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 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.
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::novec
orjob::vec
.If
jobz = job::novec
, then only eigenvalues are computed.If
jobz = job::vec
, then eigenvalues and eigenvectors are computed.- uplo
Must be
uplo::upper
oruplo::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 of size
a(lda,*)
containing the upper or lower triangle of the symmetric matrixA
, as specified by uplo.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
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 matrixZ
which contains the eigenvectors ofA
.- w
Buffer holding array of size at least n. If
info = 0
, contains the eigenvalues of the matrixA
in 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 |