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geqrf_batch (Group 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, iϵ{1...batch_size}, where batch_size is a sum of all parameter group sizes as provided with the group_sizes array. No pivoting is performed during factorization.

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.

Total number of problems to solve, batch_size, is a sum of sizes of all of the groups of parameters as provided by group_sizesarray.

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,
  T **tau,
  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 parameters.

Each of m_g specifies the number of rows in the matrices A_i from array a, belonging to group g.

n

Array of group_count parameters n_g parameters.

Each of n_g specifies the number of columns in the matrices A_i from array a, belonging to group g.

a

Array of batch_size pointers to input matrices A_i, each being of size lda_g*n_g (g is an index of group to which A_i belongs).

lda

Array of group_countlda_g parameters, each representing the leading dimensions of input matrices A_i, from array a, 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 geqrf_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 the factorization data as follows:

The elements on and above the diagonal of A_i contain the min(mg,mng)-by-n_g upper trapezoidal matrices R_i (R_i is upper triangular if mg≥ng); the elements below the diagonal, with the array tau_i, present the orthogonal matrix Q_i as a rpoduct of min(mg,ng) elementary reflectors.

Here, g is an index of parameters group corresponding to i-th decomposition.

tau

Array of pointers to store tau_i, each of size m_g,n_g, containing scalars that define elementary reflectors for the matrices Q_i in its decomposition in a product of elementary reflectors.

Here, g is an index of parameters group corresponding to i-th decomposition.

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 (Buffer Strided Version) geqrf_batch (USM Strided Version)