SRC/sgelqf.f(3)            Library Functions Manual            SRC/sgelqf.f(3)

NAME
       SRC/sgelqf.f

SYNOPSIS
   Functions/Subroutines
       subroutine sgelqf (m, n, a, lda, tau, work, lwork, info)
           SGELQF

Function/Subroutine Documentation
   subroutine sgelqf (integer m, integer n, real, dimension( lda, * ) a,
       integer lda, real, dimension( * ) tau, real, dimension( * ) work,
       integer lwork, integer info)
       SGELQF

       Purpose:


           !>
           !> SGELQF computes an LQ factorization of a real M-by-N matrix A:
           !>
           !>    A = ( L 0 ) *  Q
           !>
           !> where:
           !>
           !>    Q is a N-by-N orthogonal matrix;
           !>    L is a lower-triangular M-by-M matrix;
           !>    0 is a M-by-(N-M) zero matrix, if M < N.
           !>
           !>

       Parameters
           M

           !>          M is INTEGER
           !>          The number of rows of the matrix A.  M >= 0.
           !>

           N

           !>          N is INTEGER
           !>          The number of columns of the matrix A.  N >= 0.
           !>

           A

           !>          A is REAL array, dimension (LDA,N)
           !>          On entry, the M-by-N matrix A.
           !>          On exit, the elements on and below the diagonal of the array
           !>          contain the m-by-min(m,n) lower trapezoidal matrix L (L is
           !>          lower triangular if m <= n); the elements above the diagonal,
           !>          with the array TAU, represent the orthogonal matrix Q as a
           !>          product of elementary reflectors (see Further Details).
           !>

           LDA

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

           TAU

           !>          TAU is REAL array, dimension (min(M,N))
           !>          The scalar factors of the elementary reflectors (see Further
           !>          Details).
           !>

           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 >= 1, if MIN(M,N) = 0, and LWORK >= M, otherwise.
           !>          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

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

       Author
           Univ. of Tennessee


           Univ. of California Berkeley


           Univ. of Colorado Denver


           NAG Ltd.

       Further Details:


           !>
           !>  The matrix Q is represented as a product of elementary reflectors
           !>
           !>     Q = H(k) . . . H(2) H(1), where k = min(m,n).
           !>
           !>  Each H(i) has the form
           !>
           !>     H(i) = I - tau * v * v**T
           !>
           !>  where tau is a real scalar, and v is a real vector with
           !>  v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n),
           !>  and tau in TAU(i).
           !>

       Definition at line 143 of file sgelqf.f.

Author
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LAPACK                          Version 3.12.0                 SRC/sgelqf.f(3)