Feature #13208: Vector.zero(n) and vector.zero?

• Status: Closed
• Assignee: marcandre (Marc-Andre Lafortune)
• Target version: -

[qitar888 (Chia-sheng Chen)]

Found that I need this recently, and class Matrix has these two function while Vector not.
So I add two function based on Matrix counterpart and also add test.

Usage

require 'matrix'
v = Vector.zero(3)  # => Vector[0, 0, 0]
v.zero?  # => true
w = Vector[1, 0, 0]
w.zero?  # => false

[shevegen (Robert A. Heiler)]

I think the method is fine but of course that is just my own opinion,
the core team and matz will decide that.

One hopefully small request though:

• Do you think you could make the description for the method a
  bit more explicit? Right now the documentation to it states only:

"Return a zero vector."

Perhaps this is obvious to others but I am not entirely sure
what a zero vector per se is, although of course the example is
explicit enough to infer from it (I assume a zero vector is one that
contains only 0 as its members but from the documentation alone,
without the example, I am not sure everyone may be able to infer
this completely correctly so.)

[marcandre (Marc-Andre Lafortune)]

• Assignee set to marcandre (Marc-Andre Lafortune)

Looks good.

I think the short description is probably good enough. The example makes it clear if someone has doubts...

I'm travelling, will commit in a few days.

[marcandre (Marc-Andre Lafortune)]

Thanks for the patch.
Committed.
PS: I allowed Vector.zero(0).

[marcandre (Marc-Andre Lafortune)]

• Status changed from Open to Closed

[stomar (Marcus Stollsteimer)]

Just curious:

Vector.zero(0).zero?  # => true or false?

Not sure what I would expect in this case.

[duerst (Martin Dürst)]

stomar (Marcus Stollsteimer) wrote:

Just curious:

Vector.zero(0).zero?  # => true or false?

Not sure what I would expect in this case.

Definitely true. More generally,

Vector.zero(x).zero?  # => true

for any value of x.

Colloquially, all the values in the vector are zero, even if there aren't that many values there.

That also matches how Mathematics works.

It also works best that way in programming. The simplest implementation of zero? is something like

class Vector
  def zero?
    all { |e| e.zero? }
  end
end

which will automatically give the right result.

[stomar (Marcus Stollsteimer)]

Granted, in the case of #zero? returning true might suggest itself, but is "nothing" really the same as "zero"...? If there was a method Vector.one with Vector.one(3) => Vector[1, 1, 1], should Vector.one(0).one? be true? (All the values in the vector are 1, even if there aren't that many values there...). In that case, for Vector[] both #one? and #zero? would be true at the same time...

Generally speaking: I'm a bit sceptical about allowing zero size for these creator methods and about allowing these properties for zero size vectors/matrices, and I'm not sure what mathematics says about it.

It's easier to demonstrate the possible problems using the Matrix class (which has more methods to play around). The current behavior is a bit strange and contradictory:

size = 0

z = Matrix.zero(size)
z.zero? && z.orthogonal? && z.unitary?  # => true  (a zero matrix that's also orthogonal!)
z.det    # => 1  (should be 0 for *any* `size')

i = Matrix.identity(size)
i.zero?  # => true  (should be false for *any* `size')

# and of course:
i == z  # true  (!)

The question is whether the methods that generate those special matrices/vectors should allow size 0 (since the generated objects do not have all the expected properties), and/or whether the methods that query these properties should return a value or not (since the property might not be very meaningful).

[marcandre (Marc-Andre Lafortune)]

Martin is exactly right. See https://en.wikipedia.org/wiki/Vacuous_truth