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::lapacknamespace.

Syntax

cl::sycl::event ungqr_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 cl::sycl::vector_class<cl::sycl::event> &events = {})

Function supports the following precisions and devices.

T

Devices supported

std::complex<float>

Host, CPU, and GPU

std::complex<double>

Host, CPU, and GPU

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, ...)

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).

n

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

k

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

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.

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

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.