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Module « scipy.linalg »

Fonction solve_triangular - module scipy.linalg

Signature de la fonction solve_triangular

def solve_triangular(a, b, trans=0, lower=False, unit_diagonal=False, overwrite_b=False, check_finite=True) 

Description

help(scipy.linalg.solve_triangular)

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``
lower : bool, 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_diagonal : bool, optional
    If True, diagonal elements of `a` are assumed to be 1 and
    will not be referenced.
overwrite_b : bool, optional
    Allow overwriting data in `b` (may enhance performance)
check_finite : bool, 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
-----
.. versionadded:: 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.])

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