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getrs_batch (Group Version)

Solves a batch of systems 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 (iϵ{1...batch_size}) 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 (Group Version) to compute the LU factorization of A₁.

The total number of problems to solve, batch_size, is a sum of sizes of all of the groups of parameters as provided by``group_sizes`` array.

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 **ipiv,
  T **b,
  std::int64_t *ldb,
  std::int64_t group_count,
  std::int64_t *group_sizes,
  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

Array of group_count parameters trans_g indicating the form of the equations for the group g:

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

Array of group_count parameters n_g specifying the order of the matrices A_i and the number of rows in matrices B_i (0 ≤ n_g) belonging to group g.

nrhs

Array of group_count parameters nrhs_g specifying the number of right hand sides(0≤nrhs)for group g.

a

Array of batch_size pointers to factorization of the matricesA_i, as returned by getrf_batch (Group Version).

lda

Array of group_count parameters lda_g specifying the leading dimension of A_i from group g.

ipiv

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

b

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

ldb

Array of group_count parameters ldb_g specifying the leading dimensions of B_i in the group g.

group_count

Specifies the number of groups of parameters. Must be at least 0.

group_sizes

Array of group_count integers. Array element with index g specifies the number of problems to solve for each of the groups of parameters g. So the total number of problems to solve, batch_size, is a sum of all parameter group sizes.

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 getrs_batch_scratchpad_size (Group Version).

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 (Buffer Strided Version) getrs_batch (USM Strided Version)