flopscope.numpy.linalg.eigvalsh
fnp.linalg.eigvalsh(a, UPLO='L')[flopscope source][numpy source]
Compute the eigenvalues of a complex Hermitian or real symmetric matrix.
Adapted from NumPy docs np.linalg.eigvalsh
Symmetric eigenvalues. Cost: $n^3$.
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 flops.linalg documentation for details.
The eigenvalues are computed using LAPACK routines _syevd, _heevd.
Examples
>>> import flopscope.numpy as fnp
>>> from numpy import linalg as LA
>>> a = flops.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 = flops.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 = flops.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])