getting slope information from griddedInterpolant

Question

dominik 2014-1-30

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https://ww2.mathworks.cn/matlabcentral/answers/114286-getting-slope-information-from-griddedinterpolant

评论： Matt J 2014-1-31

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

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dominik 2014-1-31

编辑：dominik 2014-1-31

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 2014-1-31

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

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