Hi guys, I'm gonna give you a quick
crash course tutorial on MathLab for

first timers or
approximately first timers.

When you first open MathLab you're
gonna see stuff like these,

get rid of these as soon as you can,
that's just getting in the way.

You can still use them, they're
still there, you just have to hover.

This is the command window.

You can use it like a calculator.

Do all of your code immediately,
and get response back.

I like to open up a script, and open
up the editor so I can write a script.

And it's really clean in here.

And then you can evaluate,
over in the command line.

Notice, they're right next to each other.

You can see.

All the code heightwise.

You can actually do this as well,
minimize the tool strip if you wanted to.

I've already got a file here
that we're gonna run through.

And then go through all of
this as quickly as possible.

So just pause, rewind if you have to.

When you start evaluating code in
the editor, you can set these break points

here to evaluate up to that point,
and then you can continue stepping.

You can also set modify condition,
so this is a Boolean condition here.

So to run, I like to use hotkeys.

This is function F5, to run.

Or you can just use one of the arrows,
up here, when there's a run arrow.

Anyway, so
now that it's running in debug mode,

I can continue stepping by clicking
this or just use the hotkey.

So this first line, I stored a row vector,

an array in a row into x1.

And it goes from minus 2 pi to 2 pi.

Or at least it's supposed to
go from minus 2 pi to 2 pi.

It defaults,
when it's just one colon there,

it defaults to integer value increment.

So you see over here it went
from -2 pi but it didn't quite

hit positive 2 pi because
the incrementation didn't allow it.

So the next line here allows
it to do that because I

enforced the conditions that it
reaches a total range of 4 pi.

And it reaches that over 13 increments,
so there was a total of 14 points.

And if you look at here, X2,
it goes from minus 2 pi to 2 pi.

And he's our way to do this without
having to think about how to increment,

is just to use the linspace command.

And you just tell it how
many points you want.

This one, in this case, it's 14 points
that it's identical to this, x2 and

x3 are identical, if you look over here,
they're identical.

Just easier to use lens space sometimes.

There's also log space.

I created lens space again,
and using these for later.

100 points for log spacing.

This log space gives me ten to
the zero to ten to the six.

So it goes from one to a million
over a hundred points.

So if you see, you look over here,

this is the very largest number,

it's a 1 times 10 to the sixth,
it's a million.

Here's a matrix.

It's a this is the first row,
second row, and they're separated,

rows are separated by a semi colon.

This a row vector B,
this is a column vector C.

The same values just one is
a transpose of the other.

It was three by four matrix of zeros,
three rows, four columns.

Matrix of ones,
three by three identity matrix.

Now, when we started
doing matrix operations,

let's take a look at how to solve this,
A times Y is equal to B.

If we know A and we know B,
how do we solve for Y?

So we invert A, so
I'm gonna grab this and put it down here.

This operator says,
invert A and operate on B.

This is going to give me an error because
the matrix dimensions must agree,

which means MathLab doesn't know how
to operate a matrix on a row vector.

So this row vector for the least,

the less obscure mathematical operation,
which is just matrix

multiplication that has to be a column
vector, it has to be a column vector.

There's also a way to do a row
vector here but it's a more

obscure operation,
out of product of some sort.

MathLab doesn't know how to
do it unless you massage it.

So you come over here and you put this
transpose operator, this tick mark, and

that'll allow it to do
the correct operation.

So that gives me a solution.

My solution Y for this linear system.

And then YY is gonna be the same thing
because C is already the transpose of B.

[COUGH]
This is to check to make sure that I get

B back, so there's B back.

When I got my solution Y.

Now here if I have an array of
input values into this function,

then this function automatically
loops through all those values, so

you don't have to write
your own four loop.

So that's the output here is the sign
of every one of those individually.

Now I'm gonna use these down below here.

So this dot here

doesn't mean dot product it means
element wise multiplication or

in this case element wise multiplication,
down here it's element wise division.

So it just takes the first element here
multiply it with the first element here.

Second element here, multiply it by
the second element here, and so forth.

And stores it in W.

So if you look at the size of w, compare
it with the size of either Y1 or Y2,

it doesn't matter,
they're both the same size.

And size returns all dimensions.

As compared to length which I
have suppressed the output so

I have to actually bring it over.

Let's say for example, length of B,
B if you look up here,

B is 3 by 4 and C is 4 by 3.

So the length of either of these

is the same because length
finds the longest dimension.

So going into the plotting,

you can just call up the plot function and
it brings up a figure.

Applies to that figure, you can come in
here and insert labels, title, legend and

all the stuff right here
if you wanted to but

I suggest since we're gonna be coding
a lot just get used to writing your code

to do everything for
you at least as much as possible.

So there we added a title to it,
we added a label.

Now if I wanna add another
plot to the same figure

I have to hold on to the figure.

[COUGH] So then I can throw in another
plot under that same set of axis,

let go the figure.

Just because I've let go of it,
you might assume that you can now

start another plot and it'll create a new
figure for that plot, but it doesn't.

It overwrites on top of this,
it writes to the same figure.

So that's an obvious problem,
the way to get over that is by explicitly

calling the figure,
this is just a quirkyness with MathLab,

there's probably a way around it,
I just, I'm not aware of it.

So create a whole new figure,
and then plot to that.

So it's the same thing with subplot.

If I just start subplotting, it's gonna
write over the top of this figure.

Then it's gonna create a subplot axis or
set of axis and

then it's gonna plot to that set of axis
and it's gonna tie it all to that axis.

Now this X label, notice how I've
done this, it's a carrot for

a super script and
then an underscore for a subscript.

And the curly braces are if you have
multiple characters that you need to

include in the scripts,
in the subscripts, super script.

So then the subplot it says
make me a 2 by 1 region

and here is populate in
the first region and

now it's populating in the second region,
these plots.

So there's the second region of the plot,
title, label, okay?

So if I continue going now since
I have called figure again,

this is going to override this and that's
fine because I'm done looking at all this.

Well okay, so notice that it
didn't override the whole thing,

it just overwrites the current axis.

So this is an exponential.

We have a linear set of
points on the input and

then we have the exponential
set of the output.

I want to get rid of,
I want to look at this on,

let's call our new figure, whoops.

So now I can look at both of these
if I choose to at the same time.

So notice how I have.

Just gone from plot to send their log Y.

So it suppress the exponential
growth in the Y direction by scaling

it logarithmically.

Now, if I give inputs that
are growing exponential and

then the output is exponential
of the exponential input.

It wants to be a double
exponential growth.

So let's see what that looks like.

Well, the problem here, you won't be
able to see it, unless we plot it.

That's a straight line,
notice the X-axis here

doesn't come any where near
the largest X values of X log.

Remember this is,
one million is the largest value.

So what's happened is it's gone to
the maximum that this can possibly go to,

on the Y value.

That's the maximum it can go to, before it
thinks that all the numbers are infinity.

So this actually goes infinitely higher,
and this goes much further to the right.

So this is a totally garbage,
a total garbage plot here.

It doesn't, it's meaningless.

So I'm gonna rescale, I'm gonna create

X log small enough that it'll
actually plot those values.

So now you can see,
I should probably get rid of these dots.

Let's replot this new set of points.

Just a default solid line.

So this is,
this actually is the exponential growth

of the inputs and it goes over all
possible values of the inputs.

So that's still not very
appealing to look at so

let's create a new figure and
suppress the logarithmic or

the exponential growth in the X-axis now.

So we we semi log X and
notice that I don't have

to repause a million times,
but let's do this.

So it is an exponential growth, it's
doubled the exponential because the input

is, the inputs are growing exponentially
and the output is growing exponentially.

It's tough to see it's exponential because
there, it's doubled the exponential.

So if you have a doubly
exponential growth,

the input and the output then do log log.

And that shows you
the exponential characteristic.

All right, that's about it for this video.

The next one will go into more depth.