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import sympy as sp
class HighLevel():
def __init__(self, j):
self.j = j
def initial(self):
j = self.j
#init parameters
h, b, n, u = 0.1, None, None, None
x, y, z, px, py, pz = None, 0.1, 0.001, 0.01, None, 0.0001
xa, ya, za, pxa, pya, pza = None, None, None, None, None, None
if j == 1:
b = 5.0 / 4
n = b / (1 + b) ** 2
u = 1.0 / (1.0 / b + b + 2.0)
x = 10.0
py = 0.5
elif j == 2:
b = 3.0 / 4
n = b / (1 + b) ** 2
u = 1.0 / (1.0 / b + b + 2.0)
x = 8.3
py = 0.6
elif j == 3:
b = 3.0 / 2
x = 12.0
py = 0.4
elif j == 4:
b = 7.0 / 4
n = b / (1 + b) ** 2
u = 1.0 / (1.0 / b + b + 2.0)
x = 15.0
py = 0.35
elif j == 5:
b = 1.0
n = b / (1 + b) ** 2
u = 1.0 / (1.0 / b + b + 2.0)
x = 18.0
py = 0.3
elif j == 6:
b = 3.0 / 5
n = b / (1 + b) ** 2
u = 1.0 / (1.0 / b + b + 2.0)
x = 20.0
py = 0.25
elif j == 7:
b = 5.0 / 7
n = b / (1 + b) ** 2
u = 1.0 / (1.0 / b + b + 2.0)
x = 22.0
py = 0.22
elif j == 8:
b = 2.0
x = 26.0
py = 0.2
elif j == 9:
b = 0.5
n = b / (1 + b) ** 2
u = 1.0 / (1.0 / b + b + 2.0)
x = 30.0
y = 0.5
z = 0.1
pz = 0.01
elif j == 10:
b = 5.0
n = b / (1 + b) ** 2
u = 1.0 / (1.0 / b + b + 2.0)
x = 35.0
y = 2.0
z = 0.1
pz = 0.03
py = 0.15
xa, ya, za, pxa, pya, pza = x, y, z, px, py, pz
return j, h, b, n, x, y, z, xa, ya, za, px, py, pz, pxa, pya, pza
def f(self, x, y, z, px, py, pz, b):
x_val, y_val, z_val, px_val, py_val, pz_val, b_val = x, y, z, px, py, pz, b
x, y, z, px, py, pz, b = sp.symbols('x y z px py pz b')
c = 1.0
u = 1 / (1 / b + b + 2)
ht = px ** 2 / 2 + py ** 2 / 2 + pz ** 2 / 2
hv = -1 / (x ** 2 + y ** 2 + z ** 2) ** (1 / 2)
h1pn = 1 / (2 * x ** 2 + 2 * y ** 2 + 2 * z ** 2) - (((u + 3) * (px ** 2 + py ** 2 + pz ** 2)) / 2 + (u * (
(px * x) / (x ** 2 + y ** 2 + z ** 2) ** (1 / 2) + (py * y) / (x ** 2 + y ** 2 + z ** 2) ** (
1 / 2) + (pz * z) / (x ** 2 + y ** 2 + z ** 2) ** (1 / 2)) ** 2) / 2) / (
x ** 2 + y ** 2 + z ** 2) ** (1 / 2) + ((3 * u) / 8 - 1 / 8) * (
px ** 2 + py ** 2 + pz ** 2) ** 2
e = ht + hv + h1pn
de_dx = sp.diff(e, x)
de_dy = sp.diff(e, y)
de_dz = sp.diff(e, z)
de_dpx = sp.diff(e, px)
de_dpy = sp.diff(e, py)
de_dpz = sp.diff(e, pz)
de_dx_val = de_dx.subs({x: x_val, y: y_val, z: z_val, px: px_val, py: py_val, pz: pz_val, b: b_val})
de_dy_val = de_dy.subs({x: x_val, y: y_val, z: z_val, px: px_val, py: py_val, pz: pz_val, b: b_val})
de_dz_val = de_dz.subs({x: x_val, y: y_val, z: z_val, px: px_val, py: py_val, pz: pz_val, b: b_val})
de_dpx_val = de_dpx.subs({x: x_val, y: y_val, z: z_val, px: px_val, py: py_val, pz: pz_val, b: b_val})
de_dpy_val = de_dpy.subs({x: x_val, y: y_val, z: z_val, px: px_val, py: py_val, pz: pz_val, b: b_val})
de_dpz_val = de_dpz.subs({x: x_val, y: y_val, z: z_val, px: px_val, py: py_val, pz: pz_val, b: b_val})
e_val = e.subs({x: x_val, y: y_val, z: z_val, px: px_val, py: py_val, pz: pz_val, b: b_val})
return de_dx_val, de_dy_val, de_dz_val, de_dpx_val, de_dpy_val, de_dpz_val, e_val
def rejust(self, x, y, z, px, py, pz, xa, ya, za, pxa, pya, pza):
x = (x + xa) / 2
y = (y + ya) / 2
z = (z + za) / 2
px = (px + pxa) / 2
py = (py + pya) / 2
pz = (pz + pza) / 2
xa = x
ya = y
za = z
pxa = px
pya = py
pza = pz
return x, y, z, px, py, pz, xa, ya, za, pxa, pya, pza
def symplectic(self, h, x, y, z, px, py, pz, xa, ya, za, pxa, pya, pza, b):
vxa, vya, vza, vpx, vpy, vpz, e = self.f(xa, ya, za, px, py, pz, b)
x = x + h / 2 * vpx
y = y + h / 2 * vpy
z = z + h / 2 * vpz
pxa = pxa - h / 2 * vxa
pya = pya - h / 2 * vya
pza = pza - h / 2 * vza
vx, vy, vz, vpxa, vpya, vpza, e = self.f(x, y, z, pxa, pya, pza, b)
xa = xa + h * vpxa
ya = ya + h * vpya
za = za + h * vpza
px = px - h * vx
py = py - h * vy
pz = pz - h * vz
vxa, vya, vza, vpx, vpy, vpz, e = self.f(xa, ya, za, px, py, pz, b)
x = x + h / 2 * vpx
y = y + h / 2 * vpy
z = z + h / 2 * vpz
pxa = pxa - h / 2 * vxa
pya = pya - h / 2 * vya
pza = pza - h / 2 * vza
return x, y, z, px, py, pz, xa, ya, za, pxa, pya, pza |