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dorgbr examples
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Man Page Details
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NAME
       DORGBR  -  one  of the real orthogonal matrices Q or P**T determined by
       DGEBRD when reducing a real matrix A to bidiagonal form

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

           CHARACTER      VECT

           INTEGER        INFO, K, LDA, LWORK, M, N

           DOUBLE         PRECISION A( LDA, * ), TAU( * ), WORK( * )

PURPOSE
       DORGBR generates one of the real orthogonal matrices Q or  P**T  deter-
       mined by DGEBRD when reducing a real matrix A to bidiagonal form: A = Q
       * B * P**T.  Q and P**T are defined as products of  elementary  reflec-
       tors 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  DORGBR  returns  the  first  n
       columns of Q, where m >= n >= k;
       if  m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR 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 DORGBR 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 DORGBR 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 DGEBRD:
               = '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 DGEBRD.  If VECT = 'P', the number of rows in
               the original K-by-N matrix reduced by DGEBRD.  K >= 0.

       A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
               On  entry,  the vectors which define the elementary reflectors,
               as returned by DGEBRD.  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) DOUBLE PRECISION 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 DGEBRD in  its
               array argument TAUQ or TAUP.

       WORK       (workspace/output)   DOUBLE   PRECISION   array,   dimension
       (MAX(1,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 opti-
               mal 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

