dorgtr(3S)

NAME
     DORGTR - generate a real orthogonal matrix Q which is defined as the
     product of n-1 elementary reflectors of order N, as returned by DSYTRD

SYNOPSIS
     SUBROUTINE DORGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO )

         CHARACTER      UPLO

         INTEGER        INFO, LDA, LWORK, N

         DOUBLE         PRECISION A( LDA, * ), 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
     DORGTR generates a real orthogonal matrix Q which is defined as the
     product of n-1 elementary reflectors of order N, as returned by DSYTRD:
     if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),

     if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).


ARGUMENTS
     UPLO    (input) CHARACTER*1
             = 'U': Upper triangle of A contains elementary reflectors from
             DSYTRD; = 'L': Lower triangle of A contains elementary reflectors
             from DSYTRD.

     N       (input) INTEGER
             The order of the matrix Q. N >= 0.

     A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
             On entry, the vectors which define the elementary reflectors, as
             returned by DSYTRD.  On exit, the N-by-N orthogonal matrix Q.

     LDA     (input) INTEGER
             The leading dimension of the array A. LDA >= max(1,N).
     TAU     (input) DOUBLE PRECISION array, dimension (N-1)
             TAU(i) must contain the scalar factor of the elementary reflector
             H(i), as returned by DSYTRD.

     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. LWORK >= max(1,N-1).  For
             optimum performance LWORK >= (N-1)*NB, 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)

     This man page is available only online.