{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "87c27add-caff-4614-8fe3-5791ab80e1dc",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "# Adjoint optimization of an integrated bandpass filter\n",
    "\n",
    "In this notebook, we will use broadband optimization to design a bandpass filter in an integrated photonic device.\n",
    "\n",
    "In short, this device takes in broadband light through a waveguide and encourages transmission to the output waveguide for a certain frequency range, while suppressing transmission outside of this range.\n",
    "<!-- \n",
    "<img src=\"img/adjoint_9.png\" width=400 alt=\"Schematic of the waveguide division multiplexer\"> -->\n",
    "\n",
    "<img src=\"img/adjoint_17.png\" width=400 alt=\"Schematic of the bandpass filter \">\n",
    "\n",
    "If you are unfamiliar with inverse design, we also recommend our [intro to inverse design tutorials](https://www.flexcompute.com/tidy3d/learning-center/inverse-design/) and our [primer on automatic differentiation with tidy3d](https://www.flexcompute.com/tidy3d/examples/notebooks/Autograd1Intro/).\n"
   ]
  },
  {
   "cell_type": "code",
   "id": "77c1e025-acd7-4e75-a5ce-4a0134a69e79",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-18T10:47:26.472691Z",
     "start_time": "2026-03-18T10:47:24.426029Z"
    }
   },
   "source": [
    "import autograd as ag\n",
    "import autograd.numpy as np\n",
    "import matplotlib.pylab as plt\n",
    "import tidy3d as td\n",
    "import tidy3d.web as web"
   ],
   "outputs": [],
   "execution_count": 1
  },
  {
   "cell_type": "markdown",
   "id": "4cffcb65-9591-45ce-bd2b-c485e856d0b8",
   "metadata": {},
   "source": [
    "## Setup\n",
    "\n",
    "First, we define some parameters that set up our optimization, such as the frequency points we are interested in as well as the geometric, material, and source parameters."
   ]
  },
  {
   "cell_type": "code",
   "id": "3ae4ea7e-8cae-47f8-93a7-e6ffde9d018f",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T10:47:26.477552Z",
     "start_time": "2026-03-18T10:47:26.475562Z"
    }
   },
   "source": [
    "wvl_min, wvl_max = 0.8, 1.2\n",
    "fmin, fmax = td.C_0 / wvl_max, td.C_0 / wvl_min\n",
    "\n",
    "num_freqs = 51\n",
    "freqs = np.linspace(fmin, fmax, num_freqs)\n",
    "\n",
    "freq0 = np.mean(freqs)\n",
    "lambda0 = td.C_0 / freq0\n",
    "fwidth = freq0 / 10\n",
    "run_time = 100 / fwidth\n",
    "\n",
    "wvl0 = td.C_0 / freq0"
   ],
   "outputs": [],
   "execution_count": 2
  },
  {
   "cell_type": "markdown",
   "id": "89b954c8-14ba-4b7e-bf06-167fe3188289",
   "metadata": {},
   "source": [
    "We will use a photonic integrated circuit with a 2D design region, so we set up some parameters to define that region."
   ]
  },
  {
   "cell_type": "code",
   "id": "74107971-385d-4e77-b186-d4379f56b1ed",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T10:47:26.521188Z",
     "start_time": "2026-03-18T10:47:26.519651Z"
    }
   },
   "source": [
    "size_design_x = 10 * wvl0\n",
    "size_design_y = 5 * wvl0\n",
    "\n",
    "width_wg = 0.4 * wvl0\n",
    "\n",
    "length_wg = 2 * wvl0\n",
    "\n",
    "size_buffer = 1.5 * wvl0"
   ],
   "outputs": [],
   "execution_count": 3
  },
  {
   "cell_type": "markdown",
   "id": "ef28f0f6-7423-4791-9e04-f7f996959599",
   "metadata": {},
   "source": [
    "And then some positions and length scales to help us keep track of things later on."
   ]
  },
  {
   "cell_type": "code",
   "id": "b626a5a1-5a67-4909-8872-540a40b4bd63",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T10:47:26.565308Z",
     "start_time": "2026-03-18T10:47:26.563636Z"
    }
   },
   "source": [
    "size_sim_x = length_wg + size_design_x + length_wg\n",
    "size_sim_y = size_buffer + size_design_y + size_buffer\n",
    "\n",
    "center_wg_in_x = -size_sim_x / 2 + length_wg / 2\n",
    "center_wg_in_y = 0\n",
    "\n",
    "center_wg_out_x = +size_sim_x / 2 - length_wg / 2\n",
    "center_wg_out_y = 0\n",
    "\n",
    "center_design_x = 0\n",
    "center_design_y = 0"
   ],
   "outputs": [],
   "execution_count": 4
  },
  {
   "cell_type": "markdown",
   "id": "90aedfcb-6d2f-406f-abf5-7829360f6f30",
   "metadata": {},
   "source": [
    "Our material will just be a simple dielectric with relative permittivity of 4."
   ]
  },
  {
   "cell_type": "code",
   "id": "7608f6e1-34b7-4232-abdc-c47eb5cffbd2",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T10:47:26.609321Z",
     "start_time": "2026-03-18T10:47:26.607853Z"
    }
   },
   "source": [
    "eps_mat = 4.0\n",
    "mat = td.Medium(permittivity=eps_mat)"
   ],
   "outputs": [],
   "execution_count": 5
  },
  {
   "cell_type": "markdown",
   "id": "cdcb1842-a9f6-47c8-bafc-1a8eeb897d96",
   "metadata": {},
   "source": [
    "Next, we define some discretization parameters for our simulation and design region."
   ]
  },
  {
   "cell_type": "code",
   "id": "511333d4-a136-4d46-bd3a-5b3a36e53c4d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T10:47:26.653272Z",
     "start_time": "2026-03-18T10:47:26.651825Z"
    }
   },
   "source": [
    "min_steps_per_wvl = 25\n",
    "dl_design_region = 0.015"
   ],
   "outputs": [],
   "execution_count": 6
  },
  {
   "cell_type": "code",
   "id": "f8e1ee66-d0e1-4572-9a29-95de19a18793",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T10:47:26.698060Z",
     "start_time": "2026-03-18T10:47:26.696484Z"
    }
   },
   "source": [
    "nx = int(np.ceil(size_design_x / dl_design_region))\n",
    "ny = int(np.ceil(size_design_y / dl_design_region))"
   ],
   "outputs": [],
   "execution_count": 7
  },
  {
   "cell_type": "markdown",
   "id": "e8034d36-ef07-4211-8d46-61af5dd210fb",
   "metadata": {},
   "source": [
    "### Static Components\n",
    "\n",
    "In the next step, we will define the \"static\" tidy3d simulation components that do not change over the course of optimization. For example, the sources, monitors, and many of the structures.\n",
    "\n",
    "We'll put these into a base simulation, which we can easily update with our optimizing components later."
   ]
  },
  {
   "cell_type": "code",
   "id": "a6de18cc-8fd2-4355-bfa2-5d4654002041",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T10:47:26.758861Z",
     "start_time": "2026-03-18T10:47:26.740980Z"
    }
   },
   "source": [
    "waveguide_in = td.Structure(\n",
    "    geometry=td.Box(\n",
    "        center=(center_wg_in_x - length_wg, center_wg_in_y, 0),\n",
    "        size=(3 * length_wg, width_wg, td.inf),\n",
    "    ),\n",
    "    medium=mat,\n",
    ")\n",
    "\n",
    "waveguide_out = td.Structure(\n",
    "    geometry=td.Box(\n",
    "        center=(center_wg_out_x + length_wg, center_wg_out_y, 0),\n",
    "        size=(3 * length_wg, width_wg, td.inf),\n",
    "    ),\n",
    "    medium=mat,\n",
    ")\n",
    "\n",
    "design_region_static = td.Structure(\n",
    "    geometry=td.Box(\n",
    "        size=(size_design_x, size_design_y, td.inf),\n",
    "        center=(center_design_x, center_design_y, 0),\n",
    "    ),\n",
    "    medium=td.Medium(permittivity=np.mean([1, eps_mat])),\n",
    ")"
   ],
   "outputs": [],
   "execution_count": 8
  },
  {
   "cell_type": "code",
   "id": "49a4469b-1b78-4b35-93af-b3b5af7eaae0",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T10:47:26.808921Z",
     "start_time": "2026-03-18T10:47:26.795687Z"
    }
   },
   "source": [
    "mode_plane_size = 5 * width_wg\n",
    "num_modes = 1\n",
    "mode_spec = td.ModeSpec(num_modes=num_modes)\n",
    "mode_index = 0\n",
    "\n",
    "src_mode = td.ModeSource(\n",
    "    size=(0, mode_plane_size, td.inf),\n",
    "    center=(center_wg_in_x, center_wg_in_y, 0),\n",
    "    direction=\"+\",\n",
    "    mode_spec=mode_spec,\n",
    "    mode_index=mode_index,\n",
    "    num_freqs=10,\n",
    "    source_time=td.GaussianPulse(\n",
    "        freq0=freq0,\n",
    "        fwidth=fwidth,\n",
    "    ),\n",
    ")\n",
    "\n",
    "mnt_mode = td.ModeMonitor(\n",
    "    size=(0, mode_plane_size, td.inf),\n",
    "    center=(center_wg_out_x, center_wg_out_y, 0),\n",
    "    freqs=freqs,\n",
    "    mode_spec=mode_spec,\n",
    "    name=\"mode\",\n",
    ")\n",
    "\n",
    "mnt_field_0 = td.FieldMonitor(\n",
    "    size=(td.inf, td.inf, 0), center=(0, 0, 0), freqs=[freq0], name=\"field_single\"\n",
    ")\n",
    "\n",
    "mnt_field_all = mnt_field_0.updated_copy(freqs=freqs)"
   ],
   "outputs": [],
   "execution_count": 9
  },
  {
   "cell_type": "code",
   "id": "8355e7d6-24ea-4abd-8a76-94a852f73353",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T10:47:26.936992Z",
     "start_time": "2026-03-18T10:47:26.845947Z"
    }
   },
   "source": [
    "# mesh override structure over the design region helps keep the resolution constant across this space\n",
    "override_structure_design = td.MeshOverrideStructure(\n",
    "    geometry=design_region_static.geometry,\n",
    "    dl=3 * [dl_design_region],\n",
    ")\n",
    "\n",
    "sim_base = td.Simulation(\n",
    "    size=(size_sim_x, size_sim_y, 0),\n",
    "    structures=[waveguide_in, waveguide_out, design_region_static],\n",
    "    sources=[src_mode],\n",
    "    monitors=[mnt_mode],\n",
    "    grid_spec=td.GridSpec.auto(\n",
    "        wavelength=wvl0,\n",
    "        min_steps_per_wvl=min_steps_per_wvl,\n",
    "        override_structures=[override_structure_design],\n",
    "    ),\n",
    "    boundary_spec=td.BoundarySpec.pml(x=True, y=True, z=False),\n",
    "    run_time=run_time,\n",
    ")"
   ],
   "outputs": [],
   "execution_count": 10
  },
  {
   "cell_type": "code",
   "id": "353dc3d1-a210-4d85-8205-bc4e026fbe5d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T10:47:27.170356Z",
     "start_time": "2026-03-18T10:47:26.940299Z"
    }
   },
   "source": [
    "_, (ax1, ax2) = plt.subplots(1, 2, tight_layout=True, figsize=(10, 4))\n",
    "sim_base.plot(z=0, ax=ax1)\n",
    "sim_base.plot_eps(z=0, ax=ax2)\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x400 with 3 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 11
  },
  {
   "cell_type": "markdown",
   "id": "95b1ecb6-68a7-47b4-830d-a840c285ebe4",
   "metadata": {},
   "source": [
    "## Design Region Parameterization\n",
    "\n",
    "Next, we define the functions that allow us to generate our design region using topology optimization.\n",
    "\n",
    "We'll apply several functions that enable us to filter and project our optimization parameters into a permittivity grid, and then turn this permittivity grid into a structure that can be added to our base simulation as the optimization progresses."
   ]
  },
  {
   "cell_type": "code",
   "id": "a3ad0889-cbdb-4c0e-80f6-68cbe93143fe",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T10:47:27.589407Z",
     "start_time": "2026-03-18T10:47:27.174405Z"
    }
   },
   "source": [
    "from tidy3d.plugins.autograd import make_filter_and_project, rescale\n",
    "\n",
    "# radius of the circular filter (um) and the threshold strength\n",
    "radius = 0.120  # <= larger radius = bigger feature sizes\n",
    "beta = 50  # <= higher beta = more binarized\n",
    "beta_penalty = 10\n",
    "\n",
    "filter_project = make_filter_and_project(radius, dl_design_region)\n",
    "\n",
    "\n",
    "def get_density(params: np.ndarray, beta: float) -> np.ndarray:\n",
    "    \"\"\"Get the material density values (0, 1) array as a function of the parameters (0, 1)\"\"\"\n",
    "    return filter_project(params, beta)\n",
    "\n",
    "\n",
    "def get_eps(params: np.ndarray, beta: float) -> np.ndarray:\n",
    "    \"\"\"Get the permittivity values (1, eps_mat) array as a function of the parameters (0, 1)\"\"\"\n",
    "    processed_params = get_density(params, beta)\n",
    "    eps = rescale(processed_params, 1, eps_mat)\n",
    "    return eps\n",
    "\n",
    "\n",
    "def get_design_region(params, beta) -> td.Structure:\n",
    "    \"\"\"Get the design region evaluated at a set of parameters.\"\"\"\n",
    "\n",
    "    xmin = center_design_x - size_design_x / 2.0\n",
    "    xmax = center_design_x + size_design_x / 2.0\n",
    "    ymin = center_design_y - size_design_y / 2.0\n",
    "    ymax = center_design_y + size_design_y / 2.0\n",
    "\n",
    "    coord_bounds_x = np.linspace(xmin, xmax, nx + 1)\n",
    "    coord_bounds_y = np.linspace(ymin, ymax, ny + 1)\n",
    "\n",
    "    coord_centers_x = 0.5 * (coord_bounds_x[1:] + coord_bounds_x[:-1])\n",
    "    coord_centers_y = 0.5 * (coord_bounds_y[1:] + coord_bounds_y[:-1])\n",
    "\n",
    "    coords = dict(x=coord_centers_x, y=coord_centers_y, z=[0])\n",
    "\n",
    "    eps = get_eps(params, beta=beta).reshape((nx, ny, 1))\n",
    "    permittivity = td.SpatialDataArray(eps, coords=coords)\n",
    "    medium = td.CustomMedium(permittivity=permittivity)\n",
    "    return design_region_static.updated_copy(medium=medium)\n",
    "\n",
    "\n",
    "def get_sim(params, beta) -> td.Simulation:\n",
    "    \"\"\"Get the design region evaluated at a set of parameters.\"\"\"\n",
    "    design_region = get_design_region(params=params, beta=beta)\n",
    "    new_structures = list(sim_base.structures)\n",
    "    new_structures[-1] = design_region\n",
    "    return sim_base.updated_copy(structures=new_structures)"
   ],
   "outputs": [],
   "execution_count": 12
  },
  {
   "cell_type": "code",
   "id": "a431a13e-1c1a-43ab-8742-83abe417c8a0",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T10:47:27.675325Z",
     "start_time": "2026-03-18T10:47:27.594795Z"
    }
   },
   "source": [
    "# get simulation at a set of starting parameters and try it out\n",
    "np.random.seed(0)  # fix a random seed for reproducibility\n",
    "params0 = np.random.random((nx, ny))\n",
    "sim0 = get_sim(params0, beta=beta)"
   ],
   "outputs": [],
   "execution_count": 13
  },
  {
   "cell_type": "code",
   "id": "382022c3-2a0d-40db-9398-abc0f6f3fb7a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T10:47:28.087794Z",
     "start_time": "2026-03-18T10:47:27.678686Z"
    }
   },
   "source": [
    "_, (ax1, ax2) = plt.subplots(1, 2, tight_layout=True, figsize=(10, 4))\n",
    "sim0.plot(z=0, ax=ax1)\n",
    "sim0.plot_eps(z=0, ax=ax2)\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x400 with 3 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 14
  },
  {
   "cell_type": "markdown",
   "id": "d7b94105-a4db-4a7a-843e-4595f4bdc2a6",
   "metadata": {},
   "source": [
    "## Objective Function\n",
    "\n",
    "Next, we will write the code that will define our metric for optimization. Specifically, we will analyze the transmission spectrum of our device, and compute the weighted sum with a set of weights representing our ideal bandpass filter operation.\n",
    "\n",
    "We'll also include a penalty to discourage small feature sizes, which could be difficult to fabricate."
   ]
  },
  {
   "cell_type": "code",
   "id": "69e3afc1-ab3a-4f90-9dbf-486d738ebda3",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T10:47:28.095508Z",
     "start_time": "2026-03-18T10:47:28.093291Z"
    }
   },
   "source": [
    "def get_transmission(params, beta, step_num: int, verbose: bool, use_broadband: bool) -> np.ndarray:\n",
    "    \"\"\"Compute transmission amplitudes as function of frequency.\"\"\"\n",
    "    sim = get_sim(params=params, beta=beta)\n",
    "    task_name = \"bandpass_invdes\"\n",
    "    if step_num is not None:\n",
    "        task_name += \"_step_\" + str(step_num)\n",
    "    data = web.run(sim, task_name=task_name, verbose=verbose)\n",
    "    amps = data[mnt_mode.name].amps.sel(direction=\"+\", mode_index=mode_index)\n",
    "    if not use_broadband:\n",
    "        amps = amps.interp(f=freq0)\n",
    "    return np.abs(amps) ** 2"
   ],
   "outputs": [],
   "execution_count": 15
  },
  {
   "cell_type": "code",
   "id": "7fa5ad7d-be8e-4f20-986c-2d150b0dae49",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T10:47:28.180087Z",
     "start_time": "2026-03-18T10:47:28.138390Z"
    }
   },
   "source": [
    "bandwidth_um = 0.1\n",
    "\n",
    "import xarray as xr\n",
    "\n",
    "\n",
    "def target(freq: float) -> xr.DataArray:\n",
    "    \"\"\"Target transmission as a function of frequency.\"\"\"\n",
    "    wvl_min = lambda0 - bandwidth_um / 2.0\n",
    "    wvl_max = lambda0 + bandwidth_um / 2.0\n",
    "    wvl = td.C_0 / freq\n",
    "    values = 1.0 * (np.logical_and(wvl > wvl_min, wvl < wvl_max))\n",
    "    return xr.DataArray(values, coords=dict(f=freq))\n",
    "\n",
    "\n",
    "target_spectrum = target(freqs)\n",
    "target_spectrum.plot.scatter()\n",
    "plt.ylabel(\"transmission\")\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 16
  },
  {
   "cell_type": "code",
   "id": "e8b67ae9-9d49-450d-89a3-0581fb055c12",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T10:47:28.187994Z",
     "start_time": "2026-03-18T10:47:28.186150Z"
    }
   },
   "source": [
    "def get_metric(transmission: xr.DataArray) -> float:\n",
    "    in_band = target_spectrum\n",
    "    out_band = 1 - target_spectrum\n",
    "\n",
    "    avg_T_in_band = np.sum(in_band * transmission).values / np.sum(in_band).values\n",
    "    avg_T_out_band = np.sum(out_band * transmission).values / np.sum(out_band).values\n",
    "\n",
    "    # ideally,  (avg_T_in_band = 1 and avg_T_out_band = 0) -> metric = 1\n",
    "    # at worst, (avg_T_in_band = 0 and avg_T_out_band = 1) -> metric = -1\n",
    "\n",
    "    return avg_T_in_band - avg_T_out_band"
   ],
   "outputs": [],
   "execution_count": 17
  },
  {
   "cell_type": "markdown",
   "id": "3cccf15e-c5bb-40d7-817d-1c1f8521d7fb",
   "metadata": {},
   "source": [
    "### Fabrication Penalty\n",
    "\n",
    "Next, we introduce a built-in fabrication penalty function that evaluates our design region to reduce our objective function if any small feature sizes are measured compared to the `radius` defined earlier."
   ]
  },
  {
   "cell_type": "code",
   "id": "3003837c-b401-413d-89c3-cb7d5679afc9",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T10:47:28.232969Z",
     "start_time": "2026-03-18T10:47:28.230589Z"
    }
   },
   "source": [
    "from tidy3d.plugins.autograd import make_erosion_dilation_penalty\n",
    "\n",
    "penalty = make_erosion_dilation_penalty(radius, dl_design_region, beta=beta_penalty)"
   ],
   "outputs": [],
   "execution_count": 18
  },
  {
   "cell_type": "code",
   "id": "f35aa79e-712e-4bb6-8257-489d217e4ce1",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T10:47:28.277976Z",
     "start_time": "2026-03-18T10:47:28.275787Z"
    }
   },
   "source": [
    "# for debugging, can be helpful to be able to change our objective function behavior\n",
    "use_metric = True\n",
    "use_penalty = True\n",
    "use_broadband = True\n",
    "\n",
    "\n",
    "def objective(\n",
    "    params: np.ndarray,\n",
    "    beta: float,\n",
    "    step_num: int = 0,\n",
    "    verbose: bool = False,\n",
    "    use_metric: bool = use_metric,\n",
    "    use_penalty: bool = use_penalty,\n",
    "    use_broadband: bool = use_broadband,\n",
    ") -> float:\n",
    "    metric = 0.0\n",
    "    penalty_val = 0.0\n",
    "\n",
    "    if use_metric:\n",
    "        transmission = get_transmission(\n",
    "            params=params,\n",
    "            beta=beta,\n",
    "            step_num=step_num,\n",
    "            verbose=verbose,\n",
    "            use_broadband=use_broadband,\n",
    "        )\n",
    "        metric = get_metric(transmission)\n",
    "\n",
    "    if use_penalty:\n",
    "        penalty_weight = 1.0  # np.minimum(1, beta / 25)\n",
    "        density = get_density(params, beta)\n",
    "        penalty_val = penalty_weight * penalty(density)\n",
    "\n",
    "    return metric - penalty_val"
   ],
   "outputs": [],
   "execution_count": 19
  },
  {
   "cell_type": "code",
   "id": "b5fcbd67-4a6a-4dfc-8e69-9dc221fb8042",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T10:47:28.322390Z",
     "start_time": "2026-03-18T10:47:28.320889Z"
    }
   },
   "source": [
    "grad_fn = ag.value_and_grad(objective)"
   ],
   "outputs": [],
   "execution_count": 20
  },
  {
   "cell_type": "code",
   "id": "19ec2d7d-7cad-4bdd-af11-8354585e5ef0",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T10:53:41.402362Z",
     "start_time": "2026-03-18T10:47:28.368154Z"
    }
   },
   "source": [
    "val, grad = grad_fn(params0, beta=beta, verbose=True)\n",
    "print(grad.shape)"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001B[2;36m11:47:29 CET\u001B[0m\u001B[2;36m \u001B[0mCreated task \u001B[32m'bandpass_invdes_step_0'\u001B[0m with resource_id             \n",
       "\u001B[2;36m             \u001B[0m\u001B[32m'fdve-c700b3a5-89a6-4dc4-9a74-f69793295694'\u001B[0m and task_type \u001B[32m'FDTD'\u001B[0m.  \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">11:47:29 CET </span>Created task <span style=\"color: #008000; text-decoration-color: #008000\">'bandpass_invdes_step_0'</span> with resource_id             \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #008000; text-decoration-color: #008000\">'fdve-c700b3a5-89a6-4dc4-9a74-f69793295694'</span> and task_type <span style=\"color: #008000; text-decoration-color: #008000\">'FDTD'</span>.  \n",
       "</pre>\n"
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       "\u001B[2;36m            \u001B[0m\u001B[2;36m \u001B[0mView task using web UI at                                          \n",
       "\u001B[2;36m             \u001B[0m\u001B]8;id=860050;https://tidy3d.simulation.cloud/workbench?taskId=fdve-c700b3a5-89a6-4dc4-9a74-f69793295694\u001B\\\u001B[32m'https://tidy3d.simulation.cloud/workbench?\u001B[0m\u001B]8;;\u001B\\\u001B]8;id=737968;https://tidy3d.simulation.cloud/workbench?taskId=fdve-c700b3a5-89a6-4dc4-9a74-f69793295694\u001B\\\u001B[32mtaskId\u001B[0m\u001B]8;;\u001B\\\u001B]8;id=860050;https://tidy3d.simulation.cloud/workbench?taskId=fdve-c700b3a5-89a6-4dc4-9a74-f69793295694\u001B\\\u001B[32m=\u001B[0m\u001B]8;;\u001B\\\u001B]8;id=285030;https://tidy3d.simulation.cloud/workbench?taskId=fdve-c700b3a5-89a6-4dc4-9a74-f69793295694\u001B\\\u001B[32mfdve\u001B[0m\u001B]8;;\u001B\\\u001B]8;id=860050;https://tidy3d.simulation.cloud/workbench?taskId=fdve-c700b3a5-89a6-4dc4-9a74-f69793295694\u001B\\\u001B[32m-c700b3a5-89a\u001B[0m\u001B]8;;\u001B\\\n",
       "\u001B[2;36m             \u001B[0m\u001B]8;id=860050;https://tidy3d.simulation.cloud/workbench?taskId=fdve-c700b3a5-89a6-4dc4-9a74-f69793295694\u001B\\\u001B[32m6-4dc4-9a74-f69793295694'\u001B[0m\u001B]8;;\u001B\\.                                         \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>View task using web UI at                                          \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-c700b3a5-89a6-4dc4-9a74-f69793295694\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-c700b3a5-89a</span></a>\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-c700b3a5-89a6-4dc4-9a74-f69793295694\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">6-4dc4-9a74-f69793295694'</span></a>.                                         \n",
       "</pre>\n"
      ]
     },
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    {
     "data": {
      "text/plain": [
       "\u001B[2;36m            \u001B[0m\u001B[2;36m \u001B[0mTask folder: \u001B]8;id=621712;https://tidy3d.simulation.cloud/folders/folder-df61810d-cad6-4474-8ea9-e4f00d5dfcb0\u001B\\\u001B[32m'default'\u001B[0m\u001B]8;;\u001B\\.                                            \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>Task folder: <a href=\"https://tidy3d.simulation.cloud/folders/folder-df61810d-cad6-4474-8ea9-e4f00d5dfcb0\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'default'</span></a>.                                            \n",
       "</pre>\n"
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    {
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       "Output()"
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
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       "Output()"
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       "version_major": 2,
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     "metadata": {},
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    {
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ]
     },
     "metadata": {},
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    {
     "data": {
      "text/plain": [
       "\u001B[2;36m11:47:44 CET\u001B[0m\u001B[2;36m \u001B[0mstatus = queued                                                    \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">11:47:44 CET </span>status = queued                                                    \n",
       "</pre>\n"
      ]
     },
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     "jetTransient": {
      "display_id": null
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    },
    {
     "data": {
      "text/plain": [
       "\u001B[2;36m            \u001B[0m\u001B[2;36m \u001B[0mTo cancel the simulation, use \u001B[32m'web.abort\u001B[0m\u001B[32m(\u001B[0m\u001B[32mtask_id\u001B[0m\u001B[32m)\u001B[0m\u001B[32m'\u001B[0m or              \n",
       "\u001B[2;36m             \u001B[0m\u001B[32m'web.delete\u001B[0m\u001B[32m(\u001B[0m\u001B[32mtask_id\u001B[0m\u001B[32m)\u001B[0m\u001B[32m'\u001B[0m or abort/delete the task in the web UI.      \n",
       "\u001B[2;36m             \u001B[0mTerminating the Python script will not stop the job running on the \n",
       "\u001B[2;36m             \u001B[0mcloud.                                                             \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>To cancel the simulation, use <span style=\"color: #008000; text-decoration-color: #008000\">'web.abort(task_id)'</span> or              \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #008000; text-decoration-color: #008000\">'web.delete(task_id)'</span> or abort/delete the task in the web UI.      \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>Terminating the Python script will not stop the job running on the \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>cloud.                                                             \n",
       "</pre>\n"
      ]
     },
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       "Output()"
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       "model_id": "119600f7c92749378139140f212b7f41"
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ]
     },
     "metadata": {},
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    {
     "data": {
      "text/plain": [
       "\u001B[2;36m11:47:58 CET\u001B[0m\u001B[2;36m \u001B[0mstarting up solver                                                 \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">11:47:58 CET </span>starting up solver                                                 \n",
       "</pre>\n"
      ]
     },
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    },
    {
     "data": {
      "text/plain": [
       "\u001B[2;36m11:47:59 CET\u001B[0m\u001B[2;36m \u001B[0mrunning solver                                                     \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">11:47:59 CET </span>running solver                                                     \n",
       "</pre>\n"
      ]
     },
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    {
     "data": {
      "text/plain": [
       "\u001B[2;36m11:48:15 CET\u001B[0m\u001B[2;36m \u001B[0mearly shutoff detected at \u001B[1;36m18\u001B[0m%, exiting.                            \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">11:48:15 CET </span>early shutoff detected at <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">18</span>%, exiting.                            \n",
       "</pre>\n"
      ]
     },
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ]
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    {
     "data": {
      "text/plain": [
       "\u001B[2;36m11:48:16 CET\u001B[0m\u001B[2;36m \u001B[0mstatus = postprocess                                               \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">11:48:16 CET </span>status = postprocess                                               \n",
       "</pre>\n"
      ]
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       "Output()"
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     "data": {
      "text/plain": [
       "\u001B[2;36m11:48:38 CET\u001B[0m\u001B[2;36m \u001B[0mstatus = success                                                   \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">11:48:38 CET </span>status = success                                                   \n",
       "</pre>\n"
      ]
     },
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ]
     },
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    {
     "data": {
      "text/plain": [
       "\u001B[2;36m11:48:40 CET\u001B[0m\u001B[2;36m \u001B[0mView simulation result at                                          \n",
       "\u001B[2;36m             \u001B[0m\u001B]8;id=764015;https://tidy3d.simulation.cloud/workbench?taskId=fdve-c700b3a5-89a6-4dc4-9a74-f69793295694\u001B\\\u001B[4;34m'https://tidy3d.simulation.cloud/workbench?\u001B[0m\u001B]8;;\u001B\\\u001B]8;id=121193;https://tidy3d.simulation.cloud/workbench?taskId=fdve-c700b3a5-89a6-4dc4-9a74-f69793295694\u001B\\\u001B[4;34mtaskId\u001B[0m\u001B]8;;\u001B\\\u001B]8;id=764015;https://tidy3d.simulation.cloud/workbench?taskId=fdve-c700b3a5-89a6-4dc4-9a74-f69793295694\u001B\\\u001B[4;34m=\u001B[0m\u001B]8;;\u001B\\\u001B]8;id=624924;https://tidy3d.simulation.cloud/workbench?taskId=fdve-c700b3a5-89a6-4dc4-9a74-f69793295694\u001B\\\u001B[4;34mfdve\u001B[0m\u001B]8;;\u001B\\\u001B]8;id=764015;https://tidy3d.simulation.cloud/workbench?taskId=fdve-c700b3a5-89a6-4dc4-9a74-f69793295694\u001B\\\u001B[4;34m-c700b3a5-89a\u001B[0m\u001B]8;;\u001B\\\n",
       "\u001B[2;36m             \u001B[0m\u001B]8;id=764015;https://tidy3d.simulation.cloud/workbench?taskId=fdve-c700b3a5-89a6-4dc4-9a74-f69793295694\u001B\\\u001B[4;34m6-4dc4-9a74-f69793295694'\u001B[0m\u001B]8;;\u001B\\\u001B[4;34m.\u001B[0m                                         \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">11:48:40 CET </span>View simulation result at                                          \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-c700b3a5-89a6-4dc4-9a74-f69793295694\" target=\"_blank\"><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-c700b3a5-89a</span></a>\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-c700b3a5-89a6-4dc4-9a74-f69793295694\" target=\"_blank\"><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">6-4dc4-9a74-f69793295694'</span></a><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">.</span>                                         \n",
       "</pre>\n"
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ]
     },
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    {
     "data": {
      "text/plain": [
       "\u001B[2;36m11:48:44 CET\u001B[0m\u001B[2;36m \u001B[0mLoading results from simulation_data.hdf5                          \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">11:48:44 CET </span>Loading results from simulation_data.hdf5                          \n",
       "</pre>\n"
      ]
     },
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     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
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    },
    {
     "data": {
      "text/plain": [
       "\u001B[2;36m11:48:45 CET\u001B[0m\u001B[2;36m \u001B[0mStarted working on Batch containing \u001B[1;36m1\u001B[0m tasks.                       \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">11:48:45 CET </span>Started working on Batch containing <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1</span> tasks.                       \n",
       "</pre>\n"
      ]
     },
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    {
     "data": {
      "text/plain": [
       "\u001B[2;36m11:49:08 CET\u001B[0m\u001B[2;36m \u001B[0mMaximum FlexCredit cost: \u001B[1;36m0.062\u001B[0m for the whole batch.                \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">11:49:08 CET </span>Maximum FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.062</span> for the whole batch.                \n",
       "</pre>\n"
      ]
     },
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     }
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     "data": {
      "text/plain": [
       "\u001B[2;36m            \u001B[0m\u001B[2;36m \u001B[0mUse \u001B[32m'Batch.real_cost\u001B[0m\u001B[32m(\u001B[0m\u001B[32m)\u001B[0m\u001B[32m'\u001B[0m to get the billed FlexCredit cost after    \n",
       "\u001B[2;36m             \u001B[0mcompletion.                                                        \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>Use <span style=\"color: #008000; text-decoration-color: #008000\">'Batch.real_cost()'</span> to get the billed FlexCredit cost after    \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>completion.                                                        \n",
       "</pre>\n"
      ]
     },
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    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "604a661124b7458782b8bebef6465c6c"
      }
     },
     "metadata": {},
     "output_type": "display_data",
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    },
    {
     "data": {
      "text/plain": [
       "\u001B[2;36m11:53:33 CET\u001B[0m\u001B[2;36m \u001B[0mBatch complete.                                                    \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">11:53:33 CET </span>Batch complete.                                                    \n",
       "</pre>\n"
      ]
     },
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     }
    },
    {
     "data": {
      "text/plain": [],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ]
     },
     "metadata": {},
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    {
     "data": {
      "text/plain": [
       "Output()"
      ],
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       "version_major": 2,
       "version_minor": 0,
       "model_id": "1bd21230441d4debb1165ecdb0023edf"
      }
     },
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    },
    {
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      "text/plain": [],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
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    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(640, 320)\n"
     ]
    }
   ],
   "execution_count": 21
  },
  {
   "cell_type": "code",
   "id": "ecd26376-0dda-4faa-a6b2-756a7a39464b",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T10:53:41.426020Z",
     "start_time": "2026-03-18T10:53:41.414918Z"
    }
   },
   "source": [
    "print(np.linalg.norm(grad))\n",
    "val"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.07879764775310094\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "np.float64(-0.7059607115923544)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 22
  },
  {
   "cell_type": "markdown",
   "id": "c58fb201-c09d-4a1e-b2f1-84f18b50dd89",
   "metadata": {},
   "source": [
    "## Optimization\n",
    "\n",
    "Now that we have a function to compute our gradient, we can use an open source gradient-based optimizer to perform inverse design of our device.\n",
    "\n",
    "In this case, we use Tidy3D's built-in Adam optimizer, which performs gradient-ascent with some extra terms to improve the performance and convergence."
   ]
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T13:28:05.352075Z",
     "start_time": "2026-03-18T10:53:41.473794Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# assert False\n",
    "from tidy3d.plugins.autograd import adam, apply_updates\n",
    "\n",
    "# hyperparameters\n",
    "num_steps = 35\n",
    "learning_rate = 0.1\n",
    "\n",
    "# initialize adam optimizer with starting parameters\n",
    "params = np.ones_like(params0) * 0.5\n",
    "optimizer = adam(learning_rate=learning_rate)\n",
    "opt_state = optimizer.init(params)\n",
    "\n",
    "# store history\n",
    "objective_history = []\n",
    "params_history = [params]\n",
    "beta_history = []\n",
    "\n",
    "# gradually increase the binarization strength\n",
    "beta0 = 1\n",
    "beta_max = 50\n",
    "\n",
    "for i in range(num_steps):\n",
    "    # compute gradient and current objective function value\n",
    "    density = get_density(params, beta)\n",
    "\n",
    "    plt.subplots(1, 1, figsize=(2, 2))\n",
    "    plt.imshow(np.flipud(1 - density.T), cmap=\"gray\", vmin=0, vmax=1)\n",
    "    plt.axis(\"off\")\n",
    "    plt.show()\n",
    "\n",
    "    perc_done = i / (num_steps - 1)\n",
    "\n",
    "    beta = beta0 + perc_done * (beta_max - beta0)\n",
    "    value, gradient = grad_fn(params, step_num=i + 1, beta=beta)\n",
    "\n",
    "    # outputs\n",
    "    print(f\"step = {i + 1}\")\n",
    "    print(f\"\\tbeta = {beta:.4e}\")\n",
    "    print(f\"\\tJ = {value:.4e}\")\n",
    "    print(f\"\\tgrad_norm = {np.linalg.norm(gradient):.4e}\")\n",
    "\n",
    "    # compute and apply updates to the optimizer based on gradient (-1 sign to maximize obj_fn)\n",
    "    updates, opt_state = optimizer.update(-gradient, opt_state, params)\n",
    "    params[:] = apply_updates(params, updates)\n",
    "\n",
    "    # cap the parameters\n",
    "    params = np.clip(np.array(params), 0.0, 1.0)\n",
    "\n",
    "    # save history\n",
    "    objective_history.append(value)\n",
    "    params_history.append(params.copy())\n",
    "    beta_history.append(beta)\n",
    "\n",
    "power = objective(params_history[-1], beta=beta)\n",
    "objective_history.append(power)"
   ],
   "id": "da4397c008cebdc9",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
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    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 1\n",
      "\tbeta = 1.0000e+00\n",
      "\tJ = -1.0779e+00\n",
      "\tgrad_norm = 2.7160e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 2\n",
      "\tbeta = 2.4412e+00\n",
      "\tJ = -8.2619e-01\n",
      "\tgrad_norm = 6.2687e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 3\n",
      "\tbeta = 3.8824e+00\n",
      "\tJ = -7.2141e-01\n",
      "\tgrad_norm = 6.7354e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 4\n",
      "\tbeta = 5.3235e+00\n",
      "\tJ = -4.8807e-01\n",
      "\tgrad_norm = 5.5690e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 5\n",
      "\tbeta = 6.7647e+00\n",
      "\tJ = -4.3455e-01\n",
      "\tgrad_norm = 4.1122e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 6\n",
      "\tbeta = 8.2059e+00\n",
      "\tJ = -2.6478e-01\n",
      "\tgrad_norm = 3.4645e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 7\n",
      "\tbeta = 9.6471e+00\n",
      "\tJ = -1.4979e-01\n",
      "\tgrad_norm = 1.9463e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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lL38hKpWKSCQSEhAQ4LXn5lof6nQQCoUkLS2NfPnll8RgMHh0247kKKHeL/rY7XZiMBhIbW0t2bVrF3njjTfIggULiL+/v8+eLV8ePp9P4uPjyeOPP0727NlDqqqqSFtbG9HpdMwZQOvn6lr19rFYLOT5559nzhEOh0OEQiERi8W/6FhxOBwilUrZe7hcLsnJySFlZWUeXcxWq9VbkSRer7wjmb8aGxvx3XffMVMNPVBcy3ZLZyMtg8fjQSaTQS6XQyKRQKlUws/Pj9lwHQ4H8vPzkZOTw/SlofX1tBJ70onpyTk+Ph6xsbGYOnUqbr75ZnzwwQf44osv0N/f77Ge9PGmbfS99PN8Ph8FBQX4wx/+gIkTJ0KhUAzbPYaqQVfaWYbWxWg0ory8HDabDVwuFxEREZg2bRr8/PxQV1eHpqYmaLVa6PV6mM1mr9U8b2A2m93aW1paimeffRbPPfcc0tPTWUAR7Qtv4bPaQCtgt9vR1dWFkydPQiKRIDo6GlarFTqdDhaLxS16yhdB5vP5mDZtGmbNmsXsp/RgERQUBIlEArFYDB6Ph8HBQZSWlqKyshIZGRkIDQ0dVcf1hJEmGjVXicVixMbG4u6770ZbWxv27dsHg8HA6srn8+FwONzswJ7q4FouHSAqIAkJCXj22Wcxbdo0j7Zrb9pBQd9ptVrR3d3NFpMTJ06gsLAQABAYGIg//vGPuO222yCRSGCxWKDT6aDT6dDW1oby8nLU19ejpaUFJSUlaG1tvarFiMO5HMlHD5TU3u5wOLBr1y40Njbi6aefxpIlS4Y5m7zBVem8ZrMZJ0+exNatW9Hc3IwJEyZg1qxZkEgkOHToEL744gt0dXUxc5Tdbr+i7kRXpOzsbLz99ttITU294ioTEBCAsLAwZGZmwmazMfeo3W6H0WiEQCBgoYIjvdN1MtJDIJ0chBCYTCa0traipqYGUqkUarWaOSQ86YWjeSJdQe24IpEImZmZiIuL87i7eSpjJJMk/Zm6fb/99ltoNBpwuVz09fWht7cXAoEA+fn5mD9/PtRqNYDLLmh/f38AQFpaGmbNmsUEraqqCmvXrsWhQ4d81n/5fD7kcjkCAgKQlpYGpVKJ06dPMz9BRUUFXnvtNYSHh2Py5Mk+mckAH4SXdpLD4UBlZSU++eQTlJSUQCKRIC8vD1lZWQgICIBKpcIPP/zAjNverLxyuRxxcXHMTJaSkuLVoYsQArFYjMDAQJSUlGDbtm1obm5GR0cHtFot1Go1Zs2ahenTpyMkJASDg4Po6OhAeHg4wsPDweVy4XQ60dXVhWPHjuHs2bMQiUSYPHkyUlJSMDAwgAMHDmDv3r1obGyEwWBwU4uoNWKoyuC68g4VPqfTCbvdDofDwQ5b3d3d+OGHH5CVlQWlUgmlUslMRhwOBw6HA2azmbmx6Tvoe41GI9vtysrK8M477+DgwYPDDmA8Hg/h4eGYN28egoKC3OrqCqoO8Xg85OTk4K233sIzzzyDEydOQKfTea1SUL+A1WpFUFAQMjIyoNFo0NvbC6fTCbVajeDgYNTV1SEzMxMqlWrEOnmC104KKoRarRbfffcdtm/fDpPJBIvFArlcjvnz5yMnJwdnzpzB3/72N7S1tXnUA2nH0PKEQiHmzZuHxx9/HMnJyQgODnbTga4E8qOL9/vvv8cf//hHXLp0iblcqSMlLi4OY8aMgUajQVNTE9LT0/HUU08hJSUFtbW1eO+997B//34MDAyAz+cjOTkZU6ZMgUajweHDh9HV1QWHwwEul8t03NGcF6OtjEPB5/OhVCoRHh4OsVgMu90OPz8/FtykUChw8uRJnD9/HnFxcVi6dCkSEhLcBP/rr79GY2MjuFwuDh48iLKyMhZ7wePxIBQKIZfLkZCQgMWLF+OOO+5AWFiYm114tP4lhKC3txfFxcXYvXs3/vvf/6Kjo8Or8aFqklqtRlBQEPR6PbhcLubNm4dFixYhLCwMhBBmZaE2em/g04GN/Ggsp1t6Z2cnDhw4gKKiIpSWliIsLAwajQZdXV0eB5bD4SAyMhJ5eXkwmUxob29HamoqnnzySWRlZbHAGF8hEAiQnJwMqVQ6TEUxGAwoLy9HVVUVgMuTsKWlBS0tLbjhhhtQWVmJiooKpjLYbDbm+bFarSwIh37XG/iiH9rtdmg0GgwMDLAJzeFwUFFRgerqaohEIhw9ehQajQbBwcGQy+W45557oFAoYDKZ8P3332PDhg3o7+8Hh8NBf38/q69QKER6ejomTpyIzMxM5OXlITExERKJxCvBBX6aiEFBQZg7dy4mTZqEgoICvPHGG2hoaGDq1eDgoMc4Dbq49PT0oK+vj2VozJw5E5MmTYJAIIDdbofFYmET0lv47GFTKpW48cYbkZaWhrKyMhw6dAg6nY4JLa3sUNA0oBdeeAEFBQVwOp0YGBiAXC6HSqUadbaNJgx0UsXHx+O2226D2WyGxWKBwWBg6SsA3LY6q9WKCxcuoKKiAg6Hg/2N2lkjIyMRGRkJg8GA5uZmGAyGX9RFTFUQ1zZJpVIolUpYrVZmu3Y4HGhsbERZWRnkcjnOnTuHjz/+2C3M0G63g8PhQC6X45ZbbsGaNWuQmprK4j9G2hWudKilUCgUWLZsGcaPH4/W1lZIpVJYLBbs2LEDn3/+OTo7O0e1x3O5XPT396OlpQV2ux1CoZA9vuKqTGV8Ph9+fn4IDw8Hj8djkVmeviOTyRAVFYV58+Zh5cqVSExMZGX5+/u76YX08STItHyqcjgcDhYdBlw+ZP32t7/F9OnTQQhBd3c3Pv74Y+zbt8/jZKJC66oPisViqNVqyOVy6PV66PV6CAQC8Pl8r1zbPwcEAgECAwORn5+PrKws9Pb2orGxkUXFHTx4ECUlJdDr9WhpaXGboMDlPlepVFi5ciV+97vfISwszGN/WiwW9Pf3QyKRwM/Pj33XFa5C6GpF4fP5iIuLQ1xcHPt7Xl4e5s6diw8++ABHjhxBb2+vR93Y6XRicHAQRUVFWLJkiU+7wFD4fGBzrQQN9PZUSaoH33HHHcjJyWGuXvpd6iqklgCDwcAGIzQ0FFFRUZBIJHA4HGhtbUVxcTGcTicCAgLQ3t6Onp4ejB8/ntl2ORwOAgIC2Ana4XBAKpWitLQULS0tV2wX7Tyz2YzW1lZ0dnaygxJd+X7pAB2ZTIaYmBhkZmYiNTWV9QkNEDKZTNBqtaMehAkhUKlUWLBggUfBpTtjfX09jh49ioyMDIwbNw4CgYBZTqirmR4Ge3p6YDAYoFarERgY6DH4SSgUYurUqcjLy0NFRQW+//57bNu2DdXV1cMWD6vViqKiItTV1SE4ONgtKs4XeC28JpOJNYSaXb777jtUVVUN60Qul4tJkybh5ZdfZiF7TqcTJpMJnZ2dKCwsZH7v1NRUBAQE4OLFizh48CDa29sREBCAgoICZGRkoLe3F7t27UJ5eTl4PB5UKhVTDU6fPo3HH38cY8eOdQvGoR3qrfLvajmw2WzsUOEaI+DqjPglIBQKERgYyASupqYG7e3tuHTpEvr6+mA2m70yOQLA4ODgFTMSpFIpEhISEBQUxPrMZDKhuLgY1dXVkMvlcDqdKC0tRVFREXQ6HRITEzF//nzccMMNLCoMAFJTUxETEwORSAQej4esrCzccMMNmDNnDp5++mkUFhYOq0tdXR3+8pe/YPXq1SgoKGAHdcB7a4PXwvvUU0+htrYW9fX1GBwchNVqZSvCUHA4HGi1WpSXlzOBLSkpwdmzZ1FaWoqmpiYWpSSRSCCRSGA2m2E0GtmsLyoqYqdvs9nMgkzMZjMzI7W2tmLXrl3gcDhISEiATCZjq7ter0dxcbGbR2w0uNqkR9rG6ETw1vHiyUM2VPi4XC74fD5zFlRWVqKyshJWq5VZc3x19Oj1epw9exb5+fks+8N1UgsEAkRGRiI0NJTZm51OJy5evIgXXngBpaWlbLLq9Xpmhrtw4QIOHToElUoFvV4PjUbDTF7JyckIDQ0Fn89HZGQkxo0bB5FIBJlMxvR1VzgcDhw9ehTnzp1DSkoK5s2bh7lz5yI2Nhbh4eFetdNrU5lAIGC5+8MK+XGVE4vFrMP5fD6CgoIgl8vR19eHgYGBEb/vDWj00ZQpUzBhwgSYzWbm/ZHJZAgLC0NAQADTobq7u3HixAnU19f/bK5OavukOvdIoOYh6soODw9HSEgILBYLqqur0d7eziaJUChkLm2j0ejGa3C14PP5SE9Px/z585GamoqwsDBER0cjNDTULaLLFdTc+D//8z9obW29qj6jZfJ4PISEhCAoKAhNTU0YGBhwU888tY3P5yM6OhpZWVnYunWrd+30tmIjpatwuVyoVCrceOONCA0NxaFDh9Dc3AybzeZbhNAVwOPxEBQUhAkTJmDChAmoq6vD3r17UVZWxkL2hp6k6eP6e2qrvZogc2rfHXpKdx0QapFJTU1l2+eYMWMQHBwMh8OBwsJCfPbZZ7hw4QIsFgtzLTscjlGzS0bCUGGgTo2ysjJUVVUxx0ZoaCiysrKQm5uL5ORkJCcnIzIy0m3itLe3s5X+auDqrezo6EB3dzdTx+jhXSQSsdXcFQ6HA93d3aioqPD6fT67h/l8PtuGuFwuRCIR1Go1uFwuYz251sAcT3A4HCwTtaSkBPX19SgtLfUqSFogELgxuVBh8RVDV0SBQICYmBj4+/ujtbUVOp0OISEhuPPOO7F06VJERkay99LDEHUvv/76625WBFr+1YBOSHq2oB48h8PhZjasqqrCN998A4lEgqioKMyZMwdz5syBSqVCVVUVtm3bBp1ON8xDOFLdRvub6zkCANuJXLNuaPn0LJOXl4eMjAyv2+1T9jCHw4G/vz/S09NZstz58+fR29vLHBi0w7yJZVAoFIiNjYVSqYRGo0Frayv0ej0IIayxVO+i5bkOkrcrBE2udDgc7NBzrZNLIBBg7NixWLNmDaKionD+/Hm0trZi3LhxmD17NpRKpZue6ypQTU1NWLduHbZt2+ZToPdo4HK5zODv7cQUCAQICAiATCbD4OAgU+2kUikiIiIQERGBwMBAcLlcdHR0oKOjAxzO5YzpiIgIyGQy1NTUoKSkxGMsMH34fD4UCgWjIqD14/F4kEgkkMlkCA0NRVJSElQqFT766COv6u9z6rtUKsXy5ctx99134+jRo3j77bcxMDDAPiOXywGACSEF5UwQCoUwGAwIDQ3F73//e8yfPx9yuRw6nQ5lZWU4ffo0zGYzYmJiEB4ejoqKCmzYsMFrd6SvoPopTUYUCoVQKBTg8/nQarXQarXM1ENNZiKRCCkpKXjssccwd+5cdthyOByQy+VuYZl0AKmaQp0zW7duxVtvvYVLly6xwbySrjvaSgfgZ7GIKJVK3HXXXbjnnnsQHx8PiUQC4LIpk6bcKxQKiMViEELQ1taGLVu2YPfu3ejq6sLAwAA70FNhjomJwfTp03H48GE3jg4ej8dMm5SvDrgsO97AZ7WBrjgZGRlsJlKIxWIsWrQIfn5+2Lhxo5tQx8bGYtWqVYiKikJlZSViYmKwdOlSJuwKhQLh4eGYNWsWW8UBYNasWfDz88Nf//pXdHd3+1rdEcHj8eDv74/U1FRkZ2czAsGQkBAkJiZCJpOhvr4e33zzDY4dO4bBwUEIBAIEBQUhKysLCxcuxLQf42GpQANwM80N1UXpQUmhUGDq1Kno7u7G7t270dzczPRA11VJJpMxWzc9sPr7+7Os3qFBMtdqhw4ICMBjjz2GRx99FCqVym1spVIpC+ah7SGEIC4uDr/73e8wdepUnDx5Etu2bUNJSQn7HE2offjhh/Hee+/hrbfeYouBTCbDmDFj0NbWxng2fIHXwkvNHsuWLcPy5csREBCA6dOnY/Lkydi9ezc4HA5uvvlmvPDCC+DxeKisrMThw4dZ8E1OTg4WLFiAkJAQZGVlwel0MpfgUO+dK6RSKX77298iMDAQ69atw8WLF0c8PHoLsViMsWPH4oEHHsCMGTMQGBgIQi6n0otEIkilUnC5XCQmJiIyMhLh4eGoqqpi9ueCggLExMRAJpN59Me7HsJozK+rUPN4PCQmJmLVqlWYPXs2zp49i6NHj+L8+fPo7++HUChEZmYm5s2bx1LeTSYTEhISkJSUBACorKzEjh07sH//frS1tV11mhKXy4VcLkdubi4eeeQR3HLLLWy19Tb2QSaTITExER0dHSybnKoPUVFRWLJkCSIjI/HQQw/h2LFjKCoqglqtxqpVq7B8+XKcP38ezz//POrr632L/fb2g9HR0ZgyZQrWrl2LkJAQAEBoaCj++te/MjPZn/70J8TGxsJutyMvLw/Hjh2Dw+GAWCxGVFQU/Pz8IJFIEB4e7rZNXKlzRCIRli5dirS0NHz66afYu3cvWltbYTKZRqUdpSoB8NOqJJFIMH78eDz11FOYNGkSy4QmhEAmkwH4Kf9LJBIhKSkJd955J7RaLYKDgxEREcFIPTwNLnV0dHd3Y3BwEMHBwVCr1R49UsHBwQgMDERWVhamT5+OAwcOoLKyEhEREZg3bx7S0tIgEomYni4UCll74uLiUFBQgBkzZuDDDz/E2bNnWbgmnVCe3PZcLhd+fn6IiIhAXFwcMjMzMXnyZOTm5jLuDW+ElvY3PaALBAIWhxEUFMSIXObPn4+EhARwOJfT9detW4eNGzdi7ty5mD9/PiQSCRITE2Gz2fA///M/XtvlAR+Et6OjA01NTW7hhgCQnp6Ov/3tbyxWFLi8smRmZkKpVMJsNiMqKgoJCQlMr6Q6prehb3RAMjIy8PLLL+PRRx9FaWkpc/12dXWhtrYWbW1tzKFBudNycnIAXObMMpvNyMjIwL333osbb7xxWMrQ0FWUBsjQ1Y4Kj6vB3xVUxxMIBFAqlRCLxYxuaaTPc7lcyGQypKamIiQkhAUrBQQEMIfL0N2IlhMQEIAFCxYgPDwcX375Jerr66FSqRAVFQUul4uioiIUFxfDYDCAx+MhMDAQs2bNwu23346MjAyoVKphXkhfBNfVWiCRSCCXy5GUlISZM2ciJSUFPB7PzRzH5XKRn5+PxMREBAcHM0uMQCBARkYGZDKZT8Lr04FNJBLhT3/6E/74xz+6rWh6vR4ikYilchBC0NTUhG+++YYJXWJiIovXHKl8b+DacTR7gsYjnDlzBoWFhejo6EB0dDQWL16MjIwMFipoNBoREhLiFmcx0nuHBqW4fna0uo7Und58x9Uu7cu7bDYbNBoN9Ho9y/XjcDhoa2vDrl27UFlZicjISEybNg1jx451I927moAY153O1aJy8eJFdHR0YOzYsVAqlSwIRyqVMlXEYrGgq6uLWTloeRs3bsQjjzzi9Y4MXIW1Yfbs2fjqq6+gVCphsVhw7Ngx1NbW4tZbb0VoaCirDD1t0sgvatynMbtDtx1vQ/JcO3Doz9QUYzQaIRaLoVAo3FLD6UrnjWD4iqtxLoxUhi/1chX8od+l42C1WlnY4dC+HlrvK1k0gJ+CsihfHI0BoQfq4OBg9ruOjg4QQljmisFgwJYtW2AwGLB8+XKEhobC4XDgxRdfxLp163wyY/pkbZBIJMjPz2d62H//+188++yzIIQgLS2NCS8VVNekOi6Xy9zGFAaDAT/88AOLERYKheju7kZ1dTUkEgkSEhIQEBDgcdsdOsB0UGgazVB4+u5ohvcrYejK7BqNNbQMGkVns9k8Guu9fbc39R36M90RPf2dTmiaUczn89k7LBYL2tra0N7eDqfTyey+XC4XZ86cwbfffotly5YhPz+flUVNha79q9PpYLfbERYWBuCybBw4cAA//PAD6uvr8cILL0CpVGLixImIiYlhlLLewGvhlcvleOCBB7BmzRqIxWK0t7fjww8/xKVLlyAWi9Hc3My2POoMoKGKrqssDbABgLKyMjz55JOw2Wy46667kJCQgK+++grnzp0Dl8tFamoqVqxYgSVLlrD8Jk+DMNrvrgTqQKABKp4w1ORFf3Y4HNBqtWhtbUVTUxOMRiOCgoIQEhICqVQKDocDnU6HixcvorCwEE1NTfD398eiRYswY8YMtm16gif9mL6T7iCu9ADelOEJ7e3t2LdvHxISEpCXlweRSIS+vj5s3LgRGzduRGtrKwAgMjISS5cuRXR0NN555x2Ul5djcHAQY8eOZXRcdGelcE1UpaDEIhqNBt9++y1uu+02TJgwAdOnT8dHH32Ev//971esM4XXwnvjjTdi1apVzNbX19eH5uZmNvh9fX1u+pqrILj+zrWzadysyWTCv/71L8a2Q1Nyenp60NjYCKVSiYULFzLTmuugXevWb7FYoNfrhzkXhoK2zXWb1mq1KCwsZMTJNpsNY8aMwbhx49hKU19fjz179qCoqAharRZcLhfV1dUICgpidE3etoHG9FLKpKEqmK994XA4cPLkSXzwwQfskEUIwenTp/HRRx+hrq6OWWn6+/uh1WoRGhqKiooKWCwW1NXVMbZJQi4nw7oKL51krrJA+5sQwoixqdBPm3aZQNtb+BSMPpJ+NPT/V4uRVlNvrRLX+t6raYNrXIGrI8JVXRpa/v8fbfIWrvWnoJ5ET7ga1Wa07w/92RcbvtfCW1RUhA0bNuC5555j9sno6Gg0NzczH7mrruPq+XF1kbrOzKioKISHh8Nms+Gee+5hakNxcTG4XC7GjBmDu+66CzNnzhxGSvFzHbZoAPWVAqFdBY+uwv7+/sjPz0dkZCSmTJkCg8GAwMBAN7UhMjISISEhSEtLQ2NjI1Mb0tPT3frCG1CTFPVAXuvBk8fjYeLEiTCbzYiNjYVCoYBIJEJ+fj5WrlyJf//73ywLPCoqCsuXL0d0dDTefvttlJaWMnJrWgez2QypVOpmyRkagyIUCuHn58f6Lzw8HBzO5WCpH374Ae+++y727NnjXQOIlwBAJBIJ+X//7/8Ro9FIrFYr2bx5M0lISCDx8fHkyJEjbpdpGI1Gt0tGKAeY6+/0ej3Zvn07OXz4MNHr9cRqtZK2tjZy+PBhcvr0adLV1UVsNtsVr4qi8Ja3a7TPe4uhHFs2m41YrVZ2Q5DNZiN2u53YbDZisViIwWAgWq2W6PV6N64xX+BNW7z9vOvf6fVirp8zmUykvr6eHD16lBw5coTU1dURo9FILBYLOXnyJFm7di0pLCxk42m320lrayvp7+93k4PKykpSVlbGyh8YGCB33XUXCQ4OJk888QTp7+8ndrud7Ny5k0RHRxMOh+N1f/hkbaBpIlarFWKxGLfeeitCQkJQW1vL7mQAftoqzWYzM5VRxwHdUgm5nKt/8803u22zYWFhTF+k8MVUptfrYTAYIBaL3dhyCBme3OmLQX7o54f+f7Sy6FUC1NbpTZu8PZAS4m4qG/o3yh7vyepAx8F1B6DvEIlEw5IsKcaNG4eMjAy2G7qeacxmM1tZORwOsynTfufxeLjpppswceJE3HrrrVAqlXA4HDh16pTPtFI+Ca9YLMbUqVOZS1UoFGLKlCnIyclxY3IBLp9it2zZAi6Xi8zMTMb5ShP9KDyZjEaD62BRJwWlZDp9+jQKCwvR3t6O6OhoLFmyBFlZWQAAjUYDo9GI0NBQhIaGsstOfHFSUIwmWEO/54uzgU4wb9Uj+j2r1Yq+vj528KTBTq2trdixYweqqqoQFRWF6dOnIzc3d9jNQL5abihFgGs9CCHo6+tDe3s7xo4dC39/fxYaQFUoAOxKApVKxcrgcrlMBfGF1Ntr4VUoFJgwYQJuu+02toLSzuvv72fMg9QScOLECbzxxhssvHHVqlVYsWIFE3K73c5Oor6sgBaLhRHAlZaWorW1FV1dXairq0N7ezvz0PD5fBw5cgTZ2dngcDjMPZyeno77778f48aNY/qja1uGvtNut7O0d6FQ6Db5RjNnUcJBhUIxYqCL6zsp+YhWq4VCoWDho57q5Vpfg8GAoqIibNmyBQ0NDVAqlYiKigKHw0FxcTHOnz8Pk8kEHo+Hf/7zn5gxYwZuv/12ZGVlQa1WM53ftWxvQOtA62E2m1FXV4c9e/bgzJkzzD0cFRWFzMzMYW0e6uFMS0uDWq3+ZYQ3LCyM+cxpJQghKC0txUsvvcQCc1JTU1kayuDgIBwOB9ra2tDQ0MCyBsxmM0wmE0sOvBKoSlBeXs4Cc1zjGFw7kcJms6GhoQGXLl0C8FNgTnV1NVpaWvDUU09hypQpboE5rgHvdHCMRiMuXboErVaLoKAghIeHD7ttZ2hdbTYbi2vlcDgsJsKTINKs6vr6erfAnPnz5yMtLY0F0TscDrfJ4/zxMpi9e/fio48+wvnz5z0G5riSrnR0dGDz5s34/vvvER4ejtjYWGRmZmLKlCnIy8tDQECAVxxxrodWeiAzm80wGAxMgKlDZtGiRXjxxRcZ4+epU6ewadMm3HTTTbjlllsglUphtVpx/vx5r+N4KbwW3qamJvT09IDD4eD5559HaGgoOjo68Oyzz2Lv3r3gcC7fkfD666+Dz+ejqKiIGa7pajkwMACxWMxchpSZcCS4zuqtW7di/fr1qK6u9jpTgK6crjAYDDh58iRefPFF3H///Zg5cyazXZvNZrbNUUb2+vp6fP3116isrGQhkfn5+aOGRFIm8MDAQDf3qatqQVfa2tpaFhJ54cIF9Pf3QyQS4dSpUywkcmBgAEajEfHx8UhOTgYhBBUVFdi+fTsOHjyIjo4Ot5DI0cIjaTD8wMAAqqqqsHfvXrz//vsYO3YsHnnkESxcuJBN6NGE2FWA6YSlE623t5etoDt37sQ999yD7OxsNDQ04E9/+hOKi4uxfft2lJaWYvny5Th37hxefvllFv/tLbwWXuoj/+qrr5CWloYVK1bg0KFDOHHiBBOQvXv3QiqVws/PD+fOnXPTyc6dO4fvvvsOkZGRqKioQExMDMvxGrp9Aj+tfgaDAf/617/w0ksvobe316fGjQSLxYLi4mLU1tYiJSWFBaPTREUajN7Q0ICtW7fi6NGjGBgYgEAgwJkzZ5CdnY0FCxZg6tSpbLWioKqQq1DTlZLuEjabDY2Njfjyyy+xZ88etLS0QK/XM+5aADh8+DCKiopYMDo1LSmVSsZ2qdfrrzkz2ul0QqfT4ejRoygvL8fFixexZs0aluEwElwFm3oR6+rqmBOF7ob0HoyAgAB8/PHHOHv2LOx2O3p7e/H3v/8dhw8fRnt7O/PQ+gKfMylsNhsuXLiA9PR01NbWuv3NbDZjx44dANxTOQghaG5uxt/+9jcIhUIYjUYEBwfDZrNh4cKFUCgUGBwcRElJCU6fPg2j0cjy9ysrK/GPf/zjZxNcCofDAY1Gg9OnT6OoqIjdgCkQCCCXyyEQCDAwMMDSgKhjYXBwEK2traitrYXNZsPcuXMhlUoZmzhNkQHcdVNXAdbpdDh8+DA2b96M5uZmj2lATqeTpSFR0MCXkQb5WtOANBoN3n77bXR1deHee+9FQkICpFIpCLmcRzg4OAiRSMTCPQGgubkZGzduxL59+9Db24vBwUE3u67VasWmTZvQ2tqKo0ePuu0KRqMRNTU14HA47D2+4KoTMOk9uBcuXGAJmPRCOm8TMGUyGaKjo+Hn54f+/n60t7fDaDQyIzzNk6JkJMD/rQTM7OxsrF69GpGRkSwBMz8/HzfddBO7Lw7wnID517/+1eebdkbD1SZgBgYGQi6Xs4lKXc9hYWEIDw9nt5p2dnaiq6sLHM5lWi2agFlbW4uysjK3g5arekTlwlMCJrVauCZgqtVqfPjhh17V3+eQSJr6DoAxewcGBiIlJQUSiQSFhYVobW392Xm9aLpKeno6EhMTUVdXh5KSEq9Op/SgQyegtxPsSqBEGTT13WAwIDg4GHfccQeWLVvG1CK6IlJ9c+fOnXj99dfZZdWuTDy+Yqid1ZX10tNn6YWE0dHRmDNnDubOnQt/f39UVVXh888/x8mTJ5nFxtWqMpLVA/AuLV4gEDA2UK1Wy1h46I6mUqmQk5OD9PR0vPHGG1613We1gVIiUZhMJubeo+ku17qqeQKPx0NYWBgWLVqECRMmoKGhAZ988glLfxkK2vmEEHYVFvDTyn01cDXs00NXY2OjW5ubm5vxwQcf4NChQ8jMzMQNN9zAsiTsdjsKCwvx73//m92FRuNsKanf1fQdFXqqG9M2Ure3WCxGaGgoxo4dy0hHkpKSGKE1ACQmJmJgYICtoqPZua/0e9pXPB6PcTfQqxZEIpHbzkctSX19fThx4gQaGhp+fuGlF4d48mz19/fjyJEjjO4JAMvElcvl6O3thVarvaZL+SijCs2Lozc4ZmVlQaFQICwsDGq1mtlU6Wdra2vd6j3aynQluKosI6Wr0zDJ4uJilJeXQ6lUsnvVrFYrampq0NnZyeie6HZPTUm+0j15Gg8+n4+MjAwsWLAAKSkpCAkJQXR0NEJCQkake6K5hTQt6Fronvh8PkJDQxEUFITGxkZ2UxT1fnpqG5/PR0hIiE+kI14L76pVq1BbW4u6ujoMDg4yJhYqkPROYuDyKpmXl4c//elPSEhIQFdXFyPaKykpQWNjI4xGIzgcDjNNUaI9unpQd6rdbmeJljqdDidOnGCMkWq1GjfddBPmz5+PuLg4SKVSZpoyGAzYuHEjnnvuOQwODnrdIYD7Vjy0o73RtalFgTJOtrW1DTPqDy2PXmpCw0YpkaHVavVZRxcIBLj11luxatUqKJXKYV5MuhLabDbmuubxeIiLi0NiYiL0ej3jZHMl2uPz+YxGlhKKO51OqFQqpKamMs8lJdoTCoV4/fXXcejQIbfJ7trPCoUCY8aMwbx58zBnzhxER0d73U6vhffVV1+FyWRCb28vNBoNNBoNvvvuO2zatIld7URBCIGfnx+jvkxOTsakSZNY/tKZM2fYFZ+pqalQq9WM4rStrQ2BgYGYMGEC0tPTGcVpWVkZ041MJhNL7JwzZw7S09OHJRLy+Xzk5eVBrVZ7Jbx0m6OPK8Wp641Gvu4co8Ue0N9TD55SqURiYiLLzqYmJF8pTmkquycnEJ1YbW1tuHjxImJjY5GUlAQ+n4+UlBQ8//zzqK6uhkwmg8PhQGlpKYqLizE4OIikpCRGcWoymRjvcUpKCqKjo924K2w2G86dOzfM+kDB5/MxZcoUrFmzBvn5+cwm7gt8uvXdFTTh7r777sPZs2eH/V0mk2HevHm44447kJubi7CwMOYSpAPmmlVhNBrR0tKC/v5+hISEIDIyktk429racPbsWcb11d7eju7u7mHk0lS4OJzL2RxHjhzBgw8+OCq5NPDTQUYsFrN73igrJmWK+TkOeFcCPUhlZGQgNTUVfD4fdXV1uHDhAtra2pgNlT4jDV1iYiK++OIL3HjjjSOSS9fW1uLIkSPIzMxEfn6+G/G364QzmUzo6emB0WiESqVibuuR4i/0ej1KS0uxfft27NixA7W1tR5jdFNSUvDRRx+hoKDAZ15eiqui9acCIhaLERQUxBRzVxgMBvz3v//F7t27ERERgblz5+KRRx5BcnKyG8MMLYvemUaIe5Ikl8tFbGwsIiMj2c9U53Sl9Sfk8o01tbW1IISgp6cHn3zyCTo7O6/YLtctXSwWIzIyEmq1Gnq9HvX19eyyk18aRqMR9fX16O/vh9PpxIQJExAVFYWamhpwuVwoFAqEhIQgICAAer0ezc3N0Gg0w+6zoLtiREQEwsLChsUuCIVCJCUlITAwEGKx2E14hjpXFAoFFArFsIChobBYLDh+/Djef/99HD9+fFQGHIFAgNzcXMTHx/scmOWKq6L1t9vt0Ov1aG1tZT5sAExPcr0N0mAwsJvUT548ieeffx4TJkxwu1BFrVYPC9AZOllctxSaLEg/R1eIDz/8EF988QUsFguMRiOzW3oC1fWoXZSehoHLd2VERUUB8Ezc8UuC3pxz5swZyGQytsXrdDqo1WpMnz4dS5YsgUKhQElJCT766CNcuHCBtdNms6G/vx/vvfceGhsbsWbNGowZMwZSqdRtxaQHaoorRZa56v92ux3Nzc1obm5m55Xt27dj48aN6OnpGVW1oqQneXl5bmSEQ3Vhb+CTkkEPTWVlZaiurkZnZyecTif8/PwgEokQHh4OjUaDS5cuDbuAxOFw4OzZs1i5ciVyc3PZVVZjxozBU089hezs7BGvsvImLJDGIDQ0NHic8XRy0ACXzMxMpKeno7y8HGVlZSzIx2AwoLW1FX5+frBarb/4TUDATyue65ZtMpkYHwbdFXg8HuLj45Geng6FQoHExEQAwGuvvQaNRgMO5zI/Bb2Oddu2baipqcGkSZOQmZmJ3NxcJCUlsRDFqwlD1el02LFjB958803U19eDz+czuRjNQuFqvqPEKDRYiYYeUC/nLyK8wGUhrKmpwY4dO2A0GmG32zFu3Djccsst7BLB1157jQUWD7UXtrW1scAcQghqa2thtVrx+OOPIyUlxe1uAm9BdTh6S6Qrq49UKkViYiLS0tLYzTqZmZl48sknkZSUhNraWrz//vvYu3cvtFotBAIB4uPjMW7cOPT19aGjo4O5focyo48k1EN3jdHA5/Ph7++PiIgIZgMdeong1KlT2SWC8+bNY3wUMpkMN998M8xmMxobG8Hj8XDgwAGWDGq1WlFaWoqLFy+yW0YXL16MO++8ExEREcPq6gl0nLq7u3HmzBns3r0b27Ztu6I65toX1EpBLxGk6e+UXJF62lzJYLwq29cDGz2Bvvnmmzh37hwkEgkWLVqEhx56iFkNHn30URQXF7NDxZXo/OVyOWJjYxEXF4eVK1dizpw5XsX50o7V6/UoKSlBYWEhWlpa0NnZCa1Wy+iNpk6diqCgIAwODqKzsxNhYWEIDQ1l+nN3dzeOHz/O2jN58mQkJiZicHAQBw4cwJ49e9DY2Ai9Xs+uLaDhhq7OENapQ7bCoW2nOj2Px4NUKkV2djbuuOMOZGVlwd/fHwqFgt27QfucXrLnmr1A30vrBFwm4HvnnXewb98+lqXr6oELCwvD008/jfvvv59dgXCl/i0tLcXatWtx+vRpN/fulUDrGxwcjNmzZyMjIwP79u3DyZMn4XA4oFarkZCQgDvvvBOLFi1iaoTXMcXeCq9rg8xmMwoLC/Hdd9+hqakJSUlJmD59OsRiMQ4dOoRNmzaxCwUpY6I3sQ4cDgdjx47FZ599hjFjxniVhWA2m9kdD8HBwW6XsNAgm5FihofqcVQAaIA2FYy2tjacP38eu3fvdrtjjNaL6s2eutKT4Lq62EUiEWbPno3169cjNjbWI1/a0DJGW9npKvnVV1/hm2++QV9fH3g8Hnp7e9Hb2wsul4tZs2Zhw4YNiImJ8dgv1JVtsVhQXl6OtWvX4tixYz6rTwKBgAXWjxkzBn5+foy/gnJlZGRk4N1330VBQYFXscRu/XA1wgtcHrCenh7s378fH330Edra2lhOPjVq007w5RV8Ph+TJ0/GrFmzmNcpKCgI8fHxCA4OZrcH8fl8FolWVVWFjIyMEYk8vFnBR/ub1WpFWVkZXnnlFezfv5/ZtSlpIJ2gngRpKFyzR+gKlpCQgHfffRczZsxwU5mu5gRO30mZKk0mE7hcLk6ePIk///nPaG1tRUBAAP785z/jzjvvZDdYUmb0trY2lJeXo66uDi0tLSgtLWXcCr6CWpFc20v7iV4tu3btWsbJ4XN7yVWCZs1WVVWR7OxswuFwCADC4XAIl8tlP1/Nw+FwCI/HI1wul3C5XCIQCIifnx8JDw8niYmJJDc3l0yfPp0UFBSQuLg4Eh0dTe677z5SXV3Nsll9aYenx+FwEKvVSvR6PamoqCCrV68m/v7+I9bT2/Z66h8+n08mTpxItm3bRvr6+ojNZnPLsqbt8SXLeWh7+vv7ybJly9i7IyIiyJ133klWrVpFZs+eTZKSkkhwcDCRSqWEy+Ve9dh5297FixeTCxcuEKvVOqx93sJr4R0pddpkMpEXXniBqNVqIpVKSWBgIFGpVD9rB1ypY4RCIRkzZgzZvHkzMRgMHtO9R0sXdzgc7LHb7USv15Pq6mqyY8cO8tprr5Gbb76Z+Pv7X9OEvNLD5/NJXFwcWb16Ndm5cycpLy8nLS0tZHBwkKXK0/q5ps57+1gsFvL8888TkUjE+k4oFBKxWEx4PN4vOkZSqZRIJBK2GOXm5pLy8vIRFwxv4bO1gRD3jFiRSITHHnsMOTk56O/vZ5RN//jHP1BVVXVVZiaqE1KzCTWlkBG2ZafTif7+ftTV1cFgMLAwRFrHkdoBgJmVnE4nRCIRDAYDDh48iC1btqCyspJRo14t87i3sNvtaGpqwqeffopdu3YhKCgIarUa2dnZmDt3LuLj42EymdDR0QGhUIj4+HioVCo3Fsyh7SWEuPXDmDFjoFQqWToXdbeLRCJoNBpmFnQ9EF6rmTAoKAj33HMPu1/EarXivvvuQ2pqKqsX+THWgl5/lZeX51XZPgvvUHA4l5kZ58+f76YPZ2Vl4Y033sCpU6eGeYFGQ1hYGFasWIGsrCxmOqmrq8OOHTtQWVkJo9HIaO4BsLA/mvJNO9ybU6vdbkdDQwP2798Pu92OhIQEVFdX49NPP0VDQ8M1RcFdDciPTp3GxkYWanno0CF8//33uPHGG5nHTygU4qabbsKKFSvY9biAO6uPa9oRtbFmZ2cjKysLR48eZYfjxx57DCkpKWhubsahQ4fQ2dnJaAra2tqwbds2VFRU+CTEtB4SiQS33347nnnmGfj5+bGDu+tl2T/u/tBoNGhra/Opv65KeF0H1FVI6L8CgQATJ05Eeno6Kioq8OWXX2LTpk1esV4rlUosW7YMOTk5bFWZNGkS5syZg7a2NvD5fLS1tWHfvn344Ycf0NfXB4VCgSlTpqCgoIBdFzpUeD0JssPhQEVFBTZv3gy73Y78/Hy0trYyz+H/Fmj/kh8tO5WVlSw+g8ZP9/f3s9staWyHa5tdBZo+lOmR2sSXLVuG3/zmNxCLxcjMzERBQQHjthAKhbBarVAqlXj22We9uu8OuMzWTh0hmZmZWL16NWP49BQkRNOddDodkpKShnFKjAafPWwmk4mdYOldFJ5mPnDZzTpx4kSkpKTAZrPhs88+u2LaS0NDAz744AM888wziImJAY/Hg8ViAYfDQVJSEvz9/ZGTk4MpU6Zg4sSJOHHiBFJTUzFnzhzExMQM89CMtvpSqntq883NzUVubi4MBgPOnj3LQjSvNcnxWjE0nJL+S+9a9mRiGhqnAFxeCZcuXQo+n4+GhgbMmTOHxZiYzWYcOXIElZWVKCgoQGJiImNW9xTs7wlyuRxPPPEEbr/9dshkMigUimGZyLTuJpMJTU1NKC4uhkajYalT3lAhsDYSL/fFI0eOuPHM2u12hIaGYubMmVi8eDECAwM9Cgrt9Orqaqxbtw4HDhxAf3//qFeVikQi5ObmYurUqVCpVOjp6YHD4cDChQsZuTUhP1EZSSQSRn86rIGjZHY4f+Q+uHjxIoRCIRISEiAUCnHp0iXs2rULhw8fRkVFBbq6uoa5u68Vri7hoVuya3imTCZDQkICoqOjMTg4iO7ubsY68+ijjzIuDXoWGc027qrWWSwWxidhs9lw8OBBrF27FvX19ZDJZAgMDGROnStNXurJXLZsGV5++WW3mAnXulBZqKiowFtvvYWDBw+it7eXRcGlp6ePWHdP8HrlXbhwIcxm8zB75s6dO1FUVIT169cz/gNPK19KSgo2bNjAeAo2bdqEU6dOeewYi8WCU6dOoaioiH1fJpOhq6sLYrEYqampkEqlEIlEwzh1h65OdGuiqUA8Hs8tr0wulyM7O9vt98nJySwcs6GhwWP5FFQAhrqMXQWJDhp9qHC6rqauoJ/x9/fH5MmTsWTJEkRHR0On07HAl+TkZBZ/YTabWSRaUFAQFAqFR042+i+1T1NHRF1dHT7//HOmThiNRvT09IwqD8DlnSs5ORlTp07FpEmTMHv2bI8y4NpvjY2NWL16NY4fP876ih6IBwcH0d/f7zVHr9fC6xrQ7bqaGY1GbNq0CTweD7///e8RExPjRkfqOohKpRJ5eXnIycnBxIkT8fDDD6OwsHDEAXTVO61WK7Zt24a6ujrMmDGDxVIMpT4FLseU0pA86oFraWlh9PLR0dFQqVRMWAUCgRshH3DZyF9ZWYnW1lZ2RRMN7nZNh1epVJg2bRpSUlIAgLlPRSIR46QwGAzo6OhATU0NLl26BL1ef0WvI2XdoRRWMpkMKpWKZTFYLBaWkXLx4kUUFRWhu7sbcXFxmDJlCtLT05kge4rYoyf8S5cuYePGjTh48KBPmcwcDgcTJkzAm2++ifT0dDcnw1CLB9Xd6+rq8NJLL+HEiROs7dRZ0d7ejs8++ww//PADKisrvauDt2qDa8VoQHJfXx9rMJ/PR1RUFLKysjB+/HjMnz8fqampHmMUaIMOHz6Mhx56CI2NjV6f6jmcy1fELly4EOvXr2ehixQdHR345z//yRh7DAYDuru7odPp2BWylPAkMDAQQUFBiImJQWxsLNRqNQQCAfR6Pfbs2YP169ejubkZABAREYHVq1cjNjYWx44dw+HDh2EwGDB+/Hj87ne/Q1ZWltttSK6nabvdjsHBQRQXF+Pjjz/GkSNHoNPpvGqzRCJBWloapk6diri4OGi1WtTX17O+12q16OzshEajgdVqBYfDgZ+fHyIjI5GamoqFCxdi3rx58PPzcyvX+eNlJ//5z3/wwQcfMJZ7b5Gamop//vOfGD9+vEfLDm1ba2srvvnmGxw6dAgXLlxwyyyXy+VYunQpHnnkEZSVlWHt2rXQaDTeW3i8NQjjR6Mzj8cjBQUF5LXXXiNPPPEESU9PJwKBwM0wzePxSHx8PHnrrbdIT0/PiA4CyvGbmppKhEKhT4bv5ORksm/fPmKxWBg/bFVVFVm8eDEziHvyfnG5XMLn84lEIiF+fn4kIiKC5Ofnk7vuuousWbOGrFq1iixZsoQkJCQw471IJCLPP/88GRgYIDabjQwMDJALFy6Qffv2kYqKCqLX64d5xIY+drud9Pb2kv/85z9k/PjxzFkAgIjFYhISEkJkMpnH9goEAhIYGEhSU1NJUlISUalURCgUEh6PN6rjhMvlEpVKRVasWEH27dtH2tvbiV6vJ4ODg6SyspKsW7eOJCcn++SkEAqFJDMzk+zcuZM5S1xB22uz2cjx48fJ5MmTh8kHABIeHk5eeeUV0tXVRaxWK9m7dy8JDAwkPoik9x42KjQ8Ho9kZ2eTY8eOkf7+flJYWEhuvfVWIhaLh1VQLBaTGTNmkC1btpDe3l6PA6zVasm2bdvIAw88QGJjYwmfz/eqE8ViMZk3bx757LPPyL59+8g777xDsrKyfPbscTgcwufziVgsJkKhkPD5/GFlZGVlkdraWo/eoKGuXE+gn7dYLKSjo4Ns2rSJTJo0iajVapKamkpeeeUVcvr0abJhwwYSHh4+Yl15PN4VBXY0Ic7NzSVLly4lt912G8nLyyNKpdKrsjgcDlEoFGTChAlk/fr1pLS0lJFFexLaxsZG8sorr5CYmJhh5QsEAjJu3Diyc+dOYjKZ2Pe6u7vJvffeSwICAn5+4Z0xYwbJzMwkMpmMqNVq8tlnnxG73U4cDgepqakhjz/+OMnLyyNjxowh4eHhbkIok8nIvHnzyNGjR4nZbCY2m4309/eT5uZm0tXVRQYGBkhvby85ceIEWbt2LcnOziZKpZKIRKJRVwUej0fkcjnx9/f3aeX25eHxeOSRRx4her3eo6vZm3iDoSuwTqcjZ8+eJVu2bCGFhYXEaDQSp9NJdDodefzxx72ewFf7eCv8PB6PREREkLvvvpt88803pL29ncUieNpZ6uvryXPPPUfS0tLcVlulUklycnLIokWLyLp160hNTY3bhKfM8m1tbeTAgQM/v/AeP36cvPLKKyQsLIwIBAJy9913swF1OBxEq9WSxsZGUl9fT06cOEEWL17sJnhcLpdkZ2eTDRs2kHXr1pGZM2eS3Nxc8vbbb7N4BIfDQYxGIykvLyfvvPMOue2220hWVhaRSqU/y6Dx+XwilUqJWCy+4gDSuAk/Pz/yyiuvDFMNrhZD4ylcBcBqtZJPP/2U+Pn5eb2iKpVKEhYWRpRK5c8ao8DhcEhMTAz597//zaj3hwpsX18fqa6uJjU1NWT79u1k4sSJwyZedHQ02bJlC+no6CA6nW6Y8A8MDJCamhoyODjoc1CV19aG1tZW9Pb2MpNQVVUVtFotSynx8/Njh4LY2Fg8+OCDOHToEPOqOZ1OVFdX480330RPTw90Oh04HA5CQ0Nx3333MZchNYUFBQUhLS0NJ06cwFdffeUTtSkFPUhwuVxIJBIkJSXhxhtvhEajwf79+91I7IZCJBJBIpEwq4TFYmGerGvBSHZY8uPBjvaBNwe64OBg3HvvvcjMzERZWRm2b9/OeJDJCGY4b8HlcpGUlIRp06axSxldTX9msxkff/wxvvvuO8hkMrS1taGmpsZtjDgcDm655RbceuutHq8OsNvtOH78OHbs2IGVK1ciMzPzl43nvY7r+L+C/xuXgV3HdVwFrgvvdfxqcV14r+NXi+vCex2/WlwX3uv41eK68F7HrxbXhfc6frW4LrzX8avFdeG9jl8t/j+1m6zXb35DhQAAAABJRU5ErkJggg=="
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 8\n",
      "\tbeta = 1.1088e+01\n",
      "\tJ = -6.6487e-02\n",
      "\tgrad_norm = 2.2965e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 9\n",
      "\tbeta = 1.2529e+01\n",
      "\tJ = 3.9496e-02\n",
      "\tgrad_norm = 2.5447e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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TppFMJmN3Tnvf4oiICMrMzGzxiDSXVnNzc6m0tJT0ej3pdDqqrq6mkpISqqmpsbqTNZTCGUV/fn4+PXz4kKqrq8lgMJBer6eioiI6duwYTZs2jby9vVvl+GOtmc9LQEAAJScn26R+tLYeDVtRURF988031KlTJ3JyciKpVGrxvK5du1JeXl6Tc8qcOvX19ZSUlEQRERGtHqdAICBfX1+aOXMmLV++nDp37myhvVCpVPTDDz+wqlB7YBfxMuqvFStWkLu7O6lUKho4cCCdPn2ateykpaVRcHCw3UQrEAjI39+f9u7da5f7ITPRxcXFtGPHDnrvvfeoT58+FBERQXFxcbRlyxbKzMyk6upqyszMpFOnTtH9+/dZQmG82lasWEFRUVHUsWNHmjJlCu3bt482bNhA/fv3JycnJxIIBBbWxWdBwEyTyWQ0evRo2r9/PyUlJVFGRgbV1tZa9NFcz91w/JWVlZSZmUmZmZl08OBBio2NJaFQ2OSzli5d2qQO1tr8nj9/niIiIkggENg9Ni6XSx4eHvTll19SQkIC/f3vfyeRSMQ6RzGeh9ZeppZgs4UNAGsdmTBhAq5fvw6xWAwnJycEBwdj+PDh6Ny5M86fP4/FixejoqLC1ttCqVRi/PjxmDBhAiIjI1lnbHv6dfXqVYwcORLZ2dkWx7pQKISfnx8CAwORl5eHzMxMBAQEYOHChYiKisKtW7ewdOlSJCQksD4MAoEAarUaWq32mUvg1sDhcCAUCiGRSCAUCiGXy9GtWzeMGDECCoUCSUlJqKiowMCBA9GnTx/2iCUilJaW4ssvv8SFCxfA4XDw8OFDlJWVWdyfy+VCJpPB398fo0aNwqRJk+Ds7GyzloKIkJubi3PnzuH333/H0aNHUVlZadf4lEolXF1dUVpaitraWoSHh2PIkCFwcXGBRCJBTEwMq6q0ee3toXTGNr1kyRIaO3YsDR8+nHx9fUkoFJJMJiNvb+8WNQ1OTk4UFxdHgwYNIj8/PwoLC6O1a9eyvhGtEVBMJhPduXOHfHx8bN4RXFxcKCoqijw8PBr1l8PhkFgsbnL3+k80Pp9PgYGBFBAQwO76ISEhdObMGQsH/q1bt5JSqbR6IvB4PGrXrh3NmzePDh8+3MiZ3N45NplMVFNTQzt27KDIyEhSKpWkVqvJ0dHRrtNIoVDQtm3bqL6+nmVP7PXJIGoF28DwmVVVVXTjxg166aWXbO54QEAA7du3j2pqaqimpoaysrIoNze31RNq3i+NRkOzZ88mJycnksvljfg8WxuHwyGJREIeHh6kVCr/a9Y2Nzc3Gj9+PEVHR7PHtVgspvfff5+Sk5Pp3r17dODAAeratavVPsrlcpo6dSrdvn27kbrNfC1bQ8RGo5EKCgooJSWFbt26RRcuXKAPPviAVCqVTWOTy+X066+/suxha/vSKlUZ8yCtVkszZ85sdoF5PB65u7vThAkT6Nq1a80KUE0JaOZ8n16vJ61W28gJ3GQyUUVFBf3xxx904cIFOnr0KI0YMcIuTykOh0N8Pp8UCgW5u7uTQqFolafV0zaVSkWffvoppaSk0Lp168jLy4tVG8rlcgoODqaQkBB2x7VGHN999x0bXmSNTzYajaTRaJrlfW0RdM03tISEBBo/fjy5ubk1u3GIRCLasmXLU4dW2a0qowZqqOasT0FBQZgyZQqGDRsGf39/CAQC9jvGEsaYN/V6PQoLC1FWVgZXV1e4uLiw6pXCwkKcOHECGRkZMBqNyM/PB4/Hw4QJExAVFQUejwcOhwO5XI6ePXuyzwgICEBKSgoePHhg1/g0Gg3q6+tZc6a5A/fzBOPZ1qdPH8TGxkIoFEKn07HmVJPJhKqqqhZN1y4uLhg0aFCznn61tbW4ffs2vL294ebmBgCsKkuj0YDH48FkMqG4uBj379+H0WhEaGgovL29Wcd2cwgEAvTp0wc9e/bEnTt3sH//fhw8eBDp6emNrKM6nQ5nz57FqFGjIJPJWq0etJl4jUYjNBoNioqKoNFoIBAIkJKSgsOHD1tdWEdHR3z11VcYMWIES6A6nQ7Z2dk4ffo0bty4AScnJ3Tt2hUqlQpJSUk4cOAAcnNz4erqipiYGHTq1AmPHj3CwYMHkZKSwrpSmkwmcLlc3LhxAxs2bEBEREQjp2siglqthkqlsnkyyCwSgrkXNYiafV7gcrmQy+VwdnaGTqfDiRMnUFNTg4SEBBQWFtplZi8vL0dRURF8fX2b/I1QKISvry/rYkpEqKqqwpo1a5CQkMBGldy7d4+NdGnbti3ee+899O7dGxqNBnfu3IFWq0VISAiCg4Ph6OgIPp+P9u3bIywsDBMnTsS//vUv7Nixw6L/RIQDBw5ArVZj/PjxCA4OhoODA7t2z1xgW7p0KQ0dOpTatGlDarWaXF1dSSKRNHk0SCQS+uyzz+jOnTuUlpZG27Zto7Fjx5Kvry97FHM4HJJKpaRSqRoJR0xQpDW9KqNmkcvl9Pbbb1NKSgppNJpGLMm9e/coICDgv8Kz2tN4PB5JpVJydHQkmUxGDg4O5OjoyKqU7L2fQCCgdevWWXjYNWTDrLUzZ85YxNFZe7ZMJiMfHx9ycXFh18fBwYFCQ0OpX79+NHr0aFq5ciU9ePCAampqaNWqVU2q2DgcDqlUKurVqxctWbKErl+/ThUVFTazDTaryvh8frOWM5lMBicnJxQXF0Or1QJ4bMlxdXWFVqtFeXm5hSdYa+Hg4ICgoCAIBALk5ORAp9PB19cXUVFRiIyMhI+PD6RSKWpra3H48GFs3ryZ7c+zgL0sBKMGY3a4hh5xfD4fEomEzYNgzw7b3DO7d++OuXPnIjw8HEqlEg4ODo2cxM3/NplM+PnnnzFx4kTW66y14PP56Ny5M2JiYnDs2DHcvHmzxTnjcrnw8PBAx44dceTIEZue89QxbBwOB+7u7pg6dSoiIiKwePFi1iXuWYPH46Fdu3Z44403UFhYiAMHDqC0tJTlS3k8HgQCAcuv1dfXN3rhGPbiWRBJc5BIJFCr1fDy8kKXLl3QrVs3cLlcHD9+HEeOHGH14Fwul3UXtCViwVZwniQkkcvlUCgU8PX1RZcuXdCpUycEBATAz88PKpWKnY/6+nosX74cX331VYuRLrY+XyAQsOZgAOz66HQ6q/MvFAqhUqlQWFho0zPsFtgEAoFFYJ9AIEBYWBgUCgUyMjIaKcifJYxGIzIyMrBr1y5UVlayhAuADSa0RgB8Pp8VFjkcDgwGwzNZIODxicPlclFTU8P6qnbp0gVTp05FZGQklEolpFIpRCIRiAhdu3aFTCbDjh07oNFoYDKZnllfzEFPXFVra2tRUFCA27dvIz4+Hnw+HzKZDIGBgXjjjTcwePBgSKVSJCYmYufOnc/kdGSe33BcTRkgOBwO1Go1+vfvbyFwtwS7d9527drhn//8J3x9fZGdnY1NmzYhLS0NJpMJJpOJXRBboFAo0L59e8jlchQUFODhw4dsvJhUKoW3tzeMRiMePnz4VLsSl8u1CNV/VgKYh4cHpk2bBpVKhV9//RUZGRmIjo7GJ598guDgYIuFYp5rNBqRmpqK6dOn48qVK/8RYbAp8Hg8ODk5QSwWo7S0FHV1deznKpUKnp6e8PDwYFk0xkFHrVbD29sbEokEN2/eREZGhk1rbo3l4vP5kEqlCAkJQUxMDNzd3TF37lzbBmArc4wnTLaPjw9duXKF9Ho9nTt3jtzd3Rsx4U0JGXw+nyQSCYlEIgoJCaH9+/dTZWUlabVaKikpoTNnztCyZcto+fLldPLkScrNzaU///yToqKinrvAJBQKSSQSkVQqJXd3dwoMDCS1Wt2kDlupVNLChQuptLSU6urqKDs7m1JTU5vNDGQwGMhgMFBVVRV9++23Vq17/+0mEolowoQJlJiYSEVFRVRbW0t1dXVUVFREaWlplJ6eTo8ePaK6ujrSaDSUkpJCI0aMIEdHxybnisvlklKptCp8m0eISyQSkkqlNgtsdhNvYGAg3b59m0wmE8XHx5NMJrMg3O7du1NcXFwj7YFcLqd//OMftH37dlq6dCkdO3bMQkFu7s1krjUwGo2UkJBgNXXQ0zalUklDhgyhL7/8kv7nf/6HVqxYQT/99BNdu3aNMjMz6dy5czRq1CgLrQqT3Wb+/PmUk5Nj4TzTkgGG+Z7xEf7222+pS5cuTVoDuVwu+1KJxWJyc3Oj8PBwateuHTk5OT0zDzemSaVSmj17tlVTfXOGioKCAtq4cSP16tXLqkk9IiKCtm3bRr169Wq0afj6+pKTk5PF58+ceCUSCfn5+dF3333HEl1ubi516dKFfWjnzp0pNTWVcnJyqHPnzhZEPXz4cHr06BHp9Xqqqqqi6upqm72ajEYjJSYmUs+ePZ/JgnE4HAoNDaXdu3dTRUUFa7kztzgxz71//z79/e9/J19fX2rfvj1NmzaNzpw5Q5WVlc0Sq06no7q6ukbqqoZWqfv379P69eupR48eJJFIiMvlkkAgoKCgIJo1axZt2bKFvv/+e/ruu+/o7NmzlJeXR4WFhXTlyhX6/PPP7crv1tSuKJfLKSoqirZs2UI1NTV2mWmZeaqsrKTNmzc3SmXl6OhIe/bsIYPBQImJiaz/iVgsprfeeouSk5Np9+7dFBwc/PyId9CgQfTTTz+x+bqYTp86dYq6detGMTExdPnyZXZnmT59OtsZBwcH+u6779iFNBgMrCOGrRNkMj0OU//Xv/5Fbdu2bXVoOpfLpbCwMPrtt9+s7vwNdxa9Xk8PHz6kU6dOUWpqKlVXVzcbYs9ck5GRQZcvX6bi4uImw9OZe5hnyBw8eDB9+OGHlJSUxEbxNnSJNCf+8+fP00svvWSzu6K5bnXSpEm0YcMGunTpEpWXl9sVRm9tzJcuXaL+/fuTm5sbubu7U0BAAM2ZM4fdqAwGA/36668UFxdHGzduZJOUGI1GOn78OKtjthU2C2xOTk4YNmwYVq9eDScnJwvrU15eHng8Htzd3VkhZc+ePZg8eTJMJhP69u2LZcuWISwsrJG02ZokIYWFhbh27RquXr2Ku3fvIj09Hffu3WMFDgZMwg6RSMQKguHh4Zg3bx769u3bouslmWkyiMgiUre5pBpEhJqaGmi1WigUCgiFQpueU1tbi6qqKjg6OrJmU1sSiKSmpmLVqlVITk6GQCCAUqmEVqvF3bt3WZUch8OBQqHAsGHDMGXKFHTs2BFSqdSmMbUEZszZ2dk4ceIEnJyc4O/vD5lMBjc3NzZQlFm/2tpai3zCRISSkhK89NJLNumE2f7aSrwcDgcikQjffPMNPvjgA3C5XPYhTII3ZrKJCGVlZTh69CgUCgU6d+4MV1dXC2JhrrV3wsy7a3oShlRaWorExETs27cPycnJqKyshIuLC0aPHo3XXnsNMpmMNZIEBgbCw8PDZr/RhtPTmmtsua411zDXEREqKipQXFwMkUgER0dH6HQ6XLx4Edu2bUN+fj7Cw8MxZswY9O7dGxKJxOb7t9Rf8/WsqalBTU0NXFxcWH8Ma7Sh1WpZfTyDlJQUDBgwAGVlZc8v0d6IESOwa9cuCAQC1NfX48yZMyguLsbw4cNZ+zQzoebXWbuXNcJ4GmKpq6tDbm4uioqK4OLiAn9/f4hEIovf2W0//wugqSWkJ7perVYLR0dHdi5a+wKaQ6/XW2RwpyfJCRmLIvNZRUUFiAgqlYrVse/btw/Z2dkYO3Ys2rRpAwDYv38/xo4da1cGeruMFBKJhD1uDQYD1qxZw6ah9/b2RmxsrMXvzY89hqDN/6/X63H+/HkIBAJ07doVYrEYFRUVuHPnDng8HgIDA9lBNzfhzHeMvjAkJKTRdw3/ZmA+Ua09BZjjm/GUY7zczO9nMBhQV1fHRjW0NCZ70Jz108HBgTVNN/ydef8bfqfT6ZCVlYW8vDwYjUZ4eXnBz88PAoEASUlJ2LNnD8aMGWNhVDCZTBaeg0SE/Px8EBGbB06r1WLr1q04c+YMzp07hx9//BEuLi5o164dfH197fIAtJl4RSIRZsyYgXfffRccDgcZGRnYsGEDKisrweVycfXqVZZ4GxJqU0hNTcVbb70FjUaD0aNHo0ePHti7dy/++OMPAEBoaCgmT56M0aNHN5u8jcHTEB+zU9h6D4Z/y8vLw+XLl5GSkoKysjK4ubkhIiICoaGhUKvV4PF4yMvLwy+//IJTp05BIpFg2rRpGDp0aKvCncxhy7Ut/aakpATXr19HREQE1Go1AKC6uhorV67Ejz/+yB7jTk5OeP311xEWFoa1a9fi3r17yM/Px44dOyx2dHMe2mQyoba2lk3oR0/8N7Kzs6HX63Hq1CmcPXsWb775JsLCwrB582YsWLDA5vmwWbTr2rUrZWVlsZLuyZMnLfSfH330kYVnfEPJ1Zokv2fPHlZKFolE5Orq2kgV5uHhQadPn26VFNwSmH5qNBq7o1dNJhNlZmbS9OnTydvbmy0JoFKpKDY2lpYuXUpHjhyhw4cP08SJE0mhULBjioyMpIyMjFappOrq6mzKxm4LjEYj/fDDD9S1a1c6evQoq9lISEhoZHzCEz2wp6cnq5qLiIhgU5Iy6kHzPul0OkpKSqKbN2+y9JCZmUne3t6s5mPJkiUW2quMjAyb+2/zzksN/FqfRmvQFJqzfT9PtPb+jFMNwyYw9+LxeGzCanM2wvy61j7zWc8Fk1PBvP+29q81rE9L19jjW2Ez8aampmLdunVYuHAhZDIZvL294eLiguzsbHC5XIuEGdQE29Dws6CgILi5uUGj0WDs2LGIiorC3r17ce7cOQCP2YYpU6agR48eNg/IXjDeT60hCk9PT8yZMwexsbFISUlBaWkpXF1dERERgZCQEKjVanC5XPj4+MDb2xsnT56EWCzGtGnT4OXlZXc/AVgIoE9LyBwOB0OHDoWfnx/at2/P3q9Tp06YOnUqNm/ezDo/qdVqDB8+HB06dMCaNWtw+/ZttG3bFmKxmL2fwWAAl8ttpF0wd9CRSCQsDy4UChEUFATgMYtx4sQJLFiwwHavRFu3aOCxg/natWvJaDSSTqejFStWkEqlIhcXFzp37pwFS2CNbWiY2qe+vp5Onz5NiYmJVFdXR0ajkcrLyykpKYmSk5OptLTU7vyz1owNtl5nL8yPO71eT/X19aTT6axmYNfr9VRZWWmRCOU/gebmojlTtlarpTt37tDp06fpxIkTlJ6eThqNhvR6PSUlJdHcuXPpypUrFutpnluN6DFbkpaWRqmpqSxLWVNTQ0OHDiWhUEhxcXH06NEjMplMlJKSQn5+fs/HSMG8lSNHjsTOnTtZv8zz58+jtLQUQ4cOZaVo+g+qyshM6NJoNMjOzkZBQQHc3NwQEBBgsTPQ/w9VZYyxRC6XP1NVmcFgsNCqkB2qssOHDyMrKwtvvvkmPDw8AAD79u3DuHHjnp+qTCQSoV+/fiyPJBQK0b9/f7b6jTlKS0vx22+/sQk0GNe6lowU9kys6YkvbGlpKc6fP29hpHB2dsaoUaPw+uuvQyaToaysDHq9HkFBQfDy8mrEh7b0rNb0z57rWnMNcx3R4+Qjjx49glgsZo0UiYmJ2L59OwoLC9GpUyeMGTMG0dHRTRY/sefZ5tWFGOj1etTU1MDZ2Zn93tz3G3jMY7/yyiusXMAQeUhICORyuV3+4DbvvGq1Gq+++ipWrlzJvkXMxGVnZ4PP58PT05MdzO7duzFlyhQYjUb07t0by5cvR3h4+DMxDxcUFCA5ORlXr17FvXv3cPv2bdy/f7+ReVggEMDFxYU1DxMROnTogHnz5qFfv3428brMGMlO83BVVRU0Gg1UKlWLOx5zTW1tLSorKyGXy1mDjy3m4T///BMrV67E1atXwefzoVAoUF9fjwcPHrCRxox5eMiQIax52LyWR3P9awlM/3NycnDy5EkolUr4+vpCJpPBw8PDwjzMqM8YJ35z83BsbCxu3bplu4+zrfzFK6+8Qtu2bWvkmBMfH0+RkZHUq1cv+uOPP1gHjGnTprEqFplMRuvXr2f5IcYxx9a4feZ5mZmZ9Mknn1BwcPBTOea0bduWfv31V5sccwwGA2VlZdHZs2fp5s2bjZL3WeurTqejBw8e0B9//EGPHj1q0TFHp9NRWloazZs3jwYMGEAffPABXbp0qZFjTkM+WqvV0qlTpyg6Otrm/BIcDoeUSiX16NGD3n33XVq7di1duHDBbvmi4TgYXvjll19mHXP8/f1p9uzZVh1z1q9fz9YdYYoIMq6RtsIul0gfHx9av3496xGWk5NDkZGR7MR06tSJUlJSKCsry+JzDodDw4YNY8sVVVZWtlj2yHxiGN1j9+7dn5lLZEhICG3fvp3Ky8tJr9dbdYk0mUyUkZFBEydOJH9/f+rYsSPNmjWLzp8/T1VVVU/tEqnVaunu3bu0Zs0a6tatG4nFYuJyuWyqp5kzZ9LmzZtp48aNtHbtWjp+/DibZSgxMZE+/vhj8vPze2qXSEdHR+revTtt2rTJZlfVhutTUVFBmzdvblT6y9wl8ty5c6yOVyQS0bhx4+iPP/6gH3/8kfz9/dlrbIXdzugBAQFswZPjx483ckbv0qULvfLKK41c9BwcHGjatGm0efNm+vzzz+nf//63zc7op0+fthjcs2oKhYJefvllWrBgAa1evZq+/vpr2rZtG127do2ysrIoMTGRxo0bZ1GjVygUUmBgIC1YsIByc3NZ44a9zujFxcW0YcMGioyMtMga3pCwhEIh65Du7OxMoaGhFBwcTAqF4pmnopJIJDRr1iwqLS1tdAI1dTIxm9jq1aupR48ezTqjN4yI4XK55OXlRUql0uLz50a8vr6+lJSURDqdzu4wICalJZPOdOfOnVReXs6GmRw/fpw+//xzWrhwIR0+fJgyMjIoKSmJunXr9swJt+EkCgQCEgqFFmFAzs7OTe70SqWSvvjiCyopKaG6ujrKzMyk69evswW2rakJzcOANm7caNWK9d9uQqGQxowZQ2fPnqX8/Hyqrq6mmpoays3NpatXr9KNGzeooKCAamtrqba2li5fvkxDhgwhmUzWqjAggUDAhgFJpVKSyWQ2E6/d0cNSqRRpaWmorq5GdnY2AgICoNVqLZhxUxPBeOa1ijMyMjB58mSEhoZCLpejsLAQWVlZrNAlFovh6ekJk8mE7Oxse7tpAcYSxmTDoQYCgelJ8CgAtuRrS6ioqMC3334LAFCpVDh48CCysrIQHR2N+fPnWzgHmT/DaDQiPT0dP/74I4qKip5qXE8LHo8HtVoNsViMkpIS1NXVQafTYe/evYiPj4e7uzvrypqXl4fCwkJwOBw4OTnBy8sLYrEY6enpyMnJaVbIMplMqKioaNIxSigUIjg4GDExMWzqKVtgt55XIBCwkiLw2ErSvn17DB8+HFwuF2vWrMHdu3dt7oC9cHBwgIeHByorK1FSUmJT1CpjAmXGYTQan1mIN+PQzWgzeDweOnfujClTpiAiIgJKpRIymYwNfc/NzcXatWuxc+fOZ5oMxRYw1kSZTIagoCCMGDGCzWl24cIFfP3117h3757t0r6dEAqFbC1m83XjcDhQqVTo27cvunXrhk8++cS28dhLvNbg5uaGyZMno3PnzliyZMlzTToSGhqKN954A0VFRY2SjjD5GcyTjjQMmWfUT7YQ/dNAIpFApVLB3d0dkZGR6NatG3g8HuLj4xEfH88mZ35eSUe4XC6kUikUCgWbdKRr165s0hFfX18oFAqLPHJff/01Fi9e/ExebMYOYJ6IsaWkIwKBAHK5HCUlJbY9w1biFQgEzU6uVCqFSqVCaWkpu6NIJBK4u7tDq9WipKTkmUyKTCZDQEAABAIB8vPzYTAYEBgYiOjoaERERMDLy8si3dOmTZueOn2ROaxZAVv6PbPbAY/dDc3nkc/nQywWsxbCZ/FScTgc9OrVC/PmzWMTwjg4ODQqWmL+t8lkwu7du/H+++8/9Xwx/tkxMTE4cuQI0tLSWpwzJt1TeHg4jh49atNzbOZ5lyxZgsTERFy/fh11dXXg8/moqqpiY8Pq6uoseEWpVIp//vOfGDduHHQ6Ha5du4bjx4/j/PnzyM3NhV6vB5fLhUQiYY0ITFp9ZjAMn2qesqm2thZpaWmsU/eoUaPw0UcfITAw0KIQNPC4uuXhw4dx//59W4fZIuw9UumJY0pTWXEYJ3WRSASZTGaRoVKv17eqgKFAIMD48eMxZMgQq0YI5n7m9+VwOGjTpg1kMhlLvNZeVJlMBmdnZ2g0Grbyk1QqRZs2bdCmTRu4uLige/fuePXVV+Hm5gY3Nzd8/PHHVjcuLpcLlUqFsLAwDB06FEOGDIGPj4/N47SZeGfPno0PPviATaQnEAiQmpqKf/zjH8jIyGj0ex6Ph5CQEPj4+IDH46Ft27YYOXIkcnJycPbsWTbFaZcuXaBQKHD58mUcPHiwUYrT4uJiHDhwAH/++adFilPg/3mdtW3btpEbHz2xpzs5Odk8GQysRYA8TzAsjkgkgru7O/z8/BAWFoba2lpcuHABDx48sCsllKOjI7p27dqsCVyn06GsrAxyuZw1F0dGRmLmzJlISEiAVCoFh8PB/fv32RSnoaGheO+99xAdHQ2NRoO7d++yKU6DgoLYFKcM25aTk4MrV65YTdDo4OCAKVOmYNy4cQgMDGxVnl67CqoAlm+rwWDARx99hI0bN1pd4ICAAEyaNAlxcXGNdsamkkuXl5fDxcXFIrl0UVERTp48ySaXzsvLA5fLbZRcumEf7t27h6FDh9q88zL9YXxxGe2ANQ3F8wCPx2MTZE+fPh0+Pj44evQo1q1bh7y8PJtZipCQEJw8eRJt2rRpUsKvqanBrVu34O3tDQ8PD3b+9Ho9tFotS4CPHj3Cw4cPYTKZ0LZtW3h5eVlNLs1Ap9Ph5s2b2Lt3Lw4dOoT79+9blTvGjx+PjRs3PlVyads1wmZg9JgajYZmzJjRrLKcy+WSq6sr/e1vf6MrV65YzT/QVDN/nrmetKm0/qWlpXT27Fk6c+YM/fbbbzR8+HC7LHKc/yNp/RUKBc2dO5euXr1Ka9euJU9PT7aunVwup5CQEDZrjrW5VyqVtGnTpv9oWn+tVksnT56k0aNHk7Ozc4tp/b///vunTutvF/Gad7S8vJyuXr1KMTExNvsY+Pn50e7du9mMOQ8fPnyqCjXm/aqrq6Pp06eTQqEgBweHJq1WthCwRCIhd3f3/2pBFVdXVxo7diz16tXLoqDKxIkTKTk5mR48eEC//fYbRUVFNVlQZfLkyXTr1q1nXlDFYDBQXl4ea7RISEig999/v5GlrKnm6OhI+/fv/88WVDGZTJSXl0cLFy6kESNG0LBhw8jb25stZeXj49NiKSuVSkVDhgyh/v37k4+PD7Vr145Wr1791KWsbt26RV5eXjYTh7u7O/Xp04e8vLyaLGXVmqJ5z6rx+XwKCgqiwMBAtpRV27Zt6UyDUlY7d+5kd+CG42CumTNnDv373/+mzMzMVpWMYubYZHpc/XTbtm3UsWNHUigUpFKp2Iqnto5NLpfTli1bSKvVsk5arelXq4oIjh8/ni0iqFar0bZtW7zxxhuIjIzE+fPn8eWXX6K8vNzW20KpVGLcuHGYMGECOnfu3Kqo2itXruDNN99sZO0Ri8UIDAxEcHAwcnJy8PDhQwQFBeGLL75At27dkJ6ejqVLl+L06dOstkMoFMLFxQUajQbl5eXPnd9ldKJSqRRCoRAKhQLdu3dniwgmJyejvLwcAwYMQHR0tIWzd1lZGasJYgSs0tJSi/szOl9fX1+MHDkSU6dOhaurq13+wllZWThz5gyOHDmCEydOtFjUpeH4VCoV3NzcUFJSgpqaGoSFhWHw4MFsRp2YmBj4+PjYFxdn79tXX19Pq1evJk9PT1Kr1TRkyBBKSEhgj6a0tDQKCQlpVflWPz8/+vnnn5+qfOv7779PsbGx1KVLF3rjjTdo+/btlJubS7W1tZSbm0vnzp2jzMxMCyea/Px8+uabbyg6OpoiIyNpxowZdOjQIfr+++/p5ZdfJrVa/dzLt44ZM4Z++eUXSk5OpszMTLvKt1ZVVVF2djZlZ2fT4cOHaeDAgSQSiaw+SyqV0uLFi+0q33rmzBlq3759q/h/Ho9HXl5etGTJEjp//jy99dZbjcq3xsXFUVFR0fNlG5jBVFdX08mTJ+mHH36go0eP0sOHDyknJ4cuXbpEU6dOfarC2Z06dWLDwpsS4Jh+MPx3Tk6OReHsmpoaKisro7q6uhYFQuZvnU5HBQUFlJmZyfrs6vV6Ki4upvj4eDbE/a9QOLu4uJjWrl1LkZGRpFarG6VQjYyMpJycnCbnlHlhtFotXbhwgTp06NDqcTKb0syZM2nZsmUUERFhwaM7OzvTrl27WlU4225VGQCLMJza2lr87//+L7Zv346cnBxUVlY2W3ilJfB4PPTv3x+DBg2CWCyGSCSCp6cnfHx8oFAoIBaL2QQkeXl52LdvH86fP4/Bgwdj8uTJ7HdMH209gpqbBpPJhOTkZLzzzju4ffv2M2cj3N3dcejQIXTr1g3A08fX0RMnqdLSUhQWFqKwsBBbt27Fvn37YDAYIBKJMH/+fEydOhUSiQRVVVUoLS1FZWUlCgsLkZGRgZycHGRlZeHy5ctP7UDEhPwAYGtUcLlchIeHY/78+Xj99ddbF8FtF6lbeetra2vp1VdffabHKPD/XCu5XC6JRCJSq9Vsjty+ffvSyy+/TEFBQSQUConD4VBAQABduHCh1RqLhuMyP66Li4vp448/bvIoftrG5XJpzJgxlJGRYdUn+GnGwLSMjAwKDQ21YB+ioqJowIABFBISQiqViqRSKfH5/OeerZ3D4dCgQYPo3r17VqPMbcVTES8RkcFgoJUrV7J1w1xcXMjZ2fk/rmISCAQ0b948NkzJVlg7duvq6ujGjRu0Z88eWrFiBQ0fPpwcHR2fe/9jY2PpwIEDVFBQQFVVVVRTU9NIzdVawq6vr6d33nnnP7om5i+KOesSGBhI165ds6rL12g0No/Jbn/ehuByuZg8eTI6dOiAuro6+Pr6oqKiAsuWLcOpU6daxUIwli6BQAA+n4/6+voWnXqMRiPu37+Pmpoa1v3Q1uBKplQrj8dDSUkJfvzxR+zatQt5eXnss+k5axz0ej0SEhKQlpaGdu3aQalUgsfjITg4GIMHD0bbtm1RU1OD7OxsSCQShIWFQalUArAtgSCfz0dUVBR27txpYWqWy+VwcXFBWVkZKisrn7m3nbe3N7744gu4uLjg0qVLKCkpwejRo9GpUyeLvmo0GsTHx+PcuXNYtWqVTfd+auLlcB7X+xo4cKDF54GBgVixYgUOHjyIwsJCm4nY0dERo0ePRnR0NFsQ8P79+/jll19w/fp11NTUoLKyspGt38HBAWFhYaxJ2Vb+qaysDL/99huqq6vh7++PY8eOYfv27aiurrZtAp4h6EkU7fnz59nPuFwutm7dioCAANTU1KCgoABCoRADBw7EZ599hsDAQAAt88kcDgd9+/aFv78/7ty5A+CxK+vy5csRGxuLgoICHDhwAMnJyfD29oaPjw8KCwvx+++/s1WA7IVIJMK0adMwfvx48Pl8DBkyhN0kmD4RPS5Bdvr0aWzdurVZ03Mj2LxH2wlGrXbz5k2aO3euzceuv78/GyNn3qqqqujhw4dsKVjG8sThcEihUNDEiRPpzp07FgGPtvTx6tWrFB0dTZ06daJZs2ZR7969/2tWteZaQz5UIpHQmjVr2PFaG1tDrYpOp6OlS5eSVColHo9HU6ZMsYgGZ8KxGINBfX09LVq0yK75cHJyol69elH//v3ps88+o5KSkmb7p9Vq6eLFi/Tll1/SiRMnqKioyGYas5l4G6pRbFHrmBPee++9Z9MkCAQC+uSTT9iwaGt6TpPJRFlZWTRnzhwaOHAgrVq1igoLC5sNSW+qf7m5uTRnzhyaM2cOXb58mY4ePUoDBgxotXn5eRKveX/kcjnt3LnT7nRY5eXltHLlSpo0aRKlpqZaqApPnDhBq1atomvXrlFlZSVlZGTYJYwrFAraunUrlZaWUlVVVZNmf0bQv3DhAn300UfUq1cv2r59u111SojsUJX99ttvbFaW2tpaGI1GODg4oHPnzmwWluaSaqSnp2Pq1Km4fPmyhd+uNUilUsTFxWHYsGFwcHBAWVkZ1Go1YmNjIZfL2d/pdDpotVqL5Bn2WuZMJhPKy8tZjy4Oh4OioiIcPHgQu3btQkpKCuuz/J8Ew/czbpKenp5sDWcm68ynn34KZ2dnq9c2BWbMRqPRIhH01atXMWHCBDx48ABqtRoBAQGoqKjA3bt3bYrwkEgk+PDDD7Fw4cJmcykTEe7cuYOFCxciPj4eFRUVcHd3x7Fjx6wmpWkWtlI5U+HbfAfgcDjk6OhI06dPZ8Olm3rjTabH9br27t1LkyZNIjc3txZ3GoFAwEYbu7q60uLFi6moqKjRLtzcMxvu3tZUUdY+q62tpa1btzYqzdSw8Xg8kkgkJBQKG50szFy1NjmKi4sLTZgwgY4fP0737t2j9PR0NglhcXExOw86nY5KSkqoqKjI7ty9JpOJampqaNasWa0ywKhUKho+fDjt2rWrxVwcJtNj35iXXnrJYk5CQkJYB62SkhKb+k1kh7bBmrRPRKiursamTZtQWlqKefPmITg4GBKJxMJGzfzr5uaGkSNH4rXXXsPQoUMxbdo05ObmNvVSWTzz0aNHWLJkCU6dOoW4uDi8/vrr8PX1tUjBxFxHZtELdXV1KCoqskhP7+npCQcHB/D5fNZ/17yv9ETge/DggUXuLCaQU6/Xs/nZgoOD8fbbb8PJyQnZ2dnIzMyERqOBTCZjnbM1Gg0yMzNx48YNFBcX2yS8mkwmVFZWIjMzEzqdDmq1GlKplJ0X05OI3PLycly5cgVHjhxBQUEBwsPD8eqrr6JTp06Qy+XNnkj0RFg6d+4cDhw4YLdmyNvbG2vWrMHgwYObLNJCZhqdzMxMLF68GOfOnbMwIrm5ueHWrVtYvXo1Tp8+jZSUFJue36oATCYuyzxEh8N5XPy4Xbt2iIqKYtUh1hIV05Oj69ChQ5g5c2aTBNwUhEIhRowYgY0bN7J5sJj71tXV4ejRozh16hSKiopQUFCAgoICVFdXg8vlQq1WIzAwEAEBAfDw8ECbNm3Qvn17BAQEsEnhDAYDkpKS8N5777GR0EqlEu+++y66d++Ohw8fIjExEVqtFuPGjcObb74JmUzG5lIzmUxsnlrgMSFWVVXh2LFjWLx4Me7evWuz6o2pzTF+/HgMHjwYHA4HN27cQGpqKnJzc5GZmYmMjAzWssnkJAsLC0NMTAyGDx+OTp06WRQOZ56t1+tx6dIlzJs3D0lJSXapA52dnbFhwwaMGDGiyTUGgMLCQuzYsQMnTpzAzZs3UVhYyKrj+Hw+evfujdmzZ+PChQtYtWqVfWFPtm7RMDsq5HI5zZgxgxYvXmzVCYTD4ZCnpyetXr3aahIO5ggxGAx09uxZGjBgAInFYruOK09PT7p48aLFUV9QUEBTp04lR0fHZo9qxnInFApJqVRSly5daNasWbR+/Xpav349zZkzh9q1a8feQywW0+rVq1nJ3Gg0UnV1NRUXF9t0TJsLrmvXrm3EMjFJWJgietaag4MDde7cmaKiosjFxcUmSxiXyyV3d3eaMWMGJSUlUXl5OdXX11NdXR1lZGTQ+vXrKTw83C5tAofDIW9vb/rpp5+a1XQYjUb6888/qW/fvlbZEScnJ5o3bx7l5eWxucqY0gc202RriFepVNLp06dZ0+mcOXOsEp9QKKQBAwbQvn37mqxnazQaKT8/n1avXk3BwcE2TySPx6NXXnmFDh8+TNevX6dffvmlyYmyZUGYjDnWiOKll15iX8KGBGkPb2k0GqmkpISWLFlCarWaOBwOyWQymj9/PmVmZlJiYiKFh4c328/WOtg7OTlR9+7daeTIkfTaa69Ru3bt7NowRCIRhYaG0syZMykpKakR4TJzYTAYKDs7m1avXk0BAQFWaSImJobi4+MtfHjr6uroq6++orZt29pKkrYTr0gkYgmLz+fTt99+yz64vLycvvjiC+rUqRP5+vqSQqGwmGSxWEyxsbEUHx9PWq2W9Ho9VVdXU2VlJTsJer2e0tPT6bPPPqPw8PBm0weZL4pUKiUnJ6fn5nfA4XBo4cKFTx2yQmS5A+/Zs4c++OAD+uGHH9h6v0ajkZYsWfJ/Ss/s6upK48ePp71791JOTk6TiQP1ej2lpqbS7NmzKTg42MJ9UqVSUd++fWnixIm0detWNht6Q+LX6XSUn59v83zaTLw9evSwCPN47bXXWDs0o9AuKiqizMxMOn36NPXu3bvRRLi7u9OkSZNo4sSJ1KtXL4qKiqJt27ZZaA/0ej3l5OTQrl276J133qHQ0NBnFkfGOPnYcz+BQECrVq1qlcteUzAfq7mmQ6/X220UkEql5ObmRo6Ojs+c6F1dXWnfvn0WrqXmY6iqqqKUlBSKj4+nTz/9lLy9vRudDD4+PnTs2DGqrq62akAy1/bYC5uJNyQkhBwcHNhOhYSEUGFhodVFMZlM9PPPP1vdDRl1G/P/nj17UkVFhdWFzcnJoe+//97q8WNvEwqF1LlzZ/r4449p6NChNoX4cLlckkqltGDBAnYBnxeYE+y1116zmTVQKBT0+eef09mzZ2n9+vXUrl27Z+ZvDIBiY2MbsUsM9Ho9rVixgjw9PUkulze5IUyePLlZ3ri+vp5KSkrIYDDYPWet8ud9gRf4vwBuyz95gRf4v4kXxPsCf1m8IN4X+MviBfG+wF8WL4j3Bf6yeEG8L/CXxQvifYG/LF4Q7wv8ZfGCeF/gL4v/D4euK309HllBAAAAAElFTkSuQmCC"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 10\n",
      "\tbeta = 1.3971e+01\n",
      "\tJ = 1.2552e-01\n",
      "\tgrad_norm = 3.6951e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 11\n",
      "\tbeta = 1.5412e+01\n",
      "\tJ = 2.1704e-01\n",
      "\tgrad_norm = 3.9002e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 12\n",
      "\tbeta = 1.6853e+01\n",
      "\tJ = 3.1980e-01\n",
      "\tgrad_norm = 5.0512e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 13\n",
      "\tbeta = 1.8294e+01\n",
      "\tJ = 3.7750e-01\n",
      "\tgrad_norm = 1.0561e-01\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 14\n",
      "\tbeta = 1.9735e+01\n",
      "\tJ = 4.6349e-01\n",
      "\tgrad_norm = 7.6660e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 15\n",
      "\tbeta = 2.1176e+01\n",
      "\tJ = 5.1728e-01\n",
      "\tgrad_norm = 6.3994e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 16\n",
      "\tbeta = 2.2618e+01\n",
      "\tJ = 5.5467e-01\n",
      "\tgrad_norm = 6.9983e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 17\n",
      "\tbeta = 2.4059e+01\n",
      "\tJ = 5.9320e-01\n",
      "\tgrad_norm = 5.5706e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 18\n",
      "\tbeta = 2.5500e+01\n",
      "\tJ = 6.1756e-01\n",
      "\tgrad_norm = 5.0047e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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pqalBnz59mq3j2LFjkZub224LQeXGjoeHB0QiEcRisdaLO7FYjFWrViE3N7fVmaUlaEVeZRTAwoULERkZieXLl2u1AhcKhXjnnXdQXV3N6WqFhYUoKSlp1Vm9ceM13RBhWRYxMTEwMzPjpkcDA4M2EfLvUheaE00mLAcHB5w4cQI1NTWQy+Woq6vDH3/8AScnJ7X77e3tERUVpWZTbQ+wLIuHDx/i3LlzuHLlCnbt2oW+ffvythOPGjWqVUcuPtBpwdZ4AfTll1/y6gh7e3usXLlSa4+nxu+tr6/HzZs38eWXX2LLli0qPg1yuRxXr17Fd999h9jYWMTFxWHlypU6e3v9XRsTmkQqlWL58uU4dOgQfHx81P4WFBSEqVOnYsiQISpO80qxsbHB9evX22x6a2oubOm60tJSnD9/Hhs3bsSoUaOaJTLDMPj666/b5YPSirxNV6ZyuRyRkZGtdsTq1auRlZWl4nugydje+Lemv+fm5uLtt9/mVtAMw6BXr15IT09XM+IrpaamBkOGDHmuI6i2YmFhgY8++gj5+fmIi4trViVoSUaOHKm1kwvwbABITU1FTEwMjh07hh07duCDDz5AREQENm/ejMTERBXrTVNiN273gwcPIiQkROM6YsqUKXjy5AkaGhq09kdpDAbgF9YJgIqLi2ndunWUnp5OHh4eVFVVRQcPHqTy8vJm73vttdfo+++/J6FQyD0nKSmJfvjhByoqKqI+ffrQgAEDqKGhgS5fvkxJSUkklUqpb9++5O/vTwzD0KVLl2j79u2UlpamFoX66quv0vfff09isVhjmSMiIujrr7/mU8XnDrFYTMHBweTk5ESpqamUkZFBJSUlWkfeTp48mQ4fPsy1OR8AoPPnz9OsWbOouLiYABDLsirXWFhYUFhYGE2aNIkA0IMHD6iqqoq8vLzopZdeIjc3N5V+kMlklJqaSjNmzKD79+9zvwsEAvL09CR3d3cyMjIiHx8fCg8PJw8PD+1svXxZXltbi7feektrPXLkyJHIyclBUVERbt68iaVLl8LGxkZlGjE0NFSLFGYYBgYGBq3qrtbW1hotFEq/hYkTJz730ZSvMAzTLr4Ur7zyitY7jSzLtjqLKkUkEqmsCRiGgYWFBcaMGYNffvlFxS2Sbx/4+Pjgjz/+0GoE5k3eppGgmsTExESFmMqKOTg4wMXFpd38HUxNTdG7d28u/CUqKoqzN8tkMpSUlCApKQlr167VKkK2I0QsFsPBwUGrGL22ip+fHx4/fszFhikXeC1NzyzLYvHixe1S3xEjRuDMmTPIzMzEV199xTsY1s3NDevWreNNXt5qQ2vDuVQqpT179pCpqSlNnDiRqqur+TxWJ7zzzju0dOlSmjhxIsXHx5OhoSGNHDmSnJycKCsri9LS0ujJkydUXV2tNvX9XWAYhry8vGjFihU0bNgwSk1NpeXLl1NCQoLOW+favNvX15fc3d2ppqaGqqurycnJiQYMGEDdu3cna2trcnd3JxMTE+6eqqoqGj9+PF26dKldyqCvr09SqZRKS0u1ri9PSpLWAZgMw8Db2xsjR46Et7c3N6WbmZnhwIEDWLt2bYc7dLu4uGDcuHHPxXOtNVHONCtXrlSJ62LZZxG/e/fuxTvvvAM3N7fnUj6RSARDQ0MEBARgz549yMvLQ0pKCubOnduh3mXaCG9OakteHx8fZGdnQyaTITs7W8WUI5FItGoAoVAIS0tLtaldKBTC0NAQFhYWMDc3f65mKz516N69O4YNG4awsDB88cUXyMjI0GimamxlSU1NRXBw8HMtu0gkgr29PSwsLFTWFQzDcN5lXbp0gbOzs4rKaGhoCF9fX4wYMaJDPO34QmuvMktLS7K1tSWhUEhCoZBqamq4vzU0NLR6v0QiIalUSl5eXjR//nwaNGgQlZSU0MmTJykuLo6cnJxo2LBh5OrqSubm5iSTyejYsWO0du1aKi0t1ba4vCESibicYfr6+mRlZUUymYyePHnSouoRHBxM+/btI2traxIIBNwKX5OapfxNqVL88MMPFB4e3m5TtbaQy+X0119/qfzm7u5OCxcuJG9vb7K0tCRnZ2cSCoWUmJhIcXFxZGxsTH379iVvb28yMjKi5ORkmjJlCmVmZv79FdB25PXz8+NyVq1fv17tix09ejQiIyM1OoaMHj0aZ8+eRUZGhsoOS2NvLk22X7lcjuPHj8PFxaVdv3CxWIyAgAB8/PHHiI6OxvHjx3Ho0CH88ccfKCwsRHZ2NubOnasy8hsaGsLBwQG2trbo06cPbt68qbPBnWWfRTe0lDxEX18f3bp1g6+vL0xMTCASiThp7y1tT09PbsXf3KyhyQZ/9OjRdvXn5s1J3hf+34P/9a9/cZsUr776qspLAwICkJeXh/r6eowfP16FuKGhoVy8lC5gWRZJSUkYN25cu+jUdnZ22L59u0oWGk1G98LCQowePRqWlpaYOnUqrl69ioKCAuTm5qrcqytYlkVCQoLGkClvb28cPXoUZWVlKCsrw71793D27FnExsYiNjYWn376qYqjlLaizBzUrVs3/Pvf/0ZiYqJOdZHL5YiNjUW3bt00vufll1/Gli1bMGzYMLW0T7NmzYKvr2/Hk1cgEGD//v1ch507dw5OTk4QCATo2rUrNwqx7LOEckq9dd68eTr5qjYFy7KoqqrCwYMHMWLECJ3NYDY2NoiOjua1fap0t0xLS9PaG4svFAoFvvnmGxgZGYFhGNjY2GDBggXIzMxscQRUKBS4ePEinJ2dtSZt79698d133yEtLQ0VFRW8fUuaA8s+yzBkb2+v8p6+ffty9SgsLMRrr70GOzs7zJo1i1sbPHr0CEFBQR1LXoZhsGvXLpWRKS0tDQcOHFDZKGDZZ07hV65cQXJycpvDPZpC6dRz48YN/Pvf/24xUZyZmRl69uwJV1dXmJiYwNfXF7/++mu7pCxtLyiN+WfPnsWuXbuQkpKilaNSbGwsvLy8IBAIWo2CtrKywsqVK7lZsD37RS6X4+LFi9i0aRO2bNmCffv24fHjxyq8qK2tRU5Ojlpqg3PnznEbVXyhtZ33lVdeoYMHD3ILHE3XKKH8e3uEtmgCAJLL5XT9+nX69ttv6fz589zWJhGRn58fffvtt+Tn50e1tbVUWFhIVlZWZGNj02Fl0hWttWVr9+bk5NCtW7dIJpORSCSihw8f0smTJyklJYUkEgl169aNhg4dSmFhYeTr60sCgaDd26A5KjV+D/5vUcyyrMritqCggAICAuivv/7ibefVmrxBQUEUGxtLEomEEhMT6dSpU+Tt7U1jx47VLQ6pHaAkcXZ2Np07d45u3bpFpqamNH/+fOrates/jqh/BwBwH6xYLCYrKyud+qcxPTTF9rX2vKYDmFwup02bNtHly5dpxowZNGXKFBKLxVRRUUF9+/bV6L/S0sN5gUg1xVBCQgLnR6qnp4f//ve/XPYVvlDaOy9fvoycnBzU1NTg6dOniI+PR2xsLJKTk9VylLUGpS7Y3pG4zb2LZZ8lzsjOzkZhYaHG6V45XSYnJ+P+/fu88rs9TyjVmNTUVPz888/43//+h+PHj3NO46mpqdi8eTNSU1NbdZVU9oUS6enpnGXCwMAAe/bs4a5btWoVRCIR73JqRd6JEydyyd2WLFmipltqkyyNZVnEx8fDwcGBi8Lo168fvLy8YGRkBJFIBHNzcyxbtkyn4LyOhtL1b/PmzfDz84O1tTVcXV2xYMEC5Ofnq+hzT548wfTp02FiYgIzMzMsWrRIY+7ivxtKkiqDA5Sora3FkiVLYGFhwZkJxWIxRo0ahbVr18LDwwMMwyAsLAz19fUtPr+0tBSVlZXc/3/77TcVp54BAwZwnKqsrMTWrVt5l18r8m7cuJH7SqZNm6a2GNi6datW5N24cWOrK2OpVIrbt2/zrtDfBZZl8csvv2j0hlu6dCnn1cWyLLZs2aJmK75x48ZzrsH/t9G+//77Kv6/CQkJzS6CGy8GPTw8UFpa2uLzMzMzUVBQwP1/x44dKs9wc3NTiWTWZkbSKskBWtBFlKfTaIMXXRfVtOgRCARkaGio8psyJ4MSurRVR0EikZCBgYHKby0t5pr+3lofCoVClbpqqndLvGoRfFlORAgLC+PSX37wwQcqX6SlpSXu3r2r1cir1JslEgkcHBwQFBSE7t27cycKWVhYIDIy8h+rNtTW1uLbb7/FSy+9BEdHR/j5+SEqKorLn6C8rqysDBEREXBwcIC9vf0/pk7K3cum9uu6ujosW7ZMTW0IDQ3Fhg0buIDViRMnthixoVQFampquP///vvvKmrDwIEDObWhrKwMX375Je/ya0VeiUSCbdu2gWWfJYtWGscNDAywdu1arR2gFQoFHjx4gGvXruHx48eora1FWVkZ7t69i4sXLyIlJUWnBZumbeaOgHKaq6ysxJMnT1BRUdGsQ45MJsPjx4+Rm5vb7nbv9oZSF05JScHBgwfVFmwPHjzA1q1buUNmWntW42sePXrE7SYaGhpi7969XJ8tWbIEQqGQdzm1NpUNGDCAzp07R3p6epScnExnz54lHx8fGj58OInF4udmKpPJZJSRkUFnzpyhW7dukZGRES1YsIB69eqlZuJ50dUVTdDUjTU1NVRYWEgGBgZkaWlJItEzPyy+9W/6zPYwlSkUCtq+fTtduHCBpk2bRhMmTCCxWEylpaXUp08frQ5r1Jq8U6ZMoQMHDrS6SaFNBXWFkrSXLl2irVu30uXLl1U8zzw8PGjz5s3Uv39/qqqqoidPnpCdnR05ODj8Y3ROJVpqSz73ZmVl0Y0bN6ihoYEEAgFlZWXRmTNnKCMjgwwNDcnf359GjBhBY8aM4WLFntcmBRERy7IquvXjx48pMDCQCgsLO8bOKxAIsHv3bm4aUCgUuHfvHnbv3q2SMESpD549exbx8fHtbtdUmqmuXLmCWbNmtRhiY2hoCA8PD9jZ2cHAwAAeHh44cuTIP257uK6uDseOHcP//vc/3L59m7e6pDziwN3dndNPm9seVmauWb16dbtvDyutUHFxcdixYwd27NiBX3/9FcXFxWq8ePTokYqezbIsTp06xYXL80WbHHNOnz4Ne3t7MAwDNzc37vgklmWxd+9e6Ovrw8TEBDNnztQpjVNTKPXL/fv3Y8iQITrHhVlbWyMmJoa3Y051dTXy8vI6TFdVKBTYtGkTZ3YzMzPDG2+80apjjlwux7Fjx9TiBluTxo45Dx48aFZX5wtlea5fvw5XV1fu4xGJRBg6dCgXUVJYWIg5c+bA1tYWM2bMQHp6OhQKBTIyMtC3b1+ufHyhs0ukQqHA7NmzVRrF398fubm5ai6RRIT+/fvj0aNHbWqgu3fvYuzYse3iEmlvb4/du3dzSVCaivKd5eXlmD17NpycnDBv3jzcu3cPpaWlKC4u1ngWry71io+P13jEl6+vL2JiYlBZWYmKigrcv38fp0+fRnR0NGef5XvCUnMktrCwgJ+fH+bNm4fk5GSt68Oyzzz99u7d22w2yeDgYHz99ddqLpEuLi6YPn06vLy8VK7nC63J6+/vz+3IaHJGHzlyJD788EONo2L//v1x6NAh/Pnnn2rmJOWKvDln9GPHjmnt+teaSCQS9OnTB2vWrMHJkycRHR2NI0eOID4+HkVFRcjPz8f777+vYtqxsLCAl5cX3NzcMGTIECQkJLTpg2zNGV0Zb9arVy+YmZlxYecdERrl5eXFnenR0ojf+G8NDQ1YsmRJq6metHGc5wutF2zBwcF09uxZkkgklJeXR/3799cq4bJQKCR9fX1yc3OjefPm0YgRI7gwoPj4eHJ0dKQhQ4ZwYUAKhYKOHz9OGzZsaDG5SVvReAGqr69P1tbWpFAoKD8/v8Xo15EjR9LevXvJwsKi1TCgxgBAjx49ovDwcLp8+XL7VaSNcHZ2ptdff526detGNjY25ObmRkREcXFxlJCQQKamptS/f3/y9fUlAwMDOnr0KM2fP79do8V5UpI/zanRVPbw4UPU19cjLS1NJQpWX19fqyldIBDA1NRULQpYIBBAT08PJiYmMDY2bpdwl47KAikUCuHn54fhw4djwoQJWLduncZTzRuPXnK5HPfv31dxwH4eIhKJYGdn12zmT4lEAmtra9jY2KgE1urr68Pd3R2BgYEdko+CNye1JS/DMHB3d0dwcDBcXFw4UpiamuLw4cPYvHlzh5wq01hcXFwwceJErRru70phyjAMnJ2d8d///lct9P3Ro0fYtm0bd+LQ301WZQZNY2Nj9O/fH/v370deXh4SExMxc+bM554ZU1vytlvSEQMDA9q+fTvZ2NjQ5MmTOzTpyLx582jFihU0ZcoU+uOPP8jY2JjGjh1Lzs7OlJmZSSkpKfTXX39ReXn5c0064uHhQe+++y6FhIRQcnIyrV69mpKTkzu8TAKBgLp3705ubm5UXV1N9fX15OrqSgMHDiQfHx+ysrIiV1dXMjIy4u4pLS2l0NBQiouLa5cyGBoakpGREZWUlGiVdIRhGP7tw5flfNI9KWPWGv8mEAjg5OQENzc3nQ+kaypSqRQ9evSAnp4ehEIhNmzYwNlF5XI5ysvLkZaWhvXr1z/3dE9CoRDm5uYderB2U+nVqxfy8/Mhl8vR0NCAuro6jdk3G4NlWYSHh7f53RKJBGPGjMGFCxeQlZWlVbonT09PbNmyhffI2+GJ9kJDQ/H48WMUFxfjjz/+wLJly1SC9JQJ9Zp2Lt9Ee/b29sjOztbYGfX19Rg7duxzJa+20h4h7bom2luwYAGv5wsEAhVrB8MwMDMzQ2hoKI4cOcKZEJU+EmFhYa0+s1u3brh9+7ZWlhveSUf09PTo008/JUtLS8rKyiIvLy+qqqqivXv3UklJSbP32drako2NDYlEIrKwsKDAwECaPXs2/fTTT/TkyRPq1asX9evXj+rq6ujSpUuUnJzMJbbo3bt3qylOQ0NDqUuXLmrvZRiGxGIxOTk58a3ic4dIJCI/Pz+ysrKivLw8ysvLo/Lycq1dBrVJbdoY48aNoyNHjtDTp0+JZVliWVbFN8HCwoJCQ0Np/PjxJBKJKCcnh2pqasjd3Z169epF7u7uJJFIuOfV1dVRUlISpaamqrxHIBCQt7c3eXh4kJGREXl7e9Orr75K7u7uHZPiVPl1KhQKLtRFLpdj1apVLX5RUqkUK1euRHp6eovJpRuvxDXZenNycjBv3jxODWAYBv7+/i0ml66trcXw4cOf+2iqjUilUoSHhyMtLQ23bt3S6eTNCRMm6HSYolwuR3p6OmJjY3Hq1Cns378fUVFRiIyMxM6dO1XCsprb1FHugu7atQtBQUEaLRnTp09HUVERZDJZm5JLa5XuSZMjsr6+fov3VFVV0aeffko7duygOXPm0IoVK8jU1FTNMUT5b02jBsMw5OjoSFu2bOHsonp6ejRx4kRydnYmhmFILpfTlStXKCkpiby9vcnKyopOnTpF165d06aKHAQCwXNZ7FVVVdGhQ4fI2tqagoODVdJpET1bCPn5+ZGdnR2VlpbS/fv3qaioSOWa+Ph4unPnDjdz8R3NhEIheXp6kqenJxERb2chAFRWVka3b9+mO3fuUExMDF27do1kMpnatQzD0KBBg8jS0rLtjkHaML2hoQGHDx/Gm2++iXfffReLFi3S6nBsgUCAt956i9OJqqurkZ+fz6V45/P1NffFx8TEcF+5SCSCgYFBm3ahnndyP6WdtfFvdnZ2OHz4MKqqqiCTyVBXV4fbt29rTIPl4OCATz75BEVFRe3uj8Gyz8J7zp07h6tXr2LXrl3o06cPbxPp6NGj22VrXSvyJiQkaJwGlKejK6MJmsZ1NRaRSIQJEyYgIiIC/fr1g52dHZycnPCvf/1L53RDCoUCc+fO1ZocyqOsunbt+o8/ysrc3By//PKLmjdcXV0dBgwY0GwdQ0JCkJWV1S4EVg4Y58+fh6urK0QikU6Z3MViMaKiopCXl4enT5/qTGStyJuZmalybJKRkRHee+89nDhxAlevXkV+fj7KysqwevVqnUaurl276nQWG8uy+Oyzz5pNryqVSlVMZspDBEtKSqBQKJCXl4dly5Y990MEGYZB165dMXbsWIwZMwYvv/wyunbtiqCgIPz6668a9dja2loVjyxN4uvriw0bNuDUqVO4c+cOF8rFF0rPrzNnzmDTpk06pZdydHSEj48PN7CJRCJ06dIF7u7uGDp0qEaLUWvQ+vjWEydOwM/PDx4eHvj222/VpnuWbdvxrVFRUTqRt6KiAtu2bcPIkSNhY2MDiUQCCwsLLFiwAPHx8YiPj8fixYsRGBiIiIgIjce3/vnnn/jss88wf/58TJs2DR4eHh2eKLsxcadMmcK5XspkMtTU1KC0tLRFsikUCnz++eewsbGBv78/li5dirlz52q0bwuFQhgbG2Px4sW8c2ywLIsDBw7Azs5OZzPe9OnTkZ2djdLSUqxdu1ZtYDMzM0NKSopWfQ7oeA5bWVkZioqKNFoFioqKMG/ePJ2n4dmzZ2t1cLZMJlNJFFdfX49Hjx7hypUruH//vsqB0AqFAtXV1a0enK0kc0FBAU6ePIk1a9Zg8ODBHbp92qNHD5XtZG36o6GhAY8ePeKyVspkMnz11VfNbgq5uLigqKhIpc6aDkFXOpe3ZSubYRisWLECVVVVXMBq43Y0MTHBihUrWsz/0Bx4bw83B/xf3qm7d+/S8ePH6fjx43Tv3j2dV+qOjo60bt06IiJ6+vQpBQYGUkBAAInFYqqqqqKysjKysrIifX19KigooKioKLpy5QpNmjSJPvzwQzI0NGy38JbGTVNSUkLDhw+nxMTEdnl2U2zYsIEWL17cLmXH/6W/io6Opl9++YUSExPpwYMHJJfLieiZ19zPP/9MQ4cOpaSkJDp06BDl5+dT165dKTg4mKytrenhw4d0+fJlOnLkCOXl5bWpPAYGBuTv709isZju3LlDlZWVXDquadOmUY8ePUgkEmlfd63pruHL/+mnn9rkFN1UGvurGhsbY9KkSVi4cCECAgJgY2ODoUOHYsmSJQgICFDx2l+5cqVOh+dpqlNTyczM7FBnmi+++KJdI54bj6glJSVq27TW1tYICAhQSy4iEomgr6/fodYWhmGwZs2aNqdVbTN5FQoFt60oFovh7e2NPn36tJsfgzYilUpx5swZnabexqpFbm4uoqOjcfjwYZw9exZ79uzRabNAG7G2tsaXX36JrKwsVFZWori4GLm5uVxOg8bl1IXkcrkca9asUSOl0tOso+olkUgwevRoTJ48GS4uLpBKpRgyZAgKCgo0qiktZeBpinYZeTMyMrB27Vr89ttvePr0Kaqrq3Hw4EGNoS3aiEAggLGxsVZOLQsXLtRaZ05ISMC5c+dw6dIlrFy5Em5ublzEgi6nmrelvnZ2dvD394ebmxvs7e0RFhaGW7duobq6GikpKVi5ciXmzJmDkydParWLxrLPYsi6d+/OvU8kEmHZsmWIjY3F/PnzWzRx6iIMw2DhwoWoqamBTCZDQUEB7t27pxJFoyxbSUkJ1qxZg27duvGuU5vJq3x50y0+hUKBy5cvY/DgwVr795qYmGDixInYvXs37t27h9OnT2Po0KEwMTGBiYmJ2sJJIBDA09MTr7zyCi5cuMB7VGJZFleuXIGNjQ309PTafFJ8R4m5uTn69OmjEmhpYWGBc+fOaTUCsyyLrVu3cu3n6+vLEamurg6bNm2Cn58fpk2bhuXLl2PatGktJu5uibQCgQC9evVSOdxcU3nKyspw6NAhDBs2DPb29hg8eDDv+rQLeZuDcp/7hx9+0Hg6eXPy6aefqpjglKaw+/fvIyUlBbt371bxTJs+fTr++usvFcsC3/LdunULrq6ucHV1xcCBAzVuwvxTZfHixVqTt7S0FKGhoRAKhXjrrbe4WUo5C5WVlXHt2NDQgLVr1/L+oMViMebMmYMff/wRR44caTHglmWfZV0KDg6GWCyGqakpYmJitMqe2aHkVUKhUGDlypW8O2XZsmUtTv1Ke7Onpyf69u3bprB6uVyOhw8fIi8vD9XV1Th//jwCAwP/kSNwY9HX18e+fft00u//+usvHDhwgEu5z7IsiouL8dFHH+G7777j9GyWZbFz507ebTFr1iy1dKnNlSErKws9e/bk7p0xY4bW5jLe5K2vr0dDQwOXLFjp5MzHJ4FlWSQmJvLewbKyssK+fftQUFDAnbzTNBmcQqFAQUGBymZDe0DZuR988ME/bhQWiURwdHTE2LFjsX//fp0PeNHkG6JczOnp6SE8PBwxMTH4/vvv4e7u3mq5GIbBwIEDeac2qK6uxvTp01X6W5vczkrwJu+AAQMwYsQIzJ49G+Hh4QgJCUHfvn0REhKCnTt3qpyrpglyuRw7d+5Ume5bEolEAicnJzg6OsLW1hYzZ85EVlaWzuYkTQ49LV0rk8mwc+fOVlfiAoEAUqm0QyMlxGIxQkJC8MsvvyA/P1/FLbG8vBxXr17Fr7/+irNnzyIxMZHLRcEXcrkcEyZMUHmnUCjkPeKGhYXxPu1JLpdj8+bNKu36wQcf6OTCqXUAZnMjwvDhw7F7927ExcWhoKBA47SvTA81c+ZMnVa27u7uWLhwIWJiYlqdYpS7bdnZ2bh58yYOHDiAqKgofPTRR/jpp5+QlpaGyspKFSI0vf/69esq29zKPfqgoCD06NED7u7uWLp0KRISEnDp0iVERkaid+/eMDc3h1Qqha2tLfz9/TF06FB4e3vrbLWwtrbG9evX1Vbo9+/fx7Bhw2BgYMBZRqRSKQYOHIhr167xJnBZWZnKFK6NeHl58XL8UfbH4cOHVfYELCwskJSUxC3eTp8+zavMQDuRt/H0oa+vD1dXV6xfv17jtMayz5zEjx07hldffRVjxoxBv379tIoENjQ0xIkTJ5rd4m1oaMCVK1fwyiuvwNbWVs3oLhQKYWVlhd69eyMsLAzLly/HmTNnUFBQgNraWtTU1CA1NRXjxo1T6aRvvvkGjx8/Rl1dHSoqKlBYWKiySFQuUDMyMpCcnIzc3FxUVlaivr4eBQUFahmG+ArDMBg7diyX94tln0Ui9+vXr9l7nJ2dER0dzeWJa66tZDIZtmzZopOt19HRETExMS0Sl2WfBRLs3r0bkydPVvG5MDQ0RFRUFJcjeMaMGRCLxXwpqRt5BQIBRo4cicjISLzxxhsac2VJJBKsXbu22SR7SqO00gHl4MGDvAP1iAgffvih2kgkl8tx8+ZNzJgxQ6tnET07FMbFxQUvv/wy+vbtq2Id8fT0xP3797WyZGiqb2pqKhwcHHQisEAgwBtvvIH8/HwkJydjxIgRrd4jlUoxZswYbNiwAXfu3OEGE5lMhuLiYty8eROLFi3SKkjVyMgII0eOxIYNG5CWltbswlppftu1axfc3NxUBg8XFxcsWLAAsbGxHD8qKirQu3dvEHVg3gYigq2tLR4+fMgRMDo6WqM90MDAAIsWLcKDBw9a3QqUyWRYsWIF7xHAx8cHN27cQHFxMQoLCxEfH493330X5ubmOpGjJfnggw/aZVGoUCiwdetWtd1HBwcHREVFYd68eS3axAUCAVxdXXXa/DE1NcXw4cMxd+5cjB8/Hh4eHlrtgkokEgwcOBCnTp1S2fVrDOXHXV9fj9u3b2P27Nkq6qGJiQnCw8ORmZmp0anr2rVrmD9/Pu/21Im8VlZWePToEfe3hoYGREVFwdbWFiYmJiodwDAMbG1t8eabbyIuLg61tbWQy+VqsUss+yyyYt++fZg9ezZ69uzZql5sbGwMFxcXODk5dWiI+/vvv98u5FWqNHv27IGPjw+MjIzQs2dPXLx4kVM5WlIFnocIhUKEhYXh1KlTGheCygGsoqICKSkp2Lt3LyZMmMBZagQCAQYNGoSvvvoKCQkJLaa71XZm04m8YrEYZ86cUXmpTCZDTk4OUlNT8fvvv2t0kDY1NUVQUBBGjx6NcePG4b333lNLVKec/svLyxETE4MePXq0a2cYGBhonaLI09MTubm57WaSY9lnrqOJiYlcmI5SN3R1deVdLoFAAG9vbwwdOlQle1F7yqhRo5q1XshkMvz+++947bXX0KNHD5iamqotSsePH6+2Hdxe0HnBtn379mavZVkWx48f5+X/2r17dxQXFzf7nOjo6HYzQxkaGuLHH3/Eb7/9ppV6wTAMvvnmmw7pgMZ1/eabb7QiYL9+/TjTWXp6Ovz9/dudvJs3b2623jdu3ICZmVmLH9dPP/3UYe3WZn/eTnTieeGfdTBDJzqhBTrJ24kXFp3k7cQLi07yduKFRSd5O/HCopO8nXhh0UneTryw6CRvJ15YdJK3Ey8s/h8lKRLLNlFo5AAAAABJRU5ErkJggg=="
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 19\n",
      "\tbeta = 2.6941e+01\n",
      "\tJ = 6.4649e-01\n",
      "\tgrad_norm = 4.7039e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 20\n",
      "\tbeta = 2.8382e+01\n",
      "\tJ = 6.7457e-01\n",
      "\tgrad_norm = 3.0053e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 21\n",
      "\tbeta = 2.9824e+01\n",
      "\tJ = 6.8719e-01\n",
      "\tgrad_norm = 3.8986e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 22\n",
      "\tbeta = 3.1265e+01\n",
      "\tJ = 7.0528e-01\n",
      "\tgrad_norm = 2.1861e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 23\n",
      "\tbeta = 3.2706e+01\n",
      "\tJ = 7.1718e-01\n",
      "\tgrad_norm = 3.7014e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 24\n",
      "\tbeta = 3.4147e+01\n",
      "\tJ = 7.3719e-01\n",
      "\tgrad_norm = 1.8640e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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4IDg4GNeuXTPI6bu8vJyXi2BtMjY2xuzZs7FixQr4+Pi88AaKdu3a4caNGzq99ObNm9cg4wYFBaGwsLDFTOhqtRpffvkldyIZYtyRSqX44osvkJ6ejsePHyM9Pd2gi7ZeYkN+fj6WLFmCYcOGYcyYMRg5ciQkEolenV63bh2n6ystLUVeXh5KS0ubdFbXQCOT1v593aPN3NwcLi4uevXtRSOGYeoxhbe3N6KiolBRUQG1Wg2VSoXs7GyMGDGi3vPu7u7YtGlTizKuBqWlpdi4cSNCQ0Nx4sQJHDx4EH369OGlGxcIBFizZg1qamqa3Q+9mLf2ZUatVqOiogKDBg3itRje3t746aefmtXp6upqHDlyBO+++y7mzZuHixcvcjt1ZWUljhw5gt27d+Pu3bvIy8vDgQMHIJPJnjsj6ktSqRSffPIJvv7663qqLBMTE/Tu3RszZszAhAkT0LFjR51Mnpyc3Cx1m8a0/+TJE6SlpWld5upekjWX4aioKKxatQpeXl4NinC2trZIS0trkQ/KIG2Dhp4+farlStfQDjJx4kQtr3lD3llSUoLQ0FCt3dTGxkbLk6nuYimVSrz11lvPnRn1pREjRiAlJQW7du3S0s3ypblz5xokfmnk/5s3byI8PBxvvPEG7O3tYWNjg6FDh+Lw4cOorq5uVFOjufguX74cXl5e9e4+EokEu3fvRlFREcrKynRqOfiCt4UNf0WK7tu3j5KSkkgsFlNsbCxdu3atUcuMXC6nq1evkqurK2clKioqoj/++INSU1PJzs6OOnfuTBKJhB4+fEgZGRlkYmJC3bp1o44dO5JAIKBbt27R5s2b6dy5c6RWq7Xa79q1K128eJFsbW119nnt2rW0fv16PkN8YWBlZUUymYyysrJIqVTq/fzkyZPp4MGDJBDwz2wAgG7evEkzZsyg1NRUqq6urreuxsbGFBQURIsWLSIXFxeqqakhpVJJMpmMzM3NSSKRaLVXVlZGv//+O82aNYtKSkq4v4nFYnJzcyORSEQKhYLkcjmFhIRQUFAQiUQi/gPly+Xl5eWYM2eO3sK5vb097ty5g8rKSqSnp2PXrl3w9/fnBH6NPV8qlWqppaRSKTp06IBOnTo1uvuIRCKd/gwaW/qkSZOe+076d9OgQYOgUCj02sVYlsXGjRt5tW9qagpnZ2fY2dnBysoK7dq1Q79+/bBx40YkJydrRYZnZWXB1dWVV5thYWF6iZW8mffVV1812FnFxcUFvXr1arHwdGtra4wfP57zjlq+fDl3TLIsi4KCAkRFRWHGjBnP/dImEAhgY2Nj0PFvKFlaWuL06dOoqKjgjANN+diyLIuPP/642e+2s7PDpEmTcODAARw7dgzjx4/nrR+WSqUYO3Ysb+ZtkRg2zd+nTZtGLMvS999/z6dJgzFlyhTatWsXvf3223T69GmytramdevWUffu3enq1au0b98+Sk5ONujIbUlYWVlRaGgoTZ06lVJSUmjFihV0+/bt1knAUQcymYw6duxIjo6OZGVlRZ07dyZzc3MSiUTUrl076tWrF9nZ2XGiXGVlJb311lt05syZFnm/JiawrpjHBzxZkgyKHnZwcEBAQAAXqkz0TOn88ccfY+bMmX/LzjJixAgtg4lAIGh1hxJ9+jd58mTExMRoRSVkZ2fj6NGjCAsLw+zZsw0Kz28JEolE8Pb2xu7du5GamoqrV69i6tSpz8UNVBfx5kl9mdfS0hJXrlxBdXV1Pbt3XUtWU8QwDEQikc5nhEIhLC0t4ejoqNPz6UUhgUAAPz8/vPHGG5g0aRI2b96MuLg4znqnCxpn/W+++ea5ijUakabu/AqFQkgkEtja2qJnz571cnMIhUI4OTmhf//+8PDweG7Mq8fV7hmMjY3Jzc2NxGIx2dvba90O+RyHIpGIbGxsyMfHh4KCgsjb25uSk5MpIiKCkpOTqV27dhQYGEgBAQHk7u5OFhYWlJCQQEuXLqU7d+7o2129oBGNxGIxWVlZEcuylJ+f3+i4Xn/9dQoPDycrKyutHF1NvUckEtHcuXMpMTGRwsLCWsWXtimwLEsFBQVa/9e3b19asWIFyeVyksvlZG9vT1VVVXTy5En69ddfSS6X05AhQzixIzMzk6ZNm0aXL1/+2/uv985rZmaGxMREsCyLLVu2aF3ANMkxZs6cWc9EzDAM+vTpg8jISKSnp2vpCzWagfz8fK0Yqto7VVJSEgICAlpULGAYBpaWlhg5ciS2bNmC//73v/juu+8QHR2NzMxMpKenIzg4WOudAoEAtra2cHNzQ1BQEJcIxBBo9KoNuS4SPbvEDB8+HGPHjkWnTp0glUphZGTUKubsbt26NRjFqzFQ6Vqba9euNelFqM+68eZJ3j/8q+GBAweitLQUCoUCQ4cO1Xrp2LFjOQYcOHCg1jETFBSE7OzsZi10VlYWli9fzjssqDGys7PD2rVrkZCQAIVCofNGrmGuAQMGQCgUwtPTE7t27cLjx49RWFjYqGigz7guX76sM2OQpaUlvv/+eygUCqjVahQWFuLWrVuIjo5GZGQkZs+erXd8YG0SCoXw8PBAYGAgQkJCGg2YbGoMZ86c0enHzTAMRowYgX379mH69Omc0UIkEmHUqFHYunUrunfv3vrMK5FIuAQRLMti27ZtnH521KhRnOsey7JYs2YNt7N99NFHesdb6YLGl/jBgwfYvHkzunTpYhATy+VynD17lpc/Bcs+Sxp3+PBhpKent7ifAPAsGmXr1q3cwjIMA1dXVxw6dKhBS5nGD/fQoUO89Kh1ydraGtu3b0dubq7OjJ36QuN1aGtrq3VKvfrqq1wQpsa8P3fuXISHh3N+1ampqVqbHV/oxbympqZank01NTWIjo7G8ePHtZJ/aHasvXv34tq1awZ7yjcEzUTn5OTgww8/bDTQ09XVFRMnTsSAAQNgZ2eHTp064eTJk3qZT5vSkbYEFAoFjhw5gkWLFuGbb77hLY6wLIvExERMnz4dDg4OMDY2blSk0OQIi4qK4u0MxRcqlQrR0dHYunUrNm3ahIMHDyI/P7+emKHrhEtKSmr9RHuhoaFaBoGGFvXvWHDNrf3ixYt466236kU79O7dG/fu3YNKpUJVVRUeP36sM2vliwI+xoSGnlMqlUhLS0NsbCx++OEHBAUFcao4TaadMWPGYOfOncjIyGi1OeBrEKn7m+rqas4vmS/0NlJ4e3vTtWvXyMzMjB49ekTR0dHk5+dHfn5+OpPV/R0AQCqVih49ekRnzpyhW7dukY2NDb333nvk4eHxXPr0PAGAlEol3bx5k27evEn29vbUu3dvcnR0JJFIpNd81GaP2kkT6/6fPu1dv36dDh48SH5+fjRp0iSSSqVUVlZGvXr1ouTkZN6aF71VZV26dCGxWEwJCQk0YcIEevjwIVlaWtKqVato8eLFXPg4n0HU1NTQ//73PyovLydvb2+yt7ensrIyevLkCZWWlpKrqyt17ty5yQlnGIaMjIzI29ubvLy8CAD3+9ZkXM1Hk5WVRbm5uWRtbU3t2rWr11/85aQSHx9PJiYm1LVrVy6cvTXAMAyJxWIKCAiggIAAvZ/HX6UVUlJSKDY2ltLT08nDw4NGjRpFMpmM7t27RxcuXKDAwEDq0KEDr/B7zW/S09NpypQp9PDhQxKJRJSbm0srV64ksVhMHh4elJycrFdHeYH+UqVoLi3vv/++1hFtYmKCEydO8D6OWPZZHiyJRAKBQMA5kNvY2MDIyAhCoRAymQwrVqzQ28nk74DGJXTmzJlwcHCARCKBjY0Npk+fXi9LTF5eHkaPHg2xWAxTU1O8//77LeKM3VxoxI26GT4VCgVWrlwJa2trTn4WCoUYNGiQVnT42LFjGx2HxqpYVFTE/XvHjh1al2wfHx/u4hYfH6+Xb4NezLtp0yZOTnnnnXfqXQZmzJihF/Py8fiSyWSIi4vjPaC/CyzLIjQ0VOeFqHYCPJZ9lpOr9iXK0tIS9+7de84jeNa3/fv34x//+IcWE96+fZuXE7+npydKSkoabf/AgQO4cuUK9++5c+dqteHo6MglStRoUPhCr1JWaELWEQqF+jSnl7/piwhNdqDa0FTpaex3fKxwfxdMTExIJpNp/V9LroupqamWn2/dcQPQsmDq5cjDl8vpry1eo8JZvny51hdkZmamd56wgwcPcnpiKysruLu7Qy6XQyKRQCQSwdzc/IUWG3JychAcHAxnZ2eYmprC1dUVK1asQHFxsdY8lJSUYNasWTA1NYWFhQU+/PDDF0ZsUKlU9YwtGrHB0tKSO+JFIhFeffVVfPTRR/Dw8ADDMJgwYUKTYkNJSYlW5aidO3dqiQ1dunRBaWkpWJZFbGwshg8fzrv/eqvK3nzzTVRXVyMhIYGLVbK1tcU333yjd8YXhUKB//3vf/jll19w//59FBYWIiMjA9euXcOFCxcQHx+vtxVLsyAtrcNs6F1KpRJPnz7FnTt3kJ2drVOnzbLPsjDGxcUhISGhRSxzrQnN8R0fH4/w8HBs2rQJERERHJMlJydj165dvBJC11WZpaenc2WuRCIRPvnkE6jValRWVnLxkHyht6rMy8uLrl27RjKZjNLS0ujKlSvUrVs36tKly3M7DlFLVXb69GmKiYkhS0tLWrJkiVYdh/8vwF8J+S5fvkw3btwgNzc36t+/Pzk6OjaZnE9XWxq0lKrsxo0btH//fvLz86PJkyeTiYkJlZaWUo8ePSglJaX1/HmXLVv2whkpzp07h/Hjx9czUvj6+uLWrVuoqalBWVkZkpKSkJaW1mIFAVsaDTm/8HmupqYGaWlpiImJQXh4OF577TXO3VIgEMDJyQnjx4/Hzp07Wyx6t6G+6GOk0KC8vBy+vr6tax6unbZdoVDg/PnziIiI0MoPwLIscnNzsXv3bkRHR3O285aC5v2ZmZkIDQ1t1Knb3t4ew4cPh5+fH6eO+/HHH184Bq6qqsKePXswadIkrFy5Enfv3uXVR7Vajdu3b2PKlCmwt7eHRCJp1N+DYRi4u7vjxx9/bPF1UavVSEhIwHfffYc9e/bg/PnzXN0MDRoyD9+4cYNzTuILvR1zzp49y714y5YtMDExgVAoRGBgoJZjzkcffQSGYWBmZobQ0NB6Nm5DoNmZHjx4gA0bNqBTp04GOebY2dnh119/5e2YU1hYiJiYmFZJ4AE88wnQJE3R9FEulzf4kWnmuLKyEmFhYVoRLXzJzMwMH3/8MTIyMjgZ3NCxadbl9OnTcHFx4dZELBZj8uTJKCgoAMs+c8w5fPgw5syZg/DwcI6xHzx4gJ49e3J94wu9xYZBgwahrKwMCoWCqyCjoTFjxiAvL09L+NZ87cOHD8e9e/cMniTN7f6DDz6AXC5vEZfINWvW4M6dO5xvsa6LVllZGd566y0YGxujZ8+eiIiIQGZmJgoLC1tk52JZFtHR0VxthtpkY2ODY8eOQalUQq1Wo6CgANHR0di7dy8+//xzzvBh6BwIBAI4Ozvj1VdfRWhoKB4+fGjQeGpqahAeHq6z7BfDMBg9ejT27t2LKVOmcKKMSCTCG2+8gS+//LJeUka+0Jt5ZTIZx4Rbt26t54w+YMAATJs2Teekenp6Ytu2bbhz545WmlGWZVFRUYGcnByt8kwasOwzr6N+/fq1eIyahYUFRo4cia+//hrHjx/HL7/8gps3byI3NxdZWVlYs2aNVmyXkZERHB0d0b59e0yfPh1Pnz5t1o6Vm5uLfv36Ndq/cePGYdKkSfDy8mpSLGgO+fv7c2urq6+65HG1Wo1///vfTUZHt4Yzut7aBicnJ7px4wY5ODhQTk4O9erVizIyMvg0wbVjZmZG3t7e9Pbbb5Ovry/Fx8dTZGQkPX78mJydnWn06NHUr18/8vDwIHNzc7pz5w4tW7aMEhISeL9HX9QO4ZFIJGRtbU0AKDs7u1HF+dSpU2nnzp1kamrKOwxIg+rqalq8eDH95z//eS5hQLrQtWtXWrhwIXXq1IlcXV3JycmJKioq6MiRI/Tbb7+Rk5MTDRw4kPz8/Egmk9GFCxdoyZIlVFhY2GJ94DsXejOvlZUVnTx5knr06EFxcXE0duxYys3NJaJnlhn8VeOBLwQCgc4YMaFQSGZmZiSRSKi0tJSqq6t5t6nrHfr2iy9EIhH16dOHnJ2dycjIiLp27Upjxowhb2/vBtVS+Eu1FxYWRsuXL6eampoW7xcfCIVCkslkVFlZqdUHhmFIIBCQTCYjNzc3Ki0tpbS0NG6dNH8Ti8VUXFzc4ikGeK8T3y2a6siLPXr00FJNCQQCfPDBBzp9HlqarK2t8cYbb2g5oQsEggaPVF2Fs1uTrKysMH36dFy9elUr9D0zMxMRERHYvn07pk6d+lyiohmGgVgsxiuvvIIDBw7g/v37OHPmDEaMGPFCpA3QgyVbLukIEdGYMWNIpVLR6dOn+TRpMKZOnUq7du2iqVOn0vHjx8nGxoY2btxI3bt3p5iYGNq7dy8lJiY+l4pEtWFpaUkLFiygadOm0aNHj2j16tUUHx//tyUd6dChAzk5OZGVlRV17dqVrKysyNjYmDw8PKhbt25kYWHBJR3Jy8ujESNGtFiEtsbl05BTpcV33qFDhxqc4t7DwwP9+/eHs7Nzi0S9WllZYcyYMVy6p7rRHcXFxbhw4QLmz5/fqkVQ+BDDMJDJZC1e46wxsrCwwKlTp1BeXq5XuqeWODUdHR2xcOFCnD17FpcuXcLMmTN5r7m5uTnmzJnDe+flzbxlZWWYNm2a3keLk5MTkpKSUF1djadPn+K7775D3759tRZTLBbD2NhYq20TExN06NAB3t7ejR6vQqFQpx+xxogyZcqU58q8z4P69+9vUKK9d999l1f7YrEYFhYWsLCwgLm5Oezt7dG9e3esWbMGDx8+1NJK5OXl8UpMYmpqivDwcL0ypPOOpDA1NaWvvvqKKxhoaWlJV69epfPnzzd5DJqYmJBYLCYnJyeaPn06jR8/nmJiYujhw4dkYmJCHh4eJJVKKSUlhdLT00kmk5Gfnx95eXmRSCSiuLg42rhxI509e7beuzw9Pal37946XRONjIzIy8uL7xBfGIhEIjI1NaWKigpSqVR6P+/i4qJfqtC/MHPmTLpy5Qo9efKEKisrdaY4fe2112jBggXk6elJREQAyNjYmKysrEgqlXJiCMuyVFRURBcuXKiniZBKpdS+fXtiGIaqqqrIwcGBQkJCaOLEifq51er1eULbvJefn49u3bo1+kUxDINx48YhJSWlWfrQ4uJiLF26VCs9kqWlJSIjI7X0xXV1kHx3kxeJPD09cenSJYSFhRmUz2zhwoUGG4Ly8/Nx584dHDx4EBMmTICLiwtcXFwwduxYREVFNZoIWjP/qampmD9/Ptzd3euJS1KpFD/99BPKy8tRXl6OwsJCg5NLG5TWX6FQQKVSoaysrNFKNLXJw8MDe/bsaTSzdlPQxP3PmTMHc+fOxblz5ziZrqKiAj///DN27tyJuLg45Ofn48yZM7Czs3vuzKgvSSQSrF27Fvv27asX1i+RSNC7d2/MnTsX77zzDry8vOrJlD4+Pnjw4EGz3EI1Tk85OTnIzs7WcuOsK0NrTOgnT57EypUrGy086Ojo2CzDTm3oxbwFBQVYunQpBg8ejMDAQAwaNEjLHs9nUZYvX46CggKucJ2m2B9fU6vmA6pbUGXdunVcX2QyGdzc3J5bFsaWIE3dtLobQEREBMrLy7mCKjk5OToLqri5uWHNmjXIzc1tcaeokpISbNq0CatWrUJUVBQOHDiAXr168coyKRQKsW7duhapVqoX8+7evbvehU0gEEAsFsPIyAjW1tZNVuERCATw9fXFkCFD4OnpCQcHB7i5uWHChAmIiooyKMKgrKyMc6fjS1KpFCEhIVi/fj1eeeWVv7VYoCHUrl07/PnnnzovpgsXLtT5jMavoCVzVajVamzcuFErMFNfDZKpqSm+/vprPHnyBE+ePEFWVpZBXn56Me/58+e1jjFXV1fs3bsXV65cwZUrV/Do0SPOFdIQFZVUKsWBAwf0nmiFQoG33367QU2ISCSq54OxatUqbrcvLCzEjh07dFbW+TuJYRh4e3tj9OjR6N69O+zt7WFqaopu3bpxabbqQqlUYtSoUY22OWTIEBw6dAgnT57E999/j0uXLul1qy8uLkZERAT279+PTz75RO9StjKZDK+//joCAwO501AkEnFFBN3d3XHjxg291hzQk3lVKhWioqIQFBSEadOm6SxqBzzbCfUt6qehWbNm6c28Go+znTt3YsqUKejRowccHR3h6emJ0NBQXLhwAfv27UPv3r1haWmJcePGIS8vr57zT1ZWFvbt24eQkBBMmDAB3t7ef6t+dtiwYXj69ClUKhXKy8uRnp6OuLg4zqVQF9RqNZYuXcoxw6JFi7B58+Z6WRs1VkaGYWBtbY1bt27xXvNFixZxpV/1HZNAIMBXX32Fmpoa1NTUYPfu3fXECzMzM1y7dk2vNQcMLGVVV+asDbVajZiYGIN8TIkIa9eu1TuKoK4ivqKiApmZmSgoKNDSOZaWluL+/fuoqKho8sasycp49uxZzJ8/X6e7X0uSjY0NYmNjDfpwi4uL8csvvyApKYmbi23btjVazjYqKop7XqlUoqKiol5sHcs+y2DZnKLhAoEAYWFhXL8uXLjAncpGRkZwd3fHZ599ZpC4qDfz6pq8mpoaJCYm4qeffsLixYsNrvhORFi5ciUUCgVSU1Px448/4vbt2xwDFhcX4/r161yZ+6ysLKxfvx7vvPMODhw4wKUqbUloGPnChQvNSifaFC1YsMCgEqYNISMjo9EaeR999BGKiopw/vx5vP322/Dx8cEbb7yB77//Hnfv3sWZM2ewcuVKnWlL9SWNr0dwcDCnifD19cUvv/yCnJwcg7UizWZepVKJtWvXaoVJN4fMzc0xcuRIODs7c5HJq1evxp49e9CvXz8YGxvDxcUFEyZMQOfOnbl3SiQSrFu3rsVCyuuqgqKjo1uVeT///HOd4TLN6X9cXBxWrVqFBQsW4O2339ZSG5qYmKBjx471rJcCgQAmJiatWp9CIpE0WAhcH/B2zGkIBQUF1L17d3ry5AkREUkkEmIYplkujLqgsdw0BqlUSlFRUTR48GDePrWaNlmW5Vwn8/Pz6erVq5SSkkIsy1JWVhYdOXKEUlJSmj2OhtChQwf65JNPyMfHhxQKBaWmppK1tTX169ePm1MApFAoqKKigiwsLHhFAtceX2xsLAUFBWn5X0ulUhKLxVRSUtIqLqP29vY0Z84cEolEFBMTQ/n5+TRq1ChavXo1GRsb6+wnbytbs1gfzwwHc+fORadOnbB48WL88ccfuHLlCkJCQhrNm8uHjIyM4Orqyu3CTf1eJBLppa1g2Wc12/71r3/hzTffxLRp0xAUFARPT8/nUhlHKBTCzMyMy7FrbGyM4OBg5OXlQaVSISYmBiNHjoS7uzuWLl2qFY3Cd7zr1q3j3mdtbY3Tp0/j/v37WLZsmZaGqCVOUaFQiF27dnFiQU1NDaqqqrRyW2jEsqKiIhw9ehTTpk3jPZ4WkXmrq6tRWFiodTlSKpX4448/MG7cOL39Vt3c3LBw4UKcOnUKOTk5SEtLw5IlS+Di4gK5XF7P+GBqaooZM2bghx9+QFlZmV5937lz53NVjzVFtasN1c46LhQKsX37dr2ZNz4+novSHTJkCHdPUCgUOHDgAObPn489e/bgu+++Q2BgoMH6b4ZhEBAQgIKCggb7o1Kp8Oeff2LhwoXo1q0bevfujTVr1vAeT7OZtzFoJuXIkSO8b6xisRhnzpzREuI1GoWcnBxkZWXhzz//5IwSDMNwFhtDbuonT57kyjlZWlq+0Ixcl15//XW9L3lKpRJz584FwzB48803tZzla2ca0mhnJk+erFefvLy88K9//Yur3dGYVmf//v1c4KmlpSViYmL0WsNWZV4NVCoVZs+ezXunCQsLa9TiwrIsrl69iq5duyIgIKBZmb5VKhUSExNx/fp1JCcn49tvv0XHjh1fmKiChkhjZjXkg83OzsbGjRtx8eJFjlFjYmIwbdo0HD9+XMs3+ttvv+XdJ1dXV8TFxfG6bGZkZGi5Ss6aNUtvkzFv5q3dIc1XqlAoeOXdYlkWkZGRvOVIe3t77NmzB6mpqUhPT9fKLVC7zfz8/BbPpcCyLNLT07Fq1SqDddWtybAuLi4YPXo0vv32W07m1ciNmhB5PutRez2rqqq4clo2NjbYv38/srOzcevWLfTp04dX39zd3XlrEFiWxddff81tEF27duWV96wueGsbQkNDSSaTkZOTE+Xn51NCQgKlpKSQTCajWbNm0YQJE8jY2LjB229FRQUtWbKE9u/fzys0RCgUkrm5OQkEAhIKhTRu3Dj6+OOPydHRkYgMy3hee6hNZfMGQDExMTR27FjKy8vT+10tCaFQSAMGDKDg4GAaPHgw2dnZkVAoJKVSSX/88QedPXuWnj59SkVFRWRvb0+TJ0+m4cOH8761l5WVUc+ePen+/ftE9CyERy6XU2lpKZWUlDT5/LBhw2jXrl3k6enZ5LqwLEtxcXE0ceJESklJIXNzczp27BgNGTJE7zVtkRg2sVhMw4YNo9dee40sLCzIzMyM+vfvT3K5XCs5W3V1NR05coQ2bNhA9+7d06+jDEMdO3akwYMHU0BAAAUFBdXLK1sbACg3N5fi4uKoqqqK1Go15eTk0OPHj0kmk1GPHj3I19eXbG1tOVVU3TGWlJRQv379KDExkYiI2rVrR2+++SZJJBI6deoUpaWlkbu7O02ZMoWr1Hnz5k168OABlZeXExGRmZkZOTo6EsMwlJqaalBcnbW1NZ04cYL69evH9VGlUtGnn35KmzZtoqqqKq3fW1hY0N69e2ncuHG8GKKoqIh69uxpkCrQysqKzp8/T/7+/g2+C3+VcLh37x5FRkZSeHg4ZWZmEtGzIujfffcdCYVCysrKopMnT9L8+fP5vZzvFk16HG8Mw8DX1xd37tzR6QWVnp6OxYsXw9fXF/7+/ggICNCZMaYhEgqF+Oabb3QeMxqVzJEjR+Dl5cU55dS9iIlEIsjlcvTs2RNTpkzBZ599hmPHjuHWrVtISkrC7du3sXz5chgZGUEkEmHOnDlISUnhjuWcnBxcvnxZK8WVxjSdmJiIw4cPIzIyEgkJCSgpKUFJSQl27drVZHKOhqhXr164f/8+957Tp0836vLZvn173Lx5s8nEfSzL4tChQwb5cIhEIrz//vsNXho1mqjIyEgMHz5cK9s6wzDo0qULbt++zc2bJoKZN0/y/mGdjjs5OaFPnz7w9vZuUJ0ydOhQnTnKNDJaRUUFKisrUVVVhTNnzujFwIsXL9bZbnJyMubNm2eQNUwoFMLY2BhmZmYwMTHhZLLXXnutXsK4pqCLYRQKBYKCggyWefv27YvY2Fj8/vvv8PLyavL3Tk5OmD17Nnbs2MEl7qutynz69Cl27typl9+GsbExhg0bhpCQEPzwww8NzovGWy84OFjLRZZhGPj7++Pbb7/lPnwAyMrK4oqw84VBzCuXyxEXF8fpdxcsWNDgDjxx4kStoLyGoFQqMW/ePN6T2Lt3b6SmpqKsrAxFRUVISkrC5s2b4eLiYjBzNERbtmxpkUuhxjGl9ofFMAx69OiBhQsXwsfHp8m+yGQyg/I92NraYu3atYiJicGhQ4cwfvx4ODs789bjGhsbw8/PDxEREVzYTkNMy7LPkueNGjVK68SztrbG0qVLdfoXq1Qq7NmzBwMHDuQ9nwYxr6+vr1aq9vT0dPj7+zeY3MPFxQXLli3DtWvXUFBQwNUurqvByMrKwocffoigoCAEBgaiQ4cODepdGYaBk5MTunTpAg8PjxbzrdBFS5YsabGUqDU1NdiwYQOsra0hk8nw7rvvcosZHx+vZYjgS3zHzTAMV32Jb9tGRkZYsGABLl++rFXlVAPNGpaXl+PRo0e4cOECPvroI7i7u3NtODk5YfXq1bh7926j+niNXYAvDGLejh07alWBYdln9XkjIiLw448/Yv369bCxsak3EaampnBzc0Pnzp0xaNAgvPfee1pugJqJUKlUUCqVyM3NxQcffPBcTLW1yd7evkHfZX2hObLv3bunlaESADIzM+Ho6Mi7X9bW1ggJCcGBAwcQFhaGwYMHt7iRJTAwkNuodI0lMzMTq1evhr+/P6ytreutlYuLC2JjY1slH7JBzFu7/JAuqNXqenXaGqKOHTsiJydHZzss+yxeylDHdl3k5uaG+fPn6/1BzJ07t8XdLevi3LlzvGMCGYbBtm3btOTYnJwcXqKHPrRhw4YGx61UKjFp0qRGd/558+a12rw126usDW14Xni5C6G14f812pi3DS8t2pi3DS8t2pi3DS8t2pi3DS8t2pi3DS8t2pi3DS8t2pi3DS8t2pi3DS8t/g+OMMu15fFVIQAAAABJRU5ErkJggg=="
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 25\n",
      "\tbeta = 3.5588e+01\n",
      "\tJ = 7.4836e-01\n",
      "\tgrad_norm = 3.8801e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 26\n",
      "\tbeta = 3.7029e+01\n",
      "\tJ = 7.5856e-01\n",
      "\tgrad_norm = 1.7237e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 27\n",
      "\tbeta = 3.8471e+01\n",
      "\tJ = 7.6755e-01\n",
      "\tgrad_norm = 3.1975e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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G4fF4EAgEEAgE0NXVhZmZWYPCfpFIhN69eyMwMBCdO3eGk5MTevfujZCQENy8eVOr809VVRV69OihUYeamJhg4cKF+Pzzz+Hu7v5aRGOakKOjI27fvq3WDHTRokVq3xEIBJg5cyarRtYWtY9kcrkcCxYsYL/B5/M1Vu4YGBhg69atSEtLQ2JiIp4+fcpJrfwyNGLewsJChISEYMCAARgyZAh8fHw0EmKbmJhgy5YtrNyyvLwcL168aNS4+eWOrK6uVtGoKRQKrF69mmVAIyMj2Nvbv9Itv7mJx+PV6VsPDw8cPXqUPZsyDIOysjJMnTq1DtN27doV27dvbxHbj4yMDEyfPh3Tpk3Db7/9hp9//hk9e/bktGsJhUJ8++23WjHry9CIeZUdpmSe5ORkTvapPB4PnTt3RkxMTJMqLZVKER4ejhEjRmDMmDGIiYlhV+qysjIcOnQIP/zwA27fvo28vDzs2bNHrSjo3046OjoICQnBkiVL6uwIIpEInTp1wqxZszB37lz07t27DtMMGzYMhYWFTV5tKyoqcOfOHVy/fl3lkvvypZ1hauybz549ixUrVsDT07PeRc3KygoZGRla16s2tBaVMQyDS5cucbqJjhw5EtnZ2Vp3pnKFCQkJUVlNzczMcPr06TryUSWkUikGDBjw2plRU/L29satW7ewbNkyrY4zixYt0qqvlfYMd+7cwf79+9G/f38YGBhAIpHAw8MDO3fubHAlry3VWbp0KTp06FBn8RCLxdi0aRPS09ORmZmJZ8+eaT3RODOv0hopLCwM8+fPx6xZs+Dk5NRoR5qYmCAxMVGFwUpKSnDy5El888032LlzJy5evIiEhAScOHECYWFh+Omnn3Dv3j2UlZWhvLwccXFxGDVqlNqB7Ny5M4qKiuqt84oVK147M2pKOjo6MDc319pQaPTo0RrvcAzDICYmBi4uLtDT01O7cgqFQgwbNgyXLl1CZmYm8vPz8eLFC5SWlkImk9URWRYXFyM8PBx6enoq5QgEAlhbW8PW1hampqbw9PTE5s2bNbJLATRg3tLSUsyYMUPjlcDMzAyPHj1ijT+io6PRp08fFW2cSCSCrq4uW7bSEN3LywudOnVq8HYrFovVWiMpjzezZ89+7cz4qqlLly6oqKjQiBEYhsG0adM4Ty5bW1s4OTnB1dUVHh4eGDhwILZv347MzEyV40RiYiLMzMwaLVMkEmHjxo0aWclxZt6+fftqfSPv0qULZs2ahX79+nH2Vm2IzM3NMXLkSFbduWLFCvbsqzx/nT59Gp988kmTBezNQcqt91V9T19fH8ePH0dlZSVnVTPDMJg+fXqTvsvj8eDs7Ix58+YhMjISv/76q4oHMZd6T506lTPzauzD1hA6duxIRUVFrJFOS2HSpEm0Y8cOGjZsGF25coXMzc1p7dq11K1bN0pMTKStW7dSQkIC60f2umBoaEhBQUE0a9YsKigooNWrV9Nff/1FMpmsxQ2XDAwMqFOnTmRtbU2urq7k4OBAEomEpFIpWVpaUu/evcnGxoY1+CksLKShQ4fS9evXm+X7St9FhUKh8buc+4Yrl1OtGWJsbAwvLy8YGxur/D5+/Hh4e3u3+MpiZGSE3r17Q0dHh/2Nz+erHD1eJ5mYmGDy5Mn4888/VYy7S0pKcPnyZRw7dgwrVqxg7WpfFSnPscoYCqGhoYiNjcXx48fh7+//rzHGb7GVV19fn3755Rfq1asX3b17l0aPHk05OTlcilBbJp/PVzs7BQIBmZqakrOzM+Xm5lJaWtprMbNsDGKxmHr37k3W1tbEMAx17NiRhg8fTh06dGjQZBEARUdH04QJE6ikpOQV17oGPB6PdHR0qLq6WmUM+Hw+8Xg8EovFZG5uTlKplAoKCtj+5/F4ZGJiQp6enlRWVkb37t1rVnPKFlt5TU1NkZSUBAAoKChAu3btNJpVfD4f1tbWGD58OP7v//4P586dw4YNG+Dr6wsXFxcMGDAAa9euxdmzZ/Hs2TNUVFQgNTUVQ4cOfWWrk0gkgpWVVaNhkQQCAT7//HNUVFQ0aKxUH+RyOZYvX/6vWfF4PB5GjBiByMhInDt3DrGxscjJycHTp0+xbNky9OnTB0OHDsWWLVuQmJgIqVSKgoICTJw48bWsvBozr66uLhvpZNeuXSrbNI/HQ48ePTB8+HC1tr3t27fH3r17WZPG2uIzqVSKFy9eqPyuBMPURF/p1atXsw+WgYEBunbtii+++AKhoaHYtWsXLl68iPT0dKSlpWHOnDkqzMXn82Fra4tevXph3bp1TdZgFRQUoGfPnvXWUV9fHwMHDkRgYCDc3Nygp6cHkUjULLbTL/fFoEGD1Hpn1LY+U+fFnZKSgo4dOzZYviYTlDNPcn7wn4J79eqFoqKiOgYhPB4PY8eORX5+PoqKilTOvgKBACNHjkRycnKTFBUZGRmYM2cOJ9FLY2RnZ4f169fj9u3bKi7ktW/mDMMgLy+PdQu3srLCli1bkJmZqZFKu7F2Xbp0Sa3JpaGhIY4cOQKZTAa5XI6CggIkJCTgxo0buHjxIhYsWKBVWCsliUQidOnSBVOnTsXWrVuRk5OjtXIjLi5O7S7M4/EwePBgHDlyBB999BErdeHz+ejWrRuCgoLqaGm5QiPmNTQ0ZMPzMAyDNWvWQCwWQygUYvTo0awKUaFQsPp2fX19LF26tI6tqDZQGoY8ePAAa9euhYeHh1YOglZWViqBLhr7ZmJiInbu3Fkn3ldzQS6XY/v27SrybCMjI2zevLnBUEpyuRzHjx9H27ZtNe4DIyMjbNmyBSUlJZzFaQ1BaftbmxF5PB78/f3ZSVFVVYXIyEjMmDEDu3btQmFhIRQKBa5du4a33nqrZZnXwsICKSkp7G+VlZU4e/YsTpw4wXaCsiF37txBcHAwoqOj62w1TUVtNeSCBQvqaHBqk7u7O6ZMmYKAgABYWFjA3t4eERERGjFhcwxuY5DL5bh69SqWL1+OlStX4tq1a5z6TTm5PvzwQ072xzweD05OTggPD9cqXEBDUDLimjVrEBwcjL1797Lx3WrXV90O9+DBAzaOA1doxLw8Hg8rV66sE21QXQe8igFnmBqvh5iYGIwaNaqOi72vry9SUlLYWZ+SksKGjPo3Qt3Acn2vuroaaWlpuHz5MjZu3FjHOMbCwgLjx4/HgQMH8Pz58xYbFy5tUPdMdXU1G52HKzQWlbm5udGNGzfI1NSUUlNT6cqVK/T222+Tp6cnGw37VQP/eAA/ffqUTp8+TQkJCWRtbU1z584lBweH11Kn1wkAlJWVRQcOHKDbt2+Tt7c3jRs3jlxdXRv1OFZXlhLqPMM17VsAdOvWLdq3bx95enpSUFAQGRgYUGlpKXXt2pUeP37MWVTG0cf4f7CzsyOxWEyJiYk0ZswYevToEZmbm1NISAjNnTuXdHR0ODeiqqqKLly4QGVlZeTh4UE2NjZUWlpKSUlJlJaWRt7e3uTj40NCobDBTuLxeCQSicjT05M8PDwIAPt8SzKuctJkZmZSTk4OmZqakpOTU536AqCMjAy6ePEiOTo6Uo8ePVh39pYAj8cjW1tbWrJkCTEMw8ptuQIAKRQKSklJoWvXrlFiYiJ5eHjQyJEjydDQkB4+fEgxMTH03nvvUfv27Rt1v1fWiYgoPT2dJk2aRI8fPyY+n08ZGRm0bt06EgqFZGZmpllDuS7RRDWmeo8fPwbDMPj8889VtmgdHR0cOnSI83bEMAx27NgBsVgMPp8PfX192Nrasi70Sl+rZcuWaRzS6FWAYRgkJydj/PjxsLCwgFgshpmZGaZNm4YXL16o9ENycjI6deoEHo8HiUSC+fPnN5uLflMhl8tZyYkSVVVVWLp0Kdq0acMePQQCAfz8/LB8+XLWuXbw4MENtoNhavwCpVIp+/fOnTtVjjMuLi6seO7mzZsYO3Ys57prxLzbtm1jzynqBNPDhg3jbIrHMAzGjBnT6K3YzMwMT5484dygVwWFQqHWCovP52Pnzp0ql5EtW7bUuenfu3fvNbegpm7h4eGYO3euygKRkJDAyaDJ2dm5XnNUZflnzpxBYmIi+/f8+fPr9IVyfJUSFK7QKJVVYypAPl+zzFhv+llU3RGJz+eTnp6eym8SiUSlra/rbqAOurq6ZGRkpPJbc9bPwMCAxGJxvf/HS4HKNVIzc+VyIoKnpyfu378PhmGwcOFClRkkkUgQHh6u0bFh3759bHQWQ0NDODg4wNramo3XZWhoiOXLl/9rjw0ZGRkICgqCjY0NJBIJ7OzssGTJkjoZbbKzs+Hn5weRSAR9fX18/vnnLRIgRRsoFIo6IjnlscHMzIzd4oVCIQYNGoR169axcYsbC5SilPLUjkS5a9culWODo6MjK077888/MXjwYM5110rDVlJSgsTERHTs2BF8Ph9WVlbYtm2bRuc4pbrx999/x/Hjx3Hv3j3k5+cjIyMD169fR1RUFBISEtSqixsrt7E8DM0FpYjq+fPniI+PR0ZGhlrZKcMwePHiBS5cuIC4uLhGo8g3Z/1qezho8l51dTUePnyIAwcOYMWKFQgPD2dV4U+ePMHOnTvZ+09jZdV+5vnz52wyGD6fj+DgYDZOhVJRwRVNEpWlp6dTbGwseXt7k5ubm8bHhuYC/rn1P3v2jE6fPk1xcXFkZWVF8+bNo7Zt2/5rtuhXAeVwPnv2jHbt2kW3bt2irl270tSpU8nd3f1fISqLj4+nsLAwcnd3p2nTppGhoSEVFRWRj48PpaamtoxVGY/Hw+rVq/9VSgqpVIqTJ09ixIgRdWweevbsiUePHkEul6O8vBz379/H48ePm8XtuiWg3DU0tU6rvQP88ccfWLVqVR3/QnNzc4wfPx6HDh36VykplKioqECXLl1ejXqYYWpco6OionDs2DEV2wWlevjTTz/FyZMnm32bVDY8LS0N06ZNa9DFxsHBAaNGjUK3bt1gZGSENm3a4MCBA/86LZtMJsOxY8cwceJETJkyBSdPnuR0ZGKYmsyZyrN3Y+phPp+Ptm3b4sCBAxofyRoDwzB4/PgxDh48iF27diE6OrpOwJP61MPXrl1jNaRcoRHzGhgY4MqVK+wKsWLFCojFYggEAowaNUolouNHH30EohoTynnz5rH/awqUopSHDx9izZo1KhlsNCFLS0uNDHNycnJw5swZZGRktMiKJZfL8e2336r49+np6WHLli317hLKy9D+/fu18sjQ09PDypUrkZeX1ywZlhiGwR9//AFnZ2f2QiYWizFlyhTWtV0qleL48eMICgrCjh07WMOcixcvqlikcYXGF7aePXvWaxI5evRo5ObmoqSkhE0Ip/xfnz59EBsbq3VHMUxNdst58+ahTZs2WjFtbbK1tcXq1atx/fp1NoujunqVl5dj5MiREAqFaN++PX788Ufk5uY2q0nkxYsX67hUEdW4EylzEysUCuTl5eHChQvYvXs3QkNDMWbMmCY5dvL5fLi7u2PChAnYu3ev1pZ/CoUCkZGRaiODKg3cjxw5gilTprCuW3w+H927d8f06dPrRL7nCq2M0e/evQuGYbBnzx4Vo2gej4euXbsiMDBQrbG0hYUFQkJCEB8fr5I4W6mJyc3NVZsaS6nN6tmzZ7Nn6dHV1YW3tze++OIL7N+/H1FRUbh58yZycnKQnZ2NdevWqUSkEQqFcHR0RN++ffHtt982OQ5YXl4eunfvXm/9jI2NMXLkSIwfPx7t2rVjIz02Zx8omWnChAn1GqMrFIp6jdFPnToFc3PzRsvnWheu0FjaYGFhQX///Tc5OjpSQUEBde3aVePMiQYGBuTj40Njx44lV1dXun79Op06dYqys7PJycmJ/P396d1336UOHTqQlZUVZWZm0qxZs+j8+fMafUdTKIXzEomETExMiMfjUU5ODsnlcrXPC4VCWrVqFS1cuJD1ltVEwC+Xy2nZsmW0adOmf4V/Ho/Ho759+9KECRPI2tqarK2tycXFhYqKiigsLIyuXr1KxsbG5OfnR3379iV7e3u6c+cOzZ49W6vsmfWBa19o5YAZERFB7777Lt28eZMmTZpEL168YJ/RdBD4fL5arYrSAdPJyYmysrKa5E4vFouJYZh6mbAp0NPTo6FDh5K5uTmVlJSQu7s7jRgxgjp27NigQRHDMHTq1CmaPHkylZWVNXu9uIDP55NQKKTq6uo641bbAbOyspIKCwtV/q+rq8tag0ml0matF2ce4rpEU61lXZlwurYROI/Hw/Tp01XOui1FpqamCAgIUPm+QCCAgYGBWtd3oVD4Sp0cjY2NMW7cOMTExLCSFoapCX904cIFREREYMmSJVol0W4K1daWeXt7Y/fu3bh27Rr27t2rdTDwlqAWOzY0hI4dO1JhYSFlZmZyKVJrfPDBB/TDDz/Q8OHD6dKlS2Rubk4bN25kg45s27aN4uLi6iSUftXQ1dWlCRMm0Jw5c6igoIDWrVtH169fJ5lM1uLfNjAwoHfeeYdsbW3ZoCM6Ojokk8nI3t6eunfvTmZmZuxu+fTpUwoICNAqobk6KDP6aLPbNfvK27t3b60CeiglDYsXL8bgwYObJfxSmzZtMHLkSLasxYsXq4R7Ki0txeXLl7Fw4UK1t/hXTbq6uq80VrCenh5++eUXFYlIY5dKuVze5PACynBPixYtwrlz53D27FkMGjSI8/tGRkb44osvOK+8nJm3uLgYkyZN0nj7tbS0ZL2Gq6qqcPnyZQwaNEgl2o0yunrt9wwNDeHl5QUfH58Gk5kIhULExMTUqa9SJhwcHPzamfdVk4+PD8rLyzkzAVDDvIGBgZzKFwgEMDU1ha2tLRwcHODm5oYePXrgm2++QXp6usqEefz4MSfRpkgkwtatWzXSfnL2pDA0NKTt27eTn58fPXv2jIiIIiMj6f79+w2+J5fL2W1SGV3m2LFjFBcXR3fv3iUAZGVlRfr6+lRSUkIlJSWkp6dHb731Fuu28ujRI1q7di2dOHGizjbk5uZGPj4+db6rjMZjaWnJtYn/GvB4PNLT06PKykqtItG4uLhw9mhRgs/n0+jRoyk+Pp6KiorUflsoFFKPHj3os88+o3feeYf09PSIz+eTjo4OSSQS0tHRYY8hDMNQUVERXblyhcrLy1XKEYvFZGtryyZEtLCwoBkzZtDMmTNZqQ0naDQ9a4Fhanz1uSTXGD58eJO0UwxTE1x68eLFKiu2kZGRSrrWl7dHuVyO999//7WvhJqSra0tzp07h6+//lqrBC9Lly7VWtmQkZGB+/fv48iRIxg+fDgsLCxgZmaGPn364ODBgw0qMpT9n5qaiv/85z9wdnauU399fX0cPnwYeXl5yMzMRFJSEvLz87VS12sc1l+hUEAmk6G6uhqPHj3inBfYy8sLv/32W5Pc4Kuqqlj9/4QJE3DmzBl2mykrK8OPP/6Ibdu24c6dOygsLER0dHSzBCh51SQWi7Fy5Ur88MMPdTRoQqEQnTp1wqefforg4GC1GYzGjBnToNaQ61hXVVUhPT0dqampKsqjlw2IGKYmweOZM2ewbNky1t5XHbm6ujaYTFsTaJxQ5YsvvoCvry/8/f01DvphYGCAVatWoaioCNXV1SgsLEROTg6Ki4s5xxBQnmVrP88wDNauXctq9YyMjODq6tpoNJmW0FQ1F6m7Bzg7O+PQoUMqjFlfQpXOnTtj48aNGifX5tL/ycnJmDJlCqZPn46TJ08iPDwc3bt35xSCSiQS4fvvv3/1CVUOHTpU58LG5/PZ2Fn6+vowNzdvUCohEAjQqVMn+Pn5oV27drC2toanpycmTpyIo0ePsgGRNYE2qawsLS2xZcsWrF+/Hp06dWr22F/NTQ4ODvj777/Vqm6/+uqreifA6NGjWWbXFrUvYNXV1fj4449Vxl/TS7yhoSF27NiB58+fIyUlhY2mrik0Yt4///xTJbCHg4MD9u7di7/++gt//vknEhISkJycjDVr1mh1VhOJRNi0aZPGHS2XyzF79ux6J43SG7n2oG7atInd9l68eIGIiAj4+vq+9iSC7u7ueO+999C+fXvo6emxnionTpxQ2y8KhQKTJk2qt0w+n49Ro0bh5MmTOH36NMLCwhAVFcXZ64VhGDx8+BArV67EunXrMH/+fJUE3FzIxMQE48ePx7Bhw9h3hUIhzM3NYWpqCmdnZ9y/f1+jMQc0ZF65XI7z589j6tSp+OijjxAfH6+2Q4uLi9GhQwetBjAoKEhj5mWYmlD+Bw8exMyZM+Hv7w8XFxd07NgRCxcuxLlz57Bz5054eXlBV1cX/v7+yMvLq1NGWVkZfv75ZwwZMgTt2rWDo6Njg6Gkmpv69OmD58+fQy6Xo7CwEH///Td++eUX3L9/v96VSaFQYN68eeDxeNDR0cHo0aPx9ddf1zFGr71CSiQSzplGy8vLNQrNr47Wr18PuVwOmUyG77//vs5KbWxsjLt372o05oCWibMbEnwzDIO7d+/CxsZGq5WnORJny2QyFBUVsT5XSsrPz8etW7caTJ2kfL+4uBj5+fmIjY3FwoULYWlp2aKMa2RkpDYxDJf2Z2dnY+fOnYiMjGSPXQcPHmxwO1+3bp1Kf9VO5qiEQqHAr7/+qiLh0YZWrFjBGr6fOHGCPaKJxWK4u7tj+/btWjnZai0qq915VVVVSExMxIkTJ7B69WqtjcSFQiGio6NZL43bt28jLS1NxWzy9u3bSE1NRWVlJZvnePr06fj555+1Oi9zaZ9CocDp06dbNCnKBx98oLWXtLrFJDs7u07y7No0btw4pKamIjIyEsOGDYObmxv8/Pzw008/ITExkQ36Z21t3eS26enpYdSoUfjwww/ZYHoeHh44e/ZsnQAtmqDJzFtVVYXg4GAYGxs3Sz6I7t27Y9u2bRg6dCj09fXh4OCAtWvX4uDBg/Dz84Oenh4sLS3RrVs3ldVdLBZjzpw5GmuW1EHdan7x4sVmyWRUH3333Xd15NVNvWSdP38egYGB8Pf3x9ChQ+Hg4MB+TyAQqI0qqTRwaupq2xAJBAIcPny4yQsNZ8Oc+pCamkpdunSh/Px8IlLvYdoc4GJuKRQK6fDhwzRhwgTONrUAqLq6mqRSKenq6hKfz6fc3Fw6f/48xcXFERFRRUUF/f7775SamtrkdtSHt99+mzZs2EBWVlaUnp5Ojx49Int7ewoMDGSDluCf+G7l5eVkZGTUaAw3/BNzDP/EbktLS6OJEyey7SIisrW1JR0dHUpNTW3WvBJKODk50dSpU6m0tJT+/vtvKikpoT59+tD69evJwMBApa5KcPZIbhLro+ZyFhAQACsrK0yePBkRERGIiIjA5MmTmxS1m/5ZTZ2dnTlvXQKBAFu2bOE8oxmmxolzzJgxaNeuHbtCtW3b9rXkiXg5maJIJMKCBQtYOXhcXBwGDBgAR0dHzJw5U+Mtl2EY/Pjjj2zb3Nzc8PDhQ+Tk5OCrr75iL6fqknZrQzo6OoiKimJ3kaqqKpSXl9eR0UulUmRkZODEiROYO3cu5/Y0y5m3qKgI6enpKmmbZDIZrl27hqCgoAYNa9SRg4MD5s6di+joaOTl5SEpKQkzZsyAtbU12rZtW0erZ2BggA8//BA//vhjg7Gz1NV9zZo1r5xJNSGBQICePXti7NixKu3m8/lYtWqVxltveno67OzsQEQIDAxkpRgymQzHjx/Hl19+iWPHjuHQoUPo1q2b1kyszHHR0DFOKpVi//798PPzg62tLXr06IGtW7dybkuTmbchKIXav//+O2c1slAoRGRkpIqjpnIyZGVlIS8vD0+ePGEDEfN4PHz99ddaqZ2VK5GBgQGEQiEkEsm/Wuv2Mvn7+2scNkqhUCAkJAR8Ph/jxo1TMSV9mbKysjRW/lhYWGDWrFlsKtf6xkShUGD9+vXsmdvY2JhNGcEVLcq8SigUCgQFBXGesUq5YH1gGAZPnz5F//798d577yEnJ0fruslkMsTFxeHSpUu4ceMGtm/fDnd39389EwsEAixfvlyrCVtYWIgffvgBsbGxLKNevnwZ8+fPx9WrV1UWjfq0d+rIyMgIUVFRnDzE09LSVFz2p06dqvFE1Ip5a59huAbG2L9/P+dzpLGxMVatWoW7d+8iOTkZaWlpdQKXMAyD8vLyJnvvqqtreno6Vq1apXI7/zeQQCCAvb09AgMDsWfPHhU5tkwmQ2lpKUpLSxtVtb4szagdJ8zBwQExMTGoqKhASkoKevfuzalubdu2RVhYGCebBYZhVEwNvL29kZSUpPE4cmbeZcuWYe/evTh27Bh++uknzJkzB++++y769euHAwcONCpjLSgowIgRIzQSp+nr68PExATm5uaYNGkSG6qpuWW5L0M5sAkJCaxc8nWSUChEQEAAIiIikJWVxR6RKisrERUVhfnz52PAgAHw8vJCp06dEBoaqlHQw9zcXJWYCwYGBvDx8eHcdq5pypQy8ydPnrChnUxNTfHXX39pJR7U2IdNnchKLBbToEGDKCAggEpLS4lhGAoICKCuXbuyxsUAqKysjCIiImjDhg2UlJTE5bMqsLW1pV69elGPHj3oo48+IlNT03qfxT9+WXFxcQSATVNaXFxMIpGIHB0dyc3Njdq0aUMSiUSt2EkqlZKvry/duHGDeDweOTs708iRI0koFNKJEycoJSWFbG1tqV+/fiQQCCg/P5+ePHlCqamprAG2SCQiGxsb0tXVpbS0NKqsrNS43fb29nT27Fnq0KEDW8eqqipavHgx7dixo45PnI6ODu3evZs++OADTmKnFy9eUOfOnSklJUXjupmZmdHly5dV6vYyGIahjIwM+uuvv+jixYsUExPDih2DgoJo3759xOfz6d69exQWFkbfffcdt49z5XLScLUwNjbGTz/9pNYK6tmzZ5gxYwbc3d3h4eEBT09PjYw9eDxevSIx5SXx6NGjKivHy2dYoVAIMzMzeHp6YtCgQQgODsa+ffsQFRWF+Ph43Lx5E19++SUkEgkkEgkWLVrEGtQzTE1ywdjYWNYiimFqTDVLSkoQHx+PvXv3Ytu2bYiJiWGjCP33v//VWPKipD59+rCrm/Ki2ZAiwcnJCQkJCY2Ge2UYBsePH9fKx47P5+PTTz9tMFdcbm4uli5dCjs7uzrHRicnJ9Y+Jj8/H2+//TY0YEnNI+YoydLSEm+99VaDNgyOjo54+PChWgaWy+Ws/UFZWRmOHDmikRFMcHCw2nKTk5Px2Wefae3oKRAIWIZVMvwHH3ygUVC6+uw/5HI55s2bp/XxoU+fPrh58yaio6PVhlZ6mezt7REUFITQ0FDcunWrjmShsrISp06d0igJoY6ODvz9/fHJJ59gz5499XpWMExNWldfX986C4e9vT0WL16sEt/33r177Jhx5knOD7708YSEBFRUVODZs2fo379/vY319fVFYmJiozdQqVSKYcOGce7E9957D/n5+aisrERhYSHu3buH9evX17Gmag7asWNHs5yzGaYmembt0Eg6OjoYM2YMlixZ0mj+XqKaG702ampzc3OEhoYiKysLjx8/xtatW9GvXz/OC4ZEIoG7uzsOHz7M3m8aWs2Tk5PRt29f9n1ldMovvvgCSUlJdS6VUqkUX331FXx8fDj3p1bMGxAQwIo1GIbBlStXGvQQtbOzw+LFi3Ht2jVkZ2cjPz+fvRXXFss8ePAAn3zyCaZMmYJPPvkEffv2rXeg+Hw+OnTogJ49e8LFxQVGRkYtJt6q7VrfVMjlcmzbtg1WVlawtbXF1q1bWWuuBw8eaGW9xuPxOElyBAIBm3GJa19JJBKEhITg6tWr9Ub6ZJgac9KUlBRcv34du3fvVpmIzs7O2L17d4NG58rLXEVFBee+1Ip5u3fvzqYnAv6XtvPrr7/Gli1b6k3oLJFIYG1tDXt7e3h7e2P69Om4du2aCgPX9o2qrKxEeHi41ufE+gZaUxtdKysrxMXFNZuUQy6XIy0tDenp6SqDWVxcrDb5dH3Upk0bLF68GJGRkTh16hQWL17MySFWExo9enSDkovS0lJ8++23eOedd9CmTRuIxWKViWFjY6PWA6Q5oBXzent7NzhD5HK52lRX6sjFxQWZmZn1llVdXd2sHsADBw7EX3/9pRGTENUI0Vs6IPXjx485B0lRXlprX8jkcjmWLl3arMwbGhra4PHgu+++a1D8OXHixBbrtyZblbWiFa8LrycDSita0QxoZd5WvLFoZd5WvLFoZd5WvLFoZd5WvLFoZd5WvLFoZd5WvLFoZd5WvLFoZd5WvLH4fxPSomFMwdbAAAAAAElFTkSuQmCC"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 28\n",
      "\tbeta = 3.9912e+01\n",
      "\tJ = 7.7714e-01\n",
      "\tgrad_norm = 1.5292e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 29\n",
      "\tbeta = 4.1353e+01\n",
      "\tJ = 7.8253e-01\n",
      "\tgrad_norm = 2.5060e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 30\n",
      "\tbeta = 4.2794e+01\n",
      "\tJ = 7.9181e-01\n",
      "\tgrad_norm = 1.6373e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 31\n",
      "\tbeta = 4.4235e+01\n",
      "\tJ = 8.0041e-01\n",
      "\tgrad_norm = 1.9507e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 32\n",
      "\tbeta = 4.5676e+01\n",
      "\tJ = 8.0708e-01\n",
      "\tgrad_norm = 1.5625e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 33\n",
      "\tbeta = 4.7118e+01\n",
      "\tJ = 8.1259e-01\n",
      "\tgrad_norm = 1.5900e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 34\n",
      "\tbeta = 4.8559e+01\n",
      "\tJ = 8.1908e-01\n",
      "\tgrad_norm = 1.2210e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 35\n",
      "\tbeta = 5.0000e+01\n",
      "\tJ = 8.2519e-01\n",
      "\tgrad_norm = 1.2090e-02\n"
     ]
    }
   ],
   "execution_count": 23
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T13:28:05.433737Z",
     "start_time": "2026-03-18T13:28:05.427902Z"
    }
   },
   "cell_type": "code",
   "source": "params_final = params_history[-1]",
   "id": "e0f1f3b7bc518976",
   "outputs": [],
   "execution_count": 24
  },
  {
   "cell_type": "markdown",
   "id": "98b1ebc5-643a-49d2-90ea-483403d52db5",
   "metadata": {},
   "source": [
    "## Analyzing Results\n",
    "\n",
    "Now we can take a look at our optimization results and make some figures.\n",
    "\n",
    "We'll first plot the objective function value history, and then look at the transmission spectrum and field profiles of our final device."
   ]
  },
  {
   "cell_type": "code",
   "id": "58ae6972-9f74-4ec7-891a-5a11e6a95161",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T13:28:05.531648Z",
     "start_time": "2026-03-18T13:28:05.478580Z"
    }
   },
   "source": [
    "plt.plot(objective_history)\n",
    "plt.xlabel(\"iterations\")\n",
    "plt.ylabel(\"objective function\")\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 25
  },
  {
   "cell_type": "code",
   "id": "23dd95a6-0112-4c57-a945-cca3b5e548a1",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T13:28:05.638268Z",
     "start_time": "2026-03-18T13:28:05.542915Z"
    }
   },
   "source": [
    "mnt_fld = td.FieldMonitor(\n",
    "    size=(td.inf, td.inf, 0), center=(0, 0, 0), freqs=[fmin, freq0, fmax], name=\"fields\"\n",
    ")\n",
    "\n",
    "sim_final = get_sim(params_final, beta=beta)\n",
    "\n",
    "sim_final = sim_final.updated_copy(monitors=list(sim_final.monitors) + [mnt_fld])"
   ],
   "outputs": [],
   "execution_count": 26
  },
  {
   "cell_type": "code",
   "id": "a0db3c79-03ca-45cc-b4a0-3402de15ff7f",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T13:28:05.837411Z",
     "start_time": "2026-03-18T13:28:05.643092Z"
    }
   },
   "source": [
    "sim_final.plot_eps(z=0, monitor_alpha=0.0, source_alpha=0.0)\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 27
  },
  {
   "cell_type": "code",
   "id": "f203c7e5-f791-4bd1-bdbc-cecebe3e9c2a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T13:28:24.514567Z",
     "start_time": "2026-03-18T13:28:05.844260Z"
    }
   },
   "source": [
    "transmission = get_transmission(\n",
    "    params=params_final, beta=beta, step_num=None, verbose=True, use_broadband=True\n",
    ")"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001B[2;36m14:28:06 CET\u001B[0m\u001B[2;36m \u001B[0mCreated task \u001B[32m'bandpass_invdes'\u001B[0m with resource_id                    \n",
       "\u001B[2;36m             \u001B[0m\u001B[32m'fdve-decf0647-8e6b-4299-9ddc-e33804549d9c'\u001B[0m and task_type \u001B[32m'FDTD'\u001B[0m.  \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:28:06 CET </span>Created task <span style=\"color: #008000; text-decoration-color: #008000\">'bandpass_invdes'</span> with resource_id                    \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #008000; text-decoration-color: #008000\">'fdve-decf0647-8e6b-4299-9ddc-e33804549d9c'</span> and task_type <span style=\"color: #008000; text-decoration-color: #008000\">'FDTD'</span>.  \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001B[2;36m            \u001B[0m\u001B[2;36m \u001B[0mView task using web UI at                                          \n",
       "\u001B[2;36m             \u001B[0m\u001B]8;id=571454;https://tidy3d.simulation.cloud/workbench?taskId=fdve-decf0647-8e6b-4299-9ddc-e33804549d9c\u001B\\\u001B[32m'https://tidy3d.simulation.cloud/workbench?\u001B[0m\u001B]8;;\u001B\\\u001B]8;id=618298;https://tidy3d.simulation.cloud/workbench?taskId=fdve-decf0647-8e6b-4299-9ddc-e33804549d9c\u001B\\\u001B[32mtaskId\u001B[0m\u001B]8;;\u001B\\\u001B]8;id=571454;https://tidy3d.simulation.cloud/workbench?taskId=fdve-decf0647-8e6b-4299-9ddc-e33804549d9c\u001B\\\u001B[32m=\u001B[0m\u001B]8;;\u001B\\\u001B]8;id=895263;https://tidy3d.simulation.cloud/workbench?taskId=fdve-decf0647-8e6b-4299-9ddc-e33804549d9c\u001B\\\u001B[32mfdve\u001B[0m\u001B]8;;\u001B\\\u001B]8;id=571454;https://tidy3d.simulation.cloud/workbench?taskId=fdve-decf0647-8e6b-4299-9ddc-e33804549d9c\u001B\\\u001B[32m-decf0647-8e6\u001B[0m\u001B]8;;\u001B\\\n",
       "\u001B[2;36m             \u001B[0m\u001B]8;id=571454;https://tidy3d.simulation.cloud/workbench?taskId=fdve-decf0647-8e6b-4299-9ddc-e33804549d9c\u001B\\\u001B[32mb-4299-9ddc-e33804549d9c'\u001B[0m\u001B]8;;\u001B\\.                                         \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>View task using web UI at                                          \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-decf0647-8e6b-4299-9ddc-e33804549d9c\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-decf0647-8e6</span></a>\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-decf0647-8e6b-4299-9ddc-e33804549d9c\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">b-4299-9ddc-e33804549d9c'</span></a>.                                         \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001B[2;36m            \u001B[0m\u001B[2;36m \u001B[0mTask folder: \u001B]8;id=117274;https://tidy3d.simulation.cloud/folders/folder-df61810d-cad6-4474-8ea9-e4f00d5dfcb0\u001B\\\u001B[32m'default'\u001B[0m\u001B]8;;\u001B\\.                                            \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>Task folder: <a href=\"https://tidy3d.simulation.cloud/folders/folder-df61810d-cad6-4474-8ea9-e4f00d5dfcb0\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'default'</span></a>.                                            \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "709f05e2c51d425882404fd2905f3204"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001B[2;36m14:28:19 CET\u001B[0m\u001B[2;36m \u001B[0mEstimated FlexCredit cost: \u001B[1;36m0.025\u001B[0m. Minimum cost depends on task     \n",
       "\u001B[2;36m             \u001B[0mexecution details. Use \u001B[32m'web.real_cost\u001B[0m\u001B[32m(\u001B[0m\u001B[32mtask_id\u001B[0m\u001B[32m)\u001B[0m\u001B[32m'\u001B[0m to get the billed  \n",
       "\u001B[2;36m             \u001B[0mFlexCredit cost after a simulation run.                            \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:28:19 CET </span>Estimated FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.025</span>. Minimum cost depends on task     \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>execution details. Use <span style=\"color: #008000; text-decoration-color: #008000\">'web.real_cost(task_id)'</span> to get the billed  \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>FlexCredit cost after a simulation run.                            \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001B[2;36m14:28:21 CET\u001B[0m\u001B[2;36m \u001B[0mstatus = success                                                   \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:28:21 CET </span>status = success                                                   \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "2ee0f6c73ec64d989a0dc1e28bc43dad"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001B[2;36m14:28:24 CET\u001B[0m\u001B[2;36m \u001B[0mLoading results from simulation_data.hdf5                          \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:28:24 CET </span>Loading results from simulation_data.hdf5                          \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 28
  },
  {
   "cell_type": "code",
   "id": "7a573b70-a661-4ad4-ab0a-2eb919953f50",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T13:28:24.599894Z",
     "start_time": "2026-03-18T13:28:24.520130Z"
    }
   },
   "source": [
    "plt.scatter(freqs / 1e12, target(freqs), label=\"target\")\n",
    "plt.plot(freqs / 1e12, transmission, label=\"measured\")\n",
    "plt.xlabel(\"frequency (THz)\")\n",
    "plt.ylabel(\"transmission (P_out / P_in)\")\n",
    "plt.legend()\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 29
  },
  {
   "cell_type": "markdown",
   "id": "181882cc-ca9e-43ce-8b6e-e68db7b810c2",
   "metadata": {},
   "source": [
    "We see that the final transmission spectrum more or less matches our expected bandpass filter!"
   ]
  },
  {
   "cell_type": "code",
   "id": "1e086827-fa39-47e1-b83f-fbef91fb9f6c",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T13:29:21.190472Z",
     "start_time": "2026-03-18T13:28:24.607277Z"
    }
   },
   "source": [
    "sim_data_final = web.run(sim_final, task_name=\"final\")"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001B[2;36m            \u001B[0m\u001B[2;36m \u001B[0mCreated task \u001B[32m'final'\u001B[0m with resource_id                              \n",
       "\u001B[2;36m             \u001B[0m\u001B[32m'fdve-7e7b2744-cf25-430f-9df7-e5a6a9909899'\u001B[0m and task_type \u001B[32m'FDTD'\u001B[0m.  \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>Created task <span style=\"color: #008000; text-decoration-color: #008000\">'final'</span> with resource_id                              \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #008000; text-decoration-color: #008000\">'fdve-7e7b2744-cf25-430f-9df7-e5a6a9909899'</span> and task_type <span style=\"color: #008000; text-decoration-color: #008000\">'FDTD'</span>.  \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001B[2;36m            \u001B[0m\u001B[2;36m \u001B[0mView task using web UI at                                          \n",
       "\u001B[2;36m             \u001B[0m\u001B]8;id=175716;https://tidy3d.simulation.cloud/workbench?taskId=fdve-7e7b2744-cf25-430f-9df7-e5a6a9909899\u001B\\\u001B[32m'https://tidy3d.simulation.cloud/workbench?\u001B[0m\u001B]8;;\u001B\\\u001B]8;id=990224;https://tidy3d.simulation.cloud/workbench?taskId=fdve-7e7b2744-cf25-430f-9df7-e5a6a9909899\u001B\\\u001B[32mtaskId\u001B[0m\u001B]8;;\u001B\\\u001B]8;id=175716;https://tidy3d.simulation.cloud/workbench?taskId=fdve-7e7b2744-cf25-430f-9df7-e5a6a9909899\u001B\\\u001B[32m=\u001B[0m\u001B]8;;\u001B\\\u001B]8;id=562566;https://tidy3d.simulation.cloud/workbench?taskId=fdve-7e7b2744-cf25-430f-9df7-e5a6a9909899\u001B\\\u001B[32mfdve\u001B[0m\u001B]8;;\u001B\\\u001B]8;id=175716;https://tidy3d.simulation.cloud/workbench?taskId=fdve-7e7b2744-cf25-430f-9df7-e5a6a9909899\u001B\\\u001B[32m-7e7b2744-cf2\u001B[0m\u001B]8;;\u001B\\\n",
       "\u001B[2;36m             \u001B[0m\u001B]8;id=175716;https://tidy3d.simulation.cloud/workbench?taskId=fdve-7e7b2744-cf25-430f-9df7-e5a6a9909899\u001B\\\u001B[32m5-430f-9df7-e5a6a9909899'\u001B[0m\u001B]8;;\u001B\\.                                         \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>View task using web UI at                                          \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-7e7b2744-cf25-430f-9df7-e5a6a9909899\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-7e7b2744-cf2</span></a>\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-7e7b2744-cf25-430f-9df7-e5a6a9909899\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">5-430f-9df7-e5a6a9909899'</span></a>.                                         \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001B[2;36m            \u001B[0m\u001B[2;36m \u001B[0mTask folder: \u001B]8;id=881461;https://tidy3d.simulation.cloud/folders/folder-df61810d-cad6-4474-8ea9-e4f00d5dfcb0\u001B\\\u001B[32m'default'\u001B[0m\u001B]8;;\u001B\\.                                            \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>Task folder: <a href=\"https://tidy3d.simulation.cloud/folders/folder-df61810d-cad6-4474-8ea9-e4f00d5dfcb0\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'default'</span></a>.                                            \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "b34db62846a84a12a331faa581097569"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001B[2;36m14:28:36 CET\u001B[0m\u001B[2;36m \u001B[0mEstimated FlexCredit cost: \u001B[1;36m0.025\u001B[0m. Minimum cost depends on task     \n",
       "\u001B[2;36m             \u001B[0mexecution details. Use \u001B[32m'web.real_cost\u001B[0m\u001B[32m(\u001B[0m\u001B[32mtask_id\u001B[0m\u001B[32m)\u001B[0m\u001B[32m'\u001B[0m to get the billed  \n",
       "\u001B[2;36m             \u001B[0mFlexCredit cost after a simulation run.                            \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:28:36 CET </span>Estimated FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.025</span>. Minimum cost depends on task     \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>execution details. Use <span style=\"color: #008000; text-decoration-color: #008000\">'web.real_cost(task_id)'</span> to get the billed  \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>FlexCredit cost after a simulation run.                            \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001B[2;36m14:28:37 CET\u001B[0m\u001B[2;36m \u001B[0mstatus = queued                                                    \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:28:37 CET </span>status = queued                                                    \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001B[2;36m            \u001B[0m\u001B[2;36m \u001B[0mTo cancel the simulation, use \u001B[32m'web.abort\u001B[0m\u001B[32m(\u001B[0m\u001B[32mtask_id\u001B[0m\u001B[32m)\u001B[0m\u001B[32m'\u001B[0m or              \n",
       "\u001B[2;36m             \u001B[0m\u001B[32m'web.delete\u001B[0m\u001B[32m(\u001B[0m\u001B[32mtask_id\u001B[0m\u001B[32m)\u001B[0m\u001B[32m'\u001B[0m or abort/delete the task in the web UI.      \n",
       "\u001B[2;36m             \u001B[0mTerminating the Python script will not stop the job running on the \n",
       "\u001B[2;36m             \u001B[0mcloud.                                                             \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>To cancel the simulation, use <span style=\"color: #008000; text-decoration-color: #008000\">'web.abort(task_id)'</span> or              \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #008000; text-decoration-color: #008000\">'web.delete(task_id)'</span> or abort/delete the task in the web UI.      \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>Terminating the Python script will not stop the job running on the \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>cloud.                                                             \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
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      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "10b76b8176ae46e3a5162b9cbcf5cd75"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001B[2;36m14:28:49 CET\u001B[0m\u001B[2;36m \u001B[0mstatus = preprocess                                                \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:28:49 CET </span>status = preprocess                                                \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001B[2;36m14:28:54 CET\u001B[0m\u001B[2;36m \u001B[0mstarting up solver                                                 \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:28:54 CET </span>starting up solver                                                 \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001B[2;36m14:28:55 CET\u001B[0m\u001B[2;36m \u001B[0mrunning solver                                                     \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:28:55 CET </span>running solver                                                     \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "cda34cc2f5d841a99a57eb7d9ae43211"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001B[2;36m14:28:58 CET\u001B[0m\u001B[2;36m \u001B[0mearly shutoff detected at \u001B[1;36m23\u001B[0m%, exiting.                            \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:28:58 CET </span>early shutoff detected at <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">23</span>%, exiting.                            \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
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     }
    },
    {
     "data": {
      "text/plain": [],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ]
     },
     "metadata": {},
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     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001B[2;36m14:28:59 CET\u001B[0m\u001B[2;36m \u001B[0mstatus = postprocess                                               \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:28:59 CET </span>status = postprocess                                               \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
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       "version_major": 2,
       "version_minor": 0,
       "model_id": "36f371c0b7a04773b7e487b0cab54648"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001B[2;36m14:29:02 CET\u001B[0m\u001B[2;36m \u001B[0mstatus = success                                                   \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:29:02 CET </span>status = success                                                   \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001B[2;36m14:29:04 CET\u001B[0m\u001B[2;36m \u001B[0mView simulation result at                                          \n",
       "\u001B[2;36m             \u001B[0m\u001B]8;id=42371;https://tidy3d.simulation.cloud/workbench?taskId=fdve-7e7b2744-cf25-430f-9df7-e5a6a9909899\u001B\\\u001B[4;34m'https://tidy3d.simulation.cloud/workbench?\u001B[0m\u001B]8;;\u001B\\\u001B]8;id=751307;https://tidy3d.simulation.cloud/workbench?taskId=fdve-7e7b2744-cf25-430f-9df7-e5a6a9909899\u001B\\\u001B[4;34mtaskId\u001B[0m\u001B]8;;\u001B\\\u001B]8;id=42371;https://tidy3d.simulation.cloud/workbench?taskId=fdve-7e7b2744-cf25-430f-9df7-e5a6a9909899\u001B\\\u001B[4;34m=\u001B[0m\u001B]8;;\u001B\\\u001B]8;id=778542;https://tidy3d.simulation.cloud/workbench?taskId=fdve-7e7b2744-cf25-430f-9df7-e5a6a9909899\u001B\\\u001B[4;34mfdve\u001B[0m\u001B]8;;\u001B\\\u001B]8;id=42371;https://tidy3d.simulation.cloud/workbench?taskId=fdve-7e7b2744-cf25-430f-9df7-e5a6a9909899\u001B\\\u001B[4;34m-7e7b2744-cf2\u001B[0m\u001B]8;;\u001B\\\n",
       "\u001B[2;36m             \u001B[0m\u001B]8;id=42371;https://tidy3d.simulation.cloud/workbench?taskId=fdve-7e7b2744-cf25-430f-9df7-e5a6a9909899\u001B\\\u001B[4;34m5-430f-9df7-e5a6a9909899'\u001B[0m\u001B]8;;\u001B\\\u001B[4;34m.\u001B[0m                                         \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:29:04 CET </span>View simulation result at                                          \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-7e7b2744-cf25-430f-9df7-e5a6a9909899\" target=\"_blank\"><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-7e7b2744-cf2</span></a>\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-7e7b2744-cf25-430f-9df7-e5a6a9909899\" target=\"_blank\"><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">5-430f-9df7-e5a6a9909899'</span></a><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">.</span>                                         \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
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    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "2e407aaecb704b5592fdcbadbb6ca642"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001B[2;36m14:29:20 CET\u001B[0m\u001B[2;36m \u001B[0mLoading results from simulation_data.hdf5                          \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:29:20 CET </span>Loading results from simulation_data.hdf5                          \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 30
  },
  {
   "cell_type": "code",
   "id": "5dbbbec3-9713-48e6-ac30-9df21d822ada",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T13:29:24.311061Z",
     "start_time": "2026-03-18T13:29:21.195034Z"
    }
   },
   "source": [
    "f, axes = plt.subplots(3, 1, tight_layout=True, figsize=(10, 6))\n",
    "\n",
    "for ax, f in zip(axes, (mnt_fld.freqs)):\n",
    "    sim_data_final.plot_field(mnt_fld.name, field_name=\"E\", val=\"abs^2\", f=f, ax=ax)\n",
    "    ax.set_title(f\"wvl={1000 * f / td.C_0:.0f} (nm)\")"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x600 with 6 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 31
  },
  {
   "cell_type": "markdown",
   "id": "724f1448-a601-4a47-abd6-2b33b5515bc7",
   "metadata": {},
   "source": [
    "We see that the field patterns at the middle and edges of our spectrum behave as we would expect, respectively blocking and transmitting the light."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f3109463-6b77-4bcc-9b0a-82008dc21413",
   "metadata": {},
   "source": [
    "## Using Inverse Design Plugin\n",
    "\n",
    "Tidy3D now supports a higher level syntax for defining inverse design problems in a simpler way.\n",
    "\n",
    "Here we'll show how to set up this same problem using that tool and run it for 2 iterations.\n",
    "\n",
    "For a full tutorial, refer to [this example](https://docs.simulation.cloud/projects/tidy3d/en/latest/notebooks/InverseDesign.html)."
   ]
  },
  {
   "cell_type": "code",
   "id": "aca68595-7d54-4069-880b-668214b0fc54",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T13:29:24.595975Z",
     "start_time": "2026-03-18T13:29:24.326115Z"
    }
   },
   "source": [
    "import tidy3d.plugins.invdes as tdi"
   ],
   "outputs": [],
   "execution_count": 32
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T13:29:24.952613Z",
     "start_time": "2026-03-18T13:29:24.600648Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# transformations on the parameters that lead to the material density array (0,1)\n",
    "filter_project = tdi.FilterProject(radius=radius, beta=beta_history[-1])\n",
    "\n",
    "# penalties applied to the state of the material density, after these transformations are applied\n",
    "penalty = tdi.ErosionDilationPenalty(weight=1.0, length_scale=radius)\n",
    "\n",
    "design_region = tdi.TopologyDesignRegion(\n",
    "    size=design_region_static.geometry.size,\n",
    "    center=design_region_static.geometry.center,\n",
    "    eps_bounds=(\n",
    "        1.0,\n",
    "        eps_mat,\n",
    "    ),  # the minimum and maximum permittivity values in the final grid\n",
    "    transformations=[filter_project],\n",
    "    penalties=[penalty],\n",
    "    pixel_size=dl_design_region,\n",
    "    initialization_spec=tdi.CustomInitializationSpec(\n",
    "        params=params_history[-1].reshape((nx, ny, 1)),\n",
    "    ),\n",
    ")"
   ],
   "id": "25ae155d1892f931",
   "outputs": [],
   "execution_count": 33
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T13:29:25.150398Z",
     "start_time": "2026-03-18T13:29:24.964669Z"
    }
   },
   "cell_type": "code",
   "source": [
    "design = tdi.InverseDesign(\n",
    "    simulation=sim_base,\n",
    "    design_region=design_region,\n",
    "    task_name=\"invdes\",\n",
    ")"
   ],
   "id": "914357a03cda2e91",
   "outputs": [],
   "execution_count": 34
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T13:29:25.163252Z",
     "start_time": "2026-03-18T13:29:25.160357Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def post_process_fn(sim_data, **kwargs) -> float:\n",
    "    amps = sim_data[mnt_mode.name].amps.sel(direction=\"+\", mode_index=mode_index)\n",
    "    transmission = np.abs(amps) ** 2\n",
    "    return get_metric(transmission)"
   ],
   "id": "8908e5a8a6e46c5f",
   "outputs": [],
   "execution_count": 35
  },
  {
   "cell_type": "code",
   "id": "bf58d5f4-ab86-458c-b3e3-a4992634b1b9",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T13:29:25.238172Z",
     "start_time": "2026-03-18T13:29:25.205242Z"
    }
   },
   "source": [
    "optimizer = tdi.AdamOptimizer(\n",
    "    design=design,\n",
    "    num_steps=1,\n",
    "    learning_rate=learning_rate,\n",
    "    results_cache_fname=\"data/invdes_history_filter.hdf5\",\n",
    ")"
   ],
   "outputs": [],
   "execution_count": 36
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T13:33:17.810943Z",
     "start_time": "2026-03-18T13:29:25.283047Z"
    }
   },
   "cell_type": "code",
   "source": "result = optimizer.run(post_process_fn=post_process_fn)",
   "id": "5ca7f3597464321b",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step (1/1)\n",
      "\tobjective_fn_val = 7.101e-01\n",
      "\tgrad_norm = 9.824e-03\n",
      "\tpost_process_val = 8.863e-01\n",
      "\tpenalty = 1.762e-01\n"
     ]
    }
   ],
   "execution_count": 37
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T13:33:18.132838Z",
     "start_time": "2026-03-18T13:33:17.834296Z"
    }
   },
   "cell_type": "code",
   "source": [
    "sim_last = result.sim_last\n",
    "ax = sim_last.plot_eps(z=0, monitor_alpha=0.0, source_alpha=0.0)"
   ],
   "id": "7090c5ca348dd4a1",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 38
  }
 ],
 "metadata": {
  "applications": [
   "Passive photonic integrated circuit components"
  ],
  "description": "This notebook demonstrates the inverse design of an integrated bandpass filter with permittivity binarization and minimum feature size control.",
  "feature_image": "./img/adjoint_17.png",
  "features": [
   "Adjoint inverse design",
   "2D simulation"
  ],
  "kernelspec": {
   "display_name": ".venv",
   "language": "python",
   "name": "python3"
  },
  "keywords": "inverse design, silicon photonics, filter, photonic integrated circuits, design optimization, adjoint, Tidy3D, FDTD",
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.10"
  },
  "title": "Inverse Design of an Integrated Bandpass Filter in Tidy3D | Flexcompute"
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
