如何用numpy找到Wronskian行列式

Question

我试图找到这3个函数的Wronskian行列式，但代码中有“TypeError:没有找到与指定签名和ufunc det转换匹配的循环”。我怎样才能解决它

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,f,g],[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 

Answer 1

很简单：

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,f,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

有关更多信息，请参见sympy矩阵docs

编辑#1 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,f,g],x)
print(wronskian)

返回相同的值

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

wronskian方法也记录在sympydocs中