cungrq.f −

**Functions/Subroutines**

subroutine **cungrq** (M, N, K, A, LDA, TAU, WORK, LWORK, INFO)

CUNGRQ

**subroutine cungrq (integerM, integerN, integerK, complex, dimension( lda, * )A, integerLDA, complex, dimension( * )TAU, complex, dimension( * )WORK, integerLWORK, integerINFO)
CUNGRQ**

**Purpose:**

CUNGRQ generates an M-by-N complex matrix Q with orthonormal rows,

which is defined as the last M rows of a product of K elementary

reflectors of order N

Q = H(1)**H H(2)**H . . . H(k)**H

as returned by CGERQF.

**Parameters:**

*M*

M is INTEGER

The number of rows of the matrix Q. M >= 0.

*N*

N is INTEGER

The number of columns of the matrix Q. N >= M.

*K*

K is INTEGER

The number of elementary reflectors whose product defines the

matrix Q. M >= K >= 0.

*A*

A is COMPLEX array, dimension (LDA,N)

On entry, the (m-k+i)-th row must contain the vector which

defines the elementary reflector H(i), for i = 1,2,...,k, as

returned by CGERQF in the last k rows of its array argument

A.

On exit, the M-by-N matrix Q.

*LDA*

LDA is INTEGER

The first dimension of the array A. LDA >= max(1,M).

*TAU*

TAU is COMPLEX array, dimension (K)

TAU(i) must contain the scalar factor of the elementary

reflector H(i), as returned by CGERQF.

*WORK*

WORK is COMPLEX array, dimension (MAX(1,LWORK))

On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

*LWORK*

LWORK is INTEGER

The dimension of the array WORK. LWORK >= max(1,M).

For optimum performance LWORK >= M*NB, where NB is the

optimal blocksize.

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.

*INFO*

INFO is INTEGER

= 0: successful exit

< 0: if INFO = -i, the i-th argument has an illegal value

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

November 2011

Definition at line 129 of file cungrq.f.

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