sorghr(3S)

NAME
     SORGHR - generate a real orthogonal matrix Q which is defined as the
     product of IHI-ILO elementary reflectors of order N, as returned by
     SGEHRD

SYNOPSIS
     SUBROUTINE SORGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )

         INTEGER        IHI, ILO, INFO, LDA, LWORK, N

         REAL           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
     SORGHR generates a real orthogonal matrix Q which is defined as the
     product of IHI-ILO elementary reflectors of order N, as returned by
     SGEHRD: Q = H(ilo) H(ilo+1) . . . H(ihi-1).


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

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

     A       (input/output) REAL array, dimension (LDA,N)
             On entry, the vectors which define the elementary reflectors, as
             returned by SGEHRD.  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) REAL array, dimension (N-1)
             TAU(i) must contain the scalar factor of the elementary reflector
             H(i), as returned by SGEHRD.
     WORK    (workspace/output) REAL array, dimension (LWORK)
             On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

     LWORK   (input) INTEGER
             The dimension of the array WORK. LWORK >= IHI-ILO.  For optimum
             performance LWORK >= (IHI-ILO)*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)

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