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sgeqrf

 NAME
      SGEQRF - compute a QR factorization of a real M-by-N matrix
      A

 SYNOPSIS
      SUBROUTINE SGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO )

          INTEGER        INFO, LDA, LWORK, M, N

          REAL           A( LDA, * ), TAU( * ), WORK( LWORK )

 PURPOSE
      SGEQRF computes a QR factorization of a real M-by-N matrix
      A: A = Q * R.

 ARGUMENTS
      M       (input) INTEGER
              The number of rows of the matrix A.  M >= 0.

      N       (input) INTEGER
              The number of columns of the matrix A.  N >= 0.

      A       (input/output) REAL array, dimension (LDA,N)
              On entry, the M-by-N matrix A.  On exit, the ele-
              ments on and above the diagonal of the array contain
              the min(M,N)-by-N upper trapezoidal matrix R (R is
              upper triangular if m >= n); the elements below the
              diagonal, with the array TAU, represent the orthogo-
              nal matrix Q as a product of min(m,n) elementary
              reflectors (see Further Details).

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

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

      WORK    (workspace) REAL array, dimension (LWORK)
              On exit, if INFO = 0, WORK(1) returns the optimal
              LWORK.

      LWORK   (input) INTEGER
              The dimension of the array WORK.  LWORK >= max(1,N).
              For optimum performance LWORK >= N*NB, where NB is
              the optimal blocksize.

      INFO    (output) INTEGER
              = 0:  successful exit
              < 0:  if INFO = -i, the i-th argument had an illegal

              value

 FURTHER DETAILS
      The matrix Q is represented as a product of elementary
      reflectors

         Q = H(1) H(2) . . . H(k), where k = min(m,n).

      Each H(i) has the form

         H(i) = I - tau * v * v'

      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:m) is stored on exit in
      A(i+1:m,i), and tau in TAU(i).