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Lecture 8
Function Subprograms
In mathematics and engineering science, we quite often need to define, use
and evaluate a function of one or more variables. For example, we might
have the functions
f ( x) or g ( x, y ) etc.
The arguments of the functions might be scalar or vector quantities. In
Fortran, we can define a function to be a special program, sometimes
called a subprogram or subroutine, which acts very similar to functions in
mathematics. For example, suppose we have the function:
f ( x, y)  x 2  3xy  sin 2 ( x /(1  y 3 ))
We can define this function in Fortran with the following function
subprogram:
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Lecture 8
REAL FUNCTION F (X,Y)
REAL :: X,Y
F = X**2 – 3*X*Y +(SIN(X/(1.+Y**3)))**2
END
We can then use the function in a Fortran program by using its name (in
this case F) in any statement where we can normally use a variable name
(e.g., in an assignment statement). For example, suppose we need the
value of the function for values of x from 0 to1 and y from 0 to 1 in steps
of 0.1. We could write a main program followed by a function
subprogram as shown below. We will use what is called an "external
subprogram" for the function since the function subprogram is located
external to the main program (i.e., it is placed after the END statement of
main program).
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Lecture 8
PROGRAM Evaluate_function
REAL :: X,Y,F
DO I =0,10
DO J=0,10
X=I*0.1
Y=J*0.1
A=F(X,Y)
rest of program statements
END DO
END DO
END PROGRAM Evaluate_function
REAL FUNCTION F (X,Y)
REAL :: X,Y
F = X**2 – 3*X*Y +(SIN(X/(1.+Y**3)))**2
END FUNCTION F
Note that the function is an external function that is placed outside of
PROGRAM Evaluate_function (i.e., it is placed after the END
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Lecture 8
PROGRAM statement). The external function (and its resulting value) can
be used just like a variable name. For example, all of the following a valid
uses:
IF (F(X,Y) .LE. 0.) EXIT
A = 27.3/F(X,Y)**2
PRINT *, F(X,Y)
The arguments in a function subprogram are sometimes called "dummy"
arguments because they are replaced by the values placed in the argument
list when needed by another program. In other words, the necessary values
of all arguments are passed from the main program to the function
subprogram when the function is to be evaluated. The following could
have been used:
REAL FUNCTION F (A,B)
REAL :: A,B
F = A**2 – 3*A*B +(SIN(A/(1.+B**3)))**2
END
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Lecture 8
The general form of a function subprogram is given by
FUNCTION function-name (argument-list)
specification statements (if any)
executatble statements (if any)
function-name = expression
more executable statements (if needed)
END
The FUNCTION statement may also be used to "type" the function:
type-idendifier FUNCTION function-name (argument-list)
The END statement may also be written
END FUNCTION function-name
There must be at least one of the statements function-name = expression in
each functin subprogram. A RETURN statement may be placed anywehre
in the subprogram if program logic dictates that execution should be
returned to the calling program (otherwise this occurs when the END
statement is executed.
Lecture 8
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When execution is passed to a function subprogram (i.e., the function is
"called" to be evaluated), several things are important:
 Arguments of the function subprogram take on the values that are passed
to it from the program from which the function is referenced.
 The list of arguments (in both the program using the function and the
function subprogram) must exactly in type of variable/constant, number
of arguments and order of arguments.
 Execution of the function program continues until the END statement is
reached; or a RETURN statement is reached. The RETURN statement
is an executable statement that may be used to return to the calling
program (before reaching the END statement).
 Variables in a subprogram (except those in the argument list) are general
considered to be local variables, i.e., any assignment of a value to the
variable within the subprogram has no effect outside the subprogram.
These local variables are not available for use outside the subprogram.
 However, variables in the argument list are not generally local and, if the
variable is changed in the subprogram, the new value applies to the
calling program (so these would be called global varialbes). This is
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Lecture 8
because the calling program passes the address of the variable in the
argument list to the function. Note: this is the pre-Fortran 90 rule for
external subprograms. In Fortran 90 where subprograms may be internal
to the main program (see text), variables are considered to be global
unless changed by the INTENT statement.
 The local/global nature of variables in the argument list of a subprogram
may be changed by the INTENT statement. Its general form is
Type-specifier, INTENT(usage-attribute) variable-list
where usage-attribute is either IN, OUT or INOUT.
 IN means the value of a variable in the argument list will not be
altered during execution of the subprogram (the variable is used for
input to the subprogram only). Hence, the variable is considered
INput to the subroutine.
 OUT means the variable is intended to pass values back to the calling
program. Hence, the variable is considered OUTput from the
subroutine back to the calling program
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 INOUT means the variable can be used to pass information both to
and from the subroutine.
In Fortran 90, function subprograms can be made accessible to the main
program in three ways:
1. As an external subprogram (the type we have discussed here). The
function subprogram is placed after the END PROGRAM statement of
the main program.
2. As in internal subprogram. The function subprogram is placed in the
main program just before the END PROGRAM statement and after the
CONTAINS statement. The general form is given by:
PROGRAM Main
main program statements
CONTAINS
subprogram #1
more subprograms as needed
END PROGRAM Main
Lecture 8
3. As a module subprogram. The function subprogram is placed in a
module from which it can be imported into the main program.
Most programmers use external subprograms. See Chapter 6 for a
description of internal and module subprograms.
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