{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Normalization Diff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading required package: daltoolbox\n",
      "\n",
      "Registered S3 method overwritten by 'quantmod':\n",
      "  method            from\n",
      "  as.zoo.data.frame zoo \n",
      "\n",
      "\n",
      "Attaching package: ‘daltoolbox’\n",
      "\n",
      "\n",
      "The following object is masked from ‘package:base’:\n",
      "\n",
      "    transform\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# DAL ToolBox\n",
    "# version 1.0.777\n",
    "\n",
    "source(\"https://raw.githubusercontent.com/cefet-rj-dal/daltoolbox/main/jupyter.R\")\n",
    "\n",
    "#loading DAL\n",
    "load_library(\"daltoolbox\") "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Series for studying"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "data(sin_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Fahjowb9zPPKkvnIi63aFBK/JnqLYEi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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(ggplot2)\n",
    "plot_ts(x=sin_data$x, y=sin_data$y) + theme(text = element_text(size=16))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### sliding windows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A matrix: 3 × 10 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>t9</th><th scope=col>t8</th><th scope=col>t7</th><th scope=col>t6</th><th scope=col>t5</th><th scope=col>t4</th><th scope=col>t3</th><th scope=col>t2</th><th scope=col>t1</th><th scope=col>t0</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>0.0000000</td><td>0.2474040</td><td>0.4794255</td><td>0.6816388</td><td>0.8414710</td><td>0.9489846</td><td>0.9974950</td><td>0.9839859</td><td>0.9092974</td><td>0.7780732</td></tr>\n",
       "\t<tr><td>0.2474040</td><td>0.4794255</td><td>0.6816388</td><td>0.8414710</td><td>0.9489846</td><td>0.9974950</td><td>0.9839859</td><td>0.9092974</td><td>0.7780732</td><td>0.5984721</td></tr>\n",
       "\t<tr><td>0.4794255</td><td>0.6816388</td><td>0.8414710</td><td>0.9489846</td><td>0.9974950</td><td>0.9839859</td><td>0.9092974</td><td>0.7780732</td><td>0.5984721</td><td>0.3816610</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 3 × 10 of type dbl\n",
       "\\begin{tabular}{llllllllll}\n",
       " t9 & t8 & t7 & t6 & t5 & t4 & t3 & t2 & t1 & t0\\\\\n",
       "\\hline\n",
       "\t 0.0000000 & 0.2474040 & 0.4794255 & 0.6816388 & 0.8414710 & 0.9489846 & 0.9974950 & 0.9839859 & 0.9092974 & 0.7780732\\\\\n",
       "\t 0.2474040 & 0.4794255 & 0.6816388 & 0.8414710 & 0.9489846 & 0.9974950 & 0.9839859 & 0.9092974 & 0.7780732 & 0.5984721\\\\\n",
       "\t 0.4794255 & 0.6816388 & 0.8414710 & 0.9489846 & 0.9974950 & 0.9839859 & 0.9092974 & 0.7780732 & 0.5984721 & 0.3816610\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 3 × 10 of type dbl\n",
       "\n",
       "| t9 | t8 | t7 | t6 | t5 | t4 | t3 | t2 | t1 | t0 |\n",
       "|---|---|---|---|---|---|---|---|---|---|\n",
       "| 0.0000000 | 0.2474040 | 0.4794255 | 0.6816388 | 0.8414710 | 0.9489846 | 0.9974950 | 0.9839859 | 0.9092974 | 0.7780732 |\n",
       "| 0.2474040 | 0.4794255 | 0.6816388 | 0.8414710 | 0.9489846 | 0.9974950 | 0.9839859 | 0.9092974 | 0.7780732 | 0.5984721 |\n",
       "| 0.4794255 | 0.6816388 | 0.8414710 | 0.9489846 | 0.9974950 | 0.9839859 | 0.9092974 | 0.7780732 | 0.5984721 | 0.3816610 |\n",
       "\n"
      ],
      "text/plain": [
       "     t9        t8        t7        t6        t5        t4        t3       \n",
       "[1,] 0.0000000 0.2474040 0.4794255 0.6816388 0.8414710 0.9489846 0.9974950\n",
       "[2,] 0.2474040 0.4794255 0.6816388 0.8414710 0.9489846 0.9974950 0.9839859\n",
       "[3,] 0.4794255 0.6816388 0.8414710 0.9489846 0.9974950 0.9839859 0.9092974\n",
       "     t2        t1        t0       \n",
       "[1,] 0.9839859 0.9092974 0.7780732\n",
       "[2,] 0.9092974 0.7780732 0.5984721\n",
       "[3,] 0.7780732 0.5984721 0.3816610"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "       t0          \n",
       " Min.   :-0.99929  \n",
       " 1st Qu.:-0.55091  \n",
       " Median : 0.05397  \n",
       " Mean   : 0.02988  \n",
       " 3rd Qu.: 0.63279  \n",
       " Max.   : 0.99460  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sw_size <- 10\n",
    "ts <- ts_data(sin_data$y, sw_size)\n",
    "ts_head(ts, 3)\n",
    "summary(ts[,10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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aqasTjgd8Ku31C1SFPhFV5DG2ANPIIdQQxxVxSqWqSdcCevoQ0wEqZiRxBE2DXu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\nX+iDiqN9kabCK9gRhDkWfSV2BFUlxzbyNoD2RdoBd2NHEOZz6I8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T/Er8ip2DhIWKVNAW303YEfyyygaKBE9hByFhoSKd4ZqI/7AjZDsZ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\nAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(ggplot2)\n",
    "plot_ts(y=ts[,10]) + theme(text = element_text(size=16))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### normalization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A matrix: 3 × 9 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>t8</th><th scope=col>t7</th><th scope=col>t6</th><th scope=col>t5</th><th scope=col>t4</th><th scope=col>t3</th><th scope=col>t2</th><th scope=col>t1</th><th scope=col>t0</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>0.9982009</td><td>0.9672887</td><td>0.9073861</td><td>0.8222178</td><td>0.7170790</td><td>0.5985067</td><td>0.4738732</td><td>0.3509276</td><td>0.23731412</td></tr>\n",
       "\t<tr><td>0.9672887</td><td>0.9073861</td><td>0.8222178</td><td>0.7170790</td><td>0.5985067</td><td>0.4738732</td><td>0.3509276</td><td>0.2373141</td><td>0.14009662</td></tr>\n",
       "\t<tr><td>0.9073861</td><td>0.8222178</td><td>0.7170790</td><td>0.5985067</td><td>0.4738732</td><td>0.3509276</td><td>0.2373141</td><td>0.1400966</td><td>0.06531964</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 3 × 9 of type dbl\n",
       "\\begin{tabular}{lllllllll}\n",
       " t8 & t7 & t6 & t5 & t4 & t3 & t2 & t1 & t0\\\\\n",
       "\\hline\n",
       "\t 0.9982009 & 0.9672887 & 0.9073861 & 0.8222178 & 0.7170790 & 0.5985067 & 0.4738732 & 0.3509276 & 0.23731412\\\\\n",
       "\t 0.9672887 & 0.9073861 & 0.8222178 & 0.7170790 & 0.5985067 & 0.4738732 & 0.3509276 & 0.2373141 & 0.14009662\\\\\n",
       "\t 0.9073861 & 0.8222178 & 0.7170790 & 0.5985067 & 0.4738732 & 0.3509276 & 0.2373141 & 0.1400966 & 0.06531964\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 3 × 9 of type dbl\n",
       "\n",
       "| t8 | t7 | t6 | t5 | t4 | t3 | t2 | t1 | t0 |\n",
       "|---|---|---|---|---|---|---|---|---|\n",
       "| 0.9982009 | 0.9672887 | 0.9073861 | 0.8222178 | 0.7170790 | 0.5985067 | 0.4738732 | 0.3509276 | 0.23731412 |\n",
       "| 0.9672887 | 0.9073861 | 0.8222178 | 0.7170790 | 0.5985067 | 0.4738732 | 0.3509276 | 0.2373141 | 0.14009662 |\n",
       "| 0.9073861 | 0.8222178 | 0.7170790 | 0.5985067 | 0.4738732 | 0.3509276 | 0.2373141 | 0.1400966 | 0.06531964 |\n",
       "\n"
      ],
      "text/plain": [
       "     t8        t7        t6        t5        t4        t3        t2       \n",
       "[1,] 0.9982009 0.9672887 0.9073861 0.8222178 0.7170790 0.5985067 0.4738732\n",
       "[2,] 0.9672887 0.9073861 0.8222178 0.7170790 0.5985067 0.4738732 0.3509276\n",
       "[3,] 0.9073861 0.8222178 0.7170790 0.5985067 0.4738732 0.3509276 0.2373141\n",
       "     t1        t0        \n",
       "[1,] 0.3509276 0.23731412\n",
       "[2,] 0.2373141 0.14009662\n",
       "[3,] 0.1400966 0.06531964"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "       t0         \n",
       " Min.   :0.00000  \n",
       " 1st Qu.:0.06333  \n",
       " Median :0.29337  \n",
       " Mean   :0.40975  \n",
       " 3rd Qu.:0.75129  \n",
       " Max.   :1.00000  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Lt63CmBs2mqQdRB7AicjeCzMZ1GRXoclgicTU/HYm7EjsDbKj73/2pUpM9goMDZ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\nAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "preproc <- ts_norm_diff()\n",
    "preproc <- fit(preproc, ts)\n",
    "tst <- transform(preproc, ts)\n",
    "ts_head(tst, 3)\n",
    "summary(tst[,9])\n",
    "plot_ts(y=ts[,9]) + theme(text = element_text(size=16))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "4.3.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}