Elementwise Vectorized Operations Practice Problem

This data science coding problem helps you practice Broadcasting & Vectorization, elementwise vectorized operations, and implementation skills. Read the problem statement, write your solution, and strengthen your understanding of Broadcasting & Vectorization.

• Problem ID: 106
• Problem key: 106-elementwise-vectorized-operations
• URL: https://datacrack.app/solve/106-elementwise-vectorized-operations
• Difficulty: easy
• Topic: Broadcasting & Vectorization
• Module: NumPy Foundations

Problem Statement

# 🧩 Elementwise Vectorized Operations

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### 🎯 Goal
Vectorized operations apply a function to **every element** of an array simultaneously — without writing a single Python loop. This problem teaches you to implement three essential ML activation functions (`relu`, `sigmoid`, `tanh`) using pure NumPy. These functions are the building blocks of every neural network, and understanding their vectorized implementation is the first step toward building ML models from scratch.

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### 🔍 The Three Activation Functions

| Function | Formula | Output Range | Use |
|:---------|:--------|:-------------|:----|
| **ReLU** | $\max(0, x)$ | $[0, +\infty)$ | Hidden layers in deep networks |
| **Sigmoid** | $\frac{1}{1 + e^{-x}}$ | $(0, 1)$ | Binary classification output |
| **Tanh** | $\tanh(x)$ | $(-1, 1)$ | Hidden layers; centered around 0 |

All three can be implemented with a **single NumPy expression** — no loops, no list comprehensions:
```python
relu    = np.maximum(0, arr)
sigmoid = 1 / (1 + np.exp(-arr))
tanh    = np.tanh(arr)
```

---

### 💻 Task
Implement `apply_activation(data, func_name)` that dispatches to the correct activation function.

---

### 📥 Input
- `data`: list of numbers (1D or 2D)
- `func_name`: string — `"relu"`, `"sigmoid"`, or `"tanh"`

### 📤 Output
- Transformed array as a Python list (same shape as input)

---

### 🧩 Starter Code
```python
import numpy as np

def apply_activation(data, func_name):
    """
    Apply an activation function element-wise.

    Args:
        data (list): Input numbers (1D or 2D)
        func_name (str): "relu", "sigmoid", or "tanh"

    Returns:
        list: Transformed array as a Python list
    """
    arr = np.array(data, dtype=float)
    # 🧠 TODO: Check which activation function was requested
    # 🧠 TODO: Apply the correct NumPy operation to the whole array
    # 🧠 TODO: Return the result as a Python list
    pass
```

---

### 💡 Example
```python
apply_activation([-2, -1, 0, 1, 2], "relu")
# Expected: [0.0, 0.0, 0.0, 1.0, 2.0]

apply_activation([-2, -1, 0, 1, 2], "sigmoid")
# Expected: [0.119..., 0.269..., 0.5, 0.731..., 0.881...]

apply_activation([[-1, 2], [-3, 4]], "relu")
# Expected: [[0.0, 2.0], [0.0, 4.0]]
```

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### 🔑 Key Concepts
- `np.maximum(0, arr)` applies `max(0, x)` to every element — this is vectorized ReLU
- `np.exp(-arr)` computes $e^{-x}$ for every element simultaneously
- These operations work on **any shape** — 1D, 2D, or higher — without code changes
- The loop equivalent `[max(0, x) for x in data]` only works on 1D and is much slower for large arrays