| Greg Heath 2008-01-13, 7:27 pm |
| On Jan 13, 8:18 am, Shaihan <shaihan_ma...@yahoo.com> wrote:
> Thank you both for your replies. Firstly,
>
>
> I have looked into some of these briefly but found them quite
> confusing to implement. Do you have any feeling as to which would be
> most suitable. Perhaps simulated annealing? Another possibility is to
> relax from a solution to the linear problem to this one. I'm not sure
> of an optimal method for that.]
>
>
>
> Thanks for that suggestion; unfortunately it doesn't help because
> doing this constrains the solution achieved (i.e. Ax) to be real,
> which is not necessary and leads to solutions that are undesirable
> from a physical point of view.
You should try to quantify the physicality
constraint.
> The product Ax can have any phase
> variation, the goal is only to match its magnitude to that of b.
Corect me if I'm wrong:
0. Assume size(A) = [m n], size(b) = [ m 1]
1. A and b are known and complex
2. A may be rank deficient
3. A has no symmetries to exploit
4. The solution x is complex
5. x may not be unique
6. You are unable to quantify the meaning of
"solutions that are undesirable from a physical point of view"
7. You want to find x, possibly nonunique, satisfying
|| abs(A*x) - abs(b)|| is a min
You can, at least, get good starting solutions from
looping over solutions to
A*x = R*b
where
R = diag(exp(2*pi*i*rand(m,1)))
Hope this helps.
Greg
|