Compute Jacobian matrix by Sympy

Computing the Jacobian matrix is not easy, but we can use the python symbolical package Sympy to get it.

Here is a simple example.

import sympy as sym
from sysmpy import init_printing
from sympy import sin,cos,Matrix

init_printing()

x,y=sym.symbols('x y')
F=Matrix([x*cos(y),x*sin(y),x**2])
X=Matrix([x,y])
print(F.jacobian(X))
print(F.jacbian(X).subs([(x,0),(y,1)]))

Reference:

https://docs.sympy.org/latest/modules/matrices/matrices.html

https://www.sympy.org/scipy-2017-codegen-tutorial/notebooks/20-ordinary-differential-equations.html