The MORpH toolbox enables three different strategies to reduce large-scale pH models in a structure-preserving way.
The algorithms in the folder pH-MOR directly enforce the pH structure on the reduced-order model (ROM). The algorithms in this category follow this syntax:
ph_rom = <pHMOR_function>(ph_fom, redOrder, Opts);
This creates a reduced pH model ph_rom (represented as a phsRed object) with dimension redOrder for the full-order pH model ph_fom. The Opts struct can be used to configure the algorithm's parameters.
Since every pH model is inherently passive, one may also apply passivity-preserving MOR methods to pH models. Algorithms for this purpose are in the folder pa-MOR. To use them, we first convert the phs object to a sparse sss object (the class sss is defined in the sss toolbox):
pa_fom = phs2sss(ph_fom);
Then we can use any function in the pa-MOR folder to reduce the passive pa_fom as follows:
pa_rom = <paMOR_function>(sss_fom, redOrder, Opts);
This creates a reduced, passive model pa_rom (represented as a ss object) with dimension redOrder. Note that the pH form is generally lost in this process. However, since the reduced passive model pa_rom can be assumed to be minimal, it may be transformed back to pH form via
ph_rom = ss2phs(pa_rom);
The function ss2phs solves the Kalman-Yakubovich-Popov (KYP) inequality for this transformation.
One can also use traditional, unstructured MOR methods to reduce pH models. The MORpH toolbox includes the sssMOR toolbox for this purpose. With sssMOR, you can reduce pH systems in the following way:
fom = phs2sss(ph_fom);
rom = <sssMOR_function>(fom, redOrder, Opts)
Note that the created ROM rom is generally neither passive nor in pH form - its structure is destroyed! However, we can restore passivity of rom by applying passivity enforcement techniques which are located in the folder pa-ENF. They are called as follows:
pa_rom = <paENF_function>(rom, Opts);
Since the ROM pa_rom is passive, we can again transform it back to pH form via
ph_rom = ss2phs(pa_rom);