Centre Blaise Pascal » Bench4GPU

#!/usr/bin/env python

#!/usr/bin/env python

#

# Ising2D model using mpi4py MPI implementation for Python

#

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

#

# Thanks to Lisandro Dalcin for MPI4PY :

# http://mpi4py.scipy.org/

import sys

import numpy

#import pylab

from PIL import Image

from math import exp

from random import random

import time

# MPI librairie call

from mpi4py import MPI

import getopt

import matplotlib.pyplot as plt

LAPIMAGE=False

def partition ( lst, n ):

    return [ lst[i::n] for i in xrange(n) ]

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 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()

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))

if __name__=='__main__':

    ToSave=[]

    # MPI Init

    comm = MPI.COMM_WORLD

    rank = comm.Get_rank()

    # Define number of Nodes on with computing is performed (exclude 0)

    NODES=comm.Get_size()-1

    # pass explicit MPI datatypes

    if rank == 0:

        # 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=","units"])

        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 = arg

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

                    Tstep = numpy.uint32(arg)

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

                    Iterations = int(arg)

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

                    Size = int(arg)

        print "Coupling Factor J : %s" % J

        print "Magnetic Field B :  %s" % B

        print "Size of 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_MPI_%i_Initial" % (Size))

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

        sigmaIn=numpy.where(numpy.random.randn(Size,Size)>0

                            ,1,-1).astype(numpy.int8)

        numpy.random.seed(int(time.time()))

        # Master control distribution of computing

        print "Distributing work to %i node(s)..." % NODES

        Distribution=numpy.array_split(Trange,NODES)

        for i in range(NODES):

            Input=Distribution[i]

            print "Send from 0 to %i %s" % (i+1,Input)

            ToSend=sigmaIn,J,B,Iterations,Input

            # Send MPI call to each node

            comm.send(ToSend, dest=i+1, tag=11)

        print "Retreive results..."

        Results=[]

        for i in range(NODES):

            # Receive MPI call from each node

            Output=comm.recv(source=i+1,tag=11)

            print "Result from %i: %s" % (i+1,Output)

            Results+=Output

        E=numpy.array(Results)[:,1]

        M=numpy.array(Results)[:,2]

        numpy.savez("Ising2D_MPI_%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))

        if Curves:

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

    else:

        numpy.random.seed(int(time.time()/rank))

        # Slave applies simulation to set provided by master

        # Receive MPI call with Input set

        ToSplit=comm.recv(source=0, tag=11)

        sigmaIn,J,B,Iterations,Input=ToSplit

        print "Rank %i receive with %ix%i lattice at J=%.2f, B=%.2f with %i iterations and T=%s" % (rank,sigmaIn.shape[0],sigmaIn.shape[1],J,B,Iterations,Input)

        Output=[]

        # Launch simulations on the set, one by one

        for T in Input:

            print "Processing T=%.2f on rank %i" % (T,rank)

            # Reinitialize to original

            sigma=numpy.copy(sigmaIn)

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

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

            E=Energy(sigma,J,B)

            M=Magnetization(sigma,0.)

            ImageOutput(sigma,"Ising2D_MPI_%i_%1.1f_Final" %

                        (sigmaIn.shape[0],T))

            Output.append([T,E,M])

        comm.send(Output, dest=0, tag=11)