Thu Sep 29 16:44:43 2022

chance_test():
  Python version: 3.6.9
  Test chance().

dice_test():
  Simulate the Newton-Pepys dice puzzle.
  Case 1  probability estimate is  0.654
  Case 2  probability estimate is  0.609
  Case 3  probability estimate is  0.563

logistic_sample_test():
  Use the inverse CDF of the logistic distribution
  to produce 1000 sample points.

normal_plot_test():
  Plot the normal PDF for several parameter sets.

numpy_random_test():
  Demonstrate some features of the numpy random number generators.
  x = rng.random ( ): 
0.987915058288835
  s = rng.random ( size = 1 ): 
[0.84087992]
  s = rng.random ( size = 2 ): 
[0.84087992]
  a = rng.random ( size = [ 3, 4 ] ): 
[[0.18914764 0.45141033 0.63141279 0.40365929]
 [0.40399219 0.35194093 0.56167349 0.89788789]
 [0.14428344 0.93645137 0.05544609 0.67355051]]

  rng.seed() can reset the seed:

  rng = default_rng ( 123456789 ): 
  x = rng.random ( ): 
0.02771273928251694
  x = rng.random ( ): 
0.9067000554840227
  rng = default_rng ( 123456789 ): 
  x = rng.random ( ): 
0.02771273928251694

  x = rng.uniform(low=a,high=b,size=?) returns values in [a,b]

  Interval is [ 10 , 15 ]
  x = rng.uniform ( low = a, high = b ): 
14.533500277420114
  v = rng.uniform (  low = a, high = b, size = 5 ): 
[14.40696777 13.12448638 13.95357406 14.12954007 14.20852918]

  x = rng.standard_normal(size=?)
  returns normal random values with mean 0, standard deviation 1.

  v = rng.standard_normal ( size = [ 3, 4 ] ): 
[[ 1.14633764  1.7473833   0.12327598 -0.34086587]
 [ 0.1500319   0.84465446  0.90357677 -0.28058986]
 [-0.98720833  1.02633847 -1.04710489  2.80647303]]

  x = rng.normal(loc=mu,scale=sigma,size=?)
  returns normal random values with mean mu, standard deviation sigma.

  v = rng.normal ( loc = 10, scale = 0.5, size = [ 3, 4 ] ): 
[[11.16313724 10.60769281 10.16467977  9.46862195]
 [ 9.37408693 10.02587798 10.70765444  9.45749705]
 [10.16592167  9.4671201   9.99310197 10.26246305]]

spd_test():
  Matrix A is SPD if x'Ax > 0 for all nonzero vectors x
dif2 matrix passes SPD test #1
dif2 matrix passes SPD test #2
fibonacci matrix passes SPD test #1
fibonacci matrix fails SPD test #2

chance_test():
  Normal end of execution.
Thu Sep 29 16:44:44 2022