* New module: wpylib.math.stats.array_stats, for studying statistics of

an array (e.g., sparsity, difference, etc).

math/stats/array_stats.py

@@ -0,0 +1,160 @@
+# $Id: __init__.py,v 1.1 2010-10-07 15:57:29 wirawan Exp $
+#
+# wpylib.math.stats.array_stats module
+# Created: 20140404
+# Wirawan Purwanto
+#
+
+"""
+wpylib.math.stats.array_stats module
+Tools for studying the statistics of an array, the difference of
+two or more arrays, etc.
+
+"""
+
+import os
+import sys
+import numpy
+
+
+# Functions below were imported from V2b_inspect.py, 20140404
+
+"""
+CONVENTIONS
+
+- Usually, M1 is the matrix under examination, M2 is the reference matrix.
+"""
+
+def report_diff_stat(M1, M2, out=sys.stdout):
+  # Original function name: statdiff
+  """Studies the difference of two arrays (or matrices).
+  Usually, M1 is the matrix under examination, M2 is the reference
+  matrix.
+  Prints out standard report to a given text file, or returns
+  the report as a string.
+  """
+  dM = M1 - M2
+  if len(M1.shape) == 2:
+    dM_diag = numpy.diagonal(dM)
+    stats = (
+      dM.max(),
+      dM.min(),
+      dM.mean(),
+      numpy.abs(dM).mean(),
+      rms(dM),
+      dM_diag.max(),
+      dM_diag.min(),
+      dM_diag.mean(),
+      numpy.abs(dM_diag).mean(),
+      rms(dM_diag),
+    )
+    if out == tuple:
+      return stats
+
+    rslt = """\
+- max difference  = %13.6e
+- min difference  = %13.6e
+- mean difference = %13.6e
+- mean abs diff   = %13.6e
+- rms difference  = %13.6e
+- max difference  = %13.6e   on diagonal
+- min difference  = %13.6e   on diagonal
+- mean difference = %13.6e   on diagonal
+- mean abs diff   = %13.6e   on diagonal
+- rms difference  = %13.6e   on diagonal
+""" % stats
+  else:
+    stats = (
+      dM.max(),
+      dM.min(),
+      dM.mean(),
+      numpy.abs(dM).mean(),
+      rms(dM),
+    )
+    if out == tuple:
+      return stats
+
+    rslt = """\
+- max difference  = %13.6e
+- min difference  = %13.6e
+- mean difference = %13.6e
+- mean abs diff   = %13.6e
+- rms difference  = %13.6e
+""" % stats
+
+  if out == str:
+    return rslt
+  else:
+    out.write(rslt)
+    out.flush()
+
+
+def maxadiff(M1, M2):
+  # Original function name: maxdiff
+  """Returns the maximum absolute difference between two matrices.
+  Used for checking whether two matrices are identical."""
+  return numpy.abs(M1 - M2).max()
+
+
+def maxadiff_by_col(M1, M2):
+  # Original function name: maxdiff_by_col
+  """Assuming two-dimensional array (where first index is the row
+  index), computes the maximum absolute difference.
+  """
+  return numpy.abs(M1 - M2).max(axis=0)
+
+
+def maxradiff(M1, M2, ztol=1e-15):
+  # Original function name: maxrdiff
+  """Prints the maximum *relative* absolute difference between two matrices.
+  Used for checking whether two matrices are identical.
+
+  CAVEATS:
+  - Zero elements in M2 (reference matrix) are converted to unity for
+    calculating the relative difference.
+  """
+  (mapprox, mref) = (M1, M2)
+  diff = numpy.asarray(numpy.abs(mapprox - mref))
+  mref0 = numpy.asarray(numpy.abs(mref))
+  numpy.putmask(mref0, mref0 < ztol, [1.0])
+  
+  return (diff / mref0).max()
+
+
+class ArrayStat(object):
+  """A class to compute the statistics of an array.
+  """
+  def __init__(self, mat, save=False):
+    mat = numpy.asarray(mat)
+    amat = numpy.abs(mat)
+    if save:
+      self.mat = mat
+    self.min = mat.min()
+    self.max = mat.max()
+    self.mean = mat.mean()
+    self.amin = amat.min()
+    self.amax = amat.max()
+    self.amean = amat.mean()
+    self.rms = numpy.sqrt(numpy.sum(amat**2) / amat.size)
+
+  def report(self, out=sys.stdout):
+    """Prints out a standard report.
+    """
+    #print_histogram(study_sparsity(self.diff, (log_delta-5.5,log_delta+4.5+0.1)), xaxis='left_edge')
+    rslt = """\
+. min       = %12.6g
+. max       = %12.6g
+. mean      = %12.6g
+. absmin    = %12.6g
+. absmax    = %12.6g
+. absmean   = %12.6g
+. rms       = %12.6g
+""" % (self.min, self.max, self.mean,
+       self.amin, self.amax, self.amean,
+       self.rms)
+
+    if out == str:
+      return rslt
+    else:
+      out.write(rslt)
+      out.flush()