Nir,
Setup two one dimensional variables, y1 and y2 and a 2-D variable y
with the same points. In this case a circle with the 5th point equal
to the first. Run csape with the periodic condition and then inspect
the structures produced. y should yield the same coefficients as y1
and y2, just stacked into an array:
>>> x = linspace(0, 2*pi, 5);
>>> y1 = cos(x);
>>> y2 = sin(x);
>>> pp1 = csape(x, y1, 'periodic');
>>> pp2 = csape(x, y2, 'periodic');
>>> y = [y1; y2];
>>> pp = csape(x, y, 'periodic');
>>> pp1.P
ans =
0.12901 -0.60793 0.00000 1.00000
0.12901 0.00000 -0.95493 0.00000
-0.12901 0.60793 0.00000 -1.00000
-0.12901 0.00000 0.95493 -0.00000
>>> pp2.P
ans =
-0.12901 -0.00000 0.95493 0.00000
0.12901 -0.60793 0.00000 1.00000
0.12901 -0.00000 -0.95493 0.00000
-0.12901 0.60793 -0.00000 -1.00000
>>> pp.P
ans =
-0.12901 -0.00000 -0.31831 1.00000
0.12901 -0.60793 -0.00000 0.00000
0.12901 -0.00000 0.31831 -1.00000
-0.12901 0.60793 0.00000 -0.00000
0.00000 0.00000 0.63662 0.00000
0.00000 0.00000 -0.63662 1.00000
0.00000 0.00000 -0.63662 0.00000
0.00000 0.00000 0.63662 -1.00000
As you see they are quite different. This is from a saved session
using spline 1.0.7, but I have had similar results with the latest
splines 1.1.0. Actually, it looks like the only thing that has changed
between 1.0.7 and 1.1.0 is the function mkpp now has different
filednames. The latest edit noted in the comments of csape.m is Feb.
19th 2001 in both versions.
All this is easy to see in a plot of the points overlaid with the
splines too:
>>> xpp = linspace(0, 2*pi, 201);
>>> plot(y1, y2, 'ko', ppval(pp1, xpp), ppval(pp2, xpp), 'b-')
>>> figure
>>> yy = ppval(pp, xpp);
>>> plot(y(1,:), y(2,:), 'ko', yy(1,:), yy(2,:), 'b-')
Now, after editing csape.m per my recommendation:
>>> pp = csape(x, y, 'periodic');
>>> pp.P
ans =
0.12901 -0.60793 0.00000 1.00000
0.12901 0.00000 -0.95493 0.00000
-0.12901 0.60793 0.00000 -1.00000
-0.12901 0.00000 0.95493 -0.00000
-0.12901 -0.00000 0.95493 0.00000
0.12901 -0.60793 0.00000 1.00000
0.12901 -0.00000 -0.95493 0.00000
-0.12901 0.60793 -0.00000 -1.00000
Just looking at idx in csape.m ( idx = ones (columns(a),1); ), you can
see that using it in a matrix index on the left side of an equation
makes no sense anyway.
Ted
On Nov 21, 2012, at 1:09 PM, Nir Krakauer wrote:
> Dear Ted,
>
> Can you give an example where it fails?
>
> Nir
>
> On Wed, Nov 21, 2012 at 3:25 AM, Ted Rippert <ted.ripp...@gmail.com>
> wrote:
>> csape(x, y, "cond") with a boundary condition of "periodic" will work
>> for a one dimensional vector, but not for a matrix value for y. This
>> is fixed by changing line 162 in csape.m from:
>>
>> c(2:n,idx) = z(:,2:end) - z(:,1) * fact;
>>
>> to:
>>
>> c(2:n,:) = z(:,2:end) - z(:,1) * fact;
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