View source for Grace/C3/Fit-an-Exponential-Decay-Curve/English-timed

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|| '''Time'''
|| '''Narration'''

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|| 00:01
|| Welcome to the tutorial on '''Fit an exponential Decay Curve'''.

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|| 00:07
|| In this tutorial, we will learn to, Add multiple graph panels to the canvas

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|| 00:14
|| Remove dataset from the graph panel and

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|| 00:19
|| Fit a given set of data points with non-linear regression method.

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|| 00:26
|| To record this tutorial, I am using

'''Ubuntu Linux''' 16.04 OS

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|| 00:35
|| '''Grace''' 5.1.25

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|| 00:41
|| '''Gedit''' 3.18.3

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|| 00:46
|| To follow this tutorial, Learner must be familiar with the '''Grace''' interface.

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|| 00:53
|| For pre-requisite tutorials, please visit this site.

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|| 00:58
|| Two input files used in this tutorial are provided in the code files link.

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|| 01:05
||Please download and extract the files.


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|| 01:09
|| I have downloaded and saved them on my '''Desktop'''.

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|| 01:14
|| I have opened the '''Grace''' interface. 

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|| 01:18
|| Click on '''File''', '''Open''' to open a project.

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|| 01:22
|| Open the '''regression.agr''' project file from the '''Desktop''' directory.

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|| 01:29
|| A straight line graph is plotted on this plot window.

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|| 01:34
||Let's add another graph panel to the canvas.

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|| 01:38
|| Go to the '''Edit''' menu, select '''Arrange graphs''' option.

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|| 01:44
||The '''Arrange graphs''' window opens.

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|| 01:48
|| Under '''Matrix''', in the '''Cols''' drop-down increase the number of columns to 2.

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|| 01:55
|| Click on '''Apply''' and then on click '''Close'''.

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|| 01:59
||Notice that one more graph panel is added to the white canvas.

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|| 02:05
|| Notice that the graph panels are now elongated.

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|| 02:10
||I will resize the graph panels to two squares as seen on the screen.

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|| 02:17
|| I will also reposition the legends in the canvas.

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|| 02:22
|| To select a graph, click on it. 

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|| 02:25
||The selected graph is highlighted with the black squares on the corners.

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|| 02:31
|| Select the newly added graph panel.

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|| 02:35
|| Go to '''Data, Import, ASCII''' in the menu.

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|| 02:41
||Select the file, '''exponential.txt''' from '''Desktop''' directory.

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|| 02:47
|| Load the data as an '''XY''' dataset.

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|| 02:51
||Click on '''Ok''' to plot the graph.

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|| 02:55
||Then, click on '''Cancel''' to close the window.

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|| 02:59
|| From a visual inspection, the data points follow an exponential decay curve.

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|| 03:06
|| Double click on the curve to open the set appearance window.

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|| 03:11
|| Add '''symbols''' of your choice and choose no line.

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|| 03:17
||This helps to differentiate the fitted data from the starting dataset.

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|| 03:23
|| Go to '''Data''' and select '''Transformations'''.

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|| 03:27
|| A sub-menu opens with many options for data fitting.

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|| 03:32
|| Choose '''Regression''' from the sub-menu.

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|| 03:36
||New '''Regression dialog box''' opens.

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|| 03:40
|| Choose the data set of interest from '''Apply to set'''.

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|| 03:45
||Currently only a single set is loaded, shown as '''(S0)'''.

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|| 03:51
||It is in the graph panel '''G1''' and set is named '''S0'''.

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|| 03:57
|| Choose '''Exponential''' for '''Type of fit'''.

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|| 04:01
||This drop-down has few choices with sample functions to do data fitting.

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|| 04:08
|| In the '''Load''' drop-down, choose '''Fitted values'''.

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|| 04:12
|| For '''restrictions''' choose '''None'''.

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|| 04:15
|| Click on '''Accept''' to run the data fitting.

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|| 04:19
|| The '''Grace: console''' dialog box opens.

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|| 04:23
||Close the dialog box and the generated log file.

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|| 04:28
|| Notice the fitted data in the graph.

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|| 04:32
|| Often, the data may follow a complex mathematical equation. 

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|| 04:37
||Then, we have to define the equation and do a non-linear regression.

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|| 04:43
|| I will demonstrate it.

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|| 04:46
||I will not save the details of the data fitting. 

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|| 04:50
||I will close the dialog box.

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|| 04:53
||Let’s delete the fitted dataset loaded on the graph.

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|| 04:58
|| Go to '''Edit''' menu and open the '''Set Operations''' dialog box.

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|| 05:04
|| In the '''Source''' section, select Graph '''G1''' as seen.

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|| 05:10
|| In the '''set''' section, select the set '''G1 S1'''.

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|| 05:16
||Right click to open the '''context menu''' and choose '''Kill data'''.

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|| 05:22
|| A '''warning popup''' dialog box opens to confirm the process.

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|| 05:28
||Click on '''OK''' to kill the dataset.

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|| 05:32
|| Different types of set operations are possible in this window. 

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|| 05:37
|| I will click on '''Close''', to close the dialog box.

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|| 05:42
||You may explore further if desired.

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|| 05:46
|| Notice that the fitted data is removed from the graph.

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|| 05:51
|| We can also access the context menu from the '''set appearance''' window.

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|| 05:57
|| Select the desired dataset from the '''Select set''' form. 

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|| 06:02
||Right click to open the '''context menu''' and choose '''Kill data''' to remove the data.

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|| 06:08
|| Click on '''Close''', to close the dialog box.

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|| 06:12
||I will demonstrate to set up '''non-linear regression''' process. 

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|| 06:19
||  For data fitting, select an equation to fit the data.
 
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|| 06:24
||Make an initial guess for the value of the coefficients.

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|| 06:29
|| Run the data fitting algorithm.

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|| 06:32
||  Convergence is usually obtained with few iterations.
 
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|| 06:37
||Examine the output parameters for goodness of the fit.

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|| 06:42
|| Plot the function and the data together for visual representation.

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|| 06:49
|| Go to '''Data''', '''Transformations''' and select '''Non-linear curve fitting'''.

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|| 06:55
|| Under the '''Main''' tab, we will enter the desired equation.

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|| 07:00
|| Select '''2''' for '''Parameters'''.

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|| 07:04
||Two parameters '''A0''' and '''A1''' appear in the form below.

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|| 07:10
|| I will use an exponential decay curve as seen on the interface.

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|| 07:16
||Let’s type the equation as seen.

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|| 07:20
|| There is also an option to input starting values and define bounds.

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|| 07:26
||Set '''Iterations''' to 20 using the black, up triangle button as seen on the screen.

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|| 07:34
|| Set '''A0''' and '''A1''' initial guess.

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|| 07:39
|| We can make an educated guess for starting values of '''A0''' and '''A1''' from the graph.

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|| 07:47
||From the graph, '''A0''' could be around point four to point 5.

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|| 07:53
||Value of '''A1''' is around -0.25.

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||07:58
|| Set the initial guess values of the coefficients slightly away.

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|| 08:04
||Then, the iterative process in the regression algorithm can be observed.

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|| 08:11
||Input 0.4 for '''A0''' and -0.2 for '''A1''' as initial guess.

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|| 08:21
|| You may apply bounds check box if necessary by clicking on the bounds buttons.

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|| 08:28
|| In the '''Set''' section, select the set, '''G1 S0'''.

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|| 08:34
|| Click on '''Apply'''  to run the iterations.

The algorithm runs.

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|| 08:41
|| In this window, fitting parameter '''Chi-square''' is seen.

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|| 08:46
||'''Correlation coefficient, RMS, relative error''' and '''Theil coefficient''' are also seen.

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|| 08:54
|| Examine the '''chi-square''' values obtained. 

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|| 08:58
||Low '''chi-square''' means, the resulting function is a good fit for the data.

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|| 09:04
|| '''Residual''' is the difference between the observed and the fitted values.

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|| 09:10
||The '''sum of squares''' of residuals is minimized in the least square fitting method.

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|| 09:17
|| You may note down the values or save the results.

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|| 09:22
||Click on '''File, Save''' option to save the results.

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|| 09:27
|| A '''Grace:save logs''' form appear prompting to give a file name.

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|| 09:34
||In the form, type ''''fitted-values.txt'''' and click on '''Apply'''.

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|| 09:41
|| Click on '''Close''', to close the dialog box.

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|| 09:45
|| Use '''File, close''' to close the '''Grace:console''' window.

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|| 09:50
|| A curve generated from data fitting, is automatically loaded on the graph.

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|| 09:57
||The fitted curve traverse between the given data points.

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|| 10:03
|| Click on '''close''' to close the '''non-linear curve fitting''' window.

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|| 10:08
|| Click on '''File, save''' to save the project.

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|| 10:12
|| From top menu, choose '''File, exit''' to exit '''Grace'''.

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|| 10:19
|| Now, let’s summarize.

In this tutorial, we  Added multiple graph panels in the canvas

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|| 10:29
|| Learned to delete data sets from a graph panel
 
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|| 10:34
||Performed non-linear regression on an exponential decay curve.

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|| 10:41
|| For assignment, please do the following.

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|| 10:45
|| Fit the data given in the file '''assignment1.txt''' to a parabola.

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|| 10:51
|| Use an equation of the type, as seen here.

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|| 10:56
||  Fit the given data in the file '''assignment2.txt''', to '''atan(x)'''.

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|| 11:03
|| Your complete assignment look similar to this.

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|| 11:09
|| This video summarises the '''Spoken Tutorial''' Project.

Please download and watch it.

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|| 11:17
|| The '''Spoken Tutorial Project '''team: conducts workshops and gives certificates.

For more details, please write to us.

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||11:28
|| Please post your timed queries in this forum.

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|| 11:32
|| '''Spoken Tutorial''' Project is funded by '''MHRD''', '''Government of India'''.


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|| 11:39
|| This is Rani, from IIT Bombay. Thank you for joining.

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