dlaqr1-f(3)

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 (integerN, double precision, dimension( ldh, * )H, integerLDH, double precisionSR1, double precisionSI1, double precisionSR2, double precisionSI2, 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 is integer
 Order of the matrix H. N must be either 2 or 3.

 H is DOUBLE PRECISION array of 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.GE.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 is DOUBLE PRECISION array of 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.

Date:

September 2012

Contributors:

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

Definition at line 122 of file dlaqr1.f.

Author

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