Final Project (Group 6) - Notes

Data format

The data files are organized as a series of events (rows) where each event consist of the coordinates of the hits recorded in that event (N.B.: as the number of hits for even is not fixed, the dataset cannot be seen as a unique big table with a defined number of "columns"). More specifically every raw consists of:

• event number
• number of recorded hits (N)
• hit 1 coordinates
• ...
• hit N coordinates

where N could be zero too and the hits coordinates are:

• chamber, which of the four detector registered the hit (numbering is in the range $0-4$)
• layer, which layer of that detector
• xleft, the x position of the hit in the local detector coordinates assuming the track passed at the left of the wire
• xright, the x position of the hit in the local detector coordinates assuming the track passed at the right of the wire
• time, the drift time (redundant)

The local detector coordinates are defined with respect to one side (the left one) of the detector. All the detectors however were placed rotated by 180 degrees, i.e. the x axes of the local and global coordinates have different orientation.

Notes on data format

• for each recordered hit we have 5 coordinates; this means that the length of a row is 2 + 5N
• the chambers are numbered in this way:
  • chamber[0]: top-right
  • chamber[1]: bottom-right
  • chamber[2]: top-left
  • chamber[3]: bottom-left
• layers are numbered from bottom (layer = 1) to top (layer = 4)
• assuming each row is a python list (i.e. list[0] = event number, list[1] = N, ...) and $i \in [0, 1, ..., N-1]$:
  • chamber: list[2+5i]
  • layer: list[3+5i]
  • xleft: list[4+5i]
  • xright: list[5+5i]
  • time: list[6+5i]
  • the possible layout for a Pandas DataFrame could be:

Ev_Number	($n \in [1, N]$)	chamber	layer	XL_local	XR_local	Z_local	time	XL_global	XR_global	Z_global

The hit number is used as the index of the Dataframe.

Coordinates transformation

The relevant dimensions and the overall coordinate transformations in $z$ and $x$ are given below. Note that all the quantities are expressed in $mm$.

# Cell dimensions
XCELL = 42.
ZCELL = 13.

# X coordinates translation
global_x_shifts = [994.2, 947.4,-267.4,-261.5,]

# Z coordinates translations
local_z_shifts = [z*ZCELL for z in range(0,4)]
global_z_shifts = [823.5, 0, 823.5, 0]

Notes on the transformation

# '-' sign is due to 180° degrees rotation of detectors
x_global =  global_x_shifts[chamber] - x_local

z_local = local_z_shifts[layer]
z_global = global_z_shifts[chamber] + z_local

Functions

Read data

• Input: 1 row of data_file.txt, e.g. 1 event, passed as a list
• Output: Pandas DataFrame as in the Data Format paragraph, Number of the Event, Number of hits in the Event

This function takes in input one event at time, and then outputs a Pandas DataFrame as described in the previous section. In addition, the transformation from local to global coordinates is performed.

Plot background

• Input: None
• Output: list[pyplot Axes] (global image + 4 detectors zooms)

Five plots are given as output: one image of the whole detector, and one for each of the 4 chambers. This function is made in order to do the plot of the background only one time, instead of doing that for every Event.

In order to plot the Axes in the list, and get a good layout:

gridsize = (5, 2)
fig = plt.figure(figsize = (12, 24))
axes = plot_background()
plt.show()

Plot events

• Input: Pandas DataFrame (1 event) + event number
• Output: list[pyplot Axes] (global image + 4 detectors zooms)

The input of the function is the Pandas DataFrame made by the Read Data function, and the event number (this is due to the fact that, if the are no hits, the DataFrame is empty, and therefore we can't get the Event number from that). Five plots are given as output: one image of the whole detector, and one for each of the 4 chambers. In the images there will be the points of the hits tracked in the event (left/right positions must have different colors).

Select Events (Calibration)

• Input: Pandas DataFrame (1 event)
• Output: True/False

The input of the function is the Pandas DataFrame made by the Read Data function. The output is a boolean value, which labels the good calibration events.

We need to plot the histogram of the frequency of the number of hits, in order to find out the best requirements for good events.

Possible choice (to be evalueted): Good events requires at least 6 hits (in different layers) either in the left or in the right side of the detector.

Local linear fit

• Input: Pandas DataFrame (1 event)
• Output: [[slope, intercept] for each chamber]

The input of the function is the Pandas DataFrame made by the Read Data function. The output is a list of list with the coefficients of the linear regression (e.g. scipy.stats.linregress) for each chamber.

The fit is only made for good events, which means the return of Select Events (Calibration) function is True. If there are no hits in the chamber, the list returned should be [False, False].

The fit has to be made considering all of the possible permutation of the left/right signals; the result will be chosen by selecting the fit with the lowest $\chi^2$.

Global linear fit

• Input: Pandas DataFrame (1 event)
• Output: [[slope, intercept] for each side (left/right)]

The input of the function is the Pandas DataFrame made by the Read Data function. The output is a list of list with the coefficients of the linear regression (e.g. scipy.stats.linregress) for each side.

The fit is only made for good events, which means the return of Select Events (Calibration) function is True, for calibration runs, or Select Events (Physics) function is True, for physics runs. If there are no hits in one of the sides (calibration runs), the list returned should be [False, False].

The fit has to be made considering all of the possible permutation of the left/right signals; the result will be chosen by selecting the fit with the lowest $\chi^2$.

This part is a draft, and should be analyze better

The fit should be made using a fixed number of points (e.g. 6 in different layers), even if we have more. If we have more signals, they should be used to check the goodness of the fit (compare the measured position with ones calculated with fit results).

Plot events with fit

• Input: pyplot figure + fit parameters
• Output: pyplot Figure (global image)

The input of the function is the image of the global detector made by the Plot Events function, and the lists of parameters retrieved from Local linea fit and Global linear fit. The plot of the whole detector with hits and linear regressions is given as output; global fit will be dislayed with solid lines, while local one with dashed lines.