Mon May 22 08:42:18 2023

hermite_exactness_test():
  Python version: 3.8.10
  Test hermite_exactness().

hermite_exactness():
  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.

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

  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:

[4.31065263e-06 7.58070934e-04 1.91115805e-02 1.35483703e-01
 3.44642335e-01 3.44642335e-01 1.35483703e-01 1.91115805e-02
 7.58070934e-04 4.31065263e-06]

  Abscissas X:

[-4.85946283 -3.58182348 -2.48432584 -1.46598909 -0.48493571  0.48493571
  1.46598909  2.48432584  3.58182348  4.85946283]

  Region R:

[-1.e+30  1.e+30]

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

  Degree      Error

   0        0.0000000000000002
   1        0.0000000000000000
   2        0.0000000000000000
   3        0.0000000000000001
   4        0.0000000000000003
   5        0.0000000000000000
   6        0.0000000000000000
   7        0.0000000000000004
   8        0.0000000000000003
   9        0.0000000000000080
  10        0.0000000000000001
  11        0.0000000000003126
  12        0.0000000000000000
  13        0.0000000000004547
  14        0.0000000000000004
  15        0.0000000000145519
  16        0.0000000000000006
  17        0.0000000002328306
  18        0.0000000000000009

hermite_exactness_test():
  Normal end of execution.
Mon May 22 08:42:18 2023