zunmtr(3)

NAME

ZUNMTR - overwrite the general complex M-by-N matrix C

with SIDE = 'L' SIDE = 'R' TRANS = 'N'

SYNOPSIS

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

PURPOSE

ZUNMTR overwrites the general complex M-by-N matrix C with

SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C':

Q**H * C C * Q**H

where Q is a complex unitary matrix of order nq, with nq =

m if SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the

product of nq-1 elementary reflectors, as returned by ZHETRD:

if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);

if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).

ARGUMENTS

SIDE (input) CHARACTER*1

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

UPLO (input) CHARACTER*1

= 'U': Upper triangle of A contains elementary re

flectors from ZHETRD; = 'L': Lower triangle of A contains elemen

tary reflectors from ZHETRD.

TRANS (input) CHARACTER*1

= 'N': No transpose, apply Q;
= 'C': Conjugate 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.

A (input) COMPLEX*16 array, dimension

(LDA,M) if SIDE = 'L' (LDA,N) if SIDE = 'R' The

vectors which define the elementary reflectors, as returned by

ZHETRD.

LDA (input) INTEGER

The leading dimension of the array A. LDA >=

max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.

TAU (input) COMPLEX*16 array, dimension

(M-1) if SIDE = 'L' (N-1) if SIDE = 'R' TAU(i)

must contain the scalar factor of the elementary reflector H(i),

as returned by ZHETRD.

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

(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 ille

gal value

LAPACK version 3.0 15 June 2000

ZUNMTR(3)