code: import time
  from scipy import fftpack
  import book_format
  book_format.set_style()
  import kf_book.kf_internal as kf_internal
  from kf_book.kf_internal import DogSimulation
  from kf_book import book_plots as book_plots
  import numpy as np
  from matplotlib import pyplot
  import scipy.io
  import pandas as pd
  import pandas_datareader as pdr
  import seaborn as sns
  from pykrige.ok import OrdinaryKriging
  import matplotlib.pyplot as plt
  import numpy as np
  import sys
  sys.path.insert(0, '../../results')
  
  
  jj = 50
  
  with open('Lat_new.txt', 'r') as f1:
          data1 = f1.read().split(); floats1 = []
          for elem1 in data1:
              try:
                  floats1.append(float(elem1))
              except ValueError:
                  pass
  
  lat = np.array(data1, dtype = np.float64);lat = np.array_split(lat, 86)
  x1 = lat
  
  with open('Long_new.txt', 'r') as f2:
          data2 = f2.read().split(); floats2 = []
          for elem2 in data2:
              try:
                  floats2.append(float(elem2))
              except ValueError:
                  pass
              
  longdat = np.array(data2, dtype = np.float64);longdat = np.array_split(longdat, 86)
  x2 = longdat
  
  x = np.linspace(0, 405, 405)
  x_benchmark = np.linspace(0, 405, 405)# 550
  xpred = np.linspace(405, 750, 345)#440 - 550
  y_lat = x1[jj][0:405]
  y_long = x2[jj][0:405]
  # y_benchmark = x1[jj][0:550]
  
  y_fft_lat = fftpack.dct(y_lat, norm="ortho")
  y_fft_lat[5:] = 0
  y_filter_lat = fftpack.idct(y_fft_lat, norm="ortho")
  
  y_fft_long = fftpack.dct(y_long, norm="ortho")
  y_fft_long[5:] = 0
  y_filter_long = fftpack.idct(y_fft_long, norm="ortho")
  
  
  t_lat = time.time()
  
  uk_fourier_lat = OrdinaryKriging(
      x, np.zeros(x.shape), y_filter_lat, variogram_model="power"#, exact_values=False
  )
  y_fft_pred_lat, y_fft_std_lat = uk_fourier_lat.execute("grid", xpred, np.array([0.0]), backend="loop")
  
  time_fourierkriging_lat = time.time() - t_lat
  
  
  uk_lat = OrdinaryKriging(
      x, np.zeros(x.shape), y_lat, variogram_model="power"#, exact_values=False
  )
  y_pred_lat, y_std_lat = uk_lat.execute("grid", xpred, np.array([0.0]), backend="loop")
  
  time_kriging_lat = time.time() - t_lat
  
  
  t_long = time.time()
  
  uk_fourier_long = OrdinaryKriging(
      x, np.zeros(x.shape), y_filter_long, variogram_model="power"#, exact_values=False
  )
  y_fft_pred_long, y_fft_std_long = uk_fourier_long.execute("grid", xpred, np.array([0.0]), backend="loop")
  
  time_fourierkriging_long = time.time() - t_long
  
  
  uk_long = OrdinaryKriging(
      x, np.zeros(x.shape), y_long, variogram_model="power"#, exact_values=False
  )
  y_pred_long, y_std_long = uk_long.execute("grid", xpred, np.array([0.0]), backend="loop")
  
  time_kriging_long = time.time() - t_long
  
  
  y_pred_lat = np.squeeze(y_pred_lat)
  y_std_lat = np.squeeze(y_std_lat)
  y_fft_pred_lat = np.squeeze(y_fft_pred_lat)
  y_fft_std_lat = np.squeeze(y_fft_std_lat)
  
  y_pred_long = np.squeeze(y_pred_long)
  y_std_long = np.squeeze(y_std_long)
  y_fft_pred_long = np.squeeze(y_fft_pred_long)
  y_fft_std_long = np.squeeze(y_fft_std_long)
  
  
  dat_24_lat = y_fft_pred_lat[135:161]
  dat_26_lat = y_fft_pred_lat[184:207]
  dat_28_lat = y_fft_pred_lat[230:253]
  dat_30_lat = y_fft_pred_lat[276:299]
  dat_2_lat = y_fft_pred_lat[322:345]
  
  dat_24_long = y_fft_pred_long[135:161]
  dat_26_long = y_fft_pred_long[184:207]
  dat_28_long = y_fft_pred_long[230:253]
  dat_30_long = y_fft_pred_long[276:299]
  dat_2_long = y_fft_pred_long[322:345]
  
  # =====================================
  
  pred_24_lat = np.mean(dat_24_lat)
  pred_26_lat = np.mean(dat_26_lat)
  pred_28_lat = np.mean(dat_28_lat)
  pred_30_lat = np.mean(dat_30_lat)
  pred_2_lat = np.mean(dat_2_lat)
  
  pred_24_long = np.mean(dat_24_long)
  pred_26_long = np.mean(dat_26_long)
  pred_28_long = np.mean(dat_28_long)
  pred_30_long = np.mean(dat_30_long)
  pred_2_long = np.mean(dat_2_long)
  
  # ========SAVE FINAL DATA PREDICTION=========
  
  final_pred = [[pred_24_lat, pred_26_lat, pred_28_lat, pred_30_lat, pred_2_lat],[pred_24_long, pred_26_long, pred_28_long, pred_30_long, pred_2_long]]
  
  np.savetxt(('id'+str(jj)+'.txt'),final_pred)
  
apis: numpy.squeeze numpy.zeros scipy.fftpack.dct scipy.fftpack.idct numpy.array_split numpy.array numpy.linspace numpy.mean