# dlaqp2.f man page

dlaqp2.f —

## Synopsis

### Functions/Subroutines

subroutinedlaqp2(M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2, WORK)DLAQP2computes a QR factorization with column pivoting of the matrix block.

## Function/Subroutine Documentation

### subroutine dlaqp2 (integerM, integerN, integerOFFSET, double precision, dimension( lda, * )A, integerLDA, integer, dimension( * )JPVT, double precision, dimension( * )TAU, double precision, dimension( * )VN1, double precision, dimension( * )VN2, double precision, dimension( * )WORK)

**DLAQP2** computes a QR factorization with column pivoting of the matrix block.

**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.
```

**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 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*

```
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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N)`

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

November 2013

**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 149 of file dlaqp2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

dlaqp2(3) is an alias of dlaqp2.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK