interactive_test.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Riemann interactive\n",
    "\n",
    "In this notebook, we show interactive solutions of two Riemann problems for shallow water equations and acoustics. The user can interactively modify the phase planes and x-t planes and see its corresponding solutions. The code to produce these apps uses the mpld3 library, and it can be found on the clawpack folder riemann/riemann_interactive.py. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we need to load the mpld3 and numpy libraries as well as the riemann_interactive code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import mpld3\n",
    "import numpy as np\n",
    "from clawpack.riemann import riemann_interactive"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Shallow water equations\n",
    "In this section we show the interactive riemann solution of the exact solver for the shallow water equations. We first define the initial left and right state, the $g$ paramter and the plot range, then we call our riemann interactive plotting and display it. The commented line \"mpld3.save_html\" can be uncommented to save the output as html. On the app feel free to drag and drop the $q_l$ and $q_r$ states in the phase plane. The time can also be adjusted by dragging up and down the black dot in the horizontal time bar in the $x-t$ plane. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "<style>\n",
       "\n",
       "</style>\n",
       "\n",
       "<div id=\"fig_el283411397794207036323196724884\"></div>\n",
       "<script>\n",
       "function mpld3_load_lib(url, callback){\n",
       "  var s = document.createElement('script');\n",
       "  s.src = url;\n",
       "  s.async = true;\n",
       "  s.onreadystatechange = s.onload = callback;\n",
       "  s.onerror = function(){console.warn(\"failed to load library \" + url);};\n",
       "  document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
       "}\n",
       "\n",
       "if(typeof(mpld3) !== \"undefined\" && mpld3._mpld3IsLoaded){\n",
       "   // already loaded: just create the figure\n",
       "   !function(mpld3){\n",
       "       \n",
       "    // init custom PPLaneNL plugin\n",
       "    mpld3.register_plugin(\"drag\", PPlaneNLPlugin);\n",
       "    PPlaneNLPlugin.prototype = Object.create(mpld3.Plugin.prototype);\n",
       "    PPlaneNLPlugin.prototype.constructor = PPlaneNLPlugin;\n",
       "    PPlaneNLPlugin.prototype.requiredProps = [\"id\", \"idmpoint\", \n",
       "                                              \"idg\", \"iditer\", \"iditer_charac\", \"idtime\", \"idhmax\", \"idoffm\",\n",
       "                                              \"idhugol\", \"idhugor\", \"idintcl\", \"idintcr\",\n",
       "                                              \"idhugol2\", \"idhugor2\", \"idintcl2\", \"idintcr2\", \n",
       "                                              \"idqlm\", \"idqmm\", \"idqrm\", \n",
       "                                              \"idshock1\", \"idshock2\", \"idrar1\", \"idrar2\",\n",
       "                                              \"idrar1a\", \"idrar2a\", \"idrar1b\", \"idrar2b\",\n",
       "                                              \"idrar1c\", \"idrar2c\", \"idrar1d\", \"idrar2d\",\n",
       "                                              \"idtimedot\", \"idtimeline\",\n",
       "                                              \"idq1\", \"idq2\"];\n",
       "    PPlaneNLPlugin.prototype.defaultProps = {}\n",
       "    function PPlaneNLPlugin(fig, props){\n",
       "        mpld3.Plugin.call(this, fig, props);\n",
       "        mpld3.insert_css(\"#\" + fig.figid + \" path.dragging\",\n",
       "                         {\"fill-opacity\": \"1.0 !important\",\n",
       "                          \"stroke-opacity\": \"1.0 !important\"});\n",
       "    };\n",
       "\n",
       "    // Call draw function, this function is being looped all the time\n",
       "    PPlaneNLPlugin.prototype.draw = function(){\n",
       "        // Get elements into script variables\n",
       "        var obj = mpld3.get_element(this.props.id);\n",
       "        var midpoint = mpld3.get_element(this.props.idmpoint);\n",
       "        var g = this.props.idg;\n",
       "        var iter = this.props.iditer;\n",
       "        var iter_charac = this.props.iditer_charac;\n",
       "        var time = this.props.idtime;\n",
       "        var hmax = this.props.idhmax;\n",
       "        var offm = this.props.idoffm;\n",
       "        var hugol = mpld3.get_element(this.props.idhugol);\n",
       "        var hugor = mpld3.get_element(this.props.idhugor);\n",
       "        var intcl = mpld3.get_element(this.props.idintcl);\n",
       "        var intcr = mpld3.get_element(this.props.idintcr);\n",
       "        var hugol2 = mpld3.get_element(this.props.idhugol2);\n",
       "        var hugor2 = mpld3.get_element(this.props.idhugor2);\n",
       "        var intcl2 = mpld3.get_element(this.props.idintcl2);\n",
       "        var intcr2 = mpld3.get_element(this.props.idintcr2);\n",
       "        var qlm = mpld3.get_element(this.props.idqlm);\n",
       "        var qmm = mpld3.get_element(this.props.idqmm);\n",
       "        var qrm = mpld3.get_element(this.props.idqrm);\n",
       "        var shock1 = mpld3.get_element(this.props.idshock1);\n",
       "        var shock2 = mpld3.get_element(this.props.idshock2);\n",
       "        var rar1 = mpld3.get_element(this.props.idrar1);\n",
       "        var rar2 = mpld3.get_element(this.props.idrar2);\n",
       "        var rar1a = mpld3.get_element(this.props.idrar1a);\n",
       "        var rar2a = mpld3.get_element(this.props.idrar2a);\n",
       "        var rar1b = mpld3.get_element(this.props.idrar1b);\n",
       "        var rar2b = mpld3.get_element(this.props.idrar2b);\n",
       "        var rar1c = mpld3.get_element(this.props.idrar1c);\n",
       "        var rar2c = mpld3.get_element(this.props.idrar2c);\n",
       "        var rar1d = mpld3.get_element(this.props.idrar1d);\n",
       "        var rar2d = mpld3.get_element(this.props.idrar2d);\n",
       "        var timedot = mpld3.get_element(this.props.idtimedot);\n",
       "        var timeline = mpld3.get_element(this.props.idtimeline);\n",
       "        var q1 = mpld3.get_element(this.props.idq1);\n",
       "        var q2 = mpld3.get_element(this.props.idq2);\n",
       "        \n",
       "        // Set initial conditions for javascript calculations\n",
       "        //var qleft = obj.offsets[0];\n",
       "        //var qright = obj.offsets[1];\n",
       "        //var qmid = midpoint.offsets[0];\n",
       "        var offx = obj.ax.x(offm);\n",
       "        var offy = offx;\n",
       "        // Define initial values of hl, hr, hul and hur\n",
       "        var hl = obj.offsets[0][0];\n",
       "        var hul = obj.offsets[0][1];\n",
       "        var hr = obj.offsets[1][0];\n",
       "        var hur = obj.offsets[1][1];\n",
       "        hmfinal = 0;\n",
       "        humfinal = 0;\n",
       "        \n",
       "        // Main d3 drag function\n",
       "        var drag = d3.behavior.drag()\n",
       "            .origin(function(d) { return {x:obj.ax.x(d[0]),\n",
       "                                          y:obj.ax.y(d[1])}; }) \n",
       "            .on(\"dragstart\", dragstarted)\n",
       "            .on(\"drag\", dragged)\n",
       "            .on(\"dragend\", dragended);\n",
       "        \n",
       "        // Dragtime function for draggable time-dot (analog to main)\n",
       "        var dragtime = d3.behavior.drag()\n",
       "            .origin(function(d) { return {x:timedot.ax.x(d[0]),\n",
       "                                          y:timedot.ax.y(d[1])}; })                              \n",
       "            .on(\"dragstart\", dragstarted)\n",
       "            .on(\"drag\", dragged)\n",
       "            .on(\"dragend\", dragended);\n",
       "    \n",
       "        // Set elements of ql and qr draggable points and call main drag function\n",
       "        obj.elements()\n",
       "           .data(obj.offsets)\n",
       "           .style(\"cursor\", \"default\")\n",
       "           .call(drag);\n",
       "            \n",
       "        // Set elements for timedot draggable point and call dragtime function  \n",
       "        timedot.elements()\n",
       "           .data(timedot.offsets)\n",
       "           .style(\"cursor\", \"default\")\n",
       "           .call(dragtime);\n",
       "\n",
       "        // Begin phi and phi prime function\n",
       "        function phi(h,hl,hr,hul,hur) {\n",
       "            var ul = hul/hl;\n",
       "            var ur = hur/hr;\n",
       "            if (h < hl) {\n",
       "                var termIC1 = 2.0*Math.sqrt(g*hl);\n",
       "                var termIC2 = 2.0*Math.sqrt(g*h);\n",
       "                var phil = ul + termIC1 - termIC2;\n",
       "                var philp = -Math.sqrt(g/h);\n",
       "            }\n",
       "            if (h >= hl) {\n",
       "                var termHL1 = (h - hl);\n",
       "                var termHL2 = Math.sqrt(0.5*g*(1.0/h + 1.0/hl));\n",
       "                var termHL3 = termHL1*termHL2;\n",
       "                var phil = ul - termHL3 ;\n",
       "                var nume = termHL2*4*h*h;\n",
       "                var philp = -termHL2 + termHL1*g/nume;\n",
       "            }\n",
       "            if (h < hr) {\n",
       "                var termIC1 = 2.0*Math.sqrt(g*hr);\n",
       "                var termIC2 = 2.0*Math.sqrt(g*h);\n",
       "                var phir = ur - termIC1 + termIC2;\n",
       "                var phirp = Math.sqrt(g/h);\n",
       "            }\n",
       "            if (h >= hr) {\n",
       "                var termHL1 = (h - hr);\n",
       "                var termHL2 = Math.sqrt(0.5*g*(1.0/h + 1.0/hr));\n",
       "                var termHL3 = termHL1*termHL2;\n",
       "                var phir = ur + termHL3 ;\n",
       "                var nume = termHL2*4*h*h;\n",
       "                var phirp = termHL2 - termHL1*g/nume;\n",
       "            }\n",
       "            var phi = phil-phir;\n",
       "            var phiprime = philp - phirp\n",
       "            var um = 0.5*(phil + phir);\n",
       "            return [phi,phiprime,um];\n",
       "        }\n",
       "        \n",
       "        // Begin Newton iteration\n",
       "        function newton(hstar,hl,hr,hul,hur) {\n",
       "            var hn = hstar;\n",
       "            var error = 1;\n",
       "            while (error > 0.005) {\n",
       "                var hold = hn;\n",
       "                var phin = phi(hn,hl,hr,hul,hur);\n",
       "                var hn = hold - phin[0]/phin[1];\n",
       "                var um = phin[2];\n",
       "                error = Math.abs(hold - hn);\n",
       "            }\n",
       "            return [hn,um];\n",
       "        }\n",
       "        \n",
       "        // Calculate hugoniot loci\n",
       "        function hugoloci(hm,hside,huside,sign) {\n",
       "                var termHL1 = hm*(hm - hside);\n",
       "                if (hm == 0) {\n",
       "                    var termHL2 = 1.0; }\n",
       "                else {\n",
       "                   var termHL2 = Math.sqrt(0.5*g*(1.0/hm + 1.0/hside));}\n",
       "                   var termHL3 = termHL1*termHL2;\n",
       "                   var hloci = hm*huside/hside + sign*termHL3;\n",
       "            return hloci;} \n",
       "            \n",
       "        // Calculate integral curve\n",
       "        function integralcurve(hm,hside,huside,sign) {\n",
       "                var termIC1 = 2.0*hm*Math.sqrt(g*hside);\n",
       "                var termIC2 = 2.0*hm*Math.sqrt(g*hm);\n",
       "                var intcurve = hm*huside/hside - sign*(termIC1 - termIC2);\n",
       "            return intcurve;}\n",
       "            \n",
       "        // Calculate solution plot of h and hu as function of x\n",
       "        function solplot(hl,hm,hr,hul,hum,hur) {\n",
       "            var lam = [];\n",
       "            lam.push([-1000000, 0,0])\n",
       "            var ul = hul/hl;\n",
       "            var um = hum/hm;\n",
       "            var ur = hur/hr;\n",
       "            var shock1 = false;\n",
       "            var shock2 = false;\n",
       "            var qsol1 = d3.range(iter);\n",
       "            var qsol2 = d3.range(iter);\n",
       "            if (hm >= hl) {\n",
       "                var s1 = time*(hum - hul)/(hm - hl);\n",
       "                shock1 = true;\n",
       "            } else {\n",
       "                var s1b = [0,0];\n",
       "                s1b[0] = time*(ul - Math.sqrt(g*hl));\n",
       "                s1b[1] = time*(um - Math.sqrt(g*hm));\n",
       "                s1b.sort(d3.ascending);\n",
       "            }\n",
       "            if (hm >= hr) {\n",
       "                var s2 = time*(hur - hum)/(hr - hm);\n",
       "                shock2 = true;\n",
       "            } else {\n",
       "                var s2b = [0,0];\n",
       "                s2b[0] = time*(um + Math.sqrt(g*hm));\n",
       "                s2b[1] = time*(ur + Math.sqrt(g*hr));\n",
       "                s2b.sort(d3.ascending);\n",
       "            }\n",
       "            \n",
       "            for (var ii=0; ii <2*iter; ii++){\n",
       "                var xx = q1.data[ii][0];\n",
       "                // Calculate plot solution for 1 charactersitic (shock or rarefaction)\n",
       "                if (shock1) {\n",
       "                    if (xx <= s1){ qsol1[ii] = hl; qsol2[ii] = hul;}\n",
       "                    else { qsol1[ii] = hm; qsol2[ii] = hum;}\n",
       "                }\n",
       "                else {\n",
       "                    if (xx <= s1b[0]) { qsol1[ii] = hl; qsol2[ii] = hul;}\n",
       "                    else if (xx <= s1b[1]) {\n",
       "                        var m1 = (hm - hl)/(s1b[1] - s1b[0]);\n",
       "                        var m2 = (hum - hul)/(s1b[1] - s1b[0]);\n",
       "                        qsol1[ii] = m1*(xx - s1b[0]) + hl;\n",
       "                        qsol2[ii] = m2*(xx - s1b[0]) + hul;}\n",
       "                    else { qsol1[ii] = hm; qsol2[ii] = hum;}\n",
       "                }\n",
       "                // Calculate plot solution for 2 charactersitic (shock or rarefaction)\n",
       "                if (shock2) {\n",
       "                    if (xx > s2) {qsol1[ii] = hr; qsol2[ii] = hur;}\n",
       "                }\n",
       "                else{\n",
       "                    if (xx > s2b[0] && xx < s2b[1]) {\n",
       "                        var m1 = (hr - hm)/(s2b[1] - s2b[0]);\n",
       "                        var m2 = (hur - hum)/(s2b[1] - s2b[0]);\n",
       "                        qsol1[ii] = m1*(xx - s2b[0]) + hm;\n",
       "                        qsol2[ii] = m2*(xx - s2b[0]) + hum;}\n",
       "                    else if (xx > s2b[1]) { qsol1[ii] = hr; qsol2[ii] = hur;}\n",
       "                }\n",
       "            }\n",
       "            var solution = [qsol1,qsol2];\n",
       "            return solution;\n",
       "        }\n",
       "\n",
       "        // Function to update middle state   \n",
       "        function update_midstate(){\n",
       "            var hstar = 0.05*(hl + hr);\n",
       "            var solution = newton(hstar,hl,hr,hul,hur);\n",
       "            hmfinal = solution[0];\n",
       "            humfinal = solution[1]*hmfinal;\n",
       "            var xx = obj.ax.x(hmfinal);\n",
       "            var yy = obj.ax.y(humfinal);\n",
       "            // Update middle state point and marker position\n",
       "            midpoint.elements().transition().duration(5)\n",
       "            .attr(\"transform\", \"translate(\" + [xx, yy] + \")\");\n",
       "            // Move marker\n",
       "            qmm.elements().transition().duration(1)\n",
       "              .attr(\"transform\", \"translate(\" + [xx + 0.7*offx, yy + 0.7*offy] + \")\");\n",
       "        }\n",
       "        \n",
       "        // Functon to update xt-plane\n",
       "        function update_xtplane() {\n",
       "         // Calculate shcok speeds from R-H conditions\n",
       "         var lam1 = (humfinal - hul)/(hmfinal - hl);   \n",
       "         var lam2 = (hur - humfinal)/(hr - hmfinal);   \n",
       "         var lam1m = humfinal/hmfinal - Math.sqrt(g*hmfinal);\n",
       "         var lam2m = humfinal/hmfinal + Math.sqrt(g*hmfinal);\n",
       "         var lam1l = hul/hl - Math.sqrt(g*hl);\n",
       "         var lam2r = hur/hr + Math.sqrt(g*hr);\n",
       "         var color1 = \"red\";\n",
       "         var color2 = \"red\";\n",
       "         var thick1 = 4;\n",
       "         var thick2 = 4;\n",
       "         var fan = 0;\n",
       "         for (var ii=0; ii<iter_charac; ii++) {\n",
       "             if (hmfinal >= hl) {\n",
       "                 shock1.data[ii][1] = shock1.data[ii][0]/lam1;\n",
       "                 rar1.data[ii][1] = rar1.data[ii][0]/lam1;\n",
       "                 rar1a.data[ii][1] = rar1a.data[ii][0]/lam1;\n",
       "                 rar1b.data[ii][1] = rar1b.data[ii][0]/lam1;\n",
       "                 rar1c.data[ii][1] = rar1c.data[ii][0]/lam1;\n",
       "                 rar1d.data[ii][1] = rar1d.data[ii][0]/lam1;\n",
       "                 console.log(rar2a.data);\n",
       "                 color1 = \"red\";\n",
       "                 thick1 = 4;\n",
       "             } else {\n",
       "                 shock1.data[ii][1] = shock1.data[ii][0]/lam1l;\n",
       "                 rar1.data[ii][1] = rar1.data[ii][0]/lam1m;\n",
       "                 fan = Math.abs(lam1m - lam1l)/5;\n",
       "                 rar1a.data[ii][1] = rar1a.data[ii][0]/(lam1l + fan);\n",
       "                 rar1b.data[ii][1] = rar1b.data[ii][0]/(lam1l + 2*fan);\n",
       "                 rar1c.data[ii][1] = rar1c.data[ii][0]/(lam1l + 3*fan);\n",
       "                 rar1d.data[ii][1] = rar1d.data[ii][0]/(lam1l + 4*fan);\n",
       "                 color1 = \"blue\";\n",
       "                 thick1 = 1;\n",
       "             }\n",
       "             if (hmfinal >= hr) {\n",
       "                 shock2.data[ii][2] = shock2.data[ii][0]/lam2;\n",
       "                 rar2.data[ii][2] = rar2.data[ii][0]/lam2;\n",
       "                 rar2a.data[ii][2] = rar2a.data[ii][0]/lam2;\n",
       "                 rar2b.data[ii][2] = rar2b.data[ii][0]/lam2;\n",
       "                 rar2c.data[ii][2] = rar2c.data[ii][0]/lam2;\n",
       "                 rar2d.data[ii][2] = rar2d.data[ii][0]/lam2;\n",
       "                 color2 = \"red\";\n",
       "                 thick2 = 4;\n",
       "            } else {\n",
       "                 shock2.data[ii][2] = shock2.data[ii][0]/lam2r;\n",
       "                 rar2.data[ii][2] = rar2.data[ii][0]/lam2m;\n",
       "                 fan = Math.abs(lam2r - lam2m)/5;\n",
       "                 rar2a.data[ii][2] = rar2a.data[ii][0]/(lam2m + fan);\n",
       "                 rar2b.data[ii][2] = rar2b.data[ii][0]/(lam2m + 2*fan);\n",
       "                 rar2c.data[ii][2] = rar2c.data[ii][0]/(lam2m + 3*fan);\n",
       "                 rar2d.data[ii][2] = rar2d.data[ii][0]/(lam2m + 4*fan);\n",
       "                 color2 = \"blue\";\n",
       "                 thick2 = 1;\n",
       "            }                     \n",
       "         }\n",
       "         // Do transitions\n",
       "         shock1.elements().transition().duration(5)\n",
       "             .attr(\"d\", shock1.datafunc(shock1.data))\n",
       "             .style(\"stroke\", color1)\n",
       "             .style(\"stroke-width\", thick1);\n",
       "         shock2.elements().transition().duration(5)\n",
       "             .attr(\"d\", shock2.datafunc(shock2.data))\n",
       "             .style(\"stroke\", color2)\n",
       "             .style(\"stroke-width\", thick2);\n",
       "         rar1.elements().transition().duration(5)\n",
       "             .attr(\"d\", rar1.datafunc(rar1.data))\n",
       "             .style(\"stroke\", color1)\n",
       "             .style(\"stroke-width\", thick1);\n",
       "         rar2.elements().transition().duration(5)\n",
       "             .attr(\"d\", rar2.datafunc(rar2.data))\n",
       "             .style(\"stroke\", color2)\n",
       "             .style(\"stroke-width\", thick2);\n",
       "         rar1a.elements().transition().duration(5)\n",
       "             .attr(\"d\", rar1a.datafunc(rar1a.data))\n",
       "             .style(\"stroke\", color1)\n",
       "             .style(\"stroke-width\", thick1);\n",
       "         rar2a.elements().transition().duration(5)\n",
       "             .attr(\"d\", rar2a.datafunc(rar2a.data))\n",
       "             .style(\"stroke\", color2)\n",
       "             .style(\"stroke-width\", thick2);\n",
       "         rar1b.elements().transition().duration(5)\n",
       "             .attr(\"d\", rar1b.datafunc(rar1b.data))\n",
       "             .style(\"stroke\", color1)\n",
       "             .style(\"stroke-width\", thick1);\n",
       "         rar2b.elements().transition().duration(5)\n",
       "             .attr(\"d\", rar2b.datafunc(rar2b.data))\n",
       "             .style(\"stroke\", color2)\n",
       "             .style(\"stroke-width\", thick2);\n",
       "         rar1c.elements().transition().duration(5)\n",
       "             .attr(\"d\", rar1c.datafunc(rar1c.data))\n",
       "             .style(\"stroke\", color1)\n",
       "             .style(\"stroke-width\", thick1);\n",
       "         rar2c.elements().transition().duration(5)\n",
       "             .attr(\"d\", rar2c.datafunc(rar2c.data))\n",
       "             .style(\"stroke\", color2)\n",
       "             .style(\"stroke-width\", thick2);\n",
       "         rar1d.elements().transition().duration(5)\n",
       "             .attr(\"d\", rar1d.datafunc(rar1d.data))\n",
       "             .style(\"stroke\", color1)\n",
       "             .style(\"stroke-width\", thick1);\n",
       "         rar2d.elements().transition().duration(5)\n",
       "             .attr(\"d\", rar2d.datafunc(rar2d.data))\n",
       "             .style(\"stroke\", color2)\n",
       "             .style(\"stroke-width\", thick2);\n",
       "        }\n",
       "        \n",
       "        // Function to update solution plots\n",
       "        function update_solplots() {\n",
       "            var qsol = solplot(hl,hmfinal,hr,hul,humfinal,hur);\n",
       "                for (var ii=0; ii<2*iter; ii++){\n",
       "                    q1.data[ii][1] = qsol[0][ii]; \n",
       "                    q2.data[ii][2] = qsol[1][ii]; \n",
       "                }\n",
       "                // Do transitions\n",
       "                 q1.elements().transition().duration(5)\n",
       "                     .attr(\"d\", q1.datafunc(q1.data));\n",
       "                 q2.elements().transition().duration(5)\n",
       "                     .attr(\"d\", q2.datafunc(q2.data));\n",
       "        }\n",
       "        \n",
       "        // Initialize solution with given initial states before interacting\n",
       "        update_midstate();\n",
       "        update_xtplane();\n",
       "        update_solplots();\n",
       "        \n",
       "        // Begin drag function\n",
       "        function dragstarted(d) {\n",
       "          d3.event.sourceEvent.stopPropagation();\n",
       "          d3.select(this).classed(\"dragging\", true);\n",
       "        }\n",
       "   \n",
       "        // The drag function called while dragging is happening (meat of code here)\n",
       "        function dragged(d,i) {\n",
       "          if (i == 0  || i ==1) {\n",
       "              // Convert mouse coordinates in drag event (d3.event) to python coordinates d\n",
       "              d[0] = obj.ax.x.invert(d3.event.x);\n",
       "              d[1] = obj.ax.y.invert(d3.event.y);             \n",
       "              // Move ql and qr stored in obj (they have been selected in drag)\n",
       "              d3.select(this)\n",
       "                .attr(\"transform\", \"translate(\" + [d3.event.x,d3.event.y] + \")\");\n",
       "              // If obj corresponds to ql, move all the other left elements \n",
       "              }\n",
       "          if (i==0){\n",
       "              // Move marker\n",
       "              qlm.elements().transition().duration(1)\n",
       "                  .attr(\"transform\", \"translate(\" + [d3.event.x + offx, d3.event.y + offy] + \")\");     \n",
       "              // Re-calculate inital left variables when dragging \n",
       "              hl = obj.offsets[0][0];\n",
       "              hul = obj.offsets[0][1];\n",
       "              \n",
       "              // Draw Hugoniot loci through left state    \n",
       "              for (var ii=0; ii<iter; ii++) {\n",
       "                //Left from hl\n",
       "                hugol.data[ii][0] = ii*d[0]/(1.0*iter);\n",
       "                var hm = hugol.data[ii][0];\n",
       "                hugol.data[ii][1] = hugoloci(hm,hl,hul,-1) ;\n",
       "                //Right from hl\n",
       "                hugol2.data[ii][0] = d[0] + ii*(hmax-d[0])/(1.0*iter);\n",
       "                var hm2 = hugol2.data[ii][0];\n",
       "                hugol2.data[ii][1] = hugoloci(hm2,hl,hul,-1) ;\n",
       "                }\n",
       "              // Do transitions      \n",
       "              hugol.elements().transition().duration(5)\n",
       "                  .attr(\"d\", hugol.datafunc(hugol.data))\n",
       "                  .style(\"stroke-dasharray\", (\"7,7\"));\n",
       "              hugol2.elements().transition().duration(5)\n",
       "                  .attr(\"d\", hugol2.datafunc(hugol2.data));\n",
       "                               \n",
       "                  \n",
       "              // Draw integral curve through left state (note index bug for intcl.data[ii][j])\n",
       "              // and intcl2 it should be j =0,1 not j=1,2. Arrays somehow grow of sixe in mpld3\n",
       "              for (var ii=0; ii<iter; ii++) {\n",
       "                //Left from hl\n",
       "                intcl.data[ii][1] = ii*d[0]/(1.0*iter);\n",
       "                var hm = intcl.data[ii][1];\n",
       "                intcl.data[ii][2] = integralcurve(hm,hl,hul,-1);\n",
       "                //Right from hl\n",
       "                intcl2.data[ii][1] = d[0] + ii*(hmax-d[0])/(1.0*iter);\n",
       "                var hm2 = intcl2.data[ii][1];\n",
       "                intcl2.data[ii][2] = integralcurve(hm2,hl,hul,-1);\n",
       "              }\n",
       "              // Do transitions      \n",
       "              intcl.elements().transition().duration(5)\n",
       "                  .attr(\"d\", intcl.datafunc(intcl.data));\n",
       "              intcl2.elements().transition().duration(5)\n",
       "                  .attr(\"d\", intcl2.datafunc(intcl2.data))\n",
       "                  .style(\"stroke-dasharray\", (\"7,7\"));\n",
       "                  \n",
       "          }      \n",
       "          // if element corresponds to qr\n",
       "          else if (i==1) {\n",
       "              // Move marker\n",
       "              qrm.elements().transition().duration(1)\n",
       "                  .attr(\"transform\", \"translate(\" + [d3.event.x + offx, d3.event.y + offy] + \")\");\n",
       "              // Re-calculate inital right variables when dragging\n",
       "              hr = obj.offsets[1][0];\n",
       "              hur = obj.offsets[1][1];\n",
       "              \n",
       "              // Draw Hugoniot loci through right state    \n",
       "              for (var ii=0; ii<iter; ii++) {\n",
       "                //Left from hr\n",
       "                hugor.data[ii][0] = ii*d[0]/(1.0*iter);\n",
       "                var hm = hugor.data[ii][0];\n",
       "                hugor.data[ii][1] = hugoloci(hm,hr,hur,1) ;\n",
       "                //Right from hr\n",
       "                hugor2.data[ii][0] = d[0] + ii*(hmax-d[0])/(1.0*iter);\n",
       "                var hm2 = hugor2.data[ii][0];\n",
       "                hugor2.data[ii][1] = hugoloci(hm2,hr,hur,1) ;\n",
       "                }\n",
       "              // Do transitions      \n",
       "              hugor.elements().transition().duration(5)\n",
       "                  .attr(\"d\", hugor.datafunc(hugor.data))\n",
       "                  .style(\"stroke-dasharray\", (\"7,7\"));\n",
       "              hugor2.elements().transition().duration(5)\n",
       "                  .attr(\"d\", hugor2.datafunc(hugor2.data));\n",
       "                    \n",
       "              // Draw integral curve through right state (note index bug for intcr.data[ii][j])\n",
       "              // and intcr2 it should be j =0,1 not j=1,2. Arrays somehow grow of sixe in mpld3   \n",
       "              for (var ii=0; ii<iter; ii++) {\n",
       "                //Left from hr\n",
       "                intcr.data[ii][1] = ii*d[0]/(1.0*iter);\n",
       "                var hm = intcr.data[ii][1];\n",
       "                intcr.data[ii][2] = integralcurve(hm,hr,hur,1);\n",
       "                //Right from hr\n",
       "                intcr2.data[ii][1] = d[0] + ii*(hmax-d[0])/(1.0*iter);\n",
       "                var hm2 = intcr2.data[ii][1];\n",
       "                intcr2.data[ii][2] = integralcurve(hm2,hr,hur,1);\n",
       "              }\n",
       "              // Do transitions      \n",
       "              intcr.elements().transition().duration(5)\n",
       "                  .attr(\"d\", intcl.datafunc(intcr.data));\n",
       "              intcr2.elements().transition().duration(5)\n",
       "                  .attr(\"d\", intcr2.datafunc(intcr2.data))\n",
       "                  .style(\"stroke-dasharray\", (\"7,7\"));\n",
       "            }\n",
       "            // If time marker is moved\n",
       "            else if (i==2) {\n",
       "                // Convert mouse coordinates in drag event (d3.event) to python coordinates d\n",
       "                d[0] = timedot.ax.x.invert(d3.event.x);\n",
       "                d[1] = timedot.ax.y.invert(d3.event.y);      \n",
       "                d3.select(this)\n",
       "                    .attr(\"transform\", \"translate(\" + [d3.event.x,d3.event.y] + \")\");\n",
       "                // Calculate timedot position and assign it\n",
       "                var ty = timedot.ax.y.invert(d3.event.y);\n",
       "                if (ty >=0) {\n",
       "                    timeline.data[0][1] = ty;\n",
       "                    timeline.data[1][1] = ty;\n",
       "                    timeline.data[2][1] = ty;\n",
       "                    time = ty;\n",
       "                }\n",
       "                // Do transitions\n",
       "                timeline.elements().transition().duration(5)\n",
       "                    .attr(\"d\", timeline.datafunc(timeline.data));\n",
       "            }\n",
       "            \n",
       "            // Calculate middle state    \n",
       "            update_midstate();\n",
       "                  \n",
       "            // Calculate solution plots of h and hu\n",
       "            update_solplots();\n",
       "            \n",
       "            // Update characteristic in x-t plane\n",
       "            update_xtplane();\n",
       "             \n",
       "        }\n",
       "        // End dragging\n",
       "        function dragended(d) {\n",
       "          d3.select(this).classed(\"dragging\", false);\n",
       "        }\n",
       "    }\n",
       "    mpld3.register_plugin(\"drag\", PPlaneNLPlugin); \n",
       "    \n",
       "       mpld3.draw_figure(\"fig_el283411397794207036323196724884\", {\"axes\": [{\"xlim\": [0.0, 10.0], \"yscale\": \"linear\", \"axesbg\": \"#FFFFFF\", \"texts\": [{\"v_baseline\": \"hanging\", \"h_anchor\": \"middle\", \"color\": \"#000000\", \"text\": \"h\", \"coordinates\": \"axes\", \"zorder\": 3, \"alpha\": 1, \"fontsize\": 17.0, \"position\": [0.5, -0.10781249999999987], \"rotation\": -0.0, \"id\": \"el28341139779399108752\"}, {\"v_baseline\": \"auto\", \"h_anchor\": \"middle\", \"color\": \"#000000\", \"text\": \"hu\", \"coordinates\": \"axes\", \"zorder\": 3, \"alpha\": 1, \"fontsize\": 17.0, \"position\": [-0.12054227941176469, 0.50000000000000022], \"rotation\": -90.0, \"id\": \"el28341139779399172048\"}, {\"v_baseline\": \"auto\", \"h_anchor\": \"middle\", \"color\": \"#000000\", \"text\": \"Phase plane\", \"coordinates\": \"axes\", \"zorder\": 3, \"alpha\": 1, \"fontsize\": 18.0, \"position\": [0.5, 1.0249565972222223], \"rotation\": -0.0, \"id\": \"el28341139779398855568\"}, {\"v_baseline\": \"auto\", \"h_anchor\": \"start\", \"color\": \"#000000\", \"text\": \"None\", \"coordinates\": \"axes\", \"zorder\": 1000003.0, \"alpha\": 1, \"fontsize\": 12.0, \"position\": [-0.12647058823529411, -1.587499999999999], \"rotation\": -0.0, \"id\": \"el28341139779402276368\"}, {\"v_baseline\": \"auto\", \"h_anchor\": \"start\", \"color\": \"#000000\", \"text\": \"Hugoniot Loci\", \"coordinates\": \"axes\", \"zorder\": 1000003.0, \"alpha\": 1, \"fontsize\": 8.0, \"position\": [0.10398692810457516, 0.93261718750000044], \"rotation\": -0.0, \"id\": \"el28341139779399092496\"}, {\"v_baseline\": \"auto\", \"h_anchor\": \"start\", \"color\": \"#000000\", \"text\": \"Hugoniot Loci (unphysical)\", \"coordinates\": \"axes\", \"zorder\": 1000003.0, \"alpha\": 1, \"fontsize\": 8.0, \"position\": [0.10398692810457516, 0.87222222222222268], \"rotation\": -0.0, \"id\": \"el28341139779402187600\"}, {\"v_baseline\": \"auto\", \"h_anchor\": \"start\", \"color\": \"#000000\", \"text\": \"Integral Curves\", \"coordinates\": \"axes\", \"zorder\": 1000003.0, \"alpha\": 1, \"fontsize\": 8.0, \"position\": [0.10398692810457516, 0.81182725694444446], \"rotation\": -0.0, \"id\": \"el28341139779402190224\"}, {\"v_baseline\": \"auto\", \"h_anchor\": \"start\", \"color\": \"#000000\", \"text\": \"Integral Curves (unphysical)\", \"coordinates\": \"axes\", \"zorder\": 1000003.0, \"alpha\": 1, \"fontsize\": 8.0, \"position\": [0.10398692810457516, 0.7514322916666667], \"rotation\": -0.0, \"id\": \"el28341139779402274896\"}], \"zoomable\": true, \"images\": [], \"xdomain\": [0.0, 10.0], \"ylim\": [-15.0, 15.0], \"paths\": [{\"edgecolor\": \"#000000\", \"facecolor\": \"#FFFFFF\", \"edgewidth\": 1.0, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"axes\", \"dasharray\": \"10,0\", \"zorder\": 1000001.0, \"alpha\": 1, \"xindex\": 0, \"data\": \"data10\", \"id\": \"el28341139779399092048\"}], \"sharey\": [], 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4.332292645379066], [4.2727272727272725, 4.224795956173441, 4.258426491928066], [4.343434343434343, 4.141587588436732, 4.180932300726905], [4.414141414141414, 4.054189860060298, 4.099839725475321], [4.484848484848484, 3.962606746134305, 4.015177704407634], [4.555555555555555, 3.86684202470541, 3.9269744886092637], [4.626262626262626, 3.7668992890181068, 3.835257668788654], [4.696969696969697, 3.6627819588419728, 3.740054200611195], [4.767676767676767, 3.554493290964503, 3.641390428693108], [4.838383838383838, 3.442036388921271, 3.5392921093448617], [4.909090909090909, 3.3254142120281367, 3.433784432146899], [4.979797979797979, 3.204629583773915, 3.32489204043352], [5.05050505050505, 3.079685199626325, 3.212639050754918], [5.121212121212121, 2.9505836342991376, 3.0970490713821466], [5.191919191919192, 2.8173273485238743, 2.978145219914511], [5.262626262626263, 2.6799186953654583, 2.855950140044726], [5.333333333333333, 2.5383599261176872, 2.730486017532881], [5.404040404040404, 2.3926531958111026, 2.6017745954366127], [5.474747474747474, 2.242800568363003, 2.4698371886413835], [5.545454545454545, 2.0888040213967125, 2.334694697731763], [5.616161616161616, 1.9306654507548648, 2.1963676222415742], [5.686868686868687, 1.768386674729391, 2.0548760733182228], [5.757575757575758, 1.6019694380289247, 1.9102397858341664], [5.828282828282829, 1.431415415502629, 1.7624781299760688], [5.898989898989899, 1.256726215637915, 1.6116101223403643], [5.96969696969697, 1.0779033838480085, 1.4576544365617874], [6.04040404040404, 0.8949484055641399, 1.3006294135000207], [6.111111111111111, 0.7078627091458589, 1.1405530710076537], [6.181818181818182, 0.5166476686219621, 0.9774431133014065], [6.252525252525253, 0.32130460627350566, 0.8113169399570612], [6.3232323232323235, 0.12183479506954242, 0.6421916545473536], [6.393939393939394, -0.08176053903467029, 0.47008407294075916], [6.4646464646464645, -0.28948021492789877, 0.29501073127819666], [6.535353535353535, -0.5013230942932605, 0.11698789364345963], [6.6060606060606055, -0.7172880796708974, -0.06396844055757], [6.6767676767676765, -0.9373741126258093, -0.2478425294949833], [6.747474747474747, -1.1615801720141956, -0.43461888207683685], [6.818181818181818, -1.3899052723421654, -0.6242822513625921], [6.888888888888889, -1.6223484622110291, -0.8168176282163806], [6.959595959595959, -1.8589088228438602, -1.0122102351887055], [7.03030303030303, -2.0995854666884632, -1.2104455206164637], [7.101010101010101, -2.34437753609196, -1.4115091529310302], [7.171717171717171, -2.5932842020428915, -1.6153870151653535], [7.242424242424242, -2.84630466297674, -1.8220651996509947], [7.313131313131313, -3.103438143641135, -2.031530002896906], [7.383838383838384, -3.364683894017306, -2.2437679206418455], [7.454545454545454, -3.630041188294536, -2.4587656430731233], [7.525252525252525, -3.8995093238945575, -2.6765100502044117], [7.595959595959596, -4.173087620543049, -2.8969882074059488], [7.666666666666666, -4.450775419385634, -3.1201873610807045], [7.737373737373737, -4.732572082145856, -3.3460949344805027], [7.808080808080808, -5.018476990322792, -3.5746985236561706], [7.878787878787879, -5.308489544426211, -3.8059858935364748], [7.949494949494949, -5.6026091632470845, -4.039944974130407], [8.02020202020202, -5.900835283161788, -4.276563856848048], [8.09090909090909, -6.203167357467848, -4.515830790935116], [8.161616161616163, -6.509604855749924, -4.757734180016964], [8.232323232323232, -6.820147263274098, -5.00226257874743], [8.303030303030303, -7.134794080409298, -5.249404689558778], [8.373737373737374, -7.4535448220742, -5.499149359508682], [8.444444444444445, -7.7763990172083854, -5.751485577220619], [8.515151515151516, -8.103356208266627, -6.0064024699140415], [8.585858585858585, -8.4344159507349, -6.263889300521141], [8.656565656565657, -8.769577812667299, -6.523935464886884], [8.727272727272727, -9.108841374242457, -6.786530489049165], [8.797979797979798, -9.452206227339, -7.05166402659639], [8.868686868686869, -9.79967197512853, -7.319325856099427], [8.93939393939394, -10.151238231685776, -7.589505878615411], [9.01010101010101, -10.50690462161472, -7.862194115260785], [9.08080808080808, -10.866670779690198, -8.137380704851152], [9.151515151515152, -11.230536350514056, -8.415055901605596], [9.222222222222221, -11.598500988185139, -8.695210072913062], [9.292929292929292, -11.970564355982784, -8.977833697159028], [9.363636363636363, -12.34672612606271, -9.26291736160997], [9.434343434343434, -12.72698597916509, -9.550451760353951], [9.505050505050505, -13.111343604334126, -9.840427692295288], [9.575757575757574, -13.499798698648544, -10.132836059201566], [9.646464646464647, -13.892350966962642, -10.427667863801204], [9.717171717171716, -14.289000121657185, -10.724914207929864], [9.787878787878787, -14.689745882400086, -11.024566290724305], [9.858585858585858, -15.094587975915953, -11.32661540686179], [9.929292929292929, -15.503526135764563, -11.631052944843955], [10.0, -15.91656010212753, -11.937870385323382]], \"data13\": [[-11.1, -169.76593783806587, 169.76593783806587], [11.1, 169.76593783806587, -169.76593783806587]], \"data01\": [[-1.0, -1.0]]}, \"id\": \"el28341139779420703632\"});\n",
       "   }(mpld3);\n",
       "}else if(typeof define === \"function\" && define.amd){\n",
       "   // require.js is available: use it to load d3/mpld3\n",
       "   require.config({paths: {d3: \"https://mpld3.github.io/js/d3.v3.min\"}});\n",
       "   require([\"d3\"], function(d3){\n",
       "      window.d3 = d3;\n",
       "      mpld3_load_lib(\"https://mpld3.github.io/js/mpld3.v0.2.js\", function(){\n",
       "         \n",
       "    // init custom PPLaneNL plugin\n",
       "    mpld3.register_plugin(\"drag\", PPlaneNLPlugin);\n",
       "    PPlaneNLPlugin.prototype = Object.create(mpld3.Plugin.prototype);\n",
       "    PPlaneNLPlugin.prototype.constructor = PPlaneNLPlugin;\n",
       "    PPlaneNLPlugin.prototype.requiredProps = [\"id\", \"idmpoint\", \n",
       "                                              \"idg\", \"iditer\", \"iditer_charac\", \"idtime\", \"idhmax\", \"idoffm\",\n",
       "                                              \"idhugol\", \"idhugor\", \"idintcl\", \"idintcr\",\n",
       "                                              \"idhugol2\", \"idhugor2\", \"idintcl2\", \"idintcr2\", \n",
       "                                              \"idqlm\", \"idqmm\", \"idqrm\", \n",
       "                                              \"idshock1\", \"idshock2\", \"idrar1\", \"idrar2\",\n",
       "                                              \"idrar1a\", \"idrar2a\", \"idrar1b\", \"idrar2b\",\n",
       "                                              \"idrar1c\", \"idrar2c\", \"idrar1d\", \"idrar2d\",\n",
       "                                              \"idtimedot\", \"idtimeline\",\n",
       "                                              \"idq1\", \"idq2\"];\n",
       "    PPlaneNLPlugin.prototype.defaultProps = {}\n",
       "    function PPlaneNLPlugin(fig, props){\n",
       "        mpld3.Plugin.call(this, fig, props);\n",
       "        mpld3.insert_css(\"#\" + fig.figid + \" path.dragging\",\n",
       "                         {\"fill-opacity\": \"1.0 !important\",\n",
       "                          \"stroke-opacity\": \"1.0 !important\"});\n",
       "    };\n",
       "\n",
       "    // Call draw function, this function is being looped all the time\n",
       "    PPlaneNLPlugin.prototype.draw = function(){\n",
       "        // Get elements into script variables\n",
       "        var obj = mpld3.get_element(this.props.id);\n",
       "        var midpoint = mpld3.get_element(this.props.idmpoint);\n",
       "        var g = this.props.idg;\n",
       "        var iter = this.props.iditer;\n",
       "        var iter_charac = this.props.iditer_charac;\n",
       "        var time = this.props.idtime;\n",
       "        var hmax = this.props.idhmax;\n",
       "        var offm = this.props.idoffm;\n",
       "        var hugol = mpld3.get_element(this.props.idhugol);\n",
       "        var hugor = mpld3.get_element(this.props.idhugor);\n",
       "        var intcl = mpld3.get_element(this.props.idintcl);\n",
       "        var intcr = mpld3.get_element(this.props.idintcr);\n",
       "        var hugol2 = mpld3.get_element(this.props.idhugol2);\n",
       "        var hugor2 = mpld3.get_element(this.props.idhugor2);\n",
       "        var intcl2 = mpld3.get_element(this.props.idintcl2);\n",
       "        var intcr2 = mpld3.get_element(this.props.idintcr2);\n",
       "        var qlm = mpld3.get_element(this.props.idqlm);\n",
       "        var qmm = mpld3.get_element(this.props.idqmm);\n",
       "        var qrm = mpld3.get_element(this.props.idqrm);\n",
       "        var shock1 = mpld3.get_element(this.props.idshock1);\n",
       "        var shock2 = mpld3.get_element(this.props.idshock2);\n",
       "        var rar1 = mpld3.get_element(this.props.idrar1);\n",
       "        var rar2 = mpld3.get_element(this.props.idrar2);\n",
       "        var rar1a = mpld3.get_element(this.props.idrar1a);\n",
       "        var rar2a = mpld3.get_element(this.props.idrar2a);\n",
       "        var rar1b = mpld3.get_element(this.props.idrar1b);\n",
       "        var rar2b = mpld3.get_element(this.props.idrar2b);\n",
       "        var rar1c = mpld3.get_element(this.props.idrar1c);\n",
       "        var rar2c = mpld3.get_element(this.props.idrar2c);\n",
       "        var rar1d = mpld3.get_element(this.props.idrar1d);\n",
       "        var rar2d = mpld3.get_element(this.props.idrar2d);\n",
       "        var timedot = mpld3.get_element(this.props.idtimedot);\n",
       "        var timeline = mpld3.get_element(this.props.idtimeline);\n",
       "        var q1 = mpld3.get_element(this.props.idq1);\n",
       "        var q2 = mpld3.get_element(this.props.idq2);\n",
       "        \n",
       "        // Set initial conditions for javascript calculations\n",
       "        //var qleft = obj.offsets[0];\n",
       "        //var qright = obj.offsets[1];\n",
       "        //var qmid = midpoint.offsets[0];\n",
       "        var offx = obj.ax.x(offm);\n",
       "        var offy = offx;\n",
       "        // Define initial values of hl, hr, hul and hur\n",
       "        var hl = obj.offsets[0][0];\n",
       "        var hul = obj.offsets[0][1];\n",
       "        var hr = obj.offsets[1][0];\n",
       "        var hur = obj.offsets[1][1];\n",
       "        hmfinal = 0;\n",
       "        humfinal = 0;\n",
       "        \n",
       "        // Main d3 drag function\n",
       "        var drag = d3.behavior.drag()\n",
       "            .origin(function(d) { return {x:obj.ax.x(d[0]),\n",
       "                                          y:obj.ax.y(d[1])}; }) \n",
       "            .on(\"dragstart\", dragstarted)\n",
       "            .on(\"drag\", dragged)\n",
       "            .on(\"dragend\", dragended);\n",
       "        \n",
       "        // Dragtime function for draggable time-dot (analog to main)\n",
       "        var dragtime = d3.behavior.drag()\n",
       "            .origin(function(d) { return {x:timedot.ax.x(d[0]),\n",
       "                                          y:timedot.ax.y(d[1])}; })                              \n",
       "            .on(\"dragstart\", dragstarted)\n",
       "            .on(\"drag\", dragged)\n",
       "            .on(\"dragend\", dragended);\n",
       "    \n",
       "        // Set elements of ql and qr draggable points and call main drag function\n",
       "        obj.elements()\n",
       "           .data(obj.offsets)\n",
       "           .style(\"cursor\", \"default\")\n",
       "           .call(drag);\n",
       "            \n",
       "        // Set elements for timedot draggable point and call dragtime function  \n",
       "        timedot.elements()\n",
       "           .data(timedot.offsets)\n",
       "           .style(\"cursor\", \"default\")\n",
       "           .call(dragtime);\n",
       "\n",
       "        // Begin phi and phi prime function\n",
       "        function phi(h,hl,hr,hul,hur) {\n",
       "            var ul = hul/hl;\n",
       "            var ur = hur/hr;\n",
       "            if (h < hl) {\n",
       "                var termIC1 = 2.0*Math.sqrt(g*hl);\n",
       "                var termIC2 = 2.0*Math.sqrt(g*h);\n",
       "                var phil = ul + termIC1 - termIC2;\n",
       "                var philp = -Math.sqrt(g/h);\n",
       "            }\n",
       "            if (h >= hl) {\n",
       "                var termHL1 = (h - hl);\n",
       "                var termHL2 = Math.sqrt(0.5*g*(1.0/h + 1.0/hl));\n",
       "                var termHL3 = termHL1*termHL2;\n",
       "                var phil = ul - termHL3 ;\n",
       "                var nume = termHL2*4*h*h;\n",
       "                var philp = -termHL2 + termHL1*g/nume;\n",
       "            }\n",
       "            if (h < hr) {\n",
       "                var termIC1 = 2.0*Math.sqrt(g*hr);\n",
       "                var termIC2 = 2.0*Math.sqrt(g*h);\n",
       "                var phir = ur - termIC1 + termIC2;\n",
       "                var phirp = Math.sqrt(g/h);\n",
       "            }\n",
       "            if (h >= hr) {\n",
       "                var termHL1 = (h - hr);\n",
       "                var termHL2 = Math.sqrt(0.5*g*(1.0/h + 1.0/hr));\n",
       "                var termHL3 = termHL1*termHL2;\n",
       "                var phir = ur + termHL3 ;\n",
       "                var nume = termHL2*4*h*h;\n",
       "                var phirp = termHL2 - termHL1*g/nume;\n",
       "            }\n",
       "            var phi = phil-phir;\n",
       "            var phiprime = philp - phirp\n",
       "            var um = 0.5*(phil + phir);\n",
       "            return [phi,phiprime,um];\n",
       "        }\n",
       "        \n",
       "        // Begin Newton iteration\n",
       "        function newton(hstar,hl,hr,hul,hur) {\n",
       "            var hn = hstar;\n",
       "            var error = 1;\n",
       "            while (error > 0.005) {\n",
       "                var hold = hn;\n",
       "                var phin = phi(hn,hl,hr,hul,hur);\n",
       "                var hn = hold - phin[0]/phin[1];\n",
       "                var um = phin[2];\n",
       "                error = Math.abs(hold - hn);\n",
       "            }\n",
       "            return [hn,um];\n",
       "        }\n",
       "        \n",
       "        // Calculate hugoniot loci\n",
       "        function hugoloci(hm,hside,huside,sign) {\n",
       "                var termHL1 = hm*(hm - hside);\n",
       "                if (hm == 0) {\n",
       "                    var termHL2 = 1.0; }\n",
       "                else {\n",
       "                   var termHL2 = Math.sqrt(0.5*g*(1.0/hm + 1.0/hside));}\n",
       "                   var termHL3 = termHL1*termHL2;\n",
       "                   var hloci = hm*huside/hside + sign*termHL3;\n",
       "            return hloci;} \n",
       "            \n",
       "        // Calculate integral curve\n",
       "        function integralcurve(hm,hside,huside,sign) {\n",
       "                var termIC1 = 2.0*hm*Math.sqrt(g*hside);\n",
       "                var termIC2 = 2.0*hm*Math.sqrt(g*hm);\n",
       "                var intcurve = hm*huside/hside - sign*(termIC1 - termIC2);\n",
       "            return intcurve;}\n",
       "            \n",
       "        // Calculate solution plot of h and hu as function of x\n",
       "        function solplot(hl,hm,hr,hul,hum,hur) {\n",
       "            var lam = [];\n",
       "            lam.push([-1000000, 0,0])\n",
       "            var ul = hul/hl;\n",
       "            var um = hum/hm;\n",
       "            var ur = hur/hr;\n",
       "            var shock1 = false;\n",
       "            var shock2 = false;\n",
       "            var qsol1 = d3.range(iter);\n",
       "            var qsol2 = d3.range(iter);\n",
       "            if (hm >= hl) {\n",
       "                var s1 = time*(hum - hul)/(hm - hl);\n",
       "                shock1 = true;\n",
       "            } else {\n",
       "                var s1b = [0,0];\n",
       "                s1b[0] = time*(ul - Math.sqrt(g*hl));\n",
       "                s1b[1] = time*(um - Math.sqrt(g*hm));\n",
       "                s1b.sort(d3.ascending);\n",
       "            }\n",
       "            if (hm >= hr) {\n",
       "                var s2 = time*(hur - hum)/(hr - hm);\n",
       "                shock2 = true;\n",
       "            } else {\n",
       "                var s2b = [0,0];\n",
       "                s2b[0] = time*(um + Math.sqrt(g*hm));\n",
       "                s2b[1] = time*(ur + Math.sqrt(g*hr));\n",
       "                s2b.sort(d3.ascending);\n",
       "            }\n",
       "            \n",
       "            for (var ii=0; ii <2*iter; ii++){\n",
       "                var xx = q1.data[ii][0];\n",
       "                // Calculate plot solution for 1 charactersitic (shock or rarefaction)\n",
       "                if (shock1) {\n",
       "                    if (xx <= s1){ qsol1[ii] = hl; qsol2[ii] = hul;}\n",
       "                    else { qsol1[ii] = hm; qsol2[ii] = hum;}\n",
       "                }\n",
       "                else {\n",
       "                    if (xx <= s1b[0]) { qsol1[ii] = hl; qsol2[ii] = hul;}\n",
       "                    else if (xx <= s1b[1]) {\n",
       "                        var m1 = (hm - hl)/(s1b[1] - s1b[0]);\n",
       "                        var m2 = (hum - hul)/(s1b[1] - s1b[0]);\n",
       "                        qsol1[ii] = m1*(xx - s1b[0]) + hl;\n",
       "                        qsol2[ii] = m2*(xx - s1b[0]) + hul;}\n",
       "                    else { qsol1[ii] = hm; qsol2[ii] = hum;}\n",
       "                }\n",
       "                // Calculate plot solution for 2 charactersitic (shock or rarefaction)\n",
       "                if (shock2) {\n",
       "                    if (xx > s2) {qsol1[ii] = hr; qsol2[ii] = hur;}\n",
       "                }\n",
       "                else{\n",
       "                    if (xx > s2b[0] && xx < s2b[1]) {\n",
       "                        var m1 = (hr - hm)/(s2b[1] - s2b[0]);\n",
       "                        var m2 = (hur - hum)/(s2b[1] - s2b[0]);\n",
       "                        qsol1[ii] = m1*(xx - s2b[0]) + hm;\n",
       "                        qsol2[ii] = m2*(xx - s2b[0]) + hum;}\n",
       "                    else if (xx > s2b[1]) { qsol1[ii] = hr; qsol2[ii] = hur;}\n",
       "                }\n",
       "            }\n",
       "            var solution = [qsol1,qsol2];\n",
       "            return solution;\n",
       "        }\n",
       "\n",
       "        // Function to update middle state   \n",
       "        function update_midstate(){\n",
       "            var hstar = 0.05*(hl + hr);\n",
       "            var solution = newton(hstar,hl,hr,hul,hur);\n",
       "            hmfinal = solution[0];\n",
       "            humfinal = solution[1]*hmfinal;\n",
       "            var xx = obj.ax.x(hmfinal);\n",
       "            var yy = obj.ax.y(humfinal);\n",
       "            // Update middle state point and marker position\n",
       "            midpoint.elements().transition().duration(5)\n",
       "            .attr(\"transform\", \"translate(\" + [xx, yy] + \")\");\n",
       "            // Move marker\n",
       "            qmm.elements().transition().duration(1)\n",
       "              .attr(\"transform\", \"translate(\" + [xx + 0.7*offx, yy + 0.7*offy] + \")\");\n",
       "        }\n",
       "        \n",
       "        // Functon to update xt-plane\n",
       "        function update_xtplane() {\n",
       "         // Calculate shcok speeds from R-H conditions\n",
       "         var lam1 = (humfinal - hul)/(hmfinal - hl);   \n",
       "         var lam2 = (hur - humfinal)/(hr - hmfinal);   \n",
       "         var lam1m = humfinal/hmfinal - Math.sqrt(g*hmfinal);\n",
       "         var lam2m = humfinal/hmfinal + Math.sqrt(g*hmfinal);\n",
       "         var lam1l = hul/hl - Math.sqrt(g*hl);\n",
       "         var lam2r = hur/hr + Math.sqrt(g*hr);\n",
       "         var color1 = \"red\";\n",
       "         var color2 = \"red\";\n",
       "         var thick1 = 4;\n",
       "         var thick2 = 4;\n",
       "         var fan = 0;\n",
       "         for (var ii=0; ii<iter_charac; ii++) {\n",
       "             if (hmfinal >= hl) {\n",
       "                 shock1.data[ii][1] = shock1.data[ii][0]/lam1;\n",
       "                 rar1.data[ii][1] = rar1.data[ii][0]/lam1;\n",
       "                 rar1a.data[ii][1] = rar1a.data[ii][0]/lam1;\n",
       "                 rar1b.data[ii][1] = rar1b.data[ii][0]/lam1;\n",
       "                 rar1c.data[ii][1] = rar1c.data[ii][0]/lam1;\n",
       "                 rar1d.data[ii][1] = rar1d.data[ii][0]/lam1;\n",
       "                 console.log(rar2a.data);\n",
       "                 color1 = \"red\";\n",
       "                 thick1 = 4;\n",
       "             } else {\n",
       "                 shock1.data[ii][1] = shock1.data[ii][0]/lam1l;\n",
       "                 rar1.data[ii][1] = rar1.data[ii][0]/lam1m;\n",
       "                 fan = Math.abs(lam1m - lam1l)/5;\n",
       "                 rar1a.data[ii][1] = rar1a.data[ii][0]/(lam1l + fan);\n",
       "                 rar1b.data[ii][1] = rar1b.data[ii][0]/(lam1l + 2*fan);\n",
       "                 rar1c.data[ii][1] = rar1c.data[ii][0]/(lam1l + 3*fan);\n",
       "                 rar1d.data[ii][1] = rar1d.data[ii][0]/(lam1l + 4*fan);\n",
       "                 color1 = \"blue\";\n",
       "                 thick1 = 1;\n",
       "             }\n",
       "             if (hmfinal >= hr) {\n",
       "                 shock2.data[ii][2] = shock2.data[ii][0]/lam2;\n",
       "                 rar2.data[ii][2] = rar2.data[ii][0]/lam2;\n",
       "                 rar2a.data[ii][2] = rar2a.data[ii][0]/lam2;\n",
       "                 rar2b.data[ii][2] = rar2b.data[ii][0]/lam2;\n",
       "                 rar2c.data[ii][2] = rar2c.data[ii][0]/lam2;\n",
       "                 rar2d.data[ii][2] = rar2d.data[ii][0]/lam2;\n",
       "                 color2 = \"red\";\n",
       "                 thick2 = 4;\n",
       "            } else {\n",
       "                 shock2.data[ii][2] = shock2.data[ii][0]/lam2r;\n",
       "                 rar2.data[ii][2] = rar2.data[ii][0]/lam2m;\n",
       "                 fan = Math.abs(lam2r - lam2m)/5;\n",
       "                 rar2a.data[ii][2] = rar2a.data[ii][0]/(lam2m + fan);\n",
       "                 rar2b.data[ii][2] = rar2b.data[ii][0]/(lam2m + 2*fan);\n",
       "                 rar2c.data[ii][2] = rar2c.data[ii][0]/(lam2m + 3*fan);\n",
       "                 rar2d.data[ii][2] = rar2d.data[ii][0]/(lam2m + 4*fan);\n",
       "                 color2 = \"blue\";\n",
       "                 thick2 = 1;\n",
       "            }                     \n",
       "         }\n",
       "         // Do transitions\n",
       "         shock1.elements().transition().duration(5)\n",
       "             .attr(\"d\", shock1.datafunc(shock1.data))\n",
       "             .style(\"stroke\", color1)\n",
       "             .style(\"stroke-width\", thick1);\n",
       "         shock2.elements().transition().duration(5)\n",
       "             .attr(\"d\", shock2.datafunc(shock2.data))\n",
       "             .style(\"stroke\", color2)\n",
       "             .style(\"stroke-width\", thick2);\n",
       "         rar1.elements().transition().duration(5)\n",
       "             .attr(\"d\", rar1.datafunc(rar1.data))\n",
       "             .style(\"stroke\", color1)\n",
       "             .style(\"stroke-width\", thick1);\n",
       "         rar2.elements().transition().duration(5)\n",
       "             .attr(\"d\", rar2.datafunc(rar2.data))\n",
       "             .style(\"stroke\", color2)\n",
       "             .style(\"stroke-width\", thick2);\n",
       "         rar1a.elements().transition().duration(5)\n",
       "             .attr(\"d\", rar1a.datafunc(rar1a.data))\n",
       "             .style(\"stroke\", color1)\n",
       "             .style(\"stroke-width\", thick1);\n",
       "         rar2a.elements().transition().duration(5)\n",
       "             .attr(\"d\", rar2a.datafunc(rar2a.data))\n",
       "             .style(\"stroke\", color2)\n",
       "             .style(\"stroke-width\", thick2);\n",
       "         rar1b.elements().transition().duration(5)\n",
       "             .attr(\"d\", rar1b.datafunc(rar1b.data))\n",
       "             .style(\"stroke\", color1)\n",
       "             .style(\"stroke-width\", thick1);\n",
       "         rar2b.elements().transition().duration(5)\n",
       "             .attr(\"d\", rar2b.datafunc(rar2b.data))\n",
       "             .style(\"stroke\", color2)\n",
       "             .style(\"stroke-width\", thick2);\n",
       "         rar1c.elements().transition().duration(5)\n",
       "             .attr(\"d\", rar1c.datafunc(rar1c.data))\n",
       "             .style(\"stroke\", color1)\n",
       "             .style(\"stroke-width\", thick1);\n",
       "         rar2c.elements().transition().duration(5)\n",
       "             .attr(\"d\", rar2c.datafunc(rar2c.data))\n",
       "             .style(\"stroke\", color2)\n",
       "             .style(\"stroke-width\", thick2);\n",
       "         rar1d.elements().transition().duration(5)\n",
       "             .attr(\"d\", rar1d.datafunc(rar1d.data))\n",
       "             .style(\"stroke\", color1)\n",
       "             .style(\"stroke-width\", thick1);\n",
       "         rar2d.elements().transition().duration(5)\n",
       "             .attr(\"d\", rar2d.datafunc(rar2d.data))\n",
       "             .style(\"stroke\", color2)\n",
       "             .style(\"stroke-width\", thick2);\n",
       "        }\n",
       "        \n",
       "        // Function to update solution plots\n",
       "        function update_solplots() {\n",
       "            var qsol = solplot(hl,hmfinal,hr,hul,humfinal,hur);\n",
       "                for (var ii=0; ii<2*iter; ii++){\n",
       "                    q1.data[ii][1] = qsol[0][ii]; \n",
       "                    q2.data[ii][2] = qsol[1][ii]; \n",
       "                }\n",
       "                // Do transitions\n",
       "                 q1.elements().transition().duration(5)\n",
       "                     .attr(\"d\", q1.datafunc(q1.data));\n",
       "                 q2.elements().transition().duration(5)\n",
       "                     .attr(\"d\", q2.datafunc(q2.data));\n",
       "        }\n",
       "        \n",
       "        // Initialize solution with given initial states before interacting\n",
       "        update_midstate();\n",
       "        update_xtplane();\n",
       "        update_solplots();\n",
       "        \n",
       "        // Begin drag function\n",
       "        function dragstarted(d) {\n",
       "          d3.event.sourceEvent.stopPropagation();\n",
       "          d3.select(this).classed(\"dragging\", true);\n",
       "        }\n",
       "   \n",
       "        // The drag function called while dragging is happening (meat of code here)\n",
       "        function dragged(d,i) {\n",
       "          if (i == 0  || i ==1) {\n",
       "              // Convert mouse coordinates in drag event (d3.event) to python coordinates d\n",
       "              d[0] = obj.ax.x.invert(d3.event.x);\n",
       "              d[1] = obj.ax.y.invert(d3.event.y);             \n",
       "              // Move ql and qr stored in obj (they have been selected in drag)\n",
       "              d3.select(this)\n",
       "                .attr(\"transform\", \"translate(\" + [d3.event.x,d3.event.y] + \")\");\n",
       "              // If obj corresponds to ql, move all the other left elements \n",
       "              }\n",
       "          if (i==0){\n",
       "              // Move marker\n",
       "              qlm.elements().transition().duration(1)\n",
       "                  .attr(\"transform\", \"translate(\" + [d3.event.x + offx, d3.event.y + offy] + \")\");     \n",
       "              // Re-calculate inital left variables when dragging \n",
       "              hl = obj.offsets[0][0];\n",
       "              hul = obj.offsets[0][1];\n",
       "              \n",
       "              // Draw Hugoniot loci through left state    \n",
       "              for (var ii=0; ii<iter; ii++) {\n",
       "                //Left from hl\n",
       "                hugol.data[ii][0] = ii*d[0]/(1.0*iter);\n",
       "                var hm = hugol.data[ii][0];\n",
       "                hugol.data[ii][1] = hugoloci(hm,hl,hul,-1) ;\n",
       "                //Right from hl\n",
       "                hugol2.data[ii][0] = d[0] + ii*(hmax-d[0])/(1.0*iter);\n",
       "                var hm2 = hugol2.data[ii][0];\n",
       "                hugol2.data[ii][1] = hugoloci(hm2,hl,hul,-1) ;\n",
       "                }\n",
       "              // Do transitions      \n",
       "              hugol.elements().transition().duration(5)\n",
       "                  .attr(\"d\", hugol.datafunc(hugol.data))\n",
       "                  .style(\"stroke-dasharray\", (\"7,7\"));\n",
       "              hugol2.elements().transition().duration(5)\n",
       "                  .attr(\"d\", hugol2.datafunc(hugol2.data));\n",
       "                               \n",
       "                  \n",
       "              // Draw integral curve through left state (note index bug for intcl.data[ii][j])\n",
       "              // and intcl2 it should be j =0,1 not j=1,2. Arrays somehow grow of sixe in mpld3\n",
       "              for (var ii=0; ii<iter; ii++) {\n",
       "                //Left from hl\n",
       "                intcl.data[ii][1] = ii*d[0]/(1.0*iter);\n",
       "                var hm = intcl.data[ii][1];\n",
       "                intcl.data[ii][2] = integralcurve(hm,hl,hul,-1);\n",
       "                //Right from hl\n",
       "                intcl2.data[ii][1] = d[0] + ii*(hmax-d[0])/(1.0*iter);\n",
       "                var hm2 = intcl2.data[ii][1];\n",
       "                intcl2.data[ii][2] = integralcurve(hm2,hl,hul,-1);\n",
       "              }\n",
       "              // Do transitions      \n",
       "              intcl.elements().transition().duration(5)\n",
       "                  .attr(\"d\", intcl.datafunc(intcl.data));\n",
       "              intcl2.elements().transition().duration(5)\n",
       "                  .attr(\"d\", intcl2.datafunc(intcl2.data))\n",
       "                  .style(\"stroke-dasharray\", (\"7,7\"));\n",
       "                  \n",
       "          }      \n",
       "          // if element corresponds to qr\n",
       "          else if (i==1) {\n",
       "              // Move marker\n",
       "              qrm.elements().transition().duration(1)\n",
       "                  .attr(\"transform\", \"translate(\" + [d3.event.x + offx, d3.event.y + offy] + \")\");\n",
       "              // Re-calculate inital right variables when dragging\n",
       "              hr = obj.offsets[1][0];\n",
       "              hur = obj.offsets[1][1];\n",
       "              \n",
       "              // Draw Hugoniot loci through right state    \n",
       "              for (var ii=0; ii<iter; ii++) {\n",
       "                //Left from hr\n",
       "                hugor.data[ii][0] = ii*d[0]/(1.0*iter);\n",
       "                var hm = hugor.data[ii][0];\n",
       "                hugor.data[ii][1] = hugoloci(hm,hr,hur,1) ;\n",
       "                //Right from hr\n",
       "                hugor2.data[ii][0] = d[0] + ii*(hmax-d[0])/(1.0*iter);\n",
       "                var hm2 = hugor2.data[ii][0];\n",
       "                hugor2.data[ii][1] = hugoloci(hm2,hr,hur,1) ;\n",
       "                }\n",
       "              // Do transitions      \n",
       "              hugor.elements().transition().duration(5)\n",
       "                  .attr(\"d\", hugor.datafunc(hugor.data))\n",
       "                  .style(\"stroke-dasharray\", (\"7,7\"));\n",
       "              hugor2.elements().transition().duration(5)\n",
       "                  .attr(\"d\", hugor2.datafunc(hugor2.data));\n",
       "                    \n",
       "              // Draw integral curve through right state (note index bug for intcr.data[ii][j])\n",
       "              // and intcr2 it should be j =0,1 not j=1,2. Arrays somehow grow of sixe in mpld3   \n",
       "              for (var ii=0; ii<iter; ii++) {\n",
       "                //Left from hr\n",
       "                intcr.data[ii][1] = ii*d[0]/(1.0*iter);\n",
       "                var hm = intcr.data[ii][1];\n",
       "                intcr.data[ii][2] = integralcurve(hm,hr,hur,1);\n",
       "                //Right from hr\n",
       "                intcr2.data[ii][1] = d[0] + ii*(hmax-d[0])/(1.0*iter);\n",
       "                var hm2 = intcr2.data[ii][1];\n",
       "                intcr2.data[ii][2] = integralcurve(hm2,hr,hur,1);\n",
       "              }\n",
       "              // Do transitions      \n",
       "              intcr.elements().transition().duration(5)\n",
       "                  .attr(\"d\", intcl.datafunc(intcr.data));\n",
       "              intcr2.elements().transition().duration(5)\n",
       "                  .attr(\"d\", intcr2.datafunc(intcr2.data))\n",
       "                  .style(\"stroke-dasharray\", (\"7,7\"));\n",
       "            }\n",
       "            // If time marker is moved\n",
       "            else if (i==2) {\n",
       "                // Convert mouse coordinates in drag event (d3.event) to python coordinates d\n",
       "                d[0] = timedot.ax.x.invert(d3.event.x);\n",
       "                d[1] = timedot.ax.y.invert(d3.event.y);      \n",
       "                d3.select(this)\n",
       "                    .attr(\"transform\", \"translate(\" + [d3.event.x,d3.event.y] + \")\");\n",
       "                // Calculate timedot position and assign it\n",
       "                var ty = timedot.ax.y.invert(d3.event.y);\n",
       "                if (ty >=0) {\n",
       "                    timeline.data[0][1] = ty;\n",
       "                    timeline.data[1][1] = ty;\n",
       "                    timeline.data[2][1] = ty;\n",
       "                    time = ty;\n",
       "                }\n",
       "                // Do transitions\n",
       "                timeline.elements().transition().duration(5)\n",
       "                    .attr(\"d\", timeline.datafunc(timeline.data));\n",
       "            }\n",
       "            \n",
       "            // Calculate middle state    \n",
       "            update_midstate();\n",
       "                  \n",
       "            // Calculate solution plots of h and hu\n",
       "            update_solplots();\n",
       "            \n",
       "            // Update characteristic in x-t plane\n",
       "            update_xtplane();\n",
       "             \n",
       "        }\n",
       "        // End dragging\n",
       "        function dragended(d) {\n",
       "          d3.select(this).classed(\"dragging\", false);\n",
       "        }\n",
       "    }\n",
       "    mpld3.register_plugin(\"drag\", PPlaneNLPlugin); \n",
       "    \n",
       "         mpld3.draw_figure(\"fig_el283411397794207036323196724884\", {\"axes\": [{\"xlim\": [0.0, 10.0], \"yscale\": \"linear\", \"axesbg\": \"#FFFFFF\", \"texts\": [{\"v_baseline\": \"hanging\", \"h_anchor\": \"middle\", \"color\": \"#000000\", \"text\": \"h\", \"coordinates\": \"axes\", \"zorder\": 3, \"alpha\": 1, \"fontsize\": 17.0, \"position\": [0.5, -0.10781249999999987], \"rotation\": -0.0, \"id\": \"el28341139779399108752\"}, {\"v_baseline\": \"auto\", \"h_anchor\": \"middle\", \"color\": \"#000000\", \"text\": \"hu\", \"coordinates\": \"axes\", \"zorder\": 3, \"alpha\": 1, \"fontsize\": 17.0, \"position\": [-0.12054227941176469, 0.50000000000000022], \"rotation\": -90.0, \"id\": \"el28341139779399172048\"}, {\"v_baseline\": \"auto\", \"h_anchor\": \"middle\", \"color\": \"#000000\", \"text\": \"Phase plane\", \"coordinates\": \"axes\", \"zorder\": 3, \"alpha\": 1, \"fontsize\": 18.0, \"position\": [0.5, 1.0249565972222223], \"rotation\": -0.0, \"id\": \"el28341139779398855568\"}, {\"v_baseline\": \"auto\", \"h_anchor\": \"start\", \"color\": \"#000000\", \"text\": \"None\", \"coordinates\": \"axes\", \"zorder\": 1000003.0, \"alpha\": 1, \"fontsize\": 12.0, \"position\": [-0.12647058823529411, -1.587499999999999], \"rotation\": -0.0, \"id\": \"el28341139779402276368\"}, {\"v_baseline\": \"auto\", \"h_anchor\": \"start\", \"color\": \"#000000\", \"text\": \"Hugoniot Loci\", \"coordinates\": \"axes\", \"zorder\": 1000003.0, \"alpha\": 1, \"fontsize\": 8.0, \"position\": [0.10398692810457516, 0.93261718750000044], \"rotation\": -0.0, \"id\": \"el28341139779399092496\"}, {\"v_baseline\": \"auto\", \"h_anchor\": \"start\", \"color\": \"#000000\", \"text\": \"Hugoniot Loci (unphysical)\", \"coordinates\": \"axes\", \"zorder\": 1000003.0, \"alpha\": 1, \"fontsize\": 8.0, \"position\": [0.10398692810457516, 0.87222222222222268], \"rotation\": -0.0, \"id\": \"el28341139779402187600\"}, {\"v_baseline\": \"auto\", \"h_anchor\": \"start\", \"color\": \"#000000\", \"text\": \"Integral Curves\", \"coordinates\": \"axes\", \"zorder\": 1000003.0, \"alpha\": 1, \"fontsize\": 8.0, \"position\": [0.10398692810457516, 0.81182725694444446], \"rotation\": -0.0, \"id\": \"el28341139779402190224\"}, {\"v_baseline\": \"auto\", \"h_anchor\": \"start\", \"color\": \"#000000\", \"text\": \"Integral Curves (unphysical)\", \"coordinates\": \"axes\", \"zorder\": 1000003.0, \"alpha\": 1, \"fontsize\": 8.0, \"position\": [0.10398692810457516, 0.7514322916666667], \"rotation\": -0.0, \"id\": \"el28341139779402274896\"}], \"zoomable\": true, \"images\": [], \"xdomain\": [0.0, 10.0], \"ylim\": [-15.0, 15.0], \"paths\": [{\"edgecolor\": \"#000000\", \"facecolor\": \"#FFFFFF\", \"edgewidth\": 1.0, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"axes\", \"dasharray\": \"10,0\", \"zorder\": 1000001.0, \"alpha\": 1, \"xindex\": 0, \"data\": \"data10\", \"id\": \"el28341139779399092048\"}], \"sharey\": [], 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[8.868686868686869, -9.79967197512853, -7.319325856099427], [8.93939393939394, -10.151238231685776, -7.589505878615411], [9.01010101010101, -10.50690462161472, -7.862194115260785], [9.08080808080808, -10.866670779690198, -8.137380704851152], [9.151515151515152, -11.230536350514056, -8.415055901605596], [9.222222222222221, -11.598500988185139, -8.695210072913062], [9.292929292929292, -11.970564355982784, -8.977833697159028], [9.363636363636363, -12.34672612606271, -9.26291736160997], [9.434343434343434, -12.72698597916509, -9.550451760353951], [9.505050505050505, -13.111343604334126, -9.840427692295288], [9.575757575757574, -13.499798698648544, -10.132836059201566], [9.646464646464647, -13.892350966962642, -10.427667863801204], [9.717171717171716, -14.289000121657185, -10.724914207929864], [9.787878787878787, -14.689745882400086, -11.024566290724305], [9.858585858585858, -15.094587975915953, -11.32661540686179], [9.929292929292929, -15.503526135764563, -11.631052944843955], [10.0, -15.91656010212753, -11.937870385323382]], \"data13\": [[-11.1, -169.76593783806587, 169.76593783806587], [11.1, 169.76593783806587, -169.76593783806587]], \"data01\": [[-1.0, -1.0]]}, \"id\": \"el28341139779420703632\"});\n",
       "      });\n",
       "    });\n",
       "}else{\n",
       "    // require.js not available: dynamically load d3 & mpld3\n",
       "    mpld3_load_lib(\"https://mpld3.github.io/js/d3.v3.min.js\", function(){\n",
       "         mpld3_load_lib(\"https://mpld3.github.io/js/mpld3.v0.2.js\", function(){\n",
       "                 \n",
       "    // init custom PPLaneNL plugin\n",
       "    mpld3.register_plugin(\"drag\", PPlaneNLPlugin);\n",
       "    PPlaneNLPlugin.prototype = Object.create(mpld3.Plugin.prototype);\n",
       "    PPlaneNLPlugin.prototype.constructor = PPlaneNLPlugin;\n",
       "    PPlaneNLPlugin.prototype.requiredProps = [\"id\", \"idmpoint\", \n",
       "                                              \"idg\", \"iditer\", \"iditer_charac\", \"idtime\", \"idhmax\", \"idoffm\",\n",
       "                                              \"idhugol\", \"idhugor\", \"idintcl\", \"idintcr\",\n",
       "                                              \"idhugol2\", \"idhugor2\", \"idintcl2\", \"idintcr2\", \n",
       "                                              \"idqlm\", \"idqmm\", \"idqrm\", \n",
       "                                              \"idshock1\", \"idshock2\", \"idrar1\", \"idrar2\",\n",
       "                                              \"idrar1a\", \"idrar2a\", \"idrar1b\", \"idrar2b\",\n",
       "                                              \"idrar1c\", \"idrar2c\", \"idrar1d\", \"idrar2d\",\n",
       "                                              \"idtimedot\", \"idtimeline\",\n",
       "                                              \"idq1\", \"idq2\"];\n",
       "    PPlaneNLPlugin.prototype.defaultProps = {}\n",
       "    function PPlaneNLPlugin(fig, props){\n",
       "        mpld3.Plugin.call(this, fig, props);\n",
       "        mpld3.insert_css(\"#\" + fig.figid + \" path.dragging\",\n",
       "                         {\"fill-opacity\": \"1.0 !important\",\n",
       "                          \"stroke-opacity\": \"1.0 !important\"});\n",
       "    };\n",
       "\n",
       "    // Call draw function, this function is being looped all the time\n",
       "    PPlaneNLPlugin.prototype.draw = function(){\n",
       "        // Get elements into script variables\n",
       "        var obj = mpld3.get_element(this.props.id);\n",
       "        var midpoint = mpld3.get_element(this.props.idmpoint);\n",
       "        var g = this.props.idg;\n",
       "        var iter = this.props.iditer;\n",
       "        var iter_charac = this.props.iditer_charac;\n",
       "        var time = this.props.idtime;\n",
       "        var hmax = this.props.idhmax;\n",
       "        var offm = this.props.idoffm;\n",
       "        var hugol = mpld3.get_element(this.props.idhugol);\n",
       "        var hugor = mpld3.get_element(this.props.idhugor);\n",
       "        var intcl = mpld3.get_element(this.props.idintcl);\n",
       "        var intcr = mpld3.get_element(this.props.idintcr);\n",
       "        var hugol2 = mpld3.get_element(this.props.idhugol2);\n",
       "        var hugor2 = mpld3.get_element(this.props.idhugor2);\n",
       "        var intcl2 = mpld3.get_element(this.props.idintcl2);\n",
       "        var intcr2 = mpld3.get_element(this.props.idintcr2);\n",
       "        var qlm = mpld3.get_element(this.props.idqlm);\n",
       "        var qmm = mpld3.get_element(this.props.idqmm);\n",
       "        var qrm = mpld3.get_element(this.props.idqrm);\n",
       "        var shock1 = mpld3.get_element(this.props.idshock1);\n",
       "        var shock2 = mpld3.get_element(this.props.idshock2);\n",
       "        var rar1 = mpld3.get_element(this.props.idrar1);\n",
       "        var rar2 = mpld3.get_element(this.props.idrar2);\n",
       "        var rar1a = mpld3.get_element(this.props.idrar1a);\n",
       "        var rar2a = mpld3.get_element(this.props.idrar2a);\n",
       "        var rar1b = mpld3.get_element(this.props.idrar1b);\n",
       "        var rar2b = mpld3.get_element(this.props.idrar2b);\n",
       "        var rar1c = mpld3.get_element(this.props.idrar1c);\n",
       "        var rar2c = mpld3.get_element(this.props.idrar2c);\n",
       "        var rar1d = mpld3.get_element(this.props.idrar1d);\n",
       "        var rar2d = mpld3.get_element(this.props.idrar2d);\n",
       "        var timedot = mpld3.get_element(this.props.idtimedot);\n",
       "        var timeline = mpld3.get_element(this.props.idtimeline);\n",
       "        var q1 = mpld3.get_element(this.props.idq1);\n",
       "        var q2 = mpld3.get_element(this.props.idq2);\n",
       "        \n",
       "        // Set initial conditions for javascript calculations\n",
       "        //var qleft = obj.offsets[0];\n",
       "        //var qright = obj.offsets[1];\n",
       "        //var qmid = midpoint.offsets[0];\n",
       "        var offx = obj.ax.x(offm);\n",
       "        var offy = offx;\n",
       "        // Define initial values of hl, hr, hul and hur\n",
       "        var hl = obj.offsets[0][0];\n",
       "        var hul = obj.offsets[0][1];\n",
       "        var hr = obj.offsets[1][0];\n",
       "        var hur = obj.offsets[1][1];\n",
       "        hmfinal = 0;\n",
       "        humfinal = 0;\n",
       "        \n",
       "        // Main d3 drag function\n",
       "        var drag = d3.behavior.drag()\n",
       "            .origin(function(d) { return {x:obj.ax.x(d[0]),\n",
       "                                          y:obj.ax.y(d[1])}; }) \n",
       "            .on(\"dragstart\", dragstarted)\n",
       "            .on(\"drag\", dragged)\n",
       "            .on(\"dragend\", dragended);\n",
       "        \n",
       "        // Dragtime function for draggable time-dot (analog to main)\n",
       "        var dragtime = d3.behavior.drag()\n",
       "            .origin(function(d) { return {x:timedot.ax.x(d[0]),\n",
       "                                          y:timedot.ax.y(d[1])}; })                              \n",
       "            .on(\"dragstart\", dragstarted)\n",
       "            .on(\"drag\", dragged)\n",
       "            .on(\"dragend\", dragended);\n",
       "    \n",
       "        // Set elements of ql and qr draggable points and call main drag function\n",
       "        obj.elements()\n",
       "           .data(obj.offsets)\n",
       "           .style(\"cursor\", \"default\")\n",
       "           .call(drag);\n",
       "            \n",
       "        // Set elements for timedot draggable point and call dragtime function  \n",
       "        timedot.elements()\n",
       "           .data(timedot.offsets)\n",
       "           .style(\"cursor\", \"default\")\n",
       "           .call(dragtime);\n",
       "\n",
       "        // Begin phi and phi prime function\n",
       "        function phi(h,hl,hr,hul,hur) {\n",
       "            var ul = hul/hl;\n",
       "            var ur = hur/hr;\n",
       "            if (h < hl) {\n",
       "                var termIC1 = 2.0*Math.sqrt(g*hl);\n",
       "                var termIC2 = 2.0*Math.sqrt(g*h);\n",
       "                var phil = ul + termIC1 - termIC2;\n",
       "                var philp = -Math.sqrt(g/h);\n",
       "            }\n",
       "            if (h >= hl) {\n",
       "                var termHL1 = (h - hl);\n",
       "                var termHL2 = Math.sqrt(0.5*g*(1.0/h + 1.0/hl));\n",
       "                var termHL3 = termHL1*termHL2;\n",
       "                var phil = ul - termHL3 ;\n",
       "                var nume = termHL2*4*h*h;\n",
       "                var philp = -termHL2 + termHL1*g/nume;\n",
       "            }\n",
       "            if (h < hr) {\n",
       "                var termIC1 = 2.0*Math.sqrt(g*hr);\n",
       "                var termIC2 = 2.0*Math.sqrt(g*h);\n",
       "                var phir = ur - termIC1 + termIC2;\n",
       "                var phirp = Math.sqrt(g/h);\n",
       "            }\n",
       "            if (h >= hr) {\n",
       "                var termHL1 = (h - hr);\n",
       "                var termHL2 = Math.sqrt(0.5*g*(1.0/h + 1.0/hr));\n",
       "                var termHL3 = termHL1*termHL2;\n",
       "                var phir = ur + termHL3 ;\n",
       "                var nume = termHL2*4*h*h;\n",
       "                var phirp = termHL2 - termHL1*g/nume;\n",
       "            }\n",
       "            var phi = phil-phir;\n",
       "            var phiprime = philp - phirp\n",
       "            var um = 0.5*(phil + phir);\n",
       "            return [phi,phiprime,um];\n",
       "        }\n",
       "        \n",
       "        // Begin Newton iteration\n",
       "        function newton(hstar,hl,hr,hul,hur) {\n",
       "            var hn = hstar;\n",
       "            var error = 1;\n",
       "            while (error > 0.005) {\n",
       "                var hold = hn;\n",
       "                var phin = phi(hn,hl,hr,hul,hur);\n",
       "                var hn = hold - phin[0]/phin[1];\n",
       "                var um = phin[2];\n",
       "                error = Math.abs(hold - hn);\n",
       "            }\n",
       "            return [hn,um];\n",
       "        }\n",
       "        \n",
       "        // Calculate hugoniot loci\n",
       "        function hugoloci(hm,hside,huside,sign) {\n",
       "                var termHL1 = hm*(hm - hside);\n",
       "                if (hm == 0) {\n",
       "                    var termHL2 = 1.0; }\n",
       "                else {\n",
       "                   var termHL2 = Math.sqrt(0.5*g*(1.0/hm + 1.0/hside));}\n",
       "                   var termHL3 = termHL1*termHL2;\n",
       "                   var hloci = hm*huside/hside + sign*termHL3;\n",
       "            return hloci;} \n",
       "            \n",
       "        // Calculate integral curve\n",
       "        function integralcurve(hm,hside,huside,sign) {\n",
       "                var termIC1 = 2.0*hm*Math.sqrt(g*hside);\n",
       "                var termIC2 = 2.0*hm*Math.sqrt(g*hm);\n",
       "                var intcurve = hm*huside/hside - sign*(termIC1 - termIC2);\n",
       "            return intcurve;}\n",
       "            \n",
       "        // Calculate solution plot of h and hu as function of x\n",
       "        function solplot(hl,hm,hr,hul,hum,hur) {\n",
       "            var lam = [];\n",
       "            lam.push([-1000000, 0,0])\n",
       "            var ul = hul/hl;\n",
       "            var um = hum/hm;\n",
       "            var ur = hur/hr;\n",
       "            var shock1 = false;\n",
       "            var shock2 = false;\n",
       "            var qsol1 = d3.range(iter);\n",
       "            var qsol2 = d3.range(iter);\n",
       "            if (hm >= hl) {\n",
       "                var s1 = time*(hum - hul)/(hm - hl);\n",
       "                shock1 = true;\n",
       "            } else {\n",
       "                var s1b = [0,0];\n",
       "                s1b[0] = time*(ul - Math.sqrt(g*hl));\n",
       "                s1b[1] = time*(um - Math.sqrt(g*hm));\n",
       "                s1b.sort(d3.ascending);\n",
       "            }\n",
       "            if (hm >= hr) {\n",
       "                var s2 = time*(hur - hum)/(hr - hm);\n",
       "                shock2 = true;\n",
       "            } else {\n",
       "                var s2b = [0,0];\n",
       "                s2b[0] = time*(um + Math.sqrt(g*hm));\n",
       "                s2b[1] = time*(ur + Math.sqrt(g*hr));\n",
       "                s2b.sort(d3.ascending);\n",
       "            }\n",
       "            \n",
       "            for (var ii=0; ii <2*iter; ii++){\n",
       "                var xx = q1.data[ii][0];\n",
       "                // Calculate plot solution for 1 charactersitic (shock or rarefaction)\n",
       "                if (shock1) {\n",
       "                    if (xx <= s1){ qsol1[ii] = hl; qsol2[ii] = hul;}\n",
       "                    else { qsol1[ii] = hm; qsol2[ii] = hum;}\n",
       "                }\n",
       "                else {\n",
       "                    if (xx <= s1b[0]) { qsol1[ii] = hl; qsol2[ii] = hul;}\n",
       "                    else if (xx <= s1b[1]) {\n",
       "                        var m1 = (hm - hl)/(s1b[1] - s1b[0]);\n",
       "                        var m2 = (hum - hul)/(s1b[1] - s1b[0]);\n",
       "                        qsol1[ii] = m1*(xx - s1b[0]) + hl;\n",
       "                        qsol2[ii] = m2*(xx - s1b[0]) + hul;}\n",
       "                    else { qsol1[ii] = hm; qsol2[ii] = hum;}\n",
       "                }\n",
       "                // Calculate plot solution for 2 charactersitic (shock or rarefaction)\n",
       "                if (shock2) {\n",
       "                    if (xx > s2) {qsol1[ii] = hr; qsol2[ii] = hur;}\n",
       "                }\n",
       "                else{\n",
       "                    if (xx > s2b[0] && xx < s2b[1]) {\n",
       "                        var m1 = (hr - hm)/(s2b[1] - s2b[0]);\n",
       "                        var m2 = (hur - hum)/(s2b[1] - s2b[0]);\n",
       "                        qsol1[ii] = m1*(xx - s2b[0]) + hm;\n",
       "                        qsol2[ii] = m2*(xx - s2b[0]) + hum;}\n",
       "                    else if (xx > s2b[1]) { qsol1[ii] = hr; qsol2[ii] = hur;}\n",
       "                }\n",
       "            }\n",
       "            var solution = [qsol1,qsol2];\n",
       "            return solution;\n",
       "        }\n",
       "\n",
       "        // Function to update middle state   \n",
       "        function update_midstate(){\n",
       "            var hstar = 0.05*(hl + hr);\n",
       "            var solution = newton(hstar,hl,hr,hul,hur);\n",
       "            hmfinal = solution[0];\n",
       "            humfinal = solution[1]*hmfinal;\n",
       "            var xx = obj.ax.x(hmfinal);\n",
       "            var yy = obj.ax.y(humfinal);\n",
       "            // Update middle state point and marker position\n",
       "            midpoint.elements().transition().duration(5)\n",
       "            .attr(\"transform\", \"translate(\" + [xx, yy] + \")\");\n",
       "            // Move marker\n",
       "            qmm.elements().transition().duration(1)\n",
       "              .attr(\"transform\", \"translate(\" + [xx + 0.7*offx, yy + 0.7*offy] + \")\");\n",
       "        }\n",
       "        \n",
       "        // Functon to update xt-plane\n",
       "        function update_xtplane() {\n",
       "         // Calculate shcok speeds from R-H conditions\n",
       "         var lam1 = (humfinal - hul)/(hmfinal - hl);   \n",
       "         var lam2 = (hur - humfinal)/(hr - hmfinal);   \n",
       "         var lam1m = humfinal/hmfinal - Math.sqrt(g*hmfinal);\n",
       "         var lam2m = humfinal/hmfinal + Math.sqrt(g*hmfinal);\n",
       "         var lam1l = hul/hl - Math.sqrt(g*hl);\n",
       "         var lam2r = hur/hr + Math.sqrt(g*hr);\n",
       "         var color1 = \"red\";\n",
       "         var color2 = \"red\";\n",
       "         var thick1 = 4;\n",
       "         var thick2 = 4;\n",
       "         var fan = 0;\n",
       "         for (var ii=0; ii<iter_charac; ii++) {\n",
       "             if (hmfinal >= hl) {\n",
       "                 shock1.data[ii][1] = shock1.data[ii][0]/lam1;\n",
       "                 rar1.data[ii][1] = rar1.data[ii][0]/lam1;\n",
       "                 rar1a.data[ii][1] = rar1a.data[ii][0]/lam1;\n",
       "                 rar1b.data[ii][1] = rar1b.data[ii][0]/lam1;\n",
       "                 rar1c.data[ii][1] = rar1c.data[ii][0]/lam1;\n",
       "                 rar1d.data[ii][1] = rar1d.data[ii][0]/lam1;\n",
       "                 console.log(rar2a.data);\n",
       "                 color1 = \"red\";\n",
       "                 thick1 = 4;\n",
       "             } else {\n",
       "                 shock1.data[ii][1] = shock1.data[ii][0]/lam1l;\n",
       "                 rar1.data[ii][1] = rar1.data[ii][0]/lam1m;\n",
       "                 fan = Math.abs(lam1m - lam1l)/5;\n",
       "                 rar1a.data[ii][1] = rar1a.data[ii][0]/(lam1l + fan);\n",
       "                 rar1b.data[ii][1] = rar1b.data[ii][0]/(lam1l + 2*fan);\n",
       "                 rar1c.data[ii][1] = rar1c.data[ii][0]/(lam1l + 3*fan);\n",
       "                 rar1d.data[ii][1] = rar1d.data[ii][0]/(lam1l + 4*fan);\n",
       "                 color1 = \"blue\";\n",
       "                 thick1 = 1;\n",
       "             }\n",
       "             if (hmfinal >= hr) {\n",
       "                 shock2.data[ii][2] = shock2.data[ii][0]/lam2;\n",
       "                 rar2.data[ii][2] = rar2.data[ii][0]/lam2;\n",
       "                 rar2a.data[ii][2] = rar2a.data[ii][0]/lam2;\n",
       "                 rar2b.data[ii][2] = rar2b.data[ii][0]/lam2;\n",
       "                 rar2c.data[ii][2] = rar2c.data[ii][0]/lam2;\n",
       "                 rar2d.data[ii][2] = rar2d.data[ii][0]/lam2;\n",
       "                 color2 = \"red\";\n",
       "                 thick2 = 4;\n",
       "            } else {\n",
       "                 shock2.data[ii][2] = shock2.data[ii][0]/lam2r;\n",
       "                 rar2.data[ii][2] = rar2.data[ii][0]/lam2m;\n",
       "                 fan = Math.abs(lam2r - lam2m)/5;\n",
       "                 rar2a.data[ii][2] = rar2a.data[ii][0]/(lam2m + fan);\n",
       "                 rar2b.data[ii][2] = rar2b.data[ii][0]/(lam2m + 2*fan);\n",
       "                 rar2c.data[ii][2] = rar2c.data[ii][0]/(lam2m + 3*fan);\n",
       "                 rar2d.data[ii][2] = rar2d.data[ii][0]/(lam2m + 4*fan);\n",
       "                 color2 = \"blue\";\n",
       "                 thick2 = 1;\n",
       "            }                     \n",
       "         }\n",
       "         // Do transitions\n",
       "         shock1.elements().transition().duration(5)\n",
       "             .attr(\"d\", shock1.datafunc(shock1.data))\n",
       "             .style(\"stroke\", color1)\n",
       "             .style(\"stroke-width\", thick1);\n",
       "         shock2.elements().transition().duration(5)\n",
       "             .attr(\"d\", shock2.datafunc(shock2.data))\n",
       "             .style(\"stroke\", color2)\n",
       "             .style(\"stroke-width\", thick2);\n",
       "         rar1.elements().transition().duration(5)\n",
       "             .attr(\"d\", rar1.datafunc(rar1.data))\n",
       "             .style(\"stroke\", color1)\n",
       "             .style(\"stroke-width\", thick1);\n",
       "         rar2.elements().transition().duration(5)\n",
       "             .attr(\"d\", rar2.datafunc(rar2.data))\n",
       "             .style(\"stroke\", color2)\n",
       "             .style(\"stroke-width\", thick2);\n",
       "         rar1a.elements().transition().duration(5)\n",
       "             .attr(\"d\", rar1a.datafunc(rar1a.data))\n",
       "             .style(\"stroke\", color1)\n",
       "             .style(\"stroke-width\", thick1);\n",
       "         rar2a.elements().transition().duration(5)\n",
       "             .attr(\"d\", rar2a.datafunc(rar2a.data))\n",
       "             .style(\"stroke\", color2)\n",
       "             .style(\"stroke-width\", thick2);\n",
       "         rar1b.elements().transition().duration(5)\n",
       "             .attr(\"d\", rar1b.datafunc(rar1b.data))\n",
       "             .style(\"stroke\", color1)\n",
       "             .style(\"stroke-width\", thick1);\n",
       "         rar2b.elements().transition().duration(5)\n",
       "             .attr(\"d\", rar2b.datafunc(rar2b.data))\n",
       "             .style(\"stroke\", color2)\n",
       "             .style(\"stroke-width\", thick2);\n",
       "         rar1c.elements().transition().duration(5)\n",
       "             .attr(\"d\", rar1c.datafunc(rar1c.data))\n",
       "             .style(\"stroke\", color1)\n",
       "             .style(\"stroke-width\", thick1);\n",
       "         rar2c.elements().transition().duration(5)\n",
       "             .attr(\"d\", rar2c.datafunc(rar2c.data))\n",
       "             .style(\"stroke\", color2)\n",
       "             .style(\"stroke-width\", thick2);\n",
       "         rar1d.elements().transition().duration(5)\n",
       "             .attr(\"d\", rar1d.datafunc(rar1d.data))\n",
       "             .style(\"stroke\", color1)\n",
       "             .style(\"stroke-width\", thick1);\n",
       "         rar2d.elements().transition().duration(5)\n",
       "             .attr(\"d\", rar2d.datafunc(rar2d.data))\n",
       "             .style(\"stroke\", color2)\n",
       "             .style(\"stroke-width\", thick2);\n",
       "        }\n",
       "        \n",
       "        // Function to update solution plots\n",
       "        function update_solplots() {\n",
       "            var qsol = solplot(hl,hmfinal,hr,hul,humfinal,hur);\n",
       "                for (var ii=0; ii<2*iter; ii++){\n",
       "                    q1.data[ii][1] = qsol[0][ii]; \n",
       "                    q2.data[ii][2] = qsol[1][ii]; \n",
       "                }\n",
       "                // Do transitions\n",
       "                 q1.elements().transition().duration(5)\n",
       "                     .attr(\"d\", q1.datafunc(q1.data));\n",
       "                 q2.elements().transition().duration(5)\n",
       "                     .attr(\"d\", q2.datafunc(q2.data));\n",
       "        }\n",
       "        \n",
       "        // Initialize solution with given initial states before interacting\n",
       "        update_midstate();\n",
       "        update_xtplane();\n",
       "        update_solplots();\n",
       "        \n",
       "        // Begin drag function\n",
       "        function dragstarted(d) {\n",
       "          d3.event.sourceEvent.stopPropagation();\n",
       "          d3.select(this).classed(\"dragging\", true);\n",
       "        }\n",
       "   \n",
       "        // The drag function called while dragging is happening (meat of code here)\n",
       "        function dragged(d,i) {\n",
       "          if (i == 0  || i ==1) {\n",
       "              // Convert mouse coordinates in drag event (d3.event) to python coordinates d\n",
       "              d[0] = obj.ax.x.invert(d3.event.x);\n",
       "              d[1] = obj.ax.y.invert(d3.event.y);             \n",
       "              // Move ql and qr stored in obj (they have been selected in drag)\n",
       "              d3.select(this)\n",
       "                .attr(\"transform\", \"translate(\" + [d3.event.x,d3.event.y] + \")\");\n",
       "              // If obj corresponds to ql, move all the other left elements \n",
       "              }\n",
       "          if (i==0){\n",
       "              // Move marker\n",
       "              qlm.elements().transition().duration(1)\n",
       "                  .attr(\"transform\", \"translate(\" + [d3.event.x + offx, d3.event.y + offy] + \")\");     \n",
       "              // Re-calculate inital left variables when dragging \n",
       "              hl = obj.offsets[0][0];\n",
       "              hul = obj.offsets[0][1];\n",
       "              \n",
       "              // Draw Hugoniot loci through left state    \n",
       "              for (var ii=0; ii<iter; ii++) {\n",
       "                //Left from hl\n",
       "                hugol.data[ii][0] = ii*d[0]/(1.0*iter);\n",
       "                var hm = hugol.data[ii][0];\n",
       "                hugol.data[ii][1] = hugoloci(hm,hl,hul,-1) ;\n",
       "                //Right from hl\n",
       "                hugol2.data[ii][0] = d[0] + ii*(hmax-d[0])/(1.0*iter);\n",
       "                var hm2 = hugol2.data[ii][0];\n",
       "                hugol2.data[ii][1] = hugoloci(hm2,hl,hul,-1) ;\n",
       "                }\n",
       "              // Do transitions      \n",
       "              hugol.elements().transition().duration(5)\n",
       "                  .attr(\"d\", hugol.datafunc(hugol.data))\n",
       "                  .style(\"stroke-dasharray\", (\"7,7\"));\n",
       "              hugol2.elements().transition().duration(5)\n",
       "                  .attr(\"d\", hugol2.datafunc(hugol2.data));\n",
       "                               \n",
       "                  \n",
       "              // Draw integral curve through left state (note index bug for intcl.data[ii][j])\n",
       "              // and intcl2 it should be j =0,1 not j=1,2. Arrays somehow grow of sixe in mpld3\n",
       "              for (var ii=0; ii<iter; ii++) {\n",
       "                //Left from hl\n",
       "                intcl.data[ii][1] = ii*d[0]/(1.0*iter);\n",
       "                var hm = intcl.data[ii][1];\n",
       "                intcl.data[ii][2] = integralcurve(hm,hl,hul,-1);\n",
       "                //Right from hl\n",
       "                intcl2.data[ii][1] = d[0] + ii*(hmax-d[0])/(1.0*iter);\n",
       "                var hm2 = intcl2.data[ii][1];\n",
       "                intcl2.data[ii][2] = integralcurve(hm2,hl,hul,-1);\n",
       "              }\n",
       "              // Do transitions      \n",
       "              intcl.elements().transition().duration(5)\n",
       "                  .attr(\"d\", intcl.datafunc(intcl.data));\n",
       "              intcl2.elements().transition().duration(5)\n",
       "                  .attr(\"d\", intcl2.datafunc(intcl2.data))\n",
       "                  .style(\"stroke-dasharray\", (\"7,7\"));\n",
       "                  \n",
       "          }      \n",
       "          // if element corresponds to qr\n",
       "          else if (i==1) {\n",
       "              // Move marker\n",
       "              qrm.elements().transition().duration(1)\n",
       "                  .attr(\"transform\", \"translate(\" + [d3.event.x + offx, d3.event.y + offy] + \")\");\n",
       "              // Re-calculate inital right variables when dragging\n",
       "              hr = obj.offsets[1][0];\n",
       "              hur = obj.offsets[1][1];\n",
       "              \n",
       "              // Draw Hugoniot loci through right state    \n",
       "              for (var ii=0; ii<iter; ii++) {\n",
       "                //Left from hr\n",
       "                hugor.data[ii][0] = ii*d[0]/(1.0*iter);\n",
       "                var hm = hugor.data[ii][0];\n",
       "                hugor.data[ii][1] = hugoloci(hm,hr,hur,1) ;\n",
       "                //Right from hr\n",
       "                hugor2.data[ii][0] = d[0] + ii*(hmax-d[0])/(1.0*iter);\n",
       "                var hm2 = hugor2.data[ii][0];\n",
       "                hugor2.data[ii][1] = hugoloci(hm2,hr,hur,1) ;\n",
       "                }\n",
       "              // Do transitions      \n",
       "              hugor.elements().transition().duration(5)\n",
       "                  .attr(\"d\", hugor.datafunc(hugor.data))\n",
       "                  .style(\"stroke-dasharray\", (\"7,7\"));\n",
       "              hugor2.elements().transition().duration(5)\n",
       "                  .attr(\"d\", hugor2.datafunc(hugor2.data));\n",
       "                    \n",
       "              // Draw integral curve through right state (note index bug for intcr.data[ii][j])\n",
       "              // and intcr2 it should be j =0,1 not j=1,2. Arrays somehow grow of sixe in mpld3   \n",
       "              for (var ii=0; ii<iter; ii++) {\n",
       "                //Left from hr\n",
       "                intcr.data[ii][1] = ii*d[0]/(1.0*iter);\n",
       "                var hm = intcr.data[ii][1];\n",
       "                intcr.data[ii][2] = integralcurve(hm,hr,hur,1);\n",
       "                //Right from hr\n",
       "                intcr2.data[ii][1] = d[0] + ii*(hmax-d[0])/(1.0*iter);\n",
       "                var hm2 = intcr2.data[ii][1];\n",
       "                intcr2.data[ii][2] = integralcurve(hm2,hr,hur,1);\n",
       "              }\n",
       "              // Do transitions      \n",
       "              intcr.elements().transition().duration(5)\n",
       "                  .attr(\"d\", intcl.datafunc(intcr.data));\n",
       "              intcr2.elements().transition().duration(5)\n",
       "                  .attr(\"d\", intcr2.datafunc(intcr2.data))\n",
       "                  .style(\"stroke-dasharray\", (\"7,7\"));\n",
       "            }\n",
       "            // If time marker is moved\n",
       "            else if (i==2) {\n",
       "                // Convert mouse coordinates in drag event (d3.event) to python coordinates d\n",
       "                d[0] = timedot.ax.x.invert(d3.event.x);\n",
       "                d[1] = timedot.ax.y.invert(d3.event.y);      \n",
       "                d3.select(this)\n",
       "                    .attr(\"transform\", \"translate(\" + [d3.event.x,d3.event.y] + \")\");\n",
       "                // Calculate timedot position and assign it\n",
       "                var ty = timedot.ax.y.invert(d3.event.y);\n",
       "                if (ty >=0) {\n",
       "                    timeline.data[0][1] = ty;\n",
       "                    timeline.data[1][1] = ty;\n",
       "                    timeline.data[2][1] = ty;\n",
       "                    time = ty;\n",
       "                }\n",
       "                // Do transitions\n",
       "                timeline.elements().transition().duration(5)\n",
       "                    .attr(\"d\", timeline.datafunc(timeline.data));\n",
       "            }\n",
       "            \n",
       "            // Calculate middle state    \n",
       "            update_midstate();\n",
       "                  \n",
       "            // Calculate solution plots of h and hu\n",
       "            update_solplots();\n",
       "            \n",
       "            // Update characteristic in x-t plane\n",
       "            update_xtplane();\n",
       "             \n",
       "        }\n",
       "        // End dragging\n",
       "        function dragended(d) {\n",
       "          d3.select(this).classed(\"dragging\", false);\n",
       "        }\n",
       "    }\n",
       "    mpld3.register_plugin(\"drag\", PPlaneNLPlugin); \n",
       "    \n",
       "                 mpld3.draw_figure(\"fig_el283411397794207036323196724884\", {\"axes\": [{\"xlim\": [0.0, 10.0], \"yscale\": \"linear\", \"axesbg\": \"#FFFFFF\", \"texts\": [{\"v_baseline\": \"hanging\", \"h_anchor\": \"middle\", \"color\": \"#000000\", \"text\": \"h\", \"coordinates\": \"axes\", \"zorder\": 3, \"alpha\": 1, \"fontsize\": 17.0, \"position\": [0.5, -0.10781249999999987], \"rotation\": -0.0, \"id\": \"el28341139779399108752\"}, {\"v_baseline\": \"auto\", \"h_anchor\": \"middle\", \"color\": \"#000000\", \"text\": \"hu\", \"coordinates\": \"axes\", \"zorder\": 3, \"alpha\": 1, \"fontsize\": 17.0, \"position\": [-0.12054227941176469, 0.50000000000000022], \"rotation\": -90.0, \"id\": \"el28341139779399172048\"}, {\"v_baseline\": \"auto\", \"h_anchor\": \"middle\", \"color\": \"#000000\", \"text\": \"Phase plane\", \"coordinates\": \"axes\", \"zorder\": 3, \"alpha\": 1, \"fontsize\": 18.0, \"position\": [0.5, 1.0249565972222223], \"rotation\": -0.0, \"id\": \"el28341139779398855568\"}, {\"v_baseline\": \"auto\", \"h_anchor\": \"start\", \"color\": \"#000000\", \"text\": \"None\", \"coordinates\": \"axes\", \"zorder\": 1000003.0, \"alpha\": 1, \"fontsize\": 12.0, \"position\": [-0.12647058823529411, -1.587499999999999], \"rotation\": -0.0, \"id\": \"el28341139779402276368\"}, {\"v_baseline\": \"auto\", \"h_anchor\": \"start\", \"color\": \"#000000\", \"text\": \"Hugoniot Loci\", \"coordinates\": \"axes\", \"zorder\": 1000003.0, \"alpha\": 1, \"fontsize\": 8.0, \"position\": [0.10398692810457516, 0.93261718750000044], \"rotation\": -0.0, \"id\": \"el28341139779399092496\"}, {\"v_baseline\": \"auto\", \"h_anchor\": \"start\", \"color\": \"#000000\", \"text\": \"Hugoniot Loci (unphysical)\", \"coordinates\": \"axes\", \"zorder\": 1000003.0, \"alpha\": 1, \"fontsize\": 8.0, \"position\": [0.10398692810457516, 0.87222222222222268], \"rotation\": -0.0, \"id\": \"el28341139779402187600\"}, {\"v_baseline\": \"auto\", \"h_anchor\": \"start\", 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-15.91656010212753, -11.937870385323382]], \"data13\": [[-11.1, -169.76593783806587, 169.76593783806587], [11.1, 169.76593783806587, -169.76593783806587]], \"data01\": [[-1.0, -1.0]]}, \"id\": \"el28341139779420703632\"});\n",
       "            })\n",
       "         });\n",
       "}\n",
       "</script>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Define left and right state (h,hu)\n",
    "ql = np.array([3.0, 5.0])\n",
    "qr = np.array([3.0, -5.0])\n",
    "# Defineoptional parameters (otherwise chooses default values)\n",
    "plotopts = {'g':1.0, 'time':2.0, 'tmax':5, 'hmax':10, 'humin':-15, 'humax':15}\n",
    "# Call interactive function (can be called without any argument)\n",
    "pt = riemann_interactive.shallow_water(ql,qr,**plotopts)\n",
    "#mpld3.save_html(pt,\"test2.html\")\n",
    "mpld3.display()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Acoustic equations\n",
    "Here we show the exact solution for the Riemann problem of linear acoustics. We again determine the initial left and right states, and we provide the eigenvectors ($r_1,r_2$) and eigenvalues ($\\lambda_1,\\lambda_2$) of the solution. It is written in this way, so one can easily input the eigenvalues of any other two dimensional linear Riemann problem. Additional optional input can be added to adjust the plotted window. In this case, the time is fixed in \"plotopts\" and only the left and right states ($q_l,q_r$) can be moved interactively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "<style>\n",
       "\n",
       "</style>\n",
       "\n",
       "<div id=\"fig_el283411397794015650083559607981\"></div>\n",
       "<script>\n",
       "function mpld3_load_lib(url, callback){\n",
       "  var s = document.createElement('script');\n",
       "  s.src = url;\n",
       "  s.async = true;\n",
       "  s.onreadystatechange = s.onload = callback;\n",
       "  s.onerror = function(){console.warn(\"failed to load library \" + url);};\n",
       "  document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
       "}\n",
       "\n",
       "if(typeof(mpld3) !== \"undefined\" && mpld3._mpld3IsLoaded){\n",
       "   // already loaded: just create the figure\n",
       "   !function(mpld3){\n",
       "       \n",
       "    // init custom PPLane plugin\n",
       "    mpld3.register_plugin(\"drag\", PPlanePlugin);\n",
       "    PPlanePlugin.prototype = Object.create(mpld3.Plugin.prototype);\n",
       "    PPlanePlugin.prototype.constructor = PPlanePlugin;\n",
       "    PPlanePlugin.prototype.requiredProps = [\"id\", \"idmpoint\", \n",
       "                                            \"idlinesla\", \"idlineslb\", \"idlinesra\", \"idlinesrb\",  \n",
       "                                            \"idqlm\", \"idqmm\", \"idqrm\", \"idqone\", \"idqtwo\", \n",
       "                                            \"idrl0\", \"idrl1\", \"idrr0\", \"idrr1\"];\n",
       "    PPlanePlugin.prototype.defaultProps = {}\n",
       "    function PPlanePlugin(fig, props){\n",
       "        mpld3.Plugin.call(this, fig, props);\n",
       "        mpld3.insert_css(\"#\" + fig.figid + \" path.dragging\",\n",
       "                         {\"fill-opacity\": \"1.0 !important\",\n",
       "                          \"stroke-opacity\": \"1.0 !important\"});\n",
       "    };\n",
       "\n",
       "    // Call draw function, this function is being looped all the time\n",
       "    PPlanePlugin.prototype.draw = function(){\n",
       "        // Get elements into script variables\n",
       "        var obj = mpld3.get_element(this.props.id);\n",
       "        var midpoint = mpld3.get_element(this.props.idmpoint);\n",
       "        var linesla = mpld3.get_element(this.props.idlinesla);\n",
       "        var lineslb = mpld3.get_element(this.props.idlineslb);\n",
       "        var linesra = mpld3.get_element(this.props.idlinesra);\n",
       "        var linesrb = mpld3.get_element(this.props.idlinesrb);\n",
       "        var qlm = mpld3.get_element(this.props.idqlm);\n",
       "        var qmm = mpld3.get_element(this.props.idqmm);\n",
       "        var qrm = mpld3.get_element(this.props.idqrm);\n",
       "        var qone = mpld3.get_element(this.props.idqone);\n",
       "        var qtwo = mpld3.get_element(this.props.idqtwo);\n",
       "        var rl0 = this.props.idrl0;\n",
       "        var rl1 = this.props.idrl1;\n",
       "        var rr0 = this.props.idrr0;\n",
       "        var rr1 = this.props.idrr1;\n",
       "        \n",
       "        // Set initial conditions for javascript calculations\n",
       "        var qleft = obj.offsets[0];\n",
       "        var qright = obj.offsets[1];\n",
       "        var qmid = midpoint.offsets[0];\n",
       "        var off = 13;\n",
       "        // Calculate slopes for eigenlines\n",
       "        var ml = rl1/rl0;\n",
       "        var mr = rr1/rr0;\n",
       "        \n",
       "        // Main d3 drag function\n",
       "        var drag = d3.behavior.drag()\n",
       "            .origin(function(d) { return {x:obj.ax.x(d[0]),\n",
       "                                          y:obj.ax.y(d[1])}; })                              \n",
       "            .on(\"dragstart\", dragstarted)\n",
       "            .on(\"drag\", dragged)\n",
       "            .on(\"dragend\", dragended);\n",
       "    \n",
       "        // Set elements of ql and qr points and call main drag function\n",
       "        obj.elements()\n",
       "           .data(obj.offsets)\n",
       "           .style(\"cursor\", \"default\")\n",
       "           .call(drag);      \n",
       "\n",
       "        // Begin drag function\n",
       "        function dragstarted(d) {\n",
       "          d3.event.sourceEvent.stopPropagation();\n",
       "          d3.select(this).classed(\"dragging\", true);\n",
       "        }\n",
       "    \n",
       "        // The drag function called while dragging is happening (meat of code here)\n",
       "        function dragged(d,i) {\n",
       "          // Convert mouse coordinates in drag event (d3.event) to python coordinates d\n",
       "          d[0] = obj.ax.x.invert(d3.event.x);\n",
       "          d[1] = obj.ax.y.invert(d3.event.y);             \n",
       "          // Move ql and qr stored in obj (they have been selected in drag)\n",
       "          d3.select(this)\n",
       "            .attr(\"transform\", \"translate(\" + [d3.event.x, d3.event.y] + \")\");\n",
       "          // If obj corresponds to ql, move all the other left elements \n",
       "          if (i==0){\n",
       "              // Move text marker\n",
       "              qlm.elements().transition().duration(1)\n",
       "                  .attr(\"transform\", \"translate(\" + [d3.event.x + off, d3.event.y + off] + \")\");\n",
       "                  \n",
       "              // Move eigenlines\n",
       "              for (var ii=0; ii<2; ii++) {\n",
       "                linesla.data[ii][1] = ml*(linesla.data[ii][0] - d[0]) + d[1];\n",
       "                lineslb.data[ii][1] = mr*(lineslb.data[ii][0] - d[0]) + d[1]; }\n",
       "                \n",
       "              // In script calculations of middle state\n",
       "              qleft = [d[0], d[1]];\n",
       "              var det = rl0*rr1 - rr0*rl1;\n",
       "              var alphal = (rr1*(qright[0] - qleft[0]) - rr0*(qright[1] - qleft[1]))/det\n",
       "              qmid[0] = qleft[0] + alphal*rl0;\n",
       "              qmid[1] = qleft[1] + alphal*rl1;\n",
       "              var xx = obj.ax.x(qmid[0]);\n",
       "              var yy = obj.ax.y(qmid[1]); \n",
       "             \n",
       "                }\n",
       "          // if element corresponds to qr\n",
       "          else {\n",
       "              // Move text marker\n",
       "              qrm.elements().transition().duration(1)\n",
       "                  .attr(\"transform\", \"translate(\" + [d3.event.x + off, d3.event.y + off] + \")\");\n",
       "                  \n",
       "              // Move eigenlines\n",
       "              for (var ii=0; ii<2; ii++) {\n",
       "                linesra.data[ii][1] = ml*(linesra.data[ii][0] - d[0]) + d[1];\n",
       "                linesrb.data[ii][1] = mr*(linesrb.data[ii][0] - d[0]) + d[1]; }\n",
       "                \n",
       "              // In script calculations of middle state    \n",
       "              qright = [d[0], d[1]];\n",
       "              var det = rl0*rr1 - rr0*rl1;\n",
       "              var alphal = (rr1*(qright[0] - qleft[0]) - rr0*(qright[1] - qleft[1]))/det\n",
       "              qmid[0] = qleft[0] + alphal*rl0;\n",
       "              qmid[1] = qleft[1] + alphal*rl1;\n",
       "              var xx = obj.ax.x(qmid[0]);\n",
       "              var yy = obj.ax.y(qmid[1]);\n",
       "                }\n",
       "              // Update middle state point and marker position\n",
       "              midpoint.elements().transition().duration(5)\n",
       "                .attr(\"transform\", \"translate(\" + [xx, yy] + \")\");\n",
       "              qmm.elements().transition().duration(5)\n",
       "                .attr(\"transform\", \"translate(\" + [xx + 0.7*off, yy + 0.7*off] + \")\"); \n",
       "                \n",
       "              // Update eigenlines\n",
       "              linesla.elements().transition().duration(5)\n",
       "                  .attr(\"d\", linesla.datafunc(linesla.data));\n",
       "              lineslb.elements().transition().duration(5)\n",
       "                  .attr(\"d\", lineslb.datafunc(lineslb.data));\n",
       "              linesra.elements().transition().duration(5)\n",
       "                  .attr(\"d\", linesra.datafunc(linesra.data));\n",
       "              linesrb.elements().transition().duration(5)\n",
       "                  .attr(\"d\", linesrb.datafunc(linesrb.data));\n",
       "                \n",
       "              // Update subplots of q1 and q2\n",
       "              qone.data[0][1] = qleft[0];\n",
       "              qone.data[1][1] = qleft[0];\n",
       "              qone.data[2][1] = qmid[0];\n",
       "              qone.data[3][1] = qmid[0];\n",
       "              qone.data[4][1] = qright[0];\n",
       "              qone.data[5][1] = qright[0];\n",
       "              qtwo.data[0][2] = qleft[1];\n",
       "              qtwo.data[1][2] = qleft[1];\n",
       "              qtwo.data[2][2] = qmid[1];\n",
       "              qtwo.data[3][2] = qmid[1];\n",
       "              qtwo.data[4][2] = qright[1];\n",
       "              qtwo.data[5][2] = qright[1];\n",
       "              qone.elements().transition().duration(5)\n",
       "                .attr(\"d\", qone.datafunc(qone.data));\n",
       "              qtwo.elements().transition().duration(5)\n",
       "                .attr(\"d\", qtwo.datafunc(qtwo.data));  \n",
       "        }\n",
       "        // End dragging\n",
       "        function dragended(d) {\n",
       "          d3.select(this).classed(\"dragging\", false);\n",
       "        }\n",
       "    }\n",
       "    mpld3.register_plugin(\"drag\", PPlanePlugin); \n",
       "    \n",
       "       mpld3.draw_figure(\"fig_el283411397794015650083559607981\", {\"axes\": [{\"xlim\": [-5.0, 5.0], \"yscale\": \"linear\", \"axesbg\": \"#FFFFFF\", \"texts\": [{\"v_baseline\": \"hanging\", \"h_anchor\": \"middle\", \"color\": \"#000000\", \"text\": \"Pressure\", \"coordinates\": \"axes\", \"zorder\": 3, \"alpha\": 1, \"fontsize\": 12.0, \"position\": [0.5, -0.085714285714285715], \"rotation\": -0.0, \"id\": \"el28341139779401150416\"}, {\"v_baseline\": \"auto\", \"h_anchor\": \"middle\", \"color\": \"#000000\", \"text\": \"Velocity\", \"coordinates\": \"axes\", \"zorder\": 3, \"alpha\": 1, \"fontsize\": 12.0, \"position\": [-0.1064950980392157, 0.5], \"rotation\": -90.0, \"id\": \"el28341139779419851664\"}, {\"v_baseline\": \"auto\", \"h_anchor\": \"middle\", \"color\": \"#000000\", \"text\": \"Phase Plane\", \"coordinates\": \"axes\", \"zorder\": 3, \"alpha\": 1, \"fontsize\": 18.0, \"position\": [0.5, 1.0198412698412698], \"rotation\": -0.0, \"id\": \"el28341139779401183504\"}], \"zoomable\": true, \"images\": [], \"xdomain\": [-5.0, 5.0], \"ylim\": [-5.0, 5.0], \"paths\": [], \"sharey\": [], \"sharex\": [], \"axesbgalpha\": null, \"axes\": [{\"scale\": \"linear\", \"tickformat\": null, \"grid\": {\"color\": \"#000000\", \"alpha\": 0.1, \"dasharray\": \"6,6\", \"gridOn\": true}, \"fontsize\": 12.0, \"position\": \"bottom\", \"nticks\": 7, \"tickvalues\": null}, {\"scale\": \"linear\", \"tickformat\": null, \"grid\": {\"color\": \"#000000\", \"alpha\": 0.1, \"dasharray\": \"6,6\", \"gridOn\": true}, \"fontsize\": 12.0, \"position\": \"left\", \"nticks\": 7, \"tickvalues\": null}], \"lines\": [{\"color\": \"#000000\", \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"10,0\", \"zorder\": 2, \"alpha\": 1, \"xindex\": 0, \"linewidth\": 1.0, \"data\": \"data01\", \"id\": \"el28341139779400856784\"}, {\"color\": \"#000000\", \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"10,0\", \"zorder\": 2, \"alpha\": 1, \"xindex\": 0, \"linewidth\": 1.0, \"data\": \"data02\", \"id\": \"el28341139779398496336\"}, {\"color\": \"#000000\", \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"10,0\", \"zorder\": 2, \"alpha\": 1, \"xindex\": 0, \"linewidth\": 1.0, \"data\": \"data03\", \"id\": \"el28341139779398498256\"}, {\"color\": \"#000000\", \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"10,0\", \"zorder\": 2, \"alpha\": 1, \"xindex\": 0, \"linewidth\": 1.0, \"data\": \"data04\", \"id\": \"el28341139779398499856\"}, {\"color\": \"#000000\", \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"10,0\", \"zorder\": 2, \"alpha\": 1, \"xindex\": 0, \"linewidth\": 1.0, \"data\": \"data09\", \"id\": \"el28341139779398081744\"}], \"markers\": [{\"edgecolor\": \"#000000\", \"facecolor\": \"#000000\", \"edgewidth\": 1, \"yindex\": 1, \"coordinates\": \"data\", \"zorder\": 2, \"markerpath\": [[[0.0, 5.0], [1.3260155, 5.0], [2.597899353924267, 4.473168457941209], [3.5355339059327378, 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{\"xlim\": [-5.0, 5.0], \"yscale\": \"linear\", \"axesbg\": \"#FFFFFF\", \"texts\": [{\"v_baseline\": \"hanging\", \"h_anchor\": \"middle\", \"color\": \"#000000\", \"text\": \"x\", \"coordinates\": \"axes\", \"zorder\": 3, \"alpha\": 1, \"fontsize\": 12.0, \"position\": [0.5, -0.085714285714285715], \"rotation\": -0.0, \"id\": \"el28341139779400910160\"}, {\"v_baseline\": \"auto\", \"h_anchor\": \"middle\", \"color\": \"#000000\", \"text\": \"Pressure\", \"coordinates\": \"axes\", \"zorder\": 3, \"alpha\": 1, \"fontsize\": 18.0, \"position\": [0.5, 1.0198412698412698], \"rotation\": -0.0, \"id\": \"el28341139779400642192\"}], \"zoomable\": true, \"images\": [], \"xdomain\": [-5.0, 5.0], \"ylim\": [-5.0, 5.0], \"paths\": [], \"sharey\": [], \"sharex\": [], \"axesbgalpha\": null, \"axes\": [{\"scale\": \"linear\", \"tickformat\": null, \"grid\": {\"color\": \"#000000\", \"alpha\": 0.1, \"dasharray\": \"6,6\", \"gridOn\": true}, \"fontsize\": 12.0, \"position\": \"bottom\", \"nticks\": 7, \"tickvalues\": null}, {\"scale\": \"linear\", \"tickformat\": null, \"grid\": {\"color\": \"#000000\", \"alpha\": 0.1, \"dasharray\": \"6,6\", \"gridOn\": true}, \"fontsize\": 12.0, \"position\": \"left\", \"nticks\": 7, \"tickvalues\": null}], \"lines\": [{\"color\": \"#000000\", \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"10,0\", \"zorder\": 2, \"alpha\": 1.0, \"xindex\": 0, \"linewidth\": 4.0, \"data\": \"data10\", \"id\": \"el28341139779398150352\"}], \"markers\": [], \"id\": \"el28341139779400857104\", \"ydomain\": [-5.0, 5.0], \"collections\": [], \"xscale\": \"linear\", \"bbox\": [0.34621212121212119, 0.20000000000000007, 0.25757575757575757, 0.69999999999999996]}, {\"xlim\": [-5.0, 5.0], \"yscale\": \"linear\", \"axesbg\": \"#FFFFFF\", \"texts\": [{\"v_baseline\": \"hanging\", \"h_anchor\": \"middle\", \"color\": \"#000000\", \"text\": \"x\", \"coordinates\": \"axes\", \"zorder\": 3, \"alpha\": 1, \"fontsize\": 12.0, \"position\": [0.50000000000000044, -0.085714285714285715], \"rotation\": -0.0, \"id\": \"el28341139779400136080\"}, {\"v_baseline\": \"auto\", \"h_anchor\": \"middle\", \"color\": \"#000000\", \"text\": \"Velocity\", \"coordinates\": \"axes\", \"zorder\": 3, \"alpha\": 1, \"fontsize\": 18.0, \"position\": [0.50000000000000044, 1.0198412698412698], \"rotation\": -0.0, \"id\": \"el28341139779419905808\"}], \"zoomable\": true, \"images\": [], \"xdomain\": [-5.0, 5.0], \"ylim\": [-5.0, 5.0], \"paths\": [], \"sharey\": [], \"sharex\": [], \"axesbgalpha\": null, \"axes\": [{\"scale\": \"linear\", \"tickformat\": null, \"grid\": {\"color\": \"#000000\", \"alpha\": 0.1, \"dasharray\": \"6,6\", \"gridOn\": true}, \"fontsize\": 12.0, \"position\": \"bottom\", \"nticks\": 7, \"tickvalues\": null}, {\"scale\": \"linear\", \"tickformat\": null, \"grid\": {\"color\": \"#000000\", \"alpha\": 0.1, \"dasharray\": \"6,6\", \"gridOn\": true}, \"fontsize\": 12.0, \"position\": \"left\", \"nticks\": 7, \"tickvalues\": null}], \"lines\": [{\"color\": \"#000000\", \"yindex\": 2, \"coordinates\": \"data\", \"dasharray\": \"10,0\", \"zorder\": 2, \"alpha\": 1.0, \"xindex\": 0, \"linewidth\": 4.0, \"data\": \"data10\", \"id\": \"el28341139779398149008\"}], \"markers\": [], \"id\": \"el28341139779400083024\", \"ydomain\": [-5.0, 5.0], \"collections\": [], \"xscale\": \"linear\", \"bbox\": [0.64242424242424234, 0.20000000000000007, 0.25757575757575757, 0.69999999999999996]}], \"height\": 400.0, \"width\": 1080.0, \"plugins\": [{\"idlinesla\": \"el28341139779400856784\", \"idlineslb\": \"el28341139779398496336\", \"idrr1\": 1.0, \"idrr0\": 2.0, \"idqtwo\": \"el28341139779398149008\", \"idlinesra\": \"el28341139779398498256\", \"idqone\": \"el28341139779398150352\", \"idqlm\": \"el28341139779398552144pts\", \"idqmm\": \"el28341139779398081744pts\", \"idrl0\": -2.0, \"idrl1\": 1.0, \"idqrm\": \"el28341139779398553360pts\", \"idlinesrb\": \"el28341139779398499856\", \"idmpoint\": \"el28341139779398080144pts\", \"type\": \"drag\", \"id\": \"el28341139779398550672pts\"}], \"data\": {\"data10\": [[-5.0, -2.0, 2.0], [-2.0, -2.0, 2.0], [-2.0, 4.0, -1.0], [2.0, 4.0, -1.0], [2.0, 0.0, -3.0], [5.0, 0.0, -3.0]], \"data08\": [[4.0, -1.0]], \"data09\": [[4.4, -1.28]], \"data06\": [[-1.6, 1.6]], \"data07\": [[0.4, -3.4]], \"data04\": [[-5.00000000003, -0.5], [5.00000000003, -5.5]], \"data05\": [[-2.0, 2.0], [0.0, -3.0]], \"data02\": [[-5.00000000001, 0.49999999997], [5.00000000001, 5.50000000007]], \"data03\": [[-5.00000000002, -5.50000000005], [5.00000000002, -0.49999999995]], \"data01\": [[-5.0, 3.5], [5.0, -1.5]]}, \"id\": \"el28341139779401565008\"});\n",
       "   }(mpld3);\n",
       "}else if(typeof define === \"function\" && define.amd){\n",
       "   // require.js is available: use it to load d3/mpld3\n",
       "   require.config({paths: {d3: \"https://mpld3.github.io/js/d3.v3.min\"}});\n",
       "   require([\"d3\"], function(d3){\n",
       "      window.d3 = d3;\n",
       "      mpld3_load_lib(\"https://mpld3.github.io/js/mpld3.v0.2.js\", function(){\n",
       "         \n",
       "    // init custom PPLane plugin\n",
       "    mpld3.register_plugin(\"drag\", PPlanePlugin);\n",
       "    PPlanePlugin.prototype = Object.create(mpld3.Plugin.prototype);\n",
       "    PPlanePlugin.prototype.constructor = PPlanePlugin;\n",
       "    PPlanePlugin.prototype.requiredProps = [\"id\", \"idmpoint\", \n",
       "                                            \"idlinesla\", \"idlineslb\", \"idlinesra\", \"idlinesrb\",  \n",
       "                                            \"idqlm\", \"idqmm\", \"idqrm\", \"idqone\", \"idqtwo\", \n",
       "                                            \"idrl0\", \"idrl1\", \"idrr0\", \"idrr1\"];\n",
       "    PPlanePlugin.prototype.defaultProps = {}\n",
       "    function PPlanePlugin(fig, props){\n",
       "        mpld3.Plugin.call(this, fig, props);\n",
       "        mpld3.insert_css(\"#\" + fig.figid + \" path.dragging\",\n",
       "                         {\"fill-opacity\": \"1.0 !important\",\n",
       "                          \"stroke-opacity\": \"1.0 !important\"});\n",
       "    };\n",
       "\n",
       "    // Call draw function, this function is being looped all the time\n",
       "    PPlanePlugin.prototype.draw = function(){\n",
       "        // Get elements into script variables\n",
       "        var obj = mpld3.get_element(this.props.id);\n",
       "        var midpoint = mpld3.get_element(this.props.idmpoint);\n",
       "        var linesla = mpld3.get_element(this.props.idlinesla);\n",
       "        var lineslb = mpld3.get_element(this.props.idlineslb);\n",
       "        var linesra = mpld3.get_element(this.props.idlinesra);\n",
       "        var linesrb = mpld3.get_element(this.props.idlinesrb);\n",
       "        var qlm = mpld3.get_element(this.props.idqlm);\n",
       "        var qmm = mpld3.get_element(this.props.idqmm);\n",
       "        var qrm = mpld3.get_element(this.props.idqrm);\n",
       "        var qone = mpld3.get_element(this.props.idqone);\n",
       "        var qtwo = mpld3.get_element(this.props.idqtwo);\n",
       "        var rl0 = this.props.idrl0;\n",
       "        var rl1 = this.props.idrl1;\n",
       "        var rr0 = this.props.idrr0;\n",
       "        var rr1 = this.props.idrr1;\n",
       "        \n",
       "        // Set initial conditions for javascript calculations\n",
       "        var qleft = obj.offsets[0];\n",
       "        var qright = obj.offsets[1];\n",
       "        var qmid = midpoint.offsets[0];\n",
       "        var off = 13;\n",
       "        // Calculate slopes for eigenlines\n",
       "        var ml = rl1/rl0;\n",
       "        var mr = rr1/rr0;\n",
       "        \n",
       "        // Main d3 drag function\n",
       "        var drag = d3.behavior.drag()\n",
       "            .origin(function(d) { return {x:obj.ax.x(d[0]),\n",
       "                                          y:obj.ax.y(d[1])}; })                              \n",
       "            .on(\"dragstart\", dragstarted)\n",
       "            .on(\"drag\", dragged)\n",
       "            .on(\"dragend\", dragended);\n",
       "    \n",
       "        // Set elements of ql and qr points and call main drag function\n",
       "        obj.elements()\n",
       "           .data(obj.offsets)\n",
       "           .style(\"cursor\", \"default\")\n",
       "           .call(drag);      \n",
       "\n",
       "        // Begin drag function\n",
       "        function dragstarted(d) {\n",
       "          d3.event.sourceEvent.stopPropagation();\n",
       "          d3.select(this).classed(\"dragging\", true);\n",
       "        }\n",
       "    \n",
       "        // The drag function called while dragging is happening (meat of code here)\n",
       "        function dragged(d,i) {\n",
       "          // Convert mouse coordinates in drag event (d3.event) to python coordinates d\n",
       "          d[0] = obj.ax.x.invert(d3.event.x);\n",
       "          d[1] = obj.ax.y.invert(d3.event.y);             \n",
       "          // Move ql and qr stored in obj (they have been selected in drag)\n",
       "          d3.select(this)\n",
       "            .attr(\"transform\", \"translate(\" + [d3.event.x, d3.event.y] + \")\");\n",
       "          // If obj corresponds to ql, move all the other left elements \n",
       "          if (i==0){\n",
       "              // Move text marker\n",
       "              qlm.elements().transition().duration(1)\n",
       "                  .attr(\"transform\", \"translate(\" + [d3.event.x + off, d3.event.y + off] + \")\");\n",
       "                  \n",
       "              // Move eigenlines\n",
       "              for (var ii=0; ii<2; ii++) {\n",
       "                linesla.data[ii][1] = ml*(linesla.data[ii][0] - d[0]) + d[1];\n",
       "                lineslb.data[ii][1] = mr*(lineslb.data[ii][0] - d[0]) + d[1]; }\n",
       "                \n",
       "              // In script calculations of middle state\n",
       "              qleft = [d[0], d[1]];\n",
       "              var det = rl0*rr1 - rr0*rl1;\n",
       "              var alphal = (rr1*(qright[0] - qleft[0]) - rr0*(qright[1] - qleft[1]))/det\n",
       "              qmid[0] = qleft[0] + alphal*rl0;\n",
       "              qmid[1] = qleft[1] + alphal*rl1;\n",
       "              var xx = obj.ax.x(qmid[0]);\n",
       "              var yy = obj.ax.y(qmid[1]); \n",
       "             \n",
       "                }\n",
       "          // if element corresponds to qr\n",
       "          else {\n",
       "              // Move text marker\n",
       "              qrm.elements().transition().duration(1)\n",
       "                  .attr(\"transform\", \"translate(\" + [d3.event.x + off, d3.event.y + off] + \")\");\n",
       "                  \n",
       "              // Move eigenlines\n",
       "              for (var ii=0; ii<2; ii++) {\n",
       "                linesra.data[ii][1] = ml*(linesra.data[ii][0] - d[0]) + d[1];\n",
       "                linesrb.data[ii][1] = mr*(linesrb.data[ii][0] - d[0]) + d[1]; }\n",
       "                \n",
       "              // In script calculations of middle state    \n",
       "              qright = [d[0], d[1]];\n",
       "              var det = rl0*rr1 - rr0*rl1;\n",
       "              var alphal = (rr1*(qright[0] - qleft[0]) - rr0*(qright[1] - qleft[1]))/det\n",
       "              qmid[0] = qleft[0] + alphal*rl0;\n",
       "              qmid[1] = qleft[1] + alphal*rl1;\n",
       "              var xx = obj.ax.x(qmid[0]);\n",
       "              var yy = obj.ax.y(qmid[1]);\n",
       "                }\n",
       "              // Update middle state point and marker position\n",
       "              midpoint.elements().transition().duration(5)\n",
       "                .attr(\"transform\", \"translate(\" + [xx, yy] + \")\");\n",
       "              qmm.elements().transition().duration(5)\n",
       "                .attr(\"transform\", \"translate(\" + [xx + 0.7*off, yy + 0.7*off] + \")\"); \n",
       "                \n",
       "              // Update eigenlines\n",
       "              linesla.elements().transition().duration(5)\n",
       "                  .attr(\"d\", linesla.datafunc(linesla.data));\n",
       "              lineslb.elements().transition().duration(5)\n",
       "                  .attr(\"d\", lineslb.datafunc(lineslb.data));\n",
       "              linesra.elements().transition().duration(5)\n",
       "                  .attr(\"d\", linesra.datafunc(linesra.data));\n",
       "              linesrb.elements().transition().duration(5)\n",
       "                  .attr(\"d\", linesrb.datafunc(linesrb.data));\n",
       "                \n",
       "              // Update subplots of q1 and q2\n",
       "              qone.data[0][1] = qleft[0];\n",
       "              qone.data[1][1] = qleft[0];\n",
       "              qone.data[2][1] = qmid[0];\n",
       "              qone.data[3][1] = qmid[0];\n",
       "              qone.data[4][1] = qright[0];\n",
       "              qone.data[5][1] = qright[0];\n",
       "              qtwo.data[0][2] = qleft[1];\n",
       "              qtwo.data[1][2] = qleft[1];\n",
       "              qtwo.data[2][2] = qmid[1];\n",
       "              qtwo.data[3][2] = qmid[1];\n",
       "              qtwo.data[4][2] = qright[1];\n",
       "              qtwo.data[5][2] = qright[1];\n",
       "              qone.elements().transition().duration(5)\n",
       "                .attr(\"d\", qone.datafunc(qone.data));\n",
       "              qtwo.elements().transition().duration(5)\n",
       "                .attr(\"d\", qtwo.datafunc(qtwo.data));  \n",
       "        }\n",
       "        // End dragging\n",
       "        function dragended(d) {\n",
       "          d3.select(this).classed(\"dragging\", false);\n",
       "        }\n",
       "    }\n",
       "    mpld3.register_plugin(\"drag\", PPlanePlugin); \n",
       "    \n",
       "         mpld3.draw_figure(\"fig_el283411397794015650083559607981\", {\"axes\": [{\"xlim\": [-5.0, 5.0], \"yscale\": \"linear\", \"axesbg\": \"#FFFFFF\", \"texts\": [{\"v_baseline\": \"hanging\", \"h_anchor\": \"middle\", \"color\": \"#000000\", \"text\": \"Pressure\", \"coordinates\": \"axes\", \"zorder\": 3, \"alpha\": 1, \"fontsize\": 12.0, \"position\": [0.5, -0.085714285714285715], \"rotation\": -0.0, \"id\": \"el28341139779401150416\"}, {\"v_baseline\": \"auto\", \"h_anchor\": \"middle\", \"color\": \"#000000\", \"text\": \"Velocity\", \"coordinates\": \"axes\", \"zorder\": 3, \"alpha\": 1, \"fontsize\": 12.0, \"position\": [-0.1064950980392157, 0.5], \"rotation\": -90.0, \"id\": \"el28341139779419851664\"}, {\"v_baseline\": \"auto\", \"h_anchor\": \"middle\", \"color\": \"#000000\", \"text\": \"Phase Plane\", \"coordinates\": \"axes\", \"zorder\": 3, \"alpha\": 1, \"fontsize\": 18.0, \"position\": [0.5, 1.0198412698412698], \"rotation\": -0.0, \"id\": \"el28341139779401183504\"}], \"zoomable\": true, \"images\": [], \"xdomain\": [-5.0, 5.0], \"ylim\": [-5.0, 5.0], \"paths\": [], \"sharey\": [], \"sharex\": [], \"axesbgalpha\": null, \"axes\": [{\"scale\": \"linear\", \"tickformat\": null, \"grid\": {\"color\": \"#000000\", \"alpha\": 0.1, \"dasharray\": \"6,6\", \"gridOn\": true}, \"fontsize\": 12.0, \"position\": \"bottom\", \"nticks\": 7, \"tickvalues\": null}, {\"scale\": \"linear\", \"tickformat\": null, \"grid\": {\"color\": \"#000000\", \"alpha\": 0.1, \"dasharray\": \"6,6\", \"gridOn\": true}, \"fontsize\": 12.0, \"position\": \"left\", \"nticks\": 7, \"tickvalues\": null}], \"lines\": [{\"color\": \"#000000\", \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"10,0\", \"zorder\": 2, \"alpha\": 1, \"xindex\": 0, \"linewidth\": 1.0, \"data\": \"data01\", \"id\": \"el28341139779400856784\"}, {\"color\": \"#000000\", \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"10,0\", \"zorder\": 2, \"alpha\": 1, 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\"L\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"L\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"L\", \"S\", \"M\", \"S\", \"S\", \"L\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"M\", \"S\", \"L\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"L\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"L\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"L\", \"S\", \"S\", \"S\", \"S\", \"S\", \"L\", \"S\", \"S\", \"S\", \"S\", \"S\", \"S\", \"L\", \"S\", \"S\", \"S\", \"S\"]], \"alpha\": 1, \"xindex\": 0, \"data\": \"data09\", \"id\": \"el28341139779398081744pts\"}], \"id\": \"el28341139779401148304\", \"ydomain\": [-5.0, 5.0], \"collections\": [], \"xscale\": \"linear\", \"bbox\": [0.050000000000000003, 0.20000000000000007, 0.25757575757575757, 0.69999999999999996]}, {\"xlim\": [-5.0, 5.0], \"yscale\": \"linear\", \"axesbg\": \"#FFFFFF\", \"texts\": [{\"v_baseline\": \"hanging\", \"h_anchor\": \"middle\", \"color\": \"#000000\", \"text\": \"x\", \"coordinates\": \"axes\", \"zorder\": 3, \"alpha\": 1, \"fontsize\": 12.0, \"position\": [0.5, -0.085714285714285715], \"rotation\": -0.0, \"id\": \"el28341139779400910160\"}, {\"v_baseline\": \"auto\", \"h_anchor\": \"middle\", \"color\": \"#000000\", \"text\": \"Pressure\", \"coordinates\": \"axes\", \"zorder\": 3, \"alpha\": 1, \"fontsize\": 18.0, \"position\": [0.5, 1.0198412698412698], \"rotation\": -0.0, \"id\": \"el28341139779400642192\"}], \"zoomable\": true, \"images\": [], \"xdomain\": [-5.0, 5.0], \"ylim\": [-5.0, 5.0], \"paths\": [], \"sharey\": [], \"sharex\": [], \"axesbgalpha\": null, \"axes\": [{\"scale\": \"linear\", \"tickformat\": null, \"grid\": {\"color\": \"#000000\", \"alpha\": 0.1, \"dasharray\": \"6,6\", \"gridOn\": true}, \"fontsize\": 12.0, \"position\": \"bottom\", \"nticks\": 7, \"tickvalues\": null}, {\"scale\": \"linear\", \"tickformat\": null, \"grid\": {\"color\": \"#000000\", \"alpha\": 0.1, \"dasharray\": \"6,6\", \"gridOn\": true}, \"fontsize\": 12.0, \"position\": \"left\", \"nticks\": 7, \"tickvalues\": null}], \"lines\": [{\"color\": \"#000000\", \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"10,0\", \"zorder\": 2, \"alpha\": 1.0, \"xindex\": 0, \"linewidth\": 4.0, \"data\": \"data10\", \"id\": \"el28341139779398150352\"}], \"markers\": [], \"id\": \"el28341139779400857104\", \"ydomain\": [-5.0, 5.0], \"collections\": [], \"xscale\": \"linear\", \"bbox\": [0.34621212121212119, 0.20000000000000007, 0.25757575757575757, 0.69999999999999996]}, {\"xlim\": [-5.0, 5.0], \"yscale\": \"linear\", \"axesbg\": \"#FFFFFF\", \"texts\": [{\"v_baseline\": \"hanging\", \"h_anchor\": \"middle\", \"color\": \"#000000\", \"text\": \"x\", \"coordinates\": \"axes\", \"zorder\": 3, \"alpha\": 1, \"fontsize\": 12.0, \"position\": [0.50000000000000044, -0.085714285714285715], \"rotation\": -0.0, \"id\": \"el28341139779400136080\"}, {\"v_baseline\": \"auto\", \"h_anchor\": \"middle\", \"color\": \"#000000\", \"text\": \"Velocity\", \"coordinates\": \"axes\", \"zorder\": 3, \"alpha\": 1, \"fontsize\": 18.0, \"position\": [0.50000000000000044, 1.0198412698412698], \"rotation\": -0.0, \"id\": \"el28341139779419905808\"}], \"zoomable\": true, \"images\": [], \"xdomain\": [-5.0, 5.0], \"ylim\": [-5.0, 5.0], \"paths\": [], \"sharey\": [], \"sharex\": [], \"axesbgalpha\": null, \"axes\": [{\"scale\": \"linear\", \"tickformat\": null, \"grid\": {\"color\": \"#000000\", \"alpha\": 0.1, \"dasharray\": \"6,6\", \"gridOn\": true}, \"fontsize\": 12.0, \"position\": \"bottom\", \"nticks\": 7, \"tickvalues\": null}, {\"scale\": \"linear\", \"tickformat\": null, \"grid\": {\"color\": \"#000000\", \"alpha\": 0.1, \"dasharray\": \"6,6\", \"gridOn\": true}, \"fontsize\": 12.0, \"position\": \"left\", \"nticks\": 7, \"tickvalues\": null}], \"lines\": [{\"color\": \"#000000\", \"yindex\": 2, \"coordinates\": \"data\", \"dasharray\": \"10,0\", \"zorder\": 2, \"alpha\": 1.0, \"xindex\": 0, \"linewidth\": 4.0, \"data\": \"data10\", \"id\": \"el28341139779398149008\"}], \"markers\": [], \"id\": \"el28341139779400083024\", \"ydomain\": [-5.0, 5.0], \"collections\": [], \"xscale\": \"linear\", \"bbox\": [0.64242424242424234, 0.20000000000000007, 0.25757575757575757, 0.69999999999999996]}], \"height\": 400.0, \"width\": 1080.0, \"plugins\": [{\"idlinesla\": \"el28341139779400856784\", \"idlineslb\": \"el28341139779398496336\", \"idrr1\": 1.0, \"idrr0\": 2.0, \"idqtwo\": \"el28341139779398149008\", \"idlinesra\": \"el28341139779398498256\", \"idqone\": \"el28341139779398150352\", \"idqlm\": \"el28341139779398552144pts\", \"idqmm\": \"el28341139779398081744pts\", \"idrl0\": -2.0, \"idrl1\": 1.0, \"idqrm\": \"el28341139779398553360pts\", \"idlinesrb\": \"el28341139779398499856\", \"idmpoint\": \"el28341139779398080144pts\", \"type\": \"drag\", \"id\": \"el28341139779398550672pts\"}], \"data\": {\"data10\": [[-5.0, -2.0, 2.0], [-2.0, -2.0, 2.0], [-2.0, 4.0, -1.0], [2.0, 4.0, -1.0], [2.0, 0.0, -3.0], [5.0, 0.0, -3.0]], \"data08\": [[4.0, -1.0]], \"data09\": [[4.4, -1.28]], \"data06\": [[-1.6, 1.6]], \"data07\": [[0.4, -3.4]], \"data04\": [[-5.00000000003, -0.5], [5.00000000003, -5.5]], \"data05\": [[-2.0, 2.0], [0.0, -3.0]], \"data02\": [[-5.00000000001, 0.49999999997], [5.00000000001, 5.50000000007]], \"data03\": [[-5.00000000002, -5.50000000005], [5.00000000002, -0.49999999995]], \"data01\": [[-5.0, 3.5], [5.0, -1.5]]}, \"id\": \"el28341139779401565008\"});\n",
       "      });\n",
       "    });\n",
       "}else{\n",
       "    // require.js not available: dynamically load d3 & mpld3\n",
       "    mpld3_load_lib(\"https://mpld3.github.io/js/d3.v3.min.js\", function(){\n",
       "         mpld3_load_lib(\"https://mpld3.github.io/js/mpld3.v0.2.js\", function(){\n",
       "                 \n",
       "    // init custom PPLane plugin\n",
       "    mpld3.register_plugin(\"drag\", PPlanePlugin);\n",
       "    PPlanePlugin.prototype = Object.create(mpld3.Plugin.prototype);\n",
       "    PPlanePlugin.prototype.constructor = PPlanePlugin;\n",
       "    PPlanePlugin.prototype.requiredProps = [\"id\", \"idmpoint\", \n",
       "                                            \"idlinesla\", \"idlineslb\", \"idlinesra\", \"idlinesrb\",  \n",
       "                                            \"idqlm\", \"idqmm\", \"idqrm\", \"idqone\", \"idqtwo\", \n",
       "                                            \"idrl0\", \"idrl1\", \"idrr0\", \"idrr1\"];\n",
       "    PPlanePlugin.prototype.defaultProps = {}\n",
       "    function PPlanePlugin(fig, props){\n",
       "        mpld3.Plugin.call(this, fig, props);\n",
       "        mpld3.insert_css(\"#\" + fig.figid + \" path.dragging\",\n",
       "                         {\"fill-opacity\": \"1.0 !important\",\n",
       "                          \"stroke-opacity\": \"1.0 !important\"});\n",
       "    };\n",
       "\n",
       "    // Call draw function, this function is being looped all the time\n",
       "    PPlanePlugin.prototype.draw = function(){\n",
       "        // Get elements into script variables\n",
       "        var obj = mpld3.get_element(this.props.id);\n",
       "        var midpoint = mpld3.get_element(this.props.idmpoint);\n",
       "        var linesla = mpld3.get_element(this.props.idlinesla);\n",
       "        var lineslb = mpld3.get_element(this.props.idlineslb);\n",
       "        var linesra = mpld3.get_element(this.props.idlinesra);\n",
       "        var linesrb = mpld3.get_element(this.props.idlinesrb);\n",
       "        var qlm = mpld3.get_element(this.props.idqlm);\n",
       "        var qmm = mpld3.get_element(this.props.idqmm);\n",
       "        var qrm = mpld3.get_element(this.props.idqrm);\n",
       "        var qone = mpld3.get_element(this.props.idqone);\n",
       "        var qtwo = mpld3.get_element(this.props.idqtwo);\n",
       "        var rl0 = this.props.idrl0;\n",
       "        var rl1 = this.props.idrl1;\n",
       "        var rr0 = this.props.idrr0;\n",
       "        var rr1 = this.props.idrr1;\n",
       "        \n",
       "        // Set initial conditions for javascript calculations\n",
       "        var qleft = obj.offsets[0];\n",
       "        var qright = obj.offsets[1];\n",
       "        var qmid = midpoint.offsets[0];\n",
       "        var off = 13;\n",
       "        // Calculate slopes for eigenlines\n",
       "        var ml = rl1/rl0;\n",
       "        var mr = rr1/rr0;\n",
       "        \n",
       "        // Main d3 drag function\n",
       "        var drag = d3.behavior.drag()\n",
       "            .origin(function(d) { return {x:obj.ax.x(d[0]),\n",
       "                                          y:obj.ax.y(d[1])}; })                              \n",
       "            .on(\"dragstart\", dragstarted)\n",
       "            .on(\"drag\", dragged)\n",
       "            .on(\"dragend\", dragended);\n",
       "    \n",
       "        // Set elements of ql and qr points and call main drag function\n",
       "        obj.elements()\n",
       "           .data(obj.offsets)\n",
       "           .style(\"cursor\", \"default\")\n",
       "           .call(drag);      \n",
       "\n",
       "        // Begin drag function\n",
       "        function dragstarted(d) {\n",
       "          d3.event.sourceEvent.stopPropagation();\n",
       "          d3.select(this).classed(\"dragging\", true);\n",
       "        }\n",
       "    \n",
       "        // The drag function called while dragging is happening (meat of code here)\n",
       "        function dragged(d,i) {\n",
       "          // Convert mouse coordinates in drag event (d3.event) to python coordinates d\n",
       "          d[0] = obj.ax.x.invert(d3.event.x);\n",
       "          d[1] = obj.ax.y.invert(d3.event.y);             \n",
       "          // Move ql and qr stored in obj (they have been selected in drag)\n",
       "          d3.select(this)\n",
       "            .attr(\"transform\", \"translate(\" + [d3.event.x, d3.event.y] + \")\");\n",
       "          // If obj corresponds to ql, move all the other left elements \n",
       "          if (i==0){\n",
       "              // Move text marker\n",
       "              qlm.elements().transition().duration(1)\n",
       "                  .attr(\"transform\", \"translate(\" + [d3.event.x + off, d3.event.y + off] + \")\");\n",
       "                  \n",
       "              // Move eigenlines\n",
       "              for (var ii=0; ii<2; ii++) {\n",
       "                linesla.data[ii][1] = ml*(linesla.data[ii][0] - d[0]) + d[1];\n",
       "                lineslb.data[ii][1] = mr*(lineslb.data[ii][0] - d[0]) + d[1]; }\n",
       "                \n",
       "              // In script calculations of middle state\n",
       "              qleft = [d[0], d[1]];\n",
       "              var det = rl0*rr1 - rr0*rl1;\n",
       "              var alphal = (rr1*(qright[0] - qleft[0]) - rr0*(qright[1] - qleft[1]))/det\n",
       "              qmid[0] = qleft[0] + alphal*rl0;\n",
       "              qmid[1] = qleft[1] + alphal*rl1;\n",
       "              var xx = obj.ax.x(qmid[0]);\n",
       "              var yy = obj.ax.y(qmid[1]); \n",
       "             \n",
       "                }\n",
       "          // if element corresponds to qr\n",
       "          else {\n",
       "              // Move text marker\n",
       "              qrm.elements().transition().duration(1)\n",
       "                  .attr(\"transform\", \"translate(\" + [d3.event.x + off, d3.event.y + off] + \")\");\n",
       "                  \n",
       "              // Move eigenlines\n",
       "              for (var ii=0; ii<2; ii++) {\n",
       "                linesra.data[ii][1] = ml*(linesra.data[ii][0] - d[0]) + d[1];\n",
       "                linesrb.data[ii][1] = mr*(linesrb.data[ii][0] - d[0]) + d[1]; }\n",
       "                \n",
       "              // In script calculations of middle state    \n",
       "              qright = [d[0], d[1]];\n",
       "              var det = rl0*rr1 - rr0*rl1;\n",
       "              var alphal = (rr1*(qright[0] - qleft[0]) - rr0*(qright[1] - qleft[1]))/det\n",
       "              qmid[0] = qleft[0] + alphal*rl0;\n",
       "              qmid[1] = qleft[1] + alphal*rl1;\n",
       "              var xx = obj.ax.x(qmid[0]);\n",
       "              var yy = obj.ax.y(qmid[1]);\n",
       "                }\n",
       "              // Update middle state point and marker position\n",
       "              midpoint.elements().transition().duration(5)\n",
       "                .attr(\"transform\", \"translate(\" + [xx, yy] + \")\");\n",
       "              qmm.elements().transition().duration(5)\n",
       "                .attr(\"transform\", \"translate(\" + [xx + 0.7*off, yy + 0.7*off] + \")\"); \n",
       "                \n",
       "              // Update eigenlines\n",
       "              linesla.elements().transition().duration(5)\n",
       "                  .attr(\"d\", linesla.datafunc(linesla.data));\n",
       "              lineslb.elements().transition().duration(5)\n",
       "                  .attr(\"d\", lineslb.datafunc(lineslb.data));\n",
       "              linesra.elements().transition().duration(5)\n",
       "                  .attr(\"d\", linesra.datafunc(linesra.data));\n",
       "              linesrb.elements().transition().duration(5)\n",
       "                  .attr(\"d\", linesrb.datafunc(linesrb.data));\n",
       "                \n",
       "              // Update subplots of q1 and q2\n",
       "              qone.data[0][1] = qleft[0];\n",
       "              qone.data[1][1] = qleft[0];\n",
       "              qone.data[2][1] = qmid[0];\n",
       "              qone.data[3][1] = qmid[0];\n",
       "              qone.data[4][1] = qright[0];\n",
       "              qone.data[5][1] = qright[0];\n",
       "              qtwo.data[0][2] = qleft[1];\n",
       "              qtwo.data[1][2] = qleft[1];\n",
       "              qtwo.data[2][2] = qmid[1];\n",
       "              qtwo.data[3][2] = qmid[1];\n",
       "              qtwo.data[4][2] = qright[1];\n",
       "              qtwo.data[5][2] = qright[1];\n",
       "              qone.elements().transition().duration(5)\n",
       "                .attr(\"d\", qone.datafunc(qone.data));\n",
       "              qtwo.elements().transition().duration(5)\n",
       "                .attr(\"d\", qtwo.datafunc(qtwo.data));  \n",
       "        }\n",
       "        // End dragging\n",
       "        function dragended(d) {\n",
       "          d3.select(this).classed(\"dragging\", false);\n",
       "        }\n",
       "    }\n",
       "    mpld3.register_plugin(\"drag\", PPlanePlugin); \n",
       "    \n",
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   "source": [
    "# Define left and right state \n",
    "ql = np.array([-2.0, 2.0]) \n",
    "qr = np.array([0.0, -3.0])\n",
    "# Define two eigenvectors and eigenvalues (acoustics)\n",
    "zz = 2.0\n",
    "rho0 = 1.0\n",
    "r1 = np.array([zz,1.0])\n",
    "r2 = np.array([-zz,1.0])\n",
    "lam1 = zz/rho0\n",
    "lam2 = -zz/rho0\n",
    "plotopts={'q1min':-5, 'q1max':5, 'q2min':-5, 'q2max':5, 'domain':5, 'time':1, \n",
    "          'title1':\"Pressure\", 'title2':\"Velocity\"}\n",
    "riemann_interactive.linear_phase_plane(ql,qr,r1,r2,lam1,lam2,**plotopts)\n",
    "mpld3.display()"
   ]
  }
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