Assignment #6 - Using a Scientific Plotting Package - PSI-Plot

Set March 18 - due April 1

The purpose of this exercise is to show you how easy it is to create graphs with a modern plotting package; also to show you some of the power of doing mathematics using some of the many built-in functions and options that are available. Such packages are usually better than spreadsheets for doing detailed plots. Note that PSI-Plot is a relatively lightweight program; there are many much more sophisticated packages available (e.g. Sigma Plot, Origin ..).

[LC] = left click, [RC] = right click

1. XY Plot with Error Bars.

You will import a file and plot it. The file contains measured values of absolute gravity (with errors) and relative gravity (both in units of microgal) at specified times (in days) over roughly a two year period at a geodetic observatory.

• Start PSI-Plot; a basic opening screen appears
• Select File/New/Sheet; a more elaborate screen appears in spreadsheet format
• Select File/Import Data/; change to your home directory and select ex3t.txt; select Open and New Sheet
• The table will import immediately; change column titles to Time (in days), Absg, Error, and Relg and save the table as the sheet file ex6a.pdw
• Select Plot/2D Curve/Error Bar; the 2D XY-Line Plot dialog box will open; make sure Time is the x axis, Absg the y axis and the errors are taken from the column 'Error'; click OK to open the plot in its own window and then save it as ex6a.pgw
• [RC] on the line plot (between symbols) and a Normal Curve Format dialog box appears; select the following options: Style - filled diamond, Symbol size - 75, Line size - 10, Line Connected, Line Type - dashed, Pattern - choose some fill pattern; also choose colors for the symbol and fill, choose OK
• [RC] on graph background (inside the graph area) to bring up the Frame Format dialog box; select a two-color background fill style that you think is appropriate to the plot [Hint: use light colors], click OK
• Make sure axes are properly labelled (with units), add a title and print ONE FINAL COPY to LJ3 (the color printer in Room 331); close the plot file and save as ex6a.pgw (do not close PSI-Plot yet).

2. Using Mathematical Features of PSI-PLOT

Save the file ex6b.dat in your home directory; it contains a plot of relative gravity (in microgal) versus time (in day). You will fit mathematical functions to this data.

• Start a new PSI-Plot sheet and import ex6b.dat; save as ex6b.pdw
• Change the column headings to Time and Relg
• Select Math/Fitting/Line; the Straight Line dialog box opens; select Calculated Data, Best Fit Parameters, [LC] OK.
• The Line Fitting Report Opens; make a note of the most important parameters of the fit.
  
• Q1: What are the most important parameters of the fit?
  Q2: What is the equation of the best fit straight line?
  
• [LC] OK and the Report windows closes and the sheet is updated
• You should now identify the new columns created on the sheet (Ind3, Dep4)
  
  Q3: What are they?

• Now delete the column representing the independent parameters and change the number notation of the two remaining columns to match that of the input data.

3. User defined fit

Now you will do a non-linear fit using a user-defined exponential; as you go along, note the differences from the linear fit.

• Select Math/Fitting/User Define; the User Defined Fitting dialog box appears. Now you will edit in this window, but make sure YOU DO NOT OVERWRITE OR ALTER THE TEXT IN BRACKETS e.g. (INDVAR). You should edit the various options to fit the following formula:

Relg = A*EXP (-B*Time)+C

        Q4: Write down the equation for this formula. 

• Note that the parameters to be fitted are A, B and C and the independent and dependent variable names must match those in the sheet. Try as starting values A=-30, B=0.001 and C=20. When you are ready, click on Compile to make sure your formula is valid and click OK when successful
• Now click Solve to start the iterations. These could take some time, so be patient (!) and watch the number of iterations and the Sum of Squares change in the Fitting Progress dialog box. When the fitting has converged
  
  Q5: How many iterations? what is the final sum of squares?

• Make sure you click on Best Fit Parameters before viewing the Fitting Report. You should save the report in a file before you close it
  
  Q6: Is the fit obtained using an exponential better than a straight line? How do you know this?

• The data sheet should now show 3 more columns; repeat the steps in above to get rid of the unwanted column
• Finally plot the original data (Relg) and the two fitted functions (i.e. the straight line and the exponential) using the Plot/2D Curve/XY Lines options
• Choose suitable columns to plot 

        Q7: What are the suitable columns to plot?

• After you have chosen each selection, [LC] on Add Curve and then go on to the next data. As you proceed, make sure the symbol sizes are set to zero and the line size is small, otherwise big symbols will be plotted for all the large number of points! When finished, choose OK to view the plot
• When your first attempt appears, you can right click on the line to bring up the Normal Curve Format dialog box to choose line types and colors to distinguish the 3 lines
• Select the plot ([LC]) and choose Option/Add Legend to add a legend; use options Clean BKGrid and With Frame. Move the legend to where you want it (e.g. the bottom right hand corner). The you can edit the elements of the legend (i.e. the text and the line types to match those in the plot) after using Option/Ungroup. Note that once the elements are ungrouped for editing, the legend as a whole cannot be moved without re-grouping!
• When you are happy with the result, save the plot as ex6b.pgw print ONE FINAL COPY to the color printer.

Read the discussion of your first document (Assignment #2) particularly with respect to Figure 7.

Q8: Discuss the significance of the fitted lines

Submit your answers to the 8 questions and attach your color graphs ex6a.pgw and ex6b.pgw.

End of Assignment 6.