Multiple Dimensions

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As we alluded to in the applications above, it’s possible to make a nested numpy.array (can think of it as an array of arrays). A core concept for a numpy.array is its shape. The shape determines the number of dimensions and how many elements are in one. The numpy.ones function actually takes a tuple specifying the shape instead of just a number.

import numpy as np

x = np.ones((3, 4))
print(x)

Notice how it prints out as an array of arrays. Since we passed in (3, 4) as the desired shape, it creates a numpy.array with 3 rows and 4 columns.

You can also use the reshape function to transform an numpy.array from one shape to another. For example, we can use reshape to change a single-dimension array to one with two-dimensions. This will only work if the numpy.array you are reshaping has the same number of elements as the target shape; it would break if you had 3 values that you tried to reshape into a 10x10.

import numpy as np

# Create an array of the values 0 to 20 (exclusive)
x = np.arange(20)
print('Before reshape')
print(x)
print()

# Reshape it so it has dimensions 5x4 (5 rows, 4 columns)
x = x.reshape((5, 4))
print('After reshape')
print(x)

Accessing Data

When you have one of these 2D arrays, you can use syntax very similar to pandas’ .loc to access a particular row or column. You can even use the “slice” syntax from before to access multiple rows and columns.

import numpy as np

x = np.arange(20).reshape((5, 4))
print('x')
print(x)
print()

# Access one value
print('First - x[1, 2]')
print(x[1, 2])
print()

# Access a subset of the values
# Just like with lists/strs, a:b starts at a (inclusive) and goes to b (exclusive)
print('Second - x[2:4, 1:] ')
print(x[2:4, 1:])
print()

# Access an entire row
print('Third - x[3, :]')
print(x[3, :])  # Can also leave off the : at the end (default is :)
print()

# Access an entire column
print('Fourth - x[:, 2]')
print(x[:, 2])

Shape

Since the shape of a numpy.array is so important, it is common that you will want to access it. The numpy.array has a property called shape that returns a tuple describing the shape of the array. If it returns (a, b), that means it’s a 2D array with a rows and b columns.

import numpy as np

x = np.arange(4)

y = x.reshape((4, 1))

print('y.shape')
print(y.shape)
print()

print('y')
print(y)
print()

z = x.reshape((1, 4))
print('z.shape')
print(z.shape)
print()

print('z')
print(z)

Notice that y and z have different shapes since we specified the reshape differently. y has 4 rows and 1 column (which is why it prints “upright”) while z has 1 row and 4 columns (which is why it prints on one line). If I wanted to get the value 2 from y or z , we would need to change how we index since you always specify row first, then column. So for this example, it would be y[2, 0] and z[0, 2].

You might be wondering, what’s the shape of x from the last example?

import numpy as np

x = np.arange(4)
print('x.shape')
print(x.shape)
print()

print('x')
print(x)

The way to read this shape is a tuple with one element inside of it (and that element is the value 4). This is because when we passed in a number to arange, it returns a numpy.array with just one dimension! That means to access the value 2, you would write x[2] (since you only need to specify one value). There are two analogies here:

• A 2D numpy.array is kind of like a pandas.DataFrame. You have to specify a row & column to get a single value. A 1D numpy.array is like a pandas.Series. You only need to specify the index to get a value.

• Think of an analogy to geometry. A 1D numpy.array with shape (4,) is like a line of length 4. A 2D numpy.array with shape (1, 4) is like a rectangle with height 1 and width 4. Since the line only has one dimension, you just have to specify one value to indicate a position.