Fortran - Arrays

Arrays can store a fixed-size sequential collection of elements of the same type. An array is used to store a collection of data, but it is often more useful to think of an array as a collection of variables of the same type.
All arrays consist of contiguous memory locations. The lowest address corresponds to the first element and the highest address to the last element.

Numbers(1)

Numbers(2)

Numbers(3)

Numbers(4)

…

Arrays can be one- dimensional (like vectors), two-dimensional (like matrices) and Fortran allows you to create up to 7-dimensional arrays.

Declaring Arrays

Arrays are declared with the dimension attribute.
For example, to declare a one-dimensional array named number, of real numbers containing 5 elements, you write,

real, dimension(5) :: numbers

The individual elements of arrays are referenced by specifying their subscripts. The first element of an array has a subscript of one. The array numbers contains five real variables –numbers(1), numbers(2), numbers(3), numbers(4), and numbers(5).
To create a 5 x 5 two-dimensional array of integers named matrix, you write:

integer, dimension (5,5) :: matrix  

You can also declare an array with some explicit lower bound, for example:

real, dimension(2:6) :: numbers
integer, dimension (-3:2,0:4) :: matrix  

Assigning Values

You can either assign values to individual members, like,

numbers(1) = 2.0

or, you can use a loop,

do i=1,5
   numbers(i) = i * 2.0
end do

One dimensional array elements can be directly assigned values using a short hand symbol, called array constructor, like,

numbers = (/1.5, 3.2,4.5,0.9,7.2 /)

please note that there are no spaces allowed between the brackets ‘( ‘and the back slash ‘/’
Example
The following example demonstrates the concepts discussed above.

program arrayProg

   real :: numbers(5) !one dimensional integer array
   integer :: matrix(3,3), i , j !two dimensional real array
   
   !assigning some values to the array numbers
   do i=1,5
      numbers(i) = i * 2.0
   end do
   
   !display the values
   do i = 1, 5
      Print *, numbers(i)
   end do
   
   !assigning some values to the array matrix
   do i=1,3
      do j = 1, 3
         matrix(i, j) = i+j
      end do
   end do
   
   !display the values
   do i=1,3
      do j = 1, 3
         Print *, matrix(i,j)
      end do
   end do
   
   !short hand assignment
   numbers = (/1.5, 3.2,4.5,0.9,7.2 /)
   
   !display the values
   do i = 1, 5
      Print *, numbers(i)
   end do
   
end program arrayProg

When the above code is compiled and executed, it produces the following result:

 2.00000000    
 4.00000000    
 6.00000000    
 8.00000000    
 10.0000000    
         2
         3
         4
         3
         4
         5
         4
         5
         6
 1.50000000    
 3.20000005    
 4.50000000    
0.899999976    
 7.19999981    

Some Array Related Terms

The following table gives some array related terms:

Term	Meaning
Rank	It is the number of dimensions an array has. For example, for the array named matrix, rank is 2, and for the array named numbers, rank is 1.
Extent	It is the number of elements along a dimension. For example, the array numbers has extent 5 and the array named matrix has extent 3 in both dimensions.
Shape	The shape of an array is a one-dimensional integer array, containing the number of elements (the extent) in each dimension. For example, for the array matrix, shape is (3, 3) and the array numbers it is (5).
Size	It is the number of elements an array contains. For the array matrix, it is 9, and for the array numbers, it is 5.

Passing Arrays to Procedures

You can pass an array to a procedure as an argument. The following example demonstrates the concept:

program arrayToProcedure      
implicit none      

   integer, dimension (5) :: myArray  
   integer :: i
   
   call fillArray (myArray)      
   call printArray(myArray)
   
end program arrayToProcedure


subroutine fillArray (a)      
implicit none      

   integer, dimension (5), intent (out) :: a
   
   ! local variables     
   integer :: i     
   do i = 1, 5         
      a(i) = i      
   end do  
   
end subroutine fillArray 


subroutine printArray(a)

   integer, dimension (5) :: a  
   integer::i
   
   do i = 1, 5
      Print *, a(i)
   end do
   
end subroutine printArray

When the above code is compiled and executed, it produces the following result:

1
2
3
4
5

In the above example, the subroutine fillArray and printArray can only be called with arrays with dimension 5. However, to write subroutines that can be used for arrays of any size, you can rewrite it using the following technique:

program arrayToProcedure      
implicit  none    

   integer, dimension (10) :: myArray  
   integer :: i
   
   interface 
      subroutine fillArray (a)
         integer, dimension(:), intent (out) :: a 
         integer :: i         
      end subroutine fillArray      

      subroutine printArray (a)
         integer, dimension(:) :: a 
         integer :: i         
      end subroutine printArray   
   end interface 
   
   call fillArray (myArray)      
   call printArray(myArray)
   
end program arrayToProcedure


subroutine fillArray (a)      
implicit none      
   integer,dimension (:), intent (out) :: a      
   
   ! local variables     
   integer :: i, arraySize  
   arraySize = size(a)
   
   do i = 1, arraySize         
      a(i) = i      
   end do  
   
end subroutine fillArray 


subroutine printArray(a)
implicit none

   integer,dimension (:) :: a  
   integer::i, arraySize
   arraySize = size(a)
   
   do i = 1, arraySize
     Print *, a(i)
   end do
   
end subroutine printArray

Please note that the program is using the size function to get the size of the array.
When the above code is compiled and executed, it produces the following result:

1
2
3
4
5
6
7
8
9
10

Array Sections

So far we have referred to the whole array, Fortran provides an easy way to refer several elements, or a section of an array, using a single statement.
To access an array section, you need to provide the lower and the upper bound of the section, as well as a stride (increment), for all the dimensions. This notation is called a subscript triplet:

array ([lower]:[upper][:stride], ...)

When no lower and upper bounds are mentioned, it defaults to the extents you declared, and stride value defaults to 1.
The following example demonstrates the concept:

program arraySubsection

   real, dimension(10) :: a, b
   integer:: i, asize, bsize
   
   a(1:7) = 5.0 ! a(1) to a(7) assigned 5.0
   a(8:) = 0.0  ! rest are 0.0 
   b(2:10:2) = 3.9
   b(1:9:2) = 2.5
   
   !display
   asize = size(a)
   bsize = size(b)
   
   do i = 1, asize
      Print *, a(i)
   end do
   
   do i = 1, bsize
      Print *, b(i)
   end do
   
end program arraySubsection

When the above code is compiled and executed, it produces the following result:

5.00000000    
5.00000000    
5.00000000    
5.00000000    
5.00000000    
5.00000000    
5.00000000    
0.00000000E+00
0.00000000E+00
0.00000000E+00
2.50000000    
3.90000010    
2.50000000    
3.90000010    
2.50000000    
3.90000010    
2.50000000    
3.90000010    
2.50000000    
3.90000010 

Array Intrinsic Functions

Fortran 90/95 provides several intrinsic procedures. They can be divided into 7 categories.

• Vector and matrix multiplication
• Reduction
• Inquiry
• Construction
• Reshape
• Manipulation
• Location