Skip to content

Instantly share code, notes, and snippets.

@firmai
Created January 17, 2022 15:09
Show Gist options
  • Save firmai/80d9a58f16b427f0e59d548b12274d9b to your computer and use it in GitHub Desktop.
Save firmai/80d9a58f16b427f0e59d548b12274d9b to your computer and use it in GitHub Desktop.
Linear Regression - Coding Example.ipynb
Display the source blob
Display the rendered blob
Raw
{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "Linear Regression - Coding Example.ipynb",
"provenance": [],
"include_colab_link": true
},
"language_info": {
"name": "python",
"version": "3.6.3",
"mimetype": "text/x-python",
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"pygments_lexer": "ipython3",
"nbconvert_exporter": "python",
"file_extension": ".py"
},
"kernelspec": {
"name": "python3",
"language": "python",
"display_name": "Python 3"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/firmai/80d9a58f16b427f0e59d548b12274d9b/linear-regression-coding-example.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"metadata": {
"id": "K_d8erbixuUI"
},
"cell_type": "markdown",
"source": [
"**Chapter 4 – Training Linear Models**"
]
},
{
"metadata": {
"id": "MZKINbTAxuUM"
},
"cell_type": "markdown",
"source": [
"# Setup"
]
},
{
"metadata": {
"id": "_5NDv05OxuUO"
},
"cell_type": "code",
"source": [
"from __future__ import division, print_function, unicode_literals\n",
"\n",
"# Common imports\n",
"import numpy as np\n",
"import os\n",
"\n",
"# to make this notebook's output stable across runs\n",
"np.random.seed(42)\n",
"\n",
"# To plot pretty figures\n",
"%matplotlib inline\n",
"import matplotlib as mpl\n",
"import matplotlib.pyplot as plt\n",
"mpl.rc('axes', labelsize=14)\n",
"mpl.rc('xtick', labelsize=12)\n",
"mpl.rc('ytick', labelsize=12)\n",
"\n",
"# Where to save the figures\n",
"PROJECT_ROOT_DIR = \"../..\"\n",
"CHAPTER_ID = \"training_linear_models\"\n",
"\n",
"\n",
"def save_fig(fig_id, tight_layout=True):\n",
" path = os.path.join(PROJECT_ROOT_DIR, \"images\", CHAPTER_ID, fig_id + \".png\")\n",
" print(\"Saving figure\", fig_id)\n",
" if tight_layout:\n",
" plt.tight_layout()\n",
" try:\n",
" plt.savefig(path, format='png', dpi=300)\n",
" except:\n",
" plt.savefig(fig_id + \".png\", format='png', dpi=300)\n",
"\n",
"# Ignore useless warnings (see SciPy issue #5998)\n",
"import warnings\n",
"warnings.filterwarnings(action=\"ignore\", message=\"^internal gelsd\")"
],
"execution_count": null,
"outputs": []
},
{
"metadata": {
"id": "xWptt254xuUa"
},
"cell_type": "markdown",
"source": [
"# Linear regression using the Normal Equation"
]
},
{
"metadata": {
"id": "lzlfUO4dxuUe",
"outputId": "1a103018-5a7d-4cef-bdf3-f128d876c043",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 322
}
},
"cell_type": "code",
"source": [
"from pathlib import Path\n",
"import pandas as pd\n",
"import numpy as np\n",
"\n",
"github_p = \"https://raw.githubusercontent.com/Finance-781/FinML/master/Lecture%204%20-%20Linear%20Models/Inclass/\"\n",
"\n",
"my_file = Path(\"data/returns.csv\") # Defines path\n",
"if my_file.is_file(): # See if file exists\n",
" print(\"Local file found\") \n",
" df = pd.read_csv('data/returns.csv')\n",
" rf = pd.read_csv('data/rf.csv')\n",
"else:\n",
" print(\"Be patient: loading from github (2 minutes)\")\n",
" df = pd.read_csv(github_p+'data/returns.csv')\n",
" rf = pd.read_csv(github_p+'data/rf.csv')\n",
" \n",
" print(\"Done\")\n",
"df = df.set_index(\"date\",drop=True)\n",
"df.head()"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"text": [
"Be patient: loading from github (2 minutes)\n",
"Done\n"
],
"name": "stdout"
},
{
"output_type": "execute_result",
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>A</th>\n",
" <th>AAME</th>\n",
" <th>AAON</th>\n",
" <th>AAP</th>\n",
" <th>AAPL</th>\n",
" <th>AAWW</th>\n",
" <th>ABC</th>\n",
" <th>ABCB</th>\n",
" <th>ABG</th>\n",
" <th>ABM</th>\n",
" <th>...</th>\n",
" <th>YORW</th>\n",
" <th>YRCW</th>\n",
" <th>YUM</th>\n",
" <th>ZBRA</th>\n",
" <th>ZEUS</th>\n",
" <th>ZION</th>\n",
" <th>ZIOP</th>\n",
" <th>ZIXI</th>\n",
" <th>ZN</th>\n",
" <th>ZUMZ</th>\n",
" </tr>\n",
" <tr>\n",
" <th>date</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>20071231</th>\n",
" <td>-0.028813</td>\n",
" <td>-0.200000</td>\n",
" <td>0.049921</td>\n",
" <td>0.058120</td>\n",
" <td>0.087038</td>\n",
" <td>0.029820</td>\n",
" <td>-0.011020</td>\n",
" <td>0.009507</td>\n",
" <td>-0.100956</td>\n",
" <td>-0.000490</td>\n",
" <td>...</td>\n",
" <td>-0.015684</td>\n",
" <td>-0.035008</td>\n",
" <td>0.030148</td>\n",
" <td>-0.100337</td>\n",
" <td>0.213083</td>\n",
" <td>-0.144402</td>\n",
" <td>0.038123</td>\n",
" <td>0.179487</td>\n",
" <td>0.032747</td>\n",
" <td>-0.123741</td>\n",
" </tr>\n",
" <tr>\n",
" <th>20080131</th>\n",
" <td>-0.078389</td>\n",
" <td>0.135714</td>\n",
" <td>-0.101917</td>\n",
" <td>-0.058173</td>\n",
" <td>-0.316640</td>\n",
" <td>-0.078938</td>\n",
" <td>0.038110</td>\n",
" <td>-0.063502</td>\n",
" <td>-0.055149</td>\n",
" <td>0.022315</td>\n",
" <td>...</td>\n",
" <td>-0.005161</td>\n",
" <td>0.071387</td>\n",
" <td>-0.103475</td>\n",
" <td>-0.114986</td>\n",
" <td>0.065595</td>\n",
" <td>0.172414</td>\n",
" <td>-0.067797</td>\n",
" <td>-0.226087</td>\n",
" <td>-0.060100</td>\n",
" <td>-0.210591</td>\n",
" </tr>\n",
" <tr>\n",
" <th>20080229</th>\n",
" <td>-0.095983</td>\n",
" <td>-0.025157</td>\n",
" <td>-0.072472</td>\n",
" <td>-0.062605</td>\n",
" <td>-0.076389</td>\n",
" <td>0.013216</td>\n",
" <td>-0.102727</td>\n",
" <td>-0.098859</td>\n",
" <td>0.001758</td>\n",
" <td>-0.041506</td>\n",
" <td>...</td>\n",
" <td>0.006550</td>\n",
" <td>-0.248498</td>\n",
" <td>0.008489</td>\n",
" <td>0.084989</td>\n",
" <td>0.223439</td>\n",
" <td>-0.119839</td>\n",
" <td>-0.063636</td>\n",
" <td>0.101124</td>\n",
" <td>-0.014324</td>\n",
" <td>-0.085803</td>\n",
" </tr>\n",
" <tr>\n",
" <th>20080331</th>\n",
" <td>-0.025482</td>\n",
" <td>-0.012903</td>\n",
" <td>0.213204</td>\n",
" <td>0.016995</td>\n",
" <td>0.147816</td>\n",
" <td>0.086957</td>\n",
" <td>-0.017737</td>\n",
" <td>0.139240</td>\n",
" <td>-0.018545</td>\n",
" <td>0.129909</td>\n",
" <td>...</td>\n",
" <td>-0.025325</td>\n",
" <td>-0.046512</td>\n",
" <td>0.080116</td>\n",
" <td>0.000000</td>\n",
" <td>0.092010</td>\n",
" <td>-0.046073</td>\n",
" <td>-0.048544</td>\n",
" <td>-0.012755</td>\n",
" <td>0.008081</td>\n",
" <td>-0.107509</td>\n",
" </tr>\n",
" <tr>\n",
" <th>20080430</th>\n",
" <td>0.012739</td>\n",
" <td>0.555556</td>\n",
" <td>-0.097354</td>\n",
" <td>0.018502</td>\n",
" <td>0.212195</td>\n",
" <td>0.103273</td>\n",
" <td>-0.010493</td>\n",
" <td>-0.067248</td>\n",
" <td>0.210029</td>\n",
" <td>-0.061275</td>\n",
" <td>...</td>\n",
" <td>0.057961</td>\n",
" <td>0.238567</td>\n",
" <td>0.097286</td>\n",
" <td>0.102941</td>\n",
" <td>0.135255</td>\n",
" <td>0.017563</td>\n",
" <td>0.040816</td>\n",
" <td>-0.018088</td>\n",
" <td>0.024000</td>\n",
" <td>0.335245</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>5 rows × 1779 columns</p>\n",
"</div>"
],
"text/plain": [
" A AAME AAON AAP AAPL AAWW \\\n",
"date \n",
"20071231 -0.028813 -0.200000 0.049921 0.058120 0.087038 0.029820 \n",
"20080131 -0.078389 0.135714 -0.101917 -0.058173 -0.316640 -0.078938 \n",
"20080229 -0.095983 -0.025157 -0.072472 -0.062605 -0.076389 0.013216 \n",
"20080331 -0.025482 -0.012903 0.213204 0.016995 0.147816 0.086957 \n",
"20080430 0.012739 0.555556 -0.097354 0.018502 0.212195 0.103273 \n",
"\n",
" ABC ABCB ABG ABM ... YORW \\\n",
"date ... \n",
"20071231 -0.011020 0.009507 -0.100956 -0.000490 ... -0.015684 \n",
"20080131 0.038110 -0.063502 -0.055149 0.022315 ... -0.005161 \n",
"20080229 -0.102727 -0.098859 0.001758 -0.041506 ... 0.006550 \n",
"20080331 -0.017737 0.139240 -0.018545 0.129909 ... -0.025325 \n",
"20080430 -0.010493 -0.067248 0.210029 -0.061275 ... 0.057961 \n",
"\n",
" YRCW YUM ZBRA ZEUS ZION ZIOP \\\n",
"date \n",
"20071231 -0.035008 0.030148 -0.100337 0.213083 -0.144402 0.038123 \n",
"20080131 0.071387 -0.103475 -0.114986 0.065595 0.172414 -0.067797 \n",
"20080229 -0.248498 0.008489 0.084989 0.223439 -0.119839 -0.063636 \n",
"20080331 -0.046512 0.080116 0.000000 0.092010 -0.046073 -0.048544 \n",
"20080430 0.238567 0.097286 0.102941 0.135255 0.017563 0.040816 \n",
"\n",
" ZIXI ZN ZUMZ \n",
"date \n",
"20071231 0.179487 0.032747 -0.123741 \n",
"20080131 -0.226087 -0.060100 -0.210591 \n",
"20080229 0.101124 -0.014324 -0.085803 \n",
"20080331 -0.012755 0.008081 -0.107509 \n",
"20080430 -0.018088 0.024000 0.335245 \n",
"\n",
"[5 rows x 1779 columns]"
]
},
"metadata": {
"tags": []
},
"execution_count": 2
}
]
},
{
"metadata": {
"id": "onNW5NsfxuUr"
},
"cell_type": "markdown",
"source": [
"\n",
"<!-- \n",
"## Risk Free actually cancels out\n",
"\n",
"import datetime\n",
"\n",
"df.index = pd.to_datetime(df.index, format='%Y%m%d')\n",
"rf[\"TB4WK\"] = rf[\"TB4WK\"]/100\n",
"rf = rf.set_index(\"DATE\",drop=True)\n",
"rf.index = pd.to_datetime(rf.index, format='%Y-%m-%d')- datetime.timedelta(days=1)\n",
"df = df.join(rf['TB4WK']) \n",
"df[\"TB4WK\"] = df[\"TB4WK\"].fillna(method=\"ffill\").fillna(method=\"bfill\")\n",
"df = df.drop(\"TB4WK\",axis=1).subtract(df[\"TB4WK\"], axis='index') # Deducting RF -->"
]
},
{
"metadata": {
"id": "i9CKQGdYxuUt",
"outputId": "bca99b96-1c9b-4f4a-f09e-3bc63b6ac120",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 224
}
},
"cell_type": "code",
"source": [
"from sklearn.linear_model import LinearRegression\n",
"df[\"label\"] = 1 \n",
"reg = LinearRegression(fit_intercept=False).fit(df.drop([\"label\"],axis=1), df[\"label\"])\n",
"\n",
"df_coeff = pd.DataFrame(df.drop([\"label\"],axis=1).columns)\n",
"df_coeff.columns = [\"TICKER\"]\n",
"df_coeff[\"coeff\"] = reg.coef_\n",
"df_coeff[\"weight\"] = (df_coeff[\"coeff\"].abs() / df_coeff[\"coeff\"].abs().sum())*100\n",
"\n",
"print(\"Normal Regression Weights\")\n",
"df_coeff[df_coeff[\"weight\"]>0.1].head(5) ### Stocks where portfolio weights are more thn 0.1%"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"text": [
"Normal Regression Weights\n"
],
"name": "stdout"
},
{
"output_type": "execute_result",
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>TICKER</th>\n",
" <th>coeff</th>\n",
" <th>weight</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>ABG</td>\n",
" <td>0.159363</td>\n",
" <td>0.149399</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td>ABMD</td>\n",
" <td>0.227337</td>\n",
" <td>0.213124</td>\n",
" </tr>\n",
" <tr>\n",
" <th>12</th>\n",
" <td>ACAD</td>\n",
" <td>0.138325</td>\n",
" <td>0.129677</td>\n",
" </tr>\n",
" <tr>\n",
" <th>13</th>\n",
" <td>ACET</td>\n",
" <td>-0.110286</td>\n",
" <td>0.103391</td>\n",
" </tr>\n",
" <tr>\n",
" <th>36</th>\n",
" <td>AES</td>\n",
" <td>-0.107767</td>\n",
" <td>0.101029</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" TICKER coeff weight\n",
"8 ABG 0.159363 0.149399\n",
"10 ABMD 0.227337 0.213124\n",
"12 ACAD 0.138325 0.129677\n",
"13 ACET -0.110286 0.103391\n",
"36 AES -0.107767 0.101029"
]
},
"metadata": {
"tags": []
},
"execution_count": 3
}
]
},
{
"metadata": {
"id": "i0EPT2kixuU2",
"outputId": "aba0cefb-4dd5-470b-bb50-9c79e3d88a00"
},
"cell_type": "code",
"source": [
"from sklearn.linear_model import Lasso\n",
"df[\"label\"] = 1 \n",
"reg = Lasso(fit_intercept=False,alpha=0.0005, positive=True).fit(df.drop([\"label\"],axis=1), df[\"label\"])\n",
"\n",
"df_coeff = pd.DataFrame(df.drop([\"label\"],axis=1).columns)\n",
"df_coeff.columns = [\"TICKER\"]\n",
"df_coeff[\"coeff\"] = reg.coef_\n",
"df_coeff[\"weight\"] = (df_coeff[\"coeff\"].abs() / df_coeff[\"coeff\"].abs().sum())*100\n",
"\n",
"\n",
"print(\"Lasso Regression Weights, alpha=0.0005\")\n",
"df_coeff[df_coeff[\"weight\"]>1].head(5) ### Stocks where portfolio weights are more thn 1%"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"text": [
"Lasso Regression Weights, alpha=0.0005\n"
],
"name": "stdout"
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
" TICKER coeff weight\n",
"255 CACC 0.827974 3.474682\n",
"311 CHD 1.019468 4.278307\n",
"326 CIZN 0.363135 1.523936\n",
"373 CPK 0.680863 2.857315\n",
"493 DLTR 1.444784 6.063195"
],
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>TICKER</th>\n",
" <th>coeff</th>\n",
" <th>weight</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>255</th>\n",
" <td>CACC</td>\n",
" <td>0.827974</td>\n",
" <td>3.474682</td>\n",
" </tr>\n",
" <tr>\n",
" <th>311</th>\n",
" <td>CHD</td>\n",
" <td>1.019468</td>\n",
" <td>4.278307</td>\n",
" </tr>\n",
" <tr>\n",
" <th>326</th>\n",
" <td>CIZN</td>\n",
" <td>0.363135</td>\n",
" <td>1.523936</td>\n",
" </tr>\n",
" <tr>\n",
" <th>373</th>\n",
" <td>CPK</td>\n",
" <td>0.680863</td>\n",
" <td>2.857315</td>\n",
" </tr>\n",
" <tr>\n",
" <th>493</th>\n",
" <td>DLTR</td>\n",
" <td>1.444784</td>\n",
" <td>6.063195</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
]
},
"metadata": {
"tags": []
},
"execution_count": 10
}
]
},
{
"metadata": {
"id": "4PolZTKExuVA",
"outputId": "e0f79451-994c-4674-99cf-cfd470f5d513"
},
"cell_type": "code",
"source": [
"from sklearn.linear_model import Ridge\n",
"\n",
"df[\"label\"] = 1 \n",
"reg = Ridge(fit_intercept=False,alpha=1).fit(df.drop([\"label\"],axis=1), df[\"label\"])\n",
"\n",
"df_coeff = pd.DataFrame(df.drop([\"label\"],axis=1).columns)\n",
"df_coeff.columns = [\"TICKER\"]\n",
"df_coeff[\"coeff\"] = reg.coef_\n",
"df_coeff[\"weight\"] = (df_coeff[\"coeff\"].abs() / df_coeff[\"coeff\"].abs().sum())*100\n",
"\n",
"print(\"Ridge Regression Weights\")\n",
"df_coeff[df_coeff[\"weight\"]>0.1].head(5) ### Stocks where portfolio weights are more thn 0.1%"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"text": [
"Ridge Regression Weights\n"
],
"name": "stdout"
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
" TICKER coeff weight\n",
"8 ABG 0.141935 0.148249\n",
"10 ABMD 0.207163 0.216379\n",
"12 ACAD 0.123340 0.128827\n",
"13 ACET -0.100802 0.105286\n",
"38 AEY -0.123495 0.128989"
],
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>TICKER</th>\n",
" <th>coeff</th>\n",
" <th>weight</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>ABG</td>\n",
" <td>0.141935</td>\n",
" <td>0.148249</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td>ABMD</td>\n",
" <td>0.207163</td>\n",
" <td>0.216379</td>\n",
" </tr>\n",
" <tr>\n",
" <th>12</th>\n",
" <td>ACAD</td>\n",
" <td>0.123340</td>\n",
" <td>0.128827</td>\n",
" </tr>\n",
" <tr>\n",
" <th>13</th>\n",
" <td>ACET</td>\n",
" <td>-0.100802</td>\n",
" <td>0.105286</td>\n",
" </tr>\n",
" <tr>\n",
" <th>38</th>\n",
" <td>AEY</td>\n",
" <td>-0.123495</td>\n",
" <td>0.128989</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
]
},
"metadata": {
"tags": []
},
"execution_count": 16
}
]
},
{
"metadata": {
"id": "v_N84QJExuVL"
},
"cell_type": "code",
"source": [
"### Each month, calculate the weight and the portfolios, choosing Lasso\n",
"### Use 5 years data and roll forward, monthtly basis"
],
"execution_count": null,
"outputs": []
},
{
"metadata": {
"id": "5kgypAnCxuVU",
"outputId": "a23f1d9f-fca3-4eb8-f3c5-e28ffacf52ec"
},
"cell_type": "code",
"source": [
"df.head()"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
" A AAME AAON AAP AAPL AAWW \\\n",
"date \n",
"20071231 -0.028813 -0.200000 0.049921 0.058120 0.087038 0.029820 \n",
"20080131 -0.078389 0.135714 -0.101917 -0.058173 -0.316640 -0.078938 \n",
"20080229 -0.095983 -0.025157 -0.072472 -0.062605 -0.076389 0.013216 \n",
"20080331 -0.025482 -0.012903 0.213204 0.016995 0.147816 0.086957 \n",
"20080430 0.012739 0.555556 -0.097354 0.018502 0.212195 0.103273 \n",
"\n",
" ABC ABCB ABG ABM ... YRCW YUM \\\n",
"date ... \n",
"20071231 -0.011020 0.009507 -0.100956 -0.000490 ... -0.035008 0.030148 \n",
"20080131 0.038110 -0.063502 -0.055149 0.022315 ... 0.071387 -0.103475 \n",
"20080229 -0.102727 -0.098859 0.001758 -0.041506 ... -0.248498 0.008489 \n",
"20080331 -0.017737 0.139240 -0.018545 0.129909 ... -0.046512 0.080116 \n",
"20080430 -0.010493 -0.067248 0.210029 -0.061275 ... 0.238567 0.097286 \n",
"\n",
" ZBRA ZEUS ZION ZIOP ZIXI ZN \\\n",
"date \n",
"20071231 -0.100337 0.213083 -0.144402 0.038123 0.179487 0.032747 \n",
"20080131 -0.114986 0.065595 0.172414 -0.067797 -0.226087 -0.060100 \n",
"20080229 0.084989 0.223439 -0.119839 -0.063636 0.101124 -0.014324 \n",
"20080331 0.000000 0.092010 -0.046073 -0.048544 -0.012755 0.008081 \n",
"20080430 0.102941 0.135255 0.017563 0.040816 -0.018088 0.024000 \n",
"\n",
" ZUMZ label \n",
"date \n",
"20071231 -0.123741 1 \n",
"20080131 -0.210591 1 \n",
"20080229 -0.085803 1 \n",
"20080331 -0.107509 1 \n",
"20080430 0.335245 1 \n",
"\n",
"[5 rows x 1780 columns]"
],
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>A</th>\n",
" <th>AAME</th>\n",
" <th>AAON</th>\n",
" <th>AAP</th>\n",
" <th>AAPL</th>\n",
" <th>AAWW</th>\n",
" <th>ABC</th>\n",
" <th>ABCB</th>\n",
" <th>ABG</th>\n",
" <th>ABM</th>\n",
" <th>...</th>\n",
" <th>YRCW</th>\n",
" <th>YUM</th>\n",
" <th>ZBRA</th>\n",
" <th>ZEUS</th>\n",
" <th>ZION</th>\n",
" <th>ZIOP</th>\n",
" <th>ZIXI</th>\n",
" <th>ZN</th>\n",
" <th>ZUMZ</th>\n",
" <th>label</th>\n",
" </tr>\n",
" <tr>\n",
" <th>date</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>20071231</th>\n",
" <td>-0.028813</td>\n",
" <td>-0.200000</td>\n",
" <td>0.049921</td>\n",
" <td>0.058120</td>\n",
" <td>0.087038</td>\n",
" <td>0.029820</td>\n",
" <td>-0.011020</td>\n",
" <td>0.009507</td>\n",
" <td>-0.100956</td>\n",
" <td>-0.000490</td>\n",
" <td>...</td>\n",
" <td>-0.035008</td>\n",
" <td>0.030148</td>\n",
" <td>-0.100337</td>\n",
" <td>0.213083</td>\n",
" <td>-0.144402</td>\n",
" <td>0.038123</td>\n",
" <td>0.179487</td>\n",
" <td>0.032747</td>\n",
" <td>-0.123741</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>20080131</th>\n",
" <td>-0.078389</td>\n",
" <td>0.135714</td>\n",
" <td>-0.101917</td>\n",
" <td>-0.058173</td>\n",
" <td>-0.316640</td>\n",
" <td>-0.078938</td>\n",
" <td>0.038110</td>\n",
" <td>-0.063502</td>\n",
" <td>-0.055149</td>\n",
" <td>0.022315</td>\n",
" <td>...</td>\n",
" <td>0.071387</td>\n",
" <td>-0.103475</td>\n",
" <td>-0.114986</td>\n",
" <td>0.065595</td>\n",
" <td>0.172414</td>\n",
" <td>-0.067797</td>\n",
" <td>-0.226087</td>\n",
" <td>-0.060100</td>\n",
" <td>-0.210591</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>20080229</th>\n",
" <td>-0.095983</td>\n",
" <td>-0.025157</td>\n",
" <td>-0.072472</td>\n",
" <td>-0.062605</td>\n",
" <td>-0.076389</td>\n",
" <td>0.013216</td>\n",
" <td>-0.102727</td>\n",
" <td>-0.098859</td>\n",
" <td>0.001758</td>\n",
" <td>-0.041506</td>\n",
" <td>...</td>\n",
" <td>-0.248498</td>\n",
" <td>0.008489</td>\n",
" <td>0.084989</td>\n",
" <td>0.223439</td>\n",
" <td>-0.119839</td>\n",
" <td>-0.063636</td>\n",
" <td>0.101124</td>\n",
" <td>-0.014324</td>\n",
" <td>-0.085803</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>20080331</th>\n",
" <td>-0.025482</td>\n",
" <td>-0.012903</td>\n",
" <td>0.213204</td>\n",
" <td>0.016995</td>\n",
" <td>0.147816</td>\n",
" <td>0.086957</td>\n",
" <td>-0.017737</td>\n",
" <td>0.139240</td>\n",
" <td>-0.018545</td>\n",
" <td>0.129909</td>\n",
" <td>...</td>\n",
" <td>-0.046512</td>\n",
" <td>0.080116</td>\n",
" <td>0.000000</td>\n",
" <td>0.092010</td>\n",
" <td>-0.046073</td>\n",
" <td>-0.048544</td>\n",
" <td>-0.012755</td>\n",
" <td>0.008081</td>\n",
" <td>-0.107509</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>20080430</th>\n",
" <td>0.012739</td>\n",
" <td>0.555556</td>\n",
" <td>-0.097354</td>\n",
" <td>0.018502</td>\n",
" <td>0.212195</td>\n",
" <td>0.103273</td>\n",
" <td>-0.010493</td>\n",
" <td>-0.067248</td>\n",
" <td>0.210029</td>\n",
" <td>-0.061275</td>\n",
" <td>...</td>\n",
" <td>0.238567</td>\n",
" <td>0.097286</td>\n",
" <td>0.102941</td>\n",
" <td>0.135255</td>\n",
" <td>0.017563</td>\n",
" <td>0.040816</td>\n",
" <td>-0.018088</td>\n",
" <td>0.024000</td>\n",
" <td>0.335245</td>\n",
" <td>1</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>5 rows × 1780 columns</p>\n",
"</div>"
]
},
"metadata": {
"tags": []
},
"execution_count": 18
}
]
},
{
"metadata": {
"id": "hcfGhN7lxuVj",
"outputId": "3a8297e5-4980-4d09-cf44-256746416508"
},
"cell_type": "code",
"source": [
"from sklearn.linear_model import Lasso\n",
"\n",
"years_lookback = 5 \n",
"reg_periods = df.shape[0]-(12*years_lookback)\n",
"\n",
"\n",
"reg_type=\"Lasso\" \n",
"#reg_type = \"Normal\"\n",
"\n",
"print(reg_type)\n",
"\n",
"for n in range(len(df)-reg_periods-1):\n",
" df_reg = df.iloc[n:reg_periods+n,:].copy()\n",
" weight_date = df.iloc[reg_periods+n+1].copy().name\n",
" df_reg[\"label\"] = 1 \n",
" if reg_type == \"Lasso\":\n",
" reg = Lasso(fit_intercept=False,alpha=0.0005, positive=True,random_state=22).fit(df_reg.drop([\"label\"],axis=1), df_reg[\"label\"])\n",
" elif reg_type == \"Normal\":\n",
" reg = LinearRegression(fit_intercept=False).fit(df.drop([\"label\"],axis=1), df[\"label\"])\n",
" else:\n",
" print(\"please set reg = to Lasso or Normal\")\n",
" break\n",
" \n",
" df_coeff = pd.DataFrame(df_reg.drop([\"label\"],axis=1).columns)\n",
" df_coeff.columns = [\"TICKER\"]\n",
" df_coeff[\"coeff\"] = reg.coef_\n",
" df_coeff[\"coeff_norm\"] = (df_coeff[\"coeff\"]-df_coeff[\"coeff\"].min())/(df_coeff[\"coeff\"].max()-df_coeff[\"coeff\"].min()) # unity-based normalization or called min-max normalization\n",
" df_coeff[weight_date] = df_coeff[\"coeff_norm\"]/df_coeff[\"coeff_norm\"].sum()\n",
"\n",
"\n",
" df_coeff = df_coeff.set_index(\"TICKER\")\n",
"\n",
" df_coeff = df_coeff[[weight_date]].T\n",
" df_coeff = df_coeff.replace(0., np.nan)\n",
"\n",
" if n ==0:\n",
" df_all = df_coeff\n",
" else:\n",
" df_all = pd.concat((df_all,df_coeff),axis=0)\n",
"\n",
"df_all.head()\n",
"\n",
"df_ret = df.loc[df_all.index[0]:].drop(\"label\",axis=1) # select returns of original dataframe to match weights dataframe\n",
"\n",
"df_port_returns = df_all*df_ret.values\n",
"\n",
"df_port_returns[\"monthly_returns\"] = df_port_returns.sum(axis=1) # equal weighted returns\n",
"\n",
"df_port_returns[\"monthly_compounded_regression_equal_return\"]= ((df_port_returns[\"monthly_returns\"]+1).cumprod())\n",
"\n",
"\n",
"##bench\n",
"df_port_returns[\"monthly_returns_bench_equal\"] = df_ret.mean(axis=1) # equal weighted returns\n",
"\n",
"df_port_returns[\"monthly_compounded_bench_equal_return\"]= ((df_port_returns[\"monthly_returns_bench_equal\"]+1).cumprod())\n",
"\n",
"df_port_returns.index = pd.to_datetime(df_port_returns.index, format='%Y%m%d')\n",
" \n",
"df_port_returns[[\"monthly_compounded_regression_equal_return\",\"monthly_compounded_bench_equal_return\"]].plot.line()\n"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"text": [
"Lasso\n"
],
"name": "stdout"
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x1a24dab128>"
]
},
"metadata": {
"tags": []
},
"execution_count": 19
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<matplotlib.figure.Figure at 0x1a26dc04e0>"
],
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAD3CAYAAAAe5+9lAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n"
},
"metadata": {
"tags": []
}
}
]
},
{
"metadata": {
"id": "zJg3C08DxuVs"
},
"cell_type": "markdown",
"source": [
"### This part forward follows the original notebook"
]
},
{
"metadata": {
"id": "-tU6kwJbxuVu"
},
"cell_type": "code",
"source": [
"import numpy as np\n",
"\n",
"X = 2 * np.random.rand(100, 1)\n",
"y = 4 + 3 * X + np.random.randn(100, 1)"
],
"execution_count": null,
"outputs": []
},
{
"metadata": {
"id": "PTZYLya7xuV0",
"outputId": "174b4904-563a-4f38-f5ce-c791235afb99"
},
"cell_type": "code",
"source": [
"plt.plot(X, y, \"b.\")\n",
"plt.xlabel(\"$x_1$\", fontsize=18)\n",
"plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
"plt.axis([0, 2, 0, 15])\n",
"save_fig(\"generated_data_plot\")\n",
"plt.show()"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"text": [
"Saving figure generated_data_plot\n"
],
"name": "stdout"
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<matplotlib.figure.Figure at 0x1a24d875c0>"
],
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAagAAAEYCAYAAAAJeGK1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAAElFTkSuQmCC\n"
},
"metadata": {
"tags": []
}
}
]
},
{
"metadata": {
"id": "NixC2yGixuV8"
},
"cell_type": "code",
"source": [
"X_b = np.c_[np.ones((100, 1)), X] # add x0 = 1 to each instance\n",
"theta_best = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y)"
],
"execution_count": null,
"outputs": []
},
{
"metadata": {
"id": "2e2GFITgxuWB",
"outputId": "5619e21a-9395-4c5d-cf2d-e6c134198c41"
},
"cell_type": "code",
"source": [
"theta_best"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([[4.20831857],\n",
" [2.79226572]])"
]
},
"metadata": {
"tags": []
},
"execution_count": 23
}
]
},
{
"metadata": {
"id": "6zINTgeXxuWI",
"outputId": "a1f9f54f-069f-4d80-cf76-2df7770020c3"
},
"cell_type": "code",
"source": [
"X_new = np.array([[0], [2]])\n",
"X_new_b = np.c_[np.ones((2, 1)), X_new] # add x0 = 1 to each instance\n",
"y_predict = X_new_b.dot(theta_best)\n",
"y_predict"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([[4.20831857],\n",
" [9.79285 ]])"
]
},
"metadata": {
"tags": []
},
"execution_count": 24
}
]
},
{
"metadata": {
"id": "5sz2v1Q_xuWQ",
"outputId": "e8aa6967-9f86-48a3-d7f1-0842a7e2fb6a"
},
"cell_type": "code",
"source": [
"plt.plot(X_new, y_predict, \"r-\")\n",
"plt.plot(X, y, \"b.\")\n",
"plt.axis([0, 2, 0, 15])\n",
"plt.show()"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAYAAAAD/CAYAAAD4xAEfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a68328438>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"metadata": {
"id": "Ux1sxxcdxuWf"
},
"cell_type": "markdown",
"source": [
"The figure in the book actually corresponds to the following code, with a legend and axis labels:"
]
},
{
"metadata": {
"id": "0nYPXbfSxuWh",
"outputId": "31779b25-df79-43bd-86e3-53f030567203"
},
"cell_type": "code",
"source": [
"plt.plot(X_new, y_predict, \"r-\", linewidth=2, label=\"Predictions\")\n",
"plt.plot(X, y, \"b.\")\n",
"plt.xlabel(\"$x_1$\", fontsize=18)\n",
"plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
"plt.legend(loc=\"upper left\", fontsize=14)\n",
"plt.axis([0, 2, 0, 15])\n",
"save_fig(\"linear_model_predictions\")\n",
"plt.show()"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"text": [
"Saving figure linear_model_predictions\n"
],
"name": "stdout"
},
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAagAAAEYCAYAAAAJeGK1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nMdeqJrmCrScAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a69e08c88>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"metadata": {
"id": "chp4WubNxuWv",
"outputId": "9d33f194-b701-4cb0-cc6b-c75c3a5233f1"
},
"cell_type": "code",
"source": [
"from sklearn.linear_model import LinearRegression\n",
"lin_reg = LinearRegression()\n",
"lin_reg.fit(X, y)\n",
"lin_reg.intercept_, lin_reg.coef_"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"(array([3.95574706]), array([[3.073125]]))"
]
},
"metadata": {
"tags": []
},
"execution_count": 417
}
]
},
{
"metadata": {
"id": "MiX6LB5mxuW_",
"outputId": "3a247e5b-ea72-4a1f-f6b0-8de5acb019c7"
},
"cell_type": "code",
"source": [
"lin_reg.predict(X_new)"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([[ 3.95574706],\n",
" [10.10199706]])"
]
},
"metadata": {
"tags": []
},
"execution_count": 418
}
]
},
{
"metadata": {
"id": "EStqkEDnxuXF"
},
"cell_type": "markdown",
"source": [
"The `LinearRegression` class is based on the `scipy.linalg.lstsq()` function (the name stands for \"least squares\"), which you could call directly:"
]
},
{
"metadata": {
"id": "j49-rCumxuXH",
"outputId": "4a776a2b-4f61-4e7f-9d90-42058d4d13b1"
},
"cell_type": "code",
"source": [
"theta_best_svd, residuals, rank, s = np.linalg.lstsq(X_b, y, rcond=1e-6)\n",
"theta_best_svd"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([[3.95574706],\n",
" [3.073125 ]])"
]
},
"metadata": {
"tags": []
},
"execution_count": 419
}
]
},
{
"metadata": {
"id": "2wbwPItWxuXM"
},
"cell_type": "markdown",
"source": [
"This function computes $\\mathbf{X}^+\\mathbf{y}$, where $\\mathbf{X}^{+}$ is the _pseudoinverse_ of $\\mathbf{X}$ (specifically the Moore-Penrose inverse). You can use `np.linalg.pinv()` to compute the pseudoinverse directly:"
]
},
{
"metadata": {
"id": "s3BLfJVhxuXO",
"outputId": "0eb283ad-10fe-4ce8-d6ba-e98d26495d0c"
},
"cell_type": "code",
"source": [
"np.linalg.pinv(X_b).dot(y)"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([[3.95574706],\n",
" [3.073125 ]])"
]
},
"metadata": {
"tags": []
},
"execution_count": 420
}
]
},
{
"metadata": {
"id": "GeXzq6DNxuXS"
},
"cell_type": "markdown",
"source": [
"**Note**: the first releases of the book implied that the `LinearRegression` class was based on the Normal Equation. This was an error, my apologies: as explained above, it is based on the pseudoinverse, which ultimately relies on the SVD matrix decomposition of $\\mathbf{X}$ (see chapter 8 for details about the SVD decomposition). Its time complexity is $O(n^2)$ and it works even when $m < n$ or when some features are linear combinations of other features (in these cases, $\\mathbf{X}^T \\mathbf{X}$ is not invertible so the Normal Equation fails), see [issue #184](https://github.com/ageron/handson-ml/issues/184) for more details. However, this does not change the rest of the description of the `LinearRegression` class, in particular, it is based on an analytical solution, it does not scale well with the number of features, it scales linearly with the number of instances, all the data must fit in memory, it does not require feature scaling and the order of the instances in the training set does not matter."
]
},
{
"metadata": {
"id": "D_170qJkxuXV"
},
"cell_type": "markdown",
"source": [
"# Linear regression using batch gradient descent"
]
},
{
"metadata": {
"id": "aIxt26CIxuXW"
},
"cell_type": "code",
"source": [
"eta = 0.1\n",
"n_iterations = 1000\n",
"m = 100\n",
"theta = np.random.randn(2,1)\n",
"\n",
"for iteration in range(n_iterations):\n",
" gradients = 2/m * X_b.T.dot(X_b.dot(theta) - y)\n",
" theta = theta - eta * gradients"
],
"execution_count": null,
"outputs": []
},
{
"metadata": {
"id": "VFJjmSfbxuXZ",
"outputId": "e5ba2ac3-a564-4e32-8fdb-ee407c401d3d"
},
"cell_type": "code",
"source": [
"theta"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([[3.95574706],\n",
" [3.073125 ]])"
]
},
"metadata": {
"tags": []
},
"execution_count": 422
}
]
},
{
"metadata": {
"id": "JUEUQLC2xuXj",
"outputId": "59c386f4-dd6d-4694-8aca-aba2f1d59a9f"
},
"cell_type": "code",
"source": [
"X_new_b.dot(theta)"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([[ 3.95574706],\n",
" [10.10199706]])"
]
},
"metadata": {
"tags": []
},
"execution_count": 423
}
]
},
{
"metadata": {
"id": "-DYNlwOCxuXo"
},
"cell_type": "code",
"source": [
"theta_path_bgd = []\n",
"\n",
"def plot_gradient_descent(theta, eta, theta_path=None):\n",
" m = len(X_b)\n",
" plt.plot(X, y, \"b.\")\n",
" n_iterations = 1000\n",
" for iteration in range(n_iterations):\n",
" if iteration < 10:\n",
" y_predict = X_new_b.dot(theta)\n",
" style = \"b-\" if iteration > 0 else \"r--\"\n",
" plt.plot(X_new, y_predict, style)\n",
" gradients = 2/m * X_b.T.dot(X_b.dot(theta) - y)\n",
" theta = theta - eta * gradients\n",
" if theta_path is not None:\n",
" theta_path.append(theta)\n",
" plt.xlabel(\"$x_1$\", fontsize=18)\n",
" plt.axis([0, 2, 0, 15])\n",
" plt.title(r\"$\\eta = {}$\".format(eta), fontsize=16)"
],
"execution_count": null,
"outputs": []
},
{
"metadata": {
"id": "BmSqd5RrxuXt",
"outputId": "b106220d-a897-4faa-8808-79c52da0182b"
},
"cell_type": "code",
"source": [
"np.random.seed(42)\n",
"theta = np.random.randn(2,1) # random initialization\n",
"\n",
"plt.figure(figsize=(10,4))\n",
"plt.subplot(131); plot_gradient_descent(theta, eta=0.02)\n",
"plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
"plt.subplot(132); plot_gradient_descent(theta, eta=0.1, theta_path=theta_path_bgd)\n",
"plt.subplot(133); plot_gradient_descent(theta, eta=0.5)\n",
"\n",
"save_fig(\"gradient_descent_plot\")\n",
"plt.show()"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"text": [
"Saving figure gradient_descent_plot\n"
],
"name": "stdout"
},
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAsgAAAEYCAYAAABBfQDEAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzsnXeYE1UXxt/ZBZYuSFFAaYqoKKg0EUGaFRFE7AiKBVQU\nsCuKiIiNT0SwICrFCipSxAJIUWCRqiJKVXpfBZayNef742VMWFImySSZyZ7f8+TZ3ey9M3cmc3LP\nnHnvOYaIQFEURVEURVEUkpLoASiKoiiKoiiKk1AHWVEURVEURVF8UAdZURRFURRFUXxQB1lRFEVR\nFEVRfFAHWVEURVEURVF8UAdZURRFURRFUXxQB1lRFEVRFEVRfFAHWVEURVEURVF8UAdZ8YthGKca\nhvGFYRj7DcM4YBjGJMMwqtvZ3zCMLoZhfGkYxibDMI4YhrHGMIwXDcMoY/8RKUryE43dGoZximEY\nIwzDSDcM47BhGGIYRs3YjlhRChdR2miro3ZZ8LUv1uMujBhaSU8piGEYJQH8CiAbwNMABMBgACUB\n1BeRQ3b0NwxjEYDNAKYA2ArgfAADAawGcJGIeOw+NkVJVmyw21YAJgBYBiAVwGUAaonIxtiNWlEK\nDzbZ6BwADwJY4vOvPBFZGosxF2aKJHoAiiO5G0BtAHVFZD0AGIbxG4B1AHoCeM2m/h1EZI9Pv3mG\nYfwDYByAVgBm23I0ilI4iNZufxSRk472uwt0kBVFsY9obdTkTxFZFJshKiYqsXABhmE8fVSCcI5h\nGFMNw8g0DGO7YRhDDMMwYrDLawAsMg0YAETkbwALAHS0q38B59jEvCuuFsG4FcUxuM1u9YmNUthw\nm40q8UUdZHdwPoAsAB8AmAzgWtCgngTQpGBjgxSx8EoNsL96AH738/4qAGdbGG80/S85+vNPC/tR\nFCfjNrtVlMKGW230Y8Mw8g3DyDAM45Nw1gcp1lGJhTs4D8AhAFeKSAYAGIaxGUAXADUB/Fyg/SWg\nTikU80ApQ0FOBPCvn/f/AVDewnYj6m8YRjUAgwDMUj2VkgS4zW4VpbDhNhvdD+B/R7d/AHTwnwKQ\nbhjG+SKy28I2FIuog+xwDMMoC6AWgGdMAz5K8aM//ckUlgFobGHzmVEOzzYMwygNLtbLA3BHgoej\nKFFRWOxWUdyKG21URFYAWOHz1jzDMH4EsBhcuPd0LPZbWFEH2fmcB8AAMKvA+/WP/lzpp89BAL9Y\n2HagFCb/wv/dbKC736j6G4ZRAsA0cPHCJSKy1cI+FMXJuNFuFaUwkRQ2KiLLDcNYC2uOuxIGqkF2\nPucDyAfwW4H3LwCwJcBCt0sA5Fp4/RBgn6tArVRBzgbwh4UxW+5vGEZRAF8AaATgKhHx96WkKG7D\njXarKIWJZLNRzdlrMxpBdj7nAVgjIkcKvN8QfNzjj2gfA00FMNQwjNoi8hcAHC0Y0BzAExa2a6m/\nYRgpAD4G0AbA1Zq2Rkki3Gi3ilKYSAobNQyjEYC6YKBJsREtFOJwDMP4BcDvItLV5z0DFOu/IiKD\nY7DPUmAy8yPwJjN/HkAZMJn5waPtLgHvlHuIyPgI+r8NoBeAFwB8XWAYW1VqobgVN9rt0f91Ofpr\nW9A27wO1mHtEZJ7dY1aUROFGGzUM42MAfwNYDmAfGAV/EsBhABeIyF67x1yYUYmFgzEMoxj46KWg\n5ukM0KAC3eVGxdFqPm0ArAXwIRjl/RtAG9OAzSGCFbdSIux/5dGf/QGkF3jdZe9RKUp8cKvdHuXz\no69eR/9+6+jfz8VizIqSCFxso7+DuZTHAPgeQF8AkwA0VefYfjSC7EIMw7gZwCcATtK0LoriDtRu\nFcXZqI0qvmgE2Z00BCUIasCK4h7UbhXF2aiNKv+hDrI7aQhqkBRFcQ9qt4ribNRGlf9QiYWiKIqi\nKIqi+KARZEVRFEVRFEXxwfF5kCtWrCg1a9ZM9DAUJa4sW7Zsr4hUSvQ4rKA2qhRG1EZjQ04OsGoV\nUKoUcMYZ4fXduBHIyADq1AHKlg2v765dwNatQJUqQNWq4fX1eIB164BDh4DTTw9/37m5wJo1/HnG\nGTx2JXqitVHHO8g1a9bE0qVLEz0MRYkrhmFsSvQYrKI2qhRG1Ebtx+MB2ralg7hyJVCjhvW+48YB\nt98OPP008Pzz4e13+nSgQwegSxdgwgQgJYxn6/n57PfLL8CnnwI33hjevnftAlq1AooWBWbPBi66\nKLz+SmCitVHHO8iKoiiKoiQ/I0YAc+cC778fnnO8ahVw7710NAcODG+fq1YBN98MnH8+nexwnGMR\n4L77gMmTgTfeCN853rOHNwSbNwPffqvOsdNQB1lRFEVRlISyZg3wxBPA1VcDd9xhvd/Bg8D111PW\n8MknQGqq9b579zJyXKoUMGUKULJkeGMeOBB4913gqaeABx4Ir+8//wCXXgps2MAIdsuW4fVXYo86\nyIqiKIqiJIy8PKBbNzqo774LGIa1fiKMHK9ZA8ycSf2wVXJyKI3Yvh2YNw845ZTwxvzWW8CgQUCP\nHsDgMItS79sHXHYZ8OefwLRpQJs24fVX4oM6yIqiKIqiJIxXXgEWLwY++yw8J/f994GPPgKeey48\nJ1ME6N2bjvHHHwNNm4Y33i++YP8OHYBRo6w79ABw4ABwxRXAb78BX31FR1lxJuogK4qiKIqSEH79\nlVKFG28MT8P722+UNbRrB/TvH94+33gDGD2a0ohbbgmv79y5wK23As2a0aEvEoYXdfAgcNVVwLJl\ndLLbtw9v30p8UQdZURRFUZS4k51NaUWFCsCbb1rvd+AA5RHlyzMCHI7u+PvvgYceAjp1Cj/bxS+/\nAB07MpXbtGnhaZYPH6a+etEiOtYdO4a3byX+qIOsKIqiKErcGTSIkeBp0+gkW0EEuOceLm6bMweo\nXNn6/lavZpT63HOBDz8ML2PFX38BV14JnHACnewTT7Te98gROsQ//cT9duliva+SONRBVhRFURQl\nrixaBLz0Ehe5XX219X7vvMNcxUOGhJf54Z9/qBlOS2PGitKlrffdvRu4/HIu7Js9O7wFfdnZQOfO\nwA8/AGPGhC/pUBKHOsiKoiiKosSNw4eB7t3paA4bZr3f8uVA376M5D7+uPV+ublMBbd5M6PO4eRY\nzsykbnjbNjq5Z51lva+ZKeO774D33uMxK+4hjAcMoTEMo7dhGEsNw8g2DGNsgDYDDMMQwzDa2blv\nRVFCozaqKM6mMNjoU08Ba9cyomq1LPP+/XRyK1cGxo8PTx7Rpw8jv6NHh1eMIycHuO46ao8nTuTC\nPKvk5gI33QR8/TXw9tvAnXda76s4A7sjyNsBDAZwOYASBf9pGMZpAK4HsMPm/SqKYg21UUVxNklt\no3PmAMOHMwOF1dRsIpRibN7M1GwVK1rf31tv0UF97DEuCLSKx8PS1TNn0pEPRwaSlwd07co0bsOH\nA716We+rOAdbI8giMklEJgPICNDkTQCPA8ixc7+KolhDbVRRnE0y2+iBA6ySV6cO9cdWGTECmDQJ\nePHF8CLAs2YBDz5I53bIEOv9RJjp4tNPOc7bb7feNz+f7SdOBIYO5f4VdxI3DbJhGNcDyBaRb4wQ\nWbUNw7gHwD0AUL169TiMTlEUtVFFcTZut9GHHgK2bAHmz7eeIm3xYuCRR7jA7uGHre9r3TpKMs46\nK/wS1K+8wshv376MPFvF4wHuuoup54YMCW+8ivOwNYIcCMMwygAYAqCPlfYi8q6INBKRRpUqVYrt\n4BRFURtVFIfjdhudPp2V7x57zLqW959/gBtuAKpWBcaOtV6xbt8+OtRFigBTpwJlylgf59ixwBNP\nADffDPzvf9b36fFQSjF2LAufPPmk9X0qziReEeSBAD4UkY1x2p+iKOExEGqjiuJkBsKlNpqRwcjq\nuefSebSCCOUY27cz4mw173BeHnMd//UXJRa1alkf5/TpHGe7dnR0rS4EFKGUwqzON2CA9X0qziUu\nEWQAbQE8aBjGTsMwdgI4FcBEwzDCSNSiKEoMURtVFGfjWhvt3ZtO8vjxzENshddeY/T31VeBJk2s\n7+vhh4EZM7gwL5w8yenplGScdx71zsWKWetn6pXffJNSkMGDrUedFWdjawTZMIwiR7eZCiDVMIzi\nAPJAwy7q03QJgIcAfGvn/hVFCY7aqKI4m2Sz0YkTWVp58GA6n1ZYuJAyh86dw1vk9u67wBtvAP36\nhZdW7Y8/gPbtgWrVgG++sS7JEOE4X3+d43zlFXWOkwm7I8hPAzgC4AkAXY/+/rSIZIjITvMFIB/A\nvyJy0Ob9K4oSHLVRRXE2SWOjO3cC990HNG5svbDH3r2USFSvTs2yVYdz7lzg/vuBK65g1NkqW7aw\nSl5aGiPP4ZSufvZZOsX33ksnWZ3j5MLWCLKIDAR1UqHa1bRzv4qiWENtVFGcTbLYqAhw993AoUOU\nVhSx4G14PMxVvHs3JQ/lylnb14YNLOhRpw6j1VYzVvzzDx3q/fuBH38MT6/8/PN83XknMHKkOsfJ\niJaaVhRFURTFVsaNYxW5YcOAM8+01ueVV4Bvv6We94ILrPU5cIAZKwBqlk84wVq/w4eBa64B1q9n\nKWir8g8AePllLsTr1o2yjnCq+inuQR1kRVEURVFsY/Nmlne+5BLrGuIffwSefpryinvvtdYnP5/p\n2Natozzi9NOt9cvLYxnohQupkW7d2lo/gIsHn3gCuOUW4IMP1DlOZtRBVhRFURTFFjwepmfzeFii\n2YoDuXs3HdbatRmRtSpXeOwxLqp75x3rTq4I0LMnMG0ay1B36WKtH0ApxcMPs8+4ceEVH1HchzrI\niqIoiqLYwltvAbNn09G1ounNzwe6dgX+/ZfyirJlre3ngw8YzX3gATq8Vnn6afYdMMB6pBoARo3i\nvjp2ZGU+K5pqxd3oR6woiqIoStSsW8eo7pVXsuCGFYYMAWbOpEPdoIG1Pj/9xKp1l15KJ9kqI0Zw\nf/fcY71gCUCHulcvpoKbMAEoWjR0H8X9qHpGURRFUZSoyM8HuncHihcH3nvPmkxi9mw6ql27Wneo\nN25kfuRateisWo3kTphAXXSnTlwEaFXG8dFHHNtllwFffGG90InifjSCrCiKoihKVAwdytRsH38M\nVK0auv3OnVzodsYZrHpnxWHNzGTGirw8aojLl7c2tlmzgNtuAy6+ODx5xIQJdPpbtwYmT6bzrxQe\n1EFWFEVRFCViVq6kpve665hVIhT5+XSODxyg81q6tLU+t94K/PkntcpnnGFtbMuXA9dey1RzU6cC\nJUpY6zdpEvfXvHl4/ZTkQR1kRVEURVEiIieH+YDLlbMeCX7uOWDOHGa5OOcca/vp359R4xEjqD22\nwvr11ENXqMBcx1YLj0ybxnRzTZoA06cDpUpZ66ckF+ogK4qiKIoSEYMHA7/8QglCpUqh28+YwT53\n3AHcfru1fYwfz+IcvXqxnLQVdu5kCen8fOD7763JPgBGp7t0Ac4/n7+XKWOtn5J8qIOsKIqiKErY\nLFnCrBDduzP9WSi2baNsoV495hS2Qno6S1a3bg288Ya1CPWBA8BVV9FJnj0bqFvX2r5mzqQco149\nOtVWq/IpyYk6yIqiKIqihMWRI5RWVKkCvP566PZ5edQnHzkCfP45ULJk6D6bNzPrxKmnso+V9GrZ\n2XRyV66kVKJp09B9AEo+rrmGzvTMmdYXACrJizrIiqIoiqKExdNPA6tXUzJhRdv7zDPMX/zRR1ww\nF4qDB+mwZmUBc+dSRxyK/Hxmq5g9m7KMK64I3QfguK6+mpX8Zs2yti8l+VEHWVEURVEUy8ybBwwb\nBtx3n7UFc9OnAy+9xAIdt94aur3Hw+j0ypXse9ZZofuIMM/x558z5dxtt4XuA1DCcdVVjFL/8IM1\nHbVSOFAHWVEURVEUS2RmcoFd7drAK6+Ebr95M53dBg2sSTEApoz76is64VajwEOGsADIww/zZYWl\nS7n9k09m1Pnkk631UwoH6iAriqIoimKJRx9lNbuffgqd/iw3F7jpJv78/HNruYQ/+QR44QVWr+vT\nx9qY3nuPko+uXa057QCwYgWj3xUq0Dm2muVCKTyog6woiqIoSki++w4YNYpOcvPmods/+SQlDBMm\nAHXqhG6/eDHQowfQsqX1ctBTpwI9ezIS/MEHQEpK6D4rV9I5LlOGzvGpp4buoxQ+LFxK1jEMo7dh\nGEsNw8g2DGOsz/sXGoYx0zCMfwzD2GMYxueGYVSxc9+KooRGbVRRnI1TbfTff4E772QKtEGDQref\nMgX43/+Yt/iGG0K337qVqeKqVAG+/BIoVix0n/nzWdCjUSPrWS7++ANo2xZIS2Pmipo1Q/dRCie2\nOsgAtgMYDOCDAu+XB/AugJoAagDIBDDG5n0rihIatVFFcTaOtNEHHgB27wbGjQOKFw/e9u+/WQSk\nYUM6yaE4fJjp3A4eZGq2ihVD9/n9d6BDB6BGDS7ks1Kueu1aOsepqYwcn3Za6D5K4cVWiYWITAIA\nwzAaATjF5/1vfdsZhjESwDw7960oSmjURhXF2TjRRr/8Evj4Y2DgQDq9wcjOZlRXBJg4kZHaYHg8\ndKaXL6dcwkrp6c2bKakoWZIFPaw41Bs2AG3aMBXc3LnWi4cohZdEaZBbAlgV6J+GYdwD4B4AqF69\nerzGpCiKF7VRRXE2cbHR3btZ4rlhQ+Cpp0K3f/RRVtibNImZLkLx/POUR7z6KnMRhyIjgyWkDx7k\nQsEaNUL32biRznFWFmUVZ58duo+i2C2xCIlhGPUBDADwaKA2IvKuiDQSkUaVNCmhosQVtVFFcTbx\nslERLoDLzKS0IpTG94svgBEjgL59Wc0uFJ9/zqh09+7WUrMdOgS0b08Jx9SpwLnnhu6zZQud4wMH\nWCHPSh9FAeIcQTYM43QA3wLoIyI/xXPfiqKERm1UUZxNPG30o4+AyZMZ3a1XL3jbDRu4iK9JE+Dl\nl0Nve9kyOsYXXcTMGKEyVuTmcrHfkiWUfLRsGXof27YBrVsz6jxrFnD++aH7KIpJ3BxkwzBqAJgF\n4HkR+TBe+1UUxRpqo4ribOJpo1u2cGHexRcD/foFb5uVBVx/PRe/TZwYOgPFjh3MWFGpEguChNIp\nizAv8jff0Jnu1Cn0+Hfu5IK8XbsYOW7cOHQfRfHFVgfZMIwiR7eZCiDVMIziAPIAnARgNoCRIvKO\nnftUFDeQns6FIa1aAc2aJW4caqOK4h+1US8ijAbn5QFjx9LxDUa/fiy8MXVqaE3wkSN0jvftAxYs\nACpXDj2eJ54Axo9nerl77gndfs8eOsdbtnAR34UXhu6jOJ+426iI2PYCMBCAFHgNBPDs0d8P+r6s\nbLNhw4aiKG5m4UKREiVEUlP5c+HC0H0ALBUbbVPURhUlIGqjx/L22yIAf4bik0/Y9tFHQ7f1eERu\nvpntv/rK2lhee43t77uP/UOxd69I/fr8HOfMsbYPxfkkwkZtXaQnIgNFxCjwGigizx39vbTvy859\nK4pTmTsXyMlheqGcHP6dKNRGFeV41Ea9bNgAPPIIK8317Bm87Zo1jOhedBHLQ4diyBDg00/504pM\n4uOPgYceAq67DnjjjdA65X//5bjXrGGhklatQu9DcQeJsNG4Z7FQlMJGq1bU5KWm8qd+aSuKs1Ab\nJfn5zElcpAjLNgdzSI8coe44LY2lpENluPjqK+Dpp4Fbb6VkIhQzZnAsrVpxsWAomcf+/Uz/tmoV\n93XppaH3obiHRNhoovIgK0qhoVkz4IcfnKFvVBTleNRGybBhLN88fjxwyinB2z7wALByJfDtt6Hb\n/vIL0LUr0LQp8N57oSPBS5YAnTszc8bkyaEr92VmAlddRR30l18CV14ZvL3iPhJho+ogK0ocaNas\n8E66iuIGCruNrloF9O9P6UPXrsHbfvgh8P77LBxyxRXB2+7aBVxzDXDiidac3bVr6exWrkzn+4QT\ngrc/dIgFRn7+mZHsa64J3l5xL/G2UXWQFUVRFKUQk5vLnMRly4bOSfzHH6ysd8klwHPPBd9uVhYL\nhuzdy8j0yScHb79jB2UShsHsE1WqBG9/5Agd4vnzqVe+7rrg7RUlHNRBVhRFUZRCzJAhLNzx5ZfB\n064dOkTdcalSwCefUKscCBEu4EtPZ4W9Cy4IPob9+xmN3rOHj9Hr1AnePiuL0e45c1jl76abgrdX\nlHBRB1lREoRT8q4qiuKfwmCjy5YBgwdz8VznzoHbiQD33Qf8+ScX0FWtGny7r75KKcagQaEju1lZ\nzI3855/A9OlAo0bB22dnc5szZlDqcdttwdsryUssbVQdZEVJAOnpTGSfk8MVuT/8kLwTsKK4kcJg\no1lZQLdujBqPGBG87ZgxXLz37LNAu3bB206dykwVN97IzBXByM+ncz5vHqPSobJP5OZyu998A7zz\nDtCjR/D2SvISaxvVNG+KkgCclHdVUZTjKQw2OmAANcXvvw+ULx+43W+/AfffT2fkmWeCb3PlSjq8\nDRvSqQ6mZxbhdidNAl5/Hbj55uDbzssDbrmFOY5HjAidp1lJbmJto+ogK0qMSE8HXnyRPwuieVcV\nJfEUZhtdsAAYOpQ64WCZKDIzqTsuV44L4YLlI96zh4vmypRhxooSJYKPYdAgLgp8/HGgT5/gbfPz\nGe3+4gvgtdeA3r2Dt1eSg0TaqEosFCUGhHr0o3lXFSWxFGYbPXiQWStq1qSTHAgRRmnXr+e5OOmk\nwG2zs6lh3rkT+PFHoFq14GMYNQoYOJDjePHF4G09HkopPv0UeOkloF+/4O2V5CDRNqoOsqLEAH+P\nfgoab2HPu6ooiaQw2+jjjwN//cVjLlMmcLt336VTOnhw8OicCHDvvUy39umnQOPGwfc/aRIX/LVv\nD4weHVyG4fHQSR8/nhHnxx8Pvm0leUi0jarEQlFiQLI/nlUUt1NYbXTmTOCttxiFbdkycLsVKyh7\nuPxy4Mkng29z2DDqjZ95JnS6tXnzqCNu0gSYODF4iWoRSinee4+L/ULpn5XkItE2qhFkRYkByfx4\nVlGSgcJoo/v2Uapw5pmMCgdi/37qjitWZKq2lCChtG++AR59lGnXBg4Mvv9ff6VGuXZt4OuvgZIl\nA7cVoRP/9tvAY48xeqwULhJto+ogK0qMSNbHs4qSLBQ2G+3bl9Xq0tMDL6ATAe66C9i4kY5JpUqB\nt/fHH8w80aABi3UEc6Q3buRiwDJlWCWvQoXAbUXoFA8fzjG/9FJwGYaSvCTSRlVioSgJINjKXEVR\nEksy2ueUKXRin3oquEb4zTeZKWLIEODiiwO3y8gAOnSgoz1lCqvrBWLPHko1srLoHJ96auC2IpRT\nDB1KnfJrr6lzrBxPPGxUI8iKEmcKQwECRXEryWifeXlM53b++cELdyxZAjz0EBfPPfJI4HY5OUCX\nLsC2bYwyB3N4Dx7k9jZvBmbNAurVCz7WQYPonN99N3Mdq3OsFCReNqoRZMVVJENkpzAUIFAKL263\nUSv2eehQvEcVHZs2UX88bhwdCn/8+y9www3AyScHl0uIAA88wPPy/vvAhRcG3m9ODrXJy5dzQV7z\n5sHHOWQIdcy3384qecEkG0pkuN0+gfjNobZefoZh9DYMY6lhGNmGYYwt8L+2hmGsNgzjsGEYcwzD\nqGHnvpXkx7xrfOYZ/nSrgRdcmVuhQvy+sNRGlViSDDbqb+W86VR8/z3w3HNA1aqx238sbHTfPkZm\nzz3X//9FgDvuALZupSMbTB88ciTTvz35JCvmBcLMXTxjBtt36BB8jEOHAv37c5vvvafOcSxIBvsE\ngtuoncdkt8RiO4DBAC4H8N8SAMMwKgKYBOAuANMAPA9gAoAg956KcixWciK6Ad+VuRUqcBFKHB/n\nqo0qMSMZbLTgynkAaNOG+tk4YbuNlioVXDLx+uvUEb/2WvCI8IwZ/L7q2DF4FgyAmS0+/hh44QU6\nysF44w22v+EGYOzY4NX6lMhJBvsE/NtoLCQXtt6jicgkEZkMIKPAvzoDWCUin4tIFoCBABoYhnGm\nnftXkptE50S0k2bNGIHJyIiv3EJtVIklyWKjpn2eeCJw//3HOsfFigFFYrh6JxY2WqtWYKdz0SJm\njOjUic5vINasoQN7zjnARx8Fj/AOHUpn+4EHQudQfvtt5lu+9lpuN5bntrCTLPYJeG20WbPYSS7i\n9RCjHoBfzT9E5BCADUffVxRLmHeNzz/v/w7RjdoqB31hqY0qUZMsNrpkCfP1nnUWC2b4kp8PdOuW\nkGFFbKNpaf7fz8ig03vKKcAHHwReEPfPP5RIFCsGTJ0KlC4deF/jx3ujwa+/HnyR3fvvM1PF1VcD\nn30WvGiIEj2h7BNwj436Eqt5NF73aqUB7Cnw3n4AfotcGoZxD4B7AKB69eqxHZniKgLlRAy2qjU9\n3bnFABKdCN0HtVHFFtxqoyIc03PPsWSySfnyXMBWrBijnPXr05lMALbaqMcDdO8O7NoFLFjA4/RH\nbi6d3U2bgNmzgRpBVM/ffEM5Rdu2dJSDRZnHj2emiiuuYFq5QIsHFXsJllfY6TYaiFjNo/FykA8C\nKFvgvbIAMv01FpF3AbwLAI0aNZLYDk1JBgJpq9yQsskhxQrURpWY4lQbzc8HvvqKjvHvv3vfL1eO\ni9vS0pgaLTeXEc8JE1gmecOG+I3xKLba6NChwPTpTKXWqFHgnfbrx89kzJjgWSgWLWL1vQYNgEmT\nAketAeDTT7kosE2b0G2V+OFUG7VCLObReEksVgFoYP5hGEYpAKcdfV9RgmLlkU+gRyyJSqkWyWOq\nBD/aUhtVIsaNNjpvHlOQVatGx+733xnxLHM0HlupEheidehAZ/Lll1mi+e67gWHD4jPGAthmo/Pn\ns2DI9ddTYx2It99m4ZBHHmHqtUCsXs1cx1WqMIpctqAb78MXXwC33Qa0aEG5RqCKfop9WJ1bnGaj\n4c6Jts+hImLbC4xIFwfwIoAPj/5eBEAl8FHQdUffexnAIivbbNiwoSiFl4ULRUqUEElN5c+FC4O3\nHTLE22bhQpFevUSKFbPWPxFjDtQHKPOn2GibojaqxAi32eiBAyK9e4tQVMFXkSKm3Yk0aSLy4osi\nnTuLGAYGTB6UAAAgAElEQVTHduedIp984j3O4sXda6O7d4tUrSpy+uki+/YFPk8//MBjbd9eJC8v\ncLutW0WqVxepXFlk/frg537yZJ7r5s1FMjODt1XsIdz5yAk2Gum4C7YHsFSiscVoOh+3Ma6qlQKv\ngUf/1w7AagBHAMwFUNPKNnXyLdwMGcILHuDPIUOs9fM1lrQ0Gng8jFoksjEX7ANU2yqxmXzVRhVb\ncYuN7t4t8tRTIqVKHescm6/LLxd54QWRiy/m3+XKiTz5pMj27d7jTEnx7eM+G83P53GmpYmsWBH4\nXK1dK1K+vEi9eiL79wdu988/IuecI1KmjMjy5cHP//TpIkWLijRtGnybir1Eap8i7ppH/bWP1kG2\nVYMsIgOPGre//80CoCmjlLAwH/mY2ierq1N9HwkBQPXq8dNMRTLmgn2OHDngV1cYLWqjit043UY3\nbQJeeYXFJ3Jy+F5aGpCdzd9TUigfSE9noYrq1SmhuPNOyi08HmDaNEoDPB72SU0F8vPdZ6NmsZN3\n3gHOO89/m337KCtJSaEEIpBc4sgRZvpYuxb49luWsQ7EjBlA584sVPLdd8ElGIq9RGqfgLvm0WiO\nMxCacVBxNJGuTq1QgV/wIvFPn9asGdMbffklNY5WxlzwOC+6KNNlxWyVwopTbfT331mkYuJEr2Nb\nujRw8CBTj118MbBlCzNUfPABHcaPP6Yut2hRlpN++23a8tq1TIV2//3MjXzlle6z0TlzgAEDgJtv\nBu65x3+bvDzgppu4AHHWLKB27eDtFixgerY2bQLvd/ZsFhY580xg5kwuflTiR6T2mZ4ObN7szUvt\n9Hk0Jpksogk/x+Olj2+VcDEfC6WkUO82alRs9uGr0/K3/2j0Wojy0VA8X2qjSrjE0kYXLhS57DI5\nRj5Rpgx/nniiSN++Ip06ef+XkiIyfLiIx8P+27ZRWnHiifx/48Yin34qkpNz7H7cZKP16zeUk08W\nqVuXGuxA9OnDYx49OnAbj0fkrrvYbsSIwO1ERObNEylZklKN3buDt1Wcg+8cVqxY7KQVTp9HNYKs\nJB3mYyGPh5GijIL1qKIkVMqbZCnnqSixwm4bFeGj+4EDgcWLj/9/qVLAvfcCGzcyrZkI92v+PHSI\nBUGGDWMat/x8VpZ76CHgoouCF7twA3//zajvjBneLB0FGT0aGD6c1fTuuivwtp59lnKV/v2B3r0D\nt1u4ELjqKj6W/+EHZgVR3EE8pBVumEfjleZNUeJGNFV1rKSJCZXyxkHV8RTFkdhlo3l5zKl75pl0\nxhYvpjPrW67YMOggv/IKU5D16cPHtsWLU+KRmkp9ccOGwOTJrOy2bh3bNG/ufucYADIzgZEjqQH2\nx7x5PO7LLwdefTXwdt58k1XY7ryTPwOxeDFlKFWrUmJx0knRjV+JL7GeQwGXzKPRhJ/j8dLHt0ok\nBHt0E6yPlUc6VtpFsn9f4KLHt2qjSiREY6OmNKNiRflPKmE+DgZEzj/fu6IdYLuXXhL5919u5+BB\nkYcfFqlQgf8/9VSRV1/1/j8Y27aJDBjgLhutUKHhfxKSgmzYwPNw5pnB075NnMi0d9dcI5KbG7jd\nsmXMAFK7tsiWLYHbKc4mlnOo1baJnkdVYqEkFb7lMJ98Mry+Vh/pWFkM4JDqeIriOKKx0e++A7Ky\n6PZ6PMDevVxQ5/HQbtu3B2rVYnW2/HygcmXKBQYMYOaKbdtY8GPUKC7Oa9KEUdHrrjs26lwQEeCn\nn9jW3LabqF7dfyT8wAFmrPB4mLHihBP89589G+jalRH1zz4LfK5++w249FJmqZg9mwsbFfcRaVnp\ncGQRbphH1UFWkoZwymH6+wIwH+lkZ3MyqVAh8L4SbbiK4kYitdFatYD//c+rHy7ITTexItvnn9PR\nu+QSZqC48krKKJYvB157jfpijwe49lrqi5s1Cy6hOHSImS1GjgRWrmQGhj59qGc+/XQ7zkh8SPEj\npszPZ0aLtWuZ+q1OHf99V6ygHrtOneCV71at4mdbogQzZtSoYd/4lfgRzTzqm2otNZVZMNLTgzvJ\nTp5H1UFWwiLSO8t4EOru1Rx7hQpciFLwC8BMK9O7N7fRty81e047TkUJRjLZqHmzCnijtkWLArm5\n/D01FWjZkqnc8vMZCX70UaBxY/49bRoX3s2bxxRvvXsDDz5IhzsY69YBb70FjBkD7N8PNGjAhWk3\n3wyULGnzSUkQTzxBTfbbbwdO0/bXX7zJKFeO0fvy5f23W7OGTlXRonSOA6WHU5xtn0D08+gPPwDj\nx9N2Ro8Gxo0L7mQ7GXWQFcuEc2eZCIIlCvcdu2EwiuTxHP8FkJER+H9WcfoXoJK8JIuNAsfLGEqW\nBA4fplQiL4+R5Px84Mcfmdf3oYfomB06RCnE668D69dTXvC//3FhmSkh8Gej+fksePHmm3QGixQB\nunShU50MmSx8GTsWGDqUeZ179fLfZtcu4LLLeDMyZ05gucT69XSwRXi9BYpEK863TyD6ebRZM/6e\nlxddBgonzKPqICuWcULalWAE0zT5jt1cuW6udvd9DBRtNR43fAEqyYubbXTOHEaMzaIeBalYkdHM\nuXMZsQRov1Om8P2tWxkVHTWK1eCaNmWhkM6dj9XMFrTRr76ifOKtt5gOrUoV4LnngLvv5u/JxoIF\nvKFo1443Ef7IzGRWkO3bqSU+6yz/7f7+m85xdjY/l0DtFOJ0+wTCn0cB/u4rSUyaeTSaFX7xeOkK\needgR+LuRFFw7KNGMfl5sWLHH8+oUSw0EEnxgmjq3vsCF62QVxt1Dm600fx8kSlTRE4/XY4p7mHa\nkWEc+36dOiK33irSti1tdMkSkVtuYVaLlBSRLl2CH7evjRoG+wEiLVuKTJhwfEGQQLjRRv/+W6RS\nJZ7Df/7xf1xZWTy3qaki06cHPv5Nm0Rq1BApX15kxQpr56yw40b79KXg+B97zGt3BY8nGeZRjSAr\nlolJKcc44W/sL77IO+GCeRhNXdVPP4WvQW7VitEqj4c/NQeyEk/cZKO5ucxh/OyzLOABeEtPiwCt\nW1PytGKFt8+tt1IScOmltNE5c2hrZcoADzxAfXHNmoH3mZPjLVACcD/t2wODBgH168fqSJ1BZiZw\nzTU8/mnT/OuJPR6ge3deQ+PGMYrsj23b+Pns28e2550X27EnC26yT38UHP/cud6MMr4R8fT05JhH\nLTnIhmG8A6AngGoisr3A/+oCWAngHRF50P4hKvHCiubH6atOgcDHUXDs/h4D2fEITOTYn4piB1Y1\neU630cOHWYVt9GjqhQFOgqbmuEMH2uPXXzOlm5mBIS0NuOMOpmnLyvJu76qr6GiXLRt4n9u2UXrx\n7rvU1poULQo8/njyO8cA07T98QcX5tWte/z/RYB+/Zjp4+WXgW7d/G9nxw7KKvbsAWbOZIEVhST7\nHAocP35/UoqkmUethJkBdAcgADr5+d83APYCKB9NKDvQSx/fxodYPPqJNsl3pPsM5zgKjjHa8+CU\nR0PxfKmNxp5YPZqNp41mZIg8+6xIyZJyjGQC4DHdcIPI5ZdT9pCWJnL33SKrV3Nsjz1GWUW5cmyf\nksJX8eKBx+7xiMydS8lFaiq3e/XVIrffzr6FyUZPPrmhACJvvBH4eF58keekXz8JWFRk1y6Rs84S\nKVVKZP78cM5W8pMMNmruL5o5NJJtFMQp86hVicWioz+bAJhsvmkYRnsAVwK4X0T+tcNhVxKDHXd8\nvnedgP0ieyt35+EeR8G74WgfgUW7OEFR/GHX4p5E2OjWrSzzPGqUN0OFL/Xrs+zzxIl87P/UU5RL\nnHQSsHQpcx9PnEhXuksXRjlFAtvowYPe3MW//85t9uvH3MW1a3OMEyYULhvduRPo2ZMZOfwxZgyL\nttxyC7Nb+MvYsXcvF/Zt3MhsH82bx3TIrsMNNhqPOdR8LynmUSteNAADQAaAWT7vFQWwBpRXpEbj\npQd7aXQqPkR7x1ewf69e9twBhjs+JyyCsOOOHy6KTqmNxh47rut42+innzLq61vyOS1NjoseA1zs\nNXy4SGamSF6eyKRJIhdfzP+VLSvy0ENcYBaMNWtE+vRhe0DkvPNE3n9f5NAh/2ONxkZ//dVdNlq6\ndMOAiw+nTuVndNllItnZ/ttkZPB8Fi8uMmtWuGercOB0G3XTHGqOI9HzqKUIsoiIYRiLADQ3DMM4\nuuM+AM4A0E5EXFZ4UylItHd8Be86gfDuAEPd2dpZBjrWuEFjprgLO67reNrokSMsqmFi7qdOHaYC\nmzWLpZ7r1gUGDmRkOCuLkczXX2eBipo1WeSjR4/A+uL8fGpqR44EZsygptjMXRysSl4kNvrPP8An\nn3CMy5eH1zfRnHYaz01BFi4EbrgBuOAC4Msv+TkVZP9+4PLLqV+eMoURTeV4nG6jbppDzXEkfB61\n6kkDeAbUIZ8JoDKA/QC+isY7t/LS6JQ78HfXafUO0ModayR3tYnQQNsFXBSdUht1B7G0UY+HEeCC\nKdnMFGrNmol07OjVH19xhcgPP4gsWODVF59wAv930UUin38ukpsbeDx794q88opIzZrsU7WqyKBB\nIjt2RH+efMnLE/n2W+qjixWT/yLTw4e730Z//50p2urUEdm92//xHzggcuGFIkWLikybFtEpVMIg\nljYaaWS4MM+j1hsC7Y46yN0AvAcgC0DtsHYG1AQX9f0LYCeAkQCKBOujk681nHARRzoGq4L8cLbv\nlMdEkZKoyVdtNHYko43m5dGZPfNM+c8pNgyvo9y2rcill7JPkSIi3bqJ/PYb+7733rHyi7ZtRRYt\nCj6OZctE7riDj/oBkUsuEZk40XruYqusWyfy1FMip5zC/Zx4osiDDx6b79fNNrp5M4/t5JNF/vrL\n/zk4eJAyl9RUSl4KA8loo9Fsu7DPo+EYZVkA+QB+PPrzpbB3RqMeC6A4gJNB/fKDwfro5Bsat1/E\nsRi/XatgE0UCJ1+10RiQbDY6d67I6NEi1ap5HVzT3ooVE7nqKkYeAZEyZUQeeURkyxY61F9+KdK8\nubefmZUikI1mZYl89BGj0ACj0D17eh1tu8jMFPngA5EWLbxjuvJK3gBkZR3f3q02mpHBTBRly4r8\n8ov/c3HokEjr1jwHEyZEcDJdSLLZqM6j0duo5UIhInLAMIw/ALQ4etf6gtW+PtQCMFJEsgDsNAzj\nOwD1ItiO4oMbylcGIxaaJ8esgnUfaqMxIFls9Pvvmf/22mupIQaYwzgvDyhVCmjZEli/nrrgatWY\nveKee5jL+IMPgOHDWZ64Vi2gTx9mtsjN9W+jW7d6cxfv3k398uuvs5BFuXL2HJcIMH8+dcUTJzIv\nc506LCJ02208BgcSsY0ePgxcfTU13t9/DzRocHybrCygUydeox9+SI1yYSBZbFTnURsJx5sG8D4o\ns7g9Em8cLDYyHkBJANUA/A7gWj/t7gGwFMDS6tWrx+C+Irlw+51vrHDC47JIQeKiU2qjMcDtNrp7\nt8gTTxybw7hoUf48+WSR9u1FqlTh3+ecIzJ2LDMibNok8vDD3swSzZszgpyXx+0WtFGPR2TOHJHr\nrvPmLu7QQeS771iS2i62bBF54QXqbwGR0qVFevRgbt9AOYAL4jYbzcnh52QY/Az8kZXFqDkgMmaM\n1bOZHLjdRmNFYZ5HwzHKogA2AFgCwIhoZ8BZAJYByDvqaI8Nta1kenwbywvNzRexciwLF4oA1bZK\nYiZftVG10f/YuFHknnu8zrCvY3zaaVxsV6YM/27dWuSbb+hg/vyzyI030tlITRW56Sa+F4jMTJG3\n3hKpV0/+0/w++mhgfWwkZGVRLnDFFd5CIS1b0pnPzAxvW2600Tvu4DG//bb/Y8rO5s0IIDJqVHjn\nI56ojSqhMD9HoMyfEicH+UkAHgAXRrQjIAXAJgD9AaQBqABgCoBXgvVLlslX706jpzB8eZnXCdBQ\nJP4Tr9qo2qiIMMNBly7HZqUwM1LUry/SqhXPU0oKHeGlSxkVfuEFkerV2e6EE6g93rQp8H5Wr+bi\nNzPCfP751AEfPmzfsSxfLtK7N51ugIvTnn5aZP36yLbnRhs1K+k9+6z/Y8rJEencmedn5MjIzks8\nUBuNnmSfR32vEeCCfImVgwzgRAA3A3jx6N3q0Ih3BFQ8erd7gs97nQD8HqyfGydffxeg28Tu4aSW\niYexhfvFGMm4nPDF4b1OEjL5qo0WchtduJDZJAouoAO46K5pU/lvodyDDzLCu3+/yLBhXomFGWWe\nOdP/PvLyRKZMEWncWP5zvG+9lfsOJm8I5zj27BF5/XWRBg24j7Q0OvLff++Vd0SKG20UaCg9e/o/\nv7m5jPAD/BydgtpobMYTy3nUWXOoCHCBR6Kxt6D/pHMsAHYBeBVRVswD8BeAJwAUAVAOwFcAPgnW\nx22Tb6AL0E13vlbHGs9jCueLMZJxOeXz8UanojPsSF9qo4m/Bqxgp416PJRGXHCB18E1I8epqZQh\nnH02/65cWWTwYGZC2LiRFe7M6G+NGl5n2p+N7t0r8vLLbOe7n+LFrU3UoY4jN1fk66+pXzZlIA0b\nirz5psg//1g5q9Zwo42WK9fQ741BXp7IbbfxXL3yin3nKFrURmNDLOdRp3w2dkaQUxAEEflURAwR\nOUlEHpXoK+Z1BnAFgD0A1gPIBdAvym06Cn8rYQHvCtPnn4++nnokpKdzZXZ6eui2gY4h0nZ2YK6m\nTU0NvZo2knHF81iCYV4nwK7tiRmB2mhhsdG8PODTT5m14aqrWB0u5eiMUKIEcMklQJUqwI8/su27\n7wKbNrGS2r33sjrb8OFA+/bA4sXcVlra8Ta6bBlwxx3MCPH448xgccst3JcIs1iEsrdgx7FmDfDE\nE0D16szQMG8eK+n99huwdClw331A+fKhz6lV3GijtWvzc/HF42GGkQ8/BAYPBh59NEajjQC10dgQ\ny3nUaXPo888DwLq1UW0sGu86Hq9kiU65aUxOvPM192dXZT47+sQSuLxKl5Nx2mcdyZiisdEjRxhV\nPekkOS6HcfnyLL7hW9Xuq6+4gOvzz725iE84gRXwNm8+fn9DhjBP8ocfenMhlyol0quXyMqV9hzv\nzJnMw3zRRd7xd+jAghbZ2ZZOedS42UY9HuaSBkQGDLD1tNhCYbfRWBKredSJn1m0Nppwww31ctvk\nK+IMHY4vkei2nKadChe3apBN3Dz5ugEnfdYi8bHRGTNEnn/eK4nwdYyrVWMKtmLFKHu49lqWgd6/\nX+S117yyiNNOE3njjcBZHzZvFunfX6RSJbY/4wyWZd63L/Lxm8yfL3LXXUxDZqabO+ssSgPsLjFt\nBbfaqMcj8sADPH9PPGE9rV28KYw26pRjNXGjBtkXdZCVkNh9Z+c0I0gEsT4Hbp18lciIpY3u2CHS\nt6+3PLOvY1ynjkijRvLfQraePUXWrBH5+2+Rfv28KdxatGAk2Z+O1eMRmT2bWRDM3MXXXMMFcXbk\nLt60SWTQIJHatTmWsmWZei493b5FfZHgRhv1eKgbB/jTqc6xE9F51H6cbqMJN9xQL5187cGuC9GJ\nj1HiTTzOgRsnXyU67LbRlBRvKraCGSnOPZfRVzPn8DPPiOzaxb7XX892RYqI3HKLyJIl/vdz4ABz\nF5sL+E48kbILO3IXHz4s8sknIpde6l0w2KYNZRuHDlk/B2qjXhv1eBgxBpj2Tp3j8NF51D7cYKOW\nS00r8Sc93b6ykc2a2bOgwe3lOO1Az4Fi4kQb/eQT4MiR4983DOD881m2eeVKLpYbMYIllWfMADp2\nBBYtYhnnRx/lQrdTTjl+O6tXA2+9BYwdC2RmAhdcwFLNN97IxX2RIsJFdWPGcMHfvn1AjRrAgAEs\nL12rlvVtqY0ez8CBwEsvAT17Am+8weuhMOBEG9Xr0x3nQB1kh5KeztXiZg30RKzY9Uehr80OPQcK\ncZKNigA//QQ89RSwYMGx/ytShI7xhg3MKNGoETB0KMc+bhzQoAGzU5x+Oh3m228HSpc+dhv5+cDX\nXwMjRwKzZgFFi9Ihvv9+oGnT6Jyt3buBjz6iY/z770Dx4sB11zHzRevW3swa4aA2eiw7dgCDBvGc\nvvVW4XKOnWKjvuj16Y5zoA6yQwnn7irQHXI4d85W25opVOy6I3cjeg4UwBk26vEA06YB/fsDq1bx\nPcOgw1ysGNN7bdoELFnCVG6PPsp0aCNGAHfdxQhwy5ZM13b11cenAtu7F3j/feDtt7mdU05hSrC7\n7gJOOim88+VLbi7w7bd0ir/+mmnkmjYF3nmHjne5cpFvG1AbLcj27UDXrsDo0ZHdcLgVJ9ioP/T6\ndMk5iEafEY9XYdQ3LlzIlEhpaZGniAlH37NwoXf1erFihVMP5TTgMn1jYcLUIY4aFV0ap2hs9Mcf\nRcaMETn1VDlOX1yxIivIGQYLZtx+O9OrLVjAIhqmvvjWW1ki2h9Lloh0787vIECkdWuRL79kMY5o\nWLWK5afNFHMnncS/V62KbruJwE02Wr58w6g/OzfhBBvVeTTxRGujGkGOEDt1TQW3az4SSk0F7r4b\n6NYt8D5875CzsoDx49k2nDvn8ePZBuBPcxuK4mZiYaMFH9m+/jqQkRF8H7Gw0UsvBbKz+XdKCiPJ\nVapQGrFmDds8+iiLZCxaxIjvzz8zMvvYY9QXV6t27D6ys4GJEymjWLwYKFUK6NGDMop69SI/Z/v3\nA599xmjxzz9T8nH11Xzcf+WVlGu4hZ07galTgSlTEj2S8KhVi+fdaSSzjeo86n4caDLOJ5a6Jl+D\nBPg4NNi2W7WiI52fzzjSmDF0qN2g71GUWBErGy04YWZkAE8+GbyPHTaalXXs39nZXse4dm1uY/Nm\nSiCGDgVuuIHObsuWfP/00+n4du9+vL54yxZKG0aPBvbsAerW5SKubt2AE04I/xwBHNecOTzWL7/k\n+OvVA/73Pz7qr1w5su0mgtWrgcmT6RQvWsT3wlkw6AScqDlONhtVko9CpEayD393mybhlKL01zac\nUpAAv1B69PB+Aeblee9yrZbk7NaNJWINgz+7dQs9dkVxMnPn0onMz+dP37Kn0dhouPYJRGejW7cy\nCvzRR8f/r25doEIFYP16OrLjx3MB3ZYtwNlnA488Qud5yhRGle+/3+sciwCzZwOdOwM1azK7wUUX\nATNnAn/+CTzwQGTO8caNzJZQuzbQrh31xXfcwYj0ypXAQw853znOzwcWLmSkvW5d4Kyz6GDl5fGz\n+u03LnhUoiNZbNRE59EkJBp9RjxeTtQ3mlojU/uXlsb3wtUrBWobSfWaaPMJatJyZwEX6RudaKOj\nRnntE+DfIvbYaKRVGsOx0dWrRW644dgcxgD1jbVqeSvJtW0r8u23Ij/9xEIdpr64a1eRZcuO3+6B\nAyIjR3pzIFeoIPL44ywMEimHDjE/cZs23jFeeinzGB8+HPl248nhwyLTprFSX+XKPI4iRXgcb74p\nsmXL8X3URqPD7TYaaBs6jzqHaG1UJRYRYN5tjhpF0zbvNgHreqVg2qZwcy0WXA0K8I46HF2XXfkd\nFcUJZGR4JQgpKfwbCE9TGKhtJLZi1UaXLmWqtpkzj+1fvDgf669dS8nEDTcAffsCf/0FPPssI7Tl\nywOPP85IcUF98erVwJtvMq1bZiZTvY0dy4wRxYuHdywAv/d+/pmPoj/7DDhwgFHjQYMo46hePfxt\nxpuMDGD6dEbYv/8eOHQIKFOG2T46dqQ+OtpsGkpg3Gqjobah82gSEY13HY+XE+98RfzfbdoVQbZ7\nXImg4J203lmHBzQ6FRV2rUqPh40uWCAyc6ZIw4bHRtTMssp16vD3UqVE+vQR+fVXkVde8WawqFOH\nFe0OHjx2P7m5LA/dti3bFSsmctttIj//7B1HuDa6Ywf3bUagS5YU6dZNZM4ce8pKx5q//hIZNkyk\nVStvue2qVUXuvVfku+9EsrKsb0ttNDrcZKOJmLf82aPOo+ERrY0m3HBDvZxo2CbRXsDRXuz++g8Z\n4v3iT03l3/Gm4JeL1VQ7ihedfKMnkH05yUYNgzIHXwkFIFKpktcBPukkkRdeEFm+XOTBB+kom6nX\npk493jHdvZv7qF6d7U45hf137Tp2XFZtNDtbZNIkkQ4dvOO+6CKR0aNF9u+P7LzEC4+HUpMBA0Tq\n1/ee53r1RPr3F1m8OHLHXm00etxgo4mYR6MNwClEHeRCih1337FiyBCvdjIlReSyyxLvtLsNnXzd\nTyBbnDuX+taC2mIzmlmxIn+vW1fk3XdFZs0SufZab17j226js1yQxYsZzTXXR7RpQ8fWX/5bKzb6\n228i/frRWQdEqlShXvnPP2N73qIlJ4cR+d69vTcZKSkiLVqIDB0qsm6dPftRG3U/Tp1HC95E9+qV\neKfdjURro6pBjjN25X0Mpr0KVZ0mVjmcTSpUoK4M4M/zzmMZXE2Vo7iBWNno998D8+YxY0Re3rFt\nq1dn1brt24EWLaiDXbECeO016odPPJGZFO6/H6ha1dsvK8ubu3jJEmapuOsutjv77MBjC2SjZvq4\n8eOphS5aFLjmGmaiuPxyZ+bSBair/u47pmP75htg3z6gRAngssuA555j3uVKlRI9SsUukn0e9Zd2\n7o03NOVcvHHo111yYmfex2D5Gc1tmgsHC5bNjHVt+oKLL8qVi21JyVg7/ErhIRY2ahb0eOkl7+8m\n5cvTudu8mSnXevWik/fUU5wYDYMFPwYOBEqW9PbbvNmbu3jvXqYjGzGCqaXKlg09Nl8bNQzmP27e\nnHaUm+stsHDrrUDFipEdvy+xsNEdO1i0Y/JkpqzLyeFYr72Wi+wuvfTYc6YkB4VhHvWXCCAjQ+fR\nuBNN+DmSF4CbAPwJ4BCADQBaBGvv5kdDBbVNdj8iCabfCvR4KB6PaeL5eCrRj8JiBRL4+FZt1B77\n2LhRpH3741O1FSlCuYL5d2qqyBtviDzwgFdf7Fs+2hyDx0O5RadOfD8lhb/PmsX/hXvcaWl8fGvK\nO2pcLOcAACAASURBVMqXpyxh2bLwtxdqX3bYqMfDktRDhog0aeI9R6edJvLwwyy/nZdn37hDoTYa\nH3Qe1Xk0UqK10bhGkA3DuBTAywBuBLAYQJV47j+e+LvDjFdVnmBpcuIxBiuPp+winJRASmjURqO3\nj1WrgP79Gd2kL0NKlGDEePt2ll82yc8H+vShfOHmm4E2bYB77/WOoXFjSijefJNyi4oVWcSiVy+g\nRo3wxnboEPDFF3xkm53N6HHTpkC/fpRSRJLyLRTR2Gh+Pj+nKVP4WreO7zduDAweDHTqRCmJEyvF\nxQq1UZ1H7Ubn0QBE412H+wKwEMCd4fRx651voDtMu9K0BLvjC3U3mEypYvTOV200Uuy20YULuRCs\nYKo231ft2owWP/WUN3ILiHTvLrJ9+7Hb6ttX5LrrREqXZpvGjUXGjRM5ciS8cXk8IvPni9x5p3db\np5/OzBb+CmDYTbg2evgws3P06OFdIFi0qMjllzOd3datsR+zFdRGY4/Oo/FB59EAthZN57B2BKQC\nyAHwBID1ALYCGAmghJ+29wBYCmBp9erVY3LiYk2sL7hQj3iSyXhDkYzHmojJV200/G14PCLTp4uc\nc47X2TUdX7Panfm67jpep9Wq8e/q1UU6dhSZPdu7vdxcZp4wq9IVK8bMFGbu4nDYtk3kxRdFzjhD\n/sujfMcdlCLYKaGwQigb3bNHZOxYSkbM81a2rMjNN4t89pnIvn3xHa8V1EZjj86j8SMZj9VNDnJV\nAHLUYKsAqAhgAYAXgvVz652vSGwvuGS941NIgiZftVGL5OaKfPSRSI0axzrBZt5iM9VaSgod5pQU\nkeLF+V7btnSqffPv7trFiK6ZluzUUzmu3bvDG1dWlsjnn4tcdZVX+9yihcgHH4hkZoa3rVizYYPI\na6+JtGzpHWu1aiL33ScyYwbzLzsZtdH4oPOoEilucpDLHzXs7j7vXQdgRbB+bjbsWJOMd3wKSdDk\nqzYagiNHRIYP9+Yq9n1VqUJnuFgxRmrHjaNzahhcmHf77SK//HLs9n7+mXmNTYe6bVtWv/OXuzgY\nK1awiIhZdKRaNco41q6179ijxeMRWbJE5OmnRc4913vezj2X7y1dGv/IdjSojSYHOo8mL9HaaNwW\n6YnIv4ZhbD1q3P+9HYt9OSVdiTmOChWYosXu8Wjd9+Rixw5eL2ZaoXhTWG10/Hj+3q1b4LHs38+c\nxK+9Bhw86H3fMJhfd/du4PBh4JFHmNN4zBi+KlTggr377gOqHF1KlZUFTJjAhXdLlzJ38T33sM1Z\nZ1kfe0YG8Mkn3M+KFVws1KkTcxZfeinzqCaanBzmfp48mYsWt25lerkWLXguO3YEatdO9Cjdg9qo\n/WPReVQJSDTedbgvAIMALAFQGbwT/gnA88H6hHvn65RHJuY4fKtVFSvGijixGpPeCbuLHTtEPv1U\npGdPVk0zI2plyyYmOiWF0EbNyC3AtGejRh1rQzt2MPWZbzszVVv58vKfHGLwYJGBA7364jPP5LYO\nH/bub+NGka5dvRrbs84SGTkyvHLNeXki33wjcv313jFdcIHIiBEiGRn2np9I2b+fuuGbbzavZX7O\n115LnfGePYkeoT2ojcaegjZatGhs51BznzqPJgfR2mi8C4U8D2qm1gLIAjARwAt27sAp6UrMcfhW\nq8rJYeLvcePsTywejwIgSnTs2sVo2ty5wJw5TNkFAGXKAC1bsgJa69asapbAimWFykZzc71/Z2cD\nvXvTVosU4WcyezbHaVKiBP+XmclIcf/+wPr1wJAhjCC3a8fiHZdfzkipCDBrFqPF06Z5vw+KFQPe\new+46CJrY123jpHi8eOBbdsYmb73XkaLGzSw7ZREzLZtjBBPmcJzlpvLyHqXLoxqt2vHc6fYQqG1\n0dzc2M2hgM6jyrHEdRoWkVwA9x19xYR45Ui0Oo7sbG+1KvM+OBZfOIn8QnPKozinsWcPHeI5c3h+\n/viD75cuzUfMPXrwnJ1/vnNK+BY2Gy1alOMAKEnIy6ON5ucDM2d625Ypw3ZHjlC+cNllwI8/sspd\n0aKsONe3L1C/PtsfOMBJ/M03gTVrmLu4RQuWc/Z4uP1584I7yJmZwOef0zGeP58O95VXAsOHAx06\n8NxZxW4bFeH1PHkyneIlS/j+6aczp3OnTsCFFzpD5pFsFGYbBWI3hwI6jyrH4pBp2T7imVzb6jgq\nVAC+/ZYRJJHYfOEk6gtN77i97N3rjRDPnQv8/jvfL1WKzlG3bvxcGjZ0jkOcCJxko3Pn0pHdvp1O\n3s6dx7YpV47O7qFDwI03AvXqAV9+Sce4YkXgmWcYyT35ZLZftYpO8YcfUqvcpAmjvtdfT52wr634\ns1EROtFjxtA5PnSIZaRfegm47TagatXwj9MuG83PBxYu9DrFGzbw/aZNGUHv2JEa6sJUtCNZcZqN\njh9P25w+nTexqamxmeN0HlV8Scpp2imie3Mc6emMLonQsF9/PTYLDXwdcn/142OBUx7FJYKMDEYR\nTcnEypV8v2RJ4OKLGVU0HeKiRa1vV2Ky5MZZOMFGPR7KXubMAdauPfZ/JUtSMpGbC/TsyQjyRx8B\nn35KJ/Ddd4GuXSkbyMsDJk2ijGLOHCAtDbjpJuD++1nxzSSYjW7dSkd97FhKNsqUYVW9Hj0YiY3G\n6YzGRg8fZiR9yhTe4O/dywm8TRveJHToEJnTrjgfJ9io7zjS0xloAmJ3E6bzqOJLUjrITsNXj2wY\ndKwKYsfjFbNfPO9EnfIoLh78+y8dYlMy8dtvdGZLlKBDfNNNPP7GjcNziPPygF9/BRYs4Gv+/Fgd\ngQLQ6R0/ntHfHTv8t0lNBR5+GNi3j47r4cP8XC+7jFrx5s2ZueK114B33qGDW7068OKLwJ13Un/r\nD18bzc7mfi64AFi8mNdSq1bAgAFA58588mAH4dronj3A11/TKZ4xg7KSE04A2rendOLyy4GyZe0Z\nm6JYZe5crwQqL+94J9IuiYLOo4qJOshBsMvgQl38dj5eifedqFMexcWCffuOjRD/+iu/nIsXp4M0\naBAX1TVuHJ4e9MABfuamQ/zzz3yUDgCnnsrFYZ99FpNDSjrCsdHDhyl/GDKEn61JSgo/v6ws/p2a\nCpx7Lp3fokUZKW7dmqnYli1jFLlVK14TOTlcgDZyJHD11aE1tyLAxx9zXyK8aV6zBnj6aeD222OT\n8syKja5fT4d4yhRekx4Pr8U776R04pJLwrvpUxSTeMyjdksUdB5VAHWQA2KnwYW6+O00xkTciTrl\nUVy07N9P/acZIV6xgk5MWhoXUz33HM9nkyZ8zwoiwObNXmd4wQJv5DklhRkI7riDDnfz5nRKAHWQ\nrWDVRv/5B3j5ZWDECEZDTYoU4WeQk8PPtGpVfu47dzJrxIAB1BefdBJvhkynNjub7Xr2ZO7iM88M\nPdY9e+gYjxnDzx/g06SiRRmtbd7cjjMSmII26vHQ2Tf1xKtW8f369emsd+zIxaOqJ1aiIV7zqN0O\nrc6jCpAEDnKsVn6OH++dEO0wuGAXv53GqHei1jlwgHIG0yFevpyOQ1oaz9uzz/IcNm3KqLEVCsol\nFixgCiyA2SvM7TZvzu2WKROro3MOibLRbdt4rseN4+diUrw4ZRb5+cBVV9ExnjKFTwvOPht4/nnq\nx0uUADZuBB5/nKmlTG246dS2axd8fHl5wHff0SmeNo37bNwYePttRoqXLYuvjebk8Fo3I8XbtzPi\n3aIF10Vccw1Qq1Z8xqI4C7fPo3Y7tDqPKgDiWygkklewBOejRjFxeEqKvcnMFy5k0QAzMVuxYrFP\nGq7JyWPPgQMssvDYYyKNG3uLuBQrJtKypciAASJz5rCcsFX27xf5/nv2bdNGpFQp73Vz6qkiN93E\nIg7Ll4dXPhgJKkIQyctpNrp6tUinTizx7Fvcw/xsihcXueUWFrIoUYLvXXaZyHffsdRxfj4/02uu\n4TZSU0U6d+bn+MILoY/hzz95jZ18MrddqZLIQw+JrFxpz7GHw759Ip98InLjjd6iHSVL8njGjxfZ\nuzf+Y0oW1EaDE+95VOdQpSDR2qhrI8jp6VwlbkaGzMeedoj2zcUAAB8x9uhhrX80d+FWH69orkTr\nHDzICK4ZIV66lFHDokUZve3f33serRQxED9yiZUrGXUOJpcorMTbRosUoVb2xx+PbVuqFDXexYtT\n3712LUs0p6VRX9y3L3DOOZTYjBhBnfLatVxo99RTlFKE+iwPHGD56DFjeEwpKZTlvPMOo9Tx1O9u\n3eqNEs+dy8h15crADTdQOtG2rRbtUIjT5lGdQxUn4VoHee5cb1Uq4Pi8iNFonwo+runWLXSfeOQx\njOU+kuFL49Ah5mk1HeIlS/gFXaQIHeInnuBiq2bNmMYrFHl51IuamSUKyiUuvJCZEJo35+/RyCUy\nM/nIfckSb9EFtxMPGzUzQcycSWfUlxIlqDk++WRmGZk/35smqkgR5jNu35762/vu4+PgQ4d4rXz4\nIXMXB9OaezzMez1mDPDFF9xXrVrctqnxrVzZPuc4kI2KMOf2lCnUFC9bxvfPOAPo149OcdOmWrRD\nOR4nzaM6hypOwzUOcsGLr1UrTl7Z2YzWjBwZWrRvvh/qAo5EfxSPVa+x2odbk5QfPkyH2MwysXix\n1yFu3Bh47DF+fhddZC1l1oEDwKJF3ujwokXHZpdo0cIbHT733MiLfWRn0/FesoRjXrIE+PNPr8a1\nZs3Itpto4mmjTZoATz4JDBvG9Htm0QrAOynXqwfUqcPSx+PG0Vk1K1p6PFw0N3Qo95eWxrzD998P\nNGoU/Dg3bfLmLP77b6Y869aNEbJZs7i4zywtHysb/f577sOMFP/1F9tdeCGLinTsaG3xoFJ48OfA\nOWke1TlUcRqucJADXXzBjK9CBU6GZgqnChXCu4DDXVEaj1WvsdpHvFPaRMqRI7wWzAjxzz/z8XFq\nKh3iRx7hOWnenBHeUPjKJebPP1YuUb8+026ZDnH16pGNOT+fabxMR3jJEi7iM0unVq7Msd94I382\nasRH+27LHhCujaan8/ybUU2rNpqdDbz3HjOK7NnjfT8lhT89HkaLS5emE7l0KXDFFYykli7tzT/s\n8TBdW40azHDRowcr4wXiyBHgq68YLf7hBzrZbdsCgwcD117rlSzk58fORs1xZ2XxmA4f5j7ateNC\nwg4dgCpV7NmfklwcOuTftmJho76EM4/qHKo4DVc4yIEuvkDGZ1au83i8lesyMmJ7Acdj1au/fdjx\nWMepScqzsrzHN3cuI7o5OXSGGjWi09O6NR3YUPIGX7mE+dq6lf8rKJdo2jSyQggijC6ajvDixXzc\nffAg/1+mDMfdty+d4SZNGJl2mzPsj3Bs1NeZLlIEuPtuRmCDTTKZmYwWDx3K302KFPGWnm3Xjo7A\n7NmMit12G8/12Wfz2nnzTW+hgcaNmc6sffvA0gMRfo5jxtCZ3r+f0f2BA4Hu3elcF8RuG929mxkz\nvvnG+yhchE8z7rqLRTsKQyYUJToyMwPbll02Gi2JmkOB6OdRp86hSnS4wkEO9+IzjdicUL78Erju\nuthfwPHIY+i7D7se6zglpU12Nh0ZUzKxaJH30d8FFwB9+nB8F18c2oEtKJf4+Wevo3rKKd7IcPPm\njBZHIpfYs+dYmcSSJd6oZrFiwHnn0ZFq0oQOWd263khnshGOjfpOsr7vVahw/Db27GGUdtQoXgsm\nRYvy6UGpUnQWN2ygvrhyZUaXe/Wi4/jZZ5zYly/nNXPffXzVrRt4fLt2saz0mDHUJ5cowe+PHj24\nCDDUZxitja5b59UTL1xIh7h6dWqiy5blNdWiRfBtKIovZcowH3i4c6gVG7WTeM+hgD3zqFPmUMVe\nXOEgh3vx+S7g8XioC/zpJ28k2eoF7HTRvZ138/H4YipIdjadS1MykZ7OqLFh0CHu3ZsR4osvZqnb\nYPgrxuErl+jePTq5RMFFdIsXM1oMcLxnn81Kao0b81W/fnjV9dxOODbq60ynptIRzcvje6aN1q1L\nPeSECcdO0ma/k07iOU5PZ4S1dm3ggw+oI96xg5Hm99+nU1CvHnMPd+0aWHqTm8so7ZgxwPTpHM+F\nFwLvvsvsD6Guv0BYsVGPh9eUqSf+4w++f9551DN36sQMKcnwpCEZ2LkT+OWXRI8iPEqVimwODWaj\nVrbj9DkUsG8eTcQcqsQWVzjIQHgXnzlZDxxI59hcMJORwYU9VrBbdB+LLwq3PdbJyaFjaUaIFy70\nOsTnnceqZa1bMzpWrlzg7eTlUS9sZpbwlUuUKkXH5umn6VhHIpcItYiuVi1ut3dvRocvuMCa5jnZ\nsWqjvs705s3A6NHeyemPP6jZ7t/fe74Bb8S4dm0W9liwgA5tSgpf27ZRAnHDDXSYU1LoWPbuzahv\nIOdy1SpO/h9+SDlDmTLUg/fvD5x1VvTnJJCNZmfTBiZPBqZOpVOfmsqx9uzJoh1uXayZLHg8LMG9\nYgUdYvPnrl2JHllkRDKH+rNRq/OoG+ZQwH3zqBI/XOMgh0uzZnSQf/opsgvfzuhsrFa4Ov2xTk4O\nF0mZDvGCBd5Svw0a8DF4q1bMTVu+fODtZGYen13CLrlEpIvo7MLjYQaCX3/1vsxSxMmMOVmnpzMj\nRFYWz8Xw4ce2S0nh+2YEdckSVrfr1o2p+kaM4P+zs6lJr1yZzm3Pnrw2/LFvH6UXY8bwcy9ShNfO\nvn3UME+axGwWdh2naaMNGzLrxbBhrLCXmckbuiuvZNaJq64CTjzRnv0q4XHkCFPl/fKL1xn+7Tdv\nFpsiRfgk4oorWIL7vPOS35EqaKPhzqNumEMB58+jSuJIWgcZiO7Ct/OuMtYLG5xi0Lm5lCGYkon5\n87nSHqDjevfd3ghxhQqBt7Nly7G5h33lEueeS+eoeXNGiMORS/guojMd4nguojt0iJHvgs6wuf+U\nFOaubdqUTmCyI8JoVKVKjFIVJDWVn8GePbzRqlwZGDSIN1Y7d3rTqQE8d888w8iWv9zFHg8X740Z\nQwc4K4vX0rBhLCv93nu83uxOz7ZlC6+x2bM53rw8ykNuuokR7jZtrJcxV+whI+NYR/iXX4DVq71S\nnjJl6ADfeSd/nnceJVTBcmInM5HOo26ZQwFnzaOKc0iIg2wYRh0AKwF8ISJdY7mvSC98O+8qk/UR\nTl4eJ38zQjx/vjfics45nGDMCHGgFFr5+cdnl9iyhf/zlUuYxTjCkUvs3u2NCsdzEZ0Ij8HXEf71\nVz6uNWUDZcsyKnr77fzZoAEjVGYBkwkToh9HNMTSRvPymIO4f39v4RXAGy0uVYrnY+1aRo7OPZeO\nbZcujLxefz0LdKSlMQtFzZp0cv3Z6N9/M1/xuHG8OSpXjovtevSgNMa8+bHLRkV4EzR5MvXEy5fz\n/TPPBB5+mE5xkybJu1jTSYjwRrOgM2x+vwBAtWqMCF97Lb8Pzj+f15MbPh+nz6M6hypuxxBfoV+8\ndmoYMwCUALAplGE3atRI/t/euYdHVZ37/7tyIYGQcE1IAuQCCUkItyCXClZBCxVRoMWqqLV4Odpa\n9dTbUWu9tNraeuzFtmJrVdRzbP1pTxXt+fVY+1S0Kj85KAS8RBC5FLkot5AACclk/f74Zj17z957\nJjPJZPbM5P08zzyTzJqdrOzsd9Z3vfu9rFu3zvV6LOOR4pFIkAzJCl3R3s5FxniI//EPy/tZW8u/\nbc4cxlGGCkMIFy4xcqTlGY42XMKeRGe8w/YkutpaK4FuxgyKrlgk0bW0MI7VKYYPH7beM2aMJYIn\nT+ZCXFoa3jOtlHpHa91Fy4reozdstKWFpdZ++EM29zAYYZyfz/ju+nqGTJx1FsMmjh8HfvlLipv9\n+ylgrr6aItfrTsSxY6xcs3Ilr1WlgHnz+P7Fi0N7bLtro+3t3BwaUbx9O3/nySfz9y1eHL5qhtBz\nTpxgnoBdCG/YwLh0gNdYVZUVHlFXR1vsSbhUKtpod5E1VEhEemqjcfcgK6UuAHAYwFsAKrrzM2IZ\njxSvDjjJeAsnEOAiYxfER45wrKaGdWbnzqUgLijw/hkmXMI86usphpSiADbhEqa6RCThDCaJzh43\n7JVEd+21FMSxSKLTmrf1nUL4o4+sW7MDBlB4n3eeJYYnTuxeTWU/ibWNZmbynDz3nBWDDljCeNQo\nnqP33uNG5xvfYEm/w4eZR/DKK9b7778fuOEGd+1irbnZWrmS8cVNTcDYsSwRd8klDJXpimhs9OhR\nNiJ54QVWvTh4kB7tefPoGT/nHIZSCLHnyBHanl0Iv/++lTfQvz9tb9kySwxPmBBZe/lkIZHWUVlD\nhVQlrgJZKZUH4AcATgdwRZj3XQngSgAo8QgyjWU80lNP0bOltXTACQS48JiQiddftwRxVRVw4YWW\nl9hr8e8qXGLmzOjDJQIBxgfay6vV1zPeGaAwnzHDSqKbPj18R7RIOHGCv9Mphu2d20aP5iL8la9Y\nYnjs2NBNJ5KFWNqoKbMYCNDOrGNpbxUVfM+OHbye7rmH4viVV1iSbf16d9ynaQpi2LOHFShWruT/\nbMAAhmBcdhlj3WNZGm3fPuCll+glfuUVzn3IEJb3W7IEmD9fqpnEEq2B3bvdXmF7W/H8fArg73zH\n8g5XVia/HYYj0dZRu623tvbtNVRILeLtQb4HwGNa610qzMqltX4EwCMAbw05x2MVj7RmDWunGs9j\nRkbfim3q6KCgNR7i11+3QgPGjWMikfEQe7WwbWpiAw57uITpcmbCJW66ic+TJ3cdLhFpEt3111tx\nwz1Notu/3y2EP/jAEuBZWQzPOPtsSwhPmpTS1QZ6bKNbt9K7ahLo7Jia0bt3M8Z40iTGCM+YQVuc\nPJnhFxMmsHbxiRP0JgP8ecOG8bU//5mi+C9/4QI/ezbrHn/ta7HtLLd5sxU6sWYNr9GyMiYKLl5M\nEd6dJjNCMIEAz7VdCG/YELwpraigCL70UksMFxX1yfrQCbWODhtm2bqxUUFIBeL20a6UmgLgSwDq\nevqzIg3+7ypmafVq6/a4UvzgTeWdb0cHE4hWr+bjtdesWNCKCiZBGUE8cqT7+HDhEhMnMuQimnAJ\nZxLd2rUUrICVRLd8ueUZ7kkSnVmAnWJ4927rPYWFFGhf/rIlhquq4iOA2tuZUNbQwIcf9NRGN2zg\n5mX1avdYVhY97B9/zNvhCxfS67dxI3DfffzfpKXRI3/NNUzsVIpjJhRDKXqib7+d10lxMfBv/8Zr\nZNy4nvzlFh0dvA6NKDb/i7o6hnssXkxR3wdFWcw4doyfQ/b6wps2WeE3/fpxg3TOOZYQnjQp+UKV\neoNEXEcPHLBsNC2N3wtCKhBP38ccAGUAdnbuegcCSFdKjddaT432h3UVjxRJXJRzB33JJdHOIrHp\n6KAYMSETr73GWEmAYuWrX7VCJpw1YwMBLlpGDL/xhjtc4vbbrXCJrjqNhUuiS0ujV/Gcc2KTRHf4\nMIWXXQi/9x5DaQAK3poaltiyJ8+FiqOOJU1Nlgi2P7ZssbzWPjIH3bDRpiaKmPp691heHs/rxx9z\nA3DZZdyIvvUWn02Dl4wM4I9/pAC1M3Uqb5d3dNB7+/bbDGe47DLG+8Zi89LSwjJsq1axacfevfy5\np53GesiLFnWv+6JAD7DdK7x+PTdDxuM4eDCvnauussRwTQ3j1gVP5iAB19GsLKkwIaQe8RTIjwB4\nxvb9TaChfysWP9y5y40kvirVCoRrzfAAEzLx2muWR7a8nOLDeIidC35zs7u6hAmXKC5mZYlIwyVa\nWymW7J7hhobYJ9F5Ndmor7eEN8DbfZMns0ufEcI1Nb1b01Rrli/zEsL2smbp6fTcV1dzc1BdzUdV\nlW8hHN2y0c2b3a/l5/Ma2bOHccH33st43See4KOlxbrLoLV17S5eTJv9298YQvH889w4FBUx5Of2\n22NzC/fQISbXrVrF0nHNzbwGFyygAF+wIHzzGiGYjg5ugJxd5+x3aEpKKIDPP9+qL9xVNRfBhayj\nghAn4iaQtdbHABwz3yulmgG0aK0/D31UZJhdbmsrvZEPPRR5fFVPM2P9LD2jNas3mJCJ1autmL3S\nUsbNGg9xaWnwsbt2BYdLbNgQHC5x8cVWuES4RcyeRGc8w15JdBdc0LMkuuZmd5ONTZvcTTa+8AV6\no4wYLi7uvQW4tZWeUbsA/vBDVrYw8wLoRa2u5jVaXU2BXl3N8m+xKDUXK2Jho6NGMbHz8895/u+9\nl5uRBx7gNcafS6G7cGGwd6qigkmcTz7J63PoUMb6XnopxVR3MTZaVcWfu2oVN4+BAIX3RRdRmJ9+\net9tBhENra28M2X3CtfXWxvq9HRe42ecYQnhKVNSOm4/bsg6Kgjxw5c6yNEQqn6jnfvu48Jqbttl\nZnIBBHrX6OJV3sagNcWXCZlYvZpxvACT1ebO5d86dy4TiQzOcIk337Q6lw0YQFFpxHC4cAmTRGcv\nr+aVRGcS6LqTRKc15+b0Cm/d6m6yYX/Ym2zEmoMHgwWw+fqTT4IT0UaPDhbA5lFYGL1I97vGajQo\nNU2XlKzDnj3cGJ19NuOC33sPeOQRehGHDGHoi/kfGhs9dozJeFu3UmylpTEG/LLL6FXviWDVmjHL\nV1zBGG9DTQ29xIsX8xpNhqYQfnHoEO3P7hX+4APrfJqmLvb6wrW1faM7YDLZqKyjQl8k6eog9wZz\n5lhJAgAF4erVbDvbm4bW2+0vtWZsqhHDq1czPhJgEt38+ZYoLi+3RFhzMz9kjBhesyY4XGL2bNaS\nNeESoeL97El0RhTbk+jq6qwkuhkz6MGNRmyYJhsbNgS3XrY32Rg7lnP8+tctMdwbt2UDAQpzuwA2\nD3smfVYW/866OtZZNSJ43Li+XeLr88/ZOfHUU1kKbdkyiuUzzwR++1vGms6dawmr9naG2Bhve2Ul\nF+ivf907QTRS2tpYr3vVKj7s4TZKMYnwpz/t2d+aipjuj86SavaW54WFvO4XLrTE8NixssFItvNb\newAAIABJREFUFVJ1HRWE7pISAvnkk3k76JpraGSZmRQ7a9b0rqHFuv2l1rxlbw+ZMDF8xcXcZRsP\n8ZgxlkjctQt49tng6hKBQHThEiaJzu4d9kqiM97haJLoImmykZPDn3n++cFNNmJZsgtgg4fNm90i\nePNmK4kPYBhIdTW9jHZvcFlZatdY7Q5FRcAttzC2+De/4R2Ib3+b3e4qK6333Xsv8N3vWgl3GzdS\nQN9yCzBrVvc3Pc3NjCNetYpxxYcO0YM5bx7DJ372Mwrnfv1YqaWv097Oa94phk0Cr1L8v82caSXP\nTZ5MgSykLqmyjgpCrEiJEAvDmjW8pfr44zTweNyu6UnslNa8TW8PmTBJXIWFFMLGQ1xRwYUrEOCt\na1NZwhkuMXNmcLjE4MHu3xtJEp09TCKaJLpImmyUlLhDJGLpidKaTR28kuTsHsW0NP6tdgFcU8NY\n1Z42G+kpyXT7NiNjmg4E1mHiRC6uF13EDQ/Aa+3FF5lwZ2ojFxXx7oTW9Mh3x0b37uXPXbWKx7e2\nMsb1nHO4qZk/35pDX45vbG7mRsQuhjdt4vkCuJGYONGKE66r4/d9+W5IpCSTjabyOioIoZAQCxsm\n6zYQiN/tmmiSE7TmLUt7yIQpnTZihCWG58zhLXuluMC9/Tbwhz9Y1SVMd7tIwiW6SqIbMYIi+IIL\nKIqnTYtcHEbSZMPUM7U32YhVdYC2Nm4wvOKDGxut9+XkUPyecgrjUY0YrqhInFjJQICbo23bgm9r\nJwN5eawbbO9ct349RfHTT9MzOXo0vcfLl/Nuxx13UCxHY6MNDRTEL7xAm9CaG5yrr6Yonj3bu7pK\nX2lRu3ev2yu8ZYu18R06lAL4mmusmOF41fkWkodEX0cFIV6k3Edjot2u2b492ENsvL0FBZzbbbdR\nGFdVUVx8+imF8IoV9BDbwyUmTGC7Z+MhLisLvi1tBHhXSXQ33BBdEl17OxfacE02iooogM880xLD\n48bFZvFtbGQ4hjM++OOPg5OviospfC+6KNgrPHKk/3GSHR0UMNu3WyJ42zbr6507g/+WZGLMGMYe\nHzhAQbxyJcVZVhYbf1x6KcODTGhKpDba0cENoRHFppzcSScB3/8+E+0mTOh7ZcI6OnjtO+sL79tn\nvae8nAL4oossMTxqVN87V0L3SLR1VBD8IKVCLAx+3q7ZuTNYEBtv4PDhVvzwnDm8ld/RYYVLmIcJ\nAYgkXMIk0dkFsTOJzgjhSJPoImmyMX68O0QiP79n562jg7HUXmERe/ZY78vIYHykXQCbh5+dtrTm\nuXcKX/O8fbt1W9swYgSFTHk5Nzv258rK5Ll9W1k5TU+Zsg6rVtGrP20aRfGyZaHvFoSy0ZYW1kBe\ntYrJfvv28X8+dy69xIsWcVPXV2hpof3Z6wtv3MhYeoDnprbWCo+YMoX26BVaJcSWVA2xMEjYg5Ds\n9NRGU1Igx5Nduywx/OqrFEQAmxmYcIk5c7iIHTvGW8MmftgeLlFUZInh2bO50NnDJZxJdGvXWt5o\nk0RnhHAkSXSRNNkYPtwthGtqela7t6WF3minCP7oI2vRB5joZcql2cumlZf712Xr8GFv7695ts8f\n4DXgFL7m69LS8GXpkmnxVWqazs9fh4svpjCeODG64w8eZHLdCy8wTvnoUd7tOOssiuIFC/qG4Dtw\nwPIIGzHc0GAlsubmBscKT5lCu5fazf6QTDaa6OuoIPQGEoMcZz79NNhDvHUrXx86lB3qvvMdertq\na+n5fPNN4He/s5pxRBIu0drKxTFUEt2YMdzRX3cdBXFdXfikmkiabFRV8Wd+85uWGC4q6v4t2f37\n3Q00GhooJu17stJSCuBTTw32BhcUxP92cHOzOwTC/mwvPwdQsJSXM5Z53rxgMVxW5q9HO56MHcvY\n82g2Ttu3W6ET//gH7aK4mO3eFy+22temIiYUyi6EN2yw8hEAhgVNmcIQFSOKy8v9DxUSBEHoK4hA\n7oLdu4PLrm3ZwteHDKEgvvZaLubjx1MEvvEG8OMfB4dL9O/PcIlbb2WimD1cwiTRPflk+CS6Zcv4\nHC6JLpImG4MGMVFu+XJLCE+YwDlGSyDAhd6ZINfQQG+YITubAnz6dNa5tdcO7q3mHl60tPB/EsoL\nbMJTDP37W4LXbGLsXuAhQySmE+C13JU41poi8IUXKIzr6/l6bS3LvC1ZwtjiVBOAbW3cPDiT50wS\nqdmcfvGLwV3nehqyJAiCIPSMpBLI8YiJ2rvXEsOvvmolBg0aREH8rW9ZdYjXraMQvuUWzs0ZLvGd\n7wSHS5hOdH/9a+gkuunTrSS6GTNCJ9YcP84mG3Yh3FtNNpqbGQLhVTv4xAnrfQUFFL5LlwaXTSsp\niY/waWujF84r/GHbtuBYZoCirrSUgreuzh0KkZ8vAjha7DY6bRrw+usUxS++yM1bWhpt4oEH6Cmu\nqPB7xrHjyBF317n337dspH9/bk6XLbPCJCZMiO8mURAktlgQIiNpBHJvtaPct4/tNE3IREMDX8/L\n423/q67iB0l+PmOG33iDpcLs4RK1tVz0Zs+mh9iES5gkunvvDZ1Et3y5FTfslUSnNb3YTq/w5s2x\nbbKhNQWkV5Kc/dZvWhqFd3U1Y0NNfHBVFcNMehNTCi1UJYhdu4JbP6enM6GrvJzVNZwJcUVFqeex\n9JM1a4DTT6eNKkXh19REYTh/PnD33WxDnezeUWOTzhAJE24F8G+sq+Mm2YjhykppMiP4i7R1FoTI\nSRqBHKt2lJ9/Hhwy8cEHfD03l4L48st5u7NfPwriN98EfvUrqxqFPVxi9mzOYfBgeo/eeQd47rnQ\nSXRddaI7cYKhCk4xbL/1b5psLF3avSYbJ05wIfeKDzbtqM35qK7m5sAeGzx2bO/FhpqOe17hD9u2\nuUuhKcW41fJyevedCXGjRkmN13jQ1sZ20j/7WXA3wspK4M47GZ+drF7SQICbUWeIhL3xTUUFBfCl\nl1rJcz2J3xeE3kLaOgtC5CSNfOhuXcb9++khNiET77/P1wcOpBD+xjcYE9zaSkH8t78B99xjhUsU\nFlIIX3cdn+vq6KU0neieeYbP0SbROZtsbNhAoepssrFoUfeabBw+7C2Ct261PM8ARWR1Nc+DXQgX\nF8d+gdeascle4Q/btjH8xC6wAMZgl5XxPJ53XrAXuKQkuRO5tGYFh717+dizx/o6mdi4kcmdI0dy\nQ9LRQRv99a+Ta/E9dozJq3YhvHEjw5kA/k2m8Y3xCk+a1HeSMYXkR+obC0LkJFWZt0hipw4cYNyj\nCZnYtImv5+Qw/MFUmGhutjzE69cHh0vYy62VlDD+1l5r2CuJzniGnUl00TTZsD8iabLR0cHwB2eC\nXENDcNOAfv3ctYNravg7ognDiITGxtAxwNu3W/HWhqFDvesAm0oQyeh5bGnh+XeKXvO1/TVzHdnJ\nzgZaWpKnhNTIkdP0yy+vQ20tbSoZ4hs//zzYK7x+PT3FJkRn8GB3SbXq6p6VOBRSi2Qt8yYxyEJf\noc/XQT54kILYeIg3buTrAwZQEJ96KkVuY6MliO3hEjNm8H2mGcfhw8Hl1d59151EZ2++YU+i66rJ\nRmYmhWm0TTaOH+fi7VU72Hi3AHqXvWoHl5XFLtTg6NHQMcDbtoUuheasAGGek8X7Zvf2eole+9eH\nDrmPV4obp6Ii3pUwz15f5+YCaWnJufgmGh0dvC6dXefsG9SSErcY7k4yq9C3SFaBLAh9hT5XB/nQ\nIdZNNR7i+nqKl/79KXLvvJNC5MABNuX493+3Sio5wyVGjuSCuXYt44wvucSK983K4kLplURnmmys\nXcsax+GabFx9dWRNNrSmV8srSW77dit8QymKy+pqJkTZvcLDh/d8UW9pYaxvKC+wPfYS4Hk3gvfk\nk91iONFLoXl5e0MJYC9vb//+lsCtqeH/xEv05uf71+Ckr9DaypwCu1e4vt6KrU9Pt/5H9q5zw4b5\nO29BEAQh8Uh4gRwIAH/+syWI16+nWMzOBmbNAm66iR63zz6jh/iHP7RibGtrWdnhlFMYK3jgAEuz\nvfUW8ItfuJPoFi2yvMMmic402Vi9GnjwwZ432Whvp9D0ig+2ex7796fo/cIXKNKNCK6s7F7NYoMp\nhRaqG5zdswZQ1JlSaEuWuL3AfjT06IquvL3210J5e/PzLYE7frzb22uec3MT7+/vCxw+7O4698EH\nVhJnTg7t8JJLLO/whAn83BAEQRCErohbiIVSKgvACgBfAjAUwFYAt2mt/xL+uGkaWIesLArimhou\ncnv2UBCb1s4mXGL2bD7n5ATHDjuT6OxhEnV1fH8kTTac4RG1td6CtamJv98ZH7xlS7AnsrAw2Ats\nwiNGjepeCbJAgCI3VCJcqFJoXjHA5eVM1kuUUmjG29tViEMk3t5wIQ6J4O314/Ztd220N2/fas0N\nnbOkmgmTAvh/s4dH1NVFV9lFELqD2KggJDbJFGKRAeCfAE4DsBPAWQCeVUpN1FpvD3XQsGFsKPDP\nf1LsvvoqXx84kAlx3/42RVxzMxfPl19mWEW4TnQ5OVaTjeeeA773PXeTjYoKywNlxHBJSbC3UGvW\n5fUKi/j0U+t96en8eTU19FIbIVxVZXXUixStKRJDxQDv3BksDk0ptLIyxmM7RfCoUf6KQePt7Ur0\n7tnjjm8Ggr29RUWWt9dLAIu3t0u6ZaNedCcRqL2dtuMUwwcPclwp3kGZOZP1yY1nuLAwmpkJQlLj\nq40KQl/C1yQ9pdRGAN/XWv9X6PfQg1xbSw9yVhbwm99wMU1L4/cmUS0vjwLYnkiXnu5OnPvoI8uL\nmpPD8Au7V3jixOCybK2twMcfewthe1WGvLzg5DjzGDMm8ux3IxjDVYJwlkIrKPD2/paX+1cKzent\nDSWAu+vtNc+J4O3tDRIlASgSG3V6pyJpRtDcTLu0C+FNm2hrAK/ZiRODvcJOuxQEP0l1GxWEZCeZ\nPMhBKKVGABgH4P1w7ysqAi6+mNUgnn8+uGlGRwcXz299i8I2EOAiW18PPPwwY4Lt7y8t5fvOPdcS\nw2PGWLdiDx6k6H322eD44E8+CQ5LKCmh8L3ssmAhXFgYmYeysTF8JQhnKbQhQyh2x48HFi4MFsGl\npRT58SCct9f5mnh7k59IbdSJsxnBSy/xmreL4S1brNCloUMpgK+5xhLDVVXS5EUQuiJWNioNQwTB\njS8eZKVUJoC/ANiqtb7KY/xKAFfyu5NOSkujB3n6dIZcPPggvY7p6cCXvsSYW3uTjexsJuTYvcKT\nJjGcIRBgGII9Oc487BUasrJYtcIeF1xdzde6EqSmFJqX93fbNndi2MCB3iXQzPOgQdGf42hoaQn2\n6IYSwPv2hff2hovrLSykp1tET2T47Z2KxkZLSkpO2rFjBzo6eKfl2WeB738/uOuhobzcXVLNXipR\nEJKFZLRRg3iQhb5A0tVBVkqlAfg9gDwAi7XWHpLLorx8mr7zznX46CMrRGLPHmu8uNidOFdZScP/\n6CN3SMTmzcEhCsOHu+sGV1fTM5ue7j2n1laWdAtVCeKzz4Lfn50dug5weTk9aL3Rtc7u7Q0X4xuJ\ntzdcYpt4e92cOEGv6eHDwc+RvnbwoH+Lb7Q2WlAwTVdWrkN9PTeHAG2noIAieN48Pk+eHH3MvSAk\nKn4K5Ght1CtJT2KQhVQnqQSyUkoBeBxAGYCztNbHwx9hxSBnZvKWvDNWuKPDOzbYXpM4LY2hFM7Y\n4Kqq4K53hvZ2JgWGqgSxZ491exhgDGxJiVsAm69HjIidgAzl7XWK3u54e+2v9WVvb0cHW41HI2id\nrznjxL3Iy6NgHDSID/vXK1b4s/h2x0bT06fp2bPXBXmFx49P7jbggtAVfgnk7tioVLEQ+iLJFoP8\nMIAaAF+KxKgBCsw//pG3gT75hOJ30yZWn2hoCPZ+5uRQ+J5yCnDFFcG1g+2LdSBAEfnhh95e4F27\nrFrKAAW2KYU2f77bC1xcHNrbHAlas0ZzVyEOe/eG9/YagTt+fGgBPHBgant7tWbSZjTi1jnW1BS8\nAfIiO9stbktKvAWv83nQIHrdw10zK1bE9rxEQdQ2WlfHbpaCIMSFqG1UEIToiZtAVkqVArgKQCuA\nvcpSaVdprZ8OddzevWyWYY9nLC6m8L3wwuDwiJEjKf60ZpjDtm0U0y+9FCyAd+xwe1eLiyl4TznF\n7QXubik0u7c3XIhDJN7e2lrGW3uFOKSSt7e9vXshCfavvc6lnbQ0t2gdM8ZbyHq9NmhQanpHu2uj\ngiDEB7FRQYgfcZNVWusdAKL2XWZns12zPSwiN5fxtUbwrl/PChdGBG/fbpV+M+TnU+xOnQosXRos\ngktKIu+wFcrb6yWAo/X2Or2+yebt1ZoVOLobd9vYaMWwhmPgwGDRWlDA5MmuxK15zslJrvMaL7pr\no4IgxAexUUGIHwnvdxw2jILynXcYamFEcFNT8PuGDKHgrakBFixwh0F0VXmiK2+veQ7l7R0wwBK4\noby9pktbonp7W1u7L24PH2bcrr0cnhf9+rlFa3FxaG+t87W8vMQ9f4IgCIIgpAYJLzW2bgWuv54C\n14Q8zJ0bLH7Lyryz4zs6rKYbXdXuDeXtLSiwhO6ECaET2/z29gYCVmJZd0WuadIQCqWCE8tM3G1X\n8bb21yL11AuCIAiCIPhFwgvk6mrgH/+gJ9kIUOPt3bOH4nfNGm8BHK231xniEC9vr9bAsWM9E7dO\nj7oXAwYEi9ahQxl7Gy7e1v7awIFWUxVBEARBEIRUJeEF8sGDwHXXJba319S87W5SWWOjd1MFOxkZ\nbtFaWRlZxQTzdSq2ZBYEQRAEQYg1CS+Q9+8H1q61RK/T22ueu+vt7eig97UnZcGcCYFe5OYGi9ai\nInrHu6qYYL4eMEASywRBEARBEOJBwgvkujogVH1zrRlu0djIFrfd8eAeOdJ1zdusLLd4HT068rJg\neXk9q5MsJD4dHbyT0NbG51BfR/qaIAiCIAj+kfACedcu4PLLQ4vcrsREWppbvJqkvkjLgqVizdtE\nRWuGm8RCZPbGMaHGu6reIQiCIAhC8pDwAvnzz4H/+R9LrObnAxUVkZcF87u6hJ8EAv4LymiP6arJ\nR0/JzGSpOfMc6uvMTFbcyMuL7phIXovkmPz83j0PgiAIgiCEJuEFcrgQi3ihdeIKynDHdBU60hPS\n06MTh/37966gjOSYjIy+u1kSBEEQBCFyEl4gHznCVtF+itCuKkz0lHDizin0Bgygd9wPr6b9NSn3\nJgiCIAhCqpLwAnnLFmDRosjem5ERndDLyfHfq5meLl5NQRAEQRCERCLhBXJ1NfCf/9m1CM3IEK+m\nIAiCIAiC0HMSXiDn5AAnneT3LARBEARBEIS+QsILZGzbxhiLzEzrMXUqcP31HL/nHqC5OXh83Djg\n3HM5/vvfA62twW7n4mJg5kyOr13LGl324wcN4nsAtvJLS5NML0EIxZYtwOLFwTa0YAGwbBkD+W+7\nLXgsM5P2d/rpDPJ/4ongsX792CaytpalWNascR8/fDgfWgMHDgSPiY0KQjBeNnrppcDcuayl+vOf\nu21swQJgyhR263rhBfd4XR1QWsr1d8MG93hREdfStjYmE9nHJLZQSAISXyC3twP//KdVA6ytLbhl\n3lNPWeOmGO3ZZ1sC+cYb2Z/azsKFwJ//zK8XLw4/XlvrHl+0CFi1il9PnMgPELvxn3EG8NBDHP/K\nV1i42S7QZ84Ebr2V4zffDBw9Gnx8bS1w8cUc/+1v3QK/tBQ47TSO//3vFBH244cNA8aO5fjOnfwg\nsh+flcWvBSEWtLcDO3YE2+i4cRxrbeU1bF43pVVuvJEC+fhx4Mor3T/zhhuAn/6UtvHFL4Yeb2ry\nrol3883A/fdz8S4vdy/el18O3HQTcOwY8OUvuwX6kiXAJZewE9F117mPP/VU4MwzuQH49a/dx0+Y\nQAHR3g688or7+OJiYORIfmbt2OE+PiuLXwtCLGhvB7ZvD7bRM8/k2GefAb/5jbvO5vDhFMjbtgH/\n8i/un/nb39J2P/zQ20bNeH09MH26e/x3vwOuuILiet48t43ccw/X8YYG/hzn+NVXs7Xu9u3Aj37k\nHv/qV4Fp07h+/+EP7vGTT2bN2MZG4K233OPl5TwHra3Anj3u8f79pQNYipP4ArmyMnydty1brK87\nOoIXYQB4911e4PYPhpwca/yZZ7hI2scLC63xe+/l7tde4qKy0hpfuJBeZvvxo0db42lpFLAtLdbx\nI0da4y+/TOOzH3/WWZZAvuMOFoO2s2iRJZAvuMB73Aj46dP5ARhqvLTU7YFbsAB49FGOn3EGP0CM\nuM7MBE45Bbj7bo5/85tugT9lCj/4AIoYI/DNo6KCogQAXnyRH9728cJCbhIAfvgCweM5OfRMANaG\nSbwR/lFTE9pGc3MpUg2BAP9n5v81cKB7A9zWxoUJ4CL017+6x6uqOJ6VBfzyl8FjJ04As2ZxPC0N\n+NrX3McXFFjzyczka+Zz4MQJy6ZaW1lGx3l8IECBcfQoxb6Tm2+mQG5qoj17jd9/Pz9bxowJPd7Y\nCIwY4V6cv/1teuabmihOnAL7/PNpg8eOcTPgPH7ePH4OtLTw9zjHTzqJG/kTJ7y9h2VlnHcgAHzw\ngXs8N5f/W9P5R2zUX8LZ6NSpvI4B/r+MjRpH1OTJdLQ4bWDUKI6PG8d1zDk+YwbHR48GHnzQPT5l\nCscHD6YQdo4PGWLNKT2dttjcbI03NnL84EGuI87jx46lQN6+nRtqJ48+yrWoocHbRh99lLazYQPw\nhS+EHv/f/6UN2tfIzEzggQdoh5s2cbPttJEbb+RnyMcfA3fe6R6/8EL+3k8/BR5/3D0+dy6TtA4c\noKPMOV5Tw7X02DHgk0/c44MHs9h/Rwcf4tV3kfgCORrS0txt74qKwh9jhGYoLr88/PiPfxx+/L/+\nK/z4xo3hx7duddegy862xv/yF3rh7B8Mdo/agw9aHyrmePuCbNoU2o+fPNkaHzmSv88cf/w4H4b1\n6ykm7McfPmwJ5PvuowHb+cpXLIF82WXe43/6E78+9VR66O0sWQI8/zy/Li7meEaGZfhLlgBPPsnx\nGTPct/fOOIMeB4AfQseOBX+4zZhB7wTAjYBT4NfU8M4DADz9NAWA/fhRo6zA+bVr+Ww/ftAgaxN2\n6FBwUelU90ikpwf/jWlp1kLrhRFzocjKAq69NvT4gAHAihWhx3NzubiEYtAgbmBDMXgwr3enQDcb\nuNxchog4F29jg9nZwMqV7uONxy0zE/jXf3UfX1FhzaG0NHjs6FFeswB/1jvvuI8fNowC+ehR4K67\n3H/XrbdSIDc1cZH3Gr/vPn52TJrkHr/lFn42HjrE3wUElxm64QaKgsOHKWKci/fy5dx8NzUxVMcu\n/jMzeZdw6VLa7l13uY+fNYuipbXVyvK2Hz9uHMVFWxsFjvP44cOBoUMpHMwdQHN8KmeDK8X/k/0u\nbb9+wU4fJ4MGAfPnhx4fMYJ3YUJRVgY8/HDo8Zoa4NVXQ49Pneq+y2tn+nReh04bMOvk+PH0IDvH\nzTpYXk6B6hw3NlpQwL/POW7CNDMzef6cNmrqxzY18Rp0Hj9zJgXyjh20FScrV/Ia/ugj4LzzvMeX\nL6cH3zgM7Dz+OMNs3n7bGrfbwIoVXB/Xr+fPd9rIHXdwY9HQwA29c/yKK4DZs7lBWbHCPb5wIR1h\n+/YB//3f7k1+XR3XhiNHgPffdx9fWMjP17Y2d5htjGw0tQRyKpKbG368qwzGCy4IP+5leHaeeir8\n+Ntvhx//7DOrd7QxfPuH7xtvuD38xnMAAI895vbwl5Za47feyg8Y+/iECdZ4XZ1bwNg3GHv2uO8A\n2DdZv/udtQEwnHuuJZCvuYY/387SpcAf/8ivzzyTH86hxseODR5XyvvDTkhMlLLEsBcZGd7eJ0N2\nNhexUAwYAPzkJ6HHc3Otu0FeDB4MbN4cenzYMMtjaBfo/ftzfNAg4L33QnsPc3KA554L7R3Mzuat\ncud4XR3H09IoBJzjJgSsvd19h62tjaIJoNB46CG+Zi9Yf/vtFMiNjdZm3c53vwv88Ie03dmz3eO3\n3cZN9IED1t0GQ1oaf76QHKSn0w5CkZvLcItQFBRQSIaitJR3YUJRXU0Pdyjq6oLvhDuZNYvXttMG\njDaYMoVeaue4uctWWQk8+6x73PzNo0YBP/iBtwce4GfQ9OnucbOOt7TQy+0cX7iQ47t3A7/6FV8L\nBKy/q6iIAnnzZm9H5JNP0vO+caN3CM8TTwDf+AY1iHM8PZ3jPUTp3my35vxlSg0F8BiA+QD2A7hN\na/37cMdMmzZNr/O7lZ4g2G89ApaA2LXL3Ss7L8/y8P39724P/6hR9IwDjP07ejT4+PHjoS688B2t\n9bR4/5lio0LSYsI52tq4QGZl0Wbti7exsxEjaIetrcDq1e7FvbaWwuPoUd5Kdx5/2mlQ8+eLjQpC\nNJi2xGYTnJlJG9y7122DpaW8k3PoEEWwc3zWLN6J+/RT9yb9xAng3HOhpk7tkY3GWyD/AUAagMsB\nTAHw3wBmaa3fD3WMGLbQF1FK+bX4io0KQgQkk40qNU2Xla1DSQl1h/3ZPOypOYKQCvTURuMWYqGU\nygGwFMAErXUzgDeUUi8C+DqAW+M1D0EQvBEbFYTEprs2WljISJIdO4DXXqPTzX63G2C0jV00O4V0\nQYHkcAl9i3jGII8D0K61tgfE1QNwZckppa4EYGo/tSql3ovD/HqL4eBtsGQkmecOJPf8q3z4nWKj\nyUcyzx1I7vknlY0+/XR4Gz1wgI93343ZXGNFMl8jgMzfT3pko/EUyAMBHHG81gjAlYWmtX4EwCMA\noJRa58dtrFiRzPNP5rkDyT1/pZQfMQtio0lGMs8dSO75i43Gh2SeOyDz95Oe2mg869U0A8hzvJYH\noCmOcxAEITRio4KQ2IiNCkKciKdA3gwgQylVaXttMoCQiQWCIMQVsVFBSGzERgUhTsSRXOwMAAAH\nN0lEQVRNIGutjwL4E4AfKKVylFKzASwG8B9dHPpIr0+ud0nm+Sfz3IHknn/c5y42mpQk89yB5J6/\n2Gh8SOa5AzJ/P+nR3P2og/w4gHkADgC4tav6jYIgxA+xUUFIbMRGBSE+xFUgC4IgCIIgCEKik8JN\n5QVBEARBEAQhekQgC4IgCIIgCIIN3wWyUmqoUup5pdRRpdQOpdSFId6nlFI/UUod6Hz8RCn/+/pE\nMf+7lVJtSqlm22NMvOfrmNM1Sql1SqlWpdQTXbz3eqXUXqXUEaXU40qprDhNM9ycIpq/Umq5Uirg\nOPdz4jdTzzllKaUe67xmmpRSG5RSC8K837fzLzbqH2Kj/iE2Gj/ERv0hme2zc169aqO+C2QADwE4\nAWAEgIsAPKyUqvV435UAloAlbSYBOAfAVfGaZBginT8A/B+t9UDb45O4zdKb3QDuBRM+QqKU+jLY\nxvQMAKUAxgD4fq/Prmsimn8naxznfnXvTq1LMgD8E+yANQjA9wA8q5Qqc74xAc6/2Kh/iI36h9ho\n/BAb9Ydktk+gt21Ua+3bA0AOaBTjbK/9B4Afe7z3LQBX2r6/HMD/S6L53w3gP/2cb5i/414AT4QZ\n/z2AH9m+PwPAXr/nHcX8lwN4w+95RvB3bASwNJHOv9hoYjzERhPjITbq+/zFRv2Ze1LYZ+dcY2aj\nfnuQQ/WV99o51naOdfW+eBLN/AHgHKXUQaXU+0qpb/X+9GKG17kfoZQa5tN8ukOdUmq/UmqzUuoO\npVQ826x3iVJqBHg9eRX89/P8i40mB2KjvYzYaK8hNpocJLR9ArG3Ub8FcsR95Tvf2+h430Cf46ei\nmf+zAGoA5AP4FwB3KqWW9e70YobXuQe8/85E5HUAEwAUAFgKYBmAm32dkQ2lVCaApwE8qbVu8HiL\nn+dfbDQ5EBvtRcRGexWx0cQnoe0T6B0b9VsgR9NX3vnePADNutNX7hMRz19r/YHWerfWOqC1fgvA\ngwDOjcMcY4HXuQe8/08Jh9b6E631Nq11h9Z6E4AfIEHOvVIqDbydeALANSHe5uf5FxtNDsRGewmx\n0V5HbDTBSWT7BHrPRv0WyNH0lX+/c6yr98WTaObvRAPwPXs4QrzO/T6t9QGf5tNTEuLcd3ptHgMT\nU5ZqrdtCvNXP8y82mhyIjfYCYqNxQWw0+UiY896bNuqrQNbR9ZV/CsANSqmRSqliADcCeCJuk/Ug\nmvkrpRYrpYYoMgPAdQBWxXfGrjllKKWyAaQDSFdKZYeIK3oKwOVKqfFKqcFgpugTcZyqJ5HOXym1\noDM2CUqpagB3wOdz38nD4O3Cc7TWx8O8z7fzLzYqNtoTxEZ7H7FRsdHukgL2CfSmjSZAxuFQAC8A\nOApgJ4ALO1//Injrx7xPAbgfwMHOx/3obJWdJPP/A4ADoJu/AcB1CTD3u8GdoP1xN4CSznmW2N57\nA4B9YKzYSgBZyTJ/AA90zv0ogE/A20OZPs+9tHO+LZ1zNY+LEu38i40m/jXu9zXS0/mLjcbtGhcb\njf3ck9ZGk9k+O+fVqzaqOg8SBEEQBEEQBAH+xyALgiAIgiAIQkIhAlkQBEEQBEEQbIhAFgRBEARB\nEAQbIpAFQRAEQRAEwYYIZEEQBEEQBEGwIQJZEARBEARBEGyIQBYEQRAEQRAEGyKQBUEQBEEQBMGG\nCGRBEARBEARBsCECuQ+jlOqvlNqllNqplMpyjD2qlAoopS7wa36C0NcRGxWExEZsNHURgdyH0Vof\nB3AXgNEArjavK6XuA3A5gGu11s/4ND1B6POIjQpCYiM2mroorbXfcxB8RCmVDqAeQAGAMQCuAPBz\nAHdprX/g59wEQRAbFYRER2w0NRGBLEApdTaAlwD8HcBcAL/WWl/n76wEQTCIjQpCYiM2mnqIQBYA\nAEqpdwHUAXgGwIXacWEopc4DcB2AKQD2a63L4j5JQejDiI0KQmIjNppaSAyyAKXU+QAmd37b5DTq\nTg4B+DWA2+M2MUEQAIiNCkKiIzaaeogHuY+jlJoP3hZ6CUAbgK8BmKi1/jDE+5cA+IXsfAUhPoiN\nCkJiIzaamogHuQ+jlJoJ4E8A3gRwEYDvAegAcJ+f8xIEgYiNCkJiIzaauohA7qMopcYD+L8ANgNY\norVu1VpvBfAYgMVKqdm+TlAQ+jhio4KQ2IiNpjYikPsgSqkSAC+D8VALtNZHbMP3ADgO4H4/5iYI\ngtioICQ6YqOpT4bfExDij9Z6J1jU3GtsN4AB8Z2RIAh2xEYFIbERG019RCALEdFZCD2z86GUUtkA\ntNa61d+ZCYIAiI0KQqIjNppciEAWIuXrAFbavj8OYAeAMl9mIwiCE7FRQUhsxEaTCCnzJgiCIAiC\nIAg2JElPEARBEARBEGyIQBYEQRAEQRAEGyKQBUEQBEEQBMGGCGRBEARBEARBsCECWRAEQRAEQRBs\niEAWBEEQBEEQBBsikAVBEARBEATBxv8HPKrgSfGPU1cAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a6c3a2080>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"metadata": {
"id": "zvp4HYdExuXy"
},
"cell_type": "markdown",
"source": [
"# Stochastic Gradient Descent"
]
},
{
"metadata": {
"id": "8Dto25R9xuX0"
},
"cell_type": "code",
"source": [
"theta_path_sgd = []\n",
"m = len(X_b)\n",
"np.random.seed(42)"
],
"execution_count": null,
"outputs": []
},
{
"metadata": {
"id": "TEHZbSOwxuX4",
"outputId": "1e9286cb-988a-4be7-983b-462700014f9c"
},
"cell_type": "code",
"source": [
"n_epochs = 50\n",
"t0, t1 = 5, 50 # learning schedule hyperparameters\n",
"\n",
"def learning_schedule(t):\n",
" return t0 / (t + t1)\n",
"\n",
"theta = np.random.randn(2,1) # random initialization\n",
"\n",
"for epoch in range(n_epochs):\n",
" for i in range(m):\n",
" if epoch == 0 and i < 20: # not shown in the book\n",
" y_predict = X_new_b.dot(theta) # not shown\n",
" style = \"b-\" if i > 0 else \"r--\" # not shown\n",
" plt.plot(X_new, y_predict, style) # not shown\n",
" random_index = np.random.randint(m)\n",
" xi = X_b[random_index:random_index+1]\n",
" yi = y[random_index:random_index+1]\n",
" gradients = 2 * xi.T.dot(xi.dot(theta) - yi)\n",
" eta = learning_schedule(epoch * m + i)\n",
" theta = theta - eta * gradients\n",
" theta_path_sgd.append(theta) # not shown\n",
"\n",
"plt.plot(X, y, \"b.\") # not shown\n",
"plt.xlabel(\"$x_1$\", fontsize=18) # not shown\n",
"plt.ylabel(\"$y$\", rotation=0, fontsize=18) # not shown\n",
"plt.axis([0, 2, 0, 15]) # not shown\n",
"save_fig(\"sgd_plot\") # not shown\n",
"plt.show() # not shown"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"text": [
"Saving figure sgd_plot\n"
],
"name": "stdout"
},
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAagAAAEYCAYAAAAJeGK1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nVBIoACoJFACVPl7ONK0tSzxZAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a69e108d0>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"metadata": {
"id": "YBNA6G9axuYA",
"outputId": "ff378835-1ef8-42e8-a025-815b569b943f"
},
"cell_type": "code",
"source": [
"theta"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([[3.92793287],\n",
" [3.06981492]])"
]
},
"metadata": {
"tags": []
},
"execution_count": 428
}
]
},
{
"metadata": {
"id": "4cw3QKkYxuYG",
"outputId": "9e931686-053c-4fee-a985-72293700702a"
},
"cell_type": "code",
"source": [
"from sklearn.linear_model import SGDRegressor\n",
"sgd_reg = SGDRegressor(max_iter=50, tol=-np.infty, penalty=None, eta0=0.1, random_state=42)\n",
"sgd_reg.fit(X, y.ravel())"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"SGDRegressor(alpha=0.0001, average=False, epsilon=0.1, eta0=0.1,\n",
" fit_intercept=True, l1_ratio=0.15, learning_rate='invscaling',\n",
" loss='squared_loss', max_iter=50, n_iter=None, penalty=None,\n",
" power_t=0.25, random_state=42, shuffle=True, tol=-inf, verbose=0,\n",
" warm_start=False)"
]
},
"metadata": {
"tags": []
},
"execution_count": 429
}
]
},
{
"metadata": {
"id": "xt_ZIVRfxuYL",
"outputId": "9f6eb215-6918-4fa6-d721-e0cbd60daa00"
},
"cell_type": "code",
"source": [
"sgd_reg.intercept_, sgd_reg.coef_"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"(array([3.88184084]), array([2.96620713]))"
]
},
"metadata": {
"tags": []
},
"execution_count": 430
}
]
},
{
"metadata": {
"id": "Hsz2d_LqxuYS"
},
"cell_type": "markdown",
"source": [
"# Mini-batch gradient descent"
]
},
{
"metadata": {
"id": "v_FSf5ZrxuYT"
},
"cell_type": "code",
"source": [
"theta_path_mgd = []\n",
"\n",
"n_iterations = 50\n",
"minibatch_size = 20\n",
"\n",
"np.random.seed(42)\n",
"theta = np.random.randn(2,1) # random initialization\n",
"\n",
"t0, t1 = 200, 1000\n",
"def learning_schedule(t):\n",
" return t0 / (t + t1)\n",
"\n",
"t = 0\n",
"for epoch in range(n_iterations):\n",
" shuffled_indices = np.random.permutation(m)\n",
" X_b_shuffled = X_b[shuffled_indices]\n",
" y_shuffled = y[shuffled_indices]\n",
" for i in range(0, m, minibatch_size):\n",
" t += 1\n",
" xi = X_b_shuffled[i:i+minibatch_size]\n",
" yi = y_shuffled[i:i+minibatch_size]\n",
" gradients = 2/minibatch_size * xi.T.dot(xi.dot(theta) - yi)\n",
" eta = learning_schedule(t)\n",
" theta = theta - eta * gradients\n",
" theta_path_mgd.append(theta)"
],
"execution_count": null,
"outputs": []
},
{
"metadata": {
"id": "QMLwUwCexuYX",
"outputId": "cb545f51-0383-4aee-f45b-06b95857aecb"
},
"cell_type": "code",
"source": [
"theta"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([[4.25214635],\n",
" [2.7896408 ]])"
]
},
"metadata": {
"tags": []
},
"execution_count": 24
}
]
},
{
"metadata": {
"id": "N5Bti8hGxuYd"
},
"cell_type": "code",
"source": [
"theta_path_bgd = np.array(theta_path_bgd)\n",
"theta_path_sgd = np.array(theta_path_sgd)\n",
"theta_path_mgd = np.array(theta_path_mgd)"
],
"execution_count": null,
"outputs": []
},
{
"metadata": {
"id": "nsXEAG4xxuYi",
"outputId": "24cd254c-bc35-46a4-a119-68b602d6ed31"
},
"cell_type": "code",
"source": [
"plt.figure(figsize=(7,4))\n",
"plt.plot(theta_path_sgd[:, 0], theta_path_sgd[:, 1], \"r-s\", linewidth=1, label=\"Stochastic\")\n",
"plt.plot(theta_path_mgd[:, 0], theta_path_mgd[:, 1], \"g-+\", linewidth=2, label=\"Mini-batch\")\n",
"plt.plot(theta_path_bgd[:, 0], theta_path_bgd[:, 1], \"b-o\", linewidth=3, label=\"Batch\")\n",
"plt.legend(loc=\"upper left\", fontsize=16)\n",
"plt.xlabel(r\"$\\theta_0$\", fontsize=20)\n",
"plt.ylabel(r\"$\\theta_1$ \", fontsize=20, rotation=0)\n",
"plt.axis([2.5, 4.5, 2.3, 3.9])\n",
"save_fig(\"gradient_descent_paths_plot\")\n",
"plt.show()"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"text": [
"Saving figure gradient_descent_paths_plot\n"
],
"name": "stdout"
},
{
"output_type": "display_data",
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 504x288 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"metadata": {
"id": "1_RXMxEWxuYl"
},
"cell_type": "markdown",
"source": [
"# Polynomial regression"
]
},
{
"metadata": {
"id": "BlyJBgUoxuYm"
},
"cell_type": "code",
"source": [
"import numpy as np\n",
"import numpy.random as rnd\n",
"\n",
"np.random.seed(42)"
],
"execution_count": null,
"outputs": []
},
{
"metadata": {
"id": "uc-arzgsxuYp"
},
"cell_type": "code",
"source": [
"m = 100\n",
"X = 6 * np.random.rand(m, 1) - 3\n",
"y = 0.5 * X**2 + X + 2 + np.random.randn(m, 1)"
],
"execution_count": null,
"outputs": []
},
{
"metadata": {
"id": "sPmD9PHDxuYr",
"outputId": "9ab35e7e-688d-4a6c-90d4-2e53fe76965f"
},
"cell_type": "code",
"source": [
"plt.plot(X, y, \"b.\")\n",
"plt.xlabel(\"$x_1$\", fontsize=18)\n",
"plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
"plt.axis([-3, 3, 0, 10])\n",
"save_fig(\"quadratic_data_plot\")\n",
"plt.show()"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"text": [
"Saving figure quadratic_data_plot\n"
],
"name": "stdout"
},
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAagAAAEYCAYAAAAJeGK1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvOIA7rQAAF29JREFUeJzt3XuMZnddx/H3t9tCdduiDaWJwaWKUISoVCaakQCrrSJ4gbBeKuWiEVch4CVqwmIXVhaz8RIgyEVXyyXKRbS1EUREqqugS3BrUKiWCiKIQKRcbLuUbdl+/eOZodNxnpnncs7v/M4571eymZ15nnme33meec7n/C7neyIzkSSpNmd03QBJkrZiQEmSqmRASZKqZEBJkqpkQEmSqmRASZKqZEBJkqrUaEBFxLMj4kREnIqI12667dKIuDEivhARfxMRD2jyuSVJw9J0D+oTwIuAV2/8YUTcF7gGOAicD5wA/qjh55YkDciZTT5YZl4DEBErwP033PQk4IbM/OO12w8BN0fEQzLzxibbIEkahkYDahsPA/55/ZvMPBkRH177+f8LqIjYD+wH2L179yMe8pCHFGqmJKkJJ0/CBz8ImRABF18Mu3dPbrv++utvzswLdnqMUgF1DvDpTT/7X+Dcre6cmUeBowArKyt54sSJdlsnSWrUkSNw8CCcPg1nnAFPexocODC5LSI+OstjlFrFdxtw3qafnQfcWuj5JUkF7d0L97oX7No1+bp37/yPUaoHdQPw9PVvImI38MC1n0uSBmZ1Fa67Do4dm4TT6ur8j9FoQEXEmWuPuQvYFRFnA18C/hT4zYjYB/w58HzgX1wgIUnDtbq6WDCta3qI70rgduC5wFPW/n9lZn4a2Af8GvA54NuByxt+bknSgDS9zPwQcGjKbe8EXI4nSZqJpY4kSVUyoCRJVTKgJElVMqAkSVUyoCRJVTKgJElVMqAkSVUyoCRJVTKgJElVMqAkSVUyoCRJVTKgJElLOX58coHC48ebfdxS14OSJA3Q8eNw6aVwxx2TCxNed91yl9jYyB6UJGlhx45Nwun06cnXY8eae2wDSpK0sCYu7T6NQ3ySpIU1cWn3aQwoSdJSlr20+zQO8UmSqmRASZKqZEBJkqpkQEmSqmRASZKqZEBJkqpkQEmSqmRASZKqZEBJkqpkQElS5dq6nEXtLHUkSRVr83IWtbMHJUkVa/NyFrUzoCSpYm1ezqJ2DvFJUsWaupzF8eOLP8Yyv7sMA0qSKrfs5SzmncfaGEjQ3RyYASVJA7fVPNa0kNkcZk9/+uy/2zTnoCRp4OaZx9ocZtDdHFjRHlREXAS8ElgFTgF/Avx8Zn6pZDskaUzmmcdaD7P1HtTTngaXXAJXXw379pWdg4rMLPdkEW8D/gf4GeCrgL8Cfi8zXzbtd1ZWVvLEiROFWihJansOKiKuz8yVne5Xeojv64A3Z+YXM/NTwNuBhxVugyQNTpPVJlZX4cCBydcuz8MqvUjipcDlEXEM+GrgccDBzXeKiP3AfoA9e/aUbJ8k9U6b1SY2D/mVnIMq3YP6OyY9pluAjwMngGs33ykzj2bmSmauXHDBBYWbKEn90mYvZ33+6vDh8mWWigVURJzBZEjvGmA3cF8mvahfL9UGSRqitqtNbBzyK6lkD+p8YA/w8sw8lZmfAV4DPL5gGyRpcBbt5TQxb9VmpfVic1CZeXNEfAR4ZkT8FnAO8HTgX0q1QZKGat5qE03MW7Vdab30HNSTgO8FPg18CLgT+IXCbZCk0Wti3qrtFX5FV/Fl5vuAvSWfU5L0/zWxOq/tFX7W4pOkEWqiSnpTldanKVpJYhFWkpCkYam1koQkSTMxoCRJVTKgJElVMqAkSVUyoCRJVTKgJElVMqAkSVUyoCRJVTKgJElVMqAkSVUyoCRJVTKgJElVMqAkSVUyoCRJVTKgJElVMqAkSVUyoCRJCzl+HI4cmXxtg5d8l6SCjh9v7xLpJR0/DpdeCnfcAfe61+TS701vjwElSYWU2KmXCsBjxybbcfr05OuxYwaUJPVW2zv1EgG4bu/eyXOsP9fevc0/hwElSYW0vVMv0atZt7o6CcA2e2sGlCQV0vZOvUSvZqPV1XaHEQ0oSSqozZ16iV5NSQaUJA1I272akjwPSpJUJQNKklQlA0qSVCUDSpJUJQNKklQlA0qSVCUDSpJUJQNKknqg7Utb1Kj4iboRcTnwAmAP8CngxzPzXaXbIUl9UbIIbE2K9qAi4ruBXwd+AjgXeDTwHyXbIGl4ht672KoI7BiU7kH9KvDCzHzP2vf/Xfj5JQ1Mzb2Lpq7NVLoIbC2KBVRE7AJWgD+LiA8BZwPXAr+cmbdvuu9+YD/Anj17SjVRUg+VvMTEPJoMzqEVgZ1VySG+C4GzgB8CHgU8HLgEuHLzHTPzaGauZObKBRdcULCJkvpmvXexa1ddvYumh+VWV+HAgfGEE5QNqPVe0m9n5icz82bgxcDjC7ZB0sCs9y4OH65reK/W4OyTYkN8mfm5iPg4kBt/XOr5JQ1XjZeYGOuwXJNKL5J4DfCciHg7cCfwC8BbC7dBkoqoMTj7pHRAHQbuC9wEfBF4M/BrhdsgSeqBogGVmXcCz1r7J0mD0dSSct1tpkUSEfE7EZER8TVb3HZxRNwRES9rvnmSVL/1JeUHD06+DvWE4dJmXcW3/nJ/2xa3vQS4hUn5IkkanY1Lyk+dgkOHDKkmzBpQ65Uf7hFQEfF9wOOA52fm55psmCQtq1QJpPUl5WecAXfdBe98pz2pJswaUDcBn2VDQEXEWUzOY/oA8LvNN02SFldy2G19Sflll90dUtudnDv02oFNmWmRRGZmRLwHeGRERGYm8HPAg4HLMvN0m42UpHmVLoG0ujoZ2nvXu7avmVdz7cDazFNJ4j3AfYCLI+J+wEHg2sy8rpWWSdISuqjkMEtVi7FWJl/EPMvMNy6UeDRwb+AXG2+RJDWgq0oOO52cO9bK5IuYJ6DeC9wFPAN4JPCbmem1nCRVq8ZKDpZAmt3MAZWZt0TEvzKpRP4prAAhSQupMThrNG818/eufT2Qmbc23RhJktbNHFBry8r3AieA17XVIEmSYL45qF8Cvg64Ym2ZuSRJrdk2oCLifOCxwDcDvwy8ODPfs93vSJLUhJ16UI8F3gD8D5Oae89tvUWSJLFDQGXmG4E3FmpL9SynL0nllL5gYW9ZnkSSypp3mfloWZ5EksoyoGbURV0vSRozh/hmZHkSSc5Dl2VAzcHyJBord8zOQ3fBgJK0rb7umJsO1dLXl5IBJWkHfdwxtxGqXiajPANK0rb6uGNuI1Sdhy7PgJK0rT7umBcJ1VmGBJ2HLsuAkrSjvu2Y5w3Vvs6zDZ3nQUkapNVVOHBg8v8jRyYhNM12J+IfP77z76sd9qAkDdasPaNpQ4L2rLplD0rSYM1aomx9SPDw4XuGkCXOujXKHpQnHUrjMM9iia3m2fq4gnFIRhdQdtmlYZh11d2iKxDXH/+lL4XPfMYD2i4MLqB2+qPt40mHku5pngPNRVYgeiBbh17PQW1eXbP+R3Xw4OTrVqturEou9V/bc0POPdWhtz2orY5wZukd9fGkQ0n31PbckHNPdehtQG0VRrP+UfXtpMONXOAhtX+g6YFsHToJqIh4EPB+4E8y8ymLPMZWYTT0PyrHxaW79flAU7Ppqgf1CuAfl3mAaWE05D9aF3hIZXgwWIfiARURlwOfB/4B+IZZfmfasNaQw2grjotLZXgwWIeiARUR5wEvBL4LeMY299sP7Ae48MIHeiSzZuhDmFItPBisQ+ke1GHgqsz8eERMvVNmHgWOAtz//ivpkczdxtZrlLrgwWAdigVURDwcuAy4ZJ7fO/dc+OxnPZKRVJYHg90r2YPaC1wEfGyt93QOsCsiHpqZ3zrtl3bv9khGksaoZEAdBd604ftfYhJYz9zpFz2SkdQFzzvsVrGAyswvAF9Y/z4ibgO+mJmfLtUGSZqVS82711ktvsw8tOhJupLUNuvxda/XxWIlTXhZ8uZZWLp7va3FJ2liqENRs8z/tDlH5FLz7vU+oJzE1Nh1WfWgrc/fLKFbIphdoNWtXgfUsn+ghpuGoKuqB20GxCyhazmi4et1QC3zBzrUYRGNT1dDUW0GxCyhazmi4et1QM3yBzqtl+TRl4aki6GoNgNiltB1jmj4IjO7bsO2VlZW8sSJE1Nv326Ybrtekj0oaXkOk2sREXF9Zq7sdL9e96Bg+yPH7XpJHn1Jy3MRgdrU+4Dazk5DEMt+uDx6lKT2DDqg2uwlOUSoMfKgTCUNOqCgvSGIacOHfoA1VB6UqbTBB1Rbtho+9AOsIXPlq0obdS2+ZeqXrQ8fHj58dxBZXHIx1pHrB2vTqbTR9qCa6O1sHj70xMH52evsD1e+qrTRBtRWvZ33vx+uvhr27YP9++d/TD/A83PYqF9cVq6SRhtQm3s7n/88PO95k9ve8Y7J10VDyg/wdJsXkdjrbI4LdDQ0ow2ozb2dQ4fuefvVVy8WUG3r805o2nCevc7lOVSqIRptQME9ezv79t3dc1r/vjZ93wlNG86z17k8h0o1RKMOqI3We0vLzEG1re87IYfz2uNrqyHqfbHYMel7Dwr6PURZO19b9cWsxWINqJ5xJySp70ZTzXxsnK+RNBajriQhSaqXASXpy0qWnbLElXbiEJ8koOwinCEs+FH77EEV5BGjalay2LGFlTULe1CFbHfEWPPKvJrbpmaVPJfK87Y0CwOqkO0ucFjrUEfNbVPzmio7NctBjSWuNAsDqpBpR4zLVodos4fT98oVmt+ypzHMc1DjKRPaiQHVgq1CY9oR4zJDHW0PG5YahhnqMOJQt2s7HtSoSQZUw7YLja2OGJcZ6mh72LDEMMxQhxGHul07cW5JTTKgGrbIEeSiQx1tDRs20bZZDfWIe6jbtRPnltQkA6phTR5B7jRE1MawYWl9aus8hrpds3BuSU0ZfLHYLuYBmnjOZYeI+jT/0ae2zqPJ7Rrqa6Rxqq5YbETcG3glcBlwPvBh4EBm/kVbz9nVPEATR5DLDhH16Si2T22dR1PbNdb5LKlkJYkzgf8CHgPcB7gSeHNEXNTWE/b5bPX1IaJdu+4eIrISRVlbvd5dvAdd/h37N6cuFetBZeZJ4NCGH701Ij4CPAL4zzaes8/zAJvnl8Cj6JK26rVAN+9BV3/H9tzUtc4WSUTEhcCDgRu2uG0/sB9gz549Cz9H31cUbRwiOnJknKvCujKt19LFe9DV3/FYVyKqHp0EVEScBbweeF1m3rj59sw8ChyFySKJZZ6rD/Mbs0yA97k32EfTXu+u3oMu/o79m1PXiq/ii4gzgDcA5wFPyMw7t7v/0C/5Ps8wiiu5Jkq9Dls9T5fvQV9XpEqbVbeKDyAiArgKuBB4/E7hNAbzDKPU2BssvQMrOS8yrfJHF+9Bn1ekSosqPcT3KuAbgcsy8/bCz12lPg+jdLHTHOu8yFi3W+NWbJl5RDwA+Gng4cCnIuK2tX9XlGpDjdYnwA8f7t8qqS6WP2+1/H4Mltlul4qrr0ouM/8oEKWer7Rlhrr6OozSRe9vuxVtQ54vWXQln0vF1WfW4mvAWHcCs+40mw6OrQJ9DO/BIgcyDg2qzwyoBox5J7B5p7k5jEoFx5jfg+30eY5TMqB20JdzlGoY3toqjEoFRw3vQY36frK6xs2A2sasR/9d7wRqGd7aKoxKBUfX70HN+jrHKRlQ2+jLOUq1DG9tFUYlg8MdsTQsBtQ2+jJsVEs7p4WRwSFpEYO/YOGyapjbmUVf2ilJs5Y6MqA0l9qCsO32jK32nlRClbX41G+1LMYo1Z4ut7fr19pwVA1KXlFXPVfbFYrbbk+X29v1VXQvvRQOHpx8tUSSumJAaWa11cFruz0ltndanbwuX+vaDkQ0Xg7xaWa1nWvUdnvafvzthvG6fK1rWRUquUhC6siRI5NhtNOnJz2lw4fhwIGuWzXhHJTa5CIJqXI191Q8d001MKCkjtQ2ZCrVxoCSOmRPRZrOVXySpCoZUGqdlxyfztdGms4hPrXKigjTdf3a7KTm107jYECpVV1eCqT2AJj1tekiKGp/7TQODvGpVVZEmG6W16arskO1v3YaB3tQapUVEaab5bXpqgda+2uncbCShAat7/MoXVdU7/Nrp3p5PahKjflDP+ZtX4avm4bGUkcVautouA87MCfdF+fJvBorF0kU1MbEc1+u3eOku6R5GVAFtbGirS87/tquJSWpfg7xFdTGira+rLYacmHUPgyxSn3kIokBGMoOso/b4dyaND8XSYzIECbRZ93R1xZiXVbKkIbOgFIVZtnR19hb6csQq9RHBpSqMMuOvsbeypDn1qSuGVCqwiw7+lp7K0MYYpVqZECpUcvMEe20o7e3Io1L0YCKiPOBq4DvAW4GDmTmG0q2Qe0pMUdkb0Uaj9In6r4CuAO4ELgCeFVEPKxwG9SSvpw0LKkfigVUROwG9gEHM/O2zHw38GfAU0u1Qe2yWoSkJpUc4nsw8KXMvGnDz/4ZeMzmO0bEfmD/2renIuIDBdpXm/syGQbtmXN3w3nn3n77Lbd+x3fcenLBB+npti/N7R6XsW43wMWz3KlkQJ0D3LLpZ/8LnLv5jpl5FDgKEBEnZjnjeGjGut0w3m13u8dlrNsNk22f5X4l56BuA87b9LPzgFsLtkGS1BMlA+om4MyIeNCGn30LcEPBNkiSeqJYQGXmSeAa4IURsTsiHgk8AfiDHX71aOuNq9NYtxvGu+1u97iMdbthxm0vWs187TyoVwPfDXwGeK7nQUmStlL95TYkSePkFXUlSVUyoCRJVepFQEXEH0bEJyPiloi4KSKe0XWbSoiIe0fEVRHx0Yi4NSLeFxGP67pdJUTEsyPiRESciojXdt2eNkXE+RHxpxFxcu29fnLXbSphTO/xRiP/XM+1L+9FQAFHgIsy8zzgB4EXRcQjOm5TCWcC/8Wk2sZ9gCuBN0fERR22qZRPAC9isqhm6MZao3JM7/FGY/5cz7Uv70VAZeYNmXlq/du1fw/ssElFZObJzDyUmf+ZmXdl5luBjwCDD+fMvCYzr2Wy2nOwxlyjcizv8WYj/1zPtS/vRUABRMQrI+ILwI3AJ4G3ddyk4iLiQiY1DT25eTim1agcQw9KjO9zPc++vDcBlZnPYlK371FMTvg9tf1vDEtEnAW8HnhdZt7YdXvUmJlrVGp4xvi5nmdf3nlARcSxiMgp/9698b6ZeXptCOT+wDO7aXFzZt32iDiDScWNO4Bnd9bghszzno+ANSpHamif63nMui/v/JLvmbl3gV87kwHMQc2y7RERTK5CfCHw+My8s+12tW3B93yovlyjMjP/fe1n1qgcuCF+rhe07b688x7UTiLifhFxeUScExG7IuKxwI8B13XdtkJeBXwj8AOZeXvXjSklIs6MiLOBXcCuiDg7Ijo/oGraEjUqe28s7/EUo/tcL7Qvz8yq/wEXAH8LfJ7JWP37gZ/qul2Ftv0BTFa5fJHJUND6vyu6bluBbT/E3at81v8d6rpdLW3r+cC1wEngY8CTu26T73Gr2z3Kz/Ui+3Jr8UmSqlT9EJ8kaZwMKElSlQwoSVKVDChJUpUMKElSlQwoSVKVDChJUpUMKElSlQwoSVKVDCipkIj4ioj4eER8LCLuvem234+I0xFxeVftk2pjQEmF5KQo6AuArwWetf7ziDgC/CTwnMx8U0fNk6pjLT6poIjYxeSKufcDvh54BvAS4AWZ+cIu2ybVxoCSCouI7wfeAvw18J3AyzPzZ7ttlVQfA0rqQET8E3AJ8CYml9fITbf/CPCzwMOBmzPzouKNlDrmHJRUWET8KJOr5gLcujmc1nwOeDnwK8UaJlXGHpRUUER8D5PhvbcAdwI/DHxTZv7blPs/EXipPSiNkT0oqZCI+HYml3f/e+AK4ErgLuBIl+2SamVASQVExEOBtwE3AU/MzFOZ+WHgKuAJEfHIThsoVciAkloWEXuAv2Qyr/S4zLxlw82HgduB3+iibVLNzuy6AdLQZebHmJycu9VtnwC+smyLpH4woKQKrZ3Qe9bav4iIs4HMzFPdtkwqx4CS6vRU4DUbvr8d+ChwUSetkTrgMnNJUpVcJCFJqpIBJUmqkgElSaqSASVJqpIBJUmqkgElSaqSASVJqtL/AS+2ndCgFVXaAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"metadata": {
"id": "BtQo2i_PxuYu",
"outputId": "349b8c3b-25f3-424a-9cf0-5932f7ccb574"
},
"cell_type": "code",
"source": [
"from sklearn.preprocessing import PolynomialFeatures\n",
"poly_features = PolynomialFeatures(degree=2, include_bias=False)\n",
"X_poly = poly_features.fit_transform(X)\n",
"X[0]"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([-0.75275929])"
]
},
"metadata": {
"tags": []
},
"execution_count": 30
}
]
},
{
"metadata": {
"id": "Rn4gNpI1xuYw",
"outputId": "ddf176a9-51fb-4e9e-86b6-4dd80fc9d38b"
},
"cell_type": "code",
"source": [
"X_poly[0]"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([-0.75275929, 0.56664654])"
]
},
"metadata": {
"tags": []
},
"execution_count": 31
}
]
},
{
"metadata": {
"id": "IOYXY7ezxuYz",
"outputId": "91a10bdf-0e91-41cb-d9ac-3d60137cfb21"
},
"cell_type": "code",
"source": [
"lin_reg = LinearRegression()\n",
"lin_reg.fit(X_poly, y)\n",
"lin_reg.intercept_, lin_reg.coef_"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"(array([1.78134581]), array([[0.93366893, 0.56456263]]))"
]
},
"metadata": {
"tags": []
},
"execution_count": 32
}
]
},
{
"metadata": {
"id": "QZsnTTamxuY2",
"outputId": "dd90619f-199d-4d8e-8d1b-4568aa8ea716"
},
"cell_type": "code",
"source": [
"X_new=np.linspace(-3, 3, 100).reshape(100, 1)\n",
"X_new_poly = poly_features.transform(X_new)\n",
"y_new = lin_reg.predict(X_new_poly)\n",
"plt.plot(X, y, \"b.\")\n",
"plt.plot(X_new, y_new, \"r-\", linewidth=2, label=\"Predictions\")\n",
"plt.xlabel(\"$x_1$\", fontsize=18)\n",
"plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
"plt.legend(loc=\"upper left\", fontsize=14)\n",
"plt.axis([-3, 3, 0, 10])\n",
"save_fig(\"quadratic_predictions_plot\")\n",
"plt.show()"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"text": [
"Saving figure quadratic_predictions_plot\n"
],
"name": "stdout"
},
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAagAAAEYCAYAAAAJeGK1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvOIA7rQAAIABJREFUeJzt3Xd8VFX+//HXSQgklCAoTaQpSFlYC4gbXAEVFQviihVZKSoqFlaXn4qCICqsgqvuKrrsV9DVxY4gKCCwoKhRmggoTQULRUDpBAjJ+f1xCCGQMpPM3Htn5v18POYxmXbvuTOZ+dzTPsdYaxEREQmaJL8LICIiUhgFKBERCSQFKBERCSQFKBERCSQFKBERCSQFKBERCSQFKBERCaSIBihjzB3GmAXGmH3GmJeOeOw8Y8wKY8weY8xsY0yDSO5bRETiS6RrUOuBR4Gxh99pjDkOmAAMBqoDC4A3IrxvERGJI+UiuTFr7QQAY0wb4ITDHroC+Npa+9bBx4cCW4wxzay1KyJZBhERiQ8RDVDF+B3wVd4Na+1uY8x3B+8/KkAZY/oCfQEqVarUulmzZh4VU0REImH3bli5EqwFY6BpU6hUyT22cOHCLdbaGiVtw6sAVRnYfMR924EqhT3ZWjsGGAPQpk0bu2DBguiWTkREImrECBg8GHJyICkJbrgBBg50jxljfghlG16N4tsFpB9xXzqw06P9i4iIhzp2hPLlITnZXXfsGP42vKpBfQ30zLthjKkEnHTwfhERiTMZGTBrFsyZ44JTRkb424hogDLGlDu4zWQg2RiTChwA3gVGGmO6Ae8DDwFLNEBCRCR+ZWSULjDliXQT3yAgC7gf6HHw70HW2s1AN+AxYCtwJnBthPctIiJxJNLDzIcCQ4t4bCag4XgiIonsjdCnwHrVBxU1O3bsYNOmTWRnZ/tdFPFISkoKNWvWJD39yHE3IhJon3wC110X8tNjOkDt2LGDX375hbp165KWloYxxu8iSZRZa8nKymLdunUAClIisWLPHujTx02MClFMJ4vdtGkTdevWpWLFigpOCcIYQ8WKFalbty6bNm3yuzgiEqrBg2H1amjZMuSXxHSAys7OJi0tze9iiA/S0tLUrCsSKz77DJ56yk2KGjcu5JfFdIACVHNKUPrcRWJEVlZ+096990KbNiG/NOYDlIiIBNiQIS4pX/Pm8NBDYb1UAUpERKIjMxOefNIl4xs3DlJTw3q5AlSca9myJUOHDj10u2HDhowaNapM2+zYsSN33HFHGUsmInEtKwt69YLcXBgwAM48M+xNKED5oFevXhhjMMaQkpLCiSeeyIABA9i9e3fU9z1//nz69esX0nNfeuklKleufNT9EyZMYMSIEZEumojEk0GDYNUqaNECHn64VJuI6XlQsaxTp0688sorZGdnM3fuXG666SZ2797N888/f9Rzs7OzSUlJich+a9QocQmWElWvXj0CJRGRuDV3bv6ovZdfDrtpL49qUD6pUKECtWvXpl69enTv3p3rr7+eiRMnMmfOHIwxfPDBB7Rt25by5cszffp0ACZPnkzr1q1JTU2lUaNGPPjgg+zfv//QNjdt2kTXrl1JS0ujQYMGjB079qj9HtnEt337dm677Tbq1KlDamoqzZs354033mDOnDn07t2b3bt3H6rt5TUVHtnEt3XrVnr27Em1atVIS0ujU6dOfP11fqL6vJrYrFmzaNmyJZUqVeKcc85hzZo1h57z008/0bVrV6pXr07FihVp1qwZr7/+esTebxHxyO7d0Lu3G7U3cGBYo/aOFH81KL+GH4cxO7owR87rue+++3jyySdp3LgxVapUYfr06Vx//fU888wztG/fnh9//JFbb72Vffv2HQo4vXr14ocffmDmzJlUrFiRu+++m7Vr1xZTZMvFF1/M1q1bGTduHCeffDIrV65k7969tGvXjqeffpoHHniA7777DqDQ5r68/a5cuZJJkyZRrVo1HnzwQTp37syqVasOzVPbt28fI0aMYOzYsaSmptKzZ09uvfXWQ8G3X79+7N27l9mzZ5Oens7KlSvL9H6KiHcyMw9bVmP8/fDdd/D737vJuWVhrQ30pXXr1rYo33zzzdF3ulDh/SUMPXv2tJdccsmh21988YU99thj7dVXX21nz55tAfv2228XeM3ZZ59thw0bVuC+d99911aqVMnm5ubalStXWsB+8sknhx5fu3atTUpKskOGDDl0X4MGDezIkSOttdZ++OGH1hhT+PtorR03bpytVKnSUfd36NDB3n777dZaa1etWmUB+9FHHx16fNu2bTY9Pd3++9//PrQdwK5YseLQc1599VVbvnx5m5uba621tlWrVnbo0KFFv2mFKKrcIuKdzz6zNi3N2uRkay8qP9P9HpYrZ+2iRUW+BlhgQ/j9j78aVBlrMl6ZNm0alStX5sCBA2RnZ9O1a1f++c9/8s033wDQ5ohq8cKFC5k3bx6PP/74oftyc3PJyspi48aNLF++nKSkJNq2bXvo8QYNGnD88ccXWYYvv/ySOnXq0Lx581IfR95+Mw5b9KVq1aq0atXq0LGAa9Js2rTpodvHH388+/fvZ+vWrVSvXp3+/ftz6623Mm3aNM477zz+9Kc/0bp161KXS0S8MWcO7N8PlXK280JOb3fnkCFw2mll3rb6oHzSvn17Fi9efKhJbcKECdSsWfPQ45UqVSrw/NzcXIYMGcLixYsPXZYsWcLq1asLDHwIUoaFw8tSrly5Qh/Lzc0F4MYbb2TNmjX07t2bVatW0a5duwLD40UkmPKWdv+H6U99fmJni7Zw//0R2bYClE8qVqxI48aNadCgQUgj9E4//XRWrFhB48aNj7qUK1eOZs2akZuby7x58w695scff2T9+vVFbvO0005jw4YNLF++vNDHy5cvT05OTrHlat68Obm5uWRmZh66b8eOHSxdupQWLVqUeFyHO+GEE+jbty9vvvkmw4YNY8yYMWG9XkS8l5EBix6aSE/7MrnlU6ky4T9QLjKNcwpQMeKhhx5i/PjxPPTQQyxbtowVK1bw9ttvc++99wLQtGlTOnfuzC233EJmZiaLFy+mV69exSbTPe+88zjzzDPp1q0b06dPZ82aNcyYMYOJEycCbsTf3r17mTFjBlu2bGHPnj1HbaNJkyZ07dqVW265hblz57J06VJ69OhBeno63bt3D/n4+vfvz7Rp0/j+++9ZvHgx06ZNCzvAiYgPNm2i2d/7ApA08nE4rCm/rBSgYsSFF17I+++/z+zZs2nbti1t27blb3/7G/Xr1z/0nJdeeolGjRpx7rnn0qVLF7p3707Dhg2L3GZSUhJTp07lrLPOokePHjRv3pz+/fsfGrrerl07br31Vq677jpq1KjBE088Ueh2xo0bR9u2bbnsssto27Yte/bsYdq0aWFlms/NzeXOO++kRYsWnH/++dSqVYuXX3455NeLiA+shVtugc2b4ZxzIMIZZowN+KCCNm3a2AULFhT62PLly8vUwS+xTZ+/iM/GjXOZytPTYckSaNAgpJcZYxZaa0ucIKUalIiIhG/NGrjrLvf3s8+GHJzCoQAlIiLhycmBG26AXbvgyiuhR4+o7EYBSkREwjNqFHzyCdSpAy+8ELUMPgpQIiISusWL81MYjR0Lxx4btV3FfIAK+iAPiQ597iI+2LMHuneH7Gzo1w86d47q7mI6QKWkpJCVleV3McQHWVlZEVuCRERCdO+9sHw5NGsGI0dGfXcxHaBq1qzJunXr2LNnj86oE4S1lj179rBu3boCqaFEJMo++ACeew5SUmD8eKhYMeq7jOlksenp6QCsX7++wFIVEt9SUlKoVavWoc9fJN4VWM4io6RnR8GmTW6NJ4BHH41IIthQxHSAAhek9EMlIvEqMxPOO89lDC9fHmbN8jhIWQs33uiCVMeO8Ne/erbrmG7iExGJd3nLWeTkuOs5czwuwOjRMGUKHHMM/Oc/bhl3jyhAiYgEWN5yFsnJ7rpjRw93vmxZfo1pzBioV8/DncdBE5+ISDzLyHDNemXtgwq7HysrC667Dvbt45cuNzL226vomOlt86IClIhIwGVklC0whNuPlZkJKffcS5tly8iqfzK/m/EM2z7wvg9MTXwiInEunH6szEwY1XEKbT5/lv2k8NQZr7Etu5IvfWCqQYmIxLm8fqy8GlRx/VgLJq3jhf1uSPmDZgS7apwe8msjzdMAZYxpCIwGMoB9wNvAX6y1B7wsh4hIIgm5Hysnhxtm9KAqW/iQCxhd4W5m3uCmPb3zDnTrFt99UKOBTUAd4BhgBtAP+IfH5RARSSgh9WONGEHVRXPYX70Wy2/5DzO7uF6gv/zF1aDmzoVWreK3D6oR8Ka1dq+1diMwDfidx2UQEYk7mZkwYoS7LpW5c2HIEADKv/4K/YfXIiPD33lYXtegngauNcbMAaoBFwGDj3ySMaYv0Begfv36XpZPRCTmlDnbxG+/uSzlublw331w/vmHHgqn/yrSvK5BfYyrMe0AfgYWABOPfJK1doy1to21tk2NGjU8LqKISGwpUy3HWujTB37+Gc48Ex55pMDDef1XjzzifZolzwKUMSYJ16Q3AagEHIerRT3uVRlEROJRmbJNPPMMTJoEVavCa6+5bOVHyMiAgQO9T1TrZQ2qOlAfeNZau89a+yswDrjYwzKIiMSd0tZylrw4n5wB97obY8dCo0Zh77vMfV/F8KwPylq7xRizBrjNGDMKqAz0BJZ4VQYRkXgVbraJeR9uo8bN15Bss3k++Q5OrXMF4VaQop1p3es+qCuAzsBm4FsgG7jb4zKIiCQ2a0m/5yYa2TUs5HT+akeVanRetEf4eTqKz1q7GOjo5T5FROQIzz1Hs6/fYQdV6J70BlSoUKrRedEe4adURyIiiWT+fLjnHgA2PvJ/9EpuXOos6ZHKtF4UBSgRkUSxdStcdRVkZ8Mdd3DyoKsZWMZNljXTenGUzVxEJBHk5kLPnvDDD3DGGTBqlN8lKpEClIhIInjySZg8GapVgzffhAoV/C5RiRSgRETi3dy5bqYtwH/+Aw0b+lqcUClAiYjEs40b4eqr3Vjwe++FSy/1u0QhU4ASEYlXBw7ANde4INWxIzz2mN8lCosClIhIvHrgAfj4Y6hTB15/HcrF1sBtBSgRkXg0YQKMHOkyyL75JtSq5XeJwqYAJSISb1auhF693N8jR8If/+hrcUpLAUpEJJ7s3Al/+pO7vuoqt157jFKAEhGJF3mLDy5fDi1auCU0jPG7VKWmACUiEi9GjYK334b0dHj3Xahc2e8SlYkClIhIPJg1C+6/3/39yitw8sn+licCFKBERGLd2rVuvlNuLgwaBJdd5neJIkIBSkQklu3ZA5dfDr/+ChddBEOH+l2iiFGAEhGJVdbCjTfCV19BkyYwfryb9xQnFKBERGLVqFEuQ0TlyjBxIhxzjN8liigFKBGRWDR9esFBES1aeF6EzEwYMcJdR0NsJWYSEYlxmZkRWCJ91ar8QRGDB7s+KI9lZsJ558H+/VC+vBtEqCXfRURiVER+1Ldvd6P0tm93gemIQRERCYAhmDPHHUdOjrueM0cBSkQkZpX5Rz0nB667zuXaa9XKNe0l5ffUeFGrydOxo9tH3r46doz8PhSgREQ8UuYf9YEDYepUOPZYmDTpqEwRXtRq8mRkuAAYzdqaApSIiEfK9KP+n/+4zOTlyrl0Ro0aHfUUL2o1h8vIiG4zogKUiIiHSvWj/umncPPN7u9//KPIyONFrcZLClAiIkG2dq1bPmP/frjjDrjttmKfHu1ajZc0D0pEJKh27oQuXWDzZrjgAnjqKb9L5CkFKBGRIMrJge7dYdkyaNoU3njD9T8lEAUoEZEgGjAApkyBatVg8uS4S2MUCgUoEZGgGT0ann4aUlLcwoNNmvhdIl8oQImIBMm0aXDXXe7vf/8bOnTwtzw+UoASEQmKZcvg6qtd/9ODD0LPnn6XyFcKUCIiQbBhA1xyiRu5d801MGyY3yXynQKUiIjfdu2CSy+FH390k5jGjSuQYw+iv7RFEHk+ZtEYcy0wBKgPbAR6WWvnel0OEZFAOHDA1ZgWLYKTTnI59tLSCjzFyySwQeJpDcoYcz7wONAbqAK0B773sgwiEn9itnZhLdx5J3zwgUsAO3Uq1Khx1NMKSwKbCLyuQT0MDLPWfn7w9jqP9y8icSbItYsS12Z64gl44QWoUAHee6/I4eReJ4ENCs8ClDEmGWgDvGeM+RZIBSYC/89am3XEc/sCfQHq16/vVRFFJAZ5ucREOEoMnP/9b8El29u1K3Jb8ZYENlReNvHVAlKAK4GzgVOB04BBRz7RWjvGWtvGWtumRiHVXRGRPHm1i+TkYNUuim2WmzkTevd2fz/1FFx1VYnby8hwy0ElSnACbwNUXi3pn9baDdbaLcDfgYs9LIOIxJm82sUjjwSrea/IwLl4MVxxBWRnwz33wF/+4mMpg82zJj5r7VZjzM+APfxur/YvIvEriEtMFNos98MPcPHF+XOdRo70uZTB5vUgiXHAncaYaUA2cDcwxeMyiIh4okDgzFsyY8MGF7FefvmouU5SkNcB6hHgOGAVsBd4E3jM4zKIiHhr1y6XJWLVKjjlFJg40Y3ck2J5GqCstdlAv4MXEZG4UeSQ8v37XZ/T/PnQqJGb61S1qk+ljC0h1S+NMS8YY6wx5vhCHmtqjNlvjPlH5IsnIhJ8eUPKBw9214cmDOfmQq9eMGOGm4A7fTrUqeNnUWNKqA2geW9320IeewrYgUtfJCKScA4fUr5vHwwdCpmfWbdsxmuvQeXKruaUoOs6lVaoASov80OBAGWMuQS4CHjIWrs1kgUTESkrr1Ig5Q0pT0pylaaZM2FOhyHw3HPugUmToHXr6BYiDoUaoFYBv3FYgDLGpODmMS0D/hX5oomIlF6RzW5RkDekvFMnF6Tuyn2KgQceIdckwRtvwLnnHlW2mMwd6LGQBklYa60x5nPgLGOMsdZaoD9wMtDJWpsTzUKKiITL6xRIGRmuaa/+7Jd5KvceAL5/4EUaX355gecFOXdg0IQzCP9zoCrQ1BhTExgMTLTWzopKyUREysCPFEgZ695mTE4fANbe9XcaP9rrqOckamby0ghnmPnhAyXaAxWAv0a8RCIiEeB5gtUPPoDu3TG5uTB4MA2H3V3o0xI1M3lphBOg5gG5wE3AWcBIa63WchKRwPIsBdKcOdCtW35+vYcfLrZMiZiZvDRCDlDW2h3GmG9wmcg3ogwQIiLwxRfQpQvs3Qt9+8KoUWBMsS8JYu7AIAo3EdS8g9cDrbU7I10YEZGYsmgRXHihS2V0/fUwenSJwUlCF3KAOjisvCOwAHg5WgUSEYkJS5bA+efD9u0uldFLL7kRGRIx4fRBDQAaAdcfHGYuIpKYvvnGTXr67TfXvPfaa1DO69zb8a/Yd9QYUx24EPg98P+Av1trPy/uNSIicW3VKjeRafNm17z31ltuOJ5EXEkh/0JgPLAJl3Pv/qiXSEQkqFavhnPOgY0bXXaId9/VshlRVGyAsta+BrzmUVkCr8h0+iIS/1avdl/+9euhQwd47z1IS/O7VHFNjaYhUnoSkQT27beu5pQXnN5/HypV8rtUcU/rDYdI6UlEElRezWndOmjfXsHJQwpQIfIjr5eI+GzFCldjWrcOzj5bwcljauILkdKTiCSYr7927fq//OK+9FOmkLmkkn4DPKQAFQalJ5FElXADhJYscfOcNm9215MmkflVRfVDe0wBSkSKFasDhEodVBcuhAsucJNwO3eGCRMgLc3z9aVEAUpEShCLP8ylDqqffgoXXww7dsCll7pJuKmpgJbJ8IMGSYhIsWJxgFCpRt3OmuVqTjt2wFVXwTvvHApOkN8P/cgjsVOLjHWqQYlIsWJxgFDYtZ0pU8jtdiVJ+/ex6eKe1Bz/f4Xm1lM/tLcUoESkRLH2wxxWUB0/ntwbepKUc4DnzW0M+N+zzJyfFFPHG6/UxCcicSkjAwYOdH+PGOH6pY4yejT06EFSzgFGmnvpZ59jX3ZSgSbBzMxiXi9RpRqUiMStIgdLWAuPPQaDBwPww21/Y8hL95F8RJNgrI5gjBeqQYlI3Cp0sERuLvz1ry44GQNjxtBg9H2FDoBQijN/JWQNKuEmHYokqCMHS5xz1n74c28YPx5SUuDVV+Hqq4HC+9k0tNxfCRegVGUXiQ+hnGgePlji3La7OHP4lTB9OlSu7NZy6tSpxO0//TT8+qtOaP0QdwGqpH/aWJx0KCIFhXOimZEBGY03u4m38+ZBjRowdSq0bh2R7Uv0xHQf1JGja/L+qQYPdteFjbqJxUmHIlJQWH1D334L7dq54NSokcsWUUxwCnv7EjUxW4Mq7AwnlNpRLE46FJGCQu4b+uILV3PasgVOP90tl1G7duS2L1EVswGqsGAU6j9VrE06PJwGeIiEeKI5eTJccw1kZbmkr2++CVWqRG77EnW+BChjTBNgKfC2tbZHsU/evbvQuwsLRvH+T6V2cZF8xZ5oPvss9O/vhpT37g3/+pcbtScxxa8a1HPA/JCeuXKlO/M5OBQ0T1HBKJZrRyXRAA+REuTkuDlOzzzjbg8Z4i7GhLUZnQwGg+cByhhzLbAN+AxoXOILrIVrrmHOi99SYchAMtrl/6PFczAqjNrFRYqxaxd07+6a9lJS4MUX4c9/LtWmdDIYDJ6O4jPGpAPDgHtKeF5fY8wCY8yC7ZWPJRdDxw8f5Nv2ffj84/3eFDaAlO5fpAg//wwdOrjgVK0azJhR6uAEGu0bFMZa693OjHkGWG+tfdwYMxRoXFIf1AkntLFtNwzildzrqcQefmzYnvrz34HjjvOkzCIScPPmweWXw4YNcNJJbqRe06Zl3qwGJEWPMWahtbZNSc/zrAZljDkV6AQ8Fc7rqlSBaRUu55ykj1nP8dRf+zG0bQvLlkWnoCISO15/3dWcNmxw1198EZHgBPnZ0BWc/ONlE19HoCHwozFmIzAA6GaMWVTciypVcs1Zf3q0NRsmzYM2bWDNGvdfM3ly9EstIsGTmwsPPQTXXQd798LNN8OHH8Kxx/pdMokgz5r4jDEVgfTD7hqAC1i3WWs3F/W6Nm3a2AULFuTfkZUFffq4MydjYPhwuO++sEfpiEiM2rHD9S+99x4kJcGTT7oh5VH4DVAzX3SE2sTn2Sg+a+0eYE/ebWPMLmBvccGpUGlpLhNxy5YwaJCrgy9aBOPGueqWiMSvb7+Frl3hm2/gmGPcieqFF0ZlVxpq7j/fcvFZa4eWOEm3KMbAgw/CpEmuk+qtt9x/zvffR7iUIhIY06bBGWe44NSiBcyfH7XgBMrHFwQxnSyWyy5zI3hOPhmWLnX/vNOn+10qEc/F9bLkubnw6KNw8cWwbZurQX3+OTQueRplWWiouf88HWZeGkf1QRVm+3bo0QOmTHG1q4cfdjWspNiOvyKhiNemqMxMyJy6jV6zb6D6J5ML/W5Hu49IfVDREbg+qGhx/0BV6Xj/JDLaPubSmjz0kBtu+sorbtKeSBzzM+tBtH7AMzOh/zlLeHXflVRnNQeqVKPcG/+Fiy4q8JxoB+ZEy1YTNDEdoAr+gyYxa9ZgMs44A66/3k3Wa93a9U8VsfaLzo4kHviVAiuaAeLXJ8fx0b5+pLGXxZxC5i0TuO2iEws8R+mI4l9Mt4EV2onZuTMsXOiC0po1bqGy0aNdTr/DhLK4oUgs8CsFVlQGEezZA336cOk7fUhjL2NNH85NzeTUK0486qnqI4p/MV2DKvLMsWFD+OQTl9V49Gi4/Xa2TPiY4yaMgXQ3FUtnXxJP/GiKinjNbcUKt2rB0qWQmsq394zml8q9eb9j4ccW78vrSBwMkiiumS4zE57v8DrPZd9MFXaRdUJj0ia+Dq1bx23HsoiXItJMbi28/DLcfrurQTVp4prmTzklgiWVIAl1kETMB6jijBjhmvBOylnJm1zNKSxxafgffxz+8hcyPzc6+xLx086d0K8fvPqqu929O7zwQsgr30psClyyWD/kNUF8l9yUjqlfsLHb7ZCdDffcA126kNF4c5mSQcb13BORaJs/3/UVv/oqVKwIY8e6vxWc5KCY7oMqScE26lRqZzwLEzu5XH7vvw+//71LkdS5c9jbVhOhJKKINOnl5MDIka5548ABaNXKpSxq0SKCJZV4ENc1KCgkZf7ll8NXX0H79rBxo5tXcdddLgltGIoawaRalcSriIx8/fln6NTJfSkPHHBJXufNU3CSQsV9gCpUvXrwv/+5SFKuHPzzn24Zjy+/DHkThQ1x1dB1iWdlGlZuLfz3vy7J85w5ULMmfPABPP00pKZGp8AS8xIzQAEkJ5PZ4X7G3fI5WfVPdgko27Z1Ob8OHCjx5YXNPVFyydJRrTM2lHre0ZYtbvh4jx4uLVmXLrBkSYGsECKFstYG+tK6dWsbDZ99Zm1amrXJydYem7rLrr/yDmvdeZ61Z5xh7fLlZdpmWpq7LcXTexZbPvvM2uHDw/ic3nvP2tq13feqcmVrX3zR2tzcqJZRgg9YYEP4/U/YGtThtZ1t2ZV46fR/8v5fZrAptZ4bXXTaaa4jNycn5G36NaM/lqnWGVtCXgZ961a44Qa34sDGjXD22a7W1KePFheVkCVsgDqyuWLbNrj06U402buUcfRyy0jfe69LlfTNNyFvN+QvcII6sjlP6WoiJzBNpZMnw+9+55I1p6bC3/8Os2dDo0Y+F0xiTijVLD8v0Wris7Zgc8UFF+S38IG1D572vrV167ob5ctb++ij1u7fH7WylKbMsaao5rxYPqagCERT6S+/WHvttflforPOsnbVKh8KIkGHmvhKdnhtp1u3go/Vv/Vi+PpruPlm1/Y0aJCbVPjFF/4UltgfJVhUc55qnWXna1NpXqqi5s3dfKaKFV2t6aOPXNoikVJK6AB1uL594V//ggsucNd9+wJVq8KYMTBjBpx4oktimZHh5k3t3Ol5GWO9v0bNedHj23u7erX70vTqBb/9BuefD8uWwd13u8KIlEFc5+KLqD17YNgwGDXKRYi6dd0cjm7dPOv0jYfsFVqDK3o8fW/37XM5LYcPd39Xrw5PPQV//rMGQUiJlCzVvamMAAASA0lEQVQ2Wr76yjX7zZ/vbnfu7Cb6Nm7sye71Ay++mznTZR5ftcrd7tULnngCatTwtVgSOxSgoiknB/79b9dxsm0bVKjgRvzdf79rfxeJRz/+6BItv/OOu928OTz/PHTo4G+5JOYom3k0JSfDrbfCypVurse+fW7yU7Nmbh2bgAd9kbDs3QuPPeb+v995x52EjRgBixcrOElUKUCVRc2abvTS3LluYu9PP7mULuee6768IjGmwFwqa90JV/PmbhRrVhZcc407Mbv/ftcRGql9iRQirpfb8Mwf/+j6pF58ER54wHUSnX469O7tcvvVqeN3CUVKdPggnDPLLWRqs7tJ/2que7BlS3jmGXfyFeF9xeqAH4k+1aAiJTnZjU1ftSp/iO3YsW4eyLBhsHu3zhgl0ObMgTr71vJSTg8+3dfGBafjjnMr3H75ZcSCU96+YnnKhHhDASrSqld3kxS/+Qb+9CfYvRuGDGF//ZN4vcPzPDwo+6hJtkEOXEEum0TQb7/Rc+kAvsltSg/+yz7Ks777APj2W7jlFrcsTQRpTpyEJJR0E35eopnqyBNz5ljbtu2h9C8raWKvNa/b4Y/mWGsDkqKmCEEum0TIzp0ujVfVqof+R5ee2sMufGdNqTcZauoqpbhKXISY6kh9UNHWoQN8/jkrh79D0uAHONmu5jV7LbtfGg6tHmHOsi7s328KNHWE0xYfzXlRhTXDqJ8gTuzd65ruhg+HzZvdfZ06weOP0/L000u92XD6ljIy9P8kxVMTXxQc1SxmDE0fvJJfP/qaqV1fYF+NulT6dgl07cqdr57JpclTSU6yYTd1FJebLxJNc141w8RrM2Igj2vvXjex/KSTXF/p5s0uSvzvfy6lVxmCE6hvSSIslGqWn5dYa+ILqVksK8vap5+2tlatQ80q6+u2scsfnxTWYm7Dh7v9gLsePjyMMoRxPNFshonXZsTAHdeePdY+84y1derkZxs/5RRrp0yJ6AKCgTtuCSSUzdwfIZ1BpqZC//7w3XduUcSaNamzbgHN7uvqzmDfeCOkZeeLquFE8iw22pnG4/WMOzDHtX27q8Y1bOj+5zZsgFNPhXffhUWL4JJLIpo7T4t2SkSFEsX8vMRlDepIu3e7GtXhZ7cnnmi/GzDaPvHwnmK3UVgNJ5bOYmOprOHw/bjWr7d24EBr09Pz/6dat7Z2Uni1dJFoIMQaVNzn4vMjuWqp97l3r8tMMXKkq10Bm6jBv8v144KJ/TjjkprRL4MPYqms4YjkcYW8rWXL4MknYfx4V3UDOOccVw3u1EmZxiUQQs3F51lNCKgAvAj8AOwEFgMXlfS6stSgfD+LLa0DB+yEa9+wCzj90NlvdrkK1vbpY+2SJX6XTjxW4v9xTo61kycXXBbaGGuvuMLazExfyixSHALYB1UO+AnoAFQFBgFvGmMaRmuHgekHCFdyMrXvupqzUxdwXtJspiRdRnLOfpeZ4ve/Z8dpHVw/VXa23yWNa4WNwvNjZF6R/8dbt7pJ4U2aQJcu8OGHLpHrHXe4hQTfeQf+8Icy7TuQIxElYXg2D8pauxsYethdU4wxa4DWwNpo7DNvEEHenIxYmq2ekQGz/meYM6cjx3bsyOKfVvN593/QI+cl0hd/DNd+DLVrw003wY03uk5wiZjC5vOAP/njCvwfp1guPfZz6PUvePNNl8AV3Od/++3Qp4/LZhIBypcnfvNtFJ8xphZwMvB1IY/1NcYsMMYs2Jw3ibAUYn1E0eEj6KZ914Q7+SfHs547zHNsqdEcNm50yWhPPNEtu/3WW27pDymzwmotftXIMzLgo3e2MPWif7C57im0uqWd66vMynJLrE+a5FISDRgQseAEMdwCIfEjlHbASF+AFGAm8K+Snhtro/hKI5S5Rkf1Q3yaa+3s2dZ2725thQr5fQ/Vq1vbr5+1X3yh0VplUFi/j+d9mvv3W/vee64vKSUl/zOuUcPa++6zdvXqqO4+ZvtwJfAI6ig+Y0wSMB5IB7paa4vtSAnkiroRFE4zSpEjuX77DV591S33sWRJ/v3NmsF117lLkyZRPApveTXqr7D9RH3fubnw6aduFN5bb8Gvv7r7k5LYemZn5jTsRZ1bu/KH9mVbiylU8TrCUvwVuFF8BwOhAcYBs4G0UF4T7zWoorJBlNrixdbefbe1NWvmn3GDtaefbu0TT1j73XcRKXcerxN+xuVZfU6OO5C777a2Xr2Cn1uLFtY+/ridP2ld/B23JCwCmiz2eaA50Mlam+XxvgMp4gM5TjnFjex6/HFXHXv99fysAYsWwb33uudccQVcfjm0alXquTF+dKLHTQLb/fvh44/hvffc5/Pzz/mP1asH3bu7y8HPZ8aIODlukTB4FqCMMQ2AW4B9wEaT/6N4i7X2v16VI2jyBnJEvBklJQU6d3aXF16AqVPh7bdh8mT46it3GTIE6teHSy91l44dIS0t5F34ESxieWQmv/zihoK//777PHbsyH+sXj248kp3+cMfIKng+KWyHLea6SRWxX0mCa/EzI/Avn0uIk6YAFOmuB/NPBUqwNlnuxGBF1zgzt6Tih7o6dcw5KLe68B9BllZrlCzZsG0aa4Ge7iWLd38pa5doW3bEmuypTk+DRWXIAq1D0oBKgJi9kcgNxcWLnSBasqUo39Aq1d361l17OiuW7Z0mWkPE8qPpheBIxCfwe7dMG8efPIJzJ4Nn31WcNh/aqp7Ezp3doHpxBOjXqQRI9xyLDk57qN75BE3dUHET6EGKC1YGAEx2y+SlARnnOEuDz/s1gaaOdM1Q82c6fpF3n3XXQCqVIEzz4R27dx169ZkZNQqthbjVeDw/DOw1s09mj/fXT79FL788ugs9KecAueeCxdeCO3bh9WEGgkx3SQqCU8BqgShnP0H4UcgIrWUGjXyh6VbC2vW5M9Q/eQTd3vmTHfJc8IJ0Lo1nHoqKyv8nr4Pt2Jl9omUq5B8qG/Ni8AR1c9g715YuRIWL87vv/vyS5dq6HBJSW65lLPOcjXODh3guOMiWJDwRa2PU8QDauIrRkTmKHnAs+atDRvczj77zNUaFi2CXbuOetoe0lhJUyq0akqVM5ry0CsnszrnRNaVb8T4WbXIaBedjNpl+gxycuCnn1wW+e++c7WjFStg+XL4/nvXHHqk2rVd7bNtW1ej/MMfXC1TRIqlJr4ICOfsPyPDv7NTz5q36tRxw9OvuMLdzs2FVatcP9bSpWz9eAl7MpdQl3WcxmJYuhiWuolvAOwFOqW5EWt16+Zfatd2NY0aNdz1McdAejpUreoibogKfAbWuv6fbdvcZetWN6H5l19g0yZ3Wb/eBaWff3Z/F7VIZFKSm+h8yin5l1NPdbVHLV8hEjUKUMUIQtNdKHwrZ1KSy1bRrBkA1YAVmfDG1G2cX38lrVJWuKax1ath7VrXRPjrry6orVoV2j7Kl3f9NmlpbpBB3hLCSUnuYq0LLAcOuOzue/fCnj3ukpMT3vEcfzycdFL+pWlTaN7cBacKFcLbloiUmZr4ShC4octFiJVysmOHq7WsXw/r1rnLpk1ugMbmzbBli1umfMcOd11UrSYUKSmuNlatWv51rVpQs6a7rl3b1ebq1XPBKTU1cscpIkXSMHOJCk8DYV4zXVaWqxllZblqYm6uu+Tk8NXSJL5YWI4zMspx2hnlXE2rYkV3nZJS5iL43bcYEycdImFSH5REnOdzjYxxtZoiajaZmXBe34Pl+Vfky+Pn3Cq/53UpOEoQ+LYelMSeoK0PFO3y+Hm8fu47LzgOHuyutZqu+EUBSkKWNxgjOTkYg0aiXR4vjreoJdX9fK+DdiIiiUtNfBKyoE36jHZ5or394prx/HyvY2X0qsQ/DZIQ8UmQ8+SpD0qiSYMkRAIuyDUVPyeei+RRgBLxSdCaTEWCRgFKxEeqqYgUTaP4REQkkBSgJOqKGkotem9EiqMmPokqZUQomt/vTUmC/N5JYlCAkqjyc7XhoAeAUN8bPwJF0N87SQxq4pOoUkaEooXy3viVdijo750kBtWgJKqUEaFoobw3ftVAg/7eSWJQJgmJa7Hej+J3RvVYfu8kuLQeVEAl8pc+kY+9LPS+SbxRqqMAitbZcCz8gKnTvfQ0mVcSlQZJeCgaHc+xsnaPOt1FJFwKUB6Kxoi2WPnhD9paUiISfGri81A0RrTFymireE6MGgtNrCKxSIMk4kC8/EDG4nGob00kfBokkUDioRM91B/6oAUxPzNliMQ7BSgJhFB+6INYW4mVJlaRWKQAJYEQyg99EGsr8dy3JuI3BSgJhFB+6INaW4mHJlaRIFKAkogqSx9RST/0qq2IJBZPA5QxpjrwInABsAUYaK0d72UZJHq86CNSbUUkcXg9Ufc5YD9QC7geeN4Y8zuPyyBREiuThkUkNngWoIwxlYBuwGBr7S5r7SfAe8CfvSqDRJeyRYhIJHnZxHcycMBau+qw+74COhz5RGNMX6DvwZv7jDHLPChf0ByHawaNMVUqQXqVrKwdO9u127m7lBuJ0WMvMx13YknU4wZoGsqTvAxQlYEdR9y3Hahy5BOttWOAMQDGmAWhzDiON4l63JC4x67jTiyJetzgjj2U53nZB7ULSD/ivnRgp4dlEBGRGOFlgFoFlDPGNDnsvlOArz0sg4iIxAjPApS1djcwARhmjKlkjDkL6Aq8UsJLx0S9cMGUqMcNiXvsOu7EkqjHDSEeu6fZzA/OgxoLnA/8CtyveVAiIlKYwC+3ISIiiUkr6oqISCApQImISCDFRIAyxrxqjNlgjNlhjFlljLnJ7zJ5wRhTwRjzojHmB2PMTmPMYmPMRX6XywvGmDuMMQuMMfuMMS/5XZ5oMsZUN8a8a4zZffCz7u53mbyQSJ/x4RL8ex3Wb3lMBChgBNDQWpsOXAY8aoxp7XOZvFAO+AmXbaMqMAh40xjT0McyeWU98ChuUE28S9QclYn0GR8ukb/XYf2Wx0SAstZ+ba3dl3fz4OUkH4vkCWvtbmvtUGvtWmttrrV2CrAGiPvgbK2dYK2diBvtGbcSOUdlonzGR0rw73VYv+UxEaAAjDGjjTF7gBXABuADn4vkOWNMLVxOQ01ujh9F5ahMhBqUkHjf63B+y2MmQFlr++Hy9p2Nm/C7r/hXxBdjTArwX+Bla+0Kv8sjERNyjkqJP4n4vQ7nt9z3AGWMmWOMsUVcPjn8udbanINNICcAt/lT4sgJ9diNMUm4jBv7gTt8K3CEhPOZJwDlqExQ8fa9Dkeov+W+L/lure1YipeVIw76oEI5dmOMwa1CXAu42FqbHe1yRVspP/N4dShHpbV29cH7lKMyzsXj97qUiv0t970GVRJjTE1jzLXGmMrGmGRjzIXAdcAsv8vmkeeB5kAXa22W34XxijGmnDEmFUgGko0xqcYY30+oIq0MOSpjXqJ8xkVIuO91qX7LrbWBvgA1gI+Abbi2+qXAzX6Xy6Njb4Ab5bIX1xSUd7ne77J5cOxDyR/lk3cZ6ne5onSs1YGJwG7gR6C732XSZxzV407I73VpfsuVi09ERAIp8E18IiKSmBSgREQkkBSgREQkkBSgREQkkBSgREQkkBSgREQkkBSgREQkkBSgREQkkBSgREQkkBSgRDxijEkzxvxsjPnRGFPhiMf+zxiTY4y51q/yiQSNApSIR6xLCjoEqAf0y7vfGDMCuBG401r7uk/FEwkc5eIT8ZAxJhm3Ym5N4ETgJuApYIi1dpifZRMJGgUoEY8ZYy4FJgP/A84BnrXW3uVvqUSCRwFKxAfGmEXAacDruOU17BGPXw3cBZwKbLHWNvS8kCI+Ux+UiMeMMdfgVs0F2HlkcDpoK/As8KBnBRMJGNWgRDxkjLkA17w3GcgGrgJaWWuXF/H8y4GnVYOSRKQalIhHjDFn4pZ3/xS4HhgE5AIj/CyXSFApQIl4wBjTAvgAWAVcbq3dZ639DngR6GqMOcvXAooEkAKUSJQZY+oD03H9ShdZa3cc9vAjQBbwhB9lEwmycn4XQCTeWWt/xE3OLeyx9UBFb0skEhsUoEQC6OCE3pSDF2OMSQWstXafvyUT8Y4ClEgw/RkYd9jtLOAHoKEvpRHxgYaZi4hIIGmQhIiIBJIClIiIBJIClIiIBJIClIiIBJIClIiIBJIClIiIBJIClIiIBNL/Bz0jvuH4XFJLAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"metadata": {
"id": "a6CM5RaXxuY5",
"outputId": "4b4a33bc-5ce5-4b43-fe10-3729697d6000"
},
"cell_type": "code",
"source": [
"from sklearn.preprocessing import StandardScaler\n",
"from sklearn.pipeline import Pipeline\n",
"\n",
"for style, width, degree in ((\"g-\", 1, 300), (\"b--\", 2, 2), (\"r-+\", 2, 1)):\n",
" polybig_features = PolynomialFeatures(degree=degree, include_bias=False)\n",
" std_scaler = StandardScaler()\n",
" lin_reg = LinearRegression()\n",
" polynomial_regression = Pipeline([\n",
" (\"poly_features\", polybig_features),\n",
" (\"std_scaler\", std_scaler),\n",
" (\"lin_reg\", lin_reg),\n",
" ])\n",
" polynomial_regression.fit(X, y)\n",
" y_newbig = polynomial_regression.predict(X_new)\n",
" plt.plot(X_new, y_newbig, style, label=str(degree), linewidth=width)\n",
"\n",
"plt.plot(X, y, \"b.\", linewidth=3)\n",
"plt.legend(loc=\"upper left\")\n",
"plt.xlabel(\"$x_1$\", fontsize=18)\n",
"plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
"plt.axis([-3, 3, 0, 10])\n",
"save_fig(\"high_degree_polynomials_plot\")\n",
"plt.show()"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"text": [
"Saving figure high_degree_polynomials_plot\n"
],
"name": "stdout"
},
{
"output_type": "display_data",
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"metadata": {
"id": "F4nk8mB8xuY8"
},
"cell_type": "code",
"source": [
"from sklearn.metrics import mean_squared_error\n",
"from sklearn.model_selection import train_test_split\n",
"\n",
"def plot_learning_curves(model, X, y):\n",
" X_train, X_val, y_train, y_val = train_test_split(X, y, test_size=0.2, random_state=10)\n",
" train_errors, val_errors = [], []\n",
" for m in range(1, len(X_train)):\n",
" model.fit(X_train[:m], y_train[:m])\n",
" y_train_predict = model.predict(X_train[:m])\n",
" y_val_predict = model.predict(X_val)\n",
" train_errors.append(mean_squared_error(y_train[:m], y_train_predict))\n",
" val_errors.append(mean_squared_error(y_val, y_val_predict))\n",
"\n",
" plt.plot(np.sqrt(train_errors), \"r-+\", linewidth=2, label=\"train\")\n",
" plt.plot(np.sqrt(val_errors), \"b-\", linewidth=3, label=\"val\")\n",
" plt.legend(loc=\"upper right\", fontsize=14) # not shown in the book\n",
" plt.xlabel(\"Training set size\", fontsize=14) # not shown\n",
" plt.ylabel(\"RMSE\", fontsize=14) # not shown"
],
"execution_count": null,
"outputs": []
},
{
"metadata": {
"id": "b9BjXP_1xuY-",
"outputId": "e6c5bbcf-b0c5-43e2-ef0e-722ba10254fa"
},
"cell_type": "code",
"source": [
"lin_reg = LinearRegression()\n",
"plot_learning_curves(lin_reg, X, y)\n",
"plt.axis([0, 80, 0, 3]) # not shown in the book\n",
"save_fig(\"underfitting_learning_curves_plot\") # not shown\n",
"plt.show() # not shown"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"text": [
"Saving figure underfitting_learning_curves_plot\n"
],
"name": "stdout"
},
{
"output_type": "display_data",
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAagAAAEYCAYAAAAJeGK1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvOIA7rQAAIABJREFUeJzt3XucVHX9x/HXB3aBXe4iF0WREEjxAiqZlig/MRNN6RdaamimplZo3hL7qbGov7Q076RRmpp4yQvqz0zDa2pqgkUKmslVuQgrCOyyCwv7+f3xnWlmh9nd2dnZue37+Xicx8w5c+acz8zOns/5fs/3fL/m7oiIiOSbDrkOQEREJBklKBERyUtKUCIikpeUoEREJC8pQYmISF5SghIRkbykBCUiInkpqwnKzO4zs5VmtsHMPjCzM5tY9wIzWxVZ9y4z65zNWEVEJLcsmzfqmtlewIfuvtnM9gBeAo5x97kJ630VuBc4HFgBzALecPdLsxasiIjkVFZLUO4+3903R2cj0+5JVv0OcGdk/XXAVcBp2YlSRETyQUm2d2hmvyIkmzLg78DTSVbbC3gibn4e0N/M+rj7pwnbOws4C6Br164H7LHHHm0RtoiIpGnu3LmV7t63pe/LeoJy9x+Y2bnAwcBYYHOS1boB6+Pmo8+7Aw0SlLvPAGYAjB492ufMmZPpkEVEpBXMbGk678tJKz533+burwK7AN9PskoV0CNuPvp8Y1vHJiIi+SHXzcxLSH4Naj4wMm5+JPBJYvWeiIgUr6wlKDPrZ2Ynmlk3M+sYaal3EvB8ktXvBc4wsxFm1gu4HLg7W7GKiEjuZbME5YTqvI+BdcD1wPnu/qSZDTKzKjMbBODuzwC/AF4ElgFLgalZjFVERHIsa40k3H0NcFgjry0jNIyIX3YDcEMWQhMRkTyU9VZ8IiL5ZMOGDaxevZq6urpch1KQSktL6devHz169Gh+5RZSghKRdmvDhg188sknDBw4kLKyMsws1yEVFHenpqaG5cuXA2Q8SeW6FZ+ISM6sXr2agQMHUl5eruSUBjOjvLycgQMHsnr16oxvXwlKRNqturo6ysrKch1GwSsrK2uTKlIlKBFp11Ryar22+g6VoEREJC8pQYmISF5SghIRacfGjh3L5MmTcx1GUmpmLiJSYMaOHcvee+/Nbbfd1uptPfbYY5SWlmYgqsxTCUpEJBMqKnIdQQOptqrbYYcd6N69extHkx4lKBGRTJg2LSu7Oe2003j55ZeZPn06ZoaZcffdd2NmPP300xx44IF06tSJZ599loULFzJhwgQGDBhA165d2X///XnqqacabC+xim/w4MFcffXVnH322fTo0YNddtmF6667LiufLZESlIhIlFn6U2ve3wI333wzBx98MN/97ndZuXIlK1euZNdddwVgypQpXH311bz//vt88YtfpKqqivHjxzN79mzmzZvHxIkT+cY3vsH777/f5D5uvPFG9tlnH95++22mTJnCJZdcwuuvv57WV9oaSlAiIgWkZ8+edOrUifLycgYMGMCAAQPo2LEjABUVFRx55JEMGTKEvn37MnLkSM455xz22Wcfhg4dymWXXcb+++/PI4880uQ+jjzySCZPnszQoUM599xzGTp0KM8/n2xkpLalRhIiIlHu6b/XrHXvz4DRo0c3mK+urmbatGk89dRTrFy5krq6Ompra9l3332b3E7i6zvvvHObdGXUHCUoEZEi0bVr1wbzF198Mc888wzXX389w4YNo7y8nFNPPZUtW7Y0uZ3EVn1mRn19fcbjbY4SlIhIJkzN3piqnTp1Ytu2bc2u9+qrr3LqqacyceJEAGpra1m4cCHDhw9v6xAzQtegREQyIYvNzAcPHszf/vY3lixZQmVlZaOlm+HDhzNr1izefvtt3nnnHSZNmkRtbW3W4mwtJSgRkQJz8cUX06lTJ0aMGEHfvn1ZtmxZ0vVuuOEG+vXrx5gxYxg/fjwHHXQQY8aMyXK06TPP8UW9TBo9erTPmTMn12GISIF477332HPPPXMdRlFo6rs0s7nuPjrpi01QCUpERPKSEpSIiOQlJSgREclLSlAiIpKXlKBERCQvKUGJiEheUoISEZG8pAQlIiJ5KWsJysw6m9mdZrbUzDaa2T/MbHwj655mZtvMrCpuGputWEVEJPeyWYIqAT4CDgN6ApcDfzCzwY2s/7q7d4ubXspKlCIiRS5xFN18lbXezN29GqiIW/SUmS0GDgCWZCsOEREpDDm7BmVm/YHhwPxGVtnPzCrN7AMzu8LMNDSIiEg7kpMEZWalwEzgHnd/P8kqfwH2BvoBE4GTgB83sq2zzGyOmc1Zs2ZNW4UsIpIXZsyYQf/+/bcbD+rkk0/muOOOY+HChUyYMIEBAwbQtWtX9t9/f5566qkcRds6WU9QZtYB+D2wBUhaCerui9x9sbvXu/s7wJXA8Y2sO8PdR7v76L59+7ZZ3CJS/MxyN6XqhBNOYP369cyePfs/y6qqqnjiiSeYNGkSVVVVjB8/ntmzZzNv3jwmTpzIN77xDd5/P1lZIL9lNUGZmQF3Av2Bie5el+JbHWjBn1BEpDj17t2bo48+mpkzZ/5n2eOPP05JSQnHHXccI0eO5JxzzmGfffZh6NChXHbZZey///488sgjOYw6PdkuQd0O7Akc6+41ja1kZuMj16gwsz2AK4AnshOiiEh+mzRpEo8//jibNm0CYObMmUycOJEuXbpQXV3NJZdcwogRI+jduzfdunVjzpw5jQ5qmM+y1vDAzHYDzgY2A6ssVqY9G3gFWACMcPdlwDjgbjPrBnwC3Af8LFuxikj7VCjjtx5zzDGUlJTwxBNPMG7cOJ577jmeffZZIIy2+8wzz3D99dczbNgwysvLOfXUU9myZUuOo265bDYzX0rT1XTd4ta9GLi4zYMSESlAnTt35oQTTmDmzJlUVlYyYMAAxo4dC8Crr77KqaeeysSJEwGora1l4cKFDB8+PIcRp6eomm4vWAArVsDOO+c6EhGRtjVp0iTGjRvH4sWLOemkk+jQIVyxGT58OLNmzWLChAmUlpYybdo0amtrcxxteoqqL76aGvj1r3MdhYhI2xszZgwDBw5kwYIFTJo06T/Lb7jhBvr168eYMWMYP348Bx10EGPGjMlhpOkzL5RK1xSYjfb+/eewbBl06pTraEQk37333nvsueeeuQ6jKDT1XZrZXHcf3dJtFlUJCuCTT+Dhh3MdhYiItFbRJSiAW2/NdQQiItJaRZWgoi3X33wT3nort7GIiEjrFFWC2mGH2HOVokRECltRJah+/WLPH3oIVq/OXSwiUhiKqaFYrrTVd1hUCaq8HA46KDzfsgVmzMhtPCKS30pLS6mpabTXNUlRTU0NpaWlGd9uUSUogHPPjT2//XaoS7U7WhFpd/r168fy5cvZtGmTSlJpcHc2bdrE8uXL6RdfhZUhRdWTBMDxx8NFF8GqVaFXiVmz4JvfzHVUIpKPevToAcCKFSuo09lsWkpLS+nfv/9/vstMKroE1akTnH02TJsW5m+5RQlKRBrXo0ePNjm4SusVXRUfhARVEkm9r72mJuciIoWoKBPUTjvBiSfG5q+7LnexiIhIeooyQQFcHDdYx6OPwqJFuYtFRERarmgT1MiRcOSR4Xl9PdxwQ27jERGRlinaBAUNS1F33QWVlbmLRUREWqaoE9QRR8CoUeF5TQ386le5jUdERFJX1AnKrGEp6rbbQqISEZH8V9QJCsI9ULvuGp6vWQP33JPbeEREJDVFn6BKS+GCC2Lzv/wlbNuWu3hERCQ1RZ+gAM48E3r2DM8//BCeeCK38YiISPPaRYLq3h2+//3YvMaKEhHJf+0iQQH88IfQsWN4/tJLMH9+TsMREZFmtJsEtcsu8PWvx+anT89dLCIi0rx2k6AAJk+OPb/3Xli/PnexiIhI09pVgjrsMNhrr/C8ujokqbby8cewcmXbbV9EpNi1qwRlFq5FRU2fDm0xiOaLL8KQITBsmIb6EBFJV9YSlJl1NrM7zWypmW00s3+Y2fgm1r/AzFaZ2QYzu8vMOmcijkmTQqs+gH/9C55/PhNbbWjq1DDUfHU1VFQ0ve7atfDUU/CTn4QS3rBhcPfdmY9JRKTQZLMEVQJ8BBwG9AQuB/5gZoMTVzSzrwKXAuOA3YAhwLRMBNG9O5x2Wmw+040lFiyAV16JzT/9NPz739uvt2gRHHgg9OkDxx4L114Lf/lLuE/re9+Dd9/NbFwiIoUmawnK3avdvcLdl7h7vbs/BSwGDkiy+neAO919vruvA64CTstULD/4Qez5k0/CsmUte//atY03sJgxY/tlyZLgD37QePXf1q1hVOD6+pbFJSJSTHJ2DcrM+gPDgWR3JO0FzIubnwf0N7M+SbZzlpnNMbM5a9asSWnfe+wRejqHkATuuKP59yxeDNdfDwcfHEo9u+4ahpOPV1OTvOHF734HVVWx+dmz4dlno/GHktT558Ovfx26ZgL461+TJzsRkXbD3bM+AaXAc8CvG3l9IXBUwvoODG5quwcccICnatYs99BEwr1rV/fZs5Ov99BD7vvvH1s3fho2zL2mJrbuvffGXhsyxP3zn4/NT58e1tm61X3kyNjyM89suL/LL4+91qOH+/LlsddqatwrKtwPPNB9zBj3CRPcv/td94suCp+nvj7ljy8ikjXAHE8nV6TzptZMhFLbg8DTQGkj68wDvhk33yeSoPo0te2WJKi6OvehQ2PJoKTE/b77Yq9v2OB+yinJE1P8dPnlsfccckhs+TXXuN96a2x+jz1CArn77tiy8nL3FSsaxlVTExJfdJ3jjw/L33rLfcSIpmOZONH9s89S/gpERLKiIBIUYMDvgBeBsibWux/437j5w4FVzW2/JQnK3f3dd90HDmx4kP/5z93ffNN9990bLu/Uyf2YY9zvusv9F7+ILS8tDdt5992GyW7VqpDkunePLX/iCfdddonN//SnyeN64YWG+z7xRPeOHZtPltGS29y5LfoaRETaVKEkqDuAN4Buzax3FLAKGAH0Al4Arm1u+y1NUO7uy5a577VXw4O8WcP573zHfe3a2Hu2bXP/0pdir3/pS+6TJ8fmo6Ued/dzz40t79Yt9rx/f/eNGxuP67TTkiegrl3db7nF/cUX3R991P03v3E//fTtk+n06aryE5H8kG6CsvDetmdmuwFLgM3A1riXzgZeARYAI9x9WWT9C4EpQBnwKHCOu29uah+jR4/2OXPmtDi2zz4L/fS9/HLD5T16hAYUJ520/Xvmz4f99gv3O4V4Yzf9zp4da4TxwQfw+c9v//477ggt9Rrz6aehMUdlZWzZoYeGBhdDhmy//sMPwxlnwMaNsWXHHQe33w4779z4fjKtrg5eeCG0jFy3Lkxr10JZWWjeP2pU9mIRkfxgZnPdfXSL35hOVsvXKZ0SVFRNjfsJJ8RKIQcd5L5oUdPvueyy7Us4Q4aEEla8r3614Tp77hmugTXn0UdD1V5ZmftNN22/3UQffOA+alTDffXsGUpZbV2a2rbN/YEHGl4/SzadeGKIM96mTe4vveT+5JOFcw1tyZJQOj72WPcf/cj99ttD1exHH4Xq3Y8+cl+40P39990XL3avrc11xCK5Q76XoLIh3RJUVH09PPZYuA9p4sRYk+/G1NbCvvs2vBH32mthypSG6/3xj/C1r8Xmn3wy3JybilWrQukjOuBic2pr4aKL4Fe/arj8v/4rxDZ0KPTuHUp8Udu2wSefhH3ttFOYEi1dGu7nevRRKCmBgw6KTStWwGWXwbx5278vmY4d4fTTYcCAMPTJm2/Cli3htc6dQ8lv0iQ46ijo1Cm1bWbCunWhFP388yGubdtgwoRQ8ouWgtevh2uugZtugs1Nlue3t+OOMHBg6Fn/4IPDb2LffRv+LUSKUbolKCWoVnrhBRg3LjwvKQmdxPbv33Cd+no48shw4PvmN+HBB9v+oPTSS6FHig8/3P61Ll1CtV/PnrHEFH9T8IgRoYryK1+Brl1DYpo1K/Ubh3v1ClWmffqEZNirFzz3HDz+eMs+ww47wKBBsGlTbDKLHeR33TU8mjVcp3NnGD06JM9hw5r+rquq4J57wjR3buOf8eCDQ5L/zW8gxdvtUrLLLnD00eG7HjUqVN92aFc9ZEp7oARFbhIUwM03h5tqL7ggDC+fzObNoRQydGj2DkA1NaEvwOuvz06vFOXl8KMfwY9/HBJTojfegP/5n9CZbqI99giJJdVSWKp22CEkqtGjYeTIMH3uc+FE4rbbQsL57LP0tv2FL4QeQVasCP06/utfoQsrs1D6jk6bNoWTgG3bmt9meXnocX+ffWD33WHwYNhtt/DYq1coaUanurqwr+jUoUM46ejRI73PI03bujXUUNTWhn42q6vDCU5VVfjuhw4NJ08qEW9PCYrcJah8N3cuXH116Cdw+fLwj5Voxx2hb19YuDBW3ZZo3Dg477yw3htvhOn118M/7Le+Far5BgxoOhb3UJp66KFQfTd2bGj8EX3fggUwcybcd1/Lu6BKVffuIWkkJowOHUIiO/zwMNXUhI57/+//wsEpatCgUM134ompn2xEq1FXrID33oM//QmeeSZUK2Zanz4huUWnnXcOpfoBA8LUty9066YDaV1dqLLt1SvUfkRVV8Orr4bf6fPPh4ZOtbWpn2AMHx6S1bZtoYHQp5+Gx/r6cKIxZEiYPve58Pfo0yecSPXpE6rza2rCVFsbTmx79Ah/s85pdpddXx9+Z927Z7fKPJ4SFEpQqdq4MSSqDRtiB67oj3/TptDZ7XPPhdaIa9eGa0HnnQd77529GOvrQ0vJurrwT19eHqob6+pC6eejj8Lj8uXhmlZ5efjnLi8PVXDRBLp2bfP7Gjo0lPwmTQoHq0Rr1sD994fv5NBDw8CXZWWt/4xbt4YE//TToV/Gd96B1atbv91UdOoUDojRalj3cECNTvX1YVl9fex5hw4Np8QE16lTqFLde+9QCtxrr7D9urrwWevqUjvIJ2te06FD+DuXlIQpWiOxZEmYPvooxNmlS/jbdOkSppKSUIotKQnbWLYM3n8/nCQsXBg78ejVK8TarVs4SYq2zs0n3brFTi7q6mIl6a1bQ4KLXj/eaafwXSxcGKr4Fy4MCQ/CiWh0nX79QvLr0SNW8u7ePbase/ewr+j/X3l5OE7U1IRSY7QEWV0dqqoHDWo8diUo2lGCqqhofhwPwT38g775JvzjH6H68B//iDXdP/zw0AfiMcfkz3Wf1atDolqwoOEBeOnScDDo3Dkkgk6dYo144pNJZWXLG29Iajp0iCW+rl3DwTv6WFMTSlptUSIuBNdcA5de2vjrSlAUcYJKTEjxN11Ji7iHkY47dGi+OrIQ1deHasSFC8O0ZEm4/rVqVaxBzJo1sTPq9q5nz1CTkPjvtPfeoUr7iCNCA5mePRtWAzamsjIkqkWLwslEfPVdfX3odHrRojAtWRL+FtFqwE8/DScXZWWxUmCnTqEasrKyYTVzS3XrFko6bXXYuPxyuOqqxl9XgqKIE5RZaJv+5z+H6YMPwh278QNbpUIlr8xL9p0WwPdcUxMOiJWV4QBoFqrQolNidR40rPJLVlW3cWOoOnv33VA9u2BB2E98NVvHjqld+4pv+GEW9rl1a9jv1q1hO7vuGmtEsttuseqn6PWb2tqwbvw0YEBokLPHHuFaUdeuYZuffRa+i3XrwjazdvKS4m/FPcQYPbmIlqI7dQrfUWVlOPFasSI8QsPrkDvsED7/6tXh9ZUrY8MGbdgQpvXrw99w48bYsurqWOvY6PdaVrZ9CfKUUxoOY5RIN+q28kbdvLR5c7iztak7X6dOTX170GahtpmWfL5cSPadJi7L98+Q7/EVi2Tfcy5/K2nsK90b/knzRt08qXlvxxo7e6qoCKeEDz7YcPnpp8eem4WmQMm2E52vqwt37e66a5jP1lX4dMTH/PrrcMstMC0jAylnTkVFOM2+7TbYf/+wrFu32FX26F3Od94ZO5VN9zNkqxSWb99xMZo7N3zP114LV1wR7kn5/vfDa3fdFZoLLlyY/G/R2P92U5Ktk7gsjX1lveVnOlktX6eCK0HNmdN4qebDD927dImVlOJFx/OI9mwbHcMjcZ0//MG9d+/Wl7yyYdWqENfRRzfsVRfcjzjC/dVXw3q5jPull0I8qXYtD+477RQe//WvhttK/BzZPLuObmfNGverrgr7mTLF/bXXwoBlmdxXe3bFFe4PP9ywZ+lUplGjwkBvt9zi/sorYdmnn8b6R0t2zEj8eyWuU1sblj3+eBiy4YwzwvyFF4b5u+92/9OfwrI5c9znzw99dKWyrxR+KxRCb+ZtPRVUgpo1K9Zt+osvNnytvt79yCPDa5MmNX6gik9SEDqHmzzZ/Yc/bPiDHz684UBUZWXu99+fPwehjz92HzSo+X/cz30uPCbWM7T156ivd7/00lgcZuHv89BDYX7DBvd169wrK0MHfNB4p4TjxoVkBSEhzJrlfscdYf7qq8MYLJde6n7JJWHZm2+6V1eHONJJWI0lvv32Sx5fWVmsK/0NG1q2r2zKdTxN7X/dOvfrrmv6t/yVr8QGjNt339QSF8TG7/nv/w6/lYcfdv/nP8OyO+90/5//iV0W2Hff8H8VP+ZPOtNOO7mPHet+1lnuv/xlWLZgQayDycZOsuMoQXkBJagzz0z+Q4j+6O+/P8z37u3+ySeN/zNMnZraDyw6qiLEzpyiUyq91ral6IG4se8Cwplo/D/ZsGHhzH/x4tg6zUn3YF5fH4YvbizGZPuOLquuDj3gQhgeuTUHiT59wuM557hPmxZ6AIZwZt3UZwD3LVtCMrzqqu0/y9FHh8cf/Sh2AhCdSktD6fWmm5J/znS/00xIN550pFq6XbzY/fzzG9YADBvmftttYWydpn4r8fOvvup+1FGt+700N0X/7r/4hfvBB6e3DTP33XYLz5vp5VkJygskQS1eHAaDglCMj/6xe/cOZ0KXXOLer19Y9tvfprbNP/85rH/zzaFaIHpmVlXVcL2pU8MBd/r0MKoihAPWRx9l+lOmZtOm2DDEe+7Z+D9wU4n40EPDY3x34elWlyVbJ7rvjh3D2Woq20mWJGpq3L/1rdT+8Q8/PFb11rdv8weJAw4IVXTR38ETT4TfwgUXhPmuXRt/f3yS/elPm97XsGGhlP700yH5NvddbNuW2vfVUo88ErZ77LGhtHfxxbHahJUrm95XGtVTDmHguIcfdr/oovD3AfeTT3Y/7zz3K68M8x06pPY9N7X/ppLYtm2hdAZh+O8vfzn5vr7+9fD49tvhePPZZ8n/FqkmzEWL3L/97dR+u418n0pQXgAJasqU2IH4iCPCmS24H3dceIwmrmjiaG58jXip/PjcGz/Yn3RS7PVsqKsLVY8Qhhletiz1f+BnnnHfe+/knyN6UP7ss7DeFVfEzhavvrphlcjLL4eqz4oK9+99Lyx7/nn39etj+4oeeB58MLaspVJJhk0dLGpqwjDJ4D5+fGoHimTT6NGxg3sq8f34x41vq3Pn8Pjzn4cDYfQAuHat+733un/jG+7l5WHZUUeFUt/s2an9jRuTao3B4MGxaq7XXgsnQi353qdODQl41iz3U05J/fstKQnr//3vybfdmirZ5mJOZ53W7mvz5lh1dTPaNEEBPwPK4+aPJm7IdqAHcG86AWRyyusEtXlz7Ie8116xIvHUqeEANG5c7PXS0nCRsiXSPTOMr0o4//yUfmytVl8fq+bs3dv93XfD8lRjjlq/PlbVFZ2iDRgSh0Vu6RRtXNKhQ6hyjcpUAk/1QNnce6qrY9cpE6cjjgiPy5c3v69U4nv11carO8vKGn7/TU0HHuj+k5+4P/dcSB6pHsjnzm1YGpw1K5SiUkkco0bFTkImTgwl7+jJ4iGHhNLQpZe633hj7D3JtnXYYe5PPRWeR0sqiVN89XQmZKpBTToJMt0ktt1b2jZBbQP6xc1vAIbEzfcHtqUTQCanvE5Q114bvu4BA8Jod/EaOzNs69IMhDPf665r+A85ZUrLkkZL/fa3sX299lrL3tvYP0z0wn7idPDBoTVj9HmydQ45JFSNgvvOO2fnb5HOCUVLqoOaWicT+/rkk7AscYTM6DR+vPvSpeH58cc3njyiJbFp00KJNtraLNH554f/HYhVNyX77Fdc0fi+WjodeGDs/zaxYU6mvudMyeW+ct2KD6hPSFAblaBS1JLkEz2bbOvhb+NjayrGaJXj3/4WqiMT35eOCy/MfAKIf++KFWF78dU67qkdUKLLamvd33gj+Tr5JBdN05Ptq74+VtWT2Ggj2ff+9NONnyxES2BXXhlLWNHrLhBak9XWtuzMfuNG97/8JdbY46GHwvDH77wT5l94wX3ChMZ/l6kkn3z/reSYElS+Jij3UIUXPVNcu7bpdXP5Q49eRzjrLPdevRr+o5aVheqNn/wkzDeXsBprERe93nbMMW33WdM9oBTDQSeXZ9LpfKeVlWHZF77QeMIaODA833PPpv9/MlXCTCfJ57rZe55TgsrnBBW9wTOVA16uf+jxZ41NTT17hgvRM2eG+c8+C/fNVFWFhJzssz7wQFjeo0doOdhWCSBTB5Rc/y0KTSYaAUSrDidPjrVmTbe0nW4rvkI8Mclz2UhQPwUujEw1wP/GzU9VgmrCtGn+nzrtfNfYWWhTLboam15/Pbadiy9233HHsHzGjOT7kvapqZJPZaX7H/+Y3aSh32XGpZugUurN3MyWAM2u6O6fa3ZjbShvezM/4ojQ19Yjj8DEibmOpmWSDe1hBueeC7femto2zjsv9KsHYRCm557TcK7SuGQ9fGuImYKm4TbI0wS1ZUvoSLSmJnTU2rdvriNqmVQOFonzGzaEAXS6dAn985eWxobGfeedMN61SEsUwBAm0rh0E5R6M29rc+aE5DRiROElJ0h+UJg6ten39OgRHs85JzxGx8/etCkMTqMDjbSUfjPtUkoJysxGmtl/JSz7tpktMrPVZnaHmXVqmxAL3Msvh8dDD81tHJmUeLBIlrCmToUbbwwlq7//PSzbti3M62AjIilItQR1NXBIdMbMRgC/A/4NPAB8G5iS8eiKQTRBHXaXsKYTAAAXO0lEQVRYbuNoS82NPTNqVHjsoAK7iKQu1SPG/sCf4+ZPBBa4+1fd/UfA+cC3Mh1cwdu6FV57LTwv5gSViuaqBUVEEqSaoPoAK+LmDwX+L27+JWBQcxsxs8lmNsfMNpvZ3U2sd5qZbTOzqrhpbIqx5o+//x2qqmDYsNhIq+2VqvVEpIVSTVBrgIEAZtYROAB4M+71ToR7pZqzglBdeFcK677u7t3ippdSjDV/FOP1JxGRLEk1Qb0ETDWzIcBFkWUvxr0+AljS3Ebc/TF3fxz4tAUxFq72cP1JRKSNlKS43hXAc8CHhJ7Nz3P36rjXTwGez3Bs+5lZJbAW+D1wjbtvTVzJzM4CzgIYNKjZWsbs2bYNXnklPFeCEhFpsZQSlLsvMbM9gL2ANe6+ImGVqcDHGYzrL8DewNLIPh8CtgLXJIltBjADwo26GYyhdd55B9avh912g3xKnCIiBSLldr/uvtXd5yVJTkSWZ6zazt0Xuftid69393eAK4HjM7X9rFD1nohIq6RUgjKzC1NZz91vaF04jW8aKKzO25SgRERaJdVrUNcDlUAVjScKB5pMUGZWEtlnR6CjmXUBtiZeWzKz8cDb7v5JpGrxCuDhFGPNvfp6+MtfwnMlKBGRtKRaxfcWUA68DJzi7p9LMqXSA+jlhKE6LgUmRZ5fbmaDIvc6RS/WjAP+aWbVwNPAY8DPWvC5cqeiAjp2hE8jNZ5Dh4bOVHUfkIhIi6Tcm7mZ7QWcQUgs64A7gXvc/ZO2C69l8qY388sug59F8mkR9RYvIpKONu/N3N3nu/uFhBt2LwPGAkvM7Akz69zSHRe1J57IdQQiIgUv1WtQ/+HudcAjZraBUO13DFAGbM5wbIVp4UKYPz8MOXHeebmORkSkYLWoe2kzG2xmV5rZUuA3wCvAMHf/rE2iawttfS0oWno6+mi46qq23ZeISBFLdTyob5vZ88AC4PPA2cBgd7/C3Re3ZYAZtXw5TJvWtvt48snwOGFC2+5HRKTIpVrF93tgGXATobn5CGCEWcMW5214H1RmjB0bHpcvh4EDM7/9Tz8N3RuVlMBRR2V++yIi7UiqCWoZ4T6nk5pYp9n7oHKmoqJhyWmXXcLj1KmZrfL74x/DPVCHHw69emVuuyIi7VCqffENbm4dM9u11dG0lYoKuOQS6No1zJeXw9KlsOOOmd1P9PqTqvdERFqt1WNwm9kAM7sN+CAD8bSdqqrY802b4KabWvb+5kpatbXw7LPh+XHHtWzbIiKynVQbSfQys5lmtsbMVpjZeRZMBRYBBwGnt2mkrVUdGR2kQ+Qj33orfJZC48O6OnjmmeYbV7zwQtjHqFHqvVxEJANSLUH9jDDM+z2E8ZluBJ4EDgPGu/tod3+gbULMkGgJas89Q2OJDRtg+vTm33fhhTB+fPPrqXpPRCSjUk1QxwDfdfeLgeMIHcYudPfD3f3lNosuk6IlqK5d4fLLw/Mbb4wtT+bss+G222LzZsn71auvh5kzw3MlKBGRjEg1Qe1MuAcKd18E1BJu1C0c0RJU166hld0Xvxiahc+Ykfz6Un09/POf4fmQIbHHqqrt158zJyS6QYNCFZ+IiLRaqgmqA1AXN78N2JT5cNpQtKTUrVsoBV12WZi//vrk15fuvhveeAMGDIC//S0sW7QIfvrThuutWRPr0ujYY8O2RUSk1VJNUAbcZ2ZPmtmTQBfgN9H5uOX5K76KD+BrX4ORI2FFZIDg2trYuuvWwZQp4fn110OfPvC974UGFjfdBG++GV6bPBn69YvNT5+uoTVERDIk1Rt170mYvy/TgbS5aBVft27hcdo0mDcv9npZWXicOjXccFtZCYceCiefHJbPmAG9e8MvfgGnnw4HHABPPRVeO+AAmDtXQ2uIiGRQqjfqfretA2lziSWoioowvfUWHHhgWFZaCmvXhmtKHTvGSkRRFRXw2GOwYEGYIFTrPfBALPGJiEhGtPpG3YKRWIKK+sIXwuMPfxjuebr11jB/3nmw994N1y0rg9/+NjZ/7rkwa1ZIelOntk3cIiLtVPtJUIklqHhTp27f7dGNN25/PamiItbhLIRkVlISK42JiEjGtHjAwoLVWAkKYsmloiI0L+/YMfn1pPhEZKZrTiIibUglqEQd2s9XIiKSz9rP0bipElSiVK4n6ZqTiEibaj8JKtUSFKR2PUnXnERE2lT7SVAtKUGJiEjOtZ8E1ZISlIiI5Fz7SVAqQYmIFJT2k6BUghIRKSjtJ0GpBCUiUlCymqDMbLKZzTGzzWZ2dzPrXmBmq8xsg5ndZWadW7VzlaBERApKtktQK4CrgbuaWsnMvgpcCowDdgOGAEkGbUrRli2wdWvoDLZTp7Q3IyIi2ZPVBOXuj7n748Cnzaz6HeBOd5/v7uuAq4DT0t5x/Gi6IiJSEPL1GtReQNxgTcwD+ptZn8QVzeysSLXhnDVr1iTfmqr3REQKTr4mqG7A+rj56PPuiSu6+wx3H+3uo/v27Zt8a2ogISJScPI1QVUBPeLmo883prU1laBERApOviao+cDIuPmRwCfu3ty1q+RUghIRKTjZbmZeYmZdgI5ARzPrYmbJxqS6FzjDzEaYWS/gcuDutHesEpSISMHJdgnqcqCG0IR8UuT55WY2yMyqzGwQgLs/A/wCeBFYBiwF0h/fQiUoEZGCk9URdd29Aqho5OUG2cPdbwBuyMiOVYISESk4+XoNKrNUghIRKTjtI0GpBCUiUnDaR4JSCUpEpOC0jwSlEpSISMFpXwlKJSgRkYLRPhKUOosVESk47SNBqQQlIlJw2keCUglKRKTgtI8EpRKUiEjBaR8JSiUoEZGC0z4SlJqZi4gUnPaRoHSjrohIwWkfCUolKBGRglP8CWrbNqitBTMoK8t1NCIikqLiT1DxpSez3MYiIiIpK/4EpetPIiIFqfgTlK4/iYgUpOJPUCpBiYgUpOJPUCpBiYgUpPaToFSCEhEpKMWfoNTNkYhIQSr+BKUSlIhIQSr+BKUSlIhIQSr+BKUSlIhIQSr+BKUSlIhIQSr+BKUSlIhIQSr+BKUSlIhIQcpqgjKzHcxslplVm9lSMzu5kfUqzKzOzKripiFp7VQ36oqIFKSSLO9vOrAF6A+MAv5oZvPcfX6SdR9y90mt3qO6OhIRKUhZK0GZWVdgInCFu1e5+6vAk8ApbbpjlaBERApSNqv4hgNb3f2DuGXzgL0aWf9YM1trZvPN7Ptp71UlKBGRgpTNBNUN2JCwbD3QPcm6fwD2BPoC3wN+amYnJduomZ1lZnPMbM6aNWu2X0ElKBGRgpTNBFUF9EhY1gPYmLiiuy9w9xXuvs3d/wrcDByfbKPuPsPdR7v76L59+ybZq0pQIiKFKJsJ6gOgxMyGxS0bCSRrIJHIgfTGa1cJSkSkIGUtQbl7NfAYcKWZdTWzLwMTgN8nrmtmE8ystwUHAucBT6S1Y92oKyJSkLJ9o+4PgDJgNfAA8H13n29mY8ysKm69E4EPCdV/9wI/d/d7Wrw391iCKi9vXeQiIpJVWb0Pyt3XAl9PsvwVQiOK6HzSBhEtVlMTklRZGXTsmJFNiohIdhR3V0fq5khEpGAVd4LS9ScRkYJV3AlKJSgRkYJV3AlKJSgRkYJV3AlKJSgRkYJV3AlKJSgRkYJV3AlKJSgRkYJV3AlK3RyJiBSs4k5Q6ihWRKRgFXeCUglKRKRgtY8EpRKUiEjBKe4EpUYSIiIFq7gTlEpQIiIFq7gTlEpQIiIFq7gTlEpQIiIFq7gTlEpQIiIFq7gTlEpQIiIFq7gTlEpQIiIFq7gTlEpQIiIFq7gTlEpQIiIFq3gTlLu6OhIRKWDFm6C2bIGtW6G0FDp1ynU0IiLSQsWboHT9SUSkoBVvgtL1JxGRgla8CUrXn0REClrxJyhV8YmIFKTiTVCq4hMRKWjFm6BUghIRKWhZTVBmtoOZzTKzajNbamYnN7KemdnPzezTyPRzM7Nmd7BiRex5tAS1ZEkmQhcRkSwryfL+pgNbgP7AKOCPZjbP3ecnrHcW8HVgJODAbGAxcEeTW1+5EubODc8XLGj4KCIiBcXcPTs7MusKrAP2dvcPIst+Dyx390sT1v0rcLe7z4jMnwF8z90Pamofo818TrIXsvQZRURke2Y2191Ht/R92SxBDQe2RpNTxDzgsCTr7hV5LX69vZJt1MzOIpS46AMk/QYitYOfwMqPYUWyVXJoR6Ay10G0kGLOjkKLudDiBcWcLZ9P503ZTFDdgA0Jy9YD3RtZd33Cet3MzDyhyBcpZUVLWnMq08jSuWRmc9I5s8glxZwdhRZzocULijlbzCxp5VZzstlIogrokbCsB7AxhXV7AFWJyUlERIpXNhPUB0CJmQ2LWzYSSGwgQWTZyBTWExGRIpW1BOXu1cBjwJVm1tXMvgxMAH6fZPV7gQvNbKCZ7QxcBNydwm5mZCreLFLM2aGY216hxQuKOVvSijlrrfgg3AcF3AV8BfgUuNTd7zezMcCf3L1bZD0Dfg6cGXnrb4EpquITEWk/spqgREREUlW8XR2JiEhBU4ISEZG8VBQJKtU+/nLJzCab2Rwz22xmdye8Ns7M3jezTWb2opntlqMw42PqbGZ3Rr7PjWb2DzMbH/d63sUMYGb3mdlKM9tgZh+Y2Zlxr+VlzFFmNszMas3svrhlJ0f+BtVm9njkOm7OmdlLkVirItO/4l7Ly5gBzOxEM3svEtvCyPXvvPxtxH230Wmbmd0a93o+xjzYzJ42s3VmtsrMbjOzkshro8xsbiTeuWY2qtkNunvBT8ADwEOEG3wPIdzYu1eu40qI8RuE/gVvJ3TjFF2+YyTeE4AuwHXAG3kQb1egAhhMOJH5GuGetcH5GnMk7r2AzpHnewCrgAPyOea42P8MvALcF/dZNgKHRn7b9wMP5jrOSGwvAWc28v3na8xfAZYCB0V+0wMjUyH8NroR7g89NDKflzEDTxNaXHcBBgDvAOcBnSLf/QVA58iypUCnJreX6w+UgS+kK6ED2uFxy34PXJvr2BqJ9+qEBHUW8NeEz1MD7JHrWJPE/k9gYqHETOheZSXwzXyPGTgR+EPkpCCaoH4G3B+3zu6R33r3PIi3sQSVzzH/FTgjyfK8/m1EYvoOsIhYw7a8jBl4Dzg6bv464NfAkcDyaPyR15YBRzW1vWKo4musj7+kfffloQb9Dnq4X2wheRa/mfUnfNfzyfOYzexXZrYJeJ+QoJ4mj2M2sx7AlcCFCS8lxryQyMlY9qJr0jVmVmlmr5nZ2MiyvIzZzDoSuursa2YfmtnHkeqnMvL4txHnO8C9Hjmyk78x3wScaGblZjYQGA88Q4jrn3HxQzjhbTLeYkhQLenjLx8l9jsIeRa/mZUCM4F73P198jxmd/8BIZYxhJvDN5PfMV8F3OnuHycsz+eYpwBDCFVkM4D/M7Pdyd+Y+wOlwPGE38UoYD/gcvI3ZgAi15YOA+6JW5yvMf+FkHQ2AB8Dc4DHSTPeYkhQLenjLx/ldfxm1oFQZboFmBxZnNcxA7j7Nnd/FdgF+D55GnPkQvERwI1JXs7LmAHc/U133+jum939HuA14GjyN+aayOOt7r7S3SuBG8jvmKNOAV5198Vxy/Iu5six4hnCSWFXwnWy3oROF9KKtxgSVEv6+MtHDfodtDBu1u7kQfyRHj3uJJx9TnT3ushLeRtzEiXEYsvHmMcSGp4sM7NVwMXARDN7m+1jHkK4wPzB9pvJOQeMPI3Z3dcRzujjq5iiz/P1txF1Kg1LT5CfMe8ADAJui5y4fAr8jnASMB/YN3JMidqX5uLN9cW/DF2Ye5DQkq8r8GXysxVfCaFlyzWEEkmXyLK+kXgnRpb9nDxojROJ+Q7gDaBbwvK8jBnoR2hs0A3oCHwVqAaOy+OYywmtnaLT9cAjkXijVSVjIr/t+8iDFnFAr8h3G/0NfzvyPQ/P15gjcV8JvBX5nfQmtJi8Kl9/G5GYvxT5brsnLM/LmAkNOS6N/C56AbMILTmjrfh+RDhhmUx7aMUX+VJ2INRzVhNahpyc65iSxFhBOGOLnyoirx1BuKBfQ2gdNTgP4t0tEmMtoXgenb6dxzH3BV4GPoscJN8hjMQcfT3vYm7kd3Jf3PzJkd90NfAEsEMexNg3cqDfGPmu3wC+ks8xR+IqBX4ViXkVcAvQJZ9/G4QWcL9v5LW8i5lwbe8lwujplYSWqf0jr+0HzI3E+zawX3PbU198IiKSl4rhGpSIiBQhJSgREclLSlAiIpKXlKBERCQvKUGJiEheUoISEZG8pAQlksDMHjSzR1r4njfM7Pq2iimfmNkeZuZmtneuY5HipvugpOCYWXM/2nvc/bRWbL8n4X/jsxa8Zwegzt3zpf+2pMzsQaDE3Y9vxTY6Em7WrXT3rRkLTiRBSa4DEEnDTnHPvwb8JmFZDUmYWanH+hNslLsn9rrcLHdf29L3FCp330boiUGkTamKTwqOu6+KToRuaxosc/f1cdVQJ5jZy2ZWC3zHzPqb2UNmtjwy9PS7Zvbt+O0nVvFFqu9uNLPrzGxtZCjra+I7vkys4ousM8XM7jKzjWb2kZmdl7CfEZGxlGrNbIGZfcXMtprZiY19djPbLzLc+sbI9HczOyTu9X3M7JnIEOGfmNl9ZtY38tq1wLcIndF6ZDqopftJrOKLfHZPMh0Ueb2Lmf0y8p1Xm9mbZnZ4c39nESUoKXbXEoay2JMwcGEZoe+4Y4C9gduBe+IP8o04ndA55xeBi4BLgK83856Lgb8R+iC7GbjZzPYHMLMSQj91G4EDCSOk/ozm/yf/ACwmDL63H2GE5s2Rbe5KGI/nLcIw918lDHnwaOS9V0f2+RShxLkToW+0Fu0niaPjtrcToQfr5cCHkddnRj7jtwg9WD8E/MnM9mzms0o7pyo+KXY3uPvjCcvix16abmZfIfSC/moT23nb3a+OPP+3mZ0DjCP01tyYp9z9jsjz683sR8DhhI4yjyF0yPtld18NYGZTgOcb21ikxLYr8Iy7/yuy+MO4Vc4lDAN+Rdx7TgNWmtm+7v7PSEmyJFL6THc/DcRXb5rZdwiJaIy7V5rZCEIi39ndP4msdoOZHQl8j+1HERb5DyUoKXZz4mciJZfLCCOrDiQMA9AZ+FMz2/lnwvwKwrAN6b5nD2BJNDlFvNnUxtzdzexG4D4zOxN4AXjE3f8dWeUAYIyZVSV5++5J4kl3P0mZ2cGEIVomufvbcTF1ABY2HAqIzjReIhMBVMUnxa86Yf4y4IeEcbn+izA8wNOERNWUxMYVTvP/P+m8p0nu/hNC1eTTwKHA/LhraB0Iw86MSpiGAbMzuJ/tmNkgQmnyand/NO6lDoTvYb+EmPYEzmlJTNL+qAQl7c0hwCx3vx/+M0z1cMLgadn0PrCbmfV19zWRZQem8sZItdu/gBvN7HfAGYTrPG8DRwGLIy3tktlCKL20Zj8NREZzfRJ4zt3/N+HltwnjMO3o7q+nsl+RKJWgpL35APiqmR0cuUj/a2DnHMTxR8KgfveY2b5m9mVCg47oYJbbMbOeZnaLmR1mZruZ2ZeAg4EFkVVuJjRSuN/MvmBmQ8zsSDO708yiJcQlwEgzG2ZmO0aqPFu6n0R3EU52LzOzAXFTqbu/Q2ikMdPM/tvMPheJbYqZHdvyr03aEyUoaW+mEq7FzCaM/LmaMMR6VkVucJ1AGBb7LeC3hCHJIYxinEwd4RrW7wmJ9mHgRWBKZJvLCEOEdyZ8vncJo8ZWAdES1e2E1nl/B9YQWum1aD9JHEYY6n0JsDJuOiDy+rcJw37fQCiRPQkcREjQIo1STxIiecLMvkhoAr+3u8/PdTwiuaYEJZIjZnYCsI7QhHt34CZgk7t/MaeBieQJNZIQyZ2ehNaEuwCfEu6B0n1BIhEqQYmISF5SIwkREclLSlAiIpKXlKBERCQvKUGJiEheUoISEZG89P/+Fr24KLrwzAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"metadata": {
"id": "j3LWcQg8xuZB",
"outputId": "7f5d5a79-7a09-4e2a-bde7-ad6a89375db8"
},
"cell_type": "code",
"source": [
"from sklearn.pipeline import Pipeline\n",
"\n",
"polynomial_regression = Pipeline([\n",
" (\"poly_features\", PolynomialFeatures(degree=10, include_bias=False)),\n",
" (\"lin_reg\", LinearRegression()),\n",
" ])\n",
"\n",
"plot_learning_curves(polynomial_regression, X, y)\n",
"plt.axis([0, 80, 0, 3]) # not shown\n",
"save_fig(\"learning_curves_plot\") # not shown\n",
"plt.show() # not shown"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"text": [
"Saving figure learning_curves_plot\n"
],
"name": "stdout"
},
{
"output_type": "display_data",
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"metadata": {
"id": "0MxEwiE3xuZG"
},
"cell_type": "markdown",
"source": [
"# Regularized models"
]
},
{
"metadata": {
"id": "1xK9m00exuZH",
"outputId": "1843efad-fb2a-49f5-8d0e-b2e741afb3b2"
},
"cell_type": "code",
"source": [
"from sklearn.linear_model import Ridge\n",
"\n",
"np.random.seed(42)\n",
"m = 20\n",
"X = 3 * np.random.rand(m, 1)\n",
"y = 1 + 0.5 * X + np.random.randn(m, 1) / 1.5\n",
"X_new = np.linspace(0, 3, 100).reshape(100, 1)\n",
"\n",
"def plot_model(model_class, polynomial, alphas, **model_kargs):\n",
" for alpha, style in zip(alphas, (\"b-\", \"g--\", \"r:\")):\n",
" model = model_class(alpha, **model_kargs) if alpha > 0 else LinearRegression()\n",
" if polynomial:\n",
" model = Pipeline([\n",
" (\"poly_features\", PolynomialFeatures(degree=10, include_bias=False)),\n",
" (\"std_scaler\", StandardScaler()),\n",
" (\"regul_reg\", model),\n",
" ])\n",
" model.fit(X, y)\n",
" y_new_regul = model.predict(X_new)\n",
" lw = 2 if alpha > 0 else 1\n",
" plt.plot(X_new, y_new_regul, style, linewidth=lw, label=r\"$\\alpha = {}$\".format(alpha))\n",
" plt.plot(X, y, \"b.\", linewidth=3)\n",
" plt.legend(loc=\"upper left\", fontsize=15)\n",
" plt.xlabel(\"$x_1$\", fontsize=18)\n",
" plt.axis([0, 3, 0, 4])\n",
"\n",
"plt.figure(figsize=(8,4))\n",
"plt.subplot(121)\n",
"plot_model(Ridge, polynomial=False, alphas=(0, 10, 100), random_state=42)\n",
"plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
"plt.subplot(122)\n",
"plot_model(Ridge, polynomial=True, alphas=(0, 10**-5, 1), random_state=42)\n",
"\n",
"save_fig(\"ridge_regression_plot\")\n",
"plt.show()"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"text": [
"Saving figure ridge_regression_plot\n"
],
"name": "stdout"
},
{
"output_type": "display_data",
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 576x288 with 2 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"metadata": {
"id": "Y0LTCew8xuZS",
"outputId": "d61aac89-0a4c-4a3a-f11c-027a193959c7"
},
"cell_type": "code",
"source": [
"from sklearn.linear_model import Ridge\n",
"ridge_reg = Ridge(alpha=1, solver=\"cholesky\", random_state=42)\n",
"ridge_reg.fit(X, y)\n",
"ridge_reg.predict([[1.5]])"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([[1.55071465]])"
]
},
"metadata": {
"tags": []
},
"execution_count": 39
}
]
},
{
"metadata": {
"id": "-IWIoVeWxuZV",
"outputId": "e40c2248-85f9-40c1-ba41-222143a3ea5a"
},
"cell_type": "code",
"source": [
"sgd_reg = SGDRegressor(max_iter=50, tol=-np.infty, penalty=\"l2\", random_state=42)\n",
"sgd_reg.fit(X, y.ravel())\n",
"sgd_reg.predict([[1.5]])"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([1.49905184])"
]
},
"metadata": {
"tags": []
},
"execution_count": 40
}
]
},
{
"metadata": {
"id": "m8_xgOYyxuZY",
"outputId": "26d8bbc2-729f-42fc-a9e0-9d331c27aba4"
},
"cell_type": "code",
"source": [
"ridge_reg = Ridge(alpha=1, solver=\"sag\", random_state=42)\n",
"ridge_reg.fit(X, y)\n",
"ridge_reg.predict([[1.5]])"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([[1.5507201]])"
]
},
"metadata": {
"tags": []
},
"execution_count": 41
}
]
},
{
"metadata": {
"id": "4a3vdxJFxuZb",
"outputId": "3d15360a-d937-417b-dc58-6f24bd1ade3a"
},
"cell_type": "code",
"source": [
"from sklearn.linear_model import Lasso\n",
"\n",
"plt.figure(figsize=(8,4))\n",
"plt.subplot(121)\n",
"plot_model(Lasso, polynomial=False, alphas=(0, 0.1, 1), random_state=42)\n",
"plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
"plt.subplot(122)\n",
"plot_model(Lasso, polynomial=True, alphas=(0, 10**-7, 1), tol=1, random_state=42)\n",
"\n",
"save_fig(\"lasso_regression_plot\")\n",
"plt.show()"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"text": [
"Saving figure lasso_regression_plot\n"
],
"name": "stdout"
},
{
"output_type": "display_data",
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 576x288 with 2 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"metadata": {
"id": "t7yPQ9rgxuZi",
"outputId": "2fce9198-3dd7-4089-a962-af4b08bb37c6"
},
"cell_type": "code",
"source": [
"from sklearn.linear_model import Lasso\n",
"lasso_reg = Lasso(alpha=0.1)\n",
"lasso_reg.fit(X, y)\n",
"lasso_reg.predict([[1.5]])"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([1.53788174])"
]
},
"metadata": {
"tags": []
},
"execution_count": 43
}
]
},
{
"metadata": {
"id": "nlHiQGs9xuZn",
"outputId": "456002e7-da80-47b1-9ba8-50ff74537586"
},
"cell_type": "code",
"source": [
"from sklearn.linear_model import ElasticNet\n",
"elastic_net = ElasticNet(alpha=0.1, l1_ratio=0.5, random_state=42)\n",
"elastic_net.fit(X, y)\n",
"elastic_net.predict([[1.5]])"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"array([1.54333232])"
]
},
"metadata": {
"tags": []
},
"execution_count": 44
}
]
},
{
"metadata": {
"scrolled": true,
"id": "q57peOiExuZ0",
"outputId": "ff75ee4a-238d-4c6f-dc89-e391d71046cd"
},
"cell_type": "code",
"source": [
"np.random.seed(42)\n",
"m = 100\n",
"X = 6 * np.random.rand(m, 1) - 3\n",
"y = 2 + X + 0.5 * X**2 + np.random.randn(m, 1)\n",
"\n",
"X_train, X_val, y_train, y_val = train_test_split(X[:50], y[:50].ravel(), test_size=0.5, random_state=10)\n",
"\n",
"poly_scaler = Pipeline([\n",
" (\"poly_features\", PolynomialFeatures(degree=90, include_bias=False)),\n",
" (\"std_scaler\", StandardScaler()),\n",
" ])\n",
"\n",
"X_train_poly_scaled = poly_scaler.fit_transform(X_train)\n",
"X_val_poly_scaled = poly_scaler.transform(X_val)\n",
"\n",
"sgd_reg = SGDRegressor(max_iter=1,\n",
" tol=-np.infty,\n",
" penalty=None,\n",
" eta0=0.0005,\n",
" warm_start=True,\n",
" learning_rate=\"constant\",\n",
" random_state=42)\n",
"\n",
"n_epochs = 500\n",
"train_errors, val_errors = [], []\n",
"for epoch in range(n_epochs):\n",
" sgd_reg.fit(X_train_poly_scaled, y_train)\n",
" y_train_predict = sgd_reg.predict(X_train_poly_scaled)\n",
" y_val_predict = sgd_reg.predict(X_val_poly_scaled)\n",
" train_errors.append(mean_squared_error(y_train, y_train_predict))\n",
" val_errors.append(mean_squared_error(y_val, y_val_predict))\n",
"\n",
"best_epoch = np.argmin(val_errors)\n",
"best_val_rmse = np.sqrt(val_errors[best_epoch])\n",
"\n",
"plt.annotate('Best model',\n",
" xy=(best_epoch, best_val_rmse),\n",
" xytext=(best_epoch, best_val_rmse + 1),\n",
" ha=\"center\",\n",
" arrowprops=dict(facecolor='black', shrink=0.05),\n",
" fontsize=16,\n",
" )\n",
"\n",
"best_val_rmse -= 0.03 # just to make the graph look better\n",
"plt.plot([0, n_epochs], [best_val_rmse, best_val_rmse], \"k:\", linewidth=2)\n",
"plt.plot(np.sqrt(val_errors), \"b-\", linewidth=3, label=\"Validation set\")\n",
"plt.plot(np.sqrt(train_errors), \"r--\", linewidth=2, label=\"Training set\")\n",
"plt.legend(loc=\"upper right\", fontsize=14)\n",
"plt.xlabel(\"Epoch\", fontsize=14)\n",
"plt.ylabel(\"RMSE\", fontsize=14)\n",
"save_fig(\"early_stopping_plot\")\n",
"plt.show()"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"text": [
"Saving figure early_stopping_plot\n"
],
"name": "stdout"
},
{
"output_type": "display_data",
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"metadata": {
"id": "1HtN5-F-xuZ-"
},
"cell_type": "code",
"source": [
"from sklearn.base import clone\n",
"sgd_reg = SGDRegressor(max_iter=1, tol=-np.infty, warm_start=True, penalty=None,\n",
" learning_rate=\"constant\", eta0=0.0005, random_state=42)\n",
"\n",
"minimum_val_error = float(\"inf\")\n",
"best_epoch = None\n",
"best_model = None\n",
"for epoch in range(1000):\n",
" sgd_reg.fit(X_train_poly_scaled, y_train) # continues where it left off\n",
" y_val_predict = sgd_reg.predict(X_val_poly_scaled)\n",
" val_error = mean_squared_error(y_val, y_val_predict)\n",
" if val_error < minimum_val_error:\n",
" minimum_val_error = val_error\n",
" best_epoch = epoch\n",
" best_model = clone(sgd_reg)"
],
"execution_count": null,
"outputs": []
},
{
"metadata": {
"id": "Iq28hJDCxuaB",
"outputId": "710757fd-f253-481a-ba35-11669d43e578"
},
"cell_type": "code",
"source": [
"best_epoch, best_model"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"(239,\n",
" SGDRegressor(alpha=0.0001, average=False, early_stopping=False, epsilon=0.1,\n",
" eta0=0.0005, fit_intercept=True, l1_ratio=0.15,\n",
" learning_rate='constant', loss='squared_loss', max_iter=1,\n",
" n_iter=None, n_iter_no_change=5, penalty=None, power_t=0.25,\n",
" random_state=42, shuffle=True, tol=-inf, validation_fraction=0.1,\n",
" verbose=0, warm_start=True))"
]
},
"metadata": {
"tags": []
},
"execution_count": 47
}
]
},
{
"metadata": {
"id": "gIiRVE8yxuaF"
},
"cell_type": "code",
"source": [
"t1a, t1b, t2a, t2b = -1, 3, -1.5, 1.5\n",
"\n",
"# ignoring bias term\n",
"t1s = np.linspace(t1a, t1b, 500)\n",
"t2s = np.linspace(t2a, t2b, 500)\n",
"t1, t2 = np.meshgrid(t1s, t2s)\n",
"T = np.c_[t1.ravel(), t2.ravel()]\n",
"Xr = np.array([[-1, 1], [-0.3, -1], [1, 0.1]])\n",
"yr = 2 * Xr[:, :1] + 0.5 * Xr[:, 1:]\n",
"\n",
"J = (1/len(Xr) * np.sum((T.dot(Xr.T) - yr.T)**2, axis=1)).reshape(t1.shape)\n",
"\n",
"N1 = np.linalg.norm(T, ord=1, axis=1).reshape(t1.shape)\n",
"N2 = np.linalg.norm(T, ord=2, axis=1).reshape(t1.shape)\n",
"\n",
"t_min_idx = np.unravel_index(np.argmin(J), J.shape)\n",
"t1_min, t2_min = t1[t_min_idx], t2[t_min_idx]\n",
"\n",
"t_init = np.array([[0.25], [-1]])"
],
"execution_count": null,
"outputs": []
},
{
"metadata": {
"id": "aAOmLVicxuaN",
"outputId": "8d04910e-061c-4198-b236-247f696d5e88"
},
"cell_type": "code",
"source": [
"def bgd_path(theta, X, y, l1, l2, core = 1, eta = 0.1, n_iterations = 50):\n",
" path = [theta]\n",
" for iteration in range(n_iterations):\n",
" gradients = core * 2/len(X) * X.T.dot(X.dot(theta) - y) + l1 * np.sign(theta) + 2 * l2 * theta\n",
"\n",
" theta = theta - eta * gradients\n",
" path.append(theta)\n",
" return np.array(path)\n",
"\n",
"plt.figure(figsize=(12, 8))\n",
"for i, N, l1, l2, title in ((0, N1, 0.5, 0, \"Lasso\"), (1, N2, 0, 0.1, \"Ridge\")):\n",
" JR = J + l1 * N1 + l2 * N2**2\n",
" \n",
" tr_min_idx = np.unravel_index(np.argmin(JR), JR.shape)\n",
" t1r_min, t2r_min = t1[tr_min_idx], t2[tr_min_idx]\n",
"\n",
" levelsJ=(np.exp(np.linspace(0, 1, 20)) - 1) * (np.max(J) - np.min(J)) + np.min(J)\n",
" levelsJR=(np.exp(np.linspace(0, 1, 20)) - 1) * (np.max(JR) - np.min(JR)) + np.min(JR)\n",
" levelsN=np.linspace(0, np.max(N), 10)\n",
" \n",
" path_J = bgd_path(t_init, Xr, yr, l1=0, l2=0)\n",
" path_JR = bgd_path(t_init, Xr, yr, l1, l2)\n",
" path_N = bgd_path(t_init, Xr, yr, np.sign(l1)/3, np.sign(l2), core=0)\n",
"\n",
" plt.subplot(221 + i * 2)\n",
" plt.grid(True)\n",
" plt.axhline(y=0, color='k')\n",
" plt.axvline(x=0, color='k')\n",
" plt.contourf(t1, t2, J, levels=levelsJ, alpha=0.9)\n",
" plt.contour(t1, t2, N, levels=levelsN)\n",
" plt.plot(path_J[:, 0], path_J[:, 1], \"w-o\")\n",
" plt.plot(path_N[:, 0], path_N[:, 1], \"y-^\")\n",
" plt.plot(t1_min, t2_min, \"rs\")\n",
" plt.title(r\"$\\ell_{}$ penalty\".format(i + 1), fontsize=16)\n",
" plt.axis([t1a, t1b, t2a, t2b])\n",
" if i == 1:\n",
" plt.xlabel(r\"$\\theta_1$\", fontsize=20)\n",
" plt.ylabel(r\"$\\theta_2$\", fontsize=20, rotation=0)\n",
"\n",
" plt.subplot(222 + i * 2)\n",
" plt.grid(True)\n",
" plt.axhline(y=0, color='k')\n",
" plt.axvline(x=0, color='k')\n",
" plt.contourf(t1, t2, JR, levels=levelsJR, alpha=0.9)\n",
" plt.plot(path_JR[:, 0], path_JR[:, 1], \"w-o\")\n",
" plt.plot(t1r_min, t2r_min, \"rs\")\n",
" plt.title(title, fontsize=16)\n",
" plt.axis([t1a, t1b, t2a, t2b])\n",
" if i == 1:\n",
" plt.xlabel(r\"$\\theta_1$\", fontsize=20)\n",
"\n",
"save_fig(\"lasso_vs_ridge_plot\")\n",
"plt.show()"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"text": [
"Saving figure lasso_vs_ridge_plot\n"
],
"name": "stdout"
},
{
"output_type": "display_data",
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 864x576 with 4 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
}
]
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment