Numerical Computations

Fortran and C/C++ for Numerical Computation

Suppose you are writing a Fortran Subroutine to implement the Gauss Elimination method to solve a set of linear simultaneous equations. The main program and the Gauss subroutine would look as follows:

C234567890

PARAMETER (MAXSZ = 1000)

REAL A(MAXSZ*MAXSZ), X(MAXSZ), B(MAXSZ)

WRITE(*,*) 'Enter number of equations'

READ(*,*) M

IF (M .GT. MAXSZ)

WRITE(*,*) 'Increase MAXSZ. Program aborted'

ENDIF

WRITE(*,*) 'Enter coefficient matrix row by row'

CALL READMAT(M, M, A)

WRITE(*,*) 'Enter right hand side vector'

CALL READMAT(M, 1, B)

CALL GAUSS(M, A, B, X)

WRITE(*,*) 'Solution Vector'

CALL PRINTMAT(M, 1, X)

STOP

END

C--- Subroutine to read a matrix of M rows and N columns, row by row

SUBROUTINE READMAT(M, N, A)

REAL A(M, N)

DO I = 1, M

READ(*,*) (A(I,J), J = 1, N)

END DO

RETURN

END

C--- Subroutine to solve a set of linear simultaneous equations

SUBROUTINE GAUSS(M, A, B, X)

REAL A(M, M), B(M, 1), X(M, 1)

......

RETURN

END

There are several points worth noting

• • A one dimensioned array in the main program may be viewed as a two-dimensioned (or multi-dimensioned) array inside a subroutine, as long as you understand how it is to be done.

  • When passing an array to a subroutine, its size (number of rows and columns) must also be sent as arguments to the subroutine. Subroutine does not automatically know the size of the array argument it receives.