adding leastsquarefitting algoritm + testcases

VectoCommon/VectoCommon/Utils/VectoMath.cs

@@ -378,6 +378,41 @@ namespace TUGraz.VectoCommon.Utils
 		{
 			return x < 0 ? -Math.Pow(-x, 1.0 / 3.0) : Math.Pow(x, 1.0 / 3.0);
 		}
+
+
+		public static void LeastSquaresFitting<T>(IEnumerable<T> entries, Func<T, double> getX, Func<T, double> getY,
+			out double k, out double d, out double r)
+		{
+			// algoritm taken from http://mathworld.wolfram.com/LeastSquaresFitting.html (eqn. 27 & 28)
+			var count = 0;
+			var sumX = 0.0;
+			var sumY = 0.0;
+			var sumXSquare = 0.0;
+			var sumYSquare = 0.0;
+			var sumXY = 0.0;
+			foreach (var entry in entries) {
+				var x = getX(entry);
+				var y = getY(entry);
+				sumX += x;
+				sumY += y;
+				sumXSquare += x * x;
+				sumYSquare += y * y;
+				sumXY += x * y;
+				count++;
+			}
+			if (count == 0) {
+				k = 0;
+				d = 0;
+				r = 0;
+				return;
+			}
+			var ssxx = sumXSquare - sumX * sumX / count;
+			var ssxy = sumXY - sumX * sumY / count;
+			var ssyy = sumYSquare - sumY * sumY / count;
+			k = ssxy / ssxx;
+			d = (sumY - k * sumX) / count;
+			r = ssxy * ssxy / ssxx / ssyy;
+		}
 	}
 
 	[DebuggerDisplay("(X:{X}, Y:{Y}, Z:{Z})")]

VectoCore/VectoCoreTest/Utils/VectoMathTest.cs

@@ -104,5 +104,46 @@ namespace TUGraz.VectoCore.Tests.Utils
 				Assert.AreEqual(0, cmp, 1e-15);
 			}
 		}
+
+		[TestCase()]
+		public void TestLeastSquaresFittingExact()
+		{
+			var entries = new[] {
+				new { X = 0, Y = 4 },
+				new { X = 10, Y = 8 },
+				new { X = 20, Y = 12 }
+			};
+
+			double k, d, r;
+			VectoMath.LeastSquaresFitting(entries, x => x.X, x => x.Y, out k, out d, out r);
+
+			Assert.AreEqual(4, d, 1e-6);
+			Assert.AreEqual(0.4, k, 1e-6);
+			Assert.AreEqual(1, r, 1e-6);
+		}
+
+		[TestCase()]
+		public void TestLeastSquaresFittingEx1()
+		{
+			var entries = new[] {
+				new { X = 12, Y = 34.12 },
+				new { X = 19, Y = 40.94 },
+				new { X = 23, Y = 33.58 },
+				new { X = 30, Y = 38.95 },
+				new { X = 22, Y = 35.42},
+				new { X = 11, Y = 32.12 },
+				new { X = 13, Y = 28.57 },
+				new { X = 28, Y = 40.97 },
+				new { X = 10, Y = 32.06 },
+				new { X = 11, Y = 30.55 },
+			};
+
+			double k, d, r;
+			VectoMath.LeastSquaresFitting(entries, x => x.X, x => x.Y, out k, out d, out r);
+
+			Assert.AreEqual(27.003529, d, 1e-6);
+			Assert.AreEqual(0.431535, k, 1e-6);
+			//Assert.AreEqual(1, r, 1e-3);
+		}
 	}
 }
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