Working with Arrays and Plotting (NumPy and Matplotlib)

Why arrays, not loops

Engineering computation is mostly arithmetic on lots of numbers — a temperature at every node of a mesh, a voltage at every time step. Plain Python lists can hold those numbers, but operating on them element by element with explicit loops is both slow and verbose. NumPy introduces the ndarray, a fixed-type, n-dimensional array, and lets you express whole-array operations at once ¹.

import numpy as np

x = np.linspace(0, 2 * np.pi, 100)   # 100 evenly spaced points
y = np.sin(x)                        # applies sin to every element at once
energy = 0.5 * y**2                  # arithmetic is element-wise
peak = y.max()

There is no loop. np.sin(x) operates on the entire array, and y**2 squares every element — this is vectorization. It is shorter to read and dramatically faster, because the looping happens in compiled code rather than the Python interpreter ¹.

Broadcasting and slicing

Two array ideas do most of the heavy lifting. Slicing selects subarrays — x[0], x[-1], x[10:20], or A[:, 0] for the first column of a 2-D array. Broadcasting lets arrays of different shapes combine: adding a scalar to an array adds it to every element, and a row vector can combine with a column vector to fill a grid ¹. Together they replace most of the loops a newcomer is tempted to write.

Plotting with Matplotlib

Numbers become insight through plots. Matplotlib is the standard plotting library; its pyplot interface mirrors the steps you would take by hand — draw the data, then label it.

import matplotlib.pyplot as plt

plt.plot(x, y, label="model  y = sin(x)")   # a line
plt.scatter(sx, sy, label="measurements")    # points
plt.xlabel("x"); plt.ylabel("y")
plt.legend()
plt.savefig("figure.png")   # or plt.show()

The figure below was produced by essentially this code — a continuous model curve plus scattered measurements, with axis labels and a legend.

Every figure in this program is generated exactly this way: a short script computes arrays and renders a raster image. Mastering ndarray operations and a handful of plotting calls covers the large majority of day-to-day engineering computation, and sets up the numerical methods in the next module, which are all expressed as operations on arrays.