simu_covid.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider the system \n",
    "$$\\left\\{\\begin{array}{l}\n",
    "S'=-u\\beta SI\\\\\n",
    "I'=u\\beta SI-\\nu I\\\\\n",
    "R'=\\nu I\\\\\n",
    "S(t_0)=1-I_0,I(t_0)=\\frac{I_0}{N},R(t_0)=0\n",
    "\\end{array}\\right.$$\n",
    "where $S_0+I_0+R_0=1$.\n",
    "\n",
    "The goal is to solve the optimal control proplem\n",
    "$$\\inf\\limits_{u\\in\\mathcal{U}}J(u)$$\n",
    "where \n",
    "$$\n",
    "J(u)=S(T)+I(T)-\\frac{\\nu}{\\beta}\\ln(S(T))=S_0+I_0-\\frac{\\nu}{\\beta}\\ln(S_0)+\\int_0^T\\nu I(u-1),\n",
    "$$\n",
    " and\n",
    "$$\\mathcal{U}=\\{u\\in L^{\\infty}(0,T):\\alpha\\leqslant u\\leqslant 1\\}$$\n",
    "\n",
    "One has \n",
    "$$\n",
    "DJ(u)\\cdot h=\\int_0^T[\\nu -\\beta S(P_I-P_S)]Ih,\n",
    "$$\n",
    "where\n",
    "\\begin{equation*}\n",
    "\\left\\{\\begin{array}{l}\n",
    " -\\frac{d }{d t}\\begin{pmatrix} P_S \\\\ P_I \\end{pmatrix} = \\begin{pmatrix}-u\\beta I & u\\beta I\\\\ -u\\beta S & u\\beta S-\\nu \\end{pmatrix}\\begin{pmatrix}P_S \\\\ P_I \\end{pmatrix}+\\begin{pmatrix} 0\\\\ -(u-1)I \\end{pmatrix},\\\\\n",
    "P_S(T)=0, \\ P_I(T)=0\n",
    "\\end{array}\\right.\n",
    "\\end{equation*}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from __future__ import division\n",
    "from IPython.display import display, Math, Markdown\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Parameters of the model\n",
    "beta=0.29\n",
    "nu=0.1\n",
    "t0=0\n",
    "alpha_conf = 0.231\n",
    "\n",
    "# state initialization \n",
    "N=6.7e7\n",
    "I0=1000/N\n",
    "S0=1-I0\n",
    "R0=0\n",
    "init=np.array([S0, I0,R0,0.0]) \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def f(u,y):\n",
    "\tdy = np.array([-u*beta*y[0]*y[1],u*beta*y[0]*y[1]-nu*y[1],nu*y[1],nu*y[1]*(u-1.0)])\n",
    "\treturn dy\n",
    "\n",
    "def RK4_state(u,init):\n",
    "\t# solved in the time interval [a,b] \n",
    "\t# initial conditions = vector alpha\n",
    "\t# number of subdivisions  in the interval [a,b] = N\n",
    "\tw = np.zeros((NT,4))\n",
    "\tw[0,:] = init    #initial conditions\n",
    "\tfor i in range(NT-1):\n",
    "\t\tk1 = h*f(u[i], w[i,:])\n",
    "\t\tk2 = h*f(0.5*(u[i]+u[i+1]), w[i,:]+0.5*k1)\n",
    "\t\tk3 = h*f(0.5*(u[i]+u[i+1]), w[i,:]+0.5*k2) \n",
    "\t\tk4 = h*f(u[i+1], w[i,:]+k3)\n",
    "\t\tw[i+1,:] = w[i,:] + (k1 + 2*k2 + 2*k3 + k4)/6\n",
    "\treturn w\n",
    "\n",
    "def f_dual(i,u_i,ystate,p_i):\n",
    "\ta11=-beta*u_i*ystate[i,1]\n",
    "\ta12=-beta*u_i*ystate[i,0]\n",
    "\ta21=beta*u_i*ystate[i,1]\n",
    "\ta22=beta*u_i*ystate[i,0]-nu\n",
    "\tA=np.matrix([[a11, a12],[a21 ,a22]])\n",
    "\treturn np.transpose(np.transpose(A)*np.transpose(np.matrix(p_i)))-np.matrix([0,nu*(u_i-1.0)])\n",
    "\n",
    "def RK4_adj(u,ystate):\n",
    "\t# solved in the time interval [a,b] \n",
    "\t# initial conditions = vector alpha\n",
    "\t# number of subdivisions  in the interval [a,b] = N\n",
    "\tpT = np.zeros((NT,2))\n",
    "\tpT[-1,:] = np.array([0.0,0.0])\n",
    "\tfor i in list(reversed(range(1,NT))):\n",
    "\t\tk1 = h*f_dual(i,u[i],ystate,pT[i,:])\n",
    "\t\tk2 = h*f_dual(i,0.5*(u[i]+u[i-1]),ystate,pT[i,:]+0.5*k1)\n",
    "\t\tk3 = h*f_dual(i,0.5*(u[i]+u[i-1]),ystate,pT[i,:]+0.5*k2) \n",
    "\t\tk4 = h*f_dual(i,u[i-1],ystate,pT[i,:]+k3)\n",
    "\t\tpT[i-1,:] = pT[i,:] + (k1 + 2*k2 + 2*k3 + k4)/6\n",
    "\treturn pT\n",
    "\n",
    "def J(y):\n",
    "    return S0+I0-(nu/beta)*np.log(S0)+y[-1,-1]\n",
    "\n",
    "def DJ(y,p):\n",
    "    return y[:,1]*(nu-beta*y[:,0]*(p[:,1]-p[:,0]))\n",
    "\n",
    "\n",
    "def Dicho_S_inf(val):\n",
    "    S_inf_min = 0.0 # borne gauche de l'intervalle initial\n",
    "    S_inf_max = nu/beta # borne gauche de l'intervalle initial b>a\n",
    "    val_max = S_inf_min-(nu/beta)*np.log(S_inf_min)\n",
    "    val_min = S_inf_max-(nu/beta)*np.log(S_inf_max)\n",
    "    while S_inf_max-S_inf_min > 1e-5:\n",
    "            S_inf=0.5*(S_inf_max+S_inf_min)\n",
    "            val_test=S_inf-(nu/beta)*np.log(S_inf)\n",
    "            if val_test > val:\n",
    "                    S_inf_min=S_inf\n",
    "            else:\n",
    "                    S_inf_max=S_inf\n",
    "    return 0.5*(S_inf_max+S_inf_min);\n",
    "\n",
    "def optimSIR(uinit,init,info):\n",
    "\tu=uinit\n",
    "\tyval=RK4_state(u,init)\n",
    "\tpval=RK4_adj(u,yval)\n",
    "\tJnew=J(yval)\n",
    "\tJval = [Jnew]\n",
    "\tDelta2=1\n",
    "\t#norm_grad = 1\n",
    "\ti=0\n",
    "\trho=1000 # pas dans la methode de gradient\n",
    "\twhile (abs(Delta2)>1e-10 and i<ITER):        \n",
    "\t\trho=100*rho#np.minimum(100*rho,1000.0)\n",
    "\t\tyval=RK4_state(u,init)\n",
    "\t\tpval=RK4_adj(u,yval)\n",
    "\t\tDelta=1\n",
    "\t\tk1=0\n",
    "\t\twhile (Delta>0) and (k1<100): # recherche du pas\n",
    "\t\t\trho=rho/1.2\n",
    "\t\t\tutest=u-rho*DJ(yval,pval)\n",
    "\t\t\tutest=np.maximum(alpha,np.minimum(utest,1))\n",
    "\t\t\tyval_test=RK4_state(utest,init)\n",
    "\t\t\tJnew=J(yval_test)\n",
    "\t\t\tDelta=Jnew-Jval[-1]\n",
    "\t\t\tk1=k1+1\n",
    "\t\tk2=0\n",
    "\t\tutest2=utest\n",
    "\t\tJnew2=Jnew\n",
    "\t\tDelta=-1\n",
    "\t\twhile (Delta<0) and (k2<100): # recherche du pas\n",
    "\t\t\trho=rho/1.2\n",
    "\t\t\tJnew1=Jnew2     \n",
    "\t\t\tutest1=utest2 \n",
    "\t\t\tutest2=u-rho*DJ(yval,pval)\n",
    "\t\t\tutest2=np.maximum(alpha,np.minimum(utest2,1))\n",
    "\t\t\tyval_test=RK4_state(utest2,init)\n",
    "\t\t\tJnew2=J(yval_test)\n",
    "\t\t\tDelta=Jnew2-Jnew1\n",
    "\t\t\tk2=k2+1\n",
    "\t\tDelta1=Jnew-Jval[-1]\n",
    "\t\tDelta2=Jnew1-Jval[-1]\n",
    "\t\tnorm_grad = np.linalg.norm(DJ(yval,pval))\n",
    "\t\tprint('norm grad',norm_grad)\n",
    "\t\tif info == True:\n",
    "\t\t\tprint('i=',i,'and J=',Jnew,'rho=',rho)  \n",
    "\t\t\tprint('k1=',k1,'k2=',k2,'delta2',Delta2)      \n",
    "\t\tu=np.copy(utest1)\n",
    "\t\tJval.append(Jnew1)\n",
    "\t\ti=i+1\n",
    "\tif (i==iter):\n",
    "\t\tprint('maximal number of iterations reached')\n",
    "\tprint('end of computations')\n",
    "\treturn u, i, Jnew, Jval, yval\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "def optimSIR_dic_finite_dim(T,init):\n",
    "\tT0_ind_min = 0 # borne gauche de l'intervalle initial\n",
    "\tT0_ind_max = NT-1 # borne gauche de l'intervalle initial b>a\n",
    "\twhile T0_ind_max-T0_ind_min>2:\n",
    "\t\tT0_ind_test1=int(T0_ind_min+1/3*(T0_ind_max-T0_ind_min))\n",
    "\t\tT0_ind_test2=int(T0_ind_min+2/3*(T0_ind_max-T0_ind_min))\n",
    "\t\tu1=np.ones(int(NT))\n",
    "\t\tfor i in range(T0_ind_test1,int(NT)):\n",
    "\t\t\tu1[i]=alpha\n",
    "\t\tyval1=RK4_state(u1,init)\n",
    "\t\tJ1 = J(yval1)\n",
    "\t\tu2=np.ones(int(NT))\n",
    "\t\tfor i in range(T0_ind_test2,int(NT)):\n",
    "\t\t\tu2[i]=alpha\n",
    "\t\tyval2=RK4_state(u2,init)\n",
    "\t\tJ2 = J(yval2)    \n",
    "\t\tif J1 < J2:\n",
    "\t\t\tT0_ind_max=T0_ind_test2\n",
    "\t\telse:\n",
    "\t\t\tT0_ind_min=T0_ind_test1\n",
    "\treturn u1, J1, yval1, tval[T0_ind_test1]\n",
    "\n",
    "\n",
    "def exact_value_T0(T,alpha):\n",
    "    tval=np.linspace(t0,T,NT) # discretized time interval [t0,t0+h,...,T]\n",
    "    h = (T-t0)/(NT-1)        #the time step\n",
    "    Sherd = nu/beta\n",
    "    T0_ind_min = 0 # borne gauche de l'intervalle initial\n",
    "    T0_ind_max = int(NT-1) # borne gauche de l'intervalle initial b>a\n",
    "    while T0_ind_max - T0_ind_min>1:\n",
    "        T0_ind=int(0.5*(T0_ind_min+T0_ind_max))\n",
    "        u=np.ones(int(NT))\n",
    "        for ind in range(T0_ind,NT):\n",
    "            u[ind]=alpha\n",
    "        yval = RK4_state(u,init)\n",
    "        if alpha == 0:\n",
    "            phi = yval[T0_ind,0]*(1-np.exp(nu*(tval[T0_ind]-T))) - Sherd\n",
    "        else:\n",
    "            #phi=(1.0-alpha)*yval[-1,1]*(1.0/yval[T0_ind,1]+nu*h*sum(1.0/yval[i,1] for i in range(T0_ind,NT)))-1.0\n",
    "            phi=yval[-1,1]*(1.0-alpha)*beta*h*sum(yval[i,0]/yval[i,1] for i in range(T0_ind,NT))-1.0\n",
    "        if phi <=0:\n",
    "            T0_ind_max=T0_ind\n",
    "        else:\n",
    "            T0_ind_min=T0_ind\n",
    "    T0 = tval[T0_ind]\n",
    "    S_inf = Dicho_S_inf(J(yval))\n",
    "    return S_inf, max(T0,0.0), u, J(yval), yval, tval\n",
    "\n",
    "# functions to plot and save datas\n",
    "\n",
    "def write_to_file(f,A,B):\n",
    "    f.write('\\n')\n",
    "    for i in range(len(A)):\n",
    "        f.write('(')\n",
    "        f.write(str(A[i]))\n",
    "        f.write(',')\n",
    "        f.write(str(B[i]))\n",
    "        f.write(')')\n",
    "        f.write('\\n')\n",
    "    f.write('\\n')\n",
    "    f.write('\\n')\n",
    "    return;\n",
    "\n",
    "def plot_save_example(yval,u,tval,text):\n",
    "    # Plot\n",
    "    plt.figure(1)\n",
    "    plt.plot(tval,yval[:,0],'r-',linewidth=2,label=r'$S$')\n",
    "    plt.plot(tval,yval[:,1],'g-',linewidth=2,label=r'$I$')\n",
    "    plt.plot(tval,yval[:,2],'b-',linewidth=2,label=r'$R$')\n",
    "    plt.plot(tval,(1.0/2.9)*np.ones(len(tval)),'k--',linewidth=2,label=r'$S_{herd}$')\n",
    "    plt.legend(loc='best')\n",
    "    plt.xlabel('Time')\n",
    "    plt.savefig(\"fig1_simu_covid{2}_T_{0}_alpha_{1}_S.png\".format(T,alpha,text))\n",
    "    plt.figure(2)\n",
    "    plt.plot(tval,u,'-',linewidth=2,label=r'$u$')\n",
    "    plt.legend(loc='best')\n",
    "    plt.xlabel('Time')\n",
    "    plt.axis([0, max(tval), 0, 1.05*max(u)])\n",
    "    plt.savefig(\"fig1_simu_covid{2}_T_{0}_alpha_{1}_u.png\".format(T,alpha,text))\n",
    "    plt.show()\n",
    "\n",
    "\n",
    "    # Save the values for tikz\n",
    "    File = open('fig1_simu_covid{2}_T_{0}_alpha_{1}.txt'.format(T,alpha,text),'w')\n",
    "    File.write('\\\\addplot[color=red] coordinates { ')\n",
    "    write_to_file(File,tval,yval[:,0])\n",
    "    File.write(' };\\n')\n",
    "    File.write('\\\\addplot[color=black!60!green] coordinates { ')\n",
    "    write_to_file(File,tval,yval[:,1])\n",
    "    File.write(' };\\n')\n",
    "    File.write('\\\\addplot[color=blue] coordinates { ')\n",
    "    write_to_file(File,tval,yval[:,2])\n",
    "    File.write(' };\\n')\n",
    "    File.write('\\\\addplot[color=black] coordinates {')\n",
    "    write_to_file(File,tval,u)\n",
    "    File.write(' };\\n')\n",
    "    File.close()\n",
    "    return ;\n",
    "\n",
    "\n",
    "def plot_save_opt_sol(Jval1,yval1,u1,yval2,u2,tval,fig):\n",
    "    # Plot\n",
    "    plt.figure(1)\n",
    "    plt.plot(Jval1,'b-',linewidth=2,label=r'$J(u)$')\n",
    "    plt.legend(loc='best')\n",
    "    plt.xlabel('iterations')\n",
    "    plt.axis([0, len(Jval1)-1, min(Jval1), max(Jval1)])\n",
    "    plt.savefig(\"fig{2}_simu_covid_infinite_dim_T_{0}_alpha_{1}_J.png\".format(T,alpha,fig))\n",
    "    plt.figure(2)\n",
    "    plt.plot(tval,yval1[:,0],'r-',linewidth=2,label=r'$S(u)$')\n",
    "    plt.plot(tval,yval1[:,1],'g-',linewidth=2,label=r'$I(u)$')\n",
    "    plt.plot(tval,yval1[:,2],'b-',linewidth=2,label=r'$R(u)$')\n",
    "    plt.legend(loc='best')\n",
    "    plt.xlabel('Time')\n",
    "    plt.savefig(\"fig{2}_simu_covid_infinite_dim_T_{0}_alpha_{1}_S.png\".format(T,alpha,fig))\n",
    "    plt.figure(3)\n",
    "    plt.plot(tval,u1,'-',linewidth=2,label=r'$u$')\n",
    "    plt.legend(loc='best')\n",
    "    plt.xlabel('Time')\n",
    "    plt.axis([0, max(tval), 0, 1.05*max(u1)])\n",
    "    plt.savefig(\"fig{2}_simu_covid_infinite_dim_T_{0}_alpha_{1}_u.png\".format(T,alpha,fig))\n",
    "    \n",
    "    plt.figure(4)\n",
    "    plt.plot(tval,yval2[:,0],'r-',linewidth=2,label=r'$S(T_0)$')\n",
    "    plt.plot(tval,yval2[:,1],'g-',linewidth=2,label=r'$I(T_0)$')\n",
    "    plt.plot(tval,yval2[:,2],'b-',linewidth=2,label=r'$R(T_0)$')\n",
    "    plt.legend(loc='best')\n",
    "    plt.xlabel('Time')\n",
    "    plt.savefig(\"fig{2}_simu_covid_finite_dim_T_{0}_alpha_{1}_S.png\".format(T,alpha,fig))\n",
    "    plt.figure(5)\n",
    "    plt.plot(tval,u2,'-',linewidth=2,label=r'$u(T_0)$')\n",
    "    plt.legend(loc='best')\n",
    "    plt.xlabel('Time')\n",
    "    plt.axis([0, max(tval), 0, 1.05*max(u2)])\n",
    "    plt.savefig(\"fig{2}_simu_covid_finite_dim_T_{0}_alpha_{1}_u.png\".format(T,alpha,fig))\n",
    "    plt.show()\n",
    "\n",
    "\n",
    "    # Save the values for tikz\n",
    "    File = open('fig{2}_simu_covid_T_{0}_alpha_{1}_sol.txt'.format(T,alpha,fig),'w')\n",
    "    File.write('\\\\addplot[color=red,opacity = 0.25,line width=1mm] coordinates { ')\n",
    "    write_to_file(File,tval,yval1[:,0])\n",
    "    File.write(' };\\n')\n",
    "    File.write('\\\\addplot[color=red] coordinates { ')\n",
    "    write_to_file(File,tval,yval2[:,0])\n",
    "    File.write(' };\\n')\n",
    "    File.write('\\\\addplot[color=black!60!green,opacity = 0.25,line width=1mm] coordinates { ')\n",
    "    write_to_file(File,tval,yval1[:,1])\n",
    "    File.write(' };\\n')\n",
    "    File.write('\\\\addplot[color=black!60!green] coordinates { ')\n",
    "    write_to_file(File,tval,yval2[:,1])\n",
    "    File.write(' };\\n')\n",
    "    File.write('\\\\addplot[color=blue,opacity = 0.25,line width=1mm] coordinates { ')\n",
    "    write_to_file(File,tval,yval1[:,2])\n",
    "    File.write(' };\\n')\n",
    "    File.write('\\\\addplot[color=blue] coordinates { ')\n",
    "    write_to_file(File,tval,yval2[:,2])\n",
    "    File.write(' };\\n')\n",
    "    File.close()\n",
    "    File = open('fig{2}_simu_covid_T_{0}_alpha_{1}_control.txt'.format(T,alpha,fig),'w')\n",
    "    File.write('\\\\addplot[color=black,opacity = 0.25,line width=1mm] coordinates {')\n",
    "    write_to_file(File,tval,u1)\n",
    "    File.write(' };\\n')\n",
    "    File.write('\\\\addplot[color=black] coordinates {')\n",
    "    write_to_file(File,tval,u2)\n",
    "    File.write(' };\\n')\n",
    "    File.close()\n",
    "    return ;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/duprez/.local/lib/python2.7/site-packages/ipykernel_launcher.py:52: RuntimeWarning: divide by zero encountered in log\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('$S_{inf}:', 0.06677824875404095)\n",
      "('$S_{herd}:', 0.3448275862068966)\n",
      "('$(S_{herd}-S_{inf})/(1-S_{inf}):', 0.2979456244795276)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8eb00cf790>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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5lkOdbZ99hP5El2zoS5LHAB8DXltV3wLeATwVeCZwF4O3gH17VlWdwuDKp69M8py+C1pMBif0nQ1cPmyaxvE8kKncXpO8EXgQ+OCw6S7ghKo6GXgd8KEkj+2rPhZ/nadyPIHzeOjEpNfxXCCHFu26QNsBx7OP0J/ksg69SLKCwUB/sKr+CaCqvl5V36+qHwD/yBF6K3ogVXXn8PfdwMcZ1PT1/W/rhr/v7q/ChzgT+FxVfR2mczyHFhu/qdtek7wE+E3gRTXcsTvcXbJvuHwdg33lT+urxgO8ztM4nscCvwt8ZH9bn+O5UA7R4fbZR+hPclmHI264T+/dwO6q+ruR9tH9Y78D9HqRuCSPTrJq/zKDD/Zu4qGXwngJ8Il+KnyYh8ygpm08Ryw2fjuAFw+PkjgNuHf/2+w+ZPCFRn8BnF1V3xlpX5vBd1+Q5CnAJuC2fqo84Ou8Azg3ySOTbGRQ52ePdH1jTge+UFXz+xv6Gs/Fcogut88j/en0yCfOX2Twv+cb+6hhgZp+hcHbol3A9cOfs4APADcO23cAT+65zqcwOPrhBuDm/ePH4FLWVwNfGv5+whSM6U8w+Ca1x4209T6eDP4Tugt4gMFM6aWLjR+Dt8+XDLfVG4GZnuucY7APd/82+s5h398bbg83AJ8DfqvnOhd9nYE3DsfzVuDMPusctr8XeMVY317G8wA51Nn26Rm5ktQQz8iVpIYY+pLUEENfkhpi6EtSQwx9SWrIRF+iIh3Nkuw/3A3gp4DvA3uH69+pql/upTCpBx6yqaYkuRD4dlX9Td+1SH1w946aluTbw9/PHV5Y67IkX0xycZIXJflsBt9d8NRhv7VJPpbk2uHPs/r9F0gHx9CXfuTngNcAJwF/BDytqk4F3gW8atjnbcBbq+oXGJy1+a4+CpUOlfv0pR+5tobXLUnyZeCqYfuNwK8Nl08HNg8ukQLAY5OsqsG1z6WpZ+hLP/K9keUfjKz/gB/9rTwC+KWq+u6RLEzqirt3pINzFXD+/pUkz+yxFumgGfrSwXk1MDP8RqhbgFf0XZB0MDxkU5Ia4kxfkhpi6EtSQwx9SWqIoS9JDTH0Jakhhr4kNcTQl6SGGPqS1JD/BxTNwtIP3ZB8AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8eb0013ad0>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('Time of switch:', 62.2)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8eadf6c850>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8eade417d0>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# examples of controls (figure 1)\n",
    "T=200.0\n",
    "alpha=0.0\n",
    "# discretisation parameters\n",
    "NT=int(10001) # number of time step\n",
    "ITER = 5e4 # number of step in optimisation\n",
    "tval=np.linspace(t0,T,NT) # discretized time interval [t0,t0+h,...,T]\n",
    "h = (T-t0)/(NT-1)        #the time step\n",
    "\n",
    "\n",
    "\n",
    "# Conpute the first solution\n",
    "u=np.ones(int(NT))\n",
    "yval=RK4_state(u,init)\n",
    "ind_max_I = np.argmax(yval[:,1])\n",
    "tval=tval[::50]\n",
    "yval=yval[::50,:]\n",
    "u=u[::50]\n",
    "\n",
    "Sinf = Dicho_S_inf(J(yval))\n",
    "print(\"$S_{inf}:\",Sinf)\n",
    "Sherd = nu/beta\n",
    "print(\"$S_{herd}:\",Sherd)\n",
    "print(\"$(S_{herd}-S_{inf})/(1-S_{inf}):\",(Sherd-Sinf)/(1.0-Sinf))\n",
    "\n",
    "# plot and save solution and control 1\n",
    "plot_save_example(yval,u,tval,'_example1')\n",
    "\n",
    "# compute the second solution\n",
    "tval=np.linspace(t0,T,NT)\n",
    "u=np.ones(int(NT))\n",
    "for i in range(int(ind_max_I+1),int(NT)):\n",
    "    u[i]=0.0\n",
    "yval=RK4_state(u,init)\n",
    "print('Time of switch:',tval[ind_max_I])\n",
    "tval=tval[::50]\n",
    "yval=yval[::50,:]\n",
    "u=u[::50]\n",
    "\n",
    "\n",
    "# plot and save solution and control 2\n",
    "plot_save_example(yval,u,tval,'_example2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('norm grad', 0.9365656588536552)\n",
      "('i=', 0, 'and J=', 0.9999593575942789, 'rho=', 15.823413952872837)\n",
      "('k1=', 1, 'k2=', 47, 'delta2', -0.18616579464189686)\n",
      "('norm grad', 0.7835701051793977)\n",
      "('i=', 1, 'and J=', 0.7255987049986359, 'rho=', 102.70261436495491)\n",
      "('k1=', 1, 'k2=', 14, 'delta2', -0.09033607884591177)\n",
      "('norm grad', 0.3472619901639989)\n",
      "('i=', 2, 'and J=', 0.7218050958682789, 'rho=', 2.3401526128400825)\n",
      "('k1=', 42, 'k2=', 4, 'delta2', -0.003425349195015137)\n",
      "('norm grad', 0.037521949596226366)\n",
      "('i=', 3, 'and J=', 0.72005297414375, 'rho=', 26.246368874162023)\n",
      "('k1=', 7, 'k2=', 5, 'delta2', -0.00016336282111695244)\n",
      "('norm grad', 0.07438751414318154)\n",
      "('i=', 4, 'and J=', 0.7198463477269147, 'rho=', 2.57147246568511)\n",
      "('k1=', 34, 'k2=', 4, 'delta2', -0.0001519922612499558)\n",
      "('norm grad', 0.036815597035385436)\n",
      "('i=', 5, 'and J=', 0.7197386600587312, 'rho=', 16.690263288309485)\n",
      "('k1=', 11, 'k2=', 4, 'delta2', -8.972425313147347e-05)\n",
      "('norm grad', 0.06236540743831456)\n",
      "('i=', 6, 'and J=', 0.7196378572474782, 'rho=', 2.8256578675659783)\n",
      "('k1=', 31, 'k2=', 4, 'delta2', -0.00010617324550965535)\n",
      "('norm grad', 0.037311888763583406)\n",
      "('i=', 7, 'and J=', 0.7195534917052384, 'rho=', 8.844553252574618)\n",
      "('k1=', 15, 'k2=', 4, 'delta2', -5.277448447493782e-05)\n",
      "('norm grad', 0.04793109305755719)\n",
      "('i=', 8, 'and J=', 0.7186299494900015, 'rho=', 614.2050869843486)\n",
      "('k1=', 1, 'k2=', 1, 'delta2', -0.000883947480491365)\n",
      "('norm grad', 0.0779603744508652)\n",
      "('i=', 9, 'and J=', 0.7186203875978091, 'rho=', 50.14698341182782)\n",
      "('k1=', 34, 'k2=', 5, 'delta2', -2.9781494953917687e-05)\n",
      "('norm grad', 0.05068898717202613)\n",
      "('i=', 10, 'and J=', 0.7185882936648071, 'rho=', 390.5776324312637)\n",
      "('k1=', 9, 'k2=', 5, 'delta2', -2.919315013660828e-05)\n",
      "('norm grad', 0.07638497607805714)\n",
      "('i=', 11, 'and J=', 0.7185692590288337, 'rho=', 66.12470641776659)\n",
      "('k1=', 30, 'k2=', 5, 'delta2', -2.2948339677641982e-05)\n",
      "('norm grad', 0.05133653717054246)\n",
      "('i=', 12, 'and J=', 0.7185452430499719, 'rho=', 618.0271558692895)\n",
      "('k1=', 7, 'k2=', 6, 'delta2', -2.1200072233273914e-05)\n",
      "('norm grad', 0.072964989907665)\n",
      "('i=', 13, 'and J=', 0.7185199479480419, 'rho=', 87.19321684670903)\n",
      "('k1=', 32, 'k2=', 4, 'delta2', -1.587259602353619e-05)\n",
      "('norm grad', 0.051030177666560865)\n",
      "('i=', 14, 'and J=', 0.7185109008230812, 'rho=', 471.60973772359364)\n",
      "('k1=', 10, 'k2=', 6, 'delta2', -8.8978940450124e-06)\n",
      "('norm grad', 0.06489178552928473)\n",
      "('i=', 15, 'and J=', 0.7184987284631055, 'rho=', 114.97453033734025)\n",
      "('k1=', 29, 'k2=', 4, 'delta2', -6.98694384937415e-06)\n",
      "('norm grad', 0.05087408565057623)\n",
      "('i=', 16, 'and J=', 0.7184936267716051, 'rho=', 431.85625603045224)\n",
      "('k1=', 13, 'k2=', 5, 'delta2', -5.003749713239358e-06)\n",
      "('norm grad', 0.06160867264007573)\n",
      "('i=', 17, 'and J=', 0.7184887019054916, 'rho=', 151.60746563040595)\n",
      "('k1=', 27, 'k2=', 4, 'delta2', -4.190838430839783e-06)\n",
      "('norm grad', 0.05020822190994504)\n",
      "('i=', 18, 'and J=', 0.7184847251302093, 'rho=', 329.54476790642764)\n",
      "('k1=', 17, 'k2=', 4, 'delta2', -2.8118156009115935e-06)\n",
      "('norm grad', 0.05915515352437293)\n",
      "('i=', 19, 'and J=', 0.71848250641338, 'rho=', 166.59358937610105)\n",
      "('k1=', 24, 'k2=', 5, 'delta2', -2.714934971725924e-06)\n",
      "('norm grad', 0.051188771269092354)\n",
      "('i=', 20, 'and J=', 0.7184798859209776, 'rho=', 521.4523278586809)\n",
      "('k1=', 14, 'k2=', 5, 'delta2', -2.7439522787275905e-06)\n",
      "('norm grad', 0.05941031234601794)\n",
      "('i=', 21, 'and J=', 0.7184763206971337, 'rho=', 183.06106434673382)\n",
      "('k1=', 27, 'k2=', 4, 'delta2', -2.4392113412430305e-06)\n",
      "('norm grad', 0.05141898698873749)\n",
      "('i=', 22, 'and J=', 0.7184745361169682, 'rho=', 572.9969472497966)\n",
      "('k1=', 14, 'k2=', 5, 'delta2', -2.0657421969660916e-06)\n",
      "('norm grad', 0.05823085718414663)\n",
      "('i=', 23, 'and J=', 0.7184726612124516, 'rho=', 201.15631943137907)\n",
      "('k1=', 26, 'k2=', 5, 'delta2', -1.7313318196876537e-06)\n",
      "('norm grad', 0.05196709563822068)\n",
      "('i=', 24, 'and J=', 0.7184709907009139, 'rho=', 1088.0121468079162)\n",
      "('k1=', 11, 'k2=', 5, 'delta2', -2.0235844034877104e-06)\n",
      "('norm grad', 0.059202990974669724)\n",
      "('i=', 25, 'and J=', 0.7184683855934388, 'rho=', 221.04025774993252)\n",
      "('k1=', 30, 'k2=', 4, 'delta2', -1.8179408785012896e-06)\n",
      "('norm grad', 0.05229903928932561)\n",
      "('i=', 26, 'and J=', 0.7184669744589504, 'rho=', 1721.606658469551)\n",
      "('k1=', 9, 'k2=', 5, 'delta2', -1.66407475854502e-06)\n",
      "('norm grad', 0.05868281713798691)\n",
      "('i=', 27, 'and J=', 0.7184655916209985, 'rho=', 242.88968740464523)\n",
      "('k1=', 31, 'k2=', 5, 'delta2', -1.3715293381011406e-06)\n",
      "('norm grad', 0.05301112604357031)\n",
      "('i=', 28, 'and J=', 0.7184603531576877, 'rho=', 16867.339403100366)\n",
      "('k1=', 1, 'k2=', 1, 'delta2', -4.137135662385383e-06)\n",
      "('norm grad', 0.05608662327480299)\n",
      "('i=', 29, 'and J=', 0.7184602037195719, 'rho=', 553.4415458910125)\n",
      "('k1=', 40, 'k2=', 4, 'delta2', -3.0714147214450094e-07)\n",
      "('norm grad', 0.05322811505857013)\n",
      "('i=', 30, 'and J=', 0.7184598151754583, 'rho=', 15445.537827480339)\n",
      "('k1=', 1, 'k2=', 6, 'delta2', -3.4109945157290156e-07)\n",
      "('norm grad', 0.05150695351677221)\n",
      "('i=', 31, 'and J=', 0.7184596971998941, 'rho=', 875.7334679351359)\n",
      "('k1=', 36, 'k2=', 5, 'delta2', -8.724159417106137e-08)\n",
      "('norm grad', 0.05291945437303445)\n",
      "('i=', 32, 'and J=', 0.718459603115014, 'rho=', 11786.32034958418)\n",
      "('k1=', 5, 'k2=', 6, 'delta2', -8.009135510356202e-08)\n",
      "('norm grad', 0.05395687352248384)\n",
      "('i=', 33, 'and J=', 0.7184595264270304, 'rho=', 1662.8511810627058)\n",
      "('k1=', 32, 'k2=', 4, 'delta2', -3.536797588132856e-08)\n",
      "('norm grad', 0.0529319174179934)\n",
      "('i=', 34, 'and J=', 0.7184594952521446, 'rho=', 10792.813997259227)\n",
      "('k1=', 11, 'k2=', 4, 'delta2', -2.6839994005101175e-08)\n",
      "('norm grad', 0.05376095172409115)\n",
      "('i=', 35, 'and J=', 0.7184594711937375, 'rho=', 1827.2210124985202)\n",
      "('k1=', 30, 'k2=', 5, 'delta2', -2.140026378327775e-08)\n",
      "('norm grad', 0.053074050533557335)\n",
      "('i=', 36, 'and J=', 0.7184593725244327, 'rho=', 126890.34809017502)\n",
      "('k1=', 1, 'k2=', 1, 'delta2', -8.145114838153944e-08)\n",
      "('norm grad', 0.05289078133635257)\n",
      "('i=', 37, 'and J=', 0.7184593718849307, 'rho=', 7194.448378663751)\n",
      "('k1=', 37, 'k2=', 4, 'delta2', -1.7469689028715152e-09)\n",
      "('norm grad', 0.05311222290743524)\n",
      "('i=', 38, 'and J=', 0.7184593705588043, 'rho=', 22519.24500074137)\n",
      "('k1=', 14, 'k2=', 5, 'delta2', -1.3034836543468487e-09)\n",
      "('norm grad', 0.05294189317616604)\n",
      "('i=', 39, 'and J=', 0.7184593688721977, 'rho=', 7905.60658737301)\n",
      "('k1=', 27, 'k2=', 4, 'delta2', -1.1898176888180956e-09)\n",
      "('norm grad', 0.053115031335091864)\n",
      "('i=', 40, 'and J=', 0.7184593681260804, 'rho=', 20621.026363014633)\n",
      "('k1=', 15, 'k2=', 5, 'delta2', -1.221922674154996e-09)\n",
      "('norm grad', 0.052948456173271645)\n",
      "('i=', 41, 'and J=', 0.7184593666798927, 'rho=', 8687.061498650102)\n",
      "('k1=', 26, 'k2=', 4, 'delta2', -1.132324123354067e-09)\n",
      "('norm grad', 0.05312860827440555)\n",
      "('i=', 42, 'and J=', 0.7184593654884803, 'rho=', 15735.678832710477)\n",
      "('k1=', 18, 'k2=', 4, 'delta2', -1.0132749084235115e-09)\n",
      "('norm grad', 0.05296409640953922)\n",
      "('i=', 43, 'and J=', 0.7184593648348393, 'rho=', 9545.761814389203)\n",
      "('k1=', 23, 'k2=', 5, 'delta2', -1.0278776718664062e-09)\n",
      "('norm grad', 0.05313598317223281)\n",
      "('i=', 44, 'and J=', 0.7184593636131942, 'rho=', 14409.268518485927)\n",
      "('k1=', 19, 'k2=', 4, 'delta2', -9.627678654311467e-10)\n",
      "('norm grad', 0.052966608621771126)\n",
      "('i=', 45, 'and J=', 0.7184593626802369, 'rho=', 8741.11925258142)\n",
      "('k1=', 21, 'k2=', 7, 'delta2', -7.211441443999433e-10)\n",
      "('norm grad', 0.053066934291682924)\n",
      "('i=', 46, 'and J=', 0.7184593616835409, 'rho=', 607022.1703181543)\n",
      "('k1=', 1, 'k2=', 1, 'delta2', -5.213102172163531e-10)\n",
      "('norm grad', 0.052961019400566745)\n",
      "('i=', 47, 'and J=', 0.7184593616800405, 'rho=', 13831.434834502224)\n",
      "('k1=', 41, 'k2=', 5, 'delta2', -3.68376329440423e-10)\n",
      "('norm grad', 0.05305515378975575)\n",
      "('i=', 48, 'and J=', 0.7184593613090842, 'rho=', 30064.99029184193)\n",
      "('k1=', 14, 'k2=', 7, 'delta2', -7.406308899504666e-11)\n",
      "end of computations\n",
      "('norm grad', 1.2771543662394993)\n",
      "('i=', 0, 'and J=', 0.8529098195995845, 'rho=', 81.64534041559588)\n",
      "('k1=', 29, 'k2=', 10, 'delta2', -0.1462839063723752)\n",
      "('norm grad', 0.07772703885107217)\n",
      "('i=', 1, 'and J=', 0.7200932521803898, 'rho=', 306.6683632519255)\n",
      "('k1=', 9, 'k2=', 9, 'delta2', -0.0010596041375409149)\n",
      "('norm grad', 0.05337880788213056)\n",
      "('i=', 2, 'and J=', 0.7191528825175695, 'rho=', 2.808183135408099)\n",
      "('k1=', 47, 'k2=', 4, 'delta2', -6.451075911084736e-05)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('norm grad', 0.03355176782394491)\n",
      "('i=', 3, 'and J=', 0.7190290490058812, 'rho=', 45.353725414551974)\n",
      "('k1=', 6, 'k2=', 4, 'delta2', -0.00017729379833064662)\n",
      "('norm grad', 0.06417994126732283)\n",
      "('i=', 4, 'and J=', 0.7189107167516501, 'rho=', 170.35329474357977)\n",
      "('k1=', 12, 'k2=', 6, 'delta2', -8.861645889512992e-05)\n",
      "('norm grad', 0.031721884871128696)\n",
      "('i=', 5, 'and J=', 0.7188344181211666, 'rho=', 13.908552740257905)\n",
      "('k1=', 35, 'k2=', 4, 'delta2', -4.2215090364727814e-05)\n",
      "('norm grad', 0.0480718867147679)\n",
      "('i=', 6, 'and J=', 0.7187893500667193, 'rho=', 187.19240978912623)\n",
      "('k1=', 5, 'k2=', 6, 'delta2', -0.00010734178475102496)\n",
      "('norm grad', 0.07469898034373848)\n",
      "('i=', 7, 'and J=', 0.7186919076172446, 'rho=', 54.76314251382261)\n",
      "('k1=', 27, 'k2=', 5, 'delta2', -2.8564090153948563e-05)\n",
      "('norm grad', 0.04801417238705375)\n",
      "('i=', 8, 'and J=', 0.7186604589203196, 'rho=', 142.84447284573443)\n",
      "('k1=', 15, 'k2=', 5, 'delta2', -2.6920840290656223e-05)\n",
      "('norm grad', 0.07243827798844521)\n",
      "('i=', 9, 'and J=', 0.7186375024239273, 'rho=', 60.17638009419338)\n",
      "('k1=', 25, 'k2=', 5, 'delta2', -2.2335139038931473e-05)\n",
      "('norm grad', 0.048842410200030696)\n",
      "('i=', 10, 'and J=', 0.7186145358798677, 'rho=', 188.3572687264967)\n",
      "('k1=', 14, 'k2=', 5, 'delta2', -2.1590354922995658e-05)\n",
      "('norm grad', 0.07159195951626805)\n",
      "('i=', 11, 'and J=', 0.718595714705575, 'rho=', 66.12470641776659)\n",
      "('k1=', 26, 'k2=', 5, 'delta2', -1.859682262572715e-05)\n",
      "('norm grad', 0.049543973151561865)\n",
      "('i=', 12, 'and J=', 0.7185764239059498, 'rho=', 248.3712528409889)\n",
      "('k1=', 13, 'k2=', 5, 'delta2', -1.6973505356454588e-05)\n",
      "('norm grad', 0.07036536333871042)\n",
      "('i=', 13, 'and J=', 0.7185600300308014, 'rho=', 72.66101403892412)\n",
      "('k1=', 27, 'k2=', 5, 'delta2', -1.5193055490803076e-05)\n",
      "('norm grad', 0.050575384817056604)\n",
      "('i=', 14, 'and J=', 0.7185431652377618, 'rho=', 393.00811476966106)\n",
      "('k1=', 11, 'k2=', 5, 'delta2', -1.4936880111449113e-05)\n",
      "('norm grad', 0.06995996585498793)\n",
      "('i=', 15, 'and J=', 0.7185290270573568, 'rho=', 79.84342384537507)\n",
      "('k1=', 29, 'k2=', 5, 'delta2', -1.3047377761310486e-05)\n",
      "('norm grad', 0.05200540481515788)\n",
      "('i=', 16, 'and J=', 0.7185185881457761, 'rho=', 1074.5965590056926)\n",
      "('k1=', 3, 'k2=', 8, 'delta2', -1.8866283147955798e-05)\n",
      "('norm grad', 0.07013970218263606)\n",
      "('i=', 17, 'and J=', 0.7184946391334941, 'rho=', 105.28296224333728)\n",
      "('k1=', 34, 'k2=', 4, 'delta2', -1.0962962071037197e-05)\n",
      "('norm grad', 0.05232359761420998)\n",
      "('i=', 18, 'and J=', 0.7184885449575057, 'rho=', 2040.4543422575778)\n",
      "('k1=', 1, 'k2=', 8, 'delta2', -1.0286849637441975e-05)\n",
      "('norm grad', 0.0669191963594538)\n",
      "('i=', 19, 'and J=', 0.7184754303524772, 'rho=', 138.82799114675063)\n",
      "('k1=', 36, 'k2=', 4, 'delta2', -6.437861441943582e-06)\n",
      "('norm grad', 0.05346753333386918)\n",
      "('i=', 20, 'and J=', 0.718462141761758, 'rho=', 9640.83271852435)\n",
      "('k1=', 1, 'k2=', 1, 'delta2', -1.0084329447046514e-05)\n",
      "('norm grad', 0.04821421349497603)\n",
      "('i=', 21, 'and J=', 0.7184620182923895, 'rho=', 263.60793265929624)\n",
      "('k1=', 40, 'k2=', 5, 'delta2', -7.741173109199195e-07)\n",
      "('norm grad', 0.05228399686771375)\n",
      "('i=', 22, 'and J=', 0.7184611357029003, 'rho=', 1710.9597165367345)\n",
      "('k1=', 10, 'k2=', 5, 'delta2', -5.342839808353261e-07)\n",
      "('norm grad', 0.054307437279431936)\n",
      "('i=', 23, 'and J=', 0.7184607850025817, 'rho=', 720.7794615851838)\n",
      "('k1=', 25, 'k2=', 5, 'delta2', -1.5256277974273758e-07)\n",
      "('norm grad', 0.052496087561518016)\n",
      "('i=', 24, 'and J=', 0.7184606167294212, 'rho=', 1880.0849896840787)\n",
      "('k1=', 16, 'k2=', 4, 'delta2', -1.5649612128409984e-07)\n",
      "('norm grad', 0.05458739329790979)\n",
      "('i=', 25, 'and J=', 0.7184604746853598, 'rho=', 660.0226729971744)\n",
      "('k1=', 26, 'k2=', 5, 'delta2', -1.5146406895372166e-07)\n",
      "('norm grad', 0.05279862919139915)\n",
      "('i=', 26, 'and J=', 0.718460332409699, 'rho=', 5140.689936483543)\n",
      "('k1=', 8, 'k2=', 6, 'delta2', -2.2413248590424928e-07)\n",
      "('norm grad', 0.05495728620787726)\n",
      "('i=', 27, 'and J=', 0.7184600631454425, 'rho=', 725.264720355272)\n",
      "('k1=', 32, 'k2=', 4, 'delta2', -1.6137690184159226e-07)\n",
      "('norm grad', 0.052931615376873874)\n",
      "('i=', 28, 'and J=', 0.718459924537995, 'rho=', 16867.339403100366)\n",
      "('k1=', 1, 'k2=', 7, 'delta2', -2.3115886493840776e-07)\n",
      "('norm grad', 0.05513013928737397)\n",
      "('i=', 29, 'and J=', 0.7184597509319067, 'rho=', 796.955826083058)\n",
      "('k1=', 37, 'k2=', 5, 'delta2', -1.3286160605030517e-07)\n",
      "('norm grad', 0.05332953467076708)\n",
      "('i=', 30, 'and J=', 0.7184595939470246, 'rho=', 6207.215240596205)\n",
      "('k1=', 9, 'k2=', 5, 'delta2', -7.743763996703734e-08)\n",
      "('norm grad', 0.05248151544856591)\n",
      "('i=', 31, 'and J=', 0.7184595449165238, 'rho=', 1815.9209191102989)\n",
      "('k1=', 27, 'k2=', 5, 'delta2', -2.5119039626098072e-08)\n",
      "('norm grad', 0.0532821065132379)\n",
      "('i=', 32, 'and J=', 0.7184595206544583, 'rho=', 4736.657805099101)\n",
      "('k1=', 15, 'k2=', 5, 'delta2', -1.6748389231047156e-08)\n",
      "('norm grad', 0.052602506897621144)\n",
      "('i=', 33, 'and J=', 0.7184594990330424, 'rho=', 2394.5057007302976)\n",
      "('k1=', 25, 'k2=', 4, 'delta2', -1.7026983600842982e-08)\n",
      "('norm grad', 0.0533173793460876)\n",
      "('i=', 34, 'and J=', 0.7184594815056379, 'rho=', 3614.4915703698484)\n",
      "('k1=', 18, 'k2=', 5, 'delta2', -1.4725566988005312e-08)\n",
      "('norm grad', 0.05275501107340636)\n",
      "('i=', 35, 'and J=', 0.7184594679284033, 'rho=', 3157.437909597446)\n",
      "('k1=', 22, 'k2=', 4, 'delta2', -1.0819964701980211e-08)\n",
      "('norm grad', 0.05329930571717636)\n",
      "('i=', 36, 'and J=', 0.7184594605631143, 'rho=', 3971.777524106354)\n",
      "('k1=', 19, 'k2=', 5, 'delta2', -9.502147735318545e-09)\n",
      "('norm grad', 0.05283024301226879)\n",
      "('i=', 37, 'and J=', 0.7184594479075974, 'rho=', 4163.453922837823)\n",
      "('k1=', 21, 'k2=', 4, 'delta2', -9.45819511599666e-09)\n",
      "('norm grad', 0.053352349754075386)\n",
      "('i=', 38, 'and J=', 0.7184594383227467, 'rho=', 3636.983790083983)\n",
      "('k1=', 22, 'k2=', 4, 'delta2', -9.577709514374533e-09)\n",
      "('norm grad', 0.05282172885651989)\n",
      "('i=', 39, 'and J=', 0.7184594312736914, 'rho=', 3812.5031767809696)\n",
      "('k1=', 20, 'k2=', 5, 'delta2', -7.995380579828293e-09)\n",
      "('norm grad', 0.053216925759595544)\n",
      "('i=', 40, 'and J=', 0.7184594223676608, 'rho=', 6905.94000604647)\n",
      "('k1=', 18, 'k2=', 4, 'delta2', -6.130392637970772e-09)\n",
      "('norm grad', 0.05280839854153219)\n",
      "('i=', 41, 'and J=', 0.718459417611663, 'rho=', 3491.1351830351873)\n",
      "('k1=', 24, 'k2=', 5, 'delta2', -6.2270250067442134e-09)\n",
      "('norm grad', 0.05317833540553928)\n",
      "('i=', 42, 'and J=', 0.7184594108782763, 'rho=', 10927.554744937841)\n",
      "('k1=', 14, 'k2=', 5, 'delta2', -7.779931920914862e-09)\n",
      "('norm grad', 0.05270278339099589)\n",
      "('i=', 43, 'and J=', 0.7184594033567311, 'rho=', 3196.8563175118193)\n",
      "('k1=', 27, 'k2=', 5, 'delta2', -7.642960375697783e-09)\n",
      "('norm grad', 0.053127744767737274)\n",
      "('i=', 44, 'and J=', 0.7184593964808605, 'rho=', 61957.21715697986)\n",
      "('k1=', 8, 'k2=', 1, 'delta2', -6.354500259320162e-10)\n",
      "('norm grad', 0.0523145726583878)\n",
      "('i=', 45, 'and J=', 0.7184593922060374, 'rho=', 2032.9049663968544)\n",
      "('k1=', 39, 'k2=', 5, 'delta2', -1.4911854973043148e-08)\n",
      "('norm grad', 0.05287946699406663)\n",
      "('i=', 46, 'and J=', 0.7184593781561346, 'rho=', 13194.665539704956)\n",
      "('k1=', 11, 'k2=', 4, 'delta2', -8.087398639666787e-09)\n",
      "('norm grad', 0.05313573518214539)\n",
      "('i=', 47, 'and J=', 0.718459373328965, 'rho=', 8004.3025662628625)\n",
      "('k1=', 21, 'k2=', 7, 'delta2', -1.4875453091534041e-09)\n",
      "('norm grad', 0.052975143719722916)\n",
      "('i=', 48, 'and J=', 0.7184593715762864, 'rho=', 10068.70441765325)\n",
      "('k1=', 20, 'k2=', 4, 'delta2', -9.863546646116106e-10)\n",
      "('norm grad', 0.05313802336548826)\n",
      "('i=', 49, 'and J=', 0.7184593704750717, 'rho=', 12665.53929100196)\n",
      "('k1=', 20, 'k2=', 4, 'delta2', -9.581431203997681e-10)\n",
      "('norm grad', 0.05298568513759031)\n",
      "('i=', 50, 'and J=', 0.7184593696113057, 'rho=', 11063.977636781026)\n",
      "('k1=', 22, 'k2=', 4, 'delta2', -9.591896166227798e-10)\n",
      "('norm grad', 0.05314423599847582)\n",
      "('i=', 51, 'and J=', 0.718459368577379, 'rho=', 11597.92078344326)\n",
      "('k1=', 21, 'k2=', 4, 'delta2', -9.457288285830145e-10)\n",
      "('norm grad', 0.05299201541413777)\n",
      "('i=', 52, 'and J=', 0.71845936774467, 'rho=', 12157.631813341248)\n",
      "('k1=', 21, 'k2=', 4, 'delta2', -9.55782786249415e-10)\n",
      "('norm grad', 0.053152655737011625)\n",
      "('i=', 53, 'and J=', 0.7184593667103338, 'rho=', 10620.295228532988)\n",
      "('k1=', 22, 'k2=', 4, 'delta2', -9.505090048378406e-10)\n",
      "('norm grad', 0.052997557510164495)\n",
      "('i=', 54, 'and J=', 0.7184593658685048, 'rho=', 13359.391727021848)\n",
      "('k1=', 20, 'k2=', 4, 'delta2', -9.636086373276953e-10)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('norm grad', 0.05316096997397753)\n",
      "('i=', 55, 'and J=', 0.7184593647747988, 'rho=', 9725.076834652644)\n",
      "('k1=', 23, 'k2=', 4, 'delta2', -9.727730843067661e-10)\n",
      "('norm grad', 0.0530047331947323)\n",
      "('i=', 56, 'and J=', 0.7184593640580493, 'rho=', 14679.943434392462)\n",
      "('k1=', 12, 'k2=', 11, 'delta2', -9.968268432913874e-10)\n",
      "('norm grad', 0.05316573347266142)\n",
      "('i=', 57, 'and J=', 0.7184593631960865, 'rho=', 8905.319240636754)\n",
      "('k1=', 23, 'k2=', 5, 'delta2', -9.892046071158234e-10)\n",
      "('norm grad', 0.05301511549089901)\n",
      "('i=', 58, 'and J=', 0.7184593619468507, 'rho=', 57800.3944339634)\n",
      "('k1=', 11, 'k2=', 4, 'delta2', -1.0724731103195495e-09)\n",
      "('norm grad', 0.05307601900355032)\n",
      "('i=', 59, 'and J=', 0.7184593612426763, 'rho=', 16909.506327249426)\n",
      "('k1=', 28, 'k2=', 4, 'delta2', -2.376765451117535e-12)\n",
      "end of computations\n",
      "('norm grad', 4.487587653360454e-05)\n",
      "('i=', 0, 'and J=', 0.9999859560972275, 'rho=', 69444.44444444445)\n",
      "('k1=', 1, 'k2=', 1, 'delta2', -4.265926048629964e-06)\n",
      "('norm grad', 7.195376350073778e-05)\n",
      "('i=', 1, 'and J=', 0.9582929494523734, 'rho=', 4822530.864197532)\n",
      "('k1=', 1, 'k2=', 1, 'delta2', -0.04169300664485409)\n",
      "('norm grad', 0.50397421578152)\n",
      "('i=', 2, 'and J=', 0.9556259071647423, 'rho=', 223.24170563467644)\n",
      "('k1=', 60, 'k2=', 20, 'delta2', -0.2374306426311631)\n",
      "('norm grad', 0.07893945475620608)\n",
      "('i=', 3, 'and J=', 0.7207453211576338, 'rho=', 2.9437049331690575)\n",
      "('k1=', 45, 'k2=', 4, 'delta2', -0.00021833525617709348)\n",
      "('norm grad', 0.04398625684301971)\n",
      "('i=', 4, 'and J=', 0.7205671571652076, 'rho=', 68.46116847655439)\n",
      "('k1=', 3, 'k2=', 5, 'delta2', -0.0008736617739432129)\n",
      "('norm grad', 0.12312375580558933)\n",
      "('i=', 5, 'and J=', 0.7196651097344009, 'rho=', 28.84077496219879)\n",
      "('k1=', 26, 'k2=', 4, 'delta2', -0.00023377797962909064)\n",
      "('norm grad', 0.04084155151738199)\n",
      "('i=', 6, 'and J=', 0.7194937943355575, 'rho=', 43.534971727988705)\n",
      "('k1=', 18, 'k2=', 5, 'delta2', -0.0001571063130441086)\n",
      "('norm grad', 0.09319415888718759)\n",
      "('i=', 7, 'and J=', 0.7193438303631894, 'rho=', 38.02996007904349)\n",
      "('k1=', 21, 'k2=', 5, 'delta2', -0.000123881388729985)\n",
      "('norm grad', 0.041574079407632546)\n",
      "('i=', 8, 'and J=', 0.7192193948053394, 'rho=', 47.83832493601257)\n",
      "('k1=', 19, 'k2=', 5, 'delta2', -0.00010316435312096583)\n",
      "('norm grad', 0.08413833314709776)\n",
      "('i=', 9, 'and J=', 0.7191140896080203, 'rho=', 50.14698341182782)\n",
      "('k1=', 21, 'k2=', 4, 'delta2', -8.508160263753783e-05)\n",
      "('norm grad', 0.03794642597924128)\n",
      "('i=', 10, 'and J=', 0.7190324700750901, 'rho=', 43.80588068718555)\n",
      "('k1=', 22, 'k2=', 4, 'delta2', -7.135440126981862e-05)\n",
      "('norm grad', 0.07674081156185564)\n",
      "('i=', 11, 'and J=', 0.7189772310242608, 'rho=', 55.10392201480549)\n",
      "('k1=', 19, 'k2=', 5, 'delta2', -6.277143334043611e-05)\n",
      "('norm grad', 0.04043136248433129)\n",
      "('i=', 12, 'and J=', 0.7189136330221063, 'rho=', 57.76321530695785)\n",
      "('k1=', 21, 'k2=', 4, 'delta2', -5.30760071586478e-05)\n",
      "('norm grad', 0.07731391803098482)\n",
      "('i=', 13, 'and J=', 0.718869946187698, 'rho=', 50.459037527030645)\n",
      "('k1=', 21, 'k2=', 5, 'delta2', -4.739042004320293e-05)\n",
      "('norm grad', 0.04400544018717177)\n",
      "('i=', 14, 'and J=', 0.7188304338319571, 'rho=', 76.1676055875762)\n",
      "('k1=', 18, 'k2=', 5, 'delta2', -4.2101981673425826e-05)\n",
      "('norm grad', 0.07544702671573289)\n",
      "('i=', 15, 'and J=', 0.7187897060520911, 'rho=', 55.44682211484381)\n",
      "('k1=', 22, 'k2=', 5, 'delta2', -3.7179001526554956e-05)\n",
      "('norm grad', 0.04424944613351351)\n",
      "('i=', 16, 'and J=', 0.7187382825979654, 'rho=', 83.69663562578945)\n",
      "('k1=', 19, 'k2=', 4, 'delta2', -3.1875309486784076e-05)\n",
      "('norm grad', 0.07263334224901755)\n",
      "('i=', 17, 'and J=', 0.718720327240342, 'rho=', 60.927640187116516)\n",
      "('k1=', 22, 'k2=', 5, 'delta2', -2.8944066572167415e-05)\n",
      "('norm grad', 0.045193223375301406)\n",
      "('i=', 18, 'and J=', 0.7186898936268069, 'rho=', 91.96989666455767)\n",
      "('k1=', 18, 'k2=', 5, 'delta2', -2.5081124385595288e-05)\n",
      "('norm grad', 0.0692997747377423)\n",
      "('i=', 19, 'and J=', 0.7186623231418131, 'rho=', 66.95022721197466)\n",
      "('k1=', 22, 'k2=', 5, 'delta2', -2.2174621982840037e-05)\n",
      "('norm grad', 0.04653849001808517)\n",
      "('i=', 20, 'and J=', 0.7186358246305866, 'rho=', 121.27314551051958)\n",
      "('k1=', 18, 'k2=', 4, 'delta2', -2.042722019668375e-05)\n",
      "('norm grad', 0.06979900010879934)\n",
      "('i=', 21, 'and J=', 0.718617267160367, 'rho=', 73.56813607041437)\n",
      "('k1=', 24, 'k2=', 4, 'delta2', -1.8880589271130788e-05)\n",
      "('norm grad', 0.046241759360648255)\n",
      "('i=', 22, 'and J=', 0.7186042534091553, 'rho=', 111.05064715161656)\n",
      "('k1=', 18, 'k2=', 5, 'delta2', -1.5287768326155415e-05)\n",
      "('norm grad', 0.0651025905147061)\n",
      "('i=', 23, 'and J=', 0.7185851788296607, 'rho=', 97.0082558986202)\n",
      "('k1=', 22, 'k2=', 4, 'delta2', -1.3575281371802639e-05)\n",
      "('norm grad', 0.045445507731999575)\n",
      "('i=', 24, 'and J=', 0.7185760276501647, 'rho=', 101.68983562583615)\n",
      "('k1=', 20, 'k2=', 5, 'delta2', -1.1945078773778484e-05)\n",
      "('norm grad', 0.06197748264166756)\n",
      "('i=', 25, 'and J=', 0.7185601586605681, 'rho=', 127.9168158275072)\n",
      "('k1=', 20, 'k2=', 4, 'delta2', -1.0796271664337276e-05)\n",
      "('norm grad', 0.04502730411459279)\n",
      "('i=', 26, 'and J=', 0.7185514318559859, 'rho=', 93.11807661500012)\n",
      "('k1=', 22, 'k2=', 5, 'delta2', -9.770815485810047e-06)\n",
      "('norm grad', 0.058915039799180204)\n",
      "('i=', 27, 'and J=', 0.7185424107265057, 'rho=', 202.40807283720426)\n",
      "('k1=', 16, 'k2=', 5, 'delta2', -9.992330949004646e-06)\n",
      "('norm grad', 0.04394837572263713)\n",
      "('i=', 28, 'and J=', 0.7185312135118018, 'rho=', 102.32263005378297)\n",
      "('k1=', 25, 'k2=', 4, 'delta2', -8.633948056946394e-06)\n",
      "('norm grad', 0.058894483773868876)\n",
      "('i=', 29, 'and J=', 0.7185245873161321, 'rho=', 185.34645392976398)\n",
      "('k1=', 17, 'k2=', 5, 'delta2', -7.136128926665819e-06)\n",
      "('norm grad', 0.046067313744871566)\n",
      "('i=', 30, 'and J=', 0.7185171251325994, 'rho=', 112.43703695053301)\n",
      "('k1=', 23, 'k2=', 5, 'delta2', -6.239403864682913e-06)\n",
      "('norm grad', 0.05729086690076905)\n",
      "('i=', 31, 'and J=', 0.7185117780852052, 'rho=', 293.2813665227729)\n",
      "('k1=', 15, 'k2=', 5, 'delta2', -6.528822886875396e-06)\n",
      "('norm grad', 0.044788949567871564)\n",
      "('i=', 32, 'and J=', 0.7185042740434437, 'rho=', 123.55123467380156)\n",
      "('k1=', 26, 'k2=', 4, 'delta2', -5.76690521680856e-06)\n",
      "('norm grad', 0.057418347182212774)\n",
      "('i=', 33, 'and J=', 0.7184984778098217, 'rho=', 268.5597492566006)\n",
      "('k1=', 17, 'k2=', 4, 'delta2', -4.407679394358155e-06)\n",
      "('norm grad', 0.04636157715400869)\n",
      "('i=', 34, 'and J=', 0.718495674068028, 'rho=', 135.76405073834022)\n",
      "('k1=', 24, 'k2=', 5, 'delta2', -4.258195101303208e-06)\n",
      "('norm grad', 0.05622315049019417)\n",
      "('i=', 35, 'and J=', 0.7184902178502433, 'rho=', 354.1276736305771)\n",
      "('k1=', 15, 'k2=', 5, 'delta2', -4.0001378679432875e-06)\n",
      "('norm grad', 0.047088954510492505)\n",
      "('i=', 36, 'and J=', 0.7184871099327261, 'rho=', 149.18408157997146)\n",
      "('k1=', 25, 'k2=', 5, 'delta2', -3.2993662931746215e-06)\n",
      "('norm grad', 0.05552788444344897)\n",
      "('i=', 37, 'and J=', 0.7184843082867542, 'rho=', 466.95906433537283)\n",
      "('k1=', 13, 'k2=', 6, 'delta2', -3.4364805204800675e-06)\n",
      "('norm grad', 0.047385791731622516)\n",
      "('i=', 38, 'and J=', 0.7184805349929131, 'rho=', 163.93065819576665)\n",
      "('k1=', 26, 'k2=', 5, 'delta2', -2.6606686904795396e-06)\n",
      "('norm grad', 0.05500120653832581)\n",
      "('i=', 39, 'and J=', 0.7184778691100969, 'rho=', 738.8886574024785)\n",
      "('k1=', 12, 'k2=', 5, 'delta2', -2.878451293208961e-06)\n",
      "('norm grad', 0.04654227973415338)\n",
      "('i=', 40, 'and J=', 0.7184746736334984, 'rho=', 180.1349072360085)\n",
      "('k1=', 29, 'k2=', 4, 'delta2', -2.473576797612509e-06)\n",
      "('norm grad', 0.054898274339757074)\n",
      "('i=', 41, 'and J=', 0.7184727517406635, 'rho=', 676.6053872200147)\n",
      "('k1=', 13, 'k2=', 5, 'delta2', -1.8066191869170467e-06)\n",
      "('norm grad', 0.047996650447143734)\n",
      "('i=', 42, 'and J=', 0.7184708295198025, 'rho=', 197.9409169831745)\n",
      "('k1=', 27, 'k2=', 5, 'delta2', -1.6771707810336878e-06)\n",
      "('norm grad', 0.05399413954302468)\n",
      "('i=', 43, 'and J=', 0.7184690951898909, 'rho=', 2220.0391093832072)\n",
      "('k1=', 6, 'k2=', 6, 'delta2', -2.570637144705401e-06)\n",
      "('norm grad', 0.04645064675658033)\n",
      "('i=', 44, 'and J=', 0.7184668463528543, 'rho=', 181.2558488215282)\n",
      "('k1=', 34, 'k2=', 5, 'delta2', -1.7009217352370598e-06)\n",
      "('norm grad', 0.05263505124370225)\n",
      "('i=', 45, 'and J=', 0.7184644899125874, 'rho=', 4215.431738320513)\n",
      "('k1=', 1, 'k2=', 7, 'delta2', -2.394207428757511e-06)\n",
      "('norm grad', 0.058022599459757844)\n",
      "('i=', 46, 'and J=', 0.7184624882613708, 'rho=', 344.1703592738856)\n",
      "('k1=', 35, 'k2=', 4, 'delta2', -9.146244397406633e-07)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('norm grad', 0.05277776092268611)\n",
      "('i=', 47, 'and J=', 0.7184618488401758, 'rho=', 5558.543448793654)\n",
      "('k1=', 2, 'k2=', 8, 'delta2', -7.932902239549122e-07)\n",
      "('norm grad', 0.0567953339568783)\n",
      "('i=', 48, 'and J=', 0.7184608994152746, 'rho=', 453.82917209163844)\n",
      "('k1=', 35, 'k2=', 4, 'delta2', -4.95102429165506e-07)\n",
      "('norm grad', 0.053029185440869334)\n",
      "('i=', 49, 'and J=', 0.7184596181885915, 'rho=', 31515.91472858601)\n",
      "('k1=', 1, 'k2=', 1, 'delta2', -9.839035786107786e-07)\n",
      "('norm grad', 0.05458042433749293)\n",
      "('i=', 50, 'and J=', 0.7184596159516601, 'rho=', 1034.0822669609604)\n",
      "('k1=', 39, 'k2=', 5, 'delta2', -7.812550106844895e-08)\n",
      "('norm grad', 0.053191568751074766)\n",
      "('i=', 51, 'and J=', 0.7184595387402177, 'rho=', 13917.504940131921)\n",
      "('k1=', 4, 'k2=', 7, 'delta2', -6.452339962326192e-08)\n",
      "('norm grad', 0.05244382575722883)\n",
      "('i=', 52, 'and J=', 0.7184594744431705, 'rho=', 1963.5254125738138)\n",
      "('k1=', 31, 'k2=', 5, 'delta2', -1.9027718733966026e-08)\n",
      "('norm grad', 0.05311101921735226)\n",
      "('i=', 53, 'and J=', 0.7184594137173108, 'rho=', 113629.9428572809)\n",
      "('k1=', 1, 'k2=', 2, 'delta2', -5.2445996101546655e-08)\n",
      "('norm grad', 0.05216709849717688)\n",
      "('i=', 54, 'and J=', 0.7184593995538675, 'rho=', 2157.61634792645)\n",
      "('k1=', 43, 'k2=', 4, 'delta2', -1.7966283571979602e-08)\n",
      "('norm grad', 0.05290438039843232)\n",
      "('i=', 55, 'and J=', 0.7184593860528008, 'rho=', 20165.919324335737)\n",
      "('k1=', 8, 'k2=', 5, 'delta2', -1.4344802568011517e-08)\n",
      "('norm grad', 0.05313978349555332)\n",
      "('i=', 56, 'and J=', 0.7184593713464617, 'rho=', 7079.448029703166)\n",
      "('k1=', 24, 'k2=', 7, 'delta2', -1.452354903008768e-09)\n",
      "('norm grad', 0.05299054514325825)\n",
      "('i=', 57, 'and J=', 0.7184593701170989, 'rho=', 10686.38308876412)\n",
      "('k1=', 18, 'k2=', 5, 'delta2', -9.498897224347047e-10)\n",
      "('norm grad', 0.053134720247345994)\n",
      "('i=', 58, 'and J=', 0.7184593688240101, 'rho=', 13442.524407821187)\n",
      "('k1=', 20, 'k2=', 4, 'delta2', -9.72157354617309e-10)\n",
      "('norm grad', 0.05298047598591293)\n",
      "('i=', 59, 'and J=', 0.7184593682832618, 'rho=', 9785.593939380471)\n",
      "('k1=', 22, 'k2=', 5, 'delta2', -9.641902831702964e-10)\n",
      "('norm grad', 0.05312933333583923)\n",
      "('i=', 60, 'and J=', 0.7184593674141393, 'rho=', 14771.293630316084)\n",
      "('k1=', 18, 'k2=', 5, 'delta2', -1.0064640232343436e-09)\n",
      "('norm grad', 0.05297329530869931)\n",
      "('i=', 61, 'and J=', 0.718459366233412, 'rho=', 8960.735166524359)\n",
      "('k1=', 23, 'k2=', 5, 'delta2', -9.825958935394397e-10)\n",
      "('norm grad', 0.05312053055744263)\n",
      "('i=', 62, 'and J=', 0.7184593650165166, 'rho=', 19477.691144327106)\n",
      "('k1=', 17, 'k2=', 4, 'delta2', -1.1099868801878188e-09)\n",
      "('norm grad', 0.05294402567794012)\n",
      "('i=', 63, 'and J=', 0.7184593639124606, 'rho=', 8205.406357753469)\n",
      "('k1=', 25, 'k2=', 5, 'delta2', -1.166007512765077e-09)\n",
      "('norm grad', 0.05312020829730611)\n",
      "('i=', 64, 'and J=', 0.7184593629300385, 'rho=', 12386.010232723022)\n",
      "('k1=', 18, 'k2=', 5, 'delta2', -9.682642465591584e-10)\n",
      "('norm grad', 0.053007017709376526)\n",
      "('i=', 65, 'and J=', 0.7184593617238335, 'rho=', 55827.76627725643)\n",
      "('k1=', 14, 'k2=', 3, 'delta2', -9.157257174763345e-10)\n",
      "('norm grad', 0.053094221967630265)\n",
      "('i=', 66, 'and J=', 0.7184593612672272, 'rho=', 16332.4139280746)\n",
      "('k1=', 27, 'k2=', 5, 'delta2', -2.613576022270081e-11)\n",
      "end of computations\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/duprez/.local/lib/python2.7/site-packages/ipykernel_launcher.py:52: RuntimeWarning: divide by zero encountered in log\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('number of iterations in the optimisation of u:', 60)\n",
      "('J(u):', 0.7184593612426763)\n",
      "('J(T0):', 0.7184594534472071)\n",
      "('T0:', 61.940000000000005)\n",
      "('S_inf', 0.28217973380253236)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8eade4c510>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8eaddeab10>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8eadea8e10>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8eb0013f10>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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enFVtHWbdsqiNfSaB5S3PR4DnZ+4k6ULgk8C5EbGvM+VZr/keuR7pW9raGc9sBFZIGpM0BFwNrG/dQdIZwP8ELouIFztfpvVKMdKv6fyOl1a21M0b+hFxAFgDPARsB+6PiKck3Srpsny3zwFvBx6Q9ISk9XN8O+tzdV9a2VfkWuramd4hIjYAG2ZsW9vy+MIO12UVqfucvqd3LHU+XWUltV97Z9pLK1vaHPpW0lhSeKquoe8rci1xDn0rqXuffnh6xxLn0LeSwdovw5B9dJ++pcovbSsplmGYrraOqvhErqXOoW8l7t5xn76lzaFvJXXv0w/36VviHPpW4qWVPb1jaXPoW0njBGZ9p3eyjx7pW6rauiK3V958800mJyfZu3dv1aX0zOLFixkZGeGoo46quhSgdU6/4kIq4jl9S11fhf7k5CRLlixhdHS0Fr90EcGePXuYnJxkbGys6nIA3yO32adfcSFmXdJX0zt79+5l6dKltQh8yAJ26dKlffXOxksrZx89p2+p6qvQh/q9re63f69bNn0i19LWd6Fv1ar7PXKnphtz+hUXYtYlDn0r8do72UeP9C1VDv0FeOONNzj33HOZmprijjvu4PTTT+f0009nYGCgeHzTTTe95ev279/POeecw4EDByqoemF85yyfyLW09VX3Tr+78847ueKKKxgcHOTGG2/kxhtv5LnnnuODH/wgTzzxxJxfNzQ0xAUXXMB9993Htdde28OKF67u0zvNBdec+pYmj/RncfbZZ7Nr1y4AnnvuOcbHxwG4++67WbVqVWnfrVu3ctppp837PS+//HLuvvvujtfaaY2wq+lA3ydyLXkO/RkigmeeeYaTTz4ZgM2bN3Paaaexf/9+du7cyejoaGn/LVu2cOqpp877fU899VQ2btzYjZI7qu7dO+7Tt9T17fTO6M0PduX77vr0fzjo5ycmJhgbGytOaDZC/6WXXuK44457y/5bt27lwx/+cPH8Jz/5CR//+McZGhrivPPOK6ZzBgcHGRoa4vXXX2fJkiUd/Bd1lvv0s48e6VuqPNKfYcuWLaXpmk2bNvGBD3yAY445ZtaLqGaO9L/xjW9w5ZVXcscdd7B+/frSvvv27WPx4sXdK74D6j7S9zIMlrq+HenPNyLvlpdffpljjjkGgO3bt/Pggw9y2223cfzxxzM1NcXevXuL4J6enubpp5/m/e9/f/H1k5OTxX8ag4ODxfY9e/YwPDzcN2vszEU+kQt4esfS5ZH+DB/96Ed55JFHuOqqq3jggQdYunQp73nPewD4yEc+wje/+c1i34mJCUZGRjj66KOLbSMjI0xOTgLZfwoNjz76KJdcckmP/hWHru4LrvkeuZa6vh3pV2X58uVs3ry5eL527dri8Zo1a/j85z/PhRdeCMApp5zCtm3bSl9/xRVXsGbNGh588EEuvfTSYvs999zDpz71qS5Xf/hqv57+tE/kWtoc+gtwxhlncP755zM1NVWauml17LHH8uUvf7m0bf/+/Vx++eW8733v60WZh6XZp19tHVVp/Ls9p2+pcugv0PXXX7/grxkaGuK6667rQjWdV/elld2nb6nznL6V1H2k73vkWuoc+lZS+zn9xkjfqW+JcuhbSd379KfCSytb2vou9Os2wuy3f28j7KamD75fqry0sqWur0J/8eLF7Nmzp++CsFsa98jtp6t0az+945ZNS1xfde80LmzavXt31aX0zOLFixkZGam6jMLgQL2ndxonsAc90rdEtRX6ki4C/gQYBL4UEZ+e8fmjgbuAfwfsAX41InYttJijjjqKsbGxhX6ZdVDdu3e89o6lbt7pHUmDwO3AxcBK4BpJK2fsdgPwSkT8LPAF4DOdLtR6o+59+l6GwVLXzkj/LGAiInYCSLoXWAW0rj+wCrglf/yXwG2SFHWdGD6CNUb6e/dPsWXy1WqLqcAPX8tWUvWcvqWqndA/EXi25fkk8Atz7RMRByS9CiwFXupEkdY7iwayN3/Pv7qXS2/75jx7p8t9+paqdkJ/tlf/zBF8O/sgaTWwOn+6T9LWNv7+qi3jyPjPy3V2zrI1n+GlNVVXMb8j4ViC6+y0w1rEq53QnwSWtzwfAZ6fY59JSYuAdwIvz/xGEbEOWAcgaVNEjB9K0b3kOjvrSKjzSKgRXGenHUl1Hs7Xt9OnvxFYIWlM0hBwNbB+xj7rgY/lj68E/t7z+WZm/WfekX4+R78GeIisZfPOiHhK0q3ApohYD/wF8DVJE2Qj/Ku7WbSZmR2atvr0I2IDsGHGtrUtj/cCv7LAv3vdAveviuvsrCOhziOhRnCdnVaLOuVZGDOz+uirtXfMzKy7Kgl9SRdJ2iFpQtLNVdQwk6Tlkh6VtF3SU5J+O99+i6TnJD2R/6n87uaSdknaktezKd/2Lkl/J+np/OPxFdf4vpZj9oSk1yT9Tj8cT0l3SnqxtWV4ruOnzJ/mr9XNks6suM7PSfqXvJa/lnRcvn1U0hstx/WLFdc5589Z0ify47lD0kcrrvO+lhp3SXoi317J8TxIDnXu9RkRPf1DdjL4e8B7gSHgSWBlr+uYpa4TgDPzx0uA75ItO3EL8HtV1zej1l3AshnbPgvcnD++GfhM1XXO+Jn/EDi5H44ncA5wJrB1vuMHXAL8Ldm1KGcD36q4zo8Ai/LHn2mpc7R1vz44nrP+nPPfqSeBo4GxPAsGq6pzxuf/GFhb5fE8SA517PVZxUi/WNYhIvYDjWUdKhURL0TEt/PHrwPbya40PlKsAr6aP/4qcHmFtcx0AfC9iPhB1YUARMQ/8tbrSOY6fquAuyLzGHCcpBOqqjMiHo6IA/nTx8ium6nUHMdzLquAeyNiX0R8H5ggy4SuO1idkgRcBXy9F7XM5SA51LHXZxWhP9uyDn0VrpJGgTOAb+Wb1uRvne6setokF8DDkh5XdpUzwHsi4gXIXjjAuyur7q2upvzL1G/HE+Y+fv38er2ebJTXMCbpO5L+j6RfqqqoFrP9nPv1eP4S8KOIeLplW6XHc0YOdez1WUXot7VkQ1UkvR34K+B3IuI14M+BnwFOB14gewtYtQ9FxJlkK5/+hqRzqi5oLsou6LsMeCDf1I/H82D68vUq6ZPAAeDufNMLwEkRcQZwE3CPpHdUVR9z/5z78ngC11AemFR6PGfJoTl3nWXbQY9nFaHfzrIOlZB0FNmBvjsivgEQET+KiKmImAbuoEdvRQ8mIp7PP74I/DVZTT9qvK3LP75YXYUlFwPfjogfQX8ez9xcx6/vXq+SPgb8MnBt5BO7+XTJnvzx42Rz5adUVeNBfs79eDwXAVcA9zW2VXk8Z8shOvj6rCL021nWoefyOb2/ALZHxOdbtrfOj/1HoNJF4iQdK2lJ4zHZib2tlJfC+BjwN9VU+BalEVS/Hc8Wcx2/9cB1eZfE2cCrjbfZVVB2Q6P/DlwWET9t2T6s7N4XSHovsALYWU2VB/05rweulnS0pDGyOv+51/XNcCHwLxEx2dhQ1fGcK4fo5Ouz12enW844f5fsf89PVlHDLDX9Itnbos3AE/mfS4CvAVvy7euBEyqu871k3Q9PAk81jh/ZUtaPAE/nH9/VB8f0bWR3Untny7bKjyfZf0IvAG+SjZRumOv4kb19vj1/rW4Bxiuuc4JsDrfxGv1ivu9/yl8PTwLfBi6tuM45f87AJ/PjuQO4uMo68+1fAX59xr6VHM+D5FDHXp++ItfMrEZ8Ra6ZWY049M3MasShb2ZWIw59M7MaceibmdVIWzdRMTuSSWq0uwH8G2AK2J0//2lEfLCSwswq4JZNqxVJtwA/jog/qroWsyp4esdqTdKP84/n5Qtr3S/pu5I+LelaSf+s7N4FP5PvNyzpryRtzP98qNp/gdnCOPTNmn4O+G3gNOC/AKdExFnAl4DfzPf5E+ALEfHzZFdtfqmKQs0Olef0zZo2Rr5uiaTvAQ/n27cA5+ePLwRWZkukAPAOSUsiW/vcrO859M2a9rU8nm55Pk3zd2UA+PcR8UYvCzPrFE/vmC3Mw8CaxhNJp1dYi9mCOfTNFua3gPH8jlDbgF+vuiCzhXDLpplZjXikb2ZWIw59M7MaceibmdWIQ9/MrEYc+mZmNeLQNzOrEYe+mVmNOPTNzGrkXwHSy7pFplCSzAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8eb0070050>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# minimisation with respect to u and T0 for alpha = 0 (figure 3)\n",
    "\n",
    "# parameters\n",
    "T=100.0\n",
    "alpha  = 0.0\n",
    "NT=int(5001) # number of time step\n",
    "ITER = 5e4 # number of step in optimisation\n",
    "T_end = 200.0\n",
    "tval=np.linspace(t0,T,NT) # discretized time interval [t0,t0+h,...,T]\n",
    "tval_end = np.linspace(t0,T_end,2*NT-1)#np.concatenate((tval,np.linspace(T,T_end,NT)),axis=0)\n",
    "h = (T-t0)/(NT-1)        #the time step\n",
    "\n",
    "# optimisation of u\n",
    "u=np.ones(int(NT))\n",
    "u1, i1, Jnew1, Jval1, yval1=optimSIR(u,init,True)\n",
    "u_test=np.ones(int(NT))\n",
    "for ind in range(int(NT/2),NT):\n",
    "    u_test[ind] = alpha\n",
    "u_test, i_test, Jnew_test, Jval_test, yval_test=optimSIR(u_test,init,True)\n",
    "if Jval_test<Jval1:\n",
    "    u1, i1, Jnew1, Jval1, yval1 = u_test, i_test, Jnew_test, Jval_test, yval_test\n",
    "u_test=alpha*np.ones(int(NT))\n",
    "u_test, i_test, Jnew_test, Jval_test, yval_test=optimSIR(u_test,init,True)\n",
    "if Jval_test<Jval1:\n",
    "    u1, i1, Jnew1, Jval1, yval1 = u_test, i_test, Jnew_test, Jval_test, yval_test\n",
    "# u=1 on the last interval\n",
    "u_end = np.ones(NT)\n",
    "y_end = RK4_state(u_end,yval1[-1,:]) \n",
    "yval1 = np.concatenate((yval1,y_end[1:,:]),axis=0)\n",
    "u1 = np.concatenate((u1,u_end[1:]),axis=0)\n",
    "\n",
    "\n",
    "\n",
    "# optimisation of T0\n",
    "tval=np.linspace(t0,T,NT) # discretized time interval [t0,t0+h,...,T]\n",
    "h = (T-t0)/(NT-1)        #the time step\n",
    "u2, Jval2, yval2, T02 = optimSIR_dic_finite_dim(T,init)\n",
    "# compute Sinf\n",
    "Sinf = Dicho_S_inf(J(yval2))\n",
    "#S_inf, T0, u2, Jval2, yval2, tval = exact_value_T0(T,alpha)\n",
    "#u2, i2, Jnew2, Jval2, yval2, T0 =optimSIR_finite_dim(T/2,init,10000)\n",
    "# u=1 on the last interval\n",
    "u_end = np.ones(NT)\n",
    "y_end = RK4_state(u_end,yval2[-1,:]) \n",
    "tval = np.concatenate((tval,np.linspace(T,T_end,NT)),axis=0)\n",
    "yval2 = np.concatenate((yval2,y_end[1:,:]),axis=0)\n",
    "u2 = np.concatenate((u2,u_end[1:]),axis=0)\n",
    "T=T_end\n",
    "\n",
    "\n",
    "\n",
    "# extract the values \n",
    "yval1=yval1[::50,:]\n",
    "yval2=yval2[::50,:]\n",
    "u1=u1[::50]\n",
    "u2=u2[::50]\n",
    "tval_end=tval_end[::50]\n",
    "\n",
    "\n",
    "# post processing - resultats et figures\n",
    "print('number of iterations in the optimisation of u:',i1)\n",
    "print('J(u):',Jnew1)\n",
    "#print('number of iterations in the optimisation of T0:',i2)\n",
    "print('J(T0):',Jval2)\n",
    "print('T0:',T02)\n",
    "print('S_inf',Sinf)\n",
    "plot_save_opt_sol(Jval1,yval1,u1,yval2,u2,tval_end,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('norm grad', 0.9365656588536552)\n",
      "('i=', 0, 'and J=', 0.9999186278472526, 'rho=', 15.823413952872837)\n",
      "('k1=', 1, 'k2=', 47, 'delta2', -0.18616579464189686)\n",
      "('norm grad', 0.7835701051793977)\n",
      "('i=', 1, 'and J=', 0.7498478538091571, 'rho=', 59.43438331305262)\n",
      "('k1=', 1, 'k2=', 17, 'delta2', -0.08131333423661469)\n",
      "('norm grad', 0.38789137748221325)\n",
      "('i=', 2, 'and J=', 0.7313809318465259, 'rho=', 2.808183135408099)\n",
      "('k1=', 38, 'k2=', 4, 'delta2', -0.004596377281186559)\n",
      "('norm grad', 0.08120508702284586)\n",
      "('i=', 3, 'and J=', 0.7252376204828117, 'rho=', 195.01271773667358)\n",
      "('k1=', 1, 'k2=', 1, 'delta2', -0.0026920200762897695)\n",
      "('norm grad', 0.11510614070948298)\n",
      "('i=', 4, 'and J=', 0.7252118999261243, 'rho=', 33.01560979772107)\n",
      "('k1=', 30, 'k2=', 5, 'delta2', -6.885470619855116e-05)\n",
      "('norm grad', 0.07916417064136363)\n",
      "('i=', 5, 'and J=', 0.7251615938403606, 'rho=', 71.76507715393848)\n",
      "('k1=', 16, 'k2=', 5, 'delta2', -4.450624183005569e-05)\n",
      "('norm grad', 0.10563904757595073)\n",
      "('i=', 6, 'and J=', 0.7251108866556621, 'rho=', 52.24196607358644)\n",
      "('k1=', 22, 'k2=', 5, 'delta2', -3.373888156144034e-05)\n",
      "('norm grad', 0.08245673337340176)\n",
      "('i=', 7, 'and J=', 0.7250820629968238, 'rho=', 113.55685231666256)\n",
      "('k1=', 16, 'k2=', 5, 'delta2', -3.094962992800099e-05)\n",
      "('norm grad', 0.1054003625563525)\n",
      "('i=', 8, 'and J=', 0.7250540518740407, 'rho=', 57.40598992321505)\n",
      "('k1=', 24, 'k2=', 5, 'delta2', -2.5267197514833306e-05)\n",
      "('norm grad', 0.08404643921409116)\n",
      "('i=', 9, 'and J=', 0.7250292955253628, 'rho=', 179.68570813917987)\n",
      "('k1=', 14, 'k2=', 5, 'delta2', -2.2720960828004344e-05)\n",
      "('norm grad', 0.1046681604183755)\n",
      "('i=', 10, 'and J=', 0.7250065703351007, 'rho=', 63.08046818954718)\n",
      "('k1=', 26, 'k2=', 5, 'delta2', -1.9349590013262308e-05)\n",
      "('norm grad', 0.08608819227696757)\n",
      "('i=', 11, 'and J=', 0.7249869966693364, 'rho=', 409.42675314739233)\n",
      "('k1=', 9, 'k2=', 6, 'delta2', -2.062935024194079e-05)\n",
      "('norm grad', 0.10430115046564585)\n",
      "('i=', 12, 'and J=', 0.7249643709686091, 'rho=', 83.17903004201933)\n",
      "('k1=', 30, 'k2=', 4, 'delta2', -1.4825949587238263e-05)\n",
      "('norm grad', 0.08657994493943645)\n",
      "('i=', 13, 'and J=', 0.7249539054971317, 'rho=', 539.8774165359894)\n",
      "('k1=', 9, 'k2=', 6, 'delta2', -1.0381110365220714e-05)\n",
      "('norm grad', 0.09930731370464137)\n",
      "('i=', 14, 'and J=', 0.7249455105837126, 'rho=', 109.68135204610984)\n",
      "('k1=', 29, 'k2=', 5, 'delta2', -7.311607930216013e-06)\n",
      "('norm grad', 0.08758022305253359)\n",
      "('i=', 15, 'and J=', 0.7249365424331086, 'rho=', 1771.415069435335)\n",
      "('k1=', 1, 'k2=', 9, 'delta2', -8.613222951314725e-06)\n",
      "('norm grad', 0.09801090458274567)\n",
      "('i=', 16, 'and J=', 0.7249297046861731, 'rho=', 144.6277863613644)\n",
      "('k1=', 34, 'k2=', 5, 'delta2', -4.208845445941023e-06)\n",
      "('norm grad', 0.08930225213729936)\n",
      "('i=', 17, 'and J=', 0.7249255564208443, 'rho=', 1622.0968707194615)\n",
      "('k1=', 5, 'k2=', 7, 'delta2', -2.651500652595118e-06)\n",
      "('norm grad', 0.0848840380460151)\n",
      "('i=', 18, 'and J=', 0.7249231781381054, 'rho=', 329.54476790642764)\n",
      "('k1=', 30, 'k2=', 4, 'delta2', -1.0466819493348822e-06)\n",
      "('norm grad', 0.08938780364487653)\n",
      "('i=', 19, 'and J=', 0.72492241517078, 'rho=', 859.5863292319617)\n",
      "('k1=', 15, 'k2=', 5, 'delta2', -4.7119766366510163e-07)\n",
      "('norm grad', 0.08659664107752217)\n",
      "('i=', 20, 'and J=', 0.7249220720327868, 'rho=', 521.4523278586805)\n",
      "('k1=', 23, 'k2=', 5, 'delta2', -4.6676842380133365e-07)\n",
      "('norm grad', 0.08949172387351748)\n",
      "('i=', 21, 'and J=', 0.7249215273995402, 'rho=', 655.9408909947805)\n",
      "('k1=', 19, 'k2=', 5, 'delta2', -2.5857393626260716e-07)\n",
      "('norm grad', 0.08753545682092094)\n",
      "('i=', 22, 'and J=', 0.7249212511904503, 'rho=', 990.1387248476484)\n",
      "('k1=', 18, 'k2=', 5, 'delta2', -3.0903303782636726e-07)\n",
      "('norm grad', 0.08970977065780535)\n",
      "('i=', 23, 'and J=', 0.7249210416750387, 'rho=', 600.6495513209868)\n",
      "('k1=', 23, 'k2=', 5, 'delta2', -1.8564491199857258e-07)\n",
      "('norm grad', 0.08789946709181656)\n",
      "('i=', 24, 'and J=', 0.7249207856555335, 'rho=', 2256.101987620895)\n",
      "('k1=', 13, 'k2=', 5, 'delta2', -2.753729363424995e-07)\n",
      "('norm grad', 0.09008813501409554)\n",
      "('i=', 25, 'and J=', 0.7249205622928936, 'rho=', 550.018894164312)\n",
      "('k1=', 28, 'k2=', 5, 'delta2', -1.7740795044129953e-07)\n",
      "('norm grad', 0.08837709327441366)\n",
      "('i=', 26, 'and J=', 0.7249198049298285, 'rho=', 38195.75653918833)\n",
      "('k1=', 1, 'k2=', 1, 'delta2', -6.160771248708841e-07)\n",
      "('norm grad', 0.0887806851526213)\n",
      "('i=', 27, 'and J=', 0.7249198047448101, 'rho=', 1503.908924128692)\n",
      "('k1=', 38, 'k2=', 5, 'delta2', -3.913121826570887e-09)\n",
      "('norm grad', 0.08852232441206413)\n",
      "('i=', 28, 'and J=', 0.7249198007408959, 'rho=', 2724.1694820985886)\n",
      "('k1=', 17, 'k2=', 5, 'delta2', -1.6462921026416666e-09)\n",
      "('norm grad', 0.08836139967343044)\n",
      "('i=', 29, 'and J=', 0.72491976644264, 'rho=', 91231.88476892674)\n",
      "('k1=', 1, 'k2=', 5, 'delta2', -3.515264213049818e-08)\n",
      "('norm grad', 0.08859227810259832)\n",
      "('i=', 30, 'and J=', 0.72491976421778, 'rho=', 0.05312476942793524)\n",
      "('k1=', 100, 'k2=', 4, 'delta2', 3.219646771412954e-15)\n",
      "end of computations\n",
      "('norm grad', 1.3600101228127992)\n",
      "('i=', 0, 'and J=', 0.806568125186134, 'rho=', 27.34285931056426)\n",
      "('k1=', 40, 'k2=', 5, 'delta2', -0.08413498624043436)\n",
      "('norm grad', 0.09297366537874446)\n",
      "('i=', 1, 'and J=', 0.7296227796767758, 'rho=', 16.587045597323097)\n",
      "('k1=', 24, 'k2=', 4, 'delta2', -0.0012728071887544434)\n",
      "('norm grad', 0.18687576411521)\n",
      "('i=', 2, 'and J=', 0.7285108064050148, 'rho=', 20.865035760330898)\n",
      "('k1=', 20, 'k2=', 4, 'delta2', -0.0008910311420182726)\n",
      "('norm grad', 0.07840370326000645)\n",
      "('i=', 3, 'and J=', 0.7277097387016226, 'rho=', 18.226645051501407)\n",
      "('k1=', 22, 'k2=', 4, 'delta2', -0.0006119375844074737)\n",
      "('norm grad', 0.1530847982045704)\n",
      "('i=', 4, 'and J=', 0.7273032082953371, 'rho=', 22.927506803972967)\n",
      "('k1=', 19, 'k2=', 5, 'delta2', -0.0004670118858568495)\n",
      "('norm grad', 0.07267133910060328)\n",
      "('i=', 5, 'and J=', 0.7268292729937342, 'rho=', 20.0283159459714)\n",
      "('k1=', 21, 'k2=', 5, 'delta2', -0.00036093528690672727)\n",
      "('norm grad', 0.1302850389213607)\n",
      "('i=', 6, 'and J=', 0.726415459756286, 'rho=', 30.23261925554774)\n",
      "('k1=', 18, 'k2=', 5, 'delta2', -0.00029086913082143617)\n",
      "('norm grad', 0.07063176773728004)\n",
      "('i=', 7, 'and J=', 0.7261540498678742, 'rho=', 22.008078749446497)\n",
      "('k1=', 22, 'k2=', 5, 'delta2', -0.0002265690482112781)\n",
      "('norm grad', 0.11647915641477474)\n",
      "('i=', 8, 'and J=', 0.7259539995730021, 'rho=', 47.838324936012604)\n",
      "('k1=', 16, 'k2=', 5, 'delta2', -0.00019991687802556335)\n",
      "('norm grad', 0.06722919226356859)\n",
      "('i=', 9, 'and J=', 0.7257448878070112, 'rho=', 20.152947937495128)\n",
      "('k1=', 25, 'k2=', 5, 'delta2', -0.00015795082464098442)\n",
      "('norm grad', 0.10185663386092104)\n",
      "('i=', 10, 'and J=', 0.7256269888513016, 'rho=', 130.8036588378451)\n",
      "('k1=', 7, 'k2=', 8, 'delta2', -0.00021739556429445361)\n",
      "('norm grad', 0.06408927599826472)\n",
      "('i=', 11, 'and J=', 0.7254060838848795, 'rho=', 18.454191989912058)\n",
      "('k1=', 31, 'k2=', 5, 'delta2', -0.00010648977115479408)\n",
      "('norm grad', 0.08940460084603355)\n",
      "('i=', 12, 'and J=', 0.7249804945897169, 'rho=', 1281.5411104105597)\n",
      "('k1=', 1, 'k2=', 1, 'delta2', -0.0003293622814104502)\n",
      "('norm grad', 0.11367844526779945)\n",
      "('i=', 13, 'and J=', 0.7249696453410627, 'rho=', 72.66101403892428)\n",
      "('k1=', 37, 'k2=', 4, 'delta2', -2.6902810570383906e-05)\n",
      "('norm grad', 0.08816383377341226)\n",
      "('i=', 14, 'and J=', 0.7249265775988165, 'rho=', 5045.903752703075)\n",
      "('k1=', 1, 'k2=', 1, 'delta2', -2.7014180330020565e-05)\n",
      "('norm grad', 0.0980972397807908)\n",
      "('i=', 15, 'and J=', 0.7249260642224072, 'rho=', 165.56332368577014)\n",
      "('k1=', 39, 'k2=', 5, 'delta2', -3.3772804477472107e-06)\n",
      "('norm grad', 0.0902492735968633)\n",
      "('i=', 16, 'and J=', 0.724922569468841, 'rho=', 895.4971325047466)\n",
      "('k1=', 11, 'k2=', 5, 'delta2', -1.64835651861317e-06)\n",
      "('norm grad', 0.08748742433436724)\n",
      "('i=', 17, 'and J=', 0.7249214388894856, 'rho=', 938.7134668515412)\n",
      "('k1=', 20, 'k2=', 5, 'delta2', -3.6087846466692497e-07)\n",
      "('norm grad', 0.08999344055254768)\n",
      "('i=', 18, 'and J=', 0.7249211108929571, 'rho=', 569.4533589423073)\n",
      "('k1=', 24, 'k2=', 4, 'delta2', -2.2596178328448957e-07)\n",
      "('norm grad', 0.08780052614778794)\n",
      "('i=', 19, 'and J=', 0.7249209202892634, 'rho=', 1485.3651769128314)\n",
      "('k1=', 14, 'k2=', 6, 'delta2', -2.639983026631043e-07)\n",
      "('norm grad', 0.08970802116904258)\n",
      "('i=', 20, 'and J=', 0.7249206894714579, 'rho=', 625.7427934304171)\n",
      "('k1=', 25, 'k2=', 5, 'delta2', -1.4547664772823765e-07)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('norm grad', 0.088102072454914)\n",
      "('i=', 21, 'and J=', 0.7249205382284956, 'rho=', 4873.695726856669)\n",
      "('k1=', 7, 'k2=', 7, 'delta2', -2.710790818483133e-07)\n",
      "('norm grad', 0.09016916020823093)\n",
      "('i=', 22, 'and J=', 0.7249202386352266, 'rho=', 687.5963366997565)\n",
      "('k1=', 32, 'k2=', 4, 'delta2', -1.455419188500784e-07)\n",
      "('norm grad', 0.08839086986863966)\n",
      "('i=', 23, 'and J=', 0.7249197840179444, 'rho=', 47749.74560414976)\n",
      "('k1=', 1, 'k2=', 1, 'delta2', -3.550077066760693e-07)\n",
      "('norm grad', 0.08847813540808108)\n",
      "('i=', 24, 'and J=', 0.7249197840177835, 'rho=', 175.72003596144523)\n",
      "('k1=', 51, 'k2=', 5, 'delta2', -1.1246559239452836e-12)\n",
      "end of computations\n",
      "('norm grad', 0.0002172881166276885)\n",
      "('i=', 0, 'and J=', 0.9988209026564531, 'rho=', 69444.44444444445)\n",
      "('k1=', 1, 'k2=', 1, 'delta2', -0.0011507567997084411)\n",
      "('norm grad', 0.015203016761258969)\n",
      "('i=', 1, 'and J=', 0.9870417066472241, 'rho=', 2278.5716092136886)\n",
      "('k1=', 1, 'k2=', 43, 'delta2', -0.26487940918817054)\n",
      "('norm grad', 0.1336376257771431)\n",
      "('i=', 2, 'and J=', 0.7267483790196596, 'rho=', 131861.782940607)\n",
      "('k1=', 1, 'k2=', 2, 'delta2', -0.00719672754889622)\n",
      "('norm grad', 0.32221033067683585)\n",
      "('i=', 3, 'and J=', 0.7262740742051168, 'rho=', 37.79477117879335)\n",
      "('k1=', 66, 'k2=', 4, 'delta2', -0.001329193869451628)\n",
      "('norm grad', 0.11300526645946968)\n",
      "('i=', 4, 'and J=', 0.7253312645745931, 'rho=', 294.37049331690605)\n",
      "('k1=', 9, 'k2=', 5, 'delta2', -0.0003371251206440995)\n",
      "('norm grad', 0.08924639743011813)\n",
      "('i=', 5, 'and J=', 0.7249306930277888, 'rho=', 20442.39536922959)\n",
      "('k1=', 1, 'k2=', 1, 'delta2', -0.00014775390150179035)\n",
      "('norm grad', 0.10330337428451146)\n",
      "('i=', 6, 'and J=', 0.7249286088650949, 'rho=', 155.9936748242721)\n",
      "('k1=', 48, 'k2=', 4, 'delta2', -5.828010262165506e-06)\n",
      "('norm grad', 0.09158106978564409)\n",
      "('i=', 7, 'and J=', 0.7249239894859087, 'rho=', 1214.9811622117638)\n",
      "('k1=', 9, 'k2=', 5, 'delta2', -3.5382738132749836e-06)\n",
      "('norm grad', 0.08851822060783755)\n",
      "('i=', 8, 'and J=', 0.7249197977334029, 'rho=', 58592.84154184819)\n",
      "('k1=', 1, 'k2=', 3, 'delta2', -1.5484011889332905e-06)\n",
      "('norm grad', 0.08861782631245746)\n",
      "('i=', 9, 'and J=', 0.7249197783012222, 'rho=', 1112.5665436700979)\n",
      "('k1=', 42, 'k2=', 5, 'delta2', -2.8219160341791394e-10)\n",
      "('norm grad', 0.08855021371758555)\n",
      "('i=', 10, 'and J=', 0.7249197780434108, 'rho=', 562.4317907010206)\n",
      "('k1=', 25, 'k2=', 4, 'delta2', -3.2736924282517066e-11)\n",
      "end of computations\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/duprez/.local/lib/python2.7/site-packages/ipykernel_launcher.py:52: RuntimeWarning: divide by zero encountered in log\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('number of iterations in the optimisation of u:', 25)\n",
      "('J(u):', 0.7249197840177835)\n",
      "('J(T0):', 0.7249198457710275)\n",
      "('T0:', 59.18)\n",
      "('S_inf', 0.25874960011449355)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8eadce7d90>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8eadcca750>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8eadc41e50>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8eb00a7d50>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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DZuRKqBT6wmmvn89N9/Ty/O69ZZfSFeb1zeGtx80vuwyRjlDoC28ZPJLRj59bdhkiMgv0IlZEJCIthb6ZLTOzbWY2ZmbXNPn41Wb2oJltNLO7zezY9pcqIiIHatrQN7MKsAY4H1gMXGZmixt2uw8Ydvc3Ad8FPtPuQkVE5MC1MtI/FRhz9+3uvge4BViR38Hd17v7H5Kn9wAD7S1TRETaoZXQPxp4LPd8PNk2lauAHzX7gJmtMrNRMxvduXNn61WKiEhbtBL6zWapNJ26aWZ/DQwDn232cXdf6+7D7j7c39/fepUiItIWrVyyOQ4szD0fAJ5o3MnMzgE+Bpzh7i+1pzwREWmnVkb6G4BFZjZkZr3ApcBIfgczWwL8K3CBuz/d/jJFRKQdpg19d98LrAbuBLYCt7n7FjO7zswuSHb7LPBK4HYzu9/MRqb4ciIiUqKWZuS6+zpgXcO2a3OPz2lzXSIi0gGakSsiEhGFvohIRBT6IiIRUeiLiEREoS8iEhGFvohIRBT6IiIRUeiLiEREoS8iEpGuukfuyy+/zPj4OLt37y67lFnT19fHwMAAc+fOLbsUEYlAV4X++Pg48+bNY3BwELNmKzqHxd3ZtWsX4+PjDA0NlV2OiESgq9o7u3fvZv78+VEEPoCZMX/+/Khe2YhIuboq9IFoAj8V279XRMrVdaEvIiKdo9AXEYmIQn8GXnzxRc444wyq1SrXX389J598MieffDI9PT3Z46uvvrrweXv27OH0009n7969JVQtIlLXVVfvdLsbbriBiy66iEqlwsqVK1m5ciWPP/44p512Gvfff/+Un9fb28vZZ5/NrbfeyuWXXz6LFYuITKaRfhNLly5lx44dADz++OMMDw8DcPPNN7NixYpJ+27evJmTTjpp2q954YUXcvPNN7e9VhGRmVDoN3B3Hn30UY499lgANm7cyEknncSePXvYvn07g4ODk/bftGkTJ5544rRf98QTT2TDhg2dKFlEpGVd294ZvOaOjnzdHZ/6031+fGxsjKGhoexSyjT0n3nmGQ4//PDC/ps3b+bcc8/Nnr/wwgu8733vo7e3lzPPPDNr51QqFXp7e3n++eeZN29eG/9FIiKt00i/waZNmya1a0ZHR3nTm97EoYce2nQSVeNI//vf/z4XX3wx119/PSMjI5P2femll+jr6+tc8SIi0+jakf50I/JOefbZZzn00EMB2Lp1K3fccQdf/vKXOeKII6hWq+zevTsL7omJCR566CHe8IY3ZJ8/Pj6e/dKoVCrZ9l27dtHf3681dkSkVBrpNzjvvPO4++67ueSSS7j99tuZP38+r33tawF45zvfyU9/+tNs37GxMQYGBjjkkEOybQMDA4yPjwO1Xwqp9evXs3z58ln6V4iINGfuXso3Hh4e9tHR0Unbtm7dyhvf+MZS6mnFfffdx+c//3luuummKfd54YUXWL16NX19fbz97W/PevoXXXQRn/zkJznhhBMKn9Pt/24R6R5mdq+7D+/v53dte6cbLVmyhLPOOotqtTqpdZN32GGH8Y1vfGPStj179nDhhRc2DXwRkdmk0J+hK6+8csaf09vbyxVXXNGBakREZkY9fRGRiCj0RUQiotAXEYlI14V+WVcTlSW2f6+IlKurQr+vr49du3ZFE4TpPXI1S1dEZktXXb2TTmzauXNn2aXMmr6+PgYGBsouQ0Qi0VLom9ky4ItABfiau3+q4eOHADcCfwzsAv7K3XfMtJi5c+cyNDQ0008TEZEWTdveMbMKsAY4H1gMXGZmixt2uwr4rbu/HvgC8Ol2FyoiIgeulZ7+qcCYu2939z3ALcCKhn1WAN9KHn8XONvStYlFRKRrtBL6RwOP5Z6PJ9ua7uPue4HngPntKFBERNqnlZ5+sxF74+U1reyDma0CViVPXzKzzS18/7ItAJ4pu4gWqM72ORhqBNXZbgdLnQe0iFcroT8OLMw9HwCemGKfcTObA7waeLbxC7n7WmAtgJmNHshKcbNFdbbXwVDnwVAjqM52O5jqPJDPb6W9swFYZGZDZtYLXAqMNOwzArw7eXwx8J8ey8X2IiIHkWlH+u6+18xWA3dSu2TzBnffYmbXAaPuPgJ8HbjJzMaojfAv7WTRIiKyf1q6Tt/d1wHrGrZdm3u8G3jXDL/32hnuXxbV2V4HQ50HQ42gOtstijpLu3OWiIjMvq5ae0dERDqrlNA3s2Vmts3MxszsmjJqaGRmC81svZltNbMtZvahZPsnzOxxM7s/+VP63c3NbIeZbUrqGU22HWlm/2FmDyV/H1FyjSfkjtn9ZvY7M/twNxxPM7vBzJ7OXzI81fGzmi8l5+pGMzul5Do/a2a/TGr5gZkdnmwfNLMXc8f1qyXXOeX/s5l9NDme28zsvJLrvDVX4w4zuz/ZXsrx3EcOte/8dPdZ/UPtzeCHgdcBvcADwOLZrqNJXUcBpySP5wG/orbsxCeAvyu7voZadwALGrZ9BrgmeXwN8Omy62z4P/8NcGw3HE/gdOAUYPN0xw9YDvyI2lyUpcDPSq7zncCc5PGnc3UO5vfrguPZ9P85+Zl6ADgEGEqyoFJWnQ0f/2fg2jKP5z5yqG3nZxkj/VaWdZh17v6ku/8iefw8sJXizONull8K41vAhSXW0uhs4GF3/3XZhQC4+08oziOZ6vitAG70mnuAw83sqLLqdPe7vDbrHeAeavNmSjXF8ZzKCuAWd3/J3R8BxqhlQsftq85k2ZhLgO/MRi1T2UcOte38LCP0W1nWoVRmNggsAX6WbFqdvHS6oey2ScKBu8zsXqvNcgZ4rbs/CbUTB3hNadUVXcrkH6ZuO54w9fHr5vP1SmqjvNSQmd1nZv9lZu8oq6icZv/P3Xo83wE85e4P5baVejwbcqht52cZod/Skg1lMbNXAt8DPuzuvwO+AhwHnAw8Se0lYNne5u6nUFv59P1mdnrZBU3FahP6LgBuTzZ14/Hcl648X83sY8Be4OZk05PAMe6+BLga+LaZvaqs+pj6/7krjydwGZMHJqUezyY5NOWuTbbt83iWEfqtLOtQCjObS+1A3+zu3wdw96fcveruE8D1zNJL0X1x9yeSv58GfkCtpqfSl3XJ30+XV+Ek5wO/cPenoDuPZ2Kq49d156uZvRv4M+ByTxq7SbtkV/L4Xmq98uPLqnEf/8/deDznABcBt6bbyjyezXKINp6fZYR+K8s6zLqkp/d1YKu7fz63Pd8f+wug1EXizOwwM5uXPqb2xt5mJi+F8W7gh+VUWDBpBNVtxzNnquM3AlyRXCWxFHgufZldBqvd0OgfgAvc/Q+57f1Wu/cFZvY6YBGwvZwq9/n/PAJcamaHmNkQtTp/Ptv1NTgH+KW7j6cbyjqeU+UQ7Tw/Z/vd6dw7zr+i9tvzY2XU0KSmt1N7WbQRuD/5sxy4CdiUbB8Bjiq5ztdRu/rhAWBLevyoLWV9N/BQ8veRXXBMX0HtTmqvzm0r/XhS+yX0JPAytZHSVVMdP2ovn9ck5+omYLjkOseo9XDTc/Sryb5/mZwPDwC/AP685Dqn/H8GPpYcz23A+WXWmWz/JvDehn1LOZ77yKG2nZ+akSsiEhHNyBURiYhCX0QkIgp9EZGIKPRFRCKi0BcRiUhLN1EROZiZWXq5G8AfAVVgZ/L8D+5+WimFiZRAl2xKVMzsE8Dv3f1zZdciUga1dyRqZvb75O8zk4W1bjOzX5nZp8zscjP7udXuXXBcsl+/mX3PzDYkf95W7r9AZGYU+iJ1bwY+BJwE/A1wvLufCnwN+ECyzxeBL7j7W6jN2vxaGYWK7C/19EXqNniybomZPQzclWzfBJyVPD4HWFxbIgWAV5nZPK+tfS7S9RT6InUv5R5P5J5PUP9Z6QHe6u4vzmZhIu2i9o7IzNwFrE6fmNnJJdYiMmMKfZGZ+SAwnNwR6kHgvWUXJDITumRTRCQiGumLiEREoS8iEhGFvohIRBT6IiIRUeiLiEREoS8iEhGFvohIRBT6IiIR+X+MCwp0wGhd5QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8eadaf7c50>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# minimisation with respect to u and T0 for alpha = 0.231 (figure 4)\n",
    "T=100\n",
    "alpha = alpha_conf\n",
    "NT=int(5001) # number of time step\n",
    "ITER = 5e4 # number of step in optimisation\n",
    "T_end = 200.0\n",
    "tval=np.linspace(t0,T,NT) # discretized time interval [t0,t0+h,...,T]\n",
    "tval_end = np.linspace(t0,T_end,2*NT-1)#np.concatenate((tval,np.linspace(T,T_end,NT)),axis=0)\n",
    "h = (T-t0)/(NT-1)        #the time step\n",
    "\n",
    "# optimisation of u\n",
    "u=np.ones(int(NT))\n",
    "u1, i1, Jnew1, Jval1, yval1=optimSIR(u,init,True)\n",
    "u_test=np.ones(int(NT))\n",
    "for ind in range(int(NT/2),NT):\n",
    "    u_test[ind] = alpha\n",
    "u_test, i_test, Jnew_test, Jval_test, yval_test=optimSIR(u_test,init,True)\n",
    "if Jval_test<Jval1:\n",
    "    u1, i1, Jnew1, Jval1, yval1 = u_test, i_test, Jnew_test, Jval_test, yval_test\n",
    "u_test=alpha*np.ones(int(NT))\n",
    "u_test, i_test, Jnew_test, Jval_test, yval_test=optimSIR(u_test,init,True)\n",
    "if Jval_test<Jval1:\n",
    "    u1, i1, Jnew1, Jval1, yval1 = u_test, i_test, Jnew_test, Jval_test, yval_test\n",
    "# u=1 on the last interval\n",
    "u_end = np.ones(NT)\n",
    "y_end = RK4_state(u_end,yval1[-1,:]) \n",
    "yval1 = np.concatenate((yval1,y_end[1:,:]),axis=0)\n",
    "u1 = np.concatenate((u1,u_end[1:]),axis=0)\n",
    "\n",
    "\n",
    "\n",
    "# optimisation of T0\n",
    "u2, Jval2, yval2, T02 = optimSIR_dic_finite_dim(T,init)\n",
    "#S_inf, T0, u2, Jval2, yval2, tval = exact_value_T0(T,alpha)\n",
    "#u2, i2, Jnew2, Jval2, yval2, T0 =optimSIR_finite_dim(T/2,init,10000)\n",
    "# u=1 on the last interval\n",
    "u_end = np.ones(NT)\n",
    "y_end = RK4_state(u_end,yval2[-1,:]) \n",
    "tval = np.concatenate((tval,np.linspace(T,T_end,NT)),axis=0)\n",
    "yval2 = np.concatenate((yval2,y_end[1:,:]),axis=0)\n",
    "u2 = np.concatenate((u2,u_end[1:]),axis=0)\n",
    "T=T_end\n",
    "\n",
    "# compute Sinf\n",
    "Sinf = Dicho_S_inf(J(yval2))\n",
    "\n",
    "# extract the values \n",
    "yval1=yval1[::50,:]\n",
    "yval2=yval2[::50,:]\n",
    "u1=u1[::50]\n",
    "u2=u2[::50]\n",
    "tval_end=tval_end[::50]\n",
    "\n",
    "\n",
    "# post processing - resultats et figures\n",
    "print('number of iterations in the optimisation of u:',i1)\n",
    "print('J(u):',Jnew1)\n",
    "#print('number of iterations in the optimisation of T0:',i2)\n",
    "print('J(T0):',Jval2)\n",
    "print('T0:',T02)\n",
    "print('S_inf',Sinf)\n",
    "plot_save_opt_sol(Jval1,yval1,u1,yval2,u2,tval_end,4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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     "text": [
      "/home/duprez/.local/lib/python2.7/site-packages/ipykernel_launcher.py:52: RuntimeWarning: divide by zero encountered in log\n"
     ]
    },
    {
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     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5d7cc00950>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5d7cb9d450>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5d7aa15550>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5d7a9aae10>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#graphique S infini et T0 en fonction de T (figure 5-6) \n",
    "\n",
    "# parameters\n",
    "min_T=1\n",
    "max_T=300\n",
    "nb_T = 100\n",
    "Time = np.linspace(min_T,max_T,nb_T)\n",
    "alpha_array=[0.0,alpha_conf,0.7,0.8]\n",
    "color_plt=['r-','g-','b-','c-','m-','y-','b--','g--','r--']\n",
    "color_tikz=['red','black!60!green','blue','black','yellow']\n",
    "\n",
    "# Computation of T0 Sinf theoretical\n",
    "NT=int(10000) # number of time step\n",
    "S_inf_theo_array =  np.zeros((len(Time),len(alpha_array)))\n",
    "T0_theo_array =  np.zeros((len(Time),len(alpha_array)))\n",
    "min_zero =  np.zeros(len(alpha_array))\n",
    "for ind_alpha in range(len(alpha_array)):\n",
    "    alpha = alpha_array[ind_alpha]\n",
    "    for ind_T in range(len(Time)):\n",
    "        T = Time[ind_T]\n",
    "        print('##############################################')\n",
    "        print('Iteration '+str(ind_T+1)+'/'+str(len(Time))+' and '+str(ind_alpha+1)+'/'+str(len(alpha_array)))\n",
    "        print('##############################################')\n",
    "        print(\"T=\",T)\n",
    "        tval=np.linspace(t0,T,NT) # discretized time interval [t0,t0+h,...,T]\n",
    "        h = (T-t0)/(NT-1)        #the time step\n",
    "        S_inf, T0, u, Jval, yval, tval =  exact_value_T0(T,alpha)\n",
    "        #T0init = T/2\n",
    "        #u, Jval, yval, T0 = optimSIR_dic_finite_dim(T,init)\n",
    "        #u, i, Jnew, Jval, yval, T0 =  optimSIR_finite_dim(T0init,init)\n",
    "        print('T0=',T0)\n",
    "        print('S_inf=',S_inf)\n",
    "        S_inf_theo_array[ind_T,ind_alpha] = S_inf\n",
    "        T0_theo_array[ind_T,ind_alpha] = T0\n",
    "    ind_T = nb_T-1\n",
    "    min_zero[ind_alpha] = max_T\n",
    "    while T0_theo_array[ind_T,ind_alpha]<=1 and ind_T>=0:\n",
    "        min_zero[ind_alpha] = Time[ind_T]\n",
    "        ind_T=ind_T-1\n",
    "\n",
    "        \n",
    "# Computation of T0 Sinf theoretical by optimisation\n",
    "NT=int(10000) # number of time step\n",
    "T0_opt_array =  np.zeros((len(Time),len(alpha_array)))\n",
    "S_inf_opt_array =  np.zeros((len(Time),len(alpha_array)))\n",
    "for ind_alpha in range(len(alpha_array)):\n",
    "    alpha = alpha_array[ind_alpha]\n",
    "    for ind_T in range(len(Time)):\n",
    "        print('##############################################')\n",
    "        print('Iteration J Num '+str(ind_T+1)+'/'+str(len(Time))+' and '+str(ind_alpha+1)+'/'+str(len(alpha_array)))\n",
    "        print('##############################################')\n",
    "        T = Time[ind_T]\n",
    "        print('T',T)\n",
    "        print('alpha',alpha)\n",
    "        tval=np.linspace(t0,T,NT) # discretized time interval [t0,t0+h,...,T]\n",
    "        h = (T-t0)/(NT-1)        #the time step\n",
    "        u, Jval, yval, T0 = optimSIR_dic_finite_dim(T,init)\n",
    "        S_inf = Dicho_S_inf(J(yval))\n",
    "        T0_opt_array[ind_T,ind_alpha] = T0\n",
    "        S_inf_opt_array[ind_T,ind_alpha] = S_inf\n",
    "        print('J',np.round(Jval,3))\n",
    "        print('T0',T0)\n",
    "        print('S_inf',S_inf)\n",
    "        plt.show()\n",
    "\n",
    "# post processing - resultats et figures\n",
    "# Plot\n",
    "plt.figure(1)\n",
    "for ind_alpha in range(len(alpha_array)):\n",
    "    plt.plot(Time,S_inf_theo_array[:,ind_alpha],'{0}'.format(color_plt[ind_alpha]),linewidth=2,label=r'$S_\\infty$ for alpha={0}'.format(round(alpha_array[ind_alpha],2)))\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('T')\n",
    "plt.axis([0, max(Time),0.0, np.max(S_inf_theo_array)])\n",
    "plt.savefig(\"fig5_simu_covid_S_infinity_with_respect_to_T_theo.png\")\n",
    "plt.figure(2)\n",
    "for ind_alpha in range(len(alpha_array)):\n",
    "    plt.plot(Time,T0_theo_array[:,ind_alpha],'{0}'.format(color_plt[ind_alpha]),linewidth=2,label=r'$T_0$ for alpha={0} $T_0=0$ at $T=${1}'.format(round(alpha_array[ind_alpha],2),round(min_zero[ind_alpha],0)))\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('T')\n",
    "plt.axis([0, max(Time), 0.0, np.max(T0_theo_array)])\n",
    "plt.savefig(\"fig6_simu_covid_T0_with_respect_to_T_theo.png\")\n",
    "plt.figure(3)\n",
    "for ind_alpha in range(len(alpha_array)):\n",
    "    plt.plot(Time,S_inf_opt_array[:,ind_alpha],'{0}'.format(color_plt[ind_alpha]),linewidth=2,label=r'$S_\\infty$ for alpha={0}'.format(round(alpha_array[ind_alpha],2)))\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('T')\n",
    "plt.axis([0, max(Time),0.0, np.max(S_inf_opt_array)])\n",
    "plt.savefig(\"fig5_simu_covid_S_infinity_with_respect_to_T_opt.png\")\n",
    "plt.figure(4)\n",
    "for ind_alpha in range(len(alpha_array)):\n",
    "    plt.plot(Time,T0_opt_array[:,ind_alpha],'{0}'.format(color_plt[ind_alpha]),linewidth=2,label=r'$T_0$ for alpha={0}'.format(round(alpha_array[ind_alpha],2)))\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('T')\n",
    "plt.axis([0, max(Time), 0.0, np.max(T0_opt_array)])\n",
    "plt.savefig(\"fig6_simu_covid_T0_with_respect_to_T_opt.png\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "# Save the values for tikz\n",
    "File = open('fig5_simu_covid_S_infinity_with_respect_to_T.txt','w')\n",
    "for ind_alpha in range(len(alpha_array)):\n",
    "    File.write('\\\\addplot[color={0},opacity = 0.25,line width=1mm]'.format(color_tikz[ind_alpha]))\n",
    "    File.write(' coordinates { ')\n",
    "    write_to_file(File,Time,S_inf_opt_array[:,ind_alpha])\n",
    "    File.write(' };\\n\\n')\n",
    "    File.write('\\\\addplot[color={0}]'.format(color_tikz[ind_alpha]))\n",
    "    File.write(' coordinates { ')\n",
    "    write_to_file(File,Time,S_inf_theo_array[:,ind_alpha])\n",
    "    File.write(' };\\n\\n')\n",
    "File.close()\n",
    "File = open('fig6_simu_covid_T0_with_respect_to_T.txt','w')\n",
    "for ind_alpha in range(len(alpha_array)):\n",
    "    File.write('\\\\addplot[color={0},opacity = 0.25,line width=1mm]'.format(color_tikz[ind_alpha]))\n",
    "    File.write(' coordinates { ')\n",
    "    write_to_file(File,Time,T0_opt_array[:,ind_alpha])\n",
    "    File.write(' };\\n\\n')\n",
    "    File.write('\\\\addplot[color={0}]'.format(color_tikz[ind_alpha]))\n",
    "    File.write(' coordinates { ')\n",
    "    write_to_file(File,Time,T0_theo_array[:,ind_alpha])\n",
    "    File.write(' };\\n\\n')\n",
    "File.close()\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "##############################################\n",
      "('T=', 100)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/duprez/.local/lib/python2.7/site-packages/ipykernel_launcher.py:52: RuntimeWarning: divide by zero encountered in log\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5d7a90b350>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5d7aa64810>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5d7cb8c690>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5d7cb6eb10>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#graphique S infini et T0 en fonction de alpha (figure 5-6)\n",
    "\n",
    "# parameters\n",
    "nb_alpha = 100\n",
    "min_alpha = 0.0\n",
    "max_alpha = 0.99\n",
    "alpha_array = np.linspace(min_alpha,max_alpha,nb_alpha)\n",
    "Time=[100,200,400]\n",
    "color_plt=['r-','g-','b-','c-','m-','y-','b--','g--','r--']\n",
    "color_tikz=['red','black!60!green','blue','black','yellow']\n",
    "\n",
    "\n",
    "NT=int(10000) # number of time step\n",
    "S_inf_theo_array =  np.zeros((len(alpha_array),len(Time)))\n",
    "T0_theo_array =  np.zeros((len(alpha_array),len(Time)))\n",
    "for ind_alpha in range(len(alpha_array)):\n",
    "    alpha = alpha_array[ind_alpha]\n",
    "    for ind_T in range(len(Time)):\n",
    "        T = Time[ind_T]\n",
    "        print('##############################################')\n",
    "        print('Iteration T: '+str(ind_T+1)+'/'+str(len(Time))+' and alpha: '+str(ind_alpha+1)+'/'+str(len(alpha_array)))\n",
    "        print('##############################################')\n",
    "        print(\"T=\",T)\n",
    "        tval=np.linspace(t0,T,NT) # discretized time interval [t0,t0+h,...,T]\n",
    "        h = (T-t0)/(NT-1)        #the time step\n",
    "        S_inf, T0, u, Jval, yval, tval =  exact_value_T0(T,alpha)\n",
    "        #T0init = T/2\n",
    "        #u, Jval, yval, T0 = optimSIR_dic_finite_dim(T,init)\n",
    "        #u, i, Jnew, Jval, yval, T0 =  optimSIR_finite_dim(T0init,init)\n",
    "        print('T0=',T0)\n",
    "        S_inf = Dicho_S_inf(J(yval))\n",
    "        print('S_inf=',S_inf)\n",
    "        S_inf_theo_array[ind_alpha,ind_T] = S_inf\n",
    "        T0_theo_array[ind_alpha,ind_T] = T0\n",
    "\n",
    "# Computation of the numerical value of J optimal\n",
    "NT=int(10000) # number of time step\n",
    "T0_opt_array =  np.zeros((len(alpha_array),len(Time)))\n",
    "S_inf_opt_array =   np.zeros((len(alpha_array),len(Time)))\n",
    "for ind_alpha in range(len(alpha_array)):\n",
    "    alpha = alpha_array[ind_alpha]\n",
    "    for ind_T in range(len(Time)):\n",
    "        print('##############################################')\n",
    "        print('Iteration J Num '+str(ind_T+1)+'/'+str(len(Time))+' and '+str(ind_alpha+1)+'/'+str(len(alpha_array)))\n",
    "        print('##############################################')\n",
    "        T = Time[ind_T]\n",
    "        tval=np.linspace(t0,T,NT) # discretized time interval [t0,t0+h,...,T]\n",
    "        h = (T-t0)/(NT-1)        #the time step\n",
    "        u, Jval, yval, T0 = optimSIR_dic_finite_dim(T,init)\n",
    "        S_inf = Dicho_S_inf(J(yval))\n",
    "        T0_opt_array[ind_alpha,ind_T] = T0\n",
    "        S_inf_opt_array[ind_alpha,ind_T] = S_inf\n",
    "        print('J',np.round(Jval,3))\n",
    "\n",
    "\n",
    "\n",
    "# post processing - resultats et figures\n",
    "# Plot\n",
    "plt.figure(1)\n",
    "for ind_T in range(len(Time)):\n",
    "    plt.plot(alpha_array,S_inf_theo_array[:,ind_T],'{0}'.format(color_plt[ind_T]),linewidth=2,label=r'$S_\\infty$ for T={0}'.format(Time[ind_T]))\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel(r'$\\alpha$')\n",
    "plt.axis([0, max(alpha_array),0.0, np.max(S_inf_theo_array)])\n",
    "plt.savefig(\"fig5_simu_covid_S_infinity_with_respect_to_alpha_theo.png\")\n",
    "plt.figure(2)\n",
    "for ind_T in range(len(Time)):\n",
    "    plt.plot(alpha_array,T0_theo_array[:,ind_T],'{0}'.format(color_plt[ind_T]),linewidth=2,label=r'$T_0$ for T={0}'.format(Time[ind_T]))\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel(r'$\\alpha$')\n",
    "plt.axis([0, max(alpha_array), 0.0, np.max(T0_theo_array)])\n",
    "plt.savefig(\"fig6_simu_covid_T0_with_respect_to_alpha_theo.png\")\n",
    "plt.figure(3)\n",
    "for ind_T in range(len(Time)):\n",
    "    plt.plot(alpha_array,S_inf_opt_array[:,ind_T],'{0}'.format(color_plt[ind_T]),linewidth=2,label=r'$S_\\infty$ for T={0}'.format(Time[ind_T]))\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel(r'$\\alpha$')\n",
    "plt.axis([0, max(alpha_array),0.0, np.max(S_inf_opt_array)])\n",
    "plt.savefig(\"fig5_simu_covid_S_infinity_with_respect_to_alpha_opt.png\")\n",
    "plt.figure(4)\n",
    "for ind_T in range(len(Time)):\n",
    "    plt.plot(alpha_array,T0_opt_array[:,ind_T],'{0}'.format(color_plt[ind_T]),linewidth=2,label=r'$T_0$ for T={0}'.format(Time[ind_T]))\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel(r'$\\alpha$')\n",
    "plt.axis([0, max(alpha_array), 0.0, np.max(T0_opt_array)])\n",
    "plt.savefig(\"fig6_simu_covid_T0_with_respect_to_alpha_opt.png\")\n",
    "plt.show()\n",
    "\n",
    "# Save the values for tikz\n",
    "File = open('fig5_simu_covid_S_infinity_with_respect_to_alpha.txt','w')\n",
    "for ind_T in range(len(Time)):\n",
    "    File.write('\\\\addplot[color={0},opacity = 0.25,line width=1mm]'.format(color_tikz[ind_T]))\n",
    "    File.write(' coordinates { ')\n",
    "    write_to_file(File,alpha_array,S_inf_opt_array[:,ind_T])\n",
    "    File.write(' };\\n\\n')\n",
    "    File.write('\\\\addplot[color={0}]'.format(color_tikz[ind_T]))\n",
    "    File.write(' coordinates { ')\n",
    "    write_to_file(File,alpha_array,S_inf_theo_array[:,ind_T])\n",
    "    File.write(' };\\n\\n')\n",
    "File.close()\n",
    "File = open('fig6_simu_covid_T0_with_respect_to_alpha.txt','w')\n",
    "for ind_T in range(len(Time)):\n",
    "    File.write('\\\\addplot[color={0},opacity = 0.25,line width=1mm]'.format(color_tikz[ind_T]))\n",
    "    File.write(' coordinates { ')\n",
    "    write_to_file(File,alpha_array,T0_opt_array[:,ind_T])\n",
    "    File.write(' };\\n\\n')\n",
    "    File.write('\\\\addplot[color={0}]'.format(color_tikz[ind_T]))\n",
    "    File.write(' coordinates { ')\n",
    "    write_to_file(File,alpha_array,T0_theo_array[:,ind_T])\n",
    "    File.write(' };\\n\\n')\n",
    "File.close()\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Argmin de J pour T=200: [62.626 60.606 56.566 34.343 10.101  0.   ]\n",
      "Argmin de J pour T=300: [63.636 60.606 57.576 15.152  0.     0.   ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5d7ccc6850>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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A7du3k5GRwebNm9m1q77iuKdz/UG3MCIAc+fC+PFw8iS8+KJ/790vqh+zUmYhCB/v/xhmz9a1Wb76CrKz/TuYdsZWbWP3vN2U7SojfEQ4o5eOxhLS+Gv19IkT/PPkSYKV4qPRoxkXEcGaNXpND8Crr9fwzMmrOFV6iguix/H677YRaAP+9S9jQNqCDjO1/9YM6enpTJyoC3GfPHmSiIgI5x9eT7/Kk5KSOHGiTpMuIyODvn37Nrq+t/0cNJyJfPDBB8ybN49FixaxbNkyNx9b08/Y0Fh5s4ivuZlIUlISSUlJzlnGvHnz+Oabb+pdIyYmhhkzZrBy5cp6x70515d0GyNiscDvf69fL1rk33UjAFcM0+WFl+1fpvOPZ87Ug3DzBe5KHLj3AAVrCghKCGLMijGNXFgAm4qKePTwYQDeSk1lRmwsR47A9dfrLKzf/AbWhz/AhhMb6BfWm/88fZSgais8/LBe5GPocoSEhJCRkQHAo48+SrVLMNLTr/IpU6Zw4MABjhw5QnV1Ne+88w5Xuqld5KnfRRddVM+1ZbPZOHDgACNGjHAey8jIcLrDAtxUkDj//PP58MMPKS8vp6ysjKVLl3LeeecBcPz4cWf205IlSzj33HOJjIykxL5Q1h3NzUQSExPp378/+/btA+Czzz5j5MiR5ObmUlhYCEBFRQVr1qyp9xyezvUbbYnKd6atqewsV6qrReLj9U+p9PRmu7crGUUZwgIk7I9hUl5dLvLSS3ogl17q34G0I9n/yZY00uTz0M+laHOR2z6FNTUyaONGIS1NHj54UEREyspExo/Xj3/ZZSKvbH1dWIAEPxEsX88aqRuuuEKkttafj3PG0Bmys06cOCETJ06UYcOGyTPPPCPXX3+93H///V6d+/HHH8vQoUMlJSVF/vjHP9Zru/TSSyUzM7PJflarVZKTk6W8vNx5zr59+yQ1NbXedd544w1Zvny5iIhcf/31bsfxzDPPyKhRo2TUqFHy7LPPiojOwkpNTZV77rlHxowZI9dcc42UlZWJiMiNN94oo0aNkocffrjRWL0hPT1dJk2aJGPGjJGrrrpK8vPzZceOHTJ+/HgZM2aMjBo1Sv7whz+4/SzcnesOX2Rndfgf//bavDEiIiL33quf+sEHvererkx+cbKwAFm+b7lIdraIxSISHCxS5P4PcGem4kSFfBHzhaSRJhnPZzTZb/7u3UJamkzcskWqrFYREXn4Yf1vMGSIyPYjRyX8T+HCAmTRn+bqhqQkkcJCfz3KGUdnMCIdxc6dO+WBBx5otl9paancdttt8qMf/UjefPNNr6/fHqm8HYlJ8W0Hbr5Z799+G2pr/Xtvp0tr3zJddvicc3TO8Sef+HcgbURswne3fkdtYS1xl8fR90fufdFvZmXxVk4O4RYLb48cSbDFwjffaPVgiwXeekt4ZMOPKK8p5/r+l3Ln4//TJ770khGKMrSK0aNH87e//a3Zfj169ODVV1/lhRdeYP78+X4Y2ZlLtzMiU6fC0KGQlQVr1/r33lcO1z7b5fuXYxMbXH21buhiWVoZz2ZQuLaQoF5BjHh5hNvA4smqKn5y4AAAfx86lOHh4dTWwp136jjIz34Gh8P/w8qDK4kJjWHha9lQVQV33KHL5hsMnZCBAwc2yo7q7nQ7I6KUXjcCsHixf+89rvc4+kf1J6s0i20nt+kSwwArVug/oF2Asr1lHP61DpIPf2U4wb2D3fZ79PBhSqxWroiP5/bEREArTqan60rtD/66gPtX3g/AX2wz6f3FN5CUBM88458HMRgM7UK3MyJQZ0Q++ABKSz33bU+UUvVdWoMGadnckhL/T4tagYhw8IGDSLXQ584+9Px+T7f9NhcX80Z2NsFK8eyQISilOHKkLjvuhRfg8Y2/JKcsh/MSp3HHE3Y31osvGjeWwdDF6JZGJCVFhyPKy/3vSXJ1aQFdyqWVvyKfglUFBEQHMOjPg9z2ERHuP3gQgAeSkhgcFqZfP6A/7xtugLixm3gp/SWCLEH8e+dALBWVelZmVqQbDF2ObmlEoC7A/uab/r3vjIEziAiOYEf2Do4VHoMr9Myks89EbNU2Dj6ojcPAxwYS3Mu9G+vtnBw2FReTGBzMbwYMAGDrVl32Kjwcnn0Wfpf2OwAeTr2D1H+/r6PsDr0Vg8HQpei2RuTaa3U5lDVrdBkrfxESGMIlg3XgeOXBlTB2rF69fuiQfwfSQjL/mUnF/grChoXR795+bvuUWa386tAhAP48aBCRgVo401EA89574WD1l6w5vIaokCge/jBHp8jddpsRlTIYuijd1ojExcHZZ+tMIX9PAs5NPheAb059A0FB2pCAFlnqhFTnVnP0D0cBGPK3IViC3X9t/p6RQWZ1NZMiIrjVHkzftEnnDfToAb/4BSxYtwCA+wdcT9xbH9Qvs2wwGLoc3daIAFx8sd5/+ql/7zshcQIA32TZ69vYawzhx3o3LeHYE8ewFlmJvSSWuMvi3PapsFp5zl7m4qmUFCz2tF+HffjZz+C78i/47MhnRIdE88CSo7rh3nt1upbBYOiSGCOC/43I+MTxAOzM3kmNtaZTG5Hq7GpOLToFwOC/Dm6y2NzrWVnk1NQwKSKCi2JjAdiwQX+2kZHw0EOw4PMFAPy831xil6/WDY8+6pfnMBgMvqFbG5GJE7Vb68gRHZLwF9Gh0aTEplBlreK709/BpEm6Yds2/w3CSzIWZmCrtBF/ZTwRYyLc9rGK8LS9ouovk5OdhsYxC7n/fthdup61R9YSHRLNz1fk64b77oNevXz+DIauhTeytydOnODCCy8kNTWVUaNGsXDhQrf9uro8Lnj3eRh5XD/WzmrIddfpck3PP9+q01vNvP/OExYgr6W/JlJZKRIYKKKUiF0KszNQU1gj66PWSxppUrix6VpW/83OFtLSZPDGjVJrs4mIyNat+nONihLJzxe5ZPElwgJkwbIHRQIC9JbRdM0tQ+vpyrWzvJW9PXnypGzbtk1ERIqLi2Xo0KFnpDyut5+HkcftQDo6LpKela6zs0aP1qXhd+zw70A8kPl8JtZiKzEXxhB9lvtFgCLC/zt+HICH+/cnwD4L+de/dPvtt0MBh1l1aBUhASHct1mB1QrXXAP93Gd5Gc4MfCmP26dPH6deSWRkJKmpqR6VDbuqPK43n0dHy+MG+u1OnZRZs/R+7VqoqdHJUv6gnhEB7Vvbvl3HReziPR2JtdxKxrM6UJ78aNOB77TCQraVlpIQFOTMyCoq0gUuQYs4Ltq2CIDrRswl7l57rZn77vPd4A1O1B+aF0xqDfKYZ0Eehzzuu+++S0pKCiNGjGDSpElOeVx32htPP/00hYWFjWRvv/76a4/3Onr0KOnp6Y1kY11pizyuiDBt2jQuuOACYmNj2bdvHy+//DLnnHMOt99+u1Med9euXWxvIsPS0zPPnDmznsTtjh07mDRpEgsXLnQrA9zw82jq3B49enj9vG3BpzMRpdRspdQ+pdRBpdQjbtoHKKU+U0p9q5Rap5RKcmmzKqW22zefKTclJ2v99eJi2LzZV3dpzMQ++lfU9qztuhhjJwuun3r5FDW5NUROjiR2ZmyT/f5qj4X8LCmJMLu4z+LFenX6hRdCytBqXtmuteTvKRgMOTk6pfncc33/EIYOw9fyuA5KS0uZO3cuzz33HFFRUU3266ryuN58Hh0tj+uzmYhSKgD4JzALyAC2KKWWicgel25PA2+IyOtKqe8BTwL2teRUiMh4X43PlYsvhu++0y4tf00Cekf0pk9EH06VnuJwwWGGOILrncCI2GptnHhaG4fkR5Ob/E98rLKSVfn5hFos/NguTSpS58r60Y/go+8+Iqcsh9EJozn75VW64b77dCVMg89pbsbgK5qTx23qV3lLZG9ramqYO3cu8+fP55prrvE4np07d/LAAw843zvkca+44gquv/76RuXg3f3xdtBaeVxPMxF3ErdPPfUUl112WbOfR1Pn+gtfzkSmAgdF5LCIVAPvAFc16DMS+Mz+Os1Nu1/osLhIH7tL61S6/nVuscDu3VBR4d+BNCD/k3yqjlcRNiSMnle7L7IIsDgrCwHm9OxJnN0PuGGDfoTevXVZsH9v+zcA9/Scjfp6M8TGwg9+4I/HMHQgvpbHFRHuuOMOUlNTG2VanUnyuN58Hh0tj+tLI9IPOOHyPsN+zJUdwFz76zlApFIq3v4+VCm1VSm1SSl1tbsbKKXutvfZmpub2+qBXnCBjoVs3gwFBa2+TIuZmKh/qaVnpevCUqmpOui8c6f/BuGGUy/qdSF97u6Dsrj/lSUivJaVBcBt9lgI1M1C7rgDjpUc4LMjnxEWGMZNKzPrGsLDfTd4Q6fgBz/4AevXr2f48OGMGzeO6dOn8/Of/7zZ8wIDA/m///s/LrnkElJTU7nuuusYNWqUs/2yyy7j5MmTbNiwgcWLF7N27Vpn2u6KFSuw2WwcPHiQuLi6RbEHDx4kKSmJkJAQ57GkpCSnkbPZbI3GMXHiRG677TamTp3KtGnTuPPOO5kwQf/oS01N5fXXX2fs2LHk5+fz4x//mPj4eM455xxGjx7tDKw7xuot//jHP5g/fz5jx45l+/bt/PrXv/b4ebhe3925fqMtqV2eNuBa4CWX9zcD/2jQpy/wAZAOLEQbmmhHm32fAhwFBnu6X2tTfB3MmKFTUt9/v02XaRHv73lfWIDMfnO2PnDzzXoQL7zgv0E0oOJ4haRZ0mRd0Dqpyq5qst/6ggIhLU36bdjgTOvNydFqv0qJHDki8vCqh4UFyA/fv1kkMlI/2/79fnqS7ktXTvFtK0Ye1zO+SPH1ZXZWBtDf5X0SUM8si8hJ4BoApVQEMFdEilzaEJHDSql1wATAZ0sCZ8yAdeu0O6YZ92q74Sx/cuobRAQ1aZKOSndgXCTrlSywQc95PQlOcF+pF3DOQm5JTHSm9S5erNV+L78c+vav5rV3XwPgnvKRULJYL6ocOtTnz2DovrRUHtfQdnzpztoCDFVKDVJKBQM3APWyrJRSPZVSjjE8CrxiPx6rlApx9AHOAVwD8u3O2Wfr/Vdf+fIu9RkYM5CY0BhyynI4VXqqwzO0xCqcekm7svre7T6YCbpa73/t7sNbXVxZ776r97feCmsOr+F0+WlGJ4xm6nL781x/vW8GbjD4CSOP2xifGRERqQV+CqwC9gL/FZHdSqnHlVKOyNAMYJ9Saj/QG3CISqQCW5VSO9AB96ekflZXuzNtmk4Y2rYNKit9eac6lFJ160VOpcN4ezLazp36J72fyV+ZT1VGFaGDQ4m5sOnFSh/k5lJqtTI9Korh9vjGiRO6Ym9YGFx2Gby/530Arh1yFep/H+sTr7vO589gMBj8i0/XiYjIChEZJiKDReRP9mO/F5Fl9tfvichQe587RaTKfvwrERkjIuPs+5d9OU6AqCgYM0YvONy61dd3q8PVpUVkpHb3VFfrnGM/c/JF7W3se1ffJgPqgNuA+vvaZnD55RASVstH+/Sq2rkno/WikenTwS5SZTAYzhy6fdkTVzrCpeVM83WsXB82TO8PH/bfIICqzCry/peHClIk/jCxyX7HKitZW1hIqMXCdS7FE997T+/nzYPPj35OXkUeI3qOYOSHG3TDDTf4cvgGg6GDMEbEhY4wImN7a0GqPbl2b90gu3b5kSP+GwSQ/Wa2Dqhf5TmgvtQeC7kiPp4Y+9qQzEydkBAaqmci7+3RFmVuyvdRKz7RfsJ583z/EAaDwe8YI+KCqxHxsGC1XUmJTQHgaOFRXf7EYUT8PBPJeScHgN439fbY76O8PACu7lm3CPGDD/T+0kshLNzK0u+WAjA3I0q75i64AJpYdWwwGLo2xoi4kJICCQmQm+s/fZGI4AgSeiRQZa3iVMkpPQjw60ykfF85pdtLCYgOIG62e+VCgPyaGr4oLCRQKS5zWczl6sr66sRXZJdlMyhmEOOX2qd0JivLYDhjMUbEBaXqamf506U1KEbPPg4XHO6QmUjOf/QspNecXlhCmv5KfJyXhxW4IDra6crKyoIvvtDV7L//fXh/r46wz0v5Pmr1GggIgLlzm7ymwWDo2hgj0gCHS2vDBv/d0+HSOlJ4pH5MxA8+NRFxurJ6Xe9ZZXCZ3ZUoHIJAAAAgAElEQVR1VQNXlghccglERNqcRmRuQR+ordXVeo16ocFwxmKMSAM6IrjuMCKHCw7rXOP4eL1YxZ5K60vKdpVRvrecwPhAYi9quuR7lc3Gynwta3ulixFxdWVtydxCRnEGSVFJTPnC7g+cPdtnYzecmXgjB+vAarUyYcIEvv/977tt70ryuAMHDmTMmDGMHz+eyZMnA7Bv3z7nmMePH09UVJRTIKvh/TtKHrfbi1I1ZOJECA7WlWgLC8EfAmH13FmgZyN5eXo20qePT+/tnIXM64UlqOnfFGsLCii1WhnXowcDQkMBKCnRriyLRbuynv5GFyS4ZsQcLM9+qE+85BKfjt9wZmG1Wrn33ntZvXo1SUlJTJkyhSuvvLLJqrQLFy4kNTWV4uJit+133XUXd911F5mZmZx99tlNika1FYcR+clPftKm66SlpdHT5Ufa8OHDnWO2Wq3069ePOXPmNDrv/vvvZ/bs2bz33ntUV1dTXl7epnG0BDMTaUBoqC7xJALNCKq1G/XcWeC34LqrKyvh+gSPfT86fRqo78r6/HPtsZo6VVd4X3NkDQCzQ0bpJewJCTBunI9Gb+js+FIeF3Q5948//pg777yz2bF0dnlcb/jss88YPHgwAxos2jXyuJ2Qs8+GjRu1S8sfP6TrubPAb8H1km0lVB6uJDgxmJjzm/7S2UTcxkNWr9b7WbOgoKKArSe3EmQJ4rwdhbrh4ov1NMXQYfhK+6u5cJ0/5HF//vOf85e//MWjjoeDzi6PC7oM0sUXX4xSinvuuYe77767Xt933nmHG2+8sdE1zmh53K6Kv+MiSVFJBFoCOVlykoqaCr/NRJyurOt6oQKa/muztaSEU9XV9A8JYUJEhPP4Gj3xYNYsWHd0HTaxMb3/dCI+XacbjCur2+Jredz//e9/JCQkMMmhCNoMnV0eF2DDhg188803fPLJJ/zzn/9k/fr1zrbq6mqWLVvGtdde2+jaHS2Pa4yIG846S++3bAE3ejXtToAlgAHReop6rOiYX2YiIsLp97WLKuE6z66sZXZX1pXx8c7/0JmZsGcPREToz2vNYW1RZvafof1cUCcZaegwtIhL+2/N0Zw8rmuw2LGtWbPGa3ncDRs2sGzZMgYOHMgNN9zA2rVruemmm5ocT8OZiEMed9GiRSxbtqxRf3fGzEFr5XGbemYHjudMSEhgzpw5bN682dn2ySefMHHiRHr3brwY2J087jd+rARu3Flu6NsX+vXTfygPHIDhw31/z0GxgzhUcIjDBYcZMcheP8uHM5GyXWVUHq0kKCGIqOlRHvuutss9Xh4f7zzm+O7PmKFVIT87olWOZxbFaXnfCRN0TMTQLWlOHrcpamtrnXKw/fr145133uHtt99u1O/JJ5/kySefBGDdunU8/fTTvPnmm4CWx33jjTfo108LqTYlj+uYmTQlj3vbbbfxyCOPICIsXbqUxYsXA3XyuNOnT2+RPK4nysrKsNlsREZGUlZWxqeffsrvf/97Z/uSJUvcurKgvjzu8OHDzyh53C7N1Kl67/JjwKekxLjERZKTdSzhxAmflYTPW6ZjHPFXxHus2FtUW8vWkhICleK86GjncUc8ZOZMOFF0gn15+4gMjmTKV8d0g3FldWt8LY/bFF1VHjc7O5tzzz2XcePGMXXqVC6//HJm29Pjy8vLWb16Ndc0UMs74+Vx/b21VR63IU8+qSfuP/1pu162SZ764ilhAfLgygf1geRkPYADB3xyv61Tt0oaaZL7Ua7Hfstzc4W0NDl72zbnMZtNpHdvPbzdu0VeTX9VWIBc8fYVIqNH64a0NJ+M29A8Rh7XyOM2RVeTx+3S+HsmMijWvlak0B4HSUmB48e1S2vIkHa9V9WpKko2l2AJtRA7s+kFhgBphTrT6nuxdf127oTsbO32S02FPy+1x0PiJsOu5TpQ4shOMBj8iJHH9T/GndUEkybp9Mjt26Gqyvf382eab97/tCsrdlYsAeGN/cGurLUbkQtd8s5dU3tB6uIhx+zXuvBCvWLTYDjDMPK4jTFGpAmio2HECB2S+PZb39/PueCw4IjODPFhmq8zHnJlvOd+NTVsLy0lRCmmR9UF312NyJ7cPWSVZtEnog+pGw/ohosuavcxGwyGzokxIh7wp0srNjSWqJAoSqpLyKvI89lMxFpmpWCNzraK/75nI/K5fRYyPTqaMHsGS2UlONLXZ86sS+29KOUi1Ff2ej2OUsgGg+GMxxgRD0yZovf+MCJKqfouLR8pHOavzsdWaSNyWiQhiSEe+661p/Z+z8WV9fXXOoN3zBjo3buu1MnMXtNg/34IDzelTgyGboQxIh7we5qvi0vL6c5q55mIw5XV88qezfSsC6q7xkMcq/jPPx9sYuOLYzr//XtZYbph6lS9cMRgMHQLjBHxwNixOj783XdQVOT7+9Wr5tu7N4SFQX4+NFGhtKWIVZxB9ebiIVlVVewpLyfcYmGqSzzEUWF6+nTYd3ofRVVFJEUl0X+rPR5isrIMhm6FMSIeCAmB8eP1661bfX+/eu4spdrdpVW8pZia3BpCB4XSY5Tn4mzr7LOQc6OjCbYXURSpb0Q2ZWwC4Kyks+pUvIwRMRi6FcaINIM/XVqOmYizJHw7B9fzP9GiUnGXxTVb72etm/Uhhw7B6dO6msmgQS5GJHGyLjQG2roYDIZugzEizeBPI9LkWpF2mok4jEj8pZ5dWeCyyNAlHuI6C1EKNmXajUhZrF5Mk5oKLuUmDAbDmY8xIs3gTyMyIGYACsXxouPU2mrrjMjRo22+dnVuNSVbS1DBipgZngVrsqqqOFhRQURAQL3S765GpKSqhF05uwi0BDJxt87iMq4sQ3vgrTyuN5KwXUke9/bbbychIaGR7ok72VxXTpw4wYUXXkhqaiqjRo1i4cKFbRpHi2lLzZTOtLV37SwHVqtIdLQuB3XihE9uUY9+z/QTFiCH8g+JLFmibzxvXpuvm/VmlqSRJttnbW+274f2elnfS0+vd3z8eD2czz8XWXt4rbAAmfTvSSJz5+qGV15p8zgNbacr186qra2VlJQUOXTokFRVVcnYsWNl9+7dbvvecsstsmjRIhERqaqqkoKCgiavm5GRIcnJyT4Zs0j71NT6/PPPZdu2bY2uM2DAAMnNbbrG3cmTJ2WbvbZdcXGxDB06tMnPzBe1s8xMpBkslrrZiD/kcpOjkwHILM6ExER98NSpNl837xOdlRV3afPupk32bLCzXLKySkv1yv3AQJg82TWoPs0E1Q1u8aU8bkslYbuCPO75559fr/qwt/Tp08ep3RIZGUlqaiqZmZmtGkNrMAUYveCss3Spj6+/hrlzfXuvvpFamOZkyUnoY08Ny8pq0zXFJhSs0i6n1hoRh0DXhAl6PaEzHhIyRI8vLg6GDWvTOA3tj1q3zifXlRkzPLb7Wh63pZKwXUEetymak8115ejRo6SnpzsFqvyBT42IUmo2sBAIAF4SkacatA8AXgF6AfnATSKSYW+7FfitvesfReR1X47VEw6lw02bfH+vPhF9ADhVegpGXqoPnjql82tbKZhdsq2EmtM1hA4MJXx4uMe+VhG22I3INBcj4lhkOH26doE6ZyLH7VoMZ5/tO0FvQ5fDVR4XaCSP2xTvvvtuo2PuMgkdkrD/+Mc/mDZtGvfffz9PPfUUTzzxhNvr7tq1i1m6YiigRaB+8pOfEBwczIwZM5g/f369/q7yuIBTHvfKK69sJI/797//nXnz5nn6OJoVpfLEhg0b6Nu3Lzk5OcyaNYsRI0Zw/vnnN+pXWlrK3Llzee6554iK8iw01574zIgopQKAfwKzgAxgi1JqmYjscen2NPCGiLyulPoe8CRws1IqDngMmAwIsM1+boGvxusJhztr61aoqfHtgux6M5HISL3gsLwcSkqglV8MZ2rv7OZTe3eXlVFmszEoNJQEl0q8jpjl2WfD0cKj5JTlEB8Wz+AtB3WDqZfVKWluxuArmpPHbepXubfyuO4kYT0F4Xfu3MkDDzzgfO+Qx73iiiu4/vrrGxkRHSpwT2vlcVs7E3Enm9vQiNTU1DB37lzmz5/fSLzK1/hyJjIVOCgihwGUUu8AVwGuRmQk4PiXTQM+tL++BFgtIvn2c1cDs4ElPhxvk/TsqSU9Dh6EXbu0S8dX9Il0mYkoBX366HUiWVltNyKtdGWJ1M3Cpk+HjS6LDNXbLtbFYLDja3lcT5KwXVEetymak80FbfDuuOMOUlNT2z3rzBt8GVjvB5xweZ9hP+bKDsARZZgDRCql4r08F6XU3UqprUqprbm5ue02cHf4y6XlcGedLLHLavbR71sbXK/Jq6F4c7FO7f2e59ReqDMirq6sAwcgL0/H+QcMaLDIcPdubewmTWrV+AxnJv6Qx3UnCdtV5XEBbrzxRqZPn86+fftISkri5Zdf9iib67j+hg0bWLx4MWvXrnWmMK9YscLr+7aZtqR2edqAa9FxEMf7m4F/NOjTF/gASEfHTjKAaOAXwG9d+v0OeMjT/XyV4uvgH//QWay33OLT28i3Wd8KC5DU/0vVB+bN0zdesqRV18taolN70y9Kb76ziIz8+mshLU02FRU5j732mh7CnDn6/dRFU4UFyOpP/qkbRoxo1dgMvqErp/i2FSOP65muJo+bAfR3eZ8E1DPLInISuAZAKRUBzBWRIqVUBjCjwbnrfDjWZvHbTCSywUzEkebbygwt13hIcxTW1LCnvJxgpRjvssjQ1ZVVVVvF9qztKBRTjtfqBkeBMYOhgzHyuP7Hl+6sLcBQpdQgpVQwcAOwzLWDUqqnUsoxhkfRmVoAq4CLlVKxSqlY4GL7sQ5j7FgIDdWSGfn5vrtPfFg8QZYgiqqKKK8pb5M7S2xC/irvS51ssft0J0REEGKp+2qkp+v9lCmwPWs71dZqUnulEv3tft3gyyCRwdCJMPK4jfGZERGRWuCn6D/+e4H/ishupdTjSqkr7d1mAPuUUvuB3sCf7OfmA0+gDdEW4HH7sQ4jOLjO7e/LEihKqbrgesmpNhmR0h2l1GTXEJIUQvhIz6m9AF+7CapbrXXywOPGQXqWtiiT+06usy7GiBgM3RafrlgXkRUiMkxEBouIw0D8XkSW2V+/JyJD7X3uFJEql3NfEZEh9q1TzDsd63d87dJypPmeKj3VJneWa1aWN2mITQXVKyp0QD02FnZk7QBgXK8xsEO/Nu4sg6H7YsqetABHXMTX5U/qZWi1YSaSv9L7eIiIuE3vdUw2HHZiR7Y2HGNr46GsDPr1g169Wjw2g8FwZuAxsK70z9ep6PRaQQfGN9sj+t0OVyNis+m6Wr7AORMpOQWDLtAHW2hEaotqKfqqCBWoiL0ottn+hysryautJSEoiIGhoc7jjioO48drOdxvs7Vva1yGPahuXFkGQ7emSSOilLoYeB44ADiqeSUBQ5RSPxGRT/0wvk5FUhL07QsnT2o3z/DhvrlPvZlIz57aWuXlQXW1Ds54QcFnBWCFqPOjCIxuPgnP1ZXl6vpyNSKHCw5TVlNGn4g+9Np5SDcYI2IwdGs8/ZZeCMwUkUvt8Yo7RWQ2uoyJnwvWdw6U8k9cpF5MJCBA660DZGd7fY2WpPYCpNszsyZHRjqPidR3ZznjIYnjTFDdYDAAno1IIHqtR0MyAR9Wj+rcONRfHdXPfUGjtSItjIuISIviIQDppaUA9USosrIgNxdiYnRg3REPGZcwtnGwxGAwdEs8+TleQRdNfIe6EiT90es9Xvb1wDorjrpn69f77h71ZiLQ4gyt8j3lVGVUEZwYTMT4iGb7i4jTiLguMnR1ZSnlYkRCBtRZl4EDvRqTwWA4M2lyJiIiTwLzAQVMB862v55vb+uWTJyo9TT27WuRd6lFOMvBl9iNSAtnIg4BqthLYr1K7T1RVUVBbS3xgYEkudQXcjUi4OLOylF1Dab8u6Gd8VYe99lnn2XUqFGMHj2aG2+8kcrKykZ9upI8rjfP7e1n41e8qY0CxAGxbamv4uvN17WzXJk5U5eMevdd31zfarNK0ONBwgKkvLpc5Le/1Td87DGvzk+/KF3SSJOsJVle9XfI4c7cXl8699pr9W1fe02koKJAWICEPBEiNY8v0A1e1Cgy+J+uXDvLW3ncjIwMGThwoJSXl4uIyLXXXiuvvvpqk9ft7PK43jx3S6SDm8Kv8rhKqWSl1DtKqRzga2CzUirHfmygPwxcZ8Xh0vr8c99c36IsJEZoF1ZWaVaL3FnWCitFXxSBgrhZ3sVDtrtxZUH9mYgjtXd0wmgCd+ysazAYmsCX8rigy8ZXVFRQW1tLeXm5W90RB51dHteb527JZ+NPPMVE/gM8h3ZfWcEpNHUt8A5wlu+H1znxV1zkRPEJTpacZFAL3FnFXxUj1ULExAiC4r3Lf0h3qZnloKRE66cEBUFqKvw73e7K6j0O0tfpTiYzq9OzTq3zyXVnyAyP7b6Wx+3Xrx8PP/wwycnJhIWFcfHFF3PxxRc3OZ7OLo+bmZnZ7HN706cj8GREeorIf1wP2I3JO0op9xqU3YRp0/RyjZ07dTHGOO9+8LeIeuJUfexSKl4YkYK1Wvwx5sLmtUMcuMvM2rlTp/iOGqWf1RlUjx4Gh1+BkBBwEfkxGFzxtTxuQUEBH330EUeOHCEmJoZrr72WN998k5tuusntdTu7PK64Wb/d8Lm96dMReDIi25RSzwOvUz8761a0/ke3JTRUG5IvvtCpvldc0f736BvhIpObaK/86IU7q3BtIQCx32t+lTpAfk0Nx6uqCLNYGBZeV6SxUVDdYUSK7X1Gj/atTrChXWhuxuArfC2Pu2bNGgYNGkQve8mda665hq+++qpJI9LZ5XG9eW5vPxt/48mI3ALcAfwBXfZEodeNLKMbp/g6OP98bUQ+/9w3RqReJd9xdndWVpaeHjTxpa0tqaV4SzEEQPR50V7dxxEPGdujBwFuVqpPmAC1tlp25ejy12Mza3RDC/3Lhu6Fr+Vxk5OT2bRpE+Xl5YSFhfHZZ58xefJkoGvK406ZMqXZ5/amT0fgKcW3WkReEJHZIjJGREbbXz8vLtV2uyu+jos41oqcLD2ppz4xMVBTo8ufNEHRF0W61MnUKAIjvdMbc7qyXFaqQ/2ZyIG8A1TWVpIcnUzsd8d0Q2pqC5/I0J3wtTzutGnTmDdvHhMnTmTMmDHYbDbuvvvuLiuP6+m5Hddp7rPpMJpK2wLCgV+ipWpD0W6sZcBfgIi2pIT5YvNniq+ISEmJSECA3oqL2//6K/avEBYgs96YpQ+MGKHTanfubPKcAw8dkDTS5NCvD3l9n5v27BHS0uRfmZnOY7W1IqGh+nYFBSJLdi4RFiBXvH1FXX7z8uWtfjaDb+nKKb5txcjjesavKb7Aa2ihqEHAx8AU4Gm0W+sFH9m0LkNEhBapslrhq6/a//qtKX3S0ngIuM/MOnwYKiuhf389AXIuMuw9Dvbu1Z3MTMTQCWmpPO4LL7zQKB5iaBmefB7DROQ6ezn4U+hijKKU+gLY4Z/hdW7OP1+rHK5fD5dc0r7XblT6pBkjUpNfQ+n2UlSwIursKLd9GlJhtfJdeTkWYLQ9CwVgzx69HzlS73fn7gZgTORgyMzU7jVT7sTQDTHyuI1pVhHDPt1ZYd873ndLPZGG+HLRYc/wngRaAsmvyKeytrLZBYeFnxeCQPTZ0QSENQ4UumNXWRlWYER4OOEuwUXHZMNhRPae1gdGFtnL0I8YoasLGwyGbo8nI7JVKRUBICK3Ow4qpQYDTachdCPOO09LfXz9tV6c1540WrXezEzE4cpq6/oQqD8Tqaqt4nDBYSzKwtDjur9xZRkMBgeesrPuFJFSN8cPAef5dFRdhJgYrXZYWwtr17b/9Vsik+tcZPg9741IU+VOHEYkNRUO5B/AJjZSYlMI2XtANzimKAaDodvjlcCrUmqE697h2jLA7Nl6v3Jl+1+7nkyuw53lxohUZ1dTvqccS7iFqKnexUOgzoi4pvfabPVj59+d/g6AET1HmKC6wWBohLcq4W832BvsuBqR9jatbmcibmIip5efBvQCQ0uwd/+kIsKusjJALzR0cPw4lJdrmxUXB3tzteFI7ZnaOOJuMBi6Pd4aEQcdX6ilkzFxIsTHw9GjsH9/+167XoaWB3dW1mvasCTckOD1tY9XVVFitZIQFEQvF932hkH17/LsM5GoQfohAwNhyJAWPonBYDhTaakRMTQgIAAcxUPb26XlCKxnl2brAExgoI7gV9UVDCg/UE7xhmIsPSz0mtfL62s7ZiGuqb1QPx4CLjOR0jA91Ro61NTMMhgMTowRaQd8FRdJ6KFnFjnlObpelr3YHLm5zj7OWci1CQRGeFfqBJo3IiNHgk1s7MvbB8CIzOq6BoPBYLDTUiNiAupucMxE1q2Dior2u67DiGSX2nV4GxgRsQrZb+i2xB8mtuja3hiRE0UnKK8pp3eP3sTuP64bTFDd4GNuv/12EhISmtX/8EYq1sjj+h5vjYhqsDe4kJioq91WVrZvQcbeEb0ByCnL0QccRiRHvy/4rICqjCpCU0K9rtrrwGFExrgYEZH6RqReZpYJqhv8xG233cbKZqb1VquVe++9l08++YQ9e/awZMkS9ji+oy7cddddbN++nY8//pj+/fuzfft2tm/f7lVplJbQViPizfN4+8z+xlsjcl6DvaEBDpfWqlXtd02nO6ssRxfFbDATcbiyEm9LbJE4Ta3Nxl67ERnpYkROnYLiYp2V1atX3Up1k5llaA2tkccFXYY9rhmlt5ZKxRp5XN/RpBNdKfWpiFwM4Fh06G7xoSeUUrOBhUAA8JKIPNWgPRktehVj7/OIiKywa7jvBfbZu24SkR+15N7+ZvZsePJJHRdprx85PYJ6EBYYRkVtBWU1ZUQk2LOvcnOpKazh9NLToCDxlpa5sg5WVFAlwoCQEKIC674CrnZCKZeZSOwQOLhIHxw2rF2ezeAf1q3zjfNgxgzPnu3WyuPOnDnTq/u3VCrWyOP6Dk+RWO9Tfdxg12P/JzALLWa1RSm1TERc51+/Bf4rIi8opUYCK4CB9rZDIjK+LWPwJ9OnQ2SkTpE9dgwGDGj7NZVSJPRI4FjRMbJLs4lwmYnk/icXW6WNmItiCB0Q2qLrehMPAZeZSGWkLlc8eDCEhbX+gQzdhtbK43qLu/XOnmbjRh7Xd3gyItFKqWuaahSRD5q59lTgoIgcBlBKvQNcBbgaEQEcS6yjAe8UXDohQUEwaxZ88AEsXw4//Wn7XLd3RG+OFR0jpyyHwXYjIlm5ZHykBXUSb2vZLAS8NyLOmUi2VR8wQfUuR3MzBl/RWnlcb2ciLZWKNfK4vsOjEQG+j/tgugDNGZF+1Gmzg56NTGvQZwHwqVLqPqAH4PoNGqSUSgeKgd+KSNt/vviYq6/WRuTDD9vPiLjGRbC7s3K+jaF8TzkhA0JIuM77BYYOnEF1D4UX8yvyySnLoUdQD5IOZNc1GAxe0Fp5XG/xJBVr5HH9i6fA+jERuV1Efuhmu93DeQ6aMj6u3Ai8JiJJwGXAYqWUBa1fkiwiE4AHgbeVUo2KQiml7lZKbVVKbc11WTvRUVx+uV58uG4dFBS0zzUTwl2MSK9eCBaO7ZkCwIDfDPC6zIkrO5uYibirmTW853As3+2razAYvKC18rgAN954I9OnT2ffvn0kJSXx8ssvO9uak4o18rgdQFOSh0B6WyQTgenAKpf3jwKPNuizG+jv8v4wkODmWuuAyZ7u52953Ka46CKtHvvGG+1zvUdWPyIsQJ74/AmR776TLL4naaTJxoEbxVplbfH1ymtrxZKWJgFpaVJRW+s8npOjxx0ZKWKziby07SVhATL//fkikybpxg0b2uehDD7FyOMaedym8IU8rid31s1ttE9bgKFKqUFAJnAD8IMGfY4DFwGvKaVS0VruuUqpXkC+iFiVUinAULuB6fRcfTV89pl2ad3c1k+Q+mtFJK4nx7gFgOTfJLdqFvJdeTk2tBBVqMs0vsnMrPjhcGC5bjQ1swydnJbK4xrajic9kTZpQIpILfBTYBU6Xfe/IrJbKfW4UupKe7eHgLuUUjuAJcBtdst4PvCt/fh7wI9EJL8t4/EXV12l9ytXts/qddeYSM6qGsoZQCinSLzBex11V5oKqjes8u7MzArppxePREXVrVMxGLopRh63Md4XW2oFIrICnbbreuz3Lq/3AOe4Oe994H1fjs1X9O8PkyfD1q2wejVceWXz53jCYUROF57m6NPHABjAm1iKzoeIfi2+nruV6lBXgXj4cL13zERSi+1+5KFD9RTFYDAYXPDoD1FKBSil3vTXYM4Urr5a7z/8sO3XchiR6UumU7GvgrDgHHqzyln6pKU0FVQ/YBctHDZMS+IeKTyCRVkYfNI+nRo6tHUPYDAYzmg8GhERsQK9lFLBnvoZ6uMwIsuWaencttC7R2+m7Z/GRWsvQgUqUscsx4K1XiXfltCUO8sxExk6FI4UHsEmNgbGDCTk4NG6BkOXQYz4qKEBvvpOeBOZPQpsUEr9Tin1oGPzyWjOEEaO1H9z8/Jgw4a2XSuiMIJHPnwEgAFPDCBqqN0qtcKIFNXWcqKqihClGOyy8rymBg7b0xaGDIEDeXpaMiRuSN0UxRiRLkNoaCh5eXnGkBiciAh5eXmEhrasuoU3eBMTOWnfLEBkM30N6NDB1VfDX/8KS5fCBRe07jpiFQ7ceoCY8hi2pGxh+E+Gw28ba4p4y277LCS1Rw8CXOIbR4/qGVNysq5qcjD/IABD44bCga90J2NEugyONRCdYe2UofMQGhpKUlJSu1+3WSMiIn8AUEpF6rctK8LYXZkzRxuRDz+EZ59teUzaVmNj/937KVxbSHFkMU/OeZJLKi6hT4Ny8C1hj92IjAoPr3e84WTDYUSGxA6GA6/XbzR0eoKCghg0aFBHD8PQTWjWnaWUGm0vP3AuFI8AAB1YSURBVLIL2K2U2qaU6gTLJDs306ZpWfRjxyA9vWXn1hbXsvPynWS9loUlzMKHP/6QgsgC56p1oHUzkfJyAEY1EQ9xFOg9kG93Z1l6QmkpxMZqIXmDwWBogDcxkReBB0VkgIgMQK/tWOTbYXV9LJa6APsHzVUZc6Eqs4r089MpWF1AUEIQ4z8fT/kU/cfftX5Wa4yIcybSjBFxurMK7F8PMwsxGAxN4I0R6SEiaY43IrIOXSzR0AzX2GsgL13afF9rmZWjfzzK5tTNlO0oI2xYGBM3TiRqSlR9mdw2uLMcMZGRHtxZ1dZqjhUdw6IsDMwsrWswGAwGN3gTWD+slPodsNj+/ibgiO+GdOZwwQXaE7RnD+zbV7eQz5XqnGpy3snh2J+PUZNdA0Dc5XGkvp5KUHwQoNN8wT4TSWqdO6uotpbM6mpCLRYGNdAEcZ2JHC082ji915Q7MRgMTeDNTOR2tEDVB/atJ/BDXw7qTCEoCK64Qr92zEasFVaKtxRz4rkTpF+Qzld9vuLg/Qepya4hcmok49aOY+z/xjoNCLgvB99SI+JwZY0ID6+XmVVRAcePQ2AgDBxYl96rM7NMeq/BYPCMJ3ncxSJyM3CLiPzMj2PqEohVsNXYkBrBVmXDVqE3a7mV2sJarEVWagpquMFWTQxVRPy/aja/Xk75/nJwqTytghSxl8TS584+9JzT063AjdOIlOdATIyuN19UBNXVEOzdOtA9jqB6A1fWQR3+ICVFGz1nZlbcEDho0nsNBoNnPLmzJimlBgC3K6XeoIE+SGcriFi6o5QNiV6s7BM3r+17EdGv7ZvzvQ3EJohVwKoNSCNllCYIA+YAFEJ5IRAA4aPCiZwQSdxlccRfFk9gtGevYr2YiMUCPXtCdraejfTzrn6WMx7SRLkTt+m9B9+o32gwGAwN8PTX61/ASiAF2EZ9IyL2450GqRVnTMEvKD2LUEEKS4gFS5iFgLAALOEWAmMCCYwOJDAmkODEYN5aFcJn3wZz08Nh3P5EOAGhjZXUPOFaDh7QwfUWGhFvM7Mc6b1DVTyUlenU3tjWVQw2GAxnPk0aERH5O/B3pdQLIvJjP46pVUSMjWD6qule9a3nMlKN90op/V6BsthfW0AFqHqbtwweB4/dBJatcFcrqg64xkREBNWKuIhjjUjDzKym0nuHmPReg8HgBd6sWO/0BgT0rCAkMaT5jh3A5ZfreMP69ZCfDy7KnV7RI6gHYYFhVNRWUFZTRkQLFxwW1daSYa+ZldIgM8vVnVVjreFo4VEUikGZZXUNBoPB0AQtl8YztJiYGDjvPLDZ4NNPW36+UqpNa0X2NpGZBY3Te61iJTk6mVBTvddgMHiBMSJ+4rLL9H7FCs/9mqJeXKSFM5Gmyp0UFmo7FBamQyv1MrNMeq/BYPCCJo2IUqpEKVXcxJarlNqklLrIn4PtyjiMyCef6BlJS2nLWpE9XmRmWSzGiBgMhpbjSWM9UkSi3G1AInAPsNBvI+3ijBihF/OdPq2lc1tKQriLEWnpTMTL6r3Owouxg+HQIX3QrFY3GAweaJU7S0SsIrID+Ec7j+eMRam2ubScMZGylsdE9nhZvddZeFHF66XsPXtCdHTLB2swGLoNbYqJiMi/22sg3YG2GJF6MZEWuLOKXdQMG2ZmNZneW2RP2hs8uOUDNRgM3QoTWPcjF14IISGwZYteK9gS6sVEWuDO2mufhbjLzHJ1Z9XaajlSqOtqppyq1A0pnWo9qcFg6IQYI+JHwsO1IQFYtapl59ZzZ8XG6vpZhYW6fpYHmip3IlLfiBwrPEatrZb+Uf0JO5qhG8xMxGAwNIMxIn6mtS6tejMRi6VOafD0aY/nNaUhkp+vazhGRuqJTb3MLEdQ3cxEDAZDMxgj4mcuvVTvV62C2lrvz3NoimSX2v1gXsZFdtmNyJiIiHrHHbOQIUN00N9hRAbHDobDh3WjmYkYDIZmMEbEzwwZogPZhYWwaZP35/UM74lFWcivyKfGWuN1XMRhREY3cGc5SsA7MngPFejZh5mJGAyGlmCMSAfgmI2sXu39OQGWAHqG90QQcstz62YiHtJ882tqOFldTZjFwqDQ+pUfHUbEsUbEYURSwvpowxQSAn37ej9Ag8HQLTFGpAOYMUPvP/+8ZeclRiQCdpeWw4h4SPPa7VL+3dIgM6vhTORwgXZhDS61i1wNGqRjLwaDweAB81eiAzjvPL3ftAkqK70/zxEXySrNgt76tScj4oyHNHBlQX0jIiJ1RiTXHqgx8RCDweAFPjUiSqnZSql9SqmDSqlH3LQnK6XSlFLpSqlvlVKXubQ9aj9vn1LqEl+O09/Ex8OYMVBVBZs3e3+eYyZSz4h4cGc1FQ+B+oH1rNIsymvKiQuLI/polm4w8RCDweAFPjMiSqkA4J/ApcBI4Eal1MgG3X4L/FdEJgA3AM/bzx1pfz8KmA08b7/eGcMFF+h9S1xazgytMu/cWTubMCL5+Xrr0QMSE11cWSYzy2AwtBBfzkSmAgdF5LCIVAPvAFc16CNAlP11NHDS/voq4B0RqRKRI8BB+/XOGFpjRNzORJowIiLS5Ezk/7d377FxVmcex7/PjK+JE99yIY5zcRLHCbdcSLmUbsQW6FJYEaoWGsq2XRX1si3VttuVSlUJsZUqlVW7rFaqiqjKblvRUhbKQrthKVsC2yZAEsiFhJA4F+fiOHEudhzfY/vsH+cde8b22OOxJzOe/D6S9c6c94zznryOn5zznHPe6L0VzQaS6ovLFmtmloiMSSqDyFzgWNT740FZtEeBvzGz48AG4Otj+Cxm9iUz22Zm206P4VGxmWDtWn/cvHnURef9+hPrbadGHc5q6O6mqaeH0pwc5uTlxZyLl1RfVLJIPRERGZNUBpHhHkLuBr2/H/gP51wlcCfwSzMLJfhZnHNPOufWOOfWzIysm5gkZs2C5cv9ZrmJbg0f2YTxZOvJ2OEsN+SvJiapbqPMzOrviRQvhLo6X1hVlXBbROTylcogchyYF/W+koHhqogHgWcBnHNvAgXAjAQ/O+mNdUgrZorvlClQVOS7MefPD6mbaFId4OC5IIj0TPPL6Csq/OMORURGkcogshWoNrMqM8vDJ8pfGlTnKHArgJktxweR00G99WaWb2ZVQDUwhnlMk8NYg0jMFF8YMS8yUhCJO5x1LujRKB8iIglKWRBxzvUADwGvAHvxs7D2mNn3zOzuoNq3gC+a2U7g18DfOm8PvofyPvA/wNecc72putZ0iQSRTZsS20erfEo5YQvT1NlEV0/XiHmRRIJIdTW0drdyqu0U+eF85h5v8SeUDxGRBOWk8ps75zbgE+bRZY9EvX4fuDnOZ78PfD+V15duc+b4X+S1tfDuu3D9KPPPQhZi1tRZNLQ20NjWyLw4PZE+5/pXqw8OIufP+11NCgv9n7/7tO+FVJVWETrknyeinoiIJEor1tMs6bzICGtFDnd20t7Xx9y8PEpzc2PORXohixf7XU36h7JKNTNLRMZOQSTNxpwXKRp965Ox5EP6k+qlWiMiImOnIJJmH/mIP7711rAzdYeImaEVJycypiAS2b1XPRERSYKCSJotWOBHpc6eHfgdPpJENmFMNKkOUVue5M7yDzmZOnXgWSUiIqNQEEkzM7jhBv/67bdHrx+z9UmcnEgyPZHFLcEci8WL/UWJiCRAQSQDRGZlJbKjb8wmjMMMZ3X39fFBezsGLB9loWFPXw91zXUAVJ3s8ieUDxGRMVAQyQBJ90SGGc6q7eigxzmqCgqYGo7d+PjCBV81Px8qK+F4y3F6+nqomFZB4eFgqzIFEREZAwWRDPChD/nj9u2jb8YYM8V3+nTIy4PWVmhvB2KfZjhYZChr0SI/vXfYmVmRcS4RkQQoiGSAkhKoqfEPqdq1a+S6MVN8zYb0RkYKIvv3+2NNjT/GzMwanCwREUmAgkiGSHRIq7SglNxQLi1dLXRc7BiSF+kPIlOmDPlsJIgsXeqPMQ+jivRENL1XRMZAQSRDJJpcN7P+3khMcj3SEwmGtYabmTU4iPTPzCqaB/X1kJMD8+ePoxUicrlREMkQySTXT7XGbn3S1ddHbXs7IWBZAj2RSE5kUVvw0KqFC30gERFJkIJIhrj2Wj9rat8+v+ZvJPEWHO5rb6cXWFxYSMGgmVnOxQYR5xy15/x83+ozff6E8iEiMkYKIhkiLw9WrfKvt24duW68x+SOlFQ/fdoHp+Ji33lpbGuktbuV0oJSyuuCdSbKh4jIGCmIZJDIkNZoeZF4PZFEk+pm9PdClpQtUVJdRJKmIJJBIsn10fIi8bY+iSTVR5reG8mH1J4NhrLKqzW9V0SSpiCSQaJ7IiPt6BtvdlYia0QiQeTAOR84qsuq1RMRkaQpiGSQRYugvNzP1j16NH694bY+6Whu5mBHB2GgZoThrMhCw/7hrOKFcOSIH+PSliciMkYKIhnEbGALlG3b4teLmeJbXg6hEB8UFdEHVE+ZQn5o6G3dt88f+4ezIjOzuqf5B7zPnQsFBRPVFBG5TCiIZJjrrvPHkYJITGI9FIKZM9mzcCEwfFK9tzf2OSLOuYHhrDPBuJnyISKSBAWRDLNmjT++8078OtPzp1OQU0DbxTZau1th9uyBIDJMPuToUb+xY0UFFBX5XEpkem/ZEU3vFZHkKYhkmOieSLzkupkNPFckeEzuSEFkxJlZSqqLyDgoiGSYyko/a7epCerq4teLWXA4a1ZCQSSSVI+ZmaXpvSIyDgoiGcZsYEgrkeT6iQsnaKuo4NDcueT09VFdWDikbrykuhYaish4KYhkoMiQ1kh5kfnFfrfdI81H2LtgAQBL29rIG2Zm1pDhrMjMrNLFcMhvB68gIiLJ0JatGSiRnkhVSRUAh5sPkzfnowCsinpMbrS4Cw37SqGjA2bM8JtqiYiMkYJIBoruiTjnh7gGqyodCCJHZvsAcPv77w+p19HhZ2fl5EBVVbB7b5BYX3IuqKR8iIgkScNZGaiiAq64wu+6GxltGizSEznUfJSNwTNAbtu0aUi9gwd9IFq0CHJz/dqStottlBWWaXqviIybgkgGSiS5vrBkIQCHegtpc46rDh9m7q5dQ+YFD06qD7tnlnoiIpKklAYRM7vDzPaZ2QEze3iY84+b2Y7ga7+ZNUed640691IqrzMTjZZcLy4oprSglO7p1wLwsffeg85OOHMmpl68pLpmZonIREhZTsTMwsCPgduB48BWM3vJOdc/cO+c+2ZU/a8Dq6K+RYdzbmWqri/TJZRcL62iqdRHm4+dOOELjx6FmTP76+ze7Y/Ll/tj/0LDsmrY/6IvVE9ERJKUyp7I9cAB59wh51w38AywboT69wO/TuH1TCqRnsi770Jf3/B1KkqXw7QacnCs7eryhYO2/92xwx9XrPDHA03BcFbpYti71xdGIoyIyBilMojMBY5FvT8elA1hZguAKuC1qOICM9tmZm+Z2T1xPveloM6206dPT9R1Z4Q5c3yC/fz5gVGnIUpXg4WYz3mmVFT4smMDf+WdnT4nEgrB1Vf7sv6ZWe0FvkJlJZSUpLAlIpLNUhlEhpmYSrxHLa0HnnPO9UaVzXfOrQE+A/yrmQ0ZuHfOPemcW+OcWzMzaggnW4w2pHWuwM/QKu88DPP94sPonsiePX4H35oaKCwctHtvfaevdNVVKbl2Ebk8pDKIHAfmRb2vBE7EqbueQUNZzrkTwfEQ8Dqx+ZLLQmRIa+vWoeecc9Q6vz7EmrYNG0R27vTHyFBWQ2sDbRfbKC8sp3TfEV+oICIi45DKILIVqDazKjPLwweKIbOszKwGKAXejCorNbP84PUM4GZg6Eq6LHfjjf741ltDz+3v6OB0bwi6mzhzegvMC+J1VBAZnA/Z3eiz7MtmLBvIuEfGuUREkpCyIOKc6wEeAl4B9gLPOuf2mNn3zOzuqKr3A884F7PAYTmwzcx2AhuBH0TP6rpc3HCDXzPyzjs+fRHtD+eC5eZN73Ls/BF6K4N0U1ROJNITWRnMcdt50hesvGKlH+sC9UREZFxSuu2Jc24DsGFQ2SOD3j86zOc2A9ek8tomg+Ji/zt+924/S+vDHx4491/BepDpHftp6btI/TTH/FAIGhqguxuXmzdkOGvHKd81WTnzGtj3U1945ZWXqjkikoW0Yj3DRQLH5s0DZfvb23mtuZkpoRA1zs9KO3zhmH9OunNQX8/Ro35m18yZfgsVGOiJrOgu9Y86XLjQP+pQRCRJCiIZbrgg8mSwsPD+WbOoLp4D+I0Yo5Pr0fkQM+js6eSDMx8QshBX11/0JzWUJSLjpCCS4SJB5M03fSejs7eXfz95EoCvVFSwsHghAHXNdTHJ9cH5kD2Ne+h1vdSU11C4N3iaoZLqIjJO2go+wy1Z4h/3cfKkf1zupsLTnOvp4bqiItZMn86OqC3h+3six44NzYecDPIhV6yE14OZWeqJiMg4qSeS4czgppv8682b4YlgKOsrwQr1/odTNcUOZ8ULIitmr9DMLBGZMAoik0BkSOt3u1vZ1NLC9HCY9bNmAbEPp4oEkZaDpzl4EPLyYNky/9mdp4LpveVXQW2tj07aM0tExklBZBKIBJE/TvW9kM/Onk1R8CCqedPnEbIQ9S31dFXMBuC9g1MA39HIzfWr2/uDSGsR9PT47d8LCy9xS0Qk2yiITAJr1kB4ZhdnVvlnqH85stkikBvOZd70eTgcR0v9dmU7G3wvJTKUVddcR0tXC7Onzmb2QZ+U11CWiEwEBZFJoLDQMe2R/TC1l+tdGdcMWtsRecphXV8TTJ3Kzk7/BKphk+qRfIhmZonIBFAQmQR+1dhI89VnoTXM2q1Lh5zvz4ucr4P589mBn9fbv91JMJS1YvaKgT2z1BMRkQmgIJLhGrq6+HqtfwYIP1nCntcLhtSJnqHVVlHNDlZi5kbuiSiIiMgEUBDJYM45vrx/P009PdxSWAYbrmDTJog8xDAiEkQONh3ktdBtdJPP9QsaKS315/t7IiU1/glX4bB/yIiIyDgpiGQo5xyP1tXxu7NnKQ6H+eWKpaxcabS0wIYNsXWvq/APHtlYt5H/bvKLSu6atwuA5s5m6prrKMgpYGntOf+s3eXLIT//krZHRLKTgkgG6uzt5bN79/K9I0cIAU8sXUplQQEPPODPP/10bP3lM5azpGwJZ9rO8MLBJQDcOfUNAHad8sHk6llXk/Pcb/0H7r4bEZGJoCCSYU53d3Przp083dhIUTjMS9dcw/rZfv3H/ff7NYK//73foTfCzFhXsw4ar6KxqYTZnGRV658A2N6wHYCVs66F55/3H7j33kvaJhHJXgoiGeJkVxffOXSIJW+/zeaWFirz8/nzqlXcVV7eX2fuXLjlFp8TicSDiHuW3QO1dwLwcV4mdOwIzjl+tftXANzUVgaNjVBdPTD3V0RknLQBYxqd6e7mjfPn2XD2LE+fOkVX8HDH20pL+cWyZcwZJm/xwAOwcaMf0vrCFwbKb6q8idxDxkXg6ukboL6eN4/8mS31WygrLGP9n5p8xXvv9d0ZEZEJoCCSQj19fZzr6eHMxYucuXiRY11d1La3c6Cjg/fa2tjV1hZT/xMzZvDt+fO5Yfr0uN/zk5+Er37VB5L6et87AWi9EKan7kawHs7dvAVe7uHxZ/8BgC+v+iJTfviUr3jffSlpq4hcnrImiOxrb+eW7dsxMwz6v4AhZRb8Tzy6zmAu8hX0DhzQB/Q5Rx/Q6xy9ztHjHBedo7uvj27n6Ozro623l7be3v6eRTz5Zny4uJiPlpTwyZkzWT516qjtLCmBu+6CF16AZ56Bb33Ll7/6Kri+MCx4g1fWhvnim/Dbtm3k5uTyUM9qOP2YH8q69tpR/wwRkURlTRBp7e3ljehscwYwoCwnhxm5uczIzWVOfj7VhYUsKSxkaWEha6ZNoyAcHvP3feABH0SefnogiESm/eYu+1/e6TrMtz83h75QA59pnEXFi6/5k/fdp6EsEZlQWRNElk6ZwhMrVgzbg4gui/QNImUjienNAGEzQkGvJmxGjhlhIDcUIs+MvFCIfDOmhsMUhcMUhEL9vZ6JdNddUFwM27fDgw/CbbfByy/7c39x6wVea4dnyxoA+Obz9XD6Z/6kZmWJyATLmiAyLRzmLyNLtLNcQYFPqj/+ODz1lP8CqKyEz92+mtde9O/X5i9ldcN+oAeWLtVQlohMOE3xnaR+9CPYsgUeewzuuANmzoRvfAP+euldhM0PkX1z3Q/8SYBPf1pDWSIy4cyNkvydLMzsArAv3deRQjOAM+m+iBRS+ya3bG5fNrcNoMY5Ny3ZD2fNcBawzzm3Jt0XkSpmtk3tm7zUvskrm9sGvn3j+byGs0REJGkKIiIikrRsCiJPpvsCUkztm9zUvskrm9sG42xf1iTWRUTk0sumnoiIiFxiCiIiIpK0rAgiZnaHme0zswNm9nC6r2cimFmdmb1nZjsiU/DMrMzMXjWz2uA4aZbom9lTZtZoZrujyoZtj3n/FtzPXWa2On1XPro4bXvUzOqD+7fDzO6MOvedoG37zOyv0nPViTOzeWa20cz2mtkeM/v7oDxb7l+89mXFPTSzAjPbYmY7g/b9U1BeZWZvB/fvN2aWF5TnB+8PBOcXjvgHOOcm9RcQBg4Ci4A8YCdwZbqvawLaVQfMGFT2z8DDweuHgcfSfZ1jaM9aYDWwe7T2AHcCL+O3LLsReDvd159E2x4F/nGYulcGP6P5QFXwsxtOdxtGad8cYHXwehqwP2hHtty/eO3LinsY3Iei4HUu8HZwX54F1gflTwB/F7z+KvBE8Ho98JuRvn829ESuBw445w4557qBZ4B1ab6mVFkH/Dx4/XPgnjRey5g45/4PODeoOF571gG/cN5bQImZzbk0Vzp2cdoWzzrgGedcl3PuMHAA/zOcsZxzDc65d4PXF4C9wFyy5/7Fa188k+oeBvehNXibG3w54KPAc0H54PsXua/PAbfaCDvJZkMQmQsci3p/nJF/ACYLB/zBzN4xsy8FZbOdcw3gf/CBWWm7uokRrz3Zck8fCoZznooaepzUbQuGNlbh/zebdfdvUPsgS+6hmYXNbAfQCLyK7z01O+d6girRbehvX3D+PFBOHNkQRIaLkNkwb/lm59xq4OPA18xsbbov6BLKhnv6E2AxsBJoAH4UlE/atplZEfA88A3nXMtIVYcpy/g2DtO+rLmHzrle59xKoBLfa1o+XLXgOKb2ZUMQOQ7Mi3pfCZxI07VMGOfcieDYCLyAv/GnIsMCwbExfVc4IeK1Z9LfU+fcqeAfbh/wUwaGOyZl28wsF/8L9mnn3G+D4qy5f8O1L9vuIYBzrhl4HZ8TKTGzyP6J0W3ob19wvpgRhmuzIYhsBaqDmQZ5+ETQS2m+pnExs6lmNi3yGvgYsBvfrs8H1T4PvJieK5ww8drzEvC5YJbPjcD5yLDJZDEoB/AJ/P0D37b1wQyYKqAa2HKpr28sgvHwnwF7nXP/EnUqK+5fvPZlyz00s5lmVhK8LgRuw+d9NgKfCqoNvn+R+/op4DUXZNmHle6ZAxM0++BO/IyKg8B30309E9CeRfjZHzuBPZE24ccl/wjUBseydF/rGNr0a/yQwEX8/3QejNcefHf6x8H9fA9Yk+7rT6JtvwyufVfwj3JOVP3vBm3bB3w83defQPs+gh/O2AXsCL7uzKL7F699WXEPgWuB7UE7dgOPBOWL8MHvAPCfQH5QXhC8PxCcXzTS99e2JyIikrRsGM4SEZE0URAREZGkKYiIiEjSFERERCRpCiIiIpI0BRGRCWRm5VG7vp4ctAvs3ZZlu02LaIqvSIqY2aNAq3Puh2YWxq9luh2/lmQrcL9z7v00XqLIuKknInJpXE67TctlREFE5NKYdDu/iiRCQUTk0ph0O7+KJEJBROTSmLQ7v4qMREFE5NLIut2mRQByRq8iIuPlnOsxs4eAV4Aw8JRzbk+aL0tk3DTFV0REkqbhLBERSZqCiIiIJE1BREREkqYgIiIiSVMQERGRpCmIiIhI0hREREQkaf8PQRGbQFK3x7EAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5d7cbd0950>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# calcul de J pour toute les valeurs de T0 (figure 7)\n",
    "\n",
    "# parameters\n",
    "NT=int(5e2) # number of time step\n",
    "ITER = 5e4 # number of step in optimisation\n",
    "alpha_array = np.linspace(0,1,6)\n",
    "color=['r-','g-','b-','c-','m-','y-','b--','g--','r--']\n",
    "color_tikz=['red','black!60!green','blue','yellow','brown','black']\n",
    "\n",
    "T=200\n",
    "tval=np.linspace(t0,T,NT) # discretized time interval [t0,t0+h,...,T]\n",
    "h = (T-t0)/(NT-1)  \n",
    "T0_array = np.linspace(0,T,100)\n",
    "Jval_array = np.zeros((len(T0_array),len(alpha_array)))\n",
    "argmin_J = np.zeros(len(alpha_array))\n",
    "for ind_alpha in range(len(alpha_array)):\n",
    "    alpha = alpha_array[ind_alpha]\n",
    "    for ind in range(len(T0_array)):\n",
    "        T0 = T0_array[ind]\n",
    "        u=np.ones(int(NT))\n",
    "        for ii in range(int(T0*NT/T)-1,int(NT)):\n",
    "            u[ii]=alpha\n",
    "        yval=RK4_state(u,init)\n",
    "        Jval=J(yval)\n",
    "        #print(Jval)\n",
    "        Jval_array[ind,ind_alpha] = Jval\n",
    "    ind_min = np.argmin(Jval_array[:,ind_alpha])\n",
    "    argmin_J[ind_alpha] = T0_array[ind_min]\n",
    "    \n",
    "\n",
    "# Plot\n",
    "plt.figure(1)\n",
    "for ind_alpha in range(len(alpha_array)):\n",
    "    plt.plot(T0_array,Jval_array[:,ind_alpha],'{0}'.format(color[ind_alpha]),linewidth=2,label=r'$\\alpha$={0},$T_0$ opt.={1}'.format(alpha_array[ind_alpha],round(argmin_J[ind_alpha],1)))\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('T0')\n",
    "plt.ylabel('J for T={0}'.format(T))\n",
    "plt.axis([0,T,np.min(Jval_array),np.max(Jval_array)])\n",
    "plt.savefig(\"fig7_simu_covid_values_J_T_{0}.png\".format(T))\n",
    "\n",
    "# Save the values for tikz\n",
    "File = open('fig7_simu_covid_values_J_T_{0}.txt'.format(T),'w')\n",
    "for ind_alpha in range(len(alpha_array)):\n",
    "    File.write('\\\\addplot[color={0}]'.format(color_tikz[ind_alpha]))\n",
    "    File.write(' coordinates { ')\n",
    "    write_to_file(File,T0_array,Jval_array[:,ind_alpha])\n",
    "    File.write(' };\\n\\n')\n",
    "File.close()\n",
    "\n",
    "print('Argmin de J pour T={0}: '.format(T)+str(np.round(argmin_J,3)))\n",
    "\n",
    "T=300\n",
    "tval=np.linspace(t0,T,NT) # discretized time interval [t0,t0+h,...,T]\n",
    "h = (T-t0)/(NT-1)  \n",
    "T0_array = np.linspace(0,T,100)\n",
    "Jval_array = np.zeros((len(T0_array),len(alpha_array)))\n",
    "argmin_J = np.zeros(len(alpha_array))\n",
    "for ind_alpha in range(len(alpha_array)):\n",
    "    alpha = alpha_array[ind_alpha]\n",
    "    for ind in range(len(T0_array)):\n",
    "        T0 = T0_array[ind]\n",
    "        u=np.ones(int(NT))\n",
    "        for ii in range(int(T0*NT/T)-1,int(NT)):\n",
    "            u[ii]=alpha\n",
    "        yval=RK4_state(u,init)\n",
    "        Jval=J(yval)\n",
    "        #print(Jval)\n",
    "        Jval_array[ind,ind_alpha] = Jval\n",
    "    ind_min = np.argmin(Jval_array[:,ind_alpha])\n",
    "    argmin_J[ind_alpha] = T0_array[ind_min]\n",
    "\n",
    "\n",
    "# Plot\n",
    "plt.figure(2)\n",
    "for ind_alpha in range(len(alpha_array)):\n",
    "    plt.plot(T0_array,Jval_array[:,ind_alpha],'{0}'.format(color[ind_alpha]),linewidth=2,label=r'$\\alpha$={0},$T_0$ opt.={1}'.format(alpha_array[ind_alpha],round(argmin_J[ind_alpha],1)))\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('T0')\n",
    "plt.ylabel('J for T={0}'.format(T))\n",
    "plt.axis([0,T,np.min(Jval_array),np.max(Jval_array)])\n",
    "plt.savefig(\"fig7_simu_covid_values_J_T_{0}.png\".format(T))\n",
    "\n",
    "\n",
    "# Save the values for tikz\n",
    "File = open('fig7_simu_covid_values_J_T_{0}.txt'.format(T),'w')\n",
    "for ind_alpha in range(len(alpha_array)):\n",
    "    File.write('\\\\addplot[color={0}]'.format(color_tikz[ind_alpha]))\n",
    "    File.write(' coordinates { ')\n",
    "    write_to_file(File,T0_array,Jval_array[:,ind_alpha])\n",
    "    File.write(' };\\n\\n')\n",
    "File.close()\n",
    "print('Argmin de J pour T={0}: '.format(T)+str(np.round(argmin_J,3)))\n",
    "\n",
    "plt.show()\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
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