syevd#
Computes all eigenvalues and, optionally, all eigenvectors of a real
symmetric matrix using divide and conquer algorithm. This routine
belongs to the oneapi::mkl::lapack namespace.
Description#
The routine computes all the eigenvalues, and optionally all the
eigenvectors, of a real symmetric matrix A. In other words, it
can compute the spectral factorization of A as: A = Z*λ*ZT.
Here Λ is a diagonal matrix whose diagonal elements are the
eigenvalues λi, and Z is the orthogonal matrix whose
columns are the eigenvectors zi. 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.
API#
Syntax#
namespace oneapi::mkl::lapack {
void syevd(sycl::queue &queue,
mkl::job jobz,
mkl::uplo uplo,
int64_t n,
sycl::buffer<T> &a,
int64_t lda,
sycl::buffer<T> &w,
sycl::buffer<T> &scratchpad,
int64_t scratchpad_size)
}
syevd supports the following precision and devices.
T |
Devices Supported |
|---|---|
|
CPU and GPU* |
|
CPU and GPU* |
*Interface support only; all computations are performed on the CPU.
Input Parameters#
- queue
Device queue where calculations will be performed.
- jobz
Must be
job::novecorjob::vec.If
jobz = job::novec, then only eigenvalues are computed.If
jobz = job::vec, then eigenvalues and eigenvectors are computed.- uplo
Must be
uplo::upperoruplo::lower.If
uplo = uplo::upper, a stores the upper triangular part ofA.If
uplo = uplo::lower, a stores the lower triangular part ofA.- n
The order of the matrix
A(0 ≤ n).- a
Buffer holding the array containing the upper or lower triangle of the symmetric matrix
A, as specified by uplo. The size ofamust be at leastlda*n.- lda
The leading dimension of a. Must be at least
max(1,n).- scratchpad
Buffer holding scratchpad memory to be used by the routine for storing intermediate results.
- 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 the syevd_scratchpad_size function.
Output Parameters#
- a
If
jobz = job::vec, then on exit this buffer is overwritten by the orthogonal matrixZwhich contains the eigenvectors ofA.- w
Buffer holding array of size at least n. If
info = 0, contains the eigenvalues of the matrixAin ascending order.
Exceptions#
Exception |
Description |
|---|---|
|
This exception is thrown when problems occur during calculations. You can obtain the info code of the problem using the info() method of the exception object: If If If If |