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from IPython.display import HTML
import requests
HTML(requests.get("https://git.io/fh5WI").text)
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Python and Jupyter for Programmers
Part 3: Computing with Numpy
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import numpy as np
Converting a list into a numpy array:
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x = np.array([1, 2, 3])
x
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x[0]
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x[0] = 100
x
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We can perform computations on the whole numpy arrays at once:
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x
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y = np.array([2, 3, 4])
y
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x + y
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10*x
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x**2
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np.sin(x)
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2. Performance Advantage
Numpy computations are typically a lot faster than computations done using pure Python.
Example.
Calculate an array of squares of integers from 0 to 1,000,000 using numpy:
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np.arange(10)
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%%timeit -n 5
x = np.arange(10**6)
y = x**2
The same computation using list comprehensions:
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%%timeit -n 5
x = range(10**6)
y = [n**2 for n in x]
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import bokeh.plotting as bk
bk.output_notebook() # show plots in the notebook
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x = [1, 2, 3, 4]
y = [4, 3, 2, 3]
p = bk.figure(plot_width=300, plot_height=300)
p.line(x, y, color='blue')
p.circle(x, y, size = 10, color='red')
bk.show(p)
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x = np.linspace(0, 1, 5)
x
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x = np.linspace(0, 12, 200)
y = np.sin(x)
z = np.cos(x)
p = bk.figure(plot_width=600, plot_height=300)
p.line(x, y, color='blue', line_width=2)
p.line(x, z, color='red', line_width=2)
bk.show(p)
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4. Operations on Numpy Arrays
4.1 Slicing
Array slicing works the same as for lists:
my_array[start : stop]
my_array[start : stop : step]
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a = np.arange(15)
a
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a[6:10]
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a[1:10:2]
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Boolean arrays let us select elements of an array using a logical condition.
4.2 Boolean Arrays
Boolean arrays let us select elements of an array using a logical condition.
Create an array of 15 random integers from the range 0-100:
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a = np.random.randint(0, 100, 15)
a
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large = (a > 50)
large
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Create a subarray of elements of
a for which large is true:
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a[large]
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a[a>50]
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This can be used to modify arrays:
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a
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a[a>50] = 0
a
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a = np.arange(70).reshape(10, 7)
a
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a[1, 2]
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a[1,2] = -1
a
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a[2:6, :3]
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a[1, :]
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a[:, 2]
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a[a%2 == 0] = 0
a
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b = a**2
b
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6. Example: Image Manipulation
- We will use multidimensional numpy arrays to modify an image.
- We will use Matplotlib which is another Python plotting library.
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import matplotlib.pyplot as plt
Read an image file and represent it as a 3-dimensional numpy array:
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x = plt.imread("bird.jpg")
x
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RGB Coordinates
Color of each pixel is represented by 3 integers, which give intensities of its Red, Green, and Blue components:- 0 = color off
- 255 = full on
Shape of the image array (rows, columns, depth):
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x.shape
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For image manipulation it is convenient to convert RGB coordinates to floats in the range 0-1:
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x = x/255
x
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We will use the following function to display an image:
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def imshow(x):
plt.figure(figsize=(10,10))
plt.imshow(x)
plt.show()
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imshow(x)
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imshow(x/2)
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imshow(np.minimum(1, x*2))
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imshow(x[300:750, 600:1400, :])
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y = x.copy()
y[:,:,1] = 0
y[:,:,2] = 0
imshow(y)
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z = x.copy()
z[300:700, 600:1400, 0] = 1
z[700:1100, 600:1400, 1] = 1
z[1100:1500, 600:1400, 2] = 1
imshow(z)
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