# slaqr1.f man page

slaqr1.f —

## Synopsis

### Functions/Subroutines

subroutineslaqr1(N, H, LDH, SR1, SI1, SR2, SI2, V)SLAQR1sets 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

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

slaqr1(3) is an alias of slaqr1.f(3).