CODEWITHSUNDEEP
matlabinterpolationlinear-interpolation
InfiniteVariance
InfiniteVariance

Reputation: 81

Matlab reversed 2d interpolation interp2

I have a function V that is computed from two inputs (X,Y). Since the computation is quite demanding I just perform it on a grid of points and would like to rely on 2d linear interpolation. I now want to inverse that function for fixed Y. So basically my starting point is:

X = [1,2,3];
Y = [1,2,3];
V =[3,4,5;6,7,8;9,10,11];

Is is of course easy to obtain V at any combination of (X,Y), for instance:

Vq = interp2(X,Y,V,1.8,2.5)

gives

Vq =

    8.3000

But how would I find X for given V and Y using 2d linear interploation? I will have to perform this task a lot of times, so I would need a quick and easy to implement solution.

Thank you for your help, your effort is highly appreciated.

P.

Upvotes: 3

Views: 2891

Answers (2)

InfiniteVariance
InfiniteVariance

Reputation: 81

Nras, thank you very much. I did something else in the meantime:

function [G_inv] = G_inverse (lambda,U,grid_G_inverse,range_x,range_lambda)



for t = 1:size(U,1)

        for i = 1:size(U,2) 

            xf = linspace(range_x(1), range_x(end),10000);
            [Xf,Yf] = meshgrid(xf,lambda);
            grid_fine = interp2(range_x,range_lambda,grid_G_inverse',Xf,Yf);
            idx = find (abs(grid_fine-U(t,i))== min(min(abs(grid_fine-U(t,i))))); % find min distance point and take x index
            G_inv(t,i)=xf(idx(1));

        end

end

G_inv is supposed to contain x, U is yq in the above example and grid_G_inverse contains Vq. range_x and range_lambda are the corresponding vectors for the grid axis. What do you think about this solution, also compared to yours? I would guess mine is faster but less accurate. Spped is, however, a major issue in my code.

Upvotes: 0

Nras
Nras

Reputation: 4311

EDIT using additional info

If not both x and y have to be found, but one of them is given, this problem reduces to finding a minimum in only 1 direction (i.e. in x-direction). A simple approach is formulating this in a problem which can be minizmied by an optimization routine such as fminsearch. Therefore we define the function f which returns the difference between the value Vq and the result of the interpolation. We try to find the x which minimizes this difference, after we give an intial guess x0. Depending on this initial guess the result will be what we are looking for:

% Which x value to choose if yq and Vq are fixed?
xq = 1.8; % // <-- this one is to be found
yq = 2.5; % // (given)
Vq = interp2(X,Y,V,xq,yq); % // 8.3 (given)

% this function will be minimized (difference between Vq and the result
% of the interpolation)
f = @(x) abs(Vq-interp2(X, Y, V, x, yq));
x0 = 1; % initial guess)
x_opt = fminsearch(f, x0) % // solution found: 1.8

Upvotes: 1

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