Centre Blaise Pascal » Bench4GPU

#!/usr/bin/env python

#

# Ising2D model in serial mode

#

# CC BY-NC-SA 2011 : <emmanuel.quemener@ens-lyon.fr> 

import sys

import numpy

from PIL import Image

from math import exp

from random import random

import time

import getopt

import matplotlib.pyplot as plt

def ImageOutput(sigma,prefix):

    Max=sigma.max()

    Min=sigma.min()

    # Normalize value as 8bits Integer

    SigmaInt=(255*(sigma-Min)/(Max-Min)).astype('uint8')

    image = Image.fromarray(SigmaInt)

    image.save("%s.jpg" % prefix)

def Metropolis(sigma,J,B,T,iterations): 

    start=time.time()

    SizeX,SizeY=sigma.shape

    for p in xrange(0,iterations):

        # Random access coordonate

        X,Y=numpy.random.randint(SizeX),numpy.random.randint(SizeY)

        DeltaE=sigma[X,Y]*(2.*J*(sigma[X,(Y+1)%SizeY]+

                                 sigma[X,(Y-1)%SizeY]+

                                 sigma[(X-1)%SizeX,Y]+

                                 sigma[(X+1)%SizeX,Y])+B)

        if DeltaE < 0. or random() < exp(-DeltaE/T):

            sigma[X,Y]=-sigma[X,Y]

    duration=time.time()-start

    return(duration)

def Magnetization(sigma,M):

    return(numpy.sum(sigma)/(sigma.shape[0]*sigma.shape[1]*1.0))

def Energy(sigma,J,B):

    # Copier et caster 

    E=numpy.copy(sigma).astype(numpy.float32)

    # Appel par slice

    E[1:-1,1:-1]=E[1:-1,1:-1]*(2.*J*(E[:-2,1:-1]+E[2:,1:-1]+

                                     E[1:-1,:-2]+E[1:-1,2:])+B)

    # Bien nettoyer la peripherie

    E[:,0]=0

    E[:,-1]=0

    E[0,:]=0

    E[-1,:]=0

    Energy=numpy.sum(E)

    return(Energy/(E.shape[0]*E.shape[1]*1.0))

def CriticalT(T,E):

    Epoly=numpy.poly1d(numpy.polyfit(T,E,T.size/3))

    dEpoly=numpy.diff(Epoly(T))

    dEpoly=numpy.insert(dEpoly,0,0)

    return(T[numpy.argmin(dEpoly)])

def DisplayCurves(T,E,M,J,B):

    plt.xlabel("Temperature")

    plt.ylabel("Energy")

    Experience,=plt.plot(T,E,label="Energy") 

    plt.legend()

    plt.show()

if __name__=='__main__':

    # Set defaults values

    # Coupling factor

    J=1.

    # Magnetic Field

    B=0.

    # Size of Lattice

    Size=256

    # Default Temperatures (start, end, step)

    Tmin=0.1

    Tmax=5

    Tstep=0.1

    # Default Number of Iterations

    Iterations=Size*Size*Size

    # Curves is True to print the curves

    Curves=False

    try:

        opts, args = getopt.getopt(sys.argv[1:],"hcj:b:z:i:s:e:p:",["coupling=","magneticfield=","size=","iterations=","tempstart=","tempend=","tempstep="])

    except getopt.GetoptError:

        print '%s -j <Coupling Factor> -b <Magnetic Field> -z <Size of Square Lattice> -i <Iterations> -s <Minimum Temperature> -e <Maximum Temperature> -p <steP Temperature> -c (Print Curves)' % sys.argv[0]

        sys.exit(2)

    for opt, arg in opts:

        if opt == '-h':

            print '%s -j <Coupling Factor> -b <Magnetic Field> -z <Size of Square Lattice> -i <Iterations> -s <Minimum Temperature> -e <Maximum Temperature> -p <steP Temperature> -c (Print Curves)' % sys.argv[0]

            sys.exit()

        elif opt == '-c':

            Curves=True

        elif opt in ("-j", "--coupling"):

            J = float(arg)

        elif opt in ("-b", "--magneticfield"):

            B = float(arg)

        elif opt in ("-s", "--tempmin"):

            Tmin = float(arg)

        elif opt in ("-e", "--tempmax"):

            Tmax = float(arg)

        elif opt in ("-p", "--tempstep"):

            Tstep = float(arg)

        elif opt in ("-i", "--iterations"):

            Iterations = int(arg)

        elif opt in ("-z", "--size"):

            Size = int(arg)

    print "Coupling Factor : %s" % J

    print "Magnetic Field :  %s" % B

    print "Size of square lattice : %s" % Size

    print "Iterations : %s" % Iterations

    print "Temperature on start : %s" % Tmin

    print "Temperature on end : %s" % Tmax

    print "Temperature step : %s" % Tstep

    LAPIMAGE=False

    sigmaIn=numpy.where(numpy.random.randn(Size,Size)>0,1,-1).astype(numpy.int8)

    ImageOutput(sigmaIn,"Ising2D_Serial_%i_Initial" % (Size))

    Trange=numpy.arange(Tmin,Tmax+Tstep,Tstep)

    E=[]

    M=[]

    for T in Trange:

        # Indispensable d'utiliser copy : [:] ne fonctionne pas avec numpy !

        sigma=numpy.copy(sigmaIn)

        duration=Metropolis(sigma,J,B,T,Iterations)

        E=numpy.append(E,Energy(sigma,J,B))

        M=numpy.append(M,Magnetization(sigma,B))

        ImageOutput(sigma,"Ising2D_Serial_%i_%1.1f_Final" % (Size,T))

        print "CPU Time : %f" % (duration)

        print "Total Energy at Temperature %f : %f" % (T,E[-1])

        print "Total Magnetization at Temperature %f : %f" % (T,M[-1])

    if Curves:

        DisplayCurves(Trange,E,M,J,B)

    # Save output

    numpy.savez("Ising2D_Serial_%i_%.8i" % (Size,Iterations),(Trange,E,M))

    # Estimate Critical temperature

    print "The critical temperature on %ix%i lattice with J=%f, B=%f is %f " % (Size,Size,J,B,CriticalT(Trange,E))