Data Analysis with SciPy - GeeksforGeeks

Statistics (scipy.stats) — SciPy v1.11.1 Manual

Introduction to Scipy

Scipy is a Python-based ecosystem of open-source software for mathematics, science, and engineering. It is built on top of the NumPy library and provides a collection of algorithms and functions for numerical integration, optimization, signal and image processing, linear algebra, and more. Scipy is widely used in scientific computing and data analysis.

Applications of Scipy

Here are some of the areas where Scipy can be used:

• Optimization: Scipy provides optimization routines for finding the minimum or maximum of a function.
• Integration: Scipy provides routines for numerical integration of functions.
• Interpolation: Scipy provides interpolation routines for finding a function that passes through a set of given points.
• Signal and Image Processing: Scipy provides signal processing routines for filtering, Fourier analysis, and more. It also provides image processing routines for image manipulation, filtering, and more.
• Linear Algebra: Scipy provides routines for solving linear systems, eigenvalue problems, and more.

How to Use Scipy

Before using Scipy, you need to install it using pip or conda. Once installed, you can import the library and its submodules in your Python script or Jupyter notebook:

import scipy
from scipy import optimize, integrate, interpolate, signal, linalg

Here are some examples of how to use Scipy:

• Optimization: Find the minimum of a function using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm:

  def f(x):
      return x**2 - 4*x + 3
  
  result = optimize.minimize(f, x0=0)
  print(result)
  

• Integration: Integrate a function numerically:

  from numpy import sin, cos
  
  def f(x):
      return sin(x)
  
  result = integrate.quad(f, 0, 2*cos(1))
  print(result)
  

• Interpolation: Interpolate a set of points to find a function that passes through them:

  import matplotlib.pyplot as plt
  
  x = [0, 1, 2, 3, 4]
  y = [0, 1, 4, 9, 16]
  
  f = interpolate.interp1d(x, y, kind='cubic')
  xnew = [0.5, 1.5, 2.5, 3.5]
  ynew = f(xnew)
  
  plt.plot(x, y, 'o', xnew, ynew, '-')
  plt.show()
  

• Signal and Image Processing: Filter a signal using a Butterworth filter:

  from scipy import signal
  import numpy as np
  import matplotlib.pyplot as plt
  
  # Generate a noisy signal
  t = np.linspace(0, 10, 1000)
  x = np.sin(t) + 0.1*np.random.randn(len(t))
  
  # Filter the signal using a Butterworth filter
  b, a = signal.butter(4, 0.1, 'low')
  y = signal.filtfilt(b, a, x)
  
  # Plot the original and filtered signal
  fig, (ax0, ax1) = plt.subplots(nrows=2)
  ax0.plot(t, x, 'b')
  ax0.set_title('Original signal')
  ax1.plot(t, y, 'r')
  ax1.set_title('Filtered signal')
  plt.show()