# dlaqr1.f - Man Page

SRC/dlaqr1.f

## Synopsis

### Functions/Subroutines

subroutine dlaqr1 (n, h, ldh, sr1, si1, sr2, si2, v)
DLAQR1 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 dlaqr1 (integer n, double precision, dimension( ldh, * ) h, integer ldh, double precision sr1, double precision si1, double precision sr2, double precision si2, double precision, dimension( * ) v)

DLAQR1 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, DLAQR1 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 DOUBLE PRECISION 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```

SR1

`          SR1 is DOUBLE PRECISION`

SI1

`          SI1 is DOUBLE PRECISION`

SR2

`          SR2 is DOUBLE PRECISION`

SI2

```          SI2 is DOUBLE PRECISION
The shifts in (*).```

V

```          V is DOUBLE PRECISION 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 120 of file dlaqr1.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dlaqr1(3) is an alias of dlaqr1.f(3).

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