IntegratedOnlineStationaryAlgo.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Integrated Online Stationary Algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Author: D.Kufel**\n",
    "\n",
    "**08/21/2019**\n",
    "\n",
    "*Completed at IPAM, University of Califronia Los Angeles; RIPS2019 programme working on the Alibaba project*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**This is the implementation of the integrated online stationary algorithm developed for the generalized online matching problem. The integrated algorithm merges online gradient descent and upper confidence bound algorithm in the context of the online product recommendation. See: https://arxiv.org/abs/1911.07409 for details**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ReadMe: \n",
    "\n",
    "1. The first two cells are to run the online stationary code. They require files generated from the other jupyter notebook called generating_past_and_future_data.ipynb. \n",
    "2. The rest of the cells is to plot certain statistics from the simulation.\n",
    "3. The last paragraph runs the offline code for benchmark of the online.\n",
    "\n",
    "Commands %matplotlib notebook is for interactive plots. %%capture is to shut all the print statements in a given cell"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "m=5 #number of customer types\n",
    "d=4 #number of items\n",
    "\n",
    "#Loading the past/future customer arrivals\n",
    "##################\n",
    "pastdata_rewards=np.load('pastcustomerdata_beta_rewards.npy')\n",
    "pastdata_type=np.load('pastcustomerdata_beta_customertype.npy')\n",
    "\n",
    "newdata_rewards=np.load('newcustomerdata_beta_rewards.npy')\n",
    "newdata_type=np.load('newcustomerdata_beta_customertype.npy')\n",
    "##################\n",
    "N=newdata_rewards.shape[0] #number of newly arriving customers\n",
    "\n",
    "#np.random.seed(20)\n",
    "\n",
    "def f_k(Lambda):\n",
    "    #Dual problem objective function\n",
    "    star=0\n",
    "    for j in range(0,m):\n",
    "        pj=prob_type[j] #selected row of pij matrix - for a given customer type j\n",
    "        pjmax=np.max(pj)\n",
    "        if pjmax==0:\n",
    "            pjmax=np.min(prob_type[prob_type>0])\n",
    "        #print(pjmax)\n",
    "        a=np.max(pj*(r-Lambda)/(pjmax*mu))\n",
    "        modtermj=a+np.log(np.sum(np.exp(pj*(r-Lambda)/(pjmax*mu)-a)))\n",
    "        starj=modtermj*arrival_rates[j]/np.sum(arrival_rates)*pjmax\n",
    "        star+=starj\n",
    "    return mu*star+np.dot(Lambda,budget)/N\n",
    "\n",
    "\n",
    "def true_dual(Lambda):\n",
    "    #Dual problem objective function\n",
    "    star=0\n",
    "    for j in range(0,m):\n",
    "        pj=true_prob_type[j] #selected row of pij matrix - for a given customer type j\n",
    "        pjmax=np.max(pj)\n",
    "        if pjmax==0:\n",
    "            pjmax=np.min(prob_type[prob_type>0])\n",
    "        #print(pjmax)\n",
    "        a=np.max(pj*(r-Lambda)/(pjmax*mu))\n",
    "        modtermj=a+np.log(np.sum(np.exp(pj*(r-Lambda)/(pjmax*mu)-a)))\n",
    "        starj=modtermj*arrival_rates[j]/np.sum(arrival_rates)*pjmax\n",
    "        star+=starj\n",
    "    return mu*star+np.dot(Lambda,budget)/N\n",
    "\n",
    "\n",
    "def partialderivative(Lambda,i,deltay):\n",
    "    #Calculating partial derivative of the dual problem objective function w.r.t. particular item\n",
    "    y=np.copy(Lambda)\n",
    "    y[i]=y[i]+deltay\n",
    "    fk_y=f_k(y)\n",
    "    fk_x=f_k(Lambda)\n",
    "    return (fk_y-fk_x)/deltay\n",
    "\n",
    "\n",
    "def explicitpartialderivative(Lambda,i):\n",
    "    star=0\n",
    "    for j in range(0,m):\n",
    "        pj=prob_type[j]\n",
    "        pjmax=np.max(pj)\n",
    "        if pjmax==0:\n",
    "            pjmax=np.min(prob_type[prob_type>0])\n",
    "        a=np.max(pj*(r-Lambda)/(pjmax*mu))\n",
    "        starj=arrival_rates[j]/np.sum(arrival_rates)*pj[i]*np.exp((r[i]-Lambda[i])*pj[i]/(pjmax*mu)-a)/np.sum(np.exp((r-Lambda)*pj/(pjmax*mu)-a))\n",
    "        star+=starj\n",
    "    return -star+budget[i]/N\n",
    "\n",
    "\n",
    "def lambdastoys(x):\n",
    "    ylist=[]\n",
    "    for j in range(0,m):\n",
    "        pj=prob_type[j]\n",
    "        pjmax=np.max(pj)\n",
    "        if pjmax==0:\n",
    "            pjmax=np.min(prob_type[prob_type>0])\n",
    "        a=np.max(pj*(r-x)/(pjmax*mu))\n",
    "        v=pj*(r-x)/(pjmax*mu)-a-np.log(np.sum(np.exp(pj*(r-x)/(pjmax*mu)-a)))\n",
    "        y=np.exp(v)\n",
    "        ylist.append(y)\n",
    "    return np.array(ylist) #should be a vector with length n\n",
    "\n",
    "def primal(x):\n",
    "    return np.sum(np.array([r[i]*prob_type[j,i]*lambdastoys(x)[j,i]*arrival_rates[j] for j in range(m) for i in range(d)]))\n",
    "\n",
    "\n",
    "def true_primal(x):\n",
    "    ylist=[]\n",
    "    for j in range(0,m):\n",
    "        pj=true_prob_type[j]\n",
    "        pjmax=np.max(pj)\n",
    "        if pjmax==0:\n",
    "            pjmax=np.min(true_prob_type[true_prob_type>0])\n",
    "        a=np.max(pj*(r-x)/(pjmax*mu))\n",
    "        v=pj*(r-x)/(pjmax*mu)-a-np.log(np.sum(np.exp(pj*(r-x)/(pjmax*mu)-a)))\n",
    "        y=np.exp(v)\n",
    "        ylist.append(y)\n",
    "    print(ylist[j])\n",
    "    return np.sum(np.array([r[i]*true_prob_type[j,i]*ylist[j][i]*arrival_rates[j] for j in range(m) for i in range(d)]))\n",
    "####################\n",
    "\n",
    "\n",
    "#dealing with the past data\n",
    "#################################\n",
    "\n",
    "rewardsums_item=np.sum(pastdata_rewards,axis=0) #number of shoppings of a particular item\n",
    "rewardsums_type=np.zeros((m,d)) \n",
    "prob_type=np.zeros((m,d))\n",
    "ncustomers_type=np.zeros(m)\n",
    "\n",
    "for customertype in range(0,m):\n",
    "    rewardsums_type[customertype]=np.sum(pastdata_rewards[pastdata_type==customertype],axis=0) #number of shoppings of a particular item within a type\n",
    "    ncustomers_type[customertype]=pastdata_rewards[pastdata_type==customertype].shape[0] #number of customers within a type\n",
    "    prob_type[customertype]=rewardsums_type[customertype]/ncustomers_type[customertype] #probability of shoping a given item within a given type\n",
    "    \n",
    "arrival_rates=np.array(ncustomers_type/np.sum(ncustomers_type)) #arrival rates of each customer type\n",
    "\n",
    "init_nofferings_type=np.tile(ncustomers_type.reshape(m,1),(1,d))*np.ones((m,d)) \n",
    "nofferings_type=np.copy(init_nofferings_type)\n",
    "#number of offerings of the particular item to a particular customer type\n",
    "\n",
    "init_prob_type=np.copy(prob_type)\n",
    "\n",
    "print('Initial probability matrix: \\n', init_prob_type)\n",
    "print('Customer arrival rates: ',arrival_rates)\n",
    "    \n",
    "##################################\n",
    "\n",
    "\n",
    "#a posteriori dealing with the new data (for benchmark)\n",
    "##################################\n",
    "new_rewardsums_item=np.sum(pastdata_rewards,axis=0) #number of shoppings of a particular item\n",
    "new_rewardsums_type=np.zeros((m,d)) \n",
    "true_prob_type=np.zeros((m,d))\n",
    "new_ncustomers_type=np.zeros(m)\n",
    "for customertype in range(0,m):\n",
    "    new_rewardsums_type[customertype]=np.sum(newdata_rewards[newdata_type==customertype],axis=0) #number of shoppings of a particular item within a type\n",
    "    new_ncustomers_type[customertype]=newdata_rewards[newdata_type==customertype].shape[0] #number of customers within a type\n",
    "    true_prob_type[customertype]=new_rewardsums_type[customertype]/new_ncustomers_type[customertype] #probability of shoping a given item within a given type\n",
    "\n",
    "true_arrival_rates=new_ncustomers_type/np.sum(new_ncustomers_type)\n",
    "print('True probability matrix: \\n', true_prob_type)\n",
    "print('New Customer measured arrival rates: ',true_arrival_rates)\n",
    "init_prob_diff=true_prob_type-prob_type\n",
    "#########################################\n",
    "\n",
    "#online gradient descent stuff\n",
    "#########################\n",
    "init_Lambda=np.ones(d) #np.array([0.9,0.9,0.5,0.5])#np.ones(d)*0.5 #initial value of the dual variable\n",
    "\n",
    "\n",
    "#b0=np.ones(d-1)*0.08*N #budget is not updated with each customer\n",
    "#b1=np.append(b0,1000)\n",
    "#budget=np.append(b0,0.8*N)\n",
    "\n",
    "\n",
    "#budget=np.array([0.4*N,0.4*N,0.8*N,0.1*N])\n",
    "#budget=np.append(b1,70)\n",
    "#b0=np.ones(d-1)*50\n",
    "#budget=np.append(b0,1000)\n",
    "\n",
    "r0=np.ones(d-1) #reward vector\n",
    "r=np.append(r0,1)\n",
    "#r=np.ones(d)\n",
    "\n",
    "mu=1e-2#regularization\n",
    "#delta=1e-9 #accuracy of partial derivative\n",
    "ball_size = 1e-1 #used to set step size\n",
    "maxgradnorm=0.0 #maximum value of the norm of the gradient\n",
    "\n",
    "next_Lambda=np.copy(init_Lambda) #used for the looping\n",
    "\n",
    "\n",
    "syn=np.sum(arrival_rates.reshape(m,1)/(np.sum(arrival_rates))*lambdastoys(init_Lambda)*true_prob_type,axis=0)*N\n",
    "\n",
    "syn[syn<1e-3]=np.mean(syn[syn>1e-3])\n",
    "budget=(np.random.rand(d)+1)*syn #make such random budget values for each item which will not be violated\n",
    "\n",
    "############\n",
    "\n",
    "#probability update code\n",
    "UCB=np.zeros((m,d)) #setting a dummy vector for the UCB\n",
    "\n",
    "print('Budget: ',budget)\n",
    "print('Shoppings from the past data',rewardsums_item)\n",
    "print('Init number of offerings: \\n',init_nofferings_type)\n",
    "print('Init reward values: \\n',rewardsums_type)\n",
    "\n",
    "listdual=[]\n",
    "listprimal=[]\n",
    "listtrueprimal=[]\n",
    "listprobdiff=[]\n",
    "regretUCB_sum=0\n",
    "modregretUCB_sum=0\n",
    "\n",
    "for n in range(0,N): #going through each newly arriving customer\n",
    "    \n",
    "    #UCB to determine actions for each possible type of the customer (not knowing its type still)\n",
    "    #########################################\n",
    "    Uhatt=np.sqrt(3/2*np.log(n+1)/nofferings_type)\n",
    "    #Uhatt=np.sqrt(3/2*6.5*np.log(n+1+100)/(nofferings_type))\n",
    "    #Uhatt=np.sqrt(3/200*np.log((n+1))/(nofferings_type))\n",
    "    #Uhatt=0\n",
    "\n",
    "\n",
    "    UCB[:,(rewardsums_item<budget)]=(Uhatt+prob_type*r)[:,(rewardsums_item<budget)] #select only these columns which do not violate budget\n",
    "    UCB[:,rewardsums_item>=budget]=-1 #set the UCB of budgets violating UCB to be negative\n",
    "    UCB[(np.isnan(UCB)) | (np.isinf(UCB))]=1e10 #set the UCB for unused items to be very large - ifology to get rid of nans/infs from Uhatt\n",
    "    print('UCB, iter: ',n,'value: \\n',UCB)\n",
    "    print('Uhatt: ',Uhatt)\n",
    "    print('Probability matrix: \\n',prob_type)\n",
    "    print('Number of offerings: \\n',nofferings_type)\n",
    "    prob_diff=np.mean(np.abs(true_prob_type-prob_type))\n",
    "    listprobdiff.append(prob_diff)\n",
    "    \n",
    "    action_vec=[]\n",
    "    for customertype in range(0,m):\n",
    "        action=np.random.choice(np.where(UCB[customertype]==np.max(UCB[customertype]))[0]) #pick a random item out of all items with maximum UCB\n",
    "        action_vec.append(action)\n",
    "    print('Action vector: ',action_vec)\n",
    "    #######################################\n",
    "    \n",
    "    \n",
    "    #gradient descent code to update Lambdas based on the previous data (customer yet haven't arrived)\n",
    "    #######################################\n",
    "    gradlist=[] \n",
    "    for i in range(0,d):\n",
    "        current_Lambda=next_Lambda \n",
    "        if next_Lambda[i]!=0.0: \n",
    "            #gradlist.append(partialderivative(current_Lambda,i,delta)) \n",
    "            gradlist.append(explicitpartialderivative(current_Lambda,i)) \n",
    "        else:\n",
    "            gradlist.append(0.0)\n",
    "    grad=np.array(gradlist)\n",
    "    gradnorm=np.linalg.norm(grad)\n",
    "    if np.abs(gradnorm)>maxgradnorm:\n",
    "        maxgradnorm=np.abs(gradnorm)\n",
    "            \n",
    "    next_Lambda = current_Lambda - ball_size*grad/(maxgradnorm*np.sqrt(n+1)) #updating Lambda using L-Lipshitz smoothness\n",
    "    next_Lambda[next_Lambda<0]=0.0 #proximal setting\n",
    "    \n",
    "    listdual.append(f_k(current_Lambda)) #used for plotting\n",
    "    listprimal.append(primal(current_Lambda))\n",
    "    listtrueprimal.append(true_primal(current_Lambda))\n",
    "\n",
    "    #######################################\n",
    "    \n",
    "    #customer arrives now\n",
    "    current_type=newdata_type[n]\n",
    "    print('Customer just arrived... Its type: ',current_type)\n",
    "    item_offered=action_vec[current_type]\n",
    "    \n",
    "    reward_value=newdata_rewards[n][item_offered]\n",
    "\n",
    "    #probability update part\n",
    "    #######################\n",
    "    nofferings_type[current_type][item_offered]+=1 #update the number of offerings\n",
    "    rewardsums_type[current_type][item_offered]+=reward_value #update the rewards for each type\n",
    "    ncustomers_type[current_type]+=1 #update the number of customers of a given type\n",
    "    rewardsums_item[item_offered]+=reward_value #update the rewards for each item\n",
    "    prob_type[current_type,(rewardsums_item<budget)]= rewardsums_type[current_type,(rewardsums_item<budget)]/nofferings_type[current_type, (rewardsums_item<budget)] #update the probabilities\n",
    "    ######################\n",
    "    \n",
    "    #regret calculation\n",
    "    regretUCB_term=(np.max(true_prob_type[current_type])-true_prob_type[current_type][item_offered])\n",
    "    regretUCB_sum+=regretUCB_term\n",
    "    modregretUCB_term=np.abs(true_dual(current_Lambda)-f_k(current_Lambda))\n",
    "    modregretUCB_sum+=modregretUCB_term\n",
    "    print('--------------------')\n",
    "final_prob_diff=true_prob_type-prob_type"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean inital diff:  0.20635222097777714\n",
      "Mean final diff:  0.08113642295519087\n",
      "Inital: \n",
      " [[0.52380952 0.54761905 0.78571429 0.61904762]\n",
      " [0.77142857 0.68571429 0.62857143 0.74285714]\n",
      " [0.16216216 0.78378378 0.45945946 0.35135135]\n",
      " [0.4        0.55       0.65       0.65      ]\n",
      " [0.63043478 0.7826087  0.58695652 0.17391304]]\n",
      "Final: \n",
      " [[0.83384615 0.69436202 0.57657658 0.46753247]\n",
      " [0.56302521 0.63645224 0.49693252 0.60469012]\n",
      " [0.16216216 0.72073343 0.89898256 0.29545455]\n",
      " [0.42156863 0.65714286 0.68878166 0.57848837]\n",
      " [0.45283019 0.59678653 0.57020548 0.17647059]]\n",
      "True: \n",
      "  [[0.84367121 0.71659102 0.32022189 0.34341906]\n",
      " [0.52471293 0.62456316 0.46180729 0.5771343 ]\n",
      " [0.84241824 0.71555996 0.9122894  0.14420218]\n",
      " [0.42469136 0.64987654 0.68740741 0.58024691]\n",
      " [0.34398782 0.59614409 0.53881279 0.26940639]]\n",
      "Nofferings: \n",
      " [[1626.  337.  111.   77.]\n",
      " [ 357. 1026.  163.  597.]\n",
      " [  37.  709. 1376.   44.]\n",
      " [ 102.  910.  829.  344.]\n",
      " [ 212. 1307.  585.   51.]]\n",
      "Mean over items:  [0.48668647 0.66109542 0.64629576 0.42452722]\n",
      "Mean over customer types:  [0.6430793  0.57527502 0.51933317 0.58649538 0.4490732 ]\n"
     ]
    }
   ],
   "source": [
    "print('Mean inital diff: ',np.mean(np.abs(init_prob_diff)))\n",
    "print('Mean final diff: ',np.mean(np.abs(final_prob_diff)))\n",
    "\n",
    "print('Inital: \\n',init_prob_type)\n",
    "print('Final: \\n',prob_type)\n",
    "print('True: \\n ',true_prob_type)\n",
    "print('Nofferings: \\n',nofferings_type)\n",
    "\n",
    "print('Mean over items: ', np.mean(prob_type,axis=0)) #mean probability of buy over each item - should be very close to the generated mean \n",
    "print('Mean over customer types: ',np.mean(prob_type,axis=1)) #mean probability of buy over each customer type - should be somewhere between new and old"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected value of the regret for the UCB:  0.04642440516222255\n",
      "Expected value of the modified regret for the UCB:  0.008678349889985603\n"
     ]
    }
   ],
   "source": [
    "print('Expected value of the regret for the UCB: ',regretUCB_sum/N)\n",
    "print('Expected value of the modified regret for the UCB: ',modregretUCB_sum/N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1702. 2776. 2287.  618.]\n",
      "[1701.08992295 2942.93963645 2286.12485    1780.48361719]\n"
     ]
    }
   ],
   "source": [
    "print(rewardsums_item)\n",
    "print(budget)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
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       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x112e71dd8>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.title('Convergence plots for the online algorithm')\n",
    "plt.xlabel('Customer number')\n",
    "plt.ylabel('Value of the objective functions')\n",
    "plt.plot((np.array(listdual)),'b.',label='Dual objective')\n",
    "plt.plot((np.array(listprimal)),'r.',label='Primal objective')\n",
    "plt.plot((np.array(listtrueprimal)),'g.',label='True primal objective')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[8.41555894e-01, 1.58444097e-01, 8.32510288e-09, 2.15635410e-11],\n",
       "       [2.66128926e-11, 4.02363726e-01, 8.53503350e-12, 5.97636274e-01],\n",
       "       [2.21926116e-33, 9.68687985e-07, 9.99999031e-01, 2.07255814e-25],\n",
       "       [9.72056674e-19, 6.37208391e-01, 3.61598639e-01, 1.19297029e-03],\n",
       "       [2.64831096e-15, 9.99864705e-01, 1.35294575e-04, 5.64680629e-29]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lambdastoys(next_Lambda)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1472.24640148 1648.12427249 1445.61207983  944.51690419]\n",
      "[1490.03874289 2878.04675005 2184.7153299   605.39005048]\n",
      "[3.76450836e-08 6.00254278e-09 4.97302633e+03 1.01120070e+03]\n",
      "[1472.24640148 1648.12427249 1445.61207983  944.51690419]\n",
      "[1701.08992295 2942.93963645 2286.12485    1780.48361719]\n"
     ]
    }
   ],
   "source": [
    "print(np.sum(arrival_rates.reshape(m,1)/(np.sum(arrival_rates))*lambdastoys(init_Lambda)*true_prob_type,axis=0)*N)\n",
    "print(np.sum(arrival_rates.reshape(m,1)/(np.sum(arrival_rates))*lambdastoys(current_Lambda)*true_prob_type,axis=0)*N)\n",
    "print(np.sum(arrival_rates.reshape(m,1)/(np.sum(arrival_rates))*lambdastoys([0.9,0.9,0.5,0.5])*true_prob_type,axis=0)*N)\n",
    "print(np.sum(arrival_rates.reshape(m,1)/(np.sum(arrival_rates))*lambdastoys([1,1,1,1])*true_prob_type,axis=0)*N)\n",
    "\n",
    "\n",
    "print(budget)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A posteriori offline problem solution (for benchmark)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration:  0\n",
      "Iteration:  100\n",
      "Iteration:  200\n",
      "Iteration:  300\n",
      "Iteration:  400\n",
      "Iteration:  500\n",
      "Iteration:  600\n",
      "Iteration:  700\n",
      "Iteration:  800\n",
      "Iteration:  900\n",
      "Iteration:  1000\n",
      "Iteration:  1100\n",
      "Iteration:  1200\n",
      "Iteration:  1300\n",
      "Iteration:  1400\n",
      "Iteration:  1500\n",
      "Iteration:  1600\n",
      "Iteration:  1700\n",
      "Iteration:  1800\n",
      "Iteration:  1900\n",
      "Iteration:  2000\n",
      "Iteration:  2100\n",
      "Iteration:  2200\n",
      "Iteration:  2300\n",
      "Iteration:  2400\n",
      "Iteration:  2500\n",
      "Iteration:  2600\n",
      "Iteration:  2700\n",
      "Iteration:  2800\n",
      "Iteration:  2900\n",
      "Iteration:  3000\n",
      "Iteration:  3100\n",
      "Iteration:  3200\n",
      "Iteration:  3300\n",
      "Iteration:  3400\n",
      "Iteration:  3500\n",
      "Iteration:  3600\n",
      "Iteration:  3700\n",
      "Iteration:  3800\n",
      "Iteration:  3900\n",
      "Iteration:  4000\n",
      "Iteration:  4100\n",
      "Iteration:  4200\n",
      "Iteration:  4300\n",
      "Iteration:  4400\n",
      "Iteration:  4500\n",
      "Iteration:  4600\n",
      "Iteration:  4700\n",
      "Iteration:  4800\n",
      "Iteration:  4900\n"
     ]
    },
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support. ' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
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     "output_type": "display_data"
    },
    {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x113b469b0>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "init_x=np.ones(d)#*0.1 # np.copy(current_Lambda)+0.05 #np.copy(current_Lambda) #initial value of the dual variable\n",
    "ball_size = 5e-1 #used to set step size\n",
    "maxgradnorm=0.0 #maximum value of the norm of the gradient\n",
    "maxiter=5000\n",
    "\n",
    "next_x=np.copy(init_x) #used for the looping\n",
    "\n",
    "def f_k(x):\n",
    "    #Dual problem objective function\n",
    "    star=0\n",
    "    for j in range(0,m):\n",
    "        pj=true_prob_type[j] #selected row of pij matrix - for a given customer type j\n",
    "        pjmax=np.max(pj)\n",
    "        a=np.max(pj*(r-x)/(pjmax*mu))\n",
    "        modtermj=a+np.log(np.sum(np.exp(pj*(r-x)/(pjmax*mu)-a)))\n",
    "        starj=modtermj*true_arrival_rates[j]/np.sum(true_arrival_rates)*pjmax\n",
    "        star+=starj\n",
    "    return mu*star+np.dot(x,budget)/N\n",
    "\n",
    "\n",
    "def partialderivative(x,i,deltay):\n",
    "    #Calculating partial derivative of the dual problem objective function w.r.t. particular item\n",
    "    y=np.copy(x)\n",
    "    y[i]=y[i]+deltay\n",
    "    fk_y=f_k(y)\n",
    "    fk_x=f_k(x)\n",
    "    return (fk_y-fk_x)/deltay\n",
    "\n",
    "def explicitpartialderivative(Lambda,i):\n",
    "    star=0\n",
    "    for j in range(0,m):\n",
    "        pj=true_prob_type[j]\n",
    "        pjmax=np.max(pj)\n",
    "        if pjmax==0:\n",
    "            pjmax=np.min(true_prob_type[true_prob_type>0])\n",
    "        a=np.max(pj*(r-Lambda)/(pjmax*mu))\n",
    "        starj=true_arrival_rates[j]/np.sum(true_arrival_rates)*pj[i]*np.exp((r[i]-Lambda[i])*pj[i]/(pjmax*mu)-a)/np.sum(np.exp((r-Lambda)*pj/(pjmax*mu)-a))\n",
    "        star+=starj\n",
    "    return -star+budget[i]/N\n",
    "\n",
    "\n",
    "def lambdastoys(x):\n",
    "    ylist=[]\n",
    "    for j in range(0,m):\n",
    "        pj=true_prob_type[j]\n",
    "        pjmax=np.max(pj)\n",
    "        a=np.max(pj*(r-x)/(pjmax*mu))\n",
    "        v=pj*(r-x)/(pjmax*mu)-a-np.log(np.sum(np.exp(pj*(r-x)/(pjmax*mu)-a)))\n",
    "        y=np.exp(v)\n",
    "        ylist.append(y)\n",
    "    return np.array(ylist) #should be a vector with length n\n",
    "\n",
    "def primal(x):\n",
    "    return np.sum(np.array([r[i]*true_prob_type[j,i]*lambdastoys(x)[j,i]*true_arrival_rates[j] for j in range(m) for i in range(d)]))\n",
    "####################\n",
    "\n",
    "listdual_offline=[]\n",
    "listprimal_offline=[]\n",
    "\n",
    "for iteration in range(0,maxiter): #going through each newly arriving customer\n",
    "    \n",
    "    if iteration%100==0:\n",
    "        print('Iteration: ',iteration)\n",
    "    \n",
    "    #gradient descent code to update Lambdas based on the previous data (customer yet haven't arrived)\n",
    "    #######################################\n",
    "    gradlist=[] \n",
    "    current_x=next_x\n",
    "\n",
    "    for i in range(0,d):\n",
    "        if next_x[i]!=0.0: \n",
    "            gradlist.append(explicitpartialderivative(current_x,i)) \n",
    "        else:\n",
    "            gradlist.append(0.0)\n",
    "    grad=np.array(gradlist)\n",
    "    gradnorm=np.linalg.norm(grad)\n",
    "\n",
    "    if gradnorm>maxgradnorm:\n",
    "        maxgradnorm=gradnorm\n",
    "            \n",
    "    next_x = current_x - ball_size*grad/(maxgradnorm*np.sqrt(n+1)) #updating Lambda using L-Lipshitz smoothness\n",
    "    next_x[next_x<0]=0.0 #proximal setting\n",
    "    \n",
    "    listdual_offline.append(f_k(current_x)) #used for plotting\n",
    "    listprimal_offline.append(primal(current_x))\n",
    "    \n",
    "\n",
    "plt.figure()  \n",
    "plt.title('Convergence plots for the offline algorithm')\n",
    "plt.xlabel('Customer number')\n",
    "plt.ylabel('Value of the objective functions')\n",
    "plt.plot(listdual_offline,'b.')\n",
    "plt.plot(listdual_offline,'b',label='dual')\n",
    "plt.plot(listprimal_offline,'r.')\n",
    "plt.plot(listprimal_offline,'r',label='primal')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.19543094 0.05386122 0.1029872  0.        ]\n",
      "[[0.52360518 0.47639482 0.         0.        ]\n",
      " [0.         0.90094803 0.         0.09905197]\n",
      " [0.0000002  0.00000019 0.99999961 0.        ]\n",
      " [0.         0.43582367 0.56134717 0.00282916]\n",
      " [0.         0.99999868 0.00000132 0.        ]]\n",
      "0.7168801788214592\n"
     ]
    }
   ],
   "source": [
    "np.set_printoptions(suppress=True)\n",
    "print(next_Lambda)\n",
    "print(lambdastoys(next_Lambda))\n",
    "print(primal(next_Lambda))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.09466053 0.06577683 0.12314471 0.        ]\n",
      "[[0.9999861  0.0000139  0.         0.        ]\n",
      " [0.00000002 0.73423995 0.         0.26576003]\n",
      " [0.01653715 0.00000054 0.98346231 0.        ]\n",
      " [0.         0.6454299  0.34164511 0.01292499]\n",
      " [0.         0.9999993  0.0000007  0.        ]]\n",
      "0.7252559862448924\n"
     ]
    }
   ],
   "source": [
    "print(next_x)\n",
    "print(lambdastoys(next_x))\n",
    "print(primal(next_x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "REGRET dual:  0.011354189248162047\n"
     ]
    }
   ],
   "source": [
    "REGdual=np.sum(np.abs(np.array(listdual)-f_k(np.array(next_x))))/N\n",
    "#REGprimal=(np.sum(np.array(listprimal)-primal(next_x)))/N\n",
    "print('REGRET dual: ',REGdual)\n",
    "#print('REGRET primal: ',REGprimal)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.020032539138147648\n"
     ]
    }
   ],
   "source": [
    "combinedregret=REGdual+modregretUCB_sum/N\n",
    "print(combinedregret)"
   ]
  }
 ],
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