SLAQP2  -  compute a QR factorization with column pivoting
       of the block A(OFFSET+1:M,1:N)


SYNOPSIS

       SUBROUTINE SLAQP2( M, N, OFFSET, A, LDA, JPVT,  TAU,  VN1,
                          VN2, WORK )

           INTEGER        LDA, M, N, OFFSET

           INTEGER        JPVT( * )

           REAL           A( LDA, * ), TAU( * ), VN1( * ), VN2( *
                          ), WORK( * )


PURPOSE

       SLAQP2 computes a QR factorization with column pivoting of
       the  block A(OFFSET+1:M,1:N). The block A(1:OFFSET,1:N) is
       accordingly pivoted, but not factorized.


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.

       OFFSET  (input) INTEGER
               The number of rows of the matrix A  that  must  be
               pivoted but no factorized. OFFSET >= 0.

       A       (input/output) REAL array, dimension (LDA,N)
               On entry, the M-by-N matrix A.  On exit, the upper
               triangle of block A(OFFSET+1:M,1:N) is the  trian­
               gular  factor  obtained;  the  elements  in  block
               A(OFFSET+1:M,1:N)  below  the  diagonal,  together
               with  the  array  TAU,  represent  the  orthogonal
               matrix Q as a product  of  elementary  reflectors.
               Block  A(1:OFFSET,1:N)  has  been accordingly piv­
               oted, but no factorized.

       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.

               The scalar factors of the elementary reflectors.

       VN1     (input/output) REAL array, dimension (N)
               The vector with the partial column norms.

       VN2     (input/output) REAL array, dimension (N)
               The vector with the exact column norms.

       WORK    (workspace) REAL array, dimension (N)


FURTHER DETAILS

       Based on contributions by
         G.  Quintana-Orti,  Depto.  de  Informatica, Universidad
       Jaime I, Spain
         X. Sun, Computer Science Dept., Duke University, USA


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