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



NAME
       DLAQPS

SYNOPSIS
       SUBROUTINE DLAQPS (M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1, VN2,
           AUXV, F, LDF)



PURPOSE
            DLAQPS computes a step of QR factorization with column pivoting
            of a real M-by-N matrix A by using Blas-3.  It tries to factorize
            NB columns from A starting from the row OFFSET+1, and updates all
            of the matrix with Blas-3 xGEMM.

            In some cases, due to catastrophic cancellations, it cannot
            factorize NB columns.  Hence, the actual number of factorized
            columns is returned in KB.

            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 A that have been factorized in
                     previous steps.

           NB        (input)
                     NB is INTEGER
                     The number of columns to factorize.

           KB        (output)
                     KB is INTEGER
                     The number of columns actually factorized.

           A         (input/output)
                     A is DOUBLE PRECISION array, dimension (LDA,N)
                     On entry, the M-by-N matrix A.
                     On exit, block A(OFFSET+1:M,1:KB) is the triangular
                     factor obtained and block A(1:OFFSET,1:N) has been
                     accordingly pivoted, but no factorized.
                     The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has
                     been updated.

           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)
                     JPVT(I) = K <==> Column K of the full matrix A has been
                     permuted into position I in AP.

           TAU       (output)
                     TAU is DOUBLE PRECISION array, dimension (KB)
                     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.

           AUXV      (input/output)
                     AUXV is DOUBLE PRECISION array, dimension (NB)
                     Auxiliar vector.

           F         (input/output)
                     F is DOUBLE PRECISION array, dimension (LDF,NB)
                     Matrix F**T = L*Y**T*A.

           LDF       (input)
                     LDF is INTEGER
                     The leading dimension of the array F. LDF >= max(1,N).



LAPACK routine                  31 October 2017                      DLAQPS(3)