Thu May 25 08:05:04 2023

laguerre_exactness_test():
  Python version: 3.8.10
  Test laguerre_exactness().

laguerre_exactness():
  Investigate the exactness of a Gauss-Laguerre
  quadrature rule for integrating monomials
  with density exp(-x) or density 1
  over the [A,+oo) interval.

User input:
  Quadrature rule X file = "lag_o04_x.txt".
  Quadrature rule W file = "lag_o04_w.txt".
  Quadrature rule R file = "lag_o04_r.txt".
  Maximum degree to check =  8
  OPTION = 0, integrate exp(-x)*f(x).

  The quadrature rule to be tested is
  a Gauss-Laguerre quadrature rule of ORDER =  4
  for integrals of the type:
    Integral (  0.0  <= x < +oo ) f(x) exp(-x) dx

  Weights W:

[6.03154104e-01 3.57418692e-01 3.88879085e-02 5.39294706e-04]

  Abscissas X:

[0.32254769 1.7457611  4.5366203  9.39507091]

  Region R:

[0.e+00 1.e+30]

  A Gauss-Laguerre rule would be able to exactly
  integrate monomials up to and including 
  degree =  7

  Degree      Error

   0        0.0000000000000002
   1        0.0000000000000002
   2        0.0000000000000001
   3        0.0000000000000001
   4        0.0000000000000000
   5        0.0000000000000005
   6        0.0000000000000013
   7        0.0000000000000020
   8        0.0142857142857114
   9        0.0650793650793619

laguerre_exactness_test():
  Normal end of execution.
Thu May 25 08:05:05 2023