#!/usr/bin/env python
# Copyright (c) 2012 Cloudera, Inc. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#
# Utility functions for calculating common mathematical measurements. Note that although
# some of these functions are available in external python packages (ex. numpy), these
# are simple enough that it is better to implement them ourselves to avoid extra
# dependencies.

import math

def calculate_avg(values):
  return sum(values) / float(len(values))

def calculate_stddev(values):
  """Return the standard deviation of a numeric iterable."""
  avg = calculate_avg(values)
  return math.sqrt(calculate_avg([(val - avg)**2 for val in values]))

def calculate_median(values):
  """Return the median of a numeric iterable."""
  if all([v is None for v in values]): return None
  sorted_values = sorted(values)
  length = len(sorted_values)
  if length % 2 == 0:
    return (sorted_values[length / 2] + sorted_values[length / 2 - 1]) / 2
  else:
    return sorted_values[length / 2]

def calculate_geomean(values):
  """ Calculates the geometric mean of the given collection of numerics """
  if len(values) > 0:
    return (reduce(lambda x, y: float(x) * float(y), values)) ** (1.0 / len(values))

def calculate_tval(avg, stddev, iters, ref_avg, ref_stddev, ref_iters):
  """
  Calculates the t-test t value for the given result and refrence.

  Uses the Welch's t-test formula. For more information see:
  http://en.wikipedia.org/wiki/Student%27s_t-distribution#Table_of_selected_values
  http://en.wikipedia.org/wiki/Student's_t-test
  """
  # SEM (standard error mean) = sqrt(var1/N1 + var2/N2)
  # t = (X1 - X2) / SEM
  sem = math.sqrt((math.pow(stddev, 2) / iters) + (math.pow(ref_stddev, 2) / ref_iters))
  return (avg - ref_avg) / sem