1 May 2009   2:02:06.513 PM
 
PIECEWISE_LINEAR_PRODUCT_INTEGRAL_PRB
  FORTRAN90 version
 
TEST01
  Test PIECEWISE_LINEAR_PRODUCT_INTEGRAL on a very simple problem.
  F and G are both defined over a single common
  interval, so that F(X) = G(X) = X.
 
           A           B      Integral        Exact
 
      1.0000      1.0000     0.00000         0.00000    
      1.0000      2.0000     2.33333         2.33333    
      1.0000      3.0000     8.66667         8.66667    
      1.0000      4.0000     21.0000         21.0000    
      1.0000      5.0000     41.3333         41.3333    
 
TEST02
  Test PIECEWISE_LINEAR_PRODUCT_INTEGRAL on a simple problem.
  F and G are both defined over separate, multiple
  intervals, but still true that F(X) = G(X) = X.
 
           A           B      Integral        Exact
 
      1.0000      1.0000     0.00000         0.00000    
      1.0000      2.0000     2.33333         2.33333    
      1.0000      3.0000     8.66667         8.66667    
      1.0000      4.0000     21.0000         21.0000    
      1.0000      5.0000     41.3333         41.3333    
 
TEST03
  Test PIECEWISE_LINEAR_PRODUCT_INTEGRAL on a simple problem.
  F and G are defined over separate, multiple
  intervals.
 
  F(X) interpolates SIN(X),
  G(X) interpolates 2*COS(X).
 
  We compare:
 
  INTEGRAL, our value for the integral,
  QUAD, a quadrature estimate for the integral, and
  CLOSE, the value of the integral of 2*COS(X)*SIN(X)
 
           A           B      Integral        Quad            Close
 
      0.0000      0.0000     0.00000         0.00000        -0.00000    
      0.0000      0.5236    0.247447        0.247447        0.250000    
      0.0000      1.0472    0.743259        0.743259        0.750000    
      0.0000      1.5708    0.990786        0.990786         1.00000    
      0.0000      2.0944    0.743259        0.743259        0.750000    
      0.0000      2.6180    0.247447        0.247447        0.250000    
      0.0000      3.1416   -0.256739E-14    0.362637E-15    -0.00000    
 
TEST04
  Test PIECEWISE_LINEAR_PRODUCT_INTEGRAL.
  The nodes are at 0, 1, and 2.
  F(X) = ( 0, 1, 0 ).
  G(X) = ( 1, 0, 0 ).
 
  Integral F(X) * F(X) dx =   0.666667    
  Integral F(X) * G(X) dx =   0.166667    
  Integral G(X) * G(X) dx =   0.333333    
 
TEST04
  Test PIECEWISE_LINEAR_PRODUCT_INTEGRAL.
  F_X = ( 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ).
  F_V = F_X^2
  G_X = ( 0,    2,    4,    6,    8,    10 ).
  Compute projections of F onto G with 
  G_V = ( 0,    0,    0,    0,    0,     0 )
  except that the I-th value is 1.
 
         1    0.833333    
         2     9.66667    
         3     33.6667    
         4     73.6667    
         5     129.667    
         6     87.5000 
   
         1    0.833333    
         2     9.66667    
         3     33.6667    
         4     73.6667    
         5     129.667    
         6     87.5000    
 
PIECEWISE_LINEAR_PRODUCT_INTEGRAL_PRB
  Normal end of execution.
 
 1 May 2009   2:02:06.518 PM