How to plot a surface of vector z in a 2D grid made of vectors x and y?

I have a vector z which consists of function values defined on a 2D plane. I do not know the function though. I have tried interpolation with griddata and reshape to get z into a matrix but nothing seems to work. Perhaps I'm doing something fundamentally wrong so that's it's impossible to get the result I want? Help is much appreciated!

N = 100;              % Amount of grid points
L = 1;                % System extends from -L/2 to L/2
h = L/(N-1);          % Grid step size
x = h*(0:N-1) - L/2;  % Coordinates of grid points
y=x;

coeff = -1/((pi)^2*h^2) ;
coeff = ones(100,1)*coeff;
B=[coeff coeff -4*coeff coeff coeff];
H=spdiags(B,[-3 -1 0 1 3],N,N);

[V,D]=eigs(H,N);

z=V(:,100);

[X,Y] = meshgrid(x,y) ;
Z = reshape(z,size(X)) ;
figure
surf(X,Y,Z)

EDIT: As far as I know my problem lied in the construction of the matrix 'H'. It does not yield eigenvectors that are a lengthy enough to define a surface over the entire grid. For this you need a rank 3 tensor I think. Though I use the kronecker tensor product 'kron' to get all the same spacial information into a second order tensor. This way the eigenvectors are of correct size to 'reshape' them over the grid.

%---Set up the Hamiltonian operator matrix
coeff = -h_bar^2/(2*mass*h^2) ;
I=speye(N,N);
o=ones(N,1);
t=-2*ones(N,1);
D=spdiags([o t o] ,[-1 0 1],N,N);
H=kron(D,I).*coeff+kron(I,D).*coeff;

[Star Strider]

To get a general idea of the problem, do this:

figure
stem3(x, y, z)
grid on
view(-65,45)

[Ivan Verstraeten]

I see, thank you! So is this vector does not contain information in 3D? Is it even possible to get a vector that does out of a matrix then?

[KALYAN ACHARJYA]

Both, there are 2D or 3D vectors and all matrices are vectors.

[Star Strider]

My pleasure!

It does contain information in 3D, however the ‘z’ vector is not randomly distributed with respect to the ‘x’ and ‘y’ coordinates, as griddata requires.

I am not certain what you are doing. I am not certain you can create a surface from ‘z’.

[Ivan Verstraeten]

I'm trying to plot the eigenvectors of a particle in a 2D potential well; the eigenvectors of the hamiltonian 'H'.

Answer 1

[Star Strider]

I am not certain what you want the plots to look like, since I am not at all familiar with what you are doing.

Try this:

figure
mesh(X,Y,D)
figure
mesh(X,Y,V)

See if one of those does what you want.

[Ivan Verstraeten]

It's in the alley but I only want to plot one columnvector of 'V'. It should (I'm hoping) be a surface in 3D space. Something like the image below (for V(:,99)). (This is not made with the code I posted before ofcourse)

[Star Strider]

The problem is that ‘V(:,99)’ would only plot one column vector (as you noted), not a surface. You are doing something that iis vary far from my areas of expertise, so if you have an paper or online reference explaning (in very basic terms) what you are doing, I might be able to help. (Otherwise, I will eventualy delete my Answer as not actually being one, and hope that someone who understands what you are doing sees this and responds.)

[Ivan Verstraeten]

Here is some background:

http://www.scielo.org.mx/pdf/rmfe/v54n2/v54n2a3.pdf

https://cmt.uantwerpen.be/numericalmethods/files/P11/practicum11_EN.pdf

But only read it if you have the time for it and/or really want to :) , because I think my problem can be narrowed down to 'plotting a surface of a column vector' (if it's possible with what I have). I was actually following the answer to basically the same question:https://nl.mathworks.com/matlabcentral/answers/412639-creating-surface-plot-from-a-matrix-with-3-columns

But the 'reshape' command gives the error: 'To RESHAPE the number of elements must not change'.