MATLAB: Plotting several quadratic functions

plotting

would like to plot 3 to 4 qaudratic functions (a*x^2+1) on the same coordinates by changing the value of a from -1:1:2. can i use the for loop for this? many thanks

Best Answer

Yes, I think that it is good idea:

figure
hold all
x = linspace(0,1);
for a=-1:1:2
    plot(x,a*x.^2+1)    
end
hold off
legend('a=-1','a=0','a=1','a=2')

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MATLAB: Subplots made by multiple plots

Each subplot needs to be held individually.

figure;  hold on
subplot(121)
hold on
plot(1:3)
plot(rand(1,3))
subplot(122)
hold on
plot(4:6)
plot(rand(1,3))

MATLAB: Quadratic Programming (quadprog):

Using your posted A matrix I find that

>> cond(H)
ans =
   7.5703e+18

For numerical purposes, this is a singular matrix and shouldn't be treated as positive definite (but rather positive semi-definite). The test you did with chol() isn't reproducible,

 >> [~,p] = chol(H); p
p =
     1

but even if p had been 0, it would be irrelevant. chol's judgement on whether a matrix is sufficiently positive definite to compute a Cholesky decomposition does not mean it is sufficiently positive definite for everything.

For quadprog, the only thing that matters here is that, due to the ill-conditioning of H, the equations H*x+f=0 will have a non-unique set of solutions that all approximately minimize the quadprog objective. You simply cannot be sure which of these solutions different algorithms will produce, with such an ill-conditioned H.

As for why the residual is so much worse for quadprog, that is likely because quadprog is an iterative solver and cannot use the residual to decide when to stop iterating (because it doesn't have access to A and B). In fact, it almost certainly uses something like a stopping tolerance on the gradient norm,

gradnorm = norm(H*x+f)^2 < tolerance

Since H*x+f=2*A.'*(A*x-B), we can see that the gradient norm can be significantly smaller than the residual vector r= A*x-B depending on the values of A.'

Best Answer

Related Solutions

MATLAB: Subplots made by multiple plots

MATLAB: Quadratic Programming (quadprog):

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