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geqrf_batch (USM Strided Version)

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

Description

The routine forms the Q_iR_i factorizations of a general m-by-n matrix A_i. No pivoting is performed.

The routine does not form the matrix Q_i explicitly. Instead, Q_i is represented as a product of min(m, n) elementary reflectors. Routines are provided to work with Q_i in this representation.

API

Syntax

namespace oneapi::mkl::lapack {
  cl::sycl::event geqrf_batch(cl::sycl::queue &queue,
  std::int64_t m,
  std::int64_t n,
  T *a,
  std::int64_t lda,
  std::int64_t stride_a,
  T *tau,
  std::int64_t stride_tau,
  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.

m

The number of rows in the matrices A_i (0 ≤ m).

n

The number of columns in the matrices A_i (0 ≤ n).

a

Array holding input matrices A_i.

lda

The leading dimension of A_i .

stride_a

The stride between the beginnings of matrices A_i inside the batch array a.

stride_tau

The stride between the beginnings of arrays tau_i inside the array tau.

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 than the value returned by geqrf_batch_scratchpad_size (Strided 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:

The elements on and above the diagonal of the array contain the min(m,n)-by-n upper trapezoidal matrices R_i (R_i is upper triangular if m≥n); the elements below the diagonal, with the array taui, present the orthogonal matrix Q_i as a product of min(m,n) elementary reflectors.

tau

Array to store batch of tau_i, each of size min(m,n), containing scalars that define elementary reflectors for the matrices Q_i in its decomposition in a product of elementary reflectors.

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.

Return Values

Output event to wait on to ensure computation is complete.

geqrf_batch (Group Version) geqrf_batch_scratchpad_size (Group Version)