Optimize a zscore algorithm

I wrote a zscore algorithm in Ruby that runs fine, but is incredibly slow when I have 8000+ entries to score. Can anyone help me figure out a way to improve my code, please?

module Enumerable
def mean
reduce(:+).to_f / length
end

def sample_variance
sum = inject(0){ |acc, i| acc + (i - mean)**2 }
1 / length.to_f * sum
end

def standard_deviation
Math.sqrt(sample_variance)
end

def zscore
if standard_deviation.zero?
Array.new(length, 0)
else
collect { |v| (v - mean) / standard_deviation }
end
end
end


The float is giving every score an accuracy of up to 17 decimal places. Would making it only 8 decimal places speed things up?

class Array
def mean(len=self.length)
reduce(:+).to_f / len
end

def sample_variance
len = length
m = mean(len)
sum = reduce { |acc, i| acc + (i - m)**2 }
sum.to_f / len
end

def standard_deviation
Math.sqrt(sample_variance)
end

def zscore
stdev = standard_deviation
m = mean
stdev.zero? ? Array.new(length, 0) : collect { |v| (v - m) / stdev }
end
end

-
If that is a sample variance (as opposed to a population variance), you need to divide by n-1 (not n) for it to be an unbiased estimator (though in this case the difference is negligible). Also, I suggest you write that sum / (length + 1.0). –  Cary Swoveland May 21 '14 at 8:38
@CarySwoveland I'm not a very mathy person...would you be so kind as to explain why I need to do sum/(length + 1.0) for sample variance? Thanks! Also, this is a population variance as I am running it on all records. –  DaniG2k May 21 '14 at 12:16
Unfortunately, it's a mathy answer. I think sum.to_f / len reads better than 1 / len.to_f * sum. –  Cary Swoveland May 21 '14 at 16:28

The problem is here: collect { |v| (v - mean) / standard_deviation }. standard_deviation is constant but, being inside a block, it is called on each iteration. Set the value to a local variable before. As noted by Flambino, the same principle applies to sample_variance (which uses mean inside a block).

In a functional language (where immutability is honored) the compiler would be able to do the right thing, but not in an imperative language plagued with side-effects like Ruby.

• module Enumerable: But you call .length, which is not a method that an enumerable is required to implement. Consider adding them to Array (which includes Enumerable).
• reduce and then inject. I'd use just one of the alias.
@DaniG2k You can do the same local var trick with mean in your zscore and sample_variance methods. Not as big a boost as storing standard_deviation, but the principle's the same –  Flambino May 18 '14 at 21:42
@tokland I'm confused: the reduce method should be called on an Enumerable but length should be called on an Array. Which is better to use? –  DaniG2k May 18 '14 at 21:53
@DaniG2k: Array includes Enumerable. –  tokland May 18 '14 at 21:58