?orgrq

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 4/28/2026

Version

Public

?orgrq

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

Syntax

lapack_intLAPACKE_sorgrq ( intmatrix_layout , lapack_intm , lapack_intn , lapack_intk , float*a , lapack_intlda , constfloat*tau );

lapack_intLAPACKE_dorgrq ( intmatrix_layout , lapack_intm , lapack_intn , lapack_intk , double*a , lapack_intlda , constdouble*tau );

Include Files

mkl.h

Description

sorgrq dorgrq orgrq

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 , work

REAL for sorgrq DOUBLE PRECISION for dorgrq

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 second dimension of a must be at least max(1, n ). The size of tau must be at least max(1, k ). work is a workspace array, its dimension max(1, lwork) .

lda

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

lwork

The size of the work array; at least max(1, m ).

If lwork = -1 , then a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued by xerbla . See Application Notes for the suggested value of lwork .

Output Parameters

a: Overwritten by the last m rows of the n -by- n orthogonal matrix Q .
work(1): If info = 0 , on exit work(1) contains the minimum value of lwork required for optimum performance. Use this lwork for subsequent runs.

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.

LAPACK 95 Interface Notes

There exist FORTRAN 77 and FORTRAN 95 interfaces for this routine. See the Intel® oneMKL Fortran Developer Reference for details.

Application Notes

The complex counterpart of this routine is ungrq .

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?orgrq

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

LAPACK 95 Interface Notes

Application Notes