max value of a function
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Hello everyone. I'm having a problem with finding a maximum y of a function. In general I use:
x= double(solve(diff(func)));
ymax=eval(func);
But in some cases this gives me a solution that is clearly not the maximum. Let's say, that the function is:
func = exp(-(x - 1)^2) + exp(-(x + 2)^2)
if i try to use max() i get an error "Input arguments must be convertible to floating-point numbers.".
Please let me know where is the mistake in my thinking.
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Matt J
le 8 Août 2022
Modifié(e) : Matt J
le 8 Août 2022
In general I use: x= double(solve(diff(func)));
This assumes there are no local min/max or saddle points.
if i try to use max() i get an error "Input arguments must be convertible to floating-point numbers.".
You cannot use max() with symbolic variables.
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Matt J
le 9 Août 2022
Modifié(e) : Matt J
le 9 Août 2022
If you can identify a finite search interval [a,b] where the solution lies, you can do something like this:
a=-10; b=+10;
func = @(x) exp(-(x - 1).^2) + exp(-(x + 2).^2); %Note the element-wise .^
X=linspace(a,b,1e4);
Y=func(X);
[~,i0]=max(Y);
[xmax,ymax] = fminbnd(@(z) -func(z), X(i0-1), X(i0+1));
ymax=-ymax;
fplot(func,[a,b]); hold on
plot(xmax,ymax,'or','MarkerSize',10); hold off; axis padded
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Torsten
le 8 Août 2022
Modifié(e) : Torsten
le 8 Août 2022
syms x
func = exp(-(x - 1)^2) + exp(-(x + 2)^2);
dfunc = diff(func,x);
ddfunc = diff(dfunc,x);
xc= double(vpasolve(dfunc==0,[0 2]))
xnum = double(subs(ddfunc,x,xc));
if xnum < 0
disp('Local maximum');
elseif xnum == 0
disp('Unknown type')
else
disp('Local minimum')
end
funcnum = matlabFunction(func);
x = 0:0.01:2;
plot(x,funcnum(x))
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