- Select the user mode.
- Select types of interest.
- Pick a model.
- Select the search target parameter .
- Establish the bracket of the search for a solution.
- Use the calculator to modify a parameter.
- Change measuring unit.
- Indicate the uncertainty of the values.
- Use a reference table to modify a field value.
- Modify parameters of the problem solving process.
- Start the search.
- Set the number of significant digits used and initialization modes.
- Validate the results obtained using a diagram.
- Input the report’s contextual data.
- Generate a solution report.
- Unlock fields.
Presently the application can be used in expert mode or not. The user modes have been introduced to remove fields and functions in order to simplify the user interface. Here are all fields and functions which are not displayed when expert mode is disabled :
- Field for minimum value.
- Field for maximum value
- Field for error value.
- Button to access parameters associated to the solving process.
Please notice that even if the application is not in expert user mode, search limits available in this mode are still effective (see software limitations).
Here you can select which types you want to be displayed.
The user can access to a certain number of models/equations; the user cannot import his own models/equations into the application.
The illustration below shows how the selection of a model is done according to the items selected in the three tables which allow the user to choose, in order :
- The type of model.
- A certain model or a group comprised of variants of given model.
- The variant of a given model if there are variants to the model.
Click on the arrow that appears below the symbol for the parameter to make that parameter the new search target.
- The user selection is confirmed when the arrow below the chosen parameter is animated.
- The user will then be able to input the search limits in the two new fields that have appeared on the screen .
The selection of a new target parameter adds two new fields in which the user can input the limits of the search.
- The application can only find solutions that fall within the established search limits.
The calculator appears on the screen after the user clicks on one of the model’s parameter fields.
The figure below presents an overview of the steps to use the calculator:
- The calculator appears on the screen when the user clicks on a fields.
- The user can modify the value shown in the right portion of the calculator’s display by using the calculator’s keypad (operant field).
- The calculator’s display is shown in blue (at the top).
- The “C” key (Clear) resets the fields associated with the calculator’s display fields.
- The “Copy” key allows the user reuse a value, either within EzFormulaPro or another application installed on the device.
- Just click outside the calculator to hide it without modifying the value in the field used to display the calculator.
Note: EzFormulaPro replaces the scientific notation used with a decimal notation to avoid the use of “E0”.
- To accept the modification, click on the checkmark button.
- To cancel the action, click on the hand button.
Specify, if applicable, the uncertainty for each of the model’s parameters in order to estimate the error of the solution (not to be confused with the tolerance defined for the problem solving process).
- The values entered in the various parameters’ uncertainty fields do not affect the problem solving process.
- The absolute value of the each uncertainty is used to calculate the solution’s uncertainty.
- The error’s sign is not taken into account.
- The measurement unit of an uncertainty value is the same as the one established for the associated parameter.
A parameter’s table of reference allows for initialization with different values widely accepted in the littérature.
Number of iterations:
It refers to the number of tries the problem solving process will run before the error on the solution falls below the established tolerance. Default value is 50.
It is the maximum acceptable deviation on the function before the problem solving process comes to a stop. Default value is 1E-4.
It refers to the interval used to calculate a parameter’s derivative at a given point (all other parameters are considered constant). Default value is 1E-3.
The coefficient applied to the correction calculated by the problem solving method. Default value is 0.5.
The scientific notation makes it easier to enter the solver’s parameters. The figure below illustrates the interface used by EzFormulaPro to configure its solver.
- The shaded field contains the effective value of the parameter.
- Field 2 is for adjusting the mantissa, which is the part multiplied by 10 power the value defined by the number displayed in field 3.
- Field 3 is to specify the value of the exponent of 10.
- Field 4 is to specify the prefix (+ or -) of the exponent of 10.
- The 5th item is a controller that allows the user to modulate the effective value displayed in the shaded field (1), going from zero to the nominal value originating from fields 2, 3 and 4.
The search process can be initiated by clicking on the “Solve/resolve” button. Window 1 will appear on the screen when a solution is found. Otherwise, Window 2 is shown.
- To be valid, the solution found has to fall within the established search limits.
- When no solution is found, one of the following explanatory messages is displayed:
- The maximum number of iterations has been reached.
- The solution is outside of the established limits
- The upper limit can not be the same as the lower limit.
- An error has occurred during the search process.
- When the problem solving process fails to provide a solution, the user can adjust the limits or parameters established for the process.
- EzFormulaPro will show the last value found in the parameter field. If it correspond to one of the set limits, it is recommended to increase that limit in order to find a solution.
- The hybrid method used, which combines the Newton-Raphson method and the bisectionmethod , is sensitive to local minima. It is possible for a solution within the limits established to generate a message saying otherwise. This situation is likely for the functions with peaks and valleys like the response to an increment (step) of an underdamped second order model (see formula in the control section). In that case, adjusting the limits as described above can lead to the discovery of a solution.
- When a solution is found, all values used in the search are automatically locked in order to avoid corrupting the integrity of the data belonging to the solution.
- The number of significant digits displayed can be modified as illustrated in the figure below.
- The number of significant digits used in the model’s diagram is constant, and therefore is not affected by this configuration.
- Automatic transfer to the calculator of the selected value (recommended for users working with a model for which values have already been entered).
- Calculator initialized to zero (recommended when starting fresh with a model).
For each formula, the user can view a diagram of the model to get an overall picture of the values.
- This is particularly useful for quickly validating a group of values associated with a solution or when the application has failed to provide a solution.
- It is important to note that the diagrams are static and only the numerical values are updated.
- When the diagram is a curve, it is presented with a satisfactory degree of accuracy as to allow the data to be used to adjust the parameters.
With EzFormulaPro, the user can generate report that can be sent via email. In order to facilitate report creation, EzFormulaPro uses the contextual data entered in the preference window.
- This information can be found under “Project information”. Click on the button in the banner to display this information.
When ready, the user can generate an email report by clicking on the “report” button. This button is only displayed when a solution has been found. An email report containing the following information is then created:
It largely includes the data defined in the preference section that can be used to define the context of the calculation.
The use can enter additional comments.
This section presents the formula used and the parameter for which a solution was found.
This section presents the value of the parameters used by the problem solving process.
Schéma du modèle:
Diagram of the model: This section contains an image of the diagram window. It allows the user to keep a copy of the model that cannot be easily modified with an text editing program.
The locked fields, with blue or green background, can be unlocked by clicking on the blue and green button marked “unlock”. Activating this button places EzFormulaPro in a position to start an other investigation.
- When the fields are unlocked, the “report” button replaces the “unlock” button.