Day 8 exercise solutions¶
Simple arrays¶
5 minutes.
Create this array:
2 7 12 0
3 9 3 4
4 0 1 3
>>> import numpy as np
>>> a = np.array([[2, 7, 12, 0], [3, 9, 3, 4], [4, 0, 1, 3]])
>>> a
array([[ 2, 7, 12, 0],
[ 3, 9, 3, 4],
[ 4, 0, 1, 3]])
What is the array shape?
>>> a.shape
(3, 4)
What is the array ndim?
>>> a.ndim
2
How about the len of the array?
>>> len(a)
3
Can you get the ndim and len from the shape?
>>> len(a.shape) == a.ndim
True
>>> a.shape[0] == len(a)
True
Creating arrays using functions¶
10 minutes.
- Create a 1D array from 2 through 5 inclusive.
>>> np.arange(2, 6)
array([2, 3, 4, 5])
- Make an array with 10 elements between 2 and 5 inclusive.
>>> np.linspace(2, 5, 10)
array([ 2. , 2.333333, 2.666667, 3. , 3.333333, 3.666667,
4. , 4.333333, 4.666667, 5. ])
- Make an all-ones array shape (4, 4).
>>> np.ones((4, 4))
array([[ 1., 1., 1., 1.],
[ 1., 1., 1., 1.],
[ 1., 1., 1., 1.],
[ 1., 1., 1., 1.]])
- Make an identity array shape (6, 6).
>>> np.eye(6)
array([[ 1., 0., 0., 0., 0., 0.],
[ 0., 1., 0., 0., 0., 0.],
[ 0., 0., 1., 0., 0., 0.],
[ 0., 0., 0., 1., 0., 0.],
[ 0., 0., 0., 0., 1., 0.],
[ 0., 0., 0., 0., 0., 1.]])
Make this array with a single Python / numpy command:
1 0 0 0 2 0 0 0 3
>>> np.diag([1, 2, 3])
array([[1, 0, 0],
[0, 2, 0],
[0, 0, 3]])
Look at the docstring for np.random.randn. Make a shape (3, 5) array with random numbers from a mean=0, variance = 1 normal distribution.
>>> rand_arr = np.random.rand(3, 5)
>>> rand_arr.shape
(3, 5)
Simple visualizations¶
7 minutes.
- Make an array
xwith 100 evenly spaced values between 0 and 2 * pi;
>>> x = np.linspace(0, 2 * np.pi, 100)
>>> x.shape
(100,)
- Make an array
ywhich contains the cosine of the corresponding value inx- soy[i] = cos(x[i])(hint:np.lookfor('cosine')).
>>> y = np.cos(x)
>>> y.shape
(100,)
- Plot
xagainsty;
>>> import matplotlib.pyplot as plt
>>> plt.plot(x, y)
[<...matplotlib.lines.Line2D object at ...>]
- Make a 10 by 20 array of mean 0 variance 1 normal random numbers;
>>> rand_arr = np.random.randn(10, 20)
>>> rand_arr.shape
(10, 20)
- Display this array as an image;
>>> plt.imshow(rand_arr)
<...matplotlib.image.AxesImage object at ...>
- Investigate
plt.cm. See if you can work out how to make the displayed image be grayscale instead of color.
>>> plt.imshow(rand_arr, cmap=plt.cm.gray)
<...matplotlib.image.AxesImage object at ...>
Indexing and slicing, array creation¶
10 minutes.
Create the following array, call this
a(you did this before):2 7 12 0 3 9 3 4 4 0 1 3
>>> a = np.array([[2, 7, 12, 0], [3, 9, 3, 4], [4, 0, 1, 3]])
- Get the 2nd row of
a([ 3 9 3 4]);
>>> a[1]
array([3, 9, 3, 4])
- Get the 3rd column of
a([12 3 1]);
>>> a[:, 2]
array([12, 3, 1])
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.]]
Par on course: 3 statements for each
Hint: Individual array elements can be accessed similarly to a list, e.g.
a[1]ora[1, 2].Hint: Examine the docstring for
diag.
>>> arr1 = np.ones((4, 4), dtype=np.int64) # Would be float by default
>>> arr1[3, 1] = 6
>>> arr1[2, 3] = 2
>>> arr1
array([[1, 1, 1, 1],
[1, 1, 1, 1],
[1, 1, 1, 2],
[1, 6, 1, 1]])
>>> arr2 = np.diag([2., 3., 4, 5, 6], -1) # Need a float input to diag for float output
>>> arr2[:, :-1]
array([[ 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.]])
Skim through the documentation for
np.tile, and use this function to construct the 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]]
>>> np.tile([[4, 3], [2, 1]], (2, 3))
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]])
Fancy indexing using boolean arrays¶
5 minutes.
Create the following array
a(same as before):2 7 12 0 3 9 3 4 4 0 1 3
>>> a = np.array([[2, 7, 12, 0], [3, 9, 3, 4], [4, 0, 1, 3]])
Use
>to make a mask that is true where the elements are greater than 5, like this:False True True False False True False False False False False False
>>> mask = a > 5
>>> mask
array([[False, True, True, False],
[False, True, False, False],
[False, False, False, False]], dtype=bool)
- Return all the elements in
athat are greater than 5.
>>> a[mask]
array([ 7, 12, 9])
Set all the elements greater than 5 to be equal to 5, to get this:
2 5 5 0 3 5 3 4 4 0 1 3
>>> a[mask] = 5
>>> a
array([[2, 5, 5, 0],
[3, 5, 3, 4],
[4, 0, 1, 3]])
Elementwise operations¶
10 minutes.
Remember our array a:
2 7 12 0
3 9 3 4
4 0 1 3
- Use array slicing to get a new array composed of the even columns (0, 2) of
a. Now get array that contains the odd columns (1, 3) ofa. Add these two arrays.
>>> a = np.array([[2, 7, 12, 0], [3, 9, 3, 4], [4, 0, 1, 3]])
>>> even_columns = a[:, ::2]
>>> odd_columns = a[:, 1::2]
>>> even_columns + odd_columns
array([[ 9, 12],
[12, 7],
[ 4, 4]])
Generate this array:
[2**0, 2**1, 2**2, 2**3, 2**4]
>>> 2 ** np.arange(5)
array([ 1, 2, 4, 8, 16])
Generate an array length 10 such that this is true of the elements (where
x[i]is the element ofxat indexi):x[i] = 2 ** (3 * i) - i
>>> inds = np.arange(10)
>>> x = 2 ** (3 * inds) - inds
>>> x
array([ 1, 7, 62, 509, 4092, 32763,
262138, 2097145, 16777208, 134217719])
Summary functions¶
Remember our array a:
2 7 12 0
3 9 3 4
4 0 1 3
>>> a = np.array([[2, 7, 12, 0], [3, 9, 3, 4], [4, 0, 1, 3]])
What are the:
- sum of all the values?
>>> a.sum()
48
- sum of the columns?
>>> a.sum(axis=0) # Sum over the first axis, leaving the second
array([ 9, 16, 16, 7])
- sum of the rows?
>>> a.sum(axis=1) # Sum over the second axis, leaving the first
array([21, 19, 8])
- mean?
>>> a.mean()
4.0
- min?
>>> a.min()
0
- max?
>>> a.max()
12
