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 | #include "CylinderForm" |
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5 | |
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6 | // calculates the form factor of a cylinder with polydispersity of length |
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7 | // the length distribution is a Schulz distribution, and any normalized distribution |
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8 | // could be used, as the average is performed numerically |
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9 | // |
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10 | // since the cylinder form factor is already a numerical integration, the size average is a |
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11 | // second integral, and significantly slows the calculation, and smearing adds a third integration. |
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12 | // |
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13 | //CORRECTED 12/5/2000 - Invariant is now correct vs. monodisperse cylinders |
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14 | // + upper limit of integration has been changed to account for skew of |
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15 | //Schulz distribution at high (>0.5) polydispersity |
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16 | //Requires 20 gauss points for integration of the radius (5 is not enough) |
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17 | //Requires either CylinderFit XOP (MacOSX only) or the normal CylinderForm Function |
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18 | // |
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19 | Proc PlotCyl_PolyLength(num,qmin,qmax) |
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20 | Variable num=100,qmin=0.001,qmax=0.7 |
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21 | Prompt num "Enter number of data points for model: " |
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22 | Prompt qmin "Enter minimum q-value (^-1) for model: " |
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23 | Prompt qmax "Enter maximum q-value (^-1) for model: " |
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24 | |
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25 | make/o/d/n=(num) xwave_cypl,ywave_cypl |
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26 | xwave_cypl = alog(log(qmin) + x*((log(qmax)-log(qmin))/num)) |
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27 | make/o/d coef_cypl = {1.,20.,1000,0.2,3.0e-6,0.01} |
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28 | make/o/t parameters_cypl = {"scale","radius (A)","length (A)","polydispersity of Length","SLD diff (A^-2)","incoh. bkg (cm^-1)"} |
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29 | Edit parameters_cypl,coef_cypl |
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30 | |
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31 | Variable/G root:g_cypl |
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32 | g_cypl := Cyl_PolyLength(coef_cypl,ywave_cypl,xwave_cypl) |
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33 | Display ywave_cypl vs xwave_cypl |
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34 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
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35 | Label bottom "q (\\S-1\\M)" |
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36 | Label left "Intensity (cm\\S-1\\M)" |
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37 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
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38 | End |
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39 | |
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40 | // - sets up a dependency to a wrapper, not the actual SmearedModelFunction |
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41 | Proc PlotSmearedCyl_PolyLength(str) |
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42 | String str |
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43 | Prompt str,"Pick the data folder conatining the resolution you want",popup,getAList(4) |
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44 | |
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45 | // if any of the resolution waves are missing => abort |
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46 | if(ResolutionWavesMissingDF(str)) //updated to NOT use global strings (in GaussUtils) |
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47 | Abort |
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48 | endif |
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49 | |
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50 | SetDataFolder $("root:"+str) |
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51 | |
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52 | // Setup parameter table for model function |
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53 | make/o/D smear_coef_cypl = {1.,20.,1000,0.2,3.0e-6,0.01} |
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54 | make/o/t smear_parameters_cypl = {"scale","radius (A)","length (A)","polydispersity of Length","SLD diff (A^-2)","incoh. bkg (cm^-1)"} |
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55 | Edit smear_parameters_cypl,smear_coef_cypl |
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56 | |
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57 | // output smeared intensity wave, dimensions are identical to experimental QSIG values |
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58 | // make extra copy of experimental q-values for easy plotting |
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59 | Duplicate/O $(str+"_q") smeared_cypl,smeared_qvals |
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60 | SetScale d,0,0,"1/cm",smeared_cypl |
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61 | |
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62 | Variable/G gs_cypl=0 |
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63 | gs_cypl := fSmearedCyl_PolyLength(smear_coef_cypl,smeared_cypl,smeared_qvals) //this wrapper fills the STRUCT |
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64 | |
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65 | Display smeared_cypl vs smeared_qvals |
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66 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
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67 | Label bottom "q (\\S-1\\M)" |
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68 | Label left "Intensity (cm\\S-1\\M)" |
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69 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
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70 | |
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71 | SetDataFolder root: |
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72 | End |
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73 | |
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74 | |
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75 | |
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76 | //AAO version, uses XOP if available |
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77 | // simply calls the original single point calculation with |
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78 | // a wave assignment (this will behave nicely if given point ranges) |
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79 | Function Cyl_PolyLength(cw,yw,xw) : FitFunc |
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80 | Wave cw,yw,xw |
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81 | |
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82 | #if exists("Cyl_PolyLengthX") |
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83 | yw = Cyl_PolyLengthX(cw,xw) |
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84 | #else |
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85 | yw = fCyl_PolyLength(cw,xw) |
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86 | #endif |
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87 | return(0) |
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88 | End |
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89 | |
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90 | //calculate the form factor averaged over the size distribution |
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91 | // both integrals are done using quadrature, although both may benefit from an |
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92 | // adaptive integration |
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93 | Function fCyl_PolyLength(w,x) : FitFunc |
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94 | Wave w |
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95 | Variable x |
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96 | |
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97 | //The input variables are (and output) |
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98 | //[0] scale |
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99 | //[1] avg RADIUS (A) |
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100 | //[2] Length (A) |
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101 | //[3] polydispersity (0<p<1) |
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102 | //[4] contrast (A^-2) |
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103 | //[5] background (cm^-1) |
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104 | Variable scale,radius,pd,delrho,bkg,zz,length |
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105 | scale = w[0] |
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106 | radius = w[1] |
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107 | length = w[2] |
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108 | pd = w[3] |
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109 | delrho = w[4] |
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110 | bkg = w[5] |
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111 | |
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112 | zz = (1/pd)^2-1 |
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113 | // |
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114 | // the OUTPUT form factor is <f^2>/Vavg [cm-1] |
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115 | // |
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116 | // local variables |
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117 | Variable nord,ii,a,b,va,vb,contr,vcyl,nden,summ,yyy,zi,qq |
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118 | Variable answer,zp1,zp2,zp3,vpoly |
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119 | String weightStr,zStr |
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120 | |
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121 | // nord = 5 |
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122 | // weightStr = "gauss5wt" |
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123 | // zStr = "gauss5z" |
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124 | nord = 20 |
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125 | weightStr = "gauss20wt" |
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126 | zStr = "gauss20z" |
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127 | |
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128 | // 5 Gauss points (not enough for cylinder radius = high q oscillations) |
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129 | // use 20 Gauss points |
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130 | if (WaveExists($weightStr) == 0) // wave reference is not valid, |
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131 | Make/D/N=(nord) $weightStr,$zStr |
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132 | Wave wtGau = $weightStr |
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133 | Wave zGau = $zStr |
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134 | Make20GaussPoints(wtGau,zGau) |
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135 | //Make5GaussPoints(wtGau,zGau) |
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136 | else |
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137 | if(exists(weightStr) > 1) |
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138 | Abort "wave name is already in use" |
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139 | endif |
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140 | Wave wtGau = $weightStr |
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141 | Wave zGau = $zStr |
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142 | endif |
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143 | |
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144 | // set up the integration |
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145 | // end points and weights |
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146 | // limits are technically 0-inf, but wisely choose non-zero region of distribution |
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147 | Variable range=3.4 //multiples of the std. dev. fom the mean |
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148 | a = length*(1-range*pd) |
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149 | if (a<0) |
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150 | a=0 //otherwise numerical error when pd >= 0.3, making a<0 |
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151 | endif |
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152 | If(pd>0.3) |
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153 | range = 3.4 + (pd-0.3)*18 |
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154 | Endif |
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155 | b = length*(1+range*pd) // is this far enough past avg length? |
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156 | // printf "a,b,len_avg = %g %g %g\r", a,b,length |
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157 | va =a |
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158 | vb =b |
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159 | |
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160 | qq = x //current x point is the q-value for evaluation |
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161 | summ = 0.0 // initialize integral |
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162 | ii=0 |
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163 | do |
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164 | //printf "top of nord loop, i = %g\r",i |
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165 | // Using 5 Gauss points |
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166 | zi = ( zGau[ii]*(vb-va) + vb + va )/2.0 |
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167 | yyy = wtGau[ii] * len_kernel(qq,radius,length,zz,delrho,zi) |
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168 | summ = yyy + summ |
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169 | ii+=1 |
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170 | while (ii<nord) // end of loop over quadrature points |
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171 | // |
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172 | // calculate value of integral to return |
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173 | answer = (vb-va)/2.0*summ |
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174 | |
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175 | // contrast^2 is included in integration rad_kernel |
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176 | // answer *= delrho*delrho |
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177 | //normalize by polydisperse volume |
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178 | // now volume depends on polydisperse Length - so normalize by the FIRST moment |
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179 | // 1st moment = volume! |
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180 | vpoly = Pi*(radius)^2*length |
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181 | //Divide by vol, since volume has been "un-normalized" out |
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182 | answer /= vpoly |
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183 | //convert to [cm-1] |
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184 | answer *= 1.0e8 |
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185 | //scale |
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186 | answer *= scale |
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187 | // add in the background |
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188 | answer += bkg |
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189 | |
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190 | Return (answer) |
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191 | End //End of function PolyRadCylForm() |
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192 | |
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193 | Function len_kernel(qw,rad,len_avg,zz,delrho,len) |
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194 | Variable qw,rad,len_avg,zz,delrho,len |
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195 | |
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196 | Variable Pq,vcyl,dl |
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197 | |
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198 | //calculate the orientationally averaged P(q) for the input rad |
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199 | //this is correct - see K&C (1983) or Lin &Tsao JACryst (1996)29 170. |
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200 | Make/O/n=5 kernpar |
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201 | Wave kp = kernpar |
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202 | kp[0] = 1 //scale fixed at 1 |
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203 | kp[1] = rad |
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204 | kp[2] = len |
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205 | kp[3] = delrho |
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206 | kp[4] = 0 //bkg fixed at 0 |
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207 | |
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208 | #if exists("CylinderFormX") |
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209 | Pq = CylinderFormX(kp,qw) |
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210 | #else |
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211 | Pq = fCylinderForm(kp,qw) |
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212 | #endif |
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213 | |
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214 | // undo the normalization that CylinderForm does |
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215 | //CylinderForm returns P(q)/V, we want P(q) |
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216 | vcyl=Pi*rad*rad*len |
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217 | Pq *= vcyl |
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218 | //un-convert from [cm-1] |
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219 | Pq /= 1.0e8 |
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220 | |
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221 | // calculate normalized distribution at len value |
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222 | dl = Schulz_Point_pollen(len,len_avg,zz) |
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223 | |
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224 | return (Pq*dl) |
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225 | End |
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226 | |
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227 | Function Schulz_Point_pollen(x,avg,zz) |
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228 | Variable x,avg,zz |
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229 | |
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230 | Variable dr |
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231 | |
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232 | dr = zz*ln(x) - gammln(zz+1)+(zz+1)*ln((zz+1)/avg)-(x/avg*(zz+1)) |
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233 | |
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234 | return (exp(dr)) |
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235 | End |
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236 | |
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237 | //wrapper to calculate the smeared model as an AAO-Struct |
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238 | // fills the struct and calls the ususal function with the STRUCT parameter |
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239 | // |
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240 | // used only for the dependency, not for fitting |
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241 | // |
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242 | Function fSmearedCyl_PolyLength(coefW,yW,xW) |
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243 | Wave coefW,yW,xW |
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244 | |
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245 | String str = getWavesDataFolder(yW,0) |
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246 | String DF="root:"+str+":" |
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247 | |
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248 | WAVE resW = $(DF+str+"_res") |
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249 | |
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250 | STRUCT ResSmearAAOStruct fs |
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251 | WAVE fs.coefW = coefW |
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252 | WAVE fs.yW = yW |
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253 | WAVE fs.xW = xW |
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254 | WAVE fs.resW = resW |
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255 | |
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256 | Variable err |
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257 | err = SmearedCyl_PolyLength(fs) |
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258 | |
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259 | return (0) |
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260 | End |
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261 | |
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262 | // this is all there is to the smeared calculation! |
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263 | Function SmearedCyl_PolyLength(s) :FitFunc |
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264 | Struct ResSmearAAOStruct &s |
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265 | |
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266 | // the name of your unsmeared model (AAO) is the first argument |
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267 | s.yW = Smear_Model_20(Cyl_PolyLength,s.coefW,s.xW,s.resW) |
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268 | |
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269 | return(0) |
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270 | End |
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271 | |
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