28-Oct-2022 09:13:13

circle_integrals_test():
  MATLAB/Octave version 4.2.2.
  Test circle_integrals().

circle_integrals_test01()
  circle01_sample() compares exact and
  estimated integrals along the circumference 
  of the unit circle in 2D.

  Number of sample points used is 4192

  If any exponent is odd, the integral is zero.
  We restrict this test to randomly chosen even exponents.

  Ex  Ey     MC-Estimate           Exact      Error

   0   0         6.28319         6.28319    8.88e-16
   0   8         1.76456         1.71806    4.65e-02
   4   2        0.387656        0.392699    5.04e-03
   4   8       0.0419863       0.0429515    9.65e-04
   2   6        0.243051        0.245437    2.39e-03
   4   4        0.143907        0.147262    3.36e-03
   0   0         6.28319         6.28319    8.88e-16
   2   6        0.243051        0.245437    2.39e-03
   8   2        0.171641        0.171806    1.65e-04
   4   8       0.0419863       0.0429515    9.65e-04
   8   8       0.0064992      0.00671117    2.12e-04
   0   4         2.39457         2.35619    3.84e-02
  10   4       0.0273562       0.0276117    2.55e-04
   8  10      0.00324279      0.00335558    1.13e-04
   4   4        0.143907        0.147262    3.36e-03
  10   2        0.129346        0.128854    4.92e-04
   6   4        0.072108       0.0736311    1.52e-03
  10   2        0.129346        0.128854    4.92e-04
   0   0         6.28319         6.28319    8.88e-16
   4   0         2.33939         2.35619    1.68e-02

circle_integrals_test():
  Normal end of execution.

28-Oct-2022 09:13:13