1 | <?php |
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2 | /*======================================================================= |
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3 | // File: JPGRAPH_REGSTAT.PHP |
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4 | // Description: Regression and statistical analysis helper classes |
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5 | // Created: 2002-12-01 |
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6 | // Ver: $Id: jpgraph_regstat.php 1131 2009-03-11 20:08:24Z ljp $ |
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7 | // |
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8 | // Copyright (c) Asial Corporation. All rights reserved. |
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9 | //======================================================================== |
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10 | */ |
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11 | |
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12 | //------------------------------------------------------------------------ |
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13 | // CLASS Spline |
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14 | // Create a new data array from an existing data array but with more points. |
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15 | // The new points are interpolated using a cubic spline algorithm |
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16 | //------------------------------------------------------------------------ |
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17 | class Spline { |
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18 | // 3:rd degree polynom approximation |
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19 | |
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20 | private $xdata,$ydata; // Data vectors |
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21 | private $y2; // 2:nd derivate of ydata |
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22 | private $n=0; |
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23 | |
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24 | function __construct($xdata,$ydata) { |
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25 | $this->y2 = array(); |
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26 | $this->xdata = $xdata; |
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27 | $this->ydata = $ydata; |
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28 | |
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29 | $n = count($ydata); |
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30 | $this->n = $n; |
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31 | if( $this->n !== count($xdata) ) { |
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32 | JpGraphError::RaiseL(19001); |
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33 | //('Spline: Number of X and Y coordinates must be the same'); |
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34 | } |
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35 | |
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36 | // Natural spline 2:derivate == 0 at endpoints |
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37 | $this->y2[0] = 0.0; |
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38 | $this->y2[$n-1] = 0.0; |
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39 | $delta[0] = 0.0; |
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40 | |
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41 | // Calculate 2:nd derivate |
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42 | for($i=1; $i < $n-1; ++$i) { |
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43 | $d = ($xdata[$i+1]-$xdata[$i-1]); |
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44 | if( $d == 0 ) { |
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45 | JpGraphError::RaiseL(19002); |
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46 | //('Invalid input data for spline. Two or more consecutive input X-values are equal. Each input X-value must differ since from a mathematical point of view it must be a one-to-one mapping, i.e. each X-value must correspond to exactly one Y-value.'); |
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47 | } |
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48 | $s = ($xdata[$i]-$xdata[$i-1])/$d; |
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49 | $p = $s*$this->y2[$i-1]+2.0; |
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50 | $this->y2[$i] = ($s-1.0)/$p; |
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51 | $delta[$i] = ($ydata[$i+1]-$ydata[$i])/($xdata[$i+1]-$xdata[$i]) - |
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52 | ($ydata[$i]-$ydata[$i-1])/($xdata[$i]-$xdata[$i-1]); |
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53 | $delta[$i] = (6.0*$delta[$i]/($xdata[$i+1]-$xdata[$i-1])-$s*$delta[$i-1])/$p; |
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54 | } |
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55 | |
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56 | // Backward substitution |
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57 | for( $j=$n-2; $j >= 0; --$j ) { |
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58 | $this->y2[$j] = $this->y2[$j]*$this->y2[$j+1] + $delta[$j]; |
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59 | } |
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60 | } |
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61 | |
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62 | // Return the two new data vectors |
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63 | function Get($num=50) { |
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64 | $n = $this->n ; |
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65 | $step = ($this->xdata[$n-1]-$this->xdata[0]) / ($num-1); |
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66 | $xnew=array(); |
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67 | $ynew=array(); |
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68 | $xnew[0] = $this->xdata[0]; |
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69 | $ynew[0] = $this->ydata[0]; |
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70 | for( $j=1; $j < $num; ++$j ) { |
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71 | $xnew[$j] = $xnew[0]+$j*$step; |
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72 | $ynew[$j] = $this->Interpolate($xnew[$j]); |
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73 | } |
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74 | return array($xnew,$ynew); |
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75 | } |
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76 | |
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77 | // Return a single interpolated Y-value from an x value |
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78 | function Interpolate($xpoint) { |
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79 | |
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80 | $max = $this->n-1; |
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81 | $min = 0; |
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82 | |
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83 | // Binary search to find interval |
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84 | while( $max-$min > 1 ) { |
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85 | $k = ($max+$min) / 2; |
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86 | if( $this->xdata[$k] > $xpoint ) |
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87 | $max=$k; |
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88 | else |
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89 | $min=$k; |
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90 | } |
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91 | |
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92 | // Each interval is interpolated by a 3:degree polynom function |
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93 | $h = $this->xdata[$max]-$this->xdata[$min]; |
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94 | |
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95 | if( $h == 0 ) { |
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96 | JpGraphError::RaiseL(19002); |
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97 | //('Invalid input data for spline. Two or more consecutive input X-values are equal. Each input X-value must differ since from a mathematical point of view it must be a one-to-one mapping, i.e. each X-value must correspond to exactly one Y-value.'); |
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98 | } |
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99 | |
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100 | |
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101 | $a = ($this->xdata[$max]-$xpoint)/$h; |
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102 | $b = ($xpoint-$this->xdata[$min])/$h; |
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103 | return $a*$this->ydata[$min]+$b*$this->ydata[$max]+ |
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104 | (($a*$a*$a-$a)*$this->y2[$min]+($b*$b*$b-$b)*$this->y2[$max])*($h*$h)/6.0; |
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105 | } |
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106 | } |
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107 | |
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108 | //------------------------------------------------------------------------ |
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109 | // CLASS Bezier |
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110 | // Create a new data array from a number of control points |
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111 | //------------------------------------------------------------------------ |
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112 | class Bezier { |
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113 | /** |
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114 | * @author Thomas Despoix, openXtrem company |
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115 | * @license released under QPL |
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116 | * @abstract Bezier interoplated point generation, |
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117 | * computed from control points data sets, based on Paul Bourke algorithm : |
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118 | * http://local.wasp.uwa.edu.au/~pbourke/geometry/bezier/index2.html |
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119 | */ |
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120 | private $datax = array(); |
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121 | private $datay = array(); |
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122 | private $n=0; |
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123 | |
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124 | function __construct($datax, $datay, $attraction_factor = 1) { |
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125 | // Adding control point multiple time will raise their attraction power over the curve |
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126 | $this->n = count($datax); |
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127 | if( $this->n !== count($datay) ) { |
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128 | JpGraphError::RaiseL(19003); |
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129 | //('Bezier: Number of X and Y coordinates must be the same'); |
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130 | } |
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131 | $idx=0; |
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132 | foreach($datax as $datumx) { |
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133 | for ($i = 0; $i < $attraction_factor; $i++) { |
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134 | $this->datax[$idx++] = $datumx; |
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135 | } |
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136 | } |
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137 | $idx=0; |
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138 | foreach($datay as $datumy) { |
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139 | for ($i = 0; $i < $attraction_factor; $i++) { |
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140 | $this->datay[$idx++] = $datumy; |
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141 | } |
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142 | } |
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143 | $this->n *= $attraction_factor; |
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144 | } |
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145 | |
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146 | /** |
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147 | * Return a set of data points that specifies the bezier curve with $steps points |
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148 | * @param $steps Number of new points to return |
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149 | * @return array($datax, $datay) |
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150 | */ |
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151 | function Get($steps) { |
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152 | $datax = array(); |
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153 | $datay = array(); |
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154 | for ($i = 0; $i < $steps; $i++) { |
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155 | list($datumx, $datumy) = $this->GetPoint((double) $i / (double) $steps); |
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156 | $datax[$i] = $datumx; |
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157 | $datay[$i] = $datumy; |
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158 | } |
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159 | |
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160 | $datax[] = end($this->datax); |
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161 | $datay[] = end($this->datay); |
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162 | |
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163 | return array($datax, $datay); |
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164 | } |
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165 | |
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166 | /** |
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167 | * Return one point on the bezier curve. $mu is the position on the curve where $mu is in the |
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168 | * range 0 $mu < 1 where 0 is tha start point and 1 is the end point. Note that every newly computed |
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169 | * point depends on all the existing points |
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170 | * |
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171 | * @param $mu Position on the bezier curve |
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172 | * @return array($x, $y) |
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173 | */ |
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174 | function GetPoint($mu) { |
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175 | $n = $this->n - 1; |
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176 | $k = 0; |
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177 | $kn = 0; |
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178 | $nn = 0; |
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179 | $nkn = 0; |
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180 | $blend = 0.0; |
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181 | $newx = 0.0; |
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182 | $newy = 0.0; |
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183 | |
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184 | $muk = 1.0; |
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185 | $munk = (double) pow(1-$mu,(double) $n); |
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186 | |
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187 | for ($k = 0; $k <= $n; $k++) { |
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188 | $nn = $n; |
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189 | $kn = $k; |
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190 | $nkn = $n - $k; |
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191 | $blend = $muk * $munk; |
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192 | $muk *= $mu; |
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193 | $munk /= (1-$mu); |
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194 | while ($nn >= 1) { |
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195 | $blend *= $nn; |
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196 | $nn--; |
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197 | if ($kn > 1) { |
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198 | $blend /= (double) $kn; |
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199 | $kn--; |
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200 | } |
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201 | if ($nkn > 1) { |
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202 | $blend /= (double) $nkn; |
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203 | $nkn--; |
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204 | } |
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205 | } |
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206 | $newx += $this->datax[$k] * $blend; |
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207 | $newy += $this->datay[$k] * $blend; |
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208 | } |
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209 | |
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210 | return array($newx, $newy); |
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211 | } |
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212 | } |
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213 | |
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214 | // EOF |
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215 | ?> |
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