Find path along steepest gradient in an array

I want to find the path along the steepest gradient in an array of data points. I started using the 'diff function' and the 'for loop' to get information about the maximum difference between two data points. I got stuck. Would be great if someone know how to do that. Attached is the data file.

[KSSV]

Can you tell me what do you mean by path along steepest gradient? A pictorial demo of the path will be helpful..

[Phil A]

I plotted the data attached. They are depth in meters. The cyan lines are paths. Now I want to add another path that runs along the the steepest gradient. For example, I start at the deepest point, e.g. -680 meter. From there I want to pick the point next to it with the greatest difference in these points. So if the neighbored points are -650m, -658m, and -656m I want to chose -650m because -680m - (-650m) = -30m which is the greatest difference between the stated points. Did that make it more clear?

[Jan]

Do you want to consider the 4 surrounding points, or the 8 points including the diagonally neighboring elements?

If the matrix is a real measurment, the method of the steepest descent will probably end in a local maximum cause by noise. It is not really useful to create a simple code, which checks the values of the direct neighbors only, but fitting the local neighborhood by a polynomial and a line-search algorithm might be more stable.

[Phil A]

Also the diagonally points.

Answer 1

[John D'Errico]

You have what appears to be a complete surface, a noisy one, but still.

Why cannot you just use a tool like gradient to compute gradients at any point. Then use quiver to show the lines of steepest descent? Effectively, the direction of steepest descent at any point is simply the negative gradient. That also gives you local magnitude of the gradient, so the length of the vector will show the size of the local descent.

Since it seems a bit noisy, you might wish to smooth the surface first a bit. There are many smoothing tools available.