added script to calculate the correlation integral of a large number …

…of points in an iterative and statistical fashion, documentation to follow

analysis/dynamical_systems/correlation_integral/correlation_integral.pig

@@ -0,0 +1,34 @@
+--
+-- Correlation Integral
+-- 
+-- C(e) = lim N->inf (1/N^2)*SUM( H( e - distance(x_i,x_j) ) )
+--
+-- where H is the Heaviside step function { 0 if distance(x_i,x_j) > e, 1 if distance(x_i,x_j) < e }
+-- where x_i and x_j are different points on the attractor
+--
+-- Here we take a sample n < N to calculate it for a given e (EPS)
+--
+REGISTER /usr/local/share/pig/contrib/piggybank/java/piggybank.jar;
+%default ATTRACTOR    'data/points.tsv'
+%default SAMPLE_FRAC  '0.1'  -- higher precentage = better accuracy but slower and more intensive        
+%default SAMPLE_SIZE  '100'  -- should be less than or equal to what is pulled out from the SAMPLE command
+%default EPS          '0.5'  -- independent variable in the correlation integral
+%default OUT          'data/corr_iter_00'
+
+attractor = LOAD '$ATTRACTOR' AS (x1:double, x2:double);
+first     = SAMPLE attractor $SAMPLE_FRAC;
+second    = SAMPLE attractor $SAMPLE_FRAC;
+sample_1  = LIMIT first  $SAMPLE_SIZE;
+sample_2  = LIMIT second $SAMPLE_SIZE;
+crossed   = CROSS sample_1, sample_2; -- careful
+dists     = FOREACH crossed
+            {
+                sq_dist = (sample_1::x1 - sample_2::x1)*(sample_1::x1 - sample_2::x1) + (sample_1::x2 - sample_2::x2)*(sample_1::x2 - sample_2::x2);
+                GENERATE org.apache.pig.piggybank.evaluation.math.SQRT(sq_dist) AS dist;
+            };
+to_sum    = FILTER dists BY dist < $EPS;
+grouped   = GROUP to_sum ALL;
+corr      = FOREACH grouped GENERATE (float)SIZE(to_sum)/((float)$SAMPLE_SIZE*(float)$SAMPLE_SIZE) AS corr_val, $EPS AS eps;;
+
+rmf $OUT;
+STORE corr INTO '$OUT';

analysis/dynamical_systems/correlation_integral/henon_map.rb

@@ -0,0 +1,18 @@
+#!/usr/bin/env ruby
+
+def henon_map
+  steps = 1000000
+  a = 1.4
+  b = 0.3
+  x = 0.631354477
+  y = 0.189406343
+
+  steps.times do
+    x_old = x
+    x = y + 1 - a*x*x
+    y = b*x_old
+    puts [x,y].join("\t") + "\n"
+  end
+end
+
+henon_map

analysis/dynamical_systems/correlation_integral/iterate.rb

@@ -0,0 +1,28 @@
+#!/usr/bin/env ruby
+
+#
+# Pass these in via args
+#
+raise "\n\nUsage: ./iterate.rb /path/to/attractor <num_iters> /path/to/output_dir\n" unless ARGV.length == 3
+attractor = ARGV[0]
+num_iters = ARGV[1]
+work_dir  = ARGV[2]
+
+#
+# Parameters that are constant throughout the calculation
+#
+eps_min         = 0.001
+eps_increment   = 0.025
+sample_size     = 5000
+sample_fraction = 0.001
+
+iter = 0
+eps  = eps_min
+num_iters.to_i.times do
+  next_file = "corr_iter_" + iter.to_s
+  next_dir  = File.join(work_dir, next_file)
+  system %Q{ pig -param ATTRACTOR=#{attractor} -param OUT=#{next_dir} -param EPS=#{eps} -param SAMPLE_SIZE=#{sample_size} -param SAMPLE_FRAC=#{sample_fraction} correlation_integral.pig }
+  iter += 1
+  eps += eps_increment
+end
+

network_analysis/pagerank/iterate_pagerank.sh → analysis/network_analysis/pagerank/iterate_pagerank.sh

@@ -7,7 +7,7 @@ for (( curr=0 , next=1 ; "$curr" < "$num_iters" ; curr++ , next++ )) ; do
   next_str=`printf "%03d" ${next}`
   curr_dir=${work_dir}/pagerank_graph_${curr_str}
   next_dir=${work_dir}/pagerank_graph_${next_str}
-  pig -x local -param PRGRPH="${curr_dir}" -param OUT="${next_dir}" pagerank.pig
-  # pig -param PRGRPH="${curr_dir}" -param OUT="${next_dir}" pagerank.pig
+  # pig -x local -param PRGRPH="${curr_dir}" -param OUT="${next_dir}" pagerank.pig
+  pig -param PRGRPH="${curr_dir}" -param OUT="${next_dir}" pagerank.pig
 done