potrs (USM Version)

Intel® oneAPI Math Kernel Library (oneMKL) - Data Parallel C++ Developer Reference

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ID 772045

Date 12/16/2022

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potrs (USM Version)

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
API

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:

`A` = `U`^T`U` for real data, `A` = `U`^H`U` for complex data	if uplo=`mkl::uplo::upper`
`A` = `L``L`^T for real data, `A` = `L``L`^H for complex data	if uplo=`mkl::uplo::lower`

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 (USM Version) to compute the Cholesky factorization of A.

API

Syntax

namespace oneapi::mkl::lapack {
   sycl::event potrs(
      sycl::queue &queue,
      mkl::uplo uplo,
      std::int64_t n,
      std::int64_t nrhs,
      T *a,
      std::int64_t lda,
      T *b,
      std::int64_t ldb,
      T *scratchpad,
      std::int64_t scratchpad_size,
      const std::vector<sycl::event> &events = {})
}

potrs (USM version) supports the following precisions and devices:

T	Devices supported
`float`	CPU and GPU
`double`	CPU and GPU
`std::complex<float>`	CPU and GPU
`std::complex<double>`	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 triangle U of A is stored, where A = U^T*U for real data, A = U^H*U for complex data.

If uplo=mkl::uplo::lower, the upper triangle L of A is stored, where A = L*L^T for real data, A = L*L^H for complex data.

n

The order of matrix A (0 ≤ n).

nrhs

The number of right-hand sides (0 ≤ nrhs).

a

Pointer to factorization of the matrix A, as returned by potrf (USM Version). The second dimension of a must be at least max(1, n).

lda

The leading dimension of a.

b

Pointer to the data of matrix B whose columns are the right-hand sides for the systems of equations. The second dimension of b must be at least max(1,nrhs).

ldb

The leading dimension of b.

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 potrs_scratchpad_size function.

events

List of events to wait for before starting computation. Defaults to empty list.

Output Parameters

b: The memory pointed to by pointer b is overwritten by the solution matrix X.

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`, the `i`-th diagonal element of the Cholesky factor is zero, and the solve could not be completed. 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.

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, the i-th diagonal element of the Cholesky factor is zero, and the solve could not be completed.

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.

Return Values

Output event to wait on to ensure computation is complete.

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Intel® oneAPI Math Kernel Library (oneMKL) - Data Parallel C++ Developer Reference

potrs (USM Version)

Description

API