# dlaqp2 (l) - Linux Man Pages

## dlaqp2: computes a QR factorization with column pivoting of the block A(OFFSET+1:M,1:N)

## NAME

DLAQP2 - computes a QR factorization with column pivoting of the block A(OFFSET+1:M,1:N)## SYNOPSIS

- SUBROUTINE DLAQP2(
- M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2, WORK )

- INTEGER LDA, M, N, OFFSET

- INTEGER JPVT( * )

- DOUBLE PRECISION A( LDA, * ), TAU( * ), VN1( * ), VN2( * ), WORK( * )

## PURPOSE

DLAQP2 computes a QR factorization with column pivoting of the block A(OFFSET+1:M,1:N). The 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 the matrix A that must be pivoted but no factorized. OFFSET >= 0.
- A (input/output) DOUBLE PRECISION 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 obtained; the elements in block A(OFFSET+1:M,1:N) below the diagonal, 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (N)

## FURTHER DETAILS

Based on contributions byPartial column norm updating strategy modified by

For more details see LAPACK Working Note 176.