⚡ Efficient Numerical Computations
Let’s see how NumPy can be leveraged for efficient numerical computations, via some code examples.
Basic Array Operations
NumPy arrays support a wide range of mathematical operations that can be performed efficiently and with concise syntax.
You can create an array like so:
import numpy as np
# Create a 1D array
a = np.array([1, 2, 3])
# Create a 2D array (matrix)
b = np.array([[1, 2, 3], [4, 5, 6]])
# Create an array filled with zeros
c = np.zeros((2, 3))
# Create an array filled with ones
d = np.ones((3, 2))
# Create an identity matrix
e = np.eye(3)
Operations are element-wise and can be used to efficiently perform computations across arrays:
x = np.array([1, 2, 3])
y = np.array([4, 5, 6])
# Addition
print(x + y)
# Subtraction
print(x - y)
# Multiplication
print(x * y)
# Division
print(x / y)
Advanced Array Operations
NumPy provides advanced functionalities, including broadcasting, vectorised operations, and complex slicing.
Broadcasting allows NumPy to work with arrays of different shapes during arithmetic operations:
a = np.array([1, 2, 3])
b = np.array([[0], [10], [20], [30]])
# Broadcasting allows these to be added even though they're different shapes
print(a + b)
Vectorised operations enable operations to be performed on arrays without explicit loops:
# Calculate the sine of each element
angles = np.array([0, np.pi/2, np.pi])
print(np.sin(angles))
Linear Algebra
NumPy also provides a set of functions for linear algebra operations, making it simple to perform tasks like matrix multiplication, finding determinants, solving linear systems, and more:
# Matrix multiplication
A = np.array([[1, 2], [3, 4]])
B = np.array([[5, 6], [7, 8]])
print(np.dot(A, B))
# Determinant
print(np.linalg.det(A))
# Solve linear system Ax = b
b = np.array([1, 2])
x = np.linalg.solve(A, b)
print(x)
Statistical Functions
Finally, NumPy includes functions for performing statistical operations on arrays, such as finding the mean, median, or standard deviation:
data = np.array([1, 2, 3, 4, 5])
# Mean
print(np.mean(data))
# Median
print(np.median(data))
# Standard deviation
print(np.std(data))