Special Functions: add Mittag-Leffler function

Author: diluculo

src/Numerics.Tests/SpecialFunctionsTests/MittagLefflerTests.cs

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+// <copyright file="MittagLefflerTests.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// https://numerics.mathdotnet.com
+// https://github.com/mathnet/mathnet-numerics
+//
+// Copyright (c) 2009-$CURRENT_YEAR$ 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 NUnit.Framework;
+
+namespace MathNet.Numerics.Tests.SpecialFunctionsTests
+{
+    using Complex = System.Numerics.Complex;
+
+    /// <summary>
+    /// Marcum Q functions tests.
+    /// </summary>
+    [TestFixture, Category("Functions")]
+    public class MittagLefflerTests
+    {
+        // E_0.5(z) = e^(z^2) erfc(-z)
+        [TestCase(0.5, 2.0, 0.0, 108.9409043899779724123554, 0.0, 14)]
+        [TestCase(0.5, -1.0, 1.0, 0.3047442052569125924571388, 0.2082189382028316272874373, 14)]
+        // E_1(z) = e^z
+        [TestCase(1.0, 0.0, 0.0, 1.0, 0.0, 14)]
+        [TestCase(1.0, -1.0, 0.0, 0.3678794411714423215955238, 0.0, 13)]
+        [TestCase(1.0, 1.0, 0.0, 2.718281828459045235360287, 0.0, 14)]
+        [TestCase(1.0, 1.0, 1.0, 1.468693939915885157138968, 2.287355287178842391208172, 14)]
+        [TestCase(1.0, 0.0, 1.0, 0.5403023058681397174009366, 0.8414709848078965066525023, 13)]
+        [TestCase(1.0, 0.0, -1.0, 0.5403023058681397174009366, -0.8414709848078965066525023, 13)]
+        [TestCase(1.0, 100.0, -100.0, 2.318014142308082065958914E43, 1.361170159893859825171534E43, 12)]
+        // E_2(z) = cosh(sqrt(z))
+        [TestCase(2.0, 1.0, 0.0, 1.543080634815243778477906, 0.0, 14)]
+        [TestCase(2.0, -1.0, 0.0, 0.5403023058681397174009366, 0.0, 14)]
+        // E_3(z) = 1/3 (e^(z^(1/3)) + 2 e^(-z^(1/3)/2) cos(1/2 sqrt(3) z^(1/3)))
+        [TestCase(3.0, 1.0, 1.0, 1.1666611468490602090051780, 0.1694499559052291264367060, 14)]
+        [TestCase(3.0, 100.0, -25.0, 33.06086298199622791072148, -13.33913169891245601081196, 14)]
+        // E_4(z) = 1/2 (cos(z^(1/4)) + cosh(z^(1/4)))
+        [TestCase(4.0, 1.0, -1.0, 1.0416666624911240883556243, -0.0417162740166212371993211, 12)]
+        [TestCase(4.0, 10.0, -10.0, 1.416662489403313747387247, -0.421631159478217275004827, 14)]
+        public void MittagLeffler(double alpha, double z1, double z2, double exp1, double exp2, int decimalPlaces)
+        {
+            AssertHelpers.AlmostEqualRelative(
+                new Complex(exp1, exp2),
+                SpecialFunctions.MittagLefflerE(alpha, new Complex(z1, z2)),
+                decimalPlaces
+                );
+        }
+
+        [TestCase(0.5, 0.5, 0.5, 0.0, 1.5403698281390346, 0.0, 14)]
+        [TestCase(1.5, 0.5, 0.5, 0.0, 1.1448466286155243, 0.0, 14)]
+        [TestCase(2.3, 1.0, 0.7, 2.0, 1.201890136368392, 0.7895394560075035, 13)]
+        public void GeneralizedMittagLeffler(double alpha, double beta, double z1, double z2, double exp1, double exp2, int decimalPlaces)
+        {
+            AssertHelpers.AlmostEqualRelative(
+                new Complex(exp1, exp2),
+                SpecialFunctions.MittagLefflerE(alpha, beta, new Complex(z1, z2)),
+                decimalPlaces
+                );
+        }
+
+        [TestCase(0.75, 1.0, 1.2, -10, 1.0, 8.72265651199321222E-03, 1.30548998870915031E-03, 13)]
+        public void ThreeParameterMittagLeffler(double alpha, double beta, double gamma, double z1, double z2, double exp1, double exp2, int decimalPlaces)
+        {
+            AssertHelpers.AlmostEqualRelative(
+                new Complex(exp1, exp2),
+                SpecialFunctions.MittagLefflerE(alpha, beta, gamma, new Complex(z1, z2)),
+                decimalPlaces
+                );
+        }
+    }
+}