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sgerqf

 NAME
      SGERQF - compute an RQ factorization of a real M-by-N matrix
      A

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

          INTEGER        INFO, LDA, LWORK, M, N

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

 PURPOSE
      SGERQF computes an RQ factorization of a real M-by-N matrix
      A: A = R * Q.

 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, if m <= n,
              the upper triangle of the subarray A(1:m,n-m+1:n)
              contains the M-by-M upper triangular matrix R; if m
              >= n, the elements on and above the (m-n)-th subdi-
              agonal contain the M-by-N upper trapezoidal matrix
              R; the remaining elements, with the array TAU,
              represent the orthogonal 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,M).
              For optimum performance LWORK >= M*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(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on
      exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i).