Module « numpy.linalg »

Fonction eigvalsh - module numpy.linalg

Signature de la fonction eigvalsh

def eigvalsh(a, UPLO='L') 

Description

eigvalsh.__doc__

    Compute the eigenvalues of a complex Hermitian or real symmetric matrix.

    Main difference from eigh: the eigenvectors are not computed.

    Parameters
    ----------
    a : (..., M, M) array_like
        A complex- or real-valued matrix whose eigenvalues are to be
        computed.
    UPLO : {'L', 'U'}, optional
        Specifies whether the calculation is done with the lower triangular
        part of `a` ('L', default) or the upper triangular part ('U').
        Irrespective of this value only the real parts of the diagonal will
        be considered in the computation to preserve the notion of a Hermitian
        matrix. It therefore follows that the imaginary part of the diagonal
        will always be treated as zero.

    Returns
    -------
    w : (..., M,) ndarray
        The eigenvalues in ascending order, each repeated according to
        its multiplicity.

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

    See Also
    --------
    eigh : eigenvalues and eigenvectors of real symmetric or complex Hermitian
           (conjugate symmetric) arrays.
    eigvals : eigenvalues of general real or complex arrays.
    eig : eigenvalues and right eigenvectors of general real or complex
          arrays.
    scipy.linalg.eigvalsh : Similar function in SciPy.

    Notes
    -----

    .. versionadded:: 1.8.0

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

    The eigenvalues are computed using LAPACK routines ``_syevd``, ``_heevd``.

    Examples
    --------
    >>> from numpy import linalg as LA
    >>> a = np.array([[1, -2j], [2j, 5]])
    >>> LA.eigvalsh(a)
    array([ 0.17157288,  5.82842712]) # may vary

    >>> # demonstrate the treatment of the imaginary part of the diagonal
    >>> a = np.array([[5+2j, 9-2j], [0+2j, 2-1j]])
    >>> a
    array([[5.+2.j, 9.-2.j],
           [0.+2.j, 2.-1.j]])
    >>> # with UPLO='L' this is numerically equivalent to using LA.eigvals()
    >>> # with:
    >>> b = np.array([[5.+0.j, 0.-2.j], [0.+2.j, 2.-0.j]])
    >>> b
    array([[5.+0.j, 0.-2.j],
           [0.+2.j, 2.+0.j]])
    >>> wa = LA.eigvalsh(a)
    >>> wb = LA.eigvals(b)
    >>> wa; wb
    array([1., 6.])
    array([6.+0.j, 1.+0.j])