xorbits.numpy.linalg.eigvalsh#
- xorbits.numpy.linalg.eigvalsh(a, UPLO='L')#
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 – The eigenvalues in ascending order, each repeated according to its multiplicity.
- Return type
(…, M,) ndarray
- Raises
LinAlgError – If the eigenvalue computation does not converge.
See also
Notes
New in version 1.8.0(numpy.linalg).
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])
Warning
This method has not been implemented yet. Xorbits will try to execute it with numpy.linalg.
This docstring was copied from numpy.linalg.