| Two Dimensional Array |
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| 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. |
| Example: |
| 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. |
| Example: |
| real A(3,5) |
| integer i,j |
| c |
| c |
| 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. |
| Example: |
| Let us consider three two dimensional arrays with this example |
| Program: |
| This program is of two dimension which display the output in the matrix form. |
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| Output: |
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| 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) |