Advanced Fortran 90
This document is derived from an HTML page written at the San Diego Supercomper Center many years ago. Its purpose is to Introduce Fortran 90 concepts to Fortran 77 programers. It does this by presenting an example program and introducing concepts as various routines of the program are presented. The original web page has been used over the years and has been translated into several languages.
Note: See our Fortran Overview page for basic getting started instructions and compiler/toolchain information.
- We will "develop" an application
- Incorporate f90 features
- Show source code
- Explain what and why as we do it
- Application is a genetic algorithm
- Easy to understand and program
- Offers rich opportunities for enhancement
- We also provide an summary of F90 syntax, key words, operators, constants, and functions
What was in mind of the language writers? What were they thinking?
- Enable portable codes
- Same precision
- Include many common extensions
- More reliable programs
- Getting away from underlying hardware
- Move toward parallel programming
- Run old programs
- Ease of programming
- Writing
- Maintaining
- Understanding
- Reading
- Recover C and C++ users
Why Fortran?
Famous Quote: "I don't know what the technical characteristics of
the standard language for scientific and engineering
computation in the year 2000 will be... but I know it
will be called Fortran." John Backus.
Note: He claimed that he never said this.
- Language of choice for Scientific programming
- Large installed user base.
- Fortran 90 has most of the features of C . . . and then some
- The compilers produce better programs
Justification of topics
- Enhance performance
- Enhance portability
- Enhance reliability
- Enhance maintainability
Classification of topics
- New useful features
- Old tricks
- Power features
- Overview of F90
What is a Genetic Algorithm
- A "suboptimization" system
- Find good, but maybe not optimal, solutions to difficult problems
- Often used on NP-Hard or combinatorial optimization problems
- Requirements
- Solution(s) to the problem represented as a string
- A fitness function
- Takes as input the solution string
- Output the desirability of the solution
- A method of combining solution strings to generate new solutions
- Find solutions to problems by Darwinian evolution
- Potential solutions ar though of as living entities in a population
- The strings are the genetic codes for the individuals
- Fittest individuals are allowed to survive to reproduce
Simple algorithm for a GA
- Generate a initial population, a collection of strings
- do for some time
- evaluate each individual (string) of the population using the fitness function
- sort the population with fittest coming to the top
- allow the fittest individuals to "sexually" reproduce replacing the old
population
- allow for mutation
- end do
Our example problem
- Instance:Given a map of the N states or countries and a fixed number of colors
- Find a coloring of the map, if it exists, such that no two states that share a boarder have the same color
- Notes
- In general, for a fixed number of colors and an arbitrary map the only
known way to find if there is a valid coloring is a brute force search
with the number of combinations = (NUMBER_OF_COLORS)**(NSTATES)
- The strings of our population are integer vectors represent the coloring
- Our fitness function returns the number of boarder violations
- The GA searches for a mapping with few, hopefully 0 violations
- This problem is related to several important NP_HARD problems in computer science
- Processor scheduling
- Communication and grid allocation for parallel computing
- Routing
Start of real Fortran 90 discussion
Comparing a FORTRAN 77 routine to a Fortran 90 routine
- The routine is one of the random number generators from: Numerical Recipes, The Art of Scientific Computing. Press, Teukolsky, Vetterling and Flannery. Cambridge University Press 1986.
- Changes
- correct bugs
- increase functionality
- aid portability
Original
function ran1(idum)
real ran1
integer idum
real r(97)
parameter ( m1=259200,ia1=7141,ic1=54773)
parameter ( m2=134456,ia2=8121,ic2=28411)
parameter ( m3=243000,ia3=4561,ic3=51349)
integer j
integer iff,ix1,ix2,ix3
data iff /0/
if (idum.lt.0.or.iff.eq.0)then
rm1=1.0/m1
rm2=1.0/m2
iff=1
ix1=mod(ic1-idum,m1)
ix1=mod(ia1*ix1+ic1,m1)
ix2=mod(ix1,m2)
ix1=mod(ia1*ix1+ic1,m1)
ix3=mod(ix1,m3)
do 11 j=1,97
ix1=mod(ia1*ix1+ic1,m1)
ix2=mod(ia2*ix2+ic2,m2)
r(j)=(real(ix1)+real(ix2)*rm2)*rm1
11 continue
idum=1
endif
ix1=mod(ia1*ix1+ic1,m1)
ix2=mod(ia2*ix2+ic2,m2)
ix3=mod(ia3*ix3+ic3,m3)
j=1+(97*ix3)/m3
if(j.gt.97.or.j.lt.1)then
write(*,*)' error in ran1 j=',j
stop
endif
ran1=r(j)
r(j)=(real(ix1)+real(ix2)*rm2)*rm1
return
end
Fortran 90
module ran_mod
contains
function ran1(idum)
use numz
implicit none !note after use statement
real (b8) ran1
integer , intent(inout), optional :: idum
real (b8) r(97),rm1,rm2
integer , parameter :: m1=259200,ia1=7141,ic1=54773
integer , parameter :: m2=134456,ia2=8121,ic2=28411
integer , parameter :: m3=243000,ia3=4561,ic3=51349
integer j
integer iff,ix1,ix2,ix3
data iff /0/
save ! corrects a bug in the original routine
if(present(idum))then
if (idum.lt.0.or.iff.eq.0)then
rm1=1.0_b8 m1
rm2=1.0_b8 m2
iff=1
ix1=mod(ic1-idum,m1)
ix1=mod(ia1*ix1+ic1,m1)
ix2=mod(ix1,m2)
ix1=mod(ia1*ix1+ic1,m1)
ix3=mod(ix1,m3)
do j=1,97
ix1=mod(ia1*ix1+ic1,m1)
ix2=mod(ia2*ix2+ic2,m2)
r(j)=(real(ix1,b8)+real(ix2,b8)*rm2)*rm1
enddo
idum=1
endif
endif
ix1=mod(ia1*ix1+ic1,m1)
ix2=mod(ia2*ix2+ic2,m2)
ix3=mod(ia3*ix3+ic3,m3)
j=1+(97*ix3)/m3
if(j.gt.97.or.j.lt.1)then
write(*,*)' error in ran1 j=',j
stop
endif
ran1=r(j)
r(j)=(real(ix1,b8)+real(ix2,b8)*rm2)*rm1
return
end function ran1
- Modules are a way of encapsulating functions an data. More below.
- The use numz line is similar to an include file. In this case it defines our real data type.
- real (b8) is a new way to specify percision for data types in a portable way.
- integer , intent(inout), optional :: idum we are saying idum is an optional input parameter
- integer , parameter :: just a different syntax
- The save statement is needed for program correctness
- present(idum) is a function to determine if ran1 was called with the optional parameter
Obsolescent features
The following are available in Fortran 90. On the other hand, the concept of "obsolescence" is introduced. This means that some constructs may be removed in the future.
- Arithmetic IF-statement
- Control variables in a DO-loop which are floating point or double-precision floating-point
- Terminating several DO-loops on the same statement
- Terminating the DO-loop in some other way than with CONTINUE or END DO
- Alternate return
- Jump to END IF from an outer block
- PAUSE
- ASSIGN and assigned GOTO and assigned FORMAT , that is the whole "statement number variable" concept.
- Hollerith editing in FORMAT.
Summary
- ! now indicates the start of a comment
- & indicates the next line is a continuation
- Lines can be longer than 72 characters
- Statements can start in any column
- Use ; to put multiple statements on one line
- New forms for the do loop
- Many functions are generic
- 32 character names
- Many new array assignment techniques
Features
- Flexibility can aid in program readability
- Readability decreases errors
- Got ya!
- Can no longer use C to start a comment
- Character in column 5 no longer is continue
- Tab is not a valid character (may produce a warning)
- Characters past 72 now count
program darwin
real a(10), b(10), c(10), d(10), e(10), x, y
integer odd(5),even(5)
! this line is continued by using "&"
write(*,*)"starting ",&
"darwin" ! this line in a continued from above
! multiple statement per line --rarely a good idea
x=1; y=2; write(*,*)x,y
do i=1,10 ! statement lable is not required for do
e(i)=i
enddo
odd= (/ 1,3,5,7,9 /) ! array assignment
even=(/ 2,4,6,8,10 /) ! array assignment
a=1 ! array assignment, every element of a = 1
b=2
c=a+b+e ! element by element assignment
c(odd)=c(even)-1 ! can use arrays of indices on both sides
d=sin(c) ! element by element application of intrinsics
write(*,*)d
write(*,*)abs(d) ! many intrinsic functions are generic
a_do_loop : do i=1,10
write(*,*)i,c(i),d(i)
enddo a_do_loop
do
if(c(10) .lt. 0.0 ) exit
c(10)=c(10)-1
enddo
write(*,*)c(10)
do while (c(9) .gt. 0)
c(9)=c(9)-1
enddo
write(*,*)c(9)
end program
New data declaration method
integer,parameter :: in2 = 14
real, parameter :: pi = 3.141592653589793239
real, save, dimension(10) :: cpu_times,wall_times
!**** the old way of doing the same ****!
!**** real cpu_times(10),wall_times(10) ****!
!**** save cpu_times, wall_times ****!
Kind facility
- Motivation
- Assume we have a program that we want to run on two different machines
- We want the same representation of reals on both machines (same number
of significant digits)
- Problem: different machines have different representations for reals
Digits of precision for some (old) machines and data type
| Machine |
Real |
Double Precision |
| IBM (SP) |
6 |
15 |
| Cray (T90) |
15 |
33 |
| Cray (T3E) |
15 |
15 |
* or *
- We may want to run with at least 6 digits today and at least 14 digits tomorrow
- Use the Select_Real_Kind(P) function to create a data type with P digits of precision
program darwin
! e has at least 4 significant digits
real(selected_real_kind(4))e
! b8 will be used to define reals with 14 digits
integer, parameter:: b8 = selected_real_kind(14)
real(b8), parameter :: pi = 3.141592653589793239_b8 ! note usage of _b8
! with a constant
! to force precision
e= 2.71828182845904523536
write(*,*)"starting ",& ! this line is continued by using "&"
"darwin" ! this line in a continued from above
write(*,*)"pi has ",precision(pi)," digits precision ",pi
write(*,*)"e has ",precision(e)," digits precision ",e
end program
Example output
sp001 % darwin
starting darwin
pi has 15 digits precision 3.14159265358979312
e has 6 digits precision 2.718281746
sp001 %
- Can convert to/from given precision for all variables created using "b8" by changing definition of "b8"
- Use the Select_Real_Kind(P,R) function to create a data type with P digits of precision and exponent range of R
Modules
module numz
integer,parameter:: b8 = selected_real_kind(14)
real(b8),parameter :: pi = 3.141592653589793239_b8
integergene_size
end module
program darwin
use numz
implicit none ! now part of the standard, put it after the use statements
write(*,*)"pi has ",precision(pi),"
digits precision ",pi
call set_size()
write(*,*)"gene_size=",gene_size
end program
subroutine set_size
use numz
gene_size=10
end subroutine
An example run
pi has 15 digits precision 3.14159265358979312
gene_size=10
Module functions and subroutines
Exersize 1: Write a program that returns 10 uniform random numbers.
Allocatable arrays (the basics)
module numz
integer, parameter:: b8 = selected_real_kind(14)
integer gene_size,num_genes
integer,allocatable :: a_gene(:),many_genes(:,:)
end module
program darwin
use numz
implicit none
integer ierr
call set_size()
allocate(a_gene(gene_size),stat=ierr) !stat= allows for an error code return
if(ierr /= 0)write(*,*)"allocation error" ! /= is .ne.
allocate(many_genes(gene_size,num_genes),stat=ierr) !2d array
if(ierr /= 0)write(*,*)"allocation error"
write(*,*)lbound(a_gene),ubound(a_gene) ! get lower and upper bound
! for the array
write(*,*)size(many_genes),size(many_genes,1) !get total size and size
!along 1st dimension
deallocate(many_genes) ! free the space for the array and matrix
deallocate(a_gene)
allocate(a_gene(0:gene_size)) ! now allocate starting at 0 instead of 1
write(*,*)allocated(many_genes),allocated(a_gene) ! shows if allocated
write(*,*)lbound(a_gene),ubound(a_gene)
end program
subroutine set_size
use numz
write(*,*)'enter gene size:'
read(*,*)gene_size
write(*,*)'enter number of genes:'
read(*,*)num_genes
end subroutine set_size
Example run
enter gene size:
10
enter number of genes:
20
1 10
200 10
F T
0 10
Passing arrays to subroutines
- There are several ways to specify arrays for subroutines
- Explicit shape
- integer, dimension(8,8)::an_explicit_shape_array
- Assumed size
- integer, dimension(i,*)::an_assumed_size_array
- Assumed Shape
- integer, dimension(:,:)::an_assumed_shape_array
Example
subroutine arrays(an_explicit_shape_array,&
i ,& !note we pass all bounds except the last
an_assumed_size_array ,&
an_assumed_shape_array)
! Explicit shape
integer, dimension(8,8)::an_explicit_shape_array
! Assumed size
integer, dimension(i,*)::an_assumed_size_array
! Assumed Shape
integer, dimension(:,:)::an_assumed_shape_array
write(*,*)sum(an_explicit_shape_array)
write(*,*)lbound(an_assumed_size_array) ! why does sum not work here?
write(*,*)sum(an_assumed_shape_array)
end subroutine
Interface for passing arrays
- !!!!Warning!!!! When passing assumed shape arrays as arguments you must provide an interface
- Similar to C prototypes but much more versatile
- The interface is a copy of the invocation line and the argument definitions
- Modules are a good place for interfaces
- If a procedure is part of a "contains" section in a module an interface
is not required
- !!!!Warning!!!! The compiler may not tell you that you need an interface
module numz
integer, parameter:: b8 = selected_real_kind(14)
integer,allocatable :: a_gene(:),many_genes(:,:)
end module module face
interface fitness
function fitness(vector)
use numz
implicit none
real(b8) fitness
integer, dimension(:) :: vector
end function fitness
end interface
end module program darwin
use numz
use face
implicit none
integer i
integer vect(10) ! just a regular array
allocate(a_gene(10));allocate(many_genes(3,10))
a_gene=1 !sets every element of a_gene to 1
write(*,*)fitness(a_gene)
vect=8
write(*,*)fitness(vect) ! also works with regular arrays
many_genes=3 !sets every element to 3
many_genes(1,:)=a_gene !sets column 1 to a_gene
many_genes(2,:)=2*many_genes(1,:)
do i=1,3
write(*,*)fitness(many_genes(i,:))
enddo
write(*,*)fitness(many_genes(:,1)) !go along other dimension
!!!!write(*,*)fitness(many_genes)!!!!does not work
end program
function fitness(vector)
use numz
implicit none
real(b8) fitness
integer, dimension(:):: vector ! must match interface
fitness=sum(vector)
end function
Exersize 2: Run this program using the "does not work line".
Why? Using intrinsic functions make it work?
Exersize 3: Prove that f90 does not "pass by address".
Optional arguments and intent
- Motivation:
- We may have a function or subroutine that we may not want to always pass
all arguments
- Initialization
- Two examples
- Seeding the intrinsic random number generator requires keyword arguments
- To define an optional argument in our own function we use the optional
attribute
becomes
integer, optional :: my_seed
Used like this:
! ran1 returns a uniform random number between 0-1
! the seed is optional and used to reset the generator
contains
function ran1(my_seed)
use numz
implicit none
real(b8) ran1,r
integer, optional ,intent(in) :: my_seed ! optional argument not changed in the routine
integer,allocatable :: seed(:)
integer the_size,j
if(present(my_seed))then ! use the seed if present
call random_seed(size=the_size) ! how big is the intrisic seed?
allocate(seed(the_size)) ! allocate space for seed
do j=1,the_size ! create the seed
seed(j)=abs(my_seed)+(j-1) ! abs is generic
enddo
call random_seed(put=seed) ! assign the seed
deallocate(seed) ! deallocate space
endif
call random_number(r)
ran1=r
end function ran1
end module program darwin
use numz
use ran_mod ! interface required if we have
! optional or intent arguments
real(b8) x,y
x=ran1(my_seed=12345) ! we can specify the name of the argument
y=ran1()
write(*,*)x,y
x=ran1(12345) ! with only one optional argument we don't need to
y=ran1()
write(*,*)x,y
end program
- Intent is a hint to the compiler to enable optimization
- intent(in)
- We will not change this value in our subroutine
- intent(out)
- We will define this value in our routine
- intent(inout)
Derived data types
-
Motivation:
- Derived data types can be used to group different types of data together
(integers, reals, character, complex)
- Can not be done in F77 although people have "faked" it
-
Example
- In our GA we define a collection of genes as a 2d array
- We call the fitness function for every member of the collection
- We want to sort the collection of genes based on result of fitness function
- Define a data type that holds the fitness value and an index into the 2d
array
- Create an array of this data type, 1 for each member of the collection
- Call fitness function with the result being placed into the new data type
along with a pointer into the array
- Again modules are a good place for data type definitions
module galapagos
use numz
type thefit !the name of the type
sequence ! sequence forces the data elements
! to be next to each other in memory
! where might this be useful?
real(b8) val ! our result from the fitness function
integer index ! the index into our collection of genes
end type thefit
end module
Using defined types
- Use the % to reference various components of the derived data type
program darwin
use numz
use galapagos ! the module that contains the type definition
use face ! contains various interfaces
implicit none
! define an allocatable array of the data type
! than contains an index and a real value
type (thefit),allocatable ,target :: results(:)
! create a single instance of the data type
type (thefit) best
integer,allocatable :: genes(:,:) ! our genes for the genetic algorithm
integer j
integer num_genes,gene_size
num_genes=10
gene_size=10
allocate(results(num_genes)) ! allocate the data type
! to hold fitness and index
allocate(genes(num_genes,gene_size)) ! allocate our collection of genes
call init_genes(genes) ! starting data
write(*,'("input")' ) ! we can put format in write statement
do j=1,num_genes
results(j)%index =j
results(j)%val =fitness(genes(j,:)) ! just a dummy routine for now
write(*,"(f10.8,i4)")results(j)%val,results(j)%index
enddo
end program
User defined operators
Recursive functions introduction
-
Notes
- Recursive function is one that calls itself
- Anything that can be done with a do loop can be done using a recursive
function
-
Motivation
- Sometimes it is easier to think recursively
- Divide an conquer algorithms are recursive by nature
- Fast FFTs
- Searching
- Sorting
Algorithm of searching for minimum of an array
function findmin(array)
is size of array 1?
min in the array is first element
else
find minimum in left half of array using findmin function
find minimum in right half of array using findmin function
global minimum is min of left and right half
end function
Fortran 90 recursive functions
- Recursive functions should have an interface
- The result and recursive keywords are required as part of the function definition
- Example is a function finds the minimum value for an array
recursive function realmin(ain) result (themin)
! recursive and result are required for recursive functions
use numz
implicit none
real(b8) themin,t1,t2
integer n,right
real(b8) ,dimension(:) :: ain
n=size(ain)
if(n == 1)then
themin=ain(1) ! if the size is 1 return value
return
else
right=n/2
t1=realmin(ain(1:right)) ! find min in left half
t2=realmin(ain(right+1:n)) ! find min in right half
themin=min(t1,t2) ! find min of the two sides
endif
end function
- Example 2 is the same except the input data is our derived data type
!this routine works with the data structure thefit not reals
recursive function typemin(ain) result (themin)
use numz
use sort_mod
use galapagos
implicit none
real(b8) themin,t1,t2
integer n,right
type (thefit) ,dimension(:) :: ain ! this line is different
n=size(ain)
if(n == 1)then
themin=ain(1)%val ! this line is different
return
else
right=n/2
t1=typemin(ain(1:right))
t2=typemin(ain(right+1:n))
themin=min(t1,t2)
endif
end function
Pointers
-
Motivation
- Can increase performance
- Can improve readability
- Required for some derived data types (linked lists and trees)
- Useful for allocating "arrays" within subroutines
- Useful for referencing sections of arrays
-
Notes
- Pointers can be thought of as an alias to another variable
- In some cases can be used in place of an array
- To assign a pointer use => instead of just =
- Unlike C and C++, pointer arithmetic is not allowed
-
First pointer example
- Similar to the last findmin routine
- Return a pointer to the minimum
recursive function pntmin(ain) result (themin) ! return a pointer
use numz
use galapagos
use sort_mod ! contains the .lt. operator for thefit type
implicit none
type (thefit),pointer:: themin,t1,t2
integer n,right
type (thefit) ,dimension(:),target :: ain
n=size(ain)
if(n == 1)then
themin=>ain(1) !this is how we do pointer assignment
return
else
right=n/2
t1=>pntmin(ain(1:right))
t2=>pntmin(ain(right+1:n))
if(t1 .lt. t2)then; themin=>t1; else; themin=>t2; endif
endif
end function
Exercise 4: Carefully write a recursive N! program.
Function and subroutine overloading
-
Motivation
- Allows us to call functions or subroutine with the same name with different
argument types
- Increases readability
-
Notes:
- Similar in concept to operator overloading
- Requires an interface
- Syntax for subroutines is same as for functions
- Many intrinsic functions have this capability
- abs (reals,complex,integer)
- sin,cos,tan,exp(reals, complex)
- array functions(reals, complex,integer)
- Example
- Recall we had two functions that did the same thing but with different argument types
recursive function realmin(ain) result (themin)
real(b8) ,dimension(:) :: ain recursive function typemin(ain) result (themin)
type (thefit) ,dimension(:) :: ain
! note we have two functions within the same interface
! this is how we indicate function overloading
! both functions are called "findmin" in the main program
interface findmin
! the first is called with an array of reals as input
recursive function realmin(ain) result (themin)
use numz
real(b8) themin
real(b8) ,dimension(:) :: ain
end function ! the second is called with a array of data structures as input
recursive function typemin(ain) result (themin)
use numz
use galapagos
real(b8) themin
type (thefit) ,dimension(:) :: ain
end function
end interface
Example usage
program darwin
use numz
use ran_mod
use galapagos ! the module that contains the type definition
use face ! contains various interfaces
use sort_mod ! more about this later it
! contains our sorting routine
! and a few other tricks
implicit none
! create an allocatable array of the data type
! than contains an index and a real value
type (thefit),allocatable ,target :: results(:)
! create a single instance of the data type
type (thefit) best
! pointers to our type
type (thefit) ,pointer :: worst,tmp
integer,allocatable :: genes(:,:) ! our genes for the ga
integer j
integer num_genes,gene_size
real(b8) x
real(b8),allocatable :: z(:)
real(b8),pointer :: xyz(:) ! we'll talk about this next
num_genes=10
gene_size=10
allocate(results(num_genes)) ! allocate the data type to
allocate(genes(num_genes,gene_size)) ! hold our collection of genes
call init_genes(genes) ! starting data
write(*,'("input")')
do j=1,num_genes
results(j)%index=j
results(j)%val=fitness(genes(j,:)) ! just a dummy routine
write(*,"(f10.8,i4)")results(j)%val,results(j)%index
enddo allocate(z(size(results)))
z=results(:)%val ! copy our results to a real array ! use a recursive subroutine operating on the real array
write(*,*)"the lowest fitness: ",findmin(z)
! use a recursive subroutine operating on the data structure
write(*,*)"the lowest fitness: ",findmin(results)
end program
Fortran Minval and Minloc routines
- Fortran has routines for finding minimum and maximum values in arrays and
the locations
- minval
- maxval
- minloc (returns an array)
- maxloc (returns an array)
! we show two other methods of getting the minimum fitness
! use the built in f90 routines on a real array
write(*,*)"the lowest fitness: ",minval(z),minloc(z)
Pointer assignment
- This is how we use the pointer function defined above
- worst is a pointer to our data type
- note the use of =>
! use a recursive subroutine operating on the data
! structure and returning a pointer to the result
worst=>pntmin(results) ! note pointer assignment
! what will this line write?
write(*,*)"the lowest fitness: ",worst
More pointer usage, association and nullify
-
Motivation
- Need to find if pointers point to anything
- Need to find if two pointers point to the same thing
- Need to deallocate and nullify when they are no longer used
-
Usage
- We can use associated() to tell if a pointer has been set
- We can use associated() to compare pointers
- We use nullify to zero a pointer
! This code will print "true" when we find a match,
! that is the pointers point to the same object
do j=1,num_genes
tmp=>results(j)
write(*,"(f10.8,i4,l3)")results(j)%val, &
results(j)%index, &
associated(tmp,worst)
enddo
nullify(tmp)
- Notes:
- If a pointer is nullified the object to which it points is not deallocated.
- In general, pointers as well as allocatable arrays become undefined on leaving a subroutine
- This can cause a memory leak
Pointer usage to reference an array without copying
- Motivation
- Our sort routine calls a recursive sorting routine
- It is messy and inefficient to pass the array to the recursive routine
- Solution
- We define a "global" pointer in a module
- We point the pointer to our input array
module Merge_mod_types
use galapagos
type(thefit),allocatable :: work(:) ! a "global" work array
type(thefit), pointer:: a_pntr(:) ! this will be the pointer to our input array
end module Merge_mod_types
subroutine Sort(ain, n)
use Merge_mod_types
implicit none
integer n
type(thefit), target:: ain(n)
allocate(work(n))
nullify(a_pntr)
a_pntr=>ain ! we assign the pointer to our array
! in RecMergeSort we reference it just like an array
call RecMergeSort(1,n) ! very similar to the findmin functions
deallocate(work)
return
end subroutine Sort
- In our main program sort is called like this:
! our sort routine is also recursive but
! also shows a new usage for pointers
call sort(results,num_genes)
do j=1,num_genes
write(*,"(f10.8,i4)")results(j)%val, &
results(j)%index
enddo
Data assignment with structures
! we can copy a whole structure
! with a single assignment
best=results(1)
write(*,*)"best result ",best
Using the user defined operator
! using the user defined operator to see if best is worst
! recall that the operator .converged. checks to see if %index matches
worst=>pntmin(results)
write(*,*)"worst result ",worst
write(*,*)"converged=",(best .converged. worst)
Passing arrays with a given arbitrary lower bounds
if(allocated(z))deallocate(z)
allocate(z(-10:10)) ! a 21 element array
do j=-10,10
z(j)=j
enddo ! pass z and its lower bound
! in this routine we give the array a specific lower
! bound and show how to use a pointer to reference
! different parts of an array using different indices
call boink1(z,lbound(z,1)) ! why not just lbound(z) instead of lbound(z,1)?
! lbound(z) returns a rank 1 array
subroutine boink1(a,n)
use numz
implicit none
integer,intent(in) :: n
real(b8),dimension(n:):: a ! this is how we set lower bounds in a subroutine
write(*,*)lbound(a),ubound(a)
end subroutine
Warning: because we are using an assumed shape array we need an interface
Using pointers to access sections of arrays
- Motivation
- Can increase efficiency
- Can increase readability
call boink2(z,lbound(z,1))
subroutine boink2(a,n)
use numz
implicit none
integer,intent(in) :: n
real(b8),dimension(n:),target:: a
real(b8),dimension(:),pointer::b
b=>a(n:) ! b(1) "points" to a(-10)
write(*,*)"a(-10) =",a(-10),"b(1) =",b(1)
b=>a(0:) ! b(1) "points" to a(0)
write(*,*)"a(-6) =",a(-6),"b(-5) =",b(-5)
end subroutine
Allocating an array inside a subroutine and passing it back
- Motivation
- Size of arrays are calculated in the subroutine
module numz
integer, parameter:: b8 = selected_real_kind(14)
end module
program bla
use numz
real(b8), dimension(:) ,pointer :: xyz
interface boink
subroutine boink(a)
use numz
implicit none
real(b8), dimension(:), pointer :: a
end subroutine
end interface
nullify(xyz) ! nullify sets a pointer to null
write(*,'(l5)')associated(xyz) ! is a pointer null, should be
call boink(xyz)
write(*,'(l5)',advance="no")associated(xyz)
if(associated(xyz))write(*,'(i5)')size(xyz)
end program
subroutine boink(a)
use numz
implicit none
real(b8),dimension(:),pointer:: a
if(associated(a))deallocate(a)
allocate(a(10))
end subroutine
An example run
Our fitness function
Given a fixed number of colors, M, and a description of a map of a collection
of N states.
Find a coloring of the map such that no two states that share a boarder
have the same coloring.
22
ar ok tx la mo xx
az ca nm ut nv xx
ca az nv or xx
co nm ut wy ne ks xx
ia mo ne sd mn xx
id wa or nv ut wy mt xx
ks ne co ok mo xx
la tx ar xx
mn ia sd nd xx
mo ar ok ks ne ia xx
mt wy id nd xx
nd mt sd wy xx
ne sd wy co ks mo ia xx
nm az co ok tx mn xx
nv ca or id ut az xx
ok ks nm tx ar mo xx
or ca wa id xx
sd nd wy ne ia mn xx
tx ok nm la ar xx
ut nv az co wy id xx
wa id or mt xx
wy co mt id ut nd sd ne xx
Our fitness function takes a potential coloring, that is, an integer
vector of length N and a returns the number of boarders that have states
of the same coloring
- How do we represent the map in memory?
- One way would be to use an array but it would be very sparse
- Linked lists are often a better way
Linked lists
module list_stuff
type llist
integer index ! data
type(llist),pointer::next ! pointer to the
! next element
end type llist
end module
Linked list usage
One way to fill a linked list is to use a recursive function
`fortran
recursive subroutine insert (item, root)
use list_stuff
implicit none
type(llist), pointer :: root
integer item
if (.not. associated(root)) then
allocate(root)
nullify(root%next)
root%index = item
else
call insert(item,root%next)
endif
end subroutine
- - -
- - -
## Our map representation
- An array of the derived data type states
- State is name of a state
- Linked list containing boarders
```fortran
type states
character(len=2)name
type(llist),pointer:: list
end type states
Date and time functions
! all arguments are optional
call date_and_time(date=c_date, & ! character(len=8) ccyymmdd
time=c_time, & ! character(len=10) hhmmss.sss
zone=c_zone, & ! character(len=10) +/-hhmm (time zone)
values=ivalues) ! integer ivalues(8) all of the above
call system_clock(count=ic, & ! count of system clock (clicks)
count_rate=icr, & ! clicks / second
count_max=max_c) ! max value for count
Non advancing and character IO
Internal IO
character (len=12)tmpstr
write(tmpstr,"(a12)")(c_date(5:8)//c_time(1:4)//".dat") ! // does string concatination
write(*,*)"name of file= ",tmpstr
open(14,file=tmpstr)
name of file= 03271114.dat
- Example 2: Creating a format statement at run time (array of integers and a real)
! test_vect is an array that we do not know its length until run time
nstate=9 ! the size of the array
write(fstr,'("(",i4,"i1,1x,f10.5)")')nstates
write(*,*)"format= ",fstr
write(*,fstr)test_vect,fstr
format= ( 9i1,1x,f10.5)
- Example 3: Reading from a string
integer ht,minut,sec
read(c_time,"(3i2)")hr,minut,sec
Inquire function
inquire(iolength=len_real)1.0
inquire(iolength=len_b8)1.0_b8
write(*,*)"len_b8 ",len_b8
write(*,*)"len_real",len_real
iratio=len_b8/len_real
select case (iratio)
case (1)
my_mpi_type=mpi_real
case(2)
my_mpi_type=mpi_double_precision
case default
write(*,*)"type undefined"
my_mpi_type=0
end select
An example run
Namelist
- Now part of the standard
- Motivation
- A convenient method of doing I/O
- Good for cases where you have similar runs but change one or two variables
- Good for formatted output
-
Notes:
- A little flaky
- No options for overloading format
-
Example:
integer ncolor
logical force
namelist /the_input/ncolor,force
ncolor=4
force=.true.
read(13,the_input)
write(*,the_input)
& THE_INPUT NCOLOR=4,FORCE = F /
&THE_INPUT
NCOLOR = 4,
FORCE = F
/
Vector valued functions
- Motivation
- May want a function that returns a vector
-
Notes
- Again requires an interface
- Use explicit or assumed size array
- Do not return a pointer to a vector unless you really want a pointer
-
Example:
- Take an integer input vector which represents an integer in some base and
add 1
- Could be used in our program to find a "brute force" solution
function add1(vector,max) result (rtn)
integer, dimension(:),intent(in) :: vector
integer,dimension(size(vector)) :: rtn
integer max
integer len
logical carry
len=size(vector)
rtn=vector
i=0
carry=.true.
do while(carry) ! just continue until we do not do a carry
i=i+1
rtn(i)=rtn(i)+1
if(rtn(i) .gt. max)then
if(i == len)then ! role over set everything back to 0
rtn=0
else
rtn(i)=0
endif
else
carry=.false.
endif
enddo
end function
Usage
test_vect=0
do
test_vect=add1(test_vect,3)
result=fitness(test_vect)
if(result .lt. 1.0_b8)then
write(*,*)test_vect
stop
endif
enddo
Complete source for recent discussions
Exersize 5 Modify the program to use the random
number generator given earlier.
Some array specific intrinsic functions
program matrix
real w(10),x(10),mat(10,10)
call random_number(w)
call random_number(mat)
x=matmul(w,mat) ! regular matrix multiply USE IT
write(*,'("dot(x,x)=",f10.5)'),dot_product(x,x)
end program
program allit
character(len=10):: f1="(3l1)"
character(len=10):: f2="(3i2)"
integer b(2,3),c(2,3),one_d(6)
logical l(2,3)
one_d=(/ 1,3,5 , 2,4,6 /)
b=transpose(reshape((/ 1,3,5 , 2,4,6 /),shape=(/3,2/)))
C=transpose(reshape((/ 0,3,5 , 7,4,8 /),shape=(/3,2/)))
l=(b.ne.c)
write(*,f2)((b(i,j),j=1,3),i=1,2)
write(*,*)
write(*,f2)((c(i,j),j=1,3),i=1,2)
write(*,*)
write(*,f1)((l(i,j),j=1,3),i=1,2)
write(*,*)
write(*,f1)all ( b .ne. C ) !is .false.
write(*,f1)all ( b .ne. C, DIM=1) !is [.true., .false., .false.]
write(*,f1)all ( b .ne. C, DIM=2) !is [.false., .false.]
end
1 3 5
2 4 6
0 3 5
7 4 8
TFF
TFT
F
TFF
FF
The rest of our GA
gfortran
- .f, .for, .ftn .f77
- fixed-format Fortran source; compile
- .f90, .f95
- free-format Fortran source; compile
- -fbacktrace
- Add debug information for runtime traceback
- -ffree-form -ffixed-form
- -O0, -O1, -O2, -O3
- .fpp, .FPP, .F, .FOR, .FTN, .F90, .F95, .F03 or .F08
- Fortran source file with preprocessor directives
- -fopenmp
Intel
- .f, .for, .ftn
- fixed-format Fortran source; compile
- .f90, .f95
- free-format Fortran source; compile
- -O0, -O1, -O2, -O3, -O4
- .fpp, .F, .FOR, .FTN, .FPP, .F90
- Fortran source file with preprocessor directives
- -g
- compile for debug * -traceback -notraceback (default)
- Add debug information for runtime traceback
- -nofree, -free
- Source is fixed or free format
- -fopenmp
Portland Group (x86)
- .f, .for, .ftn
- fixed-format Fortran source; compile
- .f90, .f95, .f03
- free-format Fortran source; compile
- .cuf
- free-format CUDA Fortran source; compile
-
.CUF
- free-format CUDA Fortran source; preprocess, compile
-
-O0, -O1, -O2, -O3, -O4
-
-g
- compile for debug * -traceback (default) -notraceback
- Add debug information for runtime traceback
- -Mfixed, -Mfree
- Source is fixed or free format
- -qmp
IBM xlf
- xlf, xlf_r, f77, fort77
- Compile FORTRAN 77 source files. _r = thread safe
- xlf90, xlf90_r, f90
- Compile Fortran 90 source files. _r = thread safe
- xlf95, xlf95_r, f95
- Compile Fortran 95 source files. _r = thread safe
- xlf2003, xlf2003_r,f2003 * Compile Fortran 2003 source files. _r = thread safe
- xlf2008, xlf2008_r, f2008 * Compile Fortran 2008 source files.
- .f, .f77, .f90, .f95, .f03, .f08
- .F, .F77, .F90, .F95, .F03, .F08
- Fortran source file with preprocessor directives
- -qtbtable=full
- Add debug information for runtime traceback
- -qsmp=omp
- -O0, -O1, -O2, -O3, -O4, O5
- -g , g0, g1,...g9
Summary
Introduction to Fortran Language
Brought to you by ANSI committee X3J3 and ISO-IEC/JTC1/SC22/WG5 (Fortran)
This is neither complete nor precisely accurate, but hopefully, after
a small investment of time it is easy to read and very useful.
This is the free form version of Fortran, no statement numbers,
no C in column 1, start in column 1 (not column 7),
typically indent 2, 3, or 4 spaces per each structure.
The typical extension is .f90 .
Continue a statement on the next line by ending the previous line with
an ampersand & . Start the continuation with & for strings.
The rest of any line is a comment starting with an exclamation mark ! .
Put more than one statement per line by separating statements with a
semicolon ; . Null statements are OK, so lines can end with semicolons.
Separate words with space or any form of "white space" or punctuation.
<xxx> means fill in something appropriate for xxx and do not type
the "<" or ">" .
... ellipsis means the usual, fill in something, one or more lines
[stuff] means supply nothing or at most one copy of "stuff"
[stuff1 [stuff2]] means if "stuff1" is included, supply nothing
or at most one copy of stuff2.
"old" means it is in the language, like almost every feature of past
Fortran standards, but should not be used to write new programs.
Structure of files that can be compiled
program <name> usually file name is <name>.f90
use <module_name> bring in any needed modules
implicit none good for error detection
<declarations>
<executable statements> order is important, no more declarations
end program <name>
block data <name> old
<declarations> common, dimension, equivalence now obsolete
end block data <name>
module <name> bring back in with use <name>
implicit none good for error detection
<declarations> can have private and public and interface
end module <name>
subroutine <name> use: call <name> to execute
implicit none good for error detection
<declarations>
<executable statements>
end subroutine <name>
subroutine <name>(par1, par2, ...)
use: call <name>(arg1, arg2,... ) to execute
implicit none optional, good for error detection
<declarations> par1, par2, ... are defined in declarations
and can be specified in, inout, pointer, etc.
<executable statements>
return optional, end causes automatic return
entry <name> (par...) old, optional other entries
end subroutine <name>
function <name>(par1, par2, ...) result(<rslt>)
use: <name>(arg1, arg2, ... argn) as variable
implicit none optional, good for error detection
<declarations> rslt, par1, ... are defined in declarations
<executable statements>
<rslt> = <expression> required somewhere in execution
[return] optional, end causes automatic return
end function <name>
old
<type> function(...) <name> use: <name>(arg1, arg2, ... argn) as variable
<declarations>
<executable statements>
<name> = <expression> required somewhere in execution
[return] optional, end causes automatic return
end function <name>
Executable Statements and Constructs
<statement> will mean exactly one statement in this section
a construct is multiple lines
<label> : <statement> any statement can have a label (a name)
<variable> = <expression> assignment statement
<pointer> >= <variable> the pointer is now an alias for the variable
<pointer1> >= <pointer2> pointer1 now points same place as pointer2
stop can be in any executable statement group,
stop <integer> terminates execution of the program,
stop <string> can have optional integer or string
return exit from subroutine or function
do <variable>=<from>,<to> [,<increment>] optional: <label> : do ...
<statements>
exit \_optional or exit <label>
if (<boolean expression>) exit /
exit the loop
cycle \_optional or cycle <label>
if (<boolean expression>) cycle /
continue with next loop iteration
end do optional: end do <name>
do while (<boolean expression>)
... optional exit and cycle allowed
end do
do
... exit required to end the loop
optional cycle can be used
end do
if ( <boolean expression> ) <statement> execute the statement if the
boolean expression is true
if ( <boolean expression1> ) then
... execute if expression1 is true
else if ( <boolean expression2> ) then
... execute if expression2 is true
else if ( <boolean expression3> ) then
... execute if expression3 is true
else
... execute if none above are true
end if
select case (<expression>) optional <name> : select case ...
case (<value>)
<statements> execute if expression == value
case (<value1>:<value2>)
<statements> execute if value1 ≤ expression ≤ value2
...
case default
<statements> execute if no values above match
end select optional end select <name>
real, dimension(10,12) :: A, R a sample declaration for use with "where"
...
where (A /= 0.0) conditional assignment, only assignment allowed
R = 1.0/A
elsewhere
R = 1.0 elements of R set to 1.0 where A == 0.0
end where
go to <statement number> old
go to (<statement number list>), <expression> old
for I/O statements, see: section 10.0 Input/Output Statements
many old forms of statements are not listed
Declarations
There are five (5) basic types: integer, real, complex, character and logical.
There may be any number of user derived types. A modern (not old) declaration
starts with a type, has attributes, then ::, then variable(s) names
integer i, pivot, query old
integer, intent (inout) :: arg1
integer (selected_int_kind (5)) :: i1, i2
integer, parameter :: m = 7
integer, dimension(0:4, -5:5, 10:100) :: A3D
double precision x old
real (selected_real_kind(15,300) :: x
complex :: z
logical, parameter :: what_if = .true.
character, parameter :: me = "Jon Squire"
type <name> a new user type, derived type
declarations
end type <name>
type (<name>) :: stuff declaring stuff to be of derived type <name>
real, dimension(:,:), allocatable, target :: A
real, dimension(:,:), pointer :: P
Attributes may be:
allocatable no memory used here, allocate later
dimension vector or multi dimensional array
external will be defined outside this compilation
intent argument may be in, inout or out
intrinsic declaring function to be an intrinsic
optional argument is optional
parameter declaring a constant, can not be changed later
pointer declaring a pointer
private in a module, a private declaration
public in a module, a public declaration
save keep value from one call to the next, static
target can be pointed to by a pointer
Note: not all combinations of attributes are legal
Key words (other than I/O)
note: "statement" means key word that starts a statement, one line
unless there is a continuation "&"
"construct" means multiple lines, usually ending with "end ..."
"attribute" means it is used in a statement to further define
"old" means it should not be used in new code
allocatable attribute, no space allocated here, later allocate
allocate statement, allocate memory space now for variable
assign statement, old, assigned go to
assignment attribute, means subroutine is assignment (=)
block data construct, old, compilation unit, replaced by module
call statement, call a subroutine
case statement, used in select case structure
character statement, basic type, intrinsic data type
common statement, old, allowed overlaying of storage
complex statement, basic type, intrinsic data type
contains statement, internal subroutines and functions follow
continue statement, old, a place to put a statement number
cycle statement, continue the next iteration of a do loop
data statement, old, initialized variables and arrays
deallocate statement, free up storage used by specified variable
default statement, in a select case structure, all others
do construct, start a do loop
double precision statement, old, replaced by selected_real_kind(15,300)
else construct, part of if else if else end if
else if construct, part of if else if else end if
elsewhere construct, part of where elsewhere end where
end block data construct, old, ends block data
end do construct, ends do
end function construct, ends function
end if construct, ends if
end interface construct, ends interface
end module construct, ends module
end program construct, ends program
end select construct, ends select case
end subroutine construct, ends subroutine
end type construct, ends type
end where construct, ends where
entry statement, old, another entry point in a procedure
equivalence statement, old, overlaid storage
exit statement, continue execution outside of a do loop
external attribute, old statement, means defines else where
function construct, starts the definition of a function
go to statement, old, requires fixed form statement number
if statement and construct, if(...) statement
implicit statement, "none" is preferred to help find errors
in a keyword for intent, the argument is read only
inout a keyword for intent, the argument is read/write
integer statement, basic type, intrinsic data type
intent attribute, intent(in) or intent(out) or intent(inout)
interface construct, begins an interface definition
intrinsic statement, says that following names are intrinsic
kind attribute, sets the kind of the following variables
len attribute, sets the length of a character string
logical statement, basic type, intrinsic data type
module construct, beginning of a module definition
namelist statement, defines a namelist of input/output
nullify statement, nullify(some_pointer) now points nowhere
only attribute, restrict what comes from a module
operator attribute, indicates function is an operator, like +
optional attribute, a parameter or argument is optional
out a keyword for intent, the argument will be written
parameter attribute, old statement, makes variable real only
pause old, replaced by stop
pointer attribute, defined the variable as a pointer alias
private statement and attribute, in a module, visible inside
program construct, start of a main program
public statement and attribute, in a module, visible outside
real statement, basic type, intrinsic data type
recursive attribute, allows functions and derived type recursion
result attribute, allows naming of function result result(Y)
return statement, returns from, exits, subroutine or function
save attribute, old statement, keep value between calls
select case construct, start of a case construct
stop statement, terminate execution of the main procedure
subroutine construct, start of a subroutine definition
target attribute, allows a variable to take a pointer alias
then part of if construct
type construct, start of user defined type
type ( ) statement, declaration of a variable for a users type
use statement, brings in a module
where construct, conditional assignment
while construct, a while form of a do loop
backspace statement, back up one record
close statement, close a file
endfile statement, mark the end of a file
format statement, old, defines a format
inquire statement, get the status of a unit
open statement, open or create a file
print statement, performs output to screen
read statement, performs input
rewind statement, move read or write position to beginning
write statement, performs output
Operators
** exponentiation
* multiplication
/ division
+ addition
- subtraction
// concatenation
== .eq. equality
/= .ne. not equal
< .lt. less than
> .gt. greater than
<= .le. less than or equal
>= .ge. greater than or equal
.not. complement, negation
.and. logical and
.or. logical or
.eqv. logical equivalence
.neqv. logical not equivalence, exclusive or
.eq. == equality, old
.ne. /= not equal. old
.lt. < less than, old
.gt. > greater than, old
.le. <= less than or equal, old
.ge. >= greater than or equal, old
Other punctuation:
/ ... / used in data, common, namelist and other statements
(/ ... /) array constructor, data is separated by commas
6*1.0 in some contexts, 6 copies of 1.0
(i:j:k) in some contexts, a list i, i+k, i+2k, i+3k, ... i+nk≤j
(:j) j and all below
(i:) i and all above
(:) undefined or all in range
Constants
Logical constants:
.true. True
.false. False
Integer constants:
0 1 -1 123456789
Real constants:
0.0 1.0 -1.0 123.456 7.1E+10 -52.715E-30
Complex constants:
(0.0, 0.0) (-123.456E+30, 987.654E-29)
Character constants:
"ABC" "a" "123'abc$%#@!" " a quote "" "
'ABC' 'a' '123"abc$%#@!' ' a apostrophe '' '
Derived type values:
type name
character (len=30) :: last
character (len=30) :: first
character (len=30) :: middle
end type name
type address
character (len=40) :: street
character (len=40) :: more
character (len=20) :: city
character (len=2) :: state
integer (selected_int_kind(5)) :: zip_code
integer (selected_int_kind(4)) :: route_code
end type address
type person
type (name) lfm
type (address) snail_mail
end type person
type (person) :: a_person = person( name("Squire","Jon","S."), &
address("106 Regency Circle", "", "Linthicum", "MD", 21090, 1936))
a_person%snail_mail%route_code == 1936
open (<unit number>)
open (unit=<unit number>, file=<file name>, iostat=<variable>)
open (unit=<unit number>, ... many more, see below )
close (<unit number>)
close (unit=<unit number>, iostat=<variable>,
err=<statement number>, status="KEEP")
read (<unit number>) <input list>
read (unit=<unit number>, fmt=<format>, iostat=<variable>,
end=<statement number>, err=<statement number>) <input list>
read (unit=<unit number>, rec=<record number>) <input list>
write (<unit number>) <output list>
write (unit=<unit number>, fmt=<format>, iostat=<variable>,
err=<statement number>) <output list>
write (unit=<unit number>, rec=<record number>) <output list>
print *, <output list>
print "(<your format here, use apostrophe, not quote>)", <output list>
rewind <unit number>
rewind (<unit number>, err=<statement number>)
backspace <unit number>
backspace (<unit number>, iostat=<variable>)
endfile <unit number>
endfile (<unit number>, err=<statement number>, iostat=<variable>)
inquire ( <unit number>, exists = <variable>)
inquire ( file=<"name">, opened = <variable1>, access = <variable2> )
inquire ( iolength = <variable> ) x, y, A ! gives "recl" for "open"
namelist /<name>/ <variable list> defines a name list
read(*,nml=<name>) reads some/all variables in namelist
write(*,nml=<name>) writes all variables in namelist
&<name> <variable>=<value> ... <variable=value> / data for namelist read
Input / Output specifiers
access one of "sequential" "direct" "undefined"
action one of "read" "write" "readwrite"
advance one of "yes" "no"
blank one of "null" "zero"
delim one of "apostrophe" "quote" "none"
end = <integer statement number> old
eor = <integer statement number> old
err = <integer statement number> old
exist = <logical variable>
file = <"file name">
fmt = <"(format)"> or <character variable> format
form one of "formatted" "unformatted" "undefined"
iolength = <integer variable, size of unformatted record>
iostat = <integer variable> 0==good, negative==eof, positive==bad
name = <character variable for file name>
named = <logical variable>
nml = <namelist name>
nextrec = <integer variable> one greater than written
number = <integer variable unit number>
opened = <logical variable>
pad one of "yes" "no"
position one of "asis" "rewind" "append"
rec = <integer record number>
recl = <integer unformatted record size>
size = <integer variable> number of characters read before eor
status one of "old" "new" "unknown" "replace" "scratch" "keep"
unit = <integer unit number>
Individual questions
direct = <character variable> "yes" "no" "unknown"
formatted = <character variable> "yes" "no" "unknown"
read = <character variable> "yes" "no" "unknown"
readwrite = <character variable> "yes" "no" "unknown"
sequential = <character variable> "yes" "no" "unknown"
unformatted = <character variable> "yes" "no" "unknown"
write = <character variable> "yes" "no" "unknown"
format an explicit format can replace * in any
I/O statement. Include the format in
apostrophes or quotes and keep the parenthesis.
examples:
print "(3I5,/(2X,3F7.2/))", <output list>
write(6, '(a,E15.6E3/a,G15.2)' ) <output list>
read(unit=11, fmt="(i4, 4(f3.0,TR1))" ) <input list>
A format includes the opening and closing parenthesis.
A format consists of format items and format control items separated by comma.
A format may contain grouping parenthesis with an optional repeat count.
Format Items, data edit descriptors:
key: w is the total width of the field (filled with *** if overflow)
m is the least number of digits in the (sub)field (optional)
d is the number of decimal digits in the field
e is the number of decimal digits in the exponent subfield
c is the repeat count for the format item
n is number of columns
cAw data of type character (w is optional)
cBw.m data of type integer with binary base
cDw.d data of type real -- same as E, old double precision
cEw.d or Ew.dEe data of type real
cENw.d or ENw.dEe data of type real -- exponent a multiple of 3
cESw.d or ESw.dEe data of type real -- first digit non zero
cFw.d data of type real -- no exponent printed
cGw.d or Gw.dEe data of type real -- auto format to F or E
nH n characters follow the H, no list item
cIw.m data of type integer
cLw data of type logical -- .true. or .false.
cOw.m data of type integer with octal base
cZw.m data of type integer with hexadecimal base
"<string>" literal characters to output, no list item
'<string>' literal characters to output, no list item
Format Control Items, control edit descriptors:
BN ignore non leading blanks in numeric fields
BZ treat nonleading blanks in numeric fields as zeros
nP apply scale factor to real format items old
S printing of optional plus signs is processor dependent
SP print optional plus signs
SS do not print optional plus signs
Tn tab to specified column
TLn tab left n columns
TRn tab right n columns
nX tab right n columns
/ end of record (implied / at end of all format statements)
: stop format processing if no more list items
<input list> can be:
a variable
an array name
an implied do ((A(i,j),j=1,n) ,i=1,m) parenthesis and commas as shown
note: when there are more items in the input list than format items, the
repeat rules for formats applies.
<output list> can be:
a constant
a variable
an expression
an array name
an implied do ((A(i,j),j=1,n) ,i=1,m) parenthesis and commas as shown
note: when there are more items in the output list than format items, the
repeat rules for formats applies.
Repeat Rules for Formats:
Each format item is used with a list item. They are used in order.
When there are more list items than format items, then the following
rule applies: There is an implied end of record, /, at the closing
parenthesis of the format, this is processed. Scan the format backwards
to the first left parenthesis. Use the repeat count, if any, in front
of this parenthesis, continue to process format items and list items.
Note: an infinite loop is possible
print "(3I5/(1X/))", I, J, K, L may never stop
Intrinsic Functions
Intrinsic Functions are presented in alphabetical order and then grouped
by topic. The function name appears first. The argument(s) and result
give an indication of the type(s) of argument(s) and results.
[,dim=] indicates an optional argument "dim".
"mask" must be logical and usually conformable.
"character" and "string" are used interchangeably.
A brief description or additional information may appear.
Intrinsic Functions (alphabetical):
abs(integer_real_complex) result(integer_real_complex)
achar(integer) result(character) integer to character
acos(real) result(real) arccosine |real| ≤ 1.0 0≤result≤Pi
adjustl(character) result(character) left adjust, blanks go to back
adjustr(character) result(character) right adjust, blanks to front
aimag(complex) result(real) imaginary part
aint(real [,kind=]) result(real) truncate to integer toward zero
all(mask [,dim]) result(logical) true if all elements of mask are true
allocated(array) result(logical) true if array is allocated in memory
anint(real [,kind=]) result(real) round to nearest integer
any(mask [,dim=}) result(logical) true if any elements of mask are true
asin(real) result(real) arcsine |real| ≤ 1.0 -Pi/2≤result≤Pi/2
associated(pointer [,target=]) result(logical) true if pointing
atan(real) result(real) arctangent -Pi/2≤result≤Pi/2
atan2(y=real,x=real) result(real) arctangent -Pi≤result≤Pi
bit_size(integer) result(integer) size in bits in model of argument
btest(i=integer,pos=integer) result(logical) true if pos has a 1, pos=0..
ceiling(real) result(real) truncate to integer toward infinity
char(integer [,kind=]) result(character) integer to character [of kind]
cmplx(x=real [,y=real] [kind=]) result(complex) x+iy
conjg(complex) result(complex) reverse the sign of the imaginary part
cos(real_complex) result(real_complex) cosine
cosh(real) result(real) hyperbolic cosine
count(mask [,dim=]) result(integer) count of true entries in mask
cshift(array,shift [,dim=]) circular shift elements of array, + is right
date_and_time([date=] [,time=] [,zone=] [,values=]) y,m,d,utc,h,m,s,milli
dble(integer_real_complex) result(real_kind_double) convert to double
digits(integer_real) result(integer) number of bits to represent model
dim(x=integer_real,y=integer_real) result(integer_real) proper subtraction
dot_product(vector_a,vector_b) result(integer_real_complex) inner product
dprod(x=real,y=real) result(x_times_y_double) double precision product
eoshift(array,shift [,boundary=] [,dim=]) end-off shift using boundary
epsilon(real) result(real) smallest positive number added to 1.0 /= 1.0
exp(real_complex) result(real_complex) e raised to a power
exponent(real) result(integer) the model exponent of the argument
floor(real) result(real) truncate to integer towards negative infinity
fraction(real) result(real) the model fractional part of the argument
huge(integer_real) result(integer_real) the largest model number
iachar(character) result(integer) position of character in ASCII sequence
iand(integer,integer) result(integer) bit by bit logical and
ibclr(integer,pos) result(integer) argument with pos bit cleared to zero
ibits(integer,pos,len) result(integer) extract len bits starting at pos
ibset(integer,pos) result(integer) argument with pos bit set to one
ichar(character) result(integer) pos in collating sequence of character
ieor(integer,integer) result(integer) bit by bit logical exclusive or
index(string,substring [,back=]) result(integer) pos of substring
int(integer_real_complex) result(integer) convert to integer
ior(integer,integer) result(integer) bit by bit logical or
ishft(integer,shift) result(integer) shift bits in argument by shift
ishftc(integer, shift) result(integer) shift circular bits in argument
kind(any_intrinsic_type) result(integer) value of the kind
lbound(array,dim) result(integer) smallest subscript of dim in array
len(character) result(integer) number of characters that can be in argument
len_trim(character) result(integer) length without trailing blanks
lge(string_a,string_b) result(logical) string_a ≥ string_b
lgt(string_a,string_b) result(logical) string_a > string_b
lle(string_a,string_b) result(logical) string_a ≤ string_b
llt(string_a,string_b) result(logical) string_a < string_b
log(real_complex) result(real_complex) natural logarithm
log10(real) result(real) logarithm base 10
logical(logical [,kind=]) convert to logical
matmul(matrix,matrix) result(vector_matrix) on integer_real_complex_logical
max(a1,a2,a3,...) result(integer_real) maximum of list of values
maxexponent(real) result(integer) maximum exponent of model type
maxloc(array [,mask=]) result(integer_vector) indices in array of maximum
maxval(array [,dim=] [,mask=]) result(array_element) maximum value
merge(true_source,false_source,mask) result(source_type) choose by mask
min(a1,a2,a3,...) result(integer-real) minimum of list of values
minexponent(real) result(integer) minimum(negative) exponent of model type
minloc(array [,mask=]) result(integer_vector) indices in array of minimum
minval(array [,dim=] [,mask=]) result(array_element) minimum value
mod(a=integer_real,p) result(integer_real) a modulo p
modulo(a=integer_real,p) result(integer_real) a modulo p
mvbits(from,frompos,len,to,topos) result(integer) move bits
nearest(real,direction) result(real) nearest value toward direction
nint(real [,kind=]) result(real) round to nearest integer value
not(integer) result(integer) bit by bit logical complement
pack(array,mask [,vector=]) result(vector) vector of elements from array
present(argument) result(logical) true if optional argument is supplied
product(array [,dim=] [,mask=]) result(integer_real_complex) product
radix(integer_real) result(integer) radix of integer or real model, 2
random_number(harvest=real_out) subroutine, uniform random number 0 to 1
random_seed([size=] [,put=] [,get=]) subroutine to set random number seed
range(integer_real_complex) result(integer_real) decimal exponent of model
real(integer_real_complex [,kind=]) result(real) convert to real
repeat(string,ncopies) result(string) concatenate n copies of string
reshape(source,shape,pad,order) result(array) reshape source to array
rrspacing(real) result(real) reciprocal of relative spacing of model
scale(real,integer) result(real) multiply by 2**integer
scan(string,set [,back]) result(integer) position of first of set in string
selected_int_kind(integer) result(integer) kind number to represent digits
selected_real_kind(integer,integer) result(integer) kind of digits, exp
set_exponent(real,integer) result(real) put integer as exponent of real
shape(array) result(integer_vector) vector of dimension sizes
sign(integer_real,integer_real) result(integer_real) sign of second on first
sin(real_complex) result(real_complex) sine of angle in radians
sinh(real) result(real) hyperbolic sine of argument
size(array [,dim=]) result(integer) number of elements in dimension
spacing(real) result(real) spacing of model numbers near argument
spread(source,dim,ncopies) result(array) expand dimension of source by 1
sqrt(real_complex) result(real_complex) square root of argument
sum(array [,dim=] [,mask=]) result(integer_real_complex) sum of elements
system_clock([count=] [,count_rate=] [,count_max=]) subroutine, all out
tan(real) result(real) tangent of angle in radians
tanh(real) result(real) hyperbolic tangent of angle in radians
tiny(real) result(real) smallest positive model representation
transfer(source,mold [,size]) result(mold_type) same bits, new type
transpose(matrix) result(matrix) the transpose of a matrix
trim(string) result(string) trailing blanks are removed
ubound(array,dim) result(integer) largest subscript of dim in array
unpack(vector,mask,field) result(v_type,mask_shape) field when not mask
verify(string,set [,back]) result(integer) pos in string not in set
Intrinsic Functions (grouped by topic):
Intrinsic Functions (Numeric)
abs(integer_real_complex) result(integer_real_complex)
acos(real) result(real) arccosine |real| ≤ 1.0 0≤result≤Pi
aimag(complex) result(real) imaginary part
aint(real [,kind=]) result(real) truncate to integer toward zero
anint(real [,kind=]) result(real) round to nearest integer
asin(real) result(real) arcsine |real| ≤ 1.0 -Pi/2≤result≤Pi/2
atan(real) result(real) arctangent -Pi/2≤result≤Pi/2
atan2(y=real,x=real) result(real) arctangent -Pi≤result≤Pi
ceiling(real) result(real) truncate to integer toward infinity
cmplx(x=real [,y=real] [kind=]) result(complex) x+iy
conjg(complex) result(complex) reverse the sign of the imaginary part
cos(real_complex) result(real_complex) cosine
cosh(real) result(real) hyperbolic cosine
dble(integer_real_complex) result(real_kind_double) convert to double
digits(integer_real) result(integer) number of bits to represent model
dim(x=integer_real,y=integer_real) result(integer_real) proper subtraction
dot_product(vector_a,vector_b) result(integer_real_complex) inner product
dprod(x=real,y=real) result(x_times_y_double) double precision product
epsilon(real) result(real) smallest positive number added to 1.0 /= 1.0
exp(real_complex) result(real_complex) e raised to a power
exponent(real) result(integer) the model exponent of the argument
floor(real) result(real) truncate to integer towards negative infinity
fraction(real) result(real) the model fractional part of the argument
huge(integer_real) result(integer_real) the largest model number
int(integer_real_complex) result(integer) convert to integer
log(real_complex) result(real_complex) natural logarithm
log10(real) result(real) logarithm base 10
matmul(matrix,matrix) result(vector_matrix) on integer_real_complex_logical
max(a1,a2,a3,...) result(integer_real) maximum of list of values
maxexponent(real) result(integer) maximum exponent of model type
maxloc(array [,mask=]) result(integer_vector) indices in array of maximum
maxval(array [,dim=] [,mask=]) result(array_element) maximum value
min(a1,a2,a3,...) result(integer-real) minimum of list of values
minexponent(real) result(integer) minimum(negative) exponent of model type
minloc(array [,mask=]) result(integer_vector) indices in array of minimum
minval(array [,dim=] [,mask=]) result(array_element) minimum value
mod(a=integer_real,p) result(integer_real) a modulo p
modulo(a=integer_real,p) result(integer_real) a modulo p
nearest(real,direction) result(real) nearest value toward direction
nint(real [,kind=]) result(real) round to nearest integer value
product(array [,dim=] [,mask=]) result(integer_real_complex) product
radix(integer_real) result(integer) radix of integer or real model, 2
random_number(harvest=real_out) subroutine, uniform random number 0 to 1
random_seed([size=] [,put=] [,get=]) subroutine to set random number seed
range(integer_real_complex) result(integer_real) decimal exponent of model
real(integer_real_complex [,kind=]) result(real) convert to real
rrspacing(real) result(real) reciprocal of relative spacing of model
scale(real,integer) result(real) multiply by 2**integer
set_exponent(real,integer) result(real) put integer as exponent of real
sign(integer_real,integer_real) result(integer_real) sign of second on first
sin(real_complex) result(real_complex) sine of angle in radians
sinh(real) result(real) hyperbolic sine of argument
spacing(real) result(real) spacing of model numbers near argument
sqrt(real_complex) result(real_complex) square root of argument
sum(array [,dim=] [,mask=]) result(integer_real_complex) sum of elements
tan(real) result(real) tangent of angle in radians
tanh(real) result(real) hyperbolic tangent of angle in radians
tiny(real) result(real) smallest positive model representation
transpose(matrix) result(matrix) the transpose of a matrix
Intrinsic Functions (Logical and bit)
all(mask [,dim]) result(logical) true if all elements of mask are true
any(mask [,dim=}) result(logical) true if any elements of mask are true
bit_size(integer) result(integer) size in bits in model of argument
btest(i=integer,pos=integer) result(logical) true if pos has a 1, pos=0..
count(mask [,dim=]) result(integer) count of true entries in mask
iand(integer,integer) result(integer) bit by bit logical and
ibclr(integer,pos) result(integer) argument with pos bit cleared to zero
ibits(integer,pos,len) result(integer) extract len bits starting at pos
ibset(integer,pos) result(integer) argument with pos bit set to one
ieor(integer,integer) result(integer) bit by bit logical exclusive or
ior(integer,integer) result(integer) bit by bit logical or
ishft(integer,shift) result(integer) shift bits in argument by shift
ishftc(integer, shift) result(integer) shift circular bits in argument
logical(logical [,kind=]) convert to logical
matmul(matrix,matrix) result(vector_matrix) on integer_real_complex_logical
merge(true_source,false_source,mask) result(source_type) choose by mask
mvbits(from,frompos,len,to,topos) result(integer) move bits
not(integer) result(integer) bit by bit logical complement
transfer(source,mold [,size]) result(mold_type) same bits, new type
Intrinsic Functions (Character or string)
achar(integer) result(character) integer to character
adjustl(character) result(character) left adjust, blanks go to back
adjustr(character) result(character) right adjust, blanks to front
char(integer [,kind=]) result(character) integer to character [of kind]
iachar(character) result(integer) position of character in ASCII sequence
ichar(character) result(integer) pos in collating sequence of character
index(string,substring [,back=]) result(integer) pos of substring
len(character) result(integer) number of characters that can be in argument
len_trim(character) result(integer) length without trailing blanks
lge(string_a,string_b) result(logical) string_a ≥ string_b
lgt(string_a,string_b) result(logical) string_a > string_b
lle(string_a,string_b) result(logical) string_a ≤ string_b
llt(string_a,string_b) result(logical) string_a < string_b
repeat(string,ncopies) result(string) concatenate n copies of string
scan(string,set [,back]) result(integer) position of first of set in string
trim(string) result(string) trailing blanks are removed
verify(string,set [,back]) result(integer) pos in string not in set
Fortran 95
- New Features
- The statement FORALL as an alternative to the DO-statement
- Partial nesting of FORALL and WHERE statements
- Masked ELSEWHERE
- Pure procedures
- Elemental procedures
- Pure procedures in specification expressions
- Revised MINLOC and MAXLOC
- Extensions to CEILING and FLOOR with the KIND keyword argument
- Pointer initialization
- Default initialization of derived type objects
- Increased compatibility with IEEE arithmetic
- A CPU_TIME intrinsic subroutine
- A function NULL to nullify a pointer
- Automatic deallocation of allocatable arrays at exit of scoping unit
- Comments in NAMELIST at input
- Minimal field at input
- Complete version of END INTERFACE
- Deleted Features
- real and double precision DO loop index variables
- branching to END IF from an outer block
- PAUSE statements
- ASSIGN statements and assigned GO TO statements and the use of an assigned
integer as a FORMAT specification
- Hollerith editing in FORMAT
- See http://www.nsc.liu.se/~boein/f77to90/f95.html#17.5
References