Path integral in Matlab

I know that doing Feynman path Integral on Matlab is time consuming compare to Fortran or C.

However, do someone have a Matlab code of harmonic oscillator via path integral? I didn't manage to find any on the web (and even on Matlab forum).

Below a Fortran code which I don't know how to translate to Matlab (I am novice) Thanks, Joni

!         qmc . f90 : Feynman path i n t e g r a l for ground s t a t e wave Function
Program  qmc
  Implicit   none
  Integer   ::   i,j ,  max ,   element ,  prop ( 100 )
  Real *8   ::   change ,   ranDom , energy , newE , oldE , out , path ( 100 )
  max = 250000
  open ( 9 , FILE  =  ’qmc.dat’ , Status  =  ’Unknown’ )
                                             !   initial   path  and  开发者_Python百科probability
  Do  j  = 1 , 100
    path (j) = 0.0
    prop (j) = 0
  End  Do
                                              !   find   energy of initial path
  oldE  =  energy(path , 100)
                                     !   pick  random  element ,   change  by  random
  Do   i = 1 ,  max
    element  =  ranDom ( )*100 + 1
    change   =  ((ranDom() - 0.5)*2)
    path (element) =  path(element) + change
    newE  =  energy ( path , 100)       !   find  new  energy
                                      !   Metropolis   algorithm
    If   ((newE > oldE) .AND. (exp( - newE + oldE )  <  ranDom ()))   then
      path (element)  =  path (element) - change
    EndIf
                                                     !   add  up probabilities
    Do  j = 1 , 100
      element = path(j)*10 + 50
      prop (element) = prop(element) + 1
    End  Do
    oldE = newE
  End  Do
                                !   write  output data to file
  Do   j = 1 , 100
    out  =  prop(j)
    write (9 , *) j - 50 , out/max
  End  Do
  close (9)
  Stop  ’data  saved  in  qmc.dat’
End  Program  qmc
!   Function   calculates   energy   of   the  system
Function   energy ( array ,  max )
  Implicit   none
  Integer ::   i ,  max
  Real*8   ::   energy , array (max)
  energy = 0
  Do  i = 1 , (max - 1)
    energy = energy + (array(i+ 1) - array(i))**2 + array(i)**2
    End  Do
  Return
End

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This is an open source code for calculating Feynman integrals in MATLAB: http://arxiv.org/pdf/1205.6872v1.pdf which can be run on any ordinary CPU and much faster on a GPU.

Since it only uses extremely efficient built-in MATLAB functions which are compiled to machine code, it's not expected to be significantly slower than FORTRAN or C (keeping in mind that the computational cost of calculating Feynman integrals scales exponentially with respect to the number of time steps, meaning that FORTRAN, C, and MATLAB will all be slow in many cases, and the differences between them will be much smaller than the difference between taking 12 time steps and 13 time steps).

If you run this MATLAB code on a GPU it will in fact be faster than the FORTRAN or C implementation (only a CUDA FORTRAN or CUDA C code will be able to compare).

If you have more questions about this code you can email the author at dattani.nike@gmail.com