$: Array index to facilitate array operations (H)

• $ is the current array index in expressions of the type
  array = some_expression_involving_the_linear_array_index
• The global variable $ is set to 1 at the start of each script line.
• A

  block array operation

  array = F($, ...) is equivalent to
  • DO $=1, len_array, 1
  •     array($) = F($, ...)
  • ENDDO

• vector elements = f(element index)

  :
  • vector = $ ! evaluates to vector = (1,2,3,4,....)
  • vector = ($ - 1) * 1.001 ! set vector to (0.000, 1.001, 2.002, 3.003, ...)

• factorial n

  n!, execution sequence is $ = 1, 2, 3, ...
  • vector = vector($ - 1) * $ + ($ == 1) ! overflow for $ > 170 because 171! > 1E308
  • If an index is beyond the range of the array, the expression is 0 (e.g. vector($-1) for $ == 1)
  • ($==1) is 1 for $=1, else it is 0. See Logicals

• set matrix rows

  of a n x n matrix MX to 0, 1, 2, 3, 4, ...
  • MX = MOD($-1, n)