# zlaqr1.f man page

zlaqr1.f —

## Synopsis

### Functions/Subroutines

subroutinezlaqr1(N, H, LDH, S1, S2, V)ZLAQR1sets 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 (integerN, complex*16, dimension( ldh, * )H, integerLDH, complex*16S1, complex*16S2, 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 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
```

*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 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 108 of file zlaqr1.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

zlaqr1(3) is an alias of zlaqr1.f(3).