1 | #ifndef MARS_MExtralgoSpline
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2 | #define MARS_MExtralgoSpline
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3 |
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4 | #ifndef ROOT_TROOT
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5 | #include <TROOT.h>
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6 | #endif
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7 |
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8 | #include <iostream>
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9 | class TComplex;
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10 |
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11 | class MExtralgoSpline
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12 | {
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13 | public:
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14 | enum ExtractionType_t { kAmplitude, kIntegral }; //! Possible time and charge extraction types
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15 |
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16 | private:
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17 | ExtractionType_t fExtractionType;
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18 |
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19 | private:
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20 | //Bool_t fIsOwner; // Owner of derivatives....
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21 |
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22 | // Input
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23 | Float_t *fVal;
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24 | Int_t fNum;
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25 |
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26 | Float_t *fDer1;
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27 | Float_t *fDer2;
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28 |
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29 | Float_t fRiseTime;
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30 | Float_t fFallTime;
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31 |
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32 | Float_t fResolution;
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33 |
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34 | // Result
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35 | Float_t fTime;
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36 | Float_t fTimeDev;
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37 | Float_t fSignal;
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38 | Float_t fSignalDev;
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39 |
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40 | Double_t ReMul(const TComplex &c1, const TComplex &th) const;
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41 |
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42 | inline Float_t Eval(Float_t val, Float_t a, Float_t deriv) const
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43 | {
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44 | return a*val + (a*a*a-a)*deriv;
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45 | }
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46 |
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47 | // Evaluate value of spline in the interval i with x=[0;1[
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48 | inline Float_t Eval(const Int_t i, const Float_t x) const
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49 | {
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50 | // Eval(i,x) = (fDer2[i+1]-fDer2[i])*x*x*x + 3*fDer2[i]*x*x +
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51 | // (fVal[i+1]-fVal[i] -2*fDer2[i]-fDer2[i+1])*x + fVal[i];
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52 |
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53 | // x := [0; 1[
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54 | return Eval(fVal[i], 1-x, fDer2[i]) + Eval(fVal[i+1], x, fDer2[i+1]);
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55 | }
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56 |
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57 | /*
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58 | inline Float_t EvalAt(const Float_t x) const
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59 | {
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60 | Int_t i = TMath::FloorNint(x);
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61 |
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62 | // handle under- and overflow of the array-range by extrapolation
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63 | if (i<0)
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64 | i=0;
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65 | if (i>fNum-2)
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66 | i = fNum-2;
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67 |
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68 | return Eval(i, x-i);
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69 | }
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70 | */
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71 |
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72 | // Evaluate first derivative of spline in the interval i with x=[0;1[
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73 | inline Double_t EvalDeriv1(const Float_t x, const Int_t i) const
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74 | {
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75 | // x := [0; 1[
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76 | const Double_t difval = fVal[i+1]-fVal[i];
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77 | const Double_t difder = fDer2[i+1]-fDer2[i];
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78 |
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79 | return 3*difder*x*x + 6*fDer2[i]*x - 2*fDer2[i] - fDer2[i+1] + difval;
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80 | }
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81 |
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82 | // Evaluate second derivative of spline in the interval i with x=[0;1[
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83 | inline Double_t EvalDeriv2(const Float_t x, const Int_t i) const
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84 | {
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85 | // x := [0; 1[
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86 | return 6*(fDer2[i+1]*x + fDer2[i]*(1-x));
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87 | }
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88 |
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89 | Double_t FindY(Int_t i, Double_t y=0, Double_t min=0, Double_t max=1) const;
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90 | Double_t SearchY(Float_t maxpos, Float_t y) const;
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91 | /*
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92 | // Evaluate first solution for a possible maximum (x|first deriv==0)
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93 | inline Double_t EvalDerivEq0S1(const Int_t i) const
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94 | {
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95 | // return the x value [0;1[ at which the derivative is zero (solution1)
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96 |
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97 | Double_t sumder = fDer2[i]+fDer2[i+1];
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98 | Double_t difder = fDer2[i]-fDer2[i+1];
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99 |
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100 | Double_t sqt1 = sumder*sumder - fDer2[i]*fDer2[i+1];
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101 | Double_t sqt2 = difder*(fVal[i+1]-fVal[i]);
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102 |
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103 | Double_t x = 3*fDer2[i] - sqrt(3*sqt1 + 3*sqt2);
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104 |
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105 | Double_t denom = 3*(fDer2[i+1]-fDer2[i]);
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106 |
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107 | return -x/denom;
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108 | }
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109 |
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110 | // Evaluate second solution for a possible maximum (x|first deriv==0)
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111 | inline Double_t EvalDerivEq0S2(const Int_t i) const
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112 | {
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113 | // return the x value [0;1[ at which the derivative is zero (solution2)
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114 |
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115 | Double_t sumder = fDer2[i]+fDer2[i+1];
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116 | Double_t difder = fDer2[i]-fDer2[i+1];
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117 |
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118 | Double_t sqt1 = sumder*sumder - fDer2[i]*fDer2[i+1];
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119 | Double_t sqt2 = difder*(fVal[i+1]-fVal[i]);
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120 |
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121 | Double_t x = 3*fDer2[i] + sqrt(3*sqt1 + 3*sqt2);
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122 |
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123 | Double_t denom = 3*(fDer2[i+1]-fDer2[i]);
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124 |
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125 | return -x/denom;
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126 | }
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127 | */
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128 |
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129 | inline void EvalDerivEq0(const Int_t i, Float_t &rc1, Float_t &rc2) const
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130 | {
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131 | Double_t sumder = fDer2[i]+fDer2[i+1];
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132 | Double_t difder = fDer2[i]-fDer2[i+1];
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133 |
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134 | Double_t sqt1 = sumder*sumder - fDer2[i]*fDer2[i+1];
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135 | Double_t sqt2 = difder*(fVal[i+1]-fVal[i]);
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136 | Double_t sqt3 = sqrt(3*sqt1 + 3*sqt2);
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137 | Double_t denom = 3*(fDer2[i+1]-fDer2[i]);
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138 |
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139 | rc1 = -(3*fDer2[i] + sqt3)/denom;
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140 | rc2 = -(3*fDer2[i] - sqt3)/denom;
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141 | }
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142 |
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143 | // Calculate the "Stammfunktion" of the Eval-function
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144 | inline Double_t EvalPrimitive(Int_t i, Float_t x) const
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145 | {
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146 | /* TO BE CHECKED!
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147 | if (x==0)
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148 | return 0;
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149 |
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150 | if (x==1)
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151 | return (fVal[i+1]+fVal[i])/2 - fDer2[i+1]/4;
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152 | */
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153 | Align(i, x);
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154 |
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155 | const Double_t x2 = x*x;
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156 | const Double_t x4 = x2*x2;
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157 | const Double_t x1 = 1-x;
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158 | const Double_t x14 = x1*x1*x1*x1;
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159 |
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160 | return x2*fVal[i+1]/2 + (x4/2-x2)*fDer2[i+1]/2 + (x-x2/2)*fVal[i] + (x2/2-x-x14/4)*fDer2[i];
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161 | }
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162 |
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163 | inline void Align(Int_t &i, Float_t &x) const
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164 | {
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165 | if (i<0)
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166 | {
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167 | x += i;
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168 | i=0;
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169 | }
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170 | if (i>=fNum-1)
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171 | {
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172 | x += i-(fNum-2);
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173 | i=fNum-2;
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174 | }
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175 | }
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176 |
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177 | // Calculate the intgeral of the Eval-function in
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178 | // bin i from a=[0;1[ to b=[0;1[
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179 | inline Double_t EvalInteg(Int_t i, Float_t a=0, Float_t b=1) const
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180 | {
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181 | // This is to make sure that we never access invalid
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182 | // memory, even if this should never happen.
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183 | // If it happens anyhow we extraolate the spline
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184 | Align(i, a);
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185 | Align(i, b);
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186 |
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187 | return EvalPrimitive(i, b)-EvalPrimitive(i, a);
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188 | }
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189 |
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190 | // Calculate the intgeral of the Eval-function betwen x0 and x1
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191 | inline Double_t EvalInteg(Float_t x0, Float_t x1) const
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192 | {
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193 | const Int_t min = TMath::CeilNint(x0);
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194 | const Int_t max = TMath::FloorNint(x1);
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195 |
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196 | // This happens if x0 and x1 are in the same interval
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197 | if (min>max)
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198 | return EvalInteg(max, x0-max, x1-max);
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199 |
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200 | // Sum complete intervals
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201 | Double_t sum = 0;
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202 | for (int i=min; i<max; i++)
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203 | sum += EvalInteg(i);
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204 |
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205 | // Sum the incomplete intervals at the beginning and end
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206 | sum += EvalInteg(min-1, 1-(min-x0), 1);
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207 | sum += EvalInteg(max, 0, x1-max);
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208 |
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209 | // return result
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210 | return sum;
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211 | }
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212 |
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213 | // We search for the maximum from x=i-1 to x=i+1
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214 | // (Remeber: i corresponds to the value in bin i, i+1 to the
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215 | // next bin and i-1 to the last bin)
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216 | inline void GetMaxAroundI(Int_t i, Float_t &xmax, Float_t &ymax) const
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217 | {
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218 | Float_t xmax1, xmax2;
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219 | Float_t ymax1, ymax2;
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220 |
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221 | Bool_t rc1 = i>0 && GetMax(i-1, xmax1, ymax1);
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222 | Bool_t rc2 = i<fNum-1 && GetMax(i, xmax2, ymax2);
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223 |
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224 | // In case the medium bin is the first or last bin
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225 | // take the lower or upper edge of the region into account.
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226 | if (i==0)
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227 | {
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228 | xmax1 = 0;
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229 | ymax1 = fVal[0];
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230 | rc1 = kTRUE;
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231 | }
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232 | if (i>fNum-2)
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233 | {
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234 | xmax2 = fNum-1;
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235 | ymax2 = fVal[fNum-1];
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236 | rc2 = kTRUE;
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237 | }
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238 |
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239 | // Take a default in case no maximum is found
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240 | xmax=i;
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241 | ymax=fVal[i];
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242 |
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243 | if (rc1)
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244 | {
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245 | ymax = ymax1;
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246 | xmax = xmax1;
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247 | }
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248 | else
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249 | if (rc2)
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250 | {
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251 | ymax = ymax2;
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252 | xmax = xmax2;
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253 | }
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254 |
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255 | if (rc2 && ymax2>ymax)
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256 | {
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257 | ymax = ymax2;
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258 | xmax = xmax2;
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259 | }
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260 | /*
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261 | // Search real maximum in [i-0.5, i+1.5]
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262 | Float_t xmax1, xmax2, xmax3;
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263 | Float_t ymax1, ymax2, ymax3;
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264 |
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265 | Bool_t rc1 = i>0 && GetMax(i-1, xmax1, ymax1, 0.5, 1.0);
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266 | Bool_t rc2 = GetMax(i, xmax2, ymax2, 0.0, 1.0);
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267 | Bool_t rc3 = i<fNum-1 && GetMax(i+1, xmax3, ymax3, 0.0, 0.5);
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268 |
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269 | // In case the medium bin is the first or last bin
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270 | // take the lower or upper edge of the region into account.
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271 | if (i==0)
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272 | {
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273 | xmax1 = 0;
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274 | ymax1 = Eval(0, 0);
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275 | rc1 = kTRUE;
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276 | }
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277 | if (i==fNum-1)
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278 | {
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279 | xmax3 = fNum-1e-5;
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280 | ymax3 = Eval(fNum-1, 1);
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281 | rc3 = kTRUE;
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282 | }
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283 |
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284 | // Take a real default in case no maximum is found
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285 | xmax=i+0.5;
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286 | ymax=Eval(i, 0.5);
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287 |
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288 | //if (!rc1 && !rc2 && !rc3)
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289 | // cout << "!!!!!!!!!!!!!!!" << endl;
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290 |
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291 | if (rc1)
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292 | {
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293 | ymax = ymax1;
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294 | xmax = xmax1;
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295 | }
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296 | else
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297 | if (rc2)
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298 | {
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299 | ymax = ymax2;
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300 | xmax = xmax2;
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301 | }
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302 | else
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303 | if (rc3)
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304 | {
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305 | ymax = ymax3;
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306 | xmax = xmax3;
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307 | }
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308 |
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309 | if (rc2 && ymax2>ymax)
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310 | {
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311 | ymax = ymax2;
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312 | xmax = xmax2;
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313 | }
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314 | if (rc3 && ymax3>ymax)
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315 | {
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316 | ymax = ymax3;
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317 | xmax = xmax3;
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318 | }
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319 | */ }
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320 |
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321 | inline Bool_t GetMax(Int_t i, Float_t &xmax, Float_t &ymax, Float_t min=0, Float_t max=1) const
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322 | {
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323 | // Find analytical maximum in the bin i in the interval [min,max[
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324 |
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325 | Float_t x1, x2;
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326 | EvalDerivEq0(i, x1, x2);
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327 | // const Float_t x1 = EvalDerivEq0S1(i);
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328 | // const Float_t x2 = EvalDerivEq0S2(i);
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329 |
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330 | const Bool_t ismax1 = x1>=min && x1<max && EvalDeriv2(x1, i)<0;
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331 | const Bool_t ismax2 = x2>=min && x2<max && EvalDeriv2(x2, i)<0;
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332 |
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333 | if (!ismax1 && !ismax2)
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334 | return kFALSE;
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335 |
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336 | if (ismax1 && !ismax2)
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337 | {
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338 | xmax = i+x1;
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339 | ymax = Eval(i, x1);
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340 | return kTRUE;
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341 | }
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342 |
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343 | if (!ismax1 && ismax2)
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344 | {
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345 | xmax = i+x2;
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346 | ymax = Eval(i, x2);
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347 | return kTRUE;
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348 | }
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349 |
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350 | // Somehting must be wrong...
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351 | return kFALSE;
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352 | /*
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353 | std::cout << "?????????????" << std::endl;
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354 |
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355 | const Double_t y1 = Eval(i, x1);
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356 | const Double_t y2 = Eval(i, x2);
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357 |
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358 | if (y1>y2)
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359 | {
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360 | xmax = i+x1;
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361 | ymax = Eval(i, x1);
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362 | return kTRUE;
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363 | }
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364 | else
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365 | {
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366 | xmax = i+x2;
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367 | ymax = Eval(i, x2);
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368 | return kTRUE;
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369 | }
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370 |
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371 | return kFALSE;*/
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372 | }
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373 | /*
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374 | inline Int_t GetMaxPos(Int_t i, Float_t &xmax, Float_t &ymax) const
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375 | {
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376 | Double_t x[3];
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377 |
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378 | x[0] = 0;
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379 | // x[1] = 1; // This means we miss a possible maximum at the
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380 | // upper edge of the last interval...
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381 |
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382 | x[1] = EvalDerivEq0S1(i);
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383 | x[2] = EvalDerivEq0S2(i);
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384 |
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385 | //y[0] = Eval(i, x[0]);
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386 | //y[1] = Eval(i, x[1]);
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387 | //y[1] = Eval(i, x[1]);
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388 | //y[2] = Eval(i, x[2]);
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389 |
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390 | Int_t rc = 0;
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391 | Double_t max = Eval(i, x[0]);
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392 |
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393 | for (Int_t j=1; j<3; j++)
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394 | {
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395 | if (x[j]<=0 || x[j]>=1)
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396 | continue;
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397 |
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398 | const Float_t y = Eval(i, x[j]);
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399 | if (y>max)
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400 | {
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401 | max = y;
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402 | rc = j;
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403 | }
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404 | }
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405 |
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406 | if (max>ymax)
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407 | {
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408 | xmax = x[rc]+i;
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409 | ymax = max;
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410 | }
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411 |
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412 | return rc;
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413 | }
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414 |
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415 | inline void GetMaxPos(Int_t min, Int_t max, Float_t &xmax, Float_t &ymax) const
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416 | {
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417 | Float_t xmax=-1;
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418 | Float_t ymax=-FLT_MAX;
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419 |
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420 | for (int i=min; i<max; i++)
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421 | GetMaxPos(i, xmax, ymax);
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422 |
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423 | for (int i=min+1; i<max; i++)
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424 | {
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425 | Float_t y = Eval(i, 0);
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426 | if (y>ymax)
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427 | {
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428 | ymax = y;
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429 | xmax = i;
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430 | }
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431 | }
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432 |
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433 | }*/
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434 |
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435 |
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436 | void InitDerivatives() const;
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437 | Float_t CalcIntegral(Float_t start) const;
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438 |
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439 | public:
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440 | MExtralgoSpline(Float_t *val, Int_t n, Float_t *der1, Float_t *der2)
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441 | : fExtractionType(kIntegral), fVal(val), fNum(n), fDer1(der1), fDer2(der2), fTime(0), fTimeDev(-1), fSignal(0), fSignalDev(-1)
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442 | {
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443 | InitDerivatives();
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444 | }
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445 |
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446 | void SetRiseFallTime(Float_t rise, Float_t fall) { fRiseTime=rise; fFallTime=fall; }
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447 | void SetExtrationType(ExtractionType_t typ) { fExtractionType = typ; }
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448 | void SetResolution(Float_t res) { fResolution=res; }
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449 |
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450 | Float_t GetTime() const { return fTime; }
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451 | Float_t GetSignal() const { return fSignal; }
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452 |
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453 | Float_t GetTimeDev() const { return fTimeDev; }
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454 | Float_t GetSignalDev() const { return fSignalDev; }
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455 |
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456 | void GetSignal(Float_t &sig, Float_t &dsig) const { sig=fSignal; dsig=fSignalDev; }
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457 | void GetTime(Float_t &sig, Float_t &dsig) const { sig=fTime; dsig=fTimeDev; }
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458 |
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459 | Float_t ExtractNoise(Int_t iter);
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460 | void Extract(Byte_t sat, Int_t maxpos);
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461 | };
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462 |
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463 | #endif
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