An array section is a portion of an array that is an array itself.
It is an array subobject. A section subscript list (appended to
the array or array component) determines which portion is being
referred to. A reference to an array section takes the following
form:
array [(sect-s-list)] [(substring-range)]
array Is the name of an array.
sect-s-list Is a list of one or more section
subscripts (subscripts, subscript
triplets, or vector subscripts)
indicating a set of elements along
a particular dimension.
At least one of the items in the section
subscript list must be a subscript
triplet or vector subscript. Each
subscript and subscript triplet must be
a scalar numeric expression. Each vector
subscript must be a rank-one integer
expression.
substring-range Is a substring range in the form
[expr]:[expr]. Each expression specified
must be a scalar numeric expression.
The array (or array component) preceding
the substring range must be of type character.
If no section subscript list is specified, the rank and shape of
the array section is the same as the parent array.
Otherwise, the rank of the array section is the number of vector
subscripts and subscript triplets that appear in the list. Its
shape is a rank-one array where each element is the number of
integer values in the sequence indicated by the corresponding
subscript triplet or vector subscript.
If any of these sequences is empty, the array section has a size of
zero. The subscript order of the elements of an array section is
that of the array object that the array section represents.
Each array section inherits the type, kind type parameter, and
certain attributes (INTENT, PARAMETER, and TARGET) of the parent
array. An array section cannot inherit the POINTER attribute.
The following shows valid references to array sections:
REAL, DIMENSION(20) :: B
...
PRINT *, B(2:20:5) ! the section consists of elements
! B(2), B(7), B(12), and B(17)
K = (/3, 1, 4/)
B(K) = 0.0 ! section B(K) is a rank-one array with
! shape (3) and size 3. (0.0 is assigned to
! B(1), B(3), and B(4).)
Consider the following declaration:
CHARACTER(LEN=15) C(10,10)
An array section referenced as C(:,:)(1:3) is an array of shape
(10,10) whose elements are substrings of length 3 of the
corresponding elements of C.
1 – Triplets
A subscript triplet consists of three parts: the first two parts
designate a range of subscript values and the third part designates
the increment (stride) between each value. It takes the following
form:
[subscript-1] : [subscript-2] [:stride]
subscript-1 Is a scalar numeric expression representing
the first value in the subscript sequence.
If omitted, the declared lower bound of the
dimension is used.
subscript-2 Is a scalar numeric expression representing
the last value in the subscript sequence.
If omitted, the declared upper bound of the
dimension is used.
When indicating sections of an assumed-size
array, this subscript must be specified.
stride Is a scalar numeric expression representing
the increment between successive subscripts
in the sequence. It must have a nonzero value.
If it is omitted, it is assumed to be 1.
The stride has the following effects:
o If the stride is positive, the subscript range starts with the
first subscript and is incremented by the value of the stride,
until the largest value less than or equal to the second
subscript is attained.
For example, if an array has been declared as B(6,3,2), the
array section specified as B(2:4,1:2,2) is a rank-two array
with shape (3,2) and size 6. It consists of the following six
elements:
B(2,1,2) B(2,2,2)
B(3,1,2) B(3,2,2)
B(4,1,2) B(4,2,2)
If the first subscript is greater than the second subscript,
the range is empty.
o If the stride is negative, the subscript range starts with the
value of the first subscript and is decremented by the absolute
value of the stride, until the smallest value greater than or
equal to the second subscript is attained.
For example, if an array has been declared as A(15), the array
section specified as A(10:3:-2) is a rank-one array with shape
(4) and size 4. It consists of the following four elements:
A(10)
A(8)
A(6)
A(4)
If the second subscript is greater than the first subscript,
the range is empty.
If a range specified by the stride is empty, the array section has
a size of zero.
A subscript in a subscript triplet need not be within the declared
bounds for that dimension if all values used to select the array
elements are within the declared bounds. For example, if an array
has been declared as A(15), the array section specified as
A(4:16:10) is valid. The section is a rank-one array with shape
(2) and size 2. It consists of elements A(4) and A(14).
If the subscript triplet does not specify bounds or stride, but
only a colon (:), the entire declared range for the dimension is
used.
2 – Vector Subscripts
A vector subscript is a rank-one array of integer values (within
the declared bounds for the dimension). It is used to select a
sequence of elements from a parent array. The sequence does not
have to be in order, and it can contain duplicate values.
For example, A is a rank-two array of shape (4,6). B and C are
rank-one arrays of shape (2) and (3), respectively, with the
following values:
B = (/1,4/)
C = (/2,1,1/) ! Will result in a many-one
! array section
Array section A(3,B) consists of elements A(3,1) and A(3,4). Array
section A(C,1) consists of elements A(2,1), A(1,1), and A(1,1).
Array section A(B,C) consists of the following elements:
A(1,2) A(1,1) A(1,1)
A(4,2) A(4,1) A(4,1)
An array section with a vector subscript that has two or more
elements with the same value is called a many-one array section. A
many-one section must not appear on the left of the equals sign in
an assignment statement, or as an input item in a READ statement.
The following assignments to C also show examples of vector
subscripts:
INTEGER A(2), B(2), C(2)
...
B = (/1,2/)
C(B) = A(B)
C = A((/1,2/))
An array section with a vector subscript must not be any of the
following:
o An internal file
o An actual argument associated with a dummy array that is
defined or redefined (if the INTENT attribute is specified, it
must be INTENT(IN))
o The target in a pointer assignment statement
If the sequence specified by the vector subscript is empty, the
array section has a size of zero.