I have a question about using the lsqnonlin function.
In my case I have two functions:
f_1=#(t,x)sin(t+x.^2);
f_2=#(t,x)cos(x.^2)+3.*t.^2;
f = {f_1, f_2};
I want to find the values of the arguments t and x which would result in the least square error, defined as: f_1(t,x)^2+f_2(t,x)^2. In other words, argmin for LSE.
My code is as follow with initial guess [1,2]:
lsqnonlin(f,[1,2])
And I'm getting the error:
Error in lsqnonlin (line 196)
initVals.F = feval(funfcn{3},xCurrent,varargin{:});
Caused by:
Failure in initial objective function evaluation. LSQNONLIN cannot continue.
lsqnonlin can be used for vector function and vector input according to the documentation. I wonder how to prepare corresponding codes for it. Could anyone suggest the solution?
You are getting an error because lsqnonlin expects a scalar function handle that maps a vector to a vector, whereas you specify a cell array of function handles. To fix this, instead of a vector of functions outputting one scalar each, you need to rewrite it into a single function that accepts a vector of inputs and also outputs a vector:
f = #(xt)[sin(xt(2)+xt(1).^2), cos(xt(1).^2)+3.*xt(2).^2];
% xt = [x,t]
% f = [f_1(xt), f_2(xt)]
so f and xt are both vectors of 2 elements.
Then, the solver works:
lsqnonlin(f,[1,2])
ans =
1.6144 0.5354
Related
I have a use case as follows:
Inside F.m I have a function F that takes as its argument a 2 x 1 matrix x. F needs to matrix multiply the matrix kmat by x. kmat is a variable that is generated by a script.
So, what I did was set kmat to be global in the script:
global kmat;
kmat = rand(2);
In F.m:
function result = F(x)
global kmat;
result = kmat*x;
end
Then finally, in the script I have (x_0 has already been defined as an appropriate 2 x 1 matrix, and tstart and tend are positive integers):
xs = ode45(F, [tstart, tend], x_0);
However, this is causing the error:
Error using F (line 3)
Not enough input arguments.
Error in script (line 12)
xs = ode45(F, [tstart, tend], x_0);
What is going on here, and what can I do to fix it? Alternatively, what is the right way to pass kmat to F?
Firstly, the proper way to handle kmat is to make it an input argument to F.m
function result = F(x,kmat)
result = kmat*x;
end
Secondly, the input function to ode45 must be a function with inputs t and x (possibly vectors, t is the dependent variable and x is the dependent). Since your F function doesn't have t as an input argument, and you have an extra parameter kmat, you have to make a small anonymous function when you call ode45
ode45(#(t,x) F(x,kmat),[tstart tend],x_0)
If your derivative function was function result=derivative(t,x), then you simply do ode45(#derivative,[tstart tend],x_0) as Erik said.
I believe F in ode45(F,...) should be a function handle, i.e. #F. Also, you can have a look at this page of the MATLAB documentation for different methods to pass extra parameters to functions.
I am solving a very simple constrained optimization problem. At this point, I have only entered a constraint that makes the (L-2) vector norm equal 1 and later I hope to add non-negativity constraints.
Fmincon is giving me a "Too many output arguments" on the my constraint. I don't understand why.
Objective function: A simple Quadratic form. Actually a variance covariance Matrix, I am entering as a pre-calculated global variable.
function [y, grady] = quadobj(x)
global Q
y = x*Q*x';
if nargout > 1
grady = 2*Q*x;
end
Equality Constraint: that vector L2 norm should be 1.
function outeq = confuneq2(x)
% Nonlinear equality constraints
outeq = x*x'-1;
end
Fmincon.
x0 = [0.7,0.1, -0.69];
options = optimoptions(#fmincon,'Algorithm','sqp');
[x,fval] = fmincon(#quadobj,x0,[],[],[],[],[],[],...
#confuneq2,options);
But it's not working. I am getting the following error.
Error using confuneq2
Too many output arguments.
Error in fmincon (line 632)
[ctmp,ceqtmp] = feval(confcn{3},X,varargin{:});
Caused by:
Failure in initial user-supplied nonlinear constraint function evaluation. FMINCON cannot continue
Please help!
Confusingly, the problem is that your function has too few output arguments. If you look at the error, it is telling you that MATLAB is trying to call your function with two output arguments but you've programmed it to take only one. Thus it errors because it has called your function with too many output arguments.
All the examples in the docs have two outputs so try create your function this way:
function [out, outeq] = confuneq2(x)
out = x*x'-1;
outeq = [];
end
I have a function of 2 different vector. These are the control vector (decision variables) of the function. I want to use fmincon to optimize this function and also get the both control vector results separately.
I have tried to use handle ,#, but I got an error.
The function is:
function f = myFS(x,sv) % x is a vector (5,1)
f = norm(x)^2-sigma*(sv(1)+sv(2));
end
%% I tried to write fmincone to consider both control vectors (x and sv)
[Xtemp(:,h2),Fval, fiasco] = fmincon(#(x,sv)myFS(x,sv)...
,xstart,[],[],[],[],VLB,VUB,#(x,sv)myCon(sv),options);
Here is the error I get:
Error using myFS (line 12) Not enough input arguments.
Error in fmincon (line 564)
initVals.f =
feval(funfcn{3},X,varargin{:});
Error in main_Econstraint (line 58) [Xtemp(:,h2),Fval, fiasco] =
fmincon('myFS',xstart,[],[],[],[],VLB,VUB,#(x,sv)myCon(sv),options);
Thanks
fmincon expects your function to be of a single variable, there is no getting around that, but see:
http://se.mathworks.com/help/optim/ug/passing-extra-parameters.html
for example, if both x, cv are variables of the optimization you can combine them and then split them in the actual objective
for example
x_cv = vertcat(x, cv) and then x = x_cv(1:5); cv = x_cv(6:end)'
if cv is not a variable of the optimization, then 'freeze it' as the link above suggests
here is my code:
C=#(k) [k,k,2.*k;3,2.*k,5;1,k,k];
AV=#(k,t) [3*t, 6, 9]*C(k)*[3*t ;6 ;9];
avaint=#(k,a,b) quadgk(#(k) AV(k,t),a,b);
AVAR=#(t) avaint(t,0,87600);
Is shows:
Error using vertcat
Dimensions of matrices being concatenated are not consistent.
when I want to print AVAR(3)
Source of Error
The quadgk function passes a vector of integration points to the function handle given to it.
From the documentation:
The function y = fun(x) should accept a vector argument x and return a vector result y, where y is the integrand evaluated at each element of x.
This creates the dimension mismatch causing the error.
Solutions
To get around this implementation, you can perform the numerical integration using the integral function with the ('ArrayValued',true) option pair:
avaint = #(t,a,b) integral(#(k) AV(k,t),a,b,'ArrayValued',true);
Or, you can use arrayfun within AV to abide by the requirement of quadgk:
AV = #(k,t) arrayfun(#(k_el) [3*t, 6, 9]*(C(k_el)*[3*t ;6 ;9]),k);
i'm stuck with this error:
In an assignment A(I) = B, the number of elements in B and I must be the same.
yres(1)=((u - uc).^2) + ((y - yc).^2) -(d.^2);
i don't understand, why this won't get a skalar?since the elements are all scalar. what should be changed to get a scalar?
best regards
edit: thanks sloede, all inputs are scalar, but i still get this error
In an assignment A(I) = B, the number of elements in B and I must be the
same.
Error in myfun (line 7)
yres(1)=sqrt(((u - uc).^2) + ((y - yc).^2) ) -d;
Error in fsolve (line 241)
fuser = feval(funfcn{3},x,varargin{:});
Error in modfsolve (line 26)
x= fsolve(#myfun,x0,options,uc,d,spacing_amplitude,spacing_width);
Caused by:
Failure in initial user-supplied objective function evaluation. FSOLVE
cannot continue.*
The "." before an operator means that the following operation should be applied element-wise and not on the vector as a whole. Thus
a = b.^2
will give you as a result all elements of b squared and saved back to a. Therefore, in your code statement above, if any of u, uc, y, yc, d are not scalar but a vector, your result will be a vector as well.
Otherwise there seems to be nothing wrong with your code.
read the documentation of fsolve: http://www.mathworks.nl/help/toolbox/optim/ug/fsolve.html
it states:
fun
The nonlinear system of equations to solve. fun is a function that accepts a vector x and returns a vector F, the nonlinear equations evaluated at x.
Obviously your function myfun doesn't handle vector input.
You can solve this by adding the following construction inside your function (and of course change it to your needs/your parameters):
function out = myfun(in)
if ~isscalar(in)
% assuming it's a matrix or vector
out = reshape(arrayfun(#myfun,in(:)),size(in));
else
% your actual function execution statements
out = dostuffon(in);
end
end
or properly vectorize your function (if that's possible)