mdipierro/nlib

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

Annotated Algorithms in Python

With applications in Physics, Biology, and Finance

The complete book in PDF is now available under a Creative Commons BY-NC-ND License:

DOWNLOAD BOOK IN PDF

The book is also available in printed form from Amazon:

Amazon

The nlib library

The book builds a numerical library from the ground up, called 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 (http://experts4solutions.com) @2016 BSDv3 License