numerica 0.3.0

Numerical Analysis methods with Python (experimental)

Numerica

My own experimental implementations of numerical methods as homework.
Use documentation to see how to use, and check test.py for real examples.

Table of Contents

• Usage
  • Importing
  • Function Definition
  • Matrix Definition
• Documentation
  • 1- Solving Nonlinear Equations
    • Root Bracketing Methods
      • Graph
      • Bisection
      • Regula-Falsi
    • Iterative Methods
      • Fixed-Point Iteration
      • Newton-Raphson
      • Secant
  • 2- Matrix Operations
    • Basic Operations
      • Definition
      • Creating an Identity Matrix by n
      • Getting Dimensions of a Matrix
      • Transpose of a Matrix
    • Finding Inverse of a Matrix
      • Gauss-Jordan Method
    • Matrix Utils
      • Concat Matrices by Row (Horizontal)
      • Concat Matrices by Column (Vertical)
      • Map a Row of Matrix
      • Map all Matrix Cells
      • Is Matrix Check
      • Slice Matrix Vertically
  • 3- Solving Systems of Linear Equations
    • Gauss Elimination
    • Jacobi
    • Gauss-Seidel
  • 4- Solving Systems of Nonlinear Equations
  • 5- Numerical Integration
    • Trapezoidal
    • Simpson
  • 6- Numerical Differentiation
    • Euler Methods
      • Backward
      • Forward
      • Midpoint
  • 7- Finite Differences
    • Determine Degree of a Polynomial
  • 8- Interpolation
    • Lagrange
  • 9- Regression
    • Least Squares
• Resources
• Testing Package
• 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)
n.reg_leastsquares([(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/*