Defining equations with interpolant cfit model (ex. linearinterp, pchipinterp)

Question

Ho-Jun Suk 2016-2-20

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/269115-defining-equations-with-interpolant-cfit-model-ex-linearinterp-pchipinterp

评论： Benedikt Trolp 2017-11-12

采纳的回答： Anish Mitra

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Hi,

does anyone know how to define equations to be used in solve or vpasolve using interpolant cfit model?

I have pchipinterp (pchip_int_fn) and linearinterp (lin_int_fn) cfit models from my raw data and I want to define an equation like the following:

syms x y z
eqn = x*pchip_int_fn(x)*lin_int_fn(x) + y*pchip_int_fn(y)*lin_int_fn(y) + x*pchip_int_fn(z)*lin_int_fn(z) == 0
solve(eqn)

Matlab gives me an error message saying

"Error using cfit/subsref>iParenthesesReference (line 46)
Cannot evaluate CFIT model for some reason.
Error in cfit/subsref (line 16)
        out = iParenthesesReference( obj, currsubs );"

Does anyone know how to resolve this issue?

Thank you so much for your help!

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Answer 1

Anish Mitra 2016-2-24

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https://ww2.mathworks.cn/matlabcentral/answers/269115-defining-equations-with-interpolant-cfit-model-ex-linearinterp-pchipinterp#answer_211007

cfit objects do not work with inputs as symbolic variables. To work around this, you could re-write the cfit model equation using symbolic variables and then use it in 'eqn', instead of calling the cfit object.

The other option you could explore to find results for x,y,z is using the Optimization Toolbox, and minimizing the square of the value of 'eqn'. This would be a numerical optimization, and symbolic variables would not be used.

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Anish Mitra 2016-2-25

Yes, the first option would not be possible for piecewise polynomials. It would work for continuous functions (regular polynomials or exponentials).

Benedikt Trolp 2017-11-12

Hello Anish, I'm facing a similar Problem to the original poster, but having a hard time executing your second Option. Could you maybe explain it in Detail ? Thanks alot in advance

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