SORMBR (3lapack)

VECT = 'Q', SORMBR overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'

SYNOPSIS

  SUBROUTINE SORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK,
                     LWORK, INFO )

      CHARACTER      SIDE, TRANS, VECT

      INTEGER        INFO, K, LDA, LDC, LWORK, M, N

      REAL           A( LDA, * ), C( LDC, * ), TAU( * ), WORK( LWORK )

PURPOSE

  If VECT = 'Q', SORMBR overwrites the general real M-by-N matrix C with
                  SIDE = 'L'     SIDE = 'R' TRANS = 'N':      Q * C
  C * Q TRANS = 'T':      Q**T * C       C * Q**T

  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) CHARACTER*1
          = 'Q': apply Q or Q**T;
          = 'P': apply P or P**T.

  SIDE    (input) CHARACTER*1
          = 'L': apply Q, Q**T, P or P**T from the Left;
          = 'R': apply Q, Q**T, P or P**T from the Right.

  TRANS   (input) CHARACTER*1
          = 'N':  No transpose, apply Q  or P;
          = 'T':  Transpose, apply Q**T or P**T.

  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.

  K       (input) INTEGER
          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) REAL 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 SGEBRD.

  LDA     (input) 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     (input) REAL 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 SGEBRD in the
          array argument TAUQ or TAUP.

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

  WORK    (workspace/output) REAL array, dimension (LWORK)
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

  LWORK   (input) INTEGER
          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.

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