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  1. import sympy as sp
  2. from sympy import Symbol
  3. import numpy as np
  4. import matplotlib.pyplot as plt
  5. %matplotlib inline
  6. plt.rcParams['figure.figsize'] = 7, 7
  7.  
  8. def lag_sym(data_points):
  9.     x = Symbol('x')
  10.     L = np.zeros(data_points.shape) # this stores our basis functions.
  11.     L = []
  12.     for i, xi in enumerate(data_points):
  13.         temp_product = 1.0
  14.         other_data_points = np.delete(data_points, i)
  15.        
  16.         for xj in other_data_points: # compute product
  17.             temp_product *= (x-xj)/(xi-xj)
  18.         L.append(temp_product)
  19. #         L[i] = temp_product  # store the product.
  20.     # finished computing all basis functions.
  21.     return L
  22.  
  23. def fun_eval(F, mesh):
  24.     # F should be a list of basis polynomials of sympy.Mul class
  25.     return np.sum(np.array([[F[i].evalf(subs={'x':mesh[k]}) for i in range(len(F))] for k in range(len(mesh)) ]).transpose(), axis=1)
  26.  
  27. def herm_sym(L, data_points):
  28.     x = Symbol('x')
  29.     H = []
  30.     for i, xi in enumerate(data_points):
  31.         H.append( (1 - 2*(x - xi)*L[i].diff() ) * L[i]**2 )
  32.     return H
  33.  
  34.  
  35.  
  36.  
  37.  
  38. mesh_resolution = [5]
  39. for n in mesh_resolution:
  40.     plt.figure()
  41. #    plt.title('data points =')
  42.    
  43.     data_l = np.linspace(-1, 1, 2*n)
  44.     lag_fun = lag_sym(data_l)
  45.  
  46.     data_h = np.linspace(-1, 1, n)
  47.     L = lag_sym(data_h)
  48. #     herm_fun = herm_sym(L, data_h)
  49.    
  50.     plot_mesh = np.linspace(-1,1,100)
  51.     lag_eval =  fun_eval(lag_fun, plot_mesh)
  52. #     herm_eval = fun_eval(herm_fun, plot_mesh)
  53.     plt.plot(plot_mesh,lag_eval)
  54. #     plt.plot(plot_mesh,herm_eval)
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