import pylab as pl
import numpy as np
import matplotlib.pyplot as plt
"""
This is all from the tutorial located at :

http://scipy-lectures.github.io/intro/matplotlib/matplotlib.html

"""


# Create a figure of size 8x6 inches, 80 dots per inch
pl.figure(figsize=(10, 6), dpi=80)


# Create a new subplot from a grid of 1x1
pl.subplot(1, 1, 1)


#X = np.linspace(-np.pi, np.pi, 256, endpoint=True)
X = np.linspace(-5, 5, 500, endpoint=True)


C = (1/X**2)-5
#P = Y-5


#C, S = np.cos(X), np.sin(X)


"""
# Plot sine with a green continuous line of width 1 (pixels)
pl.plot(X, S, color="green", linewidth=1.0, linestyle="-")
"""
# Set x limits
#pl.xlim(-4.0, 44.0)

# Set x ticks
#pl.xticks(np.linspace(-4, 4, 9, endpoint=True))

# Set y limits
#pl.ylim(-1.0, 1.0)

# Set y ticks
#pl.yticks(np.linspace(-1, 1, 5, endpoint=True))

# Save figure using 72 dots per inch
# savefig("exercice_2.png", dpi=72)

"""
Editing the above - this is to change the color of the lines and also to alter
the thickness of the lines

"""

pl.plot(X, C, color="blue", linewidth=2.5, linestyle="-")
#pl.plot(X, S, color="red", linewidth=2.5, linestyle="-")

"""
Makes is so that the lines aren't right at the edge of the screen
easier to actually read the graph like this
"""

pl.xlim(X.min() * 1.1, X.max() * 1.1)
pl.ylim(C.min() * 1.1, C.max() * 1.1)

"""
Changes the x and y ticks so that they show the values of pi

Also uses latex to show the values explicitly with symbols
"""

#pl.xticks([-np.pi, -np.pi/2, 0, np.pi/2, np.pi],
         # [r'$-\pi$', r'$-\pi/2$', r'$0$', r'$+\pi/2$', r'$+\pi$'])
#pl.yticks([-1,0,1])

"""
Alters the position of the axis - moves them to the centre
"""
ax = pl.gca()  # gca stands for 'get current axis'
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.spines['bottom'].set_position(('data',0))
ax.yaxis.set_ticks_position('left')
ax.spines['left'].set_position(('data',0))

"""

"""
pl.plot(X, C, color="blue", linewidth=2.5, linestyle="-", label="y = 4 - 1/x^2")
#pl.plot(X, S, color="red",  linewidth=2.5, linestyle="-", label="sine")

pl.legend(loc='upper left')

"""
Annotate the graph!
"""

"""


t = 2 * np.pi / 3
pl.plot([t, t], [0, np.cos(t)], color='blue', linewidth=2.5, linestyle="--")
pl.scatter([t, ], [np.cos(t), ], 50, color='blue')

pl.annotate(r'$sin(\frac{2\pi}{3})=\frac{\sqrt{3}}{2}$',
            xy=(t, np.sin(t)), xycoords='data',
            xytext=(+10, +30), textcoords='offset points', fontsize=16,
            arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.2"))

pl.plot([t, t],[0, np.sin(t)], color='red', linewidth=2.5, linestyle="--")
pl.scatter([t, ],[np.sin(t), ], 50, color='red')

pl.annotate(r'$cos(\frac{2\pi}{3})=-\frac{1}{2}$',
            xy=(t, np.cos(t)), xycoords='data',
            xytext=(-90, -50), textcoords='offset points', fontsize=16,
            arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.2"))


"""


"""

"""

for label in ax.get_xticklabels() + ax.get_yticklabels():
    label.set_fontsize(16)
    label.set_bbox(dict(facecolor='white', edgecolor='None', alpha=0.65))


plt.ylim((-7,20))


# Show result on screen
pl.show()