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getrf_batch (Group Version)

Computes the batch of LU factorizations of a general m-by-n matrices. This routine belongs to the oneapi::mkl::lapack namespace.

Description

The routine computes the LU factorizations of a batch of general m-by-n matrices A_i, (iϵ{1...batch_size}) as

Where P_i is a permutation matrix, L_i is lower triangular with unit diagonal elements (lower trapezoidal if m > n) and U_i is upper triangular (upper trapezoidal if m < n). The routine uses partial pivoting with row interchanges.

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 getrf_batch(cl::sycl::queue &queue,
  std::int64_t *m,
  std::int64_t *n,
  T **a,
  std::int64_t *lda,
  std::int64_t **ipiv,
  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.

m

Array of group_count parameters m_g specifying the number of rows in the matrices A_i (0 ≤ mg) belonging to group g.

n

Array of group_count parameters n_g specifying the number of columns in the matrices A_i (0 ≤ ng) belonging to group g.

a

Array of batch_size pointers to input matricesA_i.

lda

Array of group_count parameters lda_g specifying the leading dimension of A_i belonging to 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 getrf_batch_scratchpad_size (Group Version).

events

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

Output Parameters

a

Matrices pointed to by array a are overwritten by L_i and U_i. The unit diagnonal elements of L_i are not stored.

ipiv

Arrays of batch_size pointers to arrays containing pivot indices ipiv_i each of size at least max(1,min(mg,ng)); for 1 ≤ k ≤ min(mg,ng), row k of A_i was interchanged with row ipiv_i(k).

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.

getrf_batch (Buffer Strided Version) getrf_batch (USM Strided Version)