hemi_dist.ipynb

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 "cells": [
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# imports ----------------------------------\n",
    "import math\n",
    "import random as rnd\n",
    "import numpy as np\n",
    "\n",
    "from matplotlib.transforms import Bbox\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# constants / aliases -----------------------\n",
    "vec = np.array\n",
    "vlen = np.linalg.norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# normal generators -------------------------\n",
    "\n",
    "def normalize(v):\n",
    "    norm=np.linalg.norm(v, ord=2)\n",
    "    if norm==0:\n",
    "        norm=np.finfo(v.dtype).eps\n",
    "    return v/norm\n",
    "\n",
    "def random_normal(x_s=(-1.0, 1.0), y_s=(-1.0, 1.0), z_s=(-1.0, 1.0)):\n",
    "    return normalize(vec( (x_s[0]+(x_s[1]-x_s[0])*rnd.random(), \n",
    "                           y_s[0]+(y_s[1]-y_s[0])*rnd.random(), \n",
    "                           z_s[0]+(z_s[1]-z_s[0])*rnd.random()) ))\n",
    "\n",
    "def random_angled_normal():\n",
    "    u = rnd.random() * math.pi/2.0\n",
    "    v = rnd.random() * math.pi/2.0\n",
    "    return normalize(vec( (sin(u)*cos(v), sin(u)*sin(v), cos(u)) ))\n",
    "\n",
    "def random_angled_normal_2d():\n",
    "    u = rnd.random() * math.pi/2.0\n",
    "    return normalize(vec( (sin(u), cos(u), 0) ))\n",
    "\n",
    "def random_sqrt_normal():\n",
    "    ru = rnd.random()\n",
    "    su, cu = sqrt(ru), sqrt(1.0-ru)\n",
    "\n",
    "    rv = rnd.random()\n",
    "    sv, cv = sqrt(rv), sqrt(1.0-rv)\n",
    "\n",
    "    return normalize(vec( (su*cv, su*sv, cu) ))\n",
    "\n",
    "def random_sqrt_normal_2d():\n",
    "    ru = rnd.random()\n",
    "    su, cu = sqrt(ru), sqrt(1.0-ru)\n",
    "    return normalize(vec( (su, cu, 0) ))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# plot helpers -----------------------\n",
    "\n",
    "def add_axes(ax, x=1, y=None, z=None, colval=1.0, lstyle=(0, (1, 5)), negatives=False):\n",
    "    if y is None:\n",
    "        y = x\n",
    "    if z is None:\n",
    "        z = x\n",
    "    ax.quiver((0,), (0,), (0,), (x,), (0,), (0,), colors=(colval, 0, 0, colval), linestyles=lstyle, arrow_length_ratio=0.1, zorder=99)\n",
    "    ax.quiver((0,), (0,), (0,), (0,), (y,), (0,), colors=(0, colval, 0, colval), linestyles=lstyle, arrow_length_ratio=0.1, zorder=99)\n",
    "    ax.quiver((0,), (0,), (0,), (0,), (0,), (z,), colors=(0, 0, colval, colval), linestyles=lstyle, arrow_length_ratio=0.1, zorder=99)\n",
    "    if negatives:\n",
    "        ax.quiver((0,), (0,), (0,), (-x,), (0,), (0,), colors=(colval, 0, 0, colval), linestyles=lstyle, arrow_length_ratio=0.1, zorder=99)\n",
    "        ax.quiver((0,), (0,), (0,), (0,), (-y,), (0,), colors=(0, colval, 0, colval), linestyles=lstyle, arrow_length_ratio=0.1, zorder=99)\n",
    "        ax.quiver((0,), (0,), (0,), (0,), (0,), (-z,), colors=(0, 0, colval, colval), linestyles=lstyle, arrow_length_ratio=0.1, zorder=99)\n",
    "    \n",
    "    ax.set_xlabel('x'); ax.set_xlim([-x, x]); ax.set_xticks([-1.0, 0.0, 1.0]);\n",
    "    ax.set_ylabel('y'); ax.set_ylim([y, -y]); ax.set_yticks([-1.0, 0.0, 1.0]);\n",
    "    ax.set_zlabel('z'); ax.set_zlim([-z, z]); ax.set_zticks([-1.0, 0.0, 1.0]);\n",
    "\n",
    "def quiver_vectors(ax, veclist, color=(0, 0.2, 0.8), arrow_length_ratio=0.3):\n",
    "    quiv = list()\n",
    "    for v in list(veclist):\n",
    "        quiv.append([0]*3 + list(v))\n",
    "    X, Y, Z, U, V, W = zip(*quiv)\n",
    "    ax.quiver(X, Y, Z, U, V, W, colors=color, arrow_length_ratio=arrow_length_ratio)\n",
    "\n",
    "def quiver_origin_vector(ax, vec, color=(0, 0.2, 0.8), arrow_length_ratio=0.3):\n",
    "    X, Y, Z, U, V, W = zip([0]*3 + list(vec))\n",
    "    ax.quiver(X, Y, Z, U, V, W, colors=color, arrow_length_ratio=arrow_length_ratio)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using matplotlib backend: nbAgg\n",
      "Populating the interactive namespace from numpy and matplotlib\n",
      "min/max(mv_x): 0.0018597318582742786 - 0.9988695372281022\n",
      "min/max(mv_y): 0.0018597318582889882 - 0.9988695372281016\n"
     ]
    }
   ],
   "source": [
    "# generate sample set ------------------------\n",
    "\n",
    "%matplotlib inline  \n",
    "%matplotlib notebook\n",
    "%pylab\n",
    "\n",
    "plot_normals=False\n",
    "\n",
    "if plot_normals:\n",
    "    # prepare figure & plot\n",
    "    fig = plt.figure(figsize=(14, 14))\n",
    "    fig.set_tight_layout(True)\n",
    "    ax = fig.add_subplot(111, projection='3d')\n",
    "    add_axes(ax, 1.0, colval=.5, negatives=True)\n",
    "\n",
    "# arrays to collect samples per axis\n",
    "mv_x, mv_y, mv_z = ([], [], [])\n",
    "mv_xy = []\n",
    "\n",
    "for i in range(1,100000):\n",
    "    #r = random_angled_normal_2d()\n",
    "    r = random_sqrt_normal_2d()\n",
    "    mv_x.append(arccos(r[0])*2/math.pi)\n",
    "    mv_y.append(arcsin(r[1])*2/math.pi)\n",
    "    mv_z.append(r[2])\n",
    "    mv_xy.append([r[0], r[1]])\n",
    "    #print(np.linalg.norm(r))\n",
    "    if plot_normals and i <= 10000:\n",
    "        quiver_origin_vector(ax, r, (0.2, 0.2, 0.7), arrow_length_ratio=0.1)\n",
    "\n",
    "print(f\"min/max(mv_x): {numpy.amin(mv_x)} - {numpy.amax(mv_x)}\")\n",
    "print(f\"min/max(mv_y): {numpy.amin(mv_y)} - {numpy.amax(mv_y)}\")\n",
    "\n",
    "# NOTE: sometimes the graphs would fail to render correctly\n",
    "# (interacting with it and) running this cell again would fix it..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "scrolled": false
   },
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using matplotlib backend: nbAgg\n",
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    },
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       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "};\n",
       "\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",
       "\n",
       "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
       "// prettier-ignore\n",
       "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\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.on(\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",
       "    fig.resizeObserverInstance.unobserve(fig.canvas_div);\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",
       "    if (event.target !== this) {\n",
       "        // Ignore bubbled events from children.\n",
       "        return;\n",
       "    }\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"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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width=\"1008\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1325f8a2b0>]"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import multivariate_normal as scipy_mv_normal\n",
    "from scipy.stats import uniform as scipy_uniform\n",
    "from scipy.stats import norm as scipy_norm\n",
    "\n",
    "use_dist = scipy_uniform\n",
    "\n",
    "mu_x, std_x = use_dist.fit(mv_x)\n",
    "fit_x = use_dist()\n",
    "var_x = fit_x.var()\n",
    "mu_y, std_y = use_dist.fit(mv_y)\n",
    "fit_y = use_dist()\n",
    "var_y = fit_y.var()\n",
    "mu_z, std_z = use_dist.fit(mv_z)\n",
    "fit_z = use_dist()\n",
    "var_z = fit_z.var()\n",
    "\n",
    "gridX, gridY = np.meshgrid(np.linspace(-1,1,100),np.linspace(-1,1,100))\n",
    "pos = np.empty(gridX.shape + (2,))\n",
    "pos[:,:,0] = gridX\n",
    "pos[:,:,1] = gridY\n",
    "\n",
    "mvn = scipy_mv_normal([mu_x, mu_y], [[var_x, 0], [0, var_y]])\n",
    "\n",
    "%matplotlib inline  \n",
    "%matplotlib notebook\n",
    "%pylab\n",
    "\n",
    "fig = plt.figure(figsize=(9, 14), dpi=112)\n",
    "fig.set_tight_layout(True)\n",
    "\n",
    "x = np.linspace(use_dist.ppf(0.01),\n",
    "                use_dist.ppf(0.99), 100)\n",
    "\n",
    "ax = fig.add_subplot(311)\n",
    "\n",
    "ax.plot(x, fit_x.pdf(x))\n",
    "ax.hist(mv_x, density=True, histtype='stepfilled', bins=25, alpha=0.2)\n",
    "\n",
    "\n",
    "ax = fig.add_subplot(312)\n",
    "\n",
    "ax.plot(x, fit_y.pdf(x))\n",
    "ax.hist(mv_y, density=True, histtype='stepfilled', bins=25, alpha=0.2)\n",
    "\n",
    "ax = fig.add_subplot(313, aspect='equal')\n",
    "ax.plot(mv_x, mv_y, 'b.', markersize=.05) # *list(zip(*mv_xy))\n",
    "\n",
    "\n",
    "#ax = fig.add_subplot(414, projection='3d')\n",
    "#ax.plot_surface(gridX, gridY, mvn.pdf(pos), cmap='viridis',linewidth=0)\n",
    "#print(mvn.pdf(pos))\n",
    "#ax.plot_surface(gridX, gridY, np.array(mv_xy), cmap='viridis',linewidth=0)"
   ]
  },
  {
   "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": "3.9.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}