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RootFinding: auto zero-crossing bracketing expansion in FindRoots.OfFunction; include missing R# settings, apply

pull/265/head
Christoph Ruegg 12 years ago
parent
304bdb86b3
commit
3991084de6
8 changed files with 429 additions and 385 deletions
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  1. 30
      MathNet.Numerics.sln.DotSettings
  2. 12
      src/Numerics/FindRoots.cs
  3. 10
      src/Numerics/RootFinding/Bisection.cs
  4. 46
      src/Numerics/RootFinding/Brent.cs
  5. 12
      src/Numerics/RootFinding/ZeroCrossingBracketing.cs
  6. 326
      src/UnitTests/RootFindingTests/BisectionTest.cs
  7. 323
      src/UnitTests/RootFindingTests/BrentTest.cs
  8. 55
      src/UnitTests/RootFindingTests/FindRootsTest.cs

30
MathNet.Numerics.sln.DotSettings
View File

@ -1,9 +1,20 @@
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<s:String x:Key="/Default/CodeStyle/CodeCleanup/RecentlyUsedProfile/@EntryValue">Full Cleanup (Math.NET)</s:String>
<s:String x:Key="/Default/CodeStyle/CodeCleanup/RecentlyUsedProfile/@EntryValue">Default: Reformat Code</s:String>
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12
src/Numerics/FindRoots.cs
View File

@ -50,6 +50,11 @@ namespace MathNet.Numerics
{
double root;
if (!ZeroCrossingBracketing.Expand(f, ref lowerBound, ref upperBound, 1.6, 100))
{
throw new NonConvergenceException(Resources.RootFindingFailed);
}
if (Brent.TryFindRoot(f, lowerBound, upperBound, accuracy, maxIterations, out root))
{
return root;
@ -79,12 +84,7 @@ namespace MathNet.Numerics
return root;
}
if (Bisection.TryFindRoot(f, lowerBound, upperBound, accuracy, maxIterations, out root))
{
return root;
}
throw new NonConvergenceException(Resources.RootFindingFailed);
return OfFunction(f, lowerBound, upperBound, accuracy, maxIterations);
}
/// <summary>

10
src/Numerics/RootFinding/Bisection.cs
View File

@ -3,9 +3,9 @@
// http://numerics.mathdotnet.com
// http://github.com/mathnet/mathnet-numerics
// http://mathnetnumerics.codeplex.com
//
//
// Copyright (c) 2009-2013 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
@ -14,10 +14,10 @@
// 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
@ -34,7 +34,7 @@ using MathNet.Numerics.Properties;
namespace MathNet.Numerics.RootFinding
{
/// <summary>
/// Bisection root-finding algorithm without any recovery measures in case of lacking bracketing.
/// Bisection root-finding algorithm.
/// </summary>
public static class Bisection
{

46
src/Numerics/RootFinding/Brent.cs
View File

@ -3,9 +3,9 @@
// http://numerics.mathdotnet.com
// http://github.com/mathnet/mathnet-numerics
// http://mathnetnumerics.codeplex.com
//
// Copyright (c) 2009-2013 Math.NET
//
//
// 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
@ -14,10 +14,10 @@
// 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
@ -39,6 +39,22 @@ namespace MathNet.Numerics.RootFinding
/// </summary>
public static class Brent
{
/// <summary>Find a solution of the equation f(x)=0.</summary>
/// <param name="f">The function to find roots from.</param>
/// <param name="guessLowerBound">Guess for the low value of the range where the root is supposed to be. Will be expanded if needed.</param>
/// <param name="guessUpperBound">Guess for the high value of the range where the root is supposed to be. Will be expanded if needed.</param>
/// <param name="accuracy">Desired accuracy. The root will be refined until the accuracy or the maximum number of iterations is reached. Default 1e-8.</param>
/// <param name="maxIterations">Maximum number of iterations. Default 100.</param>
/// <param name="expandFactor">Factor at which to expand the bounds, if needed. Default 1.6.</param>
/// <param name="maxExpandIteratons">Maximum number of expand iterations. Default 100.</param>
/// <returns>Returns the root with the specified accuracy.</returns>
/// <exception cref="NonConvergenceException"></exception>
public static double FindRootExpand(Func<double, double> f, double guessLowerBound, double guessUpperBound, double accuracy = 1e-8, int maxIterations = 100, double expandFactor = 1.6, int maxExpandIteratons = 100)
{
ZeroCrossingBracketing.Expand(f, ref guessLowerBound, ref guessUpperBound, expandFactor, maxExpandIteratons);
return FindRoot(f, guessLowerBound, guessUpperBound, accuracy, maxIterations);
}
/// <summary>Find a solution of the equation f(x)=0.</summary>
/// <param name="f">The function to find roots from.</param>
/// <param name="lowerBound">The low value of the range where the root is supposed to be.</param>
@ -103,9 +119,9 @@ namespace MathNet.Numerics.RootFinding
}
// convergence check
double xAcc1 = 2.0 * Precision.DoublePrecision * Math.Abs(root) + 0.5 * accuracy;
double xAcc1 = 2.0*Precision.DoublePrecision*Math.Abs(root) + 0.5*accuracy;
double xMidOld = xMid;
xMid = (upperBound - root) / 2.0;
xMid = (upperBound - root)/2.0;
if (Math.Abs(xMid) <= xAcc1 || froot.AlmostEqualNormRelative(0, froot, accuracy))
{
@ -121,20 +137,20 @@ namespace MathNet.Numerics.RootFinding
if (Math.Abs(e) >= xAcc1 && Math.Abs(fmin) > Math.Abs(froot))
{
// Attempt inverse quadratic interpolation
double s = froot / fmin;
double s = froot/fmin;
double p;
double q;
if (lowerBound.AlmostEqualRelative(upperBound))
{
p = 2.0 * xMid * s;
p = 2.0*xMid*s;
q = 1.0 - s;
}
else
{
q = fmin / fmax;
double r = froot / fmax;
p = s * (2.0 * xMid * q * (q - r) - (root - lowerBound) * (r - 1.0));
q = (q - 1.0) * (r - 1.0) * (s - 1.0);
q = fmin/fmax;
double r = froot/fmax;
p = s*(2.0*xMid*q*(q - r) - (root - lowerBound)*(r - 1.0));
q = (q - 1.0)*(r - 1.0)*(s - 1.0);
}
if (p > 0.0)
@ -144,11 +160,11 @@ namespace MathNet.Numerics.RootFinding
}
p = Math.Abs(p);
if (2.0 * p < Math.Min(3.0 * xMid * q - Math.Abs(xAcc1 * q), Math.Abs(e * q)))
if (2.0*p < Math.Min(3.0*xMid*q - Math.Abs(xAcc1*q), Math.Abs(e*q)))
{
// Accept interpolation
e = d;
d = p / q;
d = p/q;
}
else
{

12
src/Numerics/RootFinding/ZeroCrossingBracketing.cs
View File

@ -3,9 +3,9 @@
// http://numerics.mathdotnet.com
// http://github.com/mathnet/mathnet-numerics
// http://mathnetnumerics.codeplex.com
//
//
// Copyright (c) 2009-2013 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
@ -14,10 +14,10 @@
// 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
@ -100,12 +100,12 @@ namespace MathNet.Numerics.RootFinding
if (Math.Abs(fmin) < Math.Abs(fmax))
{
lowerBound += factor * (lowerBound - upperBound);
lowerBound += factor*(lowerBound - upperBound);
fmin = f(lowerBound);
}
else
{
upperBound += factor * (upperBound - lowerBound);
upperBound += factor*(upperBound - lowerBound);
fmax = f(upperBound);
}
}

326
src/UnitTests/RootFindingTests/BisectionTest.cs
View File

@ -3,9 +3,9 @@
// http://numerics.mathdotnet.com
// http://github.com/mathnet/mathnet-numerics
// http://mathnetnumerics.codeplex.com
//
//
// Copyright (c) 2009-2013 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
@ -14,10 +14,10 @@
// 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
@ -41,7 +41,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
public void MultipleRoots()
{
// Roots at -2, 2
Func<double, double> f1 = x => x * x - 4;
Func<double, double> f1 = x => x*x - 4;
Assert.AreEqual(0, f1(Bisection.FindRoot(f1, 0, 5, 1e-14)));
Assert.AreEqual(0, f1(Bisection.FindRootExpand(f1, 3, 4, 1e-14)));
Assert.AreEqual(-2, Bisection.FindRoot(f1, -5, -1, 1e-14));
@ -51,7 +51,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
Assert.AreEqual(2, Bisection.FindRoot(x => -f1(x), 1, 4, 1e-14));
// Roots at 3, 4
Func<double, double> f2 = x => (x - 3) * (x - 4);
Func<double, double> f2 = x => (x - 3)*(x - 4);
Assert.AreEqual(0, f2(Bisection.FindRoot(f2, 3.5, 5, 1e-14)), 1e-14);
Assert.AreEqual(3, Bisection.FindRoot(f2, -5, 3.5, 1e-14));
Assert.AreEqual(4, Bisection.FindRoot(f2, 3.2, 5, 1e-14));
@ -62,7 +62,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
[Test]
public void LocalMinima()
{
Func<double, double> f1 = x => x * x * x - 2 * x + 2;
Func<double, double> f1 = x => x*x*x - 2*x + 2;
Assert.AreEqual(0, f1(Bisection.FindRoot(f1, -5, 5, 1e-14)), 1e-14);
Assert.AreEqual(0, f1(Bisection.FindRoot(f1, -2, 4, 1e-14)), 1e-14);
}
@ -70,7 +70,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
[Test]
public void NoRoot()
{
Func<double, double> f1 = x => x * x + 4;
Func<double, double> f1 = x => x*x + 4;
Assert.That(() => Bisection.FindRoot(f1, -5, 5, 1e-14), Throws.TypeOf<NonConvergenceException>());
}
@ -78,7 +78,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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;
Func<double, double> f1 = z => 8*Math.Pow((4 - z)*z, 2)/(Math.Pow(6 - 3*z, 2)*(2 - z)) - 0.186;
double x = Bisection.FindRoot(f1, 0.1, 0.9, accuracy: 1e-9, maxIterations: 80);
Assert.AreEqual(0.277759543089215, x, 1e-9);
Assert.AreEqual(0, f1(x), 1e-16);
@ -94,15 +94,15 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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 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 = Bisection.FindRoot(f1, 0, 100);
@ -120,13 +120,13 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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 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 = Bisection.FindRoot(f1, 0, 100);
@ -138,7 +138,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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;
Func<double, double> f1 = T => Math.Exp(21000/T)/(T*T) - 1.11e11;
double x = Bisection.FindRoot(f1, 550, 560, 1e-2);
Assert.AreEqual(551.773822885233, x, 1e-5);
Assert.AreEqual(0, f1(x), 1e-2);
@ -152,7 +152,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
{
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;
return A*B*(B*Math.Pow(1 - x, 2) - A*x*x)/Math.Pow(x*(A - B) + B, 2) + 0.14845;
};
double r = Bisection.FindRoot(f1, 0, 1);
@ -170,7 +170,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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));
return DH + TR*(ALPHA + TR*(BETA/2 + TR*GAMMA/3)) - 298.0*(ALPHA + 298.0*(BETA/2 + 298.0*GAMMA/3));
};
double x = Bisection.FindRoot(f1, 3000, 5000);
@ -192,17 +192,17 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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);
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;
return R*T/V + Beta/(V*V) + Gama/(V*V*V) + Delta/(V*V*V*V) - P;
};
double x = Bisection.FindRoot(f1, 0.1, 1);
Assert.AreEqual(0.174749531708621, x, 1e-5);
Assert.AreEqual(0, f1(x), 1e-12);
}
}
[Test]
public void Oneeq6b()
@ -218,23 +218,23 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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);
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;
return R*T*V*V*V + Beta*V*V + Gama*V + Delta - P*V*V*V*V;
};
double x = Bisection.FindRoot(f1, 0.1, 1);
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;
Func<double, double> f1 = x => x/(1 - x) - 5*Math.Log(0.4*(1 - x)/(0.4 - 0.5*x)) + 4.45977;
double r = Bisection.FindRoot(f1, 0, 0.79, 1e-2);
Assert.AreEqual(0.757396293891, r, 1e-5);
Assert.AreEqual(0, f1(r), 1e-13);
@ -250,7 +250,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
const double b = 40;
const double c = 200;
return a * v * v + b * Math.Pow(v, 7 / 4) - c;
return a*v*v + b*Math.Pow(v, 7/4) - c;
};
double x = Bisection.FindRoot(f1, 0.01, 1);
@ -269,7 +269,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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);
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 = Bisection.FindRoot(f1, 1, 50);
@ -284,7 +284,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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);
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 = Bisection.FindRoot(f1, .01, 0.35);
Assert.AreEqual(0.036210083704, r, 1e-5);
@ -306,7 +306,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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;
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 = Bisection.FindRoot(f1, 0, 0.25);
@ -329,13 +329,13 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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;
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 = Bisection.FindRoot(f1, 0.01, 0.45);
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
// Could not test the following root, since Math.Pow(y,1/3) does not work for y<0
// r = Bisection.FindRoot(f1, 0.55, 0.7);
// Assert.AreEqual(0.600323117488527, r, 1e-5);
// Assert.AreEqual(0, f1(r), 1e-14);
@ -353,7 +353,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
const double T = 430.85;
const double R = 82.05;
return (R * T / P) * (1 + b / v + c / (v * v)) - v;
return (R*T/P)*(1 + b/v + c/(v*v)) - v;
};
double x = Bisection.FindRoot(f1, 100, 300);
@ -372,10 +372,10 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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;
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;
return R*Math.Pow(T, 1.5)*V*(V + B)/(P*Math.Sqrt(T)*V*(V + B) + A) + B - V;
};
double x = Bisection.FindRoot(f1, .01, .3);
@ -397,10 +397,10 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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);
double DT1 = T1 - t1 - Q/(M*Cp);
double DT2 = T1 - t1 - Q/(m*cp);
return U * A * (DT2 - DT1) / Math.Log(DT2 / DT1) - Q;
return U*A*(DT2 - DT1)/Math.Log(DT2/DT1) - Q;
};
double x = Bisection.FindRoot(f1, 1000000, 7000000);
@ -412,7 +412,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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;
Func<double, double> f1 = h => h*(1 + h*(3 - h)) - 2.4 - h;
double x = Bisection.FindRoot(f1, -2, 0);
Assert.AreEqual(-0.795219754733581, x, 1e-5);
@ -429,7 +429,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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;
Func<double, double> f1 = h => 2.4/(h*(3 - h)) - h;
double x = Bisection.FindRoot(f1, -2, -0.5);
Assert.AreEqual(-0.795219745444464, x, 1e-5);
@ -453,18 +453,18 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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 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;
return 212798*y*xx + 372820*z*xx + H0 - Hf;
};
double r = Bisection.FindRoot(f1, 1000, 3000);
@ -476,7 +476,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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)));
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 = Bisection.FindRoot(f1, 0, 0.00035);
Assert.AreEqual(0.000340568862275, x, 1e-5);
@ -489,12 +489,12 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
// 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;
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;
return 1.296*(T - Tp) + 10369*k*Pp;
};
double x = Bisection.FindRoot(f1, 500, 725);
@ -514,12 +514,12 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
// 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;
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;
return 1.3*(T - Tp) + 1.04e4*k*Pp;
};
double x = Bisection.FindRoot(f1, 500, 1500);
@ -537,25 +537,25 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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;
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 = Bisection.FindRoot(f1, -0.5, -0.02);
@ -579,25 +579,25 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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;
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 = Bisection.FindRoot(f1, -0.5, 1.2);
@ -613,14 +613,14 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
{
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);
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;
double ra = (-k1*P0*(1 - xa)/xa1 + k2*P0*P0*xa*xa/(xa1*xa1))/den;
return -ra / FA0;
return -ra/FA0;
};
double x = Bisection.FindRoot(f1, 0.75, 1.02);
@ -636,13 +636,13 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
{
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));
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));
double ra = (-k1*P0*(1 - xa)/xa1 + k2*P0*P0*xa*xa/(xa1*xa1));
return -ra / FA0;
return -ra/FA0;
};
double x = Bisection.FindRoot(f1, 0.75, 1.02);
@ -656,37 +656,37 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
// 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;
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;
double dg = 4*ag/(sg + si)*d;
const double ugs = -0.0295;
double ug = ugs * 3.1415927 / 4 / ag;
double ug = ugs*3.1415927/4/ag;
const double uls = -0.00001;
double ul = uls * 3.1415927 / 4 / al;
double ul = uls*3.1415927/4/al;
double sl = 3.1415927 - sg;
double dl = 4 * al / (sl) * d;
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;
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));
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));
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 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);
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;
return -tg*sg*al + tl*sl*ag - ti*si*(al + ag) + d*(rol - rog)*al*ag*g;
};
double x = Bisection.FindRoot(f1, 0, 0.3);
@ -700,37 +700,37 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
// 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;
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;
double dg = 4*ag/(sg + si)*d;
const double ugs = -0.029;
double ug = ugs * 3.1415927 / 4 / ag;
double ug = ugs*3.1415927/4/ag;
const double uls = -0.00001;
double ul = uls * 3.1415927 / 4 / al;
double ul = uls*3.1415927/4/al;
double sl = 3.1415927 - sg;
double dl = 4 * al / (sl) * d;
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;
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));
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));
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 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);
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;
return -tg*sg*al + tl*sl*ag - ti*si*(al + ag) + d*(rol - rog)*al*ag*g;
};
double x = Bisection.FindRoot(f1, 0, 0.1);

323
src/UnitTests/RootFindingTests/BrentTest.cs
View File

@ -3,9 +3,9 @@
// http://numerics.mathdotnet.com
// http://github.com/mathnet/mathnet-numerics
// http://mathnetnumerics.codeplex.com
//
// Copyright (c) 2009-2013 Math.NET
//
//
// 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
@ -14,10 +14,10 @@
// 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
@ -41,8 +41,9 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
public void MultipleRoots()
{
// Roots at -2, 2
Func<double, double> f1 = x => x * x - 4;
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)));
@ -50,7 +51,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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);
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));
@ -61,7 +62,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
[Test]
public void LocalMinima()
{
Func<double, double> f1 = x => x * x * x - 2 * x + 2;
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);
}
@ -83,7 +84,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
[Test]
public void NoRoot()
{
Func<double, double> f1 = x => x * x + 4;
Func<double, double> f1 = x => x*x + 4;
Assert.That(() => Brent.FindRoot(f1, -5, 5, 1e-14, 50), Throws.TypeOf<NonConvergenceException>());
}
@ -91,7 +92,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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;
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);
@ -107,15 +108,15 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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 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);
@ -133,13 +134,13 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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 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);
@ -151,7 +152,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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;
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);
}
@ -163,7 +164,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
{
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;
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);
@ -182,7 +183,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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));
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);
@ -204,11 +205,11 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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);
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;
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);
@ -228,11 +229,11 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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);
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;
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);
@ -244,7 +245,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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;
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);
}
@ -258,7 +259,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
const double b = 40;
const double c = 200;
return a * v * v + b * Math.Pow(v, 7 / 4) - c;
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);
@ -275,7 +276,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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);
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);
@ -290,7 +291,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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);
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);
@ -312,7 +313,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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;
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);
@ -335,7 +336,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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;
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);
@ -359,7 +360,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
const double T = 430.85;
const double R = 82.05;
return (R * T / P) * (1 + b / v + c / (v * v)) - v;
return (R*T/P)*(1 + b/v + c/(v*v)) - v;
};
double x = Brent.FindRoot(f1, 100, 300, 1e-14);
@ -378,10 +379,10 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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;
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;
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);
@ -403,10 +404,10 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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);
double DT1 = T1 - t1 - Q/(M*Cp);
double DT2 = T1 - t1 - Q/(m*cp);
return U * A * (DT2 - DT1) / Math.Log(DT2 / DT1) - Q;
return U*A*(DT2 - DT1)/Math.Log(DT2/DT1) - Q;
};
double x = Brent.FindRoot(f1, 1000000, 7000000, 1e-9);
@ -418,7 +419,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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;
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);
@ -435,7 +436,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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;
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);
@ -459,18 +460,18 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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 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;
return 212798*y*xx + 372820*z*xx + H0 - Hf;
};
double r = Brent.FindRoot(f1, 1000, 3000);
@ -482,7 +483,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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)));
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);
@ -495,12 +496,12 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
// 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;
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;
return 1.296*(T - Tp) + 10369*k*Pp;
};
double x = Brent.FindRoot(f1, 500, 725);
@ -520,12 +521,12 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
// 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;
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;
return 1.3*(T - Tp) + 1.04e4*k*Pp;
};
double x = Brent.FindRoot(f1, 500, 1500);
@ -541,27 +542,27 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
{
const double P = 200;
const double Pc = 33.5;
const double T = 631 * 2;
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;
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);
@ -585,25 +586,25 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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;
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);
@ -619,14 +620,14 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
{
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);
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;
double ra = (-k1*P0*(1 - xa)/xa1 + k2*P0*P0*xa*xa/(xa1*xa1))/den;
return -ra / FA0;
return -ra/FA0;
};
double x = Brent.FindRoot(f1, 0.75, 1.02);
@ -642,13 +643,13 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
{
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));
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));
double ra = (-k1*P0*(1 - xa)/xa1 + k2*P0*P0*xa*xa/(xa1*xa1));
return -ra / FA0;
return -ra/FA0;
};
double x = Brent.FindRoot(f1, 0.75, 1.02, 1e-10);
@ -662,37 +663,37 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
// 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;
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;
double dg = 4*ag/(sg + si)*d;
const double ugs = -0.0295;
double ug = ugs * 3.1415927 / 4 / ag;
double ug = ugs*3.1415927/4/ag;
const double uls = -0.00001;
double ul = uls * 3.1415927 / 4 / al;
double ul = uls*3.1415927/4/al;
double sl = 3.1415927 - sg;
double dl = 4 * al / (sl) * d;
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;
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));
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));
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 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);
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;
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);
@ -706,37 +707,37 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
// 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;
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;
double dg = 4*ag/(sg + si)*d;
const double ugs = -0.029;
double ug = ugs * 3.1415927 / 4 / ag;
double ug = ugs*3.1415927/4/ag;
const double uls = -0.00001;
double ul = uls * 3.1415927 / 4 / al;
double ul = uls*3.1415927/4/al;
double sl = 3.1415927 - sg;
double dl = 4 * al / (sl) * d;
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;
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));
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));
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 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);
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;
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);

55
src/UnitTests/RootFindingTests/FindRootsTest.cs
View File

@ -3,9 +3,9 @@
// http://numerics.mathdotnet.com
// http://github.com/mathnet/mathnet-numerics
// http://mathnetnumerics.codeplex.com
//
//
// Copyright (c) 2009-2013 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
@ -14,10 +14,10 @@
// 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
@ -37,6 +37,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
using Complex = Numerics.Complex;
#else
using Complex = System.Numerics.Complex;
#endif
[TestFixture, Category("RootFinding")]
@ -46,7 +47,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
public void MultipleRoots()
{
// Roots at -2, 2
Func<double, double> f1 = x => x * x - 4;
Func<double, double> f1 = x => x*x - 4;
Assert.AreEqual(0, f1(FindRoots.OfFunction(f1, 0, 5, 1e-14)));
Assert.AreEqual(-2, FindRoots.OfFunction(f1, -5, -1, 1e-14));
Assert.AreEqual(2, FindRoots.OfFunction(f1, 1, 4, 1e-14));
@ -55,7 +56,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
Assert.AreEqual(2, FindRoots.OfFunction(x => -f1(x), 1, 4, 1e-14));
// Roots at 3, 4
Func<double, double> f2 = x => (x - 3) * (x - 4);
Func<double, double> f2 = x => (x - 3)*(x - 4);
Assert.AreEqual(0, f2(FindRoots.OfFunction(f2, 3.5, 5, 1e-14)), 1e-14);
Assert.AreEqual(3, FindRoots.OfFunction(f2, -5, 3.5, 1e-14));
Assert.AreEqual(4, FindRoots.OfFunction(f2, 3.2, 5, 1e-14));
@ -66,7 +67,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
[Test]
public void LocalMinima()
{
Func<double, double> f1 = x => x * x * x - 2 * x + 2;
Func<double, double> f1 = x => x*x*x - 2*x + 2;
Assert.AreEqual(0, f1(FindRoots.OfFunction(f1, -5, 5, 1e-14)), 1e-14);
Assert.AreEqual(0, f1(FindRoots.OfFunction(f1, -2, 4, 1e-14)), 1e-14);
}
@ -74,7 +75,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
[Test]
public void NoRoot()
{
Func<double, double> f1 = x => x * x + 4;
Func<double, double> f1 = x => x*x + 4;
Assert.That(() => FindRoots.OfFunction(f1, -5, 5, 1e-14), Throws.TypeOf<NonConvergenceException>());
}
@ -82,8 +83,8 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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;
double x = FindRoots.OfFunction(f1, 550, 560, 1e-2);
Func<double, double> f1 = T => Math.Exp(21000/T)/(T*T) - 1.11e11;
double x = FindRoots.OfFunction(f1, 550, 560, 1e-12);
Assert.AreEqual(551.773822885233, x, 1e-5);
Assert.AreEqual(0, f1(x), 1e-2);
}
@ -98,12 +99,12 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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));
return DH + TR*(ALPHA + TR*(BETA/2 + TR*GAMMA/3)) - 298.0*(ALPHA + 298.0*(BETA/2 + 298.0*GAMMA/3));
};
double x = FindRoots.OfFunction(f1, 3000, 5000, 1e-10);
Assert.AreEqual(4305.30991366774, x, 1e-5);
Assert.AreEqual(0, f1(x), 1e-10);
Assert.AreEqual(0, f1(x), 1e-8);
}
[Test]
@ -120,26 +121,26 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
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);
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;
return R*T/V + Beta/(V*V) + Gama/(V*V*V) + Delta/(V*V*V*V) - P;
};
double x = FindRoots.OfFunction(f1, 0.1, 1);
Assert.AreEqual(0.174749531708621, x, 1e-5);
Assert.AreEqual(0, f1(x), 1e-12);
Assert.AreEqual(0, f1(x), 1e-5);
}
[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;
double r = FindRoots.OfFunction(f1, 0, 0.79, 1e-2);
Assert.AreEqual(0.757396293891, r, 1e-5);
Assert.AreEqual(0, f1(r), 1e-13);
Func<double, double> f1 = x => x/(1 - x) - 5*Math.Log(0.4*(1 - x)/(0.4 - 0.5*x)) + 4.45977;
double r = FindRoots.OfFunction(f1, 0, 0.79, 1e-10);
Assert.AreEqual(0.757396293891, r, 1e-6);
Assert.AreEqual(0, f1(r), 1e-6);
}
[Test]
@ -152,15 +153,15 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
const double b = 40;
const double c = 200;
return a * v * v + b * Math.Pow(v, 7 / 4) - c;
return a*v*v + b*Math.Pow(v, 7/4) - c;
};
double x = FindRoots.OfFunction(f1, 0.01, 1);
Assert.AreEqual(0.842524411168525, x, 1e-2);
Assert.AreEqual(0, f1(x), 1e-12);
Assert.AreEqual(0, f1(x), 1e-5);
}
private void AssertComplexEqual(Complex expected, Complex actual, double delta)
void AssertComplexEqual(Complex expected, Complex actual, double delta)
{
Assert.AreEqual(expected.Real, actual.Real, delta);
Assert.AreEqual(expected.Imaginary, actual.Imaginary, delta);
@ -180,7 +181,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
// Expected Roots: -u, -v
Complex r1 = new Complex(-u, 0d), r2 = new Complex(-v, 0d);
Assert.IsTrue(x1.AlmostEqualRelative(r1, 1e-14) && x2.AlmostEqualRelative(r2, 1e-14)
|| x1.AlmostEqualRelative(r2, 1e-14) && x2.AlmostEqualRelative(r1, 1e-14));
|| x1.AlmostEqualRelative(r2, 1e-14) && x2.AlmostEqualRelative(r1, 1e-14));
// Verify they really are roots
AssertComplexEqual(Complex.Zero, c + b*x1 + a*x1*x1, 1e-14);
@ -200,7 +201,7 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
// Expected roots?
Complex r1 = new Complex(x1R, x1I), r2 = new Complex(x2R, x2I);
Assert.IsTrue(x1.AlmostEqualRelative(r1, 1e-14) && x2.AlmostEqualRelative(r2, 1e-14)
|| x1.AlmostEqualRelative(r2, 1e-14) && x2.AlmostEqualRelative(r1, 1e-14));
|| x1.AlmostEqualRelative(r2, 1e-14) && x2.AlmostEqualRelative(r1, 1e-14));
// Verify they really are roots
AssertComplexEqual(Complex.Zero, c + b*x1 + a*x1*x1, 1e-14);

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