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/*---------------------------------------------------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration |
\\ / A nd | Copyright (C) 2011 OpenFOAM Foundation
\\/ M anipulation |
-------------------------------------------------------------------------------
License
This file is part of OpenFOAM.
OpenFOAM is free software: you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
for more details.
You should have received a copy of the GNU General Public License
along with OpenFOAM. If not, see <http://www.gnu.org/licenses/>.
Application
PolynomialTest
Description
Test application for the templated Polynomial class
\*---------------------------------------------------------------------------*/
#include "IStringStream.H"
#include "Polynomial.H"
#include "polynomialFunction.H"
#include "Random.H"
#include "cpuTime.H"
using namespace Foam;
const int PolySize = 8;
const scalar coeff[] = { 0.11, 0.45, -0.94, 1.58, -2.58, 0.08, 3.15, -4.78 };
const char* polyDef = "(0.11 0.45 -0.94 1.58 -2.58 0.08 3.15 -4.78)";
scalar polyValue(const scalar x)
{
// Hard-coded polynomial 8 coeff (7th order)
return
coeff[0]
+ coeff[1]*x
+ coeff[2]*sqr(x)
+ coeff[3]*pow3(x)
+ coeff[4]*pow4(x)
+ coeff[5]*pow5(x)
+ coeff[6]*pow6(x)
+ coeff[7]*x*pow6(x);
}
scalar intPolyValue(const scalar x)
{
// Hard-coded integral form of above polynomial
return
coeff[0]*x
+ coeff[1]/2.0*sqr(x)
+ coeff[2]/3.0*pow3(x)
+ coeff[3]/4.0*pow4(x)
+ coeff[4]/5.0*pow5(x)
+ coeff[5]/6.0*pow6(x)
+ coeff[6]/7.0*x*pow6(x)
+ coeff[7]/8.0*x*x*pow6(x);
}
scalar polyValue1(const scalar x)
{
// "normal" evaluation using pow()
scalar value = coeff[0];
for (int i=1; i < PolySize; ++i)
{
value += coeff[i]*pow(x, i);
}
return value;
}
scalar polyValue2(const scalar x)
{
// calculation avoiding pow()
scalar value = coeff[0];
scalar powX = x;
for (int i=1; i < PolySize; ++i)
{
value += coeff[i] * powX;
powX *= x;
}
return value;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
int main(int argc, char *argv[])
{
const label n = 10000;
const label nIters = 1000;
scalar sum = 0.0;
Info<< "null poly = " << (Polynomial<8>()) << nl
<< "null poly = " << (polynomialFunction(8)) << nl
<< endl;
Polynomial<8> poly(coeff);
Polynomial<9> intPoly(poly.integral(0.0));
IStringStream is(polyDef);
polynomialFunction polyfunc(is);
Info<< "poly = " << poly << nl
<< "intPoly = " << intPoly << nl
<< endl;
Info<< "2*poly = " << 2*poly << nl
<< "poly+poly = " << poly + poly << nl
<< "3*poly = " << 3*poly << nl
<< "poly+poly+poly = " << poly + poly + poly << nl
<< "3*poly - 2*poly = " << 3*poly - 2*poly << nl
<< endl;
Info<< nl << "--- as polynomialFunction" << nl << endl;
Info<< "polyf = " << polyfunc << nl
<< "intPoly = " << poly.integral(0.0) << nl
<< endl;
Info<< "2*polyf = " << 2*polyfunc << nl
<< "polyf+polyf = " << polyfunc + polyfunc << nl
<< "3*polyf = " << 3*polyfunc << nl
<< "polyf+polyf+polyf = " << polyfunc + polyfunc + polyfunc << nl
<< "3*polyf - 2*polyf = " << 3*polyfunc - 2*polyfunc << nl
<< endl;
Polynomial<8> polyCopy = poly;
Info<< "poly, polyCopy = " << poly << ", " << polyCopy << nl << endl;
polyCopy = 2.5*poly;
Info<< "2.5*poly = " << polyCopy << nl << endl;
Random rnd(123456);
for (int i=0; i<10; i++)
{
scalar x = rnd.scalar01()*100;
scalar px = polyValue(x);
scalar ipx = intPolyValue(x);
scalar pxTest = poly.value(x);
scalar ipxTest = intPoly.value(x);
Info<<"\nx = " << x << endl;
Info<< " px, pxTest = " << px << ", " << pxTest << endl;
Info<< " ipx, ipxTest = " << ipx << ", " << ipxTest << endl;
if (mag(px - pxTest) > SMALL)
{
Info<< " *** WARNING: px != pxTest: " << px - pxTest << endl;
}
if (mag(ipx - ipxTest) > SMALL)
{
Info<< " *** WARNING: ipx != ipxTest: " << ipx - ipxTest << endl;
}
Info<< endl;
}
//
// test speed of Polynomial:
//
Info<< "start timing loops" << nl
<< "~~~~~~~~~~~~~~~~~~" << endl;
cpuTime timer;
for (int loop = 0; loop < n; ++loop)
{
sum = 0.0;
for (label iter = 0; iter < nIters; ++iter)
{
sum += poly.value(loop+iter);
}
}
Info<< "value: " << sum
<< " in " << timer.cpuTimeIncrement() << " s\n";
for (int loop = 0; loop < n; ++loop)
{
sum = 0.0;
for (label iter = 0; iter < nIters; ++iter)
{
sum += polyfunc.value(loop+iter);
}
}
Info<< "via function: " << sum
<< " in " << timer.cpuTimeIncrement() << " s\n";
for (int loop = 0; loop < n; ++loop)
{
sum = 0.0;
for (label iter = 0; iter < nIters; ++iter)
{
sum += polyValue(loop+iter);
}
}
Info<< "hard-coded 0: " << sum
<< " in " << timer.cpuTimeIncrement() << " s\n";
for (int loop = 0; loop < n; ++loop)
{
sum = 0.0;
for (label iter = 0; iter < nIters; ++iter)
{
sum += polyValue1(loop+iter);
}
}
Info<< "hard-coded 1: " << sum
<< " in " << timer.cpuTimeIncrement() << " s\n";
for (int loop = 0; loop < n; ++loop)
{
sum = 0.0;
for (label iter = 0; iter < nIters; ++iter)
{
sum += polyValue2(loop+iter);
}
}
Info<< "hard-coded 2: " << sum
<< " in " << timer.cpuTimeIncrement() << " s\n";
Info<< nl << "Done." << endl;
return 0;
}
// ************************************************************************* //
|
