From a88e042a15e895d2496ba1f4fe2eba522c97834e Mon Sep 17 00:00:00 2001
From: Christoph Ruegg <git@cdrnet.ch>
Date: Sun, 14 Oct 2018 15:46:58 +0200
Subject: [PATCH] Fit.Curve: non-linear least-squares curve fitting (scalar)
 #597

---
 MathNet.Numerics.sln.DotSettings |  1 +
 src/Numerics.Tests/FitTests.cs   | 19 +++++++++++++++++++
 src/Numerics/FindMinimum.cs      | 11 +++++++++++
 src/Numerics/Fit.cs              | 20 ++++++++++++++++++++
 4 files changed, 51 insertions(+)

diff --git a/MathNet.Numerics.sln.DotSettings b/MathNet.Numerics.sln.DotSettings
index 5bbf624a..14b3d43d 100644
--- a/MathNet.Numerics.sln.DotSettings
+++ b/MathNet.Numerics.sln.DotSettings
@@ -81,5 +81,6 @@ OTHER DEALINGS IN THE SOFTWARE.&#xD;
 	<s:Boolean x:Key="/Default/Environment/SettingsMigration/IsMigratorApplied/=JetBrains_002EReSharper_002EPsi_002ECSharp_002ECodeStyle_002ESettingsUpgrade_002ECSharpPlaceAttributeOnSameLineMigration/@EntryIndexedValue">True</s:Boolean>
 	<s:Boolean x:Key="/Default/Environment/SettingsMigration/IsMigratorApplied/=JetBrains_002EReSharper_002EPsi_002ECSharp_002ECodeStyle_002ESettingsUpgrade_002EMigrateBlankLinesAroundFieldToBlankLinesAroundProperty/@EntryIndexedValue">True</s:Boolean>
 	<s:Boolean x:Key="/Default/Environment/SettingsMigration/IsMigratorApplied/=JetBrains_002EReSharper_002EPsi_002ECSharp_002ECodeStyle_002ESettingsUpgrade_002EMigrateThisQualifierSettings/@EntryIndexedValue">True</s:Boolean>
+	<s:Boolean x:Key="/Default/UserDictionary/Words/=Numerics/@EntryIndexedValue">True</s:Boolean>
 	
 	</wpf:ResourceDictionary>
diff --git a/src/Numerics.Tests/FitTests.cs b/src/Numerics.Tests/FitTests.cs
index e4e4eb70..c17c225f 100644
--- a/src/Numerics.Tests/FitTests.cs
+++ b/src/Numerics.Tests/FitTests.cs
@@ -320,5 +320,24 @@ namespace MathNet.Numerics.UnitTests
                 Assert.AreEqual(4.02159*Math.Sin(z) - 1.46962*Math.Cos(z) - 0.287476, resf(z), 1e-4);
             }
         }
+
+        [Test]
+        public void FitsCurveToBestLineThroughOrigin()
+        {
+            // Mathematica: Fit[{{1,4.986},{2,2.347},{3,2.061},{4,-2.995},{5,-2.352},{6,-5.782}}, {x}, x]
+            // -> -0.467791 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.Curve(x, y, (s,t) => s*t, -1.0);
+            Assert.AreEqual(-0.467791, resp, 1e-4);
+
+            var resf = Fit.CurveFunc(x, y, (s, t) => s * t, -1.0, 1e-10);
+            foreach (var z in Enumerable.Range(-3, 10))
+            {
+                Assert.AreEqual(-0.467791 * z, resf(z), 1e-4);
+            }
+        }
     }
 }
diff --git a/src/Numerics/FindMinimum.cs b/src/Numerics/FindMinimum.cs
index b37bcfcd..76b02944 100644
--- a/src/Numerics/FindMinimum.cs
+++ b/src/Numerics/FindMinimum.cs
@@ -46,6 +46,17 @@ namespace MathNet.Numerics
             return result.MinimizingPoint;
         }
 
+        /// <summary>
+        /// Find vector x that minimizes the function f(x) using the Nelder-Mead Simplex algorithm.
+        /// For more options and diagnostics consider to use <see cref="NelderMeadSimplex"/> directly.
+        /// </summary>
+        public static double OfScalarFunction(Func<double, double> function, double initialGuess, double tolerance = 1e-8, int maxIterations = 1000)
+        {
+            var objective = ObjectiveFunction.Value(v => function(v[0]));
+            var result = NelderMeadSimplex.Minimum(objective, CreateVector.Dense(new[] { initialGuess }), tolerance, maxIterations);
+            return result.MinimizingPoint[0];
+        }
+
         /// <summary>
         /// Find vector x that minimizes the function f(x) using the Nelder-Mead Simplex algorithm.
         /// For more options and diagnostics consider to use <see cref="NelderMeadSimplex"/> directly.
diff --git a/src/Numerics/Fit.cs b/src/Numerics/Fit.cs
index 34d8a0cf..8116a5f5 100644
--- a/src/Numerics/Fit.cs
+++ b/src/Numerics/Fit.cs
@@ -32,6 +32,7 @@ using System.Linq;
 using MathNet.Numerics.LinearAlgebra;
 using MathNet.Numerics.LinearRegression;
 using MathNet.Numerics.Providers.LinearAlgebra;
+using MathNet.Numerics.Statistics;
 
 namespace MathNet.Numerics
 {
@@ -334,5 +335,24 @@ namespace MathNet.Numerics
             var parameters = LinearGeneric(x, y, method, functions);
             return z => functions.Zip(parameters, (f, p) => p * f(z)).Sum();
         }
+
+        /// <summary>
+        /// Non-linear least-squares fitting the points (x,y) to an arbitrary function y : x -> f(p, x),
+        /// returning its best fitting parameter p.
+        /// </summary>
+        public static double Curve(double[] x, double[] y, Func<double, double, double> f, double initialGuess, double tolerance = 1e-8, int maxIterations = 1000)
+        {
+            return FindMinimum.OfScalarFunction(p => Distance.Euclidean(Generate.Map(x, t => f(p, t)), y), initialGuess, tolerance, maxIterations);
+        }
+
+        /// <summary>
+        /// Least-Squares fitting the points (x,y) to a line y : x -> a+b*x,
+        /// returning a function y' for the best fitting line.
+        /// </summary>
+        public static Func<double, double> CurveFunc(double[] x, double[] y, Func<double, double, double> f, double initialGuess, double tolerance = 1e-8, int maxIterations = 1000)
+        {
+            var parameters = Curve(x, y, f, initialGuess, tolerance, maxIterations);
+            return z => f(parameters, z);
+        }
     }
 }