# SLAQR1 (3) - Linux Manuals

slaqr1.f -

## SYNOPSIS

### Functions/Subroutines

subroutine slaqr1 (N, H, LDH, SR1, SI1, SR2, SI2, V)
SLAQR1 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 slaqr1 (integerN, real, dimension( ldh, * )H, integerLDH, realSR1, realSI1, realSR2, realSI2, real, dimension( * )V)

SLAQR1 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, SLAQR1 sets v to a
scalar multiple of the first column of the product

(*)  K = (H - (sr1 + i*si1)*I)*(H - (sr2 + i*si2)*I)

scaling to avoid overflows and most underflows. It
is assumed that either

1) sr1 = sr2 and si1 = -si2
or
2) si1 = si2 = 0.

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 REAL array of 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
```

SR1

```          SR1 is REAL
```

SI1

```          SI1 is REAL
```

SR2

```          SR2 is REAL
```

SI2

```          SI2 is REAL
The shifts in (*).
```

V

```          V is REAL array of 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:

September 2012

Contributors:

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

Definition at line 122 of file slaqr1.f.

## Author

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