How can I optimize the below function using "fsolve". It only takes input argument in the form of vectors but I have to pass input arguments to the below function in the form of matrix.
I am getting the below error while using the optimization toolbox
Error running optimization. Inner matrix dimensions must agree.
function f = object(w)
k=10;
B=20;
f = sum ((w(1,:)/(w(2,:).^w(3,:)*k)+((w(3,:)-1)*w(4,:)/B*w(3,:))));
end
You're very brief in your problem description about the outer circumstances but from your function it looks like the function might expect a w argument of size 4 x N. Did I guess correctly? If so, try
w_initial = rand(4*N,1); % resonable initialization. maybe random? maybe zeros?
fsolve(#(w) object(reshape(w,4,N)), w_initial, ...)
Related
I'm trying to vectorize one function in Matlab, but I have a problem with assigning values.
function [val] = clenshaw(coeffs,x)
b=zeros(1,length(coeffs)+2);
for k=length(coeffs):-1:2
b(k)=coeffs(k)-b(k+2)+2*b(k+1).*x;
end
val=coeffs(1)-b(3)+b(2).*x;
The purpose of this function is to use Clenshaw's algorithm to compute a value of one polynomial with coefficients "coeffs" at point x.
It work fine when x is a single value, but I'd like it to work with vector of arguments too.
When I try to pass a vector I get an error:
Unable to perform assignment because the left
and right sides have a different number of
elements.
Error in clenshaw (line 7)
b(k)=coeffs(k)-b(k+2)+2*b(k+1).*x;
I understand that there is a problem, because I'm trying to assign vector to a scalar variable b(k).
I tried making b a matrix instead of a vector, however I still cannot get the return output I'd like to have which would be a vector of values of this function at points from vector x.
Thank you for helping and sorry if something isn't entirely clear, because English is not my native language.
The vectorized version of your function looks like this:
function [val] = clenshaw(coeffs,x)
b=zeros(length(x),length(coeffs)+2);
for k=length(coeffs):-1:2
b(:,k)=coeffs(k)-b(:,k+2)+2*b(:,k+1).*transpose(x);
end
val=coeffs(1)-b(:,3)+b(:,2).*transpose(x);
end
b needs to be a matrix. In your loop, you have to perform every operation per row of b. So you need to write b(:,k) instead of b(k). Since b(:,k) is a vector and not a scalar, you also have to be careful with the dimensions when using the .* operator. To get the correct results, you need to transpose x. The same goes for the calculation of val. If you don't like the transposition, just swap the rows and cols of b and you get this:
function [val] = clenshaw(coeffs,x)
b=zeros(length(coeffs)+2, length(x));
for k=length(coeffs):-1:2
b(k,:)=coeffs(k)-b(k+2,:)+2*b(k+1,:).*x;
end
val=coeffs(1)-b(3,:)+b(2,:).*x;
end
However, the first version returns a column vector and the second a row vector. So you might need to transpose the result if the vector type is important.
I have some troubles to understand how to implement the following MIQP (Mixed Integer Quadratic Programming) with linear constraints in Matlab calling Gurobi.
Let me explain in a schematic way my setting.
(1) x is the unknown and it is a column vector with size 225x1.
(2) The objective function (which should be minimised wrto x) looks like
which can be rewritten as
I have a Matlab script computing alpha, Q,c (Q,c sparse) when some_known_parameters1 are given:
function [alpha, Q,c]=matrix_objective_function(some_known_parameters1)
%...
end
(3) The constraints are linear in x, include equalities and inequalities, and are written in the form
I have a Matlab script computing Aeq,beq,Aineq,bineq (Aeq,Aineq sparse) when some_known_parameters2 is given:
function [Aeq,beq,Aineq,bineq]=constraints(some_known_parameters2)
%...
end
(4) Some components of x are restricted to be in {0,1}. I have a Matlab script producing a string of letters B (binary), C (continous) when some_known_parameters3 is given:
function type=binary_continuous(some_known_parameters3)
%...
end
Now, I need to put together (1)-(4) using Gurobi. I am struggling to understand how. I found this example but it looks very cryptic to me. Below I report some lines I have attempted to write, but they are incomplete and I would like your help to complete them.
clear
rng default
%Define some_known_parameters1,
some_known_parameters2,some_known_parameters3 [...]
%1) generate alpha,Q,c,Aeq,beq,Aineq,bineq,type with Q,c,Aeq, Aineq sparse
[alpha, Q,c]=matrix_objective_function(some_known_parameters1)
[Aeq,beq,Aineq,bineq]=constraints(some_known_parameters2)
type=binary_continuous(some_known_parameters3)
%2) Set up Gurobi
clear model;
model.A=[Aineq; Aeq];
model.rhs=full([bineq(:); beq(:)]);
model.sense=[repmat('<', size(Aineq,1),1); repmat('=', size(Aeq,1),1)];
model.Q=Q; %not sure?
model.alpha=alpha; %not sure?
model.c=c; %not sure?
model.vtype=type;
result=gurobi(model); %how do I get just the objective function here without the minimiser?
Questions:
(1) I'm not sure about
model.Q=Q;
model.alpha=alpha;
model.c=c;
I'm just trying to set the matrices of the objective function using the letters provided here but it gives me error. The example here seems to me doing
model.Q=Q;
model.obj=c;
But then how do I set alpha? Is it ignoring it because it does not change the set of solutions?
(2) How do I get as output stored in a matrix just the minimum value of the objective function without the corresponding x?
(1) You're right, there's no need to pass the constant alpha since it doesn't affect the optimal solution. Gurobi's MATLAB API only accepts sparse matrices. Furthermore model.obj is always the c vector in the problem statement:
model.Q = sparse(Q);
model.obj = c;
(2) To get the optimal objective value, you first need to pass your model to gurobi and solve it. Then you can access it via the objval attribute:
results = gurobi(model);
val = results.objval + alpha
I want to solve a system of linear equalities of the type Ax = b+u, where A and b are known. I used a function in MATLAB like this:
x = #(u) gmres(A,b+u);
Then I used fmincon, where a value for u is given to this expression and x is computed. For example
J = #(u) (x(u)' * x(u) - x^*)^2
and
[J^*,u] = fmincon(J,...);
withe the dots as matrices and vectors for the equalities and inequalities.
My problem is, that MATLAB delivers always an output with information about the command gmres. But I have no idea, how I can stop this (it makes the Program much slower).
I hope you know an answer.
Patsch
It's a little hidden in the documentation, but it does say
No messages are displayed if the flag output is specified.
So you need to call gmres with at least two outputs. You can do this by making a wrapper function
function x = gmresnomsg(varargin)
[x,~] = gmres(varargin{:});
end
and use that for your handle creation
x = #(u) gmresnomsg(A,b+u);
I'm an electrical engineer who not familiar with MATLAB. My question is how can I pass other variable that use for calculate cost function when I call "fmincon"command. First I start with making a cost function name "Sum_Square_error.m" for calculate sum square error from estimated output (output that estimate from using Neural network) and real output.In this function I will use weight from welled train network multiply with shrinkage coefficient matrix(c) and call it "modify_input_weight". Then I evaluate neural network with modify_input_weight.So I get the estimate output. After that I get sum square error. My objective is to minimize Sum_square_error by adjust weight of neural network by using shrinkage coefficient matrix(c).
I have already read "fmincon" function reference. I can passing extra parameter for by three method
1. Anonymous Functions
2. Nested Functions
3. Global Variables
For this kind of problem which method is best fit. I tried to use Anonymous Functions like this
------------------------------------------- Sum_Square_error.m -------------------------------------------------------
f = #(c) Sum_Square_error(c,input_weight,X_test,Y_test);
for i=1:10
modify_input_weight(:,i) = c(i,1)*input_weight(:,i);
end
net.IW{1,1}= modify_input_weight;
y = net(X_test);
e = gsubtract(Y_test,y);
f = sum(e)^2;
end
-------------------------------------------------- Main program ----------------------------------------------------------
A = ones(1,10);
b = s;
lb = zeros(1,10);
[c,fval] = fmincon(#Sum_Square_error,c0,A,b,[],[],lb,[]);
but after I tried to run this program, it show many error message. Could someone please help me to passing "c,input_weight,X_test,Y_test" to optimize this cost function.
in Sum_Square_error.m you dont declare an anonymous function make it a regular function so change
f = #(c) Sum_Square_error(c,input_weight,X_test,Y_test);
to
function f = Sum_Square_error(c,input_weight,X_test,Y_test)
now in your main, when you say #fun you actually need to pass in the paremeters explicitly
fmincon(#Sum_Square_error(c,input_Weight,X_test,Y_test),c0,A,b,[],[],lb,[]);
where you replace c,input_Weight,X_test,Y_test with actual data
Trying to find a way to call the exponentiation function ( ^ ) used in a custom function for every item in a matrix in GNU Octave.
I am quite a beginner, and I suppose that this is very simple, but I can't get it to work.
The code looks like this:
function result = the_function(the_val)
result = (the_val - 5) ^ 2
endfunction
I have tried to call it like this:
>> A = [1,2,3];
>> the_function(A);
>> arrayfun(#the_function, A);
>> A .#the_function 2;
None of these have worked (the last one I believe is simply not correct syntax), throwing the error:
error: for A^b, A must be a square matrix
This, I guess, means it is trying to square the matrix, not the elements inside of it.
How should I do this?
Thanks very much!
It is correct to call the function as the_function(A), but you have to make sure the function can handle a vector input. As you say, (the_val - 5)^2 tries to square the matrix (and it thus gives an error if the_val is not square). To compute an element-wise power you use .^ instead of ^.
So: in the definition of your function, you need to change
result = (the_val-5)^2;
to
result = (the_val-5).^2;
As an additional note, since your code as it stands does work with scalar inputs, you could also use the arrayfun approach. The correct syntax would be (remove the #):
arrayfun(the_function, A)
However, using arrayfun is usually slower than defining your function such that it works directly with vector inputs (or "vectorizing" it). So, whenever possible, vectorize your function. That's what my .^suggestion above does.