Example of how to use the MPRebinSpectra module.

A discrete 2D spectrum of electron energies (for $2\nu\beta\beta$ decay) is given as an ascii text file where:

column1 = E1, column2 = E2, column3 = multiplicity(dGdE)

The premise of MPRebinSpectra module is the use of segmential linear approximation of the discrete spectral points in order to transform the spectrum to a semi-continuous (subsequently continuous), normalized (to volume = 1) spectrum. Such spectrum can be saved as a new ascii file to use in further analysis (i.e. for sampling energies).

using MPRebinSpectra, StatsPlots, FHist, CSV, DataFrames, ColorSchemes
Base.displaysize() = (8, 80) # this is just to show "only" 5 rows of dataframes

gr()

Plots.GRBackend()

inFile = "spectrumG0.dat"

"spectrumG0.dat"

The MPRebinSpectra works with dataframes. The headers must be ["E1", "E2", "dGdE"] (at some point I plan to change this, so that headers could be user-defined.

Each column must contain only Float64 variables.

df_raw = CSV.File(inFile, delim = "    ", header = ["E1", "E2", "dGdE"]) |> DataFrame
df_raw.E1 = parse.(Float64, df_raw.E1)
df_raw.E2 = parse.(Float64, df_raw.E2);

p_raw = scatter(df_raw[1:1000:end, 1], df_raw[1:1000:end,2], df_raw[1:1000:end,3],
                zlims = (minimum(df_raw.dGdE), maximum(df_raw.dGdE)), legend = :false,
                xlabel = "E1 [MeV]", ylabel = "E2 [MeV]", zlabel = "dGdE", 
                title = "Raw spectrum, every 1000 pts", c = :blue, markeralpha = 1, ms = 2.5,
                markerstrokewidth = 0.2, camera = (55,45))
p_raw_side = scatter(df_raw[1:1000:end, 1], df_raw[1:1000:end,2], df_raw[1:1000:end,3],
                zlims = (minimum(df_raw.dGdE), 1.1*maximum(df_raw.dGdE)), legend = :false,
                 ylabel = "E2 [MeV]", zlabel = "dGdE", 
                title = "Projection", c = :blue, markeralpha = 0.6, ms = 4,
                markerstrokewidth = 0.2, camera = (90,0), zticks = :none)
plot(p_raw, p_raw_side, size = (900, 400), bottom_margin = 6Plots.mm, left_margin = 6Plots.mm)

---

Rebinned dataframe contains columns:

E1 - defines constant E1 for which the linear approximation of the spectral points was made
minE - minimum energy E2 for the segment of the linear approximation 
maxE - maximum energy E2 for the segment of the linear approximation (E1 of next row is E2 of previous - continuity)
minG - dGdE value corresponding to minE 
maxG - dGdE value corresponding to maxE (this will probably be deleted in future)
a - approximation parameter from y = ax + b
b - approximation parameter from y = ax + b

The argument _prec of rebin2D(df, _prec, _dx) is the precision with which the approximation is to be made. For example _prec = 0.001 means that the approximation is made with an uncertainty of 1 promile. The argument _dx is the energy step of the spectrum (by default set to 0.001MeV).

---

df = rebin2D(df_raw, 0.001)

614,474 rows × 7 columns

	E1	minE	maxE	minG	maxG	a	b
	Float64	Float64	Float64	Float64	Float64	Float64	Float64
1	0.00093	0.0	0.00093	0.0	1.34513e-47	1.44638e-44	0.0
2	0.00093	0.00093	0.01493	1.34513e-47	1.37867e-47	2.39571e-47	1.3429e-47
3	0.00093	0.01493	0.02693	1.37867e-47	1.40984e-47	2.5975e-47	1.33989e-47
4	0.00093	0.02693	0.04093	1.40984e-47	1.45085e-47	2.92929e-47	1.33095e-47
5	0.00093	0.04093	0.05893	1.45085e-47	1.50717e-47	3.12889e-47	1.32278e-47
6	0.00093	0.05893	0.10993	1.50717e-47	1.66716e-47	3.13706e-47	1.3223e-47
7	0.00093	0.10993	0.13393	1.66716e-47	1.73789e-47	2.94708e-47	1.34319e-47
8	0.00093	0.13393	0.15693	1.73789e-47	1.80181e-47	2.77913e-47	1.36568e-47
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮

---

normalize2D!(df) normalizes the dataframe to the total volume of 1.

---

E1 = 0.10093
x = df_raw[df_raw.E1 .== E1 , 2]
y = df_raw[df_raw.E1 .== E1 , 3]
p_approx = scatter(x[1:50:end], y[1:50:end],
                    ylims = (0, 1.1*maximum(df_raw[df_raw.E1 .== E1 , 3])),
                    xlims = (0,3),
                    xlabel = "E2 [MeV]", ylabel = "dG/dE1dE2", title = "E1 = $E1 MeV; every 50 points",
                    label = "SpectrumG0 points"
                    )

for row in eachrow(df[df.E1 .== E1, :])
    plot!( [row.minE, row.maxE], 
           [get_line_point(row.minE, row.a, row.b), get_line_point(row.maxE, row.a, row.b)], 
           label = ifelse(row[:maxE] == 0.00093, "linear approximation", ""), 
           lw = 4, a=0.1, minorgrid =:true, framestyle = :box )
end
p_approx

df = normalize2D!(df)

614,474 rows × 7 columns

	E1	minE	maxE	minG	maxG	a	b
	Float64	Float64	Float64	Float64	Float64	Float64	Float64
1	0.00093	0.0	0.00093	0.0	0.402019	432.278	0.0
2	0.00093	0.00093	0.01493	0.402019	0.412043	0.716006	0.401353
3	0.00093	0.01493	0.02693	0.412043	0.421358	0.776314	0.400452
4	0.00093	0.02693	0.04093	0.421358	0.433615	0.875475	0.397782
5	0.00093	0.04093	0.05893	0.433615	0.450447	0.93513	0.39534
6	0.00093	0.05893	0.10993	0.450447	0.498264	0.937572	0.395196
7	0.00093	0.10993	0.13393	0.498264	0.519403	0.880794	0.401438
8	0.00093	0.13393	0.15693	0.519403	0.538506	0.830598	0.408161
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮

Last step is to add a column of CDF values - probabilities.

df = get_cdf!(df)

614,474 rows × 8 columns

	E1	minE	maxE	minG	maxG	a	b	cdf
	Float64	Float64	Float64	Float64	Float64	Float64	Float64	Float64
1	0.00093	0.0	0.00093	0.0	0.402019	432.278	0.0	1.86939e-7
2	0.00093	0.00093	0.01493	0.402019	0.412043	0.716006	0.401353	5.88537e-6
3	0.00093	0.01493	0.02693	0.412043	0.421358	0.776314	0.400452	1.08858e-5
4	0.00093	0.02693	0.04093	0.421358	0.433615	0.875475	0.397782	1.68706e-5
5	0.00093	0.04093	0.05893	0.433615	0.450447	0.93513	0.39534	2.48272e-5
6	0.00093	0.05893	0.10993	0.450447	0.498264	0.937572	0.395196	4.90193e-5
7	0.00093	0.10993	0.13393	0.498264	0.519403	0.880794	0.401438	6.12313e-5
8	0.00093	0.13393	0.15693	0.519403	0.538506	0.830598	0.408161	7.33972e-5
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮

cdfs = df[:, :cdf]

scatter(cdfs[1:10000:end], title= "Cumulative Distribution function CDF; every 1e3",
        xlabel = "energy segments (E1 + E2)", ylabel = "CDF", minorgrid = :true, 
        xlims=(0, 60), ylims = (0, 1.1), legend = :false, framestyle = :box)

Approximated spectrum shown as lines build out of linear segments. Each line represents one constant E1

c = palette(:thermal)

p = plot_lines(50, df, c)
p = plot!(ylims = (minimum(df.minG), 1.1*maximum(df.maxG)), ylabel = "dG/dE1dE2")

Output can be saved as a csv file which can be read off into new dataframe with ease

CSV.write("spectrumG0_Rebinned_prec0001.csv", df)

"spectrumG0_Rebinned_prec0001.csv"