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COSC 4364 Numerical Methods - Lecture02_MATLAB_Intro
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00:01 so, mm hmm. What I I should do. Mhm Start a
00:10 bit all over so the outline of doesn't want to do as the following
00:17 I said, so we'll see how interact with them kind of training users
00:26 virtually Alright. So these are some the aspects of that time that will
00:34 covered today and that was than the coming assignments for the class. Mhm
00:44 that stands for Matrix lab and it originally created by Professor Clean moller when
00:55 was faculty in New Mexico University in university, New Mexico maybe it is
01:03 Albuquerque and he also worked a lot the national Tv labs, particularly those
01:11 and Oregon mhm And the uh tools created um got picked up by quite
01:26 few in the academic world to use teaching numerical analysis to simplify kind of
01:38 assignment by having it effectively both the and associated um support functions and the
01:48 emphasis would be on the numerical the algorithms and not so much about
01:54 programming and it's really caught on. I would say the software package known
02:04 Meth lab today is probably the most or is the most successful software packages
02:14 not only in your algebra a lot other things too, it has really
02:22 developed by academics mostly that does new and their courses and and then this
02:35 known as math works that is responsible the math lab products is and taking
02:42 of it up and thank you too and support it. So a lot
02:47 the content and the math is really from academia and also verify that things
02:59 of good american quality and because of very large user base it also got
03:06 well developed. So nowadays it's put as a collection of toolboxes that covers
03:19 wide range of domains and there's just list of a few um we will
03:26 engage with and they are the toolboxes my recollection and what they do is
03:33 do the basic, simple the neuralgia that doesn't require in one of the
03:41 boxes. Mm hmm. And here kind of very brief listing of what's
03:50 Math lab as well as a companion in on a similar thing so that
03:55 things sort of comes together and it was listed on there previous slide as
04:02 . A lot of things also in kind of usage in terms of deep
04:09 and hey I as well as signal and all kinds of other stuff and
04:16 for stimulation tech tools. So it a very wide range including also cogeneration
04:26 not just standard processors, you know in the IBM and whatever you have
04:35 also for actually being able to generate for F P G A. S
04:39 programmable devices at the hardware level. they also have application tool boxes for
04:48 domains. So it's indeed quite a set of tools so that and because
04:56 the wide distribution is released, something very valuable to know, not just
05:02 this course, but for life after the course and or to age or
05:10 academia or in industry since it's so used. All right now, a
05:16 bit about the overall structure on that . So on this side, I
05:25 the first thing on the top is the task, graphical user interface and
05:32 sure suggestions on demo how to use graphical user interface and then there's a
05:38 of other ways and that you can that you do work. But matt
05:45 it has kind of its own set files types, what's known as m
05:52 , meta files of codes and matt are data files and then there's also
05:59 command line interface. So I think some of all three of these or
06:05 of these things will be touched upon suraj from a graphical user interface and
06:13 can do a lot of things access boxes, built in functions and report
06:21 and performance measurement tools and it kind looks like this. But I'm not
06:26 to go through the different fields. sure josh will do that. And
06:34 as I said, there are files code. So yes, you can
06:37 things that they want to do directly the prompts from meth lab, but
06:45 it may be more effective in actually the script and then saving it as
06:52 the top M file and then you the script file and then they want
06:58 , the change makes changes and playing the trial and errors for algorithms or
07:07 . It's kind of very easy then make yourself m fights. And the
07:14 part is the data files that are of binary files that Math Lab uses
07:21 store variables and the specifics for the that you use and running your bad
07:32 scripts at one point about this in addition to that statement is that
07:42 Math Club does file compression and so store files, unless you for something
07:51 are compressed funds. So that means takes a little bit of time to
07:58 . But of course the weakest system part in the system when it comes
08:05 larger data set is the data path storage or disks that compared to many
08:13 things in the systems are quite So even though it says here that
08:18 , it does tend to increase the for store for writing, but it
08:26 speeds up things when you're loaning because , un compression is pretty fast compared
08:32 the data bowling rates but of depending upon how effective the compression
08:40 there's no guarantee that you always, when it finally small already to start
08:45 , it probably doesn't pay. And the file is such that it's hard
08:53 get a large fire science reduction and them, it doesn't really improve
09:02 The loading either. So compression depends basically finding patterns yet you can describe
09:10 effectively than the data itself. So of things about racism. Out time
09:23 designed to work with the race. it's kind of the language, the
09:29 and languages a language with a narration and in that regard it's not all
09:35 different from other languages that also have syntax. So that means two operations
09:45 be done on a race and conceptually way as you operate in single
09:52 If you can I had the rage doing sort of a plus operation and
09:57 right thing happens. You don't have explicitly create oops that as each individual
10:08 pair of elements individually. So I'll a little bit about that but that
10:14 sure when the coverage Yeah some detailed Swedish and talk briefly about data types
10:22 storage and referencing which is just a feature. Um that one can use
10:29 times. So I will do things quickly. So as I said,
10:36 ray are the it's designed for the . So that's basically it's the premier
10:42 type in math lab. So even you asked that the scalar, it's
10:48 basically stored as if it were in right arrangement. Having a number of
10:53 that you're is convenient for the So it's not just one or 2
10:59 like typical dr emergencies so it can any number of dimensions but it is
11:06 to the point that for every dimension to every other dimension, the number
11:11 elements needs to be the same. basically it in two dimensions will be
11:18 of a square dr ray and but did mention some form of empathetic structure
11:26 in the degenerate case cube, it be ragged. Um Then size is
11:37 of an important function that is coming that plan and the sizes of actress
11:44 says that tells you how many dimensions already has and how many elements there
11:50 in each of the dimension. And probably demo mode. And another thing
12:01 um as it says and then thinking you reference an element in the array
12:11 his on the right hand side which sort of the middle example you point
12:19 something that is not part of the . That's an arab. On the
12:24 hand, if it's on the left side that means kind of assigning values
12:32 something that originally was not included in array the Iraq has extended. So
12:40 illegal. And the thing to Okay. And then he was just
12:46 as various forms of assignment and I suggestion will probably demo that. But
12:51 one part I wanted to stress is by being in language or with raising
13:02 it tends to use or triplet notation often the work can is legal and
13:08 has the structure. It's the first an increment and I last and If
13:14 is submitted, that means the increment by the 4th 1. So it's
13:19 of an easy way of initialize things basically having the looping built into the
13:31 structure. I will go through. didn't want to take too much time
13:38 I'll let this. There are examples the slides that you can look at
13:43 and I'm sure. And so the demonstrate, there's a couple of things
13:51 variable naming that it is case So one has to be careful and
13:57 unused variable names to make sure you kind of mess up by not paying
14:04 to exactly once you do um to data types as available, you
14:15 single and double. The one thing want stressful, I want to stress
14:21 get to be stressed and assignment is default, everything is in double
14:28 So I'm when my wants to study effects are the accuracy outcome using single
14:37 double position. One needs to be clear and explicitly declare things variables as
14:43 in single position and also make sure um in sort of consistency things does
14:53 get promoted to double precision in Um Okay, that was what I
15:02 on that. So here's what I to point out in terms song,
15:10 the race are these calls, sequence storage associations or if you are multidimensional
15:18 raise, they always get flat into dimensional erase before things are laid out
15:24 memory that happens in C. And and everything. So it's just
15:28 Rised when it's signed to memory and uses call a major order. So
15:38 just shows how then this um array to a what kind of a matrix
15:50 . But it also means that since are effectively laid out As one dimensional
15:59 and look here at the memory, means one can reference elements within the
16:09 but just figure out what if location is in memories of a component.
16:14 doesn't have to have multiple indices to a particular element. One can just
16:21 by its order in the linear And I will let probably you can
16:29 at the slides and different ways of it and you can get subsections and
16:35 it on with that. So it's convenient to into um subsections of arrays
16:41 blocks of arrays and work with blocks this section and type form function in
16:50 . Yeah. And I'll try to something about theory operations. So,
16:57 that's probably what the bulk of the will be and telling you about how
17:02 can reference elements in this thing. then it's sort of one thing that
17:08 amazing. Often convenient is then how can Reshape arrays between one and 2
17:17 or and the number of dimensions from linear space to some multidimensional array or
17:28 or introduce a number of dimensions by a revision. And I guess that
17:36 and I like to look at the on the slides, transport diseases in
17:42 time. This prime thing that allows to um change your order between there
17:49 the arguments it supports reduction, which and it also has a built in
17:56 brand that shows here and some that things along various dimensions depending upon how
18:04 use this argument. Um and uh comes quickly as I've warned because the
18:14 is really On the demo and I to take not more than about 15
18:20 to see Ashley has enough time to his demo and then time for doing
18:25 couple of simple exercises. But let see. And so you can do
18:33 concatenation of a race that has to shaped consistent and then here's something built
18:39 functions that are quite useful already mentioned . And the number of function you
18:45 also initialize erasing the different ways to or ones by using the corresponding in
18:55 but that was really quick and a bit um not a good job but
19:00 because that should hopefully be covered but heads up for things to pay attention
19:08 when um so just do the So I think you can take over
19:16 here. Yeah, I'll start Okay, can you see my
19:27 Yes. Okay, great. so we're just starting with what the
19:35 workspace looks like in in Math So when when you open it you'll
19:40 a window. Probably something like you won't have these many scripts open
19:46 . Um so there are mainly two for writing Math lab scripts. One
19:53 just using a simple dot m script you can use open using this new
19:58 , but then over here in the tab, um and then another using
20:03 live script, which I'll show you that looks like later on for
20:07 I'll simply just work with the dot scripts. Then here in between you'll
20:14 your workspace where you write your commands everything in the bottom, you have
20:21 command window where you'll see most of outputs and you can have your workspace
20:27 as well, which contains all the basically that you declared through throughout the
20:34 of your script. Um So so one thing I would suggest everyone
20:43 to use these two commands first, your in your script, always because
20:48 been sort of helpful for me and me not run into many issues.
20:54 first cl c c stands for a console. So if you do the
20:58 you run this command then it basically out the whole command window where you
21:02 your any output that you may have from your previous executions, it just
21:08 remove all the clutter get makes things confusing. And the second is clear
21:14 which you can also achieve by just this clear workspace um button on the
21:19 and what that does is it basically all these variables that you that you
21:24 have in your workspace. So in , whenever you run the, run
21:28 program, all the variables get stored the workspace and if you run the
21:32 again and you try to redefine that's the variables with the same name
21:38 you try to do something else. Math lab throws an error because it
21:42 confused between two variables of the same . So it's generally a good idea
21:47 clear your workspace every time you run code, it may not be the
21:53 idea. If you have loaded a very big data set in that
21:57 try to avoid that because loading a dataset takes time, in that case
22:02 do that. But if you're just simple programs, you can simply just
22:05 that and clear out your workspace so you avoid any issues later on for
22:14 demo, I'll just close the it's not going to be needed.
22:17 can simply drag and drop command window well for now, I'll just put
22:22 on the right side um to run of any of your scripts, just
22:29 go to the editor tab on the and press the run button. So
22:35 will clear out the command window and will come out. Clear out the
22:40 and once you run it, I'll to this plot later on.
22:46 starting from variable description, if you used python then it's very similar to
22:53 you do in python. Just without data type, you can just simply
22:56 any variables and their assigned values against against the hence the command. But
23:04 you emit the semicolon, that's still valid statement. Mad love. Will
23:10 give you any other what that basically is whatever is the output of executing
23:15 particular line will also be show reflected the in the command output in the
23:21 window. So if you don't want see output of every single line that
23:26 execute, just put a semicolon at end and as dr johnson just said
23:32 the variables that you define are by . Double precision. Yeah. So
23:38 these two variables are double precision. can also check the type by using
23:43 class function. So here this is output here that tells you that class
23:48 a is double. If you want cast it to single precision then just
23:53 a typecasting as you would do in other programming language using the single statement
23:59 that converts that variable into a single variable. And here we store that
24:05 to see um operators, multiplication. as any other programming languages. If
24:13 multiply two double precision numbers, the you get is double precision. I
24:19 think it printed it printed up So double precision divan. If you
24:27 double precision numbers and cast it to precision then the output a single precision
24:32 that's the two which is a single number here. Um Addition of a
24:40 and single precision results in single precision which again you see here the three
24:45 a single precision number and multiplication of and single precision results in a single
24:52 number. So before here is a precision number. Um The power
25:01 you can use it to raise any to any power that you want.
25:06 here just squaring up a so a whatever the way what value was got
25:12 and got stored into T. one colon operator again as you saw in
25:18 slides that generates a vector. And here the initial value of the vector
25:25 one we gave it an instrument of and the upper limit was 10.
25:30 so the vector that was generated, had all these values from 1-9.
25:36 that's all Values in increments of two till 10. Um Similarly you can
25:45 um use um this colon operator to um an interval with equally distant values
25:55 you can use inbuilt functions like sine provided the the variable as input that's
26:04 times T. So that's by times whole the vector that you generated.
26:12 that will give you the value of function for all those values as a
26:20 and that will be stored in And if you want to plot it
26:25 can simply give it. Uh I X comma Yes. Oh sorry
26:31 Yeah X comma. Y. And will be a plot those values.
26:38 Inside a inside a line plot So that's generating plots is also very
26:48 . Um Right if you want to input from a user that's also very
26:53 , you can just use the function input and if you want to associate
27:00 message with that you can simply give string as an input to that function
27:03 whatever message you want to show up that and that causes the program to
27:10 until you get input from the let's say I give it 10.
27:15 then you can use the F. F function which has a similar
27:21 A few of you see before you percentage of F as the variable declaration
27:27 variable definer, for a floating point and just a message and then the
27:33 name to get the output on the . So any questions on that.
27:41 are just some very simple concepts to started with. Alright, I have
27:54 questions so feel free to just bother in between if you have any
28:03 Alright um you can also write conditional . So the syntax for the NFL's
28:14 in Math lab is like this you if then your conditional on the condition
28:21 you wanted to run for whatever you to do for that condition and then
28:26 F followed by else and then each or I should say any structured block
28:34 Math lab ends with whatever keyword it's to start with and then it ends
28:40 the keyword end. So that marks end of that structured statement. So
28:47 and marks the state end of this structured block. Um you can also
28:55 switch statements like any other programming So here I defined a variable called
29:01 with a string that has been it then the switch statements Sin taxes like
29:07 , a switch and then the variable which it's supposed to run for.
29:12 then you define all the cases for you want to run different statements for
29:21 if I remember correctly, she has uh as the default keyword for the
29:29 where you have no specific input for Math lab, that's the same
29:35 Can be achieved by using the otherwise . Um Yeah. And if I
29:43 it. Yeah. So if X 50, So the else if statement
29:48 executed for the first part so I X is equal to 50 and then
29:53 switch statements since grade was be the be got executed and great, bigger
30:00 out there on the console. Any on the switch? Can you do
30:10 fall through between cases? Like you see languages, I'm sorry say that
30:16 . Can you do a fall through say I have case A and then
30:19 case B basically a case that handles cases. Uh I'm not sure I
30:28 really tried that. You might be to I don't, I don't think
30:32 this should be a big deal. you can give a comma here,
30:35 not aware of the right syntax but can, you can probably do
30:45 Alright. Um then there was conditional you can also write for loops and
30:50 loops in math lab. So let just quickly run that so we can
30:54 the output as well. So here equal stem and then you can write
31:00 while loop by using this syntax awhile less than 20 condition and then inside
31:06 via loop you also give the increment A and then you finish it up
31:11 the end statement and so that runs Those 10 penetrations from 10 to
31:22 Um Yeah. Ah for loop you also, you have a couple of
31:30 ways to to run it um here for loop I defined for x equals
31:38 . And remember this is the colon . So by default the increment as
31:45 . So this uh this for luck run from Then all the way to
31:50 . And remember, these are the indexes where whenever you use a colon
31:56 . So 10 and 20 are included the in the sequence that you run
32:03 . If you want to change the , let's say bye to rather than
32:08 default of one you can provide to the increment in that colon operator.
32:13 then the loop will run for The are implemented by two from 10 to
32:18 . And as any other structure you ended with the with the end
32:26 . Any questions on that. So are just simple ways to run the
32:33 . Look, I'll show you how run them with vectors and matrices as
32:41 . So yeah, just quick Is that it's not a big deal
32:45 matt lauer, it's just a slight in in the in syntax of how
32:50 write it. But otherwise the whole , it's pretty much the same as
32:54 other programming languages. You might have no one thing to remember that array
33:03 disease when default starts by one. Maryland was supposed like fortune, but
33:11 that starts at zero. Right. , I was about to get to
33:15 . Okay, Alright. Yeah. , okay. I think and chad
33:23 said that for fall through case for cases, switch statement is conditioned one
33:29 condition too. So you can just multiple conditions separated by commerce.
33:37 Thank you for that. All So yeah. Alright, I run
33:47 code again, so we can see output. Um Again I haven't given
33:52 colons everywhere, so we can see output right away rather than putting everything
33:57 print effort. Any display commands. is another command called display which you
34:01 use to print out state anything on console. Um Alright, so Coming
34:10 vectors, just simple one directors. you can define a row vector um
34:18 elements spaced by just blank spaces, it also works with commas. So
34:25 can just simply provide commas in And that also defines a row
34:31 Ah Right. For column vector, define each column, each roll separated
34:38 a semi column. So every semi basically starts a new new role.
34:45 if you have one element in each that basically makes it makes it a
34:50 vector. So here B is a vector where each row is 4567 all
34:56 way to 10. So that's one vector over there. Right? Um
35:01 yeah, here's the indexing part. indexes in math lab start from
35:06 Uh as compared to zero in other languages. So the first element you
35:12 if you index using uh these uh place is over here. Um You
35:21 from one. So the first the first element in one was
35:25 So you get that four. Second was five, you got five and
35:29 on. Um you can also get of the elements of from the
35:38 So that you can do, we using the colon operator. So here
35:44 can provide the start and end index which you want the elements from.
35:51 again these indexes are inclusive. So get index 234 and five from
35:57 So that's 56 and 78 values in . Um If you want something from
36:06 specific index all the way up to end of that vector, you can
36:11 provide the end keyword as the as last index. And that should give
36:18 all the indexes, all the values from whatever. Starting index you give
36:23 what whatever. And the last index that vector, if you want specific
36:33 from our vector, let's say I Element at Index one. Index 5
36:40 Index six. Then I can simply a list containing all those indexes as
36:45 Parameter ah to the to the indexing . And that returns those specific uh
36:56 from that particular vector. If if want kind of a reversed reverse order
37:05 the of the elements, you can simply switch the statement to just to
37:11 the starting index from end. But you have to provide the increment or
37:16 I should say a detriment um value that it knows how many elements elements
37:22 jump every time while going back and the way up to the index number
37:27 . So here is upset four. the values from last index jumping to
37:34 every time and all the way up The second index in the in the
37:39 the vector. So that's 10, and six in the a vector over
37:44 . If you want to just reverse entire entire vector and store it in
37:51 variable or even in the same you can do that, you can
37:56 the command flip and provide the name the vector that you want to reverse
38:00 that that will give you a reversed . Um looping through a vector again
38:09 couple of ways to do that. First is simply you can provide the
38:17 uh the indexes starting from 12 length A. That that means the number
38:24 elements in the um in that So it starts from 12 length
38:30 And then you can index it um this indexing statement here and that will
38:37 you the loop output for all those the variables, all the elements in
38:45 question. Um So um this is mike working for. Okay so can
38:51 like put like a set like at own vector? For like a for
38:54 like that. So let's say you a vector that's like 1567. You
39:00 do that with the for loop to you you can do that too.
39:04 simply just replace this with like I above and it will run for these
39:11 values. So that's 15 and six then you can index using the ai
39:17 or whatever indexing variable you've used. was what my next example was going
39:24 be. You can simply just assign to the name of that vector.
39:29 here I equals if you write that the output is simply just printing out
39:37 values. And in this case i not the index but those are the
39:41 values inside the vector. So you look through a vector just by directly
39:49 its value to the indexing variable as . Does that answer your question
39:58 Yes. Okay. Mhm. Um right. So for vectors you can
40:08 perform transport and that's simply just the operator. So remember be was a
40:16 vector and if you transpose it you a roll victor. So that's
40:24 Um addition of two vectors is element edition. So if you add A
40:31 B transports, it's going to simply add each pair wise elements with each
40:38 . The multiplication operation is the one need to be careful about. So
40:43 are two versions of multiplication operation. is just simply the asterisk operation and
40:50 other is dot and asterisk, just simple asterisk is a matrix multiplication.
40:58 that's going to perform a inner product an outer product based on whatever the
41:03 of two vectors are the dot star the element wise multiplication. So here
41:10 line 43 what I'm performing is an wise um product of A and
41:18 Transport. So in that case it multiplies be transposed. Which was this
41:25 and A which was this guy. that's just basically square of each elements
41:34 16, and so on Online what I'm doing is a matrix
41:41 So that's only just the asterisk operator . And that in this case is
41:48 row vector times a column vector. it was a row vector and B
41:51 a column vector. So that performs inner product. And inner product is
41:56 , if you're aware it's a multiply operation, you perform element wise multiplication
42:01 then you add up all the all all the products. So that's uh
42:09 the output of that operation is there's 71. So be careful whenever you're
42:16 multiplication of two vectors or two you should know what operation you are
42:22 . And then use the right operator that. No. All right,
42:30 appending vectors with each other. So , just like when you were defining
42:39 as I said, having columns or commas or just spaces between elements creates
42:47 row vector and having semi columns between creates a column vector. The same
42:54 goes for when you're when you append vectors with each other. So here
43:01 I append A will be transposed and have the column as a comma.
43:08 the as the operator in between That means you add all the all
43:14 elements of B transpose to the to columns of A. So in this
43:22 it's just basically a one D. pending operations so to say. So
43:27 just gets appended after all the elements the road victory. If you have
43:33 semi colons as the as the operator between them, then the new elements
43:39 get appended goes and go to the row. So in this case it
43:44 A um to Arturo matrix basically because new elements that from B transports they
43:52 to the next next door. Ah thing that BB was a column vector
44:01 all the way to 10. If append B again using the comma then
44:07 goes to the next column. So rest of the 45 all the way
44:11 10 goes to the next column. you append using a semi column then
44:18 get appended below it. That means go to the next draw. So
44:23 this way you can append column vectors row vectors with each other in different
44:31 . Any questions on that comment? worked nicely because A. And B
44:40 the same number of elements. Yes. If you if you have
44:44 number of elements in um in in in the vectors then for one of
44:53 dimensions it will complain. Um So say if um the number of uh
45:02 when performing this operation when adding be to be the number of elements in
45:09 operations was not the same then it have created a ragged array. That
45:16 Let's say we had from 4 to in the left in the first column
45:20 only had 456 and seven in the column. That means that the number
45:26 elements are not equal in one of dimensions. And then matt love would
45:30 complained. So you have to be when you're appending vectors with each other
45:39 the same would happen if you tried multiply two vectors whose dimensions do not
45:55 . All right. Um Right. to define matrix it's a it's a
46:03 simple yes chat question. How does lab handle operations? Multiplication or addition
46:10 the vector? Mix with in danger strength. That's a good question.
46:19 I don't exactly know. I haven't but my guess is that it gives
46:25 an error because of data type I don't think it performs multiplication of
46:33 data types exceptional. Eric yeah except America if they are double or single
46:40 it's fine. It doesn't complain but they are numbers and strings then it
46:45 complain. All right. Um Yeah to define a matrix again I'll just
47:02 it. Um Yeah so to define matrix you can just simply define a
47:11 of row vectors separated by semi which is basically a matrix. So
47:18 in this case 12345 is one row is another row and rows are separated
47:24 semicolons. So you get this matrix here, you can perform transpose of
47:31 matrix again using the apostrophe out So that gives you the transports again
47:40 starting start from one in math So you get if you want to
47:45 a certain element, you just start from one. And let's say if
47:50 do three comma four, that means 3rd row which is this row and
47:55 column which is this column. So element value six as the that's how
48:01 can index it if you want to let's say all the rules of the
48:07 the matrix, but only a few . So for Rose you can just
48:14 write the colon operator, which basically for that. I want to hold
48:18 Rose and then you can tell it I want only to the columns two
48:25 three. So that's two and three the call an operator again And that
48:31 you a column two and 3 and the rows of the matrix simply if
48:36 want all the columns, but only rows one and two. You can
48:43 this syntax to do that and that you the first two rows and all
48:48 columns of those two rows. So how you can just get slices or
48:54 ah the matrix that you want. Again here the asterisk or print is
49:02 matrix multiplication operation. So it performs times column for each row of of
49:07 left hand operator. And that gives the output for matrix multiplication. If
49:13 want to perform element wise multiplication of matrices. The operator uses dot followed
49:21 the asterisk and that's that's what gives the element wise uh multiplication. Um
49:32 . Right. You can also compute inverse of a matrix determinant of a
49:39 . There are simple, simple commands do that. I envy transport inverse
49:44 stands for determinant. Um Right. then there are some special functions that
49:52 can use to define matrices with either zeros, all ones or random random
50:02 in the matrix. So zero's three it defines a three by three matrix
50:08 all zeros in it. So that's one. If you want the matrix
50:14 two rows and three columns all with , you can use this syntax 02
50:18 three. And that gives your matrix of size two x 3 with all
50:24 in it. Same if you want rather than zeros, then you can
50:29 do once and provide two comma And that gives you a matrix of
50:34 by three with all once. If want a matrix with random values,
50:39 can use the function rand. Ah then give the dimensions. So let's
50:44 we give three by three That gives a matrix with random values of dimensions
50:51 x 3. And the important point using random function you get all the
50:57 that are uniformly distributed in the in interval zero comma one. So if
51:05 want a matrix that has values outside domain, you need to multiply each
51:12 of the value with that whatever scaling , you need to get it into
51:16 different different range. Alright. Any on that? All right. Um
51:35 . Next is how you define functions in math lab. The first point
51:42 that functions inside a dot M script to be defined at the end of
51:50 script. You cannot define it, it before any of the assignment statement
51:56 any other commands. You need to them at the end of the
51:59 Otherwise model gives you an error. The syntax to define a function is
52:05 you have to write the keyword function you need to provide the name of
52:10 variable. That will have the return of of the of whatever is computed
52:16 that, in that function uh followed equal sign. And then the function
52:23 and then the parameters that that function us input. So A and B
52:29 are the input R E. Is the is the return variable which
52:34 contain the return value. So in , in this function I'm basically comparing
52:39 numbers. It is bigger than The R E S variable contains a
52:45 it contains the value of P. I define X and Y as five
52:51 10 I called the function compare with X and Y variables. And note
53:00 the name of the variables that you here while calling the function does not
53:04 to be same as the function parameters and that's similar to any other programming
53:13 . Um so you call that you give five and 10 as the
53:18 since then is the bigger number? function should return then in this R
53:23 . S, variable. And then return value from that function is stored
53:28 that in a variable called camp. here as you can see the return
53:32 we got was 10 in camp. If you want to return multiple values
53:41 the function, you can simply just the list of the return variables as
53:49 rather than just providing one variable, as the written written variable. So
53:55 this function returns two values that some mull And again it takes two variables
54:01 inputs. Uh stores the sum of two variables in some and the product
54:07 those two variables in mall it returns two. So if we call that
54:12 X and y here Some in Mulch contain 15 and 50. So that's
54:20 some 15 miles has contained 50, questions on that. So just the
54:32 concept. Just different syntax. All . And yes, you can also
54:45 um You can also solve equations um perform differentiation and integration using symbolic
54:55 I don't think I should go into . I'll just post this demo on
54:59 blackboard and you can take a look think for the tutorial they only need
55:06 stuff. We can cover these other later on maybe. Yeah. Um
55:15 guess everyone is everyone ready but their lab environment is everything set up for
55:21 guys. Just just an F. . I focus on the smallest of
55:25 he even does try to experiment that like there's a symbolic math toolbox that
55:31 have to install. Right? If you try to run that and
55:35 don't have the toolbox installed. Matara automatically tell you that you need that
55:40 box. It will give you a to install it. I forgot about
55:43 part. Yeah. So it's a not a big deal. It's if
55:48 if you're missing a toolbox metal up tells you that you're missing something.
55:51 will give you an error in the window along with a a link that
55:56 take you to whatever web page or small window that will allow you to
56:01 that toolbox. So there's not much out to do if you're missing something
56:06 your environment. Mhm. That's Medlab generally a very helpful tool in that
56:12 ? Unless the chat question, is also true for the online version?
56:18 don't know. I believe online version I should have all the toolboxes automatically
56:24 if if it doesn't it should automatically it from whatever server it's running
56:31 I don't think that's required on the version, but if if not it
56:37 it will probably give you again some way to do it. It won't
56:41 a complicated process to do it. . I only have a few exercises
56:54 you guys want to go through Oh, before going to that,
56:59 me tell you the easier way to your codes for these exercises. So
57:05 till now I was showing everything in dot M scripts, right? Which
57:09 just simple scripts to save and run codes for the exercises. You can
57:14 use the live scripts. And those generally more helpful in debugging your code
57:21 you can go to new and open live script from there. And what
57:26 does is it basically allows you to the output of your program as you
57:31 . So let's say if I define equals five, it will show you
57:35 output of whatever I did and If did X Square, it will show
57:41 output 25 years. So it's easier debug your code as you go in
57:47 scripts feel free to use that if more comfortable with dot M scripts feel
57:51 to do that. Is there a um, when I'm trying to do
57:59 you did with the ml xing of live editor, but I'm not seeing
58:04 outputs on the right side. Uh do you not see this window
58:13 the right side? That's what I . I see the window on the
58:16 side, but there's no there are um you need to you need to
58:20 a run in the live editor tab in the live editor tab.
58:27 I got it. I see it . Okay. What's another question having
58:34 lab opens uh low system resources. , in that case you may want
58:41 use the online version. If you to install Maglev on your laptop using
58:47 university license, you can simply go the Mat lab online version and login
58:52 the same same credentials and that should you access to the online version.
59:03 you still want to run it on laptop, you may need more
59:08 Yes. Metal optics quite a bit RAM. All right, let me
59:18 the exercises on top, let's start exercise one and to only have 20
59:25 , I'll Give maybe four or 5 to get them done. It's they're
59:31 as difficult. Um if it if feels like that we're running out of
59:38 , I'll simply just go through the quickly. But let's see if there
59:43 people who can do it. So question was just starting to get enough
59:49 . Well I'm running with 16 so should be fine. Yes. So
59:54 making me wonder how much is How much is depending on what your
59:58 is? If it's yeah if you has 8 gig and it's um the
60:12 and the exercises are on the The demo is on on blackboard.
60:17 haven't posted the exercises yet and if curious the exercises are actually from dr
60:26 slides which are probably for the next . And there is they are at
60:31 end of that particular lecture. So are the exercises from the lecture slides
60:40 . All right. Yeah let's do exercise one and two elevator a couple
60:44 minutes before. Yeah you guys get try it. I'm not sure if
60:55 are from the book. Sorry I not remember. Keep in check but
61:02 will have them posted. Yeah I'll them anyway that's fine. Alright that's
61:22 Okay I'll wait till two or 5 guess. Okay. Yeah and also
61:28 exercises are on my slides I guess next lecture we encourage you to do
61:35 and as well as whatever gets posted passion if you have trouble send us
61:42 so we can work with you if don't get time to do it now
61:46 the election because an email or you trouble on hulu. So you can
62:00 your feedback. Excuse me. I one question. So the vector is
62:44 vector or a It's a it's a vector because the elements are separated by
62:53 . Mhm. The first one. first one on the first one as
62:59 . Yeah. And for the and the second question, um index position
63:06 at one or a zero. Yeah. Math Club and Math Lab
63:11 starts from one. Yeah. Just the summer Into what or reminder what
63:36 has already said. So list of separated by spaces or commas results in
63:44 row. Doctor. If they are by semicolons, it becomes a column
63:53 . So it's just two options for and one for creating a role factor
64:00 one for creating economy. That's Alright. Uh should I talk about
64:15 Solutions for these 2? Has anyone ? We're a bit tight on
64:22 So you may not get a chance do all of them, but feel
64:27 to try them on your own later . If you if you don't get
64:30 chance any volunteers for the first Okay, sure. Yeah. Go
64:42 . I just want to You want share my screen. Is that what
64:44 mean? Yeah. Yeah, Let me allow David Wright.
64:51 I think I did it. Yeah. You should be able to
64:56 it now. All right. Is ? Sure. Can you see?
65:08 , I think it's good. I it's sure. Okay. There we
65:12 . I was seeing the preview. see. So your screen. I
65:19 see yours that says I'm sharing. hmm. Did in one line you
65:28 just type in chat. Yeah, do that. This one's pretty
65:33 Yeah. Stop sharing. I don't what to do with it. Mm
65:40 . Right. Yeah, that's the answer I think. Yeah.
65:47 If you want 74, um, can simply do that using the colon
65:51 . Right. And with the increment two, Alright, for the second
65:58 you can just probably try to Yeah, it's a little bit hard
66:02 explain everything. Yeah. Just try put in the chat. Um or
66:08 easy way as I can go through solution and maybe you guys can check
66:12 and if you happen to have a solution, let me know.
66:18 So problem too. If you want define a vector again, just use
66:23 elements based ah Like this. If want to add 16 to each
66:31 that's simple. Offly an addition The next thing was to add 3
66:37 only the odd indexed elements. So that or was it even or
66:45 Okay, interesting. I did it even I don't know why I did
66:48 , but anyway, For that, simply created a vector that started from
66:54 all the way to length of a yeah, so that contained all the
67:04 all the even indexes and then I provided that vector as an input um
67:10 the scripting syntax and added three to . So that's basically what it does
67:16 adds three to all the even numbers indexed elements there. You can do
67:22 same thing for odds um to perform square root, you can simply do
67:31 dot and they and the caret operator negative power of one by two,
67:39 computes the square root. Or otherwise can simply use the function sq.
67:43 in medlab and again then to compute wise, square of each element.
67:49 you can do dot carrot and to the square of each element.
67:58 I'll post the solutions as well on on the on the blackboard. So
68:01 don't have to worry if you miss . Alright, let's see if you
68:05 can get through exercise three and Mhm wow. And note that here
69:08 and Y are column vectors. There a apostrophe after that. After their
69:14 of their column vectors. So that's way you can create a column
69:21 If you don't want to write semi after everything, you can just declare
69:25 row vector and put apostrophe after Mhm. Right. Mhm.
70:35 Mhm. What? All right. that was enough time to go through
73:47 of them. Mm hmm. Um right. So the third problem.
73:55 again we defined X and Y as vectors. So that's 3 to 684135
74:01 X. And Y. The first said at the some of the elements
74:06 X to Y. So you have first perform some of all the elements
74:12 X and then add that's some to of the element of why And to
74:19 that, that the simple statement that needed to do was why? Plus
74:25 sum function that had X as the . So some of x is the
74:32 huh. Some of all the elements X. And then add that to
74:36 . And since plus is already a wise operations. So you don't need
74:41 write dot plus. It's simply So that's first and raise each element
74:49 X to the power specified by corresponding in Y. So that's again a
74:55 X dot and then carried Y. that's element wise power operations. So
75:04 zero powered Y zero or I should X one? Power Y one,
75:08 two, power Y two and so . So that's this statement performs that
75:15 similarly. If you want to perform element wise division, that's why
75:21 And the division operator X element wise is dot uh star of Y.
75:30 And then Added the elements in Z and assign the variable, assign it
75:36 variable w. So again, performing is just simply calling the function sum
75:42 in case anyone used loops to do . That's also right. But using
75:48 some function is a rather straightforward Any questions on that? All
76:00 For exercise four. Ah It was just using the colon operator correctly.
76:08 first it's just a series of even starting from two. So here I
76:14 Now I use the colon operator to the initial value increment of two and
76:19 till 10. So that's a serious of even numbers. If he wanted
76:27 reversed kind of vectors starting from Going all the way to -4.
76:33 can provide the initial value of stem decree mint of two. So that's
76:39 and the final value is -4. that gives you a vector starting from
76:44 , going Back to -4. Uh anyone get the 3rd and 4th
76:52 Right. Yes. Okay, Yeah, that was a little bit
77:01 one if you haven't used these ones . So here are the simple things
77:05 notice is the enumerators in all the is one. So that's the simple
77:12 . And then the denominator again starts one. So if I can write
77:16 as one by one as well. ? The denominators start from one and
77:20 by one every time we go. simple. And the simple way to
77:24 it is having one as the numerator then element wise divide, divide and
77:32 denominator is simply A vector going from to 10 And that gives you that
77:40 of one x 1, one x and so on. And in the
77:45 1 you have basically 0x1, you say it. So numerator goes from
77:51 to all positive whole numbers and numerator from one to positive whole numbers.
78:00 again the numerator here, rather than one. In the previous cases you
78:04 have a vector of 0-10 and then wise divide and the nominator goes from
78:10 . So that gives you that kind a vector. There any questions on
78:18 comments, were there Number three Right. The scalar gets promoted to
78:25 vector automatically. Right? Yes, you're divided by a vector basically.
78:33 , extending something networks. Alright. think we have just 558 minutes.
78:44 ? Basically should stop now. that's fine. I have dated have
78:50 Guatemala after this class. That's alright stop 10 minutes before they have.
78:59 you. Yeah. And you know questions or send the email if you
79:06 them otherwise and well not otherwise, on Wednesday will be combined lecture classroom
79:13 . All taxes. Yeah. And sure everyone joins the prologue group.
79:17 don't think many people have joined Okay. Yeah. All right,
79:25 you for today. Thank you. bye. We should stop recording here
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