08-Mar-2024 07:45:13

nintlib_test():
  MATLAB/Octave version 5.2.0
  Test nintlib().

  Test routines for estimating the integral of
  of F(X) in the hypercube [A,B]^DIM_NUM.



  DIM_NUM =        2


  A(1:DIM_NUM) = 0.000000
  B(1:DIM_NUM) = 1.000000


  F(X(1:DIM_NUM)) = 1

  BOX_ND:               1.000000000000        25
  P5_ND:                1.000000000000         9
  ROMBERG_ND:           1.000000000000       500
  SAMPLE_ND:            1.000000000000       120
  P5_ND + :             1.000000000000         9
  P5_ND + :             1.000000000000        36
  P5_ND + :             1.000000000000       144
  P5_ND + :             1.000000000000       576
  P5_ND + :             1.000000000000      2304
  P5_ND + :             1.000000000000      9216
  MONTE_CARLO_ND:       1.000000000000     80000
  MONTE_CARLO_ND:       1.000000000000    640000
  MONTE_CARLO_ND:       1.000000000000   5120000


  F(X(1:DIM_NUM)) = sum ( X(1:DIM_NUM) )

  BOX_ND:               1.000000000000        25
  P5_ND:                1.000000000000         9
  ROMBERG_ND:           1.000000000000       500
  SAMPLE_ND:            1.000000000000       120
  P5_ND + :             1.000000000000         9
  P5_ND + :             1.000000000000        36
  P5_ND + :             1.000000000000       144
  P5_ND + :             1.000000000000       576
  P5_ND + :             1.000000000000      2304
  P5_ND + :             1.000000000000      9216
  MONTE_CARLO_ND:       1.000408153591     80000
  MONTE_CARLO_ND:       0.999978740429    640000
  MONTE_CARLO_ND:       1.000130017743   5120000


  F(X(1:DIM_NUM)) = sum( X(1:DIM_NUM)^2 )

  BOX_ND:               0.666666666667        25
  P5_ND:                0.666666666667         9
  ROMBERG_ND:           0.666666666667      1400
  SAMPLE_ND:            0.665987531604       120
  P5_ND + :             0.666666666667         9
  P5_ND + :             0.666666666667        36
  P5_ND + :             0.666666666667       144
  P5_ND + :             0.666666666667       576
  P5_ND + :             0.666666666667      2304
  P5_ND + :             0.666666666667      9216
  MONTE_CARLO_ND:       0.665881789519     80000
  MONTE_CARLO_ND:       0.667390386305    640000
  MONTE_CARLO_ND:       0.666786678442   5120000


  F(X(1:DIM_NUM)) = sum ( X(1:DIM_NUM)^3 )

  BOX_ND:               0.500000000000        25
  P5_ND:                0.500000000000         9
  ROMBERG_ND:           0.500000000000      1400
  SAMPLE_ND:            0.499693384220       120
  P5_ND + :             0.500000000000         9
  P5_ND + :             0.500000000000        36
  P5_ND + :             0.500000000000       144
  P5_ND + :             0.500000000000       576
  P5_ND + :             0.500000000000      2304
  P5_ND + :             0.500000000000      9216
  MONTE_CARLO_ND:       0.499888994276     80000
  MONTE_CARLO_ND:       0.498951898044    640000
  MONTE_CARLO_ND:       0.500198629940   5120000


  F(X(1:DIM_NUM)) = exp(sum(X(1:DIM_NUM)))

  BOX_ND:               2.952492442010        25
  P5_ND:                2.952489609987         9
  ROMBERG_ND:           2.952492134614       500
  SAMPLE_ND:            2.949428500673       120
  P5_ND + :             2.952489609987         9
  P5_ND + :             2.952492396633        36
  P5_ND + :             2.952492441299       144
  P5_ND + :             2.952492442001       576
  P5_ND + :             2.952492442012      2304
  P5_ND + :             2.952492442013      9216
  MONTE_CARLO_ND:       2.959505239786     80000
  MONTE_CARLO_ND:       2.953107767545    640000
  MONTE_CARLO_ND:       2.953297265765   5120000


  F(X(1:DIM_NUM)) = 1/(1+sum(X(1:DIM_NUM)^2))

  BOX_ND:               0.639510304013        25
  P5_ND:                0.639380432842         9
  ROMBERG_ND:           0.639510327294       500
  SAMPLE_ND:            0.639697555310       120
  P5_ND + :             0.639380432842         9
  P5_ND + :             0.639510041677        36
  P5_ND + :             0.639510349723       144
  P5_ND + :             0.639510351837       576
  P5_ND + :             0.639510351870      2304
  P5_ND + :             0.639510351870      9216
  MONTE_CARLO_ND:       0.639377561550     80000
  MONTE_CARLO_ND:       0.639744771827    640000