Multiplies a complex matrix by the unitary matrix Q of the RQ factorization formed by ?gerqf.

## Syntax

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

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

• mkl.h

## Description

The routine multiplies a complex m-by-n matrix C by Q or QH, where Q is the complex unitary matrix defined as a product of k elementary reflectors H(i) of order n: Q = H(1)H* H(2)H*...*H(k)Has 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, QH*C, C*Q, or C*QH (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 QH is applied to C from the left.

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

trans

Must be either 'N' or 'C'.

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

If trans = 'C', the routine multiplies C by QH.

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 H(i), for i = 1,2,...,k, as returned by cgerqf/zgerqf 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 cgerqf/zgerqf.

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

c(size max(1, ldc*n) for column major layout and max(1, ldc*m for row major layout) 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, QH*C, C*Q, or C*QH (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 real counterpart of this routine is ormrq.