how can I vectorize my code when multiple variables are present

Hi All,

This is a follow up to my previous question here.

I'm trying to figure out how to vectorize my code when multiple variables are present. The following is the toy model with odes for 2 variables (Please note the code may not make much sense, in my real system variables w and u are coupled. Also, in the actual system the number of variables in the model is uder-defined. For this reason, I am looping through the variables in the for-loop).

global mat1 mat2 k nvar var npts
k = 2;
nvar =2;
var = ["w", "x"];
npts=10;
mat1=[ 
       1    -2     1     0     0     0     0     0     0     0;
       0     1    -2     1     0     0     0     0     0     0;
       0     0     1    -2     1     0     0     0     0     0;
       0     0     0     1    -2     1     0     0     0     0;
       0     0     0     0     1    -2     1     0     0     0;
       0     0     0     0     0     1    -2     1     0     0;
       0     0     0     0     0     0     1    -2     1     0;
       0     0     0     0     0     0     0     1    -2     1;
       ];

mat2 = [
        1    -1     0     0     0     0     0     0     0     0;
        0     1    -1     0     0     0     0     0     0     0;
        0     0     1    -1     0     0     0     0     0     0;
        0     0     0     1    -1     0     0     0     0     0;
        0     0     0     0     1    -1     0     0     0     0;
        0     0     0     0     0     1    -1     0     0     0;
        0     0     0     0     0     0     1    -1     0     0;
        0     0     0     0     0     0     0     1    -1     0;
        ];


w0 = [2 0 0 0 0 0 0 0 0 0]';
x0 = [1 0 0 0 0 0 0 0 0 0]';
z0 = [w0; x0];
tspan = 0:0.01:0.5;

f0 = fun(0, z0);
joptions = struct('diffvar', 2, 'vectvars', 2, 'thresh', 1e-8, 'fac', []);
J = odenumjac(@fun,{0 z0}, f0, joptions); 
sparsity_pattern = sparse(J~=0.);
options = odeset('Stats', 'on', 'Vectorized', 'on'); %, 'JPattern', sparsity_pattern);

ttic = tic();
[t, sol]  =  ode15s(@(t,z) fun(t,z), tspan , z0, options);
ttoc = toc(ttic)
fprintf('runtime %f seconds ...\n', ttoc)
plot(t, sol)

function Zstruct = get_Zstruct(z)
global nvar var npts
    temp = reshape(z, npts, []);
    for i = 1:nvar
        Zstruct.(var(i)) = temp(:,i); 
    end
end

function dz = fun(t,z)
global nvar var mat1 mat2 
fprintf('size of z %d %d...\n', size(z))
dz = zeros(size(z), 'like', z);
Zstruct = get_Zstruct(z);

F =[];
for i = 1:nvar
x  = Zstruct.(var(i));
f = zeros(size(x), 'like', x);    
f(1,:) = 0;
f(2:9,:) = mat1*x + mat2*x;
f(10,:) = 2*(x(end-1) - x(end));
end
F(:,:) = vertcat(F,f);
end

I tried to check the size of z and it inconsistent for different function calls.

size of z 20 1...
size of z 20 20...
size of z 20 1...
size of z 20 1...
:
size of z 20 1...
size of z 20 1...
size of z 20 1...
size of z 20 20...

I'm sure the mistake is in the function Zstruct = get_Zstruct(z). I'm not sure how to vectorize here. Could someone please help me with this?

[Deepa Maheshvare]

Any suggestions?

[Walter Roberson]

    for i = 1:nvar
        Zstruct.(var(i)) = temp(:,i); 
    end

cell2struct() instead of the loop.

[Deepa Maheshvare]

@Walter Roberson I'm sorry, I didn't understand your comment completely .

temp is a double, sorry, I'm a bit confused how to use cell2struct() here. Also, I couldn't understand why the size of `z` varies from 20 x 1 to 20 x 20.

Answer 1

[darova]

Try to remove parenthesis

[Deepa Maheshvare]

when I try removing the paranthesis

Unable to perform assignment because the indices on the left side are not compatible with the size of the right side.

Error in cse_2_21_21>get_Zstruct (line 50)
        Zstruct.var(i) = temp(:,i);

Error in cse_2_21_21>fun (line 58)
Zstruct = get_Zstruct(z);

Error in cse_2_21_21 (line 34)
f0 = fun(0, z0);