potrs_batch (USM Strided Version)

oneMKL - Data Parallel C++ Developer Reference

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ID 772045

Date 3/22/2024

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potrs_batch (USM Strided Version)

Solves a system of linear equations with a Cholesky-factored symmetric (Hermitian) positive-definite coefficient matrices. This routine belongs to the oneapi::mkl::lapack namespace.

Description
API

Description

The routine solves for X_i the system of linear equations A_i*X_i = B_i with a symmetric positive-definite or, for complex data, Hermitian positive-definite matrices A_i, given the Cholesky factorization of A_i, i ϵ{1...batch_size} :

A_i = U_i^T*U_i for real data, A_i = U_i^H*U_i for complex data if uplo=mkl::uplo::upper
A_i = L_i*L_i^T for real data, A_i = L_i*L_i^H for complex data if uplo=mkl::uplo::lower

where L_i is a lower triangular matrix and U_i is upper triangular. The system is solved with multiple right-hand sides stored in the columns of the matrix B_i.

Before calling this routine, matrices A_i should be factorized by a call to potrf_batch (USM Strided Version).

API

Syntax

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

This function 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_i of A_i is stored, where A_i = U_i^T*U_i for real data, A_i = U_i^H*U_i for complex data.

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

n

The order of the matrices A_i (n ≥ 0).

nrhs

The number of right hand sides (nrhs ≥ 0).

a

Array containing the batch of factorizations of the matrices A_i, as returned by potrf_batch (USM Strided Version).

lda

The leading dimension of A_i (lda ≥ max(1, n)).

stride_a

The stride between the beginnings of matrices inside the batch array a (stride_a ≥ max(1, lda * n)).

b

The array containing the batch of matrices B_i whose columns are the right-hand sides for the systems of equations.

ldb

The leading dimensions of B_i (ldb ≥ max(1, n)).

stride_b

The stride between the beginnings of matrices B_i inside the batch array b (stride_b ≥ max(1, ldb * nrhs)).

batch_size

The number of problems in a batch (batch_size ≥ 0).

scratchpad

Scratchpad memory to be used by 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 then the value returned by stride version of potrs_batch_scratchpad_size (Strided Version) function.

events

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

Output Parameters

b: The memory pointed to by pointer batch array b is overwritten by the solution matrix X_i.

Exceptions

Exception	Description
`mkl::lapack::batch_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 = -n`, the `n`-th parameter had an illegal value. If `info` equals the value passed as scratchpad size, and detail() returns non-zero, then the passed scratchpad is of insufficient size, and the required size should be not less then value returned by the detail() method of the exception object. If `info` is zero, then the diagonal element of some of `U`_i is zero, and the solve could not be completed. The indexes of such matrices in the batch can be obtained with the `ids()` method of the exception object. You can obtain the indexes of the first zero diagonal elements in these `U`_i matrices using the `infos()` method of the exception object.

Exception

Description

mkl::lapack::batch_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 = -n, the n-th parameter had an illegal value.

If info equals the value passed as scratchpad size, and detail() returns non-zero, then the passed scratchpad is of insufficient size, and the required size should be not less then value returned by the detail() method of the exception object.

If info is zero, then the diagonal element of some of U_i is zero, and the solve could not be completed. The indexes of such matrices in the batch can be obtained with the ids() method of the exception object. You can obtain the indexes of the first zero diagonal elements in these U_i matrices using the infos() method of the exception object.

Return Values

Output event to wait on to ensure computation is complete.

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oneMKL - Data Parallel C++ Developer Reference

potrs_batch (USM Strided Version)

Description

API