geqrf

Computes the QR factorization of a general m-by-n matrix. This routine belongs to the oneapi::mkl::lapacknamespace.

Syntax

void geqrf(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)

geqrf supports the following precisions and devices:

T

Devices supported

float

Host, CPU, and GPU

double

Host, CPU, and GPU

std::complex<float>

Host, CPU, and GPU

std::complex<double>

Host, CPU, and GPU

Description

The routine forms the QR 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.

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 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 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 the geqrf_scratchpad_size function.

Output Parameters

a

Overwritten by the factorization data as follows:

The elements on and above the diagonal of the array contain the min(m,n)-by-n upper trapezoidal matrix R (R is upper triangular if m≥n); the elements below the diagonal, with the array tau, present the orthogonal matrix Q as a product of min(m,n) elementary reflectors.

tau

Array, size at least max (1, 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.