I'm having trouble trying to understand how to implement the following:
Layer: Bi-LSTM 1
Input: (None,50,25)
Output: (None,50,25)
I know that the first argument is units, since the model has a None value, it can be anything? However, for the last two arguments I don't know how I can implement it.
The only other arguments that take numbers are: dropout and recurrent_dropout however, they are floats between 0 and 1.
Can someone please explain how I am supposed to recreate this model?
Related
I have the IJVM Simulator I got with the download example code. I don't understand what the numbers next to the methods mean.
First example
Second example
I understand that I am calling the add method above, but then what are those 3 and 1 next to add? Why am I including them?
Or the 2 and 0 for fak?
In the PyTorch geometric tutorial for creating Message Passing Networks they have this paragraph at the start when explaining what the class does:
MessagePassing(aggr="add", flow="source_to_target", node_dim=-2): Defines the aggregation scheme to use ("add", "mean" or "max") and the flow direction of message passing (either "source_to_target" or "target_to_source"). Furthermore, the node_dim attribute indicates along which axis to propagate.
I don't understand what this node_dim is referring to, and why it is -2. I have looked at the documentation for the MessagePassing class and it says there that it is the axis which to propagate -- this still doesn't really clarify what we are doing here and why the default is -2 (presumably that is how you propagate information at a node level). Could someone offer some explanation of this to me please?
After referring to here and here, I think the thing related to it is the output of the 'message' function.
In most cases, the shape of the output is [edge_num, emb_out], and if we set the node_dim as -2, it means that we will aggregate along the edge_num using indices of the target nodes.
This is exactly the process that aggregates the information from source nodes.
The result after aggregation is [node_num, emb_out].
I start with a simple Maxima question, the answer to which may provide the answer to the actual problem I'm grappling with.
Related Simple Question:
How can I get maxima to calculate:
bfloat((1+%i)^0.3);
Might there be an option variable that can be set so that this evaluates to a complex number?
Actual Question:
In evaluating approximations for numerical time integration for finite element methods, for this purpose I'm using spectral analysis, which requires the calculation of the eigenvalues of a 4 x 4 matrix. This matrix "cav" is also calculated within maxima, using some of the algebra capabilities of maxima, but sustituting numerical values, so that matrix is entirely numerical, i.e. containing no variables. I've calculated the eigenvalues with Mathematica and it returns 4 real eigenvalues. However Maxima calculates horrenduously complicated expressions for this case, which apparently it does not "know" how to simplify, even numerically as "bigfloat". Perhaps this problem arises because Maxima first approximates the matrix "cac" by rational numbers (i.e. fractions) and then tries to solve the problem fully exactly, instead of simply using numerical "bigfloat" computations throughout. Is there I way I can change this?
Note that if you only change the input value of gzv to say 0.5 it works fine, and returns numerical values of complex eigenvalues.
I include the code below. Note that all of the code up until "cav:subst(vs,ca)$" is just for the definition of the matrix cav and seems to work fine. It is in the few statements thereafter that it fails to calculate numerical values for the eigenvalues.
v1:v0+ (1-gg)*a0+gg*a1$
d1:d0+v0+(1/2-gb)*a0+gb*a1$
obf:a1+(1+ga)*(w^2*d1 + 2*gz*w*(d1-d0)) -
ga *(w^2*d0 + 2*gz*w*(d0-g0))$
obf:expand(obf)$
cd:subst([a1=1,d0=0,v0=0,a0=0,g0=0],obf)$
fd:subst([a1=0,d0=1,v0=0,a0=0,g0=0],obf)$
fv:subst([a1=0,d0=0,v0=1,a0=0,g0=0],obf)$
fa:subst([a1=0,d0=0,v0=0,a0=1,g0=0],obf)$
fg:subst([a1=0,d0=0,v0=0,a0=0,g0=1],obf)$
f:[fd,fv,fa,fg]$
cad1:expand(cd*[1,1,1/2-gb,0] - gb*f)$
cad2:expand(cd*[0,1,1-gg,0] - gg*f)$
cad3:expand(-f)$
cad4:[cd,0,0,0]$
cad:matrix(cad1,cad2,cad3,cad4)$
gav:-0.05$
ggv:1/2-gav$
gbv:(ggv+1/2)^2/4$
gzv:1.1$
dt:0.01$
wv:bfloat(dt*2*%pi)$
vs:[ga=gav,gg=ggv,gb=gbv,gz=gzv,w=wv]$
cav:subst(vs,ca)$
cav:bfloat(cav)$
evam:eigenvalues(cav)$
evam:bfloat(evam)$
eva:evam[1]$
The main problem here is that Maxima tries pretty hard to make computations exact, and it's hard to tell it to ease up and allow inexact results.
Is there a mistake in the code you posted above? You have cav:subst(vs,ca) but ca is not defined. Is that supposed to be cav:subst(vs,cad) ?
For the short problem, usually rectform can simplify complex expressions to something more usable:
(%i58) rectform (bfloat((1+%i)^0.3));
`rat' replaced 1.0B0 by 1/1 = 1.0B0
(%o58) 2.59023849130283b-1 %i + 1.078911979230303b0
About the long problem, if fixed-precision (i.e. ordinary floats, not bigfloats) is acceptable to you, then you can use the LAPACK function dgeev to compute eigenvalues and/or eigenvectors.
(%i51) load (lapack);
<bunch of messages here>
(%o51) /usr/share/maxima/5.39.0/share/lapack/lapack.mac
(%i52) dgeev (cav);
(%o52) [[- 0.02759949957202372, 0.06804641655485913, 0.997993508502892, 0.928429191717788], false, false]
If you really need variable precision, I don't know what to try. In principle it's possible to rework the LAPACK code to work with variable-precision floats, but that's a substantial task and I'm not sure about the details.
I have been trying to get my hands dirty with Information Retrieval.My professor gave us this problem to solve, but I can't get my way around it. The matrix given, if it is a distance matrix, the diagonal elements should all be 0. But in the table, they're given as 1. The other entries are also less than 1. How is this possible? Can someone please explain?
Please see question 5.c. I could not enter the table manually and apologize for that.
In every similarity measurement, 1 means totally similar and 0 means there is no similarity between documents.
I am trying to run this code but it keeps crashing:
log10(x):=log(x)/log(10);
char(x):=floor(log10(x))+1;
mantissa(x):=x/10**char(x);
chop(x,d):=(10**char(x))*(floor(mantissa(x)*(10**d))/(10**d));
rnd(x,d):=chop(x+5*10**(char(x)-d-1),d);
d:5;
a:10;
Ibwd:[[30,rnd(integrate((x**60)/(1+10*x^2),x,0,1),d)]];
for n from 30 thru 1 step -1 do Ibwd:append([[n-1,rnd(1/(2*n-1)-a*last(first(Ibwd)),d)]],Ibwd);
Maxima crashes when it evaluates the last line. Any ideas why it may happen?
Thank you so much.
The problem is that the difference becomes negative and your rounding function dies horribly with a negative argument. To find this out, I changed your loop to:
for n from 30 thru 1 step -1 do
block([],
print (1/(2*n-1)-a*last(first(Ibwd))),
print (a*last(first(Ibwd))),
Ibwd: append([[n-1,rnd(1/(2*n-1)-a*last(first(Ibwd)),d)]],Ibwd),
print (Ibwd));
The last difference printed before everything fails miserably is -316539/6125000. So now try
rnd(-1,3)
and see the same problem. This all stems from the fact that you're taking the log of a negative number, which Maxima interprets as a complex number by analytic continuation. Maxima doesn't evaluate this until it absolutely has to and, somewhere in the evaluation code, something's dying horribly.
I don't know the "fix" for your specific example, since I'm not exactly sure what you're trying to do, but hopefully this gives you enough info to find it yourself.
If you want to deconstruct a floating point number, let's first make sure that it is a bigfloat.
say z: 34.1
You can access the parts of a bigfloat by using lisp, and you can also access the mantissa length in bits by ?fpprec.
Thus ?second(z)*2^(?third(z)-?fpprec) gives you :
4799148352916685/140737488355328
and bfloat(%) gives you :
3.41b1.
If you want the mantissa of z as an integer, look at ?second(z)
Now I am not sure what it is that you are trying to accomplish in base 10, but Maxima
does not do internal arithmetic in base 10.
If you want more bits or fewer, you can set fpprec,
which is linked to ?fpprec. fpprec is the "approximate base 10" precision.
Thus fpprec is initially 16
?fpprec is correspondingly 56.
You can easily change them both, e.g. fpprec:100
corresponds to ?fpprec of 335.
If you are diddling around with float representations, you might benefit from knowing
that you can look at any of the lisp by typing, for example,
?print(z)
which prints the internal form using the Lisp print function.
You can also trace any function, your own or system function, by trace.
For example you could consider doing this:
trace(append,rnd,integrate);
If you want to use machine floats, I suggest you use, for the last line,
for n from 30 thru 1 step -1 do :
Ibwd:append([[n-1,rnd(1/(2.0*n- 1.0)-a*last(first(Ibwd)),d)]],Ibwd);
Note the decimal points. But even that is not quite enough, because integration
inserts exact structures like atan(10). Trying to round these things, or compute log
of them is probably not what you want to do. I suspect that Maxima is unhappy because log is given some messy expression that turns out to be negative, even though it initially thought otherwise. It hands the number to the lisp log program which is perfectly happy to return an appropriate common-lisp complex number object. Unfortunately, most of Maxima was written BEFORE LISP HAD COMPLEX NUMBERS.
Thus the result (log -0.5)= #C(-0.6931472 3.1415927) is entirely unexpected to the rest of Maxima. Maxima has its own form for complex numbers, e.g. 3+4*%i.
In particular, the Maxima display program predates the common lisp complex number format and does not know what to do with it.
The error (stack overflow !!!) is from the display program trying to display a common lisp complex number.
How to fix all this? Well, you could try changing your program so it computes what you really want, in which case it probably won't trigger this error. Maxima's display program should be fixed, too. Also, I suspect there is something unfortunate in simplification of logs of numbers that are negative but not obviously so.
This is probably waaay too much information for the original poster, but maybe the paragraph above will help out and also possibly improve Maxima in one or more places.
It appears that your program triggers an error in Maxima's simplification (algebraic identities) code. We are investigating and I hope we have a bug fix soon.
In the meantime, here is an idea. Looks like the bug is triggered by rnd(x, d) when x < 0. I guess rnd is supposed to round x to d digits. To handle x < 0, try this:
rnd(x, d) := if x < 0 then -rnd1(-x, d) else rnd1(x, d);
rnd1(x, d) := (... put the present definition of rnd here ...);
When I do that, the loop runs to completion and Ibwd is a list of values, but I don't know what values to expect.