Autograd4MultiObjective.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "df03ca2b-256f-472c-bcaf-e35a529143c6",
   "metadata": {},
   "source": [
    "# Multi-objective adjoint optimization\n",
    "\n",
    "> Note: native autograd support is an experimental feature in tidy3d 2.7. To see the original implementation of this notebook using jax and the adjoint plugin, refer to [this notebook](https://www.flexcompute.com/tidy3d/examples/notebooks/AdjointPlugin4MultiObjective/).\n",
    "\n",
    "In this notebook, we will show how to use the adjoint plugin efficiently for objectives involving several simulations.\n",
    "\n",
    "One common application of this involves defining an objective function that may depend on several different definitions of your structures, each with some geometric or material modification. For example, including the performance of devices with slightly larger or smaller feature sizes into one's objective can serve to make optimization more robust to fabrication errors. For more details, see this [paper](https://link.springer.com/article/10.1007/s10409-009-0240-z). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "5accbf7e-221b-46b8-8aa4-b010fde0a816",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "import autograd as ag\n",
    "import autograd.numpy as anp\n",
    "\n",
    "import matplotlib.pylab as plt\n",
    "\n",
    "import tidy3d as td\n",
    "import tidy3d.web as web"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a908597-1bb4-45ff-8fc9-dca626011d5c",
   "metadata": {},
   "source": [
    "### Setup\n",
    "\n",
    "First, let's define the frequency that our objective will depend on"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "247c3045-6b11-4a86-9bc7-d9ba1a8c173e",
   "metadata": {},
   "outputs": [],
   "source": [
    "freq0 = 2e14\n",
    "wavelength = td.C_0 / freq0"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d96aca0f-a9da-4f8a-833c-5cefe8a3bb7f",
   "metadata": {},
   "source": [
    "Now we set up some physical parameters.\n",
    "\n",
    "We will be putting a `td.Box` in the center of a domain with a point source on one side and a diffraction monitor on the other.\n",
    "\n",
    "The objective will involve summing the power of the 0th order diffraction order.\n",
    "\n",
    "The gradient of this objective will be computed with respect to the permittivity of the box.\n",
    "\n",
    "We will adjust the size of the box by `dy` in the y direction and define a combined objective function that returns the average power when the box is either perturbed by `+dy`, `0`, or `-dy`, which emulates a treatment for enhancing device robustness via dilation and erosion effects, as described in the paper linked at the top of this notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6894b8a3-4889-431f-bb68-f3bd28b73369",
   "metadata": {},
   "outputs": [],
   "source": [
    "permittivity_val = 2.0\n",
    "\n",
    "# box sizes (original design)\n",
    "lx = wavelength\n",
    "ly = wavelength\n",
    "lz = wavelength\n",
    "\n",
    "# amount by which we will change the box size in y\n",
    "dy = ly / 5.0\n",
    "\n",
    "buffer = 2 * wavelength\n",
    "\n",
    "Lx = lx + 2 * buffer\n",
    "Ly = ly + dy + 2 * buffer\n",
    "Lz = lz + 2 * buffer\n",
    "\n",
    "\n",
    "src_pos_x = -Lx / 2 + buffer / 2\n",
    "mnt_pos_x = +Lx / 2 - buffer / 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7257c894-0eb8-4813-bc86-8d5ee9b4d639",
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_sim(permittivity: float, dy_sign: int) -> td.Simulation:\n",
    "    \"\"\"Make a simulation as a function of the box permittivity and the frequency.\"\"\"\n",
    "\n",
    "    box_size = ly + dy_sign * dy\n",
    "\n",
    "    box = td.Structure(\n",
    "        geometry=td.Box(center=(0.0, 0.0, 0.0), size=(lx, box_size, lz)),\n",
    "        medium=td.Medium(permittivity=permittivity),\n",
    "    )\n",
    "\n",
    "    src = td.PointDipole(\n",
    "        center=(src_pos_x, 0, 0),\n",
    "        polarization=\"Ey\",\n",
    "        source_time=td.GaussianPulse(\n",
    "            freq0=freq0,\n",
    "            fwidth=freq0 / 10,\n",
    "        ),\n",
    "    )\n",
    "\n",
    "    mnt = td.DiffractionMonitor(\n",
    "        center=(mnt_pos_x, 0, 0),\n",
    "        size=(0, td.inf, td.inf),\n",
    "        freqs=[freq0],\n",
    "        name=\"diffraction\",\n",
    "    )\n",
    "\n",
    "    return td.Simulation(\n",
    "        size=(Lx, Ly, Lz),\n",
    "        structures=[box],\n",
    "        monitors=[mnt],\n",
    "        sources=[src],\n",
    "        grid_spec=td.GridSpec.auto(wavelength=td.C_0 / freq0),\n",
    "        boundary_spec=td.BoundarySpec(\n",
    "            x=td.Boundary.pml(), y=td.Boundary.periodic(), z=td.Boundary.periodic()\n",
    "        ),\n",
    "        run_time=200 / src.source_time.fwidth,\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e11b1338-e831-47f6-85d7-d3abe2aef5d5",
   "metadata": {},
   "source": [
    "Let's make a simulation for each of the perturbed size values and visualize them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c03a39c5-83e4-4e0d-84a2-c8bf86446b60",
   "metadata": {},
   "outputs": [
    {
     "data": {
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bzWLdunX13x911FH1m0E88sgj+Otf/4ovfelLWLRoEe66666WP+PPf/5zfc/GeDyO9773vc4fOBGRCzgjiYha43wkrzF0U1dYuHAh1q5di6OPPhq33nor9txzT68PiYhIGJyRREStcT6SGxi6iYiIiIiIiBzCz3QTEREREREROYShm4iIiIiIiMghoYkf0j1qtRq2bNmC3t5eSJLk9eEQkSBUVcXw8DBmzpyJQMCf70VyPhKRHr/PSM5HItJjdD76KnRv2bIFl112GXp6eupfkyQJkUik/vtKpYJKpeL6scmyXC9UrVbDjh078Ktf/QojIyOuHwuRXXp6enDaaaeN6jkrmvtDURQ7Dm+Um266CRs3bsSsWbNs/9mdoNV81ONGPcYzMjLC+Ugdz6752EooFBq1B3GpVEK7t/Dx84w0Mx9bcaIe4+GMpG7g5Ixs1m4eNDIffRW6e3t70dPTg0MPPXTUCzs0NFRfNPb19XnyLq6iKBgaGgKwaxuCQCCAb3zjG5g8ebLrx0IdSMkCG+8e/bXZpwJyyoujqduxYwfuvfdeBIPBUQsOsxr7I5lMQpZluw4RwK4FEID69iF+pDcfW3G6HuOpVCqoVqucj2SOgDPSrvnYSq1WQyaTAbDrTbJkMtnWz/P7jDQzH1uxux7j4Ywk0wScj4CzM7IVq3nQ6Hz0VejWLgmKRCL1d02Gh4dRq9UQj8dRKpWwc+dO14O3oijYsWMHJk2aBADYuXMn4vE44vE4EomEa8dBHUypAr2TRn8tkQBkb///qVQqCAaDiEajloNZc3+MjIygp6fHkaDn58sGW83HVtysh97zazOS85EME3BG2jEfW9ECXjgcRiQSQbFYRLVatSUw+3VGGp2PrThZj1YURUGxWOSMJOMEnI+AczOyFTvy4ETz0X8fzGkwPDyMXC6HRCKBvr4+TJ06FeVyGZlMBrVazZVjUBQF6XQa4XAYU6dOxdSpUxEKhVy/XJNIRK36IxwOI51Os0c8IEI9VFVl7Yl0aAGvXC5j6tSp6OvrQyKRQC6Xw/DwsNeH5zusB5H43MqDvg3djS+w9m6jLMuuBu/GBaz2bkogEEAqlfLtu8lEGr3+6OvrY/D2gAj1qNVqyGazjn4WkqhTNQc87cxQb28vg54HWA8i8bmZB30ZukdGRsa8wBq3gnerBaxGkiRXPyNJJJrx+oPB230i1ENbwFYqFc5HoiZ6AU/DoOcu1oPIHk7e3LpV4NY4kQd9F7pDoRAKhULLF1jjdPAebwGr4Zlu8isj/cHg7R4R6tG4gE2lUr7csohIz0QBT8Og5w7Wg8g+5XIZhULB9p87XuDW2J0HfbdyCYVCiMViE97AwqngbWQBS+RXZvqDwdt5ItSjeQEbDodt+blE3cBowNMw6DlLlHp4sfUtkRPC4TDy+byt/WEkcGvszIO+S3yVSsXwnSftDt4M3ET6rPQHg7dzRKiH2QUskZ9Y7Q8Gb2eIUo9CoYByudz2zyESQSgUQjwet60/zARujV150Hepz+y7f3a90AzcRPra6Q8Gb/uJUA8GbvIDq2uKdvuDwdteotRjeHgY+XyeVwRRV4nFYrb1h9nArbEjDzL5GdDuC83ATaTPjv5oN+i5tUVgJ6hUKkLUg4Gb/EBRFNNnJe3qDwZve4hSDy1QxONxhEIhS8dAJCq7+sNK4Na0mweZ/gyy+kIzcBPps7M/rAa9Wq2GXC5n+Xm7iSRJGBoa8rweDNzkF5IkIZvNetYfDN7tEaUejYEiFou1dQxEorKjP6wGbk07wZsJ0ASzLzQDN5E+J/rDbNDTFkzVarXt5+4GkUgEwWDQ83owcJNfyLKMUCjkaX8weFsjSj3sDBREohOhP6wGb6ZAk4y+0AzcRPqc7A+jQa9xwZRMJm17/k5Wq9WQSCQ8rwcDN/mFJElIpVKe9weDtzmi1IOBm/xIhP5ozINGr5ZkErRgouDNwE20m6qqo37vRn9MFPSaF0z8/NsuiqIIUQ8GbvITSZKE6A8Gb2NEqQcDN/mZCP2h5UGjV0syDVqkF7wZuIlGUxSlHrzd7A+9oMeA5w3Wg0ifKP2ht5AdGRlx9Hk7hSj1YOAmEqM/ZFk2fLUkT++0QQve6XQamUwGiUQCmUyGgZuogaqqyGazSKVSrveHtpDNZDJIp9Po6+tDLpdjwPMI60GkT5T+0BapjZdMFgoFV55bZIFAoP6aeF0PBm6iXUToD6NXSzJ0t0kL3oODgzzDTdSCLMsYHh72rD+0hWw6nUY6nQYA9Pf3M+B5hPUg0idKfzQvZHlH7F3/lpXLZcyYMcPzejBwE+3WKf3BZEhERERERETkEIbuNmmfUdXOeFcqFUsbphN1K0VREA6HPesP7TN4lUqlfkmgmX2jyV6sB5E+Ufqj8TORiUSCl5dj979lItSDN7sj2q1T+oOhuw3NN4WKRCKWN0wn6lbaljhe9EfzTW8ikYipfaPJXqwHkT5R+qP5JkS9vb28vBy7t1QUoR4iBwsiN4nQH5VKxdDjGLot0rsLs9UN04m6lSzLkCSp/t9u9YfeXWaN7htN9mI9iPSJ0h96d/3t6elx9Hk7hSj1YPAmEqM/FEXB0NCQoccydFsw0bZHDN5Eu2mBW+NGf0y0rUvzwsnou5TdTpZlIerB4E1+oqqqEP3BbaiMEaUeDN7kZyL0h5YHg8GgocczdJtkdJ9hBm8ifU72h9F9VBsXTkbfpex22pY4XteDwZv8QttS0ev+YOA2R5R6MHiTH4nQH415MJFIGPoehm4TjAZuDYM3kT4n+sNowNNoCyej71J2u1KphGq16nk9GLzJLxRFGXXTtPE41R8M3NaIUg8Gb/ITEfrDbB7UMHQbZPUFZvAm0mdnf5gNeJpAIGD4Xcpup6oqksmk5/Vg8Ca/UFUVqVTKs/5g4G6PKPVoDBa80zx1Kzv6o93gbTUPAgzdhrTzAgMM3kTjsaM/rAY8jdme7mahUEiIejB4kx/IsoxwOGzqe+zqDwZue4hSDy1Y5PN53qeEuo5d/dFO8G43D/pupRkKhUw9vt0XWMPgTaSvnf5oN+DRWCLUg8Gb/MDqmqLd/mDgtpco9ejt7UU8Hke5XLb8M4hEUygUbOsPq8Hbjjzoy9A9MjJi6LF2BW4NgzeRPiv9wcDtHBHqweBNpM9qfzBwO0OUesRiMdNXTxCJqlKpIJ/P29YfVoK3XXnQd6G7UqmgUChM+ELbHbg1DN5E+sz0BwO380SoR/NClmdwiHYzG/QYuJ0lSj3MXtVJJKpyuYx4PG5rf5gJ3nbmQV+G7lgsNu4L7VTg1hhZyKqqautzEnUKI/3BwO0eEerRuJDNZrN8s5KogdGgx8DtDtaDyD7hcBixWMz2n2skeNudB30XugGgp6dH94V2OnBrxlvIqqrKyyjJ18brDwZu94lQD20hGwqFOB+JmkwU9Bjw3MV6ENnDyas2xgveTuRBX4ZuoPUL7Vbg1rRayNZqNWSzWZ7pJt/T6w8Gbm+IUI9AIIBUKgVJkhx9HqJOpBf0GPC8wXoQic/NPOjrD31owy6Xy0FRFJRKJdcCt0ZbyKbTaaTTaQC7LoGPx+OuPD+RyPT6g4HbGyLUQ5Ik1p5Ihxb0MpkM0uk0IpEIisUiA55HWA8i8bmVB317plvT29uLaDSKYrEIVVVdDdwaWZbR19eHcrmMcrmMyZMnc99gorc190dfXx9Dl4dEqAfPdBPp04KeqqooFouIRqMMeB5iPYjE50Ye9H2y097R0BQKBdePoVarIZfL1X+fz+d5eTnR25r7I5fL8UZaHmI9iMTXuJYplUq8D4LHWA8isbmRB30duhuv2Z8xY4blDdPb0fiZyP7+fvT396NSqXAgE6F1f3C7Pe+IUo9KpeLacxF1msbPDM+YMYP73HuM9SASm1t50Lehu9WH5K1smN6OVjchkmUZqVSKZ7rJ9/T6g/vce0OUehQKBe7VTaSj+SZdZveNJnuxHkRiczMP+jJ0VyoV3bvSuRW8x7vrbzgc5mdWydfG6w8Gb/eJUo/h4WHk83mEw2HHnoOoU+ndFZtBzxusB1H7nFxTjHeXcifyoO9CtyRJGBoaGveudE4HbyPb7PBGauRXRvqDwds9otRDW8DG43FH9+0k6kQTbUPFoOcu1oPIHoqiOHJ1m5FtwezOg75LdpFIBMFgcMK70jkVvLnPMJE+M/3B4O08UerRuICNxWK2/VyibmB032cGPXeIUA/+e0jdQpIkZLNZW/vDzD7cdubBjgndV155Jd7znvegt7cX06ZNw6mnnopXXnnF9M+p1WpIJBKGziTbHbwZuIn0WekPBu/d7JqRGlHqYXQBS+RHZvvDr8Hb7vmoR4R6lMtl39SVup8sywiFQrb1h5nArbErD3ZM6P7973+PZcuW4amnnsLq1atRLpdxwgknmL6lu6Iopi7dtuuFZuAm0tdOfzB472LXjATEqQcDN3W7dm6aarU//Bi87ZyPekSoh6IoyGazkCTJ8s8gEokkSUilUrb1h9nArbEjD3bMB+Puv//+Ub+/5ZZbMG3aNKxbtw7HHnuso8+tDU9tb1qziz8GbiJ9dvSHFvTS6TQymYzpYdoN7JqRotSDgZv8QFEURKNR09/Xbn9oQS+TySCdTnf92sTpNaQI9dACRSgU6upakv9IkmRbf1gJ3Jp282DHrkqHhoYAAFOmTHHl+ay+w8HATaTPzv5o5wzryMiI5ecVldUZmcvlPK8HAzf5haqqyGaznvSHH894a+xcQ4pQj8ZAkUqleKabuo5d/dHuSZl2znh3ZOiu1Wq46KKLcPTRR+OQQw7RfVypVEIulxv1qx1mX2gGbiJ9TvSHlaA3PDxs6yWGIjAyI1vNR1mWUa1WPa8HAzf5hSzLqFQqnvWHH4O31fnYigj1aA4UDNzUrezoDzuugrQavDsydC9btgwvvfQSbr/99nEfd+WVVyKZTNZ/zZ49u+3nNvpCM3AT6XOyP8wEPW3B1G13xDYyI1vNx0AggGQy6Xk9GLjJLwKBAFKplKf94bfgbXU+NhOhHk4ECiKRidIfjXnQ6NWSHdedy5cvx7333os1a9Zg1qxZ4z52xYoVGBoaqv/auHGjLccwUfBm4CbS50Z/GAl6jQumnp4e24/BK0ZnZKv5WCqVHNkD22w9GLjJT8LhsOf94Zfg3c58bCRCPRi4ya9E6Q8tDxq9WrJjOlRVVSxfvhy//vWv8cgjj2CfffaZ8HsikQgSicSoX3bRC94M3ESjVSqV+n+72R/jBb1uDHhmZ2Sr+djOnZQn4rd6EJkhQn+Mt5BtnOOdyI75qBGhHgzc5Hei9Edvb6/hqyU7pkuXLVuGW2+9FT/72c/Q29uLgYEBDAwMYOfOnZ4dU3PwZuAmGqtcLqNQKHjSH60Wst0a8ESckc38VA8is0Toj1YLWUVR6jce61R2zceRkREh6sHATSROfxi9WrJjtgy78cYbAQALFy4c9fWbb74ZS5cudf+A3tZ4+/hcLgdJkhi4iRqEw2Hk83mMjIx40h+N21dt3boVALoy4Ik6I5v5pR5EVojQH43bVw0ODgIAgsGga8/vBDvmYzQaRaFQwJQpUzyvhyzLDNxE6Kz+6JjQ7eRlj+2KxWL1O1tGIhEGbqIGjYs1r/pDlmVEIhEUi0UA6LobpwFiz8hmfqgHkVUi9EcgEEAikUA6nQZg/EyOqOycjyLUI5FICBcoiLzSKf0h3hF1GO2SWUmSEI1GUSwWTe/bRtTNFEXxvD+Gh4dRLBYRjUYhSZLpfaPJXqwHkT4R+kNRFGQyGYTDYYTDYa5rsGu9FwgEhKhHJpPp2pvdEZnVKf3B0N2G5s+o9vX1Wd4wnahbqaqKVCrlWX80fiayr6/P9L7RZC/Wg0ifCP3R+JnIqVOnYurUqR1/ebkdFEVBMpkUoh7dfpd5IqNE6A+js4Ch2yK9m0JZ3TCdqFvJsoxwOAzA/f5odRMiM/tGk71YDyJ9IvRHq5sQaZduEhAKhYSohx+2dyOaiAj9UavV6h8xnghDtwUT3YWZwZtot+bP1bjVH+Pd9ZdBrzUn9ujWsB5E+kToj/Hu+ivi5yO9Iko9GLzJz0ToDy0PVqtVQ4/nFDXJ6LZHDN5E+pzuDyPb7DQunIy+S9ntQqEQRkZGbP+5ZuvB4E1+UigUPO8PbkNljgj1YPAmvxKhPxrzYDKZNPQ9nKommN1nmMGbSJ9T/WFmX1tt4WT0XcpuV6lUUCgUPK8Hgzf5RaVSQT6f97Q/GLitEaEeDN7kNyL0R3MeNHqVICerQWYDt4bBm0if3f1hJuBpZFk2/C5lt6tUKvUtEL2sB4M3+UW5XEY8HvesPxi42yNCPZqDRblcbusYiERlR3+0G7yt5kGAoduQdl5ggMGbaDx29YeVgKdx8rPMnaanp8fzejB4k1+Ew2HT+z7b1R8M3PYQoR6NwSKbzXJmUtexqz/aCd7t5kHfTVhJkkw9vt0XWMPgTaSv3f5oJ+DRWCLUg8Gb/MDqG37t9gcDt71EqIcWLEKhEC8zp65SLpdt6w+rwduOPOi7KRuJRFCpVAw91q7ArWHwJtJntT8YuJ0hQj0YvIn0We0PBm5niFCPQCCAVCpl+gQTkahqtRqy2axt/WEleNuVB303aWu1GoaGhiZ8oe0O3BoGbyJ9ZvuDgdtZItSjeSGrqqotP5eoG5gNegzczhKhHpIk2bZmJfKaoigIhUK29YfZ4G1nHvTdtFUUBcFgcNwX2qnArWHwJtJntD8YuN0hQj0aF7LZbJbBm6iB0aDHwO0OEerBM93ULSRJQiqVsrU/jAZvu/OgLyduIpHQfaGdDtyaiRayRi+BJ+pGE/UHA7e7RKiHtpCtVCr8vCJRk4mCHgO3u1gPInvIsuzIm0gTBW8n8qAvu1zvhXYrcGv0FrKFQkGoLR8GnnoKCs/Ik8v0+oOB2xsi1EOWZaRSKaHOdOc2bMCO117z+jCIdIMeA543WA+gMjKCLY8/LtTMps7i5FUbbufB7u30CTS/0KVSydXArWleyA4PDyOfzyMcDrvy/BPJb96MZy+/HH+/+26vD4V8qFV/MHB7R4R6hMNhYT6vqKoqXvj2t7Huqqug8iZvJIDmoFcqlXwT8ETk93q8cd99eO6b38TQ3/7m9aEQteRmHuzubp9A4/YK2jscbgZuTeNCNpfLIR6PC7Nv8OZHH0Uxk8GbDzyAWrXq9eGQDzX3BwO3t0SohygL1eENG5Bdvx7Db7yBt/76V68PhwjA7qCnnVG18yZEZJ5f66GqKt544AHsHBzE5jVrvD4cIl1u5cHu7nhqi1qrYeODD0KSJBS2bEH6hRe8PiQiImFsWrMG1WIRNUXhopKIqMGO9euR+/vfEQgGsfGhh1DlvTjI53wdurVr9iuVSv0dDSsbprer8RLNRCKBfD4vxI3U0n/+M/KbNiHa1we1UsGmRx7x+pDIh5r7g3f995YI9RBhv+5auYyNq1cjEA4jGIlg05o1qOzc6fVhEdXPqDbefJD73HvHr/XYtGYNaoqCaH8/dm7fju3PPuv1IRG15FYe9G3obv6QfCQSsbRheruaPxPZ29uLeDwuxI3UNj3yCGrlMgKRCILRKLY+/jhvqEauatUfDN7eEaEe5XJZiLuXDz73HEa2bUO4txfheBylt97CwJNPen1Y5HPNN+mKRCKm9o0me/m1HpViEZseeQQBWUZQlqFWq9j08MNeHxbRGG7mQV+Gbr270pndML1dejchisVint9IrVwoYMtjjyEYjUKSpF2LyqEhbH3iCU+Pi/xDrz8YvL0hQj0URUE2mxViD9qNDz8MtVJBUJYRCIeh1mpcVJKn9O6KbXTfaLKXn+ux7emnUUynIb/9b0WopwcDTz2F4ltveXxk1GmcvPO923lQjLt1uSyXywFAyw/Jay90JpNBOp127MZqE9311+sbqQ2sXYvSjh2ITpkCAAi8fTwbV6/G3ied5OWhkQ9M1B/a17Re5o3VnCVCPRpvQuT13ctLO3Zg69q1CE2aVP9aKBbD9nXrMDIwgJ7p0z08OvKjibah0oJeOp1GJpPxxY28vOT3emx6+GGotRoCb59ACsdi2JlOY8vjj2PfU07x9Nj+83/FenP0xv84zutDEJqiKIhGo7b/3Im2BXMiD3ZPhxskyzKq1eq4L57TZ7w7YdujjatXA6paD9sAEI7HkXnpJQy/+aaHR0bdzmh/8Iy3O0SoR+MCNpVKeX6me+sf/oDy8DDC8Xj9a+FYDJWdO7H5scc8PDLyI6P7PvvhDKsIRKiHl/ti7xwcxPann0YoFqt/TQoGAQAbH3yQe3aTKaqqIpvN2tofRvfhtjsP+i50BwIBJJPJCd+tcCp4d0Lgzm/ejPSf/oRww8AEdl0eVN25E5sffdSbA6OuZ7Y/GLydJUI9mhewXgduVVXx5urVAHYvJAFACgQgBQJ484EHuGc3ucZowNMweDtLhHqoqurpfS+2PPYYyiMjY9aQcm8vdrz6KvfsJlNkWbb15oNGA7fGzjzou9BdKpUMX7ptd/DuhMAN7Nqbu1IsItTTM+rrkiRBCoXw5oMPcs9usp3V/mDwdoYI9TC7gHXD8IYNyL788qiz3Jpwby/37CbXWO0PBm9niFCPWq2GbDbr2dlkbW9uSBKkpr9/cNIkVEslbq9IpgQCAaRSKdv6w0zgbjwGO/Kg7z7TbXYQ2XVNf6cE7vre3G+ftWkm9/bW9+yedsQRHhwhdaN2+4Of8baXCPUQMXADu/fmlpPJMX8WjESg7NiBzWvWoO+QQzw4ul34mcXOYXV70Hb7o9s/U+w2EerRuO1RvMWbgm7Q9uaWW8x8SZIQkGVsfOghHLhkCYIe35uDOkc4HLatP8wGbo0deZAT1oB23+HolMAN7N6bu9XABHYtKrlnN9nJrv5o5wyr1YVvNxoZGfG8HqIG7sa9uVtd5i5JEvfsJlPK5TIKhYKp77GrP3jG2x4i1KMxUKRSKc9mprY3d1DnxlfheJx7dpMldvVHOzdEazcPirGS6QBWX+hOCtzA6L259XDPbrKL3f1hJegpioKhoaG2n7sbhEIhFAoFz+shYuAGRu/NrSfc28s9u8mwcDiMfD7vWX8weLdHhHo0Bwqvtpxt3Jtb794b3LOb2mFHf7R9B/I2grfvLi9vh9lLCzotcDfvza0nHI+jmMlg6xNPeLZ9mEiXT/LSSWuc6g8zlzZrC6Zgww2x/CwUCiEWi3leDxEDNzB6b249gVAIqqpi08MPY9b73+/i0VEnCoVCiMfjnvYHLzW3RoR6tAoUXt1ETdubO5JKjfu4xj27tW1piYxqtz/s0JwHjX6cg1PVJKPvcHRa4AZ2783d6gZBjRr37Caywun+MHKGtXHBlEgkbD+GTlSpVNDTdANFO5ith4iL/lZ7c+sJ9fTU9+wmmkgsFvO8P3jG2xwR6uFUoLBq08MPQ1XV+t7cesKxGMr5PLY8/rhLR0bdRoT+aMyDRq+WFGtV0yEmCt6dGLiB1ntz6+Ge3WRU8zB0qz/GC3qiBzyvOPnZ9k6vR6u9ufVwz24yS4T+GG8hyxC+myj1EClw1/fmNvCmLffsJjuI0B9aHjR6taR4K5sOoRe8OzVwj2zfjsxLL0GtVrFz+3aMbN8+5jPbtUoFI9u2Yef27Sjn86js3ImtTzzh0RFTp1AUBeVyGYD7/dFqIdsJAa9bdXI9Nv/+96gpCoqZDHZu346d6fSYx2h/VkynUVMUbOYNJ8kEEfqj1UK2VqvVL3/3u0qlIkQ9RArcADDw5JMo79yJysjIrjXkwABqb/+7rykXCvU1pFqtYuhvf8PwG294dMTUDUToj0AgYPhqSX6muw3N1/RHIhEUi8WOC9wAICcSeOfZZ9fvuLvlD3/A8D/+ATT8PWpvf5Zxzoc+VD/bw23DaCKSJCGbzaJYLHrSH42fKVYUBaVSSfiA1806tR57f+ADSB14IAAgt2EDtrQ4i61Wq9jjfe/D5P33BwDEZ81y9Rip84nQH42fmUy//eZStVp15blFJssyhoaGEI1GPa9HpVIRJnADQN+hh+LAc84BAFRLJfzjnntQLZdHXWpe3bkT8T33xKzjdt0HJxiJYNLUqZ4cL3UPEfrD6Cxg6G6TFry3bt2KYrGIaDTacYEbAELRKA7493+v/37HK6/sCt0t7Psv/4LevfZy69Cow8myXA/cXvVHb28vFEVBsVgEAOEDXrfrxHrMWrQIWLQIALDh3ntbhm4A6D/8cLzjzDPdPDTqMiL0hyzL6Ovrqy9iO3FdY7dAIIBarSZEPUQK3ACQmDMHB3384wB2XfHzj3vuafk4OZGoP47ILqL3h0bsVU6HaNxjs1QqeXbnSCIRNZ4h8ao/tDNGGrP74pK9WA8ifSL0R/Ml5SMjI64fg6hEqEcul+Pn7Ine1in9wdDdpsbPqM6YMcPyhulE3apcLiMej3vWH42fiZwxY4bpfaPJXqwHkT4R+qPxM5H9/f3o7+/n5eUAisUiYrGYEPXgXeaJdumk/mDobkPzTaHa2TCdqFuFw2HEYjFP+qPVTYiMbF9FzmA9iPSJ0B+tbkIkyzKSyaTjz90Jenp6hKgHt3cjEqc/jF4JxNBtkd5dmLsteKuqikK1gKHKEHZWd4KbO5BZoYYt6Nzsj/Hu+sug15okSY797G6sR+N8LFQLnI9kmQj9Md5df0MGthL1CxHq0RHBm/ORHCRKfwwPDxv+yEnHhe7vfe97mDNnDqLRKI466ig8/fTTrh/DRNsedUvwLtVKeL34Ot4ovYHNymZsLW/BdmUbnsw96fWhUQdzoz+MbLPTuHDqls8rtjsfI5GII3t1m61HJwRvpaaMmo9vlN7AW+UMXims9/rQqMOUy2XP+0PEbaicYNcaUoR6iBy8d9Z2YpOyadR8TJfTSJczXh8adQFR+kPLg7FYzNDjOyp0/+IXv8DFF1+MlStX4rnnnsNhhx2GE088Edu3b3ftGIzuM9zpwXuglsZwOYdoWkFvRkVvRsWkYUAJ1nDl5qvwSJb7z5J1TvaHmX1ttYVTN9zIy475WKvVMDQ05Hk9RA/efym+jB3S6PnYm1FRlWq4M/srzkcyrFarIZvNetoffgncdq8hRaiHiMH7D/m1GFTfQihfGTUfUaniL8p6zkdqiyj90ZgHe3p6DH2P6dC9ZMkSPKazVYrTvv3tb+P888/Heeedh4MOOgjf//730dPTg//93/915fmNBm5NpwbvqlrF7ce/iYeWhsf8emRJCLmpEq7ddC2qKm+sQtY50R9mAp6mt7fX8LuURng1I+2Yj4qiIBgMel4PkYN3Va3iptkP4ZFzWszHc8N47cgg5yMZpigKQqGQZ/3hduDutjWkCPVoDhaq6t2F3FW1im/lbsBDS0It15BPnBHifCTL7OgPO4K32TyoMf0hnaGhISxevBh77703zjvvPCxZsgR77rmn2R9jmqIoWLduHVasWFH/WiAQwOLFi/Hkk60vdy6VSqO23Wi8nbxZVl9gLVhkMhmk0+mOeBf5+fzz+Ft/FugP6j5mW3kbns8/jyN7j3TxyKjb2NkfVgKexui7lEZ4MSPtnI+JRAI7d+70tB7ajNWOSaQ9gp/PP4/N4TRwhP58LHI+kkGSJCGVSnnSH16c4e6UNaSZ9aMI9dCCRTqdRjabxaRJkywdQ7uezz+P7eXtwMH68xGcj2SBXf2RyWRMr0kaWc2DgIUz3XfffTc2b96M//zP/8QvfvELzJkzByeffDLuvPNOlMtlsz/OsHQ6jWq1ij322GPU1/fYYw8MDAy0/J4rr7wSyWSy/mv27NmWnrudFxjovDPe6XLa1scRjceO/mgn4NnNixlp53wUpR6invHmfCQ7ybJs6QaG7faHV5eUd8oa0uz6UYR6aMGiUql4ts7kfCQnqKpqW3+0c8a77Txo+jsA9Pf34+KLL8af/vQn/PGPf8T++++Pc845BzNnzsRnP/tZvPbaa1Z+rO1WrFiBoaGh+q+NGzdClmVTL3S7L7Cmk4L31PBUWx9HNJF2+kOkwK3phBnZaj5qRKmHiMGb85Hs1M6OAVb7w+vPcHf6fNQjQj1kWUYqlfLsEnPOR7KbqqrIZrO29YfV4G1HHmxrdbp161asXr0aq1evRjAYxAc+8AG8+OKLOOigg/Cd73ynnR89xtSpUxEMBrFt27ZRX9+2bRumT5/e8nsikQgSicSoX4FAALlcztALbVfg1nRK8D48fjimhaeN+5g9wnvg8PjhLh0R+YGV/hAxcDdya0baNR8biVIP0YI35yOJxGx/eB24G4m8hpxoPuoRoR7hcNizunI+kt0URUGlUrGtP6wEb9tOwJr9hnK5jF/96lf40Ic+hL333ht33HEHLrroImzZsgU/+clP8NBDD+GXv/wlvva1r1k+qFZkWcYRRxyBhx9+uP61Wq2Ghx9+GO973/sM/5xSqYRqtTrhC2134NZ0QvAOSkFcMusS3T+XIOHzsz6PoDTOZ3aILDDTH6IGbi9mpF3zsZko9WhcyHp9p3nORxKN0aAnQuDu9DWkESLUw6t/DzkfyW6qqiKVStnaH2aCt5150PSN1GbMmIFarYaPfvSjePrppzF37twxj1m0aBEmT57c1oG1cvHFF2PJkiU48sgjMW/ePFx33XUoFAo477zzDP8MVVWRTCaRz+d1P0zvVODWGLl5lNfbPrw/9X5cg2twzaZrdt0U4217hPfA52d9Hu9Pvd/Do6NuZqQ/RA3cgHcz0o752Ioo9dBm8Y4dO2y927wVnI8kmolu5iVC4AY6fw1pVKfUwwmcj2QnWZYRDocd+bkT3VzN7jxoOnR/5zvfwRlnnIFoNKr7mMmTJ+Mf//hHWwfWyllnnYXBwUF8+ctfxsDAAObOnYv7779/zI0xJhIKhXRfaKcDt2a8hWy5XBbiDPj7U+/HgskL8Hz+eaTLaUwNT8Xh8cP5DiU5brz+EDlwA97NSLvmYyui1KO3t9fTmwQ14nwk0egFPZECXjesIY3qhHo4hfOR7OLkmmK84O1EHjQdus855xxbntiq5cuXY/ny5W3/nFYvdKFQcCVwa1otZAEgm80iEok4/vxGBKUgt3UgT+j1h8iBG/B2Rto1H1sRpR6xWMzTfWgbcT6SaJqDXiwWEyrgdcsa0ijR6+EkzkfqBG7mQdOhu5s0vtBbt24FANcCt6ZxITs4OAhg15n4bh7EREa16g9ZloUN3N1OlHqEQr7+p4toXI1BL5fLQZKkrg94ImM9iMTmVh70/apVluVRZ5W9+KxgIBAYdWfMeDze1jYiRN2kuT+0XQjIG6wHkfga1zKRSIQBz2OsB5HY3MiDvl8pDQ8Po1gsIhqNQpIkyxumt0NRFGQyGYTDYYTDYezYscPzG6kRiaK5PzKZjBCf6fUrEeohyuXlRCLSPjMsSRKi0SiKxaIQ2+35FetBJD438qCvQ3fjh+T7+vosb5jejsabEE2dOhVTp05FKBRiqCBC6/4Qebu9bidCPVRVZe2JdDTfpKuvr0+ofe79hvUgEp9bedC3obvVXemsbJjejlZ3/Q0EAkilUry8nHxPrz9E3+e+W4lQj1qthmw2yzPdRC3o3RXb6L7RZC/Wg0h8buZBX4bukZER3bvSuRW8x9tmR5Ikft6HfG28/mDwdp8I9dAWsJVKhfORqMlE21Ax6LmL9SCyR6VScexnj7ctmBN50HehOxQKoVAojHtXOqeDt5F9bXmmm/zKSH8weLtHhHo0LmBTqRRv3EbUwOi+zwx67mA9iOxTLpdRKBRs/7lG9uG2Ow/6buUSCoUQi8UmvA28U8HbyAKWyK/M9AeDt/NEqEfzAjYcDtvyc4m6gdGAp2HQc5Yo9XDy7CCRm8LhMPL5vK39YSRwa+zMg77b7LRSqaCnp8fQY1ttmN5OSGbgts+N/3Gc14dANrPSH437RqfTae59aiMR6tFqAcs3V4h2MRvwNI37Rjf+ntojSj0KhQLK5XJbP4NIFKFQCPF43Lb+MBO4NXblQd+lPrPv/tn1DgcDN5G+dvqDZ7ztJ0I9rC5giTqJ1TVFu/3BM972EqUew8PDyOfzvCKIukosFrOtP8wGbo0deZDJz4B2X2gGbiJ9dvRHu0HPrS0CO0GlUhGiHgzc5AeKopg+K2lXfzB420OUemiBIh6PIxTy3YWs1OXs6g8rgVvTbh5kVxpk9dICBm4ifXb2h9VLm2u1Wv2yJb+TJAlDQ0OIRqOe1oOBuz38+E3nkCQJ2WwW4XDYk/7gpebtEaUejYEiEomgWCy2dRxEIrKjP9qdca3yoFFMgCaYfYeDgZtInxP9YfYMq7ZgqlarbT93N4hEIggGg57Xg4Gb/EKWZYRCIU/7g2e8rRGlHnYGCiLRidAfVs94MwWaZPSFZuAm0udkfxgNeo0LpmQyadvzd7JarYZEIuF5PRi4yS8kSUIqlfK8Pxi8zRGlHgzc5Eci9EdjHjR6tSSToAUTBW8GbqLdVFUd9Xs3+mOioNe8YOLn33ZRFEWIejBwk59IkiREfzB4GyNKPRi4yc9E6A8tDxq9WpIrTYv0PuPNwE00mqIoiEaj9f92qz/0PlPcasHEPU2dZ6YeRH4jSn/ofWZyZGTE0eftFKLUg4HbOt7zonuI0B+yLBu+WpKhuw3NwTuRSCCTyTBwEzVQVRXZbBapVMr1/mheyPb19SGXyzHgeYT1INInSn80L2SBXXs/+10gEKi/Jl7Xg4GbaBcR+sPo1ZIM3W3Sgvfg4CDPcBO1IMsyhoeHPesPbSGbTqeRTqcBAP39/Qx4HmE9iPSJ0h/NC9lYLObq84tIlmWUy2XMmDHD83owcBPt1in9wWRIRERERERE5BCG7jZpn1HVznhXKhVLG6YTdStFURAOhz3rD+0zeJVKpX5JoJHtecgZrAeRPlH6o/EzkYlEgpeXY/e/ZSLUgze7I9qtU/qDobsNzTeFikQilvZtI+pm2pY4XvRH801vIpGIqX2jyV6sB5E+Ufqj+SZEvb29vLwcu7dUFKEeIgcLIjeJ0B9Gb8bL0G2R3l2YrW6YTtStZFmGJEn1/3arP/TuMmt032iyF+tBpE+U/tC7629PT4+jz9spRKkHgzeRGP2hKAqGhoYMPZah24KJtj1i8CbaTQvcGjf6Y6JtXZoXTtwybBdtiyK7ma0Hgzf5iaqqQvQHt6EyRpR6MHiTn4nQH1oeDAaDhh7P0G2S0X2GGbyJ9DnZH0b3UW1cOBl9l7LbaVvieF0PBm/yC21LRa/7g4HbHFHqweBNfiRCfzTmwUQiYeh7GLpNMBq4NQzeRPqc6A+jAU+jLZyMvkvZ7UqlEqrVquf1YPAmv1AUZdRN08bjVH8wcFsjSj0YvMlPROgPs3lQw9BtkNUXmMGbSJ+d/WE24GkCgYDhdym7naqqSCaTnteDwZv8QlVVpFIpz/qDgbs9otSjMVjwTvPUrezoj3aDt9U8CDB0G9LOCwwweBONx47+sBrwNGZ7upuFQiEh6sHgTX4gyzLC4bCp77GrPxi47SFKPbRgkc/neZ8S6jp29Uc7wbvdPOi7lWYoFDL1+HZfYA2DN5G+dvqj3YBHY4lQDwZv8gOra4p2+4OB216i1KO3txfxeBzlctnyzyASTaFQsK0/rAZvO/KgL0P3yMiIocfaFbg1DN5E+qz0BwO3c0SoB4M3kT6r/cHA7QxR6hGLxUxfPUEkqkqlgnw+b1t/WAneduVB34XuSqWCQqEw4Qttd+DWMHgT6TPTHwzczhOhHs0LWZ7BIdrNbNBj4HaWKPUwe1UnkajK5TLi8bit/WEmeNuZB30ZumOx2LgvtFOBW2NkIauqqq3PSdQpjPQHA7d7RKhH40I2m83yzUqiBkaDHgO3O1gPIvuEw2HEYjHbf66R4G13HvRd6AaAnp4e3Rfa6cCtGW8hq6oqL6MkXxuvPxi43SdCPbSFbCgU4nwkajJR0GPAcxfrQWQPJ6/aGC94O5EHfRm6gdYvtFuBW9NqIVur1ZDNZnmmm3xPrz8YuL0hQj0CgQBSqRQkSXL0eYg6kV7QY8DzButBJD4386CvP/ShDbtcLgdFUVAqlVwL3BptIZtOp5FOpwHsugQ+Ho+78vxEItPrDwZub4hQD0mSWHsiHVrQy2QySKfTiEQiKBaLDHgeYT2IxOdWHvTtmW5Nb28votEoisUiVFV1NXBrZFlGX18fyuUyyuUyJk+ezH2Did7W3B99fX0MXR4SoR48002kTwt6qqqiWCwiGo0y4HmI9SASnxt50PfJTntHQ1MoFFw/hlqthlwuV/99Pp/n5eVEb2vuj1wuxxtpeYj1IBJf41qmVCrxPggeYz2IxOZGHvR16G68Zn/GjBmWN0xvR+NnIvv7+9Hf349KpcKBTITW/cHt9rwjSj0qlYprz0XUaRo/Mzxjxgzuc+8x1oNIbG7lwY4I3Rs2bMDHP/5x7LPPPpg0aRL2228/rFy5sq2B1epD8lY2TG9Hq5sQybKMVCrFM93ke3r9wX3uR3NiPrYiSj0KhQL36ibS0XyTLrP7Rncjt2ZkK6wHkdjczIMdcSO19evXo1ar4aabbsL++++Pl156Ceeffz4KhQKuvfZa0z+vUqlgx44dLT8k3/hh+sbf2228u/6Gw2F+ZpV8bbz+aLyZVyaT8eQ+DCKxez62Iko9hoeHkc/nHdmzk6jT6d0Vu/lmXn67EaUbM7IV1oOofU6+mT/eXcqdyIMdEbpPOukknHTSSfXf77vvvnjllVdw4403mh6YkiRhaGgI0WhUd3HodPA2ss2On0ME+ZuR/mDw3s3O+diKKPXQFrDxeBzBYNDWn03U6SbahsrPQc/pGdkK60FkD0VRHDkZaWRbMLvzYMeuUoeGhjBlypRxH1MqlZDL5Ub9ikQiCAaDEy4Knbq0gPsME+kz0x+81Fyf1fnYTJR6NC5geZabaDSj+z7z0ubdJpqRRuajHhHqwX8PqVtIkoRsNmtrf5jZh9vOPNiRofv111/H9ddfj09+8pPjPu7KK69EMpms/5o9ezZqtRoSiYShszB2B28GbiJ9VvqDwXusduZjI1HqYXQBS+RHZvuDwdvYjJxoPuoRoR7lctmXdaXuJMsyQqGQbf1hJnBr7MqDnobuSy+9FJIkjftr/fr1o75n8+bNOOmkk3DGGWfg/PPPH/fnr1ixAkNDQ/VfGzduhKIopi57tOuFZuAm0tdOf3Rr8PZiPmpEqQcDN3W7dm6aarU/uiV4Ozkjx5uPekSoh6IoyGazkCTJ8s8gEokkSUilUrb1h9nArbEjD3r6me7Pfe5zWLp06biP2Xfffev/vWXLFixatAjz58/HD37wgwl/fiQSQSQSafcw276mn4GbSJ8d/dGNn/H2aj6KUg8GbvIDRVEQjUZNf1+7/dENnyl2ckaaXT+KUA8tUIRCoY6rJdF4JEmyrT+sBG5Nu3nQ09Ct7fNqxObNm7Fo0SIcccQRuPnmm11fUFt9oRm4ifTZ2R/tBL2RkRHLz+sUr+ajNuO8rAcDN/mFqqrIZrOYNm2a6/3R6cFblDWkCPVoDBSJRAKlUsnycRCJyK7+aPekTDvBuyNOBW3evBkLFy7EXnvthWuvvRaDg4MYGBjAwMCAq8dh9tICBm4ifU70h5VLm4eHh1EoFNp+bq/YOR9lWUa1WvW8Hgzc5BeyLKNSqXjWH91yqfl4nFxDilCP5kDBS8upW9nRH3a84Wb1UvOO2DJs9erVeP311/H6669j1qxZo/6snc9DWWH0HQ4GbiJ9TvaHmTOs2oKpk++Ibed8DAQCSCaTnteDgZv8IhAIIJVKYWhoyLP+6PQz3hNxag0pQj2cCBREIhOlPxrzoNGPonREdy5duhSqqrb85YWJ3uFg4CbS50Z/GDnD2rhg6unpsf0Y3GLnfCyVSgiF7H8v1mw9GLjJT8LhsOf90c1nvJ1YQ4pQDwZu8itR+kPLg0avlmSHWqQXvBm4iUarVCr1/3azP8YLegx4rTn5RibrQaRPhP4YbyHbOMf9ToR6MHCT34nSH729vYavlmSXtqE5eDNwE41VLpdRKBQ86Y9WC1kGPO+wHkT6ROiPVgtZRVEwNDTk+HN3gpGRESHqwcBNJE5/GL1asiM+0y2yxmv6c7kcJEli4CZqEA6Hkc/nMTIy4kl/NH6meOvWrQDAgOch1oNInwj90fiZycHBQQBAMBh07flFFY1GUSgUMGXKFM/rIcsyAzcROqs/xDqaDtV4WUEkEmHgJmrQuFjzqj9kWR51o4tOvnFaN2A9iPSJ0B+BQACJRKL++06+74XdRKhHIpEQLlAQeaVT+kO8I+ow2iWzkiQhGo2iWCyaun08UbdTFMXz/hgeHkaxWEQ0GoUkSYa35yFnsB5E+kToD0VRkMlkEA6HEQ6Hua7BrvVeIBAQoh6ZTKarbnZH1I5O6Q+G7jY0f0a1r6/P0r5tRN1MVVWkUinP+qPxM5F9fX2m940me7EeRPpE6I/Gz0ROnToVU6dO5eXl2PW6JJNJIerRjXeZJ7JChP4wOgsYui3SuymU1Q3TibqVLMsIh8MA3O+PVjchMrJ9FTmD9SDSJ0J/tLoJUfOlm34WCoWEqEe3bu9GZIYI/VGr1ZDL5Qw9lqHbgonuwszgTbRb8+dq3OqP8e76y6DXmhN7dGtYDyJ9IvTHeHf9FfHzkV4RpR4M3uRnIvSHlger1aqhx3OKmmR02yMGbyJ9TveHkW12GhdORt+l7HahUAgjIyO2/1yz9WDwJj8pFAqe9we3oTJHhHoweJNfidAfjXkwmUwa+h5OVRPM7jPM4E2kz6n+MLOvrbZwMvouZberVCooFAqe14PBm/yiUqkgn8972h8M3NaIUA8Gb/IbEfqjOQ8avUqQk9Ugs4Fbw+BNpM/u/jAT8DSyLBt+l7LbVSoVxGIxz+vB4E1+US6XEY/HPesPBu72iFCP5mBRLpfbOgYiUdnRH+0Gb6t5EGDoNqSdFxhg8CYaj139YSXgaZz8LHOn6enp8bweDN7kF+Fw2PS+z3b1BwO3PUSoR2OwyGaznJnUdezqj3aCd7t50HcTVpIkU49v9wXWMHgT6Wu3P9oJeDSWCPVg8CY/sPqGX7v9wcBtLxHqoQWLUCjEy8ypq5TLZdv6w2rwtiMP+m7KRiIRVCoVQ4+1K3BrGLyJ9FntDwZuZ4hQDwZvIn1W+4OB2xki1CMQCCCVSpk+wUQkqlqthmw2a1t/WAneduVB303aWq2GoaGhCV9ouwO3hsGbSJ/Z/mDgdpYI9WheyKqqasvPJeoGZoMeA7ezRKiHJEm2rVmJvKYoCkKhkG39YTZ425kHfTdtFUVBMBgc94V2KnBrGLyJ9BntDwZud4hQj8aFbDabZfAmamA06DFwu0OEevBMN3ULSZKQSqVs7Q+jwdvuPOjLiZtIJHRfaKcDt2aihazRS+CJutFE/cHA7S4R6qEtZCuVCj+vSNRkoqDHwO0u1oPIHrIsO/Im0kTB24k86Msu13uh3QrcGr2FbKFQ4JYP5Ht6/cHA7Q0R6iHLMlKpFM90E7WgF/QY8LzBehC1z8mrNtzOg77dJ0d7oTOZDNLpNPr6+pDL5VwL3BptkZrL5epfy+fzprcQIepGrfqDgds7ItQjHA7z84pEOrSgl06nkclkkEgkkMlkGPA8wnoQic3NPOjb0A3sfqHT6TTS6TQAoL+/3/UFXfNCNh6PIxgMunoMRKJq7g8Gbm+JUA8uVIn0aUFvcHCQZ1QFwHoQic2tPMiOJyIiIiIiInKIr0O3ds1+pVKpX0JgZcP0djV+JjKRSCCfz/NGakRva+4P3vXfWyLUg/t1E+nTPjPcePNB7nPvHdaDSGxu5UHfhu7mD8lHIhFLG6a3q/kmRL29vYjH47yRGhFa9weDt3dEqEe5XObdy4l0NN+kKxKJmNo3muzFehCJzc086MvQrXdXOrMbprdL766/sVgM4XDY0ecmEp1efzB4e0OEeiiKgmw2yz1oiVrQuyu20X2jyV6sB1H7nNytxO086MvQPd5d6dwK3hNtsxMK+foed+RzE/UHg7e7RKiHtoANhUK8ezlRk4m2oWLQcxfrQWQPRVEcCd4TbQvmRB70XeiWZRnVanXc28A7Hby5zzCRPqP9weDtDhHq0biATaVSPNNN1MDovs8Meu4QoR5Onh0kcpOqqshms7b2h9F9uO3Og74L3YFAAMlkcsIzJU4FbwZuIn1m+4PB21ki1KN5AcvATbSb0YCnYfB2lgj1UFWV972griHLsq03HzQauDV25kHfhe5SqWT40m27gzcDN5E+q/3B4O0MEephdgFL5CdW+4PB2xki1KNWqyGbzfJMN3WNQCCAVCplW3+YCdyNx2BHHvTdCsbsILLrhWbgJtLXbn8weNtLhHowcJMfWN0etN3+YPC2lwj1aNz2iPe9oG4SDodt6w+zgVtjRx7kKsaAdl9oBm4ifXb1RztBz+rCtxuNjIx4Xg8GbvKLcrmMQqFg6nvs6g8Gb3uIUI/GQJFKpTgzqevY1R9WArem3TzIrjTI6gvNwE2kz+7+sBL0FEXB0NBQ28/dDUKhEAqFguf1YOAmvwiHw8jn8571B4N3e0SoR3Og4Jaz1K3s6I92rwJpJ3hzNWOC2ReagZtIn1P9YSboaQumYDBo2/N3slAohFgs5nk9GLjJL0KhEOLxuKf9weBtjQj1sDtQEIlOhP5ozoNGr5bkisYko8GbgZtIn9P9YSToNS6YEomE7cfQiSqVCnp6emz/uWbrwcBNfhKLxTzvDwZvc0SoBwM3+ZUI/dGYB41eLclVjQUTBW8GbqLdmoehW/0xXtBjwGvNyc+2sx5E+kToj/EWsgzhu4lSDwZu8jMR+kPLg0avluTKxiK94M3ATTSaoigol8sA3O+PVgtZBjzvsB5E+kToj1YL2Vqthlwu5+jzdopKpSJEPRi4icToj0AgYPhqSWMbVlNLWvDOZDJIp9OIRCIoFosM3EQNJElCNptFsVj0pD+058rlclAUBaVSiQHPQ6wHkT4R+kNbyKbTaaTTaQBAtVp15blFJssyhoaGEI1GPa9HpVJh4CaCGP1hdBZwhdMmLXirqopisYhoNMrATdRAlmXP+6O3txfRaBTFYhGqqjLgeYz1INInQn/Isoy+vj6Uy2WUy2Wua7BrvVer1YSoR19fHwM30ds6pT+4yrFB4x6bpVLJ0obpRN2q8QyJV/2hnTHSmN0Xl+zFehDpE6E/mi8pHxkZcf0YRCVCPXK5HD9nT/S2TukPX11erqoqAIz6x6xdIyMjKBQKiMViiEajyOVy2LZtG5LJJEIhay9vuVxGrVZDPp+3/DPIZ5QcMLxz9NdyOUD2diusfD4PRVEgyzJisZgt/WFWpVLB0NAQgsEgkskkisUi3nrrLZRKpfqdurWZoM0IP3JiPrZipB7j4XwkSwSckfl8HtVqFcVisX4Tw3b7ww7aArZarSKZTAIA3nrrLQD+nZHa1VqRSESIegwNDWFgYACJRGLMWXfOSDJNwPkItJ6Rzcz2hxOMriEl1UcTdNOmTZg9e7bXh0FEgtq4cSNmzZrl9WF4gvORiCbi1xnJ+UhEE5loPvoqdNdqNWzZsgW9vb2QJMnrw0Eul8Ps2bOxcePGjtwnuJOPv5OPHeDx201VVQwPD2PmzJm+/Wwx56O9ePze4vHby+8zkvPRXjx+b/H47WV0PvrqupNAICDkO7SJREKI/2ms6uTj7+RjB3j8dtIuS/Irzkdn8Pi9xeO3j59nJOejM3j83uLx28fIfPTf25VERERERERELmHoJiIiIiIiInIIQ7eHIpEIVq5ciUgk4vWhWNLJx9/Jxw7w+Kn7dfr/Izx+b/H4qZt1+v8fPH5v8fi94asbqRERERERERG5iWe6iYiIiIiIiBzC0E1ERERERETkEIZuIiIiIiIiIocwdBMRERERERE5hKFbMKVSCXPnzoUkSXjhhRe8PhxDNmzYgI9//OPYZ599MGnSJOy3335YuXIlFEXx+tB0fe9738OcOXMQjUZx1FFH4emnn/b6kAy58sor8Z73vAe9vb2YNm0aTj31VLzyyiteH5ZlV111FSRJwkUXXeT1oVAH4Hx0B+ejGDgfySzOSHdwRnqvE+cjQ7dgvvCFL2DmzJleH4Yp69evR61Ww0033YS//OUv+M53voPvf//7uOyyy7w+tJZ+8Ytf4OKLL8bKlSvx3HPP4bDDDsOJJ56I7du3e31oE/r973+PZcuW4amnnsLq1atRLpdxwgknoFAoeH1opj3zzDO46aabcOihh3p9KNQhOB+dx/koBs5HsoIz0nmckd7r2PmokjB+97vfqQceeKD6l7/8RQWgPv/8814fkmXf/OY31X322cfrw2hp3rx56rJly+q/r1ar6syZM9Urr7zSw6OyZvv27SoA9fe//73Xh2LK8PCw+o53vENdvXq1umDBAvXCCy/0+pBIcJyP7uB89B7nI1nBGekOzkhvdfJ85JluQWzbtg3nn38+Vq1ahZ6eHq8Pp21DQ0OYMmWK14cxhqIoWLduHRYvXlz/WiAQwOLFi/Hkk096eGTWDA0NAYCQr/V4li1bhg9+8IOj6kCkh/PRHZyPYuB8JLM4I93BGem9Tp6PIa8PgABVVbF06VJ86lOfwpFHHokNGzZ4fUhtef3113H99dfj2muv9fpQxkin06hWq9hjjz1GfX2PPfbA+vXrPToqa2q1Gi666CIcffTROOSQQ7w+HMNuv/12PPfcc3jmmWe8PhTqAJyP7uF89B7nI5nFGekezkhvdfp85JluB1166aWQJGncX+vXr8f111+P4eFhrFixwutDHsXo8TfavHkzTjrpJJxxxhk4//zzPTpyf1i2bBleeukl3H777V4fimEbN27EhRdeiNtuuw3RaNTrwyEPcT5yPjqJ85E6HWckZ6STOm1GdsN8lFRVVb0+iG41ODiITCYz7mP23XdfnHnmmfjtb38LSZLqX69WqwgGg/jYxz6Gn/zkJ04faktGj1+WZQDAli1bsHDhQrz3ve/FLbfcgkBAvPd0FEVBT08P7rzzTpx66qn1ry9ZsgQ7duzAPffc493BmbB8+XLcc889eOyxx7DPPvt4fTiG3X333fiXf/kXBIPB+teq1SokSUIgEECpVBr1Z9S9OB85H53C+UjdgDOSM9IpnTgju2E+MnQL4M0330Qul6v/fsuWLTjxxBNx55134qijjsKsWbM8PDpjNm/ejEWLFuGII47ArbfeKvT/+EcddRTmzZuH66+/HsCuS2z22msvLF++HJdeeqnHRzc+VVXxX//1X/j1r3+NRx99FO94xzu8PiRThoeH8cYbb4z62nnnnYcDDzwQX/ziFzvmEidyD+ejuzgfvcP5SFZwRrqLM9Ib3TAf+ZluAey1116jfh+PxwEA++23X8cMy4ULF2LvvffGtddei8HBwfqfTZ8+3cMja+3iiy/GkiVLcOSRR2LevHm47rrrUCgUcN5553l9aBNatmwZfvazn+Gee+5Bb28vBgYGAADJZBKTJk3y+Ogm1tvbO2YwxmIx9PX1dcTAJPdxPrqL89E7nI9kBWekuzgjvdEN85Ghm9q2evVqvP7663j99dfHDHgRL6Q466yzMDg4iC9/+csYGBjA3Llzcf/994+5MYaIbrzxRgDAwoULR3395ptvxtKlS90/ICIaF+ejezgfiToPZ6R7OCO9xcvLiYiIiIiIiBwi3l0KiIiIiIiIiLoEQzcRERERERGRQxi6iYiIiIiIiBzC0E1ERERERETkEIZuIiIiIiIiIocwdBMRERERERE5hKGbiIiIiIiIyCEM3UREREREREQOYegmIiIiIiIicghDNxEREREREZFDGLrJVwYHBzF9+nRcccUV9a+tXbsWsizj4Ycf9vDIiIi8xflIRNQa5yO1S1JVVfX6IIjc9Lvf/Q6nnnoq1q5di3e+852YO3cuTjnlFHz729/2+tCIiDzF+UhE1BrnI7WDoZt8admyZXjooYdw5JFH4sUXX8QzzzyDSCTi9WEREXmO85GIqDXOR7KKoZt8aefOnTjkkEOwceNGrFu3Du9617u8PiQiIiFwPhIRtcb5SFbxM93kS3/729+wZcsW1Go1bNiwwevDISISBucjEVFrnI9kFc90k+8oioJ58+Zh7ty5eOc734nrrrsOL774IqZNm+b1oREReYrzkYioNc5HagdDN/nOJZdcgjvvvBN/+tOfEI/HsWDBAiSTSdx7771eHxoRkac4H4mIWuN8pHbw8nLylUcffRTXXXcdVq1ahUQigUAggFWrVuHxxx/HjTfe6PXhERF5hvORiKg1zkdqF890ExERERERETmEZ7qJiIiIiIiIHMLQTUREREREROQQhm4iIiIiIiIihzB0ExERERERETmEoZuIiIiIiIjIIQzdRERERERERA5h6CYiIiIiIiJyCEM3ERERERERkUMYuomIiIiIiIgcwtBNRERERERE5BCGbiIiIiIiIiKHMHQTEREREREROeT/A5KVz97NIGPgAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 1000x400 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, axes = plt.subplots(1, 3, tight_layout=True, figsize=(10, 4))\n",
    "\n",
    "for ax, dy_sign in zip(axes, (-1, 0, 1)):\n",
    "    sim = make_sim(permittivity=permittivity_val, dy_sign=dy_sign)\n",
    "    ax = sim.plot(z=0, ax=ax)\n",
    "    ax.set_title(f\"size[y]={sim.structures[0].geometry.size[1]:.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2aa83e08-2983-4d8d-b85b-31584c96872d",
   "metadata": {},
   "source": [
    "### Define Objective\n",
    "\n",
    "Now let's define our objective function, first we defined how to postprocess a `SimulationData` to give the desired power."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e673c7d6-e44f-4086-bf98-d201739201fc",
   "metadata": {},
   "outputs": [],
   "source": [
    "def post_process(sim_data: td.SimulationData) -> float:\n",
    "    \"\"\"O-th order diffracted power.\"\"\"\n",
    "    amp = sim_data[\"diffraction\"].amps.sel(orders_x=0, orders_y=0).values\n",
    "    return anp.sum(anp.abs(amp) ** 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56d3acce-0f8b-493d-9cf7-0568720827f5",
   "metadata": {},
   "source": [
    "And then we write our combined, multi-objective over all of the `dy` values.  We use the `web.run_async` function to run a list of these three simulations simultaneously."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "86e4ec1c-89ca-474c-83d1-68c6c3bcbdb3",
   "metadata": {},
   "outputs": [],
   "source": [
    "def objective(permittivity: float) -> float:\n",
    "    \"\"\"Average of O-th order diffracted power over all dy_sign values.\"\"\"\n",
    "    sims = {f\"sign = {dy_sign}\": make_sim(permittivity, dy_sign=dy_sign) for dy_sign in (-1, 0, 1)}\n",
    "\n",
    "    batch_data = web.run_async(sims, path_dir=\"data\", verbose=True)\n",
    "\n",
    "    power = sum(post_process(sim_data) for sim_data in batch_data.values()) / len(batch_data)\n",
    "    return power"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "318b2a19-5536-4332-9903-8f63ce8ae502",
   "metadata": {},
   "source": [
    "### Multi-Objective Gradient Calculation\n",
    "\n",
    "Finally, we are ready to use `ag.value_and_grad` to differentiate this function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "15546df4-05b5-480f-8a10-32a69f434088",
   "metadata": {},
   "outputs": [
    {
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     "text": [
      "average power = 2.62e+00\n",
      "derivative of average power wrt permittivity = -8.43e-01\n"
     ]
    }
   ],
   "source": [
    "grad_objective = ag.value_and_grad(objective)\n",
    "\n",
    "power_average, grad_power_min = grad_objective(permittivity_val)\n",
    "print(f\"average power = {power_average:.2e}\")\n",
    "print(f\"derivative of average power wrt permittivity = {grad_power_min:.2e}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cbb1fa38-7212-48d2-bd3c-6538f39d378a",
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   "source": [
    "### Sanity Checking: Manual Loop over size\n",
    "\n",
    "Now we will implement the brute force approach to computing the multi-objective gradient by the naive approach of looping over dy values and computing the individual gradient contributions one by one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "722f8199-6316-49d0-a53d-2e39c3f649cd",
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    "def grad_manual(permittivity: float) -> float:\n",
    "    \"\"\"Average of O-th order diffracted power over all dy_sign values.\"\"\"\n",
    "\n",
    "    grad_avg = 0.0\n",
    "\n",
    "    for dy_sign in (-1, 0, 1):\n",
    "        print(f\"working on dy_sign = {dy_sign}\")\n",
    "\n",
    "        def objective_fn(p):\n",
    "            sim = make_sim(p, dy_sign=dy_sign)\n",
    "            sim_data = td.web.run(sim, task_name=f\"dy_sign={dy_sign}\", verbose=False)\n",
    "            return post_process(sim_data)\n",
    "\n",
    "        grad_fn = ag.grad(objective_fn)\n",
    "\n",
    "        gradient = grad_fn(permittivity)\n",
    "        grad_avg += gradient / 3.0\n",
    "\n",
    "    return grad_avg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "4662f3ea-ec95-4d40-8ac9-255ca3228b18",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "working on dy_sign = -1\n",
      "working on dy_sign = 0\n",
      "working on dy_sign = 1\n"
     ]
    }
   ],
   "source": [
    "grad_man = grad_manual(permittivity_val)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "274b87fc-b3d4-4d33-a782-d0338b694220",
   "metadata": {},
   "source": [
    "We can see that they match, as expected."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "24aa18da-fa10-4307-acde-ca0ac24bf98e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gradient (batched) = -8.4287e-01\n",
      "gradient (looped) = -8.4287e-01\n"
     ]
    }
   ],
   "source": [
    "print(f\"gradient (batched) = {grad_power_min:.4e}\")\n",
    "print(f\"gradient (looped) = {grad_man:.4e}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2386142b-fe8e-4fa2-b80d-942db85b4d0c",
   "metadata": {},
   "source": [
    "## Takeaways\n",
    "\n",
    "The main thing to note here is that, using `web.run_async`, all of the individual simulations were uploaded at roughly the same time.\n",
    "\n",
    "This means that the server is able to work on them concurrently rather than needing to wait for the previously uploaded one to finish. The time savings for applications with several simulations can be enormous.\n"
   ]
  }
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