Thread: Circle problem

I need to write this:

f(x,y) = hardlim(sqrt(x^2+y^2)-1) (hardlim(x) = 0 if x <= 0 and 1 otherwise)

but without using any multiplication or the square root. Only thing I can use is summation, multiplication by a value (x*5), and the hardlim or hyperbolic tangent functions.

(I basically need to build a neural net classifier thingie that will return 1 if a point is in the unit circle and 0 otherwise.)

Originally Posted by madflame991

I need to write this:

f(x,y) = hardlim(sqrt(x^2+y^2)) (hardlim(x) = 0 if x <= 0 and 1 otherwise)

but without using any multiplication or the square root. Only thing I can use is summation, multiplication by a value (x*5), and the hardlim or hyperbolic tangent functions.

(I basically need to build a neural net classifier thingie that will return 1 if a point is in the unit circle and 0 otherwise.)

I'm not sure that I understand the question. That function f(x,y) is always 1 except at the origin. I don't see what that has to do with a function that will return 1 if a point is in the unit circle and 0 otherwise.

You can define the given function f(x,y) in terms of the hardlim function by

f(x,y) = hardlim( hardlim(x) + hardlim((–1)*x) + hardlim(y) + hardlim((–1)*y) ).

My bad, I forgot a -1 there. It should be ok now.

Originally Posted by madflame991

My bad, I forgot a -1 there. It should be ok now.

In that case, it seems to me that what you want is not possible. You can easily eliminate the square root function, because hardlim(sqrt(x^2+y^2)-1) is the same as hardlim(x^2+y^2-1). But I don't see any way of avoiding multiplication. I also don't see that the tanh function can be any help at all here.