Average data according to a category (or key or index) wave

#pragma rtGlobals=3     // Use modern global access method and strict wave access.
function /WAVE averageByKey(waveToAvg, dataKeys[, keyTol])
// Given a wave waveToAvg and a wave dataKeys,
// determines the number of unique entries (categories/keys/...) in dataKeys
// and averages waveToAvg according to those entries.
// The standard error of the mean, # of points averaged, and corresponding
// categories are also saved.
// e.g.
//  averageByKey(calibrationData, calibrationSolution)  // Key by entry in calibrationSolution
//  make /n=(numpnts(signal)) signalInt=round(signal); averageByKey(signal,signalInt) // Average to nearest integer
//
// OUTPUT:
    // averageByKey(data, keys), produces:
    // wave data_Keys -- a list of the unique data keys found in keyWave
    // wave data_Kavg -- the mean of the data corresponding to the keys
    // wave data_KSE  -- the standard error of the mean
    // wave data_Knum -- the # of points used for calculating the Avg & SD
   
wave waveToAvg
wave dataKeys
variable keyTol // Optional: the tolerance of keys, e.g. is 1.001 a "1" or not?
if (ParamIsDefault(keyTol))
    keyTol= 1e-07
endif
   
    // get list of unique keys
    wave keys = getKeys(dataKeys, tol=keyTol, wname=nameOfWave(waveToAvg) + "_Keys")
    variable nkeys = numpnts(keys)
   
    // try to predict memory overflow
    variable np=numpnts(waveToAvg)
    if (np*nkeys > 2147000000)
        abort "averageByKey() was given too many keys / data points. Make a smaller selection."
    endif
   
    // prepare waves for saving summary stats
    make /d/n=(nkeys)/o $(nameOfWave(waveToAvg) + "_KAvg")      /WAVE=out_avg
    make /d/n=(nkeys)/o $(nameOfWave(waveToAvg) + "_KSE")       /WAVE=out_SE
    make /d/n=(nkeys)/o $(nameOfWave(waveToAvg) + "_Knum")      /WAVE=out_n
    out_avg=nan
    out_SE=nan
    out_n=nan
   
    // prepare output matrix
    make /FREE /d/n=(np,nkeys) outmat=nan // each column represents one key & contains only that key's data
    variable i,colkey
    for (i=0; i<nkeys; i+=1)
        SetDimLabel 1, i, $num2str(keys[i]), outmat  // label for later sorting
    endfor
   
    // go through the data, insert appropriate results into outmat
    string Sthiskey
    for (i=0; i<np; i+=1)
        Sthiskey = num2str(dataKeys[i])
        outmat[i][% $Sthiskey]=waveToAvg[i]
    endfor
   
    // get the desired summary statistics
    for (i=0; i<nkeys; i+=1)
        ImageStats /G={0, np-1, i,i} outmat
        if (V_flag < 0) // probably unnecessary: avoid saving the previous loop's stats
            abort "averageByKey(): unknown error"
        endif
        out_n[i]=V_npnts
        if (V_npnts>0) // for V_npnts==1, V_sdev is set to NaN
            out_avg[i]=V_avg
            out_SE[i]=V_sdev / sqrt(V_npnts)
        endif
    endfor
    return keys
end
 
function /WAVE getKeys(keys[, tol, wname])
// Given a list of keys (e.g. laser on/off = 0/1),
// return a wave of the unique keys only (in e.g. above, {0,1})
 
wave keys
variable tol // optional, allow 1.0001==1 to be true.
string wname // optional name of output wave
if (ParamIsDefault(tol))
    tol= 1e-07
endif
if (ParamIsDefault(wname))
    wname= nameOfWave(keys) + "_uniqKeys"
endif
 
    // create output wave
    make /d/o/n=0 $wname /WAVE=outw
    outw=nan
 
    // special case of an empty key wave, or one with only NaN/inf
    wavestats /Q/M=1 keys
    if (V_npnts==0)
        return outw
    endif
 
    // go through input wave & save any new entries
    variable i=0, np=numpnts(keys)
    do
        if (getIndex(keys[i], outw, tol=tol) == -1)
            appendWave(outw, {keys[i]})
            SetDimLabel 0, (numpnts(outw)-1), $num2str(keys[i]), outw // label for ease of use (but tol!=0 must be considered)
        endif
        i += 1
    while (i<np)
 
    return outw
end
 
function getIndex(v, w, [tol, rev, start])
// Finds the index of the given variable var in the given wave w.
// Optional variable tolerance gives the ± acceptance range. Default 1.0E-7.
// Optional variable rev searches in reverse if set.
// Capable of finding NaNs.
// Returns -1 if not found.
// see also FindValue
 
    variable v
    wave w
    variable tol
    variable rev
    variable start // default == 0
 
 
    if (paramIsDefault(tol)) // TODO: change this to an autodetected spacing from w
        tol = 1.0E-7
    elseif (tol < 0)
        tol = abs(tol)
    endif
 
    variable i, n = numpnts(w)
 
    if ((rev))
        if (ParamIsDefault(start))
            start = n-1
        endif
        if (start < 0)
            abort "Cannot start at a negative index."
            // Strictly speaking getIndex() is not responsible for this, but it helps with debugging.
        endif
 
        for (i =start; i >= 0; i -= 1)
            if (abs(w[i] - v) < tol)
                return i
            endif
        endfor
 
    else
 
        for (i =start; i < n; i += 1)
            if (abs(w[i] - v) < tol)
                return i
            endif
        endfor
 
    endif
 
    return -1
end
 
function appendWave(taker, appendThis)
// Concatenate alias. Given a wave "appendThis", appends its data to "taker". 1D waves only.
    wave taker, appendThis
    concatenate /NP=0 {appendThis}, taker
end