Coverage for local/lib/python2.7/site-packages/sage/interacts/library_cython.pyx : 86%

r""" 

Library of cythonized methods 

AUTHORS: 

- Harald Schilly (2011-01-16): initial version (#9623) partially based on work by Lauri Ruotsalainen 

""" 

#***************************************************************************** 

# Copyright (C) 2011 Harald Schilly <harald.schilly@gmail.com> 

# 

# Distributed under the terms of the GNU General Public License (GPL) 

# as published by the Free Software Foundation; either version 2 of 

# the License, or (at your option) any later version. 

# http://www.gnu.org/licenses/ 

#***************************************************************************** 

from sage.misc.all import prod 

cpdef julia(ff_j, z, int iterations): 

""" 

Helper function for the Julia Fractal interact example. 

INPUT: 

- ``ff_j`` -- fast callable for the inner iteration 

- ``z`` -- complex number 

- ``iterations`` -- number of loops 

TESTS:: 

sage: from sage.interacts.library_cython import julia 

sage: z = var('z') 

sage: c_real, c_imag = 1, 1 

sage: f = symbolic_expression(z**2 + c_real + c_imag * CDF.gen()).function(z) 

sage: ff_m = fast_callable(f, vars=[z], domain=CDF) 

sage: julia(ff_m, CDF(1,1), 3) 

1.0 + 3.0*I 

""" 

for i in range(iterations): 

z = ff_j(z) 

if z.abs() > 2: break 

return z 

cpdef mandel(ff_m, z, int iterations): 

""" 

Helper function for the Mandelbrot Fractal interact example. 

INPUT: 

- ``ff_m`` -- fast callable for the inner iteration 

- ``z`` -- complex number 

- ``iterations`` -- number of loops 

TESTS:: 

sage: from sage.interacts.library_cython import mandel 

sage: z, c = var('z, c') 

sage: f = symbolic_expression(z**2 + c).function(z,c) 

sage: ff_m = fast_callable(f, vars=[z,c], domain=CDF) 

sage: mandel(ff_m, CDF(1,1), 3) 

1.0 + 3.0*I 

""" 

c = z 

for i in range(iterations): 

z = ff_m(z, c) 

if z.abs() > 2: break 

return z 

cpdef cellular(rule, int N): 

""" 

Cythonized helper function for the cellular_automata fractal. 

Yields a matrix showing the evolution of a Wolfram's cellular automaton. 

Based on work by Pablo Angulo. 

http://wiki.sagemath.org/interact/misc#CellularAutomata 

INPUT: 

- ``rule`` -- determines how a cell's value is updated, depending 

on its neighbors 

- ``N`` -- number of iterations 

TESTS:: 

sage: from sage.interacts.library_cython import cellular 

sage: rule = [1, 0, 1, 0, 0, 1, 1, 0] 

sage: N = 3 

sage: print(cellular(rule, N)) 

[[0 0 0 1 0 0 0 0] 

[1 1 0 1 0 1 0 0] 

[0 1 1 1 1 1 0 0]] 

""" 

from numpy import zeros 

cdef int j, k, l 

M=zeros((N, 2*N+2), dtype=int) 

M[0,N]=1 

for j in range(1, N): 

for k in range(0, 2*N): 

l = 4 * M[j-1, k-1] + 2 * M[j-1, k] + M[j-1, k+1] 

M[j,k] = rule[l] 

return M