MATLAB: Solving for an x value using ppval

fsolvefunctionsinterp1interpolationMATLABppvalunknown

I have created a linear piecewise function using interp1 which works beautifully given the x value. Is there a way for which I could solve for an x value given the Y value? Example:

 hotStreamInterp = interp1(B,Hhotpt, 'linear', 'pp')';
 x = fsolve(480 = ppval(hotStreamInterp, x_unknown));

How could I properly write this? Thank you.

Best Answer

It depends - if x and y are 1-1, you can just switch them in the above two lines. In general, however, there is probably more than one x value for a given y value. Then you'll have to decide whether you want x from a particular interval or all the values of x. If you know where the extrema in x are, you could interpolate in the intervals between extrema.

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MATLAB: How to use the ppval, pp and spline in this situation

Given data vectors x and y. f = spline(x, y) function returns a piecewise-polynomial which models the best relation (in the least square sense) f:x->y. After estimating the polynomial, if you want to find the value of y at some arbitrary value of x, you can just evaluate piecewise polynomial f at. In MATLAB you can use ppval function to evaluate the piecewise polynomial f.

MATLAB: Derivative of piecewise polynomial using ppval

Well, you could always use ppder. I've not looked at the code, but I imagine it might work.

For a cubic spline, a derivative is actually pretty easy to do, as just a matrix multiply. (For that matter any order spline in a pp form is trivial to differentiate.)

% pd is the polynomial degree of the polynomial segments,
% so for a spline created by spline, we have pd=3.
pd = 3; 
D = diag(pd:-1:1,1);
% given deriv as the order of the derivative to compute
% just loop
for i = 1:deriv
  pp.coefs = pp.coefs*D;
end

Untested code, but it should work.

Best Answer

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MATLAB: How to use the ppval, pp and spline in this situation

MATLAB: Derivative of piecewise polynomial using ppval

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