• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS

NAME

zunmbr - VECT = 'Q', CUNMBR overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'

SYNOPSIS

  SUBROUTINE ZUNMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, 
 *      WORK, LWORK, INFO)
  CHARACTER * 1 VECT, SIDE, TRANS
  DOUBLE COMPLEX A(LDA,*), TAU(*), C(LDC,*), WORK(*)
  INTEGER M, N, K, LDA, LDC, LWORK, INFO

  SUBROUTINE ZUNMBR_64( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, 
 *      LDC, WORK, LWORK, INFO)
  CHARACTER * 1 VECT, SIDE, TRANS
  DOUBLE COMPLEX A(LDA,*), TAU(*), C(LDC,*), WORK(*)
  INTEGER*8 M, N, K, LDA, LDC, LWORK, INFO

F95 INTERFACE

  SUBROUTINE UNMBR( VECT, SIDE, [TRANS], [M], [N], K, A, [LDA], TAU, 
 *       C, [LDC], [WORK], [LWORK], [INFO])
  CHARACTER(LEN=1) :: VECT, SIDE, TRANS
  COMPLEX(8), DIMENSION(:) :: TAU, WORK
  COMPLEX(8), DIMENSION(:,:) :: A, C
  INTEGER :: M, N, K, LDA, LDC, LWORK, INFO

  SUBROUTINE UNMBR_64( VECT, SIDE, [TRANS], [M], [N], K, A, [LDA], 
 *       TAU, C, [LDC], [WORK], [LWORK], [INFO])
  CHARACTER(LEN=1) :: VECT, SIDE, TRANS
  COMPLEX(8), DIMENSION(:) :: TAU, WORK
  COMPLEX(8), DIMENSION(:,:) :: A, C
  INTEGER(8) :: M, N, K, LDA, LDC, LWORK, INFO

C INTERFACE

#include <sunperf.h>

void zunmbr(char vect, char side, char trans, int m, int n, int k, doublecomplex *a, int lda, doublecomplex *tau, doublecomplex *c, int ldc, int *info);

void zunmbr_64(char vect, char side, char trans, long m, long n, long k, doublecomplex *a, long lda, doublecomplex *tau, doublecomplex *c, long ldc, long *info);

PURPOSE

zunmbr 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).

ARGUMENTS

• VECT (input)
  

   = 'Q': apply Q or Q**H;

   = 'P': apply P or P**H.

• SIDE (input)
  

   = '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 (input)
  

   = 'N':  No transpose, apply Q or P;

   = 'C':  Conjugate transpose, apply Q**H or P**H.

• M (input)
  The number of rows of the matrix C. M > = 0.

• N (input)
  The number of columns of the matrix C. N > = 0.

• K (input)
  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 (input)
  (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 (input)
  The leading dimension of the array A. If VECT = 'Q', LDA > = max(1,nq); if VECT = 'P', LDA > = max(1,min(nq,K)).

• TAU (input)
  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 (input/output)
  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 (input)
  The leading dimension of the array C. LDC > = max(1,M).

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

• LWORK (input)
  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)
  

   = 0:  successful exit

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