Gnuplot/C2/Error-bars-and-data-fitting/English
| Visual Cue | Narration |
| Slide Number 1
Title Slide Data fitting and error bars |
Welcome to the tutorial on Data fitting and error bars |
| Slide Number 2
Learning Objectives |
In this tutorial, we will learn,
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| Slide Number 3
System and Software Requirement |
*Debian Linux 9 .3
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| Slide Number 4
Pre-requisites |
To follow this tutorial, learner’s must be familiar with,
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| Go to Desktop. | First, we will first learn to incorporate error bars in a graph.
First, Go to Desktop. I have a, x y yerror type data, in a text file. |
| Double click to open the file. | It is saved in Desktop directory for me.
Double click on the file icon to open it in a text editor. The file opens in gedit for me. This file is provided to you with the tutorial. |
| Hover mouse over columns | The first column is x data.
Second column is y data. The third column is y data error bar in measurement. |
| Close gedit | Close gedit by clicking on the x-sign. |
| Press ctrl alt t
cd ~/Desktop |
Press ctrl alt t keys together to open a terminal.
Change directory to Desktop as seen on the screen. |
| gnuplot | Open gnuplot.
Type gnuplot and enter |
| Show qt on screen. | Set terminal as necessary.
For me it is already in qt. |
| Ctrl-l | I will clear screen with command control l.
This takes terminal prompt to top of the screen for clarity in video. |
| First, let's plot the data to see the trend and for visual inspection. | |
| plot 'error-bar.txt' using 1:2:3 with yerrorbars | Enter the plot command as seen on the screen. |
| If error limits are on the x data, we can use, x error bars term for plotting.
The graphic window opens. | |
| The colon 3 with y error bars in the plot command adds the error to the plot. | |
| Hover mouse over decay curve. | Next, let's fit this graph to an equation. |
| This data likely represent an exponential decay. | |
| The points may be off the ideal curve due to measurement errors. | |
| We will fit the given data points to an exponential decay function. | |
| Let's see a few steps involved in fitting data points to an equation. | |
| Slide Number 5
Steps in data fitting |
First, define a function to represent the data
Make initial guess values for constants A good fitting, measured by chi square value Find the 'optimal' value of the constants in the function and Display the fitted data |
| f(x) = a * exp(-k*x) | First, let's define the function.
Type f of x is equal to a times e to the power minus k x Use the syntax as seen on the screen |
| Go to graphical window. | Let's make an educated initial guess for the initial guess values of a and k
Go to graphical window. |
| From the graph, I will place the initial value of a at one lakh fitfty thousand | |
| For an exponential decay, I will place the initial guess of k around 0.5 | |
| Close the graphical window and go to gnuplot terminal prompt. | |
| a=150000
k=0.5 |
Enter commands to set the values of a and k
Enter a equal to fifteen hundred thousand Enter k equal to zero point five |
| fit f(x) “error-bar.txt” using 1:2:3 via a,k | To fit the data use command as seen on the screen.
Fit space f of x space in double quotes error hyphen bar dot txt. Then Space using space 1 colon 2 colon 3 via a comma k |
| If column 3 is not mentioned, the y axis uncertainties is not considered for data fitting. | |
| The software does the fitting and gives output values. | |
| Let's scroll up the screen. | |
| I see an error , warning message on top | |
| Notice a table with chi square and new values of a and k after each iteration. | |
| Program reports, the fitting process converged after a few iterations.
It is 8 iteractions. | |
| Many fitting parameters are reported in the output.
Program reports, final sum of square of residuals. | |
| Notice, relative change in values after the last iteration.
The number is very small | |
| Degrees of freedom is 9 | |
| The root mean square or RMS is around 0.17 | |
| Updated values of a and k and their error in estimation is also shown. | |
| The correlation matrix of variables is at the end of the output. | |
| Now we have a function that fits the given data points. | |
| Let's plot the data points and function together. | |
| Then, we can see, how well the equation fit the given points.
I will clear the screen with command control l for clarity in video again. | |
| plot f(x) lw 2 title 'fitted data', "error-bar-fitting.txt" using 1:2:3 with yerrorbars pt 7 ps 1.5 notitle | Then, enter the plot command as seen on the screen. |
| I will modify to change legend as fitted data for f of x.
It is represented by a line with width 2. | |
| I have specified no legend title for the starting data set.
Data points are represented only by symbols with error bar and have no line. I have specified a filled circle symbol and 1.5 for point size | |
| set xrange [0.95:5.05] | Please pause video as necessary to practice.
Let's also set x axis limits with set xrange command as seen in the video. |
| replot | Replot to see the results. |
| Slide Number 6
Summary |
Now let’s summarize.
In this tutorial, we learned to
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| Slide Number 7
Assignment |
For assignment activity, please do the following.
For data file assignment.txt, plot x and y error bars in graph. The file is provided to you along with the tutorial. Fit the data to a double exponential decay curve. |
| Slide Number 8
Spoken Tutorial Project |
This video summarises the Spoken Tutorial Project
Please download and watch it. |
| Slide Number 9
Spoken Tutorial workshops |
We conduct workshops and give certificates.
Please write to us. |
| Slide Number 10
Forum for specific questions: |
Post your timed queries in the forum. |
| Slide Number 11
Acknowledgement |
Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India. |
| Thank you for joining. |
