Live CEOing Ep 752: Language Design Review of System Modeling and Control Systems Features for 14.0

All right, here we are with another version 14 design review. This one is about control and control theory and system modeling. All right. Every time we do one of these, every learn a tiny bit more about this topic area, which is not one that I've ever really practiced. Okay.

So the first functionality is something that we plan to do more of. So if you have a model, how, you know, tolerant is that of uncertainty in some of the things that go in. Let's say it's an engineering model and you actually, it's a device you're going to build, then you're unlikely to be able to produce identical parts. There are tolerances involved and whatnot.

Yeah, yeah, yeah.

Okay, so how much did the whole system degrade or vary in its performance? Does it even stop working? I mean would you even write in an aircraft that hasn't been seriously validated for that? Yeah, and you could say the same if you. If what the model you do is just kind of like a prediction model, more science thing or business thing.

Show me an example of one of these plots.

When the thing is bad, go to system uncertainty plot.

Okay, which one do I press here? Is it the, the.

Do.

We have an error here? Somebody knocked up please. Self test error and axes box.

Yeah.

Okay, got it. Yep.

So what it describes is the kinds of systems it can take. How do you specify uncertainty? You can use a round. You can use distributions, intervals, regions. And you can even have sort of varying input, you know, like a random process.

These fonts should be smaller, certainly no bigger than the axes fonts. Does that make sense? Okay. Yeah, It's a little bit confusing that, that outer interval which is the bounding. Yeah, I don't even know whether going up to 100% makes sense. Do you have that parameterizable? Yes, you can choose Solar Quantiles. This is kind of nice functionality. It's an interesting idea. I mean I'm kind of wondering, you know, in like ND Solve, why don't we have a similar thing?

Yeah, so parametric and we can build something, a new function that does it. So parametric and diesel would be like a building block to achieve that with. Yeah, that's kind of why we built built it. But I think that there's a bunch of these end user functions that one can build with that. And what this does, it's not that you couldn't program it yourself. And so it does basically Monte Carlo simulation parallelizes that.

Yeah, I understand.

Does the processing on top of it, et cetera. It's not that you couldn't Build it. It's just tedious as hell.

Yeah. But I'm kind of wondering for this functionality, why isn't there a general Monte Carlo given a function as a function of T or whatever it is? Why isn't this just a general thing? Why is it specific to system modeling, the ability to make that type of plot like this type of plot? How would I make that type of plot is that. That's not a distribution plot, is it?

No, no, no.

What is it? So we should have something that makes this type of plot from data, right? It's kind of like a version of a histogram plot.

Yeah, I think that, that we should probably do that for plot and other things. That makes it easy if you specify. That, you know, the, the. The sort of arounds, you know, that depends on, on your variable and things like that.

I think both plot and list plot need to be able to make plots like this. Am I making sense?

Yeah. You mean list line plot.

Right.

So list plot already does intervals and stuff.

No, I, I understand that, but I'm saying, I'm saying this type of plot where you're showing the smooth, you know, not so smooth, you know, this, this sort of graduated color level thing. Yeah, I don't see why we wouldn't do that for, you know, given a list plot. Well, maybe list line plot, but I don't even know whether it's that function or whether it's a, you know. You know, more like a sort of un, you know, distribution or uncertainty or something variant of list list plot. Just like we have list step plot. This seems like another variant of that family where what's happening is it's kind of list histogram plot. Right. Where at every point, I mean, we had a design.

But the thing that's been put in now for a point uncertainty for points. If you want uncertainty for curves and surfaces, that's what this could be, for instance. Or maybe it is an outer variant.

Yeah, I mean, I think this is a generally useful kind of plot where you've got data and.

But you need a full distribution at every point.

Exactly, exactly.

But I mean, this is, you know.

A histogram is just one slice. And this is a, you know, histogram is a function of a parameter.

Yeah. And these are slice distributions, as we call them, for random processes.

Well, I thought we had a function like this for distribution. I mean, what, what is our distribution plot function?

Well, we have for finite, you know, this distribution chart. And there is box whisker chart or things to compare many.

Why is this. Okay. Arnode, you've got to trace why that documentation took forever to launch.

Yep.

With us. Right. So this is another version of how to do this, but only with discrete points. Whereas here we. We're. We're having a, you know, a distribution as a function of parameter.

Yeah.

And it seems like. It really seems like a generally useful thing that we should support. And we should also support it in a function that you plot. If that function has sort of uncertainty parameters. I don't know what happens if you say. What happens if I say plot around sin x, you know, 0.2 cos x.

I don't think it does anything at this point.

Nothing.

Yeah, we have prototypes for these. These things, but it's. We have to come back to uncertainty.

Why did they put that race. Lovely. Interesting choice that. It cut the things off here. Oh, no, no. Maybe they're zero. Yeah, sorry, there's zero there. Yeah, it's lovely. Okay, so in a sense, this is a continuum limit of this, right?

Yes, yes. I mean, this one shows we show quantiles there. This one shows standard deviation. Like around shows it's based on standard deviation, not on quantiles.

Yeah, yeah, right, I understand. I really think this is a useful kind of plot for both plot and list plot. Now, in terms of your very specific use here, I mean, God knows, I don't know, I'm not in this business. It looks nice.

Think that this packages up a lot of results in a killer app, which is to be able to look at it and see. Is that where you need to be or do you need to do further analysis?

Yes, but now if I want the results in a computable form, how do.

I get them in the future we will do more functions. This generates massive amounts of data. I think it's good to have things that can reduce the data. One of the things that you want to do is certain kinds of conditions that you want the system to always satisfy. For instance, can we validate that? Can we verify what's the probability that.

It will always do this?

Exactly, exactly.

So what's the range of. Of x values for which that will always be guaranteed?

Right, exactly. So that's for the future.

That's within some confidence interval, some quantile.

Yes. So the various ways of quantifying that. And so we'll. We'll do that, you know, but. But what it does is automate a lot of data analysis on this. Massive amounts of data.

Yeah, okay, that's great. So how long do these things take to run? I mean, if I Just do this.

Depends on the system. So it's going to do a lot of simulations, you know, of the same. That's probably a very simple system, so it's probably not too bad.

Be lovely if there was a little bit more indication of what's actually happening. Okay. Loading documentation examples. It's unclear why I would need to load documentation examples for this, but whatever. I mean, at least it's honest about what it's doing. Plotting progress. What do you mean it's plotting progress? It's not plotting progress. What the hell are you doing there? What are you talking about? Way to say it. Okay, who's. Who's making sure. How does this work? How do we get these things edited?

I can.

I can't fix the title. No, no, no, no, no, no. Who. I want to know the process by which we figure out. Okay, I don't. I have no idea why this plot is so tiny, but. But I guess I can make it bigger. And I assume you can switch off this legend, right? Yeah. So, okay, let's talk about progress monitoring in general. What. Who do we have from project management here, Eli? Okay, so I'd like to know, you know, all kinds of kernel developers are adding progress monitoring, which is good. Roger, maybe you have a comment on this? How are we centrally dealing with the wording for that progress monitoring?

I don't think we are, Steven. So I think it's a gap.

Okay, fine. All right, so where should that be done? What should the process be? I mean, at the very least, it has to go to dqa.

But I think. But now that I think about it, I don't think I've ever even seen the. The text for any progress monitor. But I, you know, and I should actually review that too, just as we do documentation.

Yep. So, okay, so look, let's get a process.

The DQA wouldn't. DQA wouldn't have caught what you caught.

No, no, it would not have caught that, but it will catch other things, which, you know, the last thing we want is a spelling mistake which could.

Happen there without dqa.

So, I mean, well, you're reviewing documentation, but whatever process reviews documentation. Where are these progress. I mean, are these things, you know, burnt into the code or are they in resources?

I think they're all burnt into code.

Okay, fine. Well then. Then we need our node. We need some way to extract these and tag whether they have been reviewed or not. I mean, for example, they certainly will be in pull requests right onode.

Yeah, I'm thinking. I think we need to. I need to check on this. But yeah, with Roger or ITAI or somebody that knows how this is implemented, these progress monitors, because I don't know if you can easily programmatically extract all of them. I don't think that's how that works.

Okay, well, so.

Or even like, you know, like, I'm not even sure it can be localized, for example. I don't think it's that organized. It's. I mean.

Okay, well then developer needs.

This is probably hard coded in the source code somewhere.

Yeah, I agree. Which is what needs to happen for a lot of these progress monitoring things. But we just need a process where people understand, just like, you know, we know we have to review what the plot looks like in the end. But the progress monitor is also something that is seen, so to speak, but.

Like the, you know, messages are in a separate resource file. And that's absolutely something that's going to easily be done by dqa. This is, this is sort of like, you know, it's not quite as nice.

Okay. Simulation progress is not really. What, what should it be saying? Running simulation running. No, I mean, what does this mean? Running 51 of. This is just totally muddled, right? Running 51. 51 of 200 simulation instances. It probably should say top things.

Should.

No, no, no, but, but you know, I need to see the actual list of these. Okay, we need to see the list of all of these things and then go through. So again, I don't know what we are consistently doing for this top level piece. Running simulation, I suspect is what we should be saying. All right, and here, you know, 151 or running simulations. Plural. Okay. And then at the bottom, you know, 151 of 200 simulation instances or something. I don't know. But it got to be, you know, it's got to be consistent with the, you know, and I don't even know about the capitalization of that thing at the top. Blah, blah, blah. I mean, we just need standards and we need to know how we're getting these reviewed. Fair. Yep. And Roger, Eli can. I don't know how we should centralize this because a bunch of different groups. I mean, I think many of the progress monitoring people are in the Roger Empire, but not all.

No, but I, I mean, now that you, you pointed that out, I'll certainly change how we do things, you know, and we'll, We'll. We'll extract them out so we can actually look at them as a cartoon.

Fine, fine, fine, fine. But we just need, we need a standard for what they're supposed to say we have, you know, Itai, I think, was the one who defined a bunch of them, and he probably knows what some of those standards are. So maybe he's a reasonable reviewer for these things. Or pick one or two reviewers who know the standards for these progress monitors, at least for the next, you know, couple of versions those people can review and then other people can learn how those things should be set up.

And then if Eli can take a note and send it to like T lcc then that's probably a good place to review that, that system.

T lcc? Yes, I think so.

It's as, as good a place as any place. And it's, it'll. It's the right group of people that can, you know, where that can be discussed.

Yeah, it is an LCC issue actually. So.

Yeah. Yeah. Okay. Well, looks nice, like a nice function, but for goodness sake, let's figure out how to move it out into the general plotting functions as well.

Yep. No, that, that was the intention and this might be a driver for that. So, okay, the next. Unless you have more things to go over.

No, I don't on that one.

No, the next one is. So when you have a discrete device like a computer interfacing with a continuous device, like physics.

I don't think physics is continuous, but not the scale you're talking about. It's continuous. Go ahead.

Exactly. I knew you would say that. But so the thing is that you want to simulate them together. You want to see how they behave together. So you need to be able to simulate mixed continuous time, discrete time systems. And this is what this adds. And specifically what you have is that the way you go from continuous time to discrete time is to sample. And the way you go from discrete time to continuous time is in some form of extrapolation. And they are usually called hold, zero, order, hold, first order, hold.

Those are unbelievably engineering terms, but that's.

Exactly what people recognize.

Wow. Okay, so, okay, so.

So if you're a hardcore engineer like Musk or someone like that, you know exactly what we're talking about.

Okay. The, the. If I took an interpolating function and I applied sampler model to it, would I get the step thing?

Yes, yes. If interpolation order zero.

No, no, I know that, but I'm just saying if I take an actual interpolation.

Yeah, but it's, it's.

By the way, by the way, this, this typing is dragging. Something is very, very wrong here. Our node typing is dragging in this version with what I'm doing. Am I making sense?

Yeah. I'm gonna save the notebook and I see if it's a notebook issue or if it's a.

No, it's. I don't think it is. I've been seeing this issue for a while.

But it's something. It's docu tools. It's. You know, one of those notes we have open. It's a dynamic that's off screen. I mean, there's like 20 different things it could be. So kind of the very least, I'm going to need that notebook to try to design reviews.

Okay. Okay. So if I now say Eli, make.

A note of that. So I.

Sorry. God, it's just crazy. This thing is just crazy. I think it's something to do with the autocompleter. I mean, there was this. There was this clue that the first two letters might be slow, but it's slow all the way through.

Yeah, it's the prototype, but it needs to be splattered. It's the prototype built, Steven. So there might be some.

So we can't release this. Okay. So that.

We're not releasing. We're not releasing.

This is not a function, Stephen. It's a model.

Oh, yeah.

You have to hook it up with that simulation function. Input output model. Simulate is the sec. Yeah. The second example.

Oh, boy, I hope people are using all this stuff. It's its own world.

It's a big world.

When did we introduce this?

The input output model simulation is new for this. This part of this design review.

I see. So.

But there need to be two model blocks that are the bridges between discrete and continuous time. And those. That's. That's what those two are.

Why is there a sample model open close.

Sorry, what?

Well, why does it say sample model open closed.

That's the default. Assumes that. It assumes parameters in that model. But then there are. You can specify. You can customize that model based on.

Well, it's assuming basically that that model is just saying X equals X, so to speak.

It's just giving them sample time. 1. That's a very slow sample time for most systems.

Okay, so how would I do something. God, I hate the way that this is. R equals. I hate that. But anyway, whatever. You guys always do that. Hate it. How do I specify a much shorter sampling time?

Yeah, you. You'll give an associ.

Okay.

Yeah. And then sampling period goes to whatever you want.

Okay, now that's different from what I would get if I said plot sin x x 02 PI interpolation order. Oh, God. This is Driving me crazy. This speed thing. Interpolation order zero. Oh, we don't have that for plot. No, no, thought we did.

Well, we do actually. But wait a minute. It's just for list plot. Yeah, it's for list plot.

For plot.

We don't.

For.

For. For this line plot. We do.

I see. Why don't we. For. Well, it doesn't make any sense for plot because it's really changing the function.

Right.

Okay. So that's pretty funky what it's doing here.

Yeah, yeah.

It doesn't look right. It looks like some kind of anti aliasing or aliasing phenomenon.

I think that that's. Where. What's the problem there Suba is that.

Yeah, I have to follow. That's what's coming from ND solven when event. Yeah, I'm not doing that. It's what is. Yeah, there's something I wanted. I wanted to. Yeah. Towards the end I will. I was going to bring it up with that team.

Do you think that's missing events which is.

Which is at least easy to answer? The reason that autocomplete is not sorted?

Yeah, I'm not sure what's. Yeah, yeah. I. I either to whether it's missing events or it's that the plot is missing it. This plot sampling is missing it.

Yeah.

Seems unlikely. Anyway, we can answer Sanders question on the live stream. The reason these things are not sorted is because it wouldn't be useful to sort them. They want to put the things that are most likely first in. Has a lot of very obscure things that it could be. It could be an inverse Jacobe function. Probably not what you want. I mean that's the whole art of autocomplete is how you sort it. Okay, so this is then returning.

Yeah. By. By default it returns the output response of that. Of that model.

I don't understand. How does plot work here? I mean this thing. What is this thing? If I want to find out the value of this at that point, what do I do? Can I take.

Yeah, you can substitute T. You can replace T with that.

But I mean here. Oh, I see. I see. Here I've got it to an interpolating function.

Yeah.

Right. So then all of the workflows that are available for that are now you plugged into those workflows.

Model simulate basically turns this into a univariate interpolating function. In this case.

Yeah. It can be vector valued but.

Yeah. Okay. Okay. So this is the. This is the way of going from a model. So I mean I could. Could I take some other Kind of model, like one of your.

Yeah, it accepts all those models.

Yeah.

Sorry, so you mean if I could take one of these. What are they called? The ones, the ones that you feed into Arduinos. What are those called?

Yeah, the state space model transfer function. Yeah, yeah, it accepts all of them.

Okay, so I could finally find out what a state space model.

Needs to be a numeric model, not symbols in it. Right.

So yeah, if Dissolve can handle it, then it can be symbols. But. Yeah, but generally not.

Okay, so now this I want to say here.

Why is it pink?

I don't have a clue. Now, how do I give variables here?

Yeah, you just. If you want, you want to give an input like sine T. Just like before the input is. Does one input. So just sign t and then T goes from zero to two. PI. Yeah.

Just percent. Not super exciting. Oh, there's no dynamics.

Yeah, there is no dynamics.

That first matrix there is zero. So there's no. Nothing happening in it particularly.

Okay, so what do I do? I added.

Make it a negative value. So it's.

Yeah, negative value. Otherwise it's unstable.

Okay, okay, so that's. Now is there an analytical. Might there be an analytical version of this?

Yeah, this one for sure.

Yeah, you can just give T. Oh, yeah. Instead of T going, you can. The range, you just give it T.

Wow. So. But that has nothing to do with simulate.

Well, solving and simulating is sort of the same, right?

Yeah, but it's not because this is an analytical result.

Right.

And I would never guess that a function which had the name simulate could give an analytical result. This is kind of nice. I mean, this kind of turns this. I mean, we haven't had this level of simplicity in getting output from control system stuff before, have we?

There has been state response and output response. You could get that result in this case. The, the, the case that you give there, we could do before.

But how does. What does state response take as input?

The state space model.

The same thing. So if you. Yeah, so yeah, the.

Okay, and then what?

Just give the same arguments sine tt.

Okay. Yeah.

And yeah, the re. The reason. Yeah. Because the state response and output response does not give all the internal signals when we have like interconnected models. That's why we, we now have this new design with the simulate and the data function.

So when you put, when you wire systems together, you don't want to flatten it and get rid of it. So you often want to put like little probes, like an oscilloscope somewhere, you know, like measure what does this. What's the signal on this wire and that wire? So for instance, when you wire up a control system to a plant, which means a physical model, then you kind of want to know what's the control effort? How much energy am I pumping into the system? Can I even do it?

Okay, so if I take a thing like this, I don't even know how many sort of input wires the thing has.

Yeah, this also has one.

How do you know that?

Well, dimensionality of the matrices.

Yeah. Okay. I just don't know which dimension.

Right, right.

I mean, it's very similar to what's happening with tensors in, in machine learning pipelines, is it not? I mean, this thing is. Can you not put these in series and so on?

Yes.

Okay. So again, that's a. Okay, it's got one input. If it had multiple inputs, I would just give a vector there.

Yes, yeah.

And you got a list of two because that model has two states.

Okay, okay. Okay. So now what's the relationship between input output model simulate and state response?

So input output model simulate is sort of next level up in sophistication for two reasons. Two important reasons. One is what Subha mentioned, that you can say what it is that you want to get out, which is incredibly hard, which takes a lot of coding because you have to kind of do it yourself with the previous ones.

What do you mean you want to say what you want to get out? Where do you say?

Look at that.

Look at the reference page for input output model simulate.

Yeah, that first illustration will show.

So.

So now we can place probes anywhere in that model.

Okay, so this is what can go in.

Yes.

Not just a differential equation.

Difference. Differential difference and combination of those.

Yeah, but, but how are those packaged? I mean, if I just give Y.

Double dot, you can't give it right in here, I hope. But you know, when you create the state space model, you can give a set of differential equations. Yeah, equations.

If you give Y double dot, you will wrap it around state space model or one of those models and get that. And get one of these model space model around it.

Yes.

Around the differential equation. Yeah.

Yeah. Okay. Okay. Okay. So now this is what you can get out. Output response, etc. Is that correct?

Yeah, yes.

So I mean, in this case here, for example, if I went here and I said. And this. And I said something like.

The last argument.

Which is not auto completing. Please fix.

Yeah. Because the documentation is still.

Well, one, sometimes they have names. Steven. The models can store names. This one didn't have any. So there's just a default number. You know, position names, basically. Yeah, this, you know, sometimes like particularly real world systems, you often have names. You say like this is the hydraulic.

I understand, I understand. Why did this not work?

Yeah, yeah. So I'm deciding what to do with this. This one has no subsystems. That subsystem only works for systems connections models.

Okay, so produce a message and.

Yeah, yeah, yeah, because I, Yeah, I'm, I'm still. Yeah, if, if it returns any value, I'm going to generate a message. Yes.

Okay. All right, let's talk about the name again. Input output model simulate. So is it true that, I mean, input output models are like a name in economics and so on. They mean something quite different from this. I think there. Am I making sense?

Yeah. Input output model just means a model with inputs and outputs.

I know, but is it a standard term? Var. Control theory?

Yes.

Okay, but how does it relate to the input output models of economics?

It's similar, you know, they, they, the inputs are usually called exogenous inputs, you know.

For whom? For control theory?

No, for, you know, in economics, you know, so there, there, there are two kinds of models that frequently use there then dynamic models. One is where, where there's only basically noise input like Arma, Massachusetts. Those kinds of things. Then when you also have exogenous input that you can actually measure, they're usually called rmax, arcs, max, etc. So x is for the exogenous input side.

Okay.

And. They often use state space models and so then they need an output too because it's usually you're not interested in the full state.

Okay, so we already have the function system model simulate, right? Yes, but that really is doing simulation. Yes, but this might be doing simulation or it might be doing exact solving.

Yes.

What would happen if we call this input output model solve? Does that not make any sense? I mean, it really is. Look, it's a thing where you're giving an input and you ask what is the thing going to do?

Yes. I think SOL feels strange in this context.

Strange because it isn't really solving. It's not, there's no X solving for. It's just running the model with that input.

Right.

So input output model response. Is it consistent with state response?

Yeah, actually it could be. Yeah.

Yeah.

I think that's a neutral word that doesn't say whether it's.

No, it's not a bad idea, Stephen. It's very consistent with the previous names.

Yes.

Well, what about just input output response? Let's get the model.

I think that's Even better.

Okay. All right, so we got another function, then we got input output response. Well, we got input output response data. Is it data or is it a function?

Yeah, so you can. So from this, you can ask just the property data, and then it'll return that data object, and then we can do. We can query properties.

I'm asking, is the quotes data object actually a function? Really?

No.

What is. How. How is it primarily used? It's just something with an association inside that you can pick at pieces of and things.

Yeah. Yeah. So. Yeah.

So is it lazy? Is it lazy meaning that it computes things only when it needs it?

Some of them it compute. Yeah. So it depends what comes out of that simulation. So all what is there it has, and then if it's something new, it computes later.

Okay.

Yeah, but in the simulation itself covers the vast majority it has.

So, for example, if I took it outside the range there, 2pi, would it know what to do? Or is it.

No, no, it will not. It'll. Yes, it only.

Yeah.

Okay, so, okay, but so you think input output response data makes sense. What. What are some other star data things in the. In the control systems world?

Yeah, right now. So we've been. We've been moving from the name system. We have systems model controller data.

Okay.

That. Yeah. And then we have. Yeah, systems model controller data. We, We. We unified all the controllers into that.

Okay, okay. But that's a star data that works more or less the same way as this input, output, response data will work.

Yeah. Yeah.

Okay. All right. Well, seems reasonable. Let's take a look at this. So I mean, if it's called input, output, response, do these properties make sense? Is it just output then? I don't know.

No, it makes sense because it's the. Yeah, they all responses. What? We are getting out all those properties, the various responses.

Okay. Okay.

State response output.

Well, they respond. You know, they respond in a sense that you give it an input. How does the model respond over time?

Yeah. Are we doing webinars and things about all this stuff? Because all this stuff is really quite complicated. I mean, it kind of. I mean, do we have a course yet about control theory?

We have one that's about to launch. We've just developed one over the summer.

Great.

And yes, we will be doing more, actually. So here's a game plan. So this is the Wolfram modeling series, which will be jointly done by the system Modeler team, the Numerics team, Control Suba and calculus and algebra to some extent. And the format will be kind of Like a cooking show or a home remodeling show. So we'll do like a modeling project. You know, there's going to be a goal. You're going to go through the. You know, to, you know, how do you think about it? You showcase some things. It's like when you cook, you don't necessarily wait 45 minutes for something to cook.

I do think the name might. I mean, there are these things called Wolfram models that come out of the physics project. So we have to, you know, I guess Wolfram modeling is sufficiently different from that that people won't get confused. But that would be. I mean, I. I think you might add system modeling or something like that, if that's what it is. Making sense.

Yeah.

I mean, it's pde, this PDE modeling. There's the sort of ODE modeling that system modeler does, and there's uses of those ODE models like in control systems. And there are sort of other kinds of analysis, like asymptotics from calculus.

Now, it's very different. I mean, the. Well, probably. So long as it's modeling, it's okay. Makes sense. Yeah.

I think that this will be. I think we'll run a lot of episodes of this.

Yeah, I think sounds like a really good idea.

So we're about to kick that off, actually. Will be weekly episodes, is the idea.

Good. Good. All right. Anything else we should make sure to look at?

Yeah, I just want to clarify. So is that name you say, Input output, model response?

No.

No. Input output response.

Okay. We don't think. We don't need model. Okay.

I don't know. Why would we put model in? They're all about models, aren't they? The thing you're feeding it as a model.

Yeah.

You asking for the input output response of that model?

Yeah. Okay, got it.

Yeah. It's kind of important in these meetings that we actually. I mean. Yeah, I think that's what we decided. Okay. What else should we look at here?

That's it.

Okay. Nice stuff.

Great. Thank you.

All right. See you in another design review soon.

Thank you.

See you. Bye. Bye.