 Hull Butterfly Oscillator [LuxAlgo]
// This work is licensed under a Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) https://creativecommons.org/licenses/by-nc-sa/4.0/
// © LuxAlgo

//@version=5
indicator("Hull Butterfly Oscillator [LuxAlgo]", "Hull Butterfly Oscillator [LuxAlgo]")
//-----------------------------------------------------------------------------}
//Settings
//----------------------------------------------------a-------------------------{
length = input(14)

mult = input(2., 'Levels Multiplier')

src = input(close)

//Style
bull_css_0 = input.color(color.new(#0cb51a, 50), 'Bullish Gradient'
  , inline = 'inline0'
  , group = 'Style')

bull_css_1 = input.color(#0cb51a, ''
  , inline = 'inline0'
  , group = 'Style')

bear_css_0 = input.color(color.new(#ff1100, 50), 'Bearish Gradient'
  , inline = 'inline1'
  , group = 'Style')

bear_css_1 = input.color(#ff1100, ''
  , inline = 'inline1'
  , group = 'Style')

//-----------------------------------------------------------------------------}
//Normalization variables
//-----------------------------------------------------------------------------{
var short_len = int(length / 2)
var hull_len = int(math.sqrt(length))

var den1 = short_len * (short_len + 1) / 2
var den2 = length * (length + 1) / 2
var den3 = hull_len * (hull_len + 1) / 2

//-----------------------------------------------------------------------------}
//Hull coefficients
//-----------------------------------------------------------------------------{
var lcwa_coeffs = array.new_float(hull_len, 0)
var hull_coeffs = array.new_float(0)

if barstate.isfirst
    //Linearly combined WMA coeffs
    for i = 0 to length-1
        sum1 = math.max(short_len - i, 0)
        sum2 = length - i
    
        array.unshift(lcwa_coeffs, 2 * (sum1 / den1) - (sum2 / den2))
    
    //Zero padding of linearly combined WMA coeffs
    for i = 0 to hull_len-2
        array.unshift(lcwa_coeffs, 0)
    
    //WMA convolution of linearly combined WMA coeffs
    for i = hull_len to array.size(lcwa_coeffs)-1
        sum3 = 0.
        for j = i-hull_len to i-1
            sum3 += array.get(lcwa_coeffs, j) * (i - j)
        
        array.unshift(hull_coeffs, sum3 / den3)

//-----------------------------------------------------------------------------}
//Hull squeeze oscillator
//-----------------------------------------------------------------------------{
var os  = 0
var len = array.size(hull_coeffs)-1
hma     = 0.
inv_hma = 0.

for i = 0 to len
    hma += src[i] * array.get(hull_coeffs, i)
    inv_hma += src[len-i] * array.get(hull_coeffs, i)
    
hso = hma - inv_hma

cmean = ta.cum(math.abs(hso)) / bar_index * mult

os := ta.cross(hso, cmean) or ta.cross(hso, -cmean) ? 0
  : hso < hso[1] and hso > cmean ? -1
  : hso > hso[1] and hso < -cmean ? 1
  : os

//-----------------------------------------------------------------------------}
//Plot
//-----------------------------------------------------------------------------{
//Colors
css0 = color.from_gradient(hso, 0, cmean, bull_css_0, bull_css_1)
css1 = color.from_gradient(hso, -cmean, 0, bear_css_1, bear_css_0)
css = hso > 0 ? css0 : css1

//Oscillator line/histogram
plot(hso, 'Hull Butterfly', css
  , style = plot.style_histogram)

plot(hso, 'Hull Butterfly', chart.fg_color)

//Dots
plot(os > os[1] and os == 1 ? hso : na, 'Bullish Dot'
  , bull_css_1
  , 2
  , plot.style_circles)
  
plot(os < os[1] and os == -1 ? hso : na, 'Bearish Dot'
  , bear_css_1
  , 2
  , plot.style_circles)


//Levels
plot(cmean, color = color.gray, editable = false)

plot(cmean / 2, color = color.gray, editable = false)

plot(-cmean / 2, color = color.gray, editable = false)

plot(-cmean, color = color.gray, editable = false)

//-----------------------------------------------------------------------------}
