拉格朗日Lagrange多项式计算源代码

#property indicator_chart_window
#property indicator_buffers 3
#property indicator_color1 SkyBlue
#property indicator_color2 Crimson
#property indicator_color3 Crimson
//----
extern int Pow=3;
extern int Depth=12;точками
extern int Mode=MODE_HIGH;//MODE_HIGH, MODE_LOW, MODE_CLOSE
extern int TimeFrame=0;
extern int Shift=10;
//----
double Lx[];
double Lx0[];
double Pnt[];

int X[];
double Y[];
double C[];
//----------------------------------------------------------- Lagrange
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);
}
//----------------------------------------------------------- Lagrange
int start()
{
if (Pow<=1) Pow = 2;
if (Pow>=21) Pow = 20;
FindPoint();
Lagrange();
return(0);
}
//----------------------------------------------------------- FindPoint
void FindPoint()
{
int pos, pos2, pos_prev = -1;
if (Depth<=0) Depth=2;
int i=Depth;
int n=0;
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;
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];
}
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;
}
}
for (i = 0; i<Pow; i++) Pnt[X[i]] = Y[i];
ArrayInitialize(Lx0, EMPTY_VALUE);
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;
}
}
}
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