Error "Jacobian not correct size" while trying to supply system's Jacobian within fsolve

Hello,

I am having some trouble supplying the Jacobian matrix of a system of non-linear equations to fsolve. I thought adding "jacobian" to the fsolve output would generate the system's Jacobian (which it does); however, whenever I add either " 'SpecifyObjectiveGradient',true " or " 'Jacobian','on' " to the solver's options, hoping that it would recognise jacobian as the Jacobian matrix, I receive the following error:

Supplied Jacobian is not the correct size: the Jacobian matrix should be 562-by-593.

The code I have is as follows:

options = optimoptions('fsolve','Display','iter','Algorithm','Levenberg-Marquardt','SpecifyObjectiveGradient',true);%'Jacobian','on');
.
.
.
[xss,x,exitflag,output,jacobian] = fsolve(xss,x0,options); % Where xss is a function handle, function with simultaneous equations in another file

If I run the simple check

size(jacobian)

I get the size mentioned above, i.e. 562x593:

ans =
562   593

If jacobian has the correct dimensions but it is not recognised by options, does this mean that I have to supply the Jacobian manually? And if so, how may I go about doing it? I tried doing so, but I did not know where to place the 'jacobian' function itself. I am assuming it should be placed at the end of the function file, but I never managed to generate it successfully. For reference, my function file, when summarised, looks like this:

function [xss,xout] = function_name(x,inputs)
% Endogenous variables
A = x(1:12);
.
.
.
Z = x(587:593);
%Equations
xss1 = (equation here); xss{1} = xss1;
.
.
.
xss59 = (equation here); xss{59} = xss59;
xss = cell2mat(xss);

xout = [(vector of endogenous variables)];

end

Would anybody be able to help with this? I have had a look at the documentation for both jacobian and fsolve, but as I could not find an example similar enough to mine I could not figure it out. Thank you very much for the time and help!

Answer 1

[Matt J]

When you set SpecfiyObjectiveFunction=true it means you are planning to do your own manual calculation of the Jacobian within your objective function. Assuming you are not using the JacobianMultiplyFcn or JacobPattern options, your objective function code should look like this.

function [xss,jacobianMatrix] = function_name(x,inputs)

 ...
  xss=____
  if nargout>1
     jacobianMatrix=_______
  end
 end
 

In the present case, the output jacobianMatrix should be 562x593.

[Mark]

Thank you for this! However, in my case providing the whole Jacobian manually would be quite laborious, given the high number of equations and variables. Is there any way to automate the process, e.g. some in-built function or equivalent? I tried using J = jacobian(xss,x) or the like but none of my attempts were successful.

[Matt J]

It's Matlab. You should be using vector/matrix arithmetic to generate the Jacobian, not calculating each element with its own separate command.

[Mark]

Alright -- I thinks I got it. Thanks again!