Difference between revisions of "Modern Fortran"

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Line 128: Line 128:
 
==Free Format: some highlights==
 
==Free Format: some highlights==
 
{|
 
{|
 +
|- valign="top"
 
|
 
|
 
* Columns no longer significant; can start at left margin
 
* Columns no longer significant; can start at left margin
Line 652: Line 653:
 
==Modules==
 
==Modules==
 
{|
 
{|
 +
|- valign="top"
 
|
 
|
 
* Easiest to show by example
 
* Easiest to show by example
Line 658: Line 660:
 
* “Use” goes before “implicit none”
 
* “Use” goes before “implicit none”
 
|
 
|
−
samples/procedures/simplemod/simplemod.f90
+
<source lang="fortran">
 +
module gravity
 +
    implicit none
 +
    real, parameter :: G  = 6.67e-11  ! MKS units
 +
 
 +
contains
 +
    real function gravforce(x1,x2,m1,m2)
 +
        implicit none
 +
        real, dimension(3), intent(in) :: x1,x2
 +
        real, intent(in) :: m1, m2
 +
        real :: dist
 +
 
 +
        dist = sqrt(sum((x1-x2)**2))
 +
        gravforce = G * m1 * m2 / dist**2
 +
    end function gravforce
 +
end module gravity
 +
 
 +
program simplemod
 +
    use gravity
 +
    implicit none
 +
 
 +
    print *, 'Gravitational constant = ', G
 +
    print *, 'Force between 2 1kg masses at [1,0,0] &
 +
              &and [0,0,1] is'
 +
 
 +
    print *, gravforce([1.,0.,0.],[0.,0.,1.],1.,1.)
 +
 
 +
end program simplemod
 +
</source>
 +
(from samples/procedures/simplemod/simplemod.f90)
 
|
 
|
 
|}
 
|}
Line 664: Line 695:
 
==Compiling & Running==
 
==Compiling & Running==
 
{|
 
{|
 +
|- valign="top"
 
|
 
|
 
* When compiling the code a gravity.mod file is created
 
* When compiling the code a gravity.mod file is created
Line 669: Line 701:
 
* Not compatible between different compilers, versions.
 
* Not compatible between different compilers, versions.
 
|
 
|
 +
<source lang="bash">
 +
$ ls
 +
simplemod.f90
 +
 +
$ gfortran -o simplemod simplemod.f90 -Wall
 +
 +
$ ls
 +
gravity.mod    simplemod    simplemod.f90
 +
 +
$ ./simplemod
 +
Gravitational constant =  6.6700000E-11
 +
Force between 2 1kg masses at [1,0,0] and [0,0,1] is
 +
  3.3350003E-11
 +
</source>
 
|}
 
|}
  
 
==Modules==
 
==Modules==
 
{|
 
{|
 +
|- valign="top"
 
|
 
|
 
* function gravforce can “see” the modulewide parameter defined above.
 
* function gravforce can “see” the modulewide parameter defined above.
 
* So can main program, through use statement.
 
* So can main program, through use statement.
 
|
 
|
−
samples/procedures/simplemod/simplemod.f90
+
<source lang="fortran">
−
|}
+
<source lang="fortran">
 +
module gravity
 +
    implicit none
 +
    real, parameter :: G  = 6.67e-11  ! MKS units
  
−
==use module, only :==
+
contains
 +
    real function gravforce(x1,x2,m1,m2)
 +
        implicit none
 +
        real, dimension(3), intent(in) :: x1,x2
 +
        real, intent(in) :: m1, m2
 +
        real :: dist
 +
 
 +
        dist = sqrt(sum((x1-x2)**2))
 +
        gravforce = G * m1 * m2 / dist**2
 +
    end function gravforce
 +
end module gravity
 +
 
 +
program simplemod
 +
    use gravity
 +
    implicit none
 +
 
 +
    print *, 'Gravitational constant = ', G
 +
    print *, 'Force between 2 1kg masses at [1,0,0] &
 +
              &and [0,0,1] is'
 +
 
 +
    print *, gravforce([1.,0.,0.],[0.,0.,1.],1.,1.)
 +
 
 +
end program simplemod
 +
</source>
 +
(from samples/procedures/simplemod/simplemod.f90)
 +
|}
 +
 
 +
==use module, only :==
 
{|
 
{|
 +
|- valign="top"
 +
|
 
* Best practice is to only pull in from the module what you need
 
* Best practice is to only pull in from the module what you need
 
* Otherwise, everything.
 
* Otherwise, everything.
Line 687: Line 766:
 
* (Note syntax for continuation of a string...)
 
* (Note syntax for continuation of a string...)
 
|
 
|
 +
<source lang="fortran">
 +
module gravity
 +
    implicit none
 +
    real, parameter :: G  = 6.67e-11  ! MKS units
 +
 +
contains
 +
    real function gravforce(x1,x2,m1,m2)
 +
        implicit none
 +
        real, dimension(3), intent(in) :: x1,x2
 +
        real, intent(in) :: m1, m2
 +
        real :: dist
 +
 +
        dist = sqrt(sum((x1-x2)**2))
 +
        gravforce = G * m1 * m2 / dist**2
 +
    end function gravforce
 +
end module gravity
 +
 +
program simplemod2
 +
    use gravity, only : G, gravforce
 +
    implicit none
 +
 +
    print *, 'Gravitational constant = ', G
 +
    print *, 'Force between 2 1kg masses at [1,0,0] &
 +
              &and [0,0,1] is'
 +
   
 +
    print *, gravforce([1.,0.,0.],[0.,0.,1.],1.,1.)               
 +
 +
end program simplemod2
 +
</source>
 
samples/procedures/simplemod/simplemod2.f90
 
samples/procedures/simplemod/simplemod2.f90
 
|}
 
|}
Line 692: Line 800:
 
==Modules usually get their own files==
 
==Modules usually get their own files==
 
{|
 
{|
 +
|- valign="top"
 
|
 
|
 
* For encapsulation
 
* For encapsulation
Line 699: Line 808:
 
* (Main program hasn’t changed much).
 
* (Main program hasn’t changed much).
 
|
 
|
−
samples/procedures/multifilemod/gravity.f90
+
<source lang="fortran">
−
|}
+
module gravity
 +
    implicit none
 +
    private
 +
 
 +
    character (len=8), parameter, public :: massunit="kilogram"
 +
    character (len=8), parameter, public :: forceunit="Newton"
 +
    public :: gravforce
 +
 
 +
    real, parameter :: G  = 6.67e-11  ! MKS units
 +
 
 +
contains
 +
    real function distance(x1,x2)
 +
        implicit none
 +
        real, dimension(3), intent(in) :: x1, x2
 +
 
 +
        distance = sqrt(sum((x1-x2)**2))
 +
    end function distance
 +
 
 +
    real function gravforce(x1,x2,m1,m2)
 +
        implicit none
 +
        real, dimension(3), intent(in) :: x1,x2
 +
        real, intent(in) :: m1, m2
 +
        real :: dist
 +
 
 +
        dist = distance(x1,x2)
 +
        gravforce = G * m1 * m2 / dist**2
 +
    end function gravforce
 +
end module gravity
 +
</source>
 +
(from samples/procedures/multifilemod/gravity.f90 )
 +
|}
  
 
==Modules usually get their own files==
 
==Modules usually get their own files==
 
{|
 
{|
 +
|- valign="top"
 +
|
 
* Compiling gravity.f90 now gives both an .o file (containing the code) and the .mod file as before.
 
* Compiling gravity.f90 now gives both an .o file (containing the code) and the .mod file as before.
 
* Compiling the main program (multifilemod.f90) requires the .mod file.
 
* Compiling the main program (multifilemod.f90) requires the .mod file.
 
|
 
|
−
samples/procedures/multifilemod/Makefile
+
<source lang="make">
 +
FC=gfortran
 +
FFLAGS=-O3 -Wall
 +
 +
multifilemod: multifilemod.o gravity.o
 +
$(FC) -o $@ multifilemod.o gravity.o
 +
 
 +
%.mod: %.f90
 +
$(FC) $(FFLAGS) -c $<
 +
 
 +
multifilemod.o: multifilemod.f90 gravity.mod
 +
$(FC) $(FFLAGS) -c $<
 +
 
 +
clean:
 +
rm -f *.o *~ *.mod multifilemod
 +
</source>
 +
(from samples/procedures/multifilemod/Makefile)
 
|}
 
|}
  
 
==.mod needed for compilation==
 
==.mod needed for compilation==
 
{|
 
{|
 +
|- valign="top"
 
|
 
|
 
* ...because needs the type information of the constants,
 
* ...because needs the type information of the constants,
Line 717: Line 875:
 
* Can’t compile without these
 
* Can’t compile without these
 
|
 
|
−
samples/procedures/multifilemod/multifilemod.f90
+
<source lang="fortran">
 +
program simplemod2
 +
    use gravity, only : gravforce, massunit, forceunit
 +
    implicit none
 +
 
 +
    print *, 'Force between 2 1 ', massunit ,' masses ', &
 +
            ' at [1,0,0] and [0,0,1] is'
 +
   
 +
    print *, gravforce([1.,0.,0.],[0.,0.,1.],1.,1.), forceunit
 +
 
 +
end program simplemod2
 +
</source>
 +
(from samples/procedures/multifilemod/multifilemod.f90)
 
|}
 
|}
  
 
==.o needed for linking==
 
==.o needed for linking==
 
{|
 
{|
 +
|- valign="top"
 +
|
 
* Linking, however, doesn’t require the .mod file
 
* Linking, however, doesn’t require the .mod file
 
* Only requires the .o file from the module code.
 
* Only requires the .o file from the module code.
 
* .mod file analogous (but better than) .h files for C code.
 
* .mod file analogous (but better than) .h files for C code.
 
|
 
|
−
samples/procedures/multifilemod/Makefile
+
<source lang="make">
 +
FC=gfortran
 +
FFLAGS=-O3 -Wall
 +
 +
multifilemod: multifilemod.o gravity.o
 +
$(FC) -o $@ multifilemod.o gravity.o
 +
 
 +
%.mod: %.f90
 +
$(FC) $(FFLAGS) -c $<
 +
 
 +
multifilemod.o: multifilemod.f90 gravity.mod
 +
$(FC) $(FFLAGS) -c $<
 +
 
 +
clean:
 +
rm -f *.o *~ *.mod multifilemod
 +
</source>
 +
(from samples/procedures/multifilemod/Makefile)
 
|}
 
|}
  
 
==Compiling and running==
 
==Compiling and running==
 
{|
 
{|
 +
|- valign="top"
 +
|
 
* So compile files with modules first, so those that need them have the .mod files
 
* So compile files with modules first, so those that need them have the .mod files
 
* Link the .o files
 
* Link the .o files
 +
|
 +
<source lang="bash">
 +
$ make
 +
gfortran -O3 -Wall  -c gravity.f90
 +
gfortran -O3 -Wall  -c multifilemod.f90
 +
gfortran -o multifilemod multifilemod.o gravity.o
 +
reposado-$ ./multifilemod
 +
Force between 2 1 kilogram masses  at [1,0,0] and [0,0,1] is
 +
  3.33500033E-11 Newton
 +
</source>
 
|}
 
|}
  
 
==Private and public==
 
==Private and public==
 
{|
 
{|
−
|-
+
|- valign="top"
 
|
 
|
 
* Not all of a module’s content need be public
 
* Not all of a module’s content need be public
Line 744: Line 944:
 
* Allows hiding implementation specific routines
 
* Allows hiding implementation specific routines
 
|
 
|
 +
<source lang="fortran">
 +
module gravity
 +
    implicit none
 +
    private
 +
 +
    character (len=8), parameter, public :: massunit="kilogram"
 +
    character (len=8), parameter, public :: forceunit="Newton"
 +
    public :: gravforce
 +
 +
    real, parameter :: G  = 6.67e-11  ! MKS units
 +
 +
contains
 +
    real function distance(x1,x2)
 +
        implicit none
 +
        real, dimension(3), intent(in) :: x1, x2
 +
 +
        distance = sqrt(sum((x1-x2)**2))
 +
    end function distance
 +
 +
    real function gravforce(x1,x2,m1,m2)
 +
        implicit none
 +
        real, dimension(3), intent(in) :: x1,x2
 +
        real, intent(in) :: m1, m2
 +
        real :: dist
 +
 +
        dist = distance(x1,x2)
 +
        gravforce = G * m1 * m2 / dist**2
 +
    end function gravforce
 +
end module gravity
 +
</source>
 
( from samples/procedures/multifilemod/gravity.f90 )
 
( from samples/procedures/multifilemod/gravity.f90 )
 
|}
 
|}
Line 749: Line 979:
 
==Procedures==
 
==Procedures==
 
{|
 
{|
−
|-
+
|- valign="top"
 
|
 
|
 
* We’ve already seen procedures defined in new style; let’s look more closely.
 
* We’ve already seen procedures defined in new style; let’s look more closely.
Line 759: Line 989:
 
* Also documentation of a sort.
 
* Also documentation of a sort.
 
|
 
|
−
( from samples/procedures/funcsub/procedures.f90 )
+
<source lang="fortran">
−
|}
+
module procedures
 +
 
 +
contains
 +
 
 +
function square(x) result(xsquared)
 +
      implicit none
 +
      real :: xsquared
 +
      real, intent(IN) :: x
 +
 
 +
      xsquared = x*x
 +
end function square
 +
 
 +
function cube(x)
 +
      implicit none
 +
      real :: cube
 +
      real, intent(IN) :: x
 +
 
 +
      cube = x*x*x
 +
end function cube
 +
 
 +
subroutine squareAndCube(x, squarex, cubex)
 +
      implicit none
 +
      real, intent(in) :: x
 +
      real, intent(out) :: squarex
 +
      real, intent(out) :: cubex
 +
 
 +
      squarex = square(x)
 +
      cubex  = cube(x)
 +
end subroutine squareAndCube
 +
 
 +
end module procedures
 +
</source>
 +
( from samples/procedures/funcsub/procedures.f90 )
 +
|}
  
 
==Functions==
 
==Functions==
 
{|
 
{|
−
|-
+
|- valign="top"
 
|
 
|
 
* Can be typed a couple of ways.
 
* Can be typed a couple of ways.
Line 772: Line 1,035:
 
* Function return values don’t take intent - always out
 
* Function return values don’t take intent - always out
 
|
 
|
 +
<source lang="fortran">
 +
function square(x) result(xsquared)
 +
      implicit none
 +
      real :: xsquared
 +
      real, intent(IN) :: x
 +
 +
      xsquared = x*x
 +
end function square
 +
 +
function cube(x)
 +
      implicit none
 +
      real :: cube
 +
      real, intent(IN) :: x
 +
 +
      cube = x*x*x
 +
end function cube
 +
 +
subroutine squareAndCube(x, squarex, cubex)
 +
      implicit none
 +
      real, intent(in) :: x
 +
      real, intent(out) :: squarex
 +
      real, intent(out) :: cubex
 +
 +
      squarex = square(x)
 +
      cubex  = cube(x)
 +
end subroutine squareAndCube
 +
</source>
 
( from samples/procedures/funcsub/procedures.f90 )
 
( from samples/procedures/funcsub/procedures.f90 )
 
|}
 
|}
Line 777: Line 1,067:
 
==Procedure interfaces==
 
==Procedure interfaces==
 
{|
 
{|
−
|-
+
|- valign="top"
 
|
 
|
 
* The interface to a procedure consists of
 
* The interface to a procedure consists of
Line 786: Line 1,076:
 
* Like a C prototype, but more detailed info
 
* Like a C prototype, but more detailed info
 
* .mod files contain explicit interfaces to all public module procedures.
 
* .mod files contain explicit interfaces to all public module procedures.
−
|}
+
|
 +
<source lang="fortran">
 +
function square(x) result(xsquared)
 +
      implicit none
 +
      real :: xsquared
 +
      real, intent(IN) :: x
 +
 
 +
      xsquared = x*x
 +
end function square
 +
 
 +
function cube(x)
 +
      implicit none
 +
      real :: cube
 +
      real, intent(IN) :: x
  
−
==Procedure interfaces==
+
      cube = x*x*x
−
{|
+
end function cube
−
|- valign="top"
+
 
 +
subroutine squareAndCube(x, squarex, cubex)
 +
      implicit none
 +
      real, intent(in) :: x
 +
      real, intent(out) :: squarex
 +
      real, intent(out) :: cubex
 +
 
 +
      squarex = square(x)
 +
      cubex  = cube(x)
 +
end subroutine squareAndCube
 +
</source>
 +
( from samples/procedures/funcsub/procedures.f90 )
 +
|}
 +
 
 +
==Procedure interfaces==
 +
{|
 +
|- valign="top"
 
|
 
|
 
* To see where interfaces become necessary, consider this sketch of a routine to do trapezoid-rule integration
 
* To see where interfaces become necessary, consider this sketch of a routine to do trapezoid-rule integration
Line 797: Line 1,116:
 
* You do that for procedures with interfaces
 
* You do that for procedures with interfaces
 
|
 
|
−
http://en.wikipedia.org/wiki/File:Trapezoidal_rule_illustration_small.svg
+
<source lang="fortran">
 +
function integratefx(xlo, xhi, f, n)
 +
    ! integrate with trapezoid rule
 +
    ! ....
 +
 
 +
    integer :: i
 +
    real :: dx, xleft, xright
 +
 
 +
    integratefx = 0.
 +
    dx = (xhi-xlo)/n
 +
    xleft = xlo
 +
    do i=0, n-1
 +
        xright = xleft + dx
 +
        integratefx = integratefx + dx*(f(xright)+f(xleft))/2.
 +
        xleft = xright
 +
    enddo
 +
end function integratefx
 +
</source>
 +
(from samples/procedures/interface/integrate.f90 )
 +
 
 +
[[File:Wiki_trapezoidal.png|300px]]
 +
 
 +
(from http://en.wikipedia.org/wiki/File:Trapezoidal_rule_illustration_small.svg )
 
|}
 
|}
  
Line 807: Line 1,148:
 
* Can then use it, and at compile time compiler ensures function passed in matches thisinterface.
 
* Can then use it, and at compile time compiler ensures function passed in matches thisinterface.
 
|
 
|
 +
<source lang="fortran">
 +
function integratefx(xlo, xhi, f, n)
 +
    ! integrate with trapezoid rule
 +
    implicit none
 +
    real, intent(in) :: xlo, xhi
 +
    interface
 +
        function f(x)
 +
            implicit none
 +
            real :: f
 +
            real, intent(in) :: x       
 +
        end function f
 +
    end interface
 +
    integer, intent(in) :: n
 +
    real :: integratefx
 +
 +
    integer :: i
 +
    real :: dx, xleft, xright
 +
 +
    integratefx = 0.
 +
    dx = (xhi-xlo)/n
 +
    xleft = xlo
 +
    do i=0, n-1
 +
        xright = xleft + dx
 +
        integratefx = integratefx + dx*(f(xright)+f(xleft))/2.
 +
        xleft = xright
 +
    enddo
 +
end function integratefx
 +
 +
</source>
 
(from samples/procedures/interface/integrate.f90 )
 
(from samples/procedures/interface/integrate.f90 )
 
|}
 
|}
Line 819: Line 1,189:
 
* Recursive functions '''must''' use “result” keyword to return value.
 
* Recursive functions '''must''' use “result” keyword to return value.
 
|
 
|
−
( from samples/procedures/recursive/integrate.f90)
+
<source lang="fortran">
−
|}
+
recursive function integratefx(xlo, xhi, f, tol) result(integral)
 +
    ! integrate with trapezoid rule, simpsons rule;
 +
    ! if difference between two is larger than
 +
    ! relevant tolerance, subdivide region.
 +
 
 +
    ! ...variable declarations as before...
 +
 
 +
    dx = xhi-xlo
 +
    xmid = (xlo+xhi)/2.
 +
    trapezoid = dx*(f(xlo)+f(xhi))/2.
 +
    simpsons = dx/6.*(f(xlo)+4.*f(xmid)+f(xhi))
 +
    error = abs(trapezoid-simpsons)/(0.5*(trapezoid+simpsons))
 +
 
 +
    if (error > tol) then
 +
        ! too coarse; subdivide
 +
        integral = integratefx(xlo,xmid,f,tol) + &
 +
                  integratefx(xmid,xhi,f,tol)
 +
    else
 +
        integral = trapezoid
 +
    endif
 +
end function integratefx
 +
</source>
 +
( from samples/procedures/recursive/integrate.f90)
 +
|}
  
 
==Pure procedures==
 
==Pure procedures==
Line 835: Line 1,228:
 
* Almost all the procedures we’ve seen so far are pure.
 
* Almost all the procedures we’ve seen so far are pure.
 
|
 
|
 +
<source lang="fortran">
 +
    pure subroutine axpy(a, x, y)
 +
        ! y = y + a*x
 +
        implicit none
 +
        real, intent(IN) :: a, x
 +
        real, intent(INOUT) :: y
 +
 +
        y = y + a*x
 +
    end subroutine axpy
 +
 +
    subroutine printaxpy(a, x, y)
 +
        ! y = y + a*x
 +
        implicit none
 +
        real, intent(IN) :: a, x
 +
        real, intent(INOUT) :: y
 +
 +
        print *, a, '*', x, ' + ', y, &
 +
                ' = ', a*x+y
 +
        y = a*x + y
 +
    end subroutine printaxpy
 +
</source>
 
(from  samples/procedures/purity/purity.f90)
 
(from  samples/procedures/purity/purity.f90)
 
|}
 
|}
Line 844: Line 1,258:
 
* Can make arguments optional by using the optional attribute.
 
* Can make arguments optional by using the optional attribute.
 
* Use present to test.
 
* Use present to test.
 +
* Often useful to clarify calling of procedure if many parameters have sensible defaults.
 +
* Avoid code duplication, wrappers of having one version of routine with default values, one with user-supplied
 
* Can’t use tol if not present; have to use another variable.
 
* Can’t use tol if not present; have to use another variable.
 
|
 
|
 +
<source lang="fortran">
 +
recursive function integratefx(xlo, xhi, f, tol) result(integral)
 +
    ! ....
 +
    real, intent(in), optional :: tol
 +
    ! ....
 +
 +
    real :: errtol
 +
 +
    ! use parameter if passed,
 +
    ! else use default
 +
    if (present(tol)) then
 +
        errtol = tol
 +
    else
 +
        errtol = 1.e-6
 +
    endif
 +
 +
    ! ....
 +
 +
    if (error > errtol) then
 +
        ! too coarse; subdivide
 +
        integral = integratefx(xlo,xmid,f,errtol) + &
 +
                  integratefx(xmid,xhi,f,errtol)
 +
    else
 +
        integral = trapezoid
 +
    endif
 +
end function integratefx
 +
 +
</source>
 
(from  samples/procedures/optional/integrate.f90)
 
(from  samples/procedures/optional/integrate.f90)
 
|}
 
|}
  
−
==Keyword Arguments==
+
==Optional Arguments==
 
{|
 
{|
 
|- valign="top"
 
|- valign="top"
Line 855: Line 1,299:
 
* When calling the procedure, can use the optional argument or not.
 
* When calling the procedure, can use the optional argument or not.
 
* Makes sense to leave optional arguments at end - easier to figure out what’s what when it’s omitted.
 
* Makes sense to leave optional arguments at end - easier to figure out what’s what when it’s omitted.
 +
 +
|
 +
<source lang="fortran">
 +
    print *, 'Integrating using default tol'
 +
    approx = integratefx(0., 2*pi, sinesquared)
 +
    print *, 'Approximate integral = ', approx
 +
    print *, 'Exact integral = ', exact
 +
 +
    print *, ''
 +
    print *, 'Integrating using coarser tol'
 +
    approx = integratefx(0., 2*pi, sinesquared, 0.01)
 +
    print *, 'Approximate integral = ', approx
 +
 +
    ! ....
 +
</source>
 +
(from  samples/procedures/optional/optional.f90)
 +
|}
 +
 +
==Keyword Arguments==
 +
{|
 +
|- valign="top"
 +
|
 
* To avoid ambiguity with omitted arguments - or really whenever you want - you can specify which value is which explicitly.
 
* To avoid ambiguity with omitted arguments - or really whenever you want - you can specify which value is which explicitly.
 
* Don’t have to be in order.
 
* Don’t have to be in order.
−
* Can clarify calls of routines with many arguments.
+
* Can clarify calls of routines with many arguments
 
|
 
|
 +
<source lang="fortran">
 +
    ! ....
 +
    print *, 'Integrating using still coarser tol'
 +
    approx = integratefx(xhi=2*pi, xlo=0., tol=0.5, &
 +
                        f=sinesquared)
 +
    print *, 'Approximate integral = ', approx
 +
</source>
 
(from  samples/procedures/optional/optional.f90)
 
(from  samples/procedures/optional/optional.f90)
 
|}
 
|}
 +
  
 
==Procedures and Modules Summary==
 
==Procedures and Modules Summary==
Line 886: Line 1,360:
 
|}
 
|}
  
−
==Fortran arrays==
+
=Fortran arrays=
 +
{|
 +
|- valign="top"
 +
|
 
* Fortran made for dealing with scientific data
 
* Fortran made for dealing with scientific data
 
* Arrays built into language
 
* Arrays built into language
−
* The type information associated with an
+
* The type information associated with an array includes rank (# of dimension), size, element type, stride..
−
array includes rank (# of dimension), size,
+
* Enables powerful optimizations, programmer-friendly features.
−
element type, stride..
+
* Can be manipulated like simple scalar variables
−
* Enables powerful optimizations,
+
* Elementwise addition, multiplication.. 
−
programmer-friendly features.
+
|
 +
<source lang="fortran">
 +
program basicarrays
 +
    implicit none
 +
    integer, dimension(5) :: a, b, c
 +
    integer :: i
  
−
==Fortran arrays==
+
    a = [1,2,3,4,5]
−
* Can be manipulated
+
    b = [(2*i+1, i=1,5)]
−
like simple scalar
 
−
variables
 
−
* Elementwise
 
−
addition,
 
−
multiplication..
 
−
samples/arrays/basic.f90
 
  
−
==Array constructors==
 
−
* Can have array
 
−
constants like
 
−
numerical constants
 
−
* use [] or (/ /), then
 
−
comma-separated
 
−
list of values.
 
−
* Implied do loops
 
−
can be used in
 
−
constructors
 
−
* (Variables have to
 
−
be defined)
 
  
−
[1,2,3,4,5] or (/1,2,3,4,5/)
+
    print *, 'a = ', a
−
[ (i,i=1,5)]
+
    print *, 'b = ', b
−
[ ((i*j,j=1,3),i=1,5)]
 
  
−
==Elementwise operations==
+
    c = a+b
−
* Elementwise operations
+
    print *, 'c = ', c
−
can be */+-, or
 
−
application of an
 
−
elemental function.
 
−
* Math intrinsics are all
 
−
elemental - applied to
 
−
array, applies to every
 
−
element.
 
−
* Order of execution
 
−
undefined - allows
 
−
vectorization,
 
−
parallelization.
 
  
−
samples/arrays/elementwise.f90
+
    c = a*b + 1
 +
    print *, 'a*b+1=', c
 +
end program basicarrays
 +
</source>
 +
(from samples/arrays/basic.f90 )
 +
|}
  
−
==Elemental Functions==
+
==Array constructors==
−
* User can create their
+
{|
−
own elemental functions
+
|- valign="top"
−
* Label any scalar function
+
|
−
with “elemental” should (until recently,
+
* Can have array constants like numerical constants
−
must) be pure, so can be
+
* use [] or (/ /), then comma-separated list of values.
−
applied everywhere at
+
* Implied do loops can be used in constructors
−
same time.
+
* (Implied do-loop variables have to be defined)
−
* Faster than in loop.
+
|
−
* Can also take multiple
+
<source lang="fortran">
−
arguments: eg
+
      x = [1,2,3,4,5]
−
z = addsquare(x,y)
+
      x = (/1,2,3,4,5/)
 +
      x = [ (i,i=1,5)]
 +
      a = [ ((i*j,j=1,3),i=1,5)]
 +
</source>
 +
|}
  
−
samples/arrays/elemental.f90
+
==Elementwise operations==
 +
{|
 +
|- valign="top"
 +
|
 +
* Elementwise operations can be */+-, or application of an elemental function.
 +
* Math intrinsics are all elemental - applied to array, applies to every element.
 +
* Order of execution undefined - allows vectorization, parallelization.
 +
|
 +
<source lang="fortran">
 +
program elementwise
 +
    implicit none
 +
    real, dimension(10) :: x,y,z
 +
    integer :: i
 +
    real, parameter:: pi = 4.*atan(1.)
  
−
==Array comparisons==
+
    x = [(2*pi*(i-1)/9.,i=1,10)]
−
* Array comparisons
+
   
−
return an array of
+
    y = sin(x)
−
logicals of the same size
+
    z = x*x
−
of the arrays.
 
−
* Can use any and all to
 
−
see if any or all of those
 
−
logicals are true.
 
−
samples/arrays/compare.f90
 
  
−
==Array masks==
+
    print *, x
−
* These logical arrays can
+
    print *, y
−
be used to mask several
+
    print *, z
−
operations
+
end program elementwise
−
* Only do sums, mins, etc
+
</source>
−
where the mask is true
+
(from samples/arrays/elementwise.f90 )
−
* Eg, only pick out positive
+
|}
−
values.
 
−
* Many array intrinsics
 
−
have this mask option
 
  
−
samples/arrays/mask.f90
+
==Elemental Functions==
−
 
+
{|
−
==Where construct==
+
|- valign="top"
−
* The where construct
+
|
−
can be used to easily
+
* User can create their own elemental functions
−
manipulate sections of
+
* Label any scalar function with “elemental” should (until recently, must) be pure, so can be applied everywhere at same time.
−
array based on arbitrary
+
* Can be faster than loop.
−
comparisons.
+
* Can also take multiple arguments: eg z = addsquare(x,y)
−
* Where construct => for
+
|
−
whatever indices the
+
<source lang="fortran">
−
comparison is true, set
+
program elementalfn
−
values as follow;
+
    implicit none
−
otherwise, set other
+
    real, dimension(10) :: x,y,z
−
values.
+
    integer :: i
 +
    real, parameter:: pi = 4.*atan(1.)
 +
 
 +
    x = [(2*pi*(i-1)/9.,i=1,10)]
 +
   
 +
    y = sinesquared(x)
 +
    z = sin(x)*sin(x)
  
−
samples/arrays/where.f90
+
    print *, x
 +
    print *, y
 +
    print *, z
 +
    print *,z(::3)
 +
contains
 +
    elemental function sinesquared(x)
 +
    implicit none
 +
    real :: sinesquared
 +
    real, intent(in) :: x
 +
 
 +
    sinesquared = sin(x)**2
 +
    end function sinesquared
 +
end program elementalfn
 +
</source>
 +
(from samples/arrays/elemental.f90 )
 +
|}
  
−
==Forall construct==
+
==Array comparisons==
−
* Forall is an array
+
{|
−
assignment statement
+
|- valign="top"
−
* Each line in forall has to be
+
|
−
independent. All done “at
+
* Array comparisons return an array of logicals of the same size of the arrays.
−
once” - no guarantees as
+
* Can use any and all to see if any or all of those logicals are true.
−
to order
+
|
−
* If (say) 2 lines in the forall,
+
<source lang="fortran">
−
all of the first line is done,
+
program comparearrays
−
then all of the second.
+
    implicit none
−
* Any functions called must
+
    integer, dimension(5) :: a, b
−
be pure
+
    integer :: i
−
* Can be vectorized or
 
−
parallelized by compiler
 
  
−
samples/arrays/forall.f90
+
    a = [1,2,3,4,5]
 +
    b = [(2*i-3, i=1,5)]
  
−
==Array Sections==
+
    print *, 'A = ', a
−
* Generalization of array
+
    print *, 'B = ', b
−
indexing
 
−
* Familiar to users of
 
−
Matlab, IDL, Python..
 
−
* Can use “slices” of an
 
−
array using “index
 
−
triplet”
 
−
* [start]:[end][:step]
 
−
* Default start=1, default
 
−
end=size, default step=1.
 
−
* Can be used for each
 
−
index of multid array
 
  
−
a([start]:[end][:step])
+
    if (any(a > b)) then
−
a = [1,2,3,4,5,6,7,8,9,10]
+
        print *, 'An A is larger than a B'
−
a(7:) == [7,8,9,10]
+
    endif           
−
a(:3) == [1,2,3]
+
    if (all(a > b)) then
−
a(2:4) == [2,3,4]
+
        print *, 'All As ares larger than Bs'
−
a(::3) == [1,4,7,10]
+
    else if (all(b > a)) then
−
a(2:4:2) == [2,4]
+
        print *, 'All Bs are larger than As'
−
a(2) == 2
+
    else
−
a(:) == [1,2,3,4,5,6,7,8,9,10]
+
        print *, 'A, B values overlap'
 +
    endif
  
−
==Array Sections==
+
end program comparearrays
−
* This sort of thing is very
+
</source>
−
handy in numerical
+
(from samples/arrays/compare.f90)
−
computation
+
|}
−
* Replace do-loops with
 
−
clearer, shorter, possibly
 
−
vectorized array
 
−
operations
 
−
* Bigger advantage for
 
−
multidimensional arrays
 
  
−
samples/arrays/derivative.f90
+
==Array masks==
 +
{|
 +
|- valign="top"
 +
|
 +
* These logical arrays can be used to mask several operations
 +
* Only do sums, mins, etc where the mask is true
 +
* Eg, only pick out positive values.
 +
* Many array intrinsics have this mask option
 +
|
 +
<source lang="fortran">
 +
program mask
 +
    implicit none
 +
    integer, dimension(10) :: a
 +
    logical, dimension(10) :: pos
 +
    integer :: i
  
−
==Array Sections==
+
    a = [(2*i-7, i=1,10)]
−
* The previous sorts of array
+
    pos = (a > 0)
−
sections - shifting things leftward
 
−
and rightward - are so common
 
−
there are intrinsics for them
 
−
* +ve shift shifts elements
 
−
leftwards (or array bounds
 
−
rightwards).
 
−
* cshift does circular shift - shifting
 
−
off the end of the array “wraps
 
−
around”.
 
−
* eoshift fills with zeros, or
 
−
optional filling.
 
−
* Can work on given dimension
 
  
−
a = [1,2,3,4,5]
+
    print '(A,10(I4,1X))','A = ', a
−
cshift(a,1) == [2,3,4,5,1]
+
    print *,'# of positive values:  ', count(pos)
−
cshift(a,-1) == [5,1,2,3,4]
+
    print *,'Sum of positive values: ', sum(a,pos)
−
eoshift(a,1) ==[2,3,4,5,0]
+
    print *,'Minimum positive value: ', minval(a,pos)
−
eoshift(a,-1)==[0,1,2,3,4]
 
  
−
==Other important array==
+
end program mask
−
intrinsics
+
</source>
−
* minval/maxval - finds min, max element in an array.
+
( from samples/arrays/mask.f90 )
−
* minloc/maxloc - finds location of min/max element
+
<source lang="bash">
−
* product/sum - returns product/sum of array elements
+
$ ./mask
−
* reshape - Adjusts shape of array data. Eg:
+
A =  -5  -3  -1    1    3    5    7    9  11  13
−
1,4
+
# of positive values:              7
−
reshape([1,2,3,4,5,6],[3,2]) == 2,5
+
Sum of positive values:           49
−
3,6
+
Minimum positive value:            1
 +
</source>
 +
|}
  
−
==Linear algebra in Fortran==
+
==Where construct==
−
* Comes built in with transpose, matmul,
+
{|
−
dot_product for dealing with arrays.
+
|- valign="top"
−
* matmul also does matrix-vector multiplication
+
|
−
* Either use these or system-provided BLAS
+
* The where construct can be used to easily manipulate sections of array based on arbitrary comparisons.
−
libraries - never, ever write yourself.
+
* Where construct => for whatever indices the comparison is true, set values as follow; otherwise, set other values.
 +
|
 +
<source lang="fortran">
 +
program wherearray
 +
    implicit none
 +
    real, dimension(6) :: a, diva
 +
    integer :: i
  
−
==Matmul times==
+
    a = [(2*i-6, i=1,6)]
−
$ ./matmul 2500
+
    where (a /= 0)
−
Experiment with matrix size
+
        diva = 1/a
−
2500
+
    elsewhere
−
Triple-loop time:
+
        diva = -999
−
149.63400
+
    endwhere
−
matmul intrinsic time:
 
−
10.370000
 
−
SGEMM lapack call time:
 
−
1.4809999
 
  
−
(gfortran 4.6, compiled -O3 -march=native
+
    print *,'a = '
−
using Intel MKL 10.3 for sgemm)
+
    print '(6(F8.3,1X))',a
 +
    print *,'1/a = '
 +
    print '(6(F8.3,1X))',diva
  
−
samples/arrays/matmul.f90
+
end program wherearray
 +
</source>
 +
(from samples/arrays/where.f90)
 +
<source lang="bash">
 +
$ ./where
 +
a =
 +
  -4.000  -2.000    0.000    2.000    4.000    6.000
 +
1/a =
 +
  -0.250  -0.500 -999.000    0.500    0.250    0.167
 +
</source>
 +
|}
  
−
==Linear algebra in Fortran==
+
==Forall construct==
 +
{|
 +
|- valign="top"
 +
|
 +
* Forall is an array assignment statement
 +
* Each line in forall has to be independent. All done “at once” - no guarantees as to order
 +
* If (say) 2 lines in the forall, all of the first line is done, then all of the second.
 +
* Any functions called must be pure
 +
* Can be vectorized or parallelized by compiler
 +
|
 +
<source lang="fortran">
 +
program forallarray
 +
    implicit none
 +
    integer, dimension(6,6) :: a
 +
    integer :: i,j
  
−
samples/arrays/matrix.f90
+
    a = -999
 +
    forall (i=1:6, j=1:6, i/=j)
 +
        a(i,j) = i-j
 +
    endforall
  
−
==Array sizes and Assumed Shape==
+
    do i=1,6
−
* Printmat routine here is
+
        print '(6(I5,1X))',(a(i,j),j=1,6)
−
interesting - don’t pass
+
    enddo
−
(a,rows,cols), just a.
+
end program forallarray
−
* Can assume a rank-2 array,
+
</source>
−
and get size at runtime.
+
(from samples/arrays/forall.f90)
−
* Simplifies call, and eliminates
+
<source lang="bash">
−
possible inconsistency: what if
+
$ ./forall
−
rows, cols is wrong?
+
-999    -1    -2    -3    -4    -5
−
* size(array,dim) gets the size of
+
    1  -999    -1    -2   -3    -4
−
array in the dim dimension.
+
    2    1  -999    -1    -2    -3
 +
    3    2    1  -999    -1    -2
 +
    4    3    2    1  -999    -1
 +
    5    4    3    2    1  -999
 +
</source>
 +
|}
  
−
samples/arrays/matrix.f90
+
==Array Sections==
 +
{|
 +
|- valign="top"
 +
|
 +
* Generalization of array indexing
 +
* Familiar to users of Matlab, IDL, Python..
 +
* Can use “slices” of an array using “index triplet”
 +
* [start]:[end][:step]
 +
* Default start=1, default end=size, default step=1.
 +
* Can be used for each index of multid array
 +
|
 +
<source lang="fortran">
  
−
==Array sizes and Assumed Shape==
+
a([start]:[end][:step])
−
* Assumed shape arrays (eg,
 
−
dimension(:,:)) much better
 
−
than older ways of passing
 
−
arrays:
 
−
integer nx, ny
 
−
integer a(nx,ny)
 
−
or worse,
 
−
integer a(*,ny)
 
−
* Information is thrown away,
 
−
possibility of inconsistency.
 
−
* Here, (:,:) means we know the
 
−
rank, but don’t know the size
 
−
yet.
 
  
−
samples/arrays/matrix.f90
+
a = [1,2,3,4,5,6,7,8,9,10]
  
−
==Allocatable Arrays==
+
a(7:) == [7,8,9,10]
−
* So far, all our programs have had fixed-size
+
a(:3) == [1,2,3]
−
arrays, set at compile time.
+
a(2:4) == [2,3,4]
−
* To change problem size, have to edit code,
+
a(::3) == [1,4,7,10]
−
recompile.
+
a(2:4:2) == [2,4]
−
* Has some advantages (optimization,
+
a(2) == 2
−
determinism) but very inflexible.
+
a(:) == [1,2,3,4,5,6,7,8,9,10]
−
* Would like to be able to request memory
+
</source>
−
at run time, make array of desired size.
+
|}
−
* Allocatable arrays are arguably most
 
−
important addition to Fortran.
 
−
 
 
−
==Allocate(), Deallocate()==
 
−
* Give array a deferred size (eg,
 
−
dimension(:)) and the attribute
 
−
allocatable.
 
−
* When time to allocate it, use
 
−
allocate(a(n)).
 
−
* Deallocate with deallocate(a).
 
−
samples/arrays/allocatable.f90
 
−
* In between, arrays can be used
 
−
as any other array.
 
  
−
==Allocate(), Deallocate()==
+
==Array Sections==
−
* If allocation fails (not enough memory available for
+
{|
−
request), program will exit.
+
|- valign="top"
−
* Can control this by checking for an optional error code,
+
|
−
allocate(a(n),stat=ierr)
+
* This sort of thing is very handy in numerical computation
−
* Can then test if ierr>0 (failure condition) and handle
+
* Replace do-loops with clearer, shorter, possibly vectorized array operations
−
gracefully.
+
* Bigger advantage for multidimensional arrays
−
* In scientific programming, the default behaviour is often
+
|
−
fine, if abrupt - you either have enough memory to run
+
<source lang="fortran">
−
the problem, or you don’t.
+
program derivative
 +
    implicit none
 +
    real, dimension(10) :: x
 +
    real, dimension(9) :: derivx
 +
    integer :: i
 +
    real, parameter:: pi = 4.*atan(1.), h=1.
  
−
==get_command_argument()==
+
    x = [(2*pi*(i-1)/9.,i=1,10)]
−
* Previous version still
+
   
−
depended on a compiled-in
+
    derivx = ((x(2:10)-x(1:9))/h)
−
number.
+
    print *, derivx
−
* Can read from file or from
 
−
console, but Fortran now has
 
−
standard way to get
 
−
command-line arguments
 
−
* Get the count of arguments,
 
−
and if there’s at least one
 
−
argument there, get it, read it
 
−
as integer, and allocate array.
 
−
samples/arrays/allocatable2.f90
 
  
−
==get_command_argument()==
+
    do i=1,9
 +
        derivx(i) = (x(i+1)-x(i))/h
 +
    enddo
 +
    print *, derivx
 +
end program derivative
 +
</source>
 +
(from samples/arrays/derivative.f90)
 +
|}
  
−
samples/arrays/allocatable2.f90
+
==Array Sections==
−
 
+
{|
−
==Hands on #3==
+
|- valign="top"
−
* Use array functionality to simplify hydro code
+
|
−
-- don't need to pass, array size, and can
+
* The previous sorts of array sections - shifting things leftward and rightward - are so common there are intrinsics for them
−
simplify mathematics using array operations.
+
* positive shift shifts elements leftwards (or array bounds rightwards).
−
* In workedexamples/arrays, have modified
+
* cshift does circular shift - shifting off the end of the array “wraps around”.
−
hydro to allocate u, and pbm to just take array.
+
* eoshift fills with zeros, or optional filling.
−
* Do the same with the fluid dynamic routines in
+
* Can work on given dimension
−
solver.f90
+
|
−
* ~30 min
+
<source lang="fortran">
  
−
==Fortran Pointers==
 
−
* Pointers, or references,
 
−
refer to another
 
−
variable.
 
−
* Eg, p does not contain a
 
−
real value, but a
 
−
reference to another
 
−
real variable.
 
−
* Once associated with
 
−
another variable, can
 
−
read/write to it as if it
 
−
were stored “in” p.
 
  
−
real, target :: x = 3.2
+
a = [1,2,3,4,5]
−
real, pointer:: p
 
−
p => x
 
−
p
 
  
−
x
+
cshift(a,1) == [2,3,4,5,1]
−
3.2
+
cshift(a,-1) == [5,1,2,3,4]
 +
eoshift(a,1) ==[2,3,4,5,0]
 +
eoshift(a,-1)==[0,1,2,3,4]
 +
</source>
 +
|}
  
−
==Fortran Pointers==
+
==Other important array intrinsics==
 +
{|
 +
|- valign="top"
 +
|
 +
* minval/maxval - finds min, max element in an array.
 +
* minloc/maxloc - finds location of min/max element
 +
* product/sum - returns product/sum of array elements
 +
* reshape - Adjusts shape of array data. Eg:
  
−
samples/pointers/ptr1.f90
+
<source lang="fortran">
  
−
==Fortran Pointers==
 
−
* Pointers are either
 
−
associated, null, or
 
−
undefined; start out life
 
−
undefined.
 
−
* Can associate them to
 
−
a variable with => , or
 
−
mark them as not
 
−
associated with any
 
−
valid variable by
 
−
pointing it to null().
 
  
−
real, target :: x = 3.2
+
                                1,4
−
real, pointer:: p
+
reshape([1,2,3,4,5,6],[3,2]) == 2,5
−
p => null()
+
                                3,6
−
p
+
</source>
 +
|}
  
−
x
+
==Linear algebra in Fortran==
 +
{|
 +
|- valign="top"
 +
|
 +
* Comes built in with transpose, matmul, dot_product for dealing with arrays.
 +
* matmul also does matrix-vector multiplication
 +
* Either use these or system-provided BLAS libraries - never, ever write yourself.
 +
* Consider the following timings for a matrix multiplication - a naive triple loop, a clal to that  matmul intrinsic, or an explicit call to a BLAS package.
 +
* factor of 100 difference!
 +
* Note that you can build gfortran to use fast (BLAS) routines for intrinsics...
 +
|
 +
|}
  
−
==Fortran Pointers==
+
==Matrix Multiplication Times==
−
real, target :: x = 3.2
+
{|
−
real, pointer:: p
+
|- valign="top"
−
* Reading value from or
+
|
−
writing value to a null
+
<source lang="fortran">
−
pointer will cause
+
!...
−
errors, probably crash.
+
 
 +
    print *, 'Experiment with matrix size ', n
 +
    print *, 'Times in seconds.'
  
−
p => null()
+
    allocate(a(n,n))
−
p
+
    allocate(b(n,n))
 +
    allocate(c(n,n))
 +
    call random_number(a)
 +
    call random_number(b)
  
−
x
+
    call tick(starttime)
 +
    do j=1,n
 +
        do i=1,n
 +
            c(i,j) = 0.
 +
            do k=1,n
 +
                c(i,j) = c(i,j)+a(i,k)*b(k,j)
 +
            enddo
 +
        enddo
 +
    enddo
 +
    looptime = tock(starttime)
  
−
==Fortran Pointers==
+
    call tick(starttime)
−
* Fortran pointers can’t
+
    c = matmul(a,b)
−
point just anywhere.
+
    matmultime = tock(starttime)
−
* Must reference a
 
−
variable with the same
 
−
type, that has the target
 
−
attribute.
 
  
−
real, target :: x = 3.2
+
    call tick(starttime)
−
real, pointer:: p
+
    call sgemm('N','N',n,n,n,1.,a,n,b,n,0.,c,n)
−
p => x
+
    sgemmtime = tock(starttime)
−
p
 
  
−
x
 
−
3.2
 
  
−
==Fortran Pointers==
+
    print *, 'Triple-loop time:      ', looptime
−
real, target :: x = 3.2
+
    print *, 'matmul intrinsic time: ', matmultime
−
real, pointer:: p1, p2
+
    print *, 'SGEMM lapack call time:', sgemmtime
−
* Pointers can reference
+
!...
−
other pointers.
+
</source>
−
* Actually references
+
|
−
what they’re pointing
+
<source lang="bash">
−
to.
+
$ ./matmul 2500
 +
Experiment with matrix size
 +
    2500
 +
Triple-loop time:
 +
    149.63400
 +
matmul intrinsic time:
 +
    10.370000
 +
SGEMM lapack call time:
 +
    1.4809999
 +
</source>
 +
(gfortran 4.6, compiled -O3 -march=native using Intel MKL 10.3 for sgemm)
 +
(program from samples/arrays/matmul.f90)
 +
|}
  
−
p1 => x
+
==Linear algebra in Fortran==
−
p2 => p1
+
{|
−
p1
+
|- valign="top"
−
p2
+
|
 +
* Things like transposes work, too:
 +
* see samples/arrays/matrix.f90
 +
<source lang="fortran">
 +
program matvec
 +
    implicit none
 +
    integer, dimension(4,5) :: a
 +
    integer, dimension(5,4) :: at
 +
    integer, dimension(4,4) :: aat
 +
    integer :: i
  
−
x
+
    a = reshape([(i,i=1,4*5)],[4,5])
−
3.2
+
    at = transpose(a)
 +
    print *,'A = '
 +
    call printmat(a)
 +
    print *,'A^T = '
 +
    call printmat(at)
  
−
==Allocating a pointer==
+
    aat = matmul(a,at)
−
* Pointer doesn’t
+
    print *,'A . A^T = '
−
necessarily have to have
+
    call printmat(aat)
−
another variable to
+
    !...
−
target
+
</source>
−
* Can allocate memory
+
|
−
for p to point to that
+
<source lang="bash">
−
does not belong to any
+
$ ./matrix
−
other pointer.
+
A =  
−
* Must deallocate it when
+
  1    5    9  13  17
−
done
+
  2    6  10  14  18
 +
  3    7  11  15  19
 +
  4    8  12  16  20
 +
A^T =  
 +
  1    2    3    4
 +
  5    6    7    8
 +
  9  10  11  12
 +
  13  14  15  16
 +
  17  18  19  20
 +
A . A^T =
 +
565  610  655  700
 +
610  660  710  760
 +
655  710  765  820
 +
700  760  820  880
 +
A . A^T subarray =
 +
610  660  710
 +
655  710  765
 +
700  760  820
 +
</source>
 +
|}
  
−
real, pointer:: p
+
==Array sizes and Assumed Shape==
−
allocate(p)
+
{|
−
p = 7.9
+
|- valign="top"
−
p
+
|
−
7.9
+
* Printmat routine here is interesting - don’t pass (a,rows,cols), just a.
 +
* Can assume a rank-2 array, and get size at runtime.
 +
* Simplifies call, and eliminates possible inconsistency: what if rows, cols is wrong?
 +
* size(array,dim) gets the size of array in the dim dimension.
 +
* Assumed shape arrays (eg, dimension(:,:)) much better than older ways of passing arrays:
  
−
==Allocating a Pointer==
+
integer nx, ny
  
−
samples/pointers/ptr2.f90
+
integer a(nx,ny)
  
−
==What are they good==
+
or worse,
−
for? (1)
 
−
* Pointers are essential for
 
−
creating, maintaining
 
−
dynamic data structures
 
−
* Linked lists, trees, heaps..
 
−
* Some of these can be
 
−
sort-of implemented in
 
−
arrays, but very
 
−
awkward
 
−
* Adaptive meshes, treebased particle solvers
 
−
need these structures.
 
  
−
http://en.wikipedia.org/wiki/File:Singly-linked-list.svg
+
integer a(*,ny)
  
−
http://en.wikipedia.org/wiki/File:Max-Heap.svg
+
* Information is thrown away, possibility of inconsistency.
 +
* Here, (:,:) means we know the rank, but don’t know the size yet.
 +
|
 +
<source lang="fortran">
 +
    subroutine printmat(a)
 +
    implicit none
 +
    integer, dimension(:,:) :: a
 +
    integer :: nr, nc, i, j
  
−
==What are they good==
+
    nr = size(a,1)
−
for? (2)
+
    nc = size(a,2)
−
* A pointer can be of
+
    do i=1,nr
−
array type, not just
+
        print '(99(I4,1X))', (a(i,j), j=1,nc)
−
scalar
+
    enddo
−
* Fortran pointers +
+
    end subroutine printmat
−
fortran arrays are quite
+
</source>
−
interesting; can create
+
(from samples/arrays/matrix.f90)
−
“views” of subarrays
+
|}
  
−
real, target, dimension(7) :: x
 
−
real, pointer:: p(:)
 
−
p => x(2:6)
 
  
−
p
+
==Allocatable Arrays==
−
x
+
{|
−
1
+
|- valign="top"
 +
|
 +
* So far, all our programs have had fixed-size arrays, set at compile time.
 +
* To change problem size, have to edit code, recompile.
 +
* Has some advantages (optimization, determinism) but very inflexible.
 +
* Would like to be able to request memory at run time, make array of desired size.
 +
* Allocatable arrays are arguably most important addition to Fortran.
 +
|}
  
−
2
+
==Allocate(), Deallocate()==
 +
{|
 +
|- valign="top"
 +
|
 +
* Give array a deferred size (eg, dimension(:)) and the attribute allocatable.
 +
* When time to allocate it, use allocate(a(n)).
 +
* Deallocate with deallocate(a).
 +
* In between, arrays can be used as any other array.
 +
* If allocation fails (not enough memory available for request), program will exit.
 +
* Can control this by checking for an optional error code, allocate(a(n),stat=ierr)
 +
* Can then test if ierr>0 (failure condition) and handle gracefully.
 +
* In scientific programming, the default behaviour is often fine, if abrupt - you either have enough memory to run the problem, or you don’t.
 +
|
 +
<source lang="fortran">
 +
program allocarray
 +
    implicit none
 +
    integer :: i, n
 +
    integer, dimension(:), allocatable :: a
  
−
3
+
    n = 10
 +
    allocate(a(n))
 +
    a = [(i, i=2,20,2)]
  
−
4
+
    print *,'A = '
 +
    print *,a
  
−
5
+
    deallocate(a)
 +
end program allocarray
 +
</source>
 +
(from samples/arrays/allocatable.f90 )
 +
|}
  
−
6
+
==get_command_argument()==
 +
{|
 +
|- valign="top"
 +
|
 +
* Previous version still depended on a compiled-in number.
 +
* Can read from file or from console, but Fortran now has standard way to get command-line arguments
 +
* Get the count of arguments, and if there’s at least one argument there, get it, read it as integer, and allocate array.
 +
|
 +
<source lang="fortran">
 +
program allocarray2
 +
    implicit none
 +
    integer :: i, n
 +
    integer, dimension(:), allocatable :: a
 +
    character(len=30) :: arg
  
−
7
+
    if (command_argument_count() < 1) then
 +
        print *,'Use: allocatable N, '//&
 +
                ' where N is array size.'
 +
        stop
 +
    endif
  
−
==Array Views==
+
    call get_command_argument(1, arg)
 +
    read( arg,'(I30)'), n
 +
   
 +
    print *,'Allocating array of size ', n
 +
    allocate(a(n))
  
−
samples/pointers/views.f90
+
    a = [(i,i=1,n)]
 +
    print *, a
 +
   
 +
    deallocate(a)
 +
end program allocarray2
 +
</source>
 +
(from samples/arrays/allocatable2.f90)
 +
<source lang="bash">
 +
$ ./allocatable2
 +
Use: allocatable N,  where N is array size.
  
−
==Hands on #4==
+
$ ./allocatable2 3
−
* Use pointers to provide views into subsets of
+
Allocating array of size     3
−
the arrays in solver.f90 to clarify the functions.
+
  1       2   3
−
* In workedexamples/pointers, have started
 
−
the process with cfl, hydroflux; try tackling
 
−
tvd1d, others.
 
−
* ~30 min
 
  
−
==Derived Types and Objects==
+
$ ./allocatable2 5
−
* Often, groups of
+
Allocating array of size     5
−
variables naturally go
+
  1       2   3       4   5
−
together to represent a
+
</source>
−
larger structure
+
|}
−
* Whenever you find
 
−
yourself passing the
 
−
same group of variables
 
−
to several routines, a
 
−
good candidate for a
 
−
derived type.
 
  
−
type griddomain
+
==Hands on #3==
−
real :: xmin, xmax
+
{|
−
real :: ymin, ymax
+
|- valign="top"
−
real :: nx, ny
+
|
−
real, dimension(:,:) :: u
+
* Use array functionality to simplify hydro code -- don't need to pass, array size, and can simplify mathematics using array operations.
−
endtype griddomain
+
* In workedexamples/arrays, have modified hydro to allocate u, and pbm to just take array.
−
type(griddomain) :: g
+
* Do the same with the fluid dynamic routines in solver.f90
−
g % xmin = -1
+
* ~30 min
−
g % xmax = +1
+
|
−
 
+
|}
−
==Derived Types and Objects==
 
−
* Consider interval
 
−
arithmetic (good for
 
−
quantification of
 
−
uncertainties, etc).
 
−
* An interval inherently
 
−
has two values
 
−
associated with it - the
 
−
end points.
 
−
* Can make this a type.
 
−
samples/derivedtypes/simple/intervalmath.f90
 
−
 
 
−
==Derived Types and Objects==
 
−
* Note can access the
 
−
fields in the type with
 
−
“%”
 
−
* typename
 
−
(field1val,field2val..)
 
−
initializes a value of that
 
−
type.
 
−
* Can pass values of this
 
−
type to functions, etc.,
 
−
just like a built-in type.
 
−
samples/derivedtypes/simple/intervalmath.f90
 
−
 
 
−
==Procedures using types==
 
−
* Can start creating
 
−
library of routines that
 
−
operate on these new
 
−
interval types.
 
−
* Procedures can take
 
−
the new type as
 
−
arguments, functions
 
−
can return the new
 
−
type.
 
−
samples/derivedtypes/intervalfunctions/intervalmath.f90
 
−
 
 
−
==Procedures using types==
 
−
* Can start creating
 
−
library of routines that
 
−
operate on these new
 
−
interval types.
 
−
* Procedures can take
 
−
the new type as
 
−
arguments, functions
 
−
can return the new
 
−
type.
 
−
 
 
−
samples/derivedtypes/intervalfunctions/interval1.f90
 
−
 
 
−
==Procedures using types==
 
−
* Would prefer not to
 
−
have to treat integer
 
−
and real intervals so
 
−
differently in main
 
−
program
 
−
* Different types, but
 
−
adding should be
 
−
similar.
 
−
samples/derivedtypes/intervalfunctions/intervalmath.f90
 
  
−
==Procedures using types==
+
=Fortran Pointers=
 
{|
 
{|
 +
|- valign="top"
 
|
 
|
−
* Would like to be able to call “addintervals” and have language call the right subroutine, do the right thing.
+
* Pointers, or references, refer to another variable.
−
* Similar to how intrinsics work - sin() works on any kind of real, matmult() works on integer, real, or complex matricies.
+
* Eg, p does not contain a real value, but a reference to another real variable.
 +
* Once associated with another variable, can read/write to it as if it were stored “in” p.
 
|
 
|
−
samples/derivedtypes/genericintervals/interval2.f90
+
<source lang="fortran">
−
|}
+
real, target :: x = 3.2
 +
real, pointer:: p
 +
p => x
  
−
==Generic Interfaces==
+
p
 +
 
 +
x
 +
3.2
 +
</source>
 +
samples/pointers/ptr1.f90
 +
|}
 +
 
 +
==Fortran Pointers==
 
{|
 
{|
−
* Generic Interfaces
+
|- valign="top"
−
* addintintervals and addrealintervals share the same interface, (two input parameters, one function return), but different types.
+
|
−
* Put them behind the same interface.
+
* Pointers are either associated, null, or undefined; start out life undefined.
−
* Now, a call to addintervals is resolved at compile time to one or the other.
+
* Can associate them to a variable with => , or mark them as not associated with any valid variable by pointing it to null(). 
 +
* Reading value from or writing value to a null pointer will cause errors, probably crash.
 +
* Fortran pointers can’t point just anywhere.
 +
* Must reference a variable with the same type, that has the target attribute.
 +
|
 +
<source lang="fortran">
 +
real, target :: x = 3.2
 +
real, pointer:: p
 +
p => null()
 +
p
 +
 
 +
x
 +
</source>
 
|
 
|
−
samples/derivedtypes/genericintervals/intervalmath.f90
 
 
|}
 
|}
  
−
==Generic Interfaces==
+
==Fortran Pointers==
−
* Note that everything is
+
{|
−
private except what is
+
|- valign="top"
−
explicitly made public.
+
|
−
* Types are public.
+
* Pointers can reference other pointers.
−
* Generic interfaces are
+
* Actually references what they’re pointing to.
−
public.
+
|
−
* Type specific routines
+
<source lang="fortran">
−
are not.
+
real, target :: x = 3.2
−
* Program using interval
+
real, pointer:: p1, p2
−
math sees only the
+
p1 => x
−
generic interfaces.
+
p2 => p1
−
samples/derivedtypes/genericintervals/intervalmath.f90
+
p1
 +
p2
  
−
==Generic interfaces==
+
x
−
* Call to addintervals or
+
3.2
−
subtract intervals goes
+
</source>
−
to the correct typespecific routine.
+
|}
−
* As does print interval.
 
−
* Could create routines
 
−
to add real to int
 
−
interval, etc and add to
 
−
the same interface.
 
−
samples/derivedtypes/genericintervals/interval2.f90
 
  
−
==Operator overloading==
+
==Allocating a pointer==
−
* An infix operator is
+
{|
−
really just “syntactic
+
|- valign="top"
−
sugar” for a function
+
|
−
which takes two
+
* Pointer doesn’t necessarily have to have another variable to target
−
operands and returns a
+
* Can allocate memory for p to point to that does not belong to any other pointer.
−
third.
+
* Must deallocate it when done
−
 
+
|
−
a = b (op) c
+
<source lang="fortran">
−
=>
+
real, pointer:: p
−
function op(b,c)
+
allocate(p)
−
returns a
+
p = 7.9
 +
p
 +
7.9
 +
|
 +
</source>
 +
samples/pointers/ptr2.f90
 +
|}
  
−
==Operator overloading==
+
==What are they good for? (1)==
−
* An assignment
+
{|
−
operator is really just
+
|- valign="top"
−
“syntactic sugar” for a
+
|
−
subroutine which takes
+
* Pointers are essential for creating, maintaining dynamic data structures
−
two operands and sets
+
* Linked lists, trees, heaps..
−
the first from the
+
* Some of these can be sort-of implemented in arrays, but very awkward
−
second.
+
* Adaptive meshes, treebased particle solvers need these structures.
 +
|
 +
http://en.wikipedia.org/wiki/File:Singly-linked-list.svg
 +
http://en.wikipedia.org/wiki/File:Max-Heap.svg
 +
|}
  
−
a=b
+
==What are they good for? (2)==
−
=>
+
{|
−
subroutine assign(a,b)
+
|- valign="top"
 +
|
 +
* A pointer can be of array type, not just scalar
 +
* Fortran pointers + fortran arrays are quite interesting; can create “views” of subarrays
 +
|
 +
<source lang="fortran">
 +
real, target, dimension(7) :: x
 +
real, pointer:: p(:)
 +
p => x(2:6)
  
−
==Operator overloading==
+
p
−
* Here, we’ve defined
+
x
−
two subroutines which
+
1
−
set intervals based on
 
−
an array - 2 ints for an
 
−
integer interval, or 2
 
−
reals for a real interval
 
  
−
samples/derivedtypes/intervaloperators/intervalmath.f90
+
2
  
−
==Generic interfaces==
+
3
−
* Once this is done, can
 
−
use assignment
 
−
operator,
 
−
* Or add, subtract
 
−
multiply intervals.
 
−
* Can even compose
 
−
them in complex
 
−
expressions! Functions
 
−
automatically
 
−
composed.
 
−
samples/derivedtypes/intervaloperators/interval3.f90
 
  
−
==Type bound procedures==
+
4
−
* Types can have not only
 
−
variables, but
 
−
procedures.
 
−
* Takes us from a type to
 
−
what is usually called a
 
−
class.
 
  
−
samples/derivedtypes/intervaltypebound/
+
5
−
intervalmath.f90
 
  
−
==Type bound procedures==
+
6
−
* Called like one accesses
 
−
a field - %
 
−
* Operates on data of
 
−
the particular variable it
 
−
is invoked from
 
  
−
samples/derivedtypes/intervaltypebound/interval3.f90
+
7
 +
</source>
 +
samples/pointers/views.f90
 +
|}
  
−
==Type bound procedures==
+
==Hands on #4==
−
* It is implicitly passed as
+
{|
−
it’s first parameter the
+
|- valign="top"
−
variable itself.
+
|
−
* Can take other
+
* Use pointers to provide views into subsets of the arrays in solver.f90 to clarify the functions.
−
arguments as well.
+
* In workedexamples/pointers, have started the process with cfl, hydroflux; try tackling tvd1d, others.
−
 
+
* ~30 min
−
samples/derivedtypes/intervaltypebound/
+
|
−
intervalmath.f90
+
|}
  
−
==Object oriented==
+
=Derived Types and Objects=
−
programming
+
{|
−
* F2003 onwards can do full object oriented
+
|- valign="top"
−
programing.
+
|
−
* Types can be derived from other types, inheriting
+
* Often, groups of variables naturally go together to represent a larger structure
−
their fields and type-bound procedures, and
+
* Whenever you find yourself passing the same group of variables to several routines, a good candidate for a derived type.
−
extending them.
+
<source lang="fortran">
−
* Goes beyond scope of today, but this is the
+
type griddomain
−
starting-off point.
+
    real :: xmin, xmax
 +
    real :: ymin, ymax
 +
    real :: nx, ny
 +
    real, dimension(:,:) :: u
 +
endtype griddomain
  
−
==Interoperability with==
+
type(griddomain) :: g
−
other languages
+
g % xmin = -1
−
* Large scientific software now frequently uses
+
g % xmax = +1
−
multiple languages, either within a single code
+
</source>
−
or between codes.
+
|}
−
* Right tool for the job!
 
−
* Need to know how to make software
 
−
interact.
 
−
* Here we’ll look at C/Fortran code calling
 
−
each other, and calling Fortran code from
 
−
python.
 
  
−
==C-interoperability==
+
==Derived Types and Objects==
−
* iso_c_binding module contains definitions for
+
{|
−
interacting with C
+
|- valign="top"
−
* Types, ways to bind procedures to C, etc.
+
|
−
* Allows you to call C routines, or bind Fortran
+
* Consider interval arithmetic (good for quantification of uncertainties, etc).
−
routines in a way that they can be called by C.
+
* An interval inherently has two values associated with it - the end points.
 +
* Can make this a type.
 +
* Note can access the fields in the type with “%”
 +
* typename (field1val,field2val..) initializes a value of that type.
 +
* Can pass values of this type to functions, etc., just like a built-in type.
 +
|
 +
(from samples/derivedtypes/simple/intervalmath.f90 )
 +
|
 +
|}
  
−
==Calling a C routine==
+
==Procedures using types==
−
from Fortran
+
{|
−
* As with the case of
+
|- valign="top"
−
calling a passed-in
+
|
−
function, need an
+
* Can start creating library of routines that operate on these new interval types.
−
explicit prototype.
+
* Procedures can take the new type as arguments, functions can return the new type.
−
* Tells compiler what
+
|
−
to do with “sqrtc”
+
(from samples/derivedtypes/intervalfunctions/intervalmath.f90 )
−
function when called.
+
|}
−
samples/C-interop/call-c-fn/main.f90
 
  
−
==Calling a C routine==
+
==Procedures using types==
−
from Fortran
+
{|
−
* BIND(C) - tells compiler/
+
|- valign="top"
−
linker will have a C-style,
+
|
−
rather than fortran-style
+
* Would prefer not to have to treat integer and real intervals so differently in main program
−
name in object file.
+
* Different types, but adding should be similar.
−
* Can optionally supply
+
* Would like to be able to call “addintervals” and have language call the right subroutine, do the right thing.
−
another name; otherwise,
+
* Similar to how intrinsics work - sin() works on any kind of real, matmult() works on integer, real, or complex matricies.
−
will default to procedure
+
|
−
name.
+
samples/derivedtypes/genericintervals/interval2.f90
−
* Here we’re calling it sqrtc
+
|}
−
to avoid Fortran sqrt()
 
−
function.
 
  
−
==Calling a C routine==
+
==Generic Interfaces==
−
from Fortran
+
{|
−
* The value the function
+
|- valign="top"
−
takes and returns are C
+
|
−
doubles; that is, reals of
+
{|
−
kind(c_double).
+
* Generic Interfaces
−
* Also defined: c_float,
+
* addintintervals and addrealintervals share the same interface, (two input parameters, one function return), but different types.
−
integers of kind c_int,
+
* Put them behind the same interface.
−
c_long, etc.
+
* Now, a call to addintervals is resolved at compile time to one or the other.
 +
|
 +
samples/derivedtypes/genericintervals/intervalmath.f90
 +
|}
  
−
==Calling a C routine==
+
==Generic Interfaces==
−
from Fortran
+
{|
−
* C function arguments by
+
|- valign="top"
−
default are passed by
+
|
−
value; Fortran by default
+
* Note that everything is private except what is explicitly made public.
−
are passed by reference.
+
* Types are public.
−
* Passed by value - values
+
* Generic interfaces are public.
−
copied into function
+
* Type specific routines are not.
−
* Passed by reference pointers to values copied
+
* Program using interval math sees only the generic interfaces.
−
in.
+
|
−
* value attribute for C-style
+
samples/derivedtypes/genericintervals/intervalmath.f90
−
arguments.
+
|}
−
 
 
−
==Calling a C routine==
 
−
from Fortran C math
 
−
lib.
 
  
−
* Compiling - just make
+
==Generic interfaces==
−
sure to link in C library
+
{|
−
you’re calling
+
|- valign="top"
−
* And that’s it.
+
|
 +
* Call to addintervals or subtract intervals goes to the correct typespecific routine.
 +
* As does print interval.
 +
* Could create routines to add real to int interval, etc and add to the same interface.
 +
|
 +
samples/derivedtypes/genericintervals/interval2.f90
 +
|}
  
−
$ make
+
==Operator overloading==
−
gfortran -c main.f90
+
{|
−
gfortran -o main main.o -lm
+
|- valign="top"
 +
|
 +
* An infix operator is really just “syntactic sugar” for a function which takes two operands and returns a third.
 +
|
 +
<source lang="fortran"
 +
a = b (op) c
 +
=>
 +
function op(b,c)
 +
returns a
  
−
$ ./main
+
a=b
−
x =
+
=>
−
2.0000000000000000
+
subroutine assign(a,b)
−
C
+
</source>
−
sqrt(x) =
+
|}
−
1.4142135623730951
 
−
Fortran sqrt(x) =
 
−
1.4142135623730951
 
  
−
==C strings==
+
==Operator overloading==
−
* When using C
+
{|
−
strings, you have to
+
|- valign="top"
−
remember that C
+
|
−
terminates strings
+
* Here, we’ve defined two subroutines which set intervals based on an array - 2 ints for an integer interval, or 2 reals for a real interval
−
with a special
+
|
−
character
+
samples/derivedtypes/intervaloperators/intervalmath.f90
−
* C_NULL_CHAR
+
|}
−
* Dealing with functions
 
−
that return strings is
 
−
hairier, as they return
 
−
a pointer, not an array.
 
  
−
$ make
+
==Generic interfaces==
−
gfortran-mp-4.4 -c main.f90
+
{|
−
gfortran-mp-4.4 -o main main.o -lc
+
|- valign="top"
−
$ ./main
+
|
−
1234 =
+
* Once this is done, can use assignment operator,
−
1234
+
* Or add, subtract multiply intervals.
 +
* Can even compose them in complex expressions! Functions automatically composed.
 +
|
 +
samples/derivedtypes/intervaloperators/interval3.f90
 +
|}
  
−
samples/C-interop/c-strings/main.f90
+
==Type bound procedures==
 +
{|
 +
|- valign="top"
 +
|
 +
* Types can have not only variables, but procedures.
 +
* Takes us from a type to what is usually called a class.
 +
|
 +
(from samples/derivedtypes/intervaltypebound/intervalmath.f90 )
 +
|}
  
−
==Calling Fortran from C==
+
==Type bound procedures==
−
* To write Fortran
+
{|
−
routines callable from
+
|- valign="top"
−
C, bind the subroutine
+
|
−
to a C name
+
* Called like one accesses a field - %
−
* Can optionally give it a
+
* Operates on data of the particular variable it is invoked from
−
different name, as above
+
|
−
* And make sure
+
samples/derivedtypes/intervaltypebound/interval3.f90
−
arguments are of C
+
|}
−
types.
 
  
−
samples/C-interop/c-call-fortran/froutine.f90
+
==Type bound procedures==
 +
{|
 +
|- valign="top"
 +
|
 +
* It is implicitly passed as it’s first parameter the variable itself.
 +
* Can take other arguments as well.
 +
|
 +
samples/derivedtypes/intervaltypebound/intervalmath.f90
 +
|}
  
−
==Calling Fortran from C==
+
==Object oriented programming==
−
* Here, we’ll do
+
{|
−
something a little
+
|- valign="top"
−
trickier and pass C
+
|
−
dynamic arrays
+
* F2003 onwards can do full object oriented programing.
−
 
+
* Types can be derived from other types, inheriting their fields and type-bound procedures, and extending them.
−
samples/C-interop/c-call-fortran/froutine.f90
+
* Goes beyond scope of today, but this is the starting-off point.
 +
|
 +
|}
  
−
==Calling Fortran from C==
+
=Interoperability with other languages=
−
* In Fortran, we accept
+
{|
−
the arguments as C
+
|- valign="top"
−
pointers
+
|
−
* We then associate
+
* Large scientific software now frequently uses multiple languages, either within a single code or between codes.
−
them with fortran
+
* Right tool for the job!
−
pointers to arrays of
+
* Need to know how to make software interact.
−
shape [nx] (1d arrays
+
* Here we’ll look at C/Fortran code calling each other, and calling Fortran code from python.
−
here)
+
|
−
* Then we can do the
+
|}
−
usual Fortran array
 
−
operations with them.
 
  
−
samples/C-interop/c-call-fortran/froutine.f90
+
==C-interoperability==
 +
{|
 +
|- valign="top"
 +
|
 +
* iso_c_binding module contains definitions for interacting with C
 +
* Types, ways to bind procedures to C, etc.
 +
* Allows you to call C routines, or bind Fortran routines in a way that they can be called by C.
 +
|
 +
|}
  
−
==Calling Fortran from C==
+
==Calling a C routine from Fortran==
−
* The single scalar
+
{|
−
argument passed back
+
|- valign="top"
−
we just treat as an
+
|
−
intent(out) variable
+
* As with the case of calling a passed-in function, need an explicit prototype.
−
* Of type c_float.
+
* Tells compiler what to do with “sqrtc” function when called.
−
samples/C-interop/c-call-fortran/froutine.f90
+
|
 +
samples/C-interop/call-c-fn/main.f90
 +
|}
  
−
==More advanced==
+
==Calling a C routine from Fortran==
−
* Handling arbitrary C code is possible
+
{|
−
* Passing C structs -- create a Fortran derived
+
|- valign="top"
−
type with the same fields, use BIND(C) in
+
|
−
defining the type.
+
* BIND(C) - tells compiler/ linker will have a C-style, rather than fortran-style name in object file.
−
* C “multidimensional arrays” - have to be
+
* Can optionally supply another name; otherwise, will default to procedure name.
−
careful, they may not be contiguous! Follow
+
* Here we’re calling it sqrtc to avoid Fortran sqrt() function.
−
pointers.
+
* The value the function takes and returns are C doubles; that is, reals of kind(c_double).
−
* Even taking passed function pointers to C
+
* Also defined: c_float, integers of kind c_int, c_long, etc.
−
functions is possible (samples/C-interop/
+
|
−
functionptr)
+
|}
  
−
==Example of==
+
==Calling a C routine from Fortran==
−
Fortran calling
+
{|
−
C, which calls
+
|- valign="top"
−
Fortran
+
|
 +
* C function arguments by default are passed by value; Fortran by default are passed by reference.
 +
* Passed by value - values copied into function
 +
* Passed by reference pointers to values copied in.
 +
* value attribute for C-style arguments.
 +
* Compiling - just make sure to link in C library you’re calling
 +
* And that’s it.
 +
|
 +
<source lang="bash">
 +
$ make
 +
gfortran -c main.f90
 +
gfortran -o main main.o -lm
  
−
samples/C-interop/valueref/driver.f90
+
$ ./main
 +
x =
 +
2.0000000000000000
 +
C
 +
sqrt(x) = 1.4142135623730951
 +
Fortran sqrt(x) = 1.4142135623730951
 +
</source>
 +
|}
  
−
==samples/C-interop/valueref/croutine.c==
+
==C strings==
−
 
+
{|
−
==samples/C-interop/valueref/froutine.f90==
+
|- valign="top"
 +
|
 +
* When using C strings, you have to remember that C terminates strings with a special character
 +
* C_NULL_CHAR
 +
* Dealing with functions that return strings is hairier, as they return a pointer, not an array.
 +
|
 +
<source lang="bash">
 +
$ make
 +
gfortran-mp-4.4 -c main.f90
 +
gfortran-mp-4.4 -o main main.o -lc
 +
$ ./main
 +
1234 =
 +
1234
 +
</source>
 +
(from samples/C-interop/c-strings/main.f90 )
 +
|}
  
−
==$ ./main==
+
==Calling Fortran from C==
−
(1) In the FORTRAN routine before call to C
+
{|
−
(1) i =
+
|- valign="top"
−
15 x =
+
|
−
2.0000000000000000
+
* To write Fortran routines callable from C, bind the subroutine to a C name
−
(2) In the C routine, got i=15, *x=2.000000
+
* Can optionally give it a different name, as above
−
(2) Changed x
+
* And make sure arguments are of C types.
−
(3) In the FORTRAN routine called by C
+
|
−
(3) Got product p =
+
samples/C-interop/c-call-fortran/froutine.f90
−
30.000000000000000
+
|}
−
(1) In the FORTRAN routine after call to C
 
−
(1) i =
 
−
15 x =
 
−
3.0000000000000000
 
−
prod =
 
−
30.000000000000000
 
  
−
==samples/C-interop/valueref/Makefile==
+
==Calling Fortran from C==
 +
{|
 +
|- valign="top"
 +
|
 +
* Here, we’ll do something a little trickier and pass C dynamic arrays
 +
* In Fortran, we accept the arguments as C pointers
 +
* We then associate them with fortran pointers to arrays of shape [nx] (1d arrays here)
 +
* Then we can do the usual Fortran array operations with them. 
 +
* The single scalar argument passed back we just treat as an intent(out) variable
 +
* Of type c_float.
 +
|
 +
(from samples/C-interop/c-call-fortran/froutine.f90 )
 +
|}
  
−
==F2py==
+
==More advanced==
−
* Comes with scipy,
+
{|
−
a widely-installed
+
|- valign="top"
−
(by scientists)
+
|
−
python package.
+
* Handling arbitrary C code is possible
−
* Wraps fortran in
+
* Passing C structs -- create a Fortran derived type with the same fields, use BIND(C) in defining the type.
−
python, allows you
+
* C “multidimensional arrays” - have to be careful, they may not be contiguous! Follow pointers.
−
to easily interface.
+
* Even taking passed function pointers to C
−
* fwrap is another
+
functions is possible
−
option
+
|
 +
(from samples/C-interop/functionptr )
 +
|}
  
−
http://www.scipy.org/F2py
+
==Fortran calling C, which calls Fortran==
−
 
+
{|
−
==* Will only use solver module.==
+
|- valign="top"
−
* Unfortunately, f2py isn’t quite smart enough to understand
+
|
−
using parameters to size arrays, so global replace ‘nvars’=4
+
samples/C-interop/valueref/driver.f90
−
* module load use.experimental gcc python/2.7.1 intel/12
+
|
−
* “f2py -m hydro_solver -h hydro_solver.pyf solver.f90”
+
|}
  
−
==* generates the following header file (hydro_solver.pyf)==
+
==samples/C-interop/valueref/croutine.c==
 +
{|
 +
|- valign="top"
 +
|
 +
|
 +
|}
  
−
* Comment out stuff we don’t need (lower-level routines)
+
==samples/C-interop/valueref/froutine.f90==
−
* f2py -c --fcompiler=gfortran hydro_solver.pyf solver.f90
+
{|
 +
|- valign="top"
 +
|
 +
|
 +
|}
  
−
==$ ipython==
+
==$ ./main==
−
In [1]: import hydro_solver
+
{|
−
In [2]: hydro_solver.solver.
+
|- valign="top"
−
hydro_solver.solver.cfl
+
|
−
hydro_solver.solver.gamma
+
<source lang="bash">
−
hydro_solver.solver.hydroflux
+
$ ./main
−
hydro_solver.solver.idens
+
(1) In the FORTRAN routine before call to C
−
hydro_solver.solver.iener
+
(1) i =
−
hydro_solver.solver.imomx
+
15 x =
 +
2.0000000000000000
 +
(2) In the C routine, got i=15, *x=2.000000
 +
(2) Changed x
 +
(3) In the FORTRAN routine called by C
 +
(3) Got product p =
 +
30.000000000000000
 +
(1) In the FORTRAN routine after call to C
 +
(1) i = 15 x = 3.0000000000000000 prod = 30.000000000000000
 +
</source>
 +
|
 +
|}
  
−
hydro_solver.solver.imomy
+
==samples/C-interop/valueref/Makefile==
−
hydro_solver.solver.initialconditions
+
{|
−
hydro_solver.solver.timestep
+
|- valign="top"
−
hydro_solver.solver.tvd1d
+
|
−
hydro_solver.solver.xsweep
+
|
−
hydro_solver.solver.xytranspose
+
|}
  
−
In [2]: hydro_solver.solver.idens
+
==F2py==
−
Out[2]: array(1, dtype=int32)
+
{|
−
In [3]: import numpy
+
|- valign="top"
−
In [4]: u = hydro_solver.solver.initialconditions(100,100)
+
|
−
In [5]: import pylab
+
* Comes with scipy, a widely-installed (by scientists) python package.
−
In [6]: pylab.imshow(u[1,:,:])
+
* Wraps fortran in python, allows you to easily interface.
−
In [7]: for i in range(100)
+
* fwrap is another option
−
...dt = hydro_solver.solver.timestep(u)
+
|
−
In [8]: pylab.imshow(u[1,:,:])
+
http://www.scipy.org/F2py
 +
|}
  
−
==Coarrays==
+
==* Will only use solver module.==
−
* In F2008, objects
+
{|
−
can also have a
+
|- valign="top"
−
“codimension”.
+
|
−
* An object with a
+
* Unfortunately, f2py isn’t quite smart enough to understand using parameters to size arrays, so global replace ‘nvars’=4
−
codimension can be
+
* module load use.experimental gcc python/2.7.1 intel/12
−
“seen” across
+
* “f2py -m hydro_solver -h hydro_solver.pyf solver.f90”
−
processes
+
|
−
* Right now, only intel
+
|}
−
v 12 supports this
 
−
samples/coarrays/simple.f90
 
  
−
==Coarrays==
+
==* generates the following header file (hydro_solver.pyf)==
−
1
+
{|
 +
|- valign="top"
 +
|
 +
* Comment out stuff we don’t need (lower-level routines)
 +
* f2py -c --fcompiler=gfortran hydro_solver.pyf solver.f90
 +
|
 +
|}
  
−
A
+
==$ ipython==
−
B
+
{|
−
 
+
|- valign="top"
−
2
+
|
−
 
+
<source lang="bash">
−
A
+
In [1]: import hydro_solver
−
B
+
In [2]: hydro_solver.solver.
 +
hydro_solver.solver.cfl
 +
hydro_solver.solver.gamma
 +
hydro_solver.solver.hydroflux
 +
hydro_solver.solver.idens
 +
hydro_solver.solver.iener
 +
hydro_solver.solver.imomx
  
−
N
+
hydro_solver.solver.imomy
 +
hydro_solver.solver.initialconditions
 +
hydro_solver.solver.timestep
 +
hydro_solver.solver.tvd1d
 +
hydro_solver.solver.xsweep
 +
hydro_solver.solver.xytranspose
  
−
...
+
In [2]: hydro_solver.solver.idens
 +
Out[2]: array(1, dtype=int32)
 +
In [3]: import numpy
 +
In [4]: u = hydro_solver.solver.initialconditions(100,100)
 +
In [5]: import pylab
 +
In [6]: pylab.imshow(u[1,:,:])
 +
In [7]: for i in range(100)
 +
...dt = hydro_solver.solver.timestep(u)
 +
In [8]: pylab.imshow(u[1,:,:])
 +
</source>
 +
|}
  
−
A
+
=Coarrays=
−
B
+
{|
−
 
+
|- valign="top"
−
num_images
+
|
−
independant
+
* In F2008, objects can also have a “codimension”.
−
processes
+
* An object with a codimension can be “seen” across processes
 +
* Right now, only intel v 12 supports this
 +
|
 +
samples/coarrays/simple.f90
 +
|}
  
 
==Coarrays==
 
==Coarrays==
 +
{|
 +
|- valign="top"
 +
|
 
1
 
1
  
Line 1,885: Line 2,562:
 
independant
 
independant
 
processes
 
processes
 +
|
 +
|}
  
−
A[1]
+
==Coarrays==
−
B[N]
+
{|
 +
|- valign="top"
 +
|
 +
1
  
−
Independent, parallel tasks can
+
A
−
“see” each other’s data as easily as an array index.
+
B
  
−
==Sychronization==
+
2
−
* When accessing other
 
−
processor’s data, must
 
−
ensure that tasks are
 
−
synchronized
 
−
* Don’t want to read
 
−
task 1’s data before
 
−
read is complete!
 
−
* sync all
 
−
samples/coarrays/broadcast.f90
 
  
−
==Sychronization==
+
A
−
* Other synchronization
+
B
−
tools:
 
−
* sync images([..]) syncs
 
−
only images in the list
 
−
provided
 
−
* critical - only one
 
−
image can enter block
 
−
at a time
 
−
* lock - finer-grained
 
−
control than critical.
 
−
* atomic operations.
 
  
−
samples/coarrays/broadcast.f90
+
N
  
−
==1d Diffusion Eqn==
+
...
−
* Calculate heat
 
−
diffusion along a bar
 
−
* Finite difference;
 
−
calculate second
 
−
derivative using
 
−
neighbours
 
−
* Get new
 
−
temperature from
 
−
old temperatures
 
  
−
1 -2 1
+
A
 +
B
  
−
==1d Diffusion Eqn==
+
num_images
−
* Initial conditions:
+
independant
−
* Use pointers to
+
processes
−
point to new, old
 
−
temperatures
 
−
* 1..totpoints+2 (pts 1,
 
−
totpoints+1 “ghost
 
−
cells)
 
−
* Setup x, orig
 
−
temperature, expected
 
−
values
 
  
−
samples/coarrays/diffusion/diffusion.f90
+
A[1]
 +
B[N]
  
−
==1d Diffusion Eqn==
+
Independent, parallel tasks can
−
* Evolution:
+
“see” each other’s data as easily as an array index.
−
* Apply BCs
+
|
−
* Apply finite
+
|}
−
difference stencil to
 
−
all real data points
 
−
samples/coarrays/diffusion/diffusion.f90
 
  
−
==1d Diffusion Eqn==
+
==Sychronization==
−
* Output calculated
+
{|
−
values and theory to
+
|- valign="top"
−
file output.txt
+
|
−
* Note: Fortran2008,
+
* When accessing other processor’s data, must ensure that tasks are synchronized
−
can use “newunit”
+
* Don’t want to read task 1’s data before read is complete!
−
to find, use an
+
* sync all
−
unused IO unit
+
|
 +
samples/coarrays/broadcast.f90
 +
|}
  
−
samples/coarrays/diffusion/diffusion.f90
+
==Sychronization==
 +
{|
 +
|- valign="top"
 +
|
 +
* Other synchronization tools:
 +
* sync images([..]) syncs only images in the list provided
 +
* critical - only one image can enter block at a time
 +
* lock - finer-grained control than critical.
 +
* atomic operations.
 +
|
 +
samples/coarrays/broadcast.f90
 +
|}
  
−
==$ ./diffusion==
+
==1d Diffusion Eqn==
−
[..]
+
{|
−
$ gnuplot
+
|- valign="top"
−
[..]
+
|
−
gnuplot> plot 'output.txt' using 1:2 with points title 'Simulated',
+
* Calculate heat diffusion along a bar
−
'output.txt' using 1:3 with lines title 'Theory'
+
* Finite difference; calculate second derivative using neighbours
 +
* Get new temperature from old temperatures
 +
1 -2 1
 +
|
 +
|}
  
−
==Coarray Diffusion==
+
==1d Diffusion Eqn==
−
* Now we’ll try this in
+
{|
−
parallel
+
|- valign="top"
−
* Each image runs it’s part
+
|
−
of the problem
+
* Initial conditions:
−
(totpoints/num_images())
+
* Use pointers to point to new, old temperatures
−
* Communications is like
+
* 1..totpoints+2 (pts 1, totpoints+1 “ghost cells)
−
boundary condition
+
* Setup x, orig temperature, expected values
−
handling - except
+
|
−
boundary data must be
+
samples/coarrays/diffusion/diffusion.f90
−
obtained from
+
|}
−
neighbouring image.
 
  
−
==Coarray Diffusion==
+
==1d Diffusion Eqn==
−
* Everything’s the same
+
{|
−
except we are only
+
|- valign="top"
−
responsible for locpoints
+
|
−
points, starting at start.
+
* Evolution:
−
* Once calculated, we
+
* Apply BCs
−
never need totpoints
+
* Apply finite difference stencil to all real data points
−
again. All arrays are of
+
|
−
size (locpoints), etc.
+
samples/coarrays/diffusion/diffusion.f90
−
* For simplicity, we
+
|}
−
assume here everything
+
 
−
divides evenly.
+
==1d Diffusion Eqn==
−
 
+
{|
−
samples/coarrays/diffusion/diffusion-coarray.f90
+
|- valign="top"
 +
|
 +
* Output calculated values and theory to file output.txt
 +
* Note: Fortran2008, can use “newunit” to find, use an unused IO unit
 +
|
 +
samples/coarrays/diffusion/diffusion.f90
 +
|}
 +
 
 +
==$ ./diffusion==
 +
{|
 +
|- valign="top"
 +
|
 +
[..]
 +
$ gnuplot
 +
[..]
 +
gnuplot> plot 'output.txt' using 1:2 with points title 'Simulated',
 +
'output.txt' using 1:3 with lines title 'Theory'
 +
|
 +
|}
  
 
==Coarray Diffusion==
 
==Coarray Diffusion==
−
* Boundary exchange; if we
+
{|
−
have interior neighbours,
+
|- valign="top"
−
get updated data from
+
|
−
them so we can calculate
+
* Now we’ll try this in parallel
−
our new data
+
* Each image runs it’s part of the problem (totpoints/num_images())
−
* Note: can’t use pointers
+
* Communications is like boundary condition handling - except boundary data must be obtained from neighbouring image.
−
here, coarrays can’t be
+
|
−
targets.
+
|}
−
* Sync all around boundary
 
−
exchange a little heavy
 
−
handed; could just sync
 
−
neighbours.
 
−
samples/coarrays/diffusion/diffusion-coarray.f90
 
  
 
==Coarray Diffusion==
 
==Coarray Diffusion==
−
 
+
{|
−
temperature()[leftneigh]
+
|- valign="top"
−
 
+
|
−
temperature()
+
* Everything’s the same except we are only responsible for locpoints points, starting at start.
 +
* Once calculated, we never need totpoints again. All arrays are of size (locpoints), etc.
 +
* For simplicity, we assume here everything divides evenly.
 +
|
 +
samples/coarrays/diffusion/diffusion-coarray.f90
 +
|}
 +
 
 +
==Coarray Diffusion==
 +
{|
 +
|- valign="top"
 +
|
 +
* Boundary exchange; if we have interior neighbours, get updated data from them so we can calculate our new data
 +
* Note: can’t use pointers here, coarrays can’t be targets.
 +
* Sync all around boundary exchange a little heavy handed; could just sync neighbours.
 +
|
 +
samples/coarrays/diffusion/diffusion-coarray.f90
 +
|}
 +
 
 +
==Coarray Diffusion==
 +
{|
 +
|- valign="top"
 +
|
 +
<source lang="fortran">
 +
temperature()[leftneigh]
 +
 
 +
temperature()
 
temperature()[rightneigh]
 
temperature()[rightneigh]
  
Line 2,024: Line 2,723:
  
 
lnpts+2
 
lnpts+2
 +
</source>
 +
|}
  
 
==Coarray Diffusion==
 
==Coarray Diffusion==
−
* Everything else exactly
+
{|
−
the same.
+
|- valign="top"
−
* For I/O, we each output
+
|
−
our own file, prefixed by
+
* Everything else exactly the same.
−
our image number
+
* For I/O, we each output our own file, prefixed by our image number
 
* (eg, 1-output.txt, 2output.txt...)
 
* (eg, 1-output.txt, 2output.txt...)
−
 
+
|
 
samples/coarrays/diffusion/diffusion-coarray.f90
 
samples/coarrays/diffusion/diffusion-coarray.f90
 +
|}
  
 
==$ export FOR_COARRAY_NUM_IMAGES=3==
 
==$ export FOR_COARRAY_NUM_IMAGES=3==
 +
{|
 +
|- valign="top"
 +
|
 +
<source lang="fortran">
 
# 3 images
 
# 3 images
 
$ ./diffusion-coarray
 
$ ./diffusion-coarray
Line 2,043: Line 2,749:
 
gnuplot> plot '1-ics.txt' using 1:2, '2-ics.txt' using 1:2, '3-ics.txt'
 
gnuplot> plot '1-ics.txt' using 1:2, '2-ics.txt' using 1:2, '3-ics.txt'
 
using 1:2
 
using 1:2
 +
</source>
 +
|}
  
 
==gnuplot> plot '1-output.txt' using 1:2, '2-output.txt' using 1:2, '3output.txt' using 1:2, '1-output.txt' using 1:3 with lines title 'Theory',==
 
==gnuplot> plot '1-output.txt' using 1:2, '2-output.txt' using 1:2, '3output.txt' using 1:2, '1-output.txt' using 1:3 with lines title 'Theory',==
 +
{|
 +
|- valign="top"
 +
|
 
'2-output.txt' using 1:3 with lines title 'Theory', '3-output.txt' using 1:3
 
'2-output.txt' using 1:3 with lines title 'Theory', '3-output.txt' using 1:3
 
with lines title 'Theory'
 
with lines title 'Theory'
 +
|
 +
|}
  
 
==Parallel Matrix Multiplication==
 
==Parallel Matrix Multiplication==
−
* Consider matrix
+
{|
−
operations, where
+
|- valign="top"
−
matrix is
+
|
−
decomposed onto
+
* Consider matrix operations, where matrix is decomposed onto images in blocks
−
images in blocks
+
* A given image has corresponding blocks in A, B, responsible for that block in C.
−
* A given image has
 
−
corresponding blocks
 
−
in A, B, responsible
 
−
for that block in C.
 
  
 
A
 
A
Line 2,065: Line 2,774:
 
C
 
C
 
=
 
=
 +
|
 +
|}
  
 
==Parallel Matrix Multiplication==
 
==Parallel Matrix Multiplication==
 +
{|
 +
|- valign="top"
 +
|
 
* Block matrix multiply exactly like matrix multiply, except each operation is a submatrix operation
 
* Block matrix multiply exactly like matrix multiply, except each operation is a submatrix operation
 
* matmul instead of “*”.
 
* matmul instead of “*”.
Line 2,077: Line 2,791:
 
C
 
C
 
=
 
=
 +
|
 +
|}
  
 
==Parallel Matrix Multiplication==
 
==Parallel Matrix Multiplication==
 +
{|
 +
|- valign="top"
 +
|
 
* Each image gets its own block of a, b, c.
 
* Each image gets its own block of a, b, c.
 
* Note [nrows,*].  Coarrays can have any corank(eg, number of codimensions)
 
* Note [nrows,*].  Coarrays can have any corank(eg, number of codimensions)
Line 2,085: Line 2,804:
  
 
samples/coarrays/blockmatrix.f90
 
samples/coarrays/blockmatrix.f90
 +
|
 +
|}
  
 
==Parallel Matrix Multiplication==
 
==Parallel Matrix Multiplication==
 +
{|
 +
|- valign="top"
 +
|
 
* Allocation, deallocation of coarrays is like a sync all
 
* Allocation, deallocation of coarrays is like a sync all
 
* Forces synchronization across all images
 
* Forces synchronization across all images
Line 2,092: Line 2,816:
  
 
samples/coarrays/blockmatrix.f90
 
samples/coarrays/blockmatrix.f90
 +
|
 +
|}
  
 
==Parallel Matrix Multiplication==
 
==Parallel Matrix Multiplication==
 +
{|
 +
|- valign="top"
 +
|
 
* This is the entire parallel multiplication operation.
 
* This is the entire parallel multiplication operation.
 
* a[myrow,k] gets the entire a block from image at myrow,k.
 
* a[myrow,k] gets the entire a block from image at myrow,k.
Line 2,099: Line 2,828:
  
 
samples/coarrays/blockmatrix.f90
 
samples/coarrays/blockmatrix.f90
 +
|
 +
|}
  
 
==Coarray Summary==
 
==Coarray Summary==
 +
{|
 +
|- valign="top"
 +
|
 
* Coarrays are powerful, simple-to-use addition to parallel programming models available
 
* Coarrays are powerful, simple-to-use addition to parallel programming models available
 
* Will be widely available soon
 
* Will be widely available soon
Line 2,106: Line 2,840:
 
* Typically implemented with MPI under the hood; can give performance similar to MPI with fewer lines of code.
 
* Typically implemented with MPI under the hood; can give performance similar to MPI with fewer lines of code.
 
* Other languages have similar extensions (UPC based on C, Titanium based on Java) but are not part of languages’ standard.
 
* Other languages have similar extensions (UPC based on C, Titanium based on Java) but are not part of languages’ standard.
 +
|
 +
|}
  
 
==Closing Hints==
 
==Closing Hints==
 +
{|
 +
|- valign="top"
 +
|
 
* Always give the compiler info it needs to help you by being as explicit as possible
 
* Always give the compiler info it needs to help you by being as explicit as possible
 
* implicit none, end [construct] [name], parameters for constants, intent in/out, use only, etc.
 
* implicit none, end [construct] [name], parameters for constants, intent in/out, use only, etc.
 
* Always get as much info from compiler as possible - always use -Wall (gfortran) or -warn all (ifort).
 
* Always get as much info from compiler as possible - always use -Wall (gfortran) or -warn all (ifort).
 +
|
 +
|}
  
 
==Useful Resources==
 
==Useful Resources==
 +
{|
 +
|- valign="top"
 +
|
 
* http://fortranwiki.org/
 
* http://fortranwiki.org/
 
** Reference source; has all standards; Fortran2003/2008 status of major compilers
 
** Reference source; has all standards; Fortran2003/2008 status of major compilers
Line 2,119: Line 2,863:
 
* http://stackoverflow.com/questions/tagged/fortran
 
* http://stackoverflow.com/questions/tagged/fortran
 
** ( Programmers Questions & Answers
 
** ( Programmers Questions & Answers
 +
|}

Latest revision as of 14:59, 23 August 2012

Modern Fortran for FORTRAN77 users

Jonathan Dursi

This is the Wiki-fied version of the slides used for the Modern Fortran course at SciNet. To follow along, with both the examples and the hands on, you will want to download the source code and make sure you have a working Fortran 2003 compiler.


Course Overview

  • Intro, History (10 min)
  • New syntax (30 min)
  • Hands On 1(60 min)
  • Functions, Modules (45 min)
  • #Hands On 2 (30 min)
  • Lunch (1 hr)
  • New Array Features (15 min)
  • Hands on #3 (30 min)
  • Pointers & Interfaces (30 min)
  • Hands on #4 (30 min)
  • Derived Data Types and Objects (30 min)
  • Interoperability with C,Python (30 min)
  • Coarrays (30 min)

A Brief History of Fortran

  • Only major compiled programming language designed specifically for scientific programming.
  • Powerful array operations; many mathematical functions (Bessel functions!) built in; designed to enable compiler optimizations for fast code
  • Oldest (54-57 yrs) still-used programming language.
  • Most people come to Fortran via being given old code by someone.
  • Can’t understand the old code, or quirks of modern language, without understanding it’s history
  • 1957 - J.W. Backus et al. In Proceedings Western Joint Computer Conference, Los Angeles, California, February 1957.
  • IBM 704
  • (Arguably) first modern compiled programming language.
  • Idea of compilers at all was controversial at time.
(from http://www.softwarepreservation.org/projects/FORTRAN/ )
(from http://en.wikipedia.org/wiki/File:Fortran_acs_cover.jpeg )

FORTRAN (1957)

  • Fixed-column format to simplify punched cards
  • C in column 1 - comment
  • Line labels in cols 2-5
  • Continuation character in col 6
  • Code in cols 7-72.
  • Continued until Fortran90!
  • Variables did not need declaration
  • Any variables used starting with i,j,k,l,m,n were assumed integer, all others real.
  • Saved punched cards.
  • Idea is with us today terrible idea.
  • Already had multidimensional arrays!
(from http://en.wikipedia.org/wiki/File:FortranCardPROJ039.agr.jpg )


Incremental changes

  • FORTRAN II (1958) - subroutines and functions (good!) common blocks (terrible, terrible).
  • Still machine dependent (READ INPUT TAPE)
  • FORTRAN III - inline assembly - never released
  • FORTRAN IV (1961) - removed machine dependancies


FORTRAN66

  • With implementation of standard, loss of machine dependency, started gaining wide use on many computers
  • Many implementations
  • double precision, complex, logical types
  • intrinsic and external routines

FORTRAN77

  • The most common to see “in the wild” of old code today
  • if/else/endif, better do loops, control of implicit typing
  • Character strings, saved variables, IO improvements
  • Approved in 1978, beginning long tradition of “optimistic” naming of standards by year.

The interregnum

  • Programming languages and techniques were moving quite quickly
  • Several attempts were made to make new version, but standardization process very slow, failed repeatedly.
  • Absent new real standard, implementations began to grow in many different directions
  • Some extensions became quasi-standard, many were peculiar to individual compilers.

Fortran90

  • Enormous changes; the basis of modern Fortran (not FORTRAN!)
  • Free form, array slices, modules, dynamic memory allocation, derived types...
  • Changes so major that took several years for compilers to catch up.
  • Modern fortran

And since...

  • Fortran95 - modest changes to Fortran90, killed off some deprecated F77 constructs.
  • Fortran 2003 - bigger change; object-oriented, C interoperability. Most compilers have pretty good F2003 support.
  • Fortran 2008 - mostly minor changes, with one big addition (coarray), other parallel stuff. Compiler-writers getting there.

F90, F95, F2003, F2008..

  • We won’t distinguish between versions; we’ll just show you a lot of useful features of modern fortran.
  • Will only show widely-implemented features from 2003 and 8, with exception of coarrays; these are being implemented and are very important.

New Format, New Syntax

Free Format: some highlights

  • Columns no longer significant; can start at left margin
  • Implicit none. Always, always use.
  • Variable declaration syntax changed (more later)
  • Lines can be up to 132 char long; to continue, put & at end of line.
  • ! for comments; comments out rest of line.
  • Numeric line labels are strongly discouraged, but control structures can be named (more later)
  • <, > vs .lt., .gt.
  • <=, >= vs .le., .ge.
  • ==, /= vs .eq., .neq.
  • Program, procedure can contain other procedures
  • “program x” or “function y” ended by “end program x” or “end function y”
  • Case doesn’t matter (except strings)
  • Lines can start anywhere, can be 132 cols long
  • Continue with an & at end of line
  • Can continue a single line 255 times
  • Comments - !, can start anywhere, comments out rest of line
  • Compilers can usually handle both old fixed format and modern free format, but not within the same file.
  • (From samples/freeform/freeform.f90)

<source lang="fortran"> program example 

   implicit none
   integer, parameter :: npts = 10000
   real, parameter :: startx=0., endx=1.
   real, parameter :: dx = (endx-startx)/npts

   real :: integral, xleft, xright, xmid
   integer :: i

   if (npts < 2) then
       print *,'Too few points!'
   else
       integral = 0.  ! Simpson's Rule
       xleft = 0.

  int: do i=0,npts-1
           xright = (i+1)*dx
           xmid = (xleft+xright)/2.

           integral = integral + (dx/6.)*(f(xleft) + 4.*f(xmid) + &
                                          f(xright))
           xleft = xright
        end do int

        print *,'Numerical integral is ', integral
        print *,'Exact soln is ', (endx-startx)/2.  - &
                                    (sin(2*endx)-sin(2*startx))/4.
    endif


contains 

   function f(x)
       implicit none
       real :: f
       real, intent(in) :: x
       f = sin(x)**2
   end function f

end program example </source>

Variable Declarations

  • Implicit none turns off all implicit typing.
  • Was a common F77 extension, but not part of a standard.
  • DO THIS. Without, (eg) variable typos don’t get caught.
  • This is going to be a recurring theme for several features.
  • You do a little more typing and make things explicit to compiler.
  • Then compiler can catch errors, optimize, better.
  • The “::” separating type and name is new
  • Type declarations can now have a lot more information
  • Many attributes of variables set on declaration line
  • :: makes it easier for you, compiler, to see where attributes stop and variable names begin
  • Parameter attribute for values which will be constants.
  • Compiler error if try to change them.
  • Useful for things which shouldn’t change.
  • F77 equivalent:

<source lang="fortran"> integer i parameter (i=5) </source>

  • Initialization of variables at declaration time
    • Required for parameters (because can’t change them later), can be done for other variables.
    • Can do anything that compiler can figure out at compile time, including math with other parameters.

<source lang="fortran"> 

   implicit none
   integer, parameter :: npts = 10000
   real, parameter :: startx=0., endx=1.
   real, parameter :: dx = (endx-startx)/npts

   real :: integral, xleft, xright, xmid
   integer :: i

</source>

Variable Initialization

  • Initializing variables this way gives unexpected behaviour in functions/subroutines “for historical reasons”.
  • Initialized variables given the “save” attribute
  • eg, integer, save, i=5
  • Value saved between calls. Can be handy - but not threadsafe.
  • Initialization done only first time through.
  • Not a problem for main program, parameters.

<source lang="fortran">

...

subroutine testvarinit 

   implicit none
   integer :: i = 5

   print '(A,I3)', 'On entry; i = ', i
   i = 7
   print '(A,I3)', 'Now set;  i = ', i

end subroutine testvarinit

...


program initialization 

   use inittest
... 
   call testvarinit
   call testvarinit
...

end program initialization

</source>

( From samples/variables/initialization/initialization.f90)

<source lang="bash"> $ gfortran initialization.f90 -o initialization $ ./initialization On entry; i = 5 Now set; i = 7 On entry; i = 7 Now set; i = 7 </source>

Real Kinds

  • Reals, Double precisions, really different “kinds” of same “type” - floating point real numbers.
  • Kinds introduced to give enhanced version of functionality of non-standard but ubiquitous constructs like REAL*8
  • real32, real64 defined in iso_fortran_env in newest compilers (gfortran 4.6, ifort 12)
  • selected_real_kind(N): returns kind parameter for reals with N decimal digits of precision
  • Default real is generally 4-byte (32bit) real, has 6 digits of precision and a range of 37 in the exponent.
  • Many built-in (‘intrinsic’) functions which give info about properties of a variable’s numerical type.
  • precision - #digits of precision in decimal * range - of exponent
  • tiny, huge - smallest, largest positive represented number
  • epsilon - machine epsilon
  • several others

<source lang="fortran"> program realkinds 

   use iso_fortran_env
   implicit none

   real :: x
   real(kind=real32) :: x32
   real(kind=real64) :: x64
   real(kind=real128):: x128

   real(kind=selected_real_kind(6)) :: y6
   real(kind=selected_real_kind(15)):: y15

   print *,'Default:'
   print *, precision(x), range(x)
   print *,'Real32:'
   print *, precision(x32), range(x32)
   print *,'Real64:'
   print *, precision(x64), range(x64)
   print *,'Real128:'
   print *, precision(x128), range(x128)

   print *,

   print *,'Selected Real Kind 6:'
   print *, precision(y6), range(y6)

   print *,'Selected Real Kind 15:'
   print *, precision(y15), range(y15)

end program realkinds </source> (from samples/variables/kinds/realkinds.f90)

<source lang="bash"> $ ./realkinds 

Default:
          6          37
Real32:
          6          37
Real64:
         15         307
Real128:
         18        4931

Selected Real Kind 6:
          6          37
Selected Real Kind 15:
         15         307

</source>

Integer Kinds

  • Similar constructs for integers
  • selected int kind(N): kind can represent all N-digit decimal numbers.
  • huge(N): largest positive number of that type samples/variables/kinds/intkinds.f90

<source lang="fortran"> program integerkinds 

   use iso_fortran_env
   implicit none
   
   integer :: i
   integer(kind=int8)  :: i8
   integer(kind=int16) :: i16
   integer(kind=int32) :: i32
   integer(kind=int64) :: i64

   integer(kind=selected_int_kind(6)) :: j6
   integer(kind=selected_int_kind(15)):: j15

   print *,'Default:'
   print *, huge(i)
   print *,'Int8:'
   print *, huge(i8)
   print *,'Int16:'
   print *, huge(i16)
   print *,'Int32:'
   print *, huge(i32)
   print *,'Int64:'
   print *, huge(i64)
   
   print *,

   print *,'Selected Integer Kind 6:'
   print *, huge(j6)
   
   print *,'Selected Integer Kind 15:'
   print *, huge(j15)

end program integerkinds </source>

(from samples/variables/kinds/intkinds.f90)

<source lang="bash"> $ ./intkinds 

Default:
 2147483647
Int8:
 127
Int16:
 32767
Int32:
 2147483647
Int64:
 9223372036854775807

Selected Integer Kind 6:
 2147483647
Selected Integer Kind 15:
 9223372036854775807

</source>

Strings

  • Character types are usually used for strings
  • Specify length
  • Padded by blanks
  • Intrinsic trim() gets rid of blanks at end
  • Can compare strings with <,>,==, etc.
  • Concatenate with //
  • Characters have kinds too
  • gfortran has partial support for selected_char_kind(“ISO_10646”) for unicode strings.

<source lang="fortran"> program strings 

   implicit none
   character(len=20) :: hello 
   character(len=20) :: world
   character(len=30) :: helloworld

   hello = "Hello"
   world = "World!"
   
   helloworld = trim(hello) // " " // trim(world)
   
   print *, helloworld

   if (hello < world) then
       print *, '<', hello, '> is smaller.'
   else
       print *, '<', world, '> is larger.'
   endif

end program strings </source>

(from samples/variables/strings/strings.f90)

<source lang="bash"> $ ./strings 

Hello World!                  
<Hello               > is smaller.

</source>

Array declarations

  • Array declarations have changed, too:
  • dimension is now an attribute
  • Can easily declare several arrays with same dimension

<source lang="fortran"> program arrays 

   implicit none
   real, dimension(3) :: x, y

   x = [1,2,3]
   y = 2*x

   print *, x
   print *, y

end program arrays </source> ( from samples/variables/arrays/arrays.f90) <source lang="bash"> $ ./arrays 

  1.0000000       2.0000000       3.0000000    
  2.0000000       4.0000000       6.0000000

</source>


Do loops

  • Do loops syntax has had some changes
  • do/enddo - was a common extension, now standard.
  • All constructs now have end constructname to end.
  • Named constructs (program, subroutine) require, eg, end program doi.
  • Helps catch various simple errors (mismatched ends, etc.)

<source lang="fortran"> program doi 

       implicit none
       integer :: i

       do i=1,10
           print *, i, i**2, i**3
       enddo

end program doi </source> ( from samples/variables/doloops/doi.f90 ) <source lang="bash"> $ ./doi 

          1           1           1
          2           4           8
          3           9          27
          4          16          64
          5          25         125
          6          36         216
          7          49         343
          8          64         512
          9          81         729
         10         100        1000

</source>

Named loops

  • Can name control structures like do, if statements now, too.
  • Handy for documentation, or to distinguish deeply-nested loops.
  • Again, can help catch mismatched loops.
  • enddo or end do; fortran isn’t picky about spaces.

<source lang="fortran"> program nameddo 

   implicit none
   integer :: i, j

   outer: do i=1,3
       inner: do j=1,3
           print *, i, j, i*i+j*j
       enddo inner
   end do outer

end program nameddo </source> ( from samples/variables/doloops/nameddo.f90 ) <source lang="bash"> $ ./nameddo 

          1           1           2
          1           2           5
          1           3          10
          2           1           5
          2           2           8
          2           3          13
          3           1          10
          3           2          13
          3           3          18

</source>

Cycle/exit

  • Do loops don’t even need a i=1,n
  • do/enddo
  • Will loop forever
  • Can control looping with cycle, exit
  • exit - exits loop. (exit loopname can exit out of nested loops)
  • cycle - jumps back to do

<source lang="fortran"> program cycleexit 

   implicit none
   integer :: i

   do 
       print *, 'Enter a number between 1-13'
       read *,  i
       if (i>=1 .and. i<=13) exit
       print *, 'Wrong; try again.'
   enddo 

   print *, 'Good; you entered ', i

end program cycleexit </source> ( from samples/variables/doloops/cycleexit.f90 ) <source lang="bash"> $ more cycleexit-out.txt $ ./cycleexit 

Enter a number between 1-13

23 

Wrong; try again.
Enter a number between 1-13

-1 

Wrong; try again.
Enter a number between 1-13

12 

Good; you entered           12

</source>


Do while

  • do while - repeats as long as precondition is true.
  • Seems like it should be useful, but in practice, just do/enddo with exit condition is usually cleaner.

<source lang="fortran"> program dowhile 

   implicit none
   integer :: i

   i = -1  
   do while (i < 1 .or. i > 13)
       print *, 'Enter a number between 1-13'
       read *,  i
       if (i<1 .or. i>13) print *, 'Wrong; try again.'
   enddo 

   print *, 'Good; you entered ', i

end program dowhile </source> ( from samples/variables/doloops/dowhile.f90 )

Hands On 1

  • In workedexample/f77 is a simplified, F77ized version of a fluid-dynamics code from Ue-Li Pen, CITA, U of Toronto (http://www.cita.utoronto.ca/~pen/MHD/)
  • For the purposes of this class, we've turned it from a perfectly good f90 code to something that looks more like something your supervisor would dust off and give to you.
  • Today we’ll be translating this version into a very modern Fortran
  • Compile (using make) and run (./hydro)
  • Outputs a .pbm file; use “display dens.pbm” to see the result of dense blob of fluid moving through a light medium.
  • In workedexamples/freeform, have partly converted the program to new freeform format, with enddos, ending procedures, implicit nones, and new variable declaration syntax.
  • Finish doing so - just need to do program hydro, subroutine color, subroutine outputpbm, function cfl. Fix indenting (Don't need to start at col 7 anymore).
  • ~1 hr (for getting logged in and everything working)

Procedures and Modules

  • Several enhancements to how procedures (functions, subroutines) are defined
  • Modules are ways of organizing procedures, definitions, into sensible units for ease of code maintenance, clarity

Modules

  • Easiest to show by example
  • Here, the gravity module defines a constant, and contains a function
  • Main program “use”s the module, has access to both.
  • “Use” goes before “implicit none”

<source lang="fortran"> module gravity 

   implicit none
   real, parameter :: G  = 6.67e-11   ! MKS units

contains 

   real function gravforce(x1,x2,m1,m2)
       implicit none
       real, dimension(3), intent(in) :: x1,x2
       real, intent(in) :: m1, m2
       real :: dist

       dist = sqrt(sum((x1-x2)**2))
       gravforce = G * m1 * m2 / dist**2
   end function gravforce

end module gravity

program simplemod 

   use gravity
   implicit none

   print *, 'Gravitational constant = ', G
   print *, 'Force between 2 1kg masses at [1,0,0] &
             &and [0,0,1] is'

   print *, gravforce([1.,0.,0.],[0.,0.,1.],1.,1.)

end program simplemod </source> (from samples/procedures/simplemod/simplemod.f90)

Compiling & Running

  • When compiling the code a gravity.mod file is created
  • Machine-generated and readable “header” file containing detailed type, other information about contents of module
  • Not compatible between different compilers, versions.

<source lang="bash"> $ ls simplemod.f90

$ gfortran -o simplemod simplemod.f90 -Wall

$ ls gravity.mod simplemod simplemod.f90

$ ./simplemod 

Gravitational constant =   6.6700000E-11
Force between 2 1kg masses at [1,0,0] and [0,0,1] is
 3.3350003E-11

</source>

Modules

  • function gravforce can “see” the modulewide parameter defined above.
  • So can main program, through use statement.

<source lang="fortran"> <source lang="fortran"> module gravity 

   implicit none
   real, parameter :: G  = 6.67e-11   ! MKS units

contains 

   real function gravforce(x1,x2,m1,m2)
       implicit none
       real, dimension(3), intent(in) :: x1,x2
       real, intent(in) :: m1, m2
       real :: dist

       dist = sqrt(sum((x1-x2)**2))
       gravforce = G * m1 * m2 / dist**2
   end function gravforce

end module gravity

program simplemod 

   use gravity
   implicit none

   print *, 'Gravitational constant = ', G
   print *, 'Force between 2 1kg masses at [1,0,0] &
             &and [0,0,1] is'

   print *, gravforce([1.,0.,0.],[0.,0.,1.],1.,1.)

end program simplemod </source> (from samples/procedures/simplemod/simplemod.f90)

use module, only :

  • Best practice is to only pull in from the module what you need
  • Otherwise, everything.
  • Adds some clarity and documentation, good for maintainability
  • (Note syntax for continuation of a string...)

<source lang="fortran"> module gravity 

   implicit none
   real, parameter :: G  = 6.67e-11   ! MKS units

contains 

   real function gravforce(x1,x2,m1,m2)
       implicit none
       real, dimension(3), intent(in) :: x1,x2
       real, intent(in) :: m1, m2
       real :: dist

       dist = sqrt(sum((x1-x2)**2))
       gravforce = G * m1 * m2 / dist**2
   end function gravforce

end module gravity

program simplemod2 

   use gravity, only : G, gravforce
   implicit none

   print *, 'Gravitational constant = ', G
   print *, 'Force between 2 1kg masses at [1,0,0] &
             &and [0,0,1] is'
   
   print *, gravforce([1.,0.,0.],[0.,0.,1.],1.,1.)

end program simplemod2 </source> samples/procedures/simplemod/simplemod2.f90

Modules usually get their own files

  • For encapsulation
  • For ease of re-use
  • Here’s a slightly expanded module;
  • Let’s see how to compile it.
  • (Main program hasn’t changed much).

<source lang="fortran"> module gravity 

   implicit none
   private

   character (len=8), parameter, public :: massunit="kilogram"
   character (len=8), parameter, public :: forceunit="Newton"
   public :: gravforce

   real, parameter :: G  = 6.67e-11   ! MKS units

contains 

   real function distance(x1,x2)
       implicit none
       real, dimension(3), intent(in) :: x1, x2

       distance = sqrt(sum((x1-x2)**2))
   end function distance

   real function gravforce(x1,x2,m1,m2)
       implicit none
       real, dimension(3), intent(in) :: x1,x2
       real, intent(in) :: m1, m2
       real :: dist

       dist = distance(x1,x2)
       gravforce = G * m1 * m2 / dist**2
   end function gravforce

end module gravity </source> (from samples/procedures/multifilemod/gravity.f90 )

Modules usually get their own files

  • Compiling gravity.f90 now gives both an .o file (containing the code) and the .mod file as before.
  • Compiling the main program (multifilemod.f90) requires the .mod file.

<source lang="make"> FC=gfortran FFLAGS=-O3 -Wall

multifilemod: multifilemod.o gravity.o $(FC) -o $@ multifilemod.o gravity.o

%.mod: %.f90 $(FC) $(FFLAGS) -c $<

multifilemod.o: multifilemod.f90 gravity.mod $(FC) $(FFLAGS) -c $<

clean: rm -f *.o *~ *.mod multifilemod </source> (from samples/procedures/multifilemod/Makefile)

.mod needed for compilation

  • ...because needs the type information of the constants,
  • and type information, number and type of parameters, for the function call.
  • Can’t compile without these

<source lang="fortran"> program simplemod2 

   use gravity, only : gravforce, massunit, forceunit
   implicit none

   print *, 'Force between 2 1 ', massunit ,' masses ', &
            ' at [1,0,0] and [0,0,1] is'
   
   print *, gravforce([1.,0.,0.],[0.,0.,1.],1.,1.), forceunit

end program simplemod2 </source> (from samples/procedures/multifilemod/multifilemod.f90)

.o needed for linking

  • Linking, however, doesn’t require the .mod file
  • Only requires the .o file from the module code.
  • .mod file analogous (but better than) .h files for C code.

<source lang="make"> FC=gfortran FFLAGS=-O3 -Wall

multifilemod: multifilemod.o gravity.o $(FC) -o $@ multifilemod.o gravity.o

%.mod: %.f90 $(FC) $(FFLAGS) -c $<

multifilemod.o: multifilemod.f90 gravity.mod $(FC) $(FFLAGS) -c $<

clean: rm -f *.o *~ *.mod multifilemod </source> (from samples/procedures/multifilemod/Makefile)

Compiling and running

  • So compile files with modules first, so those that need them have the .mod files
  • Link the .o files

<source lang="bash"> $ make gfortran -O3 -Wall -c gravity.f90 gfortran -O3 -Wall -c multifilemod.f90 gfortran -o multifilemod multifilemod.o gravity.o reposado-$ ./multifilemod 

Force between 2 1 kilogram masses  at [1,0,0] and [0,0,1] is
 3.33500033E-11 Newton

</source>

Private and public

  • Not all of a module’s content need be public
  • Can give individual items public or private attribute
  • “private” makes everything private by default
  • Allows hiding implementation specific routines

<source lang="fortran"> module gravity 

   implicit none
   private

   character (len=8), parameter, public :: massunit="kilogram"
   character (len=8), parameter, public :: forceunit="Newton"
   public :: gravforce

   real, parameter :: G  = 6.67e-11   ! MKS units

contains 

   real function distance(x1,x2)
       implicit none
       real, dimension(3), intent(in) :: x1, x2

       distance = sqrt(sum((x1-x2)**2))
   end function distance

   real function gravforce(x1,x2,m1,m2)
       implicit none
       real, dimension(3), intent(in) :: x1,x2
       real, intent(in) :: m1, m2
       real :: dist

       dist = distance(x1,x2)
       gravforce = G * m1 * m2 / dist**2
   end function gravforce

end module gravity </source> ( from samples/procedures/multifilemod/gravity.f90 )

Procedures

  • We’ve already seen procedures defined in new style; let’s look more closely.
  • Biggest change: intent attribute to “dummy variables” (eg, parameters passed in/out).
  • Again, make expectations more explicit, compiler can catch errors, optimize.
  • Intent(in) - read only. Error to change.
  • Intent(out) - write only. Value undefined before set.
  • Intent(inout) - read/write. (eg, modify region of an array)
  • Also documentation of a sort.

<source lang="fortran"> module procedures

contains

function square(x) result(xsquared) 

     implicit none
     real :: xsquared
     real, intent(IN) :: x

     xsquared = x*x

end function square

function cube(x) 

     implicit none
     real :: cube
     real, intent(IN) :: x

     cube = x*x*x

end function cube

subroutine squareAndCube(x, squarex, cubex) 

     implicit none
     real, intent(in) :: x
     real, intent(out) :: squarex
     real, intent(out) :: cubex

     squarex = square(x)
     cubex   = cube(x)

end subroutine squareAndCube

end module procedures </source> ( from samples/procedures/funcsub/procedures.f90 )

Functions

  • Can be typed a couple of ways.
  • Old-style still works (real function square..)
  • Give a result variable different from function name; set that, type that result (xsquared)
  • Explicitly type the function name, set that as return value (cube)
  • Function return values don’t take intent - always out

<source lang="fortran"> function square(x) result(xsquared) 

     implicit none
     real :: xsquared
     real, intent(IN) :: x

     xsquared = x*x

end function square

function cube(x) 

     implicit none
     real :: cube
     real, intent(IN) :: x

     cube = x*x*x

end function cube

subroutine squareAndCube(x, squarex, cubex) 

     implicit none
     real, intent(in) :: x
     real, intent(out) :: squarex
     real, intent(out) :: cubex

     squarex = square(x)
     cubex   = cube(x)

end subroutine squareAndCube </source> ( from samples/procedures/funcsub/procedures.f90 )

Procedure interfaces

  • The interface to a procedure consists of
    • A procedure’s name
    • The arguments, their names, types and all attributes
    • For functions, the return value name and type
  • Eg, the procedure, with all the real code stripped out.
  • Like a C prototype, but more detailed info
  • .mod files contain explicit interfaces to all public module procedures.

<source lang="fortran"> function square(x) result(xsquared) 

     implicit none
     real :: xsquared
     real, intent(IN) :: x

     xsquared = x*x

end function square

function cube(x) 

     implicit none
     real :: cube
     real, intent(IN) :: x

     cube = x*x*x

end function cube

subroutine squareAndCube(x, squarex, cubex) 

     implicit none
     real, intent(in) :: x
     real, intent(out) :: squarex
     real, intent(out) :: cubex

     squarex = square(x)
     cubex   = cube(x)

end subroutine squareAndCube </source> ( from samples/procedures/funcsub/procedures.f90 )

Procedure interfaces

  • To see where interfaces become necessary, consider this sketch of a routine to do trapezoid-rule integration
  • We want to integrate a passed-in function f, but we don’t know anything about it - type, # of arguments, etc.
  • Need to “type” f the same way you do with xlo, xhi, n.
  • You do that for procedures with interfaces

<source lang="fortran"> function integratefx(xlo, xhi, f, n)

integrate with trapezoid rule .... 
   integer :: i
   real :: dx, xleft, xright

   integratefx = 0.
   dx = (xhi-xlo)/n
   xleft = xlo
   do i=0, n-1
       xright = xleft + dx
       integratefx = integratefx + dx*(f(xright)+f(xleft))/2.
       xleft = xright
   enddo

end function integratefx </source> (from samples/procedures/interface/integrate.f90 )

Wiki trapezoidal.png

(from http://en.wikipedia.org/wiki/File:Trapezoidal_rule_illustration_small.svg )

Procedure interfaces

  • Define f as a parameter, give its type via an interface.
  • Can then use it, and at compile time compiler ensures function passed in matches thisinterface.

<source lang="fortran"> function integratefx(xlo, xhi, f, n)

integrate with trapezoid rule 
   implicit none
   real, intent(in) :: xlo, xhi
   interface
       function f(x)
           implicit none
           real :: f
           real, intent(in) :: x        
       end function f
   end interface
   integer, intent(in) :: n
   real :: integratefx

   integer :: i
   real :: dx, xleft, xright

   integratefx = 0.
   dx = (xhi-xlo)/n
   xleft = xlo
   do i=0, n-1
       xright = xleft + dx
       integratefx = integratefx + dx*(f(xright)+f(xleft))/2.
       xleft = xright
   enddo

end function integratefx

</source> (from samples/procedures/interface/integrate.f90 )

Recursive procedures

  • By default, Fortran procedures cannot call themselves (recursion)
  • Can be enabled by giving the procedure the recursive attribute
  • Subroutines, functions
  • Recursive functions must use “result” keyword to return value.

<source lang="fortran"> recursive function integratefx(xlo, xhi, f, tol) result(integral)

integrate with trapezoid rule, simpsons rule; if difference between two is larger than relevant tolerance, subdivide region. ...variable declarations as before... 
   dx = xhi-xlo
   xmid = (xlo+xhi)/2.
   trapezoid = dx*(f(xlo)+f(xhi))/2.
   simpsons = dx/6.*(f(xlo)+4.*f(xmid)+f(xhi))
   error = abs(trapezoid-simpsons)/(0.5*(trapezoid+simpsons))

   if (error > tol) then
too coarse; subdivide 
       integral = integratefx(xlo,xmid,f,tol) + &
                  integratefx(xmid,xhi,f,tol) 
   else
       integral = trapezoid
   endif

end function integratefx </source> ( from samples/procedures/recursive/integrate.f90)

Pure procedures

  • Procedures are pure or impure depending on whether or not they have “side effects”:
    • Changing things other than their dummy arguments
  • Modifying save variables
  • Modifying module data
  • Printing, etc.
  • Optimizations can be made for pure routines which can’t for impure
  • Label known-pure routines with the pure attribute.
  • Almost all the procedures we’ve seen so far are pure.

<source lang="fortran"> 

   pure subroutine axpy(a, x, y)
y = y + a*x 
       implicit none
       real, intent(IN) :: a, x
       real, intent(INOUT) :: y

       y = y + a*x 
   end subroutine axpy

   subroutine printaxpy(a, x, y)
y = y + a*x 
       implicit none
       real, intent(IN) :: a, x
       real, intent(INOUT) :: y

       print *, a, '*', x, ' + ', y, &
                ' = ', a*x+y
       y = a*x + y
   end subroutine printaxpy

</source> (from samples/procedures/purity/purity.f90)

Optional Arguments

  • Can make arguments optional by using the optional attribute.
  • Use present to test.
  • Often useful to clarify calling of procedure if many parameters have sensible defaults.
  • Avoid code duplication, wrappers of having one version of routine with default values, one with user-supplied
  • Can’t use tol if not present; have to use another variable.

<source lang="fortran"> recursive function integratefx(xlo, xhi, f, tol) result(integral)

.... 
   real, intent(in), optional :: tol
.... 
   real :: errtol
use parameter if passed, else use default 
   if (present(tol)) then
       errtol = tol
   else
       errtol = 1.e-6
   endif
.... 
   if (error > errtol) then
too coarse; subdivide 
       integral = integratefx(xlo,xmid,f,errtol) + &
                  integratefx(xmid,xhi,f,errtol) 
   else
       integral = trapezoid
   endif

end function integratefx

</source> (from samples/procedures/optional/integrate.f90)

Optional Arguments

  • When calling the procedure, can use the optional argument or not.
  • Makes sense to leave optional arguments at end - easier to figure out what’s what when it’s omitted.

<source lang="fortran"> 

   print *, 'Integrating using default tol'
   approx = integratefx(0., 2*pi, sinesquared)
   print *, 'Approximate integral = ', approx
   print *, 'Exact integral = ', exact

   print *, 
   print *, 'Integrating using coarser tol'
   approx = integratefx(0., 2*pi, sinesquared, 0.01)
   print *, 'Approximate integral = ', approx
....

</source> (from samples/procedures/optional/optional.f90)

Keyword Arguments

  • To avoid ambiguity with omitted arguments - or really whenever you want - you can specify which value is which explicitly.
  • Don’t have to be in order.
  • Can clarify calls of routines with many arguments

<source lang="fortran">

.... 
   print *, 'Integrating using still coarser tol'
   approx = integratefx(xhi=2*pi, xlo=0., tol=0.5, &
                        f=sinesquared)
   print *, 'Approximate integral = ', approx

</source> (from samples/procedures/optional/optional.f90)


Procedures and Modules Summary

  • Modules let you bundle procedures, constants in useful packages.
  • Can have public, private components
  • Compiling them generates a .mod file (needed for compiling anything that does a “use modulename”) and an .o file (where the code goes, needed to link together the program).
  • New syntax for functions/subroutines: intent (IN/OUT/INOUT)
  • New syntax for function return values; result or explicit typing of function in argument list.
  • Procedures have interfaces, which are needed for (eg) passing functions
  • Optional/keyword arguments
  • Pure/recursive procedures

Hands On 2

  • In workedexamples/modules, have have pulled the PBM stuff out into a module.
  • Do the same with the hydro routines. What needs to be private? Public?
  • The common block (thankfully) only contains constants, can make those module parameters
  • ~30 min

Fortran arrays

  • Fortran made for dealing with scientific data
  • Arrays built into language
  • The type information associated with an array includes rank (# of dimension), size, element type, stride..
  • Enables powerful optimizations, programmer-friendly features.
  • Can be manipulated like simple scalar variables
  • Elementwise addition, multiplication..

<source lang="fortran"> program basicarrays 

   implicit none
   integer, dimension(5) :: a, b, c
   integer :: i

   a = [1,2,3,4,5]
   b = [(2*i+1, i=1,5)]



   print *, 'a = ', a
   print *, 'b = ', b

   c = a+b
   print *, 'c = ', c

   c = a*b + 1
   print *, 'a*b+1=', c

end program basicarrays </source> (from samples/arrays/basic.f90 )

Array constructors

  • Can have array constants like numerical constants
  • use [] or (/ /), then comma-separated list of values.
  • Implied do loops can be used in constructors
  • (Implied do-loop variables have to be defined)

<source lang="fortran"> 

      x = [1,2,3,4,5]
      x = (/1,2,3,4,5/)
      x = [ (i,i=1,5)]
      a = [ ((i*j,j=1,3),i=1,5)]

</source>

Elementwise operations

  • Elementwise operations can be */+-, or application of an elemental function.
  • Math intrinsics are all elemental - applied to array, applies to every element.
  • Order of execution undefined - allows vectorization, parallelization.

<source lang="fortran"> program elementwise 

   implicit none
   real, dimension(10) :: x,y,z
   integer :: i
   real, parameter:: pi = 4.*atan(1.)

   x = [(2*pi*(i-1)/9.,i=1,10)]
   
   y = sin(x)
   z = x*x

   print *, x
   print *, y
   print *, z

end program elementwise </source> (from samples/arrays/elementwise.f90 )

Elemental Functions

  • User can create their own elemental functions
  • Label any scalar function with “elemental” should (until recently, must) be pure, so can be applied everywhere at same time.
  • Can be faster than loop.
  • Can also take multiple arguments: eg z = addsquare(x,y)

<source lang="fortran"> program elementalfn 

   implicit none
   real, dimension(10) :: x,y,z
   integer :: i
   real, parameter:: pi = 4.*atan(1.)

   x = [(2*pi*(i-1)/9.,i=1,10)]
   
   y = sinesquared(x)
   z = sin(x)*sin(x)

   print *, x
   print *, y
   print *, z
   print *,z(::3)

contains 

   elemental function sinesquared(x)
   implicit none
   real :: sinesquared
   real, intent(in) :: x

   sinesquared = sin(x)**2
   end function sinesquared

end program elementalfn </source> (from samples/arrays/elemental.f90 )

Array comparisons

  • Array comparisons return an array of logicals of the same size of the arrays.
  • Can use any and all to see if any or all of those logicals are true.

<source lang="fortran"> program comparearrays 

   implicit none
   integer, dimension(5) :: a, b
   integer :: i

   a = [1,2,3,4,5]
   b = [(2*i-3, i=1,5)]

   print *, 'A = ', a
   print *, 'B = ', b

   if (any(a > b)) then
       print *, 'An A is larger than a B'
   endif            
   if (all(a > b)) then
       print *, 'All As ares larger than Bs'
   else if (all(b > a)) then
       print *, 'All Bs are larger than As'
   else 
       print *, 'A, B values overlap'
   endif

end program comparearrays </source> (from samples/arrays/compare.f90)

Array masks

  • These logical arrays can be used to mask several operations
  • Only do sums, mins, etc where the mask is true
  • Eg, only pick out positive values.
  • Many array intrinsics have this mask option

<source lang="fortran"> program mask 

   implicit none
   integer, dimension(10) :: a
   logical, dimension(10) :: pos
   integer :: i

   a = [(2*i-7, i=1,10)]
   pos = (a > 0)

   print '(A,10(I4,1X))','A = ', a
   print *,'# of positive values:   ', count(pos)
   print *,'Sum of positive values: ', sum(a,pos)
   print *,'Minimum positive value: ', minval(a,pos)

end program mask </source> ( from samples/arrays/mask.f90 ) <source lang="bash"> $ ./mask A = -5 -3 -1 1 3 5 7 9 11 13 

# of positive values:              7
Sum of positive values:           49
Minimum positive value:            1

</source>

Where construct

  • The where construct can be used to easily manipulate sections of array based on arbitrary comparisons.
  • Where construct => for whatever indices the comparison is true, set values as follow; otherwise, set other values.

<source lang="fortran"> program wherearray 

   implicit none
   real, dimension(6) :: a, diva
   integer :: i

   a = [(2*i-6, i=1,6)]
   where (a /= 0)
       diva = 1/a
   elsewhere
       diva = -999
   endwhere

   print *,'a = '
   print '(6(F8.3,1X))',a
   print *,'1/a = '
   print '(6(F8.3,1X))',diva

end program wherearray </source> (from samples/arrays/where.f90) <source lang="bash"> $ ./where 

a = 
 -4.000   -2.000    0.000    2.000    4.000    6.000
1/a = 
 -0.250   -0.500 -999.000    0.500    0.250    0.167

</source>

Forall construct

  • Forall is an array assignment statement
  • Each line in forall has to be independent. All done “at once” - no guarantees as to order
  • If (say) 2 lines in the forall, all of the first line is done, then all of the second.
  • Any functions called must be pure
  • Can be vectorized or parallelized by compiler

<source lang="fortran"> program forallarray 

   implicit none
   integer, dimension(6,6) :: a
   integer :: i,j

   a = -999
   forall (i=1:6, j=1:6, i/=j)
       a(i,j) = i-j
   endforall

   do i=1,6
       print '(6(I5,1X))',(a(i,j),j=1,6)
   enddo

end program forallarray </source> (from samples/arrays/forall.f90) <source lang="bash"> $ ./forall 

-999    -1    -2    -3    -4    -5
   1  -999    -1    -2    -3    -4
   2     1  -999    -1    -2    -3
   3     2     1  -999    -1    -2
   4     3     2     1  -999    -1
   5     4     3     2     1  -999

</source>

Array Sections

  • Generalization of array indexing
  • Familiar to users of Matlab, IDL, Python..
  • Can use “slices” of an array using “index triplet”
  • [start]:[end][:step]
  • Default start=1, default end=size, default step=1.
  • Can be used for each index of multid array

<source lang="fortran">

a([start]:[end][:step])

a = [1,2,3,4,5,6,7,8,9,10]

a(7:) == [7,8,9,10] a(:3) == [1,2,3] a(2:4) == [2,3,4] a(::3) == [1,4,7,10] a(2:4:2) == [2,4] a(2) == 2 a(:) == [1,2,3,4,5,6,7,8,9,10] </source>

Array Sections

  • This sort of thing is very handy in numerical computation
  • Replace do-loops with clearer, shorter, possibly vectorized array operations
  • Bigger advantage for multidimensional arrays

<source lang="fortran"> program derivative 

   implicit none
   real, dimension(10) :: x
   real, dimension(9) :: derivx
   integer :: i
   real, parameter:: pi = 4.*atan(1.), h=1.

   x = [(2*pi*(i-1)/9.,i=1,10)]
   
   derivx = ((x(2:10)-x(1:9))/h)
   print *, derivx

   do i=1,9
       derivx(i) = (x(i+1)-x(i))/h
   enddo
   print *, derivx

end program derivative </source> (from samples/arrays/derivative.f90)

Array Sections

  • The previous sorts of array sections - shifting things leftward and rightward - are so common there are intrinsics for them
  • positive shift shifts elements leftwards (or array bounds rightwards).
  • cshift does circular shift - shifting off the end of the array “wraps around”.
  • eoshift fills with zeros, or optional filling.
  • Can work on given dimension

<source lang="fortran">


a = [1,2,3,4,5]

cshift(a,1) == [2,3,4,5,1] cshift(a,-1) == [5,1,2,3,4] eoshift(a,1) ==[2,3,4,5,0] eoshift(a,-1)==[0,1,2,3,4] </source>

Other important array intrinsics

  • minval/maxval - finds min, max element in an array.
  • minloc/maxloc - finds location of min/max element
  • product/sum - returns product/sum of array elements
  • reshape - Adjusts shape of array data. Eg:

<source lang="fortran"> 


                               1,4

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

                               3,6

</source>

Linear algebra in Fortran

  • Comes built in with transpose, matmul, dot_product for dealing with arrays.
  • matmul also does matrix-vector multiplication
  • Either use these or system-provided BLAS libraries - never, ever write yourself.
  • Consider the following timings for a matrix multiplication - a naive triple loop, a clal to that matmul intrinsic, or an explicit call to a BLAS package.
  • factor of 100 difference!
  • Note that you can build gfortran to use fast (BLAS) routines for intrinsics...

Matrix Multiplication Times

<source lang="fortran">

... 
   print *, 'Experiment with matrix size ', n
   print *, 'Times in seconds.'

   allocate(a(n,n))
   allocate(b(n,n))
   allocate(c(n,n))
   call random_number(a)
   call random_number(b)

   call tick(starttime)
   do j=1,n
       do i=1,n
           c(i,j) = 0.
           do k=1,n
               c(i,j) = c(i,j)+a(i,k)*b(k,j)
           enddo
       enddo
   enddo
   looptime = tock(starttime)

   call tick(starttime)
   c = matmul(a,b)
   matmultime = tock(starttime)

   call tick(starttime)
   call sgemm('N','N',n,n,n,1.,a,n,b,n,0.,c,n)
   sgemmtime = tock(starttime)



   print *, 'Triple-loop time:      ', looptime
   print *, 'matmul intrinsic time: ', matmultime
   print *, 'SGEMM lapack call time:', sgemmtime
...

</source>

<source lang="bash"> $ ./matmul 2500 Experiment with matrix size 

   2500

Triple-loop time: 

   149.63400

matmul intrinsic time: 

   10.370000

SGEMM lapack call time: 

   1.4809999

</source> (gfortran 4.6, compiled -O3 -march=native using Intel MKL 10.3 for sgemm) (program from samples/arrays/matmul.f90)

Linear algebra in Fortran

  • Things like transposes work, too:
  • see samples/arrays/matrix.f90

<source lang="fortran"> program matvec 

   implicit none
   integer, dimension(4,5) :: a
   integer, dimension(5,4) :: at
   integer, dimension(4,4) :: aat
   integer :: i

   a = reshape([(i,i=1,4*5)],[4,5])
   at = transpose(a)
   print *,'A = '
   call printmat(a)
   print *,'A^T = '
   call printmat(at)

   aat = matmul(a,at)
   print *,'A . A^T = '
   call printmat(aat)
...

</source>

<source lang="bash"> $ ./matrix 

A = 
  1    5    9   13   17
  2    6   10   14   18
  3    7   11   15   19
  4    8   12   16   20
A^T = 
  1    2    3    4
  5    6    7    8
  9   10   11   12
 13   14   15   16
 17   18   19   20
A . A^T = 
565  610  655  700
610  660  710  760
655  710  765  820
700  760  820  880
A . A^T subarray = 
610  660  710
655  710  765
700  760  820

</source>

Array sizes and Assumed Shape

  • Printmat routine here is interesting - don’t pass (a,rows,cols), just a.
  • Can assume a rank-2 array, and get size at runtime.
  • Simplifies call, and eliminates possible inconsistency: what if rows, cols is wrong?
  • size(array,dim) gets the size of array in the dim dimension.
  • Assumed shape arrays (eg, dimension(:,:)) much better than older ways of passing arrays:

integer nx, ny

integer a(nx,ny)

or worse,

integer a(*,ny)

  • Information is thrown away, possibility of inconsistency.
  • Here, (:,:) means we know the rank, but don’t know the size yet.

<source lang="fortran"> 

   subroutine printmat(a)
   implicit none
   integer, dimension(:,:) :: a
   integer :: nr, nc, i, j

   nr = size(a,1)
   nc = size(a,2)
   do i=1,nr
       print '(99(I4,1X))', (a(i,j), j=1,nc)
   enddo
   end subroutine printmat

</source> (from samples/arrays/matrix.f90)


Allocatable Arrays

  • So far, all our programs have had fixed-size arrays, set at compile time.
  • To change problem size, have to edit code, recompile.
  • Has some advantages (optimization, determinism) but very inflexible.
  • Would like to be able to request memory at run time, make array of desired size.
  • Allocatable arrays are arguably most important addition to Fortran.

Allocate(), Deallocate()

  • Give array a deferred size (eg, dimension(:)) and the attribute allocatable.
  • When time to allocate it, use allocate(a(n)).
  • Deallocate with deallocate(a).
  • In between, arrays can be used as any other array.
  • If allocation fails (not enough memory available for request), program will exit.
  • Can control this by checking for an optional error code, allocate(a(n),stat=ierr)
  • Can then test if ierr>0 (failure condition) and handle gracefully.
  • In scientific programming, the default behaviour is often fine, if abrupt - you either have enough memory to run the problem, or you don’t.

<source lang="fortran"> program allocarray 

   implicit none
   integer :: i, n
   integer, dimension(:), allocatable :: a

   n = 10
   allocate(a(n))
   a = [(i, i=2,20,2)]

   print *,'A = '
   print *,a

   deallocate(a)

end program allocarray </source> (from samples/arrays/allocatable.f90 )

get_command_argument()

  • Previous version still depended on a compiled-in number.
  • Can read from file or from console, but Fortran now has standard way to get command-line arguments
  • Get the count of arguments, and if there’s at least one argument there, get it, read it as integer, and allocate array.

<source lang="fortran"> program allocarray2 

   implicit none
   integer :: i, n
   integer, dimension(:), allocatable :: a
   character(len=30) :: arg

   if (command_argument_count() < 1) then
       print *,'Use: allocatable N, '//&
               ' where N is array size.'
       stop
   endif

   call get_command_argument(1, arg)
   read( arg,'(I30)'), n
    
   print *,'Allocating array of size ', n
   allocate(a(n))

   a = [(i,i=1,n)]
   print *, a
   
   deallocate(a)

end program allocarray2 </source> (from samples/arrays/allocatable2.f90) <source lang="bash"> $ ./allocatable2 

Use: allocatable N,  where N is array size.

$ ./allocatable2 3 

Allocating array of size	     3

1 2 3

$ ./allocatable2 5 

Allocating array of size	     5

1 2 3 4 5 </source>

Hands on #3

  • Use array functionality to simplify hydro code -- don't need to pass, array size, and can simplify mathematics using array operations.
  • In workedexamples/arrays, have modified hydro to allocate u, and pbm to just take array.
  • Do the same with the fluid dynamic routines in solver.f90
  • ~30 min

Fortran Pointers

  • Pointers, or references, refer to another variable.
  • Eg, p does not contain a real value, but a reference to another real variable.
  • Once associated with another variable, can read/write to it as if it were stored “in” p.

<source lang="fortran"> real, target :: x = 3.2 real, pointer:: p p => x

p

x 3.2 </source> samples/pointers/ptr1.f90

Fortran Pointers

  • Pointers are either associated, null, or undefined; start out life undefined.
  • Can associate them to a variable with => , or mark them as not associated with any valid variable by pointing it to null().
  • Reading value from or writing value to a null pointer will cause errors, probably crash.
  • Fortran pointers can’t point just anywhere.
  • Must reference a variable with the same type, that has the target attribute.

<source lang="fortran"> real, target :: x = 3.2 real, pointer:: p p => null() p

x </source>

Fortran Pointers

  • Pointers can reference other pointers.
  • Actually references what they’re pointing to.

<source lang="fortran"> real, target :: x = 3.2 real, pointer:: p1, p2 p1 => x p2 => p1 p1 p2

x 3.2 </source>

Allocating a pointer

  • Pointer doesn’t necessarily have to have another variable to target
  • Can allocate memory for p to point to that does not belong to any other pointer.
  • Must deallocate it when done

<source lang="fortran"> real, pointer:: p allocate(p) p = 7.9 p 7.9

</source> samples/pointers/ptr2.f90

What are they good for? (1)

  • Pointers are essential for creating, maintaining dynamic data structures
  • Linked lists, trees, heaps..
  • Some of these can be sort-of implemented in arrays, but very awkward
  • Adaptive meshes, treebased particle solvers need these structures.

http://en.wikipedia.org/wiki/File:Singly-linked-list.svg http://en.wikipedia.org/wiki/File:Max-Heap.svg

What are they good for? (2)

  • A pointer can be of array type, not just scalar
  • Fortran pointers + fortran arrays are quite interesting; can create “views” of subarrays

<source lang="fortran"> real, target, dimension(7) :: x real, pointer:: p(:) p => x(2:6)

p x 1

2

3

4

5

6

7 </source> samples/pointers/views.f90

Hands on #4

  • Use pointers to provide views into subsets of the arrays in solver.f90 to clarify the functions.
  • In workedexamples/pointers, have started the process with cfl, hydroflux; try tackling tvd1d, others.
  • ~30 min

Derived Types and Objects

  • Often, groups of variables naturally go together to represent a larger structure
  • Whenever you find yourself passing the same group of variables to several routines, a good candidate for a derived type.

<source lang="fortran"> type griddomain 

   real :: xmin, xmax
   real :: ymin, ymax
   real :: nx, ny
   real, dimension(:,:) :: u

endtype griddomain

type(griddomain) :: g g % xmin = -1 g % xmax = +1 </source>

Derived Types and Objects

  • Consider interval arithmetic (good for quantification of uncertainties, etc).
  • An interval inherently has two values associated with it - the end points.
  • Can make this a type.
  • Note can access the fields in the type with “%”
  • typename (field1val,field2val..) initializes a value of that type.
  • Can pass values of this type to functions, etc., just like a built-in type.

(from samples/derivedtypes/simple/intervalmath.f90 )

Procedures using types

  • Can start creating library of routines that operate on these new interval types.
  • Procedures can take the new type as arguments, functions can return the new type.

(from samples/derivedtypes/intervalfunctions/intervalmath.f90 )

Procedures using types

  • Would prefer not to have to treat integer and real intervals so differently in main program
  • Different types, but adding should be similar.
  • Would like to be able to call “addintervals” and have language call the right subroutine, do the right thing.
  • Similar to how intrinsics work - sin() works on any kind of real, matmult() works on integer, real, or complex matricies.

samples/derivedtypes/genericintervals/interval2.f90

Generic Interfaces

  • Generic Interfaces
  • addintintervals and addrealintervals share the same interface, (two input parameters, one function return), but different types.
  • Put them behind the same interface.
  • Now, a call to addintervals is resolved at compile time to one or the other.

samples/derivedtypes/genericintervals/intervalmath.f90

Generic Interfaces

  • Note that everything is private except what is explicitly made public.
  • Types are public.
  • Generic interfaces are public.
  • Type specific routines are not.
  • Program using interval math sees only the generic interfaces.

samples/derivedtypes/genericintervals/intervalmath.f90

Generic interfaces

  • Call to addintervals or subtract intervals goes to the correct typespecific routine.
  • As does print interval.
  • Could create routines to add real to int interval, etc and add to the same interface.

samples/derivedtypes/genericintervals/interval2.f90

Operator overloading

  • An infix operator is really just “syntactic sugar” for a function which takes two operands and returns a third.

<source lang="fortran" a = b (op) c => function op(b,c) returns a

a=b => subroutine assign(a,b) </source>

Operator overloading

  • Here, we’ve defined two subroutines which set intervals based on an array - 2 ints for an integer interval, or 2 reals for a real interval

samples/derivedtypes/intervaloperators/intervalmath.f90

Generic interfaces

  • Once this is done, can use assignment operator,
  • Or add, subtract multiply intervals.
  • Can even compose them in complex expressions! Functions automatically composed.

samples/derivedtypes/intervaloperators/interval3.f90

Type bound procedures

  • Types can have not only variables, but procedures.
  • Takes us from a type to what is usually called a class.

(from samples/derivedtypes/intervaltypebound/intervalmath.f90 )

Type bound procedures

  • Called like one accesses a field - %
  • Operates on data of the particular variable it is invoked from

samples/derivedtypes/intervaltypebound/interval3.f90

Type bound procedures

  • It is implicitly passed as it’s first parameter the variable itself.
  • Can take other arguments as well.

samples/derivedtypes/intervaltypebound/intervalmath.f90

Object oriented programming

  • F2003 onwards can do full object oriented programing.
  • Types can be derived from other types, inheriting their fields and type-bound procedures, and extending them.
  • Goes beyond scope of today, but this is the starting-off point.

Interoperability with other languages

  • Large scientific software now frequently uses multiple languages, either within a single code or between codes.
  • Right tool for the job!
  • Need to know how to make software interact.
  • Here we’ll look at C/Fortran code calling each other, and calling Fortran code from python.

C-interoperability

  • iso_c_binding module contains definitions for interacting with C
  • Types, ways to bind procedures to C, etc.
  • Allows you to call C routines, or bind Fortran routines in a way that they can be called by C.

Calling a C routine from Fortran

  • As with the case of calling a passed-in function, need an explicit prototype.
  • Tells compiler what to do with “sqrtc” function when called.

samples/C-interop/call-c-fn/main.f90

Calling a C routine from Fortran

  • BIND(C) - tells compiler/ linker will have a C-style, rather than fortran-style name in object file.
  • Can optionally supply another name; otherwise, will default to procedure name.
  • Here we’re calling it sqrtc to avoid Fortran sqrt() function.
  • The value the function takes and returns are C doubles; that is, reals of kind(c_double).
  • Also defined: c_float, integers of kind c_int, c_long, etc.

Calling a C routine from Fortran

  • C function arguments by default are passed by value; Fortran by default are passed by reference.
  • Passed by value - values copied into function
  • Passed by reference pointers to values copied in.
  • value attribute for C-style arguments.
  • Compiling - just make sure to link in C library you’re calling
  • And that’s it.

<source lang="bash"> $ make gfortran -c main.f90 gfortran -o main main.o -lm

$ ./main x = 2.0000000000000000 C sqrt(x) = 1.4142135623730951 Fortran sqrt(x) = 1.4142135623730951 </source>

C strings

  • When using C strings, you have to remember that C terminates strings with a special character
  • C_NULL_CHAR
  • Dealing with functions that return strings is hairier, as they return a pointer, not an array.

<source lang="bash"> $ make gfortran-mp-4.4 -c main.f90 gfortran-mp-4.4 -o main main.o -lc $ ./main 1234 = 1234 </source> (from samples/C-interop/c-strings/main.f90 )

Calling Fortran from C

  • To write Fortran routines callable from C, bind the subroutine to a C name
  • Can optionally give it a different name, as above
  • And make sure arguments are of C types.

samples/C-interop/c-call-fortran/froutine.f90

Calling Fortran from C

  • Here, we’ll do something a little trickier and pass C dynamic arrays
  • In Fortran, we accept the arguments as C pointers
  • We then associate them with fortran pointers to arrays of shape [nx] (1d arrays here)
  • Then we can do the usual Fortran array operations with them.
  • The single scalar argument passed back we just treat as an intent(out) variable
  • Of type c_float.

(from samples/C-interop/c-call-fortran/froutine.f90 )

More advanced

  • Handling arbitrary C code is possible
  • Passing C structs -- create a Fortran derived type with the same fields, use BIND(C) in defining the type.
  • C “multidimensional arrays” - have to be careful, they may not be contiguous! Follow pointers.
  • Even taking passed function pointers to C

functions is possible

(from samples/C-interop/functionptr )

Fortran calling C, which calls Fortran

samples/C-interop/valueref/driver.f90

samples/C-interop/valueref/croutine.c

samples/C-interop/valueref/froutine.f90

$ ./main

<source lang="bash"> $ ./main (1) In the FORTRAN routine before call to C (1) i = 15 x = 2.0000000000000000 (2) In the C routine, got i=15, *x=2.000000 (2) Changed x (3) In the FORTRAN routine called by C (3) Got product p = 30.000000000000000 (1) In the FORTRAN routine after call to C (1) i = 15 x = 3.0000000000000000 prod = 30.000000000000000 </source>

samples/C-interop/valueref/Makefile

F2py

  • Comes with scipy, a widely-installed (by scientists) python package.
  • Wraps fortran in python, allows you to easily interface.
  • fwrap is another option

http://www.scipy.org/F2py

* Will only use solver module.

  • Unfortunately, f2py isn’t quite smart enough to understand using parameters to size arrays, so global replace ‘nvars’=4
  • module load use.experimental gcc python/2.7.1 intel/12
  • “f2py -m hydro_solver -h hydro_solver.pyf solver.f90”

* generates the following header file (hydro_solver.pyf)

  • Comment out stuff we don’t need (lower-level routines)
  • f2py -c --fcompiler=gfortran hydro_solver.pyf solver.f90

$ ipython

<source lang="bash"> In [1]: import hydro_solver In [2]: hydro_solver.solver. hydro_solver.solver.cfl hydro_solver.solver.gamma hydro_solver.solver.hydroflux hydro_solver.solver.idens hydro_solver.solver.iener hydro_solver.solver.imomx

hydro_solver.solver.imomy hydro_solver.solver.initialconditions hydro_solver.solver.timestep hydro_solver.solver.tvd1d hydro_solver.solver.xsweep hydro_solver.solver.xytranspose

In [2]: hydro_solver.solver.idens Out[2]: array(1, dtype=int32) In [3]: import numpy In [4]: u = hydro_solver.solver.initialconditions(100,100) In [5]: import pylab In [6]: pylab.imshow(u[1,:,:]) In [7]: for i in range(100) ...dt = hydro_solver.solver.timestep(u) In [8]: pylab.imshow(u[1,:,:]) </source>

Coarrays

  • In F2008, objects can also have a “codimension”.
  • An object with a codimension can be “seen” across processes
  • Right now, only intel v 12 supports this

samples/coarrays/simple.f90

Coarrays

1

A B

2

A B

N

...

A B

num_images independant processes

Coarrays

1

A B

2

A B

N

...

A B

num_images independant processes

A[1] B[N]

Independent, parallel tasks can “see” each other’s data as easily as an array index.

Sychronization

  • When accessing other processor’s data, must ensure that tasks are synchronized
  • Don’t want to read task 1’s data before read is complete!
  • sync all

samples/coarrays/broadcast.f90

Sychronization

  • Other synchronization tools:
  • sync images([..]) syncs only images in the list provided
  • critical - only one image can enter block at a time
  • lock - finer-grained control than critical.
  • atomic operations.

samples/coarrays/broadcast.f90

1d Diffusion Eqn

  • Calculate heat diffusion along a bar
  • Finite difference; calculate second derivative using neighbours
  • Get new temperature from old temperatures

1 -2 1

1d Diffusion Eqn

  • Initial conditions:
  • Use pointers to point to new, old temperatures
  • 1..totpoints+2 (pts 1, totpoints+1 “ghost cells)
  • Setup x, orig temperature, expected values

samples/coarrays/diffusion/diffusion.f90

1d Diffusion Eqn

  • Evolution:
  • Apply BCs
  • Apply finite difference stencil to all real data points

samples/coarrays/diffusion/diffusion.f90

1d Diffusion Eqn

  • Output calculated values and theory to file output.txt
  • Note: Fortran2008, can use “newunit” to find, use an unused IO unit

samples/coarrays/diffusion/diffusion.f90

$ ./diffusion

[..] $ gnuplot [..] gnuplot> plot 'output.txt' using 1:2 with points title 'Simulated', 'output.txt' using 1:3 with lines title 'Theory'

Coarray Diffusion

  • Now we’ll try this in parallel
  • Each image runs it’s part of the problem (totpoints/num_images())
  • Communications is like boundary condition handling - except boundary data must be obtained from neighbouring image.

Coarray Diffusion

  • Everything’s the same except we are only responsible for locpoints points, starting at start.
  • Once calculated, we never need totpoints again. All arrays are of size (locpoints), etc.
  • For simplicity, we assume here everything divides evenly.

samples/coarrays/diffusion/diffusion-coarray.f90

Coarray Diffusion

  • Boundary exchange; if we have interior neighbours, get updated data from them so we can calculate our new data
  • Note: can’t use pointers here, coarrays can’t be targets.
  • Sync all around boundary exchange a little heavy handed; could just sync neighbours.

samples/coarrays/diffusion/diffusion-coarray.f90

Coarray Diffusion

<source lang="fortran"> temperature()[leftneigh]

temperature() temperature()[rightneigh]

1 2 3 ...

lnpts+2 </source>

Coarray Diffusion

  • Everything else exactly the same.
  • For I/O, we each output our own file, prefixed by our image number
  • (eg, 1-output.txt, 2output.txt...)

samples/coarrays/diffusion/diffusion-coarray.f90

$ export FOR_COARRAY_NUM_IMAGES=3

<source lang="fortran">

  1. 3 images

$ ./diffusion-coarray [..] $ gnuplot [..] gnuplot> plot '1-ics.txt' using 1:2, '2-ics.txt' using 1:2, '3-ics.txt' using 1:2 </source>

gnuplot> plot '1-output.txt' using 1:2, '2-output.txt' using 1:2, '3output.txt' using 1:2, '1-output.txt' using 1:3 with lines title 'Theory',

'2-output.txt' using 1:3 with lines title 'Theory', '3-output.txt' using 1:3 with lines title 'Theory'

Parallel Matrix Multiplication

  • Consider matrix operations, where matrix is decomposed onto images in blocks
  • A given image has corresponding blocks in A, B, responsible for that block in C.

A

B X C =

Parallel Matrix Multiplication

  • Block matrix multiply exactly like matrix multiply, except each operation is a submatrix operation
  • matmul instead of “*”.
  • For simplicity, we’ll assume square decomposition.

A

B X C =

Parallel Matrix Multiplication

  • Each image gets its own block of a, b, c.
  • Note [nrows,*]. Coarrays can have any corank(eg, number of codimensions)
  • Here, we make decomposition nrows x ncols.
  • Can set decomposition array-by-array.

samples/coarrays/blockmatrix.f90

Parallel Matrix Multiplication

  • Allocation, deallocation of coarrays is like a sync all
  • Forces synchronization across all images
  • Any particular coarray must have same size, co-size across all images

samples/coarrays/blockmatrix.f90

Parallel Matrix Multiplication

  • This is the entire parallel multiplication operation.
  • a[myrow,k] gets the entire a block from image at myrow,k.
  • matmul works with those blocks, updates c with new term.

samples/coarrays/blockmatrix.f90

Coarray Summary

  • Coarrays are powerful, simple-to-use addition to parallel programming models available
  • Will be widely available soon
  • Basic model implemented in Cray fortran for ~10 yrs; well tested and understood.
  • Typically implemented with MPI under the hood; can give performance similar to MPI with fewer lines of code.
  • Other languages have similar extensions (UPC based on C, Titanium based on Java) but are not part of languages’ standard.

Closing Hints

  • Always give the compiler info it needs to help you by being as explicit as possible
  • implicit none, end [construct] [name], parameters for constants, intent in/out, use only, etc.
  • Always get as much info from compiler as possible - always use -Wall (gfortran) or -warn all (ifort).

Useful Resources
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