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Revive package#3

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ErikQQY wants to merge 1 commit intoHPMolSim:mainfrom
ErikQQY:qqy/revive
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Revive package#3
ErikQQY wants to merge 1 commit intoHPMolSim:mainfrom
ErikQQY:qqy/revive

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@ErikQQY ErikQQY commented Sep 16, 2025

This PR does several things:

  1. Add a weighted_balanced_truncation::Bool keyword argument for choosing the weighted balanced truncation method in model reduction.
  2. Revert to the previous usage of the main function VPMR_cal. (It's really weird to only keep the N here since the de la Vallée-Poussin approximation does need $n_c$ and $n$ here).
  3. Other maintenance chores.

The newly added weighted balanced truncation method for model reduction in the current implementation is the same as the VPMR implementation. The advantage may be only obvious when using some other weight function(the Gramians with using Heaviside weight function is the same with solving continuous Lyapunov equation), but to take that advantage we may need to compute the weighted integral $I_w(x,y)=\int_{-\infty}^{+\infty}e^{-(x+y)t}w(t)w^*(t)dt$, which is heavily dependent on the choice of weight function. So we might provide a way to specify the weight function and compute the integral to obtain the Gramians.

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