From: "theosib@..." <theosib@...>
Date: 2007-11-02T09:07:06+09:00
Subject: Fastest way to compute dot product (inner product) in Ruby?

Ruby seems to provide some nice, abstract ways of doing some
computationally intensive things quickly.  For instance, String#unpack
is a very nice and efficient way to convert between formats when doing
I/O and such.  Unfortunately, it doesn't seem to have an efficient way
to compute functions on vectors.  It sure would be nice, for instance,
if I could add two vectors and get another vector which is the
component-wise sum.  But alas, it's also important to be able to
concatenate arrays.  Anyhow, so I'm trying to find the fastest way to
compute a dot product, and I was hoping I could get some help from
others out there who surely know more about this than I do.

I'd like to begin by saying that Array#zip sucks.  Ok, I'm sure
there's a case where it's useful, but I haven't found it.  Every one
of the dot product suggestions I've found through Google suggests
using zip, and I have found that zip imposes a huge amount of
overhead.  I suspect the main problem is that zip isn't lazy about
creating the new array but instead actually allocates the memory and
fully computes the combined array before passing it on.  That takes a
long time, even though it's being done "under the hood" in C where it
should be faster.

To make a long story short, I've put together a benchmark that
compares a number of different solutions.  Unfortunately, the
"dumbest" most straight-forward solution seems to be, by far, the
fastest.  There's got to be a better way, and I'm hoping someone on
this newsgroup can make a suggestion.

To jump to the answer, this one is consistently the winner:

def dot_product_e l1, l2
    sum = 0
    for i in 0...l1.size
        sum += l1[i] * l2[i]
    end
    sum
end


Here's the benchmark I ran:

require 'benchmark'


# The following from http://c2.com/cgi/wiki?DotProductInManyProgrammingLanguages
def dot_product_a l1, l2
    l1.zip(l2).inject(0) { |sum,els| sum+els[0]*els[1] }
end

def dot_product_b l1, l2
    l1.zip(l2).map { |a,b| a*b }.inject {|sum,el| sum+el}
end

def dot_product_c l1, l2
    sum=0
    for a,b in l1.zip(l2)
        sum+= a*b
    end
    sum
end

def dot_product_d l1, l2
    sum=0
    l1.zip(l2){|a, b| sum+=a*b}
    sum
end


# The next two, I wrote
def dot_product_e l1, l2
    sum = 0
    for i in 0...l1.size
        sum += l1[i] * l2[i]
    end
    sum
end

def dot_product_f l1, l2
    sum = 0
    l1.each_index do |i|
        sum += l1[i] * l2[i]
    end
    sum
end

# And lastly, I copied code from the standard matrix.rb module
def each2(v1, v2)
    0.upto(v1.size - 1) do |i|
        yield v1[i], v2[i]
    end
end

def dot_product_g l1, l2
    sum = 0
    each2(l1, l2) { |a,b| sum += a*b }
    sum
end

a = []
b = []
for i in 0...1000000
    a.push(rand)
    b.push(rand)
end

n = 500000
Benchmark.bm do |x|
  x.report { dot_product_a(a, b) }
  x.report { dot_product_b(a, b) }
  x.report { dot_product_c(a, b) }
  x.report { dot_product_d(a, b) }
  x.report { dot_product_e(a, b) }
  x.report { dot_product_f(a, b) }
  x.report { dot_product_g(a, b) }
end


On an Apple MacBook Pro with a Core 2 Duo, 2.33GHz, with Ruby compiled
through Fink, these are the results (repeated runs nearly identical):

      user     system      total        real
  1.960000   0.050000   2.010000 (  2.022095)
  1.890000   0.140000   2.030000 (  2.046605)
  1.230000   0.020000   1.250000 (  1.261263)
  1.270000   0.010000   1.280000 (  1.277588)
  0.790000   0.000000   0.790000 (  0.793650)
  1.180000   0.000000   1.180000 (  1.198618)
  1.340000   0.000000   1.340000 (  1.344791)