Question about two dimensional PCA analysis

Question

Jaime de la Mota 2018-6-19

0
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https://ww2.mathworks.cn/matlabcentral/answers/406367-question-about-two-dimensional-pca-analysis

编辑： Jaime de la Mota 2018-6-19

Hello everybody. I have a file containing wind data in directions S-N and W-E for some places and at some times denoted by latitudes and longitudes. I have written the following code:

if true
  clear all
close all 
clc
ncdisp('solicitud_31082016_00_12-60_ext.nc')
longitud = ncread('solicitud_31082016_00_12-60_ext.nc', 'longitude');
latitud = ncread('solicitud_31082016_00_12-60_ext.nc', 'latitude');
numero = ncread('solicitud_31082016_00_12-60_ext.nc', 'number');
tiempo =  ncread('solicitud_31082016_00_12-60_ext.nc', 'time');
mat_u = ncread('solicitud_31082016_00_12-60_ext.nc', 'u');
mat_v = ncread('solicitud_31082016_00_12-60_ext.nc', 'v');
mat_t = ncread('solicitud_31082016_00_12-60_ext.nc', 't');
latitudes = size (mat_u, 2);
longitudes=size (mat_u, 1);
for contador_latitudes = 1:latitudes
  for contador_longitudes =1: longitudes
      U =(squeeze(mat_u(contador_longitudes,contador_latitudes,:,:)))';
      V =(squeeze(mat_v(contador_longitudes,contador_latitudes,:,:)))'; 
      module=sqrt(U.^2+V.^2);
      t=size(V,1);
      num_realizations=size(V,2);
      Autocovariance=cov(module');
[eigenvectors,eigenvalues]=eig(Autocovariance);
[coeff, score, latent, tsquared, explained, mu]=pca(module,'Centered',false);T=score*coeff';TT=T';
useful_pcs=9;
coeff_global(:,:,contador_latitudes, contador_longitudes)=coeff;
score_global(:,:,contador_latitudes, contador_longitudes)=score;
tsquared_global(:,:,contador_latitudes, contador_longitudes)=tsquared;
explained_global(:,contador_latitudes, contador_longitudes)=explained;
mu_global(:, contador_latitudes, contador_longitudes)=mu;
  end
end
end

However, I don't want to know just the module of the wind velocity for all these places at all these times. I want to know what is the relationship between both directions and not just the variation of the module of the wind.

Can someone please tell me how to do that?

Edit: I want to see not the unidimensional eigenvectors, instead I want to visualize a surface with the eigenvectors in both directions.

Thanks