-- Available @ https://fxcodebase.com/code/viewtopic.php?f=17&t=74473

--+------------------------------------------------------------------------------------------------+
--|                                                            Copyright © 2023, Gehtsoft USA LLC  | 
--|                                                                         http://fxcodebase.com  |
--+------------------------------------------------------------------------------------------------+
--|                                                                   Developed by : Mario Jemic   |                    
--|                                                                       mario.jemic@gmail.com    |
--|                                                        https://AppliedMachineLearning.systems  | 
--+------------------------------------------------------------------------------------------------+

--+------------------------------------------------------------------------------------------------+
--|                                           Our work would not be possible without your support. |
--+------------------------------------------------------------------------------------------------+
--|                                                               Paypal:  https://goo.gl/9Rj74e   |
--|                                                             Patreon :  https://goo.gl/GdXWeN   |
--|                                                      Buy Me a Coffee:  http://tiny.cc/pjh9vz   |  
--+------------------------------------------------------------------------------------------------+



-- Indicator profile initialization routine
-- Defines indicator profile properties and indicator parameters
-- TODO: Add minimal and maximal value of numeric parameters and default color of the streams
function Init()
    indicator:name("Gaussian Smoothing");
    indicator:description("");
    indicator:requiredSource(core.Tick);
    indicator:type(core.Indicator);

  
 	indicator.parameters:addGroup("Calculation");	
 
    indicator.parameters:addInteger("Period", "Period", "", 20, 1, 2000);

	
	 indicator.parameters:addGroup("Line Style");	
    indicator.parameters:addInteger("width", "Line width", "", 1, 1, 5);
    indicator.parameters:addInteger("style", "Line style", "", core.LINE_SOLID);
    indicator.parameters:setFlag("style", core.FLAG_LINE_STYLE);
	
	 indicator.parameters:addColor("color", "Line Color", "", core.rgb(0, 255, 255)); 

end

-- Indicator instance initialization routine
-- Processes indicator parameters and creates output streams
-- TODO: Refine the first period calculation for each of the output streams.
-- TODO: Calculate all constants, create instances all subsequent indicators and load all required libraries
-- Parameters block
 
	
local first;
local source = nil;
local Period;
	
-- Routine
 function Prepare(nameOnly)   
 
    
	Period=instance.parameters.Period;
	source = instance.source
 
    local name = profile:id() .. "(" ..  instance.source:name().. "," ..  Period  .. ")";
    instance:name(name); 


    if   (nameOnly) then
        return;
    end

 
	 
	first=source:first()+Period ; 
 
	
	
    Line = instance:addStream("Line", core.Line, name, "Line", instance.parameters.color, first );
    Line:setPrecision(math.max(2, instance.source:getPrecision()));
    Line:setWidth(instance.parameters.width);
    Line:setStyle(instance.parameters.style);
    Line:addLevel(0);	
 
end


function Update(period, mode)

	 

	if period <= first
	or  not source:hasData(period) 
	then
	return;
	end
	
	 
    CalculateGaussianSmoothing(period)	
	 
end

function CalculateGaussianSmoothing(period)
     local maximum_value=mathex.max(source, period-Period+1, period );
        half_maximum = maximum_value / 2;
		
		-- Find indices where the data is above half the maximum
		local above_half_max = {}
		for i = period-Period+1 , period, 1 do
			if source[i] >= half_maximum then
				table.insert(above_half_max, i)
			end
		end
        local kernel = {}		
		local fwhm = above_half_max[#above_half_max] - above_half_max[1]
        local sigma = fwhm / (2 * math.sqrt(2 * math.log(2)))
		
        for i = 1, Period do
			local x = i - (Period + 1) / 2
			local value = math.exp(-(x * x) / (2 * sigma * sigma))
			table.insert(kernel, value)
        end		
		
	-- Normalize the kernel
		local sum = 0
		for _, value in ipairs(kernel) do
			sum = sum + value
		end
		for i, value in ipairs(kernel) do
			kernel[i] = value / sum
		end
	
       -- Apply the moving average
        local kernel_size = #kernel
        local half_kernel = (kernel_size - 1) / 2	
		

		
 					   
		local result = 0;
		for i = 1, Period , 1  do					   
		result = result + source[period - Period+i] * kernel[i]  									   
		end
		Line[period]=result;    
						
		

end


--+------------------------------------------------------------------------------------------------+
--|                                                                    We appreciate your support. | 
--+------------------------------------------------------------------------------------------------+
--|                                                               Paypal: https://goo.gl/9Rj74e    |
--|                                                             Patreon :  https://goo.gl/GdXWeN   |  
--|                                                     Buy Me a Coffee: http://tiny.cc/pjh9vz     |
--+------------------------------------------------------------------------------------------------+
--|  Cryptocurrency  |  Network                    |  Address                                      |
--+------------------------------------------------+-----------------------------------------------+
--|  USDT            |  ERC20 (ETH Ethereum)       |  0xe53aab6bc468a963a02d1319660ee60cf80fc8e7   | 
--|  USDT            |  TRC20 (Tron)               |  TTBXsfuPm2rk36AkdemY7muNXGjyziC86g           |
--|  USDT            |  BEP20 (BSC BNB Smart Chain)|  0xe53aab6bc468a963a02d1319660ee60cf80fc8e7   |
--|  USDT            |  Matic Polygon              |  0xe53aab6bc468a963a02d1319660ee60cf80fc8e7   |
--|  USDT            |  SOL Solana                 |  3nh5rpUKopcYLNU4zGCdUFAkM3iRQq8VVUmuzVG6VDf2 |
--|  USDT            |  ARBITRUM Arbitrum One      |  0xe53aab6bc468a963a02d1319660ee60cf80fc8e7   |
--+------------------------------------------------+-----------------------------------------------+