NAME¶

ZUNMRQ - overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'

SYNOPSIS¶

SUBROUTINE ZUNMRQ(

SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO )

CHARACTER SIDE, TRANS INTEGER INFO, K, LDA, LDC, LWORK, M, N COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )

PURPOSE¶

ZUNMRQ overwrites the general complex M-by-N matrix C with TRANS = 'C': Q**H * C C * Q**H
where Q is a complex unitary matrix defined as the product of k elementary reflectors
Q = H(1)' H(2)' . . . H(k)'
as returned by ZGERQF. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

ARGUMENTS¶

SIDE (input) CHARACTER*1

= 'L': apply Q or Q**H from the Left;
= 'R': apply Q or Q**H from the Right.

TRANS (input) CHARACTER*1

= 'N': No transpose, apply Q;
= 'C': Transpose, apply Q**H.

M (input) INTEGER

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

N (input) INTEGER

The number of columns of the matrix C. N >= 0.

K (input) INTEGER

The number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0.

A (input) COMPLEX*16 array, dimension

(LDA,M) if SIDE = 'L', (LDA,N) if SIDE = 'R' The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by ZGERQF in the last k rows of its array argument A. A is modified by the routine but restored on exit.

LDA (input) INTEGER

The leading dimension of the array A. LDA >= max(1,K).

TAU (input) COMPLEX*16 array, dimension (K)

TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by ZGERQF.

C (input/output) COMPLEX*16 array, dimension (LDC,N)

On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.

LDC (input) INTEGER

The leading dimension of the array C. LDC >= max(1,M).

WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))

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

LWORK (input) INTEGER

The dimension of the array WORK. If SIDE = 'L', LWORK >= max(1,N); if SIDE = 'R', LWORK >= max(1,M). For optimum performance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE = 'R', 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 (output) INTEGER

= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value