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Numerica\n[![PyPI version](https://badge.fury.io/py/numerica.svg)](https://badge.fury.io/py/numerica)\n\nMy own experimental implementations of numerical methods as homework.\u003cbr /\u003e\nUse [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.\n\n# Table of Contents\n  - [Usage](#usage)\n    - [Importing](#importing)\n    - [Function Definition](#function-definition)\n    - [Matrix Definition](#matrix-definition)\n  - [Documentation](#documentation)\n    - [1- Solving Nonlinear Equations](#1--solving-nonlinear-equations)\n      - [Root Bracketing Methods](#root-bracketing-methods)\n        - [Graph](#graph)\n        - [Bisection](#bisection)\n        - [Regula-Falsi](#regula-falsi)\n      - [Iterative Methods](#iterative-methods)\n        - [Fixed-Point Iteration](#fixed-point-iteration)\n        - [Newton-Raphson](#newton-raphson)\n        - [Secant](#secant)\n    - [2- Matrix Operations](#2--matrix-operations)\n      - [Basic Operations](#basic-operations)\n        - [Definition](#matrix-definition)\n        - [Creating an Identity Matrix by n](#identity-matrix)\n        - [Getting Dimensions of a Matrix](#size-of-matrix)\n        - [Transpose of a Matrix](#transpose-of-a-matrix)\n      - [Finding Inverse of a Matrix](#finding-inverse-of-a-matrix)\n        - [Gauss-Jordan Method](#gauss-jordan-method)\n      - [Matrix Utils](#matrix-utils)\n        - [Concat Matrices by Row (Horizontal)](#concat-matrices-by-row-horizontal)\n        - [Concat Matrices by Column (Vertical)](#concat-matrices-by-column-vertical)\n        - [Map a Row of Matrix](#map-a-row-of-matrix)\n        - [Map all Matrix Cells](#map-all-matrix-cells)\n        - [Is Matrix Check](#is-matrix-check)\n        - [Slice Matrix Vertically](#slice-matrix-vertically)\n    - [3- Solving Systems of Linear Equations](#3--solving-systems-of-linear-equations)\n      - [Gauss Elimination](#gauss-elimination)\n      - [Jacobi](#jacobi)\n      - [Gauss-Seidel](#gauss-seidel)\n    - [4- Solving Systems of Nonlinear Equations](#4--solving-systems-of-nonlinear-equations)\n    - [5- Numerical Integration](#5--numerical-integration)\n      - [Trapezoidal](#trapezoidal)\n      - [Simpson](#simpson)\n    - [6- Numerical Differentiation](#6--numerical-differentiation)\n      - [Euler Methods](#euler-methods)\n        - [Backward](#backward)\n        - [Forward](#forward)\n        - [Midpoint](#midpoint)\n    - [7- Finite Differences](#7--finite-differences)\n        - [Determine  Degree of a Polynomial](#determine-degree-of-a-polynomial)\n    - [8- Interpolation](#8--interpolation)\n      - [Lagrange](#lagrange)\n    - [9- Regression](#9--regression)\n      - [Least Squares](#least-squares)\n  - [Resources](#resources)\n  - [Testing Package](#testing-package)\n  - [Uploading to PyPI](#uploading-to-pypi)\n\n# Usage\n**python \u003e= 3.8 is required**\n\n## Importing\n    import numerica as n\n    from numerica import f // function definition\n    from numerica import m // matrix definition\n\n## Function Definition\n    f('expression')\n\n    fx = f('3x^2 + 2x + 3')\n    fx(2)\n\n## Matrix Definition\n    m(\n        a11, a12, a13;\n        a21, a22, a23;\n        a31, a32, a33\n    )\n\n    matrix = m('1,2,3; 4,5,6; 7,8,9');\n\n# Documentation\n## 1- Solving Nonlinear Equations\n### Root Bracketing Methods\n#### Graph\n    n.nl_graph(fx, dx, epsilon, x)\n\n#### Bisection\n    n.nl_bisection(fx, epsilon, a, b)\n\n#### Regula-Falsi\n    n.nl_regulafalsi(fx, epsilon, a, b)\n\n### Iterative Methods\n#### Fixed-Point Iteration\n    n.nl_fixedpoint(hx, epsilon, x)\n\n#### Newton-Raphson\n    n.nl_newtonraphson(fx, epsilon, x)\n\n#### Secant\n    n.nl_secant(fx, epsilon, x0, x1)\n\n## 2- Matrix Operations\n### Basic Operations\n#### Matrix Definition\n    m(\n        a11, a12, a13;\n        a21, a22, a23;\n        a31, a32, a33\n    )\n\n#### Identity Matrix\n    n.m_id(n)\n\n#### Size of Matrix\n    (m, n) = n.m_size(A)\n\n#### Transpose of a Matrix\n    n.m_transpose(A)\n\n### Finding Inverse of a Matrix\n#### Gauss-Jordan Method\n    n.mi_gaussjordan(A)\n\n### Matrix Utils\n#### Concat Matrices by Row (Horizontal)\n    n.m_rowconcat(A, B)\n\n#### Concat Matrices by Column (Vertical)\n    n.m_colconcat(A, B)\n\n#### Map a Row of Matrix\n    n.m_rowmap(A, i, iteratee)\n\n#### Map all Matrix Cells\n    n.m_cellmap(A, iteratee)\n\n#### Is Matrix Check\n    n.is_matrix(A)\n\n#### Slice Matrix Vertically\n    n.m_rowslice(A, start, stop, step)\n\n## 3- Solving Systems of Linear Equations\n### Gauss Elimination\n    n.ls_gauss(A, C)\n\n### Jacobi\n    n.ls_jacobi(A, C, X, epsilon=0.001)\n\n### Gauss-Seidel\n    n.ls_gaussseidel(A, C, X, epsilon=0.001)\n\n## 4- Solving Systems of Nonlinear Equations\n## 5- Numerical Integration\n### Trapezoidal\n    n.itg_trapezoidal(fx, x0, xn, n)\n\n### Simpson\n    n.itg_simpson(fx, x0, xn, n)\n\n## 6- Numerical Differentiation\n### Euler Methods\n#### Backward\n    n.diff_backward(fx, x)\n\n#### Forward\n    n.diff_forward(fx, x)\n\n#### Midpoint\n    n.diff_midpoint(fx, x)\n\n## 7- Finite Differences\n### Determine Degree of a Polynomial\n    n.fd_degree(pair_tuples)\n    n.fd_degree([(x0,y0), (x1,y1), (x2,y3), ...])\n\n## 8- Interpolation\n### Lagrange\n    n.itp_lagrange(pair_tuples)\n    n.itp_lagrange([(x0,y0), (x1,y1), (x2,y3), ...], x)\n\n## 9- Regression\n### Least Squares\n    n.reg_leastsquares(pair_tuples, degree) // returns polynomial\n    n.reg_leastsquares_solve(pair_tuples, x, degree) // solves polynomial \n    n.reg_leastsquares_solve([(x0,y0), (x1,y1), (x2,y3), ...], x, deg)\n\n# Resources\n- YTU Numerical Analysis Lecture Notes\n- https://mat.iitm.ac.in/home/sryedida/public_html/caimna/index1.html\n\n# Testing Package\n##### Test Directly as Script\n    python3.8 -m numerica\n##### or Install Package Locally (from repo root dir)\n    pip3.8 install .\n##### and Test It from REPL\n    import numerica as n\n    # ...\n##### or Use test.py Interactively\n    python3.8 -i test.py\n    # ...\n##### or Just Test and Exit\n    python3.8 test.py\n\n# Uploading to PyPI\n##### Install Twine\n    pip3.8 install twine\n##### Build\n    rm -rf build \u0026 rm -rf dist \u0026 rm -rf numerica.egg-info\n    python3.8 setup.py sdist bdist_wheel\n##### Upload\n    twine upload dist/*","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Framesaliyev%2Fnumerica","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Framesaliyev%2Fnumerica","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Framesaliyev%2Fnumerica/lists"}