DoE-Simulations.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 7,
   "source": [
    "import IPython\n",
    "import cv2\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from scipy import fftpack\n",
    "from scipy.ndimage import convolve\n",
    "from scipy.fftpack import dct, dctn, idctn\n",
    "from scipy.linalg import circulant\n",
    "import pywt\n",
    "from sklearn import linear_model\n",
    "from IPython.display import clear_output, display\n",
    "import seaborn as sns\n",
    "import matplotlib as mpl\n",
    "mpl.rc('image', cmap='Blues')\n",
    "\n",
    "import cvxpy as cp\n",
    "import pandas as pd"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Let's load the [Shepp-Logan phantom](https://en.wikipedia.org/wiki/Shepp–Logan_phantom) and resize it to be $ 128 \\times 128 $."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "source": [
    "width = 128\n",
    "img = cv2.imread('./SheppLogan_Phantom.png',0, )\n",
    "img = cv2.resize(img, dsize=(width,width))\n",
    "N = np.prod(img.shape) # The dimension after flattening"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Here's a function that tells us the sparsity of an image, i.e. the proportion of non-zero pixels it has:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "source": [
    "def sparsity(img):\n",
    "    return (np.sum(np.abs(img) > 1e-9) / np.prod(img.shape))"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "And the next function tells us the progress in a for loop while we're waiting:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "source": [
    "def print_progress(n, i):\n",
    "    \n",
    "    if i % np.max([(n // 100), 1]) == 0:\n",
    "        clear_output(wait=True)\n",
    "        print((i + 1) * 100 // n, \"% done\")"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Since the image in the original basis is not sparse, we look at its Laplacian which is sparse. We also normalize the coefficients to be 0 or 1:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "source": [
    "thresh = 0  # A threshold to zero coefficients\n",
    "lap = cv2.Laplacian(img,cv2.CV_64F,ksize=1)\n",
    "lap_th = np.copy(lap)\n",
    "lap_th[lap_th < thresh] = 0\n",
    "lap_th[lap_th != 0] = 1\n",
    "plt.imshow(lap_th)\n",
    "print(\"Sparsity: \", sparsity(lap_th))"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Sparsity:  0.06317138671875\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ],
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQEAAAD7CAYAAABqkiE2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAgAElEQVR4nOydd3gU1feH37stm957ISGhhF5CE0TpKCgiggiiAoodFRtfK/YKFgQFFQUL+BMLNlBBQaX33kICpJFCerKbbff3xwYkkgAhZXfDvM+TB3ZmduZsmc+ee+655wgpJQoKCpcuKkcboKCg4FgUEVBQuMRRREBB4RJHEQEFhUscRQQUFC5xFBFQULjEaTAREEIMFUIcFEIkCyGmN9R1FBQU6oZoiDwBIYQaOAQMAtKBzcBNUsp99X4xBQWFOqFpoPN2B5KllCkAQoglwAigWhEICgqSzZrFNpApCgoKANu2bc2TUgb/d3tDiUAkkHbG43Sgx5kHCCGmAFMAomNiWLtxSwOZoqCgAOCuFceq2+6wwKCUcr6UMklKmRQcdJY4KSgoNBINJQIZQPQZj6MqtykoKDgZDSUCm4EWQog4IYQOGAv80EDXUlBQqAMNEhOQUlqEEPcBvwJqYIGUcm9DXEtBQaFuNFRgECnlL8AvDXV+hfqn1GghNaeM+po0FkDzEE889Q32NVOoB5RPR+E0h0+U0n/Cq2A1188JNTr+XPQ4nWL96ud8Cg2CIgKXGKVGC++uTaHQYD1r3960QqgoI6LfVQy5LLZO11mx9ihZa37lqRX7aRN1tggEuGu4v3ec4iU4Acon0MSxWG1VHheVm3njze/hZBqotWc/Qa1lVL94nh/aqk7X9dCpmPO3mrULv2ZtdQcEx3JLlztw01aNTWvUynKWxkYRgSZM2slyrnnrbyoqLKe3mYwmKMomasDVLLqzV7XPC/fT1/na9/aKZdTiZ2rcX2Iyc/2cdRQVGU9vc3PT8ONDlxMd6FHn6ytcOIoINDEKykwUG+w3/f6cIo6tXgUefmhDo04fo43vSPeO4XRuwLF6uJ/+nGJSVG6mpKSCkydOAmDOTgdDMfvHd8RWGZn0cdfg76lrMBsV7DTIAqLa0rVrklTShuuHqd/t4bM539kfWM1Qms/Qe2/jw7GdqhynUQv0WrUDLLQjpaTcZOXU12/y4u38NncheAWcHqZMvH8Us0a0cZiNTQ13rdgqpUz673bFE3BxTBYby/dnUVhhj+irhKDv6EFVjhmXFIGXkwXghBB4uv1r07ikCIy331zlGJuULNxyFIAAvY4hrcPQaZSYQX3jXN8MhVpTXmHhthdWQOp2AB5/9QHevq6ng62qPSPaRzKifWSVbS/8fogH734TABHfhdQFExQRaACU4YALsi21gIe/3QWATqfh1t5ReOvsLnTHMD9iguoeWLPaJNOW7WNXSl6tntcxPoiZ17ZBrRJ1tuFobhm7s4sAKKow89m6dEwme7zjrVEdlfyDWqIMB5oAVpukxGDmr7R8diz5GnyC0UU2Z9EtXQn1rV1E32SxUWq01LjfYpMs+20/RVtW2ze4e4N3UPUHl+SBoQSAYz3680T/BDTnEAEvveaCftFjgz2JDfYEIKvQyLS312DOzwVg5xXNiA32wNtdWy+CcymjeAIuRGaBgW6PfE95+lHIz+DZmQ8xrlMUgV66Wt8Iqw5kc8NTy2o+QNrgxBEwGQDoNXEcC8Z1qfbQWz/byqZFi+0PdO4QFg+i5pv8mxevo3/rkFrZa7HayC8zY6ucOrj7651s3pjK5jevq5cpzUsBxRNwUdJOlpOcVwpAQYWJ5i3DqWgWDHTjiphAQnzcznuOzAIDB3NKqmz7aucJOLYLz459iIip4Re+Y8Lp/47oHE5YDTfbiC7hFBRcd347judRtvMfvtrVE/EfzWoV4k2Ev3uNz9WoVVVe62UJgeTlG1h/PA//bPs0Yotgb6ICaj6HQvUonoCT88yKg8x+5j0ANC2SSP5wHD7udu0W/72TauCNP5N5+fF3qm6s/Nzffv8Rbuna7LznON+1LuR7tHDLMR66581TJ6yy7+k3HmDaFQnVPKtmisrNxN/+BdbkrQA8+OJ9PDu4bpmOTRnFE3AxsgqNPLXiAH9tsFeEGnLPrVzbIRh3nfq8N6TFamPmmiPsz7J7EBu22+u59J8ygV4JAVWOvTwm+ILF5FxcyDn6NgvmyTcerLJt7eGTrJ7/GR/+dJBd6XZvpW2ENw/1bX7eFGJ3nZp3H+nHdzvasvKDRXyx/CDp+UZeGNqqRq9F4WwUEXBCKsxWcoqMfPvxT/YxuVcAj1+ZcM4MP5tNYrLY1wlUWGx8uGwvJ3ds/vcAT38euTKeXgmBDW1+jTQP8eSRkKq/9r2i/Fj9hR8nNq1j2Sb7tnVdenBnz2bo1HbvQqdRoaom5qHTqBjXpRkt/XxY+XkAuds2snTvHu7r1Qx/Ty1uDkyGciWU4YCTYTRbGfrOP1gsNj6c0BW1SiCEINJfj4dbzZq9+3gRw176FSklGq2Geff1JtbP8/R+IQQR/voqCTrOQJnRQmahscpwIrWgjLvmrMVitqBSqfj5ycG0i/at8RzlFRYyCuznsNokty/aik6nYsXUPooQnIEyHHABThQaySmuoKLCSmCgOy3CvM7pEmfkGyg22DMF95wsQqPVIKVEq9PSMsj79PSaM+Op19AizKvKNq1ahbYy70EIwd68otOzH74e2rMCiB5u/57DYrXh56enoMDAwaxSQnzclKHBeVA8ASdi4pfb+X7hCjZ8ch/xoZ7nHRNfPXcd67/8HoCEQYP5+4l+qCrH5lq1qJexviOQUmK22r+XNinp/eIqUlatBKD3zSP56a7qVz+ewmK1kZxdRq/bZnP9pKv5+D/rJi5VavIEFBFwAtJOlvPptnQKyi1YbZJnBiYQ6F3z1N+R7FK+3JXJyTIzBpO9OEif5r7c3DXGZW/8mpBSsmjrMdalFAP2YGCgp91L8HZTM7lbDN7uZ9dFyCup4IWVyahVAn8PDRO7Rl/y04eKCDgpNptk1cEcxkx8heffvJ/7+8RXe5yU8vSKuy+3H+f+e2ax4MNHGdkhqtrjmypLd6Zzx5Q3wGaFgEh2ffkAUQHuNYrfO38fYcajs/nm0ye4smVwtQHGSwVFBJyQYoOZ6+dtINBXz0N9mxMX5Flt+q/NJrnr611s3JUFQJe2odzZI4YWIV7n9BiaIidLKjicU8qUjzeT9udvBPe8kgGXxTJnVPtqb/DsIiOpeWXMXJNCYUkF30zpgU81nsOlQE0ioCzJchAnS01kFhhJSc7FYpX0jA+sVgBKDGYyCgzsS80n7UgmaUcy0WnU9IwPvOQEACDQ242e8YF06xCGaNaOvKw89qbmk1FgoMRwdoHUUF89PZoHYLbYSEnOJbPASH6pyQGWOy+KJ+Aghr2/ns3rDrNx5ihCfN1qnLp7c3UyL73+Pd+9dSudo+15AjqNCnfdpT31VV5hOR083Hq8gFHTFvH049fVmHVYVmEhu6iCHtOW0qNPy/MGF5siiifgJKSdLOf/dqQR4e/B4EFtCfTWVSsAhWUmlu5MJ6fUTK/hlxEb4IGvhxZfD+0lLwBgnxY89X7EBnjSa/hl5JSaWboznaLysz0CTzcNgV46Bg1qR7ifB/+3I420k+UOsNz5UESgkVlxOJs773iNke1D+PyWrjWOTzMKjNxxzzuUVVj45Z7LXGLO31E0D/Hkl3suo9hg4Y573yUj31Dtcb4eWr68tSvXtQ/hzjte4/cjOY1sqXNy0cMBIUQ0sAgIBSQwX0r5jhAiAPgKiAWOAmOklAXnOtelMBzILa7grv/bSZi/O1fE+9E3NrjaJBaTxca0H/aRX1LBNR2C6RrmT8twbwdY7Hocyiph64kCftyVS36JvYrx7Zc344aOVWdQsgqN/H00l9XJhWQXGph3Y0eCLoH4SkMMByzAw1LKNkBP4F4hRBtgOrBKStkCWFX5+JKmrMJCbnEFfyzfRnmFhTGdoqsVAKPJSmGZiRVrktl7KJfRHaIUAagFLcO9uaF9FHsO5rLxu5VsXLiYxZszKSo3V+m/EO6nZ0ynaMorLPyxYge5xRWUVdRcYKWpU2+BQSHEMuC9yr8rpZRZQohwYLWU8pzrO5uyJ2Cx2hj09t/k5JTxw7S+BHrp8KuhjPYjP+7n82+28sMzVxMX5EnwBdQKUKiKlJK8EhP7TxQzYvJM0LmjConht5evo2ucf5VjC8tMnCw1MfzNNUREePPr1D5NuvlJg64dEELEAp2BjUColDKrctcJ7MOF6p4zBZgCEB0TUx9mOB0Z+QaO5pfh6akjobkbkQHu1Zb5LigzcehEKWVGM83iw4nyd1cE4CIRQhDs44bJ4kWLQQM5ejgT84FNLN3fC41K0CbSB21laTM/Tx16rZoWCYHYpGRjaj6xAZ5EXmKZhXWWPSGEF/AN8KCUsvjMfdLuZlTrakgp50spk6SUScFBwXU1wymZ9U8qw297nReHJvLdHT1qrPO/La2AoeOfp3WYJ+uf7H/OCjsKF0ZkgDsbnhrAY5MvA+CDGXO48pGvKf5PXUW9Ts33d/TghaGJDL/tdWavP9r4xjqYOnkCQggtdgH4Qkr5beXmbCFE+BnDgUs2BCslYLMiBNVms5VVWHjlj2RKjFamvXAPQ+NDLum01vpGpRIMbxlK2Uv3M/fzTZjKymo8TgBYLXy3KpkSo4Un+ydcMmJ80Z6AsCdrfwzsl1LOOmPXD8Ctlf+/FThHNcumiZT/FvjAzbPavHaL1UaJwcKcT9ey/XAuTw9qSasIJQhY37SO8OaZQS1JSIxCaHVYrLazmrRCZbUzNw9y1q3iy5mfkltc0fjGOoi6DAd6AxOA/kKIHZV/VwOvAoOEEIeBgZWPLykOnyilzcM/oFIJ1n3+CAmhZ8/xT/1uL4NfX80vL13HF5O7O8DKSwchBIvv6MGPL17LwFf/5IHv9551TEKYF+u+eIy+E8c6wELHctHDASnlP0BNvuuAiz2vK2OzSY6fLOfgyRLMFWZah+hJjPSpckxRuZnsIiOZ+eVIKWkV5k2Al9J0s6GJCfLAU69BSsjML+dQVgmhvnp8PezJWp5uGhIjfbiqfQg7O/bieEk5vrlaYgI9mvwQTVk7UI+UVVhoff83+AX6sOHZQbhpVWdNOX225RhTH57Pp+/dw5DWYbhpVE2uBoCzIqWkwmJjxYETTLxvLrNnTeHm/1RatlhtGM02es74nZLCUva9M9LpSrJdLEp5sQZmS0oBy4/kUpqRjqdPq7MEoKjczJKd6RwtqOCaO0bRJtjXoV2Bz8WetCJWptau/dh/GRgXdM66gI5ACHsn5jZBPgy/fRR7sw3MW5/KTZ2iTqdva9Qq9IDZZKE4PZ1Zf6VwVXwwSc39z31yF0YRgXripVWHWD3/MxAC0aZ1lX1SSk6Wmpj+5KcMGD+MpU4cA5BS8sHmNL545YOzegPU4iSkPnE3b0f9OxRyJm+nZbg3n03owsgPN/LBzBUMWfII3npNVRsFkJPCrCfeZeddt7C0ufN+ZnVFEYH6xMOXV1+9nd5RAacLY1ptknuW7uavzWmn+/U5K0eySxn/4UaS96WBRsejL95Fr6jaNf1cm1bIzKfm8uXSLazfbc8Zi4n04fMJXdE74+rH8iKufmMNV3SL4r1R7VGrBGqVYOkDfVk7qi3/m/6hoy1scBQRqCNGs5WicjN6rRq32ESGtQqrUstOSsnqDcfIWf8nhMYT4utcc8/Fhn/rFKbkl3FwZ4o9t6FZO0Ylhtd62jLMS8/MZu2xGA0c3n4YclNJjmpN1jX2ZdPOVNUnzM8dQuPJ+nslf9r6I69vB9gLtLaP8cXPU8uMuLboNGqyi4z4emiddghXF5TAYB3540AOox7+jJeeGHl6bHlmc1CL1UbbR38mPyefHe+Owc9T61SBptu+2M6yL/8AIKF7R5ZPuxyVEAgB3npNrXPpLVYbJUYLUtq9oF5PL+fkxtUQEMV1Nw/gk3GdG+BVXBxlFRYKysx0uu8rgiKC2PPa1VVer9UmKTaY+WJHOk+//B3fzppAv1a1a6TqTCiBwQbCYLVCTip6rQr//ywMSskpY1d2IZ07hOPhFk2gt85pfklOFBrZnJ6Pm1ZNp/7270W3ViEEeOrqNCWmUf/7PthskusGtmJrjD2optOo+XFPJt2jA2rdSr0h8HTToFYJhg/riNFs5ed9WXQI9SMuxJ7XoVYJ/D11uKkF5KTy2bZMewn0+CCn+RzrA0UEGpD31h/jk9c+ZvXip+nYrHZj64Zm/fE8Jk1+lXfff5R5Yzo0yDVUKsGb1yQCiQB8uvkot0x8mU8X/I8R7SMb5Jq1Ra9V8+n4zuw4Wki/m57njifv4PXhidUe+92sj/guLIGDn9+F3rfpiEDTXTfZwBQbzExesoOf9uUyc84j9I/7dxFU2slyRi/YzDfLz85MczRF5WYmfrmd3w7mM3POI/SNbbzFW/3iQpg55xFWHDjJ5CU7qi0D5iiiA915e/ZUrDbJ6AWbq5QeGxRvt9un6xUOtLDhUETgIjGYrHz7+Z/sTc1nUvfYKuW/TpaYWPnhYor3bAafkCoxAkdiNFnJLzXx/bJtZOaXM6l7LM2CPBrt+s2CPJjUPZa0k2V89/02CspMGCuDko4m0NuNW5NikRJWfrSkSkXi2GBPJnWPJSYuGGxWyk1Wp7G7PlCGAw3IsCk38vLViYT4Or42gJSSmxZuYd+BHNbNGu3QegWfjOtCzvC2DHnlD9q1CWXp5G5OlUdwTk6m0XXq/zFoSHuW3HZWjM0lUTyBiyAlp4y9WcXEJ7Uj6YxosdUm2Z9RzMGCYsIvH8iw9sHEBHk4TRDpeHoROcdPEO6nd2hNvWAfN8L99OQcz2LHrgx2HCsix0lW7XWO9CS8zwAOFpRwILMEq+3f2bOurYIJ6H4FtuP7OJZRfI6zuBaKJ1BLpJSM/3AjB3amcuijmwk8Y/GP0WSl/1M/4h/sz/aXhqBtwqWq6ov8DX/Q/6a/efa1e3mwb/Ut2BqT8V1iGN0xis5PrKA4v5hDc0efntKddW0bnugXT6tbMx1sZf2ifEsvAqvVBlYzKpU4azrNarFis9lQV7PPUexJK+LhH/bTLymap+/r5xSeibtOzdP396fbzTeCxYTF5vh8FbDPaGhUApvVhtVqPWufWiVAqDhyIJ0Hv9/L3nTX9wgUEagFNpvEYpX2m1ujrbKO2mqTWGwStUaNRuP4m+wUFquNHw5l88lL7zOidRDTrkhwivRdd52aaVck8PRVrUBnz6KsrtiHo1Br1KjVaixWWWVIgBCg1WE+vI2FL73PytRcxxlZTygiUAt+2ZdFu8d+5q4h8aybNRof939HUy+vOkyfF1ay8LEBLHvocqeYETieV06nJ3/ljfl/O9qUGukY5ceaxU9xJNduqzN0BVKrBD8+3JePH76S3s+v5JU/Dp/e5+uuYd1bo3ngubsdaGH9oohALUjON5Dzz2808/EgMdKnSorptqMFpG/aRKtgH+JDvZwi2m0wWclY9xcU5qBv2xMfnfPk7Z/Cx11Lhxjf07YanGDqTQhBfKgXrYJ8yNi0gVU7sziaW0ZZhQWNWkVipA+9Y5wr+asuKCJwCTD0pkEkf3Cj063vdxV2fPMDnce+yYbUk442pUFQROACKCo38+nmo2SXmhl89y3E+P2bYJORby9MER3kyXWTr8VL73wTLnqd+nSevLMyulMYQyaNYtmBbFbsy6o6DncQPu4aRky+jtDL+kFxLhVnxCzi/D0ZfM+tnCgxs3DLUafKfqwtighcALnFFTz0yIeknyznq4ndiA/1Or1vR1Yh06fOpFOkF5+M61xlytBZcIahyfkY1jacT8d35t3FW7l7zjqnCBIGervx6fjOPHxD27P2JYR58dXEbqTllfHgIx+RV+IceQ4Xg/P9bCnUGYvVxr3f7CG70MCiufeTGORz/icpXLIoInAeisrNFJabQVb9ZbLZJIXlZsrMFghLwMeJagRYbZJf/zyElJJBE5OcIi/AlfHVayAsgXKLlYIyE77u2tM5IAHebhAaR6nRQlG5+XT1YldCGQ6cA7PFxsA31jDo/gVgLK2yL7/MRIeHvmXBP8c5+MXdDE8Md5CVCg3NtW0iOPjF3Xz41zE6PPQd+WX/Li56+arW7Jp7E2PfW8ugN9c4xTCmtjjPz5cTIoGTucVgLCVh2AgGtA44vc9qk5RlZVHeIowQpXlok0avU6PXqSkvN1OalYXtjKCll94ecC3OL8Zk1OMEhbpqjSICF4BnXCv++l8/3J0g005Bob6pswgIIdTAFiBDSjlcCBEHLAECga3ABCml6VzncAXOjK/PW5/Ksu1ZUNxwvVYzCwxM/3k/ZkvN7uUzg1qe1eGoKVB49Cg3f7aNKb1iGJRYbWd7h/DK9e3Y1DOKx37aT58EP27vEedok+qF+vAEHgD2A6e+ja8Bb0kplwghPgAmA+/Xw3UaFbPFhsFkxfafMZ6Uko9/P8Lhn5aBuw/uDVA912i2klNUwY+LVoCpmjRaiwkqyrm63aPEBXvipm06XYzc3N0oLclj5fsLCfCa4lQi0KdFEIlh3iS8vYCDSa2qiIDeQ4/WTYvBbM941GpcJ9xW19bkUcAw4CVgWmWn4v7AuMpDFgIzcEERmL02hTcXbsKQvBvPlh3PPiCkOatm31bv7auNZiuDZv2NzSbZuPD+ahN8PtySxrwZc5j6ynJejI3kn2cHO7RISH3hplHx5zOD2ZKRxKS733G0OReMm0bF6hlD2JddTLsHv2Pa+K5OsSz6QqmrJ/A28Bhwqjh9IFAopbRUPk4Hqq0oKYSYAkwBiI6JqaMZ9U9yrgHDnvW4t+tFu07RZzfjcXOnWbBnvSYHZRYYyC6qQEpJcKAHzUM8qy35PTQhiK972Xu+6nQa9p8oJrvIbkeYnx5vJ8xavBCEEEQHelBqtIDKueMv+fll7EkrItxPT6C3G9GBHhQbLJTs2czh3OoLlTorF/1tEUIMB3KklFuFEFfW9vlSyvnAfLD3HbhYOxoUnTsrZgyjTaR3revvXwxP/HKAZQuXs3Hh/TUKAEDfFkEcmDUCgCKDmdZ3LsZ6zF7U9MmX7uT+3k1jrOrM5Pz9G5dv+IuXXr+be3o3d7Q5daIuPxm9gWuFEFcDeuwxgXcAPyGEptIbiAIy6m6m49CoxOmbcX9GMYt3Z3FZh3CG9YzGXVu/wmCx2sBUjvqMa1bHmcVMvNw0PDjpMv7Y1ZztS75m8Z8pFBosjBicSIsQdzROvF7AFXHXqXnw7v6s2pHI7q+XYnaCNQ515aK/xVLK/0kpo6SUscBY4A8p5XjgT+CGysNuBZbV2cpGxmqT1S5g+fVILrOfeY8RicE8O7gVHvWUJSjlGddT1y7QqNepeWpgS166ti1odKQs/5E5L3/Knd2iuadXXKN4MPWJzSaxSc7K0HQWPNw0PDu4FU9fc7bLLwDU9u+EMyyAulAa4hvyOPYgYTL2GMHHDXCNBuNAZgmdn/qV//t6Y6Ndc09aMR2fWEGrcG/++PiBiwo2tonwYeUXT9FxzA1gMnD1y78x5pPN55xidDZMFhujPt7EsJd/A7PrLchpFuTBqoWP4eOupfNTv3Ioy7kb0J6iXkRASrlaSjm88v8pUsruUsoEKeVoKaVLfZqFBhNpq5ZDST5uCR3QNcJUz4kyIxmrfsZHr6ZzrN9FJSX5emjpGufPle3DUDXvRNGuTWzefAyrC6Ww2aRky+ajFO3ahKp5J6IDHN+q7HyknjSSkW/AbLHhqdfQJc4frUqQ9scKig2W85/ACXAtX7ERmXTPNRx+/8bTfelchen9Ezg0fxxebbo62pSLxrttEofmj+PRK5x/mm3hrM9pN2kB6fkGR5ty0bjmXFIj4O2mxrsyEajYYObXgyfILTXTe9I4onwbr2tPbdFr1QhArVZTlFfA59uO0zsq0KUyC9UaNV56DW7VrH7MyDew5mjVTM04Hy96xgc0asJUMz8Pek8ez5b1R6g4dgCbC3lc/0URgQsgp6iCKQ98wPDbR/HTXb0cbc6Fc3Qnj963k+semuxULcHrwrrjedx75xtVtsUMHs72F4acncvRgLQM9+anu3pxs4eOnxccaLwLNwCKCDRl4jozZ/pA9p4wMGT2Wt4b3ZEWYV7nf54TIaXk+d8P8c9+e2nvuDBvPv54epVjjhdWMPS9tUwf3JL+rUOqO43COVBEoBIpJSVGCyeNjbfWSUpJscFCQUXDXNMnwIfr20eRUZTKps+WsPfKWEJ83PBx17jEWgOj2Up5hZWvVh4ha82v4B9BwI39ub5DVJXjNhw5yXOPvstfre5xChHwc1dDUDNKzGaKDWa89c79fisiUElZhZXuT/9K9oHDYGucsteF5WaS/vcz+UdSGv5iUjJx+hKCW7Zg80tXuUQFnM+2HuexmSvhxBGISmTje+NdonbDlB6x3LjoLsbM20B+fjmbXxjilAVoT+G8ljUyVpskNyMXLCZih15D10jv8z+pjthskvy0EwDEDr2GdsH146qrhKBPrzhOllSwISWfkgorsUOv4eiWneSmZyOdMIh1NLeM1Pwy2rSPQq0WrE/J58ed2XB0J77drqRt+0giA9xP9wU8kwAPHc2HDqPCKtlw5CTtIn0b96azWliZkovBZKVtlA9eeg3uOjVFRUZyM3KdPmioiMB/iO7Skc0zBjVqpl2rXp1Y90T/eutdqNWo+GxCFw5mldLrplcZeddotjw3mG4zBKn7j9XLNeqb534/xPfzv2Hj4sexWCW9x71iL+mmUvPFtCu5LD6wRpe6Zbg3W2YM4t5v9nDVxDdZt/h/jTsbYixl+gOzCOw1gP0zr0WrcV7XvzoUEfgPQth/ScGey//e2lQO5ZTz6DO3MqR5cANds/6blwoh7Gms0oaUErVK8PLY9mzOiOWxn/YzuHUgN3SMOt9pGg0pOT0ME8K+IaLfVdwypAXNg87f0en0fpu1UUt8PdinOc1D7mf23F+RLpQqfCaKCJwDm4R3/28nJqOJ5LmjnaKRZ20QAtB7I4SgwmxlcOswOkb40+amd0kZ0sspRFi0aF8AACAASURBVMBmk5itttO2WiubvqL3YkDPGB7v38LRJp6TpOb+tI3y4eOvtznalItGyRhswsQEebBx4f00C3Sn1QPfOWUb7T3pxbSa+h3Ngz35++N7mfTpFu7+chv/fDKVpwY4twA0FRQRaMLotWpahnvjoVVTtGUNhRUmdGpBVKf2+PvoOZhZ4pTts7y8dLQM83KJmYCmgCIClxgBXjq2PD+YMV3C6Dn2ZVYczHKoPe2ifDjw7khScsu4/Pa5LLgtiR/u6uVSNfpcHeWdvgQYFBfE9dMm82vyST7ZfAyJvVgKhhJMVscEs4wmKws2HeX3A9notWp7MM9QjFolGmXlZmNhzc/m5T+SWZuc52hTaqTpvNt1wNHz5lLKKg0t6ptOsX58dGNHVmxM4+E3V1FeUZkMVRlRb+zXL6WkrMLCw2/8zlNf7/m3AIdK7dSZdRfCmTkBQgD56cybMYeXfz/sOKPOgyICwGt/JHP5i6uwZSY75PoH1+8gacbv/HGg4foYCCH47I4eLHrmKq59by3f7crhhy+eYXVyAf1m/kVuceOVfXjut0OMmLOORc8OY/Kg5nR/7ndiAj345aOHiPB3/hoCNZG/fw89n1/J4u3HUasEX93bm7fnPgxeAed/sgNRRABYvT/HXkjEP4KwMHumYLHBzIlCI6YGyuuvQk4qqct/YHduw1aiSYz0oUdMIGlH8ygqMxEf5EWpwUzygSzM5+mhV1ZhIbPAUO1fWcWFFc8orzzHltR80o+dpGdMIG2CvElZ/iM+ejW9EgKrzQh0dgQQEhEAHr4cXfEj/6QUAdAmyof+cSGgdW5hc713vKHwCWbdnAlEB3qgUgle+fMIH8z+AQpP4Nm2u6OtqzeCvHTsmnUdvxzMou242bz+7Gjm39jpvGm23+7OYOrTX1W7b85LNzKuS7PzXvuXAye4Y/qXfPDyWIbekuSypdH/i16nZs0T/dmd0ZXht7ziaHNqTdP4FOoDlb2IyKmboajcDPkZNBt0Nb06hlfbBKSuuGnVDB3RjW27o8j569d6P391qFQCXw8t7QJ96TqkF5nFJv5IzgYg2suTrnF+VcblpUYLq5NzOJxnpOuQ6mspHMo18vPeLK6ID65WTMoqLKxOzmVvdhldh/SibZAv7jo1fx7KYWd2CV3HjaFHpG/DvOBGwsddi59eB8L1nGtFBM6F1o0v7+pFm6iGyUP30mtYfFsSv+/PZkwjicAp2sf4svLBy7l23gbefnI2AOH9rmb3q1ehPkPvsouMTLj/A4beei0rH7y82nONXrCZd177kq1LHqtWBE6WmLj5gY/oO3rQ6XPkl5q44allxLeLY/OzA10+IOjKKCJwifPiVYn81W4aT79SfWX4EB835r91B4mBNQvhs4NaMqz9RJ78ZT/xoV48N6QVaw7lMvPPIwB4u2t565UJdAn1b5DXoFA3FBG4xOkQ40tcsAfP+Z4dwS6vDPgNbRV2zuSdhMrsvsdn/80mXy8e7tuc346cZN23qwDwbdGaj8d2wrPSSzCarJRVWHDz8sDbu/7auClcHIoIKFSLxWpj2Htr2bPtKAATb+rO68Or77H3xC8HWbhkI7bj+8hXqWlxRxE3j+nGriXTANCoVVXKqN/19S7WrEvh9+evIcxPrwwFHIwiAgqoVYKky1qgVgu2Hi0gOsCDYG8dx4/lY8k4TFi3XhSVm9mSUlDt80sMZoIjg8nOcgONGyFRISRFexEdWH1V5uPZJRQePUqwj1uT6Kbs6igioICHm4af7+7FtqOFDJrwMvc/fTvPDLKv4NPHJbL5hSF8suUYg8Y9V+3zX5k1lVkjhtDi7kK8/bzZ/tKQJpX629SpkwgIIfyAj4B2gAQmAQeBr4BY4CgwRkpZ/U+IgtOgUglUArCasdokKiF4cWJXdmWV88TyA2jVKu555q5qn3s4z8jDP+yjIjsTH//WqFWiWhf/QGYJczceI6llMFd3GVFveQLp+QbeWJPCb38fqZfzXWrU9VN4B1ghpbxBCKEDPIAngFVSyleFENOB6dj7EyqcB7NVYrbY0Kirv4kazY7KhqxjO0XTI7KcrhPe5apxg1k4vjPqMzoi2yqPG/PJZlbP/wy0bmi07Wo878bMk3z28gd8uuB/jGgfWW/2pheUs+jV+fZkfQ/fRu0/0BS4aJ9NCOEL9KWy4aiU0iSlLARGAAsrD1sIXFdXIy8VXpq7hk5PriCjwOhQOz78ZA3tHv+ZlJwyIvz1rP34XtpFeZP48A/sOl50+ridx4tIfPgHVi9bBx6+fPzBQ/z0yBUNklh1IQy+czz/LHqYZkHO2yHKGanLwC0OyAU+EUJsF0J8JITwBEKllKcWqZ8AQqt7shBiihBiixBiS25ebh3McH0C9Do8OvSGohwyN66jwtw4Jc//i7tOjWf7nmAoJWf9agwmK3qtmjZRPiQGe1BeUs6+/CKOZJdyJLuUvSeLKC8pxz0klIAOSXSPCqR5iKfDvJjECB/aRvnUW8v4S4W6iIAG6AK8L6XsDJRhd/1PI+1rVKtdpyqlnC+lTJJSJgUHNUwBT1ehUzM/kt8fw8AbBzrUjlbh3hyeM5rRtw46a981bSNIfn8MH6xMJenGV0m68VU+Xn2U5PfHcOSDG9kz81oiXXgF4KVMXSQzHUiXUm6sfLwUuwhkCyHCpZRZQohwoOHWxzYR1CqBu06Nm4Mj6qpKO6orqKpRq9CoVdx2ZSy/h9hHeEPaBl3Qr26JwczXuzM4kmdk6L230foc2YcKjc9Fi4CU8oQQIk0I0UpKeRAYAOyr/LsVeLXy3+rzURVckkndY5nUPbZWzykoM/PwE5/Rd/Qglt3Zs2EMU7ho6jp4uh/4onJmIAWYiH2I8X9CiMnAMWBMHa+hoOBS/N+329hxKI9Fk7q5RL5EnURASrkDSKpm14C6nPeSRkpOlpkIKDPh7+mYvPpgLx1Etqaowkx+qQl/T61TpvZKKckvM1NUYYaoRIK8nKO/ouXQZvYd2U7BjZ0I9XX+jEgljOpsGIoZcu9HJPTswvqn+jdqO7RTTOvbnCndYxjyxhrMZitbXhhSJfffWSg1Wujx5C+EhPpw8JOJTaZISWPj/L7KJcSgNoG0uvY6MBnIzytp1HZaZ+LppiHQS0dJcTkFuYUXXYhUSsnOY4UsO5AF5vrPfbBJKMgpoKzMRJCXzimFyhVQpNOJuDUpltHto2iR2jQmVKw2ydj31nJi9XJHm6JwDhQRcDKccexdZ0LieOKREQyMC3K0JQrVoIiAwgVhsdowWaqvSKzTqM4Zu9D4B3F3r9jzFjOtDRVmK0azFTd3N9zdnSMg6KooIqBwQfy4N5O7Z62udt+8h/vV64KgC+GhZftYsfowPz59FZH+7vXe2v1SQhEBJ0MloEOXZpjNVvamFxPqpyfczzHpuJ07RpKdV86+jBL25pTj4199pt/+nHLi04pICPVqtPbtKSeKKTh8kFDfqwhz0PtTI1FtCWke5TKzFa5h5SWEm1bNj3f1ZH9GCX1veYNbHriJd0a2bXQ7NGoVS25LIiWnjB63zuaq8UPY9+bwao8dv2grr72+lG2fTSUuxLORLXU+xo7rzezr26FWCdLzDY4257woIuCEaNQqu3trrsBiO3dnoIbCZpMs3p7G7hPlTLz3Oq5tHVzjuP+uy5oRGTCC9zcdp0O4B+M6x1zS7rlKJRyS33GxKCLg5NhsEovVVmO1nga7rpTMWLSN8pJyDs0dc872YP1ahdAjNoD4u77C28+bsZ2iwWafIqzvZqdS2guZCCFAo+PSlZr6w3Xk6hJlyVcb6PjECg6fKHXI9Y2p+0l6cgVv17J019Jd6XT833Kyd2yvV3s2puTTfvpyhrQPZc37txOklCyvM4oIOCluGhUerbtAWSGZa36j2HBhTT/rHXMF+dn55JSaa/W07ZllZK9ZAb7BRDcPp75GB2kl5ZxYvZwIHx0dYnxx0ypZgnVFGQ44KXEhnhyaM5qnfz3EJ6/Md5gdbgkd2T17ND7uF/FVUWtY9sookpr5K9V+nBjlk3FS1CqBp16Dl5tjfumEEIy/ug0pOaUs259Jz4gA2kVX3zR01/EiNmXlM6Bfa1qEef0buxAqvHXaehGAsgoLv+zPYm92OX1vv5k2SmGSekMRAYVqUasEzw9txZHsUpLGvs7QW69l8W3VrRqHF1YeYuXnP7F1yWM0b6ApwsIyM1Omf0n3YX349f7eDXKNSxUlJuDkTOoaxacfPsrMv44w4bNtGEyOKUL6+2976DdzDfszik9v25deTL+Za2gb6cOS9+4mVOkm5JIoInAKm5XicjMlhtoFwBqa2GBPhreNYPeBXJYv34XZ6pi8AevhLexY8jVpxeXYbJLCMhMH8ovZ8ccWWoW4M6RN2OmGo/VNicFMqdGCJigMf29FaOobZThwiuJcet/zKUkDuiju5nkoKDfT9bEfaJUYzv4v7r24oOEFYrNJbvhoE8mHc9gwcxRBigjUO4onAAxoG0qzQVdDUTY5OY6Zjz8XAriyezSdeyTwT0qew3IGTqFRCVq3CadbQiBhfvoGj/xnZ5dSkFNAkLcbvh6us2JwT1oRvx/JaZCCKvWJ4gkAj/ZLYEqPZjSfnOloU6pFpRLMHtmW9HwDHca9Q++RV/LTXb0cZo+vh5bl917WNGsf1BNWm+SmuetIX/ULDisRdYEoInAuLCbu/3oH/dqHMb1fgkPzwU/fcFI26ncqyNuNl168jcX/HGfP0qVn29OAbEkp4L31R7nu8lgSRrZGr3Utx1VKIDCae6dey/CWzttgx7Xe1UZEp1GBmyfblnzDB0u2YbE6Xs1VlQ03NSqB0WTFamt4m3w9tNzTuzk39olp8GudwmaTGE1WvjmQzbJ3P2VIfBA3d23m1NmBFWZrtUVX1P4hPHZlPD3jAx1g1YWhiEANPDUggbVfPI572x6ONuU0IT5ubJl3KwPbBtPivqWsO5LnaJMahKN55bSZtowPPvjN0aZcEEazlSHv/MPgJ5c5/fi/OhQRqIEgbzcSwrzQezhPwQqtRkV8qBeBHhpKt/9NrqHC0SY1CBVmKwU7N4G04d/tCnz0zh0MlBIO78/EknEY365X0DbMtWoqKDEBBafl+vFX8v4NHdC4SG0Cv7ad2TNrBHonHrZUR508ASHEQ0KIvUKIPUKIxUIIvRAiTgixUQiRLIT4qrJFmUI90jnUnzGPTmFTWgnv/H2EMqODVhieg5GtQxjz0G0s3XeCTzcfrbFI6ZlYrDa+3HaML3ZlMnbqOG7rGolOo3KZAiUqlQqdWoXaRew9xUWLgBAiEpgKJEkp2wFqYCzwGvCWlDIBKAAm14ehjYWU9oIa9V0Moz5JjPRh3pgObE0+yYyXllLUwFmONpusdRCye/MA5oxqx7d/HuHRd9acVwSklJgsNqbP28iXP+/jnZHtuLyF80bUmxJ1HQ5oAHchhBnwALKA/sC4yv0LgRnA+3W8TqORtnU7XZ6GF25qz1WJ4Y42x+FkFhi4fs46Ug5mNOh15m84yvwVh5l1z2W0CfRxmSFAU+CiPQEpZQbwJnAc+81fBGwFCqWUp/zTdKDaWtRCiClCiC1CiC25ebkXa0a9oVYJQqNDQedO2u8/sT3z36w8s8lMZqGRonLnWlcQGeSJV0ws+aUmTpY0TJDQYLJycNUazJmpiPgu+OjqN0hnNFvJyDew5VgxGcdySIrwp02Uj8sMAaqjxGAms8CAn5+e0OgQ+9SuE1OX4YA/MAKIAyIAT2DohT5fSjlfSpkkpUwKDnK82+fppmbjc4NY/NqNoKoa2DEd2krXCe/yxPIDDrKueube0J71r17L0OeWM2reBmwNmDfQd8wQUhdMICnWv17Pu+N4Ie3GzyYhxIODc28kOtCjXs/vCOZtPEaHCXN5cWQ7NswYhKeDakJcKHUZDgwEUqWUuQBCiG+B3oCfEEJT6Q1EAQ3rR9YTQgi83bX4uf0bx1QJuH5IIn+F+HD4l58odjJP4FTO/uABrZFS8vXONLpHBjZI2W8PN02t8/ZVQjB6QAL7M0P4fm8GumoyLo8VVNBzeB/6xPi71LqAU+zPKGZ7dgGXX96CmCBPhIBioxXy0/HSavB2ge5IdRGB40BPIYQHYAAGAFuAP4EbgCXArcCyuhrpKDRqFW9ek0hyt2i6rfrT0eZUi4ebhgU3dWJtch7Dx7/A4y/fx/QBLRxtFmBf8/D80FYczyun49iZUJR91jHxw0aw+dmBLrsO4aVVh/l5wXds+Wo68aFejjbnorhoEZBSbhRCLAW2ARZgOzAf+BlYIoR4sXLbx/VhqMKF8cHSnaxPPsn7YzoS4e/uaHMACPTS8clbkzBVUwuhuY+XywpAU6FOswNSymeBZ/+zOQXoXpfzOgPFRivFBvM56+07E24qNQREUrRnC3/t2ULxNW2JqN/h+0XjqddwXSP3KlS4cJS04Rr4ZO4yWty5hJScMkebckG0i/Zh75f3c8WEkY42RcHFUETgP/i764gdfDX4hmBK2Y35jCSXI2mFbDyST2GZyYEWVo9eqybC353hHUOI69ef3TmF7E0vvugZAykl+zOK2ZVdSPwVl3NZgpO4FU5MqdHCppR8TFYbsYOuatCKS/WJIgL/oVWEN1ufG8yYG7qdtW//998xdPzz7EgvcoBlF8bk7rGsfWoAj324iWEv/1btOPxCsNokI95czf3v/sOa6f24r3fzera06XE8r5wht71BidHC1ucG0zLc29EmXRCuIVWNjEolquR/B3rreGLGRJb+c4xDP36PxHlTioUQ6DQqXr29G7tPlPPQ93uxSft05/R+CTQLuvB5eKvVis1mQ4jGKSLiSqTmlPH6miNEBHjwxLO3EeClI7PACFZ7npwrJTspInAB+HvqeLRfAlq14LkfHW3N+VGrBDd2jqFzVgk9bnkHSvPBauaG9k8R4adHqzm3A2i1SSosNjRaDVqdVhGAakg+WcqS1+czY9ZDPHB5PIBdBFwQZTjQhIkJ9GDdp1O55t6bQUrGvriCy1/987xl1T/aeJSOj/3E67d14Y/nrsLtPKKh4NoonkANtAzxwLdDd9KKy/HM0xATWDnnLiW7ckqI9fckOtDdqfvQ63VqEiN9uKZdMH92vhyAsjITKTlluOtqTmXdn12OxWyhbbCvyybANCY2myQt38DevCKQjukLURcUEaiB+3rHMalbDN2eXIHFbGHvrGtP75vxv3m8GNuWgx/cRICX85dLGNk+kmveuwGAnOIKOt65CPLSajz+nscncODtkfY6iwrnpcJio9+MFfZqSGbXq/akiEANaNQq9Fr7CkKT0QQSrowJZOvUSfz043YsBoMThwerolGr0FT+8Pt5ahk/vg9F55jmvKZVMPpzeAqXMkaTla93pXM4z8jwqZO4MsZeQLTCUAF+YQwd1Ycb2oU62MraoYhALegU68eiZp3pkZrP4Z3JjjbnovBx1/Le9e0cbYbLUlZhYepLv9A6qRXrn+wPcLo/ZEBsMxbd3OW8gVdnw7WsVVBQqHcUT+AcCCA41JfS0gpySyrw89DipdcQHOxJTkgQ+aUmNCrhkktgFWpPUbmZvBITWP4d95cYzBSUmfEN9MXHxw1XnE1VROAcaDUqfn+kL6k5ZXS483MmjL+Md0e246uJ3ThR2J4+j39Pj8sSWHZnT0ebqtAITPhsK39//xfkZwAdAPjf8oN8sWQjq98YRVyIp1PPFtWE61ncyPi4a+0rCXOPUVBqD6Z56TV4u2uoOJlLQZFrJogo1J6CQiOU5tNi2DUM6xEFQGFpBeSk4qXX4OMCBUSqQ/EEFBRqg18YPz3QhxBf52lKU1cUT+ACCPZxY/asKUQFejDqo00cyf63COnurUcY+eFGdh4rdKCFCo3N4ROljPpoE6v+dK66kxeDIgIXgK+Hlpu7NiPUS8sf8z/jeGE5Qgg0vgFwIoXV8z9ja7YiAk0Vs8VGqdGCTqdC4+OPEIKjBWX8MW8RxuTd4Bvq9BWFz4UiAhdJgKeWbe+O5unnJzraFIUG5pf9WcRPWczEvs3YPnsM/p7/jv0nTLuZXQsmExngHKXcLgZFBGqLlPx1rICDWaWE++lpFeRazScVak9OmQnT/o0E6HVEBVRdLxIf5E50oIdLp1i7ruUO5O2n59Jn2tcUG5yvB6CCQm0RztBzr2vXJLl24xZHm3Fe9qUXs2B7Bgu/2oTFYCB54SRKDGbmbjyO1SZx16p4pG9z/Dydf1GRwvkpKDMx868UDGYbapXgnh4xhPi48e4/qeSWmVGrBBM7R5IY6eNoUy8Id63YKqVM+u92xROoBW2ifHhjeGviWkZCZZPO6EAPXh+eSEp2CXPe/IoixTtoMhSWmZnzxmKO5Zby+vBEYoM9MZisvPbeStbtPsHrwxNdRgDOhSICF0tOCj2f+Jlpy/Y52hIFhTqhiEAtEUIQF+2LJrYdBVv+YvthezPVuBBvfFu25USRkaxCJYvQ1cksMHCi2Ihvq/bEhtgLhuYUGcksMBISF0VclK+DLaw/lIzBi2DhzV04MbwNnW/LO73tlatb8b9+8XR9dBlBoX5senagS+aRK4DFamPYrL8oyCthy+vX4K233yYTFm1ly7pDbJ99IyG+bg62sv4477dUCLFACJEjhNhzxrYAIcTvQojDlf/6V24XQoh3hRDJQohdQoguDWm8o9Br1fbyXELFsZRc5q1PJavQiIdOjbHcyPHkTD7YcJQDmSWONrXRsFht/Lgnk3nrU5m3PpX9GcWONqlOlJeZMBqMuOvUZBYY7a9pTwa20iL0WhV6bdMpunIhP1WfcnbL8enAKillC2BV5WOAq4AWlX9TgPfrx0znpXjrGqZPnckfqfZhgRAC6+EtPP3gLBZsS3ewdY1HhcXGlJl/Mn3qTKZPnckHm2ouX+YSnJEAuDIlh+lTZ1Ky7S/H2dOAnHc4IKX8SwgR+5/NI4ArK/+/EFgNPF65fZG0zztuEEL4CSHCpZRZ9WWws+DroeW7mTfz2fYMvp35EQBuWhXfP3M1yw4mMe+FeQ62sPak5JQxadEWrFaJVqvi01uSiPlPn4IXfj/Eb9syARjSNYKnBrbko42pfLk2jdfv7UOgu73azurUQvrNXMOCCUkN0iq9oVi2O4O3fk1m2g3t6BjiU6XS8g0P38H4zhH4NLH6ERcbEwg948Y+AZwqqhYJnPkTkF657SwREEJMwe4tEB0Tc5FmOA69Vs2VrYKRSL4NS8BotlFssNC9eQDebhrmhbcC4GSpCV93jdPGB8qMFoxme3msYwVl7PxnD1jNoNOTcW1bPN2qur3f/X2U1F9/hsBo9Pqe3N2jGd9syWL7jyv56ObHaV55w/99rIgdS5dROKpjo7+mi8FitVFksLAmpYida/cxZ2xnWkd4U1RupsIqISyB8Z0juLJVsKNNrXfqHBiUUkohRK0zjqSU87G3Mqdr1yTHZyxdJJc1D+TgF3fzwLe7mfHBP2x7ZzStwr05tHASr/x5hISJC1n71o20iXLO+eSp3+/h2yVrAWiV1JoDCyfbhzQ2ydUz13B0939qKZ5Mg+BYNn54O7tyikiY8BEUZoFwTpG7UA5mldLnoa+449Y+HFo4CT8PLZkFBro+uJSBA9ty8Iu78XWR3oK15WJfVfYpN18IEQ7kVG7PAKLPOC6qcluTxU2rJkSrxmi2Ys5MxWqTaDUqgn0qo8dpe1myJ4trTVY6NfN1Go8gp7iC3ZmFqBC07pYIQLc2IQR7u6FSCSxWG93bh6PX213f4ynZlO9ai3+P/rRpF06Yn57UgjLI2I9nxz60bBNxltfgSpgtNkjfD/Q5/dlZrBJzxhFMltaE+DSd2YD/crEi8ANwK/Bq5b/Lzth+nxBiCdADKGqK8YBaYbUw++nZzG/bkyPzxjqNCKw9msuk21/j3bmP8OHYs112jVrFvDEdTj+e/c8RnnloLe/fcxlD2oRVOfapSd256zKlYamrcl4REEIsxh4EDBJCpAPPYr/5/08IMRk4BoypPPwX4GogGSgHLpl1tk8PbMmVrYOY8dtB2kZ4M61vPLd3jSJm5kO88L6TRpVrsW7kVD/C6pbNu3KvwgqzlWd/O0R+qYnn37iXgXHB2GySmWuOsP9EKTOeu4XLowIcbWaDciGzAzfVsGtANcdK4N66GuWKdInzp1WEN4mff8vWQB/u6hlLy3AvWoZ78cmvhynIK8ZosqJTq5yiLr1WpQJPP8w2ebpu/rmw2iR4BVQ5vtxiXydRZrJiMFnRa1UuJQimymIhn3+/k6BQf+beMAiw9xaYv2wvJYUlzJ431l5jsgnTtF9dI+OuVfPPS8PZdaKQxKnf8Myk7tzRM45fHr6C1JNldPvfz4y5KpFXhyU62lSuTAhhy1fTeXrFQZ6et/68xw8ZmMjmxY/x4Pe7mTJrNQDlRfZkqBdmLWdOsyjWzBhKlAsV13hi+UG+/XU/Xz0+kNgAe6XguWtTePHjDRiO7MUtzvGfU2Pg+J+kJoRKJYgJ8iDKy4PS3Rv5eVcOe9OL8fPUEunrTsG+nfy1M4s9aUUUlZ+7M3BD46XXEB/qRfMQT/Se+vP+tQzxJCHMi+jAf48PiAgmoNcAsFrI370dk8U1mnEWlZvZk1bEPzszKdi/myg/j9OVgZLzjBj2rEffvA3tOjVD7UKezcWieAINyJoFi+nzpRdrFj16Ov98/7JlXP7zcpZ8+PBZATZH8NyQVjw7qOV5j1Op7DfD7OvbIUdWbWM25pPNrP7y5waxryFYfzSPm+6YBRYTeFUz3ldr+emZq+kY4zyzOQ2JIgINQIivG7c8NpkVf6eQs2E1Ukp8PbRMfmgsf2xOI3X5D7z5ezL788q4o0czh4451SqBWnXhv3bV3RT39IklMnAMH29JO30us1Uy4bFJhDrhQhurBEwGml99LQO6RePrriG7yMgHG48hBNzy2GQi/J27ckf6dwAAEO1JREFU7Xx9cmm8ykYmwt+dd0a25Zp+CaDWIiX4eWh585pE7hveEtQatnzxFc+98SNlRtcvQjIoMZTXh7Vm4bc7mD3jfWbPeB+bTfLuyHZE+DtXjMBqk9ikBLWG+4e35PXhifi4a8ksMPL28x+j06h4Z2Rbwv2aTl+B86GUF2tAMgsMpOUbeO7XA6hUgqWTulNitHAsr5zxc/4h59ARDn5+V5NoZGG1SQ5klpyeOYjw1zudABSUmbj2vXVEhXrxcN94mgV54K3XcP1HGxFC8MzgVkQHuDud3fVFTeXFlOFAAxLh706IjxsVFRays8tIzzcQ6K0jqbk/XdqHs8FoIqe4ApVKEOTtfG5zbVCrBG2dNDUaIK+kghOFRtKPn6RZuDdJzf0pKDORnm/g6NFCIiK8SYrzr9XQqKmgeAKNQHmF/df/svu+YMQNPfl0fGcMJit5JRV0m/Yt7bvE8vsDfRxtZpNFSsmAt/5m387jbJ51PUHebrjr1Nzy+TZ+/G4T62ePJybQHY8mng+geAIOxMNNQ5C3G4OvTcJTr+HLbcfo1zwUf08dVw9th1oIPv//9s48PKoqS+C/Q1WqsidAIkkIOwEhLAEdhW7EqC3YiDCtPQot2qK0Sysu2LYwfNPg2OMyiKL92SN+giO2LG4ozTQNuCC4gKBACFsSEiSEhCRAEipLLcmdP94jqZCgLKkl1P19X768d9+rd0+d996pe8+995zvfmBU9wR6JrafZbftgYNl1Xx5qJxeKbH0TB5EpygbJ6pdrMwuZevOYqg4SoTNctEbgB9DOwb9RGKsnRVT/4WMrtE8eN88thedIDrcyuLJGdw6NInp98/j430lgRbzouOjvSVMf+AFpgxLYfHkDKLCrWw/UsGD982jZMOaQIsXFGgjECAeW7yNSf+7jcoaN0NT4li0aCa5ZbVMWLiZozrd+QVTUlHH+Ne+Ia+8lkVvPEl6chyVNW5ue3MrMxYZXc/R06bw9su/IyE6tPNEaCPgZ2LtFkjoTunmjax97wvKqpxE2a3cPCQVpRSb1mdRWunkZG1gZxS2Z07WuimtcvLV+p0A3DwklSibhdIqJ+ve+4LSLRshoTu3X9mV8YNSiAoP3a4AaMeg36lxeqiocTP+pU0UrPsHJPcnc9xwVv7uSipr3JyodjF+/kZiY+1sfDIzZCastBVuTwOjn9+Aw+Fk9eNXEx8ZRmyElYmvb2HTP7fDkX30+eV4Vj0yivjIsJDyBWjHYJAQabcSabcydkR3VjnHcOSrDWTtSuLL3HL6JkaTHB/OgH4J1Dg9fH3gGJYOQgeEgSmxxF1kse3aisoaN9lHKgFjpmLHjuF0T4khOT6cYw4Xu4oqyd51BMp/ICVzLGOv6HbRzgU4H3RLIEAopTjmcJF2xxtQtBdE+M8XH2X6qD4opdh9uIqrfvMsOKvBEsYnS/+Dy3p1DLTYQcmWA8e5YcqfjdiI4dF8uXQWA7vGICK8vOkAcx9fYMROSE0nd8nddI62taslz22FbgkEGSJCtN3KvFnjKHeMAaDgmJMHP9jFU2P6kRQfzuynp7Hs83zy1/ydxz/IInNwEjOv7XtRxby/EOpc9TzzWR4bsoqh3k2fcROYlNmLpDg7xxwu5qzLYcO3haAUV02bwoSMLkTbrSFpAH4MbQQCSLjNwrQrezXu371sByvfWsv0kT3pc0kUf8jsS52ngfmfRbHz4zXsyx7E9J/1bAyJb7V0CMkZbmBEB3Y4Pby+bCvO/GywR3HzVT34Q2Zf3J4G8o46WPrKcqMlFRHDE9f24aq0iy9ScFuguwNBRGllHaVVTqa9tY1OnSJYdd8IKmvclJ90AVBW7eSe176hrtoYQnzn8WsYlZYQSJEDxqMf7WbNpnwWPzCShEhjynVCrJ3YcCsTFm5m+7f5OPdtZfikW/jrbcPo2imC6BAfBdDdgXbAJXHhxEaGERkZhsPhIqfYQWKsnf4pRkLM+MowLBYLVccq4OBO1uQOJikmnB4JkUERssyXuD0N/FBeY4Q5A45W1GK1WkhLjG5cgFVW5SSnxIHD4cIeYcc+bBTXDUlq1J+mdXRLIAhxeRrYW1RF5j1/Yer0W3hx4kDAcCa6PA28/f0hnnhoPoTZoUtf9r45laSLfOnrkRO1pE9dDMeN1G6vLrifWwanYrM2xTV89KPdvPXqSr5YNJ1+ydEAWDuIHmY1OVNLQBuBIKWkoo4563KIDreSGGUMDSbHhTE5ozsHjjp4YVM+ABYRunWKIMz0DUy8tAsDugbvar5zYW9RFR/vOwqAu0FReLyWevN5fWJ0H3olRrJ8ZyHFlcbEqrJqNzVOD3PH9KPLRbA8u63R3YF2RlJ8OAtvHcLctft5ftYroBSWtMv51zdu59KUGBZNygCMMfKeU5dAwQ7jg88+zKVezd/25gn3/lF6d3cxC2b/BUTo0Gc4+YumNM6VUEpRVethxvzPacj7DkR49M8PMX/CwECJ3m7RLYEgp+h4LbllDqa88CnVObvo9vOruOP6vjxxTV/A8JJnHaqk2gz/vWLXUb7ZaSQMHdCnM2/+Zli78Re4PQ3c+bfvySk4DkBhfgnu/Vv5/dwH+fXAJAZ3i21s2j/3aS5LPz1A4VebiLl0KEtmXENaYnRjwFBNS3RLoJ3StVOEMYtwUCrbKqspzCvi276dOZJRCxjBPIZ4BcRcm3eM/L1GTliPp4HiijqslqbWgNUMYNIhwEOLDQ2K8pNOPA1NP0LuesXunHIK85oy10nvYdyankR6aizHHK5Gx+DWghPGeV16M2BQV0anJQT8O7VXdEugneCo8+CpN0J6f7j7CI/PeRcAa+cuZL96W2MfuNZVj9PMMlxQVsO1jy2DupON14np3pNdL/0q4FOQK6pdDH5sJY7CH5oKw2PYsGAyPU5Lhx4dbqXspIshD63Ac8zwESx4+lYmDkgBjPkSoT78dzacd0tARBYD44FSpdQgs2wecBPgAg4AU5VSFeaxWcA9QD3wsFJqbZt9ixDG+yEfdkk8l40dCYDNZuGfuSXE2ozjw5I7NgYm6eKqZ+T1Q3G56lFK8f3nOzh56CDv7TpM54gmI2C3WLi6b6LPoh5XOz1syCvDVd+U6ai8xo3j0EGwRzI8cygigs1m4ZK4cOKjjKW9B8uq2V58AoCCE3V4ig5AYg8u+1k/MhLjG8/TXBg/2RIQkdGAA1jiZQTGAJ8ppTwi8jyAUupJERkILAOuAFKAT4B+SqkfzXOlWwLnT2WNm553LYGC7QA8+dwjzLwurcV5Sikun7ue/H+sanmR+CSyls+gW+fIlsfagEPlNQydNB8qj7Y41ufGiWyd84tWHZhPr8/hxX9/pVnZFXdOZu30n/tEzoud824JKKU2ikjP08rWee1uBn5tbk8EliulnECBiORhGISfznOlOS8ibBb+NmccH2RdxsqXFrHwwyw25ZQDMCA1nufG9cdqMcbSX73zMvIn9m9xDVe94om/7/FZDIOYiDBeevYObJaWL3qfuJhGA+D2NPDk/+1jv7kicPeuIhDh5hn3cF0/Y/FUeuc4n8gYyrRF++9uYIW53RXDKJzisFnWAhG5F7gXoFv37m0gRmhis3bgxvRkEiPsrOyYQkXOXr7O2QtA3uChzMrsjc0cHUhPiWVw1zgi7ZZmv7yOOg9zF2+jMm+fT2SMS7uURZMymgXvUEpR46ynQalG4+P0NLD84x3U7vkWYszp0B1T+P2VPfQKSh9yQUZARGYDHuCdc/2sUup14HUwugMXIocGhqTGkbX0kWZlB49XM+jh9/G4mhKcJHZNZPNT1xPr5ROItFn4+pkbqW8Y5xPZrJYORNiar3ysqvUwYs46yo+UN5Yppag/tIfI9CvZ+MxNjcYrsZ2HYw92ztsIiMhdGA7D61STY6EI6OZ1WqpZpvEx4TZLq336lO6JOJ2GY/DIjp0UVx7nm4LhdA5v+WLFRljpl9x28+yVUuSWOKiqdVJ0vLbZsfK6Okr27IN6DylDBze1TLp3Ib1/Aj0SIvV0Xz9xVkOEpk9gtZdj8AbgReBqpVSZ13npwFKaHIOfAmnaMRg4To2rK6W44qlPKFizCiyt2/7Ua8ay479uaLPlyZ76BjJmr6VowxkGiOo99B43gS1/au4YFNBj/j7gQoYIlwGZQIKIHAbmALMAO7DevHmblVL3K6V2i8i7wB6MbsKDP2UANL6l6YUW/vRv6Wwd0dL/4nDWs2Thag7nHebhldltZgTqGxRFeYXQMYU7772RaHvLYChXdIvRv/gBRk8W0nCy1k3aAytw5u70yfUj+g8j96+3hnxU30Cjpw1rzkik3crGZyfi8tzkk+vbrB0It+mQaMGKNgIaLB2kTR2CmvaF7oxpNCGONgIaTYijjYBGE+JoI6DRhDjaCGg0IU5QzBMQkTKgGij/qXP9QAJaDm+0HM1pz3L0UEq1yMASFEYAQES2tTaRQcuh5dBy+FYO3R3QaEIcbQQ0mhAnmIzA64EWwETL0RwtR3MuOjmCxieg0WgCQzC1BDQaTQDQRkCjCXGCwgiIyA0isl9E8kRkpp/q7CYin4vIHhHZLSKPmOWdRGS9iOSa//0S4VJELCKyXURWm/u9RGSLqZMVIuLzIPsiEi8i74vIPhHZKyIjA6EPEXnMvCfZIrJMRML9pQ8RWSwipSKS7VXWqg7E4BVTpiwRGe5jOeaZ9yZLRFaKSLzXsVmmHPtFZOw5VaaUCugfYMFIYNIbsAE7gYF+qDcZGG5uxwA5wEDgv4GZZvlM4Hk/6WEGRmi21eb+u8Akc/s14AE/yPAWMM3ctgHx/tYHRnTqAiDCSw93+UsfwGhgOJDtVdaqDoBxwBqMiGgjgC0+lmMMYDW3n/eSY6D53tiBXub7ZDnrunz9YJ3Flx0JrPXanwXMCoAcHwPXA/uBZLMsGdjvh7pTMeIxXgusNh+qcq8b3kxHPpIhznz55LRyv+rDNAKFQCeMeBergbH+1AfQ87SXr1UdAAuBya2d5ws5Tjv2K+Adc7vZOwOsBUaebT3B0B04ddNPccZcBb7CDKQ6DNgCdFFKFZuHSoAufhBhAfBHoMHc7wxUKKVOxQr3h056AWXAm2a35A0RicLP+lBKFQEvAIeAYqAS+A7/68ObM+kgkM/u3RitkAuWIxiMQEARkWjgA+BRpVSV9zFlmFWfjqGKyKk8j9/5sp6zwIrR/PwfpdQwjLUczfwzftJHR4xMVr0wIlZHATf4ss5zwR86+CkuJN9HawSDEQhYrgIRCcMwAO8opT40i4+KSLJ5PBko9bEYPwcmiMhBYDlGl+BlIF5EToV/84dODgOHlVJbzP33MYyCv/XxC6BAKVWmlHIDH2LoyN/68OZMOvD7s+uV7+N20yBdsBzBYAS2Ammm99cGTAJayZrZtogRK30RsFcp9aLXoVXAb83t32L4CnyGUmqWUipVKdUT47t/ppS6HficphyP/pCjBCgUkVPJCq/DCB3vV31gdANGiEikeY9OyeFXfZzGmXSwCrjTHCUYAVR6dRvaHDPfxx+BCUqpmtPkmyQidhHpBaQB3571hX3p5DkHB8g4DO/8AWC2n+ochdGsywJ2mH/jMPrjnwK5GFmVO/lRD5k0jQ70Nm9kHvAeYPdD/RnANlMnHwEdA6EP4ClgH5ANvI3h9faLPjCyahcDbozW0T1n0gGGA/dV87ndBVzuYznyMPr+p57X17zOn23KsR/45bnUpacNazQhTjB0BzQaTQDRRkCjCXG0EdBoQhxtBDSaEEcbAY0mxNFGQKMJcbQR0GhCnP8HxgCz9RdxwHUAAAAASUVORK5CYII="
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {
    "scrolled": true
   }
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "source": [
    "N = np.prod(img.shape)  # Size of experimental domain\n",
    "p = N  # Covariate Dimension\n",
    "n = p // 2  #Sample size; we undersample by 50%\n",
    "print('shape: ', img.shape)\n",
    "print('dim: ', p)\n",
    "print('sparsity of the original image: ', sparsity(img))\n",
    "print('sparsity of the Laplacian: ', sparsity(lap_th))"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "shape:  (128, 128)\n",
      "dim:  16384\n",
      "sparsity of the original image:  0.42742919921875\n",
      "sparsity of the Laplacian:  0.06317138671875\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "We will be (under-)sampling the [Discrete Cosine Transform](https://en.wikipedia.org/wiki/Discrete_cosine_transform) of the image, so let's look at this transform and its inverse:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "source": [
    "C = dctn(img, norm='ortho')\n",
    "# Cshift = np.log(np.abs(np.fft.fftshift(C)))\n",
    "invC = idctn(C, norm='ortho')\n",
    "plt.figure(figsize=(20,20))\n",
    "plt.subplot(131),plt.imshow(img)\n",
    "plt.title('Input Image')\n",
    "plt.subplot(132),plt.imshow(np.log(np.abs(C)))\n",
    "plt.title('DCT')\n",
    "plt.subplot(133), plt.imshow(invC)\n",
    "plt.title('iDCT')\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 1440x1440 with 3 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "The matrix of the 2d DCT transform in the vectorized basis can be obtained using Kronecker products:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "source": [
    "d = dct(np.eye(img.shape[0]), norm='ortho')\n",
    "D = np.kron(d,d).T"
   ],
   "outputs": [],
   "metadata": {
    "scrolled": true
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "We take the experimental domain to be this matrix $D$ scaled by $\\sqrt{N}$:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "source": [
    "X = np.sqrt(N) * D.copy()"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Let's say we are interested in the average intensity of the image within the gray rectangular area:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "source": [
    "c_arr = np.zeros(img.shape)\n",
    "c_arr[95:110, 50:75] = 1\n",
    "plt.figure(figsize=(20,20))\n",
    "plt.subplot(121)\n",
    "plt.imshow(lap_th, vmin=0, cmap='gray')\n",
    "plt.axis('off')\n",
    "plt.subplot(122)\n",
    "plt.imshow(np.minimum(lap_th + 0.2*c_arr, 1), vmin=0, cmap='gray')\n",
    "plt.axis('off')\n",
    "plt.savefig('shepp_lap_filter.png', format=\"png\", cmap='gray', vmin=0, dpi=700, bbox_inches='tight')"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 1440x1440 with 2 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "The true coefficient $\\beta$ is taken to be the vectorized Laplacian. $c$ is the indicator function of the rectangular area above."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "source": [
    "beta = lap_th.reshape(N)\n",
    "c = c_arr.reshape(N)\n",
    "c = c / np.sum(np.abs(c))\n",
    "gamma = beta.T @ c"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Given this value of $c$ and $X$, we need to solve the following linear program:\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\text{P1: minimize}_{w \\geq 0} &\\quad c^T \\Sigma^{-1} c \\\\\n",
    "\\text{s.t. }\\quad &\\Sigma = \\sum_{i=1}^N w_i x_i x_i^T\\\\\n",
    "&\\sum_{i=1}^N w_i = 1\n",
    "\\end{align*}\n",
    "$$"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Fortunately, this can be written as a linear program:\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\text{P2: minimize}_{a,b} &\\quad \\sum_i a_i \\\\\n",
    "\\text{s.t. }\\quad &c  = \\sum_{i=1}^N b_i x_i^T\\\\\n",
    "&a \\geq b\\\\\n",
    "&a \\geq -b\n",
    "\\end{align*}\n",
    "$$"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Given an optimal solution $(a^\\star, b^\\star)$ of $P2$, a solution of $P1$ is found by $w^\\star = |a| / \\| a\\|_1$. The following code solve $P2$ using the cvxpy package. Since it takes a long time to solve this program, I have saved the solution to a file called `w_opt.csv` which I just read it next."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "w = cp.Variable((N), nonneg = True)\n",
    "z = cp.Variable((N))\n",
    "constraints = [X.T @ z == c, z - w <= 0, -z - w <= 0]\n",
    "obj = cp.Minimize(cp.sum(w))\n",
    "prob = cp.Problem(obj, constraints)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "prob.solve(verbose = True, abstol = 1e-5)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "w_opt = w.value / np.sum(w.value)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "source": [
    "def c_optimize(X,c):\n",
    "    N = X.shape[0]\n",
    "    w = cp.Variable((N), nonneg = True)\n",
    "    z = cp.Variable((N))\n",
    "    constraints = [X.T @ z == c, z - w <= 0, -z - w <= 0]\n",
    "    obj = cp.Minimize(cp.sum(w))\n",
    "    prob = cp.Problem(obj, constraints)\n",
    "    prob.solve(verbose = True, abstol = 1e-5)\n",
    "    return(w.value / np.sum(w.value))\n",
    "    "
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "#np.savetxt(\"w_opt.csv\", w_opt, delimiter=\",\")"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Read optimal weights"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "source": [
    "w_opt = np.loadtxt(\"w_opt.csv\", delimiter=\",\")"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Let's take a look at the distirbution of the weights, or rather, their $\\log$:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "source": [
    "plt.hist(np.log(w_opt[w_opt > 0]))\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "As seen below, the optimal design improves the asymptotic standard error of the de-biased lasso estimator by a factor of $\\approx 5$:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "source": [
    "sigma_opt = np.sqrt(c.T @ np.linalg.solve( X.T @ np.diag(w_opt) @ X, c))"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "source": [
    "sigma_unif = np.sqrt(c.T @ np.linalg.solve( X.T @ X / N, c))"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "source": [
    "(sigma_unif / sigma_opt)"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "4.974722710380465"
      ]
     },
     "metadata": {},
     "execution_count": 27
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "source": [
    "from sklearn.linear_model import Lasso, LassoCV\n",
    "from random import sample"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "The next function computes the de-biased lasso estimator:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "source": [
    "def deb_lasso(x, y, c, u, lasso_tuning, beta_init):\n",
    "    n = len(y)\n",
    "    clf = Lasso(alpha=lasso_tuning, fit_intercept=False,\n",
    "               warm_start=True, max_iter = 999999, copy_X = True,\n",
    "                normalize = False)\n",
    "    norms = np.sqrt(np.mean(x**2, axis = 0))\n",
    "    clf.coef_ = beta_init  #Initialize at truth for faster computation\n",
    "    clf.fit(x / norms, y)\n",
    "    beta_hat = clf.coef_ / norms\n",
    "    gamma_hat = c.T @ beta_hat + u.T @ x.T @ (y - x @ beta_hat) / n\n",
    "    return [gamma_hat, beta_hat]"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "source": [
    "signal = X @ beta"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "We can use cross-validation to find a good value of the tuning paramter for the lasso estimator:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "source": [
    "n = N // 2\n",
    "lambda_theory = np.sqrt(np.log(N)/ n)\n",
    "indices = np.random.choice(range(N), size=n)\n",
    "\n",
    "y = signal[indices] + np.random.normal(size=n)\n",
    "\n",
    "lasso_fit = LassoCV(cv = 10, fit_intercept=False, \n",
    "                    alphas=(np.exp(np.arange(-3, 0, 1e-1)))*lambda_theory,\n",
    "                    n_jobs = -1, max_iter = 999999, verbose=True).fit(X[indices,:],y)\n",
    "\n",
    "plt.plot(lasso_fit.alphas_, np.mean(lasso_fit.mse_path_, axis = 1))\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "[Parallel(n_jobs=-1)]: Using backend ThreadingBackend with 5 concurrent workers.\n",
      "............................................................................................................................................................................................................................................................................................................[Parallel(n_jobs=-1)]: Done  10 out of  10 | elapsed:  3.0min finished\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "source": [
    "beta_hat = lasso_fit.coef_\n",
    "print(gamma)\n",
    "print(\"Error: \", np.sum(np.abs(beta - beta_hat)))\n",
    "print(np.sum(beta))\n",
    "print(lambda_theory, lasso_fit.alpha_)\n",
    "cv_lambda = lasso_fit.alpha_"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "0.10666666666666666\n",
      "Error:  42.898707944147674\n",
      "1035.0\n",
      "0.03441769459380233 0.009379916019746007\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Uniform Sampling"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "source": [
    "n = N // 2\n",
    "lambda_theory = np.sqrt(np.log(N)/ n)\n",
    "u_unif = c\n",
    "gamma = c.T @ beta\n",
    "signal = X @ beta"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "source": [
    "gamma"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "0.10666666666666666"
      ]
     },
     "metadata": {},
     "execution_count": 57
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "source": [
    "n = N // 2\n",
    "n_reps = 5\n",
    "gammas_unif = np.zeros(n_reps)\n",
    "signal = X @ beta\n",
    "beta_hat = np.zeros(N)\n",
    "\n",
    "for i in range(n_reps):\n",
    "    indices = np.random.choice(range(N), size=n)\n",
    "    y = signal[indices] + np.random.normal(size=n)    \n",
    "    gammas_unif[i], beta_hat = deb_lasso(X[indices,:], y, c, u_unif, lambda_theory, beta_hat.copy())\n",
    "    \n",
    "    print_progress(n_reps, i)\n",
    "#     print(gammas_unif[i] - gamma)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "100 % done\n",
      "-0.010557183864339681\n"
     ]
    }
   ],
   "metadata": {
    "scrolled": true
   }
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "source": [
    "np.savetxt(fname = 'unif_dist.csv', X = gammas_unif, delimiter = ',')"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "source": [
    "gammas_unif = np.loadtxt(\"unif_dist.csv\", delimiter=\",\")"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "source": [
    "sns.histplot(gammas_unif - gamma)\n",
    "plt.show()\n",
    "print(\"bias: \", np.mean(gammas_unif) - gamma)\n",
    "print(\"std: \", np.std(gammas_unif))\n",
    "print((np.linalg.norm(c) / np.sqrt(n)))"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {
      "needs_background": "light"
     }
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "bias:  -0.00115171559733028\n",
      "std:  0.0019342389201397066\n"
     ]
    },
    {
     "output_type": "error",
     "ename": "NameError",
     "evalue": "name 'n' is not defined",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-35-bbe09c358c0a>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"bias: \"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmean\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgammas_unif\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mgamma\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"std: \"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgammas_unif\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinalg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnorm\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mc\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msqrt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'n' is not defined"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "# np.savetxt(\"unif_dist.csv\", gammas_unif, delimiter=\",\")"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "source": [],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Optimal Sampling"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Next we compute $u = \\Sigma^{-1} c$ for optimal design:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "source": [
    "u_opt = np.linalg.solve(X.T @ np.diag(w_opt) @ X, c)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "n_reps = 5\n",
    "gammas_opt = np.zeros(n_reps)\n",
    "beta_hat = np.zeros(N)\n",
    "for i in range(n_reps):\n",
    "    indices = np.random.choice(range(N), size=n, p=w_opt)\n",
    "    y = signal[indices] + np.random.normal(size=n)\n",
    "\n",
    "    gammas_opt[i], beta_hat = deb_lasso(X[indices,:], y, c, u_opt, lambda_theory, beta_hat.copy())\n",
    "    \n",
    "    print_progress(n_reps, i)\n",
    "    print(gammas_opt[i] - gamma)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "source": [
    "# np.savetxt(\"opt_dist.csv\", gammas_opt, delimiter=\",\")"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "source": [
    "gammas_opt = np.loadtxt(\"opt_dist.csv\", delimiter=\",\")"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "source": [
    "sns.histplot(np.sqrt(n)*(gammas_opt - gamma))\n",
    "plt.show()\n",
    "print(\"bias: \", np.mean(gammas_opt - gamma))\n",
    "print(\"std: \", (np.std(np.sqrt(n)*(gammas_opt - gamma))))"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {
      "needs_background": "light"
     }
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "bias:  4.59230837756619e-07\n",
      "std:  0.008825489007543305\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "source": [
    "sns.histplot(np.sqrt(n)*(gammas_unif - gamma))\n",
    "plt.show()\n",
    "print(\"bias: \", np.mean(gammas_unif - gamma))\n",
    "print(\"std: \", (np.std(np.sqrt(n)*(gammas_unif - gamma))))"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {
      "needs_background": "light"
     }
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "bias:  -0.001151715597330294\n",
      "std:  0.17506732247881365\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "To see the improvements let's look at the estimation errors under optimal and uniform designs in one plot:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "source": [
    "estim_errors = pd.DataFrame({\"Optimal\": gammas_opt, \n",
    "                             \"Uniform\": gammas_unif})"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "source": [
    "sns.histplot(estim_errors - gamma)\n",
    "plt.title(\"Errors under Optimal and Uniform Designs\")\n",
    "plt.xlabel(\"Estimation Errors\")\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "As you can see in the plot, the estimation errors under the optimal design are much more concentrated around zero than when using a uniform design. "
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "# More simulations"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "The rest of the code provides more simulations with Gaussian designs along with power and error rate calculations."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "source": [
    "import numpy as np\n",
    "from scipy.linalg import toeplitz\n",
    "from sklearn.linear_model import Lasso, LassoCV\n",
    "from random import sample\n",
    "import cvxpy as cp\n",
    "from scipy.stats import norm"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "source": [
    "\n",
    "N = 1000\n",
    "p = 500\n",
    "n = 200\n",
    "ss = [5, 10]\n",
    "mc_samples = 500\n",
    "\n",
    "\n",
    "\n",
    "kappas = [0.1, 0.9]\n",
    "# Sigma = toeplitz(kappa ** np.arange(p)).T\n",
    "# u_unif = np.linalg.solve(Sigma, c)\n",
    "\n",
    "\n",
    "lambda_theory = np.sqrt(np.log(p) / n)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Uniform Sampling"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "source": [
    "np.random.seed(1)\n",
    "\n",
    "beta_hat = np.zeros(p)\n",
    "gamma_hats_unif = np.zeros([2, len(kappas), len(ss), mc_samples])\n",
    "vars_unif = np.zeros([2, len(kappas), len(ss), mc_samples])\n",
    "gammas = np.zeros([2, len(kappas), len(ss)])\n",
    "    \n",
    "for k in range(len(kappas)):\n",
    "    Sigma = toeplitz(kappas[k] ** np.arange(p)).T\n",
    "    X = np.random.multivariate_normal(mean=np.zeros(p), cov=Sigma, size=N)\n",
    "    for l in [0,1]:\n",
    "        for j in range(len(ss)):\n",
    "            beta = np.concatenate((np.arange(ss[j],0, -1), np.zeros(p - ss[j])), axis = 0) / ss[j]\n",
    "            c = np.zeros(p)\n",
    "            c[ss[j] + l - 1] = 1\n",
    "\n",
    "            u_unif = np.linalg.solve(X.T @ X / N, c)\n",
    "\n",
    "            signal = X @ beta\n",
    "            gammas[l, k,j] = c.T @ beta\n",
    "            \n",
    "            for i in range(mc_samples):\n",
    "                indices = np.random.choice(range(N), size=n)\n",
    "                y = signal[indices] + np.random.normal(size=n)\n",
    "                gamma_hats_unif[l, k, j, i], beta_hat = deb_lasso(X[indices,:], y, c, u_unif, lambda_theory, beta_hat.copy())\n",
    "                vars_unif[l, k, j, i] = u_unif.T @ X[indices,:].T @ X[indices,:] @ u_unif / (n**2)\n",
    "                print_progress(mc_samples, i)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "99 % done\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "source": [
    "np.mean(gamma_hats_unif, axis = 3) - gammas"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[[-0.00741991, -0.00499849],\n",
       "        [ 0.00338051, -0.01087915]],\n",
       "\n",
       "       [[-0.00609174, -0.01040796],\n",
       "        [-0.00483919, -0.01336414]]])"
      ]
     },
     "metadata": {},
     "execution_count": 13
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "source": [
    "np.std(gamma_hats_unif, axis = 3)"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[[0.10092128, 0.10586833],\n",
       "        [0.28455224, 0.31579955]],\n",
       "\n",
       "       [[0.10239152, 0.10247408],\n",
       "        [0.29687626, 0.3008129 ]]])"
      ]
     },
     "metadata": {},
     "execution_count": 14
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "source": [
    "np.mean(np.sqrt(vars_unif), axis = 3)"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[[0.09747906, 0.10026493],\n",
       "        [0.30239911, 0.30653389]],\n",
       "\n",
       "       [[0.10534118, 0.09685147],\n",
       "        [0.30538942, 0.30126461]]])"
      ]
     },
     "metadata": {},
     "execution_count": 15
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "# c-Optimal Sampling"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "source": [
    "np.random.seed(1)\n",
    "\n",
    "beta_hat = np.zeros(p)\n",
    "gamma_hats_opt = np.zeros([2, len(kappas), len(ss), mc_samples])\n",
    "vars_opt = np.zeros([2, len(kappas), len(ss), mc_samples])\n",
    "gammas = np.zeros([2, len(kappas), len(ss)])\n",
    "    \n",
    "for k in range(len(kappas)):\n",
    "    Sigma_init = toeplitz(kappas[k] ** np.arange(p)).T\n",
    "    X = np.random.multivariate_normal(mean=np.zeros(p), cov=Sigma_init, size=N)\n",
    "    for l in [0,1]:\n",
    "        for j in range(len(ss)):\n",
    "            beta = np.concatenate((np.arange(ss[j],0, -1), np.zeros(p - ss[j])), axis = 0) / ss[j]\n",
    "            c = np.zeros(p)\n",
    "            c[ss[j] + l - 1] = 1\n",
    "\n",
    "            signal = X @ beta\n",
    "            gammas[l, k,j] = c.T @ beta\n",
    "            w_opt = c_optimize(X, c)\n",
    "            u_opt = np.linalg.solve(X.T @ np.diag(w_opt) @ X, c)\n",
    "\n",
    "            for i in range(mc_samples):\n",
    "                indices = np.random.choice(range(N), size=n, p = w_opt)\n",
    "                y = signal[indices] + np.random.normal(size=n)\n",
    "                gamma_hats_opt[l, k, j, i], beta_hat = deb_lasso(X[indices,:], y, c, u_opt, lambda_theory, beta_hat.copy())\n",
    "                vars_opt[l, k, j, i] = u_opt.T @ X[indices,:].T @ X[indices,:] @ u_opt / (n**2)\n",
    "                print_progress(mc_samples, i)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "99 % done\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "source": [
    "np.mean(gamma_hats_opt, axis = 3) - gammas"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[[-0.0070414 , -0.01145838],\n",
       "        [-0.00760301,  0.0053687 ]],\n",
       "\n",
       "       [[-0.00617892, -0.00402471],\n",
       "        [-0.00947508,  0.01922104]]])"
      ]
     },
     "metadata": {},
     "execution_count": 20
    }
   ],
   "metadata": {
    "scrolled": true
   }
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "source": [
    "np.std(gamma_hats_opt, axis = 3) / np.std(gamma_hats_unif, axis = 3)"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[[0.7059069 , 0.70285757],\n",
       "        [0.73612518, 0.63974331]],\n",
       "\n",
       "       [[0.67328261, 0.69605469],\n",
       "        [0.67741645, 0.6861752 ]]])"
      ]
     },
     "metadata": {},
     "execution_count": 22
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "source": [
    "np.std(gamma_hats_opt, axis = 3)"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[[0.07124103, 0.07441036],\n",
       "        [0.20946607, 0.20203065]],\n",
       "\n",
       "       [[0.06893843, 0.07132756],\n",
       "        [0.20110886, 0.20641035]]])"
      ]
     },
     "metadata": {},
     "execution_count": 23
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "source": [
    "np.mean(np.sqrt(vars_opt), axis = 3)"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[[0.06499012, 0.06712503],\n",
       "        [0.20856639, 0.20622425]],\n",
       "\n",
       "       [[0.06990412, 0.065541  ],\n",
       "        [0.19831938, 0.20068078]]])"
      ]
     },
     "metadata": {},
     "execution_count": 24
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "source": [
    "np.sum((gamma_hats_opt +\n",
    "        np.sqrt(vars_opt) *\n",
    "        norm().interval(0.95)[0]) > 0, axis = 3) / mc_samples +\\\n",
    "            np.sum((gamma_hats_opt[:,:,:,:] +\n",
    "                np.sqrt(vars_opt)[:,:,:,:] *\n",
    "                norm().interval(0.95)[1]) < 0, axis = 3) / mc_samples"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[[0.806, 0.29 ],\n",
       "        [0.156, 0.078]],\n",
       "\n",
       "       [[0.048, 0.064],\n",
       "        [0.042, 0.056]]])"
      ]
     },
     "metadata": {},
     "execution_count": 25
    }
   ],
   "metadata": {
    "scrolled": true
   }
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "source": [
    "np.sum((gamma_hats_unif +\n",
    "        np.sqrt(vars_unif) *\n",
    "        norm().interval(0.95)[0]) > 0, axis = 3) / mc_samples +\\\n",
    "            np.sum((gamma_hats_unif[:,:,:,:] +\n",
    "                np.sqrt(vars_unif)[:,:,:,:] *\n",
    "                norm().interval(0.95)[1]) < 0, axis = 3) / mc_samples"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[[0.496, 0.152],\n",
       "        [0.096, 0.064]],\n",
       "\n",
       "       [[0.054, 0.058],\n",
       "        [0.048, 0.046]]])"
      ]
     },
     "metadata": {},
     "execution_count": 26
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "source": [
    "gammas_array = np.array([gammas.T] * mc_samples).T"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "np.sum(((gamma_hats_opt +\n",
    "        np.sqrt(vars_opt) *\n",
    "        norm().interval(0.95)[0]) <= gammas_array) *\\\n",
    "       ((gamma_hats_opt +\n",
    "        np.sqrt(vars_opt) *\n",
    "        norm().interval(0.95)[1]) >= gammas_array),axis = 3) / mc_samples "
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "np.sum(((gamma_hats_unif +\n",
    "        np.sqrt(vars_unif) *\n",
    "        norm().interval(0.95)[0]) <= gammas_array) *\\\n",
    "       ((gamma_hats_unif +\n",
    "        np.sqrt(vars_unif) *\n",
    "        norm().interval(0.95)[1]) >= gammas_array),axis = 3) / mc_samples "
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "np.sqrt(n) * np.std(gamma_hats_opt, axis = 3)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "np.sqrt(n) * np.std(gamma_hats_unif, axis = 3)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "# n-Nearest-Neighbor Sampling"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "source": [
    "np.random.seed(1)\n",
    "\n",
    "beta_hat = np.zeros(p)\n",
    "gamma_hats_nn = np.zeros([2, len(kappas), len(ss), mc_samples])\n",
    "vars_nn = np.zeros([2, len(kappas), len(ss), mc_samples])\n",
    "gammas = np.zeros([2, len(kappas), len(ss)])\n",
    "    \n",
    "for k in range(len(kappas)):\n",
    "    Sigma_init = toeplitz(kappas[k] ** np.arange(p)).T\n",
    "    X = np.random.multivariate_normal(mean=np.zeros(p), cov=Sigma_init, size=N)\n",
    "    for l in [0,1]:\n",
    "        for j in range(len(ss)):\n",
    "            beta = np.concatenate((np.arange(ss[j],0, -1), np.zeros(p - ss[j])), axis = 0) / ss[j]\n",
    "            c = np.zeros(p)\n",
    "            c[ss[j] + l - 1] = 1\n",
    "            distances = np.sum((X - c) ** 2, axis = 1)\n",
    "            indices = np.argsort(distances)[:n]\n",
    "            signal = X @ beta\n",
    "            gammas[l, k, j] = c.T @ beta\n",
    "            \n",
    "            # u_opt = np.linalg.solve(X[indices,:].T @ X[indices,:] / n, c)\n",
    "            u_opt = np.linalg.lstsq(X[indices, :].T @ X[indices,:] / n, c, rcond = None)[0]\n",
    "\n",
    "            for i in range(mc_samples):\n",
    "                \n",
    "                y = signal[indices] + np.random.normal(size=n)\n",
    "                gamma_hats_nn[l, k, j, i], beta_hat = deb_lasso(X[indices,:], y, c, u_opt, lambda_theory, beta_hat.copy())\n",
    "                vars_nn[l, k, j, i] = u_opt.T @ X[indices,:].T @ X[indices,:] @ u_opt / (n**2)\n",
    "                print_progress(mc_samples, i)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "99 % done\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "source": [
    "print((np.mean(gamma_hats_nn, axis = 3) - gammas))\n",
    "print((np.mean(gamma_hats_opt, axis = 3) - gammas))\n"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[[[-0.087752   -0.02561296]\n",
      "  [-0.02767169 -0.01777255]]\n",
      "\n",
      " [[ 0.00430137 -0.00360645]\n",
      "  [ 0.03143773  0.01499292]]]\n",
      "[[[-0.0070414  -0.01145838]\n",
      "  [-0.00760301  0.0053687 ]]\n",
      "\n",
      " [[-0.00617892 -0.00402471]\n",
      "  [-0.00947508  0.01922104]]]\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Standard Errors"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "source": [
    "np.sqrt(n) * np.std(gamma_hats_nn, axis = 3) "
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[[0.89005768, 0.7464554 ],\n",
       "        [0.75967769, 0.60447951]],\n",
       "\n",
       "       [[0.56018465, 0.51814282],\n",
       "        [0.46694018, 0.46100234]]])"
      ]
     },
     "metadata": {},
     "execution_count": 86
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Power & FPR"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "source": [
    "np.sum((gamma_hats_nn +\n",
    "        np.sqrt(vars_nn) *\n",
    "        norm().interval(0.95)[0]) > 0, axis = 3) / mc_samples +\\\n",
    "            np.sum((gamma_hats_nn[:,:,:,:] +\n",
    "                np.sqrt(vars_nn)[:,:,:,:] *\n",
    "                norm().interval(0.95)[1]) < 0, axis = 3) / mc_samples"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[[0.678, 0.432],\n",
       "        [0.428, 0.238]],\n",
       "\n",
       "       [[0.062, 0.056],\n",
       "        [0.1  , 0.064]]])"
      ]
     },
     "metadata": {},
     "execution_count": 91
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Coverage"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "source": [
    "np.mean( ((gamma_hats_nn +\n",
    "        np.sqrt(vars_nn) *\n",
    "        norm().interval(0.95)[0]) <= 0 ) * \n",
    "            ((gamma_hats_nn[:,:,:,:] +\n",
    "                np.sqrt(vars_nn)[:,:,:,:] *\n",
    "                norm().interval(0.95)[1]) >= 0), axis = 3)"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[[0.322, 0.568],\n",
       "        [0.572, 0.762]],\n",
       "\n",
       "       [[0.938, 0.944],\n",
       "        [0.9  , 0.936]]])"
      ]
     },
     "metadata": {},
     "execution_count": 88
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "source": [
    "np.mean( ((gamma_hats_opt +\n",
    "        np.sqrt(vars_opt) *\n",
    "        norm().interval(0.95)[0]) <= 0 ) * \n",
    "            ((gamma_hats_opt[:,:,:,:] +\n",
    "                np.sqrt(vars_opt)[:,:,:,:] *\n",
    "                norm().interval(0.95)[1]) >= 0), axis = 3)"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[[0.194, 0.71 ],\n",
       "        [0.844, 0.922]],\n",
       "\n",
       "       [[0.952, 0.936],\n",
       "        [0.958, 0.944]]])"
      ]
     },
     "metadata": {},
     "execution_count": 63
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "source": [
    "def coverage(est, var_est, param):\n",
    "    params = np.repeat(param[:, :, :, np.newaxis], est.shape[-1], axis=3)\n",
    "    return(np.mean( ((est +\n",
    "        np.sqrt(var_est) *\n",
    "        norm().interval(0.95)[0]) <= params ) * \n",
    "            ((est +\n",
    "                np.sqrt(var_est) *\n",
    "                norm().interval(0.95)[1]) >= params), axis = 3))"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "source": [
    "print(coverage(gamma_hats_nn, vars_nn, gammas))"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[[[0.4   0.78 ]\n",
      "  [0.76  0.816]]\n",
      "\n",
      " [[0.938 0.944]\n",
      "  [0.9   0.936]]]\n"
     ]
    }
   ],
   "metadata": {}
  }
 ],
 "metadata": {
  "kernelspec": {
   "name": "python3",
   "display_name": "Python 3.8.3 64-bit ('3.8.3': pyenv)"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  },
  "interpreter": {
   "hash": "6936cdb59f789db9c68afa5939721edccad207825d04799ebe59c67799651f60"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}