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So in the previous lecture, we have learned about lists, and I told you that lists are nice for storing

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some small amount of numbers or strings and for which we don't want to do any further mathematical calculations.

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However, if we want to do mathematical calculations, which we will do a lot in this course, we will

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have to use.

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Arrays and arrays are not natively implemented in Python.

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They are implemented in a module called Nampai.

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So if you followed the previous lectures, we have already imported this.

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So let me scroll up to the very top.

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We have imported Nampai, S and P, and we need this to be able to use arrays because to define an array,

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what we have to write is, for example, let me stored in the variable called array one.

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We right and p dot array.

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And then the syntax is normal brackets.

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And then here we can write the square brackets one for nine, for example.

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This would be our right.

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So of course, let me call this.

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So you see, the result would be an array which has these numbers.

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So you may wonder, why do we have these double brackets here?

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And the reason for this is that we also can define multidimensional arrays.

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So let's redefine the two lists that we have defined previously also as arrays.

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So we had here one, a three.

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And here we had two lists that emerged inside each other.

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So the first one one one two three and a second one was

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this was one four nine.

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Now you can see how the syntax works, so we need the normal brackets, basically.

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Yeah, it's it's related to the NPRA commands.

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And then here we have these two lists, you could say that emerged.

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But since we have right here array, there are not lists anymore.

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Now they are arrays.

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We can call them, for example, like this.

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And you see, this is already nicely organized in the output.

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And it looks like a matrix from mathematics.

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So, of course, we can now select individual elements like we did for lists so we can write every one

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square bracket, one which gives us the second element since we're again start counting from zero.

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And we can also select multiple of these.

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So if we want to have the first two elements done, we get these two.

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And here you realize if we just select a single number, then it's just a number.

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And if we select multiple numbers, then it will remain the property of the array so that data type

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will be on the right.

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So if we do this for the second array, which would give us one as a number and a as a string, we have

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two different data types.

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This works, but gives us as an output, another option or property, which means something like a mixed

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data type.

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Now, if we want to select elements of a multi-dimensional array, which would, in our case, be the

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array number three, this one here, then we can of course do this.

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For example, if we want to have this property here, so we have to write zero and then to.

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But so this is exactly the same as for this, but since we now have an array, we can also make it more

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easy and just right like this is what exactly the same result.

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So manipulating arrays is, of course, somewhat similar to this, but there are also important differences.

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So there you cannot use anymore the syntax that we had previously.

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Let me scroll up.

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So we have previously list Dot Append, which is something that just works for lists that are natively

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implemented in Python.

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So here we must use a different commands and this command is called Nampai Dot Prepend.

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So if we just use this command, Python doesn't know which area we want to manipulate.

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So first, we must start with the array that we want to manipulate, and then we write a comma.

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And the thing we want to add.

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So this will be the new array.

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But there's another important difference here previously for the lists, if we would write something

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similar.

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Then the list would now have been updated already here.

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This is not the case.

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If we right now, everyone, the old area appears.

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This is because here we do not have lists anymore, but we have no idea.

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So if we want to update the array, what we have to do is then write every one equals.

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This one and now.

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Sorry, I somehow switched to data time, I think.

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Yes.

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So now the one is updated, so of course, we can also use this append commands here for more general

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purposes.

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So, for example, we could now add to your true numbers at the same time, and we could do this by

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adding or by appending voucher to see a whole array.

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So we write and pray no more brackets.

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Square brackets 5.6 now.

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Oh, I did the same mistake again.

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No one will be this.

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So we have this hour and we have appended these two numbers.

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So what we can also do is we can, of course, manipulate multidimensional areas.

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So let's get back to our error number three, which is this matrix.

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So basically, we have two arrays stored inside of one array.

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So what we can do now is we can also append here some numbers or some errors so we can write and we

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don't depend on a three comma and we right here what we want to append.

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So it just will again be an array and the array will, for example, be one eight twenty seven, which

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will be the cubic numbers of these.

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So what happens if we run this?

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Oh, this, this doesn't give us what we want.

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It gives us one two three one four nine one eight twenty seven as a single one dimensional already.

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So what I wanted to do here is add another line.

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So in order to do this, we must use a bit of a different syntax.

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So let me copy this and no change it.

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So you see, the array number three starts with two square brackets, so we must now also start with

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two square brackets so that these two arrays have the same rank.

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And now it will still not work.

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Still give the same result that we do not really want.

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So we must tell it and option an additional property how we want to merge these two lists, or how we

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want to append the array here to the other array.

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And this will be axis equals zero, which means basically add or append this array on the first level.

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So see row once again since first start counting from zero means first level, and then we will get

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this nice three by three matrix.

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Of course, we could also do this differently.

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We could do this by adding a different row here instead.

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For this, we would have to, for example, overwrite four and 16.

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And now I think we have to right access one, which would be the second level on the way yet in horror.

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Let me check what's the problem here?

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Oh, yeah, right?

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Because basically, if you see we want to add it here, so we must have here these these square brackets

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as well.

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So like this?

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OK, so you see, manipulating multidimensional arrays can be a bit tricky because you have to really

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take care of the syntax.

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So you do not only need these arguments axis one and axis zero, but also you need to make sure that

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these brackets here are correct.

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By the way, I messed up here a bit.

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This is, of course, not supposed to be math.

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Is this supposed to be manipulated so we can just click here and move this to the bottom?

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Yeah.

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So now let's come to math.

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This is just really quick.

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This is where I want to show you where arrays are better than lists or more simple, so we can just

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write, for example, here everyone times two.

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And if you remember what everyone was, everyone.

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Than this was one four, nine five five six.

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And now we do not just repeat this error twice, but we really multiply every element of the array by

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a number.

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So this is really useful in a mathematical way.

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And this was not possible for lists, if you remember.

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So here was the same thing for lists.

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So we had one three, four 10 and we got one three four 10 one three four 10.

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So, of course, this also works with an addition, so we could write something like this.

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So this time, every element will be added by the number two.

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And of course, it also works with multidimensional arrays

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with the multiplication and addition and also, of course, other operations.

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So I hope you see that arrays can be quite advantageous.

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So once again, this is useful when we want to do mathematical operations, sometimes we use arrays

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instead of lists.

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And also, these arrays require much less storage to store the individual elements compared to the lists.