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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 (http://en.wikipedia.org/wiki/Punch_card)
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 (http://en.wikipedia.org/wiki/Free-form_language) 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)STOP1
S =(A + B + C)/2.0
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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
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-
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
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)GOTO50
IF(A.EQ.0 .OR. B.EQ.0 .OR. C.EQ.0)GOTO90
S =(A + B + C)/2.0
AREA =SQRT( S *(S - A)*(S - B)*(S - C))
WRITE(6,601) A,B,C,AREA GOTO10
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 D
C OUTPUT - LINE PRINTER UNIT 6, REAL OUTPUT
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C INPUT ERROR DISPAYS ERROR MESSAGE ON OUTPUT
501 FORMAT(3I5)
601 FORMAT(" A= ",I5," B= ",I5," C= ",I5," AREA= ",F10.2,"SQUARE U
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)GOTO90
S =(A + B + C)/2.0
AREA =SQRT( S *(S - A)*(S - B)*(S - C))
WRITE(6,601) A,B,C,AREA
GOTO10
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 (http://ibm1130.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
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PROGRAM EUCLID
PRINT *, 'A?'
READ *, NA
IF(NA.LE.0)THEN
PRINT *, 'A must be a positive integer.'
STOP
ENDIF
PRINT *, 'B?'
READ *, NB
IF(NB.LE.0)THEN
PRINT *, 'B must be a positive integer.'
STOP
ENDIF
PRINT *, 'The GCD of', NA, ' and', NB, ' is', NGCD(NA, NB), '.'
STOP
END
FUNCTION NGCD(NA, NB)
IA = NAIB = NB
1 IF(IB.NE.0)THEN
ITEMP = IA
IA = IB
IB =MOD(ITEMP, IB)
GOTO1
ENDIF
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 ofNA, 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 ofIA 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.
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EXP() corresponds to the exponential function ex. 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 geometricinterpretation 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 - j1.0000000e**(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
implicitnone
integer:: sum, a
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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
endif
write(10,*) a
enddo
print*, "Summation =", sum
write(10,*)"Summation =", sumclose(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
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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
implicitnone ! 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)thenwrite(*,*)'Error, invalid input.'
cycle interactive_loop
endif
! 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
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enddo yn_loop
enddo interactive_loop
endprogram 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 ofDO 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 return
! While this may not be desired behavior, it keeps this example simple
implicitnone
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_point
! 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_aver
write (*,'(''Average of negative points = '', 1g12.4)') negative_aver
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! dot_product(a,v)=a'b
tol_max =max((abs(x(i)- xk)/(1. +abs(xk)))**2, abs(A(i, i)
x(i)= xk
enddo iteration_loop
enddo convergence_loop
if(present(actual_iter)) actual_iter = iter
endfunction 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
implicitnone
! explicit interface to the gauss_sparse function
interface
function gauss_sparse(num_iter, tol, b, A, x, actual_iter)resu
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
endfunction
endinterface
! 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))]
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! 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 = "
residue, actual_iter, x
endprogram 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:
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subroutine swap_real(a1, a2)
implicitnone
! 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
endsubroutine 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)
implicitnone
! 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
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a1 = a2
a2 = a
endsubroutine swap_e
endsubroutine 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
implicitnone
! explicit interface to the swap_real subroutine
interface
subroutine swap_real(a1, a2)
real, intent(inout):: a1(:), a2(:)
endsubroutine swap_real
endinterface
! 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 swapprint '(// "after swap:")'
print '("a = [", 10f6.1, "]")', a
print '("b = [", 10f6.1, "]")', b
endprogram test_swap_real
Pointers and targets methods
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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
implicitnone
contains
elemental function A(x)result(res)
integer:: res
integer, intent(IN):: x
res = x +1
endfunctionendmodule SomeModule
program Test
use SomeModule, DoSomething => A
implicitnone
!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),
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
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! 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))
! 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))
! 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),
deallocate(A, p, q, stat = istat)
if(istat /=0)stop'Error during deallocation'
endprogram Test
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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'spublic 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 ki
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
endtype ijk
type matrix
integer m, n
real, allocatable:: a(:,:) ! Fortran 2003 feature. For Fortran 9
endtype matrix
! All the variables and procedures from this module can be accessed
! by other program units, except for AppName
public
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private:: AppName
! Generic procedure swap
interface swap
moduleprocedure swap_integer, swap_real
endinterface swap
interface GetLastError ! This adds a new, additional procedure to t
! generic procedure GetLastError
moduleprocedure GetLastError_GlobalModule
endinterface GetLastError
! Operator overloading
interfaceoperator(+)
moduleprocedure add_ijk
endinterface
! Prototype for external procedure
interface function gauss_sparse(num_iter, tol, b, A, x, actual_iter)result(
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
endfunction gauss_sparse
endinterface
! 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_
endfunction add_ijk
! Include external files
include 'swap_integer.f90'! Comments SHOULDN'T be added on include
include 'swap_real.f90'
endmodule GlobalModule
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an/Fortran examples - Wikibooks, open books for an open world http://en.wikibooks.org/wiki/Fortran/Fortran_