diff options
| author | chzhang <zch921005@126.com> | 2023-02-16 00:37:15 +0800 |
|---|---|---|
| committer | chzhang <zch921005@126.com> | 2023-02-16 00:37:15 +0800 |
| commit | fe488162d4e2d241388817c5353f553d2dc114fa (patch) | |
| tree | 95a9a3e4cdc7573cdea3c798cfdf1be4fc4f4e98 /rl | |
| parent | 13d8981e9b949046d7e457d7c654802a426eab94 (diff) | |
policy gradient
Diffstat (limited to 'rl')
| -rw-r--r-- | rl/tutorials/04_maze_env_policy_gradient.ipynb | 11012 |
1 files changed, 11012 insertions, 0 deletions
diff --git a/rl/tutorials/04_maze_env_policy_gradient.ipynb b/rl/tutorials/04_maze_env_policy_gradient.ipynb new file mode 100644 index 0000000..58959a2 --- /dev/null +++ b/rl/tutorials/04_maze_env_policy_gradient.ipynb @@ -0,0 +1,11012 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "ExecuteTime": { + "end_time": "2023-02-15T16:15:05.316900Z", + "start_time": "2023-02-15T16:15:04.747314Z" + } + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import gym\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## basics" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "- $\\theta$ 与 $\\pi_\\theta(s,a)$（给定 $\\theta$（策略参数） 关于 s, a 的函数），基于 $\\theta$ 找到 $\\pi_\\theta$\n", + " - $\\theta$ 是策略参数\n", + " - $\\pi_\\theta(s,a)$ 是策略（base $\\theta$，policy)\n", + " - $\\pi$ 表示 distribution\n", + "- 策略迭代（策略梯度，policy gradient）的含义\n", + " - $\\theta_0\\rightarrow \\pi_0$, $\\theta_0 \\rightarrow \\theta_1$, $\\theta_1 \\rightarrow \\pi_1$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 更新 pi 的计算方式" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "ExecuteTime": { + "end_time": "2023-02-15T16:15:08.056882Z", + "start_time": "2023-02-15T16:15:07.687380Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 360x360 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(figsize=(5, 5))\n", + "ax = plt.gca()\n", + "ax.set_xlim(0, 3)\n", + "ax.set_ylim(0, 3)\n", + "\n", + "# plt.plot([1, 1], [0, 1], color='red', linewidth=2)\n", + "# plt.plot([1, 2], [2, 2], color='red', linewidth=2)\n", + "# plt.plot([2, 2], [2, 1], color='red', linewidth=2)\n", + "# plt.plot([2, 3], [1, 1], color='red', linewidth=2)\n", + "\n", + "plt.plot([2, 3], [1, 1], color='red', linewidth=2)\n", + "plt.plot([0, 1], [1, 1], color='red', linewidth=2)\n", + "plt.plot([1, 1], [1, 2], color='red', linewidth=2)\n", + "plt.plot([1, 2], [2, 2], color='red', linewidth=2)\n", + "\n", + "plt.text(0.5, 2.5, 'S0', size=14, ha='center')\n", + "plt.text(1.5, 2.5, 'S1', size=14, ha='center')\n", + "plt.text(2.5, 2.5, 'S2', size=14, ha='center')\n", + "plt.text(0.5, 1.5, 'S3', size=14, ha='center')\n", + "plt.text(1.5, 1.5, 'S4', size=14, ha='center')\n", + "plt.text(2.5, 1.5, 'S5', size=14, ha='center')\n", + "plt.text(0.5, 0.5, 'S6', size=14, ha='center')\n", + "plt.text(1.5, 0.5, 'S7', size=14, ha='center')\n", + "plt.text(2.5, 0.5, 'S8', size=14, ha='center')\n", + "plt.text(0.5, 2.3, 'START', ha='center')\n", + "plt.text(2.5, 0.3, 'GOAL', ha='center')\n", + "# plt.axis('off')\n", + "plt.tick_params(axis='both', which='both', \n", + " bottom=False, top=False, \n", + " right=False, left=False,\n", + " labelbottom=False, labelleft=False\n", + " )\n", + "line, = ax.plot([0.5], [2.5], marker='o', color='g', markersize=60)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "ExecuteTime": { + "end_time": "2023-02-15T16:18:13.511216Z", + "start_time": "2023-02-15T16:18:13.501181Z" + } + }, + "outputs": [], + "source": [ + "# border & barrier\n", + "# ↑, →, ↓, ←（顺时针）\n", + "# row index: given state\n", + "# col index: posible action\n", + "# (state, action) matrix\n", + "# 跟环境对齐\n", + "theta_0 = np.asarray([[np.nan, 1, 1, np.nan], # s0\n", + " [np.nan, 1, np.nan, 1], # s1\n", + " [np.nan, np.nan, 1, 1], # s2\n", + " [1, np.nan, np.nan, np.nan], # s3 \n", + " [np.nan, 1, 1, np.nan], # s4\n", + " [1, np.nan, np.nan, 1], # s5\n", + " [np.nan, 1, np.nan, np.nan], # s6 \n", + " [1, 1, np.nan, 1]] # s7\n", + " )" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "ExecuteTime": { + "end_time": "2023-02-15T16:18:09.714487Z", + "start_time": "2023-02-15T16:18:09.710727Z" + } + }, + "outputs": [], + "source": [ + "# 基于占比, 最 naive 的概率化方式\n", + "def cvt_theta_0_to_pi(theta):\n", + " m, n = theta.shape\n", + " pi = np.zeros((m, n))\n", + " for r in range(m):\n", + " pi[r, :] = theta[r, :] / np.nansum(theta[r, :])\n", + " return np.nan_to_num(pi)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "ExecuteTime": { + "end_time": "2023-02-15T16:18:15.897321Z", + "start_time": "2023-02-15T16:18:15.891621Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[0. , 0.5 , 0.5 , 0. ],\n", + " [0. , 0.5 , 0. , 0.5 ],\n", + " [0. , 0. , 0.5 , 0.5 ],\n", + " [1. , 0. , 0. , 0. ],\n", + " [0. , 0.5 , 0.5 , 0. ],\n", + " [0.5 , 0. , 0. , 0.5 ],\n", + " [0. , 1. , 0. , 0. ],\n", + " [0.33333333, 0.33333333, 0. , 0.33333333]])" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "cvt_theta_0_to_pi(theta_0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\begin{split}\n", + "\\mathbb P_{k} & = \\frac{\\exp(z_k\\cdot \\beta)}{\\sum_i \\exp(z_i\\cdot \\beta)}\\\\\n", + "&=\\frac{\\exp(\\frac{z_k}T)}{\\sum_i \\exp(\\frac{z_i}T)}=\\frac{\\exp(\\beta\\cdot{z_k})}{\\sum_i \\exp(\\beta\\cdot{z_i})}\n", + "\\end{split}\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "ExecuteTime": { + "end_time": "2023-02-15T16:19:08.329088Z", + "start_time": "2023-02-15T16:19:08.324707Z" + } + }, + "outputs": [], + "source": [ + "# 基于 softmax，更 general 的概率化方式\n", + "def softmax_cvt_theta_0_to_pi(theta, beta=1.0):\n", + " m, n = theta.shape\n", + " pi = np.zeros((m, n))\n", + " exp_theta = np.exp(theta*beta)\n", + " for r in range(m):\n", + " pi[r, :] = exp_theta[r, :]/np.nansum(exp_theta[r, :])\n", + " pi = np.nan_to_num(pi)\n", + " return pi" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "ExecuteTime": { + "end_time": "2023-02-15T16:20:09.965106Z", + "start_time": "2023-02-15T16:20:09.957608Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[0. , 0.5 , 0.5 , 0. ],\n", + " [0. , 0.5 , 0. , 0.5 ],\n", + " [0. , 0. , 0.5 , 0.5 ],\n", + " [1. , 0. , 0. , 0. ],\n", + " [0. , 0.5 , 0.5 , 0. ],\n", + " [0.5 , 0. , 0. , 0.5 ],\n", + " [0. , 1. , 0. , 0. ],\n", + " [0.33333333, 0.33333333, 0. , 0.33333333]])" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "softmax_cvt_theta_0_to_pi(theta_0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 与环境（Env）交互" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "ExecuteTime": { + "end_time": "2023-02-15T16:20:53.049014Z", + "start_time": "2023-02-15T16:20:53.044788Z" + } + }, + "outputs": [], + "source": [ + "# 维护着状态，以及 step 函数的返回\n", + "class MazeEnv(gym.Env):\n", + " def __init__(self):\n", + " self.state = 0\n", + " pass\n", + " \n", + " def reset(self):\n", + " self.state = 0\n", + " return self.state\n", + " \n", + " def step(self, action):\n", + " if action == 0:\n", + " self.state -= 3\n", + " elif action == 1:\n", + " self.state += 1\n", + " elif action == 2:\n", + " self.state += 3\n", + " elif action == 3:\n", + " self.state -= 1\n", + " done = False\n", + " if self.state == 8:\n", + " done = True\n", + " # state, reward, done, _\n", + " return self.state, 1, done, {}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\begin{split}\n", + "&\\theta_{s_i,a_j}=\\theta_{s_i,a_j}+\\eta\\cdot \\Delta \\theta_{s,a_j}\\\\\n", + "&\\Delta \\theta_{s,a_j}=\\frac{1}T\\cdot \\left(N(s_i,a_j) - P(s_i,a_j)N(s_i,a)\\right)\n", + "\\end{split}\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "ExecuteTime": { + "end_time": "2023-02-15T16:24:35.773913Z", + "start_time": "2023-02-15T16:24:35.756275Z" + } + }, + "outputs": [], + "source": [ + "# 动作策略选择，基于当前环境的状态\n", + "class Agent:\n", + " def __init__(self):\n", + " self.actions = list(range(4))\n", + " self.theta_0 = np.asarray([[np.nan, 1, 1, np.nan], # s0\n", + " [np.nan, 1, np.nan, 1], # s1\n", + " [np.nan, np.nan, 1, 1], # s2\n", + " [1, np.nan, np.nan, np.nan], # s3 \n", + " [np.nan, 1, 1, np.nan], # s4\n", + " [1, np.nan, np.nan, 1], # s5\n", + " [np.nan, 1, np.nan, np.nan], # s6 \n", + " [1, 1, np.nan, 1]] # s7\n", + " )\n", + "# self.pi = self._cvt_theta_0_to_pi(self.theta_0)\n", + " self.theta = self.theta_0\n", + " self.pi = self._softmax_cvt_theta_to_pi()\n", + " \n", + " self.eta = 0.1\n", + " \n", + " def _cvt_theta_to_pi(self):\n", + " m, n = self.theta.shape\n", + " pi = np.zeros((m, n))\n", + " for r in range(m):\n", + " pi[r, :] = self.theta[r, :] / np.nansum(self.theta[r, :])\n", + " return np.nan_to_num(pi)\n", + " \n", + " def _softmax_cvt_theta_to_pi(self, beta=1.):\n", + " m, n = self.theta.shape\n", + " pi = np.zeros((m, n))\n", + " exp_theta = np.exp(self.theta*beta)\n", + " for r in range(m):\n", + " pi[r, :] = exp_theta[r, :] / np.nansum(exp_theta[r, :])\n", + " return np.nan_to_num(pi)\n", + " \n", + " def update_theta(self, s_a_history):\n", + " T = len(s_a_history) - 1\n", + " m, n = self.theta.shape\n", + " delta_theta = self.theta.copy()\n", + " for i in range(m):\n", + " for j in range(n):\n", + " if not(np.isnan(self.theta_0[i, j])):\n", + " sa_i = [sa for sa in s_a_history if sa[0] == i]\n", + " sa_ij = [sa for sa in s_a_history if (sa[0] == i and sa[1] == j)]\n", + " N_i = len(sa_i)\n", + " N_ij = len(sa_ij)\n", + " delta_theta[i, j] = (N_ij - self.pi[i, j]*N_i)/T\n", + " self.theta = self.theta + self.eta * delta_theta\n", + " return self.theta\n", + " \n", + " def update_pi(self):\n", + " self.pi = self._softmax_cvt_theta_to_pi()\n", + " return self.pi\n", + " \n", + " def choose_action(self, state):\n", + " # 依概率分布 \\pi_\\theta 选择 action\n", + " action = np.random.choice(self.actions, p=self.pi[state, :])\n", + " return action" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "ExecuteTime": { + "end_time": "2023-02-15T16:24:36.986021Z", + "start_time": "2023-02-15T16:24:36.982126Z" + } + }, + "outputs": [], + "source": [ + "env = MazeEnv()\n", + "agent = Agent()" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "ExecuteTime": { + "end_time": "2023-02-15T16:26:20.267851Z", + "start_time": "2023-02-15T16:26:20.265077Z" + } + }, + "outputs": [], + "source": [ + "state = env.state\n", + "# state, action\n", + "# trajectory\n", + "s_a_history = [[state, np.nan]]" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "ExecuteTime": { + "end_time": "2023-02-15T16:26:21.233154Z", + "start_time": "2023-02-15T16:26:21.224677Z" + } + }, + "outputs": [], + "source": [ + "while True:\n", + " action = agent.choose_action(state)\n", + " s_a_history[-1][1] = action\n", + " state, reward, done, _ = env.step(action)\n", + "# print(action, state, done)\n", + " s_a_history.append([state, np.nan])\n", + " if state == 8 or done:\n", + " break" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "ExecuteTime": { + "end_time": "2023-02-15T16:26:37.748993Z", + "start_time": "2023-02-15T16:26:37.745429Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "41" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(s_a_history)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## update $\\theta$ and $\\pi_\\theta$ base policy gradient" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "- $\\theta_{s_i, a_j} = \\theta_{s_i, a_j} + \\eta \\Delta\\theta_{s_i, a_j}$\n", + "- $\\Delta\\theta_{s_i, a_j}=\\frac{N(s_i, a_j)-P(s_i,a_j)\\cdot N(s_i, a)}{T}$" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "ExecuteTime": { + "end_time": "2023-02-15T16:26:59.409116Z", + "start_time": "2023-02-15T16:26:59.402036Z" + } + }, + "outputs": [], + "source": [ + "env = MazeEnv()\n", + "agent = Agent()\n", + "state = 0\n", + "# state, action\n", + "s_a_history = [[state, np.nan]]\n", + "while True:\n", + " action = agent.choose_action(state)\n", + " s_a_history[-1][1] = action\n", + " state, reward, done, _ = env.step(action)\n", + "# print(action, state, done)\n", + " s_a_history.append([state, np.nan])\n", + " if state == 8 or done:\n", + " break" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "ExecuteTime": { + "end_time": "2023-02-15T16:27:48.102978Z", + "start_time": "2023-02-15T16:27:48.095130Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ nan, 0.99852941, 1.00147059, nan],\n", + " [ nan, 1. , nan, 1. ],\n", + " [ nan, nan, 0.99926471, 1.00073529],\n", + " [1. , nan, nan, nan],\n", + " [ nan, 1.00220588, 0.99779412, nan],\n", + " [0.99926471, nan, nan, 1.00073529],\n", + " [ nan, 1. , nan, nan],\n", + " [0.9995098 , 1.00098039, nan, 0.9995098 ]])" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "agent.update_theta(s_a_history)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "ExecuteTime": { + "end_time": "2023-02-15T16:28:12.018602Z", + "start_time": "2023-02-15T16:28:12.009712Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[0. , 0.49926471, 0.50073529, 0. ],\n", + " [0. , 0.5 , 0. , 0.5 ],\n", + " [0. , 0. , 0.49963235, 0.50036765],\n", + " [1. , 0. , 0. , 0. ],\n", + " [0. , 0.50110294, 0.49889706, 0. ],\n", + " [0.49963235, 0. , 0. , 0.50036765],\n", + " [0. , 1. , 0. , 0. ],\n", + " [0.33316989, 0.33366021, 0. , 0.33316989]])" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "agent._softmax_cvt_theta_to_pi()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 完整训练及更新" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "ExecuteTime": { + "end_time": "2023-02-15T16:29:01.195968Z", + "start_time": "2023-02-15T16:29:01.193635Z" + } + }, + "outputs": [], + "source": [ + "stop_eps = 1e-4" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "ExecuteTime": { + "end_time": "2023-02-15T16:30:47.697768Z", + "start_time": "2023-02-15T16:30:37.677891Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": 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s_a_history = [[state, np.nan]]\n", + " while True:\n", + " action = agent.choose_action(state)\n", + " s_a_history[-1][1] = action\n", + " state, reward, done, _ = env.step(action)\n", + " # print(action, state, done)\n", + " s_a_history.append([state, np.nan])\n", + " if state == 8 or done:\n", + " break\n", + " \n", + " # 更新 theta\n", + " agent.update_theta(s_a_history)\n", + " pi = agent.pi.copy()\n", + " # 更新 pi\n", + " agent.update_pi()\n", + " \n", + " delta = np.sum(np.abs(agent.pi - pi))\n", + " print(len(s_a_history), delta)\n", + " if delta < stop_eps:\n", + " break" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "ExecuteTime": { + "end_time": "2023-02-15T16:31:12.707176Z", + "start_time": "2023-02-15T16:31:12.702580Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[0. , 0.98782525, 0.01217475, 0. ],\n", + " [0. , 0.98334014, 0. , 0.01665986],\n", + " [0. , 0. , 0.98558642, 0.01441358],\n", + " [1. , 0. , 0. , 0. ],\n", + " [0. , 0.01273671, 0.98726329, 0. ],\n", + " [0.01651377, 0. , 0. , 0.98348623],\n", + " [0. , 1. , 0. , 0. ],\n", + " [0.01417312, 0.97542647, 0. , 0.01040041]])" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "agent.pi" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "ExecuteTime": { + "end_time": "2023-02-15T16:32:30.039742Z", + "start_time": "2023-02-15T16:32:30.034230Z" + } + }, + "outputs": [], + "source": [ + "env = MazeEnv()\n", + "state = env.reset()\n", + "# state, action\n", + "s_a_history = [[state, np.nan]]\n", + "while True:\n", + " action = agent.choose_action(state)\n", + " s_a_history[-1][1] = action\n", + " state, reward, done, _ = env.step(action)\n", + "# print(action, state, done)\n", + " s_a_history.append([state, np.nan])\n", + " if state == 8 or done:\n", + " break" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "ExecuteTime": { + "end_time": "2023-02-15T16:32:42.568711Z", + "start_time": "2023-02-15T16:32:42.565306Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "7" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(s_a_history)" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "ExecuteTime": { + "end_time": "2023-02-15T16:32:49.888530Z", + "start_time": "2023-02-15T16:32:49.879945Z" + } + }, + "outputs": [], + "source": [ + "from matplotlib import animation\n", + "from IPython.display import HTML" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "ExecuteTime": { + "end_time": "2023-02-15T16:32:50.821265Z", + "start_time": "2023-02-15T16:32:50.814402Z" + } + }, + "outputs": [], + "source": [ + "def init():\n", + " line.set_data([], [])\n", + " return (line, )\n", + "def animate(i):\n", + " state = s_a_history[i][0]\n", + " x = (state % 3)+0.5\n", + " y = 2.5 - int(state/3)\n", + " line.set_data(x, y)" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "ExecuteTime": { + "end_time": "2023-02-15T16:32:58.428084Z", + "start_time": "2023-02-15T16:32:58.425058Z" + } + }, + "outputs": [], + "source": [ + "anim = animation.FuncAnimation(fig, animate, init_func=init, frames=len(s_a_history), interval=200, repeat=False)" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "ExecuteTime": { + "end_time": "2023-02-15T16:33:00.330427Z", + "start_time": "2023-02-15T16:32:59.624908Z" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "<link rel=\"stylesheet\"\n", + "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/\n", + "css/font-awesome.min.css\">\n", + "<script language=\"javascript\">\n", + " function isInternetExplorer() {\n", + " ua = navigator.userAgent;\n", + " /* MSIE used to detect old browsers and Trident used to newer ones*/\n", + " return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n", + " }\n", + "\n", + " /* Define the Animation class */\n", + " function Animation(frames, img_id, slider_id, interval, loop_select_id){\n", + " this.img_id = img_id;\n", + " this.slider_id = slider_id;\n", + " this.loop_select_id = loop_select_id;\n", + " this.interval = interval;\n", + " this.current_frame = 0;\n", + " this.direction = 0;\n", + " this.timer = null;\n", + " this.frames = new Array(frames.length);\n", + "\n", + " for (var i=0; i<frames.length; i++)\n", + " {\n", + " this.frames[i] = new Image();\n", + " this.frames[i].src = frames[i];\n", + " }\n", + " var slider = document.getElementById(this.slider_id);\n", + " slider.max = this.frames.length - 1;\n", + " if (isInternetExplorer()) {\n", + " // switch from oninput to onchange because IE <= 11 does not conform\n", + " // with W3C specification. It ignores oninput and onchange behaves\n", + " // like oninput. In contrast, Mircosoft Edge behaves correctly.\n", + " slider.setAttribute('onchange', slider.getAttribute('oninput'));\n", + " slider.setAttribute('oninput', null);\n", + " }\n", + " this.set_frame(this.current_frame);\n", + " }\n", + "\n", + " Animation.prototype.get_loop_state = function(){\n", + " var button_group = document[this.loop_select_id].state;\n", + " for (var i = 0; i < button_group.length; i++) {\n", + " var button = button_group[i];\n", + " if (button.checked) {\n", + " return button.value;\n", + " }\n", + " }\n", + " return undefined;\n", + " }\n", + "\n", + " Animation.prototype.set_frame = function(frame){\n", + " this.current_frame = frame;\n", + " document.getElementById(this.img_id).src =\n", + " this.frames[this.current_frame].src;\n", + " document.getElementById(this.slider_id).value = this.current_frame;\n", + " }\n", + "\n", + " Animation.prototype.next_frame = function()\n", + " {\n", + " this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n", + " }\n", + "\n", + " Animation.prototype.previous_frame = function()\n", + " {\n", + " this.set_frame(Math.max(0, this.current_frame - 1));\n", + " }\n", + "\n", + " Animation.prototype.first_frame = function()\n", + " {\n", + " this.set_frame(0);\n", + " }\n", + "\n", + " Animation.prototype.last_frame = function()\n", + " {\n", + " this.set_frame(this.frames.length - 1);\n", + " }\n", + "\n", + " Animation.prototype.slower = function()\n", + " {\n", + " this.interval /= 0.7;\n", + " if(this.direction > 0){this.play_animation();}\n", + " else if(this.direction < 0){this.reverse_animation();}\n", + " }\n", + "\n", + " Animation.prototype.faster = function()\n", + " {\n", + " this.interval *= 0.7;\n", + " if(this.direction > 0){this.play_animation();}\n", + " else if(this.direction < 0){this.reverse_animation();}\n", + " }\n", + "\n", + " Animation.prototype.anim_step_forward = function()\n", + " {\n", + " this.current_frame += 1;\n", + " if(this.current_frame < this.frames.length){\n", + " this.set_frame(this.current_frame);\n", + " }else{\n", + " var loop_state = this.get_loop_state();\n", + " if(loop_state == \"loop\"){\n", + " this.first_frame();\n", + " }else if(loop_state == \"reflect\"){\n", + " this.last_frame();\n", + " this.reverse_animation();\n", + " }else{\n", + " this.pause_animation();\n", + " this.last_frame();\n", + " }\n", + " }\n", + " }\n", + "\n", + " Animation.prototype.anim_step_reverse = function()\n", + " {\n", + " this.current_frame -= 1;\n", + " if(this.current_frame >= 0){\n", + " this.set_frame(this.current_frame);\n", + " }else{\n", + " var loop_state = this.get_loop_state();\n", + " if(loop_state == \"loop\"){\n", + " this.last_frame();\n", + " }else if(loop_state == \"reflect\"){\n", + " this.first_frame();\n", + " this.play_animation();\n", + " }else{\n", + " this.pause_animation();\n", + " this.first_frame();\n", + " }\n", + " }\n", + " }\n", + "\n", + " Animation.prototype.pause_animation = function()\n", + " {\n", + " this.direction = 0;\n", + " if (this.timer){\n", + " clearInterval(this.timer);\n", + " this.timer = null;\n", + " }\n", + " }\n", + "\n", + " Animation.prototype.play_animation = function()\n", + " {\n", + " this.pause_animation();\n", + " this.direction = 1;\n", + " var t = this;\n", + " if (!this.timer) this.timer = setInterval(function() {\n", + " t.anim_step_forward();\n", + " }, this.interval);\n", + " }\n", + "\n", + " Animation.prototype.reverse_animation = function()\n", + " {\n", + " this.pause_animation();\n", + " this.direction = -1;\n", + " var t = this;\n", + " if (!this.timer) this.timer = setInterval(function() {\n", + " t.anim_step_reverse();\n", + " }, this.interval);\n", + " }\n", + "</script>\n", + "\n", + "<style>\n", + ".animation {\n", + " display: inline-block;\n", + " text-align: center;\n", + "}\n", + "input[type=range].anim-slider {\n", + " width: 374px;\n", + " margin-left: auto;\n", + " margin-right: auto;\n", + "}\n", + ".anim-buttons {\n", + " margin: 8px 0px;\n", + "}\n", + ".anim-buttons button {\n", + " padding: 0;\n", + " width: 36px;\n", + "}\n", + ".anim-state label {\n", + " margin-right: 8px;\n", + "}\n", + ".anim-state input {\n", + " margin: 0;\n", + " vertical-align: middle;\n", + "}\n", + "</style>\n", + "\n", + "<div class=\"animation\">\n", + " <img id=\"_anim_img08373f47b35a4575bca30f51c4dc2174\">\n", + " <div class=\"anim-controls\">\n", + " <input id=\"_anim_slider08373f47b35a4575bca30f51c4dc2174\" type=\"range\" class=\"anim-slider\"\n", + " name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n", + " oninput=\"anim08373f47b35a4575bca30f51c4dc2174.set_frame(parseInt(this.value));\"></input>\n", + " <div class=\"anim-buttons\">\n", + " <button onclick=\"anim08373f47b35a4575bca30f51c4dc2174.slower()\"><i class=\"fa fa-minus\"></i></button>\n", + " <button onclick=\"anim08373f47b35a4575bca30f51c4dc2174.first_frame()\"><i class=\"fa fa-fast-backward\">\n", + " </i></button>\n", + " <button onclick=\"anim08373f47b35a4575bca30f51c4dc2174.previous_frame()\">\n", + " <i class=\"fa fa-step-backward\"></i></button>\n", + " <button onclick=\"anim08373f47b35a4575bca30f51c4dc2174.reverse_animation()\">\n", + " <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n", + " <button onclick=\"anim08373f47b35a4575bca30f51c4dc2174.pause_animation()\"><i class=\"fa fa-pause\">\n", + " </i></button>\n", + " <button onclick=\"anim08373f47b35a4575bca30f51c4dc2174.play_animation()\"><i class=\"fa fa-play\"></i>\n", + " </button>\n", + " <button onclick=\"anim08373f47b35a4575bca30f51c4dc2174.next_frame()\"><i class=\"fa fa-step-forward\">\n", + " </i></button>\n", + " <button onclick=\"anim08373f47b35a4575bca30f51c4dc2174.last_frame()\"><i class=\"fa fa-fast-forward\">\n", + " </i></button>\n", + " <button onclick=\"anim08373f47b35a4575bca30f51c4dc2174.faster()\"><i class=\"fa fa-plus\"></i></button>\n", + " </div>\n", + " <form action=\"#n\" name=\"_anim_loop_select08373f47b35a4575bca30f51c4dc2174\" class=\"anim-state\">\n", + " <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_08373f47b35a4575bca30f51c4dc2174\"\n", + " checked>\n", + " <label for=\"_anim_radio1_08373f47b35a4575bca30f51c4dc2174\">Once</label>\n", + " <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_08373f47b35a4575bca30f51c4dc2174\"\n", + " >\n", + " <label for=\"_anim_radio2_08373f47b35a4575bca30f51c4dc2174\">Loop</label>\n", + " <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_08373f47b35a4575bca30f51c4dc2174\"\n", + " >\n", + " <label for=\"_anim_radio3_08373f47b35a4575bca30f51c4dc2174\">Reflect</label>\n", + " </form>\n", + " </div>\n", + "</div>\n", + "\n", + "\n", + "<script language=\"javascript\">\n", + " /* Instantiate the Animation class. */\n", + " /* The IDs given should match those used in the template above. */\n", + " (function() {\n", + " var img_id = 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