Array properties

The number of dimensions of the array. This is fixed for a given array, and is determined from the array declaration. If an object is not an array, then it is said to be scalar and to have rank zero.

Each array dimension has a lower bound, an upper bound, and an extent that is defined as

MAX (upper bound -lower bound + 1, 0)

Bounds are integer valued and may be positive, zero, or negative. Unlike FORTRAN 77, it is permissible for the lower bound to be greater than the upper bound; if this happens then there are no elements in the dimension and the extent of the dimension is defined to be zero.

The size of an array is the total number of array elements, computed as the product of all its extents. If the extent of any dimension is zero, the size of the array is zero and the array contains no elements. An array with no elements is known as a zero-sized array.

The shape of an array is a vector of the extents of each dimension of the array; the shape can thus be expressed as a one-dimensional array of size equal to the rank of the array being described. For example, if given the following declarations:

REAL    :: a1(10)

INTEGER :: a2(2,4)

LOGICAL :: a3(5,5,0)

COMPLEX :: s1

The rank of a1 is 1 as it only has one dimension, the extent of the single dimension is 10, and the size of a1 is also 10. a1 has a shape represented by the vector [ 10 ].

a2 has been declared with two dimensions and consequently has a rank of 2, the extents of the dimensions are 2 and 4 respectively, and the size of a2 is 8. The vector [ 2, 4 ] represents the array's shape.

a3 has a rank of 3, the extent of the first two dimensions is 5, and the extent of the third dimension is zero. The size of a3 is the product of all the extents and is therefore zero. The shape of a3 is [ 5, 5, 0]

s1 is a scalar and therefore has a rank of zero, and its shape is represented by an empty vector.