1
00:00:00,000 --> 00:00:02,766
[MUSIC PLAYING]

2
00:00:02,766 --> 00:00:05,080


3
00:00:05,080 --> 00:00:08,230
SPEAKER: Well, hello, one and all
and welcome to our short on matrices

4
00:00:08,230 --> 00:00:11,980
and arrays, two structures
to store data all the same

5
00:00:11,980 --> 00:00:14,230
type in multiple dimensions.

6
00:00:14,230 --> 00:00:16,280
Now, why would you do that?

7
00:00:16,280 --> 00:00:20,170
Well, I have here an aerial view
of San Francisco and the Bay area

8
00:00:20,170 --> 00:00:21,078
more generally.

9
00:00:21,078 --> 00:00:22,870
And an interesting
thing about this area is

10
00:00:22,870 --> 00:00:27,100
that temperatures vary between the
mountains and the city and the Bay.

11
00:00:27,100 --> 00:00:31,690
We could use matrices and arrays to
model how those temperatures actually

12
00:00:31,690 --> 00:00:34,180
vary in given areas.

13
00:00:34,180 --> 00:00:36,730
Now, setting aside matrices
and arrays for now,

14
00:00:36,730 --> 00:00:40,420
let's just think through how we could
kind of pictorialize temperatures

15
00:00:40,420 --> 00:00:42,560
across this map here.

16
00:00:42,560 --> 00:00:46,060
Well, one thing I suppose we could
do is break it up into a grid

17
00:00:46,060 --> 00:00:47,830
a bit like this one here.

18
00:00:47,830 --> 00:00:52,330
Here we have a three-by-three
grid with nine cells in total

19
00:00:52,330 --> 00:00:55,688
and three rows and three columns.

20
00:00:55,688 --> 00:00:57,730
Now, it turns out, I've
said before, temperatures

21
00:00:57,730 --> 00:01:00,640
can vary between the city and
the mountains and the Bay,

22
00:01:00,640 --> 00:01:05,209
so we could slot in temperatures
to each of these cells representing

23
00:01:05,209 --> 00:01:07,400
the average temperature
in the particular area

24
00:01:07,400 --> 00:01:08,520
that we're talking about.

25
00:01:08,520 --> 00:01:11,870
So for instance, in the top
left here, in San Francisco,

26
00:01:11,870 --> 00:01:14,030
we could add in this temperature.

27
00:01:14,030 --> 00:01:19,040
Maybe it'll be 60 degrees Fahrenheit
and keep going down this column.

28
00:01:19,040 --> 00:01:22,580
Maybe just south of that it's
about 55 degrees on average,

29
00:01:22,580 --> 00:01:25,910
Fahrenheit again, and just south
of that, in the mountains now,

30
00:01:25,910 --> 00:01:29,030
it's even colder, maybe 50
degrees Fahrenheit here.

31
00:01:29,030 --> 00:01:32,310
And we can keep filling things
in now column by column.

32
00:01:32,310 --> 00:01:34,910
So maybe this column here
has these temperatures,

33
00:01:34,910 --> 00:01:38,280
and this column here has
these temperatures here.

34
00:01:38,280 --> 00:01:42,440
So each area has its own average
temperature, depending, in this case,

35
00:01:42,440 --> 00:01:46,470
on where it's located in
the time of day, as well.

36
00:01:46,470 --> 00:01:48,830
So what we've created
here is really a matrix,

37
00:01:48,830 --> 00:01:54,870
a two-dimensional grid of values all of
the same type, all numeric in this case.

38
00:01:54,870 --> 00:01:59,090
It's a 2D grid where we have, in this
case, three rows and three columns,

39
00:01:59,090 --> 00:02:02,040
a three-by-three matrix, in this case.

40
00:02:02,040 --> 00:02:07,130
So let's try to build this same idea
now in R, making use of a function

41
00:02:07,130 --> 00:02:08,960
that we'll call matrix.

42
00:02:08,960 --> 00:02:12,085
So we'll come over here
to RStudio, and let

43
00:02:12,085 --> 00:02:19,050
me make here a file called
weather.R, just like this.

44
00:02:19,050 --> 00:02:23,930
And I'll see, in my File Explorer
here, I now have this file weather.R.

45
00:02:23,930 --> 00:02:27,620
We'll save temps.R data
for a bit later here.

46
00:02:27,620 --> 00:02:31,040
Let me open up weather.R, and
the first thing I want to do,

47
00:02:31,040 --> 00:02:36,110
is think through what data I
should store in this matrix.

48
00:02:36,110 --> 00:02:39,800
Well, to do that, I'll actually
first need to make a vector.

49
00:02:39,800 --> 00:02:43,700
A vector of the pieces of data
I want to store in this matrix.

50
00:02:43,700 --> 00:02:48,650
So let's go back to our visualization
here and see what data we have.

51
00:02:48,650 --> 00:02:50,930
Well, it turns out, when
we make this matrix,

52
00:02:50,930 --> 00:02:54,480
we're going to fill it in, like
we did before, column by column.

53
00:02:54,480 --> 00:02:57,050
So I want a vector that
has all of these values

54
00:02:57,050 --> 00:02:59,670
that I could fill in to this
matrix column by column.

55
00:02:59,670 --> 00:03:03,020
So I would start perhaps, with 60
degrees Fahrenheit, top left here.

56
00:03:03,020 --> 00:03:06,290
Then maybe 55 degrees, kind
of middle left, as well,

57
00:03:06,290 --> 00:03:08,420
then 50 degrees bottom left.

58
00:03:08,420 --> 00:03:13,580
Then I would go to 60 top middle, 60
again, in the middle of the matrix here,

59
00:03:13,580 --> 00:03:17,250
and 55 down in the
middle of the bottom row.

60
00:03:17,250 --> 00:03:21,710
So let's keep going here and make up
our own vector to store in this matrix.

61
00:03:21,710 --> 00:03:26,570
We'll come back now to RStudio, and
why don't we name this vector something

62
00:03:26,570 --> 00:03:28,650
like temps, just like this.

63
00:03:28,650 --> 00:03:33,800
And to make a vector of a certain type
or to actually add in some data here,

64
00:03:33,800 --> 00:03:38,990
I can use this function called c to
basically add in individual values

65
00:03:38,990 --> 00:03:40,580
to this vector.

66
00:03:40,580 --> 00:03:44,750
So the first value, as we said before,
is going to be the one in the top left,

67
00:03:44,750 --> 00:03:46,340
60 degrees Fahrenheit.

68
00:03:46,340 --> 00:03:48,290
I'll make sure that I have 60 here.

69
00:03:48,290 --> 00:03:53,900
The next one, down below in the
column now, was 55, followed by 50.

70
00:03:53,900 --> 00:03:56,420
And that was our first column of data.

71
00:03:56,420 --> 00:03:57,710
Let's move to the next column.

72
00:03:57,710 --> 00:04:05,060
I believe that one began with 60 here,
then we had 60 again, and then 55.

73
00:04:05,060 --> 00:04:08,953
Let's check that 60, 60, and 55.

74
00:04:08,953 --> 00:04:09,620
OK, pretty good.

75
00:04:09,620 --> 00:04:11,210
Let's do the next column now.

76
00:04:11,210 --> 00:04:15,472
I'll say that one was 65, 60, and 60.

77
00:04:15,472 --> 00:04:16,430
Let's check that again.

78
00:04:16,430 --> 00:04:19,399
I see 65, 60, and 60.

79
00:04:19,399 --> 00:04:21,529
So it seems like our
vector is appropriate now

80
00:04:21,529 --> 00:04:23,660
for building this matrix.

81
00:04:23,660 --> 00:04:26,660
Let's come back now here, and
we want to make sure we actually

82
00:04:26,660 --> 00:04:29,090
store this vector temps.

83
00:04:29,090 --> 00:04:32,150
And if I type now temps in my
console, I should, hopefully,

84
00:04:32,150 --> 00:04:35,750
see all these numbers that
are part of my vector.

85
00:04:35,750 --> 00:04:39,860
Now, to make this matrix, I actually
use a function called matrix.

86
00:04:39,860 --> 00:04:42,120
And I would use it a bit like this.

87
00:04:42,120 --> 00:04:47,910
I could use matrix by typing in the
matrix function, just like this.

88
00:04:47,910 --> 00:04:51,350
And it turns out that matrix
takes a few arguments.

89
00:04:51,350 --> 00:04:54,890
One is this vector called
temps, the very first one.

90
00:04:54,890 --> 00:04:58,310
The data we want to actually
store inside of this matrix.

91
00:04:58,310 --> 00:05:00,920
So I'll type temps
here, saying that I will

92
00:05:00,920 --> 00:05:06,580
use this vector I defined earlier to
fill in this matrix I'm about to create.

93
00:05:06,580 --> 00:05:11,950
Now the next two arguments, they
are defined by the number of rows

94
00:05:11,950 --> 00:05:15,220
and the number of columns we
actually want to have in this matrix.

95
00:05:15,220 --> 00:05:17,710
So again, we had a
three-by-three matrix,

96
00:05:17,710 --> 00:05:20,590
meaning we had three
rows and three columns.

97
00:05:20,590 --> 00:05:23,500
And then when we specify
this in R is as follows,

98
00:05:23,500 --> 00:05:29,230
I can say n row, for number of rows,
and set it equal to some value, like 3,

99
00:05:29,230 --> 00:05:30,590
in this case.

100
00:05:30,590 --> 00:05:36,710
I could also do ncol, another argument
here, and set that equal to 3, as well.

101
00:05:36,710 --> 00:05:40,180
So now I've said, take this
data from my temps vector

102
00:05:40,180 --> 00:05:44,450
and turn it into a matrix that
has three rows and three columns.

103
00:05:44,450 --> 00:05:47,890
So if I'm at my console, a
little bit bigger down here,

104
00:05:47,890 --> 00:05:51,910
and I were to run this function
matrix here, what should I see?

105
00:05:51,910 --> 00:05:55,750
Well, a matrix down below
looking very similar to the grid

106
00:05:55,750 --> 00:05:58,780
we saw in our slides, albeit
without the background here.

107
00:05:58,780 --> 00:06:05,660
I see the first column of 60, 55,
and 50 next column 60, 60, 55,

108
00:06:05,660 --> 00:06:08,720
and then 65, 60, and 60 again.

109
00:06:08,720 --> 00:06:11,690
So why don't we store this
now in its own object.

110
00:06:11,690 --> 00:06:13,520
I'll call this one weather.

111
00:06:13,520 --> 00:06:16,590
And I'll assign it now to this name.

112
00:06:16,590 --> 00:06:20,750
So if I type weather, in the future, I
should now see this matrix of values,

113
00:06:20,750 --> 00:06:24,860
a three-by-three grid of these
values all of the same type.

114
00:06:24,860 --> 00:06:27,890
Now, matrices can be of any
dimension, actually, really

115
00:06:27,890 --> 00:06:29,870
of any number of rows or columns.

116
00:06:29,870 --> 00:06:31,820
They have to be two
dimensional, that is.

117
00:06:31,820 --> 00:06:35,960
Now, I can make this four
columns or four rows,

118
00:06:35,960 --> 00:06:39,350
whatever it is, as long as my
vector has enough data to fill

119
00:06:39,350 --> 00:06:42,630
in all of those rows and columns.

120
00:06:42,630 --> 00:06:45,620
So if we have this matrix,
what can we do with it?

121
00:06:45,620 --> 00:06:48,600
One thing we can do is try
to access certain values.

122
00:06:48,600 --> 00:06:52,790
So if I tried here to maybe store this
as a matrix, as I've already done,

123
00:06:52,790 --> 00:06:57,890
I could then ask the question, what
does this first row of values look like?

124
00:06:57,890 --> 00:07:01,520
I could access that first row of
values by using a syntax, actually,

125
00:07:01,520 --> 00:07:02,900
just like we saw down below.

126
00:07:02,900 --> 00:07:08,510
If I look down below here, I'll see that
the first row seems to have this syntax

127
00:07:08,510 --> 00:07:09,665
in front of it, [1,_].

128
00:07:09,665 --> 00:07:12,260


129
00:07:12,260 --> 00:07:16,880
Hmm, so if I actually go to my
program here and type weather,

130
00:07:16,880 --> 00:07:23,000
the name of our, in this case,
matrix, and then I type [1,_] space

131
00:07:23,000 --> 00:07:26,420
for style's sake, I'll hit
Enter here, command Enter,

132
00:07:26,420 --> 00:07:31,130
and I'll actually see the very
first row of values in our matrix.

133
00:07:31,130 --> 00:07:32,270
Let's check that again.

134
00:07:32,270 --> 00:07:37,940
Here, I'll go back, and I see 60, 60,
and 65 for the first row of this matrix,

135
00:07:37,940 --> 00:07:39,420
so pretty good.

136
00:07:39,420 --> 00:07:42,840
I could even try to find
values by column, too.

137
00:07:42,840 --> 00:07:47,060
So I could use weather, and then I
could leave the first part blank,

138
00:07:47,060 --> 00:07:52,200
just do comma space, and then type in
1, and that would give me, in this case,

139
00:07:52,200 --> 00:07:54,360
the first column of values.

140
00:07:54,360 --> 00:07:56,880
So to be clear, what
we're doing here is this.

141
00:07:56,880 --> 00:08:03,020
When I did weather [1,_], I was
asking for this first row of values,

142
00:08:03,020 --> 00:08:07,250
and when I did the second thing
I did here, weather [, 1],

143
00:08:07,250 --> 00:08:10,680
I'm asking for the first column
of values in this matrix.

144
00:08:10,680 --> 00:08:14,450
And I could use 1, 2, or 3
the indexes for this matrix

145
00:08:14,450 --> 00:08:18,140
here, to get any row or
any column I would like.

146
00:08:18,140 --> 00:08:19,700
Now, I can also combine these.

147
00:08:19,700 --> 00:08:26,415
So let's say I were to
type this, weather [1,1],

148
00:08:26,415 --> 00:08:29,540
I'm curious what you think that would
give me if we look back at our matrix

149
00:08:29,540 --> 00:08:30,560
here.

150
00:08:30,560 --> 00:08:34,520
Might give us, in this case,
the value in the first row

151
00:08:34,520 --> 00:08:38,570
and in the first column, which would
be this top left one 60 degrees.

152
00:08:38,570 --> 00:08:39,559
So let's try that.

153
00:08:39,559 --> 00:08:43,730
If I type this and run this
line of code here on line 11,

154
00:08:43,730 --> 00:08:48,980
I should see I get back 60 degrees from
this matrix of values I've created.

155
00:08:48,980 --> 00:08:50,660
So pretty handy here.

156
00:08:50,660 --> 00:08:53,490
And there are other options
for making matrices, too.

157
00:08:53,490 --> 00:08:57,920
So if I were to type, ?matrix to
actually open up the documentation

158
00:08:57,920 --> 00:09:02,810
for matrices, I would see exactly how I
could use this matrix function and some

159
00:09:02,810 --> 00:09:04,980
other parameters inside of it.

160
00:09:04,980 --> 00:09:07,970
So let me go over here and show
you what that could look like.

161
00:09:07,970 --> 00:09:12,260
If I scroll down, and look
at the usage now for matrix,

162
00:09:12,260 --> 00:09:15,350
I'll see that, again,
the first argument was--

163
00:09:15,350 --> 00:09:18,200
the one we gave it --in this
case, it has a name, "data,"

164
00:09:18,200 --> 00:09:21,830
but we gave the value of
temps for our vector now.

165
00:09:21,830 --> 00:09:26,870
We set these parameters here, nrow
and ncol, which are by default 1.

166
00:09:26,870 --> 00:09:31,350
And we could also change this
parameter here called byrow.

167
00:09:31,350 --> 00:09:37,318
So by default, we filled in our matrix
by column first, first the first column,

168
00:09:37,318 --> 00:09:39,110
then the next column,
and the third column,

169
00:09:39,110 --> 00:09:44,340
but we could invert that, and instead,
fill in our data by row instead.

170
00:09:44,340 --> 00:09:46,160
And there's one more
here down here, too,

171
00:09:46,160 --> 00:09:51,200
one called dimnames, which let us
name the dimensions of our matrix.

172
00:09:51,200 --> 00:09:53,360
The one going top to
bottom, and the one going

173
00:09:53,360 --> 00:09:57,080
left to right, in this case, kind
of our x- or y-axis, if you will,

174
00:09:57,080 --> 00:09:59,240
inside of our matrix.

175
00:09:59,240 --> 00:10:04,660
So this is how we can make matrices
in R and access their values.

176
00:10:04,660 --> 00:10:08,530
Now, there is a more
advanced data structure that

177
00:10:08,530 --> 00:10:10,630
might actually come in handy for us.

178
00:10:10,630 --> 00:10:12,470
One called an array.

179
00:10:12,470 --> 00:10:14,480
So let's look at why
we might use an array

180
00:10:14,480 --> 00:10:18,560
and think through, conceptually, what
it could represent for us in this case.

181
00:10:18,560 --> 00:10:22,300
So I'll come back now to
our slides, and let's think.

182
00:10:22,300 --> 00:10:26,650
So this represents temperatures
at a certain moment in time,

183
00:10:26,650 --> 00:10:30,610
maybe in the afternoon time,
but as evening approaches,

184
00:10:30,610 --> 00:10:32,950
these temperatures
might actually change.

185
00:10:32,950 --> 00:10:36,730
They might go from this to this,
getting a little bit colder

186
00:10:36,730 --> 00:10:38,290
as the night goes on.

187
00:10:38,290 --> 00:10:42,290
And maybe around midnight or so,
once it is definitively night time,

188
00:10:42,290 --> 00:10:43,570
it might be even colder.

189
00:10:43,570 --> 00:10:47,030
Maybe it changes to be a temperature
landscape more like this here.

190
00:10:47,030 --> 00:10:49,330
So temperatures can change over time.

191
00:10:49,330 --> 00:10:53,500
Each location can have its own
temperature change over time.

192
00:10:53,500 --> 00:10:57,370
Now, to represent this, you might
notice we're using multiple matrices.

193
00:10:57,370 --> 00:11:02,170
If I go back to our very first one, this
was one matrix, this was another matrix,

194
00:11:02,170 --> 00:11:04,520
and this was a third matrix.

195
00:11:04,520 --> 00:11:08,030
So how could we combine these
into one data structure?

196
00:11:08,030 --> 00:11:11,540
Well, we can do so by
thinking in three dimensions.

197
00:11:11,540 --> 00:11:15,620
So here we have a cube, a good visual
metaphor for what we're about to do.

198
00:11:15,620 --> 00:11:19,520
You can imagine, again, our first
matrix, which was two dimensional,

199
00:11:19,520 --> 00:11:21,990
had three rows and three columns.

200
00:11:21,990 --> 00:11:25,820
But you could also visualize
time on its own axis

201
00:11:25,820 --> 00:11:28,820
here, this third dimension that
stretches back, in this case,

202
00:11:28,820 --> 00:11:29,910
for instance.

203
00:11:29,910 --> 00:11:32,750
You could imagine that
these temperatures change

204
00:11:32,750 --> 00:11:35,060
over time in this third dimension.

205
00:11:35,060 --> 00:11:37,100
So for instance, if
we look at, let's say,

206
00:11:37,100 --> 00:11:40,520
the top-right cell in
each of our matrices,

207
00:11:40,520 --> 00:11:45,500
notice how it is first 65 degrees
Fahrenheit, then as evening comes,

208
00:11:45,500 --> 00:11:48,650
it stays about 65 degrees,
but then as night time comes,

209
00:11:48,650 --> 00:11:50,900
it changes to 55 degrees.

210
00:11:50,900 --> 00:11:53,930
So time, in this case, is a
third dimension stretching

211
00:11:53,930 --> 00:11:56,630
backwards from our point of view now.

212
00:11:56,630 --> 00:11:59,870
So you can have these structures
that are multi-dimensional,

213
00:11:59,870 --> 00:12:04,070
not just 2D but 3D or 4D, 5D,
however many dimensions you want,

214
00:12:04,070 --> 00:12:06,360
you can make in terms of an array.

215
00:12:06,360 --> 00:12:09,440
So let's go ahead and try
this out using this same data.

216
00:12:09,440 --> 00:12:14,330
We'll come back now to weather.R. And
let me clear what I have right now

217
00:12:14,330 --> 00:12:19,760
and instead, load in this new vector I
created and stored inside of this file

218
00:12:19,760 --> 00:12:23,760
called temps.RData, on
the right-hand side here.

219
00:12:23,760 --> 00:12:28,820
So if I were to run this,
load("temps.RData"),

220
00:12:28,820 --> 00:12:32,060
saying take whatever data
is stored inside this file,

221
00:12:32,060 --> 00:12:35,060
temps.RData and load it
into my environment, well,

222
00:12:35,060 --> 00:12:40,730
I should get now a new
value for this vector temps.

223
00:12:40,730 --> 00:12:46,460
If I hit command Enter here, you'll
see a lot more values in this vector.

224
00:12:46,460 --> 00:12:49,490
And this is because we have
enough data to fill in,

225
00:12:49,490 --> 00:12:52,520
not just that first matrix,
not just that second,

226
00:12:52,520 --> 00:12:54,770
but also that third matrix, too.

227
00:12:54,770 --> 00:12:59,690
Enough values to fill in three whole
three-by-three matrices stretching back

228
00:12:59,690 --> 00:13:01,580
in time, if you will.

229
00:13:01,580 --> 00:13:03,950
So how can we turn this
vector into an array?

230
00:13:03,950 --> 00:13:07,080
Well, we can use, in this
case, the array function.

231
00:13:07,080 --> 00:13:09,020
So I will do just that here.

232
00:13:09,020 --> 00:13:12,290
It looks very similar to our
matrix function in terms of usage.

233
00:13:12,290 --> 00:13:16,910
I could type array, just like this, and
I could give in, as the first argument

234
00:13:16,910 --> 00:13:19,040
here, this temps vector.

235
00:13:19,040 --> 00:13:23,960
So I'll say temps is the vector we'll
use to fill in this array of values.

236
00:13:23,960 --> 00:13:26,390
But then array differs
slightly from matrix,

237
00:13:26,390 --> 00:13:31,610
and it takes another argument,
another parameter one called dim, dim.

238
00:13:31,610 --> 00:13:33,860
And dim stands for dimensions.

239
00:13:33,860 --> 00:13:38,940
Now, the dimension argument actually
takes a vector as input itself.

240
00:13:38,940 --> 00:13:41,870
So here I'll define a new
vector using our c function.

241
00:13:41,870 --> 00:13:45,890
And I could say, well, what
kind of dimensions do I want?

242
00:13:45,890 --> 00:13:51,560
We saw before, when we had a 2D
matrix, it was a three-by-three matrix,

243
00:13:51,560 --> 00:13:55,520
but now if I look back at our
cube, you might notice that, well,

244
00:13:55,520 --> 00:13:57,440
there are three matrices here.

245
00:13:57,440 --> 00:14:02,930
It's kind of like we have a three by
three by three structure three rows,

246
00:14:02,930 --> 00:14:06,950
three columns, but each of those
stretches back three different times.

247
00:14:06,950 --> 00:14:10,220
And you can visualize it a bit
more like this notice how we have,

248
00:14:10,220 --> 00:14:14,240
again three rows, three
columns, but three of those rows

249
00:14:14,240 --> 00:14:16,880
and columns stretching back in time.

250
00:14:16,880 --> 00:14:18,890
So let's look at this now.

251
00:14:18,890 --> 00:14:23,180
I could actually represent this same
cube by making a vector like this,

252
00:14:23,180 --> 00:14:26,150
3,3,3.

253
00:14:26,150 --> 00:14:30,620
And this specifies I want three rows,
three columns, and each of those

254
00:14:30,620 --> 00:14:34,040
is stretched back three times
in this other dimension we have.

255
00:14:34,040 --> 00:14:37,520
So if I were to run this line
of code here on line five,

256
00:14:37,520 --> 00:14:41,360
you could then see a much more
complex output down below.

257
00:14:41,360 --> 00:14:43,520
But we can break it down
into smaller pieces.

258
00:14:43,520 --> 00:14:46,640
Notice here, that this should
look a little bit familiar.

259
00:14:46,640 --> 00:14:50,360
This is the matrix we had at the
beginning of our temperatures at one

260
00:14:50,360 --> 00:14:51,860
point in time.

261
00:14:51,860 --> 00:14:56,030
But then, we also have the
next matrix down below here,

262
00:14:56,030 --> 00:14:58,910
and the next matrix down
below here representing

263
00:14:58,910 --> 00:15:02,640
how the temperatures have
changed over time, as well.

264
00:15:02,640 --> 00:15:07,425
So how could we access this data in
this three-dimensional structure?

265
00:15:07,425 --> 00:15:10,920
Well, we could actually still
make use of this comma syntax.

266
00:15:10,920 --> 00:15:12,060
We see a hint here.

267
00:15:12,060 --> 00:15:17,670
Notice how I have comma comma 1,
this seems to give me this matrix.

268
00:15:17,670 --> 00:15:22,290
Comma comma 2, well, this gives me
this matrix, our second one here,

269
00:15:22,290 --> 00:15:26,380
and comma comma 3, gives
me our third matrix here.

270
00:15:26,380 --> 00:15:27,900
So I actually could try this.

271
00:15:27,900 --> 00:15:31,680
If I go into our file,
I could store this now

272
00:15:31,680 --> 00:15:35,280
as the new array for
this weather object.

273
00:15:35,280 --> 00:15:37,290
I'll hit command Enter to store that.

274
00:15:37,290 --> 00:15:44,610
And now, if I were to type,
on line 10, weather[,, 1],

275
00:15:44,610 --> 00:15:46,560
what do you think I should see?

276
00:15:46,560 --> 00:15:49,740
Probably the first matrix
in this 3D structure.

277
00:15:49,740 --> 00:15:53,520
So I'll hit Enter now, and I'll
actually get back that very first matrix

278
00:15:53,520 --> 00:15:54,522
from before.

279
00:15:54,522 --> 00:15:56,730
But then how did these
temperatures change over time?

280
00:15:56,730 --> 00:15:58,188
Well, I could look at the next one.

281
00:15:58,188 --> 00:16:05,920
I could say, weather[,, 2], and now I
see my second matrix, weather[,, 3],

282
00:16:05,920 --> 00:16:08,770
and now I'll see our
third matrix, again,

283
00:16:08,770 --> 00:16:12,470
visualizing how these temperatures
have changed over time.

284
00:16:12,470 --> 00:16:17,090
So similar to matrix, array does
have its own documentation too.

285
00:16:17,090 --> 00:16:20,560
So if I type ?array, to
open this documentation,

286
00:16:20,560 --> 00:16:23,920
I can see ways to create an array.

287
00:16:23,920 --> 00:16:25,680
I'll open this up for us here.

288
00:16:25,680 --> 00:16:28,640
And let's look at the
usage now for array.

289
00:16:28,640 --> 00:16:31,990
So we saw our very
first argument to array

290
00:16:31,990 --> 00:16:34,330
was a parameter that we called data.

291
00:16:34,330 --> 00:16:37,180
And we gave it the value
temps, this longer version

292
00:16:37,180 --> 00:16:40,540
of temps to fill in not
just one matrix but three.

293
00:16:40,540 --> 00:16:44,230
We then specified the
dimensions in terms of a vector.

294
00:16:44,230 --> 00:16:47,260
In this case, we gave it a
vector of length 3, where

295
00:16:47,260 --> 00:16:51,340
we asked for three rows, three
columns, and three of those structures

296
00:16:51,340 --> 00:16:53,050
to stretch back in time.

297
00:16:53,050 --> 00:16:55,720
And finally, we have a
very similar parameter,

298
00:16:55,720 --> 00:17:00,160
dimnames if we wanted to name
each of those dimensions,

299
00:17:00,160 --> 00:17:04,329
like, x, y, or z or maybe like
longitude, latitude, and time

300
00:17:04,329 --> 00:17:07,180
we could do that here if we wanted to.

301
00:17:07,180 --> 00:17:10,089
So this is a brief
foray into how we have

302
00:17:10,089 --> 00:17:13,900
tried to create our own structures
using matrices and arrays to represent

303
00:17:13,900 --> 00:17:15,978
temperatures how they
can change over time.

304
00:17:15,978 --> 00:17:18,520
I'm excited to see what you all
create with these structures.

305
00:17:18,520 --> 00:17:20,550
See you next time.

306
00:17:20,550 --> 00:17:22,000