orgqr

Generates the real orthogonal matrix Q of the QR factorization formed by geqrf. This routine belongs to the oneapi::mkl::lapacknamespace.

Syntax

void orgqr(cl::sycl::queue &queue, 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)

orgqr supports the following precisions and devices:

T

Devices supported

float

Host, CPU, and GPU

double

Host, CPU, and GPU

Description

The routine generates the whole or part of m-by-m orthogonal matrix Q of the QR factorization formed by the routine geqrf.

Usually Q is determined from the QR factorization of an m by p matrix A with m≥p. To compute the whole matrix Q, use:

mkl::orgqr(queue, m, m, p, a, lda, tau, ...)

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

mkl::orgqr(queue, m, p, p, a, lda, tau, ...)

To compute the matrix Qk of the QR factorization of leading k columns of the matrix A:

mkl::orgqr(queue, m, m, k, a, lda, tau, ...)

To compute the leading k columns of Qk (which form an orthonormal basis in the space spanned by leading k columns of the matrix A):

mkl::orgqr(queue, m, k, k, a, lda, tau, ...)

Input Parameters

queue

Device queue where calculations will be performed.

m

The number of rows in the matrix A (0≤m).

n

The number of columns in the matrix A (0≤n).

k

The number of elementary reflectors whose product defines the matrix Q (0≤k≤n).

a

Buffer holding the result of geqrf.

lda

The leading dimension of a (lda≤m).

tau

Buffer holding the result of geqrf.

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 orgqr_scratchpad_size function.

Output Parameters

a

Overwritten by n leading columns of the m-by-m orthogonal matrix Q.

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.