"Algebraic" IF Statement Evaluation

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Jim Thompson 17 years ago

I need to evaluate...

IF(t,1,0) (If t is true, output 1, if t is false, output 0 (numeric), t may be something like V11 >= 7, for example)

BUT I have no IF statement handling capability at this level of a simulation.

I do have algebraic capability.

Is there some cute way to do this algebraically?

...Jim Thompson

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qrus19 17 years ago

X=int(V11/7) X/X

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qrus19 17 years ago

gah! messed that up :S

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Tim Shoppa 17 years ago

For your example, V11>=3D7:

(abs(V11-7))/(V11-7) will be +1 for V11>7, -1 for V11

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qrus19 17 years ago

t=X/X

This will sorta work, but if x is 0 then you'll probably get errors, to a human it's the 0/0 = 1 thing not having used your emulator I can't be sure what'll happen of how to treat an error like this.

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Jim Thompson 17 years ago

I don't have INT available, I do have ABS and some trig functions

...Jim Thompson

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Jim Thompson 17 years ago

That's what I came up with, except I inserted a small "delta" (smaller than my step size) to avoid 0/0. I was hoping for something more compact :-(

...Jim Thompson

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Paul Hovnanian P.E. 17 years ago

Do you have a unit step function (u(x)) available?

Paul Hovnanian paul@hovnanian.com ---------------------------------------------------------------------- Have gnu, will travel.

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Jim Thompson 17 years ago

No :-(

...Jim Thompson

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Jim Thompson 17 years ago

I don't have function SGN :-(

...Jim Thompson

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Spehro Pefhany 17 years ago

(1+sgn(V11-7))/2 ?

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Spehro Pefhany 17 years ago

y = V11 -7

(abs(y) + y)/(2*y)

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Spehro Pefhany 17 years ago

P.S. If you want avoid awkward situations very near y == 0 you could do

(abs(y) + y)/(2* abs(y) + e)

where e is a very small positive number

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Jasen Betts 17 years ago

are there any operators or functions that can give a different mumeric result depending on the truth of the input.

many systems have false as 0 and true as 1 (or less common -1)

else maybe something like (sgn( sgn(V11-7) *2 +1 ) + 1 ) /2

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Tom Del Rosso 17 years ago

ABS has an intrinsic "if" that can do it. Spehro showed the method.

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JosephKK 17 years ago

(numeric),

Do you have a tanh() function?

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Jim Thompson 17 years ago

No, Though I'm fascinated. How would use of TANH() work in this situation?

...Jim Thompson

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James Waldby 17 years ago

tanh(x) = (e^x - e^-x) / (e^x + e^-x), so for large |x| (for example, |x| > 3) it approximates x/abs(x) quite closely but avoids divide-by-zero issues. For snappier results, consider tanh(k*x), at the risk of overflow if k is too big.

.

jiw

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Jim Thompson 17 years ago

So the equivalent of "SGN"?

...Jim Thompson

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JosephKK 17 years ago

(numeric),

With tanh(Ax-B)/2 + 1/2 you may arbitrarily make close approximation to a unit step function (including shiftability). Or do interesting cross fade like things. Mostly pretty well behaved for numerical techniques as well.

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"Algebraic" IF Statement Evaluation

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