gels_batch (Group Version)

oneMKL - Data Parallel C++ Developer Reference

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ID 772045

Date 6/24/2024

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gels_batch (Group Version)

Finds the least squares solutions for a batch of overdetermined linear systems. This routine belongs to the oneapi::mkl::lapack namespace.

Description
API

Description

Uses the QR factorization to solve a grouped batch of linear systems with full rank matrices. Each linear system is solved according to the following:

If m ≥ n and trans = transpose::nontrans the least squares solution to the overdetermined system is computed: min ||A*X - B||

If m ≥ n and trans = (transpose::trans or tranpose::conjtrans) the minimal norm solution to the underdetermined system is computed: min ||X|| s.t. A^H *X = B

On exit, the contents of B is overwritten with the solution vectors X.

Currently only m ≥ n case is supported.

API

Syntax

namespace oneapi::mkl::lapack {
  sycl::event gels_batch(sycl::queue &queue,
  mkl::transpose *trans,
  int64_t *m,
  int64_t *n,
  int64_t *nrhs,
  T **a,
  int64_t *lda,
  T **b,
  int64_t *ldb,
  int64_t group_count,
  int64_t *group_sizes,
  T *scratchpad,
  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.

trans

Array of group_count parameters trans _g. Operation applied to matrices A_i in group g. Real precisions: mkl::tranpose::nontrans or mkl::transpose::trans Complex precisions: mkl::tranpose::nontrans or mkl::transpose::conjtrans

m

Array of group_count parameters m _g The number of rows of the matrices A_i in group g (m ≥ n ≥ 0).

n

Array of group_count parameters n _g The number of columns of the matrices A_i in group g (m ≥ n ≥ 0).

nrhs

Array of group_count parameters nrhs _g The number of right-hand sides: the number of columns in B_i in group g (nrhs ≥ 0).

a

Array of batch_size pointers. Contains batch_size m-by-n matrices A_i

lda

Array of group_count parameters lda _g The leading dimension of A_i in group g (lda ≥ max(1,m)).

b

Array of batch_size pointers Contains the matrices B_i of right hand side vectors in group g. Each matrix B_i must be allocated enough space to store the solution vectors X_i, i.e. max(m,n)-by-nrhs

If trans = transpose::nontrans then B_i is m-by-nrhs, otherwise B_i is n-by-nrhs.

ldb

Array of group_count parameters ldb _g The leading dimensions of B_i in group g (ldb ≥ max(1,max(m,n))).

group_count

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

group_sizes

Array of group_count integers group_sizes _g Array element with index g specifies the number of problems to solve for each group 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 must not be less than the value returned by gels_batch_scratchpad_size (Group Version).

events

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

Output Parameters

a: Overwritten by the factorization data as follows: Contains triangular matrix R obtained on the basis of A_i used in least squares computation. The tau vectors are not recorded.
b: Overwritten by least squares solutions of the batch of problems.

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 = -i`, the `i`-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 `A`_i does not have full rank, 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 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 = -i, the i-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 A_i does not have full rank, 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 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

gels_batch (Group Version)

Description

API