WEBVTT 00:01.080 --> 00:03.000 Hello and welcome back to our costs. 00:03.000 --> 00:07.830 Soon the last session we learned that India raised containers of homogeneous data. 00:08.340 --> 00:10.800 So in particular for numerical data. 00:10.800 --> 00:15.990 And this allows us to make fast element Weiss and vector rise operations. 00:16.020 --> 00:22.920 So far we have only seen one dimensional arrays are only one sequence of elements and in linear algebra. 00:22.950 --> 00:24.330 You would call it a vector. 00:24.780 --> 00:31.200 And this is only a special case of India race and the general case is a multi-dimensional array. 00:31.200 --> 00:33.010 And in the case of two dimensions. 00:33.170 --> 00:39.720 Yeah you and Linnea argue probably would call it a matrix and the matrix S rows and columns and the 00:39.720 --> 00:41.520 amount of elements in the row. 00:41.520 --> 00:48.450 So if you count the number of elements from left to right is the size of a row and the amount of elements 00:48.450 --> 00:49.080 in a column. 00:49.080 --> 00:55.770 So we account the elements from top to the bottom is the size of the column and the size of each of 00:55.770 --> 00:57.160 those dimensions. 00:57.210 --> 01:01.920 Give us the shape so for example we have three rows and four columns. 01:01.920 --> 01:06.450 But now let's stop coding so we important umpires and P as always. 01:06.540 --> 01:13.830 Then we create a num pi array from one to twelve including and we can check the type. 01:13.890 --> 01:20.100 So should be an end the array and then we can check the shape of our end the array. 01:20.100 --> 01:27.360 So by calling the attribute shape and here you can see it's a one dimensional array so we have only 01:27.360 --> 01:28.440 one dimension here. 01:28.440 --> 01:31.120 If we had to ask me I mentioned c what if. 01:31.370 --> 01:38.250 Yeah two or three numbers here it's a one dimensional array containing of twelve elements in linear 01:38.280 --> 01:38.870 algebra. 01:38.880 --> 01:41.560 You would call it a vector of its elements. 01:41.640 --> 01:47.790 And what we got now can do we can reshape our ending array with the method. 01:47.820 --> 01:54.240 Dot reshape and then we can determine how the shape should look like the first position determines the 01:54.240 --> 01:58.110 amount of rows and the second position determines the amount of columns. 01:58.150 --> 02:04.440 Yeah we want transform our one dimensional array with both elements into an array with two rows and 02:04.500 --> 02:06.780 each row has six columns. 02:06.780 --> 02:16.670 So let's run the cell and let's have a look at a funny you can see Python returns us a two dimensional 02:16.670 --> 02:17.270 array. 02:17.330 --> 02:24.440 So we have here an outer array and this is containing two arrays so two rows here in this example. 02:24.470 --> 02:33.030 So we have the first row and the second row and each row has six columns. 02:33.090 --> 02:37.350 And we can also check now on the shape of our new two dimensional array. 02:38.760 --> 02:45.690 And it's no surprise two and six so two rows six columns of course we can also reshape our array to 02:45.690 --> 02:49.920 the shape six rows and two columns. 02:49.920 --> 02:55.110 Also here with the reshape method. 02:55.240 --> 03:00.250 So now you can see we get six rows and each row containing two elements. 03:00.250 --> 03:11.560 So we have six rows and two columns and let's also check the shape it's six rows and two columns an 03:11.600 --> 03:18.420 element y's operations or vector US operations still work in the same manner as with only a one dimensional 03:18.420 --> 03:18.680 array. 03:18.690 --> 03:20.180 So that's no problem. 03:20.190 --> 03:26.700 So if we add hundreds to a we at 100 to each element of our array. 03:26.790 --> 03:31.950 So before we add Tier 1 2 in the first row now we have 101 and 102 and so on. 03:31.950 --> 03:35.870 So now let's remind that we have in total twelve elements in our array. 03:36.000 --> 03:42.200 And she tried to reshape our array let's say into regrowth and five columns. 03:42.230 --> 03:46.110 So that would mean 15 elements. 03:46.110 --> 03:52.180 This does not work and pass and tests cannot reshape array of size twelve and to shape 3 5. 03:52.230 --> 03:58.490 And we are not limited to two dimensions so we can increase the amount of dimensions to let's say 3. 03:58.500 --> 04:05.280 So we can say okay we want to reshape the end the array and create a three dimensional array. 04:05.460 --> 04:07.800 So the first dimension is the size of two. 04:07.800 --> 04:11.970 The second is the size of two and the third dimension has to the size of three. 04:12.390 --> 04:17.370 So it's kind of a cube. 04:17.430 --> 04:23.190 So now you can see here this is the first element of the first dimension and this is the second element 04:23.190 --> 04:29.970 of the first dimension so the first dimension contains two times the matrix consisting of two rows and 04:29.970 --> 04:30.780 three columns. 04:30.990 --> 04:33.720 So let's check the shape of a. 04:34.710 --> 04:40.560 And we get the shape as a three dimensional with the size 2 2 and 3. 04:40.560 --> 04:48.300 So now let's assume we want to create a two dimensional array containing of the numbers 1 to 100 including 04:48.300 --> 04:51.150 in the shape 25 rows and 4 columns. 04:51.150 --> 04:53.610 We can do that in our 1 line of code. 04:54.030 --> 05:02.140 So first of all we create a one dimensional array consisting of the numbers 1 2 100 and then we reshape 05:02.140 --> 05:06.210 the array and get 25 rows and 4 columns. 05:06.250 --> 05:10.720 So let's see what we get. 05:10.730 --> 05:20.710 So now we have field twenty five rows and four columns and our elements and immigrated from 1 to 100. 05:21.010 --> 05:21.390 All right. 05:21.400 --> 05:26.800 So this was the introduction to multi-dimensional arrays and they are and the next session you will 05:26.800 --> 05:30.480 have a look how to index and slice multi-dimensional arrays. 05:30.640 --> 05:33.370 So hope you are it and see you in the next session by.