Array Terminology

Examples of declarations:

    REAL, DIMENSION(15)       :: A
    REAL, DIMENSION(-4:0,0:2) :: B
    REAL  :: C(5,3), D(0:4,0:2) ! Shorthand

The above are explicit-shape arrays.

Terminology:

• rank -- the number of dimensions up to and including 7 dimensions. A has rank 1, B, C and D have rank 2.
• bounds -- upper and lower limits of indices, an unspecified bound is 1. A has lower bound 1 and upper bound 15, B has lower bounds -4 and 0 and upper bounds 0 and 2, C has lower bounds of 1 and 1 with upper bounds 5 and 3, and D has bounds 0 and 0, and 4 and 2.
• extent -- number of elements in dimension (which can be zero). A has extent 15, B, C and D have extents 5 and 3.
• size -- either the total number of elements or, if particular dimension is specified, the number of elements in that dimension. All arrays have size 15.
• shape -- rank and extents. A has shape (/15/), B, C and D have shape (/5,3/).
• conformable -- two arrays are conformable if they have the same shape -- for operations between two arrays the shapes (of the sections) must (generally) conform (just like in mathematics). B, C and D have the same shape so they conform.
• there is no storage association for Fortran 90 arrays.

Explicit-shape arrays can have symbolic bounds so long as they are initialisation expressions -- evaluatable at compile time.

Now try this question

 

Consider the following declarations,

    REAL, DIMENSION(15)       :: A
    REAL, DIMENSION(-4:0,0:2) :: B
    REAL  :: C(5,3), D(0:4,0:2) ! Shorthand

Individual array elements are denoted by subscripting the array name by an INTEGER, for example, A(7) element of A, or C(3,2), 3 elements down, 2 across.

The arrays can be visualised as below:

 
Figure 1: Visualisation of Arrays

The first dimension runs up and down the page and the second dimensions runs across the page.