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{
"metadata": {
"name": "",
"signature": "sha256:f6b2be254b338b92e0cfbb6a454fd0146d0da75b9f95c693baa98c3901d06d95"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"%matplotlib inline\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Aliasing** \n",
"The code below plots sine waves of a given frequency, along with their representation on a grid with $m$ points. Try changing $p$ and notice how for $m<2p$ the function looks identical to that for $2(m+1)-p$ due to aliasing. "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from matplotlib import animation\n",
"import matplotlib.pyplot as plt\n",
"from clawpack.visclaw.JSAnimation import IPython_display\n",
"\n",
"fig = plt.figure()\n",
"ax = plt.axes(xlim=(0, 1), ylim=(-1.2, 1.2))\n",
"\n",
"m=20\n",
"x=np.linspace(0,1,m+2); # grid\n",
"xf=np.linspace(0,1,1000) # fine grid\n",
"\n",
"line1, = ax.plot([],[], '-r', lw=2)\n",
"line2, = ax.plot([],[],'o-',lw=2)\n",
"\n",
"def fplot(p):\n",
" line1.set_data(xf, np.sin(p*np.pi*xf))\n",
" line2.set_data(x,np.sin(p*np.pi*x))\n",
" ax.set_title('p='+str(p))\n",
" return line2,\n",
"\n",
"anim = animation.FuncAnimation(fig, fplot, frames=range(0,44))\n",
"IPython_display.display_animation(anim, show_buttons=True)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"\n",
"<script language=\"javascript\">\n",
" /* Define the Animation class */\n",
" function Animation(frames, img_id, slider_id, frame_id, interval, loop_select_id){\n",
" this.img_id = img_id;\n",
" this.slider_id = slider_id;\n",
" this.frame_id = frame_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",
" document.getElementById(this.slider_id).max = this.frames.length - 1;\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 = this.frames[this.current_frame].src;\n",
" document.getElementById(this.slider_id).value = this.current_frame;\n",
" document.getElementById(this.frame_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(){t.anim_step_forward();}, 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(){t.anim_step_reverse();}, this.interval);\n",
" }\n",
"</script>\n",
"\n",
"<div class=\"animation\" align=\"center\">\n",
" <img id=\"_anim_imgbfef9ea27398dd5c\" style=\"width:Nonepx\">\n",
" <br>\n",
" <input id=\"_anim_sliderbfef9ea27398dd5c\" type=\"range\" style=\"width:350px\" name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\" onchange=\"animbfef9ea27398dd5c.set_frame(parseInt(this.value));\"></input>\n",
" <br>\n",
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"rV+/blxKMZUnLgAAAABJRU5ErkJggg==\n",
"\"></button>\n",
" <button onclick=\"animbfef9ea27398dd5c.previous_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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"\"></button>\n",
" <button onclick=\"animbfef9ea27398dd5c.reverse_animation()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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"RK5CYII=\n",
"\"></button>\n",
" <button onclick=\"animbfef9ea27398dd5c.pause_animation()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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"AABJRU5ErkJggg==\n",
"\"></button>\n",
" <button onclick=\"animbfef9ea27398dd5c.play_animation()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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"\"></button>\n",
" <button onclick=\"animbfef9ea27398dd5c.next_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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"qNIwUMDAwMDAsADKS2NkGL4AAIARMlfNIfZMAAAAAElFTkSuQmCC\n",
"\"></button>\n",
" <button onclick=\"animbfef9ea27398dd5c.last_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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"FnSONdiL8Qci0lzwpOM5sQAAAABJRU5ErkJggg==\n",
"\"></button>\n",
" <button onclick=\"animbfef9ea27398dd5c.faster()\">+</button>\n",
" <form action=\"#n\" name=\"_anim_loop_selectbfef9ea27398dd5c\" class=\"anim_control\">\n",
"\n",
" <input id=\"_frame_nobfef9ea27398dd5c\" type=\"textbox\" size=\"1\" onchange=\"animbfef9ea27398dd5c.set_frame(parseInt(this.value));\" onpaste=\"this.onchange();\" oninput=\"this.onchange();\"></input>\n",
" \n",
" <input type=\"radio\" name=\"state\" value=\"once\" > Once </input>\n",
" <input type=\"radio\" name=\"state\" value=\"loop\" checked> Loop </input>\n",
" <input type=\"radio\" name=\"state\" value=\"reflect\" > Reflect </input>\n",
" </form>\n",
"\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 = \"_anim_imgbfef9ea27398dd5c\";\n",
" var slider_id = \"_anim_sliderbfef9ea27398dd5c\";\n",
" var frame_id = \"_frame_nobfef9ea27398dd5c\"\n",
" var loop_select_id = \"_anim_loop_selectbfef9ea27398dd5c\";\n",
" var frames = new Array(0);\n",
" \n",
" frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAbAAAAEgCAYAAADVKCZpAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\\\n",
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