NumPy Introduction
NumPy transforms Python into a powerhouse for numerical computing. While Python lists can hold mixed data types, NumPy arrays store homogeneous data in highly optimized structures. This design choice enables lightning-fast mathematical operations that would be impossibly slow with regular Python lists.
The core ndarray object represents n-dimensional arrays with fixed sizes and identical data types throughout. This constraint isn't limiting, it's liberating because it unlocks vectorized operations that process entire arrays in single commands. The official NumPy documentation offers comprehensive tutorials and examples for mastering these powerful capabilities.
NumPy provides several important advantages for scientific programming:
- High efficiency because it's implemented in compiled C language
- Vectorization allows operations on entire arrays without explicit loops
- Lower memory consumption compared to Python lists
- Complete and optimized mathematical operations
Vectorization is the ability to apply a single operation to an entire array at once. It's like giving commands to an entire army formation simultaneously, rather than one by one.
# Element multiplication using Python list (slow)x = [1, 2, 3, 4, 5]y = [2, 3, 4, 5, 6]z = []for i in range(len(x)): z.append(x[i] * y[i])print("List result:", z) # Output: List result: [2, 6, 12, 20, 30]# Element multiplication using NumPy (fast)import numpy as npx_np = np.array([1, 2, 3, 4, 5])y_np = np.array([2, 3, 4, 5, 6])z_np = x_np * y_npprint("NumPy result:", z_np) # Output: NumPy result: [ 2 6 12 20 30]Manual Array Creation
The most basic way to create NumPy arrays is to convert existing Python data structures into arrays.
One-dimensional arrays are like a sequence of numbers in a single row. You can create them from Python lists using the np.array() function.
import numpy as np# Create 1D array from lista = np.array([0, 1, 2, 3])print("1D Array:", a) # Output: 1D Array: [0 1 2 3]print("Data type:", type(a)) # Output: Data type: <class 'numpy.ndarray'>print("Shape:", a.shape) # Output: Shape: (4,)print("Dimensions:", a.ndim) # Output: Dimensions: 1Two-dimensional arrays are like tables with rows and columns. You can create them from nested lists.
import numpy as np# Create 2D array from nested lista = np.array([[0, 1], [2, 3]])print("2D Array:")print(a)# Output:# [[0 1]# [2 3]]print("Shape:", a.shape) # Output: Shape: (2, 2)print("Dimensions:", a.ndim) # Output: Dimensions: 2print("Total elements:", a.size) # Output: Total elements: 4Three-dimensional arrays can be illustrated as stacks of tables. Imagine like several sheets of paper stacked, where each sheet contains table data.
import numpy as np# Create 3D arraya = np.array([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]])print("3D Array:")print(a)# Output:# [[[ 1 2 3]# [ 4 5 6]]# [[ 7 8 9]# [10 11 12]]]print("Shape:", a.shape) # Output: Shape: (2, 2, 3)print("Axis 0 (planes):", a.shape[0]) # Output: Axis 0 (planes): 2print("Axis 1 (rows):", a.shape[1]) # Output: Axis 1 (rows): 2print("Axis 2 (columns):", a.shape[2]) # Output: Axis 2 (columns): 3Multidimensional Structure
| Dimension | Shape | Structure | Example | Axis |
|---|---|---|---|---|
| 1D | (4,) | Number sequence in single row | [0, 1, 2, 3] | Axis 0 for element index |
| 2D | (2, 2) | Table with rows and columns | [[0, 1], [2, 3]] | Axis 0 for rows, Axis 1 for columns |
| 3D | (2, 2, 3) | Stack of tables (planes) | 2 planes, each plane 2x3 | Axis 0 depth, Axis 1 height, Axis 2 width |
The higher the array dimension, the more complex the data structure, but the basic principle remains the same. Each axis represents one dimension of data organization.
NumPy can create arrays from various Python data structures, including lists, tuples, and mixtures of both.
import numpy as np# From listarr_from_list = np.array([0, 1, 2, 3])print("From list:", arr_from_list) # Output: From list: [0 1 2 3]# From tuplearr_from_tuple = np.array((0, 1, 2, 3))print("From tuple:", arr_from_tuple) # Output: From tuple: [0 1 2 3]# From mixture (will be converted to compatible type)arr_mixed = np.array([0, 1, 2.5, 3])print("From mixture:", arr_mixed) # Output: From mixture: [0. 1. 2.5 3. ]print("Automatic data type:", arr_mixed.dtype) # Output: Automatic data type: float64Array Creation Functions
NumPy provides various specialized functions for creating arrays with specific patterns or values. This is like having special molds for making cakes with consistent shapes.
Constant Value Functions
The np.ones() function creates arrays filled with the number 1. Useful when you need initialization with base values.
import numpy as np# 1D array with value 1a = np.ones(3)print("1D ones:", a) # Output: 1D ones: [1. 1. 1.]# 2D array with value 1a = np.ones((2, 3))print("2D ones:")print(a)# Output:# [[1. 1. 1.]# [1. 1. 1.]]# 3D array with value 1a = np.ones((2, 2, 3))print("3D ones shape:", a.shape) # Output: 3D ones shape: (2, 2, 3)print("3D ones:")print(a)# Output:# [[[1. 1. 1.]# [1. 1. 1.]]# [[1. 1. 1.]# [1. 1. 1.]]]Besides np.ones(), there are other functions for creating arrays with special patterns:
import numpy as np# Array with zero valuesa = np.zeros((2, 3))print("Zeros array:")print(a)# Output:# [[0. 0. 0.]# [0. 0. 0.]]# Identity array (diagonal 1, others 0)a = np.eye(3, 3)print("Identity matrix:")print(a)# Output:# [[1. 0. 0.]# [0. 1. 0.]# [0. 0. 1.]]# Diagonal array with specific valuesa = np.diag((1, 2, 3))print("Diagonal array:")print(a)# Output:# [[1 0 0]# [0 2 0]# [0 0 3]]Random Functions
Random functions are useful for creating simulation data or initialization with random values.
import numpy as np# Set seed for consistent resultsnp.random.seed(10)# Array with uniform random values between 0 and 1a = np.random.rand(2, 3)print("Random uniform [0,1]:")print(a)# Output:# [[0.77132064 0.02075195 0.63364823]# [0.74880388 0.49850701 0.22479665]]# Array with normal distribution (mean=0, std=1)a = np.random.randn(3)print("Random normal:", a) # Output: Random normal: [ 0.62133597 -0.72008556 0.26551159]# Array with random integers in specific rangea = np.random.randint(1, 10, size=(2, 3))print("Random integers [1,10):")print(a)# Output:# [[7 9 2]# [9 5 2]]Mathematical Functions
The np.fromfunction function enables array creation based on mathematical functions. This is like having a formula to generate the value of each element based on its position.
import numpy as np# Create array using functiondef f(i, j): return i + j# 2x3 array with values based on function f(i,j) = i + ja = np.fromfunction(f, (2, 3))print("Array from function f(i,j) = i + j:")print(a)# Output:# [[0. 1. 2.]# [1. 2. 3.]]# More complex functiondef g(i, j): return i * j + 1b = np.fromfunction(g, (3, 3))print("Array from function g(i,j) = i*j + 1:")print(b)# Output:# [[1. 1. 1.]# [1. 2. 3.]# [1. 3. 5.]]The np.empty function creates arrays without initializing element values. This is useful when you will fill the array with values later and want to save initialization time.
import numpy as np# Create empty array (undefined values)a = np.empty((3, 2))print("Empty array (random values from memory):")print(a)# Output will vary because values are not initialized# Example output:# [[0. 0.]# [0. 0.]# [0. 0.]]print("Shape:", a.shape) # Output: Shape: (3, 2)print("Dtype:", a.dtype) # Output: Dtype: float64Arrays from Sequences
NumPy provides specialized functions for creating arrays from value sequences with specific patterns.
np.arange Function
The np.arange function is the NumPy version of Python's range(), but can generate arrays with floating-point data types and directly allocate memory for elements.
import numpy as np# Array from 0 to 4a = np.arange(5)print("arange(5):", a) # Output: arange(5): [0 1 2 3 4]# Array with start, stop, and stepa = np.arange(1.5, 3., 0.5)print("arange(1.5, 3., 0.5):", a) # Output: arange(1.5, 3., 0.5): [1.5 2. 2.5]# Array with step that produces decimal valuesa = np.arange(1.5, 4.)print("arange(1.5, 4.):", a) # Output: arange(1.5, 4.): [1.5 2.5 3.5]# Parameter demonstrationprint("\nParameter arange(start, end, step):")print("- start, end, step can be float")print("- end is excluded from result")print("- step default is 1")print("- start default is 0")np.linspace Function
Unlike np.arange which uses fixed steps, np.linspace divides a range into a number of evenly spaced points.
import numpy as np# Create 5 evenly spaced points between 0 and 10a = np.linspace(0, 10, 5)print("linspace(0, 10, 5):", a) # Output: linspace(0, 10, 5): [ 0. 2.5 5. 7.5 10. ]# Create 11 evenly spaced points between -1 and 1a = np.linspace(-1, 1, 11)print("linspace(-1, 1, 11):", a)# Output: linspace(-1, 1, 11): [-1. -0.8 -0.6 -0.4 -0.2 0. 0.2 0.4 0.6 0.8 1. ]# Comparison linspace vs arangeprint("\nDifference linspace vs arange:")print("linspace: number of elements known, distance calculated")print("arange: distance known, number of elements calculated")Comparison arange vs linspace
| Aspect | np.arange | np.linspace |
|---|---|---|
| Main parameters | start, stop, step | start, stop, num |
| Control | Distance between elements | Total number of elements |
| Endpoint | Excluded | Included (default) |
| Data type | Follows input | Always float (default) |
| Usage | Sequence with fixed distance | Even range division |
Basic Operations
After creating arrays, you can perform various operations to manipulate and analyze data.
import numpy as np# Create example arraya = np.array([[1, 2, 3], [4, 5, 6]])print("Array:")print(a)# Output:# [[1 2 3]# [4 5 6]]print("Shape:", a.shape) # Output: Shape: (2, 3)print("Size (total elements):", a.size) # Output: Size (total elements): 6print("Ndim (dimensions):", a.ndim) # Output: Ndim (dimensions): 2print("Dtype (data type):", a.dtype) # Output: Dtype (data type): int64print("Itemsize (bytes per element):", a.itemsize) # Output: Itemsize (bytes per element): 8Arrays can be reshaped using the reshape() function to rearrange dimensions without changing the data:
import numpy as np# 1D array with 12 elementsa = np.arange(12)print("Original array:", a) # Output: Original array: [ 0 1 2 3 4 5 6 7 8 9 10 11]# Reshape to 3x4b = a.reshape(3, 4)print("Reshape 3x4:")print(b)# Output:# [[ 0 1 2 3]# [ 4 5 6 7]# [ 8 9 10 11]]# Reshape to 2x6c = a.reshape(2, 6)print("Reshape 2x6:")print(c)# Output:# [[ 0 1 2 3 4 5]# [ 6 7 8 9 10 11]]# Reshape with -1 (automatically calculate dimension)d = a.reshape(4, -1)print("Reshape 4x-1 (automatic):")print(d)# Output:# [[ 0 1 2]# [ 3 4 5]# [ 6 7 8]# [ 9 10 11]]