StochasticReconfiguration/Reproduce_Hetherington_PRA1984.ipynb

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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: pylab import has clobbered these variables: ['copy', 'eig']\n",
      "`%matplotlib` prevents importing * from pylab and numpy\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "%pylab inline\n",
    "\n",
    "mpl.rcParams['font.size']=12\n",
    "\n",
    "from scipy.linalg import eig \n",
    "import bisect \n",
    "import copy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reproducing \"Observations on the statistical iterations of matrices\" by J.H. Hetherington*\n",
    "\n",
    "## I. Introduction\n",
    "\n",
    "We can use stochastic iteration to effect the power method for sampling the extremal eigenvalues/eigenvectors of a matrix with sampling access to a matrix-vector product. In the context of many-body physics, this matrix might be a Hamiltonian and we might be interested in, e.g, an approximation of the affiliated Green's function as in diffusion Monte Carlo.\n",
    "\n",
    "Naive stochastic iteration can result in two effects that we would like to mitigate if we are to use it:\n",
    "\n",
    "1. Seemingly anomalous growth in variance as the number of iterations increases.\n",
    "2. Stable or reducing variance, but the introduction of bias.\n",
    "\n",
    "In this notebook, we will walk through the results in Hetherington's paper and reproduce them one by one. This culminates in a simple stochastic reconfiguration implementation for controlling variance and bias with a fixed population of walkers.\n",
    "\n",
    "*Fun fact: Hetherington is one of a select few physicists to have co-authored a paper with a domestic cat (https://en.wikipedia.org/wiki/F.D.C._Willard)\n",
    "\n",
    "## II and III. Stochastic Matrices and Markov Chains\n",
    "\n",
    "Most of us probably know what a stochastic matrix is. It is a matrix that is:\n",
    "* Comprised of non-negative entries...\n",
    "* ...and columns that sum to 1\n",
    "\n",
    "We might interpret the entries of such a matrix as probabilities. The rows and columns of our matrix comprise a discrete state space through which we might imagine a system evolving. The entry in the ith row and jth column is then to be interpreted as the probability of the system transitioning into basis state i, given that it is found in basis state j.\n",
    "\n",
    "What do we know about these matrices?\n",
    "* They have a left eigenvector proportional to all 1s, with eigenvalue 1.\n",
    "* 1 is the largest eigenvalue.\n",
    "* If the matrix cannot be put in block diagonal form via permutation, this maximum eigenvalue is non-degenerate.\n",
    "\n",
    "If we conceive of repeated application of this matrix as applying the power method to project out the largest eigenvector/eigenvalue of our matrix (which we assume to be non-degenerate), then the relationship between the properties of this type of matrix and the properties of a Markov Chain are evident. This largest eigenvector is, indeed, the stationary distribution of some Markov Chain. Thus, we see that there is a relationship between a Markov Chain generated by iterating some matrix and its extremal eigenvalues.\n",
    "\n",
    "## IV. Non-negative Matrices\n",
    "\n",
    "What happens if rather than considering matrices that are both non-negative and have columns that sum to unity, we consider more general non-negative matrices. We can factorize these matrices into a product of a stochastic matrix and a diagonal matrix. In Equation 2* of Hetherington's paper, he demonstrates that a non-negative matrix can be \"made stochastic\" given access to its extremal left eigenpair. Below we demonstrate how to do this for a contrived 2x2 example:\n",
    "\n",
    "*Note: Equation 2 has a typo, it should be $M_{ij} = \\frac{1}{\\lambda} Z_i A_{ij} Z_{j}^{-1}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
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   "outputs": [
    {
     "name": "stdout",
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     "text": [
      "Matrix A: \n",
      "[[ 2.  4.]\n",
      " [ 3.  1.]]\n"
     ]
    }
   ],
   "source": [
    "# construct an exemplary non-negative matrix\n",
    "A = zeros([2,2])\n",
    "A[0,0] = 2.0\n",
    "A[1,1] = 1.0\n",
    "A[1,0] = 3.0\n",
    "A[0,1] = 4.0\n",
    "print 'Matrix A: \\n', A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Column 0 sum:  5.0\n",
      "Column 1 sum:  5.0\n",
      "Matrix A is non-negative but the columns do not sum to 1\n"
     ]
    }
   ],
   "source": [
    "# verify that columns do not sum to 1\n",
    "print 'Column 0 sum: ', sum(A[:,0])\n",
    "print 'Column 1 sum: ', sum(A[:,1])\n",
    "print 'Matrix A is non-negative but the columns do not sum to 1'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stochastic factor of A (M): \n",
      "[[ 0.4  0.8]\n",
      " [ 0.6  0.2]]\n"
     ]
    }
   ],
   "source": [
    "# compute the eigenvalues and left/right eigenvectors\n",
    "w, vl, vr = eig(A, left=True)\n",
    "\n",
    "# fill out the entries of the stochastic part of A in the silliest way possible\n",
    "# direct application of Equation 2\n",
    "M = zeros([2,2])\n",
    "scl = 1.0/abs(w[0])\n",
    "M[0,0] = scl*vl[0,0]*A[0,0]/vl[0,0]\n",
    "M[0,1] = scl*vl[0,0]*A[0,1]/vl[1,0]\n",
    "M[1,0] = scl*vl[1,0]*A[1,0]/vl[0,0]\n",
    "M[1,1] = scl*vl[1,0]*A[1,1]/vl[1,0]\n",
    "\n",
    "print 'Stochastic factor of A (M): \\n', M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalues of M (largest is 1):  [ 1.0+0.j -0.4+0.j]\n",
      "Left eigenvectors of M (eigenvector corresponding to 1 is ~ to all 1s): \n",
      "[[ 0.70710678 -0.6       ]\n",
      " [ 0.70710678  0.8       ]]\n"
     ]
    }
   ],
   "source": [
    "# compute the eigenvalues and left/right eigenvectors\n",
    "wStoc, vlStoc, vrStoc = eig(M, left=True)\n",
    "\n",
    "print 'Eigenvalues of M (largest is 1): ', wStoc \n",
    "print 'Left eigenvectors of M (eigenvector corresponding to 1 is ~ to all 1s): \\n', vlStoc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Diagonal factor of A (w): \n",
      "[[ 5.  0.]\n",
      " [ 0.  5.]]\n"
     ]
    }
   ],
   "source": [
    "# compute the diagonal factor of A (below Equation 4)\n",
    "wDiag = eye(2)\n",
    "wDiag[0,0] *= sum(A[:,0])\n",
    "wDiag[1,1] *= sum(A[:,1])\n",
    "\n",
    "print 'Diagonal factor of A (w): \\n', wDiag"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix A: \n",
      "[[ 2.  4.]\n",
      " [ 3.  1.]]\n",
      "Product M*w: \n",
      "[[ 2.  4.]\n",
      " [ 3.  1.]]\n"
     ]
    }
   ],
   "source": [
    "print 'Matrix A: \\n', A\n",
    "print 'Product M*w: \\n', dot(M,wDiag)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## V. The Dilemma of the Symmetric Matrix\n",
    "\n",
    "Of course, none of this is particularly useful as it assumes that we know the spectrum and eigenvectors a priori. Next we move onto the central example of the paper in which we estimate the largest eigenvalue of a symmetric non-negative matrix (something that is starting to look like a Hamiltonian).\n",
    "\n",
    "## VI. Using Non-Stochastic Matrices\n",
    "\n",
    "Assume for a moment that we have access to a factorized form of a symmetric, non-negative (but non-stochastic) matrix. We will demonstrate via stochastic iteration that we can estimate the largest eigenvalue of this matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalues of A:  [ 1.10517172  0.52782145]\n"
     ]
    }
   ],
   "source": [
    "# create the SYMMETRIC A matrix of interest in the paper\n",
    "A = zeros([2,2])\n",
    "scl = 1.0/sqrt(6.0*4.0)\n",
    "A[0,0] = scl*5\n",
    "A[0,1] = scl*1\n",
    "A[1,0] = scl*1\n",
    "A[1,1] = scl*3\n",
    "\n",
    "w, vl, vr = eig(A, left=True)\n",
    "# we know that the eigenvalues are real, so just print them out as such\n",
    "print 'Eigenvalues of A: ', real(w)\n",
    "wExact = real(w[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Diagonal factor of A: \n",
      "[[ 1.22474487  0.        ]\n",
      " [ 0.          0.81649658]]\n"
     ]
    }
   ],
   "source": [
    "# create the diagonal factor of A\n",
    "w = zeros([2,2])\n",
    "w[0,0] = sum(A[:,0])\n",
    "w[1,1] = sum(A[:,1])\n",
    "print 'Diagonal factor of A: \\n', w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stochastic factor of A: \n",
      "[[ 0.83333333  0.25      ]\n",
      " [ 0.16666667  0.75      ]]\n"
     ]
    }
   ],
   "source": [
    "# create the stochastic factor of A\n",
    "M = zeros([2,2])\n",
    "M[0,0] = A[0,0]/w[0,0]\n",
    "M[0,1] = A[0,1]/w[1,1]\n",
    "M[1,0] = A[1,0]/w[0,0]\n",
    "M[1,1] = A[1,1]/w[1,1]\n",
    "print 'Stochastic factor of A: \\n', M"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To estimate the largest eigenvector of A, we will now generate a Markov Chain from the probabilities in the stochastic factor, and weight the configurations with the respective elements of the diagonal factor. We will then take the estimate of the eigenvector, and extract its associated eigenvalue."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "collapsed": false
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   "outputs": [],
   "source": [
    "# the paper makes a point of using weights that are reciprocals, \n",
    "# such that the weight of a given configuration is (6/4)**(n/2)...\n",
    "# given such a weight, this routine computes the integer n\n",
    "def getN(weight):\n",
    "    return int(log(weight**2)/log(6.0/4.0))\n",
    "\n",
    "def estimateEig(nIterations, M, w):\n",
    "    \n",
    "    # starting from state 0\n",
    "    currentState = 0\n",
    "\n",
    "    weight = zeros(nIterations)\n",
    "    weight[0] = 1.0 # start with a weight of 1\n",
    "\n",
    "    nvec = zeros(nIterations) # for keeping track of the weight (in terms of its integer power) at each iteration\n",
    "    nvec[0] = 0\n",
    "    rvec = rand(nIterations-1)\n",
    "\n",
    "    # for storing the running estimate of the largest eigenvector of A\n",
    "    eigEst = zeros([2,nIterations])\n",
    "    eigEst[0,0] = M[0,currentState]*weight[0]\n",
    "    eigEst[1,0] = M[1,currentState]*weight[0]\n",
    "\n",
    "    for i in range(1,nIterations):\n",
    "    \n",
    "        # the probability of staying in the current state is given by a diagonal element of the stochastic factor\n",
    "        # ...and because this is a 2-state example, this is enough to constrain the probability of switching into the other state\n",
    "        probStay = M[currentState,currentState]\n",
    "    \n",
    "        # if random number is greater than probability of staying, \n",
    "        # then for high probability of staying, probStay is close to 1 \n",
    "        # and it is less likely that a number will be greater than probStay\n",
    "        # so you should switch if this does happen\n",
    "        if(rvec[i-1]>probStay):\n",
    "            currentState = mod(currentState+1,2)            \n",
    "    \n",
    "        weight[i] = w[currentState,currentState]*weight[i-1]\n",
    "    \n",
    "        nvec[i] = getN(weight[i])\n",
    "    \n",
    "        eigEst[0,i] = eigEst[0,i-1] + M[0,currentState]*weight[i]\n",
    "        eigEst[1,i] = eigEst[1,i-1] + M[1,currentState]*weight[i]\n",
    "    \n",
    "    return weight, eigEst"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimate of largest eigenvalue of A:  1.07595702368\n",
      "Actual eigenvalue:  1.10517171552\n"
     ]
    }
   ],
   "source": [
    "nIterations = 1000\n",
    "weight, eigEst = estimateEig( nIterations, M, w )\n",
    "\n",
    "# given the unnormalized eigenvector estimate, normalize it and compute the associated eigenvalue\n",
    "# looks kind of like the local energy, yes?\n",
    "nrmEst = sqrt(dot(eigEst[:,nIterations-1],eigEst[:,nIterations-1]))\n",
    "eigNrm = eigEst[:,nIterations-1]/nrmEst\n",
    "print 'Estimate of largest eigenvalue of A: ', dot(eigNrm,dot(A,eigNrm))\n",
    "print 'Actual eigenvalue: ', wExact"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a decent estimate, but not perfect. Looks good, right?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
    "collapsed": false
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DwUUXwaabNr/dzJl5FJeUckzzzdfyfq0BlyRJUoeceir84Ac58ayryyUknXXY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\n5S9XP7ZqVfq3TbWlrytXQtu2MGNG6phy6aVw3XUtH6skSZJq11Iz4Cb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zz5T4bETNfzRJ\nUt6ZgEtqLQYCh8YYl9VwrDPwRYxxRQihL2m2PFtNSWsgJYnfB24MIRybGR8LHB1COCSE0C6E8Avg\na+AFgBjjQuBpYBQwO8b4Xk3Bxhi/BK4AbgohHBdC6Ji53w9CCNfV8TkrYu0ErAIWZhY5ngvsVMd1\nTfExkN2GcDipjr4vpIQ4s9C1Uy3XrynWT4AtqtWQZ7sLODeEsEsIoQOpHvylTLmJJBUcE3BJpew/\nM6cxxjkxxtdrOgb8GPhtCGER8Gsge6a2+rlVxmKMb5IWQt4SQvhejHE6cDZwI/AZafHfsTHGb7Ou\nHUOq/65p8WXlG8T4B+DiTEyfkhYX/pi6F2ZWxDUNuIG0CPVjUknHc2u6ro7XdbkSGJ0pNzk5xvga\nqQ78xkzXkulU7URT5d71iHUi6Y+dj0MIn64WeIxPApeR/uvGh0AP0iLP5vhsktTsQipPlCRJkpQL\nzoBLkiRJOWQCLkmSJOWQCbgkSZKUQybgkiRJUg6ZgEuSJEk5ZAIuSZIk5ZAJuCRJkpRDJuCSJElS\nDpmAS5IkSTn0/wD7TpmKJKNxYwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108d03790>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# weight vs iteration for the 1000 iteration Markov Chain\n",
    "figure(figsize=[12,10])\n",
    "plot(log10(weight))\n",
    "xlabel('Markov Chain Iteration')\n",
    "ylabel('Log10 Weight')\n",
    "title('Demonstration that the weights explode with the number of iterations')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It turns out that the weights used in our Markov Chain explode, which means that we cannot carry this out indefinitely to reduce variance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/local/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/ipykernel/__main__.py:6: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "/opt/local/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/ipykernel/__main__.py:7: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x109d54c10>"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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RFyd1rACwQjqadxdE2NCDCLaeToHwps/KrCwz8b4OuYFppBc3ADiVc264UscY2w4Rnir3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\n+vNSpXqeVr/6Xdaxa7alF110fWPQiLfleq1Ocizz6FlPs5/LulnsdZ2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rut/36nceViFv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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108d95610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# vary the length of the Markov chain\n",
    "iterationList = linspace(1,1000,1000)\n",
    "wEstList = zeros(len(iterationList))\n",
    "for idx,nIterations in enumerate(iterationList):\n",
    "    weight, eigEst = estimateEig( int(nIterations), M, w )\n",
    "    nrmEst = sqrt(dot(eigEst[:,nIterations-1],eigEst[:,nIterations-1]))\n",
    "    eigNrm = eigEst[:,nIterations-1]/nrmEst\n",
    "    wEstList[idx] = dot(eigNrm,dot(A,eigNrm))\n",
    "    \n",
    "# estimates vs length of Markov chain\n",
    "figure(figsize=[12,10])\n",
    "plot(iterationList, wEstList, 'o', label='Estimated eigenvalue')\n",
    "axhline(wExact, color='black', label='Exact eigenvalue')\n",
    "xlabel('Length of Markov Chain')\n",
    "ylabel('Eigenvalue estimate')\n",
    "title('Stochastic iteration to compute eigenvalue estimate from estimated eigenvector')    \n",
    "legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Running this calculation for many different chain lengths, we see that increasing the chain length does not appear to generally make things better. Of course, this calculation is only for a single walker."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## VII. Difficulties Arise\n",
    "\n",
    "Hetherington quantifies the difficulties that we are observing by plotting the distribution of weights in Figure 2. Let us reproduce this plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1082326d0>"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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pp1ZL777Ua51upVvJ1rylts384Ac/4K677iKlxP333883v/lNDhw4wIYNG3jiE5940vUs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\nhndJkiR1g6vNSJIkSauc4V2SJEnKifW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6Q9c5WVWSJHUNJ6y2gMW7JEnSiUqlQ+Tze5ic\nnKO/fw2FwigDA5uyDqvjWby3gMW7JEnSvFLpEFu3fpRicRfQA8yQy+1gbGybBfwS2W1GkiRJLZXP\n76kp3AF6KBZ3kc/vyTCq1c3iXZIkSQuanJxjvnCv6mFqai6LcITFuyRJkk6iv38NMFO3dYa+PkvI\nrJh5SZIkLahQGCWX28F8AV8e814ojGYW02rnhNUaTlhtjdJEifzuPJPTk/T39lPYXmBg80DWYUmS\n1HHa4T212m1mamqOvj67zbSK3WZawOJ96UoTJbZetZXiliKsA2YhdzDH2LVjFvCSJDXA99TuZrcZ\ntYX87vz8TQZgHRS3FMnvzmcalyRJncb3VC3E4l0tVTxSc5OpWgfFI/dlEo8kSZ1qcnpywffUqemp\nTOJRe7B4V0vdf+8MzNZtnIX77z2WSTySJHWq/t7+Bd9T+3r7MolH7cHiXS11zrpBuCk3f7OZBW7K\n8bjTB7MLSpKkDlTYXiB38MT31NzBHIXthUzjUrYs3tVST8ydBT+8Ga4fhk8Nlf/84c3knnBW1qFJ\nktRRBjYPMHbtGMNHhxkqDTF8dNjJqrLbTC27zSxdqXSIrVs/WrOUcrkf7NjYNttKSZIkVdgqsgUs\n3lvDfrCSJEmnZvHeAhbvkiRJWgn2eVdLlCZKjFw9wtDoECNXj1CaKGUdkiRJkip88l5jtT95dyU3\nSZK0HKpDaicn5+jvd0gtOGymJVZ78T5y9Qj7Nuw7cUGIWRg+Oszej+zNLC5JktS5bGaxMIfNaMlc\nyU2SpO7SDsNh8/k9NYU7QA/F4i7y+T0rHks3WJt1AGofx1dyq3vy7kpukiR1nhOGw54FzMJdV921\n4sNhJyfnmC/cq3qYmppbsRi6iU/eddybX/MW1t6y8YSV3NbespE3v+YtmcYlSZIal9+dn5/HBrAO\niluK5HfnVzSO/v41wEzd1hn6+ixDm2HWdNzHbriV39195wmro/7u7jv52A23Zh2aJElqULsMhy0U\nRsnldjBfwJfHvBcKoysaR7dw2IyOK/9a6+nwwF54YH771NTnM4tJkiQ1p12Gww4MbGJsbBv5/DU1\nCziu7smqS2HxruPmf61VOy7NX2tJktSJCtsL3HXVXQ9rAV24trDisQwMbGLv3h0r/vd2I1tF1uiG\nVpGliRL53Xkmpyfp7+2nsL2w6EkptnKSJKm7VOuCqekp+nr7GqoLtLzs894CnV68t2KRpeoiCvO/\n1nIRBUmSpFazeG+BTi/eXWRJkiS12lJ+q6+Ta7Z4d8x7FykeqfRxrbUOikfuyyQeSZLU2dqlV7zm\nOROxi9x/78x8j/aqWbj/3mOZxCNJkjpbu/SK1zyL9y5yzrpBuCl3wiJL3JTjcacPZheUJEnqWO3S\nKx7K8/JGRnYxNLSDkZFdlEqHVjyGduCwmS7yxNxZfHPfzXD9+2H9FBzrgwfeSW74C1mHJkmSOlC7\n9IpfqCPeXXetzo54TlitkfWE1aVOCLHVoyRJaqVWdLJrhZGRXezb92fUr0UzPHxNx/aPd8JqhytN\nlBi8YpDDzz58fELIgSsOMH7D+KJ/OFzBTJIktdLA5gHGrh07sVf8tSvfbaa8CnxP3dYepqbmVjSO\ndmDx3ibe9t4/LRfuNRNCDj/7MG97759y86e+vOjzuIKZJElqpYHNA5m3nHYV+Hmr7ztuU3fdfXDB\nCSHfvPtgJvFIkiS1SmmixMjVIwyNDjFy9QiliVJDxxcKo+RyOygX8FAdGlwojLY20A7gk/cWWfIC\nBsfWLzghhGPrWxypJEnSymlFr3iHBs9zwmqNZiestmIyxytf+Sfc/P++Aq8uHT8HNw1w2VNewZe/\n/OGGY5IkSWoH7bICfKl0iHx+D5OTc/T3r6FQGM20+HfCaoZOtYDBYi/KD35wO98Z/DU/uf4orD8C\nxx7L49dv4IMf3L58gUuSJC2zyenJBVeAX8le8d3UatIx73WaGYdVPFJccLx68ch9iz7HwMAmbh9/\nD8MveSpDuYsZfslTuX38PR13QUmSJNU63iu+1gr3is/n99QU7gA9FIu7yOf3rFgMreKT9zr7Nuxr\neBzW/ffOQI6H/Tro/nuPNfR32ylGkiR1m8L2AnddddfDhhcXri00dJ6lzC/splaTPnmvVzPkZbHO\nWTcIN+Xm/1c5C9yU43GnDy5DgJIkSZ2j2it++OgwQ6Uhho8ON7zIU3V+4b4N+xgfGGffhn1svWrr\nokdLzLearNV4q8lS6RAjI7sYGtrByMguSqVDDR3fCk5YrRERiZ3lz//dPc/h//6vbyzquPKqX/8B\nznw/rJ+CY33wwDsZHv6CT9IlSZKWaKmTXluxCn2rV7JvdsLqqnjyHhGPjogvRcSxiChFxB+f8oAG\nh7yUe4/eCA/cAIdvgwduIJe7cVX2HpUkSWq1yenJBecXLnbS68DAJj514yvZ/KzncMaWzWx+1nP4\n1I2vbKjobpdx86uieAeuA34DPAYYAf5HRDx1wVc2MeSl2nt0ePgahoZ2MDx8TUfOXm618fHxrEPo\nKuazdcxla5nP1jKfrWU+WyfLXC510mtposQbPjDKxIu/z69edYiJF3+fN3xgtKEmJeVx80fgzBE4\nd6j8J0caHjdfHXrTrK4v3iPiUcAfAu9JKf1LSulO4GbgPy14wPXD8MObyT3hxJ5G+w/cwcCF53PG\nBZsZuPB89h+444T91cmmt922i717dzyscH+k4xej085xsh/yTvs+lvMcjRzf7flsh2tzpeNo5xga\nOUe3X5utOIc/69nF0M75bIcYGjnHct47H+n4wvYCuYMnzi/MHcxR2F5Y1DlO1dZ7sXFs3PgrePIl\n8JZ98Ibx8p9PvoTe3l8t+hyl0iGeP/g+9v3tPQ3l5wQppa7+AC4AjtVt2w7cvMBrExxLudzb0333\nTaSq2/cfSGufsTHxLhI7SbyLtPYZG9Pt+w+kxVjq8Z16jh07dmQeQzufo9Hjuzmf7XBtZhFHu8bQ\n6Dm6+dpsxTn8Wc82hnbNZzvE0Og5luveudjj7yvdl4a3Daehy4fS8LbhdF/pvkWfY/DywfL2uo+h\ny4cWfY5LX3/Z/L6d86+59PWXLfocl112deLJA+X9kFITtW3XT1iNiIuAz6eU+mq2/WfgP6aUXlD3\n2jQ8vPNhK24NXHg+Ey/+/sMmSWz+2jMpfft7jxjDUo/v1HPs3LmTnTt3dvz3sVznaPT4bs5nO1yb\nWcSxHMdncY5uvjZbcQ5/1rONoV3z2Q4xNHqO5bp3rsT3sZgJr490jqHRIcYHxh/2dw+Vhrhtz22L\nOsc5T3smR151d3n/TpqasLoaivcLgDtSSutrtr0deF5K6bK613Z3MiRJktQ2mineV8MiTT8C1kZE\nLqVUrGzbAvyg/oXNJFCSJElaKV3/5B0gIv4nkIA3Ac8CvgI8N6W0hNkCkiRJ0srq+m4zFW8FHgUc\nAfYCb7FwlyRJUqdZFU/eJUmSpG6wWp68n1JEfDYifhoRD0ZEMSLeXbf/koi4p7JC660RcW5Wsba7\niFgXEZ+IiIlKPr8TES+ue435XKSIeGtE/ENE/CYiPrXAfnPZgIZXW9YJTnU9ei025pHuleazcad6\nLzefzYmI8yLiXyLiMzXbzGWDImK8ksfpiDgaEffU7Gs4nxbvZe8HBlJKG4GXANsi4t8DRMRZwE3A\nu4EzgW8Df51VoB1gLXAYuLiSzzzw+erFaD4bNgkUgE/W7zCXTVn8astayILXo9diU056rzSfTVvw\nvdx8Lsm1wLeqX0TE2ZjLZiTgypRSb0ppQ0rpqdD8vdNhM3Ui4snA3wOXpZS+ExFvAi5PKV1U2f8o\n4OfABSmlH2UYaseIiIPAzpTSl8xncyKiAPSnlN5Qs81cNqCSn18CT6t2noqITwOTKaV3ZRpch6m/\nHr0WW6N6rwTOxnwuSe17OXAh5rNhEfFa4JXAPwFPTCm9zp/15kTE14HPppTqf2PZVD598l4REX8V\nETPA3cCfp5S+U9n1dOBg9XUppV8DP65s1yOIiHOAJ1HOK5jPVjKXjXkS8K81LWOhnD/ztXRei0tU\nuVeeR7mNsfls0kney81ngyKiF9hFeUX62jba5rJ574+IIxFxICKeX9nWVD4t3itSSm8F1gMvBN4X\nEb9f2bUeeLDu5dPAhhUMryNFxFrK3X1uTCndW9lsPlvHXDZmPeX81DJfreG1uAQ198o9ladt5rNJ\nNe/lWym/l/9bzGcz3gt8PKU0VbfdXDbnvwJPAPqBjwO3RMQATeaz64v3iPh6RMxFxEMLfOyvfW0q\nux34G6A6ke0Y0Ft32o3A0eWPvv0sNp8REZTfjH4LbKs5hfmsaOTaPAlz2RjztXzMbZNOcq80n0tQ\neS8fZ/693Hw2IMor078Q+NACu81lE1JK/5BSmkkp/WtK6TPAncDLaDKfXb/CakppqInD1gK/rnz+\nA+Dy6o6I6AFyLLBC62rQQD4/SXnc5ktTSg/VbDefFU1em7XMZWMWvdqyGua12LyF7pXmszXWAjPA\nIcxnI54PbAIOV/5zuR5YExFPA64HRqsvNJdL1tTPetc/eX8kEfGYiPijiOiJiDWVLjOvAW6uvORL\nwNMj4lURcTqwA/iuEzNOLiKuB54CXJpSmq3bbT4bEBGnRcTvAadRLjxPj4jTKrvNZQMqYwm/CLw3\nIh4VERcBrwA+m21kneMU16PXYhNOca80nw06xXv5lzGfjbqBcgF5AeUHHNcD/xt4EeV8mssGRMTG\niHhR9X4ZEcPAxcDf0uy1mVJa1R+Un3iMAw9Q7kTxLeAVda95AXAP5f/B3wacm3Xc7foBnAvMUf7N\nxdHKxzTwx+azqXzuqOTzoZqP/2Yum87noys3y2PABPBHWcfUSR+nuh69FhvO5Snvleaz4Xye8r3c\nfC4ptzuAz5jLpvN3duV6fLByfX4DeMFS8mmrSEmSJKlDrPphM5IkSVKnsHiXJEmSOoTFuyRJktQh\nLN4lSZKkDmHxLkmSJHUIi3dJkiSpQ1i8S5IkSR3C4l2SJEnqEBbvkiRJUoeweJckSZI6hMW7JKlh\nEVGKiLdHxMGI+GVEfC4i1mUdlyR1O4t3SVKzXgO8CBgAtgCjmUYjSavA2qwDkCR1rA+nlH4GEBFf\nAS7IOB5J6no+eZckNetnNZ//GlifVSCStFpYvEuSJEkdwuJdkiRJ6hAW75KkZqSsA5Ck1ShS8v4r\nSZIkdQKfvEuSJEkdwuJdkiRJ6hAW75IkSVKHsHiXJEmSOoTFuyRJktQhLN4lSZKkDmHxLkmSJHUI\ni3dJkiSpQ1i8S5IkSR3i/wOXTuKOQBdA0AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a050910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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SpDno71/DyMhGarW3MjExRW/vCur12T+c2+nxWh1o2c8Pf/hD7rrrLjKThx56iO9+97vc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\n/4US6tRLJt8xAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109c71250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nWalkers = 500000\n",
    "nIterations = 50\n",
    "\n",
    "ensembleP = zeros([nIterations*2+1,2])\n",
    "\n",
    "def getN(weight):\n",
    "    return int(round(log(weight**2)/log(6.0/4.0)))\n",
    "\n",
    "for walker in arange(nWalkers):\n",
    "\n",
    "    # decide randomly on the initial state\n",
    "    if(rand(1)<0.5):\n",
    "        currentState = 0\n",
    "        increment = True\n",
    "    else:\n",
    "        currentState = 1\n",
    "        increment = False\n",
    "\n",
    "    nvec = zeros(nIterations,dtype=int)\n",
    "    nvec[0] = 0\n",
    "    rvec = rand(nIterations-1)\n",
    "\n",
    "    for i in range(1,nIterations):\n",
    "    \n",
    "        probStay = M[currentState,currentState]\n",
    "   \n",
    "        if(increment):\n",
    "            nvec[i] = nvec[i-1] + 1\n",
    "        else:\n",
    "            nvec[i] = nvec[i-1] - 1\n",
    "\n",
    "        if(rvec[i-1]>probStay):\n",
    "            currentState = mod(currentState+1,2)    \n",
    "            increment = not(increment)\n",
    "    \n",
    "    ensembleP[nIterations+1+nvec[-1],currentState] += 1.0 \n",
    "    \n",
    "n = linspace(-nIterations,nIterations,2*nIterations+1)\n",
    "figure(figsize=[12,10])\n",
    "plot(n,ensembleP[:,0], 'o', label='i=1')\n",
    "plot(n,ensembleP[:,1], 'o', label='i=2')\n",
    "xlabel('n')\n",
    "ylabel('p(n,i)')\n",
    "title('Reproduction of Fig. 2a')\n",
    "legend()\n",
    "xlim([-30,50])\n",
    "figure(figsize=[12,10])\n",
    "plot(n,ensembleP[:,0]*(1.5)**(n/2.), 'o', label='i=1')\n",
    "plot(n,ensembleP[:,1]*(1.5)**(n/2.), 'o', label='i=2')\n",
    "xlabel('n')\n",
    "ylabel('wn p(n,i)')\n",
    "title('Reproduction of Fig. 2b')\n",
    "xlim([-30,50])    \n",
    "legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An important thing to note in comparing this with the paper is that depending on the length of the Markov Chain (in this case 50) there are certain values of n that will never be reached. That is why every other entry (all of the even values of n) have proabability 0.\n",
    "\n",
    "For the interested reader, it might be fun to watch the separation between these two sets of peaks grow as the length of the Markov Chain increases.\n",
    "\n",
    "What is really important here? \n",
    "* The most probable answer is not the same as the average answer.\n",
    "* The variance associated with estimators from this Markov chain will grow with the length of the chain. \n",
    "* The formal variance is non-monotonic in the length of the chain but it quickly turns over to exponential growth. This means that there is an optimal sequence length, beyond which continued iteration will help less than reducing statistical error by increasing the number of walkers.\n",
    "\n",
    "Next we reproduce Figure 3. Here we demonstrate the the eigenvector estimate not only looks very different from the actual eigenvector, but that it does not resemble the eigenvector estimate predicted via matrix multiplication (i.e., deterministic power method)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x10bcabe50>"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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dpZdeekkrV67UrFmz9D//8z8J17V79+5au3atXn31VX3xxRfauHGjevbsqfHj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      "text/plain": [
       "<matplotlib.figure.Figure at 0x107ec7850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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rrxcrc8UVV+j999/X6tWrlZ2drddee03t2rUrugiyQ4cO+uijj7RhwwZt3749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\nBwCACRLAAQBgggRwAACYIAEcAAAm6P8BcRW4/NFcXmIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10bc7db90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nWalkers = 512\n",
    "nIterations = 500\n",
    "\n",
    "ensembleX = zeros([nIterations,2])\n",
    "ensembleX[0,0] = 1.0\n",
    "ensembleX[0,1] = 0.0\n",
    "\n",
    "def getN(weight):\n",
    "    return int(round(log(weight**2)/log(6.0/4.0)))\n",
    "\n",
    "for walker in arange(nWalkers):\n",
    "\n",
    "    # do not decide randomly on the initial state, you know it is 0\n",
    "    currentState = 0        \n",
    "    \n",
    "    nvec = zeros(nIterations,dtype=int)\n",
    "    nvec[0] = 0\n",
    "    rvec = rand(nIterations-1)\n",
    "    weight = zeros(nIterations)\n",
    "    weight[0] = 1.0\n",
    "\n",
    "    for i in range(1,nIterations):\n",
    "    \n",
    "        probStay = M[currentState,currentState]\n",
    "           \n",
    "        if(rvec[i-1]>probStay):\n",
    "            currentState = mod(currentState+1,2)    \n",
    "               \n",
    "        weight[i] = w[currentState,currentState]*weight[i-1]\n",
    "        ensembleX[i,:] += M[:,currentState]*weight[i]        \n",
    "        \n",
    "analX = zeros([nIterations,2])\n",
    "analX[0,0] = 1.0\n",
    "analX[0,1] = 0.0\n",
    "\n",
    "for i in range(1,nIterations):\n",
    "    analX[i,:] = dot(A,analX[i-1,:])\n",
    "    \n",
    "figure(figsize=[12,10])\n",
    "plot(arctan2(ensembleX[:,1],ensembleX[:,0]),'.', label='Stochastic Iteration')\n",
    "plot(arctan2(analX[:,1],analX[:,0]), '-', label='Matrix Multiplication')\n",
    "xlabel('N')\n",
    "ylabel('arctan($X_2/X_1$)')\n",
    "title('Exponential Growth in Error for Stochastic Eigenvector Estimate')\n",
    "legend()\n",
    "\n",
    "figure(figsize=[12,10])\n",
    "xlim([0,50])\n",
    "ylim([0,0.7])\n",
    "plot(arctan2(ensembleX[:,1],ensembleX[:,0]),'.', label='Stochastic Iteration')\n",
    "plot(arctan2(analX[:,1],analX[:,0]), '-', label='Matrix Multiplication')\n",
    "xlabel('N')\n",
    "ylabel('arctan($X_2/X_1$)')\n",
    "title('Exponential Growth in Error for Stochastic Eigenvector Estimate')    \n",
    "legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## VIII. The Weighted Average\n",
    "\n",
    "Rather than using the eigenvector itself to compute the eigenvalue estimate, this section introduces a functional form for an estimator. We use it to reproduce Figure 4."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def weightedAverage( L, nTrials ):\n",
    "    \n",
    "    nIterations = 20000\n",
    "\n",
    "    M = zeros([2,2])\n",
    "    M[0,0] = 5./6.\n",
    "    M[0,1] = 1./4.\n",
    "    M[1,0] = 1./6.\n",
    "    M[1,1] = 3./4.\n",
    "        \n",
    "    w = zeros([2,2])    \n",
    "    w[0,0] = sqrt(6./4.)\n",
    "    w[1,1] = sqrt(4./6.)\n",
    "    \n",
    "    lambdaEsts = zeros(nTrials)\n",
    "    \n",
    "    for trial in arange(nTrials):\n",
    "\n",
    "        # do not decide randomly on the initial state, you know it is 0\n",
    "        currentState = 0        \n",
    "        \n",
    "        Gnvec = zeros(nIterations)\n",
    "        wvec = zeros(nIterations)\n",
    "        rvec = rand(nIterations)\n",
    "        weightList = []\n",
    "        \n",
    "        cweight = w[currentState,currentState]\n",
    "        wvec[0] = cweight\n",
    "        Gnvec[0] = 1.0        \n",
    "        weightList.append( cweight )\n",
    "\n",
    "        for i in range(1,nIterations):\n",
    "                        \n",
    "            probStay = M[currentState,currentState]\n",
    "           \n",
    "            if(rvec[i]>probStay):\n",
    "                currentState = mod(currentState+1,2)    \n",
    "               \n",
    "            cweight = w[currentState,currentState]            \n",
    "            wvec[i] = cweight\n",
    "            \n",
    "            if(L==0):\n",
    "                Gnvec[i] = 1.0\n",
    "            else:                \n",
    "                Gnvec[i] = reduce( lambda x, y: x*y, weightList )\n",
    "            \n",
    "            weightList.append(cweight)\n",
    "            if(len(weightList)>L):\n",
    "                weightList.pop(0)\n",
    "            \n",
    "        lambdaEsts[trial] = dot(wvec,Gnvec)/sum(Gnvec)\n",
    "    \n",
    "    return mean(lambdaEsts), var(lambdaEsts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# this guy will take like 5 minutes to run\n",
    "Lvals = [0,1,2,3,4,5,6,7,12,18,20,24,30,35,41,48]\n",
    "NL = len(Lvals)\n",
    "lammeans = zeros(NL)\n",
    "lamvars = zeros(NL)\n",
    "for idx,L in enumerate(Lvals):\n",
    "    lammeans[idx], lamvars[idx] = weightedAverage( L, 50 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10c0bcf10>"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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T3D7JnsVO3rVr19d+npuby9wMdKFffvnePPSh5+TSS89Ksi3nn391Lr54Z978\n5jOEfgCATWDPnj3ZMz9kYxVt5VV63p7k25J8XWvtKxPbH5TkomyyVXpOO+2snH/+M5Jsm9h6dU49\n9eycd97OjaoWACzKKj1sRlbpWSdVdceqOqGqbraCYl6TIR3/xILtT0/ylSQXrKDsdXfllftz/bCf\nJNuyb9/+jagOAAAzYmaG9FTVaUm2J6kkd0hyo6p69rh7b2vtvInDX5DkiUnmMqyZP1/Gg5KcOP7x\nPuPzGVX1X0nSWnv+RBkvT/IjSX6rqo5L8qEkpyR5eJLd074VmGXHHHNEkquzsIf/6KM35Wc6AABW\nycwM6amqC3MgrC90UWvt5IljX5nkCUlObq1NBv6dSZ67SBmttXa9DzhVdaskv5LkkUlul+TSJC9u\nrb30IPWcySE9C8fwJ1dnxw5j+AGYXYb0sBltxiE9MxP4N4tZDfzJEPrPPPPcnH/+/px6qlV6AJg9\nlpFmsxP4t4BZDfx+gQIArD2BfwuY1cAPAMDa24yB34xOAADomMAPAAAdE/gBAKBjAj8AAHRM4AcA\ngI4J/AAA0DGBHwAAOibwAwBAx9x4a4nceAsAYGvZs2d4zP88Nzf8PDd34Oe14E67G0TgBwBgPbjT\nLgAAcEgCPwAAdEzgBwCAjgn8AADQMYEfAAA6JvADAEDHBH4AAOiYwA8AAB0T+AEAoGMCPwAAdOyo\nja4AN3T55Xtz5pnn5sor9+eYY47I7t2n57jjtm90tQAA2ISqtbbRddhUqqqt5TV7zWv25qlPPSef\n/exZSbYluTq3ve3OvPjFZ+RxjxP6AQC2iqpKa61WWo4hPTPmTW86dyLsJ8m2fPazZ+VNbzp3A2sF\nAMBmJfDPmCuv3J8DYX/etuzbt38jqgMAwCYn8M+YY445IsnVC7ZenaOP9lcFAMDSSZEz5pRTTs9t\nb7szB0L/MIb/lFNO38BaAQCwWZm0u0RrPWk3ObBKz759+3P00VbpAQDYilZr0q7Av0TrEfgBAMAq\nPQAAwCEJ/AAA0DGBHwAAOibwAwBAxwR+AADo2FHLOamq7pLkbkm+PklL8pkk/9xa+9dVrBsAALBC\nhx34q+quSZ6c5FFJ7ji/eXxu4zGfTnJBkt9rrX1oFesJAAAswyHX4a+qHUl+LckjklyT5O1J3pnk\n0iRXZQj9X5fkm5PcL8mDktwsyeuS/GJr7bK1qvxGsA4/AADrYbXW4T+cHv4PJrkkyelJXtdau/oQ\nFduW4VsWEMMkAAAZG0lEQVSAp43n3nSFdQQAAJbpcHr4f7C19sZlFV718Nbany2rZjNKDz8AAOth\ntXr4Dxn4uT6BHwCA9bBagX/Vl+Wsqp+sqg+udrkAAMDSrcU6/LdPcsIalAsAACyRG28BAEDHBH4A\nAOiYwA8AAB0T+AEAoGOHc+OtVNXPLaHM71pmXQAAgFV2WOvwV9X+JZbbWmtHLq9Ks806/AAArIfV\nWof/sHr4k5y00hcCAADWnzvtLpEefgAA1sPM3mkXAACYHYcM/FX1kOUWXlXfvdxzAQCAlTucHv6/\nqqq3VtX3V9UhJ+JW1Y2q6hFVdVGSv1h5FQEAgOU6nEm7357kt5K8MclnquotSd6V5NIk/5mkknxd\nkm9Jcr8kD0lymyR/k+Tb1qDOAADAYTrsSbtVdf8kT0ny8CS3SLLwxEry+SSvS/LS1tq7V7GeM8Ok\nXQAA1sNqTdpd8io947Ce70jyrUnukCH4fybJPyd5X2ttqWv2byoCPwAA62HDAv9WJ/ADALAeZnJZ\nzqo6sqq+r6resJrlAgAAy7Mqgb+qHlhVL0nyqSRvSnKT1SgXAABYmcNZpWeqqvq2JI9L8tgk35Rk\nb5I/TPKa1toHVqd6AADASiwp8FfVjiSPzxD0T8gwWfeqJA9orV28+tUDAABW4rCG9FTV/arqH5J8\nNMnTk7wjyXcn+cYk5yR5TFWteEIBAACwug5rlZ6q+kCSjyR5VZK/bq19ZcH+Jyf5wST/s7X2hbWo\n6KywSg8AAOthtVbpOdwhPa9orb1wsZ2ttZeNPfwXV9UPtNYuX2nFAACAlVvVdfir6qeSnJXkh1pr\nb1+1gmeIHn4AANbDevfwH5bW2kurqmUY+nP8apYNAAAs3Zrcabeqjmit7V/1gmeAHn4AANbDTN5p\nd16vYR8AADabNQn8AADAbBD4AQCgYwI/AAB0TOAHAICOCfwAANAxgR8AADom8AMAQMcEfgAA6JjA\nDwAAHRP4AQCgYwI/AAB0TOAHAICOHbXRFejZnj3J61+/NxdeeG6uuGJ/7nznI3LSSafnEY/Ynrm5\nja4dAABbQbXWNroOm0pVtcO9ZpdfvjcPfeg5ufTSs5JsS3J1duzYmTe/+Ywcd9z2Na0nAACbW1Wl\ntVYrLceQnjV05pnnToT9JNmWSy89K2eeee4G1goAgK1E4F9DV165PwfC/rxt2bdv/0ZUBwCALUjg\nX0PHHHNEkqsXbL06Rx/tsgMAsD4kzzW0e/fp2bFjZw6E/mEM/+7dp29YnQAA2Fqs0rOG9u7dnlNO\nOSMXXnj2xCo9Z2Tv3u057riNrh0AAFuBVXqWaCmr9AAAwHJZpQcAADgkgR8AADom8AMAQMcEfgAA\n6JjADwAAHRP4AQCgYwI/AAB0TOAHAICOCfwAANCxmQn8VfWsqrqgqi6tqv1Vddkyy3lYVf1dVX2h\nqq4ayzx2kWO/tar+qKouq6prquqTVfXGqnrQSt4LAADMimqtbXQdkiRVtT/JVUnem+Q+ST7XWjt+\niWU8MskfJ3lfkj9IcuskP5vkq0nu01r7t4ljT0jyniRfTvJ7Sf41ydFJfjzJnZL8QGvtL6e8RpuV\nawYAQL+qKq21WnE5sxJeq+rY1trHx58vSbJtKYG/qo5KsjdDgL9ba+2acfu9MgT7P2itPXni+N1J\nfjnJw1trfz6xfUeG8P+G1tojp7yOwA8AwJpbrcA/M0N65sP+Cjw4yTdmCPbXTJT7T0n2JHlMVR05\ncfwXx+dPLSjn00n2J/nCCusDAAAbbmYC/yq4b5KW5OIp+y5Ocqskd5nY9gdJrkjykqp6cFUdXVX3\nTfKaJJ9P8ptrXF8AAFhzPQX+o8fnK6fsm992zPyG1tpnktwvyVeSXJjkk0n+Icm3JLn/+M0AAABs\naj0F/puPz1+esu9LC45JVd0pw1CfHUl+PskPJnlGhom+f1FVxwQAADa5oza6Aqtofkz+Tabsu+mC\nY5Lkt5Mcn+TbWmsfmt9YVX+TYaWgX03yxDWoJwAArJueAv++8fmYJB9ZsG++t35yuM9Dknx4Muwn\nSWvtn6vqwxkmAU+1a9eur/08NzeXubm55dUYAABGe/bsyZ49e1a93JlZlnPSMpflfEiSNyc5s7X2\n/AX7/jbJvZPcvrV23bjtv5Psba3dfUpZH0xy69baDYb1WJYTAID10N2ynEtRVXesqhOq6mYTmy/K\nsMTmj1XV5Fj9e2Xorb9gPuyP3p3khKr6zgVl3z/Daj7vWrM3AAAA62Rmevir6rQk25NUkp9OcqMk\nvzXu3ttaO2/i2HMzjK+fa629bWL7o5K8NskHkrw8wwTcpye5LsOddj81cewDk7wlybVJXpbhZlt3\nSfLkDB+EHthae9+UeurhBwBgzfV4p90Lk5y4yO6LWmsnTxz7yiRPSHLyZOAf9z0syXOS3DPDij1v\nSfJLrbXLp7zmfZI8O8l3JblNks9m+KbgV1prH1ikngI/AABrrrvAv1kI/AAArIctPYYfAAA4PAI/\nAAB0TOAHAICOCfwAANAxgR8AADom8AMAQMcEfgAA6JjADwAAHRP4AQCgYwI/AAB0TOAHAICOCfwA\nANAxgR8AADom8AMAQMcEfgAA6JjADwAAHRP4AQCgYwI/AAB0TOAHAICOCfwAANAxgR8AADom8AMA\nQMcEfgAA6JjADwAAHRP4AQCgYwI/AAB0TOAHAICOCfwAANAxgR8AADom8AMAQMcEfgAA6JjADwAA\nHRP4AQCgYwI/AAB0TOAHAICOCfwAANAxgR8AADom8AMAQMcEfgAA6JjADwAAHRP4AQCgYwI/AAB0\nTOAHAICOCfwAANAxgR8AADom8AMAQMcEfgAA6JjADwAAHRP4AQCgYwI/AAB0TOAHAICOCfwAANAx\ngR8AADom8AMAQMcEfgAA6JjADwAAHRP4AQCgYwI/AAB0TOAHAICOCfwAANAxgR8AADom8AMAQMcE\nfgAA6JjADwAAHRP4AQCgYwI/AAB0TOAHAICOCfwAANAxgR8AADom8AMAQMcEfgAA6JjADwAAHRP4\nAQCgYwI/AAB0TOAHAICOCfwAANAxgR8AADom8AMAQMcEfgAA6JjADwAAHRP4AQCgYwI/AAB0TOAH\nAICOCfwAANAxgR8AADom8AMAQMcEfgAA6JjADwAAHRP4AQCgYwI/AAB0TOAHAICOCfwAANAxgR8A\nADom8C/DPe95Vp72tL3Zs2ejawIAAAcn8C/DJZc8I2960znZvn3vRlcFAAAOSuBflm259NKzcuaZ\n5250RQAA4KAE/mXbln379m90JQAA4KAE/mW7Okcf7fIBADDbZiaxVtWzquqCqrq0qvZX1WXLLOdh\nVfV3VfWFqrpqLPPYgxz/rVX1v6tqX1V9qao+UVWvq6o7LP4qV2fHjp3Zvfv05VQRAADWzVEbXYEJ\nz09yVZL3JrnNcgqoqkcm+eMk70vyjCS3TvKzSd5RVfdprf3bguO/J8nrk3wsye8k+XSSr09y/yS3\nSvKZaa9zj3ucnZNOOiN7927Pccctp6YAALA+qrW20XVIklTVsa21j48/X5JkW2vt+CWcf1SSvUm+\nnORurbVrxu33SvKeJH/QWnvyxPF3SPKhJBcn+cHW2mENyK+qNivXDACAflVVWmu10nJmZkjPfNhf\ngQcn+cYMwf6aiXL/KcmeJI+pqiMnjv+pJLdN8szW2v6qutn4oQEAALoxM4F/Fdw3ScvQY7/QxRmG\n6NxlYtv3Jfl8kq+rqvcnuTrJl6rqbVV1n7WuLAAArIeeAv/R4/OVU/bNbztmYtsJGeYw/FWGIT8/\nlOQXktw9yYVVddc1qicAAKybnoaw3Hx8/vKUfV9acEyS3DLDB57zWms/Or+xqt6b5MIkz03yuDWo\nJwAArJueAv8Xx+ebTNl30wXHJMk1SbYledXkga21i6rqiiRzi73Qrl27vvbz3Nxc5uYWPRQAAA7L\nnj17smfPnlUvd2ZW6Zm0zFV6finD0p4Pba29dcG+X0nyrCR3b619aNz2wQzDeu7RWvvgguPfmeTb\nW2s3zQJW6QEAYD10t0rPKnh3ksqwhv5C988wQfejE9veNT7facrxd0ry76taOwAA2ACbMvBX1R2r\n6oSqutnE5ouSfCrJj1XVzSeOvVeGJTsvaK1dN3H8qzN8QHjyxLZU1Q9kmNz7prWqPwAArJeZGdJT\nVacl2Z4hhP90khsl+a1x997W2nkTx56b5IlJ5lprb5vY/qgkr03ygSQvz3Cn3acnuS7JfVprn1rw\nmucneWyGlXr+PMmx42v/Z5L7Lrwz73iOIT0AAKy51RrSM0uB/8IkJy6y+6LW2skTx74yyROSnDwZ\n+Md9D0vynCT3zLBiz1uS/FJr7fIpr3lEkp9P8qQMYf9zSf4yyXNaa9OW9xT4AQBYF90F/s1C4AcA\nYD2YtAsAABySwA8AAB0T+AEAoGMCPwAAdEzgBwCAjgn8AADQMYEfAAA6JvADAEDHBH4AAOiYwA8A\nAB0T+AEAoGMCPwAAdEzgBwCAjgn8AADQMYEfAAA6JvADAEDHBH4AAOiYwA8AAB0T+AEAoGMCPwAA\ndEzgBwCAjgn8AADQMYEfAAA6JvADAEDHBH4AAOiYwA8AAB0T+AEAoGMCPwAAdEzgBwCAjgn8AADQ\nMYEfAAA6JvADAEDHBH4AAOiYwA8AAB0T+AEAoGMCPwAAdEzgBwCAjgn8AADQMYEfAAA6JvADAEDH\nBH4AAOiYwA8AAB0T+AEAoGMCPwAAdEzgBwCAjgn8AADQMYEfAAA6JvADAEDHBH4AAOiYwA8AAB0T\n+AEAoGMCPwAAdEzgBwCAjgn8AADQMYEfAAA6JvADAEDHBH4AAOiYwA8AAB0T+AEAoGMCPwAAdEzg\nBwCAjgn8AADQMYEfAAA6JvADAEDHBH4AAOiYwA8AAB0T+AEAoGMCPwAAdEzgBwCAjgn8AADQMYEf\nAAA6JvADAEDHBH4AAOiYwA8AAB0T+AEAoGMCPwAAdEzgBwCAjgn8AADQMYEfAAA6JvADAEDHBH4A\nAOiYwA8AAB0T+AEAoGMCPwAAdEzgBwCAjgn8AADQMYEfAAA6JvADAEDHBH4AAOiYwA8AAB0T+AEA\noGMCPwAAdEzgBwCAjgn8AADQMYEfAAA6JvADAEDHBH4AAOjYzAT+qnpWVV1QVZdW1f6qumyZ5Tys\nqv6uqr5QVVeNZR57GOfds6q+Mr72I5fz2gAAMGtmJvAneX6Sk5J8LMlnl1PAGNT/b5KbJHlGkl9P\ncmKSd1TVHQ9yXiV5eZIvJmnLeW0AAJhFsxT4j2+t3aG19j1J9i315Ko6Ksk5SfYmeVBr7WWttV9L\n8j1J7phk10FO/5kkd03yG0uuNQAAzLCZCfyttY+vsIgHJ/nGJH/QWrtmotx/SrInyWOq6siFJ1XV\nNyXZnWRnkk8kqRXWAwAAZsbMBP5VcN8Mw3EunrLv4iS3SnKXKftemmEY0e+MfzakhyXbs2fPRleB\nGaRdMI12wTTaBWupp8B/9Ph85ZR989uOmdxYVY9J8r1Jntxa27+GdaNzflEzjXbBNNoF02gXrKWe\nAv/Nx+cvT9n3pQXHpKpuk+SFSX6/tfauNa4bAABsiJ4C/xfH55tM2XfTBcckydnj87PWrEYAALDB\nqrXZG7JeVZck2dZaO34J5/xShqU9H9pae+uCfb+SIdjfvbX2oar69iT/mOS5SV47cegPJfnVJGck\n+eskn2itXbugrNm7YAAAdKm1tuIFZY5ajYrMiHdnWGHn/kneumDf/ZN8PslHxz/feXx+XoYVeia1\nJC8an++b5L3X27kKFx0AANbLpuzhH2+ideskV8wvwTmuw783ybVJ7tZa++K4/V5J3pPkD1trPzlx\n/gOmFH1Skqck+c0MK/v8bWvtc6v53gAAYD3NTA9/VZ2WZHuGXvo7JLlRVT173L23tXbexOEvSPLE\nJHNJ3pYkrbWvVtXTMgzReUdVvTzDh4KnJ/l0Jm681Vr7tySvm1KHW46vf3Fr7Qb7AQBgs5mZwJ/k\nR5OcuGDb88bni5JMBv6W5AbLaLbW/qSqfjDJczLcNffLSd6S5Jdaa586zHrM3lceAACwTDOzSk9r\n7aTW2pGLPE5ecOyPtNaOaq29bUo5f9Fae0Br7Rattdu11h7TWrv8MOvwqvH1rte7X4OfraoPVdU1\nVXVFVZ1dVTdfrCz6UVXPqqoLqurSqtpfVZcd4vi7VNUbquo/q+oLVfW2qjppverL2quqb6mq51XV\nO6vq36vq81X1vqr65Wm/F7SJrWH8ez6vqj5YVf9VVVdX1Uer6sVVddwix2sXW1BV3ayqLhv/T/nd\nKfu1jS1g/Puf9vj8lGNX1CZmqYd/lr0ww8o9f5phOc+7JvmZJN+W5Ls3sF6sj+cnuSrDBO7bHOzA\nqjo+yTszzCV5QYbJ4j+e5K+r6nsXriDFpvWkDPN93pjh28evZJgD9CtJHl1V92utfTnRJraYOyW5\nY4Yho59M8tUk98jQXh5XVfdurX080S7I7iS3y5RRBdrGlvO2JL+/YNtXJv+wGm1iJiftzpKq+tYk\nlyT509ba/5zY/tNJfjfJ41trr13sfDa/qjp24j/pQ00ovyDJI5Lcu7V2ybhtW5J/SXJNa+2u61Nr\n1lJV3TvJv7bW/nvB9t1JfjnJGa21l4zbtIktrqoeleSCJGe11s4at2kXW9T4++MfkvxCkt9K8qLW\n2s9M7Nc2toiq2p/k3Nbakw5x3IrbxMwM6Zlhjx+fX7hg+8sz3MjrtPWtDuttPuwfyjiU4weSXDj/\nD3I8/+okf5DkLlV1nzWpJOuqtfbehWF/9H8yTPy/e6JN8DVXjM9fSbSLrayqjsiQH/4iyeun7Nc2\ntqCqutEY4KftW5U2IfAf2n0yTBB+9+TG8ev692dYqx+S5J4Z7vR88ZR9F2cIgtpL375pfP638Vmb\n2IKq6iZVdbuqOqaq/t8kL8uwbPQfjodoF1vXzyW5S5KfXmS/trH1PCpDB/J/V9Wnq+p3q+pWE/tX\npU0I/Id2dJL/aK19Zcq+K5PcvoZ7AMDR4/OVU/bNbztmnerCOht77s7M0Iv7mnGzNrE1/ViSzyT5\nRJK/ytAmHtRa+/S4X7vYgsaJ27syDO36xCKHaRtbyz8k2ZnkhzIsN/+3GT4Mvm1iAYhVaROC6qHd\nPMPyntN8aeKYG8yoZsuZ/8c5rb18acEx9Od3kvyPJM9qrf3ruE2b2Jpen+RDSW6R5NszLPrwtqp6\nyLhqnHaxNb0syceS/PZBjtE2tpDW2v0XbDpvnCv4/CRPS/KrWaU2oYf/0L6Y4auUaW46cQzMt4Np\n7UVb6dg4WfepSX6vtfbrE7u0iS2otbavtfbW1tobx0m6J2XopZsPetrFFlPDzUUfkuSnWmvXHeRQ\nbYPfyLAazynjn1elTejhP7R9Se5aVTeaMqznmAzDfb66AfVi9uwbn6d9tTa/bdpXcmxiVbUrybOT\n/GFr7SkLdmsTpLV2SVW9L8mDx03axRZSVTdO8psZJur+e1XtGHfdaXy+9bjtP6JtbHmtta9W1b4k\ntx83rUqb0MN/aO/OcJ2+c3JjVd0kwzr87552ElvSJRm+clv4FV3GbS3JP65rjVhTY9h/bpJXttZ+\nfMoh2gTzbpYDd4jXLraWmyW5Q4Ye23+deFyY4e/6CUk+muRHo21seWO+vFOS+Tk/q9ImBP5D+z/j\n89MXbP+JDP+Iz1/f6jCrxiWy/m+Suaq6x/z2qrpFhkl8H22t+YDYiap6boaw/6rW2o9OO0ab2Fqq\n6hsW2X5ShqVa35JoF1vQ1RlWYnn0+Dz/+KkMK6z85bjvjdrG1lFVX7fIrl9JcmSGGzuu2u8LN946\nDONtr5+a5A0ZvpL71gyTsN7eWnvIRtaNtTeOvdye4RfzTye5UYabpSTJ3tbaeRPH7sgw6/6rGcbr\nfj7Dh8O7JXlYa+0t61h11khVPTXJORmWWnxuDvTczvv0/N+1NrF1VNXrknxjkrdmaBs3TfIdSR6b\nYbjGA8dJu9oFqartSS7PDW+8pW1sAVX1W0nul+GbnisyTPJ/WIY5P+9McvLEHdtX3CYE/sNQVZWh\nh/8nkhyb4Rf3a5PsbK2ZPNO5qrowyYmL7L6otXbyguNPyHDr6wcnuXGS9yTZ1Vq7cE0ryrqpqldm\nWEJtMddrF9rE1jDeUfeJSe6VYQhHyxDo/iLJb7TWPrPgeO1iCxsD/2UZAv/TFuzTNjpXVT+Y4Vue\nuye5XZLrMgz1+j9Jfru1du2C41fUJgR+AADomDH8AADQMYEfAPj/27VjG4ShIIiCXomEVmjCCRXR\nDc3QBz1QA0cDiAxbWs+Epx9s+IIPFBP8AABQTPADAEAxwQ8AAMUEPwAAFBP8AABQTPADAEAxwQ8A\nAMUEPwB/kWRN8k5y23sLwJEJfgAAKCb4AQCgmOAHAIBigh8AAIoJfgAAKCb4AQCgmOAHAIBigh8A\nAIoJfgAAKCb4AQCg2GnvAQDUuyY5f7m/Zua++RqAg8nM7L0BgEJJ1mVZHj+ePGfmstUegKMS/AAA\nUMwffgAAKCb4AQCgmOAHAIBigh8AAIoJfgAAKCb4AQCgmOAHAIBigh8AAIoJfgAAKCb4AQCg2Ack\n2yu3XmT7rgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a598210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=[12,10])\n",
    "errorbar(Lvals, lammeans, yerr=100*lamvars,fmt='o',label='Stochastic Estimate')\n",
    "axhline(1.10517,color='black', label='Exact Eigenvalue')\n",
    "ylim([1.04,1.14])\n",
    "mpl.rcParams['font.size']=18\n",
    "xlabel('L')\n",
    "ylabel('$\\lambda$(L)')\n",
    "title('Reproduction of Fig. 4')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we see the fundamental tradeoff that we have to deal with. Even for a Markov Chain with 20,000 iterations we have a choice between problems:\n",
    "\n",
    "* If we truncate the product of weights to L<10, we have small variance but statistical bias.\n",
    "* If we let the product of weights increase to encompass the whole chain, the variance will grow exponentially with L.\n",
    "\n",
    "Reconfiguration is the solution to this problem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## IX, X, and XI. Carrying Many Configurations Simultaneously (and More)\n",
    "\n",
    "The solution to these problems is to carry many walkers together, and to assign a global weight to the group of walkers. The algorithm implemented goes through the following:\n",
    "\n",
    "* Create a population of walkers and sum up their total weight.\n",
    "    * Randomly move each walker individually as before.\n",
    "    * Compute the population averaged weight, which will be used in the estimator.\n",
    "    * Choose to copy (or not copy) walkers among this fixed population based upon their relative weights.\n",
    "    * Repeat.\n",
    "\n",
    "The basic idea here is that a single walker is liable to have weights that explode. Rather than relying on these individual weights, we aggregate them every so often (in this case every iteration) and reconfigure the walker population relative to their cumulative weights. This has the net effect of damping out huge fluctuations in the weights, while introducing a statistical bias that scales inversely with the walker population."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# the input variables are:\n",
    "#  -L : number of iterations to average over\n",
    "#  -M : population\n",
    "#  -N : length of Markov chain\n",
    "#  -S : S+1 = number of configurations to average over at the end of the chain\n",
    "def stochasticReconfiguration( L, M, N, S ):\n",
    "    \n",
    "    # p = the probabilities of staying in state 0 or 1\n",
    "    p = zeros(2)\n",
    "    w = zeros(2)\n",
    "    p[0] = 5./6.\n",
    "    p[1] = 3./4.\n",
    "    \n",
    "    # the weights affiliated with states 0 and 1\n",
    "    w[0] = sqrt(6./4.)\n",
    "    w[1] = sqrt(4./6.)\n",
    "    \n",
    "    # all walkers start in state 0\n",
    "    popStates = zeros(M)  \n",
    "    popWeights = w[0]*ones(M)\n",
    "    \n",
    "    # allocate the global weight \n",
    "    globalWeight = zeros(N+1) \n",
    "    # initialize for the first iteration\n",
    "    globalWeight[0] = w[0]\n",
    "    \n",
    "    \n",
    "    # iterate over the length of the Markov chain\n",
    "    for i in range(1,N+1):\n",
    "        \n",
    "        # compute a set of random numbers for testing each moving in the population, at this iteration\n",
    "        rvec = rand(M)\n",
    "        # accumulate population weight\n",
    "        totalWeight = 0.0\n",
    "        \n",
    "        # accumulate the global weight\n",
    "        for walker in range(M):\n",
    "            cState = popStates[walker]\n",
    "            if(rvec[walker]>p[cState]):\n",
    "                popStates[walker] = mod(cState+1,2)\n",
    "            popWeights[walker] = w[cState]\n",
    "            totalWeight += w[cState]\n",
    "        globalWeight[i] = totalWeight/float(M)\n",
    "        \n",
    "        # reconfigure\n",
    "        cumWeights = cumsum(popWeights)     \n",
    "        rvec = rand(M)\n",
    "        tmpStates = copy.deepcopy(popStates)\n",
    "        tmpWeights = copy.deepcopy(popWeights)\n",
    "        for walker in range(M):\n",
    "            choice = bisect.bisect( cumWeights, rvec[walker]*totalWeight )\n",
    "            popStates[walker] = tmpStates[choice]\n",
    "            popWeights[walker] = tmpWeights[choice]\n",
    "        \n",
    "    Gvec = zeros(S+1)\n",
    "    for s in range(0,S+1):\n",
    "        Gvec[s] = prod( globalWeight[N-s-L:N-s] )\n",
    "        \n",
    "    lambdaEst = dot(globalWeight[N-S:],Gvec)/sum(Gvec)\n",
    "        \n",
    "    return lambdaEst, globalWeight"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/local/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/ipykernel/__main__.py:39: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "/opt/local/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/ipykernel/__main__.py:41: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "/opt/local/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/ipykernel/__main__.py:42: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n"
     ]
    }
   ],
   "source": [
    "# nTrials for statistics\n",
    "nTrials = 10\n",
    "\n",
    "# 2,000 samples per test\n",
    "LList = [0,1,2,3,4,5,6,7,12,18,20,24,30,35,41,48]\n",
    "LEst = zeros(len(LList))\n",
    "LVar = zeros(len(LList))\n",
    "\n",
    "for idx,pop in enumerate(LList):\n",
    "    \n",
    "    trialResults = zeros(nTrials)\n",
    "    M = 30\n",
    "    N = 2000\n",
    "    for trial in range(nTrials):\n",
    "        lE, gW = stochasticReconfiguration(L, M, N, N-1)\n",
    "        trialResults[trial] = lE\n",
    "    \n",
    "    LEst[idx] = mean(trialResults)\n",
    "    LVar[idx] = var(trialResults)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.04, 1.14)"
      ]
     },
     "execution_count": 158,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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d+UnOHy9aMqeq+vkMX1efl+HCFQDrTmvtQb3bAEBf67KGvKr2z1Df+Fvpd4Y+AAAs27oM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\nAAAdCeQAANDR/w8jmqfI5m2R1wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d996450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=[12,10])\n",
    "mpl.rcParams['font.size']=12\n",
    "errorbar( LList, LEst, yerr=LVar, fmt='o' )\n",
    "axhline(1.10517)\n",
    "xlabel('L')\n",
    "ylabel('Eigenvalue')\n",
    "title('For M=30 walkers, the small L bias is removed')\n",
    "ylim([1.04,1.14])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/local/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/ipykernel/__main__.py:39: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "/opt/local/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/ipykernel/__main__.py:41: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "/opt/local/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/ipykernel/__main__.py:42: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n"
     ]
    }
   ],
   "source": [
    "# nTrials for statistics\n",
    "nTrials = 10\n",
    "\n",
    "# 2,000 samples per test\n",
    "LList = [0,1,2,3,4,5,6,7,12,18,20,24,30,35,41,48]\n",
    "LEst = zeros(len(LList))\n",
    "LVar = zeros(len(LList))\n",
    "\n",
    "for idx,pop in enumerate(LList):\n",
    "    \n",
    "    trialResults = zeros(nTrials)\n",
    "    M = 2\n",
    "    N = 2000\n",
    "    for trial in range(nTrials):\n",
    "        lE, gW = stochasticReconfiguration(L, M, N, N-1)\n",
    "        trialResults[trial] = lE\n",
    "    \n",
    "    LEst[idx] = mean(trialResults)\n",
    "    LVar[idx] = var(trialResults)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.04, 1.14)"
      ]
     },
     "execution_count": 161,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ESZ0AALBg8+5DfrsnV52V5O2tta9duiItLV1WAABYbis1DvlM7pnkXotcBwAA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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b9cfe10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=[12,10])\n",
    "mpl.rcParams['font.size']=12\n",
    "errorbar( LList, LEst, yerr=LVar, fmt='o' )\n",
    "axhline(1.10517)\n",
    "xlabel('L')\n",
    "ylabel('Eigenvalue')\n",
    "title('For M=2 walkers, the small L bias is removed (and made worse)')\n",
    "ylim([1.04,1.14])"
   ]
  },
  {
   "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": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}