Grace/C3/FitanExponentialDecayCurve/Englishtimed
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Revision as of 15:40, 30 August 2022 by PoojaMoolya (Talk  contribs)
Time  Narration 
00:01  Welcome to the tutorial on Fit an exponential Decay Curve. 
00:07  In this tutorial, we will learn to, Add multiple graph panels to the canvas 
00:14  Remove dataset from the graph panel and 
00:19  Fit a given set of data points with nonlinear regression method. 
00:26  To record this tutorial, I am using
Ubuntu Linux 16.04 OS 
00:35  Grace 5.1.25 
00:41  Gedit 3.18.3 
00:46  To follow this tutorial, Learner must be familiar with the Grace interface. 
00:53  For prerequisite tutorials, please visit this site. 
00:58  Two input files used in this tutorial are provided in the code files link. 
01:05  Please download and extract the files.

01:09  I have downloaded and saved them on my Desktop. 
01:14  I have opened the Grace interface. 
01:18  Click on File, Open to open a project. 
01:22  Open the regression.agr project file from the Desktop directory. 
01:29  A straight line graph is plotted on this plot window. 
01:34  Let's add another graph panel to the canvas. 
01:38  Go to the Edit menu, select Arrange graphs option. 
01:44  The Arrange graphs window opens. 
01:48  Under Matrix, in the Cols dropdown increase the number of columns to 2. 
01:55  Click on Apply and then on click Close. 
01:59  Notice that one more graph panel is added to the white canvas. 
02:05  Notice that the graph panels are now elongated. 
02:10  I will resize the graph panels to two squares as seen on the screen. 
02:17  I will also reposition the legends in the canvas. 
02:22  To select a graph, click on it. 
02:25  The selected graph is highlighted with the black squares on the corners. 
02:31  Select the newly added graph panel. 
02:35  Go to Data, Import, ASCII in the menu. 
02:41  Select the file, exponential.txt from Desktop directory. 
02:47  Load the data as an XY dataset. 
02:51  Click on Ok to plot the graph. 
02:55  Then, click on Cancel to close the window. 
02:59  From a visual inspection, the data points follow an exponential decay curve. 
03:06  Double click on the curve to open the set appearance window. 
03:11  Add symbols of your choice and choose no line. 
03:17  This helps to differentiate the fitted data from the starting dataset. 
03:23  Go to Data and select Transformations. 
03:27  A submenu opens with many options for data fitting. 
03:32  Choose Regression from the submenu. 
03:36  New Regression dialog box opens. 
03:40  Choose the data set of interest from Apply to set. 
03:45  Currently only a single set is loaded, shown as (S0). 
03:51  It is in the graph panel G1 and set is named S0. 
03:57  Choose Exponential for Type of fit. 
04:01  This dropdown has few choices with sample functions to do data fitting. 
04:08  In the Load dropdown, choose Fitted values. 
04:12  For restrictions choose None. 
04:15  Click on Accept to run the data fitting. 
04:19  The Grace: console dialog box opens. 
04:23  Close the dialog box and the generated log file. 
04:28  Notice the fitted data in the graph. 
04:32  Often, the data may follow a complex mathematical equation. 
04:37  Then, we have to define the equation and do a nonlinear regression. 
04:43  I will demonstrate it. 
04:46  I will not save the details of the data fitting. 
04:50  I will close the dialog box. 
04:53  Let’s delete the fitted dataset loaded on the graph. 
04:58  Go to Edit menu and open the Set Operations dialog box. 
05:04  In the Source section, select Graph G1 as seen. 
05:10  In the set section, select the set G1 S1. 
05:16  Right click to open the context menu and choose Kill data. 
05:22  A warning popup dialog box opens to confirm the process. 
05:28  Click on OK to kill the dataset. 
05:32  Different types of set operations are possible in this window. 
05:37  I will click on Close, to close the dialog box. 
05:42  You may explore further if desired. 
05:46  Notice that the fitted data is removed from the graph. 
05:51  We can also access the context menu from the set appearance window. 
05:57  Select the desired dataset from the Select set form. 
06:02  Right click to open the context menu and choose Kill data to remove the data. 
06:08  Click on Close, to close the dialog box. 
06:12  I will demonstrate to set up nonlinear regression process. 
06:19  For data fitting, select an equation to fit the data. 
06:24  Make an initial guess for the value of the coefficients. 
06:29  Run the data fitting algorithm. 
06:32  Convergence is usually obtained with few iterations. 
06:37  Examine the output parameters for goodness of the fit. 
06:42  Plot the function and the data together for visual representation. 
06:49  Go to Data, Transformations and select Nonlinear curve fitting. 
06:55  Under the Main tab, we will enter the desired equation. 
07:00  Select 2 for Parameters. 
07:04  Two parameters A0 and A1 appear in the form below. 
07:10  I will use an exponential decay curve as seen on the interface. 
07:16  Let’s type the equation as seen. 
07:20  There is also an option to input starting values and define bounds. 
07:26  Set Iterations to 20 using the black, up triangle button as seen on the screen. 
07:34  Set A0 and A1 initial guess. 
07:39  We can make an educated guess for starting values of A0 and A1 from the graph. 
07:47  From the graph, A0 could be around point four to point 5. 
07:53  Value of A1 is around 0.25. 
07:58  Set the initial guess values of the coefficients slightly away. 
08:04  Then, the iterative process in the regression algorithm can be observed. 
08:11  Input 0.4 for A0 and 0.2 for A1 as initial guess. 
08:21  You may apply bounds check box if necessary by clicking on the bounds buttons. 
08:28  In the Set section, select the set, G1 S0. 
08:34  Click on Apply to run the iterations.
The algorithm runs. 
08:41  In this window, fitting parameter Chisquare is seen. 
08:46  Correlation coefficient, RMS, relative error and Theil coefficient are also seen. 
08:54  Examine the chisquare values obtained. 
08:58  Low chisquare means, the resulting function is a good fit for the data. 
09:04  Residual is the difference between the observed and the fitted values. 
09:10  The sum of squares of residuals is minimized in the least square fitting method. 
09:17  You may note down the values or save the results. 
09:22  Click on File, Save option to save the results. 
09:27  A Grace:save logs form appear prompting to give a file name. 
09:34  In the form, type 'fittedvalues.txt' and click on Apply. 
09:41  Click on Close, to close the dialog box. 
09:45  Use File, close to close the Grace:console window. 
09:50  A curve generated from data fitting, is automatically loaded on the graph. 
09:57  The fitted curve traverse between the given data points. 
10:03  Click on close to close the nonlinear curve fitting window. 
10:08  Click on File, save to save the project. 
10:12  From top menu, choose File, exit to exit Grace. 
10:19  Now, let’s summarize.
In this tutorial, we Added multiple graph panels in the canvas 
10:29  Learned to delete data sets from a graph panel 
10:34  Performed nonlinear regression on an exponential decay curve. 
10:41  For assignment, please do the following. 
10:45  Fit the data given in the file assignment1.txt to a parabola. 
10:51  Use an equation of the type, as seen here. 
10:56  Fit the given data in the file assignment2.txt, to atan(x). 
11:03  Your complete assignment look similar to this. 
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11:39  This is Rani, from IIT Bombay. Thank you for joining. 