1 | /**********************************************************
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2 | *
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3 | * BiCubicSpline.java
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4 | *
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5 | * Class for performing an interpolation on the tabulated
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6 | * function y = f(x1,x2) using a natural bicubic spline
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7 | * Assumes second derivatives at end points = 0 (natural spine)
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8 | *
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9 | * See BiCubicSplineFast.java for a faster running version
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10 | * (http://www.ee.ucl.ac.uk/~mflanaga/java/BiCubicSplineFast.html)
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11 | *
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12 | * WRITTEN BY: Dr Michael Thomas Flanagan
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13 | *
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14 | * DATE: May 2002
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15 | * UPDATE: 20 May 2003, 17 February 2006, 27 July 2007, 4 December 2007, 21 September 2008, 31 October 2009, 5 January 2011
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16 | *
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17 | * DOCUMENTATION:
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18 | * See Michael Thomas Flanagan's Java library on-line web page:
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19 | * http://www.ee.ucl.ac.uk/~mflanaga/java/BiCubicSpline.html
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20 | * http://www.ee.ucl.ac.uk/~mflanaga/java/
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21 | *
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22 | * Copyright (c) 2003 - 2011 Michael Thomas Flanagan
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23 | *
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24 | * PERMISSION TO COPY:
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25 | *
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26 | * Permission to use, copy and modify this software and its documentation for NON-COMMERCIAL purposes is granted, without fee,
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27 | * provided that an acknowledgement to the author, Dr Michael Thomas Flanagan at www.ee.ucl.ac.uk/~mflanaga, appears in all copies
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28 | * and associated documentation or publications.
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29 | *
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30 | * Redistributions of the source code of this source code, or parts of the source codes, must retain the above copyright notice, this list of conditions
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31 | * and the following disclaimer and requires written permission from the Michael Thomas Flanagan:
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32 | *
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33 | * Redistribution in binary form of all or parts of this class must reproduce the above copyright notice, this list of conditions and
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34 | * the following disclaimer in the documentation and/or other materials provided with the distribution and requires written permission from the Michael Thomas Flanagan:
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35 | *
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36 | * Dr Michael Thomas Flanagan makes no representations about the suitability or fitness of the software for any or for a particular purpose.
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37 | * Dr Michael Thomas Flanagan shall not be liable for any damages suffered as a result of using, modifying or distributing this software
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38 | * or its derivatives.
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39 | *
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40 | ***************************************************************************************/
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41 |
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42 | package agents.anac.y2015.agentBuyogV2.flanagan.interpolation;
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43 |
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44 | import agents.anac.y2015.agentBuyogV2.flanagan.math.Fmath;
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45 |
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46 | public class BiCubicSpline{
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47 |
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48 | private int nPoints = 0; // no. of x1 tabulated points
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49 | private int mPoints = 0; // no. of x2 tabulated points
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50 | private int nPointsT = 0; // no. of transposed x1 tabulated points
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51 | private int mPointsT = 0; // no. of transposed x2 tabulated points
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52 | private double[][] y = null; // y=f(x1,x2) tabulated function
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53 | private double[][] yT = null; // transposed y=f(x1,x2) tabulated function, i.e. y=f(x2,x1)
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54 | private double[] x1 = null; // x1 in tabulated function f(x1,x2)
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55 | private double[] x2 = null; // x2 in tabulated function f(x1,x2)
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56 | private double xx1 = Double.NaN; // value of x1 at which an interpolated y value is required
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57 | private double xx2 = Double.NaN; // value of x2 at which an interpolated y value is required
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58 | private double[] xMin = new double[2]; // minimum values of x1 and x2
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59 | private double[] xMax = new double[2]; // maximum values of x1 and x2
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60 | private double[][] d2ydx2inner = null; // second derivatives of first called array of cubic splines
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61 | private double[][] d2ydx2innerT = null; // second derivatives of first called transposed array of cubic splines
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62 | private CubicSpline csn[] = null; // nPoints array of CubicSpline instances
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63 | private CubicSpline csm = null; // CubicSpline instance
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64 | private CubicSpline csnT[] = null; // mPoints array of transposed CubicSpline instances
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65 | private CubicSpline csmT = null; // transposed CubicSpline instance
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66 | private double interpolatedValue = Double.NaN; // interpolated value for the original 2D matrix
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67 | private double interpolatedValueTranspose = Double.NaN; // interpolated value for the transposed 2D matrix
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68 | private double interpolatedValueMean = Double.NaN; // mean interpolated value
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69 | private boolean derivCalculated = false; // = true when the first called cubic spline derivatives have been calculated
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70 | private boolean averageIdenticalAbscissae = false; // if true: the the ordinate values for identical abscissae are averaged
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71 | // If false: the abscissae values are separated by 0.001 of the total abscissae range;
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72 | private static double potentialRoundingError = 5e-15; // potential rounding error used in checking wheter a value lies within the interpolation bounds (static value)
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73 | private static boolean roundingCheck = true; // = true: points outside the interpolation bounds by less than the potential rounding error rounded to the bounds limit (static value)
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74 |
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75 |
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76 | // Constructor
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77 | // Constructor with data arrays initialised to arrays x and y
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78 | public BiCubicSpline(double[] x1, double[] x2, double[][] y){
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79 | this.nPoints=x1.length;
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80 | this.mPoints=x2.length;
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81 | this.nPointsT=this.mPoints;
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82 | this.mPointsT=this.nPoints;
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83 | if(this.nPoints!=y.length)throw new IllegalArgumentException("Arrays x1 and y-row are of different length " + this.nPoints + " " + y.length);
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84 | if(this.mPoints!=y[0].length)throw new IllegalArgumentException("Arrays x2 and y-column are of different length "+ this.mPoints + " " + y[0].length);
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85 | if(this.nPoints<3 || this.mPoints<3)throw new IllegalArgumentException("The data matrix must have a minimum size of 3 X 3");
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86 |
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87 | this.csm = new CubicSpline(this.nPoints);
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88 | this.csn = CubicSpline.oneDarray(this.nPoints, this.mPoints);
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89 | this.csmT = new CubicSpline(this.mPoints);
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90 | this.csnT = CubicSpline.oneDarray(this.nPointsT, this.mPointsT);
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91 | this.x1 = new double[this.nPoints];
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92 | this.x2 = new double[this.mPoints];
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93 | this.y = new double[this.nPoints][this.mPoints];
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94 | this.yT = new double[this.nPointsT][this.mPointsT];
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95 | this.d2ydx2inner = new double[this.nPoints][this.mPoints];
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96 | this.d2ydx2innerT = new double[this.nPointsT][this.mPointsT];
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97 | for(int i=0; i<this.nPoints; i++){
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98 | this.x1[i]=x1[i];
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99 | }
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100 | this.xMin[0] = Fmath.minimum(this.x1);
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101 | this.xMax[0] = Fmath.maximum(this.x1);
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102 | for(int j=0; j<this.mPoints; j++){
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103 | this.x2[j]=x2[j];
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104 | }
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105 | this.xMin[1] = Fmath.minimum(this.x2);
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106 | this.xMax[1] = Fmath.maximum(this.x2);
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107 | for(int i =0; i<this.nPoints; i++){
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108 | for(int j=0; j<this.mPoints; j++){
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109 | this.y[i][j]=y[i][j];
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110 | }
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111 | }
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112 | for(int i =0; i<this.nPointsT; i++){
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113 | for(int j=0; j<this.mPointsT; j++){
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114 | this.yT[i][j]=y[j][i];
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115 | }
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116 | }
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117 |
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118 | double[] yTempn = new double[mPoints];
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119 | for(int i=0; i<this.nPoints; i++){
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120 | for(int j=0; j<mPoints; j++)yTempn[j]=y[i][j];
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121 | this.csn[i].resetData(x2,yTempn);
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122 | this.csn[i].calcDeriv();
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123 | this.d2ydx2inner[i]=this.csn[i].getDeriv();
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124 | }
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125 |
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126 | double[] yTempnT = new double[mPointsT];
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127 | for(int i=0; i<this.nPointsT; i++){
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128 | for(int j=0; j<mPointsT; j++)yTempnT[j]=yT[i][j];
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129 | this.csnT[i].resetData(x1,yTempnT);
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130 | this.csnT[i].calcDeriv();
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131 | this.d2ydx2innerT[i]=this.csnT[i].getDeriv();
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132 | }
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133 | this.derivCalculated = true;
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134 | }
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135 |
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136 | // Constructor with data arrays initialised to zero
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137 | // Primarily for use by TriCubicSpline
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138 | public BiCubicSpline(int nP, int mP){
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139 | this.nPoints=nP;
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140 | this.mPoints=mP;
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141 | if(this.nPoints<3 || this.mPoints<3)throw new IllegalArgumentException("The data matrix must have a minimum size of 3 X 3");
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142 | this.nPointsT=mP;
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143 | this.mPointsT=nP;
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144 | this.csm = new CubicSpline(this.nPoints);
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145 | this.csmT = new CubicSpline(this.nPointsT);
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146 | if(!this.roundingCheck)this.csm.noRoundingErrorCheck();
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147 |
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148 | this.csn = CubicSpline.oneDarray(this.nPoints, this.mPoints);
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149 | this.csnT = CubicSpline.oneDarray(this.nPointsT, this.mPointsT);
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150 |
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151 | this.x1 = new double[this.nPoints];
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152 | this.x2 = new double[this.mPoints];
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153 | this.y = new double[this.nPoints][this.mPoints];
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154 | this.yT = new double[this.nPointsT][this.mPointsT];
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155 | this.d2ydx2inner = new double[this.nPoints][this.mPoints];
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156 | this.d2ydx2innerT = new double[this.nPointsT][this.mPointsT];
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157 |
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158 | }
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159 |
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160 | // METHODS
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161 |
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162 | // Reset rounding error check option
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163 | // Default option: points outside the interpolation bounds by less than the potential rounding error rounded to the bounds limit
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164 | // This method causes this check to be ignored and an exception to be thrown if any point lies outside the interpolation bounds
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165 | public static void noRoundingErrorCheck(){
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166 | BiCubicSpline.roundingCheck = false;
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167 | CubicSpline.noRoundingErrorCheck();
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168 | }
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169 |
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170 | // Reset potential rounding error value
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171 | // Default option: points outside the interpolation bounds by less than the potential rounding error rounded to the bounds limit
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172 | // The default value for the potential rounding error is 5e-15*times the 10^exponent of the value outside the bounds
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173 | // This method allows the 5e-15 to be reset
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174 | public static void potentialRoundingError(double potentialRoundingError){
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175 | BiCubicSpline.potentialRoundingError = potentialRoundingError;
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176 | CubicSpline.potentialRoundingError(potentialRoundingError);
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177 | }
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178 |
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179 | // Reset the default handing of identical abscissae with different ordinates
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180 | // from the default option of separating the two relevant abscissae by 0.001 of the range
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181 | // to avraging the relevant ordinates
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182 | public void averageIdenticalAbscissae(){
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183 | this.averageIdenticalAbscissae = true;
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184 | for(int i=0; i<this.csn.length; i++)this.csn[i].averageIdenticalAbscissae();
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185 | this.csm.averageIdenticalAbscissae();
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186 | }
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187 |
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188 | // Resets the x1, x2, y data arrays
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189 | // Primarily for use in TiCubicSpline
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190 | public void resetData(double[] x1, double[] x2, double[][] y){
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191 | if(x1.length!=y.length)throw new IllegalArgumentException("Arrays x1 and y row are of different length");
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192 | if(x2.length!=y[0].length)throw new IllegalArgumentException("Arrays x2 and y column are of different length");
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193 | if(this.nPoints!=x1.length)throw new IllegalArgumentException("Original array length not matched by new array length");
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194 | if(this.mPoints!=x2.length)throw new IllegalArgumentException("Original array length not matched by new array length");
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195 |
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196 | for(int i=0; i<this.nPoints; i++){
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197 | this.x1[i]=x1[i];
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198 | }
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199 |
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200 | for(int i=0; i<this.mPoints; i++){
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201 | this.x2[i]=x2[i];
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202 | }
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203 |
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204 | for(int i=0; i<this.nPoints; i++){
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205 | for(int j=0; j<this.mPoints; j++){
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206 | this.y[i][j]=y[i][j];
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207 | this.yT[j][i]=y[i][j];
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208 | }
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209 | }
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210 |
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211 | this.csm = new CubicSpline(this.nPoints);
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212 | this.csn = CubicSpline.oneDarray(this.nPoints, this.mPoints);
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213 | double[] yTempn = new double[mPoints];
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214 |
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215 | for(int i=0; i<this.nPoints; i++){
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216 | for(int j=0; j<mPoints; j++)yTempn[j]=y[i][j];
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217 | this.csn[i].resetData(x2,yTempn);
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218 | this.csn[i].calcDeriv();
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219 | this.d2ydx2inner[i]=this.csn[i].getDeriv();
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220 | }
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221 |
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222 | this.csmT = new CubicSpline(this.nPointsT);
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223 | this.csnT = CubicSpline.oneDarray(this.nPointsT, this.mPointsT);
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224 | double[] yTempnT = new double[mPointsT];
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225 |
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226 | for(int i=0; i<this.nPointsT; i++){
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227 | for(int j=0; j<mPointsT; j++)yTempnT[j]=yT[i][j];
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228 | this.csnT[i].resetData(x1,yTempnT);
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229 | this.csnT[i].calcDeriv();
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230 | this.d2ydx2innerT[i]=this.csnT[i].getDeriv();
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231 | }
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232 |
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233 | this.derivCalculated = true;
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234 |
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235 | }
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236 |
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237 | // Returns a new BiCubicSpline setting internal array size to nP x mP and all array values to zero with natural spline default
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238 | // Primarily for use in this.oneDarray for TiCubicSpline
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239 | public static BiCubicSpline zero(int nP, int mP){
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240 | if(nP<3 || mP<3)throw new IllegalArgumentException("A minimum of three x three data points is needed");
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241 | BiCubicSpline aa = new BiCubicSpline(nP, mP);
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242 | return aa;
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243 | }
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244 |
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245 | // Create a one dimensional array of BiCubicSpline objects of length nP each of internal array size mP x lP
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246 | // Primarily for use in TriCubicSpline
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247 | public static BiCubicSpline[] oneDarray(int nP, int mP, int lP){
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248 | if(mP<3 || lP<3)throw new IllegalArgumentException("A minimum of three x three data points is needed");
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249 | BiCubicSpline[] a =new BiCubicSpline[nP];
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250 | for(int i=0; i<nP; i++){
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251 | a[i]=BiCubicSpline.zero(mP, lP);
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252 | }
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253 | return a;
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254 | }
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255 |
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256 |
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257 | // Get inner matrix of derivatives
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258 | // Primarily used by TriCubicSpline
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259 | public double[][] getDeriv(){
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260 | return this.d2ydx2inner;
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261 | }
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262 |
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263 | // Get inner matrix of transpose derivatives
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264 | // Primarily used by TriCubicSpline
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265 | public double[][] getDerivTranspose(){
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266 | return this.d2ydx2innerT;
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267 | }
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268 |
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269 |
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270 | // Get minimum limits
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271 | public double[] getXmin(){
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272 | return this.xMin;
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273 | }
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274 |
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275 | // Get maximum limits
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276 | public double[] getXmax(){
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277 | return this.xMax;
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278 | }
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279 |
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280 | // Get limits to x
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281 | public double[] getLimits(){
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282 | double[] limits = {xMin[0], xMax[0], xMin[1], xMax[1]};
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283 | return limits;
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284 | }
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285 |
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286 | // Display limits to x
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287 | public void displayLimits(){
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288 | System.out.println(" ");
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289 | for(int i=0; i<2; i++){
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290 | System.out.println("The limits to the x array " + i + " are " + xMin[i] + " and " + xMax[i]);
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291 | }
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292 | System.out.println(" ");
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293 | }
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294 |
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295 | // Set inner matrix of derivatives
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296 | // Primarily used by TriCubicSpline
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297 | public void setDeriv(double[][] d2ydx2){
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298 | this.d2ydx2inner = d2ydx2;
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299 | this.derivCalculated = true;
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300 | }
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301 |
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302 | // Set inner matrix of transpose derivatives
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303 | // Primarily used by TriCubicSpline
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304 | public void setDerivTranspose(double[][] d2ydx2){
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305 | this.d2ydx2innerT = d2ydx2;
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306 | this.derivCalculated = true;
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307 | }
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308 |
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309 | // Returns an interpolated value of y for a value of x
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310 | // from a tabulated function y=f(x1,x2)
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311 | public double interpolate(double xx1, double xx2){
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312 |
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313 | this.xx1 = xx1;
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314 | this.xx2 = xx2;
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315 |
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316 | double[] yTempm = new double[this.nPoints];
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317 |
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318 | for (int i=0;i<this.nPoints;i++){
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319 | yTempm[i]=this.csn[i].interpolate(xx2);
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320 | }
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321 | this.csm.resetData(x1,yTempm);
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322 | this.interpolatedValue = this.csm.interpolate(xx1);
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323 |
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324 | double[] yTempmT = new double[this.nPointsT];
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325 |
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326 | for (int i=0;i<this.nPointsT;i++){
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327 | yTempmT[i]=this.csnT[i].interpolate(xx1);
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328 | }
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329 | this.csmT.resetData(x2,yTempmT);
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330 | this.interpolatedValueTranspose = this.csmT.interpolate(xx2);
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331 |
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332 | this.interpolatedValueMean = (this.interpolatedValue + this.interpolatedValueTranspose)/2.0;
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333 | return this.interpolatedValueMean;
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334 | }
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335 |
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336 | // Returns mean interpolated value, interpolated value for data as entered, interpolated value for transposed matrix, xx1 value and xx2 value
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337 | public double[] getInterpolatedValues(){
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338 | double[] ret = {this.interpolatedValueMean, this.interpolatedValue, this.interpolatedValueTranspose, this.xx1, this.xx2};
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339 | return ret;
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340 | }
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341 |
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342 |
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343 |
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344 | }
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345 |
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