https://github.com/saadsalmanakram/numerical-computing
Working on core numerical computing using dedicated libraries in this genre...
https://github.com/saadsalmanakram/numerical-computing
cupy jax numpy scipy sympy theano xarray
Last synced: 4 months ago
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Working on core numerical computing using dedicated libraries in this genre...
- Host: GitHub
- URL: https://github.com/saadsalmanakram/numerical-computing
- Owner: saadsalmanakram
- Created: 2024-10-05T11:12:43.000Z (8 months ago)
- Default Branch: main
- Last Pushed: 2025-01-28T04:53:50.000Z (4 months ago)
- Last Synced: 2025-01-28T05:26:47.593Z (4 months ago)
- Topics: cupy, jax, numpy, scipy, sympy, theano, xarray
- Homepage:
- Size: 2.93 KB
- Stars: 2
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
---
# 🔢 Numerical Computing: Mastering NumPy, SciPy, SymPy, and CuPy
## 📝 Introduction
**Numerical Computing** is the foundation of scientific computing, engineering simulations, and data analysis. This repository provides a **comprehensive guide** to **NumPy, SciPy, SymPy, and CuPy**, helping learners master numerical methods, symbolic computation, and GPU-accelerated operations.
📌 **Understand the fundamentals of numerical computing**
📌 **Learn efficient matrix operations** with NumPy & CuPy
📌 **Explore scientific computing** with SciPy
📌 **Perform symbolic mathematics** using SymPy
📌 **Optimize performance** with GPU acceleration and parallel processing
---
## 🚀 Features
- 🔢 **NumPy**: Vectorized operations, linear algebra, random numbers
- ⚡ **CuPy**: GPU-accelerated numerical computing
- 🔬 **SciPy**: Scientific computing (optimization, signal processing, ODEs)
- 📝 **SymPy**: Symbolic mathematics (calculus, algebra, equation solving)
- 🏎 **Performance Optimization**: Parallelism, CUDA, memory-efficient computations
- 📈 **Practical Applications**: Signal processing, numerical integration, differential equations
---
## 📌 Prerequisites
Before getting started, ensure you have the following installed:
- **Python 3.x** → [Download Here](https://www.python.org/downloads/)
- Libraries: NumPy, SciPy, SymPy, CuPy
- Jupyter Notebook for interactive exploration
---
## 📂 Repository Structure
```
Numerical-Computing/
│── numpy/ # NumPy operations
│── scipy/ # SciPy-based scientific computing
│── sympy/ # Symbolic mathematics with SymPy
│── README.md # Documentation
└── requirements.txt # Python dependencies
```
---
## 🏆 Getting Started
### 1️⃣ Clone the Repository
```bash
git clone https://github.com/saadsalmanakram/Numerical-Computing.git
cd Numerical-Computing
```
### 2️⃣ Install Dependencies
```bash
pip install -r requirements.txt
```
### 3️⃣ Run an Example Notebook
Launch Jupyter Notebook and open one of the provided notebooks:
```bash
jupyter notebook
```
---
## 🔍 Topics Covered
### 🔢 **NumPy - The Core of Numerical Computing**
- **Creating & Manipulating Arrays**
- **Matrix Operations & Linear Algebra**
- **Broadcasting & Vectorization**
- **Random Number Generation**
- **Fourier Transforms (FFT)**
### 🔬 **SciPy - Advanced Scientific Computing**
- **Optimization (Minimization, Curve Fitting)**
- **Numerical Integration (Quad, Romberg, Simpson’s Rule)**
- **Differential Equations (ODEs, PDEs)**
- **Signal Processing (Filtering, FFT, Spectral Analysis)**
- **Statistical Functions & Distributions**
### 📝 **SymPy - Symbolic Computation**
- **Algebraic Manipulation & Equation Solving**
- **Calculus (Derivatives, Integrals, Limits)**
- **Matrix Algebra & Determinants**
- **Series Expansions & Laplace Transforms**
- **Generating LaTeX Output**
### ⚡ **CuPy - GPU-Accelerated NumPy**
- **Accelerating NumPy with CUDA**
- **Performing Fast Matrix Computations**
- **Memory Management & GPU Array Handling**
- **Parallel Processing**
### 🏎 **Performance Optimization Techniques**
- **Vectorization vs. Loops**
- **Memory Management & Broadcasting**
- **CUDA Acceleration with CuPy**
- **Parallel Computing with SciPy**
---
## 🚀 Example Code
### 🔢 **NumPy: Efficient Matrix Multiplication**
```python
import numpy as np
A = np.random.rand(1000, 1000)
B = np.random.rand(1000, 1000)
# Fast Matrix Multiplication
C = np.dot(A, B)
```
### 🔬 **SciPy: Solving a Differential Equation**
```python
from scipy.integrate import odeint
import numpy as np
def dydt(y, t):
return -y + np.sin(t)
t = np.linspace(0, 10, 100)
y0 = 1.0
solution = odeint(dydt, y0, t)
```
### 📝 **SymPy: Solving Algebraic Equations**
```python
from sympy import symbols, Eq, solve
x = symbols('x')
equation = Eq(x**2 - 5*x + 6, 0)
solution = solve(equation, x)
print(solution) # Output: [2, 3]
```
### ⚡ **CuPy: GPU-Accelerated Computations**
```python
import cupy as cp
A = cp.random.rand(1000, 1000)
B = cp.random.rand(1000, 1000)
C = cp.dot(A, B) # GPU-accelerated matrix multiplication
```
---
## 🏆 Real-World Applications
📌 **Numerical Optimization** → Solve constrained & unconstrained optimization problems
📌 **Differential Equations** → Solve physics and engineering problems
📌 **Signal Processing** → Apply FFT, wavelet transforms, and filtering
📌 **Computational Physics** → Run simulations for quantum mechanics and electromagnetism
📌 **Machine Learning & Data Science** → Feature transformations, probability distributions
---
## 🏆 Contributing
Contributions are welcome! 🚀
🔹 **Fork** the repository
🔹 Create a new branch (`git checkout -b feature-name`)
🔹 Commit changes (`git commit -m "Added CuPy optimization example"`)
🔹 Push to your branch (`git push origin feature-name`)
🔹 Open a pull request
---
## 📜 License
This project is licensed under the **MIT License** – feel free to use, modify, and share the code.
---
## 📬 Contact
For queries or collaboration, reach out via:
📧 **Email:** [email protected]
🌐 **GitHub:** [SaadSalmanAkram](https://github.com/saadsalmanakram)
💼 **LinkedIn:** [Saad Salman Akram](https://www.linkedin.com/in/saadsalmanakram/)
---
⚡ **Master Numerical Computing & Optimize Performance Efficiently!** ⚡
---