# Introduction to F

Fortran was introduced in 1957 and remains the language of choice for most scientific programming. Some of the most important features of Fortran 90 include recursive subroutines, dynamic storage allocation and pointers, user defined data structures, modules, and the ability to manipulate entire arrays.

Fortran 90 is compatible with Fortran 77 and includes syntax that is no longer desirable. F is a subset of Fortran 90 that includes only its modern features and is compact and easy to learn.

The simplest way to use the F subset of Fortran is to use the option -std=F with the g95 compiler: g95 -std=F ProductExample.f95

### 1. Introduction

An example of a simple F program.
```program ProductExample
real :: m, a, force
m = 2.0                       ! mass in kilograms
a = 4.0                       ! acceleration in mks units
force = m*a                   ! force in newtons
print *, force
end program ProductExample
```
The features of F in Program ProductExample include the following:
• The first statement must be a program statement; the last statement must have a corresponding end program statement.
• The types of all variables must be declared.
• The names of all variables must be between 1 and 31 alphanumeric characters of which the first must be a letter and the last cannot be an underscore.
• Real numbers are written as 2.0 rather than 2.
• The case is significant, but two names that differ only in the case of one or more letters cannot be used together. All keywords (words that are part of the language and cannot be redefined.) are written in lower case. Some names such as product are reserved and cannot be used as names.
• Comments begin with a ! and can be included anywhere in the program.
• Statements may contain up to 132 characters.
• The asterisk (*) following print is the default format.

We next introduce syntax that allows the user to enter the desired values of m and a from the keyboard. Note the use of the (unformatted) read statement and how character strings are printed.

```program ReadInput
real :: m, a, force
! SI units
print *, "mass m = ?"
read *, m
print *, "acceleration a = ?"
read *, a
force = m*a
print *, "force (in newtons) =", force
end program ReadInput
```

### 2. Do construct

An example of the do construct to execute the same statements more than once:
```program Series
real :: sumOfSeries       ! sum is a keyword
integer :: n
sumOfSeries = 0.0
! add first 100 terms
do n = 1, 100
sumOfSeries = sumOfSeries + 1.0/real(n)**2       ! real is example of intrinsic funcion
print *, n,sumOfSeries
end do
end program Series
```
Note that n is an integer variable. In this example the do statement specifies the first and last values of n; n increases by unity (default). The block of statements inside a loop is indented for clarity.

Because the product n*n is done using integer arithmetic, it is better to convert n to a real variable before the multiplication is done. Exponentiation is done using the operator **.

### 3. If construct

The do loop can be exited by satisfying a test.
```program SeriesTest
! illustrate use of do construct
integer :: n
! choose large value for relative change
real :: sumOfSeries, newterm, relativeChange
n = 0
sumOfSeries = 0.0
do
n = n + 1
newterm = 1.0/(n*n)
sumOfSeries = sumOfSeries + newterm
relativeChange = newterm/sumOfSeries
if (relativeChange < 0.0001) then
exit
end if
print *, n, relativeChange, sumOfSeries
end do
end program SeriesTest
```
The features included in program SeriesTest include:
• A do construct can be exited by using the exit statement.
• The if construct allows the execution of a sequence of statements (a block) to depend on a condition. The if construct is a compound statement and begins with if ... then and ends with end if. The block inside the if construct is indented for clarity. Examples of more general if constructs using else and else if statements are given in Program Factorial.
relation operator
less than <
less than or equal <=
equal ==
not equal /=
greater than >
greater than or equal >=
Table 1. Summary of relational operators.

The following program illustrates the use of the kind parameter and a named do construct:

```program SeriesDouble
! illustrate use of kind parameter and named do loop
integer, parameter :: double = 8     ! use for double precision
integer :: n
real (kind = double) :: sumOfSeries, newterm, relativeChange
n = 0
sumOfSeries = 0.0
printChange: do
n = n + 1
newterm = 1.0/real(n, kind = double)**2
sumOfSeries = sumOfSeries + newterm
relativeChange = newterm/sumOfSeries
if (relativeChange < 0.0001) then
exit printChange
end if
print *, n,relativeChange,sumOfSeries
end do printChange
end program SeriesDouble
```

A more general use of the parameter statement is given in Program drag.

• The do and end do statements must either have the same name or both be unnamed. In general, the named do construct is named to make explicit which do construct is exited for the case of nested do constructs. The use of a named do construct in program SeriesDouble is unnecessary and is for illustrative purposes only.

### 4. Subprograms

Subprograms are called from the main program or other subprograms. As an example, the following program adds and multiplies two numbers that are inputed from the keyboard. The variables x and y are public and are available to the main program.

```module common
public :: initial, add, multiply      ! subroutines
integer, parameter, public :: double = 8
real (kind = double), public :: x,y

contains

subroutine initial()
print *, "x = ?"
read *,x
print *, "y = ?"
read *,y
end subroutine initial

subroutine add(sum2)
real (kind = double), intent (in out) :: sum2
sum2 = x + y
end subroutine add

subroutine multiply(product2)
real (kind = double), intent (in out) :: product2
product2 = x*y
end subroutine multiply

end module common

program tasks            ! illustrate use of module and subroutines
! note how variables are passed
use common
real (kind = double) :: sum2, product2
call initial()                 ! initialize variables
call add(sum2)                 ! add two variables
call multiply(product2)
print *, "sum =", sum2, "product =", product2
end program tasks
```
• Subprograms (subroutines and functions) are contained in modules. The form of a module, subroutine, and a function is similar to that of a main program.
• A module is accessed in the main program by the use statement.
• Subroutines are invoked in the main program by using the call statement.
• A subprogram always has access to other entities in the module.
• The subprograms in a module are preceded by a contains statement.
• Variables and subprograms may be declared public in a module and be available to the main program (and other modules).
• Information can also be passed as an argument to each subprogram as are the variables sum2 and product2. A open parenthesis () is needed even if there are no arguments. The intent of each dummy argument of a program must be indicated.
• intent in means that the dummy argument cannot be changed within the subprogram.
• intent out means that the dummy argument cannot be used within the subprogram until it is given a value with the intent of passing a value back to the calling program.
• intent in out means that the dummy argument has an initial value which is changed and passed back to the calling program. (It also is correct to write inout.)
• The module(s) can be a separate file.

### 5. Formatted output

The structure of Program cool is similar to Program tasks. Note the use of the modulo function and the use of format specifications. We have used a format specification, which is a list of edit descriptors. An example from Program cool is

```print "(t7,a,t16,a,t28,a)", "time","T_coffee","T_coffee - T_room"
```
The t (tab) edit descriptor is used to skip to a specified position on an output line. The edit descriptor a (alphanumeric) is for character strings. An example of the f (floating point) descriptor is given by
```print "(f10.2,2f13.4)",t,T_coffee,T_coffee - T_room
```
The edit descriptor f13.4 means that a total of thirteen positions are reserved for printing a real value rounded to 4 places after the decimal point. (The decimal point and a minus sign occupy two of the thirteen positions.) The edit descriptor 2f13.4 means that the edit descriptor f13.4 is used twice. Another common edit descriptor is i (integer).

Comment on Program drag

The only new syntax in Program drag is the use of the parameter statement:

```real (kind = double), public, parameter :: g = 9.8
```
A parameter is a named constant. The value of a parameter is fixed by its declaration and cannot be changed during the execution of a program.

### 6. Files

Program saveData illustrates how to open a new file, write data in a file, close a file, and read data from an existing file.

```program saveData
! illustrate writing and reading file
integer :: i,j,x
character(len = 32) :: file_name
print *, "name of file?"
read *, file_name
open (unit=5,file=file_name,action="write",status="new")
do i = 1,4
x = i*i
write (unit=5,fmt=*) i,x
end do
close(unit=5)
! open(unit=1,file=file_name,action="read",status="old")
open(unit=1,file=file_name,position="rewind",action="read",status="old")
do i = 1,4
read (unit=1,fmt = *) j,x
print *, j,x
end do
close(unit=1)
end program saveData
```

Input/output statements refer to a particular file by specifying its unit. The read and write statements do not refer to a file directly, but refer to a file number which must be connected to a file. There are many variations on the open statement, but the above example is typical. The values of the action specifier are read, write, and readwrite (default). Values for status are old, new, replace, or scratch.

If you plan to reuse data on the same system with the same compiler, you can use unformatted input/output to save the overhead, extra space, and the roundoff error associated with the conversion of the internal representation of a value to its external representation. Of course, the latter is machine and compiler dependent. Unformatted access is very useful when data is generated by one program and then analyzed by a separate program on the same computer. To generate unformatted files, omit the format specification. Examples of programs which use direct access and records are available.

### 7. Arrays

The definition and use of arrays is illustrated in Program vector.

```module common
public :: initial,cross
contains

subroutine initial(a,b)
real, dimension (:), intent(out) :: a,b
a(1:3) = (/ 2.0, -3.0, -4.0 /)
b(1:3) = (/ 6.0, 5.0, 1.0 /)
end subroutine initial

subroutine cross(r,s)
real, dimension (:), intent(in) :: r,s
real, dimension (3) :: cross_product
! note use of dummy variables
integer :: component,i,j
do component = 1,3
i = modulo(component,3) + 1
j = modulo(i,3) + 1
cross_product(component) = r(i)*s(j) - s(i)*r(j)
end do
print *, ""     ! skip line
print *, "three components of the vector product:"
print "(a,t10,a,t16,a)", "x","y","z"
print *, cross_product
end subroutine cross

end module common

program vector            ! illustrate use of arrays
use common
real, dimension (3) :: a,b
real :: dot
call initial(a,b)
dot = dot_product(a,b)
print *, "dot product = ", dot
call cross(a,b)
end program vector
```
The main features of arrays include: An array is declared in the declaration section of a program, module, or procedure using the dimension attribute. Examples include

real, dimension (10) :: x,y
integer, dimension (-10:10) :: prob
integer, dimension (10,10) :: spin ! example of two-dimensional array
• The default value of the lower bound of an array is 1. The lower bound of an array can be negative.
• Rather than assigning each array element explicitly, we can use an array constructor to give an array a set of values. An array constructor is a one-dimensional a list of values, separated by commas, and delimited by "(/" and "/)". An example is
```a(1:3) = (/ 2.0, -3.0, -4.0 /)
```
is equivalent to the separate assignments
```a(1) = 2.0
a(2) = -3.0
a(3) = -4.0
```
• Note that the array cross_product can be referenced by a single statement:
```print *, cross_product
```

Fortran 90 has many vector and matrix multiplication functions. For example, the function dot_function operates on two vectors and returns their scalar product. Some useful array reduction functions are maxval, minval, product, and sum.

### 8. Allocate statement

The size of an array can be changed during the execution of the program. The use of the allocate and deallocate statements are illustrated in the following. Note the use of the implied do loop.

```program dynamicArray
! example of dynamic arrays
real, dimension (:), allocatable :: x
integer :: i, N
N = 2
allocate(x(N:2*N))
! implied do loop
x(N:2*N) = (/ (i*i, i = N, 2*N) /)
print *, x
deallocate(x)
allocate(x(N:3*N))
x = (/ (i*i, i = N, 3*N) /)
print *, x
end program dynamicArray
```
An example of passing arrays:
```module param
integer, public, parameter :: double = 8
end module param

module common
use param
private
public :: initial
integer, public :: N
contains

subroutine initial(x)
real (kind = double), intent(inout), dimension(:) :: x
N = 100
x(1) = 1.0
end subroutine initial
end module common

program test
use param
use common
real (kind = double), allocatable,dimension (:) :: x
N = 10
allocate(x(N))
call initial(x)
end program test
```

### 9. Random number sequences

A convenient intrinsic procedure is subroutine random_number. Although it is a good idea to write your own random number generator using an algorithm that you have tested on a particular problem of interest, it is convenient to use subroutine random_number when you are debugging your program or if accuracy is not important. The following program illustrates several uses of subroutine random_number and random_seed. Note that the argument rnd of random_number must be real, has intent out, and can be either a scalar or an array.

```program randomExample
real :: rnd
real, dimension (:), allocatable :: x
integer, dimension (:), allocatable:: seed, seed_present
integer :: L, i, m, nmin, nmax, randomInteger
! generate random integers between nmin and nmax
! dimension of seed is one in F and two in Fortran 90
call random_seed()        ! initialize random number generator
call random_number(rnd)   ! generate random number
print *, "random number = ", rnd
call random_seed(size=m)      ! random_seed in gfortran requires m integers to start
print *,"# seeds needed = ", m
allocate(seed(m))
! put is integer vector that puts the desired seeds into random number generator
do i = 1,m
seed(i) = 12345 + i
end do
call random_seed(put=seed)    ! assign seeds
! get is integer vector which reads present seeds
allocate(seed_present(m))
call random_seed(get=seed_present)         ! confirm seeds
print *, "seeds = ", seed_present
call random_number(rnd)
call random_seed(get=seed_present)
print *, "new seeds = ", seed_present      ! confirm value of new seed
! generate L random integers between nmin and nmax
L = 10         ! length of sequence
nmin = 5
nmax = 15
do i = 1, L
call random_number(rnd)
randomInteger = (nmax - nmin + 1)*rnd + nmin
print *, "random integer = ", randomInteger
end do
allocate(x(L))         ! assign random numbers to array x
call random_number(x)
print "(4f13.6)", x
call random_seed(get=seed_present)
! find new seed so can start program from where the program stopped
print *, "new seed = ", seed_present
end program randomExample
```
Note how subroutine random_seed is used to specify the seed. This specification is useful when the same random number sequence is used to test a program.

### 10. Recursion

A simple example of a recursive definition is the factorial function:

factorial(n) = n! = n(n-1)(n-2) ... 1
A recursive definition of the factorial is
factorial(1) = 1 factorial(n) = n factorial(n-1)

A program that closely parallels the above definition follows. Note how the word recursive is used.

```module fact

public :: f
contains

recursive function f(n) result (factorial_result)
integer, intent (in) :: n
integer :: factorial_result

if (n <= 1) then
factorial_result = 1
else
factorial_result = n*f(n-1)
end if
end function f

end module fact

program test_factorial
use fact
integer :: n
print *, "integer n?"
read *, n
print "(i4, a, i10)", n, "! = ", f(n)
end program test_factorial
```

A more detailed example (taken from pp. 98-99 in The Fun of Computing,John G. Kemeny, True BASIC (1990)) is given two integers, n and m, what is their greatest common divisor, that is, the largest integer that divides both? For example, if n = 1000 and m = 32, than the greatest common divisor (gcd) is gcd = 8.

One method for finding gcd is to integer divide n by m. We write n = q m + r, where q is the quotient and r is the remainder. If r = 0, then m divides n and m is the gcd. Otherwise, any divisor of m and r also divides n, and hence gcd(n,m) = gcd(m,r). Because r < m, we have made progress. As an example, take n = 1024 and m = 24. Then q = 42 and r = 16. So we want gcd(24,16). Now q = 1 and r = 8 and we calculate gcd(16,8). Finally q = 2, and r = 0 so gcd = 8. The following program implements this idea.

```module gcd_def

public :: gcd
contains

recursive function gcd(n,m) result (gcd_result)
integer, intent (in) :: n,m
integer :: gcd_result
integer :: remainder

remainder = modulo(n,m)
if (remainder == 0) then
gcd_result = m
else
gcd_result = gcd(m,remainder)
end if
end function gcd

end module gcd_def

program greatest
use gcd_def

integer :: n,m
print *, "enter two integers n, m"
read *, n,m
print "(a,i6,a,i6,a ,i6)", "gcd of",n," and",m,"=",gcd(n,m)
end program greatest
```

The volume of a d-dimensional hypersphere of unit radius can be related to the area of a (d - 1)-dimensional hypersphere. The following program uses a recursive subroutine to integrate numerically a d-dimensional hypersphere:

```module common
public :: initialize,integrate

integer, parameter, public :: double = 8
real (kind = double), parameter, public :: zero = 0.0
real (kind = double), public :: h, volume
integer, public :: d

contains

subroutine initialize()
print *, "dimension d?"
read *, d                         ! spatial dimension
print *, "integration interval h?"
read *, h
volume = 0.0
end subroutine initialize

recursive subroutine integrate(lower_r2, remaining_d)
! lower_r2 is contribution to r^2 from lower dimensions
real(kind = double),intent (in) :: lower_r2
integer, intent (in) :: remaining_d  ! # dimensions to integrate
real (kind = double) :: x
x = 0.5*h   ! mid-point approximation
if (remaining_d > 1) then
lower_d: do
call integrate(lower_r2 + x**2, remaining_d - 1)
x = x + h
if (x > 1) then
exit lower_d
end if
end do lower_d
else
last_d: do
if (x**2 + lower_r2 <= 1) then
volume = volume + h**(d - 1)*(1 - lower_r2 - x**2)**0.5
end if
x = x + h
if (x > 1) then
exit last_d
end if
end do last_d
end if
end subroutine integrate

end module common

program hypersphere
! original program by Jon Goldstein
use common
call initialize()
call integrate(zero, d - 1)
volume = (2**d)*volume         ! only consider positive octant
print *, volume
end program hypersphere
```

### 11. Character variables

The only intrinsic operator for character expressions is the concatenation operator //. For example, the concatenation of the character constants string and beans is written as

"string"//"beans"
The result, stringbeans, may be assigned to a character variable.

A useful example of concatenation is given in the following:

```program write_files
! open n files and write data
integer :: i,n
character(len = 15) :: file_name
n = 11
do i = 1,n
! assign number.dat to file_name using write statement
write(unit=file_name,fmt="(i2.2,a)") i,".dat"
! // is concatenation operator
file_name = "config"//file_name
open (unit=1,file=file_name,action="write",status="replace")
write (unit=1, fmt=*) i*i,file_name
close(unit=1)
end do
end program write_files
```
Note the use of the write statement to build a character string for numeric and character components.

### 12. Complex variables

Fortran 90 is well suited for treating complex variables. The following program illustrates the way complex variables are defined and used.

```program complexExample
integer, parameter :: double = 8
real (kind = double), parameter :: pi = 3.141592654
complex (kind = double) :: b,bstar,f,arg
real (kind = double) :: c
complex :: a
integer :: d
! A complex constant is written as two real numbers, separated by
! a comma and enclosed in parentheses.
a = (2,-3)
! Both components must have same kind
b = (0.5_double,0.8_double)
print *, "a =", a      ! note that a has less precision than b
print *, "a*a =", a*a
print *, "b =", b
print *, "a*b =", a*b
c = real(b)           ! real part of b
print *, "real part of b =", c
c = aimag(b)      ! imaginary part of b
print *, "imaginary part of b =", c
d = int(a)
print *, "real part of a (converted to integer) =", d
arg = cmplx(0.0,pi)
b = exp(arg)       ! done in two lines for ease of reading only
bstar = conjg(b)    ! complex conjugate of b
f = abs(b)       ! absolute value of b
print *, "properties of b =", b,bstar,b*bstar,f
end program complexExample
```

### 13. References and Links

Walter S. Brainerd, Charles H. Goldberg, and Jeanne C. Adams, Programmer's Guide to F, Unicomp (1996).

Michael Metcalf and John Reid, The F Programming Language, Oxford University Press (1996).

13. Links

## Acknowledgements

Program save_data was modified by Ty Faechner, 18 June 2003.

Please send comments and corrections to Harvey Gould, hgould@clarku.edu.

Updated 12 March 2013

© 2013 Harvey Gould.