#region License Information
/* HeuristicLab
* Copyright (C) 2002-2015 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
*
* This file is part of HeuristicLab.
*
* HeuristicLab is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* HeuristicLab is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with HeuristicLab. If not, see .
*/
#endregion
using System;
using System.Collections.Generic;
using System.Linq;
using HeuristicLab.Common;
using HeuristicLab.Core;
using HeuristicLab.Data;
using HeuristicLab.Parameters;
using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
namespace HeuristicLab.Algorithms.DataAnalysis {
[StorableClass]
[Item(Name = "CovariancePiecewisePolynomial",
Description = "Piecewise polynomial covariance function with compact support for Gaussian processes.")]
public sealed class CovariancePiecewisePolynomial : ParameterizedNamedItem, ICovarianceFunction {
public IValueParameter LengthParameter {
get { return (IValueParameter)Parameters["Length"]; }
}
public IValueParameter ScaleParameter {
get { return (IValueParameter)Parameters["Scale"]; }
}
public IConstrainedValueParameter VParameter {
get { return (IConstrainedValueParameter)Parameters["V"]; }
}
private bool HasFixedLengthParameter {
get { return LengthParameter.Value != null; }
}
private bool HasFixedScaleParameter {
get { return ScaleParameter.Value != null; }
}
[StorableConstructor]
private CovariancePiecewisePolynomial(bool deserializing)
: base(deserializing) {
}
private CovariancePiecewisePolynomial(CovariancePiecewisePolynomial original, Cloner cloner)
: base(original, cloner) {
}
public CovariancePiecewisePolynomial()
: base() {
Name = ItemName;
Description = ItemDescription;
Parameters.Add(new OptionalValueParameter("Length", "The length parameter of the isometric piecewise polynomial covariance function."));
Parameters.Add(new OptionalValueParameter("Scale", "The scale parameter of the piecewise polynomial covariance function."));
var validValues = new ItemSet(new IntValue[] {
(IntValue)(new IntValue().AsReadOnly()),
(IntValue)(new IntValue(1).AsReadOnly()),
(IntValue)(new IntValue(2).AsReadOnly()),
(IntValue)(new IntValue(3).AsReadOnly()) });
Parameters.Add(new ConstrainedValueParameter("V", "The v parameter of the piecewise polynomial function (allowed values 0, 1, 2, 3).", validValues, validValues.First()));
}
public override IDeepCloneable Clone(Cloner cloner) {
return new CovariancePiecewisePolynomial(this, cloner);
}
public int GetNumberOfParameters(int numberOfVariables) {
return
(HasFixedLengthParameter ? 0 : 1) +
(HasFixedScaleParameter ? 0 : 1);
}
public void SetParameter(double[] p) {
double @const, scale;
GetParameterValues(p, out @const, out scale);
LengthParameter.Value = new DoubleValue(@const);
ScaleParameter.Value = new DoubleValue(scale);
}
private void GetParameterValues(double[] p, out double length, out double scale) {
// gather parameter values
int n = 0;
if (HasFixedLengthParameter) {
length = LengthParameter.Value.Value;
} else {
length = Math.Exp(p[n]);
n++;
}
if (HasFixedScaleParameter) {
scale = ScaleParameter.Value.Value;
} else {
scale = Math.Exp(2 * p[n]);
n++;
}
if (p.Length != n) throw new ArgumentException("The length of the parameter vector does not match the number of free parameters for CovariancePiecewisePolynomial", "p");
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, int[] columnIndices) {
double length, scale;
int v = VParameter.Value.Value;
GetParameterValues(p, out length, out scale);
var fixedLength = HasFixedLengthParameter;
var fixedScale = HasFixedScaleParameter;
int exp = (int)Math.Floor(columnIndices.Count() / 2.0) + v + 1;
Func f;
Func df;
switch (v) {
case 0:
f = (r) => 1.0;
df = (r) => 0.0;
break;
case 1:
f = (r) => 1 + (exp + 1) * r;
df = (r) => exp + 1;
break;
case 2:
f = (r) => 1 + (exp + 2) * r + (exp * exp + 4.0 * exp + 3) / 3.0 * r * r;
df = (r) => (exp + 2) + 2 * (exp * exp + 4.0 * exp + 3) / 3.0 * r;
break;
case 3:
f = (r) => 1 + (exp + 3) * r + (6.0 * exp * exp + 36 * exp + 45) / 15.0 * r * r +
(exp * exp * exp + 9 * exp * exp + 23 * exp + 45) / 15.0 * r * r * r;
df = (r) => (exp + 3) + 2 * (6.0 * exp * exp + 36 * exp + 45) / 15.0 * r +
(exp * exp * exp + 9 * exp * exp + 23 * exp + 45) / 5.0 * r * r;
break;
default: throw new ArgumentException();
}
// create functions
var cov = new ParameterizedCovarianceFunction();
cov.Covariance = (x, i, j) => {
double k = Math.Sqrt(Util.SqrDist(x, i, x, j, columnIndices, 1.0 / length));
return scale * Math.Pow(Math.Max(1 - k, 0), exp + v) * f(k);
};
cov.CrossCovariance = (x, xt, i, j) => {
double k = Math.Sqrt(Util.SqrDist(x, i, xt, j, columnIndices, 1.0 / length));
return scale * Math.Pow(Math.Max(1 - k, 0), exp + v) * f(k);
};
cov.CovarianceGradient = (x, i, j) => GetGradient(x, i, j, length, scale, v, exp, f, df, columnIndices, fixedLength, fixedScale);
return cov;
}
private static IList GetGradient(double[,] x, int i, int j, double length, double scale, int v, double exp, Func f, Func df, int[] columnIndices,
bool fixedLength, bool fixedScale) {
double k = Math.Sqrt(Util.SqrDist(x, i, x, j, columnIndices, 1.0 / length));
var g = new List(2);
if (!fixedLength) g.Add(scale * Math.Pow(Math.Max(1.0 - k, 0), exp + v - 1) * k * ((exp + v) * f(k) - Math.Max(1 - k, 0) * df(k)));
if (!fixedScale) g.Add(2.0 * scale * Math.Pow(Math.Max(1 - k, 0), exp + v) * f(k));
return g;
}
}
}