1 | #pragma rtGlobals=1 // Use modern global access method. |
---|
2 | |
---|
3 | ///////////////////////////////////////////////////// |
---|
4 | // |
---|
5 | // Plot's Greg Beaucage's Rg-power Law "model" of scattering |
---|
6 | // somewhat useful for identifying length scales, but short on |
---|
7 | // physical inerpretation of the real structure of the sample. |
---|
8 | // |
---|
9 | // up to 4 "levels" can be calculated |
---|
10 | // best to start with single level, and fit a small range of |
---|
11 | // the data, and add more levels as needed |
---|
12 | // |
---|
13 | // see the help file for the original references |
---|
14 | // |
---|
15 | Proc PlotBeau_One(num,qmin,qmax) |
---|
16 | Variable num=256,qmin=0.001,qmax=0.7 |
---|
17 | Prompt num "Enter number of data points for model: " |
---|
18 | Prompt qmin "Enter minimum q-value (^-1) for model: " |
---|
19 | Prompt qmax "Enter maximum q-value (^-1) for model: " |
---|
20 | |
---|
21 | make/o/d/n=(num) xwave_b1,ywave_b1 |
---|
22 | xwave_b1 = alog(log(qmin) + x*((log(qmax)-log(qmin))/num)) |
---|
23 | make/o/d coef_b1 = {1,3,21,6e-4,2,0} |
---|
24 | make/o/t parameters_b1 = {"scale","G1 (cm-1 sr-1)","Rg1 (A)","B1 (cm-1 sr-1)","Pow1","bkg (cm-1 sr-1)"} |
---|
25 | Edit parameters_b1,coef_b1 |
---|
26 | ywave_b1 := OneLevel(coef_b1,xwave_b1) |
---|
27 | Display ywave_b1 vs xwave_b1 |
---|
28 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
---|
29 | Label bottom "q (\\S-1\\M)" |
---|
30 | Label left "Intensity (cm\\S-1\\M)" |
---|
31 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
---|
32 | End |
---|
33 | |
---|
34 | Proc PlotBeau_Two(num,qmin,qmax) |
---|
35 | Variable num=256,qmin=0.001,qmax=0.7 |
---|
36 | Prompt num "Enter number of data points for model: " |
---|
37 | Prompt qmin "Enter minimum q-value (^-1) for model: " |
---|
38 | Prompt qmax "Enter maximum q-value (^-1) for model: " |
---|
39 | |
---|
40 | make/o/d/n=(num) xwave_b2,ywave_b2 |
---|
41 | xwave_b2 = alog(log(qmin) + x*((log(qmax)-log(qmin))/num)) |
---|
42 | make/o/d coef_b2 = {1,400,200,5e-6,4,3,21,6e-4,2,0} |
---|
43 | make/o/t parameters_b2 = {"scale","G1 (cm-1 sr-1)","Rg1 (A)","B1 (cm-1 sr-1)","Pow1","G2 (cm-1 sr-1)","Rg2 (A)","B2 (cm-1 sr-1)","Pow2","bkg (cm-1 sr-1)"} |
---|
44 | Edit parameters_b2,coef_b2 |
---|
45 | ywave_b2 := TwoLevel(coef_b2,xwave_b2) |
---|
46 | Display ywave_b2 vs xwave_b2 |
---|
47 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
---|
48 | Label bottom "q (\\S-1\\M)" |
---|
49 | Label left "Intensity (cm\\S-1\\M)" |
---|
50 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
---|
51 | End |
---|
52 | |
---|
53 | Proc PlotBeau_Three(num,qmin,qmax) |
---|
54 | Variable num=256,qmin=0.001,qmax=0.7 |
---|
55 | Prompt num "Enter number of data points for model: " |
---|
56 | Prompt qmin "Enter minimum q-value (^-1) for model: " |
---|
57 | Prompt qmax "Enter maximum q-value (^-1) for model: " |
---|
58 | |
---|
59 | make/o/d/n=(num) xwave_b3,ywave_b3 |
---|
60 | xwave_b3 = alog(log(qmin) + x*((log(qmax)-log(qmin))/num)) |
---|
61 | make/o/d coef_b3 = {1,4000,600,2e-7,4,400,200,5e-6,4,3,21,6e-4,2,0} |
---|
62 | make/o/t parameters_b3 = {"scale","G1 (cm-1 sr-1)","Rg1 (A)","B1 (cm-1 sr-1)","Pow1","G2 (cm-1 sr-1)","Rg2 (A)","B2 (cm-1 sr-1)","Pow2","G3 (cm-1 sr-1)","Rg3 (A)","B3 (cm-1 sr-1)","Pow3","bkg (cm-1)"} |
---|
63 | Edit parameters_b3,coef_b3 |
---|
64 | ywave_b3 := ThreeLevel(coef_b3,xwave_b3) |
---|
65 | Display ywave_b3 vs xwave_b3 |
---|
66 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
---|
67 | Label bottom "q (\\S-1\\M)" |
---|
68 | Label left "Intensity (cm\\S-1\\M)" |
---|
69 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
---|
70 | End |
---|
71 | |
---|
72 | Proc PlotBeau_Four(num,qmin,qmax) |
---|
73 | Variable num=256,qmin=0.001,qmax=0.7 |
---|
74 | Prompt num "Enter number of data points for model: " |
---|
75 | Prompt qmin "Enter minimum q-value (^-1) for model: " |
---|
76 | Prompt qmax "Enter maximum q-value (^-1) for model: " |
---|
77 | |
---|
78 | make/o/d/n=(num) xwave_b4,ywave_b4 |
---|
79 | xwave_b4 = alog(log(qmin) + x*((log(qmax)-log(qmin))/num)) |
---|
80 | make/o/d coef_b4 = {1,40000,2000,1e-8,4,4000,600,2e-7,4,400,200,5e-6,4,3,21,6e-4,2,0} |
---|
81 | make/o/t parameters_b4 = {"scale","G1 (cm-1 sr-1)","Rg1 (A)","B1 (cm-1 sr-1)","Pow1","G2 (cm-1 sr-1)","Rg2 (A)","B2 (cm-1 sr-1)","Pow2","G3 (cm-1 sr-1)","Rg3 (A)","B3 (cm-1 sr-1)","Pow3","G4 (cm-1 sr-1)","Rg4 (A)","B4 (cm-1 sr-1)","Pow4","bkg (cm-1)"} |
---|
82 | Edit parameters_b4,coef_b4 |
---|
83 | ywave_b4 := FourLevel(coef_b4,xwave_b4) |
---|
84 | Display ywave_b4 vs xwave_b4 |
---|
85 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
---|
86 | Label bottom "q (\\S-1\\M)" |
---|
87 | Label left "Intensity (cm\\S-1\\M)" |
---|
88 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
---|
89 | End |
---|
90 | |
---|
91 | /////////// macros for smeared model calculations |
---|
92 | |
---|
93 | Proc PlotSmearedBeau_OneLevel() |
---|
94 | //no input parameters necessary, it MUST use the experimental q-values |
---|
95 | // from the experimental data read in from an AVE/QSIG data file |
---|
96 | If(ResolutionWavesMissing()) //part of GaussUtils |
---|
97 | Abort |
---|
98 | endif |
---|
99 | |
---|
100 | // Setup parameter table for model function |
---|
101 | Make/O/D smear_coef_b1 ={1,3,21,6e-4,2,0} |
---|
102 | make/o/t smear_parameters_b1 = {"scale","G1 (cm-1 sr-1)","Rg1 (A)","B1 (cm-1 sr-1)","Pow1","bkg (cm-1 sr-1)"} |
---|
103 | Edit smear_parameters_b1,smear_coef_b1 |
---|
104 | |
---|
105 | // output smeared intensity wave, dimensions are identical to experimental QSIG values |
---|
106 | // make extra copy of experimental q-values for easy plotting |
---|
107 | Duplicate/O $gQvals smeared_b1,smeared_qvals |
---|
108 | SetScale d,0,0,"1/cm",smeared_b1 |
---|
109 | |
---|
110 | smeared_b1 := SmearedOneLevel(smear_coef_b1,$gQvals) |
---|
111 | Display smeared_b1 vs smeared_qvals |
---|
112 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
---|
113 | Label bottom "q (\\S-1\\M)" |
---|
114 | Label left "Intensity (cm\\S-1\\M)" |
---|
115 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
---|
116 | End |
---|
117 | |
---|
118 | Proc PlotSmearedBeau_TwoLevel() |
---|
119 | //no input parameters necessary, it MUST use the experimental q-values |
---|
120 | // from the experimental data read in from an AVE/QSIG data file |
---|
121 | If(ResolutionWavesMissing()) //part of GaussUtils |
---|
122 | Abort |
---|
123 | endif |
---|
124 | |
---|
125 | // Setup parameter table for model function |
---|
126 | Make/O/D smear_coef_b2 = {1,400,200,5e-6,4,3,21,6e-4,2,0} |
---|
127 | make/o/t smear_parameters_b2 = {"scale","G1 (cm-1 sr-1)","Rg1 (A)","B1 (cm-1 sr-1)","Pow1","G2 (cm-1 sr-1)","Rg2 (A)","B2 (cm-1 sr-1)","Pow2","bkg (cm-1 sr-1)"} |
---|
128 | Edit smear_parameters_b2,smear_coef_b2 |
---|
129 | |
---|
130 | // output smeared intensity wave, dimensions are identical to experimental QSIG values |
---|
131 | // make extra copy of experimental q-values for easy plotting |
---|
132 | Duplicate/O $gQvals smeared_b2,smeared_qvals |
---|
133 | SetScale d,0,0,"1/cm",smeared_b2 |
---|
134 | |
---|
135 | smeared_b2 := SmearedTwoLevel(smear_coef_b2,$gQvals) |
---|
136 | Display smeared_b2 vs smeared_qvals |
---|
137 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
---|
138 | Label bottom "q (\\S-1\\M)" |
---|
139 | Label left "Intensity (cm\\S-1\\M)" |
---|
140 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
---|
141 | End |
---|
142 | |
---|
143 | Proc PlotSmearedBeau_ThreeLevel() |
---|
144 | //no input parameters necessary, it MUST use the experimental q-values |
---|
145 | // from the experimental data read in from an AVE/QSIG data file |
---|
146 | If(ResolutionWavesMissing()) //part of GaussUtils |
---|
147 | Abort |
---|
148 | endif |
---|
149 | |
---|
150 | // Setup parameter table for model function |
---|
151 | Make/O/D smear_coef_b3 = {1,4000,600,2e-7,4,400,200,5e-6,4,3,21,6e-4,2,0} |
---|
152 | make/o/t smear_parameters_b3 = {"scale","G1 (cm-1 sr-1)","Rg1 (A)","B1 (cm-1 sr-1)","Pow1","G2 (cm-1 sr-1)","Rg2 (A)","B2 (cm-1 sr-1)","Pow2","G3 (cm-1 sr-1)","Rg3 (A)","B3 (cm-1 sr-1)","Pow3","bkg (cm-1)"} |
---|
153 | Edit smear_parameters_b3,smear_coef_b3 |
---|
154 | |
---|
155 | // output smeared intensity wave, dimensions are identical to experimental QSIG values |
---|
156 | // make extra copy of experimental q-values for easy plotting |
---|
157 | Duplicate/O $gQvals smeared_b3,smeared_qvals |
---|
158 | SetScale d,0,0,"1/cm",smeared_b3 |
---|
159 | |
---|
160 | smeared_b3 := SmearedThreeLevel(smear_coef_b3,$gQvals) |
---|
161 | Display smeared_b3 vs smeared_qvals |
---|
162 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
---|
163 | Label bottom "q (\\S-1\\M)" |
---|
164 | Label left "Intensity (cm\\S-1\\M)" |
---|
165 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
---|
166 | End |
---|
167 | |
---|
168 | Proc PlotSmearedBeau_FourLevel() |
---|
169 | //no input parameters necessary, it MUST use the experimental q-values |
---|
170 | // from the experimental data read in from an AVE/QSIG data file |
---|
171 | If(ResolutionWavesMissing()) //part of GaussUtils |
---|
172 | Abort |
---|
173 | endif |
---|
174 | |
---|
175 | // Setup parameter table for model function |
---|
176 | Make/O/D smear_coef_b4 = {1,40000,2000,1e-8,4,4000,600,2e-7,4,400,200,5e-6,4,3,21,6e-4,2,0} |
---|
177 | Make/o/t smear_parameters_b4 = {"scale","G1 (cm-1 sr-1)","Rg1 (A)","B1 (cm-1 sr-1)","Pow1","G2 (cm-1 sr-1)","Rg2 (A)","B2 (cm-1 sr-1)","Pow2","G3 (cm-1 sr-1)","Rg3 (A)","B3 (cm-1 sr-1)","Pow3","G4 (cm-1 sr-1)","Rg4 (A)","B4 (cm-1 sr-1)","Pow4","bkg (cm-1)"} |
---|
178 | Edit smear_parameters_b4,smear_coef_b4 |
---|
179 | |
---|
180 | // output smeared intensity wave, dimensions are identical to experimental QSIG values |
---|
181 | // make extra copy of experimental q-values for easy plotting |
---|
182 | Duplicate/O $gQvals smeared_b4,smeared_qvals |
---|
183 | SetScale d,0,0,"1/cm",smeared_b4 |
---|
184 | |
---|
185 | smeared_b4 := SmearedFourLevel(smear_coef_b4,$gQvals) |
---|
186 | Display smeared_b4 vs smeared_qvals |
---|
187 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
---|
188 | Label bottom "q (\\S-1\\M)" |
---|
189 | Label left "Intensity (cm\\S-1\\M)" |
---|
190 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
---|
191 | End |
---|
192 | |
---|
193 | //////////Function definitions |
---|
194 | |
---|
195 | Function OneLevel(w,x) :FitFunc |
---|
196 | Wave w |
---|
197 | Variable x |
---|
198 | |
---|
199 | Variable ans,erf1,prec=1e-15 |
---|
200 | Variable G1,Rg1,B1,Pow1,bkg,scale |
---|
201 | |
---|
202 | scale = w[0] |
---|
203 | G1 = w[1] |
---|
204 | Rg1 = w[2] |
---|
205 | B1 = w[3] |
---|
206 | Pow1 = w[4] |
---|
207 | bkg = w[5] |
---|
208 | |
---|
209 | erf1 = erf( (x*Rg1/sqrt(6)) ,prec) |
---|
210 | |
---|
211 | ans = G1*exp(-x*x*Rg1*Rg1/3) |
---|
212 | ans += B1*(erf1^3/x)^Pow1 |
---|
213 | ans *= scale |
---|
214 | ans += bkg |
---|
215 | |
---|
216 | Return (ans) |
---|
217 | End |
---|
218 | |
---|
219 | Function TwoLevel(w,x) :FitFunc |
---|
220 | Wave w |
---|
221 | Variable x |
---|
222 | |
---|
223 | Variable ans,G1,Rg1,B1,G2,Rg2,B2,Pow1,Pow2,bkg |
---|
224 | Variable erf1,erf2,prec=1e-15,scale |
---|
225 | |
---|
226 | //Rsub = Rs |
---|
227 | scale = w[0] |
---|
228 | G1 = w[1] //equivalent to I(0) |
---|
229 | Rg1 = w[2] |
---|
230 | B1 = w[3] |
---|
231 | Pow1 = w[4] |
---|
232 | G2 = w[5] |
---|
233 | Rg2 = w[6] |
---|
234 | B2 = w[7] |
---|
235 | Pow2 = w[8] |
---|
236 | bkg = w[9] |
---|
237 | |
---|
238 | erf1 = erf( (x*Rg1/sqrt(6)) ,prec) |
---|
239 | erf2 = erf( (x*Rg2/sqrt(6)) ,prec) |
---|
240 | //Print erf1 |
---|
241 | |
---|
242 | ans = G1*exp(-x*x*Rg1*Rg1/3) |
---|
243 | ans += B1*exp(-x*x*Rg2*Rg2/3)*(erf1^3/x)^Pow1 |
---|
244 | ans += G2*exp(-x*x*Rg2*Rg2/3) |
---|
245 | ans += B2*(erf2^3/x)^Pow2 |
---|
246 | ans *= scale |
---|
247 | ans += bkg |
---|
248 | |
---|
249 | Return(ans) |
---|
250 | End |
---|
251 | |
---|
252 | |
---|
253 | Function ThreeLevel(w,x) :FitFunc |
---|
254 | Wave w |
---|
255 | Variable x |
---|
256 | |
---|
257 | Variable ans,G1,Rg1,B1,G2,Rg2,B2,Pow1,Pow2,bkg |
---|
258 | Variable G3,Rg3,B3,Pow3,erf3 |
---|
259 | Variable erf1,erf2,prec=1e-15,scale |
---|
260 | |
---|
261 | //Rsub = Rs |
---|
262 | scale = w[0] |
---|
263 | G1 = w[1] //equivalent to I(0) |
---|
264 | Rg1 = w[2] |
---|
265 | B1 = w[3] |
---|
266 | Pow1 = w[4] |
---|
267 | G2 = w[5] |
---|
268 | Rg2 = w[6] |
---|
269 | B2 = w[7] |
---|
270 | Pow2 = w[8] |
---|
271 | G3 = w[9] |
---|
272 | Rg3 = w[10] |
---|
273 | B3 = w[11] |
---|
274 | Pow3 = w[12] |
---|
275 | bkg = w[13] |
---|
276 | |
---|
277 | erf1 = erf( (x*Rg1/sqrt(6)) ,prec) |
---|
278 | erf2 = erf( (x*Rg2/sqrt(6)) ,prec) |
---|
279 | erf3 = erf( (x*Rg3/sqrt(6)) ,prec) |
---|
280 | //Print erf1 |
---|
281 | |
---|
282 | ans = G1*exp(-x*x*Rg1*Rg1/3) + B1*exp(-x*x*Rg2*Rg2/3)*(erf1^3/x)^Pow1 |
---|
283 | ans += G2*exp(-x*x*Rg2*Rg2/3) + B2*exp(-x*x*Rg3*Rg3/3)*(erf2^3/x)^Pow2 |
---|
284 | ans += G3*exp(-x*x*Rg3*Rg3/3) + B3*(erf3^3/x)^Pow3 |
---|
285 | ans *= scale |
---|
286 | ans += bkg |
---|
287 | |
---|
288 | Return(ans) |
---|
289 | End |
---|
290 | |
---|
291 | Function FourLevel(w,x) :FitFunc |
---|
292 | Wave w |
---|
293 | Variable x |
---|
294 | |
---|
295 | Variable ans,G1,Rg1,B1,G2,Rg2,B2,Pow1,Pow2,bkg |
---|
296 | Variable G3,Rg3,B3,Pow3,erf3 |
---|
297 | Variable G4,Rg4,B4,Pow4,erf4 |
---|
298 | Variable erf1,erf2,prec=1e-15,scale |
---|
299 | |
---|
300 | //Rsub = Rs |
---|
301 | scale = w[0] |
---|
302 | G1 = w[1] //equivalent to I(0) |
---|
303 | Rg1 = w[2] |
---|
304 | B1 = w[3] |
---|
305 | Pow1 = w[4] |
---|
306 | G2 = w[5] |
---|
307 | Rg2 = w[6] |
---|
308 | B2 = w[7] |
---|
309 | Pow2 = w[8] |
---|
310 | G3 = w[9] |
---|
311 | Rg3 = w[10] |
---|
312 | B3 = w[11] |
---|
313 | Pow3 = w[12] |
---|
314 | G4 = w[13] |
---|
315 | Rg4 = w[14] |
---|
316 | B4 = w[15] |
---|
317 | Pow4 = w[16] |
---|
318 | bkg = w[17] |
---|
319 | |
---|
320 | erf1 = erf( (x*Rg1/sqrt(6)) ,prec) |
---|
321 | erf2 = erf( (x*Rg2/sqrt(6)) ,prec) |
---|
322 | erf3 = erf( (x*Rg3/sqrt(6)) ,prec) |
---|
323 | erf4 = erf( (x*Rg4/sqrt(6)) ,prec) |
---|
324 | |
---|
325 | ans = G1*exp(-x*x*Rg1*Rg1/3) + B1*exp(-x*x*Rg2*Rg2/3)*(erf1^3/x)^Pow1 |
---|
326 | ans += G2*exp(-x*x*Rg2*Rg2/3) + B2*exp(-x*x*Rg3*Rg3/3)*(erf2^3/x)^Pow2 |
---|
327 | ans += G3*exp(-x*x*Rg3*Rg3/3) + B3*exp(-x*x*Rg4*Rg4/3)*(erf3^3/x)^Pow3 |
---|
328 | ans += G4*exp(-x*x*Rg4*Rg4/3) + B4*(erf4^3/x)^Pow4 |
---|
329 | ans *= scale |
---|
330 | ans += bkg |
---|
331 | |
---|
332 | Return(ans) |
---|
333 | End |
---|
334 | |
---|
335 | Function SmearedOneLevel(w,x) :FitFunc |
---|
336 | Wave w |
---|
337 | Variable x |
---|
338 | |
---|
339 | // Variable timer=StartMSTimer |
---|
340 | Variable ans |
---|
341 | SVAR sq = gSig_Q |
---|
342 | SVAR qb = gQ_bar |
---|
343 | SVAR sh = gShadow |
---|
344 | SVAR gQ = gQVals |
---|
345 | |
---|
346 | ans = Smear_Model_20(OneLevel,$sq,$qb,$sh,$gQ,w,x) |
---|
347 | |
---|
348 | // Print "HS elapsed time(s) = ",StopMSTimer(timer)*1e-6 |
---|
349 | return(ans) |
---|
350 | End |
---|
351 | |
---|
352 | Function SmearedTwoLevel(w,x) :FitFunc |
---|
353 | Wave w |
---|
354 | Variable x |
---|
355 | |
---|
356 | Variable ans |
---|
357 | SVAR sq = gSig_Q |
---|
358 | SVAR qb = gQ_bar |
---|
359 | SVAR sh = gShadow |
---|
360 | SVAR gQ = gQVals |
---|
361 | |
---|
362 | ans = Smear_Model_20(TwoLevel,$sq,$qb,$sh,$gQ,w,x) |
---|
363 | |
---|
364 | return(ans) |
---|
365 | End |
---|
366 | |
---|
367 | Function SmearedThreeLevel(w,x) :FitFunc |
---|
368 | Wave w |
---|
369 | Variable x |
---|
370 | |
---|
371 | Variable ans |
---|
372 | SVAR sq = gSig_Q |
---|
373 | SVAR qb = gQ_bar |
---|
374 | SVAR sh = gShadow |
---|
375 | SVAR gQ = gQVals |
---|
376 | |
---|
377 | ans = Smear_Model_20(ThreeLevel,$sq,$qb,$sh,$gQ,w,x) |
---|
378 | |
---|
379 | return(ans) |
---|
380 | End |
---|
381 | |
---|
382 | Function SmearedFourLevel(w,x) :FitFunc |
---|
383 | Wave w |
---|
384 | Variable x |
---|
385 | |
---|
386 | Variable ans |
---|
387 | SVAR sq = gSig_Q |
---|
388 | SVAR qb = gQ_bar |
---|
389 | SVAR sh = gShadow |
---|
390 | SVAR gQ = gQVals |
---|
391 | |
---|
392 | ans = Smear_Model_20(FourLevel,$sq,$qb,$sh,$gQ,w,x) |
---|
393 | |
---|
394 | return(ans) |
---|
395 | End |
---|