dlaqps (l)  Linux Manuals
dlaqps: computes a step of QR factorization with column pivoting of a real MbyN matrix A by using Blas3
NAME
DLAQPS  computes a step of QR factorization with column pivoting of a real MbyN matrix A by using Blas3SYNOPSIS
 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( * )
PURPOSE
DLAQPS computes a step of QR factorization with column pivoting of a real MbyN matrix A by using Blas3. It tries to factorize NB columns from A starting from the row OFFSET+1, and updates all of the matrix with Blas3 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 MbyN 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 Faq = L*Yaq*A.
 LDF (input) INTEGER
 The leading dimension of the array F. LDF >= max(1,N).
FURTHER DETAILS
Based on contributions byPartial column norm updating strategy modified by
For more details see LAPACK Working Note 176.