# coding: utf-8
This IPython Notebook contains simple examples of the line function. 

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# In[1]:


import numpy as np
from scipy.integrate import odeint


# In[2]:


from bokeh.plotting import figure, output_notebook, show


# In[3]:


sigma = 10
rho = 28
beta = 8.0/3
theta = 3 * np.pi / 4


# In[4]:


def lorenz(xyz, t):
    x, y, z = xyz
    x_dot = sigma * (y - x)
    y_dot = x * rho - x * z - y
    z_dot = x * y - beta* z
    return [x_dot, y_dot, z_dot]


# In[5]:


initial = (-10, -7, 35)
t = np.arange(0, 100, 0.001)


# In[6]:


solution = odeint(lorenz, initial, t)


# In[7]:


x = solution[:, 0]
y = solution[:, 1]
z = solution[:, 2]
xprime = np.cos(theta) * x - np.sin(theta) * y


# In[8]:


colors = ["#C6DBEF", "#9ECAE1", "#6BAED6", "#4292C6", "#2171B5", "#08519C", "#08306B",]


# In[9]:


output_notebook()


# In[10]:


p = figure(title="lorenz example")
p.multi_line(np.array_split(xprime, 7), np.array_split(z, 7),
           line_color=colors, line_alpha=0.8, line_width=1.5)


# In[11]:


show(p)