scipy.linalg.solve_triangular¶
- scipy.linalg.solve_triangular(a, b, trans=0, lower=False, unit_diagonal=False, overwrite_b=False, debug=None, 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:
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
New 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]
>>> 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.])