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Multidimensional Arrays
10:07Arrays can have multiple dimensions, let's see how to create and use them to our advantage.
Multidimensional is such an [LAUGH]
intimidating sounding word, isn't it?
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It sounds futuristic and outer spacey,
I mean what does many dimensions even mean,
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especially in the context of an array?
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Well, the answer is kind of boring
in comparison to how cool it sounds.
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If you think about what we've been
doing so far with our arrays,
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we've basically been building a container
where each slot represents something.
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For instance,
in the grade point average example,
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each element represented
a single year of school.
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So we could say that this
is the year dimension.
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Now let's imagine that we wanted to track
every student in my graduating class.
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Now of course, we could add
a separate variable for each student.
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But wouldn't it be nice to store
that all in the same variable.
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Well, you can.
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What you do is you add a new dimension,
the Student dimension.
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Now, we essentially have rows,
where each row represents a student, and
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each column here represents a year.
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And would you look at this?
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We have two dimension.
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And really, a two dimensional
array is just an array of arrays.
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Right, I can access the student I want,
like the third one here, and
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then I could select which year I want.
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I want the sophomore or second year.
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There is a term that is used to discuss
how many dimensions an array has.
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This is called rank.
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So this GPA example is currently rank 2.
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Now, fun fact about
two-dimensional arrays,
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you remember how single dimension arrays
are often referred to as a vector?
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Well, a two-dimensional array
is referred to as a Matrix.
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>> [SOUND] Whoa.
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>> Now, remember these are called
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ndarrays.
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And again, the n represents any number
because you can have as many dimensions
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and ranks as your heart desires.
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Like we could add another
dimension of School,
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where each school had
all of their students.
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So that's 3D, and most likely you'll need
[SOUND] to wear these glasses to see that.
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Sorry, that's a bad joke.
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But see, now we have an array.
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I'll choose the first element, and
that is our array that contains arrays.
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All right,
not as intimidating as it sounds.
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But I bet you feel like you need some
practice to fully grok it, right?
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Let's do it.
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So first, let's review our notes.
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So here's mine.
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About data types.
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So by choosing the proper data type you
can greatly reduce the size required to
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store objects.
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Remember we saw that and
again, I put the link here
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just to jump off the data type page
whenever we need it to review later.
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Think that's handy bookmark, sort of.
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Data types are maintained by wrapping
values in scalar representation.
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Remember when we pulled that
value out of the array,
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it still knew the size that it was even
though it kinda looked like it didn't and
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it was a singular value, which is scalar.
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Np.zeros is a handy way to create
an empty array filled with zeroes,
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like we did right here.
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So we did this and we pushed the data
type of the u unsigned integer 16.
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Awesome.
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Okay, so let's return to our gpa example,
which is here.
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I'm gonna click in here, put it in
command mode, and add one below, so b.
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And what I'd like to see
here is a new array.
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We will make students_gpas, so
it's a list of students GPAs and
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we'll make a multidimensional array.
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So I'll say np.array and
we're gonna pass in an iterable again and
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we are going to make this
iterable just be a list of lists.
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So first we'll push mine through here so
we have this.
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I'll Copy that, paste this here.
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And I'm gonna do a comma, and
I'm gonna add another list.
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So let's add another student,
her name is Vlada.
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She struggled at first.
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English was not her first language but
then she totally nailed it.
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So she had a 3.2 her first year.
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And then she started
getting a lot better 3.8.
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And then by the end was just sailing,
4.0, 4.0.
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Awesome, and let's see, one more.
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Let's add Quasey.
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He was on fire all through school.
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He started with a 3.96.
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He got a 3.92 his sophomore year and
he ended out with 4.0, 4.0.
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Awesome.
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So let's make sure that we grab
the right data type for this.
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So right now,
the second parameter we're leaving empty,
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let's say np., and then,
what do you think that was?
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Let's see,
let's use this link one more time.
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We'll click this,
I already have it open here in the tab so,
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this data type, let's say we, is that
float64, we definitely don't need that.
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We should be totally fine with just
this float 16, so let's use float16.
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So we will build our
student GPA with a float16.
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And then let's that a look at it too.
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We'll say, students_gpas.
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So, this is really just an interval.
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It's a list of lists.
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So each element of that
list is another list, okay.
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List of lists, multidimensional list.
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So let's go ahead and take a look at it.
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Awesome and it looks exactly like we want.
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It's an array of float16 and
it has all of the values there.
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Now, it's possible that we would have
run in to a bit of a precision error but
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we didn't.
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We haven't run that here but just in
case because we did set a data type.
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It might change precision.
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Check the teacher's notes for
more information on that.
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So we now have a two dimensional array,
right?
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We have rows and
we also have columns, right?
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We have these columns here.
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You can always look at the property on
an array to see how many are there and
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we have .ndim for number of dimensions.
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You see that it has two.
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If we wanted to see how many
elements are in each dimension,
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we can actually view that.
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That's exposed using
what is known as shape.
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So you can say students_gpas.shape.
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This is saying, three by four, and
there are three rows and four columns.
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Each element in this tuple
represents the length of each axis.
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So that's another term that you'll
see used to describe dimensions.
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The plural for axis is axes, not like what
Paul Bunion had a bunch of, he had axis.
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This axes, A-X-E-S.
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So in our case, the first axis is
students and the second axis is years.
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Axes are zero-based, so
axis zero is 3, and axis one is 4.
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Now, one thing that might bite
you if you aren't careful,
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is that if you use the size property,
so if we say students_gpas.size,
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it's gonna tell you all of them.
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Not just the first dimension.
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If you wanna see just the first dimension,
you can still use len,
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and that will just show you
how many students there are.
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Three.
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There's also a property that we
can peek at called item size.
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So again, students_gpas.itemsize, and
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that shows you how many bytes
are being used for each item.
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Which means now we can
calculate how much space we're
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taking up if we did students_gpas.itemsize
times student_gpas.size.
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We're taking up 24 bytes.
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Which lines up with exactly what you would
see if you were to use the whos command.
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So let's say whos, and
then if you follow a type ndarray,
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it will show us all the ndarrays.
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So here's the 4 by 4,
this is the singular one that we had and
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look that was 32 bytes and here is 3 by 4
and it's 24 bytes, it's already smaller.
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Data types savings for the win, right.
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This whos is a Jupiter Notebook special
command, but you could also grab this
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information and any information of a numpy
object using a function named info,
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np.info, and we can pass in students_gpas.
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And if we take a look, we could see,
there's the shape, 3 by 4,
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there's our item size, and here's
the type, and some more information.
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All right, let's access some things.
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So if I wanted to get access to the third
student's record, I could just do this.
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I could say, students_gpas [2].
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And that is the third student.
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That's Quasey's grades.
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And see how that returns me an array.
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So of course if I wanted to,
I could just chain off of it, right,
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because it is an array.
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Let's say I wanted to get the last year
here, so I could just get this last year,
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this last four here.
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So I could say, students_gpas,
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[2], so
that will get us the student there, and
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then I just get [3], and
it should return back 4, awesome.
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This is just one way of accessing this
value in the two-dimensional space, and
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remember, this 2D, or
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two-dimensional example is
synonymous with the term matrix.
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Whoah.
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Sorry for making mutlidimensionality
seem a little less futuristic
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than you probably anticipated.
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It still sounds cool, though, right?
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So make sure to drop it when
someone asks what you're learning.
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Just coding in a couple of dimensions.
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I do hope it's pretty straightforward, and
we'll get lots of practice working in in
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dimensions through
the rest of this course.
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Now that you've got a handle
on the main data type and
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most of its terminology, let's go
ahead and wrap up this first stage.
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We'll go deeper in the remainder
of this course, and
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I'll show off some great shortcuts,
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as well as how to use these powerful
multidimensional arrays to your advantage.
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For now though,
why don't you make sure you reflect a bit
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on multidimensional arrays and
add some thought to your notebook.
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And please remember to take a break and
let all your learning sink in.
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You deserve it.
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See you in a bit.
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