5 February 2008   4:07:11.098 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_x.txt".
  Quadrature rule W file = "gen_herm_o16_a1.0_w.txt".
  Quadrature rule R file = "gen_herm_o16_a1.0_r.txt".
  Maximum degree to check =       35
  Weighting function exponent ALPHA =    1.00000    
  OPTION = 0, integrate |x|^alpha*exp(-x*x)*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 = 0, standard rule:
    Integral ( -oo < x < oo ) |x|^alpha * exp(-x^2) * f(x) dx
    is to be approximated by
    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).
 
  Weights W:
 
  w( 1) =   0.5240005874357543E-09
  w( 2) =   0.4242873358136269E-06
  w( 3) =   0.4538254386679103E-04
  w( 4) =   0.1397268117612835E-02
  w( 5) =   0.1667174613060782E-01
  w( 6) =   0.8789749331858591E-01
  w( 7) =   0.2093933904071717    
  w( 8) =   0.1845942946708189    
  w( 9) =   0.1845942946708189    
  w(10) =   0.2093933904071717    
  w(11) =   0.8789749331858591E-01
  w(12) =   0.1667174613060782E-01
  w(13) =   0.1397268117612835E-02
  w(14) =   0.4538254386679103E-04
  w(15) =   0.4242873358136269E-06
  w(16) =   0.5240005874357543E-09
 
  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
 
        0.0000000000000007    0
        0.0000000000000000    1
        0.0000000000000006    2
        0.0000000000000000    3
        0.0000000000000004    4
        0.0000000000000000    5
        0.0000000000000001    6
        0.0000000000000000    7
        0.0000000000000004    8
        0.0000000000000000    9
        0.0000000000000008   10
        0.0000000000000000   11
        0.0000000000000010   12
        0.0000000000000000   13
        0.0000000000000009   14
        0.0000000000000000   15
        0.0000000000000006   16
        0.0000000000000000   17
        0.0000000000000003   18
        0.0000000000000000   19
        0.0000000000000001   20
        0.0000000000000000   21
        0.0000000000000007   22
        0.0000000000000000   23
        0.0000000000000014   24
        0.0000000000000000   25
        0.0000000000000016   26
        0.0000000000000000   27
        0.0000000000000013   28
        0.0000000000000000   29
        0.0000000000000007   30
        0.0000000000000000   31
        0.0000777000777032   32
        0.0000000000000000   33
        0.0006627359568485   34
        0.0000000000000000   35
 
INT_EXACTNESS_GEN_HERMITE_R16:
  Normal end of execution.
 
 5 February 2008   4:07:11.105 PM