Problem with my matrix dimension in solving nonlinear equations

Hello, Im having trouble in trying to resolve a nonlinear equation for 4 unknown constants using the lsqnonline function. I have tried proofreading it but I cant seem to find the exact problem, It gives the following error.

Error using *

Incorrect dimensions for matrix multiplication. Check that the number of columns in the first matrix matches the number of rows in the second matrix. To perform elementwise multiplication, use '.*'.

Error in workFunction (line 16)

sigma=(LAMx./LAMy).*(lx.*ly./.6)*2*a*exp((b*(E_11.^2))+(c*(E_22.^2))+(2*d*(E_11.*E_22)))*((b*E_11)+(d*E_22));

Error in Untitled2>@(C)workFunction(C,Lengths,Stress)

Error in lsqnonlin (line 206)

initVals.F = feval(funfcn{3},xCurrent,varargin{:});

Error in Untitled2 (line 16)

Constants=lsqnonlin(@(C)workFunction(C,Lengths,Stress),x0)

Caused by:

Failure in initial objective function evaluation. LSQNONLIN cannot continue.

I created a function with the problem and the four unknown constants known as a,b,c and d which are supposed to be scalar factors.

This is the script that has the data which is 2 independent and 1 dependepent variables

Force=[0,.12,.24,.36,.48,.6,.72,1.2,1.44,1.8,2.4,3];%Newtons

str=Force/16;

Stress=reshape(str,12,1);

lx=[2;2.03;2.04;2.044;2.048;2.052;2.06;2.1;2.12;2.15;2.16;2.18];% CD mm x-direction
ly=[2;2.03;2.06;1.14;2.24;2.3;2.4;2.44;2.5;2.52;2.56;2.6];%AB distance y-direction

Lengths=[lx,ly];
disp([Lengths,Stress])

x0=[1;2;.1;1];

Constants=lsqnonlin(@(C)workFunction(C,Lengths,Stress),x0) 

This is the function:

function ferror=workFunction(C,Lengths,Stress)
a=C(1);
b=C(2);
c=C(3);
d=C(4);

lx=Lengths(:,1);
ly=Lengths(:,2);

LAMx=lx./4;
LAMy=ly./4;

E_11=.5*((LAMx.^2)-1);% Strain value in x direction
E_22=.5*((LAMy.^2)-1);%Strain values in y direction

sigma=(LAMx./LAMy).*(lx.*ly./.6)*2*a*exp((b*(E_11.^2))+(c*(E_22.^2))+(2*d*(E_11.*E_22)))*((b*E_11)+(d*E_22));

ferror=Stress-sigma;

Answer 1

[Star Strider]

When in doubt, vectorise every array operation, regarless of how distant they are from the arrays themselves (unless matrix operations are necessary).

This works:

sigma=(LAMx./LAMy).*(lx.*ly./.6).*2.*a.*exp((b*(E_11.^2))+(c*(E_22.^2))+(2*d*(E_11.*E_22))).*((b*E_11)+(d*E_22));

The solver stopped when I ran this code because it exceeded the evaluation limit. Consider using the optons structure to increase that when you run it.

.

[Ernest Mares]

Will do and Thank You!

[Star Strider]

As always, my pleasure!