Examples: Add F# linear regressions sample (from blog)

src/FSharpExamples/FSharpExamples.fsproj

@@ -60,11 +60,12 @@
     </ProjectReference>
   </ItemGroup>
   <ItemGroup>
-    <None Include="DenseVector.fsx" />
+    <None Include="RandomAndDistributions.fsx" />
-    <None Include="Apply.fsx" />
     <None Include="Histogram.fsx" />
     <None Include="MCMC.fsx" />
-    <None Include="RandomAndDistributions.fsx" />
+    <None Include="DenseVector.fsx" />
+    <None Include="LinearRegression.fsx" />
+    <None Include="Apply.fsx" />
   </ItemGroup>
   <PropertyGroup>
     <MinimumVisualStudioVersion Condition="'$(MinimumVisualStudioVersion)' == ''">11</MinimumVisualStudioVersion>

src/FSharpExamples/LinearRegression.fsx

@@ -0,0 +1,117 @@
+// <copyright file="LinearRegression.fsx" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://numerics.mathdotnet.com
+// http://github.com/mathnet/mathnet-numerics
+// http://mathnetnumerics.codeplex.com
+//
+// Copyright (c) 2009-2013 Math.NET
+//
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+//
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+// </copyright>
+
+#r "../../out/lib/Net40/MathNet.Numerics.dll"
+#r "../../out/lib/Net40/MathNet.Numerics.FSharp.dll"
+
+open System
+open MathNet.Numerics
+open MathNet.Numerics.LinearAlgebra
+open MathNet.Numerics.LinearAlgebra.Double
+open MathNet.Numerics.Distributions
+
+// Simple Least Squares Linear Regression, from:
+// http://christoph.ruegg.name/blog/2012/9/9/linear-regression-mathnet-numerics.html
+
+let ``Fitting to a line`` =
+    printfn "Fitting to a line"
+
+    let X = DenseMatrix.ofColumnList 3 2 [ List.init 3 (fun i -> 1.0); [ 10.0; 20.0; 30.0 ] ]
+    let y = DenseVector [| 15.0; 20.0; 25.0 |]
+    let p = X.QR().Solve(y)
+
+    printfn "X: %A" X
+    printfn "y: %s" (y.ToString())
+    printfn "p: %s" (p.ToString())
+
+    (p.[0], p.[1])
+
+
+let ``Fitting to an arbitrary linear function from noisy data`` =
+    printfn "Fitting to an arbitrary linear function from noisy data"
+
+    // define our target functions
+    let f1 x = Math.Sqrt(Math.Exp(x))
+    let f2 x = SpecialFunctions.DiGamma(x*x)
+
+    // sample points
+    let xdata = [ 1.0 .. 1.0 .. 10.0 ]
+
+    // create data samples, with chosen parameters and with gaussian noise added
+    let fy (noise:IContinuousDistribution) x = 2.5*f1(x) - 4.0*f2(x) + noise.Sample()
+    let ydata = xdata |> List.map (fy (Normal.WithMeanVariance(0.0,2.0)))
+
+    // build matrix form
+    let X =
+        [
+            xdata |> List.map f1
+            xdata |> List.map f2
+        ] |> DenseMatrix.ofColumnList 10 2
+    let y = DenseVector.ofList ydata
+
+    // solve
+    let p = X.QR().Solve(y)
+
+    printfn "X: %A" X
+    printfn "y: %s" (y.ToString())
+    printfn "p: %s" (p.ToString())
+
+    (p.[0], p.[1])
+
+
+let ``Fitting to an sine from noisy data`` =
+    printfn "Fitting to an sine from noisy data"
+
+    // sample points
+    let omega = 1.0
+    let xdata = [| -1.0; 0.0; 0.1; 0.2; 0.3; 0.4; 0.65; 1.0; 1.2; 2.1; 4.5; 5.0; 6.0; |]
+
+    // generate noisy data for sample points
+    let rnd = Random(1)
+    let ydata = xdata |> Array.map (fun x -> 5.0 + 2.0*Math.Sin(omega*x + 0.2) + 2.0*(rnd.NextDouble()-0.5))
+
+    let X = [
+                Array.create xdata.Length 1.0
+                xdata |> Array.map (fun x -> Math.Sin(omega*x))
+                xdata |> Array.map (fun x -> Math.Cos(omega*x))
+            ] |> DenseMatrix.ofColumnSeq xdata.Length 3
+    let y = DenseVector ydata
+
+    let p = X.QR().Solve(y)
+    let a = p.[0]
+    let b = SpecialFunctions.Hypotenuse(p.[1], p.[2])
+    let c = Math.Atan2(p.[2], p.[1])
+
+    printfn "X: %A" X
+    printfn "y: %s" (y.ToString())
+    printfn "p: %s" (p.ToString())
+    printfn "a: %f, b: %f, c: %f" a b c
+
+    (a,b,c)