numpy.linalg.eigvalsh¶
-
numpy.linalg.
eigvalsh
(a, UPLO='L')[source]¶ Compute the eigenvalues of a 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
Notes
New in version 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])
>>> # 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])