Programming algorithm expressed in math notation

[elusiveshame]

Hey everyone,
I wasn't sure if this belonged in the general math forum or not, so I posted it here instead (mods - feel free to move if it belongs elsewhere).

What I want to know is how to properly write out a computer algorithm in proper math notation. Take this code for example:

    Height = 4
    Width = 10
    For X = 0 to Width - 1
        For Y = 0 to Height - 1
            index = x + (y * width)
        Next
    Next

To put it into a mathematical formula, how would you do it? The highest level of math completed was Single Variable Calculus, so going by what I know, it would look like:

index = x∑y∑ x + (y * x)

Is that even close?

 

[anorlunda]

$\sum_y\sum_x x + (y * width)$
or
$\sum_{y,x} x + (y * width)$

To do that in LateX here on PF, write the following except use # instead of @.

@@\sum_y\sum_x x + (y * width)@@
or
@@\sum_{y,x} x + (y * width)@@

But first you have to fix a bug in your code. As written is it not a sum at all.

index = x + (y * width)

It should be

index = index + x + (y * width)

You also need to initialize index=0 before the loops.

Note that at the bottom of the post edit window, is a button called LateX. That shows you how to do it.

 

[Ibix]

But first you have to fix a bug in your code. As written is it not a sum at all.
It should be
You also need to initialize index=0 before the loops.

...well, it should be that if you want the code to do what the maths says. Since the code looks to me like it's converting (x,y) coordinates into an index in a 1d array, I'd say the maths that has the bug.

 

[elusiveshame]

$\sum_y\sum_x x + (y * width)$
or
$\sum_{y,x} x + (y * width)$

To do that in LateX here on PF, write the following except use # instead of @.
But first you have to fix a bug in your code. As written is it not a sum at all.It should beYou also need to initialize index=0 before the loops.

Note that at the bottom of the post edit window, is a button called LateX. That shows you how to do it.

Thanks for the LaTeX tutorial =) There's no bug in the code, though, and it was just a small snippet of a much larger routine.

...well, it should be that if you want the code to do what the maths says. Since the code looks to me like it's converting (x,y) coordinates into an index in a 1d array, I'd say the maths that has the bug.

That's exactly what it's doing. Basically it's taking an array of a data type that has its own 2D (x,y) coordinate system. This just identifies the index of that data type.

 

[elusiveshame]

Here's the full loop if you're curious:

            idx = 0
            ix = 0
            iy = 0
            For X = 0 To Int(Text3.Text) - 1
                For Y = 0 To Int(Text2.Text) - 1
                    tc = X + (Int(Text3.Text) * Y)
                    For Index = 0 To 31
                        t$ = Hex(b(idx + Index))
                        If Len(t$) = 1 Then
                            t$ = "0" + t$
                        End If
                        Extract(tc).pixels(ix, iy) = CInt(CLng("&h" & Left(t$, 1)))
                        ix = ix + 1
                        Extract(tc).pixels(ix, iy) = CInt(CLng("&h" & Right(t$, 1)))
                        ix = ix + 1
                        If ix = 8 Then
                            ix = 0
                            iy = iy + 1
                        End If
                        If iy = 8 Then
                            iy = 0
                            idx = idx + 32
                        End If
                    Next
                Next
            Next

 

[Ibix]

That's exactly what it's doing. Basically it's taking an array of a data type that has its own 2D (x,y) coordinate system. This just identifies the index of that data type.

So you aren't summing anything. You are just calculating $x+y\times width$ for a sequence of $x$ and $y$ values. I don't think there's a way to express that any more cleanly.

 

[elusiveshame]

So you aren't summing anything. You are just calculating $x+y\times width$ for a sequence of $x$ and $y$ values. I don't think there's a way to express that any more cleanly.

Ah, yeah, you're right.

Thanks!

 

[FactChecker]

So you aren't summing anything. You are just calculating $x+y\times width$ for a sequence of $x$ and $y$ values. I don't think there's a way to express that any more cleanly.

So that would be $index_{x,y} = x + y * width$, for $0 \le x \le Int(Text3.Text) - 1, 0 \le y \le Int(Text2.Text) - 1$