what does this piece of fortran mean?

Question

im trying to go through a little algorithm in fortran (im not a fortran programmer unfortunately) but i need to understand what its doing: here it is,

  omega = 0.d0
  s = 1.d0
  i = 1
  j = 2
  k = 3
101 do iperm = 1, 3
     omega = omega + s * a1 (i) * a2 (j) * a3 (k)
     l = i
     i = j
     j = k
     k = l
  enddo
  i = 2
  j = 1
  k = 3
  s = - s

  if (s.lt.0.d0) goto 101

  omega = abs (omega) * alat**3

a1,a2,a3 are vectors (three elements each, real values, representing vectors in 3d space) s is a unit integer (can be 1 or -1 alternately) and i,j,k are integers while omega (which is what i need to understand how its arrived at) is a floating point value, so is alat. Now what is going on up there? especially the iperm =1,3 part, is that a vector being created? at first i thought iperm might be some fancy function/routine or iterator, but after some search i think thats not the case, whats the purpose of the iperm? is there some looping over iperm between "do" and "enddo" ?

Answer 1

All you've got is a sequence of assignments with a loop thrown in for fun. I guess you understand that statement such as

lhs = rhs

evaluates rhs and assigns the result to the variable lhs.

The line

101 do iperm = 1, 3

starts a do loop. The 101 is a statement label, it's used later. The loop comprises all the statements from that line to the line enddo. The loop will be executed 3 times (once for each of the integers in the sequence starting at 1 and ending at 3). The loop control variable iperm is assigned these values in turn. The loop is a little unusual in that the loop variable is not used inside the loop. The statement

omega = omega + s * a1 (i) * a2 (j) * a3 (k)

updates the value of omega. The term a1(i) (the space in your original is immaterial) means the i-th element of array a1. et cetera

When the line

if (s.lt.0.d0) goto 101

is executed if s is less than 0 control goes bak to the line labelled 101.

Finally, the term alat**3 calculates the cube of alat.

So now get a piece of paper and figure out what value omega gets.