AM18_ex2.ipynb

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   "cell_type": "markdown",
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    "# Example 2: active rotations in $\\unicode{0x211D}^3$\n",
    "\n",
    "In this example we study simple rotations of vectors from $\\unicode{0x211D}^3$, i.e.\n",
    "$$\\vec{r}'={\\cal{R}}\\vec{r}\\,.$$ To this end, we define functions for the multiplication \n",
    "of vectors with $3\\times 3$ matrices, as well as the product of two such matrices. \n",
    "Furthermore, we implement the calculation of the determinant of a $3\\times 3$ matrix, \n",
    "to be able to check the corresponding condition for orthogonal rotation matrices, i.e.\n",
    "$\\det({\\cal{R}})=+1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### definition of matrices and vectors for diplay purposes only (can be ignored)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.display import Markdown, Latex, Math\n",
    "\n",
    "def bmatrix(a):\n",
    "    \"\"\"Returns a LaTeX vmatrix\n",
    "\n",
    "    :a: numpy array\n",
    "    :returns: LaTeX vmatrix as a string\n",
    "    \"\"\"\n",
    "    lines = str(a).replace('[', '').replace(']', '').splitlines()\n",
    "  \n",
    "    rv = [r'\\begin{vmatrix}']\n",
    "    rv += ['  ' + ' & '.join(l.split()) + r'\\\\' for l in lines]\n",
    "    rv +=  [r'\\end{vmatrix}']\n",
    "    return '\\n'.join(rv)\n",
    "\n",
    "def lvector(a):\n",
    "    \"\"\"Returns a LaTeX vector\n",
    "\n",
    "    :a: numpy array\n",
    "    :returns: LaTeX pmatrix as a string\n",
    "    \"\"\"\n",
    "    lines = str(a).replace('[', '').replace(']', '').replace(',','').splitlines()\n",
    "  \n",
    "    rv = [r'\\begin{pmatrix}']\n",
    "    rv += [r' \\\\ '.join(l.split()) for l in lines]\n",
    "    rv +=  [r'\\end{pmatrix}']\n",
    "    return '\\n'.join(rv)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### definition of products of a matrix with another matrix or a vector, as well as the matrix determinant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "%matplotlib notebook\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import numpy as np\n",
    "from numpy import cos, sin \n",
    "import math\n",
    "\n",
    "## definition of the matix-vector multiplication\n",
    "def MatrixVectorProduct( mat, vecpre):\n",
    "    \"\"\"Returns the result of a matrix-vector Multiplication\n",
    "    \n",
    "    :mat:    3x3 Matrix\n",
    "    :vecpre: 3D vector\n",
    "    :vecnew: resulting vector\"\"\"\n",
    "    vecnew= [0,0,0]\n",
    "    if len(vecpre) == 3 :\n",
    "        for i in range (0,3):\n",
    "            for j in range (0,3):\n",
    "                vecnew[i]+=mat[i][j]*vecpre[j] \n",
    "    else :\n",
    "        print('Error: Wrong dimensions')\n",
    "    return vecnew\n",
    "\n",
    "## definition of the matix product\n",
    "def MatrixProduct( mat1, mat2):\n",
    "    \"\"\"Returns the result of a matrix Multiplication\n",
    "    \n",
    "    :mat1, mat2:    3x3 Matrix\n",
    "    :matnew: resulting matrix\"\"\"\n",
    "    matnew= [[0,0,0],[0,0,0],[0,0,0]]\n",
    "    for i in range (0,3):\n",
    "        for j in range (0,3):\n",
    "            for k in range (0,3):\n",
    "                matnew[i][j]+=mat1[i][k]*mat2[k][j] \n",
    "    return matnew\n",
    "\n",
    "## definition of the matix determinant\n",
    "def Matrix3Determinant(mat3,column):\n",
    "    \"\"\"Returns the determinant of a 3x3 Matrix\n",
    "    \n",
    "    :mat3:   3x3 Matrix\n",
    "    :column: compute determinant along column\n",
    "    :return: determinant\"\"\"\n",
    "    det = 0\n",
    "    if column < 0 or column > 2 :\n",
    "        print('Error in Maxtrix3Determinant: wrong column number')\n",
    "    #delete column \n",
    "    mat_tmp = np.delete(mat3,column,1)\n",
    "    for i in range (0,3):\n",
    "        #delete row i\n",
    "        mat2 = np.delete(mat_tmp,i,0)\n",
    "        det += pow(-1,i+column)*mat3[i][column]*Matrix2Determinant(mat2)\n",
    "    return det \n",
    "\n",
    "##definition of the 2x2 matix determinant\n",
    "def Matrix2Determinant(mat2):\n",
    "    det = mat2[0][0]*mat2[1][1]-mat2[1][0]*mat2[0][1]\n",
    "    return det\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example calculation of a matrix determinant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "\n",
       "\n",
       "$$A=\\begin{vmatrix}\n",
       "  1 & 2 & 3\\\\\n",
       "  3 & 2 & 1\\\\\n",
       "  1 & 4 & 2\\\\\n",
       "\\end{vmatrix}\\,,\\quad\\det(A)=20$$"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
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     "execution_count": 171,
     "metadata": {},
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   "source": [
    "# input of matrix to compute the determinant for\n",
    "A = [[1,2,3],[3,2,1],[1,4,2]]\n",
    "det=Matrix3Determinant(A,2)\n",
    "\n",
    "Markdown(\"\"\"\n",
    "\n",
    "$$A={x}\\\\,,\\\\quad\\\\det(A)={det}$$\"\"\".format(x=bmatrix(np.matrix(A)), det=det))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Rotations in $\\unicode{0x211D}^3$: definition of rotation angles and input vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [],
   "source": [
    "####################################################################################################################\n",
    "\n",
    "## input rotation angles here\n",
    "phix = np.pi/8\n",
    "phiy = 0.1\n",
    "phiz = 0.5\n",
    "\n",
    "## input of vector to be rotated\n",
    "vr = [1,1,1]\n",
    "\n",
    "## definition of Rotation Matrices\n",
    "Rx = [[1,0,0],[0,cos(phix),-sin(phix)],[0,sin(phix),cos(phix)]]\n",
    "Ry = [[cos(phiy),0,sin(phiy)],[0,1,0],[-sin(phiy),0,cos(phiy)]]\n",
    "Rz = [[cos(phiz),-sin(phiz),0],[sin(phiz),cos(phiz),0],[0,0,1]]\n",
    "\n",
    "## corresponding determinants \n",
    "detRx = Matrix3Determinant(Rx,0)\n",
    "detRy = Matrix3Determinant(Ry,0)\n",
    "detRz = Matrix3Determinant(Rz,0)\n",
    "\n",
    "####################################################################################################################\n",
    "\n",
    "##calculation of matrix-vector product\n",
    "## in the example: rotation of r around z-Axis by angle phiz\n",
    "vrp=MatrixVectorProduct(Rz,vr)\n",
    "\n",
    "## resulting rotation matrices for combination of two rotations\n",
    "Rxy=MatrixProduct(Rx,Ry)\n",
    "Ryx=MatrixProduct(Ry,Rx)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "\n",
       "## Illustrating the Results\n",
       "## Rotation Matrices\n",
       "$$R_x=\\begin{vmatrix}\n",
       "  1. & 0. & 0.\\\\\n",
       "  0. & 0.92 & -0.38\\\\\n",
       "  0. & 0.38 & 0.92\\\\\n",
       "\\end{vmatrix}\\,,\\quad \\det(R_x)=1.0$$\n",
       "$$R_y=\\begin{vmatrix}\n",
       "  1. & 0. & 0.1\\\\\n",
       "  0. & 1. & 0.\\\\\n",
       "  -0.1 & 0. & 1.\\\\\n",
       "\\end{vmatrix}\\,,\\quad \\det(R_y)=1.0$$\n",
       "$$R_z=\\begin{vmatrix}\n",
       "  0.88 & -0.48 & 0.\\\\\n",
       "  0.48 & 0.88 & 0.\\\\\n",
       "  0. & 0. & 1.\\\\\n",
       "\\end{vmatrix}\\,,\\quad \\det(R_z)=1.0$$\n",
       "\n",
       "## Vector to be rotated\n",
       "$$\\vec r=\\begin{pmatrix}\n",
       "1 \\\\ 1 \\\\ 1\n",
       "\\end{pmatrix}$$\n",
       "\n",
       "## Rotated Vector\n",
       "$$\\vec r'=R_z\\vec r=\\begin{pmatrix}\n",
       "0.39815702328616975 \\\\ 1.3570081004945758 \\\\ 1\n",
       "\\end{pmatrix}$$\n",
       "\n",
       "## Matrix Products \n",
       "\n",
       "$$R_{xy}=\\begin{vmatrix}\n",
       "  1. & 0. & 0.1\\\\\n",
       "  0.04 & 0.92 & -0.38\\\\\n",
       "  -0.09 & 0.38 & 0.92\\\\\n",
       "\\end{vmatrix}$$\n",
       "\n",
       "$$R_{yx}=\\begin{vmatrix}\n",
       "  1. & 0.04 & 0.09\\\\\n",
       "  0. & 0.92 & -0.38\\\\\n",
       "  -0.1 & 0.38 & 0.92\\\\\n",
       "\\end{vmatrix}$$\n",
       "\n",
       "$$\\Rightarrow R_{xy} \\neq R_{yx}$$"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "execution_count": 173,
     "metadata": {},
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   "source": [
    "Markdown(\"\"\"\n",
    "## Illustrating the Results\n",
    "## Rotation Matrices\n",
    "$$R_x={x}\\\\,,\\\\quad \\\\det(R_x)={detRx}$$\n",
    "$$R_y={y}\\\\,,\\\\quad \\\\det(R_y)={detRy}$$\n",
    "$$R_z={z}\\\\,,\\\\quad \\\\det(R_z)={detRz}$$\n",
    "\n",
    "## Vector to be rotated\n",
    "$$\\\\vec r={vr}$$\n",
    "\n",
    "## Rotated Vector\n",
    "$$\\\\vec r'=R_z\\\\vec r={vrp}$$\n",
    "\n",
    "## Matrix Products \n",
    "\n",
    "$$R_{{xy}}={xy}$$\n",
    "\n",
    "$$R_{{yx}}={yx}$$\n",
    "\n",
    "$$\\Rightarrow R_{{xy}} \\\\neq R_{{yx}}$$\"\"\".format(vr=lvector(vr),vrp=lvector(vrp),xy=bmatrix(np.around(Rxy,decimals=2)),yx=bmatrix(np.around(Ryx,decimals=2)),x=bmatrix(np.around(Rx,decimals=2)), y=bmatrix(np.around(Ry,decimals=2)),z=bmatrix(np.around(Rz,decimals=2)),detRx=detRx,detRy=detRy,detRz=detRz))\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
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       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\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",
       "\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",
       "\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'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.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, 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 * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\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 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 = $(\"#\" + 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",
       "    var width = fig.canvas.width/mpl.ratio\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 + '\" 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/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<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 () { 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",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\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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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## setup for plotting the vectors\n",
    "r_pre=np.array([0,0,0,vr[0],vr[1],vr[2]])\n",
    "r_past=np.array([0,0,0,vrp[0],vrp[1],vrp[2]])\n",
    "\n",
    "fig = plt.figure(1)\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "## plot initial vector \n",
    "vprelength=np.linalg.norm(vr)\n",
    "ax.quiver(r_pre[0],r_pre[1],r_pre[2],r_pre[3],r_pre[4],r_pre[5],color='black',\n",
    "            pivot='tail',arrow_length_ratio=0.3/vprelength, label='original vector $\\\\vec{r}$')\n",
    "\n",
    "## plot transformed vector\n",
    "vpastlength=np.linalg.norm(vrp)\n",
    "ax.quiver(r_past[0],r_past[1],r_past[2],r_past[3],r_past[4],r_past[5],color='r',\n",
    "            pivot='tail',arrow_length_ratio=0.3/vpastlength, label='resulting vector $\\\\vec{r}^,$')\n",
    "\n",
    "ax.set_xlim([-2,2])\n",
    "ax.set_ylim([-2,2])\n",
    "ax.set_zlim([-2,2])\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('y')\n",
    "ax.set_zlabel('z',labelpad=0)\n",
    "plt.title('Illustration of matrix-vector multiplication\\n',fontsize=15)\n",
    "plt.legend(bbox_to_anchor=(0.3, 0.9))\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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}