Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  computes  a  step  of  QR factorization with column pivoting of a real M-by-N
       matrix A by using Blas-3

SYNOPSIS

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

           INTEGER        KB, LDA, LDF, M, N, NB, OFFSET

           INTEGER        JPVT( * )

           REAL           A( LDA, * ), AUXV( * ), F( LDF, * ), TAU( * ), VN1( * ), VN2( * )

PURPOSE

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

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

        OFFSET  (input) INTEGER
                The number of rows of A that have been factorized in
                previous steps.

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

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

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

        JPVT    (input/output) INTEGER array, dimension (N)
                JPVT(I) = K <==> Column K of the full matrix A has been
                permuted into position I in AP.

        TAU     (output) REAL array, dimension (KB)
                The scalar factors of the elementary reflectors.

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

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

        AUXV    (input/output) REAL array, dimension (NB)
                Auxiliar vector.

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

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

FURTHER DETAILS

        Based on contributions by
          G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
          X. Sun, Computer Science Dept., Duke University, USA
        Partial column norm updating strategy modified by
          Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
          University of Zagreb, Croatia.
        -- April 2011                                                      --
        For more details see LAPACK Working Note 176.

 LAPACK auxiliary routine (version 3.3.1)   April 2011                            SLAQPS(3lapack)