ungbr

Generates the complex unitary matrix Q or Pt determined by gebrd. This routine belongs to the oneapi::mkl::lapacknamespace.

Syntax

void ungbr(cl::sycl::queue &queue, mkl::generate gen, std::int64_t m, std::int64_t n, std::int64_t k, cl::sycl::buffer<T> &a, std::int64_t lda, cl::sycl::buffer<T> &tau, cl::sycl::buffer<T> &scratchpad, std::int64_t scratchpad_size)

ungbr supports the following precisions and devices:

T

Devices supported

std::complex<float>

Host and CPU

std::complex<double>

Host and CPU

Description

The routine generates the whole or part of the unitary matrices Q and PH formed by the routines gebrd. Use this routine after a call to cgebrd/zgebrd. All valid combinations of arguments are described in Input Parameters; in most cases you need the following:

To compute the whole m-by-m matrix Q, use:

ungbr(queue, generate::q, m, m, n, a, …)

(note that the buffera must have at least m columns).

To form the n leading columns of Q if m > n, use:

ungbr(queue, generate::q, m, n, n, a, …)

To compute the whole n-by-n matrix PT, use:

ungbr(queue, generate::p, n, n, m, a, …)

(note that the array a must have at least n rows).

To form the m leading rows of PT if m < n, use:

ungbr(queue, generate::p, m, n, m, a, …)

Input Parameters

queue

Device queue where calculations will be performed.

gen

Must be generate::q or generate::p.

If gen= generate::q, the routine generates the matrix Q.

If gen= generate::p, the routine generates the matrix PT.

m

The number of rows in the matrix Q or PT to be returned (0≤m).

If gen= generate::q, m n min(m, k).

If gen= generate::p, n m min(n, k).

n

The number of rows in the matrix Q or PT to be returned (0≤n). See m for constraints.

k

If gen= generate::q, the number of columns in the original m-by-k matrix reduced by gebrd.

If gen= generate::p, the number of rows in the original k-by-n matrix reduced by gebrd.

a

Buffer holding memory returned by gebrd.

lda

The leading dimension of a.

tau

For gen= generate::q, the array tauq is returned by the gebrd function.

For gen= generate::p, the array taup is returned by the gebrd function.

The dimension of tau must be at least min(m,k) for gen = generate::q, or min(n,k) for gen = generate::p.

scratchpad

Buffer holding scratchpad memory to be used by the 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 than the value returned by the ungbr_scratchpad_size function.

Output Parameters

a

Overwritten by n leading columns of the m-by-m unitary matrix Q or PT, (or the leading rows or columns thereof) as specified by gen, m, and n.

Exceptions

mkl::lapack::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 = -i, the i-th parameter had an illegal value. If info is equal to the value passed as scratchpad size, and detail() returns non-zero, then the passed scratchpad has an insufficient size, and the required size should not be less than the value returned by the detail() method of the exception object.