source: sans/Analysis/branches/ajj_23APR07/IGOR_Package_Files/Put in User Procedures/SANS_Models_v3.00/NewModels_2006/LogNormalSphere.ipf @ 92

#pragma rtGlobals=1             // Use modern global access method.

#include "sphere"
// plots the form factor of spherical particles with a log-normal radius distribution
//
// for the integration it may be better to use adaptive routine

//Proc to setup data and coefficients to plot the model
Proc PlotLogNormalPolySphere(num,qmin,qmax)
        Variable num=128,qmin=0.001,qmax=0.7
        Prompt num "Enter number of data points for model: "
        Prompt qmin "Enter minimum q-value (^-1) for model: "
        Prompt qmax "Enter maximum q-value (^-1) for model: "
        
        Make/O/D/N=(num) xwave_lns,ywave_lns
        xwave_lns = alog( log(qmin) + x*((log(qmax)-log(qmin))/num) )
        Make/O/D coef_lns = {0.01,60,0.2,1e-6,2e-6,0}
        make/O/T parameters_lns = {"Volume Fraction (scale)","exp(mu)=median Radius (A)","sigma","SLD sphere (A-2)","SLD solvent (A-2)","bkg (cm-1 sr-1)"}
        Edit parameters_lns,coef_lns
        ywave_lns := LogNormalPolySphere(coef_lns,xwave_lns)
        Display ywave_lns vs xwave_lns
        ModifyGraph log=1,marker=29,msize=2,mode=4
        Label bottom "q (\\S-1\\M)"
        Label left "Intensity (cm\\S-1\\M)"
        AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2)
End

Proc PlotSmearLogNormPolySphere()                                                               
        //no input parameters necessary, it MUST use the experimental q-values
        // from the experimental data read in from an AVE/QSIG data file
        
        // if no gQvals wave, data must not have been loaded => abort
        if(ResolutionWavesMissing())
                Abort
        endif
        
        // Setup parameter table for model function
        Make/O/D smear_coef_lns = {0.01,60,0.2,1e-6,2e-6,0}                                     
        make/o/t smear_parameters_lns = {"Volume Fraction (scale)","exp(mu)=median Radius (A)","sigma","SLD sphere (A-2)","SLD solvent (A-2)","bkg (cm-1 sr-1)"}                
        Edit smear_parameters_lns,smear_coef_lns                                        
        
        // output smeared intensity wave, dimensions are identical to experimental QSIG values
        // make extra copy of experimental q-values for easy plotting
        Duplicate/O $gQvals smeared_lns,smeared_qvals                           
        SetScale d,0,0,"1/cm",smeared_lns                                                       

        smeared_lns := SmearLogNormSphere(smear_coef_lns,$gQvals)               
        Display smeared_lns vs smeared_qvals                                                                    
        ModifyGraph log=1,marker=29,msize=2,mode=4
        Label bottom "q (\\S-1\\M)"
        Label left "Intensity (cm\\S-1\\M)"
        AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2)
End


// calculates the model at each q-value by integrating over the normalized size distribution
// integration is done by gauss quadrature of either 20 or 76 points (nord)
// 76 points is slower, but reccommended to remove high-q oscillations
//
Function LogNormalPolySphere(w,x): FitFunc
        wave w
        variable x
        
        Variable scale,rad,sig,rho,rhos,bkg,delrho,mu,r3
        
        //set up the coefficient values
        scale=w[0]
        rad=w[1]                //rad is the median radius
        mu = ln(w[1])
        sig=w[2]
        rho=w[3]
        rhos=w[4]
        delrho=rho-rhos
        bkg=w[5]
        
//temp set scale=1 and bkg=0 for quadrature calc
        Make/O/D/N=4 sphere_temp
        sphere_temp[0] = 1
        sphere_temp[1] = rad            //changed in loop
        sphere_temp[2] = delrho
        sphere_temp[3] = 0
        
        //currently using 20 pts...
        Variable va,vb,ii,zi,nord,yy,summ,inten
        String weightStr,zStr
        
        //select number of gauss points by setting nord=20 or76 points
//      nord = 20
        nord = 76
        
        weightStr = "gauss"+num2str(nord)+"wt"
        zStr = "gauss"+num2str(nord)+"z"
        
        if (WaveExists($weightStr) == 0) // wave reference is not valid, 
                Make/D/N=(nord) $weightStr,$zStr
                Wave gauWt = $weightStr
                Wave gauZ = $zStr               // wave references to pass
                if(nord==20)
                        Make20GaussPoints(gauWt,gauZ)
                else
                        Make76GaussPoints(gauWt,gauZ)
                endif   
        else
                if(exists(weightStr) > 1) 
                         Abort "wave name is already in use"            //executed only if name is in use elsewhere
                endif
                Wave gauWt = $weightStr
                Wave gauZ = $zStr               // create the wave references
        endif
        
        // end points of integration
        // limits are technically 0-inf, but wisely choose interesting region of q where R() is nonzero
        // +/- 3 sigq catches 99.73% of distrubution
        // change limits (and spacing of zi) at each evaluation based on R()
        //integration from va to vb
        
//      va = -3*sig + rad
        va = -3.5*sig +mu               //in ln(R) space
        va = exp(va)                    //in R space
        if (va<0)
                va=0            //to avoid numerical error when  va<0 (-ve q-value)
        endif
//      vb = 3*exp(sig) +rad
        vb = 3.5*sig*(1+sig)+ mu
        vb = exp(vb)
        
        summ = 0.0              // initialize integral
        for(ii=0;ii<nord;ii+=1)
                // calculate Gauss points on integration interval (r-value for evaluation)
                zi = ( gauZ[ii]*(vb-va) + vb + va )/2.0
                sphere_temp[1] = zi
                // calculate sphere scattering
                yy = gauWt[ii] *  LogNormal_distr(sig,mu,zi) * SphereForm(sphere_temp,x)
                yy *= 4*pi/3*zi*zi*zi           //un-normalize by current sphere volume
                
                summ += yy              //add to the running total of the quadrature
        endfor
// calculate value of integral to return
        inten = (vb-va)/2.0*summ
        
        //re-normalize by polydisperse sphere volume
        //third moment
        r3 = exp(3*mu + 9/2*sig^2)              // <R^3> directly
        inten /= (4*pi/3*r3)            //polydisperse volume
        
        inten *= scale
        inten+=bkg
        
        Return(inten)
End

// this is all there is to the smeared calculation!
Function SmearLogNormSphere(w,x) :FitFunc
        Wave w
        Variable x
        
        Variable ans
        SVAR sq = gSig_Q
        SVAR qb = gQ_bar
        SVAR sh = gShadow
        SVAR gQ = gQVals
        
        //the name of your unsmeared model is the first argument
        ans = Smear_Model_20(LogNormalPolySphere,$sq,$qb,$sh,$gQ,w,x)

        return(ans)
End

// normalization is correct, using 3rd moment of lognormal distribution
//
Function LogNormal_distr(sig,mu,pt)
        Variable sig,mu,pt
        
        Variable retval
        
        retval = (1/ ( sig*pt*sqrt(2*pi)) )*exp( -0.5*((ln(pt) - mu)^2)/sig^2 )
        return(retval)
End

//calculates number density given the coefficients of the lognormal distribution
// the scale factor is the volume fraction
// then nden = phi/<V> where <V> is calculated using the 3rd moment of the radius
Macro NumberDensity_LogN()
        
        Variable nden,r3,rg,sv,i0,ravg,rpk
        
        if(WaveExists(coef_lns)==0)
                abort "You need to plot the model first to create the coefficient table"
        Endif
        
        Print "median radius (A) = ",coef_lns[1]
        Print "sigma = ",coef_lns[2]
        Print "volume fraction = ",coef_lns[0]
        
        r3 = exp(3*ln(coef_lns[1]) + 9/2*coef_lns[2]^2)         // <R^3> directly,[A^3]
        nden = coef_lns[0]/(4*pi/3*r3)          //nden in 1/A^3
        ravg = exp(ln(coef_lns[1]) + 0.5*coef_lns[2]^2)
        rpk = exp(ln(coef_lns[1]) - coef_lns[2]^2)
        rg = (3./5.)^0.5*exp(ln(coef_lns[1]) + 7.*coef_lns[2]^2)
        sv = 1.0e8*3*coef_lns[0]*exp(-ln(coef_lns[1]) - 2.5*coef_lns[2]^2)
        i0 = 1.0e8*(4*pi/3)*coef_lns[0]*(coef_lns[3]-coef_lns[4])^2*exp(3*ln(coef_lns[1]) + 13.5*coef_lns[2]^2)
        
        Print "number density (A^-3) = ",nden
        Print "mean radius (A) = ",ravg
        Print "peak dis. radius (A) = ",rpk
        Print "Guinier radius (A) = ",rg
        Print "Interfacial surface area / volume (cm-1) Sv = ",sv
        Print "Forward cross section (cm-1 sr-1) I(0) = ",i0
End

// plots the lognormal distribution based on the coefficient values
// a static calculation, so re-run each time
//
Macro PlotLogNormalDistribution()

        variable sig,mu,maxr
        
        if(WaveExists(coef_lns)==0)
                abort "You need to plot the model first to create the coefficient table"
        Endif
        sig=coef_lns[2]
        mu = ln(coef_lns[1])
        
        Make/O/D/N=1000 lognormal_distribution
        maxr = 5*sig*(1+sig)+ mu
        maxr = exp(maxr)
        SetScale/I x, 0, maxr, lognormal_distribution
        lognormal_distribution = LogNormal_distr(sig,mu,x)
        Display lognormal_distribution
        modifygraph log(bottom)=1
        legend
End