SRC/dlaqps.f(3)            Library Functions Manual            SRC/dlaqps.f(3)

NAME
       SRC/dlaqps.f

SYNOPSIS
   Functions/Subroutines
       subroutine dlaqps (m, n, offset, nb, kb, a, lda, jpvt, tau, vn1, vn2,
           auxv, f, ldf)
           DLAQPS computes a step of QR factorization with column pivoting of
           a real m-by-n matrix A by using BLAS level 3.

Function/Subroutine Documentation
   subroutine dlaqps (integer m, integer n, integer offset, integer nb,
       integer kb, double precision, dimension( lda, * ) a, integer lda,
       integer, dimension( * ) jpvt, double precision, dimension( * ) tau,
       double precision, dimension( * ) vn1, double precision, dimension( * )
       vn2, double precision, dimension( * ) auxv, double precision,
       dimension( ldf, * ) f, integer ldf)
       DLAQPS computes a step of QR factorization with column pivoting of a
       real m-by-n matrix A by using BLAS level 3.

       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.

       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 A that have been factorized in
                     previous steps.

           NB

                     NB is INTEGER
                     The number of columns to factorize.

           KB

                     KB is INTEGER
                     The number of columns actually factorized.

           A

                     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

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

           JPVT

                     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

                     TAU is DOUBLE PRECISION array, dimension (KB)
                     The scalar factors of the elementary reflectors.

           VN1

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

           VN2

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

           AUXV

                     AUXV is DOUBLE PRECISION array, dimension (NB)
                     Auxiliary vector.

           F

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

           LDF

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

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       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 175 of file dlaqps.f.

Author
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LAPACK                          Version 3.12.0                 SRC/dlaqps.f(3)