WEBVTT 00:01.740 --> 00:03.650 Hello and welcome back to our costs. 00:03.710 --> 00:10.660 So in the last session I introduced multi-dimensional and umpire race and the most common cases to remember 00:10.760 --> 00:14.310 a case where we have rows and columns. 00:14.310 --> 00:20.630 Some of this session we learn how to index that slides two dimensional arrays and also how to change 00:20.640 --> 00:24.030 singer or multiple elements in a two dimensional array. 00:24.650 --> 00:28.650 So about first of all let's s always important umpire. 00:29.220 --> 00:37.670 And then we create an umpire Ray from 1 to twelfth including and then we reshape those 12 elements to 00:37.770 --> 00:43.380 three rows and four columns. 00:43.390 --> 00:47.000 Now you could ask yourself why the elements are arranged in this manner. 00:47.080 --> 00:49.050 So we have kind of a row vice order. 00:49.060 --> 00:55.540 So we have twelve elements and reshape automatically orders them the elements row so starting in the 00:55.540 --> 00:57.600 first row one two three four. 00:57.640 --> 00:59.960 Then the second row of five six seven eight. 01:00.220 --> 01:02.710 And theoretically could also be the other way around. 01:02.710 --> 01:09.410 So starting column biased so one two three four five six and the others. 01:09.440 --> 01:11.790 And that this is the default setting and an umpire. 01:11.800 --> 01:14.790 But of course we can't change that soon. 01:14.840 --> 01:17.470 They reshape method. 01:17.520 --> 01:22.920 There is some part of me to court order and it's the default setting and see I don't want to go into 01:22.920 --> 01:33.660 details what C means but we can change here the order to F and when we rerun here ourselves then we 01:33.660 --> 01:34.710 get a different order. 01:34.710 --> 01:37.790 So now we have one two three four five six and so on. 01:37.800 --> 01:40.100 So this is flexible here. 01:40.140 --> 01:46.410 All right so let's change it to order C and run the sides again. 01:46.410 --> 01:54.420 Now again we f our let's say normal order and indexing multi-dimensional or two dimensional arrays. 01:54.460 --> 01:58.330 That's actually no difference to one dimensional arrays. 01:58.450 --> 02:05.880 So we have also zero based indexing and if we want to slice the first element of the array. 02:05.890 --> 02:08.760 So the first element here is the first row. 02:08.860 --> 02:13.150 We can do this by having the 0 in the spare brackets 02:17.710 --> 02:24.850 and now we get to the first row of our array and we can also get the second row at an exposition one 02:26.540 --> 02:38.270 and the third row at to next position to so your f in and 0 in exposition 1 and in exposition 2 and 02:38.280 --> 02:44.340 we can also slice of the last show which is actually the third row. 02:44.400 --> 02:47.390 This gives us the same result. 02:47.440 --> 02:50.900 And what if now we want to slice them in the second row. 02:51.040 --> 02:54.500 The second element so let's say here. 02:54.530 --> 02:57.290 So we want to have in the second row The second element. 02:57.320 --> 03:00.970 The sixth and we can do this by having two spat brackets. 03:00.980 --> 03:05.390 So first of all let's cross the second one year out. 03:05.800 --> 03:09.410 So first of all we are slicing the second row. 03:09.920 --> 03:11.040 Yeah. 03:11.300 --> 03:17.780 And then from the second row we are getting the second element in exposition 1 03:22.610 --> 03:23.000 and extra. 03:23.000 --> 03:29.360 We do not need to spell brackets you can put this into once bad bracket separated by a comma. 03:29.390 --> 03:35.840 So the first position gets us in the row we want to slice into the second position gets us in the column 03:36.920 --> 03:40.310 so spat bracket one come out. 03:40.310 --> 03:44.380 One should give us the same as loud as them here above buffers two step records. 03:44.390 --> 03:47.860 And that's correct. 03:47.860 --> 03:54.510 So now we can also index the element in the third row and the last column column. 03:54.520 --> 04:03.200 So let's see what it is on the third row in the last column it's twelve let's check this out and we 04:03.200 --> 04:13.480 get twelve and out if you want to select a column so all rows and all elements in a column then we can 04:13.480 --> 04:23.650 say okay I want f all rows I have a double colon and then I want to have the first column. 04:23.650 --> 04:27.130 Now this gives us the complete first column 1 5 and 9 04:30.730 --> 04:38.810 So all arrows in the first column and of course we can also select for all rows in the second column 04:40.170 --> 04:40.830 to 610 04:45.430 --> 04:51.550 and also all rows in the last column five eight twelve. 04:51.570 --> 04:58.290 Now we can also do more complicated things like getting the elements in the first two rows and column 04:58.290 --> 05:01.420 2 and 3. 05:01.590 --> 05:07.350 So in the first two rows the elements 2 and 3 so 2 3 6 7 05:12.900 --> 05:15.070 Yeah. 05:15.200 --> 05:23.540 All right so let's go back to our array and what we can also do we can switch or change the x's or transpose 05:23.570 --> 05:31.100 the Xs so to say that yeah instead of having a year one two three four as the first row we want to have 05:31.100 --> 05:37.940 it as a first column and instead of having here in the first column 1 5 9 we want to have it as the 05:37.940 --> 05:45.080 first row and we can do this by the attribute t so T capital letter 05:48.650 --> 05:55.730 and then we see a we just transposed them the our the array we switched the axis and that's also the 05:55.730 --> 05:58.040 method transpose. 05:58.280 --> 06:02.450 So we have at the brackets you can see it's a method not an attribute. 06:02.450 --> 06:07.980 And this gives us the same result. 06:08.000 --> 06:14.600 All right so now let's assume let's go back to our India rate a let's assume you want to divide the 06:14.600 --> 06:22.220 last column by 4 and actually we want to change the last column. 06:22.220 --> 06:29.390 So let's first of all divide on elements by force so we select all rows. 06:29.390 --> 06:36.770 And the last column and we will divide each element by four and then we have to assign the new values 06:37.430 --> 06:38.570 to the last column. 06:38.570 --> 06:39.560 So we have to say 06:43.880 --> 06:47.780 so please for the last column please calculate new values 06:50.950 --> 06:55.510 and now if you check a day you can see them on the last column. 06:55.680 --> 06:58.540 We have divided all elements by far. 06:59.000 --> 07:06.140 Okay so let's uh rearrange our array a well we know it already and then we can take the sum of all elements. 07:06.140 --> 07:13.680 So that's uh the method that sum which sums of all elements in the matrix. 07:13.750 --> 07:20.720 So it's seventy eight in what we can also do we can take the sum of each column so we can. 07:21.020 --> 07:28.620 So we can take the sum of column 1 it's the 15 of column two it's 18 and so on and therefore we have 07:28.620 --> 07:30.780 to define the axis. 07:30.780 --> 07:39.080 So the axis is the argument or barometer of the sum method an axis equals zero means that we take the 07:39.080 --> 07:48.520 sum of each column or to say along the rows so we sum up along the rows let's see what we get so we 07:48.520 --> 07:52.550 get 15 or 15 a seal of the some of the first column we get 18. 07:52.580 --> 08:00.280 It's the sum of the second column 21 is the sum of the third column and 24 is the sum of the fourth 08:00.280 --> 08:04.490 column and we can also take the sum of each row. 08:04.490 --> 08:11.040 So this means you take the sum along the columns. 08:11.040 --> 08:13.890 So get we get 10 26 and 42. 08:13.890 --> 08:18.690 So the sum of the first row gives us a 10. 08:18.720 --> 08:25.320 Then the sum of the second draw gives us 26 and the sum of the third row gives us 42. 08:26.340 --> 08:30.440 That's also the method come some and come some early returns. 08:30.450 --> 08:33.870 The cumulative sum of all elements. 08:33.870 --> 08:35.880 So let's see what we get. 08:35.890 --> 08:38.610 It's a cumulative means we are starting from the first element. 08:38.670 --> 08:43.120 So 1 then we are adding the second gives us three. 08:43.350 --> 08:47.830 Then we are adding the third element gives us six. 08:48.270 --> 08:57.730 Adding the fourth element gives us 10 adding the fifth element gives 15 and so on and we can also take 08:57.730 --> 09:00.100 the cumulative sum for each column 09:03.430 --> 09:05.500 from our let's secure the first column. 09:05.510 --> 09:15.220 So we start with 1 then we add 5 to 6 then we add 9 to 15 and also the second column. 09:15.220 --> 09:27.460 We have 2 adding six men we have eight adding 10 then we have 18 and we can also do the same cumulative 09:27.460 --> 09:32.110 sum for each row. 09:32.260 --> 09:33.290 All right. 09:34.720 --> 09:42.640 So let's go back to our initial array a and that's also the method thought process. 09:42.670 --> 09:46.580 So it takes the product over all elements. 09:46.590 --> 09:53.110 That's a bit a large number here actually and we can also take the product over all elements in each 09:53.110 --> 09:57.610 column so x equals zero. 09:57.630 --> 10:00.630 I guess that's the product of the column. 10:00.630 --> 10:02.890 So here we have 1 times five times line. 10:02.940 --> 10:08.470 Give us forty five and so on so two times six is twelve times ten is under 20. 10:08.550 --> 10:15.660 And yeah of course we can also take the product over all elements in each row by having the parameter 10:15.690 --> 10:19.550 X equals one. 10:19.600 --> 10:21.510 Now you can see it's the product here. 10:21.520 --> 10:22.600 Over each row. 10:22.600 --> 10:26.230 So one times two times three times four gets 24. 10:26.460 --> 10:26.680 Yeah. 10:26.680 --> 10:29.190 And so on. 10:29.200 --> 10:29.560 All right. 10:29.560 --> 10:34.490 So this is it for the session and in the next session we learn about boolean indexing. 10:34.570 --> 10:36.100 So I hope to see you there by.