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Fortran

The current, editable version of this book is available in Wikibooks, the open-content textbooks collection, at
https://en.wikibooks.org/wiki/Fortran

Permission is granted to copy, distribute, and/or modify this document under the terms of the Creative Commons Attribution-ShareAlike 3.0 License.


Why learn Fortran?

A 2020 supercomputer model of ocean velocity and sea surface temperature, generated with Fortran code. Fortran remains widely used for scientific programming, among other fields.

Fortran is a general purpose programming language mainly used by the scientific community. It is fast, portable and it has seamless handling of arrays and parallelism. It is one of the earliest high level programming languages, and many recognize the original versions which used punched cards to encode the programs. Its name is a contraction of FORmula TRANslation (old versions of the language are typically stylized as FORTRAN) and its creation marked the representation of mathematical expressions with more ease than lower level assembly language. It is still widely used today in numerical weather prediction, physical and chemical modelling, applied mathematics, and other high performance computing purposes. Fortran has a rich array of mathematical libraries and scientific codebases available. The newer standards continuously add modern functionality and are fully backward compatible.

This book is intended to help write code modern Fortran. Where appropriate the differences in usage between legacy versions and the modern standard will be highlighted as there is a significant code base written in older versions, especially FORTRAN 77.

When are other languages better?[edit | edit source]

Fortran is a very verbose, statically typed compiled language. It can take more time to write, compile and debug than other dynamically typed and interpreted languages. Therefore, many people have moved to languages (such as Python and Ruby) for productivity purposes.




History

Origins[edit | edit source]

An IBM 704, the platform Fortran originally targeted at inception.

Fortran was created by a team lead by John Backus at IBM in 1957. Originally, the name was written in all capital letters, but current standards and implementations only require the first letter to be capital. The name Fortran stands for FORmula TRANslator. Initially it was specifically aimed at scientific calculations and thereby had very limited support for working with character strings and lacked other provisions important for a general purpose programming language, which it will attain later during its extensive development that ensued after its successful debut. Until the C language became popular, Fortran had been one of the few high level languages with a reasonable degree of portability between different computer systems. Several websites indicate that the work on Fortran was started in 1954 and released commercially in 1957. It is believed that the first successful compilation of a small Fortran program took place on September 20, 1954.

Fortran Versions[edit | edit source]

A programming language family tree, focusing on Fortran/Speedcoding and COBOL/FLOW-MATIC. Aside from contemporary versions of Fortran, many programming languages were influenced by early versions of Fortran.

There have been several versions of Fortran. FORTRAN I, II, III and IV are considered obsolete and contained many machine-dependent features. FORTRAN 66 was the first standardized version and was released in 1966. All later versions of Fortran are numbered after the year the standard was released. The versions of Fortran most commonly remaining in use are FORTRAN 77, Fortran 90 and later.

In FORTRAN II, IF statements had the form: IF (numeric_expression) label_if_negative, label_if_zero, label_if_positive. It also had an odd type of string literal, called Hollerith literals (after the inventor of the keypunch and IBM). Where today one might code 'hello', FORTRAN II used 5Hhello. However, there was no string variable type.

FORTRAN IV added the IF/THEN concept, the concept of logical expressions, with operators .AND., .OR., .EQ., .NE., et cetera. Complex numbers as a basic type were also added.

FORTRAN 77 added strings as a distinct type.

Fortran 90 added various sorts of threading, and direct array processing.

Fortran 2003 added object orientated features, derived types, language interoperability with C, data manipulation and many I/O enhancements.

Fortran 2008 added coarrays and parallelism and submodules.

Fortran 2018 added even more C interoperability and parallelism features.

Although Fortran became a standardized language early, many companies had their own extensions to it. Strangely, IBM and DEC had virtually the same set of extensions.

Differences between versions[edit | edit source]

Early versions of Fortran were often used in conjunction with punch cards. Contemporary Fortran versions bears little mind to obsolete formats, beginning with FORTRAN 90.
  • FORTRAN 66 comments are denoted by the C character in column 1, while FORTRAN 77 comments may also use * in column 1 instead. Fortran 90 also allows the use of ! character.
  • FORTRAN 77 symbolic names are limited to 6 character lengths, while Fortran 90 allows names up to 31 characters long.
  • FORTRAN 77 files need 6 spaces before words begin, while Fortran 90 doesn't (as it uses the free-form code style.)



Hello world

Simple Fortran program[edit | edit source]

Below is a simple Fortran program. You can paste this into a text editor (such as Emacs or Vim). Source code must be in a plain text file, so don't use a word processor (such as Microsoft Word), because its native format is usually not plain text, or otherwise contains special formatting data. Give the file a name such as hello.f90. The filename extension .f90 is conventionally used for modern Fortran source code. Other common Fortran file extensions are .f, .FOR, .for, .f77, .f90 and .f95, which can denote the use of old or specific Fortran standards. You may also use .F, .fpp and .FPP for files that support Preprocessing.

program hello
    print *, "Hello World!"
end program
Because Fortran is case insensitive, one could just as easily write the first 'hello' program as:
Program Hello
    Print *, "Hello World!"
End Program

The only case sensitive part of this program is what contained in the quotation marks of the print statement. ("Hello World!")

Compiling[edit | edit source]

Unix[edit | edit source]

There are several Fortran compilers available for Unix. Among the most popular are:

  • GNU Fortran compiler from the GCC, which is a fork of G95. Invocation:
    gfortran -o hello hello.f90
    
    Note: the GNU Fortran compiler uses the FORTRAN 77 standard by default, so the input file must have the .f90 (or of later standard) suffix, so that the compiler can guess the desired standard automatically. Alternatively you can supply the -ffree-form option with the usual .f suffix to enable free-form format instead of the fixed-form format used by the FORTRAN 77 standard.
  • Fortran 95 optimizing compiler from Oracle Solaris Studio. Invocation:
    f95 -o hello hello.f90
    

Once the program is compiled and linked, you may execute it:

./hello

Windows[edit | edit source]

On Windows, you will need to install a compiler. You may also want to install an IDE for that compiler, which acts as an editor and allows you to compile the program more easily.

When you have a compiler, open a command prompt (MS-DOS prompt). This looks like

 C:\>

or something similar. At the prompt, you need to move into the folder containing the .f90 file. Then, to compile, type

 f95 hello.f90 -o hello.exe

This assumes the compiler is called "f95". The Intel compiler is typically "ifort". You may need to specify where this is, for example if it's in Program Files\Compiler, use:

 "C:\Program Files\Compiler\f95" hello.f90 -o hello.exe

Alternatively, you could install a text editor with support for Fortran compilers. Such as SciTE [1] The above commands produce an executable called hello.exe - to run this, just type

 hello

at the command prompt

OpenVMS[edit | edit source]

On VMS you will need the DEC Fortran90 compiler installed and licenses loaded. This is available as part of the hobbyist project. These commands work for Fortran on both Alpha and VAX.

To compile, type the following at the DCL prompt:

$ FORTRAN HELLO.F

To link the file to the Run-Time Lib (RTL) type the following:

$ LINK HELLO.OBJ

To Run the executable image, type the following:

$ RUN HELLO.EXE
Hello World!
$

Enjoy all that VMS and Fortran offers.




Beginning Fortran

Introduction[edit | edit source]

Fortran programs are made up of the main program and modules, each can contain subroutines and functions.

Code that should be executed when the program is run should be placed in a program block, like this:

program name_of_program
  ! <variable declarations> ...
  ! <program statements> ...
end program

Indentation is not required, but is recommended. The name of the program must start with a letter, and can otherwise contain letters, numbers, and the _ (underscore) character. Each statement terminates with the end of the line.

Free Form and Fixed Form[edit | edit source]

The Fortran 77 syntax requires that you give 6 spaces before any commands. These 6 spaces originate from the punched card version of Fortran. After the first 6 spaces, you may place additional spaces for indentation if you wish.

However, there is a maximum total line width of 72 characters (including the first 6 spaces). If you require extra space you can put any character (except 0 with some compilers) in column 6; this is called a "continuation character". With punched cards, this meant that you could continue the line onto a second card.

C2345678...
      PRINT *,"This is a really....
     *...long line.

On some compilers you can turn off the 6 spaces rule, and turn off fixed length lines, by specifying "free form" and not "fixed form" mode. If you use the GNU Fortran compiler (gfortran), you can use the -ffree-form command line option when compiling for the same purpose.

Commenting[edit | edit source]

Inclusion of an exclamation mark, !, on a line makes the rest of the line a comment, like this:

 a = b ! this is a comment
 c = d ! this!! is also a comment

In fixed-form mode, you can also mark a whole line as a comment by placing a * or a c in the first column.

Variables[edit | edit source]

See Variables

There are many different types and options for variables, but for now we'll stick to the basics.

real       :: a  ! Decimal number.
integer    :: b  ! Whole number.
character  :: c  ! Single character.

It is recommended to use the implicit none statement before variable declarations to avoid typing errors by forcing the explicit declaration of every program variable.

Mathematical operators[edit | edit source]

See Mathematics

  • Add, subtract, multiply, divide
  +
  -
  *
  /
  • Assignment
  =
  • To the power of ( 2**4 is two to the fourth power = 16 )
  **

The mathematical operators have a certain precedence order:

** [exponentiation] always comes first, it is right to left associative. i.e. 2**3**2 = 512, not 64

Next comes * [multiplication] and / [division], these are left to right associative, i.e., 1.0/1.0/2.0*6.0 = ((1.0/1.0)/2.0)*6.0 = 3.0, not 12.0.

Next in order is + [addition] and - [subtraction], these are left to right associative as well, so x-y+z = (x-y)+z = x+(-y)+z.

Finally comes = [assignment].

Intrinsic functions[edit | edit source]

Fortran has a wide range of functions useful in numerical work, such as sin, exp, and log. The argument of a function must have the proper type, and it is enclosed in parentheses:
x = sin(3.14159) ! Sets x equal to sin(pi), which is zero.
The intrinsic math functions of Fortran are elemental, meaning that they can take arrays as well as scalars as arguments and return a scalar or an array of the same shape:
real :: x(2), pi=3.14159
x = sin([pi, pi/2])
The above program fragment sets the two elements of array x, x(1) and x(2), equal to sin(pi) and sin(pi/2) respectively.

Comparative and Logical operators[edit | edit source]

In if statements, and in some other places, you can code relational operators =, <, >, ≤, ≥, and ≠, respectively as .eq., .lt., .gt., .le., .de., and .ne.. Another way to write these operators would be: ==, <, >, <=, >=, and /=, respectively.

You can also use the logical operators .and., .or. and .not., as well as the logical constants .true. and .false.. When combining these items, do not double up on the dots. For instance, a .and. .not. b is the same as a.and.not.b, but not a.and..not.b.

WRITE statements[edit | edit source]

See Input and Output

write (*,*) "Hello World", variablename, "More text", anothervariable

(*,*) means to use the default output with default options, usually print to screen. Things inside quotes are printed as they look in the code, and the value of the variable is printed. Objects must be separated by commas, and the write statement automatically ends the line by default.

The full formal syntax is:

write (unit=unit_num, FMT=fmt_label, err=label) "Hello World", variablename, "More text", anothervariable

Note that some versions of Fortran don't allow double-quotes, and require single-quotes. An enclosed single-quote can be represented by doubling. For instance, 'don''t'.

The first parenthesized argument to WRITE or READ is the unit number. Unit numbers are associated with input or output streams in a way determined by the operating system. In very old systems, the unit number is the device address. In IBM JCL systems, the association between unit numbers and files are done with JCL DD statements. In other versions, there is some statement that associates files and units. The UNIT= tag may be omitted. If an asterisk is used for the unit number, then the I/O involved is the standard input channel, or the standard output channel.

The second parenthesized argument to WRITE or READ is the record number. Note that this argument, if present, is separated from the unit number by a single quote. If present, this variable defines which record number is read from or written to. For instance,

record_number = 5
write (2, record_number) x, y, z

writes x, y, and z in packed machine-specific format into record number 5. Note, of course, that this usage requires that your OS or Fortran compiler know what constitutes a record. In byte-organized files, the above code would write x, y, and z starting at the file's byte #5.

The third parenthesized argument to WRITE or READ is the format number. If this third argument is present as an asterisk, as above, then the formatting is the obvious default. If you'd rather use a FORMAT statement to format the input or output, then include the statement number for the FORMAT statement. For example:

write (7,1) 'Hello, world!', i, 'More text', x
1 format (A,I,A,F)

Note that a format statement is not executable as an in-line statement. It is only used where referenced by read or write. The fmt= tag may be omitted. The entire argument may be omitted, too. However, if you omit the format argument, the I/O will be performed unformatted, using machine-specific, packed data.

The last parenthesized argument to write or read is the error handler statement label. For instance, if

write (5,err=2) x, y, z

is coded, this means that output is to be unformatted to unit 5. If an error occurs, execution continues at statement 2 (the statement with a statement label of 2 in front of it). If an error occurs, and there is no ERR= argument, then the program abnormally terminates. Thus, ERR= is the closest equivalent of catch in other languages. Although this last argument may be omitted entirely, ERR= can't be omitted from the argument once used.

Example Code[edit | edit source]

See More Examples in Fortran

program nearlyuseless
    implicit none

    real    :: temperature
    integer :: cows

    temperature = 98.6
    cows        = 9
    print *, "There are ", cows, " cows outside."
    print *, "You are probably ", temperature, " right now"
end program

Some versions of Fortran, or in some settings, use format characters. When formatting characters are used, the first character of the line determines how the line is printed. 1 means new page. 0 means 2 line-feeds before the line (double-space). - means 3 line-feeds before the line (triple-spacing). + means no line-feeds before the line (overprinting). And a space means a single line-feed before the line (normal printing).

Here's the same program in archaic form, with this forms-control character:

temperature = 98.6
i_cows = 6
write (*,*) ' There are ', i_cows, ' cows outside.'
write (*,*) ' You are probably ', temperature, ' right now.'
end




Fortran variables

Introduction[edit | edit source]

In programming, a variable is a container for data that the program can change. You typically declare variables before you use them to provide information on what kind of data they should store. However, Fortran allows variables to be created implicitly. Absent an implicit statement, undeclared variables and arguments beginning with i/I through n/N (the "in" group) will be integer, and all other undeclared variables and arguments will be real.

Many consider using variables without declaring them bad practice. If you want to be forced to declare variables, code implicit none first.

General Examples[edit | edit source]

Examples of usual variables are listed below

! Declare a constant, whose value cannot be changed.
integer, parameter :: num_days_week = 7
! Declare i as an integer, j as an array of 2 integers from j(1) to j(2), k as
! an array of 2 integers from '''k(0)''' to k(1), and m as a 2-dimensional
! array of 12 elements.
integer :: i, j(2), k(0:1), m(3,4)
! Declare c as an array of 4 floating point numbers from c(0) to c(3).
real :: c(0:3)
! Declare word as a string of length 5
character (len=5) :: word
! Declare a boolean variable with values .TRUE. or .FALSE.
logical :: tf

The following does exactly the same thing, but in the shorter, more archaic form:

INTEGER, PARAMETER :: num_days_week = 7
DIMENSION j(2), k(0:1), m(3,4), c(0:3)
CHARACTER*5 word
LOGICAL tf

If memory layout counts to you, note that m(1,1) is followed in memory by m(2,1), and not by m(1,2).

A variable can be set by placing it before an equal sign, which is followed by the value to which it is set. Given the declarations above, the following assignments are possible:

i    = 3*4                  ! Set i to 3*4 = 12         
j    = [1, 4]               ! Set j(1) to 1, j(2) to 4
c    = [1.0, 4.0, 5.0, 9.0] ! Set c(0) to 1.0, c(1) to 4.0, c(2) to 5.0, c(3) to 9.0
word = 'dog'                ! Set word = "dog  " . The variable word is padded with spaces on the right
tf   = .true.               ! Set tf to True

A variable can appear on both sides of an assignment. The right hand side is evaluated first, and the variable is then assigned to that value:

i = 3     ! i has value 3
i = i**i  ! i has value 3**3 = 27

Variables can be converted from one type to another, but unlike in C++ or Java where you would typecast the variable, in Fortran you use the intrinsic procedures:

real          :: r = 1.5
real (kind=8) :: d = 1.5
integer       :: i = 1

print *, dble(r), dble(d), dble(i)   ! Convert number to a double precision
print *, real(r), real(d), real(i)   ! Convert number to a single precision (REAL)
print *, int(r), int(d), int(i)      ! Convert number to an integer

Again, the same thing in the simpler, archaic form:

 DOUBLE PRECISION d = 1.5
 r = 1.5
 i = 1
 PRINT *, DBLE(r), DBLE(d), DBLE(i)
 PRINT *, REAL(r), REAL(d), REAL(i)
 PRINT *, INT(r), INT(d), INT(i)

Arrays[edit | edit source]

Declaration[edit | edit source]

One can declare arrays using two different notations. The following example illustrates the notations for arrays of integer type and of length 5.

integer, dimension (5) :: arr1
integer                :: arr2(5)

For multidimensional arrays one needs to specify the length of each dimension. The following example highlights the case of a 5x6 integer matrix aka a two-dimensional array of length (5,6). (Again, showing both notations.)

integer, dimension (5,6) :: arr1
integer                  :: arr2(5,6)

Initialization[edit | edit source]

To initialize arrays with actual values one has multiple options: set specific elements, specific ranges, or the whole array.

integer :: arr(3)

arr(1)   = 4            ! set specific element
arr(1:2) = [4, 5]       ! set a range aka slicing notation
arr      = [4, 5, 6]    ! set whole array

To set multidimensional arrays one need to make use of reshape, and shape commands.

integer :: arr(2,3)

arr = reshape([1,2,3,4,5,6], shape(arr))
! arr = reshape([1,2,3,4,5,6], shape=[2,1])  ! same effect as above command - hardcode the shape of arr

! arr represents matrix:
! 1 3 5
! 2 4 6

Fortran uses column-major ordering such that the upper example produces a often confusing matrix. For a row-major ordering one can use the following example which highlights the use of the order argument to specify along which dimension to sort first.

integer :: arr(2,3)

arr = reshape([1,2,3,4,5,6], shape(arr), order=[2,1])

! arr represents matrix:
! 1 2 3
! 4 5 6




Fortran simple input and output

Default output[edit | edit source]

A Fortran program reads from standard input or from a file using the read statement, and it can write to standard output using the print statement. With the write statement one can write to standard output or to a file. Before writing to a file, the file must be opened and assigned a unit number with which the programmer may reference the file. If one wishes to use the write statement to write a statement to the default output, the syntax is write(*,*). It is used as follows:

program hello_world
    implicit none
    write (*,*) "Hello World!"
end program

This code writes "Hello World!" to the default output (usually standard output, the screen), similar to if one had used the print *, statement.

File output[edit | edit source]

As a demonstration of file output, the following program reads two integers from the keyboard and writes them and their product to an output file:

program xproduct
    implicit none
    integer :: i, j
    integer, parameter :: out_unit=20

    print *, "enter two integers"
    read (*,*) i,j

    open (unit=out_unit,file="results.txt",action="write",status="replace")
    write (out_unit,*) "The product of", i, " and", j
    write (out_unit,*) "is", i*j
    close (out_unit)
end program xproduct

The file "results.txt" will contain these lines:

 The product of 2 and 3
 is 6

Each print or write statement on a new line by default starts printing on a new line. For example:

program hello_world
    implicit none

    print *, "Hello"
    print *, "World!"
end program

Prints, to standard output:

Hello
World!

If one had put "Hello World!" in one print statement, the text "Hello World!" would have appeared on one line.




Fortran control

Selection[edit | edit source]

If-then(-else) conditional[edit | edit source]

Conditional execution is done using the if, then and else statements in the following construct:

 if (logical_expression1) then
    ! Block of code
 else if (logical_expression2) then
    ! Block of code
 else
    ! Block of code
 end if

You may have as many else if statements as you desire.

The following operators can be used when making expressions:

Operation Modern Fortran Old FORTRAN
Less than < .LT.
Greater than > .GT.
Greater than/equal >= .GE.
Less than/equal <= .LE.
Equal == .EQ.
Not equal /= .NE.
Logical equivalent .EQV.
Logical not equivalent .NEQV.
Logical not .NOT.
Logical and .AND.
Logical or .OR.

Note: The Fortran standard mandates .EQ. and .NEQ. cannot be used with logicals but some compilers will not enforce the standard

To check more than one statement, use parentheses.

if ((a .gt. b) .and. .not. (a .lt. c)) then

The following program generates a random number between 0 and 1 and tests if it is between 0 and 0.3, 0.3 and 0.6, or between 0.6 and 1.0.

program xif
    implicit none
    real :: x
    real, parameter :: x1 = 0.3, x2 = 0.6

    call random_seed()
    call random_number(x)
    if (x < x1) then
        print *, x, "<",x1
    else if (x < x2) then
        print *, x, "<", x2
    else
        print *, x, ">=", x2
    end if
end program xif

There are two interesting archaic forms of IF:

      IF (<logical_expression>) GOTO <statement_label>
      IF (<arithmetic_expression>) <first_label>, <second_label>, <third_label>

In the first form, things are pretty straightforward. In the second form, the arithmetic expression is evaluated. If the expression evaluates to a negative number, then execution continues at the first line number. If the expression evaluates to zero, then execution continues at the second line number. Otherwise, execution continues at the third line number.

case (switch)[edit | edit source]

select case(...) case (...); ... end select

If an if block consists of repeated tests on a single variable, it may be possible to replace it with a select case construct. For example, the code

if (month=="January" .or. month=="December") then
    num_days = 31
else if (month=="February") then
    num_days = 28
else if (month=="March") then
    num_days = 31
else
    num_days = 30
end if

can be replaced by

select case (month)
    case ("January", "December")
        num_days = 31
    case ("February")
        num_days = 28
    case ("March")
        num_days = 31
    case default
        num_days = 30
end select

Fortran does not need a break statement.

Loops[edit | edit source]

do i=1,10 ... end do

To iterate, Fortran has a do loop. The following loop prints the squares of the integers from 1 to 10:

do i=1,10
    print *, i**2
end do

One can exit a loop early using exit, as shown in the code below, which prints the squares of integers until one of the squares exceeds 25.

do i=1,10
    isquare = i**2
    if (isquare > 25) exit
    print *, isquare
end do

Loops can be nested. The following code prints powers 2 through 4 of the integers from 1 to 10

do i=1,10
    do ipower=1,3
        print *, i, ipower, i**ipower
    end do
end do

In an archaic form of DO, a line number on which the loop(s) end is used. Here's the same loop, explicitly stating that label 1 is the last line of each loop:

      DO 1 i=1,10
          DO 1 ipower=1,3
              1 PRINT *, i, ipower, i**ipower

If using the archaic form, the loop must not end on an IF or GO TO statement. You may use a CONTINUE statement as an anchor for a the 1 label.

There is also an optional increment argument when declaring a do loop. The following will count up by two's. 2, 4, 6, ...

do i=2,10,2
    write (*,*) i
end do

Arguments to the do loop don't have to be numbers, they can be any integer that is defined elsewhere in the program. first, last, and increment can be any variable name.

do i=first,last,increment
    ! Code goes here
end do

Simple statements[edit | edit source]

goto statement_label will jump to the specified statement number.

stop exit_code will stop with the specified condition code or exit code. stop may be coded without an argument. Note that on many systems, stop 0 is still a failure. Also note that pre-Fortran 2008, the condition code must be a constant expression and not a variable.

exit will leave a loop.

continue can be used to end an archaic DO loop when it would otherwise end on an IF.

cycle will transfer the control of the program to the next end do statement.

return leaves a subroutine or function.



Fortran procedures and functions

Functions and Subroutines[edit | edit source]

In most programs, a block of code is often re-used at several places. In order to minimize duplicating code and facilitate maintaining the code, such blocks of code should be placed within a function or subroutine. A Fortran function is similar to a mathematical function, which takes one or many parameters as inputs and returns a single output value. A Fortran subroutine is a block of code that performs some operation on the input variables, and as a result of calling the subroutine, the input variables are modified.

An expression containing a function call:

! func1 is a function defined elsewhere.
! It takes an integer as an input and returns another integer as the output.
a = func1(b)

A call to a subroutine:

! sub1 is a subroutine defined elsewhere.
! sub1 performs some operation on input variables e and f.
call sub1(e, f)
! Now e or f, or both (or neither) may be modified.

Many programming languages do not distinguish between functions and subroutines (e.g. C/C++, Python, Java). Pure functional programming languages (e.g. Haskell) only allow functions, because subroutines can, in some case, modify input variables as side-effects, which can complicate the code.

Functions are simpler than subroutines. A function must return a single value, and can be invoked from within expressions, like a write statement, inside an if declaration if (function) then, etc. A subroutine does not return a value, but can return many values via its arguments and can only be used as a stand-alone command (using the keyword call).

Function[edit | edit source]

In Fortran, one can use a function to return a value or an array of values. The following program calls a function to compute the sum of the square and the cube of an integer.

function func(i) result(j)
    integer, intent (in) :: i ! input
    integer              :: j ! output

    j = i**2 + i**3
end function

program main
    implicit none
    integer :: i
    integer :: func

    i = 3
    print *, "sum of the square and cube of", i, "is", func(i)
end program

The intent (in) attribute of argument i means that i cannot be changed inside the function and in contrast, the return value j has automatic intent (out). Note that the return type of func needs to be declared. If this is omitted, some compilers will not compile. Open64 will compile the resulting code with warning, but the behavior is ill-defined.

An alternative formulation (F77 compatible) is

      FUNCTION func_name(a, b)
          INTEGER :: func_name
          INTEGER :: a
          REAL    :: b
          func_name = (2*a)+b
          RETURN
      END FUNCTION
    
      PROGRAM cows
          IMPLICIT NONE
          INTEGER :: func_name
          PRINT *, func_name(2, 1.3)
      END PROGRAM

The return type of the func_name still needs to be declared, as above. The only difference is how the return type of func_name is referenced within func_name. In this case, the return variable has the same name as the function itself.

Recursion[edit | edit source]

Fortran requires you to declare recursive functions, such as a recursive factorial function, in order for the code to compile.

recursive function fact(i) result(j)
    integer, intent (in) :: i
    integer :: j
    if (i==1) then
        j = 1
    else
        j = i * fact(i - 1)
    end if
end function fact

Subroutine[edit | edit source]

A subroutine can be used to return several values through its arguments. It is invoked with a call statement. Here is an example.

subroutine square_cube(i, isquare, icube)
    integer, intent (in)  :: i              ! input
    integer, intent (out) :: isquare, icube ! output

    isquare = i**2
    icube   = i**3
end subroutine

program main
    implicit none
    external square_cube ! external subroutine
    integer :: isq, icub

    call square_cube(4, isq, icub)
    print *, "i,i^2,i^3=", 4, isq, icub
end program

Intent[edit | edit source]

When declaring variables inside functions and subroutines that need to be passed in or out, intent may be added to the declaration. The default is no intent checking - which can allow erroneous coding to be undetected by the compiler.

intent (in) - the value of the dummy argument may be used, but not modified, within the procedure.

intent (out)- the dummy argument may be set and then modified within the procedure, and the values returned to the caller.

intent (inout) - initial values of the dummy argument may be both used and modified within the procedure, and then returned to the caller.

More on Functions vs. Subroutines[edit | edit source]

Different function result definitions[edit | edit source]

Functions can define the data type of their result in different forms: either as a separate variable or by the function name.

See the examples below

function f1(i) result (j)
  !! result's variable:  separately specified
  !! result's data type: separately specified
  integer, intent (in) :: i
  integer              :: j
  j = i + 1
end function

integer function f2(i) result (j)
  !! result's variable:  separately specified
  !! result's data type: by prefix
  integer, intent (in) :: i
  j = i + 2
end function

integer function f3(i)
  !! result's variable:  by function name
  !! result's data type: by prefix
  integer, intent(in) :: i
  f3 = i + 3
end function

function f4(i)
  !! result's variable:  by function name
  !! result's data type: separately specified
  integer, intent (in) :: i
  integer              :: f4
  f4 = i + 4
end function

program main
  implicit none
  integer :: f1, f2, f3, f4

  print *, 'f1(0)', f1(0) ! output: 1
  print *, 'f2(0)', f2(0) ! output: 2
  print *, 'f3(0)', f3(0) ! output: 3
  print *, 'f4(0)', f4(0) ! output: 4
end program

External[edit | edit source]

Procedures must be included by module use or by specifying them as external procedures. external supplies only an implicit interface which is inferior as the compiler doesn't know the number of arguments and neither their data types. Thus, it cannot yield warnings at compile time (in contrast to an explicit interface given from a module use, c.f. Fortran/OOP in Fortran).

subroutine square_cube(i, isquare, icube)
    integer, intent (in)  :: i              ! input
    integer, intent (out) :: isquare, icube ! output

    isquare = i**2
    icube   = i**3
end subroutine

integer function pow4(i)
    integer, intent (in) :: i

    pow4 = i**4
end function

program main
    implicit none
    external square_cube    ! external subroutine (only implicit interface)
    integer :: pow4         ! external function (only implicit interface)
    integer :: i, isq, icub

    i = 5
    call square_cube(i, isq, icub)
    print '(A,4I5)', "i,i^2,i^3,i^4=", i, isq, icub, pow4(i)
end program

Pure procedures[edit | edit source]

Both functions and subroutines can modify their input variables. By necessity, subroutines modify input variables, since they do not return any output value. Functions do not have to, but are allowed, by default, to modify input variables. A function can be turned into a pure function, which does not have any side-effects through the use of the intent attribute on all input variables, and further enforced through the keyword pure. The pure keyword imposes additional restrictions, which essentially prevents the function from having any side-effects.

An example of a pure function.

pure real function square(x)
    real, intent (in) :: x

    square = x*x
end function

program main
    real :: a, b, square

    a = 2.0
    b = square(a)
    ! After invoking the square(.) pure function, we can be sure that
    ! besides assigning the output value of square(a) to b,
    ! nothing else has been changed.
end program

Keyword arguments[edit | edit source]

One can use any order of the input arguments if one specifies them by their dummy name. That is possible as long as the calling procedure has an interface block of the intended procedure (which is automatically created if one includes the function by module usage uses modules).

There is also a hybrid method where one specifies some parameters by position and the rest by their dummy name.

An example is given

real function adder(a,b,c,d)
    real, intent (in) :: a, b, c, d
    adder = a+b+c+d
end function

program main
    interface
        real function adder(a,b,c,d)
            real, intent (in) :: a, b, c, d
        end function
    end interface

    print *, adder(d=1.0, b=2.0, c=1.0, a=1.0)  ! specify each parameter by dummy name
    print *, adder(1.0, d=1.0, b=2.0, c=1.0)    ! specify some parameters by dummy names, other by position
end program

Optional arguments[edit | edit source]

Arguments can be set optional. The intrinsic function present can be used to check if a specific parameter is set.

An example is given below.

real function tester(a)
    real, intent (in), optional :: a
    if (present(a)) then
        tester = a
    else
        tester = 0.0
    end if
end function 

program main
    interface
        function tester(a)
            real function tester(a)
            real, intent (in), optional :: a
        end function 
    end interface

    print *, "[no args] tester()   :", tester()    ! yields: 0.0
    print *, "[   args] tester(1.0):", tester(1.0) ! yields: 1.0
end program

Interface block[edit | edit source]

If a procedure has another procedure as dummy argument then one has to specify its type, just as the type of other parameters. An interface block is used for this case. It consists of the procedure statement with the definitions of its arguments.

Note, that each interface block has its own scope. Thus, if one needs to access outside values one needs to explicitly load them. This can be achieved by the import, or use statements.

An example is given below.

function tester(a)
    real, intent (in) :: a
    real :: tester

    tester = 2*a + 3
end function tester

program main
    interface
        function tester(a)
            real, intent (in) :: a
            real :: tester
        end function tester
    end interface

    print *, "tester(1.0):", tester(1.0) ! yields: 5.0
end program main

Save attribute[edit | edit source]

The value of a variable can be saved in-between procedure calls by explicitly giving the save attribute.

An example is given below.

subroutine f()
    implicit none
    integer, save :: i = 0

    i = i + 1
    print *, "value i:", i
end

program main
    implicit none
    interface
        subroutine f()
            integer, save :: i = 0
        end
    end interface

    call f()  ! yields: 1
    call f()  ! yields: 2
    call f()  ! yields: 3
end program main

Generic[edit | edit source]

It is possible to create generic functions with the same name for different input arguments, similar to the abs function which works for integer, real, and complex data types.

The following example illustrates how to create a function add which adds either two integers or character strings.

module add_mod
    implicit none
    private
    public :: add

    interface add
        procedure add_int, add_char
    end interface add
contains
    pure function add_int( x, y )
        integer, intent (in) :: x, y
        integer :: add_int

        add_int = x+y
    end function add_int

    pure function add_char( x, y )
        character (len=*), intent (in) :: x, y
        character (len=len(x)+len(y)), allocatable :: add_char

        add_char = x // y
    end function add_char
end module add_mod

program main
  use add_mod
  implicit none

  print *, "add ints: ", add( 1, 2 )
  print *, "add chars: ", add("abc", "def")
end program main

Deferred[edit | edit source]

One can set type-bound procedures of an abstract type as deferred such that it needs to be reimplemented in derived types. For more information see the section on abstract types.

Elemental[edit | edit source]

One can create procedures that operate parameters of arbitrary dimension. The keyword elemental is used where one defines the operation on a single object (e.g. integer) and the general case is automatically handled.

An example for the addition of arbitrary long integer dimension is given.

pure elemental function add_int(x, y)
    integer, intent (in) :: x, y
    integer :: add_int
    add_int = x + y
end function add_int

program main
    implicit none

    interface
        pure elemental function add_int(x, y)
            integer, intent (in) :: x, y
            integer :: add_int
        end function add_int
  end interface

  print *, "add ints:", add_int(1, 2) ! yields: 3
  print *, "add arrays:", add_int([1, 2], [2, 3]) ! yields: 3   5
end program main



complex types

Warning: Display title "Fortran/data types" overrides earlier display title "Fortran/Fundamentals".

Variables and data declarations must occur at the start of all Fortran program units before any executable statements. Variables may have a "kind" that specifies its size in memory. The kind parameter can have different meanings for each compiler or processor, so be sure to check what kinds are available to you in your compiler's documentation.

Declaration style[edit | edit source]

There are several ways to declare a variable. The modern Fortran style is to be verbose and explicit. The following example declares an real array with the a kind of 8 (on most compilers this means 8 bytes long, i.e. double precision).
! Modern variable declaration
! <datatype> [(kind=<num>), <attribute>, ... ::] <identifier>[, ...]
! Example:
real (kind=8), dimension (3) :: variable
The dimension attribute is quite long to type out, but may be more concise when declaring multiple arrays on a single line. If only a single variable is to be declared then it may be more concise to specify the dimension with parentheses next to the identifier.
real (kind=8) :: variable(3)
Variables may also be initialized with an assignment.
real (kind=8) :: variable(3) = 1.0
The :: is optional for backwards compatibility with older versions of Fortran. The older style of declarations use a * to denote the kind of a variable.
REAL*8 variable(3)
Furthermore, the kind may be omitted entirely to simply use the default kind for your compiler.
real variable(3)

Intrinsic data types[edit | edit source]

Integer[edit | edit source]

The integer data type stores signed integer values (i.e. ..., -3, -2, -1, 0, 1, 2, 3, ...). On most compilers, the default kind stores integers as short integers 4 bytes in size (kind=4). Long integers are usually 8 bytes (kind=8). The allowed attributes are: allocatable, intrinsic, public, asynchronous, optional, save, parameter, bind, pointer, target, dimension (dims), private, value, external, protected, volatile and intent (inout).
integer :: variable

Logical[edit | edit source]

The logical data type stores boolean vales and can only contain values .true. or .false.. The default logical kind for most compilers is 4, occupying 4 bytes. Therefore, logicals are much like integers in terms of memory, but integers and logicals are generally not compatible for most operations. The allowed attributes are: allocatable, intrinsic, public, asynchronous, optional, save, parameter, bind, pointer, target, dimension (dims), private, value, external, protected, volatile, intent (inout).
logical :: variable

Real[edit | edit source]

The real data type stores floating point data. Vales are stored in memory in scientific notation as a mantissa and an exponent. The default kind for real variables is 4, which consists of 4 bytes (32 bits). In this case 24 bits are used for the mantissa and 8 bits are used for the exponent. The allowed attributes are: allocatable, intrinsic, public, asynchronous, optional, save, parameter, bind, pointer, target, dimension (dims), private, value, external, protected, volatile, intent (inout).

All compilers support at least two kinds of real kinds for low precision and high precision numbers. But the standard does not specify what size these precisions should be. Most compilers use 32 bits for single precision and 64 bits for double precision. Therefore, many compilers support a double precision real data type that uses the higher precision that is available. However, for portablility it is much better to use the selected_real_kind intrinsic function to select the required kind parameter for your variables precision.
real :: variable
double precision :: variable2

Complex[edit | edit source]

In mathematics, a complex number has a real and an imaginary component. Complex numbers in Fortran are stored in rectangular coordinates as a pair of real numbers (real part first, followed by the imaginary part). The default kind of complex numbers is always the same as the default kind of the real data type. So a complex variable of kind 4 will contain two reals of kind 4. If kind 4 reals corresponds to 4 bytes, then the default complex variables will be 8 bytes in size. The allowed attributes are: allocatable, intrinsic, public, asynchronous, optional, save, parameter, bind, pointer, target, dimension (dims), private, value, external, protected, volatile, intent (inout).
complex :: variable

Complex operations[edit | edit source]

All of the arithmetic operators can take a complex number on either side. Fortran automatically handles complex arithmetic and the special rules of imaginary numbers.

Care must be taken in using function calls that might cause an error. For instance, taking the square root of the real number -1.0 will result in an error, because -1 is outside of the domain of real square root. Taking the square root of the complex number (-1.0,0.0) is allowed because -1 is in the domain of complex square root.

Character[edit | edit source]

The character data type stores strings of characters. The default kind of character variables is usually 1 which represents ASCII characters. Kind 2 usually represents the ISO 10646 standard characters. Character variables are unique in that they also have a len parameter in addition to kind which specifies the number of characters in the string. Typically a single character occupies 1 byte in memory. In addition to this, character data types can also be arrays.
character (len=5,kind=1), dimension (2) :: strings
The old style declarations does not have a kind parameter and only has the length parameter.
CHARACTER*5 strings(2)

Constants[edit | edit source]

Literal constants[edit | edit source]

Data embedded in expressions are referred to as literals or constants. Literals can have a particular data type depending on how they are written. For example, in the below line the value 1 is an integer.
a = a + 1
The below table demonstrate how to type literal constants.
Literal constants
Type Example literals
integer 0, -1, 9999
logical .true., .false., T, F
real 1.1, 0.0005, -99.9e-99
complex (-1.0,3), (0.5,-3e5)
character 'Hello'
Note that the parentheses notation for complex numbers cannot be used with variables. For example, (a, b) is invalid. To convert real variables to complex, use the cmplx function:
cmplx(a, b)

Any expression involving complex numbers and other numbers is promoted to complex.

Parameter constants[edit | edit source]

Constants literals are simply unnamed data. Variables can be constants too. They are declared with the parameter attribute. These variables are immutable and assigning to them after they have been declared will cause an error. They must be initialized with a value when they are declared.
real, parameter :: PI = 3.141592



Fortran structure and style

Warning: Display title "Fortran/Program structure" overrides earlier display title "Fortran/data types".

Style[edit | edit source]

Older versions of Fortran had strict guidelines on how a program was formatted. Fortran 90 lifted this restriction and would accept free format code as well as historical fixed format code.

Fixed format[edit | edit source]

Prior to Fortran 90, source code followed a well-defined fixed format. Comments are indicated with a 'C' in the first column, columns 2-5 were reserved for an optional numerical statement label, a non-blank character in column 6 indicated the current line was a continuation from the previous one, and columns 7 through 72 were available for program statements. Columns 73 through 80 were ignored and often contained line sequence numbers. Blank lines were not allowed. This rigid formatting was the result of Fortran being developed in the era of batch computing and punched card input. The sequence number was used in the case a program 'deck' was dropped; program order could be recovered if the punch cards were placed in a card reader and sorted on columns 73-80. Compiler vendors offered extensions to this formatting, but it was rarely portable (for example, interpreting tab characters as 6 spaces.)

Note that while column position was significant, white space was not. The following program illustrates legal use of white space in fixed-format Fortran:

C2345678901234567890
      PROGRAM Z
      GOTO11
   11 CONTINUE
      GO TO 780
 780  CONTINUE
      G OTO3 60
 360  CONTINUE
      STOP
      END

While this code is technically legal, it is strongly encouraged to use white space to separate keywords, labels, and data to maintain readability.

Fortran was developed before the standardization of the ASCII character set and traditionally Fortran code has been written in all-caps. Variable names were limited to six characters, but this was often extended by compiler vendors.

Free format[edit | edit source]

As of Fortran 90 and onward, source code does not require fixed column formatting. In this case, commands can freely start on any column. The 72 column limit has also been released. This allows for much more space for indentation.

program test
    implicit none
    integer four
    four = 4
    write (*,*) four
end program

Case sensitivity[edit | edit source]

Fortran is not case sensitive. Fortran was typically used on systems that only supported capital letters. In fact, the language itself was called FORTRAN (in capiltals). It remains customary, though completely unnecessary, to type Fortran commands in all capitals. This is useful to distinguish keywords in source code that is displayed on monocrome displays and print. These days, syntax highlighting is available to replace this. However it may be useful to visually distinguish older Fortran code from modern source code.

Whitespace[edit | edit source]

Whitespace and empty lines usually won't matter in Fortran 90 or above. Some statements require whitespace, for example, program, function and subroutine require whitespace between the statement keyword and the program unit identifier.

However, unlike many other languages such as C, C++, and Java, the line delimiter ';' is optional, so each line of code may stay on its own line. However, the use of the command separator character ';' is discouraged.

Structure[edit | edit source]

Program units[edit | edit source]

Fortran programs are made up of program units. A single source code file can contain several program units but it is conventional to place each program unit in its own separate source code file. At their most basic they consist of a series of Fortran statements and conclude with the end statement.

Main program[edit | edit source]

Every executable program must have a main program unit. For example, the following is a complete compilable and executable program.
write (*,*) "Hello, world"
end
However, it is much clearer to use the program statement to indicate that it is the main program unit.
program main
    write (*,*) "Hello, world!"
end program main
The main program is separated into sections. The first section should consist of module use statements. This is followed by implicit / implicit none statements that control whether undeclared variables are implicitly typed. This is followed by the declaration section where variables, types, interfaces and procedures are declared. Then comes the executable statements of the main program. The last section is the internal subprograms initiated by the contains statement.
program main
    ! Use statements section
    use module_name
    ! Implicit none statement section
    implicit none
    ! Declarations section
    integer :: a
    real :: b
    
    ! Executable section
    write (*,*) "Blah, blah, blah..."
end program main

Subprograms[edit | edit source]

Program units may also be subprograms: these can be procedures (functions and subroutines), block data, modules or submodules.

External subprograms[edit | edit source]
The following code shows a main program and a function. The increment function is external to the main program, and therefore needs a declaration in the main program on line 4.
program main
    implicit none
    integer :: a
    integer, external :: increment

    a = increment(34)
    write (*,*) a
end program main

function increment(input) result (output)
    implicit none
    integer :: output
    integer :: input

    output = input + 1
end function increment
However, the interface of the function is still implicit. To explicitly declare an external procedure, one can use an interface that declares all the inputs and outputs of external procedures. In which case, the main program would be as follows.
program main
    implicit none
    integer :: a
    interface
        integer function increment(input)
            integer :: input
        end function
    end interface

    a = increment(34)
    write (*,*) a
end program main
Internal subprograms[edit | edit source]
Internal subprograms do not need an explicit interface or a declaration, because they are part of the parent program unit. A subprogram is internal if it is contained within the contains section of a program unit.
program main
    implicit none
    integer :: a

    a = increment(34)
    write (*,*) a
    
contains

    function increment(input) result (output)
        integer :: output
        integer :: input

        output = input + 1
    end function increment

end program main

Functions[edit | edit source]

Subroutines[edit | edit source]

Block Data[edit | edit source]

Modules[edit | edit source]

Submodules[edit | edit source]



io

It is often useful, in Fortran and other languages, to specify where, and how you want something to print or be read. Fortran offers many commands and formatting specifications which can serve these purposes. In the following sections we will be considering the I/O operations (open, close, inquire, rewind, backspace, endfile, flush, print, read, write and namelist) and I/O formatting (format). In Fortran 2008, a significant addition has been the ability to extend the basic facilities with user-defined routines to output derived types including those that are themselves composed of other derived types.

Together these commands form a very powerful assembly of facilities for reading and writing formatted and unformatted files with sequential, direct or asynchronous access. Indeed, the options can look bewildering at first. However, the basic operations are simple enough but they are backed up by the power and flexibility to read or write almost any file.

However, it is worth mentioning, at this stage, what Fortran cannot do simply and directly from a language-defined perspective: Fortran will not address a file defined by a URL, files must be available locally or on a mapped network drive or equivalent. Similarly, Fortran does not natively support XML, except that XML is simple ASCII text so it can be read easily but parsing it out is down to the programmer! The Fortran language knows nothing about computer graphics; you are not going to find a language-defined draw command. Fortran will happily open and read a jpg file but there is no language-defined method of displaying the file as a picture; a suitable external library will have to be used. Finally, Fortran does not have any language-defined mouse operations or touch screen gestures.

I/O Operations[edit | edit source]

Introduction[edit | edit source]

Modern Fortran has a rich vocabulary for I/O operations. These operations can generally be used on the screen and keyboard, external files and internal files. In recent versions of Fortran, the syntax of these commands has been rationalized but most of the original syntax has been retained for backwards compatibility. I/O operations are notoriously error-prone and Fortran now supports a unified mechanism for identifying and processing errors.

Simple I/O Operations[edit | edit source]

Print[edit | edit source]

This is the classic "Hello World" operation, but is rarely used in production code. print is one of two formatted output operations and it is also much simpler that the write statement. The main purpose of the print statement is to print to the screen (standard output unit) and it has no options for file output. The general form is:

print fmt, list

Both fmt and list are optional and the fmt can be explicit or list-directed (as indicated by *), and being optional can take the name=value format. The list is a comma separated list of literals or intrinsic type variables. So here are some examples:

program hello
    implicit none
    integer :: i

    ! List-directed fmt
    print *, "Hello World"
    do i = 1, 10
        ! An explicit fmt and a two element list
        print '(A,I0)', "Hello ", i
    end do
    ! Name=value for fmt
    print fmt='(A)', 'Goodbye'
end program hello

Note that print is just about the only I/O operation that still does not support iostat and iomsg clauses, and for this reason alone should not be used in new code except for temporary output and debugging. print has no explicit mechanism for printing user-defined types and this is another reason for not using it in production code.

I/O Channels & Files[edit | edit source]

In the example on print shown above, the print statement is automatically pre-connected to the standard output device also known as the computer screen. However, in general, Fortran requires a two stage process to connect code to external files. First we have to connect the file to a Fortran channel (manually identified by a positive integer or automatically assigned a negative value): the open command, and then we can read and write to the now open channel. read and write operations to a channel that is not open, results in an error; there is no language-specified buffering until the relevant channel is opened. Once an I/O operation is complete we can close the connection between the file and the Fortran channel. If a Fortran program terminates before a channel is closed to a file, Fortran will usually close the channel without significant loss of data.

The state of availability of Fortran channels can be ascertained through one form of the inquire command. The inquire command can also be used to determine the existence and other properties of a file before it is connected to a Fortran channel.

Fortran I/O to internal files does not require a pre-connection process. Fortran input from the keyboard and output to the screen is automatically pre-connected on a special channel (*). Compiler vendors are free to assign a channel number to these standard I/O devices and the user can determine which channel numbers have been used via the intrinsic module iso_fortran_env.

Open[edit | edit source]

This is the command required to establish a connection between an external file and a Fortran channel. The open command can be used to create a new file or connect to existing files. Subsequent I/O to the file, once open, is made via this channel number. The open command has options to ensure that the file already exists or does not already exist, to ensure that it is used only for input, or only for output, or for both. The expected format of the file can be specified in the open command and errors can be trapped. The full syntax of the command can appear to be rather complicated, but generally any one call to open uses only a small subset of all the available options.

The open command originated when external files were usually card images. open can now specify that the connection to a file be fixed-format, asynchronous, a binary stream and many combinations of these. It is worth remembering that I/O is a major source of potential coding errors and where critical data are read they should be written again to confirm correct processing.

The value of the Fortran channel number has global scope within any one image of a Fortran program. Even if an integer variable is used to open a channel and that variable has very limited scope, the actual channel number is effectively ubiquitous. This needs to be considered at design time because one module can open, say, channel 10, and another module can close channel 10 without any use association between them. For this reason, in large programs, it is often the case that a single module is used to control all file i/o operations so that a clear and obvious "open - read/write - close" chain can be maintained.

Finally, as usual with Fortran, there are options and clauses which are retained for legacy purposes which should not be used in new code.

Open Command Syntax[edit | edit source]

open ([unit=]u[, olist])

Where [] indicate optional sections and olist is a comma separated list of options. In the above, u is a scalar integer expression or equivalent and is required unless the newunit option is specified. (Bad luck: we cannot open more than one file in one open statement). Technically, u is called the external file unit number, or channel number for short.

Common Options[edit | edit source]

newunit=nu where nu is a default integer variable. This allows the processor to select the channel number and, to avoid conflicts with legacy code, a negative value (not -1) will be selected that does not conflict with any current unit number in use. This is the form that should be used in all new code.

iostat=ios where ios is a default integer variable which will be set to zero if the open statement does not detect an error, but will be set to a positive value is an error does occur, and the exact value is vendor dependent. Although technically an option, this is a highly recommended option for all open commands. If this option is not present (and the err= option is not present, see below) the program will stop if there is an error. The presence of this option confers on the programmer the responsibility to check the value returned and have the program act accordingly.

iomsg=iom where iom is a scalar character variable of default kind. Again, although technically an option, this is a highly recommended option for all open commands in new code. The length of the message is error and vendor specific and may require some trial and error.

file=fln where fln is a default character variable, literal or expression which specifies the name of the external file. The file name can be a fully qualified path or a local filename. If the path points to a file on a network drive the drive must be preconnected and there is no language defined way of making this connection. (Except that we can always resort to execute_command_line)

status=stn where stn is also a default character variable, literal or expression which must evaluate (case independently) to one of 'old', 'new', 'replace', 'scratch' or 'unknown'. 'old' requires the file to exist and is typically used when the purpose of the open statement is to allow a file to be read. 'new' and 'replace' require the presence of the file= option described above, and 'new' requires the file to not exist, and 'replace' allows the file to already exist but if it does it will be overwritten. 'scratch' is special in that the file= option must not be used and the file created cannot be kept on subsequent execution of a close command. 'scratch' is typically used for the temporary warehousing of large data structures to a hard disk or similar mass storage. If 'unknown' is specified this is also the default if the status= option is not given, and the file status becomes vendor and system dependent, i.e. a manual will have to be consulted.

action=act where act is a default kind character expression, variable or value that evaluates to 'read', 'write' or 'readwrite'. Somewhat amazingly, the default is processor dependent, so the manual will have to be consulted. If 'read' is specified, the file is to be regarded as read only and attempt to execute write, print or end file statements on this channel will result in errors. Similarly if 'write' is specified, the file is to be regarded as write only and attempts to execute a read statement will result in an error. When 'write' is specified some other statements may result in an error in a processor dependent manner (e.g. backspace).

Simple Example of Open[edit | edit source]

program opena
    implicit none
    integer :: nout !channel number
    integer :: my_iostat !integer scalar to catch error status
    character (len=256) :: my_iomsg !Default-kind character variable to catch error msg

    open (newunit=nout, file="local.dat", iostat=my_iostat, iomsg=my_iomsg)
    if (my_iostat /= 0) then
        write (*,*) 'Failed to open local.dat, iomsg='//trim(my_iomsg)
        stop
    end if
    write (nout,*) 
end program

Less Common Options[edit | edit source]

access=acl where acl is a character expression, variable or literal that evaluates to either 'sequential', 'direct' or 'stream'. When opening a file that already exists, this value must correspond to an allowed value which is usually the value given when the file was created. The default for a new file is 'sequential'. 'stream' access is new at Fortran 2008 and provides some compatibility with C binary stream files. The other really important feature of 'stream' access is that a file can be positioned for write and part of the file overwritten without changing the rest of the file. For formatted stream files the new_line(nl) function will return the relevant new line characters in the character variable nl.

recl=rcl where rcl is an integer expression, variable or literal that must evaluate to a positive value. For a file to be opened for direct access this 'option' is required and must specify the length of each record. For sequential files it is optional and can be used to specify the maximum length of a record. For a file that already exists, the value or rcl must correspond to the value used to create the file. In any case, the value of rcl must also be allowed by the underlying operating system.

form=frm where frm is a character expression, variable or literal that evaluates to either 'formatted' or 'unformatted'. This option can often be omitted since the default is 'formatted' for sequential access and 'unformatted' for direct access.

blank=blk where blk is a character expression, variable or literal that provides the value 'null' or 'zero' for formatted i/o only. See bn and bz formats below.

position=psn where psn is a character expression, variable or literal that evaluates to 'asis', 'rewind' or 'append' and applies only when the access method is sequential. The default value is 'asis'. When opened, a new file is always positioned at its initial point but for existing files, the user has the option of where to position the current position.s

delim=

pad=

Options to Avoid[edit | edit source]

There is much legacy code out there and this section describes features that are still legal but which should be considered for replacement, and certainly not used in new code.

err=eno where eno is a literal integer label number. If an error occurs in the processing of the open statement the program will transfer control to the statement with label number eno. The presence of the err= option caused the program to continue if there was an error. This option should now be replaced with iostat= and iomsg=. (It is legal to specify both err= and iostat=, but without either the program will stop if an error occurs processing the open statement.)

unit=nu where nu is a default integer expression, variable or literal value which must be positive and which must not coincide with any unit already in use. If this option is placed first in the list of options the "unit=" can be omitted. This was very widely used and should now be replaced with newunit=. In very old code, nu was a fixed value and the programmer had to ensure that it did not clash with other channels in use at the same time. More recently, the inquire statement can be used to select a unit number not already in use, but this could not guard against a subsequent open statement trying to use a fixed value already in use. This is why the newunit option, and only the newunit option, is allowed to specify a negative value for the channel number.

Read[edit | edit source]

The read statement is a statement which reads from the specified input in the specified form, a variable. For example,

program reada
    implicit none
    integer :: a

    read (*,*) a
end program

will create an integer memory cell for a, and then it will read a value with the default formatting from the default input and store it in a. The first * in (*,*) signifies where the value should be read from. The second * specifies the format the user wants the number read with. Let us first discuss the format strings available. In Fortran we have at our disposal many format strings with which we may specify how we want numbers, or character strings to appear on the screen. For fixed point reals: Fw.d; w is the total number of spaces allotted for the number, and d is the number of decimal places. The decimal place always takes up one position. For example,

program reada
    inplicit none
    real :: a

    read (*,'(F5.2)') a
end program

The details of the I/O formatting e.g. '(F5.2)' will be described below

Write[edit | edit source]

Inquire[edit | edit source]

The inquire statement has two basic forms: "inquire by unit" and "inquire by file" and both are very useful and well worth getting to know. There is a more obscure form called "inquire by length" which is useful for checking the unformatted record length of potential output in order to decide what record length may be required, or whether a file with an already defined record length can cope with a given output.

Inquire by unit[edit | edit source]

Inquire by file[edit | edit source]

Inquire by length[edit | edit source]

This rather more obscure version of the inquire command is used to obtain the length of an unformatted record required to contain a given form of output and hence allow the user to either check or specify the length of a record required.

Inquire errors[edit | edit source]

Close[edit | edit source]

The close command releases the connection between a file and a Fortran channel. In the process, and depending on how the file was opened, the file can be saved or discarded. The general form of the close command is as follows:

close ([unit=]u, [, olist])

Where u is a default integer expression, variable or literal value that evaluates to the number of the channel to close, and unit= is optional. The options available in the option list are as follows:

iostat=ios where ios is a default integer variable which will return with the value 0 if the close command is executed correctly. If an error occurs the return value will be positive and a message describing the error will be provided via the iomsg option described below.

err=eno where eno is a literal integer label number. If an error occurs in the processing of the close statement, the program will transfer control to the statement with label number eno. The presence of the err= option caused the program to continue if there was an error. This option should now be replaced with iostat= and iomsg=. (It is legal to specify both err= and iostat=, but without either the program will stop if an error occurs processing the open statement.)

iomsg=iom where iom is a scalar character variable of default kind. Again, although technically an option, this is a highly recommended option for all close commands in new code. The length of the message is error and vendor specific and may require some trial and error.

status=st

Close errors[edit | edit source]

It is perhaps counter intuitive, but Fortran does not consider attempting to CLOSE a channel that is already closed to be an error. Like inquire and open, the errors close will report are effectively operating system errors. For example, close with status="delete" on a channel which is already closed is an error especially if the file no longer exists. Similarly, Fortran will report an error if a file created as 'scratch' is closed with status="keep" because the only option for scratch files is status='delete'. These limitations are predicated on the iostat (and iomsg) clause being used to allow the user to program for graceful termination when necessary, and not to obtain a full report on the performance of a close command.

I/O Formatting[edit | edit source]

List-Directed Formatting[edit | edit source]

We describe explicit formatting below but it is immediately clear that there is a whole "language within a language" so Fortran provides a short cut, or language-defined format guessing. It turns out that this default formatting is very close to a comma separated variable (CSV) processor for input. List-directed I/O is specified by a fmt=* clause, but the fmt clause is optional and can be replaced with just *.

Explicit Formatting[edit | edit source]

Fortran has a rich, but very terse, language for controlling the formatting of I/O operations. The format commands can be placed in an explicit fortmat statement or they can be placed within a clause of the relevant READ or WRITE statement either literally or stored in a character variable.



strings

Modern Fortran has a wide range of facilities for handling string or text data but some of these language-defined facilities have not been widely implemented by the compiler developers. It should be remembered that Fortran is designed for scientific computing and is probably not a good choice for writing a new word processor.

Character type[edit | edit source]

The main feature in Fortran that supports strings is the intrinsic data type character. A character literal constant can be delimited by either single or double quotes, and, where necessary, these can be escaped by using two consecutive single or double quotes. The concatenation operator is // (but this cannot be used to concatenate character entities of different KIND). Character scalar variables and arrays are allowed. Character variables have a sub-string notation to refer to and extract sub-strings.

Example

program string_1
    implicit none
    ! Declarations
    character (len=6) :: word1
    character (len=2) :: word2

    word1 = "abcdef" ! Assignment
    word2 = word1(5:6) ! Substring
    word1 = 'Don''t ' ! Escape with a double quote
    write (*,*) word2//word1 ! Concatenation
end program string_1

In the above example, the two character variables word1 and word2 are declared to have length 6 and 2 characters respectively.

In character assignment operations, if the right hand side of the assignment is shorter than the left hand side, the remaining characters on the left hand side are filled with blanks. If the right hand side is longer than the left hand side, then the right hand side is truncated. In neither case is an error raised either by the compiler or at run time.

character arrays and coarrays are permitted and can be declared and accessed in the same way as any other Fortran array. Where the array index and substring notations are to be combined, the array indices appear first and the substring expression appears second as illustrated in the final line of the following example:

character (len=120), dimension (10) :: text
text(1) = 'This is the first element of the array "text"'
text(2:3) = ' '       ! Elements 2 and 3 are blank.
text(4)(20:20) = '!'  ! Character 20 of element 4.

Unlike some programming languages, Fortran character data and variables do not require an explicit character to terminate a string. Also, unlike C-type languages, Fortran character data do not accommodate embedded and escaped control characters (e.g. /n) and all processing of output control is done via an extensive format sub-system.

Character collating sequence[edit | edit source]

Internally, Fortran maintains a collating sequence for all the permitted characters. Non-printing characters may be included in the collating sequence. The collating sequence is not specified by the language standard but most vendors support either ASCII or EBCDIC. This collating sequence means that lexical comparisons can be performed to ascertain whether e.g. 'a'<'b', but the outcome is essentially vendor specific. Hence there is a difference between functions such as ichar and iachar that is described below.

Character kind[edit | edit source]

character can also have a kind, but this is vendor-specific. It can allow compilers to support unicode, or the Russian alphabet or Japanese characters etc. It is not necessary to specify the length or kind of a character variable. If a character variable is declared with neither, the result is a variable of default kind and one character long. A single number is to indicate length, and two numbers indicate length and kind in that order. It is generally much clearer, but slightly more verbose to be explicit, as shown in lines 6-8 of the following example. The compiler vendor has control over which kinds of character are supported and the integer values assigned to access the corresponding character sets.

program string_2
    implicit none
    character :: one
    character (5) :: english_name
    character (5,2) :: japanese_name
    character (len=80) :: line
    character (len=120, kind=3) :: unicode_line
    character (kind=4, len=256) :: ebcdic_string
    !...
end program string_2

The intrinsic function selected_char_kind(name) returns the positive integer kind value of the character set with the corresponding name (e.g default, ascii, kanji, iso_10646 etc) but the only character set that must be supported is default, and if the name is not supported then -1 will be returned. Disappointingly, vendors generally have been slow to implement more than the default kind but gfortran, for instance, is a notable exception.

Language-defined Intrinsic Functions and Subprograms[edit | edit source]

Fortran has a fairly limited set of intrinsic functions to support character manipulation, searching and conversion. But the basic set is enough to construct some powerful features as required. There are some strange absences such as the ability to convert from lower-case to upper-case but this can be understood and forgiven since these concepts may not exist in many of the languages or character sets that may be represented by different character kinds. Functions such as size, lbound and ubound which apply to arrays of any data type, including character type, are not described here.

achar[edit | edit source]

achar(i, kind) returns the ith character in the ASCII collating sequence for the characters of the specified kind. The integer i must be in the range 0 < i < 127. Kind is an optional integer. If kind is not specified the default kind is assumed. achar(72) has the value 'H'. One really useful feature of achar is that it permits access to the non-printing ASCII characters such as return (achar(13)). achar will always return the ASCII character even if the processor's collating sequence is not ASCII. If kind is present, the kind parameter of the result is that specified by kind; otherwise, the kind parameter of the result is that of default character. If the processor cannot represent the result value in the kind of the result, the result is undefined. Using achar is highly recommended in preference to char, described below, because it is portable from one processor to another.

adjustl[edit | edit source]

adjustl(string) left justifies by removing leading (left) blanks from string and filling the right of string with blanks so that the result has the same length as the input string.

adjustr[edit | edit source]

adjustr(string) right justifies by removing trailing (right) blanks from string and filling the left of the string with blanks so that the result has the same length as the input string.

char[edit | edit source]

char(i, kind) returns the ith character in the processor collating sequence for the characters of the specified kind. The integer i does not have to be in the range 0 < i < 127. Kind is an optional integer. If kind is not specified the default kind is assumed. If the processor cannot represent the result value in the kind of the result, the result is undefined.

iachar[edit | edit source]

iachar(c, kind) is the inverse of achar described above. c is a single input character and iachar(c) returns the position of c in the ASCII character set as a default integer. Kind is an optional input integer and if kind is specified, it specifies the kind of the integer returned by iachar.

ichar[edit | edit source]

ichar(c, kind) is the inverse of CHAR described above. c is a single input character and ichar(c) returns the position of c in the selected character set as a default integer. Kind is an optional input integer and if kind is specified, it specifies the kind of the integer returned by ichar.

index[edit | edit source]

index(string, substring) returns a default integer representing the position of the first instance of substring in string searching from left to right. There are two optional arguments: back and kind. If the logical back is set true the search is conducted from right to left, and if the integer kind is specified, then the integer returned by index will be of that kind. If substring does not appear in string the result is 0.

len[edit | edit source]

len(c, kind) returns an integer representing the declared length of character c. This can be extremely useful in subprograms which receive character dummy arguments. c can be a character array. Kind is an optional integer which controls the kind of the integer returned by len.

len_trim[edit | edit source]

len_trimc, kind) returns the length of c excluding any trailing blanks (but including leading blanks). If c is only blanks the result is 0. Hence expressions like len_trim(adjustl(c)) can be used to count the number of characters in c between the first and last non-blank characters. Kind is an optional integer which controls the kind of the integer returned by len_trim.

new_line[edit | edit source]

new_line(c) is a character function that returns the new line character for the current processor. The kind of the returned character will be the same as the kind of c. A blank character may be returned if the character kind from which c is drawn does not contain a relevant newline character. This function is not likely to be used except in some very specific circumstances.

repeat[edit | edit source]

repeat(string, ncopies) concatenates integer ncopies of the string. Hence repeat('=',72) is a string of 72 equals signs. String must be scalar but can be of any length. Trailing blanks in string are included in the result.

scan[edit | edit source]

scan(string, set, back, kind) returns a default integer (or an integer of the optional kind) that represents the first position that any character in set appears in string. To search right to left, the optional logical back must be set true. string can be an array in which case, the result in an integer array. If string is an array then set can be an array of the same size and shape as string and each element of set is scanned for in the corresponding element of string. index, described above, is a special case of scan, because every character of set must be found and in the order of the characters in set.

selected_char_kind[edit | edit source]

selected_char_kind(name) is an integer function that returns the kind value of the character set named. The only set that must be supported by the language standard is name='DEFAULT'. If name is not supported the result is -1.

trim[edit | edit source]

trim(string) is a character valued function that returns a string with the trailing blanks removed. If string is all blanks the result has zero length.

verify[edit | edit source]

verify(string, set, back, kind) is an integer function that returns the position of the first character in string that is not in set. So verify is roughly the obverse of scan. In verify back and kind are both optional and have the same role as described in scan above. If every character in string is also in set (or string has zero length), then the function returns 0.

Regular expressions[edit | edit source]

Fortran does not have any language-defined regex or sorting capability for character data. Fortran does not have a language-defined text tokenizer but, with a little ingenuity, list directed input can provide a partial solution. However, there are Fortran libraries that wrap C regex libraries.

I/O of character data[edit | edit source]

read formatting[edit | edit source]

read for character data can be list-directed or formated using the "a" or "an" forms of this edit descriptor. In the "a" form, the width is taken from the width of the corresponding item in the list. In the "an" form, the integer n specifies the number of characters to transfer. The general edit description "gn" can also be used.

Example

character (120) :: line
open (10,"test.dat")
read (10,'(a)') line        ! Read up to 120 characters into line
read (10,'(a5)') line(115:) ! Read 5 character and put them at the end of line

write Formatting[edit | edit source]

The a and g edit descriptors exist for write as described above. The "a" form will write the whole character variable including all the trailing blanks so it is common to use trim or adjustl or both.

Example

character (len=512) :: line
!...
write (10,'(a)') trim(adjustl(line))

Internal Read and Write[edit | edit source]

Fortran has many hidden secrets and one of the most useful is that read and write statements can be used on character variables as if they were files. Hence the otherwise mystifying lack of functions to convert numbers to strings and vice versa. The character variable is treated as an 'internal file'

Example

character (120) :: text_in, text_out
integer :: i
real :: x
!...
write (text_in,'(A,I0)') 'i = ', i  ! Formatted
!...
read (text_out,*) x  ! List-directed

In addition to type conversion, this internal read/write can be used as a very flexible and bullet proof method of reading files where the contents may be of uncertain format. The external file is read line by line into a character variable, scan and verify can be used on the line to determine what is present and then an internal file read is done on the character variable to convert to real, integer, complex etc as appropriate.

Recent Extensions[edit | edit source]

character(:), allocatable[edit | edit source]

The size of character scalar data can be deferred (or "allocatable") and therefore free from being required to be declared of a specific length. The resulting scalar can then be formally allocated, or it can be automatically allocated as shown in the following example.

Example

character (:), allocatable :: string
!...
string = 'abcdef'
!...
string = '1234567890'
!...
string = trim(line)
!...

It is even possible to declare an array of assumed length elements, as illustrated below.

Example

character (:), dimension (:), allocatable :: strings

However, this feature should be used carefully and some restrictions apply

Actual/Dummy arguments of type character[edit | edit source]

It is frequently the case that a procedure may be written with a character dummy argument where the length of that argument is not known in advance. Modern Fortran allows dummy arguments to be declared with assumed length using len=*. Functions of type character can be written so that the result assumed a length related to the length of the dummy arguments.

Example

call this('Hello')
call this('Goodbye')
!...
subroutine this(string)
    implicit none
    character (len=*), intent (in) :: string
    character (len=len(string)+5)  :: temp
    !...
end subroutine

In the above example, the character variable temp is declared to have 5 more characters than string, no matter how long the actual argument is. In the next example, a function return a string, the length of which is related to the length of one or more arguments.

Example

string = that('thing', 7)
!...
function that(in_string, n) result (out_string)
    implicit none
    character (len=*), intent (in)    :: in_string
    integer, intent(in)               :: n
    character (len=len(in_string)*n)  :: out_string
    !...
end function

In circumstances where the character function has to return a string and the length of this string is not simply related to the inputs, the assumed length, allocatable form described above can be used, and is illustrated in the case conversion examples below.

character parameters[edit | edit source]

character parameters can be declared without explicitly stating the length, for example;

character (*), parameter :: place = 'COEFF_LIST_initialise'

Approaches to Case Conversion[edit | edit source]

Here are some further examples of the ideas above, but directed to the case conversion for languages where case conversion as a concept exists. In the first example, the ASCII character set functions iachar and achar are used to check each character in a string consecutively.

Example

function up_case(in) result (out)
    implicit none
    character (*), intent (in) :: in
    character (:), allocatable :: out
    integer                    :: i, j

    out = in                           ! Transfer whole array
    do i = 1, LEN_TRIM(out)            ! Each character
        j = iachar(out(i:i))           ! Get the ASCII position
        select case (j)
            case (97:122)              ! The lower case characters
                out(i:i) = ACHAR(j-32) ! Offset to the upper case
        end select
    end do
end function up_case

An alternative approach that does not rely on the ASCII representation function could be as follows:

Example

function to_upper(in) result (out)
    implicit none
    character (*), intent (in) :: in
    character (:), allocatable :: out
    integer                    :: i, j
    character (*), parameter   :: upp = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ'
    character (*), parameter   :: low = 'abcdefghijklmnopqrstuvwxyz'

    out = in                          ! Transfer all characters
    do i = 1, len_trim(out)           ! All non-blanks
        j = index(low, out(i:i))      ! Is ith character in low
        if (j>0) out(i:i) = upp(j:j)  ! Yes, then subst with upp
    end do
end function to_upper

Which routine is quicker will depend on the relative speed of the index and iachar intrinsics. In one less than very scientific test, the first method above seemed to be slightly more than twice as fast as the second method, but this will vary from vendor to vendor.



structures

Structures, structured types, or derived types(DT) were first introduced in Fortran 90.[1] Structures allow the user to create data types that hold multiple different variables.

Derived types are often implemented within modules such that one can easily reuse them. They might also hold type-bound procedures which are intended to process the structure. The arguments pass(name), nopass indicate whether the object should be passed as the first argument.

Similar to the character data type, structures can be parameterized by two different parameter types: kind, len. The kind parameters must be known at compile type (consist of constants) whereas the len parameters can change at runtime.

Simple example[edit | edit source]

As an example, we can define a new structure type, 'Fruit' which stores some basic fruit variables:

type fruit
    real      :: diameter  ! in mm
    real      :: length    ! in mm
    character :: colour
end type

We can declare two 'fruit' variables, and assign them values:

type (fruit) :: apple, banana
apple = fruit(50, 45, "red")
banana%diameter = 40
banana%length   = 200
banana%colour   = "yellow"

And we can then use the fruit variables and their child values in normal Fortran operations.

Example: type-bound procedures[edit | edit source]

!> show the usage of type-bound procedures (pass/nopass arguments)
module test_m
    implicit none
    private
    public test_type
    type test_type
        integer :: i
    contains
        procedure, nopass :: print_hello
        procedure         :: print_int
    end type
contains
    !> do not process type specific data => nopass
    subroutine print_hello
        print *, "hello"
    end subroutine

    !> process type specific data => first argument is "this" of type "class(test_type)"
    !! use class and not type below !!!!
    subroutine print_int(this)
        class(test_type), intent(in) :: this

        print *, "i", this%i
  end subroutine
end module

program main
    use test_m
    implicit none
    type (test_type) :: obj

    obj%i = 1
    call obj%print_hello
    call obj%print_int
end program

Example: parameterized type[edit | edit source]

! testing types with params: kind + len
program main
    implicit none
    type matrix(rows, cols, k)
        integer, len  :: rows, cols
        integer, kind :: k = kind(0.0)    ! optional/default value
        real (kind=k), dimension(rows, cols) :: vals
    end type 
    type (matrix(rows=3, cols=3)) :: my_obj
end program

References[edit | edit source]

  1. A Look at Fortran 90 - Lahey computer systems



memory management

Introduction and historical background[edit | edit source]

Most Fortran programs prior to the Fortran90 standard used self-contained data, without structures, and without much in the way of shared, structured data. However, it was possible to share data, in structured and unstructured ways, using common blocks. Furthermore, there used to be little memory management going on in a Fortran program. Until Fortran90 allocated storage wasn't even possible, except via certain extensions (e.g. Cray pointers). Modern Fortran, however, supports many modern programming paradigms, has full support for allocatable data (including allocatable types), and allows for the use of pointers.

Shared variables in modules[edit | edit source]

Since Fortran90, shared variables are conveniently managed by the use of modules. Common blocks were used to define global memory prior to the Fortran90 standard; their use in modern Fortran is discouraged. A Fortran module can also contain subroutines and functions, but we shall leave the discussion of these features for later. As for the management of shared variables, they may be defined in a module:

module shared_variables
    implicit none
    private
    integer, public, save :: shared_integer
    integer, public, save :: another_shared_integer
    type, public :: shared_type
        logical :: my_logical
        character :: my_character
    end type shared_type
    type (shared_type), public :: shared_stuff
end module shared_variables

Note that it is considered good practice to declare any module private, even if it contains only public variables. Although save is the default for a variable in a module, meaning that it retains its previous value whenever the variables within the modules are used, it is sometimes considered good practice to make this explicit. The module can then be used in the main program:

program my_example
    use shared_variables, only: shared_integer, shared_stuff
    implicit none
    integer :: some_local_integer

    ! This will work and assign shared_integer to some local variable.
    shared_integer = some_local_integer
    ! This will print the component my_character from type shared_stuff
    ! to stdout.
    write (*,*) shared_stuff%my_character
    ! This, however, will not work, since another_shared_integer was not
    ! imported from the module - the program will not compile.
    shared_integer = another_shared_integer
end program my_example

Common blocks[edit | edit source]

Common blocks have been replaced by the use of public variables in modules in modern Fortran standards (Fortran90 and later). They are, however, historically important due to their use in older Fortran standards (77 and prior). A common block was Fortran's way of using shared, common storage for standards prior to Fortran90. In its simplest form, a common block is a way of defining global memory. Be careful, though. In most languages, each item in common memory is shared as a globally known name separately. In Fortran, however, the common block is a shared thing. I'll show several examples, but each example will share i and another_integer, and my_array, a 10x10 array of real numbers.

In C, for instance, I can define the shared memory using:

int i;
int another_integer;
float my_array[10][10];

and use these data elsewhere with:

extern float my_array[10][10];
extern int i;
extern int another_integer;

Note that one module declares the storage, and another uses the storage. Also note that the definitions and usages are not in the same order. This is because in C, as in most languages, i, another_integer, and my_array are all shared items. Not so in Fortran. In Fortran, all routines sharing this storage would have a definition something like this:

common i, another_integer, my_array
integer another_integer
real my_array(10,10)

This common block is stored as a block of data, as a linkable named structure. The only problem is that we don't know its name. Various compilers will give various names to this block. In some systems, the block actually doesn't have a name. We can avoid this problem by giving the structure a name. For instance,

common /my_block/ i, another_integer, my_array
integer another_integer
real my_array(10,10)

Using this form, two different Fortran programs can identify the same area of storage and share it, without having to know the structure of all shared storage. Also using this format, a C or other program could share the storage. For instance, a C program wanting to share this storage would declare the same storage as follows:

extern struct {
    int i;
    int another_integer;
    float my_array[10][10];
} my_block;

In the above example, having the my_block names match is critical, as well as having the types, sizes, and order match. However, having the names internally match is not since these names are known only locally. Also note that in the above example, Fortran's my_array(i,j) matches C's my_block.my_aArray[j][i].

Byte alignment[edit | edit source]

Byte alignment of intrinsic data types can mostly be ensured simply by using the appropriate kind. Fortran does not have any way of automatically ensuring derived data types are byte aligned. However, it is quite simple for the programmer to ensure that appropriate padding for data is inserted. For example, let's say we have a derived type that contains a character and an integer
type :: my_type
    integer (kind=4) :: ival
    character (len=1) :: letter
end type
Arrays of this type will have elements of size 5 bytes. If we want the elements of an array of this type to align every 8 bytes we need to add 3 more bytes of padding. We can do this by adding characters that serve no other purpose than as padding.
type :: my_type
    integer (kind=4) :: ival
    character (len=1) :: letter
    character (len=3) :: padding
end type

Memory management with pointers[edit | edit source]

In Fortran one can use pointers as some kind of alias for other data, e.g. such as a row in a matrix.

Pointer states[edit | edit source]

Each pointer is in one of the following states

  • undefined: right after definition if it has not been initialized
  • defined
    • null/not associated: not the alias of any data
    • associated: alias of some data.

The intrinsic function associated distinguished between the second and third states.

Assignments[edit | edit source]

Overview[edit | edit source]

We will use the following example: Let a pointer ptr be the alias of some real value x.

real, target :: x
real, pointer :: ptr
ptr => x

For the next example we will use a real matrix matr as target and the pointer ptr should alias a specific row.

real, dimension (4, 4), target :: matr
real, dimension (:), pointer :: ptr
ptr => matr(2, :)

Pointers can also be appointed to other pointers. This causes them to be an alias of the same data that the first pointer is. See the example below.

real, target :: x
real, pointer :: ptr1, ptr2
ptr1 => x
ptr2 => ptr1

Ordinary vs. pointer assignments[edit | edit source]

The difference between ordinary and pointer assignments of pointers can be explained by the following equalities. Assume this setup

real, target :: x1, x2
real, pointer :: ptr1, ptr2
ptr1 => x1
ptr2 => x2

Ordinary assignments of pointers lead to assignments of the data they point to. One can see this by the following two statements which are equal.

! Two equal statements
ptr1 = ptr2
x1 = x2

In contrast, pointer assignments changes the alias of one of the pointers and no change on the underlying data. See the equal example statements.

! Two equal statements
ptr1 => ptr2
ptr1 => x2

Memory allocation[edit | edit source]

After definition of pointers one can allocate memory for it using the allocate command. The memory pointed to by a pointer is given free again by the deallocate command. See the following example.

program main
    implicit none
    real, allocatable :: ptr

    allocate (ptr)
    ptr = 1.
    print *, ptr
    deallocate (ptr)
end program main

Examples[edit | edit source]

Allocatable vs. pointer[edit | edit source]

You can declare an array to have a known number of dimensions, but an unknown size using allocation:

real, dimension (:,:), allocatable :: my_array
allocate (my_array(10,10))
deallocate (my_array)

You can also declare something as a pointer:

real, dimension (:,:), pointer :: some_pointer
allocate (some_pointer(10,10))
deallocate (some_pointer)

In archaic versions of FORTRAN (77 and before), you'd just have a big static array and use whatever portion of it you need.



error handling

Typically in an error situation, your program will stop, and you'll get an error message. The only exception to this is that at the end of read and write statements' parenthesized control list, you can add, err=label to determine which line to jump to in the event of an error.

Modern Fortran (from Fortran 90 onwards) has introduced four main areas for error capture:

1) File handling and i/o operation error handling

2) IEEE floating point error detection and reporting

3) Dynamic allocation

4) Command line operations

File handling and I/O Operations[edit | edit source]

All the external file handling statements and I/O operations (open, read, write, close, inquire, backspace, endfile, flush, rewind and wait) can now take optional iostat and iomsg clauses. iostat is an integer which returns a non-zero value if there is an error, in which case, the character variable assigned to iomsg will return a brief error message. The non-zero integers and the messages are compiler dependent but the intrinsic module, iso_fortran_env, gives access to two important values: iostat_end and iostat_eor. If an error occurs, and iostat is non-zero, execution will not stop. The ERR clause is still supported but should not be used.

Example[edit | edit source]

integer :: my_iostat
character (256) :: my_iomsg

open (file='my.dat', unit=10, iostat=my_iostat, iomsg=my_iomsg)
if (my_iostat/=0) then
    write (*,*) 'Open my.dat failed with iostat = ', my_iostat, ' iomsg = '//trim(my_iomsg)
end if
Note that the length required for the message character is vendor and error dependent.

IEEE floating point error detection and reporting[edit | edit source]

This is a big topic, but in essence modern Fortran provides access to three intrinsic modules: IEEE_arithmetic, IEEE_exceptions and IEEE_features. These features can be used to intercept errors such as divide by zero and overflow but at the expense of some performance.

The IEEE_features module controls access to the features the programmer may require, by use association in the scoping unit where the programmer places the use statement,

Example[edit | edit source]

subroutine blah
    use, intrinsic :: ieee_features
    
    ! ...
end subroutine blah
See Chapter 11 in Metcalf et al, Modern Fortran Explained, OUP. All the necessary basic facilities exist in order for the programmer to construct a try/catch system if desired.

Dynamic Allocation[edit | edit source]

Modern Fortran allows run-time allocation and deallocation of arrays of any type, and a typical error might be to try to dynamically allocate an array so large that there is not enough memory, or an attempt to deallocate an array which is not already allocated. There are optional clauses stat and errmsg which can be used to prevent program failure and allow the programmer to take evasive action.

Example[edit | edit source]

real, allocatable, dimension (:) :: x
integer :: my_stat
character (256) :: my_errmsg

allocate (x(100000000), stat=my_stat, errmsg=my_errmsg)
if (my_stat/=0) then
    write(*,*) 'Failed to allocate x with stat = ', my_stat, ' and errmsg '//trim(my_errmsg)
end if
These features are available in the equivalent coarray features.

Command Line Operations[edit | edit source]

Modern Fortran also supports error detection for the execution of command line operations,

Example[edit | edit source]

integer :: my_cmdstat
character (256) :: my_cmdmsg

call execute_command_line('my.exe', cmdstat=my_cmdstat, cmdmsg=my_cmdmsg )
if (my_cmdstat/=0) stop
In this example, the programmer of the my.exe program has the responsibility for what codes are returned and what error messages are exposed, except that -1 and -2 are reserved for allowing the compiler vendor indicating what features may be supported.



parallel processing

Parallelism is included in the Fortran 2008 standard. To use parallel features, a Fortran program must be compiled with parallelism enabled. For example, the Intel ifort compiler uses the flag -coarray.

Images[edit | edit source]

Fortran uses a Partitioned Global Address Space (PGAS) model for parallelism. For each processor, the program is executed as a separate duplicate "image" of the program, each with their own separate memory partition. Consider the following program:
program hello
    implicit none
    write (*,*) 'Hello from ', this_image(), 'of', num_images()
end program hello
The intrinsic function this_image returns the number of the image that is being executed, and the intrinsic function num_images returns the total number of images for the program. If the program is compiled and executed with 4 processors, the output might look something like this:
Hello from image 1 of 4
Hello from image 4 of 4
Hello from image 2 of 4
Hello from image 3 of 4
Note that the images are executed asynchronously and so the output may not appear in the order 1, 2, 3 then 4.

Coarrays[edit | edit source]

Coarrays are a way of communicating data in arrays across images. A coarray is just like a normal array but it has extra codimensions for each image. Codimensions can be declared and indexed using the square brackets []. For example to declare a rank 1 coarray with size of 10 and a codimension of size 4:
real :: coarr(10)[4]
! Or you can use declaration attributes to do the same thing
real, dimension (10), codimension [4] :: another_coarr
Scalar variables can also be coarrays:
integer :: scalar[*]
Here, * denotes the maximum number of available processors. The codimensions can have multiple axes just like normal dimensions, however, there is a limit of rank 15 for codimensions. Transferring data between images is as simple as indexing on the codimensions.
! Set all images to 1
coarr = 1
! Indexing
another_coarr(3)[4] = coarr(3)[3]



OOP in Fortran

Object-oriented programming[edit | edit source]

Module[edit | edit source]

Overview[edit | edit source]

Data can be gathered in modules. The general form is given by

module <name>
    [use <module_names>]
    [<declarations>]
contains
    [<subroutines and functions>]
end module [<name>]

Data access[edit | edit source]

There are three possible access properties: public, private, protected.

  • public: Outside code has read and write access.
  • private: Outside code has no access.
  • public, protected: Outside code has read access.

Using module in other code[edit | edit source]

One can include the module's public data in outside code. There are three ways.

  • use <moduleName>: includes all public data and methods
  • use <moduleName>, <renames>: includes all public data and methods, but renames some public data or methods
  • use <moduleName>, only: <subset>: includes only some public data and methods

Example[edit | edit source]

General overview[edit | edit source]
module test_m
    implicit none
    private  ! All data is by default private.
    ! These procedures are set public -> accessible outside
    public print_coords, set_coords 
    real :: x, y  ! Not accessible outside module.
contains
    subroutine print_coords
        print *, "x, y", x, y
    end subroutine

    subroutine set_coords(new_x, new_y)
        real, intent(in) :: new_x, new_y

        x = new_x
        y = new_y
    end subroutine
end module

program main
    use test_m  ! Import the "test_m" module
    implicit none

    call set_coords(1.0, 1.0)  ! Call the public procedure from test_mod
    call print_coords
end program
Data access[edit | edit source]
module data_access_m
    implicit none
    private
    public a, b
    protected b
    private c
    integer :: a = 1
    integer :: b = 1
    integer :: c = 1
end module

program main
    use data_access_m

    ! Accessing public object works.
    print *, a
    ! Editing public object works.
    a = 2
    ! Accessing protected object works.
    print *, b
    ! Editing protected object does not work.
    !b = 2 <- ERROR
    ! Accessing private object does not work
    !print *, c <- ERROR
    ! Editing private object does not work
    !c = 2 <- ERROR
end program
Using modules[edit | edit source]
module test_module
    implicit none
    private
    integer, public :: a = 1
    integer, public, protected :: b = 1
    integer, private :: c = 1
end module test_module

!> Import all public data of test_module.
program main
    use test_module

    print *, a, b
end program main

!> Import all data, and rename.
program main
    use test_module, better_name => a

    ! New name use available.
    print *, better_name
    ! Old name is not available anymore.
    !print *, a  <- ERROR
end program main

!> Import only a subset of the public data.
program main
    use test_module, only : a

    ! Only a is loaded
    print *, a
    ! b is not loaded
    !print *, b  <- ERROR
end program main

Submodule[edit | edit source]

Modules can be extended using submodules. Multiple advantages arise

  • splitting of large modules
  • splitting of interface definitions and implementations such that dependent modules do not need to be recompiled if the implementations change
  • two modules need data from each other.

Example[edit | edit source]

Splitting of definitions and implementations[edit | edit source]
!> simple module about circles
module circle_mod
    implicit none
    private
    public :: area, radius
    real            :: radius
    real, parameter :: PI = 3.1415

    interface  ! Interface block needed. Each function implemented via submodule needs an entry here.
        module function area() ! Important. Note the "module" keyword.
            real :: area
        end function 
    end interface
end module 

submodule (circle_mod) circle_subm  ! Submodule (parent_mod) child_mod.
contains
    module function area()  ! Again "module" keyword.
        area = PI*radius**2
    end function 
end submodule

program main
    use circle_mod
    implicit none

    radius = 1.0
    print *, "area:", area()
end program

Derived data types[edit | edit source]

In Fortran one can derive structures off of other structures, so called derived data types. The derived types will have the features of the parent type as well as the newly added ones and the general syntax is given by:

type, extends(<parentTypeName>) :: <newTypeName>
    <definitions>
end type

The following example shows different types of people within a company.

module company_data_mod
    implicit none
    private
    public phone_type, address_type, person_type, employee_type, salaried_worker_type, hourly_worker_type

    type phone_type
        integer :: area_code, number
    end type

    type address_type
        integer                        :: number
        character (len=:), allocatable :: street, city
        character (len=2)              :: state
        integer                        :: zip_code
    end type

    type person_type
        character (len=:), allocatable :: name
        type (address_type)            :: address
        type (phone_type)              :: phone
        character (len=:), allocatable :: remarks
    end type

    type, extends (person_type) :: employee_type
        integer :: phone_extension, mail_stop, id_number
    end type

    type, extends (employee_type) :: salaried_worker_type
        real :: weekly_salary
    end type

    type, extends (employee_type) :: hourly_worker_type
        real :: hourly_wage, overtime_factor, hours_worked
    end type
end module

program main
    use company_data_mod
    implicit none

    type (hourly_worker_type) :: obj
end program

Destructors[edit | edit source]

One can define procedures which will be invoked before the object is automatically deleted (out of scope). This is done with the statement final. The following example illustrates it

module person_m
    implicit none

    type person
        integer, allocatable :: numbers(:)
    contains
        final :: del
    end type
contains
    subroutine del(this)
        !! example for a derived type's destructor. allocatables are
        !! deallocated automatically anyways. this is just to show the usage of
        !! "final".
        type (person), intent (inout) :: this

        if (allocated(this%numbers)) deallocate (this%numbers)
    end subroutine 
end module

Abstract base type and deferred procedure[edit | edit source]

One can set the base type as abstract such that one cannot initialize objects of that type but one can derive sub-types of it (via extends). Specific procedures which should be defined in the sub-type need the property deferred as well as an explicit interface.

The following example illustrates their use.

module shape_m
    implicit none

    type, abstract :: shape
        real :: a, b
    contains
        procedure :: print => shape_print
        procedure (area_shape), deferred :: area
    end type

    interface
        real function area_shape(this)
            import :: shape
            class (shape), intent (in) :: this
        end function
    end interface
contains
    subroutine shape_print(this)
        class (shape), intent (in) :: this

        print *, 'a,b', this%a, this%b
    end subroutine
end module

module line_m
    use shape_m
    implicit none
    private
    public line

    type, extends (shape) :: line
    contains
        procedure :: area
    end type
contains
    real function area(this)
        class (line), intent (in) :: this

        area = abs(this%a - this%b)
    end function
end module

module rectangle_m
    use shape_m
    implicit none
    private
    public rectangle

    type, extends(shape) :: rectangle
    contains
        procedure :: area
    end type
contains
    real function area(this)
        class (rectangle), intent (in) :: this

        area = this%a * this%b
    end function
end module

program main
    use line_m
    use rectangle_m
    implicit none

    type (line)      :: l
    type (rectangle) :: r

    ! line
    l%a = 2.0
    l%b = 4.0
    print *, "line ...  "
    call l%print
    print *, "-> from:  ", l%a
    print *, "-> to:    ", l%b
    print *, "-> length:", l%area()

    ! rectangle
    r%a = 3.0
    r%b = 5.0
    print *
    print *, "rectangle ..."
    call r%print
    print *, "-> side a:", r%a
    print *, "-> side b:", r%b
    print *, "-> area:  ", r%area()
end program

Polymorphic Pointer[edit | edit source]

One can create pointers to child classes by using type definitions in allocate statements and the select type environment. The following example highlights its use.

module shape_m
    implicit none

    type, abstract :: shape
        ! Just an empty class used to implement a parent class.
        ! reason for abstract: there shouldnt be objects of TYPE(!) shape, just 
        ! polymorphic CLASS instances.
    end type
end module

module line_m
    use shape_m
    implicit none

    type, extends (shape) :: line
        ! A child class w/ one attribute.
        ! Reason for extends(shape): polymorphic shape pointer can point to
        ! objects of this type.
        real :: length
    end type
end module

module rectangle_m
    use shape_m
    implicit none

    type, extends (shape) :: rectangle
        ! A child class w/ another attribute
        ! Reason for extends(shape): (see explanation in line type)
        real :: area
    end type
end module

program main
    use rectangle_m
    use line_m
    implicit none

    class (shape), allocatable :: sh  ! Pointer to parent class.
    ! allocate (line :: sh)
    allocate (rectangle :: sh)  ! Allocate using child types
    select type (x => sh)   ! Associate block. "x" will be a pointer to the child object and of its type(!!)
        type is (line)      ! Select the right child type (the one we used in the allocate statement)
            x%length = 1.0
            print *, 'line length', x%length
        type is (rectangle)
            x%area = 2.0
            print *, 'rectangle area', x%area
        ! class is ()  ! Select by using classes.
        class default  ! If nothing of the above applied.
            error stop 'class/type not specified!'
    end select
end program



language extensions

Procedure Overloading[edit | edit source]

Like several other languages, Fortran 90 and newer supports the ability to select the appropriate routine from a list of routines based on the arguments passed. This selection is done at compile time and is thus unencumbered by run-time performance penalties. This feature is accessed by use of modules and the interface block.

In the following example, a module is specified which contains an interface function f which can handle arguments of various types.

module extension_m
    implicit none
    private
    public f  ! Only the interface f is accessable outside the module.

    interface f  ! The overloaded function is called "f".
          module procedure f_i  ! "f(x)" for integer argument "x" will call "f_i"
          module procedure f_r  ! "f(x)" for real    argument "x" will call "f_r"
          module procedure f_z  ! ...        complex ....                   "f_z"
   end interface
contains
   integer function f_i(x) result (y)
      integer, intent (in) :: x

      y = x**2 - 1
   end function 

   real function f_r(x) result(y)
      real, intent (in) :: x

      y = x**2 - 1.0
   end function 

   complex function f_z(x) result(y)
      complex, intent (in) :: x

      y = x**2 - 1.0
   end function 
end module

A program which uses this module now has access to a single interface function f which accepts arguments that are of integer, real, or complex type. The return type of the function is the same as the input type. In this way the routine is much like many of the intrinsic functions defined as part of the Fortran standard. An example program is given below:

program main
    use extension_m
    implicit none
    complex :: xz, yz
    integer :: xi, yi
    real    :: xr, yr

    xi = 2
    xr = 2.0
    xz = 2.0
    yi = f(xi)
    yr = f(xr)
    yz = f(xz)
end program

Intrinsic functions[edit | edit source]

One can extend intrinsic functions. This is similar to overload operators.

Here we will demonstrate this by extending the sqrt function. The intrinsic function is not implemented for arguments of integer type. This is because there is no clear idea how to define the result of non integer type (e.g. , but how to define ). We implement a method here where the result is always the nearest integer.

module sqrt_int_m
    implicit none
    private
    public sqrt
    ! use intrinsic sqrt for data types which are not overloaded
    intrinsic :: sqrt
    ! extend sqrt for integers
    interface sqrt
        module procedure sqrt_int
    end interface 
contains
  pure integer function sqrt_int(i)
    integer, intent (in) :: i

    sqrt_int = nint(sqrt(real(i)))
  end function 
end module 

program main
    use sqrt_int_m
    implicit none
    integer :: i

    ! sqrt can be called by real and integer arguments
    do i = 1, 7
        print *, "i, sqrt(i), sqrt(real(i))", i, sqrt(i), sqrt(real(i))
    end do
end program

Derived Data Types[edit | edit source]

Fortran 90 and newer supports the creation of new data types which are composites of existing types. In some ways this is similar to an array, but the components need not be all of the same type and they are referenced by name, not index. Such data types must be declared before variables of that type, and the declaration must be in scope to be used. An example of a simple 2d vector type is given below.

type :: vec_t
   real :: x,y
end type

Variables of this type can be declared much like any other variable, including variable characteristics such are pointer or dimension.

type (vec_t) :: a,b
type (vec_t), dimension (10) :: vecs

Using derived data types, the Fortran language can be extended to represent more diverse types of data than those represented by the primitive types.

Operator Overloading[edit | edit source]

Operators can be overloaded so that derived data types support the standard operations, opening the possibility of extending the Fortran language to have new types which behave nearly like the native types.

Assignment[edit | edit source]

The assignment operator = can be overloaded. We will demonstrate this by the following example. Here, we define how the assignment of a logical type on the left and an integer on the right should be performed.

module overload_assignment_m
    implicit none
    private
    public assignment (=)

    interface assignment (=)
        module procedure logical_gets_integer
    end interface
contains
    subroutine logical_gets_integer(tf, i)
        logical, intent (out) :: tf
        integer, intent (in)  :: i

        tf = (i == 0)
    end subroutine
end module

program main
    use overload_assignment_m
    implicit none
    logical :: tf

    tf = 0
    print *, "tf=0:", tf  ! Yields: T
    tf = 1
    print *, "tf=1:", tf  ! Yields: F
end program

Intrinsic operators[edit | edit source]

One can overload intrinsic operators, such as +,-,*.

In the following example we will overload the * operator to work as the logical .and..

module overload_asterisk_m
    implicit none
    private
    public operator (*)

    interface operator (*)
        module procedure logical_and
    end interface
contains
    pure logical function logical_and(log1, log2)
        logical, intent (in) :: log1, log2

        logical_and = (log1 .and. log2)
    end function
end module

program main
  use overload_asterisk_m
  implicit none
  logical, parameter :: T = .true., F = .false.

  print *, "T*T:", T*T  ! Yields: T
  print *, "T*F:", T*F  ! Yields: F
  print *, "F*T:", F*T  ! Yields: F
  print *, "F*F:", F*F  ! Yields: F
end program

New operators[edit | edit source]

One can create newly self-created operators.

We demonstrate this by the following example: We create an unary operator .even. <int> which outputs a logical if the given integer is even as well as a binary operator <reals> .cross. <reals> that performs the standard cross product of two real vectors.

module new_operators_m
    implicit none
    private
    public operator (.even.)
    public operator (.cross.)

    interface operator (.even.)
        module procedure check_even
    end interface

    interface operator (.cross.)
        module procedure cross_product
    end interface
contains
    pure logical function check_even(i)
        integer, intent (in) :: i

        check_even = (modulo(i, 2) == 0)
    end function

    function cross_product(x, y) result(z)
        real, intent (in) :: x(3), y(3)
        real :: z(3)

        z(1) = x(2)*y(3) - x(3)*y(2)
        z(2) = x(3)*y(1) - x(1)*y(3)
        z(3) = x(1)*y(2) - x(2)*y(1)
    end function
end module

program main
    use new_operators_m
    implicit none
    integer :: i
    real    :: x(3), y(3)

    do i = 1, 6
        print *, "i:", i, "even?", .even. i
    end do
    print *

    x = [ 1, 2,  3]
    y = [-1, 2, -3]
    print *, 'x', x
    print *, 'y', y
    print *, 'x cross_product y', x .cross. y
end program



Mixing languages

Types[edit | edit source]

Fortran types map quite well to intrinsic types in other compiled languages. The following is a table of Fortran-to-C types:

 Fortran            C
 =======            =
 COMMON             extern struct
 INTEGER*1          signed char
 INTEGER*2          short
 INTEGER*4          long
 INTEGER*8          long long
 INTEGER            int
 REAL               float
 REAL*4             float
 REAL*8             double
 REAL*16            long double
 LOGICAL            int
 LOGICAL*n          char [n]
 CHARACTER*n        char [n]
 DOUBLE PRECISION   double
 COMPLEX            float [2]
 COMPLEX*8          float [2]
 COMPLEX*16         double [2]
 COMPLEX*32         long double [2]

Arrays[edit | edit source]

The layout of Fortran arrays in memory contrasts with arrays in C and many C-based languages. When iterating over contiguous array elements in C, the rightmost array subscript varies the fastest, while in Fortran, the leftmost array subscript varies the fastest. Hence the element following x(1,1) in contiguous memory is x(2,1), not x(1,2). Furthermore, the element sub-scripting in C starts at 0, while Fortran starts at 1 by default. An element in Fortran may be x(1), while the equivalent value in C code would be x[0]. However, when passing a Fortran array to a C function, you do not need to (and should not) reshape the array into C-style subscripts first; the compiler will automatically do this for you.

Global Storage[edit | edit source]

See the Common Blocks section.

Subroutine and function calls[edit | edit source]

Many languages push their arguments onto the stack, some as constants and some as addresses. In most compilers, Fortran will compile a block of pointers to variables and constants, and push the address of that block. So, if we had a Fortran procedure defined as follows:

subroutine my_sub(i, j, x)

then the C definition would be:

struct my_sub_args {
    int *i;
    int *j;
    float *x;
} my_sub_args = {&i, &j, &x};
void my_sub(my_sub_args*);

The C code could call the routine as follows:

my_sub(&my_sub_args);

The PL/1 Special Case[edit | edit source]

In PL/1, you can define an external common block, subroutine, or procedure to be of type FORTRAN. When you do this, everything, down to subscript order, will be handled for you. Likewise, you can define a PL/1 item, such as a subroutine, to be of type FORTRAN, and it will then be callable by Fortran using Fortran's calling conventions.



Documenting Fortran

FORD - FORtran Documenter[edit | edit source]

A great program for documenting fortran source code is FORD.

See the github page for instructions on installing, and usage of FORD: github.com.

Documenting Fortran using Doxygen[edit | edit source]

Documentation can be created right from source code using Doxygen.

The commandline program doxygen creates the documentation using configuration files. The gui program doxygen-wizard helps creating those files.

Overview[edit | edit source]

The source code needs to be documented using special comment syntax:  !>, and  !!.

One should always set OPTIMIZE_FOR_FORTRAN = YES within the configuration file.

Doxygen commands are usually ended by an empty comment line or a new doxygen command.

Note that support for Fortran is rather bad in doxygen. Even simple constructs such as public/private statements inside of types are not supported (see here github.com).

LaTeX[edit | edit source]

One can also include LaTeX code within the documentation. Doxygen's website gives detailed information.

Examples[edit | edit source]

subroutine[edit | edit source]

!> @brief inserts a value into an ordered array
!!
!! An array "list" consisting of n ascending ordered values. The method insert a
!! "new_entry" into the array.
!! hint: use cshift and eo-shift
!!
!! @param[in,out]   list    a real array, size: max_size
!! @param[in]       n       current values in the array
!! @param[in]       max_size    size if the array
!! @param[in]       new_entry   the value to insert
subroutine insert(list, n, max_size, new_entry)
    implicit none
    real, dimension (:), intent (inout) :: list
    integer, intent (in) :: n, max_size
    real, intent (in) :: new_entry

    ! code ........
end subroutine insert

function[edit | edit source]

!> @brief calcs the angle between two given vectors
!!
!! using the standard formula:
!!  \f$\cos \theta = \frac{ \vec v \cdot \vec w}{\abs{v}\abs{w}}\f$.
!!
!! @param[in]   \f$v,w\f$   real vectors
!! @return  a real value describing the angle. 0 if \f$\abs v\f$ or \f$\abs w\f$ below a
!!          threshold.
pure function calc_angle(v, w) result (theta)
  implicit none
  real, dimension (:), intent (in) :: v, w
  real :: theta

  ! code .......
end function calc_angle

Troubleshooting[edit | edit source]

Empty documentation[edit | edit source]

If the documentation is just an empty page then one can try setting EXTRACT_ALL = YES.



prettify code

Prettify Source Code[edit | edit source]

There are tools available to automatically edit source code such that it is more easily readable. This includes topics such as

  • indentation
  • alignment
  • lower/uppercase words

fprettify[edit | edit source]

A python script fprettify for auto-indentation and whitespace formatting is readily available from github or PyPI.



Fortran examples

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). By convention most contemporary Fortran compilers select the language standard to use during compilation based on source code file name suffix: FORTRAN 77 for .f (or the less common .for), Fortran 90 for .f90, Fortran 95 for .f95. Other standards, if supported, may be selected manually with a command line option.

FORTRAN II, IV, and 77 compilers[edit | edit source]

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[edit | edit source]

Simple Fortran II program[edit | edit source]

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 -
C INTEGER VARIABLES START WITH I,J,K,L,M OR N
      READ(5,501) IA,IB,IC
  501 FORMAT(3I5)
      IF (IA) 701, 777, 701
  701 IF (IB) 702, 777, 702
  702 IF (IC) 703, 777, 703
  777 STOP 1
  703 S = (IA + IB + IC) / 2.0
      AREA = SQRT( S * (S - IA) * (S - IB) * (S - IC) )
      WRITE(6,801) IA,IB,IC,AREA
  801 FORMAT(4H A= ,I5,5H  B= ,I5,5H  C= ,I5,8H  AREA= ,F10.2,
     $13H SQUARE UNITS)
      STOP
      END

Simple Fortran IV program[edit | edit source]

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,
     $13H SQUARE 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[edit | edit source]

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[edit | edit source]

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[edit | edit source]

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)[edit | edit source]

 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[edit | edit source]

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[edit | edit source]

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[edit | edit source]

Greatest common divisor[edit | edit source]

The following introductory example in FORTRAN 77 finds the greatest common divisor for two numbers and 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[edit | edit source]

The following FORTRAN 77 example prints out the values of (where ) for values of .

*     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 , where is the imaginary unit .
  • 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 . 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 program to find the area of a triangle[edit | edit source]

program area
    implicit none
    real :: A, B, C, S

    ! area of a triangle
    read *, A, B, C
    S = (A + B + C)/2
    A = sqrt(S*(S-A)*(S-B)*(S-C))
    print *,"area =",A
    stop
end program area

Fortran 90/95 examples[edit | edit source]

Summations with a DO loop[edit | edit source]

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[edit | edit source]

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[edit | edit source]

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[edit | edit source]

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[edit | edit source]

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[edit | edit source]

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[edit | edit source]

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[edit | edit source]

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



FAQ

This article contains some frequently-asked questions (FAQs) regarding Fortran and their answers.

Q. Should I learn Fortran? Is it obsolete?[edit | edit source]

A: Fortran is not obsolete and it will not be any time soon. Fortran is a general purpose programming language and is suitable for many applications. However, it excells at numerical computation and high performance computing. It is fast, portable and it has seamless handling of arrays. Because of this, there are many high-quality Fortran libraries for numerical algorithms and it is widespread in scientific communities (e.g. numerical weather predicion). The language itself is still maintained and regularly updated with modern features; the latest version is Fortran 2018.

Q: What Fortran compiler should I use?[edit | edit source]

A: Oracle Solaris Studio, GNU Fortran, G95, and Silverfrost (Windows only) are free software Fortran 95 compilers, and Absoft, IBM, Intel, Lahey, NAG, Pathscale and PGI sell Fortran compilers. Comparative information on Fortran compilers is available at Wikipedia.

Q: How do I create numbered file names such as out_01.txt, out_02.txt etc.?[edit | edit source]

A: Use an "internal write" to create the file names, for example

write (file_name,"('out_',i2.2,'.txt')") i

A: A neater way to do this would be:

i=<file number>
WRITE(file_name, fmt = '(A4,I0,A4)')'out_',i,'.txt'

This way the formatting is clear and you are writing the correct string to the variable. I assume you wanted an integer as the number. 'I' format statement requires an Integer length, or zero in some cases. You are probably thinking of F where the decimal point denotes the number of decimals to consider.

Q: What does the open statement look like using this technique? OPEN(UNIT = __, FILE = ???, STATUS='NEW')?[edit | edit source]

A: Gfortran does not accept this block

      write(file_name,'cp',(i5.5),'.out') ITN
      open  (67,file = file_name)

Gives, ERROR, file tag must be of type CHARACTER

Can someone else help with this?

A: See the answer above. Basically the way you have written the variable file_name is incorrect.

WRITE(file_name,fmt='(A2,I0,A4)')'cp',ITN,'.out'
OPEN(UNIT=67, file=file_name, status='new')

Assuming that ITN has been declared as an integer and given a value.

Q: How can I convert a string to an integer and other types? What about the reverse?[edit | edit source]

A: Use an "internal read" or "internal write". In effect, you use a character variable as the file name and read or write the I/O list. You write things like

   read (character_variable, format) list of variables

to convert a string to another type and

   write (character_variable, format) list of variables

to convert to a string from another type, as demonstrated by the following program:

program xconvert_integer_string   
character(20) :: cnum 
integer       :: i 
i = 445 
write(cnum,'(i5)') i 
write(*,'(a)') trim(cnum) ! should output "  445" 
write(cnum,'(i5.5)') i 
write(*,'(a)') trim(cnum) ! should output "00445" 
i = 34 
write(cnum,'(i0)') i 
write(*,'(a)') trim(cnum) ! should output "34" 
end program xconvert_integer_string

This answer is based on messages in comp.lang.fortran by Paul van Delst and Dick Hendrickson.

Q. How do I issue a command to the operating system within a Fortran program?[edit | edit source]

A. The Fortran 2008 standard provides the execute_command_line intrinsic procedure to make system calls. Prior versions have no standard way to make system calls, but many compilers have an extension named "system" or something similar. Please consult the documentation of your compiler. In Fortran 2003, one can call C code, and it is possible to call the operating system from C.