NAME

       slaqps.f -

SYNOPSIS

   Functions/Subroutines
       subroutine slaqps (M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1, VN2, AUXV, F, LDF)
           SLAQPS 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 slaqps (integerM, integerN, integerOFFSET, integerNB, integerKB, real, dimension(
       lda, * )A, integerLDA, integer, dimension( * )JPVT, real, dimension( * )TAU, real,
       dimension( * )VN1, real, dimension( * )VN2, real, dimension( * )AUXV, real, dimension(
       ldf, * )F, integerLDF)
       SLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A
       by using BLAS level 3.

       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.

       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 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

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

           VN1

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

           VN2

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

           AUXV

                     AUXV is REAL array, dimension (NB)
                     Auxiliar vector.

           F

                     F is REAL 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 178 of file slaqps.f.

Author

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