03-Jul-2023 10:42:21

walker_sample_test():
  MATLAB/Octave version 5.2.0.
  Test walker_sample()

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

  Initial X:

     1:     0.769853
     2:     0.701797
     3:     0.247491
     4:     0.263604
     5:     0.519571
     6:     0.201338
     7:      0.91287

  Initial L1 norm of X(1:N) = 1.9338

  Normalized X:

     1:     0.769853
     2:      0.36291
     3:     0.127982
     4:     0.136314
     5:     0.268679
     6:     0.104115
     7:      0.91287

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

NORMALIZE_TEST
  Normal end of execution.

r8vec_print_test():
  r8vec_print() prints an R8VEC.

  The R8VEC:

     1:      123.456
     2:        5e-06
     3:       -1e+06
     4:      3.14159

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):

     1:            0
     2:       0.0625
     3:         0.25
     4:        0.375
     5:         0.25
     6:       0.0625
     7:            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_BUILD_TEST
  Normal end of execution.

walker_sampler_test():
  walker_sampler() creates Walker sample vectors Y and A
  for efficiently sampling 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       0.0179238
     2        0.161314
     3       0.0716953
     4       0.0100822
     5       0.0258103
     6       0.0403286
     7      0.00796615
     8        0.645258
     9       0.0131685
    10      0.00645258

  Built the sampler
  i Y(i) A(i):

     1        0.179238     8
     2               1     2
     3        0.716953     8
     4        0.100822     8
     5        0.258103     8
     6        0.403286     8
     7       0.0796615     8
     8        0.386855     2
     9        0.131685     8
    10       0.0645258     8

  100000 samples:
  prob   #samples:

       0.0179238    1751
        0.161314   16184
       0.0716953    7367
       0.0100822    1003
       0.0258103    2546
       0.0403286    4076
      0.00796615     794
        0.645258   64263
       0.0131685    1377
      0.00645258     639

  sumvar = 1.14161 (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):

     1:            0
     2:      0.30103
     3:     0.176091
     4:     0.124939
     5:      0.09691
     6:    0.0791812
     7:    0.0669468
     8:    0.0579919
     9:    0.0511525
    10:    0.0457575
    11:            0

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

   0   0               0
   1   1               1
   2   1        0.896612
   3   2         0.72697
   4   2         0.87219
   5   2        0.712631
   6   3        0.602521
   7   1        0.521928
   8   1        0.460373
   9   1        0.411817
  10  10               2

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

walker_verify_test():
  Normal end of execution.

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 Nin a Zipf distribution with
  parameter P.

  X for N = 5, P = 1.0

     1:            0
     2:     0.437956
     3:     0.218978
     4:     0.145985
     5:     0.109489
     6:    0.0875912
     7:            0

  X for N = 5, P = 2.0

     1:            0
     2:     0.683242
     3:      0.17081
     4:    0.0759157
     5:    0.0427026
     6:    0.0273297
     7:            0

  X for N = 10, P = 2.0

     1:            0
     2:     0.645258
     3:     0.161314
     4:    0.0716953
     5:    0.0403286
     6:    0.0258103
     7:    0.0179238
     8:    0.0131685
     9:    0.0100822
    10:   0.00796615
    11:   0.00645258
    12:            0

ZIPF_PROBABILITY_TEST
  Normal end of execution.

walker_sample_test():
  Normal end of execution.

03-Jul-2023 10:42:42