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 |
---|---|
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
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
>>> 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])
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https://docs.scipy.org/doc/numpy-1.13.0/reference/generated/numpy.linalg.eigvalsh.html