?orgrq

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/31/2023

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?orgrq

Generates the real matrix Q of the RQ factorization formed by ?gerqf.

Syntax

lapack_int LAPACKE_sorgrq (int matrix_layout, lapack_int m, lapack_int n, lapack_int k, float* a, lapack_int lda, const float* tau);

lapack_int LAPACKE_dorgrq (int matrix_layout, lapack_int m, lapack_int n, lapack_int k, double* a, lapack_int lda, const double* tau);

Include Files

mkl.h

Description

The routine generates an m-by-n real matrix with orthonormal rows, which is defined as the last m rows of a product of k elementary reflectors H(i) of order n: Q = H(1)* H(2)*...*H(k)as returned by the routines gerqf. Use this routine after a call to sgerqf/dgerqf.

Input Parameters

matrix_layout

Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).

m

The number of rows of the matrix Q (m≥ 0).

n

The number of columns of the matrix Q (n≥ m).

k

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

a, tau

Arrays: a(size max(1, lda*n) for column major layout and max(1, lda*m) for row major layout), tau.

On entry, the (m - k + i)-th row of a must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by sgerqf/dgerqf in the last k rows of its array argument a;

tau[i - 1] must contain the scalar factor of the elementary reflector H(i), as returned by sgerqf/dgerqf;

The size of tau must be at least max(1, k).

lda

The leading dimension of a; at least max(1, m)for column major layout and max(1, n) for row major layout.

Output Parameters

a: Overwritten by the last m rows of the n-by-n orthogonal matrix Q.

Return Values

This function returns a value info.

If info=0, the execution is successful.

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

Application Notes

The complex counterpart of this routine is ungrq.

Parent topic: Orthogonal Factorizations: LAPACK Computational Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?orgrq