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sgeqpf

 NAME
      SGEQPF - compute a QR factorization with column pivoting of
      a real M-by-N matrix A

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

          INTEGER        INFO, LDA, M, N

          INTEGER        JPVT( * )

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

 PURPOSE
      SGEQPF computes a QR factorization with column pivoting of a
      real M-by-N matrix A: A*P = 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 upper
              triangle of the array contains the min(M,N)-by-N
              upper triangular matrix R; the elements below the
              diagonal, together with the array TAU, represent the
              orthogonal matrix Q as a product of min(m,n) elemen-
              tary reflectors.

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

      JPVT    (input/output) INTEGER array, dimension (N)
              On entry, if JPVT(i) .ne. 0, the i-th column of A is
              permuted to the front of A*P (a leading column); if
              JPVT(i) = 0, the i-th column of A is a free column.
              On exit, if JPVT(i) = k, then the i-th column of A*P
              was the k-th column of A.

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

      WORK    (workspace) REAL array, dimension (3*N)

      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(n)

      Each H(i) has the form

         H = 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).

      The matrix P is represented in jpvt as follows: If
         jpvt(j) = i
      then the jth column of P is the ith canonical unit vector.