Numpy and scipy

numpy

• NumPy is one of the fundamental packages for scientific computing in Python.
• It contains functionality for multi-dimensional arrays, and also mathematical functions such as linear algebra operations, the Fourier transform, and pseudo-random number generators.

• Usually, numerical calculations in your code will be faster if you use numpy.

• loading library

  import numpy as np
  

• as np is not mandatory but often used.

• Using numpy array

  import numpy as np
  a = np.zeros(2)
  print(a)
  

convert list to numpy array

• numpy array can be made by defining the list first, as

  import numpy as np
  a = [1, 2, 3, 4, 5]
  b = np.array(a)
  print(a)
  print(b)
  

Array Creation

• numpy.zeros(n): array with n zeros.
• numpy.ones(n): array with n ones.
• np.arange(n): sequence of numbers with n elements.

Linear spacing

• You can have an uniformly-ditributed numbers by linspace function.

  import numpy as np
  x = np.linspace(-10, 10, 100)  # start, end, number of points
  

Random Number Generation

• numpy.random.rand(): generate random numbers from a uniform distribution.
• numpy.random.randn(): generate random numbers from a normal distribution.
• numpy.random.randint(): generate random integers.

Mathematical functions

• Several functions are available in numpy.
  • numpy.sin(): sine function
  • numpy.cos(): cosine function
  • numpy.exp(): exponential
  • numpy.log(): natural logarithm function
  • numpy.log10(): base 10 logarithm function
  • numpy.pi: $\pi = 3.141592...$

maximum and minimum

• Maximum and minimum values in an array can be easily found by numpy.max and numpy.min functions.
• The max/min argument i.e. the index corresponding to the max/min value is obtained by numpy.argmax and numpy.argmin functions.

  import numpy as np
  a = [1, 2, 4, 2, 1]
  b = np.array(a)
  print(np.max(b))
  print(np.argmax(b))
  

Exercise (numpy)

• Let's say you have sales data for a week represented as a NumPy array. Calculate the total sales for the week. answer

scipy

• SciPy is a Python library collecting scientific computing functionalities.
• It provides advanced linear algebra routines, mathematical function optimization, signal processing, special mathematical functions, and statistical distributions.

• linear algebra (linalg)

  import numpy as np
  from scipy import linalg
  
  A = np.array([[1, 3, 2], [-1, 0, 1], [2, 3, 0]])
  
  Ainv = linalg.inv(A)
  
  print(Ainv)
  print(np.matmul(Ainv, A))  # matrix-matrix multiply
  

• numerical integration

  import numpy as np
  from scipy import integrate
  
  # Define the function to integrate
  def my_func(x):
      return x**2  # Example function: x^2
  
  # Perform numerical integration using quad
  result, _ = integrate.quad(my_func, 0, 4)  # Integrate x^2 from 0 to 4
  
  print("Result of the integration:", result)
  

• ordinary differential equation (odeint); solving differential equation $\frac{dy}{dt} = -y$

  import numpy as np
  from scipy.integrate import odeint
  import matplotlib.pyplot as plt
  
  # define function for ODE
  def func_dydt(y, t):
      dydt = -y
      return dydt
  
  t_list = np.linspace(0.0, 10.0, 100)
  y_init = 1.0  # initial value
  y_list = odeint(func_dydt, y_init, t_list)
  
  # visualization
  fig, ax = plt.subplots()
  ax.plot(t_list, y_list)
  plt.show()
  

Exercise (scipy)

• Perform the numerical integration of $\exp(-x^2)$ function from -10 to 10, using SciPy's quad function.

answer