dormbr(3S)

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

SYNOPSIS
     SUBROUTINE DORMBR( 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

         DOUBLE         PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( *
                        )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

PURPOSE
     If VECT = 'Q', DORMBR 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', DORMBR 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 DGEBRD 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 DGEBRD.  If VECT = 'P', the number of rows in the
             original matrix reduced by DGEBRD.  K >= 0.

     A       (input) DOUBLE PRECISION 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
             DGEBRD.

     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) DOUBLE PRECISION 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 DGEBRD in
             the array argument TAUQ or TAUP.

     C       (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION 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.

             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

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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