covar, variance, correl

import logging, math

proc covar(vx, vy : openArray[float]) : float =
  if len(vx) != len(vy) or len(vx) < 2:
    error("Covar requires equal length arrays, length greater than 2.")

  var result : float = 0.0

  var mx = mean(vx)
  var my = mean(vy)

  for i in 0..len(vx)-1:
    var xd = vx[i] - mx
    var yd = vy[i] - my
    result += (xd * yd - result) / (float(i) + 1.0)

  return result

proc variance(vx : openArray[float]) : float =
  return covar(vx, vx)

proc correl(vx, vy : openArray[float]) : float =
  return covar(vx, vy) / (sqrt(variance(vx)) * sqrt(variance(vy)))