NAME

       slaqp2.f -

SYNOPSIS

   Functions/Subroutines
       subroutine slaqp2 (M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2, WORK)
           SLAQP2 computes a QR factorization with column pivoting of the matrix block.

Function/Subroutine Documentation

   subroutine slaqp2 (integerM, integerN, integerOFFSET, real, dimension( lda, * )A, integerLDA,
       integer, dimension( * )JPVT, real, dimension( * )TAU, real, dimension( * )VN1, real,
       dimension( * )VN2, real, dimension( * )WORK)
       SLAQP2 computes a QR factorization with column pivoting of the matrix block.

       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.

       Parameters:
           M

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

           N

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

           OFFSET

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

           A

                     A is 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 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

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

           JPVT

                     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

                     TAU is REAL array, dimension (min(M,N))
                     The scalar factors of the elementary reflectors.

           VN1

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

           VN2

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

           WORK

                     WORK is REAL array, dimension (N)

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           September 2012

       Contributors:
           G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain X. Sun, Computer
           Science Dept., Duke University, USA
            Partial column norm updating strategy modified on April 2011 Z. Drmac and Z.
           Bujanovic, Dept. of Mathematics, University of Zagreb, Croatia.

       References:
           LAPACK Working Note 176

       Definition at line 149 of file slaqp2.f.

Author

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