1 | #pragma rtGlobals=1 // Use modern global access method. |
---|
2 | #pragma IgorVersion = 6.0 |
---|
3 | |
---|
4 | #include "CylinderForm" |
---|
5 | |
---|
6 | // calculates the form factor of a cylinder with polydispersity of length |
---|
7 | // the length distribution is a Schulz distribution, and any normalized distribution |
---|
8 | // could be used, as the average is performed numerically |
---|
9 | // |
---|
10 | // since the cylinder form factor is already a numerical integration, the size average is a |
---|
11 | // second integral, and significantly slows the calculation, and smearing adds a third integration. |
---|
12 | // |
---|
13 | //CORRECTED 12/5/2000 - Invariant is now correct vs. monodisperse cylinders |
---|
14 | // + upper limit of integration has been changed to account for skew of |
---|
15 | //Schulz distribution at high (>0.5) polydispersity |
---|
16 | //Requires 20 gauss points for integration of the radius (5 is not enough) |
---|
17 | //Requires either CylinderFit XOP (MacOSX only) or the normal CylinderForm Function |
---|
18 | // |
---|
19 | Proc PlotCyl_PolyLength(num,qmin,qmax) |
---|
20 | Variable num=100,qmin=0.001,qmax=0.7 |
---|
21 | Prompt num "Enter number of data points for model: " |
---|
22 | Prompt qmin "Enter minimum q-value (^-1) for model: " |
---|
23 | Prompt qmax "Enter maximum q-value (^-1) for model: " |
---|
24 | |
---|
25 | make/o/d/n=(num) xwave_cypl,ywave_cypl |
---|
26 | xwave_cypl = alog(log(qmin) + x*((log(qmax)-log(qmin))/num)) |
---|
27 | make/o/d coef_cypl = {1.,20.,1000,0.2,3.0e-6,0.01} |
---|
28 | make/o/t parameters_cypl = {"scale","radius (A)","length (A)","polydispersity of Length","SLD diff (A^-2)","incoh. bkg (cm^-1)"} |
---|
29 | Edit parameters_cypl,coef_cypl |
---|
30 | |
---|
31 | Variable/G root:g_cypl |
---|
32 | g_cypl := Cyl_PolyLength(coef_cypl,ywave_cypl,xwave_cypl) |
---|
33 | Display ywave_cypl vs xwave_cypl |
---|
34 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
---|
35 | Label bottom "q (\\S-1\\M)" |
---|
36 | Label left "Intensity (cm\\S-1\\M)" |
---|
37 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
---|
38 | End |
---|
39 | |
---|
40 | // - sets up a dependency to a wrapper, not the actual SmearedModelFunction |
---|
41 | Proc PlotSmearedCyl_PolyLength(str) |
---|
42 | String str |
---|
43 | Prompt str,"Pick the data folder containing the resolution you want",popup,getAList(4) |
---|
44 | |
---|
45 | // if any of the resolution waves are missing => abort |
---|
46 | if(ResolutionWavesMissingDF(str)) //updated to NOT use global strings (in GaussUtils) |
---|
47 | Abort |
---|
48 | endif |
---|
49 | |
---|
50 | SetDataFolder $("root:"+str) |
---|
51 | |
---|
52 | // Setup parameter table for model function |
---|
53 | make/o/D smear_coef_cypl = {1.,20.,1000,0.2,3.0e-6,0.01} |
---|
54 | make/o/t smear_parameters_cypl = {"scale","radius (A)","length (A)","polydispersity of Length","SLD diff (A^-2)","incoh. bkg (cm^-1)"} |
---|
55 | Edit smear_parameters_cypl,smear_coef_cypl |
---|
56 | |
---|
57 | // output smeared intensity wave, dimensions are identical to experimental QSIG values |
---|
58 | // make extra copy of experimental q-values for easy plotting |
---|
59 | Duplicate/O $(str+"_q") smeared_cypl,smeared_qvals |
---|
60 | SetScale d,0,0,"1/cm",smeared_cypl |
---|
61 | |
---|
62 | Variable/G gs_cypl=0 |
---|
63 | gs_cypl := fSmearedCyl_PolyLength(smear_coef_cypl,smeared_cypl,smeared_qvals) //this wrapper fills the STRUCT |
---|
64 | |
---|
65 | Display smeared_cypl vs smeared_qvals |
---|
66 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
---|
67 | Label bottom "q (\\S-1\\M)" |
---|
68 | Label left "Intensity (cm\\S-1\\M)" |
---|
69 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
---|
70 | |
---|
71 | SetDataFolder root: |
---|
72 | End |
---|
73 | |
---|
74 | |
---|
75 | |
---|
76 | //AAO version, uses XOP if available |
---|
77 | // simply calls the original single point calculation with |
---|
78 | // a wave assignment (this will behave nicely if given point ranges) |
---|
79 | Function Cyl_PolyLength(cw,yw,xw) : FitFunc |
---|
80 | Wave cw,yw,xw |
---|
81 | |
---|
82 | #if exists("Cyl_PolyLengthX") |
---|
83 | yw = Cyl_PolyLengthX(cw,xw) |
---|
84 | #else |
---|
85 | yw = fCyl_PolyLength(cw,xw) |
---|
86 | #endif |
---|
87 | return(0) |
---|
88 | End |
---|
89 | |
---|
90 | //calculate the form factor averaged over the size distribution |
---|
91 | // both integrals are done using quadrature, although both may benefit from an |
---|
92 | // adaptive integration |
---|
93 | Function fCyl_PolyLength(w,x) : FitFunc |
---|
94 | Wave w |
---|
95 | Variable x |
---|
96 | |
---|
97 | //The input variables are (and output) |
---|
98 | //[0] scale |
---|
99 | //[1] avg RADIUS (A) |
---|
100 | //[2] Length (A) |
---|
101 | //[3] polydispersity (0<p<1) |
---|
102 | //[4] contrast (A^-2) |
---|
103 | //[5] background (cm^-1) |
---|
104 | Variable scale,radius,pd,delrho,bkg,zz,length |
---|
105 | scale = w[0] |
---|
106 | radius = w[1] |
---|
107 | length = w[2] |
---|
108 | pd = w[3] |
---|
109 | delrho = w[4] |
---|
110 | bkg = w[5] |
---|
111 | |
---|
112 | zz = (1/pd)^2-1 |
---|
113 | // |
---|
114 | // the OUTPUT form factor is <f^2>/Vavg [cm-1] |
---|
115 | // |
---|
116 | // local variables |
---|
117 | Variable nord,ii,a,b,va,vb,contr,vcyl,nden,summ,yyy,zi,qq |
---|
118 | Variable answer,zp1,zp2,zp3,vpoly |
---|
119 | String weightStr,zStr |
---|
120 | |
---|
121 | // nord = 5 |
---|
122 | // weightStr = "gauss5wt" |
---|
123 | // zStr = "gauss5z" |
---|
124 | nord = 20 |
---|
125 | weightStr = "gauss20wt" |
---|
126 | zStr = "gauss20z" |
---|
127 | |
---|
128 | // 5 Gauss points (not enough for cylinder radius = high q oscillations) |
---|
129 | // use 20 Gauss points |
---|
130 | if (WaveExists($weightStr) == 0) // wave reference is not valid, |
---|
131 | Make/D/N=(nord) $weightStr,$zStr |
---|
132 | Wave wtGau = $weightStr |
---|
133 | Wave zGau = $zStr |
---|
134 | Make20GaussPoints(wtGau,zGau) |
---|
135 | //Make5GaussPoints(wtGau,zGau) |
---|
136 | else |
---|
137 | if(exists(weightStr) > 1) |
---|
138 | Abort "wave name is already in use" |
---|
139 | endif |
---|
140 | Wave wtGau = $weightStr |
---|
141 | Wave zGau = $zStr |
---|
142 | endif |
---|
143 | |
---|
144 | // set up the integration |
---|
145 | // end points and weights |
---|
146 | // limits are technically 0-inf, but wisely choose non-zero region of distribution |
---|
147 | Variable range=3.4 //multiples of the std. dev. fom the mean |
---|
148 | a = length*(1-range*pd) |
---|
149 | if (a<0) |
---|
150 | a=0 //otherwise numerical error when pd >= 0.3, making a<0 |
---|
151 | endif |
---|
152 | If(pd>0.3) |
---|
153 | range = 3.4 + (pd-0.3)*18 |
---|
154 | Endif |
---|
155 | b = length*(1+range*pd) // is this far enough past avg length? |
---|
156 | // printf "a,b,len_avg = %g %g %g\r", a,b,length |
---|
157 | va =a |
---|
158 | vb =b |
---|
159 | |
---|
160 | qq = x //current x point is the q-value for evaluation |
---|
161 | summ = 0.0 // initialize integral |
---|
162 | ii=0 |
---|
163 | do |
---|
164 | //printf "top of nord loop, i = %g\r",i |
---|
165 | // Using 5 Gauss points |
---|
166 | zi = ( zGau[ii]*(vb-va) + vb + va )/2.0 |
---|
167 | yyy = wtGau[ii] * len_kernel(qq,radius,length,zz,delrho,zi) |
---|
168 | summ = yyy + summ |
---|
169 | ii+=1 |
---|
170 | while (ii<nord) // end of loop over quadrature points |
---|
171 | // |
---|
172 | // calculate value of integral to return |
---|
173 | answer = (vb-va)/2.0*summ |
---|
174 | |
---|
175 | // contrast^2 is included in integration rad_kernel |
---|
176 | // answer *= delrho*delrho |
---|
177 | //normalize by polydisperse volume |
---|
178 | // now volume depends on polydisperse Length - so normalize by the FIRST moment |
---|
179 | // 1st moment = volume! |
---|
180 | vpoly = Pi*(radius)^2*length |
---|
181 | //Divide by vol, since volume has been "un-normalized" out |
---|
182 | answer /= vpoly |
---|
183 | //convert to [cm-1] |
---|
184 | answer *= 1.0e8 |
---|
185 | //scale |
---|
186 | answer *= scale |
---|
187 | // add in the background |
---|
188 | answer += bkg |
---|
189 | |
---|
190 | Return (answer) |
---|
191 | End //End of function PolyRadCylForm() |
---|
192 | |
---|
193 | Function len_kernel(qw,rad,len_avg,zz,delrho,len) |
---|
194 | Variable qw,rad,len_avg,zz,delrho,len |
---|
195 | |
---|
196 | Variable Pq,vcyl,dl |
---|
197 | |
---|
198 | //calculate the orientationally averaged P(q) for the input rad |
---|
199 | //this is correct - see K&C (1983) or Lin &Tsao JACryst (1996)29 170. |
---|
200 | Make/O/n=5 kernpar |
---|
201 | Wave kp = kernpar |
---|
202 | kp[0] = 1 //scale fixed at 1 |
---|
203 | kp[1] = rad |
---|
204 | kp[2] = len |
---|
205 | kp[3] = delrho |
---|
206 | kp[4] = 0 //bkg fixed at 0 |
---|
207 | |
---|
208 | #if exists("CylinderFormX") |
---|
209 | Pq = CylinderFormX(kp,qw) |
---|
210 | #else |
---|
211 | Pq = fCylinderForm(kp,qw) |
---|
212 | #endif |
---|
213 | |
---|
214 | // undo the normalization that CylinderForm does |
---|
215 | //CylinderForm returns P(q)/V, we want P(q) |
---|
216 | vcyl=Pi*rad*rad*len |
---|
217 | Pq *= vcyl |
---|
218 | //un-convert from [cm-1] |
---|
219 | Pq /= 1.0e8 |
---|
220 | |
---|
221 | // calculate normalized distribution at len value |
---|
222 | dl = Schulz_Point_pollen(len,len_avg,zz) |
---|
223 | |
---|
224 | return (Pq*dl) |
---|
225 | End |
---|
226 | |
---|
227 | Function Schulz_Point_pollen(x,avg,zz) |
---|
228 | Variable x,avg,zz |
---|
229 | |
---|
230 | Variable dr |
---|
231 | |
---|
232 | dr = zz*ln(x) - gammln(zz+1)+(zz+1)*ln((zz+1)/avg)-(x/avg*(zz+1)) |
---|
233 | |
---|
234 | return (exp(dr)) |
---|
235 | End |
---|
236 | |
---|
237 | //wrapper to calculate the smeared model as an AAO-Struct |
---|
238 | // fills the struct and calls the ususal function with the STRUCT parameter |
---|
239 | // |
---|
240 | // used only for the dependency, not for fitting |
---|
241 | // |
---|
242 | Function fSmearedCyl_PolyLength(coefW,yW,xW) |
---|
243 | Wave coefW,yW,xW |
---|
244 | |
---|
245 | String str = getWavesDataFolder(yW,0) |
---|
246 | String DF="root:"+str+":" |
---|
247 | |
---|
248 | WAVE resW = $(DF+str+"_res") |
---|
249 | |
---|
250 | STRUCT ResSmearAAOStruct fs |
---|
251 | WAVE fs.coefW = coefW |
---|
252 | WAVE fs.yW = yW |
---|
253 | WAVE fs.xW = xW |
---|
254 | WAVE fs.resW = resW |
---|
255 | |
---|
256 | Variable err |
---|
257 | err = SmearedCyl_PolyLength(fs) |
---|
258 | |
---|
259 | return (0) |
---|
260 | End |
---|
261 | |
---|
262 | // this is all there is to the smeared calculation! |
---|
263 | Function SmearedCyl_PolyLength(s) :FitFunc |
---|
264 | Struct ResSmearAAOStruct &s |
---|
265 | |
---|
266 | // the name of your unsmeared model (AAO) is the first argument |
---|
267 | s.yW = Smear_Model_20(Cyl_PolyLength,s.coefW,s.xW,s.resW) |
---|
268 | |
---|
269 | return(0) |
---|
270 | End |
---|
271 | |
---|