Analysis of a FORTRAN Matrix Program - I

Here I present a matrix homework. I will post comments and suggestions in a series of posts. First, here is the program at the outset.

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/)

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


One thing that is missing from this program is comments. Tell me what the program is supposed to do, and what each section of the code is supposed to do. It used to be that the letter C at the beginning of the line would start a comment. Here, instead, we use the character !

Another thing to realize is that you can assign an entire matrix to another matrix with the = operator. You need not initialize copy separately, or even loop, copying elements. Rather, just use =. I will comment out the code and put in the new code in its place. My changes in red.

! 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