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

From Script | Spoken-Tutorial
Jump to: navigation, search
 
(7 intermediate revisions by 2 users not shown)
Line 1: Line 1:
  
−
{|border=1
+
{| border=1
 +
|| '''Visual Cue'''
 +
|| '''Narration'''
  
 
|-
 
|-
−
|| Visual Cue
+
|| '''Slide Number 1'''
−
|| Narration
+
'''Title Slide '''
 +
|| Welcome to the tutorial on
 +
'''Error bars and data fitting '''in '''gnuplot'''.
  
 
|-
 
|-
−
||'''Slide Number 1'''
+
|| '''Slide Number 2'''
−
'''Title Slide '''
+
'''Learning Objectives'''
−
'''Data fitting and error bars'''
+
|| In this tutorial, we will,
−
||Welcome to the tutorial on '''Data fitting and error bars'''
+
* 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 2'''
+
|| '''Slide Number 3'''
 
'''Learning Objectives'''
 
'''Learning Objectives'''
−
||In this tutorial, we will learn,
+
||  
−
*Learn to add error bars in a graph
+
* Fit the dataset to the equation  
−
*Learn data fitting
+
* Draw an arrow object in the graph
−
*Fit a given dataset to an equation  
+
−
*Run non-linear regression and generate fitting parameters
+
  
 
|-
 
|-
−
||'''Slide Number 3'''
+
|| '''Slide Number 4'''
 
'''System and Software Requirement'''
 
'''System and Software Requirement'''
−
||*Debian Linux 9 .3
+
|| To record this tutorial, I am using,
−
*Gedit 3.22.0 and
+
* '''Ubuntu Linux''' 16.04 OS
−
*gnuplot 5.2.5 installed
+
* '''Gnuplot''' version 5.2.6 and  
 +
* '''Gedit''' version 3.18
  
 
|-
 
|-
−
||'''Slide Number 4'''
+
|| '''Slide Number 5'''
 
'''Pre-requisites'''
 
'''Pre-requisites'''
−
||To follow this tutorial, learner’s must be familiar with,
+
[https://spoken-tutorials.org https://spoken-tutorials.org]
−
*Basic computer and internet skills
+
|| To follow this tutorial,  
−
*Concept of graphing and
+
* Learner must be familiar with the basics of '''gnuplot'''.
−
*College level Mathematics skills
+
* For the prerequisite tutorials, please visit this site.
  
 
|-
 
|-
−
|| Go to '''Desktop'''.
+
|| '''Slide Number 6'''
−
||First, we will first learn to incorporate error bars in a graph.
+
'''Code files'''
−
First, Go to '''Desktop'''.
+
||  
−
I have a, x y yerror type data, in a text file.  
+
* The files used in this tutorial are provided in the '''code files''' link.
 +
* Please download and extract the files.
  
 
|-
 
|-
−
|| Double click to open the file.
+
|| Go to '''Desktop'''.
−
||It is saved in '''Desktop''' directory for me.
+
|| Go to '''Desktop'''.
−
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.
+
  
−
|-
+
I have a, '''x,''' '''y,''' '''y'''-error type data, in a text file.  
−
|| 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'''
+
|| Hover mouse over '''x''', '''y''' and '''dy''' columns on the screen for the file.
−
|| Close '''gedit''' by clicking on the x-sign.
+
|| The first column is x data.
 +
 
 +
The second column is '''y''' data.
 +
 
 +
The third column is error in the '''y''' data.
  
 
|-
 
|-
−
||Press '''ctrl alt t'''
+
|| Close '''gedit'''.
−
'''cd ~/Desktop'''
+
Press '''Ctrl+Alt+T'''.
−
|| Press '''ctrl alt t''' keys together to open a '''terminal'''.
+
||  
−
Change directory to '''Desktop''' as seen on the screen.
+
 
 +
Open a '''terminal'''.
  
 
|-
 
|-
−
||'''gnuplot'''
+
|| Enter the command '''cd Desktop '''.
−
|| Open '''gnuplot'''.
+
Enter the command '''gnuplot'''.
−
Type '''gnuplot''' and '''enter'''
+
|| Change the directory to '''Desktop''' and open '''gnuplot'''.
  
 
|-
 
|-
−
|| Show qt on screen.
+
|| Press '''Ctrl+L'''.
−
||'''Set''' '''terminal''' as necessary.  
+
|| I will clear the screen.
−
For me it is already in '''qt'''.
+
  
 
|-
 
|-
−
|| '''Ctrl-l'''
+
|| Cursor on the '''terminal'''.
−
|| I will clear screen with command control l.
+
|| Let's plot the data to see the trend.  
−
This takes terminal prompt to top of the screen for clarity in video.
+
  
 
|-
 
|-
−
||  
+
|| Enter the command '''plot 'xydy.txt' using 1:2:3 with yerrorbars''' .
−
|| First, let's plot the data to see the trend and for visual inspection.
+
|| Enter the '''plot''' command as seen on the screen.
  
 
|-
 
|-
−
|| '''plot 'error-bar.txt' using 1:2:3 with yerrorbars'''
+
|| Hover mouse over ''':3''' .
−
|| Enter the plot command as seen on the screen.
+
|| 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 can use, x error bars 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.
  
 
|-
 
|-
−
||  
+
|| Hover mouse over decay curve.
−
|| The colon 3 with y error bars in the plot command adds the error to the plot.
+
|| Let's fit this graph to an equation.  
  
 
|-
 
|-
−
|| Hover mouse over decay curve.
+
|| Cursor on the graph.
−
|| Next, let's fit this graph to an equation.  
+
|| Here, the data points are likely to follow an exponential decay.
  
 
|-
 
|-
−
||  
+
|| Hover mouse on the graph.
−
|| This data likely represent an exponential decay.
+
|| The points deviate from an accurate exponential decay.
 +
 
 +
This could be due to measurement errors.
  
 
|-
 
|-
−
||  
+
|| Point mouse next to data.
−
|| The points may be off the ideal curve due to measurement errors.
+
|| We will fit the given data points to an '''exponential decay''' function.
  
 
|-
 
|-
−
||  
+
|| Cursor on the screen.
−
|| 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 7'''
 +
'''Steps for Fitting Data'''
 
||  
 
||  
−
|| Let's see a few steps involved in fitting data points to an equation.
+
* 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 5'''
+
|| '''Slide Number 8'''
−
'''Steps in data fitting'''
+
 
−
|| First, define a function to represent the data
+
'''Steps for Fitting Data'''
−
Make initial guess values for constants
+
||  
−
A good fitting, measured by '''chi square''' value
+
* Check for goodness of the fit
−
Find the 'optimal' value of the constants in the function
+
* A good fitting is measured by a low value of chi square and
−
and Display the fitted data
+
* Display the fitted data with the starting dataset
  
 
|-
 
|-
−
|| '''f(x) = a * exp(-k*x)'''
+
|| Type, '''f(x) = a * exp(-k*x)'''  
−
||First, let's define the function.
+
and press '''Enter'''.
−
Type '''f''' of '''x''' is equal to a times '''e''' to the power minus '''k x'''
+
|| First, let's define the function.
−
Use the syntax as seen on the screen
+
 
 +
In the '''gnuplot''' prompt, type f of x is equal to a times e to the power minus k x.
  
 
|-
 
|-
 
|| Go to graphical window.
 
|| Go to graphical window.
−
||Let's make an educated initial guess for the initial guess values of a and k
+
|| Make an educated initial guess for the values of '''a''' and '''k'''.
−
Go to graphical window.
+
 
 +
Go to the graphical window.
  
 
|-
 
|-
−
||  
+
|| Hover mouse near top of y axis.
−
|| From the graph, I will place the initial value of a at one lakh fitfty thousand
+
|| 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
+
|| 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 gnuplot terminal prompt.
+
|| Close the graphical window and go to the '''gnuplot terminal''' prompt.
  
 
|-
 
|-
−
||'''a=150000 '''
+
|| Enter the commands,
 +
'''a=150000 '''
 
'''k=0.5'''
 
'''k=0.5'''
−
||Enter commands to set the values of a and k
+
|| Enter commands to set initial guess values.
−
Enter a equal to fifteen hundred thousand
+
 
−
Enter k equal to zero point five
+
Set '''a''' to 150 thousand and '''k''' to 0.5 .
  
 
|-
 
|-
−
|| '''fit f(x) “error-bar.txt” using 1:2:3 via a,k'''
+
|| Type, '''fit f(x) ‘xydy.txt’ using 1:2:3 via a,k'''
−
||To fit the data use command as seen on the screen.
+
and press '''Enter'''.
−
Fit space f of x space in double quotes error hyphen bar dot txt.  
+
|| To fit the data type the command,
−
Then Space using space 1 colon 2 colon 3 via a comma k
+
 
 +
'''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''' .
−
|| If column 3 is not mentioned, the y axis uncertainties is not considered for data fitting.
+
|| 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'''.
−
|| The software does the fitting and gives output values.
+
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.
 
|| Let's scroll up the screen.
  
 
|-
 
|-
 
||  
 
||  
−
|| I see an error , warning message on top
+
|| 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 of a and k after each iteration.
+
|| Notice a table with '''chi square''' and new values for '''a''' and '''k''' after each iteration.
  
 
|-
 
|-
−
||  
+
|| Incorporate the number of iterations.
−
||Program reports, the fitting process converged after a few iterations.
+
|| The program reports that, the fitting process converged after 10 iterations.
−
It is 8 iteractions.
+
  
 
|-
 
|-
−
||  
+
|| Hover mouse over '''final sum of square of residuals'''.
−
||Many fitting parameters are reported in the output.
+
|| Many fitting parameters are reported in the output.
 
Program reports, final sum of square of residuals.
 
Program reports, final sum of square of residuals.
  
 
|-
 
|-
−
||  
+
|| Hover mouse over iteration value.
−
||Notice, relative change in values after the last iteration.
+
|| Notice, relative change in values after the last iteration.
−
The number is very small
+
 
 +
 
 +
The number is very small.
  
 
|-
 
|-
−
||  
+
|| Hover mouse over '''Degrees of freedom'''.
−
|| Degrees of freedom is 9
+
|| '''Degrees of freedom''' is 9.
  
 
|-
 
|-
−
||  
+
|| Hover mouse over '''RMS'''.
−
|| The root mean square or RMS is around 0.17
+
|| '''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.
+
|| 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.
+
|| 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.
 
|| Now we have a function that fits the given data points.
 +
 +
Let's plot the data points and the function together.
  
 
|-
 
|-
−
||  
+
|| Press '''Ctrl+L''' .
−
|| Let's plot the data points and function together.
+
|| 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''' .
−
||Then, we can see, how well the equation fit the given points.
+
|| Enter the command as seen on the screen.
−
I will clear the screen with command control l for clarity in video again.
+
 
 +
This plots the data and the function together.
 +
 
 +
We are plotting the fitted equation along with the initial data points.
  
 
|-
 
|-
−
|| '''plot f(x) lw 2 title 'fitted data', "error-bar-fitting.txt" using 1:2:3 with yerrorbars pt 7 ps 1.5 notitle'''
+
|| Hover mouse near the legend.
−
||Then, enter the plot command as seen on the screen.
+
|| 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 dataset as no '''notitle''' is mentioned.
 +
 
 +
I have specified a filled circle '''symbol''' and 1.5 for point size.
  
 
|-
 
|-
−
||  
+
|| Show the line on the graphics window.
−
||I will modify to change legend as '''fitted data''' for f of x.
+
Show symbol with error bar.
−
It is represented by a line with width 2.
+
|| Data points are represented by symbols with '''error bar''' and without a line style.
  
 
|-
 
|-
−
||  
+
|| Enter the command, '''set xrange [0.95:5.05]''' .
−
||I have specified no legend title for the starting data set.
+
|| Let's also set '''x axis''' limits with '''set xrange''' command as seen.
−
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]'''
+
|| Type '''replot''' and press '''Enter''' to see the graphics window.
−
||Please pause video as necessary to practice.
+
|| '''Replot''' to see the results.
−
Let's also set x axis limits with set xrange command as seen in the video.
+
  
 
|-
 
|-
−
|| '''replot'''
+
|| Show this web site address screen shot.
−
|| Replot to see the results.
+
'''http://gnuplot.sourceforge.net/demo/fit.html'''
 +
|| Check the '''gnuplot''' website for example '''scripts''' on data fitting.
  
 
|-
 
|-
−
||'''Slide Number 6'''
+
|| 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.
 +
 
 +
|-
 +
|| 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 9'''
 
'''Summary'''
 
'''Summary'''
−
|| Now let’s summarize.
+
|| To summarize, in this tutorial, we  
−
In this tutorial, we learned to
+
* Incorporated error bars in a plot graph
−
* Display error bars in a graph
+
* Fitted a given set of data points to an equation
−
* Fit a given set of data points to an equation<br/>and
+
* Plotted the fitted curve along with parent data
−
* Display fitted curve along with parent data
+
* Added and removed an arrow object
  
 +
|-
 +
|| '''Slide Number 10'''
 +
'''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 7'''
+
|| '''Slide Number 11'''
 
'''Assignment'''
 
'''Assignment'''
−
||For assignment activity, please do the following.
+
||  
−
For data file assignment.txt, plot x and y error bars in graph.
+
* Fit the data to a double exponential decay curve with ''yerrorbars''.
−
The file is provided to you along with the tutorial.
+
* Plot the fitted data
−
Fit the data to a double exponential decay curve.
+
* 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 8'''
+
|| '''Slide Number 12'''
 
'''Spoken Tutorial Project'''
 
'''Spoken Tutorial Project'''
−
||This video summarises the Spoken Tutorial Project  
+
|| This video summarises the '''Spoken Tutorial''' Project .
 
Please download and watch it.
 
Please download and watch it.
  
 
|-
 
|-
−
||'''Slide Number 9'''
+
|| '''Slide Number 13'''
 
'''Spoken Tutorial workshops'''
 
'''Spoken Tutorial workshops'''
−
||We conduct workshops and give certificates.  
+
|| We conduct workshops and give certificates.  
−
Please write to us.
+
 
 +
For more details, please write to us.
  
 
|-
 
|-
−
||'''Slide Number 10'''
+
|| '''Slide Number 14'''
 +
 
 
'''Forum for specific questions:'''
 
'''Forum for specific questions:'''
 
|| Post your timed queries in the forum.
 
|| Post your timed queries in the forum.
  
 
|-
 
|-
−
||'''Slide Number 11'''
+
|| '''Slide Number 15'''
 
'''Acknowledgement'''
 
'''Acknowledgement'''
−
||Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India.
+
|| Spoken Tutorial Project is funded by '''MHRD''', '''Government of India'''.
  
 
|-
 
|-
 
||  
 
||  
−
|| Thank you for joining.  
+
|| This is Rani, from '''IIT''', '''Bombay'''.
 +
Thank you for joining.
  
 +
|-
 
|}
 
|}

Latest revision as of 09:51, 4 February 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

  • 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 version 5.2.6 and
  • Gedit version 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.

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 7

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 8

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 dataset as no notitle is mentioned.

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

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.
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.
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 9

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 10

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 11

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 12

Spoken Tutorial Project

This video summarises the Spoken Tutorial Project .

Please download and watch it.

Slide Number 13

Spoken Tutorial workshops

We conduct workshops and give certificates.

For more details, please write to us.

Slide Number 14

Forum for specific questions:

Post your timed queries in the forum.
Slide Number 15

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

Retrieved from "https://script.spoken-tutorial.org/index.php?title=Gnuplot/C2/Error-bars-and-data-fitting/English&oldid=51004"