NumPy Basics: Arrays, Operations, and Broadcasting

Creating arrays

NumPy arrays are faster than Python lists for numerical operations and support vectorised operations.

import numpy as np

# From Python list
arr = np.array([1, 2, 3, 4, 5])

# Creating arrays
np.zeros((3, 4))      # 3x4 array of zeros
np.ones((2, 3))       # 2x3 array of ones
np.eye(3)             # 3x3 identity matrix
np.arange(0, 10, 2)   # [0, 2, 4, 6, 8]
np.linspace(0, 1, 5)  # [0, 0.25, 0.5, 0.75, 1.0]
np.random.randn(3, 3) # 3x3 random normal values

# Array properties
arr.shape      # (5,)
arr.dtype      # dtype('int64')
arr.ndim       # 1
arr.size       # 5 (total elements)

Array operations and vectorisation

NumPy operations apply element-wise to entire arrays — no explicit loops needed.

a = np.array([1, 2, 3, 4])
b = np.array([10, 20, 30, 40])

# Element-wise operations
a + b        # [11, 22, 33, 44]
a * b        # [10, 40, 90, 160]
a ** 2       # [1, 4, 9, 16]
np.sqrt(a)   # [1, 1.41, 1.73, 2.0]

# Aggregate operations
a.sum()       # 10
a.mean()      # 2.5
a.std()       # standard deviation
a.min()       # 1
a.argmax()    # 3 (index of max value)

# Matrix operations
A = np.array([[1, 2], [3, 4]])
B = np.array([[5, 6], [7, 8]])
A @ B          # matrix multiplication
np.dot(A, B)   # same result
A.T            # transpose

Indexing and slicing

NumPy supports advanced indexing beyond standard Python slicing.

arr = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])

arr[0, 1]          # 2 (row 0, col 1)
arr[1, :]          # [4, 5, 6] (all of row 1)
arr[:, 2]          # [3, 6, 9] (all of col 2)
arr[0:2, 1:3]      # [[2,3],[5,6]] (subarray)

# Boolean indexing
a = np.array([1, -2, 3, -4, 5])
a[a > 0]           # [1, 3, 5]
a[a < 0] = 0       # replace negatives with 0

# Fancy indexing
indices = np.array([0, 2, 4])
a[indices]         # [1, 3, 5]

Broadcasting

Broadcasting allows operations between arrays of different shapes, following strict rules.

# Rule: arrays are compatible if dimensions are equal or one of them is 1

a = np.array([[1, 2, 3],
              [4, 5, 6]])  # shape (2, 3)

b = np.array([10, 20, 30])  # shape (3,)
# b is broadcast to (2, 3)
a + b  # [[11,22,33],[14,25,36]]

# Scalar is broadcast to any shape
a * 2  # [[2,4,6],[8,10,12]]

# Column vector
c = np.array([[100], [200]])  # shape (2, 1)
# c is broadcast to (2, 3)
a + c  # [[101,102,103],[204,205,206]]

Exam tip

Broadcasting is the most-tested NumPy concept. The key rule: shapes are compared from the right — sizes must match OR one must be 1. Also know the difference between a[a > 0] (boolean indexing) and a[[0, 2]] (fancy indexing).