Mathematical/Algebraic way to model an offset?

[Manrique]

Hi, I am looking for a way to mathematically do an offset.

I want to go from a matrix that looks like this.

	2
1
3

The numbers represent duration, so it can also look like this (I have the matrix in both notations, so the starting point can be either matrix)

	1	1
1
1	1	1

And I want to offset the numbers in each row as follows (this represents a delay in the starting time)

1

2

1

So the end result should be a matrix that looks like this:

0	0	1	1	0
0	0	1	0	0
0	1	1	1	0

It's fine to use expressions such as sum, as well as the use of max, min, round, etc.

No use of Ifs, For loops, etc.

Also, there would not be a problem in having to resize the matrix.

Is there a way to model this? I greatly appreciate your help. It's driving me crazy!
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[daon2]

Without loops? How do you plan to access entries of the matrix? Matrix multiplication by itself requires a loop.

Not sure if this is adequate, but:

You could write a number n in the form "111...1" as \(\displaystyle S_n=\sum_{i=1}^n 10^i\) (as a string), and write \(\displaystyle Z_k = \underbrace{00...0}_{k\,\, times}\).

Then if your offset is \(\displaystyle k\) replace the entry "0000n000" with "0000" + \(\displaystyle Z_k + S_n\)

Then the sequence of strings will be your row vectors, resize appropriately and you'll have a square matrix of 0's and 1's in string form.