Post mathematical notations that fucked you for hours. Would it have killed this guy to give one example?
Post mathematical notations that fucked you for hours. Would it have killed this guy to give one example?
Post mathematical notations that fucked you for hours. Would it have killed this guy to give one example?
what seems to be the problem chief, this shit is clear as crystal
What do you think it says?
G: vector
diag(...): matrix
U: vector
alternatively G and U could be matrices as well but that should be clear from the context
Thanks for proving my point.
You wut mate?
i didnt prove your point.
from your snippet alone it remains unclear how the author denotes scalars, vectors and matrices. however that should become clear when looking at the whole passage.
so unless that snippet is the only thing you have, its probably is clear enough too understand
No regardless of the vectors / matrices you already made the same mistake I did right here.
>diag(...): matrix
in this case the notation is not "fucked up" is in unconventional, instead it is simply wrong
Just to clarify do you think it's diag(matrix x matrix) or diag(matrix) * matrix?
the latter
It's the former. 🙁
actually neither,
i mean diag(...)*matrix
with ... being s scalars. diag(...) is thus a square matrix
That's what I thought too then I spent a whole fucking day figuring out why it doesn't work.
now im interested in the context. can you link the paper
http://mesh.brown.edu/taubin/pdfs/Taubin-icra88.pdf
Enjoy. I sure did.
>Paper is on Computer Vision
It's all makes sense now. OP is just a CS student who thinks he knows math and isn't willing to accept that so he blames his confusion on the writer. Go learn some basic linear algebra and come back to this. You will need it anyways.
>basic linear algebra
Generalized eigenvalue problems aren't basic linear algebra. You'd know that if you did linear algebra.
Wtf are you talking about? I don't know what hack school you went to but generalized eigenvalue problems are first year intro linear algebra material. I will acknowledge that they were probably taught at the end of the first semester so depending on your program, it may have been left out for time, but still a very basic concept.
To be more precise you actually multiply each of the vector on the right by the scalars in the same order given and then take the diagonal of the final result.
are you serious?
diag(matrix*matrix) isnt even a valid operation. and from the text its clear that (U1,...Us) is a non-square matrix with dimension sxm (in general s!=m).
the correct interpretation was given multiple times like
and
>diag(matrix*matrix) isnt even a valid operation
Taking the diagonal of a matrix is perfectly valid.
Now sure, I could be wrong, but this is literally the only way it worked and I've tried the "correct interpretations".
>Taking the diagonal of a matrix is perfectly valid
yes, if that matrix is square. however the matrix product at hand is not square in general, since (s<=m).
also G is a matrix and not a set of diagonal entries, because otherwise the following steps dont make any sense such as calculating G^t.
additionally, step 6) strongly hints that G is a non-square matrix because F is non-square in general (see p.644 between (1) and (2).
how did you implement F=lambda*G*(I-T) with your current interpretarion of G?
I'm too tired to think about this now. But diag() of a vector is a square with the non-diagonal entrees as zero. But I'll think about what you said later.
G has to be a square diagonal otherwise L won't compute.
L computes and is square even for non-square G, similary to T which is square even though H is not.
this is basic matrix algebra.
>M,N,U,D,T are mxm matrices.
>G is a sxm matrix.
>H is a (m-s)xm matrix.
>L is a sxs matrix.
>lambda is a 2xs matrix
>F is a 2xm matrix
At least this is how I see it.
yes i agree. that doesnt contradict me though?
(i think in general lambda is a matrix of nxs with F being nxm, and n depends on the type of surface of the concrete problem)
Won't give the correct result.
This one is almost right actually
Except it's diag() instead of transpose.
No he's right, compute by hand what happens when you multiply a diagonal with a matrix and then you'll get it, transpose is just because he wrote it horizontally which is more natural and normal.
Why don't you try and implement the algorithm then you'll see why your way doesn't work.
Let's take a low dimensional example with [math]mathbf{U}_i=(U_{i,1},U_{i,2},U_{i,3})^T[/math], then the multiplication is [math]begin{bmatrix}
1/sqrt{d_1}&0\
0&1sqrt{d_2}
end{bmatrix}begin{bmatrix}
U_{1,1}&U_{1,2}&U_{1,3}\
U_{2,1}&U_{2,2}&U_{2,3}
end{bmatrix}[/math] and the result is a 2 by 3 matrix whose (1,2) entry is [math]U_{1,2}/sqrt{d_1}+U_{2,2}0=U_{1,2}/sqrt{d_1}[/math].
In general, multiplying a matrix by an appropriately sized diagonal matrix (from the left) means multiplying each row of the matrix with the diagonal entry from the corresponding row, exactly as
said.
So, enlighten us.
[math]G = (U_1 / sqrt{d_1}, ..., U_s / sqrt{d_s})^T[/math]
G=diag(given list)*U
seems pretty straight foreword
It's proof that mathematicians are just shitty programmers. Imagine if some H1-B programmer forgot to define his variables and then tried to gaslight everybody into thinking we "should be smart enough to figure it out anyway"
I what they say wasn't unnecessarily ofuscated how would they impress the ladies then??
>AAAHHH I CANT STOP NOTATIOOONING SHIT
STEM is full of these notationooor homosexuals that will try to represent simple shit with confusing notation just to pretend they're smarter than everyone else
pic rel facial expression these frauds be making while saying shit like these:
>oh you don't understand some complicated mathematical notation I just made up on spot???? Bet you're too unintelligent to be in this field pal
They produce hundreds upon hundreds of useless proofs every year.
Taubin has great useful papers he's just fucking unreadable probably unless you're in his class or something.
Unlike humanities which produce hundreds upon hundreds of useless poofs every year.
The diag operator is common notation.
What is the relationship between x and y in this drawing?
Or stated another way, how many CFM does y have to be to get 1” of x water column? Is the scale linear or logarithmic?
Any help would’ve appreciated anons. Is a math question and did not see a stupid questions thread.
why did you draw a fan, isnt that supposed to be a pump or something?
assuming the traditional engineering assumptions, the relation between the flow rate and the height of the water column depends on the geometry of the canister. if it is prismatic, its is linear. the formula is then:
flowrate*time=(base area of canister)*(height of water column).