Numrs

A rust native build of numpy and scipy using modern algorithms, multithreading and parallelization. Built for speed, precision and performance.

---

📂 Project Structure

Numrs ├── Cargo.toml ├── src/ │ ├── lib.rs # Main library exports │ ├── methods.rs # Core mathematical algorithms │ └── utils.rs # Helper functions for algorithms └── tests/ ├── unit/ │ ├── mod.rs # Unit test module declaration │ └── method.rs # Unit tests for methods └── integration/ └── basic.rs # Integration tests

✅ Progress

• Project restructured into a library crate (no main.rs required).
• Implemented and tested a wide range of numerical methods, including:

Linear Algebra

• LU Decomposition (with full test coverage)
• Cholesky Decomposition
• QR Decomposition
• Conjugate Gradient method for sparse systems (linbcg)
• Vandermonde & Toeplitz matrix methods

Interpolation & Approximation

• Polynomial interpolation & extrapolation (regular and rational)
• Cubic splines (spline, spline2, splin2)
• Polynomial coefficient routines (polcoe, polcof)
• Chebyshev methods (chebft, chebev, chebpc, pcshft)
• Rational approximants & Padé approximants

Numerical Integration

• Trapezoidal methods (with refinement levels)
• Simpson’s method
• Romberg integration
• Improper integrals (midpnt, midinf, midsql, midsqu, midexp)
• Gaussian quadrature methods (gauleg, gaulag, gauher, gaujac, gaucof)
• Orthogonal polynomial routines (othog.rs)
• Multidimensional integration algorithms

Series & Summation

• Euler summation (eulsum.rs)
• Efficient power series routines (pccheb)

Special Functions

• Gamma functions (gamma, gamma_series, gamma_continued)
• Factorials & Beta functions (factrl, factln, beta, bico)
• Exponential integral & incomplete beta function
• Error functions
• Bessel functions (j0, y0, j1, y1, j, k0, beschd, bessik)
• Airy functions, spherical Bessel functions, Legendre polynomials (PLGNDR.rs)
• Fresnel integrals, Cosine and Sine integrals
• Dawson integrals, Carlson Elliptical integrals (first, second, third, degenrate), Lengendre Elliptical integrals (first, second, third), Jacobian elliptical integral

Random Numbers

• Monte Carlo Vegas: Adaptive
• Monte Carlo Miser: Adaptive

Fast Fourier Transform

• FFT1
• FFT2
• Real_FT
• Sin_FT
• Fourn
• Real_FT3

Fourier and Spectral Analysis

• Convolve
• Correlation

🚧 TODO

• Fix SVD (4 unit tests currently failing)
• Add multithreading to interpolation methods (e.g., polcoe)
• Combine and refactor linear algebra routines for cleaner structure
• Link library routines internally to reduce redundancy
• Expand documentation on method usage
• Hypergeometric and Hypergeometric derivatives
• Random numbers (especially Monte Carlo Methods)
• Root finding and nonlinear sets of equations
• FFT implementations
• Manage lib dependencies
• Fourier and Spectral Analysis (Lots of calls from FFT section of lib)

---

📖 Documentation

Documentation and usage examples are coming soon. Clear examples for methods along with performance benchmarks comparing C algorithms and numpy.

---

🛠️ Tech Stack

• Language: Rust
• Testing: Unit & integration tests with robust edge case coverage
• Optimizations: Multithreading and parallelization for selected methods, Rust-native optimizations

---

📜 License

This project is licensed under the GNU General Public License v3.0 (GPL-3.0).

You may redistribute and/or modify this software under the terms of the GNU GPL as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
See the GNU General Public License for more details.