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Module « numpy.linalg »

Fonction solve - module numpy.linalg

Signature de la fonction solve

def solve(a, b) 

Description

help(numpy.linalg.solve)

Solve a linear matrix equation, or system of linear scalar equations.

Computes the "exact" solution, `x`, of the well-determined, i.e., full
rank, linear matrix equation `ax = b`.

Parameters
----------
a : (..., M, M) array_like
    Coefficient matrix.
b : {(M,), (..., M, K)}, array_like
    Ordinate or "dependent variable" values.

Returns
-------
x : {(..., M,), (..., M, K)} ndarray
    Solution to the system a x = b.  Returned shape is (..., M) if b is
    shape (M,) and (..., M, K) if b is (..., M, K), where the "..." part is
    broadcasted between a and b.

Raises
------
LinAlgError
    If `a` is singular or not square.

See Also
--------
scipy.linalg.solve : Similar function in SciPy.

Notes
-----
Broadcasting rules apply, see the `numpy.linalg` documentation for
details.

The solutions are computed using LAPACK routine ``_gesv``.

`a` must be square and of full-rank, i.e., all rows (or, equivalently,
columns) must be linearly independent; if either is not true, use
`lstsq` for the least-squares best "solution" of the
system/equation.

.. versionchanged:: 2.0

   The b array is only treated as a shape (M,) column vector if it is
   exactly 1-dimensional. In all other instances it is treated as a stack
   of (M, K) matrices. Previously b would be treated as a stack of (M,)
   vectors if b.ndim was equal to a.ndim - 1.

References
----------
.. [1] G. Strang, *Linear Algebra and Its Applications*, 2nd Ed., Orlando,
       FL, Academic Press, Inc., 1980, pg. 22.

Examples
--------
Solve the system of equations:
``x0 + 2 * x1 = 1`` and
``3 * x0 + 5 * x1 = 2``:

>>> import numpy as np
>>> a = np.array([[1, 2], [3, 5]])
>>> b = np.array([1, 2])
>>> x = np.linalg.solve(a, b)
>>> x
array([-1.,  1.])

Check that the solution is correct:

>>> np.allclose(np.dot(a, x), b)
True

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