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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 IPython Notebooks
You can run a cell by pressing [shift] + [Enter] or by pressing the "play" button in the menu.
You can get help on a function or object by pressing [shift] + [tab] after the opening parenthesis function(
You can also get help by executing function?
Numpy Arrays
Manipulating numpy arrays is an important part of doing machine learning
(or, really, any type of scientific computation) in python.  This will likely
be review for most
Step1:  There is much, much more to know, but these few operations are fundamental to what we'll
do during this tutorial.
Scipy Sparse Matrices
We won't make very much use of these in this tutorial, but sparse matrices are very nice
in some situations.  In some machine learning tasks, especially those associated
with textual analysis, the data may be mostly zeros.  Storing all these zeros is very
inefficient, and representing in a way that only contains the "non-zero" values can be much more efficient.  We can create and manipulate sparse matrices as follows
Step2:  The CSR representation can be very efficient for computations, but it is not
as good for adding elements.  For that, the LIL (List-In-List) representation
is better
Step3:  Often, once an LIL matrix is created, it is useful to convert it to a CSR format
(many scikit-learn algorithms require CSR or CSC format)
Step4:  There are several other sparse formats that can be useful for various problems
Step5:  There are many, many more plot types available.  One useful way to explore these is by
looking at the matplotlib gallery
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Python Code:
import numpy as np
# Generating a random array
X = np.random.random((3, 5))  # a 3 x 5 array
print(X)
# Accessing elements
# get a single element
print(X[0, 0])
# get a row
print(X[1])
# get a column
print(X[:, 1])
# Transposing an array
print(X.T)
# Turning a row vector into a column vector
y = np.linspace(0, 12, 5)
print(y)
# make into a column vector
print(y[:, np.newaxis])
# getting the shape or reshaping an array
print(X.shape)
print(X.reshape(5, 3))
# indexing by an array of integers (fancy indexing)
indices = np.array([3, 1, 0])
print(indices)
X[:, indices]
Explanation: IPython Notebooks
You can run a cell by pressing [shift] + [Enter] or by pressing the "play" button in the menu.
You can get help on a function or object by pressing [shift] + [tab] after the opening parenthesis function(
You can also get help by executing function?
Numpy Arrays
Manipulating numpy arrays is an important part of doing machine learning
(or, really, any type of scientific computation) in python.  This will likely
be review for most: we'll quickly go through some of the most important features.
End of explanation
from scipy import sparse
# Create a random array with a lot of zeros
X = np.random.random((10, 5))
print(X)
# set the majority of elements to zero
X[X < 0.7] = 0
print(X)
# turn X into a csr (Compressed-Sparse-Row) matrix
X_csr = sparse.csr_matrix(X)
print(X_csr)
# convert the sparse matrix to a dense array
print(X_csr.toarray())
Explanation: There is much, much more to know, but these few operations are fundamental to what we'll
do during this tutorial.
Scipy Sparse Matrices
We won't make very much use of these in this tutorial, but sparse matrices are very nice
in some situations.  In some machine learning tasks, especially those associated
with textual analysis, the data may be mostly zeros.  Storing all these zeros is very
inefficient, and representing in a way that only contains the "non-zero" values can be much more efficient.  We can create and manipulate sparse matrices as follows:
End of explanation
# Create an empty LIL matrix and add some items
X_lil = sparse.lil_matrix((5, 5))
for i, j in np.random.randint(0, 5, (15, 2)):
    X_lil[i, j] = i + j
print(X_lil)
print(X_lil.toarray())
Explanation: The CSR representation can be very efficient for computations, but it is not
as good for adding elements.  For that, the LIL (List-In-List) representation
is better:
End of explanation
print(X_lil.tocsr())
Explanation: Often, once an LIL matrix is created, it is useful to convert it to a CSR format
(many scikit-learn algorithms require CSR or CSC format)
End of explanation
%matplotlib inline
import matplotlib.pyplot as plt
# plotting a line
x = np.linspace(0, 10, 100)
plt.plot(x, np.sin(x))
# scatter-plot points
x = np.random.normal(size=500)
y = np.random.normal(size=500)
plt.scatter(x, y)
# showing images
x = np.linspace(1, 12, 100)
y = x[:, np.newaxis]
im = y * np.sin(x) * np.cos(y)
print(im.shape)
# imshow - note that origin is at the top-left by default!
plt.imshow(im)
# Contour plot - note that origin here is at the bottom-left by default!
plt.contour(im)
# 3D plotting
from mpl_toolkits.mplot3d import Axes3D
ax = plt.axes(projection='3d')
xgrid, ygrid = np.meshgrid(x, y.ravel())
ax.plot_surface(xgrid, ygrid, im, cmap=plt.cm.jet, cstride=2, rstride=2, linewidth=0)
Explanation: There are several other sparse formats that can be useful for various problems:
CSC (compressed sparse column)
BSR (block sparse row)
COO (coordinate)
DIA (diagonal)
DOK (dictionary of keys)
The scipy.sparse submodule also has a lot of functions for sparse matrices
including linear algebra, sparse solvers, graph algorithms, and much more.
Matplotlib
Another important part of machine learning is visualization of data.  The most common
tool for this in Python is matplotlib.  It is an extremely flexible package, but
we will go over some basics here.
First, something special to IPython notebook.  We can turn on the "IPython inline" mode,
which will make plots show up inline in the notebook.
End of explanation
# %load http://matplotlib.org/mpl_examples/pylab_examples/ellipse_collection.py
import matplotlib.pyplot as plt
import numpy as np
from matplotlib.collections import EllipseCollection
x = np.arange(10)
y = np.arange(15)
X, Y = np.meshgrid(x, y)
XY = np.hstack((X.ravel()[:,np.newaxis], Y.ravel()[:,np.newaxis]))
ww = X/10.0
hh = Y/15.0
aa = X*9
fig, ax = plt.subplots()
ec = EllipseCollection(ww, hh, aa, units='x', offsets=XY,
                       transOffset=ax.transData)
ec.set_array((X+Y).ravel())
ax.add_collection(ec)
ax.autoscale_view()
ax.set_xlabel('X')
ax.set_ylabel('y')
cbar = plt.colorbar(ec)
cbar.set_label('X+Y')
plt.show()
Explanation: There are many, many more plot types available.  One useful way to explore these is by
looking at the matplotlib gallery: http://matplotlib.org/gallery.html
You can test these examples out easily in the notebook: simply copy the Source Code
link on each page, and put it in a notebook using the %load magic.
For example:
End of explanation
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