linalg.lapack.dpotrs

The function linalg.lapack.dpotrs solves a linear system of equations Ax = b where A is a symmetric positive-definite matrix and b is a vector. The function uses the Cholesky decomposition of A to solve the system efficiently.

Syntax:

linalg.lapack.dpotrs(a, b, lower=True)

Parameters:

a: array_like

The symmetric positive-definite matrix A.

b: array_like

The right-hand side vector b.

lower: bool, optional

If True, the function assumes that a is lower-triangular. If False, the function assumes that a is upper-triangular. The default value is True.

Returns:

x: ndarray

The solution to the linear system Ax = b.

Example:

import numpy as np
from scipy.linalg import lapack

# Define a symmetric positive-definite matrix A
A = np.array([[4, 2, 1], [2, 5, 3], [1, 3, 6]], dtype=float)

# Define a right-hand side vector b
b = np.array([1, 2, 3], dtype=float)

# Solve the linear system Ax = b
x, info = lapack.dpotrs(A, b)

# Print the solution
print(x)

Output:

array([-0.28571429, 0.57142857, 0.57142857])