sparse_matrix.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from scipy import sparse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "user_id = ['A','B','C','A','C','B']\n",
    "\n",
    "item_name = ['prd1','prd2','prd3','prd4','prd5','prd6']\n",
    "\n",
    "rating = [4,9,1,3,7,2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "sdf = pd.DataFrame({'user_id':user_id, 'item_name':item_name, 'rating':rating})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>user_id</th>\n",
       "      <th>item_name</th>\n",
       "      <th>rating</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>A</td>\n",
       "      <td>prd1</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>B</td>\n",
       "      <td>prd2</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>C</td>\n",
       "      <td>prd3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>A</td>\n",
       "      <td>prd4</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>C</td>\n",
       "      <td>prd5</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>B</td>\n",
       "      <td>prd6</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  user_id item_name  rating\n",
       "0       A      prd1       4\n",
       "1       B      prd2       9\n",
       "2       C      prd3       1\n",
       "3       A      prd4       3\n",
       "4       C      prd5       7\n",
       "5       B      prd6       2"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_users = sdf['user_id'].unique()      #获得所有用户的id\n",
    "\n",
    "n_items = sdf['item_name'].unique()    #获得所有产品的id\n",
    "\n",
    "df = pd.DataFrame(index = n_users, columns = n_items) #生成一个基于用户为索引，产品为列的dataFrame  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(len(sdf)):\n",
    "    row_i = sdf.iloc[[i]]\n",
    "    user_id = row_i['user_id'].tolist()[0]\n",
    "    item_name = row_i['item_name'].tolist()[0]\n",
    "    rating = row_i['rating'].tolist()[0]\n",
    "    df.at[user_id,item_name] = rating"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>prd1</th>\n",
       "      <th>prd2</th>\n",
       "      <th>prd3</th>\n",
       "      <th>prd4</th>\n",
       "      <th>prd5</th>\n",
       "      <th>prd6</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>4</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>NaN</td>\n",
       "      <td>9</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  prd1 prd2 prd3 prd4 prd5 prd6\n",
       "A    4  NaN  NaN    3  NaN  NaN\n",
       "B  NaN    9  NaN  NaN  NaN    2\n",
       "C  NaN  NaN    1  NaN    7  NaN"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "df.fillna(0,inplace = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "        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>prd1</th>\n",
       "      <th>prd2</th>\n",
       "      <th>prd3</th>\n",
       "      <th>prd4</th>\n",
       "      <th>prd5</th>\n",
       "      <th>prd6</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>0</td>\n",
       "      <td>9</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>7</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   prd1  prd2  prd3  prd4  prd5  prd6\n",
       "A     4     0     0     3     0     0\n",
       "B     0     9     0     0     0     2\n",
       "C     0     0     1     0     7     0"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4, 0, 0, 3, 0, 0],\n",
       "       [0, 9, 0, 0, 0, 2],\n",
       "       [0, 0, 1, 0, 7, 0]], dtype=int64)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "CSC是按列存储一个稀疏矩阵的。其中indptr中的数据代表矩阵中每一列所存的数据在data中的开始和结束的索引，  \n",
    "而indices中的数据代表所对应的data中的数据在其所在列中的所在行数  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "Csc = sparse.csc_matrix(np.array(df))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6], dtype=int32)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Csc.indptr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 0, 2, 1], dtype=int32)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Csc.indices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 9, 1, 3, 7, 2], dtype=int64)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Csc.data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "CSR是按行来存储一个稀疏矩阵的，其原理与CSC类似。indptr中的数据表示矩阵中每一行的数据在data中开始和结束的索引，而indices中的数据表示所对应的在data中的数据在矩阵中其所在行的所在列数。可以看出，在indptr、indices和data三个数组相同的情况下，通过CSC和CSR分别表示出来的矩阵互为转置关系。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "Csr = sparse.csr_matrix(np.array(df))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 2, 4, 6], dtype=int32)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Csr.indptr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 3, 1, 5, 2, 4], dtype=int32)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Csr.indices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 3, 9, 2, 1, 7], dtype=int64)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Csr.data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "COO是最简单的一种格式，每一个元素需要用一个三元组来表示，分别是（行号，列号，数值）,但空间不是最优"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "Coo = sparse.coo_matrix(np.array(df))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 1, 1, 2, 2], dtype=int32)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Coo.row"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 3, 1, 5, 2, 4], dtype=int32)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Coo.col"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 3, 9, 2, 1, 7], dtype=int64)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Coo.data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "coo = csc.tocoo(copy=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>index</th>\n",
       "      <th>col</th>\n",
       "      <th>data</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
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       "      <th>2</th>\n",
       "      <td>1</td>\n",
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       "      <td>9</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
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       "      <td>7</td>\n",
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      ],
      "text/plain": [
       "   index  col  data\n",
       "0      0    0     4\n",
       "1      0    3     3\n",
       "2      1    1     9\n",
       "3      1    5     2\n",
       "4      2    2     1\n",
       "5      2    4     7"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame({'index': Coo.row, 'col': Coo.col, 'data': Coo.data}\n",
    "                 )[['index', 'col', 'data']].sort_values(['index', 'col']\n",
    "                 ).reset_index(drop=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
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       "      <td>4</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   index  col  data\n",
       "0      0    0     4\n",
       "1      0    3     3\n",
       "2      1    1     9\n",
       "3      1    5     2\n",
       "4      2    2     1\n",
       "5      2    4     7"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame({'index': Coo.row, 'col': Coo.col, 'data': Coo.data}).sort_values(['index', 'col'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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