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"cells": [
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Warning!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This example notebook is not up-to-date with the latest version of Plotly's Python API (version 1.0.\\*). \n",
"\n",
"Refer to Plotly's Python [User Guide](http://nbviewer.ipython.org/github/plotly/python-user-guide/blob/master/s00_homepage/s00_homepage.ipynb) \n",
"and more specifically [section 7.2](http://nbviewer.ipython.org/github/plotly/python-user-guide/blob/master/s7_streaming/s7_streaming_p2-double-pendulum.ipynb) for an updated version of this notebook.\n",
"\n",
"
"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Graphing the Double Pendulum Trajectory
\n",
"with Plotly's Real-time Streaming API"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Plotly's Streaming API enables your plotly graphs to update in real-time, without refreshing your browser.\n",
"\n",
"All viewers of the graph see the same data, at the same time.\n",
"\n",
"Learn more about real-time streaming graphs with plotly here:\n",
"\n",
"[https://github.com/plotly/streaming-demos](https://github.com/plotly/streaming-demos)"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import plotly\n",
"import time\n",
"import json\n",
"import math\n",
"from numpy import sin, cos, pi, array\n",
"import numpy as np\n",
"import scipy.integrate as integrate"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Fill in the config.json file in this directory with your plotly username, \n",
"# plotly API key, and your generated plotly streaming tokens\n",
"# Sign up to plotly here: https://plot.ly/ssu\n",
"# View your API key and streaming tokens here: https://plot.ly/settings\n",
"\n",
"with open('./config.json') as config_file:\n",
" plotly_user_config = json.load(config_file)\n",
"\n",
"username = \"Streaming-Demos\" # plotly_user_config['plotly_username'] \n",
"api_key = plotly_user_config['plotly_api_key']\n",
"stream_tokens = plotly_user_config['plotly_streaming_tokens']"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Initialize your plotly object\n",
"p = plotly.plotly(username, api_key)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Define the Double Pendulum state equations and parameters\n",
"# Code adapted from http://matplotlib.org/examples/animation/double_pendulum_animated.html (Thx!)\n",
"\n",
"G = 9.8 # acceleration due to gravity, in m/s^2\n",
"L1 = 1.0 # length of pendulum 1 in m\n",
"L2 = 1.0 # length of pendulum 2 in m\n",
"M1 = 1.0 # mass of pendulum 1 in kg\n",
"M2 = 1.0 # mass of pendulum 2 in kg\n",
"\n",
"\n",
"def derivs(state, t):\n",
"\n",
" dydx = np.zeros_like(state)\n",
" dydx[0] = state[1]\n",
"\n",
" del_ = state[2]-state[0]\n",
" den1 = (M1+M2)*L1 - M2*L1*cos(del_)*cos(del_)\n",
" dydx[1] = (M2*L1*state[1]*state[1]*sin(del_)*cos(del_)\n",
" + M2*G*sin(state[2])*cos(del_) + M2*L2*state[3]*state[3]*sin(del_)\n",
" - (M1+M2)*G*sin(state[0]))/den1\n",
"\n",
" dydx[2] = state[3]\n",
"\n",
" den2 = (L2/L1)*den1\n",
" dydx[3] = (-M2*L2*state[3]*state[3]*sin(del_)*cos(del_)\n",
" + (M1+M2)*G*sin(state[0])*cos(del_)\n",
" - (M1+M2)*L1*state[1]*state[1]*sin(del_)\n",
" - (M1+M2)*G*sin(state[2]))/den2\n",
"\n",
" return dydx\n",
"\n",
"# th1 and th2 are the initial angles (degrees)\n",
"# w10 and w20 are the initial angular velocities (degrees per second)\n",
"th1 = 120.0\n",
"w1 = 0.0\n",
"th2 = -10.0\n",
"w2 = 0.0\n",
"\n",
"rad = pi/180"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Initialize your plotly real-time streaming graph with a REST API call\n",
"# Embed your stream token in one of the traces of a plotly-data object - one token per trace\n",
"# Also embed 'maxpoints', the number of points that you want plotted at a time\n",
"\n",
"# The `iplot` command will embed our plotly graph as an iframe in this notebook\n",
"# Each plotly graph has a unique url that you can share \n",
"# Anyone can view your streaming graph in real-time - \n",
"# viewers see the same data at the same time \n",
"# (try it! Open up this notebook up in two different browser windows and observer\n",
"# that the graphs are plotting identical data!)\n",
"\n",
"# The unique URL for this graph is https://plot.ly/~streaming-demos/4\n",
"\n",
"def axes(range):\n",
" return {\n",
" \"autotick\" : True,\n",
" \"showgrid\" : False,\n",
" \"showline\" : False,\n",
" \"zeroline\" : False,\n",
" \"ticks\": '', \n",
" \"range\": range\n",
" }\n",
"p.iplot([\n",
" {\n",
" 'x': [], \n",
" 'y': [], \n",
" 'type': 'scatter', \n",
" 'mode': 'lines+markers', \n",
" 'line': {\n",
" 'opacity': 0.8\n",
" },\n",
" 'marker': {\n",
" 'size': 12\n",
" },\n",
" 'stream': {\n",
" 'token': stream_tokens[4], \n",
" }\n",
" },\n",
" {\n",
" 'x': [], \n",
" 'y': [], \n",
" 'type': 'scatter', \n",
" 'mode': 'lines', \n",
" 'line': {\n",
" 'color': 'rgba(31, 119, 180, 0.15)'\n",
" },\n",
" 'stream': {\n",
" 'token': stream_tokens[5], \n",
" 'maxpoints': 100\n",
" }\n",
" }],\n",
" layout = {\n",
" 'xaxis': axes([-2, 2]), \n",
" 'yaxis': axes([-2, 0.5]), \n",
" 'title': 'Double Pendulum Simulation',\n",
" 'showlegend': False\n",
" },\n",
" filename='streaming double pendulum', fileopt='overwrite')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
""
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 5,
"text": [
""
]
}
],
"prompt_number": 5
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Now stream data to this plot!\n",
"# Write to a plotly stream with plotly-formatted data\n",
"# In this case, we'll continually integrate the double pendulum equations 20 points a time, \n",
"# and write the solution, one point at a time\n",
"\n",
"# Our plotly-object is formatted as: {'x': x_data, 'y': y_data}\n",
"\n",
"s0 = plotly.stream(stream_tokens[4])\n",
"s1 = plotly.stream(stream_tokens[5])\n",
"state = np.array([th1, w1, th2, w2])*pi/180.\n",
"while True:\n",
" # create a time array from 0..100 sampled at 0.1 second steps\n",
" dt = 0.05\n",
" t = np.arange(0.0, 20, dt)\n",
" # solve!\n",
" y = integrate.odeint(derivs, state, t)\n",
" x1 = L1*sin(y[:,0])\n",
" y1 = -L1*cos(y[:,0])\n",
" x2 = L2*sin(y[:,2]) + x1\n",
" y2 = -L2*cos(y[:,2]) + y1\n",
" # Write the solution to plotly's servers, one point at a time\n",
" for (x1i, y1i, x2i, y2i) in zip(x1, y1, x2, y2):\n",
" s0.write({'x': [0, x1i, x2i], 'y': [0, y1i, y2i]})\n",
" s1.write({'x': x2i, 'y': y2i})\n",
" time.sleep(0.08) # plot points 80 ms at a time\n",
"\n",
" # Set the new initial state\n",
" state = np.array([y[-1,0], y[-1, 1], y[-1, 2], y[-1, 3]])"
],
"language": "python",
"metadata": {},
"outputs": []
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# When you're done, close your stream!\n",
"s.close()"
],
"language": "python",
"metadata": {},
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Give it a try yourself!\n",
"\n",
"##### More Streaming IPython Notebooks:\n",
"\n",
"[http://nbviewer.ipython.org/github/plotly/Streaming-Demos/tree/master/IPython%20examples/](http://nbviewer.ipython.org/github/plotly/Streaming-Demos/tree/master/IPython%20examples/)\n",
"\n",
"##### More about Plotly Streaming \n",
"\n",
"[https://github.com/plotly/Streaming-Demos](https://github.com/plotly/Streaming-Demos)\n",
"\n",
"##### Get in touch!\n",
"\n",
"[http://twitter.com/plotlygraphs](@plotlygraphs)\n",
"\n",
"[https://facebook.com/plotly](https://facebook.com/plotly)\n",
"\n",
""
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# CSS styling within IPython notebook\n",
"from IPython.core.display import HTML\n",
"import urllib2\n",
"def css_styling():\n",
" url = 'https://raw.githubusercontent.com/plotly/python-user-guide/master/custom.css'\n",
" styles = urllib2.urlopen(url).read()\n",
" return HTML(styles)\n",
"\n",
"css_styling()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"\n",
"\n"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 2,
"text": [
""
]
}
],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}