how to compute inverse of interpn function

I am looking for the inverse operation of interpn (VI=interpn(X1,X2,X3,X4,V,Y1,Y2,Y3,Y4)

[Y1,Y2,Y3,Y4] = inv_interpn(X1,X2,X3,X4,V,V1).

Y1,Y2,Y3,Y4 can be scalar, if only single solution exist. or it can be a vector is 2 or more solutions exist.

Linear interpolation between the grid points is good enough.

Please help me.

[Vijay Anand]

I further add to understand this problem. In 2D sense, if V = f(x1,x2) and to make it simple, V = x1 + x2.

Now, the matrix V looks like this.

The problem is, if we ask for x1,x2 values corresponding to say V = 5, there are infinite solutions exists. (1,4), (2,3), (1.1,3.9), (-5.5,10.5).

So, the right answer is anypoint on this line. Depending on the function V = f(x,y), this line may become a curve / spline. Even continuity of the curve is also not guaranteed !!!

So, for 2D problem, we are looking for a curve with some data points.

similarly, for a 3D problem, we are looking for a matrix ie a plane with data points...

Hope i made it clear.... cheers vijay

Answer 1

[bio lim]

This is how you should approach the problem. Let's study the case when V=5.

Let's say we generate 100 possible combinations of x1 and x2 that sum up to 5.

   x1 = zeros(200,1);
   x2 = zeros(200,1);

Now, we use an iteration to generate a random number, and we "scale" it.

   for i = 1:200
   rng shuffle
   X = rand(2,1,'double');
   V = 5;
   X  = X/sum(X)*V;
   X(1) = X(1) - (V-sum(X));
   x1(i) = X(1);
   x2(i) = X(2);
   end

If we plot the above,

figure(1)
grid on
plot(x1,x2,'-k');
title('V = 5')
xlabel('x1');
ylabel('x2');

We get: