sgeqpf(3F)

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)
             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) 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.