sorgbr3

!>
!> 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.
!> 

VECT

!>          VECT is 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

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

N

!>          N is 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

!>          K is 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

!>          A is 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

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

TAU

!>          TAU is 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

!>          WORK is REAL array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
!> 

LWORK

!>          LWORK is 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

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!> 

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