gerqf

Computes the RQ factorization of a general m-by-n matrix. This routine belongs to the oneapi::mkl::lapack namespace.

Syntax

void gerqf(cl::sycl::queue &queue, std::int64_t m, std::int64_t n, cl::sycl::buffer<T> &a, std::int64_t lda, cl::sycl::buffer<T> &tau, cl::sycl::buffer<T> &scratchpad, std::int64_t scratchpad_size)

gerqf supports the following precisions and devices:

T

Devices supported

float

Host and CPU

double

Host and CPU

std::complex<float>

Host and CPU

std::complex<double>

Host and CPU

Description

The routine forms the RQ factorization of a general m-by-n matrix A No pivoting is performed.

The routine does not form the matrix Q explicitly. Instead, Q is represented as a product of min(m, n) elementary reflectors. Routines are provided to work with Q in this representation.

Note

This routine supports the Progress Routine feature.

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).

a

Buffer holding input matrix A. The second dimension of a must be at least max(1, n).

lda

The leading dimension of a, at least max(1, m).

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 gerqf_scratchpad_size function.

Output Parameters

a

Overwritten by the factorization data as follows:

if m n, the upper triangle of the subarray a(1:m, n-m+1:n ) contains the m-by-m upper triangular matrix R; if m n, the elements on and above the (m-n)-th subdiagonal contain the m-by-n upper trapezoidal matrix R

In both cases, the remaining elements, with the arraytau, represent the orthogonal/unitary matrix Q as a product of min(m,n) elementary reflectors.

tau

Array, size at least min(m,n).

Contains scalars that define elementary reflectors for the matrix Q in its decomposition in a product of elementary reflectors.

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.