Histograms

src/Histograms.jl

@@ -3,15 +3,181 @@ module Histograms
 This module is mostly a convenient wrapper of Python functions (numpy, scipy).
 
 Functions in this module:
- - W1 (2 methods)
+ - W1 (8 methods)
+ - load! (3 methods)
+ - plot (2 methods)
+ - plot_raw (1 method)
 
 """
 
 import PyCall
+import NPZ
 include("ConvenienceFunctions.jl")
 
 scsta = PyCall.pyimport("scipy.stats")
 
+################################################################################
+# HistData struct ##############################################################
+################################################################################
+"""
+A simple struct to store samples for empirical PDFs (histograms, distances etc.)
+
+Functions that operate on HistData struct:
+ - W1 (4 methods)
+ - load! (3 methods)
+ - plot (2 methods)
+ - plot_raw (1 method)
+"""
+mutable struct HistData
+  samples::Dict{Symbol, AbstractVecOrMat}
+end
+
+HistData() = HistData(Dict())
+
+"""
+Load samples into a HistData object under a specific key from a vector
+
+Parameters:
+  - hd:            HistData; groups of samples accessed by keys
+  - key:           Symbol; key of the samples group to load samples to
+  - samples:       array-like; samples to load
+
+If the `key` group already exists, the samples are appended. If, in addition,
+the samples were in a matrix, they are flattened first, and then the new ones
+are added.
+"""
+function load!(hd::HistData, key::Symbol, samples::AbstractVector)
+  if haskey(hd.samples, key)
+    if isa(hd.samples[key], Matrix)
+      println(warn("load!"),
+              "hd.samples[:", key, "] is a Matrix; using vec(hd.samples)")
+    end
+    hd.samples[key] = vcat(vec(hd.samples[key]), samples)
+  else
+    hd.samples[key] = samples
+  end
+end
+
+"""
+Load samples into a HistData object under a specific key from a matrix
+
+Parameters:
+  - hd:            HistData; groups of samples accessed by keys
+  - key:           Symbol; key of the samples group to load samples to
+  - samples:       matrix-like; samples to load
+
+If the `key` group already exists, the samples are appended. If, in addition,
+the samples were in a vector, the new ones are flattened first, and then added
+to the old ones. If the samples were in a matrix and row dimensions don't match,
+the minimum of the two dimensions is chosen, the rest is discarded.
+"""
+function load!(hd::HistData, key::Symbol, samples::AbstractMatrix)
+  if haskey(hd.samples, key)
+    if isa(hd.samples[key], Vector)
+      println(warn("load!"),
+              "hd.samples[:", key, "] is a Vector; using vec(samples)")
+      hd.samples[key] = vcat(hd.samples[key], vec(samples))
+    elseif size(hd.samples[key], 1) != size(samples, 1)
+      println(warn("load!"), "sizes of hd.samples & samples don't match; ",
+              "squishing down to match the minimum of the two")
+      K = min(size(hd.samples[key], 1), size(samples,1))
+      hd.samples[key] = hcat(hd.samples[key][1:K, 1:end], samples[1:K, 1:end])
+    else
+      hd.samples[key] = hcat(hd.samples[key], samples)
+    end
+  else
+    hd.samples[key] = samples
+  end
+end
+
+"""
+Load samples into a HistData object under a specific key from a file
+
+Parameters:
+  - hd:            HistData; groups of samples accessed by keys
+  - key:           Symbol; key of the samples group to load samples to
+  - filename:      String; name of a .npy file with samples (vector/matrix)
+
+All the rules about vector/matrix interaction from two other methods apply.
+"""
+function load!(hd::HistData, key::Symbol, filename::String)
+  samples = NPZ.npzread(filename)
+  if isa(samples, Array) && ndims(samples) <= 2
+    load!(hd, key, samples)
+  else
+    throw(error("load!: ", filename, " is not a 1- or 2-d Array; abort"))
+  end
+end
+
+"""
+Plot a histogram of a range of data by a specific key
+
+Parameters:
+  - hd:     HistData; groups of samples accessed by keys
+  - plt:    a module used for plotting (only PyPlot supported)
+  - key:    Symbol; key of the samples group to construct histogram from
+  - k:      Int or UnitRange; if samples are in a matrix, which rows to use
+  - kws:    dictionary-like; keyword arguments to pass to plotting function
+
+If `hd.samples[key]` is a matrix, all the samples from `k` row(s) are combined;
+if it is a vector, `k` is ignored.
+"""
+function plot(hd::HistData, plt, key::Symbol, k::Union{Int,UnitRange}; kws...)
+  if length(hd.samples) == 0
+    println(warn("plot"), "no samples, nothing to plot")
+    return
+  end
+  is_pyplot = (Symbol(plt) == :PyPlot)
+  if !is_pyplot
+    println(warn("plot"), "only PyPlot is supported; not plotting")
+    return
+  end
+
+  if isa(hd.samples[key], Vector)
+    S = hd.samples[key]
+  else
+    S = vec(hd.samples[key][k, 1:end])
+  end
+
+  plot_raw(S, plt; kws...)
+end
+
+"""
+Plot a histogram of whole data by a specific key
+
+Parameters:
+  - hd:     HistData; groups of samples accessed by keys
+  - plt:    a module used for plotting (only PyPlot supported)
+  - key:    Symbol; key of the samples group to construct histogram from
+  - kws:    dictionary-like; keyword arguments to pass to plotting function
+"""
+plot(hd::HistData, plt, key::Symbol; kws...) =
+  plot(hd, plt, key, UnitRange(1, size(hd.samples[key], 1)); kws...)
+
+"""
+Plot a histogram of samples
+
+Parameters:
+  - S:      array-like; samples to construct histogram from
+  - plt:    a module used for plotting (only PyPlot supported)
+  - kws:    dictionary-like; keyword arguments to pass to plotting function
+
+The keyword arguments `kws` have precedence over defaults, but if left
+unspecified, these are the defaults:
+  bins     = "auto"
+  histtype = "step"
+  density  = true
+"""
+function plot_raw(S::AbstractVector, plt; kws...)
+  kwargs_local = Dict{Symbol, Any}()
+  kwargs_local[:bins]     = "auto"
+  kwargs_local[:histtype] = "step"
+  kwargs_local[:density]  = true
+
+  # the order of merge is important! kws have higher priority
+  plt.hist(S; merge(kwargs_local, kws)...)
+end
+
 ################################################################################
 # distance functions ###########################################################
 ################################################################################
@@ -27,11 +193,13 @@ Returns:
   - w1_uv:         number; the Wasserstein-1 distance
 """
 function W1(u_samples::AbstractVector, v_samples::AbstractVector;
-                     normalize = true)
-  L = maximum([u_samples; v_samples]) - minimum([u_samples; v_samples])
+                     normalize = false)
   return if !normalize
     scsta.wasserstein_distance(u_samples, v_samples)
   else
+    u_m, u_M = extrema(u_samples)
+    v_m, v_M = extrema(v_samples)
+    L = max(u_M, v_M) - min(u_m, v_m)
     scsta.wasserstein_distance(u_samples, v_samples) / L
   end
 end
@@ -45,22 +213,22 @@ Parameters:
   - V_samples:     matrix-like; samples from distributions (v1, v2, ...)
   - normalize:     boolean; whether to normalize the distances by 1/(max-min)
 
-`U_samples` and `V_samples` should have samples in the 2nd dimension (along
-rows) and have the same 1st dimension (same number of rows). If not, the minimum
-of the two (minimum number of rows) will be taken.
-
-`normalize` induces *pairwise* normalization, i.e. it max's and min's are
-computed for each pair (u_j, v_j) individually.
-
 Returns:
   - w1_UV:         array-like; the pairwise Wasserstein-1 distances:
                    w1(u1, v1)
                    w1(u2, v2)
                    ...
                    w1(u_K, v_K)
+
+`U_samples` and `V_samples` should have samples in the 2nd dimension (along
+rows) and have the same 1st dimension (same number of rows). If not, the minimum
+of the two (minimum number of rows) will be taken.
+
+`normalize` induces *pairwise* normalization, i.e. it max's and min's are
+computed for each pair (u_j, v_j) individually.
 """
 function W1(U_samples::AbstractMatrix, V_samples::AbstractMatrix;
-                     normalize = true)
+                     normalize = false)
   if size(U_samples, 1) != size(V_samples, 1)
     println(warn("W1"), "sizes of U_samples & V_samples don't match; ",
             "will use the minimum of the two")
@@ -75,6 +243,143 @@ function W1(U_samples::AbstractMatrix, V_samples::AbstractMatrix;
   return w1_UV
 end
 
+W1(U_samples::AbstractMatrix, v_samples::AbstractVector; normalize = false) =
+  W1(vec(U_samples), v_samples; normalize = normalize)
+
+W1(u_samples::AbstractVector, V_samples::AbstractMatrix; normalize = false) =
+  W1(u_samples, vec(V_samples); normalize = normalize)
+
+"""
+Compute pairs of Wasserstein-1 distances between `key` samples and the rest
+
+Parameters:
+  - hd:     HistData; groups of samples accessed by keys
+  - key:    Symbol; key of the samples group to compare everything else against
+  - k:      Int or UnitRange; if samples are in a matrix, which rows to use
+
+Returns:
+  - key2all_combined:     Dict{Symbol, Float64}; pairs of W1 distances
+
+Compute the W1-distances between `hd.samples[key]` and all other `hd.samples`.
+If any of the `hd.samples` is a matrix (not a vector) then `k` is used to access
+rows of said matrix, and then samples from these rows are combined together.
+For any of the `hd.samples` that is a vector, `k` is ignored.
+
+This function is useful when you have one reference (empirical) distribution and
+want to compare the rest against that "ground truth" distribution.
+
+Examples:
+  k2a_row1 = W1(hd, :dns, 1)
+  K = size(hd.samples[:dns], 1)
+  k2a_combined = W1(hd, :dns, 1:K)
+  println(k2a_combined[:bal])
+"""
+function W1(hd::HistData, key::Symbol, k::Union{Int,UnitRange})
+  key2all_combined = Dict{Symbol, Float64}()
+  for ki in keys(hd.samples)
+    if ki == key
+      continue
+    end
+    key2all_combined[ki] = W1(hd, ki, key, k)
+  end
+  return key2all_combined
+end
+
+"""
+Compute a pair of Wasserstein-1 distance between `key1` & `key2` samples
+
+Parameters:
+  - hd:     HistData; groups of samples accessed by keys
+  - key1:   Symbol; key of the first samples group
+  - key2:   Symbol; key of the second samples group
+  - k:      Int or UnitRange; if samples are in a matrix, which rows to use
+
+Returns:
+  - w1_key1key2:     Float64; W1 distance
+
+Compute the W1-distance between `hd.samples[key1]` and `hd.samples[key2]`.
+If either of them is a matrix (not a vector) then `k` is used to access rows of
+said matrix, and then samples from these rows are combined together.
+For vectors, `k` is ignored.
+
+Examples:
+  w1_dns_bal = W1(hd, :dns, :bal, 1)
+  K = size(hd.samples[:dns], 1)
+  w1_dns_bal_combined = W1(hd, :dns, :bal, 1:K)
+"""
+function W1(hd::HistData, key1::Symbol, key2::Symbol, k::Union{Int,UnitRange})
+  u = if isa(hd.samples[key1], Vector)
+    hd.samples[key1]
+  else
+    vec(hd.samples[key1][k, 1:end])
+  end
+  v = if isa(hd.samples[key2], Vector)
+    hd.samples[key2]
+  else
+    vec(hd.samples[key2][k, 1:end])
+  end
+  return W1(u, v)
+end
+
+"""
+Compute vectors of Wasserstein-1 distances between `key` samples and the rest
+
+Parameters:
+  - hd:     HistData; groups of samples accessed by keys
+  - key:    Symbol; key of the samples group to compare everything else against
+
+Returns:
+  - key2all_vectorized:   Dict{Symbol, Union{Vector{Float64}, Float64}};
+                          either vectors or pairs of W1 distances
+
+Compute the W1-distances between `hd.samples[key]` and all other `hd.samples`.
+For each pair of samples (`key` and something else) where both groups of samples
+are in a matrix, the returned value will be a vector (corresponding to rows of
+the matrices); for each pair where at least one of the groups is a vector, the
+returned value will be a Float64, and all samples from a matrix are combined.
+
+This function is useful when you have one reference (empirical) distribution and
+want to compare the rest against that "ground truth" distribution.
+
+Examples:
+  k2a_vectorized = W1(hd, :dns)
+  println(k2a_vectorized[:onl] .> 0.01)
+"""
+function W1(hd::HistData, key::Symbol)
+  key2all_vectorized = Dict{Symbol, Union{Vector{Float64}, Float64}}()
+  for ki in keys(hd.samples)
+    if ki == key
+      continue
+    end
+    key2all_vectorized[ki] = W1(hd, ki, key)
+  end
+  return key2all_vectorized
+end
+
+"""
+Compute a vector of Wasserstein-1 distances between `key1` & `key2` samples
+
+Parameters:
+  - hd:     HistData; groups of samples accessed by keys
+  - key1:   Symbol; key of the first samples group
+  - key2:   Symbol; key of the second samples group
+
+Returns:
+  - w1_key1key2:     Union{Vector{Float64}, Float64}; W1 distance
+
+Compute the W1-distance between `hd.samples[key1]` and `hd.samples[key2]`.
+
+If both are matrices, the returned value will be a vector (corresponding to rows
+of the matrices); if at least one of them is a vector, the returned value will
+be a Float64, and all samples from a matrix are combined.
+
+Examples:
+  w1_dns_bal = W1(hd, :dns, :bal)
+  println(w1_dns_bal .> 0.01)
+"""
+W1(hd::HistData, key1::Symbol, key2::Symbol) =
+  W1(hd.samples[key1], hd.samples[key2])
+
 end # module