dlaqps.f(3)

NAME
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 (integerM, integerN, integerOFFSET, integerNB, integerKB, double precision, dimension( lda, * )A, integerLDA, integer, dimension( * )JPVT, double precision, dimension( * )TAU, double precision, dimension( * )VN1, double precision, dimension( * )VN2, double precision, dimension( * )AUXV, double precision, dimension( ldf, * )F, integerLDF)

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)
              Auxiliar 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.

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 177 of file dlaqps.f.

Author

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