OpenFOAM: API Guide
v1912
The open source CFD toolbox
quadraticEqn.C
Go to the documentation of this file.
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/*---------------------------------------------------------------------------*\
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========= |
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\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
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\\ / O peration |
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\\ / A nd | www.openfoam.com
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\\/ M anipulation |
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-------------------------------------------------------------------------------
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Copyright (C) 2017 OpenFOAM Foundation
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-------------------------------------------------------------------------------
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License
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This file is part of OpenFOAM.
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OpenFOAM is free software: you can redistribute it and/or modify it
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under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
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ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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for more details.
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You should have received a copy of the GNU General Public License
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along with OpenFOAM. If not, see <http://www.gnu.org/licenses/>.
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\*---------------------------------------------------------------------------*/
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#include "
linearEqn.H
"
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#include "
quadraticEqn.H
"
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// * * * * * * * * * * * * * * * Member Functions * * * * * * * * * * * * * //
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Foam::Roots<2>
Foam::quadraticEqn::roots
()
const
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{
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/*
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This function solves a quadraticEqn equation of the following form:
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a*x^2 + b*x + c = 0
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x^2 + B*x + C = 0
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The quadraticEqn formula is as follows:
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x = - B/2 +- sqrt(B*B - 4*C)/2
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If the sqrt generates a complex number, this provides the result. If not
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then the real root with the smallest floating point error is calculated.
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x0 = - B/2 - sign(B)*sqrt(B*B - 4*C)/2
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The other root is the obtained using an identity.
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x1 = C/x0
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*/
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const
scalar
a
= this->
a
();
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const
scalar
b
= this->
b
();
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const
scalar
c
= this->
c
();
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if
(a == 0)
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{
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return
Roots<2>
(
linearEqn
(
b
,
c
).
roots
(),
roots::nan
, 0);
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}
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// This is assumed not to over- or under-flow. If it does, all bets are off.
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const
scalar disc =
b
*
b
/4 -
a
*
c
;
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// How many roots of what types are available?
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const
bool
oneReal = disc == 0;
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const
bool
twoReal = disc > 0;
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//const bool twoComplex = disc < 0;
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if
(oneReal)
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{
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const
Roots<1>
r =
linearEqn
(
a
,
b
/2).
roots
();
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return
Roots<2>
(r, r);
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}
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else
if
(twoReal)
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{
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const
scalar
x
= -
b
/2 -
sign
(
b
)*
sqrt
(disc);
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return
Roots<2>
(
linearEqn
(-
a
,
x
).
roots
(),
linearEqn
(-
x
,
c
).
roots
());
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}
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else
// if (twoComplex)
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{
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return
Roots<2>
(
roots::complex
, 0);
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}
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}
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// ************************************************************************* //
Foam::roots::complex
Definition:
Roots.H:57
Foam::roots::nan
Definition:
Roots.H:60
Foam::quadraticEqn::roots
Roots< 2 > roots() const
Get the roots.
Definition:
quadraticEqn.C:33
Foam::sign
dimensionedScalar sign(const dimensionedScalar &ds)
Definition:
dimensionedScalar.C:166
Foam::quadraticEqn::b
scalar b() const
Definition:
quadraticEqnI.H:61
Foam::linearEqn
Linear equation of the form a*x + b = 0.
Definition:
linearEqn.H:50
Foam::linearEqn::roots
Roots< 1 > roots() const
Get the roots.
Definition:
linearEqnI.H:91
linearEqn.H
Foam::quadraticEqn::a
scalar a() const
Definition:
quadraticEqnI.H:55
Foam::sqrt
dimensionedScalar sqrt(const dimensionedScalar &ds)
Definition:
dimensionedScalar.C:144
x
x
Definition:
LISASMDCalcMethod2.H:52
Foam::Roots
Templated storage for the roots of polynomial equations, plus flags to indicate the nature of the roo...
Definition:
Roots.H:70
quadraticEqn.H
Foam::quadraticEqn::c
scalar c() const
Definition:
quadraticEqnI.H:67
src
OpenFOAM
primitives
polynomialEqns
quadraticEqn
quadraticEqn.C
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