10-Jun-2023 06:33:30

correlation_test():
  MATLAB/Octave version 5.2.0.
  Test correlation().

correlation_test01()
  Plot correlation functions.
  Graphics saved as "besselj_plot.png".
  Graphics saved as "besselk_plot.png".
  Graphics saved as "correlation_circular_plot.png"
  Graphics saved as "constant_plot.png".
  Graphics saved as "cubic_plot.png".
  Graphics saved as "damped_cosine_plot.png".
  Graphics saved as "damped_sine_plot.png".
  Graphics saved as "exponential_plot.png".
  Graphics saved as "gaussian_plot.png".
  Graphics saved as "hole_plot.png".
  Graphics saved as "linear_plot.png".
  Graphics saved as "matern_plot.png".
  Graphics saved as "pentaspherical_plot.png".
  Graphics saved as "power_plot.png".
  Graphics saved as "rational_quadratic_plot.png".
  Graphics saved as "spherical_plot.png".
  Graphics saved as "white_noise_plot.png".

correlation_test02()
  sample_paths_cholesky() generates sample paths from the
  correlation matrix, factored using the Cholesky factor.
  It requires that the correlation matrix is nonnegative definite.

  SAMPLE_PATHS_EIGEN generates sample paths from the
  correlation matrix, factored using the eigen factorization.
  If the correlation matrix is not nonnegative definite,
  we simply suppress negative eigenvalues.

  SAMPLE_PATHS_FFT generates sample paths from the
  correlation matrix, factored using the FFT factorization
  of the correlation matrix after embedding in a circulant.

  Graphics saved as "besselj_paths.png".
  Graphics saved as "besselk_paths.png".
  Graphics saved as "circular_paths.png".
  Graphics saved as "constant_paths.png".
  Graphics saved as "cubic_paths.png".
  Graphics saved as "damped_cosine_paths.png".
  Graphics saved as "damped_sine_paths.png".
  Graphics saved as "exponential_paths.png".
  Graphics saved as "gaussian_paths.png".
  Graphics saved as "hole_paths.png".
  Graphics saved as "linear_paths.png".
  Graphics saved as "matern_paths.png".
  Graphics saved as "pentaspherical_paths.png".
  Graphics saved as "power_paths.png".
  Graphics saved as "rational_quadratic_paths.png".
  Graphics saved as "spherical_paths.png".
  Graphics saved as "white_noise_paths.png".

correlation_test03():
  Make plots of correlation functions.

  Graphics saved as "besselj_plots.png".
  Graphics saved as "besselk_plots.png".
  Graphics saved as "circular_plots.png".
  Graphics saved as "constant_plots.png".
  Graphics saved as "cubic_plots.png".
  Created "damped_cosine_plots.png".
  Graphics saved as "damped_sine_plots.png".
  Graphics saved as "exponential_plots.png".
  Graphics saved as "gaussian_plots.png".
  Graphics saved as "hole_plots.png".
  Graphics saved as "linear_plots.png".
  Graphics saved as "matern_plots.png".
  Graphics saved as "pentaspherical_plots.png".
  Graphics saved as "power_plots.png".
  Graphics saved as "rational_quadratic_plots.png".
  Graphics saved as "spherical_plots.png".
  Graphics saved as "white_noise_plots.png".

correlation_test04():
  Convert between a correlation and a covariance matrix.

  Covariance matrix K:

  Col:       1             2             3             4             5       
  Row
      1 :           1             1             1             1             1  
      2 :           1             2             2             2             2  
      3 :           1             2             3             3             3  
      4 :           1             2             3             4             4  
      5 :           1             2             3             4             5  

  Correlation matrix C:

  Col:       1             2             3             4             5       
  Row
      1 :           1      0.707107       0.57735           0.5      0.447214  
      2 :    0.707107             1      0.816497      0.707107      0.632456  
      3 :     0.57735      0.816497             1      0.866025      0.774597  
      4 :         0.5      0.707107      0.866025             1      0.894427  
      5 :    0.447214      0.632456      0.774597      0.894427             1  

  Variances:

     1:            1
     2:      1.41421
     3:      1.73205
     4:            2
     5:      2.23607

  Recovered covariance matrix K2:

  Col:       1             2             3             4             5       
  Row
      1 :           1             1             1             1             1  
      2 :           1             2             2             2             2  
      3 :           1             2             3             3             3  
      4 :           1             2             3             4             4  
      5 :           1             2             3             4             5  

correlation_test05():
  correlation_brownian_display() displays the Brownian correlation
  Graphics saved as "correlation_brownian_plots.png".

correlation_test06():
  For non-stationary correlation functions:

  sample_paths2_cholesky() generates sample paths from the
  correlation matrix, factored using the Cholesky factor.
  It requires that the correlation matrix is nonnegative definite.

  sample_paths2_eigen() generates sample paths from the
  correlation matrix, factored using the eigen factorization.
  If the correlation matrix is not nonnegative definite,
  we simply suppress negative eigenvalues.

  sample_paths2_fft() generates sample paths from the
  correlation matrix, factored using the FFT factorization
  of the correlation matrix after embedding in a circulant.

  Graphics saved as "correlation_brownian_paths.png"

correlation_test():
  Normal end of execution.

10-Jun-2023 06:33:50