From 7374ecb1b5d528bde9105db00c605ac4963a4e49 Mon Sep 17 00:00:00 2001
From: Christoph Ruegg <git@cdrnet.ch>
Date: Sun, 14 Oct 2018 18:55:39 +0200
Subject: [PATCH] Fit.Curve: extended to 2 and 3 parameters #597

---
 src/Numerics.Tests/FitTests.cs | 20 ++++++++++++++++
 src/Numerics/Fit.cs            | 42 ++++++++++++++++++++++++++++++++--
 2 files changed, 60 insertions(+), 2 deletions(-)

diff --git a/src/Numerics.Tests/FitTests.cs b/src/Numerics.Tests/FitTests.cs
index c17c225f..9b7aa949 100644
--- a/src/Numerics.Tests/FitTests.cs
+++ b/src/Numerics.Tests/FitTests.cs
@@ -339,5 +339,25 @@ namespace MathNet.Numerics.UnitTests
                 Assert.AreEqual(-0.467791 * z, resf(z), 1e-4);
             }
         }
+
+        [Test]
+        public void FitsCurveToBestLine()
+        {
+            // 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.Curve(x, y, (m, s, t) => m + s*t, 1.0, -1.0, 1e-12);
+            Assert.AreEqual(7.01013, resp.Item1, 1e-4);
+            Assert.AreEqual(-2.08551, resp.Item2, 1e-4);
+
+            var resf = Fit.CurveFunc(x, y, (m, s, t) => m + s * t, 1.0, -1.0, 1e-12);
+            foreach (var z in Enumerable.Range(-3, 10))
+            {
+                Assert.AreEqual(7.01013 - 2.08551 * z, resf(z), 1e-4);
+            }
+        }
     }
 }
diff --git a/src/Numerics/Fit.cs b/src/Numerics/Fit.cs
index 8d65c986..2802bdcb 100644
--- a/src/Numerics/Fit.cs
+++ b/src/Numerics/Fit.cs
@@ -345,13 +345,51 @@ namespace MathNet.Numerics
         }
 
         /// <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.
+        /// Non-linear least-squares fitting the points (x,y) to an arbitrary function y : x -> f(p0, p1, x),
+        /// returning its best fitting parameter p0 and p1.
+        /// </summary>
+        public static Tuple<double, double> Curve(double[] x, double[] y, Func<double, double, double, double> f, double initialGuess0, double initialGuess1, double tolerance = 1e-8, int maxIterations = 1000)
+        {
+            return FindMinimum.OfFunction((p0, p1) => Distance.Euclidean(Generate.Map(x, t => f(p0, p1, t)), y), initialGuess0, initialGuess1, tolerance, maxIterations);
+        }
+
+        /// <summary>
+        /// Non-linear least-squares fitting the points (x,y) to an arbitrary function y : x -> f(p0, p1, p2, x),
+        /// returning its best fitting parameter p0, p1 and p2.
+        /// </summary>
+        public static Tuple<double, double, double> Curve(double[] x, double[] y, Func<double, double, double, double, double> f, double initialGuess0, double initialGuess1, double initialGuess2, double tolerance = 1e-8, int maxIterations = 1000)
+        {
+            return FindMinimum.OfFunction((p0, p1, p2) => Distance.Euclidean(Generate.Map(x, t => f(p0, p1, p2, t)), y), initialGuess0, initialGuess1, initialGuess2, tolerance, maxIterations);
+        }
+
+        /// <summary>
+        /// Non-linear least-squares fitting the points (x,y) to an arbitrary function y : x -> f(p, x),
+        /// returning a function y' for the best fitting curve.
         /// </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);
         }
+
+        /// <summary>
+        /// Non-linear least-squares fitting the points (x,y) to an arbitrary function y : x -> f(p0, p1, x),
+        /// returning a function y' for the best fitting curve.
+        /// </summary>
+        public static Func<double, double> CurveFunc(double[] x, double[] y, Func<double, double, double, double> f, double initialGuess0, double initialGuess1, double tolerance = 1e-8, int maxIterations = 1000)
+        {
+            var parameters = Curve(x, y, f, initialGuess0, initialGuess1, tolerance, maxIterations);
+            return z => f(parameters.Item1, parameters.Item2, z);
+        }
+
+        /// <summary>
+        /// Non-linear least-squares fitting the points (x,y) to an arbitrary function y : x -> f(p0, p1, p2, x),
+        /// returning a function y' for the best fitting curve.
+        /// </summary>
+        public static Func<double, double> CurveFunc(double[] x, double[] y, Func<double, double, double, double, double> f, double initialGuess0, double initialGuess1, double initialGuess2, double tolerance = 1e-8, int maxIterations = 1000)
+        {
+            var parameters = Curve(x, y, f, initialGuess0, initialGuess1, initialGuess2, tolerance, maxIterations);
+            return z => f(parameters.Item1, parameters.Item2, parameters.Item3, z);
+        }
     }
 }