# zlaqp2.f - Man Page

SRC/zlaqp2.f

## Synopsis

### Functions/Subroutines

subroutine **zlaqp2** (m, n, offset, a, lda, jpvt, tau, vn1, vn2, work)**ZLAQP2** computes a QR factorization with column pivoting of the matrix block.

## Function/Subroutine Documentation

### subroutine zlaqp2 (integer m, integer n, integer offset, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) jpvt, complex*16, dimension( * ) tau, double precision, dimension( * ) vn1, double precision, dimension( * ) vn2, complex*16, dimension( * ) work)

**ZLAQP2** computes a QR factorization with column pivoting of the matrix block.

**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 accordingly pivoted, but not factorized.

**Parameters***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 the matrix A that must be pivoted but no factorized. OFFSET >= 0.

*A*A is 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 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*LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).

*JPVT*JPVT is 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*TAU is COMPLEX*16 array, dimension (min(M,N)) 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.

*WORK*WORK is COMPLEX*16 array, dimension (N)

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Contributors:**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.**References:**LAPACK Working Note 176

Definition at line **147** of file **zlaqp2.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zlaqp2(3) is an alias of zlaqp2.f(3).