在Matlab中可视化大量特征向量

Question

I have 6 matrices for which I am required to plot the eigenvectors . These matrices have dimensions from 20x20 to 320x320. I really do not know what would be the best (clearer) way to plot them. Is there any library available to your knowledge? I thought about reducing the dimension of each eigenvector but still, it would be a lot of work.

N = [40, 80, 160]; % Dimension 1-D grid

% Laplace operators
L1 = -1/((1/N(1))^2) * full( ( spdiags(repmat([1,-2,1], N(1)-1, 1), -1:1, N(1)-1, N(1)-1) ) );
L2 = -1/((1/N(2))^2) * full( ( spdiags(repmat([1,-2,1], N(2)-1, 1), -1:1, N(2)-1, N(2)-1) ) );
L3 = -1/((1/N(3))^2) * full( ( spdiags(repmat([1,-2,1], N(3)-1, 1), -1:1, N(3)-1, N(3)-1) ) );

These matrices are the Laplace operators associated to Poisson's equation. The aim is to visualize how the eigenvectors change when we change the dimension of the 1D grid I use to solve Poisson's equation.

Answer 1

As you have intuited, we cannot plot them the same way we would plot a 3D vector. If you want to visualize the spacial distance between eigenvectors, you could consider geometry preserving dimensionally reduction like isomap , but the simplest visualization, is to plot the dimensions of the eigenvectors.

First, let's get some eigenvectors. I use the same example as the eig documentation

A = gallery('lehmer',20)
[A_eig_vec, A_eig_val] = eig(A);

Then plot each column as a line. I also use multiple plots to avoid the plots getting too noisy with too many lines.

subplot(4, 1, 1);
plot(A_eig_vec(:, 1:5));

subplot(4, 1, 2);
plot(A_eig_vec(:, 6:10));

subplot(4, 1, 3);
plot(A_eig_vec(:, 11:15));

subplot(4, 1, 4);
plot(A_eig_vec(:, 16:20));

The result looks like this

You can see how the eigenvectors seem to capture different frequencies.