The Data Pane

To load the measurement data into ParX choose File > Open Data… (⌥⌘O) to show the Open File Dialog. Select the desired .json, .csv or .tsv file and choose to open the file.

Alternatively, in the Finder, drag and drop a model file directly on the data pane.

Given a model with interface variables you wish to compare with measured data, the measured data points must be matched to the model interface. For each model variable on the left, a data variable must be selected on the right. When there are matching names in de data file these will be pre-selected automatically.

When the data is loaded, its properties are displayed in the data pane.

The interface variables are shown with their range and number of steps (or number of distinct values). The total number of data points is also shown.

When the data is loaded it is drawn in the same graph as the model. The axis are automatically adjusted to encompass all data points.

The data point markers match the color of the associated model curve and y-axis title.

Error Bars

We also need a measure for the accuracy of the match between the model and the data. Therefore each data point can specify the accuracy of the measurement, or the required accuracy of the model. The clearest representation of this is the error bar.

All data points get error bars; these can be supplied in the data file for all coordinates.

Together they define not a data “point” but a data “ellipsoid” centered at the data point (drawn as a rectangle on the graph).

You will have noticed that in ParX there is no predetermined distinction between independent and dependent variables. There can be, but there doesn’t have to be. An interface variable can be made independent by assigning it a zero error, either in the data file or through the data pane by its fixed button.

When extracting the model from the data points, the distance between the model curve and a data point is determined with the error ellipsoid as the unit of measure. The distance is one when the curve touches the ellipsoid.

What is displayed in the Objective field is the average distance for all data points.

Especially when the model in strongly nonlinear, this principal of determining the shortest distance to the model curve is very beneficial in balancing the influences of data points in the flat and steep regions of the curve, as illustrated here:

The “weight” of the contributions of the data points in the result is equalized.

Tolerance Settings

The measurement accuracy is normally provided per data point in de data file. In case this information is not available, or one wishes to account for additional modelling errors, the accuracy can be set in de data pane. A global relative tolerance that applies to all variables can be specified in the "Tolerance" field. Next, each variable has its own fields for specifying a relative and an absolute tolerance. When all four tolerances are specified simultaneously, the largest is chosen.

By setting a variable to fixed, the tolerance on that variable for all data points is set to zero. This has the effect of excluding the variable from the distance calculation.

Save the Settings

The variable selections and tolerance settings can be saved to file for later re-use.

Choose File > Save Data…(⌥⌘S) and supply a file name in the Save dialogue. The file is saved with the .prxd extension.

The settings can be recreated by choosing File > Open Data… (⌥⌘O) and opening the file containing them.

Dragging and dropping a .prxd file on the data pane will also load the settings.

Re-exporting the Measurement Data

The measurement data can be re-exported to a .json file, a .csv file, or a .tsv file. The .tsv file is UTF16 encoded for better compatibility with Excel.

Choose File > Export Data To, and select a file location in the file Export dialog.

This functionality is provided mainly for the purposes of data format conversion.

The re-exported measurement data points will either retain their original error intervals, or take their intervals from the specified tolerances in the data pane. Fix the variable when no error interval is required.