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So a great job, if you made it this far, you have learned a lot about Python and Nampai already.

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So the last thing that I want to present to you in this crash course is how you can visualize your data

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and your results, because of course, we will also create figures, for example, of our results.

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So we call this plotting or creating plots and to do this in Python.

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It's very useful to import a library called Months Plot Clip.

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So it's basically a mathematical plot library.

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And then there's some some option here, which is called PI plot and you write import.

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You could read just in parts Matlock lip.

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And then every time you want to plot something, you write, plot live dot pi, plot dots and then the

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actual command.

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And since this is pretty long, we use an abbreviation, so we write import much plot loop PI plot as

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Pulte.

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So in the following, we only have to write Pulte, which is pretty similar as we did for nonpaying

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when we wrote import numpy as NP.

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So in most of our files on the following, we will basically run this command in the first cell and

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in one of the first lines.

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But here, just to make it a bit more or have a better overview of the notebook, I just keep it here.

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So we run this.

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And now we have loaded the library and we can use it and we can plot nice things.

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So the most simple thing you can do is just plot some data points with some coordinates.

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So you have some coordinates basically which have an X value and the Y value, and you have several

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of these.

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So we can just write plot dot scatter.

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This is the command for such a list, plot or scatterplot.

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And then you provide the two lists, and now it's important you do not provide x one by one.

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This is not true.

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You provide instead x one x two x three and then you provide a second list with the Y coordinates.

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So it's really important to acknowledge here the order of the two things.

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So first, all the X coordinates and then all the way coordinates, so we can just do an example here

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one, two, three and then maybe four or five.

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And for the Y coordinates, we just take some values five one minus one zero two.

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So now I made a mistake, so let me check what I did wrong here.

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I don't really see it just yet.

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It says X and Y must be the same size.

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Maybe I did a comma.

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Yes, here I made a mistake with the comma.

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So maybe it's a good idea that you saw this here.

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So just a small mistake here.

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I guess this large error message and and most of the cases, it's a good idea to scroll to the bottom

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because there it gives you the the error message.

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So now they have to stay, have the same size so I can run it.

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And you see, we have now our coordinates.

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The first point has to coordinate one and five, the second one, two and one and so on.

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So this is how you create a scatterplot.

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So now this is typically not how we get our data.

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So let me show you a bit of a more realistic example.

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So let's say, for example, we have some array which we call, I don't know, courts small.

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And as I said, it's an array.

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And typically at least this is how I program typically or most of the times is I have a first data point,

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which has some coordinates.

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And let's assume we even have three coordinates X, Y and Z.

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So the first point has the coordinates one one one.

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Then we have a second point, which has some other coordinates two for eight.

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So the next one, you see just a square and cubic numbers.

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Of course, I could also generate this list automatically.

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But just for the just for the presentation here, let's just write them down.

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OK, so now we have five different data points, which all have three coordinates.

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So in such a scatterplot which is two dimensional, we can of course only use two of these coordinates.

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We can, for example, plots the X and Y coordinates of all of these five points.

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So how are we going to do this?

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Well, we are, as I said, you really have to be careful here with the syntax because if I would just

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right here plot scatter and then quotes one, it would of course give me an error because yeah, the

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inputs has a completely wrong shape.

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So first, we must shape our data and we do this in the following way.

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First of all, he told you that you have to first provide the X coordinates and then the Y coordinates.

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So what we're going to do is we are going to transpose the array.

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So this basically just means reorder the array and now the first cell or the first brackets will contain

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this value.

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This this is this.

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So basically all the X coordinates and you do this by writing down quotes one dot capital t.

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So this Ensino has reordered this array.

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So we started from here.

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Now we are here and now what we can do is we can assign this array and individually these three rows

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here, we can assign them to new variables.

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So I call them X1 y one z one.

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And now, if I called them just to show you next, one will just be this line here.

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Why one will be the second line and so on.

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And so this is not really nice, I think, because what we can do next is we are basically we don't

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have to do anything anymore because we already have now the correct shape.

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We can just use them.

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So what we can do now is we can write, plot, scatter and just write x one comma y one.

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And that's basically all we have to do, because now you see, this has the same syntax as this one

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here.

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So I can just run it and you see we get now the plot.

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So on the x axis, we have this line here and on the y axis we have this one.

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So the values are one, four, nine, 16 and twenty five.

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So what's also nice is we can just plot in the same plot.

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The Z components as well.

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So now we have plotted the X components on the x axis and the Z component at the y axis.

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So you see, they are different No.

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One, eight, 27, 64 125.

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So maybe to just make this a bit clearer and to understand it a bit better, we should add labels to

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our plots and we can do this by writing before we do this here.

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Plot X label.

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X so now we have the X on the x axis, and to make the Y label, we write Peltier Dot Y label.

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And here we I would say we just write y commas because we plot both of them.

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The Y coordinate is blue and the Z coordinate is orange.

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OK, so now we have a nice scatterplot, and I'll show you how you can handle such data points that

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we will typically get from our calculations.

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Now, of course, there are not only these scatter plots.

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You also want to plot conventional functions and you want to connect them with a line.

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And the truth is, most of the times you do not straightforwardly plot a function as a line.

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Instead, what you do, you generate some data points which are very dense, you could say, and then

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you connect these with lines and so you emulate the real function.

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So let me show you what I mean by this.

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So what we're going to do here is we are going to first generate some data points.

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So I just write your data points.

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And then what we're going to do is we first are going to generate some X coordinates.

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And for this, we should do something like zero one two three four five like we did here.

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So this would be our data points.

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However, since we want to have a smooth function, we must make them very, very dense.

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So we should do instead something like zero, 0.1 0.2.

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And so.

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So this is, of course, very, very tedious, and you need many of these points to generate a smooth

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function.

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So to generate such a list, what you can do is you can just write and p dot little space and then you

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provide starting value, then the end value and the number of points between these two values.

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So you could, for example, write one hundred and now I can show you what this looks like.

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This is an array with 100 data points between zero and four.

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So it's often better to add you add additional data points because then we will have such nice numbers

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here.

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This is because the first and the last data point to count as well.

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So when we write here 101, we actually have a distance here of zero point zero four.

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But it wouldn't be a problem to write 100 here.

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OK, so now we have this list, and what we're going to do next is we are going to generate a loyalists

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our actual values.

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So let's say we want to plot the function just a random function one plus two times cosine, which would

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be an PIMCO's.

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And then I would just say three X. So this would be our function that we're going to plots.

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And of course, the Y values must also be a list.

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So the X values must also be a list, and we just take our list that we have just generated.

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So I run this.

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And now you see the Y values are both also a list or array betters, say, and we can plot.

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Now both of these lists together, as we did before, so we can, of course, now just load this one

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here.

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The scatterplot?

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And this will be the function, and if you now want to connect these very dense points, you can write.

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Plots are Pulte Dot plots.

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This is the correct comment.

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And now you see it gets a rather smooth line here.

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But for example, if I would decrease the number of data points to 21, then you would see these are

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really just lines connecting the data points, which make a not so smooth function.

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And of course, the higher the number goes, the smoother the function will look.

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So I see I would say 101 was just fine.

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And yeah, we can definitely work with this.

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So what else can we do here?

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Well, we can, for example, specify again the labels which we have done previously.

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But I want to show you something new.

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I want to show you the limits on the XS.

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For example, the x axis.

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And so the syntax here is x limb than normal brackets and in the cupboard or in the yeah, in the in

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these brackets, we write zero comma eight, for example.

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And so we have now changed the X range from zero to eight.

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And what I'm going to do next is I'm going to add some more data points and I want to plot.

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So let's say I want to create more data.

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So I just copy this one here and say X to Y to X two.

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And this time I want to plot the values of four x between four and eight to fill the remaining space

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here.

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So I write for Comma eight and I want to just continue with the same function.

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So now I will add another plot here.

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I will add the plots of X two and Y two.

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And of course, if I do it like this, you see, we have now merged these two plots.

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But you can also merge different types of plots.

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For example, you could write plot dot scatter.

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And now you would get such a graph.

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All right, so you see, it's really nice to are really easy to plot stuff, you just have to remember

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that you cannot just provide a function that you plot, but instead you must always generate lists or

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arrays that you then plot.

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So you have really the full control over the way you plot things.

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So the very last thing that I want to show you is that you can also export figures and save them, and

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this is pretty easy.

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Interest rate potti dot safe, fake for, say, figure.

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And then you just have to provide a name to write, test plot dot.

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And then, you know, you could, for example, use a page file.

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You run this and it gives you the output because we are in Jupyter notebook.

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If you would be in a Python notebook, it would not give you the output here, but you would then export

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the file and you can look it up in your directory where this notebook here is located.

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And you see, I have opened here the image that we have just exported.