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Let's now dive into this new section on TensorFlow indexing.

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So let's suppose we have this tensor which we'll call tensor indexed.

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And we simply define this 1D tensor with some values.

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So we have

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24904567.

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And then let's run this.

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And then we say okay we want to get um let's say this value for now.

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To obtain this value for we are going to make use of its index.

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In general, in programming, the first index is zero.

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So this is going to be 012, three, four, five six and then seven.

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So if we want to get this foyer we're going to have to specify the index one.

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If we want to get two we have to specify the index zero and so on and so forth for the rest.

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So let's after running this that's after getting or creating this tensor index, we could simply print

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out tensor index and then specify an index.

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So let's say we we want to pick out the start.

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So ten tensor index three.

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We'll put this three in a square bracket.

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We run that.

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You see that it's going to give us the value zero which matches with this arrangement.

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Now if we say we want to get the last element or if we want to get the the first element, then we'll

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specify zero.

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So the zeroth index we run that.

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And you see, we should get two.

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See, we have two.

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Now, if you want to have the last element.

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So let's say we want to have the last element.

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We could pick seven or we could say we want to have tensor indexed.

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And then we say negative one.

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So when you specify negative one then you're specifying the last element.

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Um given that we know the, the the exact index for the last element, which in this case is seven,

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then we could specify seven.

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So let's run this and then see what we get.

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There we go.

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You see, we have seven and then we have seven.

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So that's how easy it is for us to, uh, obtain a value based on its position in the tensor.

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Now let's say we want to get a segment or part of this 1D tensor.

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Let's say we want to get this segment.

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We want to get 4904.

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Now this 4904, as we could see here matches with the indices 1 to 4.

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Or let's, let's let's pick another one.

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Let's say four.

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Um 90456.

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This matches with 1 to 6 you see.

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So let's just um, run this and see what we get.

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Tensor indexed.

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Um, and here instead of um, selecting each and every one of this, we would do one because remember

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one would pick out this elements 490456.

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Then we will specify the indices um one right up to six.

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But we are not going to say one, two, three, four, five and then six and then try to run that.

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You see, we get an error here.

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So what we are going to do is we're going to say we want to go from 1 to 6 by specifying or by putting

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between one.

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That's the start index and the end index a colon.

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So we just put that colon, we run that and there we go.

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You see we have this part which we wanted.

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That's 494490456.

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But when you look at the those outputs actually 49045 now what this tells us is actually when we say

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one right up to six, we're going from um, one, uh, let's, let's put it out this way.

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When we say one up to six, we're actually going from one right up to.

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Six minus one.

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So we're actually going from one right up to five.

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And so if we want to go or if we want to pick out 490456, then we'll need to say here that we want

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to go to seven.

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So, so such that we'll go from 1 to 7 and or we'll go from 1 to 7 minus one.

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That will be 1 to 6.

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So let's take that off.

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Run that again.

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And you can see now that we have 490456.

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So in general what we'll do is um, if we want to go from um a given start.

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So we'll do a start to the end.

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But instead of um, end, we'll do start to end minus one.

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And so in general, if you want to go from index start right up to index end, we should instead do

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tensor slice or tensor index.

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Um, start right up to end plus one so that uh when we do n plus one minus one it falls back at end.

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So that's it.

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Now you could, um, pause the video at this point and try to, um, do for example, or get this first

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tree, you see that you will have two, four, nine.

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That's going to be 0 to 2.

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Uh, hopefully you got the answer.

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Let's just get that done.

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So we'll do tensor tensor um index.

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And then we'll do because we're going from 0 to 2.

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So we'll do 0 to 2 plus one.

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You see let's run.

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That could take this off so that we could see the the the original tensor indexed.

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So let's take that off.

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There we go.

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You see um 0 to 2 plus one.

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You see we have 249.

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Now if we're starting from the very first index, if we're starting from the zeroth index then we must

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not put this.

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So, uh, taking the zero off already tells us that it's actually zero.

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So we could have the zero, or you may not have the zero.

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So you see, it's the same answer.

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Now, if let's say we want to get from zero right up to the end, what we'll do here, we will have

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three right up to seven.

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So we'll do three um, up to seven remember plus one.

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So we run that again.

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And you see we, we should have 0456 704 567 exactly as we expect.

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Now given that we're going right up to the end, we could also decide not to put anything.

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So if you're going or if you're starting from the, the first the zeroth index, you may not put anything.

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Um, if you're going right up to the end, you may also decide not to put any value.

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So let's run that and see what we get.

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You see, we have exact same, um, output 04567, the same as we would have with um, seven plus 104567.

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So that's it.

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Now if you want to go right up to the last but one value, you could say we're going from three right

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up to minus one.

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So remember when we specified, um or when we had tensor tensor indexed um and then we specified minus

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one.

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The value we got was seven which was the last value.

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But when we um specify or when we go from a start index to that end index and we specify this minus

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one, obviously we'll go from start to end and the end will instead be the the value before the actual

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end.

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So it's just like what we've seen already where if we're going from let's say um, three let's take

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the start off.

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If we're going from three to to seven, then what we will actually get by doing this, if we just took

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3 to 7, what will actually get will be 3 to 2 six, you see.

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So when we do three two negative one is the same as going from 3 to 7.

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So that's actually um 3 to 6.

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So when let's run this you see we should get 0456.

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So that's it.

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Now if we want to get to the second to the last, that's 3 to -2.

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You see now we have 045.

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Then we could do third to the last we have or we should have zero four.

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So on and so forth.

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So that's it.

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Then another thing we could do is let's say we let's get back to say six.

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And the thing we could do is we could, um, get these values and steps.

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Let's take that from the beginning to the, to the, to the seat, or let's even take the seventh value.

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So let's go to seven.

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So if we run this we have from 0 to 7 then we have 2490456.

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That's fine.

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Now we could um get this values in steps of two.

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So if we put two see specifying this two would make us get two.

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And then we skip this one.

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Nine will skip this one four we'll skip this one and then six.

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So let's just run this let's print this out here.

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Tensor indexed.

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Tensor indexed and let's say goes 0 to 7.

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Let's write out explicitly 0 to 7.

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And then here we have 0 to 7.

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Bear with steps of two.

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So let's print this out.

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Let's print that out.

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There we go.

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So as you could see we have 2490456.

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But now uh when we specify steps of two we'll take two and then we'll skip four.

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We get nine.

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See that's nine here.

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And then we skip zero.

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We get four.

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Does four year and then we skip, um, six.

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All right, I will skip five.

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And then we get six and that's six there.

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So that's it.

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So essentially this is the same as um having one.

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So not skipping any value.

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So that's it.

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We've just looked at indexing with 1D tensors.

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So let's take an example of a two dimensional tensor.

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So here we have again tensor um indexed tensor indexed.

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And then we have this 2D tensor.

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We simply fill out those values.

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So we have 23456.

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And then we have say 90421.

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And then we have 001 or well 000017 um, zero.

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Okay.

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So we have this tensor which turns out to be a five or rather three by five tensor 2D.

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So we have to add this square bracket.

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There we go.

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We add the square bracket here and at this position.

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So this is our 2D tensor.

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And then we want to get a specific value.

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Now let's suppose that we want to get the value or this value nine at this position.

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So what we'll do is we'll start by saying um how many rows do we have.

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We have one two, three.

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And what we'll do is we'll locate the row in which this nine is found and the column.

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So this is the first row second row and third row.

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While this is the first column that's 290 first um colon second colon, third colon fourth colon and

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fifth column.

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Now this nine is found on the second row.

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But since we start counting from one from zero we have the zeroth row and the first row.

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So here we'll say we want to have tensor tensor indexed.

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And then we'll specify we want to have one.

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So index one because this is zero this is one.

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And then this is two.

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Now for the colon we have colon zero because this is the first colon or this is the zeroth colon or

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colon with index zero, colon index one, index two, index three and then index four.

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So since this is index zero we're going to have zero.

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But we separate this tool with a comma.

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So unlike when the 1D where we didn't separate with a comma because obviously it's one dimensional.

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Now we have two dimensions.

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So the that to the left of the comma is the first dimension.

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That to the right of the comma is the second dimension.

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Um essentially this is the rows uh to the left obviously rows and then columns.

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So let's run this and then see what we get.

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See we have um this tensor and the value in this tensor is nine.

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So that's it.

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So you see we obtain nine.

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Now let's say we want to get this two right here.

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So it will be the same row but different column.

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So this is 0123.

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So here we replace zero with three.

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We run that again and we should get two.

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So that's fine.

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Now let's suppose we want to get um this 042.

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Or let's say we want to get 170.

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Let's say we want to get this 170.

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Now um, unlike here where we had a single value.

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So we just pick out a specific index.

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Now we have a range.

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So just like what we are seeing with the 1D tensor where we could pick out the range.

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Now we're also going to pick out this range of values.

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So we have 170 which we want to pick out.

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What we'll do is we'll go again zeroth row first row second row.

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So here we pick second row.

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There we go.

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So up because all these values fall in the second row.

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We just pick the second row.

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And then for the columns because the values we want to pick um fall in a range of columns that this

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is zero, one, two.

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This is where one starts.

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So colon two is here we have two.

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Remember this is after the comma to the right of the comma.

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And then we go from two right up to this colon.

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So we have 234.

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Now again if we want to get to the fourth column then we will do four plus one just as we had seen with

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a 1D.

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So let's run this and then see what we get.

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You see we have 170.

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But if we did um two four we would have only one seven.

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So let's, let's have that four plus one and that's fine.

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So that's how we obtain this.

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Now let's say we want to obtain just six and one.

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So we want to obtain six one.

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Now in this case.

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In this case we would have um six one.

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So this six belongs to zero row zero one belongs to row two.

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So we want to go from row zero right up to row two.

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But because we want to get the specific value we'll say two plus one just as we had seen already.

241
00:15:17,490 --> 00:15:18,690
So two plus one.

242
00:15:18,690 --> 00:15:20,280
And then we have the comma.

243
00:15:20,280 --> 00:15:21,780
So this is the first.

244
00:15:21,780 --> 00:15:23,010
This is for the row.

245
00:15:23,010 --> 00:15:24,810
And then this is now for the columns.

246
00:15:24,810 --> 00:15:26,730
So the one to the right for the columns.

247
00:15:26,730 --> 00:15:30,150
Now we are having this values on the same column.

248
00:15:30,150 --> 00:15:34,050
So we'll just simply say 01234.

249
00:15:34,050 --> 00:15:35,670
So we'll specify four.

250
00:15:35,670 --> 00:15:38,160
Run that and there we go.

251
00:15:38,160 --> 00:15:42,750
You see we have 610 because we want to have only six and one.

252
00:15:42,750 --> 00:15:45,060
We are going to take off this one from here.

253
00:15:45,060 --> 00:15:52,200
Because going from 0 to 2 is simply simply having zero and then two minus one which is one.

254
00:15:52,200 --> 00:15:53,940
So that's exactly what we want to have.

255
00:15:53,940 --> 00:15:54,960
So no need.

256
00:15:54,960 --> 00:15:56,130
Um, adding plus one.

257
00:15:56,130 --> 00:15:57,660
That was actually an error.

258
00:15:57,810 --> 00:16:01,080
We would have added plus one if we wanted to get all these elements.

259
00:16:01,080 --> 00:16:02,280
That's 610.

260
00:16:02,280 --> 00:16:05,910
So let's run this again and see what we obtain.

261
00:16:05,940 --> 00:16:07,200
See we have six one.

262
00:16:07,200 --> 00:16:09,810
Now let's say we want to have 610.

263
00:16:09,810 --> 00:16:16,110
Actually if we wanted to have 610 instead of doing from 0 to 2 plus one, obviously this will give you

264
00:16:16,110 --> 00:16:17,160
610.

265
00:16:17,160 --> 00:16:21,960
We could take this off and just um, put the column.

266
00:16:21,960 --> 00:16:28,560
So now by putting the column, what you're saying is you want to work with all the rows.

267
00:16:28,560 --> 00:16:33,930
So here we work with all the rows, which is obviously the same as going from 0 to 2 plus one.

268
00:16:33,930 --> 00:16:37,470
So we run this and see what we get.

269
00:16:37,470 --> 00:16:39,510
Say we have 610.

270
00:16:39,510 --> 00:16:40,830
We could do the same for the columns.

271
00:16:40,830 --> 00:16:42,120
We could decide to.

272
00:16:42,120 --> 00:16:46,080
Obviously if you say we want to work for work with all the columns and all the rows, then you would

273
00:16:46,080 --> 00:16:48,660
have the original tensor.

274
00:16:48,660 --> 00:16:57,150
But if we pick out a specific row, let's say the row one, um, row one, or let's say we want to go

275
00:16:57,150 --> 00:16:59,880
from 0 to 1, let's run that, see what we get.

276
00:16:59,880 --> 00:17:02,700
You see we have two, three, four, five, six.

277
00:17:02,700 --> 00:17:08,490
We have this because obviously going from 0 to 1, it's like going from 0 to 1 minus one, which is

278
00:17:08,490 --> 00:17:10,800
still uh picking only the zeroth row.

279
00:17:10,800 --> 00:17:12,870
So we have two, three, four, five, six.

280
00:17:13,200 --> 00:17:15,810
Um, that's because we've picked all the columns.

281
00:17:15,810 --> 00:17:19,980
Now, another way of picking all the columns is by working with three dots.

282
00:17:19,980 --> 00:17:23,670
So if we do three dots we should get the exact same output.

283
00:17:23,670 --> 00:17:26,940
You see here we have 23456.

284
00:17:27,120 --> 00:17:31,920
Now again instead of picking or going from 0 to 1 we could just say zero.

285
00:17:31,920 --> 00:17:35,310
We run that again and we have two, three, four, five, six.

286
00:17:35,310 --> 00:17:36,270
But there is a difference.

287
00:17:36,270 --> 00:17:38,460
Let's let's put this side by side.

288
00:17:38,460 --> 00:17:43,140
So let's print out tensor indexed.

289
00:17:43,140 --> 00:17:47,760
And then we say 0 to 1.

290
00:17:47,760 --> 00:17:50,280
And then we have all the columns.

291
00:17:50,610 --> 00:17:52,680
Then yeah let's just print this out.

292
00:17:53,430 --> 00:17:54,990
So we print this out.

293
00:17:54,990 --> 00:17:57,180
And then we also print out the shape.

294
00:17:57,180 --> 00:17:58,770
So well the shape is given.

295
00:17:58,770 --> 00:17:59,970
So let's just run this.

296
00:18:00,690 --> 00:18:01,650
There we go.

297
00:18:01,650 --> 00:18:09,210
You notice that although we have the exact same values peaked, they the output has two different shapes.

298
00:18:09,210 --> 00:18:12,810
So the output of this first one is different from the output of the second one.

299
00:18:12,810 --> 00:18:20,220
And this is simply because when you pick out zero like this you are selecting a specific row.

300
00:18:20,220 --> 00:18:27,990
And so now we since you've picked out a specific role you are dealing with a 1D tensor.

301
00:18:27,990 --> 00:18:30,240
And that's why the output here is 1D.

302
00:18:30,750 --> 00:18:38,850
But when you select a set of rows, you still having to do with a 2D tensor because you this zero one,

303
00:18:38,850 --> 00:18:40,980
although it's picking only this um row.

304
00:18:40,980 --> 00:18:44,700
In this case it would have picked this, um two.

305
00:18:44,700 --> 00:18:52,560
So when you're dealing with a range there we have a 2D tensor because we this dimension still counts.

306
00:18:52,560 --> 00:18:57,450
Whereas when you pick a specific value then you're dealing with a 1D tensor.

307
00:18:57,450 --> 00:19:00,810
Now let's suppose we want to pick 4542.

308
00:19:00,810 --> 00:19:03,570
So we want to pick four five and then four two.

309
00:19:03,600 --> 00:19:06,420
What we'll do in this case is simple.

310
00:19:07,270 --> 00:19:10,810
You could pause the video and try to, to to reflect on that.

311
00:19:10,810 --> 00:19:16,030
But simply what we'll do is we will have tensor indexed.

312
00:19:16,030 --> 00:19:21,100
And then because we want to have four, five, four, two which belong to column zero.

313
00:19:21,100 --> 00:19:26,920
And column one will simply go from zero right up to one, or rather right up to two.

314
00:19:26,950 --> 00:19:28,810
Because we are we want to have zero.

315
00:19:28,810 --> 00:19:31,660
One is actually one plus one.

316
00:19:31,660 --> 00:19:33,610
That's it, which is two.

317
00:19:33,610 --> 00:19:36,340
So we go from zero right up to two.

318
00:19:36,340 --> 00:19:41,800
And then for the columns we go from this is zero, one, two, three.

319
00:19:41,800 --> 00:19:44,530
We're going from two right up to three.

320
00:19:44,530 --> 00:19:49,630
So we'll have 2 to 3 but obviously three plus one which is four.

321
00:19:49,750 --> 00:19:52,390
So let's run that and then see what we get.

322
00:19:52,390 --> 00:19:56,770
You see we have 4542 exactly as we expect.

323
00:19:57,370 --> 00:20:03,970
After exploring the 2D tensor indexing let's look at the 3D tensor indexing.

324
00:20:03,970 --> 00:20:07,330
So let's suppose that let's first of all run this.

325
00:20:07,330 --> 00:20:13,000
And then we suppose that we want to obtain this value nine which we have right here.

326
00:20:13,030 --> 00:20:14,500
Let's rearrange this a little.

327
00:20:14,500 --> 00:20:16,540
So um it's clearer.

328
00:20:17,170 --> 00:20:18,550
There we go.

329
00:20:18,550 --> 00:20:23,800
We want to have that value of nine um, which is found at this position.

330
00:20:23,800 --> 00:20:29,530
So first of all we have tensor tensor indexed.

331
00:20:29,530 --> 00:20:37,210
And then um as with the 2D where we had a single comma separating the two dimensions here we would have

332
00:20:37,210 --> 00:20:40,930
two commas separating the three dimensions.

333
00:20:40,930 --> 00:20:44,410
So we have the first, second and third dimension.

334
00:20:45,040 --> 00:20:55,060
Now if we print out this tensor indexed let's create a new cell right here and print out tensor indexed.

335
00:20:56,020 --> 00:20:58,960
You would find that let's get let's get a shape directly.

336
00:20:59,170 --> 00:21:03,640
You would find that its shape is four by two by three.

337
00:21:03,640 --> 00:21:09,430
So here we have four blocks of 2D tensors.

338
00:21:09,430 --> 00:21:12,070
There's the first there's the second there's the third.

339
00:21:12,070 --> 00:21:13,390
And this is the fourth.

340
00:21:13,390 --> 00:21:16,330
So here we have this four different blocks.

341
00:21:16,330 --> 00:21:19,390
Now nine belongs to the fourth block.

342
00:21:19,390 --> 00:21:25,060
And so if we want to obtain nine all we need to do is let's take this one off.

343
00:21:25,210 --> 00:21:32,830
All we need to do is come right here and specify that we want this, um fourth block.

344
00:21:32,830 --> 00:21:37,480
So this is 0123.

345
00:21:37,960 --> 00:21:39,760
So here we have three.

346
00:21:39,760 --> 00:21:46,870
And then once we pick out this um block that's this fourth block which is three, because we start counting

347
00:21:46,870 --> 00:21:51,520
from zero, we are then going to select a specific row.

348
00:21:51,520 --> 00:21:53,470
So this is the zeroth row.

349
00:21:53,500 --> 00:21:54,880
This is the first row.

350
00:21:54,880 --> 00:22:00,400
Or we could say first row second row knowing that we're counting from index zero um onwards.

351
00:22:00,400 --> 00:22:02,620
So this is zero.

352
00:22:02,620 --> 00:22:04,240
And this is one.

353
00:22:04,240 --> 00:22:08,200
Now nine year belongs to this um row zero.

354
00:22:08,200 --> 00:22:10,420
So here again we will say zero.

355
00:22:10,420 --> 00:22:19,420
And then for the columns this is the zeroth column or this is the first column index zero, second column

356
00:22:19,420 --> 00:22:22,480
index one and third column index two.

357
00:22:22,510 --> 00:22:24,310
So 012.

358
00:22:24,340 --> 00:22:25,870
So nine belongs to two.

359
00:22:25,900 --> 00:22:29,860
So let's um have two right there and then see what we get.

360
00:22:29,860 --> 00:22:31,930
So you see here we have nine.

361
00:22:31,930 --> 00:22:39,400
Which makes sense because um we've actually picked the exact position where nine is located.

362
00:22:39,400 --> 00:22:43,210
Now let's say we want to have um 219.

363
00:22:43,210 --> 00:22:49,990
If we want to have this 219, then it will suffice to maintain this three because 219 belongs to this,

364
00:22:50,140 --> 00:22:51,730
uh, block with index three.

365
00:22:52,180 --> 00:22:56,650
Um, and then we'll say we want to pick, um for the rows.

366
00:22:56,650 --> 00:23:01,540
We want to pick the zeroth row, but for the columns, because we want all the columns because it goes

367
00:23:01,540 --> 00:23:09,790
from zero, one, two or from 0 to 2, we are going to say we could go from 0 to 2 plus one go run that

368
00:23:09,790 --> 00:23:11,380
we should have two, one, nine.

369
00:23:11,380 --> 00:23:14,620
Or we could just simply say one to have all those values.

370
00:23:14,620 --> 00:23:16,870
We run that and that should be fine.

371
00:23:16,870 --> 00:23:18,850
See we have 219.

372
00:23:18,850 --> 00:23:28,030
Now that we have this 219, we could decide to pick out, um, let's say 214 minus three.

373
00:23:28,030 --> 00:23:36,940
In that case, again we're going to have all the rows because 214 minus three contains um, all the

374
00:23:36,940 --> 00:23:40,810
rows um are taken into consideration when picking these values.

375
00:23:40,810 --> 00:23:48,970
And then we're going to go from the zeroth column, zeroth column right up to the second to the last

376
00:23:48,970 --> 00:23:49,300
column.

377
00:23:49,300 --> 00:23:53,560
So we go 012 because obviously this is going to be two minus one.

378
00:23:53,560 --> 00:23:54,850
So let's run that.

379
00:23:54,850 --> 00:23:58,930
And then you see we have 214 minus three which makes sense.

380
00:23:58,930 --> 00:24:01,930
Or we could just simply say um minus one.

381
00:24:01,930 --> 00:24:06,610
So if we do that we should have 214 minus three now.

382
00:24:06,730 --> 00:24:13,420
Now let's suppose that for each and every block we have right here, that's for all these four blocks,

383
00:24:13,420 --> 00:24:18,370
we want to get the elements which lie on the second column.

384
00:24:18,400 --> 00:24:24,370
In that case, what we'll do is we're going to take or we're going to pick out all the different blocks,

385
00:24:24,370 --> 00:24:30,040
and then we'll pick out all the rows, and then we'll say, I want to get the elements in the second

386
00:24:30,040 --> 00:24:30,460
column.

387
00:24:30,460 --> 00:24:31,630
So let's run that.

388
00:24:32,570 --> 00:24:34,280
Are we getting an error?

389
00:24:35,270 --> 00:24:39,170
Yeah, we have multiple ellipses and slice spec not allowed.

390
00:24:39,170 --> 00:24:43,430
So we are not allowed to have multiple ellipses as we've just done.

391
00:24:43,430 --> 00:24:47,630
We just have this like this, run that and there we go.

392
00:24:47,630 --> 00:24:54,170
You see that we're going to pick now all the columns um, or all the columns of index two.

393
00:24:54,170 --> 00:24:58,160
So here we have C zero minus one.

394
00:24:58,160 --> 00:25:00,080
Here we have zero two.

395
00:25:00,110 --> 00:25:01,160
You see that here.

396
00:25:01,640 --> 00:25:03,470
Here we have zero zero.

397
00:25:03,500 --> 00:25:04,610
You can see that here.

398
00:25:04,610 --> 00:25:07,040
Here we have 932.

399
00:25:07,070 --> 00:25:08,750
You could see that right here.

400
00:25:08,750 --> 00:25:12,950
You could also just have only semicolon and run that.

401
00:25:12,950 --> 00:25:14,690
And you should have the exact same output.

402
00:25:14,690 --> 00:25:19,400
So that's it for this section on indexing we are going to move to the next section where we will work

403
00:25:19,400 --> 00:25:21,440
with math operations.