31 August 2007   4:57:54.270 PM                                                 
 
INT_EXACTNESS_LAGUERRE
  FORTRAN90 version
 
  Investigate the polynomial exactness of a Gauss-Laguerre
  quadrature rule by integrating exponentially weighted 
  monomials up to a given degree over the [0,oo) interval.
 
  The rule may be defined on another interval, [A,oo)
  in which case it is adjusted to the [0,oo) interval.
 
INT_EXACTNESS_LAGUERRE: User input:
  Quadrature rule X file = "lag_o16_x.txt".
  Quadrature rule W file = "lag_o16_w.txt".
  Quadrature rule R file = "lag_o16_r.txt".
  Maximum degree to check =       35
 
  Spatial dimension =        1
  Number of points  =       16
 
  The quadrature rule to be tested is
  a Gauss-Laguerre rule
  of ORDER =       16
  with A =      0.00000    
 
  OPTION = 0, standard rule:
    Integral ( A <= x < oo ) exp(-x) f(x) dx
    is to be approximated by
    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).
 
  Weights W:
 
  w( 1) =   0.2061517149578010    
  w( 2) =   0.3310578549508841    
  w( 3) =   0.2657957776442142    
  w( 4) =   0.1362969342963776    
  w( 5) =   0.4732892869412523E-01
  w( 6) =   0.1129990008033945E-01
  w( 7) =   0.1849070943526311E-02
  w( 8) =   0.2042719153082785E-03
  w( 9) =   0.1484458687398130E-04
  w(10) =   0.6828319330871197E-06
  w(11) =   0.1881024841079673E-07
  w(12) =   0.2862350242973883E-09
  w(13) =   0.2127079033224104E-11
  w(14) =   0.6297967002517869E-14
  w(15) =   0.5050473700035514E-17
  w(16) =   0.4161462370372855E-21
 
  Abscissas X:
 
  x( 1) =   0.8764941047892787E-01
  x( 2) =   0.4626963289150808    
  x( 3) =    1.141057774831227    
  x( 4) =    2.129283645098381    
  x( 5) =    3.437086633893207    
  x( 6) =    5.078018614549769    
  x( 7) =    7.070338535048235    
  x( 8) =    9.438314336391938    
  x( 9) =    12.21422336886616    
  x(10) =    15.44152736878162    
  x(11) =    19.18015685675314    
  x(12) =    23.51590569399191    
  x(13) =    28.57872974288214    
  x(14) =    34.58339870228664    
  x(15) =    41.94045264768835    
  x(16) =    51.70116033954334    
 
  Region R:
 
  r( 1) =    0.000000000000000    
  r( 2) =   0.1000000000000000E+31
 
  A Gauss-Laguerre rule would be able to exactly
  integrate monomials up to and including degree =       31
 
          Error          Degree  Exponents
 
        0.0000000000000001    0     0
        0.0000000000000002    1     1
        0.0000000000000004    2     2
        0.0000000000000002    3     3
        0.0000000000000002    4     4
        0.0000000000000007    5     5
        0.0000000000000007    6     6
        0.0000000000000004    7     7
        0.0000000000000013    8     8
        0.0000000000000011    9     9
        0.0000000000000016   10    10
        0.0000000000000022   11    11
        0.0000000000000027   12    12
        0.0000000000000031   13    13
        0.0000000000000038   14    14
        0.0000000000000040   15    15
        0.0000000000000042   16    16
        0.0000000000000047   17    17
        0.0000000000000044   18    18
        0.0000000000000047   19    19
        0.0000000000000042   20    20
        0.0000000000000040   21    21
        0.0000000000000036   22    22
        0.0000000000000033   23    23
        0.0000000000000036   24    24
        0.0000000000000036   25    25
        0.0000000000000033   26    26
        0.0000000000000036   27    27
        0.0000000000000042   28    28
        0.0000000000000049   29    29
        0.0000000000000058   30    30
        0.0000000000000064   31    31
        0.0000000016636638   32    32
        0.0000000274757702   33    33
        0.0000002335930378   34    34
        0.0000013619942516   35    35
 
INT_EXACTNESS_LAGUERRE:
  Normal end of execution.
 
31 August 2007   4:57:54.280 PM