sytrf (USM Version)#
Computes the Bunch-Kaufman factorization of a symmetric matrix. This
routine belongs to the oneapi::mkl::lapack namespace.
Description#
The routine computes the factorization of a real/complex symmetric
matrix A using the Bunch-Kaufman diagonal pivoting method. The
form of the factorization is:
if
uplo=uplo::upper,A=U*D*UTif
uplo=uplo::lower,A=L*D*LT
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
symmetric 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 sytrf(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 = {})
}
sytrf (USM version) supports the following precisions and devices:
T |
Devices Supported |
|---|---|
|
CPU |
|
CPU |
|
CPU |
|
CPU |
Input Parameters#
- queue
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 arrayastores the upper triangular part of the matrixA, andAis factored asU*D*UT.If
uplo = uplo::lower, the arrayastores the lower triangular part of the matrixA, andAis factored asL*D*LT.- n
The order of the matrix
A(0 ≤ n).- a
Pointer to the coefficients of matrix
Acontaining either the upper or lower triangular part of the matrixA(see uplo). The size ofamust 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 sytrf_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::upperandipiv(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::lowerandipiv(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.