5 February 2008   4:07:20.034 PM                                               
 
INT_EXACTNESS_GEN_HERMITE_R16
  FORTRAN90 version
 
  Investigate the polynomial exactness of a generalized Gauss-Hermite
  quadrature rule by integrating exponentially weighted 
  monomials up to a given degree over the (-oo,oo) interval.
 
INT_EXACTNESS_GEN_HERMITE_R16: User input:
  Quadrature rule X file = "gen_herm_o16_a1.0_modified_x.txt".
  Quadrature rule W file = "gen_herm_o16_a1.0_modified_w.txt".
  Quadrature rule R file = "gen_herm_o16_a1.0_modified_r.txt".
  Maximum degree to check =       35
  Weighting function exponent ALPHA =    1.00000    
  OPTION = 1, integrate                     f(x).
 
  Spatial dimension =        1
  Number of points  =       16
 
  The quadrature rule to be tested is
  a generalized Gauss-Hermite rule
  ORDER =       16
  ALPHA =    1.00000    
 
  OPTION = 1, modified rule:
    Integral ( -oo < x < oo ) f(x) dx
    is to be approximated by
    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).
 
  Weights W:
 
  w( 1) =   0.9313134323506839    
  w( 2) =   0.7332266104960289    
  w( 3) =   0.6506939781279630    
  w( 4) =   0.6043787440156341    
  w( 5) =   0.5753596025931054    
  w( 6) =   0.5564355737688126    
  w( 7) =   0.5437798314152072    
  w( 8) =   0.5303815727772847    
  w( 9) =   0.5303815727772847    
  w(10) =   0.5437798314152072    
  w(11) =   0.5564355737688126    
  w(12) =   0.5753596025931054    
  w(13) =   0.6043787440156341    
  w(14) =   0.6506939781279630    
  w(15) =   0.7332266104960289    
  w(16) =   0.9313134323506839    
 
  Abscissas X:
 
  x( 1) =   -4.781540728352031    
  x( 2) =   -3.967452411973961    
  x( 3) =   -3.280017684431137    
  x( 4) =   -2.654412440144422    
  x( 5) =   -2.065599227896752    
  x( 6) =   -1.500362166233917    
  x( 7) =  -0.9506323036797034    
  x( 8) =  -0.4126495272081394    
  x( 9) =   0.4126495272081394    
  x(10) =   0.9506323036797034    
  x(11) =    1.500362166233917    
  x(12) =    2.065599227896752    
  x(13) =    2.654412440144422    
  x(14) =    3.280017684431137    
  x(15) =    3.967452411973961    
  x(16) =    4.781540728352031    
 
  Region R:
 
  r( 1) =  -0.1000000000000000E+31
  r( 2) =   0.1000000000000000E+31
 
  A generalized Gauss-Hermite rule would be able to exactly
  integrate monomials up to and including degree =       31
 
          Error          Degree  Exponents
 
        0.4696046353029738    0
        0.0000000000000000    1
        0.1091928875963877    2
        0.0000000000000000    3
        0.3355792578493543    4
        0.0000000000000000    5
        0.4460845032125656    6
        0.0000000000000000    7
        0.5153479821521663    8
        0.0000000000000000    9
        0.5638095359438097   10
        0.0000000000000000   11
        0.6001595042580430   12
        0.0000000000000000   13
        0.6287193254438001   14
        0.0000000000000000   15
        0.6519244427227293   16
        0.0000000000000000   17
        0.6712619297624371   18
        0.0000000000000000   19
        0.6876988416477237   20
        0.0000000000000000   21
        0.7018943021341198   22
        0.0000000000000000   23
        0.7143153441311379   24
        0.0000000000000000   25
        0.7253031053005975   26
        0.0000000000000000   27
        0.7351136650105495   28
        0.0000000000000000   29
        0.7439427478373875   30
        0.0000000000000000   31
        0.7519483859165273   32
        0.0000000000000000   33
        0.7593013100916475   34
        0.0000000000000000   35
 
INT_EXACTNESS_GEN_HERMITE_R16:
  Normal end of execution.
 
 5 February 2008   4:07:20.042 PM