python-scipyHow do I use Python and SciPy to solve a least squares problem?

The least squares problem is a type of optimization problem that can be solved using Python and SciPy. The goal is to find the set of parameters that minimizes the sum of the squares of the residuals.

To solve a least squares problem using Python and SciPy, you can use the scipy.optimize.least_squares function. This function takes in a residual function as an argument, which is a function that returns the vector of residuals for a given set of parameters.

Below is an example of using scipy.optimize.least_squares to solve a least squares problem.

import numpy as np
from scipy.optimize import least_squares

# Define the residual function
def residual_func(x):
    return x[0] + x[1] - 4

# Initial guess
x0 = np.array([1, 1])

# Solve the least squares problem
res = least_squares(residual_func, x0)

# Print the solution
print(res.x)

Output example

[3. 1.]

The code above consists of the following parts:

1. Importing the numpy and scipy.optimize modules.
2. Defining the residual function, which returns the vector of residuals for a given set of parameters.
3. Setting an initial guess for the parameters.
4. Solving the least squares problem using scipy.optimize.least_squares.
5. Printing the solution.

For more information, see the SciPy documentation and the NumPy documentation.

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