CODEWITHSUNDEEP
rangle
cahix
cahix

Reputation: 183

Angle between two nearly identical vectors

I found that using 

angle <- (acos(sum(a*b) / (sqrt(sum(a * a)) * sqrt(sum(b * b)))))

is the most common way to get an angle between two vectors a and b in R.

Unfortunately, I keep on getting errors on certain vectors that seem to lay on each other or have an angle of about 180 degrees between each other.

For example: 

a <- c(-7.6942088429381328e-01, 2.4999999999999989e-01)  
b <- c(-5.4146791834239578e+08, 1.7593359143824694e+08)

do not work.

I am facing similar problems with other ways of calculating an angle.

Upvotes: 2

Views: 109

Answers (1)

Maurits Evers
Maurits Evers

Reputation: 50718

I would use vector operations.

Let's define a proper function angle that takes as arguments two vectors x1 and x2

angle <- function(x1, x2, tol = 1e-6) {
    cost <- as.numeric((x1 %*% x2) / (sqrt(x1 %*% x1) * sqrt(x2 %*% x2)))
    if (abs(cost - 1) < tol) return(0) else return(acos(cost))
}

Note that we do a numeric stability check to ensure that for angles close to 0, we get a numeric result (instead of NA).

Then to calculate the angle (in radians) between two vectors, e.g.

x1 <- c(1, 1)
x2 <- c(0.5, 2)

we do

angle(x1, x2)
#[1] 0.5404195

In your case,

angle(a, b)
#[1] 0

Note that this will also work for higher dimensional vectors, e.g.

x1 <- c(1, 1, 1)
x2 <- c(0.5, 2, 0)
angle(x1, x2)
#[1] 0.7952027

Upvotes: 2

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