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Welcome back.

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So I believe leave out a little bit of play around with the dot product maybe created your own matrices.

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Try it out.

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If not that's okay but remember the best way to learn is to always run the code yourself first and then

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again maybe if you are even doing that sometimes it's hard to understand like different concepts when

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you just seen numbers on a page.

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That's always good to try and back things up with a practical example.

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So let's have a look at one where the dot product might come into play.

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So this is my Google Sheet I'm tracking my nut by the sales for my future not on a business because

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my favorite food in the world is almond butter.

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And now this business we create 100 percent almond butter 100 percent peanut butter and 100 percent

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cashew butter.

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And so this is just a simple tracker to track how many jars I've sold on each day.

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Friday was a massive day because we sold 15 jars of butter.

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Now we've got the prices here of each one.

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So I'm about as 10 dollars peanut butter as eight dollars in cash but our cash is a little bit more

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expensive so cashew butter is 12 dollars per job.

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And now what my goal here is to figure out this total column because that's what I want to know is what

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days am I making the most money.

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Monday must have been a slow day.

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But if we click on this sell here and we have a look at this we can see that this formula is relatively

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the same.

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Well similar not exactly the same because there's different letters and numbers to our DOT PRODUCT formula.

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Back on our slide here.

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So a times J plus B times L plus eight times n and that equals 44.

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Well if we come back we've got B 2 which is two times B 9 which is the price of almond butter plus C

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two in the number of jars of peanut butter times the price of peanut butter and then we've done the

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same for cashew butter.

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And now we get the total.

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So this is an example of where the dot product can come into play is where we want to reduce the numbers

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we have here and find out the pattern between them.

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So I've got numbers of jars being sold here and the prices and the total price is the patent between

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these two.

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And I want to emphasize the fact that this can be replicated in pure non pi and panders not just in

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an Excel spreadsheet.

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So let's put this to the test.

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What we're going to do is create a little title here dot product example not by sales and we're going

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to recreate this example this whole set here from scratch using nothing but an umpire raise and pander.

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So let's do that and.

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We'll set a random seed so the random numbers we create are similar to the ones here.

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Hopefully that's the idea of random seed.

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Now we have sales amounts we go at MP random Rand int we want it up to 20 is a good amount of sales

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if I'm selling more than 20 jars I need to step up my supply chain sales amounts.

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So this will be we'll put a little comment here.

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Number of jars sold there we go 12 15 0 3 3 7 and now we want to create a data frame create weekly sales

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data frame.

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So this is to put it into pandas so it looks a bit more presentable than just an umpire Ray.

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So let's do that.

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Weekly sales equals PD data frame.

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We want to add our ray sales amounts which we've just created up here.

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And then for the indexes will come back our indexes are going to be days of the week so let's do that

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index man choose and run out the days of the week.

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Wed deliberate aviation so and fry.

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Wonderful and then our columns we're going to figure this out we've got a peanut butter cashew butter.

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Wonderful columns equals

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Allan butter peanut butter

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it might seem a bit tedious to type this out we could always export this is a CSB an important panders

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but it's always good practice to build your own things from scratch that way you really start to understand

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what's happening let's have a look at weekly sales OK.

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Wonderful.

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So the numbers are a bit different here from what's going on there.

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But the process is going to be the same.

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So now we've just recreated this section without the total column in a panda's data frame.

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Wonderful.

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So now we want the prices.

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So we want to create the prices array.

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We'll keep this the same.

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So what are the numbers 10 8 12.

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So we can do that with a simple umpire Ray MP or Ray we want 10 8 12.

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Wonderful.

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Let's have a look so there's a simple num pie array.

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Now we want to put that into a data frame as well create a prices data frame bottom prices equals payday

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dot data frame prices.

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Here index equals so the index is just this column here.

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So we want price.

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Wonderful price.

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And then we want columns is the same as above.

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I might just copy this usually we want to write it out but to save a little bit at time of topping this

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out we've got the same columns because if we go here same columns wonderful.

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Put that in there we've got an extra bracket there we go.

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Now let's have a look at our butter prices data from ERA.

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Mm hmm.

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Wrong number of items past one placement implies three.

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We come back.

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Shape of past values is three one indices imply 1 3.

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Now that's our problem here.

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So this is a weird thing in num pi where we go prices not shape it equals three something.

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But what panders is expecting is three columns and one row.

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But this is three rows one column.

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We want to reshape this to be one three there we go.

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Wonderful.

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So what we've done is we've recreated this little section in Paris.

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Beautiful.

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So now how do we do this.

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We need to do a dot product of sorts on this and this okay.

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Then add it to this and this and this and this and add it up and get that.

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All right.

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So let's try.

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So let's just do what we have here.

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We've got wins our total sales sales amounts

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and prizes.

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Let's make total sales equals prices which is we'll have a look at prices again.

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Prices.

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Sales amounts.

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What happens here not aligned.

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We want to have a look at our sales amounts actually from this is saying that the shapes are aligned

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so we can see that the sales amounts shape is 5 3 and the prices shape is 3 0.

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Okay.

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That makes sense.

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We've we've seen this before we've seen the shapes of dot products not fitting together the shapes on

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a line.

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We need to transpose shapes aren't aligned.

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Let's transpose go.

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Total sales.

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Which one do we have to transpose.

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Maybe if we try to transpose sales amounts total sales equals prices.

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Sales amounts T.

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There we.

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That worked.

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Total sales.

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Wonderful.

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Okay.

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Now I've got something that looks kind of like this again.

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It's with different numbers.

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But now I've got some total sales.

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Okay.

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So how would we get this as a column on the very right hand side.

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Let's have a think.

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Let's try something.

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Let's just.

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If in doubt run the code create daily sales maybe I create the same thing is here but within a panda's

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data frame so we can kind of just add the two data frames together.

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So let's put up prices which is this yeah.

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What else do we want.

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We want weekly sales Yeah.

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So we want these two.

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We want to combine these two through one shape.

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No we get weekly sales not shape as well.

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OK.

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Oh there we go.

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So now this is starting to look familiar maybe if we flip weekly sales which is our data frame flip

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that transpose that and then dot product of those two because then if we flip these two right there'll

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be three on the inside and the threes will line up daily sales equals.

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We should be out to do a dot product dot weekly sales dot t so that's a transpose their well that might

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have worked because let me prove it to you.

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Weekly sales team that's shite.

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Excellent.

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Here we go.

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We might be cooking with gas here.

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Oh beautiful.

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So this should be the totals.

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Now how do we get this onto the right hand side of our data frame.

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We want to put this on there here because that's what we're recreating right.

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We're putting this total on there.

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Okay we can do this how do we create a new column in pandas.

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We go weekly sales.

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This is our data frame here.

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Well weekly sales total maybe I'll put a little dollar sign there.

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So we know what's going on here.

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Equals daily sales daily sales is this little pandas data frame here I go type daily sales data frame

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and we want to add that data frame as a new column on the back end of our data frame here.

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So let's see what happens when we do this weekly sales off.

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That didn't work.

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What's the error here key error.

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Total

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Total maybe the column title doesn't work.

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Wrong number of items past five.

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Placement implies one because we're getting into another shape era.

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So this is a row.

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But we want noted in column form so maybe we have to transpose this.

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I cannot stay in shape and then we want the shape of our weekly sales data frame Okay so we want our

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daily sales to have the same number of rows as our weekly sales.

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And then we should be able to append it.

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Okay put a note in here doesn't work not the right shape.

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But what we can do is come down we'll make a new cell.

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Here we go weekly sales total.

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That's a terrible ways to spell it.

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Title Daniel weekly sales total equals daily sales dot t for transpose and now the A's hopefully beautiful.

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There we go.

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So now we've just replicated with a few steps in between of shifting shapes and whatnot.

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We've replicated this column here figuring out how much I made from each day Monday was a terrible day

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couldn't pay the rent without money.

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Well in this state of home it's actually a bit better.

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Wednesday was my biggest day and this one we've now seen where manipulating the shapes of arrays and

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performing a dot product can work in practice.

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So this this video was a lot to take in so I'd go back through and just have a little practice around

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maybe create your own store maybe you want to sell your own favorite food product or technology or something

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like that make our prices array here make a total column and try to replicate it using num pie panders

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and see if you can end up with something like this.

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That'll be a good practice exercise.

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Okay I forget.

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Try to run the code yourself if it doesn't work.

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Keep trying.

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Search it up and I'll see you in the next video.