When developing learning algorithms. Very
often, a few simple plots can give you a
better sense of what the algorithm is
doing, and just sanity check that
everything's going okay, and the
algorithm's doing what it's supposed to.
For example, in an earlier video, I talked
about how plotting the cause function, J
of theta, can help you make sure that
[inaudible] the sense is converging.
Often, plots of the data, or of the
learning algorithm outputs will also give
you ideas for how to improve your learning
algorithm, Fortunately, Octave has, very
simple tools to generate lots of different
plots. And when I use learning.
Algorithms. I find that plotting the data,
plotting the linear algorithm. And so on
are often. An important part of how I get
ideas for improving the algorithms. And,
in this video, I'd like to show you some
of these [inaudible] tools for plotting
and visualizing your data. Here's my
[inaudible] window. Let's quickly generate
some data. First the plots. I'm gonna set
T to be equal to, you know, this array of
numbers. Here's T, set of numbers going
from zero up to.98. Let's say Y1 equals
sine of two pi 4T. And if I want to plot.
The side function is very easy I just type
plot T, Y one, and hit enter. And up comes
this part where the horizontal axis is the
T variable and the vertical axis is Y one
which is this sort of [inaudible] sort of
function that we just computed. Let's say
Y two is to be equal to. The co-sign of
two pie four T like so and [cough] if I
plot. T, Y2 what octave will do is it will
take my [inaudible] plot and it will
replace it with this cosign function that
you know cosign of X start at one, right,
now what if I want to have, have both the
sign and the cosign plots on top of each
other what I'm going to do is I'm going to
type, plot T, Y1 so here's my sign
function and then I'm going to use the
function, hold on. And what hold on does
is it causes Octave to now plot new
figures on top of the old one and let me
now plot T Y two I'm plot the cosign
function in a different color so when we
put in R in quotation marks there and
instead of replacing current figure of
plot the cosign function on top and the R
indicates the [inaudible] color and. Here
are additional commands it's labeled times
to label the X axis or horizontal axis and
Y labeled values [inaudible] to label the
vertical axis value and I can also.
[cough] And I can also label my two lines
with this command legend, sign, cosign,
and, this plus this legend, up on the
upper right showing what the two lines
are. And finally title my plot, put a
title at the top of this figure. Lastly if
you want to save this figure, you type
print, [inaudible] d, p and g. My plot
PNG. So, PNG is a graphics file format.
And if you do this, this will actually
save this as a file. If I do that, let me
ch-, change directory to Let's see. Put
that. And then I will print that out. So,
this will take a while. Depending on how
your Octave conversions set up. This may
take a few seconds. But change the
directory to my desktop. And Octave is now
taking a few seconds to save this. If I
now go to my desktop. [cough] Let's hide
these windows [inaudible] that's the
figure saved as a PNG file also can save
in other formats as well so you can type
help plot if you want to see the other
file formats rather than PNG that we can
save figures in and lastly if you want to
get rid of the plot, the close command
[sound]. Causes a figure to go away so
there's a figure I type close you know
that figure just disappeared from my, just
disappeared from my desktop. Altiv also
lets you specify a figure of numbers you
type figure one + T one, one. That starts
up a first figure and that helps TY1 and
then if you want a second figure you
specify different figure numbers so figure
two plot T Y two like so and now on my
desktop I actually have two figures figure
one and figure two there's one plotting
the sign function one plotting the cosign
function. Here's one other neat command
that often use which is the sub plot
command so we're going to use sub plot one
two one what this does is it divides, sub
divides the plot, into A 1x2 grid that's
what the first two parameters are and it
starts to access the first element, that's
what the final parameter of one is right
so just divide my figure into 1x2 grid and
I want to access the first element right
now and so if I type that in this product
this figure is on the left and if I plot
T. Y1, it now fills up this, you know,
first element. And if I now do subplot
122, I'm gonna start to acess a second
element, and plot TY2. We'll throw in Y2
in the right hand side or in the second
element. And last command, you can also
change the access scales, and change
accesses to 1.51 minus 1.1. And this sets
the X range and Y range for the figure on
the right. And completely assess the
horizontal major values in figure on the
right that range to 0.5 to one and
vertical axis values that range from -one
to one. And you know you don't need to
memorize all these command and if you ever
need to change the axis all you need to
know is that there's axis command and you
can really get the details from the usual
[inaudible] help command. Finally just a
[inaudible] CLF here's the figure. And his
one, one matrix less than A is equal to a
five by five matrix square [inaudible] say
so A is now this five by five matrix.
Doesn't we trick lesson as used to
visualize a matrix which I can use image
as c Of A, and what this will do is this
will plot a five by five, matrix. So I'll
take my matrix and plot this as a five by
five grid of colors, where the different
colors correspond to the different values
in the A matrix. So, [inaudible], I can
also do color bar, let me use a more
sophisticated command, [inaudible] color
bar, color. Map gray. This is actually
running three commands at a time. We're
running image sc, then we're running color
bar and we're running colormap gray. And
what this does is it sets the color for
map to gray colormap and on the right it
also puts in this color bar. And so this
color bar shows what the different shades
of color correspond to. Concretely, the
upper left element of the a matrix is
seventeen and so, yeah, that corresponds
to kind of a knit shade of gray. Where as
in contrast the second element of A sort
of the one two element of A is 24 where it
says A one two is 24 so that response to
this graph here which is a nearly a shade
of white. And the small values say A, what
is that, A four five It's about a three
over here that response you can see on my
color bar, that response much darker of
shade in this image. So, here's an example
I can plot it larger [inaudible] magic
fifteen. That gives me fifteen by fifteen
matrix square and this gives me a plot of
a what my fifteen by fifteen matrix values
look like. And finally to wrap up this
video. What you see me do here is use a
comma chaining of function calls. Here's
how you actually do this. If I type A
equals one, B equals two, C equals three
And hit enter then this, this is actually
carrying out three commands at the same
time or really carrying out three commands
one after another and it prints out all
three results and this is a lot like =one
B=2 C=3 except that if I use semicolons
instead of a comma it doesn't print out
anything, so this you know this thing here
we call comma chaining of commands so
comma chaining of function calls and it's
just another convenient way in octave to
put multiple commands like image. See
color bar, color map to put muti commands
on the same line. So that's it. You now
know how to plot different figures in
[inaudible]. And, in, Nick's video, the,
the [inaudible] I wanna tell you about is,
how to write control statements. Like
if/while/for statements in [inaudible], as
well as how to define and use functions.