solve_triangular — SciPy v1.15.2 Manual (original) (raw)

scipy.linalg.

scipy.linalg.solve_triangular(a, b, trans=0, lower=False, unit_diagonal=False, overwrite_b=False, check_finite=True)[source]#

Solve the equation a x = b for x, assuming a is a triangular matrix.

Parameters:

a(M, M) array_like

A triangular matrix

b(M,) or (M, N) array_like

Right-hand side matrix in a x = b

lowerbool, optional

Use only data contained in the lower triangle of a. Default is to use upper triangle.

trans{0, 1, 2, ‘N’, ‘T’, ‘C’}, optional

Type of system to solve:

unit_diagonalbool, optional

If True, diagonal elements of a are assumed to be 1 and will not be referenced.

overwrite_bbool, optional

Allow overwriting data in b (may enhance performance)

check_finitebool, optional

Whether to check that the input matrices contain only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination) if the inputs do contain infinities or NaNs.

Returns:

x(M,) or (M, N) ndarray

Solution to the system a x = b. Shape of return matches b.

Raises:

LinAlgError

If a is singular

Notes

Added in version 0.9.0.

Examples

Solve the lower triangular system a x = b, where:

 [3  0  0  0]       [4]

a = [2 1 0 0] b = [2] [1 0 1 0] [4] [1 1 1 1] [2]

import numpy as np from scipy.linalg import solve_triangular a = np.array([[3, 0, 0, 0], [2, 1, 0, 0], [1, 0, 1, 0], [1, 1, 1, 1]]) b = np.array([4, 2, 4, 2]) x = solve_triangular(a, b, lower=True) x array([ 1.33333333, -0.66666667, 2.66666667, -1.33333333]) a.dot(x) # Check the result array([ 4., 2., 4., 2.])