# Issue while computing jacobian

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Deepa Maheshvare on 18 Feb 2021
Answered: Walter Roberson on 19 Feb 2021
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 on 19 Feb 2021
Any suggestions?

Walter Roberson on 19 Feb 2021
f = zeros(size(x), 'like', x) ;
f(1,:) = 0;
f(2:9,:) = mat1*x + mat2*x;
f(10,:) = 2*(x(end-1,:) - x(end,:));

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