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Module « scipy.linalg »

Fonction solve - module scipy.linalg

Signature de la fonction solve

def solve(a, b, lower=False, overwrite_a=False, overwrite_b=False, check_finite=True, assume_a=None, transposed=False) 

Description

help(scipy.linalg.solve)

Solves the linear equation set ``a @ x == b`` for the unknown ``x``
for square `a` matrix.

If the data matrix is known to be a particular type then supplying the
corresponding string to ``assume_a`` key chooses the dedicated solver.
The available options are

===================  ================================
 diagonal             'diagonal'
 tridiagonal          'tridiagonal'
 banded               'banded'
 upper triangular     'upper triangular'
 lower triangular     'lower triangular'
 symmetric            'symmetric' (or 'sym')
 hermitian            'hermitian' (or 'her')
 positive definite    'positive definite' (or 'pos')
 general              'general' (or 'gen')
===================  ================================

Parameters
----------
a : (N, N) array_like
    Square input data
b : (N, NRHS) array_like
    Input data for the right hand side.
lower : bool, default: False
    Ignored unless ``assume_a`` is one of ``'sym'``, ``'her'``, or ``'pos'``.
    If True, the calculation uses only the data in the lower triangle of `a`;
    entries above the diagonal are ignored. If False (default), the
    calculation uses only the data in the upper triangle of `a`; entries
    below the diagonal are ignored.
overwrite_a : bool, default: False
    Allow overwriting data in `a` (may enhance performance).
overwrite_b : bool, default: False
    Allow overwriting data in `b` (may enhance performance).
check_finite : bool, default: True
    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.
assume_a : str, optional
    Valid entries are described above.
    If omitted or ``None``, checks are performed to identify structure so the
    appropriate solver can be called.
transposed : bool, default: False
    If True, solve ``a.T @ x == b``. Raises `NotImplementedError`
    for complex `a`.

Returns
-------
x : (N, NRHS) ndarray
    The solution array.

Raises
------
ValueError
    If size mismatches detected or input a is not square.
LinAlgError
    If the matrix is singular.
LinAlgWarning
    If an ill-conditioned input a is detected.
NotImplementedError
    If transposed is True and input a is a complex matrix.

Notes
-----
If the input b matrix is a 1-D array with N elements, when supplied
together with an NxN input a, it is assumed as a valid column vector
despite the apparent size mismatch. This is compatible with the
numpy.dot() behavior and the returned result is still 1-D array.

The general, symmetric, Hermitian and positive definite solutions are
obtained via calling ?GESV, ?SYSV, ?HESV, and ?POSV routines of
LAPACK respectively.

The datatype of the arrays define which solver is called regardless
of the values. In other words, even when the complex array entries have
precisely zero imaginary parts, the complex solver will be called based
on the data type of the array.

Examples
--------
Given `a` and `b`, solve for `x`:

>>> import numpy as np
>>> a = np.array([[3, 2, 0], [1, -1, 0], [0, 5, 1]])
>>> b = np.array([2, 4, -1])
>>> from scipy import linalg
>>> x = linalg.solve(a, b)
>>> x
array([ 2., -2.,  9.])
>>> np.dot(a, x) == b
array([ True,  True,  True], dtype=bool)

Vous êtes un professionnel et vous avez besoin d'une formation ? Programmation Python
Les fondamentaux Voir le programme détaillé