2.gradient_natural_images.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "BIAPDG2670SE"
   },
   "source": [
    "# Analysis of a bias-free network\n",
    "\n",
    "A bias-free network operates on its input by applying an adaptive linear transform (adaptive, because the transform is dependent on the input image). In this notebook, we analyze the properties of this transform using singular value decomposition.\n"
   ]
  },
  {
   "cell_type": "code",
   "source": [
    "from google.colab import drive\n",
    "drive.mount('/content/drive')\n"
   ],
   "metadata": {
    "id": "ZW6TYGSR9Qfl"
   },
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "code",
   "source": [
    "# set to google drive location by default\n",
    "file_root_path = '/content/drive/MyDrive/Denoising Code/Denoising_Tutorial'\n",
    "\n",
    "# if the files are in local devices, change the file_root_path to the local location\n"
   ],
   "metadata": {
    "id": "KWeaESuY9StA"
   },
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "code",
   "source": [
    "from google.colab import drive\n",
    "drive.mount('/content/drive')\n",
    "\n",
    "import os\n",
    "import sys\n",
    "\n",
    "sys.path.append(file_root_path)"
   ],
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "XTPCDYewY0J7",
    "executionInfo": {
     "status": "ok",
     "timestamp": 1705956047841,
     "user_tz": 300,
     "elapsed": 706,
     "user": {
      "displayName": "Kangning Liu",
      "userId": "18225106579512019568"
     }
    },
    "outputId": "69ee3e41-7574-470d-946f-bdd2a91a56d5"
   },
   "execution_count": 1,
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Drive already mounted at /content/drive; to attempt to forcibly remount, call drive.mount(\"/content/drive\", force_remount=True).\n"
     ]
    }
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "id": "QloYQYJr70SF",
    "executionInfo": {
     "status": "ok",
     "timestamp": 1705956047841,
     "user_tz": 300,
     "elapsed": 1,
     "user": {
      "displayName": "Kangning Liu",
      "userId": "18225106579512019568"
     }
    }
   },
   "outputs": [],
   "source": [
    "# !pip install ipywidgets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "id": "7fjleJSY70SG",
    "executionInfo": {
     "status": "ok",
     "timestamp": 1705956047841,
     "user_tz": 300,
     "elapsed": 1,
     "user": {
      "displayName": "Kangning Liu",
      "userId": "18225106579512019568"
     }
    }
   },
   "outputs": [],
   "source": [
    "# !jupyter labextension list"
   ]
  },
  {
   "cell_type": "code",
   "source": [
    "import warnings\n",
    "\n",
    "# This line suppresses all warnings.\n",
    "warnings.filterwarnings('ignore')"
   ],
   "metadata": {
    "id": "CqSVM2h25zx2",
    "executionInfo": {
     "status": "ok",
     "timestamp": 1705956047842,
     "user_tz": 300,
     "elapsed": 2,
     "user": {
      "displayName": "Kangning Liu",
      "userId": "18225106579512019568"
     }
    }
   },
   "execution_count": 4,
   "outputs": []
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "ZRICWD5Z70SH",
    "executionInfo": {
     "status": "ok",
     "timestamp": 1705956052825,
     "user_tz": 300,
     "elapsed": 4786,
     "user": {
      "displayName": "Kangning Liu",
      "userId": "18225106579512019568"
     }
    }
   },
   "outputs": [],
   "source": [
    "\n",
    "import numpy as np\n",
    "import matplotlib.pylab as plt\n",
    "import matplotlib.patches as patches\n",
    "import os\n",
    "import torch\n",
    "from skimage import io\n",
    "# from skimage.measure.simple_metrics import compare_psnr, compare_mse\n",
    "from skimage.metrics import peak_signal_noise_ratio as compare_psnr\n",
    "from skimage.metrics import mean_squared_error  as compare_mse\n",
    "import sys\n",
    "from utils import *\n",
    "import time\n",
    "\n",
    "# %matplotlib widget\n",
    "# %matplotlib notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "71ECqrjo70SH",
    "executionInfo": {
     "status": "ok",
     "timestamp": 1705956052825,
     "user_tz": 300,
     "elapsed": 3,
     "user": {
      "displayName": "Kangning Liu",
      "userId": "18225106579512019568"
     }
    }
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "id": "yJgmK8NZ70SH",
    "executionInfo": {
     "status": "ok",
     "timestamp": 1705956052825,
     "user_tz": 300,
     "elapsed": 2,
     "user": {
      "displayName": "Kangning Liu",
      "userId": "18225106579512019568"
     }
    }
   },
   "outputs": [],
   "source": [
    "# Paths for data, pretrained models, and precomputed performance measures\n",
    "pretrained_base = file_root_path + '/bias_free_denoising/pretrained/'\n",
    "precomputed_base = file_root_path + '/bias_free_denoising/precomputed/'\n",
    "data_base = file_root_path + '/bias_free_denoising/data/'\n",
    "\n",
    "# Datasets available in the data folder\n",
    "train_folder_path = os.path.join(data_base, 'Train400/')\n",
    "test_folder_path = os.path.join(data_base, 'Test/Set68/')\n",
    "set12_path = os.path.join(data_base, 'Test/Set12/')\n",
    "kodak_path = os.path.join(data_base, 'Test/Kodak23/')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "nBDzDYeZ70SI"
   },
   "source": [
    "### Choose a model\n",
    "\n",
    "Note: we provide four pre-trained models. You can train and analyze any other model (and its bias-free counterpart) using the train script provided in the repository."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "id": "arMfGRTG70SI",
    "executionInfo": {
     "status": "ok",
     "timestamp": 1705956053032,
     "user_tz": 300,
     "elapsed": 209,
     "user": {
      "displayName": "Kangning Liu",
      "userId": "18225106579512019568"
     }
    }
   },
   "outputs": [],
   "source": [
    "# Choose a model (pre-trained options: 'dncnn', 'unet', 'rcnn', 'sdensenet')\n",
    "model = 'dncnn'\n",
    "\n",
    "# Select the range of noise levels (stdev, relative to intensities in range [0,255])\n",
    "# used during training (options are 0-10, 0-30, 0-55, 0-100).\n",
    "l = 0   # lower bound of training range\n",
    "h = 100 # upper bound of training range\n",
    "\n",
    "BF_CNN = load_model(os.path.join(pretrained_base, model, 'bias_free', str(l)+'-'+str(h)+'.pt'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "pspDFhCC70SI"
   },
   "source": [
    "### Choose a clean image\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "id": "VL_0NnM770SI",
    "executionInfo": {
     "status": "ok",
     "timestamp": 1705956053032,
     "user_tz": 300,
     "elapsed": 3,
     "user": {
      "displayName": "Kangning Liu",
      "userId": "18225106579512019568"
     }
    }
   },
   "outputs": [],
   "source": [
    "# !pip install ipympl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "id": "atmZnsIq70SI",
    "outputId": "89cc565b-b694-4e0a-f472-e5700a163a3b",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 268
    },
    "executionInfo": {
     "status": "ok",
     "timestamp": 1705956053194,
     "user_tz": 300,
     "elapsed": 164,
     "user": {
      "displayName": "Kangning Liu",
      "userId": "18225106579512019568"
     }
    }
   },
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 300x300 with 1 Axes>"
      ],
      "image/png": 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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "# choose a clean image (figure 4 in paper uses image_num=15)\n",
    "\n",
    "image_num = 15\n",
    "clean_im = single_image_loader(test_folder_path, image_num)\n",
    "\n",
    "# Crop out a 40x40 patch (optional, helps for visibility.  Same values used for Figure 4 in paper).\n",
    "clean_im = clean_im[100:140, 100:140]\n",
    "dim1, dim2 = clean_im.shape\n",
    "\n",
    "\n",
    "f , axs = plt.subplots(1,1 , figsize=(3,3))\n",
    "axs.imshow(clean_im, 'gray', vmin=0, vmax = 1)\n",
    "axs.axis('off');\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "LUM07TH970SI"
   },
   "source": [
    "## Interpretation: Nonlinear adaptive filtering\n",
    "\n",
    "Since the BF-CNN can be interpreted as applying an adaptive linear transform, each pixel in the denoised image is a weighted sum of input pixels. The weighting function is one row of the Jacobian, evaluated at the input image. Here, we examine this weighting function for selected output pixels, as shown in Figure 4 of the paper."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "-ryHulU870SI"
   },
   "source": [
    "### Interactive visualization of adaptive filters\n",
    "\n",
    "Note that all weighting functions sum to approximately one, and thus compute a local average. Their shapes vary substantially, and are adapted to the underlying image content. As the noise level increases, the spatial extent of the weight functions increases in order to average out the noise, while respecting boundaries between different regions in the image, which results in dramatically different functions for each pixel (i.e., non-convolutional)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "id": "mMS7xeBF70SI",
    "outputId": "b930b7af-d4fe-46a9-cd8c-6c5f062b6189",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 819
    },
    "executionInfo": {
     "status": "ok",
     "timestamp": 1705956058461,
     "user_tz": 300,
     "elapsed": 5270,
     "user": {
      "displayName": "Kangning Liu",
      "userId": "18225106579512019568"
     }
    }
   },
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 800x900 with 7 Axes>"
      ],
      "image/png": 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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "# Choose some noise levels to examine, relative to image intensities in range (0,255)\n",
    "# Note: Figure 4 of paper uses [10, 30, 100].\n",
    "noise_levels = [10, 30, 90]\n",
    "\n",
    "global residual_imgs, input_imgs\n",
    "input_imgs = []\n",
    "residual_imgs = []\n",
    "\n",
    "# %matplotlib notebook\n",
    "\n",
    "fig = plt.figure(figsize = (8,9))\n",
    "fig.suptitle('click on a pixel on any of the noisy images to see filters')\n",
    "plt.axis('off')\n",
    "ax_names=[]\n",
    "\n",
    "for j in range(len(noise_levels)):\n",
    "    # add noise\n",
    "    noisy_im, _ = add_noise2(clean_im.reshape(1,dim1,dim2), noise_levels[j], 'S')\n",
    "    # plot noisy\n",
    "    ax = fig.add_subplot(3,len(noise_levels),j+1)\n",
    "    ax.imshow(noisy_im[0], 'gray', vmin = 0, vmax = 1)\n",
    "    ax.tick_params(bottom=False,left=False,labelleft=False,labelbottom=False)\n",
    "    ax.set_title(r'$\\sigma = $ ' + str(noise_levels[j]) + '\\n noisy image')\n",
    "    ax_names.append(ax)\n",
    "\n",
    "    # denoise\n",
    "    inp_test = torch.tensor(noisy_im.astype('float32'),requires_grad=True).unsqueeze(1)\n",
    "    input_imgs.append(inp_test)\n",
    "    residual= BF_CNN(inp_test)\n",
    "    residual_imgs.append(residual)\n",
    "    denoised = residual.squeeze(0).squeeze(0).data.numpy()\n",
    "\n",
    "    # plot denoised\n",
    "    ax = fig.add_subplot(3,len(noise_levels),j+len(noise_levels)+1)\n",
    "    ax.imshow(denoised, 'gray', vmin = 0, vmax = 1)\n",
    "    ax.tick_params(bottom=False,left=False,labelleft=False,labelbottom=False)\n",
    "    ax.set_title( 'denoised image')\n",
    "\n",
    "global last_pa\n",
    "last_pa = []\n",
    "\n",
    "ix, iy = 0, 0\n",
    "def onclick(event):\n",
    "    print(\"Click event captured\")  # Debugging line\n",
    "\n",
    "    global ix, iy\n",
    "    ix, iy = int(event.xdata), int(event.ydata)\n",
    "\n",
    "    # remove previous pixel marker\n",
    "    if len(last_pa) != 0:\n",
    "        for i in range(len(last_pa)):\n",
    "            last_pa[i].set_visible(False)\n",
    "\n",
    "    for j in range(len(noise_levels)):\n",
    "        ax = fig.add_subplot(fig.add_subplot(3,len(noise_levels),j+len(noise_levels)*2+1))\n",
    "        filt = torch.autograd.grad(residual_imgs[j][0,0,iy,ix], input_imgs[j], retain_graph=True)[0][0,0].data.numpy()\n",
    "        limit =  max(np.abs(np.min( filt)), np.abs(np.max( filt)))\n",
    "        ax.imshow(filt, 'RdGy', vmin= -limit, vmax = limit)\n",
    "        ax.set_title('adaptive filter \\n sum = \\n' + str( np.round(np.sum(filt),2)))\n",
    "        ax.tick_params(bottom=False,left=False,labelleft=False,labelbottom=False)\n",
    "        pa = patches.Rectangle((ix-.5,iy-.5), width=1, height=1,edgecolor = [1,0,0], angle=0.0, facecolor='red', lw=1)\n",
    "        ax_names[j].add_patch(pa)\n",
    "        last_pa.append(pa)\n",
    "\n",
    "cid = fig.canvas.mpl_connect('button_press_event', onclick);\n"
   ]
  },
  {
   "cell_type": "code",
   "source": [
    "def plot_filters_for_points(points, clean_im, dim1, dim2, patch_h=1, path_w=1, angle=5):\n",
    "    \"\"\"\n",
    "    Plot noisy, denoised images, zoomed-in crops, and adaptive filters for two specified pixels, for each noise level.\n",
    "\n",
    "    Args:\n",
    "    points (list of tuples): List containing two tuples, each with the (x, y) coordinates of a pixel.\n",
    "    clean_im (array): The clean image.\n",
    "    dim1 (int): Dimension 1 of the image.\n",
    "    dim2 (int): Dimension 2 of the image.\n",
    "    \"\"\"\n",
    "    # Noise levels to examine\n",
    "    noise_levels = [10, 30]\n",
    "    width = 10  # Width for zooming and rectangle\n",
    "    linewidth = 2  # Line width for rectangle\n",
    "\n",
    "    for noise_level in noise_levels:\n",
    "        # Add noise\n",
    "        noisy_im, _ = add_noise2(clean_im.reshape(1, dim1, dim2), noise_level, 'S')\n",
    "\n",
    "        # Denoise\n",
    "        inp_test = torch.tensor(noisy_im.astype('float32'), requires_grad=True).unsqueeze(1)\n",
    "        residual = BF_CNN(inp_test)\n",
    "        denoised = residual.squeeze(0).squeeze(0).data.numpy()\n",
    "\n",
    "        # Create figure for this noise level\n",
    "        fig, axes = plt.subplots(nrows=len(points), ncols=4, figsize=(16, 9))\n",
    "#         fig.suptitle(f'Noise Level {noise_level}')\n",
    "\n",
    "        for i, point in enumerate(points):\n",
    "            ix, iy = point\n",
    "\n",
    "            # Noisy Image\n",
    "            axes[i][0].imshow(noisy_im[0], 'gray', vmin=0, vmax=1)\n",
    "            pa1 = patches.Rectangle((ix,iy), width=path_w, height=patch_h, angle=angle, edgecolor = [1,0,0], facecolor='red', lw=5)\n",
    "            axes[i][0].add_patch(pa1)\n",
    "            rect1 = patches.Rectangle((ix-width, iy-width), width*2, width*2, linewidth=linewidth, edgecolor='r', facecolor='none')\n",
    "            axes[i][0].add_patch(rect1)\n",
    "#             axes[i][0].set_title(f'Noisy Image\\nPoint ({ix}, {iy})')\n",
    "            axes[i][0].axis('off')\n",
    "\n",
    "            # Denoised Image\n",
    "            axes[i][1].imshow(denoised, 'gray', vmin=0, vmax=1)\n",
    "            pa1 = patches.Rectangle((ix,iy), width=path_w, height=patch_h, angle=angle, edgecolor = [1,0,0], facecolor='red', lw=5)\n",
    "            axes[i][1].add_patch(pa1)\n",
    "            rect2 = patches.Rectangle((ix-width, iy-width), width*2, width*2, linewidth=linewidth, edgecolor='r', facecolor='none')\n",
    "            axes[i][1].add_patch(rect2)\n",
    "#             axes[i][1].set_title('Denoised Image')\n",
    "            axes[i][1].axis('off')\n",
    "\n",
    "            # Zoomed Crop\n",
    "            zoomed_crop = denoised[iy-width:iy+width, ix-width:ix+width]\n",
    "\n",
    "            axes[i][2].imshow(zoomed_crop, 'gray', vmin=0, vmax=1)\n",
    "            pa1 = patches.Rectangle((width,width), width=path_w, height=patch_h, angle=angle, edgecolor = [1,0,0], facecolor='red', lw=5)\n",
    "            axes[i][2].add_patch(pa1)\n",
    "            rect1 = patches.Rectangle((0,0), width*2, width*2, linewidth= linewidth*3, edgecolor='r',facecolor='none')\n",
    "#             axes[i][2].set_title('Zoomed Crop')\n",
    "            axes[i][2].axis('off')\n",
    "\n",
    "            # Gradient\n",
    "            filt = torch.autograd.grad(residual[0, 0, iy, ix], inp_test, retain_graph=True)[0][0, 0].data.numpy()[iy-width:iy+width, ix-width:ix+width]\n",
    "            limit = max(np.abs(np.min(filt)), np.abs(np.max(filt)))\n",
    "            x = axes[i][3].imshow(filt, 'RdGy', vmin=-limit, vmax=limit)\n",
    "#             axes[i][3].set_title(f'Gradient at ({ix}, {iy})')\n",
    "            axes[i][3].axis('off')\n",
    "            x.set_clim(-0.1, 0.1)\n",
    "            plt.colorbar(x, ax=axes[i][3])\n",
    "\n",
    "        plt.tight_layout()\n",
    "        plt.show()"
   ],
   "metadata": {
    "id": "XESdGOjuQ0mh",
    "executionInfo": {
     "status": "ok",
     "timestamp": 1705956058461,
     "user_tz": 300,
     "elapsed": 2,
     "user": {
      "displayName": "Kangning Liu",
      "userId": "18225106579512019568"
     }
    }
   },
   "execution_count": 11,
   "outputs": []
  },
  {
   "cell_type": "code",
   "source": [
    "plot_filters_for_points([(18, 18), (25, 12)], clean_im, dim1, dim2)"
   ],
   "metadata": {
    "id": "Gu5NGxPUQ23d",
    "executionInfo": {
     "status": "ok",
     "timestamp": 1705956064556,
     "user_tz": 300,
     "elapsed": 6097,
     "user": {
      "displayName": "Kangning Liu",
      "userId": "18225106579512019568"
     }
    },
    "outputId": "7a7b386a-b755-449e-c34c-71e5290aa192",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    }
   },
   "execution_count": 12,
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 1600x900 with 10 Axes>"
      ],
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     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 1600x900 with 10 Axes>"
      ],
      "image/png": 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     },
     "metadata": {}
    }
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "id": "gjW3V0w570SJ",
    "executionInfo": {
     "status": "ok",
     "timestamp": 1705956064556,
     "user_tz": 300,
     "elapsed": 3,
     "user": {
      "displayName": "Kangning Liu",
      "userId": "18225106579512019568"
     }
    }
   },
   "outputs": [],
   "source": [
    "# exit the interactive mofig.savefig('comparison_plot_piecewise_natural_image.pdf', bbox_inches='tight', dpi=300)de\n",
    "f.canvas.mpl_disconnect(cid)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "id": "JN6mkdPu70SJ",
    "executionInfo": {
     "status": "ok",
     "timestamp": 1705956067907,
     "user_tz": 300,
     "elapsed": 3353,
     "user": {
      "displayName": "Kangning Liu",
      "userId": "18225106579512019568"
     }
    }
   },
   "outputs": [],
   "source": [
    "fig.savefig('comparison_plot_natural_image_gradient.pdf', bbox_inches='tight', dpi=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "h489r_SU70SJ"
   },
   "source": [
    "## Interpretation: Projection onto an adaptive signal subspace\n",
    "\n",
    "We can study the effect of the linear transformation, A, by looking into its column space. A singular value decomposition of A, reveals that 1) most singular values are  close to zero, implying that the network is discarding all but a very low-dimensional portion of the input image, and 2) left and right singular vectors of the signal subspace are nearly identical. This means that we can interpret the action of the network as projecting the noisy signal onto a low-dimensional subspace.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "t4WoYir-70SJ"
   },
   "source": [
    "### Compute SVD of Jacobian (adaptive linear transform) of denoiser\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "id": "KFYSrYk870SJ",
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "executionInfo": {
     "status": "ok",
     "timestamp": 1705956144122,
     "user_tz": 300,
     "elapsed": 76218,
     "user": {
      "displayName": "Kangning Liu",
      "userId": "18225106579512019568"
     }
    },
    "outputId": "8185c291-3218-443d-d229-d47cc42300aa"
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "---- Jacobian computation time --- 76.1785717010498 seconds ---\n"
     ]
    }
   ],
   "source": [
    "# Compute the Jacobian, evaluated at a noisy version of the clean image selected above.\n",
    "# WARNING: slow computation! For a 40x40 patch, it can take between 1 and 2 minutes.\n",
    "\n",
    "noisy_im = add_noise2(clean_im.reshape(1,dim1,dim2), 90, 'S')[0][0]\n",
    "\n",
    "start_time_total = time.time()\n",
    "A = calc_jacobian(noisy_im,BF_CNN)\n",
    "print(\"---- Jacobian computation time --- %s seconds ---\" % (time.time() - start_time_total))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "id": "pvEvchkj70SJ",
    "executionInfo": {
     "status": "ok",
     "timestamp": 1705956147594,
     "user_tz": 300,
     "elapsed": 3489,
     "user": {
      "displayName": "Kangning Liu",
      "userId": "18225106579512019568"
     }
    }
   },
   "outputs": [],
   "source": [
    "# Compute SVD of Jacobian\n",
    "U , S, V = np.linalg.svd( A)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Jf1JCY2d70SJ"
   },
   "source": [
    "### Plot singular values\n",
    "\n",
    "Note that most singular values are close to zero, suggesting\n",
    "the denoiser is eliminating many dimensions.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "id": "0efHo6Vg70SJ",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "executionInfo": {
     "status": "ok",
     "timestamp": 1705956148170,
     "user_tz": 300,
     "elapsed": 596,
     "user": {
      "displayName": "Kangning Liu",
      "userId": "18225106579512019568"
     }
    },
    "outputId": "684a9ed1-0886-4c10-f93f-71f5ad91de04"
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
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      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
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      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
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      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
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      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
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      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
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      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
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      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ],
      "image/png": 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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "# Plot the singular values against the axis number.\n",
    "f, ax = plt.subplots(1,1,figsize = (8,4))\n",
    "\n",
    "ax.set_xlabel('axis number ', fontsize = 12, fontname= 'Times New Roman')\n",
    "ax.set_ylabel('singular values', fontsize = 12, fontname= 'Times New Roman')\n",
    "\n",
    "for tick in ax.xaxis.get_major_ticks():\n",
    "    tick.label1.set_fontsize(10)\n",
    "    tick.label1.set_fontname(\"Times New Roman\")\n",
    "\n",
    "for tick in ax.yaxis.get_major_ticks():\n",
    "    tick.label1.set_fontsize(10)\n",
    "    tick.label1.set_fontname(\"Times New Roman\")\n",
    "\n",
    "\n",
    "ax.plot(S, '-o', alpha = 1, markersize = 2,linewidth=1);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Fkecr91x70SJ"
   },
   "source": [
    "### Visualize some example singular vectors with large singular values\n",
    "\n",
    "These are 'features' of the input image that are preserved by the denoiser."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "id": "NgDj26FA70SJ",
    "outputId": "ce9f11ea-9e47-407b-af09-6998503a4cb3",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 561
    },
    "executionInfo": {
     "status": "ok",
     "timestamp": 1705956149009,
     "user_tz": 300,
     "elapsed": 842,
     "user": {
      "displayName": "Kangning Liu",
      "userId": "18225106579512019568"
     }
    }
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family ['Times New Roman'] not found. Falling back to DejaVu Sans.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 800x300 with 4 Axes>"
      ],
      "image/png": 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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "# Show some example singular vectors with large singular values\n",
    "sing_vect_n = [1,2,3,4] # indices of the singular vectors for visualization\n",
    "\n",
    "N = dim1*dim2 # dimensionality of the space\n",
    "\n",
    "limit =  max(np.abs(np.min( U[:,sing_vect_n])), np.abs(np.max(U[:,sing_vect_n])))\n",
    "f , axs = plt.subplots(1,len(sing_vect_n) , figsize=(8,3))\n",
    "plt.subplots_adjust()\n",
    "for i in range(len(sing_vect_n)):\n",
    "    u = U[:,sing_vect_n[i]]\n",
    "    v = V[sing_vect_n[i],:]\n",
    "    axs[i].imshow(u.reshape(dim1,dim2), 'gray', vmin=-limit/2, vmax = limit/2)\n",
    "    axs[i].set_title('singular vector '+str(sing_vect_n[i]), fontsize = 10, fontname= 'Times New Roman')\n",
    "    axs[i].tick_params(bottom=False,left=False,labelleft=False,labelbottom=False)\n",
    "    axs[i].set_xlabel(r'$v^Tu$ =  '+str(np.round( np.dot(u,v) ,2))+ '\\n $s =$ '+str(np.round(S[sing_vect_n[i]],1)),\n",
    "                      fontsize = 10, fontname= 'Times New Roman');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "id": "_hketXrD70SJ",
    "outputId": "b6654ccf-6834-49e8-cf64-4b2b7cad2ad4",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 543
    },
    "executionInfo": {
     "status": "ok",
     "timestamp": 1705956150175,
     "user_tz": 300,
     "elapsed": 1169,
     "user": {
      "displayName": "Kangning Liu",
      "userId": "18225106579512019568"
     }
    }
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 800x300 with 4 Axes>"
      ],
      "image/png": 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Yj1bfe/fu3aFzq1atCtLV1dVBunfv3qF8nTt39tYDwe8Vvo8iIvv27QuOP/XUUw06Fk6YMEFKS0vjzmMdDx48GKT1O4eyoscnfA7sf0u+sHx9L+ucHl+jYF3jG5/1bxyrrHEM09a7rNsQ31HsB/1uoHxFdcyi74Vj4WOPPRZJDiNNAGMFl5SUHHECiA1lvdi6sfFlxuv0Q6IgYl30ZAgneS1atPCew/K0UOKAiC+ZFiisuzUg+uquy8dnQQESsSeA+FwobDpfogHjSFgvh4g9qUgXsXuUlpbm1QTQOufLp9sG28DK15ATwFQGfau+iX6nm1j5TZs2TThhwPcfZcn6aOgxwyczup1xPIkqP7rO1tjluxeOH9Z4p/sb6xX1O+H7Lujf+lwq4641AcT6Wu9WovOZQI+FvvMi4bbQ75yvT2Jlx8C2sSZvDTkB1PLlKy/VCSDKTaoTQPz2Wv2A51KdAPomhBZJOYIuKChIqFPGCludgg2nX7ZWrVoFafxPsba2Nq4OifLhap2IyLfffhukdZ379euX8JwO7t2nT58gvXjx4iCNq2siYQHQ9V25cmWQXr9+fZDG/zxFRE4//fQgjYMePodIWHD0xM73H4ZebcVntiZHuWpb8u2330pdXZ1p3xB1xUuX4fuoYNvq3760vrf18cFz1oQKy7cGzaj/peMgl+h3omuSAevRmFyOdujQQYqLi+PkB//ZxH/edD5sTz3uoFxs2bIlSONqmEh49a5t27ZBWo+t2KdaZnC8wlW02KpWojp27NgxYdki4fFfPzPWEcc4fa/t27cHaZQZa5KnV8bxncF+sP6RseQz0zZ9qbJv376E9cYxH/vcekbrHcfxScsQ9rke/6Lia1/rn3zEei7rn3zrH3Rfe+g6YD4to3guaj9ERZeRSpm5KdWEEEIIISRjcAJICCGEEJJncAJICCGEEJJnJG0DWFBQYBp3oj2Apb/X59DuBe1otP2az8Zg69atod9oV2LtnBw0aJD3HNq6tG/fPkhrO0fLnsVXp3feeSd07vjjjw/SuMtO29hgPXDThy4f7RT18/sMxrUNAT5XQxvbW+zdu1cOHz5sbriwjLatTRA+G0udD+UQ280yOLbaF21HdJ/jvSz7TayjZWSN8qvr69v4Ye3G1/2Az5mOnb65SFVVlZSWlpqG2Ninuu+xD/R7XFVVFaRxN6v2UoDgOKl3+qJ9tQbLRHtDXV+9kc6XD59f7ypu3bp1kEaPBdrOedGiRUEad7NqWV2zZk2Q1p4N0O4PbQ/1hgmfrGq7Mewv3272bMh6zB46HeOxrr9vZ6rVNpatZNTNbFGJuvFJ19f3juoNl/g91Tu/EbxOyxe2DbZnqrLi29yjz0WFK4CEEEIIIXkGJ4CEEEIIIXlGUipg55zU19fHLbf6ljMtVxQaVIehCkNvq0aVBao2ddnoMmHZsmWhc7gUi0u2qIbVZWA9tPuVqG5VEO2QFNUlllNIn29CkbADbayvtW09an318njsmbOhCj58+LAUFRWZqt2oLmK0OgeX/S3fTKiWxTIsmdfmC6j6wv7S/Rq1jyx1vs8X3JF8SfmOa7WKrx5Rjh8pX5R+bWg5jPlEtVxHWCpFS23Uo0ePII3vNKZ1mejORbuLQYewlpsiHNcsMxd8Zksu9LiD8r58+fKEddB1xPJ13deuXRuktYoO1d54nSW31nOhTGqn07HnStUFytEQGwut99gax6wxA9tUq+kRbaYVw+dSSiS+H3yqeGvMsFx9WeM/9hPWXZtv+Xynande+E3W98X3yJK9qGZZmM/XvtZ9NFwBJIQQQgjJMzgBJIQQQgjJM5JWASeze8faLWwtWeNuMb2jDZdfMYamjqdpRQLB2LizZs0K0lrFgmXgDjm91O8LOyQSXo5FFQvGBRbx71TW6mZU7+hdgb4QN1FDpul81lJ07Jmz4SE/pn7T/eBTv1l11DKKfW6pdCy1L4Lq1kRhFBPd11I3R1UHWxFOkKg7pHV51u5mX3skI1/WdYnOZWtXulaV+lQ5lopKh1NDFTB6ItAqKuwDjEH+97//PZQPY+hq+cFxCFXF+l5RQyRi+Xp8wvEVr9O7oLF8fC/0Tt8OHTp4y8Bdy1YILisSBGLtnI/9TiWc2dHSpEkTadKkSeRxwXoHdRm+HdjW+27tqrVC7VkRxJBUIoFYu5t95gYi4fcSv8P6m4ztFDXcpdUPFlGiWiXzTeYKICGEEEJInsEJICGEEEJInsEJICGEEEJInpGUDaAP37ZtrQ+PGp3B2j6OW67xvnqbOkYG0S4CsPz169cH6Xnz5nnri7YCWq+PNgWW+wB01aDrhL/RLcTevXtD+fC3LiOqq49U7EV8do/ZsHvp1KmTlJaWyldffRU6jv2AfWc9r2Xb5ov2ocvHdtL2XGgvorfnY30xbdlspmorh/jcG2hSsSPNNEfrYibdaBcY2LY4zmgZxPfTchHTpk2bIK1lFW3q0AZu06ZNoXw4rum+Qnnt3LlzkNbRQ9CmzpILfE49dqH7FKyvHsfQHvqLL74I0trOG11pYd1FwjaLUW1NEct+Xb/jsfon434jXbRt21ZKS0vj2gb7GeUmGddZ+MzYR5ZrEp89oEi4T6y2impvaPWlNT757MO1bR/KKO5L0G6bsO21zFt2wFGw+svnji+ZKCNcASSEEEIIyTM4ASSEEEIIyTOSUgEfOnRICgsL49xZ+FSl1pJyVLWkPo7LnrhkiwG/RcLLstozPqpit2/fHqT1c6EqxnIJgmogrR7wPRfeV5ePqh29VI7L6nqJHfNaW9Oxvrg8bqne9TJ6TE3jc1+TSTp06CDNmjWL88iPav9UQfnyebgXiR6RAmXKknkrYkhUtYd1zhfMXstrVNV5VLWvVfd0qG1jZTS0Cri2tjaIwoD41Ff6XbXU8NZ1CKqi0F1Mly5dQvmwj7V7FxwL8V56PMV7RY2yo8eTysrKII0q23Xr1oXybdy4MUjju4DPqMuzTG/wuXSdsG0wbbnz0H0Sc5+jVdkNQdu2baWsrCxurNqxY0fC/KmakFhjAV6H7Wa56dL94Lu3vm9UNaql2kZZxnpo1a4vWo9+rqjfQGssjOrCDJ/L1zZUARNCCCGEEC+cABJCCCGE5BmcABJCCCGE5BkpuYHR9j+op7bcG6BuWttYYBnWlnufLl67Laiurg7SGMZN1x9tYrTdhG8rvaWXRzc1ImH3CWizpkPc+VxGaJsdtB2wbBZwO7p2kYPP5bM9EAn3ke7LbLg8iFFXVyd1dXVy3HHHhY6j7STaZWibHcs9h8/GRMs8yp5lO4Q2Vrq/fDIVNSyShWVjEtWO0AoThViuCnx1sO5r2flYLigamkTtiLKGz6vti/Fay6YI32kdWgvzof1Zz549Q/muueaaIK3DxKF9NI4Z7du3D+XD9z2q/ad+ZvztCy0nEh4bMTydfn/wPdb2wPgs+G2w7NctdylRwphlQxZj4Vn19w/HQmuMt8Zx3zc5aohXLdfYR/o76esHS9YwnzWm6TkE/rbGJHy/8DusbT2j2jb6vrvJEMWFVzL20FwBJIQQQgjJMzgBJIQQQgjJM1JSAVvLyLgsqbem49Kk5T4Bl1gtVyeY1sue7dq1C9J6eRyXjq0lcJ/aTD8/qhXQY7iIyBlnnBGk8Rn79+8fyofqHZ/LDl2GBpfcsQ31NnWfq4pk3HRky/1G7J7OuTg1elVVVZBevXp1kNYq+6iRDDCf7gefPOh8+Ft7iY8auSUV9HOhagLTqUaJsdRlSCpRGI5lcCzAd9ByI6XBvKh60pEKUD6xT3HsExE5//zzg/Q555wTOrdz584gja6prPpa4ziO+bq/0RQFo5VotSy6e7HcMuG4Zo2LqPLTamQflvsx/VyxdyEd722yxMZCLRv4PUHVa1T3K7GyY/jUwVYZOh/2lx4nsY98alNdJwvLDYzPVY2vX/U563sS1UVSqmNhus0MuAJICCGEEJJncAJICCGEEJJnpKQC1suQuDRvLYFGDUKPy76WGhmXs61dj5YauaamxlsGqilw+Vrnw/piAGkRkSFDhgRpq218O4S0isVSsaPKCdWNVmQJLE/fy7csn2327t0r9fX1cf3aoUOHII3RBLS6Aa+z5AafWatOfCpgq7+se2EfaZVY1N1eVh9FVU/5ZCOZnblHey7qruJcwFJRocxYKlUtWygXlikHyhqqAHHnuUhY/rUKtGvXrkH6hBNOCNJfffVVKB9G64iqDrR27fquEQm3oRVdA8c//d5he+COUz1m6B2iicoWCatRffWNujs6nRw4cEAKCwvjdtXidwjrbo0ZUU2ALLMpaze/tWsX3w9sR12GZfblQ/elLwKTxlL7IlYb+r7r1rcAsdTNUcdPC64AEkIIIYTkGZwAEkIIIYTkGZwAEkIIIYTkGSnZAGobAJ/+PqqXcf0bddvafsun37a2elsuMbC+ljd1S69uuc7Q9lwxtF0C1snn3kEkbNtiufCIar+QyhZ2rFc2IoJs3rxZSktLQ1FWRMIRBHr06BGkly5dGsoX1Z4tqi2F1f9W1BGfOx7Ldiaqm5ZUI2b47P4suzzLhisVtw3JELuuoe0ECwsLpaioKK4/8L3Gd1WPY5Y9ED4L5tM2gD53Ppb7FW3zhOMTjn/du3cP5cMoSWhfrJ8LxwOffZ1I+JthuZKxbCDR1lE/M9ofWi6WsD0wnYz7rVh7JOPqJ13s2bNHDh06FOcGBm0A0SWMjgoV1Q1aOog6nmDb63bHfsW6R3VNo89FHVsttzJR7aujRmOyXGxZbRi7zmdrm/BekXMSQgghhJBGASeAhBBCCCF5RlIq4JjXcQ0uReKSveV13Qoojcu+elndp7K0lmX1MrIv6oilprHcpeB11nKw5bbAF51Eq5Bxu78VTQUjCGBaJLxE7FM3iYSfSy8rZ9P7/dq1a6W4uFjatm0bOo7P0qVLlyCN7nxE4vvZV4YVAF6r8GNYS/tR1RKpkkl1q6WKsEwRLPmKWg/LnCFbKuC6ujo5fPhw3H1RTelTQ4qExx3LlYzPJYw+Z6myUFb1OawjjhM+0xV9L9+4IBI/PmH5qIq05BbbRru32bVrV8J8+l7t27f31tfnpkOD7YSmQSLfR1PxjQmZZOfOnVJSUiIVFRWh46h+x2+GlqFUIlJEfdcsl1j6PfaZwFgmYOmIQJTKGGS5prHMd/BZtKxFjazke+dFvh9jknFHxBVAQgghhJA8gxNAQgghhJA8I6VdwHGFwLI6LjFbO12tHZEWVoQPxFJNolrZF3hdxK860WoEVA9Yz4Xl6bbBfFi+VqNbanWfaibVnbpYJ60SipWZjV3A69evlyZNmkh1dXXoOC6dt27dOkgfd9xxoXxff/11kLaW4jFtyZrlud7C8iCPpKKmiXqN9Z5YJhZRy8x0dIRsmSLU19dLfX19nPxHje6C6iArKoKlQse2xV2gyURtwR29mE41qgyOO1aEE99OX5Hw86Pad/PmzaF8lkoNf1smHz7VuX5+HHe3bt0aOhdrt2yogLdt25bQHAafC3cBx9TVibB2o6ey09VSh1rnrDr5zCMs9X2qKuCoJmCpekuIghVZRH+TYu8bdwETQgghhBAvnAASQgghhOQZnAASQgghhOQZSdkAxuxetF7atw1ae25HWwRLTx3VbiiqbYdlR4D2Jrt3745UvrU1Xevl8bdlR6Y9tPvuZdmboQ1KVNc0FpaNWqx8qw8yxYEDB6Suri4u0gDKIdoOderUKZRv/fr1QVrbxOAzo92PZdthuQGIytHailjlaSwXCT5Z0eVFfUdTiaySDDE7nXRHLTgSRUVFUlRUZI5j+D5qG0CrD7BtcQy17mXZ4lq212h/h+OftmfzRbnQx7F8/X5idAocC9Gdiy7TiuiE3xPdhlg+tr1l5xb1HdTPFXOzkg0bwF27dknTpk1Tdm2lv9EI9mUqY1wy77vPbljbh+KY7IvopdF97rPti2oDabmLs95Dq44+9y7Wdycd32SuABJCCCGE5BmcABJCCCGE5BlpcQPjc5eh1ZqWCxefqshSX+KSqs6Hy/RaTeFbRtXLzbikj8vN6C5BJOyeoEWLFqFzHTt2DNItW7YM0uidXURk+/btQRqX5S2v/pa3fmup2OfSRi9f4+9cUgGXl5dL06ZN47zfoysMDF6PUUFEJHTdunXrvOcQK1oDtnXUfBapqmV9LhL0uahe8rH/0+HOJdVIJQ0d5SMKMfWvZdZhuanA906PT1HdCuG7h2X43EMc6V7oBkurZXFsxPK2bdsWyodRd7T7JXTb1K5duyDdpk2bUL5vvvlGEqFVr1gPrcr0qT0tsxFsTx3tA01KfKpon5o8k+zevVuaNm0a9+3yuWbT3x18Lsu0C4lqbmGNGdZ7g/Ww1K1WFBcs3/ft0mXoe+G4i3Kjn8tyfeQzRbPM0hDrm+xzfZSMOQxXAAkhhBBC8gxOAAkhhBBC8gxOAAkhhBBC8oykbAAPHTokhYWFcXYUuB3fCnGEtgjaVg716pbdVNTQPZhP69F9ZVj2Majb1yHj0F4Gbc9ERLZs2RKkq6qqgjTaBopIKJQPlq9dC1i2fanYEWDasrdMJRxZppgxY4aIxLt3GTNmTJBGm0pt94LXLVq0KHTOJ79WqKmoIQ51+/rcTqQjjJtlH+h71/S5qPdKFZ99WzKhzI50PFPs2rVL9u/fL61atQodR1mzbMKiuotIxSWE7kPMZ7mSQXswbefsC7uGYRVFwuOdtiNE90s9evRImBYJv59o54zvtEi4ffU3CbHswXyhS60QkbrvrHtnmi1btkhRUVHI9lJEpFevXkHa973T5/S3JqoNYNSQkVHHOMuFmc8uWdtAotxYrtnwOi3zeM6SNcvVmyV7iK8Nk7F/pg0gIYQQQgg5IpwAEkIIIYTkGUmpgA8fPiyFhYWmWxVcetVuSlDF0Lp169A53/ZmaznTWnrG5WxLPexzpaCxVNuoArfcgOAyvXaf0KFDhyCNLhL0krL1zL7lYkvdZHl4t9o+ljcd7kFS5YUXXgj9vv7664M0Ppd2R4Qqp88++yx0zueCR7e1T0a1KwFUuVlqWUvd7HOLpNV5UaMBWO59UqmTRSquX6xrfG3Y0Crgbdu2JVT9oRuhqO+dli2f6UmU9zERlqmML3qOdqvii9SgzWHw+dHtlS5j7dq1QRrVxiJh9zGoYtfuYnC81vVA0D2UBt8Zn9svkXAECk0sr1ZDNgR79uyRwsLCONc5PjMCLbPYNrrPferLVE2FfKZHukyfeY2+Duurx3htYuYrA7/dum2wTOxb/R5a0WoQ6z1Eorpw0/3ASCCEEEIIIeSIcAJICCGEEJJnJKUCLiwslKKiorjdQrj8jmpfDP4tEvaurneI4VK/FQnEt0MmHeoRa/naUinjMnJU9Z3Ot2HDhiC9c+fOIK3VF7h7WKtEfLunreX2qAHQfc+VzI6jdKPVPm+++WaQHjVqVJDW8ooqpiFDhoTOLVy4MEhbu2Utb/W+fJqo8utTy1rvhhUJxFeHRL+TrZNFOiJ6WAHbG5K6ujqpq6uLM+XAcQzVobreqG7S8oOqLZRBKwIBqkOtqCNapYb1wl2Q1hiHqmKt9kTVm959j89sPT/uFt66dWvCOoiETWW0VwVsA7yXbhufCYweM7HdfFEssmEOU15eLkVFRaHvh4h/x7UeM9AUS++CTcWswhozLXMYrBfKshWdBM9pFbClzvepsHU+lGWUG60qx/rqbw3KNpYf1XwrqomOdY0FVwAJIYQQQvIMTgAJIYQQQvIMTgAJIYQQQvKMpGwAS0pKpKSkJE7Pjb9xu7zeOo82gdoGEO078Lp0uHfQZaD+PaotE57TtgJo92jdy/LwjWWg3YBuJ7Q/0DZw6HYBbQct25SoNpA+W7Fs2WAl4ve//32Q7tOnT5Du3bt3KB8+86BBg0Ln1qxZE6TRbY/lBgaxPNdbbnai2mJa98oVotqF+twdJCNT2XID06ZNGykpKZHNmzeHjqP9Lo5peszwuc4SibcjimG5hLDazxrjUD6jRmDw1UEkbB+nx38ckyx7MCwTbQyxbUXCtojV1dWhc507dw7SaAOI1+h7Yd0tl2A+29tsvI9VVVXStGlT2bhxY+g4RmhB+0htU442q7p9d+/eHaQt+0ifLbNlexc1morlVg3vq20AUW60HPrGp6jfbm2Lim1q1QPfL21HGtXO26pvKt/i3PyCEEIIIYSQjMEJICGEEEJInpGSCliDy7SovtDLl6ii1OpLVHXiEmuqKsaoqt10qN4sNV/UMn1bxK0oAXrrPy7ho4sE7Y7BpxK2trBrYm2aDTcwTzzxhJSVlcnNN98cOo4uI6ZOnRqkr7jiilA+NEWorKwMnaupqQnSX331VZDW/eCLLuBzEZGIqGrPdLhZSUVFGlV2LZm3vN+n8vy5YopQVVUlpaWlce2K4xi6gdGRCfB91+ovPIcqJMuFixV1JCpWlAGUa8slCvaDfi5fGZZcWFEs0BwGVZ4i4bEL32n93uK9fdEzdH0t9XBD07VrVykuLo4bq9GUpUuXLkFau8vBbwNGoxIJqzN9Zgkifvc+VtQZa8zA++pvFcoQ3iuqiY7Gmif4zll1199a37ucamSldMMVQEIIIYSQPIMTQEIIIYSQPCMpFXBRUVGcGkIkvCRuLaPjkq1WiaD6EsvTS/a4dJqq6jWqOsynKrW8xFu7dqIGefZdo++tl/137NgRpLENO3XqFMqHqnjsE+3V31qKj9U3Gyrgc845RyoqKuR3v/td6Pi//du/BenXX389SKO3e5Fwfw0YMCB0rlu3bkH6448/DtJ6N7ZPFWG1R9RdgpY6I+qubY0lez5SVT37ot9E3WV/pPITXdfQu4DLy8ulrKwstNtUJGw2gDJjef7XZjUoW5YaDscCvEaPT1bbYL1wPNFqTlQPorxrlRc+i1bZ4m98B6364bPo8Ql3d+r3Dr8neK5t27ahfD7vE1Z0llzafV9eXi4lJSUhNbeIyDfffBOk161bF6R1W6MJjO5LjDSF5kb6+X0eMqxoH/ocXofmYVu2bAnlGzhwYJBGWbN2HEeN/mKpgFMZP0XC7yXWSb/LvjE+6nwiVXJHkgkhhBBCSIPACSAhhBBCSJ7BCSAhhBBCSJ6RlA2gc07q6+vjbExQz422YpZrAnSRICKyZ8+eII0eyLXXbSTqvVJ1P4FE9XCu7Q0suwcE64/1024W0DZF26lg+WizgraBImHbCbR70W2NdkCWS5iGZvXq1VJeXi5nn3126Pi9994bpB966KEgPWvWrFA+dIug+3LIkCFBGu1N3n777VA+tJfBMrQcWjYcPtmwbOostwVWxJdM2sgdrf3e0ZSRLQ4cOCAFBQVx70xVVVWQxighe/fuDeXzRT7Q5zCt+9fX35brDEsecezC8UMkbH9nRUXA35a7LGvM9F2j2wyfU9ss4niF3xPdNmjbiO6htD0ctod+x2PjaUPboYp8Vy/nXNz3FNHjP4LfAt1faAOIbYjfahG/jFr265YNPNoAattrlEOfDaxI+LsW1WYz6jiTSsQsEXvPgs+1kH43Eu3B0PVKRg65AkgIIYQQkmdwAkgIIYQQkmckrQJOtLzoW87Xy+2YT7s+wCVsXLLW2/Z96mYraLTGp26zom74tmmL2N7PfcvPqbrEsAJqY5ti3bU6B9sX3eygCkSX7ws8nQ31XGFhoRQWFsYFL7/66quDND7z5MmTQ/mmT58epLWLGFThnXfeeUEa3cqIhNumffv2CY8fCWw7y5UQtr0lh5ZaLVU3BunEMsWI+j7kmjpYjzutWrUK0tgHqEITCau5tFoHr0NVpHaJ4ZO1ZMwQfKYdOlKTzwTGMtHR+NRhUV1JWe+FfmZfhA/9XLW1tUEav0F6LEQVvh5PY/dORzSWZDl06JAUFBTEyRC6+sJ20zKE31OtRkVXbehm5tNPPw3lw+8ffoOsPtHvMbo7wj7SEV7wOst8ycIXacZyA+Org1W2dZ3lBgddxFhzqGTcPfngCiAhhBBCSJ7BCSAhhBBCSJ7BCSAhhBBCSJ6RFhtAKz+Cth5aB472F2gvo+280N7KsnlKxabIsjFBWxltb4E2EHo7d1QXHqnYNmkbAF/76nuhvQW2rw67hzYhuoxYG2TD7mX//v1SVFQUZ7+E9jxXXnllkNb9hTaBixYtCp3DNhg2bFiQPuecc0L5/u///i9Io7uEqPabIrZNCOIrU8t8qmHisoXv+aPa4mSTuro6qaurM+uKdli6f1FWtXsTlBO0c9I2WjjWaJvqqKCNEb4n+t1Cuyyskw7piWNLVFvWqGOhZV+t20aH2kp0X5FwP2Dd27VrF8qH44K258xGOMwYMRtAXQfsV7SP0/aLX375ZZDWz+yzc8bxTiT8DbHcFlnvOObFvty2bVso3/bt24M02mtrW26f/f6R6uHLFxVLli1bZp9LsFT3NkSFK4CEEEIIIXkGJ4CEEEIIIXlGUirgw4cPS1FRUdxyu297fzKqHFQ/oFpBL1mjasJa8kxpOTSix3CtHrFcc0RVZyDJqBGjlGGpB1CdodU5uJzv68tsqOdqa2ulvr4+TnXmUytdeOGFoXwLFy4M0h9++GHoHLo7mDt3bpD+wQ9+EMo3e/bsIG15v48a5SCVpf1kVE+5qEZNRQWcDtOJdBBTAVtg/+rIEhjRANWQImEVK4412kQDXZNE7V/LdQSqTXXkEp95CdZVXxfV7U+qERgsEwocJy1TIfy+oCpTj4W67ZFYmdlQBcdUwFZb+9TBIiJffPFFkF65cmXo3EknnRSksV+1azZ0LeMzKdB10ueiygCq6RH9XL58ydzLd00ycujDKgPbxvp2+9owmefjCiAhhBBCSJ7BCSAhhBBCSJ6RlAr40KFDUlhYGKdG8EUxsHawWFEMcDlX7+bC36h+SGanT1T1g2+HcDp24iSzaxnx7RbSYNtbHtmxPXXgbdztpcuIXefbbZdJ9u/fLwUFBXHyhXVE1Q7uxhQRufHGG4P0k08+GTr3+eefB+lu3boF6bPOOiuUr2/fvkF648aNQdra0WkF8sZzqe7uxuuOpJ7MNVJRo2STQ4cOJdwB73s/dd/jrkW90xHVVxiRQqshfaYnqF7WddJ1xt+o5tMRI/B9Qhn3jQsi9piW6R3rvp2U1k58fP49e/aE8mE/6L6MPXM2zCzq6+uDP8T3TdbjU8eOHYP06tWrQ+eqq6sT5sNoNyJh8waUEy0beG9dD/yWa08aCH6j8F6WaVS6xxNdXipRliwVsM98QV+XDnMYrgASQgghhOQZnAASQgghhOQZnAASQgghhOQZKdkAar20T2dtbU3XoA0D2i9ouxd0ixB1233Uelg6dLyXtq+yXNNE9QSebqLaROCzaNcP2Pba7iVmZ6Rd4jQEhw8flsOHD8c9I9qVoC0Seo8XCXu1HzVqVOjcm2++GaSXLVsWpHv37h3KN3jw4CC9adOmIJ0O2ztLXi2ZT/XdywUsG8BsRlrwERsLNVFd+/jcXomEbZtQjrWrCwRdyej2Q5nUNrs+ez5tA4fXWWML1l2PDRitxLIVT8WmynIDY+XD31hfHe0D215HXYk9czZsV2P9ou/tcyWi+wTHQi0bX3/9dZBGG0gdMQTdwmzduvWIdRWJt/PD9tXvA4LlYx9brtmiuk6L2n/p6GdrfLZshy0b21Rcs3EFkBBCCCEkz+AEkBBCCCEkz0hKBVxfXy91dXVxy7eoOkglUoWI38O1Fe0hKlEjklhbrqNGOEnkGiIRlqsPC0uNjO2WispPqwBQDaQ9/sf6JRvquVgUBi2HvqVzq7+6d+8eOvcP//APQXr58uVBGj3mi4j07NkzSKPKYt++faF8qNpIh5d4JGrUmUyQSXOGZNwsZMtljHNOnHPmWGiNi9h3WqXoc+liqc1Q7rRK1XIrgXVEkw/dzj6Vmq6775pEZSaqg77OMg2IGjEpFfnR0VnQ/YjPDZrl5inTWGYT+hvqQ6t20R0RugXSUW3QpRHm022NEcSsaGLazQyCJgaWK6Go3+FUyMQY5CvDel/TYdbDFUBCCCGEkDyDE0BCCCGEkDwjqTXrWNBpK6A2Lu1agccTlR3DUo9oL/cxLBWLJurSKapEo+521WoAn7d+TdQIH5YncCTqTjq8r1YBW57WY32bDRXcgQMHEkakwefUagofur969OgRpPH5586dG8qHnvFRdYJqY5HwO6BVMXgulUgYlootqgf5XN8dLBLdrKQh8Y2FOD5hfyfzDGhugTKIaZGwyhav0RF9cOyyZBDrqNXN+BvHeD0+Yxl6rPa9k/o99rWVZcph7SRGoo7Bujw0h/FFVsrGWNisWTMpLi6OU6mirGA76XzW+ITPg+pgHbkGVbZolqB3UqM8aO8eKEeW+hblEMvA+onY6mFfP2V6d2868kWdJ0Ql90ZWQgghhBCSUTgBJIQQQgjJMzgBJIQQQgjJM5Let55I74w2JqiL1zYfUbfjR93eHdW2Lap9iKVTt1wp4HWpundJRZ9vuctIh00Z9qu254nZX2TDhmz79u1SWlpqyhfW12ezIxJvE4N2MIMGDQrSn3zySSgfRglBT/i6PN99k8H33uRKhIxUbVGjvocNGUEnKolsUEXCYw26ZrFsUq12QXmyXAxh+doeCutk2Y2iHZa2jd25c2eQxufW7qHwOj3u+uyhLRvAVCOB+EjVTRnaR+s2jD1nOqIAJUuXLl2ktLQ0zm0N2iyiPaCOJmN9u7AvrW8BtimOhVpesR7axhTbtGXLluJj/fr1Qdpyb7Njx46EdRc5erd1ybipikrUMtI9/nEFkBBCCCEkz+AEkBBCCCEkz0hKBXzgwAFxzsUt++MyKi7z6iVlvC5qwHftmgRVIpY6zNou7VtitVQx1rKsFQkEf1suYXzPb0VM0RztFnHLrYpeRo/9juoeJ50sW7ZMmjZtKgMGDAgdR4/0iNUWut1RRjHCR3V1dSgfunvBaCKoAhEJu0KwZDRq3+E5LQvYF1q1gXkbUm0f9b05WvV4Q6uGY1GRLHMQHLu02sxSX2G7oBpOv5+o5kOXGFrdjKo4rXrD8jFdUVERyofPgmO8dueB1+mxAdsK75VMhA8fUd2ApSon1vsTa1P9rWoIhg8fLuXl5fL++++HjqO8WeprX/+L+NWjVhuiPFgypOUQzRaaN2/uLR9lylIb47thfTMzPW4crXo4GXVzrL+ScTnFFUBCCCGEkDyDE0BCCCGEkDyDE0BCCCGEkDwjJRtA7eoCf/tccYjY9gaIFaoK9f54r1RDwUV1pYHXaFsPX0gvXb4Vqst3Lw22W1T7wFTtY/A6bc8Ta4Ns2L2sXr1aioqKpGvXrqHjlmsJXz6Nr3179eoVyvfll18G6Y0bNwZpqw11W/nuZbmtsVxkYP9b8pUOtwXkO3x2OCJ+e0CRcB/rsdDXJ9puEG3x9u7dG6St8Jna9grHbqyHtvPGZ8H76jphWDAdMiwVG+Wo7jcs+1okVddJVti5bNpD9+rVSyoqKuJCVfraRrtmQVmxvl34bDrEW5s2bYI0trt2OYP31u8Dti/aXltzDayHtnvFe+tn9n2TU7UHjGrnjGQi7FwqcAWQEEIIISTP4ASQEEIIISTPSEoFXFdXJ4cPHzaX0S2VF271tjySW97J0+k6QsRWCfhUFnqpH1UCuHwtEl5+RtVJVJJZXo66bR/zWWpT65ljaiWtUmoItm3bJoWFhXHtiXWxohpgPkuGsH21awJUP69atSpSvXU9fOYMqUY1QDm0VODHGrkS/QNp2rRpQlcuPjMPrTZEtWzUCES6T/H+OM5otRlep8dkfIdQHnUZ+P5jGXpcQFUcqqV1+dY4HtVNFxL1PbbMYaLWSX8zYuNJNsbCyspKadGiRVx9UTawj5Mx2fG5qcIoGyJhF1mWmRfKoZYNnBug7KF6WSTc9vgOWdE+9HuDbZCMyxQfUaMdpcPcxvftTrm8oy6BEEIIIYQcU3ACSAghhBCSZyStAi4sLIxTZ+ASqxV43IoSgio7a1etb4ewVaeopLqjD8/hLjiR8DJ1Kiq6TASeRqLuRvapG7Oxi3T//v1SWFgomzdvDh3v379/kPZFHdDnLHU+9rPeSdaxY8cgvWXLliCt1SNWf/naN+oOXo317pHMoHfLYrujSlD3h0/ORPxeFXTfYz68l1ZF4r0sVRlepyN8+O6l646mPdpsIt0B76OOPancN5noJLG+zcY717RpU2natGloPBIRee+99xLm18+B/ae/SdjnVhQr3I2LkZAskxftIQTPoTpYPxdeh/msCCeaVL69qX7n0mGy5sM3N0jmPlwBJIQQQgjJMzgBJIQQQgjJMzgBJIQQQgjJM5KyASwvL5fi4uI49xtoL+KzGxAJ2xtYLlEs1wc+uylti4J2L1E97UeNrGHl69ChQ+jcnj17grTP5YJI9O3dVpSUqLr/VPL57Dmy4aKjU6dOUlRUJGvWrAkd37p1a5BGmdT9iDKq7e3QRgqv0zaACLq+0HKI0RAqKipC53y2rpbbHsuFkWXrZUUQIcmzb98+qa+vj+sDlDu0D9TjnWUDaLnBQnxjob4X1lG/Cz43UNp+z2fbqOUM3WC1bt06dA7rlW5b5lSiMSRDKm6aGpIbbrgh9Pvzzz8P0p999lmQ1jarPvc+Iv5xR4+ZaIuNblu0rOE4uXPnztA5zIt2pN27dw/l27BhQ5Cura0N0vidFQm/h5Y9IN43E5FAclFWEK4AEkIIIYTkGZwAEkIIIYTkGUmpgNu1ayclJSVxbgZ8Xu21+sLndV2XgdfpyBro4RyXrK066SVg/G0F8PZ5f9dL4FgP7bkcl7Nxu7yur2+7uKUOtlzE+Mq2yjhWlrL79++f0BQBVcKoAqisrAzls/oSZQ9lw1KrWVFHsHx0WyASVgmjWlpHmPAFUbeiGmh1DpYZNWrCsUCsvtmqt+5TlBN893VkDcQXZUdjuWaxrrfUzT7TE6u+WA/LrYx2iYXmEHhdqtETUjmXCVctsWfORvSdzZs3y759++JMj26//fYg/eijjwbp+fPnh/JhP+sxDqN1oOpYR/Havn17kEaXWO3atQvl842ZIuHvIZaPbmV0ndBMAdXBItEjfOTKdy2V8cvnqiiZsrgCSAghhBCSZ3ACSAghhBCSZySlAo55HdcqKlweRhWDtZtRqyJ8URf0UjGqWHEJeNmyZaF81u4mxFoCjho0GpefV6xYETqH6hKf+lrEr2621Ap6l1XUpd+o3smtHcfZpKKiQkpKSuLMAxDcmablFVUMlvd7K7IGnkMZ1bvsUEZ1n+N1qA7Wqj58H1DlaEWu0fXNpEf6fKSwsDDhmIBygSYfWgZ90T5Ewn2Hajl9PxwLUX5wp6QuT8sgyhOaL1jRSXxli4RlVe8kxjawVMA+Mr3TN+q9fe9dVLVjOlm9erWUl5fLxo0bQ8cxgsbNN98cpKdMmRLK99FHHwVprUbFPsJxTav9sV/RDEePzygPWo28a9euII1jspY7fV0M3fYoh7oMn5xn8xuX7l3xUeEKICGEEEJInsEJICGEEEJInsEJICGEEEJInpGUDWBhYaEUFRXF6ajRBgD17Tof6t61uwx0XYB2KZaX/M6dOwdp7VkcbQK1nQraMPiiMejr0MZA2xvgvV955ZXQueOPPz5I41Z9bduI4JZ47S7G8kifihsYC59dYrYpKiqSoqIi04ULys26detC+SyXBnjOihiCoCxr+z1f9AORcJuivYy2F0NbsqiuJrR9qE/OtWz4ZMXnciDRuaj5fHZVx5KNoiUX2L/aNQvKhe5vlCcsQ0ejwXEMXW5odx5oE6jbFscXHHd1fX110vKIERm0i5yo9lapRK3J9PiUq/bQsWg02n5v9erVQRpdqVx33XWhfEOGDAnS06ZNC51bunRpkMa+1GMLyhTa8mkbwP79+wfpli1bhs6hexf8nurvP0YTwbHacs2mZd765h/L0A0MIYQQQgg5IpwAEkIIIYTkGUmrgAsLCyNHjNDL8panedy2juVrFSi6O0D13YknnhjKh17n9RZ5VG+gukTXCX+jylYvN6MqZvny5aFzb7/9dpDu1q1bkB4+fHgoX5cuXYI0Lp1bKkXdvr62t5bskVxSbRwtlqoUVWk6iDj2JbaTVtOhSwOUDcvlgJYb7BfsZ93nvkgjlqsXDbYHPotlHhHVVUeqcpMO9UuuyaxPJWxFbbH60ZJj31jQvXt3bz50j6RBUwPt6gNVb5ZpCKretCoa1YO+yA8iYfnH98lqi6guWKKqirVcWVGssukGpqSkREpLS+PMA/AbZ/U5yspNN90UOocuzdCMACN/iIh8/fXXQXrr1q1BGlXIIiLHHXdckEZ5Egl/1zGaiAbzIVpeo0b4wj7TZmnpGJ9Sce/SkC5huAJICCGEEJJncAJICCGEEJJncAJICCGEEJJnJGUD6JxLqJP26cotmye9bR3172gTokNroS0G2qygSxiRsE3g/PnzQ+fQngHtVCzXGXhfy52Hri/W8ZNPPkmY1vVH+8BBgwaF8qENhLaJ8YUuSzXUEvafz/5Gt1k28dl2WO6IdF/6bJi0SwuUX7TZ1PZMaMNkuT5COdH59G8f+MyWjGKfWXavaEejbXFzqd9zFctmDc/ptsTfltsntF9FuyltX9WjR48grW3gsF8tV1eI5RLFsm1E8H1C2RcJyzuOd9qtiGWXnW63MFZ7xPolGy5F6uvrE76LWBfLbnzHjh1BWssNum2pqakJ0trlWq9evYL0vHnzgrQOSbhy5cqE5el6WXbOUb9Dlg084rN51vfCtJaFqG6wMk0qcsgVQEIIIYSQPCPS0kJsFqudg8aIuqvU+q/M5zDXWpVD55F6RRH/w9S70fC/XlzxifJfnq6DLkP/F5GKI1MsT7e5tSsO28q3Ghi1Dvq37z+sWP0a4j+d2D1i/af7K8qKpYi/nUTC7Y1yYskyXmPtENd9iTKFu/j0aiOes/6bj7o733p+zGetAOaSY3CRhpPDI42FSNT/xK0VCt9qoEi4f1BGcFwUsXfm4nNY4xj2P16j81leIHzvli7D927pNvet+Ce6d7JYDtL1udizZGMsjPW19X5iv1orwBr81uCYpMcnlCmrX/GclkPfOKkdQeO4br2D+N5Y3wJfsAd9neU8OpMrv8nIUqweychhgYuQa926dSE3JYRo1q5dG9rmnwkoh+RIZFoOKYPkSHAsJLlAFDmMNAGsr6+XDRs2SEVFRaMKnUKOHuec7NmzR6qqqjLuB4tySHw0lBxSBokPjoUkF0hGDiNNAAkhhBBCSOOBm0AIIYQQQvIMTgAJIYQQQvIMTgAJIYQQQvIMTgAJIYQQQvKMY3YC+PTTT8sJJ5wgAwcOlOLiYjnhhBPkhBNOkKeeeirbVSN5BOWQ5AKUQ5JtKIPHHsf8LuCFCxfKLbfcInPmzMl2VUgeQzkkuQDlkGQbyuCxwzG7Ahhj8eLFoZiFhGQDyiHJBSiHJNtQBo8djvkJ4KJFi3Ja2J566inp2rWrlJaWysknnyyffPLJEa/Zs2eP3HnnnVJTUyNlZWVy6qmnyqeffhqcr6urk/vvv1+6desmZWVl0qNHD/nVr37VoIGnSZh8lEMRkfXr18t1110nbdu2lbKyMhk4cKDMnTs3U49BjkA+ymHXrl2loKAg7u+2227L5KMQD5TBY0gG3THOyJEj3fTp07NdjYS89NJLrri42P3P//yPW7x4sbvllltcq1at3DfffGNed/XVV7t+/fq5d999133xxRduwoQJrkWLFm7dunXOOecmTpzo2rZt66ZNm+ZWr17tXn31Vde8eXP3+OOPN8RjkQTkoxxu377d1dTUuBtvvNHNmTPHrVq1ys2YMcOtXLmyIR6LJCAf5XDz5s1u48aNwd/MmTOdiLjZs2c3wFMRDWXw2JHBnJ4Atm/f3j377LOhY5988okrKSlxq1atcs4516NHD7d27dq4a9966y3XrFkzV1dXFxz7/PPPnYi4LVu2ZLbi/z/Dhw93t912W/C7rq7OVVVVuYceesh7zbfffuuKiorctGnTQseHDh3q7rvvPuecc5dccokbM2ZM6Pzll1/urr322jTWnsSgHH4PyuH48ePd6aefnplKkzgoh9+DcqgZN26c69Gjh6uvr09PxUkAZfB7GoMM5rQKeODAgbJkyZLQsfHjx8u//uu/Srdu3WTfvn2yY8eOhAGP582bJwMGDAjFwps/f75UVVVJu3btEt5v0qRJ0rx5c/NvzZo1kep+8OBB+eyzz+S8884LjhUWFsp5550nH330kfe6w4cPS11dnZSWloaOl5WVyfvvvy8iIqeeeqrMmjVLVqxYISIiCxYskPfff18uuuiiSHUjyUE5/B6Uw9dff12GDRsmV111lVRWVsqQIUPk2WefjVQvkjyUw+9BOdT3eeGFF2TMmDGMkZsBKIPf0xhksEm2K2AxYMCAkLDNmDFD5s6dK6+88oqIiCxdulT69OmT8Nr58+fL4MGDQ8cWLFgQdwy59dZb5eqrrzbrVFVVFanuW7dulbq6OunQoUPoeIcOHWTZsmXe6yoqKuSUU06RX/3qV9K3b1/p0KGD/PGPf5SPPvpIevbsKSIi99xzj+zevVv69OkjRUVFUldXJxMnTpRrr702Ut1IclAOE8vhqlWr5He/+5389Kc/lZ/97Gfy6aefyh133CHFxcUyevToSPUj0aEcJpZD5LXXXpOdO3fKjTfeGKleJDkog41LBnN6Ajhw4ECZOnWqiIg45+Tee++Vu+++O/hvYejQofLBBx8kvHbevHlyxx13hI7Nnz9fhg0b5r1fmzZtpE2bNmmqfer84Q9/kDFjxkjnzp2lqKhIhg4dKj/60Y/ks88+ExGRV155RaZMmSIvvvii9O/fX+bPny933nmnVFVV8cObASiHieWwvr5ehg0bJpMmTRIRkSFDhsiiRYvk6aefphxmAMphYjlEfv/738tFF10UeVJAkoMy2LhkMKdVwAMGDJB169ZJbW2tvPTSS7Jx40b56U9/esTr9u7dK19++WXoP4v6+nqZN2+e+d9GOpeb27VrJ0VFRfLNN9+Ejn/zzTfSsWNH89oePXrIu+++K7W1tbJ27Vr55JNP5NChQ9K9e3cREbn77rvlnnvukWuuuUYGDhwo119/vfzkJz+Rhx56KFLdSHJQDhPLYadOnaRfv36ha/r27Ru5biQ5KIeJ5TDG119/LW+//bbcfPPNkepEkocy2LhkMKdXAAcMGCAi3zmWvP/+++UXv/iFlJeXH/G61atXS319fWgpesaMGbJt27YGW24uLi6WE088UWbNmiWjRo0Ske8EftasWXL77bdHKqO8vFzKy8tlx44dMmPGDHn44YdFROTbb78N2VGIiBQVFUl9fX2kcklyUA4Ty+Fpp50my5cvD+VdsWKF1NTURCqXJAflMLEcxnjuueeksrJSLrnkkkjlkeShDDYyGczuHpQj07VrV/eDH/zA9erVyx06dCjSNRs2bHAFBQXuzTffdM4599FHH7nu3bu70tJSd/jw4UxWN8RLL73kSkpK3PPPP++WLFnixo4d61q1auU2bdoU5HniiSfcOeecE7pu+vTp7q233nKrVq1yf/3rX93gwYPdySef7A4ePOicc2706NGuc+fOgRuYP//5z65du3bu//2//9dgz5ZvUA7j5fCTTz5xTZo0cRMnTnRffPGFmzJlimvWrJl74YUXGuzZ8g3KYbwcOvfdbs7q6mo3fvz4BnuefIUy2HhkMOcngCNGjHAi4l555ZWkrvv1r3/tWrdu7aqrq93o0aPd+PHj3bBhwzJUSz9PPPGEq66udsXFxW748OHu448/Dp2fMGGCq6mpCR17+eWXXffu3V1xcbHr2LGju+2229zOnTuD87t373bjxo1z1dXVrrS01HXv3t3dd9997sCBAw3xSHkJ5TBeDp1z7o033nADBgxwJSUlrk+fPu6ZZ57J9KPkNZTDxHI4Y8YMJyJu+fLlmX6EvIcy2Hhk8JiPBUwIIYQQQpIjpzeBEEIIIYSQ9MMJICGEEEJInsEJICGEEEJInsEJICGEEEJInsEJICGEEEJInsEJICGEEEJInsEJYAb429/+JiNGjJCqqiopKCiQ1157zcz/0EMPyUknnSQVFRVSWVkpo0aNiouwQEgyJCuDqV5DiAXlkOQClMPEcAKYAfbu3SuDBw+Wp556KlL+d999V2677Tb5+OOPZebMmXLo0CE5//zzZe/evRmuKWmsJCuDqV5DiAXlkOQClEMP2fZEnWnq6urcxIkTXc+ePV1JSYmrrKx0o0ePbrD7i4ibOnVqUtds3rzZiYh79913M1Mp0qAcizKYyjUkt6EcklyAcpg7NMne1LNheOihh+Tll1+WZ555Rrp37y7r16+XZcuWxeWbNGmSTJo0ySxryZIlUl1dnamqBuzatUtERNq0aZPxe5HMcyzKIGl8UA5JLkA5zB0a/QRwxowZMmLECDn77LNFRKSmpkZOPfXUuHy33nqrXH311WZZVVVVGakjUl9fL3feeaecdtppMmDAgIzfj2SeY00GSeOEckhyAcph7tDoJ4CXXXaZjB8/XubOnStXXXWVXHHFFdK6deu4fG3atMmJFbfbbrtNFi1aJO+//362q0LSxLEmg6RxQjkkuQDlMHdo9JtA7rrrLlm6dKmce+658thjj0nPnj1l9erVcfkmTZokzZs3N//WrFmT0brefvvtMm3aNJk9e7Ycd9xxGb0XaTiOJRkkjRfKIckFKIe5Q4FzzmW7Eg3F/v37pUWLFjJ16lS55JJLQue2b98u27dvN6/v2rWrNGmS3KJpQUGBTJ06VUaNGuXN45yTH//4xzJ16lR55513pFevXkndgxw75KoMpuMacuxAOSS5AOUwuzRqFfDDDz8sHTt2lJNOOkkKCwtl8uTJ0rZt24T2Bulcbq6trZWVK1cGv1evXi3z58+XNm3aSHV1tTz55JMydepUmTVrloh8p/Z98cUX5S9/+YtUVFTIpk2bRESkZcuWUlZWlpY6kexwrMhglGvIsQvlkOQClMMcI8u7kDPKAw884I4//nhXWlrq2rVr50aOHOmWLFmS8fvOnj3biUjcX2yr+4QJE1xNTU2QP1FeEXHPPfdcxutKMsuxIoNRriHHLpRDkgtQDnOLvFIBE0IIIYSQPNgEQgghhBBCwnACSAghhBCSZ3ACSAghhBCSZ3ACSAghhBCSZ3ACSAghhBCSZ3ACSAghhBCSZ3ACSAghhBCSZ3ACSAghhBCSZ3ACSAghhBCSZ3ACSAghhBCSZ3ACSAghhBCSZ3ACSAghhBCSZ/x/53i3/aQS5LsAAAAASUVORK5CYII=\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "# Show some example singular vectors with large singular values\n",
    "sing_vect_n = [10,11,12,13] # indices of the singular vectors for visualization\n",
    "\n",
    "N = dim1*dim2 # dimensionality of the space\n",
    "\n",
    "limit =  max(np.abs(np.min( U[:,sing_vect_n])), np.abs(np.max(U[:,sing_vect_n])))\n",
    "f , axs = plt.subplots(1,len(sing_vect_n) , figsize=(8,3))\n",
    "plt.subplots_adjust()\n",
    "for i in range(len(sing_vect_n)):\n",
    "    u = U[:,sing_vect_n[i]]\n",
    "    v = V[sing_vect_n[i],:]\n",
    "    axs[i].imshow(u.reshape(dim1,dim2), 'gray', vmin=-limit/2, vmax = limit/2)\n",
    "    axs[i].set_title('singular vector '+str(sing_vect_n[i]), fontsize = 10, fontname= 'Times New Roman')\n",
    "    axs[i].tick_params(bottom=False,left=False,labelleft=False,labelbottom=False)\n",
    "    axs[i].set_xlabel(r'$v^Tu$ =  '+str(np.round( np.dot(u,v) ,2))+ '\\n $s =$ '+str(np.round(S[sing_vect_n[i]],1)),\n",
    "                      fontsize = 10, fontname= 'Times New Roman');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "zfxP4eD170SJ"
   },
   "source": [
    "### Visualize some example singular vectors with small singular values\n",
    "\n",
    "These are 'features' of the input image that are discarded by the denoiser."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true,
    "id": "u2UFkIUH70SJ",
    "outputId": "cce62323-5f3d-4139-8641-d2acbc4ed654",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 543
    },
    "executionInfo": {
     "status": "ok",
     "timestamp": 1705956151111,
     "user_tz": 300,
     "elapsed": 938,
     "user": {
      "displayName": "Kangning Liu",
      "userId": "18225106579512019568"
     }
    }
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 800x300 with 4 Axes>"
      ],
      "image/png": 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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "# Show some example singular vectors with small singular values\n",
    "sing_vect_n = [N-10,N-11,N-12,N-13] # indices of the singular vectors for visualization\n",
    "\n",
    "limit =  max(np.abs(np.min( U[:,sing_vect_n])), np.abs(np.max(U[:,sing_vect_n])))\n",
    "f , axs = plt.subplots(1,len(sing_vect_n) , figsize=(8,3))\n",
    "plt.subplots_adjust()\n",
    "for i in range(len(sing_vect_n)):\n",
    "    u = U[:,sing_vect_n[i]]\n",
    "    v = V[sing_vect_n[i],:]\n",
    "    axs[i].imshow(u.reshape(dim1,dim2), 'gray', vmin=-limit/2, vmax = limit/2)\n",
    "    axs[i].set_title('singular vector '+str(sing_vect_n[i]), fontsize = 10, fontname= 'Times New Roman')\n",
    "    axs[i].tick_params(bottom=False,left=False,labelleft=False,labelbottom=False)\n",
    "    axs[i].set_xlabel(r'$v^Tu$ =  '+str(np.round( np.dot(u,v) ,2))+ '\\n $s =$ '+str(np.round(S[sing_vect_n[i]],1)),\n",
    "                      fontsize = 10, fontname= 'Times New Roman');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "nh2TibIk70SJ"
   },
   "source": [
    "### Left and right singular vectors with significant singular values are nearly identical\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "id": "g93Tu5UG70SJ",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "executionInfo": {
     "status": "ok",
     "timestamp": 1705956151636,
     "user_tz": 300,
     "elapsed": 528,
     "user": {
      "displayName": "Kangning Liu",
      "userId": "18225106579512019568"
     }
    },
    "outputId": "aad8ff5c-41ad-4a2f-d0c6-5b8bf4f1630c"
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family ['Times New Roman'] not found. Falling back to DejaVu Sans.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n",
      "WARNING:matplotlib.font_manager:findfont: Font family 'Times New Roman' not found.\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ],
      "image/png": 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+ElJH08LCQjlwkGojrOfukI4RGRmJ7t272xwOKykoKKgWREj7GwwGhIWFVZtNlH06iIg8Q1p9OuH9BMS9G+eR4INNLY2IwWCotYlC6i8hjSKxt/CbNesgwN5wV+BGjYVer4fJZFJMU25rf2mKdOthuezTQUTkGd6w+jRrPBqRqkNj7ananJGfn19j0CE1s9Q05NVoNKKyshJGo1E+rslkQkxMTK2jY1i7QUTkPaTVpwF4bPVp1ng0UVVHoeTm5taYVmpmqWmlVes5OWxNSGZvdVbWbhAReQ9vWH2agUcj4ehIkKoP/KqLslmraUl7SdUmHuvjWi/6JtWUcMQKEZH30ml1bm9escbAw8tUDTCkIbRS4GBds9CQ5eD9/f1hNpvrNE25vVqL0NDQas06lZWVyM3NZQBCRETVMPDwMlWbLqT5MCQajUbuNCqllfpuVG3ukDqT6vV66PV6FBQUyAGHM5tAbDW/mM1mu00wRETUPLFzqZep2hlTp1O2v5WVlckP9KpNIjqdTtE51Hqm0qioKMTGxioCAmcJDQ2Vgw8AiImJQXh4ODuVEhFRNazx8DJVJ/Gynl/D2vXr12E0GuHv74+ysrJqy9tX/U7i6NTndelbYj3TqVTDwU6lRERkCwMPL2Td3GLdedOaEAJCCJSVlQEACgsLoVbfrMCyWCwoKyuTp0GXOBoQ2Bu1IgUl169fl7exhoOIiOxhU4sXsm5uqSlI0Gg0ikBDCIGgoCBoNBpFutzcXIeWs7eXl6qkoERa60WtVrOWg4iI7GKNh5eo2qRhPXLF1lBYs9kMvV6P8vJyudbDZDKhW7du8myhwI2aD7PZXGMnz9qaUuzVkEjNNrZmLyUiIrKFgYeXqNqkYb3Ca02qzkQqdUTV6XTyd2q1usbl6G2dtz4CAwMRFRVVr32JiKh5YVOLh0nTlOt0OpsruKpUKsXicPYUFBQgPz9f0SHVbDZDp9PZrbWo7+iT3Nxcec4OIiKiumDg4SFSwJGTk4PKykoUFRUp1mGxXuHVz8+vxuNY9/MAbgQDYWFhir4eNa3R4uhsqFVJfTukdyIiotow8PCQqh0zVSqVYpE26wXhpD4ctlgsFsVnIQRCQ0MVAYk0nLbqInBVZxy1lcYeaa6O8PDwuheciIiaNfbx8JCwsDB57gvg5noolZWV8jwcwcHBNc7jYU2j0cBisUAIgeDgYPn4VaderzrXhq05PRzp88G5OoiIyFEMPDwgPz8fOTk58md/f3/k5OQomiwsFkuNTSRVGQwGGI1GCCHkfaxHmWRkZCg6qUrbbQUOtoKRhjbJEBERSRh4eEDVIKOmphSVSlVr/wmVSoW8vDxFOuu1WwDIQ2vVajXCw8PtBg+2ghFnjHwhIiIC2MfDI+raGbMu6YQQ1fqK6PV6eaSKdc2FRqOpV+Bgb+SLI31CiIiIWOPhAdJKsa7g4+NTbU6NS5cu4fr16zUGMg2ZRIy1IURE5AjWeHhAVFQU/P39672/v78/NBqNPMeHWq1W1HIAypoIaS0V6zVVrNka3VJXDZkHhIiImh+vDjxWrlyJ6Oho+Pv7IyEhAQcOHLCbfsWKFYiJiUFAQACioqLw7LPP2h2K6gn5+fk4efJkvfPl7++PTp06wWAwyAvFSUNqrecBkYIJ68m9agp2GhI8SMN+AbDJhYiIauW1gcemTZswa9YszJ8/H0eOHEHPnj0xbNgwXLp0yWb6DRs24IUXXsD8+fNx8uRJfPDBB9i0aRNefPFFN+e8ZtKQVnvToNemU6dOAFCtdqKm6dOloESr1cr7VmU9Z0h9NaTWhIiImg+vDTyWLVuGqVOnYtKkSejevTtWr14NnU6HdevW2Uy/d+9e3H777Xj44YcRHR2NoUOHYty4cbXWkriTMx7KZ86cQVpamjxSRSJNQCaR5v9Qq9VuaQphkwsREdWFVwYeFRUVOHz4MJKSkuRtarUaSUlJ2Ldvn819BgwYgMOHD8uBxtmzZ7Ft2zb8/ve/t5m+vLwchYWFiperOeOhbN1Eo9Fo5KnRhRCKZhXrKdcbWpshsTeCxRm1JkRE1PR55aiWy5cvw2w2w2AwKLYbDAakp6fb3Ofhhx/G5cuXcccdd0AIgevXr+OJJ56osall0aJFeOWVV5yed1fz8fGRO4lqtVpFIGI2m+Xp1qWX9SJ00qRi9Q0OOIKFiIgayitrPOojJSUFr732Gt59910cOXIEn3/+ObZu3YqFCxfaTD9nzhwUFBTIr4sXL7o8j85YxfX69evyOiy2OqhKzTlSwGE0GlFZWYmCgoIG98FgcwoRETWUV9Z4tGrVChqNptqDOjc3t8YFyV5++WU89thjmDJlCgAgLi4OJSUlePzxxzF37txqq7j6+fnZXfXVFaou6Oas41jPcKrT6eQp0i0WCzQaDbRaraLGo764NgsRETWUV9Z4+Pr6om/fvti9e7e8zWKxYPfu3UhMTLS5j8lkqhZcWPd/8AauyofUgTQyMhImk0kxk2lQUBBiYmIQFRXllD4YnKmUiIgawitrPABg1qxZmDBhAvr164f+/ftjxYoVKCkpwaRJkwAA48ePR5s2bbBo0SIAQHJyMpYtW4bevXsjISEBZ86cwcsvv4zk5GQ5AGkK/P39YTabFTORGgwGuT+HxWKRAzAhBIqLi5GRkeG0Bd7Yz4OIiBrCawOPsWPHIi8vD/PmzYPRaESvXr2wfft2ucNpVlaWoobjpZdegkqlwksvvYTffvsNYWFhSE5OxquvvuqpIjid9VwctqY5z8vLg9lslvthSJ+dGSjYWr2WiIiorlTCW9ohPKywsFBeQyUkJMQl50hLS6v3viqVChEREXaDB1vBSH5+PnJzcyGEqHVlWiIiovpw5BnqlX08mqKG9onw8fGpMWi4ePEi0tLSUFJSItdISOcLDQ2FWq2GxWJp8ARm7N9BREQNxcDDTRr60JemQLdFmi69oKAA2dnZ1YbNOmsYrHX/DgYhRERUHww83MSRh76PT/WuN/ZmVlWpVNW2ScNqpQnFnDGixTqA4dosRERUHww8vJCt5eutu+JUrW2IiIiARqOBSqWCWq1WDKt1ZmBgvRKtNHqGnUyJiMgRXjuqpampbwAg9c/Q6/WKY0lL3kudSbt16yZ/bz2sVqr5cNZwWun80ugZ62Pa6txKRERkjTUebmKvj4Y9Go0GsbGxiIqKkrdJTR5CCJu1GlJgoNFoXFLzUVOfETa/EBFRbVjj4Sb1Xf3WVsBivQCc9Zwa0ueq06M7e96NmqZO5xwfRERUGwYeblLf6VLszTxaNQCQahxMJhNiYmLc3vTBtVyIiKg2bGrxctYzj9amahMImz6IiMjbsMajkahLHxHrqdMBNn0QEZH3YY1HI2EymeqUTqrlyM7OBgCnzN9BRETkLAw83KChs3uqVKo611pYp2MTCxEReRsGHm7Q0ABACIGSkpI6pQ0NDUVkZKRTpkgnIiJyNgYebuBoABAZGQl/f3/FNmk9lrpw1hTpREREzsbOpV7IaDTKP6tUKgghFDOXApwllIiIGifWeLiBo00tFosFFosFAOSgw3rmUumY1kNluVosERE1Bgw83KChfS1sNbNUnbMjNzdXXr+FiIjIW7GpxQuo1TfiP6mWQ1oYTlK1mQWoPkuoNDOq2WxGfn4+m1+IiMgrscbDDew1tWg0GrlpRaVSITIyEt27d5eDEbVaXa2ZRWLdvBIeHl6n8xEREXkSAw83sNfUYjab5Z+lWov8/HyoVCqo1WpFQFGV0WhEZWUljEYjh9ESEVGjwMDDDWpq9qg6ZBa4UVthvay9vSYTlUqleCciIvJ2DDzcoKaRJmazWW5SkVy/fh06na5ONRdBQUGKd2mkS25uLke4EBGRV2Lg4QY19bnQ6XTVmlKEECgsLERMTAwA2A0gioqKFO/SSBchBFelJSIir8TAww1qqrkoLi5GaGhotVErUl+P2pa1r9rUIs1YGh4ezr4eRETklRh4uEFN/TTMZjPOnDkjz9MhBRBSIFJ1rg5rUi2IWq2GwWCQt2VkZABQrkrLycWIiMhbcB4PN7D3wC8rK5N/joiIUAQpVefqsCZ1QNVqtXIa6xqS0NBQeVp1s9kMi8UibyciIvIU1ni4ga2mkppGtNS1VsJWbUjVbVIgolKp2PRCRERegTUebqDT6RTTnqvVarnmITs7W95uXVtRG1u1Idbb8vPzYbFY5KYY1nQQEZE3YI2HGxQWFio+Wzd7aDQaxXfOqJXIz89HdnZ2neYCISIicicGHm4gjVKRWDd7GAwGaDQaqNVqREZGOiVIsG7aYfMKERF5Eza1uIG/v7+iE6k0R4dErVYjLCysWtAhdQ619Z0tUnqdTgeTyVTn/YiIiNyFNR5uUFlZqfh84sQJuRNpTXN1SM0ljkwEJh3LZDIphtMSERF5CwYebmC9xL30WQomapqroz7NJfbm/SAiIvIGbGrxAKlpBah5ro6wsDCHmlnsHYuIiMhbMPBwg6qdS8PDwxUTfNkKLhpLEOFoPxQiImre2NTiAVIzir21WBrLNOe1rSdDRERkjYGHB0jNLPb6ZDSWBzr7lRARkSPY1OIBUpOEveYU6z4e3qyxNAkREZF3YI2HG9hal6U20hL3ALyqyaWxNAEREZF3YuDhBtaThznK25pcvC0/RETUuDDw8AL2ahG8rQ+Ft+WHiIgaF/bxcDO9Xi//LA1FNZvNioXjrHlbHwpvyw8RETUurPFws6ioKPlnqdlCmudDp9N5KltERERuwcDDzaybU6RmC5VKBQAwmUyeyhYREZFbMPBws5ycHPlnaeRKeHg4tFotdDpdg0eMcNQJERF5MwYeblZ1+nTgZgBiMpkaPGKEo06IiMibeXXgsXLlSkRHR8Pf3x8JCQk4cOCA3fTXrl3DjBkzEBERAT8/P3Tp0gXbtm1zU27rxt6cHs4YMcJRJ0RE5M28dlTLpk2bMGvWLKxevRoJCQlYsWIFhg0bhoyMDLRu3bpa+oqKCgwZMgStW7fGZ599hjZt2uDChQto0aKF+zNvh9lsrvE7Z4wY4agTIiLyZl4beCxbtgxTp07FpEmTAACrV6/G1q1bsW7dOrzwwgvV0q9btw75+fnYu3cvtFotACA6OtqdWa6TqjURXN2ViIiaE69saqmoqMDhw4eRlJQkb1Or1UhKSsK+ffts7vPVV18hMTERM2bMgMFgQGxsLF577bUaaxjKy8tRWFioeLlD1eCiKaxQS0REVFdeGXhcvnwZZrMZBoNBsd1gMMBoNNrc5+zZs/jss89gNpuxbds2vPzyy1i6dCn+8pe/2Ey/aNEi6PV6+WU9v4Y7OXuFWgYrRETkzbwy8KgPi8WC1q1b47333kPfvn0xduxYzJ07F6tXr7aZfs6cOSgoKJBfFy9edHOOb5BGtNhqZqlPR1GOaiEiIm/mlX08WrVqBY1Gg9zcXMX23NxchIeH29wnIiICWq0WGo1G3tatWzcYjUZUVFTA19dXkd7Pzw9+fn7Oz7wT1aejaFhYmNxnxJ3YV4WIiOrCK2s8fH190bdvX+zevVveZrFYsHv3biQmJtrc5/bbb8eZM2dgsVjkbadOnUJERES1oMOTXN0EYq8GxZVY00JERHXhlYEHAMyaNQtr167FRx99hJMnT+LJJ59ESUmJPMpl/PjxmDNnjpz+ySefRH5+Pp5++mmcOnUKW7duxWuvvYYZM2Z4qggytfrmZW6qD2bOH0JERHXhlU0tADB27Fjk5eVh3rx5MBqN6NWrF7Zv3y53OM3KylI80KOiorBjxw48++yziI+PR5s2bfD000/j+eef91QRZMHBwSgoKIBKpWqyD2bOH0JERHWhErbm8G6GCgsLodfrUVBQgJCQEKceOyMjA5WVldBqtYiJiXHqsYmIiDzNkWeo1za1NCVSh1frjq9ERETNEQMPNygrK1O8ExERNVcMPNxAWhjO3gJxREREzQEDDzcoLy9XvBMRETVXDDzcQOq/y368RETU3DHwcANp2K/18F8iIqLmiE9CN5BmU7WeVZWIiKg5YuBBREREbsPAg4iIiNyGgQcRERG5Tb3XaklOTkbPnj0RGxuLuLg4dO3alTNzEhERkV31DjxycnKwe/dulJWVQaVSyeuQxMfHIy4uTn7deuutzswvERERNWL1DjwOHToEi8WC9PR0pKam4tixYzh48CA2bdqEDRs2yOnMZrNTMkpERESNX70DD+DGvBTdu3dH9+7dMW7cOADApUuXMG3aNFy+fBl//OMfnZJJIiIiahqc3rm0devW+Oyzz2AymThvBRERESm4ZFSLRqPB6NGj8dZbb7ni8I2OSqVSvBMRETVX9W5qeeqpp9CrVy/Ex8cjNja22sqrpaWlyMzMbHAGmwKu1UJERHRDvQOPTz/9FO+88w5UKhXUajU6deqEnj17olu3bjCZTFi1ahV69OjhzLwSERFRI1fvwCMvLw85OTn4+eef8fPPPyM1NRXHjx/HF198gcrKSsTHx2Pt2rXOzCtVkZ+fj7y8PISFhSE0NNTT2SEiIqpVg0a1REREICIiAsOGDZO3CSFgNpvh49OgQ1Md5OXlobKyEnl5eQw8iIioUai1c+nw4cMdOqBKpWLQ4SZhYWHQarUICwvzdFaIiIjqpNYIYe/eve7IB9VDaGgoazqIiKhR4SJxbqDX6xXvREREzVWtNR5lZWWYPXs24uPjER8fjx49ekCr1bojb01GcXGx4t1d2PmUiIi8Ta2Bh0qlQlFREVatWoW0tDRUVFSgS5cuciASHx+PESNGuCOvjZa0Xo27161h51MiIvI2tQYefn5+WLNmjfw5MzMTqamp+Pnnn7F//368//77OH36tEszSfUTFhYm13gQERF5g1oDj6qzbXbs2BEdO3bEAw884LJMkXOw8ykREXmbWjuXcr2VhsnPz5d/5jBjIiJq7moNPGpa2j4xMRHfffed0zPU1OTl5ck/X79+3YM5ISIi8rx6D6etrKzEkCFDcM8992Dfvn3OzFOTotPp5J85nJaIiJq7egcehw4dwpYtW3DlyhXccccdGDlyJI4ePerMvDUJhYWF8s+BgYEezAkREZHnNWgCsVGjRuHYsWP49NNPcf78efTr1w8PPvggTp486az8NXrWnXONRqMHc9Jw+fn5yMjIUPRbISIicoRTZi4dM2YM0tLS8NFHH+Hnn39GfHw8HnvsMWRmZjrj8E2GSqXydBYaxHpeECIiovpw2pTpKpUKjz76KNLT0/Hee+9h586d6N69u7MO3yQYDAZPZ6FBuCgdERE1VIPGd1ZWVuL06dNIT09XvDIyMlBUVNTo/8J3tsY+pwbnBSEiooaqd+DRuXNnXLhwAWazWe7HEBkZiR49emDy5Mno0aMHevTo4bSMNlZ6vR4FBQVQqVTIz8/ng5uIiJq1egce0dHRuPfee+UAo0ePHggJCXFm3pqEwMBAFBQUQAjBNVOIiKjZq3fgsWvXLmfmo8my7oip0Wg8mBMiIiLPc1rnUrLNekXasrIyD+aEiIjI8xh4uJjFYpF/5sylRETU3DHwcDG1Wi2/R0VFeTg3REREnsXAw8Wkfh3s30FERMTAw+WkReKsF4sjIiJqrhh4uFhxcTEAoKCggGucEBFRs8fAw8WsO5dyjRMiImruGHi4mNS5FADXOCEiombPqwOPlStXIjo6Gv7+/khISMCBAwfqtN/GjRuhUqkwatQo12awDoKCggA0/pVpiYiInMFrA49NmzZh1qxZmD9/Po4cOYKePXti2LBhuHTpkt39zp8/j9mzZ2PgwIFuyql9JpMJAOQp04mIiJozrw08li1bhqlTp2LSpEno3r07Vq9eDZ1Oh3Xr1tW4j9lsxiOPPIJXXnkFHTp0cGNuayaNZlGpVGxqISKiZs8rA4+KigocPnwYSUlJ8ja1Wo2kpCTs27evxv3+/Oc/o3Xr1pg8ebI7slknhYWFACCv4EtERNSc1XuROFe6fPkyzGYzDAaDYrvBYEB6errNfX766Sd88MEHOHbsWJ3OUV5ejvLycvmzFCA4m3XAwdVpiYioufPKGg9HFRUV4bHHHsPatWvRqlWrOu2zaNEi6PV6+eWO6czZ1EJERM2dV9Z4tGrVChqNBrm5uYrtubm5CA8Pr5Y+MzMT58+fR3JysrxNmj/Dx8cHGRkZ6Nixo2KfOXPmYNasWfLnwsJClwcfrO0gIqLmzisDD19fX/Tt2xe7d++Wh8RaLBbs3r0bM2fOrJa+a9euOH78uGLbSy+9hKKiIrz11ls2Awo/Pz/4+fm5JP/W1Go1LBaLYj4PIiKi5sorAw8AmDVrFiZMmIB+/fqhf//+WLFiBUpKSjBp0iQAwPjx49GmTRssWrQI/v7+iI2NVezfokULAKi23d3Cw8ORl5fHZhYiIiJ4ceAxduxY5OXlYd68eTAajejVqxe2b98udzjNyspqFLUIUvOKNIcHm1uIiKg5UwmO8wRwo4+HXq9HQUEBQkJCnHrsjIwMVFZWQqvVIiYmxqnHJiIi8jRHnqHeX2XQyOXn5+P69esAbk4mRkRE1Fwx8HCxvLw8eS4Pafp0IiKi5oqBh4tZ13KwxoOIiJo7Bh4uVlxcLP/MGg8iImruGHi4mHXfXQ6pJSKi5o6Bh4sFBwcDAPR6PYfSEhFRs8fAw8WkxedctQgdERFRY8LAw8WkphZOl0JERMTAw+X0er3inYiIqDlj4EFERERuw8DDxQoKChTvREREzRkDDxdTqVSKdyIiouaMgYeLSYvlOHvhOSIiosaIgYeLSbOVctZSIiIiBh4uFxYWBq1Wy1lLiYiIwMCDiIiI3IiBh4vl5OSgsrISOTk5ns4KERGRxzHwcDHOXEpERHQTAw8iIiJyGwYeLqZWqxXvREREzRmfhi4WHh4OrVaL8PBwT2eFiIjI43w8nYGmLjQ0FKGhoZ7OBhERkVdgjQcRERG5DWs8XOzixYsoKCiAXq9HVFSUp7NDRETkUazxcDGuTktERHQTAw8X8/f3V7wTERE1Zww8XMxsNiveiYiImjMGHi6m0WgU70RERM0ZAw8XKysrU7wTERE1Zww8XEyv1yveiYiImjMGHkREROQ2DDxcjMNpiYiIbmLg4WJsaiEiIrqJgYeLBQYGQqvVIjAw0NNZISIi8jgGHi5mNBpRWVkJo9Ho6awQERF5HAMPF1OpVIp3IiKi5oyBh4sFBQUp3omIiJozBh4uZjKZFO9ERETNGQMPF9PpdIp3IiKi5oyBh4sVFhYq3omIiJozBh4uJoRQvBMRETVnDDxczN/fX/FORETUnDHwcLGKigrFOxERUXPGwMPF2NRCRER0EwMPF1Or1Yp3IiKi5oxPQxfjBGJEREQ3eXXgsXLlSkRHR8Pf3x8JCQk4cOBAjWnXrl2LgQMHomXLlmjZsiWSkpLspneX4uJixTsREVFz5rWBx6ZNmzBr1izMnz8fR44cQc+ePTFs2DBcunTJZvqUlBSMGzcO33//Pfbt24eoqCgMHToUv/32m5tzrmSxWBTvREREzZlKeGmvx4SEBPzud7/DO++8A+DGgzsqKgr/+7//ixdeeKHW/c1mM1q2bIl33nkH48ePrzV9YWEh9Ho9CgoKEBIS0uD8S3755RcIIaBSqdCjRw+nHZeIiMhbOPIM9coaj4qKChw+fBhJSUnyNrVajaSkJOzbt69OxzCZTKisrERoaKirslkn7FxKRER0k4+nM2DL5cuXYTabYTAYFNsNBgPS09PrdIznn38ekZGRiuDFWnl5OcrLy+XPrprSPCgoCAUFBexcSkREBC+t8Wio119/HRs3bsQ///nPGmcMXbRoEfR6vfyKiopySV6KiooU70RERM2ZVwYerVq1gkajQW5urmJ7bm4uwsPD7e67ZMkSvP7669i5cyfi4+NrTDdnzhwUFBTIr4sXLzol71WpVCrFOxERUXPmlYGHr68v+vbti927d8vbLBYLdu/ejcTExBr3e+ONN7Bw4UJs374d/fr1s3sOPz8/hISEKF6uYDAYoNVqqzUbERERNUde2ccDAGbNmoUJEyagX79+6N+/P1asWIGSkhJMmjQJADB+/Hi0adMGixYtAgAsXrwY8+bNw4YNGxAdHQ2j0QjgRh8LT/avCA0N9XgHVyIiIm/htYHH2LFjkZeXh3nz5sFoNKJXr17Yvn27XHOQlZWlGCmyatUqVFRU4MEHH1QcZ/78+ViwYIE7s65w8eJFFBQUuLQfCRERUWPhtfN4uJur5vFIS0uTf46NjXXacYmIiLxFo5/HoynR6/WKdyIioubMa5tamoqoqCg2sRAREf0XAw8XYx8PIiKim9jU4mIFBQWKdyIiouaMgYeLcQIxIiKimxh4uFhERAS0Wi0iIiI8nRUiIiKPYx8PF+MEYkRERDexxoOIiIjchoGHi+Xn5yMjIwP5+fmezgoREZHHsanFxYxGIywWC4xGI5tciMhlzGYzKisrPZ0NasJ8fX0VS5XUFwMPF5NmpOfM9ETkCkIIGI1GXLt2zdNZoSZOrVajffv28PX1bdBxGHgQETViUtDRunVr6HQ6Dt0nl7BYLMjOzkZOTg7atm3boPuMgYeLqVQqCCH4y4CInM5sNstBxy233OLp7FATFxYWhuzsbFy/fh1arbbex2HnUhcLDw+HVqtFeHi4p7NCRE2M1KdDp9N5OCfUHEhNLGazuUHHYeDhYvn5+aisrOSoFiJyGdaokjs46z5j4OFiZWVlinciIqLmjIGHi0lDj5wxBImIqCkbPHgwnnnmGflzdHQ0VqxY4bH82HL+/HmoVCocO3asQcepWtbmhJ1LXcxisSjeiYiobg4ePIjAwEBPZ4OcjIGHi3FUCxFR/YSFhXns3BUVFQ2er4JsY/2/i3F1WiKi6kpKSjB+/HgEBQUhIiICS5curZbGuqlFCIEFCxagbdu28PPzQ2RkJJ566ik5bXl5OZ5//nlERUXBz88PnTp1wgcffADgxiiMyZMno3379ggICEBMTAzeeustxbkmTpyIUaNG4dVXX0VkZCRiYmIAAAcOHEDv3r3h7++Pfv364ejRo9XymZaWhhEjRiAoKAgGgwGPPfYYLl++7FBZq8rMzMR9990Hg8GAoKAg/O53v8O3334rf5+eng6dTocNGzbI2zZv3oyAgACcOHECAHDt2jVMmTIFYWFhCAkJwd13343U1FQ5fWpqKu666y4EBwcjJCQEffv2xaFDh2rNW0Mx8CAiIgDuXVvqueeeww8//IAvv/wSO3fuREpKCo4cOVJj+i1btmD58uVYs2YNTp8+jS+++AJxcXHy9+PHj8enn36Kv/71rzh58iTWrFmDoKAgADeaum+99Vb84x//wIkTJzBv3jy8+OKL2Lx5s+Icu3fvRkZGBnbt2oV//etfKC4uxr333ovu3bvj8OHDWLBgAWbPnq3Y59q1a7j77rvRu3dvHDp0CNu3b0dubi7GjBlT77ICQHFxMX7/+99j9+7dOHr0KIYPH47k5GRkZWUBALp27YolS5Zg+vTpyMrKwq+//oonnngCixcvRvfu3QEAo0ePxqVLl/DNN9/g8OHD6NOnD+655x753/eRRx7BrbfeioMHD+Lw4cN44YUXGjQ/R50JEkIIUVBQIACIgoICpx43PT1dHD9+XKSnpzv1uEREpaWl4sSJE6K0tNQpx3PX76uioiLh6+srNm/eLG+7cuWKCAgIEE8//bS8rV27dmL58uVCCCGWLl0qunTpIioqKqodLyMjQwAQu3btqnMeZsyYIf7whz/InydMmCAMBoMoLy+Xt61Zs0bccsstiuu7atUqAUAcPXpUCCHEwoULxdChQxXHvnjxogAgMjIy6lzWuujRo4d4++23FdtGjhwpBg4cKO655x4xdOhQYbFYhBBC/Pvf/xYhISGirKxMkb5jx45izZo1QgghgoODxfr16+t8fnv3myPPUPbxcLGwsDDk5eV5tK2SiKgu3PX7KjMzExUVFUhISJC3hYaGys0btowePRorVqxAhw4dMHz4cPz+979HcnIyfHx8cOzYMWg0GgwaNKjG/VeuXIl169YhKysLpaWlqKioQK9evRRp4uLiFP06Tp48ifj4ePj7+8vbEhMTFfukpqbi+++/l2tXqpZTOpcjZQVu1HgsWLAAW7duRU5ODq5fv47S0lK5xkOybt06dOnSBWq1Gr/88ovcnzA1NRXFxcXVZrQtLS1FZmYmAGDWrFmYMmUKPvnkEyQlJWH06NHo2LGj3Xw5AwMPIiICcOOB6K2raEdFRSEjIwPffvstdu3ahenTp+PNN9/EDz/8gICAALv7bty4EbNnz8bSpUuRmJiI4OBgvPnmm9i/f78iXX1G0BQXFyM5ORmLFy+u9l1ERATOnDnj8DEBYPbs2di1axeWLFmCTp06ISAgAA8++CAqKioU6VJTU1FSUgK1Wo2cnBy5P2FxcTEiIiKQkpJS7dgtWrQAACxYsAAPP/wwtm7dim+++Qbz58/Hxo0bcf/999crz3XFwMPFcnJyIIRATk6O1/6HJiJyp44dO0Kr1WL//v1o27YtAODq1as4deqU3VqLgIAAJCcnIzk5GTNmzEDXrl1x/PhxxMXFwWKx4IcffkBSUlK1/fbs2YMBAwZg+vTp8jbpr357unXrhk8++QRlZWVyrcd//vMfRZo+ffpgy5YtiI6Oho9P9Udqfcu6Z88eTJw4UQ4CiouLcf78eUWa/Px8TJw4EXPnzkVOTg4eeeQRHDlyBAEBAejTpw+MRiN8fHwQHR1d43m6dOmCLl264Nlnn8W4cePw4YcfujzwYOdSFxNCKN6JiJq7oKAgTJ48Gc899xy+++47pKWlYeLEiXYnWly/fj0++OADpKWl4ezZs/jb3/6GgIAAtGvXDtHR0ZgwYQL++Mc/4osvvsC5c+eQkpIidx7t3LkzDh06hB07duDUqVN4+eWXcfDgwVrz+fDDD0OlUmHq1Kk4ceIEtm3bhiVLlijSzJgxA/n5+Rg3bhwOHjyIzMxM7NixA5MmTYLZbK5XWaU8f/755zh27BhSU1Px8MMPV5sP6oknnkBUVBReeuklLFu2DGazWe78mpSUhMTERIwaNQo7d+7E+fPnsXfvXsydOxeHDh1CaWkpZs6ciZSUFFy4cAF79uzBwYMH0a1bt1qvS0Mx8HAxKQK2FQkTETVXb775JgYOHIjk5GQkJSXhjjvuQN++fWtM36JFC6xduxa333474uPj8e233+Lrr7+W+zCsWrUKDz74IKZPn46uXbti6tSpKCkpAQBMmzYNDzzwAMaOHYuEhARcuXJFUftRk6CgIHz99dc4fvw4evfujblz51ZrUomMjMSePXtgNpsxdOhQxMXF4ZlnnkGLFi3k4MLRsgLAsmXL0LJlSwwYMADJyckYNmwY+vTpI3//8ccfY9u2bfjkk0/g4+ODwMBA/O1vf8PatWvxzTffQKVSYdu2bbjzzjsxadIkdOnSBQ899BAuXLgAg8EAjUaDK1euYPz48ejSpQvGjBmDESNG4JVXXqn1ujSUSvBPcQBAYWEh9Ho9CgoKEBIS4rTjpqWlyT/HxsY67bhERGVlZTh37hzat2+v6ABJ5Ar27jdHnqGs8SAiIiK3YeDhYlwkjoiI6CY+DV2Mi8QRERHdxMDDxdi5lIiI6CYGHi7GGg8iIqKbGHi4GOfxICIiuomBBxEREbkNAw8iIiJyGwYeRERE5DYMPIiIiDxk8ODBeOaZZzydDbdi4OFinECMiIjoJj4NXcxgMECr1cJgMHg6K0REjVpFRYXbzymEwPXr191+3qaMgQcREQEATJUmHPjtAEyVJpefa/DgwZg5cyZmzpwJvV6PVq1a4eWXX1ZMPRAdHY2FCxdi/PjxCAkJweOPPw4A+OmnnzBw4EAEBAQgKioKTz31lLwSLQC8++676Ny5M/z9/WEwGPDggw/K31ksFixatAjt27dHQEAAevbsic8++0z+PiUlBSqVCt988w369u0LPz8/rFu3DiqVCunp6YoyLF++HB07dpQ/p6WlYcSIEQgKCoLBYMBjjz2Gy5cvy9+XlJRg/PjxCAoKQkREBJYuXVrrdcrMzMR9990Hg8GAoKAg/O53v8O3334rf5+eng6dTocNGzbI2zZv3oyAgACcOHECAHDt2jVMmTIFYWFhCAkJwd13343U1FQ5fWpqKu666y4EBwcjJCQEffv2xaFDh2rNW70JEkIIUVBQIACIgoICpx43PT1dHD9+XKSnpzv1uEREpaWl4sSJE6K0tLTBxyqpKBGd/9pZYAFE5792FiUVJU7IYc0GDRokgoKCxNNPPy3S09PF3/72N6HT6cR7770np2nXrp0ICQkRS5YsEWfOnJFfgYGBYvny5eLUqVNiz549onfv3mLixIlCCCEOHjwoNBqN2LBhgzh//rw4cuSIeOutt+Rj/uUvfxFdu3YV27dvF5mZmeLDDz8Ufn5+IiUlRQghxPfffy8AiPj4eLFz505x5swZceXKFdGvXz/x0ksvKcrQt29fedvVq1dFWFiYmDNnjjh58qQ4cuSIGDJkiLjrrrvk9E8++aRo27at+Pbbb8XPP/8s7r33XhEcHCyefvrpGq/TsWPHxOrVq8Xx48fFqVOnxEsvvST8/f3FhQsX5DQrV64Uer1eXLhwQVy8eFG0bNlSUeakpCSRnJwsDh48KE6dOiX+7//+T9xyyy3iypUrQgghevToIR599FFx8uRJcerUKbF582Zx7Nixanmxd7858gxl4PFfrgo8srKyxPHjx0VWVpZTj0tE5MzAY/+v+wUWQH7t/3W/E3JYs0GDBolu3boJi8Uib3v++edFt27d5M/t2rUTo0aNUuw3efJk8fjjjyu2/fvf/xZqtVqUlpaKLVu2iJCQEFFYWFjtnGVlZUKn04m9e/dWO+a4ceOEEDcDjy+++EKRZvny5aJjx47y54yMDAFAnDx5UgghxMKFC8XQoUMV+1y8eFEAEBkZGaKoqEj4+vqKzZs3y99fuXJFBAQE2A08bOnRo4d4++23FdtGjhwpBg4cKO655x4xdOhQ+br++9//FiEhIaKsrEyRvmPHjmLNmjVCCCGCg4PF+vXraz2vswIPLiDiYiaTSfFOROSNYlvHonNoZ5zOP43OoZ0R2zrW5ee87bbboFKp5M+JiYlYunQpzGYzNBoNAKBfv36KfVJTU/Hzzz/j73//u7xNCAGLxYJz585hyJAhaNeuHTp06IDhw4dj+PDhuP/++6HT6XDmzBmYTCYMGTJEccyKigr07t1bsa3qeR966CHMnj0b//nPf3Dbbbfh73//O/r06YOuXbvK+fr+++8RFBRUrZyZmZkoLS1FRUUFEhIS5O2hoaGIiYmxe42Ki4uxYMECbN26FTk5Obh+/TpKS0uRlZWlSLdu3Tp06dIFarUav/zyi3xdU1NTUVxcjFtuuUWRvrS0FJmZmQCAWbNmYcqUKfjkk0+QlJSE0aNHK5qQnI2Bh4uFhYUhLy8PYWFhns4KEVGNdFodjj1xDGmX0hDbOhY6rc7TWQIABAYGKj4XFxdj2rRpeOqpp6qlbdu2LXx9fXHkyBGkpKRg586dmDdvHhYsWICDBw+iuLgYALB161a0adNGsa+fn5/d84aHh+Puu+/Ghg0bcNttt2HDhg148sknFflKTk7G4sWLq+UrIiICZ86ccazg/zV79mzs2rULS5YsQadOnRAQEIAHH3ywWkfb1NRUlJSUQK1WIycnBxEREXK+IiIikJKSUu3YLVq0AAAsWLAADz/8MLZu3YpvvvkG8+fPx8aNG3H//ffXK8+1YeDhYqGhoQgNDfV0NoiIaqXT6tC/TX+3nW///v2Kz//5z3/QuXNnubbDlj59+uDEiRPo1KlTjWl8fHyQlJSEpKQkzJ8/Hy1atMB3332HIUOGwM/PD1lZWRg0aJDD+X3kkUfwpz/9CePGjcPZs2fx0EMPKfK1ZcsWREdH21yNvGPHjtBqtdi/fz/atm0LALh69SpOnTplNy979uzBxIkT5SCguLgY58+fV6TJz8/HxIkTMXfuXOTk5OCRRx7BkSNHEBAQgD59+sBoNMLHxwfR0dE1nqdLly7o0qULnn32WYwbNw4ffvihywIPjmohIiKPyMrKwqxZs5CRkYFPP/0Ub7/9Np5++mm7+zz//PPYu3cvZs6ciWPHjuH06dP48ssvMXPmTADAv/71L/z1r3/FsWPHcOHCBXz88cewWCyIiYlBcHAwZs+ejWeffRYfffQRMjMzceTIEbz99tv46KOPas3vAw88gKKiIjz55JO46667EBkZKX83Y8YM5OfnY9y4cTh48CAyMzOxY8cOTJo0CWazGUFBQZg8eTKee+45fPfdd0hLS8PEiRNrneOpc+fO+Pzzz3Hs2DGkpqbi4Ycfrrba+RNPPIGoqCi89NJLWLZsGcxmM2bPng0ASEpKQmJiIkaNGoWdO3fi/Pnz2Lt3L+bOnYtDhw6htLQUM2fOREpKCi5cuIA9e/bg4MGD6NatW63Xo95q7QXiQe+8845o166d8PPzE/379xf799vv7LR582YRExMj/Pz8RGxsrNi6dWudz8XOpUTU2Dizc6m7DRo0SEyfPl088cQTIiQkRLRs2VK8+OKLis6m7dq1E8uXL6+274EDB8SQIUNEUFCQCAwMFPHx8eLVV18VQtzoTDlo0CDRsmVLERAQIOLj48WmTZvkfS0Wi1ixYoWIiYkRWq1WhIWFiWHDhokffvhBCHGzc+nVq1dt5nvMmDECgFi3bl21706dOiXuv/9+0aJFCxEQECC6du0qnnnmGblMRUVF4tFHHxU6nU4YDAbxxhtviEGDBtntXHru3Dlx1113iYCAABEVFSXeeecdxT4fffSRCAwMFKdOnZL32b9/v9BqtWLbtm1CCCEKCwvF//7v/4rIyEih1WpFVFSUeOSRR0RWVpYoLy8XDz30kIiKihK+vr4iMjJSzJw50+Y95azOpSohvHO99k2bNmH8+PFYvXo1EhISsGLFCvzjH/9ARkYGWrduXS393r17ceedd2LRokW49957sWHDBixevBhHjhxBbGztnaQKCwuh1+tRUFCAkJAQp5UjLS1N/rku+XCm/Px8uX8Jm3uImp6ysjKcO3cO7du3h7+/v6ez45DBgwejV69eWLFihaezQnVk735z5BnqtU0ty5Ytw9SpUzFp0iR0794dq1evhk6nw7p162ymf+uttzB8+HA899xz6NatGxYuXIg+ffrgnXfecXPOlfR6veLdnfLy8lBZWYm8vDy3n5uIiMgWrww8KioqcPjwYSQlJcnb1Go1kpKSsG/fPpv77Nu3T5EeAIYNG1Zj+vLychQWFiperhAVFYXY2FhERUW55Pj2hIWFQavVckQNERF5Da8c1XL58mWYzeZq65sYDIZqU9ZKjEajzfRGo9Fm+kWLFuGVV15xToa9FEfUEJG3sjW8k5oHr6zxcIc5c+agoKBAfl28eNHTWSIiImryvLLGo1WrVtBoNMjNzVVsz83NRXh4uM19wsPDHUrv5+dXbcIYIqLGyEvHCFAT46z7zCtrPHx9fdG3b1/s3r1b3maxWLB7924kJiba3CcxMVGRHgB27dpVY3oiosZOq9UC4JIM5B7SbKn2JnirC6+s8QBuzB0/YcIE9OvXD/3798eKFStQUlKCSZMmAQDGjx+PNm3aYNGiRQCAp59+GoMGDcLSpUsxcuRIbNy4EYcOHcJ7773nyWIQEbmMRqNBixYtcOnSJQCATqdTrH1C5CwWiwV5eXnQ6XQ2Z2Z1hNcGHmPHjkVeXh7mzZsHo9GIXr16Yfv27XIH0qysLMWMbwMGDMCGDRvw0ksv4cUXX0Tnzp3xxRdfuH3uDCIid5Kak6Xgg8hV1Go12rZt2+Dg1msnEHM3V00gRkTkDmazGZWVlZ7OBjVhvr6+NU7x7sgz1GtrPIiIqO40Gk2D296J3MErO5cSERFR08TAg4iIiNyGgQcRERG5Dft4/JfUx9ZVa7YQERE1VdKzsy7jVRh4/FdRUREAeGQxNyIioqagqKio1tXYOZz2vywWC7KzsxEcHOzUCXgKCwsRFRWFixcvNsthuix/8y4/wGvQ3MsP8Bo0h/ILIVBUVITIyMgah9xKWOPxX2q1GrfeeqvLjh8SEtJkb7i6YPmbd/kBXoPmXn6A16Cpl7+2mg4JO5cSERGR2zDwICIiIrdh4OFifn5+mD9/Pvz8/DydFY9g+Zt3+QFeg+ZefoDXoLmXvyp2LiUiIiK3YY0HERERuQ0DDyIiInIbBh5ERETkNgw8iIiIyG0YeDho5cqViI6Ohr+/PxISEnDgwAG76f/xj3+ga9eu8Pf3R1xcHLZt26b4XgiBefPmISIiAgEBAUhKSsLp06ddWYQGcaT8a9euxcCBA9GyZUu0bNkSSUlJ1dJPnDgRKpVK8Ro+fLiri9EgjlyD9evXVyufv7+/Ik1TvgcGDx5crfwqlQojR46U0zSme+DHH39EcnIyIiMjoVKp8MUXX9S6T0pKCvr06QM/Pz906tQJ69evr5bG0d8rnuToNfj8888xZMgQhIWFISQkBImJidixY4cizYIFC6rdA127dnVhKerP0fKnpKTY/D9gNBoV6RrTPdBQDDwcsGnTJsyaNQvz58/HkSNH0LNnTwwbNgyXLl2ymX7v3r0YN24cJk+ejKNHj2LUqFEYNWoU0tLS5DRvvPEG/vrXv2L16tXYv38/AgMDMWzYMJSVlbmrWHXmaPlTUlIwbtw4fP/999i3bx+ioqIwdOhQ/Pbbb4p0w4cPR05Ojvz69NNP3VGcenH0GgA3Ziu0Lt+FCxcU3zfle+Dzzz9XlD0tLQ0ajQajR49WpGss90BJSQl69uyJlStX1in9uXPnMHLkSNx11104duwYnnnmGUyZMkXx4K3PPeVJjl6DH3/8EUOGDMG2bdtw+PBh3HXXXUhOTsbRo0cV6Xr06KG4B3766SdXZL/BHC2/JCMjQ1G+1q1by981tnugwQTVWf/+/cWMGTPkz2azWURGRopFixbZTD9mzBgxcuRIxbaEhAQxbdo0IYQQFotFhIeHizfffFP+/tq1a8LPz098+umnLihBwzha/qquX78ugoODxUcffSRvmzBhgrjvvvucnVWXcfQafPjhh0Kv19d4vOZ2DyxfvlwEBweL4uJieVtjuwckAMQ///lPu2n+9Kc/iR49eii2jR07VgwbNkz+3NBr6kl1uQa2dO/eXbzyyivy5/nz54uePXs6L2NuUpfyf//99wKAuHr1ao1pGvM9UB+s8aijiooKHD58GElJSfI2tVqNpKQk7Nu3z+Y++/btU6QHgGHDhsnpz507B6PRqEij1+uRkJBQ4zE9pT7lr8pkMqGyshKhoaGK7SkpKWjdujViYmLw5JNP4sqVK07Nu7PU9xoUFxejXbt2iIqKwn333YdffvlF/q653QMffPABHnroIQQGBiq2N5Z7wFG1/Q5wxjVtbCwWC4qKiqr9Hjh9+jQiIyPRoUMHPPLII8jKyvJQDl2jV69eiIiIwJAhQ7Bnzx55e3O8Bxh41NHly5dhNpthMBgU2w0GQ7W2OonRaLSbXnp35JieUp/yV/X8888jMjJS8R9s+PDh+Pjjj7F7924sXrwYP/zwA0aMGAGz2ezU/DtDfa5BTEwM1q1bhy+//BJ/+9vfYLFYMGDAAPz6668Amtc9cODAAaSlpWHKlCmK7Y3pHnBUTb8DCgsLUVpa6pT/V43NkiVLUFxcjDFjxsjbEhISsH79emzfvh2rVq3CuXPnMHDgQBQVFXkwp84RERGB1atXY8uWLdiyZQuioqIwePBgHDlyBIBzfrc2Nlydltzi9ddfx8aNG5GSkqLoXPnQQw/JP8fFxSE+Ph4dO3ZESkoK7rnnHk9k1akSExORmJgofx4wYAC6deuGNWvWYOHChR7Mmft98MEHiIuLQ//+/RXbm/o9QDdt2LABr7zyCr788ktFH4cRI0bIP8fHxyMhIQHt2rXD5s2bMXnyZE9k1WliYmIQExMjfx4wYAAyMzOxfPlyfPLJJx7MmeewxqOOWrVqBY1Gg9zcXMX23NxchIeH29wnPDzcbnrp3ZFjekp9yi9ZsmQJXn/9dezcuRPx8fF203bo0AGtWrXCmTNnGpxnZ2vINZBotVr07t1bLl9zuQdKSkqwcePGOj1EvPkecFRNvwNCQkIQEBDglHuqsdi4cSOmTJmCzZs3V2t+qqpFixbo0qVLk7gHbOnfv79ctuZ0D0gYeNSRr68v+vbti927d8vbLBYLdu/erfiL1lpiYqIiPQDs2rVLTt++fXuEh4cr0hQWFmL//v01HtNT6lN+4MaIjYULF2L79u3o169fref59ddfceXKFURERDgl385U32tgzWw24/jx43L5msM9ANwYVl5eXo5HH3201vN48z3gqNp+BzjjnmoMPv30U0yaNAmffvqpYih1TYqLi5GZmdkk7gFbjh07JpetudwDCp7u3dqYbNy4Ufj5+Yn169eLEydOiMcff1y0aNFCGI1GIYQQjz32mHjhhRfk9Hv27BE+Pj5iyZIl4uTJk2L+/PlCq9WK48ePy2lef/110aJFC/Hll1+Kn3/+Wdx3332iffv2orS01O3lq42j5X/99deFr6+v+Oyzz0ROTo78KioqEkIIUVRUJGbPni327dsnzp07J7799lvRp08f0blzZ1FWVuaRMtbG0WvwyiuviB07dojMzExx+PBh8dBDDwl/f3/xyy+/yGma8j0gueOOO8TYsWOrbW9s90BRUZE4evSoOHr0qAAgli1bJo4ePSouXLgghBDihRdeEI899pic/uzZs0Kn04nnnntOnDx5UqxcuVJoNBqxfft2OU1t19TbOHoN/v73vwsfHx+xcuVKxe+Ba9euyWn+7//+T6SkpIhz586JPXv2iKSkJNGqVStx6dIlt5evNo6Wf/ny5eKLL74Qp0+fFsePHxdPP/20UKvV4ttvv5XTNLZ7oKEYeDjo7bffFm3bthW+vr6if//+4j//+Y/83aBBg8SECRMU6Tdv3iy6dOkifH19RY8ePcTWrVsV31ssFvHyyy8Lg8Eg/Pz8xD333CMyMjLcUZR6caT87dq1EwCqvebPny+EEMJkMomhQ4eKsLAwodVqRbt27cTUqVO9/j+bI9fgmWeekdMaDAbx+9//Xhw5ckRxvKZ8DwghRHp6ugAgdu7cWe1Yje0ekIZGVn1JZZ4wYYIYNGhQtX169eolfH19RYcOHcSHH35Y7bj2rqm3cfQaDBo0yG56IW4MMY6IiBC+vr6iTZs2YuzYseLMmTPuLVgdOVr+xYsXi44dOwp/f38RGhoqBg8eLL777rtqx21M90BDqYQQwi1VK0RERNTssY8HERERuQ0DDyIiInIbBh5ERETkNgw8iIiIyG0YeBAREZHbMPAgIiIit2HgQURERG7DwIOoiZo4cSKio6M9nQ3ZggULoFKpPJ2NevG2a0nUmDHwICIiIrfx8XQGiMg11q5dC4vF4ulsEBEpsMaDqInSarXw8/PzdDZcQgiB0tJST2eDiOqBgQdRI1RUVIRnnnkG0dHR8PPzQ+vWrTFkyBAcOXJETlO1X8L58+ehUqmwZMkSvPfee+jYsSP8/Pzwu9/9DgcPHqx2jn/84x/o3r07/P39ERsbi3/+85/VjpmSkgKVSoWUlBTFvtK51q9fb7ccH374Ie6++260bt0afn5+6N69O1atWlUtXXR0NO69917s2LED/fr1Q0BAANasWWPzmDNnzkRQUBBMJlO178aNG4fw8HCYzWYAwJdffomRI0ciMjISfn5+6NixIxYuXCh/XxNHy52eno4HH3wQoaGh8Pf3R79+/fDVV18p0lRWVuKVV15B586d4e/vj1tuuQV33HEHdu3aZTcvRI0Nm1qIGqEnnngCn332GWbOnInu3bvjypUr+Omnn3Dy5En06dPH7r4bNmxAUVERpk2bBpVKhTfeeAMPPPAAzp49C61WCwDYunUrxo4di7i4OCxatAhXr17F5MmT0aZNG6eWY9WqVejRowf+53/+Bz4+Pvj6668xffp0WCwWzJgxQ5E2IyMD48aNw7Rp0zB16lTExMTYPObYsWOxcuVKbN26FaNHj5a3m0wmfP3115g4cSI0Gg0AYP369QgKCsKsWbMQFBSE7777DvPmzUNhYSHefPNNp5Txl19+we233442bdrghRdeQGBgIDZv3oxRo0Zhy5YtuP/++wHc6Hy7aNEiTJkyBf3790dhYSEOHTqEI0eOYMiQIU7JC5FX8PDquERUD3q9XsyYMcNumgkTJoh27drJn8+dOycAiFtuuUXk5+fL27/88ksBQHz99dfytri4OHHrrbeKoqIieVtKSooAoDimtET4999/rzi3dC7rJeDnz58vqv7KMZlM1fI9bNgw0aFDB8W2du3aCQBi+/btdssshBAWi0W0adNG/OEPf1Bs37x5swAgfvzxR7vnnzZtmtDpdKKsrEzeVvVaOlLue+65R8TFxSmOZ7FYxIABA0Tnzp3lbT179hQjR46stXxEjR2bWogaoRYtWmD//v3Izs52eN+xY8eiZcuW8ueBAwcCAM6ePQsAyM7OxvHjxzF+/HgEBQXJ6QYNGoS4uLgG5lwpICBA/rmgoACXL1/GoEGDcPbsWRQUFCjStm/fHsOGDav1mCqVCqNHj8a2bdtQXFwsb9+0aRPatGmDO+64w+b5i4qKcPnyZQwcOBAmkwnp6ekNKRoAID8/H9999x3GjBkjH//y5cu4cuUKhg0bhtOnT+O3334DcOPf9JdffsHp06cbfF4ib8bAg6gReuONN5CWloaoqCj0798fCxYskAOH2rRt21bxWQpCrl69CgC4cOECAKBTp07V9rW1rSH27NmDpKQkBAYGokWLFggLC8OLL74IADYDj7oaO3YsSktL5X4UxcXF2LZtG0aPHq2YS+SXX37B/fffD71ej5CQEISFheHRRx+1ef76OHPmDIQQePnllxEWFqZ4zZ8/HwBw6dIlAMCf//xnXLt2DV26dEFcXByee+45/Pzzzw3OA5G3YeBB1AiNGTMGZ8+exdtvv43IyEi8+eab6NGjB7755pta95X6N1QlhHA4HzVNCFZb50wAyMzMxD333IPLly9j2bJl2Lp1K3bt2oVnn30WAKoNBbaunajNbbfdhujoaGzevBkA8PXXX6O0tBRjx46V01y7dg2DBg1Camoq/vznP+Prr7/Grl27sHjxYpvnt1bXckvHmD17Nnbt2mXzJQVzd955JzIzM7Fu3TrExsbi/fffR58+ffD+++/XudxEjQE7lxI1UhEREZg+fTqmT5+OS5cuoU+fPnj11VcxYsSIBh23Xbt2AG78tV5V1W1Sbcm1a9cU26VaE3u+/vprlJeX46uvvlLUwnz//feOZtmmMWPG4K233kJhYSE2bdqE6Oho3HbbbfL3KSkpuHLlCj7//HPceeed8vZz587Veuy6lrtDhw4AbgxtTkpKqvW4oaGhmDRpEiZNmoTi4mLceeedWLBgAaZMmVLrvkSNBWs8iBoZs9lcrRmgdevWiIyMRHl5eYOPHxkZidjYWHz88ceKPhI//PADjh8/rkjbrl07aDQa/Pjjj4rt7777bq3nkWperGtaCgoK8OGHHzYk+7KxY8eivLwcH330EbZv344xY8bUev6Kioo65b2u5W7dujUGDx6MNWvWICcnp9px8vLy5J+vXLmi+C4oKAidOnVyyr8pkTdhjQdRI1NUVIRbb70VDz74IHr27ImgoCB8++23OHjwIJYuXeqUc7z22mu47777cPvtt2PSpEm4evUq3nnnHcTGxiqCEb1ej9GjR+Ptt9+GSqVCx44d8a9//Uvut2DP0KFD4evri+TkZEybNg3FxcVYu3YtWrdubfMh7ag+ffqgU6dOmDt3LsrLyxXNLAAwYMAAtGzZEhMmTMBTTz0FlUqFTz75pE5NTo6Ue+XKlbjjjjsQFxeHqVOnokOHDsjNzcW+ffvw66+/IjU1FQDQvXt3DB48GH379kVoaCgOHTokD5kmalI8OqaGiBxWXl4unnvuOdGzZ08RHBwsAgMDRc+ePcW7776rSFfTcNo333yz2jEBiPnz5yu2bdy4UXTt2lX4+fmJ2NhY8dVXX4k//OEPomvXrop0eXl54g9/+IPQ6XSiZcuWYtq0aSItLa1Ow2m/+uorER8fL/z9/UV0dLRYvHixWLdunQAgzp07J6dr165dvYaazp07VwAQnTp1svn9nj17xG233SYCAgJEZGSk+NOf/iR27NhRbahs1WvpSLmFECIzM1OMHz9ehIeHC61WK9q0aSPuvfde8dlnn8lp/vKXv4j+/fuLFi1aiICAANG1a1fx6quvioqKCofLTeTNVELUo0cZETVLvXr1QlhYGGfTJKJ6Yx8PIqqmsrIS169fV2xLSUlBamoqBg8e7JlMEVGTwBoPIqrm/PnzSEpKwqOPPorIyEikp6dj9erV0Ov1SEtLwy233OLpLBJRI8XOpURUTcuWLdG3b1+8//77yMvLQ2BgIEaOHInXX3+dQQcRNQhrPIiIiMht2MeDiIiI3IaBBxEREbkNAw8iIiJyGwYeRERE5DYMPIiIiMhtGHgQERGR2zDwICIiIrdh4EFERERuw8CDiIiI3Ob/Ab6hfeEMdF/QAAAAAElFTkSuQmCC\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "# Compute dot products of left and right singular vectors (u.v=1).\n",
    "subspace_dim = int(np.sum((S)**2))\n",
    "uvdots = []\n",
    "for j in range(N):\n",
    "    v = V[j,:]\n",
    "    u = U[:,j]\n",
    "    uvdots.append(abs(np.dot(v,u)))\n",
    "\n",
    "# Plot dot products as a function of associated singular value\n",
    "f, ax = plt.subplots(1,1,figsize = (6,4))\n",
    "ax.plot(S, uvdots, '.', color = 'lightgray', markersize=2 , label='discarded axes')\n",
    "ax.plot(S[0:subspace_dim], uvdots[0:subspace_dim], '.',markersize=3,color='green',alpha=1, label = 'preserved axes')\n",
    "ax.set_ylabel(r'${v}^T{u} $', fontsize = 12, fontname= 'Times New Roman')\n",
    "ax.set_xlabel('singular values', fontsize = 12, fontname= 'Times New Roman')\n",
    "plt.legend()\n",
    "for tick in ax.xaxis.get_major_ticks():\n",
    "    tick.label1.set_fontsize(10)\n",
    "    tick.label1.set_fontname(\"Times New Roman\")\n",
    "\n",
    "for tick in ax.yaxis.get_major_ticks():\n",
    "    tick.label1.set_fontsize(10)\n",
    "    tick.label1.set_fontname(\"Times New Roman\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "id": "H8g3F5xJ70SJ",
    "executionInfo": {
     "status": "ok",
     "timestamp": 1705956151801,
     "user_tz": 300,
     "elapsed": 170,
     "user": {
      "displayName": "Kangning Liu",
      "userId": "18225106579512019568"
     }
    }
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "denoisingbase",
   "language": "python",
   "name": "denoisingbase"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  },
  "colab": {
   "provenance": []
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}