geqrf_batch (Group Version)#

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

Description#

The routine forms the QiRi factorizations of a general m-by-n matrix Ai, 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 Qi explicitly. Instead, Qi is represented as a product of min(m, n) elementary reflectors. Routines are provided to work with Qi 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 {
  sycl::event geqrf_batch(sycl::queue &queue,
  int64_t *m,
  int64_t *n,
  T **a,
  int64_t *lda,
  T **tau,
  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*

*Hybrid support; some computations are performed on the CPU.

Input Parameters#

queue

Device queue where calculations will be performed.

m

Array of group_count parameters mg parameters.

Each of mg specifies the number of rows in the matrices Ai from array a, belonging to group g (mg ≥ 0).

n

Array of group_count parameters ng parameters.

Each of ng specifies the number of columns in the matrices Ai from array a, belonging to group g (ng ≥ 0).

a

Array of batch_size pointers to input matrices Ai, each being of size ldag*ng (g is an index of group to which Ai belongs).

lda

Array of group_countldag parameters, each representing the leading dimensions of input matrices Ai, from array a, belonging to group g (ldagmax(1, mg)).

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 Ai contain the min(mg,mng)-by-ng upper trapezoidal matrices Ri (Ri is upper triangular if mg ng); the elements below the diagonal, with the array taui, present the orthogonal matrix Qi as a product 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 taui, each of size min(mg,ng), containing scalars that define elementary reflectors for the matrices Qi 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.