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## sgeqlf()

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

SGEQLF

Download SGEQLF + dependencies [TGZ] [ZIP] [TXT]

Purpose:

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

Parameters

  [in]

  M

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

  [in]

  N

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

  [in,out]

  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).
      !>

  [in]

  LDA

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

  [out]

  TAU

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

  [out]

  WORK

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

  [in]

  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.
      !>

  [out]

  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).
      !>