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.

参数

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.

返回

w – The eigenvalues in ascending order, each repeated according to its multiplicity.

返回类型

(…, M,) ndarray

引发

LinAlgError – If the eigenvalue computation does not converge.

参见

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.

提示

1.8.0(numpy.linalg) 新版功能.

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

The eigenvalues are computed using LAPACK routines _syevd, _heevd.

实际案例

>>> 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])

警告

This method has not been implemented yet. Xorbits will try to execute it with numpy.linalg.

This docstring was copied from numpy.linalg.