我怎样才能找到 numpy 的 Wronskian 行列式

如何解决我怎样才能找到 numpy 的 Wronskian 行列式

我试图找到这 3 个函数的 Wronskian 行列式，但代码有“TypeError: No loop matching the specified signature and cast was found for ufunc det”。我该如何解决？

import numpy as np
import numpy.linalg
import sympy as sp
x = sp.Symbol('x')
e=sp.exp(-3*x) #inputs
f=sp.cos(2*x) 
g=sp.sin(2*x)
buneya=np.array([e,f,g],dtype=object)


a=sp.diff(buneya[0]) #first derivative
b=sp.diff(buneya[1])
c=sp.diff(buneya[2])

k=sp.diff(a)
l=sp.diff(b) #second derivative
m=sp.diff(c)
wronskian=np.array([[e,[a,b,c],[k,l,m]],dtype=object)
print (np.linalg.det(wronskian) )  #determinant

Traceback (most recent call last):

  File "C:\Users\canat\.spyder-py3\temp.py",line 20,in <module>
    print (np.linalg.det(wronskian) )

  File "<__array_function__ internals>",line 5,in det

  File "C:\ProgramData\Anaconda3\lib\site-packages\numpy\linalg\linalg.py",line 2159,in det
    r = _umath_linalg.det(a,signature=signature)

TypeError: No loop matching the specified signature and casting was found for ufunc det 

解决方法

就是这么简单：

import sympy as sp
x = sp.Symbol('x')
e=sp.exp(-3*x) #inputs
f=sp.cos(2*x) 
g=sp.sin(2*x)
buneya=[e,f,g]

a=sp.diff(buneya[0]) #first derivative
b=sp.diff(buneya[1])
c=sp.diff(buneya[2])

k=sp.diff(a)
l=sp.diff(b) #second derivative
m=sp.diff(c)
wronskian=sp.Matrix([[e,g],[a,b,c],[k,l,m]]).det()
print(wronskian)

返回

26*exp(-3*x)*sin(2*x)**2 + 26*exp(-3*x)*cos(2*x)**2

有关详细信息，请参阅 sympy 矩阵 docs。

编辑 #1 甚至更简单！

import sympy as sp
from sympy.matrices import dense

x = sp.Symbol('x')
e=sp.exp(-3*x) #inputs
f=sp.cos(2*x) 
g=sp.sin(2*x)

wronskian = dense.wronskian([e,x)
print(wronskian)

返回相同

26*exp(-3*x)*sin(2*x)**2 + 26*exp(-3*x)*cos(2*x)**2

wronskian 方法也记录在 sympy docs 中。