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