21 January 2009   3:59:14.126 PM                                                
 
INT_EXACTNESS_LEGENDRE
  FORTRAN90 version
 
  Investigate the polynomial exactness of a Gauss-Legendre
  quadrature rule by integrating weighted 
  monomials up to a given degree over the [-1,+1] interval.
 
INT_EXACTNESS_LEGENDRE: User input:
  Quadrature rule X file = "gp_o15_x.txt".
  Quadrature rule W file = "gp_o15_w.txt".
  Quadrature rule R file = "gp_o15_r.txt".
  Maximum degree to check =       25
 
  Spatial dimension =        1
  Number of points  =       15
 
  The quadrature rule to be tested is
  a Gauss-Legendre rule
  ORDER =       15
 
  Standard rule:
    Integral ( -1 <= x <= +1 ) f(x) dx
    is to be approximated by
    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).
 
  Weights W:
 
  w( 1) =   0.1700171962994026E-01
  w( 2) =   0.5160328299707975E-01
  w( 3) =   0.9292719531512456E-01
  w( 4) =   0.1344152552437842    
  w( 5) =   0.1715119091363914    
  w( 6) =   0.2006285293769890    
  w( 7) =   0.2191568584015875    
  w( 8) =   0.2255104997982067    
  w( 9) =   0.2191568584015875    
  w(10) =   0.2006285293769890    
  w(11) =   0.1715119091363914    
  w(12) =   0.1344152552437842    
  w(13) =   0.9292719531512456E-01
  w(14) =   0.5160328299707975E-01
  w(15) =   0.1700171962994026E-01
 
  Abscissas X:
 
  x( 1) =  -0.9938319632127550    
  x( 2) =  -0.9604912687080204    
  x( 3) =  -0.8884592328722570    
  x( 4) =  -0.7745966692414834    
  x( 5) =  -0.6211029467372264    
  x( 6) =  -0.4342437493468025    
  x( 7) =  -0.2233866864289669    
  x( 8) =    0.000000000000000    
  x( 9) =   0.2233866864289669    
  x(10) =   0.4342437493468025    
  x(11) =   0.6211029467372264    
  x(12) =   0.7745966692414834    
  x(13) =   0.8884592328722570    
  x(14) =   0.9604912687080204    
  x(15) =   0.9938319632127550    
 
  Region R:
 
  r( 1) =  -1.0000000000000000    
  r( 2) =   1.0000000000000000    
 
  A Gauss-Legendre rule would be able to exactly
  integrate monomials up to and including degree =       29
 
          Error          Degree
 
        0.0000000000000000    0
        0.0000000000000000    1
        0.0000000000000002    2
        0.0000000000000000    3
        0.0000000000000003    4
        0.0000000000000000    5
        0.0000000000000004    6
        0.0000000000000000    7
        0.0000000000000004    8
        0.0000000000000000    9
        0.0000000000000005   10
        0.0000000000000000   11
        0.0000000000000009   12
        0.0000000000000000   13
        0.0000000000000008   14
        0.0000000000000000   15
        0.0000000000000009   16
        0.0000000000000000   17
        0.0000000000000012   18
        0.0000000000000000   19
        0.0000000000000013   20
        0.0000000000000000   21
        0.0000000000000014   22
        0.0000000000000000   23
        0.0000000674363268   24
        0.0000000000000000   25
 
INT_EXACTNESS_LEGENDRE:
  Normal end of execution.
 
21 January 2009   3:59:14.131 PM