6 February 2008  10:08:07.761 AM                                               
 
INT_EXACTNESS_JACOBI
  FORTRAN90 version
 
  Investigate the polynomial exactness of a Gauss-Jacobi
  quadrature rule by integrating weighted 
  monomials up to a given degree over the [-1,+1] interval.
 
INT_EXACTNESS_JACOBI: User input:
  Quadrature rule X file = "jac_o16_a0.5_b1.5_x.txt".
  Quadrature rule W file = "jac_o16_a0.5_b1.5_w.txt".
  Quadrature rule R file = "jac_o16_a0.5_b1.5_r.txt".
  Maximum degree to check =       35
  Exponent of (1-x), ALPHA =   0.500000    
  Exponent of (1+x), BETA  =    1.50000    
 
  Spatial dimension =        1
  Number of points  =       16
 
  The quadrature rule to be tested is
  a Gauss-Jacobi rule
  ORDER =       16
  ALPHA =   0.500000    
  BETA  =    1.50000    
 
  Standard rule:
    Integral ( -1 <= x <= +1 ) (1-x)^alpha (1+x)^beta f(x) dx
    is to be approximated by
    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).
 
  Weights W:
 
  w( 1) =   0.3988966638936207E-03
  w( 2) =   0.3198240298907031E-02
  w( 3) =   0.1159952258657551E-01
  w( 4) =   0.2865636008049065E-01
  w( 5) =   0.5581657557108236E-01
  w( 6) =   0.9183919887761288E-01
  w( 7) =   0.1324747827148990    
  w( 8) =   0.1710802448681879    
  w( 9) =   0.2000637064771614    
  w(10) =   0.2127999546344757    
  w(11) =   0.2054979111101689    
  w(12) =   0.1784862462090924    
  w(13) =   0.1365200311515025    
  w(14) =   0.8796492067198870E-01
  w(15) =   0.4301699747981774E-01
  w(16) =   0.1138273739868221E-01
 
  Abscissas X:
 
  x( 1) =  -0.9671984819405668    
  x( 2) =  -0.9040845839929046    
  x( 3) =  -0.8119779665780460    
  x( 4) =  -0.6938290260300457    
  x( 5) =  -0.5534333596595263    
  x( 6) =  -0.3953028602480263    
  x( 7) =  -0.2245197622496786    
  x( 8) =  -0.4657307825358586E-01
  x( 9) =   0.1328178890268011    
  x(10) =   0.3078873946321201    
  x(11) =   0.4730085776933708    
  x(12) =   0.6228743183404623    
  x(13) =   0.7526678154351841    
  x(14) =   0.8582174038957007    
  x(15) =   0.9361306362220502    
  x(16) =   0.9839033190008089    
 
  Region R:
 
  r( 1) =  -1.0000000000000000    
  r( 2) =   1.0000000000000000    
 
  A Gauss-Jacobi rule would be able to exactly
  integrate monomials up to and including degree =       31
 
          Error          Degree  Exponents
 
        0.0000000000002277    0     0
        0.0000000000002279    1     1
        0.0000000000002279    2     2
        0.0000000000002274    3     3
        0.0000000000002273    4     4
        0.0000000000002276    5     5
        0.0000000000002279    6     6
        0.0000000000002273    7     7
        0.0000000000002275    8     8
        0.0000000000002275    9     9
        0.0000000000002251   10    10
        0.0000000000002280   11    11
        0.0000000000002184   12    12
        0.0000000000002281   13    13
        0.0000000000002281   14    14
        0.0000000000002225   15    15
        0.0000000000002318   16    16
        0.0000000000002310   17    17
        0.0000000000002258   18    18
        0.0000000000002201   19    19
        0.0000000000002224   20    20
        0.0000000000002257   21    21
        0.0000000000002202   22    22
        0.0000000000002385   23    23
        0.0000000000002289   24    24
        0.0000000000002193   25    25
        0.0000000000002255   26    26
        0.0000000000002133   27    27
        0.0000000000002224   28    28
        0.0000000000002347   29    29
        0.0000000000002346   30    30
        0.0000000000002153   31    31
        0.0000000149732495   32    32
        0.0000000154003196   33    33
        0.0000001343179509   34    34
        0.0000001379400340   35    35
 
INT_EXACTNESS_JACOBI:
  Normal end of execution.
 
 6 February 2008  10:08:07.768 AM