Singular Value Decomposition of a Large XYZ file

Hi everyone, I need to perform Singular Value Decomposition on a XYZ file (surface scan file with 3 columns and millions of row) to simplify the surface. In the papers I have checked in the literature, they present a 2D picture (x-z base) colouring with amplitude (y-height), and state that the fluctuating surface elevation of the surface y(x,z) should be decomposed. Any idea how to turn very narrow randomly lined xyz values into a matrix that we can implement SVD? Cheers.

Answer 1

[Christine Tobler]

First thing that occurs to me would be to interpolate the xyz data to lie on a rectangular grid in the x-z plane, and to then apply SVD to the resulting matrix (millions of rows should translate to a number of rows and columns in the thousands?).

Here is a doc example for how to interpolate xyz-data on a grid.

[Oguzhan M]

Thanks for the prompt response. When I interpolate xyz data, I get 3 matrices as expected. Should I apply SVD to x and z matrices separately to reduce number of points, if yes, how can I re-combine new x and z matrices with y matrix (unchanged) to achieve the complete simplified surface? Thanks, Oguzhan.

Answer 2

[Christine Tobler]

The way I thought of it was to use x and z as the 2d grid on which to interpolate, and y as the function value. Something like this:

 x = randn(10, 1); y = randn(10, 1); z = randn(10, 1);
 [xi,zi] = meshgrid(linspace(-1, 1), linspace(-1, 1));
 yi = griddata(x,z,y,xi,zi); % yi is a matrix with the values of y interpolated on the grid (xi, zi)

In this case, you would do SVD of the yi data, I think?

[Oguzhan M]

Sorry for the late response. You were right! SVD should be applied on yi then the final matrix can be re-composed using orthogonal matrices and inverse of the diagonal matrix. I'm now facing "out of memory error", which does not make any sense to me as there is a lot more RAM on my PC than matlab requires. .Anyways, I'll raise it on another topic. Thanks, Oguzhan.