[17772] | 1 | using HEAL.Attic;
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| 2 |
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| 3 | using HeuristicLab.Common;
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| 4 | using HeuristicLab.Core;
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| 5 | using HeuristicLab.Data;
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| 6 | using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
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| 7 | using HeuristicLab.Parameters;
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| 8 |
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| 9 | using System;
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| 10 | using System.Collections.Generic;
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| 11 | using System.Linq;
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| 12 | using System.Linq.Expressions;
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| 13 |
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| 14 | namespace HeuristicLab.Problems.DataAnalysis.Symbolic
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| 15 | {
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| 16 | [StorableType("60015D64-5D8B-408A-90A1-E4111BC114D4")]
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| 17 | [Item("IA Compiled Expression Bounds Estimator", "Compile a symbolic model into a lambda and use it to evaluate model bounds.")]
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| 18 | public class IACompiledExpressionBoundsEstimator : ParameterizedNamedItem, IBoundsEstimator
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| 19 | {
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| 20 | // interval method names
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| 21 | private static readonly Dictionary<byte, string> methodName = new Dictionary<byte, string>() {
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| 22 | { OpCodes.Add, "Add" },
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| 23 | { OpCodes.Sub, "Subtract" },
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| 24 | { OpCodes.Mul, "Multiply" },
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| 25 | { OpCodes.Div, "Divide" },
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| 26 | { OpCodes.Sin, "Sine" },
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| 27 | { OpCodes.Cos, "Cosine" },
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| 28 | { OpCodes.Tan, "Tangens" },
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| 29 | { OpCodes.Tanh, "HyperbolicTangent" },
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| 30 | { OpCodes.Log, "Logarithm" },
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| 31 | { OpCodes.Exp, "Exponential" },
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| 32 | { OpCodes.Square, "Square" },
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| 33 | { OpCodes.Cube, "Cube" },
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| 34 | { OpCodes.SquareRoot, "SquareRoot" },
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| 35 | { OpCodes.CubeRoot, "CubicRoot" },
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| 36 | { OpCodes.Absolute, "Absolute" },
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| 37 | { OpCodes.AnalyticQuotient, "AnalyticalQuotient" },
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| 38 | };
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| 39 |
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| 40 | private const string EvaluatedSolutionsParameterName = "EvaluatedSolutions";
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| 41 | private const string UseIntervalSplittingParameterName = "Use Interval splitting";
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| 42 | private const string MaxSplitParameterName = "MaxSplit";
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| 43 | private const string MinWidthParameterName = "MinWidth";
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| 44 |
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| 45 | public IFixedValueParameter<IntValue> EvaluatedSolutionsParameter {
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| 46 | get => (IFixedValueParameter<IntValue>)Parameters[EvaluatedSolutionsParameterName];
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| 47 | }
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| 48 |
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| 49 | public IFixedValueParameter<BoolValue> UseIntervalSplittingParameter {
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| 50 | get => (IFixedValueParameter<BoolValue>)Parameters[UseIntervalSplittingParameterName];
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| 51 | }
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| 52 |
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| 53 | public IFixedValueParameter<IntValue> MaxSplitParameter {
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| 54 | get => (IFixedValueParameter<IntValue>)Parameters[MaxSplitParameterName];
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| 55 | }
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| 56 |
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| 57 | public IFixedValueParameter<DoubleValue> MinWidthParameter {
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| 58 | get => (IFixedValueParameter<DoubleValue>)Parameters[MinWidthParameterName];
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| 59 | }
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| 60 |
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| 61 | public int MaxSplit {
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| 62 | get => MaxSplitParameter.Value.Value;
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| 63 | set => MaxSplitParameter.Value.Value = value;
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| 64 | }
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| 65 |
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| 66 | public double MinWidth {
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| 67 | get => MinWidthParameter.Value.Value;
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| 68 | set => MinWidthParameter.Value.Value = value;
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| 69 | }
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| 70 |
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| 71 | public int EvaluatedSolutions {
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| 72 | get => EvaluatedSolutionsParameter.Value.Value;
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| 73 | set => EvaluatedSolutionsParameter.Value.Value = value;
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| 74 | }
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| 75 |
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| 76 | public bool UseIntervalSplitting {
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| 77 | get => UseIntervalSplittingParameter.Value.Value;
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| 78 | set => UseIntervalSplittingParameter.Value.Value = value;
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| 79 | }
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| 80 |
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| 81 | private readonly object syncRoot = new object();
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| 82 |
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| 83 | public IACompiledExpressionBoundsEstimator() : base("IA Bounds Estimator",
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| 84 | "Estimates the bounds of the model with interval arithmetic, by first compiling the model into a lambda.") {
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| 85 | Parameters.Add(new FixedValueParameter<IntValue>(EvaluatedSolutionsParameterName,
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| 86 | "A counter for the total number of solutions the estimator has evaluated.", new IntValue(0)));
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| 87 | Parameters.Add(new FixedValueParameter<BoolValue>(UseIntervalSplittingParameterName,
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| 88 | "Defines whether interval splitting is activated or not.", new BoolValue(false)));
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| 89 | Parameters.Add(new FixedValueParameter<IntValue>(MaxSplitParameterName,
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| 90 | "Defines the number of iterations of splitting.", new IntValue(200)));
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| 91 | Parameters.Add(new FixedValueParameter<DoubleValue>(MinWidthParameterName,
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| 92 | "Width of interval, after the splitting should stop.", new DoubleValue(0.0)));
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| 93 | }
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| 94 |
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| 95 | [StorableConstructor]
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| 96 | private IACompiledExpressionBoundsEstimator(StorableConstructorFlag _) : base(_) { }
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| 97 |
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| 98 | private IACompiledExpressionBoundsEstimator(IACompiledExpressionBoundsEstimator original, Cloner cloner) : base(original, cloner) { }
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| 99 |
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| 100 | public override IDeepCloneable Clone(Cloner cloner) {
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| 101 | return new IACompiledExpressionBoundsEstimator(this, cloner);
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| 102 | }
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| 103 |
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| 104 |
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| 105 |
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| 106 | public double CheckConstraint(ISymbolicExpressionTree tree, IntervalCollection variableRanges, IntervalConstraint constraint) {
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| 107 | if (!UseIntervalSplitting) {
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| 108 | var modelBound = GetModelBound(tree, variableRanges);
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| 109 | if (constraint.Interval.Contains(modelBound)) return 0.0;
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| 110 | return Math.Abs(modelBound.LowerBound - constraint.Interval.LowerBound) +
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| 111 | Math.Abs(modelBound.UpperBound - constraint.Interval.UpperBound);
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| 112 | }
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| 113 |
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| 114 | if (double.IsNegativeInfinity(constraint.Interval.LowerBound) &&
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| 115 | double.IsPositiveInfinity(constraint.Interval.UpperBound)) {
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| 116 | return 0.0;
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| 117 | }
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| 118 |
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| 119 | //ContainsVariableMultipleTimes(tree, out var variables);
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| 120 |
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| 121 | lock (syncRoot) { EvaluatedSolutions++; }
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| 122 |
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| 123 | double upperBound;
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| 124 | if (double.IsNegativeInfinity(constraint.Interval.LowerBound)) {
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| 125 | upperBound = EstimateUpperBound(tree, variableRanges.GetReadonlyDictionary(), MaxSplit, MinWidth);
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| 126 |
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| 127 | return upperBound <= constraint.Interval.UpperBound
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| 128 | ? 0.0
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| 129 | : Math.Abs(upperBound - constraint.Interval.UpperBound);
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| 130 | }
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| 131 |
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| 132 | double lowerBound;
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| 133 | if (double.IsPositiveInfinity(constraint.Interval.UpperBound)) {
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| 134 | lowerBound = EstimateLowerBound(tree, variableRanges.GetReadonlyDictionary(), MaxSplit, MinWidth);
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| 135 |
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| 136 | return lowerBound <= constraint.Interval.LowerBound
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| 137 | ? 0.0
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| 138 | : Math.Abs(lowerBound - constraint.Interval.LowerBound);
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| 139 | }
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| 140 |
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| 141 | var ranges = variableRanges.GetReadonlyDictionary();
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| 142 | lowerBound = EstimateLowerBound(tree, ranges, MaxSplit, MinWidth);
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| 143 | upperBound = EstimateUpperBound(tree, ranges, MaxSplit, MinWidth);
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| 144 |
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| 145 | var res = 0.0;
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| 146 |
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| 147 | res += upperBound <= constraint.Interval.UpperBound ? 0.0 : Math.Abs(upperBound - constraint.Interval.UpperBound);
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| 148 | res += lowerBound <= constraint.Interval.LowerBound ? 0.0 : Math.Abs(lowerBound - constraint.Interval.LowerBound);
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| 149 |
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| 150 | return res;
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| 151 | }
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| 152 |
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| 153 | public void ClearState() {
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| 154 | EvaluatedSolutions = 0;
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| 155 | }
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| 156 |
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| 157 | public Interval GetModelBound(ISymbolicExpressionTree tree, IntervalCollection variableRanges) {
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| 158 | lock (syncRoot) { EvaluatedSolutions++; }
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| 159 | var resultInterval = UseIntervalSplitting
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| 160 | ? EstimateBounds(tree, variableRanges.GetReadonlyDictionary(), MaxSplit, MinWidth)
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| 161 | : EstimateBounds(tree, variableRanges.GetReadonlyDictionary());
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| 162 |
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| 163 | if (resultInterval.IsInfiniteOrUndefined || resultInterval.LowerBound <= resultInterval.UpperBound)
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| 164 | return resultInterval;
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| 165 | return new Interval(resultInterval.UpperBound, resultInterval.LowerBound);
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| 166 | }
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| 167 |
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| 168 | public IDictionary<ISymbolicExpressionTreeNode, Interval> GetModelNodesBounds(ISymbolicExpressionTree tree, IntervalCollection variableRanges) {
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| 169 | throw new NotSupportedException("Model nodes bounds are not supported.");
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| 170 | }
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| 171 |
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| 172 | public void InitializeState() {
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| 173 | EvaluatedSolutions = 0;
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| 174 | }
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| 175 |
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| 176 | public bool IsCompatible(ISymbolicExpressionTree tree) {
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| 177 | var containsUnknownSymbols = (
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| 178 | from n in tree.Root.GetSubtree(0).IterateNodesPrefix()
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| 179 | where
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| 180 | !(n.Symbol is Variable) &&
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| 181 | !(n.Symbol is Constant) &&
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| 182 | !(n.Symbol is StartSymbol) &&
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| 183 | !(n.Symbol is Addition) &&
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| 184 | !(n.Symbol is Subtraction) &&
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| 185 | !(n.Symbol is Multiplication) &&
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| 186 | !(n.Symbol is Division) &&
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| 187 | !(n.Symbol is Sine) &&
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| 188 | !(n.Symbol is Cosine) &&
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| 189 | !(n.Symbol is Tangent) &&
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| 190 | !(n.Symbol is HyperbolicTangent) &&
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| 191 | !(n.Symbol is Logarithm) &&
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| 192 | !(n.Symbol is Exponential) &&
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| 193 | !(n.Symbol is Square) &&
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| 194 | !(n.Symbol is SquareRoot) &&
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| 195 | !(n.Symbol is Cube) &&
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| 196 | !(n.Symbol is CubeRoot) &&
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| 197 | !(n.Symbol is Absolute) &&
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| 198 | !(n.Symbol is AnalyticQuotient)
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| 199 | select n).Any();
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| 200 | return !containsUnknownSymbols;
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| 201 | }
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| 202 |
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| 203 | #region compile a tree into a IA arithmetic lambda and estimate bounds
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| 204 | static Expression MakeExpr(ISymbolicExpressionTreeNode node, IReadOnlyDictionary<string, Interval> variableRanges, IReadOnlyDictionary<string, int> variableIndices, Expression args) {
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| 205 | Expression expr(ISymbolicExpressionTreeNode n) => MakeExpr(n, variableRanges, variableIndices, args);
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| 206 | var opCode = OpCodes.MapSymbolToOpCode(node);
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| 207 |
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| 208 | switch (opCode) {
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| 209 | case OpCodes.Variable: {
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| 210 | var name = (node as VariableTreeNode).VariableName;
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| 211 | var weight = (node as VariableTreeNode).Weight;
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| 212 | var index = variableIndices[name];
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| 213 | return Expression.Multiply(
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| 214 | Expression.Constant(weight, typeof(double)),
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| 215 | Expression.ArrayIndex(args, Expression.Constant(index, typeof(int)))
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| 216 | );
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| 217 | }
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| 218 | case OpCodes.Constant: {
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| 219 | var v = (node as ConstantTreeNode).Value;
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| 220 | // we have to make an interval out of the constant because this may be the root of the tree (and we are expected to return an Interval)
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| 221 | return Expression.Constant(new Interval(v, v), typeof(Interval));
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| 222 | }
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| 223 | case OpCodes.Add: {
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| 224 | var e = expr(node.GetSubtree(0));
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| 225 | foreach (var s in node.Subtrees.Skip(1)) {
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| 226 | e = Expression.Add(e, expr(s));
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| 227 | }
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| 228 | return e;
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| 229 | }
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| 230 | case OpCodes.Sub: {
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| 231 | var e = expr(node.GetSubtree(0));
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| 232 | if (node.SubtreeCount == 1) {
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| 233 | return Expression.Subtract(Expression.Constant(0.0, typeof(double)), e);
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| 234 | }
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| 235 | foreach (var s in node.Subtrees.Skip(1)) {
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| 236 | e = Expression.Subtract(e, expr(s));
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| 237 | }
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| 238 | return e;
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| 239 | }
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| 240 | case OpCodes.Mul: {
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| 241 | var e = expr(node.GetSubtree(0));
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| 242 | foreach (var s in node.Subtrees.Skip(1)) {
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| 243 | e = Expression.Multiply(e, expr(s));
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| 244 | }
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| 245 | return e;
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| 246 | }
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| 247 | case OpCodes.Div: {
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| 248 | var e1 = expr(node.GetSubtree(0));
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| 249 | if (node.SubtreeCount == 1) {
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| 250 | return Expression.Divide(Expression.Constant(1.0, typeof(double)), e1);
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| 251 | }
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| 252 | // division is more expensive than multiplication so we use this construct
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| 253 | var e2 = expr(node.GetSubtree(1));
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| 254 | foreach (var s in node.Subtrees.Skip(2)) {
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| 255 | e2 = Expression.Multiply(e2, expr(s));
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| 256 | }
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| 257 | return Expression.Divide(e1, e2);
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| 258 | }
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| 259 | // all these cases share the same code: get method info by name, emit call expression
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| 260 | case OpCodes.Exp:
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| 261 | case OpCodes.Log:
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| 262 | case OpCodes.Sin:
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| 263 | case OpCodes.Cos:
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| 264 | case OpCodes.Tan:
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| 265 | case OpCodes.Tanh:
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| 266 | case OpCodes.Square:
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| 267 | case OpCodes.Cube:
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| 268 | case OpCodes.SquareRoot:
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| 269 | case OpCodes.CubeRoot:
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| 270 | case OpCodes.Absolute:
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| 271 | case OpCodes.AnalyticQuotient: {
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| 272 | var arg = expr(node.GetSubtree(0));
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| 273 | var fun = typeof(Interval).GetMethod(methodName[opCode], new[] { arg.Type });
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| 274 | return Expression.Call(fun, arg);
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| 275 | }
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| 276 | default: {
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| 277 | throw new Exception($"Unsupported OpCode {opCode} encountered.");
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| 278 | }
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| 279 | }
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| 280 | }
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| 281 |
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| 282 | public static IReadOnlyDictionary<string, int> GetVariableIndices(ISymbolicExpressionTree tree, IReadOnlyDictionary<string, Interval> variableIntervals, out Interval[] inputIntervals) {
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| 283 | var variableIndices = new Dictionary<string, int>();
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| 284 | var root = tree.Root;
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| 285 | while (root.Symbol is ProgramRootSymbol || root.Symbol is StartSymbol) {
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| 286 | root = root.GetSubtree(0);
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| 287 | }
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| 288 | inputIntervals = new Interval[variableIntervals.Count];
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| 289 | int count = 0;
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| 290 | foreach (var node in root.IterateNodesPrefix()) {
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| 291 | if (node is VariableTreeNode varNode) {
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| 292 | var name = varNode.VariableName;
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| 293 | if (!variableIndices.ContainsKey(name)) {
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| 294 | variableIndices[name] = count;
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| 295 | inputIntervals[count] = variableIntervals[name];
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| 296 | ++count;
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| 297 | }
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| 298 | }
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| 299 | }
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| 300 | Array.Resize<Interval>(ref inputIntervals, count);
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| 301 | return variableIndices;
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| 302 | }
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| 303 |
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| 304 | public static Func<Interval[], Interval> Compile(ISymbolicExpressionTree tree, IReadOnlyDictionary<string, Interval> variableRanges, IReadOnlyDictionary<string, int> variableIndices) {
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| 305 | var root = tree.Root.GetSubtree(0).GetSubtree(0);
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| 306 | var args = Expression.Parameter(typeof(Interval[]));
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| 307 | var expr = MakeExpr(root, variableRanges, variableIndices, args);
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| 308 | return Expression.Lambda<Func<Interval[], Interval>>(expr, args).Compile();
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| 309 | }
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| 310 |
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| 311 | public static Interval EstimateBounds(ISymbolicExpressionTree tree, IReadOnlyDictionary<string, Interval> variableRanges, int n = 0, double w = 1e-5) {
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| 312 | var variableIndices = GetVariableIndices(tree, variableRanges, out Interval[] x);
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| 313 | var f = Compile(tree, variableRanges, variableIndices);
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| 314 | if (n == 0) return f(x);
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| 315 | var inf = EstimateBound(x, f, true, n, w);
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| 316 | var sup = EstimateBound(x, f, false, n, w);
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| 317 | return inf < sup ? new Interval(inf, sup) : new Interval(sup, inf);
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| 318 | }
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| 319 | public double EstimateLowerBound(ISymbolicExpressionTree tree, IReadOnlyDictionary<string, Interval> variableRanges, int n = 1000, double w = 1e-5) {
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| 320 | var variableIndices = GetVariableIndices(tree, variableRanges, out Interval[] x);
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| 321 | var f = Compile(tree, variableRanges, variableIndices);
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| 322 | var inf = EstimateBound(x, f, true, n, w);
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| 323 | return inf;
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| 324 | }
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| 325 |
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| 326 | public double EstimateUpperBound(ISymbolicExpressionTree tree, IReadOnlyDictionary<string, Interval> variableRanges, int n = 1000, double w = 1e-5) {
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| 327 | var variableIndices = GetVariableIndices(tree, variableRanges, out Interval[] x);
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| 328 | var f = Compile(tree, variableRanges, variableIndices);
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| 329 | var sup = EstimateBound(x, f, false, n, w);
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| 330 | return sup;
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| 331 | }
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| 332 |
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| 333 | static double EstimateBound(Interval[] x, Func<Interval[], Interval> f, bool m = false, int n = 1000, double w = 1e-4) {
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| 334 | double getBound(Interval iv) => m ? iv.LowerBound : -iv.UpperBound;
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| 335 | double getVolume(Interval[] box) => box.Aggregate(1.0, (acc, iv) => acc * iv.Width);
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| 336 |
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| 337 | var splits = Enumerable.Range(0, x.Length).Select(_ => new List<Interval>()).ToArray();
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| 338 | var newbox = new Interval[x.Length];
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| 339 |
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| 340 | int compare(Tuple<double, double, Interval[]> a, Tuple<double, double, Interval[]> b) {
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| 341 | var res = a.Item1.CompareTo(b.Item1);
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| 342 | if (res == 0) {
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| 343 | res = b.Item2.CompareTo(a.Item2);
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| 344 | }
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| 345 | return res;
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| 346 | }
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| 347 |
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| 348 | var q = new SortedSet<Tuple<double, double, Interval[]>>(Comparer<Tuple<double, double, Interval[]>>.Create(compare)) {
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| 349 | Tuple.Create(getBound(f(x)), getVolume(x), x)
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| 350 | };
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| 351 |
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| 352 |
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| 353 | var bestBound = double.MaxValue;
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| 354 |
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| 355 | // examine all the ordered pairs in the cartesian product
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| 356 | void next_pair(int i) {
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| 357 | if (i == splits.Length) {
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| 358 | var tmp = newbox.ToArray(); // make a copy to put in the queue
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| 359 | q.Add(Tuple.Create(getBound(f(tmp)), getVolume(tmp), tmp));
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| 360 | return;
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| 361 | }
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| 362 |
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| 363 | foreach (var iv in splits[i]) {
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| 364 | newbox[i] = iv;
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| 365 | next_pair(i + 1);
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| 366 | }
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| 367 | }
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| 368 |
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| 369 | while (q.Count > 0 && n-- > 0) {
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| 370 | var currentBound = q.Min; q.Remove(currentBound);
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| 371 | var bound = currentBound.Item1;
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| 372 | var box = currentBound.Item3;
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| 373 |
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| 374 | if (!box.Any(b => b.Width > w)) {
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| 375 | bestBound = Math.Min(bestBound, bound);
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| 376 | continue;
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| 377 | }
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| 378 |
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| 379 | // do the splits
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| 380 | for (int i = 0; i < box.Length; ++i) {
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| 381 | splits[i].Clear();
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| 382 | var iv = box[i];
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| 383 | if (iv.Width > w) {
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| 384 | var t = iv.Split();
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| 385 | splits[i].Add(t.Item1);
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| 386 | splits[i].Add(t.Item2);
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| 387 | } else {
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| 388 | splits[i].Add(iv);
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| 389 | }
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| 390 | }
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| 391 | next_pair(0);
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| 392 | }
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| 393 | if (q.Count > 0) {
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| 394 | bestBound = Math.Min(bestBound, q.First().Item1);
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| 395 | }
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| 396 | return m ? bestBound : -bestBound;
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| 397 | }
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| 398 | #endregion
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| 399 | }
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| 400 | }
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