examples/portfolio_optimization.ipynb

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      "#  Portfolio Optimization\n",
      "\n",
      "In this problem, we will find the portfolio allocation that minimizes risk while achieving a given expected return $R_\\mbox{target}$.\n",
      "\n",
      "Suppose that we know the mean returns $R \\in \\mathbf{R}^n$ and the covariance $Q \\in \\mathbf{R}^{n \\times n}$ of the $n$ assets. We would like to find a portfolio allocation $x \\in \\mathbf{R}^n$, $\\sum_i x_i = 1$, minimizing the *risk* of the portfolio, which we measure as the variance $x^T Q x$ of the portfolio. The requirement that the portfolio allocation achieve the target expected return can be expressed as $x^T R >= R_\\mbox{target}$. We suppose further that our portfolio allocation must comply with some lower and upper bounds on the allocation, $x_\\mbox{lower} \\leq x \\leq x_\\mbox{upper}$.\n",
      "\n",
      "This problem can be written as\n",
      "\n",
      "\\begin{array}{ll}\n",
      "    \\mbox{minimize}   & x^T Q x \\\\\n",
      "    \\mbox{subject to} & x^T R >= R_\\mbox{target} \\\\\n",
      "                      & \\sum_i x_i = 1 \\\\\n",
      "                      & x_\\mbox{lower} \\leq x \\leq x_\\mbox{upper}\n",
      "\\end{array}\n",
      "\n",
      "where $x \\in \\mathbf{R}^n$ is our optimization variable.\n",
      "\n",
      "We can solve this problem as follows."
     ]
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    {
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     "input": [
      "using Convex, ECOS\n",
      "\n",
      "# generate problem data\n",
      "srand(0)\n",
      "n = 50\n",
      "R = 5*randn(n)\n",
      "A = randn(n, 5)\n",
      "Q = A * A' + diagm(rand(n))\n",
      "R_target = 5\n",
      "x_lower = 0\n",
      "x_upper = 1\n",
      "\n",
      "x = Variable(length(R))\n",
      "p = minimize(quadform(x, Q), \n",
      "             x' * R >= R_target, \n",
      "             sum(x) == 1, \n",
      "             x_lower <= x, \n",
      "             x <= x_upper )\n",
      "\n",
      "solve!(p, ECOSSolver(verbose = false)) \n",
      "\n",
      "# the minimal risk\n",
      "p.optval"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "0.025263946889697284"
       ]
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     "cell_type": "markdown",
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     "source": [
      "We see that we can achieve an extremely low risk portfolio (with variance .025) with the desired expected return. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The optimal portfolio invests in only about half of the assets."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sum(x.value.>1e-4)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "27"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's take a look at the optimal portfolio we chose:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot(x=1:n,y=x.value,Geom.bar,Guide.xlabel(\"Asset Index\"),Guide.ylabel(\"Fraction of Portfolio\"))"
     ],
     "language": "python",
     "metadata": {},
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        "\n",
        "]]> </script>\n",
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        "\n",
        "(function (glob, factory) {\n",
        "    // AMD support\n",
        "    if (typeof define === \"function\" && define.amd) {\n",
        "        // Define as an anonymous module\n",
        "        define(\"Gadfly\", [\"Snap.svg\"], function (Snap) {\n",
        "            return factory(Snap);\n",
        "        });\n",
        "    } else {\n",
        "        // Browser globals (glob is window)\n",
        "        // Snap adds itself to window\n",
        "        glob.Gadfly = factory(glob.Snap);\n",
        "    }\n",
        "}(this, function (Snap) {\n",
        "\n",
        "var Gadfly = {};\n",
        "\n",
        "// Get an x/y coordinate value in pixels\n",
        "var xPX = function(fig, x) {\n",
        "    var client_box = fig.node.getBoundingClientRect();\n",
        "    return x * fig.node.viewBox.baseVal.width / client_box.width;\n",
        "};\n",
        "\n",
        "var yPX = function(fig, y) {\n",
        "    var client_box = fig.node.getBoundingClientRect();\n",
        "    return y * fig.node.viewBox.baseVal.height / client_box.height;\n",
        "};\n",
        "\n",
        "\n",
        "Snap.plugin(function (Snap, Element, Paper, global) {\n",
        "    // Traverse upwards from a snap element to find and return the first\n",
        "    // note with the \"plotroot\" class.\n",
        "    Element.prototype.plotroot = function () {\n",
        "        var element = this;\n",
        "        while (!element.hasClass(\"plotroot\") && element.parent() != null) {\n",
        "            element = element.parent();\n",
        "        }\n",
        "        return element;\n",
        "    };\n",
        "\n",
        "    Element.prototype.svgroot = function () {\n",
        "        var element = this;\n",
        "        while (element.node.nodeName != \"svg\" && element.parent() != null) {\n",
        "            element = element.parent();\n",
        "        }\n",
        "        return element;\n",
        "    };\n",
        "\n",
        "    Element.prototype.plotbounds = function () {\n",
        "        var root = this.plotroot()\n",
        "        var bbox = root.select(\".guide.background\").node.getBBox();\n",
        "        return {\n",
        "            x0: bbox.x,\n",
        "            x1: bbox.x + bbox.width,\n",
        "            y0: bbox.y,\n",
        "            y1: bbox.y + bbox.height\n",
        "        };\n",
        "    };\n",
        "\n",
        "    Element.prototype.plotcenter = function () {\n",
        "        var root = this.plotroot()\n",
        "        var bbox = root.select(\".guide.background\").node.getBBox();\n",
        "        return {\n",
        "            x: bbox.x + bbox.width / 2,\n",
        "            y: bbox.y + bbox.height / 2\n",
        "        };\n",
        "    };\n",
        "\n",
        "    // Emulate IE style mouseenter/mouseleave events, since Microsoft always\n",
        "    // does everything right.\n",
        "    // See: http://www.dynamic-tools.net/toolbox/isMouseLeaveOrEnter/\n",
        "    var events = [\"mouseenter\", \"mouseleave\"];\n",
        "\n",
        "    for (i in events) {\n",
        "        (function (event_name) {\n",
        "            var event_name = events[i];\n",
        "            Element.prototype[event_name] = function (fn, scope) {\n",
        "                if (Snap.is(fn, \"function\")) {\n",
        "                    var fn2 = function (event) {\n",
        "                        if (event.type != \"mouseover\" && event.type != \"mouseout\") {\n",
        "                            return;\n",
        "                        }\n",
        "\n",
        "                        var reltg = event.relatedTarget ? event.relatedTarget :\n",
        "                            event.type == \"mouseout\" ? event.toElement : event.fromElement;\n",
        "                        while (reltg && reltg != this.node) reltg = reltg.parentNode;\n",
        "\n",
        "                        if (reltg != this.node) {\n",
        "                            return fn.apply(this, event);\n",
        "                        }\n",
        "                    };\n",
        "\n",
        "                    if (event_name == \"mouseenter\") {\n",
        "                        this.mouseover(fn2, scope);\n",
        "                    } else {\n",
        "                        this.mouseout(fn2, scope);\n",
        "                    }\n",
        "                }\n",
        "                return this;\n",
        "            };\n",
        "        })(events[i]);\n",
        "    }\n",
        "\n",
        "\n",
        "    Element.prototype.mousewheel = function (fn, scope) {\n",
        "        if (Snap.is(fn, \"function\")) {\n",
        "            var el = this;\n",
        "            var fn2 = function (event) {\n",
        "                fn.apply(el, [event]);\n",
        "            };\n",
        "        }\n",
        "\n",
        "        this.node.addEventListener(\n",
        "            /Firefox/i.test(navigator.userAgent) ? \"DOMMouseScroll\" : \"mousewheel\",\n",
        "            fn2);\n",
        "\n",
        "        return this;\n",
        "    };\n",
        "\n",
        "\n",
        "    // Snap's attr function can be too slow for things like panning/zooming.\n",
        "    // This is a function to directly update element attributes without going\n",
        "    // through eve.\n",
        "    Element.prototype.attribute = function(key, val) {\n",
        "        if (val === undefined) {\n",
        "            return this.node.getAttribute(key, val);\n",
        "        } else {\n",
        "            return this.node.setAttribute(key, val);\n",
        "        }\n",
        "    };\n",
        "});\n",
        "\n",
        "\n",
        "// When the plot is moused over, emphasize the grid lines.\n",
        "Gadfly.plot_mouseover = function(event) {\n",
        "    var root = this.plotroot();\n",
        "    init_pan_zoom(root);\n",
        "\n",
        "    var xgridlines = root.select(\".xgridlines\"),\n",
        "        ygridlines = root.select(\".ygridlines\");\n",
        "\n",
        "    xgridlines.data(\"unfocused_strokedash\",\n",
        "                    xgridlines.attr(\"stroke-dasharray\").replace(/px/g, \"mm\"))\n",
        "    ygridlines.data(\"unfocused_strokedash\",\n",
        "                    ygridlines.attr(\"stroke-dasharray\").replace(/px/g, \"mm\"))\n",
        "\n",
        "    // emphasize grid lines\n",
        "    var destcolor = root.data(\"focused_xgrid_color\");\n",
        "    xgridlines.attr(\"stroke-dasharray\", \"none\")\n",
        "              .selectAll(\"path\")\n",
        "              .animate({stroke: destcolor}, 250);\n",
        "\n",
        "    destcolor = root.data(\"focused_ygrid_color\");\n",
        "    ygridlines.attr(\"stroke-dasharray\", \"none\")\n",
        "              .selectAll(\"path\")\n",
        "              .animate({stroke: destcolor}, 250);\n",
        "\n",
        "    // reveal zoom slider\n",
        "    root.select(\".zoomslider\")\n",
        "        .animate({opacity: 1.0}, 250);\n",
        "};\n",
        "\n",
        "\n",
        "// Unemphasize grid lines on mouse out.\n",
        "Gadfly.plot_mouseout = function(event) {\n",
        "    var root = this.plotroot();\n",
        "    var xgridlines = root.select(\".xgridlines\"),\n",
        "        ygridlines = root.select(\".ygridlines\");\n",
        "\n",
        "    var destcolor = root.data(\"unfocused_xgrid_color\");\n",
        "\n",
        "    xgridlines.attr(\"stroke-dasharray\", xgridlines.data(\"unfocused_strokedash\"))\n",
        "              .selectAll(\"path\")\n",
        "              .animate({stroke: destcolor}, 250);\n",
        "\n",
        "    destcolor = root.data(\"unfocused_ygrid_color\");\n",
        "    ygridlines.attr(\"stroke-dasharray\", ygridlines.data(\"unfocused_strokedash\"))\n",
        "              .selectAll(\"path\")\n",
        "              .animate({stroke: destcolor}, 250);\n",
        "\n",
        "    // hide zoom slider\n",
        "    root.select(\".zoomslider\")\n",
        "        .animate({opacity: 0.0}, 250);\n",
        "};\n",
        "\n",
        "\n",
        "var set_geometry_transform = function(root, tx, ty, scale) {\n",
        "    var xscalable = root.hasClass(\"xscalable\"),\n",
        "        yscalable = root.hasClass(\"yscalable\");\n",
        "\n",
        "    var old_scale = root.data(\"scale\");\n",
        "\n",
        "    var xscale = xscalable ? scale : 1.0,\n",
        "        yscale = yscalable ? scale : 1.0;\n",
        "\n",
        "    tx = xscalable ? tx : 0.0;\n",
        "    ty = yscalable ? ty : 0.0;\n",
        "\n",
        "    var t = new Snap.Matrix().translate(tx, ty).scale(xscale, yscale);\n",
        "\n",
        "    root.selectAll(\".geometry, image\")\n",
        "        .forEach(function (element, i) {\n",
        "            element.transform(t);\n",
        "        });\n",
        "\n",
        "    bounds = root.plotbounds();\n",
        "\n",
        "    if (yscalable) {\n",
        "        var xfixed_t = new Snap.Matrix().translate(0, ty).scale(1.0, yscale);\n",
        "        root.selectAll(\".xfixed\")\n",
        "            .forEach(function (element, i) {\n",
        "                element.transform(xfixed_t);\n",
        "            });\n",
        "\n",
        "        root.select(\".ylabels\")\n",
        "            .transform(xfixed_t)\n",
        "            .selectAll(\"text\")\n",
        "            .forEach(function (element, i) {\n",
        "                if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
        "                    var cx = element.asPX(\"x\"),\n",
        "                        cy = element.asPX(\"y\");\n",
        "                    var st = element.data(\"static_transform\");\n",
        "                    unscale_t = new Snap.Matrix();\n",
        "                    unscale_t.scale(1, 1/scale, cx, cy).add(st);\n",
        "                    element.transform(unscale_t);\n",
        "\n",
        "                    var y = cy * scale + ty;\n",
        "                    element.attr(\"visibility\",\n",
        "                        bounds.y0 <= y && y <= bounds.y1 ? \"visible\" : \"hidden\");\n",
        "                }\n",
        "            });\n",
        "    }\n",
        "\n",
        "    if (xscalable) {\n",
        "        var yfixed_t = new Snap.Matrix().translate(tx, 0).scale(xscale, 1.0);\n",
        "        var xtrans = new Snap.Matrix().translate(tx, 0);\n",
        "        root.selectAll(\".yfixed\")\n",
        "            .forEach(function (element, i) {\n",
        "                element.transform(yfixed_t);\n",
        "            });\n",
        "\n",
        "        root.select(\".xlabels\")\n",
        "            .transform(yfixed_t)\n",
        "            .selectAll(\"text\")\n",
        "            .forEach(function (element, i) {\n",
        "                if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
        "                    var cx = element.asPX(\"x\"),\n",
        "                        cy = element.asPX(\"y\");\n",
        "                    var st = element.data(\"static_transform\");\n",
        "                    unscale_t = new Snap.Matrix();\n",
        "                    unscale_t.scale(1/scale, 1, cx, cy).add(st);\n",
        "\n",
        "                    element.transform(unscale_t);\n",
        "\n",
        "                    var x = cx * scale + tx;\n",
        "                    element.attr(\"visibility\",\n",
        "                        bounds.x0 <= x && x <= bounds.x1 ? \"visible\" : \"hidden\");\n",
        "                    }\n",
        "            });\n",
        "    }\n",
        "\n",
        "    // we must unscale anything that is scale invariance: widths, raiduses, etc.\n",
        "    var size_attribs = [\"font-size\"];\n",
        "    var unscaled_selection = \".geometry, .geometry *\";\n",
        "    if (xscalable) {\n",
        "        size_attribs.push(\"rx\");\n",
        "        unscaled_selection += \", .xgridlines\";\n",
        "    }\n",
        "    if (yscalable) {\n",
        "        size_attribs.push(\"ry\");\n",
        "        unscaled_selection += \", .ygridlines\";\n",
        "    }\n",
        "\n",
        "    root.selectAll(unscaled_selection)\n",
        "        .forEach(function (element, i) {\n",
        "            // circle need special help\n",
        "            if (element.node.nodeName == \"circle\") {\n",
        "                var cx = element.attribute(\"cx\"),\n",
        "                    cy = element.attribute(\"cy\");\n",
        "                unscale_t = new Snap.Matrix().scale(1/xscale, 1/yscale,\n",
        "                                                        cx, cy);\n",
        "                element.transform(unscale_t);\n",
        "                return;\n",
        "            }\n",
        "\n",
        "            for (i in size_attribs) {\n",
        "                var key = size_attribs[i];\n",
        "                var val = parseFloat(element.attribute(key));\n",
        "                if (val !== undefined && val != 0 && !isNaN(val)) {\n",
        "                    element.attribute(key, val * old_scale / scale);\n",
        "                }\n",
        "            }\n",
        "        });\n",
        "};\n",
        "\n",
        "\n",
        "// Find the most appropriate tick scale and update label visibility.\n",
        "var update_tickscale = function(root, scale, axis) {\n",
        "    if (!root.hasClass(axis + \"scalable\")) return;\n",
        "\n",
        "    var tickscales = root.data(axis + \"tickscales\");\n",
        "    var best_tickscale = 1.0;\n",
        "    var best_tickscale_dist = Infinity;\n",
        "    for (tickscale in tickscales) {\n",
        "        var dist = Math.abs(Math.log(tickscale) - Math.log(scale));\n",
        "        if (dist < best_tickscale_dist) {\n",
        "            best_tickscale_dist = dist;\n",
        "            best_tickscale = tickscale;\n",
        "        }\n",
        "    }\n",
        "\n",
        "    if (best_tickscale != root.data(axis + \"tickscale\")) {\n",
        "        root.data(axis + \"tickscale\", best_tickscale);\n",
        "        var mark_inscale_gridlines = function (element, i) {\n",
        "            var inscale = element.attr(\"gadfly:scale\") == best_tickscale;\n",
        "            element.attribute(\"gadfly:inscale\", inscale);\n",
        "            element.attr(\"visibility\", inscale ? \"visible\" : \"hidden\");\n",
        "        };\n",
        "\n",
        "        var mark_inscale_labels = function (element, i) {\n",
        "            var inscale = element.attr(\"gadfly:scale\") == best_tickscale;\n",
        "            element.attribute(\"gadfly:inscale\", inscale);\n",
        "            element.attr(\"visibility\", inscale ? \"visible\" : \"hidden\");\n",
        "        };\n",
        "\n",
        "        root.select(\".\" + axis + \"gridlines\").selectAll(\"path\").forEach(mark_inscale_gridlines);\n",
        "        root.select(\".\" + axis + \"labels\").selectAll(\"text\").forEach(mark_inscale_labels);\n",
        "    }\n",
        "};\n",
        "\n",
        "\n",
        "var set_plot_pan_zoom = function(root, tx, ty, scale) {\n",
        "    var old_scale = root.data(\"scale\");\n",
        "    var bounds = root.plotbounds();\n",
        "\n",
        "    var width = bounds.x1 - bounds.x0,\n",
        "        height = bounds.y1 - bounds.y0;\n",
        "\n",
        "    // compute the viewport derived from tx, ty, and scale\n",
        "    var x_min = -width * scale - (scale * width - width),\n",
        "        x_max = width * scale,\n",
        "        y_min = -height * scale - (scale * height - height),\n",
        "        y_max = height * scale;\n",
        "\n",
        "    var x0 = bounds.x0 - scale * bounds.x0,\n",
        "        y0 = bounds.y0 - scale * bounds.y0;\n",
        "\n",
        "    var tx = Math.max(Math.min(tx - x0, x_max), x_min),\n",
        "        ty = Math.max(Math.min(ty - y0, y_max), y_min);\n",
        "\n",
        "    tx += x0;\n",
        "    ty += y0;\n",
        "\n",
        "    // when the scale change, we may need to alter which set of\n",
        "    // ticks is being displayed\n",
        "    if (scale != old_scale) {\n",
        "        update_tickscale(root, scale, \"x\");\n",
        "        update_tickscale(root, scale, \"y\");\n",
        "    }\n",
        "\n",
        "    set_geometry_transform(root, tx, ty, scale);\n",
        "\n",
        "    root.data(\"scale\", scale);\n",
        "    root.data(\"tx\", tx);\n",
        "    root.data(\"ty\", ty);\n",
        "};\n",
        "\n",
        "\n",
        "var scale_centered_translation = function(root, scale) {\n",
        "    var bounds = root.plotbounds();\n",
        "\n",
        "    var width = bounds.x1 - bounds.x0,\n",
        "        height = bounds.y1 - bounds.y0;\n",
        "\n",
        "    var tx0 = root.data(\"tx\"),\n",
        "        ty0 = root.data(\"ty\");\n",
        "\n",
        "    var scale0 = root.data(\"scale\");\n",
        "\n",
        "    // how off from center the current view is\n",
        "    var xoff = tx0 - (bounds.x0 * (1 - scale0) + (width * (1 - scale0)) / 2),\n",
        "        yoff = ty0 - (bounds.y0 * (1 - scale0) + (height * (1 - scale0)) / 2);\n",
        "\n",
        "    // rescale offsets\n",
        "    xoff = xoff * scale / scale0;\n",
        "    yoff = yoff * scale / scale0;\n",
        "\n",
        "    // adjust for the panel position being scaled\n",
        "    var x_edge_adjust = bounds.x0 * (1 - scale),\n",
        "        y_edge_adjust = bounds.y0 * (1 - scale);\n",
        "\n",
        "    return {\n",
        "        x: xoff + x_edge_adjust + (width - width * scale) / 2,\n",
        "        y: yoff + y_edge_adjust + (height - height * scale) / 2\n",
        "    };\n",
        "};\n",
        "\n",
        "\n",
        "// Initialize data for panning zooming if it isn't already.\n",
        "var init_pan_zoom = function(root) {\n",
        "    if (root.data(\"zoompan-ready\")) {\n",
        "        return;\n",
        "    }\n",
        "\n",
        "    // The non-scaling-stroke trick. Rather than try to correct for the\n",
        "    // stroke-width when zooming, we force it to a fixed value.\n",
        "    var px_per_mm = root.node.getCTM().a;\n",
        "\n",
        "    // Drag events report deltas in pixels, which we'd like to convert to\n",
        "    // millimeters.\n",
        "    root.data(\"px_per_mm\", px_per_mm);\n",
        "\n",
        "    root.selectAll(\"path\")\n",
        "        .forEach(function (element, i) {\n",
        "        sw = element.asPX(\"stroke-width\") * px_per_mm;\n",
        "        if (sw > 0) {\n",
        "            element.attribute(\"stroke-width\", sw);\n",
        "            element.attribute(\"vector-effect\", \"non-scaling-stroke\");\n",
        "        }\n",
        "    });\n",
        "\n",
        "    // Store ticks labels original tranformation\n",
        "    root.selectAll(\".xlabels > text, .ylabels > text\")\n",
        "        .forEach(function (element, i) {\n",
        "            var lm = element.transform().localMatrix;\n",
        "            element.data(\"static_transform\",\n",
        "                new Snap.Matrix(lm.a, lm.b, lm.c, lm.d, lm.e, lm.f));\n",
        "        });\n",
        "\n",
        "    if (root.data(\"tx\") === undefined) root.data(\"tx\", 0);\n",
        "    if (root.data(\"ty\") === undefined) root.data(\"ty\", 0);\n",
        "    if (root.data(\"scale\") === undefined) root.data(\"scale\", 1.0);\n",
        "    if (root.data(\"xtickscales\") === undefined) {\n",
        "\n",
        "        // index all the tick scales that are listed\n",
        "        var xtickscales = {};\n",
        "        var ytickscales = {};\n",
        "        var add_x_tick_scales = function (element, i) {\n",
        "            xtickscales[element.attribute(\"gadfly:scale\")] = true;\n",
        "        };\n",
        "        var add_y_tick_scales = function (element, i) {\n",
        "            ytickscales[element.attribute(\"gadfly:scale\")] = true;\n",
        "        };\n",
        "\n",
        "        root.select(\".xgridlines\").selectAll(\"path\").forEach(add_x_tick_scales);\n",
        "        root.select(\".ygridlines\").selectAll(\"path\").forEach(add_y_tick_scales);\n",
        "        root.select(\".xlabels\").selectAll(\"text\").forEach(add_x_tick_scales);\n",
        "        root.select(\".ylabels\").selectAll(\"text\").forEach(add_y_tick_scales);\n",
        "\n",
        "        root.data(\"xtickscales\", xtickscales);\n",
        "        root.data(\"ytickscales\", ytickscales);\n",
        "        root.data(\"xtickscale\", 1.0);\n",
        "    }\n",
        "\n",
        "    var min_scale = 1.0, max_scale = 1.0;\n",
        "    for (scale in xtickscales) {\n",
        "        min_scale = Math.min(min_scale, scale);\n",
        "        max_scale = Math.max(max_scale, scale);\n",
        "    }\n",
        "    for (scale in ytickscales) {\n",
        "        min_scale = Math.min(min_scale, scale);\n",
        "        max_scale = Math.max(max_scale, scale);\n",
        "    }\n",
        "    root.data(\"min_scale\", min_scale);\n",
        "    root.data(\"max_scale\", max_scale);\n",
        "\n",
        "    // store the original positions of labels\n",
        "    root.select(\".xlabels\")\n",
        "        .selectAll(\"text\")\n",
        "        .forEach(function (element, i) {\n",
        "            element.data(\"x\", element.asPX(\"x\"));\n",
        "        });\n",
        "\n",
        "    root.select(\".ylabels\")\n",
        "        .selectAll(\"text\")\n",
        "        .forEach(function (element, i) {\n",
        "            element.data(\"y\", element.asPX(\"y\"));\n",
        "        });\n",
        "\n",
        "    // mark grid lines and ticks as in or out of scale.\n",
        "    var mark_inscale = function (element, i) {\n",
        "        element.attribute(\"gadfly:inscale\", element.attribute(\"gadfly:scale\") == 1.0);\n",
        "    };\n",
        "\n",
        "    root.select(\".xgridlines\").selectAll(\"path\").forEach(mark_inscale);\n",
        "    root.select(\".ygridlines\").selectAll(\"path\").forEach(mark_inscale);\n",
        "    root.select(\".xlabels\").selectAll(\"text\").forEach(mark_inscale);\n",
        "    root.select(\".ylabels\").selectAll(\"text\").forEach(mark_inscale);\n",
        "\n",
        "    // figure out the upper ond lower bounds on panning using the maximum\n",
        "    // and minum grid lines\n",
        "    var bounds = root.plotbounds();\n",
        "    var pan_bounds = {\n",
        "        x0: 0.0,\n",
        "        y0: 0.0,\n",
        "        x1: 0.0,\n",
        "        y1: 0.0\n",
        "    };\n",
        "\n",
        "    root.select(\".xgridlines\")\n",
        "        .selectAll(\"path\")\n",
        "        .forEach(function (element, i) {\n",
        "            if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
        "                var bbox = element.node.getBBox();\n",
        "                if (bounds.x1 - bbox.x < pan_bounds.x0) {\n",
        "                    pan_bounds.x0 = bounds.x1 - bbox.x;\n",
        "                }\n",
        "                if (bounds.x0 - bbox.x > pan_bounds.x1) {\n",
        "                    pan_bounds.x1 = bounds.x0 - bbox.x;\n",
        "                }\n",
        "            }\n",
        "        });\n",
        "\n",
        "    root.select(\".ygridlines\")\n",
        "        .selectAll(\"path\")\n",
        "        .forEach(function (element, i) {\n",
        "            if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
        "                var bbox = element.node.getBBox();\n",
        "                if (bounds.y1 - bbox.y < pan_bounds.y0) {\n",
        "                    pan_bounds.y0 = bounds.y1 - bbox.y;\n",
        "                }\n",
        "                if (bounds.y0 - bbox.y > pan_bounds.y1) {\n",
        "                    pan_bounds.y1 = bounds.y0 - bbox.y;\n",
        "                }\n",
        "            }\n",
        "        });\n",
        "\n",
        "    // nudge these values a little\n",
        "    pan_bounds.x0 -= 5;\n",
        "    pan_bounds.x1 += 5;\n",
        "    pan_bounds.y0 -= 5;\n",
        "    pan_bounds.y1 += 5;\n",
        "    root.data(\"pan_bounds\", pan_bounds);\n",
        "\n",
        "    // Set all grid lines at scale 1.0 to visible. Out of bounds lines\n",
        "    // will be clipped.\n",
        "    root.select(\".xgridlines\")\n",
        "        .selectAll(\"path\")\n",
        "        .forEach(function (element, i) {\n",
        "            if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
        "                element.attr(\"visibility\", \"visible\");\n",
        "            }\n",
        "        });\n",
        "\n",
        "    root.select(\".ygridlines\")\n",
        "        .selectAll(\"path\")\n",
        "        .forEach(function (element, i) {\n",
        "            if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
        "                element.attr(\"visibility\", \"visible\");\n",
        "            }\n",
        "        });\n",
        "\n",
        "    root.data(\"zoompan-ready\", true)\n",
        "};\n",
        "\n",
        "\n",
        "// Panning\n",
        "Gadfly.guide_background_drag_onmove = function(dx, dy, x, y, event) {\n",
        "    var root = this.plotroot();\n",
        "    var px_per_mm = root.data(\"px_per_mm\");\n",
        "    dx /= px_per_mm;\n",
        "    dy /= px_per_mm;\n",
        "\n",
        "    var tx0 = root.data(\"tx\"),\n",
        "        ty0 = root.data(\"ty\");\n",
        "\n",
        "    var dx0 = root.data(\"dx\"),\n",
        "        dy0 = root.data(\"dy\");\n",
        "\n",
        "    root.data(\"dx\", dx);\n",
        "    root.data(\"dy\", dy);\n",
        "\n",
        "    dx = dx - dx0;\n",
        "    dy = dy - dy0;\n",
        "\n",
        "    var tx = tx0 + dx,\n",
        "        ty = ty0 + dy;\n",
        "\n",
        "    set_plot_pan_zoom(root, tx, ty, root.data(\"scale\"));\n",
        "};\n",
        "\n",
        "\n",
        "Gadfly.guide_background_drag_onstart = function(x, y, event) {\n",
        "    var root = this.plotroot();\n",
        "    root.data(\"dx\", 0);\n",
        "    root.data(\"dy\", 0);\n",
        "    init_pan_zoom(root);\n",
        "};\n",
        "\n",
        "\n",
        "Gadfly.guide_background_drag_onend = function(event) {\n",
        "    var root = this.plotroot();\n",
        "};\n",
        "\n",
        "\n",
        "Gadfly.guide_background_scroll = function(event) {\n",
        "    if (event.shiftKey) {\n",
        "        var root = this.plotroot();\n",
        "        init_pan_zoom(root);\n",
        "        var new_scale = root.data(\"scale\") * Math.pow(2, 0.002 * event.wheelDelta);\n",
        "        new_scale = Math.max(\n",
        "            root.data(\"min_scale\"),\n",
        "            Math.min(root.data(\"max_scale\"), new_scale))\n",
        "        update_plot_scale(root, new_scale);\n",
        "        event.stopPropagation();\n",
        "    }\n",
        "};\n",
        "\n",
        "\n",
        "Gadfly.zoomslider_button_mouseover = function(event) {\n",
        "    this.select(\".button_logo\")\n",
        "         .animate({fill: this.data(\"mouseover_color\")}, 100);\n",
        "};\n",
        "\n",
        "\n",
        "Gadfly.zoomslider_button_mouseout = function(event) {\n",
        "     this.select(\".button_logo\")\n",
        "         .animate({fill: this.data(\"mouseout_color\")}, 100);\n",
        "};\n",
        "\n",
        "\n",
        "Gadfly.zoomslider_zoomout_click = function(event) {\n",
        "    var root = this.plotroot();\n",
        "    init_pan_zoom(root);\n",
        "    var min_scale = root.data(\"min_scale\"),\n",
        "        scale = root.data(\"scale\");\n",
        "    Snap.animate(\n",
        "        scale,\n",
        "        Math.max(min_scale, scale / 1.5),\n",
        "        function (new_scale) {\n",
        "            update_plot_scale(root, new_scale);\n",
        "        },\n",
        "        200);\n",
        "};\n",
        "\n",
        "\n",
        "Gadfly.zoomslider_zoomin_click = function(event) {\n",
        "    var root = this.plotroot();\n",
        "    init_pan_zoom(root);\n",
        "    var max_scale = root.data(\"max_scale\"),\n",
        "        scale = root.data(\"scale\");\n",
        "\n",
        "    Snap.animate(\n",
        "        scale,\n",
        "        Math.min(max_scale, scale * 1.5),\n",
        "        function (new_scale) {\n",
        "            update_plot_scale(root, new_scale);\n",
        "        },\n",
        "        200);\n",
        "};\n",
        "\n",
        "\n",
        "Gadfly.zoomslider_track_click = function(event) {\n",
        "    // TODO\n",
        "};\n",
        "\n",
        "\n",
        "Gadfly.zoomslider_thumb_mousedown = function(event) {\n",
        "    this.animate({fill: this.data(\"mouseover_color\")}, 100);\n",
        "};\n",
        "\n",
        "\n",
        "Gadfly.zoomslider_thumb_mouseup = function(event) {\n",
        "    this.animate({fill: this.data(\"mouseout_color\")}, 100);\n",
        "};\n",
        "\n",
        "\n",
        "// compute the position in [0, 1] of the zoom slider thumb from the current scale\n",
        "var slider_position_from_scale = function(scale, min_scale, max_scale) {\n",
        "    if (scale >= 1.0) {\n",
        "        return 0.5 + 0.5 * (Math.log(scale) / Math.log(max_scale));\n",
        "    }\n",
        "    else {\n",
        "        return 0.5 * (Math.log(scale) - Math.log(min_scale)) / (0 - Math.log(min_scale));\n",
        "    }\n",
        "}\n",
        "\n",
        "\n",
        "var update_plot_scale = function(root, new_scale) {\n",
        "    var trans = scale_centered_translation(root, new_scale);\n",
        "    set_plot_pan_zoom(root, trans.x, trans.y, new_scale);\n",
        "\n",
        "    root.selectAll(\".zoomslider_thumb\")\n",
        "        .forEach(function (element, i) {\n",
        "            var min_pos = element.data(\"min_pos\"),\n",
        "                max_pos = element.data(\"max_pos\"),\n",
        "                min_scale = root.data(\"min_scale\"),\n",
        "                max_scale = root.data(\"max_scale\");\n",
        "            var xmid = (min_pos + max_pos) / 2;\n",
        "            var xpos = slider_position_from_scale(new_scale, min_scale, max_scale);\n",
        "            element.transform(new Snap.Matrix().translate(\n",
        "                Math.max(min_pos, Math.min(\n",
        "                         max_pos, min_pos + (max_pos - min_pos) * xpos)) - xmid, 0));\n",
        "    });\n",
        "};\n",
        "\n",
        "\n",
        "Gadfly.zoomslider_thumb_dragmove = function(dx, dy, x, y) {\n",
        "    var root = this.plotroot();\n",
        "    var min_pos = this.data(\"min_pos\"),\n",
        "        max_pos = this.data(\"max_pos\"),\n",
        "        min_scale = root.data(\"min_scale\"),\n",
        "        max_scale = root.data(\"max_scale\"),\n",
        "        old_scale = root.data(\"old_scale\");\n",
        "\n",
        "    var px_per_mm = root.data(\"px_per_mm\");\n",
        "    dx /= px_per_mm;\n",
        "    dy /= px_per_mm;\n",
        "\n",
        "    var xmid = (min_pos + max_pos) / 2;\n",
        "    var xpos = slider_position_from_scale(old_scale, min_scale, max_scale) +\n",
        "                   dx / (max_pos - min_pos);\n",
        "\n",
        "    // compute the new scale\n",
        "    var new_scale;\n",
        "    if (xpos >= 0.5) {\n",
        "        new_scale = Math.exp(2.0 * (xpos - 0.5) * Math.log(max_scale));\n",
        "    }\n",
        "    else {\n",
        "        new_scale = Math.exp(2.0 * xpos * (0 - Math.log(min_scale)) +\n",
        "                        Math.log(min_scale));\n",
        "    }\n",
        "    new_scale = Math.min(max_scale, Math.max(min_scale, new_scale));\n",
        "\n",
        "    update_plot_scale(root, new_scale);\n",
        "};\n",
        "\n",
        "\n",
        "Gadfly.zoomslider_thumb_dragstart = function(event) {\n",
        "    var root = this.plotroot();\n",
        "    init_pan_zoom(root);\n",
        "\n",
        "    // keep track of what the scale was when we started dragging\n",
        "    root.data(\"old_scale\", root.data(\"scale\"));\n",
        "};\n",
        "\n",
        "\n",
        "Gadfly.zoomslider_thumb_dragend = function(event) {\n",
        "};\n",
        "\n",
        "\n",
        "var toggle_color_class = function(root, color_class, ison) {\n",
        "    var guides = root.selectAll(\".guide.\" + color_class + \",.guide .\" + color_class);\n",
        "    var geoms = root.selectAll(\".geometry.\" + color_class + \",.geometry .\" + color_class);\n",
        "    if (ison) {\n",
        "        guides.animate({opacity: 0.5}, 250);\n",
        "        geoms.animate({opacity: 0.0}, 250);\n",
        "    } else {\n",
        "        guides.animate({opacity: 1.0}, 250);\n",
        "        geoms.animate({opacity: 1.0}, 250);\n",
        "    }\n",
        "};\n",
        "\n",
        "\n",
        "Gadfly.colorkey_swatch_click = function(event) {\n",
        "    var root = this.plotroot();\n",
        "    var color_class = this.data(\"color_class\");\n",
        "\n",
        "    if (event.shiftKey) {\n",
        "        root.selectAll(\".colorkey text\")\n",
        "            .forEach(function (element) {\n",
        "                var other_color_class = element.data(\"color_class\");\n",
        "                if (other_color_class != color_class) {\n",
        "                    toggle_color_class(root, other_color_class,\n",
        "                                       element.attr(\"opacity\") == 1.0);\n",
        "                }\n",
        "            });\n",
        "    } else {\n",
        "        toggle_color_class(root, color_class, this.attr(\"opacity\") == 1.0);\n",
        "    }\n",
        "};\n",
        "\n",
        "\n",
        "return Gadfly;\n",
        "\n",
        "}));\n",
        "\n",
        "\n",
        "//@ sourceURL=gadfly.js\n",
        "\n",
        "(function (glob, factory) {\n",
        "    // AMD support\n",
        "      if (typeof require === \"function\" && typeof define === \"function\" && define.amd) {\n",
        "        require([\"Snap.svg\", \"Gadfly\"], function (Snap, Gadfly) {\n",
        "            factory(Snap, Gadfly);\n",
        "        });\n",
        "      } else {\n",
        "          factory(glob.Snap, glob.Gadfly);\n",
        "      }\n",
        "})(window, function (Snap, Gadfly) {\n",
        "    var fig = Snap(\"#fig-a972841059094e5e88894088fca432c7\");\n",
        "fig.select(\"#fig-a972841059094e5e88894088fca432c7-element-5\")\n",
        "   .mouseenter(Gadfly.plot_mouseover)\n",
        ".mouseleave(Gadfly.plot_mouseout)\n",
        ".mousewheel(Gadfly.guide_background_scroll)\n",
        ".drag(Gadfly.guide_background_drag_onmove,\n",
        "      Gadfly.guide_background_drag_onstart,\n",
        "      Gadfly.guide_background_drag_onend)\n",
        ";\n",
        "fig.select(\"#fig-a972841059094e5e88894088fca432c7-element-8\")\n",
        "   .plotroot().data(\"unfocused_ygrid_color\", \"#D0D0E0\")\n",
        ";\n",
        "fig.select(\"#fig-a972841059094e5e88894088fca432c7-element-8\")\n",
        "   .plotroot().data(\"focused_ygrid_color\", \"#A0A0A0\")\n",
        ";\n",
        "fig.select(\"#fig-a972841059094e5e88894088fca432c7-element-9\")\n",
        "   .plotroot().data(\"unfocused_xgrid_color\", \"#D0D0E0\")\n",
        ";\n",
        "fig.select(\"#fig-a972841059094e5e88894088fca432c7-element-9\")\n",
        "   .plotroot().data(\"focused_xgrid_color\", \"#A0A0A0\")\n",
        ";\n",
        "fig.select(\"#fig-a972841059094e5e88894088fca432c7-element-14\")\n",
        "   .data(\"mouseover_color\", \"#cd5c5c\")\n",
        ";\n",
        "fig.select(\"#fig-a972841059094e5e88894088fca432c7-element-14\")\n",
        "   .data(\"mouseout_color\", \"#6a6a6a\")\n",
        ";\n",
        "fig.select(\"#fig-a972841059094e5e88894088fca432c7-element-14\")\n",
        "   .click(Gadfly.zoomslider_zoomin_click)\n",
        ".mouseenter(Gadfly.zoomslider_button_mouseover)\n",
        ".mouseleave(Gadfly.zoomslider_button_mouseout)\n",
        ";\n",
        "fig.select(\"#fig-a972841059094e5e88894088fca432c7-element-16\")\n",
        "   .data(\"max_pos\", 120.42)\n",
        ";\n",
        "fig.select(\"#fig-a972841059094e5e88894088fca432c7-element-16\")\n",
        "   .data(\"min_pos\", 103.42)\n",
        ";\n",
        "fig.select(\"#fig-a972841059094e5e88894088fca432c7-element-16\")\n",
        "   .click(Gadfly.zoomslider_track_click);\n",
        "fig.select(\"#fig-a972841059094e5e88894088fca432c7-element-17\")\n",
        "   .data(\"max_pos\", 120.42)\n",
        ";\n",
        "fig.select(\"#fig-a972841059094e5e88894088fca432c7-element-17\")\n",
        "   .data(\"min_pos\", 103.42)\n",
        ";\n",
        "fig.select(\"#fig-a972841059094e5e88894088fca432c7-element-17\")\n",
        "   .data(\"mouseover_color\", \"#cd5c5c\")\n",
        ";\n",
        "fig.select(\"#fig-a972841059094e5e88894088fca432c7-element-17\")\n",
        "   .data(\"mouseout_color\", \"#6a6a6a\")\n",
        ";\n",
        "fig.select(\"#fig-a972841059094e5e88894088fca432c7-element-17\")\n",
        "   .drag(Gadfly.zoomslider_thumb_dragmove,\n",
        "     Gadfly.zoomslider_thumb_dragstart,\n",
        "     Gadfly.zoomslider_thumb_dragend)\n",
        ".mousedown(Gadfly.zoomslider_thumb_mousedown)\n",
        ".mouseup(Gadfly.zoomslider_thumb_mouseup)\n",
        ";\n",
        "fig.select(\"#fig-a972841059094e5e88894088fca432c7-element-18\")\n",
        "   .data(\"mouseover_color\", \"#cd5c5c\")\n",
        ";\n",
        "fig.select(\"#fig-a972841059094e5e88894088fca432c7-element-18\")\n",
        "   .data(\"mouseout_color\", \"#6a6a6a\")\n",
        ";\n",
        "fig.select(\"#fig-a972841059094e5e88894088fca432c7-element-18\")\n",
        "   .click(Gadfly.zoomslider_zoomout_click)\n",
        ".mouseenter(Gadfly.zoomslider_button_mouseover)\n",
        ".mouseleave(Gadfly.zoomslider_button_mouseout)\n",
        ";\n",
        "    });\n",
        "]]> </script>\n",
        "</svg>\n"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": 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