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sagemath
GitHub Repository: sagemath/sagelib
 Path: blob/master/sage/interacts/library_cython.pyx
4069 views
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r"""

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Library of cythonized methods

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AUTHORS:

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

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"""

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

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#       Copyright (C) 2011 Harald Schilly <[email protected]>

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#

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

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

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

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#                  http://www.gnu.org/licenses/

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

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from sage.misc.misc import prod

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include '../ext/interrupt.pxi'

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include '../ext/cdefs.pxi'

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include "../ext/stdsage.pxi"

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cpdef julia(ff_j, z, int iterations):

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    """

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    Helper function for the Julia Fractal interact example.

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    INPUT:

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

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        - `z` -- complex number

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        - `iterations` -- number of loops

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    TESTS::

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        sage: from sage.interacts.library_cython import julia

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        sage: z = var('z')

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        sage: c_real, c_imag = 1, 1

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

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

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        sage: julia(ff_m, CDF(1,1), 3)

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        1.0 + 3.0*I

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    """

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    for i in range(iterations):

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         z = ff_j(z)

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         if z.abs() > 2: break

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    return z

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cpdef mandel(ff_m, z, int iterations):

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    """

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    Helper function for the Mandelbrot Fractal interact example.

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    INPUT:

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

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        - `z` -- complex number

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        - `iterations` -- number of loops

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    TESTS::

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        sage: from sage.interacts.library_cython import mandel

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        sage: z, c = var('z, c')

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

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

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        sage: mandel(ff_m, CDF(1,1), 3)

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        1.0 + 3.0*I

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    """

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    c = z

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    for i in range(iterations):

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        z = ff_m(z, c)

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        if z.abs() > 2: break

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    return z

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cpdef cellular(rule, int N):

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    """

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    Cythonized helper function for the cellular_automata fractal.

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

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    Based on work by Pablo Angulo.

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

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    INPUT:

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

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        - `N` -- number of iterations

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    TESTS::

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        sage: from sage.interacts.library_cython import cellular

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

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        sage: N = 3

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        sage: print cellular(rule, N)

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        [[0 0 0 1 0 0 0 0]

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         [1 1 0 1 0 1 0 0]

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         [0 1 1 1 1 1 0 0]]

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    """

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    from numpy import zeros

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    cdef int j, k, l

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    M=zeros((N, 2*N+2), dtype=int)

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    M[0,N]=1  

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    for j in range(1, N):

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        for k in range(0, 2*N):

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

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            M[j,k] = rule[l]

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    return M

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