-- More information about this indicator can be found at:
-- http://fxcodebase.com/code/viewtopic.php?f=17&t=67311

--+------------------------------------------------------------------+
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--|                                            http://fxcodebase.com |
--+------------------------------------------------------------------+
--|                                      Developed by : Mario Jemic  |
--|                                          mario.jemic@gmail.com   |
--+------------------------------------------------------------------+
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--+------------------------------------------------------------------+

-- Indicator profile initialization routine

function Init()
    indicator:name("Belkhayate Gravity Center")
    indicator:description("")
    indicator:requiredSource(core.Tick)
    indicator:type(core.Indicator)

    indicator.parameters:addGroup("Calculation")
    indicator.parameters:addInteger("bars_back", "Start Bars Back", "Bars Back", 125)
    indicator.parameters:addInteger("m", "Order", "Order", 2)
    indicator.parameters:addDouble("kstd", "Multiplier", "Multiplier", 2)

    indicator.parameters:addColor("GravityLine_color", "GravityLine Line Color", "", core.rgb(0, 255, 0))
    indicator.parameters:addColor("UC1_2_color", "UC 1-2 Color", "Color", core.colors().Red);
    indicator.parameters:addInteger("UC1_2_width", "UC 1-2 Width", "Width", 1, 1, 5);
    indicator.parameters:addInteger("UC1_2_style", "UC 1-2 Style", "Style", core.LINE_DASH);
    indicator.parameters:setFlag("UC1_2_style", core.FLAG_LINE_STYLE);
    indicator.parameters:addColor("UC2_3_color", "UC 2-3 Color", "Color", core.colors().Red);
    indicator.parameters:addInteger("UC2_3_width", "UC 2-3 Width", "Width", 1, 1, 5);
    indicator.parameters:addInteger("UC2_3_style", "UC 2-3 Style", "Style", core.LINE_DASH);
    indicator.parameters:setFlag("UC2_3_style", core.FLAG_LINE_STYLE);
    indicator.parameters:addColor("LC1_2_color", "LC 1-2 Color", "Color", core.colors().LimeGreen);
    indicator.parameters:addInteger("LC1_2_width", "LC 1-2 Width", "Width", 1, 1, 5);
    indicator.parameters:addInteger("LC1_2_style", "LC 1-2 Style", "Style", core.LINE_DASH);
    indicator.parameters:setFlag("LC1_2_style", core.FLAG_LINE_STYLE);
    indicator.parameters:addColor("LC2_3_color", "LC 2-3 Color", " Color", core.colors().LimeGreen);
    indicator.parameters:addInteger("LC2_3_width", "LC 2-3 Width", " Width", 1, 1, 5);
    indicator.parameters:addInteger("LC2_3_style", "LC 2-3 Style", " Style", core.LINE_DASH);
    indicator.parameters:setFlag("LC2_3_style", core.FLAG_LINE_STYLE);
    indicator.parameters:addColor("UC1_color", "UC1 Color", "Color", core.colors().Gray);
    indicator.parameters:addInteger("UC1_width", "UC1 Width", "Width", 1, 1, 5);
    indicator.parameters:addInteger("UC1_style", "UC1 Style", "Style", core.LINE_SOLID);
    indicator.parameters:setFlag("UC1_style", core.FLAG_LINE_STYLE);
    indicator.parameters:addColor("UC2_color", "UC2 Color", "Color", core.colors().Red);
    indicator.parameters:addInteger("UC2_width", "UC2 Width", "Width", 1, 1, 5);
    indicator.parameters:addInteger("UC2_style", "UC2 Style", "Style", core.LINE_SOLID);
    indicator.parameters:setFlag("UC2_style", core.FLAG_LINE_STYLE);
    indicator.parameters:addColor("UC3_color", "UC3 Color", "Color", core.colors().Red);
    indicator.parameters:addInteger("UC3_width", "UC3 Width", "Width", 1, 1, 5);
    indicator.parameters:addInteger("UC3_style", "UC3 Style", "Style", core.LINE_SOLID);
    indicator.parameters:setFlag("UC3_style", core.FLAG_LINE_STYLE);
    indicator.parameters:addColor("LC1_color", "LC1 Color", "Color", core.colors().Gray);
    indicator.parameters:addInteger("LC1_width", "LC1 Width", "Width", 1, 1, 5);
    indicator.parameters:addInteger("LC1_style", "LC1 Style", "Style", core.LINE_SOLID);
    indicator.parameters:setFlag("LC1_style", core.FLAG_LINE_STYLE);
    indicator.parameters:addColor("LC2_color", "LC2 Color", "Color", core.colors().LimeGreen);
    indicator.parameters:addInteger("LC2_width", "LC2 Width", "Width", 1, 1, 5);
    indicator.parameters:addInteger("LC2_style", "LC2 Style", "Style", core.LINE_SOLID);
    indicator.parameters:setFlag("LC2_style", core.FLAG_LINE_STYLE);
    indicator.parameters:addColor("LC3_color", "LC3 Color", "Color", core.colors().LimeGreen);
    indicator.parameters:addInteger("LC3_width", "LC3 Width", "Width", 1, 1, 5);
    indicator.parameters:addInteger("LC3_style", "LC3 Style", "Style", core.LINE_SOLID);
    indicator.parameters:setFlag("LC3_style", core.FLAG_LINE_STYLE);
end

local first
local source = nil

local GravityLine
local UC1, UC1_2, UC2_3
local UC2
local UC3
local LC1, LC1_2, LC2_3
local LC2
local LC3
local bars_back
local kstd, m, i, nn, p

function Prepare(nameOnly)
    local name = profile:id() .. "(" .. instance.source:name() .. ")"
    instance:name(name)
    if (nameOnly) then
        return
    end
    source = instance.source
    bars_back = instance.parameters.bars_back
    kstd = instance.parameters.kstd
    m = instance.parameters.m
    nn = m + 1
    p = bars_back
    GravityLine =
        instance:addStream(
        "GravityLine",
        core.Line,
        "GravityLine",
        "GravityLine",
        instance.parameters.GravityLine_color,
        0
    )
    UC1 = instance:addStream("UC1", core.Line, "UC1", "UC1", instance.parameters.UC1_color, 0, 0);
    UC1:setWidth(instance.parameters.UC1_width);
    UC1:setStyle(instance.parameters.UC1_style);
    UC2 = instance:addStream("UC2", core.Line, "UC2", "UC2", instance.parameters.UC2_color, 0)
    UC2:setWidth(instance.parameters.UC2_width);
    UC2:setStyle(instance.parameters.UC2_style);
    UC3 = instance:addStream("UC3", core.Line, "UC3", "UC3", instance.parameters.UC3_color, 0)
    UC3:setWidth(instance.parameters.UC3_width);
    UC3:setStyle(instance.parameters.UC3_style);
    LC1 = instance:addStream("LC1", core.Line, "LC1", "LC1", instance.parameters.LC1_color, 0)
    LC1:setWidth(instance.parameters.LC1_width);
    LC1:setStyle(instance.parameters.LC1_style);
    LC2 = instance:addStream("LC2", core.Line, "LC2", "LC2", instance.parameters.LC2_color, 0)
    LC2:setWidth(instance.parameters.LC2_width);
    LC2:setStyle(instance.parameters.LC2_style);
    LC3 = instance:addStream("LC3", core.Line, "LC3", "LC3", instance.parameters.LC3_color, 0)
    LC3:setWidth(instance.parameters.LC3_width);
    LC3:setStyle(instance.parameters.LC3_style);
    LC1_2 = instance:addStream("LC12", core.Line, "LC1-2", "LC1-2", instance.parameters.LC1_2_color, 0, 0);
    LC1_2:setWidth(instance.parameters.LC1_2_width);
    LC1_2:setStyle(instance.parameters.LC1_2_style);
    LC2_3 = instance:addStream("LC23", core.Line, "LC2-3", "LC2-3", instance.parameters.LC2_3_color, 0, 0);
    LC2_3:setWidth(instance.parameters.LC2_3_width);
    LC2_3:setStyle(instance.parameters.LC2_3_style);
    UC1_2 = instance:addStream("UC12", core.Line, "UC1-2", "UC1-2", instance.parameters.UC1_2_color, 0, 0);
    UC1_2:setWidth(instance.parameters.UC1_2_width);
    UC1_2:setStyle(instance.parameters.UC1_2_style);
    UC2_3 = instance:addStream("UC2-3", core.Line, "UC2-3", "UC2-3", instance.parameters.UC2_3_color, 0, 0);
    UC2_3:setWidth(instance.parameters.UC2_3_width);
    UC2_3:setStyle(instance.parameters.UC2_3_style);
end
local i = 0
local sx = {}
local b = {}
local ai = {}
local x = {}
local fx = {}
function Update(period, mode)
    if (period < p) then
        return
    end

    sx[1] = p + 1
    local mi, n, jj, ii, kk, mm, tt, qq
    -----------------------sx-------------------------------------------------------------------
    local sum = 0
    for mi = 1, nn * 2 - 2, 1 do
        sum = 0
        for n = i, i + p, 1 do
            sum = sum + math.pow(n, mi)
        end
        sx[mi + 1] = sum
    end
    ----------------------syx-----------
    for mi = 1, nn, 1 do
        sum = 00

        for n = i, i + p, 1 do
            if (mi == 1) then
                sum = sum + source[period - n]
            else
                sum = sum + source[period - n] * math.pow(n, mi - 1)
            end
        end
        b[mi] = sum
    end

    --===============Matrix=======================================================================================================
    for jj = 1, nn, 1 do
        ai[jj] = {}
    end

    for jj = 1, nn, 1 do
        for ii = 1, nn, 1 do
            kk = ii + jj - 1
            ai[ii][jj] = sx[kk]
        end
    end

    --===============Gauss========================================================================================================
    for kk = 1, nn - 1, 1 do
        ll = 0
        mm = 0
        for ii = kk, nn, 1 do
            if math.abs(ai[ii][kk]) > mm then
                mm = math.abs(ai[ii][kk])
                ll = ii
            end
        end

        if (ll == 0) then
            return
        end

        if (ll ~= kk) then
            for jj = 1, nn, 1 do
                tt = ai[kk][jj]
                ai[kk][jj] = ai[ll][jj]
                ai[ll][jj] = tt
            end
            tt = b[kk]
            b[kk] = b[ll]
            b[ll] = tt
        end

        for ii = kk + 1, nn, 1 do
            qq = ai[ii][kk] / ai[kk][kk]
            for jj = 1, nn, 1 do
                if (jj == kk) then
                    ai[ii][jj] = 0
                else
                    ai[ii][jj] = ai[ii][jj] - qq * ai[kk][jj]
                end
            end
            b[ii] = b[ii] - qq * b[kk]
        end
    end

    x[nn] = b[nn] / ai[nn][nn]
    for ii = nn - 1, 1, -1 do
        tt = 0
        for jj = 1, nn - ii, 1 do
            tt = tt + ai[ii][ii + jj] * x[ii + jj]
            x[ii] = (1 / ai[ii][ii]) * (b[ii] - tt)
        end
    end

    if period < source:size() - 1 then
        return
    end

    period = source:size() - 1

    --===========================================================================================================================
    for n = i, i + p, 1 do
        sum = 0
        for kk = 1, m, 1 do
            sum = sum + x[kk + 1] * math.pow(n, kk)
        end
        GravityLine[period - n] = x[1] + sum
    end

    if source:size() - 1 - p - 1 > source:first() then
        GravityLine[source:size() - 1 - p - 1] = nil
    end

    local sq = 0
    local std = 0

    for n = i, i + p, 1 do
        sq = sq + math.pow(source[period - n] - GravityLine[period - n], 2)
    end

    sq = math.sqrt(sq / (p + 1)) * kstd

    UC1[source:size() - 1 - p - 1] = nil
    LC1[source:size() - 1 - p - 1] = nil
    UC2[source:size() - 1 - p - 1] = nil
    LC2[source:size() - 1 - p - 1] = nil
    UC3[source:size() - 1 - p - 1] = nil
    LC3[source:size() - 1 - p - 1] = nil

    for n = 0, p, 1 do
        UC1[period - n] = GravityLine[period - n] + sq
        LC1[period - n] = GravityLine[period - n] - sq
        UC2[period - n] = GravityLine[period - n] + sq * 2
        LC2[period - n] = GravityLine[period - n] - sq * 2
        UC3[period - n] = GravityLine[period - n] + sq * 3
        LC3[period - n] = GravityLine[period - n] - sq * 3
        UC1_2[period - n] = (UC1[period - n] + UC2[period - n]) / 2
        UC2_3[period - n] = (UC3[period - n] + UC2[period - n]) / 2
        LC1_2[period - n] = (LC1[period - n] + LC2[period - n]) / 2
        LC2_3[period - n] = (LC3[period - n] + LC2[period - n]) / 2
    end
end