1 | #pragma rtGlobals=1 // Use modern global access method. |
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2 | #pragma IgorVersion=6.1 |
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3 | |
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4 | |
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5 | // plots the form factor of spheres with a Gaussian radius distribution |
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6 | // and a fuzzy surface |
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7 | // |
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8 | // M. Stieger, J. S. Pedersen, P. Lindner, W. Richtering, Langmuir 20 (2004) 7283-7292. |
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9 | // M. Stieger, W. Richtering, J. S. Pedersen, P. Lindner, Journal of Chemical Physics 120(13) (2004) 6197-6206. |
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10 | // |
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11 | // potentially a lorentzian could be added to the high Q, if absolutely necessary |
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12 | // |
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13 | // SRK JUL 2009 |
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14 | // |
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15 | // Include lorentzian term for *high* Q component of the scattering, calculate here, removing the #include |
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16 | // |
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17 | // AJJ Feb 2010 |
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18 | |
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19 | //#include "Lorentz_model_v40" |
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20 | |
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21 | Proc PlotFuzzySpheres(num,qmin,qmax) |
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22 | Variable num=128,qmin=0.001,qmax=0.7 |
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23 | Prompt num "Enter number of data points for model: " |
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24 | Prompt qmin "Enter minimum q-value (A^-1) for model: " |
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25 | Prompt qmax "Enter maximum q-value (A^-1) for model: " |
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26 | |
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27 | Make/O/D/N=(num) xwave_fuzz,ywave_fuzz |
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28 | xwave_fuzz = alog( log(qmin) + x*((log(qmax)-log(qmin))/num) ) |
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29 | Make/O/D coef_fuzz = {0.01,60,0.2,10,1e-6,3e-6,1,50,0.001} |
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30 | make/O/T parameters_fuzz = {"Volume Fraction (scale)","mean radius (A)","polydisp (sig/avg)","interface thickness (A)","SLD sphere (A-2)","SLD solvent (A-2)","Lorentz Scale","Lorentz length (A)","bkg (cm-1 sr-1)"} |
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31 | Edit parameters_fuzz,coef_fuzz |
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32 | |
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33 | Variable/G root:g_fuzz |
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34 | g_fuzz := FuzzySpheres(coef_fuzz,ywave_fuzz,xwave_fuzz) |
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35 | Display ywave_fuzz vs xwave_fuzz |
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36 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
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37 | Label bottom "q (A\\S-1\\M)" |
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38 | Label left "Intensity (cm\\S-1\\M)" |
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39 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
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40 | |
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41 | AddModelToStrings("FuzzySpheres","coef_fuzz","parameters_fuzz","fuzz") |
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42 | End |
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43 | |
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44 | // - sets up a dependency to a wrapper, not the actual SmearedModelFunction |
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45 | Proc PlotSmearedFuzzySpheres(str) |
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46 | String str |
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47 | Prompt str,"Pick the data folder containing the resolution you want",popup,getAList(4) |
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48 | |
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49 | // if any of the resolution waves are missing => abort |
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50 | if(ResolutionWavesMissingDF(str)) //updated to NOT use global strings (in GaussUtils) |
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51 | Abort |
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52 | endif |
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53 | |
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54 | SetDataFolder $("root:"+str) |
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55 | |
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56 | // Setup parameter table for model function |
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57 | Make/O/D smear_coef_fuzz = {0.01,60,0.2,10,1e-6,3e-6,1,50,0.001} |
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58 | make/o/t smear_parameters_fuzz = {"Volume Fraction (scale)","mean radius (A)","polydisp (sig/avg)","interface thickness (A)","SLD sphere (A-2)","SLD solvent (A-2)","Lorentz Scale","Lorentz length (A)","bkg (cm-1 sr-1)"} |
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59 | Edit smear_parameters_fuzz,smear_coef_fuzz |
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60 | |
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61 | // output smeared intensity wave, dimensions are identical to experimental QSIG values |
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62 | // make extra copy of experimental q-values for easy plotting |
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63 | Duplicate/O $(str+"_q") smeared_fuzz,smeared_qvals |
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64 | SetScale d,0,0,"1/cm",smeared_fuzz |
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65 | |
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66 | Variable/G gs_fuzz=0 |
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67 | gs_fuzz := fSmearedFuzzySpheres(smear_coef_fuzz,smeared_fuzz,smeared_qvals) //this wrapper fills the STRUCT |
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68 | |
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69 | Display smeared_fuzz vs smeared_qvals |
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70 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
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71 | Label bottom "q (A\\S-1\\M)" |
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72 | Label left "Intensity (cm\\S-1\\M)" |
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73 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
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74 | |
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75 | SetDataFolder root: |
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76 | AddModelToStrings("SmearedFuzzySpheres","smear_coef_fuzz","smear_parameters_fuzz","fuzz") |
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77 | End |
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78 | |
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79 | |
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80 | |
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81 | |
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82 | //AAO version, uses XOP if available |
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83 | // simply calls the original single point calculation with |
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84 | // a wave assignment (this will behave nicely if given point ranges) |
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85 | Function FuzzySpheres(cw,yw,xw) : FitFunc |
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86 | Wave cw,yw,xw |
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87 | |
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88 | #if exists("FuzzySpheresX") |
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89 | yw = FuzzySpheresX(cw,xw) |
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90 | #else |
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91 | yw = fFuzzySpheres(cw,xw) |
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92 | #endif |
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93 | return(0) |
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94 | End |
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95 | |
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96 | Function fFuzzySpheres(w,xx) : FitFunc |
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97 | wave w |
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98 | variable xx |
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99 | |
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100 | Variable scale,rad,pd,sig,rho,rhos,bkg,delrho,sig_surf,lor_sf,lor_len |
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101 | Variable I0, L |
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102 | I0 = w[0] |
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103 | L = w[1] |
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104 | |
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105 | //set up the coefficient values |
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106 | scale=w[0] |
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107 | rad=w[1] |
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108 | pd=w[2] |
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109 | sig=pd*rad |
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110 | sig_surf = w[3] |
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111 | rho=w[4] |
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112 | rhos=w[5] |
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113 | delrho=rho-rhos |
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114 | I0 = w[6] //for the Lorentzian |
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115 | L = w[7] |
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116 | bkg=w[8] |
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117 | |
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118 | |
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119 | //could use 5 pt quadrature to integrate over the size distribution, since it's a gaussian |
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120 | //currently using 20 pts... |
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121 | Variable va,vb,ii,zi,nord,yy,summ,inten |
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122 | Variable bes,f,vol,f2 |
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123 | String weightStr,zStr |
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124 | |
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125 | //select number of gauss points by setting nord=20 or76 points |
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126 | nord = 20 |
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127 | // nord = 76 |
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128 | |
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129 | weightStr = "gauss"+num2str(nord)+"wt" |
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130 | zStr = "gauss"+num2str(nord)+"z" |
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131 | |
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132 | if (WaveExists($weightStr) == 0) // wave reference is not valid, |
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133 | Make/D/N=(nord) $weightStr,$zStr |
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134 | Wave gauWt = $weightStr |
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135 | Wave gauZ = $zStr // wave references to pass |
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136 | if(nord==20) |
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137 | Make20GaussPoints(gauWt,gauZ) |
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138 | else |
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139 | Make76GaussPoints(gauWt,gauZ) |
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140 | endif |
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141 | else |
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142 | if(exists(weightStr) > 1) |
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143 | Abort "wave name is already in use" //executed only if name is in use elsewhere |
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144 | endif |
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145 | Wave gauWt = $weightStr |
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146 | Wave gauZ = $zStr // create the wave references |
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147 | endif |
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148 | |
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149 | // end points of integration |
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150 | // limits are technically 0-inf, but wisely choose interesting region of q where R() is nonzero |
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151 | // +/- 3 sigq catches 99.73% of distrubution |
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152 | // change limits (and spacing of zi) at each evaluation based on R() |
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153 | //integration from va to vb |
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154 | va = -4*sig + rad |
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155 | if (va<0) |
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156 | va=0 //to avoid numerical error when va<0 (-ve q-value) |
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157 | endif |
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158 | vb = 4*sig +rad |
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159 | |
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160 | summ = 0.0 // initialize integral |
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161 | for(ii=0;ii<nord;ii+=1) |
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162 | // calculate Gauss points on integration interval (r-value for evaluation) |
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163 | zi = ( gauZ[ii]*(vb-va) + vb + va )/2.0 |
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164 | |
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165 | // calculate sphere scattering |
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166 | // |
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167 | //handle q==0 separately |
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168 | If(xx==0) |
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169 | f2 = 4/3*pi*zi^3*delrho*delrho*1e8 |
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170 | f2 *= exp(-0.5*sig_surf*sig_surf*xx*xx) |
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171 | f2 *= exp(-0.5*sig_surf*sig_surf*xx*xx) |
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172 | else |
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173 | bes = 3*(sin(xx*zi)-xx*zi*cos(xx*zi))/xx^3/zi^3 |
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174 | vol = 4*pi/3*zi^3 |
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175 | f = vol*bes*delrho // [=] A |
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176 | f *= exp(-0.5*sig_surf*sig_surf*xx*xx) |
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177 | // normalize to single particle volume, convert to 1/cm |
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178 | f2 = f * f / vol * 1.0e8 // [=] 1/cm |
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179 | endif |
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180 | |
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181 | yy = gauWt[ii] * Gauss_f_distr(sig,rad,zi) * f2 |
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182 | yy *= 4*pi/3*zi*zi*zi //un-normalize by current sphere volume |
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183 | |
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184 | summ += yy //add to the running total of the quadrature |
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185 | endfor |
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186 | // calculate value of integral to return |
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187 | inten = (vb-va)/2.0*summ |
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188 | |
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189 | //re-normalize by polydisperse sphere volume |
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190 | inten /= (4*pi/3*rad^3)*(1+3*pd^2) |
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191 | |
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192 | inten *= scale |
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193 | |
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194 | //Lorentzian term |
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195 | inten += I0/(1 + (xx*L)^2) |
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196 | |
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197 | |
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198 | inten+=bkg |
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199 | |
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200 | Return(inten) |
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201 | End |
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202 | |
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203 | //wrapper to calculate the smeared model as an AAO-Struct |
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204 | // fills the struct and calls the ususal function with the STRUCT parameter |
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205 | // |
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206 | // used only for the dependency, not for fitting |
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207 | // |
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208 | Function fSmearedFuzzySpheres(coefW,yW,xW) |
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209 | Wave coefW,yW,xW |
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210 | |
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211 | String str = getWavesDataFolder(yW,0) |
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212 | String DF="root:"+str+":" |
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213 | |
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214 | WAVE resW = $(DF+str+"_res") |
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215 | |
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216 | STRUCT ResSmearAAOStruct fs |
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217 | WAVE fs.coefW = coefW |
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218 | WAVE fs.yW = yW |
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219 | WAVE fs.xW = xW |
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220 | WAVE fs.resW = resW |
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221 | |
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222 | Variable err |
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223 | err = SmearedFuzzySpheres(fs) |
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224 | |
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225 | return (0) |
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226 | End |
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227 | |
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228 | // this is all there is to the smeared calculation! |
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229 | Function SmearedFuzzySpheres(s) :FitFunc |
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230 | Struct ResSmearAAOStruct &s |
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231 | |
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232 | // the name of your unsmeared model (AAO) is the first argument |
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233 | Smear_Model_20(FuzzySpheres,s.coefW,s.xW,s.yW,s.resW) |
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234 | |
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235 | return(0) |
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236 | End |
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237 | |
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238 | |
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239 | |
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240 | Function Gauss_f_distr(sig,avg,pt) |
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241 | Variable sig,avg,pt |
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242 | |
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243 | Variable retval |
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244 | |
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245 | retval = (1/ ( sig*sqrt(2*Pi)) )*exp(-(avg-pt)^2/sig^2/2) |
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246 | return(retval) |
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247 | End |
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