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Math Help - Circle problem

  1. #1
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    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.)
    Last edited by madflame991; May 20th 2011 at 07:49 AM.
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  2. #2
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    Quote Originally Posted by madflame991 View Post
    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) ).
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  3. #3
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    My bad, I forgot a -1 there. It should be ok now.
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  4. #4
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    Quote Originally Posted by madflame991 View Post
    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.
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