Need matrix help

ok.

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Proceeding on a brutal rampage is the obvious choice.
Where to find the intensity (Updated Jan 23, 2004)

ok.

no, we''re not going to do the "ok." thing.


Anyway, what happened to the "no homework help" rule?

IIRC, it''s something to do with the projected probability that a system will be in a state, after X iterations (P*P is after 2 iteration, IIRC).

I think...

BTW, add some code tag-age to your matrix, it''s unreadable.

ok.













































There is no spoon.

quote:

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Original post by Andrew Russell
no, we''re not going to do the "ok." thing.

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Lol that''s funny coming from a mod, especially a mod who has done the "ok." thing.

About the matrix...well, that''s a pretty weird question (plus there''s sort of a no homework help rule on GDNet). Doesn''t your math book say anything?

One time in high school we had these matrices that described tennis matches.

...|.A. .B. .C.|
.A.|  -   1   1 |
.B.|  1   -   0 | = P
.C.|  0   1   - |
  

1's mean wins by the rows and 0's mean losses. For example, B beat A but lost to C. The diagonal is filled with '-' because it's meaningless.

Anyway, P*P showed indirect wins. For example, if B beat C who beat A, P(subBA would be 1).

I hope I remembered this correctly and that you can find a way to apply this to your problem.


___________________________________________________________
Proceeding on a brutal rampage is the obvious choice.
Where to find the intensity (Updated Jan 23, 2004)


[edited by - amish1234 on January 28, 2004 2:31:11 AM]

i think that if you multiply it with itself, the effect will simply be doubled, as if the same matrix applied for two years. after all, thats what matrix multiplication does in CG: adding two rotations.

quote:

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Original post by Andrew Russell
no, we''re not going to do the "ok." thing.

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Uh oh - you''re ALL about fun...

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"Finishing in second place, simply means you are the first loser." - PouyaCat

There isn''t anything about no homework help in the FAQ.

Neither my teacher nor the book described what the data would represent when multiplying matricies, they just describe how to do it. The solution in the back of the book gives the matrix I found, but doesn''t say what the data means.

This type of matrix is called a Transition Matrix.

In a transition matrix
*Each column adds up to 1

Powers of transition matrices represent what happens to a system as time progresses. For example:

    A   B
   ___ ___
A |___|___|
B |___|___|

In the above matrix the fields can be seen in this way:
AA : % that transition from state A to state A
AB : % that transition from state A to state B
BA : % that transition from state B to state A
BB : % that transition from state B to state B

An Example:
Suppose Store A exists and Store B just opens. Given a transition matrix you would be able to find out how many of your people will end up leaving A for B.

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Colin Jeanne | Invader''s Realm

I think there is an unwritten rule where: if someone is asking a question that is so obviously a homework question, but they don''t say it''s homework, then you should make fun of them and not answer the question.

But if they say it''s homework, that''s ok. As long as you are explaining the concept and not just giving the answer.

quote:

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Original post by pinacolada
I think there is an unwritten rule where: if someone is asking a question that is so obviously a homework question, but they don''t say it''s homework, then you should make fun of them and not answer the question.

But if they say it''s homework, that''s ok. As long as you are explaining the concept and not just giving the answer.

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If thats not what the rule is then it should be, why not use what resources are available to help yourself (as opposed to cheating)? It''s not like he wants us to do the whole assignment or even a whole problem, he just doesn''t understand a part of it.

If you multiplied that matrix by a matrix of voters, then you''d have the result for next year. If you multiply it by itself, I think it''s the change for two years, so if you multiply it by a matrix of voters thats what it will look like in two years. It seems correct to me, but although I just studied them a few months ago I don''t recall any problem like that and I may have misunderstood.

Now I can read the matrix and understand it, I can answer your question better.

As far as I can tell, it''s a state matrix question.

for instance, take your first matrix, P. You say you changed the figures (which didn''t really help), so I''m changing them to something sensible. This is because each row must add up to one. Presumably they did before you changed them.

|.35 .24 .41|
|.45 .25 .30| = P
|.24 .34 .42|
 

Now, we have our new matrix, P.

What this represents is the chance of entering state change (after one iteration), depending on its current state. For instance, assume we are in state one (the first row). The chance that we''ll stay in state one after an iteration, is 35 percent, there''s a 24% chance we''ll end up in state two, and 41 percent that we''ll be in state three.

Multiplying P by P, will give you a matrix for two iterations, multiplying again by P will give 3 iterations, etc.

And the way this works, is you have a starting point matrix

|1|
|0| = S
|0| 
 

This matrix is our current state. Our little guy is in state one. Multiplying as such:

S*P = |.35 .24 .41|
 

Thus, these are the chances of being in each state for our guy after one iteration. If you did S*P*P*P, that would be the chance of being in a state after three iterations.

You can expand this to populations, as such:

| 11 |
| 21 | = S
| 37 |
 

Multiplying that will give you the projected populations in each state, after as many iterations as you do multiplications.


A better example would have been the weather. We could simplify it a little, and say we have two states, rainy and sunny. Make the top row sunny, and the bottom row rainy. Here is our matrix:

| 0.8 0.2 |
| 0.5 0.5 |
 

All we need is a starting point, and then we can project the weather as many days ahead as we like. Basicly, if today is raining, there''s a 50-50 chance it will be raning or sunny tomorrow, whereas, if it''s sunny, then there''s a good chance it will stay sunny.


Another trick you can do is to trap things in a state. For instance, take pool and someone who is total crap at the game. The first row is "on the table", the second is "in a pocket".

| 0.9 0.1 |
| 0.0 1.0 |
 

As you can see, while its on the table, our guy will only pocket the ball one in 10 times, whereas, once the ball is pocketed it''s not going to ever become unpocketed.


Anyway, that covers pretty much everything I know about state matrixes, I hope this has been enlightning for you.

We missed you!

Thanks, that really helped a lot.