SRC/dgelqf.f(3)

NAME
SRC/dgelqf.f

SYNOPSIS

  Functions/Subroutines
subroutine dgelqf (m, n, a, lda, tau, work, lwork, info)
DGELQF

Function/Subroutine Documentation

  subroutine dgelqf (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer lwork, integer info)

DGELQF

Purpose:

    !>
    !> DGELQF 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (min(M,N))
    !>          The scalar factors of the elementary reflectors (see Further
    !>          Details).
    !>

    WORK

    !>          WORK is DOUBLE PRECISION 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 dgelqf.f.

Author

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