hetrf (USM Version)#
Computes the Bunch-Kaufman factorization of a complex Hermitian matrix.
This routine belongs to the oneapi::mkl::lapack namespace.
Description#
The routine computes the factorization of a complex Hermitian matrix
Ausing the Bunch-Kaufman diagonal pivoting method. The form of
the factorization is:
if
uplo=uplo::upper,A = U*D*UHif
uplo=uplo::lower,A = L*D*LH,
where A is the input matrix, U and L are products of
permutation and triangular matrices with unit diagonal (upper
triangular for U and lower triangular for L), and D is a
Hermitian block-diagonal matrix with 1-by-1 and 2-by-2 diagonal
blocks. U and L have 2-by-2 unit diagonal blocks
corresponding to the 2-by-2 blocks of D.
API#
Syntax#
namespace oneapi::mkl::lapack {
sycl::event hetrf(sycl::queue &queue,
mkl::uplo uplo,
int64_t n,
T *a,
int64_t lda,
int64_t *ipiv,
T *scratchpad,
int64_t scratchpad_size,
const std::vector<sycl::event> &events = {})
}
hetrf (USM version) supports the following precisions and
devices:
T |
Devices supported |
|---|---|
|
CPU |
|
CPU |
Input Parameters#
- queue
The device queue where calculations will be performed.
- uplo
Indicates whether the upper or lower triangular part of
Ais stored and howAis factored:.If
uplo = uplo::upper, the array a stores the upper triangular part ofAandAis factored asU*D*UH.If
uplo = uplo::lower, the array a stores the lower triangular part ofAandAis factored asL*D*LH.- n
The order of the matrix
A(0 ≤ n).- a
The pointer to coefficients of matrix
Acontaining either the upper or the lower triangular part of the matrixA(see uplo). The size of a must be at leastlda*n.- lda
The leading dimension of a.
- scratchpad
Pointer to 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 hetrf_scratchpad_size function.- events
List of events to wait for before starting computation. Defaults to empty list.
Output Parameters#
- a
The upper or lower triangular part of
ais overwritten by details of the block-diagonal matrixDand the multipliers used to obtain the factorU(orL).- ipiv
Pointer to memory array of size at least
max(1, n). Contains details of the interchanges and the block structure ofD. Ifipiv(i) = k >0, thendiiis a 1-by-1 block, and thei-th row and column ofAwas interchanged with thek-th row and column.If
uplo= mkl::uplo::upper andipiv(i) =ipiv(i-1) = -m< 0, thenDhas a 2-by-2 block in rows/columnsiandi-1, and (i-1)-th row and column ofAwas interchanged with them-th row and column.If
uplo= mkl::uplo::lower andipiv(i) =ipiv(i+1) = -m< 0, thenDhas a 2-by-2 block in rows/columnsiandi+1, and (i+1)-th row and column ofAwas interchanged with them-th row and column.
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 |
Return Values#
Output event to wait on to ensure computation is complete.