Two Dimensional Array

 Two Dimensional Array
2 4 6 8
3 5 9 11
This array represents a matrix since it is two-dimensional.
Let us consider a 4 x 3 array A which will be stored in the computer as:
A(1,1), A(2, 1), A(3,1), A(4,1), A(1,2), A(2,2), A(3,2)
A(4,2), A(1,3), A(2,3), A(3,3), A(4,3)
Here the second subscript is set to 1 when the first subscript changes from 1 to 4; the second subscript is then set to 2, first subscript changes from 1 to 4. The first subscript changes rapidly and the second less rapidly. Arrays are stored column wise in Fortran language.
Matrix: An array with a rank of 2 or greater is called a matrix
Matrices are usually represented by two-dimensional arrays.
The declaration is:
real A(3,5)
It defines a two-dimensional array of 3*5=15 real numbers. Its first index as the row index, and the second as the column index.
Hence we have:
(1,1) (1,2) (1,3) (1,4) (1,5)
(2,1) (2,2) (2,3) (2,4) (2,5)
(3,1) (3,2) (3,3) (3,4) (3,5)
The general syntax for declarations is:
name (low_index1 : hi_index1, low_index2 : hi_index2)
The total size of the array is then
size = (hi_index1-low_index1+1)*(hi_index2-low_index2+1)
It is common in Fortran to declare arrays that are larger than the matrix we want to store because Fortran does not have dynamic storage allocation.
real A(3,5)
integer i,j
do 20 j = 1, 3
do 10 i = 1, 3
A (i, j) = real (i)/real(j)
10 continue
20 continue
Here we have used only 3 by 3 numbers.
Let us consider three two dimensional arrays with this example
This program is of two dimension which display the output in the matrix form.
Three dimensional arrays
Let us consider A(2, 3, 2) is a three dimensional array which have 2 x 3 x 2 elements. These are stored in the computer and their values will be as:
A(1,1,1), A(2,1,1), A(1,2,1), A(2,2,1), A(1,3,1), A(2,3,1)
A(1,1,2), A(2,1,2), A(1,2,2), A(2,2,2), A(1,3,2), A(2,3,2)
Computer memory always stores the dimensions of the array in linear form. Fortran 77 allows arrays of up to seven dimensions.
The dimension statement
There is an alternate way to declare arrays in Fortran 77.
The statements:
real A, x
dimension x(50)
dimension A(10,20)
These are equivalent to real A(10,20), x(50)
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