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## #2 Re: Help Me ! » Calculating combinations » 2013-04-12 01:15:41

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

## #3 Re: Help Me ! » Calculating combinations » 2013-04-12 00:34:51

yes | | is the absolute value

## #4 Re: Help Me ! » Calculating combinations » 2013-04-12 00:17:33

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

## #5 Re: Help Me ! » Calculating combinations » 2013-04-12 00:12:31

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

## #6 Re: Help Me ! » Calculating combinations » 2013-04-11 23:27:34

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.

## #7 Help Me ! » Calculating combinations » 2013-04-11 18:55:52

eldoci
Replies: 12

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.