numpy: Introduction¶

A Difference in Speed¶

Let's import the numpy module.

import numpy as np

n = 5  # CHANGE ME
a1 = list(range(n)) # python list
a2 = np.arange(n)   # numpy array

if n <= 10:
    print(a1)
    print(a2)

%timeit [i**2 for i in a1]

%timeit a2**2

Numpy Arrays: much less flexible, but:

much faster
less memory

Ways to create a numpy array¶

Casting from a list

a = np.array([1,2,3,5])
print(a)
print(a.dtype)

b = np.array([1.0,2.0,3.0])
print(b)
print(b.dtype)

But also noticed that:

c = np.array([1,2,3])
print(c)
print(c.dtype)

d = np.array([1,2.,3])
print(d)
print(d.dtype)

linspace
np.linspace(start, stop, num=50,...)
num is the number of sample points

np.linspace(-1, 1, 9)

zeros

np.zeros((10,10), np.float64)

Create 2D arrays, using zeros, using reshape and from list

Operations on arrays¶

These propagate to all elements:

a = np.array([1.2, 3, 4])
b = np.array([0.5, 0, 1])

Addition, multiplication, power ... are all elementwise:

a+b

a*b

a**b

Important Attributes¶

Numpy arrays have two (most) important attributes:

A = np.random.rand(5, 4, 3)
A.shape

The .shape attribute contains the dimensionality array as a tuple. So the tuple (5,4,3) means that we're dealing with a three-dimensional array of size $5 \times 4 \times 3$.

(numpy.random.rand just generates an array of random numbers of the given shape.)

A.dtype

Other dtypes include np.complex64, np.int32, ...

Iclicker question¶

1D arrays¶

a = np.random.rand(5)
a.shape

a = np.array([2,3,5])
print(a)
print(a.shape)

2D arrays¶

a = np.array([[2],[3],[5]])
print(a)
print(a.shape)

a = np.array([[2,3,5]])
print(a)
print(a.shape)

We can change 1D numpy arrays into 2D numpy arrays using the function reshape

a = np.array([2,3,5]).reshape(3,1)
print(a)
print(a.shape)

a = np.array([2,3,5]).reshape(1,3)
print(a)
print(a.shape)

print(np.arange(1,10))
B = np.arange(1,10).reshape(3,3)
print(B)

Transpose¶

print(B)

print(B.transpose())
print(B)

print(B.swapaxes(0,1))
print(B)

print(B.T)
print(B)

C = np.transpose(B)
print(C)

What happens when we try to take the transpose of 1D array?

a = np.array([[2,3,5]])
print(a.T)

But it works with 2D arrays

a = np.array([2,3,5]).reshape(3,1)
print(a)
print(a.T)

Inner and outer products¶

Matrix multiplication is np.dot(A, B) for two 2D arrays.

A = np.random.rand(3, 2)
B = np.random.rand(2, 4)
C = np.dot(A,B)
print(C.shape)

b = np.array([5,6])

d = np.dot(A,b)
print(d.shape)

A = np.array([[1,3],[2,4]])
B = np.array([[2,1],[3,2]])
print(np.dot(A,B))
print(A@B)

a = np.array([1,2,3])
b = np.array([5,6,7])
#Inner Product
print(np.dot(a,b))
print(np.inner(a,b))

#Outer Product C[i,j] = a[i]*b[j]
C = np.outer(a,b)
print(np.shape(C))
print(C)