Problem with derivation of equation

This problem is somewhat getting a method to automatically produce a function from basically three variables, so far I couldn't get my head around it. I have 2 vectors and a quantity of MxN with, which is dependent on the x,y vectors

 x=[0:1:18];
  y=[0:1:2];
  quantity=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;
    0,0,0,0,49,73,85,86,83,78,82,67,63,59,0,0,0,0,0;
    0,0,0,54,136,193,205,196,182,187,153,142,132,123,0,0,0,0,0];

I am trying to find a way to link all of them into an equation of some sorts, so when a new set of values x,y (which have values within the original x,y lengths), so I can get the same result for quantity as in the original matrix. Basically trying to figure out a way in matlab to link the x,y with the quantity as a final result.

Any idea would help

thanks in advance

Answer 1

[Walter Roberson]

https://www.siam.org/students/siuro/vol1issue1/S01002.pdf

Answer 2

[John D'Errico]

help interp2

But no, you cannot have some simple equation that will interpolate the entire array, and be simple to write down. There is none.

[George]

Hello just a quick follow up. the interp2 function helped me to achieve the interpolation I wanted.

As you pointed out though a simple equation is not possible though if case adjusted it can provide some alternatives, for getting results by a new set of x,y values that agree with the analytical solutions.

Again thanks for the help

[Walter Roberson]

interp2 is not going to produce an equation which is what you had requested. The multivariate Lagrange interpolation I linked to would be for producing an equation .

Most of the time you do not really want an equation: most of the time you want a function and interp2() can be an important component of the function.

But if you do want a function then you should look at triscatteredinterp and similar routines such as scatteredInterpolant which will produce a function that can then be evaluated at arbitrary points, or you can look at griddata() if you are wanting to interpolate a grid of values over a different grid.