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"""
[2015-06-17] Challenge #219 [Hard] The Cave of Prosperity
https://www.reddit.com/r/dailyprogrammer/comments/3aewlg/20150617_challenge_219_hard_the_cave_of_prosperity/
#Description
NAME is out in the woods one day hiking with her backpack Steven (yes, she named her backpack Steven) when she
suddently sees a cave in the side of a hill. Curious, she walks into it and after a while she comes to a big room. In
this room is a small chest filled with gold nuggets. Suddenly, she hears a voice: "Welcome, NAME to The Cave of
Prosperity!", it says. "You may take as as much gold as you can carry from this room, but once you leave it, you may
never return!"
NAME knows that Steven can carry up to 10 kilograms of gold (Steven's not a very good backpack, as it turns out), and
luckily, there's a scale next to the chest. She sees that there are five gold nuggets in the chest and she weighs them.
Four of them weigh 2 kilograms each and the last one weighs 5 kilograms. She puts the four gold nuggets weighing 2
kilograms (for a total of 8 kilograms) into to Steven and exists the cave, happy at her good fortune.
However, as you might have realized, NAME made a mistake! If she had taken the 5 kilogram nugget and two of the 2
kilogram nuggets, she would have gotten out with 9 kilograms of gold instead of 8.
Today, you are going to visit The Cave of Prosperity, and we are going to see if you can do better than NAME
#Formal inputs & outputs
##Input
On the first line of the input, you will get the capacity of your backpack, rounded to 7 digits after the decimal
point. After that, there will be one line specifying how many gold nuggets there are in the cave. After that, there
will be one line per gold nugget specifying how much each of them weighs.
The weights of the gold nuggets will be a floating point number between 0.0 and 1.0, with seven digits after the
decimal point.
##Output
On the first line of the output, you will specify how much gold you are able to escape with by putting gold nuggets
into your backpack. This number will be as large as possible without exceeding the capacity of your backpack.
After that, you will print out the weights of the gold nuggets you have collected. In other words, the first line
should be the sum of the rest of the lines.
#Sample inputs & outputs
##Input 1
2.0000000
5
0.3958356
0.4109163
0.5924923
0.6688261
0.8720640
##Output 1
1.9518064
0.4109163
0.6688261
0.8720640
##Input 2
4.0000000
10
0.0359785
0.9185395
0.2461690
0.7862738
0.9237070
0.2655587
0.3373235
0.8795087
0.7802254
0.8158674
##Output 2
3.9970232
0.9185395
0.2655587
0.3373235
0.8795087
0.7802254
0.8158674
#Challenge inputs
##Input 1
[This 15-nugget
challenge](https://gist.githubusercontent.com/anonymous/d18c4b31a9e4aa2941c4/raw/c51cd7fdaf925a6137f8728a5b30741615ba923d/gistfile1.txt
##Input 2
[This 30-nugget
challenge](https://gist.githubusercontent.com/anonymous/2451fef8cbbd0fa30705/raw/7b877d5b5330106aa1af935ea52ec5616541c8db/gistfile1.txt
#Bonus
[This 46-nugget
challenge](https://gist.githubusercontent.com/anonymous/39899cb2d250a7fd02fa/raw/6f8be09206dfbcbe32915678260dd42c5a75a435/gistfile1.txt
#Notes
As always, if you have any suggestions for a problem, head on over to /r/dailyprogrammer_ideas and suggest them!
""" |
# This code is part of Ansible, but is an independent component.
# This particular file snippet, and this file snippet only, is BSD licensed.
# Modules you write using this snippet, which is embedded dynamically by Ansible
# still belong to the author of the module, and may assign their own license
# to the complete work.
#
# Copyright (c), NAME <EMAIL>, 2012-2013
# Copyright (c), NAME <EMAIL>, 2015
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without modification,
# are permitted provided that the following conditions are met:
#
# * Redistributions of source code must retain the above copyright
# notice, this list of conditions and the following disclaimer.
# * Redistributions in binary form must reproduce the above copyright notice,
# this list of conditions and the following disclaimer in the documentation
# and/or other materials provided with the distribution.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
# ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
# WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
# IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
# INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
# PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
# LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
# USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
#
# The match_hostname function and supporting code is under the terms and
# conditions of the Python Software Foundation License. They were taken from
# the Python3 standard library and adapted for use in Python2. See comments in the
# source for which code precisely is under this License. PSF License text
# follows:
#
# PYTHON SOFTWARE FOUNDATION LICENSE VERSION 2
# --------------------------------------------
#
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# ("PSF"), and the Individual or Organization ("Licensee") accessing and
# otherwise using this software ("Python") in source or binary form and
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# 8. By copying, installing or otherwise using Python, Licensee
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|
# from cfme.modeling.base import parent_of_type
# from cfme.utils.appliance import ViaREST, MiqImplementationContext
# from . import RegionCollection, ZoneCollection, ServerCollection, Server, Zone, Region
# @MiqImplementationContext.external_for(RegionCollection.all, ViaREST)
# def region_all(self):
# self.appliance.rest_api.collections.regions.reload()
# region_collection = self.appliance.rest_api.collections.regions
# regions = [self.instantiate(region.region) for region in region_collection]
# return regions
# @MiqImplementationContext.external_for(ZoneCollection.all, ViaREST)
# def zone_all(self):
# zone_collection = self.appliance.rest_api.collections.zones
# zones = []
# parent = self.filters.get('parent')
# for zone in zone_collection:
# zone.reload(attributes=['region_number'])
# if parent and zone.region_number != parent.number:
# continue
# zones.append(self.instantiate(
# name=zone.name, description=zone.description, id=zone.id
# ))
# # TODO: This code needs a refactor once the attributes can be loaded from the collection
# return zones
# @MiqImplementationContext.external_for(ServerCollection.all, ViaREST)
# def server_all(self):
# server_collection = self.appliance.rest_api.collections.servers
# servers = []
# parent = self.filters.get('parent')
# slave_only = self.filters.get('slave', False)
# for server in server_collection:
# server.reload(attributes=['zone_id'])
# if parent and server.zone_id != parent.id:
# continue
# if slave_only and server.is_master:
# continue
# servers.append(self.instantiate(name=server.name, sid=server.id))
# # TODO: This code needs a refactor once the attributes can be loaded from the collection
# return servers
# @MiqImplementationContext.external_for(ServerCollection.get_master, ViaREST)
# def get_master(self):
# server_collection = self.appliance.rest_api.collections.servers
# server = server_collection.find_by(is_master=True)[0]
# return self.instantiate(name=server.name, sid=server.id)
# @MiqImplementationContext.external_for(Server.zone, ViaREST)
# def zone(self):
# possible_parent = parent_of_type(self, Zone)
# if self._zone:
# return self._zone
# elif possible_parent:
# self._zone = possible_parent
# else:
# server_res = self.appliance.rest_api.collections.servers.find_by(id=self.sid)
# server = server_res[0]
# server.reload(attributes=['zone'])
# zone = server.zone
# zone_obj = self.appliance.collections.zones.instantiate(
# name=zone.name, description=zone.description, id=zone.id
# )
# self._zone = zone_obj
# return self._zone
# @MiqImplementationContext.external_for(Server.slave_servers, ViaREST)
# def slave_servers(self):
# return self.zone.collections.servers.filter({'slave': True}).all()
# @MiqImplementationContext.external_for(Zone.region, ViaREST)
# def region(self):
# possible_parent = parent_of_type(self, Region)
# if self._region:
# return self._region
# elif possible_parent:
# self._region = possible_parent
# else:
# zone_res = self.appliance.rest_api.collections.zones.find_by(id=self.id)
# zone = zone_res[0]
# zone.reload(attributes=['region_number'])
# region_obj = self.appliance.collections.regions.instantiate(number=zone.region_number)
# self._region = region_obj
# return self._region
|
# Licensed to the Apache Software Foundation (ASF) under one
# or more contributor license agreements. See the NOTICE file
# distributed with this work for additional information
# regarding copyright ownership. The ASF licenses this file
# to you under the Apache License, Version 2.0 (the
# "License"); you may not use this file except in compliance
# with the License. You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing,
# software distributed under the License is distributed on an
# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
# KIND, either express or implied. See the License for the
# specific language governing permissions and limitations
# under the License.
###########################################################################################
# Implementation of the stochastic depth algorithm described in the paper
#
# NAME et al. "Deep networks with stochastic depth." arXiv preprint arXiv:1603.09382 (2016).
#
# Reference torch implementation can be found at https://github.com/yueatsprograms/Stochastic_Depth
#
# There are some differences in the implementation:
# - A BN->ReLU->Conv is used for skip connection when input and output shapes are different,
# as oppose to a padding layer.
# - The residual block is different: we use BN->ReLU->Conv->BN->ReLU->Conv, as oppose to
# Conv->BN->ReLU->Conv->BN (->ReLU also applied to skip connection).
# - We did not try to match with the same initialization, learning rate scheduling, etc.
#
#--------------------------------------------------------------------------------
# A sample from the running log (We achieved ~9.4% error after 500 epochs, some
# more careful tuning of the hyper parameters and maybe also the arch is needed
# to achieve the reported numbers in the paper):
#
# INFO:root:Epoch[80] Batch [50] Speed: 1020.95 samples/sec Train-accuracy=0.910080
# INFO:root:Epoch[80] Batch [100] Speed: 1013.41 samples/sec Train-accuracy=0.912031
# INFO:root:Epoch[80] Batch [150] Speed: 1035.48 samples/sec Train-accuracy=0.913438
# INFO:root:Epoch[80] Batch [200] Speed: 1045.00 samples/sec Train-accuracy=0.907344
# INFO:root:Epoch[80] Batch [250] Speed: 1055.32 samples/sec Train-accuracy=0.905937
# INFO:root:Epoch[80] Batch [300] Speed: 1071.71 samples/sec Train-accuracy=0.912500
# INFO:root:Epoch[80] Batch [350] Speed: 1033.73 samples/sec Train-accuracy=0.910937
# INFO:root:Epoch[80] Train-accuracy=0.919922
# INFO:root:Epoch[80] Time cost=48.348
# INFO:root:Saved checkpoint to "sd-110-0081.params"
# INFO:root:Epoch[80] Validation-accuracy=0.880142
# ...
# INFO:root:Epoch[115] Batch [50] Speed: 1037.04 samples/sec Train-accuracy=0.937040
# INFO:root:Epoch[115] Batch [100] Speed: 1041.12 samples/sec Train-accuracy=0.934219
# INFO:root:Epoch[115] Batch [150] Speed: 1036.02 samples/sec Train-accuracy=0.933125
# INFO:root:Epoch[115] Batch [200] Speed: 1057.49 samples/sec Train-accuracy=0.938125
# INFO:root:Epoch[115] Batch [250] Speed: 1060.56 samples/sec Train-accuracy=0.933438
# INFO:root:Epoch[115] Batch [300] Speed: 1046.25 samples/sec Train-accuracy=0.935625
# INFO:root:Epoch[115] Batch [350] Speed: 1043.83 samples/sec Train-accuracy=0.927188
# INFO:root:Epoch[115] Train-accuracy=0.938477
# INFO:root:Epoch[115] Time cost=47.815
# INFO:root:Saved checkpoint to "sd-110-0116.params"
# INFO:root:Epoch[115] Validation-accuracy=0.884415
# ...
# INFO:root:Saved checkpoint to "sd-110-0499.params"
# INFO:root:Epoch[498] Validation-accuracy=0.908554
# INFO:root:Epoch[499] Batch [50] Speed: 1068.28 samples/sec Train-accuracy=0.991422
# INFO:root:Epoch[499] Batch [100] Speed: 1053.10 samples/sec Train-accuracy=0.991094
# INFO:root:Epoch[499] Batch [150] Speed: 1042.89 samples/sec Train-accuracy=0.995156
# INFO:root:Epoch[499] Batch [200] Speed: 1066.22 samples/sec Train-accuracy=0.991406
# INFO:root:Epoch[499] Batch [250] Speed: 1050.56 samples/sec Train-accuracy=0.990781
# INFO:root:Epoch[499] Batch [300] Speed: 1032.02 samples/sec Train-accuracy=0.992500
# INFO:root:Epoch[499] Batch [350] Speed: 1062.16 samples/sec Train-accuracy=0.992969
# INFO:root:Epoch[499] Train-accuracy=0.994141
# INFO:root:Epoch[499] Time cost=47.401
# INFO:root:Saved checkpoint to "sd-110-0500.params"
# INFO:root:Epoch[499] Validation-accuracy=0.906050
# ###########################################################################################
|
"""Configuration file parser.
A configuration file consists of sections, lead by a "[section]" header,
and followed by "name: value" entries, with continuations and such in
the style of RFC 822.
Intrinsic defaults can be specified by passing them into the
ConfigParser constructor as a dictionary.
class:
ConfigParser -- responsible for parsing a list of
configuration files, and managing the parsed database.
methods:
__init__(defaults=None, dict_type=_default_dict, allow_no_value=False,
delimiters=('=', ':'), comment_prefixes=('#', ';'),
inline_comment_prefixes=None, strict=True,
empty_lines_in_values=True):
Create the parser. When `defaults' is given, it is initialized into the
dictionary or intrinsic defaults. The keys must be strings, the values
must be appropriate for %()s string interpolation.
When `dict_type' is given, it will be used to create the dictionary
objects for the list of sections, for the options within a section, and
for the default values.
When `delimiters' is given, it will be used as the set of substrings
that divide keys from values.
When `comment_prefixes' is given, it will be used as the set of
substrings that prefix comments in empty lines. Comments can be
indented.
When `inline_comment_prefixes' is given, it will be used as the set of
substrings that prefix comments in non-empty lines.
When `strict` is True, the parser won't allow for any section or option
duplicates while reading from a single source (file, string or
dictionary). Default is True.
When `empty_lines_in_values' is False (default: True), each empty line
marks the end of an option. Otherwise, internal empty lines of
a multiline option are kept as part of the value.
When `allow_no_value' is True (default: False), options without
values are accepted; the value presented for these is None.
sections()
Return all the configuration section names, sans DEFAULT.
has_section(section)
Return whether the given section exists.
has_option(section, option)
Return whether the given option exists in the given section.
options(section)
Return list of configuration options for the named section.
read(filenames, encoding=None)
Read and parse the list of named configuration files, given by
name. A single filename is also allowed. Non-existing files
are ignored. Return list of successfully read files.
read_file(f, filename=None)
Read and parse one configuration file, given as a file object.
The filename defaults to f.name; it is only used in error
messages (if f has no `name' attribute, the string `<???>' is used).
read_string(string)
Read configuration from a given string.
read_dict(dictionary)
Read configuration from a dictionary. Keys are section names,
values are dictionaries with keys and values that should be present
in the section. If the used dictionary type preserves order, sections
and their keys will be added in order. Values are automatically
converted to strings.
get(section, option, raw=False, vars=None, fallback=_UNSET)
Return a string value for the named option. All % interpolations are
expanded in the return values, based on the defaults passed into the
constructor and the DEFAULT section. Additional substitutions may be
provided using the `vars' argument, which must be a dictionary whose
contents override any pre-existing defaults. If `option' is a key in
`vars', the value from `vars' is used.
getint(section, options, raw=False, vars=None, fallback=_UNSET)
Like get(), but convert value to an integer.
getfloat(section, options, raw=False, vars=None, fallback=_UNSET)
Like get(), but convert value to a float.
getboolean(section, options, raw=False, vars=None, fallback=_UNSET)
Like get(), but convert value to a boolean (currently case
insensitively defined as 0, false, no, off for False, and 1, true,
yes, on for True). Returns False or True.
items(section=_UNSET, raw=False, vars=None)
If section is given, return a list of tuples with (name, value) for
each option in the section. Otherwise, return a list of tuples with
(section_name, section_proxy) for each section, including DEFAULTSECT.
remove_section(section)
Remove the given file section and all its options.
remove_option(section, option)
Remove the given option from the given section.
set(section, option, value)
Set the given option.
write(fp, space_around_delimiters=True)
Write the configuration state in .ini format. If
`space_around_delimiters' is True (the default), delimiters
between keys and values are surrounded by spaces.
""" |
"""Configuration file parser.
A configuration file consists of sections, lead by a "[section]" header,
and followed by "name: value" entries, with continuations and such in
the style of RFC 822.
Intrinsic defaults can be specified by passing them into the
ConfigParser constructor as a dictionary.
class:
ConfigParser -- responsible for parsing a list of
configuration files, and managing the parsed database.
methods:
__init__(defaults=None, dict_type=_default_dict, allow_no_value=False,
delimiters=('=', ':'), comment_prefixes=('#', ';'),
inline_comment_prefixes=None, strict=True,
empty_lines_in_values=True):
Create the parser. When `defaults' is given, it is initialized into the
dictionary or intrinsic defaults. The keys must be strings, the values
must be appropriate for %()s string interpolation.
When `dict_type' is given, it will be used to create the dictionary
objects for the list of sections, for the options within a section, and
for the default values.
When `delimiters' is given, it will be used as the set of substrings
that divide keys from values.
When `comment_prefixes' is given, it will be used as the set of
substrings that prefix comments in empty lines. Comments can be
indented.
When `inline_comment_prefixes' is given, it will be used as the set of
substrings that prefix comments in non-empty lines.
When `strict` is True, the parser won't allow for any section or option
duplicates while reading from a single source (file, string or
dictionary). Default is True.
When `empty_lines_in_values' is False (default: True), each empty line
marks the end of an option. Otherwise, internal empty lines of
a multiline option are kept as part of the value.
When `allow_no_value' is True (default: False), options without
values are accepted; the value presented for these is None.
sections()
Return all the configuration section names, sans DEFAULT.
has_section(section)
Return whether the given section exists.
has_option(section, option)
Return whether the given option exists in the given section.
options(section)
Return list of configuration options for the named section.
read(filenames, encoding=None)
Read and parse the list of named configuration files, given by
name. A single filename is also allowed. Non-existing files
are ignored. Return list of successfully read files.
read_file(f, filename=None)
Read and parse one configuration file, given as a file object.
The filename defaults to f.name; it is only used in error
messages (if f has no `name' attribute, the string `<???>' is used).
read_string(string)
Read configuration from a given string.
read_dict(dictionary)
Read configuration from a dictionary. Keys are section names,
values are dictionaries with keys and values that should be present
in the section. If the used dictionary type preserves order, sections
and their keys will be added in order. Values are automatically
converted to strings.
get(section, option, raw=False, vars=None, fallback=_UNSET)
Return a string value for the named option. All % interpolations are
expanded in the return values, based on the defaults passed into the
constructor and the DEFAULT section. Additional substitutions may be
provided using the `vars' argument, which must be a dictionary whose
contents override any pre-existing defaults. If `option' is a key in
`vars', the value from `vars' is used.
getint(section, options, raw=False, vars=None, fallback=_UNSET)
Like get(), but convert value to an integer.
getfloat(section, options, raw=False, vars=None, fallback=_UNSET)
Like get(), but convert value to a float.
getboolean(section, options, raw=False, vars=None, fallback=_UNSET)
Like get(), but convert value to a boolean (currently case
insensitively defined as 0, false, no, off for False, and 1, true,
yes, on for True). Returns False or True.
items(section=_UNSET, raw=False, vars=None)
If section is given, return a list of tuples with (name, value) for
each option in the section. Otherwise, return a list of tuples with
(section_name, section_proxy) for each section, including DEFAULTSECT.
remove_section(section)
Remove the given file section and all its options.
remove_option(section, option)
Remove the given option from the given section.
set(section, option, value)
Set the given option.
write(fp, space_around_delimiters=True)
Write the configuration state in .ini format. If
`space_around_delimiters' is True (the default), delimiters
between keys and values are surrounded by spaces.
""" |
"""Stuff to parse Sun and NeXT audio files.
An audio file consists of a header followed by the data. The structure
of the header is as follows.
+---------------+
| magic word |
+---------------+
| header size |
+---------------+
| data size |
+---------------+
| encoding |
+---------------+
| sample rate |
+---------------+
| # of channels |
+---------------+
| info |
| |
+---------------+
The magic word consists of the 4 characters '.snd'. Apart from the
info field, all header fields are 4 bytes in size. They are all
32-bit unsigned integers encoded in big-endian byte order.
The header size really gives the start of the data.
The data size is the physical size of the data. From the other
parameters the number of frames can be calculated.
The encoding gives the way in which audio samples are encoded.
Possible values are listed below.
The info field currently consists of an ASCII string giving a
human-readable description of the audio file. The info field is
padded with NUL bytes to the header size.
Usage.
Reading audio files:
f = sunau.open(file, 'r')
where file is either the name of a file or an open file pointer.
The open file pointer must have methods read(), seek(), and close().
When the setpos() and rewind() methods are not used, the seek()
method is not necessary.
This returns an instance of a class with the following public methods:
getnchannels() -- returns number of audio channels (1 for
mono, 2 for stereo)
getsampwidth() -- returns sample width in bytes
getframerate() -- returns sampling frequency
getnframes() -- returns number of audio frames
getcomptype() -- returns compression type ('NONE' or 'ULAW')
getcompname() -- returns human-readable version of
compression type ('not compressed' matches 'NONE')
getparams() -- returns a tuple consisting of all of the
above in the above order
getmarkers() -- returns None (for compatibility with the
aifc module)
getmark(id) -- raises an error since the mark does not
exist (for compatibility with the aifc module)
readframes(n) -- returns at most n frames of audio
rewind() -- rewind to the beginning of the audio stream
setpos(pos) -- seek to the specified position
tell() -- return the current position
close() -- close the instance (make it unusable)
The position returned by tell() and the position given to setpos()
are compatible and have nothing to do with the actual position in the
file.
The close() method is called automatically when the class instance
is destroyed.
Writing audio files:
f = sunau.open(file, 'w')
where file is either the name of a file or an open file pointer.
The open file pointer must have methods write(), tell(), seek(), and
close().
This returns an instance of a class with the following public methods:
setnchannels(n) -- set the number of channels
setsampwidth(n) -- set the sample width
setframerate(n) -- set the frame rate
setnframes(n) -- set the number of frames
setcomptype(type, name)
-- set the compression type and the
human-readable compression type
setparams(tuple)-- set all parameters at once
tell() -- return current position in output file
writeframesraw(data)
-- write audio frames without pathing up the
file header
writeframes(data)
-- write audio frames and patch up the file header
close() -- patch up the file header and close the
output file
You should set the parameters before the first writeframesraw or
writeframes. The total number of frames does not need to be set,
but when it is set to the correct value, the header does not have to
be patched up.
It is best to first set all parameters, perhaps possibly the
compression type, and then write audio frames using writeframesraw.
When all frames have been written, either call writeframes('') or
close() to patch up the sizes in the header.
The close() method is called automatically when the class instance
is destroyed.
""" |
"""
Limits
======
Implemented according to the PhD thesis
http://www.cybertester.com/data/gruntz.pdf, which contains very thorough
descriptions of the algorithm including many examples. We summarize here
the gist of it.
All functions are sorted according to how rapidly varying they are at
infinity using the following rules. Any two functions f and g can be
compared using the properties of L:
L=lim log|f(x)| / log|g(x)| (for x -> oo)
We define >, < ~ according to::
1. f > g .... L=+-oo
we say that:
- f is greater than any power of g
- f is more rapidly varying than g
- f goes to infinity/zero faster than g
2. f < g .... L=0
we say that:
- f is lower than any power of g
3. f ~ g .... L!=0, +-oo
we say that:
- both f and g are bounded from above and below by suitable integral
powers of the other
Examples
========
::
2 < x < exp(x) < exp(x**2) < exp(exp(x))
2 ~ 3 ~ -5
x ~ x**2 ~ x**3 ~ 1/x ~ x**m ~ -x
exp(x) ~ exp(-x) ~ exp(2x) ~ exp(x)**2 ~ exp(x+exp(-x))
f ~ 1/f
So we can divide all the functions into comparability classes (x and x^2
belong to one class, exp(x) and exp(-x) belong to some other class). In
principle, we could compare any two functions, but in our algorithm, we
don't compare anything below the class 2~3~-5 (for example log(x) is
below this), so we set 2~3~-5 as the lowest comparability class.
Given the function f, we find the list of most rapidly varying (mrv set)
subexpressions of it. This list belongs to the same comparability class.
Let's say it is {exp(x), exp(2x)}. Using the rule f ~ 1/f we find an
element "w" (either from the list or a new one) from the same
comparability class which goes to zero at infinity. In our example we
set w=exp(-x) (but we could also set w=exp(-2x) or w=exp(-3x) ...). We
rewrite the mrv set using w, in our case {1/w, 1/w^2}, and substitute it
into f. Then we expand f into a series in w::
f = c0*w^e0 + c1*w^e1 + ... + O(w^en), where e0<e1<...<en, c0!=0
but for x->oo, lim f = lim c0*w^e0, because all the other terms go to zero,
because w goes to zero faster than the ci and ei. So::
for e0>0, lim f = 0
for e0<0, lim f = +-oo (the sign depends on the sign of c0)
for e0=0, lim f = lim c0
We need to recursively compute limits at several places of the algorithm, but
as is shown in the PhD thesis, it always finishes.
Important functions from the implementation:
compare(a, b, x) compares "a" and "b" by computing the limit L.
mrv(e, x) returns list of most rapidly varying (mrv) subexpressions of "e"
rewrite(e, Omega, x, wsym) rewrites "e" in terms of w
leadterm(f, x) returns the lowest power term in the series of f
mrv_leadterm(e, x) returns the lead term (c0, e0) for e
limitinf(e, x) computes lim e (for x->oo)
limit(e, z, z0) computes any limit by converting it to the case x->oo
All the functions are really simple and straightforward except
rewrite(), which is the most difficult/complex part of the algorithm.
When the algorithm fails, the bugs are usually in the series expansion
(i.e. in SymPy) or in rewrite.
This code is almost exact rewrite of the Maple code inside the Gruntz
thesis.
Debugging
---------
Because the gruntz algorithm is highly recursive, it's difficult to
figure out what went wrong inside a debugger. Instead, turn on nice
debug prints by defining the environment variable SYMPY_DEBUG. For
example:
[user@localhost]: SYMPY_DEBUG=True ./bin/isympy
In [1]: limit(sin(x)/x, x, 0)
limitinf(_x*sin(1/_x), _x) = 1
+-mrv_leadterm(_x*sin(1/_x), _x) = (1, 0)
| +-mrv(_x*sin(1/_x), _x) = set([_x])
| | +-mrv(_x, _x) = set([_x])
| | +-mrv(sin(1/_x), _x) = set([_x])
| | +-mrv(1/_x, _x) = set([_x])
| | +-mrv(_x, _x) = set([_x])
| +-mrv_leadterm(exp(_x)*sin(exp(-_x)), _x, set([exp(_x)])) = (1, 0)
| +-rewrite(exp(_x)*sin(exp(-_x)), set([exp(_x)]), _x, _w) = (1/_w*sin(_w), -_x)
| +-sign(_x, _x) = 1
| +-mrv_leadterm(1, _x) = (1, 0)
+-sign(0, _x) = 0
+-limitinf(1, _x) = 1
And check manually which line is wrong. Then go to the source code and
debug this function to figure out the exact problem.
""" |
# Copyright 2011,2012 NAME Copyright 2008 (C) Nicira, Inc.
#
# This file is part of POX.
#
# POX is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# POX is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with POX. If not, see <http://www.gnu.org/licenses/>.
# This file is derived from the packet library in NOX, which was
# developed by Nicira, Inc.
#======================================================================
#
# DNS Message Format
#
# 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5
# +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
# | ID |
# +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
# |QR| Opcode |AA|TC|RD|RA|Z |AD|CD| RCODE |
# +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
# | Total Questions |
# +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
# | Total Answerrs |
# +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
# | Total Authority RRs |
# +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
# | Total Additional RRs |
# +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
# | Questions ... |
# +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
# | Answer RRs ... |
# +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
# | Authority RRs.. |
# +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
# | Additional RRs. |
# +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
#
# Question format:
#
# 1 1 1 1 1 1
# 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5
# +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
# | |
# / QNAME /
# / /
# +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
# | QTYPE |
# +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
# | QCLASS |
# +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
#
#
#
# All RRs have the following format:
# 1 1 1 1 1 1
# 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5
# +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
# | |
# / /
# / NAME /
# | |
# +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
# | TYPE |
# +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
# | CLASS |
# +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
# | TTL |
# | |
# +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
# | RDLENGTH |
# +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--|
# / RDATA /
# / /
# +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
#
#
#======================================================================
# TODO:
# SOA data
# General cleaup/rewrite (code is/has gotten pretty bad)
|
# Licensed to the Apache Software Foundation (ASF) under one
# or more contributor license agreements. See the NOTICE file
# distributed with this work for additional information
# regarding copyright ownership. The ASF licenses this file
# to you under the Apache License, Version 2.0 (the
# "License"); you may not use this file except in compliance
# with the License. You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# adapted from http://www.cl.cam.ac.uk/~mgk25/ucs/wcwidth.c
# -thepaul
# This is an implementation of wcwidth() and wcswidth() (defined in
# IEEE Std 1002.1-2001) for Unicode.
#
# http://www.opengroup.org/onlinepubs/007904975/functions/wcwidth.html
# http://www.opengroup.org/onlinepubs/007904975/functions/wcswidth.html
#
# In fixed-width output devices, Latin characters all occupy a single
# "cell" position of equal width, whereas ideographic CJK characters
# occupy two such cells. Interoperability between terminal-line
# applications and (teletype-style) character terminals using the
# UTF-8 encoding requires agreement on which character should advance
# the cursor by how many cell positions. No established formal
# standards exist at present on which Unicode character shall occupy
# how many cell positions on character terminals. These routines are
# a first attempt of defining such behavior based on simple rules
# applied to data provided by the Unicode Consortium.
#
# For some graphical characters, the Unicode standard explicitly
# defines a character-cell width via the definition of the East Asian
# FullWidth (F), Wide (W), Half-width (H), and Narrow (Na) classes.
# In all these cases, there is no ambiguity about which width a
# terminal shall use. For characters in the East Asian Ambiguous (A)
# class, the width choice depends purely on a preference of backward
# compatibility with either historic CJK or Western practice.
# Choosing single-width for these characters is easy to justify as
# the appropriate long-term solution, as the CJK practice of
# displaying these characters as double-width comes from historic
# implementation simplicity (8-bit encoded characters were displayed
# single-width and 16-bit ones double-width, even for Greek,
# Cyrillic, etc.) and not any typographic considerations.
#
# Much less clear is the choice of width for the Not East Asian
# (Neutral) class. Existing practice does not dictate a width for any
# of these characters. It would nevertheless make sense
# typographically to allocate two character cells to characters such
# as for instance EM SPACE or VOLUME INTEGRAL, which cannot be
# represented adequately with a single-width glyph. The following
# routines at present merely assign a single-cell width to all
# neutral characters, in the interest of simplicity. This is not
# entirely satisfactory and should be reconsidered before
# establishing a formal standard in this area. At the moment, the
# decision which Not East Asian (Neutral) characters should be
# represented by double-width glyphs cannot yet be answered by
# applying a simple rule from the Unicode database content. Setting
# up a proper standard for the behavior of UTF-8 character terminals
# will require a careful analysis not only of each Unicode character,
# but also of each presentation form, something the author of these
# routines has avoided to do so far.
#
# http://www.unicode.org/unicode/reports/tr11/
#
# NAME -- 2007-05-26 (Unicode 5.0)
#
# Permission to use, copy, modify, and distribute this software
# for any purpose and without fee is hereby granted. The author
# disclaims all warranties with regard to this software.
#
# Latest C version: http://www.cl.cam.ac.uk/~mgk25/ucs/wcwidth.c
# auxiliary function for binary search in interval table
|
"""
Define a simple format for saving numpy arrays to disk with the full
information about them.
The ``.npy`` format is the standard binary file format in NumPy for
persisting a *single* arbitrary NumPy array on disk. The format stores all
of the shape and dtype information necessary to reconstruct the array
correctly even on another machine with a different architecture.
The format is designed to be as simple as possible while achieving
its limited goals.
The ``.npz`` format is the standard format for persisting *multiple* NumPy
arrays on disk. A ``.npz`` file is a zip file containing multiple ``.npy``
files, one for each array.
Capabilities
------------
- Can represent all NumPy arrays including nested record arrays and
object arrays.
- Represents the data in its native binary form.
- Supports Fortran-contiguous arrays directly.
- Stores all of the necessary information to reconstruct the array
including shape and dtype on a machine of a different
architecture. Both little-endian and big-endian arrays are
supported, and a file with little-endian numbers will yield
a little-endian array on any machine reading the file. The
types are described in terms of their actual sizes. For example,
if a machine with a 64-bit C "long int" writes out an array with
"long ints", a reading machine with 32-bit C "long ints" will yield
an array with 64-bit integers.
- Is straightforward to reverse engineer. Datasets often live longer than
the programs that created them. A competent developer should be
able to create a solution in their preferred programming language to
read most ``.npy`` files that he has been given without much
documentation.
- Allows memory-mapping of the data. See `open_memmep`.
- Can be read from a filelike stream object instead of an actual file.
- Stores object arrays, i.e. arrays containing elements that are arbitrary
Python objects. Files with object arrays are not to be mmapable, but
can be read and written to disk.
Limitations
-----------
- Arbitrary subclasses of numpy.ndarray are not completely preserved.
Subclasses will be accepted for writing, but only the array data will
be written out. A regular numpy.ndarray object will be created
upon reading the file.
.. warning::
Due to limitations in the interpretation of structured dtypes, dtypes
with fields with empty names will have the names replaced by 'f0', 'f1',
etc. Such arrays will not round-trip through the format entirely
accurately. The data is intact; only the field names will differ. We are
working on a fix for this. This fix will not require a change in the
file format. The arrays with such structures can still be saved and
restored, and the correct dtype may be restored by using the
``loadedarray.view(correct_dtype)`` method.
File extensions
---------------
We recommend using the ``.npy`` and ``.npz`` extensions for files saved
in this format. This is by no means a requirement; applications may wish
to use these file formats but use an extension specific to the
application. In the absence of an obvious alternative, however,
we suggest using ``.npy`` and ``.npz``.
Version numbering
-----------------
The version numbering of these formats is independent of NumPy version
numbering. If the format is upgraded, the code in `numpy.io` will still
be able to read and write Version 1.0 files.
Format Version 1.0
------------------
The first 6 bytes are a magic string: exactly ``\\x93NUMPY``.
The next 1 byte is an unsigned byte: the major version number of the file
format, e.g. ``\\x01``.
The next 1 byte is an unsigned byte: the minor version number of the file
format, e.g. ``\\x00``. Note: the version of the file format is not tied
to the version of the numpy package.
The next 2 bytes form a little-endian unsigned short int: the length of
the header data HEADER_LEN.
The next HEADER_LEN bytes form the header data describing the array's
format. It is an ASCII string which contains a Python literal expression
of a dictionary. It is terminated by a newline (``\\n``) and padded with
spaces (``\\x20``) to make the total length of
``magic string + 4 + HEADER_LEN`` be evenly divisible by 16 for alignment
purposes.
The dictionary contains three keys:
"descr" : dtype.descr
An object that can be passed as an argument to the `numpy.dtype`
constructor to create the array's dtype.
"fortran_order" : bool
Whether the array data is Fortran-contiguous or not. Since
Fortran-contiguous arrays are a common form of non-C-contiguity,
we allow them to be written directly to disk for efficiency.
"shape" : tuple of int
The shape of the array.
For repeatability and readability, the dictionary keys are sorted in
alphabetic order. This is for convenience only. A writer SHOULD implement
this if possible. A reader MUST NOT depend on this.
Following the header comes the array data. If the dtype contains Python
objects (i.e. ``dtype.hasobject is True``), then the data is a Python
pickle of the array. Otherwise the data is the contiguous (either C-
or Fortran-, depending on ``fortran_order``) bytes of the array.
Consumers can figure out the number of bytes by multiplying the number
of elements given by the shape (noting that ``shape=()`` means there is
1 element) by ``dtype.itemsize``.
Format Version 2.0
------------------
The version 1.0 format only allowed the array header to have a total size of
65535 bytes. This can be exceeded by structured arrays with a large number of
columns. The version 2.0 format extends the header size to 4 GiB.
`numpy.save` will automatically save in 2.0 format if the data requires it,
else it will always use the more compatible 1.0 format.
The description of the fourth element of the header therefore has become:
"The next 4 bytes form a little-endian unsigned int: the length of the header
data HEADER_LEN."
Notes
-----
The ``.npy`` format, including reasons for creating it and a comparison of
alternatives, is described fully in the "npy-format" NEP.
""" |
# $Id: plugin_physical_host.py,v 1.15 2012/11/27 00:48:27 phil Exp $
#
# @Copyright@
#
# Rocks(r)
# www.rocksclusters.org
# version 6.1.1 (Sand Boa)
#
# Copyright (c) 2000 - 2014 The Regents of the University of California.
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are
# met:
#
# 1. Redistributions of source code must retain the above copyright
# notice, this list of conditions and the following disclaimer.
#
# 2. Redistributions in binary form must reproduce the above copyright
# notice unmodified and in its entirety, this list of conditions and the
# following disclaimer in the documentation and/or other materials provided
# with the distribution.
#
# 3. All advertising and press materials, printed or electronic, mentioning
# features or use of this software must display the following acknowledgement:
#
# "This product includes software developed by the Rocks(r)
# Cluster Group at the San Diego Supercomputer Center at the
# University of California, San Diego and its contributors."
#
# 4. Except as permitted for the purposes of acknowledgment in paragraph 3,
# neither the name or logo of this software nor the names of its
# authors may be used to endorse or promote products derived from this
# software without specific prior written permission. The name of the
# software includes the following terms, and any derivatives thereof:
# "Rocks", "Rocks Clusters", and "Avalanche Installer". For licensing of
# the associated name, interested parties should contact Technology
# Transfer & Intellectual Property Services, University of California,
# San Diego, 9500 Gilman Drive, Mail Code 0910, La Jolla, CA 92093-0910,
# Ph: (858) 534-5815, FAX: (858) 534-7345, E-MAIL:EMAIL
#
# THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS''
# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO,
# THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
# PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS
# BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
# CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
# SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR
# BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
# WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE
# OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN
# IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
#
# @Copyright@
#
# $Log: plugin_physical_host.py,v $
# Revision 1.15 2012/11/27 00:48:27 USERNAME Copyright Storm for Emerald Boa
#
# Revision 1.14 2012/05/06 05:48:34 USERNAME Copyright Storm for Mamba
#
# Revision 1.13 2012/03/16 21:09:42 USERNAME Fix for HVM based virtual cluster on xen
#
# Revision 1.12 2011/07/23 02:30:37 USERNAME Viper Copyright
#
# Revision 1.11 2011/02/14 04:20:39 USERNAME Treat HVM virtual machines as physical.
#
# Revision 1.10 2011/01/28 22:43:22 USERNAME changed the calls to 'self.abort' to 'print' + 'sys.exit'. we can't
# call abort from a plugin
#
# Revision 1.9 2010/09/07 23:53:01 USERNAME star power for gb
#
# Revision 1.8 2010/08/20 17:57:39 USERNAME make sure the IP is not null
#
# Revision 1.7 2010/07/27 19:51:11 anoop
# Cleaned code: Moved rocks report grub to rocks report host grub
#
# Revision 1.6 2010/05/03 22:50:15 USERNAME - add the ipappend 2 line if ksdevice=bootif arg is in the db
# - add static ip information of ksdevice= is used
#
# Revision 1.5 2009/05/01 19:07:03 USERNAME chimi con queso
#
# Revision 1.4 2009/04/22 02:27:19 anoop
# Moved solaris dbreport to rocks command line
#
# Revision 1.3 2009/03/04 21:31:44 USERNAME convert all getGlobalVar to getHostAttr
#
# Revision 1.2 2009/02/13 20:21:12 USERNAME make sure physical hosts look at the 'runaction' or 'installaction'
# columns in the nodes table in order to reference the correct bootaction.
#
# Revision 1.1 2009/01/16 23:58:15 USERNAME configuring the boot action and writing the boot files (e.g., PXE host config
# files and Xen config files) are now done in exactly the same way.
#
# Revision 1.3 2009/01/14 00:20:56 USERNAME unify the physical node and VM node boot action functionality
#
# - all bootaction's are global
#
# - the node table has a 'runaction' (what bootaction should the node do when
# a node normally boots) and an 'installaction (the bootaction for installs).
#
# - the 'boot' table has an entry for each node and it dictates what the node
# will do on the next boot -- it will look up the runaction in the nodes table
# (for a normal boot) or the installaction in the nodes table (for an install).
#
# Revision 1.2 2008/12/16 00:29:11 USERNAME fix
#
# Revision 1.1 2008/12/15 22:27:21 USERNAME convert pxeboot and pxeaction tables to boot and bootaction tables.
#
# this enables merging the pxeaction and vm_profiles tables
#
#
|
"""Generic socket server classes.
This module tries to capture the various aspects of defining a server:
For socket-based servers:
- address family:
- AF_INET{,6}: IP (Internet Protocol) sockets (default)
- AF_UNIX: Unix domain sockets
- others, e.g. AF_DECNET are conceivable (see <socket.h>
- socket type:
- SOCK_STREAM (reliable stream, e.g. TCP)
- SOCK_DGRAM (datagrams, e.g. UDP)
For request-based servers (including socket-based):
- client address verification before further looking at the request
(This is actually a hook for any processing that needs to look
at the request before anything else, e.g. logging)
- how to handle multiple requests:
- synchronous (one request is handled at a time)
- forking (each request is handled by a new process)
- threading (each request is handled by a new thread)
The classes in this module favor the server type that is simplest to
write: a synchronous TCP/IP server. This is bad class design, but
save some typing. (There's also the issue that a deep class hierarchy
slows down method lookups.)
There are five classes in an inheritance diagram, four of which represent
synchronous servers of four types:
+------------+
| BaseServer |
+------------+
|
v
+-----------+ +------------------+
| TCPServer |------->| UnixStreamServer |
+-----------+ +------------------+
|
v
+-----------+ +--------------------+
| UDPServer |------->| UnixDatagramServer |
+-----------+ +--------------------+
Note that UnixDatagramServer derives from UDPServer, not from
UnixStreamServer -- the only difference between an IP and a Unix
stream server is the address family, which is simply repeated in both
unix server classes.
Forking and threading versions of each type of server can be created
using the ForkingMixIn and ThreadingMixIn mix-in classes. For
instance, a threading UDP server class is created as follows:
class ThreadingUDPServer(ThreadingMixIn, UDPServer): pass
The Mix-in class must come first, since it overrides a method defined
in UDPServer! Setting the various member variables also changes
the behavior of the underlying server mechanism.
To implement a service, you must derive a class from
BaseRequestHandler and redefine its handle() method. You can then run
various versions of the service by combining one of the server classes
with your request handler class.
The request handler class must be different for datagram or stream
services. This can be hidden by using the request handler
subclasses StreamRequestHandler or DatagramRequestHandler.
Of course, you still have to use your head!
For instance, it makes no sense to use a forking server if the service
contains state in memory that can be modified by requests (since the
modifications in the child process would never reach the initial state
kept in the parent process and passed to each child). In this case,
you can use a threading server, but you will probably have to use
locks to avoid two requests that come in nearly simultaneous to apply
conflicting changes to the server state.
On the other hand, if you are building e.g. an HTTP server, where all
data is stored externally (e.g. in the file system), a synchronous
class will essentially render the service "deaf" while one request is
being handled -- which may be for a very long time if a client is slow
to read all the data it has requested. Here a threading or forking
server is appropriate.
In some cases, it may be appropriate to process part of a request
synchronously, but to finish processing in a forked child depending on
the request data. This can be implemented by using a synchronous
server and doing an explicit fork in the request handler class
handle() method.
Another approach to handling multiple simultaneous requests in an
environment that supports neither threads nor fork (or where these are
too expensive or inappropriate for the service) is to maintain an
explicit table of partially finished requests and to use select() to
decide which request to work on next (or whether to handle a new
incoming request). This is particularly important for stream services
where each client can potentially be connected for a long time (if
threads or subprocesses cannot be used).
Future work:
- Standard classes for Sun RPC (which uses either UDP or TCP)
- Standard mix-in classes to implement various authentication
and encryption schemes
- Standard framework for select-based multiplexing
XXX Open problems:
- What to do with out-of-band data?
BaseServer:
- split generic "request" functionality out into BaseServer class.
Copyright (C) 2000 NAME <EMAIL>
example: read entries from a SQL database (requires overriding
get_request() to return a table entry from the database).
entry is processed by a RequestHandlerClass.
""" |
"""
=============================
Subclassing ndarray in python
=============================
Credits
-------
This page is based with thanks on the wiki page on subclassing by NAME - http://www.scipy.org/Subclasses.
Introduction
------------
Subclassing ndarray is relatively simple, but it has some complications
compared to other Python objects. On this page we explain the machinery
that allows you to subclass ndarray, and the implications for
implementing a subclass.
ndarrays and object creation
============================
Subclassing ndarray is complicated by the fact that new instances of
ndarray classes can come about in three different ways. These are:
#. Explicit constructor call - as in ``MySubClass(params)``. This is
the usual route to Python instance creation.
#. View casting - casting an existing ndarray as a given subclass
#. New from template - creating a new instance from a template
instance. Examples include returning slices from a subclassed array,
creating return types from ufuncs, and copying arrays. See
:ref:`new-from-template` for more details
The last two are characteristics of ndarrays - in order to support
things like array slicing. The complications of subclassing ndarray are
due to the mechanisms numpy has to support these latter two routes of
instance creation.
.. _view-casting:
View casting
------------
*View casting* is the standard ndarray mechanism by which you take an
ndarray of any subclass, and return a view of the array as another
(specified) subclass:
>>> import numpy as np
>>> # create a completely useless ndarray subclass
>>> class C(np.ndarray): pass
>>> # create a standard ndarray
>>> arr = np.zeros((3,))
>>> # take a view of it, as our useless subclass
>>> c_arr = arr.view(C)
>>> type(c_arr)
<class 'C'>
.. _new-from-template:
Creating new from template
--------------------------
New instances of an ndarray subclass can also come about by a very
similar mechanism to :ref:`view-casting`, when numpy finds it needs to
create a new instance from a template instance. The most obvious place
this has to happen is when you are taking slices of subclassed arrays.
For example:
>>> v = c_arr[1:]
>>> type(v) # the view is of type 'C'
<class 'C'>
>>> v is c_arr # but it's a new instance
False
The slice is a *view* onto the original ``c_arr`` data. So, when we
take a view from the ndarray, we return a new ndarray, of the same
class, that points to the data in the original.
There are other points in the use of ndarrays where we need such views,
such as copying arrays (``c_arr.copy()``), creating ufunc output arrays
(see also :ref:`array-wrap`), and reducing methods (like
``c_arr.mean()``.
Relationship of view casting and new-from-template
--------------------------------------------------
These paths both use the same machinery. We make the distinction here,
because they result in different input to your methods. Specifically,
:ref:`view-casting` means you have created a new instance of your array
type from any potential subclass of ndarray. :ref:`new-from-template`
means you have created a new instance of your class from a pre-existing
instance, allowing you - for example - to copy across attributes that
are particular to your subclass.
Implications for subclassing
----------------------------
If we subclass ndarray, we need to deal not only with explicit
construction of our array type, but also :ref:`view-casting` or
:ref:`new-from-template`. NumPy has the machinery to do this, and this
machinery that makes subclassing slightly non-standard.
There are two aspects to the machinery that ndarray uses to support
views and new-from-template in subclasses.
The first is the use of the ``ndarray.__new__`` method for the main work
of object initialization, rather then the more usual ``__init__``
method. The second is the use of the ``__array_finalize__`` method to
allow subclasses to clean up after the creation of views and new
instances from templates.
A brief Python primer on ``__new__`` and ``__init__``
=====================================================
``__new__`` is a standard Python method, and, if present, is called
before ``__init__`` when we create a class instance. See the `python
__new__ documentation
<http://docs.python.org/reference/datamodel.html#object.__new__>`_ for more detail.
For example, consider the following Python code:
.. testcode::
class C(object):
def __new__(cls, *args):
print('Cls in __new__:', cls)
print('Args in __new__:', args)
return object.__new__(cls, *args)
def __init__(self, *args):
print('type(self) in __init__:', type(self))
print('Args in __init__:', args)
meaning that we get:
>>> c = C('hello')
Cls in __new__: <class 'C'>
Args in __new__: ('hello',)
type(self) in __init__: <class 'C'>
Args in __init__: ('hello',)
When we call ``C('hello')``, the ``__new__`` method gets its own class
as first argument, and the passed argument, which is the string
``'hello'``. After python calls ``__new__``, it usually (see below)
calls our ``__init__`` method, with the output of ``__new__`` as the
first argument (now a class instance), and the passed arguments
following.
As you can see, the object can be initialized in the ``__new__``
method or the ``__init__`` method, or both, and in fact ndarray does
not have an ``__init__`` method, because all the initialization is
done in the ``__new__`` method.
Why use ``__new__`` rather than just the usual ``__init__``? Because
in some cases, as for ndarray, we want to be able to return an object
of some other class. Consider the following:
.. testcode::
class D(C):
def __new__(cls, *args):
print('D cls is:', cls)
print('D args in __new__:', args)
return C.__new__(C, *args)
def __init__(self, *args):
# we never get here
print('In D __init__')
meaning that:
>>> obj = D('hello')
D cls is: <class 'D'>
D args in __new__: ('hello',)
Cls in __new__: <class 'C'>
Args in __new__: ('hello',)
>>> type(obj)
<class 'C'>
The definition of ``C`` is the same as before, but for ``D``, the
``__new__`` method returns an instance of class ``C`` rather than
``D``. Note that the ``__init__`` method of ``D`` does not get
called. In general, when the ``__new__`` method returns an object of
class other than the class in which it is defined, the ``__init__``
method of that class is not called.
This is how subclasses of the ndarray class are able to return views
that preserve the class type. When taking a view, the standard
ndarray machinery creates the new ndarray object with something
like::
obj = ndarray.__new__(subtype, shape, ...
where ``subdtype`` is the subclass. Thus the returned view is of the
same class as the subclass, rather than being of class ``ndarray``.
That solves the problem of returning views of the same type, but now
we have a new problem. The machinery of ndarray can set the class
this way, in its standard methods for taking views, but the ndarray
``__new__`` method knows nothing of what we have done in our own
``__new__`` method in order to set attributes, and so on. (Aside -
why not call ``obj = subdtype.__new__(...`` then? Because we may not
have a ``__new__`` method with the same call signature).
The role of ``__array_finalize__``
==================================
``__array_finalize__`` is the mechanism that numpy provides to allow
subclasses to handle the various ways that new instances get created.
Remember that subclass instances can come about in these three ways:
#. explicit constructor call (``obj = MySubClass(params)``). This will
call the usual sequence of ``MySubClass.__new__`` then (if it exists)
``MySubClass.__init__``.
#. :ref:`view-casting`
#. :ref:`new-from-template`
Our ``MySubClass.__new__`` method only gets called in the case of the
explicit constructor call, so we can't rely on ``MySubClass.__new__`` or
``MySubClass.__init__`` to deal with the view casting and
new-from-template. It turns out that ``MySubClass.__array_finalize__``
*does* get called for all three methods of object creation, so this is
where our object creation housekeeping usually goes.
* For the explicit constructor call, our subclass will need to create a
new ndarray instance of its own class. In practice this means that
we, the authors of the code, will need to make a call to
``ndarray.__new__(MySubClass,...)``, or do view casting of an existing
array (see below)
* For view casting and new-from-template, the equivalent of
``ndarray.__new__(MySubClass,...`` is called, at the C level.
The arguments that ``__array_finalize__`` receives differ for the three
methods of instance creation above.
The following code allows us to look at the call sequences and arguments:
.. testcode::
import numpy as np
class C(np.ndarray):
def __new__(cls, *args, **kwargs):
print('In __new__ with class %s' % cls)
return np.ndarray.__new__(cls, *args, **kwargs)
def __init__(self, *args, **kwargs):
# in practice you probably will not need or want an __init__
# method for your subclass
print('In __init__ with class %s' % self.__class__)
def __array_finalize__(self, obj):
print('In array_finalize:')
print(' self type is %s' % type(self))
print(' obj type is %s' % type(obj))
Now:
>>> # Explicit constructor
>>> c = C((10,))
In __new__ with class <class 'C'>
In array_finalize:
self type is <class 'C'>
obj type is <type 'NoneType'>
In __init__ with class <class 'C'>
>>> # View casting
>>> a = np.arange(10)
>>> cast_a = a.view(C)
In array_finalize:
self type is <class 'C'>
obj type is <type 'numpy.ndarray'>
>>> # Slicing (example of new-from-template)
>>> cv = c[:1]
In array_finalize:
self type is <class 'C'>
obj type is <class 'C'>
The signature of ``__array_finalize__`` is::
def __array_finalize__(self, obj):
``ndarray.__new__`` passes ``__array_finalize__`` the new object, of our
own class (``self``) as well as the object from which the view has been
taken (``obj``). As you can see from the output above, the ``self`` is
always a newly created instance of our subclass, and the type of ``obj``
differs for the three instance creation methods:
* When called from the explicit constructor, ``obj`` is ``None``
* When called from view casting, ``obj`` can be an instance of any
subclass of ndarray, including our own.
* When called in new-from-template, ``obj`` is another instance of our
own subclass, that we might use to update the new ``self`` instance.
Because ``__array_finalize__`` is the only method that always sees new
instances being created, it is the sensible place to fill in instance
defaults for new object attributes, among other tasks.
This may be clearer with an example.
Simple example - adding an extra attribute to ndarray
-----------------------------------------------------
.. testcode::
import numpy as np
class InfoArray(np.ndarray):
def __new__(subtype, shape, dtype=float, buffer=None, offset=0,
strides=None, order=None, info=None):
# Create the ndarray instance of our type, given the usual
# ndarray input arguments. This will call the standard
# ndarray constructor, but return an object of our type.
# It also triggers a call to InfoArray.__array_finalize__
obj = np.ndarray.__new__(subtype, shape, dtype, buffer, offset, strides,
order)
# set the new 'info' attribute to the value passed
obj.info = info
# Finally, we must return the newly created object:
return obj
def __array_finalize__(self, obj):
# ``self`` is a new object resulting from
# ndarray.__new__(InfoArray, ...), therefore it only has
# attributes that the ndarray.__new__ constructor gave it -
# i.e. those of a standard ndarray.
#
# We could have got to the ndarray.__new__ call in 3 ways:
# From an explicit constructor - e.g. InfoArray():
# obj is None
# (we're in the middle of the InfoArray.__new__
# constructor, and self.info will be set when we return to
# InfoArray.__new__)
if obj is None: return
# From view casting - e.g arr.view(InfoArray):
# obj is arr
# (type(obj) can be InfoArray)
# From new-from-template - e.g infoarr[:3]
# type(obj) is InfoArray
#
# Note that it is here, rather than in the __new__ method,
# that we set the default value for 'info', because this
# method sees all creation of default objects - with the
# InfoArray.__new__ constructor, but also with
# arr.view(InfoArray).
self.info = getattr(obj, 'info', None)
# We do not need to return anything
Using the object looks like this:
>>> obj = InfoArray(shape=(3,)) # explicit constructor
>>> type(obj)
<class 'InfoArray'>
>>> obj.info is None
True
>>> obj = InfoArray(shape=(3,), info='information')
>>> obj.info
'information'
>>> v = obj[1:] # new-from-template - here - slicing
>>> type(v)
<class 'InfoArray'>
>>> v.info
'information'
>>> arr = np.arange(10)
>>> cast_arr = arr.view(InfoArray) # view casting
>>> type(cast_arr)
<class 'InfoArray'>
>>> cast_arr.info is None
True
This class isn't very useful, because it has the same constructor as the
bare ndarray object, including passing in buffers and shapes and so on.
We would probably prefer the constructor to be able to take an already
formed ndarray from the usual numpy calls to ``np.array`` and return an
object.
Slightly more realistic example - attribute added to existing array
-------------------------------------------------------------------
Here is a class that takes a standard ndarray that already exists, casts
as our type, and adds an extra attribute.
.. testcode::
import numpy as np
class RealisticInfoArray(np.ndarray):
def __new__(cls, input_array, info=None):
# Input array is an already formed ndarray instance
# We first cast to be our class type
obj = np.asarray(input_array).view(cls)
# add the new attribute to the created instance
obj.info = info
# Finally, we must return the newly created object:
return obj
def __array_finalize__(self, obj):
# see InfoArray.__array_finalize__ for comments
if obj is None: return
self.info = getattr(obj, 'info', None)
So:
>>> arr = np.arange(5)
>>> obj = RealisticInfoArray(arr, info='information')
>>> type(obj)
<class 'RealisticInfoArray'>
>>> obj.info
'information'
>>> v = obj[1:]
>>> type(v)
<class 'RealisticInfoArray'>
>>> v.info
'information'
.. _array-wrap:
``__array_wrap__`` for ufuncs
-------------------------------------------------------
``__array_wrap__`` gets called at the end of numpy ufuncs and other numpy
functions, to allow a subclass to set the type of the return value
and update attributes and metadata. Let's show how this works with an example.
First we make the same subclass as above, but with a different name and
some print statements:
.. testcode::
import numpy as np
class MySubClass(np.ndarray):
def __new__(cls, input_array, info=None):
obj = np.asarray(input_array).view(cls)
obj.info = info
return obj
def __array_finalize__(self, obj):
print('In __array_finalize__:')
print(' self is %s' % repr(self))
print(' obj is %s' % repr(obj))
if obj is None: return
self.info = getattr(obj, 'info', None)
def __array_wrap__(self, out_arr, context=None):
print('In __array_wrap__:')
print(' self is %s' % repr(self))
print(' arr is %s' % repr(out_arr))
# then just call the parent
return np.ndarray.__array_wrap__(self, out_arr, context)
We run a ufunc on an instance of our new array:
>>> obj = MySubClass(np.arange(5), info='spam')
In __array_finalize__:
self is MySubClass([0, 1, 2, 3, 4])
obj is array([0, 1, 2, 3, 4])
>>> arr2 = np.arange(5)+1
>>> ret = np.add(arr2, obj)
In __array_wrap__:
self is MySubClass([0, 1, 2, 3, 4])
arr is array([1, 3, 5, 7, 9])
In __array_finalize__:
self is MySubClass([1, 3, 5, 7, 9])
obj is MySubClass([0, 1, 2, 3, 4])
>>> ret
MySubClass([1, 3, 5, 7, 9])
>>> ret.info
'spam'
Note that the ufunc (``np.add``) has called the ``__array_wrap__`` method of the
input with the highest ``__array_priority__`` value, in this case
``MySubClass.__array_wrap__``, with arguments ``self`` as ``obj``, and
``out_arr`` as the (ndarray) result of the addition. In turn, the
default ``__array_wrap__`` (``ndarray.__array_wrap__``) has cast the
result to class ``MySubClass``, and called ``__array_finalize__`` -
hence the copying of the ``info`` attribute. This has all happened at the C level.
But, we could do anything we wanted:
.. testcode::
class SillySubClass(np.ndarray):
def __array_wrap__(self, arr, context=None):
return 'I lost your data'
>>> arr1 = np.arange(5)
>>> obj = arr1.view(SillySubClass)
>>> arr2 = np.arange(5)
>>> ret = np.multiply(obj, arr2)
>>> ret
'I lost your data'
So, by defining a specific ``__array_wrap__`` method for our subclass,
we can tweak the output from ufuncs. The ``__array_wrap__`` method
requires ``self``, then an argument - which is the result of the ufunc -
and an optional parameter *context*. This parameter is returned by some
ufuncs as a 3-element tuple: (name of the ufunc, argument of the ufunc,
domain of the ufunc). ``__array_wrap__`` should return an instance of
its containing class. See the masked array subclass for an
implementation.
In addition to ``__array_wrap__``, which is called on the way out of the
ufunc, there is also an ``__array_prepare__`` method which is called on
the way into the ufunc, after the output arrays are created but before any
computation has been performed. The default implementation does nothing
but pass through the array. ``__array_prepare__`` should not attempt to
access the array data or resize the array, it is intended for setting the
output array type, updating attributes and metadata, and performing any
checks based on the input that may be desired before computation begins.
Like ``__array_wrap__``, ``__array_prepare__`` must return an ndarray or
subclass thereof or raise an error.
Extra gotchas - custom ``__del__`` methods and ndarray.base
-----------------------------------------------------------
One of the problems that ndarray solves is keeping track of memory
ownership of ndarrays and their views. Consider the case where we have
created an ndarray, ``arr`` and have taken a slice with ``v = arr[1:]``.
The two objects are looking at the same memory. NumPy keeps track of
where the data came from for a particular array or view, with the
``base`` attribute:
>>> # A normal ndarray, that owns its own data
>>> arr = np.zeros((4,))
>>> # In this case, base is None
>>> arr.base is None
True
>>> # We take a view
>>> v1 = arr[1:]
>>> # base now points to the array that it derived from
>>> v1.base is arr
True
>>> # Take a view of a view
>>> v2 = v1[1:]
>>> # base points to the view it derived from
>>> v2.base is v1
True
In general, if the array owns its own memory, as for ``arr`` in this
case, then ``arr.base`` will be None - there are some exceptions to this
- see the numpy book for more details.
The ``base`` attribute is useful in being able to tell whether we have
a view or the original array. This in turn can be useful if we need
to know whether or not to do some specific cleanup when the subclassed
array is deleted. For example, we may only want to do the cleanup if
the original array is deleted, but not the views. For an example of
how this can work, have a look at the ``memmap`` class in
``numpy.core``.
Subclassing and Downstream Compatibility
----------------------------------------
When sub-classing ``ndarray`` or creating duck-types that mimic the ``ndarray``
interface, it is your responsibility to decide how aligned your APIs will be
with those of numpy. For convenience, many numpy functions that have a corresponding
``ndarray`` method (e.g., ``sum``, ``mean``, ``take``, ``reshape``) work by checking
if the first argument to a function has a method of the same name. If it exists, the
method is called instead of coercing the arguments to a numpy array.
For example, if you want your sub-class or duck-type to be compatible with
numpy's ``sum`` function, the method signature for this object's ``sum`` method
should be the following:
.. testcode::
def sum(self, axis=None, dtype=None, out=None, keepdims=False):
...
This is the exact same method signature for ``np.sum``, so now if a user calls
``np.sum`` on this object, numpy will call the object's own ``sum`` method and
pass in these arguments enumerated above in the signature, and no errors will
be raised because the signatures are completely compatible with each other.
If, however, you decide to deviate from this signature and do something like this:
.. testcode::
def sum(self, axis=None, dtype=None):
...
This object is no longer compatible with ``np.sum`` because if you call ``np.sum``,
it will pass in unexpected arguments ``out`` and ``keepdims``, causing a TypeError
to be raised.
If you wish to maintain compatibility with numpy and its subsequent versions (which
might add new keyword arguments) but do not want to surface all of numpy's arguments,
your function's signature should accept ``**kwargs``. For example:
.. testcode::
def sum(self, axis=None, dtype=None, **unused_kwargs):
...
This object is now compatible with ``np.sum`` again because any extraneous arguments
(i.e. keywords that are not ``axis`` or ``dtype``) will be hidden away in the
``**unused_kwargs`` parameter.
""" |
"""Configuration file parser.
A configuration file consists of sections, lead by a "[section]" header,
and followed by "name: value" entries, with continuations and such in
the style of RFC 822.
Intrinsic defaults can be specified by passing them into the
ConfigParser constructor as a dictionary.
class:
ConfigParser -- responsible for parsing a list of
configuration files, and managing the parsed database.
methods:
__init__(defaults=None, dict_type=_default_dict, allow_no_value=False,
delimiters=('=', ':'), comment_prefixes=('#', ';'),
inline_comment_prefixes=None, strict=True,
empty_lines_in_values=True):
Create the parser. When `defaults' is given, it is initialized into the
dictionary or intrinsic defaults. The keys must be strings, the values
must be appropriate for %()s string interpolation.
When `dict_type' is given, it will be used to create the dictionary
objects for the list of sections, for the options within a section, and
for the default values.
When `delimiters' is given, it will be used as the set of substrings
that divide keys from values.
When `comment_prefixes' is given, it will be used as the set of
substrings that prefix comments in empty lines. Comments can be
indented.
When `inline_comment_prefixes' is given, it will be used as the set of
substrings that prefix comments in non-empty lines.
When `strict` is True, the parser won't allow for any section or option
duplicates while reading from a single source (file, string or
dictionary). Default is True.
When `empty_lines_in_values' is False (default: True), each empty line
marks the end of an option. Otherwise, internal empty lines of
a multiline option are kept as part of the value.
When `allow_no_value' is True (default: False), options without
values are accepted; the value presented for these is None.
sections()
Return all the configuration section names, sans DEFAULT.
has_section(section)
Return whether the given section exists.
has_option(section, option)
Return whether the given option exists in the given section.
options(section)
Return list of configuration options for the named section.
read(filenames, encoding=None)
Read and parse the list of named configuration files, given by
name. A single filename is also allowed. Non-existing files
are ignored. Return list of successfully read files.
read_file(f, filename=None)
Read and parse one configuration file, given as a file object.
The filename defaults to f.name; it is only used in error
messages (if f has no `name' attribute, the string `<???>' is used).
read_string(string)
Read configuration from a given string.
read_dict(dictionary)
Read configuration from a dictionary. Keys are section names,
values are dictionaries with keys and values that should be present
in the section. If the used dictionary type preserves order, sections
and their keys will be added in order. Values are automatically
converted to strings.
get(section, option, raw=False, vars=None, fallback=_UNSET)
Return a string value for the named option. All % interpolations are
expanded in the return values, based on the defaults passed into the
constructor and the DEFAULT section. Additional substitutions may be
provided using the `vars' argument, which must be a dictionary whose
contents override any pre-existing defaults. If `option' is a key in
`vars', the value from `vars' is used.
getint(section, options, raw=False, vars=None, fallback=_UNSET)
Like get(), but convert value to an integer.
getfloat(section, options, raw=False, vars=None, fallback=_UNSET)
Like get(), but convert value to a float.
getboolean(section, options, raw=False, vars=None, fallback=_UNSET)
Like get(), but convert value to a boolean (currently case
insensitively defined as 0, false, no, off for False, and 1, true,
yes, on for True). Returns False or True.
items(section=_UNSET, raw=False, vars=None)
If section is given, return a list of tuples with (section_name,
section_proxy) for each section, including DEFAULTSECT. Otherwise,
return a list of tuples with (name, value) for each option
in the section.
remove_section(section)
Remove the given file section and all its options.
remove_option(section, option)
Remove the given option from the given section.
set(section, option, value)
Set the given option.
write(fp, space_around_delimiters=True)
Write the configuration state in .ini format. If
`space_around_delimiters' is True (the default), delimiters
between keys and values are surrounded by spaces.
""" |
"""
=====================================================
Optimization and root finding (:mod:`scipy.optimize`)
=====================================================
.. currentmodule:: scipy.optimize
Optimization
============
Local Optimization
------------------
.. autosummary::
:toctree: generated/
minimize - Unified interface for minimizers of multivariate functions
minimize_scalar - Unified interface for minimizers of univariate functions
OptimizeResult - The optimization result returned by some optimizers
OptimizeWarning - The optimization encountered problems
The `minimize` function supports the following methods:
.. toctree::
optimize.minimize-neldermead
optimize.minimize-powell
optimize.minimize-cg
optimize.minimize-bfgs
optimize.minimize-newtoncg
optimize.minimize-lbfgsb
optimize.minimize-tnc
optimize.minimize-cobyla
optimize.minimize-slsqp
optimize.minimize-dogleg
optimize.minimize-trustncg
The `minimize_scalar` function supports the following methods:
.. toctree::
optimize.minimize_scalar-brent
optimize.minimize_scalar-bounded
optimize.minimize_scalar-golden
The specific optimization method interfaces below in this subsection are
not recommended for use in new scripts; all of these methods are accessible
via a newer, more consistent interface provided by the functions above.
General-purpose multivariate methods:
.. autosummary::
:toctree: generated/
fmin - Nelder-Mead Simplex algorithm
fmin_powell - Powell's (modified) level set method
fmin_cg - Non-linear (Polak-Ribiere) conjugate gradient algorithm
fmin_bfgs - Quasi-Newton method (Broydon-Fletcher-Goldfarb-Shanno)
fmin_ncg - Line-search Newton Conjugate Gradient
Constrained multivariate methods:
.. autosummary::
:toctree: generated/
fmin_l_bfgs_b - Zhu, Byrd, and Nocedal's constrained optimizer
fmin_tnc - Truncated Newton code
fmin_cobyla - Constrained optimization by linear approximation
fmin_slsqp - Minimization using sequential least-squares programming
differential_evolution - stochastic minimization using differential evolution
Univariate (scalar) minimization methods:
.. autosummary::
:toctree: generated/
fminbound - Bounded minimization of a scalar function
brent - 1-D function minimization using Brent method
golden - 1-D function minimization using Golden Section method
Equation (Local) Minimizers
---------------------------
.. autosummary::
:toctree: generated/
leastsq - Minimize the sum of squares of M equations in N unknowns
least_squares - Feature-rich least-squares minimization.
nnls - Linear least-squares problem with non-negativity constraint
lsq_linear - Linear least-squares problem with bound constraints
Global Optimization
-------------------
.. autosummary::
:toctree: generated/
basinhopping - Basinhopping stochastic optimizer
brute - Brute force searching optimizer
differential_evolution - stochastic minimization using differential evolution
Rosenbrock function
-------------------
.. autosummary::
:toctree: generated/
rosen - The Rosenbrock function.
rosen_der - The derivative of the Rosenbrock function.
rosen_hess - The Hessian matrix of the Rosenbrock function.
rosen_hess_prod - Product of the Rosenbrock Hessian with a vector.
Fitting
=======
.. autosummary::
:toctree: generated/
curve_fit -- Fit curve to a set of points
Root finding
============
Scalar functions
----------------
.. autosummary::
:toctree: generated/
brentq - quadratic interpolation Brent method
brenth - Brent method, modified by Harris with hyperbolic extrapolation
ridder - Ridder's method
bisect - Bisection method
newton - Secant method or Newton's method
Fixed point finding:
.. autosummary::
:toctree: generated/
fixed_point - Single-variable fixed-point solver
Multidimensional
----------------
General nonlinear solvers:
.. autosummary::
:toctree: generated/
root - Unified interface for nonlinear solvers of multivariate functions
fsolve - Non-linear multi-variable equation solver
broyden1 - Broyden's first method
broyden2 - Broyden's second method
The `root` function supports the following methods:
.. toctree::
optimize.root-hybr
optimize.root-lm
optimize.root-broyden1
optimize.root-broyden2
optimize.root-anderson
optimize.root-linearmixing
optimize.root-diagbroyden
optimize.root-excitingmixing
optimize.root-krylov
optimize.root-dfsane
Large-scale nonlinear solvers:
.. autosummary::
:toctree: generated/
newton_krylov
anderson
Simple iterations:
.. autosummary::
:toctree: generated/
excitingmixing
linearmixing
diagbroyden
:mod:`Additional information on the nonlinear solvers <scipy.optimize.nonlin>`
Linear Programming
==================
Simplex Algorithm:
.. autosummary::
:toctree: generated/
linprog -- Linear programming using the simplex algorithm
linprog_verbose_callback -- Sample callback function for linprog
The `linprog` function supports the following methods:
.. toctree::
optimize.linprog-simplex
Assignment problems:
.. autosummary::
:toctree: generated/
linear_sum_assignment -- Solves the linear-sum assignment problem
Utilities
=========
.. autosummary::
:toctree: generated/
approx_fprime - Approximate the gradient of a scalar function
bracket - Bracket a minimum, given two starting points
check_grad - Check the supplied derivative using finite differences
line_search - Return a step that satisfies the strong Wolfe conditions
show_options - Show specific options optimization solvers
LbfgsInvHessProduct - Linear operator for L-BFGS approximate inverse Hessian
""" |
"""CPStats, a package for collecting and reporting on program statistics.
Overview
========
Statistics about program operation are an invaluable monitoring and debugging
tool. Unfortunately, the gathering and reporting of these critical values is
usually ad-hoc. This package aims to add a centralized place for gathering
statistical performance data, a structure for recording that data which
provides for extrapolation of that data into more useful information,
and a method of serving that data to both human investigators and
monitoring software. Let's examine each of those in more detail.
Data Gathering
--------------
Just as Python's `logging` module provides a common importable for gathering
and sending messages, performance statistics would benefit from a similar
common mechanism, and one that does *not* require each package which wishes
to collect stats to import a third-party module. Therefore, we choose to
re-use the `logging` module by adding a `statistics` object to it.
That `logging.statistics` object is a nested dict. It is not a custom class,
because that would:
1. require libraries and applications to import a third-party module in
order to participate
2. inhibit innovation in extrapolation approaches and in reporting tools, and
3. be slow.
There are, however, some specifications regarding the structure of the dict.::
{
+----"SQLAlchemy": {
| "Inserts": 4389745,
| "Inserts per Second":
| lambda s: s["Inserts"] / (time() - s["Start"]),
| C +---"Table Statistics": {
| o | "widgets": {-----------+
N | l | "Rows": 1.3M, | Record
a | l | "Inserts": 400, |
m | e | },---------------------+
e | c | "froobles": {
s | t | "Rows": 7845,
p | i | "Inserts": 0,
a | o | },
c | n +---},
e | "Slow Queries":
| [{"Query": "SELECT * FROM widgets;",
| "Processing Time": 47.840923343,
| },
| ],
+----},
}
The `logging.statistics` dict has four levels. The topmost level is nothing
more than a set of names to introduce modularity, usually along the lines of
package names. If the SQLAlchemy project wanted to participate, for example,
it might populate the item `logging.statistics['SQLAlchemy']`, whose value
would be a second-layer dict we call a "namespace". Namespaces help multiple
packages to avoid collisions over key names, and make reports easier to read,
to boot. The maintainers of SQLAlchemy should feel free to use more than one
namespace if needed (such as 'SQLAlchemy ORM'). Note that there are no case
or other syntax constraints on the namespace names; they should be chosen
to be maximally readable by humans (neither too short nor too long).
Each namespace, then, is a dict of named statistical values, such as
'Requests/sec' or 'Uptime'. You should choose names which will look
good on a report: spaces and capitalization are just fine.
In addition to scalars, values in a namespace MAY be a (third-layer)
dict, or a list, called a "collection". For example, the CherryPy
:class:`StatsTool` keeps track of what each request is doing (or has most
recently done) in a 'Requests' collection, where each key is a thread ID; each
value in the subdict MUST be a fourth dict (whew!) of statistical data about
each thread. We call each subdict in the collection a "record". Similarly,
the :class:`StatsTool` also keeps a list of slow queries, where each record
contains data about each slow query, in order.
Values in a namespace or record may also be functions, which brings us to:
Extrapolation
-------------
The collection of statistical data needs to be fast, as close to unnoticeable
as possible to the host program. That requires us to minimize I/O, for example,
but in Python it also means we need to minimize function calls. So when you
are designing your namespace and record values, try to insert the most basic
scalar values you already have on hand.
When it comes time to report on the gathered data, however, we usually have
much more freedom in what we can calculate. Therefore, whenever reporting
tools (like the provided :class:`StatsPage` CherryPy class) fetch the contents
of `logging.statistics` for reporting, they first call
`extrapolate_statistics` (passing the whole `statistics` dict as the only
argument). This makes a deep copy of the statistics dict so that the
reporting tool can both iterate over it and even change it without harming
the original. But it also expands any functions in the dict by calling them.
For example, you might have a 'Current Time' entry in the namespace with the
value "lambda scope: time.time()". The "scope" parameter is the current
namespace dict (or record, if we're currently expanding one of those
instead), allowing you access to existing static entries. If you're truly
evil, you can even modify more than one entry at a time.
However, don't try to calculate an entry and then use its value in further
extrapolations; the order in which the functions are called is not guaranteed.
This can lead to a certain amount of duplicated work (or a redesign of your
schema), but that's better than complicating the spec.
After the whole thing has been extrapolated, it's time for:
Reporting
---------
The :class:`StatsPage` class grabs the `logging.statistics` dict, extrapolates
it all, and then transforms it to HTML for easy viewing. Each namespace gets
its own header and attribute table, plus an extra table for each collection.
This is NOT part of the statistics specification; other tools can format how
they like.
You can control which columns are output and how they are formatted by updating
StatsPage.formatting, which is a dict that mirrors the keys and nesting of
`logging.statistics`. The difference is that, instead of data values, it has
formatting values. Use None for a given key to indicate to the StatsPage that a
given column should not be output. Use a string with formatting
(such as '%.3f') to interpolate the value(s), or use a callable (such as
lambda v: v.isoformat()) for more advanced formatting. Any entry which is not
mentioned in the formatting dict is output unchanged.
Monitoring
----------
Although the HTML output takes pains to assign unique id's to each <td> with
statistical data, you're probably better off fetching /cpstats/data, which
outputs the whole (extrapolated) `logging.statistics` dict in JSON format.
That is probably easier to parse, and doesn't have any formatting controls,
so you get the "original" data in a consistently-serialized format.
Note: there's no treatment yet for datetime objects. Try time.time() instead
for now if you can. Nagios will probably thank you.
Turning Collection Off
----------------------
It is recommended each namespace have an "Enabled" item which, if False,
stops collection (but not reporting) of statistical data. Applications
SHOULD provide controls to pause and resume collection by setting these
entries to False or True, if present.
Usage
=====
To collect statistics on CherryPy applications::
from cherrypy.lib import cpstats
appconfig['/']['tools.cpstats.on'] = True
To collect statistics on your own code::
import logging
# Initialize the repository
if not hasattr(logging, 'statistics'): logging.statistics = {}
# Initialize my namespace
mystats = logging.statistics.setdefault('My Stuff', {})
# Initialize my namespace's scalars and collections
mystats.update({
'Enabled': True,
'Start Time': time.time(),
'Important Events': 0,
'Events/Second': lambda s: (
(s['Important Events'] / (time.time() - s['Start Time']))),
})
...
for event in events:
...
# Collect stats
if mystats.get('Enabled', False):
mystats['Important Events'] += 1
To report statistics::
root.cpstats = cpstats.StatsPage()
To format statistics reports::
See 'Reporting', above.
""" |
# Configuration file for jupyter-notebook.
#------------------------------------------------------------------------------
# Application(SingletonConfigurable) configuration
#------------------------------------------------------------------------------
## This is an application.
## The date format used by logging formatters for %(asctime)s
#c.Application.log_datefmt = '%Y-%m-%d %H:%M:%S'
## The Logging format template
#c.Application.log_format = '[%(name)s]%(highlevel)s %(message)s'
## Set the log level by value or name.
#c.Application.log_level = 30
#------------------------------------------------------------------------------
# JupyterApp(Application) configuration
#------------------------------------------------------------------------------
## Base class for Jupyter applications
## Answer yes to any prompts.
#c.JupyterApp.answer_yes = False
## Full path of a config file.
#c.JupyterApp.config_file = u''
## Specify a config file to load.
#c.JupyterApp.config_file_name = u''
## Generate default config file.
#c.JupyterApp.generate_config = False
#------------------------------------------------------------------------------
# NotebookApp(JupyterApp) configuration
#------------------------------------------------------------------------------
## Set the Access-Control-Allow-Credentials: true header
#c.NotebookApp.allow_credentials = False
## Set the Access-Control-Allow-Origin header
#
# Use '*' to allow any origin to access your server.
#
# Takes precedence over allow_origin_pat.
#c.NotebookApp.allow_origin = ''
## Use a regular expression for the Access-Control-Allow-Origin header
#
# Requests from an origin matching the expression will get replies with:
#
# Access-Control-Allow-Origin: origin
#
# where `origin` is the origin of the request.
#
# Ignored if allow_origin is set.
#c.NotebookApp.allow_origin_pat = ''
## Whether to allow the user to run the notebook as root.
#c.NotebookApp.allow_root = False
## DEPRECATED use base_url
#c.NotebookApp.base_project_url = '/'
## The base URL for the notebook server.
#
# Leading and trailing slashes can be omitted, and will automatically be added.
#c.NotebookApp.base_url = '/'
## Specify what command to use to invoke a web browser when opening the notebook.
# If not specified, the default browser will be determined by the `webbrowser`
# standard library module, which allows setting of the BROWSER environment
# variable to override it.
#c.NotebookApp.browser = u''
## The full path to an SSL/TLS certificate file.
#c.NotebookApp.certfile = u''
## The full path to a certificate authority certificate for SSL/TLS client
# authentication.
#c.NotebookApp.client_ca = u''
## The config manager class to use
#c.NotebookApp.config_manager_class = 'notebook.services.config.manager.ConfigManager'
## The notebook manager class to use.
#c.NotebookApp.contents_manager_class = 'notebook.services.contents.largefilemanager.LargeFileManager'
## Extra keyword arguments to pass to `set_secure_cookie`. See tornado's
# set_secure_cookie docs for details.
#c.NotebookApp.cookie_options = {}
## The random bytes used to secure cookies. By default this is a new random
# number every time you start the Notebook. Set it to a value in a config file
# to enable logins to persist across server sessions.
#
# Note: Cookie secrets should be kept private, do not share config files with
# cookie_secret stored in plaintext (you can read the value from a file).
#c.NotebookApp.cookie_secret = ''
## The file where the cookie secret is stored.
#c.NotebookApp.cookie_secret_file = u''
## The default URL to redirect to from `/`
#c.NotebookApp.default_url = '/tree'
## Disable cross-site-request-forgery protection
#
# Jupyter notebook 4.3.1 introduces protection from cross-site request
# forgeries, requiring API requests to either:
#
# - originate from pages served by this server (validated with XSRF cookie and
# token), or - authenticate with a token
#
# Some anonymous compute resources still desire the ability to run code,
# completely without authentication. These services can disable all
# authentication and security checks, with the full knowledge of what that
# implies.
#c.NotebookApp.disable_check_xsrf = False
## Whether to enable MathJax for typesetting math/TeX
#
# MathJax is the javascript library Jupyter uses to render math/LaTeX. It is
# very large, so you may want to disable it if you have a slow internet
# connection, or for offline use of the notebook.
#
# When disabled, equations etc. will appear as their untransformed TeX source.
#c.NotebookApp.enable_mathjax = True
## extra paths to look for Javascript notebook extensions
#c.NotebookApp.extra_nbextensions_path = []
## Extra paths to search for serving static files.
#
# This allows adding javascript/css to be available from the notebook server
# machine, or overriding individual files in the IPython
#c.NotebookApp.extra_static_paths = []
## Extra paths to search for serving jinja templates.
#
# Can be used to override templates from notebook.templates.
#c.NotebookApp.extra_template_paths = []
##
#c.NotebookApp.file_to_run = ''
## Deprecated: Use minified JS file or not, mainly use during dev to avoid JS
# recompilation
#c.NotebookApp.ignore_minified_js = False
## (bytes/sec) Maximum rate at which stream output can be sent on iopub before
# they are limited.
#c.NotebookApp.iopub_data_rate_limit = 1000000
## (msgs/sec) Maximum rate at which messages can be sent on iopub before they are
# limited.
#c.NotebookApp.iopub_msg_rate_limit = 1000
## The IP address the notebook server will listen on.
#c.NotebookApp.ip = 'localhost'
## Supply extra arguments that will be passed to Jinja environment.
#c.NotebookApp.jinja_environment_options = {}
## Extra variables to supply to jinja templates when rendering.
#c.NotebookApp.jinja_template_vars = {}
## The kernel manager class to use.
#c.NotebookApp.kernel_manager_class = 'notebook.services.kernels.kernelmanager.MappingKernelManager'
## The kernel spec manager class to use. Should be a subclass of
# `jupyter_client.kernelspec.KernelSpecManager`.
#
# The Api of KernelSpecManager is provisional and might change without warning
# between this version of Jupyter and the next stable one.
#c.NotebookApp.kernel_spec_manager_class = 'jupyter_client.kernelspec.KernelSpecManager'
## The full path to a private key file for usage with SSL/TLS.
#c.NotebookApp.keyfile = u''
## The login handler class to use.
#c.NotebookApp.login_handler_class = 'notebook.auth.login.LoginHandler'
## The logout handler class to use.
#c.NotebookApp.logout_handler_class = 'notebook.auth.logout.LogoutHandler'
## The MathJax.js configuration file that is to be used.
#c.NotebookApp.mathjax_config = 'TeX-AMS-MML_HTMLorMML-full,Safe'
## A custom url for MathJax.js. Should be in the form of a case-sensitive url to
# MathJax, for example: /static/components/MathJax/MathJax.js
#c.NotebookApp.mathjax_url = ''
## Dict of Python modules to load as notebook server extensions.Entry values can
# be used to enable and disable the loading ofthe extensions. The extensions
# will be loaded in alphabetical order.
#c.NotebookApp.nbserver_extensions = {}
## The directory to use for notebooks and kernels.
#c.NotebookApp.notebook_dir = u''
## Whether to open in a browser after starting. The specific browser used is
# platform dependent and determined by the python standard library `webbrowser`
# module, unless it is overridden using the --browser (NotebookApp.browser)
# configuration option.
#c.NotebookApp.open_browser = True
## Hashed password to use for web authentication.
#
# To generate, type in a python/IPython shell:
#
# from notebook.auth import passwd; passwd()
#
# The string should be of the form type:salt:hashed-password.
#c.NotebookApp.password = u''
## Forces users to use a password for the Notebook server. This is useful in a
# multi user environment, for instance when everybody in the LAN can access each
# other's machine through ssh.
#
# In such a case, server the notebook server on localhost is not secure since
# any user can connect to the notebook server via ssh.
#c.NotebookApp.password_required = False
## The port the notebook server will listen on.
#c.NotebookApp.port = 8888
## The number of additional ports to try if the specified port is not available.
#c.NotebookApp.port_retries = 50
## DISABLED: use %pylab or %matplotlib in the notebook to enable matplotlib.
#c.NotebookApp.pylab = 'disabled'
## (sec) Time window used to check the message and data rate limits.
#c.NotebookApp.rate_limit_window = 3
## Reraise exceptions encountered loading server extensions?
#c.NotebookApp.reraise_server_extension_failures = False
## DEPRECATED use the nbserver_extensions dict instead
#c.NotebookApp.server_extensions = []
## The session manager class to use.
#c.NotebookApp.session_manager_class = 'notebook.services.sessions.sessionmanager.SessionManager'
## Supply SSL options for the tornado HTTPServer. See the tornado docs for
# details.
#c.NotebookApp.ssl_options = {}
## Supply overrides for terminado. Currently only supports "shell_command".
#c.NotebookApp.terminado_settings = {}
## Token used for authenticating first-time connections to the server.
#
# When no password is enabled, the default is to generate a new, random token.
#
# Setting to an empty string disables authentication altogether, which is NOT
# RECOMMENDED.
#c.NotebookApp.token = '<generated>'
## Supply overrides for the tornado.web.Application that the Jupyter notebook
# uses.
#c.NotebookApp.tornado_settings = {}
## Whether to trust or not X-Scheme/X-Forwarded-Proto and X-Real-Ip/X-Forwarded-
# For headerssent by the upstream reverse proxy. Necessary if the proxy handles
# SSL
#c.NotebookApp.trust_xheaders = False
## DEPRECATED, use tornado_settings
#c.NotebookApp.webapp_settings = {}
## Specify Where to open the notebook on startup. This is the
# `new` argument passed to the standard library method `webbrowser.open`.
# The behaviour is not guaranteed, but depends on browser support. Valid
# values are:
# 2 opens a new tab,
# 1 opens a new window,
# 0 opens in an existing window.
# See the `webbrowser.open` documentation for details.
#c.NotebookApp.webbrowser_open_new = 2
## Set the tornado compression options for websocket connections.
#
# This value will be returned from
# :meth:`WebSocketHandler.get_compression_options`. None (default) will disable
# compression. A dict (even an empty one) will enable compression.
#
# See the tornado docs for WebSocketHandler.get_compression_options for details.
#c.NotebookApp.websocket_compression_options = None
## The base URL for websockets, if it differs from the HTTP server (hint: it
# almost certainly doesn't).
#
# Should be in the form of an HTTP origin: ws[s]://hostname[:port]
#c.NotebookApp.websocket_url = ''
#------------------------------------------------------------------------------
# ConnectionFileMixin(LoggingConfigurable) configuration
#------------------------------------------------------------------------------
## Mixin for configurable classes that work with connection files
## JSON file in which to store connection info [default: kernel-<pid>.json]
#
# This file will contain the IP, ports, and authentication key needed to connect
# clients to this kernel. By default, this file will be created in the security
# dir of the current profile, but can be specified by absolute path.
#c.ConnectionFileMixin.connection_file = ''
## set the control (ROUTER) port [default: random]
#c.ConnectionFileMixin.control_port = 0
## set the heartbeat port [default: random]
#c.ConnectionFileMixin.hb_port = 0
## set the iopub (PUB) port [default: random]
#c.ConnectionFileMixin.iopub_port = 0
## Set the kernel's IP address [default localhost]. If the IP address is
# something other than localhost, then Consoles on other machines will be able
# to connect to the Kernel, so be careful!
#c.ConnectionFileMixin.ip = u''
## set the shell (ROUTER) port [default: random]
#c.ConnectionFileMixin.shell_port = 0
## set the stdin (ROUTER) port [default: random]
#c.ConnectionFileMixin.stdin_port = 0
##
#c.ConnectionFileMixin.transport = 'tcp'
#------------------------------------------------------------------------------
# KernelManager(ConnectionFileMixin) configuration
#------------------------------------------------------------------------------
## Manages a single kernel in a subprocess on this host.
#
# This version starts kernels with Popen.
## Should we autorestart the kernel if it dies.
#c.KernelManager.autorestart = True
## DEPRECATED: Use kernel_name instead.
#
# The Popen Command to launch the kernel. Override this if you have a custom
# kernel. If kernel_cmd is specified in a configuration file, Jupyter does not
# pass any arguments to the kernel, because it cannot make any assumptions about
# the arguments that the kernel understands. In particular, this means that the
# kernel does not receive the option --debug if it given on the Jupyter command
# line.
#c.KernelManager.kernel_cmd = []
## Time to wait for a kernel to terminate before killing it, in seconds.
#c.KernelManager.shutdown_wait_time = 5.0
#------------------------------------------------------------------------------
# Session(Configurable) configuration
#------------------------------------------------------------------------------
## Object for handling serialization and sending of messages.
#
# The Session object handles building messages and sending them with ZMQ sockets
# or ZMQStream objects. Objects can communicate with each other over the
# network via Session objects, and only need to work with the dict-based IPython
# message spec. The Session will handle serialization/deserialization, security,
# and metadata.
#
# Sessions support configurable serialization via packer/unpacker traits, and
# signing with HMAC digests via the key/keyfile traits.
#
# Parameters ----------
#
# debug : bool
# whether to trigger extra debugging statements
# packer/unpacker : str : 'json', 'pickle' or import_string
# importstrings for methods to serialize message parts. If just
# 'json' or 'pickle', predefined JSON and pickle packers will be used.
# Otherwise, the entire importstring must be used.
#
# The functions must accept at least valid JSON input, and output *bytes*.
#
# For example, to use msgpack:
# packer = 'msgpack.packb', unpacker='msgpack.unpackb'
# pack/unpack : callables
# You can also set the pack/unpack callables for serialization directly.
# session : bytes
# the ID of this Session object. The default is to generate a new UUID.
# username : USERNAME username added to message headers. The default is to ask the OS.
# key : bytes
# The key used to initialize an HMAC signature. If unset, messages
# will not be signed or checked.
# keyfile : filepath
# The file containing a key. If this is set, `key` will be initialized
# to the contents of the file.
## Threshold (in bytes) beyond which an object's buffer should be extracted to
# avoid pickling.
#c.Session.buffer_threshold = 1024
## Whether to check PID to protect against calls after fork.
#
# This check can be disabled if fork-safety is handled elsewhere.
#c.Session.check_pid = True
## Threshold (in bytes) beyond which a buffer should be sent without copying.
#c.Session.copy_threshold = 65536
## Debug output in the Session
#c.Session.debug = False
## The maximum number of digests to remember.
#
# The digest history will be culled when it exceeds this value.
#c.Session.digest_history_size = 65536
## The maximum number of items for a container to be introspected for custom
# serialization. Containers larger than this are pickled outright.
#c.Session.item_threshold = 64
## execution key, for signing messages.
#c.Session.key = ''
## path to file containing execution key.
#c.Session.keyfile = ''
## Metadata dictionary, which serves as the default top-level metadata dict for
# each message.
#c.Session.metadata = {}
## The name of the packer for serializing messages. Should be one of 'json',
# 'pickle', or an import name for a custom callable serializer.
#c.Session.packer = 'json'
## The UUID identifying this session.
#c.Session.session = u''
## The digest scheme used to construct the message signatures. Must have the form
# 'hmac-HASH'.
#c.Session.signature_scheme = 'hmac-sha256'
## The name of the unpacker for unserializing messages. Only used with custom
# functions for `packer`.
#c.Session.unpacker = 'json'
## Username for the Session. Default is your system username.
#c.Session.username = u'username'
#------------------------------------------------------------------------------
# MultiKernelManager(LoggingConfigurable) configuration
#------------------------------------------------------------------------------
## A class for managing multiple kernels.
## The name of the default kernel to start
#c.MultiKernelManager.default_kernel_name = 'python2'
## The kernel manager class. This is configurable to allow subclassing of the
# KernelManager for customized behavior.
#c.MultiKernelManager.kernel_manager_class = 'jupyter_client.ioloop.IOLoopKernelManager'
#------------------------------------------------------------------------------
# MappingKernelManager(MultiKernelManager) configuration
#------------------------------------------------------------------------------
## A KernelManager that handles notebook mapping and HTTP error handling
## Whether messages from kernels whose frontends have disconnected should be
# buffered in-memory.
#
# When True (default), messages are buffered and replayed on reconnect, avoiding
# lost messages due to interrupted connectivity.
#
# Disable if long-running kernels will produce too much output while no
# frontends are connected.
#c.MappingKernelManager.buffer_offline_messages = True
## Whether to consider culling kernels which are busy. Only effective if
# cull_idle_timeout is not 0.
#c.MappingKernelManager.cull_busy = False
## Whether to consider culling kernels which have one or more connections. Only
# effective if cull_idle_timeout is not 0.
#c.MappingKernelManager.cull_connected = False
## Timeout (in seconds) after which a kernel is considered idle and ready to be
# culled. Values of 0 or lower disable culling. The minimum timeout is 300
# seconds (5 minutes). Positive values less than the minimum value will be set
# to the minimum.
#c.MappingKernelManager.cull_idle_timeout = 0
## The interval (in seconds) on which to check for idle kernels exceeding the
# cull timeout value.
#c.MappingKernelManager.cull_interval = 300
##
#c.MappingKernelManager.root_dir = u''
#------------------------------------------------------------------------------
# ContentsManager(LoggingConfigurable) configuration
#------------------------------------------------------------------------------
## Base class for serving files and directories.
#
# This serves any text or binary file, as well as directories, with special
# handling for JSON notebook documents.
#
# Most APIs take a path argument, which is always an API-style unicode path, and
# always refers to a directory.
#
# - unicode, not url-escaped
# - '/'-separated
# - leading and trailing '/' will be stripped
# - if unspecified, path defaults to '',
# indicating the root path.
##
#c.ContentsManager.checkpoints = None
##
#c.ContentsManager.checkpoints_class = 'notebook.services.contents.checkpoints.Checkpoints'
##
#c.ContentsManager.checkpoints_kwargs = {}
## handler class to use when serving raw file requests.
#
# Default is a fallback that talks to the ContentsManager API, which may be
# inefficient, especially for large files.
#
# Local files-based ContentsManagers can use a StaticFileHandler subclass, which
# will be much more efficient.
#
# Access to these files should be Authenticated.
#c.ContentsManager.files_handler_class = 'notebook.files.handlers.FilesHandler'
## Extra parameters to pass to files_handler_class.
#
# For example, StaticFileHandlers generally expect a `path` argument specifying
# the root directory from which to serve files.
#c.ContentsManager.files_handler_params = {}
## Glob patterns to hide in file and directory listings.
#c.ContentsManager.hide_globs = [u'__pycache__', '*.pyc', '*.pyo', '.DS_Store', '*.so', '*.dylib', '*~']
## Python callable or importstring thereof
#
# To be called on a contents model prior to save.
#
# This can be used to process the structure, such as removing notebook outputs
# or other side effects that should not be saved.
#
# It will be called as (all arguments passed by keyword)::
#
# hook(path=path, model=model, contents_manager=self)
#
# - model: the model to be saved. Includes file contents.
# Modifying this dict will affect the file that is stored.
# - path: the API path of the save destination
# - contents_manager: this ContentsManager instance
#c.ContentsManager.pre_save_hook = None
##
#c.ContentsManager.root_dir = '/'
## The base name used when creating untitled directories.
#c.ContentsManager.untitled_directory = 'Untitled Folder'
## The base name used when creating untitled files.
#c.ContentsManager.untitled_file = 'untitled'
## The base name used when creating untitled notebooks.
#c.ContentsManager.untitled_notebook = 'Untitled'
#------------------------------------------------------------------------------
# FileManagerMixin(Configurable) configuration
#------------------------------------------------------------------------------
## Mixin for ContentsAPI classes that interact with the filesystem.
#
# Provides facilities for reading, writing, and copying both notebooks and
# generic files.
#
# Shared by FileContentsManager and FileCheckpoints.
#
# Note ---- Classes using this mixin must provide the following attributes:
#
# root_dir : USERNAME A directory against against which API-style paths are to be resolved.
#
# log : logging.Logger
## By default notebooks are saved on disk on a temporary file and then if
# succefully written, it replaces the old ones. This procedure, namely
# 'atomic_writing', causes some bugs on file system whitout operation order
# enforcement (like some networked fs). If set to False, the new notebook is
# written directly on the old one which could fail (eg: full filesystem or quota
# )
#c.FileManagerMixin.use_atomic_writing = True
#------------------------------------------------------------------------------
# FileContentsManager(FileManagerMixin,ContentsManager) configuration
#------------------------------------------------------------------------------
## Python callable or importstring thereof
#
# to be called on the path of a file just saved.
#
# This can be used to process the file on disk, such as converting the notebook
# to a script or HTML via nbconvert.
#
# It will be called as (all arguments passed by keyword)::
#
# hook(os_path=os_path, model=model, contents_manager=instance)
#
# - path: the filesystem path to the file just written - model: the model
# representing the file - contents_manager: this ContentsManager instance
#c.FileContentsManager.post_save_hook = None
##
#c.FileContentsManager.root_dir = u''
## DEPRECATED, use post_save_hook. Will be removed in Notebook 5.0
#c.FileContentsManager.save_script = False
#------------------------------------------------------------------------------
# NotebookNotary(LoggingConfigurable) configuration
#------------------------------------------------------------------------------
## A class for computing and verifying notebook signatures.
## The hashing algorithm used to sign notebooks.
#c.NotebookNotary.algorithm = 'sha256'
## The sqlite file in which to store notebook signatures. By default, this will
# be in your Jupyter data directory. You can set it to ':memory:' to disable
# sqlite writing to the filesystem.
#c.NotebookNotary.db_file = u''
## The secret key with which notebooks are signed.
#c.NotebookNotary.secret = ''
## The file where the secret key is stored.
#c.NotebookNotary.secret_file = u''
## A callable returning the storage backend for notebook signatures. The default
# uses an SQLite database.
#c.NotebookNotary.store_factory = traitlets.Undefined
#------------------------------------------------------------------------------
# KernelSpecManager(LoggingConfigurable) configuration
#------------------------------------------------------------------------------
## If there is no Python kernelspec registered and the IPython kernel is
# available, ensure it is added to the spec list.
#c.KernelSpecManager.ensure_native_kernel = True
## The kernel spec class. This is configurable to allow subclassing of the
# KernelSpecManager for customized behavior.
#c.KernelSpecManager.kernel_spec_class = 'jupyter_client.kernelspec.KernelSpec'
## Whitelist of allowed kernel names.
#
# By default, all installed kernels are allowed.
#c.KernelSpecManager.whitelist = set([])
|
"""
A multi-dimensional ``Vector`` class, take 9: operator ``@``
WARNING: This example requires Python 3.5 or later.
A ``Vector`` is built from an iterable of numbers::
>>> Vector([3.1, 4.2])
Vector([3.1, 4.2])
>>> Vector((3, 4, 5))
Vector([3.0, 4.0, 5.0])
>>> Vector(range(10))
Vector([0.0, 1.0, 2.0, 3.0, 4.0, ...])
Tests with 2-dimensions (same results as ``vector2d_v1.py``)::
>>> v1 = Vector([3, 4])
>>> x, y = v1
>>> x, y
(3.0, 4.0)
>>> v1
Vector([3.0, 4.0])
>>> v1_clone = eval(repr(v1))
>>> v1 == v1_clone
True
>>> print(v1)
(3.0, 4.0)
>>> octets = bytes(v1)
>>> octets
b'd\\x00\\x00\\x00\\x00\\x00\\x00\\x08@\\x00\\x00\\x00\\x00\\x00\\x00\\x10@'
>>> abs(v1)
5.0
>>> bool(v1), bool(Vector([0, 0]))
(True, False)
Test of ``.frombytes()`` class method:
>>> v1_clone = Vector.frombytes(bytes(v1))
>>> v1_clone
Vector([3.0, 4.0])
>>> v1 == v1_clone
True
Tests with 3-dimensions::
>>> v1 = Vector([3, 4, 5])
>>> x, y, z = v1
>>> x, y, z
(3.0, 4.0, 5.0)
>>> v1
Vector([3.0, 4.0, 5.0])
>>> v1_clone = eval(repr(v1))
>>> v1 == v1_clone
True
>>> print(v1)
(3.0, 4.0, 5.0)
>>> abs(v1) # doctest:+ELLIPSIS
7.071067811...
>>> bool(v1), bool(Vector([0, 0, 0]))
(True, False)
Tests with many dimensions::
>>> v7 = Vector(range(7))
>>> v7
Vector([0.0, 1.0, 2.0, 3.0, 4.0, ...])
>>> abs(v7) # doctest:+ELLIPSIS
9.53939201...
Test of ``.__bytes__`` and ``.frombytes()`` methods::
>>> v1 = Vector([3, 4, 5])
>>> v1_clone = Vector.frombytes(bytes(v1))
>>> v1_clone
Vector([3.0, 4.0, 5.0])
>>> v1 == v1_clone
True
Tests of sequence behavior::
>>> v1 = Vector([3, 4, 5])
>>> len(v1)
3
>>> v1[0], v1[len(v1)-1], v1[-1]
(3.0, 5.0, 5.0)
Test of slicing::
>>> v7 = Vector(range(7))
>>> v7[-1]
6.0
>>> v7[1:4]
Vector([1.0, 2.0, 3.0])
>>> v7[-1:]
Vector([6.0])
>>> v7[1,2]
Traceback (most recent call last):
...
TypeError: Vector indices must be integers
Tests of dynamic attribute access::
>>> v7 = Vector(range(10))
>>> v7.x
0.0
>>> v7.y, v7.z, v7.t
(1.0, 2.0, 3.0)
Dynamic attribute lookup failures::
>>> v7.k
Traceback (most recent call last):
...
AttributeError: 'Vector' object has no attribute 'k'
>>> v3 = Vector(range(3))
>>> v3.t
Traceback (most recent call last):
...
AttributeError: 'Vector' object has no attribute 't'
>>> v3.spam
Traceback (most recent call last):
...
AttributeError: 'Vector' object has no attribute 'spam'
Tests of hashing::
>>> v1 = Vector([3, 4])
>>> v2 = Vector([3.1, 4.2])
>>> v3 = Vector([3, 4, 5])
>>> v6 = Vector(range(6))
>>> hash(v1), hash(v3), hash(v6)
(7, 2, 1)
Most hash values of non-integers vary from a 32-bit to 64-bit Python build::
>>> import sys
>>> hash(v2) == (384307168202284039 if sys.maxsize > 2**32 else 357915986)
True
Tests of ``format()`` with Cartesian coordinates in 2D::
>>> v1 = Vector([3, 4])
>>> format(v1)
'(3.0, 4.0)'
>>> format(v1, '.2f')
'(3.00, 4.00)'
>>> format(v1, '.3e')
'(3.000e+00, 4.000e+00)'
Tests of ``format()`` with Cartesian coordinates in 3D and 7D::
>>> v3 = Vector([3, 4, 5])
>>> format(v3)
'(3.0, 4.0, 5.0)'
>>> format(Vector(range(7)))
'(0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0)'
Tests of ``format()`` with spherical coordinates in 2D, 3D and 4D::
>>> format(Vector([1, 1]), 'h') # doctest:+ELLIPSIS
'<1.414213..., 0.785398...>'
>>> format(Vector([1, 1]), '.3eh')
'<1.414e+00, 7.854e-01>'
>>> format(Vector([1, 1]), '0.5fh')
'<1.41421, 0.78540>'
>>> format(Vector([1, 1, 1]), 'h') # doctest:+ELLIPSIS
'<1.73205..., 0.95531..., 0.78539...>'
>>> format(Vector([2, 2, 2]), '.3eh')
'<3.464e+00, 9.553e-01, 7.854e-01>'
>>> format(Vector([0, 0, 0]), '0.5fh')
'<0.00000, 0.00000, 0.00000>'
>>> format(Vector([-1, -1, -1, -1]), 'h') # doctest:+ELLIPSIS
'<2.0, 2.09439..., 2.18627..., 3.92699...>'
>>> format(Vector([2, 2, 2, 2]), '.3eh')
'<4.000e+00, 1.047e+00, 9.553e-01, 7.854e-01>'
>>> format(Vector([0, 1, 0, 0]), '0.5fh')
'<1.00000, 1.57080, 0.00000, 0.00000>'
Basic tests of operator ``+``::
>>> v1 = Vector([3, 4, 5])
>>> v2 = Vector([6, 7, 8])
>>> v1 + v2
Vector([9.0, 11.0, 13.0])
>>> v1 + v2 == Vector([3+6, 4+7, 5+8])
True
>>> v3 = Vector([1, 2])
>>> v1 + v3 # short vectors are filled with 0.0 on addition
Vector([4.0, 6.0, 5.0])
Tests of ``+`` with mixed types::
>>> v1 + (10, 20, 30)
Vector([13.0, 24.0, 35.0])
>>> from vector2d_v3 import Vector2d
>>> v2d = Vector2d(1, 2)
>>> v1 + v2d
Vector([4.0, 6.0, 5.0])
Tests of ``+`` with mixed types, swapped operands::
>>> (10, 20, 30) + v1
Vector([13.0, 24.0, 35.0])
>>> from vector2d_v3 import Vector2d
>>> v2d = Vector2d(1, 2)
>>> v2d + v1
Vector([4.0, 6.0, 5.0])
Tests of ``+`` with an unsuitable operand:
>>> v1 + 1
Traceback (most recent call last):
...
TypeError: unsupported operand type(s) for +: 'Vector' and 'int'
>>> v1 + 'ABC'
Traceback (most recent call last):
...
TypeError: unsupported operand type(s) for +: 'Vector' and 'str'
Basic tests of operator ``*``::
>>> v1 = Vector([1, 2, 3])
>>> v1 * 10
Vector([10.0, 20.0, 30.0])
>>> 10 * v1
Vector([10.0, 20.0, 30.0])
Tests of ``*`` with unusual but valid operands::
>>> v1 * True
Vector([1.0, 2.0, 3.0])
>>> from fractions import Fraction
>>> v1 * Fraction(1, 3) # doctest:+ELLIPSIS
Vector([0.3333..., 0.6666..., 1.0])
Tests of ``*`` with unsuitable operands::
>>> v1 * (1, 2)
Traceback (most recent call last):
...
TypeError: can't multiply sequence by non-int of type 'Vector'
Tests of operator `==`::
>>> va = Vector(range(1, 4))
>>> vb = Vector([1.0, 2.0, 3.0])
>>> va == vb
True
>>> vc = Vector([1, 2])
>>> from vector2d_v3 import Vector2d
>>> v2d = Vector2d(1, 2)
>>> vc == v2d
True
>>> va == (1, 2, 3)
False
Tests of operator `!=`::
>>> va != vb
False
>>> vc != v2d
False
>>> va != (1, 2, 3)
True
Tests for operator `@` (Python >= 3.5), computing the dot product::
>>> va = Vector([1, 2, 3])
>>> vz = Vector([5, 6, 7])
>>> va @ vz == 38.0 # 1*5 + 2*6 + 3*7
True
>>> [10, 20, 30] @ vz
380.0
>>> va @ 3
Traceback (most recent call last):
...
TypeError: unsupported operand type(s) for @: 'Vector' and 'int'
""" |
"""
=============================
Byteswapping and byte order
=============================
Introduction to byte ordering and ndarrays
==========================================
The ``ndarray`` is an object that provide a python array interface to data
in memory.
It often happens that the memory that you want to view with an array is
not of the same byte ordering as the computer on which you are running
Python.
For example, I might be working on a computer with a little-endian CPU -
such as an Intel Pentium, but I have loaded some data from a file
written by a computer that is big-endian. Let's say I have loaded 4
bytes from a file written by a Sun (big-endian) computer. I know that
these 4 bytes represent two 16-bit integers. On a big-endian machine, a
two-byte integer is stored with the Most Significant Byte (MSB) first,
and then the Least Significant Byte (LSB). Thus the bytes are, in memory order:
#. MSB integer 1
#. LSB integer 1
#. MSB integer 2
#. LSB integer 2
Let's say the two integers were in fact 1 and 770. Because 770 = 256 *
3 + 2, the 4 bytes in memory would contain respectively: 0, 1, 3, 2.
The bytes I have loaded from the file would have these contents:
>>> big_end_str = chr(0) + chr(1) + chr(3) + chr(2)
>>> big_end_str
'\\x00\\x01\\x03\\x02'
We might want to use an ``ndarray`` to access these integers. In that
case, we can create an array around this memory, and tell numpy that
there are two integers, and that they are 16 bit and big-endian:
>>> import numpy as np
>>> big_end_arr = np.ndarray(shape=(2,),dtype='>i2', buffer=big_end_str)
>>> big_end_arr[0]
1
>>> big_end_arr[1]
770
Note the array ``dtype`` above of ``>i2``. The ``>`` means 'big-endian'
(``<`` is little-endian) and ``i2`` means 'signed 2-byte integer'. For
example, if our data represented a single unsigned 4-byte little-endian
integer, the dtype string would be ``<u4``.
In fact, why don't we try that?
>>> little_end_u4 = np.ndarray(shape=(1,),dtype='<u4', buffer=big_end_str)
>>> little_end_u4[0] == 1 * 256**1 + 3 * 256**2 + 2 * 256**3
True
Returning to our ``big_end_arr`` - in this case our underlying data is
big-endian (data endianness) and we've set the dtype to match (the dtype
is also big-endian). However, sometimes you need to flip these around.
.. warning::
Scalars currently do not include byte order information, so extracting
a scalar from an array will return an integer in native byte order.
Hence:
>>> big_end_arr[0].dtype.byteorder == little_end_u4[0].dtype.byteorder
True
Changing byte ordering
======================
As you can imagine from the introduction, there are two ways you can
affect the relationship between the byte ordering of the array and the
underlying memory it is looking at:
* Change the byte-ordering information in the array dtype so that it
interprets the underlying data as being in a different byte order.
This is the role of ``arr.newbyteorder()``
* Change the byte-ordering of the underlying data, leaving the dtype
interpretation as it was. This is what ``arr.byteswap()`` does.
The common situations in which you need to change byte ordering are:
#. Your data and dtype endianess don't match, and you want to change
the dtype so that it matches the data.
#. Your data and dtype endianess don't match, and you want to swap the
data so that they match the dtype
#. Your data and dtype endianess match, but you want the data swapped
and the dtype to reflect this
Data and dtype endianness don't match, change dtype to match data
-----------------------------------------------------------------
We make something where they don't match:
>>> wrong_end_dtype_arr = np.ndarray(shape=(2,),dtype='<i2', buffer=big_end_str)
>>> wrong_end_dtype_arr[0]
256
The obvious fix for this situation is to change the dtype so it gives
the correct endianness:
>>> fixed_end_dtype_arr = wrong_end_dtype_arr.newbyteorder()
>>> fixed_end_dtype_arr[0]
1
Note the array has not changed in memory:
>>> fixed_end_dtype_arr.tobytes() == big_end_str
True
Data and type endianness don't match, change data to match dtype
----------------------------------------------------------------
You might want to do this if you need the data in memory to be a certain
ordering. For example you might be writing the memory out to a file
that needs a certain byte ordering.
>>> fixed_end_mem_arr = wrong_end_dtype_arr.byteswap()
>>> fixed_end_mem_arr[0]
1
Now the array *has* changed in memory:
>>> fixed_end_mem_arr.tobytes() == big_end_str
False
Data and dtype endianness match, swap data and dtype
----------------------------------------------------
You may have a correctly specified array dtype, but you need the array
to have the opposite byte order in memory, and you want the dtype to
match so the array values make sense. In this case you just do both of
the previous operations:
>>> swapped_end_arr = big_end_arr.byteswap().newbyteorder()
>>> swapped_end_arr[0]
1
>>> swapped_end_arr.tobytes() == big_end_str
False
An easier way of casting the data to a specific dtype and byte ordering
can be achieved with the ndarray astype method:
>>> swapped_end_arr = big_end_arr.astype('<i2')
>>> swapped_end_arr[0]
1
>>> swapped_end_arr.tobytes() == big_end_str
False
""" |
"""
# Plotting Benchmark Results
## Usage
usage: benchmark_plot.py [-h] [--test TEST] [--kind KIND] [--show] [--save]
filename name
Plotting
positional arguments:
filename path to file with benchmark data
name type name
optional arguments:
-h, --help show this help message and exit
--test TEST
--kind KIND
--show
--save
## Compare Implementations
python -m tests.benchmark_sortedlist --bare > tests/results_sortedlist.txt
python -m tests.benchmark_plot tests/results_sortedlist.txt SortedList --save
python -m tests.benchmark_sorteddict --bare > tests/results_sorteddict.txt
python -m tests.benchmark_plot tests/results_sorteddict.txt SortedDict --save
python -m tests.benchmark_sortedset --bare > tests/results_sortedset.txt
python -m tests.benchmark_plot tests/results_sortedset.txt SortedSet --save
## Compare Python Versions
rm tests/results_runtime_sortedlist.txt
echo ". env27/bin/activate && python -m tests.benchmark_sortedlist --bare --kind SortedList --suffix _Py27 >> tests/results_runtime_sortedlist.txt" | bash
echo ". env34/bin/activate && python -m tests.benchmark_sortedlist --bare --kind SortedList --suffix _Py34 >> tests/results_runtime_sortedlist.txt" | bash
echo ". env27/bin/activate && pypy -m tests.benchmark_sortedlist --bare --kind SortedList --suffix _PyPy >> tests/results_runtime_sortedlist.txt" | bash
python -m tests.benchmark_plot tests/results_runtime_sortedlist.txt SortedList --suffix _runtime --save
rm tests/results_runtime_sorteddict.txt
echo ". env27/bin/activate && python -m tests.benchmark_sorteddict --bare --kind SortedDict --suffix _Py27 >> tests/results_runtime_sorteddict.txt" | bash
echo ". env34/bin/activate && python -m tests.benchmark_sorteddict --bare --kind SortedDict --suffix _Py34 >> tests/results_runtime_sorteddict.txt" | bash
echo ". env27/bin/activate && pypy -m tests.benchmark_sorteddict --bare --kind SortedDict --suffix _PyPy >> tests/results_runtime_sorteddict.txt" | bash
python -m tests.benchmark_plot tests/results_runtime_sorteddict.txt SortedDict --suffix _runtime --save
rm tests/results_runtime_sortedset.txt
echo ". env27/bin/activate && python -m tests.benchmark_sortedset --bare --kind SortedSet --suffix _Py27 >> tests/results_runtime_sortedset.txt" | bash
echo ". env34/bin/activate && python -m tests.benchmark_sortedset --bare --kind SortedSet --suffix _Py34 >> tests/results_runtime_sortedset.txt" | bash
echo ". env27/bin/activate && pypy -m tests.benchmark_sortedset --bare --kind SortedSet --suffix _PyPy >> tests/results_runtime_sortedset.txt" | bash
python -m tests.benchmark_plot tests/results_runtime_sortedset.txt SortedSet --suffix _runtime --save
## Compare Loads
rm tests/results_load_sortedlist.txt
python -m tests.benchmark_sortedlist --bare --kind SortedList --suffix _100 --load 100 --no-limit >> tests/results_load_sortedlist.txt
python -m tests.benchmark_sortedlist --bare --kind SortedList --suffix _1000 --load 1000 --no-limit >> tests/results_load_sortedlist.txt
python -m tests.benchmark_sortedlist --bare --kind SortedList --suffix _10000 --load 10000 --no-limit >> tests/results_load_sortedlist.txt
python -m tests.benchmark_plot tests/results_load_sortedlist.txt SortedList --suffix _load --save
rm tests/results_load_sorteddict.txt
python -m tests.benchmark_sorteddict --bare --kind SortedDict --suffix _100 --load 100 --no-limit >> tests/results_load_sorteddict.txt
python -m tests.benchmark_sorteddict --bare --kind SortedDict --suffix _1000 --load 1000 --no-limit >> tests/results_load_sorteddict.txt
python -m tests.benchmark_sorteddict --bare --kind SortedDict --suffix _10000 --load 10000 --no-limit >> tests/results_load_sorteddict.txt
python -m tests.benchmark_plot tests/results_load_sorteddict.txt SortedDict --suffix _load --save
rm tests/results_load_sortedset.txt
python -m tests.benchmark_sortedset --bare --kind SortedSet --suffix _100 --load 100 --no-limit >> tests/results_load_sortedset.txt
python -m tests.benchmark_sortedset --bare --kind SortedSet --suffix _1000 --load 1000 --no-limit >> tests/results_load_sortedset.txt
python -m tests.benchmark_sortedset --bare --kind SortedSet --suffix _10000 --load 10000 --no-limit >> tests/results_load_sortedset.txt
python -m tests.benchmark_plot tests/results_load_sortedset.txt SortedSet --suffix _load --save
""" |
# -*- encoding: utf-8 -*-
##############################################################################
#
# OpenERP, Open Source Management Solution
# Copyright (C) 2004-2009 Tiny SPRL (<http://tiny.be>).
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Affero General Public License as
# published by the Free Software Foundation, either version 3 of the
# License, or (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
##############################################################################
# SKR03
# =====
# Dieses Modul bietet Ihnen einen deutschen Kontenplan basierend auf dem SKR03.
# Gemäss der aktuellen Einstellungen ist die Firma nicht Umsatzsteuerpflichtig.
# Diese Grundeinstellung ist sehr einfach zu ändern und bedarf in der Regel
# grundsätzlich eine initiale Zuweisung von Steuerkonten zu Produkten und / oder
# Sachkonten oder zu Partnern.
# Die Umsatzsteuern (voller Steuersatz, reduzierte Steuer und steuerfrei)
# sollten bei den Produktstammdaten hinterlegt werden (in Abhängigkeit der
# Steuervorschriften). Die Zuordnung erfolgt auf dem Aktenreiter Finanzbuchhaltung
# (Kategorie: Umsatzsteuer).
# Die Vorsteuern (voller Steuersatz, reduzierte Steuer und steuerfrei)
# sollten ebenso bei den Produktstammdaten hinterlegt werden (in Abhängigkeit
# der Steuervorschriften). Die Zuordnung erfolgt auf dem Aktenreiter
# Finanzbuchhaltung (Kategorie: Vorsteuer).
# Die Zuordnung der Steuern für Ein- und Ausfuhren aus EU Ländern, sowie auch
# für den Ein- und Verkauf aus und in Drittländer sollten beim Partner
# (Lieferant/Kunde)hinterlegt werden (in Anhängigkeit vom Herkunftsland
# des Lieferanten/Kunden). Die Zuordnung beim Kunden ist 'höherwertig' als
# die Zuordnung bei Produkten und überschreibt diese im Einzelfall.
#
# Zur Vereinfachung der Steuerausweise und Buchung bei Auslandsgeschäften
# erlaubt OpenERP ein generelles Mapping von Steuerausweis und Steuerkonten
# (z.B. Zuordnung 'Umsatzsteuer 19%' zu 'steuerfreie Einfuhren aus der EU')
# zwecks Zuordnung dieses Mappings zum ausländischen Partner (Kunde/Lieferant).
# Die Rechnungsbuchung beim Einkauf bewirkt folgendes:
# Die Steuerbemessungsgrundlage (exklusive Steuer) wird ausgewiesen bei den
# jeweiligen Kategorien für den Vorsteuer Steuermessbetrag (z.B. Vorsteuer
# Steuermessbetrag Voller Steuersatz 19%).
# Der Steuerbetrag erscheint unter der Kategorie 'Vorsteuern' (z.B. Vorsteuer
# 19%). Durch multidimensionale Hierachien können verschiedene Positionen
# zusammengefasst werden und dann in Form eines Reports ausgegeben werden.
#
# Die Rechnungsbuchung beim Verkauf bewirkt folgendes:
# Die Steuerbemessungsgrundlage (exklusive Steuer) wird ausgewiesen bei den
# jeweiligen Kategorien für den Umsatzsteuer Steuermessbetrag
# (z.B. Umsatzsteuer Steuermessbetrag Voller Steuersatz 19%).
# Der Steuerbetrag erscheint unter der Kategorie 'Umsatzsteuer'
# (z.B. Umsatzsteuer 19%). Durch multidimensionale Hierachien können
# verschiedene Positionen zusammengefasst werden.
# Die zugewiesenen Steuerausweise können auf Ebene der einzelnen
# Rechnung (Eingangs- und Ausgangsrechnung) nachvollzogen werden,
# und dort gegebenenfalls angepasst werden.
# Rechnungsgutschriften führen zu einer Korrektur (Gegenposition)
# der Steuerbuchung, in Form einer spiegelbildlichen Buchung.
# SKR04
# =====
# Dieses Modul bietet Ihnen einen deutschen Kontenplan basierend auf dem SKR04.
# Gemäss der aktuellen Einstellungen ist die Firma nicht Umsatzsteuerpflichtig,
# d.h. im Standard existiert keine Zuordnung von Produkten und Sachkonten zu
# Steuerschlüsseln.
# Diese Grundeinstellung ist sehr einfach zu ändern und bedarf in der Regel
# grundsätzlich eine initiale Zuweisung von Steuerschlüsseln zu Produkten und / oder
# Sachkonten oder zu Partnern.
# Die Umsatzsteuern (voller Steuersatz, reduzierte Steuer und steuerfrei)
# sollten bei den Produktstammdaten hinterlegt werden (in Abhängigkeit der
# Steuervorschriften). Die Zuordnung erfolgt auf dem Aktenreiter Finanzbuchhaltung
# (Kategorie: Umsatzsteuer).
# Die Vorsteuern (voller Steuersatz, reduzierte Steuer und steuerfrei)
# sollten ebenso bei den Produktstammdaten hinterlegt werden (in Abhängigkeit
# der Steuervorschriften). Die Zuordnung erfolgt auf dem Aktenreiter
# Finanzbuchhaltung (Kategorie: Vorsteuer).
# Die Zuordnung der Steuern für Ein- und Ausfuhren aus EU Ländern, sowie auch
# für den Ein- und Verkauf aus und in Drittländer sollten beim Partner
# (Lieferant/Kunde) hinterlegt werden (in Anhängigkeit vom Herkunftsland
# des Lieferanten/Kunden). Die Zuordnung beim Kunden ist 'höherwertig' als
# die Zuordnung bei Produkten und überschreibt diese im Einzelfall.
#
# Zur Vereinfachung der Steuerausweise und Buchung bei Auslandsgeschäften
# erlaubt OpenERP ein generelles Mapping von Steuerausweis und Steuerkonten
# (z.B. Zuordnung 'Umsatzsteuer 19%' zu 'steuerfreie Einfuhren aus der EU')
# zwecks Zuordnung dieses Mappings zum ausländischen Partner (Kunde/Lieferant).
# Die Rechnungsbuchung beim Einkauf bewirkt folgendes:
# Die Steuerbemessungsgrundlage (exklusive Steuer) wird ausgewiesen bei den
# jeweiligen Kategorien für den Vorsteuer Steuermessbetrag (z.B. Vorsteuer
# Steuermessbetrag Voller Steuersatz 19%).
# Der Steuerbetrag erscheint unter der Kategorie 'Vorsteuern' (z.B. Vorsteuer
# 19%). Durch multidimensionale Hierachien können verschiedene Positionen
# zusammengefasst werden und dann in Form eines Reports ausgegeben werden.
#
# Die Rechnungsbuchung beim Verkauf bewirkt folgendes:
# Die Steuerbemessungsgrundlage (exklusive Steuer) wird ausgewiesen bei den
# jeweiligen Kategorien für den Umsatzsteuer Steuermessbetrag
# (z.B. Umsatzsteuer Steuermessbetrag Voller Steuersatz 19%).
# Der Steuerbetrag erscheint unter der Kategorie 'Umsatzsteuer'
# (z.B. Umsatzsteuer 19%). Durch multidimensionale Hierachien können
# verschiedene Positionen zusammengefasst werden.
# Die zugewiesenen Steuerausweise können auf Ebene der einzelnen
# Rechnung (Eingangs- und Ausgangsrechnung) nachvollzogen werden,
# und dort gegebenenfalls angepasst werden.
# Rechnungsgutschriften führen zu einer Korrektur (Gegenposition)
# der Steuerbuchung, in Form einer spiegelbildlichen Buchung.
|
"""Generic socket server classes.
This module tries to capture the various aspects of defining a server:
For socket-based servers:
- address family:
- AF_INET{,6}: IP (Internet Protocol) sockets (default)
- AF_UNIX: Unix domain sockets
- others, e.g. AF_DECNET are conceivable (see <socket.h>
- socket type:
- SOCK_STREAM (reliable stream, e.g. TCP)
- SOCK_DGRAM (datagrams, e.g. UDP)
For request-based servers (including socket-based):
- client address verification before further looking at the request
(This is actually a hook for any processing that needs to look
at the request before anything else, e.g. logging)
- how to handle multiple requests:
- synchronous (one request is handled at a time)
- forking (each request is handled by a new process)
- threading (each request is handled by a new thread)
The classes in this module favor the server type that is simplest to
write: a synchronous TCP/IP server. This is bad class design, but
save some typing. (There's also the issue that a deep class hierarchy
slows down method lookups.)
There are five classes in an inheritance diagram, four of which represent
synchronous servers of four types:
+------------+
| BaseServer |
+------------+
|
v
+-----------+ +------------------+
| TCPServer |------->| UnixStreamServer |
+-----------+ +------------------+
|
v
+-----------+ +--------------------+
| UDPServer |------->| UnixDatagramServer |
+-----------+ +--------------------+
Note that UnixDatagramServer derives from UDPServer, not from
UnixStreamServer -- the only difference between an IP and a Unix
stream server is the address family, which is simply repeated in both
unix server classes.
Forking and threading versions of each type of server can be created
using the ForkingMixIn and ThreadingMixIn mix-in classes. For
instance, a threading UDP server class is created as follows:
class ThreadingUDPServer(ThreadingMixIn, UDPServer): pass
The Mix-in class must come first, since it overrides a method defined
in UDPServer! Setting the various member variables also changes
the behavior of the underlying server mechanism.
To implement a service, you must derive a class from
BaseRequestHandler and redefine its handle() method. You can then run
various versions of the service by combining one of the server classes
with your request handler class.
The request handler class must be different for datagram or stream
services. This can be hidden by using the request handler
subclasses StreamRequestHandler or DatagramRequestHandler.
Of course, you still have to use your head!
For instance, it makes no sense to use a forking server if the service
contains state in memory that can be modified by requests (since the
modifications in the child process would never reach the initial state
kept in the parent process and passed to each child). In this case,
you can use a threading server, but you will probably have to use
locks to avoid two requests that come in nearly simultaneous to apply
conflicting changes to the server state.
On the other hand, if you are building e.g. an HTTP server, where all
data is stored externally (e.g. in the file system), a synchronous
class will essentially render the service "deaf" while one request is
being handled -- which may be for a very long time if a client is slow
to reqd all the data it has requested. Here a threading or forking
server is appropriate.
In some cases, it may be appropriate to process part of a request
synchronously, but to finish processing in a forked child depending on
the request data. This can be implemented by using a synchronous
server and doing an explicit fork in the request handler class
handle() method.
Another approach to handling multiple simultaneous requests in an
environment that supports neither threads nor fork (or where these are
too expensive or inappropriate for the service) is to maintain an
explicit table of partially finished requests and to use select() to
decide which request to work on next (or whether to handle a new
incoming request). This is particularly important for stream services
where each client can potentially be connected for a long time (if
threads or subprocesses cannot be used).
Future work:
- Standard classes for Sun RPC (which uses either UDP or TCP)
- Standard mix-in classes to implement various authentication
and encryption schemes
- Standard framework for select-based multiplexing
XXX Open problems:
- What to do with out-of-band data?
BaseServer:
- split generic "request" functionality out into BaseServer class.
Copyright (C) 2000 NAME <EMAIL>
example: read entries from a SQL database (requires overriding
get_request() to return a table entry from the database).
entry is processed by a RequestHandlerClass.
""" |
#
# XML-RPC CLIENT LIBRARY
# $Id$
#
# an XML-RPC client interface for Python.
#
# the marshalling and response parser code can also be used to
# implement XML-RPC servers.
#
# Notes:
# this version is designed to work with Python 2.1 or newer.
#
# History:
# 1999-01-14 fl Created
# 1999-01-15 fl Changed dateTime to use localtime
# 1999-01-16 fl Added Binary/base64 element, default to RPC2 service
# 1999-01-19 fl Fixed array data element (from Skip Montanaro)
# 1999-01-21 fl Fixed dateTime constructor, etc.
# 1999-02-02 fl Added fault handling, handle empty sequences, etc.
# 1999-02-10 fl Fixed problem with empty responses (from Skip Montanaro)
# 1999-06-20 fl Speed improvements, pluggable parsers/transports (0.9.8)
# 2000-11-28 fl Changed boolean to check the truth value of its argument
# 2001-02-24 fl Added encoding/Unicode/SafeTransport patches
# 2001-02-26 fl Added compare support to wrappers (0.9.9/1.0b1)
# 2001-03-28 fl Make sure response tuple is a singleton
# 2001-03-29 fl Don't require empty params element (from NAME 2001-06-10 fl Folded in _xmlrpclib accelerator support (1.0b2)
# 2001-08-20 fl Base xmlrpclib.Error on built-in Exception (from NAME 2001-09-03 fl Allow Transport subclass to override getparser
# 2001-09-10 fl Lazy import of urllib, cgi, xmllib (20x import speedup)
# 2001-10-01 fl Remove containers from memo cache when done with them
# 2001-10-01 fl Use faster escape method (80% dumps speedup)
# 2001-10-02 fl More dumps microtuning
# 2001-10-04 fl Make sure import expat gets a parser (from NAME 2001-10-10 sm Allow long ints to be passed as ints if they don't overflow
# 2001-10-17 sm Test for int and long overflow (allows use on 64-bit systems)
# 2001-11-12 fl Use repr() to marshal doubles (from NAME 2002-03-17 fl Avoid buffered read when possible (from NAME 2002-04-07 fl Added pythondoc comments
# 2002-04-16 fl Added __str__ methods to datetime/binary wrappers
# 2002-05-15 fl Added error constants (from NAME 2002-06-27 fl Merged with Python CVS version
# 2002-10-22 fl Added basic authentication (based on code from NAME 2003-01-22 sm Add support for the bool type
# 2003-02-27 gvr Remove apply calls
# 2003-04-24 sm Use cStringIO if available
# 2003-04-25 ak Add support for nil
# 2003-06-15 gn Add support for time.struct_time
# 2003-07-12 gp Correct marshalling of Faults
# 2003-10-31 mvl Add multicall support
# 2004-08-20 mvl Bump minimum supported Python version to 2.1
#
# Copyright (c) 1999-2002 by Secret Labs AB.
# Copyright (c) 1999-2002 by NAME EMAIL http://www.pythonware.com
#
# --------------------------------------------------------------------
# The XML-RPC client interface is
#
# Copyright (c) 1999-2002 by Secret Labs AB
# Copyright (c) 1999-2002 by NAME By obtaining, using, and/or copying this software and/or its
# associated documentation, you agree that you have read, understood,
# and will comply with the following terms and conditions:
#
# Permission to use, copy, modify, and distribute this software and
# its associated documentation for any purpose and without fee is
# hereby granted, provided that the above copyright notice appears in
# all copies, and that both that copyright notice and this permission
# notice appear in supporting documentation, and that the name of
# Secret Labs AB or the author not be used in advertising or publicity
# pertaining to distribution of the software without specific, written
# prior permission.
#
# SECRET LABS AB AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH REGARD
# TO THIS SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANT-
# ABILITY AND FITNESS. IN NO EVENT SHALL SECRET LABS AB OR THE AUTHOR
# BE LIABLE FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY
# DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS,
# WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS
# ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE
# OF THIS SOFTWARE.
# --------------------------------------------------------------------
|
"""
===============
Array Internals
===============
Internal organization of numpy arrays
=====================================
It helps to understand a bit about how numpy arrays are handled under the covers to help understand numpy better. This section will not go into great detail. Those wishing to understand the full details are referred to Travis Oliphant's book "Guide to Numpy".
Numpy arrays consist of two major components, the raw array data (from now on,
referred to as the data buffer), and the information about the raw array data.
The data buffer is typically what people think of as arrays in C or Fortran,
a contiguous (and fixed) block of memory containing fixed sized data items.
Numpy also contains a significant set of data that describes how to interpret
the data in the data buffer. This extra information contains (among other things):
1) The basic data element's size in bytes
2) The start of the data within the data buffer (an offset relative to the
beginning of the data buffer).
3) The number of dimensions and the size of each dimension
4) The separation between elements for each dimension (the 'stride'). This
does not have to be a multiple of the element size
5) The byte order of the data (which may not be the native byte order)
6) Whether the buffer is read-only
7) Information (via the dtype object) about the interpretation of the basic
data element. The basic data element may be as simple as a int or a float,
or it may be a compound object (e.g., struct-like), a fixed character field,
or Python object pointers.
8) Whether the array is to interpreted as C-order or Fortran-order.
This arrangement allow for very flexible use of arrays. One thing that it allows
is simple changes of the metadata to change the interpretation of the array buffer.
Changing the byteorder of the array is a simple change involving no rearrangement
of the data. The shape of the array can be changed very easily without changing
anything in the data buffer or any data copying at all
Among other things that are made possible is one can create a new array metadata
object that uses the same data buffer
to create a new view of that data buffer that has a different interpretation
of the buffer (e.g., different shape, offset, byte order, strides, etc) but
shares the same data bytes. Many operations in numpy do just this such as
slices. Other operations, such as transpose, don't move data elements
around in the array, but rather change the information about the shape and strides so that the indexing of the array changes, but the data in the doesn't move.
Typically these new versions of the array metadata but the same data buffer are
new 'views' into the data buffer. There is a different ndarray object, but it
uses the same data buffer. This is why it is necessary to force copies through
use of the .copy() method if one really wants to make a new and independent
copy of the data buffer.
New views into arrays mean the the object reference counts for the data buffer
increase. Simply doing away with the original array object will not remove the
data buffer if other views of it still exist.
Multidimensional Array Indexing Order Issues
============================================
What is the right way to index
multi-dimensional arrays? Before you jump to conclusions about the one and
true way to index multi-dimensional arrays, it pays to understand why this is
a confusing issue. This section will try to explain in detail how numpy
indexing works and why we adopt the convention we do for images, and when it
may be appropriate to adopt other conventions.
The first thing to understand is
that there are two conflicting conventions for indexing 2-dimensional arrays.
Matrix notation uses the first index to indicate which row is being selected and
the second index to indicate which column is selected. This is opposite the
geometrically oriented-convention for images where people generally think the
first index represents x position (i.e., column) and the second represents y
position (i.e., row). This alone is the source of much confusion;
matrix-oriented users and image-oriented users expect two different things with
regard to indexing.
The second issue to understand is how indices correspond
to the order the array is stored in memory. In Fortran the first index is the
most rapidly varying index when moving through the elements of a two
dimensional array as it is stored in memory. If you adopt the matrix
convention for indexing, then this means the matrix is stored one column at a
time (since the first index moves to the next row as it changes). Thus Fortran
is considered a Column-major language. C has just the opposite convention. In
C, the last index changes most rapidly as one moves through the array as
stored in memory. Thus C is a Row-major language. The matrix is stored by
rows. Note that in both cases it presumes that the matrix convention for
indexing is being used, i.e., for both Fortran and C, the first index is the
row. Note this convention implies that the indexing convention is invariant
and that the data order changes to keep that so.
But that's not the only way
to look at it. Suppose one has large two-dimensional arrays (images or
matrices) stored in data files. Suppose the data are stored by rows rather than
by columns. If we are to preserve our index convention (whether matrix or
image) that means that depending on the language we use, we may be forced to
reorder the data if it is read into memory to preserve our indexing
convention. For example if we read row-ordered data into memory without
reordering, it will match the matrix indexing convention for C, but not for
Fortran. Conversely, it will match the image indexing convention for Fortran,
but not for C. For C, if one is using data stored in row order, and one wants
to preserve the image index convention, the data must be reordered when
reading into memory.
In the end, which you do for Fortran or C depends on
which is more important, not reordering data or preserving the indexing
convention. For large images, reordering data is potentially expensive, and
often the indexing convention is inverted to avoid that.
The situation with
numpy makes this issue yet more complicated. The internal machinery of numpy
arrays is flexible enough to accept any ordering of indices. One can simply
reorder indices by manipulating the internal stride information for arrays
without reordering the data at all. Numpy will know how to map the new index
order to the data without moving the data.
So if this is true, why not choose
the index order that matches what you most expect? In particular, why not define
row-ordered images to use the image convention? (This is sometimes referred
to as the Fortran convention vs the C convention, thus the 'C' and 'FORTRAN'
order options for array ordering in numpy.) The drawback of doing this is
potential performance penalties. It's common to access the data sequentially,
either implicitly in array operations or explicitly by looping over rows of an
image. When that is done, then the data will be accessed in non-optimal order.
As the first index is incremented, what is actually happening is that elements
spaced far apart in memory are being sequentially accessed, with usually poor
memory access speeds. For example, for a two dimensional image 'im' defined so
that im[0, 10] represents the value at x=0, y=10. To be consistent with usual
Python behavior then im[0] would represent a column at x=0. Yet that data
would be spread over the whole array since the data are stored in row order.
Despite the flexibility of numpy's indexing, it can't really paper over the fact
basic operations are rendered inefficient because of data order or that getting
contiguous subarrays is still awkward (e.g., im[:,0] for the first row, vs
im[0]), thus one can't use an idiom such as for row in im; for col in im does
work, but doesn't yield contiguous column data.
As it turns out, numpy is
smart enough when dealing with ufuncs to determine which index is the most
rapidly varying one in memory and uses that for the innermost loop. Thus for
ufuncs there is no large intrinsic advantage to either approach in most cases.
On the other hand, use of .flat with an FORTRAN ordered array will lead to
non-optimal memory access as adjacent elements in the flattened array (iterator,
actually) are not contiguous in memory.
Indeed, the fact is that Python
indexing on lists and other sequences naturally leads to an outside-to inside
ordering (the first index gets the largest grouping, the next the next largest,
and the last gets the smallest element). Since image data are normally stored
by rows, this corresponds to position within rows being the last item indexed.
If you do want to use Fortran ordering realize that
there are two approaches to consider: 1) accept that the first index is just not
the most rapidly changing in memory and have all your I/O routines reorder
your data when going from memory to disk or visa versa, or use numpy's
mechanism for mapping the first index to the most rapidly varying data. We
recommend the former if possible. The disadvantage of the latter is that many
of numpy's functions will yield arrays without Fortran ordering unless you are
careful to use the 'order' keyword. Doing this would be highly inconvenient.
Otherwise we recommend simply learning to reverse the usual order of indices
when accessing elements of an array. Granted, it goes against the grain, but
it is more in line with Python semantics and the natural order of the data.
""" |
"""Stuff to parse AIFF-C and AIFF files.
Unless explicitly stated otherwise, the description below is true
both for AIFF-C files and AIFF files.
An AIFF-C file has the following structure.
+-----------------+
| FORM |
+-----------------+
| <size> |
+----+------------+
| | AIFC |
| +------------+
| | <chunks> |
| | . |
| | . |
| | . |
+----+------------+
An AIFF file has the string "AIFF" instead of "AIFC".
A chunk consists of an identifier (4 bytes) followed by a size (4 bytes,
big endian order), followed by the data. The size field does not include
the size of the 8 byte header.
The following chunk types are recognized.
FVER
<version number of AIFF-C defining document> (AIFF-C only).
MARK
<# of markers> (2 bytes)
list of markers:
<marker ID> (2 bytes, must be > 0)
<position> (4 bytes)
<marker name> ("pstring")
COMM
<# of channels> (2 bytes)
<# of sound frames> (4 bytes)
<size of the samples> (2 bytes)
<sampling frequency> (10 bytes, IEEE 80-bit extended
floating point)
in AIFF-C files only:
<compression type> (4 bytes)
<human-readable version of compression type> ("pstring")
SSND
<offset> (4 bytes, not used by this program)
<blocksize> (4 bytes, not used by this program)
<sound data>
A pstring consists of 1 byte length, a string of characters, and 0 or 1
byte pad to make the total length even.
Usage.
Reading AIFF files:
f = aifc.open(file, 'r')
where file is either the name of a file or an open file pointer.
The open file pointer must have methods read(), seek(), and close().
In some types of audio files, if the setpos() method is not used,
the seek() method is not necessary.
This returns an instance of a class with the following public methods:
getnchannels() -- returns number of audio channels (1 for
mono, 2 for stereo)
getsampwidth() -- returns sample width in bytes
getframerate() -- returns sampling frequency
getnframes() -- returns number of audio frames
getcomptype() -- returns compression type ('NONE' for AIFF files)
getcompname() -- returns human-readable version of
compression type ('not compressed' for AIFF files)
getparams() -- returns a namedtuple consisting of all of the
above in the above order
getmarkers() -- get the list of marks in the audio file or None
if there are no marks
getmark(id) -- get mark with the specified id (raises an error
if the mark does not exist)
readframes(n) -- returns at most n frames of audio
rewind() -- rewind to the beginning of the audio stream
setpos(pos) -- seek to the specified position
tell() -- return the current position
close() -- close the instance (make it unusable)
The position returned by tell(), the position given to setpos() and
the position of marks are all compatible and have nothing to do with
the actual position in the file.
The close() method is called automatically when the class instance
is destroyed.
Writing AIFF files:
f = aifc.open(file, 'w')
where file is either the name of a file or an open file pointer.
The open file pointer must have methods write(), tell(), seek(), and
close().
This returns an instance of a class with the following public methods:
aiff() -- create an AIFF file (AIFF-C default)
aifc() -- create an AIFF-C file
setnchannels(n) -- set the number of channels
setsampwidth(n) -- set the sample width
setframerate(n) -- set the frame rate
setnframes(n) -- set the number of frames
setcomptype(type, name)
-- set the compression type and the
human-readable compression type
setparams(tuple)
-- set all parameters at once
setmark(id, pos, name)
-- add specified mark to the list of marks
tell() -- return current position in output file (useful
in combination with setmark())
writeframesraw(data)
-- write audio frames without pathing up the
file header
writeframes(data)
-- write audio frames and patch up the file header
close() -- patch up the file header and close the
output file
You should set the parameters before the first writeframesraw or
writeframes. The total number of frames does not need to be set,
but when it is set to the correct value, the header does not have to
be patched up.
It is best to first set all parameters, perhaps possibly the
compression type, and then write audio frames using writeframesraw.
When all frames have been written, either call writeframes('') or
close() to patch up the sizes in the header.
Marks can be added anytime. If there are any marks, you must call
close() after all frames have been written.
The close() method is called automatically when the class instance
is destroyed.
When a file is opened with the extension '.aiff', an AIFF file is
written, otherwise an AIFF-C file is written. This default can be
changed by calling aiff() or aifc() before the first writeframes or
writeframesraw.
""" |
"""
=============
Miscellaneous
=============
IEEE 754 Floating Point Special Values:
-----------------------------------------------
Special values defined in numpy: nan, inf,
NaNs can be used as a poor-man's mask (if you don't care what the
original value was)
Note: cannot use equality to test NaNs. E.g.: ::
>>> myarr = np.array([1., 0., np.nan, 3.])
>>> np.where(myarr == np.nan)
>>> np.nan == np.nan # is always False! Use special numpy functions instead.
False
>>> myarr[myarr == np.nan] = 0. # doesn't work
>>> myarr
array([ 1., 0., NaN, 3.])
>>> myarr[np.isnan(myarr)] = 0. # use this instead find
>>> myarr
array([ 1., 0., 0., 3.])
Other related special value functions: ::
isinf(): True if value is inf
isfinite(): True if not nan or inf
nan_to_num(): Map nan to 0, inf to max float, -inf to min float
The following corresponds to the usual functions except that nans are excluded
from the results: ::
nansum()
nanmax()
nanmin()
nanargmax()
nanargmin()
>>> x = np.arange(10.)
>>> x[3] = np.nan
>>> x.sum()
nan
>>> np.nansum(x)
42.0
How numpy handles numerical exceptions:
------------------------------------------
The default is to ``'warn'`` for ``invalid``, ``divide``, and ``overflow``
and ``'ignore'`` for ``underflow``. But this can be changed, and it can be
set individually for different kinds of exceptions. The different behaviors
are:
- 'ignore' : Take no action when the exception occurs.
- 'warn' : Print a `RuntimeWarning` (via the Python `warnings` module).
- 'raise' : Raise a `FloatingPointError`.
- 'call' : Call a function specified using the `seterrcall` function.
- 'print' : Print a warning directly to ``stdout``.
- 'log' : Record error in a Log object specified by `seterrcall`.
These behaviors can be set for all kinds of errors or specific ones:
- all : apply to all numeric exceptions
- invalid : when NaNs are generated
- divide : divide by zero (for integers as well!)
- overflow : floating point overflows
- underflow : floating point underflows
Note that integer divide-by-zero is handled by the same machinery.
These behaviors are set on a per-thread basis.
Examples:
------------
::
>>> oldsettings = np.seterr(all='warn')
>>> np.zeros(5,dtype=np.float32)/0.
invalid value encountered in divide
>>> j = np.seterr(under='ignore')
>>> np.array([1.e-100])**10
>>> j = np.seterr(invalid='raise')
>>> np.sqrt(np.array([-1.]))
FloatingPointError: invalid value encountered in sqrt
>>> def errorhandler(errstr, errflag):
... print "saw stupid error!"
>>> np.seterrcall(errorhandler)
<function err_handler at 0x...>
>>> j = np.seterr(all='call')
>>> np.zeros(5, dtype=np.int32)/0
FloatingPointError: invalid value encountered in divide
saw stupid error!
>>> j = np.seterr(**oldsettings) # restore previous
... # error-handling settings
Interfacing to C:
-----------------
Only a survey of the choices. Little detail on how each works.
1) Bare metal, wrap your own C-code manually.
- Plusses:
- Efficient
- No dependencies on other tools
- Minuses:
- Lots of learning overhead:
- need to learn basics of Python C API
- need to learn basics of numpy C API
- need to learn how to handle reference counting and love it.
- Reference counting often difficult to get right.
- getting it wrong leads to memory leaks, and worse, segfaults
- API will change for Python 3.0!
2) pyrex
- Plusses:
- avoid learning C API's
- no dealing with reference counting
- can code in psuedo python and generate C code
- can also interface to existing C code
- should shield you from changes to Python C api
- become pretty popular within Python community
- Minuses:
- Can write code in non-standard form which may become obsolete
- Not as flexible as manual wrapping
- Maintainers not easily adaptable to new features
Thus:
3) cython - fork of pyrex to allow needed features for SAGE
- being considered as the standard scipy/numpy wrapping tool
- fast indexing support for arrays
4) ctypes
- Plusses:
- part of Python standard library
- good for interfacing to existing sharable libraries, particularly
Windows DLLs
- avoids API/reference counting issues
- good numpy support: arrays have all these in their ctypes
attribute: ::
a.ctypes.data a.ctypes.get_strides
a.ctypes.data_as a.ctypes.shape
a.ctypes.get_as_parameter a.ctypes.shape_as
a.ctypes.get_data a.ctypes.strides
a.ctypes.get_shape a.ctypes.strides_as
- Minuses:
- can't use for writing code to be turned into C extensions, only a wrapper
tool.
5) SWIG (automatic wrapper generator)
- Plusses:
- around a long time
- multiple scripting language support
- C++ support
- Good for wrapping large (many functions) existing C libraries
- Minuses:
- generates lots of code between Python and the C code
- can cause performance problems that are nearly impossible to optimize
out
- interface files can be hard to write
- doesn't necessarily avoid reference counting issues or needing to know
API's
7) Weave
- Plusses:
- Phenomenal tool
- can turn many numpy expressions into C code
- dynamic compiling and loading of generated C code
- can embed pure C code in Python module and have weave extract, generate
interfaces and compile, etc.
- Minuses:
- Future uncertain--lacks a champion
8) Psyco
- Plusses:
- Turns pure python into efficient machine code through jit-like
optimizations
- very fast when it optimizes well
- Minuses:
- Only on intel (windows?)
- Doesn't do much for numpy?
Interfacing to Fortran:
-----------------------
Fortran: Clear choice is f2py. (Pyfort is an older alternative, but not
supported any longer)
Interfacing to C++:
-------------------
1) CXX
2) Boost.python
3) SWIG
4) Sage has used cython to wrap C++ (not pretty, but it can be done)
5) SIP (used mainly in PyQT)
""" |
# This code is part of Ansible, but is an independent component.
# This particular file snippet, and this file snippet only, is BSD licensed.
# Modules you write using this snippet, which is embedded dynamically by Ansible
# still belong to the author of the module, and may assign their own license
# to the complete work.
#
# Copyright (c), NAME <EMAIL>, 2012-2013
# Copyright (c), NAME <EMAIL>, 2015
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without modification,
# are permitted provided that the following conditions are met:
#
# * Redistributions of source code must retain the above copyright
# notice, this list of conditions and the following disclaimer.
# * Redistributions in binary form must reproduce the above copyright notice,
# this list of conditions and the following disclaimer in the documentation
# and/or other materials provided with the distribution.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
# ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
# WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
# IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
# INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
# PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
# LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
# USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
#
# The match_hostname function and supporting code is under the terms and
# conditions of the Python Software Foundation License. They were taken from
# the Python3 standard library and adapted for use in Python2. See comments in the
# source for which code precisely is under this License. PSF License text
# follows:
#
# PYTHON SOFTWARE FOUNDATION LICENSE VERSION 2
# --------------------------------------------
#
# 1. This LICENSE AGREEMENT is between the Python Software Foundation
# ("PSF"), and the Individual or Organization ("Licensee") accessing and
# otherwise using this software ("Python") in source or binary form and
# its associated documentation.
#
# 2. Subject to the terms and conditions of this License Agreement, PSF hereby
# grants Licensee a nonexclusive, royalty-free, world-wide license to reproduce,
# analyze, test, perform and/or display publicly, prepare derivative works,
# distribute, and otherwise use Python alone or in any derivative version,
# provided, however, that PSF's License Agreement and PSF's notice of copyright,
# i.e., "Copyright (c) 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010,
# 2011, 2012, 2013, 2014 Python Software Foundation; All Rights Reserved" are
# retained in Python alone or in any derivative version prepared by Licensee.
#
# 3. In the event Licensee prepares a derivative work that is based on
# or incorporates Python or any part thereof, and wants to make
# the derivative work available to others as provided herein, then
# Licensee hereby agrees to include in any such work a brief summary of
# the changes made to Python.
#
# 4. PSF is making Python available to Licensee on an "AS IS"
# basis. PSF MAKES NO REPRESENTATIONS OR WARRANTIES, EXPRESS OR
# IMPLIED. BY WAY OF EXAMPLE, BUT NOT LIMITATION, PSF MAKES NO AND
# DISCLAIMS ANY REPRESENTATION OR WARRANTY OF MERCHANTABILITY OR FITNESS
# FOR ANY PARTICULAR PURPOSE OR THAT THE USE OF PYTHON WILL NOT
# INFRINGE ANY THIRD PARTY RIGHTS.
#
# 5. PSF SHALL NOT BE LIABLE TO LICENSEE OR ANY OTHER USERS OF PYTHON
# FOR ANY INCIDENTAL, SPECIAL, OR CONSEQUENTIAL DAMAGES OR LOSS AS
# A RESULT OF MODIFYING, DISTRIBUTING, OR OTHERWISE USING PYTHON,
# OR ANY DERIVATIVE THEREOF, EVEN IF ADVISED OF THE POSSIBILITY THEREOF.
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# 6. This License Agreement will automatically terminate upon a material
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# 7. Nothing in this License Agreement shall be deemed to create any
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|
"""Generic socket server classes.
This module tries to capture the various aspects of defining a server:
For socket-based servers:
- address family:
- AF_INET{,6}: IP (Internet Protocol) sockets (default)
- AF_UNIX: Unix domain sockets
- others, e.g. AF_DECNET are conceivable (see <socket.h>
- socket type:
- SOCK_STREAM (reliable stream, e.g. TCP)
- SOCK_DGRAM (datagrams, e.g. UDP)
For request-based servers (including socket-based):
- client address verification before further looking at the request
(This is actually a hook for any processing that needs to look
at the request before anything else, e.g. logging)
- how to handle multiple requests:
- synchronous (one request is handled at a time)
- forking (each request is handled by a new process)
- threading (each request is handled by a new thread)
The classes in this module favor the server type that is simplest to
write: a synchronous TCP/IP server. This is bad class design, but
save some typing. (There's also the issue that a deep class hierarchy
slows down method lookups.)
There are five classes in an inheritance diagram, four of which represent
synchronous servers of four types:
+------------+
| BaseServer |
+------------+
|
v
+-----------+ +------------------+
| TCPServer |------->| UnixStreamServer |
+-----------+ +------------------+
|
v
+-----------+ +--------------------+
| UDPServer |------->| UnixDatagramServer |
+-----------+ +--------------------+
Note that UnixDatagramServer derives from UDPServer, not from
UnixStreamServer -- the only difference between an IP and a Unix
stream server is the address family, which is simply repeated in both
unix server classes.
Forking and threading versions of each type of server can be created
using the ForkingMixIn and ThreadingMixIn mix-in classes. For
instance, a threading UDP server class is created as follows:
class ThreadingUDPServer(ThreadingMixIn, UDPServer): pass
The Mix-in class must come first, since it overrides a method defined
in UDPServer! Setting the various member variables also changes
the behavior of the underlying server mechanism.
To implement a service, you must derive a class from
BaseRequestHandler and redefine its handle() method. You can then run
various versions of the service by combining one of the server classes
with your request handler class.
The request handler class must be different for datagram or stream
services. This can be hidden by using the request handler
subclasses StreamRequestHandler or DatagramRequestHandler.
Of course, you still have to use your head!
For instance, it makes no sense to use a forking server if the service
contains state in memory that can be modified by requests (since the
modifications in the child process would never reach the initial state
kept in the parent process and passed to each child). In this case,
you can use a threading server, but you will probably have to use
locks to avoid two requests that come in nearly simultaneous to apply
conflicting changes to the server state.
On the other hand, if you are building e.g. an HTTP server, where all
data is stored externally (e.g. in the file system), a synchronous
class will essentially render the service "deaf" while one request is
being handled -- which may be for a very long time if a client is slow
to read all the data it has requested. Here a threading or forking
server is appropriate.
In some cases, it may be appropriate to process part of a request
synchronously, but to finish processing in a forked child depending on
the request data. This can be implemented by using a synchronous
server and doing an explicit fork in the request handler class
handle() method.
Another approach to handling multiple simultaneous requests in an
environment that supports neither threads nor fork (or where these are
too expensive or inappropriate for the service) is to maintain an
explicit table of partially finished requests and to use a selector to
decide which request to work on next (or whether to handle a new
incoming request). This is particularly important for stream services
where each client can potentially be connected for a long time (if
threads or subprocesses cannot be used).
Future work:
- Standard classes for Sun RPC (which uses either UDP or TCP)
- Standard mix-in classes to implement various authentication
and encryption schemes
XXX Open problems:
- What to do with out-of-band data?
BaseServer:
- split generic "request" functionality out into BaseServer class.
Copyright (C) 2000 NAME <EMAIL>
example: read entries from a SQL database (requires overriding
get_request() to return a table entry from the database).
entry is processed by a RequestHandlerClass.
""" |
"""
PHCpy --- a package for Polynomial Homotopy Continuation
========================================================
PHCpy is a collection of Python modules to compute solutions
of polynomial systems using PHCpack.
A homotopy defines the deformation of a start system
(system with known solutions) into the target system
(system that has to be solved).
Continuation or path tracking methods apply numerical
predictor-corrector techniques to track the solution paths
defined by the homotopy, starting at the known solutions of the
start system and ending at the solutions of the target system.
Available modules
-----------------
solver
exports the blackbox solver of PHCpack, a mixed volume calculator,
a path tracker, functions to construct start systems, and deflation
to recondition isolated singular solutions.
solutions
solutions of phcpy.solve are lists of PHCpack solution strings
and this module exports operations to convert the solution
strings into Python dictionaries, e.g. for evaluation.
polynomials
the object oriented interface starts with the class Polynomials,
which represents a system of polynomials and provides a solve method.
interface
data transfer from string representations of polynomials and solutions
as the interface between Python and the C interface of PHCpack.
trackers
offers functions to track solution paths defined by a homotopy between
a given start system with known solutions and a target system.
sweepers
homotopies to sweep a real parameter range in natural parameter homotopies.
tuning
parameters and numerical tolerances of the trackers and sweepers
are tuned by the functions in the tuning module.
sets
offers tools to work with positive dimensional solution sets.
cascades
homotopies to compute candidate generic points on all components.
factor
separates generic points in a witness set according to the
irreducible factors in a solution set.
diagonal
given two witness sets, diagonal homotopies compute the intersection
of the given sets.
examples
defines some interesting examples taken from the research literature,
the test() solves all systems, performing a regression test.
families
polynomial system often occur in families and are defined for any
number of equations and variables, e.g.: the cyclic n-roots system.
schubert
exports the hypersurface and quantum Pieri homotopies to compute
isolated solutions to problems in enumerative geometry.
polytopes
functions to work with Newton polytopes, to compute mixed volumes
of Newton polytopes, given by tuples of support sets.
tropisms
tropisms are the leading exponents of the power series solutions
and can be computed by polyhedral end games.
maps
module to work with monomial maps, defined as solution of systems
that have exactly two monomials in every equation (binomial systems).
series
Newton's method to compute truncated power series solutions.
curves
approximate algebraic curves with rational expressions: Pade approximants
dashboard
prototype of a graphical user interface with Tkinter
server
defines a simple client/server interaction to solve random trinomials.
Calling the blackbox solver
---------------------------
Polynomials and solutions are represented as strings.
Below is an illustration of a session with the blackbox solver
on a system of two random trinomials, polynomials with three
monomials with random coefficients.
>>> from phcpy.solver import random_trinomials
>>> f = random_trinomials()
>>> print f[0]
(0.583339727743+0.81222826966115*i)*x^0*y^0\
+(-0.730410130891-0.68300881450520*i)*x^5*y^5\
+(0.547878834338+0.83655769847920*i)*x^5*y^0;
>>> print f[1]
(0.830635910813+0.55681593338247*i)*x^0*y^4\
+(0.456430547798-0.88975904324518*i)*x^1*y^4\
+(0.034113254002-0.99941797357332*i)*x^2*y^1;
>>> from phcpy.solver import solve
>>> s = solve(f,silent=True)
>>> len(s)
30
>>> print s[2]
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x : -9.99963006604849E-01 8.60147787997449E-03
y : 0.00000000000000E+00 0.00000000000000E+00
== err : 4.325E-17 = rco : 2.020E-01 = res : 1.665E-16 =
>>>
The solve command returned a list of 30 strings in s,
each string represents a solution that makes the polynomials in f vanish.
The module solutions offers function to evaluate the solutions
in the polynomials given as strings.
""" |
# """
# @package ion.agents.platform.test.test_mission_executive
# @file ion/agents/platform/test/test_test_mission_executive.py
# @author NAME @brief Test cases for platform mission executive. Based on
# ion/agents/platform/test/test_platform_agent_with_rsn.py
# """
#
# import unittest
# from unittest import skip
# from mock import Mock, patch
# from pyon.util.unit_test import PyonTestCase
# from pyon.util.int_test import IonIntegrationTestCase
# from nose.plugins.attrib import attr
#
# from pyon.public import log
# from ion.agents.platform.rsn.simulator.logger import Logger
# Logger.set_logger(log)
#
# from ion.agents.mission_executive import MissionLoader, MissionScheduler
# from ion.agents.platform.test.base_test_platform_agent_with_rsn import BaseIntTestPlatform
#
# from pyon.agent.agent import ResourceAgentState
#
# from interface.objects import AgentCommand
# from interface.objects import AttachmentType
# from pyon.public import IonObject
# from pyon.public import RT, PRED
#
# from pyon.util.breakpoint import breakpoint
# import os
#
# @attr('UNIT')
# class TestParseMission(PyonTestCase):
# """
# Unit tests for the mission parser
# """
# # def setUp(self):
# # pass
#
# # def tearDownClass(self):
# # pass
#
# def test_load_YAML(self):
# mission = MissionLoader()
# filename = "ion/agents/platform/test/mission_RSN_simulator1.yml"
# self.assertTrue(mission.load_mission_file(filename))
#
# def test_validate_schedule(self):
# pass
#
#
# # @unittest.skipIf(os.getenv("OMS") is not None, "OMS environment variable is defined.")
# @attr('INT')
# class TestSimpleMission(BaseIntTestPlatform):
# """
# Test cases for the RSN OMS simulator, which is instantiated directly (ie.,
# no connection to external simulator is involved).
# """
# def load_mission(self, yaml_filename='ion/agents/platform/test/mission_RSN_simulator1.yml'):
# self.mission = MissionLoader()
# self.mission.load_mission_file(yaml_filename)
#
# def _run_startup_commands(self, recursion=True):
# self._ping_agent()
# self._initialize(recursion)
# self._go_active(recursion)
# self._run(recursion)
#
# def _run_shutdown_commands(self, recursion=True):
# try:
# self._go_inactive(recursion)
# self._reset(recursion)
# finally: # attempt shutdown anyway
# self._shutdown(True) # NOTE: shutdown always with recursion=True
#
# @skip("Work in progress...")
# def test_simple_simulator_mission(self):
#
# # Dump mission file contents to IonObject
# filename = "ion/agents/platform/test/mission_RSN_simulator1.yml"
#
# with open(filename, 'r') as rfile:
# content = rfile.read()
#
# # make an attachment
# attachment = IonObject(RT.Attachment,
# name="Example mission",
# description="Mission File",
# content=content,
# content_type="text/yml",
# keywords=["mission"],
# attachment_type=AttachmentType.ASCII)
#
# # Create a platform in the test environment
# p_root = self._create_single_platform()
#
# self.RR2.create_attachment(p_root['platform_device_id'], attachment)
#
# attachments, _ = self.RR.find_objects(p_root['platform_device_id'], PRED.hasAttachment, RT.Attachment, True)
# self.assertEqual(len(attachments), 1)
#
# a = self.RR.read_attachment(attachments[0], include_content=True)
#
# # Write contents of attached mission file to temp yaml file
# temp_file = 'temp_mission.yml'
# with open(temp_file, 'w') as wfile:
# wfile.write(a.content)
#
# self.load_mission(yaml_filename = temp_file)
#
# self._set_receive_timeout()
#
# instruments = []
#
# for missionIndex in range(len(self.mission.mission_entries)):
# instruments.append(self.mission.mission_entries[missionIndex]['instrument_id'])
#
# # p_root = self._set_up_single_platform_with_some_instruments(instruments)
#
# # for instr_key in instruments:
# # self.assertIn(instr_key, instruments_dict)
# # create and assign instruments:
# for instr_key in instruments:
# # create only if not already created:
# if instr_key in self._setup_instruments:
# i_obj = self._setup_instruments[instr_key]
# else:
# i_obj = self._create_instrument(instr_key, start_port_agent=True)
# self._assign_instrument_to_platform(i_obj, p_root)
#
# self._start_platform(p_root)
#
# self.addCleanup(self._stop_platform, p_root)
# self.addCleanup(self._run_shutdown_commands)
#
# self.missionSchedule = MissionScheduler(self._pa_client, self._setup_instruments, self.mission.mission_entries)
#
# if os.path.isfile(temp_file):
# os.remove(temp_file)
#
# # class TestPlatformMission(IonIntegrationTestCase):
# # """
# # Test cases for the RSN shallow profiler.
# # """
#
#
|
"""Drag-and-drop support for Tkinter.
This is very preliminary. I currently only support dnd *within* one
application, between different windows (or within the same window).
I an trying to make this as generic as possible -- not dependent on
the use of a particular widget or icon type, etc. I also hope that
this will work with Pmw.
To enable an object to be dragged, you must create an event binding
for it that starts the drag-and-drop process. Typically, you should
bind <ButtonPress> to a callback function that you write. The function
should call Tkdnd.dnd_start(source, event), where 'source' is the
object to be dragged, and 'event' is the event that invoked the call
(the argument to your callback function). Even though this is a class
instantiation, the returned instance should not be stored -- it will
be kept alive automatically for the duration of the drag-and-drop.
When a drag-and-drop is already in process for the Tk interpreter, the
call is *ignored*; this normally averts starting multiple simultaneous
dnd processes, e.g. because different button callbacks all
dnd_start().
The object is *not* necessarily a widget -- it can be any
application-specific object that is meaningful to potential
drag-and-drop targets.
Potential drag-and-drop targets are discovered as follows. Whenever
the mouse moves, and at the start and end of a drag-and-drop move, the
Tk widget directly under the mouse is inspected. This is the target
widget (not to be confused with the target object, yet to be
determined). If there is no target widget, there is no dnd target
object. If there is a target widget, and it has an attribute
dnd_accept, this should be a function (or any callable object). The
function is called as dnd_accept(source, event), where 'source' is the
object being dragged (the object passed to dnd_start() above), and
'event' is the most recent event object (generally a <Motion> event;
it can also be <ButtonPress> or <ButtonRelease>). If the dnd_accept()
function returns something other than None, this is the new dnd target
object. If dnd_accept() returns None, or if the target widget has no
dnd_accept attribute, the target widget's parent is considered as the
target widget, and the search for a target object is repeated from
there. If necessary, the search is repeated all the way up to the
root widget. If none of the target widgets can produce a target
object, there is no target object (the target object is None).
The target object thus produced, if any, is called the new target
object. It is compared with the old target object (or None, if there
was no old target widget). There are several cases ('source' is the
source object, and 'event' is the most recent event object):
- Both the old and new target objects are None. Nothing happens.
- The old and new target objects are the same object. Its method
dnd_motion(source, event) is called.
- The old target object was None, and the new target object is not
None. The new target object's method dnd_enter(source, event) is
called.
- The new target object is None, and the old target object is not
None. The old target object's method dnd_leave(source, event) is
called.
- The old and new target objects differ and neither is None. The old
target object's method dnd_leave(source, event), and then the new
target object's method dnd_enter(source, event) is called.
Once this is done, the new target object replaces the old one, and the
Tk mainloop proceeds. The return value of the methods mentioned above
is ignored; if they raise an exception, the normal exception handling
mechanisms take over.
The drag-and-drop processes can end in two ways: a final target object
is selected, or no final target object is selected. When a final
target object is selected, it will always have been notified of the
potential drop by a call to its dnd_enter() method, as described
above, and possibly one or more calls to its dnd_motion() method; its
dnd_leave() method has not been called since the last call to
dnd_enter(). The target is notified of the drop by a call to its
method dnd_commit(source, event).
If no final target object is selected, and there was an old target
object, its dnd_leave(source, event) method is called to complete the
dnd sequence.
Finally, the source object is notified that the drag-and-drop process
is over, by a call to source.dnd_end(target, event), specifying either
the selected target object, or None if no target object was selected.
The source object can use this to implement the commit action; this is
sometimes simpler than to do it in the target's dnd_commit(). The
target's dnd_commit() method could then simply be aliased to
dnd_leave().
At any time during a dnd sequence, the application can cancel the
sequence by calling the cancel() method on the object returned by
dnd_start(). This will call dnd_leave() if a target is currently
active; it will never call dnd_commit().
""" |
"""
==============
Array Creation
==============
Introduction
============
There are 5 general mechanisms for creating arrays:
1) Conversion from other Python structures (e.g., lists, tuples)
2) Intrinsic numpy array array creation objects (e.g., arange, ones, zeros,
etc.)
3) Reading arrays from disk, either from standard or custom formats
4) Creating arrays from raw bytes through the use of strings or buffers
5) Use of special library functions (e.g., random)
This section will not cover means of replicating, joining, or otherwise
expanding or mutating existing arrays. Nor will it cover creating object
arrays or record arrays. Both of those are covered in their own sections.
Converting Python array_like Objects to Numpy Arrays
====================================================
In general, numerical data arranged in an array-like structure in Python can
be converted to arrays through the use of the array() function. The most
obvious examples are lists and tuples. See the documentation for array() for
details for its use. Some objects may support the array-protocol and allow
conversion to arrays this way. A simple way to find out if the object can be
converted to a numpy array using array() is simply to try it interactively and
see if it works! (The Python Way).
Examples: ::
>>> x = np.array([2,3,1,0])
>>> x = np.array([2, 3, 1, 0])
>>> x = np.array([[1,2.0],[0,0],(1+1j,3.)]) # note mix of tuple and lists,
and types
>>> x = np.array([[ 1.+0.j, 2.+0.j], [ 0.+0.j, 0.+0.j], [ 1.+1.j, 3.+0.j]])
Intrinsic Numpy Array Creation
==============================
Numpy has built-in functions for creating arrays from scratch:
zeros(shape) will create an array filled with 0 values with the specified
shape. The default dtype is float64.
``>>> np.zeros((2, 3))
array([[ 0., 0., 0.], [ 0., 0., 0.]])``
ones(shape) will create an array filled with 1 values. It is identical to
zeros in all other respects.
arange() will create arrays with regularly incrementing values. Check the
docstring for complete information on the various ways it can be used. A few
examples will be given here: ::
>>> np.arange(10)
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> np.arange(2, 10, dtype=np.float)
array([ 2., 3., 4., 5., 6., 7., 8., 9.])
>>> np.arange(2, 3, 0.1)
array([ 2. , 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9])
Note that there are some subtleties regarding the last usage that the user
should be aware of that are described in the arange docstring.
linspace() will create arrays with a specified number of elements, and
spaced equally between the specified beginning and end values. For
example: ::
>>> np.linspace(1., 4., 6)
array([ 1. , 1.6, 2.2, 2.8, 3.4, 4. ])
The advantage of this creation function is that one can guarantee the
number of elements and the starting and end point, which arange()
generally will not do for arbitrary start, stop, and step values.
indices() will create a set of arrays (stacked as a one-higher dimensioned
array), one per dimension with each representing variation in that dimension.
An example illustrates much better than a verbal description: ::
>>> np.indices((3,3))
array([[[0, 0, 0], [1, 1, 1], [2, 2, 2]], [[0, 1, 2], [0, 1, 2], [0, 1, 2]]])
This is particularly useful for evaluating functions of multiple dimensions on
a regular grid.
Reading Arrays From Disk
========================
This is presumably the most common case of large array creation. The details,
of course, depend greatly on the format of data on disk and so this section
can only give general pointers on how to handle various formats.
Standard Binary Formats
-----------------------
Various fields have standard formats for array data. The following lists the
ones with known python libraries to read them and return numpy arrays (there
may be others for which it is possible to read and convert to numpy arrays so
check the last section as well)
::
HDF5: PyTables
FITS: PyFITS
Examples of formats that cannot be read directly but for which it is not hard
to convert are libraries like PIL (able to read and write many image formats
such as jpg, png, etc).
Common ASCII Formats
------------------------
Comma Separated Value files (CSV) are widely used (and an export and import
option for programs like Excel). There are a number of ways of reading these
files in Python. There are CSV functions in Python and functions in pylab
(part of matplotlib).
More generic ascii files can be read using the io package in scipy.
Custom Binary Formats
---------------------
There are a variety of approaches one can use. If the file has a relatively
simple format then one can write a simple I/O library and use the numpy
fromfile() function and .tofile() method to read and write numpy arrays
directly (mind your byteorder though!) If a good C or C++ library exists that
read the data, one can wrap that library with a variety of techniques though
that certainly is much more work and requires significantly more advanced
knowledge to interface with C or C++.
Use of Special Libraries
------------------------
There are libraries that can be used to generate arrays for special purposes
and it isn't possible to enumerate all of them. The most common uses are use
of the many array generation functions in random that can generate arrays of
random values, and some utility functions to generate special matrices (e.g.
diagonal).
""" |
"""
================
Precision-Recall
================
Example of Precision-Recall metric to evaluate classifier output quality.
Precision-Recall is a useful measure of success of prediction when the
classes are very imbalanced. In information retrieval, precision is a
measure of result relevancy, while recall is a measure of how many truly
relevant results are returned.
The precision-recall curve shows the tradeoff between precision and
recall for different threshold. A high area under the curve represents
both high recall and high precision, where high precision relates to a
low false positive rate, and high recall relates to a low false negative
rate. High scores for both show that the classifier is returning accurate
results (high precision), as well as returning a majority of all positive
results (high recall).
A system with high recall but low precision returns many results, but most of
its predicted labels are incorrect when compared to the training labels. A
system with high precision but low recall is just the opposite, returning very
few results, but most of its predicted labels are correct when compared to the
training labels. An ideal system with high precision and high recall will
return many results, with all results labeled correctly.
Precision (:math:`P`) is defined as the number of true positives (:math:`T_p`)
over the number of true positives plus the number of false positives
(:math:`F_p`).
:math:`P = \\frac{T_p}{T_p+F_p}`
Recall (:math:`R`) is defined as the number of true positives (:math:`T_p`)
over the number of true positives plus the number of false negatives
(:math:`F_n`).
:math:`R = \\frac{T_p}{T_p + F_n}`
These quantities are also related to the (:math:`F_1`) score, which is defined
as the harmonic mean of precision and recall.
:math:`F1 = 2\\frac{P \\times R}{P+R}`
Note that the precision may not decrease with recall. The
definition of precision (:math:`\\frac{T_p}{T_p + F_p}`) shows that lowering
the threshold of a classifier may increase the denominator, by increasing the
number of results returned. If the threshold was previously set too high, the
new results may all be true positives, which will increase precision. If the
previous threshold was about right or too low, further lowering the threshold
will introduce false positives, decreasing precision.
Recall is defined as :math:`\\frac{T_p}{T_p+F_n}`, where :math:`T_p+F_n` does
not depend on the classifier threshold. This means that lowering the classifier
threshold may increase recall, by increasing the number of true positive
results. It is also possible that lowering the threshold may leave recall
unchanged, while the precision fluctuates.
The relationship between recall and precision can be observed in the
stairstep area of the plot - at the edges of these steps a small change
in the threshold considerably reduces precision, with only a minor gain in
recall.
**Average precision** (AP) summarizes such a plot as the weighted mean of
precisions achieved at each threshold, with the increase in recall from the
previous threshold used as the weight:
:math:`\\text{AP} = \\sum_n (R_n - R_{n-1}) P_n`
where :math:`P_n` and :math:`R_n` are the precision and recall at the
nth threshold. A pair :math:`(R_k, P_k)` is referred to as an
*operating point*.
AP and the trapezoidal area under the operating points
(:func:`sklearn.metrics.auc`) are common ways to summarize a precision-recall
curve that lead to different results. Read more in the
:ref:`User Guide <precision_recall_f_measure_metrics>`.
Precision-recall curves are typically used in binary classification to study
the output of a classifier. In order to extend the precision-recall curve and
average precision to multi-class or multi-label classification, it is necessary
to binarize the output. One curve can be drawn per label, but one can also draw
a precision-recall curve by considering each element of the label indicator
matrix as a binary prediction (micro-averaging).
.. note::
See also :func:`sklearn.metrics.average_precision_score`,
:func:`sklearn.metrics.recall_score`,
:func:`sklearn.metrics.precision_score`,
:func:`sklearn.metrics.f1_score`
""" |
"""
=====================================
Sparse matrices (:mod:`scipy.sparse`)
=====================================
.. currentmodule:: scipy.sparse
SciPy 2-D sparse matrix package for numeric data.
Contents
========
Sparse matrix classes
---------------------
.. autosummary::
:toctree: generated/
bsr_matrix - Block Sparse Row matrix
coo_matrix - A sparse matrix in COOrdinate format
csc_matrix - Compressed Sparse Column matrix
csr_matrix - Compressed Sparse Row matrix
dia_matrix - Sparse matrix with DIAgonal storage
dok_matrix - Dictionary Of Keys based sparse matrix
lil_matrix - Row-based linked list sparse matrix
spmatrix - Sparse matrix base class
Functions
---------
Building sparse matrices:
.. autosummary::
:toctree: generated/
eye - Sparse MxN matrix whose k-th diagonal is all ones
identity - Identity matrix in sparse format
kron - kronecker product of two sparse matrices
kronsum - kronecker sum of sparse matrices
diags - Return a sparse matrix from diagonals
spdiags - Return a sparse matrix from diagonals
block_diag - Build a block diagonal sparse matrix
tril - Lower triangular portion of a matrix in sparse format
triu - Upper triangular portion of a matrix in sparse format
bmat - Build a sparse matrix from sparse sub-blocks
hstack - Stack sparse matrices horizontally (column wise)
vstack - Stack sparse matrices vertically (row wise)
rand - Random values in a given shape
random - Random values in a given shape
Save and load sparse matrices:
.. autosummary::
:toctree: generated/
save_npz - Save a sparse matrix to a file using ``.npz`` format.
load_npz - Load a sparse matrix from a file using ``.npz`` format.
Sparse matrix tools:
.. autosummary::
:toctree: generated/
find
Identifying sparse matrices:
.. autosummary::
:toctree: generated/
issparse
isspmatrix
isspmatrix_csc
isspmatrix_csr
isspmatrix_bsr
isspmatrix_lil
isspmatrix_dok
isspmatrix_coo
isspmatrix_dia
Submodules
----------
.. autosummary::
csgraph - Compressed sparse graph routines
linalg - sparse linear algebra routines
Exceptions
----------
.. autosummary::
:toctree: generated/
SparseEfficiencyWarning
SparseWarning
Usage information
=================
There are seven available sparse matrix types:
1. csc_matrix: Compressed Sparse Column format
2. csr_matrix: Compressed Sparse Row format
3. bsr_matrix: Block Sparse Row format
4. lil_matrix: List of Lists format
5. dok_matrix: Dictionary of Keys format
6. coo_matrix: COOrdinate format (aka IJV, triplet format)
7. dia_matrix: DIAgonal format
To construct a matrix efficiently, use either dok_matrix or lil_matrix.
The lil_matrix class supports basic slicing and fancy indexing with a
similar syntax to NumPy arrays. As illustrated below, the COO format
may also be used to efficiently construct matrices. Despite their
similarity to NumPy arrays, it is **strongly discouraged** to use NumPy
functions directly on these matrices because NumPy may not properly convert
them for computations, leading to unexpected (and incorrect) results. If you
do want to apply a NumPy function to these matrices, first check if SciPy has
its own implementation for the given sparse matrix class, or **convert the
sparse matrix to a NumPy array** (e.g. using the `toarray()` method of the
class) first before applying the method.
To perform manipulations such as multiplication or inversion, first
convert the matrix to either CSC or CSR format. The lil_matrix format is
row-based, so conversion to CSR is efficient, whereas conversion to CSC
is less so.
All conversions among the CSR, CSC, and COO formats are efficient,
linear-time operations.
Matrix vector product
---------------------
To do a vector product between a sparse matrix and a vector simply use
the matrix `dot` method, as described in its docstring:
>>> import numpy as np
>>> from scipy.sparse import csr_matrix
>>> A = csr_matrix([[1, 2, 0], [0, 0, 3], [4, 0, 5]])
>>> v = np.array([1, 0, -1])
>>> A.dot(v)
array([ 1, -3, -1], dtype=int64)
.. warning:: As of NumPy 1.7, `np.dot` is not aware of sparse matrices,
therefore using it will result on unexpected results or errors.
The corresponding dense array should be obtained first instead:
>>> np.dot(A.toarray(), v)
array([ 1, -3, -1], dtype=int64)
but then all the performance advantages would be lost.
The CSR format is specially suitable for fast matrix vector products.
Example 1
---------
Construct a 1000x1000 lil_matrix and add some values to it:
>>> from scipy.sparse import lil_matrix
>>> from scipy.sparse.linalg import spsolve
>>> from numpy.linalg import solve, norm
>>> from numpy.random import rand
>>> A = lil_matrix((1000, 1000))
>>> A[0, :100] = rand(100)
>>> A[1, 100:200] = A[0, :100]
>>> A.setdiag(rand(1000))
Now convert it to CSR format and solve A x = b for x:
>>> A = A.tocsr()
>>> b = rand(1000)
>>> x = spsolve(A, b)
Convert it to a dense matrix and solve, and check that the result
is the same:
>>> x_ = solve(A.toarray(), b)
Now we can compute norm of the error with:
>>> err = norm(x-x_)
>>> err < 1e-10
True
It should be small :)
Example 2
---------
Construct a matrix in COO format:
>>> from scipy import sparse
>>> from numpy import array
>>> I = array([0,3,1,0])
>>> J = array([0,3,1,2])
>>> V = array([4,5,7,9])
>>> A = sparse.coo_matrix((V,(I,J)),shape=(4,4))
Notice that the indices do not need to be sorted.
Duplicate (i,j) entries are summed when converting to CSR or CSC.
>>> I = array([0,0,1,3,1,0,0])
>>> J = array([0,2,1,3,1,0,0])
>>> V = array([1,1,1,1,1,1,1])
>>> B = sparse.coo_matrix((V,(I,J)),shape=(4,4)).tocsr()
This is useful for constructing finite-element stiffness and mass matrices.
Further Details
---------------
CSR column indices are not necessarily sorted. Likewise for CSC row
indices. Use the .sorted_indices() and .sort_indices() methods when
sorted indices are required (e.g. when passing data to other libraries).
""" |
"""
Implementation of the trigsimp algorithm by Fu et al.
The idea behind the ``fu`` algorithm is to use a sequence of rules, applied
in what is heuristically known to be a smart order, to select a simpler
expression that is equivalent to the input.
There are transform rules in which a single rule is applied to the
expression tree. The following are just mnemonic in nature; see the
docstrings for examples.
TR0 - simplify expression
TR1 - sec-csc to cos-sin
TR2 - tan-cot to sin-cos ratio
TR2i - sin-cos ratio to tan
TR3 - angle canonicalization
TR4 - functions at special angles
TR5 - powers of sin to powers of cos
TR6 - powers of cos to powers of sin
TR7 - reduce cos power (increase angle)
TR8 - expand products of sin-cos to sums
TR9 - contract sums of sin-cos to products
TR10 - separate sin-cos arguments
TR10i - collect sin-cos arguments
TR11 - reduce double angles
TR12 - separate tan arguments
TR12i - collect tan arguments
TR13 - expand product of tan-cot
TRmorrie - prod(cos(x*2**i), (i, 0, k - 1)) -> sin(2**k*x)/(2**k*sin(x))
TR14 - factored powers of sin or cos to cos or sin power
TR15 - negative powers of sin to cot power
TR16 - negative powers of cos to tan power
TR22 - tan-cot powers to negative powers of sec-csc functions
TR111 - negative sin-cos-tan powers to csc-sec-cot
There are 4 combination transforms (CTR1 - CTR4) in which a sequence of
transformations are applied and the simplest expression is selected from
a few options.
Finally, there are the 2 rule lists (RL1 and RL2), which apply a
sequence of transformations and combined transformations, and the ``fu``
algorithm itself, which applies rules and rule lists and selects the
best expressions. There is also a function ``L`` which counts the number
of trigonometric funcions that appear in the expression.
Other than TR0, re-writing of expressions is not done by the transformations.
e.g. TR10i finds pairs of terms in a sum that are in the form like
``cos(x)*cos(y) + sin(x)*sin(y)``. Such expression are targeted in a bottom-up
traversal of the expression, but no manipulation to make them appear is
attempted. For example,
Set-up for examples below:
>>> from sympy.simplify.fu import fu, L, TR9, TR10i, TR11
>>> from sympy import factor, sin, cos, powsimp
>>> from sympy.abc import x, y, z, a
>>> from time import time
>>> eq = cos(x + y)/cos(x)
>>> TR10i(eq.expand(trig=True))
-sin(x)*sin(y)/cos(x) + cos(y)
If the expression is put in "normal" form (with a common denominator) then
the transformation is successful:
>>> TR10i(_.normal())
cos(x + y)/cos(x)
TR11's behavior is similar. It rewrites double angles as smaller angles but
doesn't do any simplification of the result.
>>> TR11(sin(2)**a*cos(1)**(-a), 1)
(2*sin(1)*cos(1))**a*cos(1)**(-a)
>>> powsimp(_)
(2*sin(1))**a
The temptation is to try make these TR rules "smarter" but that should really
be done at a higher level; the TR rules should try maintain the "do one thing
well" principle. There is one exception, however. In TR10i and TR9 terms are
recognized even when they are each multiplied by a common factor:
>>> fu(a*cos(x)*cos(y) + a*sin(x)*sin(y))
a*cos(x - y)
Factoring with ``factor_terms`` is used but it it "JIT"-like, being delayed
until it is deemed necessary. Furthermore, if the factoring does not
help with the simplification, it is not retained, so
``a*cos(x)*cos(y) + a*sin(x)*sin(z)`` does not become the factored
(but unsimplified in the trigonometric sense) expression:
>>> fu(a*cos(x)*cos(y) + a*sin(x)*sin(z))
a*sin(x)*sin(z) + a*cos(x)*cos(y)
In some cases factoring might be a good idea, but the user is left
to make that decision. For example:
>>> expr=((15*sin(2*x) + 19*sin(x + y) + 17*sin(x + z) + 19*cos(x - z) +
... 25)*(20*sin(2*x) + 15*sin(x + y) + sin(y + z) + 14*cos(x - z) +
... 14*cos(y - z))*(9*sin(2*y) + 12*sin(y + z) + 10*cos(x - y) + 2*cos(y -
... z) + 18)).expand(trig=True).expand()
In the expanded state, there are nearly 1000 trig functions:
>>> L(expr)
932
If the expression where factored first, this would take time but the
resulting expression would be transformed very quickly:
>>> def clock(f, n=2):
... t=time(); f(); return round(time()-t, n)
...
>>> clock(lambda: factor(expr)) # doctest: +SKIP
0.86
>>> clock(lambda: TR10i(expr), 3) # doctest: +SKIP
0.016
If the unexpanded expression is used, the transformation takes longer but
not as long as it took to factor it and then transform it:
>>> clock(lambda: TR10i(expr), 2) # doctest: +SKIP
0.28
So neither expansion nor factoring is used in ``TR10i``: if the
expression is already factored (or partially factored) then expansion
with ``trig=True`` would destroy what is already known and take
longer; if the expression is expanded, factoring may take longer than
simply applying the transformation itself.
Although the algorithms should be canonical, always giving the same
result, they may not yield the best result. This, in general, is
the nature of simplification where searching all possible transformation
paths is very expensive. Here is a simple example. There are 6 terms
in the following sum:
>>> expr = (sin(x)**2*cos(y)*cos(z) + sin(x)*sin(y)*cos(x)*cos(z) +
... sin(x)*sin(z)*cos(x)*cos(y) + sin(y)*sin(z)*cos(x)**2 + sin(y)*sin(z) +
... cos(y)*cos(z))
>>> args = expr.args
Serendipitously, fu gives the best result:
>>> fu(expr)
3*cos(y - z)/2 - cos(2*x + y + z)/2
But if different terms were combined, a less-optimal result might be
obtained, requiring some additional work to get better simplification,
but still less than optimal. The following shows an alternative form
of ``expr`` that resists optimal simplification once a given step
is taken since it leads to a dead end:
>>> TR9(-cos(x)**2*cos(y + z) + 3*cos(y - z)/2 +
... cos(y + z)/2 + cos(-2*x + y + z)/4 - cos(2*x + y + z)/4)
sin(2*x)*sin(y + z)/2 - cos(x)**2*cos(y + z) + 3*cos(y - z)/2 + cos(y + z)/2
Here is a smaller expression that exhibits the same behavior:
>>> a = sin(x)*sin(z)*cos(x)*cos(y) + sin(x)*sin(y)*cos(x)*cos(z)
>>> TR10i(a)
sin(x)*sin(y + z)*cos(x)
>>> newa = _
>>> TR10i(expr - a) # this combines two more of the remaining terms
sin(x)**2*cos(y)*cos(z) + sin(y)*sin(z)*cos(x)**2 + cos(y - z)
>>> TR10i(_ + newa) == _ + newa # but now there is no more simplification
True
Without getting lucky or trying all possible pairings of arguments, the
final result may be less than optimal and impossible to find without
better heuristics or brute force trial of all possibilities.
Notes
=====
This work was started by NAME at the Technological School
"Electronic systems" (30.11.2011).
References
==========
http://rfdz.ph-noe.ac.at/fileadmin/Mathematik_Uploads/ACDCA/
DESTIME2006/DES_contribs/Fu/simplification.pdf
http://www.sosmath.com/trig/Trig5/trig5/pdf/pdf.html gives a formula sheet.
""" |
# """
# @package mi.instrument.ooici.mi.test_driver.test.test_driver
# @file marine-integrations/mi/instrument/ooici/mi/test_driver/driver.py
# @author NAME @brief Test cases for test_driver driver
#
# USAGE:
# Make tests verbose and provide stdout
# * From the IDK
# $ bin/test_driver
# $ bin/test_driver -u [-t testname]
# $ bin/test_driver -i [-t testname]
# $ bin/test_driver -q [-t testname]
# """
#
# __author__ = 'Bill NAME __license__ = 'Apache 2.0'
#
# import gevent
# from nose.plugins.attrib import attr
# from mock import Mock
#
# from mi.core.log import get_logger ; log = get_logger()
#
# # MI imports.
# from mi.idk.unit_test import InstrumentDriverTestCase
# from mi.idk.unit_test import InstrumentDriverUnitTestCase
# from mi.idk.unit_test import InstrumentDriverIntegrationTestCase
# from mi.idk.unit_test import InstrumentDriverQualificationTestCase
# from mi.idk.unit_test import DriverTestMixin
#
# from mi.core.instrument.chunker import StringChunker
# from mi.core.instrument.data_particle import DataParticleKey
#
# from mi.instrument.ooici.mi.test_driver.driver import InstrumentDriver
# from mi.instrument.ooici.mi.test_driver.driver import DataParticleType
# from mi.instrument.ooici.mi.test_driver.driver import InstrumentCommand
# from mi.instrument.ooici.mi.test_driver.driver import ProtocolState
# from mi.instrument.ooici.mi.test_driver.driver import ProtocolEvent
# from mi.instrument.ooici.mi.test_driver.driver import Capability
# from mi.instrument.ooici.mi.test_driver.driver import ParameterName
# from mi.instrument.ooici.mi.test_driver.driver import Protocol
# from mi.instrument.ooici.mi.test_driver.driver import Prompt
# from mi.instrument.ooici.mi.test_driver.driver import NEWLINE
#
# ###
# # Driver parameters for the tests
# ###
# InstrumentDriverTestCase.initialize(
# driver_module='mi.instrument.ooici.mi.test_driver.driver',
# driver_class="InstrumentDriver",
#
# instrument_agent_resource_id = 'TB6W7G',
# instrument_agent_name = 'ooici_mi_test_driver',
# instrument_agent_packet_config = DataParticleType(),
#
# driver_startup_config = {}
# )
#
# #################################### RULES ####################################
# # #
# # Common capabilities in the base class #
# # #
# # Instrument specific stuff in the derived class #
# # #
# # Generator spits out either stubs or comments describing test this here, #
# # test that there. #
# # #
# # Qualification tests are driven through the instrument_agent #
# # #
# ###############################################################################
#
# ###
# # Driver constant definitions
# ###
#
# ###############################################################################
# # DRIVER TEST MIXIN #
# # Defines a set of constants and assert methods used for data particle #
# # verification #
# # #
# # In python mixin classes are classes designed such that they wouldn't be #
# # able to stand on their own, but are inherited by other classes generally #
# # using multiple inheritance. #
# # #
# # This class defines a configuration structure for testing and common assert #
# # methods for validating data particles. #
# ###############################################################################
# class DriverTestMixinSub(DriverTestMixin):
# def assertSampleDataParticle(self, data_particle):
# '''
# Verify a particle is a know particle to this driver and verify the particle is
# correct
# @param data_particle: Data particle of unkown type produced by the driver
# '''
# particle = self.convert_data_particle_to_dict(data_particle)
# stream_name = particle[DataParticleKey.STREAM_NAME]
#
# if (stream_name == DataParticleType.RAW):
# self.assert_particle_raw(data_particle)
# else:
# log.error("Unknown Particle Detected: %s" % particle)
# self.assertFalse(True)
#
#
# ###############################################################################
# # UNIT TESTS #
# # Unit tests test the method calls and parameters using Mock. #
# # #
# # These tests are especially useful for testing parsers and other data #
# # handling. The tests generally focus on small segments of code, like a #
# # single function call, but more complex code using Mock objects. However #
# # if you find yourself mocking too much maybe it is better as an #
# # integration test. #
# # #
# # Unit tests do not start up external processes like the port agent or #
# # driver process. #
# ###############################################################################
# @attr('UNIT', group='mi')
# class DriverUnitTest(InstrumentDriverUnitTestCase, DriverTestMixinSub):
# def setUp(self):
# InstrumentDriverUnitTestCase.setUp(self)
#
#
# def test_driver_enums(self):
# """
# Verify that all driver enumeration has no duplicate values that might cause confusion. Also
# do a little extra validation for the Capabilites
# """
# self.assert_enum_has_no_duplicates(DataParticleType())
# self.assert_enum_has_no_duplicates(ProtocolState())
# self.assert_enum_has_no_duplicates(ProtocolEvent())
# self.assert_enum_has_no_duplicates(InstrumentCommand())
#
# # Test capabilites for duplicates, them verify that capabilities is a subset of proto events
# self.assert_enum_has_no_duplicates(Capability())
# self.assert_enum_complete(Capability(), ProtocolEvent())
#
#
# def test_chunker(self):
# """
# Test the chunker and verify the particles created.
# """
# chunker = StringChunker(Protocol.sieve_function)
#
#
# def test_got_data(self):
# """
# Verify sample data passed through the got data method produces the correct data particles
# """
# # Create and initialize the instrument driver with a mock port agent
# driver = InstrumentDriver(self._got_data_event_callback)
# self.assert_initialize_driver(driver)
#
#
# def test_protocol_filter_capabilities(self):
# """
# This tests driver filter_capabilities.
# Iterate through available capabilities, and verify that they can pass successfully through the filter.
# Test silly made up capabilities to verify they are blocked by filter.
# """
# mock_callback = Mock()
# protocol = Protocol(Prompt, NEWLINE, mock_callback)
# driver_capabilities = Capability().list()
# test_capabilities = Capability().list()
#
# # Add a bogus capability that will be filtered out.
# test_capabilities.append("BOGUS_CAPABILITY")
#
# # Verify "BOGUS_CAPABILITY was filtered out
# self.assertEquals(sorted(driver_capabilities),
# sorted(protocol._filter_capabilities(test_capabilities)))
#
#
# ###############################################################################
# # INTEGRATION TESTS #
# # Integration test test the direct driver / instrument interaction #
# # but making direct calls via zeromq. #
# # - Common Integration tests test the driver through the instrument agent #
# # and common for all drivers (minimum requirement for ION ingestion) #
# ###############################################################################
# @attr('INT', group='mi')
# class DriverIntegrationTest(InstrumentDriverIntegrationTestCase, DriverTestMixinSub):
# def setUp(self):
# InstrumentDriverIntegrationTestCase.setUp(self)
#
# def init_port_agent(self):
# pass
#
# def stop_port_agent(self):
# pass
#
# def port_agent_comm_config(self):
# return {
# 'addr': 'localhost',
# 'port': 8080,
# 'cmd_port': 8081
# }
#
# def test_driver_process(self):
# pass
#
# def test_set(self):
# self.assert_initialize_driver()
#
# # Verify defaults
# self.assert_get(ParameterName.PAYLOAD_SIZE, 1024)
# self.assert_get(ParameterName.SAMPLE_INTERVAL, 1)
#
# # Try and update
# self.assert_set(ParameterName.PAYLOAD_SIZE, 2048, False)
# self.assert_set(ParameterName.SAMPLE_INTERVAL, 2, False)
#
# def test_autosample(self):
# """
# Verify that we can enter streaming and that all particles are produced
# properly.
#
# Because we have to test for three different data particles we can't use
# the common assert_sample_autosample method
# """
# duration = 10
#
# self.assert_initialize_driver()
# self.assert_set(ParameterName.SAMPLE_INTERVAL, 1)
# self.assert_set(ParameterName.PAYLOAD_SIZE, 1024*1024)
#
# self.assert_driver_command(ProtocolEvent.START_AUTOSAMPLE, state=ProtocolState.AUTOSAMPLE, delay=1)
#
# gevent.sleep(duration)
# samples = self.get_sample_events(DataParticleType.RAW)
#
# self.assert_driver_command(ProtocolEvent.STOP_AUTOSAMPLE, state=ProtocolState.COMMAND, delay=1)
#
# self.assertGreaterEqual(len(samples), duration-1)
#
# ###############################################################################
# # QUALIFICATION TESTS #
# # Device specific qualification tests are for doing final testing of ion #
# # integration. The generally aren't used for instrument debugging and should #
# # be tackled after all unit and integration tests are complete #
# ###############################################################################
# @attr('QUAL', group='mi')
# class DriverQualificationTest(InstrumentDriverQualificationTestCase):
# def setUp(self):
# InstrumentDriverQualificationTestCase.setUp(self)
#
# def init_port_agent(self):
# pass
#
# def stop_port_agent(self):
# pass
#
# def port_agent_comm_config(self):
# return {
# 'addr': 'localhost',
# 'port': 8080,
# 'cmd_port': 8081
# }
#
# def test_autosample(self):
# '''
# start and stop autosample and verify data particle
# '''
# self.assert_enter_command_mode()
# self.assert_start_autosample()
#
# gevent.sleep(10)
#
# self.assert_stop_autosample()
#
# def test_get_set_parameters(self):
# '''
# verify that all parameters can be get set properly, this includes
# ensuring that read only parameters fail on set.
# '''
# self.assert_enter_command_mode()
# self.assert_set_parameter(ParameterName.PAYLOAD_SIZE, 2048)
# self.assert_set_parameter(ParameterName.SAMPLE_INTERVAL, 1)
#
# ###
# # Global tests that don't work with this driver
# ###
# def test_reset(self):
# pass
#
# def test_instrument_agent_common_state_model_lifecycle(self):
# pass
#
# def test_direct_access_telnet_closed(self):
# pass
#
# def test_discover(self):
# pass
#
#
#
#
|
"""
Cython Optimize Zeros API
=========================
The underlying C functions for the following root finders can be accessed
directly using Cython:
- `~scipy.optimize.bisect`
- `~scipy.optimize.ridder`
- `~scipy.optimize.brenth`
- `~scipy.optimize.brentq`
The Cython API for the zeros functions is similar except there is no ``disp``
argument. Import the zeros functions using ``cimport`` from
`scipy.optimize.cython_optimize`. ::
from scipy.optimize.cython_optimize cimport bisect, ridder, brentq, brenth
Callback Signature
------------------
The zeros functions in `~scipy.optimize.cython_optimize` expect a callback that
takes a double for the scalar independent variable as the 1st argument and a
user defined ``struct`` with any extra parameters as the 2nd argument. ::
double (*callback_type)(double, void*)
Examples
--------
Usage of `~scipy.optimize.cython_optimize` requires Cython to write callbacks
that are compiled into C. For more information on compiling Cython see the
`Cython Documentation <http://docs.cython.org/en/latest/index.html>`_.
These are the basic steps:
1. Create a Cython ``.pyx`` file, for example: ``myexample.pyx``.
2. Import the desired root finder from `~scipy.optimize.cython_optimize`.
3. Write the callback function, and call the selected zeros function passing
the callback, any extra arguments, and the other solver parameters. ::
from scipy.optimize.cython_optimize cimport brentq
# import math from Cython
from libc cimport math
myargs = {'C0': 1.0, 'C1': 0.7} # a dictionary of extra arguments
XLO, XHI = 0.5, 1.0 # lower and upper search boundaries
XTOL, RTOL, MITR = 1e-3, 1e-3, 10 # other solver parameters
# user defined struct for extra parameters
ctypedef struct test_params:
double C0
double C1
# user defined callback
cdef double f(double x, void *args):
cdef test_params *myargs = <test_params *> args
return myargs.C0 - math.exp(-(x - myargs.C1))
# Cython wrapper function
cdef double brentq_wrapper_example(dict args, double xa, double xb,
double xtol, double rtol, int mitr):
# Cython automatically casts dictionary to struct
cdef test_params myargs = args
return brentq(
f, xa, xb, <test_params *> &myargs, xtol, rtol, mitr, NULL)
# Python function
def brentq_example(args=myargs, xa=XLO, xb=XHI, xtol=XTOL, rtol=RTOL,
mitr=MITR):
'''Calls Cython wrapper from Python.'''
return brentq_wrapper_example(args, xa, xb, xtol, rtol, mitr)
4. If you want to call your function from Python, create a Cython wrapper, and
a Python function that calls the wrapper, or use ``cpdef``. Then in Python
you can import and run the example. ::
from myexample import brentq_example
x = brentq_example()
# 0.6999942848231314
5. Create a Cython ``.pxd`` file if you need to export any Cython functions.
Full Output
-----------
The functions in `~scipy.optimize.cython_optimize` can also copy the full
output from the solver to a C ``struct`` that is passed as its last argument.
If you don't want the full output just pass ``NULL``. The full output
``struct`` must be type ``zeros_full_output``, which is defined in
`scipy.optimize.cython_optimize` with the following fields:
- ``int funcalls``: number of function calls
- ``int iterations``: number of iterations
- ``int error_num``: error number
- ``double root``: root of function
The root is copied by `~scipy.optimize.cython_optimize` to the full output
``struct``. An error number of -1 means a sign error, -2 means a convergence
error, and 0 means the solver converged. Continuing from the previous example::
from scipy.optimize.cython_optimize cimport zeros_full_output
# cython brentq solver with full output
cdef brent_full_output brentq_full_output_wrapper_example(
dict args, double xa, double xb, double xtol, double rtol,
int mitr):
cdef test_params myargs = args
cdef zeros_full_output my_full_output
# use my_full_output instead of NULL
brentq(f, xa, xb, &myargs, xtol, rtol, mitr, &my_full_output)
return my_full_output
# Python function
def brent_full_output_example(args=myargs, xa=XLO, xb=XHI, xtol=XTOL,
rtol=RTOL, mitr=MITR):
'''Returns full output'''
return brentq_full_output_wrapper_example(args, xa, xb, xtol, rtol,
mitr)
result = brent_full_output_example()
# {'error_num': 0,
# 'funcalls': 6,
# 'iterations': 5,
# 'root': 0.6999942848231314}
""" |
# REQUIRES: python-psutil
# Test per test timeout using external shell
# RUN: not %{lit} \
# RUN: %{inputs}/shtest-timeout/infinite_loop.py \
# RUN: %{inputs}/shtest-timeout/quick_then_slow.py \
# RUN: %{inputs}/shtest-timeout/short.py \
# RUN: %{inputs}/shtest-timeout/slow.py \
# RUN: -j 1 -v --debug --timeout 1 --param external=1 > %t.extsh.out 2> %t.extsh.err
# RUN: FileCheck --check-prefix=CHECK-OUT-COMMON < %t.extsh.out %s
# RUN: FileCheck --check-prefix=CHECK-EXTSH-ERR < %t.extsh.err %s
#
# CHECK-EXTSH-ERR: Using external shell
# Test per test timeout using internal shell
# RUN: not %{lit} \
# RUN: %{inputs}/shtest-timeout/infinite_loop.py \
# RUN: %{inputs}/shtest-timeout/quick_then_slow.py \
# RUN: %{inputs}/shtest-timeout/short.py \
# RUN: %{inputs}/shtest-timeout/slow.py \
# RUN: -j 1 -v --debug --timeout 1 --param external=0 > %t.intsh.out 2> %t.intsh.err
# RUN: FileCheck --check-prefix=CHECK-OUT-COMMON < %t.intsh.out %s
# RUN: FileCheck --check-prefix=CHECK-INTSH-OUT < %t.intsh.out %s
# RUN: FileCheck --check-prefix=CHECK-INTSH-ERR < %t.intsh.err %s
#
# CHECK-INTSH-OUT: TIMEOUT: per_test_timeout :: infinite_loop.py
# CHECK-INTSH-OUT: Command 0 Reached Timeout: True
# CHECK-INTSH-OUT: Command 0 Output:
# CHECK-INTSH-OUT-NEXT: Running infinite loop
# CHECK-INTSH-OUT: TIMEOUT: per_test_timeout :: quick_then_slow.py
# CHECK-INTSH-OUT: Timeout: Reached timeout of 1 seconds
# CHECK-INTSH-OUT: Command Output
# CHECK-INTSH-OUT: Command 0 Reached Timeout: False
# CHECK-INTSH-OUT: Command 0 Output:
# CHECK-INTSH-OUT-NEXT: Running in quick mode
# CHECK-INTSH-OUT: Command 1 Reached Timeout: True
# CHECK-INTSH-OUT: Command 1 Output:
# CHECK-INTSH-OUT-NEXT: Running in slow mode
# CHECK-INTSH-OUT: TIMEOUT: per_test_timeout :: slow.py
# CHECK-INTSH-OUT: Command 0 Reached Timeout: True
# CHECK-INTSH-OUT: Command 0 Output:
# CHECK-INTSH-OUT-NEXT: Running slow program
# CHECK-INTSH-ERR: Using internal shell
# Test per test timeout set via a config file rather than on the command line
# RUN: not %{lit} \
# RUN: %{inputs}/shtest-timeout/infinite_loop.py \
# RUN: %{inputs}/shtest-timeout/quick_then_slow.py \
# RUN: %{inputs}/shtest-timeout/short.py \
# RUN: %{inputs}/shtest-timeout/slow.py \
# RUN: -j 1 -v --debug --param external=0 \
# RUN: --param set_timeout=1 > %t.cfgset.out 2> %t.cfgset.err
# RUN: FileCheck --check-prefix=CHECK-OUT-COMMON < %t.cfgset.out %s
# RUN: FileCheck --check-prefix=CHECK-CFGSET-ERR < %t.cfgset.err %s
#
# CHECK-CFGSET-ERR: Using internal shell
# CHECK-OUT-COMMON: TIMEOUT: per_test_timeout :: infinite_loop.py
# CHECK-OUT-COMMON: Timeout: Reached timeout of 1 seconds
# CHECK-OUT-COMMON: Command {{([0-9]+ )?}}Output
# CHECK-OUT-COMMON: Running infinite loop
# CHECK-OUT-COMMON: TIMEOUT: per_test_timeout :: quick_then_slow.py
# CHECK-OUT-COMMON: Timeout: Reached timeout of 1 seconds
# CHECK-OUT-COMMON: Command {{([0-9]+ )?}}Output
# CHECK-OUT-COMMON: Running in quick mode
# CHECK-OUT-COMMON: Running in slow mode
# CHECK-OUT-COMMON: PASS: per_test_timeout :: short.py
# CHECK-OUT-COMMON: TIMEOUT: per_test_timeout :: slow.py
# CHECK-OUT-COMMON: Timeout: Reached timeout of 1 seconds
# CHECK-OUT-COMMON: Command {{([0-9]+ )?}}Output
# CHECK-OUT-COMMON: Running slow program
# CHECK-OUT-COMMON: Expected Passes{{ *}}: 1
# CHECK-OUT-COMMON: Individual Timeouts{{ *}}: 3
# Test per test timeout via a config file and on the command line.
# The value set on the command line should override the config file.
# RUN: not %{lit} \
# RUN: %{inputs}/shtest-timeout/infinite_loop.py \
# RUN: %{inputs}/shtest-timeout/quick_then_slow.py \
# RUN: %{inputs}/shtest-timeout/short.py \
# RUN: %{inputs}/shtest-timeout/slow.py \
# RUN: -j 1 -v --debug --param external=0 \
# RUN: --param set_timeout=1 --timeout=2 > %t.cmdover.out 2> %t.cmdover.err
# RUN: FileCheck --check-prefix=CHECK-CMDLINE-OVERRIDE-OUT < %t.cmdover.out %s
# RUN: FileCheck --check-prefix=CHECK-CMDLINE-OVERRIDE-ERR < %t.cmdover.err %s
# CHECK-CMDLINE-OVERRIDE-ERR: Forcing timeout to be 2 seconds
# CHECK-CMDLINE-OVERRIDE-OUT: TIMEOUT: per_test_timeout :: infinite_loop.py
# CHECK-CMDLINE-OVERRIDE-OUT: Timeout: Reached timeout of 2 seconds
# CHECK-CMDLINE-OVERRIDE-OUT: Command {{([0-9]+ )?}}Output
# CHECK-CMDLINE-OVERRIDE-OUT: Running infinite loop
# CHECK-CMDLINE-OVERRIDE-OUT: TIMEOUT: per_test_timeout :: quick_then_slow.py
# CHECK-CMDLINE-OVERRIDE-OUT: Timeout: Reached timeout of 2 seconds
# CHECK-CMDLINE-OVERRIDE-OUT: Command {{([0-9]+ )?}}Output
# CHECK-CMDLINE-OVERRIDE-OUT: Running in quick mode
# CHECK-CMDLINE-OVERRIDE-OUT: Running in slow mode
# CHECK-CMDLINE-OVERRIDE-OUT: PASS: per_test_timeout :: short.py
# CHECK-CMDLINE-OVERRIDE-OUT: TIMEOUT: per_test_timeout :: slow.py
# CHECK-CMDLINE-OVERRIDE-OUT: Timeout: Reached timeout of 2 seconds
# CHECK-CMDLINE-OVERRIDE-OUT: Command {{([0-9]+ )?}}Output
# CHECK-CMDLINE-OVERRIDE-OUT: Running slow program
# CHECK-CMDLINE-OVERRIDE-OUT: Expected Passes{{ *}}: 1
# CHECK-CMDLINE-OVERRIDE-OUT: Individual Timeouts{{ *}}: 3
|
"""
.. versionadded:: 0.93
Geopy can calculate geodesic distance between two points using the
[Vincenty distance](https://en.wikipedia.org/wiki/Vincenty's_formulae) or
[great-circle distance](https://en.wikipedia.org/wiki/Great-circle_distance)
formulas, with a default of Vincenty available as the function
`geopy.distance.distance`.
Great-circle distance (:class:`.great_circle`) uses a spherical model of
the earth, using the average great-circle radius of 6372.795 kilometers,
resulting in an error of up to about 0.5%. The radius value is stored in
:const:`distance.EARTH_RADIUS`, so it can be customized
(it should always be in kilometers, however).
Vincenty distance (:class:`.vincenty`) uses a more accurate ellipsoidal model
of the earth. This is the default distance formula, and is thus aliased as
``distance.distance``. There are multiple popular ellipsoidal models, and
which one will be the most accurate depends on where your points are located
on the earth. The default is the WGS-84 ellipsoid, which is the most globally
accurate. geopy includes a few other
models in the distance.ELLIPSOIDS dictionary::
model major (km) minor (km) flattening
ELLIPSOIDS = {'WGS-84': (6378.137, 6356.7523142, 1 / 298.257223563),
'GRS-80': (6378.137, 6356.7523141, 1 / 298.257222101),
'Airy (1830)': (6377.563396, 6356.256909, 1 / 299.3249646),
'Intl 1924': (6378.388, 6356.911946, 1 / 297.0),
'Clarke (1880)': (6378.249145, 6356.51486955, 1 / 293.465),
'GRS-67': (6378.1600, 6356.774719, 1 / 298.25),
}
Here's an example usage of distance.vincenty::
>>> from geopy.distance import vincenty
>>> newport_ri = (41.49008, -71.312796)
>>> cleveland_oh = (41.499498, -81.695391)
>>> vincenty(newport_ri, cleveland_oh).miles
538.3904451566326
Using great-circle distance::
>>> from geopy.distance import great_circle
>>> newport_ri = (41.49008, -71.312796)
>>> cleveland_oh = (41.499498, -81.695391)
>>> great_circle(newport_ri, cleveland_oh).miles
537.1485284062816
You can change the ellipsoid model used by the Vincenty formula like so::
>>> distance.vincenty(ne, cl, ellipsoid='GRS-80').miles
The above model name will automatically be retrieved from the ELLIPSOIDS dictionary.
Alternatively, you can specify the model values directly::
>>> distance.vincenty(ne, cl, ellipsoid=(6377., 6356., 1 / 297.)).miles
Distances support simple arithmetic, making it easy to do things like
calculate the length of a path::
>>> d = distance.distance
>>> _, wa = g.geocode('Washington, DC')
>>> _, pa = g.geocode('Palo Alto, CA')
>>> (d(ne, cl) + d(cl, wa) + d(wa, pa)).miles
3276.157156868931
""" |
"""
Discrete Fourier Transform (:mod:`numpy.fft`)
=============================================
.. currentmodule:: numpy.fft
Standard FFTs
-------------
.. autosummary::
:toctree: generated/
fft Discrete Fourier transform.
ifft Inverse discrete Fourier transform.
fft2 Discrete Fourier transform in two dimensions.
ifft2 Inverse discrete Fourier transform in two dimensions.
fftn Discrete Fourier transform in N-dimensions.
ifftn Inverse discrete Fourier transform in N dimensions.
Real FFTs
---------
.. autosummary::
:toctree: generated/
rfft Real discrete Fourier transform.
irfft Inverse real discrete Fourier transform.
rfft2 Real discrete Fourier transform in two dimensions.
irfft2 Inverse real discrete Fourier transform in two dimensions.
rfftn Real discrete Fourier transform in N dimensions.
irfftn Inverse real discrete Fourier transform in N dimensions.
Hermitian FFTs
--------------
.. autosummary::
:toctree: generated/
hfft Hermitian discrete Fourier transform.
ihfft Inverse Hermitian discrete Fourier transform.
Helper routines
---------------
.. autosummary::
:toctree: generated/
fftfreq Discrete Fourier Transform sample frequencies.
rfftfreq DFT sample frequencies (for usage with rfft, irfft).
fftshift Shift zero-frequency component to center of spectrum.
ifftshift Inverse of fftshift.
Background information
----------------------
Fourier analysis is fundamentally a method for expressing a function as a
sum of periodic components, and for recovering the function from those
components. When both the function and its Fourier transform are
replaced with discretized counterparts, it is called the discrete Fourier
transform (DFT). The DFT has become a mainstay of numerical computing in
part because of a very fast algorithm for computing it, called the Fast
Fourier Transform (FFT), which was known to Gauss (1805) and was brought
to light in its current form by NAME and NAME [CT]_. Press et al. [NR]_
provide an accessible introduction to Fourier analysis and its
applications.
Because the discrete Fourier transform separates its input into
components that contribute at discrete frequencies, it has a great number
of applications in digital signal processing, e.g., for filtering, and in
this context the discretized input to the transform is customarily
referred to as a *signal*, which exists in the *time domain*. The output
is called a *spectrum* or *transform* and exists in the *frequency
domain*.
Implementation details
----------------------
There are many ways to define the DFT, varying in the sign of the
exponent, normalization, etc. In this implementation, the DFT is defined
as
.. math::
A_k = \\sum_{m=0}^{n-1} a_m \\exp\\left\\{-2\\pi i{mk \\over n}\\right\\}
\\qquad k = 0,\\ldots,n-1.
The DFT is in general defined for complex inputs and outputs, and a
single-frequency component at linear frequency :math:`f` is
represented by a complex exponential
:math:`a_m = \\exp\\{2\\pi i\\,f m\\Delta t\\}`, where :math:`\\Delta t`
is the sampling interval.
The values in the result follow so-called "standard" order: If ``A =
fft(a, n)``, then ``A[0]`` contains the zero-frequency term (the sum of
the signal), which is always purely real for real inputs. Then ``A[1:n/2]``
contains the positive-frequency terms, and ``A[n/2+1:]`` contains the
negative-frequency terms, in order of decreasingly negative frequency.
For an even number of input points, ``A[n/2]`` represents both positive and
negative Nyquist frequency, and is also purely real for real input. For
an odd number of input points, ``A[(n-1)/2]`` contains the largest positive
frequency, while ``A[(n+1)/2]`` contains the largest negative frequency.
The routine ``np.fft.fftfreq(n)`` returns an array giving the frequencies
of corresponding elements in the output. The routine
``np.fft.fftshift(A)`` shifts transforms and their frequencies to put the
zero-frequency components in the middle, and ``np.fft.ifftshift(A)`` undoes
that shift.
When the input `a` is a time-domain signal and ``A = fft(a)``, ``np.abs(A)``
is its amplitude spectrum and ``np.abs(A)**2`` is its power spectrum.
The phase spectrum is obtained by ``np.angle(A)``.
The inverse DFT is defined as
.. math::
a_m = \\frac{1}{n}\\sum_{k=0}^{n-1}A_k\\exp\\left\\{2\\pi i{mk\\over n}\\right\\}
\\qquad m = 0,\\ldots,n-1.
It differs from the forward transform by the sign of the exponential
argument and the default normalization by :math:`1/n`.
Normalization
-------------
The default normalization has the direct transforms unscaled and the inverse
transforms are scaled by :math:`1/n`. It is possible to obtain unitary
transforms by setting the keyword argument ``norm`` to ``"ortho"`` (default is
`None`) so that both direct and inverse transforms will be scaled by
:math:`1/\\sqrt{n}`.
Real and Hermitian transforms
-----------------------------
When the input is purely real, its transform is Hermitian, i.e., the
component at frequency :math:`f_k` is the complex conjugate of the
component at frequency :math:`-f_k`, which means that for real
inputs there is no information in the negative frequency components that
is not already available from the positive frequency components.
The family of `rfft` functions is
designed to operate on real inputs, and exploits this symmetry by
computing only the positive frequency components, up to and including the
Nyquist frequency. Thus, ``n`` input points produce ``n/2+1`` complex
output points. The inverses of this family assumes the same symmetry of
its input, and for an output of ``n`` points uses ``n/2+1`` input points.
Correspondingly, when the spectrum is purely real, the signal is
Hermitian. The `hfft` family of functions exploits this symmetry by
using ``n/2+1`` complex points in the input (time) domain for ``n`` real
points in the frequency domain.
In higher dimensions, FFTs are used, e.g., for image analysis and
filtering. The computational efficiency of the FFT means that it can
also be a faster way to compute large convolutions, using the property
that a convolution in the time domain is equivalent to a point-by-point
multiplication in the frequency domain.
Higher dimensions
-----------------
In two dimensions, the DFT is defined as
.. math::
A_{kl} = \\sum_{m=0}^{M-1} \\sum_{n=0}^{N-1}
a_{mn}\\exp\\left\\{-2\\pi i \\left({mk\\over M}+{nl\\over N}\\right)\\right\\}
\\qquad k = 0, \\ldots, M-1;\\quad l = 0, \\ldots, N-1,
which extends in the obvious way to higher dimensions, and the inverses
in higher dimensions also extend in the same way.
References
----------
.. [CT] NAME, NAME and John W. NAME, 1965, "An algorithm for the
machine calculation of complex Fourier series," *Math. Comput.*
19: 297-301.
.. [NR] NAME NAME NAME and NAME
2007, *Numerical Recipes: The Art of Scientific Computing*, ch.
12-13. Cambridge Univ. Press, Cambridge, UK.
Examples
--------
For examples, see the various functions.
""" |
"""
========================================
Special functions (:mod:`scipy.special`)
========================================
.. module:: scipy.special
Nearly all of the functions below are universal functions and follow
broadcasting and automatic array-looping rules. Exceptions are noted.
Error handling
==============
Errors are handled by returning nans, or other appropriate values.
Some of the special function routines will emit warnings when an error
occurs. By default this is disabled. To enable such messages use
``errprint(1)``, and to disable such messages use ``errprint(0)``.
Example:
>>> print scipy.special.bdtr(-1,10,0.3)
>>> scipy.special.errprint(1)
>>> print scipy.special.bdtr(-1,10,0.3)
.. autosummary::
:toctree: generated/
errprint
SpecialFunctionWarning -- Warning that can be issued with ``errprint(True)``
Available functions
===================
Airy functions
--------------
.. autosummary::
:toctree: generated/
airy -- Airy functions and their derivatives.
airye -- Exponentially scaled Airy functions
ai_zeros -- [+]Zeros of Airy functions Ai(x) and Ai'(x)
bi_zeros -- [+]Zeros of Airy functions Bi(x) and Bi'(x)
itairy --
Elliptic Functions and Integrals
--------------------------------
.. autosummary::
:toctree: generated/
ellipj -- Jacobian elliptic functions
ellipk -- Complete elliptic integral of the first kind.
ellipkm1 -- ellipkm1(x) == ellipk(1 - x)
ellipkinc -- Incomplete elliptic integral of the first kind.
ellipe -- Complete elliptic integral of the second kind.
ellipeinc -- Incomplete elliptic integral of the second kind.
Bessel Functions
----------------
.. autosummary::
:toctree: generated/
jv -- Bessel function of real-valued order and complex argument.
jn -- Alias for jv
jve -- Exponentially scaled Bessel function.
yn -- Bessel function of second kind (integer order).
yv -- Bessel function of the second kind (real-valued order).
yve -- Exponentially scaled Bessel function of the second kind.
kn -- Modified Bessel function of the second kind (integer order).
kv -- Modified Bessel function of the second kind (real order).
kve -- Exponentially scaled modified Bessel function of the second kind.
iv -- Modified Bessel function.
ive -- Exponentially scaled modified Bessel function.
hankel1 -- Hankel function of the first kind.
hankel1e -- Exponentially scaled Hankel function of the first kind.
hankel2 -- Hankel function of the second kind.
hankel2e -- Exponentially scaled Hankel function of the second kind.
The following is not an universal function:
.. autosummary::
:toctree: generated/
lmbda -- [+]Sequence of lambda functions with arbitrary order v.
Zeros of Bessel Functions
^^^^^^^^^^^^^^^^^^^^^^^^^
These are not universal functions:
.. autosummary::
:toctree: generated/
jnjnp_zeros -- [+]Zeros of integer-order Bessel functions and derivatives sorted in order.
jnyn_zeros -- [+]Zeros of integer-order Bessel functions and derivatives as separate arrays.
jn_zeros -- [+]Zeros of Jn(x)
jnp_zeros -- [+]Zeros of Jn'(x)
yn_zeros -- [+]Zeros of Yn(x)
ynp_zeros -- [+]Zeros of Yn'(x)
y0_zeros -- [+]Complex zeros: Y0(z0)=0 and values of Y0'(z0)
y1_zeros -- [+]Complex zeros: Y1(z1)=0 and values of Y1'(z1)
y1p_zeros -- [+]Complex zeros of Y1'(z1')=0 and values of Y1(z1')
Faster versions of common Bessel Functions
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.. autosummary::
:toctree: generated/
j0 -- Bessel function of order 0.
j1 -- Bessel function of order 1.
y0 -- Bessel function of second kind of order 0.
y1 -- Bessel function of second kind of order 1.
i0 -- Modified Bessel function of order 0.
i0e -- Exponentially scaled modified Bessel function of order 0.
i1 -- Modified Bessel function of order 1.
i1e -- Exponentially scaled modified Bessel function of order 1.
k0 -- Modified Bessel function of the second kind of order 0.
k0e -- Exponentially scaled modified Bessel function of the second kind of order 0.
k1 -- Modified Bessel function of the second kind of order 1.
k1e -- Exponentially scaled modified Bessel function of the second kind of order 1.
Integrals of Bessel Functions
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.. autosummary::
:toctree: generated/
itj0y0 -- Basic integrals of j0 and y0 from 0 to x.
it2j0y0 -- Integrals of (1-j0(t))/t from 0 to x and y0(t)/t from x to inf.
iti0k0 -- Basic integrals of i0 and k0 from 0 to x.
it2i0k0 -- Integrals of (i0(t)-1)/t from 0 to x and k0(t)/t from x to inf.
besselpoly -- Integral of a Bessel function: Jv(2* a* x) * x[+]lambda from x=0 to 1.
Derivatives of Bessel Functions
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.. autosummary::
:toctree: generated/
jvp -- Nth derivative of Jv(v,z)
yvp -- Nth derivative of Yv(v,z)
kvp -- Nth derivative of Kv(v,z)
ivp -- Nth derivative of Iv(v,z)
h1vp -- Nth derivative of H1v(v,z)
h2vp -- Nth derivative of H2v(v,z)
Spherical Bessel Functions
^^^^^^^^^^^^^^^^^^^^^^^^^^
.. autosummary::
:toctree: generated/
spherical_jn -- Spherical Bessel function of the first kind, jn(z)
spherical_yn -- Spherical Bessel function of the second kind, yn(z)
spherical_in -- Modified spherical Bessel function of the first kind, in(z)
spherical_kn -- Modified spherical Bessel function of the second kind, kn(z)
These are not universal functions:
.. autosummary::
:toctree: generated/
sph_jn -- [+]Sequence of spherical Bessel functions, jn(z)
sph_yn -- [+]Sequence of spherical Bessel functions, yn(z)
sph_jnyn -- [+]Sequence of spherical Bessel functions, jn(z) and yn(z)
sph_in -- [+]Sequence of spherical Bessel functions, in(z)
sph_kn -- [+]Sequence of spherical Bessel functions, kn(z)
sph_inkn -- [+]Sequence of spherical Bessel functions, in(z) and kn(z)
Riccati-Bessel Functions
^^^^^^^^^^^^^^^^^^^^^^^^
These are not universal functions:
.. autosummary::
:toctree: generated/
riccati_jn -- [+]Sequence of Ricatti-Bessel functions of first kind.
riccati_yn -- [+]Sequence of Ricatti-Bessel functions of second kind.
Struve Functions
----------------
.. autosummary::
:toctree: generated/
struve -- Struve function --- Hv(x)
modstruve -- Modified Struve function --- Lv(x)
itstruve0 -- Integral of H0(t) from 0 to x
it2struve0 -- Integral of H0(t)/t from x to Inf.
itmodstruve0 -- Integral of L0(t) from 0 to x.
Raw Statistical Functions
-------------------------
.. seealso:: :mod:`scipy.stats`: Friendly versions of these functions.
.. autosummary::
:toctree: generated/
bdtr -- Sum of terms 0 through k of the binomial pdf.
bdtrc -- Sum of terms k+1 through n of the binomial pdf.
bdtri -- Inverse of bdtr
bdtrik --
bdtrin --
btdtr -- Integral from 0 to x of beta pdf.
btdtri -- Quantiles of beta distribution
btdtria --
btdtrib --
fdtr -- Integral from 0 to x of F pdf.
fdtrc -- Integral from x to infinity under F pdf.
fdtri -- Inverse of fdtrc
fdtridfd --
gdtr -- Integral from 0 to x of gamma pdf.
gdtrc -- Integral from x to infinity under gamma pdf.
gdtria -- Inverse with respect to `a` of gdtr.
gdtrib -- Inverse with respect to `b` of gdtr.
gdtrix -- Inverse with respect to `x` of gdtr.
nbdtr -- Sum of terms 0 through k of the negative binomial pdf.
nbdtrc -- Sum of terms k+1 to infinity under negative binomial pdf.
nbdtri -- Inverse of nbdtr
nbdtrik --
nbdtrin --
ncfdtr -- CDF of non-central t distribution.
ncfdtridfd -- Find degrees of freedom (denominator) of noncentral F distribution.
ncfdtridfn -- Find degrees of freedom (numerator) of noncentral F distribution.
ncfdtri -- Inverse CDF of noncentral F distribution.
ncfdtrinc -- Find noncentrality parameter of noncentral F distribution.
nctdtr -- CDF of noncentral t distribution.
nctdtridf -- Find degrees of freedom of noncentral t distribution.
nctdtrit -- Inverse CDF of noncentral t distribution.
nctdtrinc -- Find noncentrality parameter of noncentral t distribution.
nrdtrimn -- Find mean of normal distribution from cdf and std.
nrdtrisd -- Find std of normal distribution from cdf and mean.
pdtr -- Sum of terms 0 through k of the Poisson pdf.
pdtrc -- Sum of terms k+1 to infinity of the Poisson pdf.
pdtri -- Inverse of pdtr
pdtrik --
stdtr -- Integral from -infinity to t of the Student-t pdf.
stdtridf --
stdtrit --
chdtr -- Integral from 0 to x of the Chi-square pdf.
chdtrc -- Integral from x to infnity of Chi-square pdf.
chdtri -- Inverse of chdtrc.
chdtriv --
ndtr -- Integral from -infinity to x of standard normal pdf
log_ndtr -- Logarithm of integral from -infinity to x of standard normal pdf
ndtri -- Inverse of ndtr (quantiles)
chndtr --
chndtridf --
chndtrinc --
chndtrix --
smirnov -- Kolmogorov-Smirnov complementary CDF for one-sided test statistic (Dn+ or Dn-)
smirnovi -- Inverse of smirnov.
kolmogorov -- The complementary CDF of the (scaled) two-sided test statistic (Kn*) valid for large n.
kolmogi -- Inverse of kolmogorov
tklmbda -- Tukey-Lambda CDF
logit --
expit --
boxcox -- Compute the Box-Cox transformation.
boxcox1p -- Compute the Box-Cox transformation of 1 + x.
inv_boxcox -- Compute the inverse of the Box-Cox tranformation.
inv_boxcox1p -- Compute the inverse of the Box-Cox transformation of 1 + x.
Information Theory Functions
----------------------------
.. autosummary::
:toctree: generated/
entr -- entr(x) = -x*log(x)
rel_entr -- rel_entr(x, y) = x*log(x/y)
kl_div -- kl_div(x, y) = x*log(x/y) - x + y
huber -- Huber loss function.
pseudo_huber -- Pseudo-Huber loss function.
Gamma and Related Functions
---------------------------
.. autosummary::
:toctree: generated/
gamma -- Gamma function.
gammaln -- Log of the absolute value of the Gamma function.
loggamma -- Principal branch of the logarithm of the Gamma function.
gammasgn -- Sign of the gamma function.
gammainc -- Incomplete gamma integral.
gammaincinv -- Inverse of gammainc.
gammaincc -- Complemented incomplete gamma integral.
gammainccinv -- Inverse of gammaincc.
beta -- Beta function.
betaln -- Log of the absolute value of the beta function.
betainc -- Incomplete beta integral.
betaincinv -- Inverse of betainc.
psi -- Logarithmic derivative of the gamma function.
rgamma -- One divided by the gamma function.
polygamma -- Nth derivative of psi function.
multigammaln -- Log of the multivariate gamma.
digamma -- Digamma function (derivative of the logarithm of gamma).
poch -- The Pochhammer symbol (rising factorial).
Error Function and Fresnel Integrals
------------------------------------
.. autosummary::
:toctree: generated/
erf -- Error function.
erfc -- Complemented error function (1- erf(x))
erfcx -- Scaled complemented error function exp(x**2)*erfc(x)
erfi -- Imaginary error function, -i erf(i x)
erfinv -- Inverse of error function
erfcinv -- Inverse of erfc
wofz -- Fadeeva function.
dawsn -- Dawson's integral.
fresnel -- Fresnel sine and cosine integrals.
fresnel_zeros -- Complex zeros of both Fresnel integrals
modfresnelp -- Modified Fresnel integrals F_+(x) and K_+(x)
modfresnelm -- Modified Fresnel integrals F_-(x) and K_-(x)
These are not universal functions:
.. autosummary::
:toctree: generated/
erf_zeros -- [+]Complex zeros of erf(z)
fresnelc_zeros -- [+]Complex zeros of Fresnel cosine integrals
fresnels_zeros -- [+]Complex zeros of Fresnel sine integrals
Legendre Functions
------------------
.. autosummary::
:toctree: generated/
lpmv -- Associated Legendre Function of arbitrary non-negative degree v.
sph_harm -- Spherical Harmonics (complex-valued) Y^m_n(theta,phi)
These are not universal functions:
.. autosummary::
:toctree: generated/
clpmn -- [+]Associated Legendre Function of the first kind for complex arguments.
lpn -- [+]Legendre Functions (polynomials) of the first kind
lqn -- [+]Legendre Functions of the second kind.
lpmn -- [+]Associated Legendre Function of the first kind for real arguments.
lqmn -- [+]Associated Legendre Function of the second kind.
Ellipsoidal Harmonics
---------------------
.. autosummary::
:toctree: generated/
ellip_harm -- Ellipsoidal harmonic E
ellip_harm_2 -- Ellipsoidal harmonic F
ellip_normal -- Ellipsoidal normalization constant
Orthogonal polynomials
----------------------
The following functions evaluate values of orthogonal polynomials:
.. autosummary::
:toctree: generated/
assoc_laguerre
eval_legendre
eval_chebyt
eval_chebyu
eval_chebyc
eval_chebys
eval_jacobi
eval_laguerre
eval_genlaguerre
eval_hermite
eval_hermitenorm
eval_gegenbauer
eval_sh_legendre
eval_sh_chebyt
eval_sh_chebyu
eval_sh_jacobi
The functions below, in turn, return the polynomial coefficients in
:class:`~.orthopoly1d` objects, which function similarly as :ref:`numpy.poly1d`.
The :class:`~.orthopoly1d` class also has an attribute ``weights`` which returns
the roots, weights, and total weights for the appropriate form of Gaussian
quadrature. These are returned in an ``n x 3`` array with roots in the first
column, weights in the second column, and total weights in the final column.
Note that :class:`~.orthopoly1d` objects are converted to ``poly1d`` when doing
arithmetic, and lose information of the original orthogonal polynomial.
.. autosummary::
:toctree: generated/
legendre -- [+]Legendre polynomial P_n(x) (lpn -- for function).
chebyt -- [+]Chebyshev polynomial T_n(x)
chebyu -- [+]Chebyshev polynomial U_n(x)
chebyc -- [+]Chebyshev polynomial C_n(x)
chebys -- [+]Chebyshev polynomial S_n(x)
jacobi -- [+]Jacobi polynomial P^(alpha,beta)_n(x)
laguerre -- [+]Laguerre polynomial, L_n(x)
genlaguerre -- [+]Generalized (Associated) Laguerre polynomial, L^alpha_n(x)
hermite -- [+]Hermite polynomial H_n(x)
hermitenorm -- [+]Normalized Hermite polynomial, He_n(x)
gegenbauer -- [+]Gegenbauer (Ultraspherical) polynomials, C^(alpha)_n(x)
sh_legendre -- [+]shifted Legendre polynomial, P*_n(x)
sh_chebyt -- [+]shifted Chebyshev polynomial, T*_n(x)
sh_chebyu -- [+]shifted Chebyshev polynomial, U*_n(x)
sh_jacobi -- [+]shifted Jacobi polynomial, J*_n(x) = G^(p,q)_n(x)
.. warning::
Computing values of high-order polynomials (around ``order > 20``) using
polynomial coefficients is numerically unstable. To evaluate polynomial
values, the ``eval_*`` functions should be used instead.
Roots and weights for orthogonal polynomials
.. autosummary::
:toctree: generated/
c_roots
cg_roots
h_roots
he_roots
j_roots
js_roots
l_roots
la_roots
p_roots
ps_roots
s_roots
t_roots
ts_roots
u_roots
us_roots
Hypergeometric Functions
------------------------
.. autosummary::
:toctree: generated/
hyp2f1 -- Gauss hypergeometric function (2F1)
hyp1f1 -- Confluent hypergeometric function (1F1)
hyperu -- Confluent hypergeometric function (U)
hyp0f1 -- Confluent hypergeometric limit function (0F1)
hyp2f0 -- Hypergeometric function (2F0)
hyp1f2 -- Hypergeometric function (1F2)
hyp3f0 -- Hypergeometric function (3F0)
Parabolic Cylinder Functions
----------------------------
.. autosummary::
:toctree: generated/
pbdv -- Parabolic cylinder function Dv(x) and derivative.
pbvv -- Parabolic cylinder function Vv(x) and derivative.
pbwa -- Parabolic cylinder function W(a,x) and derivative.
These are not universal functions:
.. autosummary::
:toctree: generated/
pbdv_seq -- [+]Sequence of parabolic cylinder functions Dv(x)
pbvv_seq -- [+]Sequence of parabolic cylinder functions Vv(x)
pbdn_seq -- [+]Sequence of parabolic cylinder functions Dn(z), complex z
Mathieu and Related Functions
-----------------------------
.. autosummary::
:toctree: generated/
mathieu_a -- Characteristic values for even solution (ce_m)
mathieu_b -- Characteristic values for odd solution (se_m)
These are not universal functions:
.. autosummary::
:toctree: generated/
mathieu_even_coef -- [+]sequence of expansion coefficients for even solution
mathieu_odd_coef -- [+]sequence of expansion coefficients for odd solution
The following return both function and first derivative:
.. autosummary::
:toctree: generated/
mathieu_cem -- Even Mathieu function
mathieu_sem -- Odd Mathieu function
mathieu_modcem1 -- Even modified Mathieu function of the first kind
mathieu_modcem2 -- Even modified Mathieu function of the second kind
mathieu_modsem1 -- Odd modified Mathieu function of the first kind
mathieu_modsem2 -- Odd modified Mathieu function of the second kind
Spheroidal Wave Functions
-------------------------
.. autosummary::
:toctree: generated/
pro_ang1 -- Prolate spheroidal angular function of the first kind
pro_rad1 -- Prolate spheroidal radial function of the first kind
pro_rad2 -- Prolate spheroidal radial function of the second kind
obl_ang1 -- Oblate spheroidal angular function of the first kind
obl_rad1 -- Oblate spheroidal radial function of the first kind
obl_rad2 -- Oblate spheroidal radial function of the second kind
pro_cv -- Compute characteristic value for prolate functions
obl_cv -- Compute characteristic value for oblate functions
pro_cv_seq -- Compute sequence of prolate characteristic values
obl_cv_seq -- Compute sequence of oblate characteristic values
The following functions require pre-computed characteristic value:
.. autosummary::
:toctree: generated/
pro_ang1_cv -- Prolate spheroidal angular function of the first kind
pro_rad1_cv -- Prolate spheroidal radial function of the first kind
pro_rad2_cv -- Prolate spheroidal radial function of the second kind
obl_ang1_cv -- Oblate spheroidal angular function of the first kind
obl_rad1_cv -- Oblate spheroidal radial function of the first kind
obl_rad2_cv -- Oblate spheroidal radial function of the second kind
Kelvin Functions
----------------
.. autosummary::
:toctree: generated/
kelvin -- All Kelvin functions (order 0) and derivatives.
kelvin_zeros -- [+]Zeros of All Kelvin functions (order 0) and derivatives
ber -- Kelvin function ber x
bei -- Kelvin function bei x
berp -- Derivative of Kelvin function ber x
beip -- Derivative of Kelvin function bei x
ker -- Kelvin function ker x
kei -- Kelvin function kei x
kerp -- Derivative of Kelvin function ker x
keip -- Derivative of Kelvin function kei x
These are not universal functions:
.. autosummary::
:toctree: generated/
ber_zeros -- [+]Zeros of Kelvin function bei x
bei_zeros -- [+]Zeros of Kelvin function ber x
berp_zeros -- [+]Zeros of derivative of Kelvin function ber x
beip_zeros -- [+]Zeros of derivative of Kelvin function bei x
ker_zeros -- [+]Zeros of Kelvin function kei x
kei_zeros -- [+]Zeros of Kelvin function ker x
kerp_zeros -- [+]Zeros of derivative of Kelvin function ker x
keip_zeros -- [+]Zeros of derivative of Kelvin function kei x
Combinatorics
-------------
.. autosummary::
:toctree: generated/
comb -- [+]Combinations of N things taken k at a time, "N choose k"
perm -- [+]Permutations of N things taken k at a time, "k-permutations of N"
Other Special Functions
-----------------------
.. autosummary::
:toctree: generated/
agm -- Arithmetic-Geometric Mean
bernoulli -- Bernoulli numbers
binom -- Binomial coefficient.
diric -- Dirichlet function (periodic sinc)
euler -- Euler numbers
expn -- Exponential integral.
exp1 -- Exponential integral of order 1 (for complex argument)
expi -- Another exponential integral -- Ei(x)
factorial -- The factorial function, n! = special.gamma(n+1)
factorial2 -- Double factorial, (n!)!
factorialk -- [+](...((n!)!)!...)! where there are k '!'
shichi -- Hyperbolic sine and cosine integrals.
sici -- Integral of the sinc and "cosinc" functions.
spence -- Spence's function, also known as the dilogarithm.
lambertw -- Lambert W function
zeta -- Riemann zeta function of two arguments.
zetac -- Standard Riemann zeta function minus 1.
Convenience Functions
---------------------
.. autosummary::
:toctree: generated/
cbrt -- Cube root.
exp10 -- 10 raised to the x power.
exp2 -- 2 raised to the x power.
radian -- radian angle given degrees, minutes, and seconds.
cosdg -- cosine of the angle given in degrees.
sindg -- sine of the angle given in degrees.
tandg -- tangent of the angle given in degrees.
cotdg -- cotangent of the angle given in degrees.
log1p -- log(1+x)
expm1 -- exp(x)-1
cosm1 -- cos(x)-1
round -- round the argument to the nearest integer. If argument ends in 0.5 exactly, pick the nearest even integer.
xlogy -- x*log(y)
xlog1py -- x*log1p(y)
exprel -- (exp(x)-1)/x
sinc -- sin(x)/x
.. [+] in the description indicates a function which is not a universal
.. function and does not follow broadcasting and automatic
.. array-looping rules.
""" |
"""
Test models for the multilingual library.
# Note: the to_str() calls in all the tests are here only to make it
# easier to test both pre-unicode and current Django.
>>> from testproject.utils import to_str
# make sure the settings are right
>>> from multilingual.languages import LANGUAGES
>>> LANGUAGES
[['en', 'English'], ['pl', 'Polish'], ['zh-cn', 'Simplified Chinese']]
>>> from multilingual import set_default_language
>>> from django.db.models import Q
>>> set_default_language(1)
### Check the table names
>>> Category._meta.translation_model._meta.db_table
'category_language'
>>> Article._meta.translation_model._meta.db_table
'articles_article_translation'
### Create the test data
# Check both assigning via the proxy properties and set_* functions
>>> c = Category()
>>> c.name_en = 'category 1'
>>> c.name_pl = 'kategoria 1'
>>> c.save()
>>> c = Category()
>>> c.set_name('category 2', 'en')
>>> c.set_name('kategoria 2', 'pl')
>>> c.save()
### See if the test data was saved correctly
### Note: first object comes from the initial fixture.
>>> c = Category.objects.all().order_by('id')[1]
>>> to_str((c.name, c.get_name(1), c.get_name(2)))
('category 1', 'category 1', 'kategoria 1')
>>> c = Category.objects.all().order_by('id')[2]
>>> to_str((c.name, c.get_name(1), c.get_name(2)))
('category 2', 'category 2', 'kategoria 2')
### Check translation changes.
### Make sure the name and description properties obey
### set_default_language.
>>> c = Category.objects.all().order_by('id')[1]
# set language: pl
>>> set_default_language(2)
>>> to_str((c.name, c.get_name(1), c.get_name(2)))
('kategoria 1', 'category 1', 'kategoria 1')
>>> c.name = 'kat 1'
>>> to_str((c.name, c.get_name(1), c.get_name(2)))
('kat 1', 'category 1', 'kat 1')
# set language: en
>>> set_default_language('en')
>>> c.name = 'cat 1'
>>> to_str((c.name, c.get_name(1), c.get_name(2)))
('cat 1', 'cat 1', 'kat 1')
>>> c.save()
# Read the entire Category objects from the DB again to see if
# everything was saved correctly.
>>> c = Category.objects.all().order_by('id')[1]
>>> to_str((c.name, c.get_name('en'), c.get_name('pl')))
('cat 1', 'cat 1', 'kat 1')
>>> c = Category.objects.all().order_by('id')[2]
>>> to_str((c.name, c.get_name('en'), c.get_name('pl')))
('category 2', 'category 2', 'kategoria 2')
### Check ordering
>>> set_default_language(1)
>>> to_str([c.name for c in Category.objects.all().order_by('name_en')])
['Fixture category', 'cat 1', 'category 2']
### Check ordering
# start with renaming one of the categories so that the order actually
# depends on the default language
>>> set_default_language(1)
>>> c = Category.objects.get(name='cat 1')
>>> c.name = 'zzz cat 1'
>>> c.save()
>>> to_str([c.name for c in Category.objects.all().order_by('name_en')])
['Fixture category', 'category 2', 'zzz cat 1']
>>> to_str([c.name for c in Category.objects.all().order_by('name')])
['Fixture category', 'category 2', 'zzz cat 1']
>>> to_str([c.name for c in Category.objects.all().order_by('-name')])
['zzz cat 1', 'category 2', 'Fixture category']
>>> set_default_language(2)
>>> to_str([c.name for c in Category.objects.all().order_by('name')])
['Fixture kategoria', 'kat 1', 'kategoria 2']
>>> to_str([c.name for c in Category.objects.all().order_by('-name')])
['kategoria 2', 'kat 1', 'Fixture kategoria']
### Check filtering
# Check for filtering defined by Q objects as well. This is a recent
# improvement: the translation fields are being handled by an
# extension of lookup_inner instead of overridden
# QuerySet._filter_or_exclude
>>> set_default_language('en')
>>> to_str([c.name for c in Category.objects.all().filter(name__contains='2')])
['category 2']
>>> set_default_language('en')
>>> to_str([c.name for c in Category.objects.all().filter(Q(name__contains='2'))])
['category 2']
>>> set_default_language(1)
>>> to_str([c.name for c in
... Category.objects.all().filter(Q(name__contains='2')|Q(name_pl__contains='kat'))])
['Fixture category', 'zzz cat 1', 'category 2']
>>> set_default_language(1)
>>> to_str([c.name for c in Category.objects.all().filter(name_en__contains='2')])
['category 2']
>>> set_default_language(1)
>>> to_str([c.name for c in Category.objects.all().filter(Q(name_pl__contains='kat'))])
['Fixture category', 'zzz cat 1', 'category 2']
>>> set_default_language('pl')
>>> to_str([c.name for c in Category.objects.all().filter(name__contains='k')])
['Fixture kategoria', 'kat 1', 'kategoria 2']
>>> set_default_language('pl')
>>> to_str([c.name for c in Category.objects.all().filter(Q(name__contains='kategoria'))])
['Fixture kategoria', 'kategoria 2']
### Check specifying query set language
>>> c_en = Category.objects.all().for_language('en')
>>> c_pl = Category.objects.all().for_language(2) # both ID and code work here
>>> to_str(c_en.get(name__contains='1').name)
'zzz cat 1'
>>> to_str(c_pl.get(name__contains='1').name)
'kat 1'
>>> to_str([c.name for c in c_en.order_by('name')])
['Fixture category', 'category 2', 'zzz cat 1']
>>> to_str([c.name for c in c_pl.order_by('-name')])
['kategoria 2', 'kat 1', 'Fixture kategoria']
>>> c = c_en.get(id=2)
>>> c.name = 'test'
>>> to_str((c.name, c.name_en, c.name_pl))
('test', 'test', 'kat 1')
>>> c = c_pl.get(id=2)
>>> c.name = 'test'
>>> to_str((c.name, c.name_en, c.name_pl))
('test', 'zzz cat 1', 'test')
### Check filtering spanning more than one model
>>> set_default_language(1)
>>> cat_1 = Category.objects.get(name='zzz cat 1')
>>> cat_2 = Category.objects.get(name='category 2')
>>> a = Article(category=cat_1)
>>> a.set_title('article 1', 1)
>>> a.set_title('artykul 1', 2)
>>> a.set_contents('contents 1', 1)
>>> a.set_contents('zawartosc 1', 1)
>>> a.save()
>>> a = Article(category=cat_2)
>>> a.set_title('article 2', 1)
>>> a.set_title('artykul 2', 2)
>>> a.set_contents('contents 2', 1)
>>> a.set_contents('zawartosc 2', 1)
>>> a.save()
>>> to_str([a.title for a in Article.objects.filter(category=cat_1)])
['article 1']
>>> to_str([a.title for a in Article.objects.filter(category__name=cat_1.name)])
['article 1']
>>> to_str([a.title for a in Article.objects.filter(Q(category__name=cat_1.name)|Q(category__name_pl__contains='2')).order_by('-title')])
['article 2', 'article 1']
### Test the creation of new objects using keywords passed to the
### constructor
>>> set_default_language(2)
>>> c_n = Category.objects.create(name_en='new category', name_pl='nowa kategoria')
>>> to_str((c_n.name, c_n.name_en, c_n.name_pl))
('nowa kategoria', 'new category', 'nowa kategoria')
>>> c_n.save()
>>> c_n2 = Category.objects.get(name_en='new category')
>>> to_str((c_n2.name, c_n2.name_en, c_n2.name_pl))
('nowa kategoria', 'new category', 'nowa kategoria')
>>> set_default_language(2)
>>> c_n3 = Category.objects.create(name='nowa kategoria 2')
>>> to_str((c_n3.name, c_n3.name_en, c_n3.name_pl))
('nowa kategoria 2', None, 'nowa kategoria 2')
########################################
###### Check if the admin behaviour for categories with incomplete translations
>>> from django.contrib.auth.models import User
>>> User.objects.create_superuser('test', 'test_email', 'test_password')
>>> from django.test.client import Client
>>> c = Client()
>>> c.login(username='test', password='test_password')
True
# create a category with only 2 translations, skipping the
# first language
>>> resp = c.post('/admin/articles/category/add/',
... {'creator': 1,
... 'translations-TOTAL_FORMS': '3',
... 'translations-INITIAL_FORMS': '0',
... 'translations-0-language_id': '1',
... 'translations-1-language_id': '2',
... 'translations-2-language_id': '3',
... 'translations-1-name': 'pl name',
... 'translations-2-name': 'zh-cn name',
... })
>>> resp.status_code
302
>>> cat = Category.objects.order_by('-id')[0]
>>> cat.name_en
>>> cat.name_pl
u'pl name'
>>> cat.name_zh_cn
u'zh-cn name'
>>> cat.translations.count()
2
""" |
"""
Simple config
=============
Although CherryPy uses the :mod:`Python logging module <logging>`, it does so
behind the scenes so that simple logging is simple, but complicated logging
is still possible. "Simple" logging means that you can log to the screen
(i.e. console/stdout) or to a file, and that you can easily have separate
error and access log files.
Here are the simplified logging settings. You use these by adding lines to
your config file or dict. You should set these at either the global level or
per application (see next), but generally not both.
* ``log.screen``: Set this to True to have both "error" and "access" messages
printed to stdout.
* ``log.access_file``: Set this to an absolute filename where you want
"access" messages written.
* ``log.error_file``: Set this to an absolute filename where you want "error"
messages written.
Many events are automatically logged; to log your own application events, call
:func:`cherrypy.log`.
Architecture
============
Separate scopes
---------------
CherryPy provides log managers at both the global and application layers.
This means you can have one set of logging rules for your entire site,
and another set of rules specific to each application. The global log
manager is found at :func:`cherrypy.log`, and the log manager for each
application is found at :attr:`app.log<cherrypy._cptree.Application.log>`.
If you're inside a request, the latter is reachable from
``cherrypy.request.app.log``; if you're outside a request, you'll have to
obtain a reference to the ``app``: either the return value of
:func:`tree.mount()<cherrypy._cptree.Tree.mount>` or, if you used
:func:`quickstart()<cherrypy.quickstart>` instead, via
``cherrypy.tree.apps['/']``.
By default, the global logs are named "cherrypy.error" and "cherrypy.access",
and the application logs are named "cherrypy.error.2378745" and
"cherrypy.access.2378745" (the number is the id of the Application object).
This means that the application logs "bubble up" to the site logs, so if your
application has no log handlers, the site-level handlers will still log the
messages.
Errors vs. Access
-----------------
Each log manager handles both "access" messages (one per HTTP request) and
"error" messages (everything else). Note that the "error" log is not just for
errors! The format of access messages is highly formalized, but the error log
isn't--it receives messages from a variety of sources (including full error
tracebacks, if enabled).
If you are logging the access log and error log to the same source, then there
is a possibility that a specially crafted error message may replicate an access
log message as described in CWE-117. In this case it is the application
developer's responsibility to manually escape data before using CherryPy's log()
functionality, or they may create an application that is vulnerable to CWE-117.
This would be achieved by using a custom handler escape any special characters,
and attached as described below.
Custom Handlers
===============
The simple settings above work by manipulating Python's standard :mod:`logging`
module. So when you need something more complex, the full power of the standard
module is yours to exploit. You can borrow or create custom handlers, formats,
filters, and much more. Here's an example that skips the standard FileHandler
and uses a RotatingFileHandler instead:
::
#python
log = app.log
# Remove the default FileHandlers if present.
log.error_file = ""
log.access_file = ""
maxBytes = getattr(log, "rot_maxBytes", 10000000)
backupCount = getattr(log, "rot_backupCount", 1000)
# Make a new RotatingFileHandler for the error log.
fname = getattr(log, "rot_error_file", "error.log")
h = handlers.RotatingFileHandler(fname, 'a', maxBytes, backupCount)
h.setLevel(DEBUG)
h.setFormatter(_cplogging.logfmt)
log.error_log.addHandler(h)
# Make a new RotatingFileHandler for the access log.
fname = getattr(log, "rot_access_file", "access.log")
h = handlers.RotatingFileHandler(fname, 'a', maxBytes, backupCount)
h.setLevel(DEBUG)
h.setFormatter(_cplogging.logfmt)
log.access_log.addHandler(h)
The ``rot_*`` attributes are pulled straight from the application log object.
Since "log.*" config entries simply set attributes on the log object, you can
add custom attributes to your heart's content. Note that these handlers are
used ''instead'' of the default, simple handlers outlined above (so don't set
the "log.error_file" config entry, for example).
""" |
#!/usr/bin/env/python
# qsgen.py - Generate XPConnect quick stubs.
#
# ***** BEGIN LICENSE BLOCK *****
# Version: MPL 1.1/GPL 2.0/LGPL 2.1
#
# The contents of this file are subject to the Mozilla Public License Version
# 1.1 (the "License"); you may not use this file except in compliance with
# the License. You may obtain a copy of the License at
# http://www.mozilla.org/MPL/
#
# Software distributed under the License is distributed on an "AS IS" basis,
# WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
# for the specific language governing rights and limitations under the
# License.
#
# The Original Code is mozilla.org code.
#
# The Initial Developer of the Original Code is
# Mozilla Foundation.
# Portions created by the Initial Developer are Copyright (C) 2008
# the Initial Developer. All Rights Reserved.
#
# Contributor(s):
# NAME <EMAIL>
#
# Alternatively, the contents of this file may be used under the terms of
# either of the GNU General Public License Version 2 or later (the "GPL"),
# or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
# in which case the provisions of the GPL or the LGPL are applicable instead
# of those above. If you wish to allow use of your version of this file only
# under the terms of either the GPL or the LGPL, and not to allow others to
# use your version of this file under the terms of the MPL, indicate your
# decision by deleting the provisions above and replace them with the notice
# and other provisions required by the GPL or the LGPL. If you do not delete
# the provisions above, a recipient may use your version of this file under
# the terms of any one of the MPL, the GPL or the LGPL.
#
# ***** END LICENSE BLOCK *****
# =About quick stubs=
# qsgen.py generates "quick stubs", custom SpiderMonkey getters, setters, and
# methods for specified XPCOM interface members. These quick stubs serve at
# runtime as replacements for the XPConnect functions XPC_WN_GetterSetter and
# XPC_WN_CallMethod, which are the extremely generic (and slow) SpiderMonkey
# getter/setter/methods otherwise used for all XPCOM member accesses from JS.
#
# There are two ways quick stubs win:
# 1. Pure, transparent optimization by partial evaluation.
# 2. Cutting corners.
#
# == Partial evaluation ==
# Partial evaluation is when you execute part of a program early (before or at
# compile time) so that you don't have to execute it at run time. In this
# case, everything that involves interpreting xptcall data (for example, the
# big methodInfo loops in XPCWrappedNative::CallMethod and the switch statement
# in XPCConert::JSData2Native) might as well happen at build time, since all
# the type information for any given member is already known. That's what this
# script does. It gets the information from IDL instead of XPT files. Apart
# from that, the code in this script is very similar to what you'll find in
# XPConnect itself. The advantage is that it runs once, at build time, not in
# tight loops at run time.
#
# == Cutting corners ==
# The XPConnect versions have to be slow because they do tons of work that's
# only necessary in a few cases. The quick stubs skip a lot of that work. So
# quick stubs necessarily differ from XPConnect in potentially observable ways.
# For many specific interface members, the differences are not observable from
# scripts or don't matter enough to worry about; but you do have to be careful
# which members you decide to generate quick stubs for.
#
# The complete list of known differences, as of this writing, after an
# assiduous search:
#
# - Quick stubs affect the handling of naming conflicts--that is, which C++
# method gets called when a script uses an XPCOM feature that is declared in
# more than one of the interfaces the object implements. Without quick
# stubs, XPConnect just walks the interfaces in the order they're listed by
# nsClassInfo. You get the first interface that implements a feature with
# that name. With quick stubs, it's the same except that non-quick-stubbed
# features are shadowed.
#
# - Quick stub methods are JSFastNative, which means that when a quick stub
# method is called, no JS stack frame is created. This doesn't affect
# Mozilla security checks because they look for scripted JSStackFrames, not
# native ones.
#
# It does affect the 'stack' property of JavaScript exceptions, though: the
# stubbed member will not appear. (Note that if the stubbed member itself
# fails, the member name will appear in the 'message' property.)
#
# - Many quick stubs don't create an XPCCallContext. In those cases, no entry
# is added to the XPCCallContext stack. So native implementations of
# quick-stubbed methods must avoid nsXPConnect::GetCurrentNativeCallContext.
#
# (Even when a quick stub does have an XPCCallContext, it never pushes it all
# the way to READY_TO_CALL state, so a lot of its members are garbage. But
# this doesn't endanger native implementations of non-quick-stubbed methods
# that use GetCurrentNativeCallContext and are called indirectly from
# quick-stubbed methods, because only the current top XPCCallContext is
# exposed--nsAXPCNativeCallContext does not expose
# XPCCallContext::GetPrevCallContext.)
#
# - Quick stubs never suspend the JS request. So they are only suitable for
# main-thread-only interfaces.
#
# - Quick stubs don't call XPCContext::SetLastResult. This is visible on the
# Components object.
#
# - Quick stubs skip a security check that XPConnect does in
# XPCWrappedNative::CallMethod. This means the security manager doesn't have
# an opportunity to veto accesses to members for which quick stubs exist.
#
# - There are many features of IDL that XPConnect supports but qsgen does not,
# including dependent types, arrays, and out parameters.
#
# - Since quick stubs are JSPropertyOps, we have to do additional work to make
# __lookup[GS]etter__ work on them.
|
"""Stuff to parse AIFF-C and AIFF files.
Unless explicitly stated otherwise, the description below is true
both for AIFF-C files and AIFF files.
An AIFF-C file has the following structure.
+-----------------+
| FORM |
+-----------------+
| <size> |
+----+------------+
| | AIFC |
| +------------+
| | <chunks> |
| | . |
| | . |
| | . |
+----+------------+
An AIFF file has the string "AIFF" instead of "AIFC".
A chunk consists of an identifier (4 bytes) followed by a size (4 bytes,
big endian order), followed by the data. The size field does not include
the size of the 8 byte header.
The following chunk types are recognized.
FVER
<version number of AIFF-C defining document> (AIFF-C only).
MARK
<# of markers> (2 bytes)
list of markers:
<marker ID> (2 bytes, must be > 0)
<position> (4 bytes)
<marker name> ("pstring")
COMM
<# of channels> (2 bytes)
<# of sound frames> (4 bytes)
<size of the samples> (2 bytes)
<sampling frequency> (10 bytes, IEEE 80-bit extended
floating point)
in AIFF-C files only:
<compression type> (4 bytes)
<human-readable version of compression type> ("pstring")
SSND
<offset> (4 bytes, not used by this program)
<blocksize> (4 bytes, not used by this program)
<sound data>
A pstring consists of 1 byte length, a string of characters, and 0 or 1
byte pad to make the total length even.
Usage.
Reading AIFF files:
f = aifc.open(file, 'r')
where file is either the name of a file or an open file pointer.
The open file pointer must have methods read(), seek(), and close().
In some types of audio files, if the setpos() method is not used,
the seek() method is not necessary.
This returns an instance of a class with the following public methods:
getnchannels() -- returns number of audio channels (1 for
mono, 2 for stereo)
getsampwidth() -- returns sample width in bytes
getframerate() -- returns sampling frequency
getnframes() -- returns number of audio frames
getcomptype() -- returns compression type ('NONE' for AIFF files)
getcompname() -- returns human-readable version of
compression type ('not compressed' for AIFF files)
getparams() -- returns a tuple consisting of all of the
above in the above order
getmarkers() -- get the list of marks in the audio file or None
if there are no marks
getmark(id) -- get mark with the specified id (raises an error
if the mark does not exist)
readframes(n) -- returns at most n frames of audio
rewind() -- rewind to the beginning of the audio stream
setpos(pos) -- seek to the specified position
tell() -- return the current position
close() -- close the instance (make it unusable)
The position returned by tell(), the position given to setpos() and
the position of marks are all compatible and have nothing to do with
the actual position in the file.
The close() method is called automatically when the class instance
is destroyed.
Writing AIFF files:
f = aifc.open(file, 'w')
where file is either the name of a file or an open file pointer.
The open file pointer must have methods write(), tell(), seek(), and
close().
This returns an instance of a class with the following public methods:
aiff() -- create an AIFF file (AIFF-C default)
aifc() -- create an AIFF-C file
setnchannels(n) -- set the number of channels
setsampwidth(n) -- set the sample width
setframerate(n) -- set the frame rate
setnframes(n) -- set the number of frames
setcomptype(type, name)
-- set the compression type and the
human-readable compression type
setparams(tuple)
-- set all parameters at once
setmark(id, pos, name)
-- add specified mark to the list of marks
tell() -- return current position in output file (useful
in combination with setmark())
writeframesraw(data)
-- write audio frames without pathing up the
file header
writeframes(data)
-- write audio frames and patch up the file header
close() -- patch up the file header and close the
output file
You should set the parameters before the first writeframesraw or
writeframes. The total number of frames does not need to be set,
but when it is set to the correct value, the header does not have to
be patched up.
It is best to first set all parameters, perhaps possibly the
compression type, and then write audio frames using writeframesraw.
When all frames have been written, either call writeframes('') or
close() to patch up the sizes in the header.
Marks can be added anytime. If there are any marks, you must call
close() after all frames have been written.
The close() method is called automatically when the class instance
is destroyed.
When a file is opened with the extension '.aiff', an AIFF file is
written, otherwise an AIFF-C file is written. This default can be
changed by calling aiff() or aifc() before the first writeframes or
writeframesraw.
""" |
"""
==============
Array indexing
==============
Array indexing refers to any use of the square brackets ([]) to index
array values. There are many options to indexing, which give numpy
indexing great power, but with power comes some complexity and the
potential for confusion. This section is just an overview of the
various options and issues related to indexing. Aside from single
element indexing, the details on most of these options are to be
found in related sections.
Assignment vs referencing
=========================
Most of the following examples show the use of indexing when
referencing data in an array. The examples work just as well
when assigning to an array. See the section at the end for
specific examples and explanations on how assignments work.
Single element indexing
=======================
Single element indexing for a 1-D array is what one expects. It work
exactly like that for other standard Python sequences. It is 0-based,
and accepts negative indices for indexing from the end of the array. ::
>>> x = np.arange(10)
>>> x[2]
2
>>> x[-2]
8
Unlike lists and tuples, numpy arrays support multidimensional indexing
for multidimensional arrays. That means that it is not necessary to
separate each dimension's index into its own set of square brackets. ::
>>> x.shape = (2,5) # now x is 2-dimensional
>>> x[1,3]
8
>>> x[1,-1]
9
Note that if one indexes a multidimensional array with fewer indices
than dimensions, one gets a subdimensional array. For example: ::
>>> x[0]
array([0, 1, 2, 3, 4])
That is, each index specified selects the array corresponding to the
rest of the dimensions selected. In the above example, choosing 0
means that remaining dimension of lenth 5 is being left unspecified,
and that what is returned is an array of that dimensionality and size.
It must be noted that the returned array is not a copy of the original,
but points to the same values in memory as does the original array.
In this case, the 1-D array at the first position (0) is returned.
So using a single index on the returned array, results in a single
element being returned. That is: ::
>>> x[0][2]
2
So note that ``x[0,2] = x[0][2]`` though the second case is more
inefficient a new temporary array is created after the first index
that is subsequently indexed by 2.
Note to those used to IDL or Fortran memory order as it relates to
indexing. Numpy uses C-order indexing. That means that the last
index usually represents the most rapidly changing memory location,
unlike Fortran or IDL, where the first index represents the most
rapidly changing location in memory. This difference represents a
great potential for confusion.
Other indexing options
======================
It is possible to slice and stride arrays to extract arrays of the
same number of dimensions, but of different sizes than the original.
The slicing and striding works exactly the same way it does for lists
and tuples except that they can be applied to multiple dimensions as
well. A few examples illustrates best: ::
>>> x = np.arange(10)
>>> x[2:5]
array([2, 3, 4])
>>> x[:-7]
array([0, 1, 2])
>>> x[1:7:2]
array([1, 3, 5])
>>> y = np.arange(35).reshape(5,7)
>>> y[1:5:2,::3]
array([[ 7, 10, 13],
[21, 24, 27]])
Note that slices of arrays do not copy the internal array data but
also produce new views of the original data.
It is possible to index arrays with other arrays for the purposes of
selecting lists of values out of arrays into new arrays. There are
two different ways of accomplishing this. One uses one or more arrays
of index values. The other involves giving a boolean array of the proper
shape to indicate the values to be selected. Index arrays are a very
powerful tool that allow one to avoid looping over individual elements in
arrays and thus greatly improve performance.
It is possible to use special features to effectively increase the
number of dimensions in an array through indexing so the resulting
array aquires the shape needed for use in an expression or with a
specific function.
Index arrays
============
Numpy arrays may be indexed with other arrays (or any other sequence-
like object that can be converted to an array, such as lists, with the
exception of tuples; see the end of this document for why this is). The
use of index arrays ranges from simple, straightforward cases to
complex, hard-to-understand cases. For all cases of index arrays, what
is returned is a copy of the original data, not a view as one gets for
slices.
Index arrays must be of integer type. Each value in the array indicates
which value in the array to use in place of the index. To illustrate: ::
>>> x = np.arange(10,1,-1)
>>> x
array([10, 9, 8, 7, 6, 5, 4, 3, 2])
>>> x[np.array([3, 3, 1, 8])]
array([7, 7, 9, 2])
The index array consisting of the values 3, 3, 1 and 8 correspondingly
create an array of length 4 (same as the index array) where each index
is replaced by the value the index array has in the array being indexed.
Negative values are permitted and work as they do with single indices
or slices: ::
>>> x[np.array([3,3,-3,8])]
array([7, 7, 4, 2])
It is an error to have index values out of bounds: ::
>>> x[np.array([3, 3, 20, 8])]
<type 'exceptions.IndexError'>: index 20 out of bounds 0<=index<9
Generally speaking, what is returned when index arrays are used is
an array with the same shape as the index array, but with the type
and values of the array being indexed. As an example, we can use a
multidimensional index array instead: ::
>>> x[np.array([[1,1],[2,3]])]
array([[9, 9],
[8, 7]])
Indexing Multi-dimensional arrays
=================================
Things become more complex when multidimensional arrays are indexed,
particularly with multidimensional index arrays. These tend to be
more unusal uses, but theyare permitted, and they are useful for some
problems. We'll start with thesimplest multidimensional case (using
the array y from the previous examples): ::
>>> y[np.array([0,2,4]), np.array([0,1,2])]
array([ 0, 15, 30])
In this case, if the index arrays have a matching shape, and there is
an index array for each dimension of the array being indexed, the
resultant array has the same shape as the index arrays, and the values
correspond to the index set for each position in the index arrays. In
this example, the first index value is 0 for both index arrays, and
thus the first value of the resultant array is y[0,0]. The next value
is y[2,1], and the last is y[4,2].
If the index arrays do not have the same shape, there is an attempt to
broadcast them to the same shape. If they cannot be broadcast to the
same shape, an exception is raised: ::
>>> y[np.array([0,2,4]), np.array([0,1])]
<type 'exceptions.ValueError'>: shape mismatch: objects cannot be
broadcast to a single shape
The broadcasting mechanism permits index arrays to be combined with
scalars for other indices. The effect is that the scalar value is used
for all the corresponding values of the index arrays: ::
>>> y[np.array([0,2,4]), 1]
array([ 1, 15, 29])
Jumping to the next level of complexity, it is possible to only
partially index an array with index arrays. It takes a bit of thought
to understand what happens in such cases. For example if we just use
one index array with y: ::
>>> y[np.array([0,2,4])]
array([[ 0, 1, 2, 3, 4, 5, 6],
[14, 15, 16, 17, 18, 19, 20],
[28, 29, 30, 31, 32, 33, 34]])
What results is the construction of a new array where each value of
the index array selects one row from the array being indexed and the
resultant array has the resulting shape (size of row, number index
elements).
An example of where this may be useful is for a color lookup table
where we want to map the values of an image into RGB triples for
display. The lookup table could have a shape (nlookup, 3). Indexing
such an array with an image with shape (ny, nx) with dtype=np.uint8
(or any integer type so long as values are with the bounds of the
lookup table) will result in an array of shape (ny, nx, 3) where a
triple of RGB values is associated with each pixel location.
In general, the shape of the resulant array will be the concatenation
of the shape of the index array (or the shape that all the index arrays
were broadcast to) with the shape of any unused dimensions (those not
indexed) in the array being indexed.
Boolean or "mask" index arrays
==============================
Boolean arrays used as indices are treated in a different manner
entirely than index arrays. Boolean arrays must be of the same shape
as the initial dimensions of the array being indexed. In the
most straightforward case, the boolean array has the same shape: ::
>>> b = y>20
>>> y[b]
array([21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34])
The result is a 1-D array containing all the elements in the indexed
array corresponding to all the true elements in the boolean array. As
with index arrays, what is returned is a copy of the data, not a view
as one gets with slices.
The result will be multidimensional if y has more dimensions than b.
For example: ::
>>> b[:,5] # use a 1-D boolean whose first dim agrees with the first dim of y
array([False, False, False, True, True], dtype=bool)
>>> y[b[:,5]]
array([[21, 22, 23, 24, 25, 26, 27],
[28, 29, 30, 31, 32, 33, 34]])
Here the 4th and 5th rows are selected from the indexed array and
combined to make a 2-D array.
In general, when the boolean array has fewer dimensions than the array
being indexed, this is equivalent to y[b, ...], which means
y is indexed by b followed by as many : as are needed to fill
out the rank of y.
Thus the shape of the result is one dimension containing the number
of True elements of the boolean array, followed by the remaining
dimensions of the array being indexed.
For example, using a 2-D boolean array of shape (2,3)
with four True elements to select rows from a 3-D array of shape
(2,3,5) results in a 2-D result of shape (4,5): ::
>>> x = np.arange(30).reshape(2,3,5)
>>> x
array([[[ 0, 1, 2, 3, 4],
[ 5, 6, 7, 8, 9],
[10, 11, 12, 13, 14]],
[[15, 16, 17, 18, 19],
[20, 21, 22, 23, 24],
[25, 26, 27, 28, 29]]])
>>> b = np.array([[True, True, False], [False, True, True]])
>>> x[b]
array([[ 0, 1, 2, 3, 4],
[ 5, 6, 7, 8, 9],
[20, 21, 22, 23, 24],
[25, 26, 27, 28, 29]])
For further details, consult the numpy reference documentation on array indexing.
Combining index arrays with slices
==================================
Index arrays may be combined with slices. For example: ::
>>> y[np.array([0,2,4]),1:3]
array([[ 1, 2],
[15, 16],
[29, 30]])
In effect, the slice is converted to an index array
np.array([[1,2]]) (shape (1,2)) that is broadcast with the index array
to produce a resultant array of shape (3,2).
Likewise, slicing can be combined with broadcasted boolean indices: ::
>>> y[b[:,5],1:3]
array([[22, 23],
[29, 30]])
Structural indexing tools
=========================
To facilitate easy matching of array shapes with expressions and in
assignments, the np.newaxis object can be used within array indices
to add new dimensions with a size of 1. For example: ::
>>> y.shape
(5, 7)
>>> y[:,np.newaxis,:].shape
(5, 1, 7)
Note that there are no new elements in the array, just that the
dimensionality is increased. This can be handy to combine two
arrays in a way that otherwise would require explicitly reshaping
operations. For example: ::
>>> x = np.arange(5)
>>> x[:,np.newaxis] + x[np.newaxis,:]
array([[0, 1, 2, 3, 4],
[1, 2, 3, 4, 5],
[2, 3, 4, 5, 6],
[3, 4, 5, 6, 7],
[4, 5, 6, 7, 8]])
The ellipsis syntax maybe used to indicate selecting in full any
remaining unspecified dimensions. For example: ::
>>> z = np.arange(81).reshape(3,3,3,3)
>>> z[1,...,2]
array([[29, 32, 35],
[38, 41, 44],
[47, 50, 53]])
This is equivalent to: ::
>>> z[1,:,:,2]
array([[29, 32, 35],
[38, 41, 44],
[47, 50, 53]])
Assigning values to indexed arrays
==================================
As mentioned, one can select a subset of an array to assign to using
a single index, slices, and index and mask arrays. The value being
assigned to the indexed array must be shape consistent (the same shape
or broadcastable to the shape the index produces). For example, it is
permitted to assign a constant to a slice: ::
>>> x = np.arange(10)
>>> x[2:7] = 1
or an array of the right size: ::
>>> x[2:7] = np.arange(5)
Note that assignments may result in changes if assigning
higher types to lower types (like floats to ints) or even
exceptions (assigning complex to floats or ints): ::
>>> x[1] = 1.2
>>> x[1]
1
>>> x[1] = 1.2j
<type 'exceptions.TypeError'>: can't convert complex to long; use
long(abs(z))
Unlike some of the references (such as array and mask indices)
assignments are always made to the original data in the array
(indeed, nothing else would make sense!). Note though, that some
actions may not work as one may naively expect. This particular
example is often surprising to people: ::
>>> x = np.arange(0, 50, 10)
>>> x
array([ 0, 10, 20, 30, 40])
>>> x[np.array([1, 1, 3, 1])] += 1
>>> x
array([ 0, 11, 20, 31, 40])
Where people expect that the 1st location will be incremented by 3.
In fact, it will only be incremented by 1. The reason is because
a new array is extracted from the original (as a temporary) containing
the values at 1, 1, 3, 1, then the value 1 is added to the temporary,
and then the temporary is assigned back to the original array. Thus
the value of the array at x[1]+1 is assigned to x[1] three times,
rather than being incremented 3 times.
Dealing with variable numbers of indices within programs
========================================================
The index syntax is very powerful but limiting when dealing with
a variable number of indices. For example, if you want to write
a function that can handle arguments with various numbers of
dimensions without having to write special case code for each
number of possible dimensions, how can that be done? If one
supplies to the index a tuple, the tuple will be interpreted
as a list of indices. For example (using the previous definition
for the array z): ::
>>> indices = (1,1,1,1)
>>> z[indices]
40
So one can use code to construct tuples of any number of indices
and then use these within an index.
Slices can be specified within programs by using the slice() function
in Python. For example: ::
>>> indices = (1,1,1,slice(0,2)) # same as [1,1,1,0:2]
>>> z[indices]
array([39, 40])
Likewise, ellipsis can be specified by code by using the Ellipsis
object: ::
>>> indices = (1, Ellipsis, 1) # same as [1,...,1]
>>> z[indices]
array([[28, 31, 34],
[37, 40, 43],
[46, 49, 52]])
For this reason it is possible to use the output from the np.where()
function directly as an index since it always returns a tuple of index
arrays.
Because the special treatment of tuples, they are not automatically
converted to an array as a list would be. As an example: ::
>>> z[[1,1,1,1]] # produces a large array
array([[[[27, 28, 29],
[30, 31, 32], ...
>>> z[(1,1,1,1)] # returns a single value
40
""" |
#!/usr/bin/env python
# (c) 2013, NAME <EMAIL>
#
# This file is part of Ansible.
#
# Ansible is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# Ansible is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with Ansible. If not, see <http://www.gnu.org/licenses/>.
#
#
# Author: NAME <EMAIL>
#
# Description:
# This module queries local or remote Docker daemons and generates
# inventory information.
#
# This plugin does not support targeting of specific hosts using the --host
# flag. Instead, it queries the Docker API for each container, running
# or not, and returns this data all once.
#
# The plugin returns the following custom attributes on Docker containers:
# docker_args
# docker_config
# docker_created
# docker_driver
# docker_exec_driver
# docker_host_config
# docker_hostname_path
# docker_hosts_path
# docker_id
# docker_image
# docker_name
# docker_network_settings
# docker_path
# docker_resolv_conf_path
# docker_state
# docker_volumes
# docker_volumes_rw
#
# Requirements:
# The docker-py module: https://github.com/dotcloud/docker-py
#
# Notes:
# A config file can be used to configure this inventory module, and there
# are several environment variables that can be set to modify the behavior
# of the plugin at runtime:
# DOCKER_CONFIG_FILE
# DOCKER_HOST
# DOCKER_VERSION
# DOCKER_TIMEOUT
# DOCKER_PRIVATE_SSH_PORT
# DOCKER_DEFAULT_IP
#
# Environment Variables:
# environment variable: DOCKER_CONFIG_FILE
# description:
# - A path to a Docker inventory hosts/defaults file in YAML format
# - A sample file has been provided, colocated with the inventory
# file called 'docker.yml'
# required: false
# default: Uses docker.docker.Client constructor defaults
# environment variable: DOCKER_HOST
# description:
# - The socket on which to connect to a Docker daemon API
# required: false
# default: Uses docker.docker.Client constructor defaults
# environment variable: DOCKER_VERSION
# description:
# - Version of the Docker API to use
# default: Uses docker.docker.Client constructor defaults
# required: false
# environment variable: DOCKER_TIMEOUT
# description:
# - Timeout in seconds for connections to Docker daemon API
# default: Uses docker.docker.Client constructor defaults
# required: false
# environment variable: DOCKER_PRIVATE_SSH_PORT
# description:
# - The private port (container port) on which SSH is listening
# for connections
# default: 22
# required: false
# environment variable: DOCKER_DEFAULT_IP
# description:
# - This environment variable overrides the container SSH connection
# IP address (aka, 'ansible_ssh_host')
#
# This option allows one to override the ansible_ssh_host whenever
# Docker has exercised its default behavior of binding private ports
# to all interfaces of the Docker host. This behavior, when dealing
# with remote Docker hosts, does not allow Ansible to determine
# a proper host IP address on which to connect via SSH to containers.
# By default, this inventory module assumes all IP_ADDRESS-exposed
# ports to be bound to localhost:<port>. To override this
# behavior, for example, to bind a container's SSH port to the public
# interface of its host, one must manually set this IP.
#
# It is preferable to begin to launch Docker containers with
# ports exposed on publicly accessible IP addresses, particularly
# if the containers are to be targeted by Ansible for remote
# configuration, not accessible via localhost SSH connections.
#
# Docker containers can be explicitly exposed on IP addresses by
# a) starting the daemon with the --ip argument
# b) running containers with the -P/--publish ip::containerPort
# argument
# default: IP_ADDRESS if port exposed on IP_ADDRESS by Docker
# required: false
#
# Examples:
# Use the config file:
# DOCKER_CONFIG_FILE=./docker.yml docker.py --list
#
# Connect to docker instance on localhost port 4243
# DOCKER_HOST=tcp://localhost:4243 docker.py --list
#
# Any container's ssh port exposed on IP_ADDRESS will mapped to
# another IP address (where Ansible will attempt to connect via SSH)
# DOCKER_DEFAULT_IP=IP_ADDRESS docker.py --list
|
# -*- encoding: utf-8 -*-
##############################################################################
#
# OpenERP, Open Source Management Solution
# Copyright (C) 2004-2009 Tiny SPRL (<http://tiny.be>).
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Affero General Public License as
# published by the Free Software Foundation, either version 3 of the
# License, or (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
##############################################################################
# SKR03
# =====
# Dieses Modul bietet Ihnen einen deutschen Kontenplan basierend auf dem SKR03.
# Gemäss der aktuellen Einstellungen ist die Firma nicht Umsatzsteuerpflichtig.
# Diese Grundeinstellung ist sehr einfach zu ändern und bedarf in der Regel
# grundsätzlich eine initiale Zuweisung von Steuerkonten zu Produkten und / oder
# Sachkonten oder zu Partnern.
# Die Umsatzsteuern (voller Steuersatz, reduzierte Steuer und steuerfrei)
# sollten bei den Produktstammdaten hinterlegt werden (in Abhängigkeit der
# Steuervorschriften). Die Zuordnung erfolgt auf dem Aktenreiter Finanzbuchhaltung
# (Kategorie: Umsatzsteuer).
# Die Vorsteuern (voller Steuersatz, reduzierte Steuer und steuerfrei)
# sollten ebenso bei den Produktstammdaten hinterlegt werden (in Abhängigkeit
# der Steuervorschriften). Die Zuordnung erfolgt auf dem Aktenreiter
# Finanzbuchhaltung (Kategorie: Vorsteuer).
# Die Zuordnung der Steuern für Ein- und Ausfuhren aus EU Ländern, sowie auch
# für den Ein- und Verkauf aus und in Drittländer sollten beim Partner
# (Lieferant/Kunde)hinterlegt werden (in Anhängigkeit vom Herkunftsland
# des Lieferanten/Kunden). Die Zuordnung beim Kunden ist 'höherwertig' als
# die Zuordnung bei Produkten und überschreibt diese im Einzelfall.
#
# Zur Vereinfachung der Steuerausweise und Buchung bei Auslandsgeschäften
# erlaubt OpenERP ein generelles Mapping von Steuerausweis und Steuerkonten
# (z.B. Zuordnung 'Umsatzsteuer 19%' zu 'steuerfreie Einfuhren aus der EU')
# zwecks Zuordnung dieses Mappings zum ausländischen Partner (Kunde/Lieferant).
# Die Rechnungsbuchung beim Einkauf bewirkt folgendes:
# Die Steuerbemessungsgrundlage (exklusive Steuer) wird ausgewiesen bei den
# jeweiligen Kategorien für den Vorsteuer Steuermessbetrag (z.B. Vorsteuer
# Steuermessbetrag Voller Steuersatz 19%).
# Der Steuerbetrag erscheint unter der Kategorie 'Vorsteuern' (z.B. Vorsteuer
# 19%). Durch multidimensionale Hierachien können verschiedene Positionen
# zusammengefasst werden und dann in Form eines Reports ausgegeben werden.
#
# Die Rechnungsbuchung beim Verkauf bewirkt folgendes:
# Die Steuerbemessungsgrundlage (exklusive Steuer) wird ausgewiesen bei den
# jeweiligen Kategorien für den Umsatzsteuer Steuermessbetrag
# (z.B. Umsatzsteuer Steuermessbetrag Voller Steuersatz 19%).
# Der Steuerbetrag erscheint unter der Kategorie 'Umsatzsteuer'
# (z.B. Umsatzsteuer 19%). Durch multidimensionale Hierachien können
# verschiedene Positionen zusammengefasst werden.
# Die zugewiesenen Steuerausweise können auf Ebene der einzelnen
# Rechnung (Eingangs- und Ausgangsrechnung) nachvollzogen werden,
# und dort gegebenenfalls angepasst werden.
# Rechnungsgutschriften führen zu einer Korrektur (Gegenposition)
# der Steuerbuchung, in Form einer spiegelbildlichen Buchung.
# SKR04
# =====
# Dieses Modul bietet Ihnen einen deutschen Kontenplan basierend auf dem SKR04.
# Gemäss der aktuellen Einstellungen ist die Firma nicht Umsatzsteuerpflichtig,
# d.h. im Standard existiert keine Zuordnung von Produkten und Sachkonten zu
# Steuerschlüsseln.
# Diese Grundeinstellung ist sehr einfach zu ändern und bedarf in der Regel
# grundsätzlich eine initiale Zuweisung von Steuerschlüsseln zu Produkten und / oder
# Sachkonten oder zu Partnern.
# Die Umsatzsteuern (voller Steuersatz, reduzierte Steuer und steuerfrei)
# sollten bei den Produktstammdaten hinterlegt werden (in Abhängigkeit der
# Steuervorschriften). Die Zuordnung erfolgt auf dem Aktenreiter Finanzbuchhaltung
# (Kategorie: Umsatzsteuer).
# Die Vorsteuern (voller Steuersatz, reduzierte Steuer und steuerfrei)
# sollten ebenso bei den Produktstammdaten hinterlegt werden (in Abhängigkeit
# der Steuervorschriften). Die Zuordnung erfolgt auf dem Aktenreiter
# Finanzbuchhaltung (Kategorie: Vorsteuer).
# Die Zuordnung der Steuern für Ein- und Ausfuhren aus EU Ländern, sowie auch
# für den Ein- und Verkauf aus und in Drittländer sollten beim Partner
# (Lieferant/Kunde) hinterlegt werden (in Anhängigkeit vom Herkunftsland
# des Lieferanten/Kunden). Die Zuordnung beim Kunden ist 'höherwertig' als
# die Zuordnung bei Produkten und überschreibt diese im Einzelfall.
#
# Zur Vereinfachung der Steuerausweise und Buchung bei Auslandsgeschäften
# erlaubt OpenERP ein generelles Mapping von Steuerausweis und Steuerkonten
# (z.B. Zuordnung 'Umsatzsteuer 19%' zu 'steuerfreie Einfuhren aus der EU')
# zwecks Zuordnung dieses Mappings zum ausländischen Partner (Kunde/Lieferant).
# Die Rechnungsbuchung beim Einkauf bewirkt folgendes:
# Die Steuerbemessungsgrundlage (exklusive Steuer) wird ausgewiesen bei den
# jeweiligen Kategorien für den Vorsteuer Steuermessbetrag (z.B. Vorsteuer
# Steuermessbetrag Voller Steuersatz 19%).
# Der Steuerbetrag erscheint unter der Kategorie 'Vorsteuern' (z.B. Vorsteuer
# 19%). Durch multidimensionale Hierachien können verschiedene Positionen
# zusammengefasst werden und dann in Form eines Reports ausgegeben werden.
#
# Die Rechnungsbuchung beim Verkauf bewirkt folgendes:
# Die Steuerbemessungsgrundlage (exklusive Steuer) wird ausgewiesen bei den
# jeweiligen Kategorien für den Umsatzsteuer Steuermessbetrag
# (z.B. Umsatzsteuer Steuermessbetrag Voller Steuersatz 19%).
# Der Steuerbetrag erscheint unter der Kategorie 'Umsatzsteuer'
# (z.B. Umsatzsteuer 19%). Durch multidimensionale Hierachien können
# verschiedene Positionen zusammengefasst werden.
# Die zugewiesenen Steuerausweise können auf Ebene der einzelnen
# Rechnung (Eingangs- und Ausgangsrechnung) nachvollzogen werden,
# und dort gegebenenfalls angepasst werden.
# Rechnungsgutschriften führen zu einer Korrektur (Gegenposition)
# der Steuerbuchung, in Form einer spiegelbildlichen Buchung.
|
#
# XML-RPC CLIENT LIBRARY
# $Id: xmlrpclib.py 65467 2008-08-04 00:50:11Z USERNAME $
#
# an XML-RPC client interface for Python.
#
# the marshalling and response parser code can also be used to
# implement XML-RPC servers.
#
# Notes:
# this version is designed to work with Python 2.1 or newer.
#
# History:
# 1999-01-14 fl Created
# 1999-01-15 fl Changed dateTime to use localtime
# 1999-01-16 fl Added Binary/base64 element, default to RPC2 service
# 1999-01-19 fl Fixed array data element (from Skip Montanaro)
# 1999-01-21 fl Fixed dateTime constructor, etc.
# 1999-02-02 fl Added fault handling, handle empty sequences, etc.
# 1999-02-10 fl Fixed problem with empty responses (from Skip Montanaro)
# 1999-06-20 fl Speed improvements, pluggable parsers/transports (0.9.8)
# 2000-11-28 fl Changed boolean to check the truth value of its argument
# 2001-02-24 fl Added encoding/Unicode/SafeTransport patches
# 2001-02-26 fl Added compare support to wrappers (0.9.9/1.0b1)
# 2001-03-28 fl Make sure response tuple is a singleton
# 2001-03-29 fl Don't require empty params element (from NAME 2001-06-10 fl Folded in _xmlrpclib accelerator support (1.0b2)
# 2001-08-20 fl Base xmlrpclib.Error on built-in Exception (from NAME 2001-09-03 fl Allow Transport subclass to override getparser
# 2001-09-10 fl Lazy import of urllib, cgi, xmllib (20x import speedup)
# 2001-10-01 fl Remove containers from memo cache when done with them
# 2001-10-01 fl Use faster escape method (80% dumps speedup)
# 2001-10-02 fl More dumps microtuning
# 2001-10-04 fl Make sure import expat gets a parser (from NAME 2001-10-10 sm Allow long ints to be passed as ints if they don't overflow
# 2001-10-17 sm Test for int and long overflow (allows use on 64-bit systems)
# 2001-11-12 fl Use repr() to marshal doubles (from NAME 2002-03-17 fl Avoid buffered read when possible (from NAME 2002-04-07 fl Added pythondoc comments
# 2002-04-16 fl Added __str__ methods to datetime/binary wrappers
# 2002-05-15 fl Added error constants (from NAME 2002-06-27 fl Merged with Python CVS version
# 2002-10-22 fl Added basic authentication (based on code from NAME 2003-01-22 sm Add support for the bool type
# 2003-02-27 gvr Remove apply calls
# 2003-04-24 sm Use cStringIO if available
# 2003-04-25 ak Add support for nil
# 2003-06-15 gn Add support for time.struct_time
# 2003-07-12 gp Correct marshalling of Faults
# 2003-10-31 mvl Add multicall support
# 2004-08-20 mvl Bump minimum supported Python version to 2.1
#
# Copyright (c) 1999-2002 by Secret Labs AB.
# Copyright (c) 1999-2002 by NAME EMAIL http://www.pythonware.com
#
# --------------------------------------------------------------------
# The XML-RPC client interface is
#
# Copyright (c) 1999-2002 by Secret Labs AB
# Copyright (c) 1999-2002 by NAME By obtaining, using, and/or copying this software and/or its
# associated documentation, you agree that you have read, understood,
# and will comply with the following terms and conditions:
#
# Permission to use, copy, modify, and distribute this software and
# its associated documentation for any purpose and without fee is
# hereby granted, provided that the above copyright notice appears in
# all copies, and that both that copyright notice and this permission
# notice appear in supporting documentation, and that the name of
# Secret Labs AB or the author not be used in advertising or publicity
# pertaining to distribution of the software without specific, written
# prior permission.
#
# SECRET LABS AB AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH REGARD
# TO THIS SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANT-
# ABILITY AND FITNESS. IN NO EVENT SHALL SECRET LABS AB OR THE AUTHOR
# BE LIABLE FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY
# DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS,
# WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS
# ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE
# OF THIS SOFTWARE.
# --------------------------------------------------------------------
#
# things to look into some day:
# TODO: sort out True/False/boolean issues for Python 2.3
|
# Compute the two-sided one-sample Kolmogorov-Smirnov Prob(Dn <= d) where:
# D_n = sup_x{|F_n(x) - F(x)|},
# F_n(x) is the empirical CDF for a sample of size n {x_i: i=1,...,n},
# F(x) is the CDF of a probability distribution.
#
# Exact methods:
# Prob(D_n >= d) can be computed via a matrix algorithm of Durbin[1]
# or a recursion algorithm due to Pomeranz[2].
# NAME Tsang & Wang[3] gave a computation-efficient way to perform
# the Durbin algorithm.
# D_n >= d <==> D_n+ >= d or D_n- >= d (the one-sided K-S statistics), hence
# Prob(D_n >= d) = 2*Prob(D_n+ >= d) - Prob(D_n+ >= d and D_n- >= d).
# For d > 0.5, the latter intersection probability is 0.
#
# Approximate methods:
# For d close to 0.5, ignoring that intersection term may still give a
# reasonable approximation.
# NAME and Korolyuk[5] gave an asymptotic formula extending
# Kolmogorov's initial asymptotic, suitable for large d. (See
# scipy.special.kolmogorov for that asymptotic)
# Pelz-Good[6] used the functional equation for Jacobi theta functions to
# transform the Li-Chien/Korolyuk formula produce a computational formula
# suitable for small d.
#
# NAME and NAME provided an algorithm to decide when to use each of
# the above approaches and it is that which is used here.
#
# Other approaches:
# Carvalho[8] optimizes Durbin's matrix algorithm for large values of d.
# NAME and NAME use FFTs to compute the convolutions.
# References:
# [1] NAME (1968).
# "The Probability that the Sample Distribution Function Lies Between Two
# Parallel Straight Lines."
# Annals of Mathematical Statistics, 39, 398-411.
# [2] NAME (1974).
# "Exact Cumulative Distribution of the Kolmogorov-Smirnov Statistic for
# Small Samples (Algorithm 487)."
# Communications of the ACM, 17(12), 703-704.
# [3] NAME NAME NAME (2003).
# "Evaluating Kolmogorov's Distribution."
# Journal of Statistical Software, 8(18), 1-4.
# [4] NAME (1956).
# "On the exact distribution of the statistics of A. N. Kolmogorov and
# their asymptotic expansion."
# NAME 6, 55-81.
# [5] NAME (1960).
# "Asymptotic analysis of the distribution of the maximum deviation in
# the Bernoulli scheme."
# Theor. Probability Appl., 4, 339-366.
# [6] NAME NAME (1976).
# "Approximating the Lower Tail-areas of the Kolmogorov-Smirnov One-sample
# Statistic."
# Journal of the Royal Statistical Society, Series B, 38(2), 152-156.
# [7] NAME, R., NAME (2011)
# "Computing the Two-Sided Kolmogorov-Smirnov Distribution",
# Journal of Statistical Software, Vol 39, 11, 1-18.
# [8] NAME (2015)
# "An Improved Evaluation of Kolmogorov's Distribution"
# Journal of Statistical Software, Code Snippets; Vol 65(3), 1-8.
# [9] Amit NAME, NAME (2017)
# "Fast calculation of boundary crossing probabilities for Poisson
# processes",
# Statistics & Probability Letters, Vol 123, 177-182.
|
#!/usr/bin/env python
# ***** BEGIN LICENSE BLOCK *****
# Version: MPL 1.1/GPL 2.0/LGPL 2.1
#
# The contents of this file are subject to the Mozilla Public License Version
# 1.1 (the "License"); you may not use this file except in compliance with
# the License. You may obtain a copy of the License at
# http://www.mozilla.org/MPL/
#
# Software distributed under the License is distributed on an "AS IS" basis,
# WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
# for the specific language governing rights and limitations under the
# License.
#
# The Original Code is font utility code.
#
# The Initial Developer of the Original Code is Mozilla Corporation.
# Portions created by the Initial Developer are Copyright (C) 2009
# the Initial Developer. All Rights Reserved.
#
# Contributor(s):
# NAME <EMAIL>
#
# Alternatively, the contents of this file may be used under the terms of
# either the GNU General Public License Version 2 or later (the "GPL"), or
# the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
# in which case the provisions of the GPL or the LGPL are applicable instead
# of those above. If you wish to allow use of your version of this file only
# under the terms of either the GPL or the LGPL, and not to allow others to
# use your version of this file under the terms of the MPL, indicate your
# decision by deleting the provisions above and replace them with the notice
# and other provisions required by the GPL or the LGPL. If you do not delete
# the provisions above, a recipient may use your version of this file under
# the terms of any one of the MPL, the GPL or the LGPL.
#
# ***** END LICENSE BLOCK ***** */
# eotlitetool.py - create EOT version of OpenType font for use with IE
#
# Usage: eotlitetool.py [-o output-filename] font1 [font2 ...]
#
# OpenType file structure
# http://www.microsoft.com/typography/otspec/otff.htm
#
# Types:
#
# BYTE 8-bit unsigned integer.
# CHAR 8-bit signed integer.
# USHORT 16-bit unsigned integer.
# SHORT 16-bit signed integer.
# ULONG 32-bit unsigned integer.
# Fixed 32-bit signed fixed-point number (16.16)
# LONGDATETIME Date represented in number of seconds since 12:00 midnight, January 1, 1904. The value is represented as a signed 64-bit integer.
#
# SFNT Header
#
# Fixed sfnt version // 0x00010000 for version 1.0.
# USHORT numTables // Number of tables.
# USHORT searchRange // (Maximum power of 2 <= numTables) x 16.
# USHORT entrySelector // Log2(maximum power of 2 <= numTables).
# USHORT rangeShift // NumTables x 16-searchRange.
#
# Table Directory
#
# ULONG tag // 4-byte identifier.
# ULONG checkSum // CheckSum for this table.
# ULONG offset // Offset from beginning of TrueType font file.
# ULONG length // Length of this table.
#
# OS/2 Table (Version 4)
#
# USHORT version // 0x0004
# SHORT xAvgCharWidth
# USHORT usWeightClass
# USHORT usWidthClass
# USHORT fsType
# SHORT ySubscriptXSize
# SHORT ySubscriptYSize
# SHORT ySubscriptXOffset
# SHORT ySubscriptYOffset
# SHORT ySuperscriptXSize
# SHORT ySuperscriptYSize
# SHORT ySuperscriptXOffset
# SHORT ySuperscriptYOffset
# SHORT yStrikeoutSize
# SHORT yStrikeoutPosition
# SHORT sFamilyClass
# BYTE panose[10]
# ULONG ulUnicodeRange1 // Bits 0-31
# ULONG ulUnicodeRange2 // Bits 32-63
# ULONG ulUnicodeRange3 // Bits 64-95
# ULONG ulUnicodeRange4 // Bits 96-127
# CHAR achVendID[4]
# USHORT fsSelection
# USHORT usFirstCharIndex
# USHORT usLastCharIndex
# SHORT sTypoAscender
# SHORT sTypoDescender
# SHORT sTypoLineGap
# USHORT usWinAscent
# USHORT usWinDescent
# ULONG ulCodePageRange1 // Bits 0-31
# ULONG ulCodePageRange2 // Bits 32-63
# SHORT sxHeight
# SHORT sCapHeight
# USHORT usDefaultChar
# USHORT usBreakChar
# USHORT usMaxContext
#
#
# The Naming Table is organized as follows:
#
# [name table header]
# [name records]
# [string data]
#
# Name Table Header
#
# USHORT format // Format selector (=0).
# USHORT count // Number of name records.
# USHORT stringOffset // Offset to start of string storage (from start of table).
#
# Name Record
#
# USHORT platformID // Platform ID.
# USHORT encodingID // Platform-specific encoding ID.
# USHORT languageID // Language ID.
# USHORT nameID // Name ID.
# USHORT length // String length (in bytes).
# USHORT offset // String offset from start of storage area (in bytes).
#
# head Table
#
# Fixed tableVersion // Table version number 0x00010000 for version 1.0.
# Fixed fontRevision // Set by font manufacturer.
# ULONG checkSumAdjustment // To compute: set it to 0, sum the entire font as ULONG, then store 0xB1B0AFBA - sum.
# ULONG magicNumber // Set to 0x5F0F3CF5.
# USHORT flags
# USHORT unitsPerEm // Valid range is from 16 to 16384. This value should be a power of 2 for fonts that have TrueType outlines.
# LONGDATETIME created // Number of seconds since 12:00 midnight, January 1, 1904. 64-bit integer
# LONGDATETIME modified // Number of seconds since 12:00 midnight, January 1, 1904. 64-bit integer
# SHORT xMin // For all glyph bounding boxes.
# SHORT yMin
# SHORT xMax
# SHORT yMax
# USHORT macStyle
# USHORT lowestRecPPEM // Smallest readable size in pixels.
# SHORT fontDirectionHint
# SHORT indexToLocFormat // 0 for short offsets, 1 for long.
# SHORT glyphDataFormat // 0 for current format.
#
#
#
# Embedded OpenType (EOT) file format
# http://www.w3.org/Submission/EOT/
#
# EOT version 0x00020001
#
# An EOT font consists of a header with the original OpenType font
# appended at the end. Most of the data in the EOT header is simply a
# copy of data from specific tables within the font data. The exceptions
# are the 'Flags' field and the root string name field. The root string
# is a set of names indicating domains for which the font data can be
# used. A null root string implies the font data can be used anywhere.
# The EOT header is in little-endian byte order but the font data remains
# in big-endian order as specified by the OpenType spec.
#
# Overall structure:
#
# [EOT header]
# [EOT name records]
# [font data]
#
# EOT header
#
# ULONG eotSize // Total structure length in bytes (including string and font data)
# ULONG fontDataSize // Length of the OpenType font (FontData) in bytes
# ULONG version // Version number of this format - 0x00020001
# ULONG flags // Processing Flags (0 == no special processing)
# BYTE fontPANOSE[10] // OS/2 Table panose
# BYTE charset // DEFAULT_CHARSET (0x01)
# BYTE italic // 0x01 if ITALIC in OS/2 Table fsSelection is set, 0 otherwise
# ULONG weight // OS/2 Table usWeightClass
# USHORT fsType // OS/2 Table fsType (specifies embedding permission flags)
# USHORT magicNumber // Magic number for EOT file - 0x504C.
# ULONG unicodeRange1 // OS/2 Table ulUnicodeRange1
# ULONG unicodeRange2 // OS/2 Table ulUnicodeRange2
# ULONG unicodeRange3 // OS/2 Table ulUnicodeRange3
# ULONG unicodeRange4 // OS/2 Table ulUnicodeRange4
# ULONG codePageRange1 // OS/2 Table ulCodePageRange1
# ULONG codePageRange2 // OS/2 Table ulCodePageRange2
# ULONG checkSumAdjustment // head Table CheckSumAdjustment
# ULONG reserved[4] // Reserved - must be 0
# USHORT padding1 // Padding - must be 0
#
# EOT name records
#
# USHORT FamilyNameSize // Font family name size in bytes
# BYTE FamilyName[FamilyNameSize] // Font family name (name ID = 1), little-endian UTF-16
# USHORT Padding2 // Padding - must be 0
#
# USHORT StyleNameSize // Style name size in bytes
# BYTE StyleName[StyleNameSize] // Style name (name ID = 2), little-endian UTF-16
# USHORT Padding3 // Padding - must be 0
#
# USHORT VersionNameSize // Version name size in bytes
# bytes VersionName[VersionNameSize] // Version name (name ID = 5), little-endian UTF-16
# USHORT Padding4 // Padding - must be 0
#
# USHORT FullNameSize // Full name size in bytes
# BYTE FullName[FullNameSize] // Full name (name ID = 4), little-endian UTF-16
# USHORT Padding5 // Padding - must be 0
#
# USHORT RootStringSize // Root string size in bytes
# BYTE RootString[RootStringSize] // Root string, little-endian UTF-16
|
# -*- encoding: utf-8 -*-
##############################################################################
#
# OpenERP, Open Source Management Solution
# Copyright (C) 2004-2009 Tiny SPRL (<http://tiny.be>).
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Affero General Public License as
# published by the Free Software Foundation, either version 3 of the
# License, or (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
##############################################################################
# SKR03
# =====
# Dieses Modul bietet Ihnen einen deutschen Kontenplan basierend auf dem SKR03.
# Gemäss der aktuellen Einstellungen ist die Firma nicht Umsatzsteuerpflichtig.
# Diese Grundeinstellung ist sehr einfach zu ändern und bedarf in der Regel
# grundsätzlich eine initiale Zuweisung von Steuerkonten zu Produkten und / oder
# Sachkonten oder zu Partnern.
# Die Umsatzsteuern (voller Steuersatz, reduzierte Steuer und steuerfrei)
# sollten bei den Produktstammdaten hinterlegt werden (in Abhängigkeit der
# Steuervorschriften). Die Zuordnung erfolgt auf dem Aktenreiter Finanzbuchhaltung
# (Kategorie: Umsatzsteuer).
# Die Vorsteuern (voller Steuersatz, reduzierte Steuer und steuerfrei)
# sollten ebenso bei den Produktstammdaten hinterlegt werden (in Abhängigkeit
# der Steuervorschriften). Die Zuordnung erfolgt auf dem Aktenreiter
# Finanzbuchhaltung (Kategorie: Vorsteuer).
# Die Zuordnung der Steuern für Ein- und Ausfuhren aus EU Ländern, sowie auch
# für den Ein- und Verkauf aus und in Drittländer sollten beim Partner
# (Lieferant/Kunde)hinterlegt werden (in Anhängigkeit vom Herkunftsland
# des Lieferanten/Kunden). Die Zuordnung beim Kunden ist 'höherwertig' als
# die Zuordnung bei Produkten und überschreibt diese im Einzelfall.
#
# Zur Vereinfachung der Steuerausweise und Buchung bei Auslandsgeschäften
# erlaubt OpenERP ein generelles Mapping von Steuerausweis und Steuerkonten
# (z.B. Zuordnung 'Umsatzsteuer 19%' zu 'steuerfreie Einfuhren aus der EU')
# zwecks Zuordnung dieses Mappings zum ausländischen Partner (Kunde/Lieferant).
# Die Rechnungsbuchung beim Einkauf bewirkt folgendes:
# Die Steuerbemessungsgrundlage (exklusive Steuer) wird ausgewiesen bei den
# jeweiligen Kategorien für den Vorsteuer Steuermessbetrag (z.B. Vorsteuer
# Steuermessbetrag Voller Steuersatz 19%).
# Der Steuerbetrag erscheint unter der Kategorie 'Vorsteuern' (z.B. Vorsteuer
# 19%). Durch multidimensionale Hierachien können verschiedene Positionen
# zusammengefasst werden und dann in Form eines Reports ausgegeben werden.
#
# Die Rechnungsbuchung beim Verkauf bewirkt folgendes:
# Die Steuerbemessungsgrundlage (exklusive Steuer) wird ausgewiesen bei den
# jeweiligen Kategorien für den Umsatzsteuer Steuermessbetrag
# (z.B. Umsatzsteuer Steuermessbetrag Voller Steuersatz 19%).
# Der Steuerbetrag erscheint unter der Kategorie 'Umsatzsteuer'
# (z.B. Umsatzsteuer 19%). Durch multidimensionale Hierachien können
# verschiedene Positionen zusammengefasst werden.
# Die zugewiesenen Steuerausweise können auf Ebene der einzelnen
# Rechnung (Eingangs- und Ausgangsrechnung) nachvollzogen werden,
# und dort gegebenenfalls angepasst werden.
# Rechnungsgutschriften führen zu einer Korrektur (Gegenposition)
# der Steuerbuchung, in Form einer spiegelbildlichen Buchung.
# SKR04
# =====
# Dieses Modul bietet Ihnen einen deutschen Kontenplan basierend auf dem SKR04.
# Gemäss der aktuellen Einstellungen ist die Firma nicht Umsatzsteuerpflichtig,
# d.h. im Standard existiert keine Zuordnung von Produkten und Sachkonten zu
# Steuerschlüsseln.
# Diese Grundeinstellung ist sehr einfach zu ändern und bedarf in der Regel
# grundsätzlich eine initiale Zuweisung von Steuerschlüsseln zu Produkten und / oder
# Sachkonten oder zu Partnern.
# Die Umsatzsteuern (voller Steuersatz, reduzierte Steuer und steuerfrei)
# sollten bei den Produktstammdaten hinterlegt werden (in Abhängigkeit der
# Steuervorschriften). Die Zuordnung erfolgt auf dem Aktenreiter Finanzbuchhaltung
# (Kategorie: Umsatzsteuer).
# Die Vorsteuern (voller Steuersatz, reduzierte Steuer und steuerfrei)
# sollten ebenso bei den Produktstammdaten hinterlegt werden (in Abhängigkeit
# der Steuervorschriften). Die Zuordnung erfolgt auf dem Aktenreiter
# Finanzbuchhaltung (Kategorie: Vorsteuer).
# Die Zuordnung der Steuern für Ein- und Ausfuhren aus EU Ländern, sowie auch
# für den Ein- und Verkauf aus und in Drittländer sollten beim Partner
# (Lieferant/Kunde) hinterlegt werden (in Anhängigkeit vom Herkunftsland
# des Lieferanten/Kunden). Die Zuordnung beim Kunden ist 'höherwertig' als
# die Zuordnung bei Produkten und überschreibt diese im Einzelfall.
#
# Zur Vereinfachung der Steuerausweise und Buchung bei Auslandsgeschäften
# erlaubt OpenERP ein generelles Mapping von Steuerausweis und Steuerkonten
# (z.B. Zuordnung 'Umsatzsteuer 19%' zu 'steuerfreie Einfuhren aus der EU')
# zwecks Zuordnung dieses Mappings zum ausländischen Partner (Kunde/Lieferant).
# Die Rechnungsbuchung beim Einkauf bewirkt folgendes:
# Die Steuerbemessungsgrundlage (exklusive Steuer) wird ausgewiesen bei den
# jeweiligen Kategorien für den Vorsteuer Steuermessbetrag (z.B. Vorsteuer
# Steuermessbetrag Voller Steuersatz 19%).
# Der Steuerbetrag erscheint unter der Kategorie 'Vorsteuern' (z.B. Vorsteuer
# 19%). Durch multidimensionale Hierachien können verschiedene Positionen
# zusammengefasst werden und dann in Form eines Reports ausgegeben werden.
#
# Die Rechnungsbuchung beim Verkauf bewirkt folgendes:
# Die Steuerbemessungsgrundlage (exklusive Steuer) wird ausgewiesen bei den
# jeweiligen Kategorien für den Umsatzsteuer Steuermessbetrag
# (z.B. Umsatzsteuer Steuermessbetrag Voller Steuersatz 19%).
# Der Steuerbetrag erscheint unter der Kategorie 'Umsatzsteuer'
# (z.B. Umsatzsteuer 19%). Durch multidimensionale Hierachien können
# verschiedene Positionen zusammengefasst werden.
# Die zugewiesenen Steuerausweise können auf Ebene der einzelnen
# Rechnung (Eingangs- und Ausgangsrechnung) nachvollzogen werden,
# und dort gegebenenfalls angepasst werden.
# Rechnungsgutschriften führen zu einer Korrektur (Gegenposition)
# der Steuerbuchung, in Form einer spiegelbildlichen Buchung.
|
# we assume that the data is formatted as
# ra dec z_obs Mr (at z=0.1) g-r (at z=0.1), g_pbs, r_obs, i_obs ,z_obs, Y_obs
# 122.339938 2.714809 1.49938 -20.0583 0.4302 23.9241 24.0125 24.0119 24.0060
# 122.340257 2.714721 1.49986 -16.7435 0.2219 27.3779 27.3258 27.2076 27.1580
# 122.344290 2.671008 1.49898 -17.3039 0.8330 26.0372 26.0523 25.9714 25.9543
# 122.329476 2.763764 1.49904 -18.8016 0.7857 23.8054 23.7478 23.6235 23.5723
# 122.350149 2.788570 1.49867 -19.5123 0.7961 22.0180 22.3088 22.5070 22.5401
# 122.349923 2.788709 1.49893 -17.3942 0.6991 26.0867 26.2018 26.2164 26.2206
# 122.350995 2.783779 1.49850 -16.9972 0.4215 27.0413 26.7375 26.3845 26.2715
# 122.361283 2.802072 1.49834 -20.8577 0.7985 22.8971 22.7835 22.6266 22.6059
# 122.361351 2.803728 1.49767 -19.9191 0.9377 23.0343 22.8713 22.6138 22.5634
# 122.360214 2.801781 1.49903 -19.4785 0.6393 23.6923 23.4421 23.1104 23.0319
# 122.333567 2.815541 1.49891 -18.8219 0.7533 24.3696 24.4226 24.3584 24.3550
# 122.333720 2.815412 1.49957 -17.6552 0.6007 25.6228 25.7226 25.7138 25.7161
# 122.332781 2.674860 1.49919 -19.4307 0.4451 23.7421 23.4469 23.0734 22.9824
|
# -*- coding: utf-8 -*-
# Spearmint
#
# Academic and Non-Commercial Research Use Software License and Terms
# of Use
#
# Spearmint is a software package to perform Bayesian optimization
# according to specific algorithms (the “Software”). The Software is
# designed to automatically run experiments (thus the code name
# 'spearmint') in a manner that iteratively adjusts a number of
# parameters so as to minimize some objective in as few runs as
# possible.
#
# The Software was developed by NAME NAME and
# NAME at Harvard University, NAME at the
# University of Toronto (“Toronto”), and NAME at the
# Université de Sherbrooke (“Sherbrooke”), which assigned its rights
# in the Software to Socpra Sciences et Génie
# S.E.C. (“Socpra”). Pursuant to an inter-institutional agreement
# between the parties, it is distributed for free academic and
# non-commercial research use by the President and Fellows of Harvard
# College (“Harvard”).
#
# Using the Software indicates your agreement to be bound by the terms
# of this Software Use Agreement (“Agreement”). Absent your agreement
# to the terms below, you (the “End User”) have no rights to hold or
# use the Software whatsoever.
#
# Harvard agrees to grant hereunder the limited non-exclusive license
# to End User for the use of the Software in the performance of End
# User’s internal, non-commercial research and academic use at End
# User’s academic or not-for-profit research institution
# (“Institution”) on the following terms and conditions:
#
# 1. NO REDISTRIBUTION. The Software remains the property Harvard,
# Toronto and Socpra, and except as set forth in Section 4, End User
# shall not publish, distribute, or otherwise transfer or make
# available the Software to any other party.
#
# 2. NO COMMERCIAL USE. End User shall not use the Software for
# commercial purposes and any such use of the Software is expressly
# prohibited. This includes, but is not limited to, use of the
# Software in fee-for-service arrangements, core facilities or
# laboratories or to provide research services to (or in collaboration
# with) third parties for a fee, and in industry-sponsored
# collaborative research projects where any commercial rights are
# granted to the sponsor. If End User wishes to use the Software for
# commercial purposes or for any other restricted purpose, End User
# must execute a separate license agreement with Harvard.
#
# Requests for use of the Software for commercial purposes, please
# contact:
#
# Office of Technology Development
# Harvard University
# Smith Campus Center, Suite 727E
# 1350 Massachusetts Avenue
# Cambridge, MA 02138 USA
# Telephone: (617) 495-3067
# Facsimile: (617) 495-9568
# E-mail: EMAIL 3. OWNERSHIP AND COPYRIGHT NOTICE. Harvard, Toronto and Socpra own
# all intellectual property in the Software. End User shall gain no
# ownership to the Software. End User shall not remove or delete and
# shall retain in the Software, in any modifications to Software and
# in any Derivative Works, the copyright, trademark, or other notices
# pertaining to Software as provided with the Software.
#
# 4. DERIVATIVE WORKS. End User may create and use Derivative Works,
# as such term is defined under U.S. copyright laws, provided that any
# such Derivative Works shall be restricted to non-commercial,
# internal research and academic use at End User’s Institution. End
# User may distribute Derivative Works to other Institutions solely
# for the performance of non-commercial, internal research and
# academic use on terms substantially similar to this License and
# Terms of Use.
#
# 5. FEEDBACK. In order to improve the Software, comments from End
# Users may be useful. End User agrees to provide Harvard with
# feedback on the End User’s use of the Software (e.g., any bugs in
# the Software, the user experience, etc.). Harvard is permitted to
# use such information provided by End User in making changes and
# improvements to the Software without compensation or an accounting
# to End User.
#
# 6. NON ASSERT. End User acknowledges that Harvard, Toronto and/or
# Sherbrooke or Socpra may develop modifications to the Software that
# may be based on the feedback provided by End User under Section 5
# above. Harvard, Toronto and Sherbrooke/Socpra shall not be
# restricted in any way by End User regarding their use of such
# information. End User acknowledges the right of Harvard, Toronto
# and Sherbrooke/Socpra to prepare, publish, display, reproduce,
# transmit and or use modifications to the Software that may be
# substantially similar or functionally equivalent to End User’s
# modifications and/or improvements if any. In the event that End
# User obtains patent protection for any modification or improvement
# to Software, End User agrees not to allege or enjoin infringement of
# End User’s patent against Harvard, Toronto or Sherbrooke or Socpra,
# or any of the researchers, medical or research staff, officers,
# directors and employees of those institutions.
#
# 7. PUBLICATION & ATTRIBUTION. End User has the right to publish,
# present, or share results from the use of the Software. In
# accordance with customary academic practice, End User will
# acknowledge Harvard, Toronto and Sherbrooke/Socpra as the providers
# of the Software and may cite the relevant reference(s) from the
# following list of publications:
#
# Practical Bayesian Optimization of Machine Learning Algorithms
# NAME, NAME and NAME Neural Information Processing Systems, 2012
#
# Multi-Task Bayesian Optimization
# NAME, NAME and NAME Advances in Neural Information Processing Systems, 2013
#
# Input Warping for Bayesian Optimization of Non-stationary Functions
# NAME, NAME, NAME and NAME Preprint, arXiv:1402.0929, http://arxiv.org/abs/1402.0929, 2013
#
# Bayesian Optimization and Semiparametric Models with Applications to
# Assistive Technology NAME, PhD Thesis, University of
# Toronto, 2013
#
# 8. NO WARRANTIES. THE SOFTWARE IS PROVIDED "AS IS." TO THE FULLEST
# EXTENT PERMITTED BY LAW, HARVARD, TORONTO AND SHERBROOKE AND SOCPRA
# HEREBY DISCLAIM ALL WARRANTIES OF ANY KIND (EXPRESS, IMPLIED OR
# OTHERWISE) REGARDING THE SOFTWARE, INCLUDING BUT NOT LIMITED TO ANY
# IMPLIED WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR
# PURPOSE, OWNERSHIP, AND NON-INFRINGEMENT. HARVARD, TORONTO AND
# SHERBROOKE AND SOCPRA MAKE NO WARRANTY ABOUT THE ACCURACY,
# RELIABILITY, COMPLETENESS, TIMELINESS, SUFFICIENCY OR QUALITY OF THE
# SOFTWARE. HARVARD, TORONTO AND SHERBROOKE AND SOCPRA DO NOT WARRANT
# THAT THE SOFTWARE WILL OPERATE WITHOUT ERROR OR INTERRUPTION.
#
# 9. LIMITATIONS OF LIABILITY AND REMEDIES. USE OF THE SOFTWARE IS AT
# END USER’S OWN RISK. IF END USER IS DISSATISFIED WITH THE SOFTWARE,
# ITS EXCLUSIVE REMEDY IS TO STOP USING IT. IN NO EVENT SHALL
# HARVARD, TORONTO OR SHERBROOKE OR SOCPRA BE LIABLE TO END USER OR
# ITS INSTITUTION, IN CONTRACT, TORT OR OTHERWISE, FOR ANY DIRECT,
# INDIRECT, SPECIAL, INCIDENTAL, CONSEQUENTIAL, PUNITIVE OR OTHER
# DAMAGES OF ANY KIND WHATSOEVER ARISING OUT OF OR IN CONNECTION WITH
# THE SOFTWARE, EVEN IF HARVARD, TORONTO OR SHERBROOKE OR SOCPRA IS
# NEGLIGENT OR OTHERWISE AT FAULT, AND REGARDLESS OF WHETHER HARVARD,
# TORONTO OR SHERBROOKE OR SOCPRA IS ADVISED OF THE POSSIBILITY OF
# SUCH DAMAGES.
#
# 10. INDEMNIFICATION. To the extent permitted by law, End User shall
# indemnify, defend and hold harmless Harvard, Toronto and Sherbrooke
# and Socpra, their corporate affiliates, current or future directors,
# trustees, officers, faculty, medical and professional staff,
# employees, students and agents and their respective successors,
# heirs and assigns (the "Indemnitees"), against any liability,
# damage, loss or expense (including reasonable attorney's fees and
# expenses of litigation) incurred by or imposed upon the Indemnitees
# or any one of them in connection with any claims, suits, actions,
# demands or judgments arising from End User’s breach of this
# Agreement or its Institution’s use of the Software except to the
# extent caused by the gross negligence or willful misconduct of
# Harvard, Toronto or Sherbrooke or Socpra. This indemnification
# provision shall survive expiration or termination of this Agreement.
#
# 11. GOVERNING LAW. This Agreement shall be construed and governed by
# the laws of the Commonwealth of Massachusetts regardless of
# otherwise applicable choice of law standards.
#
# 12. NON-USE OF NAME. Nothing in this License and Terms of Use shall
# be construed as granting End Users or their Institutions any rights
# or licenses to use any trademarks, service marks or logos associated
# with the Software. You may not use the terms “Harvard” or
# “University of Toronto” or “Université de Sherbrooke” or “Socpra
# Sciences et Génie S.E.C.” (or a substantially similar term) in any
# way that is inconsistent with the permitted uses described
# herein. You agree not to use any name or emblem of Harvard, Toronto
# or Sherbrooke, or any of their subdivisions for any purpose, or to
# falsely suggest any relationship between End User (or its
# Institution) and Harvard, Toronto and/or Sherbrooke, or in any
# manner that would infringe or violate any of their rights.
#
# 13. End User represents and warrants that it has the legal authority
# to enter into this License and Terms of Use on behalf of itself and
# its Institution.
|
"""
Objects for dealing with Chebyshev series.
This module provides a number of objects (mostly functions) useful for
dealing with Chebyshev series, including a `Chebyshev` class that
encapsulates the usual arithmetic operations. (General information
on how this module represents and works with such polynomials is in the
docstring for its "parent" sub-package, `numpy.polynomial`).
Constants
---------
- `chebdomain` -- Chebyshev series default domain, [-1,1].
- `chebzero` -- (Coefficients of the) Chebyshev series that evaluates
identically to 0.
- `chebone` -- (Coefficients of the) Chebyshev series that evaluates
identically to 1.
- `chebx` -- (Coefficients of the) Chebyshev series for the identity map,
``f(x) = x``.
Arithmetic
----------
- `chebadd` -- add two Chebyshev series.
- `chebsub` -- subtract one Chebyshev series from another.
- `chebmul` -- multiply two Chebyshev series.
- `chebdiv` -- divide one Chebyshev series by another.
- `chebpow` -- raise a Chebyshev series to an positive integer power
- `chebval` -- evaluate a Chebyshev series at given points.
- `chebval2d` -- evaluate a 2D Chebyshev series at given points.
- `chebval3d` -- evaluate a 3D Chebyshev series at given points.
- `chebgrid2d` -- evaluate a 2D Chebyshev series on a Cartesian product.
- `chebgrid3d` -- evaluate a 3D Chebyshev series on a Cartesian product.
Calculus
--------
- `chebder` -- differentiate a Chebyshev series.
- `chebint` -- integrate a Chebyshev series.
Misc Functions
--------------
- `chebfromroots` -- create a Chebyshev series with specified roots.
- `chebroots` -- find the roots of a Chebyshev series.
- `chebvander` -- Vandermonde-like matrix for Chebyshev polynomials.
- `chebvander2d` -- Vandermonde-like matrix for 2D power series.
- `chebvander3d` -- Vandermonde-like matrix for 3D power series.
- `chebgauss` -- Gauss-Chebyshev quadrature, points and weights.
- `chebweight` -- Chebyshev weight function.
- `chebcompanion` -- symmetrized companion matrix in Chebyshev form.
- `chebfit` -- least-squares fit returning a Chebyshev series.
- `chebpts1` -- Chebyshev points of the first kind.
- `chebpts2` -- Chebyshev points of the second kind.
- `chebtrim` -- trim leading coefficients from a Chebyshev series.
- `chebline` -- Chebyshev series representing given straight line.
- `cheb2poly` -- convert a Chebyshev series to a polynomial.
- `poly2cheb` -- convert a polynomial to a Chebyshev series.
Classes
-------
- `Chebyshev` -- A Chebyshev series class.
See also
--------
`numpy.polynomial`
Notes
-----
The implementations of multiplication, division, integration, and
differentiation use the algebraic identities [1]_:
.. math ::
T_n(x) = \\frac{z^n + z^{-n}}{2} \\\\
z\\frac{dx}{dz} = \\frac{z - z^{-1}}{2}.
where
.. math :: x = \\frac{z + z^{-1}}{2}.
These identities allow a Chebyshev series to be expressed as a finite,
symmetric Laurent series. In this module, this sort of Laurent series
is referred to as a "z-series."
References
----------
.. [1] NAME et al., "Combinatorial Trigonometry with Chebyshev
Polynomials," *Journal of Statistical Planning and Inference 14*, 2008
(preprint: http://www.math.hmc.edu/~benjamin/papers/CombTrig.pdf, pg. 4)
""" |
"""CPStats, a package for collecting and reporting on program statistics.
Overview
========
Statistics about program operation are an invaluable monitoring and debugging
tool. Unfortunately, the gathering and reporting of these critical values is
usually ad-hoc. This package aims to add a centralized place for gathering
statistical performance data, a structure for recording that data which
provides for extrapolation of that data into more useful information,
and a method of serving that data to both human investigators and
monitoring software. Let's examine each of those in more detail.
Data Gathering
--------------
Just as Python's `logging` module provides a common importable for gathering
and sending messages, performance statistics would benefit from a similar
common mechanism, and one that does *not* require each package which wishes
to collect stats to import a third-party module. Therefore, we choose to
re-use the `logging` module by adding a `statistics` object to it.
That `logging.statistics` object is a nested dict. It is not a custom class,
because that would:
1. require libraries and applications to import a third-party module in
order to participate
2. inhibit innovation in extrapolation approaches and in reporting tools, and
3. be slow.
There are, however, some specifications regarding the structure of the dict.::
{
+----"SQLAlchemy": {
| "Inserts": 4389745,
| "Inserts per Second":
| lambda s: s["Inserts"] / (time() - s["Start"]),
| C +---"Table Statistics": {
| o | "widgets": {-----------+
N | l | "Rows": 1.3M, | Record
a | l | "Inserts": 400, |
m | e | },---------------------+
e | c | "froobles": {
s | t | "Rows": 7845,
p | i | "Inserts": 0,
a | o | },
c | n +---},
e | "Slow Queries":
| [{"Query": "SELECT * FROM widgets;",
| "Processing Time": 47.840923343,
| },
| ],
+----},
}
The `logging.statistics` dict has four levels. The topmost level is nothing
more than a set of names to introduce modularity, usually along the lines of
package names. If the SQLAlchemy project wanted to participate, for example,
it might populate the item `logging.statistics['SQLAlchemy']`, whose value
would be a second-layer dict we call a "namespace". Namespaces help multiple
packages to avoid collisions over key names, and make reports easier to read,
to boot. The maintainers of SQLAlchemy should feel free to use more than one
namespace if needed (such as 'SQLAlchemy ORM'). Note that there are no case
or other syntax constraints on the namespace names; they should be chosen
to be maximally readable by humans (neither too short nor too long).
Each namespace, then, is a dict of named statistical values, such as
'Requests/sec' or 'Uptime'. You should choose names which will look
good on a report: spaces and capitalization are just fine.
In addition to scalars, values in a namespace MAY be a (third-layer)
dict, or a list, called a "collection". For example, the CherryPy
:class:`StatsTool` keeps track of what each request is doing (or has most
recently done) in a 'Requests' collection, where each key is a thread ID; each
value in the subdict MUST be a fourth dict (whew!) of statistical data about
each thread. We call each subdict in the collection a "record". Similarly,
the :class:`StatsTool` also keeps a list of slow queries, where each record
contains data about each slow query, in order.
Values in a namespace or record may also be functions, which brings us to:
Extrapolation
-------------
The collection of statistical data needs to be fast, as close to unnoticeable
as possible to the host program. That requires us to minimize I/O, for example,
but in Python it also means we need to minimize function calls. So when you
are designing your namespace and record values, try to insert the most basic
scalar values you already have on hand.
When it comes time to report on the gathered data, however, we usually have
much more freedom in what we can calculate. Therefore, whenever reporting
tools (like the provided :class:`StatsPage` CherryPy class) fetch the contents
of `logging.statistics` for reporting, they first call
`extrapolate_statistics` (passing the whole `statistics` dict as the only
argument). This makes a deep copy of the statistics dict so that the
reporting tool can both iterate over it and even change it without harming
the original. But it also expands any functions in the dict by calling them.
For example, you might have a 'Current Time' entry in the namespace with the
value "lambda scope: time.time()". The "scope" parameter is the current
namespace dict (or record, if we're currently expanding one of those
instead), allowing you access to existing static entries. If you're truly
evil, you can even modify more than one entry at a time.
However, don't try to calculate an entry and then use its value in further
extrapolations; the order in which the functions are called is not guaranteed.
This can lead to a certain amount of duplicated work (or a redesign of your
schema), but that's better than complicating the spec.
After the whole thing has been extrapolated, it's time for:
Reporting
---------
The :class:`StatsPage` class grabs the `logging.statistics` dict, extrapolates
it all, and then transforms it to HTML for easy viewing. Each namespace gets
its own header and attribute table, plus an extra table for each collection.
This is NOT part of the statistics specification; other tools can format how
they like.
You can control which columns are output and how they are formatted by updating
StatsPage.formatting, which is a dict that mirrors the keys and nesting of
`logging.statistics`. The difference is that, instead of data values, it has
formatting values. Use None for a given key to indicate to the StatsPage that a
given column should not be output. Use a string with formatting
(such as '%.3f') to interpolate the value(s), or use a callable (such as
lambda v: v.isoformat()) for more advanced formatting. Any entry which is not
mentioned in the formatting dict is output unchanged.
Monitoring
----------
Although the HTML output takes pains to assign unique id's to each <td> with
statistical data, you're probably better off fetching /cpstats/data, which
outputs the whole (extrapolated) `logging.statistics` dict in JSON format.
That is probably easier to parse, and doesn't have any formatting controls,
so you get the "original" data in a consistently-serialized format.
Note: there's no treatment yet for datetime objects. Try time.time() instead
for now if you can. Nagios will probably thank you.
Turning Collection Off
----------------------
It is recommended each namespace have an "Enabled" item which, if False,
stops collection (but not reporting) of statistical data. Applications
SHOULD provide controls to pause and resume collection by setting these
entries to False or True, if present.
Usage
=====
To collect statistics on CherryPy applications::
from cherrypy.lib import cpstats
appconfig['/']['tools.cpstats.on'] = True
To collect statistics on your own code::
import logging
# Initialize the repository
if not hasattr(logging, 'statistics'): logging.statistics = {}
# Initialize my namespace
mystats = logging.statistics.setdefault('My Stuff', {})
# Initialize my namespace's scalars and collections
mystats.update({
'Enabled': True,
'Start Time': time.time(),
'Important Events': 0,
'Events/Second': lambda s: (
(s['Important Events'] / (time.time() - s['Start Time']))),
})
...
for event in events:
...
# Collect stats
if mystats.get('Enabled', False):
mystats['Important Events'] += 1
To report statistics::
root.cpstats = cpstats.StatsPage()
To format statistics reports::
See 'Reporting', above.
""" |
"""Drag-and-drop support for Tkinter.
This is very preliminary. I currently only support dnd *within* one
application, between different windows (or within the same window).
I an trying to make this as generic as possible -- not dependent on
the use of a particular widget or icon type, etc. I also hope that
this will work with Pmw.
To enable an object to be dragged, you must create an event binding
for it that starts the drag-and-drop process. Typically, you should
bind <ButtonPress> to a callback function that you write. The function
should call Tkdnd.dnd_start(source, event), where 'source' is the
object to be dragged, and 'event' is the event that invoked the call
(the argument to your callback function). Even though this is a class
instantiation, the returned instance should not be stored -- it will
be kept alive automatically for the duration of the drag-and-drop.
When a drag-and-drop is already in process for the Tk interpreter, the
call is *ignored*; this normally averts starting multiple simultaneous
dnd processes, e.g. because different button callbacks all
dnd_start().
The object is *not* necessarily a widget -- it can be any
application-specific object that is meaningful to potential
drag-and-drop targets.
Potential drag-and-drop targets are discovered as follows. Whenever
the mouse moves, and at the start and end of a drag-and-drop move, the
Tk widget directly under the mouse is inspected. This is the target
widget (not to be confused with the target object, yet to be
determined). If there is no target widget, there is no dnd target
object. If there is a target widget, and it has an attribute
dnd_accept, this should be a function (or any callable object). The
function is called as dnd_accept(source, event), where 'source' is the
object being dragged (the object passed to dnd_start() above), and
'event' is the most recent event object (generally a <Motion> event;
it can also be <ButtonPress> or <ButtonRelease>). If the dnd_accept()
function returns something other than None, this is the new dnd target
object. If dnd_accept() returns None, or if the target widget has no
dnd_accept attribute, the target widget's parent is considered as the
target widget, and the search for a target object is repeated from
there. If necessary, the search is repeated all the way up to the
root widget. If none of the target widgets can produce a target
object, there is no target object (the target object is None).
The target object thus produced, if any, is called the new target
object. It is compared with the old target object (or None, if there
was no old target widget). There are several cases ('source' is the
source object, and 'event' is the most recent event object):
- Both the old and new target objects are None. Nothing happens.
- The old and new target objects are the same object. Its method
dnd_motion(source, event) is called.
- The old target object was None, and the new target object is not
None. The new target object's method dnd_enter(source, event) is
called.
- The new target object is None, and the old target object is not
None. The old target object's method dnd_leave(source, event) is
called.
- The old and new target objects differ and neither is None. The old
target object's method dnd_leave(source, event), and then the new
target object's method dnd_enter(source, event) is called.
Once this is done, the new target object replaces the old one, and the
Tk mainloop proceeds. The return value of the methods mentioned above
is ignored; if they raise an exception, the normal exception handling
mechanisms take over.
The drag-and-drop processes can end in two ways: a final target object
is selected, or no final target object is selected. When a final
target object is selected, it will always have been notified of the
potential drop by a call to its dnd_enter() method, as described
above, and possibly one or more calls to its dnd_motion() method; its
dnd_leave() method has not been called since the last call to
dnd_enter(). The target is notified of the drop by a call to its
method dnd_commit(source, event).
If no final target object is selected, and there was an old target
object, its dnd_leave(source, event) method is called to complete the
dnd sequence.
Finally, the source object is notified that the drag-and-drop process
is over, by a call to source.dnd_end(target, event), specifying either
the selected target object, or None if no target object was selected.
The source object can use this to implement the commit action; this is
sometimes simpler than to do it in the target's dnd_commit(). The
target's dnd_commit() method could then simply be aliased to
dnd_leave().
At any time during a dnd sequence, the application can cancel the
sequence by calling the cancel() method on the object returned by
dnd_start(). This will call dnd_leave() if a target is currently
active; it will never call dnd_commit().
""" |
"""
=============
Miscellaneous
=============
IEEE 754 Floating Point Special Values
--------------------------------------
Special values defined in numpy: nan, inf,
NaNs can be used as a poor-man's mask (if you don't care what the
original value was)
Note: cannot use equality to test NaNs. E.g.: ::
>>> myarr = np.array([1., 0., np.nan, 3.])
>>> np.nonzero(myarr == np.nan)
(array([], dtype=int64),)
>>> np.nan == np.nan # is always False! Use special numpy functions instead.
False
>>> myarr[myarr == np.nan] = 0. # doesn't work
>>> myarr
array([ 1., 0., NaN, 3.])
>>> myarr[np.isnan(myarr)] = 0. # use this instead find
>>> myarr
array([ 1., 0., 0., 3.])
Other related special value functions: ::
isinf(): True if value is inf
isfinite(): True if not nan or inf
nan_to_num(): Map nan to 0, inf to max float, -inf to min float
The following corresponds to the usual functions except that nans are excluded
from the results: ::
nansum()
nanmax()
nanmin()
nanargmax()
nanargmin()
>>> x = np.arange(10.)
>>> x[3] = np.nan
>>> x.sum()
nan
>>> np.nansum(x)
42.0
How numpy handles numerical exceptions
--------------------------------------
The default is to ``'warn'`` for ``invalid``, ``divide``, and ``overflow``
and ``'ignore'`` for ``underflow``. But this can be changed, and it can be
set individually for different kinds of exceptions. The different behaviors
are:
- 'ignore' : Take no action when the exception occurs.
- 'warn' : Print a `RuntimeWarning` (via the Python `warnings` module).
- 'raise' : Raise a `FloatingPointError`.
- 'call' : Call a function specified using the `seterrcall` function.
- 'print' : Print a warning directly to ``stdout``.
- 'log' : Record error in a Log object specified by `seterrcall`.
These behaviors can be set for all kinds of errors or specific ones:
- all : apply to all numeric exceptions
- invalid : when NaNs are generated
- divide : divide by zero (for integers as well!)
- overflow : floating point overflows
- underflow : floating point underflows
Note that integer divide-by-zero is handled by the same machinery.
These behaviors are set on a per-thread basis.
Examples
--------
::
>>> oldsettings = np.seterr(all='warn')
>>> np.zeros(5,dtype=np.float32)/0.
invalid value encountered in divide
>>> j = np.seterr(under='ignore')
>>> np.array([1.e-100])**10
>>> j = np.seterr(invalid='raise')
>>> np.sqrt(np.array([-1.]))
FloatingPointError: invalid value encountered in sqrt
>>> def errorhandler(errstr, errflag):
... print("saw stupid error!")
>>> np.seterrcall(errorhandler)
<function err_handler at 0x...>
>>> j = np.seterr(all='call')
>>> np.zeros(5, dtype=np.int32)/0
FloatingPointError: invalid value encountered in divide
saw stupid error!
>>> j = np.seterr(**oldsettings) # restore previous
... # error-handling settings
Interfacing to C
----------------
Only a survey of the choices. Little detail on how each works.
1) Bare metal, wrap your own C-code manually.
- Plusses:
- Efficient
- No dependencies on other tools
- Minuses:
- Lots of learning overhead:
- need to learn basics of Python C API
- need to learn basics of numpy C API
- need to learn how to handle reference counting and love it.
- Reference counting often difficult to get right.
- getting it wrong leads to memory leaks, and worse, segfaults
- API will change for Python 3.0!
2) Cython
- Plusses:
- avoid learning C API's
- no dealing with reference counting
- can code in pseudo python and generate C code
- can also interface to existing C code
- should shield you from changes to Python C api
- has become the de-facto standard within the scientific Python community
- fast indexing support for arrays
- Minuses:
- Can write code in non-standard form which may become obsolete
- Not as flexible as manual wrapping
3) ctypes
- Plusses:
- part of Python standard library
- good for interfacing to existing sharable libraries, particularly
Windows DLLs
- avoids API/reference counting issues
- good numpy support: arrays have all these in their ctypes
attribute: ::
a.ctypes.data a.ctypes.get_strides
a.ctypes.data_as a.ctypes.shape
a.ctypes.get_as_parameter a.ctypes.shape_as
a.ctypes.get_data a.ctypes.strides
a.ctypes.get_shape a.ctypes.strides_as
- Minuses:
- can't use for writing code to be turned into C extensions, only a wrapper
tool.
4) SWIG (automatic wrapper generator)
- Plusses:
- around a long time
- multiple scripting language support
- C++ support
- Good for wrapping large (many functions) existing C libraries
- Minuses:
- generates lots of code between Python and the C code
- can cause performance problems that are nearly impossible to optimize
out
- interface files can be hard to write
- doesn't necessarily avoid reference counting issues or needing to know
API's
5) scipy.weave
- Plusses:
- can turn many numpy expressions into C code
- dynamic compiling and loading of generated C code
- can embed pure C code in Python module and have weave extract, generate
interfaces and compile, etc.
- Minuses:
- Future very uncertain: it's the only part of Scipy not ported to Python 3
and is effectively deprecated in favor of Cython.
6) Psyco
- Plusses:
- Turns pure python into efficient machine code through jit-like
optimizations
- very fast when it optimizes well
- Minuses:
- Only on intel (windows?)
- Doesn't do much for numpy?
Interfacing to Fortran:
-----------------------
The clear choice to wrap Fortran code is
`f2py <https://docs.scipy.org/doc/numpy/f2py/>`_.
Pyfort is an older alternative, but not supported any longer.
Fwrap is a newer project that looked promising but isn't being developed any
longer.
Interfacing to C++:
-------------------
1) Cython
2) CXX
3) Boost.python
4) SWIG
5) SIP (used mainly in PyQT)
""" |
"""
=====================================================
Optimization and root finding (:mod:`scipy.optimize`)
=====================================================
.. currentmodule:: scipy.optimize
Optimization
============
Local Optimization
------------------
.. autosummary::
:toctree: generated/
minimize - Unified interface for minimizers of multivariate functions
minimize_scalar - Unified interface for minimizers of univariate functions
OptimizeResult - The optimization result returned by some optimizers
The `minimize` function supports the following methods:
.. toctree::
optimize.minimize-neldermead
optimize.minimize-powell
optimize.minimize-cg
optimize.minimize-bfgs
optimize.minimize-newtoncg
optimize.minimize-lbfgsb
optimize.minimize-tnc
optimize.minimize-cobyla
optimize.minimize-slsqp
optimize.minimize-dogleg
optimize.minimize-trustncg
The `minimize_scalar` function supports the following methods:
.. toctree::
optimize.minimize_scalar-brent
optimize.minimize_scalar-bounded
optimize.minimize_scalar-golden
The specific optimization method interfaces below in this subsection are
not recommended for use in new scripts; all of these methods are accessible
via a newer, more consistent interface provided by the functions above.
General-purpose multivariate methods:
.. autosummary::
:toctree: generated/
fmin - Nelder-Mead Simplex algorithm
fmin_powell - Powell's (modified) level set method
fmin_cg - Non-linear (Polak-Ribiere) conjugate gradient algorithm
fmin_bfgs - Quasi-Newton method (Broydon-Fletcher-Goldfarb-Shanno)
fmin_ncg - Line-search Newton Conjugate Gradient
Constrained multivariate methods:
.. autosummary::
:toctree: generated/
fmin_l_bfgs_b - Zhu, Byrd, and Nocedal's constrained optimizer
fmin_tnc - Truncated Newton code
fmin_cobyla - Constrained optimization by linear approximation
fmin_slsqp - Minimization using sequential least-squares programming
differential_evolution - stochastic minimization using differential evolution
Univariate (scalar) minimization methods:
.. autosummary::
:toctree: generated/
fminbound - Bounded minimization of a scalar function
brent - 1-D function minimization using Brent method
golden - 1-D function minimization using Golden Section method
Equation (Local) Minimizers
---------------------------
.. autosummary::
:toctree: generated/
leastsq - Minimize the sum of squares of M equations in N unknowns
nnls - Linear least-squares problem with non-negativity constraint
Global Optimization
-------------------
.. autosummary::
:toctree: generated/
basinhopping - Basinhopping stochastic optimizer
brute - Brute force searching optimizer
differential_evolution - stochastic minimization using differential evolution
Rosenbrock function
-------------------
.. autosummary::
:toctree: generated/
rosen - The Rosenbrock function.
rosen_der - The derivative of the Rosenbrock function.
rosen_hess - The Hessian matrix of the Rosenbrock function.
rosen_hess_prod - Product of the Rosenbrock Hessian with a vector.
Fitting
=======
.. autosummary::
:toctree: generated/
curve_fit -- Fit curve to a set of points
Root finding
============
Scalar functions
----------------
.. autosummary::
:toctree: generated/
brentq - quadratic interpolation Brent method
brenth - Brent method, modified by Harris with hyperbolic extrapolation
ridder - Ridder's method
bisect - Bisection method
newton - Secant method or Newton's method
Fixed point finding:
.. autosummary::
:toctree: generated/
fixed_point - Single-variable fixed-point solver
Multidimensional
----------------
General nonlinear solvers:
.. autosummary::
:toctree: generated/
root - Unified interface for nonlinear solvers of multivariate functions
fsolve - Non-linear multi-variable equation solver
broyden1 - Broyden's first method
broyden2 - Broyden's second method
The `root` function supports the following methods:
.. toctree::
optimize.root-hybr
optimize.root-lm
optimize.root-broyden1
optimize.root-broyden2
optimize.root-anderson
optimize.root-linearmixing
optimize.root-diagbroyden
optimize.root-excitingmixing
optimize.root-krylov
optimize.root-dfsane
Large-scale nonlinear solvers:
.. autosummary::
:toctree: generated/
newton_krylov
anderson
Simple iterations:
.. autosummary::
:toctree: generated/
excitingmixing
linearmixing
diagbroyden
:mod:`Additional information on the nonlinear solvers <scipy.optimize.nonlin>`
Linear Programming
==================
Simplex Algorithm:
.. autosummary::
:toctree: generated/
linprog -- Linear programming using the simplex algorithm
The `linprog` function supports the following methods:
.. toctree::
optimize.linprog-simplex
Utilities
=========
.. autosummary::
:toctree: generated/
approx_fprime - Approximate the gradient of a scalar function
bracket - Bracket a minimum, given two starting points
check_grad - Check the supplied derivative using finite differences
line_search - Return a step that satisfies the strong Wolfe conditions
show_options - Show specific options optimization solvers
LbfgsInvHessProduct - Linear operator for L-BFGS approximate inverse Hessian
""" |
"""
===================
Universal Functions
===================
Ufuncs are, generally speaking, mathematical functions or operations that are
applied element-by-element to the contents of an array. That is, the result
in each output array element only depends on the value in the corresponding
input array (or arrays) and on no other array elements. Numpy comes with a
large suite of ufuncs, and scipy extends that suite substantially. The simplest
example is the addition operator: ::
>>> np.array([0,2,3,4]) + np.array([1,1,-1,2])
array([1, 3, 2, 6])
The unfunc module lists all the available ufuncs in numpy. Documentation on
the specific ufuncs may be found in those modules. This documentation is
intended to address the more general aspects of unfuncs common to most of
them. All of the ufuncs that make use of Python operators (e.g., +, -, etc.)
have equivalent functions defined (e.g. add() for +)
Type coercion
=============
What happens when a binary operator (e.g., +,-,\\*,/, etc) deals with arrays of
two different types? What is the type of the result? Typically, the result is
the higher of the two types. For example: ::
float32 + float64 -> float64
int8 + int32 -> int32
int16 + float32 -> float32
float32 + complex64 -> complex64
There are some less obvious cases generally involving mixes of types
(e.g. uints, ints and floats) where equal bit sizes for each are not
capable of saving all the information in a different type of equivalent
bit size. Some examples are int32 vs float32 or uint32 vs int32.
Generally, the result is the higher type of larger size than both
(if available). So: ::
int32 + float32 -> float64
uint32 + int32 -> int64
Finally, the type coercion behavior when expressions involve Python
scalars is different than that seen for arrays. Since Python has a
limited number of types, combining a Python int with a dtype=np.int8
array does not coerce to the higher type but instead, the type of the
array prevails. So the rules for Python scalars combined with arrays is
that the result will be that of the array equivalent the Python scalar
if the Python scalar is of a higher 'kind' than the array (e.g., float
vs. int), otherwise the resultant type will be that of the array.
For example: ::
Python int + int8 -> int8
Python float + int8 -> float64
ufunc methods
=============
Binary ufuncs support 4 methods.
**.reduce(arr)** applies the binary operator to elements of the array in
sequence. For example: ::
>>> np.add.reduce(np.arange(10)) # adds all elements of array
45
For multidimensional arrays, the first dimension is reduced by default: ::
>>> np.add.reduce(np.arange(10).reshape(2,5))
array([ 5, 7, 9, 11, 13])
The axis keyword can be used to specify different axes to reduce: ::
>>> np.add.reduce(np.arange(10).reshape(2,5),axis=1)
array([10, 35])
**.accumulate(arr)** applies the binary operator and generates an an
equivalently shaped array that includes the accumulated amount for each
element of the array. A couple examples: ::
>>> np.add.accumulate(np.arange(10))
array([ 0, 1, 3, 6, 10, 15, 21, 28, 36, 45])
>>> np.multiply.accumulate(np.arange(1,9))
array([ 1, 2, 6, 24, 120, 720, 5040, 40320])
The behavior for multidimensional arrays is the same as for .reduce(),
as is the use of the axis keyword).
**.reduceat(arr,indices)** allows one to apply reduce to selected parts
of an array. It is a difficult method to understand. See the documentation
at:
**.outer(arr1,arr2)** generates an outer operation on the two arrays arr1 and
arr2. It will work on multidimensional arrays (the shape of the result is
the concatenation of the two input shapes.: ::
>>> np.multiply.outer(np.arange(3),np.arange(4))
array([[0, 0, 0, 0],
[0, 1, 2, 3],
[0, 2, 4, 6]])
Output arguments
================
All ufuncs accept an optional output array. The array must be of the expected
output shape. Beware that if the type of the output array is of a different
(and lower) type than the output result, the results may be silently truncated
or otherwise corrupted in the downcast to the lower type. This usage is useful
when one wants to avoid creating large temporary arrays and instead allows one
to reuse the same array memory repeatedly (at the expense of not being able to
use more convenient operator notation in expressions). Note that when the
output argument is used, the ufunc still returns a reference to the result.
>>> x = np.arange(2)
>>> np.add(np.arange(2),np.arange(2.),x)
array([0, 2])
>>> x
array([0, 2])
and & or as ufuncs
==================
Invariably people try to use the python 'and' and 'or' as logical operators
(and quite understandably). But these operators do not behave as normal
operators since Python treats these quite differently. They cannot be
overloaded with array equivalents. Thus using 'and' or 'or' with an array
results in an error. There are two alternatives:
1) use the ufunc functions logical_and() and logical_or().
2) use the bitwise operators & and \\|. The drawback of these is that if
the arguments to these operators are not boolean arrays, the result is
likely incorrect. On the other hand, most usages of logical_and and
logical_or are with boolean arrays. As long as one is careful, this is
a convenient way to apply these operators.
""" |
#
# ElementTree
# $Id: ElementTree.py 2326 2005-03-17 07:45:21Z USERNAME $
#
# light-weight XML support for Python 1.5.2 and later.
#
# history:
# 2001-10-20 fl created (from various sources)
# 2001-11-01 fl return root from parse method
# 2002-02-16 fl sort attributes in lexical order
# 2002-04-06 fl TreeBuilder refactoring, added PythonDoc markup
# 2002-05-01 fl finished TreeBuilder refactoring
# 2002-07-14 fl added basic namespace support to ElementTree.write
# 2002-07-25 fl added QName attribute support
# 2002-10-20 fl fixed encoding in write
# 2002-11-24 fl changed default encoding to ascii; fixed attribute encoding
# 2002-11-27 fl accept file objects or file names for parse/write
# 2002-12-04 fl moved XMLTreeBuilder back to this module
# 2003-01-11 fl fixed entity encoding glitch for us-ascii
# 2003-02-13 fl added XML literal factory
# 2003-02-21 fl added ProcessingInstruction/PI factory
# 2003-05-11 fl added tostring/fromstring helpers
# 2003-05-26 fl added ElementPath support
# 2003-07-05 fl added makeelement factory method
# 2003-07-28 fl added more well-known namespace prefixes
# 2003-08-15 fl fixed typo in ElementTree.findtext (Thomas NAME 2003-09-04 fl fall back on emulator if ElementPath is not installed
# 2003-10-31 fl markup updates
# 2003-11-15 fl fixed nested namespace bug
# 2004-03-28 fl added XMLID helper
# 2004-06-02 fl added default support to findtext
# 2004-06-08 fl fixed encoding of non-ascii element/attribute names
# 2004-08-23 fl take advantage of post-2.1 expat features
# 2005-02-01 fl added iterparse implementation
# 2005-03-02 fl fixed iterparse support for pre-2.2 versions
#
# Copyright (c) 1999-2005 by NAME All rights reserved.
#
# EMAIL
# http://www.pythonware.com
#
# --------------------------------------------------------------------
# The ElementTree toolkit is
#
# Copyright (c) 1999-2005 by NAME By obtaining, using, and/or copying this software and/or its
# associated documentation, you agree that you have read, understood,
# and will comply with the following terms and conditions:
#
# Permission to use, copy, modify, and distribute this software and
# its associated documentation for any purpose and without fee is
# hereby granted, provided that the above copyright notice appears in
# all copies, and that both that copyright notice and this permission
# notice appear in supporting documentation, and that the name of
# Secret Labs AB or the author not be used in advertising or publicity
# pertaining to distribution of the software without specific, written
# prior permission.
#
# SECRET LABS AB AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH REGARD
# TO THIS SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANT-
# ABILITY AND FITNESS. IN NO EVENT SHALL SECRET LABS AB OR THE AUTHOR
# BE LIABLE FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY
# DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS,
# WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS
# ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE
# OF THIS SOFTWARE.
# --------------------------------------------------------------------
|
#!/usr/bin/env python
# -*- Mode: Python; py-indent-offset: 4 -*-
#
# Copyright (C) 2006-2009 NAME Scan the given public .h files of a GTK module (or module using
# GTK object conventions) and generates a set of scheme defs.
#
# defsgen uses the ctypes module to extract information from the installed
# module library (or libraries) to generate the object, interface, function,
# method, virtual, enum and flags defs. defsgen uses the gobject library
# g_type_* functions. defsgen will try to open the "libgobject-2.0.so" library
# if one is not specified on the command line.
#
# Basically the operation of defsgen is:
#
# - open and initialize the gobject and module libraries
# - read each .h file into a buffer which is scrubbed of extraneous data
# - find all *_get_type() functions prototypes
# - look in the module libraries for the get_type symbols
# - if found run the get_type() function to retrieve the GType
# - find the parent type name and save the object info
# - find each function prototypes in the file and check if it has a symbol in
# the module libraries - save the info if found
# - extract the virtual prototypes from the Class or Iface structs and save
# - write out the various defs.
#
# The command line options are:
#
# -l --modulelib Adds the given module library name to the list to be used
# for finding symbols. Mor ethan one modulefile may be
# specified. (required)
# -L --libgobject Specifies the name of the gobject library (optional but
# must be specified if "libgobject-2.0.so" is not availble)
# -s --separate Create separate files for objects and function/method defs
# using the given name as the base name (optional). If this
# is not specified the combined object and function defs
# will be output to sys.stdout.
# -f --defsfile Extract defs from the given file to filter the output defs
# that is don't output defs that are defined in the
# defsfile. More than one deffile may be specified.
# -D --defines Include portions of the defsfile defs that are conditional
# on the given define, for example GDK_TARGET_X11. Only
# useful with the --defsfile option
# -m --modulename The prefix to be stripped from the front of function names
# for the given module
# -p --useprefix Use the modulename prefix as a hint to split names into
# module and name for object and enum defs. Also used for
# generating type codes.
# --onlyenums Only produce defs for enums and flags
# --onlyobjdefs Only produce defs for objects
# --onlyvirtuals Only produce defs for virtuals
# --genpropgetsets Experimental option to generate prop-getset annotations.
# Not supported by codegen.py and friends.
#
# Examples:
#
# python defsgen.py -m pango -l libpango-1.0.so \
# /usr/local/include/pango-1.0/pango/*.h >/tmp/pango.defs
#
# - Outputs all defs for the pango module.using the library module
# libpango-1.0.so.
#
# python defsgen.py -m gdk -DGDK_TARGET_X11 -l libgdk-x11-2.0.so \
# -l libgdk_pixbuf-2.0.so -s /tmp/gdk-2.10 \
# -f /usr/tmp/pygtk/gtk/gdk-base.defs \
# /usr/local/include/gtk-2.0/gdk/*.h \
# /usr/local/include/gtk-2.0/gdk-pixbuf/*.h
#
# - Outputs the gdk module defs that are not contained in the defs file
# /usr/tmp/pygtk/gtk/gdk-base.defs. Two output files are created:
# /tmp/gdk-2.10-types.defs and /tmp/gdk-2.10.defs.
#
# Based on the original h2def.py program by
# NAME <EMAIL> and
# modified by NAME <EMAIL> to output stuff in
# Havoc's new defs format. Info on this format can be seen at:
# http://www.gnome.org/mailing-lists/archives/gtk-devel-list/2000-January/0085.shtml
# Updated to be PEP-8 compatible and refactored to use OOP
# Extensively modified by NAME to use ctypes module to extract GType
# info from the given library and to create virtual defines.
#
|
"""
Discrete Fourier Transform (:mod:`numpy.fft`)
=============================================
.. currentmodule:: numpy.fft
Standard FFTs
-------------
.. autosummary::
:toctree: generated/
fft Discrete Fourier transform.
ifft Inverse discrete Fourier transform.
fft2 Discrete Fourier transform in two dimensions.
ifft2 Inverse discrete Fourier transform in two dimensions.
fftn Discrete Fourier transform in N-dimensions.
ifftn Inverse discrete Fourier transform in N dimensions.
Real FFTs
---------
.. autosummary::
:toctree: generated/
rfft Real discrete Fourier transform.
irfft Inverse real discrete Fourier transform.
rfft2 Real discrete Fourier transform in two dimensions.
irfft2 Inverse real discrete Fourier transform in two dimensions.
rfftn Real discrete Fourier transform in N dimensions.
irfftn Inverse real discrete Fourier transform in N dimensions.
Hermitian FFTs
--------------
.. autosummary::
:toctree: generated/
hfft Hermitian discrete Fourier transform.
ihfft Inverse Hermitian discrete Fourier transform.
Helper routines
---------------
.. autosummary::
:toctree: generated/
fftfreq Discrete Fourier Transform sample frequencies.
rfftfreq DFT sample frequencies (for usage with rfft, irfft).
fftshift Shift zero-frequency component to center of spectrum.
ifftshift Inverse of fftshift.
Background information
----------------------
Fourier analysis is fundamentally a method for expressing a function as a
sum of periodic components, and for recovering the function from those
components. When both the function and its Fourier transform are
replaced with discretized counterparts, it is called the discrete Fourier
transform (DFT). The DFT has become a mainstay of numerical computing in
part because of a very fast algorithm for computing it, called the Fast
Fourier Transform (FFT), which was known to Gauss (1805) and was brought
to light in its current form by NAME and NAME [CT]_. Press et al. [NR]_
provide an accessible introduction to Fourier analysis and its
applications.
Because the discrete Fourier transform separates its input into
components that contribute at discrete frequencies, it has a great number
of applications in digital signal processing, e.g., for filtering, and in
this context the discretized input to the transform is customarily
referred to as a *signal*, which exists in the *time domain*. The output
is called a *spectrum* or *transform* and exists in the *frequency
domain*.
Implementation details
----------------------
There are many ways to define the DFT, varying in the sign of the
exponent, normalization, etc. In this implementation, the DFT is defined
as
.. math::
A_k = \\sum_{m=0}^{n-1} a_m \\exp\\left\\{-2\\pi i{mk \\over n}\\right\\}
\\qquad k = 0,\\ldots,n-1.
The DFT is in general defined for complex inputs and outputs, and a
single-frequency component at linear frequency :math:`f` is
represented by a complex exponential
:math:`a_m = \\exp\\{2\\pi i\\,f m\\Delta t\\}`, where :math:`\\Delta t`
is the sampling interval.
The values in the result follow so-called "standard" order: If ``A =
fft(a, n)``, then ``A[0]`` contains the zero-frequency term (the mean of
the signal), which is always purely real for real inputs. Then ``A[1:n/2]``
contains the positive-frequency terms, and ``A[n/2+1:]`` contains the
negative-frequency terms, in order of decreasingly negative frequency.
For an even number of input points, ``A[n/2]`` represents both positive and
negative Nyquist frequency, and is also purely real for real input. For
an odd number of input points, ``A[(n-1)/2]`` contains the largest positive
frequency, while ``A[(n+1)/2]`` contains the largest negative frequency.
The routine ``np.fft.fftfreq(n)`` returns an array giving the frequencies
of corresponding elements in the output. The routine
``np.fft.fftshift(A)`` shifts transforms and their frequencies to put the
zero-frequency components in the middle, and ``np.fft.ifftshift(A)`` undoes
that shift.
When the input `a` is a time-domain signal and ``A = fft(a)``, ``np.abs(A)``
is its amplitude spectrum and ``np.abs(A)**2`` is its power spectrum.
The phase spectrum is obtained by ``np.angle(A)``.
The inverse DFT is defined as
.. math::
a_m = \\frac{1}{n}\\sum_{k=0}^{n-1}A_k\\exp\\left\\{2\\pi i{mk\\over n}\\right\\}
\\qquad m = 0,\\ldots,n-1.
It differs from the forward transform by the sign of the exponential
argument and the normalization by :math:`1/n`.
Real and Hermitian transforms
-----------------------------
When the input is purely real, its transform is Hermitian, i.e., the
component at frequency :math:`f_k` is the complex conjugate of the
component at frequency :math:`-f_k`, which means that for real
inputs there is no information in the negative frequency components that
is not already available from the positive frequency components.
The family of `rfft` functions is
designed to operate on real inputs, and exploits this symmetry by
computing only the positive frequency components, up to and including the
Nyquist frequency. Thus, ``n`` input points produce ``n/2+1`` complex
output points. The inverses of this family assumes the same symmetry of
its input, and for an output of ``n`` points uses ``n/2+1`` input points.
Correspondingly, when the spectrum is purely real, the signal is
Hermitian. The `hfft` family of functions exploits this symmetry by
using ``n/2+1`` complex points in the input (time) domain for ``n`` real
points in the frequency domain.
In higher dimensions, FFTs are used, e.g., for image analysis and
filtering. The computational efficiency of the FFT means that it can
also be a faster way to compute large convolutions, using the property
that a convolution in the time domain is equivalent to a point-by-point
multiplication in the frequency domain.
Higher dimensions
-----------------
In two dimensions, the DFT is defined as
.. math::
A_{kl} = \\sum_{m=0}^{M-1} \\sum_{n=0}^{N-1}
a_{mn}\\exp\\left\\{-2\\pi i \\left({mk\\over M}+{nl\\over N}\\right)\\right\\}
\\qquad k = 0, \\ldots, M-1;\\quad l = 0, \\ldots, N-1,
which extends in the obvious way to higher dimensions, and the inverses
in higher dimensions also extend in the same way.
References
----------
.. [CT] NAME, NAME and John W. NAME, 1965, "An algorithm for the
machine calculation of complex Fourier series," *Math. Comput.*
19: 297-301.
.. [NR] NAME NAME NAME and NAME
2007, *Numerical Recipes: The Art of Scientific Computing*, ch.
12-13. Cambridge Univ. Press, Cambridge, UK.
Examples
--------
For examples, see the various functions.
""" |
"""
Objects for dealing with Chebyshev series.
This module provides a number of objects (mostly functions) useful for
dealing with Chebyshev series, including a `Chebyshev` class that
encapsulates the usual arithmetic operations. (General information
on how this module represents and works with such polynomials is in the
docstring for its "parent" sub-package, `numpy.polynomial`).
Constants
---------
- `chebdomain` -- Chebyshev series default domain, [-1,1].
- `chebzero` -- (Coefficients of the) Chebyshev series that evaluates
identically to 0.
- `chebone` -- (Coefficients of the) Chebyshev series that evaluates
identically to 1.
- `chebx` -- (Coefficients of the) Chebyshev series for the identity map,
``f(x) = x``.
Arithmetic
----------
- `chebadd` -- add two Chebyshev series.
- `chebsub` -- subtract one Chebyshev series from another.
- `chebmul` -- multiply two Chebyshev series.
- `chebdiv` -- divide one Chebyshev series by another.
- `chebpow` -- raise a Chebyshev series to an positive integer power
- `chebval` -- evaluate a Chebyshev series at given points.
- `chebval2d` -- evaluate a 2D Chebyshev series at given points.
- `chebval3d` -- evaluate a 3D Chebyshev series at given points.
- `chebgrid2d` -- evaluate a 2D Chebyshev series on a Cartesian product.
- `chebgrid3d` -- evaluate a 3D Chebyshev series on a Cartesian product.
Calculus
--------
- `chebder` -- differentiate a Chebyshev series.
- `chebint` -- integrate a Chebyshev series.
Misc Functions
--------------
- `chebfromroots` -- create a Chebyshev series with specified roots.
- `chebroots` -- find the roots of a Chebyshev series.
- `chebvander` -- Vandermonde-like matrix for Chebyshev polynomials.
- `chebvander2d` -- Vandermonde-like matrix for 2D power series.
- `chebvander3d` -- Vandermonde-like matrix for 3D power series.
- `chebgauss` -- Gauss-Chebyshev quadrature, points and weights.
- `chebweight` -- Chebyshev weight function.
- `chebcompanion` -- symmetrized companion matrix in Chebyshev form.
- `chebfit` -- least-squares fit returning a Chebyshev series.
- `chebpts1` -- Chebyshev points of the first kind.
- `chebpts2` -- Chebyshev points of the second kind.
- `chebtrim` -- trim leading coefficients from a Chebyshev series.
- `chebline` -- Chebyshev series representing given straight line.
- `cheb2poly` -- convert a Chebyshev series to a polynomial.
- `poly2cheb` -- convert a polynomial to a Chebyshev series.
Classes
-------
- `Chebyshev` -- A Chebyshev series class.
See also
--------
`numpy.polynomial`
Notes
-----
The implementations of multiplication, division, integration, and
differentiation use the algebraic identities [1]_:
.. math ::
T_n(x) = \\frac{z^n + z^{-n}}{2} \\\\
z\\frac{dx}{dz} = \\frac{z - z^{-1}}{2}.
where
.. math :: x = \\frac{z + z^{-1}}{2}.
These identities allow a Chebyshev series to be expressed as a finite,
symmetric Laurent series. In this module, this sort of Laurent series
is referred to as a "z-series."
References
----------
.. [1] NAME et al., "Combinatorial Trigonometry with Chebyshev
Polynomials," *Journal of Statistical Planning and Inference 14*, 2008
(preprint: http://www.math.hmc.edu/~benjamin/papers/CombTrig.pdf, pg. 4)
""" |
"""
Discrete Fourier Transform (:mod:`numpy.fft`)
=============================================
.. currentmodule:: numpy.fft
Standard FFTs
-------------
.. autosummary::
:toctree: generated/
fft Discrete Fourier transform.
ifft Inverse discrete Fourier transform.
fft2 Discrete Fourier transform in two dimensions.
ifft2 Inverse discrete Fourier transform in two dimensions.
fftn Discrete Fourier transform in N-dimensions.
ifftn Inverse discrete Fourier transform in N dimensions.
Real FFTs
---------
.. autosummary::
:toctree: generated/
rfft Real discrete Fourier transform.
irfft Inverse real discrete Fourier transform.
rfft2 Real discrete Fourier transform in two dimensions.
irfft2 Inverse real discrete Fourier transform in two dimensions.
rfftn Real discrete Fourier transform in N dimensions.
irfftn Inverse real discrete Fourier transform in N dimensions.
Hermitian FFTs
--------------
.. autosummary::
:toctree: generated/
hfft Hermitian discrete Fourier transform.
ihfft Inverse Hermitian discrete Fourier transform.
Helper routines
---------------
.. autosummary::
:toctree: generated/
fftfreq Discrete Fourier Transform sample frequencies.
rfftfreq DFT sample frequencies (for usage with rfft, irfft).
fftshift Shift zero-frequency component to center of spectrum.
ifftshift Inverse of fftshift.
Background information
----------------------
Fourier analysis is fundamentally a method for expressing a function as a
sum of periodic components, and for recovering the function from those
components. When both the function and its Fourier transform are
replaced with discretized counterparts, it is called the discrete Fourier
transform (DFT). The DFT has become a mainstay of numerical computing in
part because of a very fast algorithm for computing it, called the Fast
Fourier Transform (FFT), which was known to Gauss (1805) and was brought
to light in its current form by NAME and NAME [CT]_. Press et al. [NR]_
provide an accessible introduction to Fourier analysis and its
applications.
Because the discrete Fourier transform separates its input into
components that contribute at discrete frequencies, it has a great number
of applications in digital signal processing, e.g., for filtering, and in
this context the discretized input to the transform is customarily
referred to as a *signal*, which exists in the *time domain*. The output
is called a *spectrum* or *transform* and exists in the *frequency
domain*.
Implementation details
----------------------
There are many ways to define the DFT, varying in the sign of the
exponent, normalization, etc. In this implementation, the DFT is defined
as
.. math::
A_k = \\sum_{m=0}^{n-1} a_m \\exp\\left\\{-2\\pi i{mk \\over n}\\right\\}
\\qquad k = 0,\\ldots,n-1.
The DFT is in general defined for complex inputs and outputs, and a
single-frequency component at linear frequency :math:`f` is
represented by a complex exponential
:math:`a_m = \\exp\\{2\\pi i\\,f m\\Delta t\\}`, where :math:`\\Delta t`
is the sampling interval.
The values in the result follow so-called "standard" order: If ``A =
fft(a, n)``, then ``A[0]`` contains the zero-frequency term (the sum of
the signal), which is always purely real for real inputs. Then ``A[1:n/2]``
contains the positive-frequency terms, and ``A[n/2+1:]`` contains the
negative-frequency terms, in order of decreasingly negative frequency.
For an even number of input points, ``A[n/2]`` represents both positive and
negative Nyquist frequency, and is also purely real for real input. For
an odd number of input points, ``A[(n-1)/2]`` contains the largest positive
frequency, while ``A[(n+1)/2]`` contains the largest negative frequency.
The routine ``np.fft.fftfreq(n)`` returns an array giving the frequencies
of corresponding elements in the output. The routine
``np.fft.fftshift(A)`` shifts transforms and their frequencies to put the
zero-frequency components in the middle, and ``np.fft.ifftshift(A)`` undoes
that shift.
When the input `a` is a time-domain signal and ``A = fft(a)``, ``np.abs(A)``
is its amplitude spectrum and ``np.abs(A)**2`` is its power spectrum.
The phase spectrum is obtained by ``np.angle(A)``.
The inverse DFT is defined as
.. math::
a_m = \\frac{1}{n}\\sum_{k=0}^{n-1}A_k\\exp\\left\\{2\\pi i{mk\\over n}\\right\\}
\\qquad m = 0,\\ldots,n-1.
It differs from the forward transform by the sign of the exponential
argument and the default normalization by :math:`1/n`.
Normalization
-------------
The default normalization has the direct transforms unscaled and the inverse
transforms are scaled by :math:`1/n`. It is possible to obtain unitary
transforms by setting the keyword argument ``norm`` to ``"ortho"`` (default is
`None`) so that both direct and inverse transforms will be scaled by
:math:`1/\\sqrt{n}`.
Real and Hermitian transforms
-----------------------------
When the input is purely real, its transform is Hermitian, i.e., the
component at frequency :math:`f_k` is the complex conjugate of the
component at frequency :math:`-f_k`, which means that for real
inputs there is no information in the negative frequency components that
is not already available from the positive frequency components.
The family of `rfft` functions is
designed to operate on real inputs, and exploits this symmetry by
computing only the positive frequency components, up to and including the
Nyquist frequency. Thus, ``n`` input points produce ``n/2+1`` complex
output points. The inverses of this family assumes the same symmetry of
its input, and for an output of ``n`` points uses ``n/2+1`` input points.
Correspondingly, when the spectrum is purely real, the signal is
Hermitian. The `hfft` family of functions exploits this symmetry by
using ``n/2+1`` complex points in the input (time) domain for ``n`` real
points in the frequency domain.
In higher dimensions, FFTs are used, e.g., for image analysis and
filtering. The computational efficiency of the FFT means that it can
also be a faster way to compute large convolutions, using the property
that a convolution in the time domain is equivalent to a point-by-point
multiplication in the frequency domain.
Higher dimensions
-----------------
In two dimensions, the DFT is defined as
.. math::
A_{kl} = \\sum_{m=0}^{M-1} \\sum_{n=0}^{N-1}
a_{mn}\\exp\\left\\{-2\\pi i \\left({mk\\over M}+{nl\\over N}\\right)\\right\\}
\\qquad k = 0, \\ldots, M-1;\\quad l = 0, \\ldots, N-1,
which extends in the obvious way to higher dimensions, and the inverses
in higher dimensions also extend in the same way.
References
----------
.. [CT] NAME, NAME and John W. NAME, 1965, "An algorithm for the
machine calculation of complex Fourier series," *Math. Comput.*
19: 297-301.
.. [NR] NAME NAME NAME and NAME
2007, *Numerical Recipes: The Art of Scientific Computing*, ch.
12-13. Cambridge Univ. Press, Cambridge, UK.
Examples
--------
For examples, see the various functions.
""" |
"""
=======================================
Signal processing (:mod:`scipy.signal`)
=======================================
Convolution
===========
.. autosummary::
:toctree: generated/
convolve -- N-dimensional convolution.
correlate -- N-dimensional correlation.
fftconvolve -- N-dimensional convolution using the FFT.
convolve2d -- 2-dimensional convolution (more options).
correlate2d -- 2-dimensional correlation (more options).
sepfir2d -- Convolve with a 2-D separable FIR filter.
B-splines
=========
.. autosummary::
:toctree: generated/
bspline -- B-spline basis function of order n.
cubic -- B-spline basis function of order 3.
quadratic -- B-spline basis function of order 2.
gauss_spline -- Gaussian approximation to the B-spline basis function.
cspline1d -- Coefficients for 1-D cubic (3rd order) B-spline.
qspline1d -- Coefficients for 1-D quadratic (2nd order) B-spline.
cspline2d -- Coefficients for 2-D cubic (3rd order) B-spline.
qspline2d -- Coefficients for 2-D quadratic (2nd order) B-spline.
cspline1d_eval -- Evaluate a cubic spline at the given points.
qspline1d_eval -- Evaluate a quadratic spline at the given points.
spline_filter -- Smoothing spline (cubic) filtering of a rank-2 array.
Filtering
=========
.. autosummary::
:toctree: generated/
order_filter -- N-dimensional order filter.
medfilt -- N-dimensional median filter.
medfilt2d -- 2-dimensional median filter (faster).
wiener -- N-dimensional wiener filter.
symiirorder1 -- 2nd-order IIR filter (cascade of first-order systems).
symiirorder2 -- 4th-order IIR filter (cascade of second-order systems).
lfilter -- 1-dimensional FIR and IIR digital linear filtering.
lfiltic -- Construct initial conditions for `lfilter`.
lfilter_zi -- Compute an initial state zi for the lfilter function that
-- corresponds to the steady state of the step response.
filtfilt -- A forward-backward filter.
savgol_filter -- Filter a signal using the Savitzky-Golay filter.
deconvolve -- 1-d deconvolution using lfilter.
sosfilt -- 1-dimensional IIR digital linear filtering using
-- a second-order-sections filter representation.
sosfilt_zi -- Compute an initial state zi for the sosfilt function that
-- corresponds to the steady state of the step response.
hilbert -- Compute 1-D analytic signal, using the Hilbert transform.
hilbert2 -- Compute 2-D analytic signal, using the Hilbert transform.
decimate -- Downsample a signal.
detrend -- Remove linear and/or constant trends from data.
resample -- Resample using Fourier method.
resample_poly -- Resample using polyphase filtering method.
upfirdn -- Upsample, apply FIR filter, downsample.
Filter design
=============
.. autosummary::
:toctree: generated/
bilinear -- Digital filter from an analog filter using
-- the bilinear transform.
findfreqs -- Find array of frequencies for computing filter response.
firwin -- Windowed FIR filter design, with frequency response
-- defined as pass and stop bands.
firwin2 -- Windowed FIR filter design, with arbitrary frequency
-- response.
freqs -- Analog filter frequency response.
freqz -- Digital filter frequency response.
group_delay -- Digital filter group delay.
iirdesign -- IIR filter design given bands and gains.
iirfilter -- IIR filter design given order and critical frequencies.
kaiser_atten -- Compute the attenuation of a Kaiser FIR filter, given
-- the number of taps and the transition width at
-- discontinuities in the frequency response.
kaiser_beta -- Compute the Kaiser parameter beta, given the desired
-- FIR filter attenuation.
kaiserord -- Design a Kaiser window to limit ripple and width of
-- transition region.
savgol_coeffs -- Compute the FIR filter coefficients for a Savitzky-Golay
-- filter.
remez -- Optimal FIR filter design.
unique_roots -- Unique roots and their multiplicities.
residue -- Partial fraction expansion of b(s) / a(s).
residuez -- Partial fraction expansion of b(z) / a(z).
invres -- Inverse partial fraction expansion for analog filter.
invresz -- Inverse partial fraction expansion for digital filter.
BadCoefficients -- Warning on badly conditioned filter coefficients
Lower-level filter design functions:
.. autosummary::
:toctree: generated/
abcd_normalize -- Check state-space matrices and ensure they are rank-2.
band_stop_obj -- Band Stop Objective Function for order minimization.
besselap -- Return (z,p,k) for analog prototype of Bessel filter.
buttap -- Return (z,p,k) for analog prototype of Butterworth filter.
cheb1ap -- Return (z,p,k) for type I Chebyshev filter.
cheb2ap -- Return (z,p,k) for type II Chebyshev filter.
cmplx_sort -- Sort roots based on magnitude.
ellipap -- Return (z,p,k) for analog prototype of elliptic filter.
lp2bp -- Transform a lowpass filter prototype to a bandpass filter.
lp2bs -- Transform a lowpass filter prototype to a bandstop filter.
lp2hp -- Transform a lowpass filter prototype to a highpass filter.
lp2lp -- Transform a lowpass filter prototype to a lowpass filter.
normalize -- Normalize polynomial representation of a transfer function.
Matlab-style IIR filter design
==============================
.. autosummary::
:toctree: generated/
butter -- Butterworth
buttord
cheby1 -- Chebyshev Type I
cheb1ord
cheby2 -- Chebyshev Type II
cheb2ord
ellip -- Elliptic (Cauer)
ellipord
bessel -- Bessel (no order selection available -- try butterod)
Continuous-Time Linear Systems
==============================
.. autosummary::
:toctree: generated/
freqresp -- frequency response of a continuous-time LTI system.
lti -- Linear time invariant system base class.
StateSpace -- Linear time invariant system in state space form.
TransferFunction -- Linear time invariant system in transfer function form.
ZerosPolesGain -- Linear time invariant system in zeros, poles, gain form.
lsim -- continuous-time simulation of output to linear system.
lsim2 -- like lsim, but `scipy.integrate.odeint` is used.
impulse -- impulse response of linear, time-invariant (LTI) system.
impulse2 -- like impulse, but `scipy.integrate.odeint` is used.
step -- step response of continous-time LTI system.
step2 -- like step, but `scipy.integrate.odeint` is used.
bode -- Calculate Bode magnitude and phase data.
Discrete-Time Linear Systems
============================
.. autosummary::
:toctree: generated/
dlsim -- simulation of output to a discrete-time linear system.
dimpulse -- impulse response of a discrete-time LTI system.
dstep -- step response of a discrete-time LTI system.
LTI Representations
===================
.. autosummary::
:toctree: generated/
tf2zpk -- transfer function to zero-pole-gain.
tf2sos -- transfer function to second-order sections.
tf2ss -- transfer function to state-space.
zpk2tf -- zero-pole-gain to transfer function.
zpk2sos -- zero-pole-gain to second-order sections.
zpk2ss -- zero-pole-gain to state-space.
ss2tf -- state-pace to transfer function.
ss2zpk -- state-space to pole-zero-gain.
sos2zpk -- second-order-sections to zero-pole-gain.
sos2tf -- second-order-sections to transfer function.
cont2discrete -- continuous-time to discrete-time LTI conversion.
place_poles -- pole placement.
Waveforms
=========
.. autosummary::
:toctree: generated/
chirp -- Frequency swept cosine signal, with several freq functions.
gausspulse -- Gaussian modulated sinusoid
max_len_seq -- Maximum length sequence
sawtooth -- Periodic sawtooth
square -- Square wave
sweep_poly -- Frequency swept cosine signal; freq is arbitrary polynomial
Window functions
================
.. autosummary::
:toctree: generated/
get_window -- Return a window of a given length and type.
barthann -- Bartlett-Hann window
bartlett -- Bartlett window
blackman -- Blackman window
blackmanharris -- Minimum 4-term Blackman-Harris window
bohman -- Bohman window
boxcar -- Boxcar window
chebwin -- Dolph-Chebyshev window
cosine -- Cosine window
exponential -- Exponential window
flattop -- Flat top window
gaussian -- Gaussian window
general_gaussian -- Generalized Gaussian window
hamming -- Hamming window
hann -- Hann window
hanning -- Hann window
kaiser -- Kaiser window
nuttall -- Nuttall's minimum 4-term Blackman-Harris window
parzen -- Parzen window
slepian -- Slepian window
triang -- Triangular window
tukey -- Tukey window
Wavelets
========
.. autosummary::
:toctree: generated/
cascade -- compute scaling function and wavelet from coefficients
daub -- return low-pass
morlet -- Complex Morlet wavelet.
qmf -- return quadrature mirror filter from low-pass
ricker -- return ricker wavelet
cwt -- perform continuous wavelet transform
Peak finding
============
.. autosummary::
:toctree: generated/
find_peaks_cwt -- Attempt to find the peaks in the given 1-D array
argrelmin -- Calculate the relative minima of data
argrelmax -- Calculate the relative maxima of data
argrelextrema -- Calculate the relative extrema of data
Spectral Analysis
=================
.. autosummary::
:toctree: generated/
periodogram -- Compute a (modified) periodogram
welch -- Compute a periodogram using Welch's method
csd -- Compute the cross spectral density, using Welch's method
coherence -- Compute the magnitude squared coherence, using Welch's method
spectrogram -- Compute the spectrogram
lombscargle -- Computes the Lomb-Scargle periodogram
vectorstrength -- Computes the vector strength
""" |
#!/usr/bin/env python
# This is an Nmap command line parser. It has two main parts:
#
# getopt_long_only_extras, which is like getopt_long_only with robust
# handling of unknown options.
#
# NmapOptions, a class representing a set of Nmap options.
#
# NmapOptions is the class for external use. NmapOptions.parse parses a list of
# a command followed by command-line arguments. NmapOptions.render returns a
# list of of a command followed by arguments. NmapOptions.parse_string and
# NmapOptions.render_string first split strings into lists, following certain
# quoting rules.
#
# >>> ops = NmapOptions()
# >>> ops.parse(["nmap", "-v", "--script", "safe", "localhost"])
# >>> ops.executable
# 'nmap'
# >>> ops.target_specs
# ['localhost']
# >>> ops["-v"]
# 1
# >>> ops["--script"]
# 'safe'
#
# The command line may be modified by accessing member variables:
#
# >>> ops.executable = "C:\Program Files\Nmap\nmap.exe"
# >>> ops["-v"] = 2
# >>> ops["-oX"] = "output.xml"
# >>> ops.render()
# ['C:\\Program Files\\Nmap\\nmap.exe', '-v', '-v', '-oX', 'output.xml',
# '--script', 'safe', 'localhost']
# >>> ops.render_string()
# '"C:\\Program Files\\Nmap\\nmap.exe" -v -v -oX output.xml\
# --script safe localhost'
#
# A primary design consideration was robust handling of unknown options. That
# gives this code a degree of independence from Nmap's own list of options. If
# an option is added to Nmap but not added here, that option is treated as an
# "extra," an uninterpreted string that is inserted verbatim into the option
# list. Because the unknown option may or may not take an argument, pains are
# taken to avoid interpreting any option ambiguously.
#
# Consider the following case, where -x is an unknown option:
# nmap -x -e eth0 scanme.nmap.org
# If -x, whatever it is, does not take an argument, it is equivalent to
# nmap -e eth0 scanme.nmap.org -x
# that is, a scan of scanme.nmap.org over interface eth0. But if it does take
# an argument, its argument is "-e", and the command line is the same as
# nmap eth0 scanme.nmap.org -x -e
# which is a scan of the two hosts eth0 and scanme.nmap.org, over the default
# interface. In either case scanme.nmap.org is a target but the other arguments
# are ambiguous. To resolve this, once an unknown option is found, all
# following arguments that can be interpreted ambiguously are removed with it
# and placed in the extras, with normal option processing resumed only when
# there is no more ambiguity. This ensures that such options maintain their
# relative order when rendered again to output. In this example "-x -e eth0"
# will always appear in that order, and the -e option will be uninterpreted.
#
# To add a new option, one should do the following:
# 1) Add a test case to the NmapOptionsTest::test_options() method for the new
# option and make sure it initially fails.
# 2) Add the new option to NmapOptions.SHORT_OPTIONS and/or
# NmapOptions.LONG_OPTIONS.
# 3) Add an appropriate case to NmapOptions::handle_result(). This should
# include a line something like
# self[opt] = True
# or, if the option has an argument 'arg':
# self[opt] = arg
# 4) Add an appropriate case to NmapOptions::render()
# This should include a check to make sure the option was set in
# handle_result:
# if self[opt]:
# or, if self[opt] contains arguments
# if self[opt] is not None:
# If the check passed, then opt should be added to opt_list.
# 5) Edit profile_editor.xml to display the new option in the GUI.
# 6) Depending on the option, one may need to edit
# get_option_check_auxiliary_widget in OptionBuilder.py.
# 7) Make sure the test case works now.
|
"""
[2015-05-18] Challenge #215 [Easy] Sad Cycles
https://www.reddit.com/r/dailyprogrammer/comments/36cyxf/20150518_challenge_215_easy_sad_cycles/
# [](#EasyIcon) _(Easy)_: Sad Cycles
Take a number, and add up the square of each digit. You'll end up with another number. If you repeat this process over
and over again, you'll see that one of two things happen:
* You'll reach one, and from that point you'll get one again and again.
* You'll reach a cycle of 4, 16, 37, 58, 89, 145, 42, 20, 4, 16, 37, ...
For example, starting with the number 12:
* 1^(2)+2^(2)=5
* 5^(2)=25
* 2^(2)+5^(2)=29
* 2^(2)+9^(2)=85
* 8^(2)+5^(2)=89
* 8^(2)+9^(2)=145
* From this point on, you'll join the cycle described above.
However, if we start with the number 13:
* 1^(2)+3^(2)=10
* 1^(2)+0^(2)=1
* 1^(2)=1
* 1^(2)=1
* We get the number 1 forever.
The sequence of numbers that we end up with is called a *sad cycle*, and it depends on the number you start with. If
you start the process with a number **n**, the sad cycle for **n** is the cycle which ends up eventually repeating
itself; this will either just be the cycle `1`, or the cycle `4, 16, 37, 58, 89, 145, 42, 20`.
But what if we cube the digits instead of squaring them? This gives us a different set of cycles all together. For
example, starting with 82375 and repeatedly getting the sum of the *cube* of the digits will lead us to the cycle `352,
160, 217`. Other numbers gravitate toward certain end points. These cycles are called *3-sad cycles* (as the digits are
raised to the power 3). This can be extended toward higher powers. For example, the 7-sad cycle for 1060925 is
`5141159, 4955606, 5515475, 1152428, 2191919, 14349038, 6917264, 6182897, 10080881, 6291458, 7254695, 6059210`. Your
challenge today, will be to find the *b*-sad cycle for a given *n*.
# Formal Inputs and Outputs
## Input Description
You will input the base ***b*** on the first line, and the starting number ***n*** on the second line, like so:
5
117649
## Output Description
Output a comma-separated list containing the ***b***-sad cycle for ***n***. For example, the 5-sad cycle for 117649 is:
10933, 59536, 73318, 50062
The starting point of the cycle doesn't matter - you can give a circularly permuted version of the cycle, too; rotating
the output around, wrapping from the start to the end, is also a correct output. The following outputs are equivalent
to the above output:
59536, 73318, 50062, 10933
73318, 50062, 10933, 59536
50062, 10933, 59536, 73318
# Sample Inputs and Outputs
## Sample 1
### Input
6
2
### Output
383890, 1057187, 513069, 594452, 570947, 786460, 477201, 239459, 1083396, 841700
## Sample 2
### Input
7
7
### Output
5345158, 2350099, 9646378, 8282107, 5018104, 2191663
## Sample 3
### Input
3
14
### Output
371
## Sample 4
### Input
11
2
### Output
5410213163, 416175830, 10983257969, 105122244539, 31487287760, 23479019969, 127868735735, 23572659062, 34181820005,
17233070810, 12544944422, 31450865399, 71817055715, 14668399199, 134844138593, 48622871273, 21501697322, 33770194826,
44292995390, 125581636412, 9417560504, 33827228267, 21497682212, 42315320498, 40028569325, 40435823054, 8700530096,
42360123272, 2344680590, 40391187185, 50591455115, 31629394541, 63182489351, 48977104622, 44296837448, 50918009003,
71401059083, 42001520522, 101858747, 21187545101, 10669113941, 63492084785, 50958448520, 48715803824, 27804526448,
19581408116, 48976748282, 61476706631
# Comment Order
Some people have notified us that new solutions are getting buried if you're not one of the first to submit. This is
valid concern, so today we're trialling a method of **setting the suggested sort order to** ***new*** (suggested sorts
are a newly introduced feature on Reddit). We'll take feedback on this and see how it goes. This means newer solutions
will appear at the top.
If you don't like this new sorting, you can still change the method back to **sort by** ***best***, which is the
default.
# Notes
I wasn't aware that /u/AnkePluff has made a [similar challenge
suggestion](http://www.reddit.com/r/dailyprogrammer_ideas/comments/2ydta5/easy_happy_numbers/) already - seems like
we're on the same wavelength!
""" |
# Difficulty Level: Beginner
# Can you make Python print out the song for 99 bottles of beer on the wall?
# Note: You can use range() in three different ways
# First:
# range(5) will give you a list containing [0, 1, 2, 3, 4]
# In this case, range assumes you want to start counting at 0, and the parameter you give is the number to stop *just* short of.
# Second:
# range(5, 10) will give you a list containing [5, 6, 7, 8, 9]
# In this case, the two parameters you give to range() are the number to start at and the number to stop *just* short of.
# Helpful mnemonic: range(start, stop)
# Third:
# range(5, 15, 3) will give you a list containing [5, 8, 11, 14]
# In this case, the three parameters you give to range() are the number to start at, the number to stop *just* short of, and the number to increment each time by.
# Note that normally, the number to increment each time by is assumed to be 1. (In other words, you add 1 each time through.)
# That's why it goes [0, 1, 2, 3, 4] unless you specify that third parameter, called the step.
# Helpful mnemonic: range(start, stop, step)
# Using range() and a loop, print out the song. Your output should look like this:
# 99 bottles of beer on the wall, 99 bottles of beer ...
# If one of those bottles should happen to fall, 98 bottles of beer on the wall
# 98 bottles of beer on the wall, 98 bottles of beer ...
# If one of those bottles should happen to fall, 97 bottles of beer on the wall
# 97 bottles of beer on the wall, 97 bottles of beer ...
# If one of those bottles should happen to fall, 96 bottles of beer on the wall
# 96 bottles of beer on the wall, 96 bottles of beer ...
# If one of those bottles should happen to fall, 95 bottles of beer on the wall
# 95 bottles of beer on the wall, 95 bottles of beer ...
# If one of those bottles should happen to fall, 94 bottles of beer on the wall
# 94 bottles of beer on the wall, 94 bottles of beer ...
# If one of those bottles should happen to fall, 93 bottles of beer on the wall
# 93 bottles of beer on the wall, 93 bottles of beer ...
# If one of those bottles should happen to fall, 92 bottles of beer on the wall
# 92 bottles of beer on the wall, 92 bottles of beer ...
# If one of those bottles should happen to fall, 91 bottles of beer on the wall
# 91 bottles of beer on the wall, 91 bottles of beer ...
# If one of those bottles should happen to fall, 90 bottles of beer on the wall
# 90 bottles of beer on the wall, 90 bottles of beer ...
# If one of those bottles should happen to fall, 89 bottles of beer on the wall
# 89 bottles of beer on the wall, 89 bottles of beer ...
# If one of those bottles should happen to fall, 88 bottles of beer on the wall
# 88 bottles of beer on the wall, 88 bottles of beer ...
# If one of those bottles should happen to fall, 87 bottles of beer on the wall
# 87 bottles of beer on the wall, 87 bottles of beer ...
# If one of those bottles should happen to fall, 86 bottles of beer on the wall
# 86 bottles of beer on the wall, 86 bottles of beer ...
# If one of those bottles should happen to fall, 85 bottles of beer on the wall
# 85 bottles of beer on the wall, 85 bottles of beer ...
# If one of those bottles should happen to fall, 84 bottles of beer on the wall
# 84 bottles of beer on the wall, 84 bottles of beer ...
# If one of those bottles should happen to fall, 83 bottles of beer on the wall
# 83 bottles of beer on the wall, 83 bottles of beer ...
# If one of those bottles should happen to fall, 82 bottles of beer on the wall
# 82 bottles of beer on the wall, 82 bottles of beer ...
# If one of those bottles should happen to fall, 81 bottles of beer on the wall
# 81 bottles of beer on the wall, 81 bottles of beer ...
# If one of those bottles should happen to fall, 80 bottles of beer on the wall
# 80 bottles of beer on the wall, 80 bottles of beer ...
# If one of those bottles should happen to fall, 79 bottles of beer on the wall
# 79 bottles of beer on the wall, 79 bottles of beer ...
# If one of those bottles should happen to fall, 78 bottles of beer on the wall
# 78 bottles of beer on the wall, 78 bottles of beer ...
# If one of those bottles should happen to fall, 77 bottles of beer on the wall
# 77 bottles of beer on the wall, 77 bottles of beer ...
# If one of those bottles should happen to fall, 76 bottles of beer on the wall
# 76 bottles of beer on the wall, 76 bottles of beer ...
# If one of those bottles should happen to fall, 75 bottles of beer on the wall
# 75 bottles of beer on the wall, 75 bottles of beer ...
# If one of those bottles should happen to fall, 74 bottles of beer on the wall
# 74 bottles of beer on the wall, 74 bottles of beer ...
# If one of those bottles should happen to fall, 73 bottles of beer on the wall
# 73 bottles of beer on the wall, 73 bottles of beer ...
# If one of those bottles should happen to fall, 72 bottles of beer on the wall
# 72 bottles of beer on the wall, 72 bottles of beer ...
# If one of those bottles should happen to fall, 71 bottles of beer on the wall
# 71 bottles of beer on the wall, 71 bottles of beer ...
# If one of those bottles should happen to fall, 70 bottles of beer on the wall
# 70 bottles of beer on the wall, 70 bottles of beer ...
# If one of those bottles should happen to fall, 69 bottles of beer on the wall
# 69 bottles of beer on the wall, 69 bottles of beer ...
# If one of those bottles should happen to fall, 68 bottles of beer on the wall
# 68 bottles of beer on the wall, 68 bottles of beer ...
# If one of those bottles should happen to fall, 67 bottles of beer on the wall
# 67 bottles of beer on the wall, 67 bottles of beer ...
# If one of those bottles should happen to fall, 66 bottles of beer on the wall
# 66 bottles of beer on the wall, 66 bottles of beer ...
# If one of those bottles should happen to fall, 65 bottles of beer on the wall
# 65 bottles of beer on the wall, 65 bottles of beer ...
# If one of those bottles should happen to fall, 64 bottles of beer on the wall
# 64 bottles of beer on the wall, 64 bottles of beer ...
# If one of those bottles should happen to fall, 63 bottles of beer on the wall
# 63 bottles of beer on the wall, 63 bottles of beer ...
# If one of those bottles should happen to fall, 62 bottles of beer on the wall
# 62 bottles of beer on the wall, 62 bottles of beer ...
# If one of those bottles should happen to fall, 61 bottles of beer on the wall
# 61 bottles of beer on the wall, 61 bottles of beer ...
# If one of those bottles should happen to fall, 60 bottles of beer on the wall
# 60 bottles of beer on the wall, 60 bottles of beer ...
# If one of those bottles should happen to fall, 59 bottles of beer on the wall
# 59 bottles of beer on the wall, 59 bottles of beer ...
# If one of those bottles should happen to fall, 58 bottles of beer on the wall
# 58 bottles of beer on the wall, 58 bottles of beer ...
# If one of those bottles should happen to fall, 57 bottles of beer on the wall
# 57 bottles of beer on the wall, 57 bottles of beer ...
# If one of those bottles should happen to fall, 56 bottles of beer on the wall
# 56 bottles of beer on the wall, 56 bottles of beer ...
# If one of those bottles should happen to fall, 55 bottles of beer on the wall
# 55 bottles of beer on the wall, 55 bottles of beer ...
# If one of those bottles should happen to fall, 54 bottles of beer on the wall
# 54 bottles of beer on the wall, 54 bottles of beer ...
# If one of those bottles should happen to fall, 53 bottles of beer on the wall
# 53 bottles of beer on the wall, 53 bottles of beer ...
# If one of those bottles should happen to fall, 52 bottles of beer on the wall
# 52 bottles of beer on the wall, 52 bottles of beer ...
# If one of those bottles should happen to fall, 51 bottles of beer on the wall
# 51 bottles of beer on the wall, 51 bottles of beer ...
# If one of those bottles should happen to fall, 50 bottles of beer on the wall
# 50 bottles of beer on the wall, 50 bottles of beer ...
# If one of those bottles should happen to fall, 49 bottles of beer on the wall
# 49 bottles of beer on the wall, 49 bottles of beer ...
# If one of those bottles should happen to fall, 48 bottles of beer on the wall
# 48 bottles of beer on the wall, 48 bottles of beer ...
# If one of those bottles should happen to fall, 47 bottles of beer on the wall
# 47 bottles of beer on the wall, 47 bottles of beer ...
# If one of those bottles should happen to fall, 46 bottles of beer on the wall
# 46 bottles of beer on the wall, 46 bottles of beer ...
# If one of those bottles should happen to fall, 45 bottles of beer on the wall
# 45 bottles of beer on the wall, 45 bottles of beer ...
# If one of those bottles should happen to fall, 44 bottles of beer on the wall
# 44 bottles of beer on the wall, 44 bottles of beer ...
# If one of those bottles should happen to fall, 43 bottles of beer on the wall
# 43 bottles of beer on the wall, 43 bottles of beer ...
# If one of those bottles should happen to fall, 42 bottles of beer on the wall
# 42 bottles of beer on the wall, 42 bottles of beer ...
# If one of those bottles should happen to fall, 41 bottles of beer on the wall
# 41 bottles of beer on the wall, 41 bottles of beer ...
# If one of those bottles should happen to fall, 40 bottles of beer on the wall
# 40 bottles of beer on the wall, 40 bottles of beer ...
# If one of those bottles should happen to fall, 39 bottles of beer on the wall
# 39 bottles of beer on the wall, 39 bottles of beer ...
# If one of those bottles should happen to fall, 38 bottles of beer on the wall
# 38 bottles of beer on the wall, 38 bottles of beer ...
# If one of those bottles should happen to fall, 37 bottles of beer on the wall
# 37 bottles of beer on the wall, 37 bottles of beer ...
# If one of those bottles should happen to fall, 36 bottles of beer on the wall
# 36 bottles of beer on the wall, 36 bottles of beer ...
# If one of those bottles should happen to fall, 35 bottles of beer on the wall
# 35 bottles of beer on the wall, 35 bottles of beer ...
# If one of those bottles should happen to fall, 34 bottles of beer on the wall
# 34 bottles of beer on the wall, 34 bottles of beer ...
# If one of those bottles should happen to fall, 33 bottles of beer on the wall
# 33 bottles of beer on the wall, 33 bottles of beer ...
# If one of those bottles should happen to fall, 32 bottles of beer on the wall
# 32 bottles of beer on the wall, 32 bottles of beer ...
# If one of those bottles should happen to fall, 31 bottles of beer on the wall
# 31 bottles of beer on the wall, 31 bottles of beer ...
# If one of those bottles should happen to fall, 30 bottles of beer on the wall
# 30 bottles of beer on the wall, 30 bottles of beer ...
# If one of those bottles should happen to fall, 29 bottles of beer on the wall
# 29 bottles of beer on the wall, 29 bottles of beer ...
# If one of those bottles should happen to fall, 28 bottles of beer on the wall
# 28 bottles of beer on the wall, 28 bottles of beer ...
# If one of those bottles should happen to fall, 27 bottles of beer on the wall
# 27 bottles of beer on the wall, 27 bottles of beer ...
# If one of those bottles should happen to fall, 26 bottles of beer on the wall
# 26 bottles of beer on the wall, 26 bottles of beer ...
# If one of those bottles should happen to fall, 25 bottles of beer on the wall
# 25 bottles of beer on the wall, 25 bottles of beer ...
# If one of those bottles should happen to fall, 24 bottles of beer on the wall
# 24 bottles of beer on the wall, 24 bottles of beer ...
# If one of those bottles should happen to fall, 23 bottles of beer on the wall
# 23 bottles of beer on the wall, 23 bottles of beer ...
# If one of those bottles should happen to fall, 22 bottles of beer on the wall
# 22 bottles of beer on the wall, 22 bottles of beer ...
# If one of those bottles should happen to fall, 21 bottles of beer on the wall
# 21 bottles of beer on the wall, 21 bottles of beer ...
# If one of those bottles should happen to fall, 20 bottles of beer on the wall
# 20 bottles of beer on the wall, 20 bottles of beer ...
# If one of those bottles should happen to fall, 19 bottles of beer on the wall
# 19 bottles of beer on the wall, 19 bottles of beer ...
# If one of those bottles should happen to fall, 18 bottles of beer on the wall
# 18 bottles of beer on the wall, 18 bottles of beer ...
# If one of those bottles should happen to fall, 17 bottles of beer on the wall
# 17 bottles of beer on the wall, 17 bottles of beer ...
# If one of those bottles should happen to fall, 16 bottles of beer on the wall
# 16 bottles of beer on the wall, 16 bottles of beer ...
# If one of those bottles should happen to fall, 15 bottles of beer on the wall
# 15 bottles of beer on the wall, 15 bottles of beer ...
# If one of those bottles should happen to fall, 14 bottles of beer on the wall
# 14 bottles of beer on the wall, 14 bottles of beer ...
# If one of those bottles should happen to fall, 13 bottles of beer on the wall
# 13 bottles of beer on the wall, 13 bottles of beer ...
# If one of those bottles should happen to fall, 12 bottles of beer on the wall
# 12 bottles of beer on the wall, 12 bottles of beer ...
# If one of those bottles should happen to fall, 11 bottles of beer on the wall
# 11 bottles of beer on the wall, 11 bottles of beer ...
# If one of those bottles should happen to fall, 10 bottles of beer on the wall
# 10 bottles of beer on the wall, 10 bottles of beer ...
# If one of those bottles should happen to fall, 9 bottles of beer on the wall
# 9 bottles of beer on the wall, 9 bottles of beer ...
# If one of those bottles should happen to fall, 8 bottles of beer on the wall
# 8 bottles of beer on the wall, 8 bottles of beer ...
# If one of those bottles should happen to fall, 7 bottles of beer on the wall
# 7 bottles of beer on the wall, 7 bottles of beer ...
# If one of those bottles should happen to fall, 6 bottles of beer on the wall
# 6 bottles of beer on the wall, 6 bottles of beer ...
# If one of those bottles should happen to fall, 5 bottles of beer on the wall
# 5 bottles of beer on the wall, 5 bottles of beer ...
# If one of those bottles should happen to fall, 4 bottles of beer on the wall
# 4 bottles of beer on the wall, 4 bottles of beer ...
# If one of those bottles should happen to fall, 3 bottles of beer on the wall
# 3 bottles of beer on the wall, 3 bottles of beer ...
# If one of those bottles should happen to fall, 2 bottles of beer on the wall
# 2 bottles of beer on the wall, 2 bottles of beer ...
# If one of those bottles should happen to fall, 1 bottles of beer on the wall
|
"""
Basic functions used by several sub-packages and
useful to have in the main name-space.
Type Handling
-------------
================ ===================
iscomplexobj Test for complex object, scalar result
isrealobj Test for real object, scalar result
iscomplex Test for complex elements, array result
isreal Test for real elements, array result
imag Imaginary part
real Real part
real_if_close Turns complex number with tiny imaginary part to real
isneginf Tests for negative infinity, array result
isposinf Tests for positive infinity, array result
isnan Tests for nans, array result
isinf Tests for infinity, array result
isfinite Tests for finite numbers, array result
isscalar True if argument is a scalar
nan_to_num Replaces NaN's with 0 and infinities with large numbers
cast Dictionary of functions to force cast to each type
common_type Determine the minimum common type code for a group
of arrays
mintypecode Return minimal allowed common typecode.
================ ===================
Index Tricks
------------
================ ===================
mgrid Method which allows easy construction of N-d
'mesh-grids'
``r_`` Append and construct arrays: turns slice objects into
ranges and concatenates them, for 2d arrays appends rows.
index_exp Konrad Hinsen's index_expression class instance which
can be useful for building complicated slicing syntax.
================ ===================
Useful Functions
----------------
================ ===================
select Extension of where to multiple conditions and choices
extract Extract 1d array from flattened array according to mask
insert Insert 1d array of values into Nd array according to mask
linspace Evenly spaced samples in linear space
logspace Evenly spaced samples in logarithmic space
fix Round x to nearest integer towards zero
mod Modulo mod(x,y) = x % y except keeps sign of y
amax Array maximum along axis
amin Array minimum along axis
ptp Array max-min along axis
cumsum Cumulative sum along axis
prod Product of elements along axis
cumprod Cumluative product along axis
diff Discrete differences along axis
angle Returns angle of complex argument
unwrap Unwrap phase along given axis (1-d algorithm)
sort_complex Sort a complex-array (based on real, then imaginary)
trim_zeros Trim the leading and trailing zeros from 1D array.
vectorize A class that wraps a Python function taking scalar
arguments into a generalized function which can handle
arrays of arguments using the broadcast rules of
numerix Python.
================ ===================
Shape Manipulation
------------------
================ ===================
squeeze Return a with length-one dimensions removed.
atleast_1d Force arrays to be > 1D
atleast_2d Force arrays to be > 2D
atleast_3d Force arrays to be > 3D
vstack Stack arrays vertically (row on row)
hstack Stack arrays horizontally (column on column)
column_stack Stack 1D arrays as columns into 2D array
dstack Stack arrays depthwise (along third dimension)
split Divide array into a list of sub-arrays
hsplit Split into columns
vsplit Split into rows
dsplit Split along third dimension
================ ===================
Matrix (2D Array) Manipulations
-------------------------------
================ ===================
fliplr 2D array with columns flipped
flipud 2D array with rows flipped
rot90 Rotate a 2D array a multiple of 90 degrees
eye Return a 2D array with ones down a given diagonal
diag Construct a 2D array from a vector, or return a given
diagonal from a 2D array.
mat Construct a Matrix
bmat Build a Matrix from blocks
================ ===================
Polynomials
-----------
================ ===================
poly1d A one-dimensional polynomial class
poly Return polynomial coefficients from roots
roots Find roots of polynomial given coefficients
polyint Integrate polynomial
polyder Differentiate polynomial
polyadd Add polynomials
polysub Substract polynomials
polymul Multiply polynomials
polydiv Divide polynomials
polyval Evaluate polynomial at given argument
================ ===================
Import Tricks
-------------
================ ===================
ppimport Postpone module import until trying to use it
ppimport_attr Postpone module import until trying to use its attribute
ppresolve Import postponed module and return it.
================ ===================
Machine Arithmetics
-------------------
================ ===================
machar_single Single precision floating point arithmetic parameters
machar_double Double precision floating point arithmetic parameters
================ ===================
Threading Tricks
----------------
================ ===================
ParallelExec Execute commands in parallel thread.
================ ===================
1D Array Set Operations
-----------------------
Set operations for 1D numeric arrays based on sort() function.
================ ===================
ediff1d Array difference (auxiliary function).
unique Unique elements of an array.
intersect1d Intersection of 1D arrays with unique elements.
setxor1d Set exclusive-or of 1D arrays with unique elements.
in1d Test whether elements in a 1D array are also present in
another array.
union1d Union of 1D arrays with unique elements.
setdiff1d Set difference of 1D arrays with unique elements.
================ ===================
""" |
"""
Wrappers to LAPACK library
==========================
flapack -- wrappers for Fortran [*] LAPACK routines
clapack -- wrappers for ATLAS LAPACK routines
calc_lwork -- calculate optimal lwork parameters
get_lapack_funcs -- query for wrapper functions.
[*] If ATLAS libraries are available then Fortran routines
actually use ATLAS routines and should perform equally
well to ATLAS routines.
Module flapack
++++++++++++++
In the following all function names are shown without
type prefix (s,d,c,z). Optimal values for lwork can
be computed using calc_lwork module.
Linear Equations
----------------
Drivers::
lu,piv,x,info = gesv(a,b,overwrite_a=0,overwrite_b=0)
lub,piv,x,info = gbsv(kl,ku,ab,b,overwrite_ab=0,overwrite_b=0)
c,x,info = posv(a,b,lower=0,overwrite_a=0,overwrite_b=0)
Computational routines::
lu,piv,info = getrf(a,overwrite_a=0)
x,info = getrs(lu,piv,b,trans=0,overwrite_b=0)
inv_a,info = getri(lu,piv,lwork=min_lwork,overwrite_lu=0)
c,info = potrf(a,lower=0,clean=1,overwrite_a=0)
x,info = potrs(c,b,lower=0,overwrite_b=0)
inv_a,info = potri(c,lower=0,overwrite_c=0)
inv_c,info = trtri(c,lower=0,unitdiag=0,overwrite_c=0)
Linear Least Squares (LLS) Problems
-----------------------------------
Drivers::
v,x,s,rank,info = gelss(a,b,cond=-1.0,lwork=min_lwork,overwrite_a=0,overwrite_b=0)
Computational routines::
qr,tau,info = geqrf(a,lwork=min_lwork,overwrite_a=0)
q,info = orgqr|ungqr(qr,tau,lwork=min_lwork,overwrite_qr=0,overwrite_tau=1)
Generalized Linear Least Squares (LSE and GLM) Problems
-------------------------------------------------------
Standard Eigenvalue and Singular Value Problems
-----------------------------------------------
Drivers::
w,v,info = syev|heev(a,compute_v=1,lower=0,lwork=min_lwork,overwrite_a=0)
w,v,info = syevd|heevd(a,compute_v=1,lower=0,lwork=min_lwork,overwrite_a=0)
w,v,info = syevr|heevr(a,compute_v=1,lower=0,vrange=,irange=,atol=-1.0,lwork=min_lwork,overwrite_a=0)
t,sdim,(wr,wi|w),vs,info = gees(select,a,compute_v=1,sort_t=0,lwork=min_lwork,select_extra_args=(),overwrite_a=0)
wr,(wi,vl|w),vr,info = geev(a,compute_vl=1,compute_vr=1,lwork=min_lwork,overwrite_a=0)
u,s,vt,info = gesdd(a,compute_uv=1,lwork=min_lwork,overwrite_a=0)
Computational routines::
ht,tau,info = gehrd(a,lo=0,hi=n-1,lwork=min_lwork,overwrite_a=0)
ba,lo,hi,pivscale,info = gebal(a,scale=0,permute=0,overwrite_a=0)
Generalized Eigenvalue and Singular Value Problems
--------------------------------------------------
Drivers::
w,v,info = sygv|hegv(a,b,itype=1,compute_v=1,lower=0,lwork=min_lwork,overwrite_a=0,overwrite_b=0)
w,v,info = sygvd|hegvd(a,b,itype=1,compute_v=1,lower=0,lwork=min_lwork,overwrite_a=0,overwrite_b=0)
(alphar,alphai|alpha),beta,vl,vr,info = ggev(a,b,compute_vl=1,compute_vr=1,lwork=min_lwork,overwrite_a=0,overwrite_b=0)
Auxiliary routines
------------------
a,info = lauum(c,lower=0,overwrite_c=0)
a = laswp(a,piv,k1=0,k2=len(piv)-1,off=0,inc=1,overwrite_a=0)
Module clapack
++++++++++++++
Linear Equations
----------------
Drivers::
lu,piv,x,info = gesv(a,b,rowmajor=1,overwrite_a=0,overwrite_b=0)
c,x,info = posv(a,b,lower=0,rowmajor=1,overwrite_a=0,overwrite_b=0)
Computational routines::
lu,piv,info = getrf(a,rowmajor=1,overwrite_a=0)
x,info = getrs(lu,piv,b,trans=0,rowmajor=1,overwrite_b=0)
inv_a,info = getri(lu,piv,rowmajor=1,overwrite_lu=0)
c,info = potrf(a,lower=0,clean=1,rowmajor=1,overwrite_a=0)
x,info = potrs(c,b,lower=0,rowmajor=1,overwrite_b=0)
inv_a,info = potri(c,lower=0,rowmajor=1,overwrite_c=0)
inv_c,info = trtri(c,lower=0,unitdiag=0,rowmajor=1,overwrite_c=0)
Auxiliary routines
------------------
a,info = lauum(c,lower=0,rowmajor=1,overwrite_c=0)
Module calc_lwork
+++++++++++++++++
Optimal lwork is maxwrk. Default is minwrk.
minwrk,maxwrk = gehrd(prefix,n,lo=0,hi=n-1)
minwrk,maxwrk = gesdd(prefix,m,n,compute_uv=1)
minwrk,maxwrk = gelss(prefix,m,n,nrhs)
minwrk,maxwrk = getri(prefix,n)
minwrk,maxwrk = geev(prefix,n,compute_vl=1,compute_vr=1)
minwrk,maxwrk = heev(prefix,n,lower=0)
minwrk,maxwrk = syev(prefix,n,lower=0)
minwrk,maxwrk = gees(prefix,n,compute_v=1)
minwrk,maxwrk = geqrf(prefix,m,n)
minwrk,maxwrk = gqr(prefix,m,n)
""" |
"""Generic socket server classes.
This module tries to capture the various aspects of defining a server:
For socket-based servers:
- address family:
- AF_INET{,6}: IP (Internet Protocol) sockets (default)
- AF_UNIX: Unix domain sockets
- others, e.g. AF_DECNET are conceivable (see <socket.h>
- socket type:
- SOCK_STREAM (reliable stream, e.g. TCP)
- SOCK_DGRAM (datagrams, e.g. UDP)
For request-based servers (including socket-based):
- client address verification before further looking at the request
(This is actually a hook for any processing that needs to look
at the request before anything else, e.g. logging)
- how to handle multiple requests:
- synchronous (one request is handled at a time)
- forking (each request is handled by a new process)
- threading (each request is handled by a new thread)
The classes in this module favor the server type that is simplest to
write: a synchronous TCP/IP server. This is bad class design, but
save some typing. (There's also the issue that a deep class hierarchy
slows down method lookups.)
There are five classes in an inheritance diagram, four of which represent
synchronous servers of four types:
+------------+
| BaseServer |
+------------+
|
v
+-----------+ +------------------+
| TCPServer |------->| UnixStreamServer |
+-----------+ +------------------+
|
v
+-----------+ +--------------------+
| UDPServer |------->| UnixDatagramServer |
+-----------+ +--------------------+
Note that UnixDatagramServer derives from UDPServer, not from
UnixStreamServer -- the only difference between an IP and a Unix
stream server is the address family, which is simply repeated in both
unix server classes.
Forking and threading versions of each type of server can be created
using the ForkingMixIn and ThreadingMixIn mix-in classes. For
instance, a threading UDP server class is created as follows:
class ThreadingUDPServer(ThreadingMixIn, UDPServer): pass
The Mix-in class must come first, since it overrides a method defined
in UDPServer! Setting the various member variables also changes
the behavior of the underlying server mechanism.
To implement a service, you must derive a class from
BaseRequestHandler and redefine its handle() method. You can then run
various versions of the service by combining one of the server classes
with your request handler class.
The request handler class must be different for datagram or stream
services. This can be hidden by using the request handler
subclasses StreamRequestHandler or DatagramRequestHandler.
Of course, you still have to use your head!
For instance, it makes no sense to use a forking server if the service
contains state in memory that can be modified by requests (since the
modifications in the child process would never reach the initial state
kept in the parent process and passed to each child). In this case,
you can use a threading server, but you will probably have to use
locks to avoid two requests that come in nearly simultaneous to apply
conflicting changes to the server state.
On the other hand, if you are building e.g. an HTTP server, where all
data is stored externally (e.g. in the file system), a synchronous
class will essentially render the service "deaf" while one request is
being handled -- which may be for a very long time if a client is slow
to reqd all the data it has requested. Here a threading or forking
server is appropriate.
In some cases, it may be appropriate to process part of a request
synchronously, but to finish processing in a forked child depending on
the request data. This can be implemented by using a synchronous
server and doing an explicit fork in the request handler class
handle() method.
Another approach to handling multiple simultaneous requests in an
environment that supports neither threads nor fork (or where these are
too expensive or inappropriate for the service) is to maintain an
explicit table of partially finished requests and to use select() to
decide which request to work on next (or whether to handle a new
incoming request). This is particularly important for stream services
where each client can potentially be connected for a long time (if
threads or subprocesses cannot be used).
Future work:
- Standard classes for Sun RPC (which uses either UDP or TCP)
- Standard mix-in classes to implement various authentication
and encryption schemes
- Standard framework for select-based multiplexing
XXX Open problems:
- What to do with out-of-band data?
BaseServer:
- split generic "request" functionality out into BaseServer class.
Copyright (C) 2000 NAME <EMAIL>
example: read entries from a SQL database (requires overriding
get_request() to return a table entry from the database).
entry is processed by a RequestHandlerClass.
""" |
"""
Simple config
=============
Although CherryPy uses the :mod:`Python logging module <logging>`, it does so
behind the scenes so that simple logging is simple, but complicated logging
is still possible. "Simple" logging means that you can log to the screen
(i.e. console/stdout) or to a file, and that you can easily have separate
error and access log files.
Here are the simplified logging settings. You use these by adding lines to
your config file or dict. You should set these at either the global level or
per application (see next), but generally not both.
* ``log.screen``: Set this to True to have both "error" and "access" messages
printed to stdout.
* ``log.access_file``: Set this to an absolute filename where you want
"access" messages written.
* ``log.error_file``: Set this to an absolute filename where you want "error"
messages written.
Many events are automatically logged; to log your own application events, call
:func:`cherrypy.log`.
Architecture
============
Separate scopes
---------------
CherryPy provides log managers at both the global and application layers.
This means you can have one set of logging rules for your entire site,
and another set of rules specific to each application. The global log
manager is found at :func:`cherrypy.log`, and the log manager for each
application is found at :attr:`app.log<cherrypy._cptree.Application.log>`.
If you're inside a request, the latter is reachable from
``cherrypy.request.app.log``; if you're outside a request, you'll have to
obtain a reference to the ``app``: either the return value of
:func:`tree.mount()<cherrypy._cptree.Tree.mount>` or, if you used
:func:`quickstart()<cherrypy.quickstart>` instead, via
``cherrypy.tree.apps['/']``.
By default, the global logs are named "cherrypy.error" and "cherrypy.access",
and the application logs are named "cherrypy.error.2378745" and
"cherrypy.access.2378745" (the number is the id of the Application object).
This means that the application logs "bubble up" to the site logs, so if your
application has no log handlers, the site-level handlers will still log the
messages.
Errors vs. Access
-----------------
Each log manager handles both "access" messages (one per HTTP request) and
"error" messages (everything else). Note that the "error" log is not just for
errors! The format of access messages is highly formalized, but the error log
isn't--it receives messages from a variety of sources (including full error
tracebacks, if enabled).
If you are logging the access log and error log to the same source, then there
is a possibility that a specially crafted error message may replicate an access
log message as described in CWE-117. In this case it is the application
developer's responsibility to manually escape data before
using CherryPy's log()
functionality, or they may create an application that is vulnerable to CWE-117.
This would be achieved by using a custom handler escape any special characters,
and attached as described below.
Custom Handlers
===============
The simple settings above work by manipulating Python's standard :mod:`logging`
module. So when you need something more complex, the full power of the standard
module is yours to exploit. You can borrow or create custom handlers, formats,
filters, and much more. Here's an example that skips the standard FileHandler
and uses a RotatingFileHandler instead:
::
#python
log = app.log
# Remove the default FileHandlers if present.
log.error_file = ""
log.access_file = ""
maxBytes = getattr(log, "rot_maxBytes", 10000000)
backupCount = getattr(log, "rot_backupCount", 1000)
# Make a new RotatingFileHandler for the error log.
fname = getattr(log, "rot_error_file", "error.log")
h = handlers.RotatingFileHandler(fname, 'a', maxBytes, backupCount)
h.setLevel(DEBUG)
h.setFormatter(_cplogging.logfmt)
log.error_log.addHandler(h)
# Make a new RotatingFileHandler for the access log.
fname = getattr(log, "rot_access_file", "access.log")
h = handlers.RotatingFileHandler(fname, 'a', maxBytes, backupCount)
h.setLevel(DEBUG)
h.setFormatter(_cplogging.logfmt)
log.access_log.addHandler(h)
The ``rot_*`` attributes are pulled straight from the application log object.
Since "log.*" config entries simply set attributes on the log object, you can
add custom attributes to your heart's content. Note that these handlers are
used ''instead'' of the default, simple handlers outlined above (so don't set
the "log.error_file" config entry, for example).
""" |
"""
Newick format (:mod:`skbio.io.format.newick`)
=============================================
.. currentmodule:: skbio.io.format.newick
Newick format (``newick``) stores spanning-trees with weighted edges and node
names in a minimal file format [1]_. This is useful for representing
phylogenetic trees and taxonomies. Newick was created as an informal
specification on June 26, 1986 [2]_.
Format Support
--------------
**Has Sniffer: Yes**
+------+------+---------------------------------------------------------------+
|Reader|Writer| Object Class |
+======+======+===============================================================+
|Yes |Yes |:mod:`skbio.tree.TreeNode` |
+------+------+---------------------------------------------------------------+
Format Specification
--------------------
A Newick file represents a tree using the following grammar. See below for an
explanation of the format in plain English.
Formal Grammar
^^^^^^^^^^^^^^
.. code-block:: none
NEWICK ==> NODE ;
NODE ==> FORMATTING SUBTREE FORMATTING NODE_INFO FORMATTING
SUBTREE ==> ( CHILDREN ) | null
NODE_INFO ==> LABEL | LENGTH | LABEL FORMATTING LENGTH | null
FORMATTING ==> [ COMMENT_CHARS ] | whitespace | null
CHILDREN ==> NODE | CHILDREN , NODE
LABEL ==> ' ALL_CHARS ' | SAFE_CHARS
LENGTH ==> : FORMATTING NUMBER
COMMENT_CHARS ==> any
ALL_CHARS ==> any
SAFE_CHARS ==> any except: ,;:()[] and whitespace
NUMBER ==> a decimal or integer
.. note:: The ``_`` character inside of SAFE_CHARS will be converted to a
blank space in ``skbio.tree.TreeNode`` and vice versa.
``'`` is considered the escape character. To escape ``'`` use a
preceding ``'``.
The implementation of newick in scikit-bio allows nested comments. To
escape ``[`` or ``]`` from within COMMENT_CHARS, use a preceding ``'``.
Explanation
^^^^^^^^^^^
The Newick format defines a tree by creating a minimal representation of nodes
and their relationships to each other.
Basic Symbols
~~~~~~~~~~~~~
There are several symbols which define nodes, the first of which is the
semi-colon (``;``). The semi-colon creates a root node to its left. Recall that
there can only be one root in a tree.
The next symbol is the comma (``,``), which creates a node to its right.
However, these two alone are not enough. For example imagine the following
string: ``, , , ;``. It is evident that there is a root, but the other 3 nodes,
defined by commas, have no relationship. For this reason, it is not a valid
Newick string to have more than one node at the root level.
To provide these relationships, there is another structure:
paired parenthesis (``( )``). These are inserted at the location of an existing
node and give it the ability to have children. Placing ``( )`` in a node's
location will create a child inside the parenthesis on the left-most
inner edge.
Application of Rules
~~~~~~~~~~~~~~~~~~~~
Adding a comma within the parenthesis will create two children: ``( , )``
(also known as a bifurcating node). Notice that only one comma is needed
because the parenthesis have already created a child. Adding more commas will
create more children who are siblings to each other. For example, writing
``( , , , )`` will create a multifurcating node with 4 child nodes who are
siblings to each other.
The notation for a root can be used to create a complete tree. The ``;`` will
create a root node where parenthesis can be placed: ``( );``. Adding commas
will create more children: ``( , );``. These rules can be applied recursively
ad. infinitum: ``(( , ), ( , ));``.
Adding Node Information
~~~~~~~~~~~~~~~~~~~~~~~
Information about a node can be added to improve the clarity and meaning of a
tree. Each node may have a label and/or a length (to the parent). Newick always
places the node information at the right-most edge of a node's position.
Starting with labels, ``(( , ), ( , ));`` would become
``((D, E)B, (F, G)C)A;``. There is a named root ``A`` and the root's children
(from left to right) are ``B`` and ``C``. ``B`` has the children ``D`` and
``E``, and ``C`` has the children ``F`` and ``G``.
Length represents the distance (or weight of the edge) that connects a node to
its parent. This must be a decimal or integer. As an example, suppose ``D`` is
rather estranged from ``B``, and ``E`` is very close. That can be written as:
``((D:10, E:0.5)B, (F, G)C)A;``. Notice that the colon (``:``) separates the
label from the length. If the length is provided but the label is omitted, a
colon must still precede the length (``(:0.25,:0.5):0.0;``). Without this, the
length would be interpreted as a label (which happens to be a number).
.. note:: Internally scikit-bio will cast a length to ``float`` which
technically means that even exponent strings (``1e-3``) are supported)
Advanced Label and Length Rules
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
More characters can be used to create more descriptive labels. When creating a
label there are some rules that must be considered due to limitations in the
Newick format. The following characters are not allowed within a standard
label: parenthesis, commas, square-brackets, colon, semi-colon, and whitespace.
These characters are also disallowed from occurring within a length, which has
a much stricter format: decimal or integer. Many of these characters are
symbols which define the structure of a Newick tree and are thus disallowed for
obvious reasons. The symbols not yet mentioned are square-brackets (``[ ]``)
and whitespace (space, tab, and newline).
What if these characters are needed within a label? In the simple case of
spaces, an underscore (``_``) will be translated as a space on read and vice
versa on write.
What if a literal underscore or any of the others mentioned are needed?
A label can be escaped (meaning that its contents are understood as regular
text) using single-quotes (``'``). When a label is surrounded by single-quotes,
any character is permissible. If a single-quote is needed inside of an escaped
label or anywhere else, it can be escaped with another single-quote.
For example, ``A_1`` is written ``'A_1'`` and ``'A'_1`` would be ``'''A''_1'``.
Inline Comments
~~~~~~~~~~~~~~~
Square-brackets define a comment, which are the least commonly used part of
the Newick format. Comments are not included in the generated objects and exist
only as human readable text ignored by the parser. The implementation in
scikit-bio allows for nested comments (``[comment [nested]]``). Unpaired
square-brackets can be escaped with a single-quote preceding the bracket when
inside an existing comment. (This is identical to escaping a single-quote).
The single-quote has the highest operator precedence, so there is no need to
worry about starting a comment from within a properly escaped label.
Whitespace
~~~~~~~~~~
Whitespace is not allowed within any un-escaped label or in any length, but it
is permitted anywhere else.
Caveats
~~~~~~~
Newick cannot always provide a unique representation of any tree, in other
words, the same tree can be written multiple ways. For example: ``(A, B);`` is
isomorphic to ``(B, A);``. The implementation in scikit-bio maintains the given
sibling order in its object representations.
Newick has no representation of an unrooted tree. Some biological packages make
the assumption that when a trifurcated root exists in an otherwise bifurcated
tree that the tree must be unrooted. In scikit-bio, ``skbio.tree.TreeNode``
will always be rooted at the ``newick`` root (``;``).
Format Parameters
-----------------
The only supported format parameter is `convert_underscores`. This is `True` by
default. When `False`, underscores found in unescaped labels will not be
converted to spaces. This is useful when reading the output of an external
program in which the underscores were not escaped. This parameter only affects
`read` operations. It does not exist for `write` operations; they will always
properly escape underscores.
Examples
--------
This is a simple Newick string.
>>> from StringIO import StringIO
>>> from skbio import read
>>> from skbio.tree import TreeNode
>>> f = StringIO(u"((D, E)B, (F, G)C)A;")
>>> tree = read(f, format="newick", into=TreeNode)
>>> f.close()
>>> print(tree.ascii_art())
/-D
/B-------|
| \-E
-A-------|
| /-F
\C-------|
\-G
This is a complex Newick string.
>>> f = StringIO(u"[example](a:0.1, 'b_b''':0.2, (c:0.3, d_d:0.4)e:0.5)f:0.0;")
>>> tree = read(f, format="newick", into=TreeNode)
>>> f.close()
>>> print(tree.ascii_art())
/-a
|
-f-------|--b_b'
|
| /-c
\e-------|
\-d d
Notice that the node originally labeled ``d_d`` became ``d d``. Additionally
``'b_b'''`` became ``b_b'``. Note that the underscore was preserved in `b_b'`.
References
----------
.. [1] http://evolution.genetics.washington.edu/phylip/newick_doc.html
.. [2] http://evolution.genetics.washington.edu/phylip/newicktree.html
""" |
#
# tested on | Windows native | Linux cross-compilation
# ------------------------+-------------------+---------------------------
# MSVS C++ 2010 Express | WORKS | n/a
# Mingw-w64 | WORKS | WORKS
# Mingw-w32 | WORKS | WORKS
# MinGW | WORKS | untested
#
#####
# Notes about MSVS C++ :
#
# - MSVC2010-Express compiles to 32bits only.
#
#####
# Notes about Mingw-w64 and Mingw-w32 under Windows :
#
# - both can be installed using the official installer :
# http://mingw-w64.sourceforge.net/download.php#mingw-builds
#
# - if you want to compile both 32bits and 64bits, don't forget to
# run the installer twice to install them both.
#
# - install them into a path that does not contain spaces
# ( example : "C:/Mingw-w32", "C:/Mingw-w64" )
#
# - if you want to compile faster using the "-j" option, don't forget
# to install the appropriate version of the Pywin32 python extension
# available from : http://sourceforge.net/projects/pywin32/files/
#
# - before running scons, you must add into the environment path
# the path to the "/bin" directory of the Mingw version you want
# to use :
#
# set PATH=C:/Mingw-w32/bin;%PATH%
#
# - then, scons should be able to detect gcc.
# - Mingw-w32 only compiles 32bits.
# - Mingw-w64 only compiles 64bits.
#
# - it is possible to add them both at the same time into the PATH env,
# if you also define the MINGW32_PREFIX and MINGW64_PREFIX environment
# variables.
# For instance, you could store that set of commands into a .bat script
# that you would run just before scons :
#
# set PATH=C:\mingw-w32\bin;%PATH%
# set PATH=C:\mingw-w64\bin;%PATH%
# set MINGW32_PREFIX=C:\mingw-w32\bin\
# set MINGW64_PREFIX=C:\mingw-w64\bin\
#
#####
# Notes about Mingw, Mingw-w64 and Mingw-w32 under Linux :
#
# - default toolchain prefixes are :
# "i586-mingw32msvc-" for MinGW
# "i686-w64-mingw32-" for Mingw-w32
# "x86_64-w64-mingw32-" for Mingw-w64
#
# - if both MinGW and Mingw-w32 are installed on your system
# Mingw-w32 should take the priority over MinGW.
#
# - it is possible to manually override prefixes by defining
# the MINGW32_PREFIX and MINGW64_PREFIX environment variables.
#
#####
# Notes about Mingw under Windows :
#
# - this is the MinGW version from http://mingw.org/
# - install it into a path that does not contain spaces
# ( example : "C:/MinGW" )
# - several DirectX headers might be missing. You can copy them into
# the C:/MinGW/include" directory from this page :
# https://code.google.com/p/mingw-lib/source/browse/trunk/working/avcodec_to_widget_5/directx_include/
# - before running scons, add the path to the "/bin" directory :
# set PATH=C:/MinGW/bin;%PATH%
# - scons should be able to detect gcc.
#
#####
# TODO :
#
# - finish to cleanup this script to remove all the remains of previous hacks and workarounds
# - make it work with the Windows7 SDK that is supposed to enable 64bits compilation for MSVC2010-Express
# - confirm it works well with other Visual Studio versions.
# - update the wiki about the pywin32 extension required for the "-j" option under Windows.
# - update the wiki to document MINGW32_PREFIX and MINGW64_PREFIX
#
|
# vim: set fileencoding=utf-8 :
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|
# -*- coding: utf-8 -*-
############################ Copyrights and license ############################
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|
"""
==============
Module pymorph
==============
pymorph a powerful collection of state-of-the-art gray-scale morphological
tools that can be applied to image segmentation, non-linear filtering,
pattern recognition and image analysis.
- `add4dilate()` : Addition for dilation
- `addm()` : Addition of two images, with saturation.
- `areaclose()` : Area closing
- `areaopen()` : Area opening
- `asf()` : Alternating Sequential Filtering
- `asfrec()` : Reconstructive Alternating Sequential Filtering
- `bench()` : benchmarking main functions of the toolbox.
- `binary()` : Convert a gray-scale image into a binary image
- `blob()` : Blob measurements from a labeled image.
- `bshow()` : Generate a graphical representation of overlaid binary images.
- `cbisector()` : N-Conditional bisector.
- `cdilate()` : Dilate an image conditionally.
- `center()` : Center filter.
- `cerode()` : Erode an image conditionally.
- `close_holes()` : Close holes of binary and gray-scale images.
- `close()` : Morphological closing.
- `closerec()` : Closing by reconstruction.
- `closerecth()` : Close-by-Reconstruction Top-Hat.
- `closeth()` : Closing Top Hat.
- `concat()` : Concatenate two or more images along width, height or depth.
- `cthick()` : Image transformation by conditional thickening.
- `cthin()` : Image transformation by conditional thinning.
- `cwatershed()` : Detection of watershed from markers.
- `datatype()` : Return the image datatype string
- `dilate()` : Dilate an image by a structuring element.
- `dist()` : Distance transform.
- `drawv()` : Superpose points, rectangles and lines on an image.
- `edgeoff()` : Eliminate the objects that hit the image frame.
- `endpoints()` : Interval to detect end-points.
- `erode()` : Erode an image by a structuring element.
- `flood()` : Flooding filter- h,v,a-basin and dynamics (depth, area, volume)
- `frame()` : Create a frame image.
- `freedom()` : Control automatic data type conversion.
- `gdist()` : Geodesic Distance Transform.
- `gradm()` : Morphological gradient.
- `grain()` : Gray-scale statistics for each labeled region.
- `gray()` : Convert a binary image into a gray-scale image.
- `gshow()` : Apply binary overlays as color layers on a binary or gray-scale image
- `histogram()` : Find the histogram of the image f.
- `hmax()` : Remove peaks with contrast less than h.
- `hmin()` : Remove basins with contrast less than h.
- `homothick()` : Interval for homotopic thickening.
- `homothin()` : Interval for homotopic thinning.
- `img2se()` : Create a structuring element from a pair of images.
- `infcanon()` : Intersection of inf-generating operators.
- `infgen()` : Inf-generating.
- `infrec()` : Inf-reconstruction.
- `inpos()` : Minima imposition.
- `interot()` : Rotate an interval
- `intersec()` : Intersection of images.
- `intershow()` : Visualize an interval.
- `isbinary()` : Check for binary image
- `isolines()` : Apply an iso-line color table to a gray-scale image.
- `label()` : Label a binary image.
- `labelflat()` : Label the flat zones of gray-scale images.
- `lastero()` : Last erosion.
- `lblshow()` : Display a labeled image assigning a random color for each label.
- `limits()` : Get the possible minimum and maximum of an image.
- `mat2set()` : Converts image representation from matrix to set
- `maxleveltype()` : Returns the maximum value associated to an image datatype
- `neg()` : Negate an image.
- `open()` : Morphological opening.
- `openrec()` : Opening by reconstruction.
- `openrecth()` : Open-by-Reconstruction Top-Hat.
- `openth()` : Opening Top Hat.
- `opentransf()` : Open transform.
- `pad4n()` : pad4n
- `patspec()` : Pattern spectrum (also known as granulometric size density).
- `plot()` : Plot a function.
- `randomcolor()` : Apply a random color table to a gray-scale image.
- `regmax()` : Regional Maximum.
- `regmin()` : Regional Minimum (with generalized dynamics).
- `se2hmt()` : Create a Hit-or-Miss Template (or interval) from a pair of structuring elements.
- `se2interval()` : Create an interval from a pair of structuring elements.
- `sebox()` : Create a box structuring element.
- `secross()` : Diamond structuring element and elementary 3x3 cross.
- `sedilate()` : Dilate one structuring element by another
- `sedisk()` : Create a disk or a semi-sphere structuring element.
- `seline()` : Create a line structuring element.
- `sereflect()` : Reflect a structuring element
- `serot()` : Rotate a structuring element.
- `seshow()` : Display a structuring element as an image.
- `sesum()` : N-1 iterative Minkowski additions
- `set2mat()` : Converts image representation from set to matrix
- `setrans()` : Translate a structuring element
- `seunion()` : Union of structuring elements
- `skelm()` : Morphological skeleton (Medial Axis Transform).
- `skelmrec()` : Morphological skeleton reconstruction (Inverse Medial Axis Transform).
- `skiz()` : Skeleton of Influence Zone - also know as Generalized Voronoi Diagram
- `subm()` : Subtraction of two images, with saturation.
- `supcanon()` : Union of sup-generating or hit-miss operators.
- `supgen()` : Sup-generating (hit-miss).
- `suprec()` : Sup-reconstruction.
- `symdiff()` : Symmetric difference between two images
- `text()` : Create a binary image of a text.
- `thick()` : Image transformation by thickening.
- `thin()` : Image transformation by thinning.
- `threshad()` : Threshold (adaptive)
- `toggle()` : Image contrast enhancement or classification by the toggle operator.
- `union()` : Union of images.
- `watershed()` : Watershed detection.
- `to_int32()` : Convert an image to an int32 image.
- `to_uint16()` : Convert an image to a uint16 image.
- `to_uint8()` : Convert an image to an uint8 image.
""" |
"""
:mod:`django-email-from-template` --- send emails generated entirely from Django templates
===========================================================================================
``email_from_template`` generates and sends mail defined in Django templates to
avoid presentation layer violations. It has the following features:
* HTML email support
* Context processor system
* Support for non-Django template rendering systems
Whilst Django provides a comprehensive mail framework that simplifies the
sending mechanics of email, the typical use of it is often ugly and results in
unnecessary and complicated string formatting inside views::
from django.core.mail import send_mail
from django.core.urlresolvers import reverse
from django.contrib.sites.models import Site
# Shouldn't be in views.py
send_mail(
'Hi %s, %d %s written on your wall' % (
user.username,
num_posts > 1 and 'people have' or 'person has',
),
'Hi %s\\n\\nCheck out what they wrote here:\\n\\n %s%s\\n\\n' % (
user.username,
Site.objects.get_current(),url,
reverse('profile:view', args=(user.username,)),
),
'EMAIL',
[user.email],
fail_silently=False,
)
With :mod:`django-email-from-template`, you can relegate all this formatting to
the presentation layer as well as leverage any existing templatetags and
filters. First we define our template::
{% extends email_from_template %}
{% block subject %}
Hi {{ user.username }}, {{ num_posts }} {{ num_posts|pluralize:"person has,people have" }} written on your wall
{% endblock %}
{% block body %}
Hi {{ user.username }}.
Check out what they wrote here:
{{ site.url }}{% url profile:view user.username %}
{% endblock %}
We then simply call our template-aware version of ``send_mail`` with the
appropriate context::
from email_from_template import send_mail
send_mail([user.email], 'path/to/my_email.email', {
'user': user,
'num_posts': num_posts,
}, 'EMAIL')
Now your views are not cluttered with unnecessary presentation logic.
For HTML-enabled mail readers, we can optionally include suitable content
within a "html" block::
{% block html %}
<p>Hi <strong>{{ user.username }}</strong></p>
<p>Check out what they wrote here:</p>
<a href="{{ site.url }}{% url profile:view user.username %}">
{{ site.url }}{% url profile:view user.username %}
</a>
{% endblock %}
Context processors
------------------
The ``EMAIL_CONTEXT_PROCESSORS`` setting is a tuple of callables that return a
dictionary of items to merged into the email context. It is identical to the
functionality of Django's regular ``TEMPLATE_CONTEXT_PROCESSORS`` support
except that the callables do not take a request object.
By default, ``EMAIL_CONTEXT_PROCESSORS`` is set to::
(
'email_from_template.context_processors.debug',
'email_from_template.context_processors.django_settings',
)
``debug``
~~~~~~~~~
Module: ``email_from_template.context_processors.debug``
Enabled by default: ``True``
Sets ``debug`` in the template context to the value of ``settings.DEBUG``::
def debug():
from django.conf import settings
return {'debug': settings.DEBUG}
``django_settings``
~~~~~~~~~~~~~~~~~~~
Module: ``email_from_template.context_processors.django_settings``
Enabled by default: ``True``
Sets ``settings`` in the template context to the value of Django's settings
object, ``django.conf.settings``::
def django_settings():
from django.conf import settings
return {'settings': settings}
``site``
~~~~~~~~
Module: ``email_from_template.context_processors.site``
Enabled by default: ``False``
Sets ``site`` in the template context to the value of the current
``django.contrib.sites`` ``Site`` instance::
def site():
from django.contrib.sites.models import Site
return {'site': Site.objects.get_current()}
``i18n``
~~~~~~~~
Module: ``email_from_template.context_processors.i18n``
Enabled by default: ``False``
Includes ``LANGUAGES``, ``LANGUAGE_CODE`` and ``LANGUAGE_BIDI`` in the template
context. This email context processor is parallel to the
``django.core.context_processors.i18n`` template context processor::
def i18n():
from django.utils import translation
return {
'LANGUAGES': settings.LANGUAGES,
'LANGUAGE_CODE': translation.get_language(),
'LANGUAGE_BIDI': translation.get_language_bidi(),
}
Configuration
-------------
``EMAIL_CONTEXT_PROCESSORS``
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
A tuple of callables that return a dictionary of items to merged into the email
context. See the `Context processors` section for more details.
``EMAIL_RENDER_METHOD``
~~~~~~~~~~~~~~~~~~~~~~~
Default: ``django.template.loader.render_to_string``
Method to use to actually render templates. If you are using the
`Coffin <github.com/cdleary/coffin>`_ Jinja2 adaptor for Django,
you should set this ``coffin.template.loader.render_to_string``.
Installation
------------
Add ``email_from_template`` to your ``INSTALLED_APPS``::
INSTALLED_APPS = (
...
'email_from_template',
...
)
Links
-----
View/download code
https://github.com/playfire/django-email-from-template
File a bug
https://github.com/playfire/django-email-from-template/issues
""" |
"""Generic socket server classes.
This module tries to capture the various aspects of defining a server:
For socket-based servers:
- address family:
- AF_INET{,6}: IP (Internet Protocol) sockets (default)
- AF_UNIX: Unix domain sockets
- others, e.g. AF_DECNET are conceivable (see <socket.h>
- socket type:
- SOCK_STREAM (reliable stream, e.g. TCP)
- SOCK_DGRAM (datagrams, e.g. UDP)
For request-based servers (including socket-based):
- client address verification before further looking at the request
(This is actually a hook for any processing that needs to look
at the request before anything else, e.g. logging)
- how to handle multiple requests:
- synchronous (one request is handled at a time)
- forking (each request is handled by a new process)
- threading (each request is handled by a new thread)
The classes in this module favor the server type that is simplest to
write: a synchronous TCP/IP server. This is bad class design, but
save some typing. (There's also the issue that a deep class hierarchy
slows down method lookups.)
There are five classes in an inheritance diagram, four of which represent
synchronous servers of four types:
+------------+
| BaseServer |
+------------+
|
v
+-----------+ +------------------+
| TCPServer |------->| UnixStreamServer |
+-----------+ +------------------+
|
v
+-----------+ +--------------------+
| UDPServer |------->| UnixDatagramServer |
+-----------+ +--------------------+
Note that UnixDatagramServer derives from UDPServer, not from
UnixStreamServer -- the only difference between an IP and a Unix
stream server is the address family, which is simply repeated in both
unix server classes.
Forking and threading versions of each type of server can be created
using the ForkingMixIn and ThreadingMixIn mix-in classes. For
instance, a threading UDP server class is created as follows:
class ThreadingUDPServer(ThreadingMixIn, UDPServer): pass
The Mix-in class must come first, since it overrides a method defined
in UDPServer! Setting the various member variables also changes
the behavior of the underlying server mechanism.
To implement a service, you must derive a class from
BaseRequestHandler and redefine its handle() method. You can then run
various versions of the service by combining one of the server classes
with your request handler class.
The request handler class must be different for datagram or stream
services. This can be hidden by using the request handler
subclasses StreamRequestHandler or DatagramRequestHandler.
Of course, you still have to use your head!
For instance, it makes no sense to use a forking server if the service
contains state in memory that can be modified by requests (since the
modifications in the child process would never reach the initial state
kept in the parent process and passed to each child). In this case,
you can use a threading server, but you will probably have to use
locks to avoid two requests that come in nearly simultaneous to apply
conflicting changes to the server state.
On the other hand, if you are building e.g. an HTTP server, where all
data is stored externally (e.g. in the file system), a synchronous
class will essentially render the service "deaf" while one request is
being handled -- which may be for a very long time if a client is slow
to read all the data it has requested. Here a threading or forking
server is appropriate.
In some cases, it may be appropriate to process part of a request
synchronously, but to finish processing in a forked child depending on
the request data. This can be implemented by using a synchronous
server and doing an explicit fork in the request handler class
handle() method.
Another approach to handling multiple simultaneous requests in an
environment that supports neither threads nor fork (or where these are
too expensive or inappropriate for the service) is to maintain an
explicit table of partially finished requests and to use a selector to
decide which request to work on next (or whether to handle a new
incoming request). This is particularly important for stream services
where each client can potentially be connected for a long time (if
threads or subprocesses cannot be used).
Future work:
- Standard classes for Sun RPC (which uses either UDP or TCP)
- Standard mix-in classes to implement various authentication
and encryption schemes
XXX Open problems:
- What to do with out-of-band data?
BaseServer:
- split generic "request" functionality out into BaseServer class.
Copyright (C) 2000 NAME <EMAIL>
example: read entries from a SQL database (requires overriding
get_request() to return a table entry from the database).
entry is processed by a RequestHandlerClass.
""" |
"""
===================
Universal Functions
===================
Ufuncs are, generally speaking, mathematical functions or operations that are
applied element-by-element to the contents of an array. That is, the result
in each output array element only depends on the value in the corresponding
input array (or arrays) and on no other array elements. Numpy comes with a
large suite of ufuncs, and scipy extends that suite substantially. The simplest
example is the addition operator: ::
>>> np.array([0,2,3,4]) + np.array([1,1,-1,2])
array([1, 3, 2, 6])
The unfunc module lists all the available ufuncs in numpy. Additional ufuncts
available in xxx in scipy. Documentation on the specific ufuncs may be found
in those modules. This documentation is intended to address the more general
aspects of unfuncs common to most of them. All of the ufuncs that make use of
Python operators (e.g., +, -, etc.) have equivalent functions defined
(e.g. add() for +)
Type coercion
=============
What happens when a binary operator (e.g., +,-,\\*,/, etc) deals with arrays of
two different types? What is the type of the result? Typically, the result is
the higher of the two types. For example: ::
float32 + float64 -> float64
int8 + int32 -> int32
int16 + float32 -> float32
float32 + complex64 -> complex64
There are some less obvious cases generally involving mixes of types
(e.g. uints, ints and floats) where equal bit sizes for each are not
capable of saving all the information in a different type of equivalent
bit size. Some examples are int32 vs float32 or uint32 vs int32.
Generally, the result is the higher type of larger size than both
(if available). So: ::
int32 + float32 -> float64
uint32 + int32 -> int64
Finally, the type coercion behavior when expressions involve Python
scalars is different than that seen for arrays. Since Python has a
limited number of types, combining a Python int with a dtype=np.int8
array does not coerce to the higher type but instead, the type of the
array prevails. So the rules for Python scalars combined with arrays is
that the result will be that of the array equivalent the Python scalar
if the Python scalar is of a higher 'kind' than the array (e.g., float
vs. int), otherwise the resultant type will be that of the array.
For example: ::
Python int + int8 -> int8
Python float + int8 -> float64
ufunc methods
=============
Binary ufuncs support 4 methods. These methods are explained in detail in xxx
(or are they, I don't see anything in the ufunc docstring that is useful?).
**.reduce(arr)** applies the binary operator to elements of the array in sequence. For example: ::
>>> np.add.reduce(np.arange(10)) # adds all elements of array
45
For multidimensional arrays, the first dimension is reduced by default: ::
>>> np.add.reduce(np.arange(10).reshape(2,5))
array([ 5, 7, 9, 11, 13])
The axis keyword can be used to specify different axes to reduce: ::
>>> np.add.reduce(np.arange(10).reshape(2,5),axis=1)
array([10, 35])
**.accumulate(arr)** applies the binary operator and generates an an equivalently
shaped array that includes the accumulated amount for each element of the
array. A couple examples: ::
>>> np.add.accumulate(np.arange(10))
array([ 0, 1, 3, 6, 10, 15, 21, 28, 36, 45])
>>> np.multiply.accumulate(np.arange(1,9))
array([ 1, 2, 6, 24, 120, 720, 5040, 40320])
The behavior for multidimensional arrays is the same as for .reduce(), as is the use of the axis keyword).
**.reduceat(arr,indices)** allows one to apply reduce to selected parts of an array.
It is a difficult method to understand. See the documentation at:
**.outer(arr1,arr2)** generates an outer operation on the two arrays arr1 and arr2. It will work on multidimensional arrays (the shape of the result is the
concatenation of the two input shapes.: ::
>>> np.multiply.outer(np.arange(3),np.arange(4))
array([[0, 0, 0, 0],
[0, 1, 2, 3],
[0, 2, 4, 6]])
Output arguments
================
All ufuncs accept an optional output array. The array must be of the expected output shape. Beware that if the type of the output array is of a
different (and lower) type than the output result, the results may be silently
truncated or otherwise corrupted in the downcast to the lower type. This usage
is useful when one wants to avoid creating large temporary arrays and instead
allows one to reuse the same array memory repeatedly (at the expense of not
being able to use more convenient operator notation in expressions). Note that
when the output argument is used, the ufunc still returns a reference to the
result.
>>> x = np.arange(2)
>>> np.add(np.arange(2),np.arange(2.),x)
array([0, 2])
>>> x
array([0, 2])
and & or as ufuncs
==================
Invariably people try to use the python 'and' and 'or' as logical operators
(and quite understandably). But these operators do not behave as normal
operators since Python treats these quite differently. They cannot be
overloaded with array equivalents. Thus using 'and' or 'or' with an array
results in an error. There are two alternatives:
1) use the ufunc functions logical_and() and logical_or().
2) use the bitwise operators & and \\|. The drawback of these is that if
the arguments to these operators are not boolean arrays, the result is
likely incorrect. On the other hand, most usages of logical_and and
logical_or are with boolean arrays. As long as one is careful, this is
a convenient way to apply these operators.
""" |
"""
This module contains generic generator functions for traversing tree
(and DAG) structures. It is agnostic to the underlying data structure
and implementation of the tree object. It does this through dependency
injection of the tree's accessor functions: get_parents and
get_children.
The following depth-first traversal methods are implemented:
* Pre-order: Parent yielded before children; child with multiple
parents is yielded when first encountered.
Example use cases (when DAGs are *not* supported):
1. User access. If computing a user's access to a node relies
on the user's access to the node's parents, access to the
parent has to be computed before access to the child can
be determined. To support access chains, a user's access on
a node is actually an accumulation of accesses down from the
root node through the ancestor chain to the actual node.
2. Field value percolated down. If a value for a field is
dependent on a combination of the child's and the parent's
value, the parent's value should be computed before that of
the child's. Similar to "User access", the value would be
percolated down through the entire ancestor chain.
Example: Start Date is
max(node's start date, start date of each ancestor)
This takes the most restrictive value.
3. Depth. When computing the depth of a tree, since a child's
depth value is 1 + the parent's depth value, the parent's
value should be computed before the child's.
4. Fast Subtree Deletion. If the tree is to be pruned during
traversal, an entire subtree can be deleted, without
traversing the children, as soon as the parent is determined
to be deleted.
* Topological: Parent yielded before children; child with multiple
parents yielded only after all its parents are visited.
Example use cases (when DAGs *are* supported):
1. User access. Similar to pre-order, except a user's access
is now determined by taking a *union* of the percolated
access value from each of the node's parents combined with
its own access.
2. Field value percolated down. Similar to pre-order, except the
value for a node is calculated from the array of
percolated values from each of its parents combined
with its own.
Example: Start Date is
max(node's start date, min(max(ancestry of each parent))
This takes the most permissive from all ancestry chains.
3. Depth. Similar to pre-order, except the depth of a node will
be 1 + the minimum (or the maximum depending on semantics)
of the depth of all its parents.
4. Deletion. Deletion of subtrees are not as fast as they are
for pre-order since a node can be accessed through multiple
parents.
* Post-order: Children yielded before its parents.
Example use cases:
1. Counting. When each node wants to count the number of nodes
within its sub-structure, the count for each child has to be
calculated before its parents, since a parent's value
depends on its children.
2. Map function (when order doesn't matter). If a function
needs to be evaluated for each node in a DAG and the order
that the nodes are iterated doesn't matter, then use
post-order since it is faster than topological for DAGs.
3. Field value percolated up. If a value for a field is based
on the value from it's children, the children's values need
to be computed before their parents.
Example: Minimum Due Date of all nodes within the
sub-structure.
Note: In-order traversal is not implemented as of yet. We can do so
if/when needed.
Optimization once DAGs are not supported:
Supporting Directed Acyclic Graphs (DAGs) requires us to use
topological sort, which has the following negative performance
implications:
* For a simple tree, we can immediately skip over traversing
descendants, once it is determined that a parent is not to be yielded
(based on the return value from the 'filter_func' function). However,
since we support DAGs, we cannot simply skip over descendants since
they may still be accessible through a different ancestry chain and
need to be revisited once all their parents are visited.
* For topological sort, we need the get_parents accessor function in
order to determine whether all of a node's parents have been visited.
This means the underlying implementation of the graph needs to have
an efficient way to get a node's parents, perhaps with back pointers
to each node's parents. This requires additional storage space, which
could be eliminated if DAGs are not supported.
""" |
"""
This module provides a decorator function for observing changes in a given
property. Internally the decorator is implemented using SQLAlchemy event
listeners. Both column properties and relationship properties can be observed.
Property observers can be used for pre-calculating aggregates and automatic
real-time data denormalization.
Simple observers
----------------
At the heart of the observer extension is the :func:`observes` decorator. You
mark some property path as being observed and the marked method will get
notified when any changes are made to given path.
Consider the following model structure:
::
class Director(Base):
__tablename__ = 'director'
id = sa.Column(sa.Integer, primary_key=True)
name = sa.Column(sa.String)
date_of_birth = sa.Column(sa.Date)
class Movie(Base):
__tablename__ = 'movie'
id = sa.Column(sa.Integer, primary_key=True)
name = sa.Column(sa.String)
director_id = sa.Column(sa.Integer, sa.ForeignKey(Director.id))
director = sa.orm.relationship(Director, backref='movies')
Now consider we want to show movies in some listing ordered by director id
first and movie id secondly. If we have many movies then using joins and
ordering by Director.name will be very slow. Here is where denormalization
and :func:`observes` comes to rescue the day. Let's add a new column called
director_name to Movie which will get automatically copied from associated
Director.
::
from sqlalchemy_utils import observes
class Movie(Base):
# same as before..
director_name = sa.Column(sa.String)
@observes('director')
def director_observer(self, director):
self.director_name = director.name
.. note::
This example could be done much more efficiently using a compound foreign
key from director_name, director_id to Director.name, Director.id but for
the sake of simplicity we added this as an example.
Observes vs aggregated
----------------------
:func:`observes` and :func:`.aggregates.aggregated` can be used for similar
things. However performance wise you should take the following things into
consideration:
* :func:`observes` works always inside transaction and deals with objects. If
the relationship observer is observing has a large number of objects it's
better to use :func:`.aggregates.aggregated`.
* :func:`.aggregates.aggregated` always executes one additional query per
aggregate so in scenarios where the observed relationship has only a handful
of objects it's better to use :func:`observes` instead.
Example 1. Movie with many ratings
Let's say we have a Movie object with potentially thousands of ratings. In this
case we should always use :func:`.aggregates.aggregated` since iterating
through thousands of objects is slow and very memory consuming.
Example 2. Product with denormalized catalog name
Each product belongs to one catalog. Here it is natural to use :func:`observes`
for data denormalization.
Deeply nested observing
-----------------------
Consider the following model structure where Catalog has many Categories and
Category has many Products.
::
class Catalog(Base):
__tablename__ = 'catalog'
id = sa.Column(sa.Integer, primary_key=True)
product_count = sa.Column(sa.Integer, default=0)
@observes('categories.products')
def product_observer(self, products):
self.product_count = len(products)
categories = sa.orm.relationship('Category', backref='catalog')
class Category(Base):
__tablename__ = 'category'
id = sa.Column(sa.Integer, primary_key=True)
catalog_id = sa.Column(sa.Integer, sa.ForeignKey('catalog.id'))
products = sa.orm.relationship('Product', backref='category')
class Product(Base):
__tablename__ = 'product'
id = sa.Column(sa.Integer, primary_key=True)
price = sa.Column(sa.Numeric)
category_id = sa.Column(sa.Integer, sa.ForeignKey('category.id'))
:func:`observes` is smart enough to:
* Notify catalog objects of any changes in associated Product objects
* Notify catalog objects of any changes in Category objects that affect
products (for example if Category gets deleted, or a new Category is added to
Catalog with any number of Products)
::
category = Category(
products=[Product(), Product()]
)
category2 = Category(
product=[Product()]
)
catalog = Catalog(
categories=[category, category2]
)
session.add(catalog)
session.commit()
catalog.product_count # 2
session.delete(category)
session.commit()
catalog.product_count # 1
""" |
# # Copyright (c) 2013, Web Notes Technologies Pvt. Ltd. and Contributors
# # MIT License. See license.txt
# # For license information, please see license.txt
# from __future__ import unicode_literals
# import webnotes
# from webnotes.utils import cstr, cint, flt, comma_or, nowdate, get_base_path,today
# import barcode
# import os
# from webnotes import msgprint, _
# from datetime import date
# from webnotes.model.doc import Document, make_autoname
# from selling.doctype.customer.customer import DocType
# from selling.doctype.lead.lead import create_contact
# class DocType:
# def __init__(self, d, dl):
# self.doc, self.doclist = d, dl
# def test_data(self):
# webnotes.errprint("asd")
# def autoname(self):
# #key = 'AA'
# key = webnotes.conn.get_value("LocGlobKey", None, "key")
# curr = webnotes.conn.get_value('Series','A'+str(date.today().year)[-2:]+key,'current')
# if cint(curr)==99:
# key1 = key[0]
# key2 = key[1]
# key2 = key2.replace(key2,chr(ord(key2)+1))
# key = key1 + key2
# webnotes.conn.set_value("LocGlobKey", "LocGlobKey", "key", key)
# self.doc.patient_local_id = make_autoname('A'+str(date.today().year)[-2:]+key+'.##')
# self.doc.name = self.doc.patient_local_id
# #if(self.doc.name):
# # self.doc.patient_online_id=cstr(webnotes.conn.sql("select abbr from tabCompany where name=%s", self.doc.company)[0][0])+"/"+cstr(self.doc.lab_branch)+"/"+cstr(self.doc.name)
# dt=today()
# ss="C"+cstr(dt[2:4]+cstr(dt[5:7]))+self.doc.lab_branch[1:]+"-"+key+"-"+''
# key="GID.##"
# n = ''
# l = key.split('.')
# series_set = False
# doctype=''
# for e in l:
# en = ''
# if e.startswith('#'):
# if not series_set:
# digits = len(e)
# en = self.getseries(n, digits, doctype)
# series_set = True
# else: en = e
# n+=en
# # webnotes.errprint(n[3:])
# # webnotes.errprint(ss+n[3:])
# self.doc.patient_online_id=ss+n[3:]
# def getseries(self,key, digits, doctype=''):
# current = webnotes.conn.sql("select `current` from `tabSeries` where name='GID' for update")
# if current and current[0][0] is not None:
# current = current[0][0]
# webnotes.conn.sql("update tabSeries set current = current+1 where name='GID'")
# current = cint(current) + 1
# else:
# webnotes.conn.sql("insert into tabSeries (name, current) values (GID, 1)")
# current = 1
# return ('%0'+str(digits)+'d') % current
# def on_update(self):
# #lag = webnotes.conn.sql("select ifnull(name,'') from tabProfile where name='"+self.doc.email+"'",as_list=1,debug=1)
# self.check_valid_priority()
# check_name=webnotes.conn.sql("select name from `tabCustomer` where name='"+self.doc.name+"'",as_list=1,debug=1)
# webnotes.errprint(['name',check_name])
# if not check_name:
# self.doc.master_type = "Patient Register"
# cust = self.create_customer()
# self.create_account_head(cust)
# #self.create_customer()
# if self.doc.flag=='false':
# self.create_profile()
# self.generate_barcode()
# #self.validate()
# self.create_new_contact()
# a=webnotes.conn.sql("select name from `tabEncounter` where parent='"+self.doc.name+"'",as_list=1)
# if not a:
# webnotes.errprint("hii uygsiuc sdfuksghfui")
# self.create_patient_encounter_entry()
# self.doc.flag='True'
# self.doc.save()
# def create_new_contact(self):
# details = {}
# details['first_name'] = self.doc.first_name
# details['email_id'] = self.doc.email or ''
# details['mobile_no'] = self.doc.mobile or ''
# details['link'] = self.doc.name
# details['doc'] = 'Customer'
# create_contact(details)
# def check_valid_priority(self):
# i=1
# p=s=t=0
# from webnotes.model.bean import getlist
# for d in getlist(self.doclist, 'insurance_table'):
# webnotes.errprint(d.length)
# if d.priority=='Primary ':
# p=p+1
# elif d.priority=='Secondary':
# s+=1
# elif d.priority=='Ternary':
# t+=1
# if(p>1 or s>1 or t>1):
# webnotes.msgprint(("Duplicate entry found for priority in table insurance profile at row no '"+cstr(i)+"'."), raise_exception=1)
# i+=1
# if i>6 :
# webnotes.msgprint(("Maximum 5 'Insurence Profiles' can be entered. Please remove extra entry(ies)"),raise_exception=1)
# def create_customer(self):
# webnotes.errprint('customer creation starts')
# from webnotes.model.doc import Document
# d = Document('Customer')
# d.customer_name = self.doc.name
# d.gender = self.doc.gender
# d.full_name = self.doc.first_name
# d.save()
# return d.name
# def create_account_head(self, cust):
# if self.doc.company :
# abbr = webnotes.conn.get_value('Company', self.doc.company, 'abbr')
# if not webnotes.conn.sql("select name from tabAccount where name=%s", (self.doc.name + " - " + abbr)):
# ac_bean = webnotes.bean({
# "doctype": "Account",
# 'account_name': cust,
# 'parent_account': "Accounts Receivable - " + abbr,
# 'group_or_ledger':'Ledger',
# 'company': self.doc.company,
# 'account_type': '',
# 'tax_rate': '0',
# 'master_type': 'Patient Register',
# 'master_name': self.doc.name,
# "freeze_account": "No"
# })
# ac_bean.ignore_permissions = True
# ac_bean.insert()
# webnotes.msgprint(_("Created Account Head: ") + ac_bean.doc.name)
# else :
# webnotes.msgprint("Please select Company under which you want to create account head")
# def create_profile(self):
# profile = webnotes.bean({
# "doctype":"Profile",
# "email": self.doc.email,
# "number": self.doc.mobile,
# "middle_name": self.doc.patient_online_id,
# "first_name": self.doc.first_name,
# "user_image":self.doc.user_image,
# "enabled": 1,
# "user_type": "Customer"
# })
# profile.ignore_permissions = True
# profile.insert()
# self.role_match_cond()
# def role_match_cond(self):
# ur=Document('UserRole')
# ur.parent=self.doc.patient_online_id
# ur.parentfield='user_roles'
# ur.parenttype='Profile'
# ur.role='Patient'
# ur.save(new=1)
# dv=Document('DefaultValue')
# dv.parent=self.doc.patient_online_id
# dv.parentfield='system_defaults'
# dv.parenttype='Control Panel'
# dv.defkey='patient'
# dv.defvalue=self.doc.name
# dv.save(new=1)
# dv=Document('DefaultValue')
# dv.parent=self.doc.patient_online_id
# dv.parentfield='system_defaults'
# dv.parenttype='Control Panel'
# dv.defkey='patient_id'
# dv.defvalue=self.doc.name
# dv.save(new=1)
# def generate_barcode(self):
# webnotes.errprint([self.doc.naming_series])
# # self.doc.patient_online_id=self.doc.name
# # from barcode.writer import ImageWriter
# # ean = barcode.get('code39','123322ABS232')
# # webnotes.errprint(ean)
# # path = os.path.join(get_base_path(), "public", "barcode_img")+"/"+self.doc.name
# # fullname = ean.save(path)
# # barcode_img = '<html>\
# # <table style="width: 100%; table-layout: fixed;">\
# # <tr>\
# # <td style="width:510px">\
# # <img src="'"/barcode_img/"+self.doc.name+".png"'" width="200px">\
# # </td>\
# # </tr>\
# # </table>\
# # </html>'
# #s="23232ASA343222"
# s=self.doc.name
# import barcode
# from barcode.writer import ImageWriter
# ean = barcode.get('code39', s, writer=ImageWriter())
# path = os.path.join(get_base_path(), "public", "barcode_img")+"/"+s
# filename = ean.save(path)
# barcode_img = '<html>\
# <table style="width: 100%; table-layout: fixed;">\
# <tr>\
# <td style="width:510px">\
# <img src="'"../barcode_img/"+s+".png"'" width="200px">\
# </td>\
# </tr>\
# </table>\
# </html>'
# self.doc.barcode_image = barcode_img
# self.doc.save()
# def create_patient_encounter_entry(self):
# from webnotes.model.bean import getlist
# for encounter in getlist(self.doclist,'encounter_table'):
# if encounter:
# enct = Document('Patient Encounter Entry')
# enct.encounter = encounter.encounter
# enct.encounter_date = encounter.encounter_date
# enct.radiologist_name = encounter.radiologist_name
# enct.referrer_name = encounter.referrer_name
# enct.problem_description = encounter.problem_description
# enct.metal_in = encounter.metal_in
# enct.pacemaker = encounter.pacemaker
# enct.claustrophobia = encounter.claustrophobia
# enct.pregnancy = encounter.pregnancy
# enct.others = encounter.others
# enct.procedure_alert = encounter.procedure_alert
# enct.patient = encounter.parent
# enct.entry_in_child = 'True'
# enct.save()
# webnotes.conn.sql("update tabEncounter set id = '%s' where name = '%s'"%(enct.name,encounter.name))
# Copyright (c) 2013, Web Notes Technologies Pvt. Ltd. and Contributors
# MIT License. See license.txt
# For license information, please see license.txt
|
"""
[2016-01-27] Challenge #251 [Hard] Solve a Nonogram + Bonus
https://www.reddit.com/r/dailyprogrammer/comments/42x90t/20160127_challenge_251_hard_solve_a_nonogram_bonus/
#Description
This week we are doing a challenge involving [Nonograms](https://en.wikipedia.org/wiki/Nonogram)
It is going to be a three parter:
* [Create Nonogram description
([Easy])](https://www.reddit.com/r/dailyprogrammer/comments/42lhem/20160125_challenge_251_easy_create_nonogram/)
* [Solve Nonogram
([Intermediate/Hard])](https://www.reddit.com/r/dailyprogrammer/comments/42x90t/20160127_challenge_251_hard_solve_a_nonogram_bonus/
* Working with multiple colors/characters ([Hard])
* [Bonus: Make it an interactive game
([Intermediate])](https://www.reddit.com/r/dailyprogrammer/comments/42x90t/20160127_challenge_251_hard_solve_a_nonogram_bonus/
##What is a Nonogram?
> Nonograms, also known as Hanjie, Picross or Griddlers, are picture logic puzzles in which cells in a grid must be
colored or left blank according to numbers at the side of the grid to reveal a hidden picture. In this puzzle type, the
numbers are a form of discrete tomography that measures how many unbroken lines of filled-in squares there are in any
given row or column.
In a Nonogram you are given the number of elements in the rows and columns. A row/column where containing no element
has a '0' all other rows/columns will have at least one number.
Each number in a row/column represent sets of elements next to each other.
If a row/column have multiple sets, the declaration of that row/column will have multiple numbers. These sets will
always be at least 1 cell apart.
*An example*
| | |2|1|1| |
---|---|----|----|----|----|----
| |1|1|1|2|1
|2| |*|*| |
1|2| |*| |*|*
|0| | | | |
2|1|*|*| |*|
|2| | |*|*|
#Formal Inputs & Outputs
##Input description
Today you will recieve the columns and rows of a Nonogram seperated by a `-`
0 0 1 1 0
1 2 1 1 5
-
0 1
0 2
1 1
1 1
0 5
##Output description
The Nonogram solved like this:
*
**
* *
* *
*****
##Ins
*1*
0 0 1 1 0
1 2 1 1 5
-
0 1
0 2
1 1
1 1
0 5
*2*
0 0 0 0 0 0 4 0 0 0
0 0 3 4 5 5 2 5 0 0
1 7 1 4 4 1 1 1 7 1
-
0 0 2 1
0 0 0 5
0 0 0 6
0 0 0 8
0 0 0 10
0 0 1 1
1 2 1 1
1 2 1 1
0 1 2 1
0 0 0 8
*3*
0 0 2 0 0 0 1 0 0 0 0 0 0 0 0
0 0 3 6 0 0 4 2 0 0 1 1 1 1 0
1 10 1 2 6 15 8 9 14 8 6 10 10 11 12
-
0 0 0 3
0 0 4 2
0 0 6 6
1 4 2 1
0 6 3 2
0 0 6 7
0 0 6 8
0 0 1 10
0 0 1 10
0 0 1 10
1 1 4 4
0 3 4 4
0 0 4 4
0 0 4 4
0 0 4 4
##Notes/hints
This is a hard challenge. In the [wikipage](https://en.wikipedia.org/wiki/Nonogram) you'll find ways to find what cell
you can fill and how you can exclude cells.
#Bonus challenge
Use the inputs and output from the first challenge [Create Nonogram description
([Easy])](https://www.reddit.com/r/dailyprogrammer/comments/42lhem/20160125_challenge_251_easy_create_nonogram/) to
create a game.
Create the nonogram description fron a library (the inputs) and let the user choose a difficulty:
* Easy, the user can keep on playing, even if he makes wrong calls
* Normal, give the user some 'lives'. Everytime the user gives an incorrect guess, she/he loses a life. I would say
the user would have about number of colums added up to the number of rows lives.
* Hard, the user can't make any mistake
Now make it something beautifull, or at least playable
#Finally
Have a good challenge idea?
Consider submitting it to /r/dailyprogrammer_ideas
""" |
"""
<Program Name>
depdata.py
<Purpose>
This module houses the globals to be used by resolvers and the scraper.
Data is harvested by the scraper (scrape_deps_and_detect_conflicts) into
formats described here.
This module also contains a variety of functions for dealing with that data.
I've made sample data - already crunched in the formats below for all PyPI
packages current to late 2015 - available at:
https://www.dropbox.com/sh/2x870eosiknww68/AAArQBivh2jlu6auqNLHsm1Ja?dl=0
You can pull it from dropbox at the link provided or download all of it
(52MB zipped) via shell like so:
> curl -L -o dep_data.zip https://www.dropbox.com/sh/2x870eosiknww68/AAArQBivh2jlu6auqNLHsm1Ja?dl=1
> unzip dep_data.zip
<Data Specification>
distkey (distribution key):
A distkey is the unique identifier we use for a distribution, being a
particular concatenation of the package name and version string, separated
by parentheses.
Examples:
django(1.8.3) version 1.8.3 of package 'django'
foo(1.0b3) version 1.0b3 (1.0 beta 3) of package 'foo'
We expect version strings to be compatible with the Version or
LegacyVersion classes defined in pip._vendor.packaging.version. In
practice, anything that works for pip should work for us. Given a string
version_string, pip._vendor.packaging.version.parse(version_string) should
not raise pip._vendor.packaging.version.InvalidVersion.
Package names are less rigorously constrained, but should be all lowercase
and employ '-' rather than '_'. Again, what works in pip should work here,
except for casing, where we are stricter (all lowercase for package names
and version numbers.
I'm also less thorough about not accepting special characters in distkeys
than pip likely is.
(TODO: Point to pip's specification.)
dep (dependency):
A dependency takes the form of the two-member list, the first member being
the name of the package depended on, and the second member being a
requirement or specifier string. Such strings should match the
specifications of pip._vendor.packaging.version.Specifier. The format is
also documented here:
https://pip.pypa.io/en/stable/reference/pip_install/#requirement-specifiers
In practice, feeding string x to
pip._vendor.packaging.version.SpecifierSet(x) should not result in an
error. Generally, if pip understands a specifier string, so should we.
examples:
['pymongo', '==2.5'] # a dependency on pymongo version 2.5
['six', ''] # dependency on any version of six
['foo', '<5.0.1'] # dep on any ver of foo under 5.0.1
['bar', '>=6.0,!=6.2.1,<8.0'] # ver >= 6, less than 8, and not 6.2.1
deps (dependencies dictionary):
This is often 'deps' or 'dependencies_by_dist' in the code.
The data format we use for dependency info, which I'll generally refer to
as 'deps', is a dictionary with keys being distkeys (e.g. 'django(1.8.3)').
The value associated with each distkey in the dictionary is a list of
individual dependencies, each dependency being the length-two list 'dep'
format above.
e.g., here is a deps dictionary:
{'motorengine(0.7.4)': # distribution motorengine 0.7.4
[ ['pymongo', '==2.5'], # depends on pymongo version 2.5
['tornado', ''], # and any version of tornado
['motor', ''], # and any version of motor
['six', ''], # and any version of six
['easydict', ''] # and any version of easydict
],
'django(1.8.3)': # version 1.8.3 of package django
[], # has no dependencies
'django(1.6.3)':
[],
'django(1.7)':
[],
'chembl-webservices(2.2.11)':
[ ['lxml', ''],
['pyyaml', '>=3.10'],
['defusedxml', '>=0.4.1'],
['simplejson', '==2.3.2'],
['pillow', '>=2.1.0'],
['django-tastypie', '==0.10'],
['chembl-core-model', '>=0.6.2'],
['cairocffi', '>=0.5.1'],
['numpy', '>=1.7.1'],
['mimeparse', ''],
['raven', '>=3.5.0],
['chembl-beaker', '>=0.5.34']
],
...
...
}
edep (elaborated dependency):
An elaborated dependency is a three-member list, essentially just deps
with an additional member between the two original members: the list of
available versions satisfying the dependency.
Example:
[
'foo', # str: depended-on package
['1.0', '1.1', '1.2', '1.2.5'], # list: all satisfying versions
'>=1,<1.3' # str: the specifier/requirement string
]
The additional list identifies a list of every specific version of a
depended-on package that would satisfy the depending package's dependency
on the depended-on package. (Mouthful!)
The specifier string is redundant but provided for convenience.
edeps (elaborated dependencies dictionary):
The similarly augmented version of deps.
Example:
{
'django(1.7)': [], # django 1.7 has no dependencies
'foo(1)': [ # version 1 of foo
'bar', # depends on package bar,
['1.0', '1.1', '3', '4.2.5b4'], # any of these available versions
'' # specifier was any version
],
'X(1.0)': [ # distribution X-1.0
['B', ['2.5'], '==2.5'], # depends on package B, version 2.5,
# which exists
['C', ['1', '2'], ''], # and version 1 or 2 of package C
# those being the only available versions of C
['D', ['1.9', '1.10'], '>=1.9,<1.10.3'] # and versions 1.9 or 1.10 of
# package D, as those are the
# only available versions that
# fit '>=1.9,<1.10.3'.
]
}
conflicts_db (dictionary of conflicting distributions)
A dictionary mapping distkey to boolean indicating whether or not a
dependency conflict exists for that distribution.
Stored as conflicts_1.json, conflicts_2.json, conflicts_3.json,
respectively for the associated conflict models (1, 2, or 3), defined in
README.md and docs/background.md.
Example:
{
'motorengine(0.7.2)': True,
'django(1.7.1)': False,
'foo(1)': False
}
List of functions provided in this module:
load_json_db
ensure_data_loaded
set_conflict_model_legacy
old_normalize_version_string
write_data_to_files
deps_are_equal
get_pack_and_version
get_packname
get_version
distkey_format
is_valid_distkey
get_distkey_from_dist
versions_are_equal
fix_deps_case
assume_dep_data_exists_for
is_dep_valid
are_deps_valid
normalize_distkey
normalize_package_name
normalize_version_string
old_normalize_version_string
spectuples_to_specset
spectuples_to_specstring
elaborate_dependencies
_elaborate_dependency
""" |
"""
Define a simple format for saving numpy arrays to disk with the full
information about them.
The ``.npy`` format is the standard binary file format in NumPy for
persisting a *single* arbitrary NumPy array on disk. The format stores all
of the shape and dtype information necessary to reconstruct the array
correctly even on another machine with a different architecture.
The format is designed to be as simple as possible while achieving
its limited goals.
The ``.npz`` format is the standard format for persisting *multiple* NumPy
arrays on disk. A ``.npz`` file is a zip file containing multiple ``.npy``
files, one for each array.
Capabilities
------------
- Can represent all NumPy arrays including nested record arrays and
object arrays.
- Represents the data in its native binary form.
- Supports Fortran-contiguous arrays directly.
- Stores all of the necessary information to reconstruct the array
including shape and dtype on a machine of a different
architecture. Both little-endian and big-endian arrays are
supported, and a file with little-endian numbers will yield
a little-endian array on any machine reading the file. The
types are described in terms of their actual sizes. For example,
if a machine with a 64-bit C "long int" writes out an array with
"long ints", a reading machine with 32-bit C "long ints" will yield
an array with 64-bit integers.
- Is straightforward to reverse engineer. Datasets often live longer than
the programs that created them. A competent developer should be
able to create a solution in their preferred programming language to
read most ``.npy`` files that he has been given without much
documentation.
- Allows memory-mapping of the data. See `open_memmep`.
- Can be read from a filelike stream object instead of an actual file.
- Stores object arrays, i.e. arrays containing elements that are arbitrary
Python objects. Files with object arrays are not to be mmapable, but
can be read and written to disk.
Limitations
-----------
- Arbitrary subclasses of numpy.ndarray are not completely preserved.
Subclasses will be accepted for writing, but only the array data will
be written out. A regular numpy.ndarray object will be created
upon reading the file.
.. warning::
Due to limitations in the interpretation of structured dtypes, dtypes
with fields with empty names will have the names replaced by 'f0', 'f1',
etc. Such arrays will not round-trip through the format entirely
accurately. The data is intact; only the field names will differ. We are
working on a fix for this. This fix will not require a change in the
file format. The arrays with such structures can still be saved and
restored, and the correct dtype may be restored by using the
``loadedarray.view(correct_dtype)`` method.
File extensions
---------------
We recommend using the ``.npy`` and ``.npz`` extensions for files saved
in this format. This is by no means a requirement; applications may wish
to use these file formats but use an extension specific to the
application. In the absence of an obvious alternative, however,
we suggest using ``.npy`` and ``.npz``.
Version numbering
-----------------
The version numbering of these formats is independent of NumPy version
numbering. If the format is upgraded, the code in `numpy.io` will still
be able to read and write Version 1.0 files.
Format Version 1.0
------------------
The first 6 bytes are a magic string: exactly ``\\x93NUMPY``.
The next 1 byte is an unsigned byte: the major version number of the file
format, e.g. ``\\x01``.
The next 1 byte is an unsigned byte: the minor version number of the file
format, e.g. ``\\x00``. Note: the version of the file format is not tied
to the version of the numpy package.
The next 2 bytes form a little-endian unsigned short int: the length of
the header data HEADER_LEN.
The next HEADER_LEN bytes form the header data describing the array's
format. It is an ASCII string which contains a Python literal expression
of a dictionary. It is terminated by a newline (``\\n``) and padded with
spaces (``\\x20``) to make the total length of
``magic string + 4 + HEADER_LEN`` be evenly divisible by 16 for alignment
purposes.
The dictionary contains three keys:
"descr" : dtype.descr
An object that can be passed as an argument to the `numpy.dtype`
constructor to create the array's dtype.
"fortran_order" : bool
Whether the array data is Fortran-contiguous or not. Since
Fortran-contiguous arrays are a common form of non-C-contiguity,
we allow them to be written directly to disk for efficiency.
"shape" : tuple of int
The shape of the array.
For repeatability and readability, the dictionary keys are sorted in
alphabetic order. This is for convenience only. A writer SHOULD implement
this if possible. A reader MUST NOT depend on this.
Following the header comes the array data. If the dtype contains Python
objects (i.e. ``dtype.hasobject is True``), then the data is a Python
pickle of the array. Otherwise the data is the contiguous (either C-
or Fortran-, depending on ``fortran_order``) bytes of the array.
Consumers can figure out the number of bytes by multiplying the number
of elements given by the shape (noting that ``shape=()`` means there is
1 element) by ``dtype.itemsize``.
Format Version 2.0
------------------
The version 1.0 format only allowed the array header to have a total size of
65535 bytes. This can be exceeded by structured arrays with a large number of
columns. The version 2.0 format extends the header size to 4 GiB.
`numpy.save` will automatically save in 2.0 format if the data requires it,
else it will always use the more compatible 1.0 format.
The description of the fourth element of the header therefore has become:
"The next 4 bytes form a little-endian unsigned int: the length of the header
data HEADER_LEN."
Notes
-----
The ``.npy`` format, including reasons for creating it and a comparison of
alternatives, is described fully in the "npy-format" NEP.
""" |
"""CPStats, a package for collecting and reporting on program statistics.
Overview
========
Statistics about program operation are an invaluable monitoring and debugging
tool. Unfortunately, the gathering and reporting of these critical values is
usually ad-hoc. This package aims to add a centralized place for gathering
statistical performance data, a structure for recording that data which
provides for extrapolation of that data into more useful information,
and a method of serving that data to both human investigators and
monitoring software. Let's examine each of those in more detail.
Data Gathering
--------------
Just as Python's `logging` module provides a common importable for gathering
and sending messages, performance statistics would benefit from a similar
common mechanism, and one that does *not* require each package which wishes
to collect stats to import a third-party module. Therefore, we choose to
re-use the `logging` module by adding a `statistics` object to it.
That `logging.statistics` object is a nested dict. It is not a custom class,
because that would 1) require libraries and applications to import a third-
party module in order to participate, 2) inhibit innovation in extrapolation
approaches and in reporting tools, and 3) be slow. There are, however, some
specifications regarding the structure of the dict.
{
+----"SQLAlchemy": {
| "Inserts": 4389745,
| "Inserts per Second":
| lambda s: s["Inserts"] / (time() - s["Start"]),
| C +---"Table Statistics": {
| o | "widgets": {-----------+
N | l | "Rows": 1.3M, | Record
a | l | "Inserts": 400, |
m | e | },---------------------+
e | c | "froobles": {
s | t | "Rows": 7845,
p | i | "Inserts": 0,
a | o | },
c | n +---},
e | "Slow Queries":
| [{"Query": "SELECT * FROM widgets;",
| "Processing Time": 47.840923343,
| },
| ],
+----},
}
The `logging.statistics` dict has four levels. The topmost level is nothing
more than a set of names to introduce modularity, usually along the lines of
package names. If the SQLAlchemy project wanted to participate, for example,
it might populate the item `logging.statistics['SQLAlchemy']`, whose value
would be a second-layer dict we call a "namespace". Namespaces help multiple
packages to avoid collisions over key names, and make reports easier to read,
to boot. The maintainers of SQLAlchemy should feel free to use more than one
namespace if needed (such as 'SQLAlchemy ORM'). Note that there are no case
or other syntax constraints on the namespace names; they should be chosen
to be maximally readable by humans (neither too short nor too long).
Each namespace, then, is a dict of named statistical values, such as
'Requests/sec' or 'Uptime'. You should choose names which will look
good on a report: spaces and capitalization are just fine.
In addition to scalars, values in a namespace MAY be a (third-layer)
dict, or a list, called a "collection". For example, the CherryPy StatsTool
keeps track of what each request is doing (or has most recently done)
in a 'Requests' collection, where each key is a thread ID; each
value in the subdict MUST be a fourth dict (whew!) of statistical data about
each thread. We call each subdict in the collection a "record". Similarly,
the StatsTool also keeps a list of slow queries, where each record contains
data about each slow query, in order.
Values in a namespace or record may also be functions, which brings us to:
Extrapolation
-------------
The collection of statistical data needs to be fast, as close to unnoticeable
as possible to the host program. That requires us to minimize I/O, for example,
but in Python it also means we need to minimize function calls. So when you
are designing your namespace and record values, try to insert the most basic
scalar values you already have on hand.
When it comes time to report on the gathered data, however, we usually have
much more freedom in what we can calculate. Therefore, whenever reporting
tools (like the provided StatsPage CherryPy class) fetch the contents of
`logging.statistics` for reporting, they first call `extrapolate_statistics`
(passing the whole `statistics` dict as the only argument). This makes a
deep copy of the statistics dict so that the reporting tool can both iterate
over it and even change it without harming the original. But it also expands
any functions in the dict by calling them. For example, you might have a
'Current Time' entry in the namespace with the value "lambda scope: time.time()".
The "scope" parameter is the current namespace dict (or record, if we're
currently expanding one of those instead), allowing you access to existing
static entries. If you're truly evil, you can even modify more than one entry
at a time.
However, don't try to calculate an entry and then use its value in further
extrapolations; the order in which the functions are called is not guaranteed.
This can lead to a certain amount of duplicated work (or a redesign of your
schema), but that's better than complicating the spec.
After the whole thing has been extrapolated, it's time for:
Reporting
---------
The StatsPage class grabs the `logging.statistics` dict, extrapolates it all,
and then transforms it to HTML for easy viewing. Each namespace gets its own
header and attribute table, plus an extra table for each collection. This is
NOT part of the statistics specification; other tools can format how they like.
You can control which columns are output and how they are formatted by updating
StatsPage.formatting, which is a dict that mirrors the keys and nesting of
`logging.statistics`. The difference is that, instead of data values, it has
formatting values. Use None for a given key to indicate to the StatsPage that a
given column should not be output. Use a string with formatting (such as '%.3f')
to interpolate the value(s), or use a callable (such as lambda v: v.isoformat())
for more advanced formatting. Any entry which is not mentioned in the formatting
dict is output unchanged.
Monitoring
----------
Although the HTML output takes pains to assign unique id's to each <td> with
statistical data, you're probably better off fetching /cpstats/data, which
outputs the whole (extrapolated) `logging.statistics` dict in JSON format.
That is probably easier to parse, and doesn't have any formatting controls,
so you get the "original" data in a consistently-serialized format.
Note: there's no treatment yet for datetime objects. Try time.time() instead
for now if you can. Nagios will probably thank you.
Turning Collection Off
----------------------
It is recommended each namespace have an "Enabled" item which, if False,
stops collection (but not reporting) of statistical data. Applications
SHOULD provide controls to pause and resume collection by setting these
entries to False or True, if present.
Usage
=====
To collect statistics on CherryPy applications:
from cherrypy.lib import cpstats
appconfig['/']['tools.cpstats.on'] = True
To collect statistics on your own code:
import logging
# Initialize the repository
if not hasattr(logging, 'statistics'): logging.statistics = {}
# Initialize my namespace
mystats = logging.statistics.setdefault('My Stuff', {})
# Initialize my namespace's scalars and collections
mystats.update({
'Enabled': True,
'Start Time': time.time(),
'Important Events': 0,
'Events/Second': lambda s: (
(s['Important Events'] / (time.time() - s['Start Time']))),
})
...
for event in events:
...
# Collect stats
if mystats.get('Enabled', False):
mystats['Important Events'] += 1
To report statistics:
root.cpstats = cpstats.StatsPage()
To format statistics reports:
See 'Reporting', above.
""" |
"""
===================
Universal Functions
===================
Ufuncs are, generally speaking, mathematical functions or operations that are
applied element-by-element to the contents of an array. That is, the result
in each output array element only depends on the value in the corresponding
input array (or arrays) and on no other array elements. Numpy comes with a
large suite of ufuncs, and scipy extends that suite substantially. The simplest
example is the addition operator: ::
>>> np.array([0,2,3,4]) + np.array([1,1,-1,2])
array([1, 3, 2, 6])
The unfunc module lists all the available ufuncs in numpy. Documentation on
the specific ufuncs may be found in those modules. This documentation is
intended to address the more general aspects of unfuncs common to most of
them. All of the ufuncs that make use of Python operators (e.g., +, -, etc.)
have equivalent functions defined (e.g. add() for +)
Type coercion
=============
What happens when a binary operator (e.g., +,-,\\*,/, etc) deals with arrays of
two different types? What is the type of the result? Typically, the result is
the higher of the two types. For example: ::
float32 + float64 -> float64
int8 + int32 -> int32
int16 + float32 -> float32
float32 + complex64 -> complex64
There are some less obvious cases generally involving mixes of types
(e.g. uints, ints and floats) where equal bit sizes for each are not
capable of saving all the information in a different type of equivalent
bit size. Some examples are int32 vs float32 or uint32 vs int32.
Generally, the result is the higher type of larger size than both
(if available). So: ::
int32 + float32 -> float64
uint32 + int32 -> int64
Finally, the type coercion behavior when expressions involve Python
scalars is different than that seen for arrays. Since Python has a
limited number of types, combining a Python int with a dtype=np.int8
array does not coerce to the higher type but instead, the type of the
array prevails. So the rules for Python scalars combined with arrays is
that the result will be that of the array equivalent the Python scalar
if the Python scalar is of a higher 'kind' than the array (e.g., float
vs. int), otherwise the resultant type will be that of the array.
For example: ::
Python int + int8 -> int8
Python float + int8 -> float64
ufunc methods
=============
Binary ufuncs support 4 methods.
**.reduce(arr)** applies the binary operator to elements of the array in
sequence. For example: ::
>>> np.add.reduce(np.arange(10)) # adds all elements of array
45
For multidimensional arrays, the first dimension is reduced by default: ::
>>> np.add.reduce(np.arange(10).reshape(2,5))
array([ 5, 7, 9, 11, 13])
The axis keyword can be used to specify different axes to reduce: ::
>>> np.add.reduce(np.arange(10).reshape(2,5),axis=1)
array([10, 35])
**.accumulate(arr)** applies the binary operator and generates an an
equivalently shaped array that includes the accumulated amount for each
element of the array. A couple examples: ::
>>> np.add.accumulate(np.arange(10))
array([ 0, 1, 3, 6, 10, 15, 21, 28, 36, 45])
>>> np.multiply.accumulate(np.arange(1,9))
array([ 1, 2, 6, 24, 120, 720, 5040, 40320])
The behavior for multidimensional arrays is the same as for .reduce(),
as is the use of the axis keyword).
**.reduceat(arr,indices)** allows one to apply reduce to selected parts
of an array. It is a difficult method to understand. See the documentation
at:
**.outer(arr1,arr2)** generates an outer operation on the two arrays arr1 and
arr2. It will work on multidimensional arrays (the shape of the result is
the concatenation of the two input shapes.: ::
>>> np.multiply.outer(np.arange(3),np.arange(4))
array([[0, 0, 0, 0],
[0, 1, 2, 3],
[0, 2, 4, 6]])
Output arguments
================
All ufuncs accept an optional output array. The array must be of the expected
output shape. Beware that if the type of the output array is of a different
(and lower) type than the output result, the results may be silently truncated
or otherwise corrupted in the downcast to the lower type. This usage is useful
when one wants to avoid creating large temporary arrays and instead allows one
to reuse the same array memory repeatedly (at the expense of not being able to
use more convenient operator notation in expressions). Note that when the
output argument is used, the ufunc still returns a reference to the result.
>>> x = np.arange(2)
>>> np.add(np.arange(2),np.arange(2.),x)
array([0, 2])
>>> x
array([0, 2])
and & or as ufuncs
==================
Invariably people try to use the python 'and' and 'or' as logical operators
(and quite understandably). But these operators do not behave as normal
operators since Python treats these quite differently. They cannot be
overloaded with array equivalents. Thus using 'and' or 'or' with an array
results in an error. There are two alternatives:
1) use the ufunc functions logical_and() and logical_or().
2) use the bitwise operators & and \\|. The drawback of these is that if
the arguments to these operators are not boolean arrays, the result is
likely incorrect. On the other hand, most usages of logical_and and
logical_or are with boolean arrays. As long as one is careful, this is
a convenient way to apply these operators.
""" |
"""
# ggame
The simple cross-platform sprite and game platform for Brython Server (Pygame, Tkinter to follow?).
Ggame stands for a couple of things: "good game" (of course!) and also "git game" or "github game"
because it is designed to operate with [Brython Server](http://runpython.com) in concert with
Github as a backend file store.
Ggame is **not** intended to be a full-featured gaming API, with every bell and whistle. Ggame is
designed primarily as a tool for teaching computer programming, recognizing that the ability
to create engaging and interactive games is a powerful motivator for many progamming students.
Accordingly, any functional or performance enhancements that *can* be reasonably implemented
by the user are left as an exercise.
## Functionality Goals
The ggame library is intended to be trivially easy to use. For example:
from ggame import App, ImageAsset, Sprite
# Create a displayed object at 100,100 using an image asset
Sprite(ImageAsset("ggame/bunny.png"), (100,100))
# Create the app, with a 500x500 pixel stage
app = App(500,500)
# Run the app
app.run()
## Overview
There are three major components to the `ggame` system: Assets, Sprites and the App.
### Assets
Asset objects (i.e. `ggame.ImageAsset`, etc.) typically represent separate files that
are provided by the "art department". These might be background images, user interface
images, or images that represent objects in the game. In addition, `ggame.SoundAsset`
is used to represent sound files (`.wav` or `.mp3` format) that can be played in the
game.
Ggame also extends the asset concept to include graphics that are generated dynamically
at run-time, such as geometrical objects, e.g. rectangles, lines, etc.
### Sprites
All of the visual aspects of the game are represented by instances of `ggame.Sprite` or
subclasses of it.
### App
Every ggame application must create a single instance of the `ggame.App` class (or
a sub-class of it). Creating an instance of the `ggame.App` class will initiate
creation of a pop-up window on your browser. Executing the app's `run` method will
begin the process of refreshing the visual assets on the screen.
### Events
No game is complete without a player and players produce events. Your code handles user
input by registering to receive keyboard and mouse events using `ggame.App.listenKeyEvent` and
`ggame.App.listenMouseEvent` methods.
## Execution Environment
Ggame is designed to be executed in a web browser using [Brython](http://brython.info/),
[Pixi.js](http://www.pixijs.com/) and [Buzz](http://buzz.jaysalvat.com/). The easiest
way to do this is by executing from [runpython](http://runpython.com), with source
code residing on [github](http://github.com).
When using [runpython](http://runpython.com), you will have to configure your browser
to allow popup windows.
To use Ggame in your own application, you will minimally need to create a folder called
`ggame` in your project. Within `ggame`, copy the `ggame.py`, `sysdeps.py` and
`__init__.py` files from the [ggame project](https://github.com/BrythonServer/ggame).
### Include Ggame as a Git Subtree
From the same directory as your own python sources (note: you must have an existing git
repository with committed files in order for the following to work properly),
execute the following terminal commands:
git remote add -f ggame https://github.com/BrythonServer/ggame.git
git merge -s ours --no-commit ggame/master
mkdir ggame
git read-tree --prefix=ggame/ -u ggame/master
git commit -m "Merge ggame project as our subdirectory"
If you want to pull in updates from ggame in the future:
git pull -s subtree ggame master
You can see an example of how a ggame subtree is used by examining the
[Brython Server Spacewar](https://github.com/BrythonServer/Spacewar) repo on Github.
## Geometry
When referring to screen coordinates, note that the x-axis of the computer screen
is *horizontal* with the zero position on the left hand side of the screen. The
y-axis is *vertical* with the zero position at the **top** of the screen.
Increasing positive y-coordinates correspond to the downward direction on the
computer screen. Note that this is **different** from the way you may have learned
about x and y coordinates in math class!
""" |
"""
===================
Universal Functions
===================
Ufuncs are, generally speaking, mathematical functions or operations that are
applied element-by-element to the contents of an array. That is, the result
in each output array element only depends on the value in the corresponding
input array (or arrays) and on no other array elements. Numpy comes with a
large suite of ufuncs, and scipy extends that suite substantially. The simplest
example is the addition operator: ::
>>> np.array([0,2,3,4]) + np.array([1,1,-1,2])
array([1, 3, 2, 6])
The unfunc module lists all the available ufuncs in numpy. Documentation on
the specific ufuncs may be found in those modules. This documentation is
intended to address the more general aspects of unfuncs common to most of
them. All of the ufuncs that make use of Python operators (e.g., +, -, etc.)
have equivalent functions defined (e.g. add() for +)
Type coercion
=============
What happens when a binary operator (e.g., +,-,\\*,/, etc) deals with arrays of
two different types? What is the type of the result? Typically, the result is
the higher of the two types. For example: ::
float32 + float64 -> float64
int8 + int32 -> int32
int16 + float32 -> float32
float32 + complex64 -> complex64
There are some less obvious cases generally involving mixes of types
(e.g. uints, ints and floats) where equal bit sizes for each are not
capable of saving all the information in a different type of equivalent
bit size. Some examples are int32 vs float32 or uint32 vs int32.
Generally, the result is the higher type of larger size than both
(if available). So: ::
int32 + float32 -> float64
uint32 + int32 -> int64
Finally, the type coercion behavior when expressions involve Python
scalars is different than that seen for arrays. Since Python has a
limited number of types, combining a Python int with a dtype=np.int8
array does not coerce to the higher type but instead, the type of the
array prevails. So the rules for Python scalars combined with arrays is
that the result will be that of the array equivalent the Python scalar
if the Python scalar is of a higher 'kind' than the array (e.g., float
vs. int), otherwise the resultant type will be that of the array.
For example: ::
Python int + int8 -> int8
Python float + int8 -> float64
ufunc methods
=============
Binary ufuncs support 4 methods.
**.reduce(arr)** applies the binary operator to elements of the array in
sequence. For example: ::
>>> np.add.reduce(np.arange(10)) # adds all elements of array
45
For multidimensional arrays, the first dimension is reduced by default: ::
>>> np.add.reduce(np.arange(10).reshape(2,5))
array([ 5, 7, 9, 11, 13])
The axis keyword can be used to specify different axes to reduce: ::
>>> np.add.reduce(np.arange(10).reshape(2,5),axis=1)
array([10, 35])
**.accumulate(arr)** applies the binary operator and generates an an
equivalently shaped array that includes the accumulated amount for each
element of the array. A couple examples: ::
>>> np.add.accumulate(np.arange(10))
array([ 0, 1, 3, 6, 10, 15, 21, 28, 36, 45])
>>> np.multiply.accumulate(np.arange(1,9))
array([ 1, 2, 6, 24, 120, 720, 5040, 40320])
The behavior for multidimensional arrays is the same as for .reduce(),
as is the use of the axis keyword).
**.reduceat(arr,indices)** allows one to apply reduce to selected parts
of an array. It is a difficult method to understand. See the documentation
at:
**.outer(arr1,arr2)** generates an outer operation on the two arrays arr1 and
arr2. It will work on multidimensional arrays (the shape of the result is
the concatenation of the two input shapes.: ::
>>> np.multiply.outer(np.arange(3),np.arange(4))
array([[0, 0, 0, 0],
[0, 1, 2, 3],
[0, 2, 4, 6]])
Output arguments
================
All ufuncs accept an optional output array. The array must be of the expected
output shape. Beware that if the type of the output array is of a different
(and lower) type than the output result, the results may be silently truncated
or otherwise corrupted in the downcast to the lower type. This usage is useful
when one wants to avoid creating large temporary arrays and instead allows one
to reuse the same array memory repeatedly (at the expense of not being able to
use more convenient operator notation in expressions). Note that when the
output argument is used, the ufunc still returns a reference to the result.
>>> x = np.arange(2)
>>> np.add(np.arange(2),np.arange(2.),x)
array([0, 2])
>>> x
array([0, 2])
and & or as ufuncs
==================
Invariably people try to use the python 'and' and 'or' as logical operators
(and quite understandably). But these operators do not behave as normal
operators since Python treats these quite differently. They cannot be
overloaded with array equivalents. Thus using 'and' or 'or' with an array
results in an error. There are two alternatives:
1) use the ufunc functions logical_and() and logical_or().
2) use the bitwise operators & and \\|. The drawback of these is that if
the arguments to these operators are not boolean arrays, the result is
likely incorrect. On the other hand, most usages of logical_and and
logical_or are with boolean arrays. As long as one is careful, this is
a convenient way to apply these operators.
""" |
# vim: set fileencoding=utf-8 :
# ***********************IMPORTANT NMAP LICENSE TERMS************************
# * *
# * The Nmap Security Scanner is (C) 1996-2013 Insecure.Com LLC. Nmap is *
# * also a registered trademark of Insecure.Com LLC. This program is free *
# * software; you may redistribute and/or modify it under the terms of the *
# * GNU General Public License as published by the Free Software *
# * Foundation; Version 2 ("GPL"), BUT ONLY WITH ALL OF THE CLARIFICATIONS *
# * AND EXCEPTIONS DESCRIBED HEREIN. This guarantees your right to use, *
# * modify, and redistribute this software under certain conditions. If *
# * you wish to embed Nmap technology into proprietary software, we sell *
# * alternative licenses (contact EMAIL Dozens of software *
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# * scanning, OS detection, version detection, and the Nmap Scripting *
# * Engine. *
# * *
# * Note that the GPL places important restrictions on "derivative works", *
# * yet it does not provide a detailed definition of that term. To avoid *
# * misunderstandings, we interpret that term as broadly as copyright law *
# * allows. For example, we consider an application to constitute a *
# * derivative work for the purpose of this license if it does any of the *
# * following with any software or content covered by this license *
# * ("Covered Software"): *
# * *
# * o Integrates source code from Covered Software. *
# * *
# * o Reads or includes copyrighted data files, such as Nmap's nmap-os-db *
# * or nmap-service-probes. *
# * *
# * o Is designed specifically to execute Covered Software and parse the *
# * results (as opposed to typical shell or execution-menu apps, which will *
# * execute anything you tell them to). *
# * *
# * o Includes Covered Software in a proprietary executable installer. The *
# * installers produced by InstallShield are an example of this. Including *
# * Nmap with other software in compressed or archival form does not *
# * trigger this provision, provided appropriate open source decompression *
# * or de-archiving software is widely available for no charge. For the *
# * purposes of this license, an installer is considered to include Covered *
# * Software even if it actually retrieves a copy of Covered Software from *
# * another source during runtime (such as by downloading it from the *
# * Internet). *
# * *
# * o Links (statically or dynamically) to a library which does any of the *
# * above. *
# * *
# * o Executes a helper program, module, or script to do any of the above. *
# * *
# * This list is not exclusive, but is meant to clarify our interpretation *
# * of derived works with some common examples. Other people may interpret *
# * the plain GPL differently, so we consider this a special exception to *
# * the GPL that we apply to Covered Software. Works which meet any of *
# * these conditions must conform to all of the terms of this license, *
# * particularly including the GPL Section 3 requirements of providing *
# * source code and allowing free redistribution of the work as a whole. *
# * *
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# * permission to link the code of this program with any version of the *
# * OpenSSL library which is distributed under a license identical to that *
# * listed in the included docs/licenses/OpenSSL.txt file, and distribute *
# * linked combinations including the two. *
# * *
# * Any redistribution of Covered Software, including any derived works, *
# * must obey and carry forward all of the terms of this license, including *
# * obeying all GPL rules and restrictions. For example, source code of *
# * the whole work must be provided and free redistribution must be *
# * allowed. All GPL references to "this License", are to be treated as *
# * including the terms and conditions of this license text as well. *
# * *
# * Because this license imposes special exceptions to the GPL, Covered *
# * Work may not be combined (even as part of a larger work) with plain GPL *
# * software. The terms, conditions, and exceptions of this license must *
# * be included as well. This license is incompatible with some other open *
# * source licenses as well. In some cases we can relicense portions of *
# * Nmap or grant special permissions to use it in other open source *
# * software. Please contact EMAIL with any such requests. *
# * Similarly, we don't incorporate incompatible open source software into *
# * Covered Software without special permission from the copyright holders. *
# * *
# * If you have any questions about the licensing restrictions on using *
# * Nmap in other works, are happy to help. As mentioned above, we also *
# * offer alternative license to integrate Nmap into proprietary *
# * applications and appliances. These contracts have been sold to dozens *
# * of software vendors, and generally include a perpetual license as well *
# * as providing for priority support and updates. They also fund the *
# * continued development of Nmap. Please email EMAIL for further *
# * information. *
# * *
# * If you have received a written license agreement or contract for *
# * Covered Software stating terms other than these, you may choose to use *
# * and redistribute Covered Software under those terms instead of these. *
# * *
# * Source is provided to this software because we believe users have a *
# * right to know exactly what a program is going to do before they run it. *
# * This also allows you to audit the software for security holes (none *
# * have been found so far). *
# * *
# * Source code also allows you to port Nmap to new platforms, fix bugs, *
# * and add new features. You are highly encouraged to send your changes *
# * to the EMAIL mailing list for possible incorporation into the *
# * main distribution. By sending these changes to Fyodor or one of the *
# * Insecure.Org development mailing lists, or checking them into the Nmap *
# * source code repository, it is understood (unless you specify otherwise) *
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# * license file for more details (it's in a COPYING file included with *
# * Nmap, and also available from https://svn.nmap.org/nmap/COPYING *
# * *
# ***************************************************************************/
|
#
# XML-RPC CLIENT LIBRARY
# $Id: xmlrpclib.py 33500 2003-07-12 07:53:52Z loewis $
#
# an XML-RPC client interface for Python.
#
# the marshalling and response parser code can also be used to
# implement XML-RPC servers.
#
# Notes:
# this version is designed to work with Python 1.5.2 or newer.
# unicode encoding support requires at least Python 1.6.
# experimental HTTPS requires Python 2.0 built with SSL sockets.
# expat parser support requires Python 2.0 with pyexpat support.
#
# History:
# 1999-01-14 fl Created
# 1999-01-15 fl Changed dateTime to use localtime
# 1999-01-16 fl Added Binary/base64 element, default to RPC2 service
# 1999-01-19 fl Fixed array data element (from NAME 1999-01-21 fl Fixed dateTime constructor, etc.
# 1999-02-02 fl Added fault handling, handle empty sequences, etc.
# 1999-02-10 fl Fixed problem with empty responses (from NAME 1999-06-20 fl Speed improvements, pluggable parsers/transports (0.9.8)
# 2000-11-28 fl Changed boolean to check the truth value of its argument
# 2001-02-24 fl Added encoding/Unicode/SafeTransport patches
# 2001-02-26 fl Added compare support to wrappers (0.9.9/1.0b1)
# 2001-03-28 fl Make sure response tuple is a singleton
# 2001-03-29 fl Don't require empty params element (from NAME 2001-06-10 fl Folded in _xmlrpclib accelerator support (1.0b2)
# 2001-08-20 fl Base xmlrpclib.Error on built-in Exception (from NAME 2001-09-03 fl Allow Transport subclass to override getparser
# 2001-09-10 fl Lazy import of urllib, cgi, xmllib (20x import speedup)
# 2001-10-01 fl Remove containers from memo cache when done with them
# 2001-10-01 fl Use faster escape method (80% dumps speedup)
# 2001-10-10 sm Allow long ints to be passed as ints if they don't overflow
# 2001-10-17 sm test for int and long overflow (allows use on 64-bit systems)
# 2001-11-12 fl Use repr() to marshal doubles (from NAME Copyright (c) 1999-2001 by Secret Labs AB.
# Copyright (c) 1999-2001 by NAME
#
# EMAIL http://www.pythonware.com
#
# --------------------------------------------------------------------
# The XML-RPC client interface is
#
# Copyright (c) 1999-2001 by Secret Labs AB
# Copyright (c) 1999-2001 by NAME By obtaining, using, and/or copying this software and/or its
# associated documentation, you agree that you have read, understood,
# and will comply with the following terms and conditions:
#
# Permission to use, copy, modify, and distribute this software and
# its associated documentation for any purpose and without fee is
# hereby granted, provided that the above copyright notice appears in
# all copies, and that both that copyright notice and this permission
# notice appear in supporting documentation, and that the name of
# Secret Labs AB or the author not be used in advertising or publicity
# pertaining to distribution of the software without specific, written
# prior permission.
#
# SECRET LABS AB AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH REGARD
# TO THIS SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANT-
# ABILITY AND FITNESS. IN NO EVENT SHALL SECRET LABS AB OR THE AUTHOR
# BE LIABLE FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY
# DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS,
# WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS
# ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE
# OF THIS SOFTWARE.
# --------------------------------------------------------------------
#
# things to look into:
# TODO: support basic authentication (see robin's patch)
# TODO: fix host tuple handling in the server constructor
# TODO: let transport verify schemes
# TODO: update documentation
# TODO: authentication plugins
|
"""
[2017-06-02] Challenge #317 [Hard] Poker Odds
https://www.reddit.com/r/dailyprogrammer/comments/6eublu/20170602_challenge_317_hard_poker_odds/
#DESCRIPTION
Playing Texas Hold'em is a game about weighing odds. Every player is given two cards that only they can see. Then five
cards are turned up on the table that everybody sees. The winner is the player with the best hand composed of five
cards out of the seven available (the 5 on the table, and the two personal cards).
Your job is, given four hands of two cards, and the "flop" (three of the five cards that will be flipped up), calculate
the odds every player has of getting the best hand.
#INPUT
You will be given 5 lines, the first line contains the three cards on the flop, the next four with the two-card hands
of every player. written as \[CardValue]\[CardSuit], with the values being, in order, A, 2, 3, 4, 5, 6, 7, 8, 9, 0, J,
Q, K, A (Aces `A` may be high or low, just like real poker). The suits' corresponding symbols are the first letter of
the suit name; Clubs = C; Spades = S; Diamonds = D; Hearts = H.
#OUTPUT
Four lines of text, writing...
[PlayerNum] : [Odds of Winning (rounded to 1 decimal point)] %
#SAMPLE INPUT
3D5C9C
3C7H
AS0S
9S2D
KCJC
#SAMPLE OUTPUT
1: 15.4%
2: 8.8%
3: 26.2%
4: 49.6%
# NOTES
For those unfamiliar, here is the order of hand win priority, from best up top to worst at the bottom;
* Straight Flush (5 cards of consecutive value, all the same suit; ie: 3D4D5D6D7D)
* Four of a Kind (4 of your five cards are the same value; ie: AC4DAHASAD)
* Full House (Contains a three-of-a-kind and a pair; ie: AHADAS5C5H)
* Flush (All five cards are of the same suit; ie: AH4H9H3H2H)
* Straight (All five cards are of consecutive value; ie: 3D4S5H6H7C)
* Three-of-a-kind (Three cards are of identical value; ie: AS3C3D4H7S)
* Two Pairs (Contains two pairs; ie: AH3H4D4S2C)
* Pair (Contains two cards of identical value; ie: AHAC2S6D9D)
* High-Card (If none of the above, your hand is composed of "this is my highest card", ie; JHKD0S3H4D becomes "High
Card King".)
In the event that two people have the same hand value, whichever has the *highest card that qualifies of that rank.*
ie; If you get a pair, the value of the pair is counted first, followed by high-card. If you have a full house, the
value of the triplet is tallied first, the the pair.
* Per se; two hands of 77820 and 83J77 both have pairs, of sevens, but then Person 2 has the higher "high card"
outside the ranking, a J beats a 0.
* If the high cards are the same, you go to the second-highest card, etc.
If there is a chance of a tie, you can print that separately, but for this challenge, only print out the chance of them
*winning by themselves*.
ALSO REMEMBER; There are 52 cards in a deck, there can't be two identical cards in play simultaneously.
# Credit
This challenge was suggested by /u/Mathgeek007, many thanks. If you have a suggestion for a challenge, please share it
at /r/dailyprogrammer_ideas and there's a good chance we'll use it.
""" |
"""
=================
Structured Arrays
=================
Introduction
============
NumPy provides powerful capabilities to create arrays of structured datatype.
These arrays permit one to manipulate the data by named fields. A simple
example will show what is meant.: ::
>>> x = np.array([(1,2.,'Hello'), (2,3.,"World")],
... dtype=[('foo', 'i4'),('bar', 'f4'), ('baz', 'S10')])
>>> x
array([(1, 2.0, 'Hello'), (2, 3.0, 'World')],
dtype=[('foo', '>i4'), ('bar', '>f4'), ('baz', '|S10')])
Here we have created a one-dimensional array of length 2. Each element of
this array is a structure that contains three items, a 32-bit integer, a 32-bit
float, and a string of length 10 or less. If we index this array at the second
position we get the second structure: ::
>>> x[1]
(2,3.,"World")
Conveniently, one can access any field of the array by indexing using the
string that names that field. ::
>>> y = x['bar']
>>> y
array([ 2., 3.], dtype=float32)
>>> y[:] = 2*y
>>> y
array([ 4., 6.], dtype=float32)
>>> x
array([(1, 4.0, 'Hello'), (2, 6.0, 'World')],
dtype=[('foo', '>i4'), ('bar', '>f4'), ('baz', '|S10')])
In these examples, y is a simple float array consisting of the 2nd field
in the structured type. But, rather than being a copy of the data in the structured
array, it is a view, i.e., it shares exactly the same memory locations.
Thus, when we updated this array by doubling its values, the structured
array shows the corresponding values as doubled as well. Likewise, if one
changes the structured array, the field view also changes: ::
>>> x[1] = (-1,-1.,"Master")
>>> x
array([(1, 4.0, 'Hello'), (-1, -1.0, 'Master')],
dtype=[('foo', '>i4'), ('bar', '>f4'), ('baz', '|S10')])
>>> y
array([ 4., -1.], dtype=float32)
Defining Structured Arrays
==========================
One defines a structured array through the dtype object. There are
**several** alternative ways to define the fields of a record. Some of
these variants provide backward compatibility with Numeric, numarray, or
another module, and should not be used except for such purposes. These
will be so noted. One specifies record structure in
one of four alternative ways, using an argument (as supplied to a dtype
function keyword or a dtype object constructor itself). This
argument must be one of the following: 1) string, 2) tuple, 3) list, or
4) dictionary. Each of these is briefly described below.
1) String argument.
In this case, the constructor expects a comma-separated list of type
specifiers, optionally with extra shape information. The fields are
given the default names 'f0', 'f1', 'f2' and so on.
The type specifiers can take 4 different forms: ::
a) b1, i1, i2, i4, i8, u1, u2, u4, u8, f2, f4, f8, c8, c16, a<n>
(representing bytes, ints, unsigned ints, floats, complex and
fixed length strings of specified byte lengths)
b) int8,...,uint8,...,float16, float32, float64, complex64, complex128
(this time with bit sizes)
c) older Numeric/numarray type specifications (e.g. Float32).
Don't use these in new code!
d) Single character type specifiers (e.g H for unsigned short ints).
Avoid using these unless you must. Details can be found in the
NumPy book
These different styles can be mixed within the same string (but why would you
want to do that?). Furthermore, each type specifier can be prefixed
with a repetition number, or a shape. In these cases an array
element is created, i.e., an array within a record. That array
is still referred to as a single field. An example: ::
>>> x = np.zeros(3, dtype='3int8, float32, (2,3)float64')
>>> x
array([([0, 0, 0], 0.0, [[0.0, 0.0, 0.0], [0.0, 0.0, 0.0]]),
([0, 0, 0], 0.0, [[0.0, 0.0, 0.0], [0.0, 0.0, 0.0]]),
([0, 0, 0], 0.0, [[0.0, 0.0, 0.0], [0.0, 0.0, 0.0]])],
dtype=[('f0', '|i1', 3), ('f1', '>f4'), ('f2', '>f8', (2, 3))])
By using strings to define the record structure, it precludes being
able to name the fields in the original definition. The names can
be changed as shown later, however.
2) Tuple argument: The only relevant tuple case that applies to record
structures is when a structure is mapped to an existing data type. This
is done by pairing in a tuple, the existing data type with a matching
dtype definition (using any of the variants being described here). As
an example (using a definition using a list, so see 3) for further
details): ::
>>> x = np.zeros(3, dtype=('i4',[('r','u1'), ('g','u1'), ('b','u1'), ('a','u1')]))
>>> x
array([0, 0, 0])
>>> x['r']
array([0, 0, 0], dtype=uint8)
In this case, an array is produced that looks and acts like a simple int32 array,
but also has definitions for fields that use only one byte of the int32 (a bit
like Fortran equivalencing).
3) List argument: In this case the record structure is defined with a list of
tuples. Each tuple has 2 or 3 elements specifying: 1) The name of the field
('' is permitted), 2) the type of the field, and 3) the shape (optional).
For example::
>>> x = np.zeros(3, dtype=[('x','f4'),('y',np.float32),('value','f4',(2,2))])
>>> x
array([(0.0, 0.0, [[0.0, 0.0], [0.0, 0.0]]),
(0.0, 0.0, [[0.0, 0.0], [0.0, 0.0]]),
(0.0, 0.0, [[0.0, 0.0], [0.0, 0.0]])],
dtype=[('x', '>f4'), ('y', '>f4'), ('value', '>f4', (2, 2))])
4) Dictionary argument: two different forms are permitted. The first consists
of a dictionary with two required keys ('names' and 'formats'), each having an
equal sized list of values. The format list contains any type/shape specifier
allowed in other contexts. The names must be strings. There are two optional
keys: 'offsets' and 'titles'. Each must be a correspondingly matching list to
the required two where offsets contain integer offsets for each field, and
titles are objects containing metadata for each field (these do not have
to be strings), where the value of None is permitted. As an example: ::
>>> x = np.zeros(3, dtype={'names':['col1', 'col2'], 'formats':['i4','f4']})
>>> x
array([(0, 0.0), (0, 0.0), (0, 0.0)],
dtype=[('col1', '>i4'), ('col2', '>f4')])
The other dictionary form permitted is a dictionary of name keys with tuple
values specifying type, offset, and an optional title. ::
>>> x = np.zeros(3, dtype={'col1':('i1',0,'title 1'), 'col2':('f4',1,'title 2')})
>>> x
array([(0, 0.0), (0, 0.0), (0, 0.0)],
dtype=[(('title 1', 'col1'), '|i1'), (('title 2', 'col2'), '>f4')])
Accessing and modifying field names
===================================
The field names are an attribute of the dtype object defining the structure.
For the last example: ::
>>> x.dtype.names
('col1', 'col2')
>>> x.dtype.names = ('x', 'y')
>>> x
array([(0, 0.0), (0, 0.0), (0, 0.0)],
dtype=[(('title 1', 'x'), '|i1'), (('title 2', 'y'), '>f4')])
>>> x.dtype.names = ('x', 'y', 'z') # wrong number of names
<type 'exceptions.ValueError'>: must replace all names at once with a sequence of length 2
Accessing field titles
====================================
The field titles provide a standard place to put associated info for fields.
They do not have to be strings. ::
>>> x.dtype.fields['x'][2]
'title 1'
Accessing multiple fields at once
====================================
You can access multiple fields at once using a list of field names: ::
>>> x = np.array([(1.5,2.5,(1.0,2.0)),(3.,4.,(4.,5.)),(1.,3.,(2.,6.))],
dtype=[('x','f4'),('y',np.float32),('value','f4',(2,2))])
Notice that `x` is created with a list of tuples. ::
>>> x[['x','y']]
array([(1.5, 2.5), (3.0, 4.0), (1.0, 3.0)],
dtype=[('x', '<f4'), ('y', '<f4')])
>>> x[['x','value']]
array([(1.5, [[1.0, 2.0], [1.0, 2.0]]), (3.0, [[4.0, 5.0], [4.0, 5.0]]),
(1.0, [[2.0, 6.0], [2.0, 6.0]])],
dtype=[('x', '<f4'), ('value', '<f4', (2, 2))])
The fields are returned in the order they are asked for.::
>>> x[['y','x']]
array([(2.5, 1.5), (4.0, 3.0), (3.0, 1.0)],
dtype=[('y', '<f4'), ('x', '<f4')])
Filling structured arrays
=========================
Structured arrays can be filled by field or row by row. ::
>>> arr = np.zeros((5,), dtype=[('var1','f8'),('var2','f8')])
>>> arr['var1'] = np.arange(5)
If you fill it in row by row, it takes a take a tuple
(but not a list or array!)::
>>> arr[0] = (10,20)
>>> arr
array([(10.0, 20.0), (1.0, 0.0), (2.0, 0.0), (3.0, 0.0), (4.0, 0.0)],
dtype=[('var1', '<f8'), ('var2', '<f8')])
Record Arrays
=============
For convenience, numpy provides "record arrays" which allow one to access
fields of structured arrays by attribute rather than by index. Record arrays
are structured arrays wrapped using a subclass of ndarray,
:class:`numpy.recarray`, which allows field access by attribute on the array
object, and record arrays also use a special datatype, :class:`numpy.record`,
which allows field access by attribute on the individual elements of the array.
The simplest way to create a record array is with :func:`numpy.rec.array`: ::
>>> recordarr = np.rec.array([(1,2.,'Hello'),(2,3.,"World")],
... dtype=[('foo', 'i4'),('bar', 'f4'), ('baz', 'S10')])
>>> recordarr.bar
array([ 2., 3.], dtype=float32)
>>> recordarr[1:2]
rec.array([(2, 3.0, 'World')],
dtype=[('foo', '<i4'), ('bar', '<f4'), ('baz', 'S10')])
>>> recordarr[1:2].foo
array([2], dtype=int32)
>>> recordarr.foo[1:2]
array([2], dtype=int32)
>>> recordarr[1].baz
'World'
numpy.rec.array can convert a wide variety of arguments into record arrays,
including normal structured arrays: ::
>>> arr = array([(1,2.,'Hello'),(2,3.,"World")],
... dtype=[('foo', 'i4'), ('bar', 'f4'), ('baz', 'S10')])
>>> recordarr = np.rec.array(arr)
The numpy.rec module provides a number of other convenience functions for
creating record arrays, see :ref:`record array creation routines
<routines.array-creation.rec>`.
A record array representation of a structured array can be obtained using the
appropriate :ref:`view`: ::
>>> arr = np.array([(1,2.,'Hello'),(2,3.,"World")],
... dtype=[('foo', 'i4'),('bar', 'f4'), ('baz', 'a10')])
>>> recordarr = arr.view(dtype=dtype((np.record, arr.dtype)),
... type=np.recarray)
For convenience, viewing an ndarray as type `np.recarray` will automatically
convert to `np.record` datatype, so the dtype can be left out of the view: ::
>>> recordarr = arr.view(np.recarray)
>>> recordarr.dtype
dtype((numpy.record, [('foo', '<i4'), ('bar', '<f4'), ('baz', 'S10')]))
To get back to a plain ndarray both the dtype and type must be reset. The
following view does so, taking into account the unusual case that the
recordarr was not a structured type: ::
>>> arr2 = recordarr.view(recordarr.dtype.fields or recordarr.dtype, np.ndarray)
Record array fields accessed by index or by attribute are returned as a record
array if the field has a structured type but as a plain ndarray otherwise. ::
>>> recordarr = np.rec.array([('Hello', (1,2)),("World", (3,4))],
... dtype=[('foo', 'S6'),('bar', [('A', int), ('B', int)])])
>>> type(recordarr.foo)
<type 'numpy.ndarray'>
>>> type(recordarr.bar)
<class 'numpy.core.records.recarray'>
Note that if a field has the same name as an ndarray attribute, the ndarray
attribute takes precedence. Such fields will be inaccessible by attribute but
may still be accessed by index.
""" |
# -*- encoding: utf-8 -*-
##############################################################################
#
# Copyright (c) 2009 Veritos - NAME - www.veritos.nl
#
# WARNING: This program as such is intended to be used by professional
# programmers who take the whole responsability of assessing all potential
# consequences resulting from its eventual inadequacies and bugs.
# End users who are looking for a ready-to-use solution with commercial
# garantees and support are strongly adviced to contract a Free Software
# Service Company like Veritos.
#
# This program is Free Software; you can redistribute it and/or
# modify it under the terms of the GNU General Public License
# as published by the Free Software Foundation; either version 2
# of the License, or (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program; if not, write to the Free Software
# Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
#
##############################################################################
#
# Deze module werkt in OpenERP 5.0.0 (en waarschijnlijk hoger).
# Deze module werkt niet in OpenERP versie 4 en lager.
#
# Status 1.0 - getest op OpenERP 5.0.3
#
# Versie IP_ADDRESS
# account.account.type
# Basis gelegd voor alle account type
#
# account.account.template
# Basis gelegd met alle benodigde grootboekrekeningen welke via een menu-
# structuur gelinkt zijn aan rubrieken 1 t/m 9.
# De grootboekrekeningen gelinkt aan de account.account.type
# Deze links moeten nog eens goed nagelopen worden.
#
# account.chart.template
# Basis gelegd voor het koppelen van rekeningen aan debiteuren, crediteuren,
# bank, inkoop en verkoop boeken en de BTW configuratie.
#
# Versie IP_ADDRESS
# account.tax.code.template
# Basis gelegd voor de BTW configuratie (structuur)
# Heb als basis het BTW aangifte formulier gebruikt. Of dit werkt?
#
# account.tax.template
# De BTW rekeningen aangemaakt en deze gekoppeld aan de betreffende
# grootboekrekeningen
#
# Versie IP_ADDRESS
# Opschonen van de code en verwijderen van niet gebruikte componenten.
# Versie IP_ADDRESS
# Aanpassen a_expense van 3000 -> 7000
# record id='btw_code_5b' op negatieve waarde gezet
# Versie IP_ADDRESS
# BTW rekeningen hebben typeaanduiding gekregen t.b.v. purchase of sale
# Versie IP_ADDRESS
# Opschonen van module.
# Versie IP_ADDRESS
# Opschonen van module.
# Versie IP_ADDRESS
# Foutje in l10n_nl_wizard.xml gecorrigeerd waardoor de module niet volledig installeerde.
# Versie IP_ADDRESS
# Account Receivable en Payable goed gedefinieerd.
# Versie IP_ADDRESS
# Alle user_type_xxx velden goed gedefinieerd.
# Specifieke bouw en garage gerelateerde grootboeken verwijderd om een standaard module te creeeren.
# Deze module kan dan als basis worden gebruikt voor specifieke doelgroep modules te creeeren.
# Versie IP_ADDRESS
# Correctie van rekening 7010 (stond dubbel met 7014 waardoor installatie verkeerd ging)
# versie IP_ADDRESS
# Correctie op diverse rekening types van user_type_asset -> user_type_liability en user_type_equity
# versie IP_ADDRESS
# Kleine correctie op BTW te vorderen hoog, id was hetzelfde voor beide, waardoor hoog werd overschreven door # overig. Verduidelijking van omschrijvingen in belastingcodes t.b.v. aangifte overzicht.
# versie IP_ADDRESS
# BTW omschrijvingen aangepast, zodat rapporten er beter uitzien. 2a en 5b e.d. verwijderd en enkele omschrijvingen toegevoegd.
# versie IP_ADDRESS - Switch to English
# Added properties_stock_xxx accounts for correct stock valuation, changed 7000-accounts from type cash to type expense
# Changed naming of 7020 and 7030 to Kostprijs omzet xxxx
|
#
# XML-RPC CLIENT LIBRARY
# $Id$
#
# an XML-RPC client interface for Python.
#
# the marshalling and response parser code can also be used to
# implement XML-RPC servers.
#
# Notes:
# this version is designed to work with Python 2.1 or newer.
#
# History:
# 1999-01-14 fl Created
# 1999-01-15 fl Changed dateTime to use localtime
# 1999-01-16 fl Added Binary/base64 element, default to RPC2 service
# 1999-01-19 fl Fixed array data element (from Skip Montanaro)
# 1999-01-21 fl Fixed dateTime constructor, etc.
# 1999-02-02 fl Added fault handling, handle empty sequences, etc.
# 1999-02-10 fl Fixed problem with empty responses (from Skip Montanaro)
# 1999-06-20 fl Speed improvements, pluggable parsers/transports (0.9.8)
# 2000-11-28 fl Changed boolean to check the truth value of its argument
# 2001-02-24 fl Added encoding/Unicode/SafeTransport patches
# 2001-02-26 fl Added compare support to wrappers (0.9.9/1.0b1)
# 2001-03-28 fl Make sure response tuple is a singleton
# 2001-03-29 fl Don't require empty params element (from NAME 2001-06-10 fl Folded in _xmlrpclib accelerator support (1.0b2)
# 2001-08-20 fl Base xmlrpclib.Error on built-in Exception (from NAME 2001-09-03 fl Allow Transport subclass to override getparser
# 2001-09-10 fl Lazy import of urllib, cgi, xmllib (20x import speedup)
# 2001-10-01 fl Remove containers from memo cache when done with them
# 2001-10-01 fl Use faster escape method (80% dumps speedup)
# 2001-10-02 fl More dumps microtuning
# 2001-10-04 fl Make sure import expat gets a parser (from NAME 2001-10-10 sm Allow long ints to be passed as ints if they don't overflow
# 2001-10-17 sm Test for int and long overflow (allows use on 64-bit systems)
# 2001-11-12 fl Use repr() to marshal doubles (from NAME 2002-03-17 fl Avoid buffered read when possible (from NAME 2002-04-07 fl Added pythondoc comments
# 2002-04-16 fl Added __str__ methods to datetime/binary wrappers
# 2002-05-15 fl Added error constants (from NAME 2002-06-27 fl Merged with Python CVS version
# 2002-10-22 fl Added basic authentication (based on code from NAME 2003-01-22 sm Add support for the bool type
# 2003-02-27 gvr Remove apply calls
# 2003-04-24 sm Use cStringIO if available
# 2003-04-25 ak Add support for nil
# 2003-06-15 gn Add support for time.struct_time
# 2003-07-12 gp Correct marshalling of Faults
# 2003-10-31 mvl Add multicall support
# 2004-08-20 mvl Bump minimum supported Python version to 2.1
#
# Copyright (c) 1999-2002 by Secret Labs AB.
# Copyright (c) 1999-2002 by NAME EMAIL http://www.pythonware.com
#
# --------------------------------------------------------------------
# The XML-RPC client interface is
#
# Copyright (c) 1999-2002 by Secret Labs AB
# Copyright (c) 1999-2002 by NAME By obtaining, using, and/or copying this software and/or its
# associated documentation, you agree that you have read, understood,
# and will comply with the following terms and conditions:
#
# Permission to use, copy, modify, and distribute this software and
# its associated documentation for any purpose and without fee is
# hereby granted, provided that the above copyright notice appears in
# all copies, and that both that copyright notice and this permission
# notice appear in supporting documentation, and that the name of
# Secret Labs AB or the author not be used in advertising or publicity
# pertaining to distribution of the software without specific, written
# prior permission.
#
# SECRET LABS AB AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH REGARD
# TO THIS SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANT-
# ABILITY AND FITNESS. IN NO EVENT SHALL SECRET LABS AB OR THE AUTHOR
# BE LIABLE FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY
# DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS,
# WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS
# ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE
# OF THIS SOFTWARE.
# --------------------------------------------------------------------
#
# things to look into some day:
# TODO: sort out True/False/boolean issues for Python 2.3
|
"""
Limits
======
Implemented according to the PhD thesis
http://www.cybertester.com/data/gruntz.pdf, which contains very thorough
descriptions of the algorithm including many examples. We summarize here the
gist of it.
All functions are sorted according to how rapidly varying they are at infinity
using the following rules. Any two functions f and g can be compared using the
properties of L:
L=lim log|f(x)| / log|g(x)| (for x -> oo)
We define >, < ~ according to::
1. f > g .... L=+-oo
we say that:
- f is greater than any power of g
- f is more rapidly varying than g
- f goes to infinity/zero faster than g
2. f < g .... L=0
we say that:
- f is lower than any power of g
3. f ~ g .... L!=0, +-oo
we say that:
- both f and g are bounded from above and below by suitable integral
powers of the other
Examples
========
::
2 < x < exp(x) < exp(x**2) < exp(exp(x))
2 ~ 3 ~ -5
x ~ x**2 ~ x**3 ~ 1/x ~ x**m ~ -x
exp(x) ~ exp(-x) ~ exp(2x) ~ exp(x)**2 ~ exp(x+exp(-x))
f ~ 1/f
So we can divide all the functions into comparability classes (x and x^2 belong
to one class, exp(x) and exp(-x) belong to some other class). In principle, we
could compare any two functions, but in our algorithm, we don't compare
anything below the class 2~3~-5 (for example log(x) is below this), so we set
2~3~-5 as the lowest comparability class.
Given the function f, we find the list of most rapidly varying (mrv set)
subexpressions of it. This list belongs to the same comparability class. Let's
say it is {exp(x), exp(2x)}. Using the rule f ~ 1/f we find an element "w"
(either from the list or a new one) from the same comparability class which
goes to zero at infinity. In our example we set w=exp(-x) (but we could also
set w=exp(-2x) or w=exp(-3x) ...). We rewrite the mrv set using w, in our case
{1/w, 1/w^2}, and substitute it into f. Then we expand f into a series in w::
f = c0*w^e0 + c1*w^e1 + ... + O(w^en), where e0<e1<...<en, c0!=0
but for x->oo, lim f = lim c0*w^e0, because all the other terms go to zero,
because w goes to zero faster than the ci and ei. So::
for e0>0, lim f = 0
for e0<0, lim f = +-oo (the sign depends on the sign of c0)
for e0=0, lim f = lim c0
We need to recursively compute limits at several places of the algorithm, but
as is shown in the PhD thesis, it always finishes.
Important functions from the implementation:
compare(a, b, x) compares "a" and "b" by computing the limit L.
mrv(e, x) returns the list of most rapidly varying (mrv) subexpressions of "e"
rewrite(e, Omega, x, wsym) rewrites "e" in terms of w
leadterm(f, x) returns the lowest power term in the series of f
mrv_leadterm(e, x) returns the lead term (c0, e0) for e
limitinf(e, x) computes lim e (for x->oo)
limit(e, z, z0) computes any limit by converting it to the case x->oo
All the functions are really simple and straightforward except rewrite(), which
is the most difficult/complex part of the algorithm. When the algorithm fails,
the bugs are usually in the series expansion (i.e. in SymPy) or in rewrite.
This code is almost exact rewrite of the Maple code inside the Gruntz thesis.
Debugging
---------
Because the gruntz algorithm is highly recursive, it's difficult to figure out
what went wrong inside a debugger. Instead, turn on nice debug prints by
defining the environment variable SYMPY_DEBUG. For example:
[user@localhost]: SYMPY_DEBUG=True ./bin/isympy
In [1]: limit(sin(x)/x, x, 0)
limitinf(_x*sin(1/_x), _x) = 1
+-mrv_leadterm(_x*sin(1/_x), _x) = (1, 0)
| +-mrv(_x*sin(1/_x), _x) = set([_x])
| | +-mrv(_x, _x) = set([_x])
| | +-mrv(sin(1/_x), _x) = set([_x])
| | +-mrv(1/_x, _x) = set([_x])
| | +-mrv(_x, _x) = set([_x])
| +-mrv_leadterm(exp(_x)*sin(exp(-_x)), _x, set([exp(_x)])) = (1, 0)
| +-rewrite(exp(_x)*sin(exp(-_x)), set([exp(_x)]), _x, _w) = (1/_w*sin(_w), -_x)
| +-sign(_x, _x) = 1
| +-mrv_leadterm(1, _x) = (1, 0)
+-sign(0, _x) = 0
+-limitinf(1, _x) = 1
And check manually which line is wrong. Then go to the source code and debug
this function to figure out the exact problem.
""" |
"""
========================================
Special functions (:mod:`scipy.special`)
========================================
.. currentmodule:: scipy.special
Nearly all of the functions below are universal functions and follow
broadcasting and automatic array-looping rules.
.. seealso::
`scipy.special.cython_special` -- Typed Cython versions of special functions
Error handling
==============
Errors are handled by returning NaNs or other appropriate values.
Some of the special function routines can emit warnings or raise
exceptions when an error occurs. By default this is disabled; to
query and control the current error handling state the following
functions are provided.
.. autosummary::
:toctree: generated/
geterr -- Get the current way of handling special-function errors.
seterr -- Set how special-function errors are handled.
errstate -- Context manager for special-function error handling.
SpecialFunctionWarning -- Warning that can be emitted by special functions.
SpecialFunctionError -- Exception that can be raised by special functions.
Available functions
===================
Airy functions
--------------
.. autosummary::
:toctree: generated/
airy -- Airy functions and their derivatives.
airye -- Exponentially scaled Airy functions and their derivatives.
ai_zeros -- Compute `nt` zeros and values of the Airy function Ai and its derivative.
bi_zeros -- Compute `nt` zeros and values of the Airy function Bi and its derivative.
itairy -- Integrals of Airy functions
Elliptic functions and integrals
--------------------------------
.. autosummary::
:toctree: generated/
ellipj -- Jacobian elliptic functions.
ellipk -- Complete elliptic integral of the first kind.
ellipkm1 -- Complete elliptic integral of the first kind around `m` = 1.
ellipkinc -- Incomplete elliptic integral of the first kind.
ellipe -- Complete elliptic integral of the second kind.
ellipeinc -- Incomplete elliptic integral of the second kind.
Bessel functions
----------------
.. autosummary::
:toctree: generated/
jv -- Bessel function of the first kind of real order and \
complex argument.
jve -- Exponentially scaled Bessel function of order `v`.
yn -- Bessel function of the second kind of integer order and \
real argument.
yv -- Bessel function of the second kind of real order and \
complex argument.
yve -- Exponentially scaled Bessel function of the second kind \
of real order.
kn -- Modified Bessel function of the second kind of integer \
order `n`
kv -- Modified Bessel function of the second kind of real order \
`v`
kve -- Exponentially scaled modified Bessel function of the \
second kind.
iv -- Modified Bessel function of the first kind of real order.
ive -- Exponentially scaled modified Bessel function of the \
first kind.
hankel1 -- Hankel function of the first kind.
hankel1e -- Exponentially scaled Hankel function of the first kind.
hankel2 -- Hankel function of the second kind.
hankel2e -- Exponentially scaled Hankel function of the second kind.
wright_bessel -- Wright's generalized Bessel function.
The following is not a universal function:
.. autosummary::
:toctree: generated/
lmbda -- Jahnke-Emden Lambda function, Lambdav(x).
Zeros of Bessel functions
^^^^^^^^^^^^^^^^^^^^^^^^^
These are not universal functions:
.. autosummary::
:toctree: generated/
jnjnp_zeros -- Compute zeros of integer-order Bessel functions Jn and Jn'.
jnyn_zeros -- Compute nt zeros of Bessel functions Jn(x), Jn'(x), Yn(x), and Yn'(x).
jn_zeros -- Compute zeros of integer-order Bessel function Jn(x).
jnp_zeros -- Compute zeros of integer-order Bessel function derivative Jn'(x).
yn_zeros -- Compute zeros of integer-order Bessel function Yn(x).
ynp_zeros -- Compute zeros of integer-order Bessel function derivative Yn'(x).
y0_zeros -- Compute nt zeros of Bessel function Y0(z), and derivative at each zero.
y1_zeros -- Compute nt zeros of Bessel function Y1(z), and derivative at each zero.
y1p_zeros -- Compute nt zeros of Bessel derivative Y1'(z), and value at each zero.
Faster versions of common Bessel functions
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.. autosummary::
:toctree: generated/
j0 -- Bessel function of the first kind of order 0.
j1 -- Bessel function of the first kind of order 1.
y0 -- Bessel function of the second kind of order 0.
y1 -- Bessel function of the second kind of order 1.
i0 -- Modified Bessel function of order 0.
i0e -- Exponentially scaled modified Bessel function of order 0.
i1 -- Modified Bessel function of order 1.
i1e -- Exponentially scaled modified Bessel function of order 1.
k0 -- Modified Bessel function of the second kind of order 0, :math:`K_0`.
k0e -- Exponentially scaled modified Bessel function K of order 0
k1 -- Modified Bessel function of the second kind of order 1, :math:`K_1(x)`.
k1e -- Exponentially scaled modified Bessel function K of order 1.
Integrals of Bessel functions
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.. autosummary::
:toctree: generated/
itj0y0 -- Integrals of Bessel functions of order 0.
it2j0y0 -- Integrals related to Bessel functions of order 0.
iti0k0 -- Integrals of modified Bessel functions of order 0.
it2i0k0 -- Integrals related to modified Bessel functions of order 0.
besselpoly -- Weighted integral of a Bessel function.
Derivatives of Bessel functions
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.. autosummary::
:toctree: generated/
jvp -- Compute nth derivative of Bessel function Jv(z) with respect to `z`.
yvp -- Compute nth derivative of Bessel function Yv(z) with respect to `z`.
kvp -- Compute nth derivative of real-order modified Bessel function Kv(z)
ivp -- Compute nth derivative of modified Bessel function Iv(z) with respect to `z`.
h1vp -- Compute nth derivative of Hankel function H1v(z) with respect to `z`.
h2vp -- Compute nth derivative of Hankel function H2v(z) with respect to `z`.
Spherical Bessel functions
^^^^^^^^^^^^^^^^^^^^^^^^^^
.. autosummary::
:toctree: generated/
spherical_jn -- Spherical Bessel function of the first kind or its derivative.
spherical_yn -- Spherical Bessel function of the second kind or its derivative.
spherical_in -- Modified spherical Bessel function of the first kind or its derivative.
spherical_kn -- Modified spherical Bessel function of the second kind or its derivative.
Riccati-Bessel functions
^^^^^^^^^^^^^^^^^^^^^^^^
These are not universal functions:
.. autosummary::
:toctree: generated/
riccati_jn -- Compute Ricatti-Bessel function of the first kind and its derivative.
riccati_yn -- Compute Ricatti-Bessel function of the second kind and its derivative.
Struve functions
----------------
.. autosummary::
:toctree: generated/
struve -- Struve function.
modstruve -- Modified Struve function.
itstruve0 -- Integral of the Struve function of order 0.
it2struve0 -- Integral related to the Struve function of order 0.
itmodstruve0 -- Integral of the modified Struve function of order 0.
Raw statistical functions
-------------------------
.. seealso:: :mod:`scipy.stats`: Friendly versions of these functions.
.. autosummary::
:toctree: generated/
bdtr -- Binomial distribution cumulative distribution function.
bdtrc -- Binomial distribution survival function.
bdtri -- Inverse function to `bdtr` with respect to `p`.
bdtrik -- Inverse function to `bdtr` with respect to `k`.
bdtrin -- Inverse function to `bdtr` with respect to `n`.
btdtr -- Cumulative distribution function of the beta distribution.
btdtri -- The `p`-th quantile of the beta distribution.
btdtria -- Inverse of `btdtr` with respect to `a`.
btdtrib -- btdtria(a, p, x).
fdtr -- F cumulative distribution function.
fdtrc -- F survival function.
fdtri -- The `p`-th quantile of the F-distribution.
fdtridfd -- Inverse to `fdtr` vs dfd.
gdtr -- Gamma distribution cumulative distribution function.
gdtrc -- Gamma distribution survival function.
gdtria -- Inverse of `gdtr` vs a.
gdtrib -- Inverse of `gdtr` vs b.
gdtrix -- Inverse of `gdtr` vs x.
nbdtr -- Negative binomial cumulative distribution function.
nbdtrc -- Negative binomial survival function.
nbdtri -- Inverse of `nbdtr` vs `p`.
nbdtrik -- Inverse of `nbdtr` vs `k`.
nbdtrin -- Inverse of `nbdtr` vs `n`.
ncfdtr -- Cumulative distribution function of the non-central F distribution.
ncfdtridfd -- Calculate degrees of freedom (denominator) for the noncentral F-distribution.
ncfdtridfn -- Calculate degrees of freedom (numerator) for the noncentral F-distribution.
ncfdtri -- Inverse cumulative distribution function of the non-central F distribution.
ncfdtrinc -- Calculate non-centrality parameter for non-central F distribution.
nctdtr -- Cumulative distribution function of the non-central `t` distribution.
nctdtridf -- Calculate degrees of freedom for non-central t distribution.
nctdtrit -- Inverse cumulative distribution function of the non-central t distribution.
nctdtrinc -- Calculate non-centrality parameter for non-central t distribution.
nrdtrimn -- Calculate mean of normal distribution given other params.
nrdtrisd -- Calculate standard deviation of normal distribution given other params.
pdtr -- Poisson cumulative distribution function.
pdtrc -- Poisson survival function.
pdtri -- Inverse to `pdtr` vs m.
pdtrik -- Inverse to `pdtr` vs k.
stdtr -- Student t distribution cumulative distribution function.
stdtridf -- Inverse of `stdtr` vs df.
stdtrit -- Inverse of `stdtr` vs `t`.
chdtr -- Chi square cumulative distribution function.
chdtrc -- Chi square survival function.
chdtri -- Inverse to `chdtrc`.
chdtriv -- Inverse to `chdtr` vs `v`.
ndtr -- Gaussian cumulative distribution function.
log_ndtr -- Logarithm of Gaussian cumulative distribution function.
ndtri -- Inverse of `ndtr` vs x.
chndtr -- Non-central chi square cumulative distribution function.
chndtridf -- Inverse to `chndtr` vs `df`.
chndtrinc -- Inverse to `chndtr` vs `nc`.
chndtrix -- Inverse to `chndtr` vs `x`.
smirnov -- Kolmogorov-Smirnov complementary cumulative distribution function.
smirnovi -- Inverse to `smirnov`.
kolmogorov -- Complementary cumulative distribution function of Kolmogorov distribution.
kolmogi -- Inverse function to `kolmogorov`.
tklmbda -- Tukey-Lambda cumulative distribution function.
logit -- Logit ufunc for ndarrays.
expit -- Expit ufunc for ndarrays.
boxcox -- Compute the Box-Cox transformation.
boxcox1p -- Compute the Box-Cox transformation of 1 + `x`.
inv_boxcox -- Compute the inverse of the Box-Cox transformation.
inv_boxcox1p -- Compute the inverse of the Box-Cox transformation.
owens_t -- Owen's T Function.
Information Theory functions
----------------------------
.. autosummary::
:toctree: generated/
entr -- Elementwise function for computing entropy.
rel_entr -- Elementwise function for computing relative entropy.
kl_div -- Elementwise function for computing Kullback-Leibler divergence.
huber -- Huber loss function.
pseudo_huber -- Pseudo-Huber loss function.
Gamma and related functions
---------------------------
.. autosummary::
:toctree: generated/
gamma -- Gamma function.
gammaln -- Logarithm of the absolute value of the Gamma function for real inputs.
loggamma -- Principal branch of the logarithm of the Gamma function.
gammasgn -- Sign of the gamma function.
gammainc -- Regularized lower incomplete gamma function.
gammaincinv -- Inverse to `gammainc`.
gammaincc -- Regularized upper incomplete gamma function.
gammainccinv -- Inverse to `gammaincc`.
beta -- Beta function.
betaln -- Natural logarithm of absolute value of beta function.
betainc -- Incomplete beta integral.
betaincinv -- Inverse function to beta integral.
psi -- The digamma function.
rgamma -- Gamma function inverted.
polygamma -- Polygamma function n.
multigammaln -- Returns the log of multivariate gamma, also sometimes called the generalized gamma.
digamma -- psi(x[, out]).
poch -- Rising factorial (z)_m.
Error function and Fresnel integrals
------------------------------------
.. autosummary::
:toctree: generated/
erf -- Returns the error function of complex argument.
erfc -- Complementary error function, ``1 - erf(x)``.
erfcx -- Scaled complementary error function, ``exp(x**2) * erfc(x)``.
erfi -- Imaginary error function, ``-i erf(i z)``.
erfinv -- Inverse function for erf.
erfcinv -- Inverse function for erfc.
wofz -- Faddeeva function.
dawsn -- Dawson's integral.
fresnel -- Fresnel sin and cos integrals.
fresnel_zeros -- Compute nt complex zeros of sine and cosine Fresnel integrals S(z) and C(z).
modfresnelp -- Modified Fresnel positive integrals.
modfresnelm -- Modified Fresnel negative integrals.
voigt_profile -- Voigt profile.
These are not universal functions:
.. autosummary::
:toctree: generated/
erf_zeros -- Compute nt complex zeros of error function erf(z).
fresnelc_zeros -- Compute nt complex zeros of cosine Fresnel integral C(z).
fresnels_zeros -- Compute nt complex zeros of sine Fresnel integral S(z).
Legendre functions
------------------
.. autosummary::
:toctree: generated/
lpmv -- Associated Legendre function of integer order and real degree.
sph_harm -- Compute spherical harmonics.
These are not universal functions:
.. autosummary::
:toctree: generated/
clpmn -- Associated Legendre function of the first kind for complex arguments.
lpn -- Legendre function of the first kind.
lqn -- Legendre function of the second kind.
lpmn -- Sequence of associated Legendre functions of the first kind.
lqmn -- Sequence of associated Legendre functions of the second kind.
Ellipsoidal harmonics
---------------------
.. autosummary::
:toctree: generated/
ellip_harm -- Ellipsoidal harmonic functions E^p_n(l).
ellip_harm_2 -- Ellipsoidal harmonic functions F^p_n(l).
ellip_normal -- Ellipsoidal harmonic normalization constants gamma^p_n.
Orthogonal polynomials
----------------------
The following functions evaluate values of orthogonal polynomials:
.. autosummary::
:toctree: generated/
assoc_laguerre -- Compute the generalized (associated) Laguerre polynomial of degree n and order k.
eval_legendre -- Evaluate Legendre polynomial at a point.
eval_chebyt -- Evaluate Chebyshev polynomial of the first kind at a point.
eval_chebyu -- Evaluate Chebyshev polynomial of the second kind at a point.
eval_chebyc -- Evaluate Chebyshev polynomial of the first kind on [-2, 2] at a point.
eval_chebys -- Evaluate Chebyshev polynomial of the second kind on [-2, 2] at a point.
eval_jacobi -- Evaluate Jacobi polynomial at a point.
eval_laguerre -- Evaluate Laguerre polynomial at a point.
eval_genlaguerre -- Evaluate generalized Laguerre polynomial at a point.
eval_hermite -- Evaluate physicist's Hermite polynomial at a point.
eval_hermitenorm -- Evaluate probabilist's (normalized) Hermite polynomial at a point.
eval_gegenbauer -- Evaluate Gegenbauer polynomial at a point.
eval_sh_legendre -- Evaluate shifted Legendre polynomial at a point.
eval_sh_chebyt -- Evaluate shifted Chebyshev polynomial of the first kind at a point.
eval_sh_chebyu -- Evaluate shifted Chebyshev polynomial of the second kind at a point.
eval_sh_jacobi -- Evaluate shifted Jacobi polynomial at a point.
The following functions compute roots and quadrature weights for
orthogonal polynomials:
.. autosummary::
:toctree: generated/
roots_legendre -- Gauss-Legendre quadrature.
roots_chebyt -- Gauss-Chebyshev (first kind) quadrature.
roots_chebyu -- Gauss-Chebyshev (second kind) quadrature.
roots_chebyc -- Gauss-Chebyshev (first kind) quadrature.
roots_chebys -- Gauss-Chebyshev (second kind) quadrature.
roots_jacobi -- Gauss-Jacobi quadrature.
roots_laguerre -- Gauss-Laguerre quadrature.
roots_genlaguerre -- Gauss-generalized Laguerre quadrature.
roots_hermite -- Gauss-Hermite (physicst's) quadrature.
roots_hermitenorm -- Gauss-Hermite (statistician's) quadrature.
roots_gegenbauer -- Gauss-Gegenbauer quadrature.
roots_sh_legendre -- Gauss-Legendre (shifted) quadrature.
roots_sh_chebyt -- Gauss-Chebyshev (first kind, shifted) quadrature.
roots_sh_chebyu -- Gauss-Chebyshev (second kind, shifted) quadrature.
roots_sh_jacobi -- Gauss-Jacobi (shifted) quadrature.
The functions below, in turn, return the polynomial coefficients in
``orthopoly1d`` objects, which function similarly as `numpy.poly1d`.
The ``orthopoly1d`` class also has an attribute ``weights``, which returns
the roots, weights, and total weights for the appropriate form of Gaussian
quadrature. These are returned in an ``n x 3`` array with roots in the first
column, weights in the second column, and total weights in the final column.
Note that ``orthopoly1d`` objects are converted to `~numpy.poly1d` when doing
arithmetic, and lose information of the original orthogonal polynomial.
.. autosummary::
:toctree: generated/
legendre -- Legendre polynomial.
chebyt -- Chebyshev polynomial of the first kind.
chebyu -- Chebyshev polynomial of the second kind.
chebyc -- Chebyshev polynomial of the first kind on :math:`[-2, 2]`.
chebys -- Chebyshev polynomial of the second kind on :math:`[-2, 2]`.
jacobi -- Jacobi polynomial.
laguerre -- Laguerre polynomial.
genlaguerre -- Generalized (associated) Laguerre polynomial.
hermite -- Physicist's Hermite polynomial.
hermitenorm -- Normalized (probabilist's) Hermite polynomial.
gegenbauer -- Gegenbauer (ultraspherical) polynomial.
sh_legendre -- Shifted Legendre polynomial.
sh_chebyt -- Shifted Chebyshev polynomial of the first kind.
sh_chebyu -- Shifted Chebyshev polynomial of the second kind.
sh_jacobi -- Shifted Jacobi polynomial.
.. warning::
Computing values of high-order polynomials (around ``order > 20``) using
polynomial coefficients is numerically unstable. To evaluate polynomial
values, the ``eval_*`` functions should be used instead.
Hypergeometric functions
------------------------
.. autosummary::
:toctree: generated/
hyp2f1 -- Gauss hypergeometric function 2F1(a, b; c; z).
hyp1f1 -- Confluent hypergeometric function 1F1(a, b; x).
hyperu -- Confluent hypergeometric function U(a, b, x) of the second kind.
hyp0f1 -- Confluent hypergeometric limit function 0F1.
Parabolic cylinder functions
----------------------------
.. autosummary::
:toctree: generated/
pbdv -- Parabolic cylinder function D.
pbvv -- Parabolic cylinder function V.
pbwa -- Parabolic cylinder function W.
These are not universal functions:
.. autosummary::
:toctree: generated/
pbdv_seq -- Parabolic cylinder functions Dv(x) and derivatives.
pbvv_seq -- Parabolic cylinder functions Vv(x) and derivatives.
pbdn_seq -- Parabolic cylinder functions Dn(z) and derivatives.
Mathieu and related functions
-----------------------------
.. autosummary::
:toctree: generated/
mathieu_a -- Characteristic value of even Mathieu functions.
mathieu_b -- Characteristic value of odd Mathieu functions.
These are not universal functions:
.. autosummary::
:toctree: generated/
mathieu_even_coef -- Fourier coefficients for even Mathieu and modified Mathieu functions.
mathieu_odd_coef -- Fourier coefficients for even Mathieu and modified Mathieu functions.
The following return both function and first derivative:
.. autosummary::
:toctree: generated/
mathieu_cem -- Even Mathieu function and its derivative.
mathieu_sem -- Odd Mathieu function and its derivative.
mathieu_modcem1 -- Even modified Mathieu function of the first kind and its derivative.
mathieu_modcem2 -- Even modified Mathieu function of the second kind and its derivative.
mathieu_modsem1 -- Odd modified Mathieu function of the first kind and its derivative.
mathieu_modsem2 -- Odd modified Mathieu function of the second kind and its derivative.
Spheroidal wave functions
-------------------------
.. autosummary::
:toctree: generated/
pro_ang1 -- Prolate spheroidal angular function of the first kind and its derivative.
pro_rad1 -- Prolate spheroidal radial function of the first kind and its derivative.
pro_rad2 -- Prolate spheroidal radial function of the secon kind and its derivative.
obl_ang1 -- Oblate spheroidal angular function of the first kind and its derivative.
obl_rad1 -- Oblate spheroidal radial function of the first kind and its derivative.
obl_rad2 -- Oblate spheroidal radial function of the second kind and its derivative.
pro_cv -- Characteristic value of prolate spheroidal function.
obl_cv -- Characteristic value of oblate spheroidal function.
pro_cv_seq -- Characteristic values for prolate spheroidal wave functions.
obl_cv_seq -- Characteristic values for oblate spheroidal wave functions.
The following functions require pre-computed characteristic value:
.. autosummary::
:toctree: generated/
pro_ang1_cv -- Prolate spheroidal angular function pro_ang1 for precomputed characteristic value.
pro_rad1_cv -- Prolate spheroidal radial function pro_rad1 for precomputed characteristic value.
pro_rad2_cv -- Prolate spheroidal radial function pro_rad2 for precomputed characteristic value.
obl_ang1_cv -- Oblate spheroidal angular function obl_ang1 for precomputed characteristic value.
obl_rad1_cv -- Oblate spheroidal radial function obl_rad1 for precomputed characteristic value.
obl_rad2_cv -- Oblate spheroidal radial function obl_rad2 for precomputed characteristic value.
Kelvin functions
----------------
.. autosummary::
:toctree: generated/
kelvin -- Kelvin functions as complex numbers.
kelvin_zeros -- Compute nt zeros of all Kelvin functions.
ber -- Kelvin function ber.
bei -- Kelvin function bei
berp -- Derivative of the Kelvin function `ber`.
beip -- Derivative of the Kelvin function `bei`.
ker -- Kelvin function ker.
kei -- Kelvin function ker.
kerp -- Derivative of the Kelvin function ker.
keip -- Derivative of the Kelvin function kei.
These are not universal functions:
.. autosummary::
:toctree: generated/
ber_zeros -- Compute nt zeros of the Kelvin function ber(x).
bei_zeros -- Compute nt zeros of the Kelvin function bei(x).
berp_zeros -- Compute nt zeros of the Kelvin function ber'(x).
beip_zeros -- Compute nt zeros of the Kelvin function bei'(x).
ker_zeros -- Compute nt zeros of the Kelvin function ker(x).
kei_zeros -- Compute nt zeros of the Kelvin function kei(x).
kerp_zeros -- Compute nt zeros of the Kelvin function ker'(x).
keip_zeros -- Compute nt zeros of the Kelvin function kei'(x).
Combinatorics
-------------
.. autosummary::
:toctree: generated/
comb -- The number of combinations of N things taken k at a time.
perm -- Permutations of N things taken k at a time, i.e., k-permutations of N.
Lambert W and related functions
-------------------------------
.. autosummary::
:toctree: generated/
lambertw -- Lambert W function.
wrightomega -- Wright Omega function.
Other special functions
-----------------------
.. autosummary::
:toctree: generated/
agm -- Arithmetic, Geometric Mean.
bernoulli -- Bernoulli numbers B0..Bn (inclusive).
binom -- Binomial coefficient
diric -- Periodic sinc function, also called the Dirichlet function.
euler -- Euler numbers E0..En (inclusive).
expn -- Exponential integral E_n.
exp1 -- Exponential integral E_1 of complex argument z.
expi -- Exponential integral Ei.
factorial -- The factorial of a number or array of numbers.
factorial2 -- Double factorial.
factorialk -- Multifactorial of n of order k, n(!!...!).
shichi -- Hyperbolic sine and cosine integrals.
sici -- Sine and cosine integrals.
softmax -- Softmax function.
log_softmax -- Logarithm of softmax function.
spence -- Spence's function, also known as the dilogarithm.
zeta -- Riemann zeta function.
zetac -- Riemann zeta function minus 1.
Convenience functions
---------------------
.. autosummary::
:toctree: generated/
cbrt -- Cube root of `x`.
exp10 -- 10**x.
exp2 -- 2**x.
radian -- Convert from degrees to radians.
cosdg -- Cosine of the angle `x` given in degrees.
sindg -- Sine of angle given in degrees.
tandg -- Tangent of angle x given in degrees.
cotdg -- Cotangent of the angle `x` given in degrees.
log1p -- Calculates log(1+x) for use when `x` is near zero.
expm1 -- exp(x) - 1 for use when `x` is near zero.
cosm1 -- cos(x) - 1 for use when `x` is near zero.
round -- Round to nearest integer.
xlogy -- Compute ``x*log(y)`` so that the result is 0 if ``x = 0``.
xlog1py -- Compute ``x*log1p(y)`` so that the result is 0 if ``x = 0``.
logsumexp -- Compute the log of the sum of exponentials of input elements.
exprel -- Relative error exponential, (exp(x)-1)/x, for use when `x` is near zero.
sinc -- Return the sinc function.
""" |