BGSM_isotonic.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using ConstrainedLasso, Gadfly, DataFrames, LightGraphs, CSV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "include(\"code/BGSM_general.jl\");\n",
    "include(\"code/BGSM_effective_resistance.jl\");\n",
    "include(\"code/model_selection.jl\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "pava (generic function with 1 method)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# solve NNLS\n",
    "# minimize_b (1/2) * b^T H b + a^T b\n",
    "# subject to b >= 0\n",
    "\n",
    "function nnls(x, a, H; convtol = 1e-8, sptol = 1e-5, maxiter = 100)\n",
    "\n",
    "  # Get the number of degrees of freedom in the optimization problem.\n",
    "  k = length(x);\n",
    "    \n",
    "  # Initialize the solution to the QP subproblem.\n",
    "  y      = copy(x);\n",
    "  ind    = find(x .> sptol);\n",
    "  y[ind] = 1/length(ind);\n",
    "  i = 0;\n",
    "\n",
    "  # Repeat until we reach the maximum number of iterations, or until\n",
    "  # convergence is reached.\n",
    "  for i = 1:maxiter\n",
    "        \n",
    "    # Define the smaller QP subproblem.\n",
    "    s   = length(ind);\n",
    "    H_s = H[ind,ind];\n",
    "    d   = H*y + a;\n",
    "    d_s = d[ind];\n",
    "\n",
    "    # Solve the smaller problem.\n",
    "    p      = sparse(zeros(k));\n",
    "    p_s    = -H_s\\d_s;\n",
    "    p[ind] = p_s;\n",
    "\n",
    "    # Check convergence using KKT\n",
    "    if norm(p_s) < convtol\n",
    "            \n",
    "      # Compute the Lagrange multiplier.\n",
    "      z = d;\n",
    "      if all(z .>= -convtol)\n",
    "        break\n",
    "      elseif length(ind) < k\n",
    "        notind  = setdiff(1:k,ind);\n",
    "        ind_min = notind[findmin(z[notind])[2]];\n",
    "        ind     = sort([ind; ind_min]);\n",
    "      end\n",
    "    else\n",
    "          \n",
    "      # Find a feasible step length.\n",
    "      alpha     = 1;\n",
    "      alpha0    = -y[ind]./p_s;\n",
    "      ind_block = find(p_s .< 0);\n",
    "      alpha0    = alpha0[ind_block];\n",
    "      if ~isempty(ind_block)\n",
    "        v, t = findmin(alpha0);\n",
    "        if v < 1\n",
    "\n",
    "          # Blocking constraint.\n",
    "          ind_block = ind[ind_block[t]]; \n",
    "          alpha     = v;\n",
    "              \n",
    "          # Update working set if there is a blocking constraint.\n",
    "          deleteat!(ind,find(ind - ind_block .== 0));\n",
    "        end\n",
    "      end\n",
    "          \n",
    "      # Move to the new \"inner loop\" iterate (y) along the search\n",
    "      # direction.\n",
    "      y = y + alpha * p;\n",
    "    end\n",
    "  end\n",
    "\n",
    "  # Return the solution to the quadratic program.\n",
    "  return y\n",
    "end\n",
    "\n",
    "\n",
    "# a function pava for pooled adjacent violation algorithm\n",
    "\n",
    "function pava(v; w = ones(length(v)))\n",
    "    n = length(v);\n",
    "    if n != length(w)\n",
    "        throw(DimensionMismatch(\"Lengths of values and weights mismatch\"))\n",
    "    end\n",
    "    \n",
    "    out = ones(n);\n",
    "    j = 1;\n",
    "    S = Dict(0 => 0, 1 => 1);\n",
    "    vdash = Dict(1 => v[1]);\n",
    "    wdash = Dict(1 => w[1]);\n",
    "    @inbounds begin\n",
    "        for i = 2:n\n",
    "            j = j+1;\n",
    "            vdash[j] = v[i];\n",
    "            wdash[j] = w[i];\n",
    "            while j > 1 && vdash[j] < vdash[j-1];\n",
    "                vdash[j-1] = (wdash[j] * vdash[j] + wdash[j-1] * vdash[j-1]) /\n",
    "                   (wdash[j] + wdash[j-1]);\n",
    "                wdash[j-1] = wdash[j] + wdash[j-1];\n",
    "                j = j-1;\n",
    "            end\n",
    "            S[j] = i;\n",
    "        end\n",
    "        for k = 1:j\n",
    "            for l in S[k-1]+1 : S[k]\n",
    "                out[l] = vdash[k];\n",
    "            end\n",
    "        end\n",
    "    end\n",
    "    return out\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "166×2 Array{Float64,2}:\n",
       " 1850.0  -0.375\n",
       " 1851.0  -0.223\n",
       " 1852.0  -0.224\n",
       " 1853.0  -0.271\n",
       " 1854.0  -0.246\n",
       " 1855.0  -0.271\n",
       " 1856.0  -0.352\n",
       " 1857.0  -0.46 \n",
       " 1858.0  -0.466\n",
       " 1859.0  -0.286\n",
       " 1860.0  -0.346\n",
       " 1861.0  -0.409\n",
       " 1862.0  -0.522\n",
       "    ⋮          \n",
       " 2004.0   0.45 \n",
       " 2005.0   0.544\n",
       " 2006.0   0.505\n",
       " 2007.0   0.493\n",
       " 2008.0   0.395\n",
       " 2009.0   0.506\n",
       " 2010.0   0.559\n",
       " 2011.0   0.422\n",
       " 2012.0   0.47 \n",
       " 2013.0   0.499\n",
       " 2014.0   0.567\n",
       " 2015.0   0.746"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "warming = readcsv(joinpath(Pkg.dir(\"ConstrainedLasso\"),\"docs/src/demo/misc/warming.csv\"), header=true)[1];\n",
    "year = warming[:, 1];\n",
    "y    = warming[:, 2];\n",
    "n    = length(y);\n",
    "D    = full(incidence_matrix(PathGraph(n), oriented = true)');\n",
    "X    = pinv(D);\n",
    "XTX  = X'*X;\n",
    "hcat(year, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BGSM_isotonic (generic function with 1 method)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# a function for BSGM_iso (Section 2,3)\n",
    "\n",
    "# y                  : a noisy observation of an isotonic sequence\n",
    "# init_theta         : initialization of theta, with default a pava solution\n",
    "# lambda0, lambda1   : tuning parameters\n",
    "# convtol            : convergence tolerance\n",
    "# iter               : a number of maximum allowed iteration\n",
    "\n",
    "function BGSM_isotonic(y, D; init_y = pava(y), nu = 0, eta = 1/n, \n",
    "                       v0 = 1e-1, v1 = 1e4, a = 0, b = 0, iter = 1000)\n",
    "    n = length(y);\n",
    "    \n",
    "    # initialize\n",
    "    q = 0.5 * ones(n-1);\n",
    "    alpha = mean(y);\n",
    "    theta = init_y - alpha;\n",
    "    sigma2 = sum((y - alpha - theta).^2)/n;\n",
    "    delta = theta[2:end] - theta[1:end-1];\n",
    "    \n",
    "    # loop start\n",
    "    for i = 1:1000\n",
    "        \n",
    "        # E-step: update q and tau\n",
    "        q_old = copy(q);\n",
    "        q     = 1./( 1 + (1-eta)/eta * sqrt(v0/v1) * exp.(delta.^2/sigma2*(1/v0-1/v1)) );\n",
    "        tau   = q/v0 + (1-q)/v1;\n",
    "        \n",
    "        # M-step: update sigma2, theta, delta, eta\n",
    "        delta = nnls(delta, -X'*(y - alpha), XTX + Diagonal(tau));\n",
    "        theta = X*delta;\n",
    "        sigma2 = norm(y - alpha - theta)^2 + q' * (delta.^2);\n",
    "        sigma2 = (sigma2 + b)/(2*n + a + 1);\n",
    "        eta   = sum(q)/(n-1);\n",
    "        \n",
    "        # check convergence\n",
    "        if norm(q_old - q) < 1e-10\n",
    "            break;\n",
    "        end\n",
    "        \n",
    "    end\n",
    "    \n",
    "    # return\n",
    "    return Dict([\n",
    "                (:alpha,alpha), (:theta,theta), (:sigma2, sigma2), (:q,q), (:eta,eta), (:y, y),\n",
    "                (:delta,delta), (:alpha_theta, alpha + theta), (:v0, v0), (:v1, v1), (:nu, nu),\n",
    "                (:a, a), (:b, b), (:D, D), (:n, length(y)), (:X, speye(n)), (:p, n)\n",
    "                ])\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "model_selection (generic function with 1 method)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function model_selection(out)\n",
    "    # thresholding step\n",
    "    ind = find(out[:q] .>= 0.5);\n",
    "    zind = find(out[:q] .< 0.5);\n",
    "    \n",
    "    # get original graph\n",
    "    A_orig = out[:D]'*out[:D]; A_orig = (abs.(A_orig) - A_orig)/2;\n",
    "\n",
    "    # get a thresholded graph\n",
    "    D = out[:D][ind,:]; L = D'*D;\n",
    "    g = Graph((abs.(L) - L)/2);\n",
    "    \n",
    "    # edge contraction / node merger\n",
    "    c = connected_components(g);\n",
    "    s = length(c);\n",
    "\n",
    "    Z = zeros(out[:n],s);\n",
    "    for i = 1:s\n",
    "        Z[c[i],i] = 1\n",
    "    end\n",
    "    #Z = Z ./ sqrt.(sum(Z,1));\n",
    "\n",
    "    L = out[:D][zind,:]' * out[:D][zind,:]/out[:v1];\n",
    "    W = nullspace(sum(Z,1))\n",
    "    a = -Z'*(out[:y] .- out[:alpha]);\n",
    "    H = Z'*(I + L)*Z;\n",
    "    W = nullspace(sum(Z,1))\n",
    "    x = inv(Z'*Z) * Z' * (out[:y] - out[:alpha]) + out[:alpha]\n",
    "    Ds = full(incidence_matrix(PathGraph(s), oriented = true)');\n",
    "    Xs = W*inv(Ds*W);\n",
    "    th = Xs * nnls(Ds * x, Xs'*a, Xs'*H*Xs);\n",
    "    S = th'*H*th - 2*a'*th + out[:b];\n",
    "    println(s)\n",
    "    score = -(s-1) * log(2) + (s-1)/2 * log(out[:v1]) - log(det(W'*H*W))/2 - log(beta(out[:n]-s,s+out[:n])) +\n",
    "            (out[:n]+s+out[:a]+1)/2 + (out[:n]+s+out[:a]+2) * log(S/(out[:n]+s+out[:a]+2) )/2 +\n",
    "            (out[:n]+s-1)/2 * log(2*pi)\n",
    "    \n",
    "    return Dict([(:score, score), (:beta,  out[:alpha] + Z*th)])\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "v0_range = (1e-3 * 1.4.^(1:20))[:]; s = length(v0_range);\n",
    "score = zeros(s); fit = zeros(n,s);\n",
    "D     = full(incidence_matrix(PathGraph(n), oriented = true)');\n",
    "for i = 1:s\n",
    "    out      = BGSM_isotonic(y, D, init_y = pava(y), eta = 1/2, a = 1, b = 1,\n",
    "                            v0 = v0_range[i], v1 = 1e4);\n",
    "    ms       = model_selection(out);\n",
    "    score[i] = ms[:score];\n",
    "    fit[:,i] = ms[:beta];\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.11112006825558007"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1e-3 * 1.4^14"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((113.52167001531404, 13), 0.07937147732541433)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "findmin(score), v0_range[findmin(score)[2]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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       "function(d){null==d&&(d=1);return a.format('<feColorMatrix type=\"matrix\" values=\"{a} {b} {c} 0 0 {d} {e} {f} 0 0 {g} {h} {i} 0 0 0 0 0 1 0\"/>',{a:0.393+0.607*(1-d),b:0.769-0.769*(1-d),c:0.189-0.189*(1-d),d:0.349-0.349*(1-d),e:0.686+0.314*(1-d),f:0.168-0.168*(1-d),g:0.272-0.272*(1-d),h:0.534-0.534*(1-d),i:0.131+0.869*(1-d)})};a.filter.sepia.toString=function(){return this()};a.filter.saturate=function(d){null==d&&(d=1);return a.format('<feColorMatrix type=\"saturate\" values=\"{amount}\"/>',{amount:1-\n",
       "d})};a.filter.saturate.toString=function(){return this()};a.filter.hueRotate=function(d){return a.format('<feColorMatrix type=\"hueRotate\" values=\"{angle}\"/>',{angle:d||0})};a.filter.hueRotate.toString=function(){return this()};a.filter.invert=function(d){null==d&&(d=1);return a.format('<feComponentTransfer><feFuncR type=\"table\" tableValues=\"{amount} {amount2}\"/><feFuncG type=\"table\" tableValues=\"{amount} {amount2}\"/><feFuncB type=\"table\" tableValues=\"{amount} {amount2}\"/></feComponentTransfer>',{amount:d,\n",
       "amount2:1-d})};a.filter.invert.toString=function(){return this()};a.filter.brightness=function(d){null==d&&(d=1);return a.format('<feComponentTransfer><feFuncR type=\"linear\" slope=\"{amount}\"/><feFuncG type=\"linear\" slope=\"{amount}\"/><feFuncB type=\"linear\" slope=\"{amount}\"/></feComponentTransfer>',{amount:d})};a.filter.brightness.toString=function(){return this()};a.filter.contrast=function(d){null==d&&(d=1);return a.format('<feComponentTransfer><feFuncR type=\"linear\" slope=\"{amount}\" intercept=\"{amount2}\"/><feFuncG type=\"linear\" slope=\"{amount}\" intercept=\"{amount2}\"/><feFuncB type=\"linear\" slope=\"{amount}\" intercept=\"{amount2}\"/></feComponentTransfer>',\n",
       "{amount:d,amount2:0.5-d/2})};a.filter.contrast.toString=function(){return this()}});return C});\n",
       "\n",
       "]]> </script>\n",
       "<script> <![CDATA[\n",
       "\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);\n",
       "        } else {\n",
       "            this.node.setAttribute(key, val);\n",
       "            return this;\n",
       "        }\n",
       "    };\n",
       "\n",
       "    Element.prototype.init_gadfly = function() {\n",
       "        this.mouseenter(Gadfly.plot_mouseover)\n",
       "            .mousemove(Gadfly.plot_mousemove)\n",
       "            .mouseleave(Gadfly.plot_mouseout)\n",
       "            .dblclick(Gadfly.plot_dblclick)\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",
       "        this.mouseenter(function (event) {\n",
       "            init_pan_zoom(this.plotroot());\n",
       "        });\n",
       "        return this;\n",
       "    };\n",
       "});\n",
       "\n",
       "\n",
       "Gadfly.plot_mousemove = function(event, x_px, y_px) {\n",
       "    var root = this.plotroot();\n",
       "    if (root.data(\"crosshair\")) {\n",
       "        px_per_mm = root.data(\"px_per_mm\");\n",
       "        bB = root.select('boundingbox').node.getAttribute('value').split(' ');\n",
       "        uB = root.select('unitbox').node.getAttribute('value').split(' ');\n",
       "        xscale = root.data(\"xscale\");\n",
       "        yscale = root.data(\"yscale\");\n",
       "        xtranslate = root.data(\"tx\");\n",
       "        ytranslate = root.data(\"ty\");\n",
       "\n",
       "        xoff_mm = bB[0].substr(0,bB[0].length-2)/1;\n",
       "        yoff_mm = bB[1].substr(0,bB[1].length-2)/1;\n",
       "        xoff_unit = uB[0]/1;\n",
       "        yoff_unit = uB[1]/1;\n",
       "        mm_per_xunit = bB[2].substr(0,bB[2].length-2) / uB[2];\n",
       "        mm_per_yunit = bB[3].substr(0,bB[3].length-2) / uB[3];\n",
       "         \n",
       "        x_unit = ((x_px / px_per_mm - xtranslate) / xscale - xoff_mm) / mm_per_xunit + xoff_unit;\n",
       "        y_unit = ((y_px / px_per_mm - ytranslate) / yscale - yoff_mm) / mm_per_yunit + yoff_unit;\n",
       "\n",
       "        root.select('.crosshair').select('.primitive').select('text')\n",
       "                .node.innerHTML = x_unit.toPrecision(3)+\",\"+y_unit.toPrecision(3);\n",
       "    };\n",
       "};\n",
       "\n",
       "Gadfly.helpscreen_visible = function(event) {\n",
       "    helpscreen_visible(this.plotroot());\n",
       "};\n",
       "var helpscreen_visible = function(root) {\n",
       "    root.select(\".helpscreen\").animate({opacity: 1.0}, 250);\n",
       "};\n",
       "\n",
       "Gadfly.helpscreen_hidden = function(event) {\n",
       "    helpscreen_hidden(this.plotroot());\n",
       "};\n",
       "var helpscreen_hidden = function(root) {\n",
       "    root.select(\".helpscreen\").animate({opacity: 0.0}, 250);\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",
       "\n",
       "    var keyboard_help = function(event) {\n",
       "        if (event.which == 191) { // ?\n",
       "            helpscreen_visible(root);\n",
       "        }\n",
       "    };\n",
       "    root.data(\"keyboard_help\", keyboard_help);\n",
       "    window.addEventListener(\"keydown\", keyboard_help);\n",
       "\n",
       "    var keyboard_pan_zoom = function(event) {\n",
       "        var bounds = root.plotbounds(),\n",
       "            width = bounds.x1 - bounds.x0;\n",
       "            height = bounds.y1 - bounds.y0;\n",
       "        if (event.which == 187 || event.which == 73) { // plus or i\n",
       "            increase_zoom_by_position(root, 0.1, true);\n",
       "        } else if (event.which == 189 || event.which == 79) { // minus or o\n",
       "            increase_zoom_by_position(root, -0.1, true);\n",
       "        } else if (event.which == 39 || event.which == 76) { // right-arrow or l\n",
       "            set_plot_pan_zoom(root, root.data(\"tx\")-width/10, root.data(\"ty\"),\n",
       "                    root.data(\"xscale\"), root.data(\"yscale\"));\n",
       "        } else if (event.which == 40 || event.which == 74) { // down-arrow or j\n",
       "            set_plot_pan_zoom(root, root.data(\"tx\"), root.data(\"ty\")-height/10,\n",
       "                    root.data(\"xscale\"), root.data(\"yscale\"));\n",
       "        } else if (event.which == 37 || event.which == 72) { // left-arrow or h\n",
       "            set_plot_pan_zoom(root, root.data(\"tx\")+width/10, root.data(\"ty\"),\n",
       "                    root.data(\"xscale\"), root.data(\"yscale\"));\n",
       "        } else if (event.which == 38 || event.which == 75) { // up-arrow or k\n",
       "            set_plot_pan_zoom(root, root.data(\"tx\"), root.data(\"ty\")+height/10,\n",
       "                    root.data(\"xscale\"), root.data(\"yscale\"));\n",
       "        } else if (event.which == 82) { // r\n",
       "            set_plot_pan_zoom(root, 0.0, 0.0, 1.0, 1.0);\n",
       "        } else if (event.which == 191) { // ?\n",
       "            helpscreen_hidden(root);\n",
       "        } else if (event.which == 67) { // c\n",
       "            root.data(\"crosshair\",!root.data(\"crosshair\"));\n",
       "            root.select(\".crosshair\")\n",
       "                .animate({opacity: root.data(\"crosshair\") ? 1.0 : 0.0}, 250);\n",
       "        }\n",
       "    };\n",
       "    root.data(\"keyboard_pan_zoom\", keyboard_pan_zoom);\n",
       "    window.addEventListener(\"keyup\", keyboard_pan_zoom);\n",
       "\n",
       "    var xgridlines = root.select(\".xgridlines\"),\n",
       "        ygridlines = root.select(\".ygridlines\");\n",
       "\n",
       "    if (xgridlines) {\n",
       "        xgridlines.data(\"unfocused_strokedash\",\n",
       "                        xgridlines.attribute(\"stroke-dasharray\").replace(/(\\d)(,|$)/g, \"$1mm$2\"));\n",
       "        var destcolor = root.data(\"focused_xgrid_color\");\n",
       "        xgridlines.attribute(\"stroke-dasharray\", \"none\")\n",
       "                  .selectAll(\"path\")\n",
       "                  .animate({stroke: destcolor}, 250);\n",
       "    }\n",
       "\n",
       "    if (ygridlines) {\n",
       "        ygridlines.data(\"unfocused_strokedash\",\n",
       "                        ygridlines.attribute(\"stroke-dasharray\").replace(/(\\d)(,|$)/g, \"$1mm$2\"));\n",
       "        var destcolor = root.data(\"focused_ygrid_color\");\n",
       "        ygridlines.attribute(\"stroke-dasharray\", \"none\")\n",
       "                  .selectAll(\"path\")\n",
       "                  .animate({stroke: destcolor}, 250);\n",
       "    }\n",
       "\n",
       "    root.select(\".crosshair\")\n",
       "        .animate({opacity: root.data(\"crosshair\") ? 1.0 : 0.0}, 250);\n",
       "    root.select(\".questionmark\").animate({opacity: 1.0}, 250);\n",
       "};\n",
       "\n",
       "// Reset pan and zoom on double click\n",
       "Gadfly.plot_dblclick = function(event) {\n",
       "  set_plot_pan_zoom(this.plotroot(), 0.0, 0.0, 1.0, 1.0);\n",
       "};\n",
       "\n",
       "// Unemphasize grid lines on mouse out.\n",
       "Gadfly.plot_mouseout = function(event) {\n",
       "    var root = this.plotroot();\n",
       "\n",
       "    window.removeEventListener(\"keyup\", root.data(\"keyboard_pan_zoom\"));\n",
       "    root.data(\"keyboard_pan_zoom\", undefined);\n",
       "    window.removeEventListener(\"keydown\", root.data(\"keyboard_help\"));\n",
       "    root.data(\"keyboard_help\", undefined);\n",
       "\n",
       "    var xgridlines = root.select(\".xgridlines\"),\n",
       "        ygridlines = root.select(\".ygridlines\");\n",
       "\n",
       "    if (xgridlines) {\n",
       "        var destcolor = root.data(\"unfocused_xgrid_color\");\n",
       "        xgridlines.attribute(\"stroke-dasharray\", xgridlines.data(\"unfocused_strokedash\"))\n",
       "                  .selectAll(\"path\")\n",
       "                  .animate({stroke: destcolor}, 250);\n",
       "    }\n",
       "\n",
       "    if (ygridlines) {\n",
       "        var destcolor = root.data(\"unfocused_ygrid_color\");\n",
       "        ygridlines.attribute(\"stroke-dasharray\", ygridlines.data(\"unfocused_strokedash\"))\n",
       "                  .selectAll(\"path\")\n",
       "                  .animate({stroke: destcolor}, 250);\n",
       "    }\n",
       "\n",
       "    root.select(\".crosshair\").animate({opacity: 0.0}, 250);\n",
       "    root.select(\".questionmark\").animate({opacity: 0.0}, 250);\n",
       "    helpscreen_hidden(root);\n",
       "};\n",
       "\n",
       "\n",
       "var set_geometry_transform = function(root, tx, ty, xscale, yscale) {\n",
       "    var xscalable = root.hasClass(\"xscalable\"),\n",
       "        yscalable = root.hasClass(\"yscalable\");\n",
       "\n",
       "    var old_xscale = root.data(\"xscale\"),\n",
       "        old_yscale = root.data(\"yscale\");\n",
       "\n",
       "    var xscale = xscalable ? xscale : 1.0,\n",
       "        yscale = yscalable ? yscale : 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",
       "    root.selectAll(\".geometry, image\").forEach(function (element, i) {\n",
       "            element.transform(t);\n",
       "        });\n",
       "\n",
       "    var t = new Snap.Matrix().scale(1.0/xscale, 1.0/yscale);\n",
       "    root.selectAll('.marker').forEach(function (element, i) {\n",
       "        element.selectAll('.primitive').forEach(function (element, i) {\n",
       "            element.transform(t);\n",
       "        }) });\n",
       "\n",
       "    bounds = root.plotbounds();\n",
       "    px_per_mm = root.data(\"px_per_mm\");\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",
       "        ylabels = root.select(\".ylabels\");\n",
       "        if (ylabels) {\n",
       "            ylabels.transform(xfixed_t)\n",
       "                   .selectAll(\"g\")\n",
       "                   .forEach(function (element, i) {\n",
       "                       if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
       "                           unscale_t = new Snap.Matrix();\n",
       "                           unscale_t.scale(1, 1/yscale);\n",
       "                           element.select(\"text\").transform(unscale_t);\n",
       " \n",
       "                           var y = element.attr(\"transform\").globalMatrix.f / px_per_mm;\n",
       "                           element.attr(\"visibility\",\n",
       "                               bounds.y0 <= y && y <= bounds.y1 ? \"visible\" : \"hidden\");\n",
       "                       }\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",
       "        xlabels = root.select(\".xlabels\");\n",
       "        if (xlabels) {\n",
       "            xlabels.transform(yfixed_t)\n",
       "                   .selectAll(\"g\")\n",
       "                   .forEach(function (element, i) {\n",
       "                       if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
       "                           unscale_t = new Snap.Matrix();\n",
       "                           unscale_t.scale(1/xscale, 1);\n",
       "                           element.select(\"text\").transform(unscale_t);\n",
       "\n",
       "                           var x = element.attr(\"transform\").globalMatrix.e / px_per_mm;\n",
       "                           element.attr(\"visibility\",\n",
       "                               bounds.x0 <= x && x <= bounds.x1 ? \"visible\" : \"hidden\");\n",
       "                           }\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",
       "            if (element.attribute(\"gadfly:inscale\") == null) { return; }\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",
       "            if (element.attribute(\"gadfly:inscale\") == null) { return; }\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(\"g\").forEach(mark_inscale_gridlines);\n",
       "        root.select(\".\" + axis + \"labels\").selectAll(\"g\").forEach(mark_inscale_labels);\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "var set_plot_pan_zoom = function(root, tx, ty, xscale, yscale) {\n",
       "    var old_xscale = root.data(\"xscale\"),\n",
       "        old_yscale = root.data(\"yscale\");\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, xscale, and yscale\n",
       "    var x_min = -width * xscale - (xscale * width - width),\n",
       "        x_max = width * xscale,\n",
       "        y_min = -height * yscale - (yscale * height - height),\n",
       "        y_max = height * yscale;\n",
       "\n",
       "    var x0 = bounds.x0 - xscale * bounds.x0,\n",
       "        y0 = bounds.y0 - yscale * 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 changes, we may need to alter which set of\n",
       "    // ticks are being displayed\n",
       "    if (xscale != old_xscale) {\n",
       "        update_tickscale(root, xscale, \"x\");\n",
       "    }\n",
       "    if (yscale != old_yscale) {\n",
       "        update_tickscale(root, yscale, \"y\");\n",
       "    }\n",
       "\n",
       "    set_geometry_transform(root, tx, ty, xscale, yscale);\n",
       "\n",
       "    root.data(\"xscale\", xscale);\n",
       "    root.data(\"yscale\", yscale);\n",
       "    root.data(\"tx\", tx);\n",
       "    root.data(\"ty\", ty);\n",
       "};\n",
       "\n",
       "\n",
       "var scale_centered_translation = function(root, xscale, yscale) {\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 xscale0 = root.data(\"xscale\"),\n",
       "        yscale0 = root.data(\"yscale\");\n",
       "\n",
       "    // how off from center the current view is\n",
       "    var xoff = tx0 - (bounds.x0 * (1 - xscale0) + (width * (1 - xscale0)) / 2),\n",
       "        yoff = ty0 - (bounds.y0 * (1 - yscale0) + (height * (1 - yscale0)) / 2);\n",
       "\n",
       "    // rescale offsets\n",
       "    xoff = xoff * xscale / xscale0;\n",
       "    yoff = yoff * yscale / yscale0;\n",
       "\n",
       "    // adjust for the panel position being scaled\n",
       "    var x_edge_adjust = bounds.x0 * (1 - xscale),\n",
       "        y_edge_adjust = bounds.y0 * (1 - yscale);\n",
       "\n",
       "    return {\n",
       "        x: xoff + x_edge_adjust + (width - width * xscale) / 2,\n",
       "        y: yoff + y_edge_adjust + (height - height * yscale) / 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",
       "    root.data(\"crosshair\",false);\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 > g, .ylabels > g\")\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",
       "    var xgridlines = root.select(\".xgridlines\");\n",
       "    var ygridlines = root.select(\".ygridlines\");\n",
       "    var xlabels = root.select(\".xlabels\");\n",
       "    var ylabels = root.select(\".ylabels\");\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(\"xscale\") === undefined) root.data(\"xscale\", 1.0);\n",
       "    if (root.data(\"yscale\") === undefined) root.data(\"yscale\", 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",
       "            if (element.attribute(\"gadfly:scale\")==null) { return; }\n",
       "            xtickscales[element.attribute(\"gadfly:scale\")] = true;\n",
       "        };\n",
       "        var add_y_tick_scales = function (element, i) {\n",
       "            if (element.attribute(\"gadfly:scale\")==null) { return; }\n",
       "            ytickscales[element.attribute(\"gadfly:scale\")] = true;\n",
       "        };\n",
       "\n",
       "        if (xgridlines) xgridlines.selectAll(\"g\").forEach(add_x_tick_scales);\n",
       "        if (ygridlines) ygridlines.selectAll(\"g\").forEach(add_y_tick_scales);\n",
       "        if (xlabels) xlabels.selectAll(\"g\").forEach(add_x_tick_scales);\n",
       "        if (ylabels) ylabels.selectAll(\"g\").forEach(add_y_tick_scales);\n",
       "\n",
       "        root.data(\"xtickscales\", xtickscales);\n",
       "        root.data(\"ytickscales\", ytickscales);\n",
       "        root.data(\"xtickscale\", 1.0);\n",
       "        root.data(\"ytickscale\", 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",
       "    if (xlabels) {\n",
       "        xlabels.selectAll(\"g\")\n",
       "               .forEach(function (element, i) {\n",
       "                   element.data(\"x\", element.asPX(\"x\"));\n",
       "               });\n",
       "    }\n",
       "\n",
       "    if (ylabels) {\n",
       "        ylabels.selectAll(\"g\")\n",
       "               .forEach(function (element, i) {\n",
       "                   element.data(\"y\", element.asPX(\"y\"));\n",
       "               });\n",
       "    }\n",
       "\n",
       "    // mark grid lines and ticks as in or out of scale.\n",
       "    var mark_inscale = function (element, i) {\n",
       "        if (element.attribute(\"gadfly:scale\") == null) { return; }\n",
       "        element.attribute(\"gadfly:inscale\", element.attribute(\"gadfly:scale\") == 1.0);\n",
       "    };\n",
       "\n",
       "    if (xgridlines) xgridlines.selectAll(\"g\").forEach(mark_inscale);\n",
       "    if (ygridlines) ygridlines.selectAll(\"g\").forEach(mark_inscale);\n",
       "    if (xlabels) xlabels.selectAll(\"g\").forEach(mark_inscale);\n",
       "    if (ylabels) ylabels.selectAll(\"g\").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",
       "    if (xgridlines) {\n",
       "        xgridlines\n",
       "            .selectAll(\"g\")\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",
       "                    element.attr(\"visibility\", \"visible\");\n",
       "                }\n",
       "            });\n",
       "    }\n",
       "\n",
       "    if (ygridlines) {\n",
       "        ygridlines\n",
       "            .selectAll(\"g\")\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",
       "                    element.attr(\"visibility\", \"visible\");\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",
       "    root.data(\"zoompan-ready\", true)\n",
       "};\n",
       "\n",
       "\n",
       "// drag actions, i.e. zooming and panning\n",
       "var pan_action = {\n",
       "    start: function(root, x, y, event) {\n",
       "        root.data(\"dx\", 0);\n",
       "        root.data(\"dy\", 0);\n",
       "        root.data(\"tx0\", root.data(\"tx\"));\n",
       "        root.data(\"ty0\", root.data(\"ty\"));\n",
       "    },\n",
       "    update: function(root, dx, dy, x, y, event) {\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(\"xscale\"), root.data(\"yscale\"));\n",
       "    },\n",
       "    end: function(root, event) {\n",
       "\n",
       "    },\n",
       "    cancel: function(root) {\n",
       "        set_plot_pan_zoom(root, root.data(\"tx0\"), root.data(\"ty0\"),\n",
       "                root.data(\"xscale\"), root.data(\"yscale\"));\n",
       "    }\n",
       "};\n",
       "\n",
       "var zoom_box;\n",
       "var zoom_action = {\n",
       "    start: function(root, x, y, event) {\n",
       "        var bounds = root.plotbounds();\n",
       "        var width = bounds.x1 - bounds.x0,\n",
       "            height = bounds.y1 - bounds.y0;\n",
       "        var xscalable = root.hasClass(\"xscalable\"),\n",
       "            yscalable = root.hasClass(\"yscalable\");\n",
       "        var px_per_mm = root.data(\"px_per_mm\");\n",
       "        x = xscalable ? x / px_per_mm : bounds.x0;\n",
       "        y = yscalable ? y / px_per_mm : bounds.y0;\n",
       "        var w = xscalable ? 0 : width;\n",
       "        var h = yscalable ? 0 : height;\n",
       "        zoom_box = root.rect(x, y, w, h).attr({\n",
       "            \"fill\": \"#000\",\n",
       "            \"opacity\": 0.25\n",
       "        });\n",
       "    },\n",
       "    update: function(root, dx, dy, x, y, event) {\n",
       "        var xscalable = root.hasClass(\"xscalable\"),\n",
       "            yscalable = root.hasClass(\"yscalable\");\n",
       "        var px_per_mm = root.data(\"px_per_mm\");\n",
       "        var bounds = root.plotbounds();\n",
       "        if (yscalable) {\n",
       "            y /= px_per_mm;\n",
       "            y = Math.max(bounds.y0, y);\n",
       "            y = Math.min(bounds.y1, y);\n",
       "        } else {\n",
       "            y = bounds.y1;\n",
       "        }\n",
       "        if (xscalable) {\n",
       "            x /= px_per_mm;\n",
       "            x = Math.max(bounds.x0, x);\n",
       "            x = Math.min(bounds.x1, x);\n",
       "        } else {\n",
       "            x = bounds.x1;\n",
       "        }\n",
       "\n",
       "        dx = x - zoom_box.attr(\"x\");\n",
       "        dy = y - zoom_box.attr(\"y\");\n",
       "        var xoffset = 0,\n",
       "            yoffset = 0;\n",
       "        if (dx < 0) {\n",
       "            xoffset = dx;\n",
       "            dx = -1 * dx;\n",
       "        }\n",
       "        if (dy < 0) {\n",
       "            yoffset = dy;\n",
       "            dy = -1 * dy;\n",
       "        }\n",
       "        if (isNaN(dy)) {\n",
       "            dy = 0.0;\n",
       "        }\n",
       "        if (isNaN(dx)) {\n",
       "            dx = 0.0;\n",
       "        }\n",
       "        zoom_box.transform(\"T\" + xoffset + \",\" + yoffset);\n",
       "        zoom_box.attr(\"width\", dx);\n",
       "        zoom_box.attr(\"height\", dy);\n",
       "    },\n",
       "    end: function(root, event) {\n",
       "        var xscalable = root.hasClass(\"xscalable\"),\n",
       "            yscalable = root.hasClass(\"yscalable\");\n",
       "        var zoom_bounds = zoom_box.getBBox();\n",
       "        if (zoom_bounds.width * zoom_bounds.height <= 0) {\n",
       "            return;\n",
       "        }\n",
       "        var plot_bounds = root.plotbounds();\n",
       "        var xzoom_factor = 1.0,\n",
       "            yzoom_factor = 1.0;\n",
       "        if (xscalable) {\n",
       "            xzoom_factor = (plot_bounds.x1 - plot_bounds.x0) / zoom_bounds.width;\n",
       "        }\n",
       "        if (yscalable) {\n",
       "            yzoom_factor = (plot_bounds.y1 - plot_bounds.y0) / zoom_bounds.height;\n",
       "        }\n",
       "        var tx = (root.data(\"tx\") - zoom_bounds.x) * xzoom_factor + plot_bounds.x0,\n",
       "            ty = (root.data(\"ty\") - zoom_bounds.y) * yzoom_factor + plot_bounds.y0;\n",
       "        set_plot_pan_zoom(root, tx, ty,\n",
       "                root.data(\"xscale\") * xzoom_factor, root.data(\"yscale\") * yzoom_factor);\n",
       "        zoom_box.remove();\n",
       "    },\n",
       "    cancel: function(root) {\n",
       "        zoom_box.remove();\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.guide_background_drag_onstart = function(x, y, event) {\n",
       "    var root = this.plotroot();\n",
       "    var scalable = root.hasClass(\"xscalable\") || root.hasClass(\"yscalable\");\n",
       "    var zoomable = !event.altKey && !event.ctrlKey && event.shiftKey && scalable;\n",
       "    var panable = !event.altKey && !event.ctrlKey && !event.shiftKey && scalable;\n",
       "    var drag_action = zoomable ? zoom_action :\n",
       "                      panable  ? pan_action :\n",
       "                                 undefined;\n",
       "    root.data(\"drag_action\", drag_action);\n",
       "    if (drag_action) {\n",
       "        var cancel_drag_action = function(event) {\n",
       "            if (event.which == 27) { // esc key\n",
       "                drag_action.cancel(root);\n",
       "                root.data(\"drag_action\", undefined);\n",
       "            }\n",
       "        };\n",
       "        window.addEventListener(\"keyup\", cancel_drag_action);\n",
       "        root.data(\"cancel_drag_action\", cancel_drag_action);\n",
       "        drag_action.start(root, x, y, event);\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.guide_background_drag_onmove = function(dx, dy, x, y, event) {\n",
       "    var root = this.plotroot();\n",
       "    var drag_action = root.data(\"drag_action\");\n",
       "    if (drag_action) {\n",
       "        drag_action.update(root, dx, dy, x, y, event);\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.guide_background_drag_onend = function(event) {\n",
       "    var root = this.plotroot();\n",
       "    window.removeEventListener(\"keyup\", root.data(\"cancel_drag_action\"));\n",
       "    root.data(\"cancel_drag_action\", undefined);\n",
       "    var drag_action = root.data(\"drag_action\");\n",
       "    if (drag_action) {\n",
       "        drag_action.end(root, event);\n",
       "    }\n",
       "    root.data(\"drag_action\", undefined);\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.guide_background_scroll = function(event) {\n",
       "    if (event.shiftKey) {\n",
       "        increase_zoom_by_position(this.plotroot(), 0.001 * event.wheelDelta);\n",
       "        event.preventDefault();\n",
       "    }\n",
       "};\n",
       "\n",
       "// Map slider position x to scale y using the function y = a*exp(b*x)+c.\n",
       "// The constants a, b, and c are solved using the constraint that the function\n",
       "// should go through the points (0; min_scale), (0.5; 1), and (1; max_scale).\n",
       "var scale_from_slider_position = function(position, min_scale, max_scale) {\n",
       "    if (min_scale==max_scale) { return 1; }\n",
       "    var a = (1 - 2 * min_scale + min_scale * min_scale) / (min_scale + max_scale - 2),\n",
       "        b = 2 * Math.log((max_scale - 1) / (1 - min_scale)),\n",
       "        c = (min_scale * max_scale - 1) / (min_scale + max_scale - 2);\n",
       "    return a * Math.exp(b * position) + c;\n",
       "}\n",
       "\n",
       "// inverse of scale_from_slider_position\n",
       "var slider_position_from_scale = function(scale, min_scale, max_scale) {\n",
       "    if (min_scale==max_scale) { return min_scale; }\n",
       "    var a = (1 - 2 * min_scale + min_scale * min_scale) / (min_scale + max_scale - 2),\n",
       "        b = 2 * Math.log((max_scale - 1) / (1 - min_scale)),\n",
       "        c = (min_scale * max_scale - 1) / (min_scale + max_scale - 2);\n",
       "    return 1 / b * Math.log((scale - c) / a);\n",
       "}\n",
       "\n",
       "var increase_zoom_by_position = function(root, delta_position, animate) {\n",
       "    var old_xscale = root.data(\"xscale\"),\n",
       "        old_yscale = root.data(\"yscale\"),\n",
       "        min_scale = root.data(\"min_scale\"),\n",
       "        max_scale = root.data(\"max_scale\");\n",
       "    var xposition = slider_position_from_scale(old_xscale, min_scale, max_scale),\n",
       "        yposition = slider_position_from_scale(old_yscale, min_scale, max_scale);\n",
       "    xposition += (root.hasClass(\"xscalable\") ? delta_position : 0.0);\n",
       "    yposition += (root.hasClass(\"yscalable\") ? delta_position : 0.0);\n",
       "    old_xscale = scale_from_slider_position(xposition, min_scale, max_scale);\n",
       "    old_yscale = scale_from_slider_position(yposition, min_scale, max_scale);\n",
       "    var new_xscale = Math.max(min_scale, Math.min(old_xscale, max_scale)),\n",
       "        new_yscale = Math.max(min_scale, Math.min(old_yscale, max_scale));\n",
       "    if (animate) {\n",
       "        Snap.animate(\n",
       "            [old_xscale, old_yscale],\n",
       "            [new_xscale, new_yscale],\n",
       "            function (new_scale) {\n",
       "                update_plot_scale(root, new_scale[0], new_scale[1]);\n",
       "            },\n",
       "            200);\n",
       "    } else {\n",
       "        update_plot_scale(root, new_xscale, new_yscale);\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "var update_plot_scale = function(root, new_xscale, new_yscale) {\n",
       "    var trans = scale_centered_translation(root, new_xscale, new_yscale);\n",
       "    set_plot_pan_zoom(root, trans.x, trans.y, new_xscale, new_yscale);\n",
       "};\n",
       "\n",
       "\n",
       "var toggle_color_class = function(root, color_class, ison) {\n",
       "    var escaped_color_class = color_class.replace(/([^0-9a-zA-z])/g,\"\\\\$1\");\n",
       "    var guides = root.selectAll(\".guide.\" + escaped_color_class + \",.guide .\" + escaped_color_class);\n",
       "    var geoms = root.selectAll(\".geometry.\" + escaped_color_class + \",.geometry .\" + escaped_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 g\")\n",
       "            .forEach(function (element) {\n",
       "                var other_color_class = element.data(\"color_class\");\n",
       "                if (typeof other_color_class !== 'undefined' && 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(\"#img-a0ffa6c1\");\n",
       "fig.select(\"#img-a0ffa6c1-5\")\n",
       "   .init_gadfly();\n",
       "fig.select(\"#img-a0ffa6c1-7\")\n",
       "   .plotroot().data(\"unfocused_ygrid_color\", \"#D0D0E0\")\n",
       ";\n",
       "fig.select(\"#img-a0ffa6c1-7\")\n",
       "   .plotroot().data(\"focused_ygrid_color\", \"#A0A0A0\")\n",
       ";\n",
       "fig.select(\"#img-a0ffa6c1-8\")\n",
       "   .plotroot().data(\"unfocused_xgrid_color\", \"#D0D0E0\")\n",
       ";\n",
       "fig.select(\"#img-a0ffa6c1-8\")\n",
       "   .plotroot().data(\"focused_xgrid_color\", \"#A0A0A0\")\n",
       ";\n",
       "fig.select(\"#img-a0ffa6c1-19\")\n",
       "   .mouseenter(Gadfly.helpscreen_visible)\n",
       ".mouseleave(Gadfly.helpscreen_hidden)\n",
       ";\n",
       "    });\n",
       "]]> </script>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "Plot(...)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "set_default_plot_size(15cm,10cm)\n",
    "F = Gadfly.plot(x = v0_range[[4;8;10;12;14]], y = score[[4;8;10;12;14]], Geom.line, Scale.x_log10,\n",
    "            Coord.cartesian(xmax = -0.9),\n",
    "            Guide.xlabel(\"log(v0)\"), Guide.ylabel(\"model selection score\"))\n",
    "draw(PDF(\"figure/fig_iso2.pdf\"), F);\n",
    "F"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 262,
   "metadata": {},
   "outputs": [],
   "source": [
    "using CSV\n",
    "CSV.write(\"result/isotonic1.txt\", df, delim = ',');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = DataFrame(x = repeat(1:n, outer = 5),\n",
    "                y = [pava(y) fit[:,[8;10;12;14]]][:],\n",
    "                v0 = repeat([\"0.005\";\"0.015\";\"0.03\";\"0.06\";\"0.12\"], inner = n));\n",
    "set_default_plot_size(20cm,10cm)\n",
    "F1 = layer(df, x = :x, y = :y, color = :v0, shape = :v0, Geom.line, Geom.point,\n",
    "    Theme(line_width = .6mm, point_size = 5pt))\n",
    "F2 = layer(x = 1:n, y = y, Geom.point, Theme(default_color = \"black\", point_size = 1.5pt))\n",
    "Gadfly.plot(F1,F2, Coord.cartesian(xmax = n, ymin = -0.55),\n",
    "            Guide.title(\"Isotonic regression fits for different v0 values\"));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 264,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot(df, x = :x, y = :y, color = :v0, shape = :v0, Geom.line, Geom.point,\n",
    "    Theme(line_width = .6mm, point_size = 3pt,\n",
    "        point_shapes = repeat([Shape.hexagon;Shape.diamond;Shape.xcross;Shape.cross;Shape.square],inner = n)));"
   ]
  }
 ],
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