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Rainyy21
238 lines
5.8 KiB
Markdown
238 lines
5.8 KiB
Markdown
---
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title: Introduction to NumPy
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tags:
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- python
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- numpy
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- data-science
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- numerical-computing
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category: Lesson
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difficulty: Beginner to Intermediate
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created: 2026-05-26
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---
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# Introduction to NumPy
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> [!abstract] What is NumPy?
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> **NumPy** (Numerical Python) is the foundational library for scientific computing in Python. It provides a high-performance multidimensional array object, tools for working with these arrays, and linear algebra, Fourier transform, and random number capabilities.
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>
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> ### Why use NumPy instead of standard Python lists?
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> 1. **Speed:** NumPy arrays are written in C, making mathematical operations up to 100x faster than standard Python lists.
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> 2. **Memory Efficiency:** NumPy arrays use contiguous blocks of memory, whereas Python lists store pointers to objects scattered across memory.
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> 3. **Vectorization:** It allows performing mathematical operations on whole arrays without writing slow `for` loops.
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---
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## 📐 The N-Dimensional Array (`ndarray`)
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The core of NumPy is the **`ndarray`** (N-dimensional array). It is a grid of values, all of the **same type** (homogenous), indexed by a tuple of non-negative integers.
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```mermaid
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graph TD
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A[ndarray] --> B["1D Array (Vector) <br> Shape: (n,)"]
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A --> C["2D Array (Matrix) <br> Shape: (m, n)"]
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A --> D["3D Array (Tensor) <br> Shape: (p, m, n)"]
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```
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### Essential Array Attributes
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Every array has attributes that describe its structure:
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```python
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import numpy as np
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arr = np.array([[1, 2, 3], [4, 5, 6]])
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print(arr.ndim) # Number of dimensions (axes) -> 2
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print(arr.shape) # Tuple representing sizes in each dimension -> (2, 3)
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print(arr.size) # Total number of elements -> 6
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print(arr.dtype) # Data type of the elements -> int64
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```
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---
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## 🛠️ Creating Arrays
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First, import the library using the standard alias:
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```python
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import numpy as np
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```
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### 1. From Python Lists
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```python
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# 1D Vector
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v = np.array([1, 2, 3])
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# 2D Matrix
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m = np.array([[1, 2], [3, 4]])
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```
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### 2. Built-in Placeholders
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NumPy provides functions to initialize arrays with placeholders, avoiding manual creation:
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```python
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# Array of zeros
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zeros = np.zeros((3, 4)) # 3 rows, 4 columns
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# Array of ones
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ones = np.ones((2, 3), dtype=np.int32)
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# Range of numbers (similar to range())
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range_arr = np.arange(0, 10, 2) # [0, 2, 4, 6, 8]
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# Linearly spaced numbers
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linspace_arr = np.linspace(0, 1, 5) # [0.0, 0.25, 0.5, 0.75, 1.0]
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# Identity Matrix
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eye_matrix = np.eye(3) # 3x3 identity matrix
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```
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### 3. Random Number Generation
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```python
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# Uniform random values between [0.0, 1.0)
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rand_arr = np.random.rand(2, 2)
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# Standard normal distribution (mean=0, std=1)
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randn_arr = np.random.randn(2, 2)
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# Random integers
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rand_ints = np.random.randint(1, 100, size=(5,))
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```
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---
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## ⚡ Element-wise Operations & Vectorization
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In standard Python, to add two lists element-wise, you need a list comprehension or loop. In NumPy, you do it directly.
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```python
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x = np.array([1, 2, 3])
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y = np.array([4, 5, 6])
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print(x + y) # [5, 7, 9]
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print(x * y) # [4, 10, 18]
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print(x ** 2) # [1, 4, 9]
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```
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### 📡 Broadcasting
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Broadcasting is a powerful mechanism that allows NumPy to perform arithmetic operations on arrays of **different shapes**. The smaller array is "broadcast" across the larger array so that they have compatible shapes.
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```python
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matrix = np.array([[1, 2, 3], [4, 5, 6]])
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scalar = 10
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# The scalar is added to every single element
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print(matrix + scalar)
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# [[11, 12, 13]
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# [14, 15, 16]]
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```
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---
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## 🔍 Indexing, Slicing & Masking
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### Slicing 2D Arrays
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Slicing follows the format `array[row_start:row_end, col_start:col_end]`.
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```python
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arr = np.array([
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[10, 11, 12],
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[20, 21, 22],
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[30, 31, 32]
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])
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# Get row at index 1
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print(arr[1, :]) # [20, 21, 22]
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# Get column at index 2
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print(arr[:, 2]) # [12, 22, 32]
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# Slice a subgrid (top-left 2x2)
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print(arr[0:2, 0:2])
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# [[10, 11]
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# [20, 21]]
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```
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### 🎭 Boolean Masking (Conditional Filtering)
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You can filter arrays using conditions. NumPy returns elements where the condition resolves to `True`.
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```python
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data = np.array([1, 5, 8, 12, 3, 15])
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# Create a boolean mask
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mask = data > 5 # [False, False, True, True, False, True]
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# Filter using the mask
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filtered_data = data[mask] # [8, 12, 15]
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```
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---
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## 🧮 Common Aggregations & Axis Operations
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Aggregations allow you to compute statistics over entire arrays or along specific **axes**:
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* `axis=0`: Down the columns (collapses rows).
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* `axis=1`: Across the rows (collapses columns).
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```python
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arr = np.array([[1, 2], [3, 4]])
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# Sum of all elements
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print(np.sum(arr)) # 10
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# Sum down the columns (vertical)
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print(np.sum(arr, axis=0)) # [4, 6]
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# Sum across the rows (horizontal)
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print(np.sum(arr, axis=1)) # [3, 7]
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```
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---
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## 🔄 Reshaping and Transposing
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You can change the shape of an array without changing its data using `.reshape()` or `.T` (Transpose).
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```python
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flat = np.arange(1, 7) # [1, 2, 3, 4, 5, 6]
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# Reshape into a 2x3 matrix
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matrix = flat.reshape(2, 3)
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# [[1, 2, 3]
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# [4, 5, 6]]
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# Transpose matrix (swap rows and columns)
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transposed = matrix.T
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# [[1, 4]
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# [2, 5]
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# [3, 6]]
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```
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---
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## 💡 Best Practices
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> [!important] Avoid Standard Loops
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> Standard loops in Python are interpreted, which adds massive overhead. Vectorized operations execute in compiled C, taking advantage of CPU caches and SIMD instructions.
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>
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> **Example Comparison:**
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> ```python
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> # ❌ Extremely Slow
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> values = np.random.rand(1_000_000)
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> reciprocal = [1 / x for x in values]
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>
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> # ✅ Near Instantaneous
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> reciprocal = 1 / values
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> ```
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> [!tip] Use In-place Operations to Save Memory
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> Instead of creating a new copy, perform calculations directly on the existing array if possible using syntax like `+=`, `-=`, or `*=`.
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> ```python
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> a = np.ones(1000000)
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> b = np.ones(1000000)
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>
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> # Allocates new memory
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> a = a + b
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>
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> # Modifies 'a' in-place (saves memory allocation time)
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> a += b
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> ```
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