[MUSIC] How would you store a page of text? As we've seen, two-dimensional arrays are not a good way to do it, because each row, that is each line, would have to be the same length. Storing it in a single string is not appealing either because you can't easily access individual lines. We could store each line in a separate string but then how can we group these lines together? Wouldn't it be great if we could create a vector of special objects that would link somehow to each one of these strings? Well it turns out that we can. But what are these special objects? Well, they're called pointers. To understand what pointers are, we have to take a step back. Each variable be it a scalar, a vector, an array, a struct or anything else is stored in the memory of the computer. And each memory location has a unique address. You can think of a computer memory as a very, very long vector of memory cells, and you address the cell as the index, that is a positive integer starting with one. Consecutive addresses indicate neighboring memory cells. And a pointer is simply a variable that stores a cell's address. To make it just a tad bit more confusing though, MATLAB calls a pointer a cell. And MATLAB doesn't allow you to treat a cell as if it were a number. There are strict rules on what you can and can not do with cells. But those rules are for your own good, because it would be very easy to shoot yourself in the foot with pointers repeatedly and painfully, if you could say, do arithmetic on them or whatever you wanted to do with them. Nevertheless, the cell is a very powerful and very useful data type. Because cell arrays like structs, let's you group heterogeneous data together, which is what we wanted to do with strings from a page of text. But unlike structs, cell arrays can be indexed with numbers and partly because of that, while they're a bit trickier, they're used more frequently than structs. Since cells is a new concept, it shouldn't be surprising that there are new syntax rules. To access the object that a cell points to, you need to use braces, also called curly braces or curly brackets. To actually use cells, let's solve our original problem by using them to create a variable that stores multiple lines of text. Okay, I've got a script over here named cells of text. It'll give us what we want. This script is divided into two sections. This is the first section, says The Ultimate Legend of Big John. And let's see what it does. First line sets the first element of page to the string You could find him on the field almost any day. These braces here tell you that this is going to be a cell, so this value will now be pointed at by the first element of page. Second one set to the string, Tall, dark hair, and eyes of steel gray. The third one, They say he pulled a frisbee about half a mile. You see this pair of single quotes here and you'll remember that two single quotes together inside a string translate into one single quote. On the fourth and the fifth line you see another one of those pairs, And when he'd stick it in the corner you could almost catch a smile on Big John. Hm, must be quite a guy. Anyway, let's run the first section. Course you remember how to do that, you just click Run Section. Don't see anything happen because every single one of these assignment statements has a semicolon at the end of it. But something must have happened and I think page should have gotten the value, let's check that out with the function whos. Sure enough, it's a one by five array, in other words a vector, a row vector of type cell. We can access individual elements of page by using braces. There's the first element. You could find him on the field almost any day. Let's look at the fifth one. What's in five, well it's pointing at the string On Big John. And to double check whos, let's get the type of page with the class function. So this of course means that each element of page is of type cell. But as we said, each element of page points at something else that can be of varying size and or type. In this case the sizes of the elements are different. Let's look at a couple of them. Let's look at the first one. Notice I've put the braces here. That means we're going to access the thing that the first element of page is pointing at. And it's type is char. Of course, we knew that. It's a string. Let's look at the size of it. Well it's a 47 element row vector. Fourth element also points to a char. And the size of that char is 1 by 65. It's a 65 element row vector. So we managed to put lines of text of different lengths into one homogenous array of cells, which is what we set out to do. The second section up here, this one, shows you how you might use this cell array to print out the lines using fprintf. It goes to a new line here. Then it loops through the five indices of page here, and prints each element here using the percent s format, and putting a new line after each one. And then it ends with an extra new line. Let's run it. I click anywhere in it. Turns it yellow. And I come up here and I click Run Section. And here's what we see. You could find him on the field almost any day. Tall, dark hair, and eyes, all the way down to Big John, with a space above and below. As you might have guessed, cells are not just for strings. Letâs create a cell array that refers to truly heterogeneous data. First we call the cell function to create a blank two by three cell array, where blank means that each element contains the address of the empty array. Each element is said to point to the empty array as indicated by the arrows. In this next assignment statement, the use of braces instead of parentheses for indexing the array element indicates that the address of the object on your right is assigned to that element instead of the object itself. In this case, the function pi produced that object. The scalar, which was then stored by MATLAB in a newly allocated memory location. The address of that location is then assigned to the element 2,1 of the cell array p, thus element 2,1 now points at pi. It's important to take a minute here to emphasize that even though p now refers to heterogeneous data Namely, an empty array and a scalar, which are of two different types. The array p itself is still homogeneous. The MATLAB cell array model allows individual elements to point at different types, but the elements themselves are all of the same type, and that type is cell. The next command is p, left brace, 1, 1, right brace, equals int8 minus 17. Again, following the cell model, as with the previous assignment statement, the braces on the left mean that the address of the object on the right is copied in to the element 1,1, not the object itself. And as before, the address refers to a newly allocated location in memory. In this case, MATLAB has stored minus 17 at that location, encoded as an int8. And we can do more than empty arrays that double in an eight bit integer. Here MATLAB allocates a new location in memory to hold the string Awesome and then makes the element of p on row 2 column 2 point to it. We show the pointer directed at the first character of Awesome because the address used for a vector or a ray or anything that occupies multiple cells in memory is that of its first element. Next we create a three by two array of doubles and assign its address to the element 2, 3 of p. Again, we show the pointer aimed at the first element, element 1,1. But, in fact, it makes no difference what element it points at, because MATLAB doesn't allow you either to look at the numeric address or to change it. As we mentioned earlier, MATLAB maintains strict control over its pointers. In this statement, braces are used differently. When they're not on the left side of an assignment statement, braces indicate that the object pointed at by the element is to be retrieved instead of its address. Thus in this case, p {2,3}, retrieves the 3 by 2 array pointed at by element 2,3 of p. That arrays then input to sum. And sum does what it does with any array it receives. It adds up each of the array's columns and returns the sums in a vector. From this point forward, the process is the same as for the other assignment statements above. MATLAB allocates a new memory location to store the vector from sum, and the address of that location is copied into the element 1,3 of p. Notice that we use braces twice in this last assignment statement. On the right, we use them to retrieve a value. And on the left, we use them to store a pointer. All of these uses of braces are necessary. If we were to try using parentheses, MATLAB would complain you know, in red letters. The lone cell that still points to the empty array is changed next. We create an inf of type double by dividing 1 by 0. MATLAB stores the result in memory, and then braces are used to point element 1,2 at it. With that we have a nice little cell array that refers to two types of scalars, one string, a double vector, and a double array. And it might show more clearly how it can be possible in MATLAB to construct an array that refers to a set of data of multiple types, despite the fact that MATLAB, like almost all other languages, supports only arrays whose elements all have the same type. And what is the type of p's elements? Well, we can call the class function to answer that question. And the answer is cell as expected. But if we use braces to retrieve the object pointed at by one of p's elements, in this case element 1,2, then the class function tells us the type of that retrieved object. In this case, the object is the scalar inf, which happens to be of type double. But if we use normal parentheses when indexing that same element of the cell array, then we're referring to the cell itself and not the data that it points to. So the class function returns cell. That's the difference between using parentheses and braces when it comes to cells. Well, here's a tricky one, we use both braces and parentheses, but it's all good. First p {2,3} retrieves the object that the cell at index 2,3 of the cell array points to. And that object happens to be an array of doubles. In the parentheses with the indices 3 and 2 inside them are used to index into that array. In this array indexing works as it normally would. It retrieves a second element on the third row which is 12 as shown in the figure, nice. Now let's see some more examples. Most important concept to remember is the distinction between a cell and the object it points to. MATLAB uses various notations to indicate that the elements of the cell array are not actually arrays, but are instead pointers to arrays. For example, it encloses all numeric arrays in square brackets and it encloses a string in single quotes. That notation is supposed to say to their user, these are pointers to respective objects, not the objects themselves. For example, let's create a cell array of two cells. [SOUND] The first element of c points to a scalar, 3.1416, which is just a one by one array. And to remind us that the first element is a pointer instead of a one by one array. It puts that one by one array inside brackets. The second element points to a string and reminds us that the second element of c is a pointer to this string and not the string itself. It puts the string in quotes. Now instead of assigning a value. Let's just look at the values in these cells. Once again, we use these braces here, sometimes called curly braces, to look at the object that the given cell points to instead of to set the object that it points to that we did up here. And so we get the object that it points to. Here it's the number, here it's a string. If we use regular parentheses on the other hand, we get something different. You notice the difference? Here we got the brackets saying yes, we're looking at a pointer here. Here we got the quotes saying this is a pointer to a string. But up here with the braces, we got the sort of thing we ordinarily get when we look at a number, just the number with no brackets. We get the same sort of response when we look at a string. It's not indented and there's no quotes around it. But when you use regular parentheses with a cell element, you're asking to look at the cell's pointer, and as above, MATLAB indicates this with brackets for numbers here and quotes for strings. So when you see no quotes, you're looking at a string. And when you see quotes, you're not. Feels like we're in bizarro world here. But anyway, that's how MATLAB shows you that the object that you've requested is a cell pointer. It's subtle, now you know what it means and how it works. Another subtle detail about cells is that MATLAB doesn't allow two cells to point to the same object. Let's look at a simple example here. Its consists of two elements, each pointing to a 1x2 array of type double. C1 itself, of course, is a cell. Now consider the following statement. It looks like a simple assignment operation, so we might assume that the pointers in c2 are now the same as the pointers in c1. That would mean that they both point to the same objects. In fact, that's how it appears if we look at these objects. What happens if we change one of these objects? Let's change the object at which c1 1,1 is pointing. The first element of c1 is now pointing at some nice fresh strawberries. And we know it's a pointer because there's quotes around it. If c2 1,1 contains the same pointer as c1 1,1 then when we ask MATLAB to show us what it's pointing at, we should find those same strawberries. Let's try it. Instead, we find the object pointed at by c2 1,1 is the same as it was before. The strawberries are missing and I know they were there before. I can prove it beyond a shadow of a doubt with geometric logic. But wait, let me check c1 again. Now the strawberries are there. So am I losing my mind? Well, I may be. But there's a logical explanation for what's behind these strawberries. The culprit here is MATLAB's cell pointer model. That model doesn't allow c2 to point to the same objects as c1, in fact no two cell pointers can point at the same object. Instead, in MATLAB's version of cell pointer assignments, what happens when MATLAB carries out the assignment c2 equals c1 up here, is that it first copies all the objects pointed at by c1, then makes c2 point to the copies. So we put the strawberries in the original. But the copy pointed out by c2 was left as it was. And because no two cell pointers can point at the same object, it's impossible to change an object pointed at by one cell by manipulating it via another cell. This is a strict limitation. But you need to keep in mind when working with cells. For example if you pass a cell as an argument to a function, any changes the function makes to the objects that the cell points at will not change the objects that the original cell points too. MATLAB will simply copy the cell into the input argument. And that input argument will point to copies of the objects that the original cell points to. The function can only change the new objects. Unless the objects or the cell pointing to them is returned from the function as an output argument, these changes will be lost. And the original cell that was passed in as an input object, it won't be changed with or without an output argument, until something's assigned to it, nor will the objects it points to. This ironclad rule against two cell pointers pointing at the same object is not enforced by most languages, including C, C++, and Java. And as a result their pointers are far more flexible than MATLAB's cell pointers. There are multiple pros and cons and advantages and pitfalls associated with both types of pointers. And hours of vigorous debate have been expended on them by people who care about such things. But if you hear someone say that MATLAB is a weak language because of this rule, don't believe them. It just means they don't know that MATLAB supports two types of pointers, and its second type works like the pointers of C, C++ and Java, with all the rights and privileges and pitfalls thereunto appertaining. They're part of the less well known object-oriented structures in MATLAB. They're rarely used because they're rarely needed for numerical applications. But they're there, if you want to learn how to use them. They're taught in chapter three of the textbook. Here's some built in functions that are useful for working with cells. To understand them you really need to try them out on your own. And I encourage you to do that. And in conclusion, let me just say that cells and cell arrays are essential in many real world problems that you may run across in the future. It'd be wise to invest the time you need to learn the concept well. And a wise investment now will pay dividends in the future. And with that programming and financial advice, we'll conclude lesson seven. [MUSIC] [APPLAUSE]
