Fortran/Fortran examples

Part of the Fortran WikiBook

The following Fortran code examples or sample programs show different situations depending on the compiler. The first set of examples are for the Fortran II, IV, and 77 compilers. The remaining examples can be compiled and run with any newer standard Fortran compiler (see the end of the main Fortran article for lists of compilers). Most modern Fortran compilers expect a file with a .f or .for extension (for FORTRAN 66 or FORTRAN 77 source, although the FORTRAN 66 dialect may have to be selected specifically with a command-line option) or .f90/.f95 extension (for Fortran 90/95 source, respectively).

FORTRAN II, IV, and 77 compilers

NOTE: Before FORTRAN 90, most FORTRAN compilers enforced fixed-format source code, a carryover from IBM punch cards

• comments must begin with a * or C or ! in column 1
• statement labels must occur in columns 1-5
• continuation lines must have a non-blank character in column 6
• statements must start in column 7
• the line-length may be limited to 72 characters (derived from the 80-byte width of a punch-card, with last 8 characters reserved for (optional) sequence numbers)

If errors are produced when you compile your FORTRAN code, first check the column alignment. Some compilers also offer free form source by using a compiler flag

Area Of a Triangle program

Simple Fortran II program

One data card input

If one of the input values is zero, then the program will end with an error code of "1" in the job control card listing following the execution of the program. Normal output will be one line printed with A, B, C, and AREA. No specific units are stated.

C AREA OF A TRIANGLE - HERON'S FORMULA
C INPUT - CARD READER UNIT 5, INTEGER INPUT
C OUTPUT - LINE PRINTER UNIT 6, REAL OUTPUT
C INPUT ERROR DISPAY ERROR OUTPUT CODE 1 IN JOB CONTROL LISTING
      INTEGER A,B,C
      READ(5,501) A,B,C
  501 FORMAT(3I5)
      IF(A.EQ.0 .OR. B.EQ.0 .OR. C.EQ.0) STOP 1
      S = (A + B + C) / 2.0
      AREA = SQRT( S * (S - A) * (S - B) * (S - C))
      WRITE(6,601) A,B,C,AREA
  601 FORMAT(4H A= ,I5,5H  B= ,I5,5H  C= ,I5,8H  AREA= ,F10.2,12HSQUARE UNITS)
      STOP
      END

Simple Fortran IV program

Multiple data card input

This program has two input checks: one for a blank card to indicate end-of-data, and the other for a zero value within the input data. Either condition causes a message to be printed.

C AREA OF A TRIANGLE - HERON'S FORMULA
C INPUT - CARD READER UNIT 5, INTEGER INPUT, ONE BLANK CARD FOR END-OF-DATA
C OUTPUT - LINE PRINTER UNIT 6, REAL OUTPUT
C INPUT ERROR DISPAY ERROR MESSAGE ON OUTPUT
  501 FORMAT(3I5)
  601 FORMAT(4H A= ,I5,5H  B= ,I5,5H  C= ,I5,8H  AREA= ,F10.2,12HSQUARE UNITS)
  602 FORMAT(10HNORMAL END)
  603 FORMAT(23HINPUT ERROR, ZERO VALUE)
      INTEGER A,B,C
   10 READ(5,501) A,B,C
      IF(A.EQ.0 .AND. B.EQ.0 .AND. C.EQ.0) GO TO 50
      IF(A.EQ.0 .OR.  B.EQ.0 .OR.  C.EQ.0) GO TO 90
      S = (A + B + C) / 2.0
      AREA = SQRT( S * (S - A) * (S - B) * (S - C))
      WRITE(6,601) A,B,C,AREA
      GO TO 10
   50 WRITE(6,602)
      STOP
   90 WRITE(6,603)
      STOP
      END

Simple Fortran 77 program

Multiple data card input

This program has two input checks in the READ statement with the END and ERR parameters, one for a blank card to indicate end-of-data; and the other for zero value along with valid data. In either condition, a message will be printed.

C AREA OF A TRIANGLE - HERON'S FORMULA
C INPUT - CARD READER UNIT 5, INTEGER INPUT, NO BLANK CARD FOR END OF DATA
C OUTPUT - LINE PRINTER UNIT 6, REAL OUTPUT
C INPUT ERROR DISPAYS ERROR MESSAGE ON OUTPUT
  501 FORMAT(3I5)
  601 FORMAT(" A= ",I5,"  B= ",I5,"  C= ",I5,"  AREA= ",F10.2,"SQUARE UNITS")
  602 FORMAT("NORMAL END")
  603 FORMAT("INPUT ERROR OR ZERO VALUE ERROR")
      INTEGER A,B,C
   10 READ(5,501,END=50,ERR=90) A,B,C
      IF(A=0 .OR. B=0 .OR. C=0) GO TO 90
      S = (A + B + C) / 2.0
      AREA = SQRT( S * (S - A) * (S - B) * (S - C))  
      WRITE(6,601) A,B,C,AREA
      GO TO 10
   50 WRITE(6,602)
      STOP
   90 WRITE(6,603)
      STOP
      END

"Retro" FORTRAN IV

A retro example of a FORTRAN IV (later evolved into FORTRAN 66) program deck is available on the IBM 1130 page, including the IBM 1130 DM2 JCL required for compilation and execution. An IBM 1130 emulator is available at IBM 1130.org that will allow the FORTRAN IV program to be compiled and run on a PC.

Hello, World program

In keeping with computing tradition, the first example presented is a simple program to display the words "Hello, world" on the screen (or printer).

FORTRAN 66 (also FORTRAN IV)

 C     FORTRAN IV WAS ONE OF THE FIRST PROGRAMMING
 C     LANGUAGES TO SUPPORT SOURCE COMMENTS
       WRITE (6,7)
     7 FORMAT(13H HELLO, WORLD)
       STOP
       END

This program prints "HELLO, WORLD" to Fortran unit number 6, which on most machines was the line printer or terminal. (The card reader or keyboard was usually connected as unit 5). The number 7 in the WRITE statement refers to the statement number of the corresponding FORMAT statement. FORMAT statements may be placed anywhere in the same program or function/subroutine block as the WRITE statements which reference them. Typically a FORMAT statement is placed immediately following the WRITE statement which invokes it; alternatively, FORMAT statements are grouped together at the end of the program or subprogram block. If execution flows into a FORMAT statement, it is a no-op; thus, the example above has only two executable statements, WRITE and STOP.

The initial 13H in the FORMAT statement in the above example defines a Hollerith constant, here meaning that the 13 characters immediately following are to be taken as a character constant (note that the Hollerith constant is not surrounded by delimiters). (Some compilers also supported character literals enclosed in single quotes, a practice that came to be standard with FORTRAN 77.)

The space immediately following the 13H is a carriage control character, telling the I/O system to advance to a new line on the output. A zero in this position advances two lines (double space), a 1 advances to the top of a new page and + character will not advance to a new line, allowing overprinting.

FORTRAN 77

As of FORTRAN 77, single quotes are used to delimit character literals, and inline character strings may be used instead of references to FORMAT statements. Comment lines may be indicated with either a C or an asterisk (*) in column 1.

      PROGRAM HELLO
*     The PRINT statement is like WRITE,
*     but prints to the standard output unit
        PRINT '(A)', 'Hello, world'
        STOP
      END

Fortran 90

As of Fortran 90, double quotes are allowed in addition to single quotes. An updated version of the Hello, world example (which here makes use of list-directed I/O, supported as of FORTRAN 77) could be written in Fortran 90 as follows:

 program HelloWorld
   write (*,*) 'Hello, world!'   ! This is an inline comment
 end program HelloWorld

Fortran 77 examples

Greatest common divisor

The following introductory example in FORTRAN 77 finds the greatest common divisor for two numbers $A$ and $B$ using a verbatim implementation of Euclid's algorithm.

*     euclid.f (FORTRAN 77)
*     Find greatest common divisor using the Euclidean algorithm
 
      PROGRAM EUCLID
        PRINT *, 'A?'
        READ *, NA
        IF (NA.LE.0) THEN
          PRINT *, 'A must be a positive integer.'
          STOP
        END IF
        PRINT *, 'B?'
        READ *, NB
        IF (NB.LE.0) THEN
          PRINT *, 'B must be a positive integer.'
          STOP
        END IF
        PRINT *, 'The GCD of', NA, ' and', NB, ' is', NGCD(NA, NB), '.'
        STOP
      END
 
      FUNCTION NGCD(NA, NB)
        IA = NA
        IB = NB
    1   IF (IB.NE.0) THEN
          ITEMP = IA
          IA = IB
          IB = MOD(ITEMP, IB)
          GOTO 1
        END IF
        NGCD = IA
        RETURN
      END

The above example is intended to illustrate the following:

• The PRINT and READ statements in the above use '*' as a format, specifying list-directed formatting. List-directed formatting instructs the compiler to make an educated guess about the required input or output format based on the following arguments.
• As the earliest machines running Fortran had restricted character sets, FORTRAN 77 uses abbreviations such as .EQ., .NE., .LT., .GT., .LE., and .GE. to represent the relational operators =, ≠, <, >, ≤, and ≥, respectively.
• This example relies on the implicit typing mechanism to specify the INTEGER types of NA, NB, IA, IB, and ITEMP.
• In the function NGCD(NA, NB), the values of the function arguments NA and NB are copied into the local variables IA and IB respectively. This is necessary as the values of IA and IB are altered within the function. Because argument passing in Fortran functions and subroutines utilize call by reference by default (rather than call by value, as is the default in languages such as C), modifying NA and NB from within the function would effectively have modified the corresponding actual arguments in the main PROGRAM unit which called the function.

The following shows the results of compiling and running the program.

$ g77 -o euclid euclid.f
$ euclid
 A?
24
 B?
36
 The GCD of 24 and 36 is 12.

Complex numbers

The following FORTRAN 77 example prints out the values of $e^{j i \pi / 4}$ (where $j = \sqrt{-1}$) for values of $i = 0, 1, \ldots, 7$.

*     cmplxd.f (FORTRAN 77)
*     Demonstration of COMPLEX numbers
*
*     Prints the values of e ** (j * i * pi / 4) for i = 0, 1, 2, ..., 7
*         where j is the imaginary number sqrt(-1)
 
      PROGRAM CMPLXD
        IMPLICIT COMPLEX(X)
        PARAMETER (PI = 3.141592653589793, XJ = (0, 1))
        DO 1, I = 0, 7
          X = EXP(XJ * I * PI / 4)
          IF (AIMAG(X).LT.0) THEN
            PRINT 2, 'e**(j*', I, '*pi/4) = ', REAL(X), ' - j',-AIMAG(X)
          ELSE
            PRINT 2, 'e**(j*', I, '*pi/4) = ', REAL(X), ' + j', AIMAG(X)
          END IF
    2     FORMAT (A, I1, A, F10.7, A, F9.7)
    1     CONTINUE
        STOP
      END

The above example is intended to illustrate the following:

• The IMPLICIT statement can be used to specify the implicit type of variables based on their initial letter if different from the default implicit typing scheme described above. In this example, this statement specifies that the implicit type of variables beginning with the letter X shall be COMPLEX.
• The PARAMETER statement may be used to specify constants. The second constant in this example (XJ) is given the complex-valued value $0 + j1$, where $j$ is the imaginary unit $\sqrt{-1}$.
• The first number in the DO statement specifies the number of the last statement considered to be within the body of the DO loop. In this example, as neither the END IF nor the FORMAT is a single executable statement, the CONTINUE statement (which does nothing) is used simply in order for there to be some statement to denote as the final statement of the loop.
• EXP() corresponds to the exponential function $e^x$. In FORTRAN 77, this is a generic function, meaning that it accepts arguments of multiple types (such as REAL and, in this example, COMPLEX). In FORTRAN 66, a specific function would have to be called by name depending on the type of the function arguments (for this example, CEXP() for a COMPLEX-valued argument).
• When applied to a COMPLEX-valued argument, REAL() and AIMAG() return the values of the argument's real and imaginary components, respectively.

Incidentally, the output of the above program is as follows (see the article on Euler's formula for the geometric interpretation of these values as eight points spaced evenly about a unit circle in the complex plane).

$ cmplxd
e**(j*0*pi/4) =  1.0000000 + j0.0000000
e**(j*1*pi/4) =  0.7071068 + j0.7071068
e**(j*2*pi/4) =  0.0000000 + j1.0000000
e**(j*3*pi/4) = -0.7071068 + j0.7071068
e**(j*4*pi/4) = -1.0000000 - j0.0000001
e**(j*5*pi/4) = -0.7071066 - j0.7071069
e**(j*6*pi/4) =  0.0000000 - j1.0000000
e**(j*7*pi/4) =  0.7071070 - j0.7071065

Error can be seen occurring in the last decimal place in some of the numbers above, a result of the COMPLEX data type representing its real and imaginary components in single precision. Incidentally, Fortran 90 also made standard a double-precision complex-number data type (although several compilers provided such a type even earlier).

Fortran 90/95 examples

Summations with a DO loop

In this example of Fortran 90 code, the programmer has written the bulk of the code inside of a DO loop. Upon execution, instructions are printed to the screen and a SUM variable is initialized to zero outside the loop. Once the loop begins, it asks the user to input any number. This number is added to the variable SUM every time the loop repeats. If the user inputs 0, the EXIT statement terminates the loop, and the value of SUM is displayed on screen.

Also apparent in this program is a data file. Before the loop begins, the program creates (or opens, if it has already been run before) a text file called "SumData.DAT". During the loop, the WRITE statement stores any user-inputted number in this file, and upon termination of the loop, also saves the answer.

! sum.f90
! Performs summations using in a loop using EXIT statement
! Saves input information and the summation in a data file
 
program summation
implicit none
integer :: sum, a
 
print*, "This program performs summations. Enter 0 to stop."
open(unit=10, file="SumData.DAT")
 
sum = 0
 
do
 print*, "Add:"
 read*, a
 if (a == 0) then
  exit
 else
  sum = sum + a
 end if
 write(10,*) a
end do
 
print*, "Summation =", sum
write(10,*) "Summation =", sum
close(10)
 
end

When executed, the console would display the following:

 This program performs summations.  Enter 0 to stop.
 Add:
1
 Add:
2
 Add: 
3
 Add:
0
 Summation = 6

And the file SumData.DAT would contain:

1
2
3
Summation = 6

Calculating cylinder area

The following program, which calculates the surface area of a cylinder, illustrates free-form source input and other features introduced by Fortran 90.

program cylinder
 
! Calculate the surface area of a cylinder.
!
! Declare variables and constants.
! constants=pi
! variables=radius squared and height
 
  implicit none    ! Require all variables to be explicitly declared
 
  integer :: ierr
  character(1) :: yn
  real :: radius, height, area
  real, parameter :: pi = 3.141592653589793
 
  interactive_loop: do
 
!   Prompt the user for radius and height
!   and read them.
 
    write (*,*) 'Enter radius and height.'
    read (*,*,iostat=ierr) radius,height
 
!   If radius and height could not be read from input,
!   then cycle through the loop.
 
    if (ierr /= 0) then
      write(*,*) 'Error, invalid input.'
      cycle interactive_loop
    end if
 
!   Compute area.  The ** means "raise to a power."
 
    area = 2 * pi * (radius**2 + radius*height)
 
!   Write the input variables (radius, height)
!   and output (area) to the screen.
 
    write (*,'(1x,a7,f6.2,5x,a7,f6.2,5x,a5,f6.2)') &
      'radius=',radius,'height=',height,'area=',area
 
    yn = ' '
    yn_loop: do
      write(*,*) 'Perform another calculation? y[n]'
      read(*,'(a1)') yn
      if (yn=='y' .or. yn=='Y') exit yn_loop
      if (yn=='n' .or. yn=='N' .or. yn==' ') exit interactive_loop
    end do yn_loop
 
  end do interactive_loop
 
end program cylinder

Dynamic memory allocation and arrays

The following program illustrates dynamic memory allocation and array-based operations, two features introduced with Fortran 90. Particularly noteworthy is the absence of DO loops and IF/THEN statements in manipulating the array; mathematical operations are applied to the array as a whole. Also apparent is the use of descriptive variable names and general code formatting that comport with contemporary programming style. This example computes an average over data entered interactively.

program average
 
! Read in some numbers and take the average
! As written, if there are no data points, an average of zero is returned
! While this may not be desired behavior, it keeps this example simple
 
  implicit none
  integer :: number_of_points
  real, dimension(:), allocatable :: points
  real :: average_points=0., positive_average=0., negative_average=0.
 
  write (*,*) "Input number of points to average:"
  read (*,*) number_of_points
 
  allocate (points(number_of_points))
 
  write (*,*) "Enter the points to average:"
  read (*,*) points
 
! Take the average by summing points and dividing by number_of_points
  if (number_of_points > 0) average_points = sum(points)/number_of_points
 
! Now form average over positive and negative points only
  if (count(points > 0.) > 0) positive_average = sum(points, points > 0.) &
        /count(points > 0.)
  if (count(points < 0.) > 0) negative_average = sum(points, points < 0.) &
        /count(points < 0.)
 
  deallocate (points)
 
! Print result to terminal
  write (*,'(''Average = '', 1g12.4)') average_points
  write (*,'(''Average of positive points = '', 1g12.4)') positive_average
  write (*,'(''Average of negative points = '', 1g12.4)') negative_average
 
end program average

Writing functions

Modern Fortran features available for use with procedures, including deferred-shape, protected, and optional arguments, are illustrated in the following example, a function to solve a system of linear equations.

function gauss_sparse(num_iter, tol, b, A, x, actual_iter) result(tol_max)
 
!  This function solves a system of equations (Ax = b) by using the Gauss-Seidel Method
 
   implicit none
 
   real ::  tol_max
 
!  Input: its value cannot be modified from within the function
   integer, intent(in) :: num_iter
   real, intent(in) :: tol
   real, intent(in), dimension(:) :: b, A(:,:)
 
!  Input/Output: its input value is used within the function, and can be modified
   real, intent(inout) :: x(:)
 
!  Output: its value is modified from within the function, only if the argument is required
   integer, optional, intent(out) :: actual_iter
 
!  Locals
   integer :: i, n, iter
   real :: xk
 
!  Initialize values
   n = size(b)  ! Size of array, obtained using size intrinsic function
   tol_max = 2. * tol
   iter = 0
 
!  Compute solution until convergence
   convergence_loop: do while (tol_max >= tol .and. iter < num_iter); iter = iter + 1
 
      tol_max = -1.  ! Reset the tolerance value
 
!     Compute solution for the k-th iteration
      iteration_loop: do i = 1, n
 
!        Compute the current x-value
         xk = (b(i) - dot_product(A(i,:i-1),x(:i-1)) - dot_product(A(i,i+1:n),x(i+1:n))) / A(i, i)
 
!        Compute the error of the solution
!        dot_product(a,v)=a'b
         tol_max = max((abs(x(i) - xk)/(1. + abs(xk))) ** 2, abs(A(i, i) * (x(i) - xk)), tol_max)
         x(i) = xk
      enddo iteration_loop
   enddo convergence_loop
 
   if (present(actual_iter)) actual_iter = iter
 
end function gauss_sparse

Note that an explicit interface to this routine must be available to its caller so that the type signature is known. This is preferably done by placing the function in a MODULE and then USEing the module in the calling routine. An alternative is to use an INTERFACE block, as shown by the following example:

program test_gauss_sparse
    implicit none
 
!   explicit interface to the gauss_sparse function
    interface
        function gauss_sparse(num_iter, tol, b, A, x, actual_iter) result(tol_max)
           real ::  tol_max
           integer, intent(in) :: num_iter
           real, intent(in) :: tol
           real, intent(in), dimension(:) :: b, A(:,:)
           real, intent(inout) :: x(:)
           integer, optional, intent(out) :: actual_iter
        end function
    end interface
 
!   declare variables
    integer :: i, N = 3, actual_iter
    real :: residue
    real, allocatable :: A(:,:), x(:), b(:)
 
!   allocate arrays
    allocate (A(N, N), b(N), x(N))
 
!   Initialize matrix
    A = reshape([(real(i), i = 1, size(A))], shape(A))
 
!   Make matrix diagonally dominant
    do i = 1, size(A, 1)
        A(i,i) = sum(A(i,:)) + 1
    enddo
 
!   Initialize b
    b = [(i, i = 1, size(b))]
 
!   Initial (guess) solution
    x = b
 
!   invoke the gauss_sparse function 
    residue = gauss_sparse(num_iter = 100, &
                           tol = 1E-5, &
                           b = b, &
                           A = a, &
                           x = x, &
                           actual_iter = actual_iter)
 
!   Output
    print '(/ "A = ")'
    do i = 1, size(A, 1)
        print '(100f6.1)', A(i,:)
    enddo
 
    print '(/ "b = " / (f6.1))', b
 
    print '(/ "residue = ", g10.3 / "iterations = ", i0 / "solution = "/ (11x, g10.3))', &
        residue, actual_iter, x
 
end program test_gauss_sparse

Writing subroutines

In those cases where it is desired to return values via a procedure's arguments, a subroutine is preferred over a function; this is illustrated by the following subroutine to swap the contents of two arrays:

subroutine swap_real(a1, a2)
 
   implicit none
 
!  Input/Output
   real, intent(inout) :: a1(:), a2(:)
 
!  Locals
   integer :: i
   real :: a
 
!  Swap
   do i = 1, min(size(a1), size(a2))
      a = a1(i)
      a1(i) = a2(i)
      a2(i) = a
   enddo
 
end subroutine swap_real

As in the previous example, an explicit interface to this routine must be available to its caller so that the type signature is known. As before, this is preferably done by placing the function in a MODULE and then USEing the module in the calling routine. An alternative is to use a INTERFACE block.

Internal and Elemental Procedures

An alternative way to write the swap_real subroutine from the previous example, is:

subroutine swap_real(a1, a2)
 
   implicit none
 
!  Input/Output
   real, intent(inout) :: a1(:), a2(:)
 
!  Locals
   integer :: N
 
!  Swap, using the internal subroutine
   N = min(size(a1), size(a2))
   call swap_e(a1(:N), a2(:N))
 
 contains
   elemental subroutine swap_e(a1, a2)
      real, intent(inout) :: a1, a2
      real :: a
      a = a1
      a1 = a2
      a2 = a
   end subroutine swap_e
end subroutine swap_real

In the example, the swap_e subroutine is elemental, i.e., it acts upon its array arguments, on an element-by-element basis. Elemental procedures must be pure (i.e., they must have no side effects and can invoke only pure procedures), and all the arguments must be scalar. Since swap_e is internal to the swap_real subroutine, no other program unit can invoke it.

The following program serves as a test for any of the two swap_real subroutines presented:

program test_swap_real
    implicit none
 
!   explicit interface to the swap_real subroutine
    interface
        subroutine swap_real(a1, a2)
            real, intent(inout) :: a1(:), a2(:)
        end subroutine swap_real
    end interface
 
!   Declare variables
    integer :: i
    real :: a(10), b(10)
 
!   Initialize a, b
    a = [(real(i), i = 1, 20, 2)]
    b = a + 1
 
!   Output before swap
    print '(/"before swap:")'
    print '("a = [", 10f6.1, "]")', a
    print '("b = [", 10f6.1, "]")', b
 
!   Call the swap_real subroutine
    call swap_real(a, b)
 
!   Output after swap
    print '(// "after swap:")'
    print '("a = [", 10f6.1, "]")', a
    print '("b = [", 10f6.1, "]")', b
 
end program test_swap_real

Pointers and targets methods

In Fortran, the concept of pointers differs from that in C-like languages. A Fortran 90 pointer does not merely store the memory address of a target variable; it also contains additional descriptive information such as the target's rank, the upper and lower bounds of each dimension, and even strides through memory. This allows a Fortran 90 pointer to point at submatrices.

Fortran 90 pointers are "associated" with well-defined "target" variables, via either the pointer assignment operator (=>) or an ALLOCATE statement. When appearing in expressions, pointers are always dereferenced; no "pointer arithmetic" is possible.

The following example illustrates the concept:

module SomeModule
   implicit none
 contains
    elemental function A(x) result(res)
        integer :: res
        integer, intent(IN) :: x
        res = x + 1
    end function
end module SomeModule
 
program Test
   use SomeModule, DoSomething => A
   implicit none
 
   !Declare variables
   integer, parameter :: m = 3, n = 3
   integer, pointer :: p(:)=>null(), q(:,:)=>null()
   integer, allocatable, target :: A(:,:)
   integer :: istat = 0, i, j
   character(80) :: fmt
 
!  Write format string for matrices
!  (/ A / A, " = [", 3( "[",3(i2, 1x), "]" / 5x), "]" )
   write (fmt, '("(/ A / A, "" = ["", ", i0, "( ""["",", i0, "(i2, 1x), ""]"" / 5x), ""]"" )")') m, n
 
   allocate(A(m, n), q(m, n), stat = istat)
   if (istat /= 0) stop 'Error during allocation of A and q'
 
!  Matrix A is:
!  A = [[ 1  4  7 ]
!       [ 2  5  8 ]
!       [ 3  6  9 ]
!       ]
   A = reshape([(i, i = 1, size(A))], shape(A))
   q = A
 
   write(*, fmt) "Matrix A is:", "A", ((A(i, j), j = 1, size(A, 2)), i = 1, size(A, 1))
 
!  p will be associated with the first column of A
   p => A(:, 1)
 
!  This operation on p has a direct effect on matrix A
   p = p ** 2
 
!  This will end the association between p and the first column of A
   nullify(p)
 
!  Matrix A becomes:
!  A = [[ 1  4  7 ]
!       [ 4  5  8 ]
!       [ 9  6  9 ]
!       ]
   write(*, fmt) "Matrix A becomes:", "A", ((A(i, j), j = 1, size(A, 2)), i = 1, size(A, 1))
 
!  Perform some array operation
   q = q + A
 
!  Matrix q becomes:
!  q = [[ 2  8 14 ]
!       [ 6 10 16 ]
!       [12 12 18 ]
!       ]
   write(*, fmt) "Matrix q becomes:", "q", ((q(i, j), j = 1, size(A, 2)), i = 1, size(A, 1))
 
!  Use p as an ordinary array
   allocate (p(1:m*n), stat = istat)
   if (istat /= 0) stop 'Error during allocation of p'
 
!  Perform some array operation
   p = reshape(DoSomething(A + A ** 2), shape(p))
 
!  Array operation:
!      p(1) = 3
!      p(2) = 21
!      p(3) = 91
!      p(4) = 21
!      p(5) = 31
!      p(6) = 43
!      p(7) = 57
!      p(8) = 73
!      p(9) = 91
   write(*, '("Array operation:" / (4x,"p(",i0,") = ",i0))') (i, p(i), i = 1, size(p))
 
   deallocate(A, p, q, stat = istat)
   if (istat /= 0) stop 'Error during deallocation'
 
end program Test

Module programming

A module is a program unit which contains data definitions, global data, and CONTAINed procedures. Unlike a simple INCLUDE file, a module is an independent program unit that can be compiled separately and linked in its binary form. Once compiled, a module's public contents can be made visible to a calling routine via the USE statement.

The module mechanism makes the explicit interface of procedures easily available to calling routines. In fact, modern Fortran encourages every SUBROUTINE and FUNCTION to be CONTAINed in a MODULE. This allows the programmer to use the newer argument passing options and allows the compiler to perform full type checking on the interface.

The following example also illustrates derived types, overloading of operators and generic procedures.

module GlobalModule
 
!  Reference to a pair of procedures included in a previously compiled
!  module named PortabilityLibrary
   use PortabilityLibrary, only: GetLastError, &  ! Generic procedure
                                 Date             ! Specific procedure
!  Constants
   integer, parameter :: dp_k = kind (1.0d0)      ! Double precision kind
   real, parameter :: zero = (0.)
   real(dp_k), parameter :: pi = 3.141592653589793_dp_k
 
!  Variables
   integer :: n, m, retint
   logical :: status, retlog
   character(50) :: AppName
 
!  Arrays
   real, allocatable, dimension(:,:,:) :: a, b, c, d
   complex(dp_k), allocatable, dimension(:) :: z
 
!  Derived type definitions
   type ijk
      integer :: i
      integer :: j
      integer :: k
   end type ijk
 
   type matrix
     integer m, n
     real, allocatable :: a(:,:)  ! Fortran 2003 feature. For Fortran 95, use the pointer attribute instead
   end type matrix
 
!  All the variables and procedures from this module can be accessed
!  by other program units, except for AppName
   public
   private :: AppName
 
!  Generic procedure swap
   interface swap
      module procedure swap_integer, swap_real
   end interface swap
 
   interface GetLastError  ! This adds a new, additional procedure to the
                           ! generic procedure GetLastError
      module procedure GetLastError_GlobalModule
   end interface GetLastError
 
!  Operator overloading
   interface operator(+)
      module procedure add_ijk
   end interface
 
!  Prototype for external procedure
   interface
      function gauss_sparse(num_iter, tol, b, A, x, actual_iter) result(tol_max)
         real ::  tol_max
         integer, intent(in) :: num_iter
         real, intent(in) :: tol
         real, intent(in), dimension(:) :: b, A(:,:)
         real, intent(inout) :: x(:)
         integer, optional, intent(out) :: actual_iter
      end function gauss_sparse
   end interface
 
!  Procedures included in the module
   contains
 
!  Internal function
   function add_ijk(ijk_1, ijk_2)
     type(ijk) add_ijk, ijk_1, ijk_2
     intent(in) :: ijk_1, ijk_2
     add_ijk = ijk(ijk_1%i + ijk_2%i, ijk_1%j + ijk_2%j, ijk_1%k + ijk_2%k)
   end function add_ijk
 
!  Include external files
   include 'swap_integer.f90' ! Comments SHOULDN'T be added on include lines
   include 'swap_real.f90'
end module GlobalModule