Ecosyste.ms: Awesome

An open API service indexing awesome lists of open source software.

Awesome Lists | Featured Topics | Projects

https://github.com/mdipierro/nlib

The book "Annotated Algorithms in Python" and the nlib.py library
https://github.com/mdipierro/nlib

Last synced: 20 days ago
JSON representation

The book "Annotated Algorithms in Python" and the nlib.py library

Awesome Lists containing this project

README 

        
## Annotated Algorithms in Python (3.8)



### With applications in Physics, Biology, and Finance



The complete book in PDF is now available under a [Creative Commons BY-NC-ND License](http://creativecommons.org/licenses/by-nc-nd/3.0/legalcode):



[DOWNLOAD BOOK IN PDF](https://raw.githubusercontent.com/mdipierro/nlib/master/docs/book_numerical.pdf)



The book is also available in printed form from Amazon:



[Amazon](http://www.amazon.com/Annotated-Algorithms-Python-Applications-Physics/dp/0991160401)



## The nlib library



The book builds a numerical library from the ground up, called src/nlib.py.

It is a pure python library for numerical computations. It doesn't require numpy.



## Usage



    >>> from nlib import *



## Linear algebra example



    >>> A = Matrix([[1,2],[4,9]])

    >>> print 1/A 

    >>> print (A+2)*A

    >>> B = Matrix(2,2,lambda i,j: i+j**2)



## Fitting



    >>> points = [(x0,y0,dy0), (x1,y1,dy1), (x2,y2,dy2), ...]

    >>> coefficients, chi2, fitting_function = fit_least_squares(points,POLYNOMIAL(2))

    >>> for x,y,dy in points:

    >>>     print x, y, '~', fitting_function(x)



## Solvers

    

    >>> from math import sin

    >>> def f(x): return sin(x)-1+x

    >>> x0 = solve_newton(f, 0.0, ap=0.01, rp=0.01, ns=100)

    >>> print 'f(%s)=%s ~ 0' % (x0, f(x0))



(ap is target absolute precision, rp is target relative precision, ns is max number of steps)



## Optimizers



    >>> def f(x): return (sin(x)-1+x)**2

    >>> x0 = optimize_newton(f, 0.0, ap=0.01, rp=0.01, ns=100)

    >>> print 'f(%s)=%s ~ min f' % (x0, f(x0))    

    >>> print 'f'(%s)=%s ~ 0' % (x0, D(f)(x0))    



## Statistics



    >>> x = [random.random() for k in range(100)]

    >>> print 'mu     =', mean(x)

    >>> print 'sigma  =', sd(x)

    >>> print 'E[x]   =', E(lambda x:x,    x)

    >>> print 'E[x^2] =', E(lambda x:x**2, x)

    >>> print 'E[x^3] =', E(lambda x:x**3, x)

    >>> y = [random.random() for k in range(100)]

    >>> print 'corr(x,y) = ', correlation(x,y)

    >>> print 'cov(x,y)  = ', covariance(x,y)



## Finance



    >>> google = YStock('GOOG')

    >>> current = google.current()

    >>> print current['price']                                                                          

    >>> print current['market_cap']                                                                

    >>> for day in google.historical():

    >>>     print day['date'], day['adjusted_close'], day['log_return']



## Persistant Storage



    >>> d = PersistentDictionary(path='test.sqlite')

    >>> d['key'] = 'value'

    >>> print d['key']

    >>> del d['key']



d works like a drop-in preplacement for any normal Python dictionary except that the data is stored in a sqlite database in a file called  "test.sqlite" so it is still there if you re-start the program. Kind of like the shelve module but shelve files cannot safely be accessed by multiple threads/processes unless locked and locking the entire file is not efficient.



## Neural Network



    >>> pat = [[[0,0], [0]], [[0,1], [1]], [[1,0], [1]], [[1,1], [0]]]

    >>> n = NeuralNetwork(2, 2, 1)

    >>> n.train(pat)

    >>> n.test(pat)

    [0, 0] -> [0.00...]

    [0, 1] -> [0.98...]

    [1, 0] -> [0.98...]

    [1, 1] -> [-0.00...]



## Plotting



    >>> data = [(x0,y0), ...]

    >>> Canvas(title='my plot').plot(data, color='red').save('myplot.png')



nlib plotting requires matplotlib/numpy for the Canvas object only

plots are chainable. methods: .plot, .hist, .errorbar, .ellipses



## Complete list of functions/classes



    CONSTANT

    CUBIC

    Canvas

    Cholesky

    Cluster

    D

    DD

    Dijkstra

    DisjointSets

    E

    Ellipse

    HAVE_MATPLOTLIB

    Jacobi_eigenvalues

    Kruskal

    LINEAR

    MCEngine

    MCG

    Markowitz

    MarsenneTwister

    Matrix

    NeuralNetwork

    POLYNOMIAL

    PersistentDictionary

    Prim

    PrimVertex

    QUADRATIC

    QUARTIC

    QuadratureIntegrator

    RandomSource

    StringIO

    Trader

    YStock

    bootstrap

    breadth_first_search

    compute_correlation

    condition_number

    confidence_intervals

    continuum_knapsack

    correlation

    covariance

    decode_huffman

    depth_first_search

    encode_huffman

    fib

    fit

    fit_least_squares

    gradient

    hessian

    integrate

    integrate_naive

    integrate_quadrature_naive

    invert_bicgstab

    invert_minimum_residual

    is_almost_symmetric

    is_almost_zero

    is_positive_definite

    jacobian

    lcs

    leapfrog

    make_maze

    mean

    memoize

    memoize_persistent

    needleman_wunsch

    norm

    optimize_bisection

    optimize_golden_search

    optimize_newton

    optimize_newton_multi (multi-dimentional optimizer)

    optimize_newton_multi_imporved

    optimize_secant

    partial

    random

    resample

    sd

    solve_bisection

    solve_fixed_point

    solve_newton

    solve_newton_multi (multi-dimensional solver)

    solve_secant

    variance



## License



Created by Massimo Di Pierro ([email protected]) @2016 BSDv3 License