[Octave-bug-tracker] [bug #30587] buggy implementation of bicubic interpolation in interp2/bicubic

[Thorsten Meyer]

URL:
  <http://savannah.gnu.org/bugs/?30587>

                 Summary: buggy implementation of bicubic interpolation in
interp2/bicubic
                 Project: GNU Octave
            Submitted by: tmeyier
            Submitted on: Thu 29 Jul 2010 08:53:54 AM UTC
                Category: Libraries
                Severity: 4 - Important
              Item Group: Incorrect Result
                  Status: None
             Assigned to: None
         Originator Name: Thorsten Meyer
        Originator Email: 
             Open/Closed: Open
         Discussion Lock: Any
                 Release: dev
        Operating System: GNU/Linux

    _______________________________________________________

Details:

while implementing regression tests for recent bug fixes in interp2, I came
across the following:

  A=[13,-1,12;13,-1,12;13,-1,12];
  x=[0,1,2]; y=[10,11,12];
  xi=linspace(min(x),max(x),17);
  yi=linspace(min(y),max(y),26)';

  interp2(x,y,A,xi,yi,'cubic')(1,:)

gives this:
ans =

 Columns 1 through 6:
   13.000000    9.773438    6.968750    4.585938    2.625000    1.085938
 Columns 7 through 12:
   -0.031250   -0.726562   -1.000000   -0.851562   -0.281250    0.710938
 Columns 13 through 17:
    2.125000    3.960938    6.218750    8.898437   12.000000

  in this case, the bicubic interpolation in bicubic.m is used and it gives
what I would naively expect, i.e., a parabolic fit to the three data points:

  pp=polyfit([0 1 2], [13 -1 12], 2);
  polyval(pp, linspace(0, 2, 17))

ans =

 Columns 1 through 6:

   13.000000    9.773438    6.968750    4.585937    2.625000    1.085937
 Columns 7 through 12:
   -0.031250   -0.726563   -1.000000   -0.851563   -0.281250    0.710937
 Columns 13 through 17:
    2.125000    3.960938    6.218750    8.898438   12.000000

Now, I wanted to try the other implementation of bicubic interpolation
directly within interp2, which is used for non-meshgrid xi and yi:

  interp2(x,y,A,[xi; xi], [10 * ones(size(xi)); [10 11*ones(1,
16)]],'cubic')(1,:)

And here, I get the following:
ans =
 Columns 1 through 7:
   13.00000   11.07227    8.89062    6.60742    4.37500    2.34570   
0.67188
 Columns 8 through 14:
   -0.49414   -1.00000   -0.71484    0.28125    1.82422    3.75000   
5.89453
 Columns 15 through 17:
    8.09375   10.18359   12.00000

The question is: which of the two implementations is right? 





    _______________________________________________________

Reply to this item at:

  <http://savannah.gnu.org/bugs/?30587>

_______________________________________________
  Message sent via/by Savannah
  http://savannah.gnu.org/