DLAQP2(3)      LAPACK routine of NEC Numeric Library Collection      DLAQP2(3)



NAME
       DLAQP2

SYNOPSIS
       SUBROUTINE DLAQP2 (M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2, WORK)



PURPOSE
            DLAQP2 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)
                     M is INTEGER
                     The number of rows of the matrix A. M >= 0.

           N         (input)
                     N is INTEGER
                     The number of columns of the matrix A. N >= 0.

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

           A         (input/output)
                     A is DOUBLE PRECISION 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 triangular 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 pivoted, but no factorized.

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

           JPVT      (input/output)
                     JPVT is 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)
                     TAU is DOUBLE PRECISION array, dimension (min(M,N))
                     The scalar factors of the elementary reflectors.

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

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

           WORK      (output)
                     WORK is DOUBLE PRECISION array, dimension (N)



LAPACK routine                  31 October 2017                      DLAQP2(3)