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Step-by-Step Instructions for using ipf

1. Make sure the latest version of ipf.m is in the Matlab path. Use the Matlab load or File > Import data command to get your data into the Matlab workspace as single vector, a pair of vectors (x and y), or a matrix with the independent variable (x) in the first column and the dependent variable (y) in the second column (e.g. "mydata").

2. Type ipf(y); or ipf(x,y); or ipf(mydata); 

3. Matlab displays the data in the Figure window, with the entire signal in the lower panel and a zoomed-in section in the top panel. (In the figure below, the data are from the demo script Demoipf.m
. To use those data, download Demoipf.m, place it in the Matlab path, and type "Demoipf" at the command prompt; the "true" values of the peaks without noise are printed out in the command window for comparison to your results). Note: Make sure you don't click on the “Show Plot Tools” button in the toolbar above the figure; that will disable normal program functioning. If you do; close the Figure window and start again.

4. Use the left and right cursor keys to pan back and forth across the signal...

To pan faster, use the < and > keys. To pan by one point, use the [ and ] keys.
 
Use
the up and down cursor keys to zoom in and out.

To zoom faster, use the / and ' keys.

5. To fit a peak, isolate and center that peak in the upper window, ....


6. ... select the number of peaks by pressing a number key between 1 and 9 (1 in this case), select the peak shape (G = Gaussian in this case), and press F (for Fit).

The best-fit line is shown in red in the upper panel, superimposed on the data points, along with the peak position, height, and width of the best fit model. The bottom panel displays the residuals (difference between the best-fit line and the data). The current number of peaks, the shape, and the percent fitting error are shown at the bottom of the window. Press the R key to print out the table of results in the command window.

7. Press the F key again to compute another fit with slightly different starting first guesses. This will show how stable the fit is with respect to variations in starting points (first guesses). Press R to print a report of the best-fit peak parameters in the command window.

The percent fitting error are refreshed at the bottom of the window.

In ipf.m version 13 (November 2017), there are 24 different peaks shapes are available by keystroke (e.g. L=Lorentzian, U=exponential pulse, S=sigmoid (logistic function), etc). Press K to see a list of all commands.

You can also select the shape by number from an even larger menu of 49 shapes by pressing the - (minus) key and selecting the shape by number.

8. Here's another example using the same signal: to fit the group of three overlapping peaks near x=800, press the 3 key, use the pan and zoom to isolate that group and try to line up the peaks with the magenta dotted vertical line markers, then press F.


Each time you press F the fit is repeated with slightly different starting first guesses. Keep your eye on the fitting error and stop when the error is low. The green lines in the upper panel show the individual model components; the red line is the sum of those components. 

9. If the fit seems unstable, press the X key to perform 10 silent fits and display the one with the lowest fitting error. Press R to print a report of the best-fit peak parameters in the command window.


Percent Fitting Error 1.6439%   Elapsed time = 1.3387 sec.
       Peak#    Position     Height      Width       Area
          1      800.15     3.0067      29.995      96.001
          2      849.71     1.9867      39.633      83.814
          3      899.4      1.0122      51.476      55.462

10. If the peaks don't line up under the magenta dotted vertical lines, you can manually specify the first-guess peak positions: press C, then click on your estimates of the peak positions in the upper graph, once for each peak. A fit is automatically performed after the last click. Peaks are numbered in the order clicked.


11. In the figure below, using data from the demo script Demoipf2.m, the peaks are superimposed on a gradual curving baseline. To correct for the baseline, use the T key to cycle between the four baseline correction ("autozero") modes: None, Linear, Quadratic, and Flat. Pan and zoom each group of peaks so that the signal returns to the local baseline at the edges of the selected region in the upper panel, then press F. In the sequence shown below, a pair of peaks near x=600 is selected and fit, first without baseline subtraction, then with linear, and then quadratic, baseline correction. The latter two modes work best in this case.

The current baseline correction mode is displayed at the top of the window. 

12. Alternatively, you may use multipoint background correction to subtract a linearly-interpolated baseline for the entire signal: press the Backspace key, type in the desired number of background points (14 in the example below) and press the Enter key, then click where you estimate the baseline to be in the lower panel, starting at the left of the lowest x-value and ending to the right of the highest x-value. (For greatest precision, you can maximize the figure window before this operation). After the last click, the baseline is subtracted; then you can continue with curve fitting. (If you mess up, press the \ key to restore the original background and start over). When you are done, you can measure the peaks without baseline subtraction.

The y-axis label of the bottom panel changes accordingly.

13. Some peak shapes have an extra variable parameter that modifies the shape: the Voigt profile, Pearson, exponentially-broadened Gaussian (ExpGaussian), exponentially-broadened Lorentzian (ExpLorentzian), bifurcated Gaussian, bifurcated Lorentzian, or Gaussian/Lorentzian blend. For those shapes, you control that extra variable parameter with the A and Z keys and adjust it to minimize the fitting error. The current value is displayed at the bottom of the window. In this example, the single peak near x=2800 in the file "DataMatrix3" is fit, first with a Gaussian and then with an exponentially broadened Gaussian (E key), adjusting the extra parameter (the time constant) to minimize the fitting error.

>> load DataMatrix3
>> ipf(DataMatrix3)



14. Press Q to print out a report in the command window.

Peak Shape = Exponentially-broadened Gaussian
No baseline correction
Number of peaks = 2
Time Constant = 33.1919
Fitted x range = 1663.5 - 2050.5 (dx=387)  (Center=1857) 
Percent Fitting Error = 0.090216%
      Peak#   Position       Height       Width         Area
        1       1800.4       1.8632      60.057       119.11
        2       1900.6       0.48346     59.62         30.67


15. To test the stability of your fit with respect to random noise, press the N key a few times. That will perform fits on subsets of data points (called "bootstrap samples").

If the N key gives reasonable-looking fits with peak parameters that vary somewhat from trial to trial, then you can determine the variability of the peak position, height, width, and area by pressing the V key, which will calculate the standard deviation of all the peak parameters of all the peaks in 100 such bootstrap sub-samples (this may take a minute or so). You will be asked for the number of trials per bootstrap sample; start with 1 and increase it if the fit is not stable. If the N key gives wildly different fits, with highly variable fitting errors and peak parameters, then the fit is not stable, and you should try to increase the number of trials when asked (but of course that will increase the time it takes to complete). 

Number of fit trials per bootstrap sample (0 to cancel): 1

Peak #1      Position       Height       Width       Area
Mean:        1200.004      1.9967714   100.31494    213.20131
STD:         0.1832        0.0059565     0.37247    0.7652
STD (IQR):   0.18681       0.0060577     0.37384    0.7563
%RSD:        0.015266      0.29831       0.3713     0.35891
%RSD(IQR):  0.015067      0.2985        0.37216    0.35992
Elapsed time is 3.060255 seconds.

..and so on for Peak #2 and the other peaks if a multi-peak fit.

If the RSD and the RSD (IQR) are roughly the same (as in the example above), then the distribution of bootstrap fitting results is close to normal and the fit is stable. If the RSD is substantially greater than RSD (IQR), then the RSD is biased high by "outliers" (obliviously erroneous fits that fall far from the norm), and in that case you should use the RSD (IQR) rather than the RSD, because the IQR is much less influenced by outliers. Alternatively, you could use another model or a different data set to see if that gives more stable fits.

Difference between in the F, X, N, and V keys:

16. Press K to display the complete set of keystroke commands. Click here for more details.


This page is part of "A Pragmatic Introduction to Signal Processing", created and maintained by Prof. Tom O'Haver , Department of Chemistry and Biochemistry, The University of Maryland at College Park. Comments, suggestions and questions should be directed to Prof. O'Haver at toh@umd.edu.

Last updated, November, 2017

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