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 | // plots scattering from a mass fractal object |
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5 | // uses the model of Teixeria |
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6 | // |
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7 | // REFERENCE: J. Appl. Cryst. vol 21, p781-785 |
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8 | // Uses eq.1, 4, and 16 |
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9 | // |
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10 | // - basic subunit is a polydisperse (Schulz) sphere w/ shell - SRK Jun 2009 |
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11 | // - based on two existing XOPs, so no need to write a new one |
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12 | // |
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13 | // Macro for fractal parameters added JGB 2004 |
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14 | |
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15 | Proc PlotFractalPolyCore(num,qmin,qmax) |
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16 | Variable num=128,qmin=0.001,qmax=0.5 |
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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_fraPolyCore,ywave_fraPolyCore |
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22 | xwave_fraPolyCore = alog(log(qmin) + x*((log(qmax)-log(qmin))/num)) |
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23 | Make/O/D coef_fraPolyCore = {0.05,20,0.1,5,2,100,3.5e-6,1e-6,6.35e-6,0} |
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24 | make/o/t parameters_fraPolyCore = {"Volume Fraction (scale)","Block Radius (A)","block polydispersity (0,1)","shell thickness (A)","fractal dimension","correlation length (A)","SLD block (A-2)","SLD shell (A-2)","SLD solvent (A-2)","bkgd (cm^-1 sr^-1)"} |
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25 | Edit parameters_fraPolyCore,coef_fraPolyCore |
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26 | |
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27 | Variable/G root:g_fraPolyCore |
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28 | g_fraPolyCore := FractalPolyCore(coef_fraPolyCore,ywave_fraPolyCore,xwave_fraPolyCore) |
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29 | Display ywave_fraPolyCore vs xwave_fraPolyCore |
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30 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
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31 | Label bottom "q (A\\S-1\\M)" |
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32 | Label left "Intensity (cm\\S-1\\M)" |
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33 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
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34 | |
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35 | AddModelToStrings("FractalPolyCore","coef_fraPolyCore","parameters_fraPolyCore","fraPolyCore") |
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36 | End |
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37 | |
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38 | // - sets up a dependency to a wrapper, not the actual SmearedModelFunction |
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39 | Proc PlotSmearedFractalPolyCore(str) |
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40 | String str |
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41 | Prompt str,"Pick the data folder containing the resolution you want",popup,getAList(4) |
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42 | |
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43 | // if any of the resolution waves are missing => abort |
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44 | if(ResolutionWavesMissingDF(str)) //updated to NOT use global strings (in GaussUtils) |
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45 | Abort |
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46 | endif |
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47 | |
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48 | SetDataFolder $("root:"+str) |
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49 | |
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50 | // Setup parameter table for model function |
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51 | Make/O/D smear_coef_fraPolyCore = {0.05,20,0.1,5,2,100,3.5e-6,1e-6,6.35e-6,0} |
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52 | make/o/t smear_parameters_fraPolyCore = {"Volume Fraction (scale)","Block Radius (A)","block polydispersity (0,1)","shell thickness (A)","fractal dimension","correlation length (A)","SLD block (A-2)","SLD shell (A-2)","SLD solvent (A-2)","bkgd (cm^-1 sr^-1)"} |
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53 | Edit smear_parameters_fraPolyCore,smear_coef_fraPolyCore //display parameters in a table |
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54 | |
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55 | // output smeared intensity wave, dimensions are identical to experimental QSIG values |
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56 | // make extra copy of experimental q-values for easy plotting |
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57 | Duplicate/O $(str+"_q") smeared_fraPolyCore,smeared_qvals // |
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58 | SetScale d,0,0,"1/cm",smeared_fraPolyCore // |
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59 | |
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60 | Variable/G gs_fraPolyCore=0 |
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61 | gs_fraPolyCore := fSmearedFractalPolyCore(smear_coef_fraPolyCore,smeared_fraPolyCore,smeared_qvals) //this wrapper fills the STRUCT |
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62 | |
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63 | Display smeared_fraPolyCore vs smeared_qvals |
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64 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
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65 | Label bottom "q (A\\S-1\\M)" |
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66 | Label left "I(q) (cm\\S-1\\M)" |
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67 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
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68 | |
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69 | SetDataFolder root: |
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70 | AddModelToStrings("SmearedFractalPolyCore","smear_coef_fraPolyCore","smear_parameters_fraPolyCore","fraPolyCore") |
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71 | End |
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72 | |
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73 | |
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74 | |
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75 | //calculates the physical parameters related to the |
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76 | //model parameters. See the reference at the top of the |
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77 | //file for details |
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78 | // |
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79 | // this macro is currently only appicable to the monodisperse case and must be appropriately |
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80 | // modified before use |
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81 | // |
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82 | //Macro NumberDensity_FractalPolyCore() |
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83 | // |
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84 | // Variable nden,phi,r0,Df,corr,s0,vpoly,i0,rg |
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85 | // |
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86 | // if(Exists("coef_fraPolyCore")!=1) |
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87 | // abort "You need to plot the unsmeared model first to create the coefficient table" |
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88 | // Endif |
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89 | // |
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90 | // phi = coef_fraPolyCore[0] // volume fraction of building blocks |
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91 | // r0 = coef_fraPolyCore[1] // building block radius |
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92 | // Df = coef_fraPolyCore[2] // fractal dimension |
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93 | // corr = coef_fraPolyCore[3] // fractal correlation length (of cluster) |
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94 | // |
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95 | // Print "mean building block radius (A) = ",r0 |
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96 | // Print "volume fraction = ",phi |
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97 | // |
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98 | // // average particle volume |
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99 | // vpoly = 4*Pi/3*r0^3 |
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100 | // nden = phi/vpoly //nden in 1/A^3 |
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101 | // i0 = 1.0e8*phi*vpoly*(coef_fraPolyCore[4]-coef_fraPolyCore[5])^2 // 1/cm/sr |
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102 | // rg = corr*( Df*(Df+1)/2 )^0.5 |
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103 | // s0 = exp(gammln(Df+1))*(corr/r0)^Df |
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104 | // Print "number density (A^-3) = ",nden |
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105 | // Print "Guinier radius (A) = ",rg |
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106 | // Print "Aggregation number G = ",s0 |
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107 | // Print "Forward cross section of building blocks (cm-1 sr-1) I(0) = ",i0 |
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108 | // Print "Forward cross section of clusters (cm-1 sr-1) I(0) = ",i0*s0 |
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109 | //End |
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110 | |
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111 | //AAO version, uses XOP if available |
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112 | // simply calls the original single point calculation with |
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113 | // a wave assignment (this will behave nicely if given point ranges) |
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114 | Function FractalPolyCore(cw,yw,xw) : FitFunc |
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115 | Wave cw,yw,xw |
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116 | |
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117 | #if exists("FractalPolyCoreX") |
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118 | yw = FractalPolyCoreX(cw,xw) |
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119 | #else |
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120 | yw = fFractalPolyCore(cw,xw) |
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121 | #endif |
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122 | return(0) |
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123 | End |
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124 | |
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125 | //fractal scattering function |
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126 | Function fFractalPolyCore(w,x) :FitFunc |
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127 | wave w |
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128 | variable x |
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129 | |
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130 | variable r0,Df,corr,phi,sldp,sldm,bkg |
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131 | variable pq,sq,ans,pd,thick,slds |
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132 | phi=w[0] // volume fraction of building block spheres... |
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133 | r0=w[1] // radius of building block |
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134 | pd = w[2] // polydispersity of core |
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135 | thick = w[3] // thell thickness |
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136 | Df=w[4] // fractal dimension |
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137 | corr=w[5] // correlation length of fractal-like aggregates |
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138 | sldp = w[6] // SLD of building block |
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139 | slds = w[7] //SLD of shell |
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140 | sldm = w[8] // SLD of matrix or solution |
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141 | bkg=w[9] // flat background |
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142 | |
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143 | //calculate P(q) for the spherical subunits, units cm-1 sr-1 |
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144 | Make/O/D/N=8 tmp_PolyCor |
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145 | tmp_PolyCor[0] = phi |
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146 | tmp_PolyCor[1] = r0 |
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147 | tmp_PolyCor[2] = pd |
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148 | tmp_PolyCor[3] = thick |
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149 | tmp_PolyCor[4] = sldp |
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150 | tmp_PolyCor[5] = slds |
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151 | tmp_PolyCor[6] = sldm |
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152 | tmp_PolyCor[7] = 0 |
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153 | |
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154 | #if exists("PolyCoreFormX") |
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155 | pq = PolyCoreFormX(tmp_PolyCor,x) |
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156 | #else |
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157 | pq = fPolyCoreForm(tmp_PolyCor,x) |
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158 | #endif |
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159 | |
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160 | //calculate S(q) |
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161 | sq = Df*exp(gammln(Df-1))*sin((Df-1)*atan(x*corr)) |
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162 | sq /= (x*r0)^Df * (1 + 1/(x*corr)^2)^((Df-1)/2) |
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163 | sq += 1 |
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164 | //combine and return |
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165 | ans = pq*sq + bkg |
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166 | |
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167 | return (ans) |
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168 | End |
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169 | |
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170 | //wrapper to calculate the smeared model as an AAO-Struct |
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171 | // fills the struct and calls the ususal function with the STRUCT parameter |
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172 | // |
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173 | // used only for the dependency, not for fitting |
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174 | // |
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175 | Function fSmearedFractalPolyCore(coefW,yW,xW) |
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176 | Wave coefW,yW,xW |
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177 | |
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178 | String str = getWavesDataFolder(yW,0) |
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179 | String DF="root:"+str+":" |
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180 | |
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181 | WAVE resW = $(DF+str+"_res") |
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182 | |
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183 | STRUCT ResSmearAAOStruct fs |
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184 | WAVE fs.coefW = coefW |
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185 | WAVE fs.yW = yW |
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186 | WAVE fs.xW = xW |
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187 | WAVE fs.resW = resW |
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188 | |
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189 | Variable err |
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190 | err = SmearedFractalPolyCore(fs) |
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191 | |
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192 | return (0) |
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193 | End |
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194 | |
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195 | //the smeared model calculation |
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196 | Function SmearedFractalPolyCore(s) :FitFunc |
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197 | Struct ResSmearAAOStruct &s |
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198 | |
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199 | // the name of your unsmeared model (AAO) is the first argument |
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200 | Smear_Model_20(FractalPolyCore,s.coefW,s.xW,s.yW,s.resW) |
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201 | |
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202 | return(0) |
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203 | End |
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