{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solution of the atom within LDA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we take the code from the Hydrogen project and adopt it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy import *\n",
    "from scipy import integrate\n",
    "from scipy import interpolate\n",
    "from scipy import optimize\n",
    "from scipy import weave\n",
    "\n",
    "def Numerovc(f, x0_, dx, dh_):\n",
    "    code_Numerov=\"\"\"\n",
    "    double h2 = dh*dh;\n",
    "    double h12 = h2/12.;\n",
    "    \n",
    "    double w0 = x(0)*(1-h12*f(0));\n",
    "    double w1 = x(1)*(1-h12*f(1));\n",
    "    double xi = x(1);\n",
    "    double fi = f(1);\n",
    "    for (int i=2; i<f.size(); i++){\n",
    "        double w2 = 2*w1-w0+h2*fi*xi;  // here fi=f1\n",
    "        fi = f(i);                     // fi=f2\n",
    "        xi = w2/(1-h12*fi);\n",
    "        x(i)=xi;\n",
    "        w0 = w1;\n",
    "        w1 = w2;\n",
    "    }\n",
    "    \"\"\"\n",
    "    x = zeros(len(f))\n",
    "    dh=float(dh_)\n",
    "    x[0]=x0_\n",
    "    x[1]=x0_+dh*dx\n",
    "    weave.inline(code_Numerov, ['f','dh','x'], type_converters=weave.converters.blitz, compiler = 'gcc')\n",
    "    return x\n",
    "\n",
    "def fSchrod(En, l, R):\n",
    "    return l*(l+1.)/R**2-2./R-En\n",
    "\n",
    "def ComputeSchrod(En,R,l):\n",
    "    \"Computes Schrod Eq.\" \n",
    "    f = fSchrod(En,l,R[::-1])\n",
    "    ur = Numerovc(f,0.0,-1e-7,-R[1]+R[0])[::-1]\n",
    "    norm = integrate.simps(ur**2,x=R)\n",
    "    return ur*1/sqrt(abs(norm))\n",
    "\n",
    "def Shoot(En,R,l):\n",
    "    ur = ComputeSchrod(En,R,l)\n",
    "    ur = ur/R**l\n",
    "    f0 = ur[0]\n",
    "    f1 = ur[1]\n",
    "    f_at_0 = f0 + (f1-f0)*(0.0-R[0])/(R[1]-R[0])\n",
    "    return f_at_0\n",
    "\n",
    "def FindBoundStates(R,l,nmax,Esearch):\n",
    "    n=0\n",
    "    Ebnd=[]\n",
    "    u0 = Shoot(Esearch[0],R,l)\n",
    "    for i in range(1,len(Esearch)):\n",
    "        u1 = Shoot(Esearch[i],R,l)\n",
    "        if u0*u1<0:\n",
    "            Ebound = optimize.brentq(Shoot,Esearch[i-1],Esearch[i],xtol=1e-16,args=(R,l))\n",
    "            Ebnd.append((l,Ebound))\n",
    "            if len(Ebnd)>nmax: break\n",
    "            n+=1\n",
    "            print 'Found bound state at E=%14.9f E_exact=%14.9f l=%d' % (Ebound, -1.0/(n+l)**2,l)\n",
    "        u0=u1\n",
    "    \n",
    "    return Ebnd\n",
    "\n",
    "def cmpE(x,y):\n",
    "    if abs(x[1]-y[1])>1e-4:\n",
    "        return cmp(x[1],y[1])\n",
    "    else:\n",
    "        return cmp(x[0],y[0])\n",
    "\n",
    "# This is slightly modified code from Hydrogen project\n",
    "def ChargeDensity(bst,R,Zatom):\n",
    "    rho = zeros( len(R) )\n",
    "    N=0\n",
    "    for i,(l,Ei) in enumerate(bst):\n",
    "        dN = 2*(2*l+1)\n",
    "        if N+dN<Zatom:\n",
    "            ferm=1\n",
    "        else:\n",
    "            ferm = (Zatom-N)/float(dN)\n",
    "        u = ComputeSchrod(Ei,R,l)\n",
    "        drho = u**2 / (4*pi*R**2) * dN * ferm\n",
    "        rho += drho\n",
    "        N += dN\n",
    "        print 'Adding state with l=', l, 'and E=', Ei, 'with Z=', N, 'with ferm=', ferm\n",
    "        if N>=Zatom: break\n",
    "    return rho\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found bound state at E=  -0.999922109 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.249990190 E_exact=  -0.250000000 l=0\n",
      "Found bound state at E=  -0.111108201 E_exact=  -0.111111111 l=0\n",
      "Found bound state at E=  -0.062498772 E_exact=  -0.062500000 l=0\n",
      "Found bound state at E=  -0.039999314 E_exact=  -0.040000000 l=0\n",
      "Found bound state at E=  -0.250000016 E_exact=  -0.250000000 l=1\n",
      "Found bound state at E=  -0.111111117 E_exact=  -0.111111111 l=1\n",
      "Found bound state at E=  -0.062500003 E_exact=  -0.062500000 l=1\n",
      "Found bound state at E=  -0.039999959 E_exact=  -0.040000000 l=1\n",
      "Found bound state at E=  -0.111111111 E_exact=  -0.111111111 l=2\n",
      "Found bound state at E=  -0.062500000 E_exact=  -0.062500000 l=2\n",
      "Found bound state at E=  -0.039999977 E_exact=  -0.040000000 l=2\n",
      "Found bound state at E=  -0.062500000 E_exact=  -0.062500000 l=3\n",
      "Found bound state at E=  -0.039999992 E_exact=  -0.040000000 l=3\n",
      "Adding state with l= 0 and E= -0.999922108956 with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.249990190207 with Z= 4 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.250000015612 with Z= 10 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.111108200823 with Z= 12 with ferm= 1\n",
      "Adding state with l= 1 and E= -0.111111116781 with Z= 18 with ferm= 1\n",
      "Adding state with l= 2 and E= -0.111111111147 with Z= 28 with ferm= 1.0\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgkAAAFkCAYAAACq4KjhAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niUkhQURERGL6f/5yckOpvBdaAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11168cd10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Esearch = -1.2/arange(1,20,0.2)**2\n",
    "\n",
    "R = linspace(1e-8,100,2000)\n",
    "\n",
    "nmax=5\n",
    "Bnd=[]\n",
    "for l in range(nmax-1):\n",
    "    Bnd += FindBoundStates(R,l,nmax-l,Esearch)\n",
    "    \n",
    "Bnd.sort(cmpE)\n",
    "\n",
    "Zatom=28  # Like Ni ion\n",
    "rho = ChargeDensity(Bnd,R,Zatom)\n",
    "\n",
    "from pylab import *\n",
    "%matplotlib inline\n",
    "\n",
    "plot(R,rho*(4*pi*R**2),label='charge density')\n",
    "xlim([0,25])\n",
    "show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def FuncForHartree(y,r,rhoSpline):\n",
    "    return [y[1], -8*pi*r*rhoSpline(r)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "rhoSpline = interpolate.UnivariateSpline(R,rho,s=0)\n",
    "U1 = integrate.odeint(FuncForHartree, [0.0,5.], R, args=(rhoSpline,))[:,0]\n",
    "alpha = (2*Zatom-U1[-1])/R[-1]\n",
    "U1 += alpha*R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgkAAAFkCAYAAACq4KjhAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nBBERESnq/wMZSv2s+M+llwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1103c6f10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(R,U1)\n",
    "grid()\n",
    "show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def NumerovU(U, x0, dx, dt):\n",
    "    code_NumerovU=\"\"\"\n",
    "      double h2 = dt;\n",
    "      h2 = h2*h2;\n",
    "      double h12 = h2/12;\n",
    "      \n",
    "      double w0 = x(0)-h12*U(0);\n",
    "      double w1 = x(1)-h12*U(1);\n",
    "      double xi = x(1);\n",
    "      double Ux = U(1);\n",
    "      \n",
    "      for (int i=2; i<U.size(); i++){\n",
    "        double w2 = 2*w1 - w0 + h2*Ux;\n",
    "        Ux = U(i);\n",
    "        xi = w2+h12*Ux;\n",
    "        x(i) = xi;\n",
    "        w0 = w1;\n",
    "        w1 = w2;\n",
    "      }\n",
    "    \"\"\"\n",
    "    x = zeros(len(U))\n",
    "    x[0] = x0          # first point\n",
    "    x[1] = dx*dt + x0  # second point\n",
    "    \n",
    "    weave.inline(code_NumerovU, ['U', 'x', 'dt'], type_converters=weave.converters.blitz, compiler = 'gcc')\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ux = -8*pi*R*rho\n",
    "U2 = NumerovU(ux, 0.0, 0.1, R[1]-R[0])\n",
    "alpha2 = (2*Zatom-U2[-1])/R[-1]\n",
    "U2 += alpha2*R\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgkAAAFkCAYAAACq4KjhAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n2wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113e36150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(R,U1)\n",
    "plot(R,U2)\n",
    "grid()\n",
    "show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we add exchange correlation potential. Make sure \"excor.py\" is in your working directory, so that we can import it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from excor import ExchangeCorrelation\n",
    "exc = ExchangeCorrelation()\n",
    "def rs(rho):\n",
    "    \"Given density, returns rs.\"\n",
    "    if rho<1e-100: return 1e100\n",
    "    return pow(3/(4*pi*rho),1/3.)\n",
    "\n",
    "Vxc = [2*exc.Vx(rs(rh)) + 2*exc.Vc(rs(rh)) for rh in rho]\n",
    "\n",
    "Uks = U2-2*Zatom + Vxc*R\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAhkAAAFkCAYAAACNTikJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nfPH/AIti5pbHUZd2AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113e9eed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAhUAAAFkCAYAAACXcsmHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIiIh8f+19OMbReIjeAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113ee7850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(R,Vxc, label='Exchange-correlation contribution to U')\n",
    "legend(loc='best')\n",
    "show()\n",
    "\n",
    "plot(R,Vxc*R,label='Exchange-correlation contribution')\n",
    "plot(R,U2,label='Hartree contribution')\n",
    "plot(R,Uks, label='Uks')\n",
    "legend(loc='best')\n",
    "grid()\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now it is time to reorganize the code and feed Hartree+Exchange correlation back to the Schroedinger equation.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy import *\n",
    "from scipy import integrate\n",
    "from scipy import interpolate\n",
    "from scipy import optimize\n",
    "from scipy import weave\n",
    "\n",
    "def Numerovc(f, x0_, dx, dh_):\n",
    "    code_Numerov=\"\"\"\n",
    "    double h2 = dh*dh;\n",
    "    double h12 = h2/12.;\n",
    "    \n",
    "    double w0 = x(0)*(1-h12*f(0));\n",
    "    double w1 = x(1)*(1-h12*f(1));\n",
    "    double xi = x(1);\n",
    "    double fi = f(1);\n",
    "    for (int i=2; i<f.size(); i++){\n",
    "        double w2 = 2*w1-w0+h2*fi*xi;  // here fi=f1\n",
    "        fi = f(i);                     // fi=f2\n",
    "        xi = w2/(1-h12*fi);\n",
    "        x(i)=xi;\n",
    "        w0 = w1;\n",
    "        w1 = w2;\n",
    "    }\n",
    "    \"\"\"\n",
    "    x = zeros(len(f))\n",
    "    dh=float(dh_)\n",
    "    x[0]=x0_\n",
    "    x[1]=x0_+dh*dx\n",
    "    weave.inline(code_Numerov, ['f','dh','x'], type_converters=weave.converters.blitz, compiler = 'gcc')\n",
    "    return x\n",
    "\n",
    "def NumerovU(U, x0, dx, dt):\n",
    "    code_NumerovU=\"\"\"\n",
    "      double h2 = dt;\n",
    "      h2 = h2*h2;\n",
    "      double h12 = h2/12;\n",
    "      \n",
    "      double w0 = x(0)-h12*U(0);\n",
    "      double w1 = x(1)-h12*U(1);\n",
    "      double xi = x(1);\n",
    "      double Ux = U(1);\n",
    "      \n",
    "      for (int i=2; i<U.size(); i++){\n",
    "        double w2 = 2*w1 - w0 + h2*Ux;\n",
    "        Ux = U(i);\n",
    "        xi = w2+h12*Ux;\n",
    "        x(i) = xi;\n",
    "        w0 = w1;\n",
    "        w1 = w2;\n",
    "      }\n",
    "    \"\"\"\n",
    "    x = zeros(len(U))\n",
    "    x[0] = x0          # first point\n",
    "    x[1] = dx*dt + x0  # second point\n",
    "    \n",
    "    weave.inline(code_NumerovU, ['U', 'x', 'dt'], type_converters=weave.converters.blitz, compiler = 'gcc')\n",
    "    return x\n",
    "\n",
    "def fSchrod2(En, R, l, Uks):\n",
    "    return l*(l+1.)/R**2 + Uks/R - En\n",
    "    #return l*(l+1.)/R**2-2./R-En\n",
    "\n",
    "def ComputeSchrod(En,R,l,Uks):\n",
    "    \"Computes Schrod Eq.\" \n",
    "    f = fSchrod2(En,R[::-1],l,Uks[::-1])  # do not forget to turn around Uks!\n",
    "    ur = Numerovc(f,0.0,-1e-7,-R[1]+R[0])[::-1]\n",
    "    norm = integrate.simps(ur**2,x=R)\n",
    "    return ur*1/sqrt(abs(norm))\n",
    "\n",
    "def Shoot(En,R,l,Uks):\n",
    "    ur = ComputeSchrod(En,R,l,Uks)\n",
    "    #ur = ur/R**l\n",
    "    f0 = ur[0]\n",
    "    f1 = ur[1]\n",
    "    f_at_0 = f0 + (f1-f0)*(0.0-R[0])/(R[1]-R[0])\n",
    "    return f_at_0\n",
    "\n",
    "def FindBoundStates(R,l,nmax,Esearch,Uks):\n",
    "    n=0\n",
    "    Ebnd=[]\n",
    "    u0 = Shoot(Esearch[0],R,l,Uks)\n",
    "    for i in range(1,len(Esearch)):\n",
    "        u1 = Shoot(Esearch[i],R,l,Uks)\n",
    "        #print 'looking at energy', Esearch[i], u0,u1\n",
    "        if u0*u1<0:\n",
    "            Ebound = optimize.brentq(Shoot,Esearch[i-1],Esearch[i],xtol=1e-16,args=(R,l,Uks))\n",
    "            Ebnd.append((l,Ebound))\n",
    "            if len(Ebnd)>nmax: break\n",
    "            n+=1\n",
    "            print 'Found bound state at E=%14.9f E_exact=%14.9f l=%d' % (Ebound, -1.0/(n+l)**2,l)\n",
    "        u0=u1\n",
    "    return Ebnd\n",
    "\n",
    "def cmpE(x,y):\n",
    "    if abs(x[1]-y[1])>1e-4:\n",
    "        return cmp(x[1],y[1])\n",
    "    else:\n",
    "        return cmp(x[0],y[0])\n",
    "\n",
    "# This is slightly modified code from Hydrogen project\n",
    "def ChargeDensity(bst,R,Zatom,Uks):\n",
    "    rho = zeros( len(R) )\n",
    "    N=0\n",
    "    for i,(l,Ei) in enumerate(bst):\n",
    "        dN = 2*(2*l+1)\n",
    "        if N+dN<Zatom:\n",
    "            ferm=1\n",
    "        else:\n",
    "            ferm = (Zatom-N)/float(dN)\n",
    "        u = ComputeSchrod(Ei,R,l,Uks)\n",
    "        drho = u**2 / (4*pi*R**2) * dN * ferm\n",
    "        rho += drho\n",
    "        N += dN\n",
    "        print 'Adding state with l=', l, 'and E=', Ei/2, ' Hartree with Z=', N, 'with ferm=', ferm\n",
    "        if N>=Zatom: break\n",
    "    return rho\n",
    "    \n",
    "    \n",
    "def HartreeU(R, rho):\n",
    "    ux = -8*pi*R*rho\n",
    "    dudx=0.1\n",
    "    U = NumerovU(ux, 0.0, dudx, R[1]-R[0])\n",
    "    alpha2 = (2*Zatom-U[-1])/R[-1]\n",
    "    U += alpha2*R\n",
    "    return U\n",
    "\n",
    "def rs(rho):\n",
    "    \"Given density, returns rs.\"\n",
    "    if rho<1e-100: return 1e100\n",
    "    return pow(3/(4*pi*rho),1/3.)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found bound state at E=  -0.999998807 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.249999851 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -0.499999403471  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.124999925296  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgcAAAFkCAYAAAC0KZhSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n8v8Bd4Qy02GV8owAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1144ce6d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgkAAAFkCAYAAACq4KjhAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\njVJIEBERkUb9PzcjpsjOsrTxAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114841490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found bound state at E= -12.847578370 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -1.592504356 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -6.42378918503  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.796252177996  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgcAAAFkCAYAAAC0KZhSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAAPYQAAD2EBqD+naQAAIABJREFUeJzt3Xl8FdX9//HXSQiEsMsOSkVFQXFpUkXccUF/aC51qagg\nZalWBKyo4MqiVgVaxRYUF6ho/RJKLYu2WlABK27URK3VRCkiqKgQloAJEEjO74+bxNyEJYHMmZl7\n38/H4z5C5s7M/dx38uB+cmbmjLHWIiIiIlIuye8CREREJFjUHIiIiEgMNQciIiISQ82BiIiIxFBz\nICIiIjHUHIiIiEgMNQciIiISQ82BiIiIxFBzICIiIjHUHIiIiEgMT5sDY0yyMeYhY8xqY0yRMeZ/\nxph7vHxNEREROTj1PN7/3cBQYCDwKfAzYJYxZou1dprHry0iIiIHwOvm4GRgobX2n2XfrzXGXAOc\n4vHrioiIyAHy+pyDV4DzjDFdAIwxJwKnAy97/LoiIiJygDwdObDWPm6MOQz4zBizm2gzcre1ds6e\n1jfGtAQuBL4EdnhZm4iISJxJBQ4HFllrNx7MjjxtDowxNwG/BPoRPefgJOAPxph11to/72GTC4H/\n87ImERGRONcfmH0wO/D6nIO7gHuttX8t+/4TY8zhwJ3AnpqDLwGef/55unXrVmdF5OfD3LmwaBF8\n/XV0WadOcPjh0LYttG4NzZpBWho0bBj9mpICycmQlFT9a1ISGLPv1/T6+br0wAOjuPvuKe5eUJS5\nD5S5e8rcrVWrcrn11gFQ9ll6MLxuDpKAkirLStn7uQ47ALp160Z6evpBv/iOHfDggzB5MtSrB9dc\nAz//OZx5JjRpctC7jxszZzajb9+Dz1tqTpm7p8zdU+Zu5eRU/POgD8t73RwsAO4xxnwNfAKkA6OA\nGR6/LmvWQN++8OmncPvtcMst0KKF168aTt99953fJSQcZe6eMndPmYeX183BzcC9wDSgLbAOmA7c\n7+WLrloVHR1o0ADefx9OOMHLVwu/b775xu8SEo4yd0+Zu6fMw8vrqxWKgNFlDyfy8+GCC6KHDf71\nr+g5BbJvGRkZfpeQcJS5e8rcPWUeXl6PHDhlLQweDFu3Qna2GoOauvrqq/0uIeEoc/eUuXvKPLyM\ntdbvGioYY9KB7Ozs7AM6IXHGDLjuOnjxRcjMrPv6REREgionJ6d8tCbDWpuzv/X3JW5GDgoK4K67\nYMAANQYiEh5r164lPz/f7zIkJFq1akWnTp08f524aQ4eeggKC2HiRL8rCZ/BgwfzzDPP+F1GQlHm\n7gUx87Vr19KtWzeKior8LkVCIi0tjdzcXM8bhLhoDrZsgcceg5tugo4d/a4mfHr37u13CQlHmbsX\nxMzz8/MpKiqq84nfJD7l5uYyYMAA8vPz1RzUxBNPQHEx/OY3flcSTjppyD1l7l6QM6+rid9E6orX\nd2X03O7dMHUqDBwI7dr5XY2IiEj4hb45ePVVWLcObrjB70pERETiQ+ibg1mz4LjjQCNyB2758uV+\nl5BwlLl7ylyk5kLdHGzZAgsXwi9/6fYuhvFm8uTJfpeQcJS5e8pcpOZC3Ry8/DLs3AkBPs8oFObM\nmeN3CQlHmbunzMPp2WefJSkpiZycg5rTR2op1M3BwoWQkQGHHup3JeGWlpbmdwkJR5m7p8zdmzBh\nAklJSWzatGmPz3fv3p1zzz13v/sxDoeGp0+fzrPPPuvs9YIqtM3Bzp3wyivR2zKLiEjwGGP2+cHu\n8kO/ph5//HE1B4S4OXjjDdi2DSIRvysREZGw2759e623ieeZLUPbHLz8MnTqBCec4Hcl4Td6tLM7\naksZZe6eMg+3nTt3csstt9CmTRsaN27MZZddxsaNG2PWefHFF7nkkkvo2LEjqampHHXUUfz2t7+l\ntLQ0Zr1zzjmHE044gZycHM466ywaNWrEXXfdRefOnfnkk09YtmwZSUlJJCUlVRz2mDVrFklJSfzr\nX//ixhtvpG3bthx22GEV+1y3bh1DhgyhXbt2pKam0r179z1O111cXMz48ePp0qULqampdOrUidtv\nv53i4mIPUjtwoZ0hcckSOO88XaVQF1zcxENiKXP3lHl4WWsZMWIEhxxyCBMmTODLL79kypQpjBgx\ngqysrIr1Zs2aRZMmTbj11ltp3LgxS5YsYdy4cWzbto1JkyZVrGeMIT8/nz59+nDVVVcxcOBA2rZt\nS69evRgxYgRNmjThnnvuwVpL27ZtK7YBuPHGG2nTpg3jx4+nsLAQgPXr19OjRw+Sk5O56aabaNWq\nFa+88gpDhw5l27Zt3HTTTRXvIzMzk7fffptf//rXdO3alY8//pgpU6awcuVK5s2b5yrS/bPWBuYB\npAM2Ozvb7sv69daCtc89t8/VREQCLTs729bk/7ywmjBhgk1KSrIbN27c4/Pdu3e3vXr12uc+Zs2a\nZY0x9sILL4xZfsstt9iUlBS7devWimU7duyotv0NN9xgGzdubIuLiyuWnXPOOTYpKck+/fTTNa6p\nvI6zzz7blpaWxjw3dOhQ27FjR7t58+aY5VdffbVt0aJFRV1//vOfbb169ezbb78ds96TTz5pk5KS\n7DvvvLO3GKy1+/99KX8eSLcH+XkcypGDZcuiX3v18rUMERGnioogL8/b1+jaFYJ2YYcxhuuvvz5m\n2Zlnnsmjjz7KmjVr6N69OwANGjSoeP6HH35g586dnHHGGTz11FPk5eVx/PHHVzzfoEEDBg0aVOs6\nrrvuumonUs6bN49+/fpRUlISc6ijd+/ezJkzh5ycHHr27MkLL7xAt27dOProo2PW69WrF9Zali5d\nyqmnnlqrmrwSyuZg6VLo0kWXMIpIYsnLi16+7aXsbLczzpZ/0H7//fcxy5s1a0ZqamrF95WP7wO0\naNECgM2bN1cs+/TTT7n77rtZunQpW7dujXmNgoKCmO07duxIvXq1/wg8/PDDY77fsGEDW7Zs4amn\nnuLJJ5+str4xhvXr1wOwcuVK8vLyaN269T7XC4LQNgcaNag7eXl5dO3a1e8yEooydy8eMu/aNfrh\n7fVr1JXyD/e9XQlQVFRUsU779u0xxmCtxRjDM888w8CBAyvWTU5O3uM+bPSQNAUFBZx11lk0b96c\n3/72txxxxBGkpqaSnZ3NHXfcUe2kxIYNGx7Qe6q6Xfl+BwwYwC9/+cs9bnNC2ZnzpaWlHH/88UyZ\nMqWi7sqqNkB+Cl1zkJ8f7Z7HjvW7kvgxZswYXnzxRb/LSCjK3L14yDwtLVz3kfnJT34CwGeffUbH\njh1jntu+fTtfffUVF154IQCvvfZazPPHHXdcrV5r2bJlbN68mYULF3L66adXLF+1alWt9lPbuRda\nt25NkyZNKCkp2e+ETkceeST/+c9/6BWCv25Ddynje+9FvwbksExcmDZtmt8lJBxl7p4yd++8884j\nJSWF6dOnV/tL+cknn6SkpIQ+ffoAcO6558Y8yq8SqKnk5GSstTEjBMXFxTz++OO12k+jRo3YsmVL\njddPSkri8ssv529/+xuffPJJtefz8/Mr/n3llVfy9ddf8/TTT1dbb8eOHYGaNyF0IwfvvQetWkHn\nzn5XEj90iZd7ytw9Ze5e69atGTduHGPHjuWss84iEomQlpbGW2+9xZw5c7jooou45JJL9rufPQ3B\nV11+2mmn0aJFCwYOHFhx6eDzzz9f65GAjIwMnnjiCR544AGOOuoo2rRpU/GX/t7qmDhxIsuWLaNH\njx5cd911HHvssWzatIns7GyWLFlS0SBce+21zJ07l2HDhrF06VJOP/10SkpKyM3N5a9//SuLFy8m\nPSBDQ6FrDt59NzpqoPkNRESCr3xyoWnTpnH//feze/duOnfuzP3338+YMWNqtI+9fcBXXn7IIYfw\nj3/8g1tvvZWxY8fSokULrr32Ws4999yKQxc12ee4ceNYu3Ytv/vd79i2bRtnn312RXOwt23atGnD\nihUruO+++5g/fz7Tp0+nZcuWHHfccTF3AzXGsHDhQqZMmcJzzz3HggULSEtL44gjjmDUqFEcffTR\nNcrDBbO3TsgPxph0IDs7O3uP3VNpKRxyCNx2G9xzj/v6RETqUk5ODhkZGezt/zyRyvb3+1L+PJBh\nrT2o21iG6pyDzz+HggLo0cPvSuJL5ZnDxA1l7p4yF6m5UDUH5Scjnnyyv3XEmyCdBJMolLl7ylyk\n5kLVHGRnRyc/at7c70riy7333ut3CQlHmbunzEVqzvPmwBjTwRjzZ2NMvjGmyBjzUdm5BbX20Ufw\n05/WdYUiIiJSmafNgTGmOfAWsBO4EOgG3Aps3td2e2JttDk48cS6rVFERERieT1ycAew1lr7K2tt\ntrV2jbX2NWvt6truaM2a6MmIJ53kQZUJrvIkHeKGMndPmYvUnNfNQSbwvjFmrjHme2NMjjHmVwey\no48+in7VyEHdGzJkiN8lJBxl7p4yF6k5r5uDI4BhwGdAb2A68EdjzLW13dGHH0ZnRuzQoY4rFCZM\nmOB3CQlHmbunzEVqzuvmIAnIttaOtdZ+ZK19GngauGFfG/Xp04dIJBLz+MMfetKhw4KYmREXL15M\nJBKptv3w4cOZOXNmzLKcnBwikUi1ocXx48dXu/557dq1RCIR8qrcOH3q1KmMHj06ZllRURGRSITl\ny5fHLM/KymLw4MHVauvXrx8LFiyIWeb3+0hPT4+L9wHh+XlUnsAkzO+jsqC/j1dffTWQ70PkQGRl\nZRGJROjZsyft2rUjEokwatSoOtu/pzMkGmO+BBZba6+vtOwG4G5rbbV7U+5rhsQjjoDLLoPf/96z\nckVEnNIMiVIb8TRD4lvAMVWWHQOsqc1OCgth9Wro3r3O6hIREZG98Lo5mAKcaoy50xhzpDHmGuBX\nQK3unfr559Gv3brVeX0C1YZmxXvK3D1lLlJznjYH1tr3gUuBq4GPgbuB31hr59RmP7m50a9du9Zx\ngQJEh6LELWXunjJ3q2/fvjRq1IjCwsK9rtO/f38aNGjA5s21nvpGPOb5DInW2pettSdYa9OstcdZ\na/9U233k5UH79tCsmRcVymOPPeZ3CQlHmbunzN3q378/O3bsYP78+Xt8fvv27bz44ov06dOHFi1a\nOK5O9icU91bIy9OogYhImEQiERo3bszs2bP3+PyCBQsoKiqif//+jiuTmghFc5Cbq/MNRETCJDU1\nlcsuu4zXX399j7NTzp49myZNmpCZmcmECRNITk5m6dKlMetcf/31NGjQgI8//rhi2c6dO5kwYQLH\nHHMMDRs2pEOHDlx++eWsXl3riXdlHwLfHJSURE9I1MiBiEi49O/fn127djF37tyY5Zs3b2bx4sVc\ndtllNGjQgHvuuYeTTjqJoUOHVpyjsGjRImbMmMGECRM4/vjjASgtLeXiiy/m/vvv5+STT+aRRx7h\n5ptvZuvWrfz3v/91/v7iWeCbgy+/hOJiNQde0sQs7ilz95S5e+eeey7t27evdmhh7ty57N69u+KQ\nQr169XjuuedYt24dt9xyCwUFBQwdOpRTTjmF22+/vWK7Z599liVLljBlyhSef/55hg0bxpgxY3j1\n1VfJzMx0+t7iXT2/C9if//0v+rVLF3/riGcjRozwu4SEo8zdi4fMi3YVkZeft/8VD0LXVl1JS0mr\nk30lJSVx1VVX8eijj7J27Vo6deoERA8ptG3blnPPPbdi3eOOO457772XO++8k48++ohNmzbx+uuv\nk5T049+w8+bNo3Xr1nHxswy6wDcHq1dDcjIceqjflcSv3r17+11CwlHm7sVD5nn5eWQ8leHpa2Rf\nn016+7qbrbF///5MmTKF2bNnc8cdd/DNN9+wfPlybr75Zkzl+fCB0aNHM2fOHP7973/z4IMPcswx\nsXPorVq1imOOOSamYRBvhKI5OOwwqBf4SkVEvNW1VVeyr8/2/DXqUnp6Ol27diUrK4s77rij4hDD\nNddcU23dVatWsXLlSoCYkxDFvcB/5H75JXTu7HcVIiL+S0tJq9O/6l3p378/48aN4+OPPyYrK4su\nXbqU3wOggrWWQYMG0axZM0aNGsUDDzzAFVdcwc9//vOKdY488khWrFhBSUkJycnJrt9GQgn82Mzq\n1WoOvFb17nHiPWXunjL3T//+/bHWMm7cOD788EMGDBhQbZ2HH36Yd999l6effpr77ruP0047jWHD\nhrFp06aKdS6//HI2bNjAtGm1moFfDoCaAyErK8vvEhKOMndPmfvn8MMP57TTTmPhwoUYY6odUsjN\nzWXcuHEMHjyYPn36YIxh1qxZbNu2jWHDhlWsN3DgQM455xxuueUWrrnmGqZPn87vfvc7LrroIl56\n6SXXbyuuBbo5+OEHyM9Xc+C1v/zlL36XkHCUuXvK3F/9+/fHGEOPHj044ogjKpaXlpYyaNAg2rRp\nw5QpUyqWH3XUUTz00EO88MILvPDCC0D06odXXnmFu+++mxUrVjBq1CgeffRRmjdvXjEXgtSNQJ9z\n8OWX0a9qDkREwm3YsGExowDlkpKSeO+99/a4zciRIxk5cmTMsgYNGnDfffdx3333eVKnRAV65ODr\nr6NfdRmjiIiIO4FuDr79Nvq1XTt/6xAREUkkgW8OWrWC+vX9riS+DR482O8SEo4yd0+Zi9RcoJuD\ndeugfXu/q4h/8TBzXNgoc/eUuUjNBbo5+PZbNQcuXH311X6XkHCUuXvKXKTm1ByIiIhIjMA3Bx06\n+F2FiIhIYglsc2CtzjlwZfny5X6XkHCUuXvKXKTmAtscbN4MxcVqDlyYPHmy3yUkHGXunjIXqbnA\nNgfr10e/tmnjbx2JYM6cOX6XkHCUuXvKXKTmAtsclN+Iq2VLf+tIBGlpaX6XkHCUuXvKXKTmAtsc\nbNwY/armQERExK3ANgflIweHHOJvHSIi4r033niDpKQk5s2b53cpQoCbg40boXFjTZ3swujRo/0u\nIeEoc/eUuXsTJkwgKSmJTeV/7VXRvXt3zj333IrvjTGuSpP9CHRzoEMKbnTq1MnvEhKOMndPmbtn\njNnnB37V56y1XpckNRTY5mDTJh1ScKXq/dLFe8rcPWUuUnPOmgNjzB3GmFJjzCM1WV8jByIiia24\nuJhLLrmEFi1a8O677wLwww8/cPPNN9O5c2dSU1Np27YtvXv35sMPP/S52vhSz8WLGGNOBq4HPqrp\nNps2qTkQEUlUO3bsIBKJkJOTw+uvv056ejoAv/71r5k3bx4jR46kW7dubNy4keXLl5Obm8tJJ53k\nc9Xxw/PmwBjTGHge+BUwtqbbbdwIRx/tWVlSSV5eHl27dvW7jISizN2Li8yLiiAvz9vX6NoVfJ4T\norCwkIsvvpjc3FyWLl3K8ccfX/Hcyy+/zHXXXRcz4+Vtt93mR5lxzcXIwWPAS9baJcaYGjcHOufA\nnTFjxvDiiy/6XUZCUebuxUXmeXmQkeHta2RnQ9lf6a4ZY9iyZQsXXHABX375JW+88Ua1hq558+a8\n9957fPvtt7TX/Pqe8bQ5MMZcBZwE/Ky2227ZAs2b131NUt20adP8LiHhKHP34iLzrl2jH95ev4ZD\nla9YsNZy8803s3PnTj744IM9jvRMnjyZQYMGcdhhh5GRkUGfPn0YOHAgnTt3dll2/LPWevIADgW+\nA7pXWrYUeGQf26QDtm3bthYy7QknZNrMzOjj1FNPtfPnz7eVLVq0yGZmZtqqbrzxRjtjxoyYZdnZ\n2TYzM9Nu2LAhZvm4cePsxIkTY5atWbPGZmZm2tzc3Jjlf/zjH+1tt90Ws6ywsNBmZmbaN998M2b5\n7Nmz7aBBg6rVduWVV+p96H3ofeh9VNQL2Ozs7Gr7iAcTJ060SUlJ9uuvv97j80cccYTt06ePtdba\nZcuWWWOMvfbaa21KSoodMGDAXvf73Xff2enTp9tLL73UNm7c2DZs2ND+85//9OQ9BEnl35fZs2dX\nfDa2bdvWZmZm2rPOOssCFki3B/sZfrA72OuOoS9QAhQDu8oepZWWmT1skw7YN9/MtmDt7NleRSwi\n4r94bw6ysrJsUlKSff3116s9V1RUZFNSUuywYcOstT82B3/729/sn//8Z5uUlGRvvPHG/b7Ghg0b\n7KGHHmrPPPPMOq8/aPb3+1L+fF00B14eVngNOL7KsllALjDR2r3PdlFYGP3atKlHlYmIiOfOO+88\nUlJSmD59Or169Yo5hPDkk09SUlJCnz59qm03YMAACgoKGDlyJE2bNuWhhx4CoLS0lB9++IGmlT4c\nWrVqRYcOHdi5c6f3byiBeNYcWGsLgU8rLzPGFAIbrbW5+9q2vDlo0sSr6qSySZMmcfvtt/tdRkJR\n5u4pc/dat27NuHHjGDt2LGeddRaRSIS0tDTeeust5syZw0UXXcQll1yyx22HDx/O1q1bufvuu2na\ntCl33nkn27Zt49BDD+WKK67gxBNPpHHjxrz66qu8//77PPJIjabQkRpyMs9BJTWaG7OoKPpVzYEb\nReWBizPK3D1l7o+77rqLzp07M23aNO6//352795N586duf/++xkzZkzMulWnU77zzjspKCjgnnvu\noXnz5vzqV79i+PDhLF68mPnz51NaWspRRx3F9OnTuf76612+rbhn9jG675wxJh3IfuKJbG64IZ2V\nK+Goo/yuSkTEGzk5OWRkZJCdnV0xyY/I3uzv96X8eSDDWptzMK8VyHsrlDf4OudARETEvUA2Bzrn\nQERExD+BbQ6SkyE11e9KEkN+fr7fJSQcZe6eMhepuUA2B0VF0UMK+7gNuNShIUOG+F1CwlHm7ilz\nkZoLZHPwww86pODShAkT/C4h4Shz95S5SM0FsjkoKlJz4JLOknZPmbunzEVqLpDNQWGhrlQQERHx\nS2CbA40ciIiI+MP1DIk1sn076Dbd7sycOZOhQ4f6XUZCUebuBTnz3Nx9zigvArj9PQlkc7BjB6Sl\n+V1F4sjJyQnsf5rxSpm7F8TMW7VqRVpaGgMGDPC7FAmJtLQ0WrVq5fnrBHL65G7dsjnzzHSefNLv\nikREvLV27VrNwSA11qpVKzp16rTH5+py+uTAjhw0bOh3FSIi3uvUqdNe/7MX8UsgT0jcuVOHFURE\nRPwSyOZAIwciIiL+CWRzoJEDtyKRiN8lJBxl7p4yd0+Zh1cgmwONHLg1YsQIv0tIOMrcPWXunjIP\nr0A2ByUlGjlwqXfv3n6XkHCUuXvK3D1lHl6BbA5AzYGIiIhfAtsc6LCCiIiIPwLbHGjkwJ0FCxb4\nXULCUebuKXP3lHl4BbY50MiBO1lZWX6XkHCUuXvK3D1lHl6BnD4Zsvngg3ROOsnvikRERMKhLqdP\n1siBiIiIxAhsc6BzDkRERPwR2OZAIwciIiL+CGxzoJEDdwYPHux3CQlHmbunzN1T5uEV2OYgNdXv\nChKHZjFzT5m7p8zdU+bh5enVCsaYO4FLga7AduBt4HZr7ed7WT8dyK5fP5udO9M9q0tERCTehOlq\nhTOBqUAP4HwgBVhsjNnnGQUNGnhclYiIiOxVPS93bq3tU/l7Y8wgYD2QASzf23ZqDkRERPzj+pyD\n5oAFNu1rJTUHbi1fvtc+TTyizN1T5u4p8/By1hwYYwzwKLDcWvvpvtZNSXFTk0RNnjzZ7xISjjJ3\nT5m7p8zDy9n0ycaY6cCFwOnW2m/3sk46kH300dl89plOSHSlqKiINF076pQyd0+Zu6fM3QrTCYkA\nGGOmAX2Ac/bWGFT2xRd9iEQiMY+ePXtWu8PX4sWLiUQi1bYfPnw4M2fOjFmWk5NDJBIhPz8/Zvn4\n8eOZNGlSzLK1a9cSiUTIy8uLWT516lRGjx4ds6yoqIhIJFJt+CwrK2uP1/j269cvcO8jLS0tLt4H\nhOfnUfk/zDC/j8qC/j6mTp0aF+8jTD+PvLy8uHgfQfx5ZGVlVXw2tmvXjkgkwqhRo6ptc6A8Hzko\nawz6Amdba7/Yz7rpQPZPf5pNTo5GDkRERGqqLkcOPL1awRjzOHA1EAEKjTFty54qsNbu2Nt29et7\nWZWIiIjsi9eHFW4AmgLLgHWVHlfuayM1B25VHeoS7ylz95S5e8o8vLye5+CAmg9dreBWp06d/C4h\n4Shz95S5e8o8vJxdrVAT5eccXHRRNq+8onMOREREaip0VyvUlkYORERE/BPI5kDnHIiIiPhHzYFU\nux5XvKfM3VPm7inz8Apkc6DDCm6NGTPG7xISjjJ3T5m7p8zDS82BMG3aNL9LSDjK3D1l7p4yD69A\nNgc6rOCWLjdyT5m7p8zdU+bhFcjmQCMHIiIi/glkc6CRAxEREf+oOZBqdxUT7ylz95S5e8o8vALZ\nHOiwgltFRUV+l5BwlLl7ytw9ZR5egZw++YEHsrnrLk2fLCIiUlNxP32yDiuIiIj4J5DNgQ4riIiI\n+CeQzYFGDtzKz8/3u4SEo8zdU+buKfPwCmRzoJEDt4YMGeJ3CQlHmbunzN1T5uEVyOZAIwduTZgw\nwe8SEo4yd0+Zu6fMw0vNgZCeritDXFPm7ilz95R5eAWyOdBhBREREf8EsjnQyIGIiIh/1BwIM2fO\n9LuEhKPM3VPm7inz8Apkc6DDCm7l5BzURFpyAJS5e8rcPWUeXoGcPvnNN7M54wydyCIiIlJTmj5Z\nREREPBPI5iA52e8KREREElcgmwNj/K5AREQkcQWyORC3IpGI3yUkHGXunjJ3T5mHl5oDYcSIEX6X\nkHCUuXvK3D1lHl6eNwfGmOHGmNXGmO3GmHeNMSd7/ZpSO7179/a7hISjzN1T5u4p8/DytDkwxvQD\nHgbGAz8FPgIWGWNaefm6IiIicuC8HjkYBTxprX3OWpsH3AAUAbqPp4iISEB51hwYY1KADOD18mU2\nOuPSa0BPr15Xam/BggV+l5BwlLl7ytw9ZR5e9TzcdysgGfi+yvLvgWM8fN1Qs9ZSakspsSXsLt1N\nSWnZ1/18b7EV21f9d/ksmDH/tqXY3bth1y4ee/JROh7ZEHbtwpSUwK7d2NISsBasxZaWQmkp2FKM\nJbq8tOzfpaWA/fHf1mJKo9uZsu2p6SyctZit09RmYs/azAJa43UPbmbR6X94lsN3fHlQ+5DaUebu\nKXO3Plt1h/y7AAAe7UlEQVT9Vd3tzFrryQNoD5QCPaosnwS8s5dt0gHbtm1bm5mZGfM49dRT7fz5\n821lixYtspmZmbaqG2+80c6YMSNmWXZ2ts3MzLQbNmyIWT5u3Dg7ceLEmGVr1qyxmZmZNjc3N2b5\nH//4R3vbbbfFLCssLLSZmZn2jX+9Yb/b9p394NsP7Mufv2yHPTTM9ri4h71v2X321kW32qELh9or\n5l5h257S1nYb0c3+7Kmf2e6Pd7dH/uFI2/L6ljalW4pNeyDNJt2bZJlA9HEylgi23ljsoaOwJ/0a\ne/LF2PbtsQN6Y0efj33odOzjP8P2bYu9pg32712wSw7HvtsRu6gl9twU7Btp2PyG2IL62MJ62CkG\ne9uPH9vWgi0Emwn2zSrLZ4MdVGWZBXsl2PlVli0q20fVdW8EO6PKsuyydTdUWT4O7MQqy9aUrZtb\nZfkf0fvQ+9D70PtIzPcxu2zbU8G2Lfv3WWCJPtIP9jPcs3srlB1WKAIut9a+WGn5LKCZtfbSPWyT\nDmRnZ2eTnh68eysUlxTz6YZPycvP43+b/sfKTStZuXElawvW8n3h9+wu3R2zfv3k+rRIbUGz1GY0\nT21O89TmNG3QlLSUNFKTU2mY0pDUeqk0Lq1H+++LaLOugNbfbKbFN5totGELaRsKaLhhM6mbtkb/\nCq/EGsPuJo3Y3bwppU0bU9KwIaVpDSltmIptmEppWiqlqeXfN8Cm1IeUeth6ydE7W6WkYJPrRZel\n1IN69aLLUuphkupBchLGJGGTDMYkgUnCJCdFZ6gyBlv2FWMgKbrcJlVfhjHRv7FrOrNVbWbA8ntd\nzdYlIgHy37yVXHLtMKiDeyt4dljBWrvLGJMNnAe8CGCMMWXf/9Gr161La7asYcnqJbzz9TvkfJvD\nx+s/prikGIBWaa3ockgXjjrkKM4/4nzaN25P+ybtK762adSG1Hqp1Xe6YQNkZ0NOTvTxwQewenW0\nFwRo0gSOOgoO7QTHdoCOHaFDh+ijTRto0QJatMA0a0ZKUhK6gaWIiABsTGpRZ/vy8pwDgEeAWWVN\nwgqiVy+kAbM8ft0DUlJawhtr3uBvn/6NxV8s5n+b/ofB0L1NdzI6ZDDopEGkt0/n2NbH0jy1ec12\n+v33sGzZj4+8vOjypk0hPR369oXjjoOjj4YuXaBtW/1FKiIivvK0ObDWzi2b0+A+oC3wIXChtXaD\nl69bW5+s/4Qn3n+CuZ/OZX3hen7S7Cf06dKHSedP4pzDz+GQhofUboeffQYLFkQf770XHRU45hg4\n5xwYNw5OOQU6d44OvQfA4MGDeeaZZ/wuI6Eoc/eUuXvKPLy8HjnAWvs48LjXr1Nb1lpe+vwlprw7\nhWVfLqNto7Zce8K1XHnclZzc4WRMbf9637AB/u//4Jln4D//gYYN4cIL4U9/in5t396bN1IHNIuZ\ne8rcPWXunjIPL89OSDwQLk5ItNayaNUixi4dy/vr3uf0w05n5CkjubTbpdRPrl/bncFbb8Gjj8LC\nhdHDAZmZcO210Ls3pKV58h5ERESqysnJISMjA4J8QmIQrdq0iuEvD2fRqkWcftjpLBm4hF6de9V+\nRyUlMG8ePPxw9LBB167Rf19zDbTSzNAiIhJuCdEc7C7dzeS3JnPfG/fRrnE7Fl61kMyjM2t/6MBa\nePFFuPtu+OQT6NUL/v53+H//LzDnD4iIiBysuP9EW7NlDb2e7cXYpWO5+dSb+eTGT4gcE6l9Y/D2\n23DaafDzn0evKHj3XViyBC6+OPSNwfLly/0uIeEoc/eUuXvKPLzC/am2Hy999hInPnEiawvW8sag\nN5h4/kQa1W9Uu53k58PQoXD66VBcDK++Cq+/Dj16eFO0DyZPnux3CQlHmbunzN1T5uEVl82BtZaH\n336YvnP6cs7h5/Dhrz/kjE5n1HYn8Oyz0UsQ582D6dNhxQo4/3xvivbRnDlz/C4h4Shz95S5e8o8\nvOKuOdhVsosb/n4Dt716G2NOH8O8fvNo0bCWs0Zt2ACXXQaDBkGfPtF5C264AZKTPanZb2m6qsI5\nZe6eMndPmYdXXJ2QuHn7Zn7x11/wrzX/4k+RPzH4p4Nrv5OXX4bBg6N3GJw3Dy6tdgsIERGRuBY3\nIwerNq2i58yefPDdB7x67au1bwxKSmDs2OgJhhkZ8PHHagxERCQhxUVzsOzLZZwy4xRKbSnvDn2X\nsw8/u3Y72LQp2hQ8+GD08fe/Q7t23hQbQKNHj/a7hISjzN1T5u4p8/AK9WEFay1PZT/FiFdGcPZP\nzmbuL+bW/j4In38enadgyxb45z/hggu8KTbAOnXq5HcJCUeZu6fM3VPm4RXa6ZO/2foNw/4xjJc+\nf4kbf3Yjj170KCnJtbyB8TvvRKc7btMG/vGP6M2QREREQiihp0+21vLMh89wy6JbaJjSkPn95vPz\nrj+v/Y4WLICrr47eIXHBAmhRd/fBFhERCbNQNQe7SnYxYP4A5n4yl0EnDeKR3o/U/jJFiN49ceBA\nuOKK6FwGqal1X6yIiEhIheqExDGvjmF+7nxe+MULPNP3mQNrDJ59NnrXxF/+EmbPVmMA5OXl+V1C\nwlHm7ilz95R5eIWmOVi9eTXT/j2N+3vdz+XHXn5gO3nmmegcBkOHwowZcTupUW2NGTPG7xISjjJ3\nT5m7p8zDKzTNwZ//82ca1mvIyB4jD2wH8+bBr34F110HTz4Z+psl1aVp06b5XULCUebuKXP3lHl4\nheYTcl7uPCLHREhLOYDpON94A665JnqOweOPqzGoQpcbuafM3VPm7inz8ArFp2TBjgL+8/1/OP+I\nA7jp0X//C337whlnwHPP6VCCiIjIfoSiOXjvm/ewWE477LTabbhpE0QicPjh0cMKDRp4Up+IiEg8\nCUdz8PV7HNLwELoc0qXmG+3eDVddBVu3RucxaNrUuwJDbtKkSX6XkHCUuXvK3D1lHl6hmOfg0/xP\nOb7N8Rhjar7R2LGwZAksXhwdOZC9Kioq8ruEhKPM3VPm7inz8ArF9Mk/ffKn9OjYgycueaJmO1q6\nFM47Dx56CG6/3ZtiRUREAqQup08O/GGFUlvKZ/mfcUzLY2q2webN0dkPzzkHdEcwERGRWgt8c/BV\nwVds372drq261myDkSPhhx+iMyHqkkUREZFaC/yn5xebvwDgyEOO3P/Kr70WvW/Co4/CYYd5XFn8\nyM/P97uEhKPM3VPm7inz8Ap8c/DV1q8AOLTpoftecedOGD4czjorelhBamzIkCF+l5BwlLl7ytw9\nZR5egb9a4auCr2jZsOX+Z0b8/e/hiy+i8xnU5qoGYcKECX6XkHCUuXvK3D1lHl6ejBwYY35ijJlh\njPnCGFNkjFlpjJlgjEmp7b6+2voVhzXbzyGCDRtg4kS46SY47rgDLTthVb4yRNxQ5u4pc/eUeXh5\nNXLQFTDAdcAqoDswA0gDanWbrq+2fsVhTffTHDz4YPTkw7vuOqBiRURE5EeejBxYaxdZa4daa1+3\n1n5prf078Hvgstru66uC/TQHa9ZEb6Y0ejS0bHngRYuIiAjg9oTE5sCm2m6038MKEydCs2Zw880H\nUVpimzlzpt8lJBxl7p4yd0+Zh5eT5sAYcxQwAqjhFIdRO3bvYMuOLbRv3H7PK3z/PTzzDPzmN9C4\n8cEXmqBycg5qIi05AMrcPWXunjIPr1o1B8aYh4wxpft4lBhjjq6yTUfgFeAv1to/1eR1+vTpQyQS\nITMzE2bD9Fun07NnTxYsWBCz3uJRo4js3g3DhsUsHz58eLWONScnh0gkUu262/Hjx1e7OcjatWuJ\nRCLk5eXFLJ86dSqjq8y6WFRURCQSYfny5THLs7KyGDx4cLX31q9fv+rvY/FiIpFItXVdvY/HHnss\nLt4HhOfn8dhjj8XF+6gs6O+jU6dOcfE+wvTzGDp0aFy8jyD+PLKysohEIvTs2ZN27doRiUQYNWpU\ntW0OVK3urWCMaQns78D+F9ba3WXrdwCWAm9ba6u/0+r7j7m3Qs63OWQ8lcH7171PRoeM2JULC6MT\nHf3ylzBlSo3fg4iISDyqy3sr1OpqBWvtRmBjTdYtGzFYAvwbOKCZMNYXrgegTaM21Z/MyoItW6KH\nFERERKTOeHIpY9mIwTJgNdFLF9uU327ZWvt9TfdT3hy0btS6+pNPPw0XXaTbMYuIiNQxr05IvAA4\nAjgP+ApYB3xb9rXGNhRuoEn9JqTWS4194qOPYMUKuP76uqk2we3puJt4S5m7p8zdU+bh5dU8B89a\na5OrPJKstcm12c/6wvV7HjWYMQPatYOLL66rkhPaiBEj/C4h4Shz95S5e8o8vAJ946UNRRuqn29Q\nUgJ//Stccw2k1Ho2ZtmD3r17+11CwlHm7ilz95R5eAW6OVhfuJ7WaVVGDt58Mzq/wS9+4U9RIiIi\ncS7QzcEeRw7++tfoJYw9evhTlIiISJwLdHNQbeTAWvj73+HSS3Vb5jpUdXIQ8Z4yd0+Zu6fMwyvQ\nzcGm7ZtomVZpzqX//Q/WrgUdx6pTWVlZfpeQcJS5e8rcPWUeXoFtDkpKS9i6cyvNU5v/uPC116Be\nPTjrLP8Ki0N/+ctf/C4h4Shz95S5e8o8vALbHGzduRUgtjl4/fXouQZNmvhUlYiISPwLbHOwecdm\nAFqktvhx4VtvadRARETEY4FtDrbs2AJUGjlYtw6++w5OPtnHqkREROJf4JuDFg3LRg7efz/6NSNj\nL1vIgdrTrUHFW8rcPWXunjIPr8A2B5u3Rw8rVIwcZGdD69bROQ6kTmkWM/eUuXvK3D1lHl6BbQ7K\nRw6aNWgWXZCTEx010PwGde7qq6/2u4SEo8zdU+buKfPwCmxzsHnHZpo2aEpyUtm9mnJz4dhj/S1K\nREQkAQS2OdiyY8uPhxR27oTVq6FrV3+LEhERSQCBbg4qLmNctQpKS+GYY/wtKk4tX77c7xISjjJ3\nT5m7p8zDK7DNweYdm38cOcjLi35Vc+CJyZMn+11CwlHm7ilz95R5eAW2OYg5rPDZZ9CsGbRps++N\n5IDMmTPH7xISjjJ3T5m7p8zDK9DNQcUcB599Fh010JUKnkhLS/O7hISjzN1T5u4p8/AKbHNQsKOA\npvWbRr9ZuRK6dPG3IBERkQQR2OZgW/E2mjQou8HSmjVw+OG+1iMiIpIoAtsc/FD8A03qN4Hi4uh9\nFX7yE79LilujR4/2u4SEo8zdU+buKfPwCmxzsG3nNhrXbwxffw3WqjnwUKdOnfwuIeEoc/eUuXvK\nPLwC2RzsKtnFrtJd0cMKa9ZEF6o58MzIkSP9LiHhKHP3lLl7yjy8AtkcFBYXAkQPK5Q3B+pARURE\nnAhkc1C0uwggelhhzZro/AYNG/pclYiISGIIZnOwK9ocVBxW0CEFT+WVz0Apzihz95S5e8o8vILZ\nHBRXGTlQc+CpMWPG+F1CwlHm7ilz95R5eAWzOSgfOajfBNauVXPgsWnTpvldQsJR5u4pc/eUeXh5\n3hwYY+obYz40xpQaY06oyTbl5xw0qd84OsdBx46e1pjodLmRe8rcPWXunjIPLxcjB5OBrwFb0w3K\nr1ZovKMUioqgfXuPShMREZGqPG0OjDH/D7gAuA2o8V2Ttu/aTv3k+tRfvzG6QM2BiIiIM541B8aY\ntsBTwABge222LdxVGD0Z8dtvowvUHHhq0qRJfpeQcJS5e8rcPWUeXl6OHDwDPG6t/aC2GxbtKoqe\njKjmwImioiK/S0g4ytw9Ze6eMg+vWjUHxpiHyk4s3NujxBhztDHmJqAxUN421viQAsCcO+ew6U+b\niDzwAJHkZCL9+9OzZ08WLFgQs97ixYuJRCLVth8+fDgzZ86MWZaTk0MkEiE/Pz9m+fjx46t1t2vX\nriUSiVS7Rnfq1KnVbiRSVFREJBJh+fLlMcuzsrIYPHhwtdr69esXuPdx7733xsX7gPD8PO699964\neB+VBf19pKWlxcX7CNPPo2/fvnHxPoL488jKyiISidCzZ0/atWtHJBJh1KhR1bY5UMbaGp8niDGm\nJdByP6utBuYCl1RZngzsBv7PWlv9XUf3nw5kZz6cyYZmG3gn93RYuBBWrqxxjSIiIokoJyeHjIwM\ngAxrbc7B7KtebVa21m4ENu5vPWPMSODuSos6AIuAK4EV+9t++67tPx5W6NChNiWKiIjIQfLknANr\n7dfW2k/LH8BKoocWvrDWrtvf9kW7in48IVHnG3iu6lCZeE+Zu6fM3VPm4eVyhsQaH7/YsXsHaSlp\nag4cGTJkiN8lJBxl7p4yd0+Zh1etDiscKGvtGqLnHNSImgO3JkyY4HcJCUeZu6fM3VPm4RXIeyvs\n2L2DprY+FBRAu3Z+lxP30tPT/S4h4Shz95S5e8o8vALbHLTaXnb1Y6tW/hYjIiKSYALbHBxSWBr9\nRs2BiIiIU4FsDnaW7KRFYUn0GzUHnqs64Yd4T5m7p8zdU+bhFcjmYMfuHTTftjv6jZoDz+XkHNRc\nGXIAlLl7ytw9ZR5etZoh0WvlMyRyPbzT8lpO/f0c2LkTTK1mXxYREUk4dTlDYiBHDgAab90ZHTVQ\nYyAiIuJUYJuDRlu3Q8v93cZBRERE6lpgm4O0LYU630BERMQHgW0OUrf8oObAkT3dtlS8pczdU+bu\nKfPwCmxzUH/LVjUHjowYMcLvEhKOMndPmbunzMMrsM1BvU0Fag4c6d27t98lJBxl7p4yd0+Zh1dg\nm4Pkgq3QooXfZYiIiCScQDYHSaWQ9EMhNGvmdykiIiIJJ5DNQaPisn80b+5rHYliwYIFfpeQcJS5\ne8rcPWUeXoFsDprtLpv4SCMHTmRlZfldQsJR5u4pc/eUeXgFcvrkE65M5aO5O2DFCjj5ZL/LEhER\nCby4nz75kJKU6D80ciAiIuJcIJuD5iX1ov9QcyAiIuJcIJuDZruSy/6h5kBERMS14DYHDRpAaqrf\npSSEwYMH+11CwlHm7ilz95R5eAWyOWiyy2jUwCHNYuaeMndPmbunzMMrkFcrTDytHbdvaAKff+53\nSSIiIqEQ91crNCpGIwciIiI+CWZzsLNUzYGIiIhPAtkcpKk5cGr58uV+l5BwlLl7ytw9ZR5egWwO\nUnfs1n0VHJo8ebLfJSQcZe6eMndPmYeXp82BMeZiY8y7xpgiY8wmY8y8mmyXWlwCTZt6WZpUMmfO\nHL9LSDjK3D1l7p4yD696Xu3YGHM58BRwB7AESAG612Tb+sWl0KiRV6VJFWlpaX6XkHCUuXvK3D1l\nHl6eNAfGmGTgUeBWa+2sSk/l1WT7lOIS0C+ViIiIL7w6rJAOdAAwxuQYY9YZY142xhxXk41Tindr\n5EBERMQnXjUHRwAGGA/cB1wMbAaWGWP2e6ZhSvFujRw4NHr0aL9LSDjK3D1l7p4yD69aNQfGmIeM\nMaX7eJQYY46utN/fWmsXWGs/AAYDFvhFjV5MIwfOdOrUye8SEo4yd0+Zu6fMw6u2Iwe/B7ru49EN\n+AL4tmz93PINrbXFZc/t97elDxB59FEikUjFo2fPnixYsCBmvcWLFxOJRKptP3z4cGbOnBmzLCcn\nh0gkQn5+fszy8ePHM2nSpJhla9euJRKJkJcXe4rE1KlTq3XCRUVFRCKRatfzZmVl7fGmI/369Qvc\n+xg5cmRcvA8Iz89j5MiRcfE+Kgv6+ygqKoqL9xGmn8fpp58eF+8jiD+PrKysis/Gdu3aEYlEGDVq\nVLVtDpQn91YwxjQB1gM3WmufKVuWAnwF3GOtnbGX7dKB7GwgffFiuOCCOq9NREQkHtXlvRU8uVrB\nWrvNGPMEcK8x5mtgDTCG6GGFv9ZoJzrnQERExBdeToJ0GzAHeA5YARwGnGutLajR1jrnwJmqw1/i\nPWXunjJ3T5mHl2fNgbW2xFo7xlrb3lrb3Fp7obU2d/9bltHIgTNjxozxu4SEo8zdU+buKfPwCuS9\nFQCNHDg0bdo0v0tIOMrcPWXunjIPLzUHosuNfKDM3VPm7inz8Apuc6DDCiIiIr4IZHNgk5Ohfn2/\nyxAREUlIwWwOGqgxcKnqJB7iPWXunjJ3T5mHVzCbg4YN/S4hoVSdOU68p8zdU+buKfPw8mSGxANV\nPkPiio4dOPnrb/wuR0REJDTqcobEQI4coJEDERER3wSyOUhScyAiIuKbQDYHJlXNgUtV7zQm3lPm\n7ilz95R5eAWyOSA11e8KEsqQIUP8LiHhKHP3lLl7yjy8gtkc6LCCUxMmTPC7hISjzN1T5u4p8/AK\nZnOgkQOn0tPT/S4h4Shz95S5e8o8vILZHGjkQERExDfBbA40ciAiIuKbYDYHGjlwaubMmX6XkHCU\nuXvK3D1lHl7BbA40cuBUTs5BTaQlB0CZu6fM3VPm4RXI6ZOz77yT9Acf9LscERGR0ND0ySIiIuKZ\nYDYHOqwgIiLim2A2Bxo5EBER8U0wmwONHDgViUT8LiHhKHP3lLl7yjy8gtkcaOTAqREjRvhdQsJR\n5u4pc/eUeXgFsznQyIFTvXv39ruEhKPM3VPm7inz8FJzICIiIjHUHIiIiEiMYDYHOufAqQULFvhd\nQsJR5u4pc/eUeXgFszlo0MDvChLKpEmT/C4h4Shz95S5e8o8vDxrDowxxxhjXjTG5BtjCowxbxpj\nzqnhxl6VJXvQunVrv0tIOMrcPWXunjIPLy9HDl4BDHA2kA58BPzdGNPGw9cUERGRg+RJc2CMaQkc\nDky01n5irV0F3AGkAd29eE0RERGpG540B9bajcAKYKAxJs0YUw8YBnwPZHvxmiIiIlI36nm47wiw\nCNgGlBJtDC6y1hbsY5tUgNzcXA/LkqpWrFih+647pszdU+buKXO3Kn12HvR8AMZaW/OVjXkIuH0f\nq1igG7AKeBvYAPwW2AH8CugL/Mxa+/1e9n8N8H81LkhERESq6m+tnX0wO6htc9ASaLmf1b4Azgde\nAppbawsrbf85MMNaO3kf+78Q+JJoQyEiIiI1k0r0fL9FZYf3D1itDiuUvdh+X9AYk0R0FKG0ylOl\n7OM8h7L9H1S3IyIiksDeroudeHUp49vAJuA5Y8wJxpguxpjfEe1o/uHRa4qIiEgd8OpqhS1EDw80\nAl4D/g2cBkSstR978ZoiIiJSN2p1zoGIiIjEv2DeW0FERER8o+ZAREREYgSmOTDGDDfGrDbGbDfG\nvGuMOdnvmuKJMebMshthfWOMKTXGRPawzn3GmHXGmCJjzKvGmKP8qDUeGGPuNMasMMZsNcZ8b4yZ\nb4w5eg/rKfM6Yoy5wRjzUdmN3gqMMW8bYy6qso7y9pAx5o6y/18eqbJcudcRY8z4sowrPz6tss5B\n5x2I5sAY0w94GBgP/JToTZoWGWNa+VpYfGkEfAjcSPQy0xjGmNuBEcD1wClAIdGfQX2XRcaRM4Gp\nQA+i836kAIuNMQ3LV1Dmde4ropO0pQMZwBLgRWPMsaC8vVb2B931RP//rrxcude9/wJtgXZljzPK\nn6izvK21vj+Ad4E/VPreAF8DY/yuLR4fROebiFRZtg4YVen7psB24Eq/642HB9CqLPczlLnT3DcC\ng5W35zk3Bj4DzgWWAo9Uek65123W44GcfTxfJ3n7PnJgjEkh2uW/Xr7MRt/Ra0BPv+pKJMaYzkS7\nz8o/g63Ae+hnUFeaEx2x2QTK3GvGmCRjzFVAA+BfyttzjwEvWWuXVF6o3D3TpewQ8SpjzPPGmMOg\nbvP28sZLNdUKSCZ6Y6bKvgeOcV9OQmpH9INrTz+Ddu7LiS/GGAM8Ciy31pYfG1TmHjDGdAfeITqN\nbBHRv5ZWGWN6orw9UdaEnQT8bA9P6/e87r0LDCI6UtMemEC0Ae5OHeYdhOZAJN49DhwLnO53IQkg\nDzgRaAZcAcwxxpztb0nxyxhzKNHG93xr7S6/60kE1tpFlb79rzFmBbAGuJLo73+d8P2wApAPlBA9\nuaKytsB37stJSN8RPc9DP4M6ZoyZBvQBzrHWflvpKWXuAWvtbmvtF9baD6y1dxMdTh2G8vZKBtAa\nyDHG7DLG7ALOBn5jjCkm+hercveQtbYA+Bw4ijr8Pfe9OSjrNrOB88qXlQ3Dnkcd3UBC9s1au5ro\nL07ln0FTomfa62dwgMoag75AL2vt2srPKXNnkoBk5e2Z14DjiR5WOLHs8T7wPHCitfYLlLunjDGN\niTYG6+ry9zwohxUeAWYZY7KBFcAoIA2Y5WdR8cQY04joL5ApW3SEMeZEYJO19iuiQ4P3GGP+R/SW\n2fcTvWJkoQ/lhp4x5nHgaiACFBpjyjv5Amtt+e3IlXkdMsY8CLwCrAWaAP2Bs4Dflq2ivOuYtbYQ\nqHqNfSGw0VqbW7ZIudehspsYvkT0UEJH4F5gFzCnbJU6yTsQzYG1dm7ZnAb3ER3++BC40Fq7wd/K\n4srPiF5iZMseD5ctfxYYYq2dbIxJA54kemb9m8D/s9YW+1FsHLiBaM7LqiwfDDwHoMzrXBuiv8/t\ngQLgP0T/H1kKytuhmHlUlHudOxSYDbQENgDLgVOttRuh7vLWjZdEREQkhu/nHIiIiEiwqDkQERGR\nGGoOREREJIaaAxEREYmh5kBERERiqDkQERGRGGoOREREJIaaAxEREYmh5kBERERiqDkQERGRGGoO\nREREJMb/Bx4thAAW+yJ3AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1146215d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfwAAAFkCAYAAADFZ4k9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1149ab950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "R = linspace(1e-8,50,2**12+1) # so that we can use Romberg method\n",
    "\n",
    "nmax = 2\n",
    "Zatom = 4\n",
    "\n",
    "E0=-1.2*Zatom**2\n",
    "Eshift=0.5 # sometimes energies can be positive!!!                                                                                                                        \n",
    "Esearch = -logspace(-4,log10(-E0+Eshift),200)[::-1] + Eshift\n",
    "\n",
    "exc = ExchangeCorrelation()\n",
    "Uks = -2.*ones( len(R) )     # First iteration like hydrogen atom\n",
    "\n",
    "for itt in range(2):\n",
    "    Bnd=[]\n",
    "    for l in range(nmax-1):\n",
    "        Bnd += FindBoundStates(R,l,nmax-l,Esearch,Uks)\n",
    "    Bnd.sort( cmpE )\n",
    "    \n",
    "    rho = ChargeDensity(Bnd,R,Zatom,Uks)\n",
    "    \n",
    "    U = HartreeU(R, rho)\n",
    "    \n",
    "    Vxc = [2*exc.Vx(rs(rh)) + 2*exc.Vc(rs(rh)) for rh in rho]\n",
    "    \n",
    "    Uks = U-2*Zatom + Vxc*R\n",
    "    \n",
    "    print 'Total density has weight=', integrate.simps(rho*(4*pi*R**2), x=R)\n",
    "    \n",
    "    plot(R,U, label='U-hartree')\n",
    "    plot(R,Vxc,label='Vxc')\n",
    "    plot(R, Uks, label='Uks')\n",
    "    legend(loc='best')\n",
    "    grid()\n",
    "    show()\n",
    "    plot(R, rho*(4*pi*R**2))\n",
    "    xlim([0,20])\n",
    "    show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we will include charge density mixing, which will improve convergence. We will take a fraction of the new, and a fraction of the old charge density at each iteration.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found bound state at E=  -0.999998807 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.249999851 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -0.499999403471  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.124999925296  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E= -12.847578370 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -1.592504356 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -6.42378918503  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.796252177996  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -9.809331493 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.759401416 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -4.90466574638  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.379700708221  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -6.716105845 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.215725475 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.35805292251  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.107862737501  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.565176024 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.393819734 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.78258801221  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.196909866827  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.907109199 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.464424548 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.95355459973  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.232212274037  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.704561385 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.409029832 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85228069231  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.204514915867  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.682331761 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.403695002 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.84116588064  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.201847501159  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.718367018 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.413194014 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85918350894  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.206597007022  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.716041250 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.412505071 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85802062506  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.206252535601  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.710600928 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411038588 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85530046412  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.2055192941  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.711860535 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411383126 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85593026768  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.20569156278  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712535108 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411565239 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85626755415  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205782619571  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712221919 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411479949 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.8561109595  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205739974323  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712163550 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411464155 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85608177481  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205732077673  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712223689 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411480517 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85611184467  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205740258488  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712223394 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411480430 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85611169684  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205740215146  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712213707 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411477795 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85610685372  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205738897534  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712215324 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411478235 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85610766187  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.20573911762  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712216630 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411478591 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85610831498  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205739295317  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712216157 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411478462 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85610807842  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205739230934  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712216022 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411478425 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.856108011  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205739212588  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712216120 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411478452 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85610806021  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205739225981  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712216126 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411478454 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85610806315  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205739226775  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712216109 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411478449 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85610805471  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205739224482  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712216111 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411478449 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85610805559  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205739224718  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712216114 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411478450 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85610805681  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205739225051  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712216113 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411478450 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85610805647  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205739224957  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712216113 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411478450 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85610805633  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.20573922492  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712216113 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411478450 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.8561080564  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205739224937  Hartree with Z= 4 with ferm= 1.0\n",
      "Total density has weight= 4.0\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgcAAAFkCAYAAAC0KZhSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113f393d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgkAAAFkCAYAAACq4KjhAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAAPYQAAD2EBqD+naQAAIABJREFUeJzt3XmUnVWd7//3NxMJgSRAyIAEIrMEBVMgymBQpgtcsVWW\nUso1IiIoDiv+vDj2tdW+ICJGUWi6FZbYYNnIdUDEZhRxANEEZIpESAhBMhGggJCkMuzfH7uKVCo1\nnVNneqrer7XOeuo85xk2p9vUp757P3tHSglJkqSuhtW7AZIkqTEZEiRJUrcMCZIkqVuGBEmS1C1D\ngiRJ6pYhQZIkdcuQIEmSumVIkCRJ3TIkSJKkbhkSJElStwYUEiLisxGxOSK+2cdxx0TEvIhYFxEL\nI2L2QO4rSZKqr+yQEBGHAR8G/trHcdOBG4HbgYOBbwPfj4jjy723JEmqvrJCQkTsAFwDfAh4vo/D\nPwIsSimdn1J6NKV0GXA9MKece0uSpNoot5JwGfDLlNId/Tj2jcBtXfbdDLypzHtLkqQaGFHqCRFx\nOnAIcGg/T5kCrOiybwUwLiK2Symt7+YeuwAnAk8A60ptoyRJQ9hoYDpwc0pp9UAuVFJIiIjdgW8B\nx6WUNgzkxn04Ebi2iteXJGmwex/wo4FcoNRKQhOwKzA/IqJ933DgzRHxMWC7lFLqcs5yYHKXfZOB\nF7qrIrR7AuCaa67hNa95TYlNVLnmzJnD3Llz692MIcXvvPb8zmvP77y2FixYwBlnnAHtv0sHotSQ\ncBvw2i77fgAsAL7WTUAAuBs4qcu+E9r392QdwGte8xpmzpxZYhNVrvHjx/t915jfee35ndee33nd\nDLi7vqSQkFJaAzzSeV9ErAFWp5QWtL+/AHhVSqljLoQrgPMi4iLgKuBY4DTg5AG2XZIkVVElZlzs\nWj2YCkx75cOUngBOAY4D7ic/+nhWSqnrEw+SJKmBlPx0Q1cppbd2eX9mN8fcRR7PUBXr18OaNbDz\nztW6gyRJQ0/h12548UXYf3844ABYubLerSm25ubmejdhyPE7rz2/89rzOy+uwoeEn/8cliyBVavg\nssvq3Zpi83/Ited3Xnt+57Xnd15chQ8Jv/gFvOlN0NwMN95Y79ZIkjR4FD4kzJ+fQ8KJJ+afn+9r\nJQlJktQvhQ4Jra2weDEccggcdljed9999W2TJEmDRaFDwkMP5e3rXpcHL44dC/Pm1bdNkiQNFoUO\nCYsX5+3ee8Pw4fDa18KDD9a3TZIkDRaFDglLlsAuu8AOO+T3++8Pjz5a3zZJkjRYFDokPPEETJ++\n5X1HSOh2BQlJklSSQRcSnn/eSZUkSaqEQoeEp56C3Xff8n6vvfL2iSfq0hxJkgaVQoeEFStgypQt\n7/fYI2+ffLI+7ZEkaTApbEhYvx6eew4mT96yb6ed8iBGQ4IkSQNX2JDQMe6gcyUhIlcTliypT5sk\nSRpMChsSVqzI286VBMghwUqCJEkDV9iQsHx53nauJIAhQZKkSilsSFi1Km933XXr/XvuaXeDJEmV\nUNiQ8NxzeZDiyJFb799jD3j2WXjppfq0S5KkwaKwIeH552HChG33dzwGuXRpbdsjSdJgU9iQ8Nxz\n+ZHHrpwrQZKkyihsSOipktAxkLFjYKMkSSrPoAsJo0fnCsOyZbVvkyRJg0lhQ0JP3Q2QqwlWEiRJ\nGpjChoSeKgkAU6daSZAkaaAKGxKsJEiSVF2FDQlWEiRJqq5ChoS2Nnj55d5DgpUESZIGppAh4fnn\n87a37oYXX4Q1a2rXJkmSBpuSQkJEnBsRf42I1vbXHyPif/Ry/KyI2NzltSkiJg2k0R0hobdKAlhN\nkCRpIEqtJCwFPgPMBJqAO4AbIuLAXs5JwL7AlPbX1JTSyjLa+or+VBLAcQmSJA3EiFIOTin9qsuu\nL0bER4DDgUd6OXVVSumFUhvXk+eey1srCZIkVU/ZYxIiYlhEnA5sB/yut0OB+yPi6Yi4JSKOKPee\nHfrqbpgwAUaNMiRIkjQQJVUSACLiIOBuYDTwMvDulNJjPRy+DDgH+As5TJwN3BkRb0gp3V9ek3Ml\nYdgw2HHHntoIu+4Kq1aVewdJklRySAD+BhwMjAdOA34cEbNSSvd1PTCltBBY2GnXPRGxNzAHmN3X\njebMmcP48eO32tfc3MzzzzczYUIOAz0xJEiSBruWlhZaWlq22tfa2lqx60dKaWAXiLgVWJxS+nA/\nj/86cGRK6chejpkJzJs3bx4zZ87c5vPPfx5aWmDx4p7vc8IJMG4cXH99f1olSdLgMH/+fJqamgCa\nUkrzB3KtSsyTMAwYXsLxh5C7Icr20kuwww69H2MlQZKkgSmpuyEiLgB+DTwJ7Ai8D3gz8K/tn18I\n7JZSmt3+/pPAYuBh8hiGs4G3AMcPpNFr1vQvJNy3TQeIJEnqr1LHJEwCrgamAq3AA8CJKaXftH8+\nBZjW6fhRwCXAbuRBjg8Ax6aU7hpIo9esgbFjez/GSoIkSQNT6jwJH+rj8zO7vL8YuLiMdvWqv90N\nq1fDpk0wvJTOEEmSBBR07Yb+VhJSgmefrU2bJEkabAoZEl56qe+QMKl9dQi7HCRJKk8hQ0J/By6C\nIUGSpHIVMiT0p5LQERJWDmgpKUmShq5ChoT+VBImTIARI6wkSJJUrkKGhP5UEiJg4kRDgiRJ5Spc\nSNiwAdra+q4kgHMlSJI0EIULCWvW5G1flQQwJEiSNBCFDQlWEiRJqq7ChgQrCZIkVVfhQsJLL+Wt\nlQRJkqqrcCGh1ErCM8/A5s3VbZMkSYNR4UJCqZWETZvgueeq2yZJkgajwoWEUisJkKsJkiSpNIUL\nCR2VhP6EhF12ydvVq6vXHkmSBqvChYQ1a2DUKBg5su9jDQmSJJWvcCGhP1MydzAkSJJUvsKFhP4s\n7tRh1Kh8rCFBkqTSFS4klFJJgFxNMCRIklS6woWEUioJkFeCNCRIklS6QoaE7bfv//G77OIjkJIk\nlaNwIWHt2tJDgpUESZJKV8iQMHp0/483JEiSVJ5ChoQxY/p/vCFBkqTyFC4krFtXXkhIqXptkiRp\nMCpcSCi1kjBxIrS1bVnzQZIk9c+gDwkdsy76hIMkSaUpZEgodeAiOC5BkqRSlRQSIuLciPhrRLS2\nv/4YEf+jj3OOiYh5EbEuIhZGxOyBNLjcSoIhQZKk0pRaSVgKfAaYCTQBdwA3RMSB3R0cEdOBG4Hb\ngYOBbwPfj4jjy2xvWQMXwZAgSVKpRpRycErpV112fTEiPgIcDjzSzSkfARallM5vf/9oRBwFzAFu\nLbWxUHolYYcd8rLShgRJkkpT9piEiBgWEacD2wG/6+GwNwK3ddl3M/Cmcu65YQNs2lRaSIhw/QZJ\nkspRUiUBICIOAu4GRgMvA+9OKT3Ww+FTgBVd9q0AxkXEdiml9aXce+3avC1l4CK4foMkSeUoOSQA\nfyOPLxgPnAb8OCJmpZTuq2jLgDlz5jB+/PhX3q9fD9DMmDHNJV3HWRclSYNRS0sLLS0tW+1rbW2t\n2PVLDgkppY3Aova390XEG8hjDz7czeHLgcld9k0GXuhPFWHu3LnMnDnzlfdLlsD06aV1N4AhQZI0\nODU3N9PcvPUfzvPnz6epqaki16/EPAnDgOE9fHY3cGyXfSe07y9ZR3eDIUGSpOordZ6ECyLi6IjY\nMyIOiogLgTcD17R/fmFEXN3plCuAvSLioojYPyI+Su6i+GY5jTUkSJJUO6V2N0wCrgamAq3AA8CJ\nKaXftH8+BZjWcXBK6YmIOAWYC3wCeAo4K6XU9YmHfil34KJPN0iSVLpS50n4UB+fn9nNvrvIEy8N\n2Lp1eVtOJeHFF/NCT6NGVaIlkiQNfoVau2Eg3Q1gNUGSpFIYEiRJUrcMCZIkqVuFCwkRpY8rMCRI\nklS6QoWEdevykw0RpZ230075HEOCJEn9V6iQUOoKkB2GD89BwfUbJEnqvyEREsAJlSRJKpUhQZIk\ndatwIaHU2RY7GBIkSSpNoULCunVWEiRJqpVChQS7GyRJqp0hExJc5EmSpNIMmZCwyy7w7LOweXNl\n2yRJ0mBVuJAwkIGLmzfD889Xtk2SJA1WhQoJAx24CHY5SJLUX4ULCdttV965hgRJkkpTqJCwfv3A\nuhvAkCBJUn8VLiRYSZAkqTaGTEgYPRrGjnWRJ0mS+mvIhARwQiVJkkpRqJAwkIGL4IRKkiSVolAh\nYaCVhIkT7W6QJKm/ChMSUoK2tvKfboDc3WBIkCSpfwoTEtra8tbuBkmSaqMwIWH9+ry1u0GSpNoo\nTEhYty5vB/p0wzPP5K4LSZLUu8KEhEpVEjZuhBdfrEybJEkazEoKCRHxuYi4NyJeiIgVEfGziNiv\nj3NmRcTmLq9NETGplHt3hISBDFycODFv7XKQJKlvpVYSjga+AxwOHAeMBG6JiL7WZkzAvsCU9tfU\nlNLKUm5ciUpCx9TMhgRJkvo2opSDU0ond34fER8AVgJNwO/7OH1VSumFklrXSaW6G8AnHCRJ6o+B\njkmYQK4SPNvHcQHcHxFPR8QtEXFEqTeq1MBFsJIgSVJ/lB0SIiKAbwG/Tyk90suhy4BzgHcB7wSW\nAndGxCGl3K8SlYQxY1zkSZKk/iqpu6GLy4EDgSN7OyiltBBY2GnXPRGxNzAHmN3fm1Vi4CK4yJMk\nSf1VVkiIiO8CJwNHp5SWlXGJe+kjXADMmTOH8ePHA7B8ed73q181c845zWXcMnNCJUnSYNHS0kJL\nS8tW+1pbWyt2/UglzizUHhDeDsxKKS0q66YRtwAvpJRO6+HzmcC8efPmMXPmTAD+67/g9NOhtRXG\njSvnrtmJJ8KOO8L115d/DUmSGtX8+fNpamoCaEopzR/ItUqqJETE5UAzcCqwJiImt3/UmlJa137M\nBcCrUkqz299/ElgMPAyMBs4G3gIcX8q9KzEmAXJ3w7Jyah+SJA0xpXY3nEt+muHOLvvPBH7Y/vNU\nYFqnz0YBlwC7AS8DDwDHppTuKuXGHSFh1KgSW9zFxInw4IMDu4YkSUNBqfMk9Pk0RErpzC7vLwYu\nLrFd21i/PlcRIgZ2HcckSJLUP4Vau2GgXQ2w5ekGF3mSJKl3hQkJ69ZVJiRMnAgbNrjIkyRJfSlM\nSKhUJcFFniRJ6p8hFxI6pmZ2QiVJkno35EKClQRJkvqnUCFhoFMyg4s8SZLUX4UJCZUauNixyJPd\nDZIk9a4wIaFS3Q2QqwlWEiRJ6t2QDAlOqCRJUt+GbEiwu0GSpN4VJiSsW1eZgYtgd4MkSf1RmJBg\nd4MkSbU1ZEOC3Q2SJPVuSIaEju4GF3mSJKlnQzIkuMiTJEl9K0xIqOTAxY6pme1ykCSpZ4UJCZXu\nbgAHL0qS1JvChIS2tsp2N4AhQZKk3hQqJIwaVZlrdYSEVasqcz1JkgajIRkSRo+GHXc0JEiS1JtC\nhISUKhsSACZNMiRIktSbQoSEDRvytpIhYdddYeXKyl1PkqTBphAhoa0tbys1cBFyJcGQIElSzwoV\nEird3WBIkCSpZ0M6JDgmQZKknhUiJKxfn7eOSZAkqXYKERKqVUl4+WVYs6Zy15QkaTAZ0iEBrCZI\nktSTkkJCRHwuIu6NiBciYkVE/Cwi9uvHecdExLyIWBcRCyNidin3rdbTDeC4BEmSelJqJeFo4DvA\n4cBxwEjglogY09MJETEduBG4HTgY+Dbw/Yg4vr83rUYlYddd89ZKgiRJ3RtRysEppZM7v4+IDwAr\ngSbg9z2c9hFgUUrp/Pb3j0bEUcAc4Nb+3LcaIaFj/QZDgiRJ3RvomIQJQAKe7eWYNwK3ddl3M/Cm\n/t6kGk83jBwJO+9sSJAkqSdlh4SICOBbwO9TSo/0cugUYEWXfSuAcRHRr1EG1agkgBMqSZLUm5K6\nG7q4HDgQOLJCbdnGnDlzGD9+PMuX5/dnnQWzZzfT3NxckevvuqsDFyVJxdXS0kJLS8tW+1pbWyt2\n/UgplX5SxHeBtwFHp5Se7OPY3wLzUkqf6rTvA8DclNJOPZwzE5g3b948Zs6cyXXXwXveA62tMG5c\nyc3t0WmnwYsvws03V+6akiTV0/z582lqagJoSinNH8i1Su5uaA8Ibwfe0ldAaHc3cGyXfSe07+8X\nuxskSaq9UudJuBx4H/BeYE1ETG5/je50zAURcXWn064A9oqIiyJi/4j4KHAa8M3+3rdj4OLIkaW0\ntm+GBEmSelZqJeFcYBxwJ/B0p9e7Ox0zFZjW8Sal9ARwCnlehfvJjz6elVLq+sRDj9raYPjw/Kqk\njjEJZfS4SJI06JU6T0KfoSKldGY3++4iz6VQlra2ys622GHSJNiwIY91mDCh8teXJKnICrN2Q6XH\nI4DrN0iS1BtDAoYESZK6U4iQsH59dUOCcyVIkrStQoSEalUSdtopD4a0kiBJ0rYKExKqMXBx2LC8\n0JMhQZKkbRUmJFSjkgDOlSBJUk+GfEiYPBlWdF1+SpIkGRKmTOGVBaQkSdIWhQgJ1Xq6AXJIWLas\nOteWJKnIChESqllJmDrVSoIkSd0pTEioxtMNkCsJL72UX5IkaYvChIRqdjeA1QRJkroa8iFh6tS8\nNSRIkrS1QoSEag9cBAcvSpLUVSFCQjUrCRMm5PEOVhIkSdpaYUJCtQYuRjhXgiRJ3SlMSKhWJQGc\nK0GSpO4YEnCuBEmSulOIkFDNgYtgJUGSpO4UIiTUorvBSoIkSVsrTEio1sBFyN0NK1fCpk3Vu4ck\nSUVTmJBQ7UrC5s2walX17iFJUtEYEnBqZkmSutPwIWHjxvxXfrWfbgAHL0qS1FnDh4S2trytdiUh\nAp5+unr3kCSpaAwJwMiRMGkS/OMf1buHJElFU5iQUM2nGwBe9Sp46qnq3kOSpCIpTEioZiUBYPfd\nrSRIktRZySEhIo6OiBsi4h8RsTkiTu3j+Fntx3V+bYqISf25X61CgpUESZK2Vk4lYSxwP/BRIPXz\nnATsC0xpf01NKa3sz4nr1+etlQRJkmprRKknpJT+G/hvgIiIEk5dlVJ6odT71bKSsHo1rF0LY8ZU\n916SJBVBrcYkBHB/RDwdEbdExBH9PbGWAxfBxyAlSepQi5CwDDgHeBfwTmApcGdEHNKfk2s5cBHs\ncpAkqUPJ3Q2lSiktBBZ22nVPROwNzAFm93bunDlz2LBhPAAf+xiMHQvNzc00NzdXvJ0dlQQHL0qS\niqKlpYWWlpat9rW2tlbs+lUPCT24Fziyr4Pmzp3LypUzOekk+MEPYNq06jVoxx1h3DgrCZKk4uju\nD+f58+fT1NRUkevXa56EQ8jdEH2qVXcD+BikJEmdlVxJiIixwD7kwYgAe0XEwcCzKaWlEXEhsFtK\naXb78Z8EFgMPA6OBs4G3AMf35361GrgIOSRYSZAkKSunu+FQ4DfkuQ8ScEn7/quBD5LnQejcMTCq\n/ZjdgJeBB4BjU0p39edmtawk7L47LFhQ/ftIklQE5cyT8Ft66aZIKZ3Z5f3FwMWlNy2rdXfDbbdV\n/z6SJBVBw6/dsH59XsZ5+PDq32v33WHZMti0qfr3kiSp0TV8SGhry1WEkuZ2LNO0aTkgOKGSJEkF\nCQm1GLQIMH163i5ZUpv7SZLUyAoREmoxHgFgzz3z1pAgSZIhYSs77AA77wxPPFGb+0mS1MgaPiSs\nX1+7kAC5y8FKgiRJBQgJtawkQO5yMCRIkmRI2Maee9rdIEkSFCQk1OrpBsjdDU8+CSnV7p6SJDWi\nQoSEWlcS1q2DlStrd09JkhqRIaEL50qQJClr+JBQ66cbOuZKcFyCJGmoa/iQUOtKwoQJsOOOVhIk\nSSpESKjlwMUI50qQJAkKEhJqWUkAH4OUJAkMCd3ae294/PHa3lOSpEbT8CGh1gMXAfbZBxYtystG\nS5I0VDV8SKhHJWGfffJ9ly6t7X0lSWokhQgJtRy4CLDvvnn72GO1va8kSY2kECGhHgMXR4yAv/+9\ntveVJKmRGBK6MWJEfgzSSoIkaShr+JBQj4GLkLscDAmSpKGs4UNCPSoJkAcv2t0gSRrKChESaj1w\nEXJIePxxH4OUJA1dhQgJ9epuaGuDp56q/b0lSWoEDR0SNm+GjRvr190AjkuQJA1dDR0SNm7M23qE\nhOnTYfhwxyVIkoauhg4JbW15W4+QMHJkriY88kjt7y1JUiMoOSRExNERcUNE/CMiNkfEqf0455iI\nmBcR6yJiYUTM7s+9NmzI23qEBIAZMwwJkqShq5xKwljgfuCjQOrr4IiYDtwI3A4cDHwb+H5EHN/X\nuR3dDfV4ugHgwAPh4Yfrc29JkuptRKknpJT+G/hvgIiIfpzyEWBRSun89vePRsRRwBzg1t5ObIRK\nwvLl8OyzsPPO9WmDJEn1UosxCW8Ebuuy72bgTX2d2AghAawmSJKGplqEhCnAii77VgDjIqLXjoR6\nDlwE2G+//ISDIUGSNBSV3N1QSxddNAcYz2c+A+PH533Nzc00NzfX5P7bbZcnVTIkSJIaUUtLCy0t\nLVvta21trdj1axESlgOTu+ybDLyQUlrf24kf//hcPvjBmVx++ZbSf63NmGFIkCQ1pu7+cJ4/fz5N\nTU0VuX4tuhvuBo7tsu+E9v296uhuqNfTDWBIkCQNXeXMkzA2Ig6OiEPad+3V/n5a++cXRsTVnU65\nov2YiyJi/4j4KHAa8M2+7lXvgYuQQ8LKlfDMM/VrgyRJ9VBOJeFQ4D5gHnmehEuA+cCX2z+fAkzr\nODil9ARwCnAceX6FOcBZKaWuTzxsoyMk1LOScPDBeXv//fVrgyRJ9VDOPAm/pZdwkVI6s5t9dwEl\nd5A0QnfDvvvCjjvCvHlw3HH1a4ckSbXW0Gs3NEJ3w7Bh8PrXw1/+Ur82SJJUD4UICfWsJAAcemiu\nJEiSNJQ0dEhoa8uTGQ0fXt92NDXB4sV5emZJkoaKhg4JGzbUt6uhQ8fjplYTJElDScOHhHp3NcDW\ngxclSRoqGjoktLU1RkgYNgxmzjQkSJKGloYOCY3S3QBw2GFwzz2QUr1bIklSbTR8SGiESgLA0UfD\nU0/BkiX1bokkSbXR0KtANlJIOOooiIDf/hamT693ayojJVi9GpYtgxdeyK8IGDMGtt8epkyB3Xar\n/9MlkqT6aOiQ0NbWON0NO+8Mr31tDgmzZ9e7NeVZuRLuuAN+97s8vmLhQnjuud7PGT4cpk2D170u\nP+Vx6KG5qrLjjrVpsySpfho+JDRKJQFg1iy46aZ6t6I0q1bBddfBT34Cd92Vqwf77QeHHw6nnpp/\n3n13GDcu/+KPgJdfzq+nn87dK4sWwV//Ct/+dp4rYsQIeOMb4fjj4e1vzwEiot7/pZKkSmvokLBx\nY+OFhO98B/7xD3jVq+rdmt51/FL/0Y9g06a87sT3vgennJK7EfrjkEO2fp8SPP443Hprfn3zm/Cl\nL8EBB8Dpp0Nzcw4dkqTBoaEHLjZSdwPkMjvkLodG9dBD8La35V/wt94K//IveczBr38NZ53V/4DQ\nnQjYZx/4yEfgpz/NVYqbboI3vAEuuQT23x/e+tZcteiYUluSVFwNHxIaqZIwaRLMmAG3317vlmxr\n+XI488xc+n/kEbjmmtxN8NnPwsSJ1bnnyJFw0klw9dV5vMO11+Zw8O53wx575CrDqlXVubckqfoa\nOiRs3NhYlQTIvxRvugk2b653S7LNm+E//iOX/G+8MXeHLFgA73tf/iVeK6NHw3vfmwdFPvAAvPOd\nubqw557wiU/Ak0/Wri2SpMpo6JDQaJUEyH36y5fDfffVuyXwxBNwzDFwzjnwrnfBo4/CeefVP1i9\n9rVw2WV50ONnPpMrDHvvDR/4QH6iQpJUDIaEEh15JIwfn/9qr6f/+i84+GBYujQ/1njllfkxzUay\nyy65y2HJEvj61+G22+DAA+Hss3O7JUmNraFDQiN2N3T0w//0p/W5/5o18KEP5acJTjoJ7r8f3vKW\n+rSlv3bYAebMgcceg4svhp//PC+a9alPOWZBkhpZQ4eERqwkALznPbnffcGC2t73ySdzJaOlJVcO\nWlpyVaMoRo/OYWHRIvj85+H734e99oKvfjXPyyBJaiyGhDKcdFL+5fzjH9funnffnReZev75/PMH\nP1jcCYx23BH+z/+BxYvzeIqvfjU/PnnttY0zIFSS1OAhoZFWgexsu+3gHe/IjxnW4pfaD3+YByju\ntx/8+c/5McfBYJdd4BvfyI9sHnYYnHEGHHFEDkGSpPpr+JDQiJUEyOMCFi3Kg/GqZdOm/HTA7Nn5\nkcbbboNdd63e/epln33yGI/f/CZXj444Is/e6GOTklRfhoQyHXEEHHQQXHFFda7/4ou5WvGNb+T5\nBq68snG/i0o55phcKbnqKrjzzjz3w7/+K6xbV++WSdLQ1NAhodGmZe4sIs9J8ItfwN//XtlrL16c\nQ8idd8Ivf5mfAijq+INSDR+eZ45cuBA+/nH48pdzGPvVr+rdMkkaeho6JDRyJQHy5ECTJ8MFF1Tu\nmnfdlddCePlluOceOPnkyl27SHbcES66CB58EF79avif/zOvSfH44/VumSQNHQ0dEjZtauyQMHo0\nnH8+/Od/5sF3A5ES/Nu/wbHH5r+c7703Tzw01B1wANxyC1x/fV7ZcsaM/GSEj0xKUvU1dEiAxu1u\n6HDuufkv3fPOy7/oy9HWlh8F/OhH8wqLt9ySR/4ri8jTTi9YAJ/+dK4wHHhgnpSp3O9cktS3skJC\nRJwXEYsjYm1E3BMRh/Vy7KyI2NzltSkiJvXnXo1cSYBcTbjssjx+4PLLSz9/0SKYNSuvpHjVVXDp\npbVdmKlIxo7NAxkfeiiHhHe8I89Z4XoQklQdJYeEiHgPcAnwJeD1wF+BmyOitwWJE7AvMKX9NTWl\ntLI/92v0SgLACSfkQXZz5uRVEPsjpTz/wSGHwIoVeSzCmWdWt52Dxb775oGMv/hFDggHHQSf+xy8\n9FK9WyZJg0s5lYQ5wL+nlH6YUvobcC7wMvDBPs5blVJa2fHq780avZLQ4RvfgKOOygMNb72192Mf\nfhiOPz7Pf/COd+T1Fw4/vDbtHCwi4NRT83f5hS/At76Vxy+0tNgFIUmVUlJIiIiRQBNwe8e+lFIC\nbgPe1Ns2QvHuAAAPFElEQVSpwP0R8XRE3BIRR/T3nkUJCaNG5ccVjzwSTjwxjy3429+2/MJ66SW4\n4Qb4p3/Kf/kuWZL/Gr76ahg3rr5tL7IxY/JKkwsW5KD13vfCm9+cg5ckaWBKrSRMBIYDK7rsX0Hu\nRujOMuAc4F3AO4GlwJ0RcUh/bliE7oYOY8fCTTflqsJPfgKveU1evnm33WDCBHj72/NKiFdemfvV\nh+rjjdUwfTr8v/+XqzirV0NTUx4Iunp1vVsmScU1oto3SCktBDoPLbsnIvYmd1vM7uv8olQSOgwb\nlic/OvfcPJjxgQfyjIGvelVe0nmfferdwsHtuOPyo5KXXZYrDD/+cR7seM45eaImSVL/RSqhA7e9\nu+Fl4F0ppRs67f8BMD6l9I5+XufrwJEppSN7+HwmMA/ezKxZ47cqxzc3N9Pc3NzvNmvoWrkyL0l9\n1VV5UaxLL81dEZI0WLS0tNDS0rLVvtbWVu666y6AppTS/IFcv6SQABAR9wB/Sil9sv19AE8Cl6aU\nLu7nNW4BXkgpndbD5+0hYR4LFszkgANKaqK0lT//OT998qc/wemnw8UXw+6717tVklQd8+fPp6mp\nCSoQEsp5uuGbwNkR8f6IOAC4Atge+AFARFwYEVd3HBwRn4yIUyNi74iYERHfAt4CfLc/Nytad4Ma\nz2GHwR//CD/4QV5pcr/98qyNL75Y75ZJUmMrOSSklK4DPg18BbgPeB1wYkppVfshU4BpnU4ZRZ5X\n4QHgTuC1wLEppTv7cz9Dgiph2LD8yOnChfDJT8LXv57nW/iP/4CNG+vdOklqTCV3N9RC5+6GVatm\nMrG3aZqkMjz5JHzxi3ndjQMPzF0QJ500dFbblDR41bu7oabGjKl3CzQY7bFHnvHyL3+BSZPglFPy\nBFfOryBJWzR8SBg9ut4t0GDW1AR33JEnuvrHP2DmTHj/+/OaGpI01DV0SBgxwmfbVX0R8La3wYMP\n5vkVbr0V9t8/z5r51FP1bp0k1U9Dh4Qizbao4hsxIgeDxx+HCy6A667Lk1996lN5zgVJGmoMCVIX\n228P//t/w+LFeTKmK6+EV786//zss/VunSTVTkOHBMcjqJ7GjcvzKSxeDJ/4BHz727DnnvCZz+Tl\nvSVpsGvokGAlQY1g553hwgvzYMbzzoN/+7e8oNTHPpZX85SkwaqhQ4ITKamRTJ4MX/taDgaf/zy0\ntOQxC2eeCY8+Wu/WSVLlGRKkEu20E/zzP+ewcNFFcPPNeVnwd74Tfvc7aMD5ySSpLIYEqUw77JCf\nfFi0CK64AhYsyKtMHnYYXHsttLXVu4WSNDANHRIck6AiGD0aPvxhePhhuOkm2GUXOOOM/ETEBRfA\nM8/Uu4WSVJ6GDglWElQkw4bl9R9uvhkeeghOPhm+8pW8LPUZZ9gVIal4DAlSFcyYAd/7HixdCl/9\nKvzpT7krYsaM/Cjlc8/Vu4WS1LeGDgl2N6jodt01T8z06KNw221w0EHw6U/DbrvlNSJuvx02bap3\nKyWpew0dEpxMSYPFsGFw7LF5quennoIvfQnuvhuOOy7PufC5z8Ejj9S7lZK0tYYOCVYSNBhNngyf\n/SwsXJiDwtveBv/+77kr4tBDc3fE00/Xu5WS1OAhwTEJGswi4I1vhMsvh2XL4Kc/hWnTcvfE7rvD\n0UfDpZe6EqWk+mnokDBmTL1bINXGdtvBO94BP/tZXhfiqqtg/Pg8fmHaNDjySJg7N68jIUm10tAh\nYfvt690CqfZ22gk+8AG48ca8RPXVV+e5Fz77Wdhrr9wtcf75cNddsHFjvVsraTBr6JBgJUFD3YQJ\n+SmIG26AVavg+uvh8MNzcJg1Kz890dwM11wDy5fXu7WSBpsR9W5AbwwJ0hbjxsG73pVfmzfDvHm5\n2vCrX8H/+l/5mBkz8lMUxx6bQ8T48fVts6Ria+iQYHeD1L1hw/IaEYcdBl/+cq4i3HFHnnfhF7/I\nAx47jnnrW+Goo/IgyZ13rnfLJRWJIUEaBKZMgfe+N78gLzp1++05OFx1FVx4Yd5/4IFwxBH5deSR\nsO+++SkLSepOQ4cEuxuk8uy1V36dfXZeL2LRIvjjH+EPf8jbK6/M+ydOzNWGpiaYOTNvp00zOEjK\nGjokWEmQBi4C9t47vzrGLjz/fF5P4g9/yGMbvve9/Ogl5OAwc2Z+vf71eSrpffeFkSPr998gqT4M\nCdIQNGECnHhifkGuKixblgPD/Pl5+8Mfwte+lj8fORL23z8PjJwxIweHGTNy8Bg+vH7/HZKqq6FD\ngt0NUm1E5EWndtstTxPd4Zln4OGH8+uhh/L21lvh2Wfz5yNH5m6NffeFffbJr46f99zTACEVnSFB\nr2hpaaG5ubnezRhSGv07nzgxP0o5a9aWfSnlromHH4a//Q0eewz+/nf49a/z2IcNG/JxI0fCq1+d\nF7DaY48cGvbYY8tr993rsz5Lo3/ng5HfeXGVFRIi4jzg08AU4K/Ax1NKf+7l+GOAS4AZwJPA/00p\nXd3XffwrpLb8H3LtFfE7j8hPU0yZkudj6GzjRli6NIeGxx7LryVL4P7784RQK1dufZ2pU3Ng2G23\nfL2pU7dcu+PnyZNhRAX/nCnid150fufFVfL/9CLiPeRf+B8G7gXmADdHxH4ppWe6OX46cCNwOfBe\n4Djg+xHxdErp1vKbLqnRjBiRqwevfjWccMK2n69dm0PEk09ueS1ZksdD/OEPebtqVa5WdIjIFY0p\nU2DSpDxFdefXxInb7hs/3ic0pEooJ5/PAf49pfRDgIg4FzgF+CDw9W6O/wiwKKV0fvv7RyPiqPbr\nGBKkIWTMGNhvv/zqycaNueKwfHl+LVu2ZbtqFaxenZfZfuaZ/PPatdteY/jwvAbG+PH5NW7clu2D\nD8IXvrDt/vHjYYcd8oDpsWO3bEeONHBo6CopJETESKAJuKBjX0opRcRtwJt6OO2NwG1d9t0MzC3l\n3pKGhhEjtgyi7I+1a3NYWL16S3BYvToPrnzhBWht3bJdvDh/du21W/Zt3tz79YcP3zo09LTdbrut\nX6NHb7uvr/2jRuX//pEj87bzz8OGGVZUe6VWEiYCw4EVXfavAPbv4ZwpPRw/LiK2Symt7+ac0QAL\nFiwosXkaiNbWVubPn1/vZgwpfueVtdNO+bXPPj0fM2dOK3Pn5u88JVi3Dl56Kb/Wrs3v167d+ueu\n246fn38+VznWroW2tvzasGHLdv36vK3Uap0jRuTQMnz4tj93vO9pf0QOGt29Iro/puN9T5/1dN2O\nzyD//OCDrXz84/OJ2BJ0On7uuq+3z7ru68+xpVy387Gddd1X6vvuVPqanT9fuvSV352j+25J7xr1\n6YbpAGeccUadmzH0NDU11bsJQ47fee0V9TvfuLG4y4N/97vF/M4Lbjrwx4FcoNSQ8AywCZjcZf9k\noKeFapf3cPwLPVQRIHdHvA94AlhXYhslSRrKRpMDws0DvVBJISGltCEi5gHHAjcARES0v7+0h9Pu\nBk7qsu+E9v093Wc18KNS2iZJkl4xoApCh2FlnPNN4OyIeH9EHABcAWwP/AAgIi6MiM5zIFwB7BUR\nF0XE/hHxUeC09utIkqQGVfKYhJTSdRExEfgKudvgfuDElNKq9kOmANM6Hf9ERJxCfprhE8BTwFkp\npa5PPEiSpAYSqfOsJZIkSe3K6W6QJElDgCFBkiR1q+FCQkScFxGLI2JtRNwTEYfVu02DVUR8LiLu\njYgXImJFRPwsInqZMFeVFhGfjYjNEeFA3iqKiN0i4j8j4pmIeDki/hoRM+vdrsEqIoa3D2Jf3P59\nPxYRX6x3uwaTiDg6Im6IiH+0/xtyajfHfCUinm7/v8GtEdHLNGPda6iQ0GnxqC8BryevMHlz+0BJ\nVd7RwHeAw8kLb40EbokIF+mugfYA/GHy/5+rSiJiAvAHYD1wIvAa4P8Dnqtnuwa5LwBnkdfuOQA4\nHzg/Ij5W11YNLmPJDw58FNhmcGFEfAb4GPnfmDcAa8i/T0taoL2hBi5GxD3An1JKn2x/H8BS4NKU\nUneLR6mC2sPYSuDNKaXf17s9g1lE7ADMI/8j+s/AfSmlT9W3VYNTRHwNeFNKaVa92zJURMQvgeUp\npbM77bseeDml9P76tWxwiojNwD+llG7otO9p4OKU0tz29+PISyLMTild199rN0wlodPiUbd37Es5\nwfS2eJQqawI5kT5b74YMAZcBv0wp3VHvhgwBbwP+EhHXtXerzY+ID9W7UYPcr4FjI2JfgIg4GDgS\nuKmurRoiIuLV5OkIOv8+fQH4EyX+Pm2ktRvKWTxKFdJetfkW8PuU0iP1bs9gFhGnA4cAh9a7LUPE\nXuSKzSXA/yWXXi+NiPUppf+sa8sGqZTS5RExDXg0IjaS/yD9Qkrpx3Vu2lAxhfwHX3e/T6eUcqFG\nCgmqr8uBA8lpX1USEbuTw9hxKaUN9W7PEDEMuDel9M/t7/8aEQcB5wKGhCqIiE8As4H3AI+QQ/G3\nI+Jpg1mxNEx3A+UtHqUKiIjvAicDx6SUltW7PYNcE7ArMD8iNkTEBmAW8MmIaGuv6KiylgFd151f\nAOxRh7YMFZ8HvppS+klK6eGU0rXkWXc/V+d2DRXLgaACv08bJiS0/1XVsXgUsNXiURVZqELbag8I\nbwfeklJ6st7tGQJuA15L/svq4PbXX4BrgINTI40kHjz+wLZdlvsDS+rQlqFiGPmPvs4200C/cwaz\nlNJichjo/Pt0HPlJtpJ+nzZad8M3gR+0rzR5LzCHTotHqbIi4nKgGTgVWBMRHamzNaXkEt1VkFJa\nQy6/viIi1gCrU0pd/9pVZcwF/hARnwOuI/9D+SHg7F7P0kD8HPhiRDwFPAzMJP97/v26tmoQiYix\nwD7kigHkhRQPBp5NKS0ld2t+MSIeA54AvkpeO+kXJd2n0f5waV8l8ny2LB718ZTSX+rbqsGp/bGZ\n7v4f4MyU0g9r3Z6hKiLuAO73EcjqiYiTga+R/1FdDFySUrqqvq0avCJie+DLwLvI/5Y/DfyI3AWx\nsZ5tGywiYhbwG7b9N/zqlNIH24/5F/I8CROA3wHnpZQeK+k+jRYSJElSY7B/SJIkdcuQIEmSumVI\nkCRJ3TIkSJKkbhkSJElStwwJkiSpW4YESZLULUOCJEnqliFBkiR1y5AgSZK6ZUiQJEnd+v8BpEeo\n2ZOk/DQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1140a4c90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R = linspace(1e-8,50,2**12+1) # so that we can use Romberg method\n",
    "\n",
    "nmax = 2\n",
    "Zatom = 4\n",
    "mixr = 0.5\n",
    "\n",
    "E0=-1.2*Zatom**2\n",
    "Eshift=0.5 # sometimes energies can be positive!!!                                                                                                                        \n",
    "Esearch = -logspace(-4,log10(-E0+Eshift),200)[::-1] + Eshift\n",
    "\n",
    "exc = ExchangeCorrelation()\n",
    "Uks = -2.*ones( len(R) )     # First iteration like hydrogen atom\n",
    "\n",
    "for itt in range(30):\n",
    "    Bnd=[]\n",
    "    for l in range(nmax-1):\n",
    "        Bnd += FindBoundStates(R,l,nmax-l,Esearch,Uks)\n",
    "    Bnd.sort( cmpE )\n",
    "    \n",
    "    rho_new = ChargeDensity(Bnd,R,Zatom,Uks)\n",
    "    \n",
    "    if itt>0:\n",
    "        rho = rho_new*mixr + (1-mixr)*rho_old\n",
    "    else:\n",
    "        rho = rho_new\n",
    "    rho_old = copy(rho_new)\n",
    "    \n",
    "    U = HartreeU(R, rho)\n",
    "    \n",
    "    Vxc = [2*exc.Vx(rs(rh)) + 2*exc.Vc(rs(rh)) for rh in rho]\n",
    "    \n",
    "    Uks = U-2*Zatom + Vxc*R\n",
    "    \n",
    "    print 'Total density has weight=', integrate.simps(rho*(4*pi*R**2), x=R)\n",
    "  \n",
    "\n",
    "plot(R,U, label='U-hartree')\n",
    "plot(R,Vxc,label='Vxc')\n",
    "plot(R, Uks, label='Uks')\n",
    "legend(loc='best')\n",
    "grid()\n",
    "show()\n",
    "plot(R, rho*(4*pi*R**2))\n",
    "xlim([0,10])\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally we add the total energy. At each iteration, we will evaluate \n",
    "\n",
    "\\begin{eqnarray}\n",
    "E^{LDA}_{total} &=& \\sum_{i\\in occupied}\\int d\\vec{r}\n",
    "\\psi_i^*(\\vec{r})[-\\nabla^2]\\psi_i(\\vec{r}) +\\nonumber\\\\\n",
    " &+& \\int d\\vec{r} \\rho(\\vec{r}) [V_{nucleous}(\\vec{r})+\\epsilon_H(\\vec{r}) +\n",
    "   \\epsilon_{XC}(\\vec{r})]\\nonumber\\\\\n",
    " &=& \\sum_{i\\in occupied}\\int d\\vec{r}\n",
    "\\psi_i^*(\\vec{r})[-\\nabla^2+V_{nucleous}+V_H+V_{XC}]\\psi_i(\\vec{r})\n",
    " \\nonumber\\\\\n",
    " &+& \\int d\\vec{r} \\rho(\\vec{r}) [\\epsilon_H(\\vec{r})-V_H(\\vec{r}) +\n",
    "   \\epsilon_{XC}(\\vec{r})-V_{XC}(\\vec{r})]\\nonumber\\\\\n",
    " &=& \\sum_{i\\in occupied}\\epsilon_i + \\int d\\vec{r} \\rho(\\vec{r}) [\\epsilon_H(\\vec{r})-V_H(\\vec{r}) +\n",
    "   \\epsilon_{XC}(\\vec{r})-V_{XC}(\\vec{r})]\\nonumber\\\\\n",
    " &=& \\sum_{i\\in occupied}\\epsilon_i + \\int d\\vec{r} \\rho(\\vec{r}) [-\\epsilon_H(\\vec{r}) + \\epsilon_{XC}(\\vec{r})-V_{XC}(\\vec{r})]\\\\\n",
    "  &=& \\sum_{i\\in occupied}\\epsilon_i + \\int d\\vec{r} \\rho(\\vec{r})[\n",
    "  -\\frac{1}{2} V_H(\\vec{r}) + \\epsilon_{XC}(\\vec{r})-V_{XC}(\\vec{r})]\n",
    "\\end{eqnarray}\n",
    "\n",
    "Here we used\n",
    "\n",
    "\\begin{eqnarray}\n",
    "&& E_y[\\rho] \\equiv \\int d\\vec{r}\\; \\rho(\\vec{r})\\; \\epsilon_y[\\rho(\\vec{r})]\\\\\n",
    "&& V_y[\\rho]\\equiv \\frac{\\delta E_y[\\rho]}{\\delta \\rho(\\vec{r})}\n",
    "\\end{eqnarray}\n",
    "where $y$ is one of $H$, $x$ or $c$. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found bound state at E=  -0.999999849 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.249999981 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -0.499999924717  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.124999990581  Hartree with Z= 4 with ferm= 1.0\n",
      "Itteration 0 Etot[Ry]= -6.75545868729 Etot[Hartre]= -3.37772934365 Diff= 6.75545868729\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E= -12.848578363 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -1.592599732 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -6.42428918151  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.796299866236  Hartree with Z= 4 with ferm= 1.0\n",
      "Itteration 1 Etot[Ry]= -37.3774530953 Etot[Hartre]= -18.6887265477 Diff= 30.6219944081\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -9.810074652 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.759434866 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -4.90503732579  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.379717432886  Hartree with Z= 4 with ferm= 1.0\n",
      "Itteration 2 Etot[Ry]= -36.3284654406 Etot[Hartre]= -18.1642327203 Diff= 1.0489876547\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -6.716545642 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.215722081 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.35827282096  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.10786104061  Hartree with Z= 4 with ferm= 1.0\n",
      "Itteration 3 Etot[Ry]= -26.8429411209 Etot[Hartre]= -13.4214705605 Diff= 9.48552431971\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.565688131 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.393827053 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.78284406531  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.196913526648  Hartree with Z= 4 with ferm= 1.0\n",
      "Itteration 4 Etot[Ry]= -28.0752464676 Etot[Hartre]= -14.0376232338 Diff= 1.23230534668\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.907654027 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.464436766 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.95382701368  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.232218383119  Hartree with Z= 4 with ferm= 1.0\n",
      "Itteration 5 Etot[Ry]= -29.4101089733 Etot[Hartre]= -14.7050544866 Diff= 1.33486250566\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.705086506 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.409037292 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85254325296  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.204518646216  Hartree with Z= 4 with ferm= 1.0\n",
      "Itteration 6 Etot[Ry]= -28.9494429519 Etot[Hartre]= -14.4747214759 Diff= 0.460666021414\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.682854799 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.403702113 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.84142739972  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.201851056714  Hartree with Z= 4 with ferm= 1.0\n",
      "Itteration 7 Etot[Ry]= -28.8030908126 Etot[Hartre]= -14.4015454063 Diff= 0.146352139276\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.718893859 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.413202003 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85944692959  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.206601001347  Hartree with Z= 4 with ferm= 1.0\n",
      "Itteration 8 Etot[Ry]= -28.9001949849 Etot[Hartre]= -14.4500974925 Diff= 0.0971041723328\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.716567773 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.412512969 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85828388659  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.206256484314  Hartree with Z= 4 with ferm= 1.0\n",
      "Itteration 9 Etot[Ry]= -28.9079778931 Etot[Hartre]= -14.4539889466 Diff= 0.00778290820539\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.711126838 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411046337 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85556341901  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205523168627  Hartree with Z= 4 with ferm= 1.0\n",
      "Itteration 10 Etot[Ry]= -28.8909536434 Etot[Hartre]= -14.4454768217 Diff= 0.0170242496947\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712386609 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411390916 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85619330474  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205695458245  Hartree with Z= 4 with ferm= 1.0\n",
      "Itteration 11 Etot[Ry]= -28.8924487715 Etot[Hartre]= -14.4462243857 Diff= 0.00149512806576\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.713061261 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411573049 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85653063066  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205786524678  Hartree with Z= 4 with ferm= 1.0\n",
      "Itteration 12 Etot[Ry]= -28.8949593901 Etot[Hartre]= -14.4474796951 Diff= 0.00251061862082\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712748029 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411487748 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85637401474  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205743874051  Hartree with Z= 4 with ferm= 1.0\n",
      "Itteration 13 Etot[Ry]= -28.8943106657 Etot[Hartre]= -14.4471553328 Diff= 0.00064872442514\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712689654 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411471953 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85634482684  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205735976629  Hartree with Z= 4 with ferm= 1.0\n",
      "Itteration 14 Etot[Ry]= -28.8940092999 Etot[Hartre]= -14.4470046499 Diff= 0.000301365828761\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712749802 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411488317 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85637490096  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205744158516  Hartree with Z= 4 with ferm= 1.0\n",
      "Itteration 15 Etot[Ry]= -28.8941630896 Etot[Hartre]= -14.4470815448 Diff= 0.000153789705287\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712749506 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411488230 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85637475294  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205744115107  Hartree with Z= 4 with ferm= 1.0\n",
      "Itteration 16 Etot[Ry]= -28.8941869702 Etot[Hartre]= -14.4470934851 Diff= 2.38806530817e-05\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712739818 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411485595 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85636990913  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.20574279734  Hartree with Z= 4 with ferm= 1.0\n",
      "Itteration 17 Etot[Ry]= -28.89415821 Etot[Hartre]= -14.447079105 Diff= 2.87602274369e-05\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712741435 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411486035 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85637071748  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.20574301751  Hartree with Z= 4 with ferm= 1.0\n",
      "Itteration 18 Etot[Ry]= -28.8941590005 Etot[Hartre]= -14.4470795003 Diff= 7.90549265162e-07\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712742741 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411486390 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85637137064  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205743195194  Hartree with Z= 4 with ferm= 1.0\n",
      "Itteration 19 Etot[Ry]= -28.8941635278 Etot[Hartre]= -14.4470817639 Diff= 4.52727316969e-06\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712742268 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411486262 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85637113406  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205743130819  Hartree with Z= 4 with ferm= 1.0\n",
      "Itteration 20 Etot[Ry]= -28.894162667 Etot[Hartre]= -14.4470813335 Diff= 8.60819532988e-07\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712742133 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411486225 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85637106666  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205743112502  Hartree with Z= 4 with ferm= 1.0\n",
      "Itteration 21 Etot[Ry]= -28.8941620738 Etot[Hartre]= -14.4470810369 Diff= 5.93194165788e-07\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712742232 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411486252 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.85637111585  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.20574312587  Hartree with Z= 4 with ferm= 1.0\n",
      "Itteration 22 Etot[Ry]= -28.894162309 Etot[Hartre]= -14.4470811545 Diff= 2.3523692505e-07\n",
      "Total density has weight= 4.0\n",
      "Found bound state at E=  -7.712742238 E_exact=  -1.000000000 l=0\n",
      "Found bound state at E=  -0.411486253 E_exact=  -0.250000000 l=0\n",
      "Adding state with l= 0 and E= -3.8563711188  Hartree with Z= 2 with ferm= 1\n",
      "Adding state with l= 0 and E= -0.205743126668  Hartree with Z= 4 with ferm= 1.0\n",
      "Itteration 23 Etot[Ry]= -28.894162367 Etot[Hartre]= -14.4470811835 Diff= 5.79269894274e-08\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgkAAAFkCAYAAACq4KjhAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSZIKMiRIkqSCDAmSJKkgQ4IkSSro/wf4pwV0cxOdJgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113e61cd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def ChargeDensity(bst,R,Zatom,Uks):\n",
    "    rho = zeros( len(R) )\n",
    "    N=0\n",
    "    Ebs=0.\n",
    "    for i,(l,Ei) in enumerate(bst):\n",
    "        dN = 2*(2*l+1)\n",
    "        if N+dN<Zatom:\n",
    "            ferm=1\n",
    "        else:\n",
    "            ferm = (Zatom-N)/float(dN)\n",
    "        u = ComputeSchrod(Ei,R,l,Uks)\n",
    "        drho = u**2 / (4*pi*R**2) * dN * ferm\n",
    "        rho += drho\n",
    "        N += dN\n",
    "        Ebs += Ei*dN*ferm\n",
    "        print 'Adding state with l=', l, 'and E=', Ei/2, ' Hartree with Z=', N, 'with ferm=', ferm\n",
    "        if N>=Zatom: break\n",
    "    return (rho,Ebs)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "R = linspace(1e-8,50,2**13+1) # so that we can use Romberg method\n",
    "Etol=1e-7\n",
    "nmax = 2\n",
    "Zatom = 4\n",
    "mixr = 0.5\n",
    "\n",
    "E0=-1.2*Zatom**2\n",
    "Eshift=0.5 # sometimes energies can be positive!!!                                                                                                                        \n",
    "Esearch = -logspace(-4,log10(-E0+Eshift),200)[::-1] + Eshift\n",
    "\n",
    "exc = ExchangeCorrelation()\n",
    "Uks = -2.*ones( len(R) )     # First iteration like hydrogen atom\n",
    "Eold=0\n",
    "\n",
    "for itt in range(30):\n",
    "    Bnd=[]\n",
    "    for l in range(nmax-1):\n",
    "        Bnd += FindBoundStates(R,l,nmax-l,Esearch,Uks)\n",
    "    Bnd.sort( cmpE )\n",
    "    \n",
    "    (rho_new,Ebs) = ChargeDensity(Bnd,R,Zatom,Uks)\n",
    "    \n",
    "    if itt>0:\n",
    "        rho = rho_new*mixr + (1-mixr)*rho_old\n",
    "    else:\n",
    "        rho = rho_new\n",
    "    rho_old = copy(rho_new)\n",
    "    \n",
    "    U = HartreeU(R, rho)\n",
    "    \n",
    "    Vxc = [2*exc.Vx(rs(rh)) + 2*exc.Vc(rs(rh)) for rh in rho]\n",
    "    \n",
    "    Uks = U-2*Zatom + Vxc*R\n",
    "    \n",
    "    # Total energy\n",
    "    ExcVxc = array([2*exc.EcVc(rs(rh))+2*exc.ExVx(rs(rh)) for rh in rho])\n",
    "    pot=(ExcVxc*R**2-0.5*U*R)*rho*4*pi\n",
    "    Etot = integrate.romb(pot, R[1]-R[0]) + Ebs\n",
    "    print 'Itteration', itt, 'Etot[Ry]=', Etot, 'Etot[Hartre]=', Etot/2, 'Diff=', abs(Etot-Eold)\n",
    "    if itt>0 and abs(Etot-Eold)<Etol: break\n",
    "    Eold = Etot\n",
    "    \n",
    "    print 'Total density has weight=', integrate.simps(rho*(4*pi*R**2), x=R)\n",
    "  \n",
    "\n",
    "plot(R, rho*(4*pi*R**2),'--', label='rho')\n",
    "legend(loc='best')\n",
    "xlim([0,10])\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
}