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/* Running an HDMR Sweep */
[[Image:Variable30.png|thumb|400px|Choosing HDMR sweep as the simulation mode in the Simulation Run dialog.]]
== An Overview of HDMR Method ==
In the HDMR method, you run successive evaluations of a given function of one or more [[variables]] for a number of [[variables]] samples. Then you create an optimal monomial surface representation of the computed data as a function of those [[variables]]. The resulting simplified function is characterized by a finite number of monomial coefficients. Therefore, its computation is more faster and computationally efficient than the original functions.
==Defining the HDMR Variables ==
To define the HDMR [[variables]], follow the procedure below:
* Open the Simulation '''Run Dialog''' of most of [[EM.Cube]]'s computational modules and select the '''HDMR''' option from the '''Simulation Mode''' dropdown list. * By clicking Click the '''Settings''' button, you can next to the simulation mode dropdown list to open up the HDMR Settings Dialog. * On the left side of the "[[Variables]]" section of the dialog you see the "'Independent [[Variables]] Table", which lists all the available independent [[variables]] of your project. Select an independent variable from the table and use the Right Arrow (-->) button of the dialog to move it to the "HDMR [[Variables]] Table". * Before moving the variable to the new location, the "Define [[Optimization]] Variable Dialog" opens up, where you have to define the start and stop values of the variable (ignore the precision). * Once you finish the definition of an HDMR variable, its name and attributes are added to the HDMR [[Variables]] List.
Note that you can change your mind and remove an HDMR variable from the list. To do so, select its name or row from the list and use the {{key|Left Arrow (<--)}} button to move it back to the Independent Variables Table. You can also change the attribute values of an HDMR variable after it has been defined. Select the variable from the list and click the {{key|Edit}} button of the dialog.
==Defining the HDMR Models ==
To define an HDMR model, follow the procedure below:
<table>
<tr>
<td> [[Image:Variable31.png|thumb|300px|Defining an objective HDMR model involving S Z parameters.]] </td><td> [[Image:Variable32.png|thumb|300px|Defining an objective involving antenna directivity.]] </td><td> [[Image:Variable34.png|thumb|300px|Defining an objective involving antenna directivity.]] </td>
</tr>
</table>
[[Image:Variable34.png|thumb|550px|EM.Cube's Model dialog showing a the HDMR model "Resistance.HDM" generated by EM.Tempo's FDTD simulation engine.]]
== Running an HDMR Sweep ==
After you define all of your HDMR [[variables]] and model(s), close the HDMR Settings dialog to return to the simulation Run dialog. When you click the {{key|Run}} button of the Simulation Run dialog to start the HDMR sweep process, an Output Window pops up that reports the various stages of the sweep loop and displays the progress or percentage of completion. After the sweep process is finished, an HDMR file with a '''.HDM''' file extension is added to your project's folder, which contains all the monomial coefficients of your HDMR model. You can see your new HDMR model [[EM.Cube]]'s Models Dialog, which you can open by clicking the '''Models''' button [[File:Models_icon.png]] of the Simulate Toolbar or selecting '''Menu > Simulate > Models...''' or using the keyboard shortcut {{key|Ctrl+L}}.
Note that once you generate an HDMR model, you can use it everywhere in [[EM.Cube]] just like any standard or library function or like a functional, tabular or Python model. In the above example, the syntax of your new custom function is Resistance(L) or Resistance(x). As you can see from the figure on the right, the current value of "Resistance" is about 115.2Ω because the argument of your HDMR function, i.e. "L", has a current value of 150mm, which can be verified in the [[Variables]] dialog.
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[[Image:Back_icon.png|40px]] '''[[Parametric_Modeling,_Sweep_%26_Optimization | Back to Parametric Modeling, Sweep & Optimization]]'''
