dlaqps(3S)

NAME
     DLAQPS - compute a step of QR factorization with column pivoting of a
     real M-by-N matrix A by using Blas-3

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

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

         INTEGER        JPVT( * )

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

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

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

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

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

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

     F       (input/output) DOUBLE PRECISION array, dimension (LDF,NB)
             Matrix F' = L*Y'*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


SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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