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## nlib library This is the library described and documented in this book: http://www.amazon.com/Annotated-Algorithms-Python-Applications-Physics/dp/0991160401 It is a pure python library for numerical computations. Does not 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 file "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

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