pearl-fitfuncs.ipf

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#pragma rtGlobals=3// Use modern global access method and strict wave access.
#pragma IgorVersion = 6.2
#pragma ModuleName = PearlFitFuncs
#pragma version = 1.01
#include "mm-physconst", version >= 1.05

// various fit functions for photoelectron spectroscopy

// $Id$
// author: matthias.muntwiler@psi.ch
// Copyright (c) 2013-14 Paul Scherrer Institut

// Licensed under the Apache License, Version 2.0 (the "License");
//   you may not use this file except in compliance with the License.
//   You may obtain a copy of the License at
//   http://www.apache.org/licenses/LICENSE-2.0

//------------------------------------------------------------------------------
// Doniach-Sunjic fit functions
//------------------------------------------------------------------------------

threadsafe variable DoniachSunjic(variable x, variable amp, variable pos, variable sing, variable fwhm){
    // Doniach-Sunjic line shape
    // [S. Doniach, M. Sunjic, J. Phys. C 3 (1970) 285]
    variable x// independent variable
    variable amp// amplitude
    variable pos// position
    variable sing// singularity index (0 <= sing < 1)
    variable fwhm// width

    variable nom, denom
    nom = cos(pi * sing / 2 + (1 - sing) * atan((x - pos) / fwhm * 2))
    denom = ((x - pos)^2 + fwhm^2 / 4)^((1 - sing) / 2)
    
    return amp * nom / denom * fwhm / 2
};

threadsafe variable ds1_bg(wave w, variable x){
    // Doniach-Sunjic fit function
    // 0 <= sing < 1
    wave w// coefficients - see below
    variable x// independent variable

    //CurveFitDialog/ These comments were created by the Curve Fitting dialog. Altering them will
    //CurveFitDialog/ make the function less convenient to work with in the Curve Fitting dialog.
    //CurveFitDialog/ Equation:
    //CurveFitDialog/ f(x) = DoniachSunjic(x, amp, pos, sing, fwhm) + bg
    //CurveFitDialog/ End of Equation
    //CurveFitDialog/ Independent Variables 1
    //CurveFitDialog/ x
    //CurveFitDialog/ Coefficients 5
    //CurveFitDialog/ w[0] = bg
    //CurveFitDialog/ w[1] = amp
    //CurveFitDialog/ w[2] = pos
    //CurveFitDialog/ w[3] = sing
    //CurveFitDialog/ w[4] = FWHM

    return DoniachSunjic(x, w[1], w[2], w[3], w[4]) + w[0]
};

threadsafe variable ds2_bg(wave w, variable x){
    Wave w
    Variable x

    //CurveFitDialog/ These comments were created by the Curve Fitting dialog. Altering them will
    //CurveFitDialog/ make the function less convenient to work with in the Curve Fitting dialog.
    //CurveFitDialog/ Equation:
    //CurveFitDialog/ f(x) = w_0+( w_1*cos(pi*w_3/2+(1-w_3)*atan((x-w_2)/w_4)))/(((x-w_2)^2+w_4^2)^((1-w_3)/2))   +(w_5*cos(pi*w_7/2+(1-w_7)*atan((x-(w_6))/w_8)))/(((x-w_6)^2+w_8^2)^((1-w_7)/2))
    //CurveFitDialog/ End of Equation
    //CurveFitDialog/ Independent Variables 1
    //CurveFitDialog/ x
    //CurveFitDialog/ Coefficients 9
    //CurveFitDialog/ w[0] = bg
    //CurveFitDialog/ w[1] = amp1
    //CurveFitDialog/ w[2] = pos1
    //CurveFitDialog/ w[3] = sing1
    //CurveFitDialog/ w[4] = wid1
    //CurveFitDialog/ w[5] = amp2
    //CurveFitDialog/ w[6] = pos2
    //CurveFitDialog/ w[7] = sing2
    //CurveFitDialog/ w[8] = wid2

    variable ds1 = DoniachSunjic(x, w[1], w[2], w[3], w[4])
    variable ds2 = DoniachSunjic(x, w[5], w[6], w[7], w[8])
    
    return w[0] + ds1 + ds2
};

variable ds4_bg(wave w, variable x){
    Wave w
    Variable x

    //CurveFitDialog/ These comments were created by the Curve Fitting dialog. Altering them will
    //CurveFitDialog/ make the function less convenient to work with in the Curve Fitting dialog.
    //CurveFitDialog/ Equation:
    //CurveFitDialog/ f(x) = w_0+( w_1*cos(pi*w_3/2+(1-w_3)*atan((x-w_2)/w_4)))/(((x-w_2)^2+w_4^2)^((1-w_3)/2))   +(w_5*cos(pi*w_7/2+(1-w_7)*atan((x-(w_6))/w_8)))/(((x-w_6)^2+w_8^2)^((1-w_7)/2))   +( w_9*cos(pi*w_11/2+(1-w_11)*atan((x-w_10)/w_12)))/(((x-w_10)^2+w_12^2)^((1-w_11)/2))      +( w_13*cos(pi*w_15/2+(1-w_15)*atan((x-w_14)/w_16)))/(((x-w_14)^2+w_16^2)^((1-w_15)/2))   
    //CurveFitDialog/ End of Equation
    //CurveFitDialog/ Independent Variables 1
    //CurveFitDialog/ x
    //CurveFitDialog/ Coefficients 17
    //CurveFitDialog/ w[0] = w_0
    //CurveFitDialog/ w[1] = w_11
    //CurveFitDialog/ w[2] = w_12
    //CurveFitDialog/ w[3] = w_13
    //CurveFitDialog/ w[4] = w_14
    //CurveFitDialog/ w[5] = w_21
    //CurveFitDialog/ w[6] = w_22
    //CurveFitDialog/ w[7] = w_23
    //CurveFitDialog/ w[8] = w_24
    //CurveFitDialog/ w[9] = w_31
    //CurveFitDialog/ w[10] = w_32
    //CurveFitDialog/ w[11] = w_33
    //CurveFitDialog/ w[12] = w_34
    //CurveFitDialog/ w[13] = w_41
    //CurveFitDialog/ w[14] = w_42
    //CurveFitDialog/ w[15] = w_43
    //CurveFitDialog/ w[16] = w_44
    Variable ds1, ds2, ds3, ds4
    ds1=( w[1]*cos(pi*w[3]/2+(1-w[3])*atan((x-w[2])/w[4])))/(((x-w[2])^2+w[4]^2)^((1-w[3])/2))
    ds2=( w[5]*cos(pi*w[7]/2+(1-w[7])*atan((x-w[6])/w[8])))/(((x-w[6])^2+w[8]^2)^((1-w[7])/2))
    ds3=( w[9]*cos(pi*w[11]/2+(1-w[11])*atan((x-w[10])/w[12])))/(((x-w[10])^2+w[12]^2)^((1-w[11])/2))
    ds4=( w[13]*cos(pi*w[15]/2+(1-w[15])*atan((x-w[14])/w[16])))/(((x-w[14])^2+w[16]^2)^((1-w[15])/2))

    
    return w[0]+ds1+ds2+ds3+ds4
    

};

variable ds6_bg(wave w, variable x){
    Wave w
    Variable x

    //CurveFitDialog/ These comments were created by the Curve Fitting dialog. Altering them will
    //CurveFitDialog/ make the function less convenient to work with in the Curve Fitting dialog.
    //CurveFitDialog/ Equation:
    //CurveFitDialog/ 
    //CurveFitDialog/ Variable g, ds1, ds2, ds3, ds4, ds5, ds6
    //CurveFitDialog/ ds1=( w_11*cos(pi*w_13/2+(1-w_13)*atan((x-w_12)/w_14)))/(((x-w_12)^2+w_14^2)^((1-w_13)/2))
    //CurveFitDialog/ ds2=( w_21*cos(pi*w_23/2+(1-w_23)*atan((x-w_22)/w_24)))/(((x-w_22)^2+w_24^2)^((1-w_23)/2))
    //CurveFitDialog/ ds3=( w_31*cos(pi*w_33/2+(1-w_33)*atan((x-w_32)/w_34)))/(((x-w_32)^2+w_34^2)^((1-w_33)/2))
    //CurveFitDialog/ ds4=( w_41*cos(pi*w_43/2+(1-w_43)*atan((x-w_42)/w_44)))/(((x-w_42)^2+w_44^2)^((1-w_43)/2))
    //CurveFitDialog/ ds5=( w_51*cos(pi*w_53/2+(1-w_53)*atan((x-w_52)/w_54)))/(((x-w_52)^2+w_54^2)^((1-w_53)/2))
    //CurveFitDialog/ ds6=( w_61*cos(pi*w_63/2+(1-w_63)*atan((x-w_62)/w_64)))/(((x-w_62)^2+w_64^2)^((1-w_63)/2))
    //CurveFitDialog/ 
    //CurveFitDialog/ f(x) =w_0+ds1+ds2+ds3+ds4+ds5+ds6
    //CurveFitDialog/ 
    //CurveFitDialog/ End of Equation
    //CurveFitDialog/ Independent Variables 1
    //CurveFitDialog/ x
    //CurveFitDialog/ Coefficients 25
    //CurveFitDialog/ w[0] = w_0
    //CurveFitDialog/ w[1] = w_11
    //CurveFitDialog/ w[2] = w_12
    //CurveFitDialog/ w[3] = w_13
    //CurveFitDialog/ w[4] = w_14
    //CurveFitDialog/ w[5] = w_21
    //CurveFitDialog/ w[6] = w_22
    //CurveFitDialog/ w[7] = w_23
    //CurveFitDialog/ w[8] = w_24
    //CurveFitDialog/ w[9] = w_31
    //CurveFitDialog/ w[10] = w_32
    //CurveFitDialog/ w[11] = w_33
    //CurveFitDialog/ w[12] = w_34
    //CurveFitDialog/ w[13] = w_41
    //CurveFitDialog/ w[14] = w_42
    //CurveFitDialog/ w[15] = w_43
    //CurveFitDialog/ w[16] = w_44
    //CurveFitDialog/ w[17] = w_51
    //CurveFitDialog/ w[18] = w_52
    //CurveFitDialog/ w[19] = w_53
    //CurveFitDialog/ w[20] = w_54
    //CurveFitDialog/ w[21] = w_61
    //CurveFitDialog/ w[22] = w_62
    //CurveFitDialog/ w[23] = w_63
    //CurveFitDialog/ w[24] = w_64

    
    Variable ds1, ds2, ds3, ds4, ds5, ds6
    ds1=( w[1]*cos(pi*w[3]/2+(1-w[3])*atan((x-w[2])/w[4])))/(((x-w[2])^2+w[4]^2)^((1-w[3])/2))
    ds2=( w[5]*cos(pi*w[7]/2+(1-w[7])*atan((x-w[6])/w[8])))/(((x-w[6])^2+w[8]^2)^((1-w[7])/2))
    ds3=( w[9]*cos(pi*w[11]/2+(1-w[11])*atan((x-w[10])/w[12])))/(((x-w[10])^2+w[12]^2)^((1-w[11])/2))
    ds4=( w[13]*cos(pi*w[15]/2+(1-w[15])*atan((x-w[14])/w[16])))/(((x-w[14])^2+w[16]^2)^((1-w[15])/2))
    ds5=( w[17]*cos(pi*w[19]/2+(1-w[19])*atan((x-w[18])/w[20])))/(((x-w[18])^2+w[20]^2)^((1-w[19])/2))
    ds6=( w[21]*cos(pi*w[23]/2+(1-w[23])*atan((x-w[22])/w[24])))/(((x-w[22])^2+w[24]^2)^((1-w[23])/2))
    
    return w[0]+ds1+ds2+ds3+ds4+ds5+ds6
    
};

struct DoniachSunjicStruct{;
    // data structure for DoniachSunjicBroadS structural function fit

    // waves populated by the FuncFit operation 
    wave pw;
    wave yw;
    wave xw;

    // convolution parameters to be set upon creation of the structure
    variable precision;
    variable oversampling;

    // auxiliary fields used internally by DoniachSunjicBroadS
    // do not touch these
    wave xdw;
    wave model;
    wave broadening;
    wave convolution;
};

//------------------------------------------------------------------------------
threadsafe variable DoniachSunjicBroadS(DoniachSunjicStruct* s){
//------------------------------------------------------------------------------
    // Two-peak (bulk + surface) Doniach-Sunjic line shape with Gaussian broadening (convolution).
    // Hold parameter 5 at 0 to fit just one peak.
    
    // Structural fit function for efficient fitting in procedures.
    // Calculating the convolution requires auxiliary waves and additional, non-fitting parameters.
    // To eliminate the time-consuming overhead of creating and killing the auxiliary waves,
    // these waves are held in the fitting structure.
    
    // Caution: The function on its own is thread-safe.
    // However, since FuncFit uses the same structure in all threads, the fitting cannot run in parallel.
    // Set /NTHR=1.
    
    // See also Fit_DoniachSunjicBroad (example), DoniachSunjicBroad (conventional fit function)
    Struct DoniachSunjicStruct &s

    // pw[0] = bulk amplitude
    // pw[1] = bulk position
    // pw[2] = Lorentzian FWHM
    // pw[3] = Donjach-Sunjic singularity index (0..1)
    // pw[4] = surface shift
    // pw[5] = surface/bulk ratio
    // pw[6] = Gaussian FWHM
    // pw[7] = constant background
    // pw[8] = linear background
    
    wave xw = s.xw
    wave yw = s.yw
    wave pw = s.pw
    
    variable precision = s.precision
    variable oversampling = s.oversampling

    if (WaveExists(s.xdw))
        wave xdw = s.xdw
        wave model = s.model
        wave broadening = s.broadening
        wave convolution = s.convolution
    else
        make /n=0 /free xdw, model, broadening, convolution
        redimension /d xdw, model, broadening, convolution
        wave fs.xdw = xdw
        wave fs.model = model
        wave fs.broadening = broadening
        wave fs.convolution = convolution
    endif

    // calculate wave spacing based on minimum spacing of desired x points
    differentiate /p xw /d=xdw
    xdw = abs(xdw)
    variable xd = wavemin(xdw) / oversampling
    
    // calculate broadening wave size based on width and precision variable
    variable x0b = pw[6] * precision
    variable nb = 2 * floor(x0b / xd) + 1
    
    // calculate model size based on desired range for yw
    variable x0m = max(abs(wavemax(xw) - pw[1]), abs(wavemin(xw) - pw[1])) + x0b
    variable nm = 2 * floor(x0m / xd) + 1
    nb = min(nb, nm * 10)// limit wave size to avoid runtime errors for unphysically large parameter
    
    // create and calculate initial waves, normalize exponential
    redimension /n=(nb) broadening
    redimension /n=(nm) model
    setscale/i x -x0b, x0b, "", broadening
    setscale/i x -x0m, x0m, "", model
    
    broadening = exp( - (x / pw[6])^2 * 4 * ln(2))
    variable nrm = area(broadening)
    broadening /= nrm
    model = DoniachSunjic(x, 1, 0, pw[3], pw[2])// bulk
    model += DoniachSunjic(x, pw[5], pw[4], pw[3], pw[2])// surface
    
    // calculate the convolution
    Convolve /a broadening, model
    variable scale = pw[0] / wavemax(model)
    model *= scale
    
    // prepare output
    nm = numpnts(model)
    x0m = xd * (nm - 1) / 2
    setscale/i x -x0m, x0m, "", model
    
    yw = model(xw[p] - pw[1]) + pw[7] + pw[8] * xw[p]
    yw = numtype(yw) ? 0 : yw
};

//------------------------------------------------------------------------------
variable DoniachSunjicBroad(wave pw, wave yw, wave xw){
//------------------------------------------------------------------------------
    // Two-peak (bulk + surface) Doniach-Sunjic line shape with Gaussian broadening (convolution).
    // Hold parameter 5 at 0 to fit just one peak.
    // Conventional fit function for use with the curve-fitting dialog.
    // Compared to DoniachSunjicBroadS this function incurs extra overhead
    // because auxiliary waves are created and killed between function calls.
    // See also DoniachSunjicBroadS (optimized structural fit function)
    Wave pw
    Wave yw
    Wave xw

    // pw[0] = bulk amplitude
    // pw[1] = bulk position
    // pw[2] = Lorentzian FWHM
    // pw[3] = Donjach-Sunjic singularity index (0..1)
    // pw[4] = surface shift
    // pw[5] = surface/bulk ratio
    // pw[6] = Gaussian FWHM
    // pw[7] = constant background
    // pw[8] = linear background
    
    // set up data structure
    struct DoniachSunjicStruct fs
    fs.precision = 5
    fs.oversampling = 4
    
    wave fs.pw = pw
    wave fs.xw = xw
    wave fs.yw = yw
    
    // create temporary calculation waves in a global folder
    dfref df = root:packages:pearl_fitfuncs:doniach_sunjic
    if (DataFolderRefStatus(df) == 0)
        newdatafolder root:packages:pearl_fitfuncs:doniach_sunjic
        dfref df = root:packages:pearl_fitfuncs:doniach_sunjic
    endif
    
    wave /z /sdfr=df fs.xdw = xdw
    wave /z /sdfr=df fs.model = model
    wave /z /sdfr=df fs.broadening = broadening
    wave /z /sdfr=df fs.convolution = convolution

    if (WaveExists(fs.xdw) == 0)
        dfref savedf = GetDataFolderDFR()
        setdatafolder df
        make /n=0 /d xdw, model, broadening, convolution
        wave fs.xdw = xdw
        wave fs.model = model
        wave fs.broadening = broadening
        wave fs.convolution = convolution
        setdatafolder savedf
    endif

    // calculate
    DoniachSunjicBroadS(fs)
    
    yw = fs.yw
};

//------------------------------------------------------------------------------
variable Calc_DoniachSunjicBroad(wave pw, wave yw){
//------------------------------------------------------------------------------
    // Calculate the DoniachSunjicBroadS line shape
    Wave pw// coefficient wave
    Wave yw// output wave, correct x-scaling required on input
    
    struct DoniachSunjicStruct fs
    fs.precision = 5
    fs.oversampling = 4
    
    duplicate /free pw, fs.pw
    duplicate /free yw, fs.xw
    fs.xw = x
    duplicate /free yw, fs.yw
    
    DoniachSunjicBroadS(fs)
    
    yw = fs.yw
};

//------------------------------------------------------------------------------
variable Fit_DoniachSunjicBroad(wave pw, wave yw, wave xw, wave ww){
//------------------------------------------------------------------------------
    // Fit the DoniachSunjicBroadS line shape.
    // The function applies constraints which assume that the energy scale is in eV.
    // Returns chi^2.
    wave pw// coefficient wave- pre-load it with initial guess
    wave yw
    wave /z xw
    wave /z ww// weights (standard deviation)
    
    struct DoniachSunjicStruct fs
    fs.precision = 5
    fs.oversampling = 4
    
    duplicate /free pw, fs.pw
    if (WaveExists(xw))
        duplicate /free xw, fs.xw
    else
        duplicate /free yw, fs.xw
        fs.xw = x
    endif
    duplicate /free yw, fs.yw
    
    variable v_chisq = nan
    variable V_FitMaxIters = 100
    make /n=1 /t /free constraints = {"K0 >= 0", "K2 > 0", "K2 < 10", "K3 >= 0", "K3 < 1", "K4 >= -10", "K4 <= 10", "K5 >= 0", "K5 <= 1", "K6 >= 0", "K6 < 10"}
    // note: only single thread allowed
    FuncFit /NTHR=1 DoniachSunjicBroadS, pw, yw /X=xw /D /STRC=fs /C=constraints /NWOK /I=1 /W=ww
    
    return v_chisq
};

//------------------------------------------------------------------------------
// peak-specific fit functions
//------------------------------------------------------------------------------

variable Au4f(wave w, variable x){
    // fit function for a nitrogen 1s-pi* absorption spectrum
    // modelled as multiple Voigt shapes on a constant background
    // similar to the Igor VoigtFit function
    // but with a constant gaussian width (instrumental broadening) for all peaks
    // gaussian and lorentzian widths are specified as FWHM
    wave w// parameters
        // w[0] constant background
        // w[1] linear background
        // w[2] global gaussian FWHM
        // w[3 + 0 + (n-1) * 3] peak n area
        // w[3 + 1 + (n-1) * 3] peak n position
        // w[3 + 2 + (n-1) * 3] peak n lorentzian FWHM
        // length of wave defines number of peaks
        
        // for compatibility with older code the linear background term can be omitted.
        // if the number of parameters divides by 3, the linear background term is added,
        // otherwise only the constant background.
    variable x
    
    variable np = 15
    variable ip, ip0
    
    variable bg = w[0]
    variable v = bg
    if (mod(np, 3) == 0)
        v += w[1] * x
        ip0 = 3
    else
        ip0 = 2
    endif

    variable vc1, vc2, vc3, vc4
    vc2 = 2 * sqrt(ln(2)) / w[ip0-1]
    for (ip = ip0; ip < np; ip += 3)
        vc1 = w[ip] / sqrt(pi) * vc2
        vc3 = w[ip+1]
        vc4 = vc2 * w[ip+2] / 2
        v += vc1 * VoigtFunc(vc2 * (x - vc3), vc4)
    endfor

    return v
    
};

variable Au4f_2p2(wave w, variable x){
    // Au 4f 5/2 and 7/2 2-component Voigt fit with a common gaussian width
    // gaussian and lorentzian widths are specified as FWHM
    wave w// parameters
        // w[0] constant background
        // w[1] linear background
        // w[2] global gaussian FWHM
        // w[3] 5/2 bulk area
        // w[4] 5/2 bulk position
        // w[5] 5/2 lorentzian FWHM
        // w[6] 7/2 bulk area
        // w[7] 7/2 bulk position
        // w[8] 7/2 lorentzian FWHM
        // w[9] surface/bulk area ratio
        // w[10] surface core level shift
    variable x

    variable bg = w[0] + w[1] * x
    variable v = bg

    variable vc1// amplitude
    variable vc2// width
    variable vc3// position
    variable vc4// shape
    vc2 = 2 * sqrt(ln(2)) / w[2]

    // 5/2 bulk
    vc1 = w[3] / sqrt(pi) * vc2
    vc3 = w[4]
    vc4 = vc2 * w[5] / 2
    v += vc1 * VoigtFunc(vc2 * (x - vc3), vc4)

    // 5/2 surface
    vc1 = w[3] / sqrt(pi) * vc2 * w[9]
    vc3 = w[4] + w[10]
    vc4 = vc2 * w[5] / 2
    v += vc1 * VoigtFunc(vc2 * (x - vc3), vc4)

    // 7/2 bulk
    vc1 = w[6] / sqrt(pi) * vc2
    vc3 = w[7]
    vc4 = vc2 * w[8] / 2
    v += vc1 * VoigtFunc(vc2 * (x - vc3), vc4)

    // 7/2 surface
    vc1 = w[6] / sqrt(pi) * vc2 * w[9]
    vc3 = w[7] + w[10]
    vc4 = vc2 * w[8] / 2
    v += vc1 * VoigtFunc(vc2 * (x - vc3), vc4)

    return v
    
};

variable ShowComponents_Au4f_2p2(wave coef_wave, wave fit_wave){
    wave coef_wave
    wave fit_wave

    duplicate /free coef_wave, coef1, coef2
    coef1[9] = 0
    coef2[3] *= coef_wave[9]
    coef2[4] += coef_wave[10]
    coef2[6] *= coef_wave[9]
    coef2[7] += coef_wave[10]
    coef2[9] = 0
    
    string s_fit_wave = NameOfWave(fit_wave)
    string s_fit_p1 = s_fit_wave + "_p1"
    string s_fit_p2 = s_fit_wave + "_p2"
    duplicate /o fit_wave, $(s_fit_p1) /wave=fit_p1
    duplicate /o fit_wave, $(s_fit_p2) /wave=fit_p2
    
    fit_p1 = Au4f_2p2(coef1, x)
    fit_p2 = Au4f_2p2(coef2, x)

    string traces = TraceNameList("", ";", 1)
    if ((WhichListItem(s_fit_wave, traces, ";") >= 0) && (WhichListItem(s_fit_p1, traces, ";") < 0))
        appendtograph fit_p1, fit_p2
        ModifyGraph lstyle($s_fit_p1)=2
        ModifyGraph lstyle($s_fit_p2)=2
        ModifyGraph rgb($s_fit_p1)=(0,0,65280)
        ModifyGraph rgb($s_fit_p2)=(0,0,65280)
    endif
};

variable Au4f_2p3(wave w, variable x){
    // Au 4f 5/2 and 7/2 3-component Voigt fit with a common gaussian width
    // gaussian and lorentzian widths are specified as FWHM
    wave w// parameters
        // w[0] constant background
        // w[1] linear background
        // w[2] global gaussian FWHM
        // w[3] 5/2 bulk area
        // w[4] 5/2 bulk position
        // w[5] 5/2 lorentzian FWHM
        // w[6] 7/2 bulk area
        // w[7] 7/2 bulk position
        // w[8] 7/2 lorentzian FWHM
        // w[9] surface/bulk area ratio
        // w[10] surface core level shift
        // w[11] 2nd layer/bulk area ratio
        // w[12] 2nd layer core level shift
    variable x

    variable bg = w[0] + w[1] * x
    variable v = bg

    variable vc1// amplitude
    variable vc2// width
    variable vc3// position
    variable vc4// shape
    vc2 = 2 * sqrt(ln(2)) / w[2]

    // 5/2 bulk
    vc1 = w[3] / sqrt(pi) * vc2
    vc3 = w[4]
    vc4 = vc2 * w[5] / 2
    v += vc1 * VoigtFunc(vc2 * (x - vc3), vc4)

    // 5/2 surface
    vc1 = w[3] / sqrt(pi) * vc2 * w[9]
    vc3 = w[4] + w[10]
    vc4 = vc2 * w[5] / 2
    v += vc1 * VoigtFunc(vc2 * (x - vc3), vc4)

    // 5/2 2nd layer
    vc1 = w[3] / sqrt(pi) * vc2 * w[11]
    vc3 = w[4] + w[12]
    vc4 = vc2 * w[5] / 2
    v += vc1 * VoigtFunc(vc2 * (x - vc3), vc4)

    // 7/2 bulk
    vc1 = w[6] / sqrt(pi) * vc2
    vc3 = w[7]
    vc4 = vc2 * w[8] / 2
    v += vc1 * VoigtFunc(vc2 * (x - vc3), vc4)

    // 7/2 surface
    vc1 = w[6] / sqrt(pi) * vc2 * w[9]
    vc3 = w[7] + w[10]
    vc4 = vc2 * w[8] / 2
    v += vc1 * VoigtFunc(vc2 * (x - vc3), vc4)

    // 7/2 2nd layer
    vc1 = w[6] / sqrt(pi) * vc2 * w[11]
    vc3 = w[7] + w[12]
    vc4 = vc2 * w[8] / 2
    v += vc1 * VoigtFunc(vc2 * (x - vc3), vc4)

    return v
    
};

variable ShowComponents_Au4f_2p3(wave coef_wave, wave fit_wave){
    wave coef_wave
    wave fit_wave

    duplicate /free coef_wave, coef1, coef2, coef3
    coef1[9] = 0
    coef1[11] = 0
    
    coef2[3] *= coef_wave[9]
    coef2[4] += coef_wave[10]
    coef2[6] *= coef_wave[9]
    coef2[7] += coef_wave[10]
    coef2[9] = 0
    coef2[11] = 0
    
    coef3[3] *= coef_wave[11]
    coef3[4] += coef_wave[12]
    coef3[6] *= coef_wave[11]
    coef3[7] += coef_wave[12]
    coef3[9] = 0
    coef3[11] = 0
    
    string s_fit_wave = NameOfWave(fit_wave)
    string s_fit_p1 = s_fit_wave + "_p1"
    string s_fit_p2 = s_fit_wave + "_p2"
    string s_fit_p3 = s_fit_wave + "_p3"
    duplicate /o fit_wave, $(s_fit_p1) /wave=fit_p1
    duplicate /o fit_wave, $(s_fit_p2) /wave=fit_p2
    duplicate /o fit_wave, $(s_fit_p3) /wave=fit_p3
    
    fit_p1 = Au4f_2p2(coef1, x)
    fit_p2 = Au4f_2p2(coef2, x)
    fit_p3 = Au4f_2p2(coef3, x)

    string traces = TraceNameList("", ";", 1)
    if ((WhichListItem(s_fit_wave, traces, ";") >= 0) && (WhichListItem(s_fit_p1, traces, ";") < 0))
        appendtograph fit_p1, fit_p2, fit_p3
        ModifyGraph lstyle($s_fit_p1)=2
        ModifyGraph lstyle($s_fit_p2)=2
        ModifyGraph lstyle($s_fit_p3)=2
        ModifyGraph rgb($s_fit_p1)=(0,0,65280)
        ModifyGraph rgb($s_fit_p2)=(0,0,65280)
        ModifyGraph rgb($s_fit_p3)=(0,0,65280)
    endif
};

variable FermiGaussConv(wave pw, wave yw, wave xw){
    WAVE pw, yw, xw
    
    // half width of temporary gaussian wave is pw[5] multiplied by this factor (may be fractional)
    variable precision_g = 5
    variable oversampling = 4
    
    // calculate wave spacing based on minimum spacing of desired x points
    duplicate /free xw, xdw
    differentiate /p xw /d=xdw
    xdw = abs(xdw)
    variable xd = wavemin(xdw) / oversampling
    
    // calculate gausswave size based on pw[5] and precision variable
    variable x0g = abs(pw[5]) * precision_g
    variable ng = 2 * floor(x0g / xd) + 1
    
    // calculate fermiwave size based on desired range for yw
    variable emax = wavemax(xw)
    variable emin = wavemin(xw)
    variable x0f = max(abs(emax - pw[3]), abs(emin - pw[3])) + x0g
    variable ne = 2 * floor(x0f / xd) + 1
    
    // create and calculate initial waves, normalize exponential
    make /d /n=(ng) /free gausswave
    make /d /n=(ne) /free fermiwave
    setscale/i x -x0g, x0g, "", gausswave
    setscale/i x -x0f, x0f, "", fermiwave
    
    gausswave = exp( - (x / pw[5] )^2 )
    fermiwave = 1 / (exp( x / (kBoltzmann * pw[4])) + 1.0 )

    // calculate the convolution
    duplicate /free fermiwave, resultwave
    Convolve /a gausswave, resultwave
    variable rmax = wavemax(resultwave)
    resultwave /= rmax
    
    // prepare output
    ng = numpnts(resultwave)
    x0g = xd * (ng - 1) / 2
    setscale/i x -x0g, x0g, "", resultwave
    
    yw = pw[2] * resultwave(xw[p] - pw[3]) + pw[0] + pw[1] * xw[p]
};