Contents


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 * 1 VECT
     INTEGER M, N, K, LDA, LWORK, INFO
     REAL A(LDA,*), TAU(*), WORK(*)

     SUBROUTINE SORGBR_64(VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO)

     CHARACTER * 1 VECT
     INTEGER*8 M, N, K, LDA, LWORK, INFO
     REAL A(LDA,*), TAU(*), WORK(*)

  F95 INTERFACE
     SUBROUTINE ORGBR(VECT, M, [N], K, A, [LDA], TAU, [WORK], [LWORK],
            [INFO])

     CHARACTER(LEN=1) :: VECT
     INTEGER :: M, N, K, LDA, LWORK, INFO
     REAL, DIMENSION(:) :: TAU, WORK
     REAL, DIMENSION(:,:) :: A

     SUBROUTINE ORGBR_64(VECT, M, [N], K, A, [LDA], TAU, [WORK], [LWORK],
            [INFO])

     CHARACTER(LEN=1) :: VECT
     INTEGER(8) :: M, N, K, LDA, LWORK, INFO
     REAL, DIMENSION(:) :: TAU, WORK
     REAL, DIMENSION(:,:) :: A

  C INTERFACE
     #include <sunperf.h>

     void sorgbr(char vect, int m, int n, int k,  float  *a,  int
               lda, float *tau, int *info);

     void sorgbr_64(char vect, long m, long n, long k, float  *a,
               long lda, float *tau, long *info);

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) respec-
     tively.

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

     N (input) 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) If VECT = 'Q', the number of columns in the origi-
               nal  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)
               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)
               The leading dimension  of  the  array  A.  LDA  >=
               max(1,M).

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

     WORK (workspace)
               On exit, if INFO = 0, WORK(1) returns the  optimal
               LWORK.

     LWORK (input)
               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)
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille-
               gal value