26 March 2023  11:47:26.767 AM
 
HERMITE_EXACTNESS():
  FORTRAN90 version
  Investigate the polynomial exactness of a Gauss-Hermite
  quadrature rule by integrating weighted 
  monomials up to a given degree over the (-oo,+oo) interval.
 
HERMITE_EXACTNESS: 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 =       10
 
  Spatial dimension =        1
  Number of points  =       10
 
  The quadrature rule to be tested is
  a Gauss-Hermite rule
  of ORDER =       10
 
  OPTION = 4, the probabilist normalized weighted rule for:
  Integral ( -oo < x < +oo ) f(x) * exp(-x*x/2)/sqrt(2pi) dx
 
  Weights W:
 
  w( 1) =   0.4310652630718288E-05
  w( 2) =   0.7580709343122178E-03
  w( 3) =   0.1911158050077029E-01
  w( 4) =   0.1354837029802677    
  w( 5) =   0.3446423349320192    
  w( 6) =   0.3446423349320192    
  w( 7) =   0.1354837029802677    
  w( 8) =   0.1911158050077029E-01
  w( 9) =   0.7580709343122178E-03
  w(10) =   0.4310652630718288E-05
 
  Abscissas X:
 
  x( 1) =   -4.859462828332313    
  x( 2) =   -3.581823483551928    
  x( 3) =   -2.484325841638955    
  x( 4) =   -1.465989094391158    
  x( 5) =  -0.4849357075154977    
  x( 6) =   0.4849357075154977    
  x( 7) =    1.465989094391158    
  x( 8) =    2.484325841638955    
  x( 9) =    3.581823483551928    
  x(10) =    4.859462828332313    
 
  Region R:
 
  r( 1) =  -0.1000000000000000E+31
  r( 2) =   0.1000000000000000E+31
 
  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        0.0000000000000002
   3        0.0000000000000000
   4        0.0000000000000003
   5        0.0000000000000001
   6        0.0000000000000007
   7        0.0000000000000018
   8        0.0000000000000012
   9        0.0000000000000071
  10        0.0000000000000024
 
HERMITE_EXACTNESS:
  Normal end of execution.
 
26 March 2023  11:47:26.768 AM