zlaqp2(3)

NAME

ZLAQP2 - compute a QR factorization with column pivoting

of the block A(OFFSET+1:M,1:N)

SYNOPSIS

SUBROUTINE  ZLAQP2(  M, N, OFFSET, A, LDA, JPVT, TAU, VN1,
VN2, WORK )
    INTEGER        LDA, M, N, OFFSET
    INTEGER        JPVT( * )
    DOUBLE         PRECISION VN1( * ), VN2( * )
    COMPLEX*16     A( LDA, * ), TAU( * ), WORK( * )

PURPOSE

ZLAQP2 computes a QR factorization with column pivoting of

the block A(OFFSET+1:M,1:N). The block A(1:OFFSET,1:N) is accord

ingly 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 the matrix A that must be

pivoted but no factorized. OFFSET >= 0.

A (input/output) COMPLEX*16 array, dimension (LDA,N)

On entry, the M-by-N matrix A. On exit, the upper

triangle of block A(OFFSET+1:M,1:N) is the triangular factor ob

tained; the elements in block A(OFFSET+1:M,1:N) below the diago

nal, together with the array TAU, represent the orthogonal matrix

Q as a product of elementary reflectors. Block A(1:OFFSET,1:N)

has been accordingly pivoted, but no factorized.

LDA (input) INTEGER

The leading dimension of the array A. LDA >=

max(1,M).

JPVT (input/output) INTEGER array, dimension (N)

On entry, if JPVT(i) .ne. 0, the i-th column of A

is permuted to the front of A*P (a leading column); if JPVT(i) =

0, the i-th column of A is a free column. On exit, if JPVT(i) =

k, then the i-th column of A*P was the k-th column of A.

TAU (output) COMPLEX*16 array, dimension (min(M,N))

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.

WORK (workspace) COMPLEX*16 array, dimension (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

LAPACK version 3.0 15 June 2000

ZLAQP2(3)