integrate.cc: Add a comment on the lack of symmetry of the "midpoint" integration method

git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinAnalysis/Multipole/trunk@103 4f5cb9a8-4dd8-4c2d-9bbd-173fa4467843

1 files changed, 7 insertions, 0 deletions

diff --git a/src/integrate.cc b/src/integrate.cc
index 1f64c29..93b61ee 100644
--- a/src/integrate.cc
+++ b/src/integrate.cc
@@ -41,6 +41,13 @@ CCTK_REAL Midpoint2DIntegral(CCTK_REAL const *f, int nx, int ny, CCTK_REAL hx, C
 
   assert(nx > 0); assert(ny > 0); assert (f);
 
+  // This sum should probably exclude the upper end points.  As
+  // currently implemented, it does not naturally map to the "sum of
+  // areas" definition of the integral, as there is an additional
+  // contribution from the last term in the sum.  This introduces an
+  // additional first order error to a method which is already only
+  // first order.
+
   for (iy = 0; iy <= ny; iy++)
     for (ix = 0; ix <= nx; ix++)
       integrand_sum += f[idx(ix,iy)];