# 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

Univ. of Colorado Denver

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