Examples: update to using new curve fitting routines

src/FSharpExamples/LinearRegression.fsx

@@ -40,8 +40,13 @@ 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 ``Fitting to a line (Fit)`` =
+    printfn "Fitting to a line (Fit)"
+
+    Fit.line [| 10.0; 20.0; 30.0 |] [| 15.0; 20.0; 25.0 |]
+
+let ``Fitting to a line (Linear Algebra)`` =
+    printfn "Fitting to a line (Linear Algebra)"
 
     let X = DenseMatrix.ofColumnsList 3 2 [ List.init 3 (fun i -> 1.0); [ 10.0; 20.0; 30.0 ] ]
     let y = DenseVector [| 15.0; 20.0; 25.0 |]
@@ -54,8 +59,26 @@ let ``Fitting to a line`` =
     (p.[0], p.[1])
 
 
-let ``Fitting to an arbitrary linear function from noisy data`` =
-    printfn "Fitting to an arbitrary linear function from noisy data"
+let ``Fitting to an arbitrary linear function from noisy data (Fit)`` =
+    printfn "Fitting to an arbitrary linear function from noisy data (Fit)"
+
+    // 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 |> Array.map (fy (Normal.WithMeanVariance(0.0,2.0)))
+
+    let p = Fit.linear [f1; f2] xdata ydata
+
+    (p.[0], p.[1])
+
+let ``Fitting to an arbitrary linear function from noisy data (Linear Algebra)`` =
+    printfn "Fitting to an arbitrary linear function from noisy data (Linear Algebra)"
 
     // define our target functions
     let f1 x = Math.Sqrt(Math.Exp(x))
@@ -86,8 +109,29 @@ let ``Fitting to an arbitrary linear function from noisy data`` =
     (p.[0], p.[1])
 
 
-let ``Fitting to an sine from noisy data`` =
-    printfn "Fitting to an sine from noisy data"
+let ``Fitting to an sine from noisy data (Fit)`` =
+    printfn "Fitting to an sine from noisy data (Fit)"
+
+    // 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 p = (xdata, ydata) ||> Fit.linear [(fun _ -> 1.0); (fun z -> Math.Sin(omega*z)); (fun z -> Math.Cos(omega*z))]
+    let a = p.[0]
+    let b = SpecialFunctions.Hypotenuse(p.[1], p.[2])
+    let c = Math.Atan2(p.[2], p.[1])
+
+    printfn "p: %A" p
+    printfn "a: %f, b: %f, c: %f" a b c
+
+    (a,b,c)
+
+let ``Fitting to an sine from noisy data (Linear Algebra)`` =
+    printfn "Fitting to an sine from noisy data (Linear Algebra)"
 
     // sample points
     let omega = 1.0