Difference between revisions of "Gnuplot/C2/Error-bars-and-data-fitting/English"

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* Write an equation to fit the data
 
* Write an equation to fit the data
 
* Make initial guess for value of the coefficients
 
* Make initial guess for value of the coefficients
 +
 +
|-
 +
|| '''Slide Number 3'''
 +
'''Learning Objectives'''
 +
|| In this tutorial, we will,
 
* Fit the dataset to the equation  
 
* Fit the dataset to the equation  
 
* Draw an arrow object in the graph
 
* Draw an arrow object in the graph
  
 
|-
 
|-
−
|| '''Slide Number 3'''
+
|| '''Slide Number 4'''
 
'''System and Software Requirement'''
 
'''System and Software Requirement'''
 
|| To record this tutorial, I am using,
 
|| To record this tutorial, I am using,
−
* '''Ubuntu Linux''' 16.04
+
* '''Ubuntu Linux''' 16.04 OS
−
* '''Gnuplot''' 5.2.6 and  
+
* '''Gnuplot''' v 5.2.6 and  
−
* '''Gedit''' 3.18  
+
* '''Gedit''' v 3.18  
  
 
|-
 
|-
−
|| '''Slide Number 4'''
+
|| '''Slide Number 5'''
 
'''Pre-requisites'''
 
'''Pre-requisites'''
 
[https://spoken-tutorials.org https://spoken-tutorials.org]
 
[https://spoken-tutorials.org https://spoken-tutorials.org]
Line 38: Line 43:
  
 
|-
 
|-
−
|| '''Slide Number 5'''
+
|| '''Slide Number 6'''
 
'''Code files'''
 
'''Code files'''
 
||  
 
||  
−
* The input file used in this tutorial is provided in the '''code file''' link.
+
* The files used in this tutorial are provided in the '''code files''' link.
 
* Please download and extract the files.
 
* Please download and extract the files.
  
Line 66: Line 71:
 
|| Enter the command '''cd Desktop '''.
 
|| Enter the command '''cd Desktop '''.
 
Enter the command '''gnuplot'''.
 
Enter the command '''gnuplot'''.
−
 
 
|| Change the directory to '''Desktop''' and open '''gnuplot'''.
 
|| Change the directory to '''Desktop''' and open '''gnuplot'''.
  
Line 78: Line 82:
  
 
|-
 
|-
−
|| Enter the command '''plot 'error-bar.txt' using 1:2:3 with yerrorbars''' .
+
|| Enter the command '''plot 'xydy.txt' using 1:2:3 with yerrorbars''' .
 
|| Enter the '''plot''' command as seen on the screen.
 
|| Enter the '''plot''' command as seen on the screen.
  
Line 87: Line 91:
 
|-
 
|-
 
|| Hover mouse over '''yerrorbars'''.
 
|| Hover mouse over '''yerrorbars'''.
−
|| If error limits are on the '''x''' data, we have to use, '''x''' errorbars term for plotting.
+
|| If error limits are on the '''x''' data, we have to use, '''xerrorbars''' term for plotting.
  
 
The graphic window opens.
 
The graphic window opens.
Line 101: Line 105:
 
|-
 
|-
 
|| Hover mouse on the graph.
 
|| Hover mouse on the graph.
−
|| The points may deviate from an accurate exponential decay.  
+
|| The points deviate from an accurate exponential decay.  
  
 
This could be due to measurement errors.
 
This could be due to measurement errors.
Line 111: Line 115:
 
|-
 
|-
 
|| Cursor on the screen.
 
|| Cursor on the screen.
−
|| Let's see a few steps involved in fitting data points with an equation.
+
|| Let's see a few steps involved in fitting data points to an equation.
  
 
|-
 
|-
Line 119: Line 123:
 
* Define an equation to represent the data.
 
* Define an equation to represent the data.
 
* Make initial guess values for the coefficients in the equation.
 
* Make initial guess values for the coefficients in the equation.
−
* Optimal values for the coefficients is found by an iterative process.
+
* Optimal values for the coefficients are found by an iterative process.
  
 
|-
 
|-
Line 169: Line 173:
 
'''fit f of x''' in single quotes the file name.
 
'''fit f of x''' in single quotes the file name.
  
−
Here it is '''error dash bar dot txt'''.  
+
Here it is '''xydy dot txt'''.  
  
 
Then '''using 1 colon 2 colon 3''' via a comma k .
 
Then '''using 1 colon 2 colon 3''' via a comma k .
Line 177: Line 181:
 
|-
 
|-
 
|| Hover mouse over ''':3''' .
 
|| Hover mouse over ''':3''' .
−
|| We could leave out the colon 3 in the command.  
+
|| We could leave out the colon 3 part in the command.  
−
Then, errors in the '''y''' data are not considered during the data fitting  
+
Then, errors in the '''y''' data are not considered during the data fitting process.
−
process.
+
  
 
|-
 
|-
Line 200: Line 203:
 
|-
 
|-
 
|| Hover mouse over the '''chi square''' table.
 
|| Hover mouse over the '''chi square''' table.
−
|| Notice a table with '''chi square''' and new values of '''a''' and '''k''' after each iteration.
+
|| Notice a table with '''chi square''' and new values for '''a''' and '''k''' after each iteration.
  
 
|-
 
|-
Line 224: Line 227:
 
|-
 
|-
 
|| Hover mouse over '''RMS'''.
 
|| Hover mouse over '''RMS'''.
−
|| '''RMS''' of residuals is around 0.17.
+
|| '''RMS''' of residuals is around 2.5.
  
 
|-
 
|-
Line 237: Line 240:
 
|| Cursor on the '''terminal'''.
 
|| Cursor on the '''terminal'''.
 
|| Now we have a function that fits the given data points.
 
|| Now we have a function that fits the given data points.
−
Let's plot the data points and function together.
+
Let's plot the data points and the function together.
  
 
|-
 
|-
Line 245: Line 248:
 
|-
 
|-
 
|| Enter the command, '''plot f(x) lw 2 title 'fitted data', "xydy.txt" using 1:2:3 with yerrorbars pt 7 ps 1.5 notitle''' .
 
|| Enter the command, '''plot f(x) lw 2 title 'fitted data', "xydy.txt" using 1:2:3 with yerrorbars pt 7 ps 1.5 notitle''' .
−
|| Enter the command as seen on the screen, to plot both data together.
+
|| Enter the command as seen on the screen.
 +
This plots the data and the function together.
  
−
We are plotting the fitted equation fit along with the initial data points.
+
We are plotting the fitted equation along with the initial data points.
  
 
|-
 
|-
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|-
 
|-
 
|| Cursor on the screen, around the (1.3,6000) region.
 
|| Cursor on the screen, around the (1.3,6000) region.
−
|| Let’s draw an arrow object in the graph.
+
|| Next, let’s draw an arrow object in the graph.
−
I want to draw an arrow next to a point in the graph to highlight it.
+
  
 
|-
 
|-
 
|| Move the mouse on the screen to show the arrow placement around ('''1.63,77200 to 1.7, 62000''').
 
|| Move the mouse on the screen to show the arrow placement around ('''1.63,77200 to 1.7, 62000''').
−
|| In the graph, I want to add an arrow between these two points.
+
|| In the graph, I want to add an arrow between these two points to highlight it.
  
 
|-
 
|-
Line 312: Line 315:
 
'''set arrow 2 from 1.63,77200 to 1.4, 62000''' and press '''Enter'''.
 
'''set arrow 2 from 1.63,77200 to 1.4, 62000''' and press '''Enter'''.
 
|| Go to the '''terminal''' and enter the command as seen on the screen.
 
|| Go to the '''terminal''' and enter the command as seen on the screen.
−
I will name this arrow as '''second'''.
+
I will name this arrow as '''two'''.
  
 
|-
 
|-
Line 321: Line 324:
 
|| Cursor on the graphics window.
 
|| Cursor on the graphics window.
 
|| Now we see two arrows in the graphics window.
 
|| Now we see two arrows in the graphics window.
 +
I want to remove one of the arrows.
 
To remove the object, we have to '''unset''' the object.
 
To remove the object, we have to '''unset''' the object.
  
 
|-
 
|-
 
|| Type '''unset arrow first''' and press '''Enter'''.
 
|| Type '''unset arrow first''' and press '''Enter'''.
−
|| Go to the '''terminal'''.
+
|| Hence, go to the '''terminal'''.
−
Enter the command, '''unset arrow first''' to remove the first arrow.
+
Enter the command, '''unset space arrow space one''' to remove the first arrow.
  
 
|-
 
|-
Line 334: Line 338:
 
|-
 
|-
 
|| Cursor on the graphics window.
 
|| Cursor on the graphics window.
−
|| The arrow that was named '''first''' is now removed from the graphics window,
+
|| The arrow that was named '''one''' is now removed from the graphics window,
  
 
|-
 
|-
Line 344: Line 348:
 
|| '''Slide Number 8'''
 
|| '''Slide Number 8'''
 
'''Summary'''
 
'''Summary'''
−
|| To summarize, in this tutorial, we learned to
+
|| To summarize, in this tutorial, we  
 
* Incorporated error bars in a plot graph
 
* Incorporated error bars in a plot graph
−
* Fit a given set of data points to an equation
+
* Fitted a given set of data points to an equation
 
* Plotted the fitted curve along with parent data
 
* Plotted the fitted curve along with parent data
 
* Added and removed an arrow object
 
* Added and removed an arrow object
Line 352: Line 356:
 
|-
 
|-
 
|| '''Slide Number 9'''
 
|| '''Slide Number 9'''
−
'''Assignment 1'''
+
'''Assignment'''
 
|| For the assignment activity, please do the following.
 
|| For the assignment activity, please do the following.
−
* For the data file '''assignment.txt''', make an xy graph with ''xyerrorbars'' in the graph.
+
* For the data file '''assignment.txt''', make an xy graph with ''xyerrorbars''.
 
* This file is available in the Code files link.
 
* This file is available in the Code files link.
  
 
|-
 
|-
 
|| '''Slide Number 9'''
 
|| '''Slide Number 9'''
−
'''Assignment 2'''
+
'''Assignment'''
 
||  
 
||  
 
* Fit the data to a double exponential decay curve with ''yerrorbars''.
 
* Fit the data to a double exponential decay curve with ''yerrorbars''.
 
* Plot the fitted data
 
* Plot the fitted data
 
* Draw an arrow object in the graph at the position of your choice.
 
* Draw an arrow object in the graph at the position of your choice.
 +
 +
|-
 +
|| Glimpse of assignment
 +
|| The completed assignment looks similar to this.
  
 
|-
 
|-

Revision as of 10:50, 28 January 2020

Visual Cue Narration
Slide Number 1

Title Slide

Welcome to the tutorial on

Error bars and data fitting in gnuplot.

Slide Number 2

Learning Objectives

In this tutorial, we will,
  • Learn to add error bars in a plot
  • Learn about data fitting
  • Write an equation to fit the data
  • Make initial guess for value of the coefficients
Slide Number 3

Learning Objectives

In this tutorial, we will,
  • Fit the dataset to the equation
  • Draw an arrow object in the graph
Slide Number 4

System and Software Requirement

To record this tutorial, I am using,
  • Ubuntu Linux 16.04 OS
  • Gnuplot v 5.2.6 and
  • Gedit v 3.18
Slide Number 5

Pre-requisites https://spoken-tutorials.org

To follow this tutorial,
  • Learner must be familiar with the basics of gnuplot.
  • For the prerequisite tutorials, please visit this site.
Slide Number 6

Code files

  • The files used in this tutorial are provided in the code files link.
  • Please download and extract the files.
Go to Desktop. Go to Desktop.

I have a, x, y, y-error type data, in a text file.

Hover mouse over x, y and dy columns on the screen for the file. The first column is x data.

The second column is y data.

The third column is error in the y data.

Close gedit.

Press Ctrl+Alt+T.

Close the file.

Open a terminal.

Enter the command cd Desktop .

Enter the command gnuplot.

Change the directory to Desktop and open gnuplot.
Press Ctrl+L. I will clear the screen.
Cursor on the terminal. Let's plot the data to see the trend.
Enter the command plot 'xydy.txt' using 1:2:3 with yerrorbars . Enter the plot command as seen on the screen.
Hover mouse over :3 . The command, colon 3 with y error bars adds the error to the plot.
Hover mouse over yerrorbars. If error limits are on the x data, we have to use, xerrorbars term for plotting.

The graphic window opens.

Hover mouse over decay curve. Let's fit this graph to an equation.
Cursor on the graph. Here, the data points are likely to follow an exponential decay.
Hover mouse on the graph. The points deviate from an accurate exponential decay.

This could be due to measurement errors.

Point mouse next to data. We will fit the given data points to an exponential decay function.
Cursor on the screen. Let's see a few steps involved in fitting data points to an equation.
Slide Number 6

Steps for Fitting Data

  • Define an equation to represent the data.
  • Make initial guess values for the coefficients in the equation.
  • Optimal values for the coefficients are found by an iterative process.
Slide Number 7

Steps for Fitting Data

  • Check for goodness of the fit
  • A good fitting is measured by a low value of chi square and
  • Display the fitted data with the starting dataset
Type, f(x) = a * exp(-k*x)

and press Enter.

First, let's define the function.

In the gnuplot prompt, type f of x is equal to a times e to the power minus k x.

Go to graphical window. Make an educated initial guess for the values of a and k.

Go to the graphical window.

Hover mouse near top of y axis. From the graph, I will place the initial value of a at 1,50,000.
Hover mouse to show ½ decay. For an exponential decay, I will place the initial guess of k around 0.5 .
Close the graphical window. Close the graphical window and go to the gnuplot terminal prompt.
Enter the commands,

a=150000 k=0.5

Enter commands to set initial guess values.

Set a to 150 thousand and k to 0.5 .

Type, fit f(x) ‘xydy.txt’ using 1:2:3 via a,k

and press Enter.

To fit the data type the command,

fit f of x in single quotes the file name.

Here it is xydy dot txt.

Then using 1 colon 2 colon 3 via a comma k .

Here a and k are the coefficients.

Hover mouse over :3 . We could leave out the colon 3 part in the command.

Then, errors in the y data are not considered during the data fitting process.

Press Enter.

Data fitting is seen on the screen.

Press Enter to run the data fitting algorithm.

The coefficients in the equation are optimized by an iterative process.

The output is generated on the screen.

Scroll up. Let's scroll up the screen.
I see an error warning message on the top.
Hover mouse over the chi square table. Notice a table with chi square and new values for a and k after each iteration.
Incorporate the number of iterations. The program reports that, the fitting process converged after 10 iterations.
Hover mouse over final sum of square of residuals. Many fitting parameters are reported in the output.

Program reports, final sum of square of residuals.

Hover mouse over iteration value. Notice, relative change in values after the last iteration.


The number is very small.

Hover mouse over Degrees of freedom. Degrees of freedom is 9.
Hover mouse over RMS. RMS of residuals is around 2.5.
Show a and k values on the screen. Updated values of a and k and their error in estimation is also shown.
Hover mouse over the correlation matrix. The correlation matrix of variables is at the end of the output.
Cursor on the terminal. Now we have a function that fits the given data points.

Let's plot the data points and the function together.

Press Ctrl+L . I will clear the screen.
Enter the command, plot f(x) lw 2 title 'fitted data', "xydy.txt" using 1:2:3 with yerrorbars pt 7 ps 1.5 notitle . Enter the command as seen on the screen.

This plots the data and the function together.

We are plotting the fitted equation along with the initial data points.

Hover mouse near the legend. The fitted data is represented by a line with a line.

I am specifying the legend for f of x as fitted data.

No legend title is added for the starting data set as no notitle is mentioned.

Show the line on the graphics window.

Show symbol with error bar.

Data points are represented by symbols with error bar and without a line style.

I have specified a filled circle symbol and 1.5 for point size.

Enter the command, set xrange [0.95:5.05] . Let's also set x axis limits with set xrange command as seen.
Type replot and press Enter to see the graphics window. Replot to see the results.
Show this web site address screen shot.

http://gnuplot.sourceforge.net/demo/fit.html

Check the gnuplot website for example scripts on data fitting.
Cursor on the screen, around the (1.3,6000) region. Next, let’s draw an arrow object in the graph.
Move the mouse on the screen to show the arrow placement around (1.63,77200 to 1.7, 62000). In the graph, I want to add an arrow between these two points to highlight it.
Highlight in video, the co-ordinates seen on the graph window.

(1.63,77200 to 1.7, 62000).

I will note down the coordinates as seen in the graphics window.
Go to the terminal. Go to the terminal.
Type, set arrow 1 from 1.63,77200 to 1.7, 62000 and press Enter. Enter the commands as seen on the screen.

Here, one is the name I have given for the arrow object.

Type replot and press Enter. Replot to see the updated result.
Cursor on the graphics window. I will also add a second arrow in another direction.
Type,

set arrow 2 from 1.63,77200 to 1.4, 62000 and press Enter.

Go to the terminal and enter the command as seen on the screen.

I will name this arrow as two.

Type replot and press Enter. Replot to see the updated result.
Cursor on the graphics window. Now we see two arrows in the graphics window.

I want to remove one of the arrows. To remove the object, we have to unset the object.

Type unset arrow first and press Enter. Hence, go to the terminal.

Enter the command, unset space arrow space one to remove the first arrow.

Type replot and press Enter. Replot to see the updated result.
Cursor on the graphics window. The arrow that was named one is now removed from the graphics window,
Close the graphics window.

Type quit and press Enter.

Close the graphics window and quit gnuplot.
Slide Number 8

Summary

To summarize, in this tutorial, we
  • Incorporated error bars in a plot graph
  • Fitted a given set of data points to an equation
  • Plotted the fitted curve along with parent data
  • Added and removed an arrow object
Slide Number 9

Assignment

For the assignment activity, please do the following.
  • For the data file assignment.txt, make an xy graph with xyerrorbars.
  • This file is available in the Code files link.
Slide Number 9

Assignment

  • Fit the data to a double exponential decay curve with yerrorbars.
  • Plot the fitted data
  • Draw an arrow object in the graph at the position of your choice.
Glimpse of assignment The completed assignment looks similar to this.
Slide Number 10

Spoken Tutorial Project

This video summarises the Spoken Tutorial Project .

Please download and watch it.

Slide Number 11

Spoken Tutorial workshops

We conduct workshops and give certificates.

For more details, please write to us.

Slide Number 12

Forum for specific questions:

Post your timed queries in the forum.
Slide Number 13

Acknowledgement

Spoken Tutorial Project is funded by MHRD, Government of India.
This is Rani, from IIT, Bombay.

Thank you for joining.

Contributors and Content Editors

Madhurig, Ranipv076, Snehalathak

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