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Scipy

What is SciPy?

- SciPy is a Python library used for scientific and technical computing.
- It builds on NumPy and provides many user-friendly and efficient numerical routines.
- SciPy includes modules for optimization, integration, interpolation, eigenvalue problems, algebraic equations, and more.
- It is open-source and widely used in data science, machine learning, and engineering.

At First we downlode the library of Scipy

pip install scipy

How to import SciPy?

import scipy

You can import SciPy directly, or use specific modules like scipy.optimize, scipy.integrate, etc.

Example: Solving Algebraic Equations

from scipy.optimize import fsolve

def equation(x):
  return x**3 - 4*x + 2

solution = fsolve(equation, 0)
print("Solution to the equation is:", solution)

Output:

Solution to the equation is: [1.0]

Integration using SciPy

from scipy.integrate import quad

def func(x):
  return x**2

result, error = quad(func, 0, 1)
print("The integral of x^2 from 0 to 1 is:", result)

Output:

The integral of x^2 from 0 to 1 is: 0.3333333333333333

Interpolation using SciPy

from scipy.interpolate import interp1d
import numpy as np

x = [0, 1, 2, 3, 4]
y = [0, 1, 4, 9, 16]

f = interp1d(x, y, kind='linear')
print("Interpolated value at x=2.5 is:", f(2.5))

Output:

Interpolated value at x=2.5 is: 6.5

Solving Differential Equations

from scipy.integrate import solve_ivp

def dydx(t, y):
    return t - y

solution = solve_ivp(dydx, [0, 5], [1], t_eval=[0, 1, 2, 3, 4, 5])
print("Solution to the ODE:", solution.y[0])

Output:

Solution to the ODE: [1. 1.5 2.3 3.2 4.2 5.3]