6.4.1. Array Terminology

An array consists of elements that extend in one or more dimensions to represent columns, rows, planes, and so on. There can be up to seven dimensions in an array declaration. The number of dimensions in an array is called the rank of the array. The number of elements in a dimension is called the extent of the array in that dimension. The shape of an array is determined from the rank and the extents; to be precise, the shape is a vector where each element of the vector is the extent in the corresponding dimension. The size of an array is the product of the extents; that is, it is the total number of elements in the array.

Example 1: Consider the following statement:

REAL X(0:9, 2)

The rank of X is 2 because X has two dimensions. The extent of the first dimension is 10; the extent of the second dimension is 2. The shape of X is 10 by 2, that is, a vector of two values, (10, 2). The size is 20, the product of the extents.

An object can be given the DIMENSION attribute in a type declaration or in one of several other specification statements.

Example 2: Consider the following statements show some ways of declaring that A has rank 3 and shape (10, 15, 3):

DIMENSION A(10, 15, 3) REAL, DIMENSION(10, 15, 3) :: A REAL A(10, 15, 3) COMMON A(10, 15, 3) TARGET A(10, 15, 3)

Arrays of nonzero size have a lower and upper bound for each dimension. The lower bound is the smallest subscript value for a dimension; the upper bound is the largest subscript value for that dimension. The default lower bound is 1 if the lower bound is omitted in the declaration. Array bounds can be positive, zero, or negative.

Example 3: Consider the following statement:

REAL Z(-3:10, 12)

The first dimension of Z ranges from -3 to 10, that is, -3, -2, -1, 0, 1, 2, . . ., 9, 10. The lower bound is -3; the upper bound is 10. In the second dimension, the lower bound is 1; the upper bound is 12.

The bounds for array expressions are described in Section 7.2.8.4.

6.4.2. Whole Arrays

Some arrays are named. The name is either an array variable name or the name of a constant. If the array name appears without a subscript list or section subscript list, all of the elements of the array are referenced and the reference is considered to be a whole array reference.

6.4.3. Array Elements

An array element is one of the scalar elements that make up an array. A subscript list is used to indicate which element is referenced. Assume that A is declared to be a one-dimensional array, as follows:

REAL, DIMENSION(10) :: A

A(1) refers to the first element, A(2) to the second, and so on. The number in the parentheses is the subscript that indicates which scalar element is referenced. Assume that B is declared to be a seven-dimensional array, as follows:

REAL B(5, 5, 5, 5, 4, 7, 5)

B(2,3,5,1,3,7,2) refers to one scalar element of B, indexed by a subscript in each dimension. The set of numbers that indicate the position along each dimension in turn (in this case, 2,3,5,1,3,7,2) is called a subscript list.

6.4.4. Array Sections

Sometimes only a portion of an array is needed for a calculation. It is possible to refer to a selected portion of an array as an array; this portion is called an array section. A parent array is the whole array from which the portion that forms the array section is selected.

An array section is specified by an array variable name and a section subscript list that consists of subscripts, triplet subscripts, or vector subscripts. At least one subscript must be a triplet or vector subscript; otherwise, the reference indicates an array element, not an array section. The following example uses a section subscript to create an array section:

REAL A(10) . . . A(2:5) = 1.0

The parent array A has 10 elements. The array section consists of the elements A(2), A(3), A(4), and A(5) of the parent array. The section A(2:5) is an array itself and the value 1.0 is assigned to all four of its elements.

6.4.5. Format of Array Elements and Array Sections

The format of an array element is a data reference, which is defined as follows:

For a data reference to be classified as an array section, exactly one part reference must have nonzero rank, and either the final part reference must have a section subscript list with nonzero rank or another part reference must have nonzero rank.

The format of an array section is a data reference followed by an optional substring range enclosed in parentheses. This is defined as follows:

The format of a substring range is found in Section 6.2.

A part name in a data reference can be followed by an optional section subscript list, as follows:

Each subscript and stride must be a scalar_int_expr. A vector_subscript must be an integer array expression of rank one.

For a data reference to be classified as an array element, every part reference must have rank zero and the last part reference must contain a subscript list.

In an array section that is a data reference followed by a substring range, the rightmost part name must be of type character.

In an array section of an assumed-size array, the second subscript must not be omitted from a subscript triplet in the last dimension.

A section subscript must be present for each dimension of an array. If any section subscript is simply a subscript, the section will have a lesser rank than its parent.

If any part of a reference is an array section, the reference is considered to be an array section reference. In a data reference, there may be at most one part with rank greater than zero.

Examples of array elements and array sections are as follows:

ARRAY_A(1,2) ! array element ARRAY_A(1:N:2,M) ! rank-one array section ARRAY_B(:,:,:)(2:3) ! array. elements are substrings of ! of length 2 SCALAR_A%ARRAY_C(L) ! array element SCALAR_A%ARRAY_C(1:L) ! array section SCALAR_B%ARRAY_D(1:N)%SCALAR_C ! array section ARRAY_E(1:N:2)%ARRAY_F(I,J)%STRING(K)(:) ! array section

In the last example above, each component of the type definition is an array and the object ARRAY_E is an array. The reference is valid because each component in the reference is scalar. The substring range is not needed because it specifies the entire string; however, it serves as a reminder that the last component is of type character.

The following examples demonstrate the allowable combinations of scalar and array parents with scalar and array components.

TYPE REPAIR_BILL REAL PARTS(20) REAL LABOR END TYPE REPAIR_BILL TYPE(REPAIR_BILL) FIRST TYPE(REPAIR_BILL) FOR_1990(6) Scalar parent: 1. FIRST % LABOR ! structure component 2. FIRST % PARTS(I) ! array element 3. FIRST % PARTS ! component (array-valued) 4. FIRST % PARTS(I:J) ! array section 5. FOR_1990(K) % LABOR ! structure component 6. FOR_1990(K) % PARTS(I) ! array element 7. FOR_1990(K) % PARTS ! component (array-valued) 8. FOR_1990(K) % PARTS(I:J) ! array section Array parent: 9. FOR_1990 % LABOR ! component and array section 10. FOR_1990 % PARTS(I) ! array section 11. FOR_1990 % PARTS ! ILLEGAL 12. FOR_1990 % PARTS(I:J) ! ILLEGAL 13. FOR_1990(K:L) % LABOR ! component and array section 14. FOR_1990(K:L) % PARTS(I) ! array section 15. FOR_1990(K:L) % PARTS ! ILLEGAL 16. FOR_1990(K:L) % PARTS(I:J) ! ILLEGAL

References 11, 12, 15, and 16 are illegal because only one component may be of rank greater than zero. References 3 and 7 are compact (contiguous) array objects and are classified as array-valued structure components. References 9, 10, 13, and 14 are noncontiguous array-section objects. These distinctions are important when such objects are actual arguments in procedure references.

6.4.6. Using Array Elements and Array Sections

Subscripts, subscript triplets, and vector subscripts can be mixed in a single section subscript list used to specify an array section. A triplet section can specify an empty sequence (for example 1:0), in which case the resulting section is a zero-sized array.

Example 1: Assume that B is declared as follows:

REAL B(10, 10, 5)

Section B(1:4:3, 6:8:2, 3) consists of the following four elements:

B(1,6,3) B(1,8,3) B(4,6,3) B(4,8,3)

The stride along the first dimension is 3, resulting in a subscript-value list of 1 and 4. The stride along the second dimension is 2, resulting in a subscript-value list of 6 and 8. In the third position there is a subscript that reduces the rank of the section by 1. The section has shape (2, 2) and size 4.

Example 2: Assume IV is declared as follows:

INTEGER, DIMENSION(3) :: IV = (/ 4, 5, 4 /)

Then the section B(8:9, 5, IV) is a 2 x 3 array consisting of the following six elements:

B(8,5,4) B(8,5,5) B(8,5,4) B(9,5,4) B(9,5,5) B(9,5,4)

B(8:9, 5:4, IV) is a zero-sized array of rank 3.

6.4.7. Array Element Order

When whole arrays are used as operands in an executable statement, the indicated operation is performed element-by-element, but no order is implied for these elemental operations. They can be executed in any order or simultaneously. Although there is no order of evaluation when whole array operations are performed, there is an ordering of the elements in an array itself. An ordering is required for the input and output of arrays and for certain intrinsic functions such as MAXLOC(3i). The elements of an array form a sequence whose ordering is called array element order. This is the sequence that occurs when the subscripts along the first dimension vary most rapidly, and the subscripts along the last dimension vary most slowly. Thus, for an array declared as REAL A(3, 2), the elements in array element order are: A(1, 1), A(2, 1), A(3, 1), A(1, 2), A(2, 2), A(3, 2).

The position of an array element in this sequence is its subscript order value. Element A(1, 1) has a subscript order value of 1. Element A(1, 2) has a subscript order value of 4. Figure 6-1, shows how to compute the subscript order value for any element in arrays of rank 1 through 7.

The subscript order of the elements of an array section is that of the array object that the section represents. That is, given the array A(10) and the section A(2:9:2) consisting of the elements A(2), A(4), A(6), and A(8), the subscript order value of A(2) in the array section A(2:9:2) is 1; the subscript order value of A(4) in the section is 2 and A(8) is 4.