CODEWITHSUNDEEP
matlabodedifferential-equationsnumerical-integration
Natasha
Natasha

Reputation: 1521

Finding jacobian pattern to specify `jpattern` in MATLAB

I'm trying to understand how to specify the jacobian pattern in ode settings of MATLAB's ode solver.

I've started with a simple example,

syms x y z;
F = [x*y, cos(x*z), log(3*x*z*y)]
v = [x y z]
J = jacobian(F,v)

gives,

J =
 
[           y,   x,           0]
[ -z*sin(x*z),   0, -x*sin(x*z)]
[         1/x, 1/y,         1/z]

I would like to generate the jacobian pattern Jacobian sparsity pattern, specified as the comma-separated pair consisting of 'JPattern' and a sparse matrix. The sparse matrix contains 1s where there might be nonzero entries in the Jacobian to speed up the computation.

Therefore, from J I'd like to generate the jpattern matrix,

jpattern = 
[ 1,   1,  0]
[ 1,   0,  1]
[ 1,   1,  1]

Suggestions on how to generate the jpattern from Jacobian will be really helpful.

Upvotes: 0

Views: 430

Answers (1)

Sardar Usama
Sardar Usama

Reputation: 19689

To create the desired sparse jpattern matrix, initialize it by the size of J and then find indices of possible non-zero entries of J and update the corresponding entries in jpattern to 1.

[jr, jc] = size(J);
jpattern = sparse(jr, jc);
jpattern(find(J~=0)) = 1;

>> full(jpattern)
ans =
     1     1     0
     1     0     1
     1     1     1

Upvotes: 1

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