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80 lines
3.8 KiB
80 lines
3.8 KiB
// <copyright file="Fit.fs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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// http://mathnetnumerics.codeplex.com
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//
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// Copyright (c) 2009-2013 Math.NET
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//
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
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// files (the "Software"), to deal in the Software without
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// restriction, including without limitation the rights to use,
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following
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// conditions:
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//
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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namespace MathNet.Numerics
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open System
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open MathNet.Numerics
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open MathNet.Numerics.LinearAlgebra
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open MathNet.Numerics.LinearAlgebra.Factorization
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[<CompilationRepresentation(CompilationRepresentationFlags.ModuleSuffix)>]
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module Fit =
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let private tofs (f:Func<_,_>) = fun a -> f.Invoke(a)
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/// Least-Squares fitting the points (x,y) to a line y : x -> a+b*x,
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/// returning its best fitting parameters as (a, b) tuple.
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let line x y = Fit.Line(x,y) |> properTuple2
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/// Least-Squares fitting the points (x,y) to a line y : x -> a+b*x,
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/// returning a function y' for the best fitting line.
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let lineFunc x y = Fit.LineFunc(x,y) |> tofs
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/// Least-Squares fitting the points ((x0,x1,...,xk),y) to a linear surface y : X -> p0*x0 + p1*x1 + ... + pk*xk,
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/// returning its best fitting parameters as [p0, p1, p2, ..., pk] array.
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let multiDim intercept x y = Fit.MultiDim(x,y,intercept)
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/// Least-Squares fitting the points ((x0,x1,...,xk),y) to a linear surface y : X -> p0*x0 + p1*x1 + ... + pk*xk,
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/// returning a function y' for the best fitting surface.
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let multiDimFunc intercept x y = Fit.MultiDimFunc(x,y,intercept) |> tofs
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/// Least-Squares fitting the points (x,y) to a k-order polynomial y : x -> p0 + p1*x + p2*x^2 + ... + pk*x^k,
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/// returning its best fitting parameters as [p0, p1, p2, ..., pk] array, compatible with Evaluate.Polynomial.
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let polynomial order x y = Fit.Polynomial(x,y,order)
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/// Least-Squares fitting the points (x,y) to a k-order polynomial y : x -> p0 + p1*x + p2*x^2 + ... + pk*x^k,
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/// returning a function y' for the best fitting polynomial.
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let polynomialFunc order x y = Fit.PolynomialFunc(x,y,order) |> tofs
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/// Least-Squares fitting the points (x,y) to an arbitrary linear combination y : x -> p0*f0(x) + p1*f1(x) + ... + pk*fk(x),
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/// returning its best fitting parameters as [p0, p1, p2, ..., pk] list.
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let linear functions (x:_[]) (y:float[]) =
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functions
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|> List.map (fun f -> List.init (Array.length x) (fun i -> f x.[i]))
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|> DenseMatrix.ofColumnList
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|> fun m -> m.QR(QRMethod.Thin).Solve(DenseVector.raw y).ToArray()
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|> List.ofArray
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/// Least-Squares fitting the points (x,y) to an arbitrary linear combination y : x -> p0*f0(x) + p1*f1(x) + ... + pk*fk(x),
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/// returning a function y' for the best fitting combination.
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let linearFunc functions x y =
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let parts = linear functions x y |> List.zip functions
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in fun z -> parts |> List.fold (fun s (f,p) -> s+p*(f z)) 0.0
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