🔢 NumPy Arrays — Fast Numerical Computing

NumPy enables efficient mathematical operations on arrays. Essential for data science and scientific computing.

🎯 Why NumPy?

NumPy arrays are faster and more efficient than Python lists for numerical operations.

import numpy as np
import time

# Compare list vs NumPy array
py_list = list(range(1000000))
np_array = np.arange(1000000)

# List operation
start = time.time()
result = [x * 2 for x in py_list]
print(f"List: {time.time() - start:.6f}s")

# NumPy operation
start = time.time()
result = np_array * 2
print(f"NumPy: {time.time() - start:.6f}s")  # Much faster!

📦 Creating Arrays

import numpy as np

# From list
arr1 = np.array([1, 2, 3, 4, 5])

# Ranges
arr2 = np.arange(0, 10, 2)      # Start, stop, step
arr3 = np.linspace(0, 1, 5)     # 5 evenly spaced values

# Zeros and ones
zeros = np.zeros(5)              # [0, 0, 0, 0, 0]
ones = np.ones(5)                # [1, 1, 1, 1, 1]

# Random arrays
random = np.random.rand(5)       # Random 0-1
random_int = np.random.randint(1, 100, 5)

# 2D arrays
matrix = np.array([[1, 2, 3], [4, 5, 6]])
print(matrix.shape)              # (2, 3)

🔧 Array Operations

import numpy as np

arr = np.array([1, 2, 3, 4, 5])

# Element-wise operations
print(arr + 1)          # [2, 3, 4, 5, 6]
print(arr * 2)          # [2, 4, 6, 8, 10]
print(arr ** 2)         # [1, 4, 9, 16, 25]
print(np.sqrt(arr))     # [1, 1.41, 1.73, 2, 2.24]

# Statistical operations
print(arr.mean())       # Average: 3.0
print(arr.std())        # Standard deviation
print(arr.sum())        # Total: 15
print(arr.min())        # Minimum: 1
print(arr.max())        # Maximum: 5

# Logical operations
print(arr > 3)          # [False, False, False, True, True]
print(arr[arr > 3])     # [4, 5] - filter

📊 Indexing and Slicing

import numpy as np

arr = np.array([10, 20, 30, 40, 50])

# Indexing
print(arr[0])           # 10
print(arr[-1])          # 50

# Slicing
print(arr[1:3])         # [20, 30]
print(arr[::2])         # [10, 30, 50] - every 2nd element
print(arr[::-1])        # [50, 40, 30, 20, 10] - reverse

# 2D array indexing
matrix = np.array([[1, 2, 3], [4, 5, 6]])
print(matrix[0, 1])     # 2 (row 0, col 1)
print(matrix[1, :])     # [4, 5, 6] (row 1, all columns)

🎨 Broadcasting

NumPy automatically handles operations on arrays of different shapes.

import numpy as np

# 1D array + scalar
arr = np.array([1, 2, 3])
result = arr + 10       # [11, 12, 13]

# Different shapes (broadcasting)
arr1 = np.array([[1, 2, 3]])      # Shape (1, 3)
arr2 = np.array([[10], [20]])     # Shape (2, 1)
result = arr1 + arr2               # Shape (2, 3)
# [[11, 12, 13],
#  [21, 22, 23]]

📈 Real-World Example: Temperature Data Analysis

import numpy as np

# Temperature readings (3 days, 4 locations)
temps = np.array([
    [20, 22, 21, 23],  # Day 1
    [21, 23, 22, 24],  # Day 2
    [19, 21, 20, 22]   # Day 3
])

# Average temperature per day
daily_avg = temps.mean(axis=1)
print(f"Daily average: {daily_avg}")

# Average temperature per location
location_avg = temps.mean(axis=0)
print(f"Location average: {location_avg}")

# Overall average
overall_avg = temps.mean()
print(f"Overall average: {overall_avg:.2f}")

# Hottest reading
print(f"Hottest: {temps.max()}")

# Coldest reading
print(f"Coldest: {temps.min()}")

# Days above 22C
warm_days = (temps > 22).sum(axis=1)
print(f"Readings >22C per day: {warm_days}")

🔀 Reshaping and Flattening

import numpy as np

arr = np.arange(12)
print(arr.shape)        # (12,)

# Reshape to 2D
matrix = arr.reshape(3, 4)
print(matrix.shape)     # (3, 4)

# Reshape to 3D
cube = arr.reshape(2, 2, 3)
print(cube.shape)       # (2, 2, 3)

# Flatten back to 1D
flat = matrix.flatten()
print(flat.shape)       # (12,)

# Transpose
transposed = matrix.T
print(transposed.shape) # (4, 3)

🧮 Linear Algebra

import numpy as np

# Matrix multiplication
A = np.array([[1, 2], [3, 4]])
B = np.array([[5, 6], [7, 8]])

# Matrix product
C = np.dot(A, B)

# Vector operations
v1 = np.array([1, 2, 3])
v2 = np.array([4, 5, 6])

# Dot product
dot = np.dot(v1, v2)    # 1*4 + 2*5 + 3*6 = 32

# Cross product
cross = np.cross(v1, v2)

📊 Array Functions Summary

🔑 Key Takeaways

• ✅ NumPy arrays are faster than lists for numerical operations

• ✅ Use vectorized operations instead of loops

• ✅ Broadcasting automatically handles different array shapes

• ✅ Use axis parameter for operations on specific dimensions

• ✅ NumPy supports advanced linear algebra operations

• ✅ reshape() and transpose() modify array structure

Continue: Data Visualization Basics