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 λ
i
, 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(cl::sycl::queue &queue,
mkl::job jobz,
mkl::uplo uplo,
std::int64_t n,
cl::sycl::buffer<T> &a,
std::int64_t lda,
cl::sycl::buffer<T> &w,
cl::sycl::buffer<T> &scratchpad,
std::int64_t scratchpad_size)
}
syevd
supports the following precision and devices.T | Devices Supported |
---|---|
float | Host, CPU, and GPU |
double | Host, CPU, and GPU |
Input Parameters
- queue
- Device queue where calculations will be performed.
- jobz
- Must bejob::novecorjob::vec.Ifjobz = job::novec, then only eigenvalues are computed.Ifjobz = job::vec, then eigenvalues and eigenvectors are computed.
- uplo
- Must beuplo::upperoruplo::lower.Ifuplo = job::upper, a stores the upper triangular part ofA.Ifuplo = job::lower, a stores the lower triangular part ofA.
- n
- The order of the matrixA(0≤n).
- a
- The pointer to the array containingA, size (lda,*). The second dimension of a must be at leastmax(1, n).
- lda
- The leading dimension of a. Must be at leastmax(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 typeT. Size should not be less than the value returned by the syevd_scratchpad_size function.
Output Parameters
- a
- Ifjobz = 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. Ifinfo = 0, contains the eigenvalues of the matrixAin ascending order.
Exceptions
Exception | Description |
---|---|
mkl::lapack::exception | 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 info = -i , the i -th parameter had an illegal value.If info = i , and jobz = 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 = 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 is equal to the value passed as scratchpad size, and detail() returns non zero, then the passed scratchpad has an insufficient size, and the required size should not be less than the value returned by the detail() method of the exception object. |