mathnet-numerics/src/UnitTests/InterpolationTests/LinearSplineTest.cs

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using MathNet.Numerics.Interpolation;
using NUnit.Framework;

namespace MathNet.Numerics.UnitTests.InterpolationTests
{
    /// <summary>
    /// LinearSpline test case
    /// </summary>
    [TestFixture, Category("Interpolation")]
    public class LinearSplineTest
    {
        /// <summary>
        /// Sample points.
        /// </summary>
        readonly double[] _t = { -2.0, -1.0, 0.0, 1.0, 2.0 };

        /// <summary>
        /// Sample values.
        /// </summary>
        readonly double[] _x = { 1.0, 2.0, -1.0, 0.0, 1.0 };

        /// <summary>
        /// Verifies that the interpolation matches the given value at all the provided sample points.
        /// </summary>
        [Test]
        public void FitsAtSamplePoints()
        {
            IInterpolation interpolation = LinearSpline.Interpolate(_t, _x);

            for (int i = 0; i < _x.Length; i++)
            {
                Assert.AreEqual(_x[i], interpolation.Interpolate(_t[i]), "A Exact Point " + i);

                var actual = interpolation.DifferentiateAll(_t[i]);
                Assert.AreEqual(_x[i], actual.Item1, "B Exact Point " + i);
            }
        }

        /// <summary>
        /// Verifies that at points other than the provided sample points, the interpolation matches the one computed by Maple as a reference.
        /// </summary>
        /// <param name="t">Sample point.</param>
        /// <param name="x">Sample value.</param>
        /// <param name="maxAbsoluteError">Maximum absolute error.</param>
        /// <remarks>
        /// Maple:
        /// f := x -> piecewise(x&lt;-1,3+x,x&lt;0,-1-3*x,x&lt;1,-1+x,-1+x);
        /// f(x)
        /// </remarks>
        [TestCase(-2.4, .6, 1e-15)]
        [TestCase(-0.9, 1.7, 1e-15)]
        [TestCase(-0.5, .5, 1e-15)]
        [TestCase(-0.1, -.7, 1e-15)]
        [TestCase(0.1, -.9, 1e-15)]
        [TestCase(0.4, -.6, 1e-15)]
        [TestCase(1.2, .2, 1e-15)]
        [TestCase(10.0, 9.0, 1e-15)]
        [TestCase(-10.0, -7.0, 1e-15)]
        public void FitsAtArbitraryPointsWithMaple(double t, double x, double maxAbsoluteError)
        {
            IInterpolation interpolation = LinearSpline.Interpolate(_t, _x);

            Assert.AreEqual(x, interpolation.Interpolate(t), maxAbsoluteError, "Interpolation at {0}", t);

            var actual = interpolation.DifferentiateAll(t);
            Assert.AreEqual(x, actual.Item1, maxAbsoluteError, "Interpolation as by-product of differentiation at {0}", t);
        }

        /// <summary>
        /// Verifies that the interpolation supports the linear case appropriately
        /// </summary>
        /// <param name="samples">Samples array.</param>
        [TestCase(2)]
        [TestCase(4)]
        [TestCase(12)]
        public void SupportsLinearCase(int samples)
        {
            double[] x, y, xtest, ytest;
            LinearInterpolationCase.Build(out x, out y, out xtest, out ytest, samples);
            IInterpolation interpolation = LinearSpline.Interpolate(x, y);
            for (int i = 0; i < xtest.Length; i++)
            {
                Assert.AreEqual(ytest[i], interpolation.Interpolate(xtest[i]), 1e-15, "Linear with {0} samples, sample {1}", samples, i);
            }
        }
    }
}