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#_/ ◆ Additional Mathemetics - KGC_MathReinforce ◆ XP/VX ◆
#_/ ◆ Written by TOMY     
#_/ ◆ Translation by Mr. Anonymous                  
#_/ ◆ KGC Site:                                                   
#_/ ◆  http://ytomy.sakura.ne.jp/                                   
#_/ ◆ Translator's Blog:                                             
#_/ ◆  http://mraprojects.wordpress.com     
#_/-----------------------------------------------------------------------------
#_/  Installation: Insert this script above main.
#_/=============================================================================
#_/  This script adds additional mathemetical operations only for scripting 
#_/   convenience.
#_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_

=begin
  Added functions
┠─── Module - Math ────────────────────────────
┃ average(value)
┃   value : Numeric array
┃  Calculate average value
┃
┃ devsq(value)
┃   value : Numeric array
┃  Calculate deviation square value
┃
┃ gmt(value)
┃   value : Numeric array
┃  Calculate average geometry(synergistic) value
┃
┃ stdevp(value)
┃   value : Numeric array
┃  Calculate standard deviation value
┃
┃ var(value)
┃   value : Numeric array
┃  Calculate square value
_______________________________________________
=end

module Math
  module_function
  #--------------------------------------------------------------------------
  # ● Average
  #--------------------------------------------------------------------------
  def average(value)
    n = 0.0
    value.each {|i| n += i}
    return n / value.size
  end
  #--------------------------------------------------------------------------
  # ● Deviation Square
  #--------------------------------------------------------------------------
  def devsq(value)
    n, v = 0.0, average(value)
    value.each {|i| n += (i - v) ** 2}
    return n
  end
  #--------------------------------------------------------------------------
  # ● Average Geometry(Synergistic)
  #--------------------------------------------------------------------------
  def gmt(value)
    n = 1.0
    value.each {|i| n *= i}
    return n ** (1.0 / value.size)
  end
  #--------------------------------------------------------------------------
  # ● Standard Deviation
  #--------------------------------------------------------------------------
  def stdevp(value)
    return sqrt(var(value))
  end
  #--------------------------------------------------------------------------
  # ● Square
  #--------------------------------------------------------------------------
  def var(value)
    return 0.0 if value.size < 2
    return devsq(value) / (value.size - 1)
  end
end