MATLAB: Is there a search algorithm I can apply to a dataset that I do not have a specific F(x,y) function for

Question

Hello,

I am looking for the best search algorithm for the following set of data:

I have a set of temperature values T(x,y) which I want to find a minimum of; it is important to note that I do not have a specific function (such as T(x,y)= x^2+y^2), just the points. I haven't found a search function that works on raw data (without a function handle), but I'm a little out of my element so I may have misunderstood the documentation.

What I would like to do is to have the algorithm start at the maximum T value, then show the path it takes to the minimum T value. I want to be able to overlay the path on data for presentation. For what it's worth, the data is relatively well behaved, so there is a well defined global maximum and few peaks between the maximum and minimum.

Thank you for any direction you can offer,

Matt

Edit1: This does take place on a square grid.

Answer 1

To get a path between min and max, first find out which nodes are min and max, and then create a graph() representation of the system and use shortestpath() to find the way between them.

A key bit here is that you have to decide which nodes are connected to which. You did not say that you have a grid of points, so we as onlookers cannot assume that nodes are connected in any particular manner: in what you have given so far, it is not clear that the path could not simply go from max to min in one angled step.