# Module: Measurable::Euclidean

Included in:
Measurable
Defined in:
lib/measurable/euclidean.rb

## Instance Method Summary collapse

• call-seq: euclidean(u) -> Float euclidean(u, v) -> Float.

• call-seq: euclidean_squared(u) -> Float euclidean_squared(u, v) -> Float.

## Instance Method Details

### #euclidean(u, v = nil) ⇒ Object

call-seq:

``````euclidean(u) -> Float
euclidean(u, v) -> Float
``````

Calculate the ordinary distance between arrays `u` and `v`.

If `v` isn't given, calculate the Euclidean norm of `u`.

Arguments:

• `u` -> An array of Numeric objects.

• `v` -> (Optional) An array of Numeric objects.

Returns:

• The euclidean norm of `u` or the euclidean distance between `u` and `v`.

Raises:

• `ArgumentError` -> The sizes of `u` and `v` don't match.

 ``` 21 22 23``` ```# File 'lib/measurable/euclidean.rb', line 21 def euclidean(u, v = nil) Math.sqrt(self.euclidean_squared(u, v)) end```

### #euclidean_squared(u, v = nil) ⇒ Object

call-seq:

``````euclidean_squared(u) -> Float
euclidean_squared(u, v) -> Float
``````

Calculate the same value as euclidean(u, v), but don't take the square root of it.

This isn't a metric in the strict sense, i.e. it doesn't respect the triangle inequality. However, the squared Euclidean distance is very useful whenever only the relative values of distances are important, for example in optimization problems.

Arguments:

• `u` -> An array of Numeric objects.

• `v` -> (Optional) An array of Numeric objects.

Returns:

• The squared value of the euclidean norm of `u` or of the euclidean distance between `u` and `v`.

Raises:

• `ArgumentError` -> The sizes of `u` and `v` don't match.

Raises:

• (ArgumentError)
 ``` 47 48 49 50 51 52 53 54 55 56 57 58 59 60``` ```# File 'lib/measurable/euclidean.rb', line 47 def euclidean_squared(u, v = nil) # If the second argument is nil, the method should return the norm of # vector u. For this, we need the distance between u and the origin. if v.nil? v = Array.new(u.size, 0) end # TODO: Change this to a more specific, custom-made exception. raise ArgumentError if u.size != v.size u.zip(v).reduce(0.0) do |acc, ary| acc += (ary - ary[-1]) ** 2 end end```