# nlcpy.linalg.eigvalsh

nlcpy.linalg.eigvalsh(a, UPLO='L')[ソース]

Computes 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.

`eig`

Computes the eigenvalues and right eigenvectors of a square array.

`eigvals`

Computes the eigenvalues of a general matrix.

`eigh`

Computes the eigenvalues and eigenvectors of a complex Hermitian or a real symmetric matrix.

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

Examples

```>>> import nlcpy as vp
>>> a = vp.array([[1, -2j], [2j, 5]])
>>> vp.linalg.eigvalsh(a)
array([0.17157288, 5.82842712])  # may vary
```
```>>> # demonstrate the treatment of the imaginary part of the diagonal
>>> a = vp.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 vp.linalg.eigvals()
>>> # with:
>>> b = vp.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 = vp.linalg.eigvalsh(a)
>>> wb = vp.linalg.eigvals(b)
>>> wa; wb
array([1., 6.])
array([6.+0.j, 1.+0.j])
```