implemented a function that will be used to provide a generic n-th order, nth-dimension error approximation function

.hgignore

@@ -1,3 +1,4 @@
 \.pyc$
+\.gz$
 \.blend$
 egg

bin/pattern.py

@@ -0,0 +1,12 @@
+#!/usr/bin/env python
+
+from baker import pattern
+from baker.tools import smblog
+
+smblog.info(pattern(power = 2, phicount = 3, offset = -1))
+smblog.info()
+smblog.info(pattern(power = 2, phicount = 4, offset = -1))
+smblog.info()
+smblog.info(pattern(power = 3, phicount = 3, offset = -1))
+smblog.info()
+smblog.info(pattern(power = 3, phicount = 4, offset = -1))

bin/test3d-connectivity.py

@@ -0,0 +1,69 @@
+#!/usr/bin/env python
+
+import sys
+from grid.DDD import random_grid
+from baker import get_phis, run_baker
+from baker.tools import exact_func, smberror, improved_answer, smblog
+from glob import glob
+from os import remove
+
+import numpy as np
+
+import pylab
+
+def draw_gb(bad, good):
+  pylab.xlabel('total runs')
+  pylab.ylabel('count')
+  pylab.grid(True)
+  pylab.plot(bad)
+  pylab.plot(good)
+  pylab.legend(('bad', 'good'))
+
+  pylab.show()
+
+FILE_PREFIX='/tmp/qhull-'
+
+
+if __name__ == '__main__':
+  for g in glob('%s*' % FILE_PREFIX):
+    remove(g)
+
+  try:
+    total_points   = int(sys.argv[1])
+    random_points  = int(sys.argv[2])
+    total_tries    = int(sys.argv[3])
+  except:
+    print "usage: app.py [total points in random grid] [number of random points to attempt] [total attempts]"
+    sys.exit(1)
+
+
+  print "total points", total_points
+
+
+
+  d = {True: 0, False: 0}
+  good = []
+  bad = []
+  for cur_try in xrange(total_tries):
+    g = random_grid(total_points)
+    open('%s%0.3d.txt' % (FILE_PREFIX, cur_try), 'w').write(g.for_qhull())
+
+    for i in xrange(random_points):
+      X = [np.random.rand(), np.random.rand(), np.random.rand()]
+      exact = exact_func(X)
+
+      try:
+        try:
+          answer =  g.run_baker(X)
+          d[improved_answer(answer, exact)] += 1
+        except ValueError as e:
+          smblog.error(e)
+      except smberror as e:
+        print e
+        print d
+
+    print d
+    bad.append(d[False])
+    good.append(d[True])
+
+  draw_gb(bad = bad, good = good)

lib/baker/__init__.py

@@ -3,6 +3,7 @@ from baker.tools import smblog
 import numpy as np
 import sys
 
+import itertools
 from tools import smberror
 
 def get_phis(X, R):
@@ -305,3 +306,30 @@ def run_baker_3D(X, R, S):
             }
 
   return answer
+
+def _boxings(n, k):
+  """\
+    source for this function:
+    http://old.nabble.com/Simple-combinatorics-with-Numpy-td20086915.html
+    http://old.nabble.com/Re:-Simple-combinatorics-with-Numpy-p20099736.html
+  """
+  seq, i = [n] * k + [0], k
+  while i:
+    yield tuple(seq[i] - seq[i+1] for i in xrange(k))
+    i = seq.index(0) - 1
+    seq[i:k] = [seq[i] - 1] * (k-i)
+
+def _samples_ur(items, k, offset = 0):
+  """Returns k unordered samples (with replacement) from items."""
+  n = len(items)
+  for sample in _boxings(k, n):
+    selections = [[items[i]]*count for i,count in enumerate(sample)]
+    yield tuple([x + offset  for sel in selections for x in sel])
+
+def pattern(power, phicount, offset = 0):
+  smblog.debug("(power = %s, phicount = %s)" % (power, phicount))
+  r = []
+  for i in _samples_ur(range(1, phicount + 1), power, offset):
+    if not len(set(i)) == 1:
+      r.append(i)
+  return r

lib/grid/DDD.py

@@ -1,5 +1,5 @@
 from grid import grid as basegrid
-from baker.tools import exact_func_3D
+from baker.tools import exact_func_3D, smblog
 
 import numpy as np
 
@@ -88,6 +88,13 @@ class random_grid(rect_grid):
 
     r = np.random
 
+    appx_side_res = int(np.power(num_points, 1/3.0))
+    smblog.debug("appx_side_res: %d" % appx_side_res)
+    delta = 1.0 / float(appx_side_res)
+
+    for x in xrange(appx_side_res + 1):
+      pass
+
     for i in xrange(num_points):
       cur_x = r.rand()
       cur_y = r.rand()