source: sans/Dev/trunk/NCNR_User_Procedures/Analysis/Models/NewModels_2008/Spherocylinder_v40.ipf @ 449

Last change on this file since 449 was 449, checked in by srkline, 14 years ago

Adding the model of a cylinder with spherical end caps. By taking all of the limiting cases, 5 models are added. Since the geometries are sufficiently different, I thought it best to add as separate models. Corresponding changes have been made to the Wrapper and the modelPicker

File size: 7.0 KB
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1#pragma rtGlobals=1             // Use modern global access method.
2#pragma IgorVersion = 6.0
3
4////////////////////////////////////////////////////
5//
6// calculates the scattering of a spherocylinder, that is a cylinder with spherical end caps
7// where the radius of the end caps is the same as the radius of the cylinder
8//
9// a double integral is used, both using Gaussian quadrature
10// routines that are now included with GaussUtils
11//
12// 76 point quadrature is necessary for both quadrature calls.
13//
14//
15// REFERENCE:
16//              H. Kaya, J. Appl. Cryst. (2004) 37, 223-230.
17//              H. Kaya and N-R deSouza, J. Appl. Cryst. (2004) 37, 508-509. (addenda and errata)
18//
19////////////////////////////////////////////////////
20
21//this macro sets up all the necessary parameters and waves that are
22//needed to calculate the model function.
23//
24Proc PlotSpherocylinder(num,qmin,qmax)
25        Variable num=100, qmin=.001, qmax=.7
26        Prompt num "Enter number of data points for model: "
27        Prompt qmin "Enter minimum q-value (^1) for model: "
28        Prompt qmax "Enter maximum q-value (^1) for model: "
29        //
30        Make/O/D/n=(num) xwave_SphCyl, ywave_SphCyl
31        xwave_SphCyl =  alog(log(qmin) + x*((log(qmax)-log(qmin))/num))
32        Make/O/D coef_SphCyl = {1,20,400,1e-6,6.3e-6,0}                 //CH#2
33        make/o/t parameters_SphCyl = {"Scale Factor","cylinder radius rc (A)","cylinder length (A)","SLD cylinder (A^-2)","SLD solvent (A^-2)","Incoherent Bgd (cm-1)"} //CH#3
34        Edit parameters_SphCyl, coef_SphCyl
35       
36        Variable/G root:g_SphCyl
37        g_SphCyl := Spherocylinder(coef_SphCyl, ywave_SphCyl, xwave_SphCyl)
38        Display ywave_SphCyl vs xwave_SphCyl
39        ModifyGraph marker=29, msize=2, mode=4
40        ModifyGraph log=1
41        Label bottom "q (A\\S-1\\M)"
42        Label left "I(q) (cm\\S-1\\M)"
43        AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2)
44       
45        AddModelToStrings("Spherocylinder","coef_SphCyl","SphCyl")
46//
47End
48
49
50// - sets up a dependency to a wrapper, not the actual SmearedModelFunction
51Proc PlotSmearedSpherocylinder(str)                                                             
52        String str
53        Prompt str,"Pick the data folder containing the resolution you want",popup,getAList(4)
54       
55        // if any of the resolution waves are missing => abort
56        if(ResolutionWavesMissingDF(str))               //updated to NOT use global strings (in GaussUtils)
57                Abort
58        endif
59       
60        SetDataFolder $("root:"+str)
61       
62        // Setup parameter table for model function
63        Make/O/D smear_coef_SphCyl = {1,20,400,1e-6,6.3e-6,0}           //CH#4
64        make/o/t smear_parameters_SphCyl = {"Scale Factor","cylinder radius rc (A)","cylinder length (A)","SLD cylinder (A^-2)","SLD solvent (A^-2)","Incoherent Bgd (cm-1)"}
65        Edit smear_parameters_SphCyl,smear_coef_SphCyl                                  //display parameters in a table
66       
67        // output smeared intensity wave, dimensions are identical to experimental QSIG values
68        // make extra copy of experimental q-values for easy plotting
69        Duplicate/O $(str+"_q") smeared_SphCyl,smeared_qvals                            //
70        SetScale d,0,0,"1/cm",smeared_SphCyl                                                    //
71                                       
72        Variable/G gs_SphCyl=0
73        gs_SphCyl := fSmearedSpherocylinder(smear_coef_SphCyl,smeared_SphCyl,smeared_qvals)     //this wrapper fills the STRUCT
74       
75        Display smeared_SphCyl vs smeared_qvals                                                                 //
76        ModifyGraph log=1,marker=29,msize=2,mode=4
77        Label bottom "q (A\\S-1\\M)"
78        Label left "I(q) (cm\\S-1\\M)"
79        AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2)
80       
81        SetDataFolder root:
82        AddModelToStrings("SmearedSpherocylinder","smear_coef_SphCyl","SphCyl")
83End
84
85       
86
87//AAO version, uses XOP if available
88// simply calls the original single point calculation with
89// a wave assignment (this will behave nicely if given point ranges)
90Function Spherocylinder(cw,yw,xw) : FitFunc
91        Wave cw,yw,xw
92       
93#if exists("SpherocylinderX")
94        yw = SpherocylinderX(cw,xw)
95#else
96        yw = fSpherocylinder(cw,xw)
97#endif
98        return(0)
99End
100
101//
102// - a double integral - choose points wisely - 76 for both...
103//
104Function fSpherocylinder(w,x) : FitFunc
105        Wave w
106        Variable x
107//       Input (fitting) variables are:
108        //[0] scale factor
109        //[1] cylinder radius (little r)
110        //[2] cylinder length (big L)
111        //[3] end cap radius (big R)
112        //[4] sld cylinder (A^-2)
113        //[5] sld solvent
114        //[6] incoherent background (cm^-1)
115//      give them nice names
116        Variable scale,contr,bkg,inten,sldc,slds
117        Variable len,rad,hDist,endRad
118        scale = w[0]
119        rad = w[1]
120        len = w[2]
121//      endRad = w[3]
122        sldc = w[3]
123        slds = w[4]
124        bkg = w[5]
125       
126        Make/O/D/N=7 SphCyl_tmp
127        SphCyl_tmp[0] = w[0]
128        SphCyl_tmp[1] = w[1]
129        SphCyl_tmp[2] = w[2]
130        SphCyl_tmp[3] = w[1]            //end radius is same as cylinder radius
131        SphCyl_tmp[4] = w[3]
132        SphCyl_tmp[5] = w[4]
133        SphCyl_tmp[6] = w[5]
134       
135        hDist = 0               //by definition
136               
137        contr = sldc-slds
138       
139        Variable/G root:gDumTheta=0,root:gDumT=0
140       
141        inten = IntegrateFn76(SphCyl_Outer,0,pi/2,SphCyl_tmp,x)
142       
143        inten /= pi*rad*rad*len + pi*4*endRad^3/3               //divide by volume
144        inten *= 1e8            //convert to cm^-1
145        inten *= contr*contr
146        inten *= scale
147        inten += bkg
148       
149        Return (inten)
150End
151
152// outer integral
153// x is the q-value
154Function SphCyl_Outer(w,x,dum)
155        Wave w
156        Variable x,dum
157       
158        Variable retVal
159        Variable scale,contr,bkg,inten,sldc,slds
160        Variable len,rad,hDist,endRad
161        scale = w[0]
162        rad = w[1]
163        len = w[2]
164        endRad = w[3]
165        sldc = w[4]
166        slds = w[5]
167        bkg = w[6]
168
169        hDist = 0
170                               
171        NVAR dTheta = root:gDumTheta
172        NVAR dt = root:gDumT
173        dTheta = dum
174        retval = IntegrateFn76(SphCyl_Inner,-hDist/endRad,1,w,x)
175       
176        Variable arg1,arg2
177        arg1 = x*len/2*cos(dum)
178        arg2 = x*rad*sin(dum)
179       
180        retVal += pi*rad*rad*len*sinc(arg1)*2*Besselj(1, arg2)/arg2
181       
182        retVal *= retval*sin(dum)               // = |A(q)|^2*sin(theta)
183       
184        return(retVal)
185End
186
187//returns the value of the integrand of the inner integral
188Function SphCyl_Inner(w,x,dum)
189        Wave w
190        Variable x,dum
191       
192        Variable retVal
193        Variable scale,contr,bkg,inten,sldc,slds
194        Variable len,rad,hDist,endRad
195        scale = w[0]
196        rad = w[1]
197        len = w[2]
198        endRad = w[3]
199        sldc = w[4]
200        slds = w[5]
201        bkg = w[6]
202       
203        NVAR dTheta = root:gDumTheta
204        NVAR dt = root:gDumT
205        dt = dum
206       
207        retVal = SphCyl(w,x,dt,dTheta)
208       
209        retVal *= 4*pi*endRad^3
210       
211        return(retVal)
212End
213
214Function SphCyl(w,x,tt,Theta)
215        Wave w
216        Variable x,tt,Theta
217       
218        Variable val,arg1,arg2
219        Variable scale,contr,bkg,inten,sldc,slds
220        Variable len,rad,hDist,endRad
221        scale = w[0]
222        rad = w[1]
223        len = w[2]
224        endRad = w[3]
225        sldc = w[4]
226        slds = w[5]
227        bkg = w[6]
228       
229        hDist = 0
230               
231        arg1 = x*cos(theta)*(endRad*tt+hDist+len/2)
232        arg2 = x*endRad*sin(theta)*sqrt(1-tt*tt)
233       
234        val = cos(arg1)*(1-tt*tt)*Besselj(1,arg2)/arg2
235       
236        return(val)
237end
238
239//wrapper to calculate the smeared model as an AAO-Struct
240// fills the struct and calls the ususal function with the STRUCT parameter
241//
242// used only for the dependency, not for fitting
243//
244Function fSmearedSpherocylinder(coefW,yW,xW)
245        Wave coefW,yW,xW
246       
247        String str = getWavesDataFolder(yW,0)
248        String DF="root:"+str+":"
249       
250        WAVE resW = $(DF+str+"_res")
251       
252        STRUCT ResSmearAAOStruct fs
253        WAVE fs.coefW = coefW   
254        WAVE fs.yW = yW
255        WAVE fs.xW = xW
256        WAVE fs.resW = resW
257       
258        Variable err
259        err = SmearedSpherocylinder(fs)
260       
261        return (0)
262End
263               
264// this is all there is to the smeared calculation!
265//
266// 20 points should be fine here. This function is not much different than cylinders, where 20 is sufficient
267Function SmearedSpherocylinder(s) :FitFunc
268        Struct ResSmearAAOStruct &s
269
270//      the name of your unsmeared model (AAO) is the first argument
271        Smear_Model_20(Spherocylinder,s.coefW,s.xW,s.yW,s.resW)
272
273        return(0)
274End
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