07-Jan-2022 21:41:40

hermite_exactness_test():
  MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2
  Test hermite_exactness().
07-Jan-2022 21:41:40

HERMITE_EXACTNESS
  MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2

  Investigate the polynomial exactness of a Gauss-Hermite
  quadrature rule by integrating exponentially weighted
  monomials up to a given degree over the (-oo,+oo) interval.

HERMITE_EXACTNESS: User input:
  Quadrature rule X file = "hermite_probabilist_010_x.txt".
  Quadrature rule W file = "hermite_probabilist_010_w.txt".
  Quadrature rule R file = "hermite_probabilist_010_r.txt".
  Maximum degree to check = 18

  Spatial dimension = 1
  Number of points  = 10

  Test a Gauss-Hermite quadrature rule of
  ORDER = 10

  OPTION = 4, the probabilist normalized weighted rule for:
  Integral ( -oo < x < +oo ) f(x) * exp(-x*x/2) / sqrt(2 pi) dx

  Weights W:

  w(1) =       0.0000043106526307
  w(2) =       0.0007580709343122
  w(3) =       0.0191115805007703
  w(4) =       0.1354837029802677
  w(5) =       0.3446423349320191
  w(6) =       0.3446423349320191
  w(7) =       0.1354837029802677
  w(8) =       0.0191115805007703
  w(9) =       0.0007580709343122
  w(10) =       0.0000043106526307

  Abscissas X:

  x(1) =      -4.8594628283323118
  x(2) =      -3.5818234835519269
  x(3) =      -2.4843258416389546
  x(4) =      -1.4659890943911582
  x(5) =      -0.4849357075154976
  x(6) =       0.4849357075154976
  x(7) =       1.4659890943911582
  x(8) =       2.4843258416389546
  x(9) =       3.5818234835519269
  x(10) =       4.8594628283323118

  Region R:

  r(1) = -1.000000e+30
  r(2) = 1.000000e+30

  A Gauss-Hermite rule would be able to exactly
  integrate monomials up to and including 
  degree = 19

  Degree      Error

   0        0.0000000000000000
   1        0.0000000000000000
   2        0.0000000000000002
   3        0.0000000000000000
   4        0.0000000000000001
   5        0.0000000000000002
   6        0.0000000000000001
   7        0.0000000000000000
   8        0.0000000000000000
   9        0.0000000000000142
  10        0.0000000000000000
  11        0.0000000000000000
  12        0.0000000000000002
  13        0.0000000000000000
  14        0.0000000000000004
  15        0.0000000000000000
  16        0.0000000000000005
  17        0.0000000000000000
  18        0.0000000000000009

HERMITE_EXACTNESS:
  Normal end of execution.

07-Jan-2022 21:41:40

hermite_exactness_test():
  Normal end of execution.

07-Jan-2022 21:41:40