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Alright alright alright.

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So in the previous few videos we've had a look at different ways of creating an empire raise.

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We've seen how we can view them.

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Now let's figure out the fun part.

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Let's figure out how we can manipulate and compare our different arrays.

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This is where the crux of machine learning happens right.

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It's manipulating performing calculations finding patterns in arrays of different numbers.

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Let's start it off.

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We'll put in another heading because we're keeping our notebooks nice and neat manipulating and comparing

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have I spelt it right.

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I usually get typos in these headings manipulating and comparing arrays.

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Beautiful.

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We're gonna put a little subheading here because like pandas with NUM pi if you can think of a way of

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manipulating numbers you can probably do it.

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So the first one we're going to look at is our riff Medtech.

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Here we go lucky encoding is a little bit better than my spelling ability but arithmetic is a fancy

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word for basic math equations.

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So let's have a look.

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Start off by checking out our A1 array.

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We created this earlier A1.

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Wonderful.

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We'll create another one called ones actually.

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We've already got ones yeah beautiful.

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But if you wanted to recreate it we'll go NDP dot one's three just to make sure we know what it looks

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like.

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One's wonderful Okay so we're going to have a look at is nice and simple plus.

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So what do you think this will do if we go A1 which is our right here plus ones.

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Well let's not talk about it Daniel.

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Let's run the code beautiful A1 plus once so we've got one plus one equals two two plus one equals three

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three plus one equals four.

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Excellent.

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So all this is done has just added together the different elements in the same position of both arrays.

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So the zero position one plus one it goes to the first position two plus one equals three.

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And the second position is three plus one equals four.

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All right well let's keep going.

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Let's see a few more options.

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Hey one minus one's Can you guess what'll happen here.

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Zero one two three.

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So all it's done is it subtracted ones from a one let's push forward let's try multiply i1 times ones

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Yeah well that makes sense because our one's array is just all ones and it's just times a one by one

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one times one is one one times two is two and so on.

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Let's bring another array a two.

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Here we go.

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Now this will be interesting if we multiply A1 by A2 what's going to happen huh let's see.

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Let's work through this.

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So we've got one.

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This is let's get up.

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I won again so we can see everything in one place.

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I won one times one is one two times two is four three times three point three is nine point nine.

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That makes sense.

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What about this second row here.

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Let's see if we can figure this out by looking at it 1 4 4 2 2 5 10.

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Yep three times six point five is nineteen point five.

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Let's use python to help us out for that six point five.

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It's nineteen point five huh.

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We can get rid of this cell we don't want that actually.

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Never use a toolbar escape X to get rid of that.

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So what this is done is it's taken a one these three numbers here multiplied it by this row.

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Put it in here and then done the same thing again with a one and multiply it by this row.

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Huh that's interesting.

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Let's have a look at our other array first A3 let's combine these two a two and a three a two times

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a three operations could not be broadcast together with shapes two three two three three operations

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could not be broadcast together.

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That's interesting.

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But remember right at the start the concept video where we talked about where num pi is fast because

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it vector rises code through a technique called broadcasting.

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Well this is what's happening here.

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But to be that fast broadcasting has a few rules so let's look that up.

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Num pi broadcasting.

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There we go.

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We're gonna go to the documentation broadcasting num pi click on that the term broadcasting describes

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how num pi treats arrays with different shapes during arithmetic operations which is exactly what we're

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doing.

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We're trying to use some arithmetic on arrays with different shapes so there's a three and there's a

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two they've got different shapes and that's what the errors coming up.

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So let's have a look here.

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Subject to certain constraints the smaller array is broadcast across the larger array.

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So they have compatible shapes.

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Well that explains what's happened up here with a one times eight to the smaller array is broadcast

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across the larger array.

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So they have compatible shapes that makes sense because we've got here this is a smaller array.

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It's been broadcast across this row and then across this row.

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So that the output has a compatible shape of the larger array.

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Okay.

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We'll keep going there's some examples here.

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So these are two arrays multiplied.

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They've got the same shape.

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1 2 3 2 2 2 8 times P is one times two is two.

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Two times two is four three times two is six.

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Aha.

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That makes sense.

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And then broadcasting rule relaxes this constraint when the array shape meet certain constraints.

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Okay.

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So this is good.

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This is the kind of workflow you want to start getting into right is if you come across an area like

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this and you will all the time one of these mismatch shapes errors like different shapes that are incompatible

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with each other a value area.

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These are gonna come up all the time in machine learning and part of being a data scientist or a machine

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learning engineer is reading documentation like we're doing now and trying to figure out how to fix

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our problem.

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So General broadcasting rules okay.

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When operating on two arrays none pi compares their shapes.

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Element wise it starts with the trailing dimensions and works that way forward two dimensions are compatible

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when they are equal or one of them is one.

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Now to save a little bit of time instead of going through the entire documentation I'll leave that for

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you.

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I want you to have a think about try and figure out a way how would we get these two to be of compatibility.

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How would we fulfill this broadcasting need.

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So what you may want to look into is how can you reshape A2 to be compatible with A3.

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So that might be looking at search put in another comment here how to reshape num pie array.

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So check out the broadcasting documentation along with searching something like this and then figure

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out how to make these two shapes align.

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If you can't.

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That's entirely fine.

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This takes a bit of practice but we're going to see how to do it in a future video.

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Right now we're going to continue with our arithmetic just to finish things off.

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So where were we we've done multiplication.

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Let's try A1 divided by ones.

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So this little slashes four divided by you can probably predict what's going to happen here.

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Beautiful it works fine because our rays are similar shapes.

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Okay let's try a two.

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Let's try some floor division think two divided by a one.

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Wonderful.

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But we'll see what non floor division works here.

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There we go.

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So floor division what this means if you do two slashes you might have seen this in Python.

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If not that's fine.

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Floor division removes the decimals so you can see here it rounds it down rounds down so one point zero

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point zero point zero one point one but that's been rounded down to one two point 1 6 6 6 6 7 has been

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rounded down to 2.

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Let's keep going.

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What have we missed out on.

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Let's go square a two square two.

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This is a power so to the power of so everything in here is going to be to the power of two.

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So if we look at a two on its own it's gonna be one times one two times two is four one times one is

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one three point three times three point three is ten point eight nine will confirm that with Python

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wonderful ten point eight nine that's just filled in then rounded it off actually num Pi has a square

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you can use with this so all of these functions that you see here that we've gone through arithmetic

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floor division etc num Pi has the equivalent here now which one should you use.

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Well it's going to depend on what your workflow is best at.

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So if you want to use the maths symbol operations you can use that or if you want to use Square or you

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can even go and he'd add gonna go shift tab to figure out what it does it's figure out here doc string

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adds arguments element wise let's try that a1 ones same as just doing a one plus ones wonderful.

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I got a couple more.

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I won modulo.

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This is gonna show us the remainders.

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So A1 divided by two let's see where that goes.

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A1 divided by two let's go now in PI modulo

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model.

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There we go.

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Return element y's remainder of division.

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Wonderful.

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So this is again I'm trying to exemplify the kind of workflow you go towards if you're not sure what

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something does.

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You can always look up the documentation and have a look.

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That's what we did with broadcasting.

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We've just done that with modulo if we divided every element in a one modulo two it's gonna show us

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the remainder that's left over.

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So let's do a two modulo two.

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So this is just showing us the remainder of what's left after we've divided everything by two and if

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you wanted the exponential you're not sure what this is.

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Don't worry for now it's just to highlight the kind of arithmetic that you can do and num pi is gonna

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take the exponential of everything in an array and if you want the log you might see this come up in

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future projects of an array you can use MP dot log so that was a bit of a whirlwind tour of some of

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the arithmetic functions that you can do a num pi remember if you can't imagine it.

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You can probably do it.

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This is only just scratching the surface.

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So before next video have a practice around creating some of your own arrays and then using some of

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these arithmetic functions on them.

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Remember.

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If in doubt run the code if you're not sure what something does.

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Have a look at the NUM pi documentation see if you can figure it out.

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I'll see in the next video we're going to cover a little topic called aggregation but we'll save that

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for the next video.

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See you soon.