how do i plot the following in 3D

i have x and y which are matrices

i perform operations to get U which is a coulmn vector how do i plot it agaisnt x,y which are matices. the erro i get is that z must be a matrix not scalor or vector

x=-(ngrid/2:ngrid/2-1)*0.2
[X,Y]   =  meshgrid(x,x)
u%outputs coulmn vectors

my output U from my workspace is a coulu vector of 1x2001

[Cris LaPierre]

How does U relate to x and y?

[Tlotlo Oepeng]

u is a wave travelling on the xy plane, after a series of analytical computations i get an output coordnatres of u

[Walter Roberson]

u is complex-valued . If you plot real(u) against imag(u) it will fill an ellipse that has a ratio of about 10 : 6.4

In order to plot in three dimensions, you would need to be able to relate individual X and Y values to individual uCopy values.

[Tlotlo Oepeng]

ussually we use mesh(x,y,abs(U).^2) to plot in this case it gives error

'U must be matrix"

[Tlotlo Oepeng]

heres the code

%% -- Initialize variabels --
delta   = 0.4;                      % linear-loss coefficient
epsilon = 2.2;                      % cubic-gain coefficient
mu      = 1;                        % quintic-loss parameter 
v       = 0.1;                      % accounts for the quintic self-defocusing quantic nonlinearity
beta    = 0.5;                      % diffussivity term
D       = 1;                        % group-velocity dispersion
gamma   = 0;                        % accounts for the dispersion of the linear loss...
%% -- Define of Parameters --
ngrid   = 2001;                                        % number of grid
dt      = 0.1;                                         % change of time t
tmax    = 200;                                         % the maximum of time t
dx      = 0.2;                                         % step size in x
dy      = 0.2;                                         % step size in y
L       = 50;                                          % lenght of logitudinal space
ind     = (-ngrid/2:ngrid/2-1);                        % Indices
t       = 0:dt:tmax;                                   % temporal Grid
kt      = (2*pi/tmax)*[(0:ngrid/2) (-ngrid/2:-1)];     % temporal Grid in new domain using fftshift(so that wavw numbers correspond to
                                                         %variables..)
x       = ind*dx;                                      % Grid point along x
y       = ind*dy;                                      % Grid point along y
kx      = (2*pi/L)*[(0:ngrid/2) (-ngrid/2:-1)];        % Grid point along x in new domain using fft
ky      = (2*pi/L)*[(0:ngrid/2) (-ngrid/2:-1)]; 
[X,Y]   =  meshgrid(x,x)% Grid point along y in new domain using fft
%% -- ansatz--
U       = exp(-0.5.*x.^2-0.5.*y.^2-0.5.*t.^2);

%% -- Function Handles for RK4 Scheme--
fU      = @(U,z) (-delta+(i+epsilon).*(abs(U).^2).*U+(mu-i*v).*(abs(U).^4).*U);   
%% -- Initial Conditions --
z(1)    = 0;
%% -- Step Size --
dz      = 0.1;                  % change of z
h       = dz/2;                 % step size in z
zfinal  = 100;                  % final of z 
%% -- Update Loop --
for i = 1:ceil(zfinal/h)  
    % update time
    z(i+1) = z(i) + h;
    % update R & J
    k1 = fU( z(i)       ,  U(i)        );  % first slope
    k2 = fU( z(i)+h/2   ,  U(i)+h/2*k1 );  % second slope
    k3 = fU( z(i)+h/2   ,  U(i)+h/2*k2 );  % third slope 
    k4 = fU( z(i)+h     ,  U(i)+h*k3   );  % fourth slope
       
    U(i+1) = U(i) + h/6*(k1+2*k2+2*k3+k4);
end
%% -- Fourier Transform --
for z=1:zfinal
     u = U;
     c = fftshift(fft(u));                                               % apply Fourier transform
     c = exp(-h*((0.5*i+beta)*(kx.^2+ky.^2)+(0.5*i*D-gamma)*kt.^2)).*c;  % multiply by e^D
     u = ifft(fftshift(c));                                              % inverse Fourier
end
%% -- Plot --
figure (1);
mesh (x,y,abs(u').^2);

[Walter Roberson]

U       = exp(-0.5.*x.^2-0.5.*y.^2-0.5.*t.^2);

You need to rewrite U in terms of X and Y instead of x and y . But X and Y are 2D and probably not the same size as t, so you would need to reshape t into the third dimension, or

[X, Y, T] = meshgrid(x, x, t);
U         = exp(-0.5.*X.^2-0.5.*Y.^2-0.5.*T.^2);

But now U will be 3D and you need to summarize it down to 2D in order to use a surface plot.

    k1 = fU( z(i)       ,  U(i)        );  % first slope

That whole section would need to be rewritten in terms of U being 3D.

[Tlotlo Oepeng]

thank you ill try to di that

how do i accept answer?

Answer 1

[Walter Roberson]

[Copied from comment]

U       = exp(-0.5.*x.^2-0.5.*y.^2-0.5.*t.^2);

You need to rewrite U in terms of X and Y instead of x and y . But X and Y are 2D and probably not the same size as t, so you would need to reshape t into the third dimension, or

[X, Y, T] = meshgrid(x, x, t);
U         = exp(-0.5.*X.^2-0.5.*Y.^2-0.5.*T.^2);

But now U will be 3D and you need to summarize it down to 2D in order to use a surface plot.

    k1 = fU( z(i)       ,  U(i)        );  % first slope

That whole section would need to be rewritten in terms of U being 3D.