j2t.ipynb

Kernel: Python 2 (SageMath)

# Math libraries
import numpy as np
from math import sqrt

# Matplotlib plotting libraries
import matplotlib.pyplot as plt
%matplotlib inline

# Bokeh plotting libraries
import bokeh.plotting as blt
blt.output_notebook()

WARNING: 1 intermediate output message was discarded.

import math 
import numpy as np

class JuliaSet(object):
    def __init__(self, c, m = 100):
        self._d = 0.001
        self.c = c
        self.m = m
        self._complexplane = np.array([])
        self.set = np.array([])
    def create_a_plane(self):
        self.limit = 2
        self.r = np.arange(-self.limit,self.limit,self._d)
        self._complexplane = self.r[:,np.newaxis] + self.r[np.newaxis,:]*1j
        
        
    def juliamap(self,z):
        return z**2 + self.c
    
    def iterate(self,z):
        for counter in range(1,self.m+1):
            z = self.juliamap(z)
            if math.sqrt(z.real**2 + z.imag**2) > 2 :
                return counter
        return 0
    
    def set_spacing(self,d):
        self._d = d
        self.create_a_plane()
        return self._complexplane
        
    def generate(self):
        if not self._complexplane.size:
            self.create_a_plane()
            
        vfunc = np.vectorize(self.iterate)
        self.set = vfunc(self._complexplane)
        return self.set

class JuliaSetPlot(JuliaSet):
    """Extend JuliaSet to add plotting functionality"""
    
    def __init__(self, *args, **kwargs):
        # Invoke constructor for JuliaSet first, unaltered
        super(JuliaSetPlot, self).__init__(*args, **kwargs)
        # Add one more attribute: a rendered image array
        self.img = np.array([])
    
    def get_dim(self):
        # get what should be an attribute
        return int(4.0 / self._d)
    
    def render(self):
        if not self.set: self.generate()
        # Convert inefficient list to efficient numpy array
        self.img = np.array(self.set)
        dim = self.get_dim()
        # Reshape array into a 2d complex plane
        self.img = np.reshape(self.img, (dim,dim)).T
        
    def show(self):
        if not self.img.size: self.render()
        # Specify complex plane axes efficiently
        xy = np.linspace(-2,2,self.get_dim())
        # Use matplotlib to plot image as an efficient mesh
        plt.figure(1, figsize=(12,9))
        plt.pcolormesh(xy,xy,self.img, cmap=plt.cm.hot)
        plt.colorbar()
        plt.show()
        
    def interact(self):
        from matplotlib.colors import rgb2hex
        if not self.img.size: self.render()
        # Mimic matplotlib "hot" color palette
        colormap = plt.cm.get_cmap("hot")
        bokehpalette = [rgb2hex(m) for m in colormap(np.arange(colormap.N))]
        # Use bokeh to plot an interactive image
        f = blt.figure(x_range=[-2,2], y_range=[-2,2], plot_width=600, plot_height=600)
        f.image(image=[j.img], x=[-2,2], y=[-2,2], dw=[4], dh=[4], palette=bokehpalette)
        blt.show(f)

j = JuliaSetPlot(-1.037 + 0.17j)
%time j.set_spacing(0.006)
%time j.show()

CPU times: user 0 ns, sys: 4 ms, total: 4 ms
Wall time: 16.2 ms

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-11-2a95bb0acec6> in <module>()
      1 j = JuliaSetPlot(-1.037 + 0.17j)
      2 get_ipython().magic(u'time j.set_spacing(0.006)')
----> 3 get_ipython().magic(u'time j.show()')

/projects/sage/sage-6.9/local/lib/python2.7/site-packages/IPython/core/interactiveshell.pyc in magic(self, arg_s)
   2334         magic_name, _, magic_arg_s = arg_s.partition(' ')
   2335         magic_name = magic_name.lstrip(prefilter.ESC_MAGIC)
-> 2336         return self.run_line_magic(magic_name, magic_arg_s)
   2337 
   2338     #-------------------------------------------------------------------------
/projects/sage/sage-6.9/local/lib/python2.7/site-packages/IPython/core/interactiveshell.pyc in run_line_magic(self, magic_name, line)
   2255                 kwargs['local_ns'] = sys._getframe(stack_depth).f_locals
   2256             with self.builtin_trap:
-> 2257                 result = fn(*args,**kwargs)
   2258             return result
   2259 
/projects/sage/sage-6.9/local/lib/python2.7/site-packages/IPython/core/magics/execution.pyc in time(self, line, cell, local_ns)
/projects/sage/sage-6.9/local/lib/python2.7/site-packages/IPython/core/magic.pyc in <lambda>(f, *a, **k)
    191     # but it's overkill for just that one bit of state.
    192     def magic_deco(arg):
--> 193         call = lambda f, *a, **k: f(*a, **k)
    194 
    195         if callable(arg):
/projects/sage/sage-6.9/local/lib/python2.7/site-packages/IPython/core/magics/execution.pyc in time(self, line, cell, local_ns)
   1161         if mode=='eval':
   1162             st = clock2()
-> 1163             out = eval(code, glob, local_ns)
   1164             end = clock2()
   1165         else:
<timed eval> in <module>()
<ipython-input-10-2c3d5a46376a> in show(self)
     21 
     22     def show(self):
---> 23         if not self.img.size: self.render()
     24         # Specify complex plane axes efficiently
     25         xy = np.linspace(-2,2,self.get_dim())
<ipython-input-10-2c3d5a46376a> in render(self)
     18         dim = self.get_dim()
     19         # Reshape array into a 2d complex plane
---> 20         self.img = np.reshape(self.img, (dim,dim)).T
     21 
     22     def show(self):
/projects/sage/sage-6.9/local/lib/python2.7/site-packages/numpy/core/fromnumeric.pyc in reshape(a, newshape, order)
    216     except AttributeError:
    217         return _wrapit(a, 'reshape', newshape, order=order)
--> 218     return reshape(newshape, order=order)
    219 
    220 
ValueError: total size of new array must be unchanged

j = JuliaSetPlot(-0.624 + 0.435j)
%time j.set_spacing(0.006)
%time j.interact()

%prun j.generate()

%load_ext line_profiler
%lprun -f j.generate j.generate()