MATLAB: I want to apply what the norm function does, without using norm.

circlefunctionhigher levelnorm

I am trying to write a code with some overlapping circles. I have written a code that works using the norm function, however, I want as little 'higher-level' functions as possible. Is there a way to do this?

I have the following piece of code that runs:

if norm(center(n,:)-[row col])<= radius
  circle_pattern(col,row,n) = 1;
end

And when I replace it with this code (I tried to do some research on norm), my code will not plot the same image.

if  ((center(n,:)-row).^2 + (center(n,:)-col).^2) <= radius
              circle_pattern(col,row,n) = 1;
end

Any ideas on how to fix this?

Best Answer

Since this seems to be homework, if you don't want to use canned code, I will ask you to think on your own a bit.

At the same time, for whatever reason you have chosen to not use norm here, NOT using canned code written by experts in the field is a BAD idea. You may think that you are being self sufficient. That is NOT a good idea here. Your hand written code will be often less than optimal. It will be less efficient, but often it may have subtle bugs in it that you won't even know exist. WHEREVER possible, use all the tools you have given to you. If you choose to let pride get in your way, your code will be the poorer for it.

In fact, even something as simple as norm had something in there as I recall to fix some problem that can arise, though I seem to recall it having to do with de-normalized numbers.

Anyway, a hint: A norm will have a square root in there, no? So the 2-norm will be the sqrt of the sum of squares.

Or, you can compare what you did compute to radius^2.

Related Solutions

MATLAB: How to minimize the 12th norm of a difference vector

This is quite confusing, because you have not ever explained what you really want. In your words:

"x is a weighted sum of two vectores A and B, x= weight1 *A + weigth2*B. The purpose of the minimization is to find the weights that minimize x-y."

You say that you have vector y, and two vectors A and B. Then you need to compute the weighted linear combination x of vectors A and B, that minimizes the norm (lets not worry about which norm for the moment), so

norm(x-y) = norm((w1*A + w1*B) - y)

If you really want the 12norm here, this is a straight optimization problem, but the 12 norm is really not much different from the infinity norm. Solving an inf norm problem will reduce to a linear programming problem, whereas solving the 2-norm problem is simple linear least squares.

For example, to solve the 2-norm (i.e., Euclidean distance, which you did say above) problem, all you need do is:

W12 = [A(:),B(:)]\y(:);
weight1 = W12(1);
weight2 = W12(2);

That simple. So it is trivial to do. There are at least a half dozen other ways to compute the same set of weights in MATLAB, but the above solution is simplest. It yields a set of weights that minimize the 2-norm of the difference between x and y. There are no iterations needed. That is the true solution, IF you really wanted a 2-norm.

However, if you really wanted a 12 norm, and would not be interested in the infinity norm, then some iterative scheme would be employed.

Do you really need to do this as a 12 norm? Why would you pick such an arbitrary value as 12? As I said, it will be relatively little different from the infinity norm. For example:

v = randn(1,100);
norm(v,12)
ans =
        2.926
norm(v,inf)
ans =
        2.811

Whereas, the 2-norm is quite different.

norm(v,2)
ans =
       9.8925

So if you insist on computing the solution under a 12 norm via some (unspecified iterative scheme) I can show you some ways to do so. Will ANY reasonable iterative scheme suffice?

For example, lets make up some data, then I'll solve it under a 12-norm using fminsearch.

y = randn(100,1);
A = randn(100,1);
B = randn(100,1);

The 2 norm solution is:

W12_2norm = [A(:),B(:)]\y(:)
W12_2norm =
   -0.0024203
      0.11984

Now, create an objective function to use for an optimizer.

fun_12 = @(W12) norm((A*W12(1) + B*W12(2)) - y,12);
fun_12(W12_2norm)
ans =
       2.8766

The 2-norm solution is not the minimum set of weights for the 12norm problem. But it will provide starting values for the optimization.

[W12_12norm,fval] = fminsearch(fun_12,W12_2norm)
W12_12norm =
      0.31792
     -0.11325
fval =
       2.7072

So a different set of weights has been obtained, which yields a somewhat lower value for the 12-norm.

Again, the 12-norm seems a bit arbitrary to me. A different solution comes from the infinity norm.

fun_inf = @(W12) norm((A*W12(1) + B*W12(2)) - y,inf);
[W12_infnorm,fval] = fminsearch(fun_inf,W12_2norm)
W12_infnorm =
   -0.0047671
     -0.68259
fval =
       2.7561

I need to be a bit careful there, because the inf norm is really not well-solved using fminsearch, because the inf norm will not be a smooth, differentiable function. fminsearch would prefer differentiability. I'd have been better off using a linprog solution on that, but since you have not asked at all for an inf norm solution, I'm not going to go that deeply into the solution, especially since I have no idea what you really want.

If you can explain more clearly what you really need, I could give a more precise answer. And there are lots of iterative ways I could have solved this problem (fminbnd, for example), but I don't see why any particular iterative solution would be better than what I've shown already.

MATLAB: Matrices with customized sums for rows and columns

Try randfixedsum: http://www.mathworks.com/matlabcentral/fileexchange/9700-random-vectors-with-fixed-sum

Best Answer

Related Solutions

MATLAB: How to minimize the 12th norm of a difference vector

MATLAB: Matrices with customized sums for rows and columns

Related Question