Simple graphing of Elasticsearch scoring functions.

sim_score.py

from __future__ import division
import matplotlib.pyplot as plt
import matplotlib.dates as mdates

from pylab import *
import math
from scipy.stats import beta, norm, uniform
from scipy.special import betaln
from random import random, normalvariate
import numpy as np
from datetime import *
import os
import time

def graph(x, y, title):
    plt.plot(x, y)
    plt.suptitle( title )
    plt.show()

def gauss( origin, offset, scale, decay, abs_max, x_range, title ):
    sigma = - scale**2 / ( 2 * math.log( decay ) )
    x = np.array(x_range)
    y = np.exp(-(np.maximum(0, np.absolute(x-origin) - offset)**2)/2/sigma)
    if ( abs_max > 0 ):
	y = np.minimum( abs_max, y )
    graph( x, y, title )
    return y

def exp( origin, offset, scale, decay, abs_max, x_range, title ):
    l = math.log( decay ) / scale
    x = np.array(x_range)
    y = np.exp(l * np.maximum(0, np.absolute(x-origin) - offset))
    if ( abs_max > 0 ):
	y = np.minimum( abs_max, y )
    graph( x, y, title )
    return y

def log2p( mult, abs_max, x_range, title ):
    x = np.array(x_range)
    y = mult * np.log( x + 2 )
    if ( abs_max > 0 ):
	y = np.minimum( abs_max, y )
    graph( x, y, title )
    return y

def sqrt( mult, abs_max, x_range, title ):
    x = np.array(x_range)
    y = mult * np.sqrt( x )
    if ( abs_max > 0 ):
	y = np.minimum( abs_max, y )
    graph( x, y, title )
    return y

#################################
# Equations

sqrt( 0.1, 0, np.arange( 0, 1000000, 10 ), 'sqrt(active_installs) ' )

x = np.arange( 0, 1000000, 10 )
y1 = log2p( 0.375, 0, x, 'log2p(active_installs)' )
y2 = exp( 1000000, 0, 900000, 0.75, 0, x, 'exp(active_installs)' )

graph( x, y1 * y2, 'combined log2p(active_installs) * exp(active_installs)' )

log2p( 0.25, 0, x, 'active installs' )