These exercises come from the NumPy tutorial examples.
Instructions: Create a new notebook called NumPyExercises in your NumPy directory and solve the following problems inside it. Be sure to include the problem statements in a markdown cell above your solution. You don't need to put the "helper" code in the markdown cell, just implement the helper code in your code cell with your solution.
Preliminaries: At the top of your notebook, include a "Heading 1" cell with the title NumPy Exercises. Then include the SciPy and NumPy inline functions by adding a code cell that invokes the %pylab inline magic:
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%pylab inline
import numpy as np
Create the following arrays with correct data types:
[[1 1 1 1]
[1 1 1 1]
[1 1 1 2]
[1 6 1 1]][[0. 0. 0. 0. 0.]
[2. 0. 0. 0. 0.]
[0. 3. 0. 0. 0.]
[0. 0. 4. 0. 0.]
[0. 0. 0. 5. 0.]
[0. 0. 0. 0. 6.]]You should be able to accomplish this in 3 lines of code or less for each one. The documentation for the diag method may be helpful.
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#Copy the exercise statement to a markdown cell in your notebook and then implement a solution in a code cell
Read the documentation for np.tile and use this function to construct the following array:
[[4 3 4 3 4 3]
[2 1 2 1 2 1]
[4 3 4 3 4 3]
[2 1 2 1 2 1]]
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#Copy the exercise statement to a markdown cell in your notebook and then implement a solution in a code cell
Let’s create a prime number sieve. We will use the sieve to see what numbers between 0 and 100 are prime.
(a) First, construct an array of booleans called is prime with shape (100,), filled with
True in all the elements.
is_prime = np.ones((100,), dtype=bool)
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#Copy the exercise statement to a markdown cell in your notebook and then implement a solution in a code cell
(b) The index of each boolean element represents the number. “Cross out” 0 and 1, which are not primes. You can either set them to False or 0 (which python recognizes as equivalent to False for boolean types).
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#Copy the exercise statement to a markdown cell in your notebook and then implement a solution in a code cell
(c) For each subsequent integer j starting from 2, cross out its higher multiples:
N_max = int(np.sqrt(len(is_prime)))
for j in range(2, N_max):
is_prime[2*j::j] = False
Make sure you understand what this code is doing. What does that slicing of the array mean?
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#Copy the exercise statement to a markdown cell in your notebook and then implement a solution in a code cell
(d) Look up the documentation for np.nonzero (try help(np.nonzero) or np.nonzero?) and use it to print the prime numbers.
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#Copy the exercise statement to a markdown cell in your notebook and then implement a solution in a code cell
(e) Finally, create a new function, called eratosthenes_sieve() that takes one argument, maximum, the maximum number to test for primes, and returns an array containing the prime numbers between 2 and maximum. Use the sieve algorithm developed by Eratosthenes and described on wikipedia. Print the result for the test cases where maximum = 10 and 100. (Prime numbers and prime factorization are common topics in the Project Euler exercises.)
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#Copy the exercise statement to a markdown cell in your notebook and then implement a solution in a code cell
Let’s do some manipulations on NumPy arrays by starting with a stock image provided in SciPy. It turns out that digital images are just arrays of numbers representing the relative intensity (for B/W images) or RGB values (for color images) of the pixels in the image, similar to ipythonblocks. We can use the array operations we have learned to do digital image processing!
(a) Import the SciPy stock image into an array (since it is coming from SciPy, it is a NumPy array):
from scipy import misc
lena = misc.lena()
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#Copy the exercise statement to a markdown cell in your notebook and then implement a solution in a code cell
(b) Try viewing the image in both false color and grayscale:
imshow(lena)
imshow(lena, cmap=cm.gray)
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#Copy the exercise statement to a markdown cell in your notebook and then implement a solution in a code cell
(c) Let’s crop the image by removing 30 pixels on all sides:
crop_lena = lena[30:-30,30:-30]
imshow(crop_lena)
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#Copy the exercise statement to a markdown cell in your notebook and then implement a solution in a code cell
(d) Next, let’s make a frame by blacking out all pixels except those in a circle centered on the face. We can do this with a mask. The equation for a circle is just $x^2 + y^2 = R^2$. If we want it centered on the middle of the image at (256,256) we can create a mask with
y, x = np.ogrid[0:512,0:512]
centerx, centery = (256, 256)
mask = ((y - centery)**2 + (x - centerx)**2) > 230**2
To black out the desired pixels, we just set them equal to 0 or False:
lena[mask] = 0
imshow(lena)
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#Copy the exercise statement to a markdown cell in your notebook and then implement a solution in a code cell
(e) Create a new frame for the image that is an ellipse (long axis on the vertical) centered on the face.
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#Copy the exercise statement to a markdown cell in your notebook and then implement a solution in a code cell