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Module « numpy.linalg »

Fonction eigvalsh - module numpy.linalg

Signature de la fonction eigvalsh

def eigvalsh(a, UPLO='L') 

Description

help(numpy.linalg.eigvalsh)

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

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

Examples
--------
>>> import numpy as np
>>> 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])

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