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, debug=None, check_finite=True) 

Description

solve_triangular.__doc__

    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]

    >>> 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.])