Module « scipy.linalg »

Fonction eigvals - module scipy.linalg

Signature de la fonction eigvals

def eigvals(a, b=None, overwrite_a=False, check_finite=True, homogeneous_eigvals=False) 

Description

eigvals.__doc__

    Compute eigenvalues from an ordinary or generalized eigenvalue problem.

    Find eigenvalues of a general matrix::

        a   vr[:,i] = w[i]        b   vr[:,i]

    Parameters
    ----------
    a : (M, M) array_like
        A complex or real matrix whose eigenvalues and eigenvectors
        will be computed.
    b : (M, M) array_like, optional
        Right-hand side matrix in a generalized eigenvalue problem.
        If omitted, identity matrix is assumed.
    overwrite_a : bool, optional
        Whether to overwrite data in a (may improve 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.
    homogeneous_eigvals : bool, optional
        If True, return the eigenvalues in homogeneous coordinates.
        In this case ``w`` is a (2, M) array so that::

            w[1,i] a vr[:,i] = w[0,i] b vr[:,i]

        Default is False.

    Returns
    -------
    w : (M,) or (2, M) double or complex ndarray
        The eigenvalues, each repeated according to its multiplicity
        but not in any specific order. The shape is (M,) unless
        ``homogeneous_eigvals=True``.

    Raises
    ------
    LinAlgError
        If eigenvalue computation does not converge

    See Also
    --------
    eig : eigenvalues and right eigenvectors of general arrays.
    eigvalsh : eigenvalues of symmetric or Hermitian arrays
    eigvals_banded : eigenvalues for symmetric/Hermitian band matrices
    eigvalsh_tridiagonal : eigenvalues of symmetric/Hermitian tridiagonal
        matrices

    Examples
    --------
    >>> from scipy import linalg
    >>> a = np.array([[0., -1.], [1., 0.]])
    >>> linalg.eigvals(a)
    array([0.+1.j, 0.-1.j])

    >>> b = np.array([[0., 1.], [1., 1.]])
    >>> linalg.eigvals(a, b)
    array([ 1.+0.j, -1.+0.j])

    >>> a = np.array([[3., 0., 0.], [0., 8., 0.], [0., 0., 7.]])
    >>> linalg.eigvals(a, homogeneous_eigvals=True)
    array([[3.+0.j, 8.+0.j, 7.+0.j],
           [1.+0.j, 1.+0.j, 1.+0.j]])