1 | #region License Information
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2 | /* HeuristicLab
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3 | * Copyright (C) 2002-2015 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
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4 | * and the BEACON Center for the Study of Evolution in Action.
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5 | *
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6 | * This file is part of HeuristicLab.
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7 | *
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8 | * HeuristicLab is free software: you can redistribute it and/or modify
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9 | * it under the terms of the GNU General Public License as published by
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10 | * the Free Software Foundation, either version 3 of the License, or
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11 | * (at your option) any later version.
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12 | *
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13 | * HeuristicLab is distributed in the hope that it will be useful,
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14 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
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15 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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16 | * GNU General Public License for more details.
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17 | *
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18 | * You should have received a copy of the GNU General Public License
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19 | * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
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20 | */
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21 | #endregion
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22 | using System;
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23 | using System.Collections.Generic;
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24 | using System.Diagnostics.Contracts;
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25 | using System.Linq;
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26 |
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27 | namespace HeuristicLab.Algorithms.DataAnalysis.MctsSymbolicRegression {
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28 | // evalutes expressions (on vectors)
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29 | internal class ExpressionEvaluator {
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30 | // manages it's own vector buffers
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31 | private readonly List<double[]> vectorBuffers = new List<double[]>();
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32 | private readonly List<double[]> scalarBuffers = new List<double[]>(); // scalars are vectors of length 1 (to allow mixing scalars and vectors on the same stack)
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33 |
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34 |
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35 | private double[] GetVectorBuffer() {
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36 | var v = vectorBuffers[vectorBuffers.Count - 1];
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37 | vectorBuffers.RemoveAt(vectorBuffers.Count - 1);
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38 | return v;
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39 | }
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40 | private double[] GetScalarBuffer() {
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41 | var v = scalarBuffers[scalarBuffers.Count - 1];
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42 | scalarBuffers.RemoveAt(scalarBuffers.Count - 1);
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43 | return v;
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44 | }
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45 |
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46 | private void ReleaseBuffer(double[] buf) {
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47 | (buf.Length == 1 ? scalarBuffers : vectorBuffers).Add(buf);
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48 | }
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49 |
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50 | public const int MaxStackSize = 100;
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51 | public const int MaxParams = 50;
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52 | private readonly int vLen;
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53 | private readonly double lowerEstimationLimit;
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54 | private readonly double upperEstimationLimit;
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55 | private readonly double nanReplacementValue;
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56 |
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57 | private readonly double[][] stack;
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58 | private readonly double[][][] gradientStack;
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59 |
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60 | // preallocate stack and gradient stack
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61 | public ExpressionEvaluator(int vLen, double lowerEstimationLimit = double.MinValue, double upperEstimationLimit = double.MaxValue) {
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62 | if (vLen <= 1) throw new ArgumentException("number of elements in a variable must be > 1", "vlen");
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63 | this.vLen = vLen;
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64 | this.lowerEstimationLimit = lowerEstimationLimit;
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65 | this.upperEstimationLimit = upperEstimationLimit;
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66 | this.nanReplacementValue = (upperEstimationLimit - lowerEstimationLimit) / 2.0 + lowerEstimationLimit;
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67 |
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68 | stack = new double[MaxStackSize][];
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69 | gradientStack = new double[MaxParams][][];
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70 |
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71 | for (int k = 0; k < MaxParams; k++) {
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72 | gradientStack[k] = new double[MaxStackSize][];
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73 | }
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74 |
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75 | // preallocate buffers
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76 | for (int i = 0; i < MaxStackSize; i++) {
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77 | ReleaseBuffer(new double[vLen]);
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78 | ReleaseBuffer(new double[1]);
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79 |
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80 | for (int k = 0; k < MaxParams; k++) {
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81 | ReleaseBuffer(new double[vLen]);
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82 | ReleaseBuffer(new double[1]);
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83 | }
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84 | }
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85 | }
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86 |
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87 | // pred must be allocated by the caller
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88 | // if adjustOffsetForLogAndExp is set to true we determine c in log(c + f(x)) to make sure that c + f(x) is positive
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89 | public void Exec(byte[] code, double[][] vars, double[] consts, double[] pred, bool adjustOffsetForLogAndExp = false) {
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90 | Contract.Assert(pred != null && pred.Length >= vLen);
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91 | int topOfStack = -1;
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92 | int pc = 0;
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93 | int curParamIdx = -1;
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94 | byte op;
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95 | short arg;
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96 | // checked at the end to make sure we do not leak buffers
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97 | int initialScalarCount = scalarBuffers.Count;
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98 | int initialVectorCount = vectorBuffers.Count;
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99 |
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100 | while (true) {
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101 | ReadNext(code, ref pc, out op, out arg);
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102 | switch (op) {
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103 | case (byte)OpCodes.Nop: throw new InvalidProgramException(); // not allowed
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104 | case (byte)OpCodes.LoadConst0: {
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105 | ++topOfStack;
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106 | var z = GetScalarBuffer();
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107 | z[0] = 0;
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108 | stack[topOfStack] = z;
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109 | break;
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110 | }
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111 | case (byte)OpCodes.LoadConst1: {
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112 | ++topOfStack;
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113 | var z = GetScalarBuffer();
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114 | z[0] = 1.0;
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115 | stack[topOfStack] = z;
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116 | break;
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117 | }
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118 | case (byte)OpCodes.LoadParamN: {
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119 | ++topOfStack;
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120 | var c = consts[++curParamIdx];
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121 | var z = GetScalarBuffer();
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122 | z[0] = c;
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123 | stack[topOfStack] = z;
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124 | break;
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125 | }
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126 | case (byte)OpCodes.LoadVar: {
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127 | ++topOfStack;
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128 | var z = GetVectorBuffer();
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129 | Array.Copy(vars[arg], z, vars[arg].Length);
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130 | stack[topOfStack] = z;
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131 | break;
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132 | }
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133 | case (byte)OpCodes.Add: {
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134 | topOfStack--;
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135 | var a = stack[topOfStack + 1];
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136 | var b = stack[topOfStack];
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137 | stack[topOfStack] = Add(a, b);
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138 | ReleaseBuffer(a);
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139 | ReleaseBuffer(b);
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140 | break;
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141 | }
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142 | case (byte)OpCodes.Mul: {
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143 | topOfStack--;
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144 | var a = stack[topOfStack + 1];
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145 | var b = stack[topOfStack];
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146 | stack[topOfStack] = Mul(a, b);
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147 | ReleaseBuffer(a);
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148 | ReleaseBuffer(b);
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149 | break;
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150 | }
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151 | case (byte)OpCodes.Log: {
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152 | if (adjustOffsetForLogAndExp) {
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153 | // here we assume that the last used parameter is c in log(f(x) + c)
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154 | // this must match actions for producing code in the automaton!
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155 |
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156 | // we can easily adjust c to make sure that f(x) + c is positive because at this point we all values for f(x)
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157 | var fxc = stack[topOfStack];
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158 | var minFx = fxc.Min() - consts[curParamIdx]; // stack[topOfStack] is f(x) + c
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159 |
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160 | var delta = 1.0 - minFx - consts[curParamIdx];
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161 | // adjust c so that minFx + c = 1 ... log(minFx + c) = 0
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162 | consts[curParamIdx] += delta;
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163 |
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164 | // also adjust values on stack
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165 | for (int i = 0; i < fxc.Length; i++) fxc[i] += delta;
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166 | }
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167 | var x = stack[topOfStack];
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168 | for (int i = 0; i < x.Length; i++)
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169 | x[i] = Math.Log(x[i]);
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170 | break;
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171 | }
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172 | case (byte)OpCodes.Exp: {
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173 | if (adjustOffsetForLogAndExp) {
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174 | // here we assume that the last used parameter is c in exp(f(x) * c)
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175 | // this must match actions for producing code in the automaton!
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176 |
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177 | // adjust c to make sure that exp(f(x) * c) is not too large
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178 | var fxc = stack[topOfStack];
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179 | var maxFx = fxc.Max() / consts[curParamIdx]; // stack[topOfStack] is f(x) * c
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180 |
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181 | var f = 1.0 / (maxFx * consts[curParamIdx]);
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182 | // adjust c so that maxFx*c = 1
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183 | consts[curParamIdx] *= f;
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184 |
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185 | // also adjust values on stack
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186 | for (int i = 0; i < fxc.Length; i++) fxc[i] *= f;
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187 | }
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188 |
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189 | var x = stack[topOfStack];
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190 | for (int i = 0; i < x.Length; i++)
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191 | x[i] = Math.Exp(x[i]);
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192 | break;
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193 | }
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194 | case (byte)OpCodes.Inv: {
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195 | var x = stack[topOfStack];
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196 | for (int i = 0; i < x.Length; i++)
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197 | x[i] = 1.0 / (x[i]);
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198 | break;
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199 | }
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200 | case (byte)OpCodes.Exit:
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201 | Contract.Assert(topOfStack == 0);
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202 | var r = stack[topOfStack];
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203 | if (r.Length == 1) {
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204 | var v = double.IsNaN(r[0]) ? nanReplacementValue : Math.Min(upperEstimationLimit, Math.Max(lowerEstimationLimit, r[0]));
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205 | for (int i = 0; i < vLen; i++)
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206 | pred[i] = v;
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207 | } else {
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208 | for (int i = 0; i < vLen; i++) {
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209 | var v = double.IsNaN(r[i]) ? nanReplacementValue : Math.Min(upperEstimationLimit, Math.Max(lowerEstimationLimit, r[i]));
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210 | pred[i] = v;
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211 | }
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212 | }
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213 | ReleaseBuffer(r);
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214 | Contract.Assert(vectorBuffers.Count == initialVectorCount);
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215 | Contract.Assert(scalarBuffers.Count == initialScalarCount);
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216 | return;
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217 | }
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218 | }
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219 | }
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220 |
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221 |
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222 | // evaluation with forward autodiff
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223 | // pred and gradients must be allocated by the caller
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224 | public void ExecGradient(byte[] code, double[][] vars, double[] consts, double[] pred, double[][] gradients) {
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225 | Contract.Assert(pred != null && pred.Length >= vLen);
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226 | int topOfStack = -1;
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227 | int pc = 0;
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228 | int curParamIdx = -1;
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229 | byte op;
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230 | short arg;
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231 | int nParams = consts.Length;
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232 | Contract.Assert(gradients != null && gradients.Length >= nParams && gradients.All(g => g.Length >= vLen));
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233 |
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234 | // checked at the end to make sure we do not leak buffers
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235 | int initialScalarCount = scalarBuffers.Count;
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236 | int initialVectorCount = vectorBuffers.Count;
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237 |
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238 | while (true) {
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239 | ReadNext(code, ref pc, out op, out arg);
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240 | switch (op) {
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241 | case (byte)OpCodes.Nop: throw new InvalidProgramException(); // not allowed
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242 | case (byte)OpCodes.LoadConst0: {
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243 | ++topOfStack;
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244 | var z = GetScalarBuffer();
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245 | z[0] = 0;
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246 | stack[topOfStack] = z;
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247 | for (int k = 0; k < nParams; ++k) {
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248 | var b = GetScalarBuffer();
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249 | b[0] = 0.0;
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250 | gradientStack[k][topOfStack] = b;
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251 | }
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252 | break;
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253 | }
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254 | case (byte)OpCodes.LoadConst1: {
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255 | ++topOfStack;
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256 | var z = GetScalarBuffer();
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257 | z[0] = 1.0;
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258 | stack[topOfStack] = z;
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259 | for (int k = 0; k < nParams; ++k) {
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260 | var b = GetScalarBuffer();
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261 | b[0] = 0.0;
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262 | gradientStack[k][topOfStack] = b;
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263 | }
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264 | break;
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265 | }
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266 | case (byte)OpCodes.LoadParamN: {
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267 | var c = consts[++curParamIdx];
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268 | ++topOfStack;
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269 | var z = GetScalarBuffer();
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270 | z[0] = c;
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271 | stack[topOfStack] = z;
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272 | for (int k = 0; k < nParams; ++k) {
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273 | var b = GetScalarBuffer();
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274 | b[0] = k == curParamIdx ? 1.0 : 0.0;
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275 | gradientStack[k][topOfStack] = b;
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276 | }
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277 | break;
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278 | }
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279 | case (byte)OpCodes.LoadVar: {
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280 | ++topOfStack;
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281 | var z = GetVectorBuffer();
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282 | Array.Copy(vars[arg], z, vars[arg].Length);
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283 | stack[topOfStack] = z;
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284 | for (int k = 0; k < nParams; ++k) {
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285 | var b = GetScalarBuffer();
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286 | b[0] = 0.0;
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287 | gradientStack[k][topOfStack] = b;
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288 | }
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289 | }
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290 | break;
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291 | case (byte)OpCodes.Add: {
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292 | topOfStack--;
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293 | var a = stack[topOfStack + 1];
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294 | var b = stack[topOfStack];
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295 | stack[topOfStack] = Add(a, b);
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296 | ReleaseBuffer(a);
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297 | ReleaseBuffer(b);
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298 |
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299 | // same for gradient
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300 | for (int k = 0; k < nParams; ++k) {
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301 | var ag = gradientStack[k][topOfStack + 1];
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302 | var bg = gradientStack[k][topOfStack];
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303 | gradientStack[k][topOfStack] = Add(ag, bg);
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304 | ReleaseBuffer(ag);
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305 | ReleaseBuffer(bg);
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306 | }
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307 | break;
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308 | }
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309 | case (byte)OpCodes.Mul: {
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310 | topOfStack--;
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311 | var a = stack[topOfStack + 1];
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312 | var b = stack[topOfStack];
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313 | stack[topOfStack] = Mul(a, b);
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314 |
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315 | // same for gradient
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316 | // f(x) g(x) f '(x) g(x) + f(x) g'(x)
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317 | for (int k = 0; k < nParams; ++k) {
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318 | var ag = gradientStack[k][topOfStack + 1];
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319 | var bg = gradientStack[k][topOfStack];
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320 | var t1 = Mul(ag, b);
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321 | var t2 = Mul(a, bg);
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322 | gradientStack[k][topOfStack] = Add(t1, t2);
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323 | ReleaseBuffer(ag);
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324 | ReleaseBuffer(bg);
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325 | ReleaseBuffer(t1);
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326 | ReleaseBuffer(t2);
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327 | }
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328 |
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329 | ReleaseBuffer(a);
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330 | ReleaseBuffer(b);
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331 |
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332 | break;
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333 | }
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334 | case (byte)OpCodes.Log: {
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335 | var x = stack[topOfStack];
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336 | // calc gradients first before destroying x
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337 | // log(f(x))' = f(x)'/f(x)
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338 | for (int k = 0; k < nParams; k++) {
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339 | var xg = gradientStack[k][topOfStack];
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340 | gradientStack[k][topOfStack] = Frac(xg, x);
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341 | ReleaseBuffer(xg);
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342 | }
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343 |
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344 | for (int i = 0; i < x.Length; i++)
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345 | x[i] = Math.Log(x[i]);
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346 |
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347 | break;
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348 | }
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349 | case (byte)OpCodes.Exp: {
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350 | var x = stack[topOfStack];
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351 | for (int i = 0; i < x.Length; i++)
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352 | x[i] = Math.Exp(x[i]);
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353 |
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354 | for (int k = 0; k < nParams; k++) {
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355 | var xg = gradientStack[k][topOfStack];
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356 | gradientStack[k][topOfStack] = Mul(x, xg); // e(f(x))' = e(f(x)) * f(x)'
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357 | ReleaseBuffer(xg);
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358 | }
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359 | break;
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360 | }
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361 | case (byte)OpCodes.Inv: {
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362 | var x = stack[topOfStack];
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363 | for (int i = 0; i < x.Length; i++)
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364 | x[i] = 1.0 / x[i];
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365 |
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366 | for (int k = 0; k < nParams; k++) {
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367 | var xg = gradientStack[k][topOfStack];
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368 | // x has already been inverted above
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369 | // (1/f)' = -f' / f²
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370 | var invF = Mul(xg, x);
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371 | gradientStack[k][topOfStack] = Mul(invF, x, factor: -1.0);
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372 | ReleaseBuffer(xg);
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373 | ReleaseBuffer(invF);
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374 | }
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375 | break;
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376 | }
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377 | case (byte)OpCodes.Exit:
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378 | Contract.Assert(topOfStack == 0);
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379 | var r = stack[topOfStack];
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380 | if (r.Length == 1) {
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381 | var v = double.IsNaN(r[0]) ? nanReplacementValue : Math.Min(upperEstimationLimit, Math.Max(lowerEstimationLimit, r[0]));
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382 | for (int i = 0; i < vLen; i++)
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383 | pred[i] = v;
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384 | } else {
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385 | for (int i = 0; i < vLen; i++) {
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386 | var v = double.IsNaN(r[i]) ? nanReplacementValue : Math.Min(upperEstimationLimit, Math.Max(lowerEstimationLimit, r[i]));
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387 | pred[i] = v;
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388 | }
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389 | }
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390 | ReleaseBuffer(r);
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391 |
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392 | // same for gradients
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393 | for (int k = 0; k < nParams; k++) {
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394 | var g = gradientStack[k][topOfStack];
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395 | if (g.Length == 1) {
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396 | for (int i = 0; i < vLen; i++)
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397 | gradients[k][i] = g[0];
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398 | } else
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399 | Array.Copy(g, gradients[k], vLen);
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400 | ReleaseBuffer(g);
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401 | }
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402 |
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403 | Contract.Assert(vectorBuffers.Count == initialVectorCount);
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404 | Contract.Assert(scalarBuffers.Count == initialScalarCount);
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405 | return; // break loop
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406 | }
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407 | }
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408 | }
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409 |
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410 | private double[] Add(double[] a, double[] b) {
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411 | double[] target = null;
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412 | if (a.Length > 1) {
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413 | target = GetVectorBuffer();
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414 | if (b.Length > 1) {
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415 | for (int i = 0; i < vLen; i++)
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416 | target[i] = a[i] + b[i];
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417 | } else {
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418 | // b == scalar
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419 | for (int i = 0; i < vLen; i++)
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420 | target[i] = a[i] + b[0];
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421 | }
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422 | } else {
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423 | // a == scalar
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424 | if (b.Length > 1) {
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425 | target = GetVectorBuffer();
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426 | for (int i = 0; i < vLen; i++)
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427 | target[i] = a[0] + b[i];
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428 | } else {
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429 | // b == scalar
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430 | target = GetScalarBuffer();
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431 | target[0] = a[0] + b[0];
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432 | }
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433 | }
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434 | return target;
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435 | }
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436 |
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437 | private double[] Mul(double[] a, double[] b, double factor = 1.0) {
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438 | double[] target = null;
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439 | if (a.Length > 1) {
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440 | if (b.Length > 1) {
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441 | target = GetVectorBuffer();
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442 | for (int i = 0; i < vLen; i++)
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443 | target[i] = factor * a[i] * b[i];
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444 | } else {
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445 | // b == scalar
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446 | if (Math.Abs(b[0]) < 1E-12 /* == 0 */) {
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447 | target = GetScalarBuffer();
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448 | target[0] = 0.0;
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449 | } else {
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450 | target = GetVectorBuffer();
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451 | for (int i = 0; i < vLen; i++)
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452 | target[i] = factor * a[i] * b[0];
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453 | }
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454 | }
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455 | } else {
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456 | // a == scalar
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457 | if (b.Length > 1) {
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458 | if (Math.Abs(a[0]) < 1E-12 /* == 0 */) {
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459 | target = GetScalarBuffer();
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460 | target[0] = 0.0;
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461 | } else {
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462 | target = GetVectorBuffer();
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463 | for (int i = 0; i < vLen; i++)
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464 | target[i] = factor * a[0] * b[i];
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465 | }
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466 | } else {
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467 | // b == scalar
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468 | target = GetScalarBuffer();
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469 | target[0] = factor * a[0] * b[0];
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470 | }
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471 | }
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472 | return target;
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473 | }
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474 |
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475 | private double[] Frac(double[] a, double[] b) {
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476 | double[] target = null;
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477 | if (a.Length > 1) {
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478 | target = GetVectorBuffer();
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479 | if (b.Length > 1) {
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480 | for (int i = 0; i < vLen; i++)
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481 | target[i] = a[i] / b[i];
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482 | } else {
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483 | // b == scalar
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484 | for (int i = 0; i < vLen; i++)
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485 | target[i] = a[i] / b[0];
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486 | }
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487 | } else {
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488 | // a == scalar
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489 | if (b.Length > 1) {
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490 | if (Math.Abs(a[0]) < 1E-12 /* == 0 */) {
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491 | target = GetScalarBuffer();
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492 | target[0] = 0.0;
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493 | } else {
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494 | target = GetVectorBuffer();
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495 | for (int i = 0; i < vLen; i++)
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496 | target[i] = a[0] / b[i];
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497 | }
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498 | } else {
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499 | // b == scalar
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500 | target = GetScalarBuffer();
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501 | target[0] = a[0] / b[0];
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502 | }
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503 | }
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504 | return target;
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505 | }
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506 |
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507 | private void ReadNext(byte[] code, ref int pc, out byte op, out short s) {
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508 | op = code[pc++];
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509 | s = 0;
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510 | if (op == (byte)OpCodes.LoadVar) {
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511 | s = (short)(((short)code[pc] << 8) | (short)code[pc + 1]);
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512 | pc += 2;
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513 | }
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514 | }
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515 | }
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516 | }
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