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When developing learning algorithms, very

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often a few simple plots

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can give you a better

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sense of what the algorithm

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is doing and just sanity check

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that everything is going okay

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and the algorithms doing what is supposed to.

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For example, in an earlier

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video, I talked about how

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plotting the cost function J

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of theta can help you

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make sure that gradient descent is converging.

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Often, plots of the data

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or of all the learning algorithm outputs

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will also give you ideas

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for how to improve your learning algorithm.

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Fortunately, Octave has very

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simple tools to generate lots

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of different plots and when

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I use learning algorithms, I find

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that plotting the data, plotting

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the learning algorithm and so

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on are often an important

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part of how I get

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ideas for improving the

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algorithms and in this video,

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I'd like to show you some

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of these Octave tools for plotting and visualizing your data.

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Here's my Octave window.

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Let's quickly generate some data

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for us to plot.

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So I'm going to set T

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to be equal to, you know, this array of numbers.

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Here's T, set of

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numbers going from 0 up to .98.

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Let's set y1 equals sine

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of 2 pie 40 and

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if I want to plot the sine function, it's very easy.

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I just type plot T comma Y

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1 and hit enter.

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And up comes this plot

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where the horizontal axis is

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the T variable and the vertical

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axis is y1, which

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is the sine you saw in the function that we just computed.

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Let's set y2 to be

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equal to the cosine

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of two pi, four T, like so.

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And if I plot

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T comma y2, what octave

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will I do is I'll take my

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sine plot and it

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will replace with this cosine

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function and now, you know, cosine of xi of 1.

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Now, what if I

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want to have both

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the sine and the cosine plots on top of each other?

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What I'm going to do is I'm

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going to type plot t,y1.

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So here's my sine function, and then

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I'm going to use the function hold on.

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And what hold does it closes

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octaves to now

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figures on top of the

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old one and let

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me now plot t y2.

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I'm going to plot the cosine function in a different color.

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So, let me put there

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r in quotation marks there

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and instead of replacing

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the current figure, I'll plot the

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cosine function on top and

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the r indicates the what is an event color.

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And here additional commands - x

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label times, to label the X axis, or the horizontal axis.

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And Y label values A,

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to label the vertical axis value,

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and I can also

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label my two lines

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with this command: legend sine cosine

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and this puts this

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legend up on the upper

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right showing what the 2

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lines are, and finally title

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my plot is the title at the top of this figure.

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Lastly, if you want to save

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this figure, you type print -dpng

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myplot

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.png.

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So PNG is a graphics

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file format, and if you

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do this it will let you save this as a file.

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If I do that,

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let me actually change directory to,

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let's see, like

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that, and then I will print that out.

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So this will take a

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while depending on how

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your Octave configuration is setup,

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may take a few seconds, but change

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directory to my desktop and Octave

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is now taking a few seconds to save this.

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If I now go to my desktop, Let's hide these windows.

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Here's myplot.png

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which Octave has saved, and you

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know, there's the figure saved as the PNG file.

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Octave can save thousand other formats as well.

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So, you can type help plot,

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if you want to see the

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other file formats, rather than

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PNG, that you can save

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figures in.

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And lastly, if you want

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to get rid of the plot, the

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close command causes the figure to go away.

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As I figure if I type

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close, that figure just

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disappeared from my desktop.

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Octave also lets you specify a figure and numbers.

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You type figure 1 plots t, y1.

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That starts up

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first figure, and that plots t, y1.

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And then if you want a second figure, you specify a different figure number.

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So figure two, plot t,

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y2 like so, and

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now on my desktop, I actually have 2 figures.

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So, figure 1 and figure

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2 thus 1 plotting the sine

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function, 1 plotting the cosine function.

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Here's one other neat command that

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I often use, which is the subplot command.

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So, we're going to use subplot 1 2 1.

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What it does it sub-divides

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the plot into a

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one-by-two grid with the

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first 2 parameters are, and

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it starts to access the

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first element. That's

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what the final parameter 1 is, right?

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So, divide my figure into a

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one by two grid, and I

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want to access the first

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element right now.

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And so, if I type that

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in, this product, this figure, is on the left.

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And if I plot t,

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y1, it now fills

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up this first element.

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And if I I'll do subplot 122.

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I'm going to start to

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access the second element and plot t, y2.

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Well, throw in y2 in

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the right hand side, or in the second element.

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And last command, you can

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also change the axis scales

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and change axis these to 1.51

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minus 1 1 and this

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sets the x range

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and y range for the

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figure on the right,

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and concretely, it assess the horizontal

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major values in the figure

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on the right to make sure 0.5

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to 1, and the vertical

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axis values use the range from minus one to one.

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And, you know, you don't need to memorize all these commands.

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If you ever need to

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change the access or you

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need to know is that, you know, there's an

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access command and you can

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already get the details

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from the usual octave help command.

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Finally, just a couple last

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commands CLF clear is

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a figure and here's one unique trait.

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Let's set a to be equal

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to a 5 by 5

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magic squares a. So, a

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is now this 5 by 5

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matrix does a neat

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trick that I sometimes use to

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visualize the matrix, which is

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I can use image sc

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of a what this will

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do is plot a five

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by five matrix, a five by five grid of color.

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where the different colors correspond to

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the different values in the A matrix.

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So concretely, I can also do color bar.

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Let me use a

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more sophisticated command, and image sc

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A color bar

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color map gray.

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This is actually running three commands at a time.

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I'm running image sc then running

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color bar, then running color map gray.

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And what this does, is it sets

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a color map, so a

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gray color map, and on the

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right it also puts in this color bar.

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And so this color bar

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shows what the different shades of color correspond to.

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Concretely, the upper left

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element of the A matrix

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is 17, and so that corresponds

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to kind of a mint shade of gray.

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Whereas in contrast the second

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element of A--sort of the

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1 2 element of A--is 24.

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Right, so it's A 1 2 is 24.

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So that corresponds to

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this square out here, which is

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nearly a shade of white.

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And the small value, say

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A--what is that? A

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4 5, you know, is a value

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3 over here that corresponds--

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you can see on my color bar

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that it corresponds to a

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much darker shade in this image.

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So here's another example,

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I can plot a larger, you

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know, here's a magic 15 that

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gives you a 15 by 15

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magic square and this

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gives me a plot of what

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my 15 by 15 magic squares values looks like.

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And finally to wrap

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up this video, what you've

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seen me do here is

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use comma chaining of function calls.

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Here's how you actually do this.

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If I type A equals

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1, B equals 2, C equals

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3, and hit Enter, then

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this is actually carrying out

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three commands at the same time.

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Or really carrying out three

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commands, one after another,

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and it prints out all three results.

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And this is a lot like

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A equals 1, B equals

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2, C equals 3, except

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that if I use semicolons instead

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of a comma, it doesn't print out anything.

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So, this, you know,

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this thing here we call comma

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chaining of commands, or comma chaining of function calls.

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And, it's just another

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convenient way in Octave to

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put multiple commands like image sc

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color bar, colon map

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to put multi-commands on the same line.

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So, that's it.

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You now know how to plot

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different figures and octave, and

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in next video the

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next main piece that I want

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to tell you about is how to

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write control statements like if,

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while, for statements and

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octave as well as hard to define and use functions