Wed Oct  8 09:15:48 2025

walker_sample_test():
  python version: 3.10.12
  numpy version:  1.26.4
  Test walker_sample()

normalize_test():
  normalize() normalizes entries 1 through N of a vector
  of length N+2.

  Initial X:

     0:     0.0654836
     1:      0.162889
     2:      0.734499
     3:      0.908588
     4:      0.423584
     5:       0.52204
     6:      0.252118

  Initial L1 norm of X(1:5) =     2.7516

  Normalized X:

     0:     0.0654836
     1:      0.059198
     2:      0.266935
     3:      0.330203
     4:      0.153941
     5:      0.189722
     6:      0.252118

  Final L1 norm of X(1:5) =          1

r8vec_indicator0_test():
  r8vec_indicator0() returns an indicator matrix.

  The indicator0 vector:
[0. 1. 2. 3. 4. 5. 6. 7. 8. 9.]

random_permutation_test():
  random_permutation() randomly permutes entries 1 through N of
  a vector X[0:N+1].

  Initial X:

     0:             0
     1:             1
     2:             2
     3:             3
     4:             4
     5:             5
     6:             6

  Permuted X:

     0:             0
     1:             5
     2:             2
     3:             1
     4:             3
     5:             4
     6:             6

walker_build_test():
  walker_build() builds the Walker sampler data vectors Y and A,
  given a probability vector X.

  Binomial PDF (ignore first and last entries):

     0:             0
     1:        0.0625
     2:          0.25
     3:         0.375
     4:          0.25
     5:        0.0625
     6:             0

   I    A[I]    Y[i] (ignore first and last entries)

   0   0           0
   1   3      0.3125
   2   2           1
   3   4         0.5
   4   2        0.75
   5   3      0.3125
   6   6           2

walker_sampler_test():
  walker_sampler() creates Walker sample vectors Y and A
  for efficient sampling of a discrete probability vector.
  Test the Walker sampler with a Zipf-type probability.

  Zipf probabilities
  for N = 10
  and parameter P = 2

     I     X[I]

     1          0.645258
     2          0.161314
     3         0.0716953
     4         0.0403286
     5         0.0258103
     6         0.0179238
     7         0.0131685
     8         0.0100822
     9        0.00796615
    10        0.00645258

  Randomly permuted X:

     I     X[I]

     1          0.161314
     2          0.645258
     3         0.0179238
     4         0.0403286
     5         0.0100822
     6         0.0131685
     7        0.00645258
     8         0.0258103
     9        0.00796615
    10         0.0716953

  Built the sampler
  i Y[i] A[i]:

    0                 0     0
    1                 1     1
    2          0.669902     1
    3          0.179238     2
    4          0.403286     2
    5          0.100822     2
    6          0.131685     2
    7         0.0645258     2
    8          0.258103     2
    9         0.0796615     2
   10          0.716953     1
   11                 2    11

  100000 samples:
  prob   #samples:

          0.161314   16295
          0.645258   64360
         0.0179238    1700
         0.0403286    4091
         0.0100822    1006
         0.0131685    1279
        0.00645258     594
         0.0258103    2613
        0.00796615     783
         0.0716953    7279

  sumvar = 1.51487, (should be about 1)

walker_verify_test():
  walker_verify() verifies the Walker sampler data vectors Y and A,
  for a given probability vector X.

  Benford PDF (ignore first and last entries):

     0:             0
     1:       0.30103
     2:      0.176091
     3:      0.124939
     4:       0.09691
     5:     0.0791812
     6:     0.0669468
     7:     0.0579919
     8:     0.0511525
     9:     0.0457575
    10:             0

   I    A[I]    Y[i] (ignore first and last entries)

   0   0           0
   1   1           1
   2   1      0.8966
   3   2       0.727
   4   2      0.8722
   5   2      0.7126
   6   3      0.6025
   7   1      0.5219
   8   1      0.4604
   9   1      0.4118
  10  10           2

  The verification sum = 1.38778e-16
  It should be very close to zero.

zipf_probability_test():
  zipf_probability() sets up a probablity vector X of N+2 elements
  containing in X[1:N] the probabilities of outcomes 1 through N
  in a Zipf distribution with parameter P.

  X for N = 5, P = 1.0

     0:             0
     1:      0.437956
     2:      0.218978
     3:      0.145985
     4:      0.109489
     5:     0.0875912
     6:             0

  X for N = 5, P = 2.0

     0:             0
     1:      0.683242
     2:       0.17081
     3:     0.0759157
     4:     0.0427026
     5:     0.0273297
     6:             0

  X for N = 10, P = 2.0

     0:             0
     1:      0.645258
     2:      0.161314
     3:     0.0716953
     4:     0.0403286
     5:     0.0258103
     6:     0.0179238
     7:     0.0131685
     8:     0.0100822
     9:    0.00796615
    10:    0.00645258
    11:             0

walker_sample_test():
  Normal end of execution.
Wed Oct  8 09:15:49 2025