Adam vs BFGS (Multi-variate, Batch).ipynb

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    {
      "attachments": {},
      "cell_type": "markdown",
      "id": "32b92576",
      "metadata": {
        "id": "32b92576"
      },
      "source": [
        "## 1. Implement the Adam (Batch Version) algorithm to train a multivariable linear regression model."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "id": "x07psPjFKFPm",
      "metadata": {
        "id": "x07psPjFKFPm"
      },
      "outputs": [],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "from sklearn.metrics import r2_score\n",
        "%matplotlib inline"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "o5FTMQbCKt7v",
      "metadata": {
        "id": "o5FTMQbCKt7v"
      },
      "source": [
        "## Import Data"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "id": "QQANBgTLJrqK",
      "metadata": {
        "id": "QQANBgTLJrqK"
      },
      "outputs": [],
      "source": [
        "data2 = np.genfromtxt('/content/MultiVarLR.csv',delimiter=',')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "id": "aQe4dj-fKmbj",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aQe4dj-fKmbj",
        "outputId": "fb6fb720-b2bb-402a-c112-d0d414c64e07"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(25, 3)"
            ]
          },
          "execution_count": 3,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "X2 = data2[:, :3]\n",
        "X2.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "id": "kML8xtL0Kol_",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kML8xtL0Kol_",
        "outputId": "8cdcfbd5-3675-41a5-8782-97f1e8234311"
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      "outputs": [
        {
          "data": {
            "text/plain": [
              "(25,)"
            ]
          },
          "execution_count": 4,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "y2 = data2[:, -1]\n",
        "y2.shape"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "Rn87txyIKwDH",
      "metadata": {
        "id": "Rn87txyIKwDH"
      },
      "source": [
        "## Reshape Data"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "id": "phHFyPK0KqlN",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "phHFyPK0KqlN",
        "outputId": "0cd89c6e-a302-4c70-a1ef-881a2897bc9b"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(25, 1)"
            ]
          },
          "execution_count": 5,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "y2 = y2.reshape((-1, 1))\n",
        "y2.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "id": "mjSOCEqmKsT8",
      "metadata": {
        "id": "mjSOCEqmKsT8"
      },
      "outputs": [],
      "source": [
        "m = X2.shape[0]\n",
        "X2 = np.concatenate((np.ones((m, 1)), X2), axis=1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "id": "GzVWOA6WWUHF",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GzVWOA6WWUHF",
        "outputId": "1d6dbdbf-7b24-4e41-b101-d6807be0bcc4"
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      "outputs": [
        {
          "data": {
            "text/plain": [
              "(25, 4)"
            ]
          },
          "execution_count": 7,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "X2.shape"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "c_z80uCqK4Ic",
      "metadata": {
        "id": "c_z80uCqK4Ic"
      },
      "source": [
        "## Adam Function"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "id": "QMr-NB_OK25M",
      "metadata": {
        "id": "QMr-NB_OK25M"
      },
      "outputs": [],
      "source": [
        "def adam(X, y, alpha, epsilon, beta1, beta2, epochs):\n",
        "    cost_vals = []\n",
        "    thetas = []\n",
        "    h_s = []\n",
        "\n",
        "    # 1. Initialize the parameters with zeros\n",
        "    i = 0\n",
        "    prev_cost = 0\n",
        "    m, n = X.shape\n",
        "    theta = np.zeros((n, 1))\n",
        "    mt = np.zeros((n, 1))\n",
        "    vt = np.zeros((n, 1))\n",
        "    grad = np.ones((n, 1))\n",
        "    \n",
        "    while i < epochs and np.linalg.norm(grad, 2) > 0.001:            \n",
        "        if i > 0:\n",
        "            prev_cost = cost_vals[-1]\n",
        "\n",
        "        print(f\"****************** Epoch {i} ****************** \")\n",
        "        \n",
        "        # 2. Predict the output\n",
        "        h_x = np.dot(X, theta)\n",
        "        h_s.append(h_x)\n",
        "\n",
        "        # 3. Calculate the cost function\n",
        "        error = h_x - y\n",
        "        j = (1 / (2 * m)) * np.linalg.norm(error, 2)**2\n",
        "        print(f'Error Vector: \\n{error}')\n",
        "        print(f'\\nj = {j}')\n",
        "        cost_vals.append(j)\n",
        "\n",
        "        # 4. Calculate the gradient\n",
        "        grad = np.dot(X.T, error) / m\n",
        "        print(f\"Gradient Vector: \\n{grad}\")\n",
        "        print(f\"Gradient Vector Norm: {np.linalg.norm(grad, 2)}\")\n",
        "\n",
        "        # 5. Update the parameters\n",
        "        mt = beta1 * mt + (1 - beta1) * grad\n",
        "        mt_hat = mt/(1-beta1**(i+1))\n",
        "        vt = beta2 * vt + (1-beta2) * grad**2\n",
        "        vt_hat = vt/(1-beta2**(i+1))\n",
        "        theta = theta - (alpha/(np.sqrt(vt_hat) + epsilon)) * mt_hat\n",
        "        \n",
        "        print(f'theta_new : {theta}')\n",
        "        thetas.append(theta)\n",
        "        \n",
        "        # print(f'thetas : {thetas}')\n",
        "\n",
        "        # Cost Convergence check\n",
        "        if i > 1 and abs(prev_cost - cost_vals[-1]) < 0.001:\n",
        "            break\n",
        "\n",
        "        i += 1\n",
        "    \n",
        "    return thetas[-1], cost_vals, thetas, h_s"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 48,
      "id": "EdB-jSR6LhCo",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "EdB-jSR6LhCo",
        "outputId": "9a33b698-c408-4a9d-e9e5-c47797eb7fd0"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "\u001b[1;30;43mStreaming output truncated to the last 5000 lines.\u001b[0m\n",
            " [-7247.41111638]\n",
            " [-7286.7237182 ]\n",
            " [-7470.03087363]]\n",
            "Gradient Vector Norm: 12705.539725558521\n",
            "theta_new : [[0.30913297]\n",
            " [0.30913093]\n",
            " [0.30913026]\n",
            " [0.30914543]]\n",
            "****************** Epoch 32 ****************** \n",
            "Error Vector: \n",
            "[[ -81.20798136]\n",
            " [ -99.98770296]\n",
            " [ -96.2242722 ]\n",
            " [-104.8049896 ]\n",
            " [ -77.08153209]\n",
            " [ -53.08393728]\n",
            " [ -80.68099577]\n",
            " [ -64.30169317]\n",
            " [ -95.55209714]\n",
            " [ -90.42560776]\n",
            " [ -75.15409851]\n",
            " [ -76.08147343]\n",
            " [ -97.44208202]\n",
            " [ -79.97148663]\n",
            " [ -79.37184967]\n",
            " [-105.75113642]\n",
            " [ -78.37199598]\n",
            " [-101.07901363]\n",
            " [ -94.46085459]\n",
            " [ -85.11664508]\n",
            " [ -96.93384001]\n",
            " [ -95.24298273]\n",
            " [ -98.64348165]\n",
            " [ -77.58977951]\n",
            " [-103.89636802]]\n",
            "\n",
            "j = 3917.91158671125\n",
            "Gradient Vector: \n",
            "[[  -87.53831589]\n",
            " [-7063.08766135]\n",
            " [-7101.38549802]\n",
            " [-7280.37351113]]\n",
            "Gradient Vector Norm: 12382.583927507727\n",
            "theta_new : [[0.31859675]\n",
            " [0.31859459]\n",
            " [0.31859387]\n",
            " [0.31861001]]\n",
            "****************** Epoch 33 ****************** \n",
            "Error Vector: \n",
            "[[ -79.04073815]\n",
            " [ -97.38511525]\n",
            " [ -93.65954204]\n",
            " [-102.01312274]\n",
            " [ -75.09410234]\n",
            " [ -51.6170216 ]\n",
            " [ -78.58945967]\n",
            " [ -62.74960038]\n",
            " [ -93.11985761]\n",
            " [ -88.17317913]\n",
            " [ -73.13827518]\n",
            " [ -74.09403992]\n",
            " [ -94.79217821]\n",
            " [ -77.76639066]\n",
            " [ -77.27084893]\n",
            " [-103.11069135]\n",
            " [ -76.27100464]\n",
            " [ -98.57106256]\n",
            " [ -91.93398281]\n",
            " [ -82.85476359]\n",
            " [ -94.48267348]\n",
            " [ -92.80128061]\n",
            " [ -96.30588349]\n",
            " [ -75.40361284]\n",
            " [-101.19914214]]\n",
            "\n",
            "j = 3716.783972744642\n",
            "Gradient Vector: \n",
            "[[  -85.25750277]\n",
            " [-6879.01299385]\n",
            " [-6916.2974353 ]\n",
            " [-7090.97213469]]\n",
            "Gradient Vector Norm: 12060.064039623863\n",
            "theta_new : [[0.32804712]\n",
            " [0.32804482]\n",
            " [0.32804405]\n",
            " [0.32806122]]\n",
            "****************** Epoch 34 ****************** \n",
            "Error Vector: \n",
            "[[ -76.87656502]\n",
            " [ -94.78621418]\n",
            " [ -91.09844497]\n",
            " [ -99.22521062]\n",
            " [ -73.10948789]\n",
            " [ -50.15218369]\n",
            " [ -76.50088616]\n",
            " [ -61.19970595]\n",
            " [ -90.69106324]\n",
            " [ -85.92394072]\n",
            " [ -71.12530728]\n",
            " [ -72.1094215 ]\n",
            " [ -92.14602825]\n",
            " [ -75.56441855]\n",
            " [ -75.17282418]\n",
            " [-100.47398645]\n",
            " [ -74.17298976]\n",
            " [ -96.0666639 ]\n",
            " [ -89.41069063]\n",
            " [ -80.59608631]\n",
            " [ -92.03497896]\n",
            " [ -90.36303713]\n",
            " [ -93.97159652]\n",
            " [ -73.2205433 ]\n",
            " [ -98.50573701]]\n",
            "\n",
            "j = 3521.2377994334984\n",
            "Gradient Vector: \n",
            "[[  -82.97992049]\n",
            " [-6695.19907357]\n",
            " [-6731.47155555]\n",
            " [-6901.83905001]]\n",
            "Gradient Vector Norm: 11738.001017095632\n",
            "theta_new : [[0.33748341]\n",
            " [0.33748097]\n",
            " [0.33748015]\n",
            " [0.3374984 ]]\n",
            "****************** Epoch 35 ****************** \n",
            "Error Vector: \n",
            "[[-74.71561353]\n",
            " [-92.19118171]\n",
            " [-88.54116033]\n",
            " [-96.44144846]\n",
            " [-71.12782769]\n",
            " [-48.68952614]\n",
            " [-74.41542151]\n",
            " [-59.65211839]\n",
            " [-88.2658841 ]\n",
            " [-83.67805002]\n",
            " [-69.11533573]\n",
            " [-70.12775713]\n",
            " [-89.50381744]\n",
            " [-73.36572453]\n",
            " [-73.07792229]\n",
            " [-97.84120635]\n",
            " [-72.07809828]\n",
            " [-93.56599301]\n",
            " [-86.89115475]\n",
            " [-78.34077143]\n",
            " [-89.59092786]\n",
            " [-87.92842301]\n",
            " [-91.6407842 ]\n",
            " [-71.04072378]\n",
            " [-95.81634124]]\n",
            "\n",
            "j = 3331.2636801052945\n",
            "Gradient Vector: \n",
            "[[  -80.70572852]\n",
            " [-6511.65877178]\n",
            " [-6546.92080095]\n",
            " [-6712.98750075]]\n",
            "Gradient Vector Norm: 11416.417412388773\n",
            "theta_new : [[0.34690491]\n",
            " [0.34690232]\n",
            " [0.34690145]\n",
            " [0.34692084]]\n",
            "****************** Epoch 36 ****************** \n",
            "Error Vector: \n",
            "[[-72.5580469 ]\n",
            " [-89.60021385]\n",
            " [-85.98788128]\n",
            " [-93.66204651]\n",
            " [-69.14927142]\n",
            " [-47.22915938]\n",
            " [-72.3332232 ]\n",
            " [-58.10695456]\n",
            " [-85.84450334]\n",
            " [-81.43567662]\n",
            " [-67.10851236]\n",
            " [-68.14919647]\n",
            " [-86.86574536]\n",
            " [-71.17047468]\n",
            " [-70.9863015 ]\n",
            " [-95.21254988]\n",
            " [-69.98648845]\n",
            " [-91.06923874]\n",
            " [-84.3755655 ]\n",
            " [-76.08898928]\n",
            " [-87.15070475]\n",
            " [-85.49762214]\n",
            " [-89.31362257]\n",
            " [-68.86431894]\n",
            " [-93.13115796]]\n",
            "\n",
            "j = 3146.8517649962096\n",
            "Gradient Vector: \n",
            "[[  -78.43509863]\n",
            " [-6328.40595079]\n",
            " [-6362.65911014]\n",
            " [-6524.43175031]]\n",
            "Gradient Vector Norm: 11095.33751442397\n",
            "theta_new : [[0.35631086]\n",
            " [0.3563081 ]\n",
            " [0.35630718]\n",
            " [0.35632777]]\n",
            "****************** Epoch 37 ****************** \n",
            "Error Vector: \n",
            "[[-70.4040411 ]\n",
            " [-87.0135219 ]\n",
            " [-83.43881606]\n",
            " [-90.88723144]\n",
            " [-67.17398046]\n",
            " [-45.77120251]\n",
            " [-70.25446104]\n",
            " [-56.56434046]\n",
            " [-83.42711841]\n",
            " [-79.19700335]\n",
            " [-65.10500083]\n",
            " [-66.17390086]\n",
            " [-84.23202718]\n",
            " [-68.97884805]\n",
            " [-68.89813235]\n",
            " [-92.58823142]\n",
            " [-67.89833088]\n",
            " [-88.57660472]\n",
            " [-81.86412804]\n",
            " [-73.84092354]\n",
            " [-84.71450864]\n",
            " [-83.07083274]\n",
            " [-86.9903014 ]\n",
            " [-66.69150633]\n",
            " [-90.45040618]]\n",
            "\n",
            "j = 2967.9916935729457\n",
            "Gradient Vector: \n",
            "[[  -76.168216  ]\n",
            " [-6145.455556  ]\n",
            " [-6178.70151083]\n",
            " [-6336.18717648]]\n",
            "Gradient Vector Norm: 10774.78750989196\n",
            "theta_new : [[0.36570041]\n",
            " [0.36569748]\n",
            " [0.36569651]\n",
            " [0.36571836]]\n",
            "****************** Epoch 38 ****************** \n",
            "Error Vector: \n",
            "[[-68.25378611]\n",
            " [-84.43133399]\n",
            " [-80.89418947]\n",
            " [-88.11724797]\n",
            " [-65.20212899]\n",
            " [-44.3157841 ]\n",
            " [-68.17931834]\n",
            " [-55.02441212]\n",
            " [-81.01394249]\n",
            " [-76.9622276 ]\n",
            " [-63.1049778 ]\n",
            " [-64.20204449]\n",
            " [-81.60289517]\n",
            " [-66.79103796]\n",
            " [-66.813599  ]\n",
            " [-89.9684824 ]\n",
            " [-65.81380977]\n",
            " [-86.08831073]\n",
            " [-79.35706389]\n",
            " [-71.59677248]\n",
            " [-82.28255435]\n",
            " [-80.64826882]\n",
            " [-84.67102559]\n",
            " [-64.5224776 ]\n",
            " [-87.7743223 ]]\n",
            "\n",
            "j = 2794.6725449252112\n",
            "Gradient Vector: \n",
            "[[  -73.90528054]\n",
            " [-5962.82372177]\n",
            " [-5995.06422622]\n",
            " [-6148.27038041]]\n",
            "Gradient Vector Norm: 10454.795668714663\n",
            "theta_new : [[0.37507267]\n",
            " [0.37506956]\n",
            " [0.37506853]\n",
            " [0.37509173]]\n",
            "****************** Epoch 39 ****************** \n",
            "Error Vector: \n",
            "[[-66.10748734]\n",
            " [-81.85389674]\n",
            " [-78.35424459]\n",
            " [-85.35236067]\n",
            " [-63.23390538]\n",
            " [-42.86304313]\n",
            " [-66.1079933 ]\n",
            " [-53.48731658]\n",
            " [-78.60520606]\n",
            " [-74.73156278]\n",
            " [-61.10863433]\n",
            " [-62.23381568]\n",
            " [-78.9786005 ]\n",
            " [-64.60725342]\n",
            " [-64.73290054]\n",
            " [-87.35355303]\n",
            " [-63.73312426]\n",
            " [-83.60459444]\n",
            " [-76.85461254]\n",
            " [-69.35675048]\n",
            " [-79.85507418]\n",
            " [-78.23016177]\n",
            " [-82.35601665]\n",
            " [-62.35743997]\n",
            " [-85.10316196]]\n",
            "\n",
            "j = 2626.8827850611337\n",
            "Gradient Vector: \n",
            "[[  -71.64650841]\n",
            " [-5780.52789255]\n",
            " [-5811.76479684]\n",
            " [-5960.69931126]]\n",
            "Gradient Vector Norm: 10135.39255636844\n",
            "theta_new : [[0.38442667]\n",
            " [0.38442337]\n",
            " [0.38442228]\n",
            " [0.3844469 ]]\n",
            "****************** Epoch 40 ****************** \n",
            "Error Vector: \n",
            "[[-63.96536722]\n",
            " [-79.28147729]\n",
            " [-75.81924467]\n",
            " [-82.59285609]\n",
            " [-61.26951361]\n",
            " [-41.41313016]\n",
            " [-64.04070058]\n",
            " [-51.95321313]\n",
            " [-76.20115874]\n",
            " [-72.50524003]\n",
            " [-59.1161773 ]\n",
            " [-60.26941841]\n",
            " [-76.35941516]\n",
            " [-62.42772078]\n",
            " [-62.65625259]\n",
            " [-84.74371431]\n",
            " [-61.65649004]\n",
            " [-81.12571324]\n",
            " [-74.35703337]\n",
            " [-67.12108972]\n",
            " [-77.43231967]\n",
            " [-75.81676218]\n",
            " [-80.04551451]\n",
            " [-60.19661787]\n",
            " [-82.43720198]]\n",
            "\n",
            "j = 2464.6102100070975\n",
            "Gradient Vector: \n",
            "[[  -69.39213371]\n",
            " [-5598.5869614 ]\n",
            " [-5628.82221979]\n",
            " [-5773.4934087 ]]\n",
            "Gradient Vector Norm: 9816.61127654643\n",
            "theta_new : [[0.39376136]\n",
            " [0.39375786]\n",
            " [0.39375669]\n",
            " [0.39378283]]\n",
            "****************** Epoch 41 ****************** \n",
            "Error Vector: \n",
            "[[-61.82766716]\n",
            " [-76.71436548]\n",
            " [-73.28947533]\n",
            " [-79.83904515]\n",
            " [-59.30917502]\n",
            " [-39.96620853]\n",
            " [-61.97767309]\n",
            " [-50.42227459]\n",
            " [-73.80207137]\n",
            " [-70.28351014]\n",
            " [-57.12783119]\n",
            " [-58.30907397]\n",
            " [-73.74563429]\n",
            " [-60.25268567]\n",
            " [-60.5838891 ]\n",
            " [-82.1392603 ]\n",
            " [-59.58414115]\n",
            " [-78.6519464 ]\n",
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            " [-75.01456381]\n",
            " [-73.40834198]\n",
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            "****************** Epoch 42 ****************** \n",
            "Error Vector: \n",
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            "Gradient Vector Norm: 9181.061024277395\n",
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            " [0.41236415]\n",
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            "****************** Epoch 43 ****************** \n",
            "Error Vector: \n",
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            "****************** Epoch 44 ****************** \n",
            "Error Vector: \n",
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            " [-54.3951657 ]\n",
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            "Gradient Vector: \n",
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            "theta_new : [[0.43088238]\n",
            " [0.43087793]\n",
            " [0.43087644]\n",
            " [0.4309097 ]]\n",
            "****************** Epoch 45 ****************** \n",
            "Error Vector: \n",
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            "\n",
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            "Gradient Vector: \n",
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            "****************** Epoch 46 ****************** \n",
            "Error Vector: \n",
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            "Gradient Vector: \n",
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            " [0.44928661]\n",
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            "****************** Epoch 47 ****************** \n",
            "Error Vector: \n",
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            "Gradient Vector: \n",
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            " [0.45844691]\n",
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            "****************** Epoch 48 ****************** \n",
            "Error Vector: \n",
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            "\n",
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            "Gradient Vector: \n",
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            "Gradient Vector Norm: 7293.8195125553075\n",
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            " [0.46757496]\n",
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            "****************** Epoch 49 ****************** \n",
            "Error Vector: \n",
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            " [-52.7136987 ]\n",
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            " [-55.8945735 ]\n",
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            "\n",
            "j = 1249.991710276065\n",
            "Gradient Vector: \n",
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            "Gradient Vector Norm: 6982.71936134477\n",
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            "****************** Epoch 50 ****************** \n",
            "Error Vector: \n",
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            "\n",
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            "Gradient Vector: \n",
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            "Gradient Vector Norm: 6672.799152341352\n",
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            " [0.48572426]\n",
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            "****************** Epoch 51 ****************** \n",
            "Error Vector: \n",
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            "\n",
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            "Gradient Vector: \n",
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            "Gradient Vector Norm: 6364.151650095857\n",
            "theta_new : [[0.49474669]\n",
            " [0.49473972]\n",
            " [0.4947374 ]\n",
            " [0.49478942]]\n",
            "****************** Epoch 52 ****************** \n",
            "Error Vector: \n",
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            "\n",
            "j = 941.9835930836796\n",
            "Gradient Vector: \n",
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            "Gradient Vector Norm: 6056.8805614392895\n",
            "theta_new : [[0.50371875]\n",
            " [0.50371128]\n",
            " [0.5037088 ]\n",
            " [0.50376451]]\n",
            "****************** Epoch 53 ****************** \n",
            "Error Vector: \n",
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            "\n",
            "j = 849.8657173340066\n",
            "Gradient Vector: \n",
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            "Gradient Vector Norm: 5751.102263577733\n",
            "theta_new : [[0.5126431 ]\n",
            " [0.51263509]\n",
            " [0.51263242]\n",
            " [0.51269219]]\n",
            "****************** Epoch 54 ****************** \n",
            "Error Vector: \n",
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            " [-32.5520612 ]\n",
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            "\n",
            "j = 762.9701788570928\n",
            "Gradient Vector: \n",
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            "Gradient Vector Norm: 5446.947875016921\n",
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            " [0.52150676]\n",
            " [0.52150389]\n",
            " [0.52156814]]\n",
            "****************** Epoch 55 ****************** \n",
            "Error Vector: \n",
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            " [-28.5278101 ]\n",
            " [-43.3650007 ]]\n",
            "\n",
            "j = 681.2603107480344\n",
            "Gradient Vector: \n",
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            "Gradient Vector Norm: 5144.565751110244\n",
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            " [0.53032133]\n",
            " [0.53031824]\n",
            " [0.53038744]]\n",
            "****************** Epoch 56 ****************** \n",
            "Error Vector: \n",
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            "****************** Epoch 57 ****************** \n",
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            "****************** Epoch 58 ****************** \n",
            "Error Vector: \n",
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            "****************** Epoch 59 ****************** \n",
            "Error Vector: \n",
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            "****************** Epoch 60 ****************** \n",
            "Error Vector: \n",
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            "Gradient Vector: \n",
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            "Gradient Vector Norm: 3666.081681060822\n",
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            "****************** Epoch 61 ****************** \n",
            "Error Vector: \n",
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            "Gradient Vector: \n",
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            "****************** Epoch 62 ****************** \n",
            "Error Vector: \n",
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            "Gradient Vector: \n",
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            "****************** Epoch 63 ****************** \n",
            "Error Vector: \n",
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            "\n",
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            "Gradient Vector: \n",
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            "****************** Epoch 64 ****************** \n",
            "Error Vector: \n",
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            "Gradient Vector: \n",
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            "****************** Epoch 65 ****************** \n",
            "Error Vector: \n",
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            "Gradient Vector Norm: 2272.020722184639\n",
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            "****************** Epoch 66 ****************** \n",
            "Error Vector: \n",
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            "****************** Epoch 67 ****************** \n",
            "Error Vector: \n",
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            "Gradient Vector: \n",
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            "Gradient Vector Norm: 1753.168075068363\n",
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            "****************** Epoch 68 ****************** \n",
            "Error Vector: \n",
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            "\n",
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            "Gradient Vector Norm: 1505.84397218527\n",
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            " [0.63518425]\n",
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            "****************** Epoch 69 ****************** \n",
            "Error Vector: \n",
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            "\n",
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            "Gradient Vector: \n",
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            "Gradient Vector Norm: 1268.5245261353966\n",
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            " [0.64207911]]\n",
            "****************** Epoch 70 ****************** \n",
            "Error Vector: \n",
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            "Gradient Vector Norm: 1043.0871136680603\n",
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            "****************** Epoch 71 ****************** \n",
            "Error Vector: \n",
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            "Gradient Vector: \n",
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            " [-470.59383394]\n",
            " [-472.59929715]\n",
            " [-497.10223146]]\n",
            "Gradient Vector Norm: 831.8374448740265\n",
            "theta_new : [[0.65370542]\n",
            " [0.6536468 ]\n",
            " [0.65362728]\n",
            " [0.65406266]]\n",
            "****************** Epoch 72 ****************** \n",
            "Error Vector: \n",
            "[[ -2.28519617]\n",
            " [ -5.21011408]\n",
            " [ -2.82600739]\n",
            " [ -3.13446224]\n",
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            " [  0.33728702]\n",
            " [ -4.51342177]\n",
            " [ -7.77800766]\n",
            " [ -6.97682841]\n",
            " [ -8.39677369]\n",
            " [ -1.74418153]\n",
            " [ -3.7046085 ]\n",
            " [ -0.94284839]\n",
            " [  0.32855932]\n",
            " [ -2.8593396 ]\n",
            " [ -9.59429882]\n",
            " [ -1.86353718]\n",
            " [ -9.74662112]\n",
            " [ -2.44227753]\n",
            " [ -2.747955  ]\n",
            " [ -7.66967142]\n",
            " [ -6.32365601]\n",
            " [-13.51545376]\n",
            " [  2.02037546]\n",
            " [ -5.67291194]]\n",
            "\n",
            "j = 16.40421277526637\n",
            "Gradient Vector: \n",
            "[[  -4.47872967]\n",
            " [-359.70832319]\n",
            " [-361.10369233]\n",
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            "Gradient Vector Norm: 637.5736342986684\n",
            "theta_new : [[0.65879497]\n",
            " [0.65872348]\n",
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            " [0.65923024]]\n",
            "****************** Epoch 73 ****************** \n",
            "Error Vector: \n",
            "[[ -1.11614889]\n",
            " [ -3.80593753]\n",
            " [ -1.44242316]\n",
            " [ -1.62815866]\n",
            " [ -3.63409554]\n",
            " [  1.12898775]\n",
            " [ -3.38478037]\n",
            " [ -6.94020518]\n",
            " [ -5.66426621]\n",
            " [ -7.1808116 ]\n",
            " [ -0.65650003]\n",
            " [ -2.63204468]\n",
            " [  0.4864997 ]\n",
            " [  1.51773151]\n",
            " [ -1.72552632]\n",
            " [ -8.16954713]\n",
            " [ -0.73064155]\n",
            " [ -8.39321995]\n",
            " [ -1.07936793]\n",
            " [ -1.52797198]\n",
            " [ -6.34698589]\n",
            " [ -5.00612091]\n",
            " [-12.25413004]\n",
            " [  3.19919961]\n",
            " [ -4.21780824]]\n",
            "\n",
            "j = 11.516926208519337\n",
            "Gradient Vector: \n",
            "[[  -3.24817093]\n",
            " [-260.3962916 ]\n",
            " [-261.24539915]\n",
            " [-280.81914728]]\n",
            "Gradient Vector Norm: 463.6004005095321\n",
            "theta_new : [[0.66317608]\n",
            " [0.66308751]\n",
            " [0.66305801]\n",
            " [0.66371477]]\n",
            "****************** Epoch 74 ****************** \n",
            "Error Vector: \n",
            "[[ -0.1081878 ]\n",
            " [ -2.5951078 ]\n",
            " [ -0.24942811]\n",
            " [ -0.32926184]\n",
            " [ -2.70957374]\n",
            " [  1.81179447]\n",
            " [ -2.41145634]\n",
            " [ -6.21757667]\n",
            " [ -4.53229921]\n",
            " [ -6.13195087]\n",
            " [  0.28145256]\n",
            " [ -1.70703521]\n",
            " [  1.71886872]\n",
            " [  2.54290771]\n",
            " [ -0.74771208]\n",
            " [ -6.9409055 ]\n",
            " [  0.24595633]\n",
            " [ -7.22604187]\n",
            " [  0.09568333]\n",
            " [ -0.47614671]\n",
            " [ -5.2063307 ]\n",
            " [ -3.86992747]\n",
            " [-11.16642858]\n",
            " [  4.21538968]\n",
            " [ -2.96312571]]\n",
            "\n",
            "j = 8.542791545390484\n",
            "Gradient Vector: \n",
            "[[  -2.18705774]\n",
            " [-174.75984623]\n",
            " [-175.13814056]\n",
            " [-192.70239054]]\n",
            "Gradient Vector Norm: 313.61340321632275\n",
            "theta_new : [[0.66673899]\n",
            " [0.66662765]\n",
            " [0.66659056]\n",
            " [0.66741536]]\n",
            "****************** Epoch 75 ****************** \n",
            "Error Vector: \n",
            "[[  0.71395378]\n",
            " [ -1.60729237]\n",
            " [  0.72372264]\n",
            " [  0.73040366]\n",
            " [ -1.95539084]\n",
            " [  2.36901467]\n",
            " [ -1.61726945]\n",
            " [ -5.62776883]\n",
            " [ -3.60861936]\n",
            " [ -5.27578629]\n",
            " [  1.04670688]\n",
            " [ -0.95220291]\n",
            " [  2.72401083]\n",
            " [  3.37888895]\n",
            " [  0.05018299]\n",
            " [ -5.93845574]\n",
            " [  1.04223172]\n",
            " [ -6.27364302]\n",
            " [  1.05402413]\n",
            " [  0.38169441]\n",
            " [ -4.27562368]\n",
            " [ -2.94289069]\n",
            " [-10.27898274]\n",
            " [  5.04394697]\n",
            " [ -1.93962592]]\n",
            "\n",
            "j = 6.9668170071557425\n",
            "Gradient Vector: \n",
            "[[  -1.32139081]\n",
            " [-104.89751947]\n",
            " [-104.89205787]\n",
            " [-120.81549174]]\n",
            "Gradient Vector Norm: 191.32162061367842\n",
            "theta_new : [[0.66939802]\n",
            " [0.66925647]\n",
            " [0.66920932]\n",
            " [0.67025693]]\n",
            "****************** Epoch 76 ****************** \n",
            "Error Vector: \n",
            "[[ 1.3311359 ]\n",
            " [-0.86543533]\n",
            " [ 1.45439594]\n",
            " [ 1.5262258 ]\n",
            " [-1.38907922]\n",
            " [ 2.78775097]\n",
            " [-1.02063205]\n",
            " [-5.18441003]\n",
            " [-2.91462883]\n",
            " [-4.63207835]\n",
            " [ 1.62150295]\n",
            " [-0.38503024]\n",
            " [ 3.47851604]\n",
            " [ 4.00616088]\n",
            " [ 0.64967204]\n",
            " [-5.18545522]\n",
            " [ 1.63957316]\n",
            " [-5.55809437]\n",
            " [ 1.77332107]\n",
            " [ 1.02556009]\n",
            " [-3.57644597]\n",
            " [-2.24651428]\n",
            " [-9.61238447]\n",
            " [ 5.66550555]\n",
            " [-1.17110545]]\n",
            "\n",
            "j = 6.285155998987831\n",
            "Gradient Vector: \n",
            "[[ -0.67127894]\n",
            " [-52.432356  ]\n",
            " [-52.13919758]\n",
            " [-66.82823817]]\n",
            "Gradient Vector Norm: 99.67001511121079\n",
            "theta_new : [[0.67113013]\n",
            " [0.67094912]\n",
            " [0.67088882]\n",
            " [0.67222755]]\n",
            "****************** Epoch 77 ****************** \n",
            "Error Vector: \n",
            "[[ 1.73858739]\n",
            " [-0.37522383]\n",
            " [ 1.93696351]\n",
            " [ 2.05210454]\n",
            " [-1.01499381]\n",
            " [ 3.06483421]\n",
            " [-0.62608692]\n",
            " [-4.8908346 ]\n",
            " [-2.45560056]\n",
            " [-4.20564799]\n",
            " [ 2.00144762]\n",
            " [-0.00981981]\n",
            " [ 3.97654282]\n",
            " [ 4.41982702]\n",
            " [ 1.04620092]\n",
            " [-4.68765237]\n",
            " [ 2.03329608]\n",
            " [-5.08483564]\n",
            " [ 2.24799303]\n",
            " [ 1.45045454]\n",
            " [-3.11412443]\n",
            " [-1.78611077]\n",
            " [-9.1717251 ]\n",
            " [ 6.07519103]\n",
            " [-0.66347728]]\n",
            "\n",
            "j = 6.070112427433072\n",
            "Gradient Vector: \n",
            "[[ -0.24170762]\n",
            " [-17.76687118]\n",
            " [-17.28436035]\n",
            " [-31.15455795]]\n",
            "Gradient Vector Norm: 39.813009528591735\n",
            "theta_new : [[0.67201638]\n",
            " [0.67178508]\n",
            " [0.67170803]\n",
            " [0.67341819]]\n",
            "****************** Epoch 78 ****************** \n",
            "Error Vector: \n",
            "[[ 1.95533387]\n",
            " [-0.11377286]\n",
            " [ 2.19395633]\n",
            " [ 2.33259001]\n",
            " [-0.8156695 ]\n",
            " [ 3.21319546]\n",
            " [-0.41521824]\n",
            " [-4.73334376]\n",
            " [-2.21011018]\n",
            " [-3.97659945]\n",
            " [ 2.20427688]\n",
            " [ 0.19094   ]\n",
            " [ 4.24134695]\n",
            " [ 4.63920796]\n",
            " [ 1.25827701]\n",
            " [-4.42181026]\n",
            " [ 2.24179177]\n",
            " [-4.83177775]\n",
            " [ 2.50020651]\n",
            " [ 1.67621973]\n",
            " [-2.86707936]\n",
            " [-1.54018936]\n",
            " [-8.93643473]\n",
            " [ 6.29214042]\n",
            " [-0.3930411 ]]\n",
            "\n",
            "j = 6.030558197108907\n",
            "Gradient Vector: \n",
            "[[ -0.01262255]\n",
            " [  0.71729255]\n",
            " [  1.29965962]\n",
            " [-12.1290529 ]]\n",
            "Gradient Vector Norm: 12.219562485364847\n",
            "theta_new : [[0.67225772]\n",
            " [0.67196409]\n",
            " [0.6718663 ]\n",
            " [0.67403775]]\n",
            "****************** Epoch 79 ****************** \n",
            "Error Vector: \n",
            "[[ 2.02777165]\n",
            " [-0.02533663]\n",
            " [ 2.28029266]\n",
            " [ 2.42748291]\n",
            " [-0.74854532]\n",
            " [ 3.26428062]\n",
            " [-0.343207  ]\n",
            " [-4.67865214]\n",
            " [-2.12603112]\n",
            " [-3.89661602]\n",
            " [ 2.27317679]\n",
            " [ 0.25984713]\n",
            " [ 4.32965196]\n",
            " [ 4.71148067]\n",
            " [ 1.33092855]\n",
            " [-4.33135707]\n",
            " [ 2.30999631]\n",
            " [-4.74517309]\n",
            " [ 2.58404385]\n",
            " [ 1.75126649]\n",
            " [-2.78278746]\n",
            " [-1.45643406]\n",
            " [-8.85643148]\n",
            " [ 6.3631118 ]\n",
            " [-0.30203736]]\n",
            "\n",
            "j = 6.026432844949697\n",
            "Gradient Vector: \n",
            "[[ 0.06482891]\n",
            " [ 6.96271099]\n",
            " [ 7.57709507]\n",
            " [-5.69489221]]\n",
            "Gradient Vector Norm: 11.761280285640169\n",
            "theta_new : [[0.67213441]\n",
            " [0.67176533]\n",
            " [0.67164246]\n",
            " [0.67437384]]\n",
            "****************** Epoch 80 ****************** \n",
            "Error Vector: \n",
            "[[ 2.02043777]\n",
            " [-0.03238698]\n",
            " [ 2.27235759]\n",
            " [ 2.41995046]\n",
            " [-0.75442586]\n",
            " [ 3.26181087]\n",
            " [-0.34773062]\n",
            " [-4.68048729]\n",
            " [-2.13088258]\n",
            " [-3.898535  ]\n",
            " [ 2.26820419]\n",
            " [ 0.25613105]\n",
            " [ 4.32036257]\n",
            " [ 4.70228204]\n",
            " [ 1.32676608]\n",
            " [-4.337623  ]\n",
            " [ 2.30043523]\n",
            " [-4.75028596]\n",
            " [ 2.57473938]\n",
            " [ 1.74293945]\n",
            " [-2.78821198]\n",
            " [-1.46209436]\n",
            " [-8.86206985]\n",
            " [ 6.35316578]\n",
            " [-0.31013102]]\n",
            "\n",
            "j = 6.021453151229026\n",
            "Gradient Vector: \n",
            "[[ 0.05858872]\n",
            " [ 6.45258858]\n",
            " [ 7.06129309]\n",
            " [-6.21004713]]\n",
            "Gradient Vector Norm: 11.404642805125942\n",
            "theta_new : [[0.67190945]\n",
            " [0.67145031]\n",
            " [0.67129756]\n",
            " [0.67469915]]\n",
            "****************** Epoch 81 ****************** \n",
            "Error Vector: \n",
            "[[ 1.99402316]\n",
            " [-0.06200544]\n",
            " [ 2.24198854]\n",
            " [ 2.38821514]\n",
            " [-0.77763842]\n",
            " [ 3.24691692]\n",
            " [-0.37016514]\n",
            " [-4.6953136 ]\n",
            " [-2.15648279]\n",
            " [-3.91916161]\n",
            " [ 2.24584803]\n",
            " [ 0.23550969]\n",
            " [ 4.28767917]\n",
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            " [ 1.30468677]\n",
            " [-4.36661043]\n",
            " [ 2.27189287]\n",
            " [-4.77681405]\n",
            " [ 2.54303919]\n",
            " [ 1.71456569]\n",
            " [-2.81465143]\n",
            " [-1.48873957]\n",
            " [-8.8878411 ]\n",
            " [ 6.32347017]\n",
            " [-0.34176841]]\n",
            "\n",
            "j = 6.015301908943142\n",
            "Gradient Vector: \n",
            "[[ 0.0325588 ]\n",
            " [ 4.3440398 ]\n",
            " [ 4.93770085]\n",
            " [-8.36796511]]\n",
            "Gradient Vector Norm: 10.64309502109657\n",
            "theta_new : [[0.67172583]\n",
            " [0.67115979]\n",
            " [0.67097161]\n",
            " [0.67517131]]\n",
            "****************** Epoch 82 ****************** \n",
            "Error Vector: \n",
            "[[ 1.98196681]\n",
            " [-0.07398109]\n",
            " [ 2.22878067]\n",
            " [ 2.37541348]\n",
            " [-0.78749223]\n",
            " [ 3.24231029]\n",
            " [-0.37815937]\n",
            " [-4.69907582]\n",
            " [-2.1651982 ]\n",
            " [-3.92356358]\n",
            " [ 2.23726897]\n",
            " [ 0.22874202]\n",
            " [ 4.27247755]\n",
            " [ 4.65858292]\n",
            " [ 1.29720011]\n",
            " [-4.37749557]\n",
            " [ 2.25670856]\n",
            " [-4.78595532]\n",
            " [ 2.52790727]\n",
            " [ 1.70102318]\n",
            " [-2.82419588]\n",
            " [-1.49861447]\n",
            " [-8.89760638]\n",
            " [ 6.30767577]\n",
            " [-0.35530108]]\n",
            "\n",
            "j = 6.008535542690213\n",
            "Gradient Vector: \n",
            "[[ 0.02197674]\n",
            " [ 3.48073453]\n",
            " [ 4.06555415]\n",
            " [-9.24238053]]\n",
            "Gradient Vector Norm: 10.680183717444956\n",
            "theta_new : [[0.67157719]\n",
            " [0.67088424]\n",
            " [0.67065409]\n",
            " [0.67580445]]\n",
            "****************** Epoch 83 ****************** \n",
            "Error Vector: \n",
            "[[ 1.98378755]\n",
            " [-0.06881482]\n",
            " [ 2.23219712]\n",
            " [ 2.38100993]\n",
            " [-0.78439192]\n",
            " [ 3.24777476]\n",
            " [-0.37206503]\n",
            " [-4.69196756]\n",
            " [-2.15742039]\n",
            " [-3.91199   ]\n",
            " [ 2.24210082]\n",
            " [ 0.23551908]\n",
            " [ 4.27415488]\n",
            " [ 4.65748409]\n",
            " [ 1.30396958]\n",
            " [-4.37074738]\n",
            " [ 2.25430716]\n",
            " [-4.77811753]\n",
            " [ 2.52874916]\n",
            " [ 1.70177991]\n",
            " [-2.81726299]\n",
            " [-1.49214683]\n",
            " [-8.89178447]\n",
            " [ 6.30518472]\n",
            " [-0.35128276]]\n",
            "\n",
            "j = 6.000445972320224\n",
            "Gradient Vector: \n",
            "[[ 0.02640108]\n",
            " [ 3.82675718]\n",
            " [ 4.40861437]\n",
            " [-8.86981841]]\n",
            "Gradient Vector Norm: 10.618584024747381\n",
            "theta_new : [[0.67139127]\n",
            " [0.6705476 ]\n",
            " [0.67026771]\n",
            " [0.67655205]]\n",
            "****************** Epoch 84 ****************** \n",
            "Error Vector: \n",
            "[[ 1.98418638]\n",
            " [-0.0647831 ]\n",
            " [ 2.23417349]\n",
            " [ 2.38540113]\n",
            " [-0.78232179]\n",
            " [ 3.2530913 ]\n",
            " [-0.36650619]\n",
            " [-4.68475697]\n",
            " [-2.15013423]\n",
            " [-3.90002851]\n",
            " [ 2.24621478]\n",
            " [ 0.24197588]\n",
            " [ 4.27398678]\n",
            " [ 4.65436789]\n",
            " [ 1.31032575]\n",
            " [-4.36485925]\n",
            " [ 2.2497215 ]\n",
            " [-4.77081888]\n",
            " [ 2.52768541]\n",
            " [ 1.7008316 ]\n",
            " [-2.81099826]\n",
            " [-1.48643075]\n",
            " [-8.88675202]\n",
            " [ 6.30042412]\n",
            " [-0.34869765]]\n",
            "\n",
            "j = 5.990832356547438\n",
            "Gradient Vector: \n",
            "[[ 0.02981194]\n",
            " [ 4.08885303]\n",
            " [ 4.66635133]\n",
            " [-8.58042098]]\n",
            "Gradient Vector Norm: 10.588581901478962\n",
            "theta_new : [[0.67114386]\n",
            " [0.67012143]\n",
            " [0.66978272]\n",
            " [0.67741933]]\n",
            "****************** Epoch 85 ****************** \n",
            "Error Vector: \n",
            "[[ 1.9790759 ]\n",
            " [-0.06668572]\n",
            " [ 2.22991871]\n",
            " [ 2.3834411 ]\n",
            " [-0.78497884]\n",
            " [ 3.25564814]\n",
            " [-0.36526748]\n",
            " [-4.68015659]\n",
            " [-2.14771679]\n",
            " [-3.89157139]\n",
            " [ 2.24592431]\n",
            " [ 0.24455147]\n",
            " [ 4.26695465]\n",
            " [ 4.64496583]\n",
            " [ 1.31249056]\n",
            " [-4.36464501]\n",
            " [ 2.23883413]\n",
            " [-4.76857746]\n",
            " [ 2.51990267]\n",
            " [ 1.69386988]\n",
            " [-2.80984491]\n",
            " [-1.48590939]\n",
            " [-8.88677546]\n",
            " [ 6.28911103]\n",
            " [-0.35256916]]\n",
            "\n",
            "j = 5.979391466104276\n",
            "Gradient Vector: \n",
            "[[ 0.02799961]\n",
            " [ 3.9268669 ]\n",
            " [ 4.49656067]\n",
            " [-8.7235755 ]]\n",
            "Gradient Vector Norm: 10.57075659434463\n",
            "theta_new : [[0.67085692]\n",
            " [0.6696229 ]\n",
            " [0.66921481]\n",
            " [0.67846192]]\n",
            "****************** Epoch 86 ****************** \n",
            "Error Vector: \n",
            "[[ 1.97515776]\n",
            " [-0.06635116]\n",
            " [ 2.22741592]\n",
            " [ 2.38389912]\n",
            " [-0.78615924]\n",
            " [ 3.26015768]\n",
            " [-0.36169887]\n",
            " [-4.67312196]\n",
            " [-2.14240765]\n",
            " [-3.879248  ]\n",
            " [ 2.24759418]\n",
            " [ 0.24960494]\n",
            " [ 4.26122869]\n",
            " [ 4.63597131]\n",
            " [ 1.31717113]\n",
            " [-4.36175058]\n",
            " [ 2.22796473]\n",
            " [-4.76339632]\n",
            " [ 2.51316015]\n",
            " [ 1.68784054]\n",
            " [-2.80601844]\n",
            " [-1.48284802]\n",
            " [-8.88446409]\n",
            " [ 6.27782321]\n",
            " [-0.35448455]]\n",
            "\n",
            "j = 5.965793939004783\n",
            "Gradient Vector: \n",
            "[[ 0.02812162]\n",
            " [ 3.91798559]\n",
            " [ 4.47940608]\n",
            " [-8.70469512]]\n",
            "Gradient Vector Norm: 10.544581447047578\n",
            "theta_new : [[0.67051492]\n",
            " [0.66903097]\n",
            " [0.6685413 ]\n",
            " [0.67970484]]\n",
            "****************** Epoch 87 ****************** \n",
            "Error Vector: \n",
            "[[ 1.97094247]\n",
            " [-0.06542069]\n",
            " [ 2.22496483]\n",
            " [ 2.38501909]\n",
            " [-0.78715994]\n",
            " [ 3.26582213]\n",
            " [-0.35701952]\n",
            " [-4.66442647]\n",
            " [-2.13559271]\n",
            " [-3.86412183]\n",
            " [ 2.24999592]\n",
            " [ 0.25602522]\n",
            " [ 4.25495874]\n",
            " [ 4.62571859]\n",
            " [ 1.32317498]\n",
            " [-4.35776487]\n",
            " [ 2.21545693]\n",
            " [-4.75670969]\n",
            " [ 2.50565581]\n",
            " [ 1.68113088]\n",
            " [-2.80095844]\n",
            " [-1.47870462]\n",
            " [-8.8812304 ]\n",
            " [ 6.26483992]\n",
            " [-0.35621161]]\n",
            "\n",
            "j = 5.949653030376484\n",
            "Gradient Vector: \n",
            "[[ 0.02873539]\n",
            " [ 3.9452264 ]\n",
            " [ 4.4970221 ]\n",
            " [-8.64331256]]\n",
            "Gradient Vector Norm: 10.511693338819828\n",
            "theta_new : [[0.67009933]\n",
            " [0.66832095]\n",
            " [0.66773571]\n",
            " [0.68117716]]\n",
            "****************** Epoch 88 ****************** \n",
            "Error Vector: \n",
            "[[ 1.96467143]\n",
            " [-0.06583521]\n",
            " [ 2.22055665]\n",
            " [ 2.38472476]\n",
            " [-0.78951421]\n",
            " [ 3.27169544]\n",
            " [-0.35267227]\n",
            " [-4.65498741]\n",
            " [-2.1289137 ]\n",
            " [-3.84745693]\n",
            " [ 2.25167629]\n",
            " [ 0.26249586]\n",
            " [ 4.24596041]\n",
            " [ 4.6122428 ]\n",
            " [ 1.32909013]\n",
            " [-4.35456804]\n",
            " [ 2.19935755]\n",
            " [-4.75021516]\n",
            " [ 2.49526279]\n",
            " [ 1.67183759]\n",
            " [-2.79636849]\n",
            " [-1.47520469]\n",
            " [-8.87874517]\n",
            " [ 6.24813277]\n",
            " [-0.35983954]]\n",
            "\n",
            "j = 5.930525616116641\n",
            "Gradient Vector: \n",
            "[[ 0.02813535]\n",
            " [ 3.87028887]\n",
            " [ 4.41007065]\n",
            " [-8.68075637]]\n",
            "Gradient Vector Norm: 10.477794701899287\n",
            "theta_new : [[0.66960947]\n",
            " [0.66748536]\n",
            " [0.66678867]\n",
            " [0.6829328 ]]\n",
            "****************** Epoch 89 ****************** \n",
            "Error Vector: \n",
            "[[ 1.95909431]\n",
            " [-0.06409877]\n",
            " [ 2.21752742]\n",
            " [ 2.38677362]\n",
            " [-0.7906111 ]\n",
            " [ 3.27991632]\n",
            " [-0.34571355]\n",
            " [-4.6424451 ]\n",
            " [-2.11890736]\n",
            " [-3.82575386]\n",
            " [ 2.25540056]\n",
            " [ 0.27187536]\n",
            " [ 4.23755633]\n",
            " [ 4.59814085]\n",
            " [ 1.33791594]\n",
            " [-4.3485117 ]\n",
            " [ 2.18204813]\n",
            " [-4.74034571]\n",
            " [ 2.48509953]\n",
            " [ 1.66275271]\n",
            " [-2.78881344]\n",
            " [-1.4689595 ]\n",
            " [-8.87378489]\n",
            " [ 6.23018519]\n",
            " [-0.36183374]]\n",
            "\n",
            "j = 5.907909219966753\n",
            "Gradient Vector: \n",
            "[[ 0.0293803 ]\n",
            " [ 3.93929342]\n",
            " [ 4.46571441]\n",
            " [-8.56267221]]\n",
            "Gradient Vector Norm: 10.42980615118796\n",
            "theta_new : [[0.66900525]\n",
            " [0.6664769 ]\n",
            " [0.66565107]\n",
            " [0.68499609]]\n",
            "****************** Epoch 90 ****************** \n",
            "Error Vector: \n",
            "[[ 1.94861116]\n",
            " [-0.06671268]\n",
            " [ 2.20934466]\n",
            " [ 2.38420133]\n",
            " [-0.79548425]\n",
            " [ 3.28701502]\n",
            " [-0.34121069]\n",
            " [-4.63035525]\n",
            " [-2.11142198]\n",
            " [-3.804089  ]\n",
            " [ 2.25620069]\n",
            " [ 0.27941833]\n",
            " [ 4.22285263]\n",
            " [ 4.5774804 ]\n",
            " [ 1.34461123]\n",
            " [-4.34607335]\n",
            " [ 2.15776771]\n",
            " [-4.73313336]\n",
            " [ 2.46853448]\n",
            " [ 1.64794106]\n",
            " [-2.784249  ]\n",
            " [-1.46594176]\n",
            " [-8.87209025]\n",
            " [ 6.20501073]\n",
            " [-0.36903446]]\n",
            "\n",
            "j = 5.881242645894958\n",
            "Gradient Vector: \n",
            "[[ 0.02676774]\n",
            " [ 3.69114889]\n",
            " [ 4.19996505]\n",
            " [-8.76219964]]\n",
            "Gradient Vector Norm: 10.394284274622265\n",
            "theta_new : [[0.66833074]\n",
            " [0.66533198]\n",
            " [0.66435751]\n",
            " [0.68747935]]\n",
            "****************** Epoch 91 ****************** \n",
            "Error Vector: \n",
            "[[ 1.94711826]\n",
            " [-0.05675356]\n",
            " [ 2.21255298]\n",
            " [ 2.39517301]\n",
            " [-0.79128369]\n",
            " [ 3.30273603]\n",
            " [-0.32539605]\n",
            " [-4.60828398]\n",
            " [-2.09040115]\n",
            " [-3.76723336]\n",
            " [ 2.26725648]\n",
            " [ 0.29828025]\n",
            " [ 4.21879033]\n",
            " [ 4.56415146]\n",
            " [ 1.36305778]\n",
            " [-4.32995798]\n",
            " [ 2.13963514]\n",
            " [-4.71202235]\n",
            " [ 2.46166109]\n",
            " [ 1.64180943]\n",
            " [-2.76655848]\n",
            " [-1.45013995]\n",
            " [-8.85835573]\n",
            " [ 6.18626934]\n",
            " [-0.36401133]]\n",
            "\n",
            "j = 5.84993262976341\n",
            "Gradient Vector: \n",
            "[[ 0.03512376]\n",
            " [ 4.32148976]\n",
            " [ 4.81466171]\n",
            " [-8.04773336]]\n",
            "Gradient Vector Norm: 10.32586494927237\n",
            "theta_new : [[0.66733962]\n",
            " [0.6637986 ]\n",
            " [0.66265541]\n",
            " [0.6902319 ]]\n",
            "****************** Epoch 92 ****************** \n",
            "Error Vector: \n",
            "[[ 1.90446261]\n",
            " [-0.09414793]\n",
            " [ 2.1679282 ]\n",
            " [ 2.35542525]\n",
            " [-0.82387261]\n",
            " [ 3.2935687 ]\n",
            " [-0.34620047]\n",
            " [-4.61150934]\n",
            " [-2.11153393]\n",
            " [-3.76628523]\n",
            " [ 2.24225031]\n",
            " [ 0.28300375]\n",
            " [ 4.16397615]\n",
            " [ 4.50679044]\n",
            " [ 1.34517462]\n",
            " [-4.36079684]\n",
            " [ 2.0785553 ]\n",
            " [-4.73442035]\n",
            " [ 2.40585743]\n",
            " [ 1.59188565]\n",
            " [-2.79193907]\n",
            " [-1.47759819]\n",
            " [-8.88625919]\n",
            " [ 6.12289707]\n",
            " [-0.40901128]]\n",
            "\n",
            "j = 5.813630690098479\n",
            "Gradient Vector: \n",
            "[[ 1.92804099e-03]\n",
            " [ 1.59040944e+00]\n",
            " [ 2.04608194e+00]\n",
            " [-1.07800526e+01]]\n",
            "Gradient Vector Norm: 11.087172332933411\n",
            "theta_new : [[0.66704824]\n",
            " [0.66287816]\n",
            " [0.66154163]\n",
            " [0.69424536]]\n",
            "****************** Epoch 93 ****************** \n",
            "Error Vector: \n",
            "[[ 2.0488864 ]\n",
            " [ 0.09519919]\n",
            " [ 2.34557533]\n",
            " [ 2.55896748]\n",
            " [-0.68392317]\n",
            " [ 3.4140006 ]\n",
            " [-0.18338529]\n",
            " [-4.47662531]\n",
            " [-1.91868051]\n",
            " [-3.56407118]\n",
            " [ 2.39346676]\n",
            " [ 0.44288215]\n",
            " [ 4.33749985]\n",
            " [ 4.63766466]\n",
            " [ 1.51219661]\n",
            " [-4.1605231 ]\n",
            " [ 2.19585156]\n",
            " [-4.53625552]\n",
            " [ 2.56725735]\n",
            " [ 1.73639282]\n",
            " [-2.60227995]\n",
            " [-1.29117916]\n",
            " [-8.70964429]\n",
            " [ 6.24516432]\n",
            " [-0.21996746]]\n",
            "\n",
            "j = 5.780678144226272\n",
            "Gradient Vector: \n",
            "[[ 0.16737881]\n",
            " [14.88336894]\n",
            " [15.38637905]\n",
            " [ 2.98712399]]\n",
            "Gradient Vector Norm: 21.61495446576073\n",
            "theta_new : [[0.66171271]\n",
            " [0.65696982]\n",
            " [0.65546792]\n",
            " [0.69408801]]\n",
            "****************** Epoch 94 ****************** \n",
            "Error Vector: \n",
            "[[ 1.11454377]\n",
            " [-1.00873229]\n",
            " [ 1.24752815]\n",
            " [ 1.37547243]\n",
            " [-1.53244712]\n",
            " [ 2.80747798]\n",
            " [-1.05796697]\n",
            " [-5.1092217 ]\n",
            " [-2.93202648]\n",
            " [-4.4751723 ]\n",
            " [ 1.54380931]\n",
            " [-0.38247244]\n",
            " [ 3.1913671 ]\n",
            " [ 3.66818666]\n",
            " [ 0.63762294]\n",
            " [-5.27100033]\n",
            " [ 1.26343719]\n",
            " [-5.58143428]\n",
            " [ 1.46967419]\n",
            " [ 0.75397264]\n",
            " [-3.62860016]\n",
            " [-2.31668057]\n",
            " [-9.69332325]\n",
            " [ 5.27550492]\n",
            " [-1.37230722]]\n",
            "\n",
            "j = 6.076626248809751\n",
            "Gradient Vector: \n",
            "[[ -0.80051151]\n",
            " [-63.30040547]\n",
            " [-63.2569395 ]\n",
            " [-77.35505334]]\n",
            "Gradient Vector Norm: 118.29127957936464\n",
            "theta_new : [[0.67429925]\n",
            " [0.66937988]\n",
            " [0.66782052]\n",
            " [0.70752231]]\n",
            "****************** Epoch 95 ****************** \n",
            "Error Vector: \n",
            "[[ 4.02884529]\n",
            " [ 2.49440864]\n",
            " [ 4.69778374]\n",
            " [ 5.13340964]\n",
            " [ 1.14174647]\n",
            " [ 4.78490385]\n",
            " [ 1.7594473 ]\n",
            " [-3.01555867]\n",
            " [ 0.34517777]\n",
            " [-1.43529054]\n",
            " [ 4.25807597]\n",
            " [ 2.29587558]\n",
            " [ 6.75410763]\n",
            " [ 6.63007993]\n",
            " [ 3.46852897]\n",
            " [-1.7152039 ]\n",
            " [ 4.0839859 ]\n",
            " [-2.20250886]\n",
            " [ 4.86613512]\n",
            " [ 3.79425086]\n",
            " [-0.326978  ]\n",
            " [ 0.97173713]\n",
            " [-6.54557063]\n",
            " [ 8.21035722]\n",
            " [ 2.25669549]]\n",
            "\n",
            "j = 8.267936070566352\n",
            "Gradient Vector: \n",
            "[[  2.26937768]\n",
            " [184.4447188 ]\n",
            " [185.84645733]\n",
            " [177.57792167]]\n",
            "Gradient Vector Norm: 316.38240837797224\n",
            "theta_new : [[0.66135839]\n",
            " [0.6563828 ]\n",
            " [0.65480717]\n",
            " [0.69512342]]\n",
            "****************** Epoch 96 ****************** \n",
            "Error Vector: \n",
            "[[ 1.09613292]\n",
            " [-1.02553211]\n",
            " [ 1.22798792]\n",
            " [ 1.35755192]\n",
            " [-1.54678452]\n",
            " [ 2.80256477]\n",
            " [-1.06799445]\n",
            " [-5.11204328]\n",
            " [-2.94246369]\n",
            " [-4.47703747]\n",
            " [ 1.5322832 ]\n",
            " [-0.39024641]\n",
            " [ 3.16787122]\n",
            " [ 3.6441829 ]\n",
            " [ 0.6287046 ]\n",
            " [-5.28535468]\n",
            " [ 1.23814716]\n",
            " [-5.59251141]\n",
            " [ 1.4459186 ]\n",
            " [ 0.73271528]\n",
            " [-3.64072754]\n",
            " [-2.32954842]\n",
            " [-9.70629736]\n",
            " [ 5.24920915]\n",
            " [-1.39210102]]\n",
            "\n",
            "j = 6.075905697980044\n",
            "Gradient Vector: \n",
            "[[ -0.81541491]\n",
            " [-64.52292784]\n",
            " [-64.49486234]\n",
            " [-78.58345084]]\n",
            "Gradient Vector Norm: 120.41104240461459\n",
            "theta_new : [[0.66401271]\n",
            " [0.65889792]\n",
            " [0.65728096]\n",
            " [0.69890962]]\n",
            "****************** Epoch 97 ****************** \n",
            "Error Vector: \n",
            "[[ 1.76425831]\n",
            " [-0.21916262]\n",
            " [ 2.02035973]\n",
            " [ 2.222708  ]\n",
            " [-0.93222315]\n",
            " [ 3.26055515]\n",
            " [-0.41719986]\n",
            " [-4.62547471]\n",
            " [-2.18480757]\n",
            " [-3.76933875]\n",
            " [ 2.15803785]\n",
            " [ 0.2294406 ]\n",
            " [ 3.98398484]\n",
            " [ 4.31982658]\n",
            " [ 1.28332671]\n",
            " [-4.46515282]\n",
            " [ 1.87997581]\n",
            " [-4.81137571]\n",
            " [ 2.22310431]\n",
            " [ 1.42841   ]\n",
            " [-2.87833047]\n",
            " [-1.57077224]\n",
            " [-8.98031308]\n",
            " [ 5.91715647]\n",
            " [-0.55824486]]\n",
            "\n",
            "j = 5.708991698805752\n",
            "Gradient Vector: \n",
            "[[ -0.10885006]\n",
            " [ -7.51447906]\n",
            " [ -7.17907575]\n",
            " [-19.9022866 ]]\n",
            "Gradient Vector Norm: 22.452603063095346\n",
            "theta_new : [[0.66552495]\n",
            " [0.66024927]\n",
            " [0.65858479]\n",
            " [0.70174075]]\n",
            "****************** Epoch 98 ****************** \n",
            "Error Vector: \n",
            "[[ 2.18106053e+00]\n",
            " [ 2.86057637e-01]\n",
            " [ 2.51559268e+00]\n",
            " [ 2.76483854e+00]\n",
            " [-5.47830223e-01]\n",
            " [ 3.54937746e+00]\n",
            " [-7.96378005e-03]\n",
            " [-4.31756655e+00]\n",
            " [-1.70792330e+00]\n",
            " [-3.32066203e+00]\n",
            " [ 2.55073409e+00]\n",
            " [ 6.19800165e-01]\n",
            " [ 4.49266966e+00]\n",
            " [ 4.73907465e+00]\n",
            " [ 1.69544145e+00]\n",
            " [-3.95013534e+00]\n",
            " [ 2.27719772e+00]\n",
            " [-4.31976402e+00]\n",
            " [ 2.70696522e+00]\n",
            " [ 1.86154273e+00]\n",
            " [-2.39907614e+00]\n",
            " [-1.09415895e+00]\n",
            " [-8.52453130e+00]\n",
            " [ 6.33059972e+00]\n",
            " [-3.67891267e-02]]\n",
            "\n",
            "j = 5.7328690672222535\n",
            "Gradient Vector: \n",
            "[[ 0.33378206]\n",
            " [28.19056399]\n",
            " [28.71496209]\n",
            " [16.86277808]]\n",
            "Gradient Vector Norm: 43.63165869874653\n",
            "theta_new : [[0.66273235]\n",
            " [0.65728305]\n",
            " [0.65556804]\n",
            " [0.70047031]]\n",
            "****************** Epoch 99 ****************** \n",
            "Error Vector: \n",
            "[[ 1.62511144]\n",
            " [-0.37621761]\n",
            " [ 1.85994335]\n",
            " [ 2.05460409]\n",
            " [-1.05519263]\n",
            " [ 3.18073094]\n",
            " [-0.53648834]\n",
            " [-4.70493543]\n",
            " [-2.32143918]\n",
            " [-3.88075653]\n",
            " [ 2.03935825]\n",
            " [ 0.11927144]\n",
            " [ 3.81181801]\n",
            " [ 4.16786911]\n",
            " [ 1.16569698]\n",
            " [-4.61923863]\n",
            " [ 1.73039431]\n",
            " [-4.95247814]\n",
            " [ 2.05634708]\n",
            " [ 1.27917142]\n",
            " [-3.01887818]\n",
            " [-1.71248844]\n",
            " [-9.11706606]\n",
            " [ 5.76178344]\n",
            " [-0.72558766]]\n",
            "\n",
            "j = 5.712316074724648\n",
            "Gradient Vector: \n",
            "[[ -0.24674668]\n",
            " [-18.68192644]\n",
            " [-18.42419344]\n",
            " [-31.33540133]]\n",
            "Gradient Vector Norm: 40.87093759198248\n",
            "theta_new : [[0.66480692]\n",
            " [0.65914358]\n",
            " [0.65736605]\n",
            " [0.70431414]]\n",
            "****************** Epoch 100 ****************** \n",
            "Error Vector: \n",
            "[[ 2.19513212]\n",
            " [ 0.31458654]\n",
            " [ 2.53716795]\n",
            " [ 2.79587669]\n",
            " [-0.5295632 ]\n",
            " [ 3.57553225]\n",
            " [ 0.02298981]\n",
            " [-4.28409808]\n",
            " [-1.66951175]\n",
            " [-3.26758307]\n",
            " [ 2.57626908]\n",
            " [ 0.65289657]\n",
            " [ 4.50752058]\n",
            " [ 4.74136532]\n",
            " [ 1.72908148]\n",
            " [-3.915105  ]\n",
            " [ 2.27382082]\n",
            " [-4.28040432]\n",
            " [ 2.71813386]\n",
            " [ 1.87157643]\n",
            " [-2.36366733]\n",
            " [-1.06087134]\n",
            " [-8.49391047]\n",
            " [ 6.32740444]\n",
            " [-0.01252422]]\n",
            "\n",
            "j = 5.710254689514407\n",
            "Gradient Vector: \n",
            "[[ 0.35848461]\n",
            " [30.13971181]\n",
            " [30.65609369]\n",
            " [18.93493548]]\n",
            "Gradient Vector Norm: 46.97721363357907\n",
            "theta_new : [[0.66076902]\n",
            " [0.65489068]\n",
            " [0.6530519 ]\n",
            " [0.70228839]]\n",
            "****************** Epoch 101 ****************** \n",
            "Error Vector: \n",
            "[[ 1.38357001]\n",
            " [-0.65301019]\n",
            " [ 1.57971764]\n",
            " [ 1.7581996 ]\n",
            " [-1.27059858]\n",
            " [ 3.03622394]\n",
            " [-0.74972735]\n",
            " [-4.85115916]\n",
            " [-2.56668656]\n",
            " [-4.08785591]\n",
            " [ 1.82891148]\n",
            " [-0.07916897]\n",
            " [ 3.51377636]\n",
            " [ 3.90833731]\n",
            " [ 0.95439981]\n",
            " [-4.89309312]\n",
            " [ 1.47674518]\n",
            " [-5.20559454]\n",
            " [ 1.76872532]\n",
            " [ 1.0217559 ]\n",
            " [-3.26977663]\n",
            " [-1.96470992]\n",
            " [-9.359937  ]\n",
            " [ 5.49824421]\n",
            " [-1.01850185]]\n",
            "\n",
            "j = 5.77720630588014\n",
            "Gradient Vector: \n",
            "[[ -0.48964852]\n",
            " [-38.33638376]\n",
            " [-38.20821575]\n",
            " [-51.48241785]]\n",
            "Gradient Vector Norm: 74.70090477021559\n",
            "theta_new : [[0.66648127]\n",
            " [0.66036652]\n",
            " [0.65845906]\n",
            " [0.70985131]]\n",
            "****************** Epoch 102 ****************** \n",
            "Error Vector: \n",
            "[[ 2.78881029]\n",
            " [ 1.04113673]\n",
            " [ 3.24549391]\n",
            " [ 3.57578607]\n",
            " [ 0.02112688]\n",
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            " [ 3.14305097]\n",
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            "\n",
            "j = 6.09253019416037\n",
            "Gradient Vector: \n",
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            "Gradient Vector Norm: 136.20300321530235\n",
            "theta_new : [[0.6566265 ]\n",
            " [0.65038654]\n",
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            "****************** Epoch 103 ****************** \n",
            "Error Vector: \n",
            "[[  0.61250856]\n",
            " [ -1.56770081]\n",
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            " [ -1.97252241]\n",
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            " [ -4.85192179]\n",
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            " [ -4.1229258 ]\n",
            " [ -2.81651937]\n",
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            "\n",
            "j = 6.504081183130596\n",
            "Gradient Vector: \n",
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            "Gradient Vector Norm: 187.73941963904485\n",
            "theta_new : [[0.66607702]\n",
            " [0.6597155 ]\n",
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            "****************** Epoch 104 ****************** \n",
            "Error Vector: \n",
            "[[ 2.82836972]\n",
            " [ 1.09674068]\n",
            " [ 3.29573633]\n",
            " [ 3.63577768]\n",
            " [ 0.06109668]\n",
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            " [ 3.18854813]\n",
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            " [-3.11016205]\n",
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            " [ 3.44661484]\n",
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            " [-7.78197482]\n",
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            "\n",
            "j = 6.12004474006561\n",
            "Gradient Vector: \n",
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            "Gradient Vector Norm: 143.01208137464928\n",
            "theta_new : [[0.65931359]\n",
            " [0.65282615]\n",
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            " [0.70628244]]\n",
            "****************** Epoch 105 ****************** \n",
            "Error Vector: \n",
            "[[ 1.35197229]\n",
            " [-0.67190415]\n",
            " [ 1.5503877 ]\n",
            " [ 1.73869724]\n",
            " [-1.29084413]\n",
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            " [-0.75165493]\n",
            " [-4.83529421]\n",
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            " [ 1.72324637]\n",
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            " [-3.27346825]\n",
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            " [-9.36862881]\n",
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            "\n",
            "j = 5.737339609307203\n",
            "Gradient Vector: \n",
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            " [-39.78341606]\n",
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            "Gradient Vector Norm: 77.15529813933986\n",
            "theta_new : [[0.66250207]\n",
            " [0.65585561]\n",
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            " [0.71090309]]\n",
            "****************** Epoch 106 ****************** \n",
            "Error Vector: \n",
            "[[ 2.16167112]\n",
            " [ 0.30543667]\n",
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            " [ 2.78732236]\n",
            " [-0.54604047]\n",
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            " [ 1.75021546]\n",
            " [-3.90805434]\n",
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            " [-4.2572312 ]\n",
            " [ 2.66503593]\n",
            " [ 1.82415452]\n",
            " [-2.34928375]\n",
            " [-1.0519633 ]\n",
            " [-8.4886208 ]\n",
            " [ 6.24702478]\n",
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            "\n",
            "j = 5.626488631428987\n",
            "Gradient Vector: \n",
            "[[ 0.34971514]\n",
            " [29.312637  ]\n",
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            "Gradient Vector Norm: 45.600440161657055\n",
            "theta_new : [[0.65947717]\n",
            " [0.65265557]\n",
            " [0.65055184]\n",
            " [0.7096188 ]]\n",
            "****************** Epoch 107 ****************** \n",
            "Error Vector: \n",
            "[[ 1.56889111]\n",
            " [-0.40044439]\n",
            " [ 1.81173247]\n",
            " [ 2.03037234]\n",
            " [-1.0869287 ]\n",
            " [ 3.20464106]\n",
            " [-0.52580464]\n",
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            " [ 1.97115355]\n",
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            " [-3.00961574]\n",
            " [-1.71081963]\n",
            " [-9.11998754]\n",
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            "\n",
            "j = 5.606921730085064\n",
            "Gradient Vector: \n",
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            " [-20.64646513]\n",
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            "Gradient Vector Norm: 44.06185477264539\n",
            "theta_new : [[0.66213891]\n",
            " [0.65511095]\n",
            " [0.65295077]\n",
            " [0.71418134]]\n",
            "****************** Epoch 108 ****************** \n",
            "Error Vector: \n",
            "[[ 2.2849005 ]\n",
            " [ 0.46598981]\n",
            " [ 2.6618543 ]\n",
            " [ 2.96009974]\n",
            " [-0.42731698]\n",
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            " [ 0.81112473]\n",
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            " [-8.33887905]\n",
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            "\n",
            "j = 5.649241641304168\n",
            "Gradient Vector: \n",
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            " [40.59645947]\n",
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            "Gradient Vector Norm: 65.07145135330784\n",
            "theta_new : [[0.65615756]\n",
            " [0.64894367]\n",
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            " [0.71027101]]\n",
            "****************** Epoch 109 ****************** \n",
            "Error Vector: \n",
            "[[ 1.03811863]\n",
            " [-1.02425506]\n",
            " [ 1.18936027]\n",
            " [ 1.36181645]\n",
            " [-1.56751721]\n",
            " [ 2.86485736]\n",
            " [-1.01752011]\n",
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            " [-4.3020397 ]\n",
            " [ 1.55445849]\n",
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            " [-3.58691716]\n",
            " [-2.28835085]\n",
            " [-9.67424991]\n",
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            "\n",
            "j = 5.893998859684725\n",
            "Gradient Vector: \n",
            "[[ -0.81600733]\n",
            " [-64.84360473]\n",
            " [-64.93137847]\n",
            " [-78.50482484]]\n",
            "Gradient Vector Norm: 120.76609778939388\n",
            "theta_new : [[0.66481562]\n",
            " [0.65744758]\n",
            " [0.65519643]\n",
            " [0.72024919]]\n",
            "****************** Epoch 110 ****************** \n",
            "Error Vector: \n",
            "[[ 3.09289275]\n",
            " [ 1.44790123]\n",
            " [ 3.62295263]\n",
            " [ 4.01395262]\n",
            " [ 0.31889676]\n",
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            " [-2.1511466 ]\n",
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            " [ 3.73970472]\n",
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            " [ 0.03359282]\n",
            " [-7.45178814]\n",
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            " [ 1.13672451]]\n",
            "\n",
            "j = 6.39673863950853\n",
            "Gradient Vector: \n",
            "[[  1.35038875]\n",
            " [109.97913928]\n",
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            "Gradient Vector Norm: 186.19031874486856\n",
            "theta_new : [[0.65443479]\n",
            " [0.64697885]\n",
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            " [0.71092977]]\n",
            "****************** Epoch 111 ****************** \n",
            "Error Vector: \n",
            "[[ 0.78002804]\n",
            " [-1.32601871]\n",
            " [ 0.88739177]\n",
            " [ 1.0384768 ]\n",
            " [-1.80049164]\n",
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            " [ 1.04139891]\n",
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            " [-3.86498546]\n",
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            " [-9.94166487]\n",
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            "\n",
            "j = 6.138701819665291\n",
            "Gradient Vector: \n",
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            " [ -86.23275566]\n",
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            "Gradient Vector Norm: 158.12785126055098\n",
            "theta_new : [[0.66131152]\n",
            " [0.65373978]\n",
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            "****************** Epoch 112 ****************** \n",
            "Error Vector: \n",
            "[[ 2.41934702]\n",
            " [ 0.64647183]\n",
            " [ 2.82901197]\n",
            " [ 3.15459757]\n",
            " [-0.29543002]\n",
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            " [-8.1682892 ]\n",
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            "\n",
            "j = 5.686134428662984\n",
            "Gradient Vector: \n",
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            "Gradient Vector Norm: 87.10160225361959\n",
            "theta_new : [[0.65700179]\n",
            " [0.64930322]\n",
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            " [0.71605254]]\n",
            "****************** Epoch 113 ****************** \n",
            "Error Vector: \n",
            "[[ 1.51740092]\n",
            " [-0.43185658]\n",
            " [ 1.76367254]\n",
            " [ 1.99808629]\n",
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            " [-9.13465795]\n",
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            "\n",
            "j = 5.538278994178077\n",
            "Gradient Vector: \n",
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            " [-23.0390736 ]\n",
            " [-22.9236634 ]\n",
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            "Gradient Vector Norm: 48.052254051256725\n",
            "theta_new : [[0.65911156]\n",
            " [0.65125845]\n",
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            " [0.71979204]]\n",
            "****************** Epoch 114 ****************** \n",
            "Error Vector: \n",
            "[[ 2.0959615 ]\n",
            " [ 0.26844514]\n",
            " [ 2.45068202]\n",
            " [ 2.74958732]\n",
            " [-0.58735029]\n",
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            " [-8.50317913]\n",
            " [ 6.11721546]\n",
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            "\n",
            "j = 5.5083362181651525\n",
            "Gradient Vector: \n",
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            " [26.46092292]\n",
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            "Gradient Vector Norm: 40.781791755265104\n",
            "theta_new : [[0.65577167]\n",
            " [0.64775293]\n",
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            " [0.71839124]]\n",
            "****************** Epoch 115 ****************** \n",
            "Error Vector: \n",
            "[[ 1.44791063]\n",
            " [-0.50330529]\n",
            " [ 1.6865155 ]\n",
            " [ 1.92204621]\n",
            " [-1.17874123]\n",
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            " [-9.19340613]\n",
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            "\n",
            "j = 5.53112414780514\n",
            "Gradient Vector: \n",
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            "Gradient Vector Norm: 56.82980757618428\n",
            "theta_new : [[0.65992247]\n",
            " [0.6517173 ]\n",
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            " [0.72448653]]\n",
            "****************** Epoch 116 ****************** \n",
            "Error Vector: \n",
            "[[ 2.51203565]\n",
            " [ 0.78116521]\n",
            " [ 2.9485962 ]\n",
            " [ 3.30025539]\n",
            " [-0.19994262]\n",
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            " [-3.39612196]\n",
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            " [-8.03675281]\n",
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            " [ 0.43155646]]\n",
            "\n",
            "j = 5.706615537739515\n",
            "Gradient Vector: \n",
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            "Gradient Vector Norm: 103.53040575024056\n",
            "theta_new : [[0.65119886]\n",
            " [0.6428715 ]\n",
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            " [0.71746068]]\n",
            "****************** Epoch 117 ****************** \n",
            "Error Vector: \n",
            "[[  0.6206394 ]\n",
            " [ -1.48461139]\n",
            " [  0.71265572]\n",
            " [  0.87001164]\n",
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            " [  0.84031988]\n",
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            "j = 6.225172836781923\n",
            "Gradient Vector: \n",
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            "Gradient Vector Norm: 177.97160498865708\n",
            "theta_new : [[0.66124427]\n",
            " [0.65282418]\n",
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            "****************** Epoch 118 ****************** \n",
            "Error Vector: \n",
            "[[ 2.97624368]\n",
            " [ 1.34739275]\n",
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            " [ 0.22964808]\n",
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            " [-1.31965647]\n",
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            " [-7.52415573]\n",
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            "\n",
            "j = 6.179039204538465\n",
            "Gradient Vector: \n",
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            " [102.65335131]\n",
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            "Gradient Vector Norm: 173.46095424742452\n",
            "theta_new : [[0.6528566 ]\n",
            " [0.64435161]\n",
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            "****************** Epoch 119 ****************** \n",
            "Error Vector: \n",
            "[[ 1.12652005]\n",
            " [-0.8701488 ]\n",
            " [ 1.31426461]\n",
            " [ 1.52953305]\n",
            " [-1.46495236]\n",
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            " [ 1.68853392]\n",
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            " [ 3.18014481]\n",
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            " [ 0.86438108]\n",
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            " [ 1.09073144]\n",
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            " [-3.40527703]\n",
            " [-2.11634438]\n",
            " [-9.51417902]\n",
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            "\n",
            "j = 5.665720759483245\n",
            "Gradient Vector: \n",
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            " [-54.20779566]\n",
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            "Gradient Vector Norm: 102.05702244757842\n",
            "theta_new : [[0.65699373]\n",
            " [0.64837842]\n",
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            "****************** Epoch 120 ****************** \n",
            "Error Vector: \n",
            "[[ 2.15307028e+00]\n",
            " [ 3.66955777e-01]\n",
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            " [ 1.78572259e+00]\n",
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            " [-5.51459317e-03]]\n",
            "\n",
            "j = 5.460375308072627\n",
            "Gradient Vector: \n",
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            " [33.26620935]\n",
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            "Gradient Vector Norm: 52.49458154092735\n",
            "theta_new : [[0.65390195]\n",
            " [0.64516478]\n",
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            " [0.72516761]]\n",
            "****************** Epoch 121 ****************** \n",
            "Error Vector: \n",
            "[[ 1.54455356]\n",
            " [-0.35852865]\n",
            " [ 1.81303634]\n",
            " [ 2.07889543]\n",
            " [-1.07734355]\n",
            " [ 3.2903337 ]\n",
            " [-0.44122425]\n",
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            " [ 3.68916567]\n",
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            " [ 1.2865325 ]\n",
            " [-4.54045018]\n",
            " [ 1.48132598]\n",
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            " [ 1.90977677]\n",
            " [ 1.14843963]\n",
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            " [-1.63080646]\n",
            " [-9.0502195 ]\n",
            " [ 5.50710442]\n",
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            "\n",
            "j = 5.415778332178437\n",
            "Gradient Vector: \n",
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            " [-17.99559956]\n",
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            "Gradient Vector Norm: 39.41062171083586\n",
            "theta_new : [[0.65593316]\n",
            " [0.64705124]\n",
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            " [0.72900866]]\n",
            "****************** Epoch 122 ****************** \n",
            "Error Vector: \n",
            "[[ 2.12067927]\n",
            " [ 0.33929553]\n",
            " [ 2.49735296]\n",
            " [ 2.8278044 ]\n",
            " [-0.54637638]\n",
            " [ 3.68887992]\n",
            " [ 0.12391493]\n",
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            " [-4.1364604 ]\n",
            " [ 2.57869652]\n",
            " [ 1.74724113]\n",
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            " [-0.97267449]\n",
            " [-8.42068957]\n",
            " [ 6.07908668]\n",
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            "\n",
            "j = 5.423089145033514\n",
            "Gradient Vector: \n",
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            " [31.25024205]\n",
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            "Gradient Vector Norm: 49.03966002655292\n",
            "theta_new : [[0.65138547]\n",
            " [0.64235928]\n",
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            " [0.72654416]]\n",
            "****************** Epoch 123 ****************** \n",
            "Error Vector: \n",
            "[[ 1.21091368]\n",
            " [-0.74645697]\n",
            " [ 1.42359176]\n",
            " [ 1.6634911 ]\n",
            " [-1.37769267]\n",
            " [ 3.08283715]\n",
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            " [ 1.51476194]\n",
            " [ 0.79491672]\n",
            " [-3.27145372]\n",
            " [-1.98738522]\n",
            " [-9.39272997]\n",
            " [ 5.15093319]\n",
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            "\n",
            "j = 5.536644749060502\n",
            "Gradient Vector: \n",
            "[[ -0.57387729]\n",
            " [-45.5776147 ]\n",
            " [-45.67143211]\n",
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            "Gradient Vector Norm: 86.94131983872713\n",
            "theta_new : [[0.65817753]\n",
            " [0.6490117 ]\n",
            " [0.64632824]\n",
            " [0.73500309]]\n",
            "****************** Epoch 124 ****************** \n",
            "Error Vector: \n",
            "[[ 2.86752217]\n",
            " [ 1.24843765]\n",
            " [ 3.38636629]\n",
            " [ 3.80377673]\n",
            " [ 0.14391142]\n",
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            " [-2.14664986]\n",
            " [ 3.33818682]\n",
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            " [ 2.60119867]\n",
            " [-2.90022485]\n",
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            " [ 3.44367048]\n",
            " [ 2.52157156]\n",
            " [-1.3883568 ]\n",
            " [-0.11262603]\n",
            " [-7.59840375]\n",
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            "\n",
            "j = 5.993006392706117\n",
            "Gradient Vector: \n",
            "[[ 1.17428216]\n",
            " [95.48711443]\n",
            " [96.16113164]\n",
            " [86.91048051]]\n",
            "Gradient Vector Norm: 160.995536652264\n",
            "theta_new : [[0.64762143]\n",
            " [0.63838684]\n",
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            " [0.72561058]]\n",
            "****************** Epoch 125 ****************** \n",
            "Error Vector: \n",
            "[[  0.52579945]\n",
            " [ -1.55995875]\n",
            " [  0.61673007]\n",
            " [  0.79136896]\n",
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            " [ -5.21296065]\n",
            " [ -3.28831534]\n",
            " [ -4.56783504]\n",
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            " [ -4.03042438]\n",
            " [ -2.74524484]\n",
            " [-10.11909259]\n",
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            "\n",
            "j = 6.217382371691911\n",
            "Gradient Vector: \n",
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            " [-103.16287275]\n",
            " [-103.58837636]\n",
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            "Gradient Vector Norm: 187.54465822361806\n",
            "theta_new : [[0.65637691]\n",
            " [0.64706713]\n",
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            "****************** Epoch 126 ****************** \n",
            "Error Vector: \n",
            "[[ 2.59173417]\n",
            " [ 0.92418053]\n",
            " [ 3.06292913]\n",
            " [ 3.4563616 ]\n",
            " [-0.10596512]\n",
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            " [-3.2254202 ]\n",
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            " [-3.5519168 ]\n",
            " [ 3.11882253]\n",
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            " [-1.68831123]\n",
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            " [-7.88638399]\n",
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            "\n",
            "j = 5.686709046103506\n",
            "Gradient Vector: \n",
            "[[ 0.89001307]\n",
            " [72.51746188]\n",
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            "Gradient Vector Norm: 120.8534548650649\n",
            "theta_new : [[0.6507103 ]\n",
            " [0.64131828]\n",
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            "****************** Epoch 127 ****************** \n",
            "Error Vector: \n",
            "[[ 1.37718285]\n",
            " [-0.5301906 ]\n",
            " [ 1.62737822]\n",
            " [ 1.89647845]\n",
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            " [-0.55767403]\n",
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            " [ 1.17603027]\n",
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            " [-1.7748521 ]\n",
            " [-9.19070927]\n",
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            "\n",
            "j = 5.395703458166024\n",
            "Gradient Vector: \n",
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            " [-30.36788684]\n",
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            "Gradient Vector Norm: 60.454683219415635\n",
            "theta_new : [[0.65312878]\n",
            " [0.64363566]\n",
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            " [0.73487684]]\n",
            "****************** Epoch 128 ****************** \n",
            "Error Vector: \n",
            "[[ 2.02522098]\n",
            " [ 0.25280991]\n",
            " [ 2.39629647]\n",
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            " [-1.03746652]\n",
            " [-8.48517258]\n",
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            "\n",
            "j = 5.3287104402336425\n",
            "Gradient Vector: \n",
            "[[ 0.30152128]\n",
            " [24.98725135]\n",
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            "Gradient Vector Norm: 38.35560951638892\n",
            "theta_new : [[0.65029344]\n",
            " [0.64068949]\n",
            " [0.63791954]\n",
            " [0.73383209]]\n",
            "****************** Epoch 129 ****************** \n",
            "Error Vector: \n",
            "[[ 1.49159625]\n",
            " [-0.38228002]\n",
            " [ 1.76722439]\n",
            " [ 2.05580849]\n",
            " [-1.10843779]\n",
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            " [-4.48388086]\n",
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            " [ 1.82912609]\n",
            " [ 1.07646651]\n",
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            " [-1.62995206]\n",
            " [-9.0528768 ]\n",
            " [ 5.39209501]\n",
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            "\n",
            "j = 5.322417076556125\n",
            "Gradient Vector: \n",
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            " [-19.96015403]\n",
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            "Gradient Vector Norm: 42.48174321231798\n",
            "theta_new : [[0.65297842]\n",
            " [0.64324628]\n",
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            " [0.73846641]]\n",
            "****************** Epoch 130 ****************** \n",
            "Error Vector: \n",
            "[[ 2.23116816]\n",
            " [ 0.51211213]\n",
            " [ 2.64508646]\n",
            " [ 3.01564468]\n",
            " [-0.42750429]\n",
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            " [-8.24657773]\n",
            " [ 6.12840003]\n",
            " [ 0.12104821]]\n",
            "\n",
            "j = 5.386236466449487\n",
            "Gradient Vector: \n",
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            " [43.26622675]\n",
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            " [33.34458214]]\n",
            "Gradient Vector Norm: 69.89865188554067\n",
            "theta_new : [[0.64633164]\n",
            " [0.63649227]\n",
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            " [0.73384926]]\n",
            "****************** Epoch 131 ****************** \n",
            "Error Vector: \n",
            "[[ 0.84340135]\n",
            " [-1.14802263]\n",
            " [ 1.00550199]\n",
            " [ 1.23520393]\n",
            " [-1.69737187]\n",
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            " [ 1.06729319]\n",
            " [ 0.3946027 ]\n",
            " [-3.61834638]\n",
            " [-2.34094853]\n",
            " [-9.73460324]\n",
            " [ 4.71852262]\n",
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            "\n",
            "j = 5.721499004884503\n",
            "Gradient Vector: \n",
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            " [-74.18287618]\n",
            " [-74.4971427 ]\n",
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            "Gradient Vector Norm: 136.76209941067484\n",
            "theta_new : [[0.65572215]\n",
            " [0.6458026 ]\n",
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            " [0.74440651]]\n",
            "****************** Epoch 132 ****************** \n",
            "Error Vector: \n",
            "[[ 3.06798122]\n",
            " [ 1.5271685 ]\n",
            " [ 3.63967036]\n",
            " [ 4.10519451]\n",
            " [ 0.34426698]\n",
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            " [ 1.11572029]\n",
            " [-3.32043829]\n",
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            " [ 3.65921897]\n",
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            " [ 0.1710607 ]\n",
            " [-7.33000887]\n",
            " [ 6.95669473]\n",
            " [ 1.16827563]]\n",
            "\n",
            "j = 6.20981471142857\n",
            "Gradient Vector: \n",
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            "Gradient Vector Norm: 195.2406408261644\n",
            "theta_new : [[0.64545588]\n",
            " [0.63548724]\n",
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            "****************** Epoch 133 ****************** \n",
            "Error Vector: \n",
            "[[ 0.78409588]\n",
            " [-1.21234975]\n",
            " [ 0.93823477]\n",
            " [ 1.16665606]\n",
            " [-1.74877903]\n",
            " [ 2.86124487]\n",
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            " [-4.94942069]\n",
            " [-2.9245907 ]\n",
            " [-4.17266305]\n",
            " [ 1.44531825]\n",
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            " [ 2.74594382]\n",
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            " [ 0.65448366]\n",
            " [-5.37426624]\n",
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            " [ 0.99482944]\n",
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            " [-3.67344717]\n",
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            " [-9.78907432]\n",
            " [ 4.64794801]\n",
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            "\n",
            "j = 5.761828674945947\n",
            "Gradient Vector: \n",
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            " [-78.76696305]\n",
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            "Gradient Vector Norm: 144.75692770414284\n",
            "theta_new : [[0.65144698]\n",
            " [0.64141118]\n",
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            " [0.74229177]]\n",
            "****************** Epoch 134 ****************** \n",
            "Error Vector: \n",
            "[[ 2.23177844]\n",
            " [ 0.52979717]\n",
            " [ 2.65298086]\n",
            " [ 3.03575218]\n",
            " [-0.4196311 ]\n",
            " [ 3.84641062]\n",
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            " [-3.90491853]\n",
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            " [-2.65564049]\n",
            " [ 2.79587113]\n",
            " [ 0.98673455]\n",
            " [ 4.51518897]\n",
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            " [-3.6047596 ]\n",
            " [ 2.04995239]\n",
            " [-3.89000115]\n",
            " [ 2.68097049]\n",
            " [ 1.8391216 ]\n",
            " [-2.02973692]\n",
            " [-0.7606556 ]\n",
            " [-8.22254421]\n",
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            "\n",
            "j = 5.351710999445388\n",
            "Gradient Vector: \n",
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            " [44.43270571]\n",
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            "Gradient Vector Norm: 71.95791897143141\n",
            "theta_new : [[0.64779561]\n",
            " [0.63768647]\n",
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            " [0.74008039]]\n",
            "****************** Epoch 135 ****************** \n",
            "Error Vector: \n",
            "[[ 1.49154572]\n",
            " [-0.35461697]\n",
            " [ 1.77889378]\n",
            " [ 2.08733123]\n",
            " [-1.0965127 ]\n",
            " [ 3.35189992]\n",
            " [-0.388035  ]\n",
            " [-4.4254909 ]\n",
            " [-2.11447041]\n",
            " [-3.4096164 ]\n",
            " [ 2.11231301]\n",
            " [ 0.31591685]\n",
            " [ 3.60905047]\n",
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            " [ 1.35489925]\n",
            " [-4.49954319]\n",
            " [ 1.32525231]\n",
            " [-4.73718941]\n",
            " [ 1.81571834]\n",
            " [ 1.06463667]\n",
            " [-2.85907454]\n",
            " [-1.58773946]\n",
            " [-9.01472019]\n",
            " [ 5.34878138]\n",
            " [-0.78723376]]\n",
            "\n",
            "j = 5.247071909588735\n",
            "Gradient Vector: \n",
            "[[ -0.23122001]\n",
            " [-18.14184252]\n",
            " [-18.17134689]\n",
            " [-29.71148295]]\n",
            "Gradient Vector Norm: 39.27021745971327\n",
            "theta_new : [[0.64943723]\n",
            " [0.63924019]\n",
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            " [0.74338849]]\n",
            "****************** Epoch 136 ****************** \n",
            "Error Vector: \n",
            "[[ 1.97804845]\n",
            " [ 0.23483916]\n",
            " [ 2.35683569]\n",
            " [ 2.72002172]\n",
            " [-0.64813357]\n",
            " [ 3.68875013]\n",
            " [ 0.08961913]\n",
            " [-4.06600603]\n",
            " [-1.55813575]\n",
            " [-2.88620257]\n",
            " [ 2.57056815]\n",
            " [ 0.77132556]\n",
            " [ 4.20268197]\n",
            " [ 4.32671262]\n",
            " [ 1.83587356]\n",
            " [-3.89862111]\n",
            " [ 1.7886587 ]\n",
            " [-4.16329463]\n",
            " [ 2.38041579]\n",
            " [ 1.57014915]\n",
            " [-2.29971693]\n",
            " [-1.03164167]\n",
            " [-8.48274292]\n",
            " [ 5.83133782]\n",
            " [-0.178792  ]]\n",
            "\n",
            "j = 5.228244563489297\n",
            "Gradient Vector: \n",
            "[[ 0.28530202]\n",
            " [23.52340904]\n",
            " [23.71505389]\n",
            " [13.1909996 ]]\n",
            "Gradient Vector Norm: 35.9143205642201\n",
            "theta_new : [[0.64624076]\n",
            " [0.63595078]\n",
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            " [0.74216481]]\n",
            "****************** Epoch 137 ****************** \n",
            "Error Vector: \n",
            "[[ 1.37885939]\n",
            " [-0.47857334]\n",
            " [ 1.65034853]\n",
            " [ 1.95516405]\n",
            " [-1.19498859]\n",
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            " [-2.21843067]\n",
            " [-3.48802474]\n",
            " [ 2.01999529]\n",
            " [ 0.2327452 ]\n",
            " [ 3.46860899]\n",
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            " [ 1.26598955]\n",
            " [-4.61900576]\n",
            " [ 1.1980939 ]\n",
            " [-4.84383639]\n",
            " [ 1.67881163]\n",
            " [ 0.94216231]\n",
            " [-2.9666726 ]\n",
            " [-1.69732685]\n",
            " [-9.12051918]\n",
            " [ 5.21727188]\n",
            " [-0.9210257 ]]\n",
            "\n",
            "j = 5.255132276435399\n",
            "Gradient Vector: \n",
            "[[ -0.33996795]\n",
            " [-26.96420592]\n",
            " [-27.06016698]\n",
            " [-38.72049105]]\n",
            "Gradient Vector Norm: 54.39405338271814\n",
            "theta_new : [[0.65032951]\n",
            " [0.63993682]\n",
            " [0.63704732]\n",
            " [0.74824405]]\n",
            "****************** Epoch 138 ****************** \n",
            "Error Vector: \n",
            "[[ 2.44780697]\n",
            " [ 0.81131491]\n",
            " [ 2.91797742]\n",
            " [ 3.33930694]\n",
            " [-0.21207575]\n",
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            " [ 0.56226388]\n",
            " [-3.70334683]\n",
            " [-1.00646404]\n",
            " [-2.35587258]\n",
            " [ 3.0210984 ]\n",
            " [ 1.22404268]\n",
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            " [ 2.31339744]\n",
            " [-3.30690561]\n",
            " [ 2.2245461 ]\n",
            " [-3.5938323 ]\n",
            " [ 2.9221117 ]\n",
            " [ 2.05512114]\n",
            " [-1.74681692]\n",
            " [-0.48350296]\n",
            " [-7.95892643]\n",
            " [ 6.28578317]\n",
            " [ 0.41285007]]\n",
            "\n",
            "j = 5.4549581166117\n",
            "Gradient Vector: \n",
            "[[ 0.79038223]\n",
            " [64.23643588]\n",
            " [64.63278768]\n",
            " [55.15689782]]\n",
            "Gradient Vector Norm: 106.52053801163208\n",
            "theta_new : [[0.64118992]\n",
            " [0.6307361 ]\n",
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            " [0.74072917]]\n",
            "****************** Epoch 139 ****************** \n",
            "Error Vector: \n",
            "[[  0.46686324]\n",
            " [ -1.56256471]\n",
            " [  0.57582528]\n",
            " [  0.79315408]\n",
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            " [ -5.11138798]\n",
            " [ -3.21973448]\n",
            " [ -4.39764727]\n",
            " [  1.1840542 ]\n",
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            " [  0.61001313]\n",
            " [ -0.01447605]\n",
            " [ -3.97853055]\n",
            " [ -2.70767786]\n",
            " [-10.08864268]\n",
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            " [ -2.04969493]]\n",
            "\n",
            "j = 6.055571434221373\n",
            "Gradient Vector: \n",
            "[[  -1.29004284]\n",
            " [-103.6859511 ]\n",
            " [-104.2218921 ]\n",
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            "Gradient Vector Norm: 188.26340563477763\n",
            "theta_new : [[0.65150141]\n",
            " [0.64100292]\n",
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            "****************** Epoch 140 ****************** \n",
            "Error Vector: \n",
            "[[ 2.88768349]\n",
            " [ 1.34729655]\n",
            " [ 3.44180708]\n",
            " [ 3.91484429]\n",
            " [ 0.1945896 ]\n",
            " [ 4.33352385]\n",
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            " [-3.37181334]\n",
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            " [-1.87225182]\n",
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            " [-3.06853178]\n",
            " [ 3.43119032]\n",
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            " [-1.23573031]\n",
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            " [-7.47369868]\n",
            " [ 6.71728519]\n",
            " [ 0.96468085]]\n",
            "\n",
            "j = 5.908344308991284\n",
            "Gradient Vector: \n",
            "[[  1.26002929]\n",
            " [102.10828731]\n",
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            " [ 94.17170862]]\n",
            "Gradient Vector Norm: 172.75269050726237\n",
            "theta_new : [[0.64336107]\n",
            " [0.63282005]\n",
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            " [0.7449051 ]]\n",
            "****************** Epoch 141 ****************** \n",
            "Error Vector: \n",
            "[[ 1.10049296e+00]\n",
            " [-7.95475681e-01]\n",
            " [ 1.32828079e+00]\n",
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            " [ 6.44155368e-01]\n",
            " [-3.25104614e+00]\n",
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            " [-9.39660381e+00]\n",
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            "\n",
            "j = 5.359600986146877\n",
            "Gradient Vector: \n",
            "[[ -0.6178459 ]\n",
            " [-49.46085724]\n",
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            "Gradient Vector Norm: 93.44661716045971\n",
            "theta_new : [[0.64696739]\n",
            " [0.63637185]\n",
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            " [0.74981578]]\n",
            "****************** Epoch 142 ****************** \n",
            "Error Vector: \n",
            "[[ 2.01553916]\n",
            " [ 0.30738457]\n",
            " [ 2.41284643]\n",
            " [ 2.79986596]\n",
            " [-0.60205726]\n",
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            " [ 4.33413873]\n",
            " [ 1.92161218]\n",
            " [-3.80970255]\n",
            " [ 1.78136029]\n",
            " [-4.0621466 ]\n",
            " [ 2.41067699]\n",
            " [ 1.5974266 ]\n",
            " [-2.20908423]\n",
            " [-0.94727475]\n",
            " [-8.40404716]\n",
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            "\n",
            "j = 5.1784403537247\n",
            "Gradient Vector: \n",
            "[[ 0.34862933]\n",
            " [28.52296169]\n",
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            "Gradient Vector Norm: 44.49313404569253\n",
            "theta_new : [[0.64426162]\n",
            " [0.63360642]\n",
            " [0.63069703]\n",
            " [0.748705  ]]\n",
            "****************** Epoch 143 ****************** \n",
            "Error Vector: \n",
            "[[ 1.50616813]\n",
            " [-0.29943714]\n",
            " [ 1.81211326]\n",
            " [ 2.14928745]\n",
            " [-1.06711532]\n",
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            " [-4.64132017]\n",
            " [ 1.81438387]\n",
            " [ 1.06370134]\n",
            " [-2.77661687]\n",
            " [-1.5136843 ]\n",
            " [-8.94665866]\n",
            " [ 5.3042585 ]\n",
            " [-0.74772271]]\n",
            "\n",
            "j = 5.143012592628833\n",
            "Gradient Vector: \n",
            "[[ -0.18320313]\n",
            " [-14.41875918]\n",
            " [-14.48685421]\n",
            " [-25.65246507]]\n",
            "Gradient Vector Norm: 32.800184278233985\n",
            "theta_new : [[0.64582158]\n",
            " [0.63509718]\n",
            " [0.63218533]\n",
            " [0.75209126]]\n",
            "****************** Epoch 144 ****************** \n",
            "Error Vector: \n",
            "[[ 1.98958717]\n",
            " [ 0.28665625]\n",
            " [ 2.3865497 ]\n",
            " [ 2.77843994]\n",
            " [-0.62146376]\n",
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            " [-4.0701393 ]\n",
            " [ 2.37527279]\n",
            " [ 1.56581161]\n",
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            " [-0.96050107]\n",
            " [-8.41745827]\n",
            " [ 5.78306965]\n",
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            "\n",
            "j = 5.147304875777787\n",
            "Gradient Vector: \n",
            "[[ 0.33038919]\n",
            " [27.00840418]\n",
            " [27.15966373]\n",
            " [17.0075192 ]]\n",
            "Gradient Vector Norm: 41.91021469925965\n",
            "theta_new : [[0.6416671 ]\n",
            " [0.63087433]\n",
            " [0.62796163]\n",
            " [0.75005302]]\n",
            "****************** Epoch 145 ****************** \n",
            "Error Vector: \n",
            "[[ 1.18640112]\n",
            " [-0.67146468]\n",
            " [ 1.43876381]\n",
            " [ 1.75114584]\n",
            " [-1.35532689]\n",
            " [ 3.21715836]\n",
            " [-0.60475998]\n",
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            " [ 1.14820574]\n",
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            " [-3.1171647 ]\n",
            " [-1.85556692]\n",
            " [-9.27481206]\n",
            " [ 4.96269693]\n",
            " [-1.13892745]]\n",
            "\n",
            "j = 5.242421330073107\n",
            "Gradient Vector: \n",
            "[[ -0.50931436]\n",
            " [-40.78659671]\n",
            " [-41.01858764]\n",
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            "Gradient Vector Norm: 78.26038014366539\n",
            "theta_new : [[0.6480255 ]\n",
            " [0.63716715]\n",
            " [0.63425511]\n",
            " [0.75817853]]\n",
            "****************** Epoch 146 ****************** \n",
            "Error Vector: \n",
            "[[ 2.76502597]\n",
            " [ 1.22962334]\n",
            " [ 3.30918451]\n",
            " [ 3.79092562]\n",
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            " [-1.89820138]\n",
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            " [ 3.27355835]\n",
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            " [-1.32226108]\n",
            " [-0.06879148]\n",
            " [-7.56458765]\n",
            " [ 6.54657862]\n",
            " [ 0.82875741]]\n",
            "\n",
            "j = 5.7118070203067655\n",
            "Gradient Vector: \n",
            "[[ 1.15669975]\n",
            " [93.64835899]\n",
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            "Gradient Vector Norm: 158.02148306772082\n",
            "theta_new : [[0.63722134]\n",
            " [0.62633432]\n",
            " [0.6234235 ]\n",
            " [0.74851297]]\n",
            "****************** Epoch 147 ****************** \n",
            "Error Vector: \n",
            "[[  0.37197945]\n",
            " [ -1.64071271]\n",
            " [  0.47868161]\n",
            " [  0.71211605]\n",
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            " [  2.63295942]\n",
            " [  0.3745509 ]\n",
            " [ -5.7717503 ]\n",
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            " [ -5.90987752]\n",
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            " [ -0.12905252]\n",
            " [ -4.02277612]\n",
            " [ -2.75964583]\n",
            " [-10.14094875]\n",
            " [  4.12720103]\n",
            " [ -2.14756631]]\n",
            "\n",
            "j = 6.065608910262796\n",
            "Gradient Vector: \n",
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            " [-109.37899535]\n",
            " [-110.00231264]\n",
            " [-123.23361868]]\n",
            "Gradient Vector Norm: 198.12280146034368\n",
            "theta_new : [[0.64642661]\n",
            " [0.63551019]\n",
            " [0.63260117]\n",
            " [0.75863857]]\n",
            "****************** Epoch 148 ****************** \n",
            "Error Vector: \n",
            "[[ 2.54465687]\n",
            " [ 0.9711643 ]\n",
            " [ 3.05101134]\n",
            " [ 3.51417656]\n",
            " [-0.10495235]\n",
            " [ 4.15324188]\n",
            " [ 0.72428621]\n",
            " [-3.54061474]\n",
            " [-0.81122308]\n",
            " [-2.10599229]\n",
            " [ 3.15932726]\n",
            " [ 1.39047017]\n",
            " [ 4.88209536]\n",
            " [ 4.84044089]\n",
            " [ 2.4858338 ]\n",
            " [-3.12031882]\n",
            " [ 2.24873201]\n",
            " [-3.38975567]\n",
            " [ 3.01354804]\n",
            " [ 2.13728847]\n",
            " [-1.56056586]\n",
            " [-0.30756834]\n",
            " [-7.79360298]\n",
            " [ 6.31443668]\n",
            " [ 0.55797787]]\n",
            "\n",
            "j = 5.4647284247424945\n",
            "Gradient Vector: \n",
            "[[ 0.93016374]\n",
            " [75.34031282]\n",
            " [75.729628  ]\n",
            " [66.84806287]]\n",
            "Gradient Vector Norm: 126.01852247233903\n",
            "theta_new : [[0.64068171]\n",
            " [0.62973337]\n",
            " [0.62682718]\n",
            " [0.75413294]]\n",
            "****************** Epoch 149 ****************** \n",
            "Error Vector: \n",
            "[[ 1.31736217]\n",
            " [-0.49896012]\n",
            " [ 1.60018911]\n",
            " [ 1.93744231]\n",
            " [-1.22888297]\n",
            " [ 3.32791203]\n",
            " [-0.4542685 ]\n",
            " [-4.41155177]\n",
            " [-2.18120374]\n",
            " [-3.36878117]\n",
            " [ 2.02189106]\n",
            " [ 0.27162149]\n",
            " [ 3.38056424]\n",
            " [ 3.58749653]\n",
            " [ 1.30277064]\n",
            " [-4.60973413]\n",
            " [ 1.0529626 ]\n",
            " [-4.80210623]\n",
            " [ 1.58075117]\n",
            " [ 0.85477644]\n",
            " [-2.94208037]\n",
            " [-1.68458852]\n",
            " [-9.11216007]\n",
            " [ 5.07051207]\n",
            " [-0.96735825]]\n",
            "\n",
            "j = 5.13269479510969\n",
            "Gradient Vector: \n",
            "[[ -0.35821696]\n",
            " [-28.65456961]\n",
            " [-28.84355606]\n",
            " [-40.13340212]]\n",
            "Gradient Vector Norm: 57.13014414604367\n",
            "theta_new : [[0.64275774]\n",
            " [0.6317712 ]\n",
            " [0.62886935]\n",
            " [0.75765129]]\n",
            "****************** Epoch 150 ****************** \n",
            "Error Vector: \n",
            "[[ 1.89545041]\n",
            " [ 0.19955255]\n",
            " [ 2.28612189]\n",
            " [ 2.68711869]\n",
            " [-0.69697692]\n",
            " [ 3.72544266]\n",
            " [ 0.1104521 ]\n",
            " [-3.98823462]\n",
            " [-1.52385268]\n",
            " [-2.75314902]\n",
            " [ 2.56436954]\n",
            " [ 0.8094453 ]\n",
            " [ 4.08633539]\n",
            " [ 4.17077504]\n",
            " [ 1.87100525]\n",
            " [-3.89862422]\n",
            " [ 1.60640064]\n",
            " [-4.1239632 ]\n",
            " [ 2.25261486]\n",
            " [ 1.45621706]\n",
            " [-2.28062327]\n",
            " [-1.02666713]\n",
            " [-8.48257259]\n",
            " [ 5.64676689]\n",
            " [-0.24548452]]\n",
            "\n",
            "j = 5.064540253437502\n",
            "Gradient Vector: \n",
            "[[ 0.2539168 ]\n",
            " [20.73044664]\n",
            " [20.80663993]\n",
            " [10.7072359 ]]\n",
            "Gradient Vector Norm: 31.263030206352575\n",
            "theta_new : [[0.64040938]\n",
            " [0.62938197]\n",
            " [0.62648624]\n",
            " [0.75704697]]\n",
            "****************** Epoch 151 ****************** \n",
            "Error Vector: \n",
            "[[ 1.48271498]\n",
            " [-0.29091023]\n",
            " [ 1.79987968]\n",
            " [ 2.16142683]\n",
            " [-1.07332717]\n",
            " [ 3.4536041 ]\n",
            " [-0.2796364 ]\n",
            " [-4.27259054]\n",
            " [-1.97671911]\n",
            " [-3.16424498]\n",
            " [ 2.18623078]\n",
            " [ 0.44022853]\n",
            " [ 3.58039949]\n",
            " [ 3.7449129 ]\n",
            " [ 1.4803063 ]\n",
            " [-4.3932831 ]\n",
            " [ 1.1978649 ]\n",
            " [-4.59052145]\n",
            " [ 1.76879608]\n",
            " [ 1.0231775 ]\n",
            " [-2.73822533]\n",
            " [-1.48368934]\n",
            " [-8.92044677]\n",
            " [ 5.22213175]\n",
            " [-0.75623919]]\n",
            "\n",
            "j = 5.052712619294663\n",
            "Gradient Vector: \n",
            "[[ -0.17592639]\n",
            " [-13.9816707 ]\n",
            " [-14.10464715]\n",
            " [-24.97738492]]\n",
            "Gradient Vector Norm: 31.91126594222461\n",
            "theta_new : [[0.64217323]\n",
            " [0.63110052]\n",
            " [0.62821368]\n",
            " [0.76078223]]\n",
            "****************** Epoch 152 ****************** \n",
            "Error Vector: \n",
            "[[ 2.02827326]\n",
            " [ 0.37007334]\n",
            " [ 2.44796559]\n",
            " [ 2.87098734]\n",
            " [-0.57062942]\n",
            " [ 3.83135302]\n",
            " [ 0.25615354]\n",
            " [-3.86920217]\n",
            " [-1.35279962]\n",
            " [-2.5770914 ]\n",
            " [ 2.70016989]\n",
            " [ 0.95098425]\n",
            " [ 4.24600464]\n",
            " [ 4.29331194]\n",
            " [ 2.01982261]\n",
            " [-3.71936628]\n",
            " [ 1.71723186]\n",
            " [-3.94670559]\n",
            " [ 2.40194983]\n",
            " [ 1.58998138]\n",
            " [-2.11080648]\n",
            " [-0.86004133]\n",
            " [-8.32376077]\n",
            " [ 5.76308695]\n",
            " [-0.07399222]]\n",
            "\n",
            "j = 5.081799402548283\n",
            "Gradient Vector: \n",
            "[[ 0.40331817]\n",
            " [32.74260663]\n",
            " [32.86778416]\n",
            " [23.13511229]]\n",
            "Gradient Vector Norm: 51.84366509721553\n",
            "theta_new : [[0.636735  ]\n",
            " [0.62562324]\n",
            " [0.62274682]\n",
            " [0.75752335]]\n",
            "****************** Epoch 153 ****************** \n",
            "Error Vector: \n",
            "[[ 0.9412284 ]\n",
            " [-0.92891189]\n",
            " [ 1.16426554]\n",
            " [ 1.47808947]\n",
            " [-1.56484379]\n",
            " [ 3.10490475]\n",
            " [-0.78269877]\n",
            " [-4.63374977]\n",
            " [-2.55994275]\n",
            " [-3.68469675]\n",
            " [ 1.69622056]\n",
            " [-0.03436693]\n",
            " [ 2.91526913]\n",
            " [ 3.17992116]\n",
            " [ 0.97770101]\n",
            " [-5.03359502]\n",
            " [ 0.65294707]\n",
            " [-5.19089716]\n",
            " [ 1.13129571]\n",
            " [ 0.45263177]\n",
            " [-3.32883124]\n",
            " [-2.0748489 ]\n",
            " [-9.48718142]\n",
            " [ 4.65624518]\n",
            " [-1.42326138]]\n",
            "\n",
            "j = 5.306605309121953\n",
            "Gradient Vector: \n",
            "[[ -0.73508424]\n",
            " [-59.15945123]\n",
            " [-59.55020722]\n",
            " [-71.38664058]]\n",
            "Gradient Vector Norm: 110.19374143711883\n",
            "theta_new : [[0.64533267]\n",
            " [0.63419165]\n",
            " [0.63132498]\n",
            " [0.76750775]]\n",
            "****************** Epoch 154 ****************** \n",
            "Error Vector: \n",
            "[[ 3.01040208]\n",
            " [ 1.55997428]\n",
            " [ 3.61465938]\n",
            " [ 4.14835322]\n",
            " [ 0.33431367]\n",
            " [ 4.51136498]\n",
            " [ 1.22070112]\n",
            " [-3.1429964 ]\n",
            " [-0.22962363]\n",
            " [-1.5200971 ]\n",
            " [ 3.62537023]\n",
            " [ 1.87044474]\n",
            " [ 5.44423362]\n",
            " [ 5.28053647]\n",
            " [ 2.99107554]\n",
            " [-2.5061775 ]\n",
            " [ 2.6521812 ]\n",
            " [-2.78767553]\n",
            " [ 3.54176172]\n",
            " [ 2.61035074]\n",
            " [-0.98130703]\n",
            " [ 0.2626519 ]\n",
            " [-7.24958729]\n",
            " [ 6.73692096]\n",
            " [ 1.1541896 ]]\n",
            "\n",
            "j = 5.996595663768186\n",
            "Gradient Vector: \n",
            "[[  1.44608084]\n",
            " [116.85616229]\n",
            " [117.42812183]\n",
            " [109.74780323]]\n",
            "Gradient Vector Norm: 198.72442709320518\n",
            "theta_new : [[0.63419619]\n",
            " [0.62304288]\n",
            " [0.6201816 ]\n",
            " [0.75729092]]\n",
            "****************** Epoch 155 ****************** \n",
            "Error Vector: \n",
            "[[ 0.52767329]\n",
            " [-1.4187798 ]\n",
            " [ 0.67772074]\n",
            " [ 0.95320129]\n",
            " [-1.94132373]\n",
            " [ 2.83482293]\n",
            " [-1.17100597]\n",
            " [-4.91516371]\n",
            " [-3.01054422]\n",
            " [-4.09110348]\n",
            " [ 1.31910394]\n",
            " [-0.40147026]\n",
            " [ 2.40790956]\n",
            " [ 2.7513487 ]\n",
            " [ 0.58914623]\n",
            " [-5.52672543]\n",
            " [ 0.24094321]\n",
            " [-5.6549311 ]\n",
            " [ 0.64569577]\n",
            " [ 0.01801432]\n",
            " [-3.7844874 ]\n",
            " [-2.53033322]\n",
            " [-9.92365831]\n",
            " [ 4.22818303]\n",
            " [-1.93416133]]\n",
            "\n",
            "j = 5.72463517241441\n",
            "Gradient Vector: \n",
            "[[  -1.164397  ]\n",
            " [ -93.83545752]\n",
            " [ -94.42760915]\n",
            " [-107.02405374]]\n",
            "Gradient Vector Norm: 170.813261658096\n",
            "theta_new : [[0.64130102]\n",
            " [0.63013153]\n",
            " [0.62727847]\n",
            " [0.76544999]]\n",
            "****************** Epoch 156 ****************** \n",
            "Error Vector: \n",
            "[[ 2.23192948]\n",
            " [ 0.63088764]\n",
            " [ 2.69584697]\n",
            " [ 3.15221685]\n",
            " [-0.37721904]\n",
            " [ 3.99283111]\n",
            " [ 0.47863251]\n",
            " [-3.68792343]\n",
            " [-1.09175774]\n",
            " [-2.30921621]\n",
            " [ 2.90771868]\n",
            " [ 1.16690784]\n",
            " [ 4.49093696]\n",
            " [ 4.4818187 ]\n",
            " [ 2.24693556]\n",
            " [-3.44548393]\n",
            " [ 1.88804488]\n",
            " [-3.67613379]\n",
            " [ 2.63119396]\n",
            " [ 1.79532253]\n",
            " [-1.85146611]\n",
            " [-0.60550385]\n",
            " [-8.08107758]\n",
            " [ 5.94235954]\n",
            " [ 0.18857456]]\n",
            "\n",
            "j = 5.153705471637841\n",
            "Gradient Vector: \n",
            "[[ 0.63185504]\n",
            " [51.11960416]\n",
            " [51.3207238 ]\n",
            " [42.14482661]]\n",
            "Gradient Vector Norm: 83.80701803323593\n",
            "theta_new : [[0.63736238]\n",
            " [0.62617641]\n",
            " [0.62333349]\n",
            " [0.76284883]]\n",
            "****************** Epoch 157 ****************** \n",
            "Error Vector: \n",
            "[[ 1.42858186]\n",
            " [-0.32994302]\n",
            " [ 1.74680529]\n",
            " [ 2.12186292]\n",
            " [-1.11233112]\n",
            " [ 3.45473841]\n",
            " [-0.29042704]\n",
            " [-4.25474102]\n",
            " [-1.98554937]\n",
            " [-3.1306597 ]\n",
            " [ 2.16484368]\n",
            " [ 0.43720149]\n",
            " [ 3.50769372]\n",
            " [ 3.65994266]\n",
            " [ 1.47526472]\n",
            " [-4.41806303]\n",
            " [ 1.10285464]\n",
            " [-4.59739298]\n",
            " [ 1.69256703]\n",
            " [ 0.95516204]\n",
            " [-2.75309702]\n",
            " [-1.50457415]\n",
            " [-8.94204729]\n",
            " [ 5.12571621]\n",
            " [-0.80904869]]\n",
            "\n",
            "j = 4.998787395385937\n",
            "Gradient Vector: \n",
            "[[ -0.21018559]\n",
            " [-16.8540351 ]\n",
            " [-17.03316217]\n",
            " [-27.77157904]]\n",
            "Gradient Vector Norm: 36.68094727332382\n",
            "theta_new : [[0.63859834]\n",
            " [0.62739423]\n",
            " [0.6245648 ]\n",
            " [0.76565847]]\n",
            "****************** Epoch 158 ****************** \n",
            "Error Vector: \n",
            "[[ 1.8279472 ]\n",
            " [ 0.15420282]\n",
            " [ 2.22134488]\n",
            " [ 2.64164288]\n",
            " [-0.74425242]\n",
            " [ 3.73168973]\n",
            " [ 0.10229839]\n",
            " [-3.95873526]\n",
            " [-1.52822123]\n",
            " [-2.69977528]\n",
            " [ 2.54140528]\n",
            " [ 0.81163397]\n",
            " [ 3.9948395 ]\n",
            " [ 4.06099565]\n",
            " [ 1.8707863 ]\n",
            " [-3.92425695]\n",
            " [ 1.48248503]\n",
            " [-4.12539837]\n",
            " [ 2.15588156]\n",
            " [ 1.36992973]\n",
            " [-2.29323877]\n",
            " [-1.04757953]\n",
            " [-8.50480248]\n",
            " [ 5.52119042]\n",
            " [-0.30947351]]\n",
            "\n",
            "j = 4.97079289677094\n",
            "Gradient Vector: \n",
            "[[ 0.21410158]\n",
            " [17.36939857]\n",
            " [17.37162609]\n",
            " [ 7.47068219]]\n",
            "Gradient Vector Norm: 25.67735055885828\n",
            "theta_new : [[0.63629272]\n",
            " [0.62507137]\n",
            " [0.62225865]\n",
            " [0.76523356]]\n",
            "****************** Epoch 159 ****************** \n",
            "Error Vector: \n",
            "[[ 1.43971237]\n",
            " [-0.30658681]\n",
            " [ 1.76420296]\n",
            " [ 2.14784876]\n",
            " [-1.09807657]\n",
            " [ 3.47681947]\n",
            " [-0.26365792]\n",
            " [-4.22485445]\n",
            " [-1.95304362]\n",
            " [-3.08440961]\n",
            " [ 2.18637322]\n",
            " [ 0.4653849 ]\n",
            " [ 3.51875663]\n",
            " [ 3.65967349]\n",
            " [ 1.50438836]\n",
            " [-4.38862748]\n",
            " [ 1.09714105]\n",
            " [-4.562926  ]\n",
            " [ 1.70045599]\n",
            " [ 0.96231232]\n",
            " [-2.72258992]\n",
            " [-1.4765726 ]\n",
            " [-8.91581919]\n",
            " [ 5.1207682 ]\n",
            " [-0.78961231]]\n",
            "\n",
            "j = 4.970004264776843\n",
            "Gradient Vector: \n",
            "[[ -0.18971755]\n",
            " [-15.24372899]\n",
            " [-15.42945429]\n",
            " [-26.05223864]]\n",
            "Gradient Vector Norm: 33.89977085410022\n",
            "theta_new : [[0.63845343]\n",
            " [0.62721581]\n",
            " [0.62442487]\n",
            " [0.76949168]]\n"
          ]
        }
      ],
      "source": [
        "theta, cost_vals, thetas, h_s = adam(X2, y2, alpha=0.01, epsilon=1e-08, beta1=0.2, beta2=0.7, epochs=500)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "rRgX70_bL6Pv",
      "metadata": {
        "id": "rRgX70_bL6Pv"
      },
      "source": [
        "## Plot loss"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 41,
      "id": "Dl_DdXIBL_6B",
      "metadata": {
        "id": "Dl_DdXIBL_6B"
      },
      "outputs": [],
      "source": [
        "def plot_loss_iter(losses, epochs, f_size):\n",
        "  plt.figure(figsize=f_size)\n",
        "  plt.plot(losses, epochs, marker='*')\n",
        "  plt.xlabel('Iterations')\n",
        "  plt.ylabel('Loss')\n",
        "  plt.title(\"plot loss vs iterations\")\n",
        "  plt.show()\n",
        "\n",
        "def plot_loss_theta(losses, thetas, alpha, i):\n",
        "  plt.figure(figsize=(10, 10))\n",
        "  plt.plot(thetas, losses, marker='*')\n",
        "  plt.xlabel(f'Theta {i}')\n",
        "  plt.ylabel('Loss')\n",
        "  plt.title(f\"Learning Rate = {alpha}\")\n",
        "  plt.show()\n",
        "\n",
        "def plot_loss(cost_vals, thetas, alpha, f_size=(10, 10)):\n",
        "  plot_loss_iter(np.arange(len(cost_vals)), cost_vals, f_size)\n",
        "  n = thetas[0].shape[0]\n",
        "  for i in range(n):\n",
        "    plot_loss_theta(cost_vals, np.array(thetas)[:, i], alpha, i)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 49,
      "id": "j40-a0T7L1AG",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "j40-a0T7L1AG",
        "outputId": "b2cfedf3-7ca4-4cd4-f3db-d4d1a1181f87"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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w5TMPYum6Rq65b17W5UiSpIxlOabuQ8Dk/OO9gIVtnluUb9tR++7A6jYBsbV9uyLigohoiIiGZcuWdVL52Ttm+EDefsgQfvb3uaxY35h1OZIkKUOZhLqI+ArQBPy6Oz4vpXRVSqk+pVQ/ePDg7vjIbjPh9IN4eUsz/+/uOVmXIkmSMtTtoS4iPgD8CzAupfwWCbAYGNbmtL3zbTtqXwH0j4iKbdpLzgF1u3Fe/TAmPTSfsT++j6XrNmVdkiRJykC3hrqIOB2YAJydUtrY5qmbgfdERFVE7AuMBB4GpgEj8zNde5GbTHFzPgzeA7w7//rzgZu663sUms+eOpKU4PFFa7jiztlZlyNJkjLQZTtKRMQNwEnAoIhYBFxKbrZrFXBHfieEh1JKH00pPR0RvwNmkLst+4mUUnP+fS4EbgPKgWtSSk/nP+Ii4MaIuAx4FLi6q75LIRt1yWQam15Zq27S1AVMmrqAqooyZl52RoaVSZKk7hSv3AEtDfX19amhoSHrMjrN0rWbuOzWZ7j96ZfYtKWFsoCzjhzKV95xMHU11VmXJ0mSdkFETE8p1bfnXHeU6OHqaqupqaqgsamFirKgJcGqDZsNdJIklRhDXRFYvr6RcccN58+fOIH+vSuZNn8ljU3NWZclSZK6kaGuCEwcX89l5xzGYXv144r3HsXLW1r41YPPZ12WJEnqRoa6IvOWAwdz0qjB/Oiu2azcsDnrciRJUjcx1BWhr5x5MBs3N3PFXS5vIklSqTDUFaGRQ2p4zxuGMemh53lu2fqsy5EkSd3AUFekPvu2A6muLOe/b30261IkSVI3MNQVqUG7VfGJMQdw5zNLeOC55VmXI0mSupihroh98IQR7NW/N5f99RmaW0prkWlJkkqNoa6IVVeWc9EZBzHjxbVce/88zpv4IEvXbcq6LEmS1AUMdUXurCP25Kh9+vO922cybf5KrrjTGbGSJBWjiqwLUNc66Kt/o7GpZevxpKkLmDR1AVUVZcy87IwMK5MkSZ3JnroiN2XCGM4ePZSyyB1XVZQxdvRQplw0JtvCJElSpzLUFbm62mpqqipI+XkSjU0t1FRVUFdTnW1hkiSpUxnqSsDy9Y2MO3447z56LwCeW7Yh44okSVJnc0xdCZg4vh6ANS9v4e6ZywBIKRERWZYlSZI6kT11JaRf70o+e+pIHpy7gjufWZp1OZIkqRMZ6krMe4/dh/0H9+W/b32GLc0tO3+BJEnqEQx1JaaivIyvvONg5i7fwK8fej7rciRJUicx1JWgMaPqOPGAQfzwrtms2bgl63IkSVInMNSVoIjgy2cezJqXt/Dje9xhQpKkYmCoK1GHDK3lvGOGce0D83l+hUucSJLU0xnqStjn334gleVlfP3mpzlv4oMsXbcp65IkSdLrZKgrYXW11Xz0rftzz8xlTJu3kivu9FasJEk9lYsPl7BRl0ymsSm3rEkCJk1dwKSpC6iqKGPmZWdkW5wkSeoQe+pK2JQJYzh79FAqy3M7S1SWB2NHD2XKRWMyrkySJHWUoa6E1dVWU1NVQVNLIoAtzYnqinLqaqqzLk2SJHWQoa7ELV/fyLjjhvOD844E4OH5KzKuSJIkvR6OqStxE8fXb31835zl/PXxF3l+xQaG7943w6okSVJH2VOnrS46/SAqyoNv3fJM1qVIkqQOMtRpqyG11Vx48gHcPmMJ981ennU5kiSpAwx1epUPnbAv+wzsw3/95WmamluyLkeSJLWToU6vUl1ZziXvOJjZS9fz66kLsi5HkiS1k6FO/+RthwzhxAMG8b93zGLVhs1ZlyNJktrBUKd/EhF87axDWN/YxP/eMSvrciRJUjsY6rRdBw6pYfzxw/n11Oe5f85yzpv4IEvXbcq6LEmStAOGOu3QZ04dSb/elXzut48xbf5KrrhzdtYlSZKkHXDxYe3Qcd++i8amV2bATpq6gElTF1BVUcbMy87IsDJJkrQte+q0Q1MmjOGsI/Yk8sfVlWWMHT2UKReNybQuSZL0zwx12qG62mpqe1duPd60pYWaqgrqaqozrEqSJG2PoU6vafn6RsYdP5wT9t+d8oCFqzZmXZIkSdoOx9TpNU0cXw/AwpUbOeV//07/Pr0yrkiSJG2PPXVql2ED+/Cfb9mPmx57gYb5K7MuR5IkbcNQp3b72En7s0dtNf/1lxm0tKSsy5EkSW0Y6tRufXpV8KUzD+LJxWv4w/RFWZcjSZLaMNSpQ84+cijHDB/A/9z2LOs2bcm6HEmSlGeoU4dEBJeedQgrNmzm/909J+tyJElSnqFOHXbE3v3512P25pf3z2PusvVZlyNJkjDU6XX6wmmjqKoo56s3PcV5Ex9k6bpNWZckSVJJM9TpdamrqeZTpxzA/XNWMG3eSq64c3bWJUmSVNJcfFivy6hLJtPY1AJAAiZNXcCkqQuoqihj5mVnZFucJEklyJ46vS5TJozh7NFD6VWe+xWqKAvGjh7KlIvGZFyZJEmlyVCn16Wutpqaqgq2tLRQFtDUkiiL3G1ZSZLU/Qx1et2Wr29k3HHDufr8N1AW8OBzK7IuSZKkkuWYOr1uE8fXb338qVNG8sM7Z3P/nOWccMCgDKuSJKk02VOnTvHRt+7PPgP7cOnNT7M5P4FCkiR1H0OdOkV1ZTmXnnUIc5au55f3z8u6HEmSSo6hTp3mlIOHcOrBdfzortm8uOblrMuRJKmkGOrUqS4961CaWxLfuuWZrEuRJKmkGOrUqYYN7MPHTtqfvz7xIg/MWZ51OZIklQxDnTpd66SJrzlpQpKkbmOoU6drO2nix3fP5ryJD7J03aasy5IkqagZ6tQlWidN/OTeOUybv5Ir7pyddUmSJBU1Fx9Wlxh1yWQa29x6nTR1AZOmLqCqooyZl52RYWWSJBUne+rUJaZMGMPZo4dSURYA9CovY+zooUy5aEzGlUmSVJy6LNRFxDURsTQinmrTNjAi7oiI2fn/Dsi3R0RcERFzIuKJiDi6zWvOz58/OyLOb9N+TEQ8mX/NFRERXfVd1HF1tdXUVFXQnBIAm5tb6NurnLqa6owrkySpOHVlT921wOnbtF0M3JVSGgnclT8GOAMYmf+5APgp5EIgcClwHHAscGlrEMyf85E2r9v2s5Sx5esbGXfccL5+1iEANDy/KuOKJEkqXl02pi6l9I+IGLFN81jgpPzj64B7gYvy7denlBLwUET0j4g98+fekVJaCRARdwCnR8S9QG1K6aF8+/XAOcDkrvo+6riJ4+u3Pp4yezkPzV3BS2s2sUc/e+skSeps3T2mbkhK6cX845eAIfnHewEL25y3KN/2Wu2LttO+XRFxQUQ0RETDsmXLdu0b6HW59KxD2dKS+Nat7jQhSVJXyGyiRL5XLnXTZ12VUqpPKdUPHjy4Oz5S29hn9z587K3785fHX+CB59xpQpKkztbdoW5J/rYq+f8uzbcvBoa1OW/vfNtrte+9nXYVsI+dtD/DBvbm0pueZkuzO01IktSZujvU3Qy0zmA9H7ipTfv787NgjwfW5G/T3ga8PSIG5CdIvB24Lf/c2og4Pj/r9f1t3ksFqrqynEv/5VBmL13PtffPz7ocSZKKSlcuaXID8CAwKiIWRcSHge8Ab4uI2cCp+WOAW4G5wBzg58DHAfITJL4JTMv/fKN10kT+nF/kX/McTpLoEU49ZAinHFTHD++cxZK1bh0mSVJniZS6ZVhbwaivr08NDQ1Zl1HSFqzYyKmX/52TDhzM6pe38OP3HeX6dZIkbUdETE8p1e/8THeUUAZaJ03cPmMJ0+a5L6wkSZ3BvV/V7druC5twX1hJkjqDPXXqdq37wvYqz+3sVlEW7gsrSdIuMtSp27XuC7ulJVEW0NSSCHBcnSRJu8BQp0y07gt77QffQEUZ3DdnOaU2aUeSpM7kmDplou2+sF8+8xC+8dcZ3PrkS7zjiD0zrEqSpJ7Lnjpl7vw3jeCwvWr5r788zdpNW7IuR5KkHslQp8yVlwXfPvdwlq1v5Ae3zcy6HEmSeiRDnQrCEXv35/3HD+f6h57n8YWrsy5HkqQex1CngvH500YxeLcqvvynJ2lqbsm6HEmSehRDnQpGbXUll551KE+/sJbrH3w+63IkSepRDHUqKGcevgcnjRrMD26fyZOLV3PexAdZum5T1mVJklTwDHUqKBHBN8ceRnNKfHzSI0yb796wkiS1h+vUqeCc+r9/p7GphYWrXgbcG1aSpPawp04FZ8qEMZx1xJ5E/ri6ssy9YSVJ2glDnQpOXW01tb0rtx5v2tJCTVWFe8NKkvQaDHUqSMvXNzLu+OG8/ZAhAMxdviHjiiRJKmyOqVNBat0bdtWGzTQ8/3de3tJMS0uirCx28kpJkkqTPXUqaAP69uIrZx7MowtWc8O0BVmXI0lSwTLUqeC98+i9eON+u/Pdyc+ybF1j1uVIklSQDHUqeBHBZecexqYtLXzrlhlZlyNJUkEy1KlH2H/wbnz0rfvx58de4L7Zy7MuR5KkgmOoU4/x8TEHMGL3Pnz1pqfYtKU563IkSSoohjr1GNWV5Vx2zuHMW76B7902031hJUlqw1CnHuXEkYMYO3oov7xvHtPmuS+sJEmtXKdOPcqoSybT2NSy9dh9YSVJyrGnTj3KlAljOHv0UCrLc4sQV5aH+8JKkoShTj1MXW01NVUVNLUkImBLc6K8LNwXVpJU8gx16nGWr29k3HHDuWp8PWWBS5xIkoRj6tQDte4LC/CF00bxP3+byd+eepHTD9szw6okScqWPXXq0T7y5v04ZM9avnrT06x5eUvW5UiSlBlDnXq0yvIyvvuuI1ixvpH/vvWZrMuRJCkzhjr1eIfv3Y+PvHk/bpy2kAeec3ydJKk0GepUFD5z6oEM370PX/7jk24hJkkqSYY6FYXevcr573MPZ/6KjXzrlmfcQkySVHIMdSoabzpgEOfV782vHnreLcQkSSXHJU1UNNpuIZZwCzFJUmmxp05FY9stxCrK3EJMklQ6DHUqGm23ECsLaGpJpJTcQkySVBIMdSoqrVuIXffBY6ksC6bMXk5KKeuyJEnqcoY6FZWJ4+u57JzDePOBg/mvsYexauMWftewMOuyJEnqcoY6Fa33vGEYx+47kG/d8gxL17q8iSSpuBnqVLTKyoLvvPNwNjW1cOnNT2ddjiRJXcpQp6K23+Dd+PQpI5n81Ev87amXsi5HkqQuY6hT0bvgLftx8J61fO2mp1jz8pasy5EkqUsY6lT0KsvL+O67Dmf5+ka+M/nZrMuRJKlLGOpUEo7Yuz8fPnFfbnh4AZOfetG9YSVJRcdQp5LxubeNYp+BfZjw+yeYNt+9YSVJxcW9X1UyRn/j9q17w4J7w0qSios9dSoZrXvD5reGpaqizL1hJUlFw1CnktG6N2xrX11jUwt9epW7N6wkqSgY6lRSWveG/frZhwAwde7KjCuSJKlzOKZOJWXi+Pqtj59YuIabHn+Bpxav4bC9+mVYlSRJu86eOpWsr511CAP79uKLf3iCzW0mUEiS1BMZ6lSy+vfpxbfOOYxnXlzLT+99LutyJEnaJYY6lbS3H7oHZx85lB/fM5tnX1qbdTmSJL1uhjqVvK+ffSj9elfyxd8/QVOzt2ElST2ToU4lb2DfXnxj7GE8uXgNP7hjlluISZJ6JEOdBJx5+J6cefgeTLz3OabNcwsxSVLP45ImEjDqksluISZJ6tHsqZN4ZQuxyvweYhVl4RZikqQexVAn8coWYk0tibKAppZEc3NyCzFJUo9hqJPyWrcQm/Qfx1FVUcY/Zi9ji7NhJUk9hKFOyps4vp7LzjmMN+0/iMv/bTRrNzXxMxclliT1EJmEuoj4bEQ8HRFPRcQNEVEdEftGxNSImBMRv42IXvlzq/LHc/LPj2jzPl/Kt8+MiNOy+C4qTmcevidnHTmUK+6ezYwXXJRYklT4uj3URcRewKeA+pTSYUA58B7gu8DlKaUDgFXAh/Mv+TCwKt9+ef48IuKQ/OsOBU4HroyI8u78Lipu3zj7UPr17sUXfv+4e8NKkgpeVrdfK4DeEVEB9AFeBE4G/pB//jrgnPzjsflj8s+fEhGRb78xpdSYUpoHzAGO7Z7yVQoG9O3Ft889jBkvruUn98zJuhxJkl5Tt4e6lNJi4PvAAnJhbg0wHVidUmrKn7YI2Cv/eC9gYf61Tfnzd2/bvp3XvEpEXBARDRHRsGzZss79Qipqbz90D849ai9+cs8cnlq8JutyJEnaoSxuvw4g18u2LzAU6Evu9mmXSSldlVKqTynVDx48uCs/SkXo0rMOYWDfXnz+d4+zcNUGtxGTJBWkLG6/ngrMSyktSyltAf4InAD0z9+OBdgbWJx/vBgYBpB/vh+wom37dl4jdZr+fXrxnXcdzswl6/jYrx5h2ny3EZMkFZ4sQt0C4PiI6JMfG3cKMAO4B3h3/pzzgZvyj2/OH5N//u6UUsq3vyc/O3ZfYCTwcDd9B5WYj016BICnXlhLSrltxEZcfAujLpmccWWSJOVkMaZuKrkJD48AT+ZruAq4CPhcRMwhN2bu6vxLrgZ2z7d/Drg4/z5PA78jFwj/BnwipdTcjV9FJWTKhDGcedgeW4+rK8vcRkySVFAqdn5K50spXQpcuk3zXLYzezWltAn41x28z7eAb3V6gdI26mqrGdC3FwEkYNOWFmqqKtxGTJJUMNxRQmqn5esbGXf8cM46Yk8AZi5Zl3FFkiS9IpOeOqknmji+HoCXNzfz1AtreWH1JtZu2kJtdWXGlUmSZE+d1GG9e5Xzg/OO5MU1L/PNv8zIuhxJkgBDnfS6HL3PAD520v78fvoi7pixJOtyJEky1Emv16dPOZCD96zlS398ghXrG7MuR5JU4gx10uvUq6KMy//tSNa+3MQlf36K3PKJkiRlw1An7YKD9qjls287kMlPvcT1Dz7vFmKSpMwY6qRddMFb9uOY4QO47JYZbiEmScqMS5pIu+iQr/2NxqaWrceTpi5g0tQFVFWUMfOyMzKsTJJUSuypk3bRlAljOHv0UCrLA4CK8nALMUlStzPUSbuorraamqoKmloSZQFNzYmWluQWYpKkbmWokzrB8vWNjDtuOL/68HFUVZRx76xlbG5zS1aSpK5mqJM6wcTx9Vx2zmGccMAg/t97j2LdpiZ+eOesrMuSJJUQQ53Uyd5+6B78W/0wfvb355g2f2XW5UiSSoShTuoCXz3rEPYe0IfP/vYx1m3aknU5kqQSYKiTusBuVRVc/m9H8sLql/nGX2ZkXY4kqQQY6qQucszwgXz8pAP4/fRF/PbhBe42IUnqUoY6qQt9+tSRHL5XP75601PuNiFJ6lLuKCF1ocMuvc3dJiRJ3cKeOqkLbbvbRKW7TUiSuoihTupC2+42saU50exuE5KkLmCok7rYP+02MXMZm7Y0Z12WJKnIGOqkLtZ2t4mf/fsxrG9s4nu3zcy6LElSkTHUSd1ozEF1nP/G4Vx93zz+MWtZ1uVIkoqIoU7qZl8682AOHLIbn//946xY35h1OZKkImGok7pZdWU5P3rPUazZuIWL/u9JUkpZlyRJKgKGOikDB+9Zy0VnHMSdzyzhNw8vyLocSVIRMNRJGfngm0bw5pGD+OZfZzB17gq3EZMk7RJDnZSRsrLgB/96JL0ry/nopOluIyZJ2iVuEyZl6M3/c4/biEmSOoU9dVKGWrcRKy/LbSPWq7zMbcQkSa+LoU7KUOs2Yi0pEcDm5hYqysJtxCRJHWaokzLWuo3Ylf9+NGUB985aRkuLy5xIkjrGUCdlrHUbsTMO25NvnnMYK9Zv5ur75mVdliSph2lXqIuIvhFRln98YEScHRGVXVuaVHred+w+nH7oHvzPbc/yxKLVWZcjSepB2ttT9w+gOiL2Am4HxgPXdlVRUqmKCL7zrsMZvFsVn7rhUdY3NmVdkiSph2hvqIuU0kbgncCVKaV/BQ7turKk0tW/Ty9++J6jWLByI1+76amsy5Ek9RDtDnUR8UZgHHBLvq28a0qSdOy+A/nkySP54yOLue6B+e42IUnaqfaGus8AXwL+lFJ6OiL2A+7psqok8cmTD+ANIwbwzb/OYNo8d5uQJL22SKljSyfkJ0zsllJa2zUlda36+vrU0NCQdRnSTo26ZPKrdpto5W4TklQ6ImJ6Sqm+Pee2d/brbyKiNiL6Ak8BMyLii7tSpKTX1rrbRGV5breJ8rJwtwlJ0g619/brIfmeuXOAycC+5GbASuoirbtNNLUkygOaWxJrNm5xtwlJ0na1N9RV5telOwe4OaW0BXDJe6mLte428X8fexMD+lRy35zlvLD65azLkiQVoPaGuonAfKAv8I+IGA70yDF1Uk/SutvE6H0G8MePn0BVRRmfvvFRmpr/eaydJKm0tSvUpZSuSCntlVI6M+U8DziwR+pG+w7qy7ffeTjT5q/ih86ElSRto70TJfpFxP9GREP+5wfkeu0kdaOxo/fi3+qH8ZN753Df7OVZlyNJKiDtvf16DbAOOC//sxb4ZVcVJWnHvn72oRwweDc+89vHXJBYkrRVe0Pd/imlS1NKc/M//wXs15WFSdq+3r3K+cm4o1nfuIVP/PoRzvvZA4Y7SVK7Q93LEXFi60FEnAA4BU/KyIFDavj6WYcybf4qHp6/yt0mJElUtPO8jwLXR0S//PEq4PyuKUnSzmy728SkqQuYNHWBu01IUglr7+zXx1NKRwJHAEeklI4CTu7SyiTtUOtuE9UVr/wRPv3QPdxtQpJKWHtvvwKQUlrbZs/Xz3VBPZLaoXW3icbmFnrltxF7bOEqdu9blXFlkqSsdCjUbSM6rQpJHda628SfP3Eix+87kJfWNvL/7nZsnSSVqvaOqdsetwmTMjRxfP3WxzdccDyf/93j/Oiu2bxhxEBOOGBQhpVJkrLwmj11EbEuItZu52cdMLSbapS0ExHBZecexgGDd+PTNz7K0rUucSJJpeY1Q11KqSalVLudn5qU0q708knqZH16VXDluKPZ0NjMJ29wf1hJKjW7MqZOUoEZOaSGb517GFPnreTyO2exdO0mzpv4oIsTS1IJMNRJReadR++d2x/2nue46P+eYNr8lS5OLEklwFuoUhH682OLAbhn5jLAxYklqRTYUycVoSkTxnDKQXVbj6sryxg7eqiLE0tSETPUSUWorraaPfpVb11MctOWFmqqKqirqc60LklS1zHUSUVq+fpGxh0/nHNG51YfemLxmowrkiR1JcfUSUWqdXHiLc0tLFr1MjNeXMvsJesYOaQm48okSV3BnjqpyFWWl/GTcUfTp1c5H500nfWNTVmXJEnqAoY6qQQMqa3mivcexbzlG7j4/54gJXf5k6Rik0moi4j+EfGHiHg2Ip6JiDdGxMCIuCMiZuf/OyB/bkTEFRExJyKeiIij27zP+fnzZ0fE+Vl8F6mneNP+g/jiaQfx1yde5NoH5mddjiSpk2XVU/cj4G8ppYOAI4FngIuBu1JKI4G78scAZwAj8z8XAD8FiIiBwKXAccCxwKWtQVDS9n30rftx6sFD+NYtz3DnjJfcbUKSiki3h7qI6Ae8BbgaIKW0OaW0GhgLXJc/7TrgnPzjscD1KechoH9E7AmcBtyRUlqZUloF3AGc3m1fROqBIoIfnHckQ/v35pM3POpuE5JURLKY/bovsAz4ZUQcCUwHPg0MSSm9mD/nJWBI/vFewMI2r1+Ub9tR+z+JiAvI9fKxzz77dM63kHqoY791J41NLVuP3W1CkopDFrdfK4CjgZ+mlI4CNvDKrVYAUm4Ud6eN5E4pXZVSqk8p1Q8ePLiz3lbqkaZMGMPZo4dSWZ5bmri8LNxtQpKKQBahbhGwKKU0NX/8B3Ihb0n+tir5/y7NP78YGNbm9Xvn23bULuk11NVWU1NVQVNLojyguSWxcv1md5uQpB6u20NdSuklYGFEjMo3nQLMAG4GWmewng/clH98M/D+/CzY44E1+du0twFvj4gB+QkSb8+3SdqJ5esbGXfccP748RMYtFsv7n9uObOWrMu6LEnSLogs1quKiNHAL4BewFzgg+QC5u+AfYDngfNSSisjIoAfk5sEsRH4YEqpIf8+HwK+nH/bb6WUfrmzz66vr08NDQ2d+4WkHmzJ2k2844r7qKmu4KYLT6C2ujLrkiRJeRExPaVU365zS20RUkOd9M8enreS9/38IU4aVcdV44+hrCyyLkmSRMdCnTtKSOLYfQdyyTsO5s5nlnDlvXOyLkeS9DoY6iQBcP6bRnDuUXvxgztm8edHF7kwsST1MIY6SUBuYeJvn3s4B+1Ry4Q/PMG0eS5MLEk9SRaLD0sqUKO/cbsLE0tSD2VPnaStWhcm7lWe+6uhPHBhYknqIQx1krZqXZh4S0sL5WVBc4IFKza6MLEk9QCGOkmv0row8c0XnsDw3fvw6MLV3Dtz6c5fKEnKlOvUSdqhjZubeOeVD/DC6pe5+cITGTGob9YlSVJJcZ06SZ2iT68Kfv7+esrLgo9c38D6xqasS5Ik7YChTtJrGjawDz9+39HMXb6Bz/32MVpaSqt3X5J6CkOdpJ064YBBfPnMg7l9xhL+391zWLp2k4sTS1KBMdRJapcPnTCCdx61F5ffOYsv/uEJps13cWJJKiQuPiypXSKCW558EYC/z1oGuDixJBUSe+oktduUCWN42yFDth5XV5S5OLEkFQhDnaR2q6utpq6misgfb2pqoW+vchcnlqQCYKiT1CHL1zcy7vjhfPbUkQDcN3t5xhVJksAxdZI6aOL4V9bAXLepiV/cN4/fTF3A+47bJ8OqJEn21El63b505sG89cDBfO2mp3ho7oqsy5Gkkmaok/S6lZcFV7z3KPbZvQ8fmzSdhSs3Zl2SJJUsQ52kXdKvdyVXn/8GmlsS/3FdA/OWb3BhYknKgKFO0i7bd1BffjLuaOYsW8/4q6e6MLEkZcCJEpI6xX9c10BzS2LRqpcBFyaWpO5mT52kTjFlwhjOPnIo5WW5Vewqy8OFiSWpGxnqJHWKutpqaqoraEmJCNjSnHh5c7MLE0tSNzHUSeo0y9c3Mu644dz4keOpqargnplLWbDCGbGS1B0ipZR1Dd2qvr4+NTQ0ZF2GVPTmLlvPuVc+wOCaKv748TdRW12ZdUmS1ONExPSUUv3Oz7SnTlIX2W/wbvz0349m/vINXPibR2lqbsm6JEkqaoY6SV3mTfsP4rJzDuMfs5bxzb/OyLocSSpqLmkiqUu959h9mLt8A1f9Yy6Da6r4x+zl/Ph9RzmBQpI6mT11krrcRacfxKkHD+H7t89i2jwXJpakrmBPnaQud8jX/kZjU25MXcKFiSWpK9hTJ6nLTZkwhrNHD6Wq4pW/ck4/dIgLE0tSJzLUSepydbXV1FRVsLm5hcry3I4TD89fxW5V3iyQpM5iqJPULVoXJr7pEycyZtRgVm7YzKdueIzmltJaK1OSuoqLD0vKxPUPzudrNz3NB08YwaVnHZp1OZJUkDqy+LD3PiRl4v1vHMH85Ru55v55DB/Yhw+csG/WJUlSj+btV0mZ+co7DuZthwzhG3+dwZ0zlrB07SbOm/ggS9dtyro0SepxDHWSMlNeFvzoPaM5bK9+fPKGR7n05qeZNt917CTp9fD2q6RM9elVwbMvrWNzUwuTn3oJcB07SXo97KmTlLn7JoxhzKjBW4+rK8oYO3qo69hJUgcY6iRlrq62mqH9exP5401NLfTpVe7+sJLUAYY6SQVh+fpGxh0/nAmnjQLgnmeX0uIadpLUbo6pk1QQJo5/ZRmm8rLgvyc/y3f+9ixfPvPgDKuSpJ7DUCep4Fzwlv14YfXLXPWPuezZr5oPuoadJO2Ut18lFZyI4GtnHcrb82vY/e2pF13DTpJ2wlAnqSCVlwVXvPcojhrWn0/f+BiX/Pkp17CTpNfg7VdJBau6spynXljL5qYWbp+xBHANO0naEXvqJBW0+yaM4dSD67YeV7mGnSRtl6FOUkGrq61mSG311jXsGpta6FVR5hp2krQNQ52kgte6ht23zjmMAO6csYRNW5qzLkuSCopj6iQVvLZr2NX0ruRTNzzKp298lCvHHUN5WbzGKyWpdNhTJ6lHOfvIoVx61iHc9vQSLvnzU6TkrhOSBIY6ST3QB0/Yl4+dtD83PLyAH9452zXsJAlvv0rqoSacNorl6xr50V2zeeC5FTQ8n1vD7rJzD8+6NEnKhKFOUo8UEdz8+AsATJu/EnANO0mlzduvknqsKRPG8I7D9yTycyV6lbuGnaTSZaiT1GPV1VbTv08lAAFsbm6hsanFNewklSRDnaQebfn6RsYdN5zrP3wsfavKuXPGEmYvWZd1WZLU7aLUlgOor69PDQ0NWZchqQs8v2ID7/7Zg5RH8PuPvpFhA/tkXZIk7ZKImJ5Sqt/5mfbUSSoiw3fvy/UfOpaNm5sYf/VUlq1rzLokSeo2hjpJReXgPWv55QffwEtrN3H+NQ/z3LL1rmEnqSQY6iQVnWOGD2Ti+HpmL13Heyc+xLT5uTXsJKmYuU6dpKJ0wfUNbGlOLF2fuwXrGnaSip09dZKK0pQJYzh79FAqy3OL2JUFjD3SNewkFS9DnaSiVFdbTU1VBU0tiYqyoCXBk4vXMKhvVdalSVKXyCzURUR5RDwaEX/NH+8bEVMjYk5E/DYieuXbq/LHc/LPj2jzHl/Kt8+MiNMy+iqSClTrGnY3X3giR+zVj7nLN/Bff3maUlvKSVJpyLKn7tPAM22OvwtcnlI6AFgFfDjf/mFgVb798vx5RMQhwHuAQ4HTgSsjorybapfUA0wcX89l5xzGIUNruenCE/jIm/flugef53u3zcy6NEnqdJmEuojYG3gH8Iv8cQAnA3/In3IdcE7+8dj8MfnnT8mfPxa4MaXUmFKaB8wBju2WLyCpx4kIvnzmwbzvuH248t7n+Mk9c7IuSZI6VVY9dT8EJgAt+ePdgdUppab88SJgr/zjvYCFAPnn1+TP39q+nde8SkRcEBENEdGwbNmyTvwaknqSiOCysYdx7lF78b3bZnLNffNYunaT69hJKgrdHuoi4l+ApSml6d31mSmlq1JK9Sml+sGDB3fXx0oqQGVlwffefQSnHTqEb/x1Bp+64VHXsZNUFLJYp+4E4OyIOBOoBmqBHwH9I6Ii3xu3N7A4f/5iYBiwKCIqgH7Aijbtrdq+RpJ2qKK8jHtn5nrtH5q3EnAdO0k9X7f31KWUvpRS2julNILcRIe7U0rjgHuAd+dPOx+4Kf/45vwx+efvTrmpazcD78nPjt0XGAk83E1fQ1IPN2XCGN5x+J6U5Zaxo7I8GDvadewk9VyFtKPERcCNEXEZ8Chwdb79auBXETEHWEkuCJJSejoifgfMAJqAT6SUmru/bEk9UV1tNf37VJKAALY0J1Zt3ExdTXXWpUnS6xKltl5TfX19amhoyLoMSQXgP3/VwOCaas45aij/+avprFy/mas/UM/JBw3JujRJAiAipqeU6tt1rqFOkmDNy1sYf/VUnn1xHT8/v563HuikKknZ60ioc5swSQL69a7k+g8dywF1u3HB9Q08MGe5y51I6lEMdZKU179PLyb9x3GM2L0vH76uga/86UmXO5HUYxTSRAlJytzAvr2Yt2IDm5tauOOZpYDLnUjqGeypk6Rt3DdhDKcdOoT8aif0qihzuRNJBc9QJ0nbqKutZtBuVRC55U42N7Xw8uZmlzuRVNAMdZK0HcvXNzLuuOFc/+Fjqamq4K5nltAwf2XWZUnSDrmkiSTtxJK1m3jvVQ+xZO0mrv3QsbxhxMCsS5JUIlzSRJI60ZDaam684HiG1FbzgWseZtr8lS53IqngGOokqR3qWoNdv2rOv+ZhLvnzUy53IqmguKSJJLVTXW01i1a+zObmFm6fsQRwuRNJhcOeOknqgPsu2ma5k3KXO5FUGAx1ktQB/7TcSXML6zY1udyJpMwZ6iSpg1qXO7nhI8czoE8l9zy7lLueWZJ1WZJKnEuaSNIuWL1xM+df8zBPv7CW//feozjj8D2zLklSEXFJE0nqJv379OJX/3EcRw7rz4U3PMpNjy12uRNJmTDUSdIuqq2u5PoPHUv98AF85reP8ekbH3W5E0ndziVNJKkT9K2q4LGFq0kJHpyb207M5U4kdSd76iSpk0yZMIZ/OWJPyvLrnVSUhcudSOo2hjpJ6iR1tdX0611JAsoCmloSc5etZ/BuVVmXJqkEGOokqRO1Lndy84Unsv+gvjy5eC3f/OszlNpKA5K6n2PqJKkTTRz/ysoDd3zurXzzlhlcc/88NjQ28e13Hk55671ZSepk9tRJUhcpKwu+9i+H8KlTRvLbhoV86sZHWbRqo8udSOoS9tRJUheKCD73tgOpqargW7c+wyPPr+KltZu44s7ZXHbu4VmXJ6mIGOokqRt8//aZALy4JtdD53Inkjqbt18lqRtMmTCGs0cPpbI8N6YugNMP28PlTiR1GkOdJHWDutpqaqoqaGpJVJYHCbhv9jIat7RkXZqkImGok6Ru0rrcyU2fOJHTDh3Cpi0tvOunD/DsS2uzLk1SEYhSWzupvr4+NTQ0ZF2GJDFryTrGXz2Vlzc3c80H3kD9iIFZlySpwETE9JRS/c7PtKdOkjJz4JAa/vDRN7H7blX8+9VTufvZJSxdu8klTyS9LoY6ScrQsIF9+P1H38gBdbvxkeun85nfPsa0+Su54s7ZWZcmqYdxSRNJytig3aqYtWQ9zS2JB55bAbjkiaSOs6dOkgrAfRPG8C9H7EnrLmLlZcHYI4e65ImkdjPUSVIBqKutpl/vShJQHtDcknh04WpqqyuzLk1SD2Gok6QC0brkyc2fPJFj9unPgpUbef81D7Nm45asS5PUA7ikiSQVqJseW8wXfv84+w7qy7UfPJaKsuDCGx7lx+87irqa6qzLk9QNXNJEkorA2NF7cd0Hj+XF1Zt455UP8F9/meHMWEk75OxXSSpgbzpgEJuamlnX2MQtT74IODNW0vbZUydJBe7+i07mbYcMIT8xlsryYOxoZ8ZKejV76iSpwNXVVlNXUwUBAWxpTsxdtp7Bu1VlXZqkAmJPnST1AK0zY//88RPYb1Bfnly8ls//7nE2N7VkXZqkAuHsV0nqYVJK/PjuOfzgjlkcv99AJv57PY1Nzc6MlYqQs18lqYhFBJ88ZSQ//LfRPPL8as796f1869ZnnBkrlTh76iSpBxv5lVvZ0vzPf487M1YqDvbUSVKJuP+ikznloDpnxkpy9qsk9WR1tdXs0a/61TNjl65nUF9nxkqlxp46Serh2s6M3X9wX558YS0X3vAIL29uzro0Sd3IMXWSVERSSvxiyjy+PfkZDhvaj5+/v56ywJmxUg/lmDpJKlERwUfesh+/eH89c5et5+wf38elNz/tzFipBNhTJ0lF6sCv3MpmZ8ZKPZo9dZIk7rvoZE4/dAiRnxpbURaMPdKZsVKxMtRJUpGqq61m9/z+sGUBTS2JhudX0ruyPOPKJHUFQ50kFbHWmbF/+eSJvGHEABav3sQ5P7mfucvWZ12apE7mmDpJKiEPPreCT/zmEbY0t3DFe4/i0D1rnRkrFTDH1EmStuuN++/OTZ84gWED+vCha6dxwa+mOzNWKhLuKCFJJWbYwD48t2w9KcFjC1cDMGnqAiZNXeDMWKkHs6dOkkrQlAljOPvIoVSU5abGBnDqwXXOjJV6MEOdJJWgutpqaqoraE6JyvIgAX+fuYzHF67JujRJr5OhTpJKVOvM2Js+cSLnHjWU3r3K+cj1DXz/tpk0t5TWJDqpGDj7VZIEwKYtzXztpqf4XcMi3jxyEF99xyFcctNTzoyVMuTsV0lSh1VXlvM/7z6S/37n4Uydu5Jzr7yfafOcGSv1FM5+lSS9ytdvfprNzS1sbs4dOzNW6hnsqZMkvcqUCWM4e/RQqite+Sdi7wG9ue0zb8mwKkk7Y6iTJL1KXW01NVUVNDa3UJUPdotWvcx/XN/ArCXrMq5O0o4Y6iRJ/6R1ZuyfPn4C/378cN4wfACrN25h7I/v5/+mLwJg6dpNnDfxQZau25RxtZIgg9mvETEMuB4YAiTgqpTSjyJiIPBbYAQwHzgvpbQqIgL4EXAmsBH4QErpkfx7nQ9ckn/ry1JK1+3s8539Kkmvz9K1m/jkDY8ydd5K/q1+GBHw24aFjDt2Hy479/Csy5OKUkdmv2YR6vYE9kwpPRIRNcB04BzgA8DKlNJ3IuJiYEBK6aKIOBP4JLlQdxzwo5TScfkQ2ADUkwuH04FjUkqrXuvzDXWS9Po1Nbcw6qt/2+46dk6kkDpfQS9pklJ6sbWnLaW0DngG2AsYC7T2tF1HLuiRb78+5TwE9M8Hw9OAO1JKK/NB7g7g9O77JpJUeirKy3jw4pM5fr+BW9sqy4Oxo4e6xZiUsUzH1EXECOAoYCowJKX0Yv6pl8jdnoVc4FvY5mWL8m07at/e51wQEQ0R0bBs2bLO+wKSVILqaqvZf/BuREAEbGlOPL5wNb0ry7MuTSppmYW6iNgN+D/gMymltW2fS7l7wp12XzildFVKqT6lVD948ODOeltJKlmtEyn+cuGJHLl3P+av2Mg7rriPxxauBpxEIWUhk8WHI6KSXKD7dUrpj/nmJRGxZ0rpxfzt1aX59sXAsDYv3zvfthg4aZv2e7uybklSzsTxrwzxuenCE5n+/Eo+dcNjvPunD/DF00axYOVGps3P7UbhJAqpe2QxUSLIjZlbmVL6TJv27wEr2kyUGJhSmhAR7wAu5JWJEleklI7NT5SYDhydf4tHyE2UWPlan+9ECUnqGms2buGob97OduZQOIlCep0KeqIEcAIwHjg5Ih7L/5wJfAd4W0TMBk7NHwPcCswF5gA/Bz4OkA9v3wSm5X++sbNAJ0nqOv36VPLgxSdz5N79trb1chKF1G26/fZrSuk+IHbw9CnbOT8Bn9jBe10DXNN51UmSdsWQfr05bK9+PLFoDQCbmxNPv7CG3arcalzqau4oIUnqVMvXNzLu+OH8+RMncOjQWuYs3eAkCqkbdPuYuqw5pk6SutdDc1fw+d89zktrN/HpU0by0pqXuWGaO1FI7VHQO0pkzVAnSd1vzctbOOobTqKQOqrQJ0pIkkpMv96VPPSlUzhmn/5b2yrLg7FHOolC6iyGOklSt6irreagPWtftRPF1Hkr2NJcWneMpK5iqJMkdZvWnSj++skTOW7fgSxd18jpl/+D3zUsJKXkJAppFzimTpKUmQUrNvLFPzzO1HkrOeWgOvr3qeSPjy52EoWU50SJ12Cok6TC0tKSOPCSyTRtZxaFkyhU6pwoIUnqMcrKggcuPpmTD6oj8kvTlwWcdugQJ1FIHWCokyRlrq62mj37VQNQURa0JLj7maXcOWMpLdtbB0XSPzHUSZIKQuskipsvPJFzRg+lprqCL//pSd73i4d4fsUGJ1FIO+GYOklSQUopceO0hXz7lmfY0tLCoXvW8sjC1U6iUElxosRrMNRJUs9y4Fcms7m55Z/anUShUuBECUlS0bjvojGcfeRQKstja9v+g/ty22fekmFVUuEx1EmSClpdbTU11RU0tSR6VeT+2Xpu2Qbe9/OHuHPGEgDH20lARdYFSJK0M62TKN537D785uEFzHppLatf3sJ/XN/A6YfuQZ9e5Uybv5Ir7pzteDuVLMfUSZJ6pM1NLRz8tb/R7KLFKmKOqZMkFb1eFWU8ePHJnHpwHWX54XYBnHjAIBctVkky1EmSeqy62mqG1FaTgMryIAH3zVnOf9/67NbxdY63U6lwTJ0kqUdrO97u+gfn8/C8FdzyxIvcOWMJn3nbgTy3dJ3j7VQSHFMnSSo685Zv4JQf3Mv2dhhzvJ16EsfUSZJK2r6D+vLgxSfzhhEDtraVBbztkDrH26loGeokSUVpSL/eHDikhggoLwtaEtz1zFKuvX8+6xubAMfbqbgY6iRJRat1vN1fLjyRdx29F3vUVnPlvc8x5vv38vuGhfzortlbx9tJPZ1j6iRJJeXRBat455UPsL1//Rxvp0LjmDpJknbgqH0G8ODFJ3P0Pv23tpUFnHKQ4+3UsxnqJEklZ4/+vTl4z9pXj7d7dimX3zGbpWtd3049k+vUSZJKUtv17X55/1ymzlvJ7xsWctNji/nIm/fjpTWbXN9OPYpj6iRJypu/fAMnu76dCohj6iRJeh1GDOrLQ186hTePHLR1P1mAo4b1594vnJRZXVJ7GOokSWqjrraafQb22bqfLMCjC1cz7uqp3PLEi7y0+mXH2qkgOaZOkqRttB1v95upz/PUC2vY0NjMJ37zCAP6VLJ64xbH2qngOKZOkqR2GHXJZBqbWv6p3bF26kqOqZMkqZNNmTCGs0cPpbry1f907j+4L3c/u4SUksugKFPefpUkqR3qaqupqaqgsamFqooyNje3cOyIgSxe/TIfuraBI/bux8A+vVwGRZmxp06SpHZqHWv3p4+fwLjjhtO/TyX3fOEkKsqCJxat4d5Zy0gJJk1dwIiLb2HUJZOzLlklxDF1kiTtoqVrN/HNv87gb0+/xJbm3L+rfXuV89m3jeT9b9yXXhVlLF27iQtveJQfv+8o6mqqM65YPYVj6iRJ6kZ1tdXU9q6kqSVRVVFGAL0qyrjslmd5y//cwy+mzOUHt8/aemtW6gr21EmS1An+81cNDK6pzi2D8vAClq3bxLjjhnP+Lx9me//UOmtW7dGRnjpDnSRJXWjp2k18/vePc/+c5Vu3H9tnYB/+591HcPx+u289x1uz2h5vv0qSVCDa7lDRqzz3z+7iVRt5z1UP8f5rHuYfs5ZxxV2zvTWrXeaSJpIkdbFX7VDx8AJeWLWRo4cP4Pu3z+Ifs5ZtPW/S1AVMmrrAW7N6Xbz9KklSRhau2sCnfvMYjy1cTeu/xvsP7sv33n0ERw8fCHhrttR5+1WSpB5g2IC+HDK0FgIqywOAucs28K6fPciHrp3GPTOX8iNvzaqdvP0qSVKGtr01u2jlRo4c1p8f3TWbu59duvU8b81qZ7z9KklSAVq0aiOfvvExHl2wauus2aH9q7n49IP4lyOGsnx9o7dlS4C3XyVJ6uH2HtCHg/aoedWs2eXrGvnUjY/x1u/fw0eub/C2rF7FUCdJUoFqvTX750+cwL8fP5y3jhpMRVmwcOXLPL5ozQ73mV26dhPnTXyQpes2ZVi9upu3XyVJ6kGWrt3EZbc+w21PvURjU8vW9r5V5Zx95F68+5i9+NMji/n1wwsYd+w+XHbu4RlWq13VkduvTpSQJKkHqautpqaqgs3NLVRVlLG5uYWTR9XRr3clNzy8gBseXrD13G0nV7g8SnHz9qskST1M623ZP338BMYdN5yK8uB//20093zhJI4a1p+yeOXcfr0ruOAt+/HC6pfduaLIeftVkqQi8pU/PclvHl5AZXkZW5paGNi3Fys2bN7uuW2XR7EXrzA5+1WSpBK1dXLFx09g3PHDqR8xgD9+7I0ctEcNbTrwGNi3ko+9dX8WrtwIYC9eEbCnTpKkErC1B68sNw5vQJ9KVm3cssPzHYdXGOypkyRJr7Lt8ijH7juQv3/xJD455gD696ncel4A+w7qy/f/9Qgam5rtwetB7KmTJKnEtfbilUfQ1JIoC7buYrEte/C6lz11kiSp3Vp78W6+8ET+/fjhnHxQHT/41yMYvnufV51XU13Bu47ei7/PWsb/3jHLHrwCY0+dJEnarlfG4QVbmhN71Fbx4trG7Z7rTNquYU+dJEnaZa+MwzuRcccP54hh/fn7F0/i+P0GUt52MTygLOD91zzMT+99jq/d9NR2e/Hcvqxr2VMnSZI6pLUHr1d5bibtmw8YxIhBffnVg8+zvVRRWR5M+8qpfP+2mdvdvsyevR2zp06SJHWZbXe06N2rnG+MPYypXz6F0w8dQmV5rhcv8j9bmhOjv3EHk6YuIKXc9mUjLr6FUZdMBra/Rp69eh1nT50kSeo02/bi/Vv9MN46ajBX3DmbmUvW7XBWbVtVFWX86zF726uHPXWSJCkj2/birdq4mTMO25Ojhw8gkQtsAbxl5CDe/8bhDNqt1z+9R2NTi716r4M9dZIkqcv9568aGFxTzfuO3YffPLyAZes2MXF8/at2utjS3MKoPXZj9ctbWLKmcbvj87bVq7yM8+r/uVdvez1627b1hF6/jvTU9fhQFxGnAz8CyoFfpJS+81rnG+okSSoc2wt7g3ar4tdTF7zqvPKyoG+vctZuaurQ+5dFbqJGY9MreacMSEDvXmVs3NxC78pgU1OiAtiS4NvnHMrvpy9mS3MLCdi0pZnnlm2gV3mwufmV9/nSGQfyn28d+fq/fDuUTKiLiHJgFvA2YBEwDXhvSmnGjl5jqJMkqbD9568amLtsA7OXrs/k8wPa1UsIMP877+jKUjoU6iq6tJKudywwJ6U0FyAibgTGAjsMdZIkqXCNumQyjU0tmdbQke6uERffAnR9uGuPnj5RYi9gYZvjRfm2V4mICyKiISIali1b1m3FSZKkjpkyYQxvP3RI1mV0yJfOODDrEoCeH+raJaV0VUqpPqVUP3jw4KzLkSRJO1BXW83g3aqyLqNDunpcXXv19FC3GBjW5njvfJskSeqhlq9vZNiA3rRuRJZVWOld2bNiUk8fUzcNGBkR+5ILc+8B3pdtSZIkaVdMHN+ueQHaRo8OdSmlpoi4ELiN3JIm16SUns64LEmSpG7Xo0MdQErpVuDWrOuQJEnKUs+6WSxJkqTtMtRJkiQVAUOdJElSETDUSZIkFQFDnSRJUhEw1EmSJBUBQ50kSVIRMNRJkiQVAUOdJElSETDUSZIkFQFDnSRJUhEw1EmSJBUBQ50kSVIRMNRJkiQVAUOdJElSETDUSZIkFQFDnSRJUhEw1EmSJBUBQ50kSVIRiJRS1jV0q4hYBjy/i28zCFjeCeWUEq9Zx3nNOsbr1XFes47zmnWM16vjtr1mw1NKg9vzwpILdZ0hIhpSSvVZ19GTeM06zmvWMV6vjvOadZzXrGO8Xh23K9fM26+SJElFwFAnSZJUBAx1r89VWRfQA3nNOs5r1jFer47zmnWc16xjvF4d97qvmWPqJEmSioA9dZIkSUXAUCdJklQEDHWvISJOj4iZETEnIi7ezvNVEfHb/PNTI2JEBmUWlHZcs7dExCMR0RQR786ixkLSjuv1uYiYERFPRMRdETE8izoLSTuu2Ucj4smIeCwi7ouIQ7Kos5Ds7Jq1Oe9dEZEioqSXoGjH79gHImJZ/nfssYj4jyzqLCTt+R2LiPPyf589HRG/6e4aC007fs8ub/M7NisiVu/0TVNK/mznBygHngP2A3oBjwOHbHPOx4Gf5R+/B/ht1nX3gGs2AjgCuB54d9Y194DrNQbok3/8MX/H2nXNats8Phv4W9Z1F/o1y59XA/wDeAioz7ruQr5ewAeAH2dda6H8tPOajQQeBQbkj+uyrrvQr9k2538SuGZn72tP3Y4dC8xJKc1NKW0GbgTGbnPOWOC6/OM/AKdERHRjjYVmp9cspTQ/pfQE0JJFgQWmPdfrnpTSxvzhQ8De3VxjoWnPNVvb5rAvUOqzwdrzdxnAN4HvApu6s7gC1N7rpVe055p9BPhJSmkVQEppaTfXWGg6+nv2XuCGnb2poW7H9gIWtjlelG/b7jkppSZgDbB7t1RXmNpzzfSKjl6vDwOTu7SiwteuaxYRn4iI54D/AT7VTbUVqp1es4g4GhiWUrqlOwsrUO39c/mu/LCIP0TEsO4prWC155odCBwYEfdHxEMRcXq3VVeY2v33f37Yzb7A3Tt7U0Od1ANExL8D9cD3sq6lJ0gp/SSltD9wEXBJ1vUUsogoA/4X+HzWtfQgfwFGpJSOAO7glTs22rEKcrdgTyLX6/TziOifZUE9yHuAP6SUmnd2oqFuxxYDbf/f1975tu2eExEVQD9gRbdUV5jac830inZdr4g4FfgKcHZKqbGbaitUHf0duxE4pysL6gF2ds1qgMOAeyNiPnA8cHMJT5bY6e9YSmlFmz+LvwCO6abaClV7/lwuAm5OKW1JKc0DZpELeaWqI3+XvYd23HoFQ91rmQaMjIh9I6IXuYt68zbn3Aycn3/8buDulB/RWKLac830ip1er4g4CphILtCV+hgUaN81a/sPxTuA2d1YXyF6zWuWUlqTUhqUUhqRUhpBbuzm2SmlhmzKzVx7fsf2bHN4NvBMN9ZXiNrzd/+fyfXSERGDyN2OnduNNRaadv17GREHAQOAB9vzpoa6HciPkbsQuI3cH9jfpZSejohvRMTZ+dOuBnaPiDnA54AdLhVQCtpzzSLiDRGxCPhXYGJEPJ1dxdlq5+/Y94DdgN/np7WXdEhu5zW7ML9kwmPk/lyev/13Kw3tvGbKa+f1+lT+d+xxcmM2P5BNtYWhndfsNmBFRMwA7gG+mFIq2TtbHfhz+R7gxvZ2GLlNmCRJUhGwp06SJKkIGOokSZKKgKFOkiSpCBjqJEmSioChTpIkqQgY6iSVrIjYPb9UzGMR8VJELM4/Xp1feqEj73VORBzSwdeMy2819WREPBARR3bsG0jSKwx1kkpWfmeA0Sml0cDPgMvzj0cDLR18u3OADoU6YB7w1pTS4cA3gas6+HpJ2spQJ0nbVx4RP88vMnt7RPQGiIj9I+JvETE9IqZExEER8SZyOwt8L9/Tt39EfCQipkXE4xHxfxHRZ9sPSCk9kFJalT98iNxWQZL0uhjqJGn7RgI/SSkdCqwG3pVvvwr4ZErpGOALwJUppQfIbfHzxXzP33PAH1NKb0gpHUluxfgP7+TzPgxM7oLvIalEVGRdgCQVqHkppcfyj6cDIyJiN+BN5LZtaz2vagevPywiLgP6k9vq7bYdfVBEjCEX6k7c9bIllSpDnSRtX2Obx81Ab3J3N1bnx93tzLXAOSmlxyPiA+Q3M99WRBwB/AI4o5T3wpS067z9KkntlFJaC8yLiH8FiJzWGavrgJo2p9cAL0ZEJTBue+8XEfsAfwTGp5RmdV3lkkqBoU6SOmYc8OGIeBx4Ghibb78R+GJEPBoR+wNfBaYC9wPP7uC9vgbsDlyZn2DR0LWlSypmkVLKugZJkiTtInvqJEmSioChTpIkqQgY6iRJkoqAoU6SJKkIGOokSZKKgKFOkiSpCBjqJEmSisD/B69rsq0T/iyYAAAAAElFTkSuQmCC",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plot_loss(cost_vals, thetas, alpha=0.01)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "gcubLs95MGn8",
      "metadata": {
        "id": "gcubLs95MGn8"
      },
      "source": [
        "## R2Score"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 50,
      "id": "TAtrdoCeMIsF",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TAtrdoCeMIsF",
        "outputId": "77d3117a-0431-4957-b975-bc5b9810b01f"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.982090023089159"
            ]
          },
          "execution_count": 50,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "r2_score(y2,h_s[-1])"
      ]
    },
    {
      "attachments": {},
      "cell_type": "markdown",
      "id": "6b51a395",
      "metadata": {
        "id": "6b51a395"
      },
      "source": [
        "## 2. BFGS optimizer"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "id": "pYbMgUuuNDUX",
      "metadata": {
        "id": "pYbMgUuuNDUX"
      },
      "outputs": [],
      "source": [
        "def cost_grad(X, y, theta):\n",
        "    # j = (1 / (2 * m)) * np.linalg.norm(error, 2)**2\n",
        "    m = X.shape[0]\n",
        "    h_x = np.dot(X, theta)\n",
        "    error = h_x - y\n",
        "    grad = np.dot(X.T, error) / m\n",
        "    return grad"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 51,
      "id": "uMs9bqa2RNQx",
      "metadata": {
        "id": "uMs9bqa2RNQx"
      },
      "outputs": [],
      "source": [
        "def calc_cost(X, y, theta):\n",
        "    m = X.shape[0]\n",
        "    h_x = np.dot(X, theta)\n",
        "    error = h_x - y\n",
        "    j = (1 / (2 * m)) * np.linalg.norm(error, 2)**2\n",
        "    return j"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 32,
      "id": "efaf8ab0",
      "metadata": {
        "id": "efaf8ab0"
      },
      "outputs": [],
      "source": [
        "def BFGS(xk_1, x0, df, X_data, y_data, alpha, epsilon):\n",
        "  theta_prev = xk_1\n",
        "  theta = x0\n",
        "  i = 0\n",
        "  n = X_data.shape[1]\n",
        "  I = np.eye(n)\n",
        "  B_inv = I\n",
        "\n",
        "  cost_vals = []\n",
        "  thetas = []\n",
        "\n",
        "  if x0 is None:\n",
        "    d_theta = df(X_data, y_data, theta_prev)\n",
        "    theta = theta_prev - alpha * np.dot(B_inv, d_theta)\n",
        "    thetas.append(theta)\n",
        "\n",
        "  while True:\n",
        "      # Calculate cost\n",
        "      j = calc_cost(X_data, y_data, theta)\n",
        "      print('cost: ', j)\n",
        "      cost_vals.append(j)\n",
        "\n",
        "      # Calculate the gradient\n",
        "      d_theta = df(X_data, y_data, theta)\n",
        "      delta_x = theta - theta_prev\n",
        "\n",
        "      y = d_theta - df(X_data, y_data, theta_prev)\n",
        "      \n",
        "      # calculate each term in the BFGS equation\n",
        "      den = np.dot(y.T, delta_x)\n",
        "      t1 = I - np.dot(delta_x, y.T)/den\n",
        "      t2 = I - np.dot(y, delta_x.T)/den\n",
        "      t3 = np.dot(delta_x, delta_x.T)/den\n",
        "      \n",
        "      # calculate B_inv\n",
        "      B_inv = np.dot(np.dot(t1, B_inv), t2) + t3\n",
        "      print('xn_1:\\n', theta_prev)\n",
        "      print('xn:\\n', theta)\n",
        "      print('Dfxn_1:\\n', df(X_data, y_data, theta_prev))\n",
        "      print('Dfxn:\\n', df(X_data, y_data, theta))\n",
        "      print('***************')\n",
        "      print('B_inv\\n', B_inv)\n",
        "      print('***************')\n",
        "\n",
        "      if len(cost_vals) > 1 and abs(cost_vals[-2] - cost_vals[-1]) < 0.001:\n",
        "            break\n",
        "\n",
        "      if np.linalg.norm(d_theta, 2) < epsilon:\n",
        "        break\n",
        "\n",
        "      # Update the parameters\n",
        "      theta_prev = theta\n",
        "      theta = theta_prev - alpha * np.dot(B_inv, d_theta)\n",
        "      thetas.append(theta)\n",
        "      i += 1\n",
        "    \n",
        "  print(f'Found solution after {i} iterations.')\n",
        "  print(f'xy_min = {theta}')\n",
        "  print(f'Gradient = {d_theta}')\n",
        "  return theta, d_theta, i, cost_vals, thetas"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "2YhjZiLvOP14",
      "metadata": {
        "id": "2YhjZiLvOP14"
      },
      "source": [
        "## Initialize theta_prev"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 33,
      "id": "Gp5Ux3uyOo1J",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Gp5Ux3uyOo1J",
        "outputId": "27989144-54f0-427a-d33a-cc058617dfb4"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(25, 4)"
            ]
          },
          "execution_count": 33,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "X2.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "id": "btHb9LZbQRqU",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "btHb9LZbQRqU",
        "outputId": "4624a8b8-91c8-47fb-c8f6-74c80048df84"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(25, 1)"
            ]
          },
          "execution_count": 34,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "y2.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 35,
      "id": "GReuqCZHOPjX",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GReuqCZHOPjX",
        "outputId": "80fd1c22-709a-4ce8-a77b-216feb415686"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(4, 1)"
            ]
          },
          "execution_count": 35,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "n = X2.shape[1]\n",
        "xk_1 = np.zeros((n, 1))\n",
        "xk_1.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 36,
      "id": "Oek0NpYNOPcl",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Oek0NpYNOPcl",
        "outputId": "b2f22f05-421b-4222-af75-d0539e0e3326"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[0.],\n",
              "       [0.],\n",
              "       [0.],\n",
              "       [0.]])"
            ]
          },
          "execution_count": 36,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "xk_1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 37,
      "id": "bQcQLxFYPKhk",
      "metadata": {
        "id": "bQcQLxFYPKhk"
      },
      "outputs": [],
      "source": [
        "x0 = None"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 43,
      "id": "v-PAFUKLNYIg",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "v-PAFUKLNYIg",
        "outputId": "b15c55bc-c27f-4505-f1fe-4b23816d15f1"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "cost:  5145882705455.929\n",
            "xn_1:\n",
            " [[0.]\n",
            " [0.]\n",
            " [0.]\n",
            " [0.]]\n",
            "xn:\n",
            " [[  162.04]\n",
            " [13075.8 ]\n",
            " [13147.2 ]\n",
            " [13467.08]]\n",
            "Dfxn_1:\n",
            " [[  -162.04]\n",
            " [-13075.8 ]\n",
            " [-13147.2 ]\n",
            " [-13467.08]]\n",
            "Dfxn:\n",
            " [[3.17574837e+06]\n",
            " [2.56317967e+08]\n",
            " [2.57728446e+08]\n",
            " [2.63739883e+08]]\n",
            "***************\n",
            "B_inv\n",
            " [[ 0.99995    -0.00403566 -0.00405787 -0.00415252]\n",
            " [-0.00403566  0.67427736 -0.32751504 -0.33515433]\n",
            " [-0.00405787 -0.32751504  0.6706827  -0.33699864]\n",
            " [-0.00415252 -0.33515433 -0.33699864  0.65514118]]\n",
            "***************\n",
            "cost:  1019.922300398132\n",
            "xn_1:\n",
            " [[  162.04]\n",
            " [13075.8 ]\n",
            " [13147.2 ]\n",
            " [13467.08]]\n",
            "xn:\n",
            " [[-0.00961902]\n",
            " [-3.39396216]\n",
            " [-3.96679272]\n",
            " [ 9.16625244]]\n",
            "Dfxn_1:\n",
            " [[3.17574837e+06]\n",
            " [2.56317967e+08]\n",
            " [2.57728446e+08]\n",
            " [2.63739883e+08]]\n",
            "Dfxn:\n",
            " [[   1.27717517]\n",
            " [ -50.57355074]\n",
            " [-117.41129038]\n",
            " [ 163.71079594]]\n",
            "***************\n",
            "B_inv\n",
            " [[ 0.99995    -0.00403566 -0.00405787 -0.00415252]\n",
            " [-0.00403566  0.67427723 -0.32751525 -0.33515419]\n",
            " [-0.00405787 -0.32751525  0.6706824  -0.33699859]\n",
            " [-0.00415252 -0.33515419 -0.33699859  0.65514161]]\n",
            "***************\n",
            "cost:  424510.8493675594\n",
            "xn_1:\n",
            " [[-0.00961902]\n",
            " [-3.39396216]\n",
            " [-3.96679272]\n",
            " [ 9.16625244]]\n",
            "xn:\n",
            " [[  -1.28745634]\n",
            " [  47.12615622]\n",
            " [ 113.39077352]\n",
            " [-154.59957452]]\n",
            "Dfxn_1:\n",
            " [[   1.27717517]\n",
            " [ -50.57355074]\n",
            " [-117.41129038]\n",
            " [ 163.71079594]]\n",
            "Dfxn:\n",
            " [[  -22.95072117]\n",
            " [  662.26945725]\n",
            " [ 2708.38523664]\n",
            " [-3290.00901236]]\n",
            "***************\n",
            "B_inv\n",
            " [[ 9.99923686e-01 -3.33097548e-03 -8.19006797e-04 -8.00210231e-03]\n",
            " [-3.33097548e-03  6.59684918e-01 -4.24744544e-01 -2.25967749e-01]\n",
            " [-8.19006797e-04 -4.24744544e-01  2.97701710e-01  1.21935357e-01]\n",
            " [-8.00210231e-03 -2.25967749e-01  1.21935357e-01  1.00600135e-01]]\n",
            "***************\n",
            "cost:  2740.927906526406\n",
            "xn_1:\n",
            " [[  -1.28745634]\n",
            " [  47.12615622]\n",
            " [ 113.39077352]\n",
            " [-154.59957452]]\n",
            "xn:\n",
            " [[ -0.24128609]\n",
            " [ 17.09645585]\n",
            " [-10.45517881]\n",
            " [ -4.40425948]]\n",
            "Dfxn_1:\n",
            " [[  -22.95072117]\n",
            " [  662.26945725]\n",
            " [ 2708.38523664]\n",
            " [-3290.00901236]]\n",
            "Dfxn:\n",
            " [[  -0.81409017]\n",
            " [ 207.92915431]\n",
            " [-157.16886496]\n",
            " [ -48.47964842]]\n",
            "***************\n",
            "B_inv\n",
            " [[ 9.99926222e-01 -3.63180098e-03 -8.03367516e-04 -7.72505548e-03]\n",
            " [-3.63180098e-03  6.74865865e-01 -3.98197293e-01 -2.66660064e-01]\n",
            " [-8.03367516e-04 -3.98197293e-01  2.58467025e-01  1.34475412e-01]\n",
            " [-7.72505548e-03 -2.66660064e-01  1.34475412e-01  1.27889780e-01]]\n",
            "***************\n",
            "cost:  374963.22114998254\n",
            "xn_1:\n",
            " [[ -0.24128609]\n",
            " [ 17.09645585]\n",
            " [-10.45517881]\n",
            " [ -4.40425948]]\n",
            "xn:\n",
            " [[   0.82712899]\n",
            " [-198.74259217]\n",
            " [ 119.48328324]\n",
            " [  78.37125274]]\n",
            "Dfxn_1:\n",
            " [[  -0.81409017]\n",
            " [ 207.92915431]\n",
            " [-157.16886496]\n",
            " [ -48.47964842]]\n",
            "Dfxn:\n",
            " [[   12.39366932]\n",
            " [-2479.5866218 ]\n",
            " [ 1612.57092783]\n",
            " [  833.82210054]]\n",
            "***************\n",
            "B_inv\n",
            " [[ 9.99908349e-01 -2.89631228e-04 -2.80139931e-03 -9.02046785e-03]\n",
            " [-2.89631228e-04  5.39307283e-02 -2.72142215e-02 -2.57660703e-02]\n",
            " [-2.80139931e-03 -2.72142215e-02  3.68328725e-02 -9.46137468e-03]\n",
            " [-9.02046785e-03 -2.57660703e-02 -9.46137468e-03  3.44463822e-02]]\n",
            "***************\n",
            "cost:  3.0303079554289813\n",
            "xn_1:\n",
            " [[   0.82712899]\n",
            " [-198.74259217]\n",
            " [ 119.48328324]\n",
            " [  78.37125274]]\n",
            "xn:\n",
            " [[-0.24464961]\n",
            " [ 0.35609101]\n",
            " [ 0.5314673 ]\n",
            " [ 1.12882923]]\n",
            "Dfxn_1:\n",
            " [[   12.39366932]\n",
            " [-2479.5866218 ]\n",
            " [ 1612.57092783]\n",
            " [  833.82210054]]\n",
            "Dfxn:\n",
            " [[ 0.07881032]\n",
            " [ 0.00164172]\n",
            " [ 0.0098016 ]\n",
            " [-0.01212267]]\n",
            "***************\n",
            "B_inv\n",
            " [[ 9.99908574e-01 -3.10574371e-04 -2.78888640e-03 -9.01234448e-03]\n",
            " [-3.10574371e-04  5.39306705e-02 -2.72142605e-02 -2.57657239e-02]\n",
            " [-2.78888640e-03 -2.72142605e-02  3.68329397e-02 -9.46155313e-03]\n",
            " [-9.01234448e-03 -2.57657239e-02 -9.46155313e-03  3.44461221e-02]]\n",
            "***************\n",
            "cost:  3.024138752497448\n",
            "xn_1:\n",
            " [[-0.24464961]\n",
            " [ 0.35609101]\n",
            " [ 0.5314673 ]\n",
            " [ 1.12882923]]\n",
            "xn:\n",
            " [[-0.32353414]\n",
            " [ 0.35598135]\n",
            " [ 0.53125605]\n",
            " [ 1.13009211]]\n",
            "Dfxn_1:\n",
            " [[ 0.07881032]\n",
            " [ 0.00164172]\n",
            " [ 0.0098016 ]\n",
            " [-0.01212267]]\n",
            "Dfxn:\n",
            " [[ 7.73671776e-02]\n",
            " [ 4.34094449e-06]\n",
            " [-2.24834553e-04]\n",
            " [-7.16079694e-04]]\n",
            "***************\n",
            "B_inv\n",
            " [[ 5.15293151e+01  5.41082434e-03 -1.24034075e-01 -5.04526503e-01]\n",
            " [ 5.41082434e-03  5.38489170e-02 -2.75556206e-02 -2.54215837e-02]\n",
            " [-1.24034075e-01 -2.75556206e-02  3.58211884e-02 -6.68116802e-03]\n",
            " [-5.04526503e-01 -2.54215837e-02 -6.68116802e-03  3.73612449e-02]]\n",
            "***************\n",
            "cost:  2.8689811504619303\n",
            "xn_1:\n",
            " [[-0.32353414]\n",
            " [ 0.35598135]\n",
            " [ 0.53125605]\n",
            " [ 1.13009211]]\n",
            "xn:\n",
            " [[-4.31060101]\n",
            " [ 0.35553809]\n",
            " [ 0.5408556 ]\n",
            " [ 1.16915126]]\n",
            "Dfxn_1:\n",
            " [[ 7.73671776e-02]\n",
            " [ 4.34094449e-06]\n",
            " [-2.24834553e-04]\n",
            " [-7.16079694e-04]]\n",
            "Dfxn:\n",
            " [[ 0.00077806]\n",
            " [-0.00602408]\n",
            " [-0.03690063]\n",
            " [ 0.04190476]]\n",
            "***************\n",
            "B_inv\n",
            " [[ 5.18572809e+01  6.20679074e-04 -1.44009306e-01 -4.84300304e-01]\n",
            " [ 6.20679074e-04  5.38478479e-02 -2.75462204e-02 -2.53720514e-02]\n",
            " [-1.44009306e-01 -2.75462204e-02  3.59154749e-02 -6.54191511e-03]\n",
            " [-4.84300304e-01 -2.53720514e-02 -6.54191511e-03  3.69334794e-02]]\n",
            "***************\n",
            "cost:  2.8689039590893612\n",
            "xn_1:\n",
            " [[-4.31060101]\n",
            " [ 0.35553809]\n",
            " [ 0.5408556 ]\n",
            " [ 1.16915126]]\n",
            "xn:\n",
            " [[-4.33596478]\n",
            " [ 0.35590873]\n",
            " [ 0.54240115]\n",
            " [ 1.16758614]]\n",
            "Dfxn_1:\n",
            " [[ 0.00077806]\n",
            " [-0.00602408]\n",
            " [-0.03690063]\n",
            " [ 0.04190476]]\n",
            "Dfxn:\n",
            " [[ 2.37440089e-05]\n",
            " [-4.43677741e-04]\n",
            " [-2.71764918e-03]\n",
            " [ 3.08661359e-03]]\n",
            "***************\n",
            "B_inv\n",
            " [[ 5.15837379e+01 -1.74053647e-04 -1.46388859e-01 -4.77908827e-01]\n",
            " [-1.74053647e-04  5.39294858e-02 -2.72194476e-02 -2.57611475e-02]\n",
            " [-1.46388859e-01 -2.72194476e-02  3.72211665e-02 -8.10677197e-03]\n",
            " [-4.77908827e-01 -2.57611475e-02 -8.10677197e-03  3.87638557e-02]]\n",
            "***************\n",
            "Found solution after 8 iterations.\n",
            "xy_min = [[-4.33596478]\n",
            " [ 0.35590873]\n",
            " [ 0.54240115]\n",
            " [ 1.16758614]]\n",
            "Gradient = [[ 2.37440089e-05]\n",
            " [-4.43677741e-04]\n",
            " [-2.71764918e-03]\n",
            " [ 3.08661359e-03]]\n"
          ]
        }
      ],
      "source": [
        "theta, grad, i, cost_vals, thetas = BFGS(xk_1, x0, cost_grad, X2, y2, alpha=1, epsilon=0.001)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "TMTMlFWbR_hu",
      "metadata": {
        "id": "TMTMlFWbR_hu"
      },
      "source": [
        "## plots"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 44,
      "id": "3yxITApoSOi8",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "3yxITApoSOi8",
        "outputId": "4396dd47-04c7-4e2a-a1e4-54e24f860f4e"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plot_loss(cost_vals, thetas, alpha=1)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "LeMh-sy7SB89",
      "metadata": {
        "id": "LeMh-sy7SB89"
      },
      "source": [
        "## R2Score"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 45,
      "id": "iHwIpyjmPt9s",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "iHwIpyjmPt9s",
        "outputId": "f7a3c78a-dbce-4801-ea27-9da74ec6f145"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.9896615775501718"
            ]
          },
          "execution_count": 45,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "h_x = np.dot(X2, theta)\n",
        "r2_score(y2,h_x)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "2M3VTrEOaaUF",
      "metadata": {
        "id": "2M3VTrEOaaUF"
      },
      "source": [
        "# Conclusion"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "iTx5TtM-ac28",
      "metadata": {
        "id": "iTx5TtM-ac28"
      },
      "source": [
        "|Alogrithm|R2_score|Epochs|\n",
        "|---------|:-------|:-----|\n",
        "|Adam     |0.9821  |159   |\n",
        "|BFGS     |0.9897  |8     |"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "QZWGE6xcb9Iy",
      "metadata": {
        "id": "QZWGE6xcb9Iy"
      },
      "source": [
        "BFGS was able to converge faster than Adam, as it only needed 8 iterations and actually got better accuracy although the difference is minimum.\n",
        "\n",
        "Since we are optimizing a convex function, then second order optimization will overbeat the first order optimization.\n",
        "Also, the BFGS solves the cost of computationaly expensive operation of the inverse of hessian matrix by dependeing on the previous first derivative.\n",
        "\n",
        "So both algorithms reach a pretty good accuracy, but BFGS is much faster."
      ]
    }
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