tutorials/VSP Regularization.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Vertical Sesimic Profiling inversion\n",
    "\n",
    "@Author: Ettore Biondi - ebiondi@caltech.edu"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are going to focus our attention to a common approach when dealing with geophysical inverse problems, regularization and prior information. In this example we will invert synthetic data from a vertical seismic profiling survey. To do so, we will discretize the following equation:\n",
    "\\begin{align}\n",
    "t(z) =  \\int_{0}^{z} \\frac{1}{v(z')}dz',\n",
    "\\end{align}\n",
    "where $t(z)$ is the traveltime from the surface to the depth $z$ and $v(z')$ represents the propagation speed of the medium. To make the problem linear we will parameterize the problem using slowness instead of speed. The discrete version for a regular $z$ sampling of it can be written as follows:\n",
    "\\begin{align}\n",
    "t_i =  \\sum_{j=0}^{N_i} s_j \\Delta z,\n",
    "\\end{align}\n",
    "where $\\Delta z$ represents the sampling interval in the $z$ direction, while $t_i$ and $s_j$ are the traveltime and slowness at $z_i=N_i \\Delta z$ depth, respectively.\n",
    "In this example we will assume that the true subsurface vertical speed is given by the following equation:\n",
    "\\begin{align}\n",
    "v(z)=3000 + \\sqrt{1000 z},\n",
    "\\end{align}\n",
    "expressed in km/s."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING! DATAPATH not found. The folder /tmp will be used to write binary files\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/nas/home/fpicetti/miniconda3/envs/occd/lib/python3.10/site-packages/dask_jobqueue/core.py:20: FutureWarning: tmpfile is deprecated and will be removed in a future release. Please use dask.utils.tmpfile instead.\n",
      "  from distributed.utils import tmpfile\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import occamypy as o\n",
    "\n",
    "o.backend.set_seed_everywhere(42)\n",
    "\n",
    "# Plotting\n",
    "from matplotlib import rcParams\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "import matplotlib.pyplot as plt\n",
    "rcParams.update({\n",
    "    'image.cmap'     : 'gray',\n",
    "    'image.aspect'   : 'auto',\n",
    "    'image.interpolation': None,\n",
    "    'axes.grid'      : True,\n",
    "    'figure.figsize' : (6, 4),\n",
    "    'savefig.dpi'    : 300,\n",
    "    'axes.labelsize' : 14,\n",
    "    'axes.titlesize' : 16,\n",
    "    'font.size'      : 14,\n",
    "    'legend.fontsize': 14,\n",
    "    'xtick.labelsize': 14,\n",
    "    'ytick.labelsize': 14,\n",
    "    'text.usetex'    : True,\n",
    "    'font.family'    : 'serif',\n",
    "    'font.serif'     : 'Latin Modern Roman',\n",
    "})\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Definition of the modeling operator forward and its adjoint\n",
    "class VSP(o.Operator):\n",
    "    \"\"\"\n",
    "    Vertical Sesimic Profiling operator\n",
    "    \"\"\"\n",
    "    \n",
    "    def __init__(self, model, data, dz: float, desampling: int):\n",
    "        \"\"\"\n",
    "        VSP constructor\n",
    "        \n",
    "        Args:\n",
    "            model: domain vector\n",
    "            data: range vector\n",
    "            dz: sampling step for depth\n",
    "            desampling: desampling of data points\n",
    "        \"\"\"\n",
    "        super(VSP, self).__init__(domain=model, range=data)\n",
    "        self.name = \"VSP\"\n",
    "        self.dz = dz\n",
    "        self.desampling = int(desampling)\n",
    "        self.M = model.shape[0]\n",
    "        self.N = data.shape[0]\n",
    "        \n",
    "        if(self.M-2) < (self.N-2)*self.desampling:\n",
    "            raise ValueError(\"ERROR! Too many data points! Change desampling or number of data points\")\n",
    "        return\n",
    "    \n",
    "    def forward(self, add, model, data):\n",
    "        \"\"\"slowness -> traveltime\"\"\"\n",
    "        self.checkDomainRange(model, data)\n",
    "        if not add:\n",
    "            data.zero()\n",
    "        \n",
    "        data[0] += model[0]*dz\n",
    "        \n",
    "        for idata in range(1,self.N-1):\n",
    "            data[idata] += np.sum(model[:(idata)*self.desampling+1])*dz\n",
    "        \n",
    "        data[-1] += np.sum(model[:])*dz\n",
    "        return\n",
    "    \n",
    "    def adjoint(self, add, model, data):\n",
    "        \"\"\"traveltime -> slowness\"\"\"\n",
    "        self.checkDomainRange(model,data)\n",
    "        if not add:\n",
    "            model.zero()\n",
    "        \n",
    "        model[0] += data[0]*dz\n",
    "        \n",
    "        for idata in range(1,self.N-1):\n",
    "            model[:(idata)*self.desampling+1] += data[idata]*dz\n",
    "\n",
    "        model[:] += data[-1]*dz\n",
    "        return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "dz = 2.\n",
    "zmax = 1000.0\n",
    "z = np.linspace(0.0,zmax,int(zmax/dz)+1)\n",
    "vel = 3000.0 + np.sqrt(1000.0*z)\n",
    "slowness = 1.0/vel\n",
    "model_true = o.VectorNumpy(slowness)\n",
    "\n",
    "# Desampling of receivers\n",
    "desampling = 10 #20 m sampling\n",
    "ndata = int(zmax/(dz*desampling))+1\n",
    "data_true = o.VectorNumpy((ndata,))\n",
    "\n",
    "VSP_10 = VSP(model_true, data_true, dz, desampling)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generating observed data\n",
    "VSP_10.forward(False,model_true,data_true)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dot-product tests of forward and adjoint operators\n",
      "--------------------------------------------------\n",
      "Applying forward operator add=False\n",
      " Runs in: 0.0005710124969482422 seconds\n",
      "Applying adjoint operator add=False\n",
      " Runs in: 0.0003707408905029297 seconds\n",
      "Dot products add=False: domain=8.561224e+01 range=8.561224e+01 \n",
      "Absolute error: 8.526513e-14\n",
      "Relative error: 9.959456e-16 \n",
      "\n",
      "Applying forward operator add=True\n",
      " Runs in: 0.0005559921264648438 seconds\n",
      "Applying adjoint operator add=True\n",
      " Runs in: 0.0003418922424316406 seconds\n",
      "Dot products add=True: domain=1.712245e+02 range=1.712245e+02 \n",
      "Absolute error: 2.842171e-14\n",
      "Relative error: 1.659909e-16 \n",
      "\n",
      "-------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "VSP_10.dotTest(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(z[::desampling], data_true.plot(),'*')\n",
    "ax.set_xlabel(\"depth [m]\")\n",
    "ax.set_ylabel(\"time [s]\")\n",
    "ax.set_xlim(0,1000)\n",
    "fig.suptitle(\"Observed traveltime\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create LCG solver\n",
    "LCGsolver = o.CG(o.BasicStopper(niter=2000))\n",
    "LCGsolver.setDefaults(save_obj=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "VSP_prob = o.LeastSquares(model_true.clone().zero(), data_true, VSP_10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "##########################################################################################\n",
      "            CG Solver\n",
      "    Restart folder: /tmp/restart_2022-04-22T01-51-41.263912/\n",
      "##########################################################################################\n",
      "\n",
      "iter = 0000, obj = 6.82008e-01, rnorm = 1.17e+00, gnorm = 2.37e+02, feval = 00002\n",
      "iter = 0001, obj = 5.39592e-03, rnorm = 1.04e-01, gnorm = 6.45e+00, feval = 00004\n",
      "iter = 0002, obj = 6.22682e-04, rnorm = 3.53e-02, gnorm = 1.27e+00, feval = 00006\n",
      "iter = 0003, obj = 1.08804e-04, rnorm = 1.48e-02, gnorm = 3.33e-01, feval = 00008\n",
      "iter = 0004, obj = 2.81691e-05, rnorm = 7.51e-03, gnorm = 1.27e-01, feval = 00010\n",
      "iter = 0005, obj = 9.57360e-06, rnorm = 4.38e-03, gnorm = 5.82e-02, feval = 00012\n",
      "iter = 0006, obj = 3.47089e-06, rnorm = 2.63e-03, gnorm = 2.81e-02, feval = 00014\n",
      "iter = 0007, obj = 1.36467e-06, rnorm = 1.65e-03, gnorm = 1.54e-02, feval = 00016\n",
      "iter = 0008, obj = 5.69594e-07, rnorm = 1.07e-03, gnorm = 8.86e-03, feval = 00018\n",
      "iter = 0009, obj = 5.21249e-07, rnorm = 1.02e-03, gnorm = 5.82e-02, feval = 00020\n",
      "iter = 0010, obj = 2.28575e-07, rnorm = 6.76e-04, gnorm = 4.99e-03, feval = 00022\n",
      "iter = 0011, obj = 9.00814e-08, rnorm = 4.24e-04, gnorm = 2.96e-03, feval = 00024\n",
      "iter = 0012, obj = 3.46365e-08, rnorm = 2.63e-04, gnorm = 1.72e-03, feval = 00026\n",
      "iter = 0013, obj = 1.21659e-08, rnorm = 1.56e-04, gnorm = 1.02e-03, feval = 00028\n",
      "iter = 0014, obj = 1.12135e-08, rnorm = 1.50e-04, gnorm = 2.63e-03, feval = 00030\n",
      "iter = 0015, obj = 3.95943e-09, rnorm = 8.90e-05, gnorm = 5.36e-04, feval = 00032\n",
      "iter = 0016, obj = 3.48371e-09, rnorm = 8.35e-05, gnorm = 5.69e-03, feval = 00034\n",
      "iter = 0017, obj = 1.25247e-09, rnorm = 5.00e-05, gnorm = 2.86e-04, feval = 00036\n",
      "iter = 0018, obj = 3.71468e-10, rnorm = 2.73e-05, gnorm = 1.60e-04, feval = 00038\n",
      "iter = 0019, obj = 3.32605e-10, rnorm = 2.58e-05, gnorm = 3.01e-04, feval = 00040\n",
      "iter = 0020, obj = 1.11595e-10, rnorm = 1.49e-05, gnorm = 7.29e-05, feval = 00042\n",
      "iter = 0021, obj = 4.19413e-11, rnorm = 9.16e-06, gnorm = 3.73e-05, feval = 00044\n",
      "iter = 0022, obj = 2.41066e-11, rnorm = 6.94e-06, gnorm = 2.27e-04, feval = 00046\n",
      "iter = 0023, obj = 2.33987e-11, rnorm = 6.84e-06, gnorm = 7.25e-05, feval = 00048\n",
      "iter = 0024, obj = 1.97771e-11, rnorm = 6.29e-06, gnorm = 2.11e-05, feval = 00050\n",
      "iter = 0025, obj = 1.23631e-11, rnorm = 4.97e-06, gnorm = 9.23e-05, feval = 00052\n",
      "iter = 0026, obj = 1.12834e-11, rnorm = 4.75e-06, gnorm = 1.48e-05, feval = 00054\n",
      "iter = 0027, obj = 5.69136e-12, rnorm = 3.37e-06, gnorm = 1.30e-05, feval = 00056\n",
      "iter = 0028, obj = 4.72410e-12, rnorm = 3.07e-06, gnorm = 2.55e-05, feval = 00058\n",
      "iter = 0029, obj = 1.67034e-12, rnorm = 1.83e-06, gnorm = 2.09e-05, feval = 00060\n",
      "iter = 0030, obj = 1.66419e-12, rnorm = 1.82e-06, gnorm = 8.46e-06, feval = 00062\n",
      "iter = 0031, obj = 3.24807e-13, rnorm = 8.06e-07, gnorm = 3.79e-06, feval = 00064\n",
      "iter = 0032, obj = 1.34127e-13, rnorm = 5.18e-07, gnorm = 6.48e-06, feval = 00066\n",
      "iter = 0033, obj = 6.07714e-14, rnorm = 3.49e-07, gnorm = 6.85e-06, feval = 00068\n",
      "iter = 0034, obj = 4.17750e-14, rnorm = 2.89e-07, gnorm = 1.37e-06, feval = 00070\n",
      "iter = 0035, obj = 5.95466e-15, rnorm = 1.09e-07, gnorm = 1.62e-06, feval = 00072\n",
      "iter = 0036, obj = 5.62763e-15, rnorm = 1.06e-07, gnorm = 1.18e-06, feval = 00074\n",
      "iter = 0037, obj = 5.60137e-15, rnorm = 1.06e-07, gnorm = 8.36e-07, feval = 00076\n",
      "iter = 0038, obj = 4.02724e-15, rnorm = 8.97e-08, gnorm = 5.60e-07, feval = 00078\n",
      "iter = 0039, obj = 5.15967e-16, rnorm = 3.21e-08, gnorm = 1.44e-07, feval = 00080\n",
      "iter = 0040, obj = 5.89965e-17, rnorm = 1.09e-08, gnorm = 9.69e-08, feval = 00082\n",
      "iter = 0041, obj = 5.17076e-17, rnorm = 1.02e-08, gnorm = 5.23e-08, feval = 00084\n",
      "iter = 0042, obj = 2.03339e-17, rnorm = 6.38e-09, gnorm = 6.17e-08, feval = 00086\n",
      "iter = 0043, obj = 1.82061e-17, rnorm = 6.03e-09, gnorm = 3.89e-07, feval = 00088\n",
      "iter = 0044, obj = 3.85147e-18, rnorm = 2.78e-09, gnorm = 1.21e-08, feval = 00090\n",
      "iter = 0045, obj = 3.38194e-19, rnorm = 8.22e-10, gnorm = 5.20e-09, feval = 00092\n",
      "iter = 0046, obj = 3.32696e-19, rnorm = 8.16e-10, gnorm = 4.84e-09, feval = 00094\n",
      "iter = 0047, obj = 1.01416e-19, rnorm = 4.50e-10, gnorm = 5.91e-09, feval = 00096\n",
      "iter = 0048, obj = 8.03687e-20, rnorm = 4.01e-10, gnorm = 5.18e-09, feval = 00098\n",
      "iter = 0049, obj = 3.51729e-20, rnorm = 2.65e-10, gnorm = 3.44e-09, feval = 00100\n",
      "iter = 0050, obj = 2.30791e-20, rnorm = 2.15e-10, gnorm = 1.79e-08, feval = 00102\n",
      "iter = 0051, obj = 1.73358e-20, rnorm = 1.86e-10, gnorm = 8.03e-10, feval = 00104\n",
      "iter = 0052, obj = 1.21927e-21, rnorm = 4.94e-11, gnorm = 2.16e-10, feval = 00106\n",
      "iter = 0053, obj = 4.77976e-22, rnorm = 3.09e-11, gnorm = 2.36e-10, feval = 00108\n",
      "iter = 0054, obj = 5.35598e-23, rnorm = 1.03e-11, gnorm = 4.20e-11, feval = 00110\n",
      "iter = 0055, obj = 8.59774e-24, rnorm = 4.15e-12, gnorm = 1.78e-10, feval = 00112\n",
      "iter = 0056, obj = 5.59196e-24, rnorm = 3.34e-12, gnorm = 2.24e-10, feval = 00114\n",
      "iter = 0057, obj = 4.79499e-24, rnorm = 3.10e-12, gnorm = 3.61e-11, feval = 00116\n",
      "iter = 0058, obj = 2.79442e-24, rnorm = 2.36e-12, gnorm = 1.44e-11, feval = 00118\n",
      "iter = 0059, obj = 2.45897e-24, rnorm = 2.22e-12, gnorm = 1.70e-11, feval = 00120\n",
      "iter = 0060, obj = 1.27595e-24, rnorm = 1.60e-12, gnorm = 9.57e-12, feval = 00122\n",
      "iter = 0061, obj = 8.36138e-26, rnorm = 4.09e-13, gnorm = 1.69e-12, feval = 00124\n",
      "iter = 0062, obj = 7.36807e-26, rnorm = 3.84e-13, gnorm = 5.05e-12, feval = 00126\n",
      "iter = 0063, obj = 3.10698e-26, rnorm = 2.49e-13, gnorm = 2.46e-11, feval = 00128\n",
      "iter = 0064, obj = 2.21573e-26, rnorm = 2.11e-13, gnorm = 2.67e-12, feval = 00130\n",
      "iter = 0065, obj = 2.91728e-27, rnorm = 7.64e-14, gnorm = 2.96e-13, feval = 00132\n",
      "iter = 0066, obj = 1.51332e-28, rnorm = 1.74e-14, gnorm = 1.99e-13, feval = 00134\n",
      "iter = 0067, obj = 1.45667e-28, rnorm = 1.71e-14, gnorm = 1.11e-13, feval = 00136\n",
      "iter = 0068, obj = 7.24182e-29, rnorm = 1.20e-14, gnorm = 8.90e-14, feval = 00138\n",
      "iter = 0069, obj = 6.01598e-29, rnorm = 1.10e-14, gnorm = 5.88e-14, feval = 00140\n",
      "iter = 0070, obj = 5.21116e-29, rnorm = 1.02e-14, gnorm = 7.56e-13, feval = 00142\n",
      "iter = 0071, obj = 2.77072e-30, rnorm = 2.35e-15, gnorm = 1.59e-14, feval = 00144\n",
      "iter = 0072, obj = 1.79259e-30, rnorm = 1.89e-15, gnorm = 9.16e-15, feval = 00146\n",
      "iter = 0073, obj = 6.79650e-31, rnorm = 1.17e-15, gnorm = 6.96e-15, feval = 00148\n",
      "iter = 0074, obj = 3.75621e-32, rnorm = 2.74e-16, gnorm = 3.43e-15, feval = 00150\n",
      "iter = 0075, obj = 3.01551e-32, rnorm = 2.46e-16, gnorm = 1.04e-15, feval = 00152\n",
      "iter = 0076, obj = 2.86623e-32, rnorm = 2.39e-16, gnorm = 5.10e-15, feval = 00154\n",
      "iter = 0077, obj = 2.81962e-32, rnorm = 2.37e-16, gnorm = 2.40e-15, feval = 00156\n",
      "iter = 0078, obj = 1.21567e-32, rnorm = 1.56e-16, gnorm = 7.75e-15, feval = 00158\n",
      "iter = 0079, obj = 7.95515e-34, rnorm = 3.99e-17, gnorm = 1.84e-16, feval = 00160\n",
      "iter = 0080, obj = 3.24664e-34, rnorm = 2.55e-17, gnorm = 1.22e-16, feval = 00162\n",
      "iter = 0081, obj = 1.37490e-34, rnorm = 1.66e-17, gnorm = 2.24e-16, feval = 00164\n",
      "iter = 0082, obj = 7.49205e-36, rnorm = 3.87e-18, gnorm = 1.58e-17, feval = 00166\n",
      "Objective function didn't reduce, will terminate solver:\n",
      "\tobj_new = 7.49205e-36\tobj_cur = 7.49205e-36\n",
      "##########################################################################################\n",
      "            CG Solver end\n",
      "##########################################################################################\n",
      "\n"
     ]
    }
   ],
   "source": [
    "LCGsolver.run(VSP_prob,verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZUAAAEpCAYAAABbU781AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAAvaklEQVR4nO3de3xU9Z3/8dd3JveEZAgkgHINCKhFJQGsWlvUoF21FyuovW8vgrbd7R3W3W738tvdNm63v962XdDd7e3XXS7adbW1lqip1noB4hUBkYDcCRAmIfdk5vv745whQzq5TJjMycy8n49HHszlzJnPfI3zzvd8z/l+jbUWERGRRPB5XYCIiKQPhYqIiCSMQkVERBJGoSIiIgmjUBERkYRRqIiISMIoVCRlGGMqjTFrjTHWGLPRGLPaGBPwui4R6WN0nYqkEmNMJbANGG+tDSZgfzVAhbV2xbnuazSM9fpE+svyugCROFUDDYkIFNdmIJCgfY2GsV6fyFnUU5GUYozZjBMqq7yuRUT+mHoqkmoWAWsTsSP3UFrk8NJs97Fq9zGAO4EK92eCtXaNMWY5cI/72Aprba0xpgKnR9EArLLWNhhjVrv3K3BCcFPUvhvcz7AMwN3vSvfxgPuaILC1f31RtUf2j/v8vcOp/9xbTWQI1lr96CclfnC+HC0QSOA+K4E9/R6rBvYA1VGP7QEqo5/v95rVUbc3Asuj7m+Oeu1ynDGhave9a9zHVvb7nCsHqW9jv9oqgM3DrV8/+hnNH539JalkyPEUY8xyY8xK9yyx6hG+TxPOX/+1UY9Feh24j5e6PZ2IoPv+FTiBsinquY3AqqjtKq21tdbaetvXe1gROZPNWtuA00uJ9fkqccLiTG3u9qVRn3fQ+kVGkw5/SSpZBtTHesL9Mg8AQescagoAe4HxI3yvhn73g0Bp1P11OEGxyv0y3+A+Xg0E+wXabM7+Qj9r3269q4BTxph6YL11D2fFsChGbZF9LgNqo+4PVr/IqFCoSCqpBv5oXCAqUEpxvuhrrbVBYwzGmAr3L/lEW4tzGGsVZ/cKAji9qeheQm2/1wb778xauyzSC8EJKgYIlsA51i0yqnT4S1JCVHD0/4IGZ3C83j2ktMLdPgBnDg0lnLvfJnfgvinqqXpiHGYa7CJNd5Ae9zPcC1QBtw+weW2s/buPbRlW8SKjSKEiqaIS59DWWSER+UKOoQa4LoHvH4jx2FrgPqKCzu2hbHXDJtptg+07xueIGYbW2nqgNvrwWmRsp984zh+9xyDPiSSMDn/JmOb+hb8Sd6DbPZUWnHGKRThh0/902+XAWvcLeLB9V+KeHmyMWW2tvXeAx1a771VqjGmK+vJeB8zuf+KAeyirxhhTituLsdauc4NgTWTfwCY3JINRdYPT67gzVi3uvla4+4/0WGZba6sG+UwD1S+ScLr4UdKK+8XdYJ1rRSpJ7NX3IjIEhYqkDTdEHo9+zFo70rO/RGQEFCoiIpIwGqgXEZGEUaiIiEjCKFRERCRhFCoiIpIwChUREUkYhYqIiCSMQkVERBJGoSIiIgmjUBERkYTxJFSMMYOuMW6MqTDGrDbGVLv/BpJUmoiInIOkT9Pizs+0zVprBtlms7V2mXu7AlhjrV010PYiIjI2eNFTqSDGyncRUdN5A2cWQxpsLQoRERkjkhoqxpjlw1jLoZIYodM/bEREZOxJ2iJdbigMZ2nX0hiPNRFj5Tp3tbyVAHl5eVXTp08/lxLTRjgcxufTORigtohQO/TJtLbwhbvJ7TxByFrCFsLukEeu3/DywbYT1tqyRL5fMld+rEz0inPW2nU4q+8xb948u2vXrkTuPmXV1dWxdOlSr8sYE9QWDrVDn0xpi8PBDh597SiTn/kbqtt/RX14LgDGQKAgm5kTC8m/8zdvJfp9kxIq7mp8tUNu6IjVKyllkHEYEZGMZi384XucPn6AfSfb2XuijeOnuwBY4v8Dz9hLWT/3Xm5cMIVr55czLi/bed2dA54vNWLJ7KncZsyZDxBwD13VugPx0eqJcQgsxnYiIgLsfPEp5m/+On6bywx8zACMH7L8Pvz+LK587+e5dsGipNSSlFCx1p7VSzHGrHUPXUXuVwBN1tqgu7Y4/Z7bkIw6RUTGtJN74MhLNJ7u4nRnL7PLCgE4f+cjhKyh2v6AyvlzuHHBFJbOKyM/J5n9BkdS39G9iHGle7sGWOv2QGqAzbjjI8AKY8xqnF5Lpa5REREB1n8EGl+nHCiPengccGrylTzx6VvJy/Z7VJwjqaFirQ0C97o/0Y+v6He/IWqb4Y7FiIikPmuh7QTYEIeCHTy+4xhtXSHursyHxtfpfcdX+NgL01kwtYQvXz+XHL8TIuNLpoLHgQJJDhURERlc89M/ouSJewA4H/hY5Iltzj9ZlR/m59fOwudL/CB7IihUREQ81ni6k0dfPcojrxzmy4d/yiQmcV/oZrL9hvmTx3HJ1ADzJo0jK3A+lFaM6ZmAFSoiIsnWcYqen99GW/NJWjt7aO8OcQVwBTDbHOax8R/iymu/wrXzyynwYLD9XKRWtSIiaWDLY79g8aEX2BZaSCfZ+IyhrCiXKYE8woEruHHZGhh/ntdljohCRURktLz+EN1vvcBbJ9vI8hlmTXROAV5w8AkabYCfzfwmN116PtdfPJmS/GyPi00MhYqIyGjo7YL/+QxZPV2cH/bhM8Be5+ysPIAr7+bHN7zdywpHhUJFRORc9HTA0VfpDYV47XALT+8+Tk6Wj1VzO6C7ld7b/ou7n5tI9YXlfPjyGWfO2srzuOzRolARERkhay3H/+cvKd/+H2QBl7k/AOwGsgvImfMufnJRoUcVJp9CRUQkTm82nuahlw7z0IuH+FnbIzzPfH7Q+34mF+fx9ooJXDl7AlNK8qBkGuRkTqCAQkVEZGin9tHz0+V0tp+moztEfjjMHcAHsZzna2L79I/z1evvZsH5JUTPXZiJFCoiIkN48Tf/ycJTu3ko9E7C1pCdZZgaKGD6hALC4wPceN1nIT/gdZljgkJFRCTi1U10H3mdvSfayPIbZpcVAXDRsUfYaafz5Py/472XncfSeWXkZnk/z9ZYpFAREQHoOAUP3kmODTPHGmeJxJ3OU7kYZl33N/zrOyu9rTEFKFREJLPYEDQfAuCNY608+toR/D7D56a/BTZM18d+zaeeyOL6iyfxkahTgHO9rDmFKFREJKNM37EWfvcYAHPdHwBeAvJKyJ1xOT//tL4aR0otJyJpr62rl8e2H+WX2w7w7WPP8bydz4OhqynI8XPJ1BIWTh/PjNICzKSLwa+vxXOh1hOR9BM8QHjz39DUfJrDzR0ca+mkIAyfpJsyfzO/Kr+La5d+kmvmlZOTNZYnkk89ChURSTsNj99PxfYHOB6eRjYwFSjI9VOcn81JLuRPP3EXFJR6XWZaUqiISOpq2gttJ2hq6yLY0UPFROcU4ClHn+SV8Cz+bNz/5ZaF53PLwvOZMcG5sr2uro6lCpRRo1ARkdTUcQr+9XIIdVEKRMdEPjC56s+pe+/SjL/CPdkUKiKSMqy1vHqomb0n2nhfzlYIddF9fQ1fqm1h7qQi7lo6mxyfH4yhfPoVzrUmklQKFREZ2+p/SvfLm2hs6eLY6U7aukKU+Qzh8S34csaRc/mn+NZiH3nZusJ9LFCoiMiY1N0b5okdx1jyq7+nt7eHY7YMgBK/obQwh3BBGb6qj4E/mzzlyZihUBER74VDcGw7hHvZc6KVx3c08rs3jpPfeZx35xzna6FPcfSCD7Fi0VSdBjzGKVRExHMdz95P/ubVAMx2f1YC5DjPf3HVKiZMm+dRdRIPhYqIeK5n5284Hi7jb3s/TmFuFm+fVcpVcyYyY0IBprCMCVMVKKlCoSIiyRHqgc1fp7ulkTcbW2nt6mXJTOdE4HFHn2Nn+Q0sf9enue7Cck0rn8IUKiIy6qy1mP3PwXM/JGvceRS1hCiw0LM/n2yfwZRMZcl774LpU7wuVc6RQkVEEischt4OwJla/oFtB3lq93EevvQ5sowP32ef49lXm5kxoZAZs0p1LUmaUaiISEL1/uwDZO19EnCmlb/H/eEPwPlVkFfC7YtLvCtQRpVCRUTOmbWWlw4E+Z/ndvD1hjpqwwt5ITyf3Cw/F51XzGXTAkwuzsPMvsbrUmWUKVREJH6tjbDzEdo6e3j5YJBt+05x7HQns8xR/FmWpyfewYJ33MyNCyZTkKOvmUyStP/axphq92YAWAyst9bWD7BtBVANNAEVwDprbTAJZYrIMPQ8WUP2tvspBK50f8h2ngvllfJ3n/lTyM7zrD7xTjL/hNgIzLLWBt1ZQ+8DqgbYdrm19t7IHWNMDbBm9EsUkYF0dIfIz3FO9c3a/wz1/ktZ1X4Xb6+YwPsvO4+rLygjJ8uHP6dIgZLBkhkqVVG9jVKcXshAlgH3Rt0PjFJNIjKQjiA89FnoOs2e4200nu5k4bTx5GUbzPEdlFet4cGr3s+00gKvK5UxJGkT6FhrG6LurgBqBtveGLPZGBNwD5ttHNXiROQsbV29hHb9BnY+Al2nMaEusmw3LW2t0NsNs97F1Hd8SIEifySpI2juWMlyYKO1tnaQTVcAjwN7gW9EHwoTkQSzFsK9ALx+pIX/emE/D798mIdnbWZabgl8uhZfUycTgfKJhd7WKmOesdYm9w2NCeD0UjZbazcNsE1kUL8CWAusiRUsxpiVuPPOlZWVVW3YsGFUak41ra2tFBUVeV3GmKC2cAzWDgu3foWS1t0xnzsxYTGvLfjaaJaWdPqd6HPNNddss9YuSuQ+kx4qcCY0NgPj+5/VFenNRELEvb8Nd5B/oH3OmzfP7tq1a9RqTiV1dXUsXbrU6zLGBLWFI1Y77DneysO/e44vvHYrj4YW81p4FrnZPi6eUsyl0wJMLMqBC98LZek1maN+J/oYYxIeKkk5/OWGSI21NnK211b331Ig2G/zauDMoTFrbYMxZt0A24rIMPh726Hhd4Ss5cX9QTa/fpRXDrVwuW8HZMFvJn6cq65aynsuOe/MGV4iI5GsMZUmYH3U/UVAQ2Tw3u2NNLk9kVqccZezrmHpN9AvInGY8+a/w+9r8eP8z7cIzqxV0ps3ge/+2YfApzCRc5eUULHW1htjKtwxEHCuT1kWtUkNzuGwdW7PpMEYsxpowOmhrE1GnSLpJhS2+H2GQPBVDgSW8OVjNzCpOI8bLp7E0nnlFOVmkRWYpkCRhEna2V8DDcq7z60Y7rYiMoCeTnjxZ9DTwb6T7Ty5q5ELyot4x8xx5Hceo/SKz3H35Dt41wVl+HyaGVhGhyblEUkT4e2/xPfrrwAwE/gEOCfl74WwyaLwohu4pqzcuwIlIyhURFKYtZZnG07y0z+8xUeOP8w78krgC68RxvCrV49QfeEk8rP9PP3Ms7wrzc7ikrFJoSKSap75Hr3Hd/PWyTZ2HW0l2NHNO4H5/np6Zi8hO68YH/CexePOvMT6sj0rVzKLQkUkhRw/vI+yzX9NO4UU2WyqAF+WIT/bT35uAf6Fd3hdomQ4hYpICnjlYJD/+P1eQq/9ku9nwce61tB7XiWfvGoWN10yhdwsnb0lY4NCRWQseu1Bwi+v53hrF/tPthPs6OEmoMJ3hG6Tw9c+fTtVFZMwWt9dxhiFishY9PS3IXiA4x0B8oFCv6G0IJvSwgnkzLuDRbMne12hSEwKFZExouF4Kw+9dJjPv2MSvsbt+N65mofa38e00gJurZxKYa7+d5WxT7+lIl5p3AmP3QOhHizQ9NYpLu8N07oji2IbhmlL+Ks5F3ldpUhckrZIl4j06Q2F2f34f2Ib6iAcwoRDTC3JYcq4bHLy8mH+zTD9Cq/LFImbeioiSdTe3cuGLQf492f28s3TT1NSMpfyTz4KgEZJJB0oVERGU6gX/vfP6A4e4nCwkyPNHVSELP8ILPK/wcGy5WjiFEknChWRUbT/9WeZ/vIveMtOpcXmkwOMz81iUnEuOUWLmH3dp70uUSShFCoiCWat5bmGJu57uoFpuzfyd9nw8e41LLjoIla+s4L5M0q9LlFk1ChURBLh5f+GNx7jRGs3O462EGzv5hZgQdY+WrIm8vPP3EJF+bghdyOS6hQqIonw+N9Ddyt52aWc19HJVL+hJD+bkvwi/JfeTrECRTKEQkVkhDq6Q2zYeoC2kwf4TMshuOEbFFx+N9u2HeQ9l2qtd8lMChWR4QoegPqfgg0B0N3RQ+tzbzHVnAA/MHURPp/htsXTvK1TxEMKFZFhan/6XynY9iOsLwsDlAB3ZVsMBhuYiZl8idclinhOoSIyhP0n2/m3p/Zwy0tP4rdzaL7jUa6Z71xdogNcImdTqIj0t/cp6GzmaEsnj75yhOf3NWGt5eLsvTw7/kbOD+R5XaHImKVQEYl25BX4yXsAZ9qUTwCfiFqJ97obboHJxZ6UJpIKFCoirh1HWnjpwQf5IPDR7r8gaAIsu3gSt1VNY3JJHvhzYeIFXpcpMqYpVCQzhcPQ2wHA60da+FHdm9TuaOT/ZG/jlG8cs5bczF1L53BeIN/jQkVSi0JFMtOPb4T9zwJwEfB9AHeopGvmtfz9+xd4VZlISlOoSMZ58c0DXLb/Oczcd8OMK2nvDvFcw0mWzCqlKDeL3Atu8LpEkZSlUJGM8oc9J/jOv69nQ66lp/ITZM9/NwXAtdd4XZlIelCoSPra93ve9uo/0XXgh+RmOVeUXGEtUwp3QS/0lF9C9hC7EJH4KFQkbZ1++keMO/kie06cx5zyInL8BgPMnFgI5XdQUHqe1yWKpB2FiqSdhuOtfPfx3XzxzS1sD1/GF+2X+PbVl3LzJU6IGI/rE0lnChVJbdbCoW3Q3Ubj6S4erD/I7988QZbtYWbOMbYWX8tTK69xrjMRkVGnUJHUtu/38JObASgH7gLuihoomTPnIgWKSBINGCrGmGJgJOueNllrW0ZeksjwBNu7efHxX3MN8LHuNXSRw9UXlHFr5VSmlORBdj7BN5q9LlMkowzWU7kH2EL8h6AXua89izGm2r0ZABYD66219QPtxBizHCfUGgCstbVx1iFp7OGXD/NXv3yVfwzVc9A3kaKLb+Dry+Yyp/8Ki7vrPKlPJFMNFipbrbUPxrtDY8xAvZuNwCxrbdAYA3AfUDXAPpYDFdbae40xFe5rY24rGeKxv4Kjr565+67OXn4YClKZtZee6Vfzww/r10NkLBgwVKy1D/R/zBjzFaDBWvugMWYDYIG11tonol533wC7rLLWBt3bpUDTIHXVWGtnu/trQIGS0WzHKcyzP6Ap93xKy51VFYuzYOF5+eTnXkrBlZ/0uEIRiYh3oH6vGyhfBfZYa+8xxlw3nBe64RCxAqiJtZ0xphIIRm4PdohMMkPLvpcpAb54+iN8/sN3Uzl9PACF3pYlIjHEGyqn3H+rgTXu7ZLhvtg9lLUc2DjIGEkF0OQeAqs1xqwG6mNtb4xZCawEKCsro66ubrilpLXW1tbUbAsbIrfL6cAebbOU5YPfZ5h89ElKgIvnzKHpzZeoaxj+MF/KtkWCqR36qC1Gl7HWDn9jY+4EtuKEwhz3sQ/EM/ZijAng9FI2W2s3xXh+Jc4hNRO1/V5r7fjB9jtv3jy7a9eu4ZaR1urq6li6dKnXZcTvV1+GLffHfq6wHL7yBpj4zhtJ2bZIMLVDH7VFH2PMNmvtokTuM96eygacnsEyY0wJzlleJ+LZgTtQvxHYbIwZHzXOEtEE1PfbPmCMqeh3CE3SSHt3L23bf0ejncVPeqvxG8N188upvmiSs8Gki+MOFBFJvrhCxVrbDPxz1EN/MZzXuacT11hrIwPuW91/S3HHT6LEGkMJMvjAvqSocNjyQP1BvvPYazzZ3cCG0E0E593BX/zJfCrKirwuT0TiNNjFj9E9kU3W2n3n8D5NwPqo+4twziJrcN+rAueiyaC1tsEY02SMCbi9lAp32+A5vL+MFT2d8PpDEOrizcZWHnnlCIebO3gfzeRkh7j+muv47HUJ7Y2LSBINdkpxM25PxBhzp/vlvgfYEO8V89baemNMhTteAs4pwsuiNqkBNgPr3PsrgHuMMXuA2cCwzjCTFPDaA/DQZwCYA3wBiMw/b42fCyqXelOXiCTEsA5/Ra49McbMAla5FzhuiWeAPtagfNRzK/rdD9J3dpmkidauXl599ndcZnO4rutb5OX4+djbZ3DHkunkZfsxOYWQP+j5GCIyxsU7prIXd0zFGLPQGPNNnAsg11trX0p8eZJO/MaQdXwHu+1U3rVkIV9cNpfycZrsUSSdjHiWYmvti8CLAMaYW40xdwAnrLXfSlRxksKeXwvB/Rxr6WB8QQ45WX7ygYVZezl9wZ/wjQ9c4nWFIjIKEjL1vTulywPu4L5kupbD8Ohqek0OhWEf1u+DLB8AWT4/4y+9yeMCRWS0nHOoGGO+EumduIP7kukadwCw/09+xk0Pw11Xz+bz1Rd4XJSIJENcoeJeUV+DM44CzrT4JYAOeQlP7DzGU2+c4G8nOqFScfEinn1bMYGCHI8rE5FkibenErDWnjW1vRs0kol218KuX9Pa3cuWfac41NTObKBt4gEKC8ugcCIBr2sUkaSKN1RiTQK5PsZjkgHs439H+NgOusL5LAAu8UNBjp+8bj+87QNelyciHoh7lmJjzAdwV2N0rQLuTlxJkgpe2HOcS4/u5Ke9y/jH3o9w04Ip/PXNF5Gv9eBFMlq8oXIXzrT30fNwVaFQyRgnW7v4xqM7eb5+G0/ndnOqYBY/vnUxS+eVe12aiIwB8YbKHmvtWZNIGmNuTWA9Mta0HoeXfk441Murh5p56o3jTOoJ8/nsRgA+/8GbyZ2lQBERR7yhEmvq+T2JKETGqPofwxP/gA+41P2JzNVFwURyz1vgVWUiMgbFGyqzjDE/Ara59w3OSo43JLQqGTuOv0Fo3PlUtfwzedl+/vrmC7nxbVMwxoDxg8/ndYUiMoaMZEylFoie9W9C4sqRsWL74WbmTy7Gf+IN/OXz+OH7L+fiKSWUFGQP/WIRyVjxhsqd7pxfZxhjBlprXlLJid3QcQqAjVsP8F9b9vPJq2Zx84ndUPlRrpw90eMCRSQVxBsqseYlvw53YklJUc0H4QeLiUyUsAJYkQNscZ+f9DaPChORVBNvqNQAiyN3oqZt0TQtKaxt/ysUYuHdNTBxDgCNLV2UF+eCPwemX+FxhSKSKuINlb3uxY+1wCacs8GGtU69jE1P7mrkpf95jC8C2ydez8VzKgDQScIiMhLxLtJ1mzu9/ePAGmvtE8aYmaNSmYyq0509/MMjO1i/9QD/kHWA09lFFJQoSkTk3AwaKm6vJJYNQIUxBpxpWm5PcF0yGp78J9j9W0539nLwVAcfCoX5SA7MzWkkZ9KFjCsr8rpCEUlxQ/VU7gU2A7HWSZkALAIqEl2UjA77wv0EQzm82DEJKGJcXhYXTSkmN3cOXKK/C0Tk3A0VKqustY8PtoExZmEC65FRsm3XPqo6TvKjng/yn7yXP7/2Au5eOpssvy5eFJHEGTBUjDGXDRUocGat+ujXXWutfSIRxcm56wmF+U7tG/z+d7/loRzoDVTw0IffwUXnFXtdmoikocF6KncYY2LN9TUYA1wPKFS8Eg5R0HYQGnfSHQrzpQ0vs/NoC0v9OwG45yM3kT1FgSIio2OwUFlP/APwFi3a5a1nvsOSLX8PWyAH+AFArvucL5vsibO9q01E0t6AoeIe1tKV8imm++DL9GSXUvi+fwGgN2zp7g1TkOOHwHTI1iJaIjJ64r34UcawfSfa6HjjNU6Fp3LhrJsZX5hDFvqPLCLJo1N/0sjU8flM4xjHsybT2RvyuhwRyUD6IzYVWQt7n4Ku0wQ7uvEZQ3FeNlm9nRTZVi6ccT5TSvK9rlJEMpBCJRUdqoefvheAQIynO4pmJrMaEZEzzjlUjDEzrbX7ElCLDFOocRd+4NM9X+ZweAKXTRvPX900n8KcLMjO59SrB70uUUQy1FBzf316GPtYgZYTTpqjzZ089cQzLLeG34cv4TPVF/PZa+bg95m+jcwh7woUkYw2VE/lLpy5v5oG2UbLCSfJcw0n+dwv6rmn6y2O+0v58Z1X8/YKNb+IjB1DhcofLR/c33CXEzbGVLs3AzgLfa231tYP43VrrbWrhvMeaaf1OLQcwmJ56KUj/Mcze5kUtiwsOkrppLlMUqCIyBgzaKjEChR3tcdKa+3dxpjr6Ft0digbgVnW2qA7Zf59QNVgLzDGVAIrcabXzzz3XQvN+zHA+4H3Z7uP9wDlV3pWlojIQOIaqDfGfBPYA9QDWGsfd9dceXAYL6+y1gbd26UMfkgtogIIDrVRWupug+b9bM6+lvVtC8nN8vGJq2axaMZ45/npb/e2PhGRGOI9+2uLtfaBftPdB4fzQmtt9OSUK3DWth+QMWa5tXaTMea+OGtMC71Nb5EFPNx2IXtK38naj1Yxd9I4r8sSERlUvKHi/pmMjXqskmHOSmyMqQCWAxuttQOOxbjbDTlDsjFmJc7hMcrKyqirqxtOGSmh9OQ2LgEKA5P46qWWwzu2cXjH8F7b2tqaVm1xLtQWDrVDH7XF6DLW2qG3imzsjKGsAU7hfOlXAjXxrJ9ijAng9FI2W2s3DbDN8shzxphT1trxsbaLNm/ePLtr167hljEm9YTCbNnXxJWzJ8KW++FXX4Yv7YTiKXHtp66ujqVLl45OkSlGbeFQO/RRW/Qxxmyz1i5K5D7j6qm4YygNOL2NCcBfDHV2WIx9BI0xG4HNxpjxUeMswJmzxIZ1RllaeP1/4dkfELaWhmOt5Hb10lxeREl3I/hzoGiS1xWKiAxbvAP137DW3gP8c5yvq8bp0UTO9trq/ltK7DGZ29wzxAAC7mGu2n7jMunhlfVw7HV8U6vILYBgbye+nAIongOX3gE+zfkpIqkj3jGVFcaYPcBWa+1LcbyuibMX71oENERCwh1DabLWBvuPtbjXqayLs86UEW4+hG/aEvjog0wPW4rauxlXlDv0C0VExqB4/wyustbeDzQbYz7gnk48JPcixwZjzEq317ECWBa1SQ1wW/RrjDEBY8xq93aNGzxpZePWAwSPNNBe4IyZ+HyGiQoUEUlh8Y6pNLv/7nUvTLzHGHO7tXbIZYcHGpR3n1sR47EgcK/7k1astfzrk2/y/d++xoq8Zurbi6n0uigRkQSId0zlRzhjICtw5gQbchoXOVtvKMzX/3c7v3h+PzONc/1n5YIFHlclIpIY8Y6pLAO+aa2dMxrFpK2jr8J/3oTt7cCGLH9jLX+bC1k+nCt+SqZ6XaGISELEGyprrLUPjEol6exQPXQ18+v89/DWaUNulo8bF0xhSkke5I6D6Vd4XaGISELEO6aiQBmB1hMHKMDwhVMrKA+M4yefXMKU8iKvyxIRSTgtJzzKDp5q58UtL/F2W8yM8gA//9TlTC7J87osEZFRoSvrRlHD8VZu+7dnKepqpDlrIhtWXaFAEZG0pp7KKAmHLXf/vJ7DzZ3MKmrh/JnzyC7M8bosEZFRpVBJFGvhsb+EE7sBpwu4qbiX/T3tzOg6jAlc6219IiJJoFBJlK7T8NwPCRdPxVdUDsA44OIAYBbAhTd7WZ2ISFIoVBKl9RgAXzt9CwvfuYoVi6Z5XJCISPJpoD5RTh8FYF/XOJ7c1Ug869SIiKQL9VQSxe2p3H3zlVy+ZCFRU/eLiGQMhco5erPxNPk5WZzv9lSuXvg2d/4VEZHMo1A5BwdPtfOR+1/AGHjsooMU+3MhL+B1WSIinlGoxOvZH8KW+wlZiw128otQmLxsP+Neb4Fxk0CHvUQkgylU4rXzEcJdp3m650Kae3soycvmqgsmYHw+qFjqdXUiIp5SqMQp3NrI86F5/GnLKmZOKGDjXVeSPU6rNYqIgE4pjks4bOk4dZRdrflMKs7lZ5+6nDIFiojIGQqVOHz3t9spDJ/mtD/Ajz+xhGmlBV6XJCIypihUhmnj1gP8d52zcvINSxZw4ZRijysSERl7FCrD8Ic3T3DPg68y0bQAMLeiwuOKRETGJg3Ux2KtM9twqJsDp9r5l/UvMceG+Ny8ZtgHFJZ5XaGIyJikUIll+y9h0ycAmAY8AJCLEygAxed5UpaIyFinUInl1D7n3+X/Ab5smjt6yM32kZflh4IJENAMxCIisShUYuloIpyVh+9ttwJQ4nE5IiKpQgP1MRw5coijPQV8e/MbXpciIpJS1FOJoef0SU7bcWT5NI+XiEg8FCoxTM/vpHXaND53zRyvSxERSSk6/BWlozvk3Gg/SVGgDJ96KiIicVGouJ5rOMnV9z7JEzuPQXuTc5aXiIjEJbMPfx3YAq3HaOsO8cuHt1PZ3k1L/ZvQGYT8Uq+rExFJOZkbKm0n4d+XAZZCoAYgB4ic8BWY7lVlIiIpK3NDpf0EYNm94Mt8fusEsv0+fvChhUwbXwD+bJg4z+sKRURSTtJCxRhT7d4MAIuB9dba+gG2rQQi2y8G7rTWBhNaUGczAN/fnsfrdiZfu+FCpl2kiSJFRM5FMnsqG4FZ1tqgcdZxvw+o6r+RMSYALLLW3uveXw48Hmvbc9LpzDh8sCObJTNL+eRVsxK6exGRTJTMs7+qonobpUDTANstAtZE3a8FKt2wSZhdbx0AoMM/jnuXX6LTh0VEEiBpoWKtbYi6uwJ3bDzGdrXu8xEV7uPBRNXS1Rvi11t2OoVceREzJxYmatciIhktqQP1xpgKYDmw0Q2PmPqNtdwO3DvA/lYCKwHKysqoq6sbVh3/u6eb8tYgZMOM7JZhvy5VtLa2pt1nGim1hUPt0EdtMbqMtTa5b+gcxqoBNltrNw1j243W2mVD7XfevHl2165dQ77/gaZ2qr/9Oz7PL7gr51F8f30cTHod+qqrq2Pp0qVelzEmqC0caoc+aos+xpht1tpFidxn0q+odw9jbQQ2DmOcpIazD4Wds1+8sJ+u3jCXTARfXknaBYqIiJeSEirGmGpjzLaoh7a6/w542boxZjWwxj1bLJCoWr56/Ty+e8dlVE7yQ15xonYrIiIkb0ylCVgfdX8R0BAZvHfHWpoig/HuacSbogbnq4FBD5UN6Nh2OLjlzF0f8D6AU29AnpbfEhFJpKSEirW23hhT4Q6sg3PNSfQ4SQ2wGVjnBsxGANN3aKqBkYbKw1+Agy/Efs5d2VFERBIjaWd/DTYob61dEXW7AUjcQEdnM/aCG7jj8O0cDnbyvQ8uZOH0gPNcYXnC3kZERDJh7q+ednpyxzNpagWNppmL58+HLM34LyIyGjIiVHLyCvne8oV09oTIUaCIiIya9P+G7W6HnAIA8rL9HhcjIpLe0jpUbDgEvR3sbbEk+yJPEZFMlNah8sIbhwF4+PVmunrDHlcjIpL+0jpUNj3vLOP4tpmTdehLRCQJ0jZUDgc7eH7XQQCq5pzvcTUiIpkhbUPl/z3/Fjm2E4CSYl05LyKSDGkZKt29Yf77hQMU0OU8kF3gbUEiIhkiLUPlyV2NnGzrZm6pO46So1AREUmGtAyVX9YfAuDa2UXOA+qpiIgkRdqFSnN7D0/sbMQYuGKaGyYKFRGRpEi7UPnN9iN0h8JcNXsi47N7nAez870tSkQkQ6RNqBgbhrYT/OGVXZTSwi1zc6HtuPNkTqG3xYmIZIi0mVCyqLUB/nk23wXIA56IPGMUKiIiSZI2oQKGjmU1PN9wklPt3dyycKrzcMk0hYqISJKkT6gYQ/5Vd7H0Kq8LERHJXGkzpmITuFikiIiMTNqEChjWPbWHVw82e12IiEjGSptQCWP4p1/v5Fu/3eV1KSIiGSutxlTuWDyNS6cFvK5ERCRjpU2oGGP45q2XeF2GiEhGS5vDXxqoFxHxXtqESsga3jrZ5nUZIiIZLW1CpSts+NZv3/C6DBGRjJY2oWIxzC0v8roMEZGMljahEsYwR6EiIuKptAkVaw2TS/K8LkNEJKOlT6hgKMnP9roMEZGMljahEsYQKMjxugwRkYyWNqFiMRTnpc21nCIiKSl9QsUYsvxp83FERFJS0v60N8ZUuzcDwGJgvbW2foBtK4DlQD1QCayz1gaHeIcEVSoiIiOVzONFG4FZ1tqgMQbgPqBqgG3XWmuXARhjGoAaYNWgezcKFRERryXzeFFVVG+jFGiKtZHbSznDWtsA3Db07hUqIiJeS1qouOEQsQKn9xFLJRDs/2D/sPkj6qmIiHguqadLRY2VbLTW1g6wWWmMx5pwxmL6728lsNK922WMeS0RdaaBicAJr4sYI9QWDrVDH7VFn3mJ3mFSQ8Va22CMWQfUGGOWW2s3neP+1gHrAIwxW621ixJRZ6pTW/RRWzjUDn3UFn2MMVsTvc+kn4PrjqtsBDYaYwIxNonVKyklxiExEREZW5ISKsaYamPMtqiHIukY61BXfazH+43JiIjIGJSsnkoTsD7q/iKgIRIUxpiKSK+lf3i44zAbhvEe6xJTalpQW/RRWzjUDn3UFn0S3hbGWpvofcZ+I2OW09cDqQJqokJlI7DZHSP5o4sfrbX3JqVIERE5J0kLFRERSX+aLEtERBImpaf1HdkcYanLGFMJROZQWwzcGfm8g7VFureTMWattXZV1P2Ma4uow8sNAJHrwDKtLdzPVI0zjlvBMD9vurSF+x1xn7W2qt/jI/rsI2oXa23K/uCMw0RuV+DMGeZ5XaP0WQPAyqj7y4Ftw2mLdG4n9xfdDvf3Ih3bwv1dWB31mTL29yLSDlH3azKlLXDC9I/+fziXzz6SdknZw18jnyMsZS0C1kTdrwUqjTGBwdoiA9qpgqhrmDK0LWqsezKLtbbBun+lZmhbLOt3PwCZ0RbW2lobY+b3kX72kbZLyoYKI50jLEVZ53DGiqiHKtzHgwzeFmnbTgPMypBRbeEe7ghG3Y6WUW0RYYzZ7P6xVY1zoTVkaFu4RvrZR9QuqRwqw54jLF30+yvkdiByqvVgbZGW7eT+Yse6IDbT2qICaHLHVBqMMauj1i7KtLYA5w+vUmAvzuUIkTkGM7EtIkb62UfULik9UJ+p3AtFK6275kyGqozRS8lEpUC17Vt/aB3OF+p4T6vyTuQwcQWw1hiD1XVuSZXKPZVMniOshrMPhQ3WFmnXTu5f4gPNcp1RbYHzmc70YN3DoZFxtoxqi8ghG3dsYR0wG7jH/SMso9qin5F+9hG1Syr3VDJyjjBjzGpgjXVW0Ay4XyIDtoW7ymY6ttNtpm8NnYC7DEItmdcWsZbkDtIXNpnUFmf9sWH7ZkUvJfPaItqIPvtI2yVlQyXqQwNxzRGWstzj5pts33ni1e79AdsiHdvJ9luLx71OZV3U/ejn0r0tGowxTZE/MCJjTe7vSDCT2gInUCLXVJwR+RLMsLY4Y6TfDyNtl5SepiWT5ghzP+uefg83WGtnRz0fsy3StZ3cwxorcQ4H3otzDn1DprWF2w734Px+zAa+YQe4eC0D2mI5znhKA85f2bVRoZLWbeEeFq6k7/+HzXaAi2CH+9lH0i4pHSoiIjK2pPJAvYiIjDEKFRERSRiFioiIJIxCRUREEkahIiIiCaNQERlDjDGVxpiaGJNDDvW65e7rAqNUmsiwKFQkoxljVhpjTo3Gl7EbENvcayeGaxHOdSaxrpQfkDsP2hZiTwIokjQKFclo7pX4CZuOIzqc3GAYaI4ykbSkUBFJkKilbKOd9KIWEa8oVEQSZ83Qm4ikt5SdUFJkpNxB8Gqc+YwC9Jve251DKTJ1/GJr7Rr3sbXAJmCz+5rF1to1/V6zzBhTCmyImvizwn3PRUCVtXZVHHXe575vg7v/2e79gPsZgtGTaYp4TaEiGcUd87gvso67+1hN1O0KnKUFIotelRpjVlpr1xljaoE9UZP0YYzZaK1dYa2tNcaswJnEr//iYbPdifjq3YH7iuFMq26trXffsyoSHMaYbcAW9z3qjTGnAIWKjBkKFck0twFb+z0WjLq9HGfK+OhTequitmuKPGit3WSM2cjQtkXdjneZ2pOcPTt1Ewk8sUAk0RQqImebgLOkQOSU3gFP7R3sNOTh9kZE0o0G6iXTbMAZ24gWiLq9HmdNijPc8ZKI6OtAqjn70FMw6nbFiCsUSWHqqUhGcVdHXOMuP7yVvpCoMcascccxatxlmyMD+dHXmsx2QyaAM1AfPei+FljjrpZX7x5Cux1oMsZsxQmaRcAq972Cg9U61OtxDuUFjDGrU3FRKUlPWqRLZJjcAf0tMQbiE/keKzn7zLF4XrscqNdhN/GSDn+JDF/A6wJExjod/hIZhqhrWyqMMeoNiAxAh79ExpCocZTNkethhvm6lTgXRn5jJIfORBJFoSIiIgmjMRUREUkYhYqIiCSMQkVERBJGoSIiIgmjUBERkYT5/7JiVKO/OzlmAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(z, 1.e-3*vel,label='true model',linewidth=2,linestyle='-.')\n",
    "ax.plot(z, 1.e-3/VSP_prob.model.plot(),label='inverted model')\n",
    "ax.set_xlabel(\"depth [m]\"), ax.set_ylabel(\"vel [km/s]\")\n",
    "ax.set_ylim(3,4), ax.set_xlim(0,1000)\n",
    "fig.suptitle(\"$L_2$ inversion\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By looking at the objective function value, we clearly see that we can perfectly match the observed traveltime values. In fact, the problem is underdetermined (i.e., we have more model parameters than observations). Because of this fact, we can only retrieve the average velocity between observation depths. Moreover, we will encounter issues when random noise is present in the recorded data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "noise = data_true.clone().randn(std=1e-3)\n",
    "noisy_data = data_true.clone().scaleAdd(noise)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(z[::desampling], noisy_data.plot(),'*')\n",
    "ax.set_xlabel(\"depth [m]\")\n",
    "ax.set_ylabel(\"time [s]\")\n",
    "ax.set_xlim(0,1000)\n",
    "fig.suptitle(\"Noisy Data\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "##########################################################################################\n",
      "            CG Solver\n",
      "    Restart folder: /tmp/restart_2022-04-22T01-51-41.263912/\n",
      "##########################################################################################\n",
      "\n",
      "iter = 0000, obj = 6.80620e-01, rnorm = 1.17e+00, gnorm = 2.37e+02, feval = 00002\n",
      "iter = 0001, obj = 5.49852e-03, rnorm = 1.05e-01, gnorm = 6.50e+00, feval = 00004\n",
      "iter = 0002, obj = 6.48304e-04, rnorm = 3.60e-02, gnorm = 1.28e+00, feval = 00006\n",
      "iter = 0003, obj = 1.26607e-04, rnorm = 1.59e-02, gnorm = 3.31e-01, feval = 00008\n",
      "iter = 0004, obj = 4.59044e-05, rnorm = 9.58e-03, gnorm = 1.29e-01, feval = 00010\n",
      "iter = 0005, obj = 2.61762e-05, rnorm = 7.24e-03, gnorm = 6.59e-02, feval = 00012\n",
      "iter = 0006, obj = 1.71345e-05, rnorm = 5.85e-03, gnorm = 4.07e-02, feval = 00014\n",
      "iter = 0007, obj = 1.15094e-05, rnorm = 4.80e-03, gnorm = 3.06e-02, feval = 00016\n",
      "iter = 0008, obj = 7.28932e-06, rnorm = 3.82e-03, gnorm = 2.62e-02, feval = 00018\n",
      "iter = 0009, obj = 6.91912e-06, rnorm = 3.72e-03, gnorm = 1.63e-01, feval = 00020\n",
      "iter = 0010, obj = 4.01952e-06, rnorm = 2.84e-03, gnorm = 1.63e-02, feval = 00022\n",
      "iter = 0011, obj = 2.11271e-06, rnorm = 2.06e-03, gnorm = 1.05e-02, feval = 00024\n",
      "iter = 0012, obj = 1.27745e-06, rnorm = 1.60e-03, gnorm = 9.21e-03, feval = 00026\n",
      "iter = 0013, obj = 7.29006e-07, rnorm = 1.21e-03, gnorm = 4.91e-03, feval = 00028\n",
      "iter = 0014, obj = 7.11750e-07, rnorm = 1.19e-03, gnorm = 1.12e-02, feval = 00030\n",
      "iter = 0015, obj = 5.05659e-07, rnorm = 1.01e-03, gnorm = 3.72e-03, feval = 00032\n",
      "iter = 0016, obj = 4.81969e-07, rnorm = 9.82e-04, gnorm = 4.14e-02, feval = 00034\n",
      "iter = 0017, obj = 3.11747e-07, rnorm = 7.90e-04, gnorm = 3.05e-03, feval = 00036\n",
      "iter = 0018, obj = 1.95713e-07, rnorm = 6.26e-04, gnorm = 2.97e-03, feval = 00038\n",
      "iter = 0019, obj = 1.84423e-07, rnorm = 6.07e-04, gnorm = 5.12e-03, feval = 00040\n",
      "iter = 0020, obj = 8.70436e-08, rnorm = 4.17e-04, gnorm = 1.84e-03, feval = 00042\n",
      "iter = 0021, obj = 3.20175e-08, rnorm = 2.53e-04, gnorm = 1.14e-03, feval = 00044\n",
      "iter = 0022, obj = 3.45353e-09, rnorm = 8.31e-05, gnorm = 2.98e-03, feval = 00046\n",
      "iter = 0023, obj = 3.34364e-09, rnorm = 8.18e-05, gnorm = 4.64e-04, feval = 00048\n",
      "iter = 0024, obj = 1.19190e-09, rnorm = 4.88e-05, gnorm = 6.82e-04, feval = 00050\n",
      "iter = 0025, obj = 1.03111e-09, rnorm = 4.54e-05, gnorm = 7.41e-04, feval = 00052\n",
      "iter = 0026, obj = 8.94920e-10, rnorm = 4.23e-05, gnorm = 2.27e-04, feval = 00054\n",
      "iter = 0027, obj = 1.60089e-10, rnorm = 1.79e-05, gnorm = 9.85e-05, feval = 00056\n",
      "iter = 0028, obj = 6.28369e-11, rnorm = 1.12e-05, gnorm = 1.61e-04, feval = 00058\n",
      "iter = 0029, obj = 2.61186e-11, rnorm = 7.23e-06, gnorm = 3.82e-05, feval = 00060\n",
      "iter = 0030, obj = 2.60225e-11, rnorm = 7.21e-06, gnorm = 8.06e-05, feval = 00062\n",
      "iter = 0031, obj = 3.63557e-12, rnorm = 2.70e-06, gnorm = 1.32e-05, feval = 00064\n",
      "iter = 0032, obj = 1.94852e-12, rnorm = 1.97e-06, gnorm = 2.14e-05, feval = 00066\n",
      "iter = 0033, obj = 7.61545e-13, rnorm = 1.23e-06, gnorm = 1.59e-05, feval = 00068\n",
      "iter = 0034, obj = 6.68729e-13, rnorm = 1.16e-06, gnorm = 6.08e-06, feval = 00070\n",
      "iter = 0035, obj = 1.59933e-13, rnorm = 5.66e-07, gnorm = 2.52e-05, feval = 00072\n",
      "iter = 0036, obj = 7.97904e-14, rnorm = 3.99e-07, gnorm = 1.95e-06, feval = 00074\n",
      "iter = 0037, obj = 7.21828e-14, rnorm = 3.80e-07, gnorm = 2.13e-05, feval = 00076\n",
      "iter = 0038, obj = 5.25302e-14, rnorm = 3.24e-07, gnorm = 2.61e-06, feval = 00078\n",
      "iter = 0039, obj = 6.47567e-15, rnorm = 1.14e-07, gnorm = 5.35e-07, feval = 00080\n",
      "iter = 0040, obj = 8.89603e-16, rnorm = 4.22e-08, gnorm = 2.01e-07, feval = 00082\n",
      "iter = 0041, obj = 7.29891e-16, rnorm = 3.82e-08, gnorm = 4.40e-07, feval = 00084\n",
      "iter = 0042, obj = 3.47879e-17, rnorm = 8.34e-09, gnorm = 4.01e-08, feval = 00086\n",
      "iter = 0043, obj = 2.79105e-17, rnorm = 7.47e-09, gnorm = 4.75e-07, feval = 00088\n",
      "iter = 0044, obj = 2.33953e-17, rnorm = 6.84e-09, gnorm = 4.43e-08, feval = 00090\n",
      "iter = 0045, obj = 4.31584e-18, rnorm = 2.94e-09, gnorm = 1.06e-07, feval = 00092\n",
      "iter = 0046, obj = 2.98742e-18, rnorm = 2.44e-09, gnorm = 1.19e-08, feval = 00094\n",
      "iter = 0047, obj = 1.58361e-18, rnorm = 1.78e-09, gnorm = 1.28e-08, feval = 00096\n",
      "iter = 0048, obj = 3.42835e-19, rnorm = 8.28e-10, gnorm = 2.02e-08, feval = 00098\n",
      "iter = 0049, obj = 1.99441e-19, rnorm = 6.32e-10, gnorm = 4.35e-09, feval = 00100\n",
      "iter = 0050, obj = 1.71756e-19, rnorm = 5.86e-10, gnorm = 3.69e-09, feval = 00102\n",
      "iter = 0051, obj = 1.71184e-19, rnorm = 5.85e-10, gnorm = 5.80e-09, feval = 00104\n",
      "iter = 0052, obj = 2.64583e-20, rnorm = 2.30e-10, gnorm = 1.00e-09, feval = 00106\n",
      "iter = 0053, obj = 7.74450e-22, rnorm = 3.94e-11, gnorm = 1.56e-10, feval = 00108\n",
      "iter = 0054, obj = 2.03872e-22, rnorm = 2.02e-11, gnorm = 2.54e-10, feval = 00110\n",
      "iter = 0055, obj = 1.78246e-22, rnorm = 1.89e-11, gnorm = 3.80e-10, feval = 00112\n",
      "iter = 0056, obj = 7.42890e-23, rnorm = 1.22e-11, gnorm = 1.31e-10, feval = 00114\n",
      "iter = 0057, obj = 3.95726e-23, rnorm = 8.90e-12, gnorm = 9.41e-10, feval = 00116\n",
      "iter = 0058, obj = 2.40071e-23, rnorm = 6.93e-12, gnorm = 9.30e-11, feval = 00118\n",
      "iter = 0059, obj = 1.78082e-23, rnorm = 5.97e-12, gnorm = 2.50e-11, feval = 00120\n",
      "iter = 0060, obj = 6.45653e-25, rnorm = 1.14e-12, gnorm = 6.74e-12, feval = 00122\n",
      "iter = 0061, obj = 3.59993e-25, rnorm = 8.49e-13, gnorm = 4.41e-12, feval = 00124\n",
      "iter = 0062, obj = 2.59526e-25, rnorm = 7.20e-13, gnorm = 4.61e-12, feval = 00126\n",
      "iter = 0063, obj = 1.74865e-26, rnorm = 1.87e-13, gnorm = 1.09e-11, feval = 00128\n",
      "iter = 0064, obj = 1.59152e-26, rnorm = 1.78e-13, gnorm = 3.30e-12, feval = 00130\n",
      "iter = 0065, obj = 1.27604e-26, rnorm = 1.60e-13, gnorm = 6.39e-13, feval = 00132\n",
      "iter = 0066, obj = 7.41571e-27, rnorm = 1.22e-13, gnorm = 5.21e-12, feval = 00134\n",
      "iter = 0067, obj = 8.28667e-28, rnorm = 4.07e-14, gnorm = 2.16e-13, feval = 00136\n",
      "iter = 0068, obj = 3.97210e-28, rnorm = 2.82e-14, gnorm = 1.99e-13, feval = 00138\n",
      "iter = 0069, obj = 3.24570e-28, rnorm = 2.55e-14, gnorm = 1.68e-13, feval = 00140\n",
      "iter = 0070, obj = 1.74098e-29, rnorm = 5.90e-15, gnorm = 1.12e-13, feval = 00142\n",
      "iter = 0071, obj = 1.72515e-29, rnorm = 5.87e-15, gnorm = 2.46e-14, feval = 00144\n",
      "iter = 0072, obj = 1.41880e-30, rnorm = 1.68e-15, gnorm = 1.76e-14, feval = 00146\n",
      "iter = 0073, obj = 1.18171e-30, rnorm = 1.54e-15, gnorm = 9.02e-15, feval = 00148\n",
      "iter = 0074, obj = 6.23159e-31, rnorm = 1.12e-15, gnorm = 7.49e-15, feval = 00150\n",
      "iter = 0075, obj = 3.06845e-31, rnorm = 7.83e-16, gnorm = 7.88e-15, feval = 00152\n",
      "iter = 0076, obj = 2.95857e-31, rnorm = 7.69e-16, gnorm = 6.12e-15, feval = 00154\n",
      "iter = 0077, obj = 1.70751e-32, rnorm = 1.85e-16, gnorm = 4.23e-15, feval = 00156\n",
      "iter = 0078, obj = 1.68184e-32, rnorm = 1.83e-16, gnorm = 1.80e-15, feval = 00158\n",
      "iter = 0079, obj = 1.58239e-32, rnorm = 1.78e-16, gnorm = 7.58e-16, feval = 00160\n",
      "iter = 0080, obj = 2.09697e-33, rnorm = 6.48e-17, gnorm = 7.14e-16, feval = 00162\n",
      "iter = 0081, obj = 4.70108e-34, rnorm = 3.07e-17, gnorm = 3.48e-16, feval = 00164\n",
      "iter = 0082, obj = 2.38086e-34, rnorm = 2.18e-17, gnorm = 8.68e-17, feval = 00166\n",
      "iter = 0083, obj = 3.54451e-35, rnorm = 8.42e-18, gnorm = 5.61e-17, feval = 00168\n",
      "Objective function didn't reduce, will terminate solver:\n",
      "\tobj_new = 3.54451e-35\tobj_cur = 3.54451e-35\n",
      "##########################################################################################\n",
      "            CG Solver end\n",
      "##########################################################################################\n",
      "\n"
     ]
    }
   ],
   "source": [
    "VSP_prob_noise = o.LeastSquares(model_true.clone().zero(), noisy_data, VSP_10)\n",
    "LCGsolver.run(VSP_prob_noise,verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(z, 1.e-3*vel,label='true model',linewidth=2,linestyle='-.')\n",
    "ax.plot(z, 1.e-3/VSP_prob_noise.model.plot(),label='inverted model')\n",
    "ax.set_xlabel(\"depth [m]\"), ax.set_ylabel(\"vel [km/s]\")\n",
    "ax.set_ylim(3,4), ax.set_xlim(0,1000)\n",
    "fig.suptitle(\"$L_2$ inversion (noisy data)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A simple method to avoid these issues is to add prior knowledge to the inversion. In fact, we can change to problem to be solved and add a regularization term. We will test two kind of regularization: one in which a smooth constraint is added and another one where a prior model is assumed and employed in the regularization term.\n",
    "\n",
    "In the first case, the objective function to be minimized is the following:\n",
    "\\begin{align}\n",
    "\\phi_{smooth}(\\mathbf{m})=\\frac{1}{2}\\|G \\mathbf{m} - \\mathbf{d}_{obs} \\|_2^2 + \\frac{\\epsilon^2}{2} \\|D_1 \\mathbf{m}\\|_2^2,\n",
    "\\end{align}\n",
    "where $\\mathbf{m}$ represents the slowness model, $\\mathbf{d}_{obs}$ is the observed traveltimes, while $G$ and $D_1$ are the modeling and a first-order derivative operators, respectively. The variable $\\epsilon$ is the trade-off weight and is going to be set on the basis of trial and error."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epsilon Scale evaluation\n",
      "\tEpsilon balancing the data-space gradients is: 4.25e+04\n"
     ]
    }
   ],
   "source": [
    "# Instantiating regularization operator\n",
    "D1 = o.FirstDerivative(model_true, dz, stencil='forward')\n",
    "\n",
    "# Instantiating regularized problem with noise-free data\n",
    "VSP_prob_regD1 = o.LeastSquaresRegularized(model_true.clone().zero(),data_true,VSP_10,epsilon=1.0,reg_op=D1)\n",
    "\n",
    "# Estimating a value for the regularization weight epsilon\n",
    "epsilon_balance = VSP_prob_regD1.estimate_epsilon(True)\n",
    "VSP_prob_regD1.epsilon = epsilon_balance * 1e-4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "##########################################################################################\n",
      "            CG Solver\n",
      "    Restart folder: /tmp/restart_2022-04-22T01-51-41.263912/\n",
      "##########################################################################################\n",
      "\n",
      "iter = 0000, obj = 6.82008e-01, rnorm = 1.17e+00, gnorm = 2.37e+02, feval = 00002\n",
      "iter = 0001, obj = 5.39593e-03, rnorm = 1.04e-01, gnorm = 6.45e+00, feval = 00004\n",
      "iter = 0002, obj = 6.22693e-04, rnorm = 3.53e-02, gnorm = 1.27e+00, feval = 00006\n",
      "iter = 0003, obj = 1.08819e-04, rnorm = 1.48e-02, gnorm = 3.33e-01, feval = 00008\n",
      "iter = 0004, obj = 2.81852e-05, rnorm = 7.51e-03, gnorm = 1.27e-01, feval = 00010\n",
      "iter = 0005, obj = 9.58737e-06, rnorm = 4.38e-03, gnorm = 5.82e-02, feval = 00012\n",
      "iter = 0006, obj = 3.47967e-06, rnorm = 2.64e-03, gnorm = 2.82e-02, feval = 00014\n",
      "iter = 0007, obj = 1.36739e-06, rnorm = 1.65e-03, gnorm = 1.54e-02, feval = 00016\n",
      "iter = 0008, obj = 5.67808e-07, rnorm = 1.07e-03, gnorm = 8.86e-03, feval = 00018\n",
      "iter = 0009, obj = 4.93062e-07, rnorm = 9.93e-04, gnorm = 6.93e-02, feval = 00020\n",
      "iter = 0010, obj = 2.24808e-07, rnorm = 6.71e-04, gnorm = 5.00e-03, feval = 00022\n",
      "iter = 0011, obj = 8.68134e-08, rnorm = 4.17e-04, gnorm = 2.93e-03, feval = 00024\n",
      "iter = 0012, obj = 3.29251e-08, rnorm = 2.57e-04, gnorm = 1.68e-03, feval = 00026\n",
      "iter = 0013, obj = 1.18229e-08, rnorm = 1.54e-04, gnorm = 9.62e-04, feval = 00028\n",
      "iter = 0014, obj = 1.06256e-08, rnorm = 1.46e-04, gnorm = 2.94e-03, feval = 00030\n",
      "iter = 0015, obj = 4.27317e-09, rnorm = 9.24e-05, gnorm = 5.17e-04, feval = 00032\n",
      "iter = 0016, obj = 3.50503e-09, rnorm = 8.37e-05, gnorm = 6.68e-03, feval = 00034\n",
      "iter = 0017, obj = 1.68763e-09, rnorm = 5.81e-05, gnorm = 2.90e-04, feval = 00036\n",
      "iter = 0018, obj = 7.38765e-10, rnorm = 3.84e-05, gnorm = 2.21e-04, feval = 00038\n",
      "iter = 0019, obj = 7.07492e-10, rnorm = 3.76e-05, gnorm = 2.27e-04, feval = 00040\n",
      "iter = 0020, obj = 3.80067e-10, rnorm = 2.76e-05, gnorm = 9.39e-05, feval = 00042\n",
      "iter = 0021, obj = 2.50347e-10, rnorm = 2.24e-05, gnorm = 5.79e-05, feval = 00044\n",
      "iter = 0022, obj = 1.90960e-10, rnorm = 1.95e-05, gnorm = 6.28e-05, feval = 00046\n",
      "iter = 0023, obj = 1.90408e-10, rnorm = 1.95e-05, gnorm = 1.91e-04, feval = 00048\n",
      "iter = 0024, obj = 1.87113e-10, rnorm = 1.93e-05, gnorm = 5.06e-05, feval = 00050\n",
      "iter = 0025, obj = 1.56292e-10, rnorm = 1.77e-05, gnorm = 1.53e-04, feval = 00052\n",
      "iter = 0026, obj = 1.53412e-10, rnorm = 1.75e-05, gnorm = 3.07e-05, feval = 00054\n",
      "iter = 0027, obj = 1.31044e-10, rnorm = 1.62e-05, gnorm = 2.41e-05, feval = 00056\n",
      "iter = 0028, obj = 1.17242e-10, rnorm = 1.53e-05, gnorm = 4.88e-05, feval = 00058\n",
      "iter = 0029, obj = 1.14014e-10, rnorm = 1.51e-05, gnorm = 2.07e-05, feval = 00060\n",
      "iter = 0030, obj = 1.02918e-10, rnorm = 1.43e-05, gnorm = 2.34e-04, feval = 00062\n",
      "iter = 0031, obj = 1.02212e-10, rnorm = 1.43e-05, gnorm = 1.61e-05, feval = 00064\n",
      "iter = 0032, obj = 9.70557e-11, rnorm = 1.39e-05, gnorm = 3.50e-05, feval = 00066\n",
      "iter = 0033, obj = 9.48105e-11, rnorm = 1.38e-05, gnorm = 3.98e-05, feval = 00068\n",
      "iter = 0034, obj = 9.41251e-11, rnorm = 1.37e-05, gnorm = 1.21e-05, feval = 00070\n",
      "iter = 0035, obj = 9.01189e-11, rnorm = 1.34e-05, gnorm = 9.99e-06, feval = 00072\n",
      "iter = 0036, obj = 9.00799e-11, rnorm = 1.34e-05, gnorm = 1.59e-05, feval = 00074\n",
      "iter = 0037, obj = 8.89976e-11, rnorm = 1.33e-05, gnorm = 1.65e-05, feval = 00076\n",
      "iter = 0038, obj = 8.82799e-11, rnorm = 1.33e-05, gnorm = 1.68e-04, feval = 00078\n",
      "iter = 0039, obj = 8.76289e-11, rnorm = 1.32e-05, gnorm = 6.10e-06, feval = 00080\n",
      "iter = 0040, obj = 8.62744e-11, rnorm = 1.31e-05, gnorm = 4.67e-06, feval = 00082\n",
      "iter = 0041, obj = 8.61514e-11, rnorm = 1.31e-05, gnorm = 1.25e-05, feval = 00084\n",
      "iter = 0042, obj = 8.55689e-11, rnorm = 1.31e-05, gnorm = 3.86e-06, feval = 00086\n",
      "iter = 0043, obj = 8.54637e-11, rnorm = 1.31e-05, gnorm = 4.51e-06, feval = 00088\n",
      "iter = 0044, obj = 8.50622e-11, rnorm = 1.30e-05, gnorm = 1.21e-05, feval = 00090\n",
      "iter = 0045, obj = 8.50604e-11, rnorm = 1.30e-05, gnorm = 2.81e-06, feval = 00092\n",
      "iter = 0046, obj = 8.48370e-11, rnorm = 1.30e-05, gnorm = 2.83e-05, feval = 00094\n",
      "iter = 0047, obj = 8.46938e-11, rnorm = 1.30e-05, gnorm = 2.39e-06, feval = 00096\n",
      "iter = 0048, obj = 8.46810e-11, rnorm = 1.30e-05, gnorm = 5.85e-06, feval = 00098\n",
      "iter = 0049, obj = 8.45297e-11, rnorm = 1.30e-05, gnorm = 3.59e-06, feval = 00100\n",
      "iter = 0050, obj = 8.44569e-11, rnorm = 1.30e-05, gnorm = 1.67e-06, feval = 00102\n",
      "iter = 0051, obj = 8.44097e-11, rnorm = 1.30e-05, gnorm = 5.29e-06, feval = 00104\n",
      "iter = 0052, obj = 8.43920e-11, rnorm = 1.30e-05, gnorm = 3.27e-05, feval = 00106\n",
      "iter = 0053, obj = 8.43408e-11, rnorm = 1.30e-05, gnorm = 1.20e-06, feval = 00108\n",
      "iter = 0054, obj = 8.42589e-11, rnorm = 1.30e-05, gnorm = 1.29e-06, feval = 00110\n",
      "iter = 0055, obj = 8.42386e-11, rnorm = 1.30e-05, gnorm = 1.56e-06, feval = 00112\n",
      "iter = 0056, obj = 8.42179e-11, rnorm = 1.30e-05, gnorm = 9.16e-06, feval = 00114\n",
      "iter = 0057, obj = 8.42009e-11, rnorm = 1.30e-05, gnorm = 2.44e-06, feval = 00116\n",
      "iter = 0058, obj = 8.41895e-11, rnorm = 1.30e-05, gnorm = 1.06e-06, feval = 00118\n",
      "iter = 0059, obj = 8.41884e-11, rnorm = 1.30e-05, gnorm = 2.46e-06, feval = 00120\n",
      "iter = 0060, obj = 8.41883e-11, rnorm = 1.30e-05, gnorm = 9.42e-07, feval = 00122\n",
      "iter = 0061, obj = 8.41686e-11, rnorm = 1.30e-05, gnorm = 4.85e-07, feval = 00124\n",
      "iter = 0062, obj = 8.41634e-11, rnorm = 1.30e-05, gnorm = 2.03e-06, feval = 00126\n",
      "iter = 0063, obj = 8.41615e-11, rnorm = 1.30e-05, gnorm = 8.32e-07, feval = 00128\n",
      "iter = 0064, obj = 8.41542e-11, rnorm = 1.30e-05, gnorm = 6.27e-07, feval = 00130\n",
      "iter = 0065, obj = 8.41528e-11, rnorm = 1.30e-05, gnorm = 4.55e-07, feval = 00132\n",
      "iter = 0066, obj = 8.41463e-11, rnorm = 1.30e-05, gnorm = 8.63e-06, feval = 00134\n",
      "iter = 0067, obj = 8.41452e-11, rnorm = 1.30e-05, gnorm = 3.20e-07, feval = 00136\n",
      "iter = 0068, obj = 8.41452e-11, rnorm = 1.30e-05, gnorm = 6.19e-07, feval = 00138\n",
      "iter = 0069, obj = 8.41396e-11, rnorm = 1.30e-05, gnorm = 2.58e-07, feval = 00140\n",
      "iter = 0070, obj = 8.41368e-11, rnorm = 1.30e-05, gnorm = 3.82e-07, feval = 00142\n",
      "iter = 0071, obj = 8.41358e-11, rnorm = 1.30e-05, gnorm = 5.84e-07, feval = 00144\n",
      "iter = 0072, obj = 8.41352e-11, rnorm = 1.30e-05, gnorm = 1.76e-07, feval = 00146\n",
      "iter = 0073, obj = 8.41346e-11, rnorm = 1.30e-05, gnorm = 5.09e-06, feval = 00148\n",
      "iter = 0074, obj = 8.41340e-11, rnorm = 1.30e-05, gnorm = 2.74e-07, feval = 00150\n",
      "iter = 0075, obj = 8.41338e-11, rnorm = 1.30e-05, gnorm = 2.86e-07, feval = 00152\n",
      "iter = 0076, obj = 8.41337e-11, rnorm = 1.30e-05, gnorm = 1.20e-07, feval = 00154\n",
      "iter = 0077, obj = 8.41336e-11, rnorm = 1.30e-05, gnorm = 5.01e-07, feval = 00156\n",
      "iter = 0078, obj = 8.41331e-11, rnorm = 1.30e-05, gnorm = 6.33e-07, feval = 00158\n",
      "iter = 0079, obj = 8.41330e-11, rnorm = 1.30e-05, gnorm = 1.04e-07, feval = 00160\n",
      "iter = 0080, obj = 8.41328e-11, rnorm = 1.30e-05, gnorm = 1.15e-07, feval = 00162\n",
      "iter = 0081, obj = 8.41328e-11, rnorm = 1.30e-05, gnorm = 4.67e-07, feval = 00164\n",
      "iter = 0082, obj = 8.41325e-11, rnorm = 1.30e-05, gnorm = 9.98e-08, feval = 00166\n",
      "iter = 0083, obj = 8.41324e-11, rnorm = 1.30e-05, gnorm = 7.72e-08, feval = 00168\n",
      "iter = 0084, obj = 8.41322e-11, rnorm = 1.30e-05, gnorm = 5.16e-08, feval = 00170\n",
      "iter = 0085, obj = 8.41321e-11, rnorm = 1.30e-05, gnorm = 9.91e-08, feval = 00172\n",
      "iter = 0086, obj = 8.41320e-11, rnorm = 1.30e-05, gnorm = 4.39e-08, feval = 00174\n",
      "iter = 0087, obj = 8.41320e-11, rnorm = 1.30e-05, gnorm = 3.12e-07, feval = 00176\n",
      "iter = 0088, obj = 8.41320e-11, rnorm = 1.30e-05, gnorm = 2.56e-07, feval = 00178\n",
      "iter = 0089, obj = 8.41320e-11, rnorm = 1.30e-05, gnorm = 4.29e-08, feval = 00180\n",
      "iter = 0090, obj = 8.41319e-11, rnorm = 1.30e-05, gnorm = 8.99e-08, feval = 00182\n",
      "iter = 0091, obj = 8.41319e-11, rnorm = 1.30e-05, gnorm = 1.21e-07, feval = 00184\n",
      "iter = 0092, obj = 8.41319e-11, rnorm = 1.30e-05, gnorm = 2.65e-08, feval = 00186\n",
      "iter = 0093, obj = 8.41319e-11, rnorm = 1.30e-05, gnorm = 1.02e-07, feval = 00188\n",
      "iter = 0094, obj = 8.41319e-11, rnorm = 1.30e-05, gnorm = 8.24e-08, feval = 00190\n",
      "iter = 0095, obj = 8.41319e-11, rnorm = 1.30e-05, gnorm = 3.18e-07, feval = 00192\n",
      "iter = 0096, obj = 8.41319e-11, rnorm = 1.30e-05, gnorm = 1.76e-08, feval = 00194\n",
      "iter = 0097, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.67e-08, feval = 00196\n",
      "iter = 0098, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 4.88e-08, feval = 00198\n",
      "iter = 0099, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.81e-08, feval = 00200\n",
      "iter = 0100, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.69e-08, feval = 00202\n",
      "iter = 0101, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.45e-07, feval = 00204\n",
      "iter = 0102, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 9.32e-09, feval = 00206\n",
      "iter = 0103, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 9.17e-09, feval = 00208\n",
      "iter = 0104, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.58e-08, feval = 00210\n",
      "iter = 0105, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.55e-08, feval = 00212\n",
      "iter = 0106, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.18e-08, feval = 00214\n",
      "iter = 0107, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.40e-08, feval = 00216\n",
      "iter = 0108, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.96e-08, feval = 00218\n",
      "iter = 0109, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 8.75e-09, feval = 00220\n",
      "iter = 0110, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.35e-08, feval = 00222\n",
      "iter = 0111, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 7.43e-09, feval = 00224\n",
      "iter = 0112, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 5.70e-09, feval = 00226\n",
      "iter = 0113, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 3.27e-09, feval = 00228\n",
      "iter = 0114, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.83e-08, feval = 00230\n",
      "iter = 0115, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 9.81e-09, feval = 00232\n",
      "iter = 0116, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 2.34e-09, feval = 00234\n",
      "iter = 0117, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.14e-08, feval = 00236\n",
      "iter = 0118, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 3.32e-09, feval = 00238\n",
      "iter = 0119, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 5.22e-09, feval = 00240\n",
      "iter = 0120, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 3.58e-09, feval = 00242\n",
      "iter = 0121, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 4.15e-08, feval = 00244\n",
      "iter = 0122, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.92e-09, feval = 00246\n",
      "iter = 0123, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.28e-09, feval = 00248\n",
      "iter = 0124, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 2.65e-09, feval = 00250\n",
      "iter = 0125, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 4.62e-09, feval = 00252\n",
      "iter = 0126, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.07e-09, feval = 00254\n",
      "iter = 0127, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 3.91e-09, feval = 00256\n",
      "iter = 0128, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 4.78e-09, feval = 00258\n",
      "iter = 0129, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.16e-09, feval = 00260\n",
      "iter = 0130, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 2.64e-09, feval = 00262\n",
      "iter = 0131, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 6.21e-10, feval = 00264\n",
      "iter = 0132, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 2.24e-09, feval = 00266\n",
      "iter = 0133, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 6.20e-09, feval = 00268\n",
      "iter = 0134, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 7.83e-10, feval = 00270\n",
      "iter = 0135, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 5.47e-10, feval = 00272\n",
      "iter = 0136, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 4.87e-10, feval = 00274\n",
      "iter = 0137, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 3.71e-09, feval = 00276\n",
      "iter = 0138, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 4.21e-10, feval = 00278\n",
      "iter = 0139, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 4.65e-10, feval = 00280\n",
      "iter = 0140, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 5.45e-09, feval = 00282\n",
      "iter = 0141, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 4.69e-10, feval = 00284\n",
      "iter = 0142, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 5.36e-10, feval = 00286\n",
      "iter = 0143, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 4.09e-10, feval = 00288\n",
      "iter = 0144, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 2.44e-10, feval = 00290\n",
      "iter = 0145, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 5.27e-10, feval = 00292\n",
      "iter = 0146, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.59e-09, feval = 00294\n",
      "iter = 0147, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 4.06e-10, feval = 00296\n",
      "iter = 0148, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 6.21e-10, feval = 00298\n",
      "iter = 0149, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.94e-10, feval = 00300\n",
      "iter = 0150, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.37e-10, feval = 00302\n",
      "iter = 0151, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 2.80e-10, feval = 00304\n",
      "iter = 0152, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 9.90e-11, feval = 00306\n",
      "iter = 0153, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 2.45e-09, feval = 00308\n",
      "iter = 0154, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 8.29e-11, feval = 00310\n",
      "iter = 0155, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.29e-10, feval = 00312\n",
      "iter = 0156, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 4.74e-10, feval = 00314\n",
      "iter = 0157, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.05e-10, feval = 00316\n",
      "iter = 0158, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.85e-10, feval = 00318\n",
      "iter = 0159, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 9.36e-11, feval = 00320\n",
      "iter = 0160, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 3.82e-10, feval = 00322\n",
      "iter = 0161, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.06e-10, feval = 00324\n",
      "iter = 0162, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 7.18e-11, feval = 00326\n",
      "iter = 0163, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 3.72e-11, feval = 00328\n",
      "iter = 0164, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 8.60e-11, feval = 00330\n",
      "iter = 0165, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.72e-10, feval = 00332\n",
      "iter = 0166, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 8.74e-10, feval = 00334\n",
      "iter = 0167, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 3.00e-11, feval = 00336\n",
      "iter = 0168, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 2.50e-11, feval = 00338\n",
      "iter = 0169, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 6.25e-11, feval = 00340\n",
      "iter = 0170, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 9.44e-11, feval = 00342\n",
      "iter = 0171, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 7.27e-11, feval = 00344\n",
      "iter = 0172, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 3.10e-10, feval = 00346\n",
      "iter = 0173, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.72e-11, feval = 00348\n",
      "iter = 0174, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 4.45e-11, feval = 00350\n",
      "iter = 0175, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.27e-10, feval = 00352\n",
      "iter = 0176, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 5.42e-11, feval = 00354\n",
      "iter = 0177, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.55e-11, feval = 00356\n",
      "iter = 0178, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.36e-11, feval = 00358\n",
      "iter = 0179, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 2.21e-10, feval = 00360\n",
      "iter = 0180, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 3.75e-11, feval = 00362\n",
      "iter = 0181, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 8.01e-12, feval = 00364\n",
      "iter = 0182, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.80e-11, feval = 00366\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter = 0183, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 3.15e-11, feval = 00368\n",
      "iter = 0184, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 5.85e-11, feval = 00370\n",
      "iter = 0185, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 9.09e-12, feval = 00372\n",
      "iter = 0186, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.00e-11, feval = 00374\n",
      "iter = 0187, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 9.54e-12, feval = 00376\n",
      "iter = 0188, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 4.98e-12, feval = 00378\n",
      "iter = 0189, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.35e-11, feval = 00380\n",
      "iter = 0190, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 2.18e-11, feval = 00382\n",
      "iter = 0191, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.19e-11, feval = 00384\n",
      "iter = 0192, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 4.29e-12, feval = 00386\n",
      "iter = 0193, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.23e-11, feval = 00388\n",
      "iter = 0194, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 2.41e-12, feval = 00390\n",
      "iter = 0195, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.62e-11, feval = 00392\n",
      "iter = 0196, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 5.42e-11, feval = 00394\n",
      "iter = 0197, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 2.86e-12, feval = 00396\n",
      "iter = 0198, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 2.67e-12, feval = 00398\n",
      "iter = 0199, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 3.69e-12, feval = 00400\n",
      "iter = 0200, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 4.12e-12, feval = 00402\n",
      "iter = 0201, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 2.82e-11, feval = 00404\n",
      "iter = 0202, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.70e-11, feval = 00406\n",
      "iter = 0203, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 2.46e-12, feval = 00408\n",
      "iter = 0204, obj = 8.41318e-11, rnorm = 1.30e-05, gnorm = 1.89e-12, feval = 00410\n",
      "Objective function didn't reduce, will terminate solver:\n",
      "\tobj_new = 8.41318e-11\tobj_cur = 8.41318e-11\n",
      "##########################################################################################\n",
      "            CG Solver end\n",
      "##########################################################################################\n",
      "\n"
     ]
    }
   ],
   "source": [
    "LCGsolver.run(VSP_prob_regD1, verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(z, 1.e-3*vel,label='true model',linewidth=2,linestyle='-.')\n",
    "ax.plot(z, 1.e-3/VSP_prob_regD1.model.plot(),label='inverted model')\n",
    "ax.set_xlabel(\"depth [m]\"), ax.set_ylabel(\"vel [km/s]\")\n",
    "ax.set_ylim(3,4), ax.set_xlim(0,1000)\n",
    "fig.suptitle(\"$L_2$ regularized inversion (noise-free)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epsilon Scale evaluation\n",
      "\tEpsilon balancing the data-space gradients is: 4.25e+04\n"
     ]
    }
   ],
   "source": [
    "# Instantiating regularized problem with noisy data\n",
    "VSP_prob_regD1 = o.LeastSquaresRegularized(model_true.clone().zero(), noisy_data,VSP_10,epsilon=1.0,reg_op=D1)\n",
    "\n",
    "# Estimating a value for the regularization weight epsilon\n",
    "epsilon_balance = VSP_prob_regD1.estimate_epsilon(True)\n",
    "VSP_prob_regD1.epsilon = epsilon_balance * 5e-2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "##########################################################################################\n",
      "            CG Solver\n",
      "    Restart folder: /tmp/restart_2022-04-22T01-51-41.263912/\n",
      "##########################################################################################\n",
      "\n",
      "iter = 0000, obj = 6.80620e-01, rnorm = 1.17e+00, gnorm = 2.37e+02, feval = 00002\n",
      "iter = 0001, obj = 7.18211e-03, rnorm = 1.20e-01, gnorm = 8.73e+01, feval = 00004\n",
      "iter = 0002, obj = 6.04819e-03, rnorm = 1.10e-01, gnorm = 3.00e+01, feval = 00006\n",
      "iter = 0003, obj = 5.79790e-03, rnorm = 1.08e-01, gnorm = 1.96e+01, feval = 00008\n",
      "iter = 0004, obj = 5.66089e-03, rnorm = 1.06e-01, gnorm = 1.64e+01, feval = 00010\n",
      "iter = 0005, obj = 5.54713e-03, rnorm = 1.05e-01, gnorm = 1.61e+01, feval = 00012\n",
      "iter = 0006, obj = 5.47938e-03, rnorm = 1.05e-01, gnorm = 8.97e+00, feval = 00014\n",
      "iter = 0007, obj = 4.84232e-03, rnorm = 9.84e-02, gnorm = 4.94e+01, feval = 00016\n",
      "iter = 0008, obj = 3.44566e-03, rnorm = 8.30e-02, gnorm = 5.56e+01, feval = 00018\n",
      "iter = 0009, obj = 2.28948e-03, rnorm = 6.77e-02, gnorm = 4.42e+01, feval = 00020\n",
      "iter = 0010, obj = 1.64106e-03, rnorm = 5.73e-02, gnorm = 3.20e+01, feval = 00022\n",
      "iter = 0011, obj = 1.15589e-03, rnorm = 4.81e-02, gnorm = 2.73e+01, feval = 00024\n",
      "iter = 0012, obj = 9.79724e-04, rnorm = 4.43e-02, gnorm = 1.45e+01, feval = 00026\n",
      "iter = 0013, obj = 9.16679e-04, rnorm = 4.28e-02, gnorm = 9.80e+00, feval = 00028\n",
      "iter = 0014, obj = 8.84591e-04, rnorm = 4.21e-02, gnorm = 7.41e+00, feval = 00030\n",
      "iter = 0015, obj = 8.64916e-04, rnorm = 4.16e-02, gnorm = 6.03e+00, feval = 00032\n",
      "iter = 0016, obj = 8.53878e-04, rnorm = 4.13e-02, gnorm = 4.06e+00, feval = 00034\n",
      "iter = 0017, obj = 8.46508e-04, rnorm = 4.11e-02, gnorm = 4.11e+00, feval = 00036\n",
      "iter = 0018, obj = 8.38829e-04, rnorm = 4.10e-02, gnorm = 4.23e+00, feval = 00038\n",
      "iter = 0019, obj = 8.30586e-04, rnorm = 4.08e-02, gnorm = 4.41e+00, feval = 00040\n",
      "iter = 0020, obj = 8.21498e-04, rnorm = 4.05e-02, gnorm = 4.66e+00, feval = 00042\n",
      "iter = 0021, obj = 8.07958e-04, rnorm = 4.02e-02, gnorm = 6.18e+00, feval = 00044\n",
      "iter = 0022, obj = 7.91404e-04, rnorm = 3.98e-02, gnorm = 6.08e+00, feval = 00046\n",
      "iter = 0023, obj = 7.74983e-04, rnorm = 3.94e-02, gnorm = 6.13e+00, feval = 00048\n",
      "iter = 0024, obj = 7.57992e-04, rnorm = 3.89e-02, gnorm = 6.29e+00, feval = 00050\n",
      "iter = 0025, obj = 7.39795e-04, rnorm = 3.85e-02, gnorm = 6.55e+00, feval = 00052\n",
      "iter = 0026, obj = 7.22643e-04, rnorm = 3.80e-02, gnorm = 5.96e+00, feval = 00054\n",
      "iter = 0027, obj = 7.04859e-04, rnorm = 3.75e-02, gnorm = 6.69e+00, feval = 00056\n",
      "iter = 0028, obj = 6.82776e-04, rnorm = 3.70e-02, gnorm = 7.40e+00, feval = 00058\n",
      "iter = 0029, obj = 6.56159e-04, rnorm = 3.62e-02, gnorm = 8.07e+00, feval = 00060\n",
      "iter = 0030, obj = 6.25090e-04, rnorm = 3.54e-02, gnorm = 8.65e+00, feval = 00062\n",
      "iter = 0031, obj = 5.82758e-04, rnorm = 3.41e-02, gnorm = 1.06e+01, feval = 00064\n",
      "iter = 0032, obj = 5.33728e-04, rnorm = 3.27e-02, gnorm = 1.04e+01, feval = 00066\n",
      "iter = 0033, obj = 4.87321e-04, rnorm = 3.12e-02, gnorm = 1.01e+01, feval = 00068\n",
      "iter = 0034, obj = 4.44172e-04, rnorm = 2.98e-02, gnorm = 9.66e+00, feval = 00070\n",
      "iter = 0035, obj = 4.04687e-04, rnorm = 2.84e-02, gnorm = 9.20e+00, feval = 00072\n",
      "iter = 0036, obj = 3.72448e-04, rnorm = 2.73e-02, gnorm = 7.89e+00, feval = 00074\n",
      "iter = 0037, obj = 3.45582e-04, rnorm = 2.63e-02, gnorm = 7.66e+00, feval = 00076\n",
      "iter = 0038, obj = 3.20568e-04, rnorm = 2.53e-02, gnorm = 7.35e+00, feval = 00078\n",
      "iter = 0039, obj = 2.97819e-04, rnorm = 2.44e-02, gnorm = 6.97e+00, feval = 00080\n",
      "iter = 0040, obj = 2.77530e-04, rnorm = 2.36e-02, gnorm = 6.55e+00, feval = 00082\n",
      "iter = 0041, obj = 2.57289e-04, rnorm = 2.27e-02, gnorm = 6.86e+00, feval = 00084\n",
      "iter = 0042, obj = 2.38574e-04, rnorm = 2.18e-02, gnorm = 6.14e+00, feval = 00086\n",
      "iter = 0043, obj = 2.23562e-04, rnorm = 2.11e-02, gnorm = 5.50e+00, feval = 00088\n",
      "iter = 0044, obj = 2.11491e-04, rnorm = 2.06e-02, gnorm = 4.94e+00, feval = 00090\n",
      "iter = 0045, obj = 2.01718e-04, rnorm = 2.01e-02, gnorm = 4.46e+00, feval = 00092\n",
      "iter = 0046, obj = 1.94251e-04, rnorm = 1.97e-02, gnorm = 3.77e+00, feval = 00094\n",
      "iter = 0047, obj = 1.88427e-04, rnorm = 1.94e-02, gnorm = 3.49e+00, feval = 00096\n",
      "iter = 0048, obj = 1.83431e-04, rnorm = 1.92e-02, gnorm = 3.24e+00, feval = 00098\n",
      "iter = 0049, obj = 1.79107e-04, rnorm = 1.89e-02, gnorm = 3.02e+00, feval = 00100\n",
      "iter = 0050, obj = 1.75324e-04, rnorm = 1.87e-02, gnorm = 2.83e+00, feval = 00102\n",
      "iter = 0051, obj = 1.71535e-04, rnorm = 1.85e-02, gnorm = 3.00e+00, feval = 00104\n",
      "iter = 0052, obj = 1.67811e-04, rnorm = 1.83e-02, gnorm = 2.81e+00, feval = 00106\n",
      "iter = 0053, obj = 1.64516e-04, rnorm = 1.81e-02, gnorm = 2.65e+00, feval = 00108\n",
      "iter = 0054, obj = 1.61547e-04, rnorm = 1.80e-02, gnorm = 2.53e+00, feval = 00110\n",
      "iter = 0055, obj = 1.58810e-04, rnorm = 1.78e-02, gnorm = 2.45e+00, feval = 00112\n",
      "iter = 0056, obj = 1.56433e-04, rnorm = 1.77e-02, gnorm = 2.20e+00, feval = 00114\n",
      "iter = 0057, obj = 1.54303e-04, rnorm = 1.76e-02, gnorm = 2.19e+00, feval = 00116\n",
      "iter = 0058, obj = 1.52164e-04, rnorm = 1.74e-02, gnorm = 2.20e+00, feval = 00118\n",
      "iter = 0059, obj = 1.49989e-04, rnorm = 1.73e-02, gnorm = 2.23e+00, feval = 00120\n",
      "iter = 0060, obj = 1.47747e-04, rnorm = 1.72e-02, gnorm = 2.27e+00, feval = 00122\n",
      "iter = 0061, obj = 1.45089e-04, rnorm = 1.70e-02, gnorm = 2.61e+00, feval = 00124\n",
      "iter = 0062, obj = 1.42023e-04, rnorm = 1.69e-02, gnorm = 2.65e+00, feval = 00126\n",
      "iter = 0063, obj = 1.38851e-04, rnorm = 1.67e-02, gnorm = 2.70e+00, feval = 00128\n",
      "iter = 0064, obj = 1.35540e-04, rnorm = 1.65e-02, gnorm = 2.77e+00, feval = 00130\n",
      "iter = 0065, obj = 1.32053e-04, rnorm = 1.63e-02, gnorm = 2.85e+00, feval = 00132\n",
      "iter = 0066, obj = 1.28609e-04, rnorm = 1.60e-02, gnorm = 2.73e+00, feval = 00134\n",
      "iter = 0067, obj = 1.25158e-04, rnorm = 1.58e-02, gnorm = 2.85e+00, feval = 00136\n",
      "iter = 0068, obj = 1.21433e-04, rnorm = 1.56e-02, gnorm = 2.95e+00, feval = 00138\n",
      "iter = 0069, obj = 1.17450e-04, rnorm = 1.53e-02, gnorm = 3.04e+00, feval = 00140\n",
      "iter = 0070, obj = 1.13234e-04, rnorm = 1.50e-02, gnorm = 3.12e+00, feval = 00142\n",
      "iter = 0071, obj = 1.08267e-04, rnorm = 1.47e-02, gnorm = 3.55e+00, feval = 00144\n",
      "iter = 0072, obj = 1.02665e-04, rnorm = 1.43e-02, gnorm = 3.56e+00, feval = 00146\n",
      "iter = 0073, obj = 9.70724e-05, rnorm = 1.39e-02, gnorm = 3.54e+00, feval = 00148\n",
      "iter = 0074, obj = 9.15660e-05, rnorm = 1.35e-02, gnorm = 3.51e+00, feval = 00150\n",
      "iter = 0075, obj = 8.61977e-05, rnorm = 1.31e-02, gnorm = 3.45e+00, feval = 00152\n",
      "iter = 0076, obj = 8.13462e-05, rnorm = 1.28e-02, gnorm = 3.16e+00, feval = 00154\n",
      "iter = 0077, obj = 7.69829e-05, rnorm = 1.24e-02, gnorm = 3.11e+00, feval = 00156\n",
      "iter = 0078, obj = 7.28234e-05, rnorm = 1.21e-02, gnorm = 3.02e+00, feval = 00158\n",
      "iter = 0079, obj = 6.89327e-05, rnorm = 1.17e-02, gnorm = 2.91e+00, feval = 00160\n",
      "iter = 0080, obj = 6.53498e-05, rnorm = 1.14e-02, gnorm = 2.78e+00, feval = 00162\n",
      "iter = 0081, obj = 6.17264e-05, rnorm = 1.11e-02, gnorm = 2.92e+00, feval = 00164\n",
      "iter = 0082, obj = 5.81709e-05, rnorm = 1.08e-02, gnorm = 2.74e+00, feval = 00166\n",
      "iter = 0083, obj = 5.50551e-05, rnorm = 1.05e-02, gnorm = 2.56e+00, feval = 00168\n",
      "iter = 0084, obj = 5.23440e-05, rnorm = 1.02e-02, gnorm = 2.39e+00, feval = 00170\n",
      "iter = 0085, obj = 4.99864e-05, rnorm = 1.00e-02, gnorm = 2.23e+00, feval = 00172\n",
      "iter = 0086, obj = 4.80341e-05, rnorm = 9.80e-03, gnorm = 1.97e+00, feval = 00174\n",
      "iter = 0087, obj = 4.64137e-05, rnorm = 9.63e-03, gnorm = 1.85e+00, feval = 00176\n",
      "iter = 0088, obj = 4.49921e-05, rnorm = 9.49e-03, gnorm = 1.73e+00, feval = 00178\n",
      "iter = 0089, obj = 4.37520e-05, rnorm = 9.35e-03, gnorm = 1.62e+00, feval = 00180\n",
      "iter = 0090, obj = 4.26712e-05, rnorm = 9.24e-03, gnorm = 1.51e+00, feval = 00182\n",
      "iter = 0091, obj = 4.16487e-05, rnorm = 9.13e-03, gnorm = 1.53e+00, feval = 00184\n",
      "iter = 0092, obj = 4.06821e-05, rnorm = 9.02e-03, gnorm = 1.43e+00, feval = 00186\n",
      "iter = 0093, obj = 3.98381e-05, rnorm = 8.93e-03, gnorm = 1.33e+00, feval = 00188\n",
      "iter = 0094, obj = 3.91017e-05, rnorm = 8.84e-03, gnorm = 1.25e+00, feval = 00190\n",
      "iter = 0095, obj = 3.84559e-05, rnorm = 8.77e-03, gnorm = 1.17e+00, feval = 00192\n",
      "iter = 0096, obj = 3.79003e-05, rnorm = 8.71e-03, gnorm = 1.07e+00, feval = 00194\n",
      "iter = 0097, obj = 3.74176e-05, rnorm = 8.65e-03, gnorm = 1.02e+00, feval = 00196\n",
      "iter = 0098, obj = 3.69837e-05, rnorm = 8.60e-03, gnorm = 9.63e-01, feval = 00198\n",
      "iter = 0099, obj = 3.65934e-05, rnorm = 8.55e-03, gnorm = 9.15e-01, feval = 00200\n",
      "iter = 0100, obj = 3.62399e-05, rnorm = 8.51e-03, gnorm = 8.72e-01, feval = 00202\n",
      "iter = 0101, obj = 3.58974e-05, rnorm = 8.47e-03, gnorm = 8.86e-01, feval = 00204\n",
      "iter = 0102, obj = 3.55628e-05, rnorm = 8.43e-03, gnorm = 8.53e-01, feval = 00206\n",
      "iter = 0103, obj = 3.52540e-05, rnorm = 8.40e-03, gnorm = 8.17e-01, feval = 00208\n",
      "iter = 0104, obj = 3.49698e-05, rnorm = 8.36e-03, gnorm = 7.85e-01, feval = 00210\n",
      "iter = 0105, obj = 3.47080e-05, rnorm = 8.33e-03, gnorm = 7.53e-01, feval = 00212\n",
      "iter = 0106, obj = 3.44727e-05, rnorm = 8.30e-03, gnorm = 7.04e-01, feval = 00214\n",
      "iter = 0107, obj = 3.42604e-05, rnorm = 8.28e-03, gnorm = 6.80e-01, feval = 00216\n",
      "iter = 0108, obj = 3.40636e-05, rnorm = 8.25e-03, gnorm = 6.52e-01, feval = 00218\n",
      "iter = 0109, obj = 3.38832e-05, rnorm = 8.23e-03, gnorm = 6.24e-01, feval = 00220\n",
      "iter = 0110, obj = 3.37180e-05, rnorm = 8.21e-03, gnorm = 5.97e-01, feval = 00222\n",
      "iter = 0111, obj = 3.35562e-05, rnorm = 8.19e-03, gnorm = 6.11e-01, feval = 00224\n",
      "iter = 0112, obj = 3.33974e-05, rnorm = 8.17e-03, gnorm = 5.86e-01, feval = 00226\n",
      "iter = 0113, obj = 3.32521e-05, rnorm = 8.16e-03, gnorm = 5.59e-01, feval = 00228\n",
      "iter = 0114, obj = 3.31203e-05, rnorm = 8.14e-03, gnorm = 5.32e-01, feval = 00230\n",
      "iter = 0115, obj = 3.30011e-05, rnorm = 8.12e-03, gnorm = 5.05e-01, feval = 00232\n",
      "iter = 0116, obj = 3.28969e-05, rnorm = 8.11e-03, gnorm = 4.64e-01, feval = 00234\n",
      "iter = 0117, obj = 3.28058e-05, rnorm = 8.10e-03, gnorm = 4.42e-01, feval = 00236\n",
      "iter = 0118, obj = 3.27241e-05, rnorm = 8.09e-03, gnorm = 4.16e-01, feval = 00238\n",
      "iter = 0119, obj = 3.26519e-05, rnorm = 8.08e-03, gnorm = 3.91e-01, feval = 00240\n",
      "iter = 0120, obj = 3.25886e-05, rnorm = 8.07e-03, gnorm = 3.65e-01, feval = 00242\n",
      "iter = 0121, obj = 3.25287e-05, rnorm = 8.07e-03, gnorm = 3.70e-01, feval = 00244\n",
      "iter = 0122, obj = 3.24715e-05, rnorm = 8.06e-03, gnorm = 3.49e-01, feval = 00246\n",
      "iter = 0123, obj = 3.24208e-05, rnorm = 8.05e-03, gnorm = 3.28e-01, feval = 00248\n",
      "iter = 0124, obj = 3.23761e-05, rnorm = 8.05e-03, gnorm = 3.08e-01, feval = 00250\n",
      "iter = 0125, obj = 3.23365e-05, rnorm = 8.04e-03, gnorm = 2.90e-01, feval = 00252\n",
      "iter = 0126, obj = 3.23025e-05, rnorm = 8.04e-03, gnorm = 2.64e-01, feval = 00254\n",
      "iter = 0127, obj = 3.22733e-05, rnorm = 8.03e-03, gnorm = 2.50e-01, feval = 00256\n",
      "iter = 0128, obj = 3.22472e-05, rnorm = 8.03e-03, gnorm = 2.35e-01, feval = 00258\n",
      "iter = 0129, obj = 3.22241e-05, rnorm = 8.03e-03, gnorm = 2.21e-01, feval = 00260\n",
      "iter = 0130, obj = 3.22038e-05, rnorm = 8.03e-03, gnorm = 2.08e-01, feval = 00262\n",
      "iter = 0131, obj = 3.21847e-05, rnorm = 8.02e-03, gnorm = 2.07e-01, feval = 00264\n",
      "iter = 0132, obj = 3.21665e-05, rnorm = 8.02e-03, gnorm = 1.98e-01, feval = 00266\n",
      "iter = 0133, obj = 3.21500e-05, rnorm = 8.02e-03, gnorm = 1.88e-01, feval = 00268\n",
      "iter = 0134, obj = 3.21351e-05, rnorm = 8.02e-03, gnorm = 1.79e-01, feval = 00270\n",
      "iter = 0135, obj = 3.21215e-05, rnorm = 8.02e-03, gnorm = 1.71e-01, feval = 00272\n",
      "iter = 0136, obj = 3.21093e-05, rnorm = 8.01e-03, gnorm = 1.62e-01, feval = 00274\n",
      "iter = 0137, obj = 3.20981e-05, rnorm = 8.01e-03, gnorm = 1.57e-01, feval = 00276\n",
      "iter = 0138, obj = 3.20877e-05, rnorm = 8.01e-03, gnorm = 1.50e-01, feval = 00278\n",
      "iter = 0139, obj = 3.20781e-05, rnorm = 8.01e-03, gnorm = 1.45e-01, feval = 00280\n",
      "iter = 0140, obj = 3.20691e-05, rnorm = 8.01e-03, gnorm = 1.40e-01, feval = 00282\n",
      "iter = 0141, obj = 3.20605e-05, rnorm = 8.01e-03, gnorm = 1.40e-01, feval = 00284\n",
      "iter = 0142, obj = 3.20520e-05, rnorm = 8.01e-03, gnorm = 1.37e-01, feval = 00286\n",
      "iter = 0143, obj = 3.20439e-05, rnorm = 8.01e-03, gnorm = 1.33e-01, feval = 00288\n",
      "iter = 0144, obj = 3.20363e-05, rnorm = 8.00e-03, gnorm = 1.30e-01, feval = 00290\n",
      "iter = 0145, obj = 3.20291e-05, rnorm = 8.00e-03, gnorm = 1.26e-01, feval = 00292\n",
      "iter = 0146, obj = 3.20222e-05, rnorm = 8.00e-03, gnorm = 1.24e-01, feval = 00294\n",
      "iter = 0147, obj = 3.20154e-05, rnorm = 8.00e-03, gnorm = 1.23e-01, feval = 00296\n",
      "iter = 0148, obj = 3.20089e-05, rnorm = 8.00e-03, gnorm = 1.20e-01, feval = 00298\n",
      "iter = 0149, obj = 3.20027e-05, rnorm = 8.00e-03, gnorm = 1.17e-01, feval = 00300\n",
      "iter = 0150, obj = 3.19968e-05, rnorm = 8.00e-03, gnorm = 1.14e-01, feval = 00302\n",
      "iter = 0151, obj = 3.19911e-05, rnorm = 8.00e-03, gnorm = 1.14e-01, feval = 00304\n",
      "iter = 0152, obj = 3.19853e-05, rnorm = 8.00e-03, gnorm = 1.13e-01, feval = 00306\n",
      "iter = 0153, obj = 3.19798e-05, rnorm = 8.00e-03, gnorm = 1.11e-01, feval = 00308\n",
      "iter = 0154, obj = 3.19744e-05, rnorm = 8.00e-03, gnorm = 1.09e-01, feval = 00310\n",
      "iter = 0155, obj = 3.19693e-05, rnorm = 8.00e-03, gnorm = 1.06e-01, feval = 00312\n",
      "iter = 0156, obj = 3.19645e-05, rnorm = 8.00e-03, gnorm = 1.04e-01, feval = 00314\n",
      "iter = 0157, obj = 3.19597e-05, rnorm = 7.99e-03, gnorm = 1.02e-01, feval = 00316\n",
      "iter = 0158, obj = 3.19552e-05, rnorm = 7.99e-03, gnorm = 9.96e-02, feval = 00318\n",
      "iter = 0159, obj = 3.19510e-05, rnorm = 7.99e-03, gnorm = 9.67e-02, feval = 00320\n",
      "iter = 0160, obj = 3.19469e-05, rnorm = 7.99e-03, gnorm = 9.41e-02, feval = 00322\n",
      "iter = 0161, obj = 3.19431e-05, rnorm = 7.99e-03, gnorm = 9.21e-02, feval = 00324\n",
      "iter = 0162, obj = 3.19394e-05, rnorm = 7.99e-03, gnorm = 9.06e-02, feval = 00326\n",
      "iter = 0163, obj = 3.19359e-05, rnorm = 7.99e-03, gnorm = 8.77e-02, feval = 00328\n",
      "iter = 0164, obj = 3.19326e-05, rnorm = 7.99e-03, gnorm = 8.43e-02, feval = 00330\n",
      "iter = 0165, obj = 3.19296e-05, rnorm = 7.99e-03, gnorm = 8.06e-02, feval = 00332\n",
      "iter = 0166, obj = 3.19267e-05, rnorm = 7.99e-03, gnorm = 7.90e-02, feval = 00334\n",
      "iter = 0167, obj = 3.19241e-05, rnorm = 7.99e-03, gnorm = 7.65e-02, feval = 00336\n",
      "iter = 0168, obj = 3.19216e-05, rnorm = 7.99e-03, gnorm = 7.32e-02, feval = 00338\n",
      "iter = 0169, obj = 3.19193e-05, rnorm = 7.99e-03, gnorm = 7.00e-02, feval = 00340\n",
      "iter = 0170, obj = 3.19172e-05, rnorm = 7.99e-03, gnorm = 6.71e-02, feval = 00342\n",
      "iter = 0171, obj = 3.19153e-05, rnorm = 7.99e-03, gnorm = 6.61e-02, feval = 00344\n",
      "iter = 0172, obj = 3.19134e-05, rnorm = 7.99e-03, gnorm = 6.48e-02, feval = 00346\n",
      "iter = 0173, obj = 3.19116e-05, rnorm = 7.99e-03, gnorm = 6.26e-02, feval = 00348\n",
      "iter = 0174, obj = 3.19099e-05, rnorm = 7.99e-03, gnorm = 6.05e-02, feval = 00350\n",
      "iter = 0175, obj = 3.19083e-05, rnorm = 7.99e-03, gnorm = 5.83e-02, feval = 00352\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter = 0176, obj = 3.19069e-05, rnorm = 7.99e-03, gnorm = 5.59e-02, feval = 00354\n",
      "iter = 0177, obj = 3.19055e-05, rnorm = 7.99e-03, gnorm = 5.47e-02, feval = 00356\n",
      "iter = 0178, obj = 3.19042e-05, rnorm = 7.99e-03, gnorm = 5.28e-02, feval = 00358\n",
      "iter = 0179, obj = 3.19031e-05, rnorm = 7.99e-03, gnorm = 5.09e-02, feval = 00360\n",
      "iter = 0180, obj = 3.19020e-05, rnorm = 7.99e-03, gnorm = 4.90e-02, feval = 00362\n",
      "iter = 0181, obj = 3.19009e-05, rnorm = 7.99e-03, gnorm = 4.94e-02, feval = 00364\n",
      "iter = 0182, obj = 3.18998e-05, rnorm = 7.99e-03, gnorm = 4.90e-02, feval = 00366\n",
      "iter = 0183, obj = 3.18988e-05, rnorm = 7.99e-03, gnorm = 4.78e-02, feval = 00368\n",
      "iter = 0184, obj = 3.18978e-05, rnorm = 7.99e-03, gnorm = 4.65e-02, feval = 00370\n",
      "iter = 0185, obj = 3.18969e-05, rnorm = 7.99e-03, gnorm = 4.52e-02, feval = 00372\n",
      "iter = 0186, obj = 3.18960e-05, rnorm = 7.99e-03, gnorm = 4.31e-02, feval = 00374\n",
      "iter = 0187, obj = 3.18952e-05, rnorm = 7.99e-03, gnorm = 4.24e-02, feval = 00376\n",
      "iter = 0188, obj = 3.18944e-05, rnorm = 7.99e-03, gnorm = 4.10e-02, feval = 00378\n",
      "iter = 0189, obj = 3.18937e-05, rnorm = 7.99e-03, gnorm = 3.95e-02, feval = 00380\n",
      "iter = 0190, obj = 3.18930e-05, rnorm = 7.99e-03, gnorm = 3.80e-02, feval = 00382\n",
      "iter = 0191, obj = 3.18924e-05, rnorm = 7.99e-03, gnorm = 3.78e-02, feval = 00384\n",
      "iter = 0192, obj = 3.18918e-05, rnorm = 7.99e-03, gnorm = 3.74e-02, feval = 00386\n",
      "iter = 0193, obj = 3.18912e-05, rnorm = 7.99e-03, gnorm = 3.62e-02, feval = 00388\n",
      "iter = 0194, obj = 3.18906e-05, rnorm = 7.99e-03, gnorm = 3.48e-02, feval = 00390\n",
      "iter = 0195, obj = 3.18901e-05, rnorm = 7.99e-03, gnorm = 3.35e-02, feval = 00392\n",
      "iter = 0196, obj = 3.18896e-05, rnorm = 7.99e-03, gnorm = 3.13e-02, feval = 00394\n",
      "iter = 0197, obj = 3.18892e-05, rnorm = 7.99e-03, gnorm = 3.02e-02, feval = 00396\n",
      "iter = 0198, obj = 3.18888e-05, rnorm = 7.99e-03, gnorm = 2.87e-02, feval = 00398\n",
      "iter = 0199, obj = 3.18885e-05, rnorm = 7.99e-03, gnorm = 2.71e-02, feval = 00400\n",
      "iter = 0200, obj = 3.18882e-05, rnorm = 7.99e-03, gnorm = 2.55e-02, feval = 00402\n",
      "iter = 0201, obj = 3.18879e-05, rnorm = 7.99e-03, gnorm = 2.52e-02, feval = 00404\n",
      "iter = 0202, obj = 3.18876e-05, rnorm = 7.99e-03, gnorm = 2.45e-02, feval = 00406\n",
      "iter = 0203, obj = 3.18874e-05, rnorm = 7.99e-03, gnorm = 2.34e-02, feval = 00408\n",
      "iter = 0204, obj = 3.18871e-05, rnorm = 7.99e-03, gnorm = 2.23e-02, feval = 00410\n",
      "iter = 0205, obj = 3.18869e-05, rnorm = 7.99e-03, gnorm = 2.12e-02, feval = 00412\n",
      "iter = 0206, obj = 3.18867e-05, rnorm = 7.99e-03, gnorm = 1.94e-02, feval = 00414\n",
      "iter = 0207, obj = 3.18866e-05, rnorm = 7.99e-03, gnorm = 1.86e-02, feval = 00416\n",
      "iter = 0208, obj = 3.18864e-05, rnorm = 7.99e-03, gnorm = 1.76e-02, feval = 00418\n",
      "iter = 0209, obj = 3.18863e-05, rnorm = 7.99e-03, gnorm = 1.65e-02, feval = 00420\n",
      "iter = 0210, obj = 3.18862e-05, rnorm = 7.99e-03, gnorm = 1.54e-02, feval = 00422\n",
      "iter = 0211, obj = 3.18861e-05, rnorm = 7.99e-03, gnorm = 1.55e-02, feval = 00424\n",
      "iter = 0212, obj = 3.18860e-05, rnorm = 7.99e-03, gnorm = 1.53e-02, feval = 00426\n",
      "iter = 0213, obj = 3.18859e-05, rnorm = 7.99e-03, gnorm = 1.47e-02, feval = 00428\n",
      "iter = 0214, obj = 3.18858e-05, rnorm = 7.99e-03, gnorm = 1.43e-02, feval = 00430\n",
      "iter = 0215, obj = 3.18857e-05, rnorm = 7.99e-03, gnorm = 1.39e-02, feval = 00432\n",
      "iter = 0216, obj = 3.18856e-05, rnorm = 7.99e-03, gnorm = 1.27e-02, feval = 00434\n",
      "iter = 0217, obj = 3.18855e-05, rnorm = 7.99e-03, gnorm = 1.25e-02, feval = 00436\n",
      "iter = 0218, obj = 3.18855e-05, rnorm = 7.99e-03, gnorm = 1.21e-02, feval = 00438\n",
      "iter = 0219, obj = 3.18854e-05, rnorm = 7.99e-03, gnorm = 1.17e-02, feval = 00440\n",
      "iter = 0220, obj = 3.18854e-05, rnorm = 7.99e-03, gnorm = 1.11e-02, feval = 00442\n",
      "iter = 0221, obj = 3.18853e-05, rnorm = 7.99e-03, gnorm = 1.14e-02, feval = 00444\n",
      "iter = 0222, obj = 3.18852e-05, rnorm = 7.99e-03, gnorm = 1.14e-02, feval = 00446\n",
      "iter = 0223, obj = 3.18852e-05, rnorm = 7.99e-03, gnorm = 1.12e-02, feval = 00448\n",
      "iter = 0224, obj = 3.18851e-05, rnorm = 7.99e-03, gnorm = 1.10e-02, feval = 00450\n",
      "iter = 0225, obj = 3.18851e-05, rnorm = 7.99e-03, gnorm = 1.08e-02, feval = 00452\n",
      "iter = 0226, obj = 3.18850e-05, rnorm = 7.99e-03, gnorm = 1.01e-02, feval = 00454\n",
      "iter = 0227, obj = 3.18850e-05, rnorm = 7.99e-03, gnorm = 1.00e-02, feval = 00456\n",
      "iter = 0228, obj = 3.18849e-05, rnorm = 7.99e-03, gnorm = 9.75e-03, feval = 00458\n",
      "iter = 0229, obj = 3.18849e-05, rnorm = 7.99e-03, gnorm = 9.39e-03, feval = 00460\n",
      "iter = 0230, obj = 3.18849e-05, rnorm = 7.99e-03, gnorm = 8.99e-03, feval = 00462\n",
      "iter = 0231, obj = 3.18848e-05, rnorm = 7.99e-03, gnorm = 8.93e-03, feval = 00464\n",
      "iter = 0232, obj = 3.18848e-05, rnorm = 7.99e-03, gnorm = 8.91e-03, feval = 00466\n",
      "iter = 0233, obj = 3.18848e-05, rnorm = 7.99e-03, gnorm = 8.65e-03, feval = 00468\n",
      "iter = 0234, obj = 3.18847e-05, rnorm = 7.99e-03, gnorm = 8.36e-03, feval = 00470\n",
      "iter = 0235, obj = 3.18847e-05, rnorm = 7.99e-03, gnorm = 8.07e-03, feval = 00472\n",
      "iter = 0236, obj = 3.18847e-05, rnorm = 7.99e-03, gnorm = 7.46e-03, feval = 00474\n",
      "iter = 0237, obj = 3.18847e-05, rnorm = 7.99e-03, gnorm = 7.36e-03, feval = 00476\n",
      "iter = 0238, obj = 3.18846e-05, rnorm = 7.99e-03, gnorm = 7.06e-03, feval = 00478\n",
      "iter = 0239, obj = 3.18846e-05, rnorm = 7.99e-03, gnorm = 6.72e-03, feval = 00480\n",
      "iter = 0240, obj = 3.18846e-05, rnorm = 7.99e-03, gnorm = 6.38e-03, feval = 00482\n",
      "iter = 0241, obj = 3.18846e-05, rnorm = 7.99e-03, gnorm = 6.16e-03, feval = 00484\n",
      "iter = 0242, obj = 3.18846e-05, rnorm = 7.99e-03, gnorm = 6.08e-03, feval = 00486\n",
      "iter = 0243, obj = 3.18845e-05, rnorm = 7.99e-03, gnorm = 5.85e-03, feval = 00488\n",
      "iter = 0244, obj = 3.18845e-05, rnorm = 7.99e-03, gnorm = 5.59e-03, feval = 00490\n",
      "iter = 0245, obj = 3.18845e-05, rnorm = 7.99e-03, gnorm = 5.33e-03, feval = 00492\n",
      "iter = 0246, obj = 3.18845e-05, rnorm = 7.99e-03, gnorm = 4.98e-03, feval = 00494\n",
      "iter = 0247, obj = 3.18845e-05, rnorm = 7.99e-03, gnorm = 4.94e-03, feval = 00496\n",
      "iter = 0248, obj = 3.18845e-05, rnorm = 7.99e-03, gnorm = 4.76e-03, feval = 00498\n",
      "iter = 0249, obj = 3.18845e-05, rnorm = 7.99e-03, gnorm = 4.57e-03, feval = 00500\n",
      "iter = 0250, obj = 3.18845e-05, rnorm = 7.99e-03, gnorm = 4.40e-03, feval = 00502\n",
      "iter = 0251, obj = 3.18844e-05, rnorm = 7.99e-03, gnorm = 4.25e-03, feval = 00504\n",
      "iter = 0252, obj = 3.18844e-05, rnorm = 7.99e-03, gnorm = 4.19e-03, feval = 00506\n",
      "iter = 0253, obj = 3.18844e-05, rnorm = 7.99e-03, gnorm = 4.09e-03, feval = 00508\n",
      "iter = 0254, obj = 3.18844e-05, rnorm = 7.99e-03, gnorm = 3.98e-03, feval = 00510\n",
      "iter = 0255, obj = 3.18844e-05, rnorm = 7.99e-03, gnorm = 3.85e-03, feval = 00512\n",
      "iter = 0256, obj = 3.18844e-05, rnorm = 7.99e-03, gnorm = 3.76e-03, feval = 00514\n",
      "iter = 0257, obj = 3.18844e-05, rnorm = 7.99e-03, gnorm = 3.71e-03, feval = 00516\n",
      "iter = 0258, obj = 3.18844e-05, rnorm = 7.99e-03, gnorm = 3.61e-03, feval = 00518\n",
      "iter = 0259, obj = 3.18844e-05, rnorm = 7.99e-03, gnorm = 3.48e-03, feval = 00520\n",
      "iter = 0260, obj = 3.18844e-05, rnorm = 7.99e-03, gnorm = 3.35e-03, feval = 00522\n",
      "iter = 0261, obj = 3.18844e-05, rnorm = 7.99e-03, gnorm = 3.27e-03, feval = 00524\n",
      "iter = 0262, obj = 3.18844e-05, rnorm = 7.99e-03, gnorm = 3.25e-03, feval = 00526\n",
      "iter = 0263, obj = 3.18844e-05, rnorm = 7.99e-03, gnorm = 3.17e-03, feval = 00528\n",
      "iter = 0264, obj = 3.18844e-05, rnorm = 7.99e-03, gnorm = 3.06e-03, feval = 00530\n",
      "iter = 0265, obj = 3.18844e-05, rnorm = 7.99e-03, gnorm = 2.95e-03, feval = 00532\n",
      "iter = 0266, obj = 3.18844e-05, rnorm = 7.99e-03, gnorm = 2.87e-03, feval = 00534\n",
      "iter = 0267, obj = 3.18844e-05, rnorm = 7.99e-03, gnorm = 2.75e-03, feval = 00536\n",
      "iter = 0268, obj = 3.18844e-05, rnorm = 7.99e-03, gnorm = 2.64e-03, feval = 00538\n",
      "iter = 0269, obj = 3.18844e-05, rnorm = 7.99e-03, gnorm = 2.51e-03, feval = 00540\n",
      "iter = 0270, obj = 3.18844e-05, rnorm = 7.99e-03, gnorm = 2.37e-03, feval = 00542\n",
      "iter = 0271, obj = 3.18844e-05, rnorm = 7.99e-03, gnorm = 2.27e-03, feval = 00544\n",
      "iter = 0272, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.23e-03, feval = 00546\n",
      "iter = 0273, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.14e-03, feval = 00548\n",
      "iter = 0274, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.04e-03, feval = 00550\n",
      "iter = 0275, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.94e-03, feval = 00552\n",
      "iter = 0276, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.87e-03, feval = 00554\n",
      "iter = 0277, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.76e-03, feval = 00556\n",
      "iter = 0278, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.67e-03, feval = 00558\n",
      "iter = 0279, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.57e-03, feval = 00560\n",
      "iter = 0280, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.47e-03, feval = 00562\n",
      "iter = 0281, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.39e-03, feval = 00564\n",
      "iter = 0282, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.38e-03, feval = 00566\n",
      "iter = 0283, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.33e-03, feval = 00568\n",
      "iter = 0284, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.28e-03, feval = 00570\n",
      "iter = 0285, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.22e-03, feval = 00572\n",
      "iter = 0286, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.21e-03, feval = 00574\n",
      "iter = 0287, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.13e-03, feval = 00576\n",
      "iter = 0288, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.09e-03, feval = 00578\n",
      "iter = 0289, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.04e-03, feval = 00580\n",
      "iter = 0290, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 9.89e-04, feval = 00582\n",
      "iter = 0291, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 9.41e-04, feval = 00584\n",
      "iter = 0292, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 9.58e-04, feval = 00586\n",
      "iter = 0293, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 9.35e-04, feval = 00588\n",
      "iter = 0294, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 9.05e-04, feval = 00590\n",
      "iter = 0295, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 8.73e-04, feval = 00592\n",
      "iter = 0296, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 8.66e-04, feval = 00594\n",
      "iter = 0297, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 8.25e-04, feval = 00596\n",
      "iter = 0298, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 7.98e-04, feval = 00598\n",
      "iter = 0299, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 7.66e-04, feval = 00600\n",
      "iter = 0300, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 7.30e-04, feval = 00602\n",
      "iter = 0301, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 6.96e-04, feval = 00604\n",
      "iter = 0302, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 6.91e-04, feval = 00606\n",
      "iter = 0303, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 6.68e-04, feval = 00608\n",
      "iter = 0304, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 6.39e-04, feval = 00610\n",
      "iter = 0305, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 6.08e-04, feval = 00612\n",
      "iter = 0306, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 5.93e-04, feval = 00614\n",
      "iter = 0307, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 5.60e-04, feval = 00616\n",
      "iter = 0308, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 5.35e-04, feval = 00618\n",
      "iter = 0309, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 5.07e-04, feval = 00620\n",
      "iter = 0310, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 4.78e-04, feval = 00622\n",
      "iter = 0311, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 4.54e-04, feval = 00624\n",
      "iter = 0312, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 4.39e-04, feval = 00626\n",
      "iter = 0313, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 4.22e-04, feval = 00628\n",
      "iter = 0314, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 4.01e-04, feval = 00630\n",
      "iter = 0315, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 3.81e-04, feval = 00632\n",
      "iter = 0316, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 3.70e-04, feval = 00634\n",
      "iter = 0317, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 3.51e-04, feval = 00636\n",
      "iter = 0318, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 3.36e-04, feval = 00638\n",
      "iter = 0319, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 3.21e-04, feval = 00640\n",
      "iter = 0320, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 3.05e-04, feval = 00642\n",
      "iter = 0321, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.93e-04, feval = 00644\n",
      "iter = 0322, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.86e-04, feval = 00646\n",
      "iter = 0323, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.78e-04, feval = 00648\n",
      "iter = 0324, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.68e-04, feval = 00650\n",
      "iter = 0325, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.58e-04, feval = 00652\n",
      "iter = 0326, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.51e-04, feval = 00654\n",
      "iter = 0327, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.45e-04, feval = 00656\n",
      "iter = 0328, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.38e-04, feval = 00658\n",
      "iter = 0329, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.31e-04, feval = 00660\n",
      "iter = 0330, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.23e-04, feval = 00662\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iter = 0331, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.20e-04, feval = 00664\n",
      "iter = 0332, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.13e-04, feval = 00666\n",
      "iter = 0333, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.08e-04, feval = 00668\n",
      "iter = 0334, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.01e-04, feval = 00670\n",
      "iter = 0335, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.92e-04, feval = 00672\n",
      "iter = 0336, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.83e-04, feval = 00674\n",
      "iter = 0337, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.82e-04, feval = 00676\n",
      "iter = 0338, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.75e-04, feval = 00678\n",
      "iter = 0339, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.68e-04, feval = 00680\n",
      "iter = 0340, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.61e-04, feval = 00682\n",
      "iter = 0341, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.58e-04, feval = 00684\n",
      "iter = 0342, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.47e-04, feval = 00686\n",
      "iter = 0343, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.42e-04, feval = 00688\n",
      "iter = 0344, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.35e-04, feval = 00690\n",
      "iter = 0345, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.27e-04, feval = 00692\n",
      "iter = 0346, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.20e-04, feval = 00694\n",
      "iter = 0347, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.16e-04, feval = 00696\n",
      "iter = 0348, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.11e-04, feval = 00698\n",
      "iter = 0349, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.05e-04, feval = 00700\n",
      "iter = 0350, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 9.97e-05, feval = 00702\n",
      "iter = 0351, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 9.82e-05, feval = 00704\n",
      "iter = 0352, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 9.11e-05, feval = 00706\n",
      "iter = 0353, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 8.78e-05, feval = 00708\n",
      "iter = 0354, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 8.39e-05, feval = 00710\n",
      "iter = 0355, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 7.98e-05, feval = 00712\n",
      "iter = 0356, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 7.49e-05, feval = 00714\n",
      "iter = 0357, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 7.37e-05, feval = 00716\n",
      "iter = 0358, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 7.08e-05, feval = 00718\n",
      "iter = 0359, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 6.75e-05, feval = 00720\n",
      "iter = 0360, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 6.44e-05, feval = 00722\n",
      "iter = 0361, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 6.41e-05, feval = 00724\n",
      "iter = 0362, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 6.00e-05, feval = 00726\n",
      "iter = 0363, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 5.84e-05, feval = 00728\n",
      "iter = 0364, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 5.65e-05, feval = 00730\n",
      "iter = 0365, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 5.46e-05, feval = 00732\n",
      "iter = 0366, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 5.20e-05, feval = 00734\n",
      "iter = 0367, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 5.03e-05, feval = 00736\n",
      "iter = 0368, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 4.83e-05, feval = 00738\n",
      "iter = 0369, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 4.60e-05, feval = 00740\n",
      "iter = 0370, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 4.35e-05, feval = 00742\n",
      "iter = 0371, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 4.28e-05, feval = 00744\n",
      "iter = 0372, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 4.04e-05, feval = 00746\n",
      "iter = 0373, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 3.91e-05, feval = 00748\n",
      "iter = 0374, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 3.76e-05, feval = 00750\n",
      "iter = 0375, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 3.63e-05, feval = 00752\n",
      "iter = 0376, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 3.47e-05, feval = 00754\n",
      "iter = 0377, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 3.25e-05, feval = 00756\n",
      "iter = 0378, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 3.10e-05, feval = 00758\n",
      "iter = 0379, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.92e-05, feval = 00760\n",
      "iter = 0380, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.73e-05, feval = 00762\n",
      "iter = 0381, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.65e-05, feval = 00764\n",
      "iter = 0382, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.50e-05, feval = 00766\n",
      "iter = 0383, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.39e-05, feval = 00768\n",
      "iter = 0384, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.28e-05, feval = 00770\n",
      "iter = 0385, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.18e-05, feval = 00772\n",
      "iter = 0386, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.08e-05, feval = 00774\n",
      "iter = 0387, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.93e-05, feval = 00776\n",
      "iter = 0388, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.83e-05, feval = 00778\n",
      "iter = 0389, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.72e-05, feval = 00780\n",
      "iter = 0390, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.62e-05, feval = 00782\n",
      "iter = 0391, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.57e-05, feval = 00784\n",
      "iter = 0392, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.46e-05, feval = 00786\n",
      "iter = 0393, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.40e-05, feval = 00788\n",
      "iter = 0394, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.33e-05, feval = 00790\n",
      "iter = 0395, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.27e-05, feval = 00792\n",
      "iter = 0396, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.22e-05, feval = 00794\n",
      "iter = 0397, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.13e-05, feval = 00796\n",
      "iter = 0398, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.08e-05, feval = 00798\n",
      "iter = 0399, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.02e-05, feval = 00800\n",
      "iter = 0400, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 9.67e-06, feval = 00802\n",
      "iter = 0401, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 9.45e-06, feval = 00804\n",
      "iter = 0402, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 8.81e-06, feval = 00806\n",
      "iter = 0403, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 8.45e-06, feval = 00808\n",
      "iter = 0404, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 8.12e-06, feval = 00810\n",
      "iter = 0405, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 7.86e-06, feval = 00812\n",
      "iter = 0406, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 7.69e-06, feval = 00814\n",
      "iter = 0407, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 7.15e-06, feval = 00816\n",
      "iter = 0408, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 6.88e-06, feval = 00818\n",
      "iter = 0409, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 6.57e-06, feval = 00820\n",
      "iter = 0410, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 6.28e-06, feval = 00822\n",
      "iter = 0411, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 6.09e-06, feval = 00824\n",
      "iter = 0412, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 5.79e-06, feval = 00826\n",
      "iter = 0413, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 5.57e-06, feval = 00828\n",
      "iter = 0414, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 5.39e-06, feval = 00830\n",
      "iter = 0415, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 5.29e-06, feval = 00832\n",
      "iter = 0416, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 5.34e-06, feval = 00834\n",
      "iter = 0417, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 4.85e-06, feval = 00836\n",
      "iter = 0418, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 4.68e-06, feval = 00838\n",
      "iter = 0419, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 4.49e-06, feval = 00840\n",
      "iter = 0420, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 4.29e-06, feval = 00842\n",
      "iter = 0421, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 4.11e-06, feval = 00844\n",
      "iter = 0422, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 3.94e-06, feval = 00846\n",
      "iter = 0423, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 3.79e-06, feval = 00848\n",
      "iter = 0424, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 3.66e-06, feval = 00850\n",
      "iter = 0425, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 3.59e-06, feval = 00852\n",
      "iter = 0426, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 3.67e-06, feval = 00854\n",
      "iter = 0427, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 3.28e-06, feval = 00856\n",
      "iter = 0428, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 3.16e-06, feval = 00858\n",
      "iter = 0429, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 3.04e-06, feval = 00860\n",
      "iter = 0430, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.92e-06, feval = 00862\n",
      "iter = 0431, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.81e-06, feval = 00864\n",
      "iter = 0432, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.67e-06, feval = 00866\n",
      "iter = 0433, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.56e-06, feval = 00868\n",
      "iter = 0434, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.48e-06, feval = 00870\n",
      "iter = 0435, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.43e-06, feval = 00872\n",
      "iter = 0436, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.49e-06, feval = 00874\n",
      "iter = 0437, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.23e-06, feval = 00876\n",
      "iter = 0438, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.14e-06, feval = 00878\n",
      "iter = 0439, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.05e-06, feval = 00880\n",
      "iter = 0440, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.98e-06, feval = 00882\n",
      "iter = 0441, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.92e-06, feval = 00884\n",
      "iter = 0442, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.78e-06, feval = 00886\n",
      "iter = 0443, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.69e-06, feval = 00888\n",
      "iter = 0444, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.61e-06, feval = 00890\n",
      "iter = 0445, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.56e-06, feval = 00892\n",
      "iter = 0446, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.57e-06, feval = 00894\n",
      "iter = 0447, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.37e-06, feval = 00896\n",
      "iter = 0448, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.28e-06, feval = 00898\n",
      "iter = 0449, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.20e-06, feval = 00900\n",
      "iter = 0450, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.14e-06, feval = 00902\n",
      "iter = 0451, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.12e-06, feval = 00904\n",
      "iter = 0452, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 9.76e-07, feval = 00906\n",
      "iter = 0453, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 9.02e-07, feval = 00908\n",
      "iter = 0454, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 8.37e-07, feval = 00910\n",
      "iter = 0455, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 7.86e-07, feval = 00912\n",
      "iter = 0456, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 7.61e-07, feval = 00914\n",
      "iter = 0457, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 6.57e-07, feval = 00916\n",
      "iter = 0458, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 5.95e-07, feval = 00918\n",
      "iter = 0459, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 5.45e-07, feval = 00920\n",
      "iter = 0460, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 5.12e-07, feval = 00922\n",
      "iter = 0461, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 5.06e-07, feval = 00924\n",
      "iter = 0462, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 4.25e-07, feval = 00926\n",
      "iter = 0463, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 3.88e-07, feval = 00928\n",
      "iter = 0464, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 3.58e-07, feval = 00930\n",
      "iter = 0465, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 3.40e-07, feval = 00932\n",
      "iter = 0466, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 3.39e-07, feval = 00934\n",
      "iter = 0467, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.93e-07, feval = 00936\n",
      "iter = 0468, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.71e-07, feval = 00938\n",
      "iter = 0469, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.57e-07, feval = 00940\n",
      "iter = 0470, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.55e-07, feval = 00942\n",
      "iter = 0471, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.78e-07, feval = 00944\n",
      "iter = 0472, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.44e-07, feval = 00946\n",
      "iter = 0473, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.42e-07, feval = 00948\n",
      "iter = 0474, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.46e-07, feval = 00950\n",
      "iter = 0475, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.63e-07, feval = 00952\n",
      "iter = 0476, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.98e-07, feval = 00954\n",
      "iter = 0477, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.80e-07, feval = 00956\n",
      "iter = 0478, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.84e-07, feval = 00958\n",
      "iter = 0479, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.96e-07, feval = 00960\n",
      "iter = 0480, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 3.24e-07, feval = 00962\n",
      "iter = 0481, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 4.02e-07, feval = 00964\n",
      "iter = 0482, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 3.38e-07, feval = 00966\n",
      "iter = 0483, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 3.35e-07, feval = 00968\n",
      "iter = 0484, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 3.30e-07, feval = 00970\n",
      "iter = 0485, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 3.38e-07, feval = 00972\n",
      "iter = 0486, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 3.67e-07, feval = 00974\n",
      "iter = 0487, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.76e-07, feval = 00976\n",
      "iter = 0488, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.34e-07, feval = 00978\n",
      "iter = 0489, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.04e-07, feval = 00980\n",
      "iter = 0490, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.97e-07, feval = 00982\n",
      "iter = 0491, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 2.51e-07, feval = 00984\n",
      "iter = 0492, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.50e-07, feval = 00986\n",
      "iter = 0493, obj = 3.18843e-05, rnorm = 7.99e-03, gnorm = 1.40e-07, feval = 00988\n",
      "Objective function didn't reduce, will terminate solver:\n",
      "\tobj_new = 3.18843e-05\tobj_cur = 3.18843e-05\n",
      "##########################################################################################\n",
      "            CG Solver end\n",
      "##########################################################################################\n",
      "\n"
     ]
    }
   ],
   "source": [
    "LCGsolver.run(VSP_prob_regD1, verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(z, 1.e-3*vel,label='true model',linewidth=2,linestyle='-.')\n",
    "ax.plot(z, 1.e-3/VSP_prob_regD1.model.plot(),label='inverted model')\n",
    "ax.set_xlabel(\"depth [m]\"), ax.set_ylabel(\"vel [km/s]\")\n",
    "ax.set_ylim(3,4), ax.set_xlim(0,1000)\n",
    "fig.suptitle(\"$L_2$ regularized inversion (noisy data)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the second case (i.e., when a prior model is employed), the objective function to be minimized is written as follows:\n",
    "\\begin{align}\n",
    "\\phi_{smooth}(\\mathbf{m})=\\frac{1}{2}\\|G \\mathbf{m} - \\mathbf{d}_{obs} \\|_2^2 + \\frac{\\epsilon^2}{2} \\|\\mathbf{m} - \\mathbf{m}_{prior}\\|_2^2,\n",
    "\\end{align}\n",
    "where $\\mathbf{m}_{prior}$ is the prior model vector expressed as the following velocity profile:\n",
    "\\begin{align}\n",
    "v_{prior}(z)  = 3100.+ 1.0 z\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "model_prior = o.VectorNumpy(1.0/(3100.0 + z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epsilon Scale evaluation\n",
      "\tEpsilon balancing the data-space gradients is: 2.04e+02\n"
     ]
    }
   ],
   "source": [
    "# Instantiating regularized problem with prior model and noisy data\n",
    "VSP_prob_prior = o.LeastSquaresRegularized(model_true.clone().zero(), noisy_data,VSP_10,epsilon=1.0,prior_model=model_prior)\n",
    "\n",
    "# Estimating a value for the regularization weight epsilon\n",
    "epsilon_balance = VSP_prob_prior.estimate_epsilon(True)\n",
    "VSP_prob_prior.epsilon = epsilon_balance * 2.5e-1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "##########################################################################################\n",
      "            CG Solver\n",
      "    Restart folder: /tmp/restart_2022-04-22T01-51-41.263912/\n",
      "##########################################################################################\n",
      "\n",
      "iter = 0000, obj = 7.31713e-01, rnorm = 1.21e+00, gnorm = 2.52e+02, feval = 00002\n",
      "iter = 0001, obj = 9.94834e-03, rnorm = 1.41e-01, gnorm = 1.06e+01, feval = 00004\n",
      "iter = 0002, obj = 9.88438e-04, rnorm = 4.45e-02, gnorm = 2.66e+00, feval = 00006\n",
      "iter = 0003, obj = 1.01552e-04, rnorm = 1.43e-02, gnorm = 4.98e-01, feval = 00008\n",
      "iter = 0004, obj = 6.56218e-05, rnorm = 1.15e-02, gnorm = 5.48e-02, feval = 00010\n",
      "iter = 0005, obj = 6.51493e-05, rnorm = 1.14e-02, gnorm = 4.49e-03, feval = 00012\n",
      "iter = 0006, obj = 6.51460e-05, rnorm = 1.14e-02, gnorm = 2.74e-04, feval = 00014\n",
      "iter = 0007, obj = 6.51460e-05, rnorm = 1.14e-02, gnorm = 1.22e-05, feval = 00016\n",
      "iter = 0008, obj = 6.51460e-05, rnorm = 1.14e-02, gnorm = 4.34e-07, feval = 00018\n",
      "iter = 0009, obj = 6.51460e-05, rnorm = 1.14e-02, gnorm = 4.20e-08, feval = 00020\n",
      "iter = 0010, obj = 6.51460e-05, rnorm = 1.14e-02, gnorm = 1.22e-08, feval = 00022\n",
      "iter = 0011, obj = 6.51460e-05, rnorm = 1.14e-02, gnorm = 2.64e-10, feval = 00024\n",
      "Objective function didn't reduce, will terminate solver:\n",
      "\tobj_new = 6.51460e-05\tobj_cur = 6.51460e-05\n",
      "##########################################################################################\n",
      "            CG Solver end\n",
      "##########################################################################################\n",
      "\n"
     ]
    }
   ],
   "source": [
    "LCGsolver.run(VSP_prob_prior,verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(z, 1.e-3*vel,label='true model',linewidth=2,linestyle='-.')\n",
    "ax.plot(z, 1.e-3/VSP_prob_prior.model.plot(),label='inverted model')\n",
    "ax.set_xlabel(\"depth [m]\"), ax.set_ylabel(\"vel [km/s]\")\n",
    "ax.set_ylim(3,4), ax.set_xlim(0,1000)\n",
    "fig.suptitle(\"$L_2$ regularized inversion (noisy data) with prior model\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}