Lgraczyk: /* Exercise */

2022-03-28T10:48:31Z

Exercise

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	== Exercise ==		== Exercise ==
	Measurements of three physical observables <code>X1, X2</code> oraz <code>X3</code> have been made. Results of the measurements are in the following files:		Measurements of three physical observables <code>X1, X2</code> oraz <code>X3</code> have been made. Results of the measurements are in the following files:
-	[http://www.if.pw.edu.pl/~lgraczyk/wiki/images/e/ed/Dane1.dat Dane1.dat], [http://www.if.pw.edu.pl/~lgraczyk/wiki/images/0/0d/Dane2.dat Dane2.dat] ~~oraz~~ [http://www.if.pw.edu.pl/~lgraczyk/wiki/images/b/ba/Dane3.dat Dane3.dat].	+	[http://www.if.pw.edu.pl/~lgraczyk/wiki/images/e/ed/Dane1.dat Dane1.dat], [http://www.if.pw.edu.pl/~lgraczyk/wiki/images/0/0d/Dane2.dat Dane2.dat] and [http://www.if.pw.edu.pl/~lgraczyk/wiki/images/b/ba/Dane3.dat Dane3.dat].

	* Please calculate the result (mean and uncertainty - standard deviation) and draw the relation between the variables <code>(X1, X2)</code>, <code>(X2, X3)</code> and <code>(X1, X3)</code>. (1 pkt)		* Please calculate the result (mean and uncertainty - standard deviation) and draw the relation between the variables <code>(X1, X2)</code>, <code>(X2, X3)</code> and <code>(X1, X3)</code>. (1 pkt)

Lgraczyk: Created page with "{| align="right" | TOC |} == Exercise == Measurements of three physical observables `X1, X2` oraz `X3` have been made. Results of the measurements ar..."

2022-03-28T10:48:13Z

Created page with "{| align="right" | __TOC__ |} == Exercise == Measurements of three physical observables <code>X1, X2</code> oraz <code>X3</code> have been made. Results of the measurements ar..."

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{| align="right"
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== Exercise ==
Measurements of three physical observables <code>X1, X2</code> oraz <code>X3</code> have been made. Results of the measurements are in the following files:
[http://www.if.pw.edu.pl/~lgraczyk/wiki/images/e/ed/Dane1.dat Dane1.dat], [http://www.if.pw.edu.pl/~lgraczyk/wiki/images/0/0d/Dane2.dat Dane2.dat] oraz [http://www.if.pw.edu.pl/~lgraczyk/wiki/images/b/ba/Dane3.dat Dane3.dat].

* Please calculate the result (mean and uncertainty - standard deviation) and draw the relation between the variables <code>(X1, X2)</code>, <code>(X2, X3)</code> and <code>(X1, X3)</code>. (1 pkt)

Variables <code>Y1, Y2</code> are related to <code>X1, X2, X3</code> via the following formulas:

<code> Y1 = 2 X1 + 5 X2 + X3

Y2 = 3 + 0.5 X1 + 4 X2</code>

Please calculate:
* covariance matrix X1, X2, X3 (1 pkt)
* mean values of Y1, Y2 in direct measurement (0.5 pkt)
* covariance matrix Y1, Y2 (1pkt)
* uncertainties of quantitites Y1, Y2 (1 pkt)
* correlation coefficients Y1 and Y2 (0.5 pkt)

== Attention ==
* Look carefully '''three first slides from lecture 5''' [http://www.if.pw.edu.pl/~lgraczyk/KADD2022/Wyklad5-2022.pdf link]
* Szczegółowy opis slajdy '''12-16 from lecture 4''' [http://www.if.pw.edu.pl/~lgraczyk/KADD2022/Wyklad4-2022.pdf link]
* Read data from file (the same as in C++):
ifstream ifile;
ifile.open("dane.dat");
double val;
while(ifile>>val)
{
cout<<val<<endl;
}
ifile.close();

* For all matrix operation (creating matrices of covariance, multiplication of matrices, transposing matrices) - use the class '''<code>TMatrixD</code>''' [https://root.cern.ch/root/html534/TMatrixT_double_.html link]
* '''Remember, that matrix operations require correct order of matrices.'''
* Uncertainty and correlation coefficient of X we obtain from TH2D histograms after reading the data; uncertainties and correlation coefficient of Y we obtain after calculating the matrix of coviarance of Y
* '''Limits of the histogram ranges in T2DH histograms in my solution are as follows:

double x1min = 1.5, x1max = 5.0;
double x2min = 0.0, x2max = 3.0;
double x3min = 4.0, x3max = 16.0;
TH2D *h12 = new TH2D("h12","Hist12",100,x1min,x1max,100,x2min,x2max);
TH2D *h13 = new TH2D("h13","Hist13",100,x1min,x1max,100,x3min,x3max);
TH2D *h23 = new TH2D("h13","Hist23",100,x2min,x2max,100,x3min,x3max);

* [http://pl.wikibooks.org/wiki/Statystyka_matematyczna/Momenty_statystyczne_w_dzia%C5%82aniu Wikibooks]

== Results ==
Plots:
[[File:Lab05_KADD2012.png]]

Output:
X1=3.00691, u(X1)=0.495242
X2=2.00581, u(X1)=0.40909
X3=9.97287, u(X3)=1.98102
rho(X1,X2)=0.156132
rho(X1,X3)=-0.00698853
rho(X2,X3)=0.00875851

after rounding to 2 significant digits:
X1=3.01, u(X1)=0.50
X2=2.01, u(X1)=0.41
X3=9.97, u(X3)=1.98

This is the matrix of covariance for X
3x3 matrix is as follows

| 0 | 1 | 2 |
--------------------------------------------
0 | 0.2453 0.0316 -0.006855
1 | 0.0316 0.1674 0.0071
2 | -0.006855 0.0071 3.924

This is the matrix of covariance for Y
2x2 matrix is as follows

| 0 | 1 |
-------------------------------
0 | 9.765 3.949
1 | 3.949 2.865

Y1=26.0157, u(Y1)=3.1249
Y2=12.5267, u(Y2)=1.6927404
rho(Y1,Y2)=0.746574
rho(Y2,Y1)=0.746574

after rounding to 2 significant digits:
Y1=26.02, u(Y1)=3.13
Y2=12.53, u(Y2)=1.70

KADD 2022 Laboratorium 5 EN - Revision history

Lgraczyk: /* Exercise */

Lgraczyk: Created page with "{| align="right" | __TOC__ |} == Exercise == Measurements of three physical observables X1, X2 oraz X3 have been made. Results of the measurements ar..."

Lgraczyk: Created page with "{| align="right" | TOC |} == Exercise == Measurements of three physical observables `X1, X2` oraz `X3` have been made. Results of the measurements ar..."