https://github.com/ramesaliyev/numerica
Numerical analysis methods implemented in Python.
https://github.com/ramesaliyev/numerica
bisection-method euler-methods fixed-point-iteration gauss-jordan-elimination gauss-seidel graph-method jacobi lagrange least-square-regression newton-raphson numerical-analysis numerical-differentiation numerical-integration numerical-methods regression regula-falsi secant-method simpson trapezoidal
Last synced: 14 days ago
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Numerical analysis methods implemented in Python.
- Host: GitHub
- URL: https://github.com/ramesaliyev/numerica
- Owner: ramesaliyev
- License: other
- Created: 2020-02-14T00:33:00.000Z (almost 6 years ago)
- Default Branch: master
- Last Pushed: 2021-03-01T10:53:22.000Z (almost 5 years ago)
- Last Synced: 2025-12-08T00:33:41.162Z (2 months ago)
- Topics: bisection-method, euler-methods, fixed-point-iteration, gauss-jordan-elimination, gauss-seidel, graph-method, jacobi, lagrange, least-square-regression, newton-raphson, numerical-analysis, numerical-differentiation, numerical-integration, numerical-methods, regression, regula-falsi, secant-method, simpson, trapezoidal
- Language: Python
- Homepage:
- Size: 72.3 KB
- Stars: 26
- Watchers: 1
- Forks: 5
- Open Issues: 1
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Numerica
[](https://badge.fury.io/py/numerica)
My own experimental implementations of numerical methods as homework.
Use [documentation](https://github.com/ramesaliyev/numerica#documentation) to see how to use, and check [test.py](https://github.com/ramesaliyev/numerica/blob/master/test.py) for real examples.
# Table of Contents
- [Usage](#usage)
- [Importing](#importing)
- [Function Definition](#function-definition)
- [Matrix Definition](#matrix-definition)
- [Documentation](#documentation)
- [1- Solving Nonlinear Equations](#1--solving-nonlinear-equations)
- [Root Bracketing Methods](#root-bracketing-methods)
- [Graph](#graph)
- [Bisection](#bisection)
- [Regula-Falsi](#regula-falsi)
- [Iterative Methods](#iterative-methods)
- [Fixed-Point Iteration](#fixed-point-iteration)
- [Newton-Raphson](#newton-raphson)
- [Secant](#secant)
- [2- Matrix Operations](#2--matrix-operations)
- [Basic Operations](#basic-operations)
- [Definition](#matrix-definition)
- [Creating an Identity Matrix by n](#identity-matrix)
- [Getting Dimensions of a Matrix](#size-of-matrix)
- [Transpose of a Matrix](#transpose-of-a-matrix)
- [Finding Inverse of a Matrix](#finding-inverse-of-a-matrix)
- [Gauss-Jordan Method](#gauss-jordan-method)
- [Matrix Utils](#matrix-utils)
- [Concat Matrices by Row (Horizontal)](#concat-matrices-by-row-horizontal)
- [Concat Matrices by Column (Vertical)](#concat-matrices-by-column-vertical)
- [Map a Row of Matrix](#map-a-row-of-matrix)
- [Map all Matrix Cells](#map-all-matrix-cells)
- [Is Matrix Check](#is-matrix-check)
- [Slice Matrix Vertically](#slice-matrix-vertically)
- [3- Solving Systems of Linear Equations](#3--solving-systems-of-linear-equations)
- [Gauss Elimination](#gauss-elimination)
- [Jacobi](#jacobi)
- [Gauss-Seidel](#gauss-seidel)
- [4- Solving Systems of Nonlinear Equations](#4--solving-systems-of-nonlinear-equations)
- [5- Numerical Integration](#5--numerical-integration)
- [Trapezoidal](#trapezoidal)
- [Simpson](#simpson)
- [6- Numerical Differentiation](#6--numerical-differentiation)
- [Euler Methods](#euler-methods)
- [Backward](#backward)
- [Forward](#forward)
- [Midpoint](#midpoint)
- [7- Finite Differences](#7--finite-differences)
- [Determine Degree of a Polynomial](#determine-degree-of-a-polynomial)
- [8- Interpolation](#8--interpolation)
- [Lagrange](#lagrange)
- [9- Regression](#9--regression)
- [Least Squares](#least-squares)
- [Resources](#resources)
- [Testing Package](#testing-package)
- [Uploading to PyPI](#uploading-to-pypi)
# Usage
**python >= 3.8 is required**
## Importing
import numerica as n
from numerica import f // function definition
from numerica import m // matrix definition
## Function Definition
f('expression')
fx = f('3x^2 + 2x + 3')
fx(2)
## Matrix Definition
m(
a11, a12, a13;
a21, a22, a23;
a31, a32, a33
)
matrix = m('1,2,3; 4,5,6; 7,8,9');
# Documentation
## 1- Solving Nonlinear Equations
### Root Bracketing Methods
#### Graph
n.nl_graph(fx, dx, epsilon, x)
#### Bisection
n.nl_bisection(fx, epsilon, a, b)
#### Regula-Falsi
n.nl_regulafalsi(fx, epsilon, a, b)
### Iterative Methods
#### Fixed-Point Iteration
n.nl_fixedpoint(hx, epsilon, x)
#### Newton-Raphson
n.nl_newtonraphson(fx, epsilon, x)
#### Secant
n.nl_secant(fx, epsilon, x0, x1)
## 2- Matrix Operations
### Basic Operations
#### Matrix Definition
m(
a11, a12, a13;
a21, a22, a23;
a31, a32, a33
)
#### Identity Matrix
n.m_id(n)
#### Size of Matrix
(m, n) = n.m_size(A)
#### Transpose of a Matrix
n.m_transpose(A)
### Finding Inverse of a Matrix
#### Gauss-Jordan Method
n.mi_gaussjordan(A)
### Matrix Utils
#### Concat Matrices by Row (Horizontal)
n.m_rowconcat(A, B)
#### Concat Matrices by Column (Vertical)
n.m_colconcat(A, B)
#### Map a Row of Matrix
n.m_rowmap(A, i, iteratee)
#### Map all Matrix Cells
n.m_cellmap(A, iteratee)
#### Is Matrix Check
n.is_matrix(A)
#### Slice Matrix Vertically
n.m_rowslice(A, start, stop, step)
## 3- Solving Systems of Linear Equations
### Gauss Elimination
n.ls_gauss(A, C)
### Jacobi
n.ls_jacobi(A, C, X, epsilon=0.001)
### Gauss-Seidel
n.ls_gaussseidel(A, C, X, epsilon=0.001)
## 4- Solving Systems of Nonlinear Equations
## 5- Numerical Integration
### Trapezoidal
n.itg_trapezoidal(fx, x0, xn, n)
### Simpson
n.itg_simpson(fx, x0, xn, n)
## 6- Numerical Differentiation
### Euler Methods
#### Backward
n.diff_backward(fx, x)
#### Forward
n.diff_forward(fx, x)
#### Midpoint
n.diff_midpoint(fx, x)
## 7- Finite Differences
### Determine Degree of a Polynomial
n.fd_degree(pair_tuples)
n.fd_degree([(x0,y0), (x1,y1), (x2,y3), ...])
## 8- Interpolation
### Lagrange
n.itp_lagrange(pair_tuples)
n.itp_lagrange([(x0,y0), (x1,y1), (x2,y3), ...], x)
## 9- Regression
### Least Squares
n.reg_leastsquares(pair_tuples, degree) // returns polynomial
n.reg_leastsquares_solve(pair_tuples, x, degree) // solves polynomial
n.reg_leastsquares_solve([(x0,y0), (x1,y1), (x2,y3), ...], x, deg)
# Resources
- YTU Numerical Analysis Lecture Notes
- https://mat.iitm.ac.in/home/sryedida/public_html/caimna/index1.html
# Testing Package
##### Test Directly as Script
python3.8 -m numerica
##### or Install Package Locally (from repo root dir)
pip3.8 install .
##### and Test It from REPL
import numerica as n
# ...
##### or Use test.py Interactively
python3.8 -i test.py
# ...
##### or Just Test and Exit
python3.8 test.py
# Uploading to PyPI
##### Install Twine
pip3.8 install twine
##### Build
rm -rf build & rm -rf dist & rm -rf numerica.egg-info
python3.8 setup.py sdist bdist_wheel
##### Upload
twine upload dist/*