1
00:00:00,330 --> 00:00:02,460
Welcome to this section on packages.

2
00:00:03,000 --> 00:00:09,290
The two packages we shall be looking at now I am apt to leave to install this.

3
00:00:09,300 --> 00:00:15,060
Just have people install numpy and then to use it.

4
00:00:15,070 --> 00:00:26,820
You could have simply known as and the number is a high performance computing library a see how to create

5
00:00:26,820 --> 00:00:28,740
a simple nonpareil.

6
00:00:29,490 --> 00:00:38,070
So we have that we have e equals and array obviously we have import it non pires mp.

7
00:00:38,070 --> 00:00:42,780
So everywhere we have an empire with simple to use and the pattern array.

8
00:00:42,780 --> 00:00:48,570
Let's have this one dimensional list and there we go.

9
00:00:48,570 --> 00:00:50,670
We have that we could not print out.

10
00:00:50,670 --> 00:00:52,560
E And that's it.

11
00:00:52,800 --> 00:00:53,860
That's our an umpire.

12
00:00:53,860 --> 00:00:59,040
Ray We could also define a two dimensional array a B.

13
00:01:00,770 --> 00:01:13,100
And Peter Del Rey, we have this two dimensional array zero negative form then.

14
00:01:15,180 --> 00:01:15,980
Six.

15
00:01:18,810 --> 00:01:20,970
We could also specify the data type.

16
00:01:21,720 --> 00:01:30,170
So your what is your specify the data type so you look for on that.

17
00:01:32,070 --> 00:01:32,820
Let's check on this.

18
00:01:32,820 --> 00:01:34,140
We're supposed to have a comma, right?

19
00:01:34,140 --> 00:01:35,160
Yeah, we're on that.

20
00:01:35,760 --> 00:01:45,510
Now, let's bring out B, which is a two dimensional array we see that is made of three rows and one,

21
00:01:45,510 --> 00:01:47,730
two, three, four, five columns.

22
00:01:50,170 --> 00:01:51,610
If you do be that ship.

23
00:01:52,120 --> 00:01:53,320
See, we have three rows.

24
00:01:53,350 --> 00:01:54,070
Five columns.

25
00:01:54,400 --> 00:01:58,030
It's very important to always come up.

26
00:01:58,720 --> 00:01:59,890
Get this ship.

27
00:02:00,010 --> 00:02:06,610
Because when debugging your code, get into know a given arrays ship is very important.

28
00:02:07,630 --> 00:02:12,070
Note that a simple list see like this.

29
00:02:14,260 --> 00:02:20,500
If you have to print out e that ship you will have this error list has no attribute ship.

30
00:02:21,340 --> 00:02:25,960
Now if you have no compiler already C that works.

31
00:02:26,440 --> 00:02:30,550
Now we could print out the non pilot array which takes an A.

32
00:02:30,940 --> 00:02:38,530
So this now is a non-priority which kicks in, which is basically made of this list.

33
00:02:40,560 --> 00:02:47,940
But this one has the advantage that we could make use of non-price methods and properties.

34
00:02:49,320 --> 00:02:59,880
We could also create a zero hour re so we have the E and the zeros and then once the a kind of array

35
00:02:59,880 --> 00:03:01,320
just never specified a ship.

36
00:03:02,250 --> 00:03:04,980
See, we have an error which is very common.

37
00:03:05,580 --> 00:03:09,480
Make sure that you put this as a double so we should have that.

38
00:03:09,780 --> 00:03:11,220
So specifying this.

39
00:03:11,220 --> 00:03:14,730
We have this ship here and that's fine.

40
00:03:14,730 --> 00:03:16,260
Now print out E.

41
00:03:18,870 --> 00:03:19,500
And there we go.

42
00:03:19,500 --> 00:03:25,740
We have this three rows and then five columns to have see it.

43
00:03:26,190 --> 00:03:29,910
See the difference graph one that the.

44
00:03:33,250 --> 00:03:40,480
And if you have any problem understanding the role colored notations, you could check out on our linear

45
00:03:40,480 --> 00:03:41,500
algebra course.

46
00:03:42,610 --> 00:03:45,190
Apart from those zeros, we could also have one.

47
00:03:45,850 --> 00:03:46,810
So just like that.

48
00:03:47,140 --> 00:03:47,800
There we go.

49
00:03:48,250 --> 00:03:52,420
If we want to have a particular number, you can simply take five by that and all this.

50
00:03:52,420 --> 00:03:54,460
So we have five times all the ones.

51
00:03:54,460 --> 00:03:55,660
So that's what we get.

52
00:03:56,200 --> 00:03:57,190
Yeah, 15.

53
00:03:58,090 --> 00:03:59,260
And basically, that's it.

54
00:04:02,530 --> 00:04:06,920
Also create an array which goes from one value to another.

55
00:04:06,970 --> 00:04:13,390
So we have in space now as a word goal, we have lean space.

56
00:04:13,930 --> 00:04:20,650
So we are going to go from C 3 to 9 while giving a space of two.

57
00:04:21,370 --> 00:04:22,360
That's pretty not a.

58
00:04:25,080 --> 00:04:27,740
You have this theory nine.

59
00:04:28,380 --> 00:04:34,860
No, actually, what the what this does is similar to the arrangement as a there's a difference.

60
00:04:35,190 --> 00:04:39,840
Let's take this off and then have arranged run that.

61
00:04:43,010 --> 00:04:44,260
They went out.

62
00:04:44,620 --> 00:04:45,080
Okay.

63
00:04:45,440 --> 00:04:48,020
So this is the end, Peter.

64
00:04:48,020 --> 00:04:51,590
Arrange and years and put up lane space.

65
00:04:53,300 --> 00:05:00,200
For the two methods we're going from this initial position to this final position for the lean space

66
00:05:00,980 --> 00:05:02,780
will define the number of.

67
00:05:04,510 --> 00:05:06,550
Different values we shall take.

68
00:05:07,030 --> 00:05:12,760
So since we've set out to work with only two values, we start with three and obviously we end with

69
00:05:12,940 --> 00:05:13,380
nine.

70
00:05:13,390 --> 00:05:15,130
So we weren't working with two values.

71
00:05:15,430 --> 00:05:21,280
Now, if we go to three values, you would have another value coming up in the middle.

72
00:05:21,280 --> 00:05:23,140
So here we have three, six, nine.

73
00:05:23,530 --> 00:05:27,880
If you go to four values, so you have three, five, four, seven, nine.

74
00:05:27,880 --> 00:05:36,310
So basically what this does is it takes nine minus three, gives us six, and it tries to break it up

75
00:05:36,310 --> 00:05:43,810
or break this sequence up such that we have four different points.

76
00:05:44,410 --> 00:05:48,550
Continuing reasons you have to work with decimals, so that is it.

77
00:05:49,480 --> 00:05:51,550
Now we have the four range.

78
00:05:51,940 --> 00:05:55,870
We are not defining the number of points which are off in our list.

79
00:05:55,870 --> 00:06:03,190
So the number of elements which are have now least with this, is that what we're defining is a step

80
00:06:03,190 --> 00:06:04,660
between each element.

81
00:06:04,660 --> 00:06:10,990
So if we say we have a step two, so almost start three plus two, we go to five plus two, we go to

82
00:06:10,990 --> 00:06:11,500
seven.

83
00:06:11,800 --> 00:06:15,610
And then we don't also take in the last element.

84
00:06:16,090 --> 00:06:18,160
So that's why we have this three, five, seven.

85
00:06:19,570 --> 00:06:21,730
Let's modify this to say a step of one.

86
00:06:21,730 --> 00:06:25,840
You see we go three, four, five, six, seven, eight, and then we don't take the last.

87
00:06:26,890 --> 00:06:35,020
This two is similar to the range function where we are from C 3 to 9, 3 to 9.

88
00:06:35,020 --> 00:06:40,630
And what happens if I that we want to for that let's bring this out.

89
00:06:42,310 --> 00:06:51,910
See, we have 392 and we have four I in range three nine.

90
00:06:53,960 --> 00:06:58,100
To keep an eye on.

91
00:06:58,100 --> 00:06:58,580
There we go.

92
00:06:58,580 --> 00:07:02,690
We have three, five, seven, which is similar to what we had here.

93
00:07:05,190 --> 00:07:09,900
We could also create an identity matrix very easily.

94
00:07:10,380 --> 00:07:13,140
Suppose we have this, we have an eye.

95
00:07:14,550 --> 00:07:18,780
We have the shape, the exact five way five.

96
00:07:20,410 --> 00:07:21,930
Arbiter that doesn't take that.

97
00:07:21,930 --> 00:07:23,820
So let's pass this way.

98
00:07:24,060 --> 00:07:29,700
Print out E so this arrow, so it means we need a partnership symbol like that.

99
00:07:29,970 --> 00:07:31,080
So would I.

100
00:07:31,080 --> 00:07:36,600
Instead of having to put the shape as a tuple, we just have to pass it this way.

101
00:07:36,600 --> 00:07:37,650
You could pass it like this.

102
00:07:37,650 --> 00:07:39,780
Simply unlike with the zeros.

103
00:07:39,780 --> 00:07:43,290
Where was a zero we have here?

104
00:07:43,560 --> 00:07:45,510
Where if we just have C.

105
00:07:47,260 --> 00:07:47,650
That.

106
00:07:47,920 --> 00:07:48,880
See, we have an arrow.

107
00:07:51,660 --> 00:07:52,770
So let's get back to this.

108
00:07:52,770 --> 00:07:54,450
Would I run it like that?

109
00:07:54,450 --> 00:08:00,810
And then we have this idea that's a metric we'd want, and this diagonal and all the other positions

110
00:08:00,810 --> 00:08:01,530
are zero.

111
00:08:02,400 --> 00:08:10,110
We could also create an empty array so we could see empty that empty see through it.

112
00:08:10,250 --> 00:08:12,780
We print out a.

113
00:08:14,920 --> 00:08:17,350
Just like with the zeros and it specify this.

114
00:08:18,850 --> 00:08:19,420
So that's it.

115
00:08:20,830 --> 00:08:23,860
Then many times we shall be working with random numbers.

116
00:08:23,860 --> 00:08:36,880
So it could have and be that random random C for let's let's have that C we have this random numbers.

117
00:08:36,880 --> 00:08:37,810
We should generate it.

118
00:08:38,380 --> 00:08:41,470
Now we could specify the shape C four or five.

119
00:08:41,890 --> 00:08:42,520
There we go.

120
00:08:43,840 --> 00:08:47,200
Now, we have seen many of this operations.

121
00:08:47,650 --> 00:08:50,870
This method is called on a single array.

122
00:08:51,430 --> 00:08:57,010
Let's suppose we define this array and with that array, let's just copy from this.

123
00:08:57,130 --> 00:08:57,700
Yeah.

124
00:08:58,840 --> 00:09:00,340
So we'll define this array.

125
00:09:02,860 --> 00:09:03,670
That is.

126
00:09:04,450 --> 00:09:07,660
Yeah, we have a, which is this.

127
00:09:07,660 --> 00:09:12,040
Ah they could bring out a ship three by five.

128
00:09:13,060 --> 00:09:25,030
Those if I'm B now B could be a random array, random of random.

129
00:09:25,150 --> 00:09:30,220
Specify the shape C three by five two.

130
00:09:31,150 --> 00:09:31,720
So that's it.

131
00:09:32,140 --> 00:09:38,980
Now we have this random array, three by five, three by five and yeah, we have B, so now let's.

132
00:09:41,410 --> 00:09:45,040
Let's print out E plus B.

133
00:09:47,410 --> 00:09:48,450
This doesn't take shape.

134
00:09:48,460 --> 00:09:49,690
So let's take that off.

135
00:09:50,320 --> 00:09:52,390
Okay, that's fine now.

136
00:09:52,420 --> 00:09:54,520
Or I didn't up this too.

137
00:09:54,520 --> 00:09:58,570
It's just like simple matrix addition.

138
00:09:58,820 --> 00:09:59,290
You see that?

139
00:09:59,410 --> 00:10:08,080
Just the an element wise addition where there's elements added on to this corresponding element in the

140
00:10:08,650 --> 00:10:11,470
the array and all the rest follow.

141
00:10:11,950 --> 00:10:12,610
So that's it.

142
00:10:13,090 --> 00:10:20,940
Now, if we had, for example, zeros here, let's say we have zeros on that and see that this area

143
00:10:21,000 --> 00:10:21,850
is going to be maintained.

144
00:10:21,850 --> 00:10:28,630
Because basically, I would add in this with zeros, it would say we want to once we notice we have

145
00:10:28,630 --> 00:10:33,510
three plus one, four, four plus one, five, six plus one, seven, so on and so forth.

146
00:10:34,690 --> 00:10:35,800
We could also.

147
00:10:38,410 --> 00:10:39,190
Subtract.

148
00:10:39,250 --> 00:10:41,740
So instead of this, we're going to have subtraction.

149
00:10:41,950 --> 00:10:42,550
That's it.

150
00:10:43,540 --> 00:10:48,100
Now, here have division C is an element.

151
00:10:48,100 --> 00:10:49,270
Y is division actually.

152
00:10:49,270 --> 00:10:57,550
So since this is once we would have this E maintained and then if we had, for example, zeros here

153
00:10:57,700 --> 00:10:58,180
c.

154
00:11:00,510 --> 00:11:09,420
We have all this in finite values because we are dividing is not a real number zero.

155
00:11:09,930 --> 00:11:13,260
Now, let's let's take this to once.

156
00:11:16,200 --> 00:11:19,890
I'm a girl so I have multiply so we could have run like that.

157
00:11:20,100 --> 00:11:26,520
There we go multiply and is we want again maintains values element wise multiplication actually.

158
00:11:27,090 --> 00:11:37,500
Now if want to do we could also do non-paid a, add a and B so do that we would do a non pilot subtract

159
00:11:38,400 --> 00:11:40,050
could do non paid out divide.

160
00:11:40,680 --> 00:11:45,480
We could do non paid up multiply c is the same.

161
00:11:45,720 --> 00:11:56,100
Now this is all I am in wise operations and I want to do the matrix multiplication that we know and

162
00:11:56,130 --> 00:11:58,350
as is actually different from this.

163
00:11:58,350 --> 00:12:04,830
And then my wife's multiplication we have the met more so run that you see that we already have an error.

164
00:12:05,130 --> 00:12:15,330
And the reason why we have error is because a shape is three five and then B ship is five is right 352.

165
00:12:15,750 --> 00:12:24,240
Now note that I recall that when doing matrix multiplication, the number of columns of the first matrix

166
00:12:24,240 --> 00:12:27,420
must be the same as the number of rows of the second matrix.

167
00:12:27,810 --> 00:12:30,030
So in this case, five is now equals three.

168
00:12:30,330 --> 00:12:31,740
That's why we have this error.

169
00:12:32,910 --> 00:12:39,720
And so to correct this, we could say, for example, we have to define this as a the transpose of this

170
00:12:40,260 --> 00:12:47,460
so that instead of having three is that you five you have a shape five three and in that case we will

171
00:12:47,460 --> 00:12:48,870
see that this to be the same.

172
00:12:49,530 --> 00:12:54,720
And if this two are the same, then we would have an output of shape three three.

173
00:12:55,200 --> 00:12:58,230
So now let's run this and see that it works fine.

174
00:12:58,230 --> 00:13:03,360
So output associated with three then our matrix multiplication on that.

175
00:13:03,720 --> 00:13:12,270
If we do multi multiply see we have an error because the element why is multiplication going to what?

176
00:13:12,270 --> 00:13:15,300
When the two then have exactly the same shape?

177
00:13:16,740 --> 00:13:17,400
No problem.

178
00:13:17,400 --> 00:13:20,820
Then the transpose is the way we could define empty, not transpose.

179
00:13:23,880 --> 00:13:24,550
That's it.

180
00:13:24,570 --> 00:13:25,290
We're on that.

181
00:13:25,980 --> 00:13:30,420
Obviously now we need to do multiplication or metric multiplication.

182
00:13:30,420 --> 00:13:30,960
That's fine.

183
00:13:32,480 --> 00:13:39,740
There are also many common functions which come up, which are which come with no empire, which we

184
00:13:39,740 --> 00:13:40,490
could use.

185
00:13:40,670 --> 00:13:46,640
Like, for example, if we have e this number E, we could have E that some.

186
00:13:47,510 --> 00:13:48,080
There we go.

187
00:13:48,080 --> 00:13:52,490
We have a 9 to 5 telling us that the sum of all these elements equals nine of five.

188
00:13:53,240 --> 00:14:05,540
We could actually see, for example, let's, let's define E to be equals and be the ones of C for two.

189
00:14:06,650 --> 00:14:09,950
So in this case, we will have a different position.

190
00:14:09,950 --> 00:14:15,710
So the sum should give us it from that c we have a sum of eight for the minimum value.

191
00:14:15,710 --> 00:14:19,250
That should be one for the maximum value that should be one.

192
00:14:19,850 --> 00:14:22,370
We look for the mean, for the mean.

193
00:14:22,850 --> 00:14:24,380
Look for the standard deviation.

194
00:14:26,960 --> 00:14:28,520
We could also do some sorting.

195
00:14:28,670 --> 00:14:35,480
So we have start that's printed out either Saad.

196
00:14:38,000 --> 00:14:39,740
All this actually does a story.

197
00:14:39,740 --> 00:14:44,750
And so that's after doing the story and we can now print out, actually.

198
00:14:45,080 --> 00:14:45,710
So that's it.

199
00:14:46,010 --> 00:14:47,240
Now let's define.

200
00:14:47,570 --> 00:14:48,800
Let's say we have this.

201
00:14:49,820 --> 00:14:50,730
Let's take this off.

202
00:14:50,750 --> 00:14:57,250
Let's say we have this in that array for one zero.

203
00:14:57,260 --> 00:14:58,310
Negative four.

204
00:14:58,340 --> 00:14:59,390
Yeah, that's fine.

205
00:14:59,750 --> 00:15:01,970
Now that's sorted and then print it out.

206
00:15:02,210 --> 00:15:05,300
So after sorting, we see that is actually we saw that.

207
00:15:06,140 --> 00:15:15,140
And also, instead of doing this way, we could just directly print out and P that sort of E so we run

208
00:15:15,140 --> 00:15:15,470
that.

209
00:15:17,490 --> 00:15:18,660
On that basis.

210
00:15:18,660 --> 00:15:19,560
Greg saw that.

211
00:15:20,190 --> 00:15:21,950
Now he could also use an axe art.

212
00:15:22,510 --> 00:15:23,540
What is actually art?

213
00:15:23,610 --> 00:15:27,030
Let's just bring out the sword.

214
00:15:27,030 --> 00:15:29,430
And Peter saw a.

215
00:15:30,870 --> 00:15:31,280
And then.

216
00:15:31,290 --> 00:15:31,850
Okay, that's.

217
00:15:32,010 --> 00:15:33,090
That's the accent.

218
00:15:33,090 --> 00:15:35,010
The sort of accent.

219
00:15:35,370 --> 00:15:36,420
Okay, let's run that away.

220
00:15:36,600 --> 00:15:38,100
So now we've done the sergeant.

221
00:15:38,400 --> 00:15:44,970
What I start does is it actually looks at the positions or the position that is negative for occupied

222
00:15:45,030 --> 00:15:45,720
initially.

223
00:15:46,290 --> 00:15:51,360
So like after Sgt, we see that the negative four comes to the first position.

224
00:15:51,360 --> 00:15:57,150
So we see that the first position we're putting out, the three, the three symbolises

225
00:15:59,640 --> 00:16:00,090
this.

226
00:16:00,690 --> 00:16:06,870
All of the sudden the first position will be occupied by the value which initially was on the third

227
00:16:06,870 --> 00:16:07,440
position.

228
00:16:07,980 --> 00:16:13,350
And then the all zero position is 00123.

229
00:16:13,800 --> 00:16:18,150
So the zero position will be occupied by the value which was initially on the third position, zero

230
00:16:18,150 --> 00:16:20,280
one, two, three, negative four, that's it.

231
00:16:20,730 --> 00:16:26,400
And then here this first position will be occupied by the value which was initially on the second position

232
00:16:26,580 --> 00:16:27,630
012.

233
00:16:27,630 --> 00:16:29,010
That's why we have that zero.

234
00:16:29,700 --> 00:16:31,230
It was initially the second position.

235
00:16:31,230 --> 00:16:33,250
So that's how we look at it with an ax.

236
00:16:33,300 --> 00:16:36,040
So it will look at your previous position, which is start.

237
00:16:36,060 --> 00:16:42,540
We actually look at you all, we actually look at a number, all the element in question and the very

238
00:16:42,540 --> 00:16:45,690
important matter is the shape.

239
00:16:46,050 --> 00:16:48,900
So let's, let's come back to this, let's use this.

240
00:16:50,490 --> 00:16:57,330
So suppose that we have this array of printed it already the shape three five and then we want to reshape

241
00:16:57,330 --> 00:17:07,380
this to say five three or we could have years and the the shape of a.

242
00:17:10,310 --> 00:17:12,140
And then we specify the ship.

243
00:17:12,290 --> 00:17:16,610
So specify the new ship, one new ship to be five three.

244
00:17:16,640 --> 00:17:18,860
One wanted to go from three five, two, five, three.

245
00:17:20,400 --> 00:17:23,700
There's no cute shape to off and that's it.

246
00:17:24,000 --> 00:17:28,140
Now that's putting out the shape of this new.

247
00:17:28,680 --> 00:17:34,800
So we have your five to we now know that if we see for example one to have a new shape five four as

248
00:17:34,800 --> 00:17:37,710
you give us an arrow and this is normal because.

249
00:17:40,190 --> 00:17:48,980
First of all, this initial array of dimension of shape three five has 15 different positions.

250
00:17:49,370 --> 00:17:56,600
One, two, three, four, five, then three units, 15 positions, whereas this new array has any position.

251
00:17:56,600 --> 00:18:03,380
So it's not possible that we do a reshape so that it will be a match between this initial array and

252
00:18:03,380 --> 00:18:05,330
its reshaped array.

253
00:18:05,960 --> 00:18:07,760
So that's why that doesn't work.

254
00:18:07,760 --> 00:18:09,080
We have to rerun that.

255
00:18:09,080 --> 00:18:14,600
We see that we now have three, four, six as a first row, three, four, six.

256
00:18:14,930 --> 00:18:19,580
You're just like the first row, then zero, -1 to 6.

257
00:18:20,600 --> 00:18:26,120
And as it follows that we could also see a one negative one.

258
00:18:26,510 --> 00:18:27,620
Now we put negative one.

259
00:18:27,620 --> 00:18:33,590
What this what happens here is number two is going to automatically get this value for you so many times

260
00:18:33,590 --> 00:18:40,010
when we want to carry out this kind of operations, put in a negative one, it just says we give number

261
00:18:40,010 --> 00:18:44,930
the liberty to tell us what value is best for us here.

262
00:18:45,350 --> 00:18:48,080
So if we do this so it gives us the answer.

263
00:18:48,800 --> 00:18:49,610
We know that shape.

264
00:18:49,790 --> 00:18:50,330
That's it.

265
00:18:50,780 --> 00:18:56,120
Now, if we had instead of that, if we had three, that's not going to be let's not take three.

266
00:18:56,480 --> 00:19:01,880
Suppose we had oh, let's add this to this perform three, this and all the value of this.

267
00:19:01,880 --> 00:19:03,680
If you put three, this is going to give you a five.

268
00:19:04,040 --> 00:19:04,550
Exactly.

269
00:19:04,590 --> 00:19:05,720
The model for you.

270
00:19:06,740 --> 00:19:14,390
If you put C two, no matter where you put your C, you must have an error because obviously having

271
00:19:14,420 --> 00:19:20,060
two means we're going to have an even number of possibilities or number of elements.

272
00:19:20,060 --> 00:19:23,300
And yeah, already we have an odd number, so it's not possible.

273
00:19:23,300 --> 00:19:26,030
Now we reshape this into an even number.

274
00:19:27,140 --> 00:19:28,190
Pick that back.

275
00:19:30,250 --> 00:19:30,850
That's fine.

276
00:19:32,500 --> 00:19:35,970
Another matter is the concatenate method.

277
00:19:35,980 --> 00:19:37,240
So suppose we have this.

278
00:19:37,750 --> 00:19:38,290
Yeah.

279
00:19:38,410 --> 00:19:39,610
Let's make it simple.

280
00:19:40,510 --> 00:19:49,750
We have your four and then we have the B and beta array with six and maybe just five.

281
00:19:50,350 --> 00:20:01,660
Now we could have NP concatenate and B from that let's modify this, put it to pull.

282
00:20:03,740 --> 00:20:04,730
That's fine.

283
00:20:04,730 --> 00:20:05,800
Now run it.

284
00:20:05,810 --> 00:20:06,530
And there we go.

285
00:20:06,770 --> 00:20:08,270
We'll see how we concatenate this.

286
00:20:08,600 --> 00:20:12,230
We have six, five, four, and then this is added on it.

287
00:20:12,980 --> 00:20:20,150
Now let's specify the axis like normally would by default as axis is zero.

288
00:20:20,600 --> 00:20:26,360
Now seen that zero simply means let's take this aid and see.

289
00:20:31,720 --> 00:20:32,080
Okay.

290
00:20:32,080 --> 00:20:41,080
By saying as zero simply means the concatenation of this to arrays is done on the zero axis.

291
00:20:42,730 --> 00:20:45,250
Which in this case is the loan axis.

292
00:20:46,410 --> 00:20:54,210
Now in this kind of area, this to the area right here, we do not have just one axis.

293
00:20:54,810 --> 00:20:56,010
Let's bring this twice.

294
00:20:56,010 --> 00:20:57,600
We have the A and B.

295
00:20:58,650 --> 00:21:01,320
Now, let's take of some of those elements.

296
00:21:01,830 --> 00:21:06,570
We have three, 3 to 2.

297
00:21:07,840 --> 00:21:16,240
So it's a three by two array that we have four be and this is five by three, we could bring this out.

298
00:21:16,450 --> 00:21:17,800
So we have a shape.

299
00:21:21,180 --> 00:21:25,920
She brings me that --.

300
00:21:28,080 --> 00:21:28,760
There we go.

301
00:21:28,770 --> 00:21:30,210
Three, five, three, two.

302
00:21:30,780 --> 00:21:32,940
Now let's do the concatenation and see what we get.

303
00:21:33,930 --> 00:21:43,830
Now the and be that concatenated of A and B now by default as the set, if we don't specify the axis

304
00:21:43,830 --> 00:21:45,840
that the default axis is zero.

305
00:21:45,930 --> 00:21:46,980
So let's run this.

306
00:21:47,880 --> 00:21:50,010
We have this error, which is normal.

307
00:21:50,580 --> 00:21:52,110
Now let's understand what's going on.

308
00:21:52,410 --> 00:21:53,880
When doing condemnation.

309
00:21:54,240 --> 00:21:59,350
What goes on is that the axis like in this case, the axis is actually zero.

310
00:21:59,370 --> 00:22:05,340
So even if we do axis equals zero, we'll still have this error because by default axis had two zero.

311
00:22:05,940 --> 00:22:12,870
So when doing a combination, as we're saying here, we have this axis always specifying axis zero.

312
00:22:13,110 --> 00:22:16,410
So what goes on is this two are somehow fixed.

313
00:22:16,830 --> 00:22:25,050
And then what Nompu tries to check now is to ensure that the other axis are the same.

314
00:22:25,860 --> 00:22:34,020
So if we want to concatenate this to O on the zero axis, then we fix the zero axis as Yeah, we'll

315
00:22:34,020 --> 00:22:37,590
fix this, we fix this, and then we verify if this two are the same.

316
00:22:37,590 --> 00:22:41,130
If they're not the same, then we cannot do the concatenation.

317
00:22:41,670 --> 00:22:47,990
So just like with this, when we fix the zero axis, we see that actually it doesn't alter axis.

318
00:22:47,990 --> 00:22:56,390
So we could simply the coordination was possible, but here where the axis where we have this first

319
00:22:56,400 --> 00:22:59,940
axis and this first axis, here they are both different.

320
00:22:59,940 --> 00:23:02,700
So we cannot the combination cannot be done.

321
00:23:03,840 --> 00:23:12,480
Now, another way of looking at this is by saying that if you have this array, the shape is given as

322
00:23:12,480 --> 00:23:13,980
the row and the column.

323
00:23:14,370 --> 00:23:20,250
So if you have an array, the shape is a row column.

324
00:23:21,030 --> 00:23:27,030
Now, if by default the axis is zero, it means you are doing concatenation across the row.

325
00:23:28,020 --> 00:23:36,630
Now, if you look at those rows here, we are having to concatenate this row with this auto one.

326
00:23:37,530 --> 00:23:42,510
And to do this, does the number of elements we have here must match up with the number of elements

327
00:23:42,510 --> 00:23:43,110
we have here?

328
00:23:43,830 --> 00:23:44,640
Same with this.

329
00:23:44,640 --> 00:23:48,660
You see, we want to continue this to the two elements.

330
00:23:48,660 --> 00:23:51,800
Our number of elements must match with this.

331
00:23:51,810 --> 00:23:59,820
Our example here, we have actually no row and no column because this is one dimensional.

332
00:24:00,210 --> 00:24:07,440
And since this is one dimensional, we could just simply use pack this or add this to the end right

333
00:24:07,440 --> 00:24:07,770
here.

334
00:24:08,250 --> 00:24:10,800
But now we're dealing with a two dimensional array.

335
00:24:11,190 --> 00:24:14,580
We have to be very careful with the way we do the cook up the nations.

336
00:24:14,910 --> 00:24:18,450
So, yeah, this kind of cannot be concatenated on this.

337
00:24:19,110 --> 00:24:23,330
This two can be concatenated and this too.

338
00:24:23,850 --> 00:24:26,520
Now, we want this to actually work.

339
00:24:26,520 --> 00:24:35,190
We must ensure that for a given axis while fixing, like if we work with the first axis as we fix this

340
00:24:35,190 --> 00:24:38,970
and we fix this, the other axis must be the same.

341
00:24:39,480 --> 00:24:42,270
So in this case, for example, we see that there is a must three.

342
00:24:42,270 --> 00:24:43,230
So this should work.

343
00:24:43,770 --> 00:24:51,540
Now looking at this and then now we will see that if we are to coordinate this two to the columns,

344
00:24:51,960 --> 00:25:00,630
then we will have three 5 to 6 zero, which is going to be added here and then 440 added again.

345
00:25:00,960 --> 00:25:02,040
So let's run this.

346
00:25:02,040 --> 00:25:03,150
So you can see that clearly.

347
00:25:03,150 --> 00:25:12,210
We have 3460, negative one is four and we have this 34260 which is added this line here and then we

348
00:25:12,210 --> 00:25:14,010
have 440, which is added.

349
00:25:14,250 --> 00:25:19,440
So yeah, we concatenate this array with this auto one.

350
00:25:20,820 --> 00:25:22,800
Now let's go ahead and modify this again.

351
00:25:22,800 --> 00:25:24,360
Suppose we have now two.

352
00:25:25,530 --> 00:25:27,240
So let's come like this.

353
00:25:28,020 --> 00:25:29,940
Now we have to run it.

354
00:25:29,940 --> 00:25:32,850
See, we have an error to go to zero.

355
00:25:32,880 --> 00:25:33,230
We'll see.

356
00:25:33,240 --> 00:25:33,780
I have an error.

357
00:25:33,780 --> 00:25:35,670
It's impossible to do the concatenation.

358
00:25:36,090 --> 00:25:44,310
So to do a concatenation, the axis we select is fixed and we monitor the order axis to be sure that

359
00:25:44,850 --> 00:25:46,470
the concatenation possible.

360
00:25:47,190 --> 00:25:53,220
Also, apart from the two, the arrays and the one the arrays, we could also define three dimensional

361
00:25:53,220 --> 00:25:53,750
arrays.

362
00:25:54,420 --> 00:25:55,380
Let's copy this.

363
00:25:57,750 --> 00:25:58,370
He's out.

364
00:25:58,380 --> 00:25:58,950
Yeah.

365
00:25:59,880 --> 00:26:05,460
Now, if I defined a three dimensional array, then we'll need an axis.

366
00:26:06,480 --> 00:26:08,580
So let's put it this way.

367
00:26:10,590 --> 00:26:19,170
This is like this is seen as regrouping two dimensional arrays, as you could see, with a two dimensional

368
00:26:19,170 --> 00:26:27,060
array where a group in this one, the area is this one is one and this one and they are seen as columns

369
00:26:27,060 --> 00:26:28,680
or rather just seen as rows here.

370
00:26:28,770 --> 00:26:31,500
This is one row, one row and a row row.

371
00:26:31,860 --> 00:26:40,380
But with three the arrays, this to the array is going to be seen as one line in our territory.

372
00:26:40,650 --> 00:26:48,330
So like this we add that that we go this out to the array.

373
00:26:49,200 --> 00:26:53,580
So we have this to the area right here and then let's copy this again.

374
00:26:55,720 --> 00:26:56,830
So that was the first line.

375
00:26:56,860 --> 00:26:57,730
The next line.

376
00:26:58,390 --> 00:27:06,310
So this our first line to the next line to the just I would add to the array we had this line one the

377
00:27:06,730 --> 00:27:14,410
one the one the for the one day we had just an element, an element, an element going to the to the

378
00:27:14,410 --> 00:27:15,340
to the three.

379
00:27:15,340 --> 00:27:19,080
Do we have to the to the.

380
00:27:20,150 --> 00:27:22,180
And so without this.

381
00:27:25,910 --> 00:27:26,510
There we go.

382
00:27:26,690 --> 00:27:27,800
So now we have this.

383
00:27:27,800 --> 00:27:30,830
One, two, three, four, five, six.

384
00:27:31,760 --> 00:27:32,420
Stop there.

385
00:27:34,280 --> 00:27:34,760
That's fine.

386
00:27:34,970 --> 00:27:36,150
So now we have this.

387
00:27:36,170 --> 00:27:37,220
And then we could close it up.

388
00:27:37,580 --> 00:27:37,910
Right?

389
00:27:37,910 --> 00:27:38,510
Yeah.

390
00:27:39,230 --> 00:27:39,790
Split up.

391
00:27:39,800 --> 00:27:40,000
Yeah.

392
00:27:40,010 --> 00:27:41,090
So we could close it up there.

393
00:27:41,090 --> 00:27:41,690
And that's fine.

394
00:27:42,080 --> 00:27:44,390
So now we've defined this.

395
00:27:44,630 --> 00:27:45,070
Let's.

396
00:27:46,100 --> 00:27:46,730
Let's have that.

397
00:27:46,970 --> 00:27:51,110
Okay, so we define our three d array in our the shape.

398
00:27:53,800 --> 00:27:59,480
See now looking at this, we have one, two, three, four, five, six, and then for each of this,

399
00:27:59,480 --> 00:28:00,670
so we should have six.

400
00:28:01,120 --> 00:28:08,440
And then for each of the six, we have, uh, one, two, three, five, six, three, five.

401
00:28:09,310 --> 00:28:11,200
This command is out of shape.

402
00:28:13,180 --> 00:28:13,710
There we go.

403
00:28:13,720 --> 00:28:22,630
We have six three, five, three knows that we have six different three by five to the Aries again.

404
00:28:22,630 --> 00:28:22,800
Yeah.

405
00:28:22,840 --> 00:28:29,690
If we have to do concatenation, suppose we have let's take this for example, this, this, this,

406
00:28:29,710 --> 00:28:30,370
we use this.

407
00:28:30,970 --> 00:28:32,290
I will bring this out.

408
00:28:33,310 --> 00:28:34,270
Take this.

409
00:28:36,580 --> 00:28:36,880
Yeah.

410
00:28:36,900 --> 00:28:44,080
We're B and then we take just two of this.

411
00:28:45,460 --> 00:28:47,590
Okay, so we have just 12 this.

412
00:28:47,590 --> 00:28:53,770
We could print out each bishop, so we have b the --.

413
00:28:54,550 --> 00:28:55,060
There we go.

414
00:28:55,360 --> 00:28:57,370
Two, three, five, six, three, five.

415
00:28:57,730 --> 00:29:02,440
Now, as you could see here, if we're in a combination so we could print out.

416
00:29:04,130 --> 00:29:11,720
And B, that concatenate of a B now in this case is going to work because if by default the axis is

417
00:29:11,720 --> 00:29:14,450
zero, the axis of zero by default amounts.

418
00:29:14,720 --> 00:29:16,670
We are fixing this and fixing this.

419
00:29:17,090 --> 00:29:19,540
Then we are going to look at the other part.

420
00:29:19,550 --> 00:29:23,390
So we have look at is to the array and compare it with the dimension of this to the array.

421
00:29:23,900 --> 00:29:29,140
So if the ship is the same as the ship, then the concatenation is possible like in this case.

422
00:29:29,140 --> 00:29:30,020
So could run that.

423
00:29:31,970 --> 00:29:32,140
Yeah.

424
00:29:32,150 --> 00:29:35,900
This arrow presupposes probably.

425
00:29:37,370 --> 00:29:38,130
And that's fine.

426
00:29:38,150 --> 00:29:39,260
Now we have this.

427
00:29:40,220 --> 00:29:41,750
We could monitor, monetize ship.

428
00:29:44,900 --> 00:29:51,200
So we have to shape the social partnership before.

429
00:29:51,440 --> 00:29:55,400
So we have this, okay, we have it by three by five.

430
00:29:55,400 --> 00:29:59,270
So the coordination has been done on this zero axis.

431
00:29:59,780 --> 00:30:05,450
Now, if you have to do that on the first axis, so we have x equals one.

432
00:30:06,410 --> 00:30:12,020
You see, normally that shouldn't work because fixing this axis, the six five doesn't match with two

433
00:30:12,020 --> 00:30:12,470
five.

434
00:30:13,610 --> 00:30:14,810
So that wouldn't work.

435
00:30:15,200 --> 00:30:23,000
Now, if we have to do on the second axis, it should work too, because fixing this six three doesn't

436
00:30:23,000 --> 00:30:24,080
match with two three.

437
00:30:24,350 --> 00:30:26,150
But then if we take this off.

438
00:30:26,360 --> 00:30:34,610
So if we take some of this off, let's take this off on that run.

439
00:30:34,610 --> 00:30:35,690
It works.

440
00:30:35,690 --> 00:30:41,720
Because when we fix this second axis to three matches with two three, so that's fine.

441
00:30:42,080 --> 00:30:50,300
Now, even if we don't have five elements, or even if we have C for this one, we could have C four

442
00:30:50,300 --> 00:30:50,990
elements.

443
00:30:51,650 --> 00:30:56,810
Four, four, four, four.

444
00:30:56,860 --> 00:30:57,370
Run it.

445
00:30:57,380 --> 00:30:59,150
C, we have four elements.

446
00:31:00,340 --> 00:31:02,520
For each of this to the race.

447
00:31:02,520 --> 00:31:04,720
So we have four columns for each editorial race.

448
00:31:04,990 --> 00:31:08,020
Now, if we fix that second act, this is still going to work.

449
00:31:10,450 --> 00:31:10,720
Yeah.

450
00:31:10,720 --> 00:31:13,570
We have this area because the axis here was zero.

451
00:31:13,720 --> 00:31:20,800
Now, let's let's have this axis equals to see that works fine.

452
00:31:21,130 --> 00:31:22,570
The shape is two, three, nine.

453
00:31:23,020 --> 00:31:28,390
We've fixed the second and then we'll compare this first two axis that same.

454
00:31:28,390 --> 00:31:30,670
So the combination is possible.

455
00:31:32,050 --> 00:31:38,360
Now also, when given an array, say we given this array, let's take this to the area.

456
00:31:39,100 --> 00:31:44,600
When given this kind of array, we could get specific elements depending on your positions.

457
00:31:44,620 --> 00:31:53,500
So if we have this a we could say we want to get e zero now a0 corresponds to the zeroth row.

458
00:31:53,680 --> 00:31:55,120
So that's the correspond to this.

459
00:31:55,750 --> 00:31:55,980
Right.

460
00:31:56,030 --> 00:31:59,500
And you see we have 3460 negative one.

461
00:32:00,140 --> 00:32:08,350
Now if 11c works we want to we have this last one don't we should try an arrow.

462
00:32:08,530 --> 00:32:15,640
So because we actually have three rows so we should go from zero one, which we have zero one and two.

463
00:32:16,750 --> 00:32:17,420
So that's it.

464
00:32:17,980 --> 00:32:23,980
Now if you want to be more specific, we could have one and then zero, meaning that we're going the

465
00:32:24,460 --> 00:32:28,450
zero one that's first row and then the zero column.

466
00:32:28,450 --> 00:32:30,910
So that's 56 and that's it.

467
00:32:30,910 --> 00:32:34,750
We have 56 if we select three, so we can have six.

468
00:32:35,200 --> 00:32:37,120
So like it we have an arrow.

469
00:32:37,840 --> 00:32:44,050
So have this 30101236.

470
00:32:44,050 --> 00:32:50,050
So right we have a six year easy way of doing this is by using the comma.

471
00:32:50,050 --> 00:32:54,580
So we have one comma, three, the first row and the third column.

472
00:32:54,970 --> 00:33:02,440
So we have the same answer also using the same command notation we could have or we could select the

473
00:33:03,010 --> 00:33:04,690
first row, for example.

474
00:33:05,050 --> 00:33:15,220
Now so the first rule was selecting all the elements in the columns we could use the column by in column

475
00:33:15,220 --> 00:33:16,600
we just simply saying in all.

476
00:33:16,600 --> 00:33:22,540
So basically this is equal to saying all columns.

477
00:33:23,320 --> 00:33:26,440
Now the columns obviously are different from the columns.

478
00:33:26,530 --> 00:33:28,090
So we have that columns.

479
00:33:28,420 --> 00:33:32,350
So we have in one that C we have 56.

480
00:33:32,350 --> 00:33:33,610
That's the first row.

481
00:33:33,670 --> 00:33:34,720
The Yeah.

482
00:33:34,720 --> 00:33:38,860
The first row there's is zero it row, first row, second row.

483
00:33:39,190 --> 00:33:46,390
Now we could pick out a second C basically what we're saying is take the second row and all those columns.

484
00:33:46,420 --> 00:33:52,510
Now if we say zero it means take the second row and the zeroth column.

485
00:33:52,510 --> 00:33:56,320
So second row zero column will restrict only this value.

486
00:33:56,470 --> 00:33:59,710
That's why you see we have just one value, so we'll do that.

487
00:33:59,860 --> 00:34:00,520
That's fine.

488
00:34:00,850 --> 00:34:03,580
Now we could also decide to work with only the columns.

489
00:34:03,820 --> 00:34:04,720
So we have that.

490
00:34:05,410 --> 00:34:11,350
Let's say we have four now we have in all the rows, but only the fourth column.

491
00:34:11,350 --> 00:34:14,110
So we go zero one, two, three, four.

492
00:34:14,170 --> 00:34:16,450
That's actually the last column on that.

493
00:34:16,450 --> 00:34:21,670
So we have negative one six two, negative one six two.

494
00:34:22,090 --> 00:34:28,360
Let's not philippines's out of spin out e so it appears looks better now is it negative one six two.

495
00:34:28,780 --> 00:34:29,380
That's fine.

496
00:34:30,490 --> 00:34:36,000
We could do some slides in with slides and let's take this one the array.

497
00:34:39,590 --> 00:34:40,510
They did put it out.

498
00:34:40,520 --> 00:34:40,970
Yeah.

499
00:34:41,660 --> 00:34:47,750
Now let's increase the 612169, eight.

500
00:34:48,530 --> 00:34:49,220
That's fine.

501
00:34:49,460 --> 00:34:51,830
Now print out the E.

502
00:34:52,190 --> 00:34:57,950
But now we actually slice it out so we could see want to work from one right up to four.

503
00:34:58,580 --> 00:35:01,070
So you go zero one as it.

504
00:35:02,740 --> 00:35:06,110
Two, three, four, two, go.

505
00:35:06,160 --> 00:35:07,990
Five, four, six, one.

506
00:35:08,410 --> 00:35:15,700
But in this notation, what is saying is go from the start to the index minus one.

507
00:35:15,730 --> 00:35:16,990
So that's why we have four.

508
00:35:17,320 --> 00:35:24,640
We have five, we have four, we have six, but we don't take one into consideration, although normally

509
00:35:24,640 --> 00:35:26,380
this is like zero.

510
00:35:29,360 --> 00:35:29,900
One.

511
00:35:31,000 --> 00:35:31,510
Two.

512
00:35:32,470 --> 00:35:33,010
Three.

513
00:35:34,750 --> 00:35:35,590
Take that.

514
00:35:35,590 --> 00:35:36,280
Three.

515
00:35:36,550 --> 00:35:36,940
Yeah.

516
00:35:38,440 --> 00:35:41,320
Four and five and then the rest.

517
00:35:41,980 --> 00:35:48,220
So yeah, we have in one, two, 4 minutes we're taking this one, two, four, but we're not taking

518
00:35:48,220 --> 00:35:49,330
the last index.

519
00:35:49,330 --> 00:35:52,590
So we just in a year and this corresponds to five, four, six.

520
00:35:52,600 --> 00:35:53,110
That's it.

521
00:35:53,830 --> 00:35:56,020
We could also do 0 to 4.

522
00:35:56,110 --> 00:35:58,450
See, we have come on that.

523
00:35:58,660 --> 00:36:00,130
So we have six now.

524
00:36:00,130 --> 00:36:04,030
We have all this zero to see nine.

525
00:36:04,360 --> 00:36:05,080
There we go.

526
00:36:06,190 --> 00:36:10,150
Then we could see we want to take all the first nine elements.

527
00:36:10,150 --> 00:36:13,030
So instead of specifying zero, we just do that.

528
00:36:13,030 --> 00:36:15,010
And it starts from the zero position.

529
00:36:15,820 --> 00:36:20,860
Now, if we want to go from a given position to the last position, we just do that.

530
00:36:20,860 --> 00:36:28,950
And it is from four as second for six 1 to 1, six, nine, eight and as it must be, not a.

531
00:36:29,770 --> 00:36:30,760
So we see that clearly.

532
00:36:31,270 --> 00:36:31,810
So that's it.

533
00:36:31,960 --> 00:36:33,890
We actually take this for.

534
00:36:34,630 --> 00:36:39,550
We could do this five C matches up with the first five elements.

535
00:36:41,350 --> 00:36:42,880
Then if we do a negative one.

536
00:36:45,290 --> 00:36:51,080
What we're saying here is start from the first elements and go right up to the.

537
00:36:53,700 --> 00:36:56,460
Last now grown ups, a lot of similar means.

538
00:36:56,460 --> 00:36:59,670
We're going to go around the last minus one index.

539
00:36:59,670 --> 00:37:01,290
That's why we have this year.

540
00:37:03,300 --> 00:37:04,770
If you want to have minus two.

541
00:37:05,340 --> 00:37:09,070
So you would go out to the last but one index.

542
00:37:09,070 --> 00:37:15,000
So we actually end up your businesses index one one, we end up now with this.

543
00:37:15,000 --> 00:37:21,660
So we go from six, five, four, six, one, two, one in about 600 business.

544
00:37:21,660 --> 00:37:23,520
Now I'm putting this to the array.

545
00:37:28,780 --> 00:37:29,610
Wrong again.

546
00:37:29,620 --> 00:37:33,860
You see, we, there's, there's the greens.

547
00:37:36,100 --> 00:37:40,960
So now we have this to the area e we taken all the elements.

548
00:37:40,960 --> 00:37:47,110
Let's say we take all the elements from the, we take the first element of the second elements is basically

549
00:37:47,110 --> 00:37:48,070
saying we're taking the.

550
00:37:49,240 --> 00:37:54,160
First row with the goal of taking the zero at row.

551
00:37:54,460 --> 00:37:56,740
We're taking the first row and that's it.

552
00:37:57,070 --> 00:37:59,410
That way we have this rule and then this row.

553
00:37:59,410 --> 00:38:05,200
We don't take this one because we're going out to index minus one or just an index minus one.

554
00:38:06,160 --> 00:38:06,580
Now.

555
00:38:06,580 --> 00:38:09,060
We haven't that we've seen that clearly.

556
00:38:09,070 --> 00:38:14,390
We could now have see zero or could see one to the end.

557
00:38:14,410 --> 00:38:20,710
I would just have to say we have towards the end, see, we take this only now we can have one, two

558
00:38:20,710 --> 00:38:30,730
and think that we could have all that's fine is the same with how it is obviously so that we will have

559
00:38:32,560 --> 00:38:41,080
all the rows, but now we decide to pick the columns so we could to go from 2 to 3.

560
00:38:42,780 --> 00:38:43,260
See that.

561
00:38:44,530 --> 00:38:45,400
Good thing for.

562
00:38:45,400 --> 00:38:47,880
Let's see for that.

563
00:38:47,890 --> 00:38:48,270
Run it.

564
00:38:48,280 --> 00:38:48,640
Okay.

565
00:38:48,910 --> 00:38:53,560
Now, what we're doing here is we've seen for the roles, take all the rules, work with all the rules

566
00:38:53,560 --> 00:38:54,550
of work with this role.

567
00:38:54,550 --> 00:39:00,580
The role on this role before the columns work with the second column, I work with the from the second

568
00:39:00,580 --> 00:39:01,720
column to the foot column.

569
00:39:02,020 --> 00:39:06,370
And obviously, since we're going up to index one as one, we're working with the second column and

570
00:39:06,370 --> 00:39:08,650
the third column does two and three.

571
00:39:08,650 --> 00:39:09,880
So when I including four.

572
00:39:10,270 --> 00:39:11,710
So that's why we go zero.

573
00:39:11,860 --> 00:39:17,740
Let's see, we go zero, one to second and then the third, this, that's fine.

574
00:39:17,740 --> 00:39:21,520
So we have 605631 and that's what we got here.

575
00:39:22,780 --> 00:39:25,360
This is similar to doing this.

576
00:39:25,360 --> 00:39:33,480
We're going to have C one, two, two and then take all the columns on that.

577
00:39:33,490 --> 00:39:34,450
C we have that.

578
00:39:35,770 --> 00:39:36,130
Yeah.

579
00:39:36,130 --> 00:39:37,210
We're picking out the.

580
00:39:38,510 --> 00:39:40,700
First all take zero.

581
00:39:40,700 --> 00:39:41,470
We don't take zero.

582
00:39:41,480 --> 00:39:45,740
Actually the one we only end we end there because we're going up to two.

583
00:39:45,740 --> 00:39:48,940
So just after and we could always take three.

584
00:39:48,950 --> 00:39:51,050
So now we could take the second.

585
00:39:51,860 --> 00:39:52,130
Yeah.

586
00:39:52,140 --> 00:39:55,340
With the second row zero four is and second.

587
00:39:55,340 --> 00:39:58,910
So we have one two before across all the columns.

588
00:40:01,000 --> 00:40:04,120
We could also go ahead and specify that we want to take the.

589
00:40:05,630 --> 00:40:07,040
First to Cullen.

590
00:40:07,040 --> 00:40:07,500
So good.

591
00:40:07,520 --> 00:40:11,540
I have to have that like that.

592
00:40:11,780 --> 00:40:16,790
So we have the one on two for the roles role one and two.

593
00:40:17,120 --> 00:40:24,880
So we have this role and this role and in this role, one and two, we have the first two columns.

594
00:40:24,890 --> 00:40:33,740
So we have this let's take from this we have role one, rule two for the columns we have up to the second.

595
00:40:33,740 --> 00:40:38,000
So we go zero one to.

596
00:40:39,440 --> 00:40:45,950
Now that we know that in this last index we'll go from zero or one and then it will be in 1 to 3.

597
00:40:46,820 --> 00:40:54,110
We have in the first on the second row, it was the first on the second.

598
00:40:54,950 --> 00:40:59,840
And then in this first and second, we're picking out the zero and the first column.

599
00:40:59,840 --> 00:41:04,520
So we have zero and first intersection happens to be the fifth 26400.

600
00:41:05,210 --> 00:41:08,060
And this we have the fifth 26400.

601
00:41:09,080 --> 00:41:13,520
Now, we could also see if we want to have all this.

602
00:41:13,850 --> 00:41:14,250
Yeah.

603
00:41:14,330 --> 00:41:15,350
Can run it like that.

604
00:41:15,890 --> 00:41:20,600
We pick out the first one, three for the rows and then we have all the columns.

605
00:41:21,080 --> 00:41:24,170
Apart from doing this, we could use three dots.

606
00:41:24,170 --> 00:41:28,490
The three dots simply means take all four, all the remaining axes.

607
00:41:28,490 --> 00:41:34,390
Now that we have just one axis here, that's ones that pick out this row axis will have one over the

608
00:41:34,400 --> 00:41:35,030
column axis.

609
00:41:35,030 --> 00:41:37,790
So basically we just have one axis year remaining.

610
00:41:38,030 --> 00:41:42,470
So within that take of the all the remaining axis so that we can have the same results.

611
00:41:43,250 --> 00:41:46,160
Now let's work with 3D input.

612
00:41:46,460 --> 00:41:47,360
Let's come to.

613
00:41:48,890 --> 00:41:50,120
You had this tree, okay?

614
00:41:50,530 --> 00:41:51,780
We had our 3-D input.

615
00:41:51,790 --> 00:41:52,150
Yeah.

616
00:41:54,870 --> 00:41:56,610
We take this off?

617
00:41:59,220 --> 00:41:59,880
Take that off.

618
00:42:01,230 --> 00:42:04,350
We have a and now we've seen this.

619
00:42:07,690 --> 00:42:08,850
Let's take this awesome New Year's.

620
00:42:10,930 --> 00:42:11,650
Yeah, that's it.

621
00:42:11,890 --> 00:42:18,550
So we have this here we this off to on that for now.

622
00:42:18,550 --> 00:42:20,230
Let's let's just have this.

623
00:42:20,290 --> 00:42:23,620
So for now we we have in the.

624
00:42:25,470 --> 00:42:29,760
First as we go from one of the three that E is e.

625
00:42:32,540 --> 00:42:38,840
So as cause this was a logistics of so it could be better.

626
00:42:39,410 --> 00:42:47,450
So aid is a and then there is this selected or sliced version of E and there's a version.

627
00:42:47,460 --> 00:42:53,240
What we're doing is we're taking out giving that a let's look at a ship that's not a ship.

628
00:42:53,240 --> 00:42:55,130
So it's clear ship.

629
00:42:55,610 --> 00:43:04,340
In this version, we're working with the first and the second axis for this first dimension where we

630
00:43:04,340 --> 00:43:06,770
have the first dimension, the second and the third dimension.

631
00:43:07,190 --> 00:43:12,590
So we were working with the first and the second axis, obviously, because we're going to go up to

632
00:43:12,590 --> 00:43:14,480
index, we go up to index minus one.

633
00:43:14,930 --> 00:43:21,440
And so if you look at this, you're working with the first and second symbol means this is the zero,

634
00:43:22,010 --> 00:43:23,210
then this is the first.

635
00:43:23,270 --> 00:43:27,830
So we're working with this and clearly this is the output we get.

636
00:43:29,120 --> 00:43:34,250
Now if after picking out this output, we want to get more specific.

637
00:43:34,490 --> 00:43:39,170
So we want to get the zero output.

638
00:43:39,170 --> 00:43:42,020
So after picking this out, we want to get a zero up.

639
00:43:42,170 --> 00:43:44,720
We could have zero run it again.

640
00:43:44,780 --> 00:43:45,320
There we go.

641
00:43:45,320 --> 00:43:48,380
We have this 3460 negative one.

642
00:43:48,620 --> 00:43:50,270
So after picking out this first.

643
00:43:51,460 --> 00:44:01,480
We take the zero that is now the the zero row year 0123 you want to take the first two have zero up

644
00:44:01,480 --> 00:44:02,740
to one.

645
00:44:02,890 --> 00:44:05,970
No up to two because we have zero and want to run that.

646
00:44:05,990 --> 00:44:09,070
See we have this and this.

647
00:44:09,580 --> 00:44:12,310
Now we could also pick that obviously pick from the beginning.

648
00:44:12,550 --> 00:44:18,610
So from the beginning here you see that with this we pick all this, we pick this one zero and then

649
00:44:18,610 --> 00:44:19,540
we also pick one.

650
00:44:20,170 --> 00:44:21,340
That's the essence of this.

651
00:44:21,910 --> 00:44:27,910
Then in this for this specific one, we pick the zero up to two.

652
00:44:28,420 --> 00:44:32,530
So that's why we have zero and one.

653
00:44:33,940 --> 00:44:34,420
That's it.

654
00:44:34,430 --> 00:44:34,860
Yeah.

655
00:44:35,680 --> 00:44:38,770
For the next one, we also p zero and one.

656
00:44:39,640 --> 00:44:44,470
Now if we have just one, you see, it just does zero.

657
00:44:44,740 --> 00:44:46,180
GOP does zero.

658
00:44:46,600 --> 00:44:55,660
If we take this to the one C we pick now just one because we pick it out in the Xs, the first Xs for

659
00:44:55,660 --> 00:44:58,360
the 000 Xs.

660
00:44:58,660 --> 00:45:01,210
We're picking the values from 1 to 3.

661
00:45:01,990 --> 00:45:05,710
So yeah, we started, we went over to take this zero Xs.

662
00:45:05,710 --> 00:45:06,880
We're going to start with one.

663
00:45:07,420 --> 00:45:12,580
And then in this one we are going to work from 0 to 1 again.

664
00:45:12,580 --> 00:45:14,170
So we just pick out just this one.

665
00:45:14,680 --> 00:45:17,440
Now, if we get this one, we want to pick out a given element.

666
00:45:17,440 --> 00:45:20,620
We could say we want to pick out see the second element.

667
00:45:20,890 --> 00:45:28,390
So we'll pick out this and then we go zero one, two over six and as soon as we have six now, we could

668
00:45:28,390 --> 00:45:30,280
also pick out a slice in this.

669
00:45:30,280 --> 00:45:32,020
So it could go from 2 to 4.

670
00:45:32,380 --> 00:45:36,310
So 01226060.

671
00:45:37,540 --> 00:45:44,410
Now forgetting that we could obviously put this swamping all we can arguments we're working with all

672
00:45:44,410 --> 00:45:49,700
the different columns now we could also use the three dots gives the same answer.

673
00:45:50,110 --> 00:45:55,030
Another interesting work with two years and the kids will want to do this.

674
00:45:55,030 --> 00:46:01,120
Let's say we want to have this all of this implements all of this.

675
00:46:01,120 --> 00:46:04,420
So we pick only the first axis.

676
00:46:04,930 --> 00:46:06,100
I just do this.

677
00:46:06,220 --> 00:46:06,970
Let's have this.

678
00:46:07,300 --> 00:46:08,770
We be to the first axis.

679
00:46:08,770 --> 00:46:15,730
I could pick only the zero axis, which is now this doesn't make a difference.

680
00:46:15,740 --> 00:46:22,990
Let's say we have 41 and then so you see that difference now.

681
00:46:23,200 --> 00:46:28,660
So here we pick out the zeros and then four for the zero we pick now.

682
00:46:30,520 --> 00:46:33,180
All the rows and then all the columns.

683
00:46:33,310 --> 00:46:34,840
That's why we have all this year.

684
00:46:34,840 --> 00:46:37,450
Odds are we print it out now.

685
00:46:37,450 --> 00:46:40,960
If we want to do this simply, we could also have three dots.

686
00:46:41,020 --> 00:46:45,220
Now, just three does, as we said, means for the rest of the axis to everything.

687
00:46:45,220 --> 00:46:46,690
So it is going to have the same.