7 September 2007  10:34:40.506 AM                                              
 
INT_EXACTNESS_GEN_HERMITE
  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: 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    
 
  Spatial dimension =        1
  Number of points  =       16
 
  The quadrature rule to be tested is
  a generalized Gauss-Hermite rule
  ORDER =       16
  A =      -0.179769    
  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) =   0.5240005874357544E-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) =   0.5240005874357544E-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) =  -0.1797693134862000    
  r( 2) =   0.1797693134862000    
 
  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
        0.0000000000000000    1     1
        0.0000000000000009    2     2
        0.0000000000000000    3     3
        0.0000000000000004    4     4
        0.0000000000000000    5     5
        0.0000000000000001    6     6
        0.0000000000000003    7     7
        0.0000000000000007    8     8
        0.0000000000000009    9     9
        0.0000000000000011   10    10
        0.0000000000000085   11    11
        0.0000000000000011   12    12
        0.0000000000000089   13    13
        0.0000000000000011   14    14
        0.0000000000005408   15    15
        0.0000000000000004   16    16
        0.0000000000025152   17    17
        0.0000000000000005   18    18
        0.0000000000401053   19    19
        0.0000000000000000   20    20
        0.0000000000035101   21    21
        0.0000000000000000   22    22
        0.0000000000920863   23    23
        0.0000000000000014   24    24
        0.0000000329710019   25    25
        0.0000000000000014   26    26
        0.0000006466871127   27    27
        0.0000000000000011   28    28
        0.0000028572976589   29    29
        0.0000000000000004   30    30
        0.0000107884407043   31    31
        0.0000777000777038   32    32
        0.0011739730834961   33    33
        0.0006627359568492   34    34
        0.0853881835937500   35    35
 
INT_EXACTNESS_GEN_HERMITE:
  Normal end of execution.
 
 7 September 2007  10:34:40.526 AM