Added support for Span<double> to SimpleRegression.FitThroughOrigin() as POC for Span support suggested in issue mathnet#1083.

Author: strMikhailPotapenko

src/Numerics.Tests/FitTests.cs

@@ -28,6 +28,7 @@
 // </copyright>
 
 using System;
+using System.Diagnostics;
 using System.Linq;
 
 using MathNet.Numerics.LinearRegression;
@@ -98,6 +99,55 @@ public void FitsToBestLineThroughOrigin()
             Assert.AreEqual(-0.467791, respSeq, 1e-4);
         }
 
+        [Test]
+        public void FitsToBestLineThroughOriginSpanInterface()
+        {
+            // 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().AsSpan();
+            var y = new Span<double> (new[] { 4.986, 2.347, 2.061, -2.995, -2.352, -5.782 });
+
+            var resp = SimpleRegression.FitThroughOrigin(x, y);
+            Assert.AreEqual(-0.467791, resp, 1e-4);            
+        }
+
+        [TestCase(10000, 100)]
+        public void FitsToBestLineThroughOriginBenchmarkSpanVsArray(int dataLength, int windowLength)
+        {            
+            var xarray = new double[dataLength];
+            var yarray = new double[dataLength];
+
+            var window = windowLength;
+
+            var resultArray = new double[dataLength];
+            var resultSpan = new double[dataLength];
+
+            Stopwatch stopwatchArraySlicing = Stopwatch.StartNew();
+            // Use Array Slicing
+            for (int i = 0; i < xarray.Length - window; ++i)
+            {
+                var xx = xarray.Skip(i).Take(window).ToArray();
+                var yy = yarray.Skip(i).Take(window).ToArray();
+                resultArray[i] = SimpleRegression.FitThroughOrigin(xx, yy);
+            }
+            stopwatchArraySlicing.Stop();
+
+            Stopwatch stopwatchSpanSlicing = Stopwatch.StartNew();
+            // Use Span Slicing
+            for (int i = 0; i < xarray.Length - window; ++i)
+            {
+                var xx = xarray.AsSpan(i, window);
+                var yy = yarray.AsSpan(i, window);
+                resultSpan[i] = SimpleRegression.FitThroughOrigin(xx, yy);
+            }
+            stopwatchSpanSlicing.Stop();
+
+            Assert.AreEqual(resultArray, resultSpan);
+
+            Console.WriteLine($"Array Slicing Timing: {stopwatchArraySlicing.Elapsed.TotalMilliseconds} ms, Span Slicing Timing: {stopwatchSpanSlicing.Elapsed.TotalMilliseconds} ms");
+        }
+
         [Test]
         public void FitsToLineSameAsExcelTrendLine()
         {

src/Numerics/LinearRegression/SimpleRegression.cs

@@ -133,6 +133,29 @@ public static double FitThroughOrigin(double[] x, double[] y)
             return mxy / mxx;
         }
 
+        public static double FitThroughOrigin(Span<double> x, Span<double> y)
+        {
+            if (x.Length != y.Length)
+            {
+                throw new ArgumentException($"All sample vectors must have the same length. However, vectors with disagreeing length {x.Length} and {y.Length} have been provided. A sample with index i is given by the value at index i of each provided vector.");
+            }
+
+            if (x.Length <= 1)
+            {
+                throw new ArgumentException($"A regression of the requested order requires at least {2} samples. Only {x.Length} samples have been provided.");
+            }
+
+            double mxy = 0.0;
+            double mxx = 0.0;
+            for (int i = 0; i < x.Length; i++)
+            {
+                mxx += x[i] * x[i];
+                mxy += x[i] * y[i];
+            }
+
+            return mxy / mxx;
+        }
+
 
         /// <summary>
         /// Least-Squares fitting the points (x,y) to a line y : x -> b*x,

src/Numerics/Numerics.csproj

@@ -29,5 +29,6 @@ many contributions, proper release notes with attributions will follow. thank yo
             <PrivateAssets>all</PrivateAssets>
             <IncludeAssets>runtime; build; native; contentfiles; analyzers; buildtransitive</IncludeAssets>
         </PackageReference>
+        <PackageReference Include="System.Memory" Version="4.5.5" />
     </ItemGroup>
 </Project>