getting slope information from griddedInterpolant

Hey when evaluating a griddedInterpolant, the computer should at some pont determine the slope of the interpolant at the query point. is there a way to modify the griddedInterpolant such that he not only provides the value at the query point but also the slope (without any additional computations).

i.e. instead of interpolant(x)=approximation(f(x)) interpolant(x)=approximation([f(x) f'(x)])

If not, does anyone have a handmade interpolant code that runs similarilye efficient?

Thanks

Dominik

[Matt J]

the computer should at some pont determine the slope of the interpolant at the query point.

I don't know if that can be assumed, even for linear interpolation. What if the computation is performed as follows?

t=(xquery-x(i))/(x(i+1) - x(i));

vi=t*v(i+1) + (1-t)*v(i);

Where is the slope, in the above? And what about for the non-linear interpolation options, e.g., 'cubic'?

[dominik]

Allright, the slope is not there but most of the calculation is done already (i assume the expensive bit is finding i, not accessing v or evaluating t or vi). All thats need to be done is (v(i)-v(i+1))/t.

Also it would be easy and not more expensive to rewrite your expression in terms of the slope.

For the spline i guess a similar point could be made (since you know the analytical expression of the interpolant between x(i) and x(i+t) you could evalute its analytical derivative at xquery) but im not sure.

But the question i guess is: can i edit the griddedInterpolant? No. So are there effieceintly coded interpolants available that can be adapted (ideally including spline and extrapolation)?

[Matt J]

There are a variety of interpolation routines on the FEX, which you could try to modify. There are also routines dedicated to splines and their derivatives, e.g.,

http://www.mathworks.com/matlabcentral/fileexchange/24996-spline-derivative

Answer 1

[Matt J]

griddedInterpolant is a built-in function and can't be modified.

Assuming you're talking about 1D interpolation, you can use this form of interp1 (see doc interp1)

 pp = interp1(...'pp');

to get the piecewise polynomial representing the interpolated data, and then apparently this FEX file

http://www.mathworks.com/matlabcentral/fileexchange/32401-splinederiv

to get derivatives, (though I haven't used it myself). Unfortunately, it appears that the above interp1 syntax is soon to be removed from MATLAB!

[dominik]

Thanks, unfortunatley i was speaking about the general case ( in my case 2D and 3D). Plus Interp1 is far to slow and uses griddedInterpolant.