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This video, I'm going to introduce some of the fundamental structures and principles of doing scientific computing in Python.

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Since the last couple of videos, I've briefly introduced Python's core structures and core data types.

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But a lot of our work is going to be working with an additional set of structures,

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a set of libraries known as scientific python or as the pie data stack.

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So learning outcomes of this video are to understand limitations of core python data types for data science to know.

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Three key rate data types particularly. Are we focusing primarily on the number high end the array?

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Also briefly introduce serious and data frame. We're going to see a lot more about those next week and the.

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To be able to perform basic vectorized operations. So in Python, we can write a list of numbers like this.

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So numbers equals I'm using the list syntax that we talked about in the earlier video.

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And I've got four numbers in here that I'm storing in this list and the variable numbers.

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Now. This seems like a perfectly natural thing to do.

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But remember, we said I said in the previous video that everything in Python is an object.

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So this isn't just a list of numbers. If we wrote this in Java or C, we would have an array of numbers where system array.

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And it's the stores, the numbers, one after the other. But in Python, that's not how it works because everything is an object.

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What our list stores is, it stores pointers to numbers.

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So we've got a list. And it's got a pointer to O point three and a pointer to nine point two, et cetera.

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So what we store is the list itself has these pointers, which are eight bytes each.

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And it has the. Numbers themselves.

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A flooding point. A double precision flooding point number takes eight bites. But the numbers aren't just numbers, they're objects.

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And every python object has at least 16 bites.

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This is all on a 64 bit system, has at least 16 bytes of header information.

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And so this whole list of numbers takes 144 bytes because we've the list has a header.

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It has pointers. The pointers are the objects that have headers in addition to the data.

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Also, the elements of a list can be different types. So when you go over the list, there's no guarantee that everything is a number.

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So if we if we want to sum our numbers, there is a python function called some that will double do a sum.

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But it's basically doing this. So we'll initialize a variable called total.

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Well, then loop over all of our numbers and we'll add each one to the total.

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And that's gonna make the total equal the total of the numbers. This works, it works just fine.

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And for a list of four numbers, it's completely fine. But Python.

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There's a couple of issues here. One python is Python. The language itself is rather slow.

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It's quite convenient, but it's slow and it's slow for two reasons.

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One is that it is interpreted the python code is compiled to an internal data structure,

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but then there's C code that runs in a loop interpreting that data structure.

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It's also dynamically typed. So remember, I said there's the the values and the numbers are in the list can have different types.

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We wrote a set of numbers there. But Python isn't guaranteed that they're all numbers.

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And so rather than saying, okay, I have a number, I'm going to keep adding it.

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What it says is I have a thing and I'm going to try to add it to the thing I already have.

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And it has to go look up how to do that, and it does that every time for each number.

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This is all very slow. Also, since it's pointers, if you've taken the computer architecture class.

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That may ring a few alarm bells for you because rather than just having an array of numbers which will be loaded into our cash very quickly accessed,

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we have an array of pointers and each pointer has to go off and look up the number in memory.

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And those numbers might be stored next to each other, but they might be stored all over the heap.

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We're gonna have cash misses which make these slow process even slower so we can write code like this and it works fine,

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but it's not an efficient way to do computation. And as we get to larger and larger data sets, you get a few hundred.

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You got a few thousand numbers. You're gonna be fine. When you've got a million numbers, when you have a hundred million or a billion numbers.

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Then things start to really get slow. So none PI is a python package that provides efficient data types for doing numeric computation.

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And NUM Pi underlies almost all of the rest of the scientific python and data science and machine learning for Python software.

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It has a data type called an NDA array. There's a variety of different ways you can create one,

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but here we're going to just create one using the array constructor and then we're going to pass it our list.

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So we're creating the list in this case. We are going to see later many ways to load arrays without having to go through a list.

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I'm just doing this here so I can demonstrate how the array works.

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But all the elements are of the same type in an array and they're also stored directly in the array.

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So this ENDI array, it's the stores, the floats, one right after each other.

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Eight bytes each. And so we don't have the indirection, three pointers. We don't have all of the overhead of storing all of these different objects.

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It's just storing the numbers, one right after each other. You can have an Endi array of objects and that's going to store the pointers.

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And that's useful in a few cases, especially for treating strings consistently with numbers.

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But it really shines when we're dealing with arrays of numbers for various scientific computing applications.

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So if you want to sum our numbers, we can use the num pi some function and it it's much shorter.

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A little python has a some function, as I mentioned, that we could have used, but also it's implemented in a compiled language.

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And when you have a num high array that's storing numbers, whether the integers,

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whether they're floating point numbers, it's stored internally in a format that's compatible with C or Fortran.

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And so a lot of num pi. Functions.

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What they're doing is they're passing the array to see code or Fortran code or

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C++ code that has a comp. loop that works on that data type and is able to very,

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very efficiently sum up those numbers. We don't have a cast mate cash issues from the indirection.

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We don't have the overhead of Python's interpreted code.

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We don't have the overhead of having to deal with the the elements of the array might be of different types.

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They're all the same type. We can work over them in in a loop, in comp.

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Machine code. So in general, don't loop. You can loop over a number high end the array.

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It's iterable just like a list. But in general, you don't want to do that.

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You want to set up your code so that num pi can do the looping for you.

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And effectively what we wind up using Python as is a scripting language to tell the underlying C, C++ and Fortran code.

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What to do.

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And the fact that Python is a slow language doesn't matter very much because the vast majority of our processing time won't be spent in Python.

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So I thought none pile. So has a feature called Vector Ization.

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There are a lot of operations that operate on an entire array at a time.

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So if I get it, I can create another array. The Linn's base function here.

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It. The land space function here.

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It creates an array of four values that are evenly spaced from zero to one inclusive.

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And then the plus operator here, remember, plus between two numbers is going to add it between two strings.

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It's going to concatenate them plus between two arrays requires them to be of compatible shapes.

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And it adds the the corresponding elements of the arrays to each other and returns a new array.

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So what if we have a bunch of number one array of numbers and we have another array of numbers?

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We want to add them together. We just add the two arrays and it does that addition again in a loop written in C or Fortran.

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And it does it very, very quickly.

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You can also add an integer or an integer or a floating point, single number to an array, and it'll add it to every element of the array.

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But this is the key point to be able to make scientific computing with Python fast.

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We setup our code and throughout. We're gonna be trying to set it up so that we use vectorized nation as much as possible.

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And we vectorized over as much data at a time as possible so we can allow the optimized loops and in num pi,

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in Pandas and Sai Pi and psychic learn to do the work and to put as much of the work as possible into those compile loops.

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So we're not spending a lot of time in slow python code. Each array has three key things.

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It has a data type called a D type, and that says what kind of elements are in the array?

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PI has data types for your standard integers of various sizes.

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Single and double precision floating point numbers. It also has D types for working with.

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Date. Date. Times. Strings and then storing arrays.

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That's where pointers to arbitrary python objects.

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The data type or the array also has a shape which is a tuple of integers that says how big the array is.

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The array may be multidimensional. So Endi array stands for N Dimensional Array.

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And it can be one, two, three, four, whatever dimensional. So if we have a 100 by 50 matrix, it's stored in a in a number PI in the array of shape.

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One hundred, comma 50. And then there's the data. It's stealth.

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That's the elements of the array. The data points themselves that are stored in the array.

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So then pandas, which we're going to see next week, builds on top of a raise with two new data types,

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a series is an array with an associated index that allows us to look up.

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So an ENDI array, like a python list is indexed using numbers starting from zero zero one, two, three, four, five.

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But sometimes for a lot of times we're gonna have some other natural index. If you've taken databases, it's equivalent to the primary key.

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So a series is an array with an associated index that might be other numbers.

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That might be strings. But some other way of accessing the points.

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It also has an efficient representations that you can have a series that's indexed zero through and minus one where N is the length of the series.

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And it does not take up a lot of space to do that. And then a data frame is a table where each column is a series.

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And they all share the same index. And we're gonna see those a lot because we load in a set of data points that's gonna be in a data frame.

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Now, an assignment zero, you're going to briefly see both of these data structures.

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I walk you through everything you have to do with them in assignment zero. And we're going to introduce them a lot more.

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Woomera's talking about how to describe data next week.

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But. Endi Arae, the number higher radiata structure is the fundamental core that all of these others are built on.

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The series augments it with an index. The data frame collects multiple series together with column names like a spreadsheet table.

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So we're still going to sometimes use Python native lists and loops.

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Oftentimes, it's going to be because for some reason, we need a list of arrays or data frames.

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Also, if we need to loop, if we have, say,

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20 input files that we need to put together to to to be our data set or we got different groups of data, we're going to loop over those.

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But the big thing we avoid doing is looping over individual data points.

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We load in a few hundred thousand records. They're going to be in a data frame.

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We don't loop over the rows of a data frame. If we can avoid it, because there's almost always a more efficient way to do that computation,

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that pushes a lot of it into the C and C++ code and Fortran code that underlies NUM, Pi, pandas, et cetera.

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So wrap up num pi provides efficient to ray data structures that are more memory compact's.

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They don't take up nearly as much space and they're also much more efficient to compute over.

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These are going to be the backbone of our data processing throughout the rest of the class.

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And we want to prefer vectorized operations that perform these loops in native comp. machine code whenever possible for a little bit of practice.

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I encourage you to take the example code from this from these slides and go and try them

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in a notebook so you can get a little more practice creating notebooks and running code.

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I will see you in class.

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