1 | #pragma rtGlobals=1 // Use modern global access method. |
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2 | |
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3 | ///////////////////////////////////////////////////// |
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4 | // |
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5 | // Plot's Greg Beaucage's Rg-power Law "model" of scattering |
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6 | // somewhat useful for identifying length scales, but short on |
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7 | // physical inerpretation of the real structure of the sample. |
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8 | // |
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9 | // up to 4 "levels" can be calculated |
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10 | // best to start with single level, and fit a small range of |
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11 | // the data, and add more levels as needed |
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12 | // |
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13 | // see the help file for the original references |
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14 | // |
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15 | Proc PlotBeau_One(num,qmin,qmax) |
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16 | Variable num=256,qmin=0.001,qmax=0.7 |
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17 | Prompt num "Enter number of data points for model: " |
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18 | Prompt qmin "Enter minimum q-value (A^-1) for model: " |
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19 | Prompt qmax "Enter maximum q-value (A^-1) for model: " |
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20 | |
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21 | make/o/d/n=(num) xwave_b1,ywave_b1 |
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22 | xwave_b1 = alog(log(qmin) + x*((log(qmax)-log(qmin))/num)) |
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23 | make/o/d coef_b1 = {1,3,21,6e-4,2,0} |
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24 | make/o/t parameters_b1 = {"scale","G1 (cm-1 sr-1)","Rg1 (A)","B1 (cm-1 sr-1)","Pow1","bkg (cm-1 sr-1)"} |
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25 | Edit parameters_b1,coef_b1 |
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26 | ywave_b1 := OneLevel(coef_b1,xwave_b1) |
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27 | Display ywave_b1 vs xwave_b1 |
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28 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
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29 | Label bottom "q (A\\S-1\\M)" |
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30 | Label left "Intensity (cm\\S-1\\M)" |
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31 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
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32 | End |
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33 | |
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34 | Proc PlotBeau_Two(num,qmin,qmax) |
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35 | Variable num=256,qmin=0.001,qmax=0.7 |
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36 | Prompt num "Enter number of data points for model: " |
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37 | Prompt qmin "Enter minimum q-value (A^-1) for model: " |
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38 | Prompt qmax "Enter maximum q-value (A^-1) for model: " |
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39 | |
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40 | make/o/d/n=(num) xwave_b2,ywave_b2 |
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41 | xwave_b2 = alog(log(qmin) + x*((log(qmax)-log(qmin))/num)) |
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42 | make/o/d coef_b2 = {1,400,200,5e-6,4,3,21,6e-4,2,0} |
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43 | make/o/t parameters_b2 = {"scale","G1 (cm-1 sr-1)","Rg1 (A)","B1 (cm-1 sr-1)","Pow1","G2 (cm-1 sr-1)","Rg2 (A)","B2 (cm-1 sr-1)","Pow2","bkg (cm-1 sr-1)"} |
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44 | Edit parameters_b2,coef_b2 |
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45 | ywave_b2 := TwoLevel(coef_b2,xwave_b2) |
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46 | Display ywave_b2 vs xwave_b2 |
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47 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
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48 | Label bottom "q (A\\S-1\\M)" |
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49 | Label left "Intensity (cm\\S-1\\M)" |
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50 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
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51 | End |
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52 | |
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53 | Proc PlotBeau_Three(num,qmin,qmax) |
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54 | Variable num=256,qmin=0.001,qmax=0.7 |
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55 | Prompt num "Enter number of data points for model: " |
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56 | Prompt qmin "Enter minimum q-value (A^-1) for model: " |
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57 | Prompt qmax "Enter maximum q-value (A^-1) for model: " |
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58 | |
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59 | make/o/d/n=(num) xwave_b3,ywave_b3 |
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60 | xwave_b3 = alog(log(qmin) + x*((log(qmax)-log(qmin))/num)) |
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61 | make/o/d coef_b3 = {1,4000,600,2e-7,4,400,200,5e-6,4,3,21,6e-4,2,0} |
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62 | make/o/t parameters_b3 = {"scale","G1 (cm-1 sr-1)","Rg1 (A)","B1 (cm-1 sr-1)","Pow1","G2 (cm-1 sr-1)","Rg2 (A)","B2 (cm-1 sr-1)","Pow2","G3 (cm-1 sr-1)","Rg3 (A)","B3 (cm-1 sr-1)","Pow3","bkg (cm-1)"} |
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63 | Edit parameters_b3,coef_b3 |
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64 | ywave_b3 := ThreeLevel(coef_b3,xwave_b3) |
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65 | Display ywave_b3 vs xwave_b3 |
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66 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
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67 | Label bottom "q (A\\S-1\\M)" |
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68 | Label left "Intensity (cm\\S-1\\M)" |
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69 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
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70 | End |
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71 | |
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72 | Proc PlotBeau_Four(num,qmin,qmax) |
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73 | Variable num=256,qmin=0.001,qmax=0.7 |
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74 | Prompt num "Enter number of data points for model: " |
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75 | Prompt qmin "Enter minimum q-value (A^-1) for model: " |
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76 | Prompt qmax "Enter maximum q-value (A^-1) for model: " |
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77 | |
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78 | make/o/d/n=(num) xwave_b4,ywave_b4 |
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79 | xwave_b4 = alog(log(qmin) + x*((log(qmax)-log(qmin))/num)) |
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80 | make/o/d coef_b4 = {1,40000,2000,1e-8,4,4000,600,2e-7,4,400,200,5e-6,4,3,21,6e-4,2,0} |
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81 | make/o/t parameters_b4 = {"scale","G1 (cm-1 sr-1)","Rg1 (A)","B1 (cm-1 sr-1)","Pow1","G2 (cm-1 sr-1)","Rg2 (A)","B2 (cm-1 sr-1)","Pow2","G3 (cm-1 sr-1)","Rg3 (A)","B3 (cm-1 sr-1)","Pow3","G4 (cm-1 sr-1)","Rg4 (A)","B4 (cm-1 sr-1)","Pow4","bkg (cm-1)"} |
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82 | Edit parameters_b4,coef_b4 |
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83 | ywave_b4 := FourLevel(coef_b4,xwave_b4) |
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84 | Display ywave_b4 vs xwave_b4 |
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85 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
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86 | Label bottom "q (A\\S-1\\M)" |
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87 | Label left "Intensity (cm\\S-1\\M)" |
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88 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
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89 | End |
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90 | |
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91 | /////////// macros for smeared model calculations |
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92 | |
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93 | Proc PlotSmearedBeau_OneLevel() |
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94 | //no input parameters necessary, it MUST use the experimental q-values |
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95 | // from the experimental data read in from an AVE/QSIG data file |
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96 | If(ResolutionWavesMissing()) //part of GaussUtils |
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97 | Abort |
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98 | endif |
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99 | |
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100 | // Setup parameter table for model function |
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101 | Make/O/D smear_coef_b1 ={1,3,21,6e-4,2,0} |
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102 | make/o/t smear_parameters_b1 = {"scale","G1 (cm-1 sr-1)","Rg1 (A)","B1 (cm-1 sr-1)","Pow1","bkg (cm-1 sr-1)"} |
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103 | Edit smear_parameters_b1,smear_coef_b1 |
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104 | |
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105 | // output smeared intensity wave, dimensions are identical to experimental QSIG values |
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106 | // make extra copy of experimental q-values for easy plotting |
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107 | Duplicate/O $gQvals smeared_b1,smeared_qvals |
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108 | SetScale d,0,0,"1/cm",smeared_b1 |
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109 | |
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110 | smeared_b1 := SmearedOneLevel(smear_coef_b1,$gQvals) |
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111 | Display smeared_b1 vs smeared_qvals |
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112 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
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113 | Label bottom "q (A\\S-1\\M)" |
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114 | Label left "Intensity (cm\\S-1\\M)" |
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115 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
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116 | End |
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117 | |
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118 | Proc PlotSmearedBeau_TwoLevel() |
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119 | //no input parameters necessary, it MUST use the experimental q-values |
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120 | // from the experimental data read in from an AVE/QSIG data file |
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121 | If(ResolutionWavesMissing()) //part of GaussUtils |
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122 | Abort |
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123 | endif |
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124 | |
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125 | // Setup parameter table for model function |
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126 | Make/O/D smear_coef_b2 = {1,400,200,5e-6,4,3,21,6e-4,2,0} |
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127 | make/o/t smear_parameters_b2 = {"scale","G1 (cm-1 sr-1)","Rg1 (A)","B1 (cm-1 sr-1)","Pow1","G2 (cm-1 sr-1)","Rg2 (A)","B2 (cm-1 sr-1)","Pow2","bkg (cm-1 sr-1)"} |
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128 | Edit smear_parameters_b2,smear_coef_b2 |
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129 | |
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130 | // output smeared intensity wave, dimensions are identical to experimental QSIG values |
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131 | // make extra copy of experimental q-values for easy plotting |
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132 | Duplicate/O $gQvals smeared_b2,smeared_qvals |
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133 | SetScale d,0,0,"1/cm",smeared_b2 |
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134 | |
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135 | smeared_b2 := SmearedTwoLevel(smear_coef_b2,$gQvals) |
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136 | Display smeared_b2 vs smeared_qvals |
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137 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
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138 | Label bottom "q (A\\S-1\\M)" |
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139 | Label left "Intensity (cm\\S-1\\M)" |
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140 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
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141 | End |
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142 | |
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143 | Proc PlotSmearedBeau_ThreeLevel() |
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144 | //no input parameters necessary, it MUST use the experimental q-values |
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145 | // from the experimental data read in from an AVE/QSIG data file |
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146 | If(ResolutionWavesMissing()) //part of GaussUtils |
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147 | Abort |
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148 | endif |
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149 | |
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150 | // Setup parameter table for model function |
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151 | Make/O/D smear_coef_b3 = {1,4000,600,2e-7,4,400,200,5e-6,4,3,21,6e-4,2,0} |
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152 | make/o/t smear_parameters_b3 = {"scale","G1 (cm-1 sr-1)","Rg1 (A)","B1 (cm-1 sr-1)","Pow1","G2 (cm-1 sr-1)","Rg2 (A)","B2 (cm-1 sr-1)","Pow2","G3 (cm-1 sr-1)","Rg3 (A)","B3 (cm-1 sr-1)","Pow3","bkg (cm-1)"} |
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153 | Edit smear_parameters_b3,smear_coef_b3 |
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154 | |
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155 | // output smeared intensity wave, dimensions are identical to experimental QSIG values |
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156 | // make extra copy of experimental q-values for easy plotting |
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157 | Duplicate/O $gQvals smeared_b3,smeared_qvals |
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158 | SetScale d,0,0,"1/cm",smeared_b3 |
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159 | |
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160 | smeared_b3 := SmearedThreeLevel(smear_coef_b3,$gQvals) |
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161 | Display smeared_b3 vs smeared_qvals |
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162 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
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163 | Label bottom "q (A\\S-1\\M)" |
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164 | Label left "Intensity (cm\\S-1\\M)" |
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165 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
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166 | End |
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167 | |
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168 | Proc PlotSmearedBeau_FourLevel() |
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169 | //no input parameters necessary, it MUST use the experimental q-values |
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170 | // from the experimental data read in from an AVE/QSIG data file |
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171 | If(ResolutionWavesMissing()) //part of GaussUtils |
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172 | Abort |
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173 | endif |
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174 | |
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175 | // Setup parameter table for model function |
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176 | Make/O/D smear_coef_b4 = {1,40000,2000,1e-8,4,4000,600,2e-7,4,400,200,5e-6,4,3,21,6e-4,2,0} |
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177 | Make/o/t smear_parameters_b4 = {"scale","G1 (cm-1 sr-1)","Rg1 (A)","B1 (cm-1 sr-1)","Pow1","G2 (cm-1 sr-1)","Rg2 (A)","B2 (cm-1 sr-1)","Pow2","G3 (cm-1 sr-1)","Rg3 (A)","B3 (cm-1 sr-1)","Pow3","G4 (cm-1 sr-1)","Rg4 (A)","B4 (cm-1 sr-1)","Pow4","bkg (cm-1)"} |
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178 | Edit smear_parameters_b4,smear_coef_b4 |
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179 | |
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180 | // output smeared intensity wave, dimensions are identical to experimental QSIG values |
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181 | // make extra copy of experimental q-values for easy plotting |
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182 | Duplicate/O $gQvals smeared_b4,smeared_qvals |
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183 | SetScale d,0,0,"1/cm",smeared_b4 |
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184 | |
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185 | smeared_b4 := SmearedFourLevel(smear_coef_b4,$gQvals) |
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186 | Display smeared_b4 vs smeared_qvals |
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187 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
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188 | Label bottom "q (A\\S-1\\M)" |
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189 | Label left "Intensity (cm\\S-1\\M)" |
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190 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
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191 | End |
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192 | |
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193 | //////////Function definitions |
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194 | |
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195 | Function OneLevel(w,x) :FitFunc |
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196 | Wave w |
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197 | Variable x |
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198 | |
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199 | Variable ans,erf1,prec=1e-15 |
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200 | Variable G1,Rg1,B1,Pow1,bkg,scale |
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201 | |
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202 | scale = w[0] |
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203 | G1 = w[1] |
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204 | Rg1 = w[2] |
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205 | B1 = w[3] |
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206 | Pow1 = w[4] |
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207 | bkg = w[5] |
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208 | |
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209 | erf1 = erf( (x*Rg1/sqrt(6)) ,prec) |
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210 | |
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211 | ans = G1*exp(-x*x*Rg1*Rg1/3) |
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212 | ans += B1*(erf1^3/x)^Pow1 |
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213 | ans *= scale |
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214 | ans += bkg |
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215 | |
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216 | Return (ans) |
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217 | End |
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218 | |
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219 | Function TwoLevel(w,x) :FitFunc |
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220 | Wave w |
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221 | Variable x |
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222 | |
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223 | Variable ans,G1,Rg1,B1,G2,Rg2,B2,Pow1,Pow2,bkg |
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224 | Variable erf1,erf2,prec=1e-15,scale |
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225 | |
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226 | //Rsub = Rs |
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227 | scale = w[0] |
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228 | G1 = w[1] //equivalent to I(0) |
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229 | Rg1 = w[2] |
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230 | B1 = w[3] |
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231 | Pow1 = w[4] |
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232 | G2 = w[5] |
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233 | Rg2 = w[6] |
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234 | B2 = w[7] |
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235 | Pow2 = w[8] |
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236 | bkg = w[9] |
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237 | |
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238 | erf1 = erf( (x*Rg1/sqrt(6)) ,prec) |
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239 | erf2 = erf( (x*Rg2/sqrt(6)) ,prec) |
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240 | //Print erf1 |
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241 | |
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242 | ans = G1*exp(-x*x*Rg1*Rg1/3) |
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243 | ans += B1*exp(-x*x*Rg2*Rg2/3)*(erf1^3/x)^Pow1 |
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244 | ans += G2*exp(-x*x*Rg2*Rg2/3) |
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245 | ans += B2*(erf2^3/x)^Pow2 |
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246 | ans *= scale |
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247 | ans += bkg |
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248 | |
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249 | Return(ans) |
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250 | End |
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251 | |
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252 | |
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253 | Function ThreeLevel(w,x) :FitFunc |
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254 | Wave w |
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255 | Variable x |
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256 | |
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257 | Variable ans,G1,Rg1,B1,G2,Rg2,B2,Pow1,Pow2,bkg |
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258 | Variable G3,Rg3,B3,Pow3,erf3 |
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259 | Variable erf1,erf2,prec=1e-15,scale |
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260 | |
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261 | //Rsub = Rs |
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262 | scale = w[0] |
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263 | G1 = w[1] //equivalent to I(0) |
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264 | Rg1 = w[2] |
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265 | B1 = w[3] |
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266 | Pow1 = w[4] |
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267 | G2 = w[5] |
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268 | Rg2 = w[6] |
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269 | B2 = w[7] |
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270 | Pow2 = w[8] |
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271 | G3 = w[9] |
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272 | Rg3 = w[10] |
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273 | B3 = w[11] |
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274 | Pow3 = w[12] |
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275 | bkg = w[13] |
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276 | |
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277 | erf1 = erf( (x*Rg1/sqrt(6)) ,prec) |
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278 | erf2 = erf( (x*Rg2/sqrt(6)) ,prec) |
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279 | erf3 = erf( (x*Rg3/sqrt(6)) ,prec) |
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280 | //Print erf1 |
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281 | |
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282 | ans = G1*exp(-x*x*Rg1*Rg1/3) + B1*exp(-x*x*Rg2*Rg2/3)*(erf1^3/x)^Pow1 |
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283 | ans += G2*exp(-x*x*Rg2*Rg2/3) + B2*exp(-x*x*Rg3*Rg3/3)*(erf2^3/x)^Pow2 |
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284 | ans += G3*exp(-x*x*Rg3*Rg3/3) + B3*(erf3^3/x)^Pow3 |
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285 | ans *= scale |
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286 | ans += bkg |
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287 | |
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288 | Return(ans) |
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289 | End |
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290 | |
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291 | Function FourLevel(w,x) :FitFunc |
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292 | Wave w |
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293 | Variable x |
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294 | |
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295 | Variable ans,G1,Rg1,B1,G2,Rg2,B2,Pow1,Pow2,bkg |
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296 | Variable G3,Rg3,B3,Pow3,erf3 |
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297 | Variable G4,Rg4,B4,Pow4,erf4 |
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298 | Variable erf1,erf2,prec=1e-15,scale |
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299 | |
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300 | //Rsub = Rs |
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301 | scale = w[0] |
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302 | G1 = w[1] //equivalent to I(0) |
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303 | Rg1 = w[2] |
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304 | B1 = w[3] |
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305 | Pow1 = w[4] |
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306 | G2 = w[5] |
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307 | Rg2 = w[6] |
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308 | B2 = w[7] |
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309 | Pow2 = w[8] |
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310 | G3 = w[9] |
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311 | Rg3 = w[10] |
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312 | B3 = w[11] |
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313 | Pow3 = w[12] |
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314 | G4 = w[13] |
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315 | Rg4 = w[14] |
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316 | B4 = w[15] |
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317 | Pow4 = w[16] |
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318 | bkg = w[17] |
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319 | |
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320 | erf1 = erf( (x*Rg1/sqrt(6)) ,prec) |
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321 | erf2 = erf( (x*Rg2/sqrt(6)) ,prec) |
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322 | erf3 = erf( (x*Rg3/sqrt(6)) ,prec) |
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323 | erf4 = erf( (x*Rg4/sqrt(6)) ,prec) |
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324 | |
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325 | ans = G1*exp(-x*x*Rg1*Rg1/3) + B1*exp(-x*x*Rg2*Rg2/3)*(erf1^3/x)^Pow1 |
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326 | ans += G2*exp(-x*x*Rg2*Rg2/3) + B2*exp(-x*x*Rg3*Rg3/3)*(erf2^3/x)^Pow2 |
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327 | ans += G3*exp(-x*x*Rg3*Rg3/3) + B3*exp(-x*x*Rg4*Rg4/3)*(erf3^3/x)^Pow3 |
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328 | ans += G4*exp(-x*x*Rg4*Rg4/3) + B4*(erf4^3/x)^Pow4 |
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329 | ans *= scale |
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330 | ans += bkg |
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331 | |
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332 | Return(ans) |
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333 | End |
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334 | |
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335 | Function SmearedOneLevel(w,x) :FitFunc |
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336 | Wave w |
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337 | Variable x |
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338 | |
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339 | // Variable timer=StartMSTimer |
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340 | Variable ans |
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341 | SVAR sq = gSig_Q |
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342 | SVAR qb = gQ_bar |
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343 | SVAR sh = gShadow |
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344 | SVAR gQ = gQVals |
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345 | |
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346 | ans = Smear_Model_20(OneLevel,$sq,$qb,$sh,$gQ,w,x) |
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347 | |
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348 | // Print "HS elapsed time(s) = ",StopMSTimer(timer)*1e-6 |
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349 | return(ans) |
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350 | End |
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351 | |
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352 | Function SmearedTwoLevel(w,x) :FitFunc |
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353 | Wave w |
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354 | Variable x |
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355 | |
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356 | Variable ans |
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357 | SVAR sq = gSig_Q |
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358 | SVAR qb = gQ_bar |
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359 | SVAR sh = gShadow |
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360 | SVAR gQ = gQVals |
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361 | |
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362 | ans = Smear_Model_20(TwoLevel,$sq,$qb,$sh,$gQ,w,x) |
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363 | |
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364 | return(ans) |
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365 | End |
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366 | |
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367 | Function SmearedThreeLevel(w,x) :FitFunc |
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368 | Wave w |
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369 | Variable x |
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370 | |
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371 | Variable ans |
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372 | SVAR sq = gSig_Q |
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373 | SVAR qb = gQ_bar |
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374 | SVAR sh = gShadow |
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375 | SVAR gQ = gQVals |
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376 | |
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377 | ans = Smear_Model_20(ThreeLevel,$sq,$qb,$sh,$gQ,w,x) |
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378 | |
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379 | return(ans) |
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380 | End |
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381 | |
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382 | Function SmearedFourLevel(w,x) :FitFunc |
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383 | Wave w |
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384 | Variable x |
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385 | |
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386 | Variable ans |
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387 | SVAR sq = gSig_Q |
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388 | SVAR qb = gQ_bar |
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389 | SVAR sh = gShadow |
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390 | SVAR gQ = gQVals |
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391 | |
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392 | ans = Smear_Model_20(FourLevel,$sq,$qb,$sh,$gQ,w,x) |
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393 | |
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394 | return(ans) |
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395 | End |
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