numpy.linalg.LinAlgError:数组的最后2个维度必须是正方形

Question

我正在尝试求解传递给a和b的方程，但我遇到了numpy.linalg.LinAlgError：数组的最后2个维度必须是正方形，我该如何解决这个问题

import sympy as sp
import numpy as np
import matplotlib.pyplot as plt
l=np.arange(1,1.5,0.01)
d=np.arange(0.005,0.015,0.0002)
Eb1=3543.75
A1=1
A2=(np.pi)*(d/2)**2/2
A3=np.pi
F11=0
F21=2*(np.arctan(0.5/l)*(180/np.pi))/360
F12=(d*np.pi*F21)
F12p=(((4/l**2)+4)**0.5-2)*(l/2)
F13=F12p-F12
F14=1-F12-F13
F23=0.5
F24=1-F21-F23
F34=F14/np.pi
rho=0.7
k=0.04
pr=0.7
cp=1005
myu=2.4*10**-5
alpha=5.68*10**-5
beta=1/500
Ra=(rho*9.81*beta*(500-293)*l)/(myu*alpha)
Nu=0.68+(0.67*Ra**0.25)/(1+(0.429/pr)**(9/16))**(4/9)
h=Nu*k
J1=3543.75+0.42*h*(500-295)
a = np.array([[F12,F13,F14], [-1*(F12+A2*F23+A2*F24),A2*F23,A2*F24], [A2*F23,-1*(A3*F34+A2*F23+F13),A3*F34]])
b = np.array([(7/3+F12+F14+F13)*J1-Eb1,-F12*J1,-F13*J1])
x = np.linalg.solve(a, b)
J2=x[0]
J3=x[1]
J4=x[2]
Eb2=((1-0.8)/(0.8*A2))*((J2-J1)*A1*F12)+J2
qrad=(Eb2-J2)/((1-0.8)/(0.8*A2))
print(qrad)

Answer 1

如果您进行一些形状重组以使解算器工作：

x = np.linalg.solve(np.moveaxis(a, 2, 0), b.T)
x = x.T

将qrad设为：

[0.04295253 0.04653147 0.05025864 0.05413453 0.0581596  0.0623343
0.06665908 0.07113439 0.07576063 0.08053823 0.08546759 0.0905491
0.09578314 0.10117008 0.10671028 0.11240411 0.11825189 0.12425396
0.13041064 0.13672224 0.14318907 0.14981142 0.15658958 0.16352382
0.1706144  0.17786158 0.18526562 0.19282674 0.20054518 0.20842117
0.21645491 0.22464661 0.23299646 0.24150466 0.25017139 0.2589968
0.26798108 0.27712437 0.28642682 0.29588858 0.30550977 0.31529051
0.32523093 0.33533114 0.34559123 0.3560113  0.36659143 0.37733172
0.38823223 0.39929302]