From Script | Spoken-Tutorial
Revision as of 15:40, 30 August 2022 by PoojaMoolya (Talk | contribs)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search
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 non-linear 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 pre-requisite 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 drop-down 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 sub-menu opens with many options for data fitting.
03:32 Choose Regression from the sub-menu.
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 drop-down has few choices with sample functions to do data fitting.
04:08 In the Load drop-down, 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 non-linear 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 non-linear 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 Non-linear 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 Chi-square is seen.
08:46 Correlation coefficient, RMS, relative error and Theil coefficient are also seen.
08:54 Examine the chi-square values obtained.
08:58 Low chi-square 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 'fitted-values.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 non-linear 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 non-linear 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.
11:09 This video summarises the Spoken Tutorial Project.

Please download and watch it.

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

For more details, please write to us.

11:28 Please post your timed queries in this forum.
11:32 Spoken Tutorial Project is funded by MHRD, Government of India.

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

Contributors and Content Editors