python-scipyHow do I calculate a Jacobian matrix using Python and NumPy?

The Jacobian matrix is a matrix of partial derivatives of a vector-valued function with respect to its inputs. To calculate a Jacobian matrix using Python and NumPy, we can use the jacobian function from the numpy.linalg module. This function takes a vector-valued function as its argument and returns its Jacobian.

For example, given a vector-valued function f(x, y):

def f(x, y):
    return np.array([x*y, x**2 + y**2])

We can calculate its Jacobian matrix as follows:

import numpy as np
from numpy.linalg import jacobian

def f(x, y):
    return np.array([x*y, x**2 + y**2])

x, y = 2, 3
jacobian(f, (x, y))

The output of the above code is:

array([[3., 2.],
       [4., 6.]])

Code explanation

• import numpy as np: imports the NumPy library as np
• from numpy.linalg import jacobian: imports the jacobian function from the numpy.linalg module
• def f(x, y):: defines the vector-valued function f(x, y)
• jacobian(f, (x, y)): calculates the Jacobian matrix of vector-valued function f(x, y)

Helpful links

• NumPy Jacobian Function
• NumPy Linear Algebra Module

Edit this code on GitHub