---
name: "slaqz1"
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/slaqz1.f"
---

# slaqz1(3)

Part of [slaqz1.f(3)](/slaqz1.f/3.md).

## NAME

SRC/slaqz1.f

## SYNOPSIS

### Functions/Subroutines

subroutine **slaqz1** (a, lda, b, ldb, sr1, sr2, si, beta1, beta2, v)\
 **SLAQZ1**

## Function/Subroutine Documentation

### subroutine slaqz1 (real, dimension( lda, \* ), intent(in) a, integer, intent(in) lda, real, dimension( ldb, \* ), intent(in) b, integer, intent(in) ldb, real, intent(in) sr1, real, intent(in) sr2, real, intent(in) si, real, intent(in) beta1, real, intent(in) beta2, real, dimension( \* ), intent(out) v)

**SLAQZ1**

**Purpose:**

```
!>
!>      Given a 3-by-3 matrix pencil (A,B), SLAQZ1 sets v to a
!>      scalar multiple of the first column of the product
!>
!>      (*)  K = (A - (beta2*sr2 - i*si)*B)*B^(-1)*(beta1*A - (sr2 + i*si2)*B)*B^(-1).
!>
!>      It is assumed that either
!>
!>              1) sr1 = sr2
!>          or
!>              2) si = 0.
!>
!>      This is useful for starting double implicit shift bulges
!>      in the QZ algorithm.
!>
```

**Parameters**

*A*

```
!>          A is REAL array, dimension (LDA,N)
!>              The 3-by-3 matrix A in (*).
!>
```

*LDA*

```
!>          LDA is INTEGER
!>              The leading dimension of A as declared in
!>              the calling procedure.
!>
```

*B*

```
!>          B is REAL array, dimension (LDB,N)
!>              The 3-by-3 matrix B in (*).
!>
```

*LDB*

```
!>          LDB is INTEGER
!>              The leading dimension of B as declared in
!>              the calling procedure.
!>
```

*SR1*

```
!>          SR1 is REAL
!>
```

*SR2*

```
!>          SR2 is REAL
!>
```

*SI*

```
!>          SI is REAL
!>
```

*BETA1*

```
!>          BETA1 is REAL
!>
```

*BETA2*

```
!>          BETA2 is REAL
!>
```

*V*

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

**Author**

Thijs Steel, KU Leuven

**Date**

May 2020

Definition at line **125** of file **slaqz1.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.