---
name: "zlaqp2.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/zlaqp2.f"
---

# zlaqp2.f(3)

## NAME

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

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