Fit: weighted MultiDim and weighted Polynomial

MathNet.Numerics.sln.DotSettings

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src/Numerics/Fit.cs

@@ -70,6 +70,15 @@ namespace MathNet.Numerics
             return MultipleRegression.NormalEquations(x, y);
         }
 
+        /// <summary>
+        /// Weighted Least-Squares fitting the points (X,y) = ((x0,x1,..,xk),y) and weights w to a linear surface y : X -> p0*x0 + p1*x1 + ... + pk*xk,
+        /// returning its best fitting parameters as [p0, p1, p2, ..., pk] array.
+        /// </summary>
+        public static double[] MultiDimWeighted(double[][] x, double[] y, double[] w)
+        {
+            return WeightedRegression.Weighted(x, y, w);
+        }
+
         /// <summary>
         /// Least-Squares fitting the points (X,y) = ((x0,x1,..,xk),y) to a linear surface y : X -> p0*x0 + p1*x1 + ... + pk*xk,
         /// returning a function y' for the best fitting combination.
@@ -90,6 +99,16 @@ namespace MathNet.Numerics
             return MultipleRegression.QR(design, Vector<double>.Build.Dense(y)).ToArray();
         }
 
+        /// <summary>
+        /// Weighted Least-Squares fitting the points (x,y) and weights w to a k-order polynomial y : x -> p0 + p1*x + p2*x^2 + ... + pk*x^k,
+        /// returning its best fitting parameters as [p0, p1, p2, ..., pk] array, compatible with Evaluate.Polynomial.
+        /// </summary>
+        public static double[] PolynomialWeighted(double[] x, double[] y, double[] w, int order)
+        {
+            var design = Matrix<double>.Build.Dense(x.Length, order + 1, (i, j) => Math.Pow(x[i], j));
+            return WeightedRegression.Weighted(design, Vector<double>.Build.Dense(y), Matrix<double>.Build.DenseOfDiagonalArray(w)).ToArray();
+        }
+
         /// <summary>
         /// Least-Squares fitting the points (x,y) to a k-order polynomial y : x -> p0 + p1*x + p2*x^2 + ... + pk*x^k,
         /// returning a function y' for the best fitting polynomial.

src/UnitTests/FitTests.cs

@@ -133,6 +133,28 @@ namespace MathNet.Numerics.UnitTests
             }
         }
 
+        [Test]
+        public void FitsToOrder2PolynomialWeighted()
+        {
+            // Mathematica: LinearModelFit[{{1,4.986},{2,2.347},{3,2.061},{4,-2.995},{5,-2.352},{6,-5.782}}, {1, x, x^2}, x, Weights -> {0.5, 1.0, 1.0, 1.0, 1.0, 0.5}]
+            // -> 7.01451 - 2.12819 x + 0.0115 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 respUnweighted = Fit.PolynomialWeighted(x, y, new[] { 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 }, 2);
+            Assert.AreEqual(3, respUnweighted.Length);
+            Assert.AreEqual(6.9703, respUnweighted[0], 1e-4);
+            Assert.AreEqual(-2.05564, respUnweighted[1], 1e-4);
+            Assert.AreEqual(-0.00426786, respUnweighted[2], 1e-6);
+
+            var resp = Fit.PolynomialWeighted(x, y, new[] { 0.5, 1.0, 1.0, 1.0, 1.0, 0.5 }, 2);
+            Assert.AreEqual(3, resp.Length);
+            Assert.AreEqual(7.01451, resp[0], 1e-4);
+            Assert.AreEqual(-2.12819, resp[1], 1e-4);
+            Assert.AreEqual(0.0115, resp[2], 1e-6);
+        }
+
         [Test]
         public void FitsToTrigonometricLinearCombination()
         {