dpnp.linalg.eigvals¶

dpnp.linalg.eigvals(a)[source]¶

Compute the eigenvalues of a general matrix.

For full documentation refer to numpy.linalg.eigvals.

Parameters:

a(..., M, M) {dpnp.ndarray, usm_ndarray}: A complex- or real-valued matrix whose eigenvalues will be computed.

Returns:

w(..., M) dpnp.ndarray: The eigenvalues, each repeated according to its multiplicity. They are not necessarily ordered, nor are they necessarily real for real matrices.

See also

dpnp.linalg.eig: Compute the eigenvalues and right eigenvectors of a square array.
dpnp.linalg.eigvalsh: Compute the eigenvalues of a complex Hermitian or real symmetric matrix.
dpnp.linalg.eigh: Return the eigenvalues and eigenvectors of a complex Hermitian (conjugate symmetric) or a real symmetric matrix.

Notes

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

Examples

Illustration, using the fact that the eigenvalues of a diagonal matrix are its diagonal elements, that multiplying a matrix on the left by an orthogonal matrix, Q, and on the right by Q.T (the transpose of Q), preserves the eigenvalues of the "middle" matrix. In other words, if Q is orthogonal, then Q * A * Q.T has the same eigenvalues as A:

>>> import dpnp as np
>>> from dpnp import linalg as LA
>>> x = np.random.random()
>>> Q = np.array([[np.cos(x), -np.sin(x)], [np.sin(x), np.cos(x)]])
>>> LA.norm(Q[0, :]), LA.norm(Q[1, :]), np.dot(Q[0, :],Q[1, :])
(array(1.), array(1.), array(0.))

Now multiply a diagonal matrix by Q on one side and by Q.T on the other:

>>> D = np.diag((-1, 1))
>>> LA.eigvals(D)
array([-1.+0.j,  1.+0.j])
>>> A = np.dot(Q, D)
>>> A = np.dot(A, Q.T)
>>> LA.eigvals(A)
array([-1.+0.j,  1.+0.j]) # random