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nicoguaro/cuerda_rigida.ipynb

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FEM code for a stiff string
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cuerda_rigida.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Pulso viajando en una cuerda rígida\n",
"\n",
"\n",
"## Problema\n",
"\n",
"Se quiere resolver la ecuación\n",
"\n",
"$$T\\frac{\\partial^2 w}{\\partial x^2} - EI\\frac{\\partial^2 u(x, t)}{\\partial x^2}\n",
"= \\mu \\frac{\\partial^2 u(x, t)}{\\partial t^2})\\, ,$$\n",
"\n",
"para $x\\in [0, L]$, con\n",
"\n",
"\\begin{align}\n",
"&u(x, 0) = g(x)\\\\\n",
"&\\frac{\\partial u(x, 0)}{\\partial t} = h(x)\\\\\n",
"&u(0, t) = u(L, t) = 0\\, ,\\\\\n",
"&\\frac{\\partial u(0, t)}{\\partial x} =\n",
"\\frac{u(L, t)}{\\partial x} = 0\\, ,\\\\\n",
"\\end{align}\n",
"\n",
"## Esquema de solución\n",
"\n",
"Al discretizar usando elementos finitos obtenemos el siguiente sistema\n",
"\n",
"$$[M]\\{\\ddot{\\mathbf{u}}\\} + [K]\\{\\mathbf{u}\\}\n",
"= \\{\\mathbf{0}\\}\\, ,$$\n",
"\n",
"y usando una diferencia finita (implícita) en el tiempo, obtenemos\n",
"\n",
"$$[M + \\Delta t^2 K]\\{\\mathbf{u}^{n+1}\\}\n",
"= [M]\\{2\\mathbf{u}^n - \\mathbf{u}^{n - 1}\\}\\, .$$\n",
"\n",
"Y para la primera iteración sería\n",
"\n",
"\n",
"$$[2M + \\Delta t^2 K]\\{\\mathbf{u}^{n+1}\\}\n",
"= 2[M]\\{2\\mathbf{u}^0 + \\Delta t\\mathbf{v}^{0}\\}\\, .$$\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import matplotlib.animation as animation\n",
"import matplotlib.font_manager as fm"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib notebook\n",
"\n",
"plt.style.use(\"https://raw.githubusercontent.com/nicoguaro/matplotlib_styles/master/styles/neon.mplstyle\")\n",
"fpath = \"./texgyreadventor-regular.otf\"\n",
"prop = fm.FontProperties(fname=fpath)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"def stiff_string_ele(coord_el, params):\n",
" k, EI, mu = params\n",
" L = coord_el[1] - coord_el[0]\n",
" stiff_loc = EI/L**3 * np.array([\n",
" [12, 6*L, -12, 6*L],\n",
" [6*L, 4*L**2, -6*L, 2*L**2],\n",
" [-12, -6*L, 12, -6*L],\n",
" [6*L, 2*L**2, -6*L, 4*L**2]])\\\n",
" + k/(30*L) * np.array([\n",
" [36, 3*L, -36, 3*L],\n",
" [3*L, 4*L**2, -3*L, -L**2],\n",
" [-36, -3*L, 36, -3*L],\n",
" [3*L, -L**2, -3*L, 4*L**2]])\n",
" mass = mu * L\n",
" mass_loc = mass/420*np.array([\n",
" [156, 22*L, 54, -13*L],\n",
" [22*L, 4*L**2, 13*L, -3*L**2],\n",
" [54, 13*L, 156, -22*L],\n",
" [-13*L, -3*L**2, -22*L, 4*L**2]])\n",
" return stiff_loc, mass_loc"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"def assem(coords, params):\n",
" \"\"\"\n",
" Ensambla la matriz de rigidez y el vector de cargas\n",
" \n",
" Parámetros\n",
" ----------\n",
" coords : ndarray, float\n",
" Coordenadas de los nodos.\n",
" params : ndarray, float\n",
" Parámetros de la viga\n",
" \n",
" Retorna\n",
" -------\n",
" stiff : ndarray, float\n",
" Matriz de rigidez del problema.\n",
" mass : ndarray, float\n",
" Matriz de masa del problema.\n",
" \"\"\"\n",
" ncoords = coords.shape[0]\n",
" stiff = np.zeros((2*ncoords, 2*ncoords))\n",
" mass = np.zeros((2*ncoords, 2*ncoords))\n",
" elems = [np.array([cont, cont + 1]) for cont in range(0, ncoords - 1)]\n",
" for el_cont, elem in enumerate(elems):\n",
" stiff_loc, mass_loc = stiff_string_ele(coords[elem], params)\n",
" dofs = [2*elem[0], 2*elem[0] + 1, 2*elem[1], 2*elem[1] + 1]\n",
" for row in range(4):\n",
" for col in range(4):\n",
" row_glob, col_glob = dofs[row], dofs[col]\n",
" stiff[row_glob, col_glob] += stiff_loc[row, col]\n",
" mass[row_glob, col_glob] += mass_loc[row, col]\n",
" return stiff, mass"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"# Condiciones iniciales\n",
"def desp_inicial(x):\n",
" \"\"\"Desplazamiento inicial de la viga\"\"\"\n",
" return np.exp(-1000*(x - 0.5)**2)\n",
"\n",
"\n",
"def vel_inicial(x):\n",
" \"\"\"Velocidad inicial de la viga\"\"\"\n",
" return np.zeros_like(x)\n",
"\n",
"npuntos = 500\n",
"x = np.linspace(0, 1, npuntos)\n",
"k = 1\n",
"mu = 1\n",
"EI = 0.1\n",
"params = k, EI, mu"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"stiff, mass = assem(x, params)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"dt = 0.001\n",
"niter = 200"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"u_total = np.zeros((2*x.shape[0], niter))\n",
"u_total[::2, 0] = desp_inicial(x)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"caso = \"fijo\"\n",
"if caso == \"patin\":\n",
" pts_libres = range(2, 2*npuntos - 1)\n",
"elif caso == \"voladizo\":\n",
" pts_libres = range(2, 2*npuntos) \n",
"else:\n",
" pts_libres = range(2, 2*npuntos - 2)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"# Primera iteración\n",
"A = 2*mass[np.ix_(pts_libres, pts_libres)] + dt**2*stiff[np.ix_(pts_libres, pts_libres)]\n",
"b = 2*(mass @ u_total[:, 0])[pts_libres]\n",
"u_total[pts_libres, 1] = np.linalg.solve(A, b)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"A = mass[np.ix_(pts_libres, pts_libres)] + dt**2*stiff[np.ix_(pts_libres, pts_libres)]\n",
"for cont in range(2, niter):\n",
" b = (mass @ (2*u_total[:, cont-1] - u_total[:, cont-2]))[pts_libres]\n",
" sol_aux = np.linalg.solve(A, b)\n",
" u_total[pts_libres, cont] = sol_aux"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"def update(data, ax):\n",
" line = neon_plot(x, data[0::2], ax)\n",
" return line"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"def neon_plot(x, y, ax=None):\n",
" if ax is None:\n",
" ax = plt.gca()\n",
" ax.clear()\n",
" line, = ax.plot(x, y, lw=1, zorder=6)\n",
" for cont in range(6, 1, -1):\n",
" ax.plot(x, y, lw=cont, color=line.get_color(), zorder=5,\n",
" alpha=0.05)\n",
" plt.plot([0, 0], [-1, 1],\n",
" color='#F241A3', alpha=0.5)\n",
" plt.plot([1, 1], [-1, 1],\n",
" color='#F241A3', alpha=0.5)\n",
" ax.set_ylim(-1.2, 1.2)\n",
" plt.xticks([])\n",
" plt.yticks([])\n",
" plt.axis(\"off\")\n",
" plt.text(1.1, -1.4, \"@nicoguaro\", fontsize=18,\n",
" horizontalalignment='right',\n",
" fontproperties=prop, alpha=0.7)\n",
" return line"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"scrolled": true
},
"outputs": [
{
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"\n",
"mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n",
" // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
" // which will in turn request a refresh of the image.\n",
" this.send_message('resize', { width: x_pixels, height: y_pixels });\n",
"};\n",
"\n",
"mpl.figure.prototype.send_message = function (type, properties) {\n",
" properties['type'] = type;\n",
" properties['figure_id'] = this.id;\n",
" this.ws.send(JSON.stringify(properties));\n",
"};\n",
"\n",
"mpl.figure.prototype.send_draw_message = function () {\n",
" if (!this.waiting) {\n",
" this.waiting = true;\n",
" this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n",
" }\n",
"};\n",
"\n",
"mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
" var format_dropdown = fig.format_dropdown;\n",
" var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
" fig.ondownload(fig, format);\n",
"};\n",
"\n",
"mpl.figure.prototype.handle_resize = function (fig, msg) {\n",
" var size = msg['size'];\n",
" if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n",
" fig._resize_canvas(size[0], size[1], msg['forward']);\n",
" fig.send_message('refresh', {});\n",
" }\n",
"};\n",
"\n",
"mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
" var x0 = msg['x0'] / fig.ratio;\n",
" var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
" var x1 = msg['x1'] / fig.ratio;\n",
" var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n",
" x0 = Math.floor(x0) + 0.5;\n",
" y0 = Math.floor(y0) + 0.5;\n",
" x1 = Math.floor(x1) + 0.5;\n",
" y1 = Math.floor(y1) + 0.5;\n",
" var min_x = Math.min(x0, x1);\n",
" var min_y = Math.min(y0, y1);\n",
" var width = Math.abs(x1 - x0);\n",
" var height = Math.abs(y1 - y0);\n",
"\n",
" fig.rubberband_context.clearRect(\n",
" 0,\n",
" 0,\n",
" fig.canvas.width / fig.ratio,\n",
" fig.canvas.height / fig.ratio\n",
" );\n",
"\n",
" fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
"};\n",
"\n",
"mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n",
" // Updates the figure title.\n",
" fig.header.textContent = msg['label'];\n",
"};\n",
"\n",
"mpl.figure.prototype.handle_cursor = function (fig, msg) {\n",
" var cursor = msg['cursor'];\n",
" switch (cursor) {\n",
" case 0:\n",
" cursor = 'pointer';\n",
" break;\n",
" case 1:\n",
" cursor = 'default';\n",
" break;\n",
" case 2:\n",
" cursor = 'crosshair';\n",
" break;\n",
" case 3:\n",
" cursor = 'move';\n",
" break;\n",
" }\n",
" fig.rubberband_canvas.style.cursor = cursor;\n",
"};\n",
"\n",
"mpl.figure.prototype.handle_message = function (fig, msg) {\n",
" fig.message.textContent = msg['message'];\n",
"};\n",
"\n",
"mpl.figure.prototype.handle_draw = function (fig, _msg) {\n",
" // Request the server to send over a new figure.\n",
" fig.send_draw_message();\n",
"};\n",
"\n",
"mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n",
" fig.image_mode = msg['mode'];\n",
"};\n",
"\n",
"mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n",
" for (var key in msg) {\n",
" if (!(key in fig.buttons)) {\n",
" continue;\n",
" }\n",
" fig.buttons[key].disabled = !msg[key];\n",
" fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
" }\n",
"};\n",
"\n",
"mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
" if (msg['mode'] === 'PAN') {\n",
" fig.buttons['Pan'].classList.add('active');\n",
" fig.buttons['Zoom'].classList.remove('active');\n",
" } else if (msg['mode'] === 'ZOOM') {\n",
" fig.buttons['Pan'].classList.remove('active');\n",
" fig.buttons['Zoom'].classList.add('active');\n",
" } else {\n",
" fig.buttons['Pan'].classList.remove('active');\n",
" fig.buttons['Zoom'].classList.remove('active');\n",
" }\n",
"};\n",
"\n",
"mpl.figure.prototype.updated_canvas_event = function () {\n",
" // Called whenever the canvas gets updated.\n",
" this.send_message('ack', {});\n",
"};\n",
"\n",
"// A function to construct a web socket function for onmessage handling.\n",
"// Called in the figure constructor.\n",
"mpl.figure.prototype._make_on_message_function = function (fig) {\n",
" return function socket_on_message(evt) {\n",
" if (evt.data instanceof Blob) {\n",
" /* FIXME: We get \"Resource interpreted as Image but\n",
" * transferred with MIME type text/plain:\" errors on\n",
" * Chrome. But how to set the MIME type? It doesn't seem\n",
" * to be part of the websocket stream */\n",
" evt.data.type = 'image/png';\n",
"\n",
" /* Free the memory for the previous frames */\n",
" if (fig.imageObj.src) {\n",
" (window.URL || window.webkitURL).revokeObjectURL(\n",
" fig.imageObj.src\n",
" );\n",
" }\n",
"\n",
" fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
" evt.data\n",
" );\n",
" fig.updated_canvas_event();\n",
" fig.waiting = false;\n",
" return;\n",
" } else if (\n",
" typeof evt.data === 'string' &&\n",
" evt.data.slice(0, 21) === 'data:image/png;base64'\n",
" ) {\n",
" fig.imageObj.src = evt.data;\n",
" fig.updated_canvas_event();\n",
" fig.waiting = false;\n",
" return;\n",
" }\n",
"\n",
" var msg = JSON.parse(evt.data);\n",
" var msg_type = msg['type'];\n",
"\n",
" // Call the \"handle_{type}\" callback, which takes\n",
" // the figure and JSON message as its only arguments.\n",
" try {\n",
" var callback = fig['handle_' + msg_type];\n",
" } catch (e) {\n",
" console.log(\n",
" \"No handler for the '\" + msg_type + \"' message type: \",\n",
" msg\n",
" );\n",
" return;\n",
" }\n",
"\n",
" if (callback) {\n",
" try {\n",
" // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
" callback(fig, msg);\n",
" } catch (e) {\n",
" console.log(\n",
" \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
" e,\n",
" e.stack,\n",
" msg\n",
" );\n",
" }\n",
" }\n",
" };\n",
"};\n",
"\n",
"// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
"mpl.findpos = function (e) {\n",
" //this section is from http://www.quirksmode.org/js/events_properties.html\n",
" var targ;\n",
" if (!e) {\n",
" e = window.event;\n",
" }\n",
" if (e.target) {\n",
" targ = e.target;\n",
" } else if (e.srcElement) {\n",
" targ = e.srcElement;\n",
" }\n",
" if (targ.nodeType === 3) {\n",
" // defeat Safari bug\n",
" targ = targ.parentNode;\n",
" }\n",
"\n",
" // pageX,Y are the mouse positions relative to the document\n",
" var boundingRect = targ.getBoundingClientRect();\n",
" var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
" var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n",
"\n",
" return { x: x, y: y };\n",
"};\n",
"\n",
"/*\n",
" * return a copy of an object with only non-object keys\n",
" * we need this to avoid circular references\n",
" * http://stackoverflow.com/a/24161582/3208463\n",
" */\n",
"function simpleKeys(original) {\n",
" return Object.keys(original).reduce(function (obj, key) {\n",
" if (typeof original[key] !== 'object') {\n",
" obj[key] = original[key];\n",
" }\n",
" return obj;\n",
" }, {});\n",
"}\n",
"\n",
"mpl.figure.prototype.mouse_event = function (event, name) {\n",
" var canvas_pos = mpl.findpos(event);\n",
"\n",
" if (name === 'button_press') {\n",
" this.canvas.focus();\n",
" this.canvas_div.focus();\n",
" }\n",
"\n",
" var x = canvas_pos.x * this.ratio;\n",
" var y = canvas_pos.y * this.ratio;\n",
"\n",
" this.send_message(name, {\n",
" x: x,\n",
" y: y,\n",
" button: event.button,\n",
" step: event.step,\n",
" guiEvent: simpleKeys(event),\n",
" });\n",
"\n",
" /* This prevents the web browser from automatically changing to\n",
" * the text insertion cursor when the button is pressed. We want\n",
" * to control all of the cursor setting manually through the\n",
" * 'cursor' event from matplotlib */\n",
" event.preventDefault();\n",
" return false;\n",
"};\n",
"\n",
"mpl.figure.prototype._key_event_extra = function (_event, _name) {\n",
" // Handle any extra behaviour associated with a key event\n",
"};\n",
"\n",
"mpl.figure.prototype.key_event = function (event, name) {\n",
" // Prevent repeat events\n",
" if (name === 'key_press') {\n",
" if (event.which === this._key) {\n",
" return;\n",
" } else {\n",
" this._key = event.which;\n",
" }\n",
" }\n",
" if (name === 'key_release') {\n",
" this._key = null;\n",
" }\n",
"\n",
" var value = '';\n",
" if (event.ctrlKey && event.which !== 17) {\n",
" value += 'ctrl+';\n",
" }\n",
" if (event.altKey && event.which !== 18) {\n",
" value += 'alt+';\n",
" }\n",
" if (event.shiftKey && event.which !== 16) {\n",
" value += 'shift+';\n",
" }\n",
"\n",
" value += 'k';\n",
" value += event.which.toString();\n",
"\n",
" this._key_event_extra(event, name);\n",
"\n",
" this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n",
" return false;\n",
"};\n",
"\n",
"mpl.figure.prototype.toolbar_button_onclick = function (name) {\n",
" if (name === 'download') {\n",
" this.handle_save(this, null);\n",
" } else {\n",
" this.send_message('toolbar_button', { name: name });\n",
" }\n",
"};\n",
"\n",
"mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n",
" this.message.textContent = tooltip;\n",
"};\n",
"mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
"\n",
"mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
"\n",
"mpl.default_extension = \"png\";/* global mpl */\n",
"\n",
"var comm_websocket_adapter = function (comm) {\n",
" // Create a \"websocket\"-like object which calls the given IPython comm\n",
" // object with the appropriate methods. Currently this is a non binary\n",
" // socket, so there is still some room for performance tuning.\n",
" var ws = {};\n",
"\n",
" ws.close = function () {\n",
" comm.close();\n",
" };\n",
" ws.send = function (m) {\n",
" //console.log('sending', m);\n",
" comm.send(m);\n",
" };\n",
" // Register the callback with on_msg.\n",
" comm.on_msg(function (msg) {\n",
" //console.log('receiving', msg['content']['data'], msg);\n",
" // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
" ws.onmessage(msg['content']['data']);\n",
" });\n",
" return ws;\n",
"};\n",
"\n",
"mpl.mpl_figure_comm = function (comm, msg) {\n",
" // This is the function which gets called when the mpl process\n",
" // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
"\n",
" var id = msg.content.data.id;\n",
" // Get hold of the div created by the display call when the Comm\n",
" // socket was opened in Python.\n",
" var element = document.getElementById(id);\n",
" var ws_proxy = comm_websocket_adapter(comm);\n",
"\n",
" function ondownload(figure, _format) {\n",
" window.open(figure.canvas.toDataURL());\n",
" }\n",
"\n",
" var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n",
"\n",
" // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
" // web socket which is closed, not our websocket->open comm proxy.\n",
" ws_proxy.onopen();\n",
"\n",
" fig.parent_element = element;\n",
" fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
" if (!fig.cell_info) {\n",
" console.error('Failed to find cell for figure', id, fig);\n",
" return;\n",
" }\n",
" fig.cell_info[0].output_area.element.one(\n",
" 'cleared',\n",
" { fig: fig },\n",
" fig._remove_fig_handler\n",
" );\n",
"};\n",
"\n",
"mpl.figure.prototype.handle_close = function (fig, msg) {\n",
" var width = fig.canvas.width / fig.ratio;\n",
" fig.cell_info[0].output_area.element.off(\n",
" 'cleared',\n",
" fig._remove_fig_handler\n",
" );\n",
"\n",
" // Update the output cell to use the data from the current canvas.\n",
" fig.push_to_output();\n",
" var dataURL = fig.canvas.toDataURL();\n",
" // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
" // the notebook keyboard shortcuts fail.\n",
" IPython.keyboard_manager.enable();\n",
" fig.parent_element.innerHTML =\n",
" '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
" fig.close_ws(fig, msg);\n",
"};\n",
"\n",
"mpl.figure.prototype.close_ws = function (fig, msg) {\n",
" fig.send_message('closing', msg);\n",
" // fig.ws.close()\n",
"};\n",
"\n",
"mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
" // Turn the data on the canvas into data in the output cell.\n",
" var width = this.canvas.width / this.ratio;\n",
" var dataURL = this.canvas.toDataURL();\n",
" this.cell_info[1]['text/html'] =\n",
" '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
"};\n",
"\n",
"mpl.figure.prototype.updated_canvas_event = function () {\n",
" // Tell IPython that the notebook contents must change.\n",
" IPython.notebook.set_dirty(true);\n",
" this.send_message('ack', {});\n",
" var fig = this;\n",
" // Wait a second, then push the new image to the DOM so\n",
" // that it is saved nicely (might be nice to debounce this).\n",
" setTimeout(function () {\n",
" fig.push_to_output();\n",
" }, 1000);\n",
"};\n",
"\n",
"mpl.figure.prototype._init_toolbar = function () {\n",
" var fig = this;\n",
"\n",
" var toolbar = document.createElement('div');\n",
" toolbar.classList = 'btn-toolbar';\n",
" this.root.appendChild(toolbar);\n",
"\n",
" function on_click_closure(name) {\n",
" return function (_event) {\n",
" return fig.toolbar_button_onclick(name);\n",
" };\n",
" }\n",
"\n",
" function on_mouseover_closure(tooltip) {\n",
" return function (event) {\n",
" if (!event.currentTarget.disabled) {\n",
" return fig.toolbar_button_onmouseover(tooltip);\n",
" }\n",
" };\n",
" }\n",
"\n",
" fig.buttons = {};\n",
" var buttonGroup = document.createElement('div');\n",
" buttonGroup.classList = 'btn-group';\n",
" var button;\n",
" for (var toolbar_ind in mpl.toolbar_items) {\n",
" var name = mpl.toolbar_items[toolbar_ind][0];\n",
" var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
" var image = mpl.toolbar_items[toolbar_ind][2];\n",
" var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
"\n",
" if (!name) {\n",
" /* Instead of a spacer, we start a new button group. */\n",
" if (buttonGroup.hasChildNodes()) {\n",
" toolbar.appendChild(buttonGroup);\n",
" }\n",
" buttonGroup = document.createElement('div');\n",
" buttonGroup.classList = 'btn-group';\n",
" continue;\n",
" }\n",
"\n",
" button = fig.buttons[name] = document.createElement('button');\n",
" button.classList = 'btn btn-default';\n",
" button.href = '#';\n",
" button.title = name;\n",
" button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
" button.addEventListener('click', on_click_closure(method_name));\n",
" button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
" buttonGroup.appendChild(button);\n",
" }\n",
"\n",
" if (buttonGroup.hasChildNodes()) {\n",
" toolbar.appendChild(buttonGroup);\n",
" }\n",
"\n",
" // Add the status bar.\n",
" var status_bar = document.createElement('span');\n",
" status_bar.classList = 'mpl-message pull-right';\n",
" toolbar.appendChild(status_bar);\n",
" this.message = status_bar;\n",
"\n",
" // Add the close button to the window.\n",
" var buttongrp = document.createElement('div');\n",
" buttongrp.classList = 'btn-group inline pull-right';\n",
" button = document.createElement('button');\n",
" button.classList = 'btn btn-mini btn-primary';\n",
" button.href = '#';\n",
" button.title = 'Stop Interaction';\n",
" button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
" button.addEventListener('click', function (_evt) {\n",
" fig.handle_close(fig, {});\n",
" });\n",
" button.addEventListener(\n",
" 'mouseover',\n",
" on_mouseover_closure('Stop Interaction')\n",
" );\n",
" buttongrp.appendChild(button);\n",
" var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
" titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
"};\n",
"\n",
"mpl.figure.prototype._remove_fig_handler = function (event) {\n",
" var fig = event.data.fig;\n",
" fig.close_ws(fig, {});\n",
"};\n",
"\n",
"mpl.figure.prototype._root_extra_style = function (el) {\n",
" el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
"};\n",
"\n",
"mpl.figure.prototype._canvas_extra_style = function (el) {\n",
" // this is important to make the div 'focusable\n",
" el.setAttribute('tabindex', 0);\n",
" // reach out to IPython and tell the keyboard manager to turn it's self\n",
" // off when our div gets focus\n",
"\n",
" // location in version 3\n",
" if (IPython.notebook.keyboard_manager) {\n",
" IPython.notebook.keyboard_manager.register_events(el);\n",
" } else {\n",
" // location in version 2\n",
" IPython.keyboard_manager.register_events(el);\n",
" }\n",
"};\n",
"\n",
"mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
" var manager = IPython.notebook.keyboard_manager;\n",
" if (!manager) {\n",
" manager = IPython.keyboard_manager;\n",
" }\n",
"\n",
" // Check for shift+enter\n",
" if (event.shiftKey && event.which === 13) {\n",
" this.canvas_div.blur();\n",
" // select the cell after this one\n",
" var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
" IPython.notebook.select(index + 1);\n",
" }\n",
"};\n",
"\n",
"mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
" fig.ondownload(fig, null);\n",
"};\n",
"\n",
"mpl.find_output_cell = function (html_output) {\n",
" // Return the cell and output element which can be found *uniquely* in the notebook.\n",
" // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
" // IPython event is triggered only after the cells have been serialised, which for\n",
" // our purposes (turning an active figure into a static one), is too late.\n",
" var cells = IPython.notebook.get_cells();\n",
" var ncells = cells.length;\n",
" for (var i = 0; i < ncells; i++) {\n",
" var cell = cells[i];\n",
" if (cell.cell_type === 'code') {\n",
" for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
" var data = cell.output_area.outputs[j];\n",
" if (data.data) {\n",
" // IPython >= 3 moved mimebundle to data attribute of output\n",
" data = data.data;\n",
" }\n",
" if (data['text/html'] === html_output) {\n",
" return [cell, data, j];\n",
" }\n",
" }\n",
" }\n",
" }\n",
"};\n",
"\n",
"// Register the function which deals with the matplotlib target/channel.\n",
"// The kernel may be null if the page has been refreshed.\n",
"if (IPython.notebook.kernel !== null) {\n",
" IPython.notebook.kernel.comm_manager.register_target(\n",
" 'matplotlib',\n",
" mpl.mpl_figure_comm\n",
" );\n",
"}\n"
],
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"<IPython.core.display.Javascript object>"
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},
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\" width=\"599.5\">"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Animacion\n",
"fig0, ax0 = plt.subplots(figsize=(6, 3))\n",
"ani = animation.FuncAnimation(fig0, update, u_total.T,\n",
" interval=niter,\n",
" repeat=True, fargs=(ax0,))\n",
"\n",
"ani.save(\"stiff_string_%g.gif\" % EI, dpi=300)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.6"
},
"varInspector": {
"cols": {
"lenName": 16,
"lenType": 16,
"lenVar": 40
},
"kernels_config": {
"python": {
"delete_cmd_postfix": "",
"delete_cmd_prefix": "del ",
"library": "var_list.py",
"varRefreshCmd": "print(var_dic_list())"
},
"r": {
"delete_cmd_postfix": ") ",
"delete_cmd_prefix": "rm(",
"library": "var_list.r",
"varRefreshCmd": "cat(var_dic_list()) "
}
},
"types_to_exclude": [
"module",
"function",
"builtin_function_or_method",
"instance",
"_Feature"
],
"window_display": false
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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