csharpfftfsharpintegrationinterpolationlinear-algebramathdifferentiationmatrixnumericsrandomregressionstatisticsmathnet
You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
754 lines
30 KiB
754 lines
30 KiB
// <copyright file="BrentTest.cs" company="Math.NET">
|
|
// Math.NET Numerics, part of the Math.NET Project
|
|
// http://numerics.mathdotnet.com
|
|
// http://github.com/mathnet/mathnet-numerics
|
|
// http://mathnetnumerics.codeplex.com
|
|
//
|
|
// Copyright (c) 2009-2014 Math.NET
|
|
//
|
|
// Permission is hereby granted, free of charge, to any person
|
|
// obtaining a copy of this software and associated documentation
|
|
// files (the "Software"), to deal in the Software without
|
|
// restriction, including without limitation the rights to use,
|
|
// copy, modify, merge, publish, distribute, sublicense, and/or sell
|
|
// copies of the Software, and to permit persons to whom the
|
|
// Software is furnished to do so, subject to the following
|
|
// conditions:
|
|
//
|
|
// The above copyright notice and this permission notice shall be
|
|
// included in all copies or substantial portions of the Software.
|
|
//
|
|
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
|
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
|
|
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
|
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
|
|
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
|
|
// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
|
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
|
|
// OTHER DEALINGS IN THE SOFTWARE.
|
|
// </copyright>
|
|
|
|
using System;
|
|
using MathNet.Numerics.RootFinding;
|
|
using NUnit.Framework;
|
|
|
|
namespace MathNet.Numerics.UnitTests.RootFindingTests
|
|
{
|
|
[TestFixture, Category("RootFinding")]
|
|
public class BrentTest
|
|
{
|
|
[Test]
|
|
public void MultipleRoots()
|
|
{
|
|
// Roots at -2, 2
|
|
Func<double, double> f1 = x => x*x - 4;
|
|
Assert.AreEqual(0, f1(Brent.FindRoot(f1, 1, 5, 1e-14, 100)));
|
|
Assert.AreEqual(0, f1(Brent.FindRootExpand(f1, 3, 5, 1e-14, 100)));
|
|
Assert.AreEqual(-2, Brent.FindRoot(f1, -5, -1, 1e-14, 100));
|
|
Assert.AreEqual(2, Brent.FindRoot(f1, 1, 4, 1e-14, 100));
|
|
Assert.AreEqual(0, f1(Brent.FindRoot(x => -f1(x), 1, 5, 1e-14, 100)));
|
|
Assert.AreEqual(-2, Brent.FindRoot(x => -f1(x), -5, -1, 1e-14, 100));
|
|
Assert.AreEqual(2, Brent.FindRoot(x => -f1(x), 1, 4, 1e-14, 100));
|
|
|
|
// Roots at 3, 4
|
|
Func<double, double> f2 = x => (x - 3)*(x - 4);
|
|
Assert.AreEqual(0, f2(Brent.FindRoot(f2, -5, 3.5, 1e-14, 100)));
|
|
Assert.AreEqual(3, Brent.FindRoot(f2, -5, 3.5, 1e-14, 100));
|
|
Assert.AreEqual(4, Brent.FindRoot(f2, 3.2, 5, 1e-14, 100));
|
|
Assert.AreEqual(3, Brent.FindRoot(f2, 2.1, 3.9, 0.001, 50), 0.001);
|
|
Assert.AreEqual(3, Brent.FindRoot(f2, 2.1, 3.4, 0.001, 50), 0.001);
|
|
}
|
|
|
|
[Test]
|
|
public void LocalMinima()
|
|
{
|
|
Func<double, double> f1 = x => x*x*x - 2*x + 2;
|
|
Assert.AreEqual(0, f1(Brent.FindRoot(f1, -5, 5, 1e-14, 100)), 1e-14);
|
|
Assert.AreEqual(0, f1(Brent.FindRoot(f1, -2, 4, 1e-14, 100)), 1e-14);
|
|
}
|
|
|
|
[Test]
|
|
public void Cubic()
|
|
{
|
|
// with complex roots (looking for the real root only): 3x^3 + 4x^2 + 5x + 6
|
|
Func<double, double> f1 = x => Evaluate.Polynomial(x, 6, 5, 4, 3);
|
|
Assert.AreEqual(-1.265328088928, Brent.FindRoot(f1, -2, -1, 1e-8, 100), 1e-6);
|
|
|
|
// real roots only: 2x^3 + 4x^2 - 50x + 6
|
|
Func<double, double> f2 = x => Evaluate.Polynomial(x, 6, -50, 4, 2);
|
|
Assert.AreEqual(-6.1466562197069, Brent.FindRoot(f2, -6.5, -5.5, 1e-8, 100), 1e-6);
|
|
Assert.AreEqual(0.12124737195841, Brent.FindRoot(f2, -0.5, 0.5, 1e-8, 100), 1e-6);
|
|
Assert.AreEqual(4.0254088477485, Brent.FindRoot(f2, 3.5, 4.5, 1e-8, 100), 1e-6);
|
|
}
|
|
|
|
[Test]
|
|
public void NoRoot()
|
|
{
|
|
Func<double, double> f1 = x => x*x + 4;
|
|
Assert.That(() => Brent.FindRoot(f1, -5, 5, 1e-14, 50), Throws.TypeOf<NonConvergenceException>());
|
|
}
|
|
|
|
[Test]
|
|
public void Oneeq1()
|
|
{
|
|
// Test case from http://www.polymath-software.com/library/nle/Oneeq1.htm
|
|
Func<double, double> f1 = z => 8*Math.Pow((4 - z)*z, 2)/(Math.Pow(6 - 3*z, 2)*(2 - z)) - 0.186;
|
|
double x = Brent.FindRoot(f1, 0.1, 0.9, 1e-14, 100);
|
|
Assert.AreEqual(0.277759543089215, x, 1e-9);
|
|
Assert.AreEqual(0, f1(x), 1e-16);
|
|
}
|
|
|
|
[Test]
|
|
public void Oneeq2a()
|
|
{
|
|
// Test case from http://www.polymath-software.com/library/nle/Oneeq2a.htm
|
|
Func<double, double> f1 = T =>
|
|
{
|
|
const double x1 = 0.332112;
|
|
const double x2 = 1 - x1;
|
|
const double G12 = 0.07858889;
|
|
const double G21 = 0.30175355;
|
|
double P2 = Math.Pow(10, 6.87776 - 1171.53/(224.366 + T));
|
|
double P1 = Math.Pow(10, 8.04494 - 1554.3/(222.65 + T));
|
|
const double t1 = x1 + x2*G12;
|
|
const double t2 = x2 + x1*G21;
|
|
double gamma2 = Math.Exp(-Math.Log(t2) - (x1*(G12*t2 - G21*t1))/(t1*t2));
|
|
double gamma1 = Math.Exp(-Math.Log(t1) + (x2*(G12*t2 - G21*t1))/(t1*t2));
|
|
double k1 = gamma1*P1/760;
|
|
double k2 = gamma2*P2/760;
|
|
return 1 - k1*x1 - k2*x2;
|
|
};
|
|
|
|
double x = Brent.FindRoot(f1, 0, 100, 1e-14, 100);
|
|
Assert.AreEqual(58.7000023925600, x, 1e-5);
|
|
Assert.AreEqual(0, f1(x), 1e-14);
|
|
}
|
|
|
|
[Test]
|
|
public void Oneeq2b()
|
|
{
|
|
// Test case from http://www.polymath-software.com/library/nle/Oneeq2b.htm
|
|
Func<double, double> f1 = T =>
|
|
{
|
|
const double x1 = 0.6763397;
|
|
const double x2 = 1 - x1;
|
|
const double A = 0.75807689;
|
|
const double B = 1.1249035;
|
|
double P2 = Math.Pow(10, 6.9024 - 1268.115/(216.9 + T));
|
|
double P1 = Math.Pow(10, 8.04494 - 1554.3/(222.65 + T));
|
|
double gamma2 = Math.Pow(10, B*Math.Pow(x1, 2)/Math.Pow(x1 + B*x2/A, 2));
|
|
double gamma1 = Math.Pow(10, A*Math.Pow(x2, 2)/Math.Pow(A*x1/B + x2, 2));
|
|
double k1 = gamma1*P1/760;
|
|
double k2 = gamma2*P2/760;
|
|
return 1 - k1*x1 - k2*x2;
|
|
};
|
|
|
|
double x = Brent.FindRoot(f1, 0, 100, 1e-14);
|
|
Assert.AreEqual(70.9000000710300, x, 1e-9);
|
|
Assert.AreEqual(0, f1(x), 1e-14);
|
|
}
|
|
|
|
[Test]
|
|
public void Oneeq3()
|
|
{
|
|
// Test case from http://www.polymath-software.com/library/nle/Oneeq3.htm
|
|
Func<double, double> f1 = T => Math.Exp(21000/T)/(T*T) - 1.11e11;
|
|
Assert.AreEqual(551.773822885233, Brent.FindRoot(f1, 550, 560, 1e-2), 1e-2);
|
|
}
|
|
|
|
[Test]
|
|
public void Oneeq4()
|
|
{
|
|
// Test case from http://www.polymath-software.com/library/nle/Oneeq4.htm
|
|
Func<double, double> f1 = x =>
|
|
{
|
|
const double A = 0.38969;
|
|
const double B = 0.55954;
|
|
return A*B*(B*Math.Pow(1 - x, 2) - A*x*x)/Math.Pow(x*(A - B) + B, 2) + 0.14845;
|
|
};
|
|
|
|
double r = Brent.FindRoot(f1, 0, 1, 1.0e-14);
|
|
Assert.AreEqual(0.691473747542323, r, 1e-5);
|
|
Assert.AreEqual(0, f1(r), 1e-14);
|
|
}
|
|
|
|
[Test]
|
|
public void Oneeq5()
|
|
{
|
|
// Test case from http://www.polymath-software.com/library/nle/Oneeq5.htm
|
|
// only solvable with reduced accuracy (1e-3 instead of 1e-10 with Bisection)
|
|
Func<double, double> f1 = TR =>
|
|
{
|
|
const double ALPHA = 7.256;
|
|
const double BETA = 2.298E-3;
|
|
const double GAMMA = 0.283E-6;
|
|
const double DH = -57798.0;
|
|
return DH + TR*(ALPHA + TR*(BETA/2 + TR*GAMMA/3)) - 298.0*(ALPHA + 298.0*(BETA/2 + 298.0*GAMMA/3));
|
|
};
|
|
|
|
double x = Brent.FindRoot(f1, 3000, 5000, 1.0e-3);
|
|
Assert.AreEqual(4305.30991366774, x, 1e-5);
|
|
Assert.AreEqual(0, f1(x), 1e-3);
|
|
}
|
|
|
|
[Test]
|
|
public void Oneeq6a()
|
|
{
|
|
// Test case from http://www.polymath-software.com/library/nle/Oneeq6a.htm
|
|
Func<double, double> f1 = V =>
|
|
{
|
|
const double R = 0.08205;
|
|
const double T = 273.0;
|
|
const double B0 = 0.05587;
|
|
const double A0 = 2.2769;
|
|
const double C = 128300.0;
|
|
const double A = 0.01855;
|
|
const double B = -0.01587;
|
|
const double P = 100.0;
|
|
const double Beta = R*T*B0 - A0 - R*C/(T*T);
|
|
const double Gama = -R*T*B0*B + A0*A - R*C*B0/(T*T);
|
|
const double Delta = R*B0*B*C/(T*T);
|
|
|
|
return R*T/V + Beta/(V*V) + Gama/(V*V*V) + Delta/(V*V*V*V) - P;
|
|
};
|
|
|
|
Assert.AreEqual(0.174749531708621, Brent.FindRoot(f1, 0.1, 1), 1e-8);
|
|
}
|
|
|
|
[Test]
|
|
public void Oneeq6b()
|
|
{
|
|
// Test case from http://www.polymath-software.com/library/nle/Oneeq6b.htm
|
|
Func<double, double> f1 = V =>
|
|
{
|
|
const double R = 0.08205;
|
|
const double T = 273.0;
|
|
const double B0 = 0.05587;
|
|
const double A0 = 2.2769;
|
|
const double C = 128300.0;
|
|
const double A = 0.01855;
|
|
const double B = -0.01587;
|
|
const double P = 100.0;
|
|
const double Beta = R*T*B0 - A0 - R*C/(T*T);
|
|
const double Gama = -R*T*B0*B + A0*A - R*C*B0/(T*T);
|
|
const double Delta = R*B0*B*C/(T*T);
|
|
|
|
return R*T*V*V*V + Beta*V*V + Gama*V + Delta - P*V*V*V*V;
|
|
};
|
|
|
|
double x = Brent.FindRoot(f1, 0.1, 1, 1e-14);
|
|
Assert.AreEqual(0.174749600398905, x, 1e-5);
|
|
Assert.AreEqual(0, f1(x), 1e-13);
|
|
}
|
|
|
|
[Test]
|
|
public void Oneeq7()
|
|
{
|
|
// Test case from http://www.polymath-software.com/library/nle/Oneeq7.htm
|
|
Func<double, double> f1 = x => x/(1 - x) - 5*Math.Log(0.4*(1 - x)/(0.4 - 0.5*x)) + 4.45977;
|
|
Assert.AreEqual(0.757396293891, Brent.FindRoot(f1, 0, 0.79, 1e-2), 1e-2);
|
|
}
|
|
|
|
[Test]
|
|
public void Oneeq8()
|
|
{
|
|
// Test case from http://www.polymath-software.com/library/nle/Oneeq8.htm
|
|
Func<double, double> f1 = v =>
|
|
{
|
|
const double a = 240;
|
|
const double b = 40;
|
|
const double c = 200;
|
|
|
|
return a*v*v + b*Math.Pow(v, 7/4) - c;
|
|
};
|
|
|
|
Assert.AreEqual(0.842524411168525, Brent.FindRoot(f1, 0.01, 1, 1e-2), 1e-2);
|
|
}
|
|
|
|
[Test]
|
|
public void Oneeq9()
|
|
{
|
|
// Test case from http://www.polymath-software.com/library/nle/Oneeq9.htm
|
|
Func<double, double> f1 = P =>
|
|
{
|
|
const double At = 0.1;
|
|
const double A = 0.12;
|
|
const double gama = 1.41;
|
|
const double Pd = 100;
|
|
|
|
return Math.Pow((gama + 1)/2, (gama + 1)/(gama - 1))*(2/(gama - 1))*(Math.Pow(P/Pd, 2/gama) - Math.Pow(P/Pd, (gama + 1)/gama)) - Math.Pow(At/A, 2);
|
|
};
|
|
|
|
double x = Brent.FindRoot(f1, 1, 50, 1e-14);
|
|
Assert.AreEqual(25.743977294088, x, 1e-5);
|
|
Assert.AreEqual(0, f1(x), 1e-14);
|
|
x = Brent.FindRoot(f1, 50, 100, 1e-14);
|
|
Assert.AreEqual(78.905412035983, x, 1e-5);
|
|
Assert.AreEqual(0, f1(x), 1e-14);
|
|
}
|
|
|
|
[Test]
|
|
public void Oneeq10()
|
|
{
|
|
// Test case from http://www.polymath-software.com/library/nle/Oneeq10.htm
|
|
Func<double, double> f1 = x => (1.0/63.0)*Math.Log(x) + (64.0/63.0)*Math.Log(1/(1 - x)) + Math.Log(0.95 - x) - Math.Log(0.9);
|
|
|
|
double r = Brent.FindRoot(f1, .01, 0.35, 1e-14);
|
|
Assert.AreEqual(0.036210083704, r, 1e-5);
|
|
Assert.AreEqual(0, f1(r), 1e-14);
|
|
r = Brent.FindRoot(f1, 0.35, 0.7);
|
|
Assert.AreEqual(0.5, r, 1e-5);
|
|
Assert.AreEqual(0, f1(r), 1e-9);
|
|
}
|
|
|
|
[Test]
|
|
public void Oneeq11a()
|
|
{
|
|
// Test case from http://www.polymath-software.com/library/nle/Oneeq11a.htm
|
|
Func<double, double> f1 = x =>
|
|
{
|
|
const double a = 0.5;
|
|
const double b = 0.8;
|
|
const double c = 0.3;
|
|
const double kp = 604500;
|
|
const double P = 0.00243;
|
|
|
|
return a - Math.Pow((c + 2*x)*(a + b + c - 2*x), 2)/(kp*P*P*Math.Pow(b - 3*x, 3)) - x;
|
|
};
|
|
|
|
double r = Brent.FindRoot(f1, 0, 0.25, 1e-14);
|
|
Assert.AreEqual(0.058654581076661, r, 1e-5);
|
|
Assert.AreEqual(0, f1(r), 1e-14);
|
|
r = Brent.FindRoot(f1, 0.3, 1, 1e-14);
|
|
Assert.AreEqual(0.600323116977323, r, 1e-5);
|
|
Assert.AreEqual(0, f1(r), 1e-14);
|
|
}
|
|
|
|
[Test]
|
|
public void Oneeq11b()
|
|
{
|
|
// Test case from http://www.polymath-software.com/library/nle/Oneeq11b.htm
|
|
Func<double, double> f1 = x =>
|
|
{
|
|
const double a = 0.5;
|
|
const double b = 0.8;
|
|
const double c = 0.3;
|
|
const double kp = 604500;
|
|
const double P = 0.00243;
|
|
|
|
return (b - Math.Pow(Math.Pow((c + 2*x)*(a + b + c - 2*x), 2)/(kp*P*P*(a - x)), 1.0/3.0))/3.0 - x;
|
|
};
|
|
|
|
double r = Brent.FindRoot(f1, 0.01, 0.45, 1e-14);
|
|
Assert.AreEqual(0.058654571042804, r, 1e-5);
|
|
Assert.AreEqual(0, f1(r), 1e-14);
|
|
// Could not test the following root, since Math.Pow(y,1/3) does not work for y<0
|
|
// r = Brent.FindRoot(f1, 0.55, 0.7);
|
|
// Assert.AreEqual(0.600323117488527, r, 1e-5);
|
|
// Assert.AreEqual(0, f1(r), 1e-14);
|
|
}
|
|
|
|
[Test]
|
|
public void Oneeq12()
|
|
{
|
|
// Test case from http://www.polymath-software.com/library/nle/Oneeq12.htm
|
|
Func<double, double> f1 = v =>
|
|
{
|
|
const double b = -159;
|
|
const double c = 9000;
|
|
const double P = 75;
|
|
const double T = 430.85;
|
|
const double R = 82.05;
|
|
|
|
return (R*T/P)*(1 + b/v + c/(v*v)) - v;
|
|
};
|
|
|
|
double x = Brent.FindRoot(f1, 100, 300, 1e-14);
|
|
Assert.AreEqual(213.001818272273, x, 1e-5);
|
|
Assert.AreEqual(0, f1(x), 1e-14);
|
|
}
|
|
|
|
[Test]
|
|
public void Oneeq13()
|
|
{
|
|
// Test case from http://www.polymath-software.com/library/nle/Oneeq13.htm
|
|
Func<double, double> f1 = V =>
|
|
{
|
|
const double Pc = 45.8;
|
|
const double Tc = 191.0;
|
|
const double P = 100;
|
|
const double T = 210.0;
|
|
const double R = 0.08205;
|
|
double A = 0.42748*(R*R*Math.Pow(Tc, 2.5))/Pc;
|
|
const double B = 0.08664*R*Tc/Pc;
|
|
|
|
return R*Math.Pow(T, 1.5)*V*(V + B)/(P*Math.Sqrt(T)*V*(V + B) + A) + B - V;
|
|
};
|
|
|
|
double x = Brent.FindRoot(f1, .01, .3, 1e-14);
|
|
Assert.AreEqual(0.075699587993613, x, 1e-9);
|
|
Assert.AreEqual(0, f1(x), 1e-14);
|
|
}
|
|
|
|
[Test]
|
|
public void Oneeq14()
|
|
{
|
|
// Test case from http://www.polymath-software.com/library/nle/Oneeq14.htm
|
|
Func<double, double> f1 = Q =>
|
|
{
|
|
const double M = 43800.0;
|
|
const double m = 149000.0;
|
|
const double Cp = 0.605;
|
|
const double U = 55.0;
|
|
const double A = 662.0;
|
|
const double T1 = 390.0;
|
|
const double t1 = 100.0;
|
|
const double cp = 0.49;
|
|
double DT1 = T1 - t1 - Q/(M*Cp);
|
|
double DT2 = T1 - t1 - Q/(m*cp);
|
|
|
|
return U*A*(DT2 - DT1)/Math.Log(DT2/DT1) - Q;
|
|
};
|
|
|
|
double x = Brent.FindRoot(f1, 1000000, 7000000, 1e-9);
|
|
Assert.AreEqual(5281024.23857737, x, 1e-5);
|
|
Assert.AreEqual(0, f1(x), 1e-9);
|
|
}
|
|
|
|
[Test]
|
|
public void Oneeq15a()
|
|
{
|
|
// Test case from http://www.polymath-software.com/library/nle/Oneeq15a.htm
|
|
Func<double, double> f1 = h => h*(1 + h*(3 - h)) - 2.4 - h;
|
|
|
|
double x = Brent.FindRoot(f1, -2, 0, 1e-14);
|
|
Assert.AreEqual(-0.795219754733581, x, 1e-5);
|
|
Assert.AreEqual(0, f1(x), 1e-14);
|
|
x = Brent.FindRoot(f1, 0, 2, 1e-14);
|
|
Assert.AreEqual(1.13413784566692, x, 1e-5);
|
|
Assert.AreEqual(0, f1(x), 1e-14);
|
|
x = Brent.FindRoot(f1, 2, 5, 1e-14);
|
|
Assert.AreEqual(2.66108192383197, x, 1e-5);
|
|
Assert.AreEqual(0, f1(x), 1e-14);
|
|
}
|
|
|
|
[Test]
|
|
public void Oneeq15b()
|
|
{
|
|
// Test case from http://www.polymath-software.com/library/nle/Oneeq15b.htm
|
|
Func<double, double> f1 = h => 2.4/(h*(3 - h)) - h;
|
|
|
|
double x = Brent.FindRoot(f1, -2, -0.5, 1e-14);
|
|
Assert.AreEqual(-0.795219745444464, x, 1e-5);
|
|
Assert.AreEqual(0, f1(x), 1e-14);
|
|
x = Brent.FindRoot(f1, 0.5, 2, 1e-14);
|
|
Assert.AreEqual(1.134137843811, x, 1e-5);
|
|
Assert.AreEqual(0, f1(x), 1e-14);
|
|
x = Brent.FindRoot(f1, 2, 2.9, 1e-14);
|
|
Assert.AreEqual(2.66108190354552, x, 1e-5);
|
|
Assert.AreEqual(0, f1(x), 1e-14);
|
|
}
|
|
|
|
[Test]
|
|
public void Oneeq16()
|
|
{
|
|
// Test case from http://www.polymath-software.com/library/nle/Oneeq16.htm
|
|
Func<double, double> f1 = T =>
|
|
{
|
|
const double y = 0.7;
|
|
const double x = 1.7;
|
|
const double z = 1 - y - 0.02;
|
|
const double CH4 = 0;
|
|
const double C2H6 = 0;
|
|
const double COtwo = y + 2*z;
|
|
const double H2O = 2*y + 3*z;
|
|
const double N2 = 0.02 + 3.76*(2*y + 7*z/2)*x;
|
|
const double O2 = (2*y + 7*z/2)*(x - 1);
|
|
const double alp = 3.381*CH4 + 2.247*C2H6 + 6.214*COtwo + 7.256*H2O + 6.524*N2 + 6.148*O2;
|
|
const double bet = 18.044*CH4 + 38.201*C2H6 + 10.396*COtwo + 2.298*H2O + 1.25*N2 + 3.102*O2;
|
|
const double gam = -4.3*CH4 - 11.049*C2H6 - 3.545*COtwo + 0.283*H2O - 0.001*N2 - 0.923*O2;
|
|
const double H0 = alp*298 + bet*0.001*298*298/2 + gam*1e-6*298*298*298/3;
|
|
double Hf = alp*T + bet*0.001*T*T/2 + gam*1e-6*T*T*T/3;
|
|
const double xx = 1;
|
|
|
|
return 212798*y*xx + 372820*z*xx + H0 - Hf;
|
|
};
|
|
|
|
double r = Brent.FindRoot(f1, 1000, 3000);
|
|
Assert.AreEqual(1779.48406483697, r, 1e-5);
|
|
Assert.AreEqual(0, f1(r), 1e-9);
|
|
}
|
|
|
|
[Test]
|
|
public void Oneeq17()
|
|
{
|
|
// Test case from http://www.polymath-software.com/library/nle/Oneeq17.htm
|
|
Func<double, double> f1 = rp => rp - 0.327*Math.Pow(0.06 - 161*rp, 0.804)*Math.Exp(-5230/(1.987*(373 + 1.84e6*rp)));
|
|
|
|
double x = Brent.FindRoot(f1, 0, 0.00035, 1e-13);
|
|
Assert.AreEqual(0.000340568862275, x, 1e-5);
|
|
Assert.AreEqual(0, f1(x), 2e-14);
|
|
}
|
|
|
|
[Test]
|
|
public void Oneeq18a()
|
|
{
|
|
// Test case from http://www.polymath-software.com/library/nle/Oneeq18a.htm
|
|
Func<double, double> f1 = T =>
|
|
{
|
|
double Tp = (269.267*T - 1752)/266.667;
|
|
double k = 0.0006*Math.Exp(20.7 - 15000/Tp);
|
|
double Pp = -(0.1/(321*(320.0/321.0 - (1 + k))));
|
|
double P = (320*Pp + 0.1)/321;
|
|
|
|
return 1.296*(T - Tp) + 10369*k*Pp;
|
|
};
|
|
|
|
double x = Brent.FindRoot(f1, 500, 725);
|
|
Assert.AreEqual(690.4486645013260, x, 1e-5);
|
|
Assert.AreEqual(0, f1(x), 1e-9);
|
|
x = Brent.FindRoot(f1, 725, 850, 1e-12);
|
|
Assert.AreEqual(758.3286948959860, x, 1e-5);
|
|
Assert.AreEqual(0, f1(x), 1e-12);
|
|
x = Brent.FindRoot(f1, 850, 1000, 1e-12);
|
|
Assert.AreEqual(912.7964911381540, x, 1e-5);
|
|
Assert.AreEqual(0, f1(x), 1e-12);
|
|
}
|
|
|
|
[Test]
|
|
public void Oneeq18b()
|
|
{
|
|
// Test case from http://www.polymath-software.com/library/nle/Oneeq18b.htm
|
|
Func<double, double> f1 = T =>
|
|
{
|
|
double Tp = (269*T - 1752)/267;
|
|
double k = 0.0006*Math.Exp(20.7 - 15000/Tp);
|
|
double Pp = -(0.1/(321*(320.0/321.0 - (1 + k))));
|
|
double P = (320*Pp + 0.1)/321;
|
|
|
|
return 1.3*(T - Tp) + 1.04e4*k*Pp;
|
|
};
|
|
|
|
double x = Brent.FindRoot(f1, 500, 1500);
|
|
Assert.AreEqual(1208.2863599396200, x, 1e-4);
|
|
Assert.AreEqual(0, f1(x), 1e-8);
|
|
}
|
|
|
|
[Test]
|
|
public void Oneeq19a()
|
|
{
|
|
// Test case from http://www.polymath-software.com/library/nle/Oneeq19a.htm
|
|
Func<double, double> f1 = z =>
|
|
{
|
|
const double P = 200;
|
|
const double Pc = 33.5;
|
|
const double T = 631*2;
|
|
const double Tc = 126.2;
|
|
const double Pr = P/Pc;
|
|
const double Tr = T/Tc;
|
|
double Asqr = 0.4278*Pr/Math.Pow(Tr, 2.5);
|
|
const double B = 0.0867*Pr/Tr;
|
|
double Q = B*B + B - Asqr;
|
|
double r = Asqr*B;
|
|
double p = (-3*Q - 1)/3;
|
|
double q = (-27*r - 9*Q - 2)/27;
|
|
double R = Math.Pow(p/3, 3) + Math.Pow(q/2, 2);
|
|
double V = (R > 0) ? Math.Pow(-q/2 + Math.Sqrt(R), 1/3) : 0;
|
|
double WW = (R > 0) ? (-q/2 - Math.Sqrt(R)) : (0);
|
|
double psi1 = (R < 0) ? (Math.Acos(Math.Sqrt((q*q/4)/(-p*p*p/27)))) : (0);
|
|
double W = (R > 0) ? (Math.Sign(WW)*Math.Pow(Math.Abs(WW), 1/3)) : (0);
|
|
double z1 = (R < 0) ? (2*Math.Sqrt(-p/3)*Math.Cos((psi1/3) + 2*3.1416*0/3) + 1/3) : (0);
|
|
double z2 = (R < 0) ? (2*Math.Sqrt(-p/3)*Math.Cos((psi1/3) + 2*3.1416*1/3) + 1/3) : (0);
|
|
double z3 = (R < 0) ? (2*Math.Sqrt(-p/3)*Math.Cos((psi1/3) + 2*3.1416*2/3) + 1/3) : (0);
|
|
double z0 = (R > 0) ? (V + W + 1/3) : (0);
|
|
|
|
return z*z*z - z*z - Q*z - r;
|
|
};
|
|
|
|
double x = Brent.FindRoot(f1, -0.5, -0.02, 1e-14);
|
|
Assert.AreEqual(-0.03241692071380, x, 1e-7);
|
|
Assert.AreEqual(0, f1(x), 1e-14);
|
|
x = Brent.FindRoot(f1, -0.02, 0.5, 1e-14);
|
|
Assert.AreEqual(-0.01234360708030, x, 1e-7);
|
|
Assert.AreEqual(0, f1(x), 1e-14);
|
|
x = Brent.FindRoot(f1, 0.5, 1.2, 1e-14);
|
|
Assert.AreEqual(1.04476050281300, x, 1e-7);
|
|
Assert.AreEqual(0, f1(x), 1e-14);
|
|
}
|
|
|
|
[Test]
|
|
public void Oneeq19b()
|
|
{
|
|
// Test case from http://www.polymath-software.com/library/nle/Oneeq19b.htm
|
|
Func<double, double> f1 = z =>
|
|
{
|
|
const double P = 200;
|
|
const double Pc = 33.5;
|
|
const double T = 631;
|
|
const double Tc = 126.2;
|
|
const double Pr = P/Pc;
|
|
const double Tr = T/Tc;
|
|
double Asqr = 0.4278*Pr/Math.Pow(Tr, 2.5);
|
|
const double B = 0.0867*Pr/Tr;
|
|
double Q = B*B + B - Asqr;
|
|
double r = Asqr*B;
|
|
double p = (-3*Q - 1)/3;
|
|
double q = (-27*r - 9*Q - 2)/27;
|
|
double R = Math.Pow(p/3, 3) + Math.Pow(q/2, 2);
|
|
double V = (R > 0) ? Math.Pow(-q/2 + Math.Sqrt(R), 1/3) : 0;
|
|
double WW = (R > 0) ? (-q/2 - Math.Sqrt(R)) : (0);
|
|
double psi1 = (R < 0) ? (Math.Acos(Math.Sqrt((q*q/4)/(-p*p*p/27)))) : (0);
|
|
double W = (R > 0) ? (Math.Sign(WW)*Math.Pow(Math.Abs(WW), 1/3)) : (0);
|
|
double z1 = (R < 0) ? (2*Math.Sqrt(-p/3)*Math.Cos((psi1/3) + 2*3.1416*0/3) + 1/3) : (0);
|
|
double z2 = (R < 0) ? (2*Math.Sqrt(-p/3)*Math.Cos((psi1/3) + 2*3.1416*1/3) + 1/3) : (0);
|
|
double z3 = (R < 0) ? (2*Math.Sqrt(-p/3)*Math.Cos((psi1/3) + 2*3.1416*2/3) + 1/3) : (0);
|
|
double z0 = (R > 0) ? (V + W + 1/3) : (0);
|
|
|
|
return z*z*z - z*z - Q*z - r;
|
|
};
|
|
|
|
double x = Brent.FindRoot(f1, -0.5, 1.2, 1e-14);
|
|
Assert.AreEqual(1.06831213384200, x, 1e-7);
|
|
Assert.AreEqual(0, f1(x), 1e-14);
|
|
}
|
|
|
|
[Test]
|
|
public void Oneeq20a()
|
|
{
|
|
// Test case from http://www.polymath-software.com/library/nle/Oneeq20a.htm
|
|
Func<double, double> f1 = xa =>
|
|
{
|
|
const double T = 313;
|
|
const double P0 = 10;
|
|
const double FA0 = 20*P0/(0.082*450);
|
|
double k1 = 1.277*1.0e9*Math.Exp(-90000/(8.31*T));
|
|
double k2 = 1.29*1.0e11*Math.Exp(-135000/(8.31*T));
|
|
double den = 1 + 7*P0*(1 - xa)/(1 + xa);
|
|
double xa1 = 1 + xa;
|
|
double ra = (-k1*P0*(1 - xa)/xa1 + k2*P0*P0*xa*xa/(xa1*xa1))/den;
|
|
|
|
return -ra/FA0;
|
|
};
|
|
|
|
double x = Brent.FindRoot(f1, 0.75, 1.02);
|
|
Assert.AreEqual(0.999251497006000, x, 1e-2);
|
|
Assert.AreEqual(0, f1(x), 1e-8);
|
|
}
|
|
|
|
[Test]
|
|
public void Oneeq20b()
|
|
{
|
|
// Test case from http://www.polymath-software.com/library/nle/Oneeq20b.htm
|
|
Func<double, double> f1 = xa =>
|
|
{
|
|
const double T = 313;
|
|
const double P0 = 10;
|
|
const double FA0 = 20*P0/(0.082*450);
|
|
double k1 = 1.277*1.0e9*Math.Exp(-90000/(8.31*T));
|
|
double k2 = 1.29*1.0e11*Math.Exp(-135000/(8.31*T));
|
|
double xa1 = 1 + xa;
|
|
double ra = (-k1*P0*(1 - xa)/xa1 + k2*P0*P0*xa*xa/(xa1*xa1));
|
|
|
|
return -ra/FA0;
|
|
};
|
|
|
|
double x = Brent.FindRoot(f1, 0.75, 1.02, 1e-10);
|
|
Assert.AreEqual(0.999984253901100, x, 1e-5);
|
|
Assert.AreEqual(0, f1(x), 1e-11);
|
|
}
|
|
|
|
[Test]
|
|
public void Oneeq21a()
|
|
{
|
|
// Test case from http://www.polymath-software.com/library/nle/Oneeq21a.htm
|
|
Func<double, double> f1 = h =>
|
|
{
|
|
double sg = Math.Acos(2*h - 1);
|
|
double si = Math.Pow(1 - Math.Pow(2*h - 1, 2), 0.5);
|
|
double ag = (sg - (2*h - 1)*si)/4;
|
|
double al = 3.1415927/4 - ag;
|
|
const double d = 1.44;
|
|
double dg = 4*ag/(sg + si)*d;
|
|
const double ugs = -0.0295;
|
|
double ug = ugs*3.1415927/4/ag;
|
|
const double uls = -0.00001;
|
|
double ul = uls*3.1415927/4/al;
|
|
double sl = 3.1415927 - sg;
|
|
double dl = 4*al/(sl)*d;
|
|
const double rol = 1;
|
|
const double rog = 0.835;
|
|
const double bt = .6;
|
|
double g = 980*Math.Sin(bt*3.1415927/180);
|
|
double dpg = (rol*al + rog*ag)*g/3.1415927*4;
|
|
const double vig = 1.0;
|
|
double reg = Math.Abs(ug)*rog*dg/vig;
|
|
double tg = -16/reg*(.5*rog*ug*Math.Abs(ug));
|
|
const double vil = .01;
|
|
double rel = Math.Abs(ul)*rol*dl/vil;
|
|
double tl = -16/rel*(.5*rol*ul*Math.Abs(ul));
|
|
const double it = 1;
|
|
double ti = -16/reg*rog*(.5*(ug - ul)*Math.Abs(ug - ul))*it;
|
|
double dpf = (tl*sl + tg*sg)*d/(al + ag)/(d*d)*4;
|
|
double dp = dpg + dpf;
|
|
double tic = (Math.Abs(ul) < Math.Abs(ug)) ? (rog/reg) : (rol/rel);
|
|
double y = (rol - rog)*g*Math.Pow(d/2, 2)/(8*vig*ugs);
|
|
|
|
return -tg*sg*al + tl*sl*ag - ti*si*(al + ag) + d*(rol - rog)*al*ag*g;
|
|
};
|
|
|
|
double x = Brent.FindRoot(f1, 0, 0.3, 1e-14);
|
|
Assert.AreEqual(0.00596133169486, x, 1e-5);
|
|
Assert.AreEqual(0, f1(x), 1e-14);
|
|
}
|
|
|
|
[Test]
|
|
public void Oneeq21b()
|
|
{
|
|
// Test case from http://www.polymath-software.com/library/nle/Oneeq21b.htm
|
|
Func<double, double> f1 = h =>
|
|
{
|
|
double sg = Math.Acos(2*h - 1);
|
|
double si = Math.Pow(1 - Math.Pow(2*h - 1, 2), 0.5);
|
|
double ag = (sg - (2*h - 1)*si)/4;
|
|
double al = 3.1415927/4 - ag;
|
|
const double d = 1.44;
|
|
double dg = 4*ag/(sg + si)*d;
|
|
const double ugs = -0.029;
|
|
double ug = ugs*3.1415927/4/ag;
|
|
const double uls = -0.00001;
|
|
double ul = uls*3.1415927/4/al;
|
|
double sl = 3.1415927 - sg;
|
|
double dl = 4*al/(sl)*d;
|
|
const double rol = 1;
|
|
const double rog = 0.835;
|
|
const double bt = .6;
|
|
double g = 980*Math.Sin(bt*3.1415927/180);
|
|
double dpg = (rol*al + rog*ag)*g/3.1415927*4;
|
|
const double vig = 1.0;
|
|
double reg = Math.Abs(ug)*rog*dg/vig;
|
|
double tg = -16/reg*(.5*rog*ug*Math.Abs(ug));
|
|
const double vil = .01;
|
|
double rel = Math.Abs(ul)*rol*dl/vil;
|
|
double tl = -16/rel*(.5*rol*ul*Math.Abs(ul));
|
|
const double it = 1;
|
|
double ti = -16/reg*rog*(.5*(ug - ul)*Math.Abs(ug - ul))*it;
|
|
double dpf = (tl*sl + tg*sg)*d/(al + ag)/(d*d)*4;
|
|
double dp = dpg + dpf;
|
|
double tic = (Math.Abs(ul) < Math.Abs(ug)) ? (rog/reg) : (rol/rel);
|
|
double y = (rol - rog)*g*Math.Pow(d/2, 2)/(8*vig*ugs);
|
|
|
|
return -tg*sg*al + tl*sl*ag - ti*si*(al + ag) + d*(rol - rog)*al*ag*g;
|
|
};
|
|
|
|
double x = Brent.FindRoot(f1, 0, 0.1, 1e-14);
|
|
Assert.AreEqual(0.00602268958797, x, 1e-5);
|
|
Assert.AreEqual(0, f1(x), 1e-14);
|
|
x = Brent.FindRoot(f1, 0.1, 0.24, 1e-14);
|
|
Assert.AreEqual(0.19925189173123, x, 1e-5);
|
|
Assert.AreEqual(0, f1(x), 1e-14);
|
|
x = Brent.FindRoot(f1, 0.24, 0.3, 1e-14);
|
|
Assert.AreEqual(0.26405262123160, x, 1e-5);
|
|
Assert.AreEqual(0, f1(x), 1e-14);
|
|
}
|
|
}
|
|
}
|
|
|