potrs#
Solves a system of linear equations with a Cholesky-factored symmetric
(Hermitian) positive-definite coefficient matrix. This routine belongs
to the oneapi::mkl::lapack namespace.
Description#
The routine solves for X the system of linear equations
A*X = B with a symmetric positive-definite or, for complex data,
Hermitian positive-definite matrix A, given the Cholesky
factorization of A:
|
if |
|
if |
where L is a lower triangular matrix and U is upper
triangular. The system is solved with multiple right-hand sides
stored in the columns of the matrix B.
Before calling this routine, you must call potrf to compute the Cholesky factorization of A.
API#
Syntax#
namespace oneapi::mkl::lapack {
void potrs(sycl::queue &queue, mkl::uplo uplo,
int64_t n,
int64_t nrhs,
sycl::buffer<T> &a,
int64_t lda,
sycl::buffer<T> &b,
int64_t ldb,
sycl::buffer<T> &scratchpad,
int64_t scratchpad_size)
}
potrs supports the following precisions and devices:
T |
Devices Supported |
|---|---|
|
CPU and GPU |
|
CPU and GPU |
|
CPU and GPU |
|
CPU and GPU |
Input Parameters#
- queue
Device queue where calculations will be performed.
- uplo
Indicates how the input matrix has been factored:
If uplo=
mkl::uplo::upper, the upper triangleUofAis stored, whereA=UT*Ufor real data,A=UH*Ufor complex data.If uplo=
mkl::uplo::lower, the upper triangleLofAis stored, whereA=L*LT for real data,A=L*LH for complex data.- n
The order of matrix
A(0 ≤ n).- nrhs
The number of right-hand sides (0 ≤ nrhs).
- a
Buffer holding factorization of the matrix
A, as returned by potrf. The size ofamust be at leastlda*n.- lda
The leading dimension of a.
- b
Buffer holding the data of matrix
Bwhose columns are the right-hand sides for the systems of equations. The size ofbmust be at leastldb*nrhs.- ldb
The leading dimension of b.
- 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 potrs_scratchpad_size function.
Output Parameters#
- b
Buffer b is overwritten by the solution matrix
X.
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 |