10-Aug-2024 07:45:08
quad_monte_carlo_test():
  MATLAB/Octave version 6.4.0
  quad_monte_carlo() is an interactive program which uses
  n random samples to estimate the integral of a
  function f(x) over the interval [a,b].

  Estimate integral ( 0.000000 < x < 1.000000 ) x.^2 dx
  quad_monte_carlo: n = 100, integral estimate q =        0.307485467034214

  Estimate integral ( 0.0 < x < 2.0 ) sqrt(x) dx
  quad_monte_carlo: n = 1000, integral estimate q =        1.856240409674573

  Estimate integral ( 0.0 < x < 2.0 ) humps(x) dx
  quad_monte_carlo: n = 1, integral estimate q =       -8.973738937526388
  quad_monte_carlo: n = 2, integral estimate q =        83.61412095913492
  quad_monte_carlo: n = 4, integral estimate q =        14.21681676869925
  quad_monte_carlo: n = 8, integral estimate q =        37.46017203615281
  quad_monte_carlo: n = 16, integral estimate q =         40.9868443662456
  quad_monte_carlo: n = 32, integral estimate q =        37.90961683429341
  quad_monte_carlo: n = 64, integral estimate q =        28.99766589560426
  quad_monte_carlo: n = 128, integral estimate q =        30.76267060498862
  quad_monte_carlo: n = 256, integral estimate q =        26.76507996694842
  quad_monte_carlo: n = 512, integral estimate q =        26.86834424961968
  quad_monte_carlo: n = 1024, integral estimate q =        29.64434015120203
  quad_monte_carlo: n = 2048, integral estimate q =         28.7056163026523
  quad_monte_carlo: n = 4096, integral estimate q =        28.15476421632259
  quad_monte_carlo: n = 8192, integral estimate q =        29.45577406193911
  quad_monte_carlo: n = 16384, integral estimate q =        29.48283664246615
  quad_monte_carlo: n = 32768, integral estimate q =        29.08238990018963
  quad_monte_carlo: n = 65536, integral estimate q =        29.25472219472647
  quad_monte_carlo: n = 131072, integral estimate q =        29.37933722920883
  quad_monte_carlo: n = 262144, integral estimate q =        29.38891527503218
  quad_monte_carlo: n = 524288, integral estimate q =        29.31757310197181
  quad_monte_carlo: n = 1048576, integral estimate q =        29.29727316461544

quad_monte_carlo_test():
  Normal end of execution.
10-Aug-2024 07:45:08