1 | #pragma rtGlobals=1 // Use modern global access method. |
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2 | #pragma IgorVersion=6.0 |
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3 | |
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4 | //////////////////////////////////////////////////// |
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5 | // calculates the scattering from a polydisperse spherical shell with a diffuse interface |
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6 | // |
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7 | // - the radius of the shell has a gaussian polydispersity |
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8 | // - the shell has a Gaussian SLD profile, rather than a slab |
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9 | // - currently normalized by the total sphere excluded volume |
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10 | // |
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11 | // M. Gradzielski, D. Langevin, L. Magid, R. Strey, JPC 99 (1995) 13232 |
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12 | // |
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13 | // keep polydispersity < 0.35 for approximations to be valid |
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14 | // |
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15 | //////////////////////////////////////////////////// |
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16 | |
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17 | // |
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18 | Proc PlotGaussianShell(num,qmin,qmax) |
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19 | Variable num=200, qmin=0.001, qmax=0.7 |
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20 | Prompt num "Enter number of data points for model: " |
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21 | Prompt qmin "Enter minimum q-value (^-1) for model: " |
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22 | Prompt qmax "Enter maximum q-value (^-1) for model: " |
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23 | // |
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24 | Make/O/D/n=(num) xwave_GaussianShell, ywave_GaussianShell |
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25 | xwave_GaussianShell = alog(log(qmin) + x*((log(qmax)-log(qmin))/num)) |
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26 | Make/O/D coef_GaussianShell = {1.,100,5,0.2,1e-6,6.34e-6,0} |
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27 | make/o/t parameters_GaussianShell = {"scale","Radius (A)","Shell thickness Std. Dev. (A)","radius polydispersity","SLD Shell (A-2)","SLD solvent (A-2)","bkgd (cm-1)"} |
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28 | Edit parameters_GaussianShell, coef_GaussianShell |
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29 | |
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30 | Variable/G root:g_GaussianShell |
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31 | g_GaussianShell := GaussianShell(coef_GaussianShell, ywave_GaussianShell, xwave_GaussianShell) |
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32 | Display ywave_GaussianShell vs xwave_GaussianShell |
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33 | ModifyGraph marker=29, msize=2, mode=4 |
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34 | ModifyGraph log=1,grid=1,mirror=2 |
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35 | Label bottom "q (\\S-1\\M) " |
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36 | Label left "I(q) (cm\\S-1\\M)" |
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37 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
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38 | |
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39 | AddModelToStrings("GaussianShell","coef_GaussianShell","GaussianShell") |
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40 | // |
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41 | End |
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42 | |
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43 | |
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44 | // |
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45 | //no input parameters are necessary, it MUST use the experimental q-values |
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46 | // from the experimental data read in from an AVE/QSIG data file |
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47 | //////////////////////////////////////////////////// |
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48 | // - sets up a dependency to a wrapper, not the actual SmearedModelFunction |
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49 | Proc PlotSmearedGaussianShell(str) |
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50 | String str |
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51 | Prompt str,"Pick the data folder containing the resolution you want",popup,getAList(4) |
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52 | |
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53 | // if any of the resolution waves are missing => abort |
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54 | if(ResolutionWavesMissingDF(str)) //updated to NOT use global strings (in GaussUtils) |
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55 | Abort |
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56 | endif |
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57 | |
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58 | SetDataFolder $("root:"+str) |
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59 | |
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60 | // Setup parameter table for model function |
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61 | Make/O/D smear_coef_GaussianShell = {1.,100,5,0.2,1e-6,6.34e-6,0} |
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62 | make/o/t smear_parameters_GaussianShell = {"scale","Radius (A)","Shell thickness Std. Dev. (A)","radius polydispersity","SLD Shell (A-2)","SLD solvent (A-2)","bkgd (cm-1)"} |
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63 | Edit smear_parameters_GaussianShell,smear_coef_GaussianShell //display parameters in a table |
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64 | |
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65 | // output smeared intensity wave, dimensions are identical to experimental QSIG values |
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66 | // make extra copy of experimental q-values for easy plotting |
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67 | Duplicate/O $(str+"_q") smeared_GaussianShell,smeared_qvals |
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68 | SetScale d,0,0,"1/cm",smeared_GaussianShell |
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69 | |
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70 | Variable/G gs_GaussianShell=0 |
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71 | gs_GaussianShell := fSmearedGaussianShell(smear_coef_GaussianShell,smeared_GaussianShell,smeared_qvals) //this wrapper fills the STRUCT |
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72 | |
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73 | Display smeared_GaussianShell vs smeared_qvals |
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74 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
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75 | Label bottom "q (\\S-1\\M)" |
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76 | Label left "I(q) (cm\\S-1\\M)" |
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77 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
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78 | |
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79 | SetDataFolder root: |
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80 | AddModelToStrings("SmearedGaussianShell","smear_coef_GaussianShell","GaussianShell") |
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81 | End |
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82 | |
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83 | |
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84 | // |
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85 | //AAO version, uses XOP if available |
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86 | // simply calls the original single point calculation with |
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87 | // a wave assignment (this will behave nicely if given point ranges) |
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88 | Function GaussianShell(cw,yw,xw) : FitFunc |
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89 | Wave cw,yw,xw |
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90 | |
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91 | #if exists("GaussianShellX") |
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92 | yw = GaussianShellX(cw,xw) |
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93 | #else |
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94 | yw = fGaussianShell(cw,xw) |
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95 | #endif |
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96 | return(0) |
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97 | End |
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98 | |
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99 | // |
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100 | // unsmeared model calculation |
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101 | // |
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102 | Function fGaussianShell(w,x) : FitFunc |
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103 | Wave w |
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104 | Variable x |
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105 | |
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106 | // variables are: |
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107 | //[0] scale |
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108 | //[1] radius () |
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109 | //[2] thick () (thickness parameter - this is the std. dev. of the Gaussian width of the shell) |
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110 | //[3] polydispersity of the radius |
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111 | //[4] sld shell (-2) |
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112 | //[5] sld solvent |
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113 | //[6] background (cm-1) |
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114 | |
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115 | Variable scale,rad,delrho,bkg,del,thick,pd,sig,zf |
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116 | Variable t1,t2,t3,t4,retval,exfact,vshell,vexcl,sldShell,sldSolvent |
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117 | scale = w[0] |
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118 | rad = w[1] |
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119 | thick = w[2] |
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120 | pd = w[3] |
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121 | sldShell = w[4] |
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122 | sldSolvent = w[5] |
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123 | bkg = w[6] |
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124 | |
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125 | delrho = w[4] - w[5] |
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126 | sig = pd*rad |
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127 | |
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128 | ///APPROXIMATION (see eqn 4 - but not a bad approximation) |
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129 | // del is the equivalent shell thickness with sharp boundaries, centered at mean radius |
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130 | del = thick*sqrt(2*pi) |
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131 | |
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132 | // calculate the polydisperse shell volume and the excluded volume |
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133 | vshell=4*pi/3*( (rad+del/2)^3 - (rad-del/2)^3 ) *(1+pd^2) |
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134 | vexcl=4*pi/3*( (rad+del/2)^3 ) *(1+pd^2) |
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135 | |
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136 | //intensity, eqn 9(a-d) |
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137 | exfact = exp(-2*sig^2*x^2) |
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138 | |
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139 | t1 = 0.5*x^2*thick^4*(1+cos(2*x*rad)*exfact) |
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140 | t2 = x*thick^2*(rad*sin(2*x*rad) + 2*x*sig^2*cos(2*x*rad))*exfact |
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141 | t3 = 0.5*rad^2*(1-cos(2*x*rad)*exfact) |
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142 | t4 = 0.5*sig^2*(1+4*x*rad*sin(2*x*rad)*exfact+cos(2*x*rad)*(4*sig^2*x^2-1)*exfact) |
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143 | |
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144 | retval = t1+t2+t3+t4 |
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145 | retval *= exp(-1*x*x*thick*thick) |
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146 | retval *= (del*del/x/x) |
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147 | retval *= 16*pi*pi*delrho*delrho*scale |
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148 | retval *= 1e8 |
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149 | |
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150 | //NORMALIZED by the AVERAGE shell volume, since scale is the volume fraction of material |
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151 | // retval /= vshell |
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152 | retval /= vexcl |
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153 | //re-normalize by polydisperse sphere volume, Gaussian distribution |
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154 | retval /= (1+3*pd^2) |
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155 | |
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156 | retval += bkg |
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157 | |
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158 | return(retval) |
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159 | |
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160 | End |
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161 | |
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162 | //CH#4 |
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163 | /////////////////////////////////////////////////////////////// |
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164 | // smeared model calculation |
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165 | // |
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166 | // you don't need to do anything with this function, as long as |
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167 | // your GaussianShell works correctly, you get the resolution-smeared |
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168 | // version for free. |
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169 | // |
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170 | // this is all there is to the smeared model calculation! |
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171 | Function SmearedGaussianShell(s) : FitFunc |
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172 | Struct ResSmearAAOStruct &s |
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173 | |
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174 | // the name of your unsmeared model (AAO) is the first argument |
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175 | Smear_Model_20(GaussianShell,s.coefW,s.xW,s.yW,s.resW) |
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176 | |
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177 | return(0) |
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178 | End |
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179 | |
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180 | |
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181 | /////////////////////////////////////////////////////////////// |
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182 | |
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183 | |
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184 | // nothing to change here |
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185 | // |
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186 | //wrapper to calculate the smeared model as an AAO-Struct |
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187 | // fills the struct and calls the ususal function with the STRUCT parameter |
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188 | // |
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189 | // used only for the dependency, not for fitting |
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190 | // |
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191 | Function fSmearedGaussianShell(coefW,yW,xW) |
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192 | Wave coefW,yW,xW |
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193 | |
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194 | String str = getWavesDataFolder(yW,0) |
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195 | String DF="root:"+str+":" |
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196 | |
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197 | WAVE resW = $(DF+str+"_res") |
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198 | |
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199 | STRUCT ResSmearAAOStruct fs |
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200 | WAVE fs.coefW = coefW |
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201 | WAVE fs.yW = yW |
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202 | WAVE fs.xW = xW |
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203 | WAVE fs.resW = resW |
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204 | |
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205 | Variable err |
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206 | err = SmearedGaussianShell(fs) |
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207 | |
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208 | return (0) |
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209 | End |
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