ungqr_batch (Group Version)#

Generates the complex unitary matrices Qi of the batch of QR factorizations formed by geqrf_batch. This routine belongs to the oneapi::mkl::lapack namespace.

Description#

The routine generates the wholes or parts of m-by-m unitary matrix Qi of the QR factorization formed by the geqrf_batch (Group Version) function.

Usually Qi is determined from the QR factorization of an m by p matrix Ai with m p. To compute the whole matrices Qi, use:

ungqr_batch(queue, m, m, p, a, ...)

To compute the leading p columns of Qi (which form an orthonormal basis in the space spanned by the columns of Ai):

ungqr_batch(queue, m, p, p, a, ...)

To compute the matrix Qik of the QR factorization of the leading k columns of the matrices Ai:

ungqr_batch(queue, m, m, k, a, ...)

To compute the leading k columns of Qik (which form an orthonormal basis in the space spanned by the leading k columns of the matrices Ai):

ungqr_batch(queue, m, k, k, a, ...)

API#

Syntax#

namespace oneapi::mkl::lapack {
  sycl::event ungqr_batch(sycl::queue &queue,
  int64_t *m,
  int64_t *n,
  int64_t *k,
  T **a,
  int64_t *lda,
  const T * const *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

std::complex<float>

CPU and GPU*

std::complex<double>

CPU and GPU*

*Interface support only; all computations are performed on the CPU.

Input Parameters#

queue

Device queue where calculations will be performed.

m

Array of group_count parameters mg as previously supplied to geqrf_batch (Group Version) (mg ≥ 0).

n

Array of group_count parameters ng as previously supplied to geqrf_batch (Group Version) (ng ≥ 0).

k

Array of group_count parameters kg. The number of elementary reflectors whose product defines the matrices Qi (0 ≤ kgng) .

a

Array resulting after a call to geqrf_batch (Group Version).

lda

Array of leading dimension of Ai as previously supplied to geqrf_batch (Group Version) (ldagmax(1, mg)).

tau

Array resulting after a call to geqrf_batch (Group Version).

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 ungqr_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 ng leading columns of the mg-by-mg unitary matrices Qi, where g is an index of group of parameters corresponding to Qi.

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.