Function solve

numpy/linalg/linalg.py:330–411

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

(a, b)

@array_function_dispatch(_solve_dispatcher)
def solve(a, b):
    """
    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 identical to `b`.

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

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

    Notes
    -----

    .. versionadded:: 1.8.0

    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.

    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``:

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