Issue while computing jacobian

Hi All,

This is a follow up to my question posted here. I'm trying to find the sparsity pattern of a jacobian in the following code

global mat1 mat2
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;
        ];



x0 = [1 0 0 0 0 0 0 0 0 0]';
tspan = 0:0.01:5;

f0 = fun(0, x0);
joptions = struct('diffvar', 2, 'vectvars', 1, 'thresh', 1e-8, 'fac', []);
J = odenumjac(@fun,{0 x0}, f0, joptions); 
sparsity_pattern = sparse(J~=0.);
options = odeset('Stats', 'on', 'JPattern', sparsity_pattern);

ttic = tic();
[t, sol]  =  ode15s(@(t,x) fun(t,x), tspan , x0); %, options);
ttoc = toc(ttic)
fprintf('runtime %f seconds ...\n', ttoc)
plot(t, sol)

function f = fun(t,x)
global mat1 mat2

fprintf('size of x: %d %d\n', size(x))

f(1,1) = 0;
f(2:9,1) = mat1*x + mat2*x;
f(10,1) = 2*(x(end-1) - x(end));
end

Unfortunately, following issue occurs while trying to evaluate the jacobian

Unable to perform assignment because the size of the left side is 8-by-1 and the size of the right side is 8-by-10.

Error in Untitled>fun (line 47)
f(2:9,1) = mat1*x + mat2*x;

Error in odenumjac (line 143)
    Fdel = feval(F,Fargs_expanded{:});

Error in Untitled (line 31)
J = odenumjac(@fun,{0 x0}, f0, joptions);
 

I see that the size of `x` changes in the second iteration.

>> test
size of x: 10 1
size of x: 10 10

I'm not sure why this happens. Suggestions on how this issue can be fixed will be of great help.

[Deepa Maheshvare]

Any suggestions?

Answer 1

[Walter Roberson]

f = zeros(size(x), 'like', x) ;
f(1,:) = 0;
f(2:9,:) = mat1*x + mat2*x;
f(10,:) = 2*(x(end-1,:) - x(end,:));