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Minimization of Internal Function

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HughPhilly

HughPhilly

Programmer
Jul 25, 2010
3
US
Hi guys,
I am a newby to Fortran programming, so this problem might be very simple to many of you.

Goal: Minimize internal function using Nelder-Mead subroutine. Internal function uses global variables..

Situation: Function is defined within program under 'contains'. So it is internal and it is defined by some global variables.. (My work environment is Linux Ubuntu 10.04, Gfortran, Fortran 90.)

Problem: When I compile the main and minimization subroutine (gfortran Internal_Function_Minimization.f90 Simples_routine.f90), I get a message 'undefined reference to internal function'.


I am attaching my code. It has two files. One is the main program file contains objective function to be minimized. The other file is Nelder-Mead Minimization subroutine.

The global variable is 'i' which is an iterator and it is used to define the internal function..


How can I hold the global variable and just minimize the internal function in terms of the local variables?


I really appreciate your help in advance.
 
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The code you posted is lousy. I corected
Code: 
    write ynewlo ! this should be always zero.
to
Code: 
    write (*,*)  ynewlo ! this should be always zero.
but then I got an error
Code: 
In file Internal_function.f90:11

    write (*,*)  ynewlo ! this should be always zero.
                 1
Error: Symbol 'ynewlo' at (1) has no IMPLICIT type
What should be ynewlo ?
And what is this ?
Code: 
    call Test01
I couldn't find any subroutine Test01 in the source you posted...

 
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Thanks mikrom. Sorry for the previous code -- I had to upload the newer version. Here is the new version but I still get the same message "undefined reference to internal_function".

ynewlo is the 'intent(out)' variable from 'nelmin' subroutine. It is the minimized value of the objective function, Internal_Function.

Thanks
Hugh
 
 http://www.mediafire.com/file/zgei68idddxa6oe/Internal_Function.f90
Upvote 0 Downvote
I changed a little bit your program, so the function now uses assumed-size array:
Code: 
Program Internal_Function_Minimization
Implicit None
integer ( kind = 4 ) n
Integer*4 :: i
Real*8 :: ynewlo
real    ( kind = 8 ) vec(2)

vec = (/1.0D+00,1.0D+00/)
Do i=1,4
    write(*,*) Internal_Function(vec)
End Do

Do i=1,4
    call minimization
    write(*,*) ynewlo ! This is a minized value. This should be always zero.
End Do


Contains

subroutine minimization


  implicit none

  integer ( kind = 4 ), parameter :: n = 2

  integer ( kind = 4 ) i
  integer ( kind = 4 ) icount
  integer ( kind = 4 ) ifault
  integer ( kind = 4 ) kcount
  integer ( kind = 4 ) konvge
  integer ( kind = 4 ) numres
  real    ( kind = 8 ) reqmin
  real    ( kind = 8 ) start(n)
  real    ( kind = 8 ) step(n)
  real    ( kind = 8 ) xmin(n)
  real    ( kind = 8 ) ynewlo

  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'TEST01'
  write ( *, '(a)' ) '  Apply NELMIN to Internal function.'

  start(1) = -1.2D+00
  start(2) =  1.0D+00

  reqmin = 1.0D-08

  step(1) = 1.0D+00
  step(2) = 1.0D+00

  konvge = 10
  kcount = 500

  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) '  Starting point X:'
  write ( *, '(a)' ) ' '
  do i = 1, n
    write ( *, '(2x,g14.6)' ) start(i)
  end do

  ynewlo = Internal_Function (start)

  write ( *, '(a)' ) ' '
  write ( *, '(a,g14.6)' ) '  F(X) = ', ynewlo

  call nelmin ( Internal_Function, n, start, xmin, ynewlo, reqmin, step, &
    konvge, kcount, icount, numres, ifault )

  write ( *, '(a)' ) ' '
  write ( *, '(a,i8)' ) '  Return code IFAULT = ', ifault
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) '  Estimate of minimizing value X*:'
  write ( *, '(a)' ) ' '
  do i = 1, n
    write ( *, '(2x,g14.6)' ) xmin(i)
  end do

  write ( *, '(a)' ) ' '
  write ( *, '(a,g14.6)' ) '  F(X*) = ', ynewlo

  write ( *, '(a)' ) ' '
  write ( *, '(a,i8)' ) '  Number of iterations = ', icount
  write ( *, '(a,i8)' ) '  Number of restarts =   ', numres

  return
end subroutine minimization

Real*8 Function Internal_Function (vec)
Implicit None
Real*8 :: vec(*)

Internal_Function = vec(1)**2 + vec(2)**2
End Function Internal_Function

End Program Internal_Function_Minimization
It compiles now with g95 and runs
Code: 
$ g95 internal_function.f90 simplex_routine.f90 -o min
But it doesn't compile with gfortran.
To compile it with gfortran you must not declare the function in the contains section together with the subroutine, but after the program:
Code: 
Program Internal_Function_Minimization
Implicit None
integer ( kind = 4 ) n
Integer*4 :: i
Real*8 :: ynewlo
real    ( kind = 8 ) vec(2)
real    ( kind = 8 ) :: internal_function

vec = (/1.0D+00,1.0D+00/)
Do i=1,4
    write(*,*) Internal_Function(vec)
End Do

Do i=1,4
    call minimization
    write(*,*) ynewlo ! This is a minized value. This should be always zero.
End Do

Contains

subroutine minimization
  implicit none

  integer ( kind = 4 ), parameter :: n = 2

  integer ( kind = 4 ) i
  integer ( kind = 4 ) icount
  integer ( kind = 4 ) ifault
  integer ( kind = 4 ) kcount
  integer ( kind = 4 ) konvge
  integer ( kind = 4 ) numres
  real    ( kind = 8 ) reqmin
  real    ( kind = 8 ) start(n)
  real    ( kind = 8 ) step(n)
  real    ( kind = 8 ) xmin(n)
  real    ( kind = 8 ) ynewlo
  real    ( kind = 8 ) :: internal_function

  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'TEST01'
  write ( *, '(a)' ) '  Apply NELMIN to Internal function.'

  start(1) = -1.2D+00
  start(2) =  1.0D+00

  reqmin = 1.0D-08

  step(1) = 1.0D+00
  step(2) = 1.0D+00

  konvge = 10
  kcount = 500

  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) '  Starting point X:'
  write ( *, '(a)' ) ' '
  do i = 1, n
    write ( *, '(2x,g14.6)' ) start(i)
  end do

  ynewlo = Internal_Function (start)

  write ( *, '(a)' ) ' '
  write ( *, '(a,g14.6)' ) '  F(X) = ', ynewlo

  call nelmin ( Internal_Function, n, start, xmin, ynewlo, reqmin, step, &
    konvge, kcount, icount, numres, ifault )

  write ( *, '(a)' ) ' '
  write ( *, '(a,i8)' ) '  Return code IFAULT = ', ifault
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) '  Estimate of minimizing value X*:'
  write ( *, '(a)' ) ' '
  do i = 1, n
    write ( *, '(2x,g14.6)' ) xmin(i)
  end do

  write ( *, '(a)' ) ' '
  write ( *, '(a,g14.6)' ) '  F(X*) = ', ynewlo

  write ( *, '(a)' ) ' '
  write ( *, '(a,i8)' ) '  Number of iterations = ', icount
  write ( *, '(a,i8)' ) '  Number of restarts =   ', numres

  return
end subroutine minimization

End Program Internal_Function_Minimization

Real*8 Function Internal_Function (vec)
Implicit None
Real*8 :: vec(*)

Internal_Function = vec(1)**2 + vec(2)**2
End Function Internal_Function
it compiles and runs
Code: 
$ gfortran internal_function.f90 simplex_routine.f90 -o min
Other solution is not to use contains section of the program and declare the function and the subroutine after the main program:
Code: 
Program Internal_Function_Minimization
Implicit None
integer ( kind = 4 ) n
Integer*4 :: i
Real*8 :: ynewlo
real    ( kind = 8 ) vec(2)
real    ( kind = 8 ) :: internal_function

vec = (/1.0D+00,1.0D+00/)
Do i=1,4
    write(*,*) Internal_Function(vec)
End Do

Do i=1,4
    call minimization
    write(*,*) ynewlo ! This is a minized value. This should be always zero.
End Do
End Program Internal_Function_Minimization

subroutine minimization
  implicit none

  integer ( kind = 4 ), parameter :: n = 2

  integer ( kind = 4 ) i
  integer ( kind = 4 ) icount
  integer ( kind = 4 ) ifault
  integer ( kind = 4 ) kcount
  integer ( kind = 4 ) konvge
  integer ( kind = 4 ) numres
  real    ( kind = 8 ) reqmin
  real    ( kind = 8 ) start(n)
  real    ( kind = 8 ) step(n)
  real    ( kind = 8 ) xmin(n)
  real    ( kind = 8 ) ynewlo
  real    ( kind = 8 ) :: internal_function

  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'TEST01'
  write ( *, '(a)' ) '  Apply NELMIN to Internal function.'

  start(1) = -1.2D+00
  start(2) =  1.0D+00

  reqmin = 1.0D-08

  step(1) = 1.0D+00
  step(2) = 1.0D+00

  konvge = 10
  kcount = 500

  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) '  Starting point X:'
  write ( *, '(a)' ) ' '
  do i = 1, n
    write ( *, '(2x,g14.6)' ) start(i)
  end do

  ynewlo = Internal_Function (start)

  write ( *, '(a)' ) ' '
  write ( *, '(a,g14.6)' ) '  F(X) = ', ynewlo

  call nelmin ( Internal_Function, n, start, xmin, ynewlo, reqmin, step, &
    konvge, kcount, icount, numres, ifault )

  write ( *, '(a)' ) ' '
  write ( *, '(a,i8)' ) '  Return code IFAULT = ', ifault
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) '  Estimate of minimizing value X*:'
  write ( *, '(a)' ) ' '
  do i = 1, n
    write ( *, '(2x,g14.6)' ) xmin(i)
  end do

  write ( *, '(a)' ) ' '
  write ( *, '(a,g14.6)' ) '  F(X*) = ', ynewlo

  write ( *, '(a)' ) ' '
  write ( *, '(a,i8)' ) '  Number of iterations = ', icount
  write ( *, '(a,i8)' ) '  Number of restarts =   ', numres

  return
end subroutine minimization

Real*8 Function Internal_Function (vec)
Implicit None
Real*8 :: vec(*)

Internal_Function = vec(1)**2 + vec(2)**2
End Function Internal_Function
It compiles and runs - however I don't know if the result is correct or not :)
Code: 
$ gfortran internal_function.f90 simplex_routine.f90 -o min

$ min
   2.0000000000000000     
   2.0000000000000000     
   2.0000000000000000     
   2.0000000000000000     
 
TEST01
  Apply NELMIN to Internal function.
 
  Starting point X:
 
    -1.20000    
     1.00000    
 
  F(X) =    2.44000    
 
  Return code IFAULT =        0
 
  Estimate of minimizing value X*:
 
   -0.641388E-04
   -0.178307E-04
 
  F(X*) =   0.443172E-08
 
  Number of iterations =       67
  Number of restarts =          1
   0.0000000000000000     
 
TEST01
  Apply NELMIN to Internal function.
 
  Starting point X:
 
    -1.20000    
     1.00000    
 
  F(X) =    2.44000    
 
  Return code IFAULT =        0
 
  Estimate of minimizing value X*:
 
   -0.641388E-04
   -0.178307E-04
 
  F(X*) =   0.443172E-08
 
  Number of iterations =       67
  Number of restarts =          1
   0.0000000000000000     
 
TEST01
  Apply NELMIN to Internal function.
 
  Starting point X:
 
    -1.20000    
     1.00000    
 
  F(X) =    2.44000    
 
  Return code IFAULT =        0
 
  Estimate of minimizing value X*:
 
   -0.641388E-04
   -0.178307E-04
 
  F(X*) =   0.443172E-08
 
  Number of iterations =       67
  Number of restarts =          1
   0.0000000000000000     
 
TEST01
  Apply NELMIN to Internal function.
 
  Starting point X:
 
    -1.20000    
     1.00000    
 
  F(X) =    2.44000    
 
  Return code IFAULT =        0
 
  Estimate of minimizing value X*:
 
   -0.641388E-04
   -0.178307E-04
 
  F(X*) =   0.443172E-08
 
  Number of iterations =       67
  Number of restarts =          1
   0.0000000000000000
 
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