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− | '''Title of script''': '''Error bars and <span style="color:#000000;">D</span><span style="color:#000000;">ata fitting'''</span>
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− | '''Author: '''Rani Parvathy
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− | '''Keywords:''' gnuplot, video tutorial, spoken tutorial, data fitting, regression, error bars
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| + | || Visual Cue |
| + | || Narration |
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| + | |- |
| + | ||'''Slide Number 1''' |
| + | '''Title Slide ''' |
| + | '''Data fitting and error bars''' |
| + | ||Welcome to the tutorial on '''Data fitting and error bars''' |
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− | {| style="border-spacing:0;width:6.8472in;"
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− | ! align=center style="background-color:#993366;border-top:1pt solid #000000;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | Visual Cue
| + | ||'''Slide Number 2''' |
− | ! align=center style="background-color:#993366;border:1pt solid #000000;padding:0.0382in;" | Narration
| + | '''Learning Objectives''' |
| + | ||In this tutorial, we will learn, |
| + | *Learn to add error bars in a graph |
| + | *Learn data fitting |
| + | *Fit a given dataset to an equation |
| + | *Run non-linear regression and generate fitting parameters |
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | <div style="color:#000000;">'''Slide Number 1'''</div> | + | ||'''Slide Number 3''' |
| + | '''System and Software Requirement''' |
| + | ||*Debian Linux 9 .3 |
| + | *Gedit 3.22.0 and |
| + | *gnuplot 5.2.5 installed |
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− | <div style="color:#000000;">'''Title Slide '''</div>
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| + | ||'''Slide Number 4''' |
| + | '''Pre-requisites''' |
| + | ||To follow this tutorial, learner’s must be familiar with, |
| + | *Basic computer and internet skills |
| + | *Concept of graphing and |
| + | *College level Mathematics skills |
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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. |
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− | <div style="color:#000000;">'''Data fitting and error bars'''</div>
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">Welcome to the tutorial on </div>
| + | || 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. |
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− | <div style="color:#000000;">'''Data fitting and error bars'''</div>
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | <div style="color:#000000;">'''Slide Number 2'''</div> | + | || 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. |
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− | <div style="color:#000000;">'''Learning Objectives'''</div>
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− | | + | || Close '''gedit''' |
− | | + | || Close '''gedit''' by clicking on the x-sign. |
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">In this tutorial, we will learn,</div> | + | |
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− | * <div style="color:#000000;">Learn to add error bars in a graph</div>
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− | * <div style="color:#000000;">Learn data fitting</div>
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− | * <div style="color:#000000;">Fit a given dataset to an equation </div>
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− | * <div style="color:#000000;">Run non-linear regression and generate fitting parameters</div>
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| + | |- |
| + | ||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. |
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | <div style="color:#000000;">'''Slide Number 3'''</div> | + | ||'''gnuplot''' |
| + | || Open '''gnuplot'''. |
| + | Type '''gnuplot''' and '''enter''' |
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− | <div style="color:#000000;">'''System and Software Requirement'''</div>
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− | <div style="color:#000000;"></div>
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">Debian Linux</div>
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− | <div style="color:#000000;">Gedit 3.22.0</div>
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− | <div style="color:#000000;">and</div>
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− | <div style="color:#000000;">Have Gnuplot 5.2.5 installed</div>
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | <div style="color:#000000;">'''Slide Number 4'''</div> | + | || Show qt on screen. |
| + | ||'''Set''' '''terminal''' as necessary. |
| + | For me it is already in '''qt'''. |
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− | <div style="color:#000000;">'''Samson Microphone'''</div>
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">To record audio, I am using '''Samson''' '''USB''' portable microphone was used.</div>
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− | <div style="color:#000000;">The model number '''SAGOMIC'''</div>
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− | <div style="color:#000000;">I bought it from '''amazon''' website, for about rupees four thousand</div>
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− | <div style="color:#000000;"><span style="background-color:transparent;">It may be available in other websites.</span></div>
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | <div style="color:#000000;">'''Slide Number 5'''</div> | + | || '''Ctrl-l''' |
− | | + | || I will clear screen with command control l. |
− | <div style="color:#000000;">'''Pre-requisites'''</div>
| + | This takes terminal prompt to top of the screen for clarity in video. |
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− | <div style="color:#000000;"></div>
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">To follow this tutorial, learner’s must be familiar with, </div> | + | |
− | | + | |
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− | <div style="color:#000000;">Basic computer and internet skills</div>
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− | <div style="color:#000000;">Concept of graphing </div>
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− | <div style="color:#000000;">and </div>
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− | <div style="color:#000000;">College level Mathematics skills</div>
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | <div style="color:#000000;">'''Slide Number 6'''</div> | + | || |
| + | || First, let's plot the data to see the trend and for visual inspection. |
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− | <div style="color:#000000;">'''Pre-requisites'''</div>
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− | <div style="color:#000000;"></div>
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <span style="background-color:transparent;color:#000000;">Please locate this tutorial on our web page, </span><span style="background-color:transparent;color:#000000;">'''spoken hyphen tutorial dot org'''</span><span style="background-color:transparent;color:#000000;"> </span>
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− | <div style="color:#000000;">Prerequisite '''spoken''' '''tutorials''', if any, will be mentioned in this page </div>
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | Go to '''Desktop'''. | + | || '''plot 'error-bar.txt' using 1:2:3 with yerrorbars''' |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">First, we will first learn to incorporate error bars in a graph.</div> | + | || Enter the plot command as seen on the screen. |
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− |
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− | <div style="color:#000000;">First, Go to '''Desktop'''.</div>
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− |
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− | <div style="color:#000000;">I have a, x y yerror type data, in a text file. </div>
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | Double click to open the file. | + | || |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">It is saved in '''Desktop''' directory for me. </div> | + | || If error limits are on the x data, we can use, x error bars term for plotting. |
| + | The graphic window opens. |
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− | <div style="color:#000000;">Double click on the file icon to open it in a text editor.</div>
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− | <div style="color:#000000;">The file opens in gedit for me.</div>
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− | <div style="color:#000000;">This file is provided to you with the tutorial.</div>
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | | + | || |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | The first column is '''x''' data. | + | || The colon 3 with y error bars in the plot command adds the error to the plot. |
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− | Second column is '''y''' data.
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− | The third column is '''y''' data error bar in measurement.
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | Close '''gedit''' | + | || Hover mouse over decay curve. |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | Close '''gedit''' by clicking on the x-sign. | + | || Next, let's fit this graph to an equation. |
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | <div style="color:#000000;">Press '''ctrl alt t'''</div>
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− | <div style="color:#000000;">'''cd ~/Desktop'''</div>
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | Press '''ctrl alt t''' keys together to open a '''terminal'''.
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− | Change directory to '''Desktop''' as seen on the screen.
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | <div style="color:#000000;">ctrl+alt+T</div> | + | || |
| + | || This data likely represent an exponential decay. |
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− | <div style="color:#000000;">>'''gnuplot'''</div>
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | Open '''gnuplot'''.
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− | Type '''gnuplot''' and '''enter'''
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | Show qt on screen. | + | || |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">'''Set''' '''terminal''' as necessary. </div> | + | || The points may be off the ideal curve due to measurement errors. |
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− | <div style="color:#000000;">For me it is already in '''qt'''.</div>
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | '''Ctrl-l''' | + | || |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | I will clear screen with command control l. | + | || We will fit the given data points to an exponential decay function. |
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− | This takes terminal prompt to top of the screen for clarity in video.
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | First, let's plot the data to see the trend and for visual inspection.
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | '''plot 'error-bar.txt' using 1:2:3 with yerrorbars'''
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | Enter the plot command as seen on the screen.
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | | + | || |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | If error limits are on the x data, we can use, x error bars term for plotting. | + | || Let's see a few steps involved in fitting data points to an equation. |
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− | The graphic window opens.
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | | + | ||'''Slide Number 5''' |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | The colon 3 with y error bars in the plot command adds the error to the plot.
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | Hover mouse over decay curve.
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | Next, let's fit this graph to an equation.
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| + | |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | This data likely represent an exponential decay.
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| + | |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | The points may be off the ideal curve due to measurement errors.
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | We will fit the given data points to an exponential decay function.
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| + | |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | Let's see a few steps involved in fitting data points to an equation.
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | <span style="color:#000000;">'''Slide Number </span><span style="color:#000000;">7'''</span>
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| '''Steps in data fitting''' | | '''Steps in data fitting''' |
− | | + | || First, define a function to represent the data |
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− | Find a function to represent the data
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− | Initial guess values for constants
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− | A good fitting, measured by chi square
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− | Find the 'optimal' value of the constants in the function
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− | <div style="color:#000000;">Display the fitted data</div>
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | First, define a function to represent the data | + | |
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| Make initial guess values for constants | | Make initial guess values for constants |
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| A good fitting, measured by '''chi square''' value | | A good fitting, measured by '''chi square''' value |
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| Find the 'optimal' value of the constants in the function | | Find the 'optimal' value of the constants in the function |
| + | and Display the fitted data |
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| + | |- |
| + | || '''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 |
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− | and Display the fitted data
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | '''f(x) = a * exp(-k*x)''' | + | || Go to graphical window. |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">First, let's define the function.</div> | + | ||Let's make an educated initial guess for the initial guess values of a and k |
| + | Go to graphical window. |
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| + | || |
| + | || From the graph, I will place the initial value of a at one lakh fitfty thousand |
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− | <div style="color:#000000;">Type '''f''' of '''x''' is equal to a times '''e''' to the power minus '''k x'''</div>
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| + | || |
| + | || For an exponential decay, I will place the initial guess of k around 0.5 |
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| + | |- |
| + | || |
| + | || Close the graphical window and go to gnuplot terminal prompt. |
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− | <div style="color:#000000;">Use the syntax as seen on the screen</div>
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | Go to graphical window. | + | ||'''a=150000 ''' |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">Let's make an educated initial guess for the initial guess values of a and k</div>
| + | '''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 |
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| + | |- |
| + | || '''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 |
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− | <div style="color:#000000;">Go to graphical window.</div>
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | | + | || |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;color:#000000;" | From the graph, I will place the initial value of a at one lakh fitfty thousand | + | || If column 3 is not mentioned, the y axis uncertainties is not considered for data fitting. |
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | | + | || |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;color:#000000;" | For an exponential decay, I will place the initial guess of k around 0.5 | + | || The software does the fitting and gives output values. |
| + | |
| |- | | |- |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | | + | || |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | Close the graphical window and go to gnuplot terminal prompt. | + | || Let's scroll up the screen. |
| + | |
| |- | | |- |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | <div style="color:#000000;">'''a=150000 '''</div> | + | || |
| + | || I see an error , warning message on top |
| | | |
− | <div style="color:#000000;">'''k=0.5'''</div>
| + | |- |
| + | || |
| + | || 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. |
| | | |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">Enter commands to set the values of a and k</div> | + | |- |
| + | || |
| + | ||Notice, relative change in values after the last iteration. |
| + | The number is very small |
| | | |
− | <div style="color:#000000;">Enter a equal to fifteen hundred thousand</div>
| + | |- |
| + | || |
| + | || Degrees of freedom is 9 |
| | | |
− | <div style="color:#000000;">Enter k equal to zero point five</div>
| |
| |- | | |- |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | '''fit f(x) “error-bar.txt” using 1:2:3 via a,k''' | + | || |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">To fit the data use command as seen on the screen.</div> | + | || The root mean square or RMS is around 0.17 |
| | | |
| + | |- |
| + | || |
| + | || Updated values of a and k and their error in estimation is also shown. |
| | | |
− | <div style="color:#000000;">Fit space f of x space in double quotes error hyphen bar dot txt. </div>
| + | |- |
| + | || |
| + | || The correlation matrix of variables is at the end of the output. |
| | | |
− |
| |
− | <div style="color:#000000;">Then Space using space 1 colon 2 colon 3 via a comma k</div>
| |
| |- | | |- |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | | + | || |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | If column 3 is not mentioned, the y axis uncertainties is not considered for data fitting. | + | || Now we have a function that fits the given data points. |
− | |-
| + | |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| + | |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | The software does the fitting and gives output values.
| + | |
− | |-
| + | |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| + | |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;color:#000000;" | Let's scroll up the screen.
| + | |
− | |-
| + | |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| + | |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;color:#000000;" | I see an error , warning message on top
| + | |
− | |-
| + | |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| + | |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;color:#000000;" | Notice a table with chi square and new values of a and k after each iteration.
| + | |
− | |-
| + | |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| + | |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">Program reports, the fitting process converged after a few iterations.</div>
| + | |
− | | + | |
| | | |
− | <div style="color:#000000;">It is 8 iteractions.</div>
| |
| |- | | |- |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | | + | || |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">Many fitting parameters are reported in the output.</div> | + | || Let's plot the data points and function together. |
| | | |
− |
| |
− | <div style="color:#000000;">Program reports, final sum of square of residuals.</div>
| |
| |- | | |- |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | | + | || |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">Notice, relative change in values after the last iteration.</div> | + | ||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. |
| | | |
− |
| |
− | <div style="color:#000000;">The number is very small</div>
| |
− | |-
| |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;color:#000000;" | Degrees of freedom is 9
| |
− | |-
| |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;color:#000000;" | The root mean square or RMS is around 0.17
| |
− | |-
| |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | Updated values of a and k and their error in estimation is also shown.
| |
− | |-
| |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | The correlation matrix of variables is at the end of the output.
| |
− | |-
| |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | Now we have a function that fits the given data points.
| |
− | |-
| |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
| |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | Let's plot the data points and function together.
| |
| |- | | |- |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | | + | || '''plot f(x) lw 2 title 'fitted data', "error-bar-fitting.txt" using 1:2:3 with yerrorbars pt 7 ps 1.5 notitle''' |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">Then, we can see, how well the equation fit the given points.</div>
| + | ||Then, enter the plot command as seen on the screen. |
| | | |
− |
| |
− | <div style="color:#000000;">I will clear the screen with command control l for clarity in video again.</div>
| |
| |- | | |- |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | '''plot f(x) lw 2 title 'fitted data', "error-bar-fitting.txt" using 1:2:3 with yerrorbars pt 7 ps 1.5 notitle''' | + | || |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">Then, enter the plot command as seen on the screen.</div>
| + | ||I will modify to change legend as '''fitted data''' for f of x. |
− | | + | It is represented by a line with width 2. |
− | | + | |
| | | |
| |- | | |- |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | | + | || |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">I will modify to change legend as '''fitted data''' for f of x.</div> | + | ||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 |
| | | |
− |
| |
− | <div style="color:#000000;">It is represented by a line with width 2.</div>
| |
| |- | | |- |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | | + | || '''set xrange [0.95:5.05]''' |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">I have specified no legend title for the starting data set.</div> | + | ||Please pause video as necessary to practice. |
| + | Let's also set x axis limits with set xrange command as seen in the video. |
| | | |
− |
| |
− | <div style="color:#000000;">Data points are represented only by symbols with error bar and have no line.</div>
| |
− |
| |
− |
| |
− | <div style="color:#000000;">I have specified a filled circle symbol and 1.5 for point size</div>
| |
| |- | | |- |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | '''set xrange [0.95:5.05]''' | + | || '''replot''' |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">Please pause video as necessary to practice.</div> | + | || Replot to see the results. |
| | | |
− |
| |
− | Let's also set x axis limits with set xrange command as seen in the video.
| |
| |- | | |- |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | '''replot''' | + | ||'''Slide Number 6''' |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | Replot to see the results.
| + | '''Summary''' |
− | |-
| + | || Now let’s summarize. |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | <div style="color:#000000;">'''Slide Number 8'''</div>
| + | |
− | | + | |
− | <div style="color:#000000;">'''Summary'''</div>
| + | |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | Now let’s summarize. | + | |
− | | + | |
− | | + | |
| In this tutorial, we learned to | | In this tutorial, we learned to |
− |
| |
− |
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| * Display error bars in a graph | | * Display error bars in a graph |
| * Fit a given set of data points to an equation<br/>and | | * Fit a given set of data points to an equation<br/>and |
Line 367: |
Line 261: |
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| |- | | |- |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | <div style="color:#000000;">'''Slide Number 9'''</div> | + | ||'''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. |
| | | |
− | <div style="color:#000000;">'''Assignment'''</div>
| + | |- |
| + | ||'''Slide Number 8''' |
| + | '''Spoken Tutorial Project''' |
| + | ||This video summarises the Spoken Tutorial Project |
| + | Please download and watch it. |
| | | |
− |
| |
− | <div style="color:#000000;"></div>
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">For assignment activity, please do the following.</div>
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− |
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− |
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− | <div style="color:#000000;">For data file assignment.txt, plot x and y error bars in graph.</div>
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− |
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− |
| |
− | <div style="color:#000000;">The file is provided to you along with the tutorial.</div>
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− |
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− |
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− | <div style="color:#000000;">Fit the data to a double exponential decay curve.</div>
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| |- | | |- |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | <div style="color:#000000;">'''Slide Number 10'''</div> | + | ||'''Slide Number 9''' |
| + | '''Spoken Tutorial workshops''' |
| + | ||We conduct workshops and give certificates. |
| + | Please write to us. |
| | | |
− | <div style="color:#000000;">'''Spoken Tutorial Project'''</div>
| |
− |
| |
− |
| |
− |
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <span style="color:#000000;">This video summarises the</span><span style="color:#000000;"> Spoken Tutorial Project </span>
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− |
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− |
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− | <div style="color:#000000;">If you do not have good bandwidth, you may download and watch it.</div>
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| |- | | |- |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | <div style="color:#000000;">'''Slide Number 11'''</div> | + | ||'''Slide Number 10''' |
| + | '''Forum for specific questions:''' |
| + | || Post your timed queries in the forum. |
| | | |
− | <div style="color:#000000;">'''Spoken Tutorial workshops'''</div>
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− |
| |
− |
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− |
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <span style="color:#000000;">We</span><span style="color:#000000;"> conduct workshops using spoken tutorials and give certificates. </span>
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− |
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− |
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− | <span style="color:#000000;">P</span><span style="color:#000000;">lease write to us.</span>
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| |- | | |- |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | <div style="color:#000000;">'''Slide Number 12'''</div> | + | ||'''Slide Number 11''' |
| + | '''Acknowledgement''' |
| + | ||Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India. |
| | | |
− | <div style="color:#000000;">'''Forum for specific questions:'''</div>
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− |
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− |
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;color:#000000;" | Post your timed queries in the forum.
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| |- | | |- |
− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;" | <div style="color:#000000;">'''Slide Number 13'''</div> | + | || |
| + | || Thank you for joining. |
| | | |
− | <span style="color:#000000;">'''Acknowledgemen'''</span><span style="color:#000000;">t</span>
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− |
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− |
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− |
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;" | <div style="color:#000000;">Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India.</div>
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− | |-
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" |
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;color:#000000;" | Thank you for joining.
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− | |-
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.0382in;color:#000000;" | '''plot f(x) lw 2, "error-bar-fitting.txt" using 1:2:3 with yerrorbars pt 7 ps 1.5'''
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− | | style="background-color:#ffffff;border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.0382in;color:#000000;" |
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− | <div style="color:#000000;margin-left:0in;margin-right:0in;"></div>
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Visual Cue
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Narration
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Slide Number 1
Title Slide
Data fitting and error bars
|
Welcome to the tutorial on Data fitting and error bars
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Slide Number 2
Learning Objectives
|
In this tutorial, we will learn,
- Learn to add error bars in a graph
- Learn data fitting
- Fit a given dataset to an equation
- Run non-linear regression and generate fitting parameters
|
Slide Number 3
System and Software Requirement
|
*Debian Linux 9 .3
- Gedit 3.22.0 and
- gnuplot 5.2.5 installed
|
Slide Number 4
Pre-requisites
|
To follow this tutorial, learner’s must be familiar with,
- Basic computer and internet skills
- Concept of graphing and
- College level Mathematics skills
|
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
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f(x) = a * exp(-k*x)
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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
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Go to graphical window.
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Let's make an educated initial guess for the initial guess values of a and k
Go to graphical window.
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From the graph, I will place the initial value of a at one lakh fitfty thousand
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For an exponential decay, I will place the initial guess of k around 0.5
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Close the graphical window and go to gnuplot terminal prompt.
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a=150000
k=0.5
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Enter commands to set the values of a and k
Enter a equal to fifteen hundred thousand
Enter k equal to zero point five
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fit f(x) “error-bar.txt” using 1:2:3 via a,k
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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
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If column 3 is not mentioned, the y axis uncertainties is not considered for data fitting.
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The software does the fitting and gives output values.
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Let's scroll up the screen.
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I see an error , warning message on top
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Notice a table with chi square and new values of a and k after each iteration.
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Program reports, the fitting process converged after a few iterations.
It is 8 iteractions.
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Many fitting parameters are reported in the output.
Program reports, final sum of square of residuals.
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Notice, relative change in values after the last iteration.
The number is very small
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Degrees of freedom is 9
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The root mean square or RMS is around 0.17
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Updated values of a and k and their error in estimation is also shown.
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The correlation matrix of variables is at the end of the output.
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Now we have a function that fits the given data points.
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Let's plot the data points and function together.
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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.
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plot f(x) lw 2 title 'fitted data', "error-bar-fitting.txt" using 1:2:3 with yerrorbars pt 7 ps 1.5 notitle
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Then, enter the plot command as seen on the screen.
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I will modify to change legend as fitted data for f of x.
It is represented by a line with width 2.
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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
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set xrange [0.95:5.05]
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Please pause video as necessary to practice.
Let's also set x axis limits with set xrange command as seen in the video.
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replot
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Replot to see the results.
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Slide Number 6
Summary
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Now let’s summarize.
In this tutorial, we learned to
- Display error bars in a graph
- Fit a given set of data points to an equation
and
- Display fitted curve along with parent data
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Slide Number 7
Assignment
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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.
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Slide Number 8
Spoken Tutorial Project
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This video summarises the Spoken Tutorial Project
Please download and watch it.
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Slide Number 9
Spoken Tutorial workshops
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We conduct workshops and give certificates.
Please write to us.
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Slide Number 10
Forum for specific questions:
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Post your timed queries in the forum.
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Slide Number 11
Acknowledgement
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Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India.
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Thank you for joining.
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