7 September 2007  10:34:54.100 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_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    
 
  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 = 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) =   0.9313134323506840    
  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) =   0.9313134323506840    
 
  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
        0.0000000000000004    2     2
        0.0000000000000000    3     3
        0.0000000000000004    4     4
        0.0000000000000001    5     5
        0.0000000000000004    6     6
        0.0000000000000002    7     7
        0.0000000000000001    8     8
        0.0000000000000006    9     9
        0.0000000000000007   10    10
        0.0000000000000010   11    11
        0.0000000000000006   12    12
        0.0000000000000098   13    13
        0.0000000000000011   14    14
        0.0000000000000147   15    15
        0.0000000000000007   16    16
        0.0000000000011596   17    17
        0.0000000000000005   18    18
        0.0000000000133582   19    19
        0.0000000000000001   20    20
        0.0000000000674163   21    21
        0.0000000000000004   22    22
        0.0000000039642600   23    23
        0.0000000000000025   24    24
        0.0000000272048055   25    25
        0.0000000000000028   26    26
        0.0000004007015377   27    27
        0.0000000000000026   28    28
        0.0000020582228899   29    29
        0.0000000000000022   30    30
        0.0001835227012634   31    31
        0.0000777000777021   32    32
        0.0038652420043945   33    33
        0.0006627359568475   34    34
        0.0015563964843750   35    35
 
INT_EXACTNESS_GEN_HERMITE:
  Normal end of execution.
 
 7 September 2007  10:34:54.211 AM