对一组函数的解的替换

Question

我一直在尝试使用矩阵传递方法求解光学系统。问题是，我想看看矩阵中的一个元素是否是常数。我用sympy来求解矩阵的一部分，我想用这些解来替换矩阵的另一个元素。我使用了sympy.subs，但似乎不起作用。代码如下

import numpy as np
import matplotlib.pyplot as plt
from sympy import *
#all distances in mm
n1 = 1
n2 = 1.77
n = n1/n2
f1 = 200
f2 = 3.3
d = np.arange(1,300,10)
d1 = d[::-1]
d2 = f2+f1
d3 = 0.5*10**(-3)
z = symbols('z')
M2 = np.array([[1, 0], [-1/f1, 1]])
M3 = np.array([[1, d2], [0, 1]])
M4 = np.array([[1, 0], [-1/f2, 1]])
M5 = np.array([[1, d3], [0, 1]])
M6 = np.array([[1, 0], [0, n]])
M7 = np.array([[1, z], [0, 1]])
s = []
Mag =[]
for i in d1:
M1 = np.array([[1, i], [0, 1]])
M = np.dot(np.dot(np.dot(np.dot(M7,M6),np.dot(M5,M4)),np.dot(M3,M2)),M1)
sol = solve(M[0,1])
Mf = M[0,0]
Mf = Mf.subs(z, sol)
Mag.append(Mf)
s.append(sol)
Mag

Output: [3.12250225675825e-17*z - 0.0165000000000002,
3.12250225675825e-17*z - 0.0165000000000002,
3.12250225675825e-17*z - 0.0165000000000002,
3.12250225675825e-17*z - 0.0165000000000002,
3.12250225675825e-17*z - 0.0165000000000002,
3.12250225675825e-17*z - 0.0165000000000002,
3.12250225675825e-17*z - 0.0165000000000002,
3.12250225675825e-17*z - 0.0165000000000002,
3.12250225675825e-17*z - 0.0165000000000002,
3.12250225675825e-17*z - 0.0165000000000002,
3.12250225675825e-17*z - 0.0165000000000002,
3.12250225675825e-17*z - 0.0165000000000002,
3.12250225675825e-17*z - 0.0165000000000002,
3.12250225675825e-17*z - 0.0165000000000002,
3.12250225675825e-17*z - 0.0165000000000002,
3.12250225675825e-17*z - 0.0165000000000002,
3.12250225675825e-17*z - 0.0165000000000002,
3.12250225675825e-17*z - 0.0165000000000002,
3.12250225675825e-17*z - 0.0165000000000002,
3.12250225675825e-17*z - 0.0165000000000002,
3.12250225675825e-17*z - 0.0165000000000002,
3.12250225675825e-17*z - 0.0165000000000002,
3.12250225675825e-17*z - 0.0165000000000002,
3.12250225675825e-17*z - 0.0165000000000002,
3.12250225675825e-17*z - 0.0165000000000002,
3.12250225675825e-17*z - 0.0165000000000002,
3.12250225675825e-17*z - 0.0165000000000002,
3.12250225675825e-17*z - 0.0165000000000002,
3.12250225675825e-17*z - 0.0165000000000002,
3.12250225675825e-17*z - 0.0165000000000002]

Answer 1

有两件事会有所帮助：

1. 求解指定变量。由于要替换z，因此应该告诉solve像在solve(M[0,1],z)中那样为z求解
2. solve的输出将是一个z值的列表——在您的情况下，似乎只有一个——而subs需要一个值，而不是列表，作为第二个参数：Mf.subs(z, sol[0])

我不使用该目录，但SymPy中有一个光学目录可能有用。