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Calculate Euclidean distance between 4-dimensional vectors

Let's say I have two 4-dimensional vectors (i.e. a and b) as follows:

a = {a1, a2, a3, a4}
b= {b1, b2, b3, b4}

How do I compute the Euclidean distance between these vectors?

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user3583442 Avatar asked Apr 29 '14 01:04

user3583442


2 Answers

The euclidian distance calculus is independent of dimensions.

In your case, the euclidian distance between a and b can be written as:

d(a,b) = sqrt( sum_{ i=1 } ^ { 4 } (a[ i ] - b[ i ])^2 )

Or, more specifically:

d(a,b) = sqrt( (a1 - b1)^2 + (a2 - b2)^2 + (a3 -b3)^2 + (a4 - b4)^2 )
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Marlos C. Machado Avatar answered Oct 11 '22 00:10

Marlos C. Machado


public static float ndistance(float[] a, float[] b) {
    float total = 0, diff;
    for (int i = 0; i < a.length; i++) {
        diff = b[i] - a[i];
        total += diff * diff;
    }
    return (float) Math.sqrt(total);
}

The function/method/code above will calculate the distance in n-dimensional space. a and b are arrays of floating point number and have the same length/size or simply the n. Since you want a 4-dimension, you simply pass a 4-length array representing the data of your 4-D vector.

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D.R.Bendanillo Avatar answered Oct 11 '22 01:10

D.R.Bendanillo