求解符号方程组仅返回 2 个准确值

Question

我必须求解满足某些条件的方程组。当我使用 Sympy 中的

solve

执行此操作时，我只得到 8 个值中的 2 个正确。

这是我的代码。

import numpy as np
from sympy import symbols, exp, Eq, solve

gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7 = symbols('gamma0 gamma1 gamma2 gamma3 gamma4 gamma5 gamma6 gamma7')
gamma = [gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7]
x = symbols('x')
a = 20
b = 5

u =[
    [0.388518*gamma0*exp(-2.012490*x) - 0.675612*gamma1*exp(-0.369901*x) + 0.336576*gamma2*exp(0.369901*x) - 0.103503*gamma3*exp(2.012490*x) + 20.168718, 
    0.163057*gamma4*exp(-2.421891*x) - 0.951601*gamma5*exp(-0.951784*x) + 0.086427*gamma6*exp(0.754538*x) - 0.045759*gamma7*exp(2.528248*x) + 2.394974],

    [-0.900008*gamma0*exp(-2.012490*x) - 0.520883*gamma1*exp(-0.369901*x) + 0.398678*gamma2*exp(0.369901*x) - 0.168303*gamma3*exp(2.012490*x) + 20.034468, 
    -0.976653*gamma4*exp(-2.421891*x) - 0.238418*gamma5*exp(-0.951784*x) + 0.122769*gamma6*exp(0.754538*x) - 0.080425*gamma7*exp(2.528248*x) + 2.329339],

    [-0.168303*gamma0*exp(-2.012490*x) - 0.398678*gamma1*exp(-0.369901*x) + 0.520883*gamma2*exp(0.369901*x) - 0.900008*gamma3*exp(2.012490*x) + 19.932869, 
    -0.095726*gamma4*exp(-2.421891*x) - 0.120587*gamma5*exp(-0.951784*x) + 0.326236*gamma6*exp(0.754538*x) - 0.963388*gamma7*exp(2.528248*x) + 2.504797], 

    [-0.103503*gamma0*exp(-2.012490*x) - 0.336576*gamma1*exp(-0.369901*x) + 0.675612*gamma2*exp(0.369901*x) + 0.388518*gamma3*exp(2.012490*x) + 19.892514, 
    -0.101960*gamma4*exp(-2.421891*x) - 0.151889*gamma5*exp(-0.951784*x) + 0.933288*gamma6*exp(0.754538*x) + 0.251633*gamma7*exp(2.528248*x) + 3.335936]
    ]

from sympy import Eq, solve

# Define the symbolic equations
eqns = [
    Eq(u[0][0].subs(x, 0), 0),
    Eq(u[1][0].subs(x, 0), 0),
    Eq(u[0][0].subs(x, b), u[0][1].subs(x, b)),
    Eq(u[1][0].subs(x, b), u[1][1].subs(x, b)),
    Eq(u[2][0].subs(x, b), u[2][1].subs(x, b)),
    Eq(u[3][0].subs(x, b), u[3][1].subs(x, b)),
    Eq(u[2][1].subs(x, a), 0),
    Eq(u[3][1].subs(x, a), 0)
]

# Solve the equations for the gamma variables
gamma_symbols = [gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7]
solutions = solve(eqns, gamma_symbols)

# Print the solutions
for symbol, value in solutions.items():
    print(f"{symbol}: {value}")

我需要获取的值如下：

gamma0: 3.3451862507144963721760546900288
gamma1: 30.086443529744653795656405805539
gamma2: -3.3917670835986188504875542362514
gamma3: 0.00013878499955117735347592615338105
gamma4: -775727.3319427781475689057795114
gamma5: -941.09415775171256674990468706789
gamma6: -0.0000010944407599058234322536821517657
gamma7: 0.00000000000000000000013958849298737787410748516872778

但是，当我运行代码时，我得到这些值：

gamma0: -2953067.95180723
gamma1: -1383474.12048191      
gamma2: -13623.4036144577      
gamma3: 1.03375979503954       
gamma4: -8212497765.78320      
gamma5: -15039124.0279307      
gamma6: -0.00000109854435279209
gamma7: 1.40162266686094E-22  

只有 gamma6 和 gamma7 是准确的。我想知道 Python 是否无法处理该系统，或者是否有其他好方法来解决它。

Answer 1

一定要使用

linsolve

：

>>> from sympy import *

# your code without solve

>>> v = [gamma0, gamma1, gamma2, gamma3, gamma4, gamma5, gamma6, gamma7]
>>> for i in zip(v, list(linsolve(eqns, v))[0]): # only one soln
...    print(i)
...
(gamma0, 3.34518073050084)
(gamma1, 30.0864601804563)
(gamma2, -3.39178380795305)
(gamma3, 0.000138785046404537)
(gamma4, -775727.547533190)
(gamma5, -941.091400437524)
(gamma6, -1.09445480076177e-6)
(gamma7, 1.39590082130360e-22)