gels_batch (Buffer Strided Version)

oneMKL - Data Parallel C++ Developer Reference

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ID 772045

Date 6/24/2024

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gels_batch (Buffer Strided 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 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 the m ≥ n and trans = transpose::nontrans case is supported.

API

Syntax

namespace oneapi::mkl::lapack {
  void gels_batch(sycl::queue &queue,
  mkl::transpose trans,
  std::int64_t m,
  std::int64_t n,
  std::int64_t nrhs,
  sycl::buffer<T> &a,
  std::int64_t lda,
  std::int64_t stride_a,
  sycl::buffer<T> &b,
  std::int64_t ldb,
  std::int64_t stride_b,
  std::int64_t batch_size,
  sycl::buffer<T> &scratchpad,
  std::int64_t scratchpad_size)
}

This function supports the following precisions and devices:

T	Devices supported
`float`	GPU
`double`	GPU
`std::complex<float>`	GPU
`std::complex<double>`	GPU

Input Parameters

queue

Device queue where calculations will be performed.

trans

Operation applied to matrices A_i. Real precisions: mkl::tranpose::nontrans or mkl::transpose::trans Complex precisions: mkl::tranpose::nontrans or mkl::transpose::conjtrans

m

The number of rows of the matrices A_i (m ≥ n ≥ 0).

n

The number of columns of the matrices A_i (m ≥ n ≥ 0).

nrhs

The number of right-hand sides: the number of columns in B_i (nrhs ≥ 0).

a

Contains batch_size m-by-n matrices A_i

lda

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

stride_a

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

b

Contains the matrices B_i of right hand side vectors. 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

The leading dimensions of B_i (ldb ≥ max(1,max(m,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 than the value returned by stride version of gels_batch_scratchpad_size (Strided Version).

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.

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oneMKL - Data Parallel C++ Developer Reference

gels_batch (Buffer Strided Version)

Description

API