source: sans/Dev/trunk/NCNR_User_Procedures/Analysis/Models/NewModels_2006/Beaucage_v40.ipf @ 570

#pragma rtGlobals=1             // Use modern global access method.
#pragma IgorVersion=6.1

/////////////////////////////////////////////////////
//
// Plot's Greg Beaucage's Rg-power Law "model" of scattering
// somewhat useful for identifying length scales, but short on
// physical inerpretation of the real structure of the sample.
//
// up to 4 "levels" can be calculated
// best to start with single level, and fit a small range of
// the data, and add more levels as needed
//
// see the help file for the original references
//
Proc PlotOnelevel(num,qmin,qmax)
        Variable num=256,qmin=0.001,qmax=0.7
        Prompt num "Enter number of data points for model: "
        Prompt qmin "Enter minimum q-value (A^-1) for model: "
        Prompt qmax "Enter maximum q-value (A^-1) for model: "
        
        make/o/d/n=(num) xwave_b1,ywave_b1
        xwave_b1 = alog(log(qmin) + x*((log(qmax)-log(qmin))/num))
        make/o/d coef_b1 = {1,3,21,6e-4,2,0}
        make/o/t parameters_b1 = {"scale","G1 (cm-1 sr-1)","Rg1  (A)","B1 (cm-1 sr-1)","Pow1","bkg (cm-1 sr-1)"}
        Edit parameters_b1,coef_b1
        
        Variable/G root:g_b1
        g_b1 := OneLevel(coef_b1,ywave_b1,xwave_b1)
        Display ywave_b1 vs xwave_b1
        ModifyGraph log=1,marker=29,msize=2,mode=4
        Label bottom "q (A\\S-1\\M)"
        Label left "Intensity (cm\\S-1\\M)"
        AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2)
        
        AddModelToStrings("OneLevel","coef_b1","parameters_b1","b1")
End

Proc PlotTwoLevel(num,qmin,qmax)
        Variable num=256,qmin=0.001,qmax=0.7
        Prompt num "Enter number of data points for model: "
        Prompt qmin "Enter minimum q-value (A^-1) for model: "
        Prompt qmax "Enter maximum q-value (A^-1) for model: "
        
        make/o/d/n=(num) xwave_b2,ywave_b2
        xwave_b2 = alog(log(qmin) + x*((log(qmax)-log(qmin))/num))
        make/o/d coef_b2 = {1,400,200,5e-6,4,3,21,6e-4,2,0}
        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)"}
        Edit parameters_b2,coef_b2
        
        Variable/G root:g_b2
        g_b2 := TwoLevel(coef_b2,ywave_b2,xwave_b2)
        Display ywave_b2 vs xwave_b2
        ModifyGraph log=1,marker=29,msize=2,mode=4
        Label bottom "q (A\\S-1\\M)"
        Label left "Intensity (cm\\S-1\\M)"
        AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2)
        
        AddModelToStrings("TwoLevel","coef_b2","parameters_b2","b2")
End

Proc PlotThreeLevel(num,qmin,qmax)
        Variable num=256,qmin=0.001,qmax=0.7
        Prompt num "Enter number of data points for model: "
        Prompt qmin "Enter minimum q-value (A^-1) for model: "
        Prompt qmax "Enter maximum q-value (A^-1) for model: "
        
        make/o/d/n=(num) xwave_b3,ywave_b3
        xwave_b3 = alog(log(qmin) + x*((log(qmax)-log(qmin))/num))
        make/o/d coef_b3 = {1,4000,600,2e-7,4,400,200,5e-6,4,3,21,6e-4,2,0}
        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)"}
        Edit parameters_b3,coef_b3
        
        Variable/G root:g_b3
        g_b3 := ThreeLevel(coef_b3,ywave_b3,xwave_b3)   
        Display ywave_b3 vs xwave_b3
        ModifyGraph log=1,marker=29,msize=2,mode=4
        Label bottom "q (A\\S-1\\M)"
        Label left "Intensity (cm\\S-1\\M)"
        AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2)
        
        AddModelToStrings("ThreeLevel","coef_b3","parameters_b3","b3")
End

Proc PlotFourLevel(num,qmin,qmax)
        Variable num=256,qmin=0.001,qmax=0.7
        Prompt num "Enter number of data points for model: "
        Prompt qmin "Enter minimum q-value (A^-1) for model: "
        Prompt qmax "Enter maximum q-value (A^-1) for model: "
        
        make/o/d/n=(num) xwave_b4,ywave_b4
        xwave_b4 = alog(log(qmin) + x*((log(qmax)-log(qmin))/num))
        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}
        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)"}
        Edit parameters_b4,coef_b4
        
        Variable/G root:g_b4
        g_b4 := FourLevel(coef_b4,ywave_b4,xwave_b4)    
        Display ywave_b4 vs xwave_b4
        ModifyGraph log=1,marker=29,msize=2,mode=4
        Label bottom "q (A\\S-1\\M)"
        Label left "Intensity (cm\\S-1\\M)"
        AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2)
        
        AddModelToStrings("FourLevel","coef_b4","parameters_b4","b4")
End

/////////// macros for smeared model calculations

// - sets up a dependency to a wrapper, not the actual SmearedModelFunction
Proc PlotSmearedOneLevel(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_b1 ={1,3,21,6e-4,2,0}                                       
        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)"}  
        Edit smear_parameters_b1,smear_coef_b1                                  
        
        // 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_b1,smeared_qvals                                
        SetScale d,0,0,"1/cm",smeared_b1                                                        
                                        
        Variable/G gs_b1=0
        gs_b1 := fSmearedOneLevel(smear_coef_b1,smeared_b1,smeared_qvals)       //this wrapper fills the STRUCT
        
        Display smeared_b1 vs smeared_qvals                                                                     
        ModifyGraph log=1,marker=29,msize=2,mode=4
        Label bottom "q (A\\S-1\\M)"
        Label left "Intensity (cm\\S-1\\M)"
        AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2)
        
        SetDataFolder root:
        AddModelToStrings("SmearedOneLevel","smear_coef_b1","smear_parameters_b1","b1")
End
        
// - sets up a dependency to a wrapper, not the actual SmearedModelFunction
Proc PlotSmearedTwoLevel(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_b2 = {1,400,200,5e-6,4,3,21,6e-4,2,0}                               
        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)"}      
        Edit smear_parameters_b2,smear_coef_b2                                  
        
        // 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_b2,smeared_qvals                                
        SetScale d,0,0,"1/cm",smeared_b2                                                        
                                        
        Variable/G gs_b2=0
        gs_b2 := fSmearedTwoLevel(smear_coef_b2,smeared_b2,smeared_qvals)       //this wrapper fills the STRUCT
        
        Display smeared_b2 vs smeared_qvals                                                                     
        ModifyGraph log=1,marker=29,msize=2,mode=4
        Label bottom "q (A\\S-1\\M)"
        Label left "Intensity (cm\\S-1\\M)"
        AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2)
        
        SetDataFolder root:
        AddModelToStrings("SmearedTwoLevel","smear_coef_b2","smear_parameters_b2","b2")
End
        
// - sets up a dependency to a wrapper, not the actual SmearedModelFunction
Proc PlotSmearedThreeLevel(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_b3 = {1,4000,600,2e-7,4,400,200,5e-6,4,3,21,6e-4,2,0}
        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)"}
        Edit smear_parameters_b3,smear_coef_b3                                  
        
        // 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_b3,smeared_qvals                                
        SetScale d,0,0,"1/cm",smeared_b3                                                        
                                        
        Variable/G gs_b3=0
        gs_b3 := fSmearedThreeLevel(smear_coef_b3,smeared_b3,smeared_qvals)     //this wrapper fills the STRUCT
        
        Display smeared_b3 vs smeared_qvals                                                                     
        ModifyGraph log=1,marker=29,msize=2,mode=4
        Label bottom "q (A\\S-1\\M)"
        Label left "Intensity (cm\\S-1\\M)"
        AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2)
        
        SetDataFolder root:
        AddModelToStrings("SmearedThreeLevel","smear_coef_b3","smear_parameters_b3","b3")
End
        
// - sets up a dependency to a wrapper, not the actual SmearedModelFunction
Proc PlotSmearedFourLevel(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_b4 = {1,40000,2000,1e-8,4,4000,600,2e-7,4,400,200,5e-6,4,3,21,6e-4,2,0}
        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)"}
        Edit smear_parameters_b4,smear_coef_b4                                  
        
        // 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_b4,smeared_qvals                                
        SetScale d,0,0,"1/cm",smeared_b4                                                        
                                        
        Variable/G gs_b4=0
        gs_b4 := fSmearedFourLevel(smear_coef_b4,smeared_b4,smeared_qvals)      //this wrapper fills the STRUCT
        
        Display smeared_b4 vs smeared_qvals                                                                     
        ModifyGraph log=1,marker=29,msize=2,mode=4
        Label bottom "q (A\\S-1\\M)"
        Label left "Intensity (cm\\S-1\\M)"
        AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2)
        
        SetDataFolder root:
        AddModelToStrings("SmearedFourLevel","smear_coef_b4","smear_parameters_b4","b4")
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 OneLevel(cw,yw,xw) : FitFunc
        Wave cw,yw,xw
        
#if exists("OneLevelX")
        yw = OneLevelX(cw,xw)
#else
        yw = fOneLevel(cw,xw)
#endif
        return(0)
End

//////////Function definitions

Function fOneLevel(w,x) :FitFunc
        Wave w
        Variable x
        
        Variable ans,erf1,prec=1e-15
        Variable G1,Rg1,B1,Pow1,bkg,scale
        
        scale = w[0]
        G1 = w[1]
        Rg1 = w[2]
        B1 = w[3]
        Pow1 = w[4]
        bkg = w[5]
        
        erf1 = erf( (x*Rg1/sqrt(6)) ,prec)
        
        ans = G1*exp(-x*x*Rg1*Rg1/3)
        ans += B1*(erf1^3/x)^Pow1
        ans *= scale
        ans += bkg
        
        Return (ans)
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 TwoLevel(cw,yw,xw) : FitFunc
        Wave cw,yw,xw
        
#if exists("TwoLevelX")
        yw = TwoLevelX(cw,xw)
#else
        yw = fTwoLevel(cw,xw)
#endif
        return(0)
End

Function fTwoLevel(w,x) :FitFunc
        Wave w
        Variable x
        
        Variable ans,G1,Rg1,B1,G2,Rg2,B2,Pow1,Pow2,bkg
        Variable erf1,erf2,prec=1e-15,scale
        
        //Rsub = Rs
        scale = w[0]
        G1 = w[1]       //equivalent to I(0)
        Rg1 = w[2]
        B1 = w[3]
        Pow1 = w[4]
        G2 = w[5]
        Rg2 = w[6]
        B2 = w[7]
        Pow2 = w[8]
        bkg = w[9]
        
        erf1 = erf( (x*Rg1/sqrt(6)) ,prec)
        erf2 = erf( (x*Rg2/sqrt(6)) ,prec)
        //Print erf1
        
        ans = G1*exp(-x*x*Rg1*Rg1/3)
        ans += B1*exp(-x*x*Rg2*Rg2/3)*(erf1^3/x)^Pow1
        ans += G2*exp(-x*x*Rg2*Rg2/3)
        ans += B2*(erf2^3/x)^Pow2
        ans *= scale
        ans += bkg
        
        Return(ans)
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 ThreeLevel(cw,yw,xw) : FitFunc
        Wave cw,yw,xw
        
#if exists("ThreeLevelX")
        yw = ThreeLevelX(cw,xw)
#else
        yw = fThreeLevel(cw,xw)
#endif
        return(0)
End

Function fThreeLevel(w,x) :FitFunc
        Wave w
        Variable x
        
        Variable ans,G1,Rg1,B1,G2,Rg2,B2,Pow1,Pow2,bkg
        Variable G3,Rg3,B3,Pow3,erf3
        Variable erf1,erf2,prec=1e-15,scale
        
        //Rsub = Rs
        scale = w[0]
        G1 = w[1]       //equivalent to I(0)
        Rg1 = w[2]
        B1 = w[3]
        Pow1 = w[4]
        G2 = w[5]
        Rg2 = w[6]
        B2 = w[7]
        Pow2 = w[8]
        G3 = w[9]
        Rg3 = w[10]
        B3 = w[11]
        Pow3 = w[12]
        bkg = w[13]
        
        erf1 = erf( (x*Rg1/sqrt(6)) ,prec)
        erf2 = erf( (x*Rg2/sqrt(6)) ,prec)
        erf3 = erf( (x*Rg3/sqrt(6)) ,prec)
        //Print erf1
        
        ans = G1*exp(-x*x*Rg1*Rg1/3) + B1*exp(-x*x*Rg2*Rg2/3)*(erf1^3/x)^Pow1
        ans += G2*exp(-x*x*Rg2*Rg2/3) + B2*exp(-x*x*Rg3*Rg3/3)*(erf2^3/x)^Pow2
        ans += G3*exp(-x*x*Rg3*Rg3/3) + B3*(erf3^3/x)^Pow3
        ans *= scale
        ans += bkg
        
        Return(ans)
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 FourLevel(cw,yw,xw) : FitFunc
        Wave cw,yw,xw
        
#if exists("FourLevelX")
        yw = FourLevelX(cw,xw)
#else
        yw = fFourLevel(cw,xw)
#endif
        return(0)
End

Function fFourLevel(w,x) :FitFunc
        Wave w
        Variable x
        
        Variable ans,G1,Rg1,B1,G2,Rg2,B2,Pow1,Pow2,bkg
        Variable G3,Rg3,B3,Pow3,erf3
        Variable G4,Rg4,B4,Pow4,erf4
        Variable erf1,erf2,prec=1e-15,scale
        
        //Rsub = Rs
        scale = w[0]
        G1 = w[1]       //equivalent to I(0)
        Rg1 = w[2]
        B1 = w[3]
        Pow1 = w[4]
        G2 = w[5]
        Rg2 = w[6]
        B2 = w[7]
        Pow2 = w[8]
        G3 = w[9]
        Rg3 = w[10]
        B3 = w[11]
        Pow3 = w[12]
        G4 = w[13]
        Rg4 = w[14]
        B4 = w[15]
        Pow4 = w[16]
        bkg = w[17]
        
        erf1 = erf( (x*Rg1/sqrt(6)) ,prec)
        erf2 = erf( (x*Rg2/sqrt(6)) ,prec)
        erf3 = erf( (x*Rg3/sqrt(6)) ,prec)
        erf4 = erf( (x*Rg4/sqrt(6)) ,prec)
        
        ans = G1*exp(-x*x*Rg1*Rg1/3) + B1*exp(-x*x*Rg2*Rg2/3)*(erf1^3/x)^Pow1
        ans += G2*exp(-x*x*Rg2*Rg2/3) + B2*exp(-x*x*Rg3*Rg3/3)*(erf2^3/x)^Pow2
        ans += G3*exp(-x*x*Rg3*Rg3/3) + B3*exp(-x*x*Rg4*Rg4/3)*(erf3^3/x)^Pow3
        ans += G4*exp(-x*x*Rg4*Rg4/3) + B4*(erf4^3/x)^Pow4
        ans *= scale
        ans += bkg
        
        Return(ans)
End

Function SmearedOneLevel(s) :FitFunc
        Struct ResSmearAAOStruct &s

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

        return(0)
End
        

Function SmearedTwoLevel(s) :FitFunc
        Struct ResSmearAAOStruct &s

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

        return(0)
End
        

Function SmearedThreeLevel(s) :FitFunc
        Struct ResSmearAAOStruct &s

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

        return(0)
End

Function SmearedFourLevel(s) :FitFunc
        Struct ResSmearAAOStruct &s

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

        return(0)
End

//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 fSmearedOneLevel(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 = SmearedOneLevel(fs)
        
        return (0)
End

//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 fSmearedTwoLevel(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 = SmearedTwoLevel(fs)
        
        return (0)
End

//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 fSmearedThreeLevel(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 = SmearedThreeLevel(fs)
        
        return (0)
End

//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 fSmearedFourLevel(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 = SmearedFourLevel(fs)
        
        return (0)
End