How to create a matrix from a for loop answer?

Hello,

I was wondering how i would create a matrix out of solutions from a for loop. Im trying to plot a meshgrid/surface and i need the final results to be a matrix to do this. Any thoughts on how i could make that happen?

Here is the code giving me trouble

%--Solving for radius to see if BC's are hit--%
      radius = sqrt(x.^2 + y.^2);

        if radius >=1
            A = sin(theta);
        elseif radius < 1
            A = 0;
        end

        sol = A;

mesh(X,Y,sol)

All of the code if below.

clear;
clc;

%--Number of simulations--%
n = 100; 
sol = zeros(1,n);
y = zeros(1,n);
x = zeros(1,n);

%--Plot of the circle--%
figure(1)
clf;
syms p
bc = sin (p);
bc2 = cos (p);
Range = [0 2*pi];
subplot(211);
h = ezplot(bc,bc2,[Range]);
hold on

[X,Y] = meshgrid(-1:0.1:1);

% 
Nsamples    = 5;
distance   = zeros(n,Nsamples);
circle      = zeros(n,Nsamples);
delta = 0.1;

for t=1:n

      %--Monte Carlo Random Walk--%
      monte = randi(4,1);
      if monte == 1
          y = y + delta;
      elseif monte == 2
          y = y - delta;
      elseif monte == 3
          x = x + delta;
      elseif monte ==4
          x = x - delta;
      end

      %--Applying BC if sin is btween pi and 2pi--%
      %--Applying it by not allowing y >= 0--%
      if y < 0
          y = 0;
      end

      %--Calculating Theta for the BC--%
      theta = atan(y./x);

       %--Solving for radius to see if BC's are hit--%
      radius = sqrt(x.^2 + y.^2);

      if radius >=1
          A = sin(theta);
      elseif radius < 1
          A = 0;
      end

      sol = A;

      %--Plotted walk on a circle plot--%
      subplot(211);
      plot(x,y,'.b');

      sol;

end

   %--Plotting Surface of Solution--%
          figure(2)
          mesh(x,y,sol)

Answer 1

[Walter Roberson]

You are initializing

y = zeros(1,n);
x = zeros(1,n);

which is good, but then in the code you have (for example)

y = y + delta;

which is going to affect all of y, not just the t'th y. You need to fix that.

Your x and y values that come out will be vectors that are scattered around, not a regular grid. You can only use mesh() when the x and y represent grids. If you want a gridded surface then you should look at triscatteredinterp() or the newer griddedinterpolant()

[Walter Roberson]

Mike commented,

Oh I didn't realize that I made that typo. The mesh was supposed to look like mesh(X,Y,sol) and not mesh(x,y,sol).

The issue I keep having is that sol is a vector and not a matrix. How would I go about making the sol a matrix?

Does it have anything to do with my initial intilization of sol=zeros(1,n)?

[Walter Roberson]

If you want a gridded surface then you should look at triscatteredinterp() or the newer griddedinterpolant(). Or even griddata()

It has nothing to do with your original initialization of sol; that initialization is correct. The problem is that your points are not gridded: you have x(t), y(t), sol(t) as a single 3-space path, but mesh() needs a sol(i,j) for every possible x(i), y(j) pair.

What, by the way, do you want to do when the path returns to the same grid location?

Also have you considered using atan2(y, x) instead of atan(y/x) ?

[Mike]

No i haven't considering using atan2 vs atan. To be honest i'm still learning MATLAB so some of this stuff isn't so obvious.

I will try using a gridded surface in place of the meshgrid.

Also i'm not sure i understand the question "what do you want to do when the path returns to the same grid location?" Could you elaborate?

Answer 2

[RAGHAVENDRA]

In addition to the Walter Roberson’s advice. I would like to say that. As per your program at line 45: if y<0 y=0; end The resulting y will be a single value(1X1 vector) . This will result in an error. Hence you need to fix that also.

[Mike]

How would you recommend that being fixed?

I was trying to satisfy a boundary condition with that line. However i think my biggest problem in all of this was the code:

%--Plotting Surface of Solution--%
          figure(2)
          mesh(x,y,sol)

Those x,y values are supposed to be capitalized rather than smaller case. I just need X and Y to be a small range and not the values i was computing before. Hence why i wrote:

[X,Y] = meshgrid(-1:0.1:1);

Think by changing all of that i would still have an issue?