Multiplies a real matrix by the orthogonal matrix Q of the RQ factorization formed by ?gerqf.

## Syntax

lapack_int LAPACKE_sormrq (int matrix_layout, char side, char trans, lapack_int m, lapack_int n, lapack_int k, const float* a, lapack_int lda, const float* tau, float* c, lapack_int ldc);

lapack_int LAPACKE_dormrq (int matrix_layout, char side, char trans, lapack_int m, lapack_int n, lapack_int k, const double* a, lapack_int lda, const double* tau, double* c, lapack_int ldc);

• mkl.h

## Description

The routine multiplies a real m-by-n matrix C by Q or QT, where Q is the real orthogonal matrix defined as a product of k elementary reflectors Hi : Q = H1H2 ... Hk as returned by the RQ factorization routine gerqf.

Depending on the parameters side and trans, the routine can form one of the matrix products Q*C, QT*C, C*Q, or C*QT (overwriting the result over C).

## Input Parameters

matrix_layout

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

side

Must be either 'L' or 'R'.

If side = 'L', Q or QT is applied to C from the left.

If side = 'R', Q or QT is applied to C from the right.

trans

Must be either 'N' or 'T'.

If trans = 'N', the routine multiplies C by Q.

If trans = 'T', the routine multiplies C by QT.

m

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

n

The number of columns in C (n 0).

k

The number of elementary reflectors whose product defines the matrix Q. Constraints:

0 km, if side = 'L';

0 kn, if side = 'R'.

a, tau, c

Arrays: a(size for side = 'L': max(1, lda*m) for column major layout and max(1, lda*k) for row major layout; for side = 'R': max(1, lda*n) for column major layout and max(1, lda*k) for row major layout), tau, c (size max(1, ldc*n) for column major layout and max(1, ldc*m) for row major layout).

On entry, the ith row of a must contain the vector which defines the elementary reflector Hi, 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 Hi, as returned by sgerqf/dgerqf.

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

c contains the m-by-n matrix C.

lda

The leading dimension of a; lda max(1, k)for column major layout. For row major layout, lda max(1, m) if side = 'L', and lda max(1, n) if side = 'R'.

ldc

The leading dimension of c; ldc max(1, m)for column major layout and max(1, n) for row major layout.

## Output Parameters

c

Overwritten by the product Q*C, QT*C, C*Q, or C*QT (as specified by side and trans).

## 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 unmrq.

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