28 March 2023   1:52:56.459 PM
 
gen_laguerre_exactness():
  FORTRAN90 version
  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.
 
gen_laguerre_exactness: User input:
  Quadrature rule X file = "gen_lag_o4_a0.5_x.txt".
  Quadrature rule W file = "gen_lag_o4_a0.5_w.txt".
  Quadrature rule R file = "gen_lag_o4_a0.5_r.txt".
  Maximum degree to check =       10
  Weighting function exponent ALPHA =   0.500000    
 
  Spatial dimension =        1
  Number of points  =        4
 
  The quadrature rule to be tested is
  a generalized Gauss-Laguerre rule
  ORDER =        4
  A =        0.00000    
  ALPHA =   0.500000    
 
  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:
 
  w( 1) =   0.4530087465586076    
  w( 2) =   0.3816169601717996    
  w( 3) =   0.5079462757224078E-01
  w( 4) =   0.8065911501100311E-03
 
  Abscissas X:
 
  x( 1) =   0.5235260767382691    
  x( 2) =    2.156648763269094    
  x( 3) =    5.137387546176711    
  x( 4) =    10.18243761381592    
 
  Region R:
 
  r( 1) =    0.000000000000000    
  r( 2) =   0.1000000000000000E+31
 
  A generalized Gauss-Laguerre rule would be able to exactly
  integrate monomials up to and including degree =        7
 
          Error          Degree
 
        0.0000000000000000    0
        0.0000000000000003    1
        0.0000000000000004    2
        0.0000000000000003    3
        0.0000000000000003    4
        0.0000000000000006    5
        0.0000000000000013    6
        0.0000000000000023    7
        0.0105306458247668    8
        0.0504362510554501    9
        0.1330978618904361   10
 
gen_laguerre_exactness:
  Normal end of execution.
 
28 March 2023   1:52:56.459 PM