diff --git a/src/Numerics/Integrate.cs b/src/Numerics/Integrate.cs index 01400e98..a01f7e4d 100644 --- a/src/Numerics/Integrate.cs +++ b/src/Numerics/Integrate.cs @@ -4,7 +4,7 @@ // http://github.com/mathnet/mathnet-numerics // http://mathnetnumerics.codeplex.com // -// Copyright (c) 2009-2010 Math.NET +// Copyright (c) 2009-2016 Math.NET // // Permission is hereby granted, free of charge, to any person // obtaining a copy of this software and associated documentation @@ -64,16 +64,18 @@ namespace MathNet.Numerics } /// - /// Approximates a definite integral using an Nth order Gauss-Legendre rule. + /// Approximates a 2-dimensional definite integral using an Nth order Gauss-Legendre rule over the rectangle [a,b] x [c,d]. /// - /// The analytic smooth function to integrate. - /// Where the interval starts, exclusive and finite. - /// Where the interval ends, exclusive and finite. + /// The 2-dimensional analytic smooth function to integrate. + /// Where the interval starts for the first (inside) integral, exclusive and finite. + /// Where the interval ends for the first (inside) integral, exclusive and finite. + /// Where the interval starts for the second (outside) integral, exclusive and finite. + /// /// Where the interval ends for the second (outside) integral, exclusive and finite. /// Defines an Nth order Gauss-Legendre rule. The order also defines the number of abscissas and weights for the rule. Precomputed Gauss-Legendre abscissas/weights for orders 2,. . ., 20, 32, 64, 96, 100, 128, 256, 512, 1024 are used, otherwise they're calulcated on the fly. /// Approximation of the finite integral in the given interval. - public static double GaussLegendre(Func f, double invervalBegin, double invervalEnd, int order) + public static double OnRectangle(Func f, double invervalBeginA, double invervalEndA, double invervalBeginB, double invervalEndB, int order) { - return GaussLegendreRule.Integrate(f, invervalBegin, invervalEnd, order); + return GaussLegendreRule.Integrate(f, invervalBeginA, invervalEndA, invervalBeginB, invervalEndB, order); } /// @@ -84,11 +86,10 @@ namespace MathNet.Numerics /// Where the interval ends for the first (inside) integral, exclusive and finite. /// Where the interval starts for the second (outside) integral, exclusive and finite. /// /// Where the interval ends for the second (outside) integral, exclusive and finite. - /// Defines an Nth order Gauss-Legendre rule. The order also defines the number of abscissas and weights for the rule. Precomputed Gauss-Legendre abscissas/weights for orders 2,. . ., 20, 32, 64, 96, 100, 128, 256, 512, 1024 are used, otherwise they're calulcated on the fly. /// Approximation of the finite integral in the given interval. - public static double GaussLegendre(Func f, double invervalBeginA, double invervalEndA, double invervalBeginB, double invervalEndB, int order) + public static double OnRectangle(Func f, double invervalBeginA, double invervalEndA, double invervalBeginB, double invervalEndB) { - return GaussLegendreRule.Integrate(f, invervalBeginA, invervalEndA, invervalBeginB, invervalEndB, order); + return GaussLegendreRule.Integrate(f, invervalBeginA, invervalEndA, invervalBeginB, invervalEndB, 32); } } } diff --git a/src/Numerics/Integration/GaussLegendreRule.cs b/src/Numerics/Integration/GaussLegendreRule.cs index 238a945e..6a14a281 100644 --- a/src/Numerics/Integration/GaussLegendreRule.cs +++ b/src/Numerics/Integration/GaussLegendreRule.cs @@ -38,8 +38,8 @@ namespace MathNet.Numerics.Integration /// public class GaussLegendreRule { - private readonly GaussPoint gaussLegendrePoint; - + private readonly GaussPoint _gaussLegendrePoint; + /// /// Initializes a new instance of the class. /// @@ -48,7 +48,7 @@ namespace MathNet.Numerics.Integration /// Defines an Nth order Gauss-Legendre rule. The order also defines the number of abscissas and weights for the rule. Precomputed Gauss-Legendre abscissas/weights for orders 2,. . ., 20, 32, 64, 96, 100, 128, 256, 512, 1024 are used, otherwise they're calulcated on the fly. public GaussLegendreRule(double intervalBegin, double intervalEnd, int order) { - gaussLegendrePoint = Map(GaussLegendrePointFactory.GetGaussPoint(order), intervalBegin, intervalEnd); + _gaussLegendrePoint = Map(GaussLegendrePointFactory.GetGaussPoint(order), intervalBegin, intervalEnd); } /// @@ -58,7 +58,7 @@ namespace MathNet.Numerics.Integration /// The ith abscissa. public double GetAbscissa(int index) { - return gaussLegendrePoint.Abscissas[index]; + return _gaussLegendrePoint.Abscissas[index]; } /// @@ -68,7 +68,7 @@ namespace MathNet.Numerics.Integration /// The ith weight. public double GetWeight(int index) { - return gaussLegendrePoint.Weights[index]; + return _gaussLegendrePoint.Weights[index]; } /// @@ -78,29 +78,29 @@ namespace MathNet.Numerics.Integration { get { - return gaussLegendrePoint.Order; + return _gaussLegendrePoint.Order; } } /// - /// Getter for the InvervalBegin. + /// Getter for the InvervalBegin. /// public double IntervalBegin { get { - return gaussLegendrePoint.IntervalBegin; + return _gaussLegendrePoint.IntervalBegin; } } /// - /// Getter for the InvervalEnd. + /// Getter for the InvervalEnd. /// public double IntervalEnd { get { - return gaussLegendrePoint.IntervalEnd; + return _gaussLegendrePoint.IntervalEnd; } } @@ -249,4 +249,4 @@ namespace MathNet.Numerics.Integration return c*a*sum; } } -} \ No newline at end of file +} diff --git a/src/Numerics/Integration/GaussRule/GaussLegendrePointFactory.cs b/src/Numerics/Integration/GaussRule/GaussLegendrePointFactory.cs index 3dbd961f..fd429537 100644 --- a/src/Numerics/Integration/GaussRule/GaussLegendrePointFactory.cs +++ b/src/Numerics/Integration/GaussRule/GaussLegendrePointFactory.cs @@ -39,7 +39,7 @@ namespace MathNet.Numerics.Integration.GaussRule static class GaussLegendrePointFactory { [ThreadStatic] - private static GaussPoint gaussLegendrePoint; + private static GaussPoint _gaussLegendrePoint; /// /// Getter for the GaussPoint. @@ -49,18 +49,18 @@ namespace MathNet.Numerics.Integration.GaussRule public static GaussPoint GetGaussPoint(int order) { // Try to get the GaussPoint from the cached static field. - if (gaussLegendrePoint != null && gaussLegendrePoint.Order == order) + if (_gaussLegendrePoint != null && _gaussLegendrePoint.Order == order) { - return gaussLegendrePoint; + return _gaussLegendrePoint; } // Try to find the GaussPoint in the precomputed dictionary. - if (!GaussLegendrePoints.TryGetValue(order, out gaussLegendrePoint)) + if (!GaussLegendrePoints.TryGetValue(order, out _gaussLegendrePoint)) { - gaussLegendrePoint = GenerateGaussLegendrePoint(order, 1e-10); // Generate the GaussPoint on the fly. + _gaussLegendrePoint = GenerateGaussLegendrePoint(order, 1e-10); // Generate the GaussPoint on the fly. } - return gaussLegendrePoint; + return _gaussLegendrePoint; } /// @@ -113,7 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0.99902152641878672000, 0.99902248289345064000 }; const double pi = 3.1415926535897932384626433832795028841971693993751; - double w0 = 0; // Weights + double w0 = 0; // Weights int m = (order + 1) >> 1; double[] abscissas = new double[m]; double[] weights = new double[m]; @@ -126,7 +126,7 @@ namespace MathNet.Numerics.Integration.GaussRule int j = 0; double x0 = Math.Cos(pi*((i << 2) - 1)*t1)*t0; // Initial guess double x1, dx; // Abscissas - double w1, dw; // Weights + double w1, dw; // Weights // Newton iterations, at least one do @@ -141,7 +141,7 @@ namespace MathNet.Numerics.Integration.GaussRule // Optimized version using lookup tables if (order < 1024) { - // Use fast algorithm for small orders + // Use fast algorithm for small orders for (k = 2; k <= order; k++) { p2 = p1; diff --git a/src/UnitTests/IntegrationTests/IntegrationTest.cs b/src/UnitTests/IntegrationTests/IntegrationTest.cs index a0bc3dfb..20f2962c 100644 --- a/src/UnitTests/IntegrationTests/IntegrationTest.cs +++ b/src/UnitTests/IntegrationTests/IntegrationTest.cs @@ -3,7 +3,9 @@ // http://numerics.mathdotnet.com // http://github.com/mathnet/mathnet-numerics // http://mathnetnumerics.codeplex.com -// Copyright (c) 2009-2010 Math.NET +// +// Copyright (c) 2009-2016 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 @@ -12,8 +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 @@ -88,22 +92,34 @@ namespace MathNet.Numerics.UnitTests.IntegrationTests private const double TargetAreaB = 11.7078776759298776163; /// - /// Test integrate portal. + /// Test Integrate facade for simple use cases. /// [Test] - public void TestIntegratePortal() + public void TestIntegrateFacade() { Assert.AreEqual( TargetAreaA, Integrate.OnClosedInterval(TargetFunctionA, StartA, StopA), 1e-5, - "Basic"); + "Interval"); Assert.AreEqual( TargetAreaA, Integrate.OnClosedInterval(TargetFunctionA, StartA, StopA, 1e-10), 1e-10, - "Basic Target 1e-10"); + "Interval, Target 1e-10"); + + Assert.AreEqual( + Integrate.OnRectangle(TargetFunctionB, StartA, StopA, StartB, StopB), + TargetAreaB, + 1e-12, + "Rectangle"); + + Assert.AreEqual( + Integrate.OnRectangle(TargetFunctionB, StartA, StopA, StartB, StopB, 22), + TargetAreaB, + 1e-10, + "Rectangle, Gauss-Legendre Order 22"); } /// @@ -220,21 +236,6 @@ namespace MathNet.Numerics.UnitTests.IntegrationTests Assert.Less(relativeError, 5e-16); } - /// - /// Gauss-Legendre rule supports integration. - /// - /// Defines an Nth order Gauss-Legendre rule. The order also defines the number of abscissas and weights for the rule. - [TestCase(19)] - [TestCase(20)] - [TestCase(21)] - [TestCase(22)] - public void TestIntegrateGaussLegendre(int order) - { - double appoximateArea = Integrate.GaussLegendre(TargetFunctionA, StartA, StopA, order); - double relativeError = Math.Abs(TargetAreaA - appoximateArea) / TargetAreaA; - Assert.Less(relativeError, 5e-16); - } - /// /// Gauss-Legendre rule supports 2-dimensional integration over the rectangle. /// @@ -260,13 +261,10 @@ namespace MathNet.Numerics.UnitTests.IntegrationTests [TestCase(22)] public void TestIntegrateGaussLegendre2D(int order) { - double appoximateArea = Integrate.GaussLegendre(TargetFunctionB, StartA, StopA, StartB, StopB, order); - double relativeError = Math.Abs(TargetAreaB - appoximateArea) / TargetAreaB; - Assert.Less(relativeError, 1e-15); } /// - /// Gauss-Legendre rule supports obtaining the abscissas/weights. In this case, they're used for integration. + /// Gauss-Legendre rule supports obtaining the abscissas/weights. In this case, they're used for integration. /// /// Defines an Nth order Gauss-Legendre rule. The order also defines the number of abscissas and weights for the rule. [TestCase(19)] @@ -309,4 +307,4 @@ namespace MathNet.Numerics.UnitTests.IntegrationTests Assert.AreEqual(gaussLegendre.IntervalEnd, StopA); } } -} \ No newline at end of file +}