4.2. Numpy¶
The basis of most scientific programming in Pyhton is the numerical Python library, numpy. NumPy gives us many tools - including a fast and efficient data type, the numpy Array - for working with numerical data.
4.2.1. Numpy Array¶
NumPy is built around the array. This is a data structure defined in NumPy which is ordered and mutable, must like the list. Although very similar to the list, the numpy array only allows numerical data as elements, like the int and float. Let’s explore!
# Frist we need to import the numpy package. It is commonly shortened to "np"
import numpy as np
The easiest way to define numpy arrays is to define a list or tuple, and convert it to an array with the numpy.array() function.
a = [0, 1, 2, 3, 4]
b = np.array(a)
print(type(a))
print(type(b))
We can index and slice numpy arrays much like lists:
print(b[0], b[1:3], b[-1])
Try running the following to get help on the NumPy array
help(np.ndarray)
Woah. That’s a really long help page. Often when you are working with a new package, help() won’t be the most convenient or easy to read way to get help. Instead, we can search for online documentation for the package we are using.
If you Google numpy documentation, you will likely see links to info about numpy and another package we will explore later, scipy. If you follow the links to NumPy, you should find a NumPy user Guide and from there, several pages of tutorials and documentation about the package. The Quickstart tutorial, will give a much more legible intro to the package.
4.2.2. Numpy Attributes¶
NumPy arrays have some built in attributes, i.e. info stored in an object, accessible with object.attribute (note: no parentheses after).
# Let's print some attributes of our b array
print("Num dimensions:", b.ndim,
"\nShape:", b.shape,
"\nSize:", b.size)
A common way to define NumPy arrays with with the arange function.
np.arange(10)
help(np.arange)
The numpy arange function allows us to quickly build integer arrays. It takes start, stop, and step as arguments.
x = np.arange(1, 10)
y = np.arange(2, 20, 2)
print(x)
print(y)
We can apply any mathematical operation to a NumPy array, and it will apply that operation to every element in the array.
x = np.arange(-3, 4)
y = x**2
print(y)
Another way to make NumPy arrays is with the linspace() function. This allows us to choose the bounds of an interval and the number of points we want to divide it into. Numpy also has useful math constants like pi and e and math functions like sin, cos, tan.
import matplotlib.pyplot as plt
x = np.linspace(-2*np.pi, 2*np.pi, 100)
y = np.sin(x)
plt.plot(x, y)
# Linspace can be useful for adding more resolution to continuous functions
xarange = np.arange(-np.pi, np.pi)
yarange = np.cos(xarange)
xlinspace = np.linspace(-np.pi, np.pi, 1000)
ylinspace = np.cos(xlinspace)
plt.subplot(1, 2, 1)
plt.plot(xarange, yarange)
plt.subplot(1, 2, 2)
plt.plot(xlinspace, ylinspace)
If we want to plot a bell curve we can use the np.random module to randomly sample a normal distribution.
norm = np.random.standard_normal(100000) # Draw 1000 random points from normal distribution
hist, bins = np.histogram(norm, bins=10, density=True) # Make histogram of our samples
plt.plot(bins[1:], hist)
hist, bins = np.histogram(norm, bins=100, density=True)
plt.plot(bins[1:], hist)
This is barely scratching the surface of the numpy package, but should be enough to get you started. The Quickstart tutorial is a great resource for more of the basics and some more advanced usage. Finally, don’t forget to use the most powerful tool at our disposal: Google. Most programmers only have the most common syntax memorized, everything else can be found with Google!
Next we will further explore the matplotlib package that we briefly introduced above!