Introduction to Fortran
Doug Sondak
Fortran History
Basic syntax
Additional syntax
• To be able to write simple Fortran programs
• To be able to understand and modify existing
Fortran code
• To be able to manage program projects using
an editor and makefile
• Matlab is great! Why do I need to learn a new
• All codes must be translated to machine language
• Interpreted language
– Matlab, Python, Java
– Translation is performed incrementally at run time
• Compiled language
– Fortran, C, C++
– Translation is performed once, then executable is run
Introduction (cont’d)
• Compiled languages run faster
– I translated a program from Matlab to C for a user,
and it ran 7 times as fast
– Large-scale computing is usually done with
compiled language
• Some convenient features of interpreted
languages (e.g., no need to declare variables)
result in performance and/or memory
• Professional programmers often work within a
programming environment
– Writing and editing code
– Running code
• On Unix systems, one typically uses an editor to
write/modify code
• Emacs and vi are most popular
– We will talk about emacs
– If you want to use vi, that’s fine
– Arguing about which is better makes the Thirty-Years'
War look tame
Emacs (cont’d)
Emacs is a wonder tool!
We will just scratch the surface
.emacs file in home directory can be customized
Commands can be executed via menus or using
the underlying character sequences
– I like the latter, so that’s what we’ll do
• Copy the file “junk” from /scratch/sondak
– This will be our example file for editing
cp /scratch/sondak/junk
Emacs Exercise
• Type “emacs”
– An emacs window will appear
– A built-in tutorial is available
• Type CTL-h t
– Hold CTL while pressing h, release CTL, then press t
• We won’t do anything with the tutorial here, but it’s a good
• The “META” key in the tutorial is “Esc”
• To read a file CTL-x CTL-f
– You will be prompted for file name at bottom of
– Type junk and hit return
– If the file doesn’t exist, emacs will create it
Emacs Exercise (cont’d)
You should now see file contents in window
To move down CTL-n (“next line”)
To move up CTL-p (“previous line”)
To move forward CTL-f (“forward”)
To move backward CTL-b (“backward”)
You can also navigate by clicking on the
desired location
– Click on the 0 in 0.282
Emacs Exercise (3)
• To delete a character CTL-d
– Hit CTL-d 3 times to delete 0.2
– Type 1.3
– You’ve now changed 0.282 to 1.382
• Highlight 0.288 with the mouse
– Don’t include spaces before or after
– CTL-w will delete the highlighted characters
– Oh no, we made a mistake! CTL-x u undoes the
previous command. Try it; 0.288 should reappear.
• another CTL-x u undoes the command previous to that, etc.
Emacs Exercise (4)
• The point is the location on the left side of the
cursor; i.e., between the character on which
the cursor resides and the character to its left.
• The mark is similar to the point, but it’s
location is set (i.e., doesn’t move with cursor).
• Suppose we want to delete all the characters
between (inclusively) 0.288 and 0.407.
Emacs Exercise (5)
• Place the cursor on the 0 in 0.288.
– can simply click on the 0
• To set the mark, CTL-spacebar
– The note “Mark set” will appear at the bottom of
the screen.
• Move the cursor to the right of 0.407
– We place it to the right of the 7 rather than on it
because the point is always to the left of the
Emacs Exercise (6)
• CTL-w will delete all characters between the mark
and the point
• For now, let’s put the characters back in by using
CTL-x u
• Move the cursor to the start of the current line
using CTL-a
– (CTL-e moves to end of current line)
• Delete (“kill”) the line with CTL-k
• Another CTL-k deletes the newline character
Emacs Exercise (7)
• “Meta” key is the Esc key
• We will use M- here to indicate the Meta key
• The Meta key is hit prior to the subsequent
key(s), not simultaneously as with CTL
• Place the cursor at the top of the file
• M-> will move the cursor to the bottom of the
• M-< will move it back to the top
Emacs Exercise (8)
• Suppose we want to swap positions of 14.747
and 14.688
• Set the mark at the 1 in 14.747
• Place the cursor on the 1 in 14.688 to set the
point to the left of the 1
• CTL-w will delete 14.747
• Place the cursor over the space to the left of the
first 1 in 16.155
• CTL-y “yanks” the previously-deleted string
Emacs Exercise (9)
• Suppose we want to swap positions of the second
and third columns
• Set the mark after the last 0 in 0.000 in the 1st
row of data
• Set the point to the right of the 8 in 0.758 in
column 2, last row
• CTL-x r k (“kill rectangle”) deletes the column
• Place the point after the 8 in 37.578
• CTL-x r y (“yank rectangle”) inserts the column
Emacs Exercise (10)
• To save the modified file, CTL-x CTL-s
– A note will appear at the bottom of the window saying the
file has been saved
• To save it under a new name, CTL-x CTL-w
– You’ll be prompted for the name at the bottom of the
– Note that when you get these kinds of prompts, you can
edit them using emacs commands
• Type a file name and then move back and forth with CTL-b and
• CTL-x CTL-c to quit
• Previous version will appear with ~ suffix in working
Fortran History
• Before Fortran, programs were written in
assembly language
• Fortran was the first widely-used high-level
computer language
– 1957
– Developed by IBM for scientific applications
Fortran History
• Fortran 66 (1966)
• Fortran 77 (1978)
• Fortran 90 (1991)
– “fairly” modern (structures, etc.)
– Current “workhorse” Fortran
• Fortran 95 (minor tweaks to Fortran 90)
• Fortran 2003
– Gradually being implemented by compiler companies
– Object-oriented support
– Interoperability with C is in the standard
• yay!
What Language Should I Use?
• I usually suggest using the language you know
• Matlab is great, but is not a good choice for
major number crunching
– Researchers often write codes in Matlab, and they
grow and grow (the codes, not the researchers)
until they are much too slow
• Then a painful translation is often required
What Language? (cont’d)
• Fortran is hard to beat for performance
• C has the potential to be as fast as Fortran if you avoid
aliasing issues and promise the optimizer your code
won’t screw up aliasing
– Fortran doesn’t have this issue due to the different nature
of its pointers
• I have not written large C++ codes, but it’s to my
understanding that object-oriented constructs tend to
be slow
• Suggestion – write computationally-intensive codes in
Fortran or C
– Can parallelize using MPI and/or OpenMP
Fortran Syntax
• Source lines are not ended with semicolons
(as in C or Matlab)
• Ampersand at end of line tells compiler that
statement is continued on next source line
• Not case-sensitive
• Spaces don’t matter except within literal
character strings
– I use them liberally to make code easy to read
• Comment character is !
Fortran Syntax (cont’d)
• Declarations – should declare each variable as
being integer, real (floating point), character,
• Integers and reals are stored differently
• Integer arithmetic will truncate result
– If i=3 and k=2, i/k=1, k/i=0
Fortran Syntax (3)
• There are sometimes several ways to do the
same thing
– For backward compatibility
– We will only use modern constructs
• Source file suffix is compiler dependent
– Usually .f90
Fortran Syntax (4)
• First statement in code is program statement
– Followed by program name
– I like to give the source file the same name as the
program myprog
(name of source file)
(first line in source code)
Fortran Syntax (5)
• implicit none
– Due to older versions of Fortran
• Had “implicit typing”
– Variables did not have to be declared
– If names started with i-n, were automatically integers
– If a-h,o-z, were automatically single-precision reals
– Implicit typing is considered bad programming practice
• Always use implicit none
• often next line after program
– Implicit none says that all variables must be declared
– If you use implicit none and don’t declare all variables,
compiler will yell at you
Fortran Syntax (6)
• A character string is enclosed by single quotes
– Characters within the quotes will be taken literally
‘This is my character string.’
• print*
– “list-directed” output
– Lazy way to produce output
• No format required
– Follow by comma, then stuff to print
print*, ’This is my character string.’
Fortran Syntax (7)
• At the end of the code is an end program
statement, followed by program name
– Paired with program statement that starts the
end program myprog
Exercise 1
• Write a “hello world” program in an editor
– Program should print a string
– 4 lines of code
– Save it to a file name with a .f90 suffix
• solution
• A compiler is a program that reads source
code and converts it to a form usable by the
• Code compiled for a given processor will not
generally run on other processors
– AMD and Intel are compatible
• On katana we have Portland Group compilers
(pgf90) and GNU compilers (gfortran)
• We’ll use pgf90, since it’s usually faster
Compilation (cont’d)
• Compilers have huge numbers of options
– See PGI compiler documentation at
– PGI Fortran reference is at
• For now, we will simply use the –o option,
which allows you to specify the name of the
resulting executable
Compilation (3)
• Can create a Unix window within emacs:
– CTL-x 2 will split the window horizontally
– CTL-x o toggles between windows
• “o” stands for “other”
– M-x will prompt for a command at the bottom of the
• Type “shell” (no quotes) for the command
• Half of emacs window will now be a Unix shell, so you can do your
compilation there
• In a normal Unix tcshell you can retrieve previous Unix commands
with the up arrow; here it’s CTL up arrow
• In a Unix window (in emacs or separate window):
pgf90 –o hello_world hello_world.f90
Compilation (4)
• Compile your code
• If it simply returns a Unix prompt it worked
• If you get error messages, read them carefully
and see if you can fix the source code and recompile
• Once it compiles correctly, type the
executable name at a Unix prompt, and it will
print your string
• Lists of variables with their associated types
• Placed in source code directly after “implicit
• Basic types:
– Integer
– Real
– Character
– logical
Declarations (cont’d)
• Examples:
integer :: i, j, k
real :: xval, time
character(20) :: name, date
logical :: isit
• +, -, *, /
• ** indicates power
2 .4
1 .5
• Built-in functions such as sin, acos, exp, etc.
• Exponential notation indicated by letter “e”
4 . 2  10
More List-Directed i/o
• read* is list-directed read, analogous to print*
• Follow with comma, then comma-delimited
list of variables you want to read
read*, x, j
• Often use list-directed read and write together
print*, ‘Enter a float and an integer:’
read*, x, j
print*, ‘float = ‘, x, ‘ integer = ‘, j
Exercise 2
• Write program to prompt for a Celcius
temperature, convert it to Fahrenheit, and
print the result.
– make sure you declare all variables
– it’s a good habit to use decimal points with all
reals, even if they’re whole numbers, e.g., 3.0
F = (9/5)C + 32
• solution
• Specify static dimensions in declaration:
real, dimension(10,3,5) :: x
• Can also specify ranges of values
integer, dimension(3:11, -15:-2) :: ival, jval
Arrays (cont’d)
• Dynamic allocation
– Need to specify no. dimensions in declaration
– Need to specify that it’s an allocatable array
real, dimension(:,:,:), allocatable :: x, y
– allocate function performs allocation
allocate( x(ni,nj,nk), y(ldim,mdim,ndim) )
– When you’re done with the variables, deallocate
deallocate(x, y)
• not necessary at very end of code; Fortran will clean them
up for you
• If variable has known, fixed value, declare as
parameter and initialize in declaration
integer, parameter :: idim = 100, jdim = 200
– Compiler substitutes values wherever variables appear
in code
– Efficient, since there are no memory accesses
– Often used for declaring arrays
integer, parameter :: idim = 100, jdim = 200
real, dimension(idim, jdim) :: x
integer, dimension(idim) :: iarray
Exercise 3
• Write program to prompt for 2 floating-point vectors of length 3,
calculate the dot product, and print the result
– Don’t name the code “dot_product” or “dot”
• Fortran has a “dot_product” intrinsic function
• there is a unix command called “dot”
– If x is an array, can use array name in list-directed read, and it
will expect the appropriate number of values (dimension)
separated by spaces
• solution
i 1
 bi
• Do loop repeats calculation over range of
do i = 1, 10
a(i) = sqrt( b(i)**2 + c(i)**2 )
• Can use increment that is not equal to 1
– Goes at end of do statement, unlike Matlab
do i = 10, -10, -2
Exercise 4
• Modify dot product program to use a do loop
• solution
• Conditional execution of block of source code
• Based on relational operators
less than
greater than
equal to
less than or equal to
greater than or equal to
not equal to
If-Then-Else (cont’d)
if( x > 0.0 .and. y > 0.0 ) then
z = 1.0/(x+y)
elseif ( x < 0.0 .and. y < 0.0) then
z = -2.0/(x+y)
print*, ’Error condition’
Exercise 5
• In dot product code, check if the magnitude of
the dot product is less than 10  6 using the
absolute value function abs. If it is, print a
message. If not, calculate the reciprocal of the
dot product and print the result.
• solution
Array Syntax
• Fortran will perform operations on entire
– Like Matlab, unlike C
• To add two arrays, simply use
• Can also specify array sections
c(-5:10) = a(0:15) + b(0:30:2)
– Here we use b(0), b(2), b(4), …
Array Syntax (cont’d)
• There are intrinsic functions to perform some
operations on entire arrays
– sum
sum(x) is the same as x(1) + x(2) + x(3) + …
– product
– minval
– maxval
Exercise 6
• Modify dot product code to use array syntax
instead of do loop
– use “sum” intrinsic to sum comnponents
• solution
• Subroutines and functions
– Function returns a single object (number, array,
etc.), and usually does not alter the arguments
• Altering arguments in a function, called “side effects,” is
sometimes considered bad programming practice
– Subroutine transfers calculated values (if any)
through arguments
• Definition starts with a return type
• End with “end function” analogous to “end program”
• Example: distance between two vectors
real function distfunc(a, b)
real, dimension(3) :: a, b
distfunc = sqrt( sum((b-a)**2) )
end function distfunc
• Use:
z = distfunc(x, y)
– Names of dummy arguments don’t have to match actual names
– distfunc must be declared in calling routine
real :: distfunc
• End with “end subroutine” analogous to “end program”
• Distance subroutine
subroutine distsub(a, b, dist)
real :: dist
real, dimension(3) :: a, b
dist = sqrt( sum((b-a)**2) )
end subroutine distfunc
• Use:
call distsub (x, y, d)
– As with function, names of dummy arguments don’t have
to match actual names
Exercise 7
• Modify dot-product program to use a
subroutine to compute the dot product
– The subroutine definition may go before or after
the main program in source code
– Don’t forget to declare arguments
• solution
Basics of Code Management
• Large codes usually consist of multiple files
• I usually create a separate file for each
– Easier to edit
– Can recompile one subprogram at a time
• Files can be compiled, but not linked, using –c
option; then object files can be linked
pgf90 –c mycode.f90
pgf90 –c myfunc.f90
pgf90 –o mycode mycode.o myfunc.o
Exercise 8
• Put dot-product subroutine and main program
in separate files
• Give main program same name you have
been using for code, e.g., “program dotprod”
and dotprod.f90
• Give subroutine same name you used for
subroutine, e.g., “subroutine dp” and dp.f90
• Compile, link, and run
• solution
• Make is a Unix utility to help manage codes
• When you make changes to files, it will
– Automatically deduce which files need to be compiled
and compile them
– Link latest object files
• Makefile is a file that tells the make utility what
to do
• Default name of file is “makefile” or “Makefile”
– Can use other names if you’d like
Makefiles (cont’d)
• Makefile contains different sections with
different functions
– The sections are not executed in order!
• Comment character is #
• There are defaults for some values, but I like
to define everything explicitly
Makefiles (3)
• example makefile:
### suffix rule
.SUFFIXES: .f90 .o
$(F90) $(COMPFLAGS) $*.f90
### compiler
F90 = pgf90
### objects
OBJ = mymain.o sub1.o sub2.o fun1.o
### compile and link
myexe: $(OBJ)
$(F90) –o $@ $(LINKFLAGS) $(OBJ)
Makefiles (4)
• variables
– Some character strings appear repeatedly in makefiles
– It’s convenient to give them names so if they are
changed, you only have to do it in one place
– To define variable:
name = string
– No quotes are required for the string
– String may contain spaces
– “name” is any name you want
– Variable names are usually all capitals
– To continue line, use \ character
Makefiles (5)
• Variables (cont’d)
– To use variable, either of these work:
• Example:
– Define compiler
F90 = pgf90
– To use elsewhere in makefile:
Makefiles (6)
• Good practice to define compiler info in
F90 = pgf90
Makefiles (7)
• Have to define all file suffixes that may be
.SUFFIXES: .o .f90
• Just to be safe, delete any default suffixes first
with a null .SUFFIXES: command
.SUFFIXES: .o .f90
Makefiles (8)
• Have to tell how to create one file suffix from
another with a suffix rule
$(F90) $(COMPFLAGS) $*.f90
• The first line indicates that the rule tells how to
create a .o file from a .f90 file
• The second line tells how to create the .o file
• The big space before $(F90) is a tab, and you
must use it!
• *$ is automatically the root of the first file
Makefiles (9)
• Usually define variable with all object file
OBJ = mymain.o sub1.o anothersub.o \
firstfunc.o func2.o
Makefiles (10)
• Finally, everything falls together with the
definition of a rule
target: prerequisites
• The target is any name you choose
– Often use name of executable
• Prerequisites are files that are required by target
– e.g., executable requires object files
• Recipe tells what you want the makefile to do
Makefiles (11)
### suffix rule
.SUFFIXES: .f90 .o
$(F90) $(COMPFLAGS) $*.f90
### compiler
F90 = pgf90
### objects
OBJ = mymain.o sub1.o sub2.o fun1.o
### compile and link
myexe: $(OBJ)
$(F90) –o $@ $(LINKFLAGS) $(OBJ)
Automatic variable for target
Makefiles (12)
• When you type “make,” it will look for a file called
“makefile” or “Makefile”
• It then searches for the first target in the file
• In our example (and the usual case) the object files are
• It checks the suffix rule to see how to create an object file
• In our case, it sees that .o files depend on .f90 files
• It checks the time stamps on the associated .o and .f90 files
to see if the .f90 is newer
• If the .f90 file is newer it performs the suffix rule
– In our case, compiles the routine
Makefiles (13)
• Once all the prerequisites are updated as
required, it performs the recipe
• In our case it links the object files and creates our
• Many makefiles have an additional target,
“clean,” that removes .o and other files
rm –f *.o
• When there are multiple targets, specify desired
target as argument to make command
make clean
Exercise 9
• Create a makefile for your dot product code
• Include two targets
– executable
– clean
• Delete your old object files using “make clean”
• Build your code using the makefile
• solution
• Declarations of variables can be modified
using “kind” parameter
• Often used for precision of reals
• Intrinsic function selected_real_kind(n)
returns kind that will have at least n significant
– n = 6 will give you “single precision”
– n = 12 will give you “double precision”
Kind (cont’d)
integer, parameter :: rk = selected_real_kind(12)
real(rk) :: x, y, z
real(rk), dimension(101,101,101) :: a
• If you want to change precision, can easily be
done by changing one line of code
Exercise 10
• Modify dot-product code to use kinds to
declare double-precision reals
– Don’t forget to modify all files
– “make” will automatically compile and link
• solution
• Program units that group variables and
• Good for global variables
• Checking of subprogram arguments
– If type or number is wrong, linker will yell at you
• Can be convenient to package variables
and/or subprograms of a given type
Modules (cont’d)
module module-name
implicit none
… variable declarations …
… subprogram definitions …
end module module-name
Modules (3)
• Only need “contains” if module contains
• I usually name my modules (and associated
files) with _mod in the name, e.g.,
solvers_mod, solvers_mod.f90
• In program unit that needs to access
components of module use module-name
• use statement must be before implicit none
Modules (4)
• use statement may specify specific components
to access by using “only” qualifier:
use solvers_mod, only: nvals, x
• A Fortran style suggestion:
– Group global variables in modules based on function
– Employ “use only” for all variables required in
program unit
– All variables then appear at top of program unit in
declarations or “use” statements
Modules (5)
• When linking object files, modules must
come first in the list
– In my makefiles I create a MODS variable
analogous to OBJS
– Link command then contains $(MODS) $(OBJS)
Exercise 11
• Create module prec_mod
– Separate file called prec_mod.f90
– Parameter rk
– Real kind for double
• Use this module in dot-product program units
• Modify makefile to compile module
– add module list to dependencies and link recipe
• solution
Derived Types
• Analogous to structures in C
• Can package a number of variables under one
type grid
integer :: nvals
real, dimension(100,100) :: x, y, jacobian
end type grid
Derived Types (cont’d)
• To declare a variable
type(grid) :: grid1
• Components are accessed using %
grid1%nvals = 20
grid1%x = 0.0
• Handy way to transfer lots of data to a
call calc_jacobian(grid1)
Exercise 12
• Create module with definition of rvec3 type
– Size of vector nvals=3
• not a paremeter – can’t have parameter in derived type
– Real 3-component vector
– Use prec_mod
• Modify code to use rvec3
• Modify makefile to include new module
• solution
• List-directed output gives little control
• write statement allows formatted output
write(unit, format) variables
• Unit is a number indicating where you want to
write data
– The number 6 is std out (write to screen)
i/o (cont’d)
• im
– For integers
– m is total number of characters in field
• am
– For character strings
– m is number of characters
– Left-justifies
– If m isn’t specified, writes number of characters in
variable declaration
i/o (3)
• fm.n
– For floating-point (real) numbers
– m is total number of characters in field
– n is number of decimal places
– If m is larger than required, right-justifies
• em.n
– Exponential notation
– Always zero left of decimal
i/o (4)
• esm.n
– scientific notation
• In format statement, put formats within ‘()’
• Example write statement
write(6, ‘(a, f6.2, i5, es15.3)’) ‘answers are ’, x, j, y
i/o (5)
• Suppose you want to write to a file?
– open statement
open(11, file=‘mydata.d’)
– “11” is unit number
• Don’t use 5 or 6
– Reserved for std in, std out
– Use this unit in your write statement
– When you’re finished writing, close the file
i/o (6)
• Can also read from file
– read rather than write
– Can use * instead of format specifier
read(11,*) j, x
Exercise 13
• Write your dot-product result to a file
• solution
Unformatted i/o
• Binary data take much less disk space than ascii
(formatted) data
• Data can be written in binary representation
– Not directly human-readable
open(199, file=‘unf.d’, form=‘unformatted’)
write(199) x(1:100000), j1, j2
read(199) x(1:100000), j1, j2
– Note that there is no format specification
• Fortran unformatted slightly different format
than C binary
– Fortran unformatted contains record delimiters
Exercise 14
• Modify dot-product program to:
– Write result to unformatted file
• don’t write character string, just number
– After file is closed, open it back up and read result
– Print result to make sure it wrote/read correctly
• solution
• Lots of books available
– I have an older edition of “Fortran 95/2003 Explained”
by Metcalf, Reid, and Cohen that I like
– Compiler
– Fortran language reference
• gfortran
• Please fill out the course survey at

Fortran for Matlab Users