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sgerq2

 NAME
      SGERQ2 - compute an RQ factorization of a real m by n matrix
      A

 SYNOPSIS
      SUBROUTINE SGERQ2( M, N, A, LDA, TAU, WORK, INFO )

          INTEGER        INFO, LDA, M, N

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

 PURPOSE
      SGERQ2 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
              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 (M)

      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).