SGEQPF  -  routine  is deprecated and has been replaced by
       routine SGEQP3


SYNOPSIS

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

           INTEGER        INFO, LDA, M, N

           INTEGER        JPVT( * )

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


PURPOSE

       This routine is deprecated and has been replaced  by  rou­
       tine SGEQP3.  SGEQPF computes a QR factorization with col­
       umn 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)
               elementary 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 col­
               umn); 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 ille­
               gal value

       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.


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