Program to establish a matrix

[wilro85]

I need to establish a matrix of "n"s and I'm hoping to figure out a programmatic way of doing so. The matrix is defined by the following:

z = abs(n1) + abs(n2) + abs(n3) ....
where z is user generated value between 3 and 31 and n# can range from 2 to 100 (again user specified).

For example if z=3 and n3 is the max value the first few entries will be:

-3 0 0
-2 -1 0
-2 0 -1
-2 0 1
-2 1 0
-1 -1 -1
-1 -1 1
etc

Does anyone have any ideas on how to approach this beast? For now it can just be stored starting in sheet1 range a1 with z and n# specified in the program.

[shg]

I don't understand ...

z = abs(n1) + abs(n2) + abs(n3) ....
where z is user generated value between 3 and 31

How are those two statements consistent?

How did you generate your example?

[wilro85]

"Matrix" was a bad word choice. The proper phrase is a series of simultaneous equations. So going to my example it would look like this:

-3 0 0
-2 -1 0
-2 0 -1
-2 0 1
-2 1 0
-1 -1 -1
-1 -1 1
etc

is derived from:
3= abs(-3) + abs(0) + abs(0)
3= abs(-2) + abs(-1) + abs(0)
3= abs(-2) + abs(0) + abs(-1)
3= abs(-2) + abs(0) + abs(1)
3=abs(-2) + abs(1) + abs(0)
3=abs(-1) + abs(-1) + abs(-1)
3=abs(-1) + abs(-1) + abs(1)
etc (this example will yield 38 equations)

The values from these equations will ultimately be used in the equation:
X(i) = A*n1 + B*n2 + C*n3 ...

The order of the equations doesn't matter as long as they are all there. Does that make enough sense?

[shg]

I'm only guessing -- is this the correct output for N=3? Each row sums, in absolute value, to 3.

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[shg]

Assuming that's correct, then the number of combinations by value of n is:

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(See http://www.research.att.com/~njas/se...lish&go=Search)

It gets out of hand pretty quickly. You could list n=7 in versions of Excel up to 2003, and n=9 in Excel 2007. N=31 would require more disk storage than has been manufactured.

[wilro85]

Yes, those 38 equations were correct. I didn't think it would get quite that out of hand. Oh well back to the drawing board.

[wilro85]

Alright, after a while of having this on the blackboard I've got another way of doing this, but I need a smaller matrix. The attached workbook has the positive half of the third, fourth, and fifth order matrices (if you compare my 3rd order to the one SHG posted in this thread, you'll see my equations are the bottom 19 of his 38. I only need half as the other half can be generated by multiplying by -1).

So ultimately, I'd like to have a program that can write a matrix of any order starting at a cell that I designate. I can create the matrices by hand, but it is tedious and I'd like to not have to store them all if possible.

If you're good at loops, see if you can come up with something.

[wilro85]

Nevermind. I've got something that will work for me.

Sub EstMat()
'Sub EstMat(C, R, order)

Dim x As Integer, y As Integer, order As Integer

C = 16
R = 2
order = 3

For i = -order To order

For j = -order To order

For k = -order To order
If (Abs(i) + Abs(j) + Abs(k) = order) Then
Cells(r, C).Value = i
Cells(r, C + 1).Value = j
Cells(r, C + 2).Value = k
r = r + 1
End If
Next

Next

Next
End Sub

[shg]

Please change the QUOTE tags to CODE tags.

Also, isn't you code correct only for order = 3? I thought there was n1, n2, ..., norder