# 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

Univ. of Colorado Denver

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