dorgrq(3S)

NAME
     DORGRQ - generate an M-by-N real matrix Q with orthonormal rows,

SYNOPSIS
     SUBROUTINE DORGRQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )

         INTEGER        INFO, K, LDA, LWORK, M, 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
     DORGRQ generates an M-by-N real matrix Q with orthonormal rows, which is
     defined as the last M rows of a product of K elementary reflectors of
     order N

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

     as returned by DGERQF.


ARGUMENTS
     M       (input) INTEGER
             The number of rows of the matrix Q. M >= 0.

     N       (input) INTEGER
             The number of columns of the matrix Q. N >= M.

     K       (input) INTEGER
             The number of elementary reflectors whose product defines the
             matrix Q. M >= K >= 0.

     A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
             On entry, the (m-k+i)-th row must contain the vector which
             defines the elementary reflector H(i), for i = 1,2,...,k, as
             returned by DGERQF in the last k rows of its array argument A.
             On exit, the M-by-N matrix Q.
     LDA     (input) INTEGER
             The first dimension of the array A. LDA >= max(1,M).

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

     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,M).  For optimum
             performance LWORK >= M*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 has an illegal value

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

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