harmonic oscillator/loss.ipynb

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    "\n",
    "## Harmonic oscillator (min T) including a control loss region (initial problem)\n",
    "\n",
    "$$\n",
    "    \\left\\{\n",
    "    \\begin{array}{l}\n",
    "        \\displaystyle \\min  T, \\\\[0.5em]\n",
    "        \\dot{x}_1(t) = x_2(t), \\; t\\in [0,T]\\\\[0.5em]\n",
    "        \\dot{x}_2(t) = u(t)-x_1(t), t\\in [0,T]  \\\\[0.5em]\n",
    "        u(t) \\in [-1, 1], \\; t\\in [0,T]\\\\[0.5em]\n",
    "        x(0) = (4.2,0) , \\quad x(T) = 0_{\\mathrm{R}^2}, \\\\[0.5em]\n",
    "        \\{x \\mid x_2 < 0\\} \\text{ is a control loss reigon.}\n",
    "    \\end{array}\n",
    "    \\right.\n",
    "$$\n",
    "\n",
    "## Harmonic oscillator (min T) including a control loss region (regularized problem)\n",
    "\n",
    "$$\n",
    "    \\left\\{\n",
    "    \\begin{array}{l}\n",
    "        \\displaystyle \\min  T + \\varepsilon \\int_0^T v^2(t)dt + \\int_0^T f_{NC}(x_2(t))u^2(t)dt, \\\\[0.5em]\n",
    "        \\dot{x}_1(t) = x_2(t), \\; t\\in [0,T]\\\\[0.5em]\n",
    "        \\dot{x}_2(t) =f_{C}(x_2(t))(u(t) - x_1(t)) + f_{NC}(x_2(t))(\\lambda(t) - x_1(t))\n",
    "        , t\\in [0,T]  \\\\[0.5em]\n",
    "        \\dot{\\lambda}(t) = f_C(x_2(t))v(t),\\; t\\in [0,T]\\\\[0.5em]\n",
    "        u(t) \\in [-1, 1] \\; t\\in [0,T]\\\\[0.5em]\n",
    "        x(0) = (4.2,0) , \\quad x(T) = 0_{\\mathrm{R}^2}.\n",
    "    \\end{array}\n",
    "    \\right.\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "c4f1fcc1",
   "metadata": {},
   "outputs": [],
   "source": [
    "using JuMP  \n",
    "using Ipopt\n",
    "using Plots\n",
    "using LaTeXStrings\n",
    "using Plots.PlotMeasures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "b8592f83",
   "metadata": {},
   "outputs": [],
   "source": [
    "mutable struct Direct\n",
    "    t; x1; x2 ; λ ; u ; xu ; xv ; p1 ; p2\n",
    "end\n",
    "\n",
    "mutable struct DirecttSol\n",
    "    t; x1; x2 ; λ ; u ; v ; xu ; xv ; p1 ; p2 ; p3\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "353ba5c3",
   "metadata": {},
   "outputs": [],
   "source": [
    "distance_squared(x, a) = x < a ? (a - x)^2 : 0 ;\n",
    "\n",
    "#Moreau Yosida regularization\n",
    "\n",
    "function MY_reg(x, a, k)\n",
    "    return 1 - exp(-k*distance_squared(x, a))\n",
    "end\n",
    "\n",
    "fNC(x) = MY_reg(x, 0.02, 1200)\n",
    "fC(x) = 1. - fNC(x)\n",
    "\n",
    "plot(fNC, -0.5, 0.5);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "300b1ce5",
   "metadata": {},
   "outputs": [],
   "source": [
    "#function F(x, alpha, a)\n",
    "#    return 1 / (1 + exp(alpha * (x - a)))\n",
    "#end\n",
    "#fNC1(x)  = F(x, 100, 0.0)\n",
    "#fC1(x)   = 1. - F(x, 100, 0.0)\n",
    "#g(x)     = fNC(x) - fNC1(x) \n",
    "#plot(g, -0.5, 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "6ffddef8",
   "metadata": {},
   "outputs": [],
   "source": [
    "function HO(x0 , ε; solution=[], nsteps=500, display=true)\n",
    "\n",
    "    # Create JuMP model, using Ipopt as the solver\n",
    "    if display\n",
    "        pl = 5\n",
    "    else\n",
    "        pl = 1\n",
    "    end\n",
    "    sys = Model(optimizer_with_attributes(Ipopt.Optimizer, \"print_level\" => pl))\n",
    "    set_optimizer_attribute(sys,\"tol\",1e-8)\n",
    "    set_optimizer_attribute(sys,\"constr_viol_tol\",1e-8)\n",
    "    set_optimizer_attribute(sys,\"max_iter\",1000)\n",
    "    \n",
    "    N  = nsteps     # Grid size\n",
    "    \n",
    "    @variables(sys, begin\n",
    "                 x1[1:N+1]    \n",
    "                 x2[1:N+1]   \n",
    "         -1.0  ≤  λ[1:N+1]  ≤ 1.0\n",
    "         -1.0  ≤  u[1:N+1]  ≤ 1.0\n",
    "          0.0  ≤ Δt         ≤ 1.0 \n",
    "                  v[1:N+1] \n",
    "         -1e1  ≤ xv[1:N+1]\n",
    "         -1e1  ≤ xu[1:N+1]\n",
    "    end)\n",
    "    \n",
    "    set_start_value(Δt, 20/N);\n",
    "    for i in 1:N+1\n",
    "        set_start_value(λ[i] , 1.0);\n",
    "        set_start_value(v[i] , 0.0);\n",
    "        set_start_value(xv[i], 0.0);\n",
    "        set_start_value(xu[i], 0.0);\n",
    "    end\n",
    "    \n",
    "    T = Δt*(N+1) ;\n",
    "    \n",
    "    # Objective\n",
    "    @objective(sys, Min, T + ε*xv[N+1] + xu[N+1])\n",
    "\n",
    "    # Boundary constraints\n",
    "    @constraints(sys, begin\n",
    "        con_xu0, xu[1]   == 0.0\n",
    "        con_xv0, xv[1]   == 0.0\n",
    "        con_x10, x1[1]   == x0[1] \n",
    "        con_x20, x2[1]   == x0[2] \n",
    "        con_x1f, x1[N+1] == 0.0 \n",
    "        con_x2f, x2[N+1] == 0.0\n",
    "        con_x30, -1. <= λ[1]    <= 1.0\n",
    "        con_x3f, -1. <= λ[N+1]  <= 1.0\n",
    "    end)\n",
    "\n",
    "    # Dynamics\n",
    "    @NLexpression(sys, dx1[j = 1:N+1], x2[j])\n",
    "    @NLexpression(sys, dx2[j = 1:N+1], fC(x2[j])*(u[j] - x1[j]) +fNC(x2[j])*(λ[j] - x1[j]))\n",
    "    @NLexpression(sys,  dλ[j = 1:N+1], fC(x2[j])*v[j])\n",
    "    @NLexpression(sys, dxv[j = 1:N+1], v[j]^2)\n",
    "    @NLexpression(sys, dxu[j = 1:N+1], fNC(x2[j])*u[j]^2)\n",
    "    \n",
    "    # Dynamics with Crank-Nicolson scheme\n",
    "    @NLconstraints(sys, begin\n",
    "        con_dx1[j=1:N], x1[j+1] == x1[j] + 0.5 * Δt * (dx1[j+1] + dx1[j])\n",
    "        con_dx2[j=1:N], x2[j+1] == x2[j] + 0.5 * Δt * (dx2[j+1] + dx2[j])\n",
    "        con_dx3[j=1:N],  λ[j+1] ==  λ[j] + 0.5 * Δt * (dλ[j+1]  + dλ[j])\n",
    "        con_dxv[j=1:N], xv[j+1] == xv[j] + 0.5 * Δt * (dxv[j+1] + dxv[j])\n",
    "        con_dxu[j=1:N], xu[j+1] == xu[j] + 0.5 * Δt * (dxu[j+1] + dxu[j])\n",
    "    end)\n",
    "    \n",
    "    \n",
    "    # Solve for the control and state\n",
    "    if display\n",
    "        println(\"Solving...\")\n",
    "    end\n",
    "    status = optimize!(sys)\n",
    "    if display\n",
    "        println()\n",
    "    end\n",
    "\n",
    "    # Display results\n",
    "    if display\n",
    "        if termination_status(sys) == MOI.OPTIMAL\n",
    "            println(\"  Solution is optimal\")\n",
    "        elseif  termination_status(sys) == MOI.LOCALLY_SOLVED\n",
    "            println(\"  (Local) solution found\")\n",
    "        elseif termination_status(sys) == MOI.TIME_LIMIT && has_values(sys)\n",
    "            println(\"  Solution is suboptimal due to a time limit, but a primal solution is available\")\n",
    "        else\n",
    "            error(\"  The model was not solved correctly.\")\n",
    "        end\n",
    "        println(\"  objective value = \", objective_value(sys))\n",
    "        println()\n",
    "    end\n",
    "\n",
    "    # Retrieves values (including duals)\n",
    "    x1 = value.(x1)[:]\n",
    "    x2 = value.(x2)[:]\n",
    "    λ  = value.(λ)[:]\n",
    "    u  = value.(u)[:]\n",
    "    v  = value.(v)[:]\n",
    "    xu  = value.(xu)[:]\n",
    "    xv  = value.(xv)[:]\n",
    "    t  = (0:N) * value.(Δt)\n",
    "    \n",
    "    \n",
    "    px10 =   dual(con_x10)\n",
    "    px20 =   dual(con_x20)\n",
    "    px1f = - dual(con_x1f)                                 \n",
    "    px2f = - dual(con_x2f) \n",
    "    \n",
    "    px30 =   dual(con_x30)\n",
    "    px3f = - dual(con_x3f) \n",
    "\n",
    "    # keep original signs for now\n",
    "    sign = 1\n",
    "    \n",
    "     px1 = [ dual(con_dx1[i]) for i in 1:N ]\n",
    "     px2 = [ dual(con_dx2[i]) for i in 1:N ]\n",
    "     px3 = [ dual(con_dx3[i]) for i in 1:N ]\n",
    "\n",
    "     px1 = sign * [px10; (px1[1:N-1]+px1[2:N])/2.; px1f]; # We add the multiplier from the limit conditions\n",
    "     px2 = sign * [px20; (px2[1:N-1]+px2[2:N])/2.; px2f]; # We add the multiplier from the limit conditions\n",
    "     px3 = sign * [px30; (px3[1:N-1]+px3[2:N])/2.; px3f]; # We add the multiplier from the limit conditions\n",
    "    \n",
    "     p1 = - [px10; px1[1:N-1]; px1f];                     # We add the multiplier from the limit conditions\n",
    "     p2 = - [px20; px2[1:N-1]; px2f];                     # We add the multiplier from the limit conditions\n",
    "     p3 = - [px30; px3[1:N-1]; px3f];                     # We add the multiplier from the limit conditions\n",
    "\n",
    "    \n",
    "    \n",
    "    \n",
    "    return DirecttSol(t, x1, x2, λ, u, v, xu, xv, p1, p2, p3)\n",
    "    \n",
    "    \n",
    "end;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "9831d7d6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solving...\n",
      "This is Ipopt version 3.14.4, running with linear solver MUMPS 5.4.1.\n",
      "\n",
      "Number of nonzeros in equality constraint Jacobian...:    16506\n",
      "Number of nonzeros in inequality constraint Jacobian.:        4\n",
      "Number of nonzeros in Lagrangian Hessian.............:    43500\n",
      "\n",
      "Total number of variables............................:     3508\n",
      "                     variables with only lower bounds:     1002\n",
      "                variables with lower and upper bounds:     1003\n",
      "                     variables with only upper bounds:        0\n",
      "Total number of equality constraints.................:     2506\n",
      "Total number of inequality constraints...............:        4\n",
      "        inequality constraints with only lower bounds:        2\n",
      "   inequality constraints with lower and upper bounds:        0\n",
      "        inequality constraints with only upper bounds:        2\n",
      "\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "   0  2.0040000e+01 4.00e+00 1.79e-02  -1.0 0.00e+00    -  0.00e+00 0.00e+00   0\n",
      "   1  4.3983741e+00 3.62e+00 4.08e+03  -1.0 5.41e+00   2.0 1.57e-01 9.58e-02f  1\n",
      "   2  3.5819933e+00 3.60e+00 9.85e+03  -1.0 8.90e+01   1.5 1.58e-02 5.36e-03f  1\n",
      "   3  3.2643537e+00 3.58e+00 1.40e+04  -1.0 8.83e+01   1.0 1.90e-03 4.11e-03f  1\n",
      "   4  3.1736139e+00 3.57e+00 1.67e+04  -1.0 7.16e+01   1.5 3.22e-04 2.35e-03f  1\n",
      "   5  3.0760157e+00 3.56e+00 1.92e+04  -1.0 6.04e+01   1.0 2.27e-03 4.16e-03f  1\n",
      "   6  3.0724238e+00 3.55e+00 2.06e+04  -1.0 2.75e+01   1.4 5.11e-03 3.39e-03f  1\n",
      "   7  3.0534321e+00 3.50e+00 9.21e+03  -1.0 2.11e+01   0.9 1.69e-02 1.48e-02f  1\n",
      "   8  2.9801126e+00 3.13e+00 1.38e+05  -1.0 1.04e+01   1.4 7.49e-02 1.05e-01f  1\n",
      "   9  2.9910591e+00 3.12e+00 1.36e+05  -1.0 4.23e+01   1.8 8.59e-03 1.86e-03h  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  10  3.0316993e+00 3.11e+00 1.30e+05  -1.0 1.05e+02   1.3 4.23e-04 2.22e-03h  1\n",
      "  11  4.1576144e+00 2.21e+00 1.08e+06  -1.0 6.57e+00   1.7 1.01e-03 2.91e-01f  1\n",
      "  12  4.1494183e+00 2.19e+00 1.07e+06  -1.0 1.19e+01   1.3 4.11e-03 9.19e-03h  1\n",
      "  13  4.1262001e+00 2.16e+00 1.05e+06  -1.0 2.10e+01   0.8 1.63e-02 1.21e-02h  1\n",
      "  14  4.0750256e+00 2.05e+00 9.80e+05  -1.0 4.41e+00   1.2 5.20e-02 5.03e-02h  1\n",
      "  15  4.0159982e+00 1.86e+00 8.24e+05  -1.0 4.63e+00   1.6 5.82e-03 9.60e-02h  1\n",
      "  16  4.0155404e+00 1.85e+00 8.23e+05  -1.0 4.52e+00   2.1 2.11e-02 1.29e-03h  1\n",
      "  17  4.0113485e+00 1.82e+00 8.08e+05  -1.0 7.10e+00   1.6 9.80e-02 1.71e-02h  1\n",
      "  18  4.0023146e+00 1.77e+00 7.86e+05  -1.0 5.27e+00   1.1 4.02e-02 2.58e-02h  1\n",
      "  19  4.0008181e+00 1.77e+00 7.82e+05  -1.0 5.85e+00   1.5 1.59e-01 4.57e-03h  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  20  3.9901999e+00 1.70e+00 7.37e+05  -1.0 1.92e+01   1.1 2.00e-02 3.64e-02h  1\n",
      "  21  3.9892361e+00 1.70e+00 7.34e+05  -1.0 2.48e+01   1.5 4.75e-02 2.93e-03h  1\n",
      "  22  3.9869398e+00 1.69e+00 7.30e+05  -1.0 2.30e+01   1.9 8.02e-02 2.62e-03h  1\n",
      "  23  3.9821323e+00 1.67e+00 6.94e+05  -1.0 3.88e+01   1.4 5.29e-03 1.39e-02h  1\n",
      "  24  3.9786372e+00 1.67e+00 6.89e+05  -1.0 4.78e+01   1.9 2.43e-02 2.39e-03h  1\n",
      "  25  3.9738305e+00 1.66e+00 6.76e+05  -1.0 6.57e+01   2.3 3.69e-04 2.26e-03h  1\n",
      "  26  3.9716699e+00 1.66e+00 6.75e+05  -1.0 1.23e+02   1.8 9.23e-04 7.73e-04h  1\n",
      "  27  3.9686783e+00 1.66e+00 6.68e+05  -1.0 1.01e+02   2.2 1.11e-02 1.32e-03h  1\n",
      "  28  3.9556900e+00 1.66e+00 6.54e+05  -1.0 7.73e+02   1.8 1.01e-05 9.59e-04f  1\n",
      "  29  3.9547345e+00 1.66e+00 6.53e+05  -1.0 1.28e+02   2.2 1.81e-03 3.00e-04h  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  30  3.9435413e+00 1.65e+00 4.63e+05  -1.0 4.82e+01   2.6 4.53e-04 3.53e-03h  1\n",
      "  31  3.9412157e+00 1.65e+00 4.37e+05  -1.0 5.54e+01   3.0 2.96e-03 7.05e-04h  1\n",
      "  32  3.9369516e+00 1.65e+00 3.70e+05  -1.0 2.63e+02   2.6 3.08e-04 7.95e-04h  1\n",
      "  33  3.9360166e+00 1.65e+00 4.54e+05  -1.0 1.75e+02   3.0 1.14e-03 2.27e-04h  1\n",
      "  34  3.9344862e+00 1.65e+00 4.74e+05  -1.0 1.25e+03   2.5 9.01e-05 5.32e-04f  1\n",
      "  35  3.9345523e+00 1.65e+00 4.82e+05  -1.0 4.59e+02   2.9 4.09e-04 1.45e-05h  1\n",
      "  36r 3.9345523e+00 1.65e+00 1.00e+03   0.2 0.00e+00   3.4 0.00e+00 2.72e-07R  5\n",
      "  37r 3.9461129e+00 1.71e+00 9.53e+02   0.2 4.21e+01    -  7.01e-02 4.65e-02f  1\n",
      "  38r 4.0891402e+00 1.70e+00 9.52e+02   0.2 6.68e-01   2.0 2.09e-01 3.40e-01f  1\n",
      "  39r 4.1561736e+00 1.67e+00 7.57e+02   0.2 3.88e-01   1.5 2.30e-01 2.66e-01f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  40r 4.1962665e+00 1.61e+00 7.09e+02   0.2 1.78e-01   1.9 3.14e-01 8.63e-01f  1\n",
      "  41r 4.2333477e+00 1.42e+00 2.49e+03   0.2 3.25e-01   1.5 3.60e-01 8.12e-01f  1\n",
      "  42r 4.2333477e+00 1.42e+00 9.99e+02   0.2 0.00e+00    -  0.00e+00 4.08e-07R 15\n",
      "  43r 4.3016205e+00 1.10e+00 2.85e+04   0.2 1.36e+00    -  3.90e-01 3.35e-01f  1\n",
      "  44r 4.3016205e+00 1.10e+00 9.99e+02   0.0 0.00e+00    -  0.00e+00 2.56e-07R 19\n",
      "  45r 4.3320879e+00 1.00e+00 9.67e+02   0.0 3.90e+00    -  3.54e-01 3.12e-02f  1\n",
      "  46r 4.6936061e+00 9.42e-02 7.83e+02   0.0 5.21e+00    -  8.25e-02 1.92e-01f  1\n",
      "  47r 4.6936061e+00 9.42e-02 9.99e+02  -1.0 0.00e+00    -  0.00e+00 2.80e-07R 19\n",
      "  48r 4.7269147e+00 6.08e-02 9.94e+02  -1.0 1.46e+01    -  6.32e-02 5.56e-03f  1\n",
      "  49r 4.7269147e+00 6.08e-02 9.98e+02  -1.0 0.00e+00    -  0.00e+00 4.76e-07R 19\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  50r 4.7684297e+00 2.85e-02 9.83e+02  -1.0 1.30e+01    -  8.42e-02 1.59e-02f  1\n",
      "  51r 4.7684297e+00 2.85e-02 9.97e+02  -1.0 0.00e+00    -  0.00e+00 4.52e-07R 19\n",
      "  52r 4.7762025e+00 2.94e-02 9.89e+02  -1.0 7.93e+00    -  1.50e-01 1.10e-02f  1\n",
      "  53r 4.7804897e+00 1.41e-01 8.98e+03  -1.0 8.17e+00    -  1.90e-01 1.02e-01f  1\n",
      "  54r 4.8511006e+00 1.75e-01 9.34e+03  -1.0 4.26e+01    -  2.29e-02 2.36e-02f  1\n",
      "  55r 4.9870122e+00 1.62e-01 1.72e+04  -1.0 3.58e+00   0.0 2.75e-01 2.29e-01f  1\n",
      "  56r 5.0647519e+00 1.53e-01 1.81e+04  -1.0 1.66e+00   0.4 4.75e-01 3.06e-01f  1\n",
      "  57r 5.1206030e+00 1.59e-01 1.80e+04  -1.0 3.18e+01  -0.1 3.14e-02 3.08e-02f  1\n",
      "  58r 5.2121899e+00 1.57e-01 1.75e+04  -1.0 5.05e+00   0.4 1.98e-01 1.94e-01f  1\n",
      "  59r 5.2670123e+00 1.50e-01 1.30e+04  -1.0 7.11e-01   0.8 1.00e+00 4.37e-01f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  60r 5.3286287e+00 1.37e-01 4.44e+03  -1.0 2.35e-01   1.2 1.00e+00 9.70e-01f  1\n",
      "  61r 5.4178085e+00 1.13e-01 3.23e+03  -1.0 2.62e+00   0.7 3.81e-01 3.30e-01f  1\n",
      "  62r 5.4754398e+00 9.83e-02 3.06e+03  -1.0 1.38e+01   0.3 7.23e-02 7.12e-02f  1\n",
      "  63r 5.5575957e+00 9.23e-02 2.09e+03  -1.0 2.25e+00   0.7 4.44e-01 2.93e-01f  1\n",
      "  64r 5.6082100e+00 8.89e-02 7.94e+02  -1.0 3.01e-01   1.1 1.00e+00 5.67e-01f  1\n",
      "  65r 5.7169462e+00 1.13e-01 1.86e+02  -1.0 4.07e+00   0.6 2.44e-01 2.36e-01f  1\n",
      "  66r 5.7731462e+00 1.07e-01 3.78e+02  -1.0 4.28e-01   1.1 1.00e+00 5.36e-01f  1\n",
      "  67r 5.8526310e+00 1.29e-01 1.25e+03  -1.0 3.02e+00   0.6 3.29e-01 2.22e-01f  1\n",
      "  68r 5.9111582e+00 1.16e-01 8.30e+02  -1.0 3.58e-01   1.0 1.00e+00 5.58e-01f  1\n",
      "  69r 5.9824812e+00 1.40e-01 1.79e+03  -1.0 3.01e+00   0.5 3.31e-01 2.24e-01f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  70r 6.0491598e+00 1.09e-01 1.13e+03  -1.0 3.76e-01   1.0 9.95e-01 5.54e-01f  1\n",
      "  71r 6.1091237e+00 1.50e-01 1.81e+03  -1.0 4.56e+00   0.5 2.14e-01 1.35e-01f  1\n",
      "  72r 6.1745528e+00 1.08e-01 1.99e+03  -1.0 7.89e+02   0.0 1.35e-03 1.34e-03f  1\n",
      "  73r 6.2981206e+00 1.20e-01 3.07e+03  -1.0 4.80e+00   0.4 1.43e-01 1.66e-01f  1\n",
      "  74r 6.3388308e+00 9.36e-02 2.18e+03  -1.0 5.56e-01   0.9 6.56e-01 3.10e-01f  1\n",
      "  75r 6.3786180e+00 8.47e-02 1.86e+02  -1.0 1.75e-01   1.3 1.00e+00 8.74e-01f  1\n",
      "  76r 6.4408330e+00 8.45e-02 8.48e+02  -1.0 8.56e-01   0.8 8.03e-01 3.97e-01f  1\n",
      "  77r 6.5315846e+00 7.94e-02 1.38e+03  -1.0 1.33e+01   0.3 7.51e-02 7.40e-02f  1\n",
      "  78r 6.5720448e+00 6.63e-02 1.40e+03  -1.0 2.32e+01  -0.1 4.30e-02 4.23e-02f  1\n",
      "  79r 6.6762826e+00 4.92e-02 1.65e+03  -1.0 1.47e+03   0.3 1.76e-04 6.68e-04f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  80r 6.7360191e+00 4.49e-02 1.08e+03  -1.0 1.93e+00   0.7 5.18e-01 3.13e-01f  1\n",
      "  81r 6.7639840e+00 4.10e-02 9.35e+02  -1.0 5.06e+00   0.2 1.98e-01 1.47e-01f  1\n",
      "  82r 6.8084975e+00 3.14e-02 4.08e+02  -1.0 1.54e+00   0.7 6.06e-01 2.43e-01f  1\n",
      "  83r 6.8243953e+00 2.56e-02 8.68e+01  -1.0 2.75e-01   1.1 1.00e+00 5.01e-01f  1\n",
      "  84  6.8244296e+00 4.47e-02 9.32e+01  -1.0 7.45e+04    -  8.38e-02 2.61e-05f 12\n",
      "  85  6.8222822e+00 4.34e-02 1.98e+03  -1.0 8.25e-01   2.9 1.00e+00 2.89e-02h  1\n",
      "  86  6.8227852e+00 3.98e-02 1.04e+04  -1.0 8.10e-01   2.4 1.00e+00 8.39e-02h  1\n",
      "  87  6.8376732e+00 3.87e-02 1.78e+04  -1.0 4.20e+00   1.9 8.73e-02 2.70e-02h  1\n",
      "  88  6.8626158e+00 3.73e-02 2.22e+04  -1.0 5.02e+00   1.5 6.46e-02 3.65e-02h  1\n",
      "  89  6.8967721e+00 3.55e-02 2.44e+04  -1.0 7.45e+00   1.0 1.40e-01 4.99e-02h  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  90  6.9271393e+00 3.48e-02 2.08e+04  -1.0 5.36e+01   0.5 9.84e-03 1.81e-02f  1\n",
      "  91  6.9710080e+00 3.32e-02 1.12e+04  -1.0 9.24e+00   0.9 3.30e-03 4.61e-02f  1\n",
      "  92  6.9745116e+00 3.30e-02 1.12e+04  -1.0 5.37e+00   1.4 7.42e-02 5.46e-03h  1\n",
      "  93  6.9901521e+00 3.22e-02 1.24e+04  -1.0 9.17e+00   0.9 9.13e-02 2.71e-02h  1\n",
      "  94  7.0096400e+00 3.14e-02 1.59e+04  -1.0 9.67e+00   1.3 6.43e-02 2.31e-02h  1\n",
      "  95  7.0150669e+00 3.11e-02 1.85e+04  -1.0 6.12e+01   0.8 1.24e-02 8.86e-03f  1\n",
      "  96  7.0341326e+00 3.04e-02 1.80e+04  -1.0 3.81e+01   0.3 2.70e-02 2.50e-02h  1\n",
      "  97  7.0357022e+00 3.03e-02 1.75e+04  -1.0 7.72e+01    -  8.18e-03 1.48e-03h  1\n",
      "  98  7.0421182e+00 3.03e-02 1.72e+04  -1.0 3.34e+02    -  3.39e-03 1.28e-03f  2\n",
      "  99  7.0606391e+00 2.96e-02 1.49e+04  -1.0 1.53e+01   0.8 1.79e-01 2.23e-02h  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 100  7.0731825e+00 2.93e-02 1.47e+04  -1.0 5.83e+01    -  1.44e-02 1.06e-02h  1\n",
      " 101  7.0794970e+00 2.93e-02 1.45e+04  -1.0 3.78e+02   0.3 2.57e-04 9.52e-04f  1\n",
      " 102  7.0800058e+00 2.92e-02 1.45e+04  -1.0 2.85e+01  -0.2 3.90e-02 7.37e-04h  1\n",
      " 103  7.0861101e+00 2.91e-02 1.44e+04  -1.0 1.44e+02    -  1.83e-03 5.72e-03f  2\n",
      " 104  7.0923450e+00 2.90e-02 1.43e+04  -1.0 3.61e+02  -0.7 3.27e-03 1.07e-03f  2\n",
      " 105  7.1000602e+00 2.90e-02 1.41e+04  -1.0 3.22e+03  -0.2 1.82e-04 1.34e-04h  1\n",
      " 106  7.1014456e+00 2.89e-02 1.41e+04  -1.0 3.15e+01    -  5.71e-02 3.16e-03h  1\n",
      " 107  7.1020251e+00 2.88e-02 1.41e+04  -1.0 9.51e+01    -  1.75e-02 3.33e-03h  1\n",
      " 108  7.1073055e+00 2.84e-02 1.61e+04  -1.0 3.38e+01    -  3.13e-02 1.37e-02h  1\n",
      " 109  7.1147468e+00 2.82e-02 1.84e+04  -1.0 5.49e+01    -  1.02e-04 7.24e-03h  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 110  7.1215517e+00 2.82e-02 1.80e+04  -1.0 3.10e+04    -  6.06e-06 1.68e-05f  1\n",
      " 111  7.1222773e+00 2.82e-02 1.80e+04  -1.0 6.44e+02    -  9.29e-03 3.28e-04h  1\n",
      " 112  7.1266502e+00 2.80e-02 2.21e+04  -1.0 1.14e+02   0.2 3.70e-02 8.83e-03h  1\n",
      " 113  7.1309259e+00 2.80e-02 2.15e+04  -1.0 4.27e+02  -0.3 7.84e-04 1.06e-03h  1\n",
      " 114  7.1308356e+00 2.79e-02 2.16e+04  -1.0 1.59e+02    -  3.89e-03 6.18e-04h  1\n",
      " 115  7.1309216e+00 2.79e-02 2.16e+04  -1.0 5.92e+01    -  2.81e-05 2.25e-04h  1\n",
      " 116  7.1353540e+00 2.79e-02 2.14e+04  -1.0 5.10e+02    -  6.46e-05 1.93e-03f  2\n",
      " 117  7.1391047e+00 2.79e-02 2.12e+04  -1.0 6.81e+02    -  3.67e-04 4.85e-04f  2\n",
      " 118  7.1392163e+00 2.79e-02 2.12e+04  -1.0 4.22e+02   0.1 3.08e-04 6.91e-05h  1\n",
      " 119  7.1450936e+00 2.78e-02 5.89e+04  -1.0 1.85e+02   0.6 2.85e-02 3.46e-03h  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 120  7.1468349e+00 2.78e-02 5.93e+04  -1.0 7.99e+02    -  2.36e-04 1.50e-04h  1\n",
      " 121  7.1525723e+00 2.77e-02 5.95e+04  -1.0 6.20e+02    -  2.45e-06 9.56e-04f  1\n",
      " 122  7.1532735e+00 2.77e-02 6.05e+04  -1.0 7.38e+02    -  1.11e-04 6.54e-04f  1\n",
      " 123  7.1455809e+00 2.77e-02 6.17e+04  -1.0 9.08e+03    -  8.23e-06 5.25e-05f  3\n",
      " 124  7.1437930e+00 2.77e-02 5.62e+04  -1.0 7.41e+02    -  3.73e-03 4.70e-04f  2\n",
      " 125  7.1438183e+00 2.77e-02 8.13e+04  -1.0 3.83e+02   0.1 1.72e-02 1.48e-05h  1\n",
      " 126  7.1470287e+00 2.77e-02 7.78e+04  -1.0 3.06e+02  -0.4 9.36e-05 1.13e-03h  1\n",
      " 127  7.1460294e+00 2.77e-02 7.81e+04  -1.0 5.72e+03    -  1.68e-06 2.81e-05f  4\n",
      " 128  7.1508814e+00 2.76e-02 1.03e+05  -1.0 5.56e+02   0.0 1.21e-02 1.32e-03h  1\n",
      " 129  7.1525693e+00 2.76e-02 1.03e+05  -1.0 9.69e+02    -  2.38e-04 3.00e-04f  3\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 130  7.1563252e+00 2.76e-02 1.01e+05  -1.0 8.44e+02    -  1.32e-03 5.19e-04f  2\n",
      " 131  7.1596374e+00 2.76e-02 1.05e+05  -1.0 6.09e+02    -  6.03e-03 7.27e-04h  1\n",
      " 132  7.1595477e+00 2.76e-02 9.69e+04  -1.0 2.56e+02    -  1.81e-05 7.17e-04h  2\n",
      " 133  7.1623925e+00 2.76e-02 9.91e+04  -1.0 1.74e+03    -  1.21e-05 2.82e-04f  3\n",
      " 134  7.1669068e+00 2.75e-02 8.09e+04  -1.0 1.43e+03    -  3.75e-03 5.16e-04f  2\n",
      " 135  7.1699512e+00 2.75e-02 7.81e+04  -1.0 1.17e+03    -  1.19e-03 3.18e-04f  2\n",
      " 136  7.1719443e+00 2.75e-02 7.58e+04  -1.0 9.24e+02    -  3.20e-03 2.04e-04h  2\n",
      " 137  7.1738562e+00 2.75e-02 1.95e+05  -1.0 1.65e+02    -  1.64e-02 1.06e-03h  1\n",
      " 138  7.1736732e+00 2.75e-02 2.10e+05  -1.0 1.41e+02    -  1.60e-03 8.40e-04h  3\n",
      " 139  7.1757688e+00 2.75e-02 2.09e+05  -1.0 5.76e+03    -  5.24e-05 3.64e-05f  4\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 140  7.1794098e+00 2.75e-02 2.07e+05  -1.0 4.03e+03    -  1.38e-04 9.11e-05f  3\n",
      " 141  7.1846229e+00 2.75e-02 1.20e+05  -1.0 3.33e+03    -  3.49e-03 1.66e-04f  2\n",
      " 142  7.1866822e+00 2.75e-02 1.15e+05  -1.0 2.81e+03    -  4.12e-04 9.96e-05f  2\n",
      " 143  7.1883645e+00 2.75e-02 8.74e+05  -1.0 4.42e+02   0.5 7.04e-02 6.38e-04h  1\n",
      " 144  7.1880680e+00 2.74e-02 1.03e+06  -1.0 3.33e+02    -  1.84e-03 8.79e-05h  3\n",
      " 145  7.1875793e+00 2.74e-02 1.53e+06  -1.0 3.94e+02    -  4.82e-03 1.15e-04h  5\n",
      " 146  7.1873788e+00 2.74e-02 2.52e+06  -1.0 5.78e+02    -  6.36e-03 3.34e-05h  8\n",
      " 147  7.1798546e+00 2.74e-02 2.52e+06  -1.0 9.22e+02    -  7.96e-04 7.96e-04s 14\n",
      " 148r 7.1798546e+00 2.74e-02 1.00e+03  -1.0 0.00e+00    -  0.00e+00 0.00e+00R  1\n",
      " 149r 7.1851833e+00 1.56e-02 9.87e+02  -1.0 1.05e+02    -  1.70e-01 5.02e-03f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 150  7.1851963e+00 1.56e-02 2.42e+04  -1.0 6.67e+03    -  4.21e-01 9.36e-05f  6\n",
      " 151r 7.1851963e+00 1.56e-02 9.99e+02  -1.0 0.00e+00    -  0.00e+00 4.75e-07R 15\n",
      " 152r 7.1949816e+00 1.54e-02 9.79e+02  -1.0 1.74e+01    -  2.97e-01 1.33e-02f  1\n",
      " 153r 7.1964824e+00 1.18e-02 7.06e+02  -1.0 1.59e+00    -  1.88e-01 2.79e-01f  1\n",
      " 154r 7.1964824e+00 1.18e-02 9.92e+02  -1.0 0.00e+00    -  0.00e+00 3.99e-07R 12\n",
      " 155r 7.1968537e+00 1.14e-02 9.52e+02  -1.0 8.59e-01    -  1.58e-01 3.90e-02f  1\n",
      " 156r 7.1964910e+00 9.58e-03 7.79e+02  -1.0 8.21e-01    -  6.47e-02 1.82e-01f  1\n",
      " 157r 7.1964910e+00 9.58e-03 9.90e+02  -1.0 0.00e+00    -  0.00e+00 3.97e-07R 16\n",
      " 158r 7.1953621e+00 7.50e-03 7.51e+02  -1.0 7.41e-01    -  3.38e-01 2.40e-01f  1\n",
      " 159r 7.1953621e+00 7.50e-03 9.87e+02  -1.0 0.00e+00    -  0.00e+00 4.13e-07R 16\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 160r 7.1917211e+00 5.15e-03 6.41e+02  -1.0 4.83e-01    -  7.00e-01 3.46e-01f  1\n",
      " 161r 7.1917211e+00 5.15e-03 9.81e+02  -1.0 0.00e+00    -  0.00e+00 3.13e-07R 17\n",
      " 162r 7.1887883e+00 3.56e-03 6.22e+02  -1.0 4.79e-01    -  1.00e+00 3.55e-01f  1\n",
      " 163r 7.1887883e+00 3.56e-03 9.72e+02  -1.0 0.00e+00    -  0.00e+00 4.38e-07R 17\n",
      " 164r 7.1866128e+00 2.61e-03 6.24e+02  -1.0 4.47e-01    -  1.00e+00 3.44e-01f  1\n",
      " 165r 7.1866128e+00 2.61e-03 9.62e+02  -1.0 0.00e+00    -  0.00e+00 2.94e-07R 18\n",
      " 166r 7.1840380e+00 1.80e-03 4.63e+02  -1.0 4.26e-01    -  1.00e+00 5.13e-01f  1\n",
      " 167r 7.1840380e+00 1.80e-03 9.46e+02  -1.0 0.00e+00    -  0.00e+00 4.42e-07R 18\n",
      " 168r 7.1832201e+00 1.68e-03 7.05e+02  -1.0 2.81e-01    -  1.00e+00 2.44e-01f  1\n",
      " 169r 7.1859313e+00 1.45e-03 2.06e+03  -1.0 4.83e-01    -  1.00e+00 1.00e+00f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 170r 7.1859313e+00 1.45e-03 9.33e+02  -1.0 0.00e+00    -  0.00e+00 4.01e-07R 15\n",
      " 171r 7.1872428e+00 1.37e-03 8.62e+02  -1.0 5.48e-01    -  1.00e+00 7.26e-02f  1\n",
      " 172r 7.1925848e+00 2.08e-03 7.27e+03  -1.0 5.32e-01    -  1.00e+00 1.00e+00f  1\n",
      " 173r 7.2022533e+00 1.36e-03 1.03e+01  -1.0 3.12e-01    -  1.00e+00 1.00e+00f  1\n",
      " 174r 7.2045637e+00 1.36e-03 6.08e-01  -1.0 2.33e-02   0.0 1.00e+00 1.00e+00h  1\n",
      " 175r 7.1780577e+00 3.77e-03 3.48e+02  -2.5 8.78e-01  -0.5 5.25e-01 4.88e-01f  1\n",
      " 176r 7.1971340e+00 5.04e-03 2.97e+02  -2.5 1.28e+01    -  7.83e-02 6.77e-02f  1\n",
      " 177r 7.1930612e+00 2.50e-03 3.42e+01  -2.5 6.99e-01  -0.1 6.52e-01 8.64e-01f  1\n",
      " 178r 7.1857164e+00 1.29e-02 6.01e+00  -2.5 6.60e-01  -0.5 8.93e-01 5.04e-01f  1\n",
      " 179r 7.1995754e+00 1.80e-02 8.98e+00  -2.5 8.73e-01  -1.0 3.67e-01 6.70e-01f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 180r 7.1985878e+00 1.78e-02 6.44e+00  -2.5 1.93e-01  -0.6 1.00e+00 2.78e-01f  1\n",
      " 181r 7.1942905e+00 1.82e-02 2.15e+00  -2.5 2.94e-01  -1.1 1.00e+00 8.71e-01f  1\n",
      " 182r 7.1900777e+00 1.89e-02 2.68e+00  -2.5 4.18e-01  -1.5 1.00e+00 1.00e+00f  1\n",
      " 183r 7.1944113e+00 1.94e-02 3.22e+00  -2.5 5.64e-01    -  1.00e+00 5.00e-01h  2\n",
      " 184r 7.2069968e+00 1.89e-02 6.67e+00  -2.5 8.47e-01    -  1.00e+00 1.00e+00H  1\n",
      " 185r 7.2037368e+00 1.89e-02 2.45e-01  -2.5 2.43e-02  -0.2 1.00e+00 1.00e+00h  1\n",
      " 186r 7.2082258e+00 1.89e-02 2.67e+00  -2.5 5.02e-01  -0.7 3.98e-01 2.50e-01h  3\n",
      " 187r 7.2151782e+00 1.87e-02 3.76e+00  -2.5 1.50e-01  -0.3 1.00e+00 1.00e+00h  1\n",
      " 188r 7.2289058e+00 1.84e-02 4.61e+00  -2.5 8.13e-01  -0.7 6.18e-01 6.46e-01f  1\n",
      " 189r 7.2331346e+00 1.79e-02 6.37e-01  -2.5 2.34e-01  -0.3 1.00e+00 1.00e+00f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 190r 7.2461356e+00 1.98e-02 2.07e+01  -2.5 9.77e-01    -  6.13e-01 6.81e-01f  1\n",
      " 191r 7.2539657e+00 2.48e-02 6.60e+00  -2.5 1.24e-01   0.1 1.00e+00 7.44e-01f  1\n",
      " 192r 7.2652990e+00 2.33e-02 2.60e+00  -2.5 2.81e-01  -0.4 1.00e+00 9.99e-01f  1\n",
      " 193r 7.2753266e+00 2.05e-02 3.45e+00  -2.5 1.26e-01   0.1 1.00e+00 9.00e-01f  1\n",
      " 194r 7.2859910e+00 1.85e-02 5.20e+00  -2.5 1.78e-01  -0.4 1.00e+00 1.00e+00f  1\n",
      " 195r 7.3074275e+00 2.76e-02 8.13e+00  -2.5 1.86e-01   0.0 9.54e-01 7.58e-01f  1\n",
      " 196r 7.3127592e+00 2.34e-02 1.91e-01  -2.5 6.89e-02   0.4 1.00e+00 1.00e+00f  1\n",
      " 197r 7.3147913e+00 2.14e-02 1.99e-01  -2.5 2.69e-02   0.9 1.00e+00 1.00e+00h  1\n",
      " 198r 7.3302220e+00 2.10e-02 1.07e+01  -2.5 1.09e-01   0.4 1.00e+00 1.00e+00f  1\n",
      " 199r 7.3336126e+00 2.05e-02 2.93e-01  -2.5 4.45e-02   0.8 1.00e+00 1.00e+00h  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 200r 7.3524293e+00 2.32e-02 1.04e+01  -2.5 1.65e-01   0.3 1.00e+00 1.00e+00f  1\n",
      " 201r 7.3696234e+00 2.53e-02 4.06e+00  -2.5 4.89e-01  -0.1 1.00e+00 7.84e-01f  1\n",
      " 202r 7.3974996e+00 3.59e-02 2.36e+01  -2.5 5.73e+00  -0.6 7.88e-02 1.17e-01f  1\n",
      " 203r 7.4062990e+00 4.04e-02 2.72e+01  -2.5 1.07e+01  -1.1 8.83e-02 3.26e-02f  1\n",
      " 204r 7.4345388e+00 3.85e-02 1.26e+01  -2.5 1.61e-01   0.2 1.00e+00 1.00e+00f  1\n",
      " 205r 7.4502205e+00 3.46e-02 1.47e+01  -2.5 6.54e-01  -0.2 3.94e-01 2.08e-01f  1\n",
      " 206r 7.4739708e+00 5.68e-02 6.95e+01  -2.5 2.26e+00  -0.7 1.92e-01 3.79e-01f  1\n",
      " 207r 7.4930110e+00 6.07e-02 3.11e+01  -2.5 1.38e-01   0.6 1.00e+00 7.30e-01f  1\n",
      " 208r 7.4974265e+00 6.13e-02 5.83e-01  -2.5 1.66e-02   1.0 1.00e+00 1.00e+00f  1\n",
      " 209r 7.5038485e+00 6.31e-02 3.41e+00  -2.5 6.52e-02   0.6 1.00e+00 1.00e+00f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 210r 7.5140262e+00 6.34e-02 8.06e+00  -2.5 2.90e-01   0.1 1.00e+00 4.51e-01f  1\n",
      " 211r 7.5366523e+00 5.77e-02 1.27e+01  -2.5 1.12e-01   0.5 1.00e+00 1.00e+00f  1\n",
      " 212r 7.5675665e+00 6.98e-02 3.67e+01  -2.5 3.81e-01   0.0 1.00e+00 1.00e+00f  1\n",
      " 213r 7.6181704e+00 8.00e-02 5.53e+01  -2.5 2.16e-01   0.5 5.76e-01 1.00e+00f  1\n",
      " 214r 7.6195890e+00 7.14e-02 2.20e+01  -2.5 8.23e-02   0.9 1.00e+00 5.96e-01h  1\n",
      " 215r 7.6442118e+00 6.31e-02 2.47e+01  -2.5 2.33e-01   0.4 1.00e+00 1.00e+00f  1\n",
      " 216r 7.6598366e+00 8.40e-02 2.54e+01  -2.5 6.40e-01  -0.1 7.83e-01 4.31e-01f  1\n",
      " 217r 7.6868167e+00 1.24e-01 6.40e+01  -2.5 8.54e+00  -0.5 3.02e-02 6.56e-02f  1\n",
      " 218r 7.6991770e+00 1.22e-01 1.19e+01  -2.5 1.10e-01   0.8 1.00e+00 1.00e+00f  1\n",
      " 219r 7.7200478e+00 1.20e-01 3.50e+01  -2.5 2.31e-01   0.3 1.00e+00 9.81e-01f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 220r 7.7516678e+00 1.02e-01 1.23e+02  -2.5 6.76e-01  -0.2 6.06e-01 7.46e-01f  1\n",
      " 221r 7.7660404e+00 1.09e-01 1.03e+02  -2.5 3.53e-01   0.3 3.57e-01 2.40e-01f  1\n",
      " 222r 7.7960109e+00 1.14e-01 3.91e+01  -2.5 9.01e-02   0.7 1.00e+00 1.00e+00f  1\n",
      " 223r 7.8026546e+00 1.14e-01 4.50e+00  -2.5 3.30e-02   1.1 1.00e+00 1.00e+00h  1\n",
      " 224r 7.8127699e+00 1.03e-01 1.29e+01  -2.5 1.16e-01   0.6 1.00e+00 8.85e-01f  1\n",
      " 225r 7.8750737e+00 1.04e-01 1.08e+02  -2.5 7.92e-01   0.2 2.68e-01 4.35e-01f  1\n",
      " 226r 7.8846678e+00 9.86e-02 9.05e+01  -2.5 1.74e-01   0.6 4.95e-01 2.15e-01f  1\n",
      " 227r 7.8868191e+00 9.81e-02 8.28e+01  -2.5 5.14e-01   0.1 6.04e-01 9.85e-02f  1\n",
      " 228r 7.8912324e+00 9.64e-02 8.02e+01  -2.5 1.72e+00  -0.4 1.26e-01 7.97e-02f  1\n",
      " 229r 7.9035550e+00 9.50e-02 6.83e+01  -2.5 5.55e-01   0.1 6.59e-01 4.19e-01f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 230r 7.9366250e+00 9.45e-02 1.15e+02  -2.5 1.55e+00   0.5 2.46e-02 4.01e-02f  1\n",
      " 231r 7.9418670e+00 9.89e-02 2.62e+02  -2.5 7.77e-01  -0.0 6.69e-01 1.64e-01f  1\n",
      " 232r 7.9560847e+00 1.14e-01 5.91e+01  -2.5 2.47e-01   0.4 9.13e-01 8.04e-01f  1\n",
      " 233r 7.9987828e+00 1.17e-01 9.23e+01  -2.5 1.03e-01   0.9 8.77e-01 1.00e+00f  1\n",
      " 234r 8.0041445e+00 1.20e-01 7.78e+00  -2.5 4.85e-02   1.3 9.98e-01 1.00e+00h  1\n",
      " 235r 8.0116768e+00 1.21e-01 2.36e+01  -2.5 1.28e-01   0.8 1.00e+00 2.21e-01f  1\n",
      " 236r 8.0320964e+00 1.22e-01 2.02e+01  -2.5 4.41e-01   0.3 9.67e-01 6.62e-01f  1\n",
      " 237r 8.0541584e+00 9.09e-02 2.81e+01  -2.5 1.35e-01   0.7 1.00e+00 1.00e+00f  1\n",
      " 238r 8.0563326e+00 9.21e-02 1.94e+01  -2.5 4.70e-02   1.2 1.00e+00 3.16e-01f  1\n",
      " 239r 8.0906475e+00 1.00e-01 5.69e+01  -2.5 1.66e-01   0.7 1.00e+00 8.86e-01f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 240r 8.0987398e+00 9.84e-02 3.88e+01  -2.5 5.40e-01   0.2 1.00e+00 3.88e-01f  1\n",
      " 241r 8.1074294e+00 1.02e-01 3.81e+01  -2.5 2.59e+00  -0.3 1.16e-01 4.82e-02f  1\n",
      " 242r 8.1398642e+00 9.74e-02 7.52e+01  -2.5 8.05e-01   0.2 3.49e-01 2.83e-01f  1\n",
      " 243r 8.1582451e+00 9.60e-02 8.88e+01  -2.5 2.36e-01   0.6 2.48e-01 1.47e-01f  1\n",
      " 244r 8.1811973e+00 8.39e-02 1.20e+02  -2.5 2.39e+00   0.1 4.58e-02 4.03e-02f  1\n",
      " 245r 8.1911345e+00 9.31e-02 1.06e+02  -2.5 2.67e-01   0.5 2.97e-01 4.14e-01f  1\n",
      " 246r 8.2047173e+00 9.25e-02 1.45e+02  -2.5 9.61e-02   1.0 1.00e+00 6.03e-01f  1\n",
      " 247r 8.2170600e+00 9.52e-02 5.95e+01  -2.5 3.46e-01   0.5 8.59e-01 2.82e-01f  1\n",
      " 248r 8.2401972e+00 9.81e-02 3.94e+01  -2.5 1.00e-01   0.9 1.00e+00 1.00e+00f  1\n",
      " 249r 8.2464293e+00 9.88e-02 9.17e-01  -2.5 4.14e-02   1.3 1.00e+00 1.00e+00f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 250r 8.2569998e+00 1.07e-01 7.15e+00  -2.5 1.35e-01   0.9 1.00e+00 8.17e-01f  1\n",
      " 251r 8.2677668e+00 1.10e-01 2.99e+01  -2.5 4.33e-01   0.4 6.61e-01 1.95e-01f  1\n",
      " 252r 8.2917854e+00 1.11e-01 4.21e+01  -2.5 1.26e-01   0.8 1.00e+00 1.00e+00f  1\n",
      " 253r 8.2987562e+00 1.12e-01 2.20e+00  -2.5 5.29e-02   1.2 1.00e+00 1.00e+00f  1\n",
      " 254r 8.3398116e+00 1.02e-01 1.46e+02  -2.5 2.16e-01   0.8 2.18e-01 2.12e-01f  1\n",
      " 255r 8.3450826e+00 7.90e-02 1.85e+01  -2.5 7.35e-02   1.2 8.23e-01 1.00e+00h  1\n",
      " 256r 8.3524786e+00 8.21e-02 1.15e+01  -2.5 2.28e-01   0.7 1.00e+00 4.88e-01f  1\n",
      " 257r 8.3689512e+00 9.01e-02 1.17e+01  -2.5 7.01e-01   0.2 4.44e-01 3.46e-01f  1\n",
      " 258r 8.3926103e+00 8.92e-02 5.33e+01  -2.5 2.33e-01   0.7 1.00e+00 5.33e-01f  1\n",
      " 259r 8.4076644e+00 9.03e-02 2.64e+01  -2.5 7.52e-02   1.1 1.00e+00 1.00e+00f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 260r 8.4180896e+00 9.49e-02 1.74e+01  -2.5 2.79e-01   0.6 8.83e-01 4.21e-01f  1\n",
      " 261r 8.4346075e+00 9.58e-02 2.71e+01  -2.5 1.01e-01   1.0 1.00e+00 1.00e+00f  1\n",
      " 262r 8.4416574e+00 9.60e-02 2.29e+01  -2.5 3.44e-01   0.6 3.85e-01 1.21e-01f  1\n",
      " 263r 8.4634585e+00 9.67e-02 3.24e+01  -2.5 1.08e-01   1.0 1.00e+00 1.00e+00f  1\n",
      " 264r 8.4762479e+00 8.78e-02 3.50e+01  -2.5 3.76e-01   0.5 6.62e-01 2.85e-01f  1\n",
      " 265r 8.5220380e+00 8.33e-02 2.27e+02  -2.5 1.22e-01   0.9 5.24e-01 6.40e-01f  1\n",
      " 266r 8.5294617e+00 8.39e-02 2.65e+01  -2.5 4.84e-02   1.4 6.72e-01 1.00e+00h  1\n",
      " 267r 8.5409894e+00 8.07e-02 5.03e+00  -2.5 1.61e-01   0.9 1.00e+00 8.51e-01f  1\n",
      " 268r 8.5844449e+00 7.51e-02 1.46e+02  -2.5 7.57e-01   0.4 9.37e-02 1.21e-01f  1\n",
      " 269r 8.5883092e+00 7.77e-02 2.37e+02  -2.5 1.80e-01   0.8 1.00e+00 1.82e-01f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 270r 8.5944806e+00 8.23e-02 3.72e+02  -2.5 7.09e-02   1.3 4.39e-01 9.91e-01f  1\n",
      " 271r 8.6403541e+00 8.77e-02 2.05e+02  -2.5 1.78e-01   0.8 4.37e-01 8.07e-01f  1\n",
      " 272r 8.6516822e+00 8.52e-02 1.54e+02  -2.5 8.64e-02   1.2 8.20e-01 3.77e-01f  1\n",
      " 273r 8.6558132e+00 8.51e-02 1.25e+02  -2.5 2.67e-01   0.7 1.00e+00 1.88e-01f  1\n",
      " 274r 8.6809409e+00 7.03e-02 1.87e+02  -2.5 1.34e+00   0.3 7.22e-02 1.00e-01f  1\n",
      " 275r 8.7339159e+00 7.81e-02 3.65e+02  -2.5 3.74e-01   0.7 2.93e-01 4.11e-01f  1\n",
      " 276r 8.7393966e+00 7.97e-02 2.56e+02  -2.5 1.23e-01   1.1 7.28e-01 2.98e-01h  1\n",
      " 277r 8.7451298e+00 8.13e-02 2.01e+01  -2.5 4.48e-02   1.5 1.00e+00 1.00e+00h  1\n",
      " 278r 8.7555186e+00 8.21e-02 6.88e+00  -2.5 1.36e-01   1.1 1.00e+00 1.00e+00f  1\n",
      " 279r 8.7629075e+00 8.43e-02 4.87e+01  -2.5 4.25e-01   0.6 8.89e-01 1.81e-01f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 280r 8.7765730e+00 8.86e-02 8.41e+00  -2.5 1.42e-01   1.0 1.00e+00 7.66e-01f  1\n",
      " 281r 8.7856960e+00 8.86e-02 2.91e+01  -2.5 4.90e-02   1.4 1.00e+00 1.00e+00f  1\n",
      " 282r 8.7931649e+00 8.95e-02 1.57e+01  -2.5 1.63e-01   1.0 1.00e+00 5.25e-01f  1\n",
      " 283r 8.8137563e+00 8.17e-02 4.99e+01  -2.5 4.82e-01   0.5 4.77e-01 3.15e-01f  1\n",
      " 284r 8.8202941e+00 8.14e-02 4.44e+01  -2.5 1.57e-01   0.9 1.00e+00 2.69e-01f  1\n",
      " 285r 8.8289192e+00 8.31e-02 6.41e+00  -2.5 5.50e-02   1.3 1.00e+00 1.00e+00f  1\n",
      " 286r 8.8975704e+00 7.83e-02 6.11e+02  -2.5 2.11e-01   0.9 2.60e-01 6.31e-01f  1\n",
      " 287r 8.9146989e+00 7.40e-02 5.54e+02  -2.5 8.24e-01   0.4 9.81e-02 1.31e-01f  1\n",
      " 288r 8.9290985e+00 8.44e-02 5.11e+02  -2.5 3.09e+00  -0.1 1.35e-01 7.23e-02f  1\n",
      " 289r 8.9428154e+00 1.88e-01 5.09e+02  -2.5 3.89e+01    -  8.82e-03 8.50e-03f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 290r 8.9504221e+00 1.87e-01 5.07e+02  -2.5 4.05e+01  -0.6 4.51e-03 3.26e-03f  1\n",
      " 291r 8.9578092e+00 1.82e-01 4.79e+02  -2.5 2.38e+00  -0.2 1.34e-01 5.17e-02f  1\n",
      " 292r 8.9669216e+00 1.63e-01 4.67e+02  -2.5 7.95e+00  -0.6 4.94e-02 2.60e-02f  1\n",
      " 293r 8.9745725e+00 1.98e-01 4.51e+02  -2.5 4.15e+00  -1.1 1.56e-01 4.00e-02f  1\n",
      " 294r 8.9788129e+00 1.97e-01 4.52e+02  -2.5 2.04e+01  -0.7 1.91e-03 2.13e-03f  1\n",
      " 295r 9.0057955e+00 1.78e-01 5.58e+02  -2.5 1.05e+00   0.6 3.09e-02 5.31e-02f  1\n",
      " 296r 9.0117568e+00 1.63e-01 4.81e+02  -2.5 6.27e-01   0.2 7.03e-01 1.44e-01h  1\n",
      " 297r 9.0229941e+00 8.93e-02 4.24e+02  -2.5 1.73e+00  -0.3 5.43e-01 1.43e-01f  1\n",
      " 298r 9.0597672e+00 8.10e-02 2.23e+02  -2.5 5.90e-02   1.0 6.18e-01 1.00e+00f  1\n",
      " 299r 9.0956031e+00 1.20e-01 4.60e+02  -2.5 2.98e-01   0.5 2.02e-01 3.73e-01f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 300r 9.1264080e+00 1.12e-01 1.20e+02  -2.5 9.91e-02   1.0 4.84e-01 1.00e+00f  1\n",
      " 301r 9.1386949e+00 1.04e-01 2.68e+01  -2.5 4.03e-02   1.4 1.00e+00 1.00e+00f  1\n",
      " 302r 9.1523180e+00 9.74e-02 3.44e+01  -2.5 1.45e-01   0.9 1.00e+00 6.45e-01f  1\n",
      " 303r 9.1637886e+00 9.12e-02 3.45e+01  -2.5 4.82e-02   1.3 1.00e+00 1.00e+00f  1\n",
      " 304r 9.1801089e+00 6.41e-02 4.97e+01  -2.5 1.76e-01   0.9 1.00e+00 7.34e-01f  1\n",
      " 305r 9.2093701e+00 6.23e-02 2.07e+02  -2.5 4.35e-02   1.3 9.21e-01 1.00e+00f  1\n",
      " 306r 9.2234076e+00 8.72e-02 2.11e+02  -2.5 4.74e+01    -  5.33e-03 8.21e-03f  1\n",
      " 307r 9.2394375e+00 8.34e-02 9.55e+01  -2.5 2.29e-01   0.8 2.36e-01 6.32e-01f  1\n",
      " 308r 9.2505622e+00 7.95e-02 8.22e+01  -2.5 6.41e-01   0.3 4.84e-01 3.04e-01f  1\n",
      " 309r 9.2579538e+00 7.38e-02 8.94e+01  -2.5 3.76e+00  -0.1 2.53e-02 1.26e-02f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 310r 9.2782822e+00 7.43e-02 7.26e+01  -2.5 6.49e-02   1.2 1.00e+00 1.00e+00f  1\n",
      " 311r 9.3051359e+00 8.03e-02 2.36e+02  -2.5 4.34e-01   0.7 9.55e-02 1.19e-01f  1\n",
      " 312r 9.3081792e+00 7.82e-02 1.39e+01  -2.5 1.23e-02   2.0 1.00e+00 1.00e+00h  1\n",
      " 313r 9.3149291e+00 7.90e-02 4.99e+00  -2.5 3.51e-02   1.6 1.00e+00 1.00e+00f  1\n",
      " 314r 9.3257176e+00 8.03e-02 3.42e+01  -2.5 1.09e-01   1.1 1.00e+00 4.97e-01f  1\n",
      " 315r 9.3348050e+00 8.10e-02 1.69e+01  -2.5 3.71e-02   1.5 1.00e+00 1.00e+00f  1\n",
      " 316r 9.3497634e+00 7.89e-02 5.29e+01  -2.5 1.27e-01   1.0 1.00e+00 9.85e-01f  1\n",
      " 317r 9.3637067e+00 6.10e-02 3.92e+01  -2.5 3.84e-02   1.5 1.00e+00 1.00e+00f  1\n",
      " 318r 9.3671804e+00 6.15e-02 7.26e+01  -2.5 1.35e-01   1.0 1.00e+00 1.41e-01f  1\n",
      " 319r 9.4013857e+00 6.22e-02 1.72e+02  -2.5 4.76e-01   0.5 4.47e-01 4.18e-01f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 320r 9.4036023e+00 6.07e-02 3.12e+01  -2.5 1.94e-02   1.8 1.00e+00 8.10e-01f  1\n",
      " 321r 9.4109378e+00 6.12e-02 5.21e+01  -2.5 4.17e-02   1.4 1.00e+00 4.00e-01f  1\n",
      " 322r 9.4336930e+00 6.86e-02 9.05e+01  -2.5 1.72e-01   0.9 1.00e+00 1.00e+00f  1\n",
      " 323r 9.4525534e+00 7.03e-02 1.80e+02  -2.5 7.10e-02   1.3 4.10e-01 4.45e-01f  1\n",
      " 324r 9.4580446e+00 7.07e-02 1.40e+02  -2.5 2.06e-01   0.8 1.00e+00 2.47e-01f  1\n",
      " 325r 9.4756958e+00 6.49e-02 1.27e+02  -2.5 7.03e-01   0.4 8.31e-01 3.39e-01f  1\n",
      " 326r 9.5250629e+00 5.30e-02 6.16e+02  -2.5 5.16e-01   0.8 6.36e-02 1.87e-01f  1\n",
      " 327r 9.5338453e+00 6.17e-02 5.71e+02  -2.5 1.16e+00   0.3 8.37e-02 8.32e-02f  1\n",
      " 328r 9.5661547e+00 7.61e-02 5.82e+02  -2.5 3.59e-01   0.7 1.76e-01 3.15e-01f  1\n",
      " 329r 9.5788900e+00 7.46e-02 5.00e+02  -2.5 8.87e-02   1.2 3.38e-01 2.20e-01f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 330r 9.5933919e+00 7.71e-02 3.78e+02  -2.5 3.76e-01   0.7 7.42e-01 2.83e-01f  1\n",
      " 331r 9.6272416e+00 7.47e-02 3.73e+02  -2.5 1.09e-01   1.1 4.62e-01 7.15e-01f  1\n",
      " 332r 9.6383619e+00 6.27e-02 3.18e+02  -2.5 3.89e-01   0.6 2.41e-01 1.99e-01f  1\n",
      " 333r 9.6654699e+00 5.07e-02 3.61e+02  -2.5 1.19e-01   1.1 4.16e-01 5.11e-01f  1\n",
      " 334r 9.6861906e+00 5.05e-02 2.25e+02  -2.5 4.09e-02   1.5 8.78e-01 1.00e+00f  1\n",
      " 335r 9.6883377e+00 5.00e-02 2.00e+02  -2.5 1.70e-01   1.0 1.00e+00 1.12e-01f  1\n",
      " 336r 9.7037885e+00 5.28e-02 1.39e+02  -2.5 5.88e-01   0.5 5.32e-01 3.16e-01f  1\n",
      " 337r 9.7101638e+00 5.09e-02 1.33e+02  -2.5 1.35e+00   0.0 2.17e-01 5.86e-02f  1\n",
      " 338r 9.7153097e+00 5.12e-02 1.29e+02  -2.5 1.75e+00   0.5 6.43e-02 3.56e-02f  1\n",
      " 339r 9.7484985e+00 5.17e-02 3.12e+02  -2.5 2.08e-01   0.9 2.02e-01 2.88e-01f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 340r 9.7581095e+00 5.47e-02 2.73e+02  -2.5 6.29e-01   0.4 7.96e-01 1.54e-01f  1\n",
      " 341r 9.7863503e+00 6.30e-02 2.96e+02  -2.5 3.39e+00  -0.1 3.42e-02 6.73e-02f  1\n",
      " 342r 9.8030711e+00 6.61e-02 2.11e+02  -2.5 7.17e-02   1.3 6.53e-01 6.37e-01f  1\n",
      " 343r 9.8117282e+00 6.69e-02 1.47e+01  -2.5 2.68e-02   1.7 1.00e+00 1.00e+00h  1\n",
      " 344r 9.8537389e+00 6.62e-02 4.91e+02  -2.5 1.63e-01   1.2 1.50e-01 3.45e-01f  1\n",
      " 345r 9.8730407e+00 6.50e-02 2.26e+02  -2.5 3.53e-02   1.7 6.10e-01 1.00e+00f  1\n",
      " 346r 9.8806959e+00 6.35e-02 1.02e+02  -2.5 1.20e-01   1.2 1.00e+00 5.58e-01f  1\n",
      " 347r 9.8839431e+00 5.80e-02 9.87e+01  -2.5 3.32e-01   0.7 8.17e-01 9.51e-02f  1\n",
      " 348r 9.9026633e+00 4.50e-02 1.01e+02  -2.5 9.15e-01   0.2 2.03e-01 2.25e-01f  1\n",
      " 349r 9.9179992e+00 4.48e-02 6.68e+01  -2.5 3.16e-02   1.5 1.00e+00 1.00e+00f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 350r 9.9354187e+00 4.65e-02 7.46e+01  -2.5 1.27e-01   1.1 1.00e+00 5.46e-01f  1\n",
      " 351r 9.9393846e+00 4.63e-02 2.07e+02  -2.5 4.84e-01   0.6 8.29e-01 9.42e-02f  1\n",
      " 352r 9.9497093e+00 4.49e-02 1.20e+02  -2.5 1.41e-01   1.0 1.00e+00 3.27e-01f  1\n",
      " 353r 9.9697140e+00 4.69e-02 8.06e+01  -2.5 4.54e-02   1.4 1.00e+00 1.00e+00f  1\n",
      " 354r 9.9899322e+00 5.10e-02 1.50e+02  -2.5 1.54e-01   1.0 7.36e-01 4.56e-01f  1\n",
      " 355r 9.9994839e+00 4.92e-02 1.57e+02  -2.5 5.93e-01   0.5 1.55e-01 6.91e-02f  1\n",
      " 356r 1.0039797e+01 4.00e-02 4.94e+02  -2.5 3.19e-01   0.9 7.89e-02 2.22e-01f  1\n",
      " 357r 1.0058972e+01 5.31e-02 5.04e+02  -2.5 5.06e-01   0.4 1.80e-01 1.73e-01f  1\n",
      " 358r 1.0063367e+01 5.19e-02 3.09e+02  -2.5 2.01e-02   1.8 7.94e-01 4.08e-01f  1\n",
      " 359r 1.0072183e+01 5.27e-02 1.51e+02  -2.5 7.33e-02   1.3 1.00e+00 5.74e-01f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 360r 1.0102287e+01 5.02e-02 3.69e+02  -2.5 2.03e-01   0.8 2.39e-01 3.59e-01f  1\n",
      " 361r 1.0132699e+01 4.69e-02 4.10e+02  -2.5 7.81e-01   0.3 1.33e-01 2.18e-01f  1\n",
      " 362r 1.0143515e+01 4.72e-02 7.88e+01  -2.5 4.60e-02   1.7 1.00e+00 1.00e+00f  1\n",
      " 363r 1.0163469e+01 4.15e-02 7.81e+01  -2.5 8.48e-02   1.2 1.00e+00 8.00e-01f  1\n",
      " 364r 1.0203417e+01 4.61e-02 3.02e+02  -2.5 2.99e-01   0.7 6.57e-01 7.13e-01f  1\n",
      " 365r 1.0225557e+01 3.37e-02 3.95e+02  -2.5 1.03e-01   1.1 2.05e-01 2.63e-01f  1\n",
      " 366r 1.0254389e+01 3.68e-02 5.74e+02  -2.5 3.60e-01   0.7 2.25e-01 3.15e-01f  1\n",
      " 367r 1.0298061e+01 3.41e-02 9.56e+02  -2.5 2.95e-01   1.1 1.01e-01 2.30e-01f  1\n",
      " 368r 1.0316857e+01 3.27e-02 2.65e+02  -2.5 3.19e-02   1.5 4.11e-01 7.82e-01h  1\n",
      " 369r 1.0328578e+01 2.85e-02 1.87e+02  -2.5 1.49e-01   1.0 8.99e-01 3.76e-01f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 370r 1.0344604e+01 2.79e-02 6.46e+01  -2.5 4.76e-02   1.5 1.00e+00 1.00e+00f  1\n",
      " 371r 1.0369450e+01 2.70e-02 1.56e+02  -2.5 1.32e-01   1.0 5.78e-01 4.40e-01f  1\n",
      " 372r 1.0396891e+01 2.92e-02 2.54e+02  -2.5 4.35e-01   0.5 3.94e-01 2.97e-01f  1\n",
      " 373r 1.0408761e+01 2.70e-02 1.13e+02  -2.5 2.10e-02   1.8 1.00e+00 1.00e+00f  1\n",
      " 374r 1.0432759e+01 2.82e-02 9.76e+01  -2.5 5.14e-02   1.4 9.62e-01 1.00e+00f  1\n",
      " 375r 1.0493715e+01 2.25e-02 2.72e+02  -2.5 1.61e+02    -  2.52e-03 4.93e-03f  1\n",
      " 376r 1.0540163e+01 2.68e-02 3.39e+02  -2.5 4.66e+02    -  1.26e-03 1.99e-03f  1\n",
      " 377r 1.0563994e+01 2.48e-02 5.73e+02  -2.5 4.55e-01   0.9 5.61e-02 1.08e-01f  1\n",
      " 378r 1.0573277e+01 2.02e-02 1.63e+02  -2.5 7.16e-02   2.2 1.87e-01 7.73e-01h  1\n",
      " 379r 1.0591305e+01 1.74e-02 8.36e+01  -2.5 2.16e-02   1.7 1.00e+00 1.00e+00f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 380r 1.0599119e+01 1.59e-02 1.67e+02  -2.5 9.23e-02   1.3 1.00e+00 2.29e-01f  1\n",
      " 381r 1.0611514e+01 1.62e-02 6.27e+01  -2.5 2.54e-02   1.7 1.00e+00 1.00e+00f  1\n",
      " 382r 1.0626100e+01 1.63e-02 7.51e+01  -2.5 7.18e-02   1.2 7.77e-01 4.33e-01f  1\n",
      " 383r 1.0647855e+01 1.44e-02 1.13e+02  -2.5 2.62e-02   1.6 1.00e+00 1.00e+00f  1\n",
      " 384r 1.0675803e+01 1.27e-02 3.73e+02  -2.5 1.29e-01   1.2 1.20e-01 2.78e-01f  1\n",
      " 385r 1.0710275e+01 1.10e-02 6.00e+02  -2.5 7.97e-02   1.6 1.83e-01 5.31e-01f  1\n",
      " 386r 1.0717524e+01 1.05e-02 5.70e+02  -2.5 5.31e+00    -  2.34e-01 4.82e-02f  1\n",
      " 387r 1.0741821e+01 9.40e-03 5.38e+02  -2.5 3.92e+00    -  1.69e-01 1.24e-01f  1\n",
      " 388r 1.0749891e+01 7.26e-03 9.07e+01  -2.5 1.63e-02   2.0 3.39e-01 1.00e+00h  1\n",
      " 389r 1.0762272e+01 7.20e-03 2.72e+01  -2.5 2.46e-02   1.5 9.08e-01 8.42e-01f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 390r 1.0808121e+01 1.35e-02 4.58e+02  -2.5 2.22e-01   1.1 8.69e-02 2.77e-01f  1\n",
      " 391r 1.0829679e+01 6.94e-03 4.30e+02  -2.5 6.31e-02   1.5 2.90e-01 4.51e-01f  1\n",
      " 392r 1.0835808e+01 2.92e-03 3.25e+01  -2.5 1.58e-02   1.9 8.80e-01 1.00e+00h  1\n",
      " 393r 1.0864529e+01 1.17e-02 2.76e+02  -2.5 1.51e-01   1.4 1.02e-01 3.55e-01f  1\n",
      " 394r 1.0888728e+01 9.29e-03 3.97e+02  -2.5 1.90e-01   1.0 2.39e-01 2.29e-01f  1\n",
      " 395r 1.0907042e+01 7.20e-03 3.70e+02  -2.5 3.19e-01   0.5 5.99e-01 2.11e-01f  1\n",
      " 396r 1.0918716e+01 6.35e-04 6.09e+01  -2.5 1.81e-02   1.8 9.20e-01 1.00e+00f  1\n",
      " 397  1.0918752e+01 2.11e-02 9.40e+01  -1.0 4.73e+04    -  3.90e-01 3.05e-05f 16\n",
      " 398  1.1262273e+01 1.34e-01 3.26e+04  -1.0 1.02e+00  -0.0 7.25e-02 5.98e-01f  1\n",
      " 399  1.1156294e+01 2.48e-02 3.29e+03  -1.0 3.94e-01   1.3 6.62e-01 1.00e+00f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 400  1.1132352e+01 1.55e-02 3.32e+03  -1.0 2.94e-01   3.5 2.49e-01 3.14e-01h  1\n",
      " 401  1.1126533e+01 1.23e-02 2.83e+03  -1.0 1.75e-01   3.1 1.27e-01 1.38e-01f  1\n",
      " 402  1.1122740e+01 1.02e-02 2.43e+03  -1.0 8.75e-02   3.5 6.05e-01 1.38e-01h  1\n",
      " 403  1.1109434e+01 3.52e-03 8.30e+03  -1.0 1.52e-01   3.0 3.33e-01 6.54e-01f  1\n",
      " 404  1.1128142e+01 1.94e-03 2.42e+04  -1.0 3.90e-01   2.5 3.12e-01 7.42e-01f  1\n",
      " 405  1.1127440e+01 1.97e-05 8.76e+02  -1.0 2.42e-01   2.1 9.85e-01 1.00e+00f  1\n",
      " 406  1.1129419e+01 2.49e-04 1.73e+02  -1.0 1.51e-01   1.6 1.00e+00 1.00e+00f  1\n",
      " 407  1.1133803e+01 5.19e-04 8.12e+01  -1.0 4.61e-02   1.1 1.00e+00 1.00e+00f  1\n",
      " 408  1.1130643e+01 1.40e-03 1.24e+02  -1.0 7.30e-02   0.6 1.00e+00 1.00e+00f  1\n",
      " 409  1.1112918e+01 1.02e-02 1.91e+02  -1.0 4.29e-01   0.2 1.00e+00 1.00e+00f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 410  1.1095807e+01 2.50e-04 1.91e+01  -1.0 7.88e-02   0.6 1.00e+00 1.00e+00f  1\n",
      " 411  1.1056899e+01 4.82e-03 1.12e+02  -1.0 2.66e-01   0.1 1.00e+00 1.00e+00f  1\n",
      " 412  1.0921333e+01 2.11e-03 2.71e+01  -1.0 2.83e-01  -0.4 1.00e+00 1.00e+00f  1\n",
      " 413  1.0888774e+01 3.69e-04 8.22e+00  -1.0 1.43e-01   0.1 1.00e+00 1.00e+00f  1\n",
      " 414  1.0778614e+01 1.77e-03 2.66e-01  -1.0 2.83e-01  -0.4 1.00e+00 1.00e+00f  1\n",
      " 415  1.0730192e+01 1.21e-04 4.28e+00  -1.7 8.58e-02  -0.9 1.00e+00 1.00e+00h  1\n",
      " 416  1.0565515e+01 9.54e-04 7.74e-01  -1.7 2.40e-01  -1.4 1.00e+00 1.00e+00f  1\n",
      " 417  1.0535755e+01 1.65e-04 7.70e-01  -1.7 1.01e-01  -0.9 1.00e+00 1.00e+00h  1\n",
      " 418  1.0459464e+01 9.84e-04 7.37e-02  -1.7 1.66e-01  -1.4 1.00e+00 1.00e+00f  1\n",
      " 419  1.0460344e+01 2.20e-05 1.22e+00  -2.5 2.37e-02  -1.0 1.00e+00 1.00e+00h  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 420  1.0425323e+01 3.07e-04 1.01e-01  -2.5 3.99e-02  -1.5 1.00e+00 1.00e+00h  1\n",
      " 421  1.0362217e+01 1.07e-03 7.91e-02  -2.5 1.09e-01  -2.0 1.00e+00 1.00e+00h  1\n",
      " 422  1.0202807e+01 8.53e-01 4.47e+00  -2.5 2.21e+01    -  2.46e-01 3.57e-01f  1\n",
      " 423  1.0160267e+01 4.00e-02 1.97e+00  -2.5 1.53e+00  -2.4 8.11e-01 1.00e+00h  1\n",
      " 424  1.0287031e+01 3.08e-02 5.29e+00  -2.5 1.11e+00  -1.1 9.14e-01 3.88e-01H  1\n",
      " 425  1.0336790e+01 1.18e-02 4.43e+00  -2.5 1.77e-01  -0.7 1.00e+00 1.00e+00f  1\n",
      " 426  1.0330552e+01 4.71e-04 1.27e+00  -2.5 1.21e-01  -1.2 1.00e+00 1.00e+00h  1\n",
      " 427  1.0300392e+01 1.83e-03 1.28e-01  -2.5 3.43e-01  -1.6 1.00e+00 1.00e+00h  1\n",
      " 428  1.0304005e+01 7.87e-04 2.05e-02  -2.5 2.30e-01  -2.1 1.00e+00 1.00e+00h  1\n",
      " 429  1.0211667e+01 3.37e-02 2.18e+01  -3.8 1.73e+00  -2.6 6.50e-01 8.68e-01h  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 430  1.0004776e+01 3.52e-02 2.78e+00  -3.8 1.72e+00  -2.2 1.15e-01 7.87e-01h  1\n",
      " 431  1.0034449e+01 2.44e-02 1.93e+00  -3.8 2.10e-01  -0.8 7.22e-02 3.06e-01h  1\n",
      " 432  1.0084509e+01 2.12e-03 1.37e+00  -3.8 3.42e-01  -1.3 4.86e-01 1.00e+00h  1\n",
      " 433  1.0056880e+01 2.94e-03 5.06e-01  -3.8 5.07e-01  -1.8 5.57e-01 1.00e+00h  1\n",
      " 434  1.0052401e+01 6.20e-04 1.41e-01  -3.8 6.84e-02  -1.4 1.00e+00 1.00e+00h  1\n",
      " 435  1.0041897e+01 4.70e-04 4.51e-03  -3.8 1.58e-01  -1.8 1.00e+00 1.00e+00h  1\n",
      " 436  1.0022858e+01 7.21e-03 8.02e-02  -3.8 4.45e-01  -2.3 1.00e+00 1.00e+00h  1\n",
      " 437  1.0005329e+01 3.05e-01 8.31e-02  -3.8 1.24e+01    -  1.00e+00 3.81e-01h  1\n",
      " 438  1.0007092e+01 9.03e-04 4.59e-02  -3.8 6.51e-01  -2.8 1.00e+00 1.00e+00h  1\n",
      " 439  9.9771845e+00 4.90e-02 1.82e-01  -3.8 5.75e+00    -  2.76e-02 3.58e-01h  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 440  9.9408126e+00 2.80e-02 8.22e-02  -3.8 1.68e+00  -2.4 1.60e-01 4.32e-01h  1\n",
      " 441  9.8814716e+00 6.58e-01 2.26e+00  -3.8 7.44e+00    -  4.78e-01 1.00e+00f  1\n",
      " 442  9.8648621e+00 1.59e-01 7.43e-01  -3.8 1.63e+00  -2.8 3.06e-01 7.99e-01h  1\n",
      " 443  9.8820104e+00 9.87e-02 4.90e-01  -3.8 4.22e-01  -2.4 3.08e-01 3.80e-01h  1\n",
      " 444  9.8977882e+00 2.47e-03 1.80e-02  -3.8 2.92e-01  -2.0 1.00e+00 1.00e+00h  1\n",
      " 445  9.8865772e+00 8.00e-03 1.98e-02  -3.8 1.17e+00  -2.5 3.65e-01 2.40e-01h  2\n",
      " 446  9.9048615e+00 2.77e-01 2.17e+00  -3.8 8.30e+00    -  1.00e+00 1.00e+00h  1\n",
      " 447  9.9027742e+00 3.85e-03 1.44e-01  -3.8 4.72e-01  -2.9 1.00e+00 1.00e+00h  1\n",
      " 448  9.9011356e+00 1.27e-03 4.29e-03  -3.8 2.55e-01  -3.4 1.00e+00 1.00e+00h  1\n",
      " 449  9.9004891e+00 6.97e-03 8.03e-03  -3.8 5.98e-01  -3.9 1.00e+00 1.00e+00h  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 450  9.8987425e+00 6.60e-02 7.44e-02  -3.8 1.55e+00  -4.4 1.00e+00 1.00e+00h  1\n",
      " 451  9.8981513e+00 3.51e-02 8.70e-02  -3.8 3.13e-01  -3.9 1.00e+00 1.00e+00h  1\n",
      " 452  9.8974279e+00 3.60e-02 8.07e-02  -3.8 1.48e+01  -4.4 6.89e-02 7.89e-03h  2\n",
      " 453  9.8972484e+00 1.91e-01 5.14e-02  -3.8 3.24e+00  -4.9 1.00e+00 1.00e+00h  1\n",
      " 454  9.8997640e+00 4.89e-03 5.07e-02  -3.8 7.69e-01  -4.5 1.00e+00 1.00e+00h  1\n",
      " 455  9.8996944e+00 5.05e-02 1.44e-03  -3.8 1.75e+00  -5.0 1.00e+00 1.00e+00h  1\n",
      " 456  9.9003159e+00 1.65e-03 9.02e-04  -3.8 4.13e-01  -4.5 1.00e+00 1.00e+00h  1\n",
      " 457  9.9006999e+00 3.19e-02 1.15e-04  -3.8 1.47e+00  -5.0 1.00e+00 1.00e+00h  1\n",
      " 458  9.9018870e+00 2.11e-01 5.11e-03  -3.8 4.04e+00  -5.5 1.00e+00 1.00e+00h  1\n",
      " 459  9.9052247e+00 6.09e-01 3.03e-03  -3.8 6.73e+00  -6.0 1.00e+00 1.00e+00h  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 460  9.9131343e+00 1.41e+00 2.22e-03  -3.8 1.03e+01  -6.4 1.00e+00 1.00e+00h  1\n",
      " 461  9.9287962e+00 3.28e+00 1.28e-03  -3.8 1.77e+01  -6.9 1.00e+00 1.00e+00h  1\n",
      " 462  9.9840638e+00 2.18e+01 6.72e-03  -3.8 5.54e+01    -  9.23e-01 1.00e+00h  1\n",
      " 463  1.0176222e+01 4.93e+01 1.46e-02  -3.8 1.96e+02    -  1.00e+00 1.00e+00h  1\n",
      " 464  1.0246355e+01 1.86e+00 9.53e-04  -3.8 7.02e+01    -  1.00e+00 1.00e+00h  1\n",
      " 465  1.0246498e+01 1.03e-01 5.56e-05  -3.8 2.69e+00    -  1.00e+00 1.00e+00h  1\n",
      " 466  1.0246503e+01 1.92e-03 4.65e-07  -3.8 3.57e-01    -  1.00e+00 1.00e+00h  1\n",
      " 467  1.0246503e+01 8.44e-09 1.50e-09  -3.8 3.95e-03    -  1.00e+00 1.00e+00h  1\n",
      " 468  1.0014456e+01 1.81e+01 2.69e-01  -5.7 3.71e+02    -  5.04e-01 5.64e-01f  1\n",
      " 469  9.9933208e+00 1.27e+01 5.39e+00  -5.7 9.09e+00  -2.0 2.77e-01 3.04e-01h  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 470  9.9806221e+00 3.82e+00 4.04e+01  -5.7 6.67e+00  -1.5 4.08e-01 7.24e-01h  1\n",
      " 471  9.9670004e+00 3.17e+00 3.30e+01  -5.7 1.70e+00  -2.0 1.35e-01 1.72e-01h  1\n",
      " 472  9.9549391e+00 2.99e-01 3.76e+00  -5.7 1.75e+00  -1.6 7.75e-01 9.17e-01h  1\n",
      " 473  9.9473176e+00 4.24e-04 4.76e-01  -5.7 1.88e-01  -2.1 3.21e-01 1.00e+00h  1\n",
      " 474  9.9452834e+00 7.32e-05 1.56e-02  -5.7 1.00e-01  -1.6 8.78e-01 1.00e+00h  1\n",
      " 475  9.9400294e+00 5.25e-04 1.77e-02  -5.7 4.72e-01  -2.1 1.87e-01 4.20e-01h  1\n",
      " 476  9.9360946e+00 3.94e-04 9.71e-03  -5.7 1.37e-01  -1.7 1.00e+00 6.04e-01f  1\n",
      " 477  9.9305066e+00 1.17e-03 1.64e-02  -5.7 5.21e-01  -2.2 6.42e-01 2.31e-01f  1\n",
      " 478  9.9250569e+00 2.21e-03 2.28e-02  -5.7 3.10e+00  -2.7 6.88e-01 2.47e-02f  1\n",
      " 479  9.8962999e+00 1.65e-02 2.37e-01  -5.7 2.28e+00  -3.1 2.76e-01 1.24e-01h  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 480  9.8934370e+00 6.49e-03 1.04e+00  -5.7 2.49e-01  -3.6 7.61e-01 9.22e-01h  1\n",
      " 481  9.8904954e+00 5.58e-03 9.10e-01  -5.7 1.73e+00  -2.3 2.70e-01 1.41e-01f  1\n",
      " 482  9.8837401e+00 5.56e-03 8.99e-01  -5.7 2.27e+01  -2.8 1.19e-02 1.53e-02f  1\n",
      " 483  9.8796277e+00 9.25e-04 3.18e-02  -5.7 3.51e-01  -3.2 1.38e-01 1.00e+00f  1\n",
      " 484  9.8764396e+00 3.28e-04 1.46e-02  -5.7 2.84e-01  -1.9 1.00e+00 8.10e-01h  1\n",
      " 485  9.8721607e+00 6.84e-04 1.90e-02  -5.7 2.18e+00  -2.4 1.06e-01 4.98e-02f  1\n",
      " 486  9.8672955e+00 7.82e-04 1.34e-02  -5.7 2.57e-01  -2.0 1.00e+00 4.43e-01f  1\n",
      " 487  9.8564154e+00 2.99e-03 1.72e-02  -5.7 6.01e-01  -2.4 6.68e-01 3.17e-01f  1\n",
      " 488  9.8481842e+00 3.31e-03 1.72e-02  -5.7 4.09e-01  -2.9 1.00e+00 2.33e-01f  1\n",
      " 489  9.8345768e+00 7.52e-03 1.63e-01  -5.7 4.05e-01  -3.4 7.07e-01 4.11e-01f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 490  9.8370448e+00 5.37e-04 5.49e-02  -5.7 3.49e-01  -2.1 9.81e-01 1.00e+00h  1\n",
      " 491  9.8317594e+00 9.09e-04 2.50e-02  -5.7 3.45e-01  -2.5 5.05e-01 9.25e-01h  1\n",
      " 492  9.6704015e+00 3.62e+01 7.27e-02  -5.7 4.52e+03    -  6.46e-02 3.54e-02f  1\n",
      " 493  9.6760711e+00 2.47e+01 5.79e-02  -5.7 5.53e+01    -  1.78e-01 3.22e-01h  1\n",
      " 494  9.6749090e+00 1.90e+01 1.22e+01  -5.7 1.56e+01  -2.1 1.84e-01 2.42e-01h  1\n",
      " 495  9.6749942e+00 1.70e+01 1.58e+01  -5.7 1.41e+01  -1.7 1.00e+00 1.10e-01h  1\n",
      " 496  9.6746585e+00 3.20e+00 5.12e+01  -5.7 1.40e+01  -2.2 1.00e+00 1.00e+00h  1\n",
      " 497  9.6747754e+00 4.72e-01 1.54e+01  -5.7 6.05e+00  -1.7 1.00e+00 1.00e+00h  1\n",
      " 498  9.6724166e+00 2.87e-01 8.42e+00  -5.7 1.08e+00  -2.2 2.86e-01 3.95e-01h  1\n",
      " 499  9.6698070e+00 4.86e-03 2.19e+00  -5.7 6.48e-01  -1.8 1.00e+00 1.00e+00f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 500  9.6675394e+00 3.61e-03 1.62e+00  -5.7 3.63e-01  -2.3 9.76e-01 2.57e-01h  1\n",
      " 501  9.6644803e+00 2.74e-03 1.23e+00  -5.7 5.48e-01  -2.7 1.00e+00 2.41e-01f  1\n",
      " 502  9.6591704e+00 2.71e-03 1.14e+00  -5.7 6.58e+01    -  1.91e-02 8.91e-03h  1\n",
      " 503  9.6571204e+00 2.50e-03 1.03e+00  -5.7 1.14e+01    -  9.15e-02 7.86e-02h  1\n",
      " 504  9.6558448e+00 2.29e-03 9.30e-01  -5.7 1.33e+01    -  5.28e-02 8.53e-02f  1\n",
      " 505  9.6556078e+00 2.23e-03 9.03e-01  -5.7 6.00e+00    -  1.10e-01 2.89e-02f  1\n",
      " 506  9.6546144e+00 2.06e-03 8.20e-01  -5.7 2.21e+01    -  1.00e+00 7.53e-02f  1\n",
      " 507  9.6532373e+00 4.84e-03 3.86e-01  -5.7 2.32e+00    -  9.24e-02 5.54e-01h  1\n",
      " 508  9.6530543e+00 4.67e-03 3.68e-01  -5.7 1.10e+01    -  7.71e-01 4.65e-02h  1\n",
      " 509  9.6526660e+00 4.49e-03 3.16e-01  -5.7 1.51e+01    -  1.00e+00 1.20e-01h  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 510  9.6520367e+00 1.76e-02 1.13e-01  -5.7 1.22e+00    -  9.26e-01 8.31e-01h  1\n",
      " 511  9.6514887e+00 1.42e-02 8.24e-02  -5.7 7.12e+00    -  9.99e-01 2.55e-01h  1\n",
      " 512  9.6494727e+00 1.86e-01 5.80e-02  -5.7 4.29e+00    -  1.00e+00 1.00e+00h  1\n",
      " 513  9.6445890e+00 1.98e+00 1.97e-02  -5.7 1.39e+01    -  8.74e-01 1.00e+00h  1\n",
      " 514  9.6465293e+00 1.37e-01 7.22e-04  -5.7 3.68e+00    -  1.00e+00 1.00e+00h  1\n",
      " 515  9.6466733e+00 3.89e-04 2.17e-06  -5.7 1.98e-01    -  1.00e+00 1.00e+00h  1\n",
      " 516  9.6466737e+00 1.71e-08 1.10e-10  -5.7 1.29e-03    -  1.00e+00 1.00e+00h  1\n",
      " 517  9.6445223e+00 7.01e-03 8.19e-03  -8.6 1.18e+00    -  5.49e-01 5.64e-01f  1\n",
      " 518  9.6430922e+00 3.59e-03 1.49e-03  -8.6 4.83e-01    -  9.14e-01 9.09e-01h  1\n",
      " 519  9.6429497e+00 8.86e-04 2.14e-04  -8.6 2.34e-01    -  1.00e+00 1.00e+00h  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      " 520  9.6429540e+00 2.34e-04 5.31e-05  -8.6 1.21e-01    -  1.00e+00 1.00e+00h  1\n",
      " 521  9.6429559e+00 5.06e-05 7.88e-06  -8.6 5.63e-02    -  1.00e+00 1.00e+00h  1\n",
      " 522  9.6429562e+00 7.32e-06 7.57e-07  -8.6 2.14e-02    -  1.00e+00 1.00e+00h  1\n",
      " 523  9.6429562e+00 3.05e-07 2.62e-08  -8.6 4.35e-03    -  1.00e+00 1.00e+00h  1\n",
      " 524  9.6429562e+00 6.28e-10 5.44e-11  -8.6 1.96e-04    -  1.00e+00 1.00e+00h  1\n",
      "\n",
      "Number of Iterations....: 524\n",
      "\n",
      "                                   (scaled)                 (unscaled)\n",
      "Objective...............:   1.9247417570542660e+00    9.6429562028418729e+00\n",
      "Dual infeasibility......:   5.4393536178247630e-11    2.7251161625302062e-10\n",
      "Constraint violation....:   6.2848823416611702e-10    6.2848823416611702e-10\n",
      "Variable bound violation:   0.0000000000000000e+00    0.0000000000000000e+00\n",
      "Complementarity.........:   2.5059502381599817e-09    1.2554810693181509e-08\n",
      "Overall NLP error.......:   2.5059502381599817e-09    1.2554810693181509e-08\n",
      "\n",
      "\n",
      "Number of objective function evaluations             = 832\n",
      "Number of objective gradient evaluations             = 261\n",
      "Number of equality constraint evaluations            = 906\n",
      "Number of inequality constraint evaluations          = 906\n",
      "Number of equality constraint Jacobian evaluations   = 541\n",
      "Number of inequality constraint Jacobian evaluations = 541\n",
      "Number of Lagrangian Hessian evaluations             = 524\n",
      "Total seconds in IPOPT                               = 17.406\n",
      "\n",
      "EXIT: Optimal Solution Found.\n",
      "\n",
      "  (Local) solution found\n",
      "  objective value = 9.642956202841873\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[33m\u001b[1m┌ \u001b[22m\u001b[39m\u001b[33m\u001b[1mWarning: \u001b[22m\u001b[39mFunction fNC automatically registered with 1 arguments.\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39m\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39mCalling the function with a different number of arguments will result in an\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39merror.\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39m\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39mWhile you can safely ignore this warning, we recommend that you manually\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39mregister the function as follows:\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39m```Julia\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39mmodel = Model()\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39mregister(model, :fNC, 1, fNC; autodiff = true)\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39m```\n",
      "\u001b[33m\u001b[1m└ \u001b[22m\u001b[39m\u001b[90m@ MathOptInterface.Nonlinear ~/.julia/packages/MathOptInterface/fTxO0/src/Nonlinear/operators.jl:370\u001b[39m\n",
      "\u001b[33m\u001b[1m┌ \u001b[22m\u001b[39m\u001b[33m\u001b[1mWarning: \u001b[22m\u001b[39mFunction fC automatically registered with 1 arguments.\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39m\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39mCalling the function with a different number of arguments will result in an\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39merror.\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39m\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39mWhile you can safely ignore this warning, we recommend that you manually\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39mregister the function as follows:\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39m```Julia\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39mmodel = Model()\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39mregister(model, :fC, 1, fC; autodiff = true)\n",
      "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39m```\n",
      "\u001b[33m\u001b[1m└ \u001b[22m\u001b[39m\u001b[90m@ MathOptInterface.Nonlinear ~/.julia/packages/MathOptInterface/fTxO0/src/Nonlinear/operators.jl:370\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "# Resolution\n",
    "x0  = [2.5; 4.0]\n",
    "ε   = 1e-3\n",
    "sol = HO(x0, ε, nsteps=500);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "b5dcbb28",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "xu = 0.006495466762635464\n",
      "xv = 0.22691120196356795\n"
     ]
    },
    {
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     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Plots\n",
    "t  = sol.t\n",
    "x1 = sol.x1\n",
    "x2 = sol.x2\n",
    "λ  = sol.λ\n",
    "u  = sol.u\n",
    "v  = sol.v\n",
    "xu = sol.xu\n",
    "xv = sol.xv\n",
    "p1 = sol.p1\n",
    "p2 = sol.p2\n",
    "p3 = sol.p3\n",
    "\n",
    "println(\"xu = \", xu[end])\n",
    "println(\"xv = \", xv[end])\n",
    "\n",
    "# Compute the differences between adjacent elements\n",
    "d = diff(u)\n",
    "\n",
    "switchings = findall(abs.(x2) .< 0.032)\n",
    "tc1   = t[switchings[1]]\n",
    "tc2   = t[switchings[2]]\n",
    "tc3   = t[switchings[3]]\n",
    "tstar = t[findall(abs.(d) .> 1.5)[]]\n",
    "\n",
    "T  = t[end];\n",
    "\n",
    "\n",
    "\n",
    "x1_plot   = plot(t,  x1, xlabel = \"t\", ylabel = \"x1\",   legend=false,  linecolor=:blue , linewidth=2)\n",
    "x2_plot   = plot(t,  x2, xlabel = \"t\", ylabel = \"x2\",    legend=false,  linecolor=:blue , linewidth=2)\n",
    "xticks!(x2_plot, [tc1,2.,tc2,tc3,8.], [L\"$\\tau_1$\",\"2\",L\"$\\tau_2$\",L\"$\\tau_3$\", \"8\"])\n",
    "vline!(x2_plot, [tc1], linestyle=:dash, linecolor=RGBA(0.5, 0.5, 0.5, 0.5), label=nothing)\n",
    "vline!(x2_plot, [tc2], linestyle=:dash, linecolor=RGBA(0.5, 0.5, 0.5, 0.5), label=nothing)\n",
    "vline!(x2_plot, [tc3], linestyle=:dash, linecolor=RGBA(0.5, 0.5, 0.5, 0.5), label=nothing)\n",
    "hline!([(0., 0), (31., 0)], linecolor=:black, linewidth=2, label=false)\n",
    "\n",
    "\n",
    "u1 = copy(u) ;\n",
    "\n",
    "u1[tc1  .<= t .<= tc2] .= λ[(switchings[1] + switchings[2]) ÷ 2]\n",
    "u1[tc3 .<= t .<=   T] .= λ[(switchings[4] + length(t)) ÷ 2]\n",
    "\n",
    "control_plot = plot(t, u1,  xlabel = \"t\", label=L\"optimal control $u$\",linecolor=:red ,linewidth=2,legend=:bottomleft) \n",
    "plot!(t, λ, xlabel = \"t\", ylabel = \"(λ,u)\",  label =L\"state $\\lambda$\", linecolor=:brown,linewidth=2)\n",
    "xticks!(control_plot, [tc1,2.,tc2,tstar,tc3,8.], [L\"$\\tau_1$\",\"2\",L\"$\\tau_2$\",L\"$\\sigma$\",L\"$\\tau_3$\", \"8\"])\n",
    "vline!(control_plot, [tc1], linestyle=:dash, linecolor=RGBA(0.5, 0.5, 0.5, 0.5), label=nothing)\n",
    "vline!(control_plot, [tc2], linestyle=:dash, linecolor=RGBA(0.5, 0.5, 0.5, 0.5), label=nothing)\n",
    "vline!(control_plot, [tc3], linestyle=:dash, linecolor=RGBA(0.5, 0.5, 0.5, 0.5), label=nothing)\n",
    "vline!(control_plot, [tstar], linestyle=:dash, linecolor=RGBA(0.5, 0.5, 0.5, 0.5), label=nothing)\n",
    "\n",
    "\n",
    "x1x2_plot = plot(x1, x2, xlabel = \"x1\", ylabel = \"x2\",  legend=false,  linecolor=:blue , linewidth=2)\n",
    "plot!(x1x2_plot, [-3, 5], [-4.0, -4.0], fillrange = 0.0, fillalpha = 0.2, fillcolor = :red, label=false)\n",
    "plot!(x1x2_plot, [-3, 5], [4.3, 4.3], fillrange = 0.0, fillalpha = 0.2, fillcolor = :green, label=false)\n",
    "plot!(x1x2_plot, [-3, 5], [0., 0.], linecolor=:black, linewidth=2, label=false)\n",
    "\n",
    "λ_plot = plot(t, λ, xlabel = \"x1\", ylabel = \"λ\",  legend = false)\n",
    "\n",
    "p1_plot   = plot(t, p1, xlabel = \"t\", ylabel = \"p1\",  legend=false, linecolor=:orange , linewidth=2)\n",
    "p2_plot   = plot(t, p2, xlabel = \"t\", ylabel = \"p2\",  legend=false, linecolor=:orange , linewidth=2)\n",
    "xticks!(p2_plot, [tc1,2,tc2,tstar,tc3,8], [L\"$\\tau_1$\",\"2\",L\"$\\tau_2$\",L\"$\\sigma$\",L\"$\\tau_3$\",\"8\"])\n",
    "vline!(p2_plot, [tc1], linestyle=:dash, linecolor=RGBA(0.5, 0.5, 0.5, 0.5), label=nothing)\n",
    "vline!(p2_plot, [tc2], linestyle=:dash, linecolor=RGBA(0.5, 0.5, 0.5, 0.5), label=nothing)\n",
    "vline!(p2_plot, [tc3], linestyle=:dash, linecolor=RGBA(0.5, 0.5, 0.5, 0.5), label=nothing)\n",
    "vline!(p2_plot, [tstar], linestyle=:dash, linecolor=RGBA(0.5, 0.5, 0.5, 0.5), label=nothing)\n",
    "\n",
    "\n",
    "\n",
    "plot(x1x2_plot, x1_plot,x2_plot, control_plot , p1_plot,p2_plot, layout = (2,3), size=(900, 500), left_margin=5mm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "92731a9c",
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v_plot   = plot(t,  v, xlabel = \"t\", ylabel = \"v\",  legend =false,linecolor=:purple, linewidth=2)\n",
    "xticks!(v_plot, [tc1,2.,tc2,tstar,tc3,8.], [L\"$\\tau_1$\",\"2\",L\"$\\tau_2$\",L\"$\\sigma$\",L\"$\\tau_3$\", \"8\"])\n",
    "vline!(v_plot, [tc1], linestyle=:dash, linecolor=:black, label=nothing)\n",
    "vline!(v_plot, [tc2], linestyle=:dash, linecolor=:black, label=nothing)\n",
    "vline!(v_plot, [tc3], linestyle=:dash, linecolor=:black, label=nothing)\n",
    "vline!(v_plot, [tstar], linestyle=:dash, linecolor=:black, label=nothing)\n",
    "\n",
    "p3_plot   = plot(t, p3, xlabel = \"t\", ylabel = \"pλ\",  legend=false, linecolor=:orange , linewidth=2)\n",
    "xticks!(p3_plot, [tc1,2.,tc2,tstar,tc3,8.], [L\"$\\tau_1$\",\"2\",L\"$\\tau_2$\",L\"$\\sigma$\",L\"$\\tau_3$\", \"8\"])\n",
    "vline!(p3_plot, [tc1], linestyle=:dash, linecolor=:black, label=nothing)\n",
    "vline!(p3_plot, [tc2], linestyle=:dash, linecolor=:black, label=nothing)\n",
    "vline!(p3_plot, [tc3], linestyle=:dash, linecolor=:black, label=nothing)\n",
    "vline!(p3_plot, [tstar], linestyle=:dash, linecolor=:black, label=nothing)\n",
    "\n",
    "plot(v_plot,p3_plot ,p1_plot,p2_plot, layout = (2,2), size=(900, 500), left_margin=10mm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "6bcb9aa6",
   "metadata": {},
   "outputs": [
    {
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1225.17,776.955 1229.21,789.494 1233.25,801.657 1237.29,813.425 1241.34,824.781 1245.38,835.707 1249.42,846.185 1253.46,856.2 1257.5,865.736 1261.54,874.777 1265.58,883.311 1269.63,891.324 1273.67,898.803 1277.71,905.736 1281.75,912.114 1285.79,917.927 1289.83,923.164 1293.88,927.819 1297.92,931.884 1301.96,936.707 1306,935.096 1310.04,932.979 1314.08,930.367 1318.12,927.266 1322.17,923.686 1326.21,919.637 1330.25,915.13 1334.29,910.176 1338.33,904.786 1342.37,898.973 1346.42,892.75 1350.46,886.13 1354.5,879.128 1358.54,871.757 1362.58,864.033 1366.62,855.971 1370.66,847.587 1374.71,838.897 1378.75,829.917 1382.79,820.665 1386.83,811.157 1390.87,801.412 1394.91,791.446 1398.96,781.279 1403,770.927 1407.04,760.411 1411.08,749.747 1415.12,738.956 1419.16,728.055 1423.2,717.064 1427.25,706.001 1431.29,694.886 1435.33,683.737 1439.37,672.573 1443.41,661.413 1447.45,650.276 1451.5,639.18 1455.54,628.143 1459.58,617.184 1463.62,606.321 1467.66,595.571 1471.7,584.952 1475.74,574.481 1479.79,564.174 1483.83,554.05 1487.87,544.122 1491.91,534.408 1495.95,524.923 1499.99,515.681 1504.03,506.696 1508.08,497.984 1512.12,489.556 1516.16,481.427 1520.2,473.608 1524.24,466.111 1528.28,458.947 1532.33,452.128 1536.37,445.662 1540.41,439.56 1544.45,433.829 1548.49,428.479 1552.53,423.516 1556.57,418.947 1560.62,414.778 1564.66,411.015 1568.7,407.662 1572.74,404.723 1576.78,402.202 1580.82,400.1 1584.87,398.42 1588.91,397.162 1592.95,396.327 1596.99,395.915 1601.03,395.924 1605.07,396.353 1609.11,397.199 1613.16,398.459 1617.2,400.128 1621.24,402.203 1625.28,404.677 1629.32,407.545 1633.36,473.607 1637.41,735.37 1641.45,812.616 1645.49,847.26 1649.53,866.038 1653.57,883.103 1657.61,900.017 1661.65,916.842 1665.7,933.565 1669.74,950.17 1673.78,966.642 1677.82,982.966 1681.86,999.127 1685.9,1015.11 1689.95,1030.9 1693.99,1046.49 1698.03,1061.85 1702.07,1076.99 1706.11,1091.87 1710.15,1106.5 1714.19,1120.85 1718.24,1134.92 1722.28,1148.69 1726.32,1162.16 1730.36,1175.3 1734.4,1188.12 1738.44,1200.59 1742.49,1212.71 1746.53,1224.47 1750.57,1235.87 1754.61,1246.88 1758.65,1257.51 1762.69,1267.74 1766.73,1277.58 1770.78,1287 1774.82,1296.01 1778.86,1304.6 1782.9,1312.77 1786.94,1320.51 1790.98,1327.81 1795.03,1334.67 1799.07,1341.1 1803.11,1347.08 1807.15,1352.61 1811.19,1357.7 1815.23,1362.34 1819.27,1366.53 1823.32,1370.27 1827.36,1373.57 1831.4,1376.41 1835.44,1378.82 1839.48,1380.77 1843.52,1382.29 1847.56,1383.37 1851.61,1384.02 1855.65,1384.24 1859.69,1384.03 1863.73,1383.4 1867.77,1382.36 1871.81,1380.91 1875.86,1379.06 1879.9,1376.81 1883.94,1374.17 1887.98,1371.15 1892.02,1367.76 1896.06,1364.01 1900.1,1359.9 1904.15,1355.45 1908.19,1350.66 1912.23,1345.54 1916.27,1340.1 1920.31,1334.36 1924.35,1328.33 1928.4,1322.01 1932.44,1315.42 1936.48,1308.56 1940.52,1301.46 1944.56,1294.12 1948.6,1286.55 1952.64,1278.76 1956.69,1270.78 1960.73,1262.61 1964.77,1254.25 1968.81,1245.74 1972.85,1237.07 1976.89,1228.27 1980.94,1219.34 1984.98,1210.29 1989.02,1201.14 1993.06,1191.91 1997.1,1182.6 2001.14,1173.23 2005.18,1163.8 2009.23,1154.34 2013.27,1144.85 2017.31,1135.35 2021.35,1125.85 2025.39,1116.35 2029.43,1106.88 2033.48,1097.44 2037.52,1088.04 2041.56,1078.7 2045.6,1069.43 2049.64,1060.23 2053.68,1051.11 2057.72,1042.09 2061.77,1033.18 2065.81,1024.38 2069.85,1015.7 2073.89,1007.16 2077.93,998.754 2081.97,990.496 2086.02,982.393 2090.06,974.452 2094.1,966.68 2098.14,959.082 2102.18,951.665 2106.22,944.433 2110.26,937.392 2114.31,930.547 2118.35,923.901 2122.39,917.458 2126.43,911.222 2130.47,905.194 2134.51,899.378 2138.55,893.775 2142.6,888.387 2146.64,883.215 2150.68,878.26 2154.72,873.52 2158.76,868.997 2162.8,864.69 2166.85,860.597 2170.89,856.716 2174.93,853.046 2178.97,849.585 2183.01,846.328 2187.05,843.274 2191.09,840.419 2195.14,837.758 2199.18,835.287 2203.22,833.001 2207.26,830.895 2211.3,828.965 2215.34,827.203 2219.39,825.604 2223.43,824.161 2227.47,822.867 2231.51,821.717 2235.55,820.701 2239.59,819.813 2243.63,819.046 2247.68,818.39 2251.72,817.838 2255.76,817.38 2259.8,817.01 2263.84,816.718 2267.88,816.494 2271.93,816.322 2275.97,816.01 2280.01,813.121 2284.05,790.663 2288.09,690.398 2292.13,286.055 \"/>\n",
       "</svg>\n"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function H(k)\n",
    "    return p1[k] * x1[k] + p2[k] * (fC(x2[k]) * (u[k] - x1[k]) + fC(x2[k]) * (λ[k] - x1[k])) + fC(x2[k]) * p3[k] * v[k] - ε * (v[k])^2 - fNC(x2[k]) * (u[k])^2\n",
    "end\n",
    "H_direct  = [H(k) for k in 1:length(x1)]\n",
    "ph_plot   = plot(t, H_direct, xlabel = \"t\", ylabel = \"H_direct\",  legend=false, linecolor=:green , linewidth=2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "97e20760",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8024686050013359"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jumpp1 = p2[switchings[1]+3] - p2[switchings[1]-2]  \n",
    "jumpp2 = p2[switchings[3]+3] - p2[switchings[3]-2]  \n",
    "lambda = λ[(switchings[3] + length(t)) ÷ 2] "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "5ed0b3da",
   "metadata": {},
   "source": [
    "# Indirect method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "3619f676",
   "metadata": {},
   "outputs": [],
   "source": [
    "using NLsolve\n",
    "using Plots\n",
    "using Plots.PlotMeasures\n",
    "include(\"flow.jl\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "76198fed",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Dynamics\n",
    "function F0(x)\n",
    "    return [ x[2], -x[1]]\n",
    "end\n",
    "\n",
    "function F1(x)\n",
    "    return [ 0.0 ,   1.0]\n",
    "end\n",
    "\n",
    "\n",
    "H0(x, p) = p' * F0(x) \n",
    "H1(x, p) = p' * F1(x)\n",
    "\n",
    "# Hamiltonians: \n",
    "H(x, p, u)  =  H0(x, p) + u*H1(x,p)                             # pseudo-Hamiltonian\n",
    "\n",
    "up(x, p) =   1.0\n",
    "um(x, p) = - 1.0\n",
    "\n",
    "Hp(x, p) = H(x, p, up(x, p))\n",
    "Hm(x, p) = H(x, p, um(x, p))\n",
    "\n",
    "\n",
    "# Hamiltonians: control loss region 2\n",
    "H2(x, b, y, p)  = H0(x, p) + b*H1(x, p) - y*p[2]                # pseudo-Hamiltonian\n",
    "Hcl(X, P)       = H2(X[1:2], X[3], X[4], P[1:2])                # control loss 2\n",
    "\n",
    "\n",
    "\n",
    "# Flows\n",
    "fp    = Flow(Hp)\n",
    "fm    = Flow(Hm)\n",
    "fcl   = Flow(Hcl) ;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "c38a0e63",
   "metadata": {},
   "outputs": [],
   "source": [
    "t0 = 0.0\n",
    "x0 = [2.5; 4.0]\n",
    "\n",
    "# Shooting function\n",
    "function SHOOT(p0, tt1, tt2, ttstar, tt3, b1, jump1, jump2, TT) \n",
    "    \n",
    "    pb0    = 0.0 \n",
    "    py0    = 0.0\n",
    "        \n",
    "    x1, p1 = fm(t0 , x0, p0, tt1) \n",
    "    \n",
    "    x2, p2 = fp(tt1, x1, p1 - [0. , jump1], tt2)\n",
    "    \n",
    "    x3, p3 = fp(tt2, x2, p2, ttstar)\n",
    "    \n",
    "    x4, p4 = fm(ttstar, x3, p3, tt3)\n",
    "    \n",
    "    X5, P5 = fcl(tt3, [x4 ; b1 ; 0.0], [p4 - [0. , jump2]; pb0 ; py0], TT)\n",
    "\n",
    "         s = zeros(eltype(p0), 10)\n",
    "    \n",
    "    s[1:2]  = X5[1:2] - [ 0.0 , 0.0 ]                     # target\n",
    "    s[3]    = H1(x3, p3)                                  # switching\n",
    "    s[4]    = x1[2] - 0.0                                 # first crossing \n",
    "    s[5]    = x2[2] - 0.0                                 # second crossing \n",
    "    s[6]    = x4[2] - 0.0                                 # third crossing \n",
    "    s[7]    = jump1 - p1[2]*(1. + 1.)/(1. - x1[1])        # jump1\n",
    "    s[8]    = jump2 - p4[2]*(b1 + 1.)/(b1 - x4[1])        # jump2\n",
    "    s[9]    = Hm(x0, p0) - 1.0                            # free final time\n",
    "    s[10]   = P5[4]                                       # averaged gradient condition \n",
    "\n",
    "    return s\n",
    "\n",
    "end;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "6bd14cf2",
   "metadata": {},
   "outputs": [],
   "source": [
    "S(ξ) = SHOOT(ξ[1:2], ξ[3], ξ[4], ξ[5],ξ[6],ξ[7],ξ[8], ξ[9], ξ[10]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "c5eabe04",
   "metadata": {},
   "outputs": [],
   "source": [
    "ξ_guess = [p1[1] , p2[1], tc1, tc2, tstar , tc3, lambda, jumpp1, jumpp2, t[end]]; # initial guess"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "41bdda45",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10-element Vector{Float64}:\n",
       "  0.03077151457444655\n",
       " -0.029578808768532912\n",
       " -0.0007059557256630849\n",
       "  0.03013812257022675\n",
       "  0.012239628743753717\n",
       "  0.02460023330776464\n",
       " -0.12575451659552692\n",
       " -1.9477889623200044\n",
       "  0.2616388965494423\n",
       "  0.02375747430798071"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S(ξ_guess)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "d3d80ceb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iter     f(x) inf-norm    Step 2-norm \n",
      "------   --------------   --------------\n",
      "     0     1.947789e+00              NaN\n",
      "     1     1.389806e-02     2.047404e+00\n",
      "     2     3.185514e-04     3.551608e-02\n",
      "     3     1.216952e-07     5.246133e-04\n",
      "     4     1.638960e-14     1.019115e-07\n",
      "Results of Nonlinear Solver Algorithm\n",
      " * Algorithm: Trust-region with dogleg and autoscaling\n",
      " * Starting Point: [0.04233787780169271, -0.31208211009790615, 0.8462959846199601, 4.000671927294357, 4.885435911215224, 6.481857882202877, 0.8024686050013359, 0.018161483077097335, -1.1800163398360546, 9.61699982522682]\n",
      " * Zero: [-0.008674974293922914, -0.2956285420501976, 0.8519663271732713, 3.9935589807630616, 4.916716539422613, 6.487512866217511, 0.82190283063157, 0.11350831730750124, 0.8384462105284638, 9.629105519807283]\n",
      " * Inf-norm of residuals: 0.000000\n",
      " * Iterations: 4\n",
      " * Convergence: true\n",
      "   * |x - x'| < 1.0e-08: false\n",
      "   * |f(x)| < 1.0e-08: true\n",
      " * Function Calls (f): 5\n",
      " * Jacobian Calls (df/dx): 5\n"
     ]
    }
   ],
   "source": [
    "# Solve\n",
    "\n",
    "indirect_sol = nlsolve(S, ξ_guess; xtol=1e-8, method=:trust_region, show_trace=true)\n",
    "println(indirect_sol)\n",
    "\n",
    "# Retrieves solution\n",
    "if indirect_sol.f_converged || indirect_sol.x_converged\n",
    "    pp0     = indirect_sol.zero[1:2]\n",
    "    tt1     = indirect_sol.zero[3]\n",
    "    tt2     = indirect_sol.zero[4]\n",
    "    ttstar  = indirect_sol.zero[5]\n",
    "    tt3     = indirect_sol.zero[6]\n",
    "    b11     = indirect_sol.zero[7]\n",
    "    jmp1    = indirect_sol.zero[8]\n",
    "    jmp2    = indirect_sol.zero[9]\n",
    "    T1      = indirect_sol.zero[10]\n",
    "\n",
    "else\n",
    "    error(\"Not converged\")\n",
    "end;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "4846dd5a",
   "metadata": {},
   "outputs": [],
   "source": [
    "t0 = 0.0\n",
    "x0 = [2.5; 4.0]\n",
    "\n",
    "ode_sol = fm((t0, tt1), x0, pp0, saveat=0.1) ;\n",
    "ttt1    = ode_sol.t ;\n",
    "xx1     = [ ode_sol[1:2, j] for j in 1:size(ttt1, 1) ] ;\n",
    "pp1     = [ ode_sol[3:4, j] for j in 1:size(ttt1, 1) ] ;\n",
    "uu1     = um.(xx1, pp1);\n",
    "\n",
    "ode_sol = fp((tt1, tt2), xx1[end], pp1[end] - [0., jmp1], saveat=0.1) ;\n",
    "ttt2    = ode_sol.t ;\n",
    "xx2     = [ ode_sol[1:2, j] for j in 1:size(ttt2, 1) ] ;\n",
    "pp2     = [ ode_sol[3:4, j] for j in 1:size(ttt2, 1) ] ;\n",
    "uu2     = up.(xx2, pp2)  ;\n",
    "\n",
    "ode_sol = fp((tt2, ttstar), xx2[end], pp2[end] , saveat=0.1) ;\n",
    "ttt3    = ode_sol.t ;\n",
    "xx3     = [ ode_sol[1:2, j] for j in 1:size(ttt3, 1) ] ;\n",
    "pp3     = [ ode_sol[3:4, j] for j in 1:size(ttt3, 1) ] ;\n",
    "uu3     = up.(xx3, pp3)  ;\n",
    "\n",
    "\n",
    "ode_sol = fm((ttstar, tt3), xx3[end], pp3[end], saveat=0.1) ;\n",
    "ttt4    = ode_sol.t ;\n",
    "xx4     = [ ode_sol[1:2, j] for j in 1:size(ttt4, 1) ] ;\n",
    "pp4     = [ ode_sol[3:4, j] for j in 1:size(ttt4, 1) ] ;\n",
    "uu4     = um.(xx4, pp4)  ;\n",
    "\n",
    "ode_sol = fcl((tt3, T1), [xx4[end] ; b11 ; 0.0], [pp4[end] - [0., jmp2]; 0. ; 0.], saveat=0.1)\n",
    "ttt5    = ode_sol.t\n",
    "xx5     = [ ode_sol[1:2, j] for j in 1:size(ttt5, 1) ]\n",
    "pp5     = [ ode_sol[5:6, j] for j in 1:size(ttt5, 1) ] \n",
    "uu5     = b11.*ones(length(ttt5)) ;\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "b847516c",
   "metadata": {},
   "outputs": [
    {
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       "</svg>\n"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = [ ttt1 ; ttt2 ; ttt3 ; ttt4 ; ttt5 ]\n",
    "x = [ xx1 ; xx2 ; xx3 ; xx4 ; xx5 ]\n",
    "p = [ pp1 ; pp2 ; pp3 ; pp4 ; pp5 ]\n",
    "u = [ uu1 ; uu2 ; uu3 ; uu4 ; uu5 ]\n",
    "\n",
    "m = length(t)\n",
    "\n",
    "x1 = [ x[i][1] for i=1:m ]\n",
    "x2 = [ x[i][2] for i=1:m ]\n",
    "p1 = [ p[i][1] for i=1:m ]\n",
    "p2 = [ p[i][2] for i=1:m ];\n",
    "\n",
    "x1_plot   = plot(t,  x1, xlabel = \"t\", ylabel = \"x1\" ,legend=false,  linecolor=:blue , linewidth=2)\n",
    "x2_plot   = plot(t,  x2, xlabel = \"t\", ylabel = \"x2\" ,legend=false,  linecolor=:blue , linewidth=2)\n",
    "xticks!(x2_plot, [ttt1[end],2,ttt2[end],ttt4[end],8], [L\"$\\tau_1^*$\",\"2\",L\"$\\tau_2^*$\",L\"$\\tau_3^*$\",\"8\"])\n",
    "vline!(x2_plot, [ttt1[end]], linestyle=:dash, linecolor=RGBA(0.5, 0.5, 0.5, 0.5), label=nothing)\n",
    "vline!(x2_plot, [ttt2[end]], linestyle=:dash, linecolor=RGBA(0.5, 0.5, 0.5, 0.5), label=nothing)\n",
    "vline!(x2_plot, [ttt4[end]], linestyle=:dash, linecolor=RGBA(0.5, 0.5, 0.5, 0.5), label=nothing)\n",
    "hline!([(0., 0), (31., 0)], linecolor=:black, linewidth=2, label=false)\n",
    "\n",
    "p1_plot   = plot(t,  p1,xlabel = \"t\", ylabel = \"p1\", legend=false, linecolor=:orange , linewidth=2)\n",
    "p2_plot   = plot(t,  p2,xlabel = \"t\", ylabel = \"p2\", legend=false,  linecolor=:orange , linewidth=2)\n",
    "xticks!(p2_plot, [ttt1[end],2,ttt2[end],ttt3[end],ttt4[end],8], [L\"$\\tau_1^*$\",\"2\",L\"$\\tau_2^*$\",L\"$\\sigma^*$\",L\"$\\tau_3^*$\",\"8\"])\n",
    "vline!(p2_plot, [ttt1[end]], linestyle=:dash, linecolor=RGBA(0.5, 0.5, 0.5, 0.5), label=nothing)\n",
    "vline!(p2_plot, [ttt2[end]], linestyle=:dash, linecolor=RGBA(0.5, 0.5, 0.5, 0.5), label=nothing)\n",
    "vline!(p2_plot, [ttt4[end]], linestyle=:dash, linecolor=RGBA(0.5, 0.5, 0.5, 0.5), label=nothing)\n",
    "vline!(p2_plot, [ttt3[end]], linestyle=:dash, linecolor=RGBA(0.5, 0.5, 0.5, 0.5), label=nothing)\n",
    "\n",
    "u_plot    = plot(t,   u,xlabel = \"t\", ylabel = \"u\", legend=false,  linecolor=:red , linewidth=2) #, linetype=:steppre)\n",
    "xticks!(u_plot, [ttt1[end],2,ttt2[end],ttt3[end],ttt4[end],8], [L\"$\\tau_1^*$\",\"2\",L\"$\\tau_2^*$\",L\"$\\sigma^*$\",L\"$\\tau_3^*$\",\"8\"])\n",
    "vline!(u_plot, [ttt1[end]], linestyle=:dash, linecolor=RGBA(0.5, 0.5, 0.5, 0.5), label=nothing)\n",
    "vline!(u_plot, [ttt2[end]], linestyle=:dash, linecolor=RGBA(0.5, 0.5, 0.5, 0.5), label=nothing)\n",
    "vline!(u_plot, [ttt3[end]], linestyle=:dash, linecolor=RGBA(0.5, 0.5, 0.5, 0.5), label=nothing)\n",
    "vline!(u_plot, [ttt4[end]], linestyle=:dash, linecolor=RGBA(0.5, 0.5, 0.5, 0.5), label=nothing)\n",
    "\n",
    "x1x2_plot = plot(x1, x2, xlabel = \"x1\", ylabel = \"x2\",legend=false,  linecolor=:blue , linewidth=2)\n",
    "plot!(x1x2_plot, [-3, 5], [-4.0, -4.0], fillrange = 0.0, fillalpha = 0.2, fillcolor = :red, label=false)\n",
    "plot!(x1x2_plot, [-3, 5], [4.3, 4.3], fillrange = 0.0, fillalpha = 0.2, fillcolor = :green, label=false)\n",
    "plot!(x1x2_plot, [-3, 5], [0., 0.], linecolor=:black, linewidth=2, label=false)\n",
    "\n",
    "x=plot( x1x2_plot, x1_plot,x2_plot, u_plot , p1_plot,p2_plot, layout = (2,3), size=(900, 500), left_margin=5mm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "c931f253",
   "metadata": {},
   "outputs": [
    {
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       "</svg>\n"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function HH(k)\n",
    "    return p1[k] * x1[k] + p2[k] *  (u[k] - x1[k]) \n",
    "end\n",
    "H_indirect  = [HH(k) for k in 1:length(x1)]\n",
    "ph_plot   = plot(t, H_indirect, xlabel = \"t\", ylabel = \"H_indirect\",  legend=false, linecolor=:green , linewidth=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "a549db55",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.45601971559771437"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function trapezoidal_integral(p, tt)\n",
    "    integral = 0.0\n",
    "    for i in 1:(length(tt) - 1)\n",
    "        integral += (p[i] + p[i + 1]) * (tt[i + 1] - tt[i]) / 2\n",
    "    end\n",
    "    return integral\n",
    "end\n",
    "p2NC = [v[2] for v in pp2]\n",
    "trapezoidal_integral(p2NC, ttt2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8ac88516",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create an animation\n",
    "animx = @animate for i = 1:length(t)\n",
    "    plot(x1[1:i], x2[1:i], xlim=(-3.,5.), ylim=(-4.,4.3), xlabel=\"x1\", ylabel=\"x2\", label=\"optimal trajectory \\$x\\$\", linecolor=:blue,  linewidth=2)\n",
    "    scatter!([x1[i]], [x2[i]], markersize=4, marker=:circle, color=:black, label=false)\n",
    "    plot!( [-3, 5], [-4.0, -4.0], fillrange = 0.0, fillalpha = 0.2, fillcolor = :red, label=false)\n",
    "    plot!( [-3, 5], [4.3, 4.3], fillrange = 0.0, fillalpha = 0.2, fillcolor = :green, label=false)\n",
    "    plot!( [-3, 5], [0., 0.], linecolor=:black, linewidth=2, label=false)\n",
    "    \n",
    "end\n",
    "\n",
    "# create an animation\n",
    "animu = @animate for i = 1:length(t)\n",
    "    plot(t[1:i], u[1:i], xlim=(0.,t[end]), ylim=(-1.2,1.2), xlabel=\"t\", ylabel=\"u\", label=\"opitmal control \\$u\\$\", linecolor=:red,  linewidth=2)\n",
    "end ;\n",
    "\n",
    "# create an animation\n",
    "animp1 = @animate for i = 1:length(t)\n",
    "    plot(t[1:i], p1[1:i], xlim=(0.,t[end]), ylim=(-1.3, 0.5), xlabel=\"t\", ylabel=\"p1\", label=\"adjoint vector \\$p1\\$\", linecolor=:orange,  linewidth=2)\n",
    "end ;\n",
    "\n",
    "# create an animation\n",
    "animp2 = @animate for i = 1:length(t)\n",
    "    plot(t[1:i], p2[1:i], xlim=(0.,t[end]), ylim=(-1.5,1.3), xlabel=\"t\", ylabel=\"p2\", label=\"adjoint vector \\$p2\\$\", linecolor=:orange,  linewidth=2)\n",
    "end ;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e5f4bc6b",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[36m\u001b[1m[ \u001b[22m\u001b[39m\u001b[36m\u001b[1mInfo: \u001b[22m\u001b[39mSaved animation to /home/anas/Documents/control-loss/harmonic oscillator/ho_x.gif\n"
     ]
    },
    {
     "data": {
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\" />"
      ],
      "text/plain": [
       "Plots.AnimatedGif(\"/home/anas/Documents/control-loss/harmonic oscillator/ho_x.gif\")"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "# display the animation\n",
    "gif(animx, \"ho_x.gif\", fps = 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d654d253",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[36m\u001b[1m[ \u001b[22m\u001b[39m\u001b[36m\u001b[1mInfo: \u001b[22m\u001b[39mSaved animation to /home/anas/Documents/control-loss/harmonic oscillator/ho_u.gif\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<img 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\" />"
      ],
      "text/plain": [
       "Plots.AnimatedGif(\"/home/anas/Documents/control-loss/harmonic oscillator/ho_u.gif\")"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# display the animation\n",
    "gif(animu, \"ho_u.gif\", fps = 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "91757fd5",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[36m\u001b[1m[ \u001b[22m\u001b[39m\u001b[36m\u001b[1mInfo: \u001b[22m\u001b[39mSaved animation to /home/anas/Documents/control-loss/harmonic oscillator/ho_p1.gif\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<img 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\" />"
      ],
      "text/plain": [
       "Plots.AnimatedGif(\"/home/anas/Documents/control-loss/harmonic oscillator/ho_p1.gif\")"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# display the animation\n",
    "gif(animp1, \"ho_p1.gif\", fps = 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c3fc189a",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[36m\u001b[1m[ \u001b[22m\u001b[39m\u001b[36m\u001b[1mInfo: \u001b[22m\u001b[39mSaved animation to /home/anas/Documents/control-loss/harmonic oscillator/ho_p2.gif\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<img 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\" />"
      ],
      "text/plain": [
       "Plots.AnimatedGif(\"/home/anas/Documents/control-loss/harmonic oscillator/ho_p2.gif\")"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# display the animation\n",
    "gif(animp2, \"ho_p2.gif\", fps = 10)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.7.2",
   "language": "julia",
   "name": "julia-1.7"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.7.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}