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**eldoci****Member**- Registered: 2013-04-11
- Posts: 7

If we have a matrix with N elements, where each element can take values G ( 0-255), we can obtain 256 power N possibilities of matrixes.

The derivative of each matrix is calculated as follows:

S=∑_(n=1)^(N-1)▒df(n)/dx=∑_(n=1)^(N-1)▒〖| f(n+1)-f(n)|〗

Since 0≤ df(n)/dx≤255 the minimum and maximum values of s are:

max S = (N-1)×255

min S = 0

I need to find how many matrixes have the same S.

Can anybody help me?

Thank you.

*Last edited by eldoci (2013-04-11 23:28:38)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,650

Hi;

Welcome to the forum. I am sorry, I can not make out your equation for S. Can you latex it or take a snapshot?

What is f?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**eldoci****Member**- Registered: 2013-04-11
- Posts: 7

Thank you for replying.

I am Sorry for not using latex.

Maybe you can understand the formula of S in this form:

S = sum (df(n)/d(x))=sum(|f (n+1)- f(n)|) for n=1,2,3...(N-1)

f(n) is the value of X in the position n of the matrix.

During calculations I have noticed that for S=0 we always get G combinations ( G matrices).

S=max we always get 2 combinations (matrices)

S=1 we get 2(N-1)*(G-1) (matrices)

Now i need to find a formula that gives me the combinations for any S.

I hope this makes the problem more clear for you.

*Last edited by eldoci (2013-04-12 01:17:29)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,650

Hi;

I hope this makes the problem more clear for you.

I still need more clarification.

f(n) is the value of X in the position n of the matrix.

How does n do that? A matrix needs 2 numbers, a row and a column to specify a position. How do you do that with one?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**eldoci****Member**- Registered: 2013-04-11
- Posts: 7

You are right about the matrix, it has 2 variables, x and z, but for simplicitz we supose that we have 1 dimension matrix( a vector) with 1 row and N elements on it

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**eldoci****Member**- Registered: 2013-04-11
- Posts: 7

You are right about the matrix, it has 2 variables, x and y, but for simplicity we suppose that we have 1 dimension matrix( a vector) with 1 row and N elements on it.

For example:

for the matrix [1 0 0 2]

S= |0-1|+ |0-0|+ |2-0|=3

f(n0)=1 f(n1)=0 f(n2)=0 and f(n3)=2

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Hi;

sum(|f (n+1)- f(n)|)

| |

That is an absolute value?

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**eldoci****Member**- Registered: 2013-04-11
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yes | | is the absolute value

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,650

Hi;

Just a bit more, Where do the combinations come in?

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**eldoci****Member**- Registered: 2013-04-11
- Posts: 7

If we have a matrix with N elements, where each element can take values G ( 0-255), we can obtain 256 power N possibilities of matrixes ( combinations of elements).

I need to calculate: how many element combinations of the matrix ( no of matrixes) can be obtained with the same S

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Hi;

Okay, I think I have enough. I will post if I get something.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**eldoci****Member**- Registered: 2013-04-11
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Thank you

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,650

Hi;

I have been unable to so far find any expression for that matrix. Are you sure there is one and can you say where the problem comes from.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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