Tools for numerical math calculations

This repository contains tools for math numerical computation such as numerical integration and interpolation. The current implementation contains:

• numerical integration using Gauss formula

  import numpy as np
  from numerical.integration import gauss
  
  def f(x):
      return np.power(x[0], 2)
  
  gauss.integrate(f, 0., 1.)  # 0.3333333

• spline functions and theirs derivatives

  import numpy as np
  from numerical import splines
  import matplotlib.pyplot as plt
  
  x = np.arange(0, 4., 0.05)
  y = splines.schoenberg(x)
  yd1 = splines.schoenberg.deriv(x, order=1)  # first derivative
  yd2 = splines.schoenberg.deriv(x, order=2)  # second derivative
  # visualize results
  plt.plot(x, y)
  plt.plot(x, yd1)
  plt.plot(x, yd2)
  plt.show()

• function interpolation

  import numpy as np
  from numerical import interpolate
  import matplotlib.pyplot as plt
  
  def fun(x):
      return 1 - np.power(x[0] - 0.5, 2)
  
  grid = np.array([np.arange(0, 1.0001, 0.25)])
  values = fun(grid)
  itp_fun = interpolate(values, grid)
  
  x = np.arange(0., 1.00001, 0.001).reshape(1, -1)
  y_intp = itp_fun(x)
  y_true = fun(x)
  
  plt.plot(x[0], y_intp)
  plt.plot(x[0], y_true)
  plt.show()