rscha-reg.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### regularización R-SCHA-2D\n",
    "ver Thebault 2006 y 2008"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy, scipy\n",
    "import trig\n",
    "import fibonacci_sphere\n",
    "import xyzfield\n",
    "from matplotlib import pyplot\n",
    "import matplotlib\n",
    "from mpl_toolkits import basemap\n",
    "%matplotlib nbagg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### parámetros"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "lon_c = 20; lat_c = 45; colat_0 = 24.8\n",
    "theta_c, phi_c, theta_0 = numpy.deg2rad((90-lat_c, lon_c, colat_0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "m_max = 1; k_max = 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "raíces"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    k     m          n\n",
      "---------------------------\n",
      "    0     0     0.0000\n",
      "    1     0     5.0483\n",
      "    1     1     3.8389\n",
      "    1    -1     3.8389\n",
      "    2     0     8.3667\n",
      "    2     1     8.3667\n",
      "    2    -1     8.3667\n",
      "    2     2     6.6876\n",
      "    2    -2     6.6876\n"
     ]
    }
   ],
   "source": [
    "import scha\n",
    "ms = numpy.arange(0, k_max+1)\n",
    "k, m, n = scha.join_roots(scha.degree(ms, theta_0, 10))\n",
    "k = numpy.array(k); m = numpy.array(m); n = numpy.array(n)\n",
    "print(\"{0:>5} {1:>5} {2:>10}\".format(\"k\", \"m\", \"n\"))\n",
    "print(\"-\"*27)\n",
    "for kk, mm, nn in zip(k, m, n):\n",
    "    print(\"{0:>5} {1:>5} {2:10.4f}\".format(kk,mm,nn))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    k     m          n\n",
      "---------------------------\n",
      "    0     0     0.0000\n",
      "    1     1     3.8389\n",
      "    1    -1     3.8389\n",
      "    2     0     8.3667\n",
      "    2     2     6.6876\n",
      "    2    -2     6.6876\n"
     ]
    }
   ],
   "source": [
    "km_even = (numpy.array(k)-numpy.abs(m)) % 2 == 0\n",
    "k_even, m_even, n_even = k[km_even], m[km_even], n[km_even]\n",
    "print(\"{0:>5} {1:>5} {2:>10}\".format(\"k\", \"m\", \"n\"))\n",
    "print(\"-\"*27)\n",
    "for kk, mm, nn in zip(k_even, m_even, n_even):\n",
    "    print(\"{0:>5} {1:>5} {2:10.4f}\".format(kk,mm,nn))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "m_mehler = numpy.array((0, 1, -1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<module 'rscha' from '/home/josecper/Programs/python/rscha.py'>"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import mfunnorm; import rscha\n",
    "import importlib; importlib.reload(rscha)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  5.79451192e-01,   0.00000000e+00,   0.00000000e+00,\n",
       "          0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
       "          0.00000000e+00,   0.00000000e+00,   0.00000000e+00],\n",
       "       [  0.00000000e+00,   5.96382742e+00,   0.00000000e+00,\n",
       "          0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
       "          0.00000000e+00,   0.00000000e+00,   0.00000000e+00],\n",
       "       [  0.00000000e+00,   0.00000000e+00,   4.73135256e+00,\n",
       "          0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
       "          0.00000000e+00,   0.00000000e+00,   0.00000000e+00],\n",
       "       [  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
       "          1.58591810e+01,   0.00000000e+00,   0.00000000e+00,\n",
       "          0.00000000e+00,   0.00000000e+00,   0.00000000e+00],\n",
       "       [  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
       "          0.00000000e+00,   8.87424619e+00,   0.00000000e+00,\n",
       "          0.00000000e+00,   0.00000000e+00,   0.00000000e+00],\n",
       "       [  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
       "          0.00000000e+00,   0.00000000e+00,   7.71988287e+00,\n",
       "          0.00000000e+00,   0.00000000e+00,   0.00000000e+00],\n",
       "       [  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
       "          0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
       "          9.30583531e-03,   0.00000000e+00,   0.00000000e+00],\n",
       "       [  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
       "          0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
       "          0.00000000e+00,   6.94914266e+01,   0.00000000e+00],\n",
       "       [  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
       "          0.00000000e+00,   0.00000000e+00,   0.00000000e+00,\n",
       "          0.00000000e+00,   0.00000000e+00,   6.94914266e+01]])"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rscha.rscha_spatial_reg_diag((k_even, m_even, n_even), m_mehler, theta_0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "n_leg = len(k_even)\n",
    "n_mehler = len(m_mehler)\n",
    "\n",
    "n_coefs = n_leg + n_mehler\n",
    "\n",
    "mp = (m_even >= 0)\n",
    "mn = (m_even < 0)\n",
    "\n",
    "c1 = numpy.zeros(n_coefs)\n",
    "c2 = c1.copy()\n",
    "c3 = c1.copy()\n",
    "leg_norm = rscha.norm_leg_even(k_even, m_even, n_even, theta_0)\n",
    "\n",
    "c1[:n_leg][mp] = (2*n_even[mp]**2+3*n_even[mp]+1)*(1+(m_even[mp] == 0))*numpy.pi*leg_norm[mp]\n",
    "c1[:n_leg][mn] = (2*n_even[mn]**2+n_even[mn])*numpy.pi*leg_norm[mn]\n",
    "\n",
    "for i, mm in enumerate(m_mehler):\n",
    "    mm_abs = numpy.abs(mm)\n",
    "    c2[n_leg+i] = (mehler.mehler_t(mm_abs, 0, theta_0, theta_0, normalized=True)*\\\n",
    "                   mehler.dmehler_t(mm_abs, 0, theta_0, theta_0, normalized=True)*numpy.sin(theta_0)-\\\n",
    "                   0.25)*(1+(mm == 0))*numpy.pi\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3.3124497578900511, 0.18099794512593123)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import mehler\n",
    "mehler.mehler_t(0, 0, theta_0, theta_0, True), mehler.dmehler_t(0, 0, theta_0, theta_0, True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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       "\n",
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       "\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]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'];\n",
       "    var y0 = fig.canvas.height - msg['y0'];\n",
       "    var x1 = msg['x1'];\n",
       "    var y1 = fig.canvas.height - msg['y1'];\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, 0, fig.canvas.width, fig.canvas.height);\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",
       "    {\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.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",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\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(\"No handler for the '\" + msg_type + \"' message type: \", msg);\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(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\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",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\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",
       "    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",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x;\n",
       "    var y = canvas_pos.y;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\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",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\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,\n",
       "                             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\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"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\";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 overriden (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 = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\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.get(0);\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",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    fig.root.unbind('remove')\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).html('<img src=\"' + dataURL + '\">');\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 dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\">';\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 () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('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",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\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",
       "    // 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",
       "\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('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img 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\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(-0.5, 530.5, 530.5, -0.5)"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig, ax = pyplot.subplots()\n",
    "ax.imshow(Mreg_t, interpolation=\"nearest\", cmap=\"viridis\")\n",
    "ax.axis('off')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0.57945119,   5.96382742,   4.73135256,  15.85918099,\n",
       "         8.87424619,   7.71988287,   0.        ,   0.        ,   0.        ])"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Mreg_s = rscha.rscha_spatial_reg_diag((k_even, m_even, n_even), m_mehler, theta_0)\n",
    "knots = numpy.arange(-1000, 1950, 50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Mreg_t = rscha.rscha_time_reg_diag(Mreg_s, knots)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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