Extrapolation

[nanfack...@yahoo.fr]

Hi!
does anyone knows how to do extrapolation in scilab?
best regards

[bruno]

What do you mean exactly ? Note that the function splin/interp,
splin2d/interp2d, splin3d/interp3d, linear_interpn, can be used
to extrapolate (but the results can be good only if you extrapolate
not far from the interpolation points).

In the interpX family there is an additionnal parameter to
precise the kind of evaluation outside the domain.

hth
Bruno

[nanfack...@yahoo.fr]

Hi bruno!
what I mean exactly is that I still facing some problems when trying to
extrapolate out of the bounds of interpolation points.When I use
splin/interp,splin2d/interp2d, splin3d/interp3d or linear_interpn,to
extrapolate, the result I can obtain is a horizontal line out of the
region of interpolation points. is there a way to solve this problem? I
guess I was clear enough.
best regards.

[thedarkclaw]

Hi guys.

I've faced a similar problem not so long ago, and what I did to solve
it was making my own version of interpolation without using any of
Scilab existing function, that, had the recurring problem of having a
limited range of action, when I was facing a problem with few data
points and great distances between them.

So what I did was basically this: (though there are probably more
efficent ways of doing this)

I had a distribution of the data points I knew in a list, coupled with
their x-y positions in a matrix like this:

datapoints=[value1, value2, value3; posx1, posx2, posx3; posy1, posy2,
posy3];

Then I define a function to get the distance between those points and
any arbitrary point I want to extrapolate their value. Something like
this: (xp & yp, are the positions of the extrapolate point)
p=4; // the higher the 'p', the less influence from distant points.
function out=dist(xp,yp,n)
out=abs( sqrt( ((xp-datapoint(2,n))^2+(yp-datapoint(3,n))^2)^(p)) );
endfunction

So now what?
I have a matrix whatever size I want (the bigger, the slower though)
that I want to extrapolate starting out from the points that I do know
the real value. So I make a cycle that starts, point by point, to
measure the distance to every known point of data, and then it makes a
weighted average of 'intensities' of them. So each known data point
contributes with a percentage to the extrapolation value depending on
how closer it is to the point to which we are extrapolating.
Something like this:

// Starts scanning the square matrix of dimensions msize*msize (it
doesn't need to be // a square matrix though)
data=ndgrid(zeros(1:msize),zeros(1:msize));
for n=1:nsize
data(datapoint(2,n),datapoint(3,n))=datapoint(1,n); // places the
known data points in
//to a blank matrix where we want to extrapolate the other points
end;
dataf=data; //the final matrix containing the extrapolated data
contrib=0;
ncontrib=0;
for xp=1:msize
for yp=1:msize
// Resets contrib counters
contrib=0;
ncontrib=0;
// Starts scanning the known data points (you need to supply the
number of data
// points you have)
for n=1:nsize
// checks if point is not itself
if dist(xp,yp,n)>0 then // (ie: the extrapolate point is not one
of the data points)
// sums up each different contribution from each different data
point with
// weighted inversely porpotional to distance and normalized
calc=(1/(dist(xp,yp,n))^2);
contrib=contrib+calc*Vp(n);
ncontrib=ncontrib+calc;
end;
end;
if data(xp,yp)==0 then
dataf(xp,yp)=dataf(xp,yp)+contrib/ncontrib; // this is the
extrapolate value
end;
end;
end;

And that's it basically. Hope I was clear enough, otherwise, ask again.
Hope it helps you out.

Pedro

[bruno]

Have you try to play with the outmode parameter of
the interp, interp2d, ... functions ? Here is an example
for splin :

// interpolation point
x = linspace(-0.5,0.5,5);
y = x.^2;
// spline coef
d = splin(x,y);

// evaluation in and out the domain
xx = linspace(-1,1,80)';
yy = interp(xx, x,y,d); // default outmode = "C0"
yy2 = interp(xx, x,y,d,"natural");
yy3 = interp(xx, x,y,d,"linear");

clf();
plot(x,y,"ko",xx,yy,"b",xx,yy2,"r",xx,yy3,"g");
legend("interp point","C0","natural","linear")

hth
Bruno

[bruno]

Hi,

may be the couple cshep2d and eval_cshep2d could have
been useful for you, have you tried it ? The help page
shows an example.

hth
Bruno

[nanfack...@yahoo.fr]

thaks a lot for your help.
you will be in touch if there is another problem.
Best regards.