Module « scipy.linalg »

Fonction solve - module scipy.linalg

Signature de la fonction solve

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

Description

solve.__doc__

    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

    ===================  ========
     generic matrix       'gen'
     symmetric            'sym'
     hermitian            'her'
     positive definite    'pos'
    ===================  ========

    If omitted, ``'gen'`` is the default structure.

    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.

    Parameters
    ----------
    a : (N, N) array_like
        Square input data
    b : (N, NRHS) array_like
        Input data for the right hand side.
    sym_pos : bool, optional
        Assume `a` is symmetric and positive definite. This key is deprecated
        and assume_a = 'pos' keyword is recommended instead. The functionality
        is the same. It will be removed in the future.
    lower : bool, optional
        If True, only the data contained in the lower triangle of `a`. Default
        is to use upper triangle. (ignored for ``'gen'``)
    overwrite_a : bool, optional
        Allow overwriting data in `a` (may enhance performance).
        Default is False.
    overwrite_b : bool, optional
        Allow overwriting data in `b` (may enhance performance).
        Default is False.
    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.
    assume_a : str, optional
        Valid entries are explained above.
    transposed: bool, optional
        If True, ``a^T x = b`` for real matrices, raises `NotImplementedError`
        for complex matrices (only for True).

    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.

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

    >>> 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)

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