SYNOPSIS

SUBROUTINE ZLAQPS(

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 VN1( * ), VN2( * )

    

COMPLEX*16 A( LDA, * ), AUXV( * ), F( LDF, * ), TAU( * )

PURPOSE

ZLAQPS computes a step of QR factorization with column pivoting of a complex 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) COMPLEX*16 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) COMPLEX*16 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) COMPLEX*16 array, dimension (NB)

Auxiliar vector.

F (input/output) COMPLEX*16 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