1 | #pragma rtGlobals=1 // Use modern global access method. |
---|
2 | #pragma IgorVersion = 6.0 |
---|
3 | |
---|
4 | //#include "GaussUtils" |
---|
5 | //#include "PlotUtils" |
---|
6 | |
---|
7 | //////////////////////////////////////////////////// |
---|
8 | // |
---|
9 | // calculates the scattering from a triaxial ellipsoid |
---|
10 | // with semi-axes a <= b <= c |
---|
11 | // |
---|
12 | // - the user must make sure that the constraints are not violated |
---|
13 | // otherwise the calculation will not be correct |
---|
14 | // |
---|
15 | // a double integral is used, both using Gaussian quadrature |
---|
16 | // routines that are now included with GaussUtils |
---|
17 | // 20-pt quadrature appears to be enough, 76 pt is available |
---|
18 | // by changing the function calls |
---|
19 | // |
---|
20 | //////////////////////////////////////////////////// |
---|
21 | |
---|
22 | //this macro sets up all the necessary parameters and waves that are |
---|
23 | //needed to calculate the model function. |
---|
24 | // |
---|
25 | Proc PlotTriaxialEllipsoid(num,qmin,qmax) |
---|
26 | Variable num=100, qmin=.001, qmax=.7 |
---|
27 | Prompt num "Enter number of data points for model: " |
---|
28 | Prompt qmin "Enter minimum q-value (^1) for model: " |
---|
29 | Prompt qmax "Enter maximum q-value (^1) for model: " |
---|
30 | // |
---|
31 | Make/O/D/n=(num) xwave_triax, ywave_triax |
---|
32 | xwave_triax = alog(log(qmin) + x*((log(qmax)-log(qmin))/num)) |
---|
33 | Make/O/D coef_triax = {1,35,100,400,6e-6,0} //CH#2 |
---|
34 | make/o/t parameters_triax = {"Scale Factor","Semi-axis A [smallest]()","Semi-axis B ()","Semi-axis C [largest]()","Contrast (^-2)","Incoherent Bgd (cm-1)"} //CH#3 |
---|
35 | Edit parameters_triax, coef_triax |
---|
36 | |
---|
37 | Variable/G root:g_triax |
---|
38 | g_triax := TriaxialEllipsoid(coef_triax, ywave_triax, xwave_triax) |
---|
39 | Display ywave_triax vs xwave_triax |
---|
40 | ModifyGraph marker=29, msize=2, mode=4 |
---|
41 | ModifyGraph log=1 |
---|
42 | Label bottom "q (\\S-1\\M) " |
---|
43 | Label left "I(q) (cm\\S-1\\M)" |
---|
44 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
---|
45 | |
---|
46 | AddModelToStrings("TriaxialEllipsoid","coef_triax","triax") |
---|
47 | // |
---|
48 | End |
---|
49 | |
---|
50 | |
---|
51 | // - sets up a dependency to a wrapper, not the actual SmearedModelFunction |
---|
52 | Proc PlotSmearedTriaxialEllipsoid(str) |
---|
53 | String str |
---|
54 | Prompt str,"Pick the data folder containing the resolution you want",popup,getAList(4) |
---|
55 | |
---|
56 | // if any of the resolution waves are missing => abort |
---|
57 | if(ResolutionWavesMissingDF(str)) //updated to NOT use global strings (in GaussUtils) |
---|
58 | Abort |
---|
59 | endif |
---|
60 | |
---|
61 | SetDataFolder $("root:"+str) |
---|
62 | |
---|
63 | // Setup parameter table for model function |
---|
64 | Make/O/D smear_coef_triax = {1,35,100,400,6e-6,0} //CH#4 |
---|
65 | make/o/t smear_parameters_triax = {"Scale Factor","A ()","B ()","C ()","Contrast (^-2)","Incoherent Bgd (cm-1)"} |
---|
66 | Edit smear_parameters_triax,smear_coef_triax //display parameters in a table |
---|
67 | |
---|
68 | // output smeared intensity wave, dimensions are identical to experimental QSIG values |
---|
69 | // make extra copy of experimental q-values for easy plotting |
---|
70 | Duplicate/O $(str+"_q") smeared_triax,smeared_qvals // |
---|
71 | SetScale d,0,0,"1/cm",smeared_triax // |
---|
72 | |
---|
73 | Variable/G gs_triax=0 |
---|
74 | gs_triax := fSmearedTriaxialEllipsoid(smear_coef_triax,smeared_triax,smeared_qvals) //this wrapper fills the STRUCT |
---|
75 | |
---|
76 | Display smeared_triax vs smeared_qvals // |
---|
77 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
---|
78 | Label bottom "q (\\S-1\\M)" |
---|
79 | Label left "I(q) (cm\\S-1\\M)" |
---|
80 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
---|
81 | |
---|
82 | SetDataFolder root: |
---|
83 | AddModelToStrings("SmearedTriaxialEllipsoid","smear_coef_triax","triax") |
---|
84 | End |
---|
85 | |
---|
86 | |
---|
87 | |
---|
88 | //AAO version, uses XOP if available |
---|
89 | // simply calls the original single point calculation with |
---|
90 | // a wave assignment (this will behave nicely if given point ranges) |
---|
91 | Function TriaxialEllipsoid(cw,yw,xw) : FitFunc |
---|
92 | Wave cw,yw,xw |
---|
93 | |
---|
94 | #if exists("TriaxialEllipsoidX") |
---|
95 | yw = TriaxialEllipsoidX(cw,xw) |
---|
96 | #else |
---|
97 | yw = fTriaxialEllipsoid(cw,xw) |
---|
98 | #endif |
---|
99 | return(0) |
---|
100 | End |
---|
101 | |
---|
102 | // calculates the form factor of an ellipsoidal solid |
---|
103 | // with semi-axes of a,b,c |
---|
104 | // - a double integral - choose points wisely |
---|
105 | // |
---|
106 | Function fTriaxialEllipsoid(w,x) : FitFunc |
---|
107 | Wave w |
---|
108 | Variable x |
---|
109 | // Input (fitting) variables are: |
---|
110 | //[0] scale factor |
---|
111 | //[1] semi-axis A (A) |
---|
112 | //[2] semi-axis B (A) |
---|
113 | //[3] semi-axis C (A) |
---|
114 | //[4] contrast (A^-2) |
---|
115 | //[5] incoherent background (cm^-1) |
---|
116 | // give them nice names |
---|
117 | Variable scale,aa,bb,cc,contr,bkg,inten,qq,ii,arg,mu |
---|
118 | scale = w[0] |
---|
119 | aa = w[1] |
---|
120 | bb = w[2] |
---|
121 | cc = w[3] |
---|
122 | contr = w[4] |
---|
123 | bkg = w[5] |
---|
124 | |
---|
125 | Variable/G root:gDumY=0,root:gDumX=0 |
---|
126 | |
---|
127 | inten = IntegrateFn20(TaE_Outer,0,1,w,x) |
---|
128 | |
---|
129 | inten *= 4*Pi/3*aa*cc*bb //multiply by volume |
---|
130 | inten *= 1e8 //convert to cm^-1 |
---|
131 | inten *= contr*contr |
---|
132 | inten *= scale |
---|
133 | inten += bkg |
---|
134 | |
---|
135 | Return (inten) |
---|
136 | End |
---|
137 | |
---|
138 | // outer integral |
---|
139 | // x is the q-value - remember that "mu" in the notation = B*Q |
---|
140 | Function TaE_Outer(w,x,dum) |
---|
141 | Wave w |
---|
142 | Variable x,dum |
---|
143 | |
---|
144 | Variable retVal,mu,aa,bb,cc,mudum,arg |
---|
145 | aa = w[1] |
---|
146 | bb = w[2] |
---|
147 | cc = w[3] |
---|
148 | |
---|
149 | NVAR dy = root:gDumY |
---|
150 | NVAR dx = root:gDumX |
---|
151 | dy = dum |
---|
152 | retval = IntegrateFn20(TaE_inner,0,1,w,x) |
---|
153 | |
---|
154 | return(retVal) |
---|
155 | End |
---|
156 | |
---|
157 | //returns the value of the integrand of the inner integral |
---|
158 | Function TaE_Inner(w,x,dum) |
---|
159 | Wave w |
---|
160 | Variable x,dum |
---|
161 | |
---|
162 | Variable aa,bb,cc,retVal |
---|
163 | |
---|
164 | NVAR dy = root:gDumY |
---|
165 | NVAR dx = root:gDumX |
---|
166 | dx = dum |
---|
167 | aa = w[1] |
---|
168 | bb = w[2] |
---|
169 | cc = w[3] |
---|
170 | retVal = TaE(x,aa,bb,cc,dx,dy) |
---|
171 | |
---|
172 | return(retVal) |
---|
173 | End |
---|
174 | |
---|
175 | Function TaE(qq,aa,bb,cc,dx,dy) |
---|
176 | Variable qq,aa,bb,cc,dx,dy |
---|
177 | |
---|
178 | Variable val,arg |
---|
179 | arg = aa*aa*cos(pi*dx/2)*cos(pi*dx/2) |
---|
180 | arg += bb*bb*sin(pi*dx/2)*sin(pi*dx/2)*(1-dy*dy) |
---|
181 | arg += cc*cc*dy*dy |
---|
182 | arg = qq*sqrt(arg) |
---|
183 | |
---|
184 | val = 9*((sin(arg) - arg*cos(arg))/arg^3 )^2 |
---|
185 | |
---|
186 | return(val) |
---|
187 | end |
---|
188 | |
---|
189 | //wrapper to calculate the smeared model as an AAO-Struct |
---|
190 | // fills the struct and calls the ususal function with the STRUCT parameter |
---|
191 | // |
---|
192 | // used only for the dependency, not for fitting |
---|
193 | // |
---|
194 | Function fSmearedTriaxialEllipsoid(coefW,yW,xW) |
---|
195 | Wave coefW,yW,xW |
---|
196 | |
---|
197 | String str = getWavesDataFolder(yW,0) |
---|
198 | String DF="root:"+str+":" |
---|
199 | |
---|
200 | WAVE resW = $(DF+str+"_res") |
---|
201 | |
---|
202 | STRUCT ResSmearAAOStruct fs |
---|
203 | WAVE fs.coefW = coefW |
---|
204 | WAVE fs.yW = yW |
---|
205 | WAVE fs.xW = xW |
---|
206 | WAVE fs.resW = resW |
---|
207 | |
---|
208 | Variable err |
---|
209 | err = SmearedTriaxialEllipsoid(fs) |
---|
210 | |
---|
211 | return (0) |
---|
212 | End |
---|
213 | |
---|
214 | // this is all there is to the smeared calculation! |
---|
215 | Function SmearedTriaxialEllipsoid(s) :FitFunc |
---|
216 | Struct ResSmearAAOStruct &s |
---|
217 | |
---|
218 | // the name of your unsmeared model (AAO) is the first argument |
---|
219 | Smear_Model_20(TriaxialEllipsoid,s.coefW,s.xW,s.yW,s.resW) |
---|
220 | |
---|
221 | return(0) |
---|
222 | End |
---|