31 March 2023  10:34:20.384 AM
 
LAGUERRE_EXACTNESS():
  FORTRAN90 version
 
  Investigate the exactness of a Gauss-Laguerre
  quadrature rule for integrating monomials 
  with density exp(-x) or density 1
  over the [0,+oo) interval.
 
LAGUERRE_EXACTNESS: 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 =       10
  OPTION = 0, integrate exp(-x)*f(x).
 
  Spatial dimension =        1
  Number of points  =        4
 
  The quadrature rule to be tested is
  a Gauss-Laguerre rule of ORDER =        4
  Integral (    0.00000     <= x < +oo ) f(x) exp ( -x ) dx
 
  Weights W:
 
  w( 1) =   0.6031541043416337    
  w( 2) =   0.3574186924377999    
  w( 3) =   0.3888790851500538E-01
  w( 4) =   0.5392947055613278E-03
 
  Abscissas X:
 
  x( 1) =   0.3225476896193923    
  x( 2) =    1.745761101158346    
  x( 3) =    4.536620296921128    
  x( 4) =    9.395070912301136    
 
  Region R:
 
  r( 1) =    0.000000000000000    
  r( 2) =   0.1000000000000000E+31
 
  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        0.0000000000000000
   3        0.0000000000000000
   4        0.0000000000000003
   5        0.0000000000000007
   6        0.0000000000000013
   7        0.0000000000000022
   8        0.0142857142857118
   9        0.0650793650793622
  10        0.1641269841269810
 
LAGUERRE_EXACTNESS:
  Normal end of execution.
 
31 March 2023  10:34:20.385 AM