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

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

     INTEGER INFO, LDA, M, N

     INTEGER JPVT( * )

     DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )



     #include <sunperf.h>

     void dgeqpf(int m, int n, double *da, int lda, int  *jpivot,
               double *tau, int *info) ;

PURPOSE
     DGEQPF 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) DOUBLE PRECISION  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
               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)   DOUBLE   PRECISION   array,   dimension
               (min(M,N))
               The scalar factors of the elementary reflectors.

     WORK      (workspace)  DOUBLE  PRECISION  array,   dimension
               (3*N)

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

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