---
name: "zlaqps.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/zlaqps.f"
---

# zlaqps.f(3)

## NAME

SRC/zlaqps.f

## SYNOPSIS

### Functions/Subroutines

subroutine **zlaqps** (m, n, offset, nb, kb, a, lda, jpvt, tau, vn1, vn2, auxv, f, ldf)\
 **ZLAQPS** computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.

## Function/Subroutine Documentation

### subroutine zlaqps (integer m, integer n, integer offset, integer nb, integer kb, 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( \* ) auxv, complex\*16, dimension( ldf, \* ) f, integer ldf)

**ZLAQPS** computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.

**Purpose:**

```
!>
!> ZLAQPS computes a step of QR factorization with column pivoting
!> of a complex M-by-N matrix A by using Blas-3.  It tries to factorize
!> NB columns from A starting from the row OFFSET+1, and updates all
!> of the matrix with Blas-3 xGEMM.
!>
!> In some cases, due to catastrophic cancellations, it cannot
!> factorize NB columns.  Hence, the actual number of factorized
!> columns is returned in KB.
!>
!> 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 A that have been factorized in
!>          previous steps.
!>
```

*NB*

```
!>          NB is INTEGER
!>          The number of columns to factorize.
!>
```

*KB*

```
!>          KB is INTEGER
!>          The number of columns actually factorized.
!>
```

*A*

```
!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          On entry, the M-by-N matrix A.
!>          On exit, block A(OFFSET+1:M,1:KB) is the triangular
!>          factor obtained and block A(1:OFFSET,1:N) has been
!>          accordingly pivoted, but no factorized.
!>          The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has
!>          been updated.
!>
```

*LDA*

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

*JPVT*

```
!>          JPVT is INTEGER array, dimension (N)
!>          JPVT(I) = K <==> Column K of the full matrix A has been
!>          permuted into position I in AP.
!>
```

*TAU*

```
!>          TAU is COMPLEX*16 array, dimension (KB)
!>          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.
!>
```

*AUXV*

```
!>          AUXV is COMPLEX*16 array, dimension (NB)
!>          Auxiliary vector.
!>
```

*F*

```
!>          F is COMPLEX*16 array, dimension (LDF,NB)
!>          Matrix F**H = L * Y**H * A.
!>
```

*LDF*

```
!>          LDF is INTEGER
!>          The leading dimension of the array F. LDF >= max(1,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 **175** of file **zlaqps.f**.

## Author

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