hegvd#
Computes all the eigenvalues, and optionally, the eigenvectors of a
complex generalized Hermitian positive-definite eigenproblem using a
divide and conquer method. This routine belongs to the
oneapi::mkl::lapack namespace.
Description#
The routine computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian positive-definite eigenproblem, of the form
A*x = λ*B*x, A*B*x = λ*x, or B*A*x = λ*x.
Here A and B are assumed to be Hermitian and B is also
positive definite.
It uses a divide and conquer algorithm.
API#
Syntax#
namespace oneapi::mkl::lapack {
void hegvd(sycl::queue &queue,
int64_t itype,
mkl::job jobz,
mkl::uplo uplo,
int64_t n,
sycl::buffer<T> &a,
int64_t lda,
sycl::buffer<T> &b,
int64_t ldb,
sycl::buffer<RT> &w,
sycl::buffer<T> &scratchpad,
int64_t scratchpad_size)
}
hegvd supports the following precision and devices.
T |
RT |
Devices Supported |
|---|---|---|
|
|
CPU and GPU* |
|
|
CPU and GPU^ |
*Interface support only; all computations are performed on the CPU.
^Hybrid support; some computations are performed on the CPU.
Input Parameters#
- queue
Device queue where calculations will be performed.
- itype
Must be 1 or 2 or 3. Specifies the problem type to be solved:
if itype
= 1, the problem type isA*x = lambda*B*x;if itype
= 2, the problem type isA*B*x = lambda*x;if itype
= 3, the problem type isB*A*x = lambda*x.- 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 and b store the upper triangular part ofAandB.If
uplo = uplo::lower, a and b stores the lower triangular part ofAandB.- n
The order of the matrices
AandB(0 ≤ n).- a
Buffer holding the array containing the upper or lower triangle of the Hermitian matrix
A, as specified by uplo. The size ofamust be at leastlda*n.- lda
The leading dimension of a; at least
max(1,n).- b
Buffer holding the array containing the upper or lower triangle of the Hermitian matrix
B, as specified by uplo. The size ofbmust be at leastldb*n.- ldb
The leading dimension of b; 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 hegvd_scratchpad_size function.
Output Parameters#
- a
On exit, if
jobz = job::vec, then ifinfo = 0, a contains the matrixZof eigenvectors. The eigenvectors are normalized as follows:if itype
= 1or2,ZH*B*Z = I;if itype
= 3,ZH*inv(B)*Z = I;If
jobz = job::novec, then on exit the upper triangle (ifuplo = uplo::upper) or the lower triangle (ifuplo = uplo::lower) ofA, including the diagonal, is destroyed.- b
On exit, if
info ≤ n, the part of b containing the matrix is overwritten by the triangular factorUorLfrom the Cholesky factorizationB = UH*UorB=L*LH.- w
Buffer holding arry of size at least n. If
info = 0, contains the eigenvalues of the matrixAin ascending order. See also info.
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 If |