Metadata-Version: 1.0
Name: big_O
Version: 0.8.1
Summary: Empirical estimation of time complexity from execution time
Home-page: https://github.com/pberkes/big_O
Author: Pietro Berkes
Author-email: pietro.berkes@googlemail.com
License: LICENSE.txt
Description: =====
        big_O
        =====
        
        big_O is a Python module to estimate the time complexity of Python code from
        its execution time.  It can be used to analyze how functions scale with inputs
        of increasing size.
        
        
        big_O executes a Python function for input of increasing size `N`, and measures
        its execution time. From the measurements, big_O fits a set of time complexity
        classes and returns the best fitting class. This is an empirical way to
        compute the asymptotic class of a function in `"Big-O"
        <http://en.wikipedia.org/wiki/Big_oh>`_.  notation. (Strictly
        speaking, we're empirically computing the Big Theta class.)
        
        Usage
        -----
        
        For concreteness, let's say we would like to compute the asymptotic behavior
        of a simple function that finds the maximum element in a list of positive
        integers:
        
            >>> def find_max(x):
            ...     """Find the maximum element in a list of positive integers."""
            ...     max_ = 0
            ...     for el in x:
            ...         if el > max_:
            ...             max_ = el
            ...     return max_
            ...
        
        To do this, we call `big_o.big_o` passing as argument the function and a
        data generator that provides lists of random integers of length N:
        
            >>> import big_o
            >>> positive_int_generator = lambda n: big_o.datagen.integers(n, 0, 10000)
            >>> best, others = big_o.big_o(find_max, positive_int_generator, n_repeats=100)
            >>> print(best)
            Linear: time = -0.0021 + 4E-06*n
        
        `big_o` inferred that the asymptotic behavior of the `find_max` fuction is
        linear, and returns an object containing the fitted coefficients for the
        complexity class. The second return argument, `others`, contains a dictionary
        of all fitted classes with the residuals from the fit as keys:
        
            >>> for class_, residuals in others.items():
            ...     print('{:<60s}    (res: {:.2G})'.format(class_, residuals))
            ...
            Logarithmic: time = -0.3 + 0.05*log(n)                      (res: 0.072)
            Cubic: time = 0.1 + 3.6E-16*n^3                             (res: 0.028)
            Quadratic: time = 0.068 + 3.8E-11*n^2                       (res: 0.011)
            Constant: time = 0.2                                        (res: 0.17)
            Exponential: time = -4.2 * 4.1E-05^n                        (res: 9.6)
            Linearithmic: time = 0.0077 + 3.5E-07*n*log(n)              (res: 0.00055)
            Polynomial: time = -11 * x^0.84                             (res: 0.12)
            Linear: time = -0.0021 + 4E-06*n                            (res: 0.00054)
        
        Submodules
        ----------
        
        - `big_o.datagen`: this sub-module contains common data generators, including an identity generator that simply returns N (`datagen.n_`), and a data generator that returns a list of random integers of length N (`datagen.integers`).
        - `big_o.complexities`: this sub-module defines the complexity classes to be fit to the execution times. Unless you want to define new classes, you don't need to worry about it.
        
        
        Standard library examples
        -------------------------
        
        Sorting a list in Python is O(n*log(n)) (a.k.a. 'linearithmic'):
        
            >>> big_o.big_o(sorted, lambda n: big_o.datagen.integers(n, -100, 100))
            (<big_o.complexities.Linearithmic object at 0x031DA9D0>, ...)
        
        Inserting elements at the beginning of a list is O(n):
        
            >>> def insert_0(lst):
            ...     lst.insert(0, 0)
            ...
            >>> print big_o.big_o(insert_0, big_o.datagen.range_n, n_repeats=100)[0]
            Linear: time = 0.00035 + 7.5E-08*n
        
        Inserting elements at the beginning of a queue is O(1):
        
            >>> from collections import deque
            >>> def insert_0_queue(queue):
            ...     lst.insert(0, 0)
            ...
            >>> def queue_generator(n):
            ...      return deque(xrange(n))
            ...
            >>> print big_o.big_o(insert_0_queue, queue_generator, n_repeats=100)[0]
            Constant: time = 0.00012
        
        `numpy` examples
        ----------------
        
        Creating an array:
        
        - `numpy.zeros` is O(n), since it needs to initialize every element to 0:
        
            >>> import numpy as np
            >>> big_o.big_o(np.zeros, big_o.datagen.n_, max_n=100000, n_repeats=100)
            (<class 'big_o.big_o.Linear'>, ...)
        
        - `numpy.empty` instead just allocates the memory, and is thus O(1):
        
            >>> big_o.big_o(np.empty, big_o.datagen.n_, max_n=100000, n_repeats=100)
            (<class 'big_o.big_o.Constant'> ...)
        
        
        License
        -------
        
        big_O is released under the GPL v3. See LICENSE.txt .
        
        Copyright (c) 2011, Pietro Berkes. All rights reserved.
        
Platform: UNKNOWN
