New sample calculation with proof

resources/run_sampling.rb

@@ -219,8 +219,10 @@ def _sample_probability_distribution(prob_dist, num_samples)
     end
 
     return_samples = {}
+    return_samples_v2 = {}
     prob_dist.each do |item|
       return_samples[item[0]] = 0
+      return_samples_v2[item[0]] = 0
     end
 
     # Sort array in descending order
@@ -239,6 +241,17 @@ def _sample_probability_distribution(prob_dist, num_samples)
     end
 
     sum = prob_dist.transpose[1].inject(0, :+)
+
+    # New style of calculating sampling distribution
+    sample_dist = prob_dist.map{|v| [v[0], (v[1]*num_samples/sum)]}
+    assigned_samples = (sample_dist.map{|val| return_samples_v2[val[0]] += val[1].to_i}).inject(0, :+)
+    remaining_samples = num_samples - assigned_samples
+    sample_dist_hash = {}
+    remaining_sample_dist = sample_dist.each_with_index.map{|v, i| [v[1] - v[1].to_i, v[0]]}.sort.reverse
+    remaining_sample_dist.map{|v| sample_dist_hash[v[1]]=v[0]}
+
+    remaining_sample_dist[0, remaining_samples].map{|v| return_samples_v2[v[1]] += 1}
+
     remaining_samples = num_samples
     while remaining_samples > 0
       # Choose highest probability item (first in array)
@@ -268,14 +281,33 @@ def _sample_probability_distribution(prob_dist, num_samples)
       end
     end
 
+    if not (return_samples == return_samples_v2)
+      # If the two sample counts (new and old) aren't equal, make sure:
+      # 1. there is no more than 1 sample difference for any options and sum of differences (extra and deficit) is zero.
+      # 2. The options for which there is one sample extra, and corresponding options for which there is one sample
+      # deficit have exact same probability.
+      # The reason for this discrepancy is as follow. Suppose, we want three samples between option=Yes and option=No
+      # If both Yes and No has same probability (0.5), the samples could be [Yes, Yes, No] or [Yes, No, No].
+      diffs = return_samples_v2.map{ |key, v| [sample_dist_hash[key], key, return_samples[key] - v]}
+      raise "Sample count diff doesn't sum to zero" unless diffs.transpose[2].inject(0, :+) == 0
+      raise "There are differences of more than 1 samples" unless diffs.transpose[2].map{|v| v.abs() <= 1}.all?
+      negative_diffs = diffs.select{|v| v[2]<0}.sort
+      positive_diffs = diffs.select{|v| v[2]>0}.sort
+      while negative_diffs.size > 0
+        negative_diff = negative_diffs.pop()
+        positive_diff = positive_diffs.pop()
+        raise "Matching diff with same probability not found" unless (negative_diff[0] - positive_diff[0]).abs < 1e-9
+      end
+    end
     # Remove items with no samples
+    return_samples_v2.delete_if { |_k, v| v == 0 }
     return_samples.delete_if { |_k, v| v == 0 }
 
-    if return_samples.values.reduce(:+) != num_samples
+    if return_samples_v2.values.reduce(:+) != num_samples
       register_error('Sampling algorithm unexpectedly failed.', nil)
     end
 
-    return return_samples
+    return return_samples_v2
   end
 
   def distribute_samples(random_seed, results_data_param, sample_results, bldgs)