solving equations with vector as the unknown variable

I need to solve the following equation which includes products between vectors and matrix:

>> F=@(x)(((x'*E)*((((Etrasp*i_covrend*E)/(Etrasp*i_covrend*uno))-((Etrasp*i_covrend*uno)/(unotrasp*i_covrend*uno)))^(-1))*(((i_covrend*E)/(Etrasp*i_covrend*uno))-((i_covrend*uno)/(unotrasp*i_covrend*uno))))-x)

>> fsolve(F,0)

Error using * Inner matrix dimensions must agree.

Error in @(x)(((x'*E)*((((Etrasp*i_covrend*E)/(Etrasp*i_covrend*uno))-((Etrasp*i_covrend*uno)/(unotrasp*i_covrend*uno)))^(-1))*(((i_covrend*E)/(Etrasp*i_covrend*uno))-((i_covrend*uno)/(unotrasp*i_covrend*uno))))-x)

Error in fsolve (line 241) fuser = feval(funfcn{3},x,varargin{:});

Caused by: Failure in initial user-supplied objective function evaluation. FSOLVE cannot continue.

I know that x must be a (10*1) vector and i'm sure that the dimensions of vectors and Matrix are correct. I don't know which command should I use to solve this equation and return a vector

Answer 1

[John D'Errico]

"I know that x must be a (10*1) vector and i'm sure that the dimensions of vectors and Matrix are correct."

However, what you don't know is how to read the help for fsolve. How did you call fsolve?

>> fsolve(F,0)

So how does fsolve know that the unknown is a vector? What length vector? You told it only that the unknown is a SCALAR, essentially a vector of length 1. The starting value is 0, a scalar.

So while YOU know that the unknown is a vector of size 10x1, fsolve thinks it is a scalar unknown. You did tell it that after all.

Unless of course, you have the mind reading toolbox installed. Then you would type this on the command line:

set(0,'readMinds','on')

Sadly, I think that toolbox is still under beta test.

[Camilla Lincetto]

Oh, right! So, how can I impose that x is a vector 10*1?

[John D'Errico]

Well, you would pass in a vector of the appropriate size. Vectors of zeros tend to be dangerous starting values, because some algorithms use finite differences, with a step size that is relative to the start point. So while I think fsolve has been written to be robust to such a thing, it never hurts to avoid zero.

I might tend to try ones(10,1) as a starting vector, but if you insist, zeros(10,1) would do what you wanted.

[Camilla Lincetto]

Can I also include a constraint like the sum of x is equal to 0? If yes, where should I include this? Thank you so much!

[Camilla Lincetto]

I need also x minimize a matricial product...

[John D'Errico]

You cannot do those things in fsolve. They would require a tool like fmincon, which you must have if you have fsolve.

[Camilla Lincetto]

I'm sorry, I have to solve the minimization of x'Vx subject to the sum of x equal to 0 and the equation reduced to ((x'*E)*((abbd)^(-1))*(ebgd))-x=0.

I tried with fmincon so:

>> Aeq1 = ones(1,10)

>> beq1 = 0

% on another script called mycon

>> function ceq = mycon(x)

>> ceq=((x'*E)*((abbd)^(-1))*(ebgd))-x

% abbd is a number, x'E a product (1*10)*(10*1) so becomes a number and ebgd is a vector (10*1)

>> x=fmincon(@(x)x'*cov_rend*x,0.00001*ones(10,1),[],[],Aeq1,beq1,[],[],@mycon)

Warning: The default trust-region-reflective algorithm does not solve problems with the constraints you have specified. FMINCON will use the active-set algorithm instead. For information on applicable algorithms, see Choosing the Algorithm in the documentation. > In fmincon at 500 Warning: Your current settings will run a different algorithm (interior-point) in a future release. > In fmincon at 505 Error using mycon Too many output arguments.

Error in fmincon (line 718) [ctmp,ceqtmp] = feval(confcn{3},X,varargin{:});

Caused by: Failure in initial user-supplied nonlinear constraint function evaluation. FMINCON cannot continue.

I know that maybe the nonlinear constraint (@mycon) isn't true, but I don't understand how I can solve this minimization. I'm not familiar with matlab because in the past I have used other programs, but now my prof forced me to use it. Thank you for all.

[John D'Errico]

The warning message merely tells you that you used the wrong algorithm.

The error message suggests you made a mistake in the constraint function. If you read the help for fmincon, it tells you that the constraint function MUST return both equality and an inequality constraint result. If no inequalities are involved, then return an empty array for that argument.