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### nth ( 1 - 8 ) Order Polynomial Fit for Amibroker (AFL)

nth ( 1 – 8 ) Order Polynomial Fit of data using Gaussian Elimination for simultaneous solution of multiple linear equations. It can extrapolate forward and/or backwards

*By Fred Tonetti*

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_SECTION_BEGIN("nth ( 1 - 8)"); //------------------------------------------------------------------------------ // // nth ( 1 - 8 ) Order Polynomial Fit of data using Gaussian Elimination for // simultaneous solution of multiple linear equations. It can extrapolate // forward and/or backwards // //------------------------------------------------------------------------------ // ********************************************************* // * // * VBS Function for Gaussian Elimination // * // * Called by PolyFit ( AFL ) // * // ********************************************************* EnableScript("VBScript"); <% function Gaussian_Elimination (GE_Order, GE_N, GE_SumXn, GE_SumYXn) Dim b(10, 10) Dim w(10) Dim Coeff(10) for i = 1 To 10 Coeff(i) = 0 next n = GE_Order + 1 for i = 1 to n for j = 1 to n if i = 1 AND j = 1 then b(i, j) = cDBL(GE_N) else b(i, j) = cDbl(GE_SumXn(i + j - 2)) end if next w(i) = cDbl(GE_SumYXn(i)) next n1 = n - 1 for i = 1 to n1 big = cDbl(abs(b(i, i))) q = i i1 = i + 1 for j = i1 to n ab = cDbl(abs(b(j, i))) if (ab >= big) then big = ab q = j end if next if (big <> 0.0) then if (q <> i) then for j = 1 to n Temp = cDbl(b(q, j)) b(q, j) = b(i, j) b(i, j) = Temp next Temp = w(i) w(i) = w(q) w(q) = Temp end if end if for j = i1 to n t = cDbl(b(j, i) / b(i, i)) for k = i1 to n b(j, k) = b(j, k) - t * b(i, k) next w(j) = w(j) - t * w(i) next next if (b(n, n) <> 0.0) then Coeff(n) = w(n) / b(n, n) i = n - 1 while i > 0 SumY = cDbl(0) i1 = i + 1 for j = i1 to n SumY = SumY + b(i, j) * Coeff(j) next Coeff(i) = (w(i) - SumY) / b(i, i) i = i - 1 wend Gaussian_Elimination = Coeff end if end function %> // ********************************************************* // * // * AFL Function for nth Order Polynomial Fit // * Calls Gaussian_Elimination ( VBS ) // * // * Y = The array to Fit // * BegBar = Beg Bar in range to fit // * EndBar = End Bar in range to fit // * Order = 1 - 8 = Order of Poly Fit (Integer) // * ExtraB = Number of Bars to Extrapolate (Backward) // * ExtraF = Number of Bars to Extrapolate (Forward) // * // ********************************************************* function PolyFit(GE_Y, GE_BegBar, GE_EndBar, GE_Order, GE_ExtraB, GE_ExtraF) { BI = BarIndex(); GE_N = GE_EndBar - GE_BegBar + 1; GE_XBegin = -(GE_N - 1) / 2; GE_X = IIf(BI < GE_BegBar, 0, IIf(BI > GE_EndBar, 0, (GE_XBegin + BI - GE_BegBar))); GE_X_Max = LastValue(Highest(GE_X)); GE_X = GE_X / GE_X_Max; X1 = GE_X; AddColumn(X1, "X1", 1.9); GE_Y = IIf(BI < GE_BegBar, 0, IIf(BI > GE_EndBar, 0, GE_Y)); GE_SumXn = Cum(0); GE_SumXn[1] = LastValue(Cum(GE_X)); GE_X2 = GE_X * GE_X; GE_SumXn[2] = LastValue(Cum(GE_X2)); GE_X3 = GE_X * GE_X2; GE_SumXn[3] = LastValue(Cum(GE_X3)); GE_X4 = GE_X * GE_X3; GE_SumXn[4] = LastValue(Cum(GE_X4)); GE_X5 = GE_X * GE_X4; GE_SumXn[5] = LastValue(Cum(GE_X5)); GE_X6 = GE_X * GE_X5; GE_SumXn[6] = LastValue(Cum(GE_X6)); GE_X7 = GE_X * GE_X6; GE_SumXn[7] = LastValue(Cum(GE_X7)); GE_X8 = GE_X * GE_X7; GE_SumXn[8] = LastValue(Cum(GE_X8)); GE_X9 = GE_X * GE_X8; GE_SumXn[9] = LastValue(Cum(GE_X9)); GE_X10 = GE_X * GE_X9; GE_SumXn[10] = LastValue(Cum(GE_X10)); GE_X11 = GE_X * GE_X10; GE_SumXn[11] = LastValue(Cum(GE_X11)); GE_X12 = GE_X * GE_X11; GE_SumXn[12] = LastValue(Cum(GE_X12)); GE_X13 = GE_X * GE_X12; GE_SumXn[13] = LastValue(Cum(GE_X13)); GE_X14 = GE_X * GE_X13; GE_SumXn[14] = LastValue(Cum(GE_X14)); GE_X15 = GE_X * GE_X14; GE_SumXn[15] = LastValue(Cum(GE_X15)); GE_X16 = GE_X * GE_X15; GE_SumXn[16] = LastValue(Cum(GE_X16)); GE_SumYXn = Cum(0); GE_SumYXn[1] = LastValue(Cum(GE_Y)); GE_YX = GE_Y * GE_X; GE_SumYXn[2] = LastValue(Cum(GE_YX)); GE_YX2 = GE_YX * GE_X; GE_SumYXn[3] = LastValue(Cum(GE_YX2)); GE_YX3 = GE_YX2 * GE_X; GE_SumYXn[4] = LastValue(Cum(GE_YX3)); GE_YX4 = GE_YX3 * GE_X; GE_SumYXn[5] = LastValue(Cum(GE_YX4)); GE_YX5 = GE_YX4 * GE_X; GE_SumYXn[6] = LastValue(Cum(GE_YX5)); GE_YX6 = GE_YX5 * GE_X; GE_SumYXn[7] = LastValue(Cum(GE_YX6)); GE_YX7 = GE_YX6 * GE_X; GE_SumYXn[8] = LastValue(Cum(GE_YX7)); GE_YX8 = GE_YX7 * GE_X; GE_SumYXn[9] = LastValue(Cum(GE_YX8)); GE_Coeff = Cum(0); GE_VBS = GetScriptObject(); GE_Coeff = GE_VBS.Gaussian_Elimination(GE_Order, GE_N, GE_SumXn, GE_SumYXn); for (i = 1; i <= GE_Order + 1; i++) printf(NumToStr(i, 1.0) + " = " + NumToStr(GE_Coeff[i], 1.9) + "\n"); GE_X = IIf(BI < GE_BegBar - GE_ExtraB - GE_ExtraF, 0, IIf(BI > GE_EndBar, 0, (GE_XBegin + BI - GE_BegBar + GE_ExtraF) / GE_X_Max)); GE_X2 = GE_X * GE_X; GE_X3 = GE_X2 * GE_X; GE_X4 = GE_X3 * GE_X; GE_X5 = GE_X4 * GE_X; GE_X6 = GE_X5 * GE_X; GE_X7 = GE_X6 * GE_X; GE_X8 = GE_X7 * GE_X; GE_X9 = GE_X8 * GE_X; GE_X10 = GE_X9 * GE_X; GE_X11 = GE_X10 * GE_X; GE_X12 = GE_X11 * GE_X; GE_X13 = GE_X12 * GE_X; GE_X14 = GE_X13 * GE_X; GE_X15 = GE_X14 * GE_X; GE_X16 = GE_X15 * GE_X; GE_Yn = IIf(BI < GE_BegBar - GE_ExtraB - GE_ExtraF, -1e10, IIf(BI > GE_EndBar, -1e10, GE_Coeff[1] + GE_Coeff[2] * GE_X + GE_Coeff[3] * GE_X2 + GE_Coeff[4] * GE_X3 + GE_Coeff[5] * GE_X4 + GE_Coeff[6] * GE_X5 + GE_Coeff[7] * GE_X6 + GE_Coeff[8] * GE_X7 + GE_Coeff[9] * GE_X8)); return GE_Yn; } // ********************************************************* // * // * Demo AFL to use PolyFit // * // ********************************************************* Filter = 1; BI = BarIndex(); PF_BegBar = BeginValue(BI); PF_EndBar = EndValue(BI); PF_Y = (H + L) / 2; PF_Order = Param("nth Order", 3, 1, 8, 1); PF_ExtraB = Param("Extrapolate Backwards", 0, 0, 50, 1); PF_ExtraF = Param("Extrapolate Forwards", 0, 0, 50, 1); Yn = PolyFit(PF_Y, PF_BegBar, PF_EndBar, PF_Order, PF_ExtraB, PF_ExtraF); GraphXSpace = 10; Plot(Yn, "nth Order Polynomial Fit - " + NumToStr(PF_Order, 1.0), IIf(BI > PF_EndBar - PF_ExtraF, colorWhite, IIf(BI < PF_BegBar - PF_ExtraF, colorWhite, colorBrightGreen)), styleThick, Null, Null, PF_ExtraF); PlotOHLC(O, H, L, C, "Close", colorLightGrey, styleCandle); _SECTION_END();

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