!siLagrange

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//|                                         		      siLagrange.mq4 |
//|                                 Copyright © 2007 Ñåðãååâ Àëåêñåé |
//|                                                los@we.kherson.ua |
//+------------------------------------------------------------------+
#property copyright "Copyright © 2007, Ñåðãååâ Àëåêñåé "
#property link      "mailto: los@we.kherson.ua"
//----
#property indicator_chart_window
#property indicator_buffers 3
#property indicator_color1 SkyBlue
#property indicator_color2 Crimson
#property indicator_color3 Crimson
//----
extern int Pow=3;//Ñòåïåíü ïîëèíîìà Ëàãðàíæà. Æåëàòåëüíî 3..8
extern int Depth=12;//ìèíèìàëüíîå ðàññòîÿíèå ìåæäó îïîðíûìè òî÷êàìè
extern int Mode=MODE_HIGH;//MODE_HIGH, MODE_LOW, MODE_CLOSE
extern int TimeFrame=0;
extern int Shift=10;//Íà ñêîëüêî áàðîâ ïðîäëåâàåì â áóäóùåå
//----
double Lx[];//Ïîëèíîì Ëàãðàíæà
double Lx0[];//Ïîëèíîì Ëàãðàíæà â áóäóùåå íà shift áàðîâ
double Pnt[];//Èíäèêàòîð îïîðíûõ òî÷åê ïîñòðîåíèÿ

int X[];//Íîìåðà áàðîâ ïî êîòîðûì ñòðîèòñÿ ïîëèíîì
double Y[];//Çíà÷åíèÿ öåíû â òî÷êàõ (O, H, L èëè C)
double C[];//Êîýôôèöèåíòû ïîëèíîìà

int init()
{	
//---- indicator line
	SetIndexBuffer(0,Lx); SetIndexStyle(0,DRAW_LINE);
	SetIndexBuffer(1,Lx0); SetIndexStyle(1,DRAW_LINE); SetIndexShift(1, Shift); 
	SetIndexBuffer(2,Pnt); SetIndexStyle(2,DRAW_ARROW); SetIndexArrow(2, 159);

	ArrayResize(X, Pow); ArrayResize(Y, Pow); ArrayResize(C, Pow);

	return(0);
}

void FindPoint()
{
	int pos, pos2, pos_prev = -1;
	if (Depth<=0) Depth=2;
	int i=Depth;
	int n=0;//ñ÷åò÷èê òî÷åê (äî Pow)
	while((i<Bars-Depth) && (n<Pow))
	{
		if (Mode==MODE_HIGH)
		{
			pos = iHighest(NULL,0,MODE_HIGH,2*Depth+1,i-Depth);	pos2 = iHighest(NULL,0,MODE_HIGH,2*Depth+1,pos-Depth); 
			if ((pos==pos2)&&(pos!=pos_prev))
			{
				X[n] = pos; Y[n]=High[pos]; n++; 
				pos_prev = pos; 
			}
		}
		if (Mode==MODE_LOW)
		{
			pos = iLowest(NULL,0,MODE_LOW,2*Depth+1,i-Depth);	pos2 = iLowest(NULL,0,MODE_LOW,2*Depth+1,pos-Depth); 
			if ((pos==pos2)&&(pos!=pos_prev))
			{
				X[n] = pos; Y[n]=Low[pos]; n++; 
				pos_prev = pos; 
			}
		}
		i++;
	}
}

void Lagrange()
{
	int i, j, b;
	//1. Íàéäåì êîýôôèöèåíòû ïîëèíîìà
	for (i = 0; i<Pow; i++)
	{
		C[i] = 1.0;
		for (j = 0; j<Pow; j++)
			 if (j != i)  C[i] = C[i]*(X[i]-X[j]);
		C[i] = Y[i]/C[i];
	}
	// 2. Òåïåðü ïðîõîäÿ ïî âñåì áàðàì äî ìàñèìàëüíîãî áàðà, óêàçàííîãî â ðàñ÷åòå ïîëèíîìà 
	//ðàñ÷èòûâàåì ñàì ïîëèíîì (èíäèêàòîð Lx)
	int bars = X[ArrayMaximum(X)];
	double sx;
	for (b = 0; b<=bars; b++)
	{
		Lx[b] = 0.0; Pnt[b] = 0;
		for (i = 0; i<Pow; i++)
		{
			sx = 1;
			for (j = 0; j<Pow; j++)
				if (j != i)	sx = sx*(b-X[j]);
			Lx[b] = Lx[b]+C[i]*sx;
		}
	}
	//3. Çàïîëíèëè ìàññèâ îïîðíûõ òî÷åê
	for (i = 0; i<Pow; i++) Pnt[X[i]] = Y[i];

	//4. È ñòðîåì èíäèêàòîð Lx0 â áóäóùåå íà Shift
	for (b = -Shift; b<=0; b++)
	{
		Lx0[b+Shift] = 0.0;
		for (i = 0; i<Pow; i++)
		{
			sx = 1;
			for (j = 0; j<Pow; j++)
				if (j != i)	sx = sx*(b-X[j]);
			Lx0[b+Shift] = Lx0[b+Shift]+C[i]*sx;
		}
	}
	
}

int start()
{
	if (Pow<=1) Pow = 2;//ïðîâåðêà êîððåêòíîñòè
	if (Pow>=21) Pow = 20;//ïðîâåðêà êîððåêòíîñòè

	//0. Îïðåäåëÿåì òàáëèöó çíà÷åíèé X è Y äëÿ ïîñòðîåíèÿ ïîëèíîìà 
	FindPoint();
	//
	Lagrange();
	//----
	return(0);
}
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