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# Restructure sys-mor tutorial#1141

Merged
merged 10 commits into from Nov 30, 2020
Merged

# Restructure sys-mor tutorial #1141

merged 10 commits into from Nov 30, 2020

## Conversation

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### pmli commented Oct 29, 2020

This is still a work in progress. The idea is to add an LTI tutorial and for the existing BT tutorial to reuse the model from there. An IRKA tutorial could be added in a new PR

added the pr:change Change in existing functionality label Oct 29, 2020
added this to the 2020.2 milestone Oct 29, 2020
 [docs] split BT tutorial in two 
 cb714d7 
 [docs] edit LTI tutorial 
 8558796 
 [docs] edit BT tutorial 
 c992cda 
 [models.iosys] fix note in eval_tf and eval_dtf 
 fc44bdc 
 [reductors.interpolation] remove wide accents 
 b043f91 
reviewed

### sdrave left a comment

Very nice!

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 .. jupyter-execute:: fom.gramian('c_lrcf')

### sdrave Nov 27, 2020

This seems a bit cryptic here. Maybe you can add a sentence about the argument and what other values are possible.

 + C^{\operatorname{T}} C & = 0. \end{align*}

### sdrave Nov 27, 2020

Maybe one sentence (and perhaps a reference), for what these Gramians are useful.

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 [docs] apply suggestions from code review for LTI and BT tutorial 
 a2d6162 
Co-authored-by: Stephan Rave <stephanrave@uni-muenster.de>
reviewed

### lbalicki left a comment

Agreed, very nice new structure!

 invertible matrix. In particular, there exist invertible transformation matrices :math:T, S \in \mathbb{R}^{n \times n} such that the realization with :math:\tilde{E} = S^{\operatorname{T}} E T = I,

### lbalicki Nov 28, 2020

This only holds if E is invertible right? Maybe it should be mentioned that we consider an LTI system with invertible E matrix at the beginning of the paragraph.

 :math:\hat{B} = W^{\operatorname{T}} B, :math:\hat{C} = C V. It is known that the reduced-order model is asymptotically stable if

### lbalicki Nov 28, 2020

I think it should also be mentioned that we assume the full order model to be asymptotically stable. Maybe we should do this when the LTI system is introduced in this tutorial.

 \sup_{u \neq 0} \frac{\lVert y \rVert_{\mathcal{L}_\infty}}{\lVert u \rVert_{\mathcal{L}_2}}. The computation of the :math:\mathcal{H}_2 is based on the system Gramians

### lbalicki Nov 28, 2020

:math:\mathcal{H}_2 norm

 [docs] add reference in LTI tutorial 
 59cd546 
 [docs] extend Gramians section in LTI tutorial 
 07b9bc7 
 [docs] fix typo in LTI tutorial 
 902f65b 
 [docs] mention assumptions in BT tutorial 
 91a5c3f 

### pmli commented Nov 29, 2020

requested review from sdrave and lbalicki November 29, 2020 21:39
approved these changes
approved these changes
merged commit 39b872b into master Nov 30, 2020
2 checks passed
deleted the sys-mor-tutorials branch November 30, 2020 09:04