numerica 0.2.0

Numerical Analysis methods with Python (experimental)

Numerica

My own experimental implementations of numerical methods as homework.

Examples

python3.8 -i test.py #includes all definitions

Preparation

import numerica as n
from numerica import f, c

fn1 = f([1, -6, 5]) # (x^2 - 6x + 5)^1
fn2 = f([1, -6.5, 13.5, -9]) # (1x^3 - 6.5x^2 + 13.5x - 9)^1

Solving Nonlinear Equations

Root Bracketing Methods

Graph Method

root1 = n.graph(fn=fn1, dx=1, epsilon=0.01, x=0)
root2 = n.graph(fn=fn1, dx=1, epsilon=0.01, x=2)

print(root1, root2) # 1, 5

Bisection Method

root1 = n.bisection(fn=fn2, epsilon=0.01, a=0, b=1.9)
root2 = n.bisection(fn=fn2, epsilon=0.01, a=1.7, b=2.9)
root3 = n.bisection(fn=fn2, epsilon=0.01, a=2.5, b=6)

print(root1, root2, root3) # 1.5, 2, 3

Regula-Falsi Method

root1 = n.regulafalsi(fn=fn2, epsilon=0.001, a=0, b=1.75)
root2 = n.regulafalsi(fn=fn2, epsilon=0.001, a=1.75, b=2.75)
root3 = n.regulafalsi(fn=fn2, epsilon=0.001, a=2.50, b=3.5)

print(root1, root2, root3) # 1.5, 2, 3

Iterative Methods

Basic Iteration

# f = x^2 - 2x - 3
# x0=4

gxfn = f([1, 0])
gxdg = f([1])

hxfn1 = f([2, 3], 1/2)
hxdh1 = f([2, 3], -1/2)

hxfn2 = c(f([3, 0]), f([1, -2], -1)) # f(x) = (3 / (x - 2))
hxdh2 = c(f([-3, 0]), f([1, -2], -2)) # f(x) = (-3 / (x - 2)^2)

hxfn3 = c(f([1/2, 0]), f([1, -3])) # f(x) = (x^2 - 3) / 2
hxdh3 = f([1, 0])

root1 = n.basic(gxfn, hxfn1, gxdg, hxdh1, epsilon=0.005, x=4)
root2 = n.basic(gxfn, hxfn2, gxdg, hxdh2, epsilon=0.005, x=4)
root3 = n.basic(gxfn, hxfn3, gxdg, hxdh3, epsilon=0.005, x=4)

print(root1, root2, root3) # 3.003, -1.003, None

Resources

• YTU Numerical Analysis Lecture Notes
• https://mat.iitm.ac.in/home/sryedida/public_html/caimna/content1.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
numerica.utils.function.f([1, -6, 5])(5) == 0

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/*