When using JacobianMultiplyFcn in lsqnonlin, why is Jinfo required to be numeric? How can I pass more general kinds of parameters to my JacobianMultiplyFcn?

What I would like to do is use the JacobianMultiplyFcn option of lsqnonlin's trust-region-reflective algorithm where Jinfo is a struct carrying parameters to be used by the Jacobian multiply operations. Below is a simplified example.

However, an error is produced indicating that Jinfo is not allowed to be a struct. I thought the whole point of JacobianMultiplyFcn option is that an actual numeric Jacobian matrix doesn't have to be constructed. What then, is Jinfo supposed to be, and how can I accomplish what I want?

A=rand(3); A(:,end)=1;

opts=optimoptions('lsqnonlin','Algorithm','trust-region-reflective',...
                             'OptimalityTol',1e-20,'FunctionTol',1e-30,'StepTol',1e-20,...
                              'SpecifyObjective', true, 'JacobianMultiplyFcn',@jmfunc);

[x,res]=lsqnonlin(@(x)resFcn(x,A), rand(3,1), [],[],opts)

Incorrect number or types of inputs or outputs for function 'nonzeros'.

Error in lsqncommon (line 18)
if any(~isfinite(nonzeros(initVals.J)))

Error in lsqnonlin (line 260)
lsqncommon(funfcn,xCurrent,lb,ub,options,defaultopt,optimgetFlag,caller,...

function [r,Jinfo]=resFcn(x,A)

   r=[A*x;x(:).^2/2]-[4;4;4;0;0;8];

   Jinfo.A=A;
   Jinfo.x=x;

end


function W=jmfunc(Jinfo,Y,flag)

  A=Jinfo.A;
  x=Jinfo.x;


 switch sign(flag)

     case 0

         W=A'*(A*Y)+Y.*x.^2;

     case 1

         W = [A*Y ;x.*Y];

     case -1

         P=Y(1:end/2); 
         Q=Y(end/2+1:end);

         W = A.'*P+x.*Q;        
 end

end

Answer 1

[Matt J]

I seem to be have been able to fool lsqnonlin into doing what I want by using the attached classdef. However, I still wonder, nervously, why the Optimization Toolbox is trying to prevent me from doing this.

A=rand(3); A(:,end)=1;


opts=optimoptions('lsqnonlin','Algorithm','trust-region-reflective',...
                             'OptimalityTol',1e-20,'FunctionTol',1e-30,'StepTol',1e-20,...
                             'SpecifyObjective', true, 'JacobianMultiplyFcn',@jmfunc);

[x,res]=lsqnonlin(@(x)resFcn(x,A), rand(3,1), [],[],opts)

Local minimum possible.

lsqnonlin stopped because the final change in the sum of squares relative to 
its initial value is less than the value of the function tolerance.

x = 3×1

-0.0000 0.0000 4.0000

res = 1.5777e-30

function [r,Jinfo]=resFcn(x,A)

   r=[A*x;x(:).^2/2]-[4;4;4;0;0;8];

   s.A=A;
   s.x=x;
   
   Jinfo=JMInfo(s);

end


function W=jmfunc(Jinfo,Y,flag)

  A=Jinfo.s.A;
  x=Jinfo.s.x;


 switch sign(flag)

     case 0

         W=A'*(A*Y)+Y.*x.^2;

     case 1

         W = [A*Y ;x.*Y];

     case -1

         P=Y(1:end/2); 
         Q=Y(end/2+1:end);

         W = A.'*P+x.*Q;        
 end

end