# dlaqz1.f - Man Page

SRC/dlaqz1.f

## Synopsis

### Functions/Subroutines

subroutine dlaqz1 (a, lda, b, ldb, sr1, sr2, si, beta1, beta2, v)
DLAQZ1

## Function/Subroutine Documentation

### subroutine dlaqz1 (double precision, dimension( lda, * ), intent(in) a, integer, intent(in) lda, double precision, dimension( ldb, * ), intent(in) b, integer, intent(in) ldb, double precision, intent(in) sr1, double precision, intent(in) sr2, double precision, intent(in) si, double precision, intent(in) beta1, double precision, intent(in) beta2, double precision, dimension( * ), intent(out) v)

DLAQZ1

Purpose:

```      Given a 3-by-3 matrix pencil (A,B), DLAQZ1 sets v to a
scalar multiple of the first column of the product

(*)  K = (A - (beta2*sr2 - i*si)*B)*B^(-1)*(beta1*A - (sr2 + i*si2)*B)*B^(-1).

It is assumed that either

1) sr1 = sr2
or
2) si = 0.

This is useful for starting double implicit shift bulges
in the QZ algorithm.```
Parameters

A

```          A is DOUBLE PRECISION array, dimension (LDA,N)
The 3-by-3 matrix A in (*).```

LDA

```          LDA is INTEGER
The leading dimension of A as declared in
the calling procedure.```

B

```          B is DOUBLE PRECISION array, dimension (LDB,N)
The 3-by-3 matrix B in (*).```

LDB

```          LDB is INTEGER
The leading dimension of B as declared in
the calling procedure.```

SR1

`          SR1 is DOUBLE PRECISION`

SR2

`          SR2 is DOUBLE PRECISION`

SI

`          SI is DOUBLE PRECISION`

BETA1

`          BETA1 is DOUBLE PRECISION`

BETA2

`          BETA2 is DOUBLE PRECISION`

V

```          V is DOUBLE PRECISION array, dimension (N)
A scalar multiple of the first column of the
matrix K in (*).```
Author

Thijs Steel, KU Leuven

Date

May 2020

Definition at line 125 of file dlaqz1.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dlaqz1(3) is an alias of dlaqz1.f(3).

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