heevd¶

Computes all eigenvalues and, optionally, all eigenvectors of a complex Hermitian matrix using divide and conquer algorithm.

heevd supports the following precisions.

T

std::complex<float>

std::complex<double>

Description

The routine computes all the eigenvalues, and optionally all the eigenvectors, of a complex Hermitian matrix A. In other words, it can compute the spectral factorization of A as: A = Z*Λ*ZH.

Here Λ is a real diagonal matrix whose diagonal elements are the eigenvalues λ_i, and Z is the (complex) unitary matrix whose columns are the eigenvectors z_i. Thus,

A*zi = λi*zi for i = 1, 2, ..., n.

If the eigenvectors are requested, then this routine uses a divide and conquer algorithm to compute eigenvalues and eigenvectors. However, if only eigenvalues are required, then it uses the Pal-Walker-Kahan variant of the QL or QR algorithm.

heevd (BUFFER Version)¶

Syntax

void onemkl::lapack::heevd(cl::sycl::queue &queue, onemkl::job jobz, onemkl::uplo upper_lower, std::int64_t n, butter<T, 1> &a, std::int64_t lda, cl::sycl::buffer<realT, 1> &w, cl::sycl::buffer<T, 1> &scratchpad, std::int64_t scratchpad_size)¶

Input Parameters

queue

The queue where the routine should be executed.

jobz

Must be job::novec or job::vec.

If jobz = job::novec, then only eigenvalues are computed.

If jobz = job::vec, then eigenvalues and eigenvectors are computed.

upper_lower

Must be uplo::upper or uplo::lower.

If upper_lower = job::upper, a stores the upper triangular part of A.

If upper_lower = job::lower, a stores the lower triangular part of A.

n

The order of the matrix A (0≤n).

a

The buffer a, size (lda,*). The buffer a contains the matrix A. The second dimension of a must be at least max(1, n).

lda

The leading dimension of a. Must be at least max(1,n).

scratchpad_size

Size of scratchpad memory as a number of floating point elements of type T. Size should not be less than the value returned by heevd_scratchpad_size function.

Output Parameters

a: If jobz = job::vec, then on exit this buffer is overwritten by the unitary matrix Z which contains the eigenvectors of A.
w: Buffer, size at least n. Contains the eigenvalues of the matrix A in ascending order.
scratchpad: Buffer holding scratchpad memory to be used by routine for storing intermediate results.

Throws

onemkl::lapack::exception

Exception is thrown in case of problems happened during calculations. The info code of the problem can be obtained by get_info() method of exception object:

If info=-i, the i-th parameter had an illegal value.

If info=i, and jobz = onemkl::job::novec, then the algorithm failed to converge; i indicates the number of off-diagonal elements of an intermediate tridiagonal form which did not converge to zero.

If info=i, and jobz = onemkl::job::vec, then the algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns info/(n+1) through mod(info,n+1).

If info equals to value passed as scratchpad size, and get_detail() returns non zero, then passed scratchpad is of insufficient size, and required size should not be less than value return by get_detail() method of exception object.

heevd (USM Version)¶