Analysis of a FORTRAN Matrix Program - II

The program already has a nice feature. It defines length to be 4 and then uses length throughout in the loops. That way, if we want to change the program to handle a 5 X 5 matrix, we can just change the declaration of our matrices to 5 X 5, and length to = 5, and the program will run. Using symbols instead of literals in this way makes the program mode readily adaptable.

The program, again:

! program to calculate whether a graph is strongly connected
! it calculates this my using matrix multiplication on the
! adjacency matrix representing the graph
PROGRAM matrix

INTEGER :: a,b, c, m(4,4), copy(4,4), total, length = 4, d, e, f

m(1, :) = (/ 1, 0, 1, 0/)
m(2, :) = (/ 1, 0, 0, 0/)
m(3, :) = (/ 1, 1, 0, 1/)
m(4, :) = (/ 0, 0, 1, 0/)

! copy(1, :) = (/ 1, 0, 1, 0/)
! copy(2, :) = (/ 1, 0, 0, 0/)
! copy(3, :) = (/ 1, 1, 0, 1/)
! copy(4, :) = (/ 0, 0, 1, 0/)

!initialize a copy of m so that we may calculate N^2
copy = m

DO a = 1, length
DO b = 1, length
total = 0
DO c = 1, length
total = m(a,c) * copy(c,b) + total
END DO
IF (total > 0) THEN
m(a,b) = 1
ELSE
m(a,b) = 0
END IF
END DO
END DO

DO f = 1, length
PRINT *, m(f,1:4)
END DO

DO e = 1, length
total = 0
DO d = 1, length
IF( m(d,e) .EQ. 1 .AND. m(e,d) .EQ. 1 ) total = total + 2
END DO
IF ( total == 8 ) THEN
PRINT *, 'Strongly Connected At: ', e
ELSE
PRINT *, 'Not Strongly Connected At: ', e
END IF
END DO

END PROGRAM matrix

However, as implemented, there are two things I would change. Firstly, length is declared as a variable. This means that somewhere in the program, I might change it by accident. It would be better to declare it a constant. But how do we do this in FORTRAN? The answer, we declare its data type and then set its value with a PARAMETER statement.

Another thing I would change: the declaration of our matrices m and copy use a literal 4. When modifying the program, I would not only have to change the definition of length but my matrix definitions as well. Instead, let us use our new constant to define the matrix size. We will also remove the old code that was commented out:

! program to calculate whether a graph is strongly connected
! it calculates this my using matrix multiplication on the
! adjacency matrix representing the graph
PROGRAM matrix

INTEGER :: length
PARAMETER (length = 4)
INTEGER :: a,b, c, m(length,length), copy(length,length), total, d, e, f

m(1, :) = (/ 1, 0, 1, 0/)
m(2, :) = (/ 1, 0, 0, 0/)
m(3, :) = (/ 1, 1, 0, 1/)
m(4, :) = (/ 0, 0, 1, 0/)

!initialize a copy of m so that we may calculate N^2
copy = m

DO a = 1, length
DO b = 1, length
total = 0
DO c = 1, length
total = m(a,c) * copy(c,b) + total
END DO
IF (total > 0) THEN
m(a,b) = 1
ELSE
m(a,b) = 0
END IF
END DO
END DO

DO f = 1, length
PRINT *, m(f,1:4)
END DO

DO e = 1, length
total = 0
DO d = 1, length
IF( m(d,e) .EQ. 1 .AND. m(e,d) .EQ. 1 ) total = total + 2
END DO
IF ( total == 8 ) THEN
PRINT *, 'Strongly Connected At: ', e
ELSE
PRINT *, 'Not Strongly Connected At: ', e
END IF
END DO

END PROGRAM matrix