scipy.linalg.

solve_triangular#

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.

The documentation is written assuming array arguments are of specified “core” shapes. However, array argument(s) of this function may have additional “batch” dimensions prepended to the core shape. In this case, the array is treated as a batch of lower-dimensional slices; see Batched Linear Operations for details.

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:

trans	system
0 or ‘N’	a x = b
1 or ‘T’	a^T x = b
2 or ‘C’	a^H x = b

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.])