SYNOPSIS

SUBROUTINE CUPMTR(

SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK, INFO )

    

CHARACTER SIDE, TRANS, UPLO

    

INTEGER INFO, LDC, M, N

    

COMPLEX AP( * ), C( LDC, * ), TAU( * ), WORK( * )

PURPOSE

CUPMTR 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 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 CHPTRD using packed storage:
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 triangular packed storage used in previous call to CHPTRD; = 'L': Lower triangular packed storage used in previous call to CHPTRD.

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.

AP (input) COMPLEX array, dimension

(M*(M+1)/2) if SIDE = 'L' (N*(N+1)/2) if SIDE = 'R' The vectors which define the elementary reflectors, as returned by CHPTRD. AP is modified by the routine but restored on exit.

TAU (input) COMPLEX array, dimension (M-1) if SIDE = 'L'

or (N-1) if SIDE = 'R' TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CHPTRD.

C (input/output) COMPLEX 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) COMPLEX array, dimension

(N) if SIDE = 'L' (M) if SIDE = 'R'

INFO (output) INTEGER

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