#!/usr/bin/env python
# coding: utf-8

# ## Graphing and Plotting

# *NOTE:* The Jupyter notebook requires some more work to display MATLAB plots:

# In[10]:


get_ipython().run_line_magic('matplotlib', 'inline')


# In[11]:


import pylab as py
import numpy as np


# Now we are ready to do some plotting with MATLAB - just note that functions are appended with np & py and comments are now # instead of %.

# In[12]:


# define some vectors for x and y
x = (1,2,3,4,5,6,7,8,9);
y = (-1,3,-2,7,8,9,3,6,8);

# plot it! Remember that normally in MATLAB it would just be plot(x,y)
py.plot(x,y)


# In[13]:


# we can also use linspace to auto-generate a range of numbers
x = np.linspace(0,20,1000)
y = np.sin(x)
py.plot(x,y)


# In[14]:


# we can use xlim() and ylim() to define the limits of the plot
py.plot(x, y)
py.xlim(5, 15)
py.ylim(-1.2, 1.2)


# In[15]:


# we can label axis' and title the plot
py.xlabel('X-Axis')
py.ylabel('Y-Axis')
py.title('My Matlab Plot')
py.plot(x, y)


# In[16]:


# LaTeX is also supported
y = np.sin(2*np.pi*x)
py.plot(x, y)
py.title(r'$\sin(2 \pi x)$')  # the `r` before the string indicates a "raw string"


# In[17]:


# the color of the plot can be changed
y = np.sin(2*np.pi*x)
py.plot(x, y, 'r')
py.title(r'$\sin(2 \pi x)$')


# #### Color and Line-Style Options for Plots

# 'r' = red 'g' = green 'b' = blue 'c' = cyan 'm' = magenta 'y' = yellow 'k' = black 'w' = white

# '-' = solid
# '--' = dashed
# ':' = dotted
# '-.' = dot-dashed
# '.' = points
# 'o' = filled circles
# '^' = filled triangles

# In[18]:


# multiple plots on the same chart with a legend
x = np.linspace(0, 20, 1000)
y1 = np.sin(x)
y2 = np.cos(x)

py.plot(x, y1, '-b', label='sine')
py.plot(x, y2, '-r', label='cosine')
py.legend(loc='upper right')
py.ylim(-1.5, 2.0)


# In[19]:


# more customization
x1 = np.linspace(0, 10, 20)
y1 = np.sin(x1)

x2 = np.linspace(0, 10, 1000)
y2 = np.sin(x2)

py.ylim(-1.5, 2.0)
py.plot(x1, y1, 'bo', label='sampled')
py.plot(x2, y2, ':k', label='continuous')
py.legend()


# In[20]:


# multiple plots are achieved with the subplot() command
x = np.linspace(-5,5);
y1 = np.sin(x);
py.subplot(1,4,1)
py.plot(x,y1)
py.title('First subplot')

y2 = np.sin(2*x);
py.subplot(1,4,2)
py.plot(x,y2)
py.title('Second subplot')

y3 = np.sin(4*x);
py.subplot(1,4,3)
py.plot(x,y3)
py.title('Third subplot')

y4 = np.sin(6*x);
py.subplot(1,4,4)
py.plot(x,y4)
py.title('Fourth subplot')

# by changing to subplot(2,2,n) we would get a 2x2 grid of plots


# ### Useful Plotting Commands

# |    Command    |          Result          |
# |------|------|
# |plot(x,y)|creates an Cartesian plot of the vectors x & y|
# |plot(y)|creates a plot of y vs. the numerical values of the elements in the y-vector|
# |semilogx(x,y)|plots log(x) vs y|
# |semilogy(x,y)|plots x vs log(y)|
# |loglog(x,y)|plots log(x) vs log(y)|
# |grid|creates a grid on the graphics plot|
# |title('text')|places a title at top of graphics plot|
# |xlabel('text')|writes 'text' beneath the x-axis of a plot|
# |ylabel('text')|writes 'text' beside the y-axis of a plot|
# |text(x,y,'text')|writes 'text' at the location (x,y)|
# |text(x,y,'text','sc')|writes 'text' at point x,y assuming lower left corner is (0,0) and upper right corner is (1,1)|
# |gtext('text')|writes text according to placement of mouse|
# |hold on|maintains the current plot in the graphics window while executing subsequent plotting commands|
# |hold off|turns OFF the 'hold on' option|
# |polar(theta,r)|creates a polar plot of the vectors r & theta where theta is in radians|
# |bar(x)|creates a bar graph of the vector x (Note also the command stairs(y))|
# |bar(x,y)|creates a bar-graph of the elements of the vector y, locating the bars according to the vector elements of 'x' (Note also the command stairs(x,y))|
# |hist(x)|creates a histogram - this differs from the bargraph in that frequency is plotted on the vertical axis|
# |mesh(z)|creates a surface in xyz space where z is a matrix of the values of the function z(x,y). z can be interpreted to be the height of the surface above some xy reference plane|
# |surf(z)|similar to mesh(z), only surface elements depict the surface rather than a mesh grid|
# |contour(z)|draws a contour map in xy space of the function or surface z|
# |meshc(z)|draws the surface z with a contour plot beneath it|
# |meshgrid [X,Y]=meshgrid(x,y)|transforms the domain specified by vectors x and y into arrays X and Y that can be used in evaluating functions for 3D mesh/surf plots|
# |print|sends the contents of graphics window to printer|
# |print filename -dps| writes the contents of current graphics to 'filename' in postscript format|