SRC/sgeqlf.f(3)

NAME
SRC/sgeqlf.f

SYNOPSIS

  Functions/Subroutines
subroutine sgeqlf (m, n, a, lda, tau, work, lwork, info)
SGEQLF

Function/Subroutine Documentation

  subroutine sgeqlf (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer lwork, integer info)

SGEQLF

Purpose:

    !>
    !> SGEQLF computes a QL factorization of a real M-by-N matrix A:
    !> A = Q * L.
    !>

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,
    !>          if m >= n, the lower triangle of the subarray
    !>          A(m-n+1:m,1:n) contains the N-by-N lower triangular matrix L;
    !>          if m <= n, the elements on and below the (n-m)-th
    !>          superdiagonal contain the M-by-N lower trapezoidal matrix L;
    !>          the remaining elements, 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 >= N, otherwise.
    !>          For optimum performance LWORK >= 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
    !>

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(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
    !>  A(1:m-k+i-1,n-k+i), and tau in TAU(i).
    !>

Definition at line 138 of file sgeqlf.f.

Author

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