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When developing learning algorithms. Very
often, a few simple plots can give you a

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better sense of what the algorithm is
doing, and just sanity check that

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everything's going okay, and the
algorithm's doing what it's supposed to.

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For example, in an earlier video, I talked
about how plotting the cause function, J

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of theta, can help you make sure that
[inaudible] the sense is converging.

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Often, plots of the data, or of the
learning algorithm outputs will also give

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you ideas for how to improve your learning
algorithm, Fortunately, Octave has, very

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simple tools to generate lots of different
plots. And when I use learning.

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Algorithms. I find that plotting the data,
plotting the linear algorithm. And so on

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are often. An important part of how I get
ideas for improving the algorithms. And,

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in this video, I'd like to show you some
of these [inaudible] tools for plotting

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and visualizing your data. Here's my
[inaudible] window. Let's quickly generate

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some data. First the plots. I'm gonna set
T to be equal to, you know, this array of

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numbers. Here's T, set of numbers going
from zero up to.98. Let's say Y1 equals

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sine of two pi 4T. And if I want to plot.
The side function is very easy I just type

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plot T, Y one, and hit enter. And up comes
this part where the horizontal axis is the

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T variable and the vertical axis is Y one
which is this sort of [inaudible] sort of

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function that we just computed. Let's say
Y two is to be equal to. The co-sign of

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two pie four T like so and [cough] if I
plot. T, Y2 what octave will do is it will

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take my [inaudible] plot and it will
replace it with this cosign function that

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you know cosign of X start at one, right,
now what if I want to have, have both the

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sign and the cosign plots on top of each
other what I'm going to do is I'm going to

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type, plot T, Y1 so here's my sign
function and then I'm going to use the

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function, hold on. And what hold on does
is it causes Octave to now plot new

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figures on top of the old one and let me
now plot T Y two I'm plot the cosign

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function in a different color so when we
put in R in quotation marks there and

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instead of replacing current figure of
plot the cosign function on top and the R

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indicates the [inaudible] color and. Here
are additional commands it's labeled times

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to label the X axis or horizontal axis and
Y labeled values [inaudible] to label the

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vertical axis value and I can also.
[cough] And I can also label my two lines

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with this command legend, sign, cosign,
and, this plus this legend, up on the

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upper right showing what the two lines
are. And finally title my plot, put a

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title at the top of this figure. Lastly if
you want to save this figure, you type

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print, [inaudible] d, p and g. My plot
PNG. So, PNG is a graphics file format.

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And if you do this, this will actually
save this as a file. If I do that, let me

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ch-, change directory to Let's see. Put
that. And then I will print that out. So,

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this will take a while. Depending on how
your Octave conversions set up. This may

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take a few seconds. But change the
directory to my desktop. And Octave is now

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taking a few seconds to save this. If I
now go to my desktop. [cough] Let's hide

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these windows [inaudible] that's the
figure saved as a PNG file also can save

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in other formats as well so you can type
help plot if you want to see the other

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file formats rather than PNG that we can
save figures in and lastly if you want to

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get rid of the plot, the close command
[sound]. Causes a figure to go away so

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there's a figure I type close you know
that figure just disappeared from my, just

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disappeared from my desktop. Altiv also
lets you specify a figure of numbers you

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type figure one + T one, one. That starts
up a first figure and that helps TY1 and

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then if you want a second figure you
specify different figure numbers so figure

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two plot T Y two like so and now on my
desktop I actually have two figures figure

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one and figure two there's one plotting
the sign function one plotting the cosign

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function. Here's one other neat command
that often use which is the sub plot

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command so we're going to use sub plot one
two one what this does is it divides, sub

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divides the plot, into A 1x2 grid that's
what the first two parameters are and it

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starts to access the first element, that's
what the final parameter of one is right

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so just divide my figure into 1x2 grid and
I want to access the first element right

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now and so if I type that in this product
this figure is on the left and if I plot

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T. Y1, it now fills up this, you know,
first element. And if I now do subplot

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122, I'm gonna start to acess a second
element, and plot TY2. We'll throw in Y2

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in the right hand side or in the second
element. And last command, you can also

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change the access scales, and change
accesses to 1.51 minus 1.1. And this sets

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the X range and Y range for the figure on
the right. And completely assess the

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horizontal major values in figure on the
right that range to 0.5 to one and

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vertical axis values that range from -one
to one. And you know you don't need to

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memorize all these command and if you ever
need to change the axis all you need to

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know is that there's axis command and you
can really get the details from the usual

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[inaudible] help command. Finally just a
[inaudible] CLF here's the figure. And his

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one, one matrix less than A is equal to a
five by five matrix square [inaudible] say

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so A is now this five by five matrix.
Doesn't we trick lesson as used to

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visualize a matrix which I can use image
as c Of A, and what this will do is this

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will plot a five by five, matrix. So I'll
take my matrix and plot this as a five by

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five grid of colors, where the different
colors correspond to the different values

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in the A matrix. So, [inaudible], I can
also do color bar, let me use a more

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sophisticated command, [inaudible] color
bar, color. Map gray. This is actually

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running three commands at a time. We're
running image sc, then we're running color

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bar and we're running colormap gray. And
what this does is it sets the color for

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map to gray colormap and on the right it
also puts in this color bar. And so this

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color bar shows what the different shades
of color correspond to. Concretely, the

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upper left element of the a matrix is
seventeen and so, yeah, that corresponds

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to kind of a knit shade of gray. Where as
in contrast the second element of A sort

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of the one two element of A is 24 where it
says A one two is 24 so that response to

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this graph here which is a nearly a shade
of white. And the small values say A, what

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is that, A four five It's about a three
over here that response you can see on my

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color bar, that response much darker of
shade in this image. So, here's an example

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I can plot it larger [inaudible] magic
fifteen. That gives me fifteen by fifteen

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matrix square and this gives me a plot of
a what my fifteen by fifteen matrix values

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look like. And finally to wrap up this
video. What you see me do here is use a

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comma chaining of function calls. Here's
how you actually do this. If I type A

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equals one, B equals two, C equals three
And hit enter then this, this is actually

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carrying out three commands at the same
time or really carrying out three commands

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one after another and it prints out all
three results and this is a lot like =one

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B=2 C=3 except that if I use semicolons
instead of a comma it doesn't print out

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anything, so this you know this thing here
we call comma chaining of commands so

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comma chaining of function calls and it's
just another convenient way in octave to

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put multiple commands like image. See
color bar, color map to put muti commands

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on the same line. So that's it. You now
know how to plot different figures in

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[inaudible]. And, in, Nick's video, the,
the [inaudible] I wanna tell you about is,

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how to write control statements. Like
if/while/for statements in [inaudible], as

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well as how to define and use functions.