dpnp.linalg.eig

dpnp.linalg.eig(a)[source]

Compute the eigenvalues and right eigenvectors of a square array.

For full documentation refer to numpy.linalg.eig.

Parameters:

a ((..., M, M) {dpnp.ndarray, usm_ndarray}) -- Matrices for which the eigenvalues and right eigenvectors will be computed.

Returns:

eigenvalues ((..., M) dpnp.ndarray) -- The eigenvalues, each repeated according to its multiplicity. The eigenvalues are not necessarily ordered. The resulting array will be of complex type, unless the imaginary part is zero in which case it will be cast to a real type. When a is real the resulting eigenvalues will be real (0 imaginary part) or occur in conjugate pairs
eigenvectors ((..., M, M) dpnp.ndarray) -- The normalized (unit "length") eigenvectors, such that the column v[:,i] is the eigenvector corresponding to the eigenvalue w[i].

Note

Since there is no proper OneMKL LAPACK function, DPNP will calculate through a fallback on NumPy call.

See also

dpnp.linalg.eigvals: Compute the eigenvalues of a general matrix.
dpnp.linalg.eigh: Return the eigenvalues and eigenvectors of a complex Hermitian (conjugate symmetric) or a real symmetric matrix.
dpnp.linalg.eigvalsh: Compute the eigenvalues of a complex Hermitian or real symmetric matrix.

Examples

>>> import dpnp as np
>>> from dpnp import linalg as LA

(Almost) trivial example with real eigenvalues and eigenvectors.

>>> w, v = LA.eig(np.diag((1, 2, 3)))
>>> w, v
(array([1., 2., 3.]),
 array([[1., 0., 0.],
        [0., 1., 0.],
        [0., 0., 1.]]))

Real matrix possessing complex eigenvalues and eigenvectors; note that the eigenvalues are complex conjugates of each other.

>>> w, v = LA.eig(np.array([[1, -1], [1, 1]]))
>>> w, v
(array([1.+1.j, 1.-1.j]),
 array([[0.70710678+0.j        , 0.70710678-0.j        ],
        [0.        -0.70710678j, 0.        +0.70710678j]]))

Complex-valued matrix with real eigenvalues (but complex-valued eigenvectors); note that a.conj().T == a, i.e., a is Hermitian.

>>> a = np.array([[1, 1j], [-1j, 1]])
>>> w, v = LA.eig(a)
>>> w, v
(array([2.+0.j, 0.+0.j]),
 array([[ 0.        +0.70710678j,  0.70710678+0.j        ], # may vary
        [ 0.70710678+0.j        , -0.        +0.70710678j]])

Be careful about round-off error!

>>> a = np.array([[1 + 1e-9, 0], [0, 1 - 1e-9]])
>>> # Theor. eigenvalues are 1 +/- 1e-9
>>> w, v = LA.eig(a)
>>> w, v
(array([1., 1.]),
 array([[1., 0.],
        [0., 1.]]))