Lesson 3.2 - Array Operations

Target: ~9 min read - 20 min hands-on

Overview

Slicing works like Python lists but extends to multiple dimensions (grid[1, :] for a row, grid[:, 2] for a column). Broadcasting lets NumPy apply an operation between arrays of different (but compatible) shapes without an explicit loop. We'll compute a temperature profile along a cooling fin using this pattern.

Why This Matters (Engineering Context)

Broadcasting is what lets you apply one design equation across an entire array of operating conditions - every ambient case, every sensor channel, every candidate size - in a single line, instead of a loop per case.

Code-Along

import numpy as np

# [Mechanical/Chemical] steady-state temperature along a cooling fin
# T(x) = T_amb + (T_base - T_amb) * exp(-m x)   (simplified long-fin form)
L = 0.10                          # m, fin length
x = np.linspace(0, L, 13)         # 13 evenly spaced positions from base (0) to tip (L)
T_base, T_amb, m = 120.0, 25.0, 45.0    # C, C, 1/m (fin parameter)

# np.exp works element-wise, so this one line gives temperature at ALL 13 points
T_x = T_amb + (T_base - T_amb) * np.exp(-m * x)
print("Position (mm):", np.round(x * 1000, 1))   # np.round rounds every element
print("Temp (C):     ", np.round(T_x, 1))

# Slicing works like lists:  [:3] first three,  [-3:] last three
print("\nFirst 3 positions (m):", x[:3])
print("Last 3 temps (C):", np.round(T_x[-3:], 1))

# --- Broadcasting: combine a (3,1) column with a (1,13) row -> a (3,13) grid ---
# reshape(3, 1) makes a column vector; NumPy "stretches" it across the 13 columns
T_amb_cases = np.array([20.0, 25.0, 30.0]).reshape(3, 1)
T_grid = T_amb_cases + (T_base - T_amb_cases) * np.exp(-m * x).reshape(1, 13)
print("\nGrid shape:", T_grid.shape)             # (3, 13): 3 cases x 13 positions
print("Fin-tip temp per ambient case (C):", np.round(T_grid[:, -1], 1))  # [:, -1] = last column

Run it: temperature is highest at the fin base (x = 0) and decays toward ambient along the length. T_grid broadcasts the 3 ambient cases against the 13-position array without a loop - its shape is (3, 13).

Practice Exercises

1. Confirm the maximum of T_x occurs at the base (index 0) using np.argmax().
2. Slice T_grid to extract the row for the 30 C ambient case.
3. Build a (3, 13) grid instead by broadcasting an array of 3 different fin parameters m = [30, 45, 60] against x - what reshaping makes the broadcast work?

# Try the practice exercises here

Knowledge Check

1. What does NumPy broadcasting allow you to do?
2. Where is temperature highest along a fin losing heat to a cooler ambient?
3. What NumPy function returns the index of the maximum value in an array?