[Octave-bug-tracker] [bug #29601] bugs in cubic and spline interpolation with interp2

[Thorsten Meyer]

URL:
  <http://savannah.gnu.org/bugs/?29601>

                 Summary: bugs in cubic and spline interpolation with interp2
                 Project: GNU Octave
            Submitted by: tmeyier
            Submitted on: Sun 18 Apr 2010 09:03:51 PM UTC
                Category: None
                Severity: 3 - Normal
              Item Group: Incorrect Result
                  Status: None
             Assigned to: None
         Originator Name: 
        Originator Email: 
             Open/Closed: Open
         Discussion Lock: Any
                 Release: dev
        Operating System: GNU/Linux

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Details:

There seem to be several bugs in the cubic and spline interpolation code of
interp2.

Reproduce with:
octave> demo interp2
[...]
interp2 example 7:
 A=[13,-1,12;5,4,3;1,6,2];
 x=[0,1,2]; y=[10,11,12];
 xi=linspace(min(x),max(x),17);
 yi=linspace(min(y),max(y),26)';
 mesh(xi,yi,interp2(x,y,A,xi,yi,'cubic'));
 [x,y] = meshgrid(x,y); 
 hold on; plot3(x(:),y(:),A(:),"b*"); hold off;

interp2 example 7: failed
mx_el_or: nonconformant arguments (op1 is 1x17, op2 is 26x1)
error: called from:
error:   /home/thorsten/hg/octave/scripts/general/interp2.m at line 352,
column 8

The offending line is
        inside = !(XI < X (1) | XI > X (end) | YI < Y (1) | YI > Y (end));

To me it seems that this works only if xi and yi are meshgrid data as well.
But this case is handled in the preceding conditional. Strange... Also
strange: the bicubic function can handle the input of the above example, i.e.
  mesh(xi,yi,bicubic(x,y,A,xi,yi));
works. So what is the purpose of the 2nd implementation of cubic
interpolation in interp2.m?

next failure of the demos:
[...]
interp2 example 8:
 [x,y,A] = peaks(10);
 x = x(1,:)'; y = y(:,1);
 xi=linspace(min(x),max(x),41);
 yi=linspace(min(y),max(y),41)';
 mesh(xi,yi,interp2(x,y,A,xi,yi,'cubic'));
 [x,y] = meshgrid(x,y); 
 hold on; plot3(x(:),y(:),A(:),"b*"); hold off;
interp2 example 8: failed
interp2: input data must have `meshgrid' format

Here, the data generated by peaks are not accepted as meshgrid data due to a
floating point problem. Also, the function isgriddata (defined in interp2.m)
seems to require not only equal lines in the grid matrix but also equally
spaced values. Is that intended (or really necessary?).

and the last failure in the demos:
interp2 example 9:
 A=[13,-1,12;5,4,3;1,6,2];
 x=[0,1,2]; y=[10,11,12];
 xi=linspace(min(x),max(x),17);
 yi=linspace(min(y),max(y),26)';
 mesh(xi,yi,interp2(x,y,A,xi,yi,'spline'));
 [x,y] = meshgrid(x,y); 
 hold on; plot3(x(:),y(:),A(:),"b*"); hold off;

interp2 example 9: failed
interp2: input data must have `meshgrid' format

Looking at the sources, the __splinen__ function that actually calculates the
interpolation is called only with the first row/column of the x and y
variables, so why require meshgrids here?

regards

Thorsten




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