# claqr1.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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claqr1.f

## SYNOPSIS

### Functions/Subroutines

subroutine claqr1 (N, H, LDH, S1, S2, V)
CLAQR1 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 claqr1 (integer N, complex, dimension( ldh, * ) H, integer LDH, complex S1, complex S2, complex, dimension( * ) V)

CLAQR1 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, CLAQR1 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 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.GE.N
```

S1

```          S1 is COMPLEX
```

S2

```          S2 is COMPLEX

S1 and S2 are the shifts defining K in (*) above.
```

V

```          V is COMPLEX 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.

Date:

June 2017

Contributors:

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

Definition at line 109 of file claqr1.f.

## Author

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