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.

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).

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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.

LAPACK Working Note 176