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Suppose I have a vector v2 = c(50,30,10,5) and I would like to calculate the angle between v2 and itself (i.e. the angle should be 0). I use the following codes:

norm_vec = function(x) sqrt(sum(x^2))

Then I call

acos( as.numeric((v2 %*% v2) / (norm_vec(v2) * norm_vec(v2))) )

However, instead of getting 0, I got the following warning message:

Warning message:
In acos(as.numeric((v2 %*% v2)/(norm_vec(v2) * norm_vec(v2)))) :
  NaNs produced

I checked the value of as.numeric((v2 %*% v2) / (norm_vec(v2) * norm_vec(v2))) as it is indeed a numeric of 1. I also checked acos(1) and the result is 0. What's wrong with my codes? Thanks!

alittleboy
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2 Answers2

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If you set x <- as.numeric((v2 %*% v2) / (norm_vec(v2) * norm_vec(v2))), you'll "see" that x is 1. However, x == 1 will return FALSE. And x-1 will return a very tiny positive number: 2.220446e-16. acos is not defined for numbers greater than 1.

The reason is that sqrt(sum(x^2)) is slightly smaller than the true square root; the true square root is an irrational number (with infinitely many digits). In this case, since you're multiplying norm_vec(v2) by itself anyways, why not just do:

acos( as.numeric(v2 %*% v2) / sum(v2^2) )
Amit Kumar Gupta
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  • thank you so much for your suggestions! Sorry I have to only accept one solution... I appreciate your help :) – alittleboy Sep 14 '13 at 23:06
2

See this answer: acos(1) returns NaN for some values, not others

And use pmin and pmax: acos(pmin(pmax(as.numeric(v2 %*% v2) / (norm_vec(v2) * norm_vec(v2)),-1.0), 1.0))

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tcash21
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