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In this new section, we shall be working with ragged tensors, and so we shall understand the reason

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why we need rag tensors, and also how to create them very easily.

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So let's get back.

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Let's suppose we have an a um tensor flow constant.

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And then here we have another, another um array.

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So we have 123.

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Well let's just end like that.

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And then here we have 456.

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Let's close this.

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We have 456.

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And then we have 789 okay.

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So here's our input.

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We could print out.

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We could print out a and then print out.

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Well let's just print out a.

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Now once we print out a here's the output we get.

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Uh we could suppose that we modify this.

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So let's let's change that and change this okay.

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So now uh our row has two columns.

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And the second the second row has three columns, while the last row has only a single column.

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Let's run this again.

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You see that obviously we get an error.

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Can convert a non rectangular Python sequence to a tensor.

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So, um, the number of columns has to be constant across the rows.

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And number of rows have to be constant across the different columns.

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So such that we have a rectangular array or rectangular tensor.

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Nonetheless in some cases you would need this kind of data.

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That is, you would need data where some rows will contain shorter columns as compared to the others.

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And so the way we deal with this is we convert this to, um, racked tensors, or we just simply create

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a racked tensor.

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So here we have racked instead of the TensorFlow constant.

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Now we have TensorFlow racked constant.

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So we run that again and you will see that we have a racked tensor.

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Now this racked tensors have different functions.

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Like we've just looked at the constant which constructs a constant rank tensor from a nested Python

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list.

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We could also have the boolean mask.

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So let's just check out the boolean mask.

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And you would uh feel free to check out the others later on.

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So for the boolean mask let's take let's take out this example.

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From here we have the data and then we have the mask.

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Um there we go.

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Let's copy this.

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Uh, let's copy this other one because we here we have um this non rectangular list.

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So let's copy that.

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And then we could simply paste this out here okay.

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So now here we have this um racked tensor right here.

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Or we have this two racked tensors.

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Let's see.

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This is the this is the input rank tensor.

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But this is the mask.

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So what this mask does is simple.

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We are going to um keep all the values.

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So let's run this.

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So you see the output.

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Um f is not defined.

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Well f is um false and t is true.

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So let's get back and then let's say here we have false false true false true and then true okay.

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Run that again.

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There we go.

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So you see that each and for every position where we have false is taken off.

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So here we have one.

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It's no more.

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It's no longer there.

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Two is no longer there because we have false to three.

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Um remains because we have true.

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So you see we are left with this three and then for the next this for false.

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So it's just taken off.

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We have this empty list and then we have the next true true.

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So five six are maintained.

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So that's it for this um boolean mask method which we have seen from the documentation.

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You could check out other methods like this cross Crosshatched range and so on and so forth.

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So we could check out those different methods.

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Um, the simple way we could check this out is by uh going through this, different examples.

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So right here we have our values.

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You see 31415926.

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So when you have this um rank tensors from row splits method and you specify the row splits.

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The way this is done is simple.

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We start from zero and then we go to four.

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So you see when we have row splits start from zero we go to four.

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So we have 0123.

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See we have 3141.

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See that.

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And then let's, let's copy this and um run the code here where we specify the row splits and we go

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from 0 to 4.

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This simply means just like with a range we're going to have um zero.

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So we will take zero.

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Then we will take one, then we will take two.

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They will take three.

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So we go from 0 to 4 minus one.

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And that's why we have three one, four one which we have here.

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And then for the next we're going to have from 4 to 4 minus one is uh, basically telling us that we

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are not going to have any elements at this position.

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And that's why, you see, we have an empty list.

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Then we go from 4 to 7, 4 to 7.

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We would have four, five, four, five and then six because we're going from 4 to 7 minus one.

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So here we have 592592.

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Then we have 7 to 8.

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So we go from seven to to eight minus one.

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So we we are at seven and that's six.

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That's a year.

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Then finally we have um 8 to 8.

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So 8 to 8 minus one is um empty.

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So that's why we have this empty list.

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So that's it.

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That's how we read this row splits.

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Now for the row lengths.

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We'll take this off.

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For the row lengths.

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We simply, um, look at this four and say, okay, we're going um, one, two, three, four.

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That's it.

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The length.

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And then the next is zero.

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So we have an empty list.

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The next is three.

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So we take the next three.

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That's it.

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The next is one.

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We take this one and finally we have zero empty list.

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So we see that where the row splits or row length, we're able to generate the same output like well

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let's just let this be.

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That's fine.

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Then we go to value row IDs.

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So for value row ids we're going to say this one.

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This three we have right here is going to be part of the zeroth um row.

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So that's that's that's where this row ID comes from.

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This this three is going to be part from part of the zeroth row.

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So that's why we have three.

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One is going to be part of the zeroth row.

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That way we have one.

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And uh for the in the zeroth row um, four is going to be part and one is going to be part.

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So that's how we have this 314.

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And then if you notice we skip one.

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What this means is we have no element belonging to the um row one.

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And that's why we have an empty list.

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And then we now look at two this next three elements.

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This next three elements belong to row two.

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And then we have three meaning that this next element belongs to row three.

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And then we have no four.

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So um, there is no elements in the row four.

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Now specify the number of rows here is important because if we just if we just, um, take this off

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or let's just say if we have considering that we have four rows.

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Then you see that there.

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We do not have this this last, uh, empty list.

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But when you say we have five rows and that you don't see the four and then you don't see this four,

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it means that that's an empty list.

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So that's it for the from row stats.

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It shows us where the row starts from.

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So this this row this row starts from position zero.

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And then the next row starts from position four.

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So this is your start from position for the other row starts again from position four.

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So because these two start from the same position it means that the there is a row which is empty.

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And that's that's how we have this four this 592.

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Because the the next starts from position seven.

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So the six and then the other one starts from position eight.

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So here we have 01234567.

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But there's no position eight.

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So we have an empty list.

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Now we also have this row limits here.

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Instead we're looking at where the row ends.

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So the the first row is going to end at position four.

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It's going to end here 0123.

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Well when we say position four um it's actually four minus one.

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So it's 0123 ends right here.

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And then the next one is going to end at that same position.

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Four.

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And because it ends at that position four um we are going to make it an empty list.

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So that's why we have the empty list since it ends at the same position where the previous one ended.

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So, um, that's why we have the empty list now for the next one we have seven.

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So 01234567.

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Obviously seven minus one.

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Remember when we when we we generally have start start to end minus one actually.

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So when you say start end it's start it's actually start end minus one.

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That's why when you delete with this limits that's with the ends we take instead of minus one.

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So we get right up to this um position because this is 0123456 right up to position six.

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We stop there and we have this 592.

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Then we have eight.

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So we go zero one um 2345678 minus one.

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Obviously we have six.

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And then the, the finally we have the empty list because um, this tool uh match.

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So that's it.

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The next we have this uniform row length.

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So we want if we want to have a uniform row length then it simply means that all this will have the

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exact same length.

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So we have 314159 and two six.

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Well this is 2468.

187
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So let's say we had seven here.

188
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You see the well let's take the start end from here.

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Run that again.

190
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We have an error because the row splits here doesn't make sense.

191
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Without taking into consideration the fact that we have added an extra element.

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Run that again.

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We for that.

194
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That was fine.

195
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But we we still, um, have some errors here anyway.

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We don't want to, um, check that out for now.

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We just wanted to test out this last one.

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So let's comment all this.

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Let's just cut that out.

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Run that.

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And we're getting an error.

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All the uniform rolling has to be specified.

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So if you specify that you see now that we have the output as expected.

204
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So let's get back and take this off.

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Run that again.

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And that should be fine.

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So that's it for this section on Rack Tensors.

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See you in the next section where we will deal with the string tensors and variables.