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ising_2d_simulation.f
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ising_2d_simulation.f
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program main
c*********************************************************************72
c
cc MAIN is the main program for ISING_2D_SIMULATION.
c
c Usage:
c
c ising_2d_simulation m n iterations thresh seed
c
c * M, N, the number of rows and columns.
c * ITERATIONS, the number of iterations.
c * THRESH, the threshhold.
c * SEED, a seed for the random number generator.
c
c Licensing:
c
c This code is distributed under the GNU LGPL license.
c
c Modified:
c
c 29 June 2013
c
c Author:
c
c John Burkardt
c
implicit none
integer i
integer iterations
integer m
integer n
double precision prob(5)
integer seed
integer step
double precision thresh
save prob
data prob /
& 0.98D+00, 0.85D+00, 0.50D+00, 0.15D+00, 0.02D+00 /
call timestamp ( )
write ( *, '(a)' ) ' '
write ( *, '(a)' ) 'ISING_2D_SIMULATION'
write ( *, '(a)' ) ' FORTRAN77 version'
write ( *, '(a)' ) ' Monte Carlo simulation of a 2D Ising model.'
c
c Get input from commandline or user.
c
call get_input ( m, n, iterations, thresh, seed )
write ( *, '(a)' ) ' '
write ( *, '(a,i8)' ) ' The number of rows is M = ', m
write ( *, '(a,i8)' ) ' The number of columns is N = ', n
write ( *, '(a,i8)' )
& ' The number of iterations taken is ITERATIONS = ', iterations
write ( *, '(a,g14.6)' ) ' The threshhold THRESH = ', thresh
write ( *, '(a,i12)' ) ' The seed SEED = ', seed
write ( *, '(a)' ) ' '
write ( *, '(a)' )
& ' The transition probability table, based on the number of'
write ( *, '(a)' ) ' neighbors with the same spin.'
write ( *, '(a)' ) ' '
write ( *, '(a)' )
& ' 1 2 3 4 5'
write ( *, '(a)' ) ' '
write ( *, '(7f10.4)' ) ( prob(i), i = 1, 5 )
c
c Do the simulation.
c I have to do this in a subroutine, so that I can dimension C1 on the fly.
c
call handle ( m, n, iterations, prob, thresh, seed )
c
c Terminate.
c
write ( *, '(a)' ) ' '
write ( *, '(a)' ) 'ISING_2D_SIMULATION'
write ( *, '(a)' ) ' Normal end of execution.'
write ( *, '(a)' ) ' '
call timestamp ( )
stop
end
subroutine ch_cap ( ch )
c*********************************************************************72
c
cc CH_CAP capitalizes a single character.
c
c Licensing:
c
c This code is distributed under the GNU LGPL license.
c
c Modified:
c
c 03 January 2007
c
c Author:
c
c John Burkardt
c
c Parameters:
c
c Input/output, character CH, the character to capitalize.
c
implicit none
character ch
integer itemp
itemp = ichar ( ch )
if ( 97 .le. itemp .and. itemp .le. 122 ) then
ch = char ( itemp - 32 )
end if
return
end
function ch_eqi ( c1, c2 )
c*********************************************************************72
c
cc CH_EQI is a case insensitive comparison of two characters for equality.
c
c Example:
c
c CH_EQI ( 'A', 'a' ) is TRUE.
c
c Licensing:
c
c This code is distributed under the GNU LGPL license.
c
c Modified:
c
c 03 January 2007
c
c Author:
c
c John Burkardt
c
c Parameters:
c
c Input, character C1, C2, the characters to compare.
c
c Output, logical CH_EQI, the result of the comparison.
c
implicit none
character c1
character c1_cap
character c2
character c2_cap
logical ch_eqi
c1_cap = c1
c2_cap = c2
call ch_cap ( c1_cap )
call ch_cap ( c2_cap )
if ( c1_cap == c2_cap ) then
ch_eqi = .true.
else
ch_eqi = .false.
end if
return
end
subroutine ch_to_digit ( c, digit )
c*********************************************************************72
c
cc CH_TO_DIGIT returns the integer value of a base 10 digit.
c
c Example:
c
c C DIGIT
c --- -----
c '0' 0
c '1' 1
c ... ...
c '9' 9
c ' ' 0
c 'X' -1
c
c Licensing:
c
c This code is distributed under the GNU LGPL license.
c
c Modified:
c
c 04 August 1999
c
c Author:
c
c John Burkardt
c
c Parameters:
c
c Input, character C, the decimal digit, '0' through '9' or blank
c are legal.
c
c Output, integer DIGIT, the corresponding integer value. If C was
c 'illegal', then DIGIT is -1.
c
implicit none
character c
integer digit
if ( lge ( c, '0' ) .and. lle ( c, '9' ) ) then
digit = ichar ( c ) - 48
else if ( c .eq. ' ' ) then
digit = 0
else
digit = -1
end if
return
end
subroutine get_input ( m, n, iterations, thresh, seed )
c*********************************************************************72
c
cc GET_INPUT gets input parameters.
c
c Licensing:
c
c This code is distributed under the GNU LGPL license.
c
c Modified:
c
c 02 November 2011
c
c Author:
c
c John Burkardt
c
c Parameters:
c
c Output, integer M, N, the number of rows and columns.
c
c Output, integer ITERATIONS, the number of iterations.
c
c Output, double precision THRESH, the threshhold.
c
c Output, integer SEED, a seed for the random
c number generator.
c
implicit none
integer arg_num
integer iarg
integer iargc
integer ierror
integer iterations
integer last
integer m
integer n
integer seed
character * ( 80 ) string
double precision thresh
arg_num = iargc ( )
if ( 1 .le. arg_num ) then
iarg = 1
call getarg ( iarg, string )
call s_to_i4 ( string, m, ierror, last )
else if ( .true. ) then
m = 10
else
write ( *, '(a)' ) ' '
write ( *, '(a)' ) ' Enter M, the number of rows:'
read ( *, * ) m
end if
if ( 2 .le. arg_num ) then
iarg = 2
call getarg ( iarg, string )
call s_to_i4 ( string, n, ierror, last )
else if ( .true. ) then
n = 10
else
write ( *, '(a)' ) ' '
write ( *, '(a)' ) ' Enter N, the number of columns:'
read ( *, * ) n
end if
if ( 3 .le. arg_num ) then
iarg = 3
call getarg ( iarg, string )
call s_to_i4 ( string, iterations, ierror, last )
else if ( .true. ) then
iterations = 15
else
write ( *, '(a)' ) ' '
write ( *, '(a)' ) ' Enter the number of iterations to take.'
read ( *, * ) iterations
end if
if ( 4 .le. arg_num ) then
iarg = 4
call getarg ( iarg, string )
call s_to_r8 ( string, thresh, ierror, last )
else if ( .true. ) then
thresh = 0.50D+00
else
write ( *, '(a)' ) ' '
write ( *, '(a)' ) ' Enter the threshhold.'
read ( *, * ) thresh
end if
if ( 5 .le. arg_num ) then
iarg = 5
call getarg ( iarg, string )
call s_to_i4 ( string, seed, ierror, last )
else if ( .true. ) then
seed = 123456789
else
write ( *, '(a)' ) ' '
write ( *, '(a)' ) ' Enter the random number seed.'
read ( *, * ) seed
end if
return
end
subroutine get_unit ( iunit )
c*********************************************************************72
c
cc GET_UNIT returns a free FORTRAN unit number.
c
c Discussion:
c
c A "free" FORTRAN unit number is a value between 1 and 99 which
c is not currently associated with an I/O device. A free FORTRAN unit
c number is needed in order to open a file with the OPEN command.
c
c If IUNIT = 0, then no free FORTRAN unit could be found, although
c all 99 units were checked (except for units 5, 6 and 9, which
c are commonly reserved for console I/O).
c
c Otherwise, IUNIT is a value between 1 and 99, representing a
c free FORTRAN unit. Note that GET_UNIT assumes that units 5 and 6
c are special, and will never return those values.
c
c Licensing:
c
c This code is distributed under the GNU LGPL license.
c
c Modified:
c
c 02 September 2013
c
c Author:
c
c John Burkardt
c
c Parameters:
c
c Output, integer IUNIT, the free unit number.
c
implicit none
integer i
integer iunit
logical value
iunit = 0
do i = 1, 99
if ( i .ne. 5 .and. i .ne. 6 .and. i .ne. 9 ) then
inquire ( unit = i, opened = value, err = 10 )
if ( .not. value ) then
iunit = i
return
end if
end if
10 continue
end do
return
end
subroutine handle ( m, n, iterations, prob, thresh, seed )
c*********************************************************************72
c
cc HANDLE does initialization, computation and output.
c
c Discussion:
c
c The main program picks up the dimensions M and N, so we have to
c call this subroutine so we can essentially allocate C1 on the fly.
c
c Licensing:
c
c This code is distributed under the GNU LGPL license.
c
c Modified:
c
c 29 June 2013
c
c Author:
c
c John Burkardt
c
c Parameters:
c
c Input, integer M, N, the number of rows and columns.
c
c Input, integer ITERATIONS, the number of iterations.
c
c Input, double precision PROB(1:5). PROB(I) represents the probability
c that the spin of a given cell will be reversed, given that it has I
c immediate neighbors (including itself) with spin the same as its own.
c
c Input, double precision THRESH, the threshhold.
c
c Input/output, integer SEED, a seed for the random number
c generator.
c
implicit none
integer m
integer n
integer c1(m,n)
integer iterations
double precision prob(1:5)
integer seed
double precision thresh
c
c Initialize the system.
c
call ising_2d_initialize ( m, n, thresh, seed, c1 )
!
! Write the initial state to a gnuplot file.
!
call plot_file ( m, n, c1, 'Initial Configuration',
& 'ising_2d_initial.txt', 'ising_2d_initial.png' )
!
! Do the simulation.
!
call transition ( m, n, iterations, prob, seed, c1 )
!
! Write the final state to a gnuplot file.
!
call plot_file ( m, n, c1, 'Final Configuration',
& 'ising_2d_final.txt', 'ising_2d_final.png' )
return
end
function i4_modp ( i, j )
c*********************************************************************72
c
cc I4_MODP returns the nonnegative remainder of integer division.
c
c Discussion:
c
c If
c NREM = I4_MODP ( I, J )
c NMULT = ( I - NREM ) / J
c then
c I = J * NMULT + NREM
c where NREM is always nonnegative.
c
c The MOD function computes a result with the same sign as the
c quantity being divided. Thus, suppose you had an angle A,
c and you wanted to ensure that it was between 0 and 360.
c Then mod(A,360) would do, if A was positive, but if A
c was negative, your result would be between -360 and 0.
c
c On the other hand, I4_MODP(A,360) is between 0 and 360, always.
c
c Example:
c
c I J MOD I4_MODP Factorization
c
c 107 50 7 7 107 = 2 * 50 + 7
c 107 -50 7 7 107 = -2 * -50 + 7
c -107 50 -7 43 -107 = -3 * 50 + 43
c -107 -50 -7 43 -107 = 3 * -50 + 43
c
c Licensing:
c
c This code is distributed under the GNU LGPL license.
c
c Modified:
c
c 30 December 2006
c
c Author:
c
c John Burkardt
c
c Parameters:
c
c Input, integer I, the number to be divided.
c
c Input, integer J, the number that divides I.
c
c Output, integer I4_MODP, the nonnegative remainder when I is
c divided by J.
c
implicit none
integer i
integer i4_modp
integer j
integer value
if ( j .eq. 0 ) then
write ( *, '(a)' ) ' '
write ( *, '(a)' ) 'I4_MODP - Fatal error!'
write ( *, '(a,i8)' ) ' Illegal divisor J = ', j
stop
end if
value = mod ( i, j )
if ( value .lt. 0 ) then
value = value + abs ( j )
end if
i4_modp = value
return
end
function i4_wrap ( ival, ilo, ihi )
c*********************************************************************72
c
cc I4_WRAP forces an I4 to lie between given limits by wrapping.
c
c Example:
c
c ILO = 4, IHI = 8
c
c I Value
c
c -2 8
c -1 4
c 0 5
c 1 6
c 2 7
c 3 8
c 4 4
c 5 5
c 6 6
c 7 7
c 8 8
c 9 4
c 10 5
c 11 6
c 12 7
c 13 8
c 14 4
c
c Licensing:
c
c This code is distributed under the GNU LGPL license.
c
c Modified:
c
c 31 December 2006
c
c Author:
c
c John Burkardt
c
c Parameters:
c
c Input, integer IVAL, an integer value.
c
c Input, integer ILO, IHI, the desired bounds for the integer value.
c
c Output, integer I4_WRAP, a "wrapped" version of IVAL.
c
implicit none
integer i4_modp
integer i4_wrap
integer ihi
integer ilo
integer ival
integer jhi
integer jlo
integer value
integer wide
jlo = min ( ilo, ihi )
jhi = max ( ilo, ihi )
wide = jhi - jlo + 1
if ( wide .eq. 1 ) then
value = jlo
else
value = jlo + i4_modp ( ival - jlo, wide )
end if
i4_wrap = value
return
end
subroutine ising_2d_agree ( m, n, c1, c5 )
c*********************************************************************72
c
cc ISING_2D_AGREE returns the number of neighbors agreeing with each cell.
c
c Discussion:
c
c The count includes the cell itself, so it is between 1 and 5.
c
c Licensing:
c
c This code is distributed under the GNU LGPL license.
c
c Modified:
c
c 22 November 2011
c
c Author:
c
c John Burkardt
c
c Parameters:
c
c Input, integer M, N, the number of cells in each
c spatial dimension.
c
c Input, integer C1(M,N), an array of 1's and -1's.
c
c Output, integer C5(M,N), the number of neighbors
c that agree. 1, 2, 3, 4, or 5.
c
implicit none
integer m
integer n
integer c1(m,n)
integer c5(m,n)
integer i
integer i4_wrap
integer im
integer ip
integer j
integer jm
integer jp
do j = 1, n
jp = i4_wrap ( j + 1, 1, n )
jm = i4_wrap ( j - 1, 1, n )
do i = 1, m
ip = i4_wrap ( i + 1, 1, m )
im = i4_wrap ( i - 1, 1, m )
c5(i,j) = c1(i,j) + c1(ip,j) + c1(im,j) + c1(i,jm) + c1(i,jp)
end do
end do
do j = 1, n
do i = 1, m
if ( 0 .lt. c1(i,j) ) then
c5(i,j) = ( 5 + c5(i,j) ) / 2
else
c5(i,j) = ( 5 - c5(i,j) ) / 2
end if
end do
end do
return
end
subroutine ising_2d_initialize ( m, n, thresh, seed, c1 )
c*********************************************************************72
c
cc ISING_2D_INITIALIZE initializes the Ising array.
c
c Licensing:
c
c This code is distributed under the GNU LGPL license.
c
c Modified:
c
c 22 November 2011
c
c Author:
c
c John Burkardt
c
c Parameters:
c
c Input, integer M, N, the number of rows and columns.
c
c Input, double precision THRESH, the threshhold.
c
c Input/output, integer SEED, a seed for the random
c number generator.
c
c Output, integer C1(M,N), the initial Ising array.
c
implicit none
integer m
integer n
integer c1(m,n)
integer i
integer j
double precision r(m,n)
double precision thresh
integer seed
call r8mat_uniform_01 ( m, n, seed, r )
do j = 1, n
do i = 1, m
if ( r(i,j) .le. thresh ) then
c1(i,j) = -1
else
c1(i,j) = +1
end if
end do
end do
return
end
subroutine ising_2d_stats ( step, m, n, c1 )
c*********************************************************************72
c
cc ISING_2D_STATS prints information about the current step.
c
c Licensing:
c
c This code is distributed under the GNU LGPL license.
c
c Modified:
c
c 22 November 2011
c
c Author:
c
c John Burkardt
c
c Parameters:
c
c Input, integer STEP, the step number.
c
c Input, integer M, N, the number of rows and columns.
c
c Input, integer C1(M,N), the current state of the system.
c
implicit none
integer m
integer n
integer c1(m,n)
integer i
integer j
integer pos_count
double precision pos_percent
integer step
integer neg_count
double precision neg_percent
if ( step == 0 ) then
write ( *, '(a)' ) ' '
write ( *, '(a)' ) ' Step Positives Negatives'
write ( *, '(a)' ) ' # % # %'
write ( *, '(a)' ) ' '
end if
pos_count = 0
do j = 1, n
do i = 1, m
if ( 0 .lt. c1(i,j) ) then
pos_count = pos_count + 1
end if
end do
end do
neg_count = m * n - pos_count
pos_percent = dble ( 100 * pos_count ) / dble ( m * n )
neg_percent = dble ( 100 * neg_count ) / dble ( m * n )
write ( *, '(2x,i4,2x,i6,2x,f6.2,2x,i6,2x,f6.2)' )
& step, pos_count, pos_percent, neg_count, neg_percent
return
end
subroutine neighbor_2d_stats ( step, m, n, c1, c5 )
c*********************************************************************72
c
cc NEIGHBOR_2D_STATS prints neighbor statistics about the current step.
c
c Licensing:
c
c This code is distributed under the GNU LGPL license.
c
c Modified:
c
c 22 November 2011
c
c Author:
c
c John Burkardt
c
c Parameters:
c
c Input, integer STEP, the step number.
c
c Input, integer M, N, the number of rows and columns.
c
c Input, integer C1(M,N), the current state of the system.
c
c Input, integer C5(M,N), the number of agreeable neighbors.
c
implicit none
integer m
integer n
integer c1(m,n)
integer c5(m,n)
integer i
integer j
integer k
integer stats(-5:5)
integer step
if ( step .eq. 0 ) then
write ( *, '(a)' ) ' '
write ( *, '(a)' ) ' Step Neighborhood Charge:'
write ( *, '(a)' )
& ' -5 -4 -3 -2 -1' //
& ' +1 +2 +3 +4 +5'
write ( *, '(a)' ) ' '
end if
do i = -5, 5
stats(i) = 0
end do
do j = 1, n
do i = 1, m
stats(c5(i,j)) = stats(c5(i,j)) + 1
end do
end do
write ( *, '(2x,i4,10(2x,i4))' )
& step, ( stats(i), i = -5,-1), ( stats(i), i = 1, 5)
return
end
subroutine plot_file ( m, n, c1, title, plot_filename,
& png_filename )
c*********************************************************************72
c
cc PLOT_FILE writes the current configuration to a GNUPLOT plot file.
c
c Licensing:
c
c This code is distributed under the GNU LGPL license.
c
c Modified:
c
c 29 June 2013
c
c Author:
c
c John Burkardt
c
c Parameters:
c
c Input, integer M, N, the number of rows and columns.
c
c Input, integer C1(M,N), the current state of the system.
c
c Input, character * ( * ) TITLE, a title for the plot.
c
c Input, character * ( * ) PLOT_FILENAME, a name for the GNUPLOT
c command file to be created.
c
c Input, character * ( * ) PNG_FILENAME, the name of the PNG graphics
c file to be created.
c
implicit none
integer m
integer n
integer c1(m,n)
integer i
integer j
character * ( * ) plot_filename
integer plot_unit
character * ( * ) png_filename
double precision ratio
character * ( * ) title
integer x1
integer x2
integer y1
integer y2
call get_unit ( plot_unit )
open ( unit = plot_unit, file = plot_filename,
& status = 'replace' )
ratio = dble ( n ) / dble ( m )
write ( plot_unit, '(a)' ) 'set term png'
write ( plot_unit, '(a)' )
& 'set output "' // trim ( png_filename ) // '"'
write ( plot_unit, '(a,i4,a)' ) 'set xrange [ 0 : ', m, ' ]'
write ( plot_unit, '(a,i4,a)' ) 'set yrange [ 0 : ', n, ' ]'
write ( plot_unit, '(a)' ) 'set nokey'
write ( plot_unit, '(a)' ) 'set title "' // trim ( title ) // '"'
write ( plot_unit, '(a)' ) 'unset tics'
write ( plot_unit, '(a,g14.6)' ) 'set size ratio ', ratio
do j = 1, n
y1 = j - 1
y2 = j
do i = 1, m
x1 = m - i
x2 = m + 1 - i
if ( c1(i,j) .lt. 0 ) then
write ( plot_unit, '(a,i3,a,i3,a,i3,a,i3,a)' )
& 'set object rectangle from ',
& x1, ',', y1, ' to ', x2, ',', y2, ' fc rgb "blue"'
else
write ( plot_unit, '(a,i3,a,i3,a,i3,a,i3,a)' )
& 'set object rectangle from ',
& x1, ',', y1, ' to ', x2, ',', y2, ' fc rgb "red"'
end if
end do
end do
write ( plot_unit, '(a)' ) 'plot 1'
write ( plot_unit, '(a)' ) 'quit'
close ( unit = plot_unit )
write ( *, '(a)' ) ' '
write ( *, '(a)' ) ' Created the gnuplot graphics file "' //
& trim ( plot_filename ) // '".'
return
end
subroutine r8mat_uniform_01 ( m, n, seed, r )
c*********************************************************************72
c
cc R8MAT_UNIFORM_01 returns a unit pseudorandom R8MAT.
c
c Discussion:
c
c An R8MAT is an array of R8's.
c
c Licensing:
c
c This code is distributed under the GNU LGPL license.
c
c Modified:
c
c 11 August 2004
c
c Author:
c
c John Burkardt
c
c Reference:
c
c Paul Bratley, Bennett Fox, Linus Schrage,
c A Guide to Simulation,
c Springer Verlag, pages 201-202, 1983.
c