{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Monte Carlo integration by Vegas" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Brute force Monte Carlo" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First we will implement the simple Monte Carlo method." ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# simple class to take care of statistically determined quantities\n", "class Cumulants:\n", " def __init__(self):\n", " self.sum=0.0 # f_0 + f_1 +.... + f_N\n", " self.sqsum=0.0 # f_0^2 + f_1^2 +....+ f_N^2\n", " self.avg = 0.0 # = 1/N\\sum_i f_i\n", " self.err = 0.0 # sqrt( -^2 )/sqrt(N)\n", " self.chisq = 0.0\n", " self.weightsum=0.0\n", " self.avgsum=0.0\n", " self.avg2sum=0.0\n", "\n", "def SimpleMC(integrant, ndim, unit, maxeval, cum):\n", " nbatch=1000 # function will be evaluated in bacthes of 1000 evaluations at one time (for efficiency and storage issues)\n", " neval=0\n", " for nsamples in range(maxeval,0,-nbatch): # loop over all_nsample evaluations in batches of nbatch\n", " n = min(nbatch,nsamples) # How many evaluations in this pass?\n", " xr = unit*random.random((n,ndim)) # generates 2-d array of random numbers in the interval [0,1)\n", " wfun = integrant(xr) # n function evaluations required in single call\n", " neval += n # We just added so many fuction evaluations\n", " cum.sum += sum(wfun) # sum_i f_i*w_i = \n", " cum.sqsum += sum(wfun*wfun) # sum_i (f_i*w_i)^2 = /all_nsamples\n", " \n", " cum.avg = cum.sum/neval\n", " w0 = sqrt(cum.sqsum/neval) # sqrt()\n", " cum.err = sqrt((w0-cum.avg)*(w0+cum.avg)/neval) # sqrt(sqsum-sum**2)\n", " cum.avg *= unit**ndim # adding units if not [0,1] interval\n", " cum.err *= unit**ndim # adding units if not [0,1] interval" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We used here a simple trick to avoid overflow, i.e.,\n", "\n", "\\begin{eqnarray}\n", "\\sqrt{\\frac{\\langle f^2\\rangle-\\langle f\\rangle^2}{N}} = \n", "\\sqrt{\\frac{(\\sqrt{\\langle f^2\\rangle}-\\langle f\\rangle)(\\sqrt{\\langle f^2\\rangle}+\\langle f\\rangle)}{N}}\n", "\\end{eqnarray}" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def my_integrant2(x):\n", " \"\"\" For testing, we are integration the function\n", " 1/(1-cos(x)*cos(y)*cos(z))/pi^3\n", " in the interval [0,pi]**3\n", " \"\"\"\n", " #nbatch,ndim = shape(x)\n", " return 1.0/(1.0-cos(x[:,0])*cos(x[:,1])*cos(x[:,2]))/pi**3" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.38924672373 +- 0.0119310201204 exact= 1.3932\n" ] } ], "source": [ "from scipy import *\n", "unit=pi\n", "ndim=3\n", "maxeval=200000\n", "exact = 1.3932 # exact value of the integral\n", " \n", "cum = Cumulants()\n", " \n", "SimpleMC(my_integrant2, ndim, pi, maxeval, cum)\n", "print cum.avg, '+-', cum.err, 'exact=', exact" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Vegas" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First we define the grid points $g(x)$. At the beginning, we just set $g(x)=x$." ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": true }, "outputs": [], "source": [ "class Grid:\n", " \"\"\"Contains the grid points g_n(x) with x=[0...1], and g=[0...1]\n", " for Vegas integration. There are n-dim g_n functions.\n", " Constraints : g(0)=0 and g(1)=1.\n", " \"\"\"\n", " def __init__(self, ndim, nbins):\n", " self.g = zeros((ndim,nbins+1))\n", " self.ndim=ndim\n", " self.nbins=nbins\n", " # At the beginning we set g(x)=x\n", " # The grid-points are x_0 = 1/N, x_1 = 2/N, ... x_{N-1}=1.0. \n", " # Note that g(0)=0, and we skip this point on the mesh.\n", " for ibin in range(nbins):\n", " w = (ibin + 1.0)/nbins \n", " self.g[:,ibin] = w # grids in all dimensions are the same at the beginning (g(x)=x)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def Vegas_step1(integrant, unit, maxeval, nstart, nincrease, grid, cum):\n", " ndim, nbins = grid.ndim,grid.nbins # dimension of the integral, size of the grid for binning in each direction\n", " unit_dim = unit**ndim # converts from unit cube integration to generalized cube with unit length\n", " nbatch=1000 # function will be evaluated in bacthes of 1000 evaluations at one time (for efficiency and storage issues)\n", " neval=0\n", " print \"\"\"Vegas parameters:\n", " ndim = \"\"\"+str(ndim)+\"\"\"\n", " unit = \"\"\"+str(unit)+\"\"\"\n", " maxeval = \"\"\"+str(maxeval)+\"\"\"\n", " nstart = \"\"\"+str(nstart)+\"\"\"\n", " nincrease = \"\"\"+str(nincrease)+\"\"\"\n", " nbins = \"\"\"+str(nbins)+\"\"\"\n", " nbaths = \"\"\"+str(nbatch)+\"\\n\"\n", "\n", " bins = zeros((nbatch,ndim),dtype=int) # in which sampled bin does this point fall?\n", " wgh = zeros(nbatch) # weights for each random point in the batch\n", " \n", " all_nsamples = nstart\n", " for nsamples in range(all_nsamples,0,-nbatch): # loop over all_nsample evaluations in batches of nbatch\n", " n = min(nbatch,nsamples) # How many evaluations in this pass?\n", " # We are integrating f(g_1(x),g_2(y),g_3(z))*dg_1/dx*dg_2/dy*dg_3/dz dx*dy*dz\n", " # This is represented as 1/all_nsamples \\sum_{x_i,y_i,z_i} f(g_1(x_i),g_2(y_i),g_3(z_i))*dg_1/dx*dg_2/dy*dg_3/dz\n", " # where dg_1/dx = diff*NBINS\n", " xr = random.random((n,ndim)) # generates 2-d array of random numbers in the interval [0,1)\n", " for i in range(n):\n", " weight = 1.0/all_nsamples\n", " for dim in range(ndim):\n", " # We want to evaluate the function f at point g(x), i.e, f(g_1(x),g_2(y),...)\n", " # Here we transform the points x,y,z -> g_1(x), g_2(y), g_3(z)\n", " # We hence want to evaluate g(x) ~ g(x[i]), where x is the random number and g is the grid function\n", " # The discretized g(t) is defined on the grid :\n", " # t[-1]=0, t[0]=1/N, t[1]=2/N, t[2]=3/N ... t[N-1]=1.\n", " # We know that g(0)=0 and g(1)=1, so that g[-1]=0.0 and g[N-1]=1.0\n", " # To interpolate g at x, we first compute i=int(x*N) and then we use linear interpolation\n", " # g(x) = g[i-1] + (g[i]-g[i-1])*(x*N-i) ; if i>0\n", " # g(x) = 0 + (g[0]-0)*(x*N-0) ; if i=0\n", " #\n", " pos = xr[i,dim]*nbins # which grid would it fit ? (x*N)\n", " ipos = int(pos) # the grid position is ipos : int(x*N)==i\n", " diff = grid.g[dim,ipos] - grid.g[dim,ipos-1] # g[i]-g[i-1]\n", " # linear interpolation for g(x) : \n", " xr[i,dim] = (grid.g[dim,ipos-1] + (pos-ipos)*diff)*unit # g(xr) ~ ( g[i-1]+(g[i]-g[i-1])*(x*N-i) )*[units]\n", " bins[i,dim]=ipos # remember in which bin this random number falls.\n", " weight *= diff*nbins # weight for this dimension is dg/dx = (g[i]-g[i-1])*N\n", " # because dx = i/N - (i-1)/N = 1/N\n", " wgh[i] = weight # total weight is (df/dx)*(df/dy)*(df/dx).../N_{samples}\n", " # Here we evaluate function f on all randomly generated x points above\n", " fx = integrant(xr) # n function evaluations required in single call\n", " neval += n # We just added so many fuction evaluations\n", "\n", " # Now we compute the integral as weighted average, namely, f(g(x))*dg/dx\n", " wfun = wgh * fx # weight * function ~ f_i*w_i\n", " cum.sum += sum(wfun) # sum_i f_i*w_i = \n", " wfun *= wfun # carefull : this is like (f_i * w_i/N)^2 hence 1/N (1/N (f_i*w_i)^2)\n", " cum.sqsum += sum(wfun) # sum_i (f_i*w_i)^2 = /all_nsamples\n", " # \n", " w0 = sqrt(cum.sqsum*all_nsamples) # w0 = sqrt()\n", " w1 = (w0 + cum.sum)*(w0 - cum.sum) # w1 = (w0^2 - ^2) = (-^2)\n", " w = (all_nsamples-1)/w1 # w ~ 1/sigma_i^2 = (N-1)/(-^2)\n", " # Note that variance of the MC sampling is Var(monte-f) = (-^2)/N == 1/sigma_i^2\n", " cum.weightsum += w # weightsum ~ \\sum_i 1/sigma_i^2\n", " cum.avgsum += w*cum.sum # avgsum ~ \\sum_i _i / sigma_i^2\n", " \n", " cum.avg = cum.avgsum/cum.weightsum # I_best = (\\sum_i _i/sigma_i^2 )/(\\sum_i 1/sigma_i^2)\n", " cum.err = sqrt(1/cum.weightsum) # err ~ sqrt(best sigma^2) = sqrt(1/(\\sum_i 1/sigma_i^2))\n", " \n", " cum.avg *= unit**ndim\n", " cum.err *= unit**ndim" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vegas parameters:\n", " ndim = 3\n", " unit = 3.14159265359\n", " maxeval = 200000\n", " nstart = 10000\n", " nincrease = 5000\n", " nbins = 128\n", " nbaths = 1000\n", "\n", "1.32583782904 +- 0.0203730373082 exact= 1.3932\n" ] } ], "source": [ "from scipy import *\n", "unit=pi\n", "ndim=3\n", "maxeval=200000\n", "exact = 1.3932 # exact value of the integral\n", " \n", "cum = Cumulants()\n", " \n", "nbins=128\n", "nstart =10000\n", "nincrease=5000\n", "grid = Grid(ndim,nbins)\n", "random.seed(0)\n", "\n", "#SimpleMC(my_integrant2, ndim, pi, maxeval, cum)\n", "Vegas_step1(my_integrant2, pi, maxeval, nstart, nincrease, grid, cum)\n", "print cum.avg, '+-', cum.err, 'exact=', exact" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "class Grid:\n", " \"\"\"Contains the grid points g_n(x) with x=[0...1], and g=[0...1]\n", " for Vegas integration. There are n-dim g_n functions.\n", " Constraints : g(0)=0 and g(1)=1.\n", " \"\"\"\n", " def __init__(self, ndim, nbins):\n", " self.g = zeros((ndim,nbins+1))\n", " self.ndim=ndim\n", " self.nbins=nbins\n", " # At the beginning we set g(x)=x\n", " # The grid-points are x_0 = 1/N, x_1 = 2/N, ... x_{N-1}=1.0. \n", " # Note that g(0)=0, and we skip this point on the mesh.\n", " for ibin in range(nbins):\n", " w = (ibin + 1.0)/nbins \n", " self.g[:,ibin] = w\n", " \n", " def RefineGrid(self, imp, SharpEdges=False):\n", " (ndim,nbins) = shape(imp)\n", " gnew = zeros((ndim,nbins+1))\n", " for idim in range(ndim):\n", " avgperbin = sum(imp[idim,:])/nbins\n", " #**** redefine the size of each bin ****\n", " newgrid = zeros(nbins)\n", " cur=0.0\n", " newcur=0.0\n", " thisbin = 0.0\n", " ibin = -1\n", " # we are trying to determine\n", " # Int[ f(g) dg, {g, g_{i-1},g_i}] == I/N_g\n", " # where I == avgperbin\n", " for newbin in range(nbins-1): # all but the last bin, which is 1.0\n", " while (thisbin < avgperbin) :\n", " ibin+=1\n", " thisbin += imp[idim,ibin]\n", " prev = cur\n", " cur = self.g[idim,ibin]\n", " # Explanation is in order : \n", " # prev -- g^{old}_{l-1}\n", " # cur -- g^{old}_l\n", " # thisbin -- Sm = f_{l-k}+.... +f_{l-2}+f_{l-1}+f_l\n", " # we know that Sm is just a bit more than we need, i.e., I/N_g, hence we need to compute how much more\n", " # using linear interpolation :\n", " # g^{new} = g_l - (g_l-g_{l-1}) * (f_{l-k}+....+f_{l-2}+f_{l-1}+f_l - I/N_g)/f_l\n", " # clearly\n", " # if I/N_g == f_{l-k}+....+f_{l-2}+f_{l-1}+f_l\n", " # we will get g^{new} = g_l\n", " # and if I/N_g == f_{l-k}+....+f_{l-2}+f_{l-1}\n", " # we will get g^{new} = g_{l-1}\n", " # and if I/N_g is between the two possibilities, we will get linear interpolation between\n", " # g_{l-1} and g_l\n", " # \n", " thisbin -= avgperbin # thisbin <- (f_{l-k}+....+f_{l-2}+f_{l-1}+f_l - I/N_g)\n", " delta = (cur - prev)*thisbin # delta <- (g_l-g_{l-1})*(f_{l-k}+....+f_{l-2}+f_{l-1}+f_l - I/N_g)\n", " if (SharpEdges):\n", " newgrid[newbin] = cur - delta/imp[idim,ibin]\n", " else:\n", " bin_m1 = ibin-1\n", " if bin_m1<0: bin_m1=0\n", " newcur = max( newcur, cur-2*delta/(imp[idim,ibin]+imp[idim,bin_m1]) )\n", " newgrid[newbin] = newcur\n", " newgrid[nbins-1]=1.0\n", " gnew[idim,:nbins]= newgrid\n", " self.g = gnew\n", " return gnew" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def Vegas_step2(integrant, unit, maxeval, nstart, nincrease, grid, cum):\n", " ndim, nbins = grid.ndim,grid.nbins # dimension of the integral, size of the grid for binning in each direction\n", " unit_dim = unit**ndim # converts from unit cube integration to generalized cube with unit length\n", " nbatch=1000 # function will be evaluated in bacthes of 1000 evaluations at one time (for efficiency and storage issues)\n", " neval=0\n", " print \"\"\"Vegas parameters:\n", " ndim = \"\"\"+str(ndim)+\"\"\"\n", " unit = \"\"\"+str(unit)+\"\"\"\n", " maxeval = \"\"\"+str(maxeval)+\"\"\"\n", " nstart = \"\"\"+str(nstart)+\"\"\"\n", " nincrease = \"\"\"+str(nincrease)+\"\"\"\n", " nbins = \"\"\"+str(nbins)+\"\"\"\n", " nbaths = \"\"\"+str(nbatch)+\"\\n\"\n", "\n", " bins = zeros((nbatch,ndim),dtype=int) # in which sampled bin does this point fall?\n", " wgh = zeros(nbatch) # weights for each random point in the batch\n", " \n", " all_nsamples = nstart\n", " fxbin = zeros((ndim,nbins)) #new2: after each iteration we reset the average function being binned\n", " for nsamples in range(all_nsamples,0,-nbatch): # loop over all_nsample evaluations in batches of nbatch\n", " n = min(nbatch,nsamples) # How many evaluations in this pass?\n", " # We are integrating f(g_1(x),g_2(y),g_3(z))*dg_1/dx*dg_2/dy*dg_3/dz dx*dy*dz\n", " # This is represented as 1/all_nsamples \\sum_{x_i,y_i,z_i} f(g_1(x_i),g_2(y_i),g_3(z_i))*dg_1/dx*dg_2/dy*dg_3/dz\n", " # where dg_1/dx = diff*NBINS\n", " xr = random.random((n,ndim)) # generates 2-d array of random numbers in the interval [0,1)\n", " for i in range(n):\n", " weight = 1.0/all_nsamples\n", " for dim in range(ndim):\n", " # We want to evaluate the function f at point g(x), i.e, f(g_1(x),g_2(y),...)\n", " # Here we transform the points x,y,z -> g_1(x), g_2(y), g_3(z)\n", " # We hence want to evaluate g(x) ~ g(x[i]), where x is the random number and g is the grid function\n", " # The discretized g(t) is defined on the grid :\n", " # t[-1]=0, t[0]=1/N, t[1]=2/N, t[2]=3/N ... t[N-1]=1.\n", " # We know that g(0)=0 and g(1)=1, so that g[-1]=0.0 and g[N-1]=1.0\n", " # To interpolate g at x, we first compute i=int(x*N) and then we use linear interpolation\n", " # g(x) = g[i-1] + (g[i]-g[i-1])*(x*N-i) ; if i>0\n", " # g(x) = 0 + (g[0]-0)*(x*N-0) ; if i=0\n", " #\n", " pos = xr[i,dim]*nbins # which grid would it fit ? (x*N)\n", " ipos = int(pos) # the grid position is ipos : int(x*N)==i\n", " diff = grid.g[dim,ipos] - grid.g[dim,ipos-1] # g[i]-g[-1]\n", " # linear interpolation for g(x) : \n", " xr[i,dim] = (grid.g[dim,ipos-1] + (pos-ipos)*diff)*unit # g(xr) ~ ( g[i-1]+(g[i]-g[i-1])*(x*N-i) )*[units]\n", " bins[i,dim]=ipos # remember in which bin this random number falls.\n", " weight *= diff*nbins # weight for this dimension is dg/dx = (g[i]-g[i-1])*N\n", " # because dx = i/N - (i-1)/N = 1/N\n", " wgh[i] = weight # total weight is (df/dx)*(df/dy)*(df/dx).../N_{samples}\n", " # Here we evaluate function f on all randomly generated x points above\n", " fx = integrant(xr) # n function evaluations required in single call\n", " neval += n # We just added so many fuction evaluations\n", "\n", " # Now we compute the integral as weighted average, namely, f(g(x))*dg/dx\n", " wfun = wgh * fx # weight * function ~ f_i*w_i\n", " cum.sum += sum(wfun) # sum_i f_i*w_i = \n", " wfun *= wfun # carefull : this is like (f_i * w_i/N)^2 hence 1/N (1/N (f_i*w_i)^2)\n", " cum.sqsum += sum(wfun) # sum_i (f_i*w_i)^2 = /all_nsamples\n", " # \n", " for dim in range(ndim): #new2\n", " # Here we make a better approximation for the function, which we are integrating.\n", " for i in range(n): #new2\n", " fxbin[dim, bins[i,dim] ] += wfun[i] #new2: just bin the function f. We saved the bin position before.\n", " \n", " w0 = sqrt(cum.sqsum*all_nsamples) # w0 = sqrt()\n", " w1 = (w0 + cum.sum)*(w0 - cum.sum) # w1 = (w0^2 - ^2) = (-^2)\n", " w = (all_nsamples-1)/w1 # w ~ 1/sigma_i^2 = (N-1)/(-^2)\n", " # Note that variance of the MC sampling is Var(monte-f) = (-^2)/N == 1/sigma_i^2\n", " cum.weightsum += w # weightsum ~ \\sum_i 1/sigma_i^2\n", " cum.avgsum += w*cum.sum # avgsum ~ \\sum_i _i / sigma_i^2\n", " \n", " cum.avg = cum.avgsum/cum.weightsum # I_best = (\\sum_i _i/sigma_i^2 )/(\\sum_i 1/sigma_i^2)\n", " cum.err = sqrt(1/cum.weightsum) # err ~ sqrt(best sigma^2) = sqrt(1/(\\sum_i 1/sigma_i^2))\n", " \n", " cum.avg *= unit**ndim\n", " cum.err *= unit**ndim\n", " \n", " return fxbin" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vegas parameters:\n", " ndim = 3\n", " unit = 3.14159265359\n", " maxeval = 200000\n", " nstart = 10000\n", " nincrease = 5000\n", " nbins = 128\n", " nbaths = 1000\n", "\n", "1.38055737023 +- 0.0384903652993 exact= 1.3932\n" ] } ], "source": [ "from scipy import *\n", "unit=pi\n", "ndim=3\n", "maxeval=200000\n", "exact = 1.3932 # exact value of the integral\n", " \n", "cum = Cumulants()\n", " \n", "nbins=128\n", "nstart =10000\n", "nincrease=5000\n", "grid = Grid(ndim,nbins)\n", "\n", "#SimpleMC(my_integrant2, ndim, pi, maxeval, cum)\n", "fxbin = Vegas_step2(my_integrant2, pi, maxeval, nstart, nincrease, grid, cum)\n", "print cum.avg, '+-', cum.err, 'exact=', exact" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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hbH6MMZ83xlyVOP/nwGnGmPcbY/YzxhwJfAW4y1pbyzUAcroARjEKWJMAhRBCNDPZEoAd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\n9QulVEAp9VSn8pDWSCmVrpR6WSlVG9RgczDaZkebkNRIKWUJTlwuCd7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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from pylab import *\n", "%matplotlib inline\n", "\n", "plot(fxbin[0])\n", "plot(fxbin[1])\n", "plot(fxbin[2])\n", "xlim([0,128])\n", "ylim([0,1e-7])\n", "show()" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def Smoothen(fxbin):\n", " (ndim,nbins) = shape(fxbin)\n", " imp = zeros(shape(fxbin))\n", " for idim in range(ndim):\n", " fxb = fxbin[idim,:]\n", " #**** smooth the f^2 value stored for each bin ****\n", " prev = fxb[0]\n", " cur = fxb[1]\n", " fxb[0] = 0.5*(prev + cur) # the first and the last point are different, as they can only be averag\n", " norm = fxb[0]\n", " for ibin in range(1,nbins-1):\n", " s = prev + cur # s=f[i-1]+f[i]\n", " prev = cur\n", " cur = fxb[ibin+1] # cur=f[i+1]\n", " fxb[ibin] = (s + cur)/3. # (f[i+1]+f[i]+f[i-1])/3.\n", " norm += fxb[ibin] # \n", " fxb[nbins-1] = 0.5*(prev+cur)\n", " norm += fxb[nbins-1]\n", " if( norm == 0 ):\n", " print 'ERROR can not refine the grid with zero grid function'\n", " return # can not refine the grid if the function is zero.\n", " fxb *= 1.0/norm # we normalize the function.\n", " # Note that normalization is such that the sum is 1.\n", " #**** compute the importance function for each bin ****\n", " #imp = zeros(nbins)\n", " avgperbin = 0.0\n", " for ibin in range(nbins):\n", " impfun = 0.0\n", " if fxb[ibin]> 0 : \n", " r = fxb[ibin] # this is the normalized function in this bin\n", " impfun = ((r - 1)/log(r))**(1.5) # this just damps the a bit. Instead of taking impfun = r,\n", " # we use g(r), where g(r)=((r-1)/log(r))^1.5 so that changes are not too rapid\n", " imp[idim,ibin] = impfun\n", " return imp" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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o8xFAuy6KiMhBoLSUOo+L6l6pTZrDmYRwkGCMU3KAhkyCyg1RNA4S1pavjbr8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\nnQ8Tz1cSy0XoZjOHuZCewDbSLZsoiD0eNMYevbe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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from pylab import *\n", "%matplotlib inline\n", "\n", "imp = Smoothen(fxbin)\n", "\n", "plot(imp[0])\n", "plot(imp[1])\n", "plot(imp[2])\n", "xlim([0,128])\n", "show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Update the class Grid, so that it can refine the grid" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vegas parameters:\n", " ndim = 3\n", " unit = 3.14159265359\n", " maxeval = 200000\n", " nstart = 10000\n", " nincrease = 5000\n", " nbins = 128\n", " nbaths = 1000\n", "\n", "1.33092497244 +- 0.0244952318512 exact= 1.3932\n" ] }, { "data": { "image/png": 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TK3D47GE2dtpIjUI1ALPO//bb8O678OGHptNfmjROjl3kIVIBICIph5+f6ddb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\nbcs3wxtRbWULXs71MlHdoij3dDnH0H+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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy import *\n", "unit=pi\n", "ndim=3\n", "maxeval=200000\n", "exact = 1.3932 # exact value of the integral\n", " \n", "cum = Cumulants()\n", " \n", "nbins=128\n", "nstart =10000\n", "nincrease=5000\n", "\n", "grid = Grid(ndim,nbins)\n", "\n", "fxbin = Vegas_step2(my_integrant2, pi, maxeval, nstart, nincrease, grid, cum)\n", "imp = Smoothen(fxbin)\n", "grid.RefineGrid(imp, SharpEdges=True)\n", "print cum.avg, '+-', cum.err, 'exact=', exact\n", "\n", "plot(grid.g[0,:nbins])\n", "plot(grid.g[1,:nbins])\n", "plot(grid.g[2,:nbins])\n", "xlim([0,128])\n", "show()" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def Vegas_step3(integrant, unit, maxeval, nstart, nincrease, grid, cum):\n", " ndim, nbins = grid.ndim,grid.nbins # dimension of the integral, size of the grid for binning in each direction\n", " unit_dim = unit**ndim # converts from unit cube integration to generalized cube with unit length\n", " nbatch=1000 # function will be evaluated in bacthes of 1000 evaluations at one time (for efficiency and storage issues)\n", " neval=0\n", " print \"\"\"Vegas parameters:\n", " ndim = \"\"\"+str(ndim)+\"\"\"\n", " unit = \"\"\"+str(unit)+\"\"\"\n", " maxeval = \"\"\"+str(maxeval)+\"\"\"\n", " nstart = \"\"\"+str(nstart)+\"\"\"\n", " nincrease = \"\"\"+str(nincrease)+\"\"\"\n", " nbins = \"\"\"+str(nbins)+\"\"\"\n", " nbaths = \"\"\"+str(nbatch)+\"\\n\"\n", "\n", " bins = zeros((nbatch,ndim),dtype=int) # in which sampled bin does this point fall?\n", " wgh = zeros(nbatch) # weights for each random point in the batch\n", " \n", " all_nsamples = nstart\n", " for iter in range(1000):\n", " fxbin = zeros((ndim,nbins)) # after each iteration we reset the average function being binned\n", " for nsamples in range(all_nsamples,0,-nbatch): # loop over all_nsample evaluations in batches of nbatch\n", " n = min(nbatch,nsamples) # How many evaluations in this pass?\n", " # We are integrating f(g_1(x),g_2(y),g_3(z))*dg_1/dx*dg_2/dy*dg_3/dz dx*dy*dz\n", " # This is represented as 1/all_nsamples \\sum_{x_i,y_i,z_i} f(g_1(x_i),g_2(y_i),g_3(z_i))*dg_1/dx*dg_2/dy*dg_3/dz\n", " # where dg_1/dx = diff*NBINS\n", " xr = random.random((n,ndim)) # generates 2-d array of random numbers in the interval [0,1)\n", " for i in range(n):\n", " weight = 1.0/all_nsamples\n", " for dim in range(ndim):\n", " # We want to evaluate the function f at point g(x), i.e, f(g_1(x),g_2(y),...)\n", " # Here we transform the points x,y,z -> g_1(x), g_2(y), g_3(z)\n", " # We hence want to evaluate g(x) ~ g(x[i]), where x is the random number and g is the grid function\n", " # The discretized g(t) is defined on the grid :\n", " # t[-1]=0, t[0]=1/N, t[1]=2/N, t[2]=3/N ... t[N-1]=1.\n", " # We know that g(0)=0 and g(1)=1, so that g[-1]=0.0 and g[N-1]=1.0\n", " # To interpolate g at x, we first compute i=int(x*N) and then we use linear interpolation\n", " # g(x) = g[i-1] + (g[i]-g[i-1])*(x*N-i) ; if i>0\n", " # g(x) = 0 + (g[0]-0)*(x*N-0) ; if i=0\n", " #\n", " pos = xr[i,dim]*nbins # which grid would it fit ? (x*N)\n", " ipos = int(pos) # the grid position is ipos : int(x*N)==i\n", " diff = grid.g[dim,ipos] - grid.g[dim,ipos-1] # g[i]-g[-1]\n", " # linear interpolation for g(x) : \n", " xr[i,dim] = (grid.g[dim,ipos-1] + (pos-ipos)*diff)*unit # g(xr) ~ ( g[i-1]+(g[i]-g[i-1])*(x*N-i) )*[units]\n", " bins[i,dim]=ipos # remember in which bin this random number falls.\n", " weight *= diff*nbins # weight for this dimension is dg/dx = (g[i]-g[i-1])*N\n", " # because dx = i/N - (i-1)/N = 1/N\n", " wgh[i] = weight # total weight is (df/dx)*(df/dy)*(df/dx).../N_{samples}\n", " \n", " # Here we evaluate function f on all randomly generated x points above\n", " fx = integrant(xr) # n function evaluations required in single call\n", " neval += n # We just added so many fuction evaluations\n", "\n", " # Now we compute the integral as weighted average, namely, f(g(x))*dg/dx\n", " wfun = wgh * fx # weight * function ~ f_i*w_i \n", " cum.sum += sum(wfun) # sum_i f_i*w_i = \n", " wfun *= wfun # carefull : this is like (f_i * w_i/N)^2 hence 1/N (1/N (f_i*w_i)^2)\n", " cum.sqsum += sum(wfun) # sum_i (f_i*w_i)^2 = /all_nsamples\n", " # \n", " for dim in range(ndim): #new2\n", " # Here we make a better approximation for the function, which we are integrating.\n", " for i in range(n): #new2\n", " fxbin[dim, bins[i,dim] ] += wfun[i] #new2: just bin the function f. We saved the bin position before.\n", "\n", " w0 = sqrt(cum.sqsum*all_nsamples) # w0 = sqrt()\n", " w1 = (w0 + cum.sum)*(w0 - cum.sum) # w1 = (w0^2 - ^2) = (-^2)\n", " w = (all_nsamples-1)/w1 # w ~ 1/sigma_i^2 = (N-1)/(-^2)\n", " # Note that variance of the MC sampling is Var(monte-f) = (-^2)/N == 1/sigma_i^2\n", " cum.weightsum += w # weightsum ~ \\sum_i 1/sigma_i^2\n", " cum.avgsum += w*cum.sum # avgsum ~ \\sum_i _i / sigma_i^2\n", " cum.avg2sum += w*cum.sum**2 # avg2cum ~ \\sum_i _i^2/sigma_i^2\n", " \n", " cum.avg = cum.avgsum/cum.weightsum # I_best = (\\sum_i _i/sigma_i^2 )/(\\sum_i 1/sigma_i^2)\n", " cum.err = sqrt(1/cum.weightsum) # err ~ sqrt(best sigma^2) = sqrt(1/(\\sum_i 1/sigma_i^2))\n", " \n", " # new in this step\n", " if iter>0:\n", " cum.chisq = (cum.avg2sum - 2*cum.avgsum*cum.avg + cum.weightsum*cum.avg**2)/iter\n", " \n", " print \"Iteration {:3d}: I= {:10.8f} +- {:10.8f} chisq= {:10.8f} number of evaluations = {:7d} \".format(iter+1, cum.avg*unit_dim, cum.err*unit_dim, cum.chisq, neval)\n", " imp = Smoothen(fxbin)\n", " grid.RefineGrid(imp, SharpEdges=True)\n", " \n", " cum.sum=0 # clear the partial sum for the next step\n", " cum.sqsum=0\n", " all_nsamples += nincrease # for the next time, increase the number of steps a bit\n", " if (neval>=maxeval): break\n", " \n", " cum.avg *= unit**ndim\n", " cum.err *= unit**ndim" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vegas parameters:\n", " ndim = 3\n", " unit = 3.14159265359\n", " maxeval = 2000000\n", " nstart = 100000\n", " nincrease = 5000\n", " nbins = 128\n", " nbaths = 1000\n", "\n", "Iteration 1: I= 1.36762346 +- 0.01023309 chisq= 0.00000000 number of evaluations = 100000 \n", "Iteration 2: I= 1.38308994 +- 0.00488295 chisq= 2.95787653 number of evaluations = 205000 \n", "Iteration 3: I= 1.38903765 +- 0.00341085 chisq= 2.92764168 number of evaluations = 315000 \n", "Iteration 4: I= 1.39085420 +- 0.00271957 chisq= 2.21131183 number of evaluations = 430000 \n", "Iteration 5: I= 1.39235286 +- 0.00238578 chisq= 1.98798517 number of evaluations = 550000 \n", "Iteration 6: I= 1.39215278 +- 0.00209328 chisq= 1.59649946 number of evaluations = 675000 \n", "Iteration 7: I= 1.39187814 +- 0.00186075 chisq= 1.34408861 number of evaluations = 805000 \n", "Iteration 8: I= 1.39040546 +- 0.00167503 chisq= 1.62389166 number of evaluations = 940000 \n", "Iteration 9: I= 1.39098400 +- 0.00155755 chisq= 1.53107506 number of evaluations = 1080000 \n", "Iteration 10: I= 1.39152488 +- 0.00144974 chisq= 1.46121875 number of evaluations = 1225000 \n", "Iteration 11: I= 1.39101550 +- 0.00135470 chisq= 1.41244571 number of evaluations = 1375000 \n", "Iteration 12: I= 1.39111487 +- 0.00127230 chisq= 1.28818899 number of evaluations = 1530000 \n", "Iteration 13: I= 1.39172957 +- 0.00120599 chisq= 1.37245777 number of evaluations = 1690000 \n", "Iteration 14: I= 1.39195626 +- 0.00114625 chisq= 1.29501238 number of evaluations = 1855000 \n", "Iteration 15: I= 1.39272504 +- 0.00110407 chisq= 1.64730521 number of evaluations = 2025000 \n", "1.39272503683 +- 0.00110407312053 exact= 1.3932 real error= 0.000340915280729\n" ] }, { "data": { "image/png": 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e+Pr6/mEsMDCQwMDAuMwrIn/h9oSZpO3/EYPSfEa3dY1xc4Ord65SK7gWGbwz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\nU0RE4gHNNCRRd8ItIWWH8sq7r3DPNz1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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy import *\n", "unit=pi\n", "ndim=3\n", "maxeval=2000000\n", "exact = 1.3932 # exact value of the integral\n", " \n", "cum = Cumulants()\n", " \n", "nbins=128\n", "nstart =100000\n", "nincrease=5000\n", "\n", "grid = Grid(ndim,nbins)\n", "\n", "random.seed(0)\n", "\n", "Vegas_step3(my_integrant2, pi, maxeval, nstart, nincrease, grid, cum)\n", "\n", "print cum.avg, '+-', cum.err, 'exact=', exact, 'real error=', abs(cum.avg-exact)/exact\n", "\n", "plot(grid.g[0,:nbins])\n", "plot(grid.g[1,:nbins])\n", "plot(grid.g[2,:nbins])\n", "show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.10" } }, "nbformat": 4, "nbformat_minor": 2 }