slarz(3S)

NAME
     SLARZ - applie a real elementary reflector H to a real M-by-N matrix C,
     from either the left or the right

SYNOPSIS
     SUBROUTINE SLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )

         CHARACTER     SIDE

         INTEGER       INCV, L, LDC, M, N

         REAL          TAU

         REAL          C( LDC, * ), V( * ), 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
     SLARZ applies a real elementary reflector H to a real M-by-N matrix C,
     from either the left or the right. H is represented in the form

           H = I - tau * v * v'

     where tau is a real scalar and v is a real vector.

     If tau = 0, then H is taken to be the unit matrix.


     H is a product of k elementary reflectors as returned by STZRZF.


ARGUMENTS
     SIDE    (input) CHARACTER*1
             = 'L': form  H * C
             = 'R': form  C * H

     M       (input) INTEGER
             The number of rows of the matrix C.
     N       (input) INTEGER
             The number of columns of the matrix C.

     L       (input) INTEGER
             The number of entries of the vector V containing the meaningful
             part of the Householder vectors.  If SIDE = 'L', M >= L >= 0, if
             SIDE = 'R', N >= L >= 0.

     V       (input) REAL array, dimension (1+(L-1)*abs(INCV))
             The vector v in the representation of H as returned by STZRZF. V
             is not used if TAU = 0.

     INCV    (input) INTEGER
             The increment between elements of v. INCV <> 0.

     TAU     (input) REAL
             The value tau in the representation of H.

     C       (input/output) REAL array, dimension (LDC,N)
             On entry, the M-by-N matrix C.  On exit, C is overwritten by the
             matrix H * C if SIDE = 'L', or C * H if SIDE = 'R'.

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

     WORK    (workspace) REAL array, dimension
             (N) if SIDE = 'L' or (M) if SIDE = 'R'

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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