Find path along steepest gradient in an array

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Phil A 2017-8-23

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编辑： John D'Errico 2017-8-23

icebase_79NG_area.mat

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.

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Jan 2017-8-23

编辑：Jan 2017-8-23

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 2017-8-23

Also the diagonally points.

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Answer 1

John D'Errico 2017-8-23

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编辑：John D'Errico 2017-8-23

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.