# zlaqr1.f - Man Page

SRC/zlaqr1.f

## Synopsis

### Functions/Subroutines

subroutine zlaqr1 (n, h, ldh, s1, s2, 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.

## Function/Subroutine Documentation

### subroutine zlaqr1 (integer n, complex*16, dimension( ldh, * ) h, integer ldh, complex*16 s1, complex*16 s2, 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, 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 >= 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, dimension (N)
A scalar multiple of the first column of the
matrix K in (*).```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Contributors:

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

Definition at line 106 of file zlaqr1.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zlaqr1(3) is an alias of zlaqr1.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK