frequency_principle/f-principle_nd.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import time\n",
    "import warnings\n",
    "import numpy as np\n",
    "import torch\n",
    "import math\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "from typing import List\n",
    "import argparse\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import datetime\n",
    "import re\n",
    "from torch.utils.data import DataLoader, Dataset, Subset, TensorDataset\n",
    "from torch.utils.data.sampler import Sampler\n",
    "from torchvision import datasets, transforms\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#   Default configuration parameter settings."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "parser = argparse.ArgumentParser(\n",
    "    description='PyTorch Training for Frequency Principle')\n",
    "\n",
    "\n",
    "parser.add_argument('--lr', default=1e-3, type=float, help='learning rate')\n",
    "parser.add_argument('--optimizer', default='nesterov',\n",
    "                    help='optimizer: sgd | adam | nesterov')\n",
    "parser.add_argument('--epochs', default=100, type=int,\n",
    "                    metavar='N', help='number of total epochs to run')\n",
    "parser.add_argument('--training_batch_size',   default=50, type=int,\n",
    "                    help='the batch size for model (default: 1000)')\n",
    "parser.add_argument('--training_size',   default=5000, type=int,\n",
    "                    help='the training size for model (default: 1000)')\n",
    "parser.add_argument('--test_batch_size',   default=50, type=int,\n",
    "                    help='the test size for model (default: 10000)')\n",
    "parser.add_argument('--act_func_name', default='ReLU',\n",
    "                    help='activation function')\n",
    "parser.add_argument('--in_channel',   default=3, type=int,\n",
    "                    help='the input channel for model (default: 3)')\n",
    "parser.add_argument('--num_classes',   default=10, type=int,\n",
    "                    help='the output dimension for model (default: 10)')\n",
    "parser.add_argument('--device',   default='cuda', type=str,\n",
    "                    help='device used to train (cpu or cuda)')\n",
    "parser.add_argument('--plot_epoch',   default=1, type=int,\n",
    "                    help='step size of plotting interval (default: 1000)')\n",
    "parser.add_argument('--ini_path', type=str,\n",
    "                    default='')\n",
    "parser.add_argument('--start_filter',   default=2, type=float,\n",
    "                    help='the start point of the filter (default: 2)')\n",
    "parser.add_argument('--end_filter',   default=100, type=float,\n",
    "                    help='the end point of the filter (default: 100)')\n",
    "parser.add_argument('--num_filter',   default=20, type=int,\n",
    "                    help='the point number of the filter (default: 20)')\n",
    "\n",
    "\n",
    "args, _ = parser.parse_known_args()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#   The storage path of the output file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "save path: 20230614154423543332\n"
     ]
    }
   ],
   "source": [
    "def mkdirs(fn):\n",
    "    \"\"\"\n",
    "    Create directories if they don't exist.\n",
    "\n",
    "    Args:\n",
    "    fn: The directory path to create.\n",
    "    \"\"\"\n",
    "\n",
    "    if not os.path.isdir(fn):\n",
    "        os.makedirs(fn)\n",
    "\n",
    "\n",
    "def create_save_dir(path_ini):\n",
    "    \"\"\"\n",
    "    Create a new directory with the current date and time as its name and return the path of the new directory.\n",
    "\n",
    "    Args:\n",
    "    path_ini: The initial path to create the new directory.\n",
    "\n",
    "    Return:\n",
    "    The path of the new directory.\n",
    "    \"\"\"\n",
    "    subFolderName = re.sub(r'[^0-9]', '', str(datetime.datetime.now()))\n",
    "    path = os.path.join(path_ini, subFolderName)\n",
    "    mkdirs(path)\n",
    "    mkdirs(os.path.join(path, 'output'))\n",
    "    return path\n",
    "\n",
    "\n",
    "args.path = create_save_dir(args.ini_path)\n",
    "print('save path: %s' % (args.path))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generation of dataloader.\n",
    "\n",
    "A dataloader is a utility in PyTorch that helps to load and preprocess data for machine learning models. It is used to efficiently load large datasets and feed them to the model in batches during training or inference. \n",
    "\n",
    "The `load_data` function defines a dataloader for the CIFAR10 dataset. The function loads the CIFAR10 dataset using the `datasets.CIFAR10` class and applies the `transform` object to the data. It creates a `Subset` object from the training dataset, which selects a subset of the data based on the `training_size` argument. \n",
    "\n",
    "The `DataLoader` class is then used to create dataloaders for the training and test datasets. The `train_loader` loads the training data in batches of size `training_batch_size`, while the `test_loader` loads the test data in batches of size `test_batch_size`. The `num_workers` argument specifies the number of subprocesses to use for data loading, while the `shuffle` argument specifies whether to shuffle the data before each epoch. \n",
    "\n",
    "\n",
    "This will return two dataloaders: `train_loader` and `test_loader`, which can be used to iterate over the training and test data in batches during training or inference.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "def load_data(training_size, training_batch_size, test_batch_size):\n",
    "    transform = transforms.Compose([\n",
    "        transforms.ToTensor(),\n",
    "        # transforms.Normalize(mean=[x/255.0 for x in [125.3, 123.0, 113.9]],\n",
    "        #                     std=[x/255.0 for x in [63.0, 62.1, 66.7]]),\n",
    "    ])\n",
    "\n",
    "    train_dataset = datasets.CIFAR10(root=\"./\",\n",
    "                                    train=True,\n",
    "                                    transform=transform,\n",
    "                                    download=True\n",
    "                                    )\n",
    "\n",
    "    test_dataset = datasets.CIFAR10(root=\"./\",\n",
    "                                    train=False,\n",
    "                                    transform=transform,\n",
    "                                    download=True)\n",
    "    \n",
    "\n",
    "    train_dataset=Subset(train_dataset,range(training_size))\n",
    "\n",
    "    train_loader = DataLoader(\n",
    "    train_dataset, batch_size=training_batch_size,  num_workers=2, shuffle=False,drop_last=True, pin_memory=True)\n",
    "\n",
    "    test_loader = DataLoader(dataset=test_dataset,\n",
    "                                 batch_size=test_batch_size,\n",
    "                                 shuffle=False, num_workers=2,drop_last=True, pin_memory=True)\n",
    "\n",
    "    return train_loader, test_loader\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Files already downloaded and verified\n",
      "Files already downloaded and verified\n"
     ]
    }
   ],
   "source": [
    "train_loader, test_loader = load_data(\n",
    "    args.training_size, args.training_batch_size, args.test_batch_size)\n",
    "\n",
    "\n",
    "train_loader, test_loader=list(train_loader), list(test_loader)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How to create a 1D datalodaer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "class DealDataset(Dataset):\n",
    "\n",
    "    def __init__(self, train_X, train_y):\n",
    "        self.x_data = train_X\n",
    "        self.y_data = train_y\n",
    "        self.len = train_X.shape[0]\n",
    "\n",
    "    def __getitem__(self, index):\n",
    "        return self.x_data[index], self.y_data[index]\n",
    "\n",
    "    def __len__(self):\n",
    "        return self.len\n",
    "\n",
    "class get_1D_data:\n",
    "    def __init__(self, args):\n",
    "        self.args = args\n",
    "\n",
    "    def get_target_func(self, x):\n",
    "\n",
    "        return torch.sin(x)+2*torch.sin(3*x)+3*torch.sin(5*x)\n",
    "    \n",
    "\n",
    "    def get_inputs(self):\n",
    "\n",
    "        args = self.args\n",
    "\n",
    "        bound=1\n",
    "\n",
    "        for i in range(2):\n",
    "            if isinstance(args.data_boundary[i], str):\n",
    "                args.data_boundary[i]=eval(args.data_boundary[i])\n",
    "\n",
    "        if args.input_dim == 1:\n",
    "\n",
    "            test_inputs = torch.reshape(torch.linspace(\n",
    "                bound*args.data_boundary[0], bound*args.data_boundary[1], args.test_size), [-1, 1])\n",
    "            train_inputs = torch.reshape(torch.linspace(\n",
    "                args.data_boundary[0], args.data_boundary[1], args.training_size), [-1, 1])\n",
    "        else:\n",
    "            test_inputs = (torch.rand(args.test_size, args.input_dim)\n",
    "                           )*(bound*args.data_boundary[1]-bound*args.data_boundary[0])+bound*args.data_boundary[0]\n",
    "            train_inputs = torch.rand(args.training_size, args.input_dim) *(args.data_boundary[1]-args.data_boundary[0])+args.data_boundary[0]\n",
    "        return test_inputs, train_inputs\n",
    "\n",
    "    def get_data(self):\n",
    "        test_inputs, train_inputs = self.get_inputs()\n",
    "        test_targets, train_targets = self.get_target_func(\n",
    "            test_inputs), self.get_target_func(train_inputs)\n",
    "        train_dataset = DealDataset(\n",
    "            train_inputs, train_targets)\n",
    "        test_dataset = DealDataset(\n",
    "            test_inputs, test_targets)\n",
    "        return train_dataset, test_dataset, test_inputs, train_inputs, test_targets, train_targets\n",
    "def load_data(training_batch_size, test_batch_size, args):\n",
    "\n",
    "    Get_data = get_1D_data(args)\n",
    "    train_dataset, test_dataset, _, _, _, _ = Get_data.get_data()\n",
    "    train_loader = DataLoader(dataset=train_dataset,\n",
    "                                batch_size=training_batch_size,\n",
    "                                shuffle=False,drop_last=True)\n",
    "    test_loader = DataLoader(dataset=test_dataset,\n",
    "                                batch_size=test_batch_size,\n",
    "                                shuffle=False,drop_last=True)\n",
    "    \n",
    "    return train_loader, test_loader\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Network model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The network structure:\n",
      "My_CNN(\n",
      "  (conv): Sequential(\n",
      "    (0): Conv2d(3, 32, kernel_size=(3, 3), stride=(1, 1))\n",
      "    (1): ReLU()\n",
      "    (2): Conv2d(32, 64, kernel_size=(3, 3), stride=(1, 1))\n",
      "    (3): ReLU()\n",
      "    (4): MaxPool2d(kernel_size=(2, 2), stride=(2, 2), padding=0, dilation=1, ceil_mode=False)\n",
      "  )\n",
      "  (mlp): Sequential(\n",
      "    (0): Linear(in_features=12544, out_features=400, bias=True)\n",
      "    (1): ReLU()\n",
      "    (2): Linear(in_features=400, out_features=10, bias=True)\n",
      "    (3): Softmax(dim=1)\n",
      "  )\n",
      ")\n"
     ]
    }
   ],
   "source": [
    "class My_CNN(nn.Module):\n",
    "    def __init__(self, in_channels=3, num_classes: int = 10, act_layer: nn.Module = nn.ReLU()):\n",
    "        super(My_CNN, self).__init__()\n",
    "        self.num_classes = num_classes\n",
    "        self.in_channels = in_channels\n",
    "        conv_layers: List[nn.Module] = []\n",
    "\n",
    "        conv_layers += [nn.Conv2d(self.in_channels,\n",
    "                             32, kernel_size=3,stride=1,padding=0), act_layer]\n",
    "        conv_layers += [nn.Conv2d(32, 64, kernel_size=3,stride=1,padding=0), act_layer]\n",
    "        conv_layers += [nn.MaxPool2d(kernel_size=(2, 2))]\n",
    "        self.conv = nn.Sequential(*conv_layers)\n",
    "        mlp_layers: List[nn.Module] = []\n",
    "        mlp_layers += [nn.Linear(14*14*64, 400), act_layer]\n",
    "        mlp_layers += [nn.Linear(400, self.num_classes), nn.Softmax(dim=1)]\n",
    "        self.mlp = nn.Sequential(*mlp_layers)\n",
    "        self._initialize_weights()\n",
    "\n",
    "    def forward(self, x):\n",
    "        x = self.conv(x)\n",
    "        x = x.view(x.size(0), -1)\n",
    "        x = self.mlp(x)\n",
    "        return x\n",
    "    \n",
    "    def _initialize_weights(self) -> None:\n",
    "        for obj in self.modules():\n",
    "            if isinstance(obj, (nn.Linear, nn.Conv2d)):\n",
    "                nn.init.xavier_uniform_(obj.weight.data)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "def get_act_func(act_func):\n",
    "    \"\"\"\n",
    "    Get activation function.\n",
    "\n",
    "    Args:\n",
    "        act_func (str): activation function name.\n",
    "\n",
    "    Returns:\n",
    "        nn.Module: activation function.\n",
    "    \"\"\"\n",
    "\n",
    "    if act_func == 'tanh':\n",
    "        return nn.Tanh()\n",
    "    elif act_func == 'ReLU':\n",
    "        return nn.ReLU()\n",
    "    elif act_func == 'Sigmoid':\n",
    "        return nn.Sigmoid()\n",
    "    else:\n",
    "        raise NameError('No such act func!')\n",
    "\n",
    "\n",
    "act_func = get_act_func(args.act_func_name)\n",
    "\n",
    "model = My_CNN(args.in_channel, args.num_classes, act_func).to(args.device)\n",
    "print(\"The network structure:\")\n",
    "print(model)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# One-step training function.\n",
    "\n",
    "The training data set is denoted as  $S=\\{(x_i,y_i)\\}_{i=1}^n$, where $x_i\\in\\mathbb{R}^d$ and $y_i\\in \\mathbb{R}^{d'}$. For simplicity, we assume an unknown function $y$ satisfying $y(x_i)=y_i$ for $i\\in[n]$. The empirical risk reads as\n",
    "\\begin{equation*}\n",
    "    R_S(\\theta)=\\frac{1}{n}\\sum_{i=1}^n\\ell(f(x_i,\\theta),y(x_i)),\n",
    "\\end{equation*}\n",
    "where the loss function $\\ell(\\cdot,\\cdot)$ is differentiable and the derivative of $\\ell$ with respect to its first argument is denoted by $\\nabla\\ell(y,y^*)$. \n",
    "\n",
    "For a one-step gradient descent, we have, \n",
    "\n",
    "\\begin{equation*}\n",
    "    \\theta_{t+1}=\\theta_t-\\eta\\nabla R_S(\\theta).\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train_one_step(model, optimizer, loss_fn,  train_loader, args):\n",
    "    \"\"\"\n",
    "    It takes in a model, optimizer, loss function, resultsaver, train_loader, and args, and returns the\n",
    "    average loss and accuracy for the training set\n",
    "\n",
    "    :param model: the model we're training\n",
    "    :param optimizer: the optimizer for training model\n",
    "    :param loss_fn: the loss function\n",
    "    :param train_loader: the training data loader\n",
    "    :param args: a dictionary containing all the parameters for the training process\n",
    "    :return: The average loss and the accuracy\n",
    "    \"\"\"\n",
    "    model.train()\n",
    "    train_loss = 0.0\n",
    "    correct = 0\n",
    "    total = 0\n",
    "    device = args.device\n",
    "\n",
    "\n",
    "    for inputs, targets in train_loader:\n",
    "\n",
    "        batch_size = inputs.size(0)\n",
    "        total += batch_size\n",
    "\n",
    "        inputs, targets = inputs.to(device), targets.to(device)\n",
    "        optimizer.zero_grad()\n",
    "        inputs, targets = torch.autograd.Variable(\n",
    "            inputs), torch.autograd.Variable(targets)\n",
    "        outputs = model(inputs)\n",
    "        loss = loss_fn(torch.log(outputs), targets)\n",
    "        loss.backward()\n",
    "        optimizer.step()\n",
    "        train_loss += loss.item()*batch_size\n",
    "        _, predicted = torch.max(outputs.data, 1)\n",
    "        correct += predicted.eq(targets.data).cpu().sum().item()\n",
    "\n",
    "    acc = 100*correct/total\n",
    "\n",
    "    return train_loss/total, acc\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# One-step test function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def test(model, loss_fn, test_loader,  args):\n",
    "    \"\"\"\n",
    "    It takes a model, a test_loader, a loss function, and some arguments, and returns the average loss\n",
    "    and accuracy of the model on the test set.\n",
    "\n",
    "    :param model: the model\n",
    "    :param loss_fn: the loss function\n",
    "    :param test_loader: a DataLoader object\n",
    "    :param args: a dictionary containing all the parameters for the training process\n",
    "    :return: The loss and accuracy of the model on the test set.\n",
    "    \"\"\"\n",
    "    model.eval()\n",
    "    train_loss = 0.0\n",
    "    correct = 0\n",
    "    total = 0\n",
    "    device = args.device\n",
    "    with torch.no_grad():\n",
    "        for inputs, targets in test_loader:\n",
    "            batch_size = inputs.size(0)\n",
    "            total += batch_size\n",
    "            inputs, targets = inputs.to(device), targets.to(device)\n",
    "            inputs, targets = torch.autograd.Variable(\n",
    "                inputs), torch.autograd.Variable(targets)\n",
    "            outputs = model(inputs)\n",
    "            loss = loss_fn(torch.log(outputs), targets)\n",
    "            train_loss += loss.item() * batch_size\n",
    "            _, predicted = torch.max(outputs.data, 1)\n",
    "            correct += predicted.eq(targets.data).cpu().sum().item()\n",
    "        acc = 100 * correct / total\n",
    "    return train_loss / total, acc\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Function to obtain model output on the full training set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def val(model, training_loader,  args):\n",
    "    \"\"\"\n",
    "    It takes a model, a test_loader, a loss function, and some arguments, and returns the average loss\n",
    "    and accuracy of the model on the test set.\n",
    "\n",
    "    :param model: the model\n",
    "    :param training_loader: a DataLoader object\n",
    "    :param args: a dictionary containing all the parameters for the training process\n",
    "    :return: the outputs of the model on the training set\n",
    "    \"\"\"\n",
    "    model.eval()\n",
    "\n",
    "    y_pred =[]\n",
    "\n",
    "    device = args.device\n",
    "    with torch.no_grad():\n",
    "        for inputs, targets in training_loader:\n",
    "\n",
    "            inputs, targets = inputs.to(device), targets.to(device)\n",
    "            inputs, targets = torch.autograd.Variable(\n",
    "                inputs), torch.autograd.Variable(targets)\n",
    "\n",
    "            outputs = model(inputs)\n",
    "\n",
    "            y_pred.append(outputs)\n",
    "\n",
    "    return torch.cat(y_pred)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot the loss value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_loss(path, loss_train, x_log=False):\n",
    "    \"\"\"\n",
    "    Plot loss.\n",
    "\n",
    "    Args:\n",
    "        path (str): path.\n",
    "        loss_train (list): list of training loss.\n",
    "        x_log (bool): whether to use log scale for x-axis.\n",
    "\n",
    "    Returns:\n",
    "        None.\n",
    "    \"\"\"\n",
    "\n",
    "    plt.figure()\n",
    "    ax = plt.gca()\n",
    "    y2 = np.asarray(loss_train)\n",
    "    plt.plot(y2, 'k-', label='Train')\n",
    "    plt.xlabel('epoch', fontsize=18)\n",
    "    ax.tick_params(labelsize=18)\n",
    "    plt.yscale('log')\n",
    "    if x_log == False:\n",
    "        fntmp = os.path.join(path, 'loss.jpg')\n",
    "\n",
    "    else:\n",
    "        plt.xscale('log')\n",
    "        fntmp = os.path.join(path, 'loss_log.jpg')\n",
    "    plt.tight_layout()\n",
    "    plt.savefig(fntmp, dpi=300)\n",
    "\n",
    "    plt.close()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Filtering\n",
    "For the original dataset $\\left\\{\\left(x_i, y_i\\right)\\right\\}_{i=0}^{n-1}$, such as MNIST or CIFAR10. $x_i$ is an image vector, $y_i$ is a one-hot vector. The low frequency part can be derived by\n",
    "$$\n",
    "y_i^{\\mathrm{low}, \\delta}=\\frac{1}{C_i} \\sum_{j=0}^{n-1} y_j G^\\delta\\left(x_i-x_j\\right),\n",
    "$$\n",
    "where $C_i=\\sum_{j=0}^{n-1} G^\\delta\\left(x_i-x_j\\right)$ is a normalization factor and\n",
    "$$\n",
    "G^\\delta\\left(x_i-x_j\\right)=\\exp \\left(-\\left|x_i-x_j\\right|^2 /(2 \\delta)\\right).\n",
    "$$\n",
    "The high frequency part can be derived by $\\boldsymbol{y}_i^{\\text {high, } \\delta} \\triangleq \\boldsymbol{y}_i-\\boldsymbol{y}_i^{\\text {low }, \\delta}$. We also compute $\\boldsymbol{h}_i^{\\text {low, } \\delta}$ and $\\boldsymbol{h}_i^{\\text {high, } \\delta}$ for each DNN output $\\boldsymbol{h}_i$.\n",
    "Then, we can examine\n",
    "$$\n",
    "\\begin{aligned}\n",
    "& e_{\\text {low }}=\\left(\\frac{\\sum_i\\left|\\boldsymbol{y}_i^{\\text {low }, \\delta}-\\boldsymbol{h}_i^{\\text {low }, \\delta}\\right|^2}{\\sum_i\\left|\\boldsymbol{y}_i^{\\text {low }, \\delta}\\right|^2}\\right)^{\\frac{1}{2}}, \\\\\n",
    "& e_{\\text {high }}=\\left(\\frac{\\sum_i\\left|\\boldsymbol{y}_i^{\\text {high }, \\delta}-\\boldsymbol{h}_i^{\\text {high }, \\delta}\\right|^2}{\\sum_i\\left|y_i^{\\text {high }, \\delta}\\right|^2}\\right)^{\\frac{1}{2}}.\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# def compute_distance(matrix):\n",
    "#     \"\"\"   \n",
    "#     A more intuitive way to calculate the pairwise Euclidean distance, but it will consume a lot of memory.\n",
    "#     \"\"\"\n",
    "#     diff = matrix[:, np.newaxis, :] - matrix[np.newaxis, :, :]\n",
    "#     return np.sum(diff**2, axis=2)\n",
    "\n",
    "\n",
    "\n",
    "def compute_distance_for_training_loader(training_loader):\n",
    "\n",
    "    \"\"\"\n",
    "    Computes the pairwise Euclidean distance between all pairs of flattened images in a training loader.\n",
    "\n",
    "    Args:\n",
    "        training_loader (DataLoader): A DataLoader object containing the training data.\n",
    "\n",
    "    Returns:\n",
    "        np.ndarray: A 2D NumPy array of shape [N, N], where N is the number of images in the training set.\n",
    "    \"\"\"\n",
    "\n",
    "    data_list = [data for data, _ in training_loader]\n",
    "\n",
    "    # Concatenate the list of data into a single tensor\n",
    "    data = torch.cat(data_list)\n",
    "    # Reshape data into [B, C*H*W]\n",
    "    flattened_images = data.view(data.shape[0], -1).numpy()\n",
    "\n",
    "    dist = -2 * np.dot(flattened_images, flattened_images.T) + np.sum(flattened_images**2, axis=1) + \\\n",
    "        np.sum(flattened_images**2, axis=1)[:, np.newaxis]\n",
    "    return dist\n",
    "\n",
    "\n",
    "def normal_kernel(dist, filter_dict):\n",
    "\n",
    "    \"\"\"\n",
    "    Computes the normalized Gaussian kernel for each filter in the filter dictionary.\n",
    "\n",
    "    Args:\n",
    "        dist (np.ndarray): A 2D NumPy array of pairwise distances between data points.\n",
    "        filter_dict (list): A list of filter values to use for each kernel.\n",
    "\n",
    "    Returns:\n",
    "        list: A list of 2D NumPy arrays, where each array is a normalized Gaussian kernel for a filter in the filter dictionary.\n",
    "    \"\"\"\n",
    "\n",
    "    kernel_dict = []\n",
    "    for filter in filter_dict:\n",
    "        kernel = np.exp(-dist / 2 / filter)\n",
    "        mean = np.sum(kernel, axis=1, keepdims=True)\n",
    "        kernel_dict.append(kernel/mean)\n",
    "    return kernel_dict\n",
    "\n",
    "\n",
    "def gauss_filiter(f_orig, kernel):\n",
    "\n",
    "    \"\"\"\n",
    "    Applies a Gaussian filter to an image output.\n",
    "\n",
    "    Args:\n",
    "        f_orig (np.ndarray): A 2D NumPy array representing the model output.\n",
    "        kernel (np.ndarray): A 2D NumPy array representing the Gaussian kernel.\n",
    "\n",
    "    Returns:\n",
    "        np.ndarray: A 2D NumPy array representing the filtered output.\n",
    "    \"\"\"\n",
    "\n",
    "    return np.matmul(kernel, f_orig)\n",
    "\n",
    "\n",
    "def get_freq_low_high(yy, kernel_dict):\n",
    "\n",
    "    \"\"\"\n",
    "    Computes the low and high frequency components of the model output using a set of Gaussian filters.\n",
    "\n",
    "    Args:\n",
    "        yy (np.ndarray): NumPy array representing the model output.\n",
    "        kernel_dict (list): A list of 2D NumPy arrays representing the Gaussian kernels to use for filtering.\n",
    "\n",
    "    Returns:\n",
    "        tuple: A tuple of two lists, where the first list contains the low frequency components of\n",
    "                the model output and the second list contains the high frequency components of the model output.\n",
    "    \"\"\"\n",
    "    f_low = []\n",
    "    f_high = []\n",
    "    for filter in range(len(kernel_dict)):\n",
    "        kernel = kernel_dict[filter]\n",
    "        f_new_norm = gauss_filiter(yy, kernel)\n",
    "        f_low.append(f_new_norm)\n",
    "        f_high_tmp = yy - f_new_norm\n",
    "        f_high.append(f_high_tmp)\n",
    "\n",
    "    return f_low, f_high \n",
    "\n",
    "def get_target_freq_distr(train_labels, dist, filter_start, filter_end, filter_num):\n",
    "\n",
    "    \"\"\"\n",
    "    Computes the target frequency distribution of a set of training labels using a set of Gaussian filters.\n",
    "\n",
    "    Args:\n",
    "        train_labels (np.ndarray): NumPy array representing the training labels.\n",
    "        dist (np.ndarray): A 2D NumPy array of pairwise Euclidean distance between all pairs of flattened images in a training loader.\n",
    "        filter_start (float): The starting value of the filter range.\n",
    "        filter_end (float): The ending value of the filter range.\n",
    "        filter_num (int): The number of filters to use in the filter range.\n",
    "\n",
    "    Returns:\n",
    "        tuple: A tuple of four elements, where the first element is a 1D NumPy array of filter values, \n",
    "                the second element is a list of 2D NumPy arrays representing the Gaussian kernels used for filtering, \n",
    "                the third element is a list of 1D NumPy arrays representing the low frequency components of the training labels, \n",
    "                and the fourth element is a list of 1D NumPy arrays representing the high frequency components of the training labels.\n",
    "    \"\"\"\n",
    "\n",
    "    filter_dict = np.linspace(\n",
    "        filter_start, filter_end, num=filter_num)\n",
    "\n",
    "    kernel_dict = normal_kernel(dist, filter_dict)\n",
    "    f_low, f_high = get_freq_low_high(train_labels, kernel_dict)\n",
    "\n",
    "    return filter_dict, kernel_dict, f_low, f_high\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Examination. \n",
    "\n",
    "Plot the relative error $e_{\\text {low }}$ and $e_{\\text {high }}$ at each training epoch."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_diff_distr(filter, lowdiff, highdiff, args):\n",
    "\n",
    "    \"\"\"\n",
    "    Plots the difference between the low and high frequency components of the predicted labels and the targets.\n",
    "\n",
    "    Args:\n",
    "        filter (float): The filter value used for filtering.\n",
    "        lowdiff (list): A list of relative distances between the low frequency components of the predicted labels and targets.\n",
    "        highdiff (list): A list of relative distances between the high frequency components of the predicted labels and targets.\n",
    "        args (argparse.Namespace): An argparse Namespace object containing the path to save the plot.\n",
    "\n",
    "    Returns:\n",
    "        None\n",
    "    \"\"\"\n",
    "\n",
    "    plt.figure(figsize=(10, 4))\n",
    "    plt.title('freq with filter {:.02f}'.format(filter))\n",
    "    plt.subplot(121)\n",
    "    plt.plot(lowdiff, 'r-', label='low_{:.02f}'.format(filter))\n",
    "    plt.plot(highdiff, 'b-', label='high_{:0.2f}'.format(filter))\n",
    "    plt.legend()\n",
    "    plt.xlabel('epoch')\n",
    "    plt.ylabel('freq')\n",
    "    plt.subplot(122)\n",
    "    tmp = np.stack([lowdiff, highdiff])\n",
    "    plt.pcolor(tmp, cmap='RdBu', vmin=0.1, vmax=1)\n",
    "    plt.colorbar()\n",
    "    plt.yticks([0.6, 1.6], ('low freq', 'high freq'), rotation='vertical')\n",
    "    plt.xlabel('epoch')\n",
    "    plt.savefig(args.path + '/hot_{:0.2f}.png'.format(filter))\n",
    "    plt.close()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Compute the high and low frequency distribution of targets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "dist = compute_distance_for_training_loader(train_loader)\n",
    "\n",
    "target_list = [target for data, target in train_loader]\n",
    "\n",
    "targets = torch.cat(target_list)\n",
    "\n",
    "\n",
    "train_labels = F.one_hot(targets, num_classes=10).detach().cpu().numpy()\n",
    "\n",
    "filter_dict, kernel_dict, f_low, f_high=get_target_freq_distr(train_labels, dist, args.start_filter, args.end_filter, args.num_filter)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Main"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] loss: 2.242450 acc: 17.92 valloss: 2.159925 valacc: 21.31 time: 1.59 s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\15853\\AppData\\Local\\Temp\\ipykernel_28172\\1689078004.py:25: UserWarning: Data has no positive values, and therefore cannot be log-scaled.\n",
      "  plt.xscale('log')\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2] loss: 2.052028 acc: 27.12 valloss: 1.996363 valacc: 25.72 time: 3.47 s\n",
      "[3] loss: 1.936158 acc: 30.56 valloss: 1.931272 valacc: 29.31 time: 5.42 s\n",
      "[4] loss: 1.868892 acc: 33.26 valloss: 1.878936 valacc: 31.99 time: 7.29 s\n",
      "[5] loss: 1.809480 acc: 35.92 valloss: 1.838458 valacc: 33.74 time: 9.25 s\n",
      "[6] loss: 1.755355 acc: 38.40 valloss: 1.805159 valacc: 35.09 time: 11.00 s\n",
      "[7] loss: 1.705256 acc: 40.20 valloss: 1.773306 valacc: 36.25 time: 12.95 s\n",
      "[8] loss: 1.658944 acc: 41.72 valloss: 1.744390 valacc: 37.58 time: 14.75 s\n",
      "[9] loss: 1.614242 acc: 43.70 valloss: 1.715700 valacc: 38.29 time: 16.56 s\n",
      "[10] loss: 1.569963 acc: 45.12 valloss: 1.689183 valacc: 39.37 time: 18.57 s\n",
      "[11] loss: 1.525250 acc: 47.24 valloss: 1.661363 valacc: 40.43 time: 20.47 s\n",
      "[12] loss: 1.479460 acc: 48.86 valloss: 1.635603 valacc: 41.47 time: 22.40 s\n",
      "[13] loss: 1.432439 acc: 50.48 valloss: 1.607664 valacc: 42.41 time: 24.40 s\n",
      "[14] loss: 1.384860 acc: 52.32 valloss: 1.580998 valacc: 43.48 time: 26.26 s\n",
      "[15] loss: 1.338627 acc: 54.18 valloss: 1.557561 valacc: 44.29 time: 28.03 s\n",
      "[16] loss: 1.291658 acc: 55.70 valloss: 1.534693 valacc: 45.24 time: 29.96 s\n",
      "[17] loss: 1.245911 acc: 57.54 valloss: 1.520419 valacc: 45.90 time: 31.68 s\n",
      "[18] loss: 1.200853 acc: 59.52 valloss: 1.505639 valacc: 46.64 time: 33.36 s\n",
      "[19] loss: 1.156061 acc: 61.20 valloss: 1.496528 valacc: 47.12 time: 35.07 s\n",
      "[20] loss: 1.111681 acc: 62.90 valloss: 1.488500 valacc: 47.57 time: 37.01 s\n",
      "[21] loss: 1.065338 acc: 64.42 valloss: 1.483422 valacc: 47.87 time: 38.81 s\n",
      "[22] loss: 1.019369 acc: 65.92 valloss: 1.480754 valacc: 48.08 time: 40.57 s\n",
      "[23] loss: 0.971426 acc: 67.84 valloss: 1.481229 valacc: 48.14 time: 42.35 s\n",
      "[24] loss: 0.922365 acc: 69.62 valloss: 1.489264 valacc: 48.27 time: 44.32 s\n",
      "[25] loss: 0.872228 acc: 71.34 valloss: 1.498970 valacc: 48.43 time: 45.96 s\n",
      "[26] loss: 0.821267 acc: 73.22 valloss: 1.512675 valacc: 48.58 time: 47.60 s\n",
      "[27] loss: 0.768954 acc: 75.58 valloss: 1.531128 valacc: 48.62 time: 49.28 s\n",
      "[28] loss: 0.715684 acc: 77.66 valloss: 1.555631 valacc: 48.70 time: 51.00 s\n",
      "[29] loss: 0.662141 acc: 79.74 valloss: 1.584454 valacc: 48.80 time: 52.94 s\n",
      "[30] loss: 0.608483 acc: 82.34 valloss: 1.618428 valacc: 48.76 time: 54.66 s\n",
      "[31] loss: 0.554494 acc: 84.28 valloss: 1.661999 valacc: 48.54 time: 56.44 s\n",
      "[32] loss: 0.502590 acc: 86.48 valloss: 1.701143 valacc: 48.47 time: 58.19 s\n",
      "[33] loss: 0.452515 acc: 88.50 valloss: 1.749106 valacc: 48.44 time: 59.98 s\n",
      "[34] loss: 0.404588 acc: 90.10 valloss: 1.798949 valacc: 48.31 time: 61.79 s\n",
      "[35] loss: 0.359553 acc: 91.70 valloss: 1.852193 valacc: 48.53 time: 63.88 s\n",
      "[36] loss: 0.317202 acc: 93.42 valloss: 1.911344 valacc: 48.31 time: 65.67 s\n",
      "[37] loss: 0.278849 acc: 94.48 valloss: 1.969513 valacc: 48.16 time: 67.45 s\n",
      "[38] loss: 0.244016 acc: 95.48 valloss: 2.031964 valacc: 48.34 time: 69.26 s\n",
      "[39] loss: 0.213388 acc: 96.64 valloss: 2.098185 valacc: 48.21 time: 70.96 s\n",
      "[40] loss: 0.186528 acc: 97.28 valloss: 2.159169 valacc: 47.95 time: 72.57 s\n",
      "[41] loss: 0.164689 acc: 97.78 valloss: 2.217817 valacc: 48.00 time: 74.16 s\n",
      "[42] loss: 0.145779 acc: 98.18 valloss: 2.271468 valacc: 48.20 time: 76.13 s\n",
      "[43] loss: 0.128995 acc: 98.40 valloss: 2.324845 valacc: 48.33 time: 77.79 s\n",
      "[44] loss: 0.115003 acc: 99.00 valloss: 2.373457 valacc: 48.37 time: 79.39 s\n",
      "[45] loss: 0.102952 acc: 99.28 valloss: 2.440753 valacc: 48.20 time: 81.07 s\n",
      "[46] loss: 0.093445 acc: 99.24 valloss: 2.501447 valacc: 48.08 time: 82.74 s\n",
      "[47] loss: 0.085656 acc: 99.38 valloss: 2.549903 valacc: 48.02 time: 84.49 s\n",
      "[48] loss: 0.078228 acc: 99.40 valloss: 2.638650 valacc: 47.89 time: 86.26 s\n",
      "[49] loss: 0.071335 acc: 99.52 valloss: 2.713143 valacc: 47.58 time: 88.00 s\n",
      "[50] loss: 0.063769 acc: 99.68 valloss: 2.674871 valacc: 48.04 time: 89.78 s\n",
      "[51] loss: 0.057586 acc: 99.70 valloss: 2.652137 valacc: 48.92 time: 91.93 s\n",
      "[52] loss: 0.052165 acc: 99.72 valloss: 2.637785 valacc: 49.28 time: 93.67 s\n",
      "[53] loss: 0.047869 acc: 99.86 valloss: 2.668156 valacc: 49.44 time: 95.42 s\n",
      "[54] loss: 0.044775 acc: 99.76 valloss: 2.728125 valacc: 49.44 time: 97.25 s\n",
      "[55] loss: 0.042492 acc: 99.78 valloss: 2.787550 valacc: 49.23 time: 99.14 s\n",
      "[56] loss: 0.039660 acc: 99.86 valloss: 2.837990 valacc: 49.26 time: 100.89 s\n",
      "[57] loss: 0.036365 acc: 99.82 valloss: 2.833091 valacc: 49.40 time: 102.63 s\n",
      "[58] loss: 0.035091 acc: 99.76 valloss: 2.833712 valacc: 49.42 time: 104.33 s\n",
      "[59] loss: 0.030627 acc: 99.76 valloss: 2.800908 valacc: 49.74 time: 106.04 s\n",
      "[60] loss: 0.025465 acc: 99.88 valloss: 2.778563 valacc: 49.93 time: 107.74 s\n",
      "[61] loss: 0.021253 acc: 99.92 valloss: 2.796755 valacc: 49.88 time: 109.91 s\n",
      "[62] loss: 0.019122 acc: 99.96 valloss: 2.821101 valacc: 49.81 time: 111.59 s\n",
      "[63] loss: 0.017305 acc: 99.96 valloss: 2.844254 valacc: 49.93 time: 113.30 s\n",
      "[64] loss: 0.015662 acc: 99.98 valloss: 2.856637 valacc: 50.12 time: 114.95 s\n",
      "[65] loss: 0.014269 acc: 100.00 valloss: 2.871623 valacc: 50.09 time: 116.63 s\n",
      "[66] loss: 0.013057 acc: 100.00 valloss: 2.897642 valacc: 50.30 time: 118.32 s\n",
      "[67] loss: 0.012155 acc: 100.00 valloss: 2.919202 valacc: 50.25 time: 119.95 s\n",
      "[68] loss: 0.011309 acc: 100.00 valloss: 2.939320 valacc: 50.32 time: 121.65 s\n",
      "[69] loss: 0.010608 acc: 100.00 valloss: 2.956045 valacc: 50.27 time: 123.36 s\n",
      "[70] loss: 0.010038 acc: 100.00 valloss: 2.968906 valacc: 50.31 time: 125.09 s\n",
      "[71] loss: 0.009527 acc: 100.00 valloss: 2.981077 valacc: 50.39 time: 126.86 s\n",
      "[72] loss: 0.009095 acc: 100.00 valloss: 2.989969 valacc: 50.40 time: 129.15 s\n",
      "[73] loss: 0.008691 acc: 100.00 valloss: 2.998950 valacc: 50.36 time: 130.92 s\n",
      "[74] loss: 0.008281 acc: 99.98 valloss: 3.007993 valacc: 50.37 time: 132.66 s\n",
      "[75] loss: 0.007778 acc: 100.00 valloss: 3.019728 valacc: 50.45 time: 134.34 s\n",
      "[76] loss: 0.007330 acc: 100.00 valloss: 3.033074 valacc: 50.38 time: 136.07 s\n",
      "[77] loss: 0.006937 acc: 100.00 valloss: 3.042401 valacc: 50.36 time: 137.80 s\n",
      "[78] loss: 0.006634 acc: 100.00 valloss: 3.050151 valacc: 50.33 time: 139.55 s\n",
      "[79] loss: 0.006343 acc: 100.00 valloss: 3.054113 valacc: 50.42 time: 141.30 s\n",
      "[80] loss: 0.006068 acc: 100.00 valloss: 3.057931 valacc: 50.40 time: 143.00 s\n",
      "[81] loss: 0.005805 acc: 100.00 valloss: 3.062328 valacc: 50.49 time: 144.71 s\n",
      "[82] loss: 0.005571 acc: 100.00 valloss: 3.069287 valacc: 50.53 time: 146.44 s\n",
      "[83] loss: 0.005358 acc: 100.00 valloss: 3.077592 valacc: 50.52 time: 148.19 s\n",
      "[84] loss: 0.005166 acc: 100.00 valloss: 3.085815 valacc: 50.65 time: 150.62 s\n",
      "[85] loss: 0.004979 acc: 100.00 valloss: 3.093081 valacc: 50.63 time: 152.38 s\n",
      "[86] loss: 0.004793 acc: 100.00 valloss: 3.100326 valacc: 50.64 time: 154.14 s\n",
      "[87] loss: 0.004622 acc: 100.00 valloss: 3.106754 valacc: 50.65 time: 155.90 s\n",
      "[88] loss: 0.004460 acc: 100.00 valloss: 3.111502 valacc: 50.65 time: 157.68 s\n",
      "[89] loss: 0.004300 acc: 100.00 valloss: 3.115537 valacc: 50.63 time: 159.46 s\n",
      "[90] loss: 0.004148 acc: 100.00 valloss: 3.119317 valacc: 50.75 time: 161.24 s\n",
      "[91] loss: 0.003991 acc: 100.00 valloss: 3.123444 valacc: 50.88 time: 162.99 s\n",
      "[92] loss: 0.003844 acc: 100.00 valloss: 3.128710 valacc: 50.91 time: 164.75 s\n",
      "[93] loss: 0.003700 acc: 100.00 valloss: 3.135732 valacc: 50.70 time: 166.49 s\n",
      "[94] loss: 0.003561 acc: 100.00 valloss: 3.144808 valacc: 50.75 time: 168.28 s\n",
      "[95] loss: 0.003429 acc: 100.00 valloss: 3.154502 valacc: 50.77 time: 170.06 s\n",
      "[96] loss: 0.003311 acc: 100.00 valloss: 3.164342 valacc: 50.64 time: 172.80 s\n",
      "[97] loss: 0.003198 acc: 100.00 valloss: 3.174051 valacc: 50.61 time: 174.58 s\n",
      "[98] loss: 0.003095 acc: 100.00 valloss: 3.183002 valacc: 50.63 time: 176.35 s\n",
      "[99] loss: 0.002997 acc: 100.00 valloss: 3.189540 valacc: 50.64 time: 178.14 s\n",
      "[100] loss: 0.002911 acc: 100.00 valloss: 3.195873 valacc: 50.61 time: 179.90 s\n",
      "[101] loss: 0.002830 acc: 100.00 valloss: 3.200736 valacc: 50.69 time: 181.70 s\n"
     ]
    }
   ],
   "source": [
    "\n",
    "loss_fn = nn.NLLLoss()\n",
    "\n",
    "if args.optimizer == 'sgd':\n",
    "    optimizer = torch.optim.SGD(model.parameters(), lr=args.lr)\n",
    "elif args.optimizer == 'nesterov':\n",
    "    optimizer = torch.optim.SGD(\n",
    "        model.parameters(), lr=args.lr, momentum=0.9, nesterov=True)\n",
    "else:\n",
    "    optimizer = torch.optim.Adam(model.parameters(), lr=args.lr)\n",
    "\n",
    "lowdiff = [[] for _ in range(len(filter_dict))]\n",
    "highdiff = [[] for _ in range(len(filter_dict))]\n",
    "\n",
    "t0 = time.time()\n",
    "\n",
    "args.loss_training_lst = []\n",
    "\n",
    "for epoch in range(args.epochs+1):\n",
    "\n",
    "    model.train()\n",
    "    loss, acc = train_one_step(\n",
    "        model, optimizer, loss_fn, train_loader, args)\n",
    "    loss_test, acc_test = test(\n",
    "        model, loss_fn, test_loader, args)\n",
    "    y_pred=val(model, train_loader, args)\n",
    "    f_train_low, f_train_high=get_freq_low_high(y_pred.detach().cpu().numpy(), kernel_dict)\n",
    "\n",
    "    for i in range(len(filter_dict)):\n",
    "        lowdiff[i].append(np.linalg.norm(\n",
    "            f_train_low[i] - f_low[i])/np.linalg.norm(f_low[i]))\n",
    "        highdiff[i].append(np.linalg.norm(\n",
    "            f_train_high[i] - f_high[i])/np.linalg.norm(f_high[i]))\n",
    "\n",
    "    args.loss_training_lst.append(loss)\n",
    "\n",
    "    if epoch % args.plot_epoch == 0:\n",
    "          print(\"[%d] loss: %.6f acc: %.2f valloss: %.6f valacc: %.2f time: %.2f s\" %\n",
    "                (epoch + 1, loss, acc, loss_test, acc_test, (time.time()-t0)))\n",
    "\n",
    "    if (epoch+1) % (args.plot_epoch) == 0:\n",
    "          plot_loss(path=args.path,\n",
    "                    loss_train=args.loss_training_lst, x_log=True)\n",
    "          plot_loss(path=args.path,\n",
    "                    loss_train=args.loss_training_lst, x_log=False)\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot the frequency difference distribution between the predicted labels and the targets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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     ]
    }
   ],
   "source": [
    "\n",
    "for filter_index, filter in enumerate(filter_dict):\n",
    "\n",
    "    lowdiff_ind, highdiff_ind = lowdiff[filter_index], highdiff[filter_index]\n",
    "\n",
    "    plot_diff_distr(filter, lowdiff_ind, highdiff_ind, args)\n"
   ]
  }
 ],
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