WEBVTT 00:00.810 --> 00:02.980 Hello and welcome back to our case study. 00:03.000 --> 00:10.170 So in this case study we want to apply our skills and a bit larger case actually and we will apply random 00:10.170 --> 00:15.890 number generation back to arrest operations and the so-called method chaining. 00:15.930 --> 00:21.780 And also we want to compare the NUM pain and the pace and standard library in terms of performance length 00:21.810 --> 00:23.420 of code readability. 00:23.940 --> 00:29.020 Yeah and actually how intuitive the respective code might be for others. 00:29.050 --> 00:32.490 So but now let's start and let's assume the following situation. 00:32.490 --> 00:39.660 So we want to create 100 random into just between 1 and 10 and then even count how many times we get 00:39.660 --> 00:41.100 the integer one. 00:41.130 --> 00:45.000 So on average I would expect that ten times out of 100. 00:45.030 --> 00:51.150 And if you do this only one time the simulation the result can be quite different to what we expect 00:51.530 --> 00:58.800 and to check if our expectation that we get 10 times the integer one we have to simulate this many times 00:58.800 --> 01:06.080 so let's say ten thousand times to get a statistically reliable result and then be similar 10000 times 01:06.090 --> 01:12.480 and then we calculate the mean of all the outcomes are all simulations and then we should be very close 01:12.480 --> 01:16.460 to to 10 on average at least I hope actually. 01:16.500 --> 01:22.980 All right so let's start and we import an umpire and this is already the whole number code. 01:22.980 --> 01:25.670 But I would like to derive the code. 01:25.800 --> 01:34.710 So first of all we want to create 100 random integers in the range one till eleven. 01:34.710 --> 01:40.190 So we get here 100 integers and then we check which of them are equal to 1. 01:40.200 --> 01:47.430 So then we should get a ending array with the boolean objects so you can see false through false false 01:48.540 --> 01:54.300 and then we want to calculate how many times you have to be in the job on and therefore we just sum 01:54.300 --> 01:55.560 up our array. 01:55.590 --> 02:02.600 So let's remember that a true stands for the value of one and a false sense for the value zeros. 02:02.610 --> 02:11.780 So if you sum up the boolean array we should get to the number of occurrences of the enter to 1 and 02:11.780 --> 02:13.540 here we have 12. 02:13.580 --> 02:17.240 So our expectation was 10 and here only with one simulation. 02:17.310 --> 02:19.400 Yet because it's random we got twelve. 02:19.460 --> 02:28.130 And now let's repeat this process ten thousand times so we create 10000 times a hundred random integers 02:28.550 --> 02:38.180 so in total of 1 million integers and then we reshape this 1 million integers to a matrix of 10000 rows 02:38.240 --> 02:43.850 and 100 columns then for each integer we check whether it's equal to 1 or not. 02:43.850 --> 02:50.960 And then we have to sum over all rows how many troops or how many times we have the occurrence of the 02:50.960 --> 02:51.620 integer 1. 02:51.650 --> 02:55.190 So we have to take Xs so equals 1. 02:55.190 --> 02:57.070 So we sum over each row. 02:57.080 --> 03:04.550 We have 10000 simulations now and if we execute this year then we can see now we get 10000 results so 03:04.550 --> 03:07.590 we simulated this process 10000 times. 03:07.880 --> 03:13.880 And in our first simulation we got 12 times the Indians are 1 9 and the second one nine times. 03:13.900 --> 03:17.740 And now we also get six times four times so this match. 03:17.750 --> 03:20.590 Uh yeah statistical variability or actually. 03:21.350 --> 03:27.530 And yeah if you want to check whether our expectation is true that we on average expect 10 occurrences 03:27.530 --> 03:35.120 of the integer one we have to take the mean of all the results and then I can see we are very close 03:35.120 --> 03:35.690 to 10. 03:36.830 --> 03:42.770 So now we created the many random numbers we use to vector us operations and also the so-called method 03:42.770 --> 03:45.980 chaining so we changed one method after another. 03:45.980 --> 03:49.620 So we started to create a random integer then we reshape that. 03:49.850 --> 03:55.770 Then we took the sum of our troops for each row and then we took the mean of all results. 03:55.790 --> 04:03.860 So this is called Method chaining and we can also measure the time that this process or this code takes 04:03.860 --> 04:05.780 on average this time. 04:05.790 --> 04:06.350 Function 04:15.900 --> 04:22.850 that takes up a time so we have one million random integers so we got here 60 milliseconds. 04:22.850 --> 04:28.970 And now what we want to do now we actually want to simulate the same process with the pace and standard 04:28.970 --> 04:31.450 library and therefore we have to impart the random module. 04:32.660 --> 04:38.750 And yes actually the code that does the same job as 0 0 an umpire code with Python standard library 04:38.930 --> 04:39.620 instrument. 04:39.630 --> 04:42.610 So let's start here with the inner for loop. 04:42.740 --> 04:47.920 So a hundred times we are creating a random integer in the range between 1 and 10. 04:47.930 --> 04:50.630 And then we check for each created random integer. 04:50.660 --> 04:55.340 If it's equal to 1 and if it's 1 We append a true to our list. 04:55.360 --> 05:00.080 Edit And if it's not equal to 1 We append files to our list. 05:00.590 --> 05:07.760 And then we calculate the sum of all of our truisms and false in our list and append this to a resides 05:07.760 --> 05:09.290 list and indeed resides. 05:09.290 --> 05:13.940 Lists are all reserved for in total ten thousand simulations. 05:13.940 --> 05:17.440 I put this whole code here into a function called simulation. 05:17.450 --> 05:20.840 So that makes it easier later yet to measure the time actually. 05:21.140 --> 05:24.500 So there's no deeper reason for it. 05:24.500 --> 05:29.750 So they can execute the Sally and then we can run our function and simulate that space in standard library 05:32.050 --> 05:34.330 and I can see we got a nine point nine. 05:34.330 --> 05:37.430 Also here we are very close to 10. 05:37.450 --> 05:43.010 Now let's measure the time of the performance of the code and compare it to an umpire. 05:52.760 --> 05:54.580 We have here one point two seconds. 05:54.580 --> 06:01.210 So this code took us one point two seconds and an umpire did actually the same job in six in milliseconds. 06:01.210 --> 06:03.400 Some umpires 100 times faster. 06:03.460 --> 06:05.510 And that's actually a huge difference. 06:05.830 --> 06:12.160 And you can also see here we have a very condensed code so we have actually only one line of code here. 06:12.220 --> 06:18.060 And in contrast with sort of the pace the standard library we have here nested for loop and if statements. 06:18.100 --> 06:22.860 However some people say that here the readability of the code is much easier. 06:22.870 --> 06:25.750 And also it's what you'd have to understand. 06:25.750 --> 06:31.060 So at least if you have done two or three times the nested blue band some statements it might be quite 06:31.060 --> 06:36.310 easy to understand what the code is doing here in comparison the vector as campaign code and method 06:36.340 --> 06:41.170 chaining might be a bit less intuitive at least if you are not used to it. 06:41.170 --> 06:41.550 All right. 06:41.560 --> 06:46.780 So this is it for the time being and in the next session we will have a look at summary statistics so 06:47.050 --> 06:48.430 help to see there by.