#region License Information /* HeuristicLab * Copyright (C) 2002-2012 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 HeuristicLab.Common; using HeuristicLab.Core; using HeuristicLab.Data; using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding; using HeuristicLab.Parameters; using HeuristicLab.Persistence.Default.CompositeSerializers.Storable; namespace HeuristicLab.Problems.DataAnalysis.Symbolic { [StorableClass] [Item("SymbolicDataAnalysisExpressionTreeInterpreter", "Interpreter for symbolic expression trees including automatically defined functions.")] public sealed class SymbolicDataAnalysisExpressionTreeInterpreter : ParameterizedNamedItem, ISymbolicDataAnalysisExpressionTreeInterpreter { private const string CheckExpressionsWithIntervalArithmeticParameterName = "CheckExpressionsWithIntervalArithmetic"; private const string EvaluatedSolutionsParameterName = "EvaluatedSolutions"; #region private classes private class InterpreterState { private double[] argumentStack; private int argumentStackPointer; private Instruction[] code; private int pc; public int ProgramCounter { get { return pc; } set { pc = value; } } internal InterpreterState(Instruction[] code, int argumentStackSize) { this.code = code; this.pc = 0; if (argumentStackSize > 0) { this.argumentStack = new double[argumentStackSize]; } this.argumentStackPointer = 0; } internal void Reset() { this.pc = 0; this.argumentStackPointer = 0; } internal Instruction NextInstruction() { return code[pc++]; } private void Push(double val) { argumentStack[argumentStackPointer++] = val; } private double Pop() { return argumentStack[--argumentStackPointer]; } internal void CreateStackFrame(double[] argValues) { // push in reverse order to make indexing easier for (int i = argValues.Length - 1; i >= 0; i--) { argumentStack[argumentStackPointer++] = argValues[i]; } Push(argValues.Length); } internal void RemoveStackFrame() { int size = (int)Pop(); argumentStackPointer -= size; } internal double GetStackFrameValue(ushort index) { // layout of stack: // [0] <- argumentStackPointer // [StackFrameSize = N + 1] // [Arg0] <- argumentStackPointer - 2 - 0 // [Arg1] <- argumentStackPointer - 2 - 1 // [...] // [ArgN] <- argumentStackPointer - 2 - N // return argumentStack[argumentStackPointer - index - 2]; } } private class OpCodes { public const byte Add = 1; public const byte Sub = 2; public const byte Mul = 3; public const byte Div = 4; public const byte Sin = 5; public const byte Cos = 6; public const byte Tan = 7; public const byte Log = 8; public const byte Exp = 9; public const byte IfThenElse = 10; public const byte GT = 11; public const byte LT = 12; public const byte AND = 13; public const byte OR = 14; public const byte NOT = 15; public const byte Average = 16; public const byte Call = 17; public const byte Variable = 18; public const byte LagVariable = 19; public const byte Constant = 20; public const byte Arg = 21; public const byte Power = 22; public const byte Root = 23; public const byte TimeLag = 24; public const byte Integral = 25; public const byte Derivative = 26; public const byte VariableCondition = 27; public const byte Square = 28; public const byte SquareRoot = 29; public const byte Gamma = 30; public const byte Psi = 31; public const byte Dawson = 32; public const byte ExponentialIntegralEi = 33; public const byte CosineIntegral = 34; public const byte SineIntegral = 35; public const byte HyperbolicCosineIntegral = 36; public const byte HyperbolicSineIntegral = 37; public const byte FresnelCosineIntegral = 38; public const byte FresnelSineIntegral = 39; public const byte AiryA = 40; public const byte AiryB = 41; public const byte Norm = 42; public const byte Erf = 43; public const byte Bessel = 44; } #endregion private Dictionary symbolToOpcode = new Dictionary() { { typeof(Addition), OpCodes.Add }, { typeof(Subtraction), OpCodes.Sub }, { typeof(Multiplication), OpCodes.Mul }, { typeof(Division), OpCodes.Div }, { typeof(Sine), OpCodes.Sin }, { typeof(Cosine), OpCodes.Cos }, { typeof(Tangent), OpCodes.Tan }, { typeof(Logarithm), OpCodes.Log }, { typeof(Exponential), OpCodes.Exp }, { typeof(IfThenElse), OpCodes.IfThenElse }, { typeof(GreaterThan), OpCodes.GT }, { typeof(LessThan), OpCodes.LT }, { typeof(And), OpCodes.AND }, { typeof(Or), OpCodes.OR }, { typeof(Not), OpCodes.NOT}, { typeof(Average), OpCodes.Average}, { typeof(InvokeFunction), OpCodes.Call }, { typeof(Variable), OpCodes.Variable }, { typeof(LaggedVariable), OpCodes.LagVariable }, { typeof(Constant), OpCodes.Constant }, { typeof(Argument), OpCodes.Arg }, { typeof(Power),OpCodes.Power}, { typeof(Root),OpCodes.Root}, { typeof(TimeLag), OpCodes.TimeLag}, { typeof(Integral), OpCodes.Integral}, { typeof(Derivative), OpCodes.Derivative}, { typeof(VariableCondition),OpCodes.VariableCondition}, { typeof(Square),OpCodes.Square}, { typeof(SquareRoot),OpCodes.SquareRoot}, { typeof(Gamma), OpCodes.Gamma }, { typeof(Psi), OpCodes.Psi }, { typeof(Dawson), OpCodes.Dawson}, { typeof(ExponentialIntegralEi), OpCodes.ExponentialIntegralEi }, { typeof(CosineIntegral), OpCodes.CosineIntegral }, { typeof(SineIntegral), OpCodes.SineIntegral }, { typeof(HyperbolicCosineIntegral), OpCodes.HyperbolicCosineIntegral }, { typeof(HyperbolicSineIntegral), OpCodes.HyperbolicSineIntegral }, { typeof(FresnelCosineIntegral), OpCodes.FresnelCosineIntegral }, { typeof(FresnelSineIntegral), OpCodes.FresnelSineIntegral }, { typeof(AiryA), OpCodes.AiryA }, { typeof(AiryB), OpCodes.AiryB }, { typeof(Norm), OpCodes.Norm}, { typeof(Erf), OpCodes.Erf}, { typeof(Bessel), OpCodes.Bessel} }; public override bool CanChangeName { get { return false; } } public override bool CanChangeDescription { get { return false; } } #region parameter properties public IValueParameter CheckExpressionsWithIntervalArithmeticParameter { get { return (IValueParameter)Parameters[CheckExpressionsWithIntervalArithmeticParameterName]; } } public IValueParameter EvaluatedSolutionsParameter { get { return (IValueParameter)Parameters[EvaluatedSolutionsParameterName]; } } #endregion #region properties public BoolValue CheckExpressionsWithIntervalArithmetic { get { return CheckExpressionsWithIntervalArithmeticParameter.Value; } set { CheckExpressionsWithIntervalArithmeticParameter.Value = value; } } public IntValue EvaluatedSolutions { get { return EvaluatedSolutionsParameter.Value; } set { EvaluatedSolutionsParameter.Value = value; } } #endregion [StorableConstructor] private SymbolicDataAnalysisExpressionTreeInterpreter(bool deserializing) : base(deserializing) { } private SymbolicDataAnalysisExpressionTreeInterpreter(SymbolicDataAnalysisExpressionTreeInterpreter original, Cloner cloner) : base(original, cloner) { } public override IDeepCloneable Clone(Cloner cloner) { return new SymbolicDataAnalysisExpressionTreeInterpreter(this, cloner); } public SymbolicDataAnalysisExpressionTreeInterpreter() : base("SymbolicDataAnalysisExpressionTreeInterpreter", "Interpreter for symbolic expression trees including automatically defined functions.") { Parameters.Add(new ValueParameter(CheckExpressionsWithIntervalArithmeticParameterName, "Switch that determines if the interpreter checks the validity of expressions with interval arithmetic before evaluating the expression.", new BoolValue(false))); Parameters.Add(new ValueParameter(EvaluatedSolutionsParameterName, "A counter for the total number of solutions the interpreter has evaluated", new IntValue(0))); } [StorableHook(HookType.AfterDeserialization)] private void AfterDeserialization() { if (!Parameters.ContainsKey(EvaluatedSolutionsParameterName)) Parameters.Add(new ValueParameter(EvaluatedSolutionsParameterName, "A counter for the total number of solutions the interpreter has evaluated", new IntValue(0))); } #region IStatefulItem public void InitializeState() { EvaluatedSolutions.Value = 0; } public void ClearState() { } #endregion public IEnumerable GetSymbolicExpressionTreeValues(ISymbolicExpressionTree tree, Dataset dataset, IEnumerable rows) { if (CheckExpressionsWithIntervalArithmetic.Value) throw new NotSupportedException("Interval arithmetic is not yet supported in the symbolic data analysis interpreter."); EvaluatedSolutions.Value++; // increment the evaluated solutions counter var compiler = new SymbolicExpressionTreeCompiler(); Instruction[] code = compiler.Compile(tree, MapSymbolToOpCode); int necessaryArgStackSize = 0; for (int i = 0; i < code.Length; i++) { Instruction instr = code[i]; if (instr.opCode == OpCodes.Variable) { var variableTreeNode = instr.dynamicNode as VariableTreeNode; instr.iArg0 = dataset.GetReadOnlyDoubleValues(variableTreeNode.VariableName); code[i] = instr; } else if (instr.opCode == OpCodes.LagVariable) { var laggedVariableTreeNode = instr.dynamicNode as LaggedVariableTreeNode; instr.iArg0 = dataset.GetReadOnlyDoubleValues(laggedVariableTreeNode.VariableName); code[i] = instr; } else if (instr.opCode == OpCodes.VariableCondition) { var variableConditionTreeNode = instr.dynamicNode as VariableConditionTreeNode; instr.iArg0 = dataset.GetReadOnlyDoubleValues(variableConditionTreeNode.VariableName); } else if (instr.opCode == OpCodes.Call) { necessaryArgStackSize += instr.nArguments + 1; } } var state = new InterpreterState(code, necessaryArgStackSize); foreach (var rowEnum in rows) { int row = rowEnum; state.Reset(); yield return Evaluate(dataset, ref row, state); } } private double Evaluate(Dataset dataset, ref int row, InterpreterState state) { Instruction currentInstr = state.NextInstruction(); switch (currentInstr.opCode) { case OpCodes.Add: { double s = Evaluate(dataset, ref row, state); for (int i = 1; i < currentInstr.nArguments; i++) { s += Evaluate(dataset, ref row, state); } return s; } case OpCodes.Sub: { double s = Evaluate(dataset, ref row, state); for (int i = 1; i < currentInstr.nArguments; i++) { s -= Evaluate(dataset, ref row, state); } if (currentInstr.nArguments == 1) s = -s; return s; } case OpCodes.Mul: { double p = Evaluate(dataset, ref row, state); for (int i = 1; i < currentInstr.nArguments; i++) { p *= Evaluate(dataset, ref row, state); } return p; } case OpCodes.Div: { double p = Evaluate(dataset, ref row, state); for (int i = 1; i < currentInstr.nArguments; i++) { p /= Evaluate(dataset, ref row, state); } if (currentInstr.nArguments == 1) p = 1.0 / p; return p; } case OpCodes.Average: { double sum = Evaluate(dataset, ref row, state); for (int i = 1; i < currentInstr.nArguments; i++) { sum += Evaluate(dataset, ref row, state); } return sum / currentInstr.nArguments; } case OpCodes.Cos: { return Math.Cos(Evaluate(dataset, ref row, state)); } case OpCodes.Sin: { return Math.Sin(Evaluate(dataset, ref row, state)); } case OpCodes.Tan: { return Math.Tan(Evaluate(dataset, ref row, state)); } case OpCodes.Square: { return Math.Pow(Evaluate(dataset, ref row, state), 2); } case OpCodes.Power: { double x = Evaluate(dataset, ref row, state); double y = Math.Round(Evaluate(dataset, ref row, state)); return Math.Pow(x, y); } case OpCodes.SquareRoot: { return Math.Sqrt(Evaluate(dataset, ref row, state)); } case OpCodes.Root: { double x = Evaluate(dataset, ref row, state); double y = Math.Round(Evaluate(dataset, ref row, state)); return Math.Pow(x, 1 / y); } case OpCodes.Exp: { return Math.Exp(Evaluate(dataset, ref row, state)); } case OpCodes.Log: { return Math.Log(Evaluate(dataset, ref row, state)); } case OpCodes.Gamma: { var x = Evaluate(dataset, ref row, state); if (double.IsNaN(x)) return double.NaN; else return alglib.gammafunction(x); } case OpCodes.Psi: { var x = Evaluate(dataset, ref row, state); if (double.IsNaN(x)) return double.NaN; else if (x.IsAlmost(0.0)) return double.NaN; else if ((Math.Floor(x) - x).IsAlmost(0)) return double.NaN; return alglib.psi(x); } case OpCodes.Dawson: { var x = Evaluate(dataset, ref row, state); if (double.IsNaN(x)) return double.NaN; return alglib.dawsonintegral(x); } case OpCodes.ExponentialIntegralEi: { var x = Evaluate(dataset, ref row, state); if (double.IsNaN(x)) return double.NaN; return alglib.exponentialintegralei(x); } case OpCodes.SineIntegral: { double si, ci; var x = Evaluate(dataset, ref row, state); if (double.IsNaN(x)) return double.NaN; else { alglib.sinecosineintegrals(x, out si, out ci); return si; } } case OpCodes.CosineIntegral: { double si, ci; var x = Evaluate(dataset, ref row, state); if (double.IsNaN(x)) return double.NaN; else { alglib.sinecosineintegrals(x, out si, out ci); return ci; } } case OpCodes.HyperbolicSineIntegral: { double shi, chi; var x = Evaluate(dataset, ref row, state); if (double.IsNaN(x)) return double.NaN; else { alglib.hyperbolicsinecosineintegrals(x, out shi, out chi); return shi; } } case OpCodes.HyperbolicCosineIntegral: { double shi, chi; var x = Evaluate(dataset, ref row, state); if (double.IsNaN(x)) return double.NaN; else { alglib.hyperbolicsinecosineintegrals(x, out shi, out chi); return chi; } } case OpCodes.FresnelCosineIntegral: { double c = 0, s = 0; var x = Evaluate(dataset, ref row, state); if (double.IsNaN(x)) return double.NaN; else { alglib.fresnelintegral(x, ref c, ref s); return c; } } case OpCodes.FresnelSineIntegral: { double c = 0, s = 0; var x = Evaluate(dataset, ref row, state); if (double.IsNaN(x)) return double.NaN; else { alglib.fresnelintegral(x, ref c, ref s); return s; } } case OpCodes.AiryA: { double ai, aip, bi, bip; var x = Evaluate(dataset, ref row, state); if (double.IsNaN(x)) return double.NaN; else { alglib.airy(x, out ai, out aip, out bi, out bip); return ai; } } case OpCodes.AiryB: { double ai, aip, bi, bip; var x = Evaluate(dataset, ref row, state); if (double.IsNaN(x)) return double.NaN; else { alglib.airy(x, out ai, out aip, out bi, out bip); return bi; } } case OpCodes.Norm: { var x = Evaluate(dataset, ref row, state); if (double.IsNaN(x)) return double.NaN; else return alglib.normaldistribution(x); } case OpCodes.Erf: { var x = Evaluate(dataset, ref row, state); if (double.IsNaN(x)) return double.NaN; else return alglib.errorfunction(x); } case OpCodes.Bessel: { var x = Evaluate(dataset, ref row, state); if (double.IsNaN(x)) return double.NaN; else return alglib.besseli0(x); } case OpCodes.IfThenElse: { double condition = Evaluate(dataset, ref row, state); double result; if (condition > 0.0) { result = Evaluate(dataset, ref row, state); SkipInstructions(state); } else { SkipInstructions(state); result = Evaluate(dataset, ref row, state); } return result; } case OpCodes.AND: { double result = Evaluate(dataset, ref row, state); for (int i = 1; i < currentInstr.nArguments; i++) { if (result > 0.0) result = Evaluate(dataset, ref row, state); else { SkipInstructions(state); } } return result > 0.0 ? 1.0 : -1.0; } case OpCodes.OR: { double result = Evaluate(dataset, ref row, state); for (int i = 1; i < currentInstr.nArguments; i++) { if (result <= 0.0) result = Evaluate(dataset, ref row, state); else { SkipInstructions(state); } } return result > 0.0 ? 1.0 : -1.0; } case OpCodes.NOT: { return Evaluate(dataset, ref row, state) > 0.0 ? -1.0 : 1.0; } case OpCodes.GT: { double x = Evaluate(dataset, ref row, state); double y = Evaluate(dataset, ref row, state); if (x > y) return 1.0; else return -1.0; } case OpCodes.LT: { double x = Evaluate(dataset, ref row, state); double y = Evaluate(dataset, ref row, state); if (x < y) return 1.0; else return -1.0; } case OpCodes.TimeLag: { var timeLagTreeNode = (LaggedTreeNode)currentInstr.dynamicNode; row += timeLagTreeNode.Lag; double result = Evaluate(dataset, ref row, state); row -= timeLagTreeNode.Lag; return result; } case OpCodes.Integral: { int savedPc = state.ProgramCounter; var timeLagTreeNode = (LaggedTreeNode)currentInstr.dynamicNode; double sum = 0.0; for (int i = 0; i < Math.Abs(timeLagTreeNode.Lag); i++) { row += Math.Sign(timeLagTreeNode.Lag); sum += Evaluate(dataset, ref row, state); state.ProgramCounter = savedPc; } row -= timeLagTreeNode.Lag; sum += Evaluate(dataset, ref row, state); return sum; } //mkommend: derivate calculation taken from: //http://www.holoborodko.com/pavel/numerical-methods/numerical-derivative/smooth-low-noise-differentiators/ //one sided smooth differentiatior, N = 4 // y' = 1/8h (f_i + 2f_i-1, -2 f_i-3 - f_i-4) case OpCodes.Derivative: { int savedPc = state.ProgramCounter; double f_0 = Evaluate(dataset, ref row, state); row--; state.ProgramCounter = savedPc; double f_1 = Evaluate(dataset, ref row, state); row -= 2; state.ProgramCounter = savedPc; double f_3 = Evaluate(dataset, ref row, state); row--; state.ProgramCounter = savedPc; double f_4 = Evaluate(dataset, ref row, state); row += 4; return (f_0 + 2 * f_1 - 2 * f_3 - f_4) / 8; // h = 1 } case OpCodes.Call: { // evaluate sub-trees double[] argValues = new double[currentInstr.nArguments]; for (int i = 0; i < currentInstr.nArguments; i++) { argValues[i] = Evaluate(dataset, ref row, state); } // push on argument values on stack state.CreateStackFrame(argValues); // save the pc int savedPc = state.ProgramCounter; // set pc to start of function state.ProgramCounter = (ushort)currentInstr.iArg0; // evaluate the function double v = Evaluate(dataset, ref row, state); // delete the stack frame state.RemoveStackFrame(); // restore the pc => evaluation will continue at point after my subtrees state.ProgramCounter = savedPc; return v; } case OpCodes.Arg: { return state.GetStackFrameValue((ushort)currentInstr.iArg0); } case OpCodes.Variable: { if (row < 0 || row >= dataset.Rows) return double.NaN; var variableTreeNode = (VariableTreeNode)currentInstr.dynamicNode; return ((IList)currentInstr.iArg0)[row] * variableTreeNode.Weight; } case OpCodes.LagVariable: { var laggedVariableTreeNode = (LaggedVariableTreeNode)currentInstr.dynamicNode; int actualRow = row + laggedVariableTreeNode.Lag; if (actualRow < 0 || actualRow >= dataset.Rows) return double.NaN; return ((IList)currentInstr.iArg0)[actualRow] * laggedVariableTreeNode.Weight; } case OpCodes.Constant: { var constTreeNode = currentInstr.dynamicNode as ConstantTreeNode; return constTreeNode.Value; } //mkommend: this symbol uses the logistic function f(x) = 1 / (1 + e^(-alpha * x) ) //to determine the relative amounts of the true and false branch see http://en.wikipedia.org/wiki/Logistic_function case OpCodes.VariableCondition: { if (row < 0 || row >= dataset.Rows) return double.NaN; var variableConditionTreeNode = (VariableConditionTreeNode)currentInstr.dynamicNode; double variableValue = ((IList)currentInstr.iArg0)[row]; double x = variableValue - variableConditionTreeNode.Threshold; double p = 1 / (1 + Math.Exp(-variableConditionTreeNode.Slope * x)); double trueBranch = Evaluate(dataset, ref row, state); double falseBranch = Evaluate(dataset, ref row, state); return trueBranch * p + falseBranch * (1 - p); } default: throw new NotSupportedException(); } } private byte MapSymbolToOpCode(ISymbolicExpressionTreeNode treeNode) { if (symbolToOpcode.ContainsKey(treeNode.Symbol.GetType())) return symbolToOpcode[treeNode.Symbol.GetType()]; else throw new NotSupportedException("Symbol: " + treeNode.Symbol); } // skips a whole branch private void SkipInstructions(InterpreterState state) { int i = 1; while (i > 0) { i += state.NextInstruction().nArguments; i--; } } } }