Wed Oct  8 08:24:53 2025

line_integrals_test():
  python version: 3.10.12
  numpy version:  1.26.4
  Test line_integrals().

line01_length_test
  line01_length returns the length of the unit line.

  line01_length() =  1.0

line01_monomial_integral_test
  line01_monomial_integral computes integrals of monomials
  along the length of the unit line in 1D.
  Compare with a Monte Carlo estimate.

  Number of sample points used is 4192

   E     MC-Estimate      Exact           Error

   0               1               1           0
   1        0.509059             0.5      0.0091
   2        0.342861        0.333333      0.0095
   3        0.258932            0.25      0.0089
   4        0.208195             0.2      0.0082
   5        0.174183        0.166667      0.0075
   6        0.149789        0.142857      0.0069
   7        0.131438           0.125      0.0064
   8         0.11713        0.111111       0.006
   9        0.105662             0.1      0.0057
  10       0.0962639       0.0909091      0.0054

line01_sample_test():
  line01_sample() samples the unit line.

  Sample points in the unit line.

     0:      0.296109
     1:      0.672723
     2:      0.853134
     3:      0.750878
     4:       0.67049
     5:       0.42745
     6:      0.914588
     7:      0.938303
     8:      0.049037
     9:      0.326541

monomial_value_1d_test():
  monomial_value_1d() evaluates a monomial of a 1D argument.

      X^(-1)       X^(0)       X^(1)       X^(2)       X^(5)

     0.11703           1     8.54485     73.0145     45553.6
    -2.03122           1   -0.492316    0.242375  -0.0289213
    0.194578           1     5.13934     26.4128     3585.39
     0.17359           1      5.7607     33.1857     6344.21
    -1.70359           1   -0.586995    0.344563  -0.0696902

line_integrals_test():
  Normal end of execution.
Wed Oct  8 08:24:53 2025