#pragma rtGlobals=1		// Use modern global access method.
#pragma IgorVersion=6.0

////////////////////////////////////////////////////
// calculates the scattering from a polydisperse spherical shell with a diffuse interface
//
// - the radius of the shell has a gaussian polydispersity
// - the shell has a Gaussian SLD profile, rather than a slab
// - currently normalized by the total sphere excluded volume
//
// M. Gradzielski, D. Langevin, L. Magid, R. Strey, JPC 99 (1995) 13232 
//
// keep polydispersity < 0.35 for approximations to be valid
//
////////////////////////////////////////////////////

//
Proc PlotGaussianShell(num,qmin,qmax)
	Variable num=200, 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_GaussianShell, ywave_GaussianShell
	xwave_GaussianShell =  alog(log(qmin) + x*((log(qmax)-log(qmin))/num))
	Make/O/D coef_GaussianShell = {1.,100,5,0.2,1e-6,6.34e-6,0}		
	make/o/t parameters_GaussianShell = {"scale","Radius (A)","Shell thickness Std. Dev. (A)","radius polydispersity","SLD Shell (A-2)","SLD solvent (A-2)","bkgd (cm-1)"}
	Edit parameters_GaussianShell, coef_GaussianShell
	
	Variable/G root:g_GaussianShell
	g_GaussianShell := GaussianShell(coef_GaussianShell, ywave_GaussianShell, xwave_GaussianShell)
	Display ywave_GaussianShell vs xwave_GaussianShell
	ModifyGraph marker=29, msize=2, mode=4
	ModifyGraph log=1,grid=1,mirror=2
	Label bottom "q (�\\S-1\\M) "
	Label left "I(q) (cm\\S-1\\M)"
	AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2)
	
	AddModelToStrings("GaussianShell","coef_GaussianShell","parameters_GaussianShell","GaussianShell")
//
End


//
//no input parameters are necessary, it MUST use the experimental q-values
// from the experimental data read in from an AVE/QSIG data file
////////////////////////////////////////////////////
// - sets up a dependency to a wrapper, not the actual SmearedModelFunction
Proc PlotSmearedGaussianShell(str)								
	String str
	Prompt str,"Pick the data folder containing the resolution you want",popup,getAList(4)
	
	// if any of the resolution waves are missing => abort
	if(ResolutionWavesMissingDF(str))		//updated to NOT use global strings (in GaussUtils)
		Abort
	endif
	
	SetDataFolder $("root:"+str)
	
	// Setup parameter table for model function
	Make/O/D smear_coef_GaussianShell = {1.,100,5,0.2,1e-6,6.34e-6,0}		
	make/o/t smear_parameters_GaussianShell = {"scale","Radius (A)","Shell thickness Std. Dev. (A)","radius polydispersity","SLD Shell (A-2)","SLD solvent (A-2)","bkgd (cm-1)"}
	Edit smear_parameters_GaussianShell,smear_coef_GaussianShell					//display parameters in a table
	
	// output smeared intensity wave, dimensions are identical to experimental QSIG values
	// make extra copy of experimental q-values for easy plotting
	Duplicate/O $(str+"_q") smeared_GaussianShell,smeared_qvals
	SetScale d,0,0,"1/cm",smeared_GaussianShell
					
	Variable/G gs_GaussianShell=0
	gs_GaussianShell := fSmearedGaussianShell(smear_coef_GaussianShell,smeared_GaussianShell,smeared_qvals)	//this wrapper fills the STRUCT
	
	Display smeared_GaussianShell vs smeared_qvals
	ModifyGraph log=1,marker=29,msize=2,mode=4
	Label bottom "q (�\\S-1\\M)"
	Label left "I(q) (cm\\S-1\\M)"
	AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2)
	
	SetDataFolder root:
	AddModelToStrings("SmearedGaussianShell","smear_coef_GaussianShell","smear_parameters_GaussianShell","GaussianShell")
End


//
//AAO version, uses XOP if available
// simply calls the original single point calculation with
// a wave assignment (this will behave nicely if given point ranges)
Function GaussianShell(cw,yw,xw) : FitFunc
	Wave cw,yw,xw
	
#if exists("GaussianShellX")
	yw = GaussianShellX(cw,xw)
#else
	yw = fGaussianShell(cw,xw)
#endif
	return(0)
End

//
// unsmeared model calculation
//
Function fGaussianShell(w,x) : FitFunc
	Wave w
	Variable x
	
	// variables are:							
	//[0] scale
	//[1] radius (�)
	//[2] thick (�) (thickness parameter - this is the std. dev. of the Gaussian width of the shell)
	//[3] polydispersity of the radius
	//[4] sld shell (�-2)
	//[5] sld solvent
	//[6] background (cm-1)
	
	Variable scale,rad,delrho,bkg,del,thick,pd,sig,zf
	Variable t1,t2,t3,t4,retval,exfact,vshell,vexcl,sldShell,sldSolvent
	scale = w[0]
	rad = w[1]
	thick = w[2]
	pd = w[3]
	sldShell = w[4]
	sldSolvent = w[5]
	bkg = w[6]
	
	delrho = w[4] - w[5]
	sig = pd*rad
	
	///APPROXIMATION (see eqn 4 - but not a bad approximation)
	// del is the equivalent shell thickness with sharp boundaries, centered at mean radius
	del = thick*sqrt(2*pi)
	
	// calculate the polydisperse shell volume and the excluded volume
	vshell=4*pi/3*( (rad+del/2)^3 - (rad-del/2)^3 ) *(1+pd^2)
	vexcl=4*pi/3*( (rad+del/2)^3 ) *(1+pd^2)
	
	//intensity, eqn 9(a-d)
	exfact = exp(-2*sig^2*x^2)
	
	t1 = 0.5*x^2*thick^4*(1+cos(2*x*rad)*exfact)
	t2 = x*thick^2*(rad*sin(2*x*rad) + 2*x*sig^2*cos(2*x*rad))*exfact
	t3 = 0.5*rad^2*(1-cos(2*x*rad)*exfact)
	t4 = 0.5*sig^2*(1+4*x*rad*sin(2*x*rad)*exfact+cos(2*x*rad)*(4*sig^2*x^2-1)*exfact)
	
	retval = t1+t2+t3+t4
	retval *= exp(-1*x*x*thick*thick)
	retval *= (del*del/x/x)
	retval *= 16*pi*pi*delrho*delrho*scale
	retval *= 1e8
	
	//NORMALIZED by the AVERAGE shell volume, since scale is the volume fraction of material
//	retval /= vshell
	retval /= vexcl
	//re-normalize by polydisperse sphere volume, Gaussian distribution
	retval /= (1+3*pd^2)
	
	retval += bkg
	
	return(retval)
	
End

//CH#4	
///////////////////////////////////////////////////////////////
// smeared model calculation
//
// you don't need to do anything with this function, as long as
// your GaussianShell works correctly, you get the resolution-smeared
// version for free.
//
// this is all there is to the smeared model calculation!
Function SmearedGaussianShell(s) : FitFunc
	Struct ResSmearAAOStruct &s

//	the name of your unsmeared model (AAO) is the first argument
	Smear_Model_20(GaussianShell,s.coefW,s.xW,s.yW,s.resW)

	return(0)
End


///////////////////////////////////////////////////////////////


// nothing to change here
//
//wrapper to calculate the smeared model as an AAO-Struct
// fills the struct and calls the ususal function with the STRUCT parameter
//
// used only for the dependency, not for fitting
//
Function fSmearedGaussianShell(coefW,yW,xW)
	Wave coefW,yW,xW
	
	String str = getWavesDataFolder(yW,0)
	String DF="root:"+str+":"
	
	WAVE resW = $(DF+str+"_res")
	
	STRUCT ResSmearAAOStruct fs
	WAVE fs.coefW = coefW	
	WAVE fs.yW = yW
	WAVE fs.xW = xW
	WAVE fs.resW = resW
	
	Variable err
	err = SmearedGaussianShell(fs)
	
	return (0)
End