dormhr(3S)

NAME
     DORMHR - overwrite the general real M-by-N matrix C with  SIDE = 'L' SIDE
     = 'R' TRANS = 'N'

SYNOPSIS
     SUBROUTINE DORMHR( SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C, LDC,
                        WORK, LWORK, INFO )

         CHARACTER      SIDE, TRANS

         INTEGER        IHI, ILO, INFO, 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
     DORMHR 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

     where Q is a real orthogonal matrix of order nq, with nq = m if SIDE =
     'L' and nq = n if SIDE = 'R'. Q is defined as the product of IHI-ILO
     elementary reflectors, as returned by DGEHRD:

     Q = H(ilo) H(ilo+1) . . . H(ihi-1).


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

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

     ILO     (input) INTEGER
             IHI     (input) INTEGER ILO and IHI must have the same values as
             in the previous call of DGEHRD. Q is equal to the unit matrix
             except in the submatrix Q(ilo+1:ihi,ilo+1:ihi).  If SIDE = 'L',
             then 1 <= ILO <= IHI <= M, if M > 0, and ILO = 1 and IHI = 0, if
             M = 0; if SIDE = 'R', then 1 <= ILO <= IHI <= N, if N > 0, and
             ILO = 1 and IHI = 0, if N = 0.

     A       (input) DOUBLE PRECISION array, dimension
             (LDA,M) if SIDE = 'L' (LDA,N) if SIDE = 'R' The vectors which
             define the elementary reflectors, as returned by DGEHRD.

     LDA     (input) INTEGER
             The leading dimension of the array A.  LDA >= max(1,M) if SIDE =
             'L'; LDA >= max(1,N) if SIDE = 'R'.

     TAU     (input) DOUBLE PRECISION array, dimension
             (M-1) if SIDE = 'L' (N-1) if SIDE = 'R' TAU(i) must contain the
             scalar factor of the elementary reflector H(i), as returned by
             DGEHRD.

     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.

     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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