geqrf

Computes the QR factorization of a general m-by-n matrix.

geqrf supports the following precisions:

T
float
double
std::complex<float>
std::complex<double>

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.

geqrf (BUFFER Version)

Syntax

void onemkl::lapack::geqrf(cl::sycl::queue &queue, std::int64_t m, std::int64_t n, cl::sycl::buffer<T, 1> &a, std::int64_t lda, cl::sycl::buffer<T, 1> &tau, cl::sycl::buffer<T, 1> &scratchpad, std::int64_t scratchpad_size)

Input Parameters

queue

The queue where the routine should be executed.

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. Must have size at least lda*n.

lda

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

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 geqrf_scratchpad_size function.

Output Parameters

a

Output buffer, 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, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors.

tau

Output buffer, 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.

scratchpad

Buffer holding scratchpad memory to be used by routine for storing intermediate results.

Throws

onemkl::lapack::exception

Exception is thrown in case of problems happened during calculations. The info code of the problem can be obtained by get_info() method of exception object:

If info=-i, the i-th parameter had an illegal value.

If info equals to value passed as scratchpad size, and get_detail() returns non zero, then passed scratchpad is of insufficient size, and required size should not be less than value return by get_detail() method of exception object.

geqrf (USM Version)

Syntax

cl::sycl::event onemkl::lapack::geqrf(cl::sycl::queue &queue, std::int64_t m, std::int64_t n, T *a, std::int64_t lda, T *tau, T *scratchpad, std::int64_t scratchpad_size, const cl::sycl::vector_class<cl::sycl::event> &events = {})

Input Parameters

queue

The queue where the routine should be executed.

m

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

n

The number of columns in A (0≤n).

a

Pointer to memory holding input matrix A. Must have size at least lda*n.

lda

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

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 geqrf_scratchpad_size function.

events

List of events to wait for before starting computation. Defaults to empty list.

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, represent 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.

scratchpad

Pointer to scratchpad memory to be used by routine for storing intermediate results.

Throws

onemkl::lapack::exception

Exception is thrown in case of problems happened during calculations. The info code of the problem can be obtained by get_info() method of exception object:

If info=-i, the i-th parameter had an illegal value.

If info equals to value passed as scratchpad size, and get_detail() returns non zero, then passed scratchpad is of insufficient size, and required size should not be less than value return by get_detail() method of exception object.

Return Values

Output event to wait on to ensure computation is complete.

Parent topic: LAPACK Linear Equation Routines