Sun May 21 14:17:10 2023

gen_laguerre_exactness_test():
  Python version: 3.8.10
  Test gen_laguerre_exactness().

gen_laguerre_exactness():
  Investigate the polynomial exactness of a generalized Gauss-Laguerre
  quadrature rule by integrating exponentially weighted
  monomials up to a given degree over the [0,+oo) interval.

  The rule may be defined on another interval, [A,+oo)
  in which case it is adjusted to the [0,+oo) interval.

User input:
  Quadrature rule X file = "gen_lag_o8_a0.5_x.txt'
  Quadrature rule W file = "gen_lag_o8_a0.5_w.txt'
  Quadrature rule R file = "gen_lag_o8_a0.5_r.txt'
  Maximum degree to check =  18
  Weighting function exponent ALPHA =  0.5
  OPTION = 0, integrate x^alpha*exp(-x)*f(x).

  Number of points =  8

  The quadrature rule to be tested is
  a generalized Gauss-Laguerre rule
  ORDER =  8
  A =      0.0
  ALPHA =  0.5

  OPTION = 0, standard rule:
    Integral ( A <= x < oo ) x^alpha exp(-x) f(x) dx
    is to be approximated by
    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).

  Weights W:

[2.27139362e-01 3.93594543e-01 2.12908971e-01 4.78774832e-02
 4.54251747e-03 1.62404600e-04 1.64237741e-06 2.17394313e-09]

  Abscissas X:

[ 0.28263365  1.1398738   2.60152484  4.72411454  7.6052563  11.41718208
 16.4994108  23.730004  ]

  Region R:

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

  A generalized Gauss-Laguerre rule would be able to exactly
  integrate monomials up to and including 
  degree =  15

      Degree  Error

   0        0.0000000000000000
   1        0.0000000000000002
   2        0.0000000000000001
   3        0.0000000000000002
   4        0.0000000000000001
   5        0.0000000000000006
   6        0.0000000000000002
   7        0.0000000000000004
   8        0.0000000000000006
   9        0.0000000000000006
  10        0.0000000000000006
  11        0.0000000000000009
  12        0.0000000000000008
  13        0.0000000000000010
  14        0.0000000000000013
  15        0.0000000000000013
  16        0.0000561671454562
  17        0.0004926661044425
  18        0.0022799523824549

gen_laguerre_exactness():
  Normal end of execution.

gen_laguerre_exactness():
  Investigate the polynomial exactness of a generalized Gauss-Laguerre
  quadrature rule by integrating exponentially weighted
  monomials up to a given degree over the [0,+oo) interval.

  The rule may be defined on another interval, [A,+oo)
  in which case it is adjusted to the [0,+oo) interval.

User input:
  Quadrature rule X file = "gen_lag_o8_a0.5_modified_x.txt'
  Quadrature rule W file = "gen_lag_o8_a0.5_modified_w.txt'
  Quadrature rule R file = "gen_lag_o8_a0.5_modified_r.txt'
  Maximum degree to check =  18
  Weighting function exponent ALPHA =  0.5
  OPTION = 1, integrate                 f(x).

  Number of points =  8

  The quadrature rule to be tested is
  a generalized Gauss-Laguerre rule
  ORDER =  8
  A =      0.0
  ALPHA =  0.5

  OPTION = 1, modified rule:
    Integral ( A <= x < oo ) f(x) dx
    is to be approximated by
    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).

  Weights W:

[0.5667959  1.1525548  1.77995022 2.48100694 3.30872386 4.36755153
 5.92027404 9.02420731]

  Abscissas X:

[ 0.28263365  1.1398738   2.60152484  4.72411454  7.6052563  11.41718208
 16.4994108  23.730004  ]

  Region R:

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

  A generalized Gauss-Laguerre rule would be able to exactly
  integrate monomials up to and including 
  degree =  15

      Degree  Error

   0        0.0000000000000001
   1        0.0000000000000002
   2        0.0000000000000001
   3        0.0000000000000000
   4        0.0000000000000000
   5        0.0000000000000002
   6        0.0000000000000000
   7        0.0000000000000001
   8        0.0000000000000001
   9        0.0000000000000002
  10        0.0000000000000006
  11        0.0000000000000007
  12        0.0000000000000008
  13        0.0000000000000007
  14        0.0000000000000005
  15        0.0000000000000008
  16        0.0000561671454584
  17        0.0004926661044444
  18        0.0022799523824566

gen_laguerre_exactness():
  Normal end of execution.

gen_laguerre_exactness_test():
  Normal end of execution.
Sun May 21 14:17:11 2023