"Dimension 1 of array has extent 4 instead of 2161727907037185" [duplicate] - fortran

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...