mathnet-numerics/src/UnitTests/FitTests.cs

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// Math.NET Numerics, part of the Math.NET Project
// http://numerics.mathdotnet.com
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// http://mathnetnumerics.codeplex.com
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using System;
using System.Linq;
using MathNet.Numerics.Statistics;
using NUnit.Framework;

namespace MathNet.Numerics.UnitTests
{
    [TestFixture]
    public class FitTests
    {
        [Test]
        public void FitsToExactLineWhenPointsAreOnLine()
        {
            var x = new[] {30.0, 40.0, 50.0, 12.0, -3.4, 100.5};
            var y = x.Select(z => 4.0 - 1.5*z).ToArray();

            var resp = Fit.Line(x, y);
            Assert.AreEqual(2, resp.Length);
            Assert.AreEqual(4.0, resp[0], 1e-12);
            Assert.AreEqual(-1.5, resp[1], 1e-12);

            var resf = Fit.LineFunc(x, y);
            foreach (var z in Enumerable.Range(-3, 10))
            {
                Assert.AreEqual(4.0 - 1.5*z, resf(z), 1e-12);
            }
        }

        [Test]
        public void FitsToBestLine()
        {
            // Mathematica: Fit[{{1,4.986},{2,2.347},{3,2.061},{4,-2.995},{5,-2.352},{6,-5.782}}, {1, x}, x]
            // -> 7.01013 - 2.08551*x

            var x = Enumerable.Range(1, 6).Select(Convert.ToDouble).ToArray();
            var y = new[] {4.986, 2.347, 2.061, -2.995, -2.352, -5.782};

            var resp = Fit.Line(x, y);
            Assert.AreEqual(2, resp.Length);
            Assert.AreEqual(7.01013, resp[0], 1e-4);
            Assert.AreEqual(-2.08551, resp[1], 1e-4);

            var resf = Fit.LineFunc(x, y);
            foreach (var z in Enumerable.Range(-3, 10))
            {
                Assert.AreEqual(7.01013 - 2.08551 * z, resf(z), 1e-4);
            }
        }

        [Test]
        public void FitsToMeanOnOrder0Polynomial()
        {
            // Mathematica: Fit[{{1,4.986},{2,2.347},{3,2.061},{4,-2.995},{5,-2.352},{6,-5.782}}, {1}, x]
            // -> -0.289167

            var x = Enumerable.Range(1, 6).Select(Convert.ToDouble).ToArray();
            var y = new[] { 4.986, 2.347, 2.061, -2.995, -2.352, -5.782 };

            var resp = Fit.Polynomial(x, y, 0);
            Assert.AreEqual(1, resp.Length);
            Assert.AreEqual(-0.289167, resp[0], 1e-4);
            Assert.AreEqual(y.Mean(), resp[0], 1e-4);
        }

        [Test]
        public void FitsToLineOnOrder1Polynomial()
        {
            // Mathematica: Fit[{{1,4.986},{2,2.347},{3,2.061},{4,-2.995},{5,-2.352},{6,-5.782}}, {1, x}, x]
            // -> 7.01013 - 2.08551 x

            var x = Enumerable.Range(1, 6).Select(Convert.ToDouble).ToArray();
            var y = new[] { 4.986, 2.347, 2.061, -2.995, -2.352, -5.782 };

            var resp = Fit.Polynomial(x, y, 1);
            Assert.AreEqual(2, resp.Length);
            Assert.AreEqual(7.01013, resp[0], 1e-4);
            Assert.AreEqual(-2.08551, resp[1], 1e-4);

            var resf = Fit.PolynomialFunc(x, y, 1);
            foreach (var z in Enumerable.Range(-3, 10))
            {
                Assert.AreEqual(7.01013 - 2.08551 * z, resf(z), 1e-4);
            }
        }

        [Test]
        public void FitsToOrder2Polynomial()
        {
            // Mathematica: Fit[{{1,4.986},{2,2.347},{3,2.061},{4,-2.995},{5,-2.352},{6,-5.782}}, {1, x, x^2}, x]
            // -> 6.9703 - 2.05564 x - 0.00426786 x^2

            var x = Enumerable.Range(1, 6).Select(Convert.ToDouble).ToArray();
            var y = new[] { 4.986, 2.347, 2.061, -2.995, -2.352, -5.782 };

            var resp = Fit.Polynomial(x, y, 2);
            Assert.AreEqual(3, resp.Length);
            Assert.AreEqual(6.9703, resp[0], 1e-4);
            Assert.AreEqual(-2.05564, resp[1], 1e-4);
            Assert.AreEqual(-0.00426786, resp[2], 1e-6);

            var resf = Fit.PolynomialFunc(x, y, 2);
            foreach (var z in Enumerable.Range(-3, 10))
            {
                Assert.AreEqual(Evaluate.Polynomial(z, resp), resf(z), 1e-4);
            }
        }

        [Test]
        public void FitsToTrigonometricLinearCombination()
        {
            // Mathematica: Fit[{{1,4.986},{2,2.347},{3,2.061},{4,-2.995},{5,-2.352},{6,-5.782}}, {1, sin(x), cos(x)}, x]
            // -> 4.02159 sin(x) - 1.46962 cos(x) - 0.287476

            var x = Enumerable.Range(1, 6).Select(Convert.ToDouble).ToArray();
            var y = new[] { 4.986, 2.347, 2.061, -2.995, -2.352, -5.782 };

            var resp = Fit.LinearCombination(x, y, z => 1.0, Math.Sin, Math.Cos);
            Assert.AreEqual(3, resp.Length);
            Assert.AreEqual(-0.287476, resp[0], 1e-4);
            Assert.AreEqual(4.02159, resp[1], 1e-4);
            Assert.AreEqual(-1.46962, resp[2], 1e-4);

            var resf = Fit.LinearCombinationFunc(x, y, z => 1.0, Math.Sin, Math.Cos);
            foreach (var z in Enumerable.Range(-3, 10))
            {
                Assert.AreEqual(4.02159*Math.Sin(z) - 1.46962*Math.Cos(z) - 0.287476, resf(z), 1e-4);
            }
        }
    }
}