x.shape = (20, 5)
print x

y.shape = (4, 20, -1)
print y.shape

# Scalar Indexing
print x[2]

# Slicing
print x[2:5]

# Advanced slicing
print "First 5 rows\n", x[:5]
print "Row 18 to the end\n", x[18:]
print "Last 5 rows\n", x[-5:]
print "Reverse the rows\n", x[::-1]

# Boolean Indexing
print x[(x % 2) == 0]

# Fancy Indexing -- Note the use of a list, not tuple!
print x[[1, 3, 8, 9, 2]]

print "Shape of X:", x.shape
print "Shape of Y:", y.shape

a = x + y
print a.shape
b = x[np.newaxis, :, :] + y
print b.shape
c = np.tile(x, (4, 1, 1)) + y
print c.shape
print "Are a and b identical?", np.all(a == b)
print "Are a and c identical?", np.all(a == c)

x = np.arange(-5, 5, 0.1)
y = np.arange(-8, 8, 0.25)
print x.shape, y.shape
z = x[np.newaxis, :] * y[:, np.newaxis]
print z.shape

# More concisely
y, x = np.ogrid[-8:8:0.25, -5:5:0.1]
print x.shape, y.shape
z = x * y
print z.shape