Fortran Programming Basics
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Contents
Introduction
Fortran Programming Language
Fortran (FORmula TRANslation) is a high level language aimed at numerical calculations. Evolved over 3040 years. All compilers should conform to the Fortran standard so that code is completely portable.
Recommended textbooks:
 Fortran 90 Explained, Metcalf and Reid, Oxford Science Publications
 Fortran 90/95 Explained, Metcalf and Reid, Oxford University Press
 Fortran 95/2003 Explained, Metcalf, Reid and Cohen, Oxford University Press
Internet resources are
 http://www.fortran.com contains a FAQ and lots of other information.
 news://comp.lang.fortran to speak directly to those who develop Fortran
Free compilers
There are a number of free compilers available
 Fortran 77 – F77 part of the GNU GCC project
 Fortran 95 – g95 based on the GNU GCC project
 Fortran 95 – gfortran part of the GNU GCC 4.0 project
 Fortran 95 – ifort Intel Fortran compilers for linux
Fortran Program Structure
Here is an example Fortran code.
program circle
real :: r, area
!This program reads a real number r and prints
!the area of a circle with radius r
read (*,*) r
area = 3.14159*r*r
write (*,*)' Area = ',area
stop
end program circle
Note that all variables are declared at the beginning of the program and before they are used.
Fortran77 Formalities
 Fortran77 requires that all lines except comment or continuation lines start in the 7th column (convention left over from Fortran coding sheets) and are restricted to 72 columns as follows:
 Col 1 : Blank or c, C or * for comments
 Col 15 : Statement label (optional)
 Col 6 : Continuation of previous line (optional)
 Col 772 : Statements
 Fortran is not case specific.
 Comments can appear anywhere in a program – use them.
 Any symbol can be used in the 6th column for continuation but the general practice is to use +, & or numbers.
 Implicit typing depending on first letter of variable name, in are integers. This easily leads to mistakes so don’t rely on it.
Fixed or Free Format
The standard Fortran77 layout (i.c. columns 772) is called fixed format but with compiler options can be extended to a line width of 132.
Some compilers accept the nonstandard tab source form where tab automatically skips to the 7th column. Then line continuations can be a number in the 8th column.
Free source form is generally used for Fortran90. Continuation lines are marked by an ampersand & at the end of the line that is to be continued.
Fortran77 or Fortran90
Fortran90 compilers are backward compatible so will interpret Fortran77 code. In fact, Fortan77 is a subset of Fortran90.
If you are modifying existing Fortran77 code you will have to continue to use the fixed format layout in any program that is already in fixed format.
Compilers decide whether code is fixed or free format depending on the extension of the file name e.g. prog.f or prog.f90
From now on we will present Fortran90 but mention any Fortran77 constructs that are now deprecated and replaced by Fortran90 constructs.
Declaration
Declaration of Variables
Start every program with the statement
implicit none
This tells the compiler that all variables are to be declared and the compiler will report an error if any variable is not declared. This is good programming practice. Do not rely on the compiler to decide if variables are integers or real. This is different from e.g. Matlab
Declaration of Variables (Contd)
Variables can be of the following types:
 LOGICAL
 CHARACTER
 INTEGER
 REAL
 COMPLEX
 user constructed called derived types
Declaration of Variables (Contd)
For example the following all declare x as a single precision real variable, that is, its representation in memory is 4 bytes long
 real :: x
 real(4) :: x
 real*4 :: x
A double precision variable z which takes 8 bytes of memory can be represented in any of the following ways:
 real(8) :: z
 real*8 :: z
 double precision :: z
Declaration of Variables (Contd)
COMPLEX
(COMPLEX*8
orCOMPLEX(4)
) – single precision complex numberCOMPLEX(8)
orCOMPLEX*16
– double precision complex numberCHARACTER(LEN=n)
,CHARACTER(n)
, orCHARACTER*n
where n is an integer value represents the number of bytes in the character variable or can be *.LOGICAL
can be.TRUE.
or.FALSE.
Declaring arrays
Here are some examples of array declarations, there are several ways to do this.
 a is a real onedimensional array of length 4, indexed 1 to 4.
real :: a(4)
 a is a real onedimensional array of length 20
integer, parameter :: n=20 real :: a(n)
 b is an integer onedimensional array of length 20, indexed 0 to 19
integer :: b(0:19)
 c is double precision 2dimensional array
double precision, dimension(10,10) :: c
In these the array a has elements a(1)
to a(20)
, b has elements b(0)
to b(19)
and c has elements c(1,1)
to c(10,10)
Example 1
Compile and execute the following code variables.f90
by doing
>f90 variables.f90 o variables
>./variables
program variables
implicit none
integer :: i
integer(2) :: j
integer(4) :: k
integer(8) :: l
real :: a
real(4) :: b
real(8) :: c
write (*,*) ' Huge: ',huge(i),huge(j),huge(k),huge(l)
write (*,*) ' Digits: ',digits(i),digits(j),digits(k),digits(l)
write (*,*) ''
write (*,*) 'Huge: ',huge(a),huge(b),huge(c)
write (*,'(a,i,i,i)') 'Digits: ',digits(a),digits(b),digits(c)
write (*,'(a8,e,e,e)') 'Epsilon: ',epsilon(a),epsilon(b),epsilon(c)
write (*,'(a9,en,en,en)') 'Epsilon: ',epsilon(a),epsilon(b),epsilon(c)
write (*,'(a10,3es)') 'Epsilon: ',epsilon(a),epsilon(b),epsilon(c)
write (*,'(a11,3e20.10e4)') 'Epsilon: ',epsilon(a),epsilon(b),epsilon(c)
end program variables
Example 1 continued
The output from variables.f90 is
Huge: 2147483647 32767 2147483647 9223372036854775807
Digits: 31 15 31 63
Huge: 3.4028235E+38 3.4028235E+38 1.797693134862316E+308
Digits: 24 24 53
Epsilon: 0.1192093E06 0.1192093E06 0.2220446049250313E15
Epsilon: 119.2092896E09119.2092896E09 222.0446049250313081E18
Epsilon: 1.1920929E07 1.1920929E07 2.2204460492503131E16
Epsilon: 0.1192092896E0006 0.1192092896E0006 0.2220446049E0015
Note how the output is presented and how this relates to the write
statements.
 * is a special character meaning standard or default
a
represents ASCII charactersi
represents integerse
represents exponential notationes
represents scientific notation (similar toe
)en
represents engineering notation and more
huge
and digits
represent intrinsic functions in the Fortran language and are defined in the standard.
huge
returns the largest number representable by a number of the same type and kind as the argument.
digits
returns the number of significant digits for numbers of the same type and kind as the argument.
Kind Parameter
In Fortran90 the KIND
parameter was introduced to allow more flexibility for the user in declaring variable precision. The following code shows how KIND can be used.
program kindtype
implicit none
integer, parameter :: i4=SELECTED_INT_KIND(4)
integer, parameter :: i8=SELECTED_INT_KIND(8)
integer, parameter :: r4=SELECTED_REAL_KIND(6,37)
integer, parameter :: r8=SELECTED_REAL_KIND(15,307)
integer(KIND=i4) :: ia
integer(KIND=i8) :: ib
real(KIND=r4) :: ra
real(KIND=r8) :: rb
print *,' Integer 4 ',huge(ia),kind(ia)
print *,' Integer 8 ',huge(ib),kind(ib)
print *,' Real 4 ',huge(ra),kind(ra)
print *,' Real 8 ',huge(rb),kind(rb)
stop
end program kindtype
Kind Example
Compile and run this example kindtype.f90
and compare the output with the results from variables.f90.
Note the use of the PARAMETER
statement used to define a constant that may be used several times throughout the program.
Try adding another variable or two with different values for the selection of the kind and see what results.
Arithmetic
Numeric Expressions
+ Addition
 Subtraction
* Multiplication
/ Division
** Exponentiation
There is an order of precedence with ** the highest followed by * and /. Next are the unary operators + and – and last the binary operators + and . For example,
A**B*C is evaluated as (A**B)*C
A/B*C is evaluated as (A/B)*C
Use parantheses to force a particular order of evaluation.
Data Type of Numeric Expressions
If every operand in a numeric expression is of the same type, the result is also of that type.
If operands of different data types are combined in an expression, the data type of the result is the same as the highest ranking operand. For example,
double precision :: x, y
y = x*2
The integer constant 2 will be promoted to double precision 2.0D0 before doing the multiplication.
Best not to rely on this but be sure that all expressions contain variables or constants of the same type.
Integer Arithmetic
Care must be taken when using all integer variables. The code segment
real :: a
a = 3/2
will produce the result a=1.0 not a=1.5
Compile and run the code exercise_int.f90 and see how the value of a can be calculated.
Do Loops
Do Loops
Loops are used for repeated of execution of similar instructions. For example,
program looping
implicit none
integer :: i, n
real*8 :: sum
n = 10
sum = 0.0D0
do i=1,n
sum = sum + dble(i)
write (*,*) ' Value of sum at step ',i,' is ',sum
enddo
stop
end program looping
Do Loops (Contd)
Things to note:
 Loop is bounded by
do
andenddo
 This can be replaced by a statement number such as
do 5 i=1,n sum = sum + dble(i) 5 continue
 Loop index is an integer.
 There can be loops within loops using a different index.
 Note 0.0D0 meaning zero in double precision.
 Note the matching of types in the summation step.
Exercise 1
Write Fortran code to calculate and print out the value of the variable a where a=5+1/i for i=1,..,n and n=10.
Then modify the code so that a is a onedimensional array and the iteration of the do loop for i calculates a(i).
Conditionals
Conditionals
Logical expressions can only have the values .TRUE. or .FALSE.
There are several relational operators, Fortran77 uses the form on the left and Fortran90 can use either form.
.LT. meaning < less than
.LE. <= less than or equal
.GT. > greater than
.GE. >= greater than or equal
.EQ. == equal
.NE. /= not equal
There are also logical operators, .AND., .OR., .NOT.
Here is an example
logical :: x,y,z
x = .TRUE.
y = x .AND. 2>1
z = x .OR. 2<1
In this example all three logical variables will be defined as .TRUE.
Conditional (IF) Statements
Can be written on one line e.g.
if (resid < 5.0D10) stop
or, in the general form e.g.
if (resid < 5.0D10) then
write (*,*)' Residual is less than 5.0D10'
stop
else
write (*,*)' Continue execution'
endif
There can even be more levels
if (resid < 5.0D10) then
write (*,*)' Residual is less than 5.0D10'
stop
elseif (num_iters > 100) then
write (*,*)' Number of iterations exceeded'
go to 25
else
write (*,*)' Continue execution'
endif
Conditional (IF) Statements
When the IF statement is used within a DO loop and you want to exit the loop but continue the code use EXIT as in the following
loop: do i=1,10
if (resid < 5.0D10) exit loop
enddo loop
Note the use of optional naming of the DO loop.
DO WHILE statements
The DO WHILE statement executes the range of a DO construct while a specified condition remains true. For example,
i=0
do while (resid >= 5.0D10)
resid = abs(x(i))
write (*,*) ' Continue execution'
i = i+1
end do
abs stands for absolute value.
Exercise 2
Extend the code you wrote for Exercise 1 so that it exits the loop when a(i) is within .01 of the asymptotic result 5.
Do this first using an IF statement then using the DO WHILE construct. For the DO WHILE case use the very first example code you wrote where a is not an array. You will need to initialise both the variable a and a variable for the iteration.
Print out the value of the iteration count at which the code completes. Do these two methods give the same answer?
Functions
Fortran Intrinsics
In the previous exercise we introduced ABS for the absolute value of a double precision variable. These are Fortran intrinsic functions. Other examples are
sin(a) sin of the angle a
cos(b) cosine of the angle b
sqrt(x) square root of x
exp(z) exponential of z
log(x) natural logarithm of x
max(a,b) maximum of a and b
mod(a,b) remainder when a is divided by b
See the Fortran Reference Manual for a complete list.
Functions and Subroutines
There are two types of subprograms in Fortran, functions and subroutines. The difference is that a function subprogram is invoked in an expression and returns a single value. A subroutine is invoked by a CALL statement and does not return a particular value.
For example,
real*8 :: x,y
x = func(y)
shows a function being used, whilst
real*8 :: x,y
call subr(x,y)
demonstrates a subroutine call where x returns the result and y contains the input value.
Subprograms are used to simplify coding by keeping the main program as uncluttered as possible and calculations which are used several times coded as subprograms.
Example Integration code
To show how to use subprograms we will use this simple integration code.
program integration1
implicit none
integer :: i, j
real(8) :: x, y, integ
integ = 0.0D0
do j=1,10
y = dble(j)*1.0D0
do i=1,10
x = dble(i) * 2.5D1
integ = integ + sin(x+y)
enddo
enddo
write (*,'(a,e20.10e3)')' Integration value = ',integ
end program integration1
Compile and run this code, integration1.f90.
Functions
We can use a function call to calculate sin(x+y) as follows:
program integration2
implicit none
integer :: i, j
real(8) :: x, y, func, integ
real(8) :: val
integ = 0.0D0
do j=1,10
y = dble(j)*1.0D0
do i=1,10
x = dble(i) * 2.5D1
val = func(x,y)
integ = integ + val
enddo
enddo
write (*,'(a,e20.10e3)')' Integration value = ',integ
end program integration2
Functions (Cont’d)
function func(x,y) result(result)
implicit none
real(8) :: x,y,result
result = sin(x+y)
end function func
Note the use of the optional Fortran90 keyword RESULT.
The function subprogram can be in a separate file from the main program and compiled separately but then linked in to create the executable.
Subroutines
The calculation of sin(x+y) can be written as a subroutine as follows:
program integration3
implicit none
integer :: i, j
real(8) :: x, y, integ
real(8) :: val
integ = 0.0D0
do j=1,10
y = dble(j)*1.0D0
do i=1,10
x = dble(i) * 2.5D1
call subr(x,y,val)
integ = integ + val
enddo
enddo
write (*,'(a,e20.10e3)')' Integration value = ',integ
end program integration3
subroutine subr(a,b,c)
implicit none
real(8) :: a,b,c
c = sin(a+b)
return
end subroutine subr
Subprogram Exercise
Start with the following code fragment
program quadratic
implicit none
real(8) :: a,b,c
complex(8) :: r1,r2
a = 2.0D0
b = 9.0D0
c = 4.0D0
then continue the program to calculate the roots of the quadratic ax**2+b*x+c=0 using a subroutine call.
If the roots are complex print a warning to that effect but not the solutions. Print the solutions if they are real.
Try with different values of a, b and c.
There are two possible solutions in quadratic.f90
and quadratic2.f90.
Using Arrays in Subroutines
In most scientific code subroutines will require using arrays for both input and output. In Fortran77 this will generally require passing the size of the arrays as a dummy argument as well as the arrays. We will look at other ways to do this in the Fortran90 course.
Using Arrays in Subroutines (Cont’d)
The integration code can be written using arrays in the subroutines.
program integrationarray
implicit none
integer :: i, j
integer, parameter :: n=10
real(8), dimension(n) :: x, y
real(8), dimension(n,n) :: val
real(8) :: integ
integ = 0.0D0
do j=1,10
y(j) = dble(j)*1.0D0
x(j) = dble(j) * 2.5D1
enddo
call subr(x,y,val,n)
do j=1,n
do i=1,n
integ = integ + val(i,j)
enddo
enddo
write (*,'(a,e20.10e3)')' Integration value = ',integ
end program integrationarray
Using Arrays in Subroutines (Cont’d)
subroutine subr(a,b,c,n)
implicit none
integer :: n, i, j
real(8) :: a(n),b(n),c(n,n)
do j=1,n
do i=1,n
c(i,j) = sin(a(i)+b(j))
enddo
enddo
return
end subroutine subr
I/O
Fortran I/O
There are many ways of writing out data.

print *,result

write (*,*) result

write (6,*) result

write (6,'(f10.4)') result

write (*,'(10F10.4)') (result(i),i=1,10)

write (*,200) result 200 format(f10.4)
Fortran I/O Cont’d
To open files and read or write data from or to them.

open (unit=2,file='ascii_data',form='formatted',status='old') read (2,'(10f20.4)') (input(i),i=1,10) close(2)

open (unit=3,file='binary_data',form='unformatted',status='unknown',iostat=ierr) if (ierr = 0) write(3,*) data close(3)
 Unit numbers 5 and 6 are conventionally reserved for STDIN and STDOUT
Putting it all Together
Copy the code integration4.f90
and the file input.dat.
Compile integration4.f90
and run it. The output all appears in the file integration4.dat.
Try editing input.dat
and rerunning the code.
Have a good look at the Fortran code and make sure you understand how it works.
Code
program integration4
implicit none
real(8) :: factor = 1.0D0
integer, parameter :: filelen=20
real(8) :: x, y, integ, init
real(8) :: userfunc
real(8), dimension(2) :: step
real(8), dimension(4) :: boundary
call loadinput('input.dat', filelen, init, boundary, step)
integ = init
y = boundary(3)
do while (y <= boundary(4))
x = boundary(1)
do while (x <=boundary(2))
integ = integ + userfunc(x,y,factor)
x = x + step(1)
enddo
y = y + step(2)
enddo
call writeoutput('integration4.dat', filelen, integ, boundary, x, y)
end program integration4
Code (Cont’d)
function userfunc(x,y,factor) result(func)
implicit none
real(8) :: x, y, func, factor
func = factor * sin(x + y)
end function userfunc
subroutine loadinput(inputfile, filelen, init, boundary, step)
implicit none
integer :: filelen
real(8) :: init
real(8), dimension(2) :: step
real(8), dimension(4) :: boundary
character(filelen) :: inputfile
open(unit=1, file=inputfile, action='read')
read(1, *) init
read(1, *) boundary
read(1, *) step
close(1)
return
end subroutine loadinput
Code (Cont’d)
subroutine writeoutput(inputfile, filelen, integ, boundary, x, y)
integer :: filelen
real(8) :: integ, x, y
real(8), dimension(4) :: boundary
character(filelen) :: inputfile
open(unit=1, file=inputfile, action='write')
write(1, *) 'Integration value = ',integ
write(1, *) 'xrange: ',boundary(1),'<= x <= ',boundary(2)
write(1, *) 'yrange: ',boundary(3),'<= y <= ',boundary(4)
write(1, *) 'Final x and y: ',x,y
close(1)
return
end subroutine writeoutput
Libraries
Using Libraries
There is a vast literature of highly optimised Fortran code for doing many things, much of it is open source.
For example, the LAPACK library provides a large suite of dense linear algebra routines. The source for LAPACK is available from NETLIB at http://netlib2.cs.utk.edu/ so you can install it anywhere.
To get more information on, enter
man lapack
To show how it is used we will call the routine ZGEEV to find the eigendecomposition of a 2dimensional complex matrix.
Read
man zgeev
to see the full documentation for this routine.
Using libraries (Cont’d)
program eigen
implicit none
integer, parameter :: n=10
integer, parameter :: lwork=3*n
complex(8), dimension(n,n) :: array, leftvectors, rightvectors
complex(8), dimension(n) :: eigenvalues
complex(8), dimension(lwork) :: work1
real(8), dimension(2*n) :: work2
real(8), dimension(2) :: rand
integer :: i, j, info
do j=1,n
do i=1,n
call random_number(rand)
array(i,j) = cmplx(rand(1),rand(2))
enddo
enddo
call zgeev('V','V',n,array,n,eigenvalues,leftvectors,n,rightvectors, &
n, work1,lwork,work2,info)
if (info==0) then
write (*,*)' Eigenvalues '
do i=1,n
write (*,*) eigenvalues(i)
enddo
else
write (*,*)' ZGEEV failed with info = ',info
endif
stop
end program eigen
Using Libraries (Cont’d)
The code eigen.f90 shows this routine in action. Have a good look at it, then compile and run it as follows to link to the LAPACK library.
f90 o eiegen eigen.f90 lcxml
./eigen
Notice that there are two work arrays declared which must be passed to the subroutine. Also an error parameter is returned to flag the success or otherwise of the routine. Always check these error parameters.
End
Conclusion
 Finish the problems
 Look at other Fortran codes
 Come to the course next week