Sat Feb  4 20:27:19 2023

random_test():
  Python version: 3.8.10
  Test random().

random_histogram() makes a histogram of n samples
  of uniform random values from numpy.random.random().
  Graphics saved as "random_histogram.png"

  mean(r) =  0.4994295687983167
  var(r)  =  0.08274190835596945

normal_histogram() makes a histogram of n samples
  of normal random values from numpy.random.normal().
  normal mean  =  2.000566918454755
  normal stdev =  1.4604906393541761

dice_test():
  Simulate the Newton-Pepys dice puzzle.
  Case 1  probability estimate is  0.628
  Case 2  probability estimate is  0.607
  Case 3  probability estimate is  0.599

logistic_sample_test():
  Use the inverse CDF of the logistic distribution
  to produce 1000 sample points.
  Graphics saved as "logistic_sample.png"

normal_plot_test():
  Plot the normal PDF for several parameter sets.
  Graphics saved as "normal_plot.png"

numpy_random_random_test():
  Demonstrate some features of the numpy random number generators.
  x = np.random.random ( ): 
0.7239424822511176
  s = np.random.random ( size = 1 ): 
[0.38323592]
  s = np.random.random ( size = 2 ): 
[0.38323592]
  a = np.random.random ( [ 3, 4 ] ): 
[[0.40055841 0.77456305 0.97019428 0.40222437]
 [0.14073362 0.51615499 0.43921489 0.5840865 ]
 [0.32627454 0.58380651 0.79915111 0.89396951]]

  np.random.seed() can reset the seed:

  np.random.seed ( seed_value ) 
  x = np.random.random ( ): 
0.532833024789759
  x = np.random.random ( ): 
0.5341366008904166
  np.random.seed ( seed_value ) 
  x = np.random.random ( ): 
0.532833024789759

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

  Interval is [ 10 , 15 ]
  x = np.random.uniform ( low = a, high = b ): 
12.670683004452084
  v = np.random.uniform (  low = a, high = b, size = 5 ): 
[12.54776518 13.56782016 11.28499477 13.76346804 14.41939592]

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

  v = np.random.standard_normal ( size = [ 3, 4 ] ): 
[[ 0.4531316  -0.91691233  1.33864041  0.85866797]
 [ 0.7272307   0.56782948 -1.09536413 -0.50974171]
 [ 0.48885947  1.27592068 -0.2999348   0.64887209]]

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

  v = np.random.normal ( loc = 10, scale = 0.5, size = [ 3, 4 ] ): 
[[10.14474608  9.9718667   9.20452301 10.12984549]
 [10.2079817   9.20913862  9.09153412  9.91753589]
 [ 9.89840189  9.31576122 10.30928274 10.38177901]]

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

random_test():
  Normal end of execution.
Sat Feb  4 20:27:27 2023