How to back interpolation to find x from z and y?

Question

ercan duzgun 2017-2-15

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评论： ercan duzgun 2019-8-15

I would like to do "back" interpolation to find an x value from the given values of z and y. (2Dimensional x,y,z matrix table is available). Is there any prepared MATLAB function for it?/ And how to do it in Simulink(Lookup Table Dynamic block is for 1D. I need 2D)?

As an example: x =[01 2 3 4 5]; y=[ 30 40 50 60]

z=[
2  3  4  5
4  5  6  7
6  7  8 10
8 10 10 13]

Table=

       1  2  3  4  5
      ---------------
  30 ! 1  2  3  4  5
  40 ! 3  4  5  6  7
  50 ! 5  6  7  8 10
  60 ! 7  8 10 10 13

According to this given values, I would like to find the x value for a given data of y=43, and z=6.8

Thanks in advance.

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Stephen23 2017-2-21

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ercan duzgun 2017-2-15

Thank you. Yes, this works.

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Answer 2

John D'Errico 2017-2-15

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Is there something already written in MATLAB to do this? No. Given that your problem is not terribly common, it would be unexpected if it was already written.

Is it possible to do? Yes. Not even that terribly difficult.

You have an array that essentially defines the relation z(x,y).

1. Use interp2 to interpolate the array along the line y = 43, so for each value of x, determine z at the given y value. The result will be a vector of z values, one for each location in x.

2. Find any pairs of locations that cross the desired z level.

3. Interpolate linearly to find x that yields the given z level exactly. (Well, exactly to within the accuracy of linear interpolation.)

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ercan duzgun 2017-2-15

Thank you. Nice programming algorithm.

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Answer 3

Phillip Resor 2019-8-14

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在 MATLAB Online 中打开

Just sorted this out using griddedInterpolant and thought others might find it useful

x = [1,2,3,4,5];
y = [30,40,50,60];
[X, Y] = ndgrid(x,y);
Z = [1,2,3,4,5;3,4,5,6,7;5,6,7,8,10;7,8,10,10,13]'; % transpose to match ndgrid
yp = 43;
zp = 6.8;
F = griddedInterpolant(X, Y, Z);
fun = @(xp)F(xp,yp)-zp;
xp = fzero(fun,mean(x))