How to preserve 2-d initial conditions after passing it into ode45?

Hi,

I pass 2d initial conditions, but ode45 linearizes it and makes the matrix into a 1-d array. How do I ensure it is handled as a 2-d array?

I have the following:

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N=60;
x(1:N, 1:2*N) = 0; x(20,20)=1;
options = odeset('RelTol',1e-7);

[t1 y] = ode45('fputest1', [0:L:t], x, options, N);

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x is a 60x120 matrix. When I step through the code in ode45, x is a 7200 x 1, 1-d array. How do I ensure x remains a 2-d matrix? Also what are the dimensions of y, when the solver has finished? Is it 2-d if x is an array? What is it in the case x is a 2-d matrix?

Answer 1

[Walter Roberson]

When I step through the code in ode45, x is a 7200 x 1, 1-d array. How do I ensure x remains a 2-d matrix?

To do that, write your own version of ode45. The Mathworks version will always pass in the boundary conditions as a column vector.

Most people deal with the situation by simply reshape() the input almost immediately.

Also what are the dimensions of y, when the solver has finished?

y will be length(t1) by numel(x).

Your function is required to return a column vector that is numel(x) by 1, and integrated versions of that column will become rows of the output.

What is it in the case x is a 2-d matrix

Then y will be length(t1) by numel(x).

You can reshape y afterwards, such as

yperm = permute(reshape(y, length(t1), size(x,1), size(x,2)),[2 3 1]);

and now yperm(:,:,iteration) will be the 2D results at time t1(iteration)

[savitha muthanna]

Thanks so much. I will try it right away. And it works well, after a few reshapes!

I have a associated question. I want to plot the yperm. For each iteration,i.e., for each time t, I would like to plot (x,y). How can I do that? Would you recommend a 3d plot? Or what sort of plot would you recommend?,

[Walter Roberson]

For plotting over time, use the original y you got back, not the permute() version

plot(t,y)

That will create one line for each derivative.

If you want a 3d plot then you need a vector of values associated with either the rows or columns of x, such as for the case where you are processing ode45 for a range of parameter values.

[savitha muthanna]

Thanks so much. If i want to plot say for each time, t, a 3-d plot, with rows (1:60), columns (1:120), do I need to create a vector of corresponding y values. If so, does it need to go row by row or column by column? And if I do so, can i then call surf on it? Or would you recommend a different 3-d plot?

for i=1:t1

surf(1:60,1:120,y values for each i)

[Walter Roberson]

for i = 1 : size(yperm,3)
   surf(yperm(:,:,i), 'edgecolor', 'none');
   pause(1);
end

or

volumeViewer(yperm)

[savitha muthanna]

Thanks so very much!