sorgbr(3S)

NAME
     SORGBR - generate one of the real orthogonal matrices Q or P**T
     determined by SGEBRD when reducing a real matrix A to bidiagonal form

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

         CHARACTER      VECT

         INTEGER        INFO, K, LDA, LWORK, M, 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
     SORGBR generates one of the real orthogonal matrices Q or P**T determined
     by SGEBRD when reducing a real matrix A to bidiagonal form: A = Q * B *
     P**T. Q and P**T are defined as products of elementary reflectors H(i) or
     G(i) respectively.

     If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q is of
     order M:
     if m >= k, Q = H(1) H(2) . . . H(k) and SORGBR returns the first n
     columns of Q, where m >= n >= k;
     if m < k, Q = H(1) H(2) . . . H(m-1) and SORGBR returns Q as an M-by-M
     matrix.

     If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T is of
     order N:
     if k < n, P**T = G(k) . . . G(2) G(1) and SORGBR returns the first m rows
     of P**T, where n >= m >= k;
     if k >= n, P**T = G(n-1) . . . G(2) G(1) and SORGBR returns P**T as an
     N-by-N matrix.


ARGUMENTS
     VECT    (input) CHARACTER*1
             Specifies whether the matrix Q or the matrix P**T is required, as
             defined in the transformation applied by SGEBRD:
             = 'Q':  generate Q;
             = 'P':  generate P**T.

     M       (input) INTEGER
             The number of rows of the matrix Q or P**T to be returned.  M >=
             0.

     N       (input) INTEGER
             The number of columns of the matrix Q or P**T to be returned.  N
             >= 0.  If VECT = 'Q', M >= N >= min(M,K); if VECT = 'P', N >= M
             >= min(N,K).

     K       (input) INTEGER
             If VECT = 'Q', the number of columns in the original M-by-K
             matrix reduced by SGEBRD.  If VECT = 'P', the number of rows in
             the original K-by-N matrix reduced by SGEBRD.  K >= 0.

     A       (input/output) REAL array, dimension (LDA,N)
             On entry, the vectors which define the elementary reflectors, as
             returned by SGEBRD.  On exit, the M-by-N matrix Q or P**T.

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

     TAU     (input) REAL array, dimension
             (min(M,K)) if VECT = 'Q' (min(N,K)) if VECT = 'P' TAU(i) must
             contain the scalar factor of the elementary reflector H(i) or
             G(i), which determines Q or P**T, as returned by SGEBRD in its
             array argument TAUQ or TAUP.

     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 >= max(1,min(M,N)).  For
             optimum performance LWORK >= min(M,N)*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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