Provided by: liblapack-doc_3.3.1-1_all

#### NAME

```       LAPACK-3 - computes a QR factorization with column pivoting of the block A(OFFSET+1:M,1:N)

```

#### SYNOPSIS

```       SUBROUTINE SLAQP2( M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2, WORK )

INTEGER        LDA, M, N, OFFSET

INTEGER        JPVT( * )

REAL           A( LDA, * ), TAU( * ), VN1( * ), VN2( * ), WORK( * )

```

#### PURPOSE

```       SLAQP2 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) REAL 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) REAL array, dimension (min(M,N))
The scalar factors of the elementary reflectors.

VN1     (input/output) REAL array, dimension (N)
The vector with the partial column norms.

VN2     (input/output) REAL array, dimension (N)
The vector with the exact column norms.

WORK    (workspace) REAL array, dimension (N)

```

#### FURTHERDETAILS

```        Based on contributions by
G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
X. Sun, Computer Science Dept., Duke University, USA
Partial column norm updating strategy modified by
Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
University of Zagreb, Croatia.
-- April 2011                                                      --
For more details see LAPACK Working Note 176.

LAPACK auxiliary routine (version 3.3.1)   April 2011                            SLAQP2(3lapack)
```