I have the same kind of problem described in this topic:
Using fzero: Undefined function or method 'isfinite' for input arguments of type 'sym'
Their answers really helped me, but I am still stuck.
I also have to find the zeros of a function of w, this function is defined in several steps:
So the only unknown is w, and I defined other objects such as:
lambda= #(w) ((16*rho(i)*A(i)*w^2*Lprime(i)^2)/(E(j)*I(i)))^0.25;
beta=#(w) lambda*b(i)^0.5;
gamma=#(w) lambda*Lprime(i)^0.5;
Then, I define a 4*4 matrix M2:
M2=#(w) [besselj(4,beta) bessely(4,beta) besseli(4,beta) besselk(4,beta);
besselj(3,beta) bessely(3,beta) besseli(3,beta) -besselk(3,beta);
besselj(2,gamma) bessely(2,gamma) besseli(2,gamma) besselk(2,gamma);
besselj(4,gamma) bessely(4,gamma) besseli(4,gamma) besselk(4,gamma)];
Then the equation to be solved is: det(M2)=0. But w=0 is one of the solutions, and I want the first non-zero solution, so I wrote:
delta = #(w) det(M2);
S(i,j)=fzero(delta,500);
Then I run the program, and Matlab says:
??? Error using ==> fzero at 235
FZERO cannot continue because user supplied function_handle ==> #(w)det(M2)
failed with the error below.
Undefined function or method 'det' for input arguments of type 'function_handle'.
Error in ==> frequencies at 57
S(i,j)=fzero(delta,500);
I also tried with the subs and the eval methods, and they don't work either, the error messages are in those cases:
??? Undefined function or method 'isfinite' for input arguments of type 'sym'.
Error in ==> fzero at 323
elseif ~isfinite(fx) || ~isreal(fx)
Error in ==> frequencies at 58
S(i,j)=fzero(#(w) subs(delta,'w',w),500);
Which is the same error as edio's I guess. And:
??? Error using ==> fzero at 307
FZERO cannot continue because user supplied function_handle ==> #(w)eval(delta)
failed with the error below.
Undefined function or method 'eval' for input arguments of type 'function_handle'.
Error in ==> frequencies at 59
S(i,j)=fzero(#(w)eval(delta),500);
Can you help me please?
Your problem appears to be that you are never evaluating your anonymous functions when you place them within other anonymous functions. For example, you define the function lambda as such:
lambda = #(w) ((16*rho(i)*A(i)*w^2*Lprime(i)^2)/(E(j)*I(i)))^0.25;
But when you use it in beta, you need to evaluate it using the input value for w, like so:
beta = #(w) lambda(w)*b(i)^0.5;
%# ^--------------Pass w to lambda to evaluate the function
As such, I believe your other anonymous functions should be defined as follows:
gamma = #(w) lambda(w)*Lprime(i)^0.5;
M2 = #(w) [besselj(4,beta(w)) bessely(4,beta(w)) besseli(4,beta(w)) ...
besselk(4,beta(w)); ...
besselj(3,beta(w)) bessely(3,beta(w)) besseli(3,beta(w)) ...
-besselk(3,beta(w)); ...
besselj(2,gamma(w)) bessely(2,gamma(w)) besseli(2,gamma(w)) ...
besselk(2,gamma(w)); ...
besselj(4,gamma(w)) bessely(4,gamma(w)) besseli(4,gamma(w)) ...
besselk(4,gamma(w))];
delta = #(w) det(M2(w));
A note about efficiency...
There is a GLARING efficiency problem I'm noticing here. By using anonymous functions instead of any other type of function (primary functions, nested functions, or subfunctions) you are going to end up evaluating the same function with the same input multiple times over.
For example, each time you evaluate M2 to create your matrix you will be evaluating both beta and gamma 8 times with the same input! Notice the improvement you could make by placing M2 in a function and passing as input w and the two function handles beta and gamma:
function newMatrix = M2(w,betaFcn,gammaFcn)
bw = betaFcn(w); %# Evaluate the beta function once
gw = gammaFcn(w); %# Evaluate the gamma function once
newMatrix = [besselj(4,bw) bessely(4,bw) besseli(4,bw) besselk(4,bw); ...
besselj(3,bw) bessely(3,bw) besseli(3,bw) -besselk(3,bw); ...
besselj(2,gw) bessely(2,gw) besseli(2,gw) besselk(2,gw); ...
besselj(4,gw) bessely(4,gw) besseli(4,gw) besselk(4,gw)];
end
And your new delta function would look like this:
delta = #(w) det(M2(w,beta,gamma));
Hi thank you very much for your help.
It works, but the last line has to change, obviously (it still took me 10 minuts for figure it out):
lambda= #(w) ((16*rho(i)*A(i)*w^2*Lprime(i)^2)/(E(j)*I(i)))^0.25;
beta=#(w) lambda(w)*b(i)^0.5;
gamma=#(w) lambda(w)*Lprime(i)^0.5;
M2=#(w) [besselj(4,beta(w)) bessely(4,beta(w)) besseli(4,beta(w)) besselk(4,beta(w));
besselj(3,beta(w)) bessely(3,beta(w)) besseli(3,beta(w)) -besselk(3,beta(w));
besselj(2,gamma(w)) bessely(2,gamma(w)) besseli(2,gamma(w)) besselk(2,gamma(w));
besselj(4,gamma(w)) bessely(4,gamma(w)) besseli(4,gamma(w)) besselk(4,gamma(w))];
delta = #(w) det(M2(w));
S(i,j)=fzero(#(w) delta(w),500);
And now it is really faster than before, in another case where the function solve could handle the resolution, it took like 10 seconds for each loop, now it's like 0.06 seconds
I will try your other solution to see the improvements.
Thank you a lot.
Related
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
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 did this
function f=objfun(w)
a=0.5
w0=[0.1;0.2;0.3];
f=(a^2)/2 + w(1)+ w(2)+ w(3);
[w,fval]=fmincon('objfun',w0,[],[],[],[],[],[],'constraint')
But I got this error message.
Error using objfun (line 3)
Not enough input arguments.
What problem is it talking about?
I learned fmincon from
http://www.math.colostate.edu/~gerhard/classes/331/lab/fmincon.html
and it tells me that codes like this
function f=objfun(x)
f=x(1)^4-x(1)^2+x(2)^2-2*x(1)+x(2);
will be the first lines to do constrained optimization.
What has gone wrong?
I believe you need to pass a function handle to fmincon. From the docs http://www.mathworks.com/help/optim/ug/fmincon.html
x = fmincon(#myfun,x0,A,b)
where myfun is a MATLAB® function such as
function f = myfun(x)
f = ... % Compute function value at x
Try passing a function handle to fmincon. I assume that constraints is your non linear constraint function, it should be a function handle as well. I also assume that you are not calling fmincon from inside your objective function. If so then I think you will have some thing like this:
objfun.m
function f = objfun(w)
a=0.5;
f=(a^2)/2 + w(1)+ w(2)+ w(3);
return
end
main.m
w0=[0.1;0.2;0.3];
[w,fval]=fmincon(#objfun,w0,[],[],[],[],[],[],#constraint)
i want to understand what is a error in the following code?code is given below
function x0=secand2d(f,g,x,dx,tol)
% find solution of f(x,y)=0 and g(x,y)=0
for i=1:20
x0=x;
f0=[feval(f,x0),feval(g,x0)];
x0=x+[dx(1),0];
fx=[feval(f,x0),feval(g,x0)];
fx=(fx-f0)/dx(1);
x0=x+[0 dx(2)];
fy=[feval(f,x0),feval(g,x0)];
fy=(fy-f0)/dx(2);
A=[fx;fy]+eps;
x=x+dx;
dx=(-A\f0'-dx')';
if(norm(dx)<tol) ;return; end;
end;
disp(norm(dx));
pause;
end
which represents of two dimensional secant method,where function f and g is defined by following form
f=#(x,y) (x-sin(x+y)); and g=#(x,y) y-cos(x-y);
i have also checked and these to function works fine on it's parameters
f(3,3)
ans =
3.2794
and
g(1,1)
ans =
0
also
x=[0.9 0.9];
dx=[0.1 0.1];
tol=1e-5;
but following code generated such kind of errors
secand2d(f,g,x,dx,tol)
Error using #(x,y)(x-sin(x+y))
Not enough input arguments.
Error in secand2d (line 5)
f0=[feval(f,x0),feval(g,x0)];
please help me to clarify reasons of this errors
You are getting that error because you are passing only x0 to f here:
f0=[feval(f,x0),feval(g,x0)];
f and g are expecting two inputs. You can fix the error like this:
f0=[feval(f,x0,y0),feval(g,x0,y0)];
If there is not a particular reason you are using feval you can do it like this:
f0 = [f(x0, y0) g(x0, y0)];
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)