Ruby/Development/Math extensions

module Math
  def Math.logb(num, base)
    log(num) / log(base)
  end
end

def hmean(x)
  sum=0
  x.each {|v| sum += (1.0/v)}
  x.size/sum
end
data = [1.1,2.3,3.3,1.2,4.5,2.1,6.6 ]
puts hm = hmean(data)  # 2.101997946

def mean(x)
  sum=0
  x.each {|v| sum += v}
  sum/x.size
end
data = [1.1,2.3,3.3,1.2,4.5,2.1,6.6 ]
puts am = mean(data)   # 3.014285714

def mean(x)
  sum=0
  x.each {|v| sum += v}
  sum/x.size
end
def variance(x)
  m = mean(x)
  sum =0.0
  x.each {|v| sum += (v-m)**2 }
  sum/x.size
end
def sigma(x)
  Math.sqrt(variance(x))
end
data = [2,3,2,2,3,4,5,5,4,3,4,1,2 ]
puts sigma(data)     # 1.20894105

def median(x)
  sorted = x.sort
  mid = x.size/2
  sorted[mid]
end
data =[7,7,7,4,4,5,4,5,7,2,2,3,3,7,3,4 ]
puts median(data)  # 4

def mode(x)
  sorted = x.sort
  a = Array.new
  b = Array.new
  sorted.each do |x|
    if a.index(x)==nil
      a << x # Add to list of values
      b << 1 # Add to list of frequencies
    else
      b[a.index(x)] += 1 # Increment existing counter
    end
  end
  maxval = b.max           # Find highest count
  where = b.index(maxval)  # Find index of highest count
  a[where]                 # Find corresponding data value
end
data =[7,7,7,4,4,5,4,5,7,2,2,3,3,7,3,4 ]
puts mode(data)            # 7

def mean(x)
  sum=0
  x.each {|v| sum += v}
  sum/x.size
end
def variance(x)
  m = mean(x)
  sum =0.0
  x.each {|v| sum += (v-m)**2 }
  sum/x.size
end
data = [2,3,2,2,3,4,5,5,4,3,4,1,2 ]
puts variance(data)  # 1.461538462

def gmean(x)
  prod=1.0
  x.each {|v| prod *= v}
  prod**(1.0/x.size)
end
data = [1.1,2.3,3.3,1.2,4.5,2.1,6.6 ]
gm = gmean(data)  # 2.508411474

module Math
  RAD2DEG = 360.0/(2.0*PI)  # Radians to degrees
  RAD2GRAD = 400.0/(2.0*PI) # Radians to grads
end
def sin_d(theta)
  Math.sin(theta/Math::RAD2DEG)
end
def sin_g(theta)
  Math.sin(theta/Math::RAD2GRAD)
end
def atan2_d(y,x)
  Math.atan2(y,x)/Math::RAD2DEG
end
def atan2_g(y,x)
  Math.atan2(y,x)/Math::RAD2GRAD
end
def arcsin(x)
Math.atan2(x,Math.sqrt(1.0-x*x))
end
def arccos(x)
Math.atan2(Math.sqrt(1.0-x*x),x)
end
def arctan(x)
Math.atan2(x,1.0)
end
def sinh(x)
  (Math.exp(x)-Math.exp(-x))/2.0
end
def cosh(x)
  (Math.exp(x)+Math.exp(-x))/2.0
end
def tanh(x)
  sinh(x)/cosh(x)
end
def asinh(x)
  Math.log(x + Math.sqrt(1.0+x**2))
end
def acosh(x)
  2.0 *Math.log(Math.sqrt((x+1.0)/2.0)+Math.sqrt((x-1)/2.0))
end
def atanh(x)
  (Math.log(1.0+x) - Math.log(1.0-x))/2.0
end