forked from denizdonmez/numethods
65 lines
1.7 KiB
Markdown
65 lines
1.7 KiB
Markdown
# numethods
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A small, 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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## 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 (NEW)
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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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### Matrix & Vector utilities
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- Minimal `Matrix` / `Vector` classes
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- `@` operator for **matrix multiplication** (NEW)
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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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---
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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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