Add smoothing of contour plots using Gaussian filtering

docs/src/plotting.md

@@ -49,7 +49,7 @@ The plot style of the mean can be customized using a `Dict`.  For `mean = true`,
 `Dict("linestyle" => :dash, "linewidth" => 1, "linecolor" => :black, "alpha" => 1, "label" => "global mode")`
 
 * `marginalmode::Union{Dict, Bool} = true`: indicate the marginal mode(s), i.e. the center of the highest histogram bin(s) (currently only for samples). The style can be passed as a `Dict`. If `marginalmode = true`, the default style is:  
-`Dict("linestyle" => :dot, "linewidth" => 1, "linecolor" => :black, "alpha" => 1, "label" => "local mode")`
+`Dict("linestyle" => :dot, "linewidth" => 1, "linecolor" => :black, "alpha" => 1, "label" => "marginal mode")`
 
 * (only for samples) `filter::Bool = false`: if `true`, `BAT.drop_low_weight_samples()` is applied before plotting
 
@@ -72,6 +72,7 @@ plot(
     std = false,
     globalmode = false,
     marginalmode = true,
+	smoothing = 0,
     diagonal = Dict(),
     upper = Dict(),
     right = Dict(),
@@ -111,7 +112,9 @@ The plot style of the mean can be customized using a `Dict`.  For `mean = true`,
 `Dict("linestyle" => :dash, "linewidth" => 1, "linecolor" => :black, "alpha" => 1, "label" => "global mode")`
 
 * `marginalmode::Union{Dict, Bool} = true`: indicate the marginalmode(s), i.e. the center of the highest histogram bin(s) (currently only for samples). The style can be passed as a `Dict`. If `marginalmode = true`, the default style is:
-`Dict("linestyle" => :dot, "linewidth" => 1, "linecolor" => :black, "alpha" => 1, "label" => "local mode")`
+`Dict("linestyle" => :dot, "linewidth" => 1, "linecolor" => :black, "alpha" => 1, "label" => "marginal mode")`
+
+* `smoothing = 0`: When plotting contours, a Gaussian filtering can be applied for smoothing the contour lines. The keyword `smoothing` accepts  positive real number (or a tuple of two positive real numbers), specifying the standard deviation of the Gaussian kernel (for each dimension) of the filtering.
 
 *  `diagonal = Dict()`: Used only for the seriestype `:marginal`. The dictionary can contain the seriestypes and plot options for 2D distributions explained above to modify the 2D plot of the marginal plot. Nested Dictionaries are possible to modify the styles of the estimators as described above
 

examples/dev-internal/plotting_examples.jl

@@ -58,7 +58,7 @@ using Plots
 
 plot(samples, :a) #default seriestype = :smallest_intervals (alias :HDR)
 #or: plot(samples, 2)
-# The default seriestype for plotting samples is `:smallest_intervals` (alias `:HDR`), highlighting the smallest intervals (the highest density region) containing 68.3, 95.5 and 99.7 perecent of the posterior probability. By default, the local mode(s) of the histogram is(are) indicated as dotted black line(s).
+# The default seriestype for plotting samples is `:smallest_intervals` (alias `:HDR`), highlighting the smallest intervals (the highest density region) containing 68.3, 95.5 and 99.7 perecent of the posterior probability. By default, the marginal mode(s) of the histogram is(are) indicated as dotted black line(s).
 
 # ### Default 1D plot of prior:
 # Priors can be plotted either by their index or by using the parameter name:
@@ -118,7 +118,7 @@ plot(samples, :a, marginalmode=false,
 # ### Default 2D plot  of samples:
 pyplot()
 plot(samples, (:a, :(b[1])), mean=true, std=true) #default seriestype = :smallest_intervals (alias :HDR)
-# The default seriestype for plotting samples is a 3-color heatmap showing the smallest intervals (highest density regions) containing 68.3%, 95.5% and 99.7% of the posterior probability. By default, the local mode
+# The default seriestype for plotting samples is a 3-color heatmap showing the smallest intervals (highest density regions) containing 68.3%, 95.5% and 99.7% of the posterior probability. By default, the marginal mode
 # of the histogram is indicated by a black square.
 
 # ### Default 2D plot  of priors:
@@ -136,9 +136,9 @@ plot(samples, (:a,:(b[2])), seriestype = :histogram)
 # (currently only correctly supported with `pyplot()` backend)
 plot(samples, (:a,:(b[2])), seriestype=:smallest_intervals_contour, bins=40)
 
-# ### smallest intervals as filled contours:
+# ### smallest intervals as filled contours with smoothing:
 # (currently only correctly supported with `pyplot()` backend)
-plot(samples, (:a,:(b[2])), seriestype=:smallest_intervals_contourf, bins=40)
+plot(samples, (:a,:(b[2])), seriestype=:smallest_intervals_contourf, bins=40, smoothing=1)
 
 # ### Customizing smallest interval plots:
 # The probability intervals to be highlighted can be specified using the `intervals` keyword.

src/algotypes/mode_estimator.jl

@@ -63,7 +63,7 @@ end
 
 *Experimental feature, not part of stable public API.*
 
-Estimates a local mode of `samples` by finding the maximum of marginalized posterior for each dimension.
+Estimates a marginal mode of `samples` by finding the maximum of marginalized posterior for each dimension.
 
 Returns a NamedTuple of the shape
 

src/plotting/recipes_MarginalDist_2D.jl

@@ -4,6 +4,7 @@
     vsel::NTuple{2,Union{Symbol, Expr, Integer}};
     intervals = default_credibilities,
     colors = default_colors,
+    smoothing = 0,
     diagonal = Dict(),
     upper = Dict(),
     right = Dict(),
@@ -43,7 +44,12 @@
         lev = calculate_levels(hist, intervals)
         x, y = get_bin_centers(marg)
         m = hist.weights
-
+
+        if smoothing != 0
+            ker = gaussian_kernel(smoothing)
+            m = convolution(m, ker, padding=:same)    
+        end
+
         # quick fix: needed when plotting contour on top of histogram
         # otherwise scaling of histogram colorbar would change scaling
         lev = lev/10000

src/plotting/recipes_samples_1D.jl

@@ -118,17 +118,17 @@
         end
     end
 
-    # local mode(s)
+    # marginal mode(s)
     if marginalmode_options != ()
         marginalmode_values = find_marginalmodes(marg)
 
         for (i, l) in enumerate(marginalmode_values)
          @series begin
             seriestype := :line
             if length(marginalmode_values)==1
-                label := get(marginalmode_options, "label", "local mode")
+                label := get(marginalmode_options, "label", "marginal mode")
             elseif i ==1
-                label := get(marginalmode_options, "label", "local modes")
+                label := get(marginalmode_options, "label", "marginal modes")
             else
                 label :=""
             end

src/plotting/recipes_samples_2D.jl

@@ -9,6 +9,7 @@
     std = false,
     globalmode = false,
     marginalmode = true,
+    smoothing = 0,
     diagonal = Dict(),
     upper = Dict(),
     right = Dict(),
@@ -92,6 +93,7 @@
             diagonal --> diagonal
             upper --> upper
             right --> right
+            smoothing --> smoothing
 
             marg, (xindx, yindx)
         end
@@ -168,9 +170,9 @@
          @series begin
             seriestype := :scatter
             if i==1 && length(marginalmode_values)==1
-                label := get(marginalmode_options, "label", "local mode")
+                label := get(marginalmode_options, "label", "marginal mode")
             elseif i ==1
-                label := get(marginalmode_options, "label", "local modes")
+                label := get(marginalmode_options, "label", "marginal modes")
             else
                 label :=""
             end

src/utils/convolution_utils.jl

@@ -0,0 +1,61 @@
+# This file is a part of BAT.jl, licensed under the MIT License (MIT).
+
+# simple 2d convolution with padding
+function convolution(input, filter; padding=:same)
+    input_r, input_c = size(input)
+    filter_r, filter_c = size(filter)
+
+    if padding == :same
+        pad_r = (filter_r - 1) ÷ 2 
+        pad_c = (filter_c - 1) ÷ 2 
+
+        input_padded = zeros(input_r+(2*pad_r), input_c+(2*pad_c))
+        for i in 1:input_r, j in 1:input_c
+            input_padded[i+pad_r, j+pad_c] = input[i, j]
+        end
+        input = input_padded
+        input_r, input_c = size(input)
+    end
+
+    result = zeros(input_r-filter_r+1, input_c-filter_c+1)
+    result_r, result_c = size(result)
+
+    for i in 1:result_r
+        for j in 1:result_c
+            for k in 1:filter_r 
+                for l in 1:filter_c 
+                    result[i,j] += input[i+k-1,j+l-1]*filter[k,l]
+                end
+            end
+        end
+    end
+
+    return result
+end
+
+
+# gaussian kernel with same σ in both dimensions
+function gaussian_kernel(σ::Real; l::Int = 4*ceil(Int,σ)+1)
+    isodd(l) || throw(ArgumentError("length must be odd"))
+    w = l>>1
+    g = σ == 0 ? [exp(0/(2*oftype(σ, 1)^2))] : [exp(-x^2/(2*σ^2)) for x=-w:w]
+    k = g/sum(g)
+    return (k * k')
+end
+
+# gaussian kernel with different σs in both dimensions
+function gaussian_kernel(
+    σs::Tuple{Real, Real}; 
+    l::Tuple{Int, Int} = (4*ceil(Int,σs[1])+1, 4*ceil(Int,σs[2])+1)
+)
+    all(isodd.(l)) || throw(ArgumentError("length must be odd"))
+    w1 = l[1]>>1
+    g1 = σs[1] == 0 ? [exp(0/(2*oftype(σs[1], 1)^2))] : [exp(-x^2/(2*σs[1]^2)) for x=-w1:w1]
+    k1 = g1/sum(g1)
+
+    w2 = l[2]>>1
+    g2 = σs[2] == 0 ? [exp(0/(2*oftype(σs[2], 1)^2))] : [exp(-x^2/(2*σs[2]^2)) for x=-w2:w2]
+    k2 = g2/sum(g2)
+
+    return (k1 * k2')  
+end

src/utils/utils.jl

@@ -2,5 +2,6 @@
 
 include("util_functions.jl")
 include("array_utils.jl")
+include("convolution_utils.jl")
 include("coord_utils.jl")
 include("valueshapes_utils.jl")

test/plotting/test_localmodes.jl

@@ -5,7 +5,7 @@ using Plots
 using StatsBase
 
 
-@testset "bin centers & local modes" begin
+@testset "bin centers & marginal modes" begin
 
     data1 = [1, 2, 3, 4, 5, 5, 6, 7, 8, 9, 9, 10]
     hist_1d = fit(Histogram, data1, nbins = 10, closed = :left)