How to plot 3D plotting

I need help on how to plot the following 2D plot in to a 3D plot.

zspan=[0,400];
v0mat = [1 0.01 1];
zsol = {};
v1sol = {};
v2sol = {};
v3sol = {};

for k=1:size(v0mat,1)
  v0=v0mat(k,:);
  [z,v]=ode45(@rhs,zspan,v0);
  zsol{k}=z;
  v1sol{k}=v(:,1);
  v2sol{k}=v(:,2);
  v3sol{k}=v(:,3);
end

for k=1:size(v0mat,1)
    figure(1)
     plot(v2sol{k},zsol{k},'g')
     hold on 
       xlabel('Velocity,w')
       ylabel('Height, z')
      grid on     
end
function parameters=rhs(z,v)
            alpha=0.116; 
            db= 2*alpha-(v(1).*v(3))./(2*v(2).^2);
            dw= (v(3)./v(2))-(2*alpha*v(2)./v(1));
            dgmark= -(2*alpha*v(3)./v(1)); 
   parameters=[db;dw;dgmark];
  end

Answer 1

[Walter Roberson]

It wasn't clear what you wanted the z to be, so I guessed that it was the initial dw, which presumably later you will vary.

zspan = linspace(0,400,50);
v0mat = [1 0.01 1];
N = size(v0mat, 1);
zsol = cell(N,1);
v1sol = cell(N,1);
v2sol = cell(N,1);
v3sol = cell(N,1);
v2in = cell(N,1);
for k=1:size(v0mat,1)
  v0 = v0mat(k,:);
  [z,v] = ode45(@rhs,zspan,v0);
  zsol{k} = z;
  v1sol{k} = v(:,1);
  v2sol{k} = v(:,2);
  v3sol{k} = v(:,3);
  v2in{k} = v0mat(2) * ones(size(v2sol{k}));
end

all_z = [zsol{:}];
all_v2 = [v2sol{:}];
all_v2in = [v2in{:}];

plot3(all_v2, all_z, all_v2in);
xlabel('Velocity,w')
ylabel('Height, z')
zlabel('initial dw')

[Dereje]

Thanks a lot!!

[Dereje]

@Walter How can I convert the inputs into matrix so that I can do Surf plot. As it is,

surf (all_v2, all_z, all_v2in) couldn't work. 

[Walter Roberson]

What problem do you observe with the above surf() call? It appears to me to work.

Note that initial velocities (all_v2in) are inputs, and height (all_z) are inputs, and that your ode output is in all_v2, so you would normally have all_v2 in the third ("z") dependent-variable position.

[Dereje]

But it returns an error which says, Z must be a matrix, not a scalar or vector.

[Walter Roberson]

This is because you only have one row in v0mat so what should be 2D arrays are coming out as vectors.

Also, all of the interesting height (z_span) is between 0 and 2, and going up to 400 is losing all of the important information.

zspan = linspace(0,2,50);
v2in_vals = linspace(0.01,0.05,10);
v0mat = [1 0.01 1];

N = size(v0mat, 1);
zsol = cell(N,1);
v1sol = cell(N,1);
v2sol = cell(N,1);
v3sol = cell(N,1);
v2in = cell(N,1);
for k=1:length(v2in_vals)
  v0 = v0mat;
  v0(2) = v2in_vals(k);
  [z,v] = ode45(@rhs,zspan,v0);
  zsol{k} = z;
  v1sol{k} = v(:,1);
  v2sol{k} = v(:,2);
  v3sol{k} = v(:,3);
  v2in{k} = v0mat(2) * ones(size(v2sol{k}));
end
all_z = [zsol{:}];
all_v2 = [v2sol{:}];
all_v2in = [v2in{:}];

subplot(1,2,1);
plot3(all_v2, all_z, all_v2in);
xlabel('Velocity,w')
ylabel('Height, z')
zlabel('initial dw')

subplot(1,2,2)
v2in_vec = v2in_vals;
z_vec = all_v2(:,1);
surf(z_vec, v2in_vec, all_v2.')
xlabel('Height, z');
ylabel('initial dw');
zlabel('Velocity,w');