crum ia a Rust crate for implementing complex numbers and matrices with a large focus on complex matrices and their use in numerical analysis.
Transcript
1 00:00:00.570 --> 00:00:02.170 Frans: This meeting is being recorded
2 00:00:02.170 --> 00:00:15.080 Gabor Szabo: So Hi, and welcome to the codeme events meetings, the meet up group. And if you're watching the Youtube video, then to the codeme events, Youtube Channel. And my name is Gabor Sabo. I
3 00:00:15.270 --> 00:00:23.110 Gabor Szabo: I'm a self-employed. I help companies introduce rust and python, help them with training, help them with testing.
4 00:00:23.220 --> 00:00:35.710 Gabor Szabo: And I also organize events, both in person meetings in Tel, Aviv, and in Python for Python and and Rust, and also these online events in English.
5 00:00:36.290 --> 00:00:50.500 Gabor Szabo: in order to share knowledge between people all around the world. And I think it's a very good way to learn about all kind of things that we can't learn or ourselves
6 00:00:50.660 --> 00:01:08.890 Gabor Szabo: this time. We have Franz, who agreed to give this presentation, and you're going to introduce yourself, or he's going to introduce himself in a bit. I'm really happy that you agreed to give this presentation, and I thank everyone who joined us in this meeting
7 00:01:08.890 --> 00:01:25.200 Gabor Szabo: feel free to ask questions after the recording, we can stay around. So if there are things that you don't want to talk about during the recording and in the Youtube, video, that's fine, we can stay around after the meeting and have a little chat as well. That's the
8 00:01:25.230 --> 00:01:28.480 Gabor Szabo: advantage of actually being in the in the meeting.
9 00:01:28.710 --> 00:01:31.369 Gabor Szabo: And also you can ask questions.
10 00:01:32.320 --> 00:01:47.709 Gabor Szabo: and if you're watching the video, then please click the like button and follow the channel. So you get notified and also join our the call me events meet up group, so you will be able to see when we have a new meetings.
11 00:01:48.430 --> 00:01:53.809 Gabor Szabo: Franz. Welcome to this meeting. Please introduce yourself, and it's yours.
12 00:01:54.540 --> 00:01:57.089 Gabor Szabo: Share your screen, if you like, and whatever
13 00:01:57.090 --> 00:02:01.689 Frans: Yeah, thanks. Thanks. Kabor. And thanks for the opportunity.
14 00:02:02.283 --> 00:02:11.110 Frans: As as I just mentioned to you. Unfortunately, I've I've I haven't got a formal presentation. But I will talk through
15 00:02:11.230 --> 00:02:24.920 Frans: this sort of process that went into what I'm doing. So 1st of all, my name is Franz Bresler slabber. That's the full spectrum of names. And I'm a programmer living in South Africa.
16 00:02:25.370 --> 00:02:30.309 Frans: I've been a programmer since I can't remember
17 00:02:30.570 --> 00:02:49.090 Frans: since 94 mainly and and oh, okay, I work for myself as well. So I do various contracts, developing mainly in the technical sort of programming space solving.
18 00:02:49.620 --> 00:02:53.009 Frans: modeling problems, etc, stuff like that.
19 00:02:54.810 --> 00:03:00.240 Frans: So my main expertise has always been c plus plus.
20 00:03:00.930 --> 00:03:19.600 Frans: Recently I had moved into Golang a bit, and then I sort of out of interest started in rust. So rust is almost I haven't. How can I say? Used it commercially, but it's it's an interest, and it's a fascinating way for me to.
21 00:03:19.810 --> 00:03:23.493 Frans: I've got a strong interest in mathematics.
22 00:03:24.270 --> 00:03:34.070 Frans: especially how it relates to a numerical computing for use in in machine learning and stuff like that
23 00:03:34.230 --> 00:03:35.530 Frans: stuff like that
24 00:03:37.020 --> 00:03:48.970 Frans: very technical term. Okay, so 1st order of business, what I did is I'm gonna share screen, because I think that's the easiest way to to go about this. That's okay. Gabor.
25 00:03:49.230 --> 00:03:50.300 Frans: obviously.
26 00:03:50.300 --> 00:03:52.039 Gabor Szabo: Sure. Sure. Sure. Go ahead.
27 00:03:52.240 --> 00:03:55.820 Frans: Okay. So I'm not too familiar.
28 00:03:58.220 --> 00:04:00.240 Gabor Szabo: Should be a big green button
29 00:04:00.240 --> 00:04:01.989 Frans: Yeah, yeah, I've got it.
30 00:04:02.870 --> 00:04:10.210 Frans: Share. Oh, yeah. Oh, not seeing it. Select window. So I'm gonna select.
31 00:04:11.310 --> 00:04:16.779 Frans: Not that one know what that doing open store.
32 00:04:17.060 --> 00:04:25.299 Frans: allow visual studio. So I've got a very big screen. So please tell me if the resolution is okay.
33 00:04:25.300 --> 00:04:30.200 Gabor Szabo: But way too small the letters. So if you can enlarge the fonts, that would be nice
34 00:04:30.380 --> 00:04:34.192 Frans: Yeah, I can just zoom in. I think that works as well.
35 00:04:34.990 --> 00:04:36.410 Frans: Just a moment.
36 00:04:37.850 --> 00:04:39.590 Frans: No, it is.
37 00:04:41.280 --> 00:04:45.380 Frans: There is a yes, somebody wants to say something
38 00:04:45.380 --> 00:04:49.949 Gabor Szabo: No, no, I just going to turn it off it. It beeps when someone joins
39 00:04:50.150 --> 00:04:51.100 Frans: All right.
40 00:04:53.500 --> 00:04:55.160 Frans: Just a moment.
41 00:05:02.250 --> 00:05:05.009 Frans: I've done this before. Sorry guys.
42 00:05:05.010 --> 00:05:06.980 Gabor Szabo: So is it. A windows
43 00:05:07.418 --> 00:05:10.929 Frans: There we go. No, it's it's a Linux
44 00:05:11.355 --> 00:05:14.759 Gabor Szabo: For me. It's control shift plus you usually
45 00:05:14.760 --> 00:05:16.020 Frans: Yeah, there we go.
46 00:05:16.260 --> 00:05:17.920 Frans: That's slightly better.
47 00:05:17.920 --> 00:05:21.180 Gabor Szabo: A little bit more, a little bit more.
48 00:05:22.180 --> 00:05:25.310 Gabor Szabo: Yeah, more, more.
49 00:05:25.310 --> 00:05:26.210 Gabor Szabo: One more sure
50 00:05:27.545 --> 00:05:28.360 Frans: Wow!
51 00:05:29.330 --> 00:05:38.159 Gabor Szabo: Yeah, okay, thanks. That's now. No, at least I can see. I don't know if anyone else still needs larger. Please let us know. For me. It's it's fine
52 00:05:38.920 --> 00:05:46.420 Frans: Okay, good stuff. So basically, let's go. Let's start at the beginning.
53 00:05:46.770 --> 00:05:57.899 Frans: So the 1st thing I started playing with is complex numbers, and the idea is to write A. What in C would be a template class
54 00:06:00.670 --> 00:06:24.770 Frans: to write the equivalent in rust, and to actually have limiting it by means of traits. Okay, so sorry. Let me just take a step back here. The whole idea that I started out with as well is that I wanted to write something. One of the main ideas is that it's completely safe code.
55 00:06:24.820 --> 00:06:35.120 Frans: So I don't call into any under the covers, call into any unsafe libraries, any C or C plus plus libraries.
56 00:06:35.360 --> 00:06:50.489 Frans: Of course, that comes with a performance penalty because you gain quite a lot by. For example, if to do your matrix, arithmetic or matrix manipulation. To do that with
57 00:06:50.630 --> 00:06:56.999 Frans: pointer arithmetic is is generally much faster, but
58 00:06:57.150 --> 00:07:14.019 Frans: I try. I stayed away from it on purpose. So this is all safe for us. Code number one. And also I. Then obviously the closest I could come in terms of performance is by using iterators extensively.
59 00:07:17.140 --> 00:07:25.969 Frans: So, okay, having said that, I started out with the basic ideas of a generic complex number class.
60 00:07:26.310 --> 00:07:37.120 Frans: and there are there are libraries out here that out there that do it, and probably do it much better. So I've got no claim that I'm doing wonderful stuff.
61 00:07:37.540 --> 00:07:43.790 Frans: and as you can see, this will look quite a bit outstanding. But okay, sorry. Let me just go to the top.
62 00:07:44.337 --> 00:07:52.080 Frans: So what I started up is just a basic structural and imaginary, with a type of generic type T.
63 00:07:52.420 --> 00:08:03.800 Frans: And because I wanted to make this compliant with num traits float and integer actually specifically
64 00:08:05.580 --> 00:08:12.919 Frans: I had to define all the traits now, some of them I haven't completed yet, because I didn't
65 00:08:13.530 --> 00:08:21.930 Frans: use the so if we go down here you will see there's some to do's in. There.
66 00:08:22.470 --> 00:08:23.499 Frans: there we go.
67 00:08:25.446 --> 00:08:26.940 Frans: Which is
68 00:08:27.110 --> 00:08:36.119 Frans: probably needs to be fleshed out at some point. So again, just reminding you that this is purely a fun project for me.
69 00:08:36.270 --> 00:08:54.100 Frans: I'm not beholden to anyone to have a finished, polished product. Of course I would like to move to that point, but hey? It's all dependent on when I have time or not. So that's my last excuse I'm going to make
70 00:08:54.480 --> 00:09:03.099 Frans: from us this evening. Okay, so complex numbers, not a big thing. There are things out there pretty much
71 00:09:04.980 --> 00:09:12.970 Frans: And I mean, I'm not going to dwell on this too too much. This is, you can imagine, this is very basic kind of coding.
72 00:09:13.370 --> 00:09:20.389 Frans: right? So, of course, that the aim of that was to start moving into matrices.
73 00:09:20.690 --> 00:09:23.740 Frans: So then
74 00:09:26.980 --> 00:09:34.670 Frans: I start. Okay, sorry. I just want to get you the matrix declaration apologies for this scrolling around.
75 00:09:34.890 --> 00:09:36.490 Frans: Oh, boom!
76 00:09:39.800 --> 00:09:48.610 Frans: So what I decided on in terms of looking towards the future
77 00:09:48.840 --> 00:09:53.970 Frans: to store the all the data in a flat vector.
78 00:09:54.490 --> 00:10:04.109 Frans: generic vector and to make it row dominant. So what that means is that if you if you look at a matrix, and
79 00:10:04.240 --> 00:10:11.780 Frans: you look at the 1st row that would be the first.st So say you've got a a
80 00:10:14.170 --> 00:10:17.920 Frans: in rows. Sorry in columns. So the 1st
81 00:10:18.150 --> 00:10:33.629 Frans: N entries in the vector is the 1st row and then the second N entries that follow onto that is the second row, so I don't know if that creates a easy visualization. But that's for those that don't.
82 00:10:34.240 --> 00:10:36.849 Frans: I haven't heard about road dominance, anyway.
83 00:10:37.090 --> 00:10:50.160 Frans: So and that was sort of then it started getting interesting. So the normal things like adding a matrix subtracting a matrix, extensive use of of just
84 00:10:50.380 --> 00:10:54.589 Frans: iterator and all the the goodies that it has with it.
85 00:10:58.050 --> 00:11:03.670 Frans: So that was pretty so interesting, but pretty straightforward.
86 00:11:03.830 --> 00:11:11.610 Frans: And then I added, stuff like, get the diagonal as a vector, etc, that kind of thing and getting a skew diagonal.
87 00:11:11.920 --> 00:11:21.890 Frans: Also, I find that I wanted to. If you have a matrix of floats, you want to round them off to some decimal place which is very nice
88 00:11:22.040 --> 00:11:48.269 Frans: for later manipulation. I find I needed upper triangular matrices. So if any of these things, these are just different forms of matrices, so upper triangular is all the elements above. The diagonal is non-zero and the one below are 0 kind of thing, and as that is, and lower triangle is triangular is the opposite.
89 00:11:48.770 --> 00:11:53.205 Frans: And we have the famous identity matrix. So
90 00:11:54.660 --> 00:12:07.240 Frans: if this is so, I I'm assuming some level of linear algebra background here. Assumption.
91 00:12:08.370 --> 00:12:16.309 Frans: Then oh, checking if it is an identity, that kind of thing. Okay, so that's pretty much
92 00:12:16.410 --> 00:12:24.000 Frans: sort of what you would think would it would have as a standard library then? Now.
93 00:12:24.200 --> 00:12:27.420 Frans: my! Oh, in this transpose.
94 00:12:30.900 --> 00:12:35.089 Frans: of course. Now this raises very interesting
95 00:12:35.640 --> 00:12:50.880 Frans: when you write this because you have to keep in mind that you have a flat vector storing the stuff. So if you have to do a transpose, you have to carefully work with what they call strides.
96 00:12:51.610 --> 00:12:53.380 Frans: In other words,
97 00:12:55.690 --> 00:13:05.180 Frans: it is normally the offset that you would get to an element in a specific row and column in a flat vector, considering a flat, vector.
98 00:13:06.510 --> 00:13:10.689 Frans: we will talk more about strides when we get to tenses.
99 00:13:11.050 --> 00:13:11.810 Frans: Okay.
100 00:13:11.940 --> 00:13:31.359 Frans: so this was sort of sub matrix. And you can see there's some tests here in a way. You know, I wrote a macro for declaring a matrix like that which is pretty straightforward, and then to get the sub matrix sticking to having this inclusive ranges that you can specify
101 00:13:31.430 --> 00:13:43.310 Frans: from this row to that row, and from this column to this this column inclusive, and it'll give you the sub matrix out of this chunk of bigger matrix, anyway. So that's sort of
102 00:13:43.980 --> 00:13:45.730 Frans: what's going on here.
103 00:13:46.890 --> 00:13:52.510 Frans: Of course, this whole process also to keep in mind is that this is me.
104 00:13:53.530 --> 00:13:59.419 Frans: As you work with iterators, more and more it becomes clearer and
105 00:13:59.540 --> 00:14:02.300 Frans: probably less clunky working with it.
106 00:14:02.680 --> 00:14:03.530 Frans: Okay?
107 00:14:06.200 --> 00:14:31.759 Frans: So also doing stuff like inserting a row, inserting a column, etc. Etc. Then, of course, there becomes augmentation as we adding a sub matrix on top as the description is up top here, the top left corner of a larger matrix. So when we when I start writing matrix, how can I say routines? This becomes important.
108 00:14:32.480 --> 00:14:43.590 Frans: determinant over 2 by 2 and then converting a real to a complex matrix. Okay, so now we start seeing why I started with complex. Because I want you to work
109 00:14:43.930 --> 00:14:50.749 Frans: my 1st aim in doing with this, or the 1st sort of goal that I had was working with complex matrices.
110 00:14:51.300 --> 00:15:13.380 Frans: and there was a very specific reason that I wanted to do it, which I'll show later, or just now put it that way. So now with matrices, you have very famous things like Lu decompositions with Gauss elimination. So this was so now it became really interesting. And I mean, I really actually
111 00:15:13.800 --> 00:15:20.900 Frans: love this stuff sadly, I do other things in life as well.
112 00:15:21.230 --> 00:15:28.340 Frans: This a side note. Humorous side note, anyway. So so that was sort of
113 00:15:29.570 --> 00:15:34.759 Frans: this. I think this was my 1st big achievement. Was it lu decomposition?
114 00:15:36.920 --> 00:15:41.400 Frans: With a partial pivot, fascinating stuff.
115 00:15:41.520 --> 00:16:03.260 Frans: So what was also what I really liked about this is I did, applied math degree long ago. But I you know you completely forget things, because if you don't work with it or not completely forget, but it's so far removed, and what was very nice is, I had to go and sort of read up on how these things work, especially
116 00:16:03.400 --> 00:16:22.099 Frans: from a numerical computing point of view, because that is different to a sort of straightforward, academic, theoretical application of matrices. Because, you know, computing isn't exact. So you always have rounding errors, and you always have to work to a certain precision.
117 00:16:22.330 --> 00:16:25.190 Frans: Anyway, that was linear solving.
118 00:16:25.620 --> 00:16:33.020 Frans: Have I got too complex yet? Sorry sorry about that. I just want to go up this.
119 00:16:33.570 --> 00:16:37.899 Frans: And we saw a real square matrix. No, we're still unreal.
120 00:16:38.410 --> 00:16:40.819 Frans: Okay? So at some point.
121 00:16:48.230 --> 00:16:50.729 Frans: sorry, it must be completely boring
122 00:16:51.480 --> 00:16:55.720 Frans: sort of looking at what I did, quite amazed that I wrote it all.
123 00:16:57.770 --> 00:17:05.419 Frans: Okay. So ultimately, the point was what to calculate eigenvalues of a matrix.
124 00:17:06.140 --> 00:17:21.600 Frans: So and here I established then complex matrix specializations, that where your generic item is a complex matrix of
125 00:17:21.829 --> 00:17:26.040 Frans: T, which you know satisfies numb traits.
126 00:17:30.390 --> 00:17:38.150 Frans: So there was just some things here, and then I think the ultimate is where I do.
127 00:17:39.371 --> 00:17:44.489 Frans: There's a random, complex matrix. By the way, kind of things is where I actually
128 00:17:45.960 --> 00:17:48.319 Frans: own a complex conjugate.
129 00:17:49.440 --> 00:17:52.770 Frans: So this is all to do with complex matrices. And
130 00:17:53.680 --> 00:18:01.819 Frans: this was also beautiful to do complex matrix. QR decomposition using householder transforms.
131 00:18:02.160 --> 00:18:08.325 Frans: This was fantastic. So, by the way, all of this has been
132 00:18:09.260 --> 00:18:13.869 Frans: how can I say ratified against Matlab
133 00:18:15.560 --> 00:18:20.830 Frans: because I wanted to make sure that I'm not putting nonsense out there.
134 00:18:28.210 --> 00:18:31.269 Frans: this is QR complex.
135 00:18:32.990 --> 00:18:44.350 Frans: QR decomposition with householder transforms. So this is all used when you're trying to find the eigenvalues of a matrix. I just want to go right down where I actually do the
136 00:18:46.520 --> 00:18:50.909 Frans: that's the household that transform scar, duck, decomposition
137 00:18:56.570 --> 00:18:58.500 Gabor Szabo: Yeah, I have a question. Franz
138 00:18:58.500 --> 00:18:59.380 Frans: Yes.
139 00:18:59.380 --> 00:19:00.393 Gabor Szabo: Do you?
140 00:19:01.680 --> 00:19:07.819 Gabor Szabo: So, besides writing the the crate, did you make any use of it?
141 00:19:07.820 --> 00:19:15.380 Frans: No, no, no. So so the that's for yourself or yeah. So I'm hoping
142 00:19:16.220 --> 00:19:28.349 Frans: to use it at some point. But at the moment this was purely, as I said in the beginning, for myself, as an entertainment, as something fascinating for me to do. And and
143 00:19:28.450 --> 00:19:43.880 Frans: I enjoy mathematics. And I enjoy solving complex software problems. And a lot of this coding is is
144 00:19:44.490 --> 00:19:54.709 Frans: I. Maybe I'm just old and slow. But I found it very involved and and quite a lot of pencil sketches had to be done
145 00:19:55.260 --> 00:19:58.510 Frans: to figure out how to do this.
146 00:19:58.830 --> 00:20:06.440 Gabor Szabo: I mean, I we use generics and all kind of interesting parts of of rust.
147 00:20:06.600 --> 00:20:13.509 Gabor Szabo: Yes. How did you? Did did you implement anything similar in in CC plus earlier
148 00:20:14.060 --> 00:20:15.890 Frans: No, I've either.
149 00:20:15.890 --> 00:20:20.959 Gabor Szabo: How do you compare what the feeling of of writing rush? That's what I'm trying to ask
150 00:20:21.190 --> 00:20:33.960 Frans: Much, much more difficult. And look, I mean, obviously, I've written C plus plus for what 20 years, you know. So and template programming template libraries is is
151 00:20:34.350 --> 00:20:41.179 Frans: is pretty because you have all these these restrictions, these these things.
152 00:20:41.360 --> 00:21:01.450 Frans: you know making. And if you so, for example, if you are doing an eigen eigenvalue decomposition you are using previous QR or Lu decompositions that you've written to actually facilitate that finding that eigenvalue and
153 00:21:01.700 --> 00:21:24.719 Frans: you have to be so. How can I say? Careful to have the right traits from the bottom up? Otherwise you can't, you know, when you get to the top one. You don't satisfy the traits required to to do it. Kind of thing. If if that makes some sort of sense, I just find it very.
154 00:21:25.200 --> 00:21:49.570 Frans: I mean, I appreciate what it's trying to do here in terms of forcing you to be very, very strict. What you can do. And obviously that is the selling point of rust. Well, one of the selling points of rust is the is safety, and and this really forces you to use it in a very specific way.
155 00:21:50.130 --> 00:22:10.590 Frans: So I do appreciate that. But I may. I mean, look, I'm a youngster in rust if you can put it like that. So maybe that's why I find it difficult, but I found it much more involved than than C plus plus. And of course, and I had to learn the whole iterator setup.
156 00:22:10.860 --> 00:22:15.950 Frans: You know what you can do with iterators, what it actually means. And and
157 00:22:16.330 --> 00:22:26.499 Frans: you know, in in c plus plus, you would have just done as I said. Pointer. Arithmetic, you know, on, on dynamic arrays, or something or static arrays doesn't matter, but
158 00:22:26.660 --> 00:22:30.999 Frans: I think it would be pretty much more straightforward.
159 00:22:32.640 --> 00:22:37.470 Frans: So so this? Why, this was challenging for me to be honest, you know
160 00:22:37.710 --> 00:22:43.045 Gabor Szabo: Do you want to go over the the details of one of the functions to see? So we can. We can,
161 00:22:43.300 --> 00:22:47.157 Frans: Well, I'm I'm just trying to get to
162 00:22:47.640 --> 00:22:51.220 Gabor Szabo: For a simple function, and then, maybe later on, a more complex one.
163 00:22:51.630 --> 00:22:52.110 Frans: Okay.
164 00:22:52.110 --> 00:22:54.929 Gabor Szabo: So so we can have a feeling of of a
165 00:22:54.930 --> 00:22:55.630 Frans: Yeah.
166 00:22:55.630 --> 00:22:56.880 Gabor Szabo: How this code looks like
167 00:22:57.360 --> 00:23:01.159 Frans: Mother, okay. So we out there. So I just want to
168 00:23:01.160 --> 00:23:04.340 Gabor Szabo: I suppose I don't know. Difficult
169 00:23:04.340 --> 00:23:08.539 Frans: Okay, yeah, I transpose this shit.
170 00:23:18.680 --> 00:23:25.519 Frans: There we go. Okay, okay, so this is
171 00:23:26.400 --> 00:23:32.560 Frans: so remember, vector matrix is a flat vector
172 00:23:32.830 --> 00:23:40.880 Frans: so basically, what I do is when I come into this function, I just declare a mutable vector
173 00:23:41.050 --> 00:23:51.370 Frans: a generic vector of type T, which is what the original type is, and it's declared with the capacity of the one that I'm entering in. So
174 00:23:53.280 --> 00:24:03.450 Frans: just to go back to something I said previously is that I was learning as well. So there may be some way of doing this in place.
175 00:24:03.640 --> 00:24:16.490 Frans: But this I just declared a new vector, kind of a result vector, which you can see. I later wrap it into the the matrix that I return, if you like.
176 00:24:17.110 --> 00:24:23.100 Frans: So and then so for each row
177 00:24:25.310 --> 00:24:31.320 Frans: index in the number of columns. So we have number of columns. So this is for each item in the row.
178 00:24:37.140 --> 00:24:39.670 Frans: I have to really scratch my brain here.
179 00:24:44.560 --> 00:25:00.700 Frans: Oh, that's right. I use the skip iter to actually skip the actual offset so that I don't want to actually use this example because this doesn't really show using
180 00:25:00.830 --> 00:25:03.370 Frans: skip, and
181 00:25:03.720 --> 00:25:12.029 Frans: the the iterator function skip and step by which I actually use quite a lot. So anyway. But we can continue with this.
182 00:25:12.340 --> 00:25:15.819 Frans: Then we have. We just
183 00:25:16.680 --> 00:25:23.319 Frans: use a skip it iterator to get to the correct one. Because, remember, if you have.
184 00:25:23.570 --> 00:25:30.109 Frans: where is the example? Here, there we go. So we want to transpose that. So that is the row
185 00:25:30.620 --> 00:25:32.929 Gabor Szabo: And we want to make the row
186 00:25:33.070 --> 00:25:39.100 Frans: The 1st column, right? So you've got to go through the 1st row and write the 1st column.
187 00:25:39.540 --> 00:26:08.629 Frans: But the problem being that you're writing it into a row dominant, vector which is what this result vector, is. So you've got to go and say, if I transpose this, you've got 1, 2, 7 going down and 3, 4, 8 going down. Okay, so you have one and 3 being the 1st row now. So one and 3 will be the 1st 2 elements of the new vector
188 00:26:11.640 --> 00:26:13.690 Frans: here that I'm writing.
189 00:26:16.230 --> 00:26:26.350 Frans: So I I. So you can see in the result. Vector sorry I'll be with you. Now, we actually, we actually just build it up, row by row.
190 00:26:28.200 --> 00:26:28.820 Gabor Szabo: Right.
191 00:26:31.090 --> 00:26:32.489 Frans: Yes, go ask a question
192 00:26:32.490 --> 00:26:39.690 Gabor Szabo: No, I was. I was just wondering if if if the transpose is not just taking the
193 00:26:40.250 --> 00:26:44.599 Gabor Szabo: Xy element in the matrix and put it in. Put it in the YX
194 00:26:44.600 --> 00:26:52.729 Frans: Right. Yes, you can. So if you which, if you have a way of accessing the elements XY,
195 00:26:53.000 --> 00:26:56.640 Frans: which I do have up here, but I'm trying to
196 00:26:56.640 --> 00:26:59.800 Gabor Szabo: An array. Right? The whole thing is just one longer
197 00:26:59.800 --> 00:27:06.580 Frans: Well, well, it's it's resembling an array, but it is stored as a flat vector that that
198 00:27:06.580 --> 00:27:07.880 Gabor Szabo: Vector, sorry. Correct.
199 00:27:07.880 --> 00:27:25.889 Frans: Yeah, flat. Vector so the thing is that I can write this by just saying, for each row, for each column, swap, go get element Xy, and make it element. Yx, and I have the accessors.
200 00:27:26.390 --> 00:27:30.819 Frans: I think I've got it. Sorry. Let me just find it up here.
201 00:27:33.410 --> 00:27:35.800 Frans: Where is? Oh, there index.
202 00:27:36.430 --> 00:27:37.559 Frans: So I've got
203 00:27:37.790 --> 00:27:51.299 Frans: index and index mutable, which will give me access to the the actual XY coordinate, if you like, or the row column coordinate, and then just make just using index to set it to
204 00:27:51.470 --> 00:27:53.630 Frans: to Yx, if you like.
205 00:27:54.050 --> 00:27:58.930 Frans: But that means that you are calling this routines many times.
206 00:27:59.260 --> 00:28:01.090 Frans: Okay in a loop.
207 00:28:01.420 --> 00:28:11.079 Frans: So I would rather, for the sake of efficiency and speed. When I look for which I've lost now.
208 00:28:20.070 --> 00:28:41.300 Frans: I would rather do it directly on the vector and pull chunks out of it than actually. So I'm saving a little bit. Okay, not much, I guess. But this to me, is more efficient than just sitting in 2 for loops and and swapping rows and columns around row and column items around.
209 00:28:42.530 --> 00:28:46.300 Frans: I could be wrong, but that was just my thought on this
210 00:28:50.230 --> 00:28:52.450 Frans: sort of happy Gabor
211 00:28:53.320 --> 00:28:58.680 Gabor Szabo: I'm trying to understand. Yeah, the skipper. What? What is that
212 00:29:00.180 --> 00:29:03.020 Frans: This is, I defined it up here.
213 00:29:11.810 --> 00:29:30.510 Frans: So that is just a way of defining an iterator that skips a certain step size through so you could. Instead of using this. And as I said this, I used in the beginning, and later on I use the iterative actual iter functions step by and skip.
214 00:29:30.690 --> 00:29:33.580 Frans: which is, which would do the same thing as this
215 00:29:35.330 --> 00:29:36.120 Gabor Szabo: Okay.
216 00:29:38.630 --> 00:29:45.700 Frans: So what I'm actually saying subtly is that this would probably needs to be rewritten.
217 00:29:48.700 --> 00:30:04.450 Frans: But for now it works okay. Because and it will become clear. Why, I just sort of went on without really being too fussed about this. Okay, so I don't.
218 00:30:04.640 --> 00:30:06.050 Frans: Okay, hang on.
219 00:30:06.450 --> 00:30:10.980 Frans: Let's get some order here, go!
220 00:30:11.350 --> 00:30:12.679 Frans: Where was that again?
221 00:30:13.250 --> 00:30:14.770 Frans: Can't remember. There we go.
222 00:30:15.100 --> 00:30:16.799 Frans: Okay. So
223 00:30:17.570 --> 00:30:28.179 Frans: that's a very easy function, which, as you rightly say, probably needs to be rewritten. I'm just trying to think if there's not something else that is probably better.
224 00:30:29.950 --> 00:30:33.139 Frans: Sub matrix. You see. Yeah.
225 00:30:33.260 --> 00:30:40.280 Frans: okay. So again, the idea is, you want to grab a chunk out of this. Okay, that's not.
226 00:30:40.660 --> 00:30:42.920 Frans: You want to grab
227 00:30:42.920 --> 00:30:43.450 Gabor Szabo: Rectangle.
228 00:30:43.450 --> 00:30:57.590 Frans: From here here. Yeah, you want to grab a little block out of it, and the way you specify it, you say inclusive. I want to from column 3 to column 7, and from Sorry row.
229 00:30:57.720 --> 00:31:06.859 Frans: row, row column. Always work, row column. So row 3, 2, including row 7, column 2. So you can. It's a little slice out of there.
230 00:31:10.720 --> 00:31:14.199 Frans: So basically, we just check that. It's the correct rows.
231 00:31:14.540 --> 00:31:15.530 Frans: Right?
232 00:31:15.690 --> 00:31:19.100 Frans: Iterate. Get an index going enumerate.
233 00:31:19.230 --> 00:31:22.759 Frans: Then we will skip.
234 00:31:26.070 --> 00:31:42.990 Frans: So we want to position ourselves. So if you imagine just visually, if you want to extract a chunk out of here and remember that it's stored row dominant. You want to 1st get to this row, and you can just strip out
235 00:31:43.160 --> 00:31:47.740 Frans: the number of row elements if you like.
236 00:31:47.860 --> 00:31:57.340 Frans: because they would, they would be adjacent in the to each other in the storage. Vector so this is this will be straightforward
237 00:31:57.470 --> 00:31:58.409 Frans: if you like.
238 00:31:58.810 --> 00:32:01.041 Frans: So you would
239 00:32:02.670 --> 00:32:18.170 Frans: remember this all up here before you get to this element here. This all will be in a flat. Vector so it's a row. Then the next row next row. So you've got to skip the number of columns times up to this row.
240 00:32:18.410 --> 00:32:22.830 Frans: and then you have to skip what the index is that you want to extract.
241 00:32:23.210 --> 00:32:26.400 Frans: So you want to skip 3 rows
242 00:32:26.540 --> 00:32:29.400 Frans: times how many columns is in a row.
243 00:32:29.550 --> 00:32:41.559 Frans: so that, and then you want to add on another little piece until you get here. So that positions you here. So I think you can see that exactly what I've done here.
244 00:32:42.140 --> 00:32:46.410 Frans: the problem, not the problem. But something that
245 00:32:46.710 --> 00:32:56.590 Frans: probably could be changed is that I'm using 0 index. Sorry one indexing for use. But
246 00:32:56.690 --> 00:33:00.270 Frans: obviously it starts at 0. It's 0 indexed.
247 00:33:00.520 --> 00:33:05.830 Frans: So that's why I always have these minus one nonsense, and it gets a bit
248 00:33:06.520 --> 00:33:18.489 Frans: tedious. But anyway, Beta estimate the number of columns times the number of rows above the element. And then, plus where the the column is that we want to extract.
249 00:33:20.020 --> 00:33:24.030 Frans: you can see calls. Start is the 1st one here in the range.
250 00:33:24.950 --> 00:33:28.020 Frans: Okay, so is, is that sort of reasonably clear
251 00:33:28.360 --> 00:33:29.700 Gabor Szabo: Yeah, I think so.
252 00:33:30.450 --> 00:33:33.470 Frans: What I'm doing right? So then.
253 00:33:33.470 --> 00:33:36.420 Gabor Szabo: We're using assert to to verify the
254 00:33:37.510 --> 00:33:38.200 Frans: Yes.
255 00:33:38.420 --> 00:33:51.300 Frans: Well, this is just to make sure that I'm not specifying in my rows and columns something that would sit outside. You know that there isn't enough rows for it to sit in here.
256 00:33:51.540 --> 00:33:52.429 Frans: if you like.
257 00:33:54.990 --> 00:34:03.689 Frans: In other words, I'm not. I'm not wanting to extract this submatrix that is larger in some dimension than the matrix. I'm given
258 00:34:04.520 --> 00:34:05.230 Gabor Szabo: Right.
259 00:34:05.800 --> 00:34:08.346 Frans: Alright. So that's all the sort of
260 00:34:09.250 --> 00:34:12.260 Frans: stuff that I this says that I do there.
261 00:34:14.860 --> 00:34:23.259 Frans: So then, the step by jeez, I'm trying to think what I did here.
262 00:34:26.800 --> 00:34:33.600 Frans: I know I extract little vectors, and then I flatten them. Obviously, this is what's happening here.
263 00:34:34.132 --> 00:34:35.098 Frans: Sorry about that.
264 00:34:35.560 --> 00:34:42.690 Frans: Step by. So I get to the right position. Then I start iterating.
265 00:34:51.400 --> 00:34:57.200 Frans: just thinking, why am I not iterating by one stepping by 1 1st of all?
266 00:35:03.860 --> 00:35:09.729 Frans: Oh, well, guys, sorry I should have spent more time prepping it so I can give better answers
267 00:35:11.410 --> 00:35:16.200 Gabor Szabo: It's fun reading code, even if it even if it's yours.
268 00:35:16.730 --> 00:35:23.520 Frans: Yeah, it's it's it's as I said, I haven't spent time on it, and I've been so in deep in
269 00:35:24.050 --> 00:35:29.630 Frans: trying to find a memory leak on a big golang server. And it's
270 00:35:29.810 --> 00:35:33.599 Frans: it's yeah. My mind has just not been on this at all.
271 00:35:35.780 --> 00:35:57.839 Frans: okay, anyway, if there's real interest. We can come back to this at some point later, when I will make time from the beginning of April, I have more time again, so maybe we can make another arrangement. I can look at this so maybe see this as a sort of a high level view to start off with.
272 00:35:57.980 --> 00:36:03.260 Frans: anyway. So the moving on from this.
273 00:36:05.090 --> 00:36:10.300 Frans: which I hadn't really considered in the beginning. But it became obvious
274 00:36:10.560 --> 00:36:30.679 Frans: that if I wanted to something that would be actually useful in terms of machine learning, I would have to move into tensors. So tensors is just a higher dimensional form of a matrix or a higher dimensional form. A matrix is a higher dimensional form of a vector
275 00:36:30.960 --> 00:36:40.019 Frans: and tensor is then a step up from that so generic N dimensions or rank.
276 00:36:43.790 --> 00:36:45.740 Frans: So this is where
277 00:36:46.500 --> 00:36:54.380 Frans: I actually did the last, my last work, and it's also probably the most from a rust perspective, the most mature.
278 00:36:56.310 --> 00:37:04.740 Frans: So again, I declare, a tensor object generic tensor object using a flat data structure.
279 00:37:07.785 --> 00:37:16.550 Frans: I have the shape of the matrix. Okay, now, I just want to actually hold there and and interrupt myself again and say that
280 00:37:17.310 --> 00:37:19.400 Frans: what I actually
281 00:37:19.630 --> 00:37:31.460 Frans: was trying to do, and I actually had to go back and change the names a bit here because I had the right idea. But I had different names for this. I think I had dims here instead of shape.
282 00:37:31.780 --> 00:37:40.189 Frans: But then I've done quite a bit of work in with tensorflow in, in python, etc. And
283 00:37:40.590 --> 00:37:44.839 Frans: and in the array, and numpy sorry.
284 00:37:45.210 --> 00:38:00.589 Frans: So I had the back of my mind. It suddenly came to me. I want to write something in rust that somebody with a python machining background would feel comfortable in well, reasonably comfortable in using.
285 00:38:00.720 --> 00:38:05.880 Frans: I don't know if that's a pipe dream. But that's sort of where I was going with this.
286 00:38:06.020 --> 00:38:08.569 Frans: So that's why I changed this to shape
287 00:38:09.390 --> 00:38:13.459 Frans: and strides I had from the beginning. So
288 00:38:14.780 --> 00:38:30.030 Frans: let's the go. So again, I'm sitting with row dominance. But whereas previously in a matrix, you have a row, followed by a row, followed by a row. You now have a more complex setup, where you can have
289 00:38:30.540 --> 00:38:35.619 Frans: in dimensions nonspecific. In other words.
290 00:38:36.060 --> 00:38:45.810 Frans: you. You can access the the way that you access an element becomes very much more obtuse
291 00:38:46.090 --> 00:38:55.260 Frans: if I can put it like that. And so that's where why, in the beginning, when I establish the struct I calculate strides
292 00:38:55.520 --> 00:39:05.800 Frans: now, strides is a way that you can use to calculate offset in the vector to get to an element
293 00:39:06.030 --> 00:39:14.780 Frans: of a certain coordinate. Given a coordinate, you can use strides to get to that element, I will demonstrate it shortly. How this works.
294 00:39:16.395 --> 00:39:17.370 Frans: So
295 00:39:18.050 --> 00:39:36.500 Frans: that was pretty straightforward, and in the next line comes to exactly what I've been talking about. So if you have an object declared like this with when you declare a new one, it automatically calculates the strides because it has got the dimensions, the shape, if you like.
296 00:39:37.070 --> 00:39:51.790 Frans: So basically, a stride, is the index of a coordinate. And you can see the coordinate you specify as a, vector because it can be of any dimension
297 00:39:52.030 --> 00:40:06.499 Frans: up to say, 1520, 30. Whatever pick a number. So obviously a good way is to present it as a vector you could probably find other ways of doing this. So here I specify, coordinate as a. Vector
298 00:40:06.640 --> 00:40:07.770 Frans: and
299 00:40:07.950 --> 00:40:19.079 Frans: we can. We can look at an example. I see I don't have an example up here. But yeah, we can look an example. So. But more importantly, you can see that I take the data, which is a vector.
300 00:40:19.240 --> 00:40:27.120 Frans: And I stepped through the coordinates that I were given the spectre. I stepped through it.
301 00:40:27.310 --> 00:40:46.150 Frans: and at the same time I'm stepping through the strides because the number of strides. This vector equals the number of coordinates. And I just do accumulated multiplication. So strides are set up that I can actually get exactly to the offset
302 00:40:46.260 --> 00:40:48.999 Frans: in the vector for this coordinate.
303 00:40:51.230 --> 00:41:01.619 Frans: it takes a bit of thinking, maybe to visual right? You can't really visualize because you're starting to work in. You know, you don't have 2 dimensions as in the matrix.
304 00:41:02.020 --> 00:41:10.629 Frans: But this is, if you think about it long enough, it will become obvious. Well, not obvious, but
305 00:41:10.830 --> 00:41:11.990 Frans: what I'm doing.
306 00:41:14.830 --> 00:41:23.189 Frans: So so there's just a mutable setting that you can assign values back.
307 00:41:25.205 --> 00:41:26.690 Frans: Right?
308 00:41:27.000 --> 00:41:29.150 Frans: So here is the sort of
309 00:41:29.410 --> 00:41:36.050 Frans: generic implementation of tensors where you have stuff like.
310 00:41:37.735 --> 00:41:40.570 Frans: Oh, no. Sorry. My apologies, that's not
311 00:41:44.750 --> 00:41:45.927 Frans: yeah. That is
312 00:41:46.850 --> 00:41:58.639 Frans: what am I saying now, here, standard functions. So anyway, this is just what I wrote, because I got tired of. I wanted to display tenses properly.
313 00:41:58.930 --> 00:42:02.689 Frans: in other words, like python would.
314 00:42:05.095 --> 00:42:08.398 Frans: So this is the sort of
315 00:42:09.370 --> 00:42:15.580 Frans: display that I that I wrote formatting it properly.
316 00:42:16.730 --> 00:42:19.170 Frans: We'll get to that in a moment as well.
317 00:42:19.480 --> 00:42:24.209 Frans: I'll actually write. We can do a real time example of of using this.
318 00:42:25.200 --> 00:42:31.139 Frans: I'm much more comfortable talking about tenses, because it's the last thing I did. So it's probably more recent in my mind.
319 00:42:31.980 --> 00:42:44.889 Frans: recent being a month and a bit ago. Okay, so these are the general functions new declaring it. So you specify a shape, you specify basically all the dimensions in the vector and then you give it the data. Vector
320 00:42:45.840 --> 00:42:54.400 Frans: so the data vector is flat, but the shape gives it its tensor characteristics if you like.
321 00:42:55.330 --> 00:43:12.430 Frans: So you can see when you declare new, you, I can easily calculate the strides, because I have the dimensions and the strides are simply just an accumulated multiplication of
322 00:43:16.820 --> 00:43:22.610 Frans: for each one. You calculate one less, I think.
323 00:43:27.770 --> 00:43:31.860 Frans: and you put it into the strides. So this is what I'm doing here.
324 00:43:32.070 --> 00:43:36.640 Frans: Yeah. So I'm starting at one where index is one.
325 00:43:36.840 --> 00:43:41.920 Frans: So this the zeroth stride is skipping. 0.
326 00:43:43.750 --> 00:43:47.540 Frans: Sorry one. Yeah. Started one skip one
327 00:43:49.450 --> 00:43:54.700 Frans: and then accumulate everyone sort of familiar with this syntax.
328 00:43:54.840 --> 00:43:57.849 Frans: the fold, the initial value, and the closure.
329 00:44:01.400 --> 00:44:04.499 Frans: What I do find very.
330 00:44:05.570 --> 00:44:14.409 Frans: I don't want to use the word annoying, but in a way it is is this sort of dereferencing
331 00:44:14.820 --> 00:44:17.629 Frans: and and and cloning
332 00:44:19.590 --> 00:44:37.580 Frans: And again. I know that's that's the that's the rust. Safety guarantees that things, you know will disappear when they need to disappear or go out of scope. But still writing the code, for it can sometimes
333 00:44:37.710 --> 00:44:42.070 Frans: get very, very challenging, I find.
334 00:44:43.925 --> 00:44:44.600 Frans: Anyway.
335 00:44:44.600 --> 00:44:45.260 Gabor Szabo: Awesome.
336 00:44:45.582 --> 00:44:46.870 Frans: Sorry. That's my dog.
337 00:44:47.640 --> 00:44:48.150 Gabor Szabo: No problem.
338 00:44:48.470 --> 00:44:57.150 Frans: Getting excited there, anyway. So this is just setting up the new new tensor. And then so you have shape strides and the actual database.
339 00:44:57.400 --> 00:44:58.120 Frans: Yeah.
340 00:45:04.170 --> 00:45:07.480 Frans: You can also. Okay. So
341 00:45:07.780 --> 00:45:11.829 Frans: just now, to sort of add on to the discussion about
342 00:45:12.000 --> 00:45:23.659 Frans: find writing something that would start to be slightly, vaguely, vaguely familiar to python users. So there's a tensor library in python called Tensory.
343 00:45:24.965 --> 00:45:29.320 Frans: I don't know if anybody has looked at. I mean go you you
344 00:45:29.320 --> 00:45:29.760 Gabor Szabo: Good.
345 00:45:29.760 --> 00:45:31.930 Frans: Do some python as well. Yeah.
346 00:45:32.690 --> 00:45:40.680 Frans: so tensely is quite an advanced library in terms of using tenses for numeric computing.
347 00:45:40.940 --> 00:45:58.699 Frans: So it's not not like tensorflow, where you specifically, maybe, you know, writing a neural network, and you're training it, etc. That kind of thing. It's more you can do what they call tensor contraction, which we'll get to in a moment.
348 00:45:58.750 --> 00:46:28.699 Frans: and you can do factorized tensor into more as the sum of more usable tensors or even usable matrices. You can sort of change it and and make it. They're all sort of numerical numerical tricks to to make it easier to work with tensors and to manipulate them, and to understand what you're actually trying to do. So
349 00:46:28.800 --> 00:46:35.730 Frans: having said that, I've never really worked with it directly myself.
350 00:46:40.690 --> 00:46:44.200 Frans: Okay, so we get to subtensor.
351 00:46:44.958 --> 00:46:47.650 Frans: Right? So one of the
352 00:46:51.680 --> 00:46:56.339 Frans: One of the big things that I discovered right in the beginning
353 00:46:56.580 --> 00:47:06.300 Frans: is that because you are in matrices. It's very easy. You are working with 2 dimensions, and there's only 2 dimensions, and that's always 2 dimensions. No problem.
354 00:47:07.120 --> 00:47:10.840 Frans: If you are writing a generic tensor that can be anything.
355 00:47:11.680 --> 00:47:19.669 Frans: Then it almost forces you to start using at nested functions within to do things.
356 00:47:19.880 --> 00:47:23.070 Frans: So this also was like a very
357 00:47:23.190 --> 00:47:28.600 Frans: tricky concept to get used to, because
358 00:47:29.150 --> 00:47:36.559 Frans: you could almost think as a tensor where you are. If you want to get to an element you have to.
359 00:47:36.710 --> 00:47:43.979 Frans: How can I put it visually? You can. You must drill down the dimensions until you get to the actual element.
360 00:47:44.130 --> 00:47:54.729 Frans: So that's sort of very strange may sound very strange. But if you write the code, one starts to understand that's sort of what is happening.
361 00:47:54.820 --> 00:48:14.720 Frans: So, for example, here, if you want to extract, get a subtensor of a tensor. You 1st have to. You have to work on all the dimension levels, and at each one you've got to drill down to the required dimension and extract an element
362 00:48:15.180 --> 00:48:21.509 Frans: that sounds very strange now that I say it out loud. But that's really the thought process that's gone on here
363 00:48:21.880 --> 00:48:27.420 Gabor Szabo: Yeah, after 3 dimensions. It's it's getting a bit hairy.
364 00:48:27.600 --> 00:48:33.549 Frans: Yeah. Well, 3 dimensions you could probably still visualize. Yes, with you know. XYZ
365 00:48:33.700 --> 00:48:39.060 Gabor Szabo: Or ZI don't know what you guys call Z in South Africa. We call it Z.
366 00:48:41.500 --> 00:49:01.749 Frans: Zeros standard stuff, you know to this is, if you just want to. So this is all. What happened is then I started looking at tensely. And I say, what did what does it have? And I want to do the same stuff. So Zeros is just to create
367 00:49:01.910 --> 00:49:24.670 Frans: a tensor of this, these dimensions or shape, if you like, so that's probably shape would be a better thing to put in there, and they all just filled with zeros. These are all filled with ones. These are filled with a certain value. T, and this is filled with a certain value range that starts at T
368 00:49:24.840 --> 00:49:25.930 Frans: and go up.
369 00:49:28.240 --> 00:49:29.130 Frans: Yeah.
370 00:49:29.130 --> 00:49:34.309 Gabor Szabo: Yeah, I think dimensions would would say that like it has 3 dimensions, or 4, or whatever right
371 00:49:34.310 --> 00:49:36.919 Frans: Yeah. Yeah. But it's just it's
372 00:49:36.920 --> 00:49:39.309 Gabor Szabo: Described, actually
373 00:49:39.430 --> 00:49:45.379 Frans: It's it's just that in in python and and tensory and and even, you know, numpy, they use shape.
374 00:49:45.560 --> 00:50:09.049 Frans: So I sort of you know there's if if I wanted to make a product that I sort of can really, commercially market or sell or punt, you know, not even commercially, but in seriousness. I would have to go through this and make it all and standardize it, and and and make it much more. How can I say rigorous?
375 00:50:09.510 --> 00:50:16.890 Frans: That's the one thing. The other thing is, I'm sure that a lot of optimization can be done which I'm
376 00:50:17.070 --> 00:50:30.078 Frans: if in a rust perspective, not I haven't gone down that road at all, and which probably needs to be gone down. So I'm not making any. I mean, I've done no benchmarking against anything else. So
377 00:50:30.730 --> 00:50:37.939 Frans: you know, there's probably there's a lot of work that needs to be done for this to be a robust, rigorous library, for sure.
378 00:50:39.420 --> 00:50:44.680 Gabor Szabo: I mean, we are getting close to the, to the, to the 1 h due to
379 00:50:45.290 --> 00:50:50.820 Frans: Do I am. Oh, I'm rambling on endlessly. My apologies, anyway, so
380 00:50:50.820 --> 00:50:52.819 Gabor Szabo: Yeah, I have to wrap up soon, I guess.
381 00:50:52.820 --> 00:51:04.640 Frans: Yeah, so so random and stuff like that. And I think the biggest and the the most difficult thing that I've done up to date was contracting a tensor.
382 00:51:04.960 --> 00:51:05.930 Frans: and
383 00:51:06.120 --> 00:51:25.789 Frans: that so using Einstein's summation notation, I don't know if anybody's familiar with that. So you have basically 2 tenses. And you basically want to contract a tensor ijkl with Mkni, which means you're taking the 3rd dimension
384 00:51:25.980 --> 00:51:28.730 Frans: and contracting it with the second dimension.
385 00:51:29.170 --> 00:51:49.360 Frans: And you're taking the 1st dimension and of the left hand tensor. And you're contracting with the right hand. And what you get basically contraction, you are shrinking the dimensions you are Melding. If I can use that word, adding these 2
386 00:51:49.760 --> 00:51:56.929 Frans: tensors together, and you will end up with a tensor of dimensions. J.
387 00:51:57.300 --> 00:51:59.120 Frans: LMN.
388 00:51:59.550 --> 00:52:12.779 Frans: Right so, and contraction was extremely difficult until it the penny drops. So yes, okay. So, Einstein, notation is just a way of writing it out understandably that that
389 00:52:12.930 --> 00:52:16.550 Frans: tensor algebraus use.
390 00:52:16.820 --> 00:52:22.980 Frans: But the actual underlying routine is the contraction routine, and that
391 00:52:24.120 --> 00:52:33.350 Frans: once you realize that a tensor you have to drill down through all the dimensions, and at the end you end up with a matrix
392 00:52:34.350 --> 00:52:45.949 Frans: at the bottom of drilling down, and once you have that sort of idea in your head, then it's just a question of rearranging
393 00:52:48.410 --> 00:52:51.100 Frans: finding the the correct
394 00:52:51.430 --> 00:52:58.419 Frans: going through the dimensional drill down to find the correct element in the matrix underneath.
395 00:52:58.870 --> 00:53:14.579 Frans: That doesn't sound very nice. But anyway, that's what it happens, anyway. So so that's basically is is sort of where I'm at. As I said, contraction was the biggest thing. Oh,
396 00:53:15.260 --> 00:53:21.029 Frans: Almost the 1st thing I did with tensors is I wanted to do a creation. Macro
397 00:53:22.050 --> 00:53:26.990 Frans: and I had to resort to.
398 00:53:27.660 --> 00:53:40.330 Frans: This was very interesting. I had to resort to writing a separate crate that contains a what's this tensor? What's this? Macro called again.
399 00:53:41.170 --> 00:53:51.880 Frans: Somebody help me here. It's it's not, you know your normal macros, or you can write it in your in your crate. But this is a specific execution, Macro. Process, Macro, sorry.
400 00:53:52.030 --> 00:53:52.700 Frans: Yeah.
401 00:53:53.470 --> 00:53:59.840 Frans: And that's the 1st time that I had to use a nested function.
402 00:54:00.180 --> 00:54:06.249 Frans: Think, here, here is it here
403 00:54:07.460 --> 00:54:11.730 Frans: flatten array? Yes, I used flatten array.
404 00:54:25.880 --> 00:54:37.260 Frans: It's the 1st time I had to use it. So what I was trying to achieve here, and this is so. If we go back to the tensor library, which uses that macro in that crate
405 00:54:37.550 --> 00:54:41.440 Frans: is that you can establish tenses by doing this.
406 00:54:41.790 --> 00:54:43.620 Frans: And that is fantastic.
407 00:54:44.000 --> 00:54:53.240 Frans: I love that because and your community, I mean, this is a like a 12 dimensional tensor.
408 00:54:53.380 --> 00:54:57.829 Frans: you know, which you can establish like. So this is just a stupid example.
409 00:54:57.990 --> 00:55:22.109 Frans: But you can see, and that establishes the shape of that and the strides of that. And that's the actual day test of the flat. Vector anyway, that's about it. So I would love to. You know, if you guys at any point want to chat more about how I did it, I'm happy to have future interaction
410 00:55:22.610 --> 00:55:30.729 Frans: on a 1 to one or one to in a group session, but only from April onwards, because at the moment things are hectic on my side.
411 00:55:31.150 --> 00:55:33.399 Frans: that's it. That's a wrap for me.
412 00:55:33.400 --> 00:55:38.660 Gabor Szabo: Well, thank you. Thank you. April. Is not that far? It's it's like 2 weeks, right? So
413 00:55:38.930 --> 00:55:51.300 Frans: Yes, no, exactly. But that's why it's a bit tense at the moment, because there's lots of pressure, and and there's a there's a substantial bonus involved. If I sort things out so you can understand
414 00:55:52.591 --> 00:56:12.020 Gabor Szabo: Good. So so thank you very much for your for your presentation. By the way, your your information. I I put the link to the to the git repository in the chat, and that if you'll be under the video as well, you will find that and the link to your. I think your Linkedin page. So people will be able to contact you if if interested.
415 00:56:12.110 --> 00:56:25.790 Gabor Szabo: So thank you very much for your presentation and for everyone who who listened, and for everyone who watched the video, and just remember to like the video and follow the channel. Thank you very much. Bye, bye.
416 00:56:25.790 --> 00:56:28.479 Frans: Thanks. Gabor, thanks, guys. Cheers. Bye-bye.
