Sat Jan 31 19:30:34 2026

correlation_test():
  python version: 3.10.12
  numpy version:  1.26.4
  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 "besselk_paths.png"
  Graphics saved as "circular_paths.png"
  Graphics saved as "damped_cosine_paths.png"
  Graphics saved as "hole_paths.png"
  Graphics saved as "linear_paths.png"
  Graphics saved as "matern_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"
  Graphics saved as "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:
array([[1., 1., 1., 1., 1.],
       [1., 2., 2., 2., 2.],
       [1., 2., 3., 3., 3.],
       [1., 2., 3., 4., 4.],
       [1., 2., 3., 4., 5.]])

  Correlation matrix C:
array([[1.        , 0.70710678, 0.57735027, 0.5       , 0.4472136 ],
       [0.70710678, 1.        , 0.81649658, 0.70710678, 0.63245553],
       [0.57735027, 0.81649658, 1.        , 0.8660254 , 0.77459667],
       [0.5       , 0.70710678, 0.8660254 , 1.        , 0.89442719],
       [0.4472136 , 0.63245553, 0.77459667, 0.89442719, 1.        ]])

  Variances sigma:
array([1.        , 1.41421356, 1.73205081, 2.        , 2.23606798])

  Recovered covariance matrix K2:
array([[1., 1., 1., 1., 1.],
       [1., 2., 2., 2., 2.],
       [1., 2., 3., 3., 3.],
       [1., 2., 3., 4., 4.],
       [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.
Sat Jan 31 19:30:40 2026