chkk-数学基础/06-线性代数(距离计算).ipynb

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   "source": [
    "# 线性代数(距离计算)\n",
    "\n",
    "不是梦回大学，那没有必要\n",
    "\n",
    "\n",
    "向量，数组计算，有转置就要转置，不转置，令人费解\n",
    "\n",
    "神经网络，基本都是矩阵连乘！\n",
    "\n",
    "智能"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "# v1=np.mat([1,2,3])\n",
    "# v2=np.mat([4,5,6])\n",
    "\n",
    "# v1=np.mat([12,34,5,6,17,8])\n",
    "# v2=np.mat([21,3,114,12,4,5])\n",
    "\n",
    "# v1=np.mat([100, 50])\n",
    "# v2=np.mat([1000, 500])\n",
    "\n",
    "# v1=np.mat([2, 10])\n",
    "# v2=np.mat([10, 50])\n",
    "\n",
    "v1=np.mat([1,2,2,1,1,1,0])\n",
    "v2=np.mat([1,2,2,1,1,2,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "48"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# L1距离，曼哈顿距离\n",
    "np.sum(abs(v1-v2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[40.79215611]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# L2距离，欧拉距离\n",
    "np.sqrt((v1-v2)*(v1-v2).T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[0.93819419]])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 余弦相似度\n",
    "np.dot(v1,v2.T)/(np.linalg.norm(v1)*np.linalg.norm(v2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.0"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm([3,4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'0.23.4'"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.__version__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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