neural_network/numpy_nn/neural_network_1.ipynb

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 "cells": [
  {
   "cell_type": "markdown",
   "id": "f4893f14",
   "metadata": {},
   "source": [
    "## 1.神经元"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94bf19cc",
   "metadata": {},
   "source": [
    "<div>\n",
    "<img src='nn1.jpg' width=45% align=left>\n",
    "<img src='nn2.jpg' width=45% align=right>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2be5b67b",
   "metadata": {},
   "source": [
    "## 2.数学模型"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8033dba5",
   "metadata": {},
   "source": [
    "<img src='math_nn.png' width=50% align=center>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "65adb74a",
   "metadata": {},
   "source": [
    "## 3.Python代码"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5a9e122",
   "metadata": {},
   "source": [
    "### 3.1 一个数据，三个特征，一个神经元"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a59d2aed",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = [1, 2, 3] #数据（3，）\n",
    "weight = [2, -1, 1] #权重\n",
    "bias = 2#偏置"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72b0c310",
   "metadata": {},
   "source": [
    "$$output = X[0] \\times weight[0] + X[1] \\times weight[1] + X[2] \\times weight[2] + bias$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "52612463",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "output = 0 \n",
    "for x, w in zip(X, weight):\n",
    "    output += x * w\n",
    "output += bias\n",
    "output"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7047e45",
   "metadata": {},
   "source": [
    "### 3.2 一个数据，三个特征，二个神经元"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "276a5d16",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = [1, 2, 3] #数据（3，）\n",
    "weight = [[2, -1, 1],\n",
    "          [2, 3, 1]] #权重\n",
    "bias = [2, 3]#偏置"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88130792",
   "metadata": {},
   "source": [
    "$$outputs[0] = X[0] \\times weight[0][0] + X[1] \\times weight[0][1] + X[2] \\times weight[0][2] + bias[0]$$\n",
    "$$outputs[1] = X[0] \\times weight[1][0] + X[1] \\times weight[1][1] + X[2] \\times weight[1][2] + bias[1]$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "171cf7ed",
   "metadata": {},
   "outputs": [],
   "source": [
    "outputs = []\n",
    "for n in range(len(weight)):\n",
    "    output = 0\n",
    "    for x, w in zip(X, weight[n]):\n",
    "        output += x * w#输入特征*权重\n",
    "    output += bias[n]#加上偏置\n",
    "    outputs.append(output)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2b29da7e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[5, 14]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "outputs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5d44a2e",
   "metadata": {},
   "source": [
    "### 3.3 三个数据，三个特征，二个神经元"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "e789cbb0",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = [[1, 2, 3],\n",
    "     [2, 3, 4],\n",
    "     [4, 5, 6]] #数据（3， 3）\n",
    "weight = [[2, -1, 1],\n",
    "          [2, 3, 1]] #权重\n",
    "bias = [2, 3]#偏置"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "ec7c1216",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_outputs = []\n",
    "for i in range(len(X)):\n",
    "    outputs = []\n",
    "    for n in range(len(weight)):\n",
    "        output = 0\n",
    "        for x, w in zip(X[i], weight[n]):\n",
    "            output += x * w#输入特征*权重\n",
    "        output += bias[n]#加上偏置\n",
    "        outputs.append(output)\n",
    "    n_outputs.append(outputs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "47bdc39b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[5, 14], [7, 20], [11, 32]]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_outputs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08742560",
   "metadata": {},
   "source": [
    "作业：请写出n_outputs，X，weight的计算"
   ]
  }
 ],
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