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domitry/hoge.ipynb

Last active August 29, 2015 14:23
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hoge.ipynb
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from math import pi, sin, cos"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 単振り子をオイラー法で解いてみる"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"time = []\n",
"result = []\n",
"l = 30.\n",
"g = 9.8\n",
"theta = 0\n",
"d_theta = 0.1\n",
"h = 1e-3\n",
"for i in xrange(0, 50000):\n",
" new_theta = theta + h*d_theta\n",
" d_theta = d_theta-h*(g/l)*sin(theta)\n",
" theta = new_theta\n",
" result.append(theta)\n",
" time.append(i*h)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f904b36ddd0>]"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x7f906592b8d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"from matplotlib import pylab\n",
"pylab.plot(time, result)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from draw import *"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<html>\n",
" <head>\n",
" <script type=\"text/javascript\">\n",
" if(typeof window.Draw == \"undefined\"){\n",
" window.Draw = {};\n",
"\n",
" require.config({\n",
" paths: {\n",
" d3: \"https://cdnjs.cloudflare.com/ajax/libs/d3/3.5.5/d3.min\",\n",
" underscore: \"http://underscorejs.org/underscore\"\n",
" }\n",
" });\n",
"\n",
" require([\"underscore\", \"d3\"], function(_, d3){\n",
" IPython.notebook.kernel.comm_manager.register_target(\"Draw\", function(comm){\n",
" window.Draw.comm = comm;\n",
"\n",
" comm.on_msg(function(msg){\n",
" var mdata = msg.content.data;\n",
" var svg = d3.select(\"#\" + mdata[\"canvas_id\"]);\n",
"\n",
" if(!_.isUndefined(svg)){\n",
" /***********************************\n",
" msg = {\n",
" queue: [{\n",
" method: \"append\",\n",
" type: \"rect\"\n",
" attr: {\n",
" width: \n",
" height: \n",
" }\n",
" selector_id: \"1234-5678-9\"\n",
" }]\n",
" }\n",
" ***********************************/\n",
" _.each(mdata[\"queue\"], function(m){\n",
" switch(m.method){\n",
" case \"append\":\n",
" var node = svg.append(m.type).attr(\"id\", m.selector_id);\n",
" break;\n",
" case \"update\":\n",
" var node = d3.select(\"#\" + m.selector_id);\n",
" break;\n",
" case \"delete\":\n",
" var node = d3.select(\"#\" + m.selector_id);\n",
" node.remove();\n",
" break;\n",
" }\n",
"\n",
" if(m.css)node.style(m.css);\n",
" if(m.attr)node.attr(m.attr);\n",
" });\n",
" }\n",
" });\n",
" });\n",
" });\n",
" }\n",
" </script>\n",
" </head>\n",
" <body>\n",
" <svg id=\"canvasc0c9bcd7-a670-46b6-a7dc-efdfc1d8cf8f\" style=\"width: 500px; background-color: white; height: 500px\">\n",
" </svg>\n",
" </body>\n",
"</html>"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"theta = pi/4\n",
"c = Canvas()\n",
"c.add(Circle(250+200*sin(theta), 200*cos(theta), 20, fill=\"#000\"))\n",
"l = Line(250, 0, 250+200*sin(theta), 200*cos(theta))\n",
"c.add(l)\n",
"c.add(Line(0, 0, 500, 0))\n",
"c.show()"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false,
"scrolled": false
},
"outputs": [
{
"data": {
"text/html": [
"<html>\n",
" <head>\n",
" <script type=\"text/javascript\">\n",
" if(typeof window.Draw == \"undefined\"){\n",
" window.Draw = {};\n",
"\n",
" require.config({\n",
" paths: {\n",
" d3: \"https://cdnjs.cloudflare.com/ajax/libs/d3/3.5.5/d3.min\",\n",
" underscore: \"http://underscorejs.org/underscore\"\n",
" }\n",
" });\n",
"\n",
" require([\"underscore\", \"d3\"], function(_, d3){\n",
" IPython.notebook.kernel.comm_manager.register_target(\"Draw\", function(comm){\n",
" window.Draw.comm = comm;\n",
"\n",
" comm.on_msg(function(msg){\n",
" var mdata = msg.content.data;\n",
" var svg = d3.select(\"#\" + mdata[\"canvas_id\"]);\n",
"\n",
" if(!_.isUndefined(svg)){\n",
" /***********************************\n",
" msg = {\n",
" queue: [{\n",
" method: \"append\",\n",
" type: \"rect\"\n",
" attr: {\n",
" width: \n",
" height: \n",
" }\n",
" selector_id: \"1234-5678-9\"\n",
" }]\n",
" }\n",
" ***********************************/\n",
" _.each(mdata[\"queue\"], function(m){\n",
" switch(m.method){\n",
" case \"append\":\n",
" var node = svg.append(m.type).attr(\"id\", m.selector_id);\n",
" break;\n",
" case \"update\":\n",
" var node = d3.select(\"#\" + m.selector_id);\n",
" break;\n",
" case \"delete\":\n",
" var node = d3.select(\"#\" + m.selector_id);\n",
" node.remove();\n",
" break;\n",
" }\n",
"\n",
" if(m.css)node.style(m.css);\n",
" if(m.attr)node.attr(m.attr);\n",
" });\n",
" }\n",
" });\n",
" });\n",
" });\n",
" }\n",
" </script>\n",
" </head>\n",
" <body>\n",
" <svg id=\"canvasa727f97e-4470-454e-96ae-757f364d8a81\" style=\"width: 500px; background-color: white; height: 500px\">\n",
" </svg>\n",
" </body>\n",
"</html>"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from math import pi, sin, cos\n",
"theta = result[0]\n",
"c = Canvas()\n",
"cr = Circle(250+200*sin(theta), 200*cos(theta), 20, fill=\"#000\")\n",
"l = Line(250, 0, 250+200*sin(theta), 200*cos(theta))\n",
"c.add(cr)\n",
"c.add(l)\n",
"c.add(Line(0, 0, 500, 0))\n",
"c.interval = 0.0005\n",
"\n",
"def func(i):\n",
" if(i > len(result)):\n",
" c.timer.stop = True\n",
" return\n",
" new_x = 250+200*sin(result[i])\n",
" new_y = 200*cos(result[i])\n",
" cr.update(cx=new_x, cy=new_y)\n",
" l.update(x2=new_x, y2=new_y)\n",
"\n",
"c.loop(func)\n",
"c.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"c.stop = True"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Lorenz Attractor"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"x_arr = []\n",
"y_arr = []\n",
"z_arr = []\n",
"p=10\n",
"r=28\n",
"b=8./3\n",
"x=1e-3\n",
"y=1e-3\n",
"z=1e-3\n",
"for i in xrange(0, 50000):\n",
" new_x = x + h*(-p*x+p*y)\n",
" new_y = y + h*(-x*z + r*x - y)\n",
" new_z = z + h*(x*y - b*z)\n",
" x_arr.append(new_x)\n",
" y_arr.append(new_y)\n",
" z_arr.append(new_z)\n",
" x = new_x\n",
" y = new_y\n",
" z = new_z"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"pylab.plot(x_arr, z_arr)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import numpy as np\n",
"def dsolve1(x0, func, num, h):\n",
" result = np.zeros((num, len(x0)))\n",
" for i in xrange(0, num):\n",
" x = x0 + h*func(x0)\n",
" result[i] = x\n",
" x0 = x\n",
" return result"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def f(y):\n",
" return np.array([\n",
" -p*y[0]+p*y[1],\n",
" -y[0]*y[2] + r*y[0] - y[1],\n",
" y[0]*y[1] - b*y[2]\n",
" ])"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"result = dsolve1(np.array([1e-3, 1e-3, 1e-3]), f, 50000, 1e-3)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"t = result.transpose()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"pylab.plot(t[0], t[2])"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [],
"source": [
"length = 50000\n",
"h = 1e-3\n",
"arr1 = dsolve1(np.array([0.0, 1.0]), lambda x: np.array([x[1], -x[0]]), length, h)\n",
"arr2 = np.array([sin(h*i) for i in range(0, length)])\n",
"pylab.plot(arr1.transpose()[0])\n",
"pylab.plot(arr2)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [],
"source": [
"pylab.plot(arr1.transpose()[0] - arr2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# RK4"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def dsolve2(x0, func, num, h):\n",
" result = np.zeros((num, len(x0)))\n",
" for i in xrange(0, num):\n",
" k1 = func(x0)\n",
" k2 = func(x0 + (h/2)*k1)\n",
" k3 = func(x0 + (h/2)*k2)\n",
" k4 = func(x0 + h*k3)\n",
" x = x0 + (h/6)*(k1 + 2*k2 + 2*k3 + k4)\n",
" result[i] = x\n",
" x0 = x\n",
" return result"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"length = 50000\n",
"h = 1e-3\n",
"arr1 = dsolve2(np.array([0.0, 1.0]), lambda x: np.array([x[1], -x[0]]), length, h)\n",
"arr2 = np.array([sin(h*i) for i in range(0, length)])\n",
"pylab.plot(arr1.transpose()[0])\n",
"pylab.plot(arr2)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"pylab.plot(arr1.transpose()[0] - arr2)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.9"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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