zunmtr (l) - Linux Manuals

zunmtr: overwrites the general complex M-by-N matrix C with SIDE = aqLaq SIDE = aqRaq TRANS = aqNaq

NAME

ZUNMTR - overwrites the general complex M-by-N matrix C with SIDE = aqLaq SIDE = aqRaq TRANS = aqNaq

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 TRANS = aqCaq: Q**H * C C * Q**H
where Q is a complex unitary matrix of order nq, with nq = m if SIDE = aqLaq and nq = n if SIDE = aqRaq. Q is defined as the product of nq-1 elementary reflectors, as returned by ZHETRD:
if UPLO = aqUaq, Q = H(nq-1) . . . H(2) H(1);
if UPLO = aqLaq, Q = H(1) H(2) . . . H(nq-1).

ARGUMENTS

SIDE (input) CHARACTER*1

= aqLaq: apply Q or Q**H from the Left;
= aqRaq: apply Q or Q**H from the Right.

UPLO (input) CHARACTER*1

= aqUaq: Upper triangle of A contains elementary reflectors from ZHETRD; = aqLaq: Lower triangle of A contains elementary reflectors from ZHETRD.

TRANS (input) CHARACTER*1

= aqNaq: No transpose, apply Q;
= aqCaq: 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 = aqLaq (LDA,N) if SIDE = aqRaq 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 = aqLaq; LDA >= max(1,N) if SIDE = aqRaq.

TAU (input) COMPLEX*16 array, dimension

(M-1) if SIDE = aqLaq (N-1) if SIDE = aqRaq 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 (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 = aqLaq, LWORK >= max(1,N); if SIDE = aqRaq, LWORK >= max(1,M). For optimum performance LWORK >= N*NB if SIDE = aqLaq, and LWORK >=M*NB if SIDE = aqRaq, 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