dpnp.linalg.eigh

dpnp.linalg.eigh(a, UPLO='L')[source]

Return the eigenvalues and eigenvectors of a complex Hermitian (conjugate symmetric) or a real symmetric matrix.

Returns two objects, a 1-D array containing the eigenvalues of a, and a 2-D square array or matrix (depending on the input type) of the corresponding eigenvectors (in columns).

For full documentation refer to numpy.linalg.eigh.

Returns:

w ((…, M) dpnp.ndarray) – The eigenvalues in ascending order, each repeated according to its multiplicity.
v ((…, M, M) dpnp.ndarray) – The column v[:, i] is the normalized eigenvector corresponding to the eigenvalue w[i].

Limitations

Parameter a is supported as dpnp.ndarray or dpctl.tensor.usm_ndarray. Input array data types are limited by supported DPNP Data types.

See also

dpnp.eig: eigenvalues and right eigenvectors for non-symmetric arrays.
dpnp.eigvals: eigenvalues of non-symmetric arrays.

Examples

>>> import dpnp as dp
>>> a = dp.array([[1, -2j], [2j, 5]])
>>> a
array([[ 1.+0.j, -0.-2.j],
       [ 0.+2.j,  5.+0.j]])
>>> w, v = dp.linalg.eigh(a)
>>> w; v
array([0.17157288, 5.82842712]),
array([[-0.92387953-0.j        , -0.38268343+0.j        ], # may vary
       [ 0.        +0.38268343j,  0.        -0.92387953j]]))