Return an array from a function and store it in th

Question

Here is the Main Program:

      PROGRAM integration
      EXTERNAL funct
      DOUBLE PRECISION funct, a , b, sum, h
      INTEGER n, i
      REAL s

      PARAMETER (a = 0, b = 10, n = 200)  

      h = (b-a)/n
      sum = 0.0

      DO i = 1, n
         sum = sum+funct(i*h+a)
      END DO

      sum = h*(sum-0.5*(funct(a)+funct(b)))

      PRINT *,sum

      CONTAINS

      END     

And below is the Function funct(x)

      DOUBLE PRECISION FUNCTION funct(x)
      IMPLICIT NONE

      DOUBLE PRECISION x
      INTEGER K

      Do k = 1,10
      funct = x ** 2 * k
      End Do

      PRINT *, 'Value of funct is', funct

      RETURN
  END

I would like the 'Sum' in the Main Program to print 10 different sums over 10 different values of k in Function funct(x).

I have tried the above program but it just compiles the last value of Funct() instead of 10 different values in sum.

Answer 1

Array results require an explicit interface. You would also need to adjust funct and sum to actually be arrays using the dimension statement. Using an explicit interface requires Fortran 90+ (thanks for the hints by @francescalus and @VladimirF) and is quite tedious:

        PROGRAM integration
        INTERFACE funct
          FUNCTION funct(x) result(r)
            IMPLICIT NONE
            DOUBLE PRECISION r
            DIMENSION r( 10 )
            DOUBLE PRECISION x
          END FUNCTION
        END INTERFACE
        DOUBLE PRECISION a , b, sum, h
        DIMENSION sum( 10)
        INTEGER n, i

        PARAMETER (a = 0, b = 10, n = 200)  

        h = (b-a)/n
        sum = 0.0

        DO i = 1, n
           sum = sum+funct(i*h+a)
        END DO

        sum = h*(sum-0.5*(funct(a)+funct(b)))

        PRINT *,sum

        END  

        FUNCTION funct(x)
        IMPLICIT NONE
        DOUBLE PRECISION funct
        DIMENSION funct( 10)
        DOUBLE PRECISION x
        INTEGER K

        Do k = 1,10
          funct(k) = x ** 2 * k
        End Do

        PRINT *, 'Value of funct is', funct

        RETURN
        END

If you can, you should switch to a more modern Standard such as Fortran 90+, and use modules. These provide interfaces automatically, which makes the code much simpler.

Alternatively, you could take the loop over k out of the function, and perform the sum element-wise. This would be valid FORTRAN 77:

        PROGRAM integration
c       ...
        DIMENSION sum( 10)
c       ...
        INTEGER K
c       ...
        DO i = 1, n
          Do k = 1,10
            sum(k)= sum(k)+funct(i*h+a, k)
          End Do
        END DO
c       ...

Notice that I pass k to the function. It needs to be adjusted accordingly:

        DOUBLE PRECISION FUNCTION funct(x,k)
        IMPLICIT NONE
        DOUBLE PRECISION x
        INTEGER K

        funct = x ** 2 * k

        PRINT *, 'Value of funct is', funct

        RETURN
        END

This version just returns a scalar and fills the array in the main program.

---

Apart from that I'm not sure it is wise to use a variable called sum. There is an intrinsic function with the same name. This could lead to some confusion...