cunmbr(3)

NAME

cunmbr.f –

SYNOPSIS

Functions/Subroutines

subroutine cunmbr (VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
CUNMBR

Function/Subroutine Documentation

subroutine cunmbr (characterVECT, characterSIDE, characterTRANS, integerM, integerN, integerK, complex, dimension( lda, * )A, integerLDA, complex, dimension( * )TAU, complex, dimension( ldc, * )C, integerLDC, complex, dimension( * )WORK, integerLWORK, integerINFO)

CUNMBR

Purpose:

If VECT = 'Q', CUNMBR 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 If VECT = 'P', CUNMBR overwrites the general complex M - by - N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' : P *C C *P TRANS = 'C' : P **H *C C *P **H Here Q and P **H are the unitary matrices determined by CGEBRD when reducing a complex matrix A to bidiagonal form : A = Q * B * P * *H.Q and P * *H are defined as products of elementary reflectors H(i) and G(i) respectively.Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'.Thus nq is the order of the unitary matrix Q or P **H that is applied.If VECT = 'Q', A is assumed to have been an NQ - by - K matrix : if nq >= k, Q = H(1) H(2)...H(k);
if nq
    < k, Q = H(1) H(2)...H(nq - 1).If VECT = 'P', A is assumed to have been a K - by - NQ matrix : if k < nq, P = G(1) G(2)...G(k);
if k
>= nq, P = G(1) G(2)...G(nq - 1).

 

Parameters:

VECT

          VECT is CHARACTER*1
          = 'Q': apply Q or Q**H;
          = 'P': apply P or P**H.

SIDE

          SIDE is CHARACTER*1
          = 'L': apply Q, Q**H, P or P**H from the Left;
          = 'R': apply Q, Q**H, P or P**H from the Right.

TRANS

          TRANS is CHARACTER*1
          = 'N':  No transpose, apply Q or P;
          = 'C':  Conjugate transpose, apply Q**H or P**H.

M

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

N

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

K

          K is INTEGER
          If VECT = 'Q', the number of columns in the original
          matrix reduced by CGEBRD.
          If VECT = 'P', the number of rows in the original
          matrix reduced by CGEBRD.
          K >= 0.

A

          A is COMPLEX array, dimension
                                (LDA,min(nq,K)) if VECT = 'Q'
                                (LDA,nq)        if VECT = 'P'
          The vectors which define the elementary reflectors H(i) and
          G(i), whose products determine the matrices Q and P, as
          returned by CGEBRD.

LDA

LDA is INTEGER
The leading dimension of the array A.If VECT = ‘Q’,
LDA >= max(1, nq);
if VECT
= ‘P’, LDA >= max(1, min(nq, K)).

TAU

          TAU is COMPLEX array, dimension (min(nq,K))
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i) or G(i) which determines Q or P, as returned
          by CGEBRD in the array argument TAUQ or TAUP.

C

          C is 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
          or P*C or P**H*C or C*P or C*P**H.

LDC

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

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.If SIDE = 'L',
                                       LWORK >= max(1, N);
if SIDE
    = 'R', LWORK >= max(1, M);
if N
    = 0 or M = 0, LWORK >= 1. For optimum performance LWORK >= max(1, N *NB) if SIDE = 'L',
           and LWORK >= max(1, M *NB) if SIDE = 'R', where NB is the optimal blocksize.(NB = 0 if M = 0 or N = 0.) 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 had an illegal value

 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 197 of file cunmbr.f.

Author

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