labs/lab-2/Ramsey Model (continuous).ipynb

{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure(figsize=(8,6))\n",
      "ax = model.plot_phase_diagram(20, cmap='winter', arrows=True)[0]\n",
      "\n",
      "# plot the unstable manifold\n",
      "init = [k_star - 1e-5, c_star + 1e-5]\n",
      "traj = model.integrate(t0=0, y0=init, T=1e3, h=0.5, integrator='lsoda')\n",
      "ax.plot(traj[:,1], traj[:,2], 'r--', label='$M_U$',)\n",
      "        \n",
      "init = [k_star + 1e-5, c_star - 1e-5]\n",
      "traj = model.integrate(t0=0, y0=init, T=1e3, h=0.5, integrator='lsoda')\n",
      "ax.plot(traj[:,1], traj[:,2], 'r--')\n",
      "\n",
      "# plot the stable manifold\n",
      "optimal_traj = model.solve_reverse_shooting(0.1 * k_star, h=1.0, eps=1e-5)\n",
      "ax.plot(optimal_traj[:,1], optimal_traj[:,2], 'r', label='$M_S$')\n",
      "\n",
      "optimal_traj_2 = model.solve_reverse_shooting(6.0 * k_star, h=1.0, eps=1e-5)\n",
      "ax.plot(optimal_traj_2[:,1], optimal_traj_2[:,2], 'r')\n",
      "\n",
      "ax.set_title('Phase diagram for the Ramsey (1928) model', fontsize=20)\n",
      "ax.legend(loc='best', frameon=False, prop={'family':'serif'})\n",
      "\n",
      "# plot two trajectories\n",
      "init = 0.999 * optimal_traj[-1,1:]\n",
      "traj = model.integrate(t0=0, y0=init, T=1e3, h=0.5, integrator='lsoda')\n",
      "ax.plot(traj[:,1], traj[:,2], color='0.5', label='')\n",
      "\n",
      "# plot two trajectories\n",
      "init = 1.001 * optimal_traj_2[-1,1:]\n",
      "traj = model.integrate(t0=0, y0=init, T=1e3, h=0.5, integrator='lsoda')\n",
      "ax.plot(traj[:,1], traj[:,2], color='0.5', label='')\n",
      "\n",
      "#plt.savefig('graphics/ramsey-phase-diagram-with-manifolds.pdf')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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rGRoaKreLe/fuVTv/9PR0WrRoETVs2JD09PSocePGtHjxYjp9+rTadV0xzooV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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x9d29890>"
       ]
      }
     ],
     "prompt_number": 168
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure(figsize=(8,6))\n",
      "\n",
      "x_min = k_star - 0.1 * c_star\n",
      "x_max = k_star + 0.1 * c_star\n",
      "\n",
      "y_min = (1 - 0.1) * c_star\n",
      "y_max = (1 + 0.1) * c_star\n",
      "\n",
      "ax = model.plot_phase_diagram(166)[0]\n",
      "ax.set_xlim(x_min, x_max)\n",
      "ax.set_ylim(y_min, y_max)\n",
      "\n",
      "X,Y = np.meshgrid(np.linspace(x_min, x_max, 10), np.linspace(y_min, y_max, 10))\n",
      "U = equation_of_motion_capital(0, np.array([X, Y]), model.args)\n",
      "V = consumption_euler_equation(0, np.array([X, Y]), model.args)\n",
      "\n",
      "Q = plt.quiver(X, Y, U, V)\n",
      "\n",
      "l,r,b,t = axis()\n",
      "dx, dy = r-l, t-b\n",
      "ax.axis([l-0.05*dx, r+0.05*dx, b-0.05*dy, t+0.05*dy])\n",
      "\n",
      "plt.title('Minimal arguments, no kwargs')\n",
      "#plt.savefig('Graphics/ramsey-model-quiver-ploy.pdf')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 158,
       "text": [
        "<matplotlib.text.Text at 0x9c38c30>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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8/fbbKC0trTNHY38aGRk178Ua6TEAOn2UlpZqtN7y8nLau3cvzZ49m1xcXHSe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\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x9b42b70>"
       ]
      }
     ],
     "prompt_number": 158
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Analytic solution "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 71
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 72
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "c_star"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 73,
       "text": [
        "1.3898982978743852"
       ]
      }
     ],
     "prompt_number": 73
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ramsey_analytic_consumption(k_star, 100, model.args)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 74,
       "text": [
        "1.3898982978743852"
       ]
      }
     ],
     "prompt_number": 74
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can generate an analytic trajectory for our Solow model like so..."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 86
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "params = {'alpha':0.33, 'delta':0.04, 'g':0.01, 'n':0.025, 'theta':3.0}\n",
      "params['rho'] = get_rho(params)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 88
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "params"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 89,
       "text": [
        "{'alpha': 0.33,\n",
        " 'delta': 0.04,\n",
        " 'g': 0.01,\n",
        " 'n': 0.025,\n",
        " 'rho': 0.004250000000000004,\n",
        " 'theta': 3.0}"
       ]
      }
     ],
     "prompt_number": 89
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# create the model object\n",
      "model = growth.RamseyModel(output=cobb_douglas_output, \n",
      "                           k_dot=equation_of_motion_capital, \n",
      "                           c_dot=consumption_euler_equation,\n",
      "                           F=ramsey_system, \n",
      "                           jacobian=ramsey_jacobian, \n",
      "                           params=params)\n",
      "\n",
      "# compute the steady state values\n",
      "model.steady_state.set_functions({'k_star':analytic_k_star, 'c_star':analytic_c_star})\n",
      "model.steady_state.set_values()\n",
      "\n",
      "# evaluate the jacobian \n",
      "k_star = model.steady_state.values['k_star']\n",
      "c_star = model.steady_state.values['c_star']\n",
      "\n",
      "eval_jac = ramsey_jacobian(0, [k_star, c_star], params)\n",
      "model.steady_state.set_eigen_star(eval_jac)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 90
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# create the grid and compute the benchmark policy function\n",
      "k_min = 0.5 * k_star \n",
      "k_max = 2.0 * k_star\n",
      "plot_grid = np.linspace(k_min, k_max, 1000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 91
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for tol in [1e-1, 1e-2, 1e-3, 1e-4]:\n",
      "    for h in [1e0, 1e-1, 1e-2]:\n",
      "        \n",
      "        # solve the model using forward shooting\n",
      "        kwargs = {'rtol':1e-9}\n",
      "        tmp_M_S = model.solve_forward_shooting(k_min, h, tol, integrator='dopri5', **kwargs)\n",
      "\n",
      "        # compute the analytic policy at the same time pts.\n",
      "        tmp_analytic_M_S = ramsey_analytic_solution(k_min, tmp_M_S[:,0], model.args)\n",
      "\n",
      "        # compute the average approximation error\n",
      "        tmp_L2_error = model.get_L2_errors(tmp_M_S, tmp_analytic_M_S)  \n",
      "        print 'L^2 error for tol=%g and h=%g using forward shooting is %g' %(tol, h, tmp_L2_error)\n",
      "    \n",
      "        # estimate the run-time\n",
      "        %timeit -n 1 -r 3 model.solve_forward_shooting(k_min, h, tol, integrator='dopri5', **kwargs)\n",
      "    print ''"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "L^2 error for tol=0.1 and h=1 using forward shooting is 1.21573\n",
        "1 loops, best of 3: 43.4 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 error for tol=0.1 and h=0.1 using forward shooting is 3.26052"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 210 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 error for tol=0.1 and h=0.01 using forward shooting is 10.2344"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 2.08 s per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        "L^2 error for tol=0.01 and h=1 using forward shooting is 0.439963"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 118 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 error for tol=0.01 and h=0.1 using forward shooting is 1.33427"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 783 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 error for tol=0.01 and h=0.01 using forward shooting is 4.19214"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 7.69 s per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        "L^2 error for tol=0.001 and h=1 using forward shooting is 0.683125"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 129 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 error for tol=0.001 and h=0.1 using forward shooting is 2.01904"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 804 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 error for tol=0.001 and h=0.01 using forward shooting is 6.36917"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 8.27 s per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        "L^2 error for tol=0.0001 and h=1 using forward shooting is 0.683125"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 134 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 error for tol=0.0001 and h=0.1 using forward shooting is 1.34184"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 2.64 s per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 error for tol=0.0001 and h=0.01 using forward shooting is 4.22663"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 27.4 s per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 93
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for tol in [1e-5, 1e-6, 1e-7, 1e-8, 1e-9]:\n",
      "        \n",
      "    # solve the model using forward shooting\n",
      "    kwargs = {'rtol':1e-9}\n",
      "    tmp_M_S = model.solve_forward_shooting(k_min, 1.0, tol, integrator='dopri5', **kwargs)\n",
      "\n",
      "    # compute the analytic policy at the same time pts.\n",
      "    tmp_analytic_M_S = ramsey_analytic_solution(k_min, tmp_M_S[:,0], model.args)\n",
      "\n",
      "    # compute the average approximation error\n",
      "    tmp_L2_error = model.get_L2_errors(tmp_M_S, tmp_analytic_M_S)  \n",
      "    print 'L^2 error for tol=%g and h=%g using forward shooting is %g' %(tol, 1.0, tmp_L2_error)\n",
      "    \n",
      "    # estimate the run-time\n",
      "    %timeit -n 1 -r 3 model.solve_forward_shooting(k_min, h, tol, integrator='dopri5', **kwargs)\n",
      "    print ''\n",
      "    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "L^2 error for tol=1e-05 and h=1 using forward shooting is 0.00850839\n",
        "1 loops, best of 3: 24.1 s per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        "L^2 error for tol=1e-06 and h=1 using forward shooting is 0.00013436"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 1min 45s per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        "L^2 error for tol=1e-07 and h=1 using forward shooting is 0.00016378"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 1min 48s per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        "L^2 error for tol=1e-08 and h=1 using forward shooting is 6.03991e-06"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 5min 3s per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        "L^2 error for tol=1e-09 and h=1 using forward shooting is 5.32365e-07"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 6min 35s per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 95
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "model.solve_multiple_shooting??"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 138
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def bc(veca, vecb):\n",
      "    \"\"\"\n",
      "    Boundary conditions for the Ramsey model.\n",
      "            \n",
      "    Args:\n",
      "        \n",
      "        veca: (array) Values of the dependent variables at the left \n",
      "              boundary.\n",
      "        \n",
      "        vecb: (array) Values of the dependent variables at the right \n",
      "              boundary.\n",
      "                      \n",
      "    Returns:\n",
      "        \n",
      "        bc: (tuple) Two arrays containing the difference between the\n",
      "            current and required values of the boundary conditions.\n",
      "            \n",
      "    \"\"\"\n",
      "    left_boundary  = np.array([veca[0] - k_min])\n",
      "    right_boundary = np.array([vecb[1] - c_star])\n",
      "    bc = (left_boundary, right_boundary)\n",
      "    return bc\n",
      "\n",
      "guess = (k_star, c_star)\n",
      "\n",
      "for tol in [1e-1, 1e-2, 1e-3, 1e-4, 1e-5, 1e-6, 1e-7, 1e-8, 1e-9]:    \n",
      "    for T in [5e2, 1e3, 5e3]:\n",
      "        solver_opts = {'tolerance':tol, 'max_subintervals':500}\n",
      "        tmp_sol = model.solve_multiple_shooting(k_min, T, guess, bc, **solver_opts)\n",
      "\n",
      "        # compute the analytic solution\n",
      "        grid = np.linspace(0, T, 1000)\n",
      "        analytic_M_S = ramsey_analytic_solution(k_min, grid, model.args)\n",
      "\n",
      "        # compute the average approximation error\n",
      "        tmp_M_S = np.hstack((grid[:,np.newaxis], tmp_sol(grid).T))\n",
      "        L2_error = model.get_L2_errors(analytic_M_S, tmp_M_S)  \n",
      "        print 'L^2 approximation error for tol=%g and T=%g is %g' %(tol, T, L2_error)\n",
      "    \n",
      "        # estimate the run-time\n",
      "        %timeit -n 1 -r 3 model.solve_multiple_shooting(k_min, T, guess, bc, **solver_opts)\n",
      "    print ''"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "L^2 approximation error for tol=0.1 and T=500 is 1.07706\n",
        "1 loops, best of 3: 23 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for tol=0.1 and T=1000 is 10.6753\n",
        "1 loops, best of 3: 27.4 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for tol=0.1 and T=5000 is 0.780274"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 253 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        "L^2 approximation error for tol=0.01 and T=500 is 2.0182\n",
        "1 loops, best of 3: 24.6 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for tol=0.01 and T=1000 is 17.3834\n",
        "1 loops, best of 3: 31.9 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for tol=0.01 and T=5000 is 0.000135369"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 261 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        "L^2 approximation error for tol=0.001 and T=500 is 0.369221\n",
        "1 loops, best of 3: 33.4 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for tol=0.001 and T=1000 is 2.43851\n",
        "1 loops, best of 3: 50.7 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for tol=0.001 and T=5000 is 0.00013557"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 302 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        "L^2 approximation error for tol=0.0001 and T=500 is 0.0269296"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 45.1 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for tol=0.0001 and T=1000 is 0.0542089"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 76.9 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for tol=0.0001 and T=5000 is 0.000133266"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 352 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        "L^2 approximation error for tol=1e-05 and T=500 is 0.00287892"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 65.2 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for tol=1e-05 and T=1000 is 0.00506856"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 112 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for tol=1e-05 and T=5000 is 0.000133079"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 383 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        "L^2 approximation error for tol=1e-06 and T=500 is 0.000282065"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 92.2 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for tol=1e-06 and T=1000 is 0.000453135"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 182 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for tol=1e-06 and T=5000 is 0.000189241"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 533 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        "L^2 approximation error for tol=1e-07 and T=500 is 2.23962e-05"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 145 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for tol=1e-07 and T=1000 is 3.89705e-05"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 255 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for tol=1e-07 and T=5000 is 1.17329e-05"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 653 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        "L^2 approximation error for tol=1e-08 and T=500 is 2.11746e-06"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 276 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for tol=1e-08 and T=1000 is 3.21072e-06"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 390 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for tol=1e-08 and T=5000 is 5.66946e-06"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 775 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        "L^2 approximation error for tol=1e-09 and T=500 is 1.94358e-07"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 424 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for tol=1e-09 and T=1000 is 3.1081e-07"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 611 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for tol=1e-09 and T=5000 is 4.76174e-07"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 1.09 s per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 139
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "analytic_M_S"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 104,
       "text": [
        "array([[    0.        ,     4.63299433,     1.1057148 ],\n",
        "       [    1.001001  ,     4.83492258,     1.12139156],\n",
        "       [    2.002002  ,     5.02956371,     1.13609264],\n",
        "       ..., \n",
        "       [  997.997998  ,     9.26598865,     1.3898983 ],\n",
        "       [  998.998999  ,     9.26598865,     1.3898983 ],\n",
        "       [ 1000.        ,     9.26598865,     1.3898983 ]])"
       ]
      }
     ],
     "prompt_number": 104
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tmp_M_S(grid).T"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 105,
       "text": [
        "array([[ 4.63299433,  1.1057148 ],\n",
        "       [ 4.83492258,  1.12139156],\n",
        "       [ 5.02956371,  1.13609264],\n",
        "       ..., \n",
        "       [ 9.26598865,  1.3898983 ],\n",
        "       [ 9.26598865,  1.3898983 ],\n",
        "       [ 9.26598865,  1.3898983 ]])"
       ]
      }
     ],
     "prompt_number": 105
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(tmp_M_S[:,1], tmp_M_S[:,2])\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "IndexError",
       "evalue": "index 2 is out of bounds for axis 1 with size 2",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mIndexError\u001b[0m                                Traceback (most recent call last)",
        "\u001b[0;32m<ipython-input-112-81c2cd6820a3>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtmp_M_S\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtmp_M_S\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshow\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;31mIndexError\u001b[0m: index 2 is out of bounds for axis 1 with size 2"
       ]
      }
     ],
     "prompt_number": 112
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "grid = np.linspace(k_min, k_max, 1000) \n",
      "analytic_pol = ramsey_analytic_consumption_policy(grid, model.args)\n",
      "\n",
      "for eps in [1e-1, 1e-2, 1e-3, 1e-4, 1e-5, 1e-6, 1e-7, 1e-8, 1e-9]:\n",
      "    for h in [1e-1, 1e-2, 1e-3]:\n",
      "    \n",
      "        kwargs = {'h':h, 'eps':eps, 'integrator':'dopri5', 'k':3, 'options':{'rtol':1e-9}}\n",
      "        tmp_policy = model.get_consumption_policy(k_min, k_max, method='reverse', **kwargs)\n",
      "\n",
      "        # compute the average approximation error\n",
      "        L2_error = get_L2_errors(analytic_pol, tmp_policy(grid))  \n",
      "        print 'L^2 approximation error for eps=%g and h=%g is %g' %(eps, h, L2_error)\n",
      "    \n",
      "        # estimate the run-time\n",
      "        %timeit -n 1 -r 3 model.get_consumption_policy(k_min, k_max, method='reverse', **kwargs)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "L^2 approximation error for eps=0.1 and h=0.1 is 5.81272e-05\n",
        "1 loops, best of 3: 39.3 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for eps=0.1 and h=0.01 is 7.88959e-05"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 362 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for eps=0.1 and h=0.001 is 8.30534e-05"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 3.63 s per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for eps=0.01 and h=0.1 is 8.38639e-08\n",
        "1 loops, best of 3: 38.4 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for eps=0.01 and h=0.01 is 1.81989e-07"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 361 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for eps=0.01 and h=0.001 is 2.36569e-07"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 3.72 s per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for eps=0.001 and h=0.1 is 6.98518e-09\n",
        "1 loops, best of 3: 38.6 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for eps=0.001 and h=0.01 is 2.91517e-10"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 363 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for eps=0.001 and h=0.001 is 2.44835e-10"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 3.91 s per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for eps=0.0001 and h=0.1 is 7.09362e-09\n",
        "1 loops, best of 3: 39 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for eps=0.0001 and h=0.01 is 1.99087e-10"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 364 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for eps=0.0001 and h=0.001 is 2.62901e-13"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 3.84 s per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for eps=1e-05 and h=0.1 is 7.10672e-09\n",
        "1 loops, best of 3: 42.9 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for eps=1e-05 and h=0.01 is 2.46788e-10"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 366 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for eps=1e-05 and h=0.001 is 8.82842e-14"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 3.99 s per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for eps=1e-06 and h=0.1 is 7.10807e-09"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 53.3 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for eps=1e-06 and h=0.01 is 2.52222e-10"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 388 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for eps=1e-06 and h=0.001 is 8.07547e-14"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 4.2 s per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for eps=1e-07 and h=0.1 is 7.1082e-09\n",
        "1 loops, best of 3: 42.5 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for eps=1e-07 and h=0.01 is 2.52614e-10"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 402 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for eps=1e-07 and h=0.001 is 9.54105e-14"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 4.1 s per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for eps=1e-08 and h=0.1 is 7.10821e-09\n",
        "1 loops, best of 3: 42.3 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for eps=1e-08 and h=0.01 is 2.53054e-10"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 399 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for eps=1e-08 and h=0.001 is 1.07808e-13"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 4.21 s per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for eps=1e-09 and h=0.1 is 7.10697e-09\n",
        "1 loops, best of 3: 42.7 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for eps=1e-09 and h=0.01 is 2.50795e-10"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 411 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for eps=1e-09 and h=0.001 is 1.72701e-13"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 4.01 s per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 130
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "grid = np.linspace(k_min, k_max, 1000) \n",
      "analytic_pol = ramsey_analytic_consumption_policy(grid, model.args)\n",
      "\n",
      "for eps in [1e-1, 1e-2, 1e-3, 1e-4, 1e-5, 1e-6, 1e-7]:\n",
      "    \n",
      "    kwargs = {'h':eps, 'eps':eps, 'integrator':'dopri5', 'k':3, 'options':{'rtol':1e-9}}\n",
      "    tmp_policy = model.get_consumption_policy(k_min, k_max, method='reverse', **kwargs)\n",
      "\n",
      "    # compute the average approximation error\n",
      "    L2_error = get_L2_errors(analytic_pol, tmp_policy(grid))  \n",
      "    print 'L^2 approximation error for eps=%g and h=%g is %g' %(eps, eps, L2_error)\n",
      "    \n",
      "    # estimate the run-time\n",
      "    %timeit -n 1 -r 3 model.get_consumption_policy(k_min, k_max, method='reverse', **kwargs)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "L^2 approximation error for eps=0.1 and h=0.1 is 5.81272e-05\n",
        "1 loops, best of 3: 38.6 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for eps=0.01 and h=0.01 is 1.81989e-07"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 362 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for eps=0.001 and h=0.001 is 2.44835e-10"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 3.68 s per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "L^2 approximation error for eps=0.0001 and h=0.0001 is 2.84974e-13"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1 loops, best of 3: 1min 19s per loop"
       ]
      },
      {
       "ename": "KeyboardInterrupt",
       "evalue": "",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
        "\u001b[0;32m<ipython-input-128-fe1076d1d2fb>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m     \u001b[0mkwargs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0;34m'h'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0meps\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'eps'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0meps\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'integrator'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m'dopri5'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'k'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'options'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m{\u001b[0m\u001b[0;34m'rtol'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m1e-9\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m     \u001b[0mtmp_policy\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmodel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_consumption_policy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mk_min\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mk_max\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmethod\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'reverse'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      8\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m     \u001b[0;31m# compute the average approximation error\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;32m/Users/clarissasweet/Projects/pyeconomics/models/growth.pyc\u001b[0m in \u001b[0;36mget_consumption_policy\u001b[0;34m(self, kmin, kmax, method, **kwargs)\u001b[0m\n\u001b[1;32m   1436\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1437\u001b[0m         \u001b[0;31m# compute the stable manifold\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1438\u001b[0;31m         \u001b[0mM_S\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_stable_manifold\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkmin\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkmax\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmethod\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1439\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1440\u001b[0m         \u001b[0;31m# construct a callable B-spline repr of the policy function\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;32m/Users/clarissasweet/Projects/pyeconomics/models/growth.pyc\u001b[0m in \u001b[0;36mget_stable_manifold\u001b[0;34m(self, kmin, kmax, method, **kwargs)\u001b[0m\n\u001b[1;32m   1280\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1281\u001b[0m             lower_M_S = self.solve_reverse_shooting(kmin, -h, eps, integrator, \n\u001b[0;32m-> 1282\u001b[0;31m                                                     **options)\n\u001b[0m\u001b[1;32m   1283\u001b[0m             upper_M_S = self.solve_reverse_shooting(kmax, h, eps, integrator, \n\u001b[1;32m   1284\u001b[0m                                                     **options)\n",
        "\u001b[0;32m/Users/clarissasweet/Projects/pyeconomics/models/growth.pyc\u001b[0m in \u001b[0;36msolve_reverse_shooting\u001b[0;34m(self, k0, h, eps, integrator, step, relax, **kwargs)\u001b[0m\n\u001b[1;32m   1128\u001b[0m             \u001b[0mode\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mintegrate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mode\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mt\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mh\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstep\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrelax\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1129\u001b[0m             \u001b[0mcurrent_step\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhstack\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mode\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mode\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1130\u001b[0;31m             \u001b[0msolution\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvstack\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msolution\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcurrent_step\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1131\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1132\u001b[0m             \u001b[0;31m# check to see if initial condition has been reached\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;32m/Users/clarissasweet/Library/Enthought/Canopy_32bit/User/lib/python2.7/site-packages/numpy/core/shape_base.pyc\u001b[0m in \u001b[0;36mvstack\u001b[0;34m(tup)\u001b[0m\n\u001b[1;32m    224\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    225\u001b[0m     \"\"\"\n\u001b[0;32m--> 226\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0m_nx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mconcatenate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0matleast_2d\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mtup\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    227\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    228\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mhstack\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtup\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 128
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tmp_policy[::-1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 122,
       "text": [
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        "       [ 9.16998865,  1.38514846],\n",
        "       [ 9.17098865,  1.38519851],\n",
        "       [ 9.17198865,  1.38524855],\n",
        "       [ 9.17298865,  1.38529859],\n",
        "       [ 9.17398865,  1.38534864],\n",
        "       [ 9.17498865,  1.38539868],\n",
        "       [ 9.17598865,  1.38544873],\n",
        "       [ 9.17698865,  1.38549878],\n",
        "       [ 9.17798865,  1.38554883],\n",
        "       [ 9.17898865,  1.38559888],\n",
        "       [ 9.17998865,  1.38564893],\n",
        "       [ 9.18098865,  1.38569899],\n",
        "       [ 9.18198865,  1.38574904],\n",
        "       [ 9.18298865,  1.3857991 ],\n",
        "       [ 9.18398865,  1.38584917],\n",
        "       [ 9.18498865,  1.38589923],\n",
        "       [ 9.18598865,  1.3859493 ],\n",
        "       [ 9.18698865,  1.38599937],\n",
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        "       [ 9.18898865,  1.38609953],\n",
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        "       [ 9.19098865,  1.3861997 ],\n",
        "       [ 9.19198865,  1.38624979],\n",
        "       [ 9.19298865,  1.38629989],\n",
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        "       [ 9.19498865,  1.3864001 ],\n",
        "       [ 9.19598865,  1.38645022],\n",
        "       [ 9.19698865,  1.38650034],\n",
        "       [ 9.19798865,  1.38655047],\n",
        "       [ 9.19898865,  1.38660061],\n",
        "       [ 9.19998865,  1.38665076],\n",
        "       [ 9.20098865,  1.38670092],\n",
        "       [ 9.20198865,  1.38675108],\n",
        "       [ 9.20298865,  1.38680126],\n",
        "       [ 9.20398865,  1.38685145],\n",
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        "       [ 9.20798865,  1.38705232],\n",
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        "       [ 9.20998865,  1.38715284],\n",
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        "       [ 9.21498865,  1.38740447],\n",
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        "       [ 9.23698865,  1.38852402],\n",
        "       [ 9.23798865,  1.38857594],\n",
        "       [ 9.23898865,  1.38862804],\n",
        "       [ 9.23998865,  1.38868035],\n",
        "       [ 9.24098865,  1.38873288],\n",
        "       [ 9.24198865,  1.38878568],\n",
        "       [ 9.24298865,  1.38883879],\n",
        "       [ 9.24398865,  1.38889224],\n",
        "       [ 9.24498865,  1.38894611],\n",
        "       [ 9.24598865,  1.38900047],\n",
        "       [ 9.24698865,  1.3890554 ],\n",
        "       [ 9.24798865,  1.38911103],\n",
        "       [ 9.24898865,  1.38916752],\n",
        "       [ 9.24998865,  1.38922509],\n",
        "       [ 9.25098865,  1.38928403],\n",
        "       [ 9.25198865,  1.38934479],\n",
        "       [ 9.25298865,  1.38940801],\n",
        "       [ 9.25398865,  1.38947481],\n",
        "       [ 9.25498865,  1.38954718],\n",
        "       [ 9.25598865,  1.38962949],\n",
        "       [ 9.25698865,  1.38973575],\n",
        "       [ 9.25764875,  1.3899045 ]])"
       ]
      }
     ],
     "prompt_number": 122
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "reverse_shooting_policies = {}\n",
      "forward_shooting_policies = {}\n",
      "\n",
      "for step in [1.0, 0.1, 0.01, 0.001]:\n",
      "    \n",
      "    kwargs = {'rtol':1e-9}\n",
      "    # compute the policy function using forward shooting\n",
      "    tmp_pol = model.get_consumption_policy(1, k_min, k_max, h=step, tol=1e-4, integrator='dopri5', **kwargs)        \n",
      "    forward_shooting_policies[step] = tmp_pol\n",
      "    \n",
      "    # compute the policy function using reverse shooting\n",
      "    tmp_pol = model.get_consumption_policy(1, k_min, k_max, h=step, eps=step, integrator='dopri5', **kwargs)\n",
      "    reverse_shooting_policies[step] = tmp_pol\n",
      "    \n",
      "    print 'Done with h=%g' %step\n",
      "    \n",
      "for step in [1.0, 0.1, 0.01, 0.001]:\n",
      "    \n",
      "    tmp_pol = forward_shooting_policies[step]\n",
      "    print np.sum((ramsey_analytic_consumption_policy(plot_grid, model.args) - tmp_pol(plot_grid))**2)**0.5\n",
      "    \n",
      "    # compute the policy function using reverse shooting\n",
      "    tmp_pol = reverse_shooting_policies[step]\n",
      "    print np.sum((ramsey_analytic_consumption_policy(plot_grid, model.args) - tmp_pol(plot_grid))**2)**0.5\n",
      "\n",
      "    print 'Done with h=%g' %step"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "      \n",
      "kwargs = {'T':1e2, 'solution_guess':guess, 'boundary_conditions':bc, 'k':1}\n",
      "benchmark_policy = model.get_consumption_policy(k_min, k_max, method='multiple', **kwargs)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 194
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "reverse_shooting_policies = {}\n",
      "forward_shooting_policies = {}\n",
      "\n",
      "for step in [1.0, 0.1, 0.01, 0.001]:\n",
      "    \n",
      "    kwargs = {'rtol':1e-9}\n",
      "    # compute the policy function using forward shooting\n",
      "    tmp_pol = model.get_consumption_policy(1, k_min, k_max, h=step, tol=1e-4, integrator='dopri5', **kwargs)        \n",
      "    forward_shooting_policies[step] = tmp_pol\n",
      "    \n",
      "    # compute the policy function using reverse shooting\n",
      "    tmp_pol = model.get_consumption_policy(1, k_min, k_max, h=step, eps=step, integrator='dopri5', **kwargs)\n",
      "    reverse_shooting_policies[step] = tmp_pol\n",
      "    \n",
      "    print 'Done with h=%g' %step\n",
      "    \n",
      "for step in [1.0, 0.1, 0.01, 0.001]:\n",
      "    \n",
      "    tmp_pol = forward_shooting_policies[step]\n",
      "    print np.sum((ramsey_analytic_consumption_policy(plot_grid, model.args) - tmp_pol(plot_grid))**2)**0.5\n",
      "    \n",
      "    # compute the policy function using reverse shooting\n",
      "    tmp_pol = reverse_shooting_policies[step]\n",
      "    print np.sum((ramsey_analytic_consumption_policy(plot_grid, model.args) - tmp_pol(plot_grid))**2)**0.5\n",
      "\n",
      "    print 'Done with h=%g' %step"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_grid = np.linspace(k_min, k_max, 1000)\n",
      "plt.figure()\n",
      "plt.plot(plot_grid, ramsey_analytic_consumption_policy(plot_grid, model.args), 'r-')\n",
      "plt.plot(plot_grid, benchmark_policy(plot_grid), 'b-')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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XiOJmLbEzwwcGRlxfm4i0T126U+cWyRDKyvG+x3Fkl3TA4UwXFjoRNSm6VeqC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\nciwZUfXDAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x9cb65f0>"
       ]
      }
     ],
     "prompt_number": 195
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# compute benchmark policy function using reverse shooting with very small h\n",
      "#kwargs = {'h':1e0, 'eps':1e-6, 'integrator':'dopri5', 'k':1.0}\n",
      "kwargs = {'T':1000, 'guess':None, 'k':1.0}\n",
      "benchmark_policy = model.get_consumption_policy(k_min, k_max, method='multiple', **kwargs)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# compute benchmark policy function using reverse shooting with very small h\n",
      "#kwargs = {'h':1e0, 'eps':1e-6, 'integrator':'dopri5', 'k':1.0}\n",
      "kwargs = {'T':1000, 'guess':None, 'k':1.0}\n",
      "benchmark_policy = model.get_consumption_policy(k_min, k_max, method='multiple', **kwargs)\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 138
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_grid = np.linspace(k_min, k_max, 1000)\n",
      "plt.figure()\n",
      "plt.plot(plot_grid, ramsey_analytic_consumption_policy(plot_grid, model.args), 'r-')\n",
      "plt.plot(plot_grid, benchmark_policy(plot_grid), 'b-')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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1XpYm4q6qOw5ccmehE1Gbol+lLgiIDYxHyi0nyK/YwrSzsdiJiIhalV6V+r/+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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x9c81ff0>"
       ]
      }
     ],
     "prompt_number": 139
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sol = model.solve_multiple_shooting(k_min, 10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 108
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "model.steady_state.values['k_star'] "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 107,
       "text": [
        "9.265988652495905"
       ]
      }
     ],
     "prompt_number": 107
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sol.solution"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 106,
       "text": [
        "array([[ 4.63299433,  5.00190629,  5.37037684,  5.73568031,  6.09519978,\n",
        "         6.44683676,  6.78654857,  7.11002733,  7.41462331,  7.69757511,\n",
        "         7.95654033,  8.19014603,  8.39737439,  8.57802651,  8.7326777 ,\n",
        "         8.86215379,  8.96814154,  9.05283843,  9.11869682,  9.16831724,\n",
        "         9.20437128,  9.22945564,  9.24599967,  9.25617471,  9.26185134,\n",
        "         9.26460633,  9.26567874,  9.26595595,  9.26598189,  9.26598542,\n",
        "         9.26598604],\n",
        "       [ 1.10571453,  1.13402695,  1.16094119,  1.18642882,  1.21047183,\n",
        "         1.23308517,  1.25415968,  1.27357992,  1.29133253,  1.30739102,\n",
        "         1.32174511,  1.33442741,  1.34547637,  1.35496026,  1.36297339,\n",
        "         1.36960929,  1.37499317,  1.37926498,  1.38256816,  1.38504638,\n",
        "         1.38684141,  1.38808752,  1.38890813,  1.38941233,  1.38969347,\n",
        "         1.38982987,  1.38988296,  1.38989668,  1.38989799,  1.3898982 ,\n",
        "         1.3898983 ]])"
       ]
      }
     ],
     "prompt_number": 106
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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IDASXNAKQyisw0/UkIAO+SfBloRNRs2JYTz6SJLzjcxTXs7ri6M0eMGljIjoR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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x9cad470>"
       ]
      }
     ],
     "prompt_number": 123
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.sum((ramsey_analytic_consumption_policy(plot_grid, model.args) - benchmark_policy(plot_grid))**2)**0.5"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 55,
       "text": [
        "0.00011831131571665765"
       ]
      }
     ],
     "prompt_number": 55
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.sum((ramsey_analytic_consumption_policy(plot_grid, model.args) - benchmark_policy(plot_grid))**2)**0.5"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 66,
       "text": [
        "4.3714282551262889"
       ]
      }
     ],
     "prompt_number": 66
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.sum((ramsey_analytic_consumption_policy(plot_grid, model.args) - benchmark_policy(plot_grid))**2)**0.5"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 58,
       "text": [
        "1.1942285268741086e-06"
       ]
      }
     ],
     "prompt_number": 58
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.sum((ramsey_analytic_consumption_policy(plot_grid, model.args) - benchmark_policy(plot_grid))**2)**0.5"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 69,
       "text": [
        "0.5644156256657098"
       ]
      }
     ],
     "prompt_number": 69
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.sum((ramsey_analytic_consumption_policy(plot_grid, model.args) - benchmark_policy(plot_grid))**2)**0.5"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 61,
       "text": [
        "1.2112922866447431e-08"
       ]
      }
     ],
     "prompt_number": 61
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.sum((ramsey_analytic_consumption_policy(plot_grid, model.args) - benchmark_policy(plot_grid))**2)**0.5"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 71,
       "text": [
        "0.14327714300320468"
       ]
      }
     ],
     "prompt_number": 71
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.sum((ramsey_analytic_consumption_policy(plot_grid, model.args) - benchmark_policy(plot_grid))**2)**0.5"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 63,
       "text": [
        "1.217247729087086e-10"
       ]
      }
     ],
     "prompt_number": 63
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Done with h=1\n",
        "Done with h=0.1"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Done with h=0.01"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Done with h=0.001"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 81
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.0970540474686\n",
        "0.0211672371143\n",
        "Done with h=1\n",
        "0.142869991476\n",
        "0.00011831133772\n",
        "Done with h=0.1\n",
        "0.143195763183\n",
        "1.19422852687e-06\n",
        "Done with h=0.01\n",
        "0.143214380603\n",
        "1.21129228664e-08\n",
        "Done with h=0.001\n"
       ]
      }
     ],
     "prompt_number": 80
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "grid = np.linspace(k_min, k_max, 100)\n",
      "forward_shooting_policies[0.0001](grid) - benchmark_policy(grid)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 298,
       "text": [
        "array([  1.01765725e-06,   1.08538537e-06,   1.15764668e-06,\n",
        "         1.23491163e-06,   1.31766221e-06,   1.40650272e-06,\n",
        "         1.50210049e-06,   1.60522988e-06,   1.71678920e-06,\n",
        "         1.83782680e-06,   1.96957204e-06,   2.11347883e-06,\n",
        "         2.27127641e-06,   2.44504033e-06,   2.63728220e-06,\n",
        "         2.85106980e-06,   3.09020032e-06,   3.35944343e-06,\n",
        "         3.66474783e-06,   4.01382311e-06,   4.41674427e-06,\n",
        "         4.88696472e-06,   5.44278294e-06,   6.10979398e-06,\n",
        "         6.92491146e-06,   7.94355839e-06,   9.25283942e-06,\n",
        "         1.09977333e-05,   1.34389418e-05,   1.70975458e-05,\n",
        "         2.31883558e-05,   3.53536373e-05,   7.18383237e-05,\n",
        "         1.40214780e-06,  -4.23401908e-05,  -2.16034104e-05,\n",
        "        -1.46812542e-05,  -1.12152994e-05,  -9.13356265e-06,\n",
        "        -7.74471761e-06,  -6.75215959e-06,  -6.00747976e-06,\n",
        "        -5.42816756e-06,  -4.96468460e-06,  -4.58548737e-06,\n",
        "        -4.26953005e-06,  -4.00224050e-06,  -3.77320457e-06,\n",
        "        -3.57478601e-06,  -3.40124864e-06,  -3.24820662e-06,\n",
        "        -3.11225223e-06,  -2.99068842e-06,  -2.88135700e-06,\n",
        "        -2.78251251e-06,  -2.69272672e-06,  -2.61082036e-06,\n",
        "        -2.53580989e-06,  -2.46686853e-06,  -2.40329598e-06,\n",
        "        -2.34449620e-06,  -2.28995825e-06,  -2.23924125e-06,\n",
        "        -2.19196321e-06,  -2.14779159e-06,  -2.10643526e-06,\n",
        "        -2.06763819e-06,  -2.03117447e-06,  -1.99684415e-06,\n",
        "        -1.96446944e-06,  -1.93389169e-06,  -1.90496878e-06,\n",
        "        -1.87757338e-06,  -1.85159089e-06,  -1.82691785e-06,\n",
        "        -1.80346060e-06,  -1.78113409e-06,  -1.75986106e-06,\n",
        "        -1.73957126e-06,  -1.72020050e-06,  -1.70169001e-06,\n",
        "        -1.68398591e-06,  -1.66703869e-06,  -1.65080279e-06,\n",
        "        -1.63523624e-06,  -1.62030028e-06,  -1.60595910e-06,\n",
        "        -1.59217953e-06,  -1.57893081e-06,  -1.56618441e-06,\n",
        "        -1.55391378e-06,  -1.54209421e-06,  -1.53070265e-06,\n",
        "        -1.51971759e-06,  -1.50911895e-06,  -1.49888791e-06,\n",
        "        -1.48900688e-06,  -1.47945935e-06,  -1.47022983e-06,\n",
        "        -1.46130377e-06])"
       ]
      }
     ],
     "prompt_number": 298
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "grid = np.linspace(k_min, k_max, 100)\n",
      "reverse_shooting_policies[0.0001](grid) - benchmark_policy(grid)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 302,
       "text": [
        "array([  1.66246461e-10,   1.77195481e-10,   1.88900451e-10,\n",
        "         2.01436312e-10,   2.14888218e-10,   2.29353203e-10,\n",
        "         2.44943732e-10,   2.61788036e-10,   2.80036327e-10,\n",
        "         2.99862579e-10,   3.21471849e-10,   3.45106166e-10,\n",
        "         3.71053965e-10,   3.99659972e-10,   4.31343072e-10,\n",
        "         4.66141237e-10,   5.05074982e-10,   5.49016055e-10,\n",
        "         5.98961880e-10,   6.56197541e-10,   7.21961491e-10,\n",
        "         7.98808020e-10,   8.89697538e-10,   9.98747529e-10,\n",
        "         1.13196952e-09,   1.29847710e-09,   1.51249169e-09,\n",
        "         1.79768378e-09,   2.19664842e-09,   2.79450174e-09,\n",
        "         3.78955300e-09,   5.77570436e-09,   1.17142875e-08,\n",
        "         0.00000000e+00,  -1.21331520e-08,  -6.19711749e-09,\n",
        "        -4.21224278e-09,  -3.21802562e-09,  -2.62077382e-09,\n",
        "        -2.22228813e-09,  -1.93749106e-09,  -1.72382419e-09,\n",
        "        -1.55761581e-09,  -1.42449741e-09,  -1.31566269e-09,\n",
        "        -1.22531052e-09,  -1.14844712e-09,  -1.08240994e-09,\n",
        "        -1.02586628e-09,  -9.75582282e-10,  -9.31288602e-10,\n",
        "        -8.91988261e-10,  -8.56894555e-10,  -8.25375768e-10,\n",
        "        -7.96922084e-10,  -7.71118058e-10,  -7.47615969e-10,\n",
        "        -7.26129157e-10,  -7.06415815e-10,  -6.88271440e-10,\n",
        "        -6.71523281e-10,  -6.56020571e-10,  -6.41633635e-10,\n",
        "        -6.28253671e-10,  -6.15780316e-10,  -6.04130301e-10,\n",
        "        -5.93228133e-10,  -5.83008308e-10,  -5.73409542e-10,\n",
        "        -5.64385427e-10,  -5.55887558e-10,  -5.47871526e-10,\n",
        "        -5.40302247e-10,  -5.33141753e-10,  -5.26370725e-10,\n",
        "        -5.19952303e-10,  -5.13863618e-10,  -5.08079134e-10,\n",
        "        -5.02591524e-10,  -4.97364594e-10,  -4.92388796e-10,\n",
        "        -4.87652807e-10,  -4.83134643e-10,  -4.78830753e-10,\n",
        "        -4.74721595e-10,  -4.70789185e-10,  -4.67038630e-10,\n",
        "        -4.63443506e-10,  -4.60014915e-10,  -4.56724658e-10,\n",
        "        -4.53568516e-10,  -4.50554039e-10,  -4.47665016e-10,\n",
        "        -4.44893011e-10,  -4.42232695e-10,  -4.39677628e-10,\n",
        "        -4.37222480e-10,  -4.34866587e-10,  -4.32615055e-10,\n",
        "        -4.30449010e-10])"
       ]
      }
     ],
     "prompt_number": 302
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "grid = np.linspace(k_min, k_max, 100)\n",
      "for step in [0.01, 0.001, 0.0001]:\n",
      "    plt.plot(grid, np.abs(forward_shooting_policies[step](grid) - benchmark_policy(grid)))\n",
      "plt.ylim(1e-16, 1e0)\n",
      "plt.yscale('log')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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KYs2aNUPbjY2NdHR0EBsbi81mG8uhRUTkc4wo9KuqqkhPT6egoGBYu8vlIjc3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\nQBT6IiIGotAXETGQ/wdKkxInLUW7jgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa241b90>"
       ]
      }
     ],
     "prompt_number": 316
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure(figsize=(8,6))\n",
      "grid = np.linspace(k_min, k_max, 1000)\n",
      "for step in [0.1, 0.01, 0.001, 0.0001]:\n",
      "    plt.plot(grid, np.abs(reverse_shooting_policies[step](grid) - benchmark_policy(grid)))\n",
      "plt.ylim(1e-16, 1e0)\n",
      "plt.yscale('log')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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MBtx+++0oKioCAOzZswe///3vO4P8+eefBwCsWbOm8zMtLS149NFHERwcDK1W\ni0ceeaR3UbyGTZ7gyy+B++4DvvsOGMzlm127xAhomzcD117r9PKIaOQY9pHOKioqoFarO1+rVCoU\nFBT02CYoKAjr1q0bcF86nQ4ajQYajQY6nQ46nc6ZpRJd3N69wC9+IVrKg+1rkZkJfPIJcPfd4paw\n+fOdWyMRyVZ+fj7y8/NhMBhgMBgc+oxTA9uZo3rl5+c7bV9El+Tbb0XL+P33gWuuGdq+5s4Vw5ne\ncQdQUiIGVeGlICKvd2FD1JH8dOp/ORISEmA0GjtfG41G9gQnedmyRTzEY8MG4NZbnbPP9HTRYv/X\nv4AbbgC6/RshInKUUwM7PT0dZWVlMBgMMJvN2LRpE+bNm+fMQxC5hs0menevXAl8/jlw003O3b9a\nDeTni8CePh14+WXAYnHuMYhoRBt0YOfk5CAjIwOlpaVQq9VYv349lEol1q5di6ysLKSkpCA7Oxta\nrdaZ9RI536lTwC23ADt3Avv3AzNnuuY4vr7iOdo7d4oObVOmAHl54tYxIqIBcGhS8l6SJDqD/dd/\nAY8+KsJUOUyPPZUk0ZL/7W8Bq1Uce+FCEepE5HU8cmhSRzCwyeX27xeDobS2Au++e/HxwV1JkkSn\ntGefFS39FSvESGnx8e6ph4jcwiOHJiVyK4NB3K41bx6wZAmwZ4/7whoAFArRue3bb4HPPgMqKoAr\nrhC9yjduFA8dISICA5u8RWkpsGwZMGOGGGK0tFS0Zj3pFPS0acCbbwInT3b1VE9IABYsEA8dqa52\nd4VE5EY8JU4jlySJlutrrwH//rd4IMejjwJRUe6uzHHnz4vBW/75T/E3JCeLDnI33yx+fPj5ubtC\nInICXsMm79TUJFqkb7whrlGvXCmuC4eGuruyoTGbgW++AfR6YOtW4KefgFmzxOAumZnAlVfK/28k\n8lIMbPIedru4z/nDD8W14DlzgF/+Erj++pE7slhdHbB7txizfNcu4OBBcbp/xoyuKS0NCA52d6VE\nNAAGNo1skgQUFYnW9McfAzExokNZTs6w9LKWJAlWSYKfp/wgaGsDfvgBOHCgayouBiZMEB3ZrrgC\nSEkRU1IS4O/v7oqJqB0Dm0Yem0307P7sM3Ft124HsrNFUA9zb++5hw7h67o6WOfMga8Tx9F3KrNZ\nhHZxMfDjj13LJ0+KINdqgcREYNKkrkmt9qzOeERegIFNI0NDA/D112KgkS1bgDFjRC/q+fOBqVPF\nrVFukL6+XE3cAAAeK0lEQVR/Pw40NaHm6qsRJbfOX62toqd8SYm4Fn7smJj/9JPojT5+fM8A7z7F\nx7OzG5GTDfvjNYmcwmYDCgvF8J1ffgkcOgRcdZXoGb1mjQgRD9BgswEA6q1W+QV2YKAYGnXKlN7v\ntbQA5eUivI8fF63x/fvFQ0uMRuDsWSA2tmeIJySIH1IdU1wcEB09cvsPELkBW9jkfpIkTtPu3Ans\n2AFs3w6MHg1kZYnp2ms9suNU3LffAgC2Tp2Kqd7UO9tqBSoruwLcaBQDvlRVienMGTE1NYn/HTsC\nvHuYx8QAo0aJqWM5NNRtZ0uI3I0tbPJMNhvw/fcinHfuFD2cw8NFMGdlAS++KFptHq7eakVqaCjq\nrVZ3lzK8lEpg3DgxXUxbm2iNdwR4R5iXlop+CNXV4j7zjsls7h3i3V9HRQEREUBkpJg6liMieIqe\nvAIDm1yvrg747jugoED8h3r3bmDsWBHQCxYAr7wii4Durs1uhx1AnJ+f9wW2owICuk6ZO6K1tWeA\ndw/0U6dED/i6OqC+vvc8IKD/MO+Yh4eLVnxoKBAW1vdyYCBb+eSxGNjkXFaruNWqoADYu1fMT50S\nz4CePVsMYLJ+vThVKmP1VisilEpEKpWoY2A7R2CguBaekHBpn5MkoLm57yDvPj91Spymb2oCGht7\nzjuWrdaBQz00FAgJAYKCxKWa7tNA64braXA0IvH/PTR4Nhtw9KjoIHbwILBvn5iPHy/C+aqrgNWr\nxf2/I+w/VFVmM0b7+WFsQAAqzWZ3l+PdFIquIL3UsL+QxdIV4H0Fese8pUXMq6oAk0m8Npl6Tn2t\n8/W9eKgHBYmzBYGBYupYvnB+qe8FBorLBjx7IGsj67+i5DptbeI+3sLCroAuKhKntqdNEy3o3/0O\nmDlTnH4c4U6bzYgPCMD4gAAUm0zuLoecxc9PXCt3xXjzkiR+EFws1FtaxL+11tbe87o6Me/rvb7W\nXfie1SoCvHuY+/mJAXQ6Jle/vnCdUiled59fuMw7DToxsKm32lpxvfDw4a5wPnJEDLAxfboI6EWL\nxD3QXhDOfalsa0O8vz/GBQZCX1Pj7nJIDhSKrqCKjBz+49vtPUPcbBaTxdK1PJjXjY2D20fHjwir\nVbzub9nHp3eQ9xfujr4/0LbLlolhfj0MA9ubtbWJgTOKinpO9fXiNPaUKeLhEg8/DKSmitN1BAAw\ntrUhPiAA4wICcLKtzd3lEA3Mx0f8G5bTv2NJEj80LhboFy4P9X2r1WMvHTCwvYHdLgbC6AjkH34Q\n8/Jy8SsyNVVMjzwi5uPH8zTUAI6aTLghKgrjAwNxorXV3eUQjUwKhbjuz6FyATCwRxa7HThxQrSa\nO6aiInHtOTpajLWdmgrcfjvw1FPi2coBAe6uWpZKTCY8qlIhUqmEHUCdxYJI3gtMRC7EwJYjs1mM\n/VxSIkYI6wjn0lLRWUarFdOMGcB994mgdsc1sxHKLkk4ajIhOTgYCoUCycHBKDaZkOGl1/OJaHgw\nsD1ZU5Po7NW9xVxSAhgMYpSpjmDOygJ+/WvRYg4Pd3fVI96ptjaEK5WIaL9VLT0sDN81NjKwicil\nGNieoLq6dyiXlADnzonnFncEc05O17OMeSrbbQ40NvYYOzw9LAz5dXVurIiIvAEDe7hIkhhp6cLT\n2CUl4hR3SkpXMM+dK+YaDTtbeKBd9fXI7NaanhkWhtyTJ91YERF5Awa2s1mt4rGEF7aWjxwRIzF1\nhHJqKnDPPWJ57FiPvY2AettZV4f/l5jY+XpySAjqrVYcb2nBRDndMkNEssLAdrayMuC227qCec4c\ncbtUcrJrRk+iYXXWbMaxlhbM7NZXwEehwM3R0fiipga/HOrQmERE/WBgO5tWCxw/7u4qyEW2VFcj\nKzoaARfcpz4/JgYvnzrFwCYil+HoGESX4JOzZ3FXbGyv9beNGoVSkwmlHFeciFyEgU3koKMmE4qa\nmzE/JqbXe/4+PlgyZgzWnT7thsqIyBswsIkc9EZFBe4fO7bX6fAOj8TH453Tp3HeYhnmyojIGwx7\nYJ86dQp33XUX7r//fuTm5g734YkG5XRbGz6sqsIj8fH9bjMhKAgLY2PxPG/xIiIXGPbALioqwt13\n34133nkHBw8eHO7DEw3KH0+cwH1jxkAdGHjR7X6r0eC9M2dQ3Nw8TJURkbcYdGAvX74ccXFxSE1N\n7bFer9cjOTkZSUlJfbagMzIy8NZbb2Hu3Lm4+eabB3t4omGzv6EBm8+dw5Pjxg24bXxAAP6o0WD5\nkSMw2+3DUB0ReQuFJEnSYD64a9cuhIaGYsmSJSgqKgIA2Gw2XH755di+fTsSEhIwc+ZMbNy4Efv3\n70dhYSEef/xx/OUvf8GMGTOQmZmJhQsX4tNPP+1dlEKBQZZF5FStNhtmFRbiP9Vq/GLMGIc+Y5ck\nzP/hB4wLCMDayy5zcYVENBI4knuDbmFnZmYi6oKBQPbt24fExERoNBr4+flh0aJFyMvLw+LFi/Hy\nyy8jPj4e119/PV555RU88sgjmDBhwmAPTzQsVpWV4fLgYNwbF+fwZ3wUCmzQarGtthavV1S4sDoi\n8iZOHTiloqICarW687VKpUJBQUGPbaZMmYK//vWvA+5Lp9NBo9FAo9FAp9NBp9M5s1SiAb1RUYHd\nDQ0omD4dikscOjZCqcQXU6ZAd+gQAhQKrLhIZzUi8j75+fnIz8+HwWCAwWBw6DNODexL/Y/axeTn\n5zttX0SXamNVFZ47cQI7pk1DmHJw/0wmBgXhq6lTccPhwzhtNuO/x4936r8RIpKvCxuijvy3wam9\nxBMSEmA0GjtfG41GqFQqZx6CyOXeO30aq48dg37KFEwa4sM8koKDsXf6dGw5fx4/LylBvdXqpCqJ\nyNs4NbDT09NRVlYGg8EAs9mMTZs2Yd68ec48BJHLSJKE/z1xAv9jMGDHtGmY3O2Z10MxNiAAO9LS\nEKVUIm3/fuzks7OJaBAGHdg5OTnIyMhAaWkp1Go11q9fD6VSibVr1yIrKwspKSnIzs6GVqt1Zr1E\nLlFvteLuH3/E36qr8e306bg8ONip+w/29cUbl12GtUlJyCkuxn0lJTjd1ubUYxDRyDbo27pcibd1\n0XD6pq4Oy44exY1RUXg5MbHfoUedpdFqxbMnTmDd6dN4VKXCYwkJiPLzc+kxicizOZJ7DGzyWk1W\nK54sL8fmc+fwWlIS7u7jKVyudMxkwrMnT2JLdTUejI/HrxISMCYgYFhrICLPwMAm6oNNkvDBmTN4\nurwcc9tb1dFubOEaWlrwgtGIjWfP4oaoKDw0diyuj4qCD3uUE3kNBjZRN5IkYWttLdYcP44gHx/8\nadIkXBkR4e6yOjVYrfioqgr/V1mJepsN2bGxyB49GmmhobwdjGiEY2ATQQwVuqW6Gs+ePAmTzYb/\n0WiwIDbWY0NQkiQcamrCX86dw1/OnoWvQoH5MTG4JToaV0dEwN/F19iJaPgxsMmrNVqt+LCqCmsr\nKhDk44P/Gj8ed8TEyOpUsyRJONDYiH+cP48vampw1GTCdZGRuDk6GtdGRkIbHOyxPzyIyHEMbPJK\nxc3NeKOiAh+fPYvrIyOxMiEB10VGjohgO2c2Y2ttLbbW1GBXfT0arFZcHRGBzIgIZEZGYmpICAJ9\nfd1dJhFdIgY2eY2zZjM2nj2LD6uqUNHWhhVjx+LBsWOhGuD51XJX0daGb+rrsauuDt/U16O0pQWX\nBQVhRlhY5zQlJARBDHEij8bAphGtzmLB5zU1+KiqCrvr6zEvJgaL4+JwfVQUfEdAa3owWm02fN/c\njAONjWJqasIRkwnqgABcERKClOBgpISE4IrgYFweHMwgJ/IQDGwacSra2pBXXY3Pqquxt6EBushI\nZI8ejfkxMQhh+PTJbLfjWEsLfmxuRrHJhOL2+bGWFsT7+yMxKAiJQUGY1DEFBmJiUBCC+X0SDRsG\nNsmeTZJQ2NiIL2tq8I/z51HW0oLbRo3C/JgYZEVFIXSQT9IiwGK343hrK461tOCn7lNrK8pbWjDK\nzw+TgoKgDggQU2Ag1AEBGNe+HK1Ujoh+AUSegIFNsmRsbe3sWLW9thZj/P1xU3Q0bouOxpzISPjx\ntiaXs0kSKtracLylBSfb2mBsa4OxtVXM26c2u70zzBMCAjDG37/PKZLBTjQgBjbJwpm2Nuyqr8fO\n+npsr61FtcWCG6KicFNUFG6MihrxHcfkqtFq7QzvirY2VJnNONNt6njdYrdjjL8/4toDPM7fH6OU\nSsT4+WFU+9S5rFQiys/Pa/sgkPdiYJPHkSQJ5a2t2FlX1xnS5y0WXNN+a9J1kZGYHhYmq3ul6eJa\nbLYeYV5lseB8t6naYsF5q1XMLRY0WK2IuCDQO4I8wtcXkUolIpRKRLZP3ZfDfX2h5BkYkiEGNrld\ni82GwqYm7GtoQEFDA3bV10MCcG37fcPXRkTgipAQBjR1strtqLVae4V5vdWKOqu199xm63xdb7Ui\n2Ne3M9g7Aj1cqUSYry9CfX17zUN9fRGmVPZe5+vLyy80bBjYNKzskoRSkwkFjY0oaA/oEpMJKcHB\nmB0ejlnh4bgmIgITAwN5TZNcwi5JaLLZeoV6o82GRpsNTd3nViuaLlzXPu9Y9gG6Ar491IN9fBDk\n44PgjuX2efAA7wX5+PTcrn3OHwUEMLDJheyShJ9aWnCwqQkHm5pwoLER3zU2IkqpxOzwcMwOC8Os\n8HBMCw3lvb4kS5IkwSxJncHeEeYtdjtMNhtM7fMWu71z2WS3o6Xbeya7vcf2F75nstmgUCgQ5OOD\nAB8fBPr4IEChEPOO1wO8F3iJ7wf4+MBPoYC/jw/8FQr4dczb1/Fsl3swsMkpzHY7ipubO8P5YFMT\nDjc1IVqpxLSwMEwLDcX00FDMCg/HaH9/d5dLJCuW9sBva59au88lqedrJ7xvliSY7XZY2udmSeqx\n7At0hrh/R7h3X74g4PsK/e7ruu/Dz8cHSoUCyvZtlReZLvb+gJ/tdhylQgEfwOPP6jGw6ZI1WK34\nvlswH2ofKWtCYCCmhYZ2BnRaaKhbnyFNRM4nSRJs7WcWOkNdkmC5MOgHCP2+tu9YZ2vf1trPdLH3\nrO37udTP2oEBw95XoYBv+3bvJidjVnj4sH73DGzqV5vdjqMmE4qam1HU1IQfmptR1NyMaosFV4SE\niHBuD+jUkBCOekVEsmUf4IeCpf39jkkTGDjsgzIxsAn29tuofmgP5qLmZvzQ3Izjra2YEBiI1JAQ\nTA4J6ZxPDAriNSwiomHGwPYikiTB2NaGEpMJJe2t5aLmZhQ3N2OUn1+PUE4NDUVycDAC2DuViMgj\nMLBHIEv7gxyOmEwinNsD+mhLC8J8faENDoY2OBipoaFIDQnBFSEhiOB420REHo2BLWPNNpsI5ebm\nrmA2mVDe0gJ1YGBnMGuDg5EcHAwtg5mISLYY2DJwzmzuDOPuAX3OYkFSUJAI5ZCQznBOCgpCIDuA\nERGNKAxsD2HvuL58QWu5pLkZVknqEcgdAa0JDOQDEIiIvAQD2w0arFZsq63t0Vo+ajIhQqns1VrW\nBgcjzt/f42/oJyIi12Jgu8GJ1lY8WlbWo7WcHBzM68tERNQvBjYREZEMOJJ7vBGXiIhIBhjYRERE\nMsDAJiIikgGXBnZ5eTlWrFiBhQsXAgCam5uxdOlSPPjgg/j4449deWgiIqIRxaWBPWHCBKxbt67z\n9d/+9jfcc889eOutt7BlyxZXHpqIiGhEcSiwly9fjri4OKSmpvZYr9frkZycjKSkJOTm5g64n4qK\nCqjVagCAL0frIiIicphDgb1s2TLo9foe62w2G1atWgW9Xo/i4mJs3LgRJSUl2LBhA1avXo3Kyspe\n+1GpVDAajQAAu93uhPKJiIi8g0OBnZmZiaioqB7r9u3bh8TERGg0Gvj5+WHRokXIy8vD4sWL8fLL\nLyM+Ph41NTV4+OGHcfDgQeTm5uKuu+7C5s2bsXLlSsybN88lfxAREdFINOjht7qf3gZE67mgoKDH\nNtHR0XjzzTd7rHv33Xcd2r9Op4NGo4FGo4FOp4NOpxtsqURERB4lPz8f+fn5MBgMMBgMDn1m0IHt\n6vGv8/PzXbp/IiIid7mwIepIpg66l3hCQkLn9WgAMBqNUKlUg90dERERXcSgAzs9PR1lZWUwGAww\nm83YtGkTr0sTERG5iEOBnZOTg4yMDJSWlkKtVmP9+vVQKpVYu3YtsrKykJKSguzsbGi1WlfXS0RE\n5JX4tC4iIiI349O6iIiIRggGNhERkQwwsImIiGSAgU1ERCQDDGwiIiIZYGATERHJAAObiIhIBhjY\nREREMsDAJiIikgEGNhERkQwwsImIiGSAgU1ERCQDDGwiIiIZYGATERHJAAObiIhIBhjYREREMsDA\nJiIikgEGNhERkQwwsImIiGSAgU1ERCQDDGwiIiIZYGATERHJAAObiIhIBhjYREREMsDAJiIikgEG\nNhERkQwwsImIiGSAgU1ERCQDDGwiIiIZYGATERHJAAObiIhIBlwe2OXl5VixYgUWLlwIAMjLy8OD\nDz6IRYsWYdu2ba4+PBER0YigkCRJGo4DLVy4EJ9++mnn67q6OvzmN7/BunXrehelUGCYyiIiInI7\nR3LP4Rb28uXLERcXh9TU1B7r9Xo9kpOTkZSUhNzcXIeLe+aZZ7Bq1SqHtyciIvJmDgf2smXLoNfr\ne6yz2WxYtWoV9Ho9iouLsXHjRpSUlGDDhg1YvXo1Kisre+1HkiQ88cQTuOWWW5CWljb0v4CIiMgL\nKB3dMDMzEwaDoce6ffv2ITExERqNBgCwaNEi5OXlYc2aNVi8eDEAoKamBk899RQOHTqE559/HiEh\nIfjqq6/Q0NCAY8eO4aGHHnLaH0NERDRSORzYfamoqIBare58rVKpUFBQ0GOb6OhovPnmmz3WPfro\nowPuW6fTQaPRQKPRQKfTQafTDaVUIiIij5Gfn4/8/HwYDIZejeH+DCmwFQrFUD5+Ufn5+S7bNxER\nkTtd2BB1JE+HdFtXQkICjEZj52uj0QiVSjWUXRIREVEfhhTY6enpKCsrg8FggNlsxqZNmzBv3jxn\n1UZERETtHA7snJwcZGRkoLS0FGq1GuvXr4dSqcTatWuRlZWFlJQUZGdnQ6vVurJeIiIirzRsA6dc\nCg6cQkRE3sSpA6cQERGR+zCwiYiIZICBTUREJAMMbCIiIhlgYBMREckAA5uIiEgGGNhEREQywMAm\nIiKSAQY2ERGRDDCwiYiIZICBTUREJAMMbCIiIhlgYBMREckAA5uIiEgGGNhEREQywMAmIiKSAQY2\nERGRDDCwiYiIZICBTUREJAMMbCIiIhlgYBMREckAA5uIiEgGGNhEREQywMAmIiKSAQY2ERGRDDCw\niYiIZICBTUREJAMMbCIiIhlgYBMREckAA5uIiEgGGNhEREQy4NLALi8vx4oVK7Bw4cLOdc3NzZg5\ncyY+//xzVx6aiIhoRHFpYE+YMAHr1q3rse6FF15Adna2Kw9LREQ04jgU2MuXL0dcXBxSU1N7rNfr\n9UhOTkZSUhJyc3MH3M+2bduQkpKC2NjYwVVLRETkpRwK7GXLlkGv1/dYZ7PZsGrVKuj1ehQXF2Pj\nxo0oKSnBhg0bsHr1alRWVvbaz44dO7B37158/PHHePvttyFJknP+CiIiohFO6chGmZmZMBgMPdbt\n27cPiYmJ0Gg0AIBFixYhLy8Pa9asweLFiwEANTU1eOqpp3Do0CHk5ubimWeeAQC8//77iI2NhUKh\ncN5fQkRENII5FNh9qaiogFqt7nytUqlQUFDQY5vo6Gi8+eabvT67dOnSAfev0+mg0Wig0Wig0+mg\n0+kGWyoREZFHyc/PR35+PgwGQ68GcX8GHdiubh3n5+e7dP9ERETucmFD1JFMHXQv8YSEBBiNxs7X\nRqMRKpVqsLsjIiKiixh0YKenp6OsrAwGgwFmsxmbNm3CvHnznFkbERERtXMosHNycpCRkYHS0lKo\n1WqsX78eSqUSa9euRVZWFlJSUpCdnQ2tVuvqeomIiLySQvLAe6sUCgVv+SIiIq/hSO5xLHEiIiIZ\nYGATERHJAAObiIhIBhjYREREMsDAJiIikgEGNhERkQwwsImIiGSAgU1ERCQDDGwiIiIZYGATERHJ\nAAObiIhIBhjYREREMsDAJiIikgEGNhERkQwwsImIiGSAgU1ERCQDDGwiIiIZYGATERHJAAObiIhI\nBhjYREREMsDAJiIikgEGNhERkQwwsImIiGSAgU1ERCQDDGwiIiIZYGATERHJAAObiIhIBhjYRERE\nMsDAJiIikgEGNhERkQwwsImIiGRA6cqdl5eX49lnn0V9fT0+/fRT2O12PP3002hsbER6ejqWLFni\nysMTERGNGC5tYU+YMAHr1q3rfJ2Xl4eKigr4+/tDpVK58tBeIT8/390lyAa/K8fwe3IcvyvH8Hty\nHocCe/ny5YiLi0NqamqP9Xq9HsnJyUhKSkJubu6A+yktLcXVV1+Nl156CX/+858HVzF14j8Ex/G7\ncgy/J8fxu3IMvyfncSiwly1bBr1e32OdzWbDqlWroNfrUVxcjI0bN6KkpAQbNmzA6tWrUVlZ2Ws/\nKpUKkZGR4sA+vHxORETkKIdSMzMzE1FRUT3W7du3D4mJidBoNPDz88OiRYuQl5eHxYsX4+WXX0Z8\nfDxqamrw8MMP4+DBg8jNzcVdd92FL7/8Eo899hh0Op0r/h4iIqKRSXJQeXm5NHny5M7Xn376qbRi\nxYrO1xs2bJBWrVrl6O4uKj4+XgLAiRMnTpw4ecUUHx8/YDYOupe4QqEY7EcHVFFR4bJ9ExERydGg\nLyQnJCTAaDR2vjYajez5TURE5CKDDuz09HSUlZXBYDDAbDZj06ZNmDdvnjNrIyIionYOBXZOTg4y\nMjJQWloKtVqN9evXQ6lUYu3atcjKykJKSgqys7Oh1WqHVEx/t49RT0ajEddddx2uuOIKTJ48Ga++\n+qq7S/JIra2tmD17NtLS0pCSkoInn3zS3SV5NJvNhmnTpuH22293dykeTaPRYMqUKZg2bRpmzZrl\n7nI8Vl1dHRYsWACtVouUlBTs3bvX3SV5pKNHj2LatGmdU0RERL//TVdIkiQNc3392rVrF0JDQ7Fk\nyRIUFRW5uxyPdebMGZw5cwZpaWloamrCjBkz8Nlnnw35B9NIZDKZEBwcDKvVimuuuQYvvfQSrrnm\nGneX5ZH+9Kc/4cCBA2hsbMSWLVvcXY7HmjBhAg4cOIDo6Gh3l+LRli5dijlz5mD58uWwWq1obm5G\nRESEu8vyaHa7HQkJCdi3bx/UanWv9z3qZui+bh+j3saMGYO0tDQAQGhoKLRabZ/3vRMQHBwMADCb\nzbDZbPyPbD9OnTqFf/3rX1ixYgU86De8x+J3dHH19fXYtWsXli9fDgBQKpUMawds374dkyZN6jOs\nAQ8LbLp0BoMBBw8exOzZs91dikey2+1IS0tDXFwcrrvuOqSkpLi7JI+0evVqvPjiixzQyAEKhQI3\n3HAD0tPT8fbbb7u7HI9UXl6O2NhYLFu2DNOnT8cDDzwAk8nk7rI83ieffIKf//zn/b7Pf50y1tTU\nhAULFuCVV15BaGiou8vxSD4+Pjh06BBOnTqFnTt3cpjEPvzzn//E6NGjMW3aNLYcHfDtt9/i4MGD\n+OKLL/D6669j165d7i7J41itVhQWFmLlypUoLCxESEgInn/+eXeX5dHMZjP+8Y9/YOHChf1uw8CW\nKYvFgrvvvhu/+MUvMH/+fHeX4/EiIiJw2223Yf/+/e4uxePs3r0bW7ZswYQJE5CTk4Ovv/6aT9K7\niLFjxwIAYmNjceedd2Lfvn1ursjzqFQqqFQqzJw5EwCwYMECFBYWurkqz/bFF19gxowZiI2N7Xcb\nBrYMSZKE+++/HykpKfj1r3/t7nI8VnV1Nerq6gAALS0t2LZtG6ZNm+bmqjzPc889B6PRiPLycnzy\nySe4/vrr8cEHH7i7LI9kMpnQ2NgIAGhubsbWrVt5V0sfxowZA7VajdLSUgDi2uwVV1zh5qo828aN\nG5GTk3PRbVz6POxLlZOTgx07duD8+fNQq9X4wx/+gGXLlrm7LI/z7bff4sMPP+y8tQQA/vd//xc3\n33yzmyvzLKdPn8bSpUtht9tht9uxePFizJ07191leTxXjmIod1VVVbjzzjsBiNO+9957L2666SY3\nV+WZXnvtNdx7770wm82YNGkS1q9f7+6SPFZzczO2b98+YJ8Ij7qti4iIiPrGU+JEREQywMAmIiKS\nAQY2ERGRDDCwiYiIZICBTUREJAMMbCIiIhlgYBMREckAA5uIiEgG/j+rtqwj0NqtQAAAAABJRU5E\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa00d550>"
       ]
      }
     ],
     "prompt_number": 315
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "model.steady_state.values['k_star']"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 191,
       "text": [
        "3.3013033273505767"
       ]
      }
     ],
     "prompt_number": 191
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "c_policy = model.get_stable_manifold(k_lower, k_upper, h=1.0, tol=1e-3, integrator='dopri5')\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 176
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "model.get_stable_manifold?"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 177
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# specify some initial conditions\n",
      "k0 = 0.5 * model.steady_state.values['k_star']\n",
      "\n",
      "k_star = model.steady_state.values['k_star']\n",
      "c_star = model.steady_state.values['c_star']\n",
      "\n",
      "model.steady_state.set_eigen_star(model.jac(0, [k_star, c_star], model.args))\n",
      "\n",
      "traj = model.solve_reverse_shooting(k0, h=1e-1, eps=1e-1, integrator='erk4')\n",
      "\n",
      "# solve the model analytically!\n",
      "analtyic_traj = ramsey_analytic_solution(k0, traj[:,0], params)\n",
      "\n",
      "model.compare_trajectories(analtyic_traj, traj[::-1])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 35,
       "text": [
        "array([[ 0.01543713,  0.00826471],\n",
        "       [ 0.01486159,  0.00795658],\n",
        "       [ 0.01429036,  0.00765076],\n",
        "       [ 0.01372633,  0.00734878],\n",
        "       [ 0.01317181,  0.00705191],\n",
        "       [ 0.01262865,  0.00676111],\n",
        "       [ 0.0120983 ,  0.00647717],\n",
        "       [ 0.01158187,  0.00620069],\n",
        "       [ 0.01108019,  0.0059321 ],\n",
        "       [ 0.01059388,  0.00567174],\n",
        "       [ 0.01012332,  0.00541981],\n",
        "       [ 0.00966876,  0.00517645],\n",
        "       [ 0.0092303 ,  0.00494171],\n",
        "       [ 0.00880793,  0.00471558],\n",
        "       [ 0.00840154,  0.004498  ],\n",
        "       [ 0.00801094,  0.00428889],\n",
        "       [ 0.00763589,  0.0040881 ],\n",
        "       [ 0.0072761 ,  0.00389547],\n",
        "       [ 0.00693121,  0.00371082],\n",
        "       [ 0.00660085,  0.00353396],\n",
        "       [ 0.00628463,  0.00336466],\n",
        "       [ 0.00598213,  0.00320271],\n",
        "       [ 0.00569292,  0.00304787],\n",
        "       [ 0.00541657,  0.00289991],\n",
        "       [ 0.00515262,  0.0027586 ],\n",
        "       [ 0.00490064,  0.0026237 ],\n",
        "       [ 0.00466019,  0.00249497],\n",
        "       [ 0.00443083,  0.00237217],\n",
        "       [ 0.00421212,  0.00225508],\n",
        "       [ 0.00400364,  0.00214346],\n",
        "       [ 0.00380497,  0.0020371 ],\n",
        "       [ 0.00361572,  0.00193578],\n",
        "       [ 0.00343547,  0.00183928],\n",
        "       [ 0.00326385,  0.0017474 ],\n",
        "       [ 0.00310048,  0.00165993],\n",
        "       [ 0.00294501,  0.00157669],\n",
        "       [ 0.00279707,  0.00149749],\n",
        "       [ 0.00265633,  0.00142214],\n",
        "       [ 0.00252247,  0.00135048],\n",
        "       [ 0.00239517,  0.00128232]])"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "model.get_stable_manifold(0.5 * k_star, 2.0 * k_star, h=1.0, eps=1e-5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 36,
       "text": [
        "array([[ 0.35012074,  0.18744722],\n",
        "       [ 0.73120832,  0.39147342],\n",
        "       [ 0.99466356,  0.53252177],\n",
        "       [ 1.16156401,  0.62187673],\n",
        "       [ 1.26359531,  0.67650213],\n",
        "       [ 1.32488681,  0.7093163 ],\n",
        "       [ 1.36136513,  0.72884601],\n",
        "       [ 1.38296208,  0.74040856],\n",
        "       [ 1.39570981,  0.74723343],\n",
        "       [ 1.40322439,  0.75125657],\n",
        "       [ 1.40764771,  0.75362473],\n",
        "       [ 1.41024976,  0.75501781],\n",
        "       [ 1.4117801 ,  0.75583712],\n",
        "       [ 1.41267863,  0.75631817],\n",
        "       [ 1.4132091 ,  0.75660218],\n",
        "       [ 1.41352059,  0.75676894],\n",
        "       [ 1.41370319,  0.7568667 ],\n",
        "       [ 1.41381041,  0.7569241 ],\n",
        "       [ 1.41387341,  0.75695783],\n",
        "       [ 1.41391015,  0.7569775 ],\n",
        "       [ 1.41393152,  0.75698894],\n",
        "       [ 1.41394402,  0.75699563],\n",
        "       [ 1.41396159,  0.75700504],\n",
        "       [ 1.41397917,  0.75701445],\n",
        "       [ 1.41399167,  0.75702114],\n",
        "       [ 1.41401304,  0.75703259],\n",
        "       [ 1.41404978,  0.75705226],\n",
        "       [ 1.41411278,  0.75708599],\n",
        "       [ 1.41422001,  0.75714339],\n",
        "       [ 1.41440264,  0.75724117],\n",
        "       [ 1.41471422,  0.75740798],\n",
        "       [ 1.41524494,  0.75769212],\n",
        "       [ 1.41614422,  0.75817357],\n",
        "       [ 1.41767668,  0.75899403],\n",
        "       [ 1.42028488,  0.7603904 ],\n",
        "       [ 1.42472597,  0.76276806],\n",
        "       [ 1.43229179,  0.76681864],\n",
        "       [ 1.44518779,  0.77372289],\n",
        "       [ 1.46721347,  0.78551497],\n",
        "       [ 1.50493221,  0.80570878],\n",
        "       [ 1.56981393,  0.84044508],\n",
        "       [ 1.68223452,  0.90063268],\n",
        "       [ 1.87926228,  1.00611716],\n",
        "       [ 2.2305181 ,  1.19417208],\n",
        "       [ 2.87182623,  1.53751485]])"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "c_k = model.get_consumption_policy(1, 0.5 * k_star, 2.0 * k_star, h=1.0, tol=1e-6, integrator='forward_euler')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 64
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "c_k(np.linspace(0, 2 * k_star)) - ramsey_analytic_consumption_policy(np.linspace(0, 2 * k_star), model.args)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 65,
       "text": [
        "array([  6.15101503e-14,   5.45327672e-14,   4.75522399e-14,\n",
        "         4.05786516e-14,   3.35981243e-14,   2.66175970e-14,\n",
        "         1.97619698e-14,   1.26010313e-14,   5.66213743e-15,\n",
        "        -1.22124533e-15,  -8.27116153e-15,  -1.51545443e-14,\n",
        "        -2.22044605e-14,  -2.91988655e-14,  -3.61377595e-14,\n",
        "        -4.31321645e-14,  -5.00710584e-14,  -5.75095527e-14,\n",
        "        -7.67164110e-14,  -9.59232693e-14,  -1.16573418e-13,\n",
        "        -1.70308212e-13,  -2.44693155e-13,  -4.27657909e-13,\n",
        "        -1.37923006e-12,  -2.20638285e-10,  -7.50792761e-11,\n",
        "        -4.75257611e-11,  -3.66253694e-11,  -2.78860268e-11,\n",
        "        -2.48689958e-11,  -2.19612106e-11,  -1.90536475e-11,\n",
        "        -1.74555925e-11,  -1.65130132e-11,  -1.55708779e-11,\n",
        "        -1.46282986e-11,  -1.36859413e-11,  -1.27433619e-11,\n",
        "        -1.22981625e-11,  -1.20079502e-11,  -1.17172938e-11,\n",
        "        -1.14268595e-11,  -1.11362031e-11,  -1.08457687e-11,\n",
        "        -1.05553344e-11,  -1.02649000e-11,  -9.97424365e-12,\n",
        "        -9.68380931e-12,  -9.39315292e-12])"
       ]
      }
     ],
     "prompt_number": 65
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "plt.plot(np.linspace(0, 2 * k_star), c_k(np.linspace(0, 2 * k_star)))\n",
      "plt.plot(np.linspace(0, 2 * k_star), ramsey_analytic_consumption_policy(np.linspace(0, 2 * k_star), model.args))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 41,
       "text": [
        "[<matplotlib.lines.Line2D at 0x9ab7210>]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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0mzd8209HfriKpU9ERkNU8VtaWgL4+86erKwsJCQkwM3NrcyY7OxsDB06FHFx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\nYv4PuYFnhLaJqsAAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x9ab2650>"
       ]
      }
     ],
     "prompt_number": 41
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ti = np.linspace(0, 3.9, 100)\n",
      "model.interpolate(traj[:,:-1], ti, k=3, ext=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "array([[ 0.        ,  1.31396159],\n",
        "       [ 0.03939394,  1.31187305],\n",
        "       [ 0.07878788,  1.3097415 ],\n",
        "       [ 0.11818182,  1.30756606],\n",
        "       [ 0.15757576,  1.30534583],\n",
        "       [ 0.1969697 ,  1.30307992],\n",
        "       [ 0.23636364,  1.30076745],\n",
        "       [ 0.27575758,  1.29840747],\n",
        "       [ 0.31515152,  1.29599904],\n",
        "       [ 0.35454545,  1.2935412 ],\n",
        "       [ 0.39393939,  1.29103297],\n",
        "       [ 0.43333333,  1.28847336],\n",
        "       [ 0.47272727,  1.28586135],\n",
        "       [ 0.51212121,  1.28319591],\n",
        "       [ 0.55151515,  1.28047598],\n",
        "       [ 0.59090909,  1.2777005 ],\n",
        "       [ 0.63030303,  1.27486838],\n",
        "       [ 0.66969697,  1.2719785 ],\n",
        "       [ 0.70909091,  1.26902975],\n",
        "       [ 0.74848485,  1.26602096],\n",
        "       [ 0.78787879,  1.26295098],\n",
        "       [ 0.82727273,  1.25981862],\n",
        "       [ 0.86666667,  1.25662266],\n",
        "       [ 0.90606061,  1.25336188],\n",
        "       [ 0.94545455,  1.25003504],\n",
        "       [ 0.98484848,  1.24664085],\n",
        "       [ 1.02424242,  1.24317802],\n",
        "       [ 1.06363636,  1.23964525],\n",
        "       [ 1.1030303 ,  1.23604118],\n",
        "       [ 1.14242424,  1.23236448],\n",
        "       [ 1.18181818,  1.22861376],\n",
        "       [ 1.22121212,  1.22478761],\n",
        "       [ 1.26060606,  1.22088461],\n",
        "       [ 1.3       ,  1.21690332],\n",
        "       [ 1.33939394,  1.21284227],\n",
        "       [ 1.37878788,  1.20869995],\n",
        "       [ 1.41818182,  1.20447487],\n",
        "       [ 1.45757576,  1.20016548],\n",
        "       [ 1.4969697 ,  1.19577021],\n",
        "       [ 1.53636364,  1.1912875 ],\n",
        "       [ 1.57575758,  1.18671572],\n",
        "       [ 1.61515152,  1.18205324],\n",
        "       [ 1.65454545,  1.17729843],\n",
        "       [ 1.69393939,  1.17244959],\n",
        "       [ 1.73333333,  1.16750502],\n",
        "       [ 1.77272727,  1.16246302],\n",
        "       [ 1.81212121,  1.15732182],\n",
        "       [ 1.85151515,  1.15207966],\n",
        "       [ 1.89090909,  1.14673476],\n",
        "       [ 1.93030303,  1.14128529],\n",
        "       [ 1.96969697,  1.13572943],\n",
        "       [ 2.00909091,  1.13006531],\n",
        "       [ 2.04848485,  1.12429107],\n",
        "       [ 2.08787879,  1.11840479],\n",
        "       [ 2.12727273,  1.11240456],\n",
        "       [ 2.16666667,  1.10628845],\n",
        "       [ 2.20606061,  1.10005448],\n",
        "       [ 2.24545455,  1.0937007 ],\n",
        "       [ 2.28484848,  1.08722509],\n",
        "       [ 2.32424242,  1.08062564],\n",
        "       [ 2.36363636,  1.07390033],\n",
        "       [ 2.4030303 ,  1.06704711],\n",
        "       [ 2.44242424,  1.06006391],\n",
        "       [ 2.48181818,  1.05294867],\n",
        "       [ 2.52121212,  1.0456993 ],\n",
        "       [ 2.56060606,  1.03831369],\n",
        "       [ 2.6       ,  1.03078974],\n",
        "       [ 2.63939394,  1.02312534],\n",
        "       [ 2.67878788,  1.01531836],\n",
        "       [ 2.71818182,  1.00736666],\n",
        "       [ 2.75757576,  0.99926813],\n",
        "       [ 2.7969697 ,  0.99102063],\n",
        "       [ 2.83636364,  0.98262202],\n",
        "       [ 2.87575758,  0.97407017],\n",
        "       [ 2.91515152,  0.96536297],\n",
        "       [ 2.95454545,  0.9564983 ],\n",
        "       [ 2.99393939,  0.94747405],\n",
        "       [ 3.03333333,  0.93828814],\n",
        "       [ 3.07272727,  0.9289385 ],\n",
        "       [ 3.11212121,  0.91942307],\n",
        "       [ 3.15151515,  0.90973984],\n",
        "       [ 3.19090909,  0.89988681],\n",
        "       [ 3.23030303,  0.88986201],\n",
        "       [ 3.26969697,  0.87966354],\n",
        "       [ 3.30909091,  0.8692895 ],\n",
        "       [ 3.34848485,  0.85873807],\n",
        "       [ 3.38787879,  0.84800748],\n",
        "       [ 3.42727273,  0.837096  ],\n",
        "       [ 3.46666667,  0.82600201],\n",
        "       [ 3.50606061,  0.81472393],\n",
        "       [ 3.54545455,  0.80326025],\n",
        "       [ 3.58484848,  0.79160962],\n",
        "       [ 3.62424242,  0.77977071],\n",
        "       [ 3.66363636,  0.76774235],\n",
        "       [ 3.7030303 ,  0.75552345],\n",
        "       [ 3.74242424,  0.74311304],\n",
        "       [ 3.78181818,  0.73051046],\n",
        "       [ 3.82121212,  0.7177151 ],\n",
        "       [ 3.86060606,  0.70472637],\n",
        "       [ 3.9       ,  0.69154367]])"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ramsey_analytic_consumption_policy(traj[:,1], model.args) - traj[:,2]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 284,
       "text": [
        "array([  0.00000000e+00,  -5.55111512e-17,   0.00000000e+00,\n",
        "         0.00000000e+00,  -5.55111512e-17,   0.00000000e+00,\n",
        "        -5.55111512e-17,  -5.55111512e-17,  -5.55111512e-17,\n",
        "        -1.11022302e-16,  -1.11022302e-16,  -1.11022302e-16,\n",
        "         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
        "        -1.11022302e-16,   0.00000000e+00,   0.00000000e+00,\n",
        "         0.00000000e+00,  -1.11022302e-16,  -1.11022302e-16,\n",
        "         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
        "         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
        "         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
        "         1.11022302e-16,   1.11022302e-16,   0.00000000e+00,\n",
        "         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
        "         1.11022302e-16,   0.00000000e+00,   1.11022302e-16,\n",
        "         1.11022302e-16])"
       ]
      }
     ],
     "prompt_number": 284
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "traj[:,2]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 265,
       "text": [
        "array([ 0.67650213,  0.7093163 ,  0.72884601,  0.74040856,  0.74723343,\n",
        "        0.75125657,  0.75362473,  0.75501781,  0.75583712,  0.75631817,\n",
        "        0.75660218,  0.75676894,  0.7568667 ,  0.7569241 ,  0.75695783,\n",
        "        0.7569775 ,  0.75698894,  0.75699563,  0.75699969])"
       ]
      }
     ],
     "prompt_number": 265
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 261,
       "text": [
        "array([[  8.97012186e-03,   4.80241297e-03],\n",
        "       [  5.35450441e-03,   2.86668808e-03],\n",
        "       [  3.17443249e-03,   1.69952382e-03],\n",
        "       [  1.87487322e-03,   1.00376735e-03],\n",
        "       [  1.10568807e-03,   5.91961938e-04],\n",
        "       [  6.48957057e-04,   3.47437843e-04],\n",
        "       [  3.80295112e-04,   2.03601936e-04],\n",
        "       [  2.22582919e-04,   1.19166173e-04],\n",
        "       [  1.29884727e-04,   6.95375280e-05],\n",
        "       [  7.67350365e-05,   4.10823108e-05],\n",
        "       [  4.33335592e-05,   2.31998684e-05],\n",
        "       [  2.40890703e-05,   1.28967773e-05],\n",
        "       [  1.32983300e-05,   7.11964377e-06],\n",
        "       [  7.09179034e-06,   3.79679411e-06],\n",
        "       [  3.47254822e-06,   1.85912864e-06],\n",
        "       [  1.64429592e-06,   8.80321125e-07],\n",
        "       [  7.96329025e-07,   4.26337632e-07],\n",
        "       [  3.65099121e-07,   1.95466315e-07],\n",
        "       [  1.18152866e-07,   6.32565381e-08]])"
       ]
      }
     ],
     "prompt_number": 261
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 217
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Task 6: Solving the linearized system!\n",
      "--------------------------------------\n",
      "\n",
      "In this task you will learn how to approximate the optimal consumption/savings decision rule for the representative household using a first-order Taylor series approximation in the neighborhood of the steady state of the Ramsey economy."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def eulerLinear(k):\n",
      "    \"\"\"This period's consumption per effective worker can be written \n",
      "    as a function of current period capital stock per effective worker.\n",
      "    \n",
      "    Inputs:\n",
      "        k_t-1: end of period t-1 level of capital per effective worker\n",
      "        \n",
      "    Returns:\n",
      "        c_t: consumption per effective worker\n",
      "    \"\"\"\n",
      "    if np.abs(ramseyEigenvalues[0]) < 1:\n",
      "        i = 0\n",
      "    elif np.abs(ramseyEigenvalues[1]) < 1:\n",
      "        i = 1\n",
      "    else:\n",
      "        print 'Ahhh! Jacobian has no stable eigenvalue!'\n",
      "\n",
      "    return analytic_c_star() + (ramseyEigenvectors[1,i] / ramseyEigenvectors[0,i]) * (k - analytic_k_star())\n",
      "\n",
      "def capitalLinear(k):\n",
      "    \"\"\"Linear approximation of the equation of motion for capital \n",
      "    per effective worker.\n",
      "    \n",
      "    Inputs:\n",
      "\n",
      "        k_t-1: end of period t-1 capital per effective worker\n",
      "        \n",
      "    Returns: next period's capital stock per effective worker, k_t\n",
      "\n",
      "    \"\"\"\n",
      "    kNext = analytic_k_star() + ramseyJacobian[0,0] * (k - analytic_k_star()) + \\\n",
      "                                ramseyJacobian[0,1] * (eulerLinear(k) - analytic_c_star())\n",
      "    return kNext\n",
      "\n",
      "def capitalQuadratic(k):\n",
      "    \"\"\"Quadratic approximation of the equation of motion for capital \n",
      "    per effective worker.\n",
      "    \n",
      "    Inputs:\n",
      "\n",
      "        k_t-1: end of period t-1 capital per effective worker\n",
      "        \n",
      "    Returns: next period's capital stock per effective worker, k_t\n",
      "\n",
      "    \"\"\"\n",
      "    pass"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 128
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Generate sample paths of the linear Ramsey model.  Because the linearized model expresses next period's capital stock per effective worker (consumption per effective worker) in terms of the current period's capital stock per effective worker (consumption per effective worker) we can make use of the Python class DS from the Solow lab to simulate trajectories of the capital and consumption per effective worker for the linearized Ramsey economy!"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Create a grid of points for plotting\n",
      "gridmax, gridsize = 200, 10000\n",
      "grid = np.linspace(0, gridmax, gridsize)\n",
      "\n",
      "# Given an initial level of capital\n",
      "k0 = analytic_k_star() / 8\n",
      "\n",
      "# Create a new instance of the class ramseyDS\n",
      "ramsey_linear = DS(F=capitalLinear)\n",
      "\n",
      "# Generate a sample path for the linearized model\n",
      "#ramsey_linear.X = k0\n",
      "#k_linear = ramsey_linear.sample_path(1000)\n",
      "#c_linear = eulerLinear(k_linear)\n",
      "\n",
      "# Create a new plot\n",
      "plt.figure(figsize=(8,6))\n",
      "model.plot_phaseSpace(gridmax=200)\n",
      "\n",
      "# Add the initial level of capital per worker\n",
      "plt.axvline(k0, color='k', ls='--', label=r'$k_{0}$')\n",
      "\n",
      "# Plot the linearized sample path\n",
      "plt.plot(grid, eulerLinear(grid), color='purple')\n",
      "\n",
      "# Add a title to the plot\n",
      "plt.title('Linear approximation of the saddle path')\n",
      "\n",
      "# Add a legend\n",
      "plt.legend(frameon=False)\n",
      "\n",
      "plt.savefig('Graphics/Ramsey-Linear-Path.png')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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kRaGJPxpPzBcxdH4vb7fIFUKI4hIREcHVq1e5c+cO/fr14+jRozZxaa8UeVEo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\nAP+1jgAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 131
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Task 7: 'Forward Shooting' to find global non-linear saddle path of the Ramsey Model.\n",
      "\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "reload(ramsey)\n",
      "model = ramsey.ramseyModel(ramsey_params)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 133
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Create a grid of points for plotting\n",
      "gridmax, gridsize = 200, 10000\n",
      "grid = np.linspace(0, gridmax, gridsize)\n",
      "\n",
      "# Create a new instance of the class ramseyDS\n",
      "model = ramsey.ramseyModel(ramsey_params)\n",
      "\n",
      "# Given an initial level of capital\n",
      "k0 = 0.5 * analytic_k_star()\n",
      "c0 = eulerLinear(k0)\n",
      "\n",
      "# Create a new plot\n",
      "plt.figure(figsize=(8,6))\n",
      "model.plot_phaseSpace(gridmax=200)\n",
      "\n",
      "# plot the sample path starting from the linearized guess\n",
      "model.k, model.c = k0, c0\n",
      "tmpPath = model.get_samplePath(T=1000) \n",
      "plt.plot(tmpPath[:, 0], tmpPath[:, 1], color='r')\n",
      "\n",
      "# Add a title to the plot\n",
      "plt.title('Linearized guess is not a \"good\" one!', fontsize=15)\n",
      "\n",
      "# Add a legend\n",
      "plt.legend(frameon=False)\n",
      "\n",
      "plt.savefig('Graphics/Ramsey-Sample-Path-Linearized-Guess.png')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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nzpySjiYiIuLWHDJcX758eQBSU1PJyMigbNmyOR5PSkqif//+BAQEMGDAALZv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\n"
      }
     ],
     "prompt_number": 135
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "reload(ramsey)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 144,
       "text": [
        "<module 'pyeconomics.models.ramsey' from '/Users/clarissasweet/Projects/pyeconomics/models/ramsey.py'>"
       ]
      }
     ],
     "prompt_number": 144
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# create an instance of the Python object representing the Ramsey model\n",
      "model = ramsey.ramseyModel(ramsey_params)\n",
      "\n",
      "# pick an initial condition for capital...\n",
      "k0 = analytic_k_star() / 8\n",
      "\n",
      "# solve the model!\n",
      "ramsey_solution_lower = model.solve_forwardShoot(k0, tol=1.5e-4)\n",
      "\n",
      "# pick an initial condition for capital...\n",
      "k0 = analytic_k_star() * 8\n",
      "\n",
      "# solve the model!\n",
      "ramsey_solution_upper = model.solve_forwardShoot(k0, tol=1.5e-4)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 145
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Create a new plot\n",
      "plt.figure(figsize=(8,6))\n",
      "\n",
      "# plot the Ramsey phase diagram\n",
      "ax = model.plot_phaseSpace(gridmax=200)[0]\n",
      "\n",
      "# Plot the full saddle-path\n",
      "ax.plot(ramsey_solution_lower[1][:, 0], ramsey_solution_lower[1][:, 1], color='r')\n",
      "ax.plot(ramsey_solution_upper[1][:, 0], ramsey_solution_upper[1][:, 1], color='r')\n",
      "\n",
      "# Plot the linearized sample path\n",
      "ax.plot(grid, eulerLinear(grid), color='purple')\n",
      "\n",
      "# Axes, labels, title, legend, etc\n",
      "ax.set_xlim(0, 200)\n",
      "ax.set_title('Saddlepath of the Ramsey economy', fontsize=20)\n",
      "\n",
      "# Add a legend\n",
      "plt.legend(frameon=False)\n",
      "\n",
      "plt.savefig('Graphics/Ramsey-Full-Nonlinear-Saddle-Path.png')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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ctWvXpkOHDgbb1otIc73IV8LHh1OtfTVK1y5t7FD0a/9+eP118PJSx6GXBC+E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\niIgEKBV5ERGRAKUiLyIiEqD+P2kbuLXe2thwAAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 146
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure(figsize=(8,6))\n",
      "ax = model.plot_phase_diagram(7.5)[0]\n",
      "\n",
      "colors = mpl.cm.cool(np.linspace(0,1,10))\n",
      "\n",
      "# compute the steady state values\n",
      "k_star = model.steady_state.values['k_star']\n",
      "c_star = model.steady_state.values['c_star']\n",
      "\n",
      "# plot the unstable manifold\n",
      "init = [k_star - 1e-5, c_star + 1e-5]\n",
      "traj = model.integrate(t0=0, y0=init, T=1e3, h=0.25, integrator='lsoda')\n",
      "ax.plot(traj[:,1], traj[:,2], label='$M_U$', color=colors[0])\n",
      "        \n",
      "init = [k_star + 1e-5, c_star - 1e-5]\n",
      "traj = model.integrate(t0=0, y0=init, T=1e3, h=0.25, integrator='lsoda')\n",
      "ax.plot(traj[:,1], traj[:,2], color=colors[0])\n",
      "\n",
      "# plot the stable manifold\n",
      "model.steady_state.set_eigen_star(model.jac(0, [k_star, c_star], model.args))\n",
      "\n",
      "optimal_traj = model.solve_reverse_shooting(0.1 * k_star, h=0.5, eps=1e-9)\n",
      "ax.plot(optimal_traj[:,1], optimal_traj[:,2], label='$M_S$', color=colors[9])\n",
      "\n",
      "optimal_traj = model.solve_reverse_shooting(2 * k_star, h=1.0, eps=1e-9)\n",
      "ax.plot(optimal_traj[:,1], optimal_traj[:,2], color=colors[9])\n",
      "\n",
      "ax.set_title('Phase diagram for the Ramsey (1928) model', fontsize=20)\n",
      "ax.legend(loc='best', frameon=False, prop={'family':'serif'})\n",
      "\n",
      "plt.savefig('Graphics/ramsey-phase-diagram-with-manifolds.pdf')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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Gqu7du6sPP/zQ7nvYHvOwrVuvb2/YoHlSD/PDPGb28OHD6o033lCNGjVSZcuW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\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xaab0110>"
       ]
      }
     ],
     "prompt_number": 243
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Task 8: Welfare Analysis\n",
      "------------------------\n",
      "\n",
      "Very much homework related! So pay attention! Two different ways to analyze welfare in the Ramsey model:\n",
      "\n",
      "1. Instantaneous welfare as measured by the flow of utility to the representative individual over time.\n",
      "2. The present discounted value of expected lifetime consumption.\n",
      "\n",
      "Can calculate both measure for the linearized and full saddle path and compare. First, need to compare the linearized solution with the full non-linear solution..."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Compare Time path of consumption between the linear and non-linear solution\n",
      "\n",
      "# Initialize the linearized and full saddle paths\n",
      "ramsey_linear.X = analytic_k_star() / 8\n",
      "\n",
      "# Simulate the time path of consumption for the linearized model\n",
      "c_linear = eulerLinear(ramsey_linear.sample_path(ramsey_solution_lower[2]))\n",
      "\n",
      "# Create a new plot\n",
      "plt.figure(figsize=(8,8))\n",
      "plt.plot(ramsey_solution_lower[1][:, 1], color='b', label=r'$c_{Full}$')\n",
      "plt.plot(c_linear, color='g', label=r'$c_{Linear}$')\n",
      "\n",
      "# Add the steady state value for capital per effective worker\n",
      "plt.axhline(analytic_c_star(), ls='--', color='k', label=r'$c^{*}$')\n",
      "\n",
      "# Don't forget to label your axes!\n",
      "plt.xlim(0, 200)\n",
      "plt.xlabel('Time')\n",
      "plt.ylabel('Consumption per effective worker, c')\n",
      "\n",
      "# Add the legend\n",
      "plt.legend(loc='best', frameon=False)\n",
      "\n",
      "# Add a title to the plot\n",
      "plt.title('Solution paths of consumption per effective worker, c', weight='bold')\n",
      "\n",
      "plt.savefig('Graphics/Full-vs-Linear-Saddlepath-Comparison.png')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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/pfDkdgncummFmzeBmzeBiAjd8eayZXW3cuVe/J5yv0wZ3fFoooIsz+6WT+36\n9eu4cOECmjRpkubxkJAQDB48WH/fxcUFN27cgIeHR26URVTgxSbFIuxpGG48vYHrT66/+PnkBu5G\n30XZYmXh4egBd0d3VLCvgDqV66BcsfKwTiiPqDulceOaFW5cBMLCgN03dT8BwN0dcHPT3WrXBrp1\n0z1WvryuVzcRmZbJwz06Ohr9+/fHrFmzUOSlr+Mi8so3EyWD3iqTJ0/W/+7l5QUvLy9jl0pklkQE\n92Pu4+LDi7j08BIuPdLdrjy6gqcJT+Hm4IZKTpXg4eSBWi610L1qd1RyqgQXqwq4cc0KV64AV08C\n564A664AV6/qArpqVd2tUiWgaVNdkLu76zqnsdMZUfYEBQUhKCjIaO2ZdLd8cnIyunTpgs6dO+t3\nvac2Z84cqNVqjBs3DgB3yxMZQkTwIOYBzv5zFuf+OYdLjy7pAv3RJVhbWKO6S3XUcKmB6s7VUd25\nOqo6V0XZYmWhUatw7Rpw/jxw7tyLn3fv6oI7JcRT3xwc3vSrJTJvefaYu4jAz88Pzs7O+P7779Od\nJqVD3aZNm7Br1y6sXLmSHeqIsiBZk4zLjy7j7D9ncebBGZz95yzOPjgLrWhRt2Rd1C5R+0WQu1SH\ns60zAODpU+D0aeDkSeDMGV2QX72qO95duzZQq9aLn5Uq6UYGI6Lcl2fD/eDBg/D09ESdOnX0u9qn\nT5+OiIgIAIC/vz8A4OOPP8aaNWvg5OSE5cuXo3r16q8WyXCnAkytVeNC5AWE3A1ByL0QnLh3Alce\nXUF5+/KoW7Iu6rr+eytZF2Xsyuj/3p48AU6d0gV5yu2ff4B69YCGDYH69XVBXr06j4MT5TV5NtyN\nieFOBYWI4Oazmzh+9zhC7oUg5G4ITt8/jfL25dG4TGM0Kd0EjUo3Qm3X2rC1epHIajUQGgocPgwc\nOgQcOwY8fKgL8AYNdGHesKFulzpPHSPK+xjuRPmYWqvG6funEXwrGAciDuDQ7UOwtrBGkzJN9LeG\npRrCvrB9mvmePgWOHn0R5seP63qiv/227vbWW0CVKgxyovyK4U6Uj8QnxyPkbggORBxA8K1gHL1z\nFBUcKsCzgic8y3uiefnmKFus7CvzPXoEBAUB+/YB+/frzhdv3FgX5M2b68Lc0TH3Xw8RmQbDnSgP\nS9YkI+RuCP4K+wt7b+7F6funUbNETXhW8ETL8i3RonwLONk4vTLfs2dAcDDw99+6QA8PB1q0ANq0\nAby8gLrPoMEIAAAgAElEQVR1edERInPGcCfKQ0QEVx9fxV9hf+GvsL+wP3w/3Bzd0N69Pdq5t8Pb\n5d5G0UJFX5lPq9X1Yt+xQ3cLDdVtjbdpA7RurTtezp7rRAUHw53oDUtQJyAoPAhbr27F1qtboREN\n2ru3R3v39mjr3hYlipRId77Hj4Hdu3VhvmuX7qImnToBHTsCnp68wAlRQcZwJ3oDHsQ8wLar27D1\n2lbsu7kPdVzroGvlruhapStquNTIcKTFW7eATZuADRt0p6l5eb0I9IoVc/UlEFEexnAnyiW3nt3C\nn5f+xLqL63Dp0SW84/EOvKt4o2OljvpBYl4mohsoZuNGXaDfvg14ewM9ewLt2umufkZE9DKGO5EJ\n3Xx6E+sursO6S+tw48kN9KjWA31r9EVrt9YoZFEow/muXAFWrdLdEhN1Yd6jh65nOzvCEVFmGO5E\nRvYg5gFWnluJledWIiIqAj2r90Sf6n3gVdELVhYZ92q7fRtYvVoX6PfvA/37AwMGAE2a8EIqRJQ9\nDHciI4hLjsOmy5uwNHQpjt45iu5Vu+PdOu/Cq6IXLFUZb2pHRwNr1wKLFwMXLgC9eukCvVUrDiBD\nRDnHcCfKIRHB/lv7seTsEmy8vBFNyzSFb11fdK/aHUUKFXnNfLqR4RYtAtav1/VsHzZM1zGuUMZ7\n6omIsszQ3OPRPypwHsU9wpIzS/DzyZ9hbWmNofWGYnqb6ShlV+q18/3zD7B0qS7URXSBfukSULJk\nLhVORJRF3HKnAkFEcCDiAH4++TO2Xd2G7tW6w7+hP5qVbZbhaWspjh0DZs8Gtm/X7XYfNkw37CuP\noxORqXC3PNFrxCTFYPGZxZh3fB4EAv+G/vCt65vukK+pJSYCf/wBzJmjG2xmzBhg6FCO305EuYPh\nTpSOO8/vYE7IHCw8tRBeFb0Q0CQAnhU8M91Kv38fmDcP+PVXoE4dICAA6NyZneOIKHfxmDtRKifv\nncSso7Ow/dp2+Nb1Rch7IXB3dM90vhs3gG++0fV89/HRXbClevVcKJiIyAQY7pTviQh23diFmQdn\nIuxpGD5s+iHmdp4Lh8IOmc4bGgrMmAH89RcwcqRu8BkXl1womojIhBjulG+JCLZd24ap+6ciNjkW\nn7X8DH1r9H3tQDMpDh3ShfqpU0BgIPDzz0CxYrlQNBFRLmC4U76jFS02X9mMqfunQq1VY2KriehV\nvRdUiirTeU+cAD77DLh6FfjoI2DdOl59jYjMD8Od8g0RwfpL6zE1eCosFAtMbDUR3ap2y1KoX7wI\nfPEFcPSo7uewYRxwhojMF8Od8oWg8CD831//B7VWjS9bf4muVbpm2vMdAG7eBKZM0Z2jPmECsGwZ\nYGubCwUTEb1BDHfK085HnsfHez7GhYcX8FWbr+BTyydLW+qPHulCfeVK4IMPgGvXAHv7XCiYiCgP\nyPy/JNEbcOf5HQzfPBxtlrRBW7e2uDzmMgbWHphpsCclAT/8oDuNTQS4fFkX8gx2IipIuOVOeUps\nUixmHJyB+Sfm4/2G7+NqwNUsndImAmzbBvznP4CbG7B/P1CjRi4UTESUBzHcKU8QEay9uBb/3f1f\ntKzQEmf8z6CcfbkszRsWphtJ7sYNYNYs3dXZOO47ERVkDHd64y5EXkDAjgA8jn+MFb1WoGWFllma\nLzER+O47XaD/5z/Ahg3sAU9EBDDc6Q2KS47DlP1T8Pvp3zGp1ST4N/KHpSprH8m//wZGjQKqVNGd\nu16xomlrJSLKTxju9EbsvrEbo7aNQtMyTXF+9HmUKFIiS/NFRelOadu5U3fFtu7dTVwoEVE+xHCn\nXPUw9iHG7x6PgxEHMa/zPHSq3CnL827bphv/vUsX4Px5DhdLRJQRhjvlmnUX1+GD7R9gUJ1BOD/q\nPIoUKpKl+Z4+BcaOBQ4eBBYvBtq2NW2dRET5HcOdTO5x3GME7AjAiXsnsKH/BjQr1yzL8+7bBwwZ\nAnTrpruCW9GipquTiMhccBAbMqmtV7eizoI6KFGkBM6MPJPlYE9M1B1bHzwY+OUXYO5cBjsRUVZx\ny51MIi45Dv/Z/R/svL4TK3utRKuKrbI874ULwMCBgLs7cPYs4OxswkKJiMwQt9zJ6EL/CUXjXxsj\nKiEKZ/zPZCvYf/8d8PLSDUqzfj2DnYgoJ7jlTkYjIpgbMhdTg6fiu/bfwbeub5au3AYAsbHAmDHA\n8eMcOpaIyFAMdzKKZwnPMGTjENx5fgeHhx1G5eKVszzvpUtAnz5Ao0ZASAhQJGud6ImIKAPcLU8G\nO/PgDBr90gjl7Mvh8PDsBfsffwCenrrhYxcvZrATERkDt9zJIIvPLMaEvyZgdsfZGFB7QJbn02iA\nL74AVq0C/voLqFfPhEUSERUwDHfKkUR1IgJ2BCD4VjCC/IJQs0TNLM/77BkwaBAQF6fbDe/iYsJC\niYgKIO6Wp2yLjI1E26Vt8SjuEULeC8lWsF++DDRtCnh4ALt3M9iJiEyB4U7ZcvbBWTT5tQnauLXB\nun7rUMw66wO8//030KoV8H//B8yeDVhZmbBQIqICjLvlKcs2XNqA97e+j7md5qJ/rf7ZmnfZMl2n\nudWrgTZtTFQgEREBYLhTFogIZh6ciXkn5mHHoB1oVLpRNuYFpk0DFi3SbbnXzPoefCIiyiGGO72W\nWqtGwI4AHLl9BEeHH0WZYmWyPG9yMuDvr7vgy9GjQMmSJiyUiIj0GO6UodikWAz4cwDi1fEIHhqc\nrePr8fFAv36AVqsbcY7nrxMR5R52qKN0RcZGos3SNnC0ccS2gduyFezPnwOdOgF2dsDGjQx2IqLc\nxnCnV4Q/C0fzRc3xjsc7WNx9MQpZFMryvA8fAq1b68aGX76cPeKJiN4EhjulcfnRZXj+7okPm3yI\naa2nZfnCLwBw545uKNmOHYGffgJU/HQREb0RPOZOeqfvn0bnlZ0xs+1M+NXzy9a8ERG6LfaRI4EJ\nE0xUIBERZQnDnQAAh28fRs81PTGv8zz0rtE7W/OmBPsHHwDjxpmoQCIiyjKGO2HfzX3ov64/lvdc\njg6VOmRrXgY7EVHew3Av4P6++Td81vlgXd91aFWxVbbmZbATEeVNDPcCbH/4fvRb1w9r+67NdrDf\nu6cbRpbBTkSU97A/cwEVfCsYfdf2xZo+a+BV0Stb8z5+DLRvD4wYwWAnIsqLFBGRN11EZhRFQT4o\nM984GHEQPdf0xOreq9HWvW225o2JAdq2Bby8gK+/Nk19REQFnaG5Z7It92HDhsHV1RW1a9dO9/n4\n+Hj4+fmhfv36aNWqFTZt2mSqUiiVE/dOoNeaXljRa0W2gz0hAejRA6hTB5g500QFEhGRwUwW7kOH\nDsXOnTszfH7JkiUoUqQITp8+jaVLl2L8+PHcOjexy48uw3uVN371/hXveLyTrXnVamDAAMDJCViw\nAMjG2DZERJTLTBbuLVu2hKOjY4bP29vbIzo6GsnJyXjy5AlsbW2zNRoaZU9EVAQ6LO+AmW1nonu1\n7tmaVwQYPRqIjdVdl93CwkRFEhGRUbyx3vIDBgzAli1b4OzsDLVajSNHjrypUsxeZGwk2i9rj8Cm\ngdkeeQ7QHVs/fhwIDgasrU1QIBERGdUbC/e5c+fC0tIS9+/fx7lz59ClSxfcunULqgwGJJ88ebL+\ndy8vL3h5eeVOofnc88Tn6LSiE/rV7IdxzbLftX31amDePODIEd1V3oiIyPiCgoIQFBRktPZM2ls+\nPDwc3t7eOHfu3CvP9evXD8OHD0eHDroR0Zo2bYolS5agWrVqrxbJ3vI5kqxJRpeVXeDu6I75XeZn\n+7DHwYNAr17Anj26TnRERJQ78mxv+cy0bdsWW7ZsgVarRVhYGJ48eZJusFPOiAhGbRuFQhaFMLfz\n3GwH+9WrQJ8+usu2MtiJiPIXk+2WHzBgAPbv349Hjx6hXLlymDJlCpKTkwEA/v7+8PHxwcWLF9Go\nUSO4uLjgxx9/NFUpBdKMgzNw6v4pBA8NhqUqe2/zkydAly7Al18C72SvUz0REeUBHMTGDK08txKf\n7P0ER4YfQWm70tmaV60GOncGatUCvv/eRAUSEdFrGZp7HFvezATfCkbgzkDs9d2b7WAHgE8/BbRa\n4JtvTFAcERHlikyPua9fvx7Pnj3T33/27Bk2btxo0qIoZ8KehqHf2n5Y0WsFarumPzLg66xcCaxb\nB6xZA1jyax8RUb6V6W75unXr4uzZs2keq1evHs6cOWPSwlLjbvnMxSTFoNnCZni/wfsIaBqQ7flP\nnQI6dAD27mUHOiKiN83kveULFy6MuLg4/f24uDhYcIiyPEUrWgzZOARNyjTBB00+yPb8Dx/qTnmb\nN4/BTkRkDjLd+dq3b1+MGjUKo0aNgohgwYIF8PHxyY3aKIu+Cv4Kd6PvYkWvFdk+5U2rBQYN0o0b\n37eviQokIqJclelu+fj4eKxZswbr1q2DiKBPnz7w8fGBjY1NbtXI3fKvsenyJnyw4wOEjAhBKbtS\n2Z7/q6+AXbuAfft4nJ2IKK8wNPd4Klw+dunhJbRa3ApbB25FkzJNsj3//v2Ajw9w4gRQpowJCiQi\nohzJtyPUkWFik2LRZ20fzGg7I0fBHhmp2x2/eDGDnYjI3HDLPR8SEfht9INKUeH37r/n6Dh7x45A\n48a63fJERJS3cBCbAmjR6UU4df8Ujo04lu1gB4AZM4CEBGDKFBMUR0REb1y2t9x/+uknODs7o3fv\n3rDMpR5Y3HJ/4eyDs2i3rB2ChwSjukv1bM9/7BjQrZvuvHbujiciypty/Zi7iODAgQPo2bNnjhdK\nOfM88Tn6ru2LHzv+mKNgj40F3n0X+OknBjsRkTl77Za7VqvFunXr0K9fv9ys6RXcctd9qRq4fiAc\nCjtgfpf5OWpj5EggPh5YssTIxRERkVGZdMtdpVJh5syZBT5Y84JloctwPvI8vn8nZ5dq27YN2LkT\nmD3byIUREVGek+kx96lTpyI6Ohp+fn4oXfrFVcacnJxMXlyKgr7lfuPJDby18C3s9d2LOq7ZHx/2\n4UOgbl1g1SqgVSsTFEhEREZl8kFsKlasmG6P7Js3b+Z4odlVkMNdrVXD83dP9KvZD4FvBWZ7fhHd\nuPGVK/MyrkRE+YXJT4ULDw/PceNkuK+Cv4KdtR0+bPphjuZftgy4cQNYvdrIhRERUZ6VaW/5xMRE\nrFmzBmPGjAEAXLt2DVu3bjV5YQQcvn0Y80/Mx+Lui6FSsj+Y4D//ABMm6Eahs7Y2fn1ERJQ3Zbrl\nPmnSJIgIgoKCAAClS5dGnz590LVrV1PXVqBFJ0bj3fXvYkHXBTm6IAwABAQAw4YBDRoYuTgiIsrT\nMg33v//+G8eOHcPu3bsBAEWKFCmwx79z04S/JqC1W2v0qNYjR/Nv2ACcOcPT3oiICqJMw71q1aqI\niorS3z969Cjq169v0qIKuj1he7D92nacG3UuR/M/fQp88IGud3wuXpmXiIjyiEzDPSAgAD169MCd\nO3fQunVr/PPPP1i2bFlu1FYgRSdGY8TmEfi568+wL2yfozYmTAC6dwc8PY1cHBER5QuZngr35MkT\nODk54eTJk9BqtWjcuDFu3rwJNze33KqxQJ0KN3rbaCSoE7Co+6Iczb93LzB0KHD+PFCsmJGLIyKi\nXGHyseW7du2KqKgoNGzYEI0bN8bFixfZmc5E9t3chy1Xt+D7DjkbhS4hAfD3B+bPZ7ATERVkmYb7\nZ599Bm9vb8TExODkyZPo27cvVqxYkRu1FSgxSTEYsXkEFnRZAIfCDjlq45tvdCPRdeli5OKIiChf\nyfSYe5cuXZCUlIT27dsjJiYG69evR9WqVXOjtgLlk72fwLOCJ7pUyVky37ypGzf+1CkjF0ZERPlO\nhuEeEBCQ5v7z58/h4eGBuXPnQlEUzOYVSIwm5G4I1l1chwujL+S4jcBAYPx4oHx5IxZGRET5Uobh\n3rBhwzRjyqfcF5F0x5qnnFFr1fDf6o9v238LJ5ucXYxn61bg0iXgjz+MXBwREeVLr+0tr1ar4efn\n98aPsZtzb/lZR2Zh27Vt+GvwXzn60hQfD9SqBcybB3ToYIICiYgo15n0wjGWlpYIDw/Hw4cP4eLi\nkuOFUPpuR93GVwe+wuHhh3O8N+Sbb4D69RnsRET0QqYd6mrWrImWLVuia9euKFVKN8a5oigYP368\nyYszdx/u/BABTQJQpXiVHM1/8yYwZw470RERUVqZhnvp0qXh4+MDAIiJieExdyPZfGUzLj68iNW9\nc34t1o8/BsaOZSc6IiJKK9MR6lIkJycDAKysrExaUHrM7Zh7bFIsasyrgcXdF6O1W+sctXHkCNCv\nH3DlCmBra+QCiYjojTL5CHU3btxA//794eHhAQ8PD/j4+CAsLCzHCyRgxsEZaFG+RY6DXUR32tuX\nXzLYiYjoVZmG+/Tp09GtWzeEhYUhLCwM3bt3x1dffZUbtZmlsKdhWHBiAb5u93WO21i7VjfU7ODB\nRiyMiIjMRqa75evVq4dTp05BpdJ9D9BoNGjYsCHOnDmTKwUC5rVbvteaXmhYqiE+8/wsR/MnJgLV\nqwO//Qa0aWPk4oiIKE8w6alwAODt7Y3AwEAMGTIEIoJly5bB29s7xwssyPaG7cXpB6exsvfKHLcx\ndy5QsyaDnYiIMpbplvvz58+xePFibNu2DYDuKnF+fn4olouXHTOHLXe1Vo36P9fHFK8p6FW9V47a\nePwYqFYNOHBA95OIiMyTobmXabjfuHEDHh4eOV6AMZhDuM8NmYsNlzdgz+A9OT6VMDAQSE4GfvrJ\nyMUREVGeYvJw9/T0xJ07d9CkSRO0bNkSnp6eqF27do4XmBP5Pdwfxz1G9Z+qY5/fPtQqUStHbURE\n6Eaiu3gRcHU1coFERJSnmDzcASAxMREnTpxAUFAQfv75Z8TExODJkyc5Xmh25fdwD9gRABHB3M5z\nc9zGe+8BLi7A9OlGLIyIiPIkk3eoO3jwIIKDg3Hw4EE8e/YMXbp0gaenZ44XWNBce3wNq86twuUP\nLue4jevXgQ0bgGvXjFgYERGZrUy33C0sLNCwYUN88skn6Ny5M6ytrXOrNr38vOXeb20/1CtZD5+2\n/DTHbbz7LlC1KvDFF0YsjIiI8iyT75Z/9uwZDh48iAMHDiAkJAQWFhZ466238OWXX+Z4odmVX8P9\n2J1j6P1Hb1wNuApbq5wNJXfhgu60t2vXgFw8QYGIiN4gk++Wd3BwgLu7O+7cuYPbt2/j8OHDSEpK\nyvECCwoRwf/t+T9M8ZqS42AHgEmTgAkTGOxERJR1mW65u7u7o2rVqvqe8k2aNEGhQoVyqz4A+XPL\nfevVrfhoz0c4O/IsLFWZfodK16lTQNeuumPuHEOeiKjgMPlueY1GAwsLixwvwBjyW7hrtBrUXVAX\nM9rOgHfVnI/m16UL0KkT8MEHRiyOiIjyPJPvln/TwZ4fLTm7BE42TuhapWuO2zh2DDh/Hli/3oiF\nERFRgZCz/cWUofjkeEwKmoS1fdfmeCQ6APjqK+Cjj4A3cHICERHlcwx3I/v55M9oWKoh3ir7Vo7b\nCA0Fjh8H1qwxYmFERFRgZHo998ePH+Prr79Gt27dAAAXL17EwoULTV5YfhSbFIuvD32NKV5TDGpn\nxgxg/HjAxsZIhRERUYGSabhPnDgRdnZ2CA8PBwBUrlwZs2bNMnVd+dL8E/PRonwL1C1ZN8dtXLsG\n7NkDjBxpxMKIiKhAyTTcT5w4gdGjR+s71llaWrKTXTpikmLw7eFvManVJIPamTkTGDMGsLMzUmFE\nRFTgZHrMvUGDBrh9+7b+/vr169GyZUuTFpUfzQ2ZizZubXJ81TdAd+W3DRt057UTERHlVKbnuV+5\ncgUTJkzAwYMH4eTkBDc3N8ybNw+VK1fOrRrz/HnuzxOfo9LsSggeGoxqztVy3M6HH+p6x3/7rRGL\nIyKifCdXLvkKAJGRkdBoNChVqlSWGh42bBi2bduGEiVK4Ny5c+lOc/z4cYwePRoxMTFwdXVFUFBQ\n+kXm8XCftn8arj25hqU9l+a4jchIoFo13VjyWVzFRERkpgzNvUyPudepUwfTp09HdHR0loMdAIYO\nHYqdO3dm+LyIYNiwYZgxYwYuXbqEdevWZbntvORZwjP8eOxHfOFp2CXbfvgB8PFhsBMRkeEyDffN\nmzfDwsIC/fr1Q6NGjfDdd98hIiIi04ZbtmwJR0fHDJ8/ceIE6tSpg3bt2gEAnJ2ds1F23vHD0R/g\nXdUblYvn/DBFTAzwyy/Af/9rxMKIiKjAyjTcK1asiI8++ggnT57EqlWrEBoaCjc3N4MXvGvXLiiK\ngpYtW8Lb2xu7du0yuM3cFp0YjZ+O/4RPW+T8Wu0AsGQJ0KoV4O5upMKIiKhAy9IIdeHh4VizZg3+\n+OMPWFhY4JtvvjF4wQkJCThz5gz27NmDuLg4tG/fHufPn4dNBiO3TJ48Wf+7l5cXvLy8DK7BUD+f\n/Blt3doatNWu1ep2yf/+uxELIyKifCUoKCjDfmc5kWm4N23aFElJSejXrx/Wrl0LdyNtXjZr1gyJ\niYkoWbIkAKBRo0YIDg5Ghw4d0p0+dbjnBQnqBHx/5HvsGLTDoHa2bgUcHIDmzY1UGBER5Tsvb7RO\nmWLYSKeZhvvSpUtRtWpVgxaSnrfeegtTpkxBXFwcEhIScPr0aTTPRwm3+MxiNCjVwKDR6ADg++91\nQ80acI0ZIiKiNDIM92XLlmHw4MHYunUrtm3blqZLvqIoGD9+/GsbHjBgAPbv349Hjx6hXLlymDJl\nCpKTkwEA/v7+KF68OIYOHYpGjRrBxcUFU6dORdGiRY30skxLrVXjm0PfYFnPZQa1c/o0cOMG0KeP\nkQojIiLCa8I9Li4OABAdHZ2jS5euWrUq02lGjRqFUaNGZbvtN23N+TUoZ18Ozcsbtqdh1iwgIACw\nsjJSYURERMjCIDYHDx5EixYtMn3MlPLSIDZa0aLO/Dr43zv/Q4dK6fcPyIp794CaNYGwMOA1ZwwS\nEVEBZPJBbAICArL0WEGx5coWWFta4x2Pdwxq56efgHffZbATEZHxZbhb/siRIzh8+DAePnyI77//\nXv8N4uHDhyhevHiuFZiXiAhmHJyBT1p8kqNDFSni4nSD1hw5YsTiiIiI/pVhuCclJSE6OhoajQbR\n0dH6x6tVq4YPP/wwV4rLaw5GHMTj+MfoWa2nQe2sXg00bQpUqmSkwoiIiFLJ9Jj7rVu3UKFChdyq\nJ1155Zh7rzW90M69HUY3Hm1QO40bA5MnA126GKcuIiIyLyY/5j5ixAg8e/ZMf//JkycZDjRjzm48\nuYEDEQfgV9fPoHZOnAAePgQ6djRSYURERC/JNNwjIyPh4OCgv+/k5IT79++btKi86MdjP+K9Bu+h\nSKEiBrWzYAHg7w9YWBipMCIiopdkOkJdrVq1cPLkSTRs2BCA7mpu1atXN3lhecnT+KdYHroc50ef\nN6idZ8+AP/8ErlwxUmFERETpyDTcP/zwQwwaNEh/3D08PBzLlhk2Mlt+8+upX9G1SleUtittUDtL\nl+p2x5coYaTCiIiI0pFph7oUx48fBwA0btzYpAWl5012qEvWJMN9tjs2+2xG/VL1c9yOiG7Qmvnz\ndZd3JSIiyojJO9QBwLFjx7B37140btwYERERCAkJyfEC85u1F9eislNlg4IdAIKDdReH8fQ0UmFE\nREQZyDTcp0+fjh9++AFLliwBABQtWhSjRxt2Klh+ISL435H/YXyz118kJyvmzwdGjuTV34iIyPQy\nDfctW7ZgxYoVKFy4MABdb/mkpCSTF5YXHIg4gJikGHSu3Nmgdv75B9i1C/D1NVJhREREr5FpuJct\nWzZNmF+6dAlVqlQxaVF5xZyQOfiwyYdQKVk6epGhRYt0l3W1tzdSYURERK+RaW95f39/eHt7IzIy\nEkOHDsWBAwfw66+/5kZtb9S96HvYG7YXC7stNKgdEV24L19upMKIiIgykWFv+Zs3b8LNzQ2A7tru\nO3bsgFarRdeuXWFjY5O7Rb6B3vKTgyYjMjYS87rMM6idAwd0g9ZcuMDj7URElDWG5l6G4d6wYUOc\nPHkSbdu2xd69e3O8AGPI7XBP1iSjwg8VsHvwbtQqUcugtoYPB6pVAyZMMFJxRERk9gzNvQx3yzs4\nOGDy5Mm4cuVKmku+pix0/HjDe5DnVRsvb0Tl4pUNDvbYWGD9euDSJSMVRkRElAUZ9hRbtmwZnJyc\n9Jd8jYmJ0d9SXwLWHP10/CeMaTzG4HbWrQNatABKljRCUURERFmU4Zb72rVrMXbsWDx79gwTJ07M\nzZreqAuRF3D18VX0qNbD4LZ+/x0ICDBCUURERNmQ4Zb70qVLAQAbNmzItWLygnkn5uG9hu+hkEUh\ng9oJC9N1ovP2NlJhREREWZThlruXlxc8PDxw//591K5dO81ziqIgNDTU5MXltujEaKw6twrnRp0z\nuK0lS4CBA4FChn1HICIiyrbXXjjm6dOnaNWqFbZs2fJKr72KFSuauja93OotP+/4POy7uQ/r+q0z\nqB2tFnB3BzZuBOrVM1JxRERUYJistzwAODo66rfQU5/3bo5EBPNPzMePHX80uK2//wYcHRnsRET0\nZmQ6rmpQUBCaNm2K1q1bAwBOnz6Nbt26mbyw3Hbs7jEkqBPQumJrg9tavBgYMsTgZoiIiHIk03D/\n9ttvsXnzZjg6OgIA6tevj7CwMJMXltt+O/UbRtQfAcXAYeSio4EtW4BBg4xUGBERUTZlOrZ8TEwM\nXF1d9fejo6NRrFgxkxaV26ITo/HnpT9xaYzho81s3Ki7ZruzsxEKIyIiyoFMt9y7d++O2bNnQ61W\nIzg4GCNHjkT//v1zo7Zc88eFP9CqQiuULGr4aDOrVgEDBhihKCIiohx6bW95AEhISMDq1avx559/\nQqvVYuDAgejTpw+sra1zq0aT95ZvtrAZPmv5GbpW6WpQOw8fApUrA3fvAkWKGKk4IiIqcEx24Zi8\nxIoaCuQAACAASURBVJThfj7yPDos74Bbgbdgqcr0KMVrzZ8PBAfrtt6JiIhyytDcy3S3vLlbeHoh\nhtQbYnCwA9wlT0REeUOB3nJPVCei7KyyODr8KDycPAxq6/Zt3Xnt9+4BuXjEgoiIzJBJt9w1Gg1m\nzZqV48bzuk1XNqGOax2Dgx0A1qwBevZksBMR0Zv32nC3sLDAihUrkJSUlFv15KrfTv2G4fWHG6Wt\nVat0Y8kTERG9aZkeaO7QoQOGDBmCgQMHonTp0vrHGzRoYNLCTC38WThO3T+FzQM2G9zWlSvA/ftA\nq1ZGKIyIiMhAmYb7oUOHoCgK/ve//6V5/O+//zZZUblh6dml8Knlg8KWhQ1ua9UqoF8/wMLCCIUR\nEREZqEB2qBMRVJ5TGSt7r0STMk0MbAuoVg1YuhRo2tRIBRIRUYFm8lPhHj9+jK+//lp/sZiLFy9i\n4cKFOV5gXnD0zlFYqCzQuHRjg9s6fRpQq4Emhn1HICIiMppMw33ixImws7NDeHg4AKBy5cr5vgf9\nstBl8K3ja/BFYgBg9Wqgf3/ACE0REREZRabhfuLECYwePRoW/x5QtrS01P+eHyVpkvDHhT8wqI7h\nl20TAdavB/r2NUJhRERERpJpuDdo0AC3b9/W31+/fj1atmxp0qJMafu17ahZoiYqOlQ0uK1z5wCN\nRjd4DRERUV6RaW/5wMBAjBkzBuHh4ahUqRLc3Nwwb9683KjNJJaeXYrBdQYbpa3164FevbhLnoiI\n8pYs95Z/+PAhNBoNSpY0/LKo2WWs3vJP4p/A7Uc3RARGwL6wvcHt1amju1hM8+YGN0VERKRnaO5l\nuuWemJiIrVu3YufOnVAUBR07dkSXLl1y9ZKvxvLHhT/QsVJHowT7tWu6S7w2a2aEwoiIiIwo03Cf\nOXMmQkNDMeDfy52tWrUK586dw6RJk0xenLEtC12GT1p8YpS2NmwAevQAVAX+unpERJTXZLpbvnr1\n6jhz5ox+Sz0xMRH16tXDpUuXcqVAwDi75W88uYG3F72NO+PuwMrCyuCa3noLmDYNaN/e4KaIiIjS\nMPkgNm+//Ta2b9+uv79jxw40y4f7opeFLoNPLR+jBPudO7rd8l5ehtdFRERkbJluudeoUQOXL1+G\nvb3uOHVUVBSqVasGCwsLKIqC0NBQ0xdp4DcYEUGVuVWwstdKNC5j+Kh0c+cCx48DS5YY3BQREdEr\nTN6hLvVWe3516v4piAgalW5klPbWrwfGjjVKU/T/7d15VFX13sfxzzGHYlBMEzXJAVRACQgZRBGy\nQdPEutlNuqtBfVrWbbhmg/fW00prrSfMJrPusyzzVvcxn9vNCefhyQOUCA6kXFMc0RQ1FE3CAcT9\n/MH1FCkekH3Y5xzer7Vccs7ZfveXtRd++O39++0NADCd03Dv1q1bI7ThWv/Y9g890PcBU243e+yY\ntGmTdOedJjQGAIALeP1cb8MwqsO9zwOm1MvIqA72664zpRwAAKbz+nBff3C9fFv4KqJDhCn1Lt6V\nDgAAd+X14X5x1G7GKfmff5YyM6Vhw0xoDAAAF3Ea7mvWrNHgwYMVEBAgf39/+fv7q3Xr1o3RW4Nd\nMC7on9//Uw/0NeeU/Jo11evb2zT8BncAALiM0wl1f/7znzV9+nT1799fzTzsdmzfHPhG7X3aK7R9\nqCn1liyRhg83pRQAAC7jNK1btmypmJiYegf72LFjFRgYqIiIK1/r3rBhg5o3b6758+fXq35d/O+/\n/lej+4w2pZZhSMuWEe4AAPfndOSelJSke+65R/fff78CAgIkVS+u/52TWWVjxozR008/rYcffrjW\nbaqqqjRp0iQNHTrUlKe+/dr5C+c1b/s85YzLMaVefr7k7y/17GlKOQAAXMZpuB89elQdO3bUN998\nU+N9Z+GelJSkoqKiK24zY8YMjRo1Shs2bHDeaT3Zi+y6qc1N6tG2hyn1OCUPAPAUTsP9008/dcmO\nDx06pEWLFunrr7/Whg0bnM5mnzx5suPrlJQUpTi5sbuZa9slaelS6b/+y7RyAAA42O122e120+rV\naeT+zjvvaPHixZKk1NRUTZw4UR06dGjQjidMmKD09HTH/XOdnZb/dbg7U1FVofnb5yt/fH6Derzo\n6FGpsFBKSjKlHAAANfx20DplypQG1XM6Sy49PV0BAQGO3yoCAgL0xhtvNGinkrRp0yaNHj1a3bt3\n17x58/THP/5RGRkZDa4rSf+39//Uu11v3dTmJlPqLV8u3X671LKlKeUAAHAppyP3r7/+Wlu2bHG8\nfvHFFxUdHd3gHe/du9fx9ZgxYzRixAilpqY2uK4kzd8xX6PCR5lSS6o+Jc/1dgCAp3A6ck9JSdG0\nadN0/PhxHTt2TO+++67T692SlJaWpsTERBUWFiooKEizZ8/WzJkzNXPmTDP6rlXVhSot2rFI94be\na0q9iorqm9dwVzoAgKdw+jz34uJivfXWW1q+fLkkadiwYXr++efVqVOnRmlQqt9zbbP2Z+lPK/5k\n2vX2r7+W/vxnKS/PlHIAADjV0Oe5Ow13d1Cfb3LCiglqd107vZL8iin7fu45qXVr6dVXTSkHAIBT\nDQ33Wq+5T506VZMmTdLTTz992Z2+//77V71TVzEMQwt2LNDSB5eaVnPpUul//se0cgAAuFyt4R4e\nHi5JiomJqbEG3TAMU56w5gqbD29Wq2taqc8NfUypt3u39NNP0i23mFIOAIBGUWu4jxgxQpLk4+Oj\n3//+9zU++/LLL13b1VWav2O+7g2717RfPpYtk+66S/Kw5+UAAJo4p7F1uTXtZqxzd4UF2xfod6FX\nvi1ufaxaJQ0ZYlo5AAAaRa0j9+XLl2vZsmU6dOiQnnnmGceF/ZKSEnXu3LnRGqyr7SXbdercKcXe\nGGtKvYoKKStLctHddwEAcJlaw71z586KiYnRokWLFBMT47jW3rVrV/Xv378xe6yTBTsW6J7Qe9TM\nZs459PXrq58A1769KeUAAGg0TpfCVVZWqkWLFjp06JBsNpslo/a6LAmI/ThWU2+fqsHdB5uyz1de\nkSorpfR0U8oBAFBnDV0K53SYu3nzZt18880aOnSohgwZosjISOW52R1dDvx0QPtO7NOgroNMq7l6\ntXTHHaaVAwCg0Ti9t/ykSZM0a9YsxcXFSZI2bNigF154wdRH0zXUwh0LNaL3CDVv5vTbqZMTJ6Rt\n26QBA0wpBwBAo3I6ci8rK1NYWJjjdVhYmMrKylzaVH0t2LHAtHvJS9LatVJionTttaaVBACg0Tgd\n6iYnJ2v48OG69957ZRiGFi1apOTkZM2fP1+S9Lvfmbf07GqcOHNCm4o36fYet5tWk1PyAABP5jTc\nS0tL1aNHD23dulWS1L17d504cUKLFy+WZH24r9yzUsndkuXTwse0mmvWSI8/blo5AAAaldNw/9TN\nF3ov3rlYd/e827R6RUXSqVNSRIRpJQEAaFROw/3gwYP6xz/+oZycHJ07d05S9RT9jIwMlzfnzPkL\n57Vi9wpNvX2qaTVXr5Zuv51bzgIAPJfTcH/ssceUkJCg8ePHq0WLFpLkNg+OyfkhR13bdFWX1l1M\nq7l6tTRsmGnlAABodE5vYtOvXz/l5eWpmYVD2doW87+4+kVd2/xavXbra6bsp6pK6tBB2rpVuvFG\nU0oCAFBvLnue+0Uvv/yynn32WY0cOVIBAQGO929xg+egLtm5RJ/e86lp9fLzpcBAgh0A4Nmchnth\nYaE+//xzbdy4US1btnS8v3btWpc25sye0j0qPVOqfp37mVaTJXAAAG/gNNxnzZqlH374QX5+fo3R\nT50t2blEw3sNN+1BMVJ1uE+caFo5AAAs4TQZIyMjdfTo0cbopV6W7Fpi6hK4s2elvDwpOdm0kgAA\nWMLpyP3kyZMKDw9XXFyc45q71UvhTp07pfUH12vBAwtMq5mbK/XpI/n7m1YSAABLOA33V155pTH6\nqJdVe1ZpQNAA+bU071JBZiajdgCAd3Aa7ikpKY3QRv0s2blEd/cy75S8VB3uXG8HAHgDp+vc/fz8\nHDetOXfunM6fPy8/Pz+dOnWqURqUaq73q7pQpU5vd1LeY3nqFtDNlPoVFVK7dtLBg1KbNqaUBADg\nqrl8nfvPP//s+Pr06dP6/PPPdeTIkaveYUNtKN6gDr4dTAt2SdqwQerVi2AHAHiHeq0j8/Hx0eOP\nP64vv/zSVf04tXz3cg3rae79YbneDgDwJk5H7vPmzXN8fe7cOWVmZioqKsqlTV3J8l3LTX1QjFQd\n7n/8o6klAQCwjNNwX7x4seOa+7XXXqsBAwbo7rvNncxWVyXlJSo8XqgBNw0wrWZlpZSTI82da1pJ\nAAAs5VHPc1+1Z5Vu7XarWl7T0vnGdbR5s9S9u3T99aaVBADAUk6vub/44ouOmfEPPPCAevfurSVL\nlri8sctZvnu5hoYMNbUm19sBAN7GabivXLlSrVu31ooVK2Sz2bR27Vq99dZbjdFbDReMC1q1Z5Xu\nCrnL1LqEOwDA2zgN94tPgpszZ47GjBmjzp076+TJky5v7Lc2FW9Se5/26hrQ1bSaVVXSt99KgwaZ\nVhIAAMs5veb+4IMPKjQ0VIGBgRoyZIh+/PFHtWrVqjF6q2HF7hWmn5L/7rvqZ7ffcIOpZQEAsJTT\nO9RJ1Tev8fHxkSSVl5errKxMHTt2dHlzF9lsNg2cPVD/mfSfGhIyxLS677wj7d4t/fWvppUEAKDB\nXH6HOkkqLS3V4sWLdfbsWcdOH3744ave6dX47sh3SuqaZGrNzEzpwQdNLQkAgOWchvvLL7+sjIwM\nJSYmOq6/S2r0cE/okiCfFj6m1btwQcrOlmbONK0kAABuwWm4L1iwQPn5+ZZcZ/+1O3vcaWq9goLq\na+2NeHUBAIBG4XS2/M0336yioqJGaOXKzLzWLlWP2pPMPcsPAIBbcDpyLykpUUREhOLi4tS2bVtJ\n1dfcMzIyXN7cr0V0iDC1Xk6OdNttppYEAMAtOJ0tb7fbf9n437P3bDabkhvxzi8NnTV4Od27S8uX\nS6GhppYFAKDBGpp7dVoKJ0m5ubmy2WyKi4u76p1dLbPD/cgRKTxcOnZMalavh94CAOB6Ll8KZ7fb\n9dhjj6lXr16SpF27dunjjz9u1JG72XJypIQEgh0A4J2chvu0adO0ZMkS9e7dW5K0c+dOTZgwwaPD\nfd06KTHR6i4AAHANp2PXEydO1LgbXWBgoCX3ljdTTo7Uv7/VXQAA4BpOR+6PPPKI7rrrLo0aNUqG\nYWjBggV69NFHG6E116iokPLzJQumDgAA0CjqNKFu69atWrJkiWw2m+6++25FRJi7LM0ZMyfU5eZK\n48dXPzQGAAB35LLZ8rt27VJxcfEl19azsrJ04403Kjg4+Kp3Wl9mhvt770mFhdJ//7cp5QAAMF1D\nc6/Wa+4TJky47C1nr7vuOk2YMOGqd2i1deu43g4A8G61hntRUZESEhIueT82Nlb79u1zaVOulJPD\nTHkAgHerNdzPnDmjkpKSS94vKSlReXm5S5tylR9+kM6elRrxigIAAI2u1nBPTk7WO++8c8n706dP\n99g17heXwNlsVncCAIDr1LoU7p133tG4cePUrVs3Jf378WnZ2dm65ZZbNGvWrEZr0EyckgcANAVO\nl8L9/PPPWrZsmWw2m+666y75+fk1Vm8OZs2Wj4+X3nxT8tATDwCAJqLRHhxjJTPC/exZqV076ccf\nJV9fkxoDAMAFXLYUrqHGjh2rwMDAWm94M2fOHEVGRioyMlIPPvigdu7c6apWJEmbNklhYQQ7AMD7\nuSzcx4wZoxUrVtT6eY8ePZSVlaUtW7ZoyJAhev31113ViiTWtwMAmg6XhXtSUpLatm1b6+f9+/dX\nmzZtJEnDhw9XZmamq1qRxMNiAABNh9MHxzSGjz76SCNGjLjiNpMnT3Z8nZKSopSUlHrtIzdXeuut\nq2gOAAAXs9vtstvtptVz6YS6oqIijRgxQgUFBbVus2bNGj3zzDNat26dAgICLt9kAycWFBdLERHS\nsWOscQcAuL+G5p6lI/etW7fq8ccf14oVK2oNdjNs2iT160ewAwCaBpddc3fmwIEDuu+++zRnzhyF\nhIS4dF8bN1aHOwAATYHLRu5paWnKzMzUsWPHFBQUpClTpqiyslKSNH78eL322msqLS3V448/Lklq\n0aKF8vLyXNLLxo3Sf/yHS0oDAOB2vP4mNoYhdexYHfBBQSY3BgCAC7jtTWzcxcGD1X936WJtHwAA\nNBavD3cm0wEAmhqvD3cm0wEAmhrCHQAAL+PVE+oMQ7rhBmnrVqlzZxc0BgCACzCh7gr275datSLY\nAQBNi1eHO6fkAQBNEeEOAICXIdwBAPAyXjuhzjCk66+XCgulDh1c1BgAAC7AhLpa7NkjtW5NsAMA\nmh6vDXdOyQMAmirCHQAAL0O4AwDgZbxyQt2FC1JAgFRUVD2pDgAAT8KEusvYubP6trMEOwCgKfLK\ncN+8WbrlFqu7AADAGl4Z7t99J0VHW90FAADW8Npwj4qyugsAAKzhdeFuGFJ+PuEOAGi6vC7ci4sl\nm03q1MnqTgAAsIbXhfvFU/I2m9WdAABgDa8NdwAAmirCHQAAL+OV4c4yOABAU+ZVt58tK5M6dpRO\nnZKuuaYRGgMAwAW4/eyvbN0q9e1LsAMAmjavCnfWtwMA4GXhvmWLdPPNVncBAIC1vCrcCwqkyEir\nuwAAwFpeM6HuwgWpdWvp4MHqZ7kDAOCpmFD3b/v2Se3aEewAAHhNuG/dKkVEWN0FAADW85pwLyhg\nMh0AAJIXhTsjdwAAqnlNuDNyBwCgmlfMlj99unoy3alTUosWjdgYAAAuwGx5Sd9/L/XuTbADACB5\nSbhv3copeQAALvKKcC8oYDIdAAAXeUW4M1MeAIBfeEW4b9tW/ahXAADgBeF+7Jh09qx0441WdwIA\ngHvw+HDftk0KD5dsNqs7AQDAPXhFuPfpY3UXAAC4D68Id663AwDwC68Id0buAAD8wqPD3TCkf/2L\ncAcA4Nc8Otx//FG6cEHq2NHqTgAAcB8eHe4XT8kzUx4AgF94RbgDAIBfEO4AAHgZwh0AAC/jseFu\nGIQ7AACX47JwHzt2rAIDAxVxhce1/eUvf1GPHj0UExOjHTt21Kv+0aPVE+k6dGhopwAAeBeXhfuY\nMWO0YsWKWj/Py8tTdna2Nm7cqOeff17PP/98verv2CGFhTFTHgCA33JZuCclJalt27a1fp6bm6tR\no0bp+uuvV1pamrZv316v+tu3V4c7AACoybJr7nl5eQoPD3e8vuGGG7Rnz546/3vCHQBQX6WlpUpP\nT1dGRoYSExNVVVVldUsu0dyqHRuGIcMwarxnu8I59smTJzu+TklJ0fbtKRo61FXdAQC8zZkzZ5Sa\nmqq5c+cqKChIt912m6655hqr25Ik2e122e120+rZjN8mrImKioo0YsQIFRQUXPLZjBkzdP78eT37\n7LOSpODg4FpH7jab7ZJfBIKCpKwsqXt38/sGALiGWfOkria5Fi1apEWLFmn27Nk13i8tLdWYMWM0\naNAgBQcHa+PGjYqLi1Nqaqpjm/LycqWmpurvf/+7HnroIc2bN08BAQEN/TZqdbncqw/LTsvHx8dr\n3rx5On78uL744guF1eMce1mZVFoqde3qwgYBAKYzDHP+XI2jR48qJCTE8dput6u8vFzXX3+9/Pz8\nNHHiREVFRWnSpEm6+eaba/xbX19fhYSEqHPnzgoJCXFpsJvBZeGelpamxMREFRYWKigoSLNnz9bM\nmTM1c+ZMSVJcXJwGDhyofv366e2339a0adPqXHvHDqlXL6mZx67SBwA0trS0NJ08eVILFy7UwoUL\n1bZtW/n6+qqqqkqlpaX67LPPNGfOHO3Zs0cffvihJOm1115TeXm5ysvL5ePjo9OnT8vHx8fi78Q5\nl11znzt3rtNt0tPTlZ6eXu/a27dLoaFX0xUAoKny9/fXm2++ecn7+fn5uuOOO/Too4/qm2++UceO\nHVVeXi5JKi4ulq+vr1avXq2EhAStW7dOCQkJjd16vXnk2PfiGncAABoqKytLMTExkqSBAwfKx8dH\n7dq10/nz59WyZUsdOnRIWVlZCg4OVmZmpoKDgy3u2DmPDHeWwQEAzLBp0yb985//VGFhoWMCm5+f\nn1q1aqWPP/5YzZs31/Hjx9W+fXvt27fP8be7c+lsebP8dtZgaKj01VdS374WNgUAgIs0dLa8x4V7\nRYXUurX0009Sq1YWNwYAgAt47FK4q7VnT/Uad4IdAIDL87hwLyxkpjwAAFficeG+c2f1GncAAHB5\nHhfuhYVS795WdwEAgPvyuHBn5A4AwJUR7gAAeBmPCveTJ6XTp6VOnazuBAAA9+VR4X5x1G7WIwMB\nAPBGHhnuAACgdh4X7syUBwDgyjwq3AsLGbkDAOCMR4U7p+UBAHDOY8LdMKRduwh3AMDVKy0tVXp6\nujIyMpSYmKiqqiqrW3IJj3kq3A8/GIqNlQ4ftrobAIAnOnPmjO644w7NnTtXQUFBKi8vl6+vr9Vt\nXVZDnwrX3MReXIpT8gDg+WxTzFnLbLxa/+BbtWqVevXqpaCgIElyBHtxcbHS0tI0cuRI/eEPf1Bg\nYKBycnJkGIYSExNN6bexEe4AgEZzNaFslqNHjyokJMTx2m63KzY2Vp07d1aLFi00ceJEx2f9+/e3\nokXTeMw19127pJ49re4CAOCp0tLSdPLkSS1cuFALFy5U27Zt5evrqxMnTiggIMCxXX5+vl588UVd\nuHBBdrtdzz33nLKzs/Xqq69q//79MgxDX3zxhdavX6+1a9dKkj755BOtXLlSzz33nCRp9erVSktL\n0wcffKAZM2Y0+vfqMSP33bulAQOs7gIA4Kn8/f315ptvXvL+t99+q6SkJMfrwMBA/fzzz2rWrJl6\n9uypU6dOKSkpSXa7XefOndPf/vY32Ww2VVRU6JZbbtGCBQsUEBCgAQMGKCsrS5KUkJCgr776Sk89\n9VSjfX+/5jEj9927pV+dTQEAwBRZWVkaOHCgpOpRe0VFhbp166ZDhw7Jz89P7dq1kyTt379fvr6+\n2rp1q0aNGqVBgwapoqJC33zzjZKSkrRu3TrFxMToyJEjqqysVPv27S37njwm3PfulYKDre4CAOBN\nvv32Wy1dulT79u3T9OnTNXXqVJWUlMjX11c2m02bN2/WrbfeKklq27atDh48qPvvv19fffWV1qxZ\no7Nnz2rYsGH67rvvdODAAe3evVsBAQHavHmzBg8ebNn35TFL4Tp1MlRcbHUnAAC4XkOXwnnMyJ1T\n8gAA1A3hDgCAlyHcAQDwMoQ7AABehnAHAMDLeEy4swwOAIC68ZilcB7QJgAApmgyS+EAAEDdEO4A\nAHgZwh0AAC9DuAMA4GUIdwBAk3fy5EkVFBRY3YZpPOZ57gAAuMKWLVuUk5Ojw4cPq7i4WEOGDLG6\npQZj5A4AaNKaNauOQsMwdM0111jcjTlY5w4AaNIMw9CRI0e0ZcsWDRkyRDabzeqWGpx7hDsAoMko\nLS3VRx99pPDwcKWnpys7O9stR+uEOwAAdXDmzBndcccdmjt3roKCglReXi5fX1+r27os7lAHAPAY\nkydPls1mu+TP5MmT67x9bds6s2rVKvXq1UtBQUGS5LbBbgZG7gCAJuGjjz7SsWPH9NJLL0mS7Ha7\nYmNj3TLkOS0PAEAdlJWV6fXXX1diYqIkqXv37oqMjLS4q8sj3AEA8DJccwcAADUQ7gAAeBnCHQAA\nL0O4AwDgZQh3AAC8DOEOAICXIdwBAPAyhDsAAF6GcAcAwMu4NNyzsrIUFhamnj17asaMGZd8fubM\nGT3yyCOKjo5WcnKyFi1a5Mp2YAG73W51C2gAjp9n4/g1XS4N9z/96U+aOXOm1qxZow8//FDHjh2r\n8flnn30mX19f5efn6/PPP9fEiRO5zayX4T8Xz8bx82wcv6bLZeH+008/SZIGDRqkrl276s4771Ru\nbm6Nbdq0aaOysjJVVlaqtLRUPj4+stlsrmoJAIAmwWXhvmHDBoWGhjpeh4eHa/369TW2SUtLU1VV\nldq3b6+BAwdqzpw5rmoHAIAmo7mVO//ggw/UvHlzHT58WAUFBRo+fLj279+vZs0u/Z2DEb3nmjJl\nitUtoAE4fp6N49c0uSzcY2Nj9cILLzheb9u2TUOHDq2xTVZWlsaNGycfHx/Fx8erc+fO2rlzZ40R\nvySuwwMAUA8uOy3fpk0bSdUBXlRUpNWrVys+Pr7GNrfddpsWL16sCxcuaO/evSotLb0k2AEAQP24\n9LT8e++9p/Hjx6uyslLPPPOM2rdvr5kzZ0qSxo8fr9GjR+v7779Xv379dMMNN2j69OmubAcAgKbB\ncGOZmZlGaGioERISYrz//vtWtwMnunbtakRERBhRUVFGbGysYRiGcerUKSM1NdUICgoyRo4caZSV\nlVncJS4aM2aM0aFDB6Nv376O9650vKZPn26EhIQYYWFhRnZ2thUt498ud+xeffVV48YbbzSioqKM\nqKgoY9myZY7POHbu5cCBA0ZKSooRHh5uJCcnG3PmzDEMw9yfP7cO96ioKCMzM9MoKioyevfubZSU\nlFjdEq6gW7duxvHjx2u8N3XqVOOpp54yzp49azz55JPGtGnTLOoOv5WVlWVs3ry5RkDUdryOHj1q\n9O7d29i/f79ht9uN6Ohoq9qGcfljN3nyZOPtt9++ZFuOnfs5fPiwkZ+fbxiGYZSUlBjdu3c3Tp06\nZerPn9vefrYu6+ThfozfTH7My8vTuHHj1KpVK40dO5Zj6EaSkpLUtm3bGu/Vdrxyc3M1dOhQ3XTT\nTUpOTpZhGCorK7Oibejyx066/ORjjp376dixo6KioiRJ7du3V58+fbRhwwZTf/7cNtzrsk4e7sVm\ns2nw4MG65557lJGRIanmcQwNDVVeXp6VLcKJ2o5Xbm6uwsLCHNv17t2bY+mGZsyYoYSEBE2dN5hm\nDgAAA51JREFUOtXxn39eXh7Hzo3t3r1b27ZtU1xcnKk/f24b7vA83377rbZs2aI33nhDEydO1JEj\nR1jG6GHqc7y494R7eeKJJ7Rv3z6tXLlSe/bscUxevtwx5di5h7KyMj3wwAN699135efnZ+rPn9uG\ne2xsrHbs2OF4vW3bNiUkJFjYEZzp1KmTJCksLEypqalavHixYmNjtX37dknS9u3bFRsba2WLcKK2\n4xUfH6/vv//esd2OHTs4lm6mQ4cOstlsatOmjZ588kktWLBAEsfOXVVWVuq+++7TQw89pJEjR0oy\n9+fPbcO9Luvk4T5Onz7tOA1YUlKilStXaujQoYqPj9fs2bN15swZzZ49m1/Q3FxtxysuLk4rV67U\ngQMHZLfb1axZM/n7+1vcLX7t8OHDkqTz58/riy++0LBhwyRx7NyRYRgaN26c+vbtqwkTJjjeN/Xn\nzwUTAU1jt9uN0NBQIzg42Jg+fbrV7eAK9u7da0RGRhqRkZHG4MGDjU8++cQwDJbCubPRo0cbnTp1\nMlq2bGl06dLFmD179hWP13vvvWcEBwcbYWFhRlZWloWd4+Kxa9GihdGlSxfjk08+MR566CEjIiLC\niImJMZ599tkaK1c4du4lOzvbsNlsRmRkpGPp4vLly039+bMZBhdFAQDwJm57Wh4AAFwdwh0AAC9D\nuAMA4GUIdwAAvAzhDjQhx48fV3R0tKKjo9WpUyd16dJF0dHR8vf311NPPWV1ewBMwmx5oImaMmWK\n/P39NXHiRKtbAWAyRu5AE3bxd3u73a4RI0ZIkiZPnqzx48dr0KBBCg4O1qpVq/TKK6+ob9++euKJ\nJxz/prCwUE888YTi4+P15JNP6vjx45Z9HwBqItwBXCI3N1dLly7V7Nmzdd999ykkJEQFBQXatWuX\nNm/eLEl64YUX9NJLLyk3N1d9+vTRrFmzLO4awEXNrW4AgHux2WxKTU2Vv7+/+vfvr3Pnzmn06NGy\n2WyKj49XTk6ObrrpJmVnZys1NVWSVFVVpW7dulnbOAAHwh3AJS4+26Fly5Zq1aqVWrVq5XhdUVGh\nqqoqtWvXTvn5+Va2CaAWnJYHUIOzObaGYahjx47q3r275s2bJ8MwVFlZWeOpVQCsRbgDTdjFZ0Lb\nbLbLfv3rbX77+q9//avWrl2rqKgoRUdHKycnp5G6BuAMS+EAAPAyjNwBAPAyhDsAAF6GcAcAwMsQ\n7gAAeBnCHQAAL0O4AwDgZf4f6oPj06W5KmwAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 213
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Then we can plot the flow of utility over time..."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# initial value for technology\n",
      "A0 = 1.0\n",
      "\n",
      "# Create a grid (useful for plotting technology...recall that consumption per worker C = c * A!)\n",
      "grid = np.arange(0, ramsey_solution[2], 1)\n",
      "\n",
      "# Create a new plot\n",
      "plt.figure(figsize=(8,8))\n",
      "plt.plot(grid, u(ramsey_solution[1][:, 1] * A0 * np.exp(g * grid)), color='b', label=r'$u_{Full}$')\n",
      "plt.plot(grid, u(c_linear * A0 * np.exp(g * grid)), color='g', label=r'$u_{Linear}$')\n",
      "\n",
      "# Add the steady state value for capital per effective worker\n",
      "plt.plot(grid, u(c_star() * A0 * np.exp(g * grid)), ls='--', color='k', label=r'$u^{*}$')\n",
      "\n",
      "# Don't forget to label your axes!\n",
      "plt.xlim(0, ramsey_solution[2])\n",
      "plt.xlabel('Time')\n",
      "plt.ylabel('Instantaneous Welfare')\n",
      "\n",
      "# Add the legend\n",
      "plt.legend(loc='best', frameon=False)\n",
      "\n",
      "# Add a title to the plot\n",
      "plt.title('Flow of welfare (i.e., utility) for representative individual')\n",
      "\n",
      "plt.savefig('Graphics/Instantaneous-utility-Ramsey-model.png')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "NameError",
       "evalue": "name 'g' is not defined",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
        "\u001b[0;32m<ipython-input-135-51902ca01fa2>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      7\u001b[0m \u001b[0;31m# Create a new plot\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfigure\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfigsize\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m8\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m8\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 9\u001b[0;31m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgrid\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mu\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mramsey_solution\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mA0\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mg\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mgrid\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcolor\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'b'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34mr'$u_{Full}$'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     10\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgrid\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mu\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mc_linear\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mA0\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mg\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mgrid\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcolor\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'g'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34mr'$u_{Linear}$'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     11\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;31mNameError\u001b[0m: name 'g' is not defined"
       ]
      }
     ],
     "prompt_number": 135
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def lifetimeUtility(X, params):\n",
      "    \"\"\"\n",
      "    \n",
      "    Function that returns the 'lifetime' utility associated with a consumption stream. \n",
      "    Note that the function automatically accounts for growth in technology and population. \n",
      "    \n",
      "    Inputs:\n",
      "        1) An array, X, representing a consumption stream\n",
      "        \n",
      "    Returns: A list containing...\n",
      "        1) Present discount value, in terms of utility, of the consumption stream\n",
      "        2) The path of discounted flow utility (for plotting)\n",
      "    \n",
      "    \"\"\"\n",
      "    # extract params\n",
      "    g = params['g']\n",
      "    n = params['n']\n",
      "    rho = params['rho']\n",
      "    \n",
      "    path = np.zeros(np.size(X))\n",
      "    for i in range(np.size(X)):\n",
      "        path[i] = (L0 / H) * np.exp((n - rho) * i) * u(X[i] * A0 * np.exp(g * i))\n",
      "    return [np.sum(path), path]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 136
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Lifetime utility is higher (barely!) following the full, non-linear consumption path\n",
      "print \"Lifetime utility from the non-linear solution: \", lifetimeUtility(ramsey_solution[1][:, 1], params)[0]\n",
      "print \"Lifetime utility from the linearized solution: \", lifetimeUtility(c_linear, params)[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "NameError",
       "evalue": "name 'params' is not defined",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
        "\u001b[0;32m<ipython-input-137-2aa5bdf8c13f>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# Lifetime utility is higher (barely!) following the full, non-linear consumption path\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0;32mprint\u001b[0m \u001b[0;34m\"Lifetime utility from the non-linear solution: \"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlifetimeUtility\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mramsey_solution\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0;32mprint\u001b[0m \u001b[0;34m\"Lifetime utility from the linearized solution: \"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlifetimeUtility\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mc_linear\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;31mNameError\u001b[0m: name 'params' is not defined"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Lifetime utility from the non-linear solution: "
       ]
      }
     ],
     "prompt_number": 137
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Analyzing a shock to the growth rate of technology\n",
      "\n",
      "In this task I will provide code to analyze a shock to the growth rate of technology.  The code starts by assuming that you are initially in the steady state of the Ramsey economy (based on same parameters we have been working with above).  I then double the quarterly growth rate of technology to $g=0.01$.  "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# reset old params\n",
      "params = {'theta':theta, 'rho':rho, 'A0':A0, 'g':g, 'L0':L0, 'n':n, 'H':H, 'delta':delta, 'alpha':alpha}\n",
      "\n",
      "# create an instance of the Python object representing the Ramsey model\n",
      "ramsey = ramseyModel(params)\n",
      "\n",
      "# start the economy in steady state...\n",
      "old_k_star, old_c_star = ramsey.SS_dict['k_star'], ramsey.SS_dict['c_star']\n",
      "ramsey.k, ramsey.c = old_k_star, old_c_star"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 183
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The first plot demonstrates the shifts in the k and c locii and the transition to the new steady state in phase space.  Note that an increas in g leads to a downward shift in the \u0394k=0 locus and a leftward shift in the \u0394c=0 locus (remember these are per effective worker variables!).  At the time of the shock c jumps up before falling monotonically towards its new, lower steady state value."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Create a grid of points for plotting\n",
      "gridmax, gridsize = 200, 10000\n",
      "grid = np.linspace(0, gridmax, gridsize)\n",
      "\n",
      "# Create a new plot\n",
      "plt.figure(figsize=(8,8))\n",
      "\n",
      "# Add the c and k locii\n",
      "plt.plot(grid, locusK(grid), color='orange', linestyle='dashed', label=r'$\\Delta k_{old}=0$', alpha=0.5)\n",
      "plt.axvline(ramsey.SS_dict['k_star'], linestyle='dashed', color='k', label=r'$\\Delta c_{old}=0$', alpha=0.5)\n",
      "plt.plot(ramsey.SS_dict['k_star'], ramsey.SS_dict['c_star'], marker='.', markersize=10, color='k', alpha=0.5)\n",
      "\n",
      "# Don't forget to label your axes!\n",
      "plt.xlim(0, 30)\n",
      "plt.xlabel('k')\n",
      "plt.ylim(0, 4)\n",
      "plt.ylabel('c', rotation='horizontal')\n",
      "\n",
      "# shock g! and create new ramseyModel object\n",
      "new_params = params\n",
      "g = 0.01\n",
      "new_params['g'] = g\n",
      "ramsey_new = ramseyModel(new_params)\n",
      "\n",
      "# Add the c and k locii\n",
      "plt.plot(grid, locusK(grid), color='orange', label=r'$\\Delta k_{new}=0$')\n",
      "plt.axvline(ramsey_new.SS_dict['k_star'], linestyle='solid', color='k', label=r'$\\Delta c_{new}=0$')\n",
      "plt.plot(ramsey_new.SS_dict['k_star'], ramsey_new.SS_dict['c_star'], marker='.', markersize=10, color='k')\n",
      "\n",
      "# solve for the non-linear saddle path\n",
      "ramsey_solution = ramsey_new.forward_shoot(old_k_star, tol=1.5e-4)\n",
      "\n",
      "# Plot the full saddle-path\n",
      "plt.plot(ramsey_solution[1][:, 0], ramsey_solution[1][:, 1], color='r', label='Saddle path')\n",
      "\n",
      "plt.title('An increase in the growth rate of technology leads to...')\n",
      "\n",
      "# add a legend\n",
      "plt.legend(loc='best', frameon=False)\n",
      "\n",
      "plt.savefig('Graphics/Shock to g in phase space!.png')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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9EBERAQDw8PDAoUOHYGVlpZHyFMXbehIRUa3bvn07lixZAhcXF6xatUppWseO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\n"
      }
     ],
     "prompt_number": 184
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This second plot shows time paths of output per effective worker, $y$, and log output per worker, $ln(Y/L)$.  Note that $y$ falls in response to the shock, while $Y/L$  jumps up! "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Suppose that economy was in its old steady state for 40 periods prior to shock to g\n",
      "y_SamplePath1 = np.repeat(f(old_k_star), 40)\n",
      "\n",
      "# y_SamplePath2 is constructed using the optimal path of k\n",
      "y_SamplePath2 = f(ramsey_solution[1][:,0])\n",
      "\n",
      "# combine the two parts of the sample path of y\n",
      "y_SamplePath = np.hstack((y_SamplePath1, y_SamplePath2))\n",
      "\n",
      "# create a new figure\n",
      "fig = plt.figure(figsize=(8,8))\n",
      "\n",
      "# define a grid of points for plotting\n",
      "grid = np.arange(0, 40 + ramsey_solution[2], 1)\n",
      "\n",
      "# create the first subplot\n",
      "ax1 = fig.add_subplot(211)\n",
      "ax1.set_title(r'A positive shock technology growth rate, g, leads to a  fall in y...')\n",
      "ax1.plot(grid, y_SamplePath, 'r', label='y')\n",
      "ax1.axhline(y=f(k_star()), xmin=0, linestyle='dashed', color='k', label=r'$y_{new}^{*}$')\n",
      "ax1.set_ylabel('y')\n",
      "ax1.legend(loc='best', frameon=False)\n",
      "\n",
      "# create the sample path of Y/L as follows...\n",
      "old_g = 0.005\n",
      "new_g = 0.01\n",
      "\n",
      "Y_SamplePath1 = f(old_k_star) * A0 * np.exp(old_g * grid[:40]) # initial bit grows at old tech growth rate\n",
      "A40 = A0 * np.exp(old_g * grid[39]) # value of A at time of shock\n",
      "Y_SamplePath2 = f(ramsey_solution[1][:,0]) * A40 * np.exp(new_g * grid[:-40]) # last bit grows at new tech growth rate\n",
      "Y_perWorkerSamplePath = np.hstack((Y_SamplePath1, Y_SamplePath2)) \n",
      "\n",
      "# create a second subplot\n",
      "ax2 = fig.add_subplot(212, sharex=ax1)\n",
      "ax2.set_title(r'but Y/L is now on a more aggressive BGP!')\n",
      "ax2.plot(grid, np.log(Y_perWorkerSamplePath), 'r', label=r'$ln\\frac{Y}{L}$')\n",
      "ax2.plot(grid, A0 + old_g * grid,'k--', label=r'$BGP_{old}$')\n",
      "ax2.set_ylabel('ln(Y/L)')\n",
      "ax2.legend(loc='best', frameon=False)\n",
      "ax.set_xlabel('Time')\n",
      "\n",
      "# tighten things up!\n",
      "plt.tight_layout()\n",
      "\n",
      "plt.savefig('Graphics/Samplepaths-of-output-following-shock.png')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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P4tatW7rHTk5O+OKLL5CWlobnn38eI0aMKHJG26N1A5R8/T3qiy++wN9//421a9fi5s2b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FAAAC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\nyBERERGnpJAjIiIiTkkhR0RERJzS/wOfpAxMlKS6ugAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 188
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}