module Nuggets::Array::MeanMixin

Calculates the arithmetic mean of the values in array.

An optional block may be passed to provide a weight for each value. Defaults to 1. Returns nil if the sum of all weights is zero (this includes array being empty).

   # File lib/nuggets/array/mean_mixin.rb
70 def arithmetic_mean(&block)
71   generalized_mean(1, &block)
72 end

Calculates the generalized mean of the values in array for exponent. Returns the geometric_mean if exponent is zero.

An optional block may be passed to provide a weight for each value. Defaults to 1. Returns nil if the sum of all weights is zero (this includes array being empty).

   # File lib/nuggets/array/mean_mixin.rb
42 def generalized_mean(exponent, &block)
43   return geometric_mean(&block) if exponent.zero?
44 
45   total, weights = 0, 0
46 
47   each { |x|
48     weight = block ? block[x] : 1
49 
50     total   += weight * x ** exponent
51     weights += weight
52   }
53 
54   (total / weights.to_f) ** (1.0 / exponent) unless weights.zero?
55 end

Calculates the geometric mean of the values in array.

An optional block may be passed to provide a weight for each value. Defaults to 1. Returns nil if the sum of all weights is zero (this includes array being empty).

    # File lib/nuggets/array/mean_mixin.rb
121 def geometric_mean
122   total, weights = 1, 0
123 
124   each { |x|
125     weight = block_given? ? yield(x) : 1
126 
127     total   *= x ** weight
128     weights += weight
129   }
130 
131   total ** (1 / weights.to_f) unless weights.zero?
132 end

Calculates the harmonic mean of the values in array.

An optional block may be passed to provide a weight for each value. Defaults to 1. Returns nil if the sum of all weights is zero (this includes array being empty).

    # File lib/nuggets/array/mean_mixin.rb
105 def harmonic_mean(&block)
106   generalized_mean(-1, &block)
107 end

Expects array to be an array of arrays (“rows”) of numeric values; the first “row” may consist of strings (labels) instead. Returns an array of strings with the mean (according to method, default mean) of each “column”, prepended with the label, if present, and appended with the standard deviation, if available; all values are subject to precision.

If array is a flat array of numeric values, it is treated as a single “column”.

Returns nil if array is empty.

Examples (with standard deviation):

[[9.4, 34.75], [9.46, 34.68], [9.51, 34.61]].report_mean
#=> ["9.4567 +/- 0.0450", "34.6800 +/- 0.0572"]

[[9.4, 34.75], [9.46, 34.68], [9.51, 34.61]].report_mean(:harmonic)
#=> ["9.4565 +/- 0.0450", "34.6799 +/- 0.0572"]

[["a", "b"], [9.4, 34.75], [9.46, 34.68], [9.51, 34.61]].report_mean(nil, 2)
#=> ["a  9.46 +/- 0.04", "b  34.68 +/- 0.06"]

CSV.read('csv', headers: true, converters: :numeric).to_a.report_mean
#=> ["a    9.4567 +/- 0.0450", "b    34.6800 +/- 0.0572"]

[9.4, 9.46, 9.51].report_mean
#=> ["9.4567 +/- 0.0450"]

[34.75, 34.68, 34.61].report_mean
#=> ["34.6800 +/- 0.0572"]

[].report_mean
#=> nil

    # File lib/nuggets/array/mean_mixin.rb
174 def report_mean(method = nil, precision = 4)
175   return if empty?
176 
177   return clone.replace(self.class.new.push(self).transpose).
178     report_mean(method, precision) unless first.is_a?(self.class)
179 
180   met, sep = [method ||= :mean, 'mean'], ['', '_']
181   lab, std = first.first.is_a?(::String), respond_to?(:std)
182 
183   fmt = ["%-#{precision}s", "%.#{precision}f", "+/- %.#{precision}f"]
184 
185   until respond_to?(method) || sep.empty?
186     method = met.join(sep.shift)
187   end
188 
189   transpose.map! { |x|
190     i, a = [], []
191 
192     i << 0 and a << x.shift if lab
193     i << 1 and a << x.send(method)
194     i << 2 and a << x.std if std
195 
196     fmt.values_at(*i).join(' ') % a
197   }
198 end

Calculates the root mean square (quadratic mean) of the values in array.

An optional block may be passed to provide a weight for each value. Defaults to 1. Returns nil if the sum of all weights is zero (this includes array being empty).

   # File lib/nuggets/array/mean_mixin.rb
88 def root_mean_square(&block)
89   generalized_mean(2, &block)
90 end