Array Operations

Element-wise operations

When you combine two arrays of the same shape with an operator, NumPy pairs up the elements in matching positions: the first with the first, the second with the second, and so on. When you combine an array with a single number, that number is used with every element. (NumPy calls this broadcasting: the single value is broadcast across the array.)

import numpy as npforce = np.array([1000.0, 2000.0, 3000.0, 4000.0])   # Narea = 20.0e-6                                        # m² (20 mm²)original_length = 50.0                                # mmextension = np.array([0.012, 0.024, 0.036, 0.049])    # mmstress = force / area / 1e6          # MPastrain = extension / original_lengthmodulus = stress / strain / 1000     # GPaprint("Stress (MPa):", stress)print("Strain:      ", strain)print("Modulus (GPa):", np.round(modulus, 1))

Mathematical functions

NumPy's mathematical functions, sometimes called universal functions, apply to every element. Use them instead of the math module whenever you work with arrays: math.exp() only accepts a single number, while np.exp() accepts a whole array.

import numpy as npd0 = 2.3e-5        # m²/sq = 148_000        # J/mol, activation energyr = 8.314          # J/(mol·K)temperatures = np.array([800, 900, 1000, 1100, 1200])   # Kdiffusivity = d0 * np.exp(-q / (r * temperatures))for temperature, d in zip(temperatures, diffusivity):    print(f"{temperature} K: {d:.2e} m²/s")

Aggregating along an axis

Functions such as np.mean() and np.max() reduce a whole array to one number by default. For a 2D table you usually want one result per row or per column. The axis argument chooses the direction: axis=0 works down the columns (one result per column), and axis=1 works across the rows (one result per row).

import numpy as np# Rows: three samples. Columns: hardness at 4 positions.hardness = np.array([    [152, 160, 158, 149],    [201, 198, 205, 199],    [175, 172, 178, 176],])print("Mean of each sample:  ", hardness.mean(axis=1))print("Mean at each position:", np.round(hardness.mean(axis=0), 1))print("Overall mean:", round(hardness.mean(), 1))

Comparisons and Boolean masks

Comparing an array with a value gives an array of True/False values, one per element. This is called a Boolean mask. Putting a mask inside square brackets selects only the elements where the mask is True. This is the NumPy way to filter data, with no loop needed.

import numpy as npdensities = np.array([2.70, 4.51, 7.87, 8.96, 19.32, 1.74])names = np.array(["Al", "Ti", "Fe", "Cu", "Au", "Mg"])is_light = densities < 5print(is_light)print(densities[is_light])print(names[is_light])print("Number of light metals:", np.sum(is_light))

The same mask can select from any array of the same length, so a mask built from densities picks the matching names. np.sum() of a mask counts the True values, because True counts as 1 and False as 0.

Combine conditions with & (and) and | (or), putting each condition in brackets. Python's and and or don't work element by element on arrays.

import numpy as npreadings = np.array([8.94, 8.97, 9.31, 8.95, 8.60, 8.96])valid = (readings > 8.9) & (readings < 9.0)print(readings[valid])print(f"Mean of valid readings: {readings[valid].mean():.3f}")