Fitting: drop old examples that use QR directly

src/FSharpExamples/LinearRegression.fsx

@@ -37,80 +37,36 @@ open MathNet.Numerics.LinearAlgebra
 open MathNet.Numerics.LinearAlgebra.Double
 open MathNet.Numerics.Distributions
 
-// Simple Least Squares Linear Regression, from:
+// Simple Least Squares Linear Regression. For the general principle see
 // http://christoph.ruegg.name/blog/2012/9/9/linear-regression-mathnet-numerics.html
 
-let ``Fitting to a line (Fit)`` =
-    printfn "Fitting to a line (Fit)"
+let ``Fitting to a line`` =
+    printfn "Fitting to a line "
 
-    Fit.line [| 10.0; 20.0; 30.0 |] [| 15.0; 20.0; 25.0 |]
+    let offset, slope = Fit.line [| 10.0; 20.0; 30.0 |] [| 15.0; 20.0; 25.0 |]
+    offset, slope
 
-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 |]
-    let p = X.QR().Solve(y)
+let ``Fitting to an arbitrary linear function from noisy data`` =
+    printfn "Fitting to an arbitrary linear function from noisy data"
 
-    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 (Fit)`` =
-    printfn "Fitting to an arbitrary linear function from noisy data (Fit)"
-
-    // define our target functions
+    // define our target function as linear combination of the following two arbitrary 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
+    // generate 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))
-    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.ofColumnsList 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])
+    p.[0], p.[1]
 
 
-let ``Fitting to an sine from noisy data (Fit)`` =
-    printfn "Fitting to an sine from noisy data (Fit)"
+let ``Fitting to an sine from noisy data`` =
+    printfn "Fitting to an sine from noisy data"
 
     // sample points
     let omega = 1.0
@@ -121,41 +77,9 @@ let ``Fitting to an sine from noisy data (Fit)`` =
     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
-    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.ofColumns 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)