dormr3(3S)

NAME
     DORMR3 - overwrite the general real m by n matrix C with  Q * C if SIDE =
     'L' and TRANS = 'N', or  Q'* C if SIDE = 'L' and TRANS = 'T', or  C * Q
     if SIDE = 'R' and TRANS = 'N', or  C * Q' if SIDE = 'R' and TRANS = 'T',

SYNOPSIS
     SUBROUTINE DORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK,
                        INFO )

         CHARACTER      SIDE, TRANS

         INTEGER        INFO, K, L, LDA, LDC, 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
     DORMR3 overwrites the general real m by n matrix C with Q * C if SIDE =
     'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if
     SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T',
     where Q is a real orthogonal matrix defined as the product of k
     elementary reflectors

           Q = H(1) H(2) . . . H(k)

     as returned by DTZRZF. Q is of order m if SIDE = 'L' and of order n if
     SIDE = 'R'.


ARGUMENTS
     SIDE    (input) CHARACTER*1
             = 'L': apply Q or Q' from the Left
             = 'R': apply Q or Q' from the Right

     TRANS   (input) CHARACTER*1
             = 'N': apply Q  (No transpose)
             = 'T': apply Q' (Transpose)
     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
             The number of elementary reflectors whose product defines the
             matrix Q.  If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >=
             0.

     L       (input) INTEGER
             The number of columns of the matrix A containing the meaningful
             part of the Householder reflectors.  If SIDE = 'L', M >= L >= 0,
             if SIDE = 'R', N >= L >= 0.

     A       (input) DOUBLE PRECISION array, dimension
             (LDA,M) if SIDE = 'L', (LDA,N) if SIDE = 'R' The i-th row must
             contain the vector which defines the elementary reflector H(i),
             for i = 1,2,...,k, as returned by DTZRZF in the last k rows of
             its array argument A.  A is modified by the routine but restored
             on exit.

     LDA     (input) INTEGER
             The leading dimension of the array A. LDA >= max(1,K).

     TAU     (input) DOUBLE PRECISION array, dimension (K)
             TAU(i) must contain the scalar factor of the elementary reflector
             H(i), as returned by DTZRZF.

     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'*C or C*Q' or C*Q.

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

     WORK    (workspace) DOUBLE PRECISION array, dimension
             (N) if SIDE = 'L', (M) if SIDE = 'R'

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

FURTHER DETAILS
     Based on contributions by
       A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

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

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