84 lines
2.3 KiB
Markdown
84 lines
2.3 KiB
Markdown
# numethods
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A lightweight, from-scratch, object-oriented Python package implementing classic numerical methods.
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**No NumPy / SciPy solvers used**, algorithms are implemented transparently for learning and research.
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## Why this might be useful
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- Great for teaching/learning numerical methods step by step.
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- Good reference for people writing their own solvers in C/Fortran/Julia.
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- Lightweight, no dependencies.
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- Consistent object-oriented API (.solve() etc).
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---
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## Features
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### Linear system solvers
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- **LU decomposition** (with partial pivoting): `LUDecomposition`
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- **Gauss-Jordan** elimination: `GaussJordan`
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- **Jacobi** iterative method: `Jacobi`
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- **Gauss-Seidel** iterative method: `GaussSeidel`
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- **Cholesky** factorization (SPD): `Cholesky`
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### Root-finding
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- **Bisection**: `Bisection`
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- **Fixed-Point Iteration**: `FixedPoint`
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- **Secant**: `Secant`
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- **Newton's method** (for roots): `NewtonRoot`
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### Interpolation
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- **Newton** (divided differences): `NewtonInterpolation`
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- **Lagrange** polynomials: `LagrangeInterpolation`
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### Orthogonalization, QR, and Least Squares
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- **Classical Gram-Schmidt**: `QRGramSchmidt`
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- **Modified Gram-Schmidt**: `QRModifiedGramSchmidt`
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- **Householder QR** (numerically stable): `QRHouseholder`
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- **QR-based linear solver** (square systems): `QRSolver`
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- **Least Squares** for overdetermined systems (via QR): `LeastSquaresSolver`
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### Numerical Differentiation
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- **Forward difference**: `ForwardDiff`
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- **Backward difference**: `BackwardDiff`
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- **Central difference (2nd order)**: `CentralDiff`
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- **Central difference (4th order)**: `CentralDiff4th`
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- **Second derivative**: `SecondDerivative`
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- **Richardson extrapolation**: `RichardsonExtrap`
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### Matrix & Vector utilities
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- Minimal `Matrix` / `Vector` classes
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- `@` operator for **matrix multiplication**
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- `*` for **scalar**–matrix multiplication
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- `.T` for transpose
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- Forward / backward substitution helpers
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- Norms, dot products, row/column access
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---
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## Install (editable)
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```bash
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pip install -e /numethods
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```
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or just add `/numethods` to `PYTHONPATH`.
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## Examples
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```bash
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python /numethods/examples/demo.py
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```
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## Notes
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- All algorithms are implemented without relying on external linear algebra solvers.
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- Uses plain Python floats and list-of-lists for matrices/vectors.
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- Tolerances use a relative criterion `|Δ| ≤ tol (1 + |value|)`.
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