1 September 2007   7:21:15.335 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_modified_x.txt".
  Quadrature rule W file = "lag_o16_modified_w.txt".
  Quadrature rule R file = "lag_o16_modified_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 = 1, modified rule:
    Integral ( A <= x < oo ) f(x) dx
    is to be approximated by
    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).
 
  Weights W:
 
  w( 1) =   0.2250363148642442    
  w( 2) =   0.5258360527623427    
  w( 3) =   0.8319613916870883    
  w( 4) =    1.146099240963750    
  w( 5) =    1.471751316966809    
  w( 6) =    1.813134687381348    
  w( 7) =    2.175517519694609    
  w( 8) =    2.565762750165028    
  w( 9) =    2.993215086371375    
  w(10) =    3.471234483102089    
  w(11) =    4.020044086444668    
  w(12) =    4.672516607732857    
  w(13) =    5.487420657986129    
  w(14) =    6.585361233289269    
  w(15) =    8.276357984364143    
  w(16) =    11.82427755165841    
 
  Abscissas X:
 
  x( 1) =   0.8764941047892792E-01
  x( 2) =   0.4626963289150808    
  x( 3) =    1.141057774831227    
  x( 4) =    2.129283645098381    
  x( 5) =    3.437086633893207    
  x( 6) =    5.078018614549768    
  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) =    34.58339870228663    
  x(15) =    41.94045264768833    
  x(16) =    51.70116033954332    
 
  Region R:
 
  r( 1) =    0.000000000000000    
  r( 2) =   0.1797693134862000    
 
  A Gauss-Laguerre rule would be able to exactly
  integrate monomials up to and including degree =       31
 
          Error          Degree  Exponents
 
        0.0000000000000027    0     0
        0.0000000000000000    1     1
        0.0000000000000002    2     2
        0.0000000000000003    3     3
        0.0000000000000001    4     4
        0.0000000000000002    5     5
        0.0000000000000001    6     6
        0.0000000000000002    7     7
        0.0000000000000000    8     8
        0.0000000000000003    9     9
        0.0000000000000003   10    10
        0.0000000000000003   11    11
        0.0000000000000003   12    12
        0.0000000000000004   13    13
        0.0000000000000006   14    14
        0.0000000000000006   15    15
        0.0000000000000003   16    16
        0.0000000000000003   17    17
        0.0000000000000004   18    18
        0.0000000000000006   19    19
        0.0000000000000002   20    20
        0.0000000000000004   21    21
        0.0000000000000003   22    22
        0.0000000000000003   23    23
        0.0000000000000004   24    24
        0.0000000000000002   25    25
        0.0000000000000003   26    26
        0.0000000000000002   27    27
        0.0000000000000000   28    28
        0.0000000000000002   29    29
        0.0000000000000002   30    30
        0.0000000000000002   31    31
        0.0000000016636708   32    32
        0.0000000274757781   33    33
        0.0000002335930469   34    34
        0.0000013619942618   35    35
 
INT_EXACTNESS_LAGUERRE:
  Normal end of execution.
 
 1 September 2007   7:21:15.360 PM