NAME

SYNOPSIS

  SUBROUTINE DORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, 
 *      WORK, LWORK, INFO)
  CHARACTER * 1 VECT, SIDE, TRANS
  INTEGER M, N, K, LDA, LDC, LWORK, INFO
  DOUBLE PRECISION A(LDA,*), TAU(*), C(LDC,*), WORK(*)
 
  SUBROUTINE DORMBR_64( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, 
 *      LDC, WORK, LWORK, INFO)
  CHARACTER * 1 VECT, SIDE, TRANS
  INTEGER*8 M, N, K, LDA, LDC, LWORK, INFO
  DOUBLE PRECISION A(LDA,*), TAU(*), C(LDC,*), WORK(*)
 

F95 INTERFACE

  SUBROUTINE ORMBR( VECT, SIDE, [TRANS], [M], [N], K, A, [LDA], TAU, 
 *       C, [LDC], [WORK], [LWORK], [INFO])
  CHARACTER(LEN=1) :: VECT, SIDE, TRANS
  INTEGER :: M, N, K, LDA, LDC, LWORK, INFO
  REAL(8), DIMENSION(:) :: TAU, WORK
  REAL(8), DIMENSION(:,:) :: A, C
 
  SUBROUTINE ORMBR_64( VECT, SIDE, [TRANS], [M], [N], K, A, [LDA], 
 *       TAU, C, [LDC], [WORK], [LWORK], [INFO])
  CHARACTER(LEN=1) :: VECT, SIDE, TRANS
  INTEGER(8) :: M, N, K, LDA, LDC, LWORK, INFO
  REAL(8), DIMENSION(:) :: TAU, WORK
  REAL(8), DIMENSION(:,:) :: A, C
 

C INTERFACE

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

void dormbr_64(char vect, char side, char trans, long m, long n, long k, double *a, long lda, double *tau, double *c, long ldc, long *info);

PURPOSE

If VECT = 'P', SORMBR overwrites the general real M-by-N matrix C with

                SIDE = 'L'     SIDE = 'R'

TRANS = 'N': P * C C * P

TRANS = 'T': P**T * C C * P**T

Here Q and P**T are the orthogonal matrices determined by SGEBRD when reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and P**T 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 orthogonal matrix Q or P**T 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)

* SIDE (input)

* TRANS (input)

* 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 SGEBRD. If VECT = 'P', the number of rows in the original matrix reduced by SGEBRD. 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 SGEBRD.

* 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 SGEBRD 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**T*C or C*Q**T or C*Q or P*C or P**T*C or C*P or C*P**T.

* 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)