homework2.1-残差分析

打开root文件

In [1]:
//%jsroot on

In [2]:
TFile *ipf=new TFile("./tracking/homework2.1.root");
TTree *tree=(TTree*) ipf->Get("tree");
TCanvas *c1=new TCanvas("c1","c1");

查看实验测量值与拟合值偏差

创建双高斯拟合函数

In [3]:
//双高斯
TF1 *total2=new TF1("total2","gaus(0)+gaus(3)");
In [4]:
TF1 *g1 = new TF1("g1","gaus");
TF1 *g2 = new TF1("g2","gaus");
TF1 *total=new TF1("total","gaus(0)+gaus(3)");
TH1F *hdx;
Double_t sigma;

查看PPAC-X

  • PPAC-1A-X
In [5]:
tree->Draw("dx[0]>>hdx0(200,-5,5)");
hdx0=(TH1F*)gROOT->FindObject("hdx0");
hdx0->Fit("g1","","",-1.5,1.5);
sigma=g1->GetParameter(2);
total->SetParameter(2,sigma);
total->SetParameter(5,5*sigma);//初始化,估计半宽为2*sigma;
hdx0->Fit("total");
gPad->SetLogy();
c1->Draw();//residual
 FCN=58318.1 FROM MIGRAD    STATUS=CONVERGED      81 CALLS          82 TOTAL
                     EDM=1.88172e-07    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  Constant     2.65849e+04   6.09460e+01   4.38149e+00   1.38981e-05
   2  Mean        -1.11359e-01   5.37625e-04   6.33821e-05  -4.44801e-01
   3  Sigma        3.84148e-01   6.99416e-04   3.91791e-05   8.04538e-01
 FCN=21046.7 FROM MIGRAD    STATUS=CONVERGED     585 CALLS         586 TOTAL
                     EDM=1.35616e-08    STRATEGY= 1  ERROR MATRIX UNCERTAINTY   1.3 per cent
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  p0           2.89611e+04   6.52248e+01  -1.72413e-01  -1.13414e-07
   2  p1          -1.09060e-01   5.26278e-04  -7.10381e-07   2.60328e-01
   3  p2           2.99911e-01   6.44501e-04   1.52556e-06   1.55236e-01
   4  p3           2.09068e+03   1.36084e+01   6.21716e-03   5.36774e-07
   5  p4          -1.02141e-01   4.04556e-03   1.40116e-05   3.82056e-02
   6  p5           1.63290e+00   5.79993e-03   4.39817e-06  -1.51008e-02
  • PPAC-1B-X
In [6]:
tree->Draw("dx[1]>>hdx1(200,-5,5)");
hdx1=(TH1F*)gROOT->FindObject("hdx1");
hdx1->Fit("g1","","",-1.5,1.5);
sigma=g1->GetParameter(2);
total->SetParameter(2,sigma);
total->SetParameter(5,5*sigma);//初始化,估计半宽为2*sigma;
hdx1->Fit("total");
gPad->SetLogy();
c1->Draw();//residual
 FCN=47883.6 FROM MIGRAD    STATUS=CONVERGED      77 CALLS          78 TOTAL
                     EDM=3.48134e-09    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  Constant     2.46122e+04   5.54115e+01   3.70540e+00   5.37022e-07
   2  Mean         1.53861e-01   5.78122e-04   6.16801e-05  -4.14439e-02
   3  Sigma        4.08422e-01   7.21403e-04   3.60061e-05  -9.88098e-02
 FCN=17568.6 FROM MIGRAD    STATUS=CONVERGED     204 CALLS         205 TOTAL
                     EDM=1.3203e-07    STRATEGY= 1  ERROR MATRIX UNCERTAINTY   1.7 per cent
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  p0           2.65043e+04   5.97200e+01  -2.30507e-01   2.00228e-06
   2  p1           1.48909e-01   5.78910e-04  -7.04439e-07   6.12138e-01
   3  p2           3.21825e-01   7.05058e-04   2.13417e-07   2.92128e-01
   4  p3           1.95901e+03   1.40548e+01   7.41594e-02   4.23232e-05
   5  p4           1.72703e-01   4.30268e-03  -1.40939e-05   6.28340e-03
   6  p5           1.67969e+00   6.68015e-03  -1.56905e-05   1.44174e-01
  • PPAC-2A-X
In [7]:
tree->Draw("dx[2]>>hdx2(200,-5,5)");
hdx2=(TH1F*)gROOT->FindObject("hdx2");
hdx2->Fit("g1","","",-1.5,1.5);
sigma=g1->GetParameter(2);
total->SetParameter(2,sigma);
total->SetParameter(5,5*sigma);//初始化,估计半宽为2*sigma;
hdx2->Fit("total");
gPad->SetLogy();
c1->Draw();//residual
 FCN=42367.6 FROM MIGRAD    STATUS=CONVERGED      70 CALLS          71 TOTAL
                     EDM=2.18004e-08    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  Constant     2.34155e+04   5.06810e+01   3.27803e+00  -6.23649e-06
   2  Mean         1.67305e-01   6.16736e-04   6.19686e-05   4.62158e-02
   3  Sigma        4.39785e-01   7.38328e-04   3.38718e-05  -5.36162e-01
 FCN=17142.1 FROM MIGRAD    STATUS=CONVERGED     164 CALLS         165 TOTAL
                     EDM=5.5162e-08    STRATEGY= 1  ERROR MATRIX UNCERTAINTY   1.2 per cent
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  p0           2.48903e+04   5.53684e+01   2.00319e-02   6.23228e-06
   2  p1           1.64158e-01   5.99290e-04   7.68368e-07   4.20590e-02
   3  p2           3.47525e-01   7.69061e-04  -1.32441e-06  -2.15976e-01
   4  p3           1.98438e+03   1.50180e+01  -1.82957e-02  -1.65043e-05
   5  p4           1.74627e-01   4.08968e-03  -9.49679e-06  -4.70104e-03
   6  p5           1.67201e+00   6.70318e-03   2.43491e-05  -3.06103e-02
  • PPAC-2B-X
In [8]:
tree->Draw("dx[3]>>hdx3(200,-5,5)");
hdx3=(TH1F*)gROOT->FindObject("hdx3");
hdx3->Fit("g1","","",-1.5,1.5);
sigma=g1->GetParameter(2);
total->SetParameter(2,sigma);
total->SetParameter(5,5*sigma);//初始化,估计半宽为2*sigma;
hdx3->Fit("total");
gPad->SetLogy();
c1->Draw();//residual
 FCN=44708.2 FROM MIGRAD    STATUS=CONVERGED      76 CALLS          77 TOTAL
                     EDM=1.2065e-08    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  Constant     2.36615e+04   5.20249e+01   3.44470e+00   5.60957e-07
   2  Mean        -2.32481e-01   6.05446e-04   6.22563e-05   3.38438e-02
   3  Sigma        4.24582e-01   7.26574e-04   3.48087e-05  -2.44227e-01
 FCN=17548.1 FROM MIGRAD    STATUS=CONVERGED     219 CALLS         220 TOTAL
                     EDM=4.48828e-09    STRATEGY= 1  ERROR MATRIX UNCERTAINTY   0.7 per cent
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  p0           2.51457e+04   5.59775e+01  -9.58797e-03  -1.53005e-06
   2  p1          -2.24414e-01   6.14252e-04  -1.93571e-07  -2.53803e-02
   3  p2           3.35814e-01   7.34304e-04  -2.44454e-07  -1.83006e-01
   4  p3           1.98809e+03   1.38354e+01   5.07450e-03  -1.80497e-05
   5  p4          -2.80553e-01   4.30066e-03   3.20035e-06   4.55424e-03
   6  p5           1.70635e+00   6.44485e-03  -5.93694e-07  -1.44554e-02
  • PPAC-3-X
In [9]:
tree->Draw("dx[4]>>hdx4(200,-5,5)");
hdx4=(TH1F*)gROOT->FindObject("hdx4");
hdx4->Fit("g1","","",-1.5,1.5);
sigma=g1->GetParameter(2);
total->SetParameter(2,sigma);
total->SetParameter(5,5*sigma);//初始化,估计半宽为2*sigma;
hdx4->Fit("total");
gPad->SetLogy();
c1->Draw();//residual
 FCN=48986 FROM MIGRAD    STATUS=CONVERGED      91 CALLS          92 TOTAL
                     EDM=1.47799e-09    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  Constant     2.01080e+04   6.79245e+01   4.18171e+00   5.00452e-07
   2  Mean         5.44376e-02   5.15574e-04   5.57108e-05   6.31410e-02
   3  Sigma        2.67876e-01   7.43318e-04   4.37514e-05  -1.63912e-02
 FCN=7290.76 FROM MIGRAD    STATUS=CONVERGED     238 CALLS         239 TOTAL
                     EDM=3.10925e-08    STRATEGY= 1  ERROR MATRIX UNCERTAINTY   1.1 per cent
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  p0           2.24955e+04   7.17190e+01   8.76052e-02  -3.18800e-06
   2  p1           5.30275e-02   5.02973e-04   4.89440e-07  -4.48702e-01
   3  p2           1.89153e-01   6.01369e-04  -9.36484e-07  -5.84838e-01
   4  p3           2.37132e+03   1.84868e+01   7.93627e-03  -1.13340e-05
   5  p4           5.79331e-02   2.92043e-03  -2.50666e-06  -1.92865e-03
   6  p5           9.84393e-01   3.98017e-03  -2.23454e-06  -3.50661e-02

查看PPAC-Y

  • PPAC-1A-Y
In [10]:
tree->Draw("dy[0]>>hdy0(200,-5,5)");
hdy0=(TH1F*)gROOT->FindObject("hdy0");
hdy0->Fit("g1","","",-1.5,1.5);
sigma=g1->GetParameter(2);
total->SetParameter(2,sigma);
total->SetParameter(5,5*sigma);//初始化,估计半宽为2*sigma;
hdy0->Fit("total");
gPad->SetLogy();
c1->Draw();//residual
 FCN=44202.4 FROM MIGRAD    STATUS=CONVERGED      69 CALLS          70 TOTAL
                     EDM=9.64202e-12    STRATEGY= 1  ERROR MATRIX UNCERTAINTY   1.6 per cent
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  Constant     2.22349e+04   4.63458e+01  -3.69228e-02   1.05798e-07
   2  Mean         6.51680e-02   6.55367e-04   8.23454e-07   7.48274e-03
   3  Sigma        4.56825e-01   7.12799e-04   3.47405e-08   7.20913e-03
 FCN=24467.8 FROM MIGRAD    STATUS=CONVERGED     179 CALLS         180 TOTAL
                     EDM=2.17042e-07    STRATEGY= 1  ERROR MATRIX UNCERTAINTY   1.2 per cent
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  p0           2.32750e+04   5.10267e+01  -2.15290e-01   1.69748e-05
   2  p1           5.03956e-02   6.79871e-04   6.78422e-06  -6.90060e-01
   3  p2           3.69671e-01   7.74319e-04   3.70823e-06   1.42037e+00
   4  p3           1.77478e+03   1.25659e+01   3.14413e-02   4.14025e-05
   5  p4           1.67610e-01   4.58101e-03   6.47779e-06  -5.14828e-02
   6  p5           1.70761e+00   6.00231e-03  -3.03994e-05  -6.47707e-02
  • PPAC-1B-Y
In [11]:
tree->Draw("dy[1]>>hdy1(200,-5,5)");
hdy1=(TH1F*)gROOT->FindObject("hdy1");
hdy1->Fit("g1","","",-1.5,1.5);
sigma=g1->GetParameter(2);
total->SetParameter(2,sigma);
total->SetParameter(5,5*sigma);//初始化,估计半宽为2*sigma;
hdy1->Fit("total");
gPad->SetLogy();
c1->Draw();//residual
 FCN=39495.3 FROM MIGRAD    STATUS=CONVERGED      81 CALLS          82 TOTAL
                     EDM=2.74572e-07    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  Constant     2.24152e+04   4.58086e+01   3.06692e+00  -1.07716e-05
   2  Mean         2.75826e-01   6.50074e-04   6.22894e-05   1.94516e-02
   3  Sigma        4.49029e-01   6.83477e-04   3.21960e-05  -2.10118e+00
 FCN=22375.7 FROM MIGRAD    STATUS=CONVERGED     197 CALLS         198 TOTAL
                     EDM=1.27964e-08    STRATEGY= 1  ERROR MATRIX UNCERTAINTY   2.2 per cent
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  p0           2.28879e+04   4.93328e+01   3.01379e-02   2.74567e-06
   2  p1           2.64890e-01   6.93744e-04  -9.89419e-08   1.95997e-01
   3  p2           3.74592e-01   7.56241e-04  -6.54463e-07   2.36242e-01
   4  p3           1.72884e+03   1.30288e+01   1.08883e-02   1.09134e-05
   5  p4           4.00404e-01   4.71308e-03   9.41257e-07  -1.23059e-02
   6  p5           1.69548e+00   6.45130e-03  -2.00513e-06   1.69498e-02
  • PPAC-2A-Y
In [12]:
tree->Draw("dy[2]>>hdy2(200,-5,5)");
hdy2=(TH1F*)gROOT->FindObject("hdy2");
hdy2->Fit("g1","","",-1.5,1.5);
sigma=g1->GetParameter(2);
total->SetParameter(2,sigma);
total->SetParameter(5,5*sigma);//初始化,估计半宽为2*sigma;
hdy2->Fit("total");
gPad->SetLogy();
c1->Draw();//residual
 FCN=31306.8 FROM MIGRAD    STATUS=CONVERGED      66 CALLS          67 TOTAL
                     EDM=1.93381e-11    STRATEGY= 1  ERROR MATRIX UNCERTAINTY   2.1 per cent
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  Constant     1.94905e+04   3.73834e+01  -1.52850e-02   1.46026e-07
   2  Mean        -3.36774e-01   8.07083e-04  -7.24442e-07   6.20355e-03
   3  Sigma        5.34576e-01   7.80427e-04   1.01309e-06  -1.18293e-03
 FCN=25738.4 FROM MIGRAD    STATUS=CONVERGED     263 CALLS         264 TOTAL
                     EDM=3.45068e-08    STRATEGY= 1  ERROR MATRIX UNCERTAINTY   0.7 per cent
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  p0           1.89411e+04   3.95362e+01   1.78773e-02   5.08738e-06
   2  p1          -3.35258e-01   8.87489e-04  -3.63869e-07  -1.18023e-01
   3  p2           4.73199e-01   9.35739e-04  -3.02678e-07   3.02224e-01
   4  p3           1.46432e+03   1.25332e+01   5.91037e-03   5.57489e-05
   5  p4          -5.07241e-01   5.52180e-03  -8.36504e-06   3.48129e-02
   6  p5           1.92619e+00   8.11343e-03  -1.42198e-06   6.34467e-02
  • PPAC-2B-Y
In [13]:
tree->Draw("dy[3]>>hdy3(200,-5,5)");
hdy3=(TH1F*)gROOT->FindObject("hdy3");
hdy3->Fit("g1","","",-1.5,1.5);
sigma=g1->GetParameter(2);
total->SetParameter(2,sigma);
total->SetParameter(5,5*sigma);//初始化,估计半宽为2*sigma;
hdy3->Fit("total");
gPad->SetLogy();
c1->Draw();//residual
 FCN=29776.3 FROM MIGRAD    STATUS=CONVERGED      67 CALLS          68 TOTAL
                     EDM=4.39522e-10    STRATEGY= 1  ERROR MATRIX UNCERTAINTY   1.7 per cent
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  Constant     1.96745e+04   3.69322e+01  -1.82684e-02   1.33307e-06
   2  Mean        -1.63407e-01   7.85528e-04  -4.61509e-07   2.13179e-02
   3  Sigma        5.36458e-01   7.27547e-04  -1.94672e-07   6.20674e-02
 FCN=25108.2 FROM MIGRAD    STATUS=CONVERGED     179 CALLS         180 TOTAL
                     EDM=1.72847e-07    STRATEGY= 1  ERROR MATRIX UNCERTAINTY   2.0 per cent
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  p0           1.93785e+04   3.97879e+01   1.91012e-01   6.36939e-06
   2  p1          -1.53125e-01   8.80806e-04  -5.83270e-06   3.28184e-01
   3  p2           4.71060e-01   9.18043e-04  -1.54030e-06  -3.89325e-01
   4  p3           1.39206e+03   1.25726e+01  -2.07204e-02   1.41774e-05
   5  p4          -2.99786e-01   5.67273e-03   6.96237e-05   7.70117e-03
   6  p5           1.87691e+00   8.20645e-03   2.23930e-05  -7.77994e-03
  • PPAC-3-Y
In [14]:
tree->Draw("dy[4]>>hdy4(200,-5,5)");
hdy4=(TH1F*)gROOT->FindObject("hdy4");
hdy4->Fit("g1","","",-1.5,1.5);
sigma=g1->GetParameter(2);
total->SetParameter(2,sigma);
total->SetParameter(5,5*sigma);//初始化,估计半宽为2*sigma;
hdy4->Fit("total");
gPad->SetLogy();
c1->Draw();//residual
 FCN=30781.1 FROM MIGRAD    STATUS=CONVERGED      85 CALLS          86 TOTAL
                     EDM=4.45698e-07    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  Constant     1.87138e+04   5.48748e+01   3.00899e+00  -2.14702e-05
   2  Mean         3.71620e-01   5.69059e-04   4.86900e-05  -7.98800e-01
   3  Sigma        3.02581e-01   6.82372e-04   3.43116e-05  -8.64357e-01
 FCN=5749.2 FROM MIGRAD    STATUS=CONVERGED     266 CALLS         267 TOTAL
                     EDM=8.51599e-07    STRATEGY= 1  ERROR MATRIX UNCERTAINTY   1.9 per cent
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  p0           1.96416e+04   5.78655e+01  -8.23516e-02  -3.40593e-06
   2  p1           3.69576e-01   5.72167e-04   1.93495e-06   1.76163e+00
   3  p2           2.33254e-01   6.81432e-04   5.49379e-07   9.04951e-02
   4  p3           1.94664e+03   1.93075e+01   3.85095e-02  -1.32823e-04
   5  p4           4.07521e-01   3.28666e-03   2.02325e-05  -2.03673e-01
   6  p5           1.00391e+00   4.80366e-03  -1.50741e-05  -3.62683e-01

PS:dx中零附近的突起,可能是在选择PPAC策略时,仅两个PPAC参与径迹重构的事件;

查看相邻PPAC-X的关联

In [15]:
gPad->SetLogy(0);
tree->Draw("dx[0]:dx[2]>>(40,-40,40,40,-40,40)");
c1->Draw();
In [16]:
gPad->SetLogy(0);
tree->Draw("dx[0]:dx[2]>>(40,-40,40,40,-40,40)","NumX==3&&WhichX[0]==0&&WhichX[1]==2&&WhichX[2]==4");
c1->Draw();

PS:在探测器组合固定下,关联谱比较干净!!!

查看chi2 vs dy[0]关联

  • 未确定PPAC组合策略
In [17]:
tree->Draw("c2ny:dy[0]>>hh(40,-10,10,200,0,1000)","","colz");
c1->SetLogy(0);
c1->Draw();//从chi2/ndf图上可看出,部分事件的径迹拟合误差很大,这部分要在后续数据处理中去掉。

PS:残差来源不同,故有多种关联的曲线

  • 确定PPAC组合策略(1A,2A,3) (WhichY[0~4]={PPAC-1A,PPAC-1B,PPAC-2A,PPAC-2B,PPAC-3});
In [18]:
tree->Draw("c2ny:dy[0]>>hh(40,-10,10,200,0,600)","NumY==3&&WhichY[0]==0&&WhichY[1]==2&&WhichY[2]==4","colz");
c1->SetLogy(0);
c1->Draw();//从chi2/ndf图上可看出,部分事件的径迹拟合误差很大,这部分要在后续数据处理中去掉。

Chi2分布

  • PPAC-X
In [19]:
tree->Draw("c2nx>>hh(200,0,1000)","","");
gPad->SetLogy();
c1->Draw();//从chi2/ndf图上可看出,部分事件的径迹拟合误差很大,这部分要在后续数据处理中去掉。
  • PPAC-Y
In [20]:
tree->Draw("c2ny>>hh(200,0,1000)","","");
gPad->SetLogy();
c1->Draw();//从chi2/ndf图上可看出,部分事件的径迹拟合误差很大,这部分要在后续数据处理中去掉。
In [21]:
!jupyter nbconvert homework2.1_Chi2 --to html
[NbConvertApp] Converting notebook homework2.1_Chi2.ipynb to html

[NbConvertApp] Writing 26336378 bytes to homework2.1_Chi2.html

In [ ]: