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getrs_batch (USM Strided Version)

Solves a system of linear equations with a batch of LU-factored square coefficient matrices, with multiple right-hand sides. This routine belongs to the oneapi::mkl::lapack namespace.

Description

The routine solves for X_i the following systems of linear equations:

• A_i * X_i = B_i If trans = mkl::transpose::notrans

• A_i^T * X_i = B_i If trans = mkl::transpose::trans

• A_i^H * X_i = B_i If trans = mkl::transpose::conjtrans

Before calling this routine you must call getrf_batch (USM Strided Version) to compute the LU factorization of A₁.

API

Syntax

namespace oneapi::mkl::lapack {
  cl::sycl::event getrs_batch(cl::sycl::queue &queue,
  mkl::transpose trans,
  std::int64_t n,
  std::int64_t nrhs,
  T *a,
  std::int64_t lda,
  std::int64_t stride_a,
  std::int64_t *ipiv,
  std::int64_t stride_ipiv,
  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<cl::sycl::event> &events = {})
}

Function supports the following precisions and devices.

T	Devices supported
float	Host, CPU, and GPU
double	Host, CPU, and GPU
std::complex<float>	Host, CPU, and GPU
std::complex<double>	Host, CPU, and GPU

Input Parameters

queue

Device queue where calculations will be performed.

trans

Indicates the form of the equations:

If trans = mkl::transpose::nontrans, then A_i*X_i = B_i is solved for X_i.

If trans = mkl::transpose::trans, then A_i^T*X_i = B_i is solved for X_i.

If trans = mkl::transpose::conjtrans, then A_i^H*X_i = B_i is solved for X_i.

n

The order of the matrices A_i and the number of rows in matrices B_i (0 ≤ n).

nrhs

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

a

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

lda

The leading dimension of A_i.

stride_a

The stride between the beginnings of matrices B_i inside the batch array b.

ipiv

The ipiv array, as returned by getrf_batch (USM Strided Version).

stride_ipiv

The stride between the beginnings of arrays ipiv_i inside the array ipiv.

b

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

ldb

The leading dimensions of B_i.

batch_size

Specifies the number of problems in a batch.

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 getrs_batch_scratchpad_size (Strided Version) function.

events

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

Output Parameters

b

Overwritten by the solution matrices 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 Ui 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 Ui matrices using the infos() method of the exception object.

Return Values

Output event to wait on to ensure computation is complete.

getrs_batch (Group Version) getrs_batch_scratchpad_size (Group Version)