Invariant_groups_Dittus.ipynb

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  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyN6WMu1BAnvoxaQLPimX9um",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/giotre/superconductors/blob/main/Invariant_groups_Dittus.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Feature grouping: invariant groups\n",
        "\n",
        "This notebook demonstrates how to build, train, and evaluate a deep learning model using TensorFlow and Keras. Additionally, we perform a feature grouping analysis to find invariant groups in the form $x_i^{\\alpha} x_j^{\\beta}$. As case study, we consider the popular Dittus-Boelter equation.\n",
        "\n",
        "## Setup\n",
        "\n",
        "We will start by importing the necessary libraries and setting up our environment.\n",
        "\n",
        "First, we install tensorflow in the version 2.15."
      ],
      "metadata": {
        "id": "-bFGkXQ_KtGc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install tensorflow==2.15"
      ],
      "metadata": {
        "id": "gRYvXUBlfVXK"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Second, we import all the necessary libraries."
      ],
      "metadata": {
        "id": "F8Ze4vgRCBIs"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.metrics import r2_score, mean_absolute_error, mean_squared_error\n",
        "from tensorflow.keras.layers import Dense\n",
        "from tensorflow.keras.models import Sequential\n",
        "from tensorflow.keras.optimizers import Adam\n",
        "import tensorflow as tf\n",
        "from keras.callbacks import EarlyStopping\n",
        "import pandas as pd\n",
        "from scipy import linalg, signal\n",
        "import tqdm\n",
        "from scipy.optimize import broyden1, least_squares\n",
        "from itertools import combinations, product\n",
        "import pickle\n",
        "import warnings\n",
        "warnings.filterwarnings(\"ignore\", category=DeprecationWarning)\n"
      ],
      "metadata": {
        "id": "t9r3MUr9Ksau"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Dataset Creation and Preprocessing\n",
        "\n",
        "The dataset used in this notebook is assumed to be in an Excel file named 'Dittus.xlsx'.\n",
        "\n",
        "Such database is created starting from the physical properties of 16 real liquids at ambient temperature and pressure.\n",
        "\n",
        "Each line of the database contains a value of the flow speed $u$, a value of the pipe diameter $d$, a value of the kinematic viscosity $\\nu$, a value of the thermal diffusivity $\\kappa$, along with the resulting Nusselt number $\\mathrm{Nu}$ according to the Dittus-Boelter equation:\n",
        "\n",
        "\\begin{equation}\n",
        "\\mathrm{Nu} = 0.023 \\mathrm{Re}_D^{4/5}\\mathrm{Pr}^{2/5}\n",
        "\\end{equation}\n",
        "\n",
        "with $\\mathrm{Re}_D = (ud/\\nu)$ and $\\mathrm{Pr} = (\\nu/\\kappa)$, or equivalently\n",
        "\n",
        "\\begin{equation}\n",
        "\\mathrm{Nu} = 0.023\\frac{u^{0.8} d^{0.8}}{\\nu^{0.4}\\kappa^{0.4}}.\n",
        "\\end{equation}\n",
        "\n",
        "Each fluid accounts for 500 value combinations $u$, $d$, thus accounting for a total of 8,000 samples."
      ],
      "metadata": {
        "id": "QvWEXw_cLG8s"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Import the data\n",
        "Data = pd.read_excel('Dittus.xlsx', index_col=0)\n",
        "Nu = np.array(Data.iloc[:, 4]).astype('float64')\n"
      ],
      "metadata": {
        "id": "ykDCL-WrKzrw"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Emulating typical experimental measurements, we add noise on top of the correct target values, sampling 8,000 points $\\eta_i$ from a Gaussian distribution, with mean $\\mu=0$\n",
        " and standard deviation $\\sigma=0.1$; the target value of each entry $\\mathrm{Nu}_i$ is then multiplied by $(1+\\eta_i)$."
      ],
      "metadata": {
        "id": "NfcLHEUaupij"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "noise = np.random.normal(loc=0.0, scale=0.1, size=len(Nu))  # create Gaussian noise\n",
        "Nu = Nu * (1 + noise)  # add noise\n",
        "Data = Data.drop(columns=['Nu']) # drop the original non-noised column\n",
        "Data.insert(4, 'Nu', Nu) # replace it with the new noised column\n",
        "Data.to_excel('Dittus Noise.xlsx') # save it in the 'Dittus Noise.xlsx' file"
      ],
      "metadata": {
        "id": "x4XTxl56un3U"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "From now onwards, we  consider only the noisy dataset and split it into training (85%) and testing (15%) sets. We also normalize the data with a normalization layer, as it is beneficial for training stability in Deep Neural Networks.\n"
      ],
      "metadata": {
        "id": "0H09rWHXL857"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Data preprocessing\n",
        "train_df, test_df = train_test_split(Data, test_size=0.15, random_state=0)\n",
        "X_train = train_df.iloc[:, :-1]\n",
        "X_test = test_df[X_train.columns]\n",
        "y_train = train_df.iloc[:, -1]\n",
        "y_test = test_df.iloc[:, -1]\n",
        "\n",
        "# Normalize the data using the normalization layer in TensorFlow\n",
        "normalizer = tf.keras.layers.Normalization(axis=-1)\n",
        "normalizer.adapt(np.array(X_train))"
      ],
      "metadata": {
        "id": "Rw-VbvkPLyaj"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Building and Training the Model\n",
        "\n",
        "Let's define and compile our deep learning model using Keras and TensorFlow, choosing a validation set as the 15% of the training set (which is 85% of the total).\n",
        "\n",
        "The deep learning model we consider is a Deep Neural Network (DNN). Our DNN takes the inputs (4-dimensional arrays), normalizes them by means of the normalization layer defined beforehand, and passes to a bunch of hidden layers with a certain number of neurons.\n",
        "\n",
        "Within each neuron, all the inputs coming from the previous layer are multiplied by the network weights (to be learned), added to the network biases (to be learned), and passed to a non-linear activation function (we choose Rectified Linear Unit -- ReLU). Notice that the non-linearity is necessary, otherwise the entire architecture would result in a trivial linear model.\n",
        "\n",
        "The structure of a neuron within the first hidden layer (after normalization layer) is like in the following image (from https://www.quora.com/Should-ReLU-be-avoided-for-input-data-that-has-a-lot-of-negative-values-in-machine-learning-models-as-an-activation-function-given-that-ReLU-totally-disregards-negative-values-by-returning-a-zero-output):\n"
      ],
      "metadata": {
        "id": "g_OC9dkHMJvM"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![neuron.png](data:image/png;base64,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)"
      ],
      "metadata": {
        "id": "gPmjkO0C_9SN"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The output layer consists of a single neuron containing the predicted $\\mathrm{Nu}_i$ for the $i$th sample of the training set.\n",
        "\n",
        "The model is trained -- i.e., weights and biases are tuned -- to reduce as more as possible the difference between the known $\\mathrm{Nu}_i$ of the training set and the predicted $\\mathrm{Nu}_i$ from the model."
      ],
      "metadata": {
        "id": "9lEx23GwAfy3"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "We also set up early stopping, i.e., we stop training if there is no improvement in the validation loss after 50 iterations, called \"epochs\" (see `patience=50`), to prevent overfitting.\n",
        "\n",
        "We create a checkpoint to save the best model over the training epochs as, by default, the last -- and not the best -- epoch would be saved."
      ],
      "metadata": {
        "id": "RZCARKY0_oy3"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Define the model\n",
        "def build_and_compile_model(norm):\n",
        "    model = Sequential([\n",
        "        norm,                                  # normalization layer defined beforehand\n",
        "        Dense(128, activation='relu'),         # layer with 128 neurons and relu activation function\n",
        "        Dense(64, activation='relu'),\n",
        "        Dense(64, activation='relu'),\n",
        "        Dense(32, activation='relu'),\n",
        "        Dense(32, activation='relu'),\n",
        "        Dense(16, activation='relu'),\n",
        "        Dense(16, activation='relu'),\n",
        "        Dense(8, activation='relu'),\n",
        "        Dense(1, activation='linear')          # output layer\n",
        "    ])\n",
        "\n",
        "    model.compile(loss='mean_absolute_error', optimizer=Adam(0.001))\n",
        "    return model\n",
        "\n",
        "# Callbacks\n",
        "es = EarlyStopping(monitor='val_loss', mode='min', verbose=1, patience=50)\n",
        "\n",
        "checkpoint_filepath = './tmp/checkpoint_dittus.tf'\n",
        "model_checkpoint_callback = tf.keras.callbacks.ModelCheckpoint(\n",
        "    filepath=checkpoint_filepath,\n",
        "    save_weights_only=True,\n",
        "    monitor='val_loss',\n",
        "    mode='min',\n",
        "    save_best_only=True\n",
        ")\n",
        "\n",
        "model = build_and_compile_model(normalizer)\n",
        "\n",
        "# Train the model\n",
        "history = model.fit(\n",
        "    X_train,\n",
        "    y_train,\n",
        "    validation_split=0.15,\n",
        "    verbose=2,\n",
        "    epochs=500,\n",
        "    callbacks=[es, model_checkpoint_callback]\n",
        ")\n",
        "\n",
        "# Save the model history\n",
        "with open('DittusHistoryDict', 'wb') as file_pi:\n",
        "    pickle.dump(history.history, file_pi)\n"
      ],
      "metadata": {
        "id": "4OXAXhIZMI4a"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Evaluating the Model\n",
        "\n",
        "After training the model, we load the best weights and evaluate the model's performance on the test set.\n",
        "\n",
        "\n",
        "We compare the real value of the $\\mathrm{Nu}$ over testing set, with the corresponding values predicted by the trained model.\n",
        "We check those performances by means of three measures:\n",
        "* coefficient of determination $R^2$, defined as\n",
        "\\begin{equation}\n",
        "R^2(\\mathbf{y}, {\\mathbf{\\hat{y}}}) = 1-\\frac{\\sum_{i=1}^k(y_i-\\hat{y_i})^2}{\\sum_{i=1}^k(y_i-\\overline{y})^2}\n",
        "\\end{equation}\n",
        "where $\\mathbf{y}$ is the $k-$dimensional vector of real values, $\\mathbf{\\hat{y}}$ is the $k-$dimensional vector of predicted values, $\\overline{y}=k^{-1}∑_{i=1}^ky_i$ is the average over real values. $R^2= 1$ if the prediction is perfect (i.e., all the red dots are on the blue line, with $y_i=\\hat{y_i}, \\forall i\\in[1,\\dots, k]$).\n",
        "\n",
        "* Mean Absolute Error $\\mathrm{MAE}$, defined as\n",
        "\\begin{equation}\n",
        "\\mathrm{MAE}(\\mathbf{y}, {\\mathbf{\\hat{y}}}) = \\frac{1}{k}\\sum_{i=1}^k|y_i - \\hat{y_i}|\n",
        "\\end{equation}\n",
        "with the same meaning of the notation.\n",
        "\n",
        "* Root Mean Squared Error $\\mathrm{RMSE}$\n",
        "\\begin{equation}\n",
        "\\mathrm{RMSE}(\\mathbf{y}, {\\mathbf{\\hat{y}}}) = \\left(\\frac{1}{k}\\sum_{i=1}^k(y_i - \\hat{y_i})^2 \\right)^{1/2}\n",
        "\\end{equation}\n",
        "with the same meaning of the notation.\n",
        "\n",
        "In our case, $k$ is the length (i.e., the number of rows) of the testing set.\n",
        "\n",
        "\n",
        "The second figure represents the behaviour of the training loss (blue) and of the validation loss (orange) over the training epochs."
      ],
      "metadata": {
        "id": "B6g8SgIYMvT9"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Load saved weights (best model)\n",
        "model.load_weights(checkpoint_filepath)\n",
        "model.save('dittus_model.tf')\n",
        "\n",
        "# Load the model history\n",
        "with open('DittusHistoryDict', \"rb\") as file_pi:\n",
        "    history = pickle.load(file_pi)\n",
        "\n",
        "# Make predictions on the test set\n",
        "test_predictions = model.predict(X_test).flatten()\n",
        "test_labels = y_test.values\n",
        "\n",
        "# Calculate evaluation metrics\n",
        "r2 = r2_score(test_labels, test_predictions)\n",
        "mae = mean_absolute_error(test_labels, test_predictions)\n",
        "rmse = np.sqrt(mean_squared_error(test_labels, test_predictions))\n",
        "\n",
        "# Plot the results\n",
        "delta = max(test_labels) - min(test_labels)\n",
        "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(7.1, 3), dpi=190)\n",
        "ax1.scatter(test_labels, test_predictions, c=\"crimson\", alpha=0.2)\n",
        "p1 = max(max(test_predictions), max(test_labels))\n",
        "p2 = min(min(test_predictions), min(test_labels))\n",
        "ax1.plot([p1, p2], [p1, p2], \"b-\")\n",
        "ax1.annotate(\"$R^2$ = %0.3f\" % r2, xy=(0.02 * delta, 0.95 * delta), xytext=(0.02 * delta, 0.95 * delta))\n",
        "ax1.annotate(\"MAE = %0.2f\" % mae, xy=(0.02 * delta, 0.85 * delta), xytext=(0.02 * delta, 0.85 * delta))\n",
        "ax1.annotate(\"RMSE = %0.2f\" % rmse, xy=(0.02 * delta, 0.75 * delta), xytext=(0.02 * delta, 0.75 * delta))\n",
        "ax1.set_xlabel(r\"True $\\overline{\\rm{Nu}}$\")\n",
        "ax1.set_ylabel(r\"Predicted $\\overline{\\rm{Nu}}$\")\n",
        "\n",
        "ax2.plot(history['loss'], label='loss')\n",
        "ax2.plot(history['val_loss'], label='validation loss')\n",
        "ax2.set_yscale('log')\n",
        "\n",
        "ax2.set_xlabel('Epoch')\n",
        "ax2.set_ylabel('MAE')\n",
        "ax2.legend(frameon = False)\n",
        "plt.subplots_adjust(wspace=0.5)\n",
        "\n",
        "\n",
        "plt.savefig('dittus_model.svg', bbox_inches='tight')\n",
        "\n",
        "plt.show()\n"
      ],
      "metadata": {
        "id": "H5ogZZQoL0Cc"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Feature Grouping Analysis\n",
        "\n",
        "This section performs feature grouping analysis using combinations of two and three features.\n",
        "\n",
        "The analysis aims to detect invariant groups of features in the form $x_i^{\\alpha}x_j^{\\beta}$."
      ],
      "metadata": {
        "id": "2YLE28dTOgne"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Load the pre-trained model\n",
        "model = tf.keras.models.load_model('dittus_model.tf')  # load saved model\n",
        "\n",
        "# List of features\n",
        "other_columns = X_train.columns\n",
        "\n",
        "# Function to calculate orthogonal vector in the null space of B\n",
        "def univec(a, b, x0, index_1, index_2):\n",
        "    B = np.zeros((1, 2))\n",
        "    B[0][0] = a / x0[index_1]\n",
        "    B[0][1] = b / x0[index_2]  # build the matrix B in x0\n",
        "    un_norm = linalg.null_space(B)  # ortho-normal basis in the null-space of B\n",
        "\n",
        "    return un_norm\n",
        "\n",
        "# Function to select random points within feature ranges\n",
        "def delta(l, Data, i):\n",
        "    x_1_min = np.min(Data[l[i][0]])\n",
        "    x_1_max = np.max(Data[l[i][0]])\n",
        "    x_2_min = np.min(Data[l[i][1]])\n",
        "    x_2_max = np.max(Data[l[i][1]])\n",
        "    return(x_1_min, x_1_max, x_2_min, x_2_max)\n",
        "\n",
        "# Generate all possible combinations of two features\n",
        "l = list(combinations(list(other_columns), 2))\n",
        "\n",
        "N = 20  # number of points evaluated per iteration\n",
        "repeat = 3  # number of iterations\n",
        "A = np.zeros([len(l), N])\n",
        "B = np.zeros([len(l), N])\n",
        "\n",
        "# Analyze each pair of features\n",
        "for i in tqdm.tqdm(range(len(l))):\n",
        "    a = 0.5 * np.ones(N)  # initial guesses for first iteration\n",
        "    b = -0.5 * np.ones(N)\n",
        "\n",
        "    for j in range(repeat):\n",
        "        beta = np.array([np.mean(a), np.mean(b)])  # initial guess for successive iterations\n",
        "\n",
        "        a = np.ones(N)\n",
        "        b = np.ones(N)\n",
        "\n",
        "        for k in range(N):\n",
        "\n",
        "            # pick two random numbers\n",
        "            w1 = np.random.uniform(0, 1)\n",
        "            w2 = np.random.uniform(0, 1)\n",
        "\n",
        "            # compute the mean of each feature\n",
        "            tx = Data[other_columns].describe().loc['mean']\n",
        "\n",
        "            # compute the x_1_min, x_1_max, x_2_min, x_2_max for the i-th couple of features\n",
        "            delta_values = delta(l, Data, i)\n",
        "\n",
        "            index_1 = pd.DataFrame(tx, columns=other_columns).columns.get_loc(l[i][0])  # get index of the first feature\n",
        "            index_2 = pd.DataFrame(tx, columns=other_columns).columns.get_loc(l[i][1])  # get index of the second feature\n",
        "\n",
        "            def MAIN(beta):\n",
        "\n",
        "                # initial guess\n",
        "                a0 = beta[0]\n",
        "                b0 = beta[1]\n",
        "\n",
        "                tx = Data[other_columns].describe().loc['mean']  # set feature values to their average\n",
        "                r = delta_values[0] + w1 * (delta_values[1] - delta_values[0])  # pick the value of the first feature at random in the interval x1_min, x1_max\n",
        "                tx[l[i][0]] = r  # set the value of the x0 component corresponding to the first feature in the couple equal to r\n",
        "                s = delta_values[2] + w2 * (delta_values[3] - delta_values[2]) #do the same for the second feature\n",
        "                tx[l[i][1]] = s\n",
        "                x0 = tf.constant(tx)\n",
        "\n",
        "                with tf.GradientTape(persistent=True) as tape:\n",
        "                    tape.watch(x0)\n",
        "                    preds1 = model(x0)  # compute the DNN model in x0\n",
        "                dy_dx1 = tape.gradient(preds1, x0)[index_1]  # evaluate the partial derivative of the model in x0 with respect to the first feature\n",
        "\n",
        "                with tf.GradientTape(persistent=True) as tape:\n",
        "                    tape.watch(x0)\n",
        "                    preds2 = model(x0) # compute the DNN model in x0\n",
        "                dy_dx2 = tape.gradient(preds2, x0)[index_2] # evaluate the partial derivative of the model in x0 with respect to the second feature\n",
        "\n",
        "                grad1 = dy_dx1.numpy()  # convert from tensor to numpy array\n",
        "                grad2 = dy_dx2.numpy()  # convert from tensor to numpy array\n",
        "\n",
        "                der = np.array([grad1, grad2])  # create derivative vector which has to be parallel to the orthogonal vector un in x0\n",
        "                der = der / np.sqrt(der[0] ** 2 + der[1] ** 2)  # normalization\n",
        "\n",
        "                tx = Data[other_columns].describe().loc['mean']  # need to create x0 again, so set features to average\n",
        "                tx[l[i][0]] = r  # set the value of the x0 component corresponding to the first feature in the couple equal to r\n",
        "                tx[l[i][1]] = s  # set the value of the x0 component corresponding to the second feature in the couple equal to r\n",
        "                x0 = tf.constant(tx)  # create x0\n",
        "\n",
        "                un = univec(a0, b0, x0.numpy(), index_1, index_2)  # get un to check for the condition of invariance (components of the gradient aligned with un in x0)\n",
        "                DIFF = np.array([np.dot(der, un)[0], a0 ** 2 + b0 ** 2 - 1], dtype=float)  # evaluate the residual\n",
        "\n",
        "                return DIFF\n",
        "\n",
        "            # Optimize to find the best fit for a and b\n",
        "            x = least_squares(MAIN, beta, method='trf', ftol=2.3e-16, verbose=1, max_nfev=50)\n",
        "\n",
        "            '''\n",
        "            Notice that x is not a variable, but rather a scipy.optimize._optimize.OptimizeResult object (check it by running type(x)).\n",
        "            Its x-th attribute -- x.x -- is the 2-dimensional variable we are looking for, containing the optimal [alpha, beta].\n",
        "            '''\n",
        "            x.x = x.x / np.linalg.norm(x.x)\n",
        "\n",
        "            a[k] = x.x[0]  # save the results for each iteration\n",
        "            b[k] = x.x[1]\n",
        "\n",
        "    A[i] = a  # create matrix with the results\n",
        "    B[i] = b\n"
      ],
      "metadata": {
        "id": "J5zn_DziNXTS"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Create a dataframe to summarize mean and standard deviation of the results\n",
        "a_b = np.array([np.mean(A, axis=1), np.std(A, axis=1), np.mean(B, axis=1), np.std(B, axis=1)]).transpose()\n",
        "a_b_frame = pd.DataFrame(a_b, columns=['mean alpha', 'std alpha', 'mean beta', 'std beta'], index=l)\n",
        "a_b_frame"
      ],
      "metadata": {
        "id": "5VA2FbrkVXj5"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "For all the six possible couples, check\n",
        "\n",
        "* If the std of either $\\alpha$ or $\\beta$ is too high w.r.t. the mean. If so, the group is not found.\n",
        "\n",
        "* If the mean of either $\\alpha$ or $\\beta$ is too near to 0. If so, this kills the group.\n",
        "\n",
        "\n",
        "These are not our cases, where all groups are found. However, notice that those groups consist of normalized coefficients, and not of the real physical coefficients of the Dittus-Boelter equation."
      ],
      "metadata": {
        "id": "wZLjtm6o342Z"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Scatter plots for feature pairs\n",
        "for ind in range(len(A)):\n",
        "    plt.figure(figsize=(6, 3), dpi=300)\n",
        "    plt.scatter(np.arange(N), A[ind], label=r'$\\alpha$')\n",
        "    plt.scatter(np.arange(N), B[ind], label=r'$\\beta$')\n",
        "    plt.title(l[ind])\n",
        "    plt.legend(bbox_to_anchor=(1.05, 1.0), loc='upper left')\n",
        "    plt.ylim(-1, 1)\n",
        "    plt.show()"
      ],
      "metadata": {
        "id": "ow2lN5Eq3k08"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "Oooi7QOc49ml"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}