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nth ( 1 - 8 ) Order Polynomial Fit for Amibroker (AFL)
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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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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 | _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 ifend 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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