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orgqr_batch (Group Version)

Generates the real orthogonal matrices Q_i of the batch of QR factorizations formed by geqrf_batch (Group Version). This routine belongs to the oneapi::mkl::lapack namespace.

Description

The routine generates the wholes or parts of the m-by-m orthogonal matrices Q₁ of the batch of QR factorizations formed by the routine geqrf_batch (Group Version). Usually, Q₁ is determined from the QR factorization of an m-by-p matrix A₁ with m ≥p.

To compute the whole matrices Q₁, use:

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

To compute the leading p columns of Q₁ (which form an orthonormal basis in the space spanned by the columns of A₁):

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

To compute the matrices Q₁^k of the QR factorizations of leading k columns of the matrices A₁:

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

To compute the leading k columns of Q₁^k (which form an orthonormal basis in the space spanned by leading k columns of the matrices A₁):

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

API

Syntax

namespace oneapi::mkl::lapack {
  cl::sycl::event orgqr_batch(cl::sycl::queue &queue,
  std::int64_t *m,
  std::int64_t *n,
  std::int64_t *k,
  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

Input Parameters

queue

Device queue where calculations will be performed.

m

Array of group_count parameters m_g as previously supplied to geqrf_batch (Group Version).

n

Array of group_count parameters n_g as previously supplied to geqrf_batch (Group Version).

k

Array of group_count parameters k_g as previously supplied to geqrf_batch (Group Version). The number of elementary reflectors whose product defines the matrices Q_i (0 ≤ k_g ≤ n_g) .

a

Array resulting after a call to geqrf_batch (Group Version) <geqrf_batch-group-version.

lda

Array of leading dimension of A_i as previously supplied to geqrf_batch (Group Version).

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 orgqr_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 n_g leading columns of the m_g-by-m_g orthogonal matrices Q_i, where g is an index of group of parameters corresponding to Q_i.

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.

orgqr_batch (Buffer Strided Version) orgqr_batch (USM Strided Version)