---
name: "zlaqr1"
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/zlaqr1.f"
---

# zlaqr1(3)

Part of [zlaqr1.f(3)](/zlaqr1.f/3.md).

## NAME

SRC/zlaqr1.f

## SYNOPSIS

### Functions/Subroutines

subroutine **zlaqr1** (n, h, ldh, s1, s2, v)\
 **ZLAQR1** sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts.

## Function/Subroutine Documentation

### subroutine zlaqr1 (integer n, complex\*16, dimension( ldh, \* ) h, integer ldh, complex\*16 s1, complex\*16 s2, complex\*16, dimension( \* ) v)

**ZLAQR1** sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts.

**Purpose:**

```
!>
!>      Given a 2-by-2 or 3-by-3 matrix H, ZLAQR1 sets v to a
!>      scalar multiple of the first column of the product
!>
!>      (*)  K = (H - s1*I)*(H - s2*I)
!>
!>      scaling to avoid overflows and most underflows.
!>
!>      This is useful for starting double implicit shift bulges
!>      in the QR algorithm.
!>
```

**Parameters**

*N*

```
!>          N is INTEGER
!>              Order of the matrix H. N must be either 2 or 3.
!>
```

*H*

```
!>          H is COMPLEX*16 array, dimension (LDH,N)
!>              The 2-by-2 or 3-by-3 matrix H in (*).
!>
```

*LDH*

```
!>          LDH is INTEGER
!>              The leading dimension of H as declared in
!>              the calling procedure.  LDH >= N
!>
```

*S1*

```
!>          S1 is COMPLEX*16
!>
```

*S2*

```
!>          S2 is COMPLEX*16
!>
!>          S1 and S2 are the shifts defining K in (*) above.
!>
```

*V*

```
!>          V is COMPLEX*16 array, dimension (N)
!>              A scalar multiple of the first column of the
!>              matrix K in (*).
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Contributors:**

Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA

Definition at line **106** of file **zlaqr1.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.