wasserstein/wasserstein-bary-reg.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![MOSEK ApS](https://www.mosek.com/static/images/branding/webgraphmoseklogocolor.png )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regularized Wasserstein Barycenters using Mosek and the exponential cone"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In a [previous notebook related to Wasserstein distances](https://nbviewer.jupyter.org/github/MOSEK/Tutorials/blob/master/wasserstein/wasserstein-bary.ipynb) we defined the linear optimization problem of computing the Wasserstein barycenter of a set of discrete measures. Here we solve an entropy-regularized variant of the same problem and to demonstrate the exponential cone capabilities of MOSEK. We also use this problem to compare Fusion and CVXPY."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a reminder, the $p$-th order Wasserstein distance $W_p(\\mu,\\upsilon)$ between discrete probability distributions $\\mu,\\upsilon$ is the objective value of the following problem:\n",
    "<br>\n",
    "<br>\n",
    "$$ \\mbox{minimize} \\quad \\sum_{i=1}\\sum_{j=1} D(X_i,Y_j)^p\\pi_{ij}$$\n",
    "<br>\n",
    "$$ \\mbox{st.} \\quad \\sum_{j=1} \\pi_{ij} = \\mu_i , \\quad i = 1,2,..n $$\n",
    "<br>\n",
    "$$ \\quad \\sum_{i=1} \\pi_{ij} = \\upsilon_j, \\quad j = 1,2,..m $$\n",
    "<br>\n",
    "$$ \\pi_{ij} \\geq 0, \\quad \\forall_{i,j}$$\n",
    "<br>\n",
    "where $D(X_i,Y_j)$ is the distance function.\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Wasserstein Barycenter with regularization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The entropy regularized barycenter problem with $p=2$ is:\n",
    "<br>\n",
    "$$ \\mbox{minimize} \\quad \\frac1N \\sum_{i,j,k}^{N} D(X_i,Y_j)^2\\pi_{ij}^k + \\frac1\\lambda\\sum_{i,j,k} \\pi_{ij}^k\\log(\\pi_{ij}^k)$$\n",
    "<br>\n",
    "$$\\mbox{st.}  \\quad \\sum_{j=1} \\pi_{ij}^{k} = \\mu_i, \\quad \\forall_{k,i} \\quad (1)$$\n",
    "<br>\n",
    "$$ \\quad \\sum_{i=1} \\pi_{ij}^{k} = \\upsilon_j^{k}, \\quad \\forall_{k,j} \\quad (2) $$\n",
    "<br>\n",
    "$$ \\pi_{ij}^{k} \\geq 0 \\quad \\forall_{k,i,j}$$\n",
    "<br>\n",
    "where $D(X_i,Y_j)$ is the euclidian distance between pixels, $\\lambda = median(D(X_i,Y_j))$ and $N$ is the number of samples.\n",
    "\n",
    "Without the entropy term the problem is just the linear problem of computing a distribution $\\mu$ minimizing the sum of distances to $\\upsilon_i$, as studied in our other notebook. Entropy regularization was suggested to us by Stefano Gualandi and appears for example in the paper by Cuturi and Doucet http://proceedings.mlr.press/v32/cuturi14.pdf. This paper contains also more details about the choice of $\\lambda$. Also more detailed information about LP aproach to Wasserstein metric can be found in [Stefano Gualandi's blogpost](http://stegua.github.io/blog/2018/12/31/wasserstein-distances-an-operations-research-perspective/).\n",
    "\n",
    "In this problem, Wasserstein Barycenter of Three's are visualized using images with size $28x28$ using $2$ handwriten '3' digits from MNIST database. Computations are carried out by Intel(R) Xeon(R) CPU E5-2687W v4 @ 3.00GHz processor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 1440x720 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import struct\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#Define the number of images for the barycenter calculation\n",
    "n=2\n",
    "number = 3\n",
    "\n",
    "#Read the images from the file\n",
    "def read_idx(filename):\n",
    "    with open(filename, 'rb') as f:\n",
    "        zero, data_type, dims = struct.unpack('>HBB', f.read(4))\n",
    "        shape = tuple(struct.unpack('>I', f.read(4))[0] for d in range(dims))\n",
    "        return np.frombuffer(f.read(), dtype=np.uint8).reshape(shape)\n",
    "    \n",
    "data = read_idx('train-images.idx3-ubyte')\n",
    "labels = read_idx('train-labels.idx1-ubyte')\n",
    "#Select the images\n",
    "digits = data[labels == number]\n",
    "train = digits[:n]\n",
    "\n",
    "plt.figure(figsize=(20,10))\n",
    "for i in range(10):\n",
    "    plt.subplot(2,5,i+1)\n",
    "    plt.imshow(digits[np.random.randint(0,digits.shape[0])])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regularized Barycenters using Mosek Fusion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mosek.fusion import *\n",
    "import time\n",
    "import sys\n",
    "\n",
    "class Wasserstein_Fusion:\n",
    "    \n",
    "    def __init__(self):\n",
    "        self.time = 0.0\n",
    "        self.M = Model('Wasserstein')\n",
    "        self.result = None\n",
    "    \n",
    "    \n",
    "    def single_pmf(self, data = None, img=False):\n",
    "        \n",
    "        ''' Takes a image or array of images and extracts the probabilty mass function'''\n",
    "        \n",
    "        if not img:\n",
    "            v=[]\n",
    "            for image in data:\n",
    "                arr = np.asarray(image).ravel(order='K')\n",
    "                v.append(arr/np.sum(arr))\n",
    "        else:\n",
    "            v = np.asarray(data).ravel(order='K')\n",
    "            v = v/np.sum(v)\n",
    "        return v\n",
    "    \n",
    "    def ms_distance(self, m ,n, constant=False):\n",
    "        \n",
    "        ''' Squared Euclidean distance calculation between the pixels '''\n",
    "        \n",
    "        if constant:\n",
    "            d = np.ones((m,m))\n",
    "        else:\n",
    "            d = np.empty((m,m))\n",
    "            coor = []\n",
    "            for i in range(n):\n",
    "                for j in range(n):\n",
    "                    coor.append(np.array([i,j]))\n",
    "            for i in range(m):\n",
    "                for j in range(m):\n",
    "                    d[i][j] = np.linalg.norm(coor[i]-coor[j])**2\n",
    "        return d\n",
    "    \n",
    "    def Wasserstein_Distance(self, bc ,data, img = False):\n",
    "        \n",
    "        ''' Calculation of wasserstein distance between a barycenter and an image by solving the minimization problem '''\n",
    "    \n",
    "        v = np.array(self.single_pmf(data, img))\n",
    "        n = v.shape[0]\n",
    "        d = self.ms_distance(n,data.shape[1])\n",
    "        with Model('Wasserstein') as M:\n",
    "            #Add variable\n",
    "            pi = M.variable('pi',[n,n], Domain.greaterThan(0.0))\n",
    "            \n",
    "            #Add constraints\n",
    "            M.constraint('c1' , Expr.sum(pi,0), Domain.equalsTo(v))\n",
    "            M.constraint('c2' , Expr.sum(pi,1), Domain.equalsTo(bc))\n",
    "            \n",
    "            M.objective('Obj.' , ObjectiveSense.Minimize, Expr.dot(d, pi))\n",
    "            \n",
    "            M.solve()\n",
    "            objective = M.primalObjValue()\n",
    "            \n",
    "        return objective\n",
    "    \n",
    "    def Wasserstein_BaryCenter(self,data):\n",
    "        \n",
    "        M = self.M\n",
    "        start_time = time.time()\n",
    "        k = data.shape[0]\n",
    "        v = np.array(self.single_pmf(data))\n",
    "        n = v.shape[1]\n",
    "        d = self.ms_distance(n,data.shape[1])\n",
    "        \n",
    "        #Add variables   \n",
    "        mu = M.variable('Mu', n, Domain.greaterThan(0.0))  \n",
    "        pi = (M.variable('Pi', [k,n,n] , Domain.greaterThan(0.0)))\n",
    "                \n",
    "        #Add constraints    \n",
    "        \n",
    "        #Constraint (1)\n",
    "        M.constraint('B', Expr.sub(Expr.sum(pi,1) , Var.repeat(mu,1,k).transpose()), Domain.equalsTo(0.0))\n",
    "        #Constraint (2)\n",
    "        M.constraint('C', Expr.sum(pi,2), Domain.equalsTo(v))\n",
    "            \n",
    "        M.objective('Obj' , ObjectiveSense.Minimize, Expr.sum(Expr.mul(Expr.mul(Expr.reshape(pi.asExpr(), k, n*n) , d.ravel()), 1/k)))\n",
    "        \n",
    "        M.setLogHandler(sys.stdout)\n",
    "        M.solve()\n",
    "        self.result = mu.level()\n",
    "        M.selectedSolution(SolutionType.Interior)\n",
    "        self.objective = M.primalObjValue()\n",
    "        self.time = time.time() - start_time\n",
    "        \n",
    "        return mu.level()\n",
    "    \n",
    "    def Wasserstein_regBaryCenter(self,data, _lambda = None, relgap = None):\n",
    "        \n",
    "        M = self.M\n",
    "        start_time = time.time()\n",
    "        k = data.shape[0]\n",
    "        v = np.array(self.single_pmf(data))\n",
    "        n = v.shape[1]\n",
    "        d = self.ms_distance(n,data.shape[1])\n",
    "        \n",
    "        if not _lambda:\n",
    "            _lambda = 60/np.median(d.ravel())\n",
    "        \n",
    "        \n",
    "        #Add variables   \n",
    "        mu = M.variable('Mu', n, Domain.greaterThan(0.0))  \n",
    "        pi = (M.variable('Pi', [k,n,n] , Domain.greaterThan(0.0)))\n",
    "        z = M.variable('z', [k,n*n]) #Artificial variable \n",
    "        \n",
    "        #Add constraints\n",
    "        #Intermediate conic constraints in form z <= -pi log(pi) \n",
    "        for i in range(1,k+1):\n",
    "            M.constraint(Expr.hstack(Expr.constTerm(n*n, 1.0),\n",
    "                                     Expr.reshape(pi.asExpr(), k*n*n).slice(0+(i-1)*n*n, n*n*i),\n",
    "                                     Expr.reshape(z.asExpr(), k*n*n).slice(0+(i-1)*n*n, n*n*i)),\n",
    "                                     Domain.inPExpCone())\n",
    "    \n",
    "        #Constraint (1)\n",
    "        M.constraint('B', Expr.sub(Expr.sum(pi,1) , Var.repeat(mu,1,k).transpose()), Domain.equalsTo(0.0))\n",
    "        #Constraint (2)\n",
    "        M.constraint('C', Expr.sum(pi,2), Domain.equalsTo(v))\n",
    "        \n",
    "            \n",
    "        M.objective('Obj' , ObjectiveSense.Minimize, Expr.sum(Expr.mul(Expr.add(Expr.mul(Expr.reshape(pi.asExpr(), k, n*n), d.ravel()),Expr.mul(Expr.sum(z,1),-1/_lambda)), 1/k)))\n",
    "        \n",
    "        #relgap is set in case of approximation\n",
    "        if relgap:\n",
    "            M.setSolverParam(\"intpntCoTolRelGap\", relgap)\n",
    "        \n",
    "        M.setLogHandler(sys.stdout)\n",
    "        M.solve()\n",
    "        self.result = mu.level()\n",
    "        self.objective = M.primalObjValue()\n",
    "        \n",
    "        self.time = time.time() - start_time\n",
    "        \n",
    "        return self.result\n",
    "        \n",
    "        \n",
    "        \n",
    "    def reset(self):\n",
    "        self.M = Model('Wasserstein')\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Problem\n",
      "  Name                   : Wasserstein     \n",
      "  Objective sense        : min             \n",
      "  Type                   : CONIC (conic optimization problem)\n",
      "  Constraints            : 3691072         \n",
      "  Cones                  : 1229312         \n",
      "  Scalar variables       : 6147345         \n",
      "  Matrix variables       : 0               \n",
      "  Integer variables      : 0               \n",
      "\n",
      "Optimizer started.\n",
      "Presolve started.\n",
      "Linear dependency checker started.\n",
      "Linear dependency checker terminated.\n",
      "Eliminator started.\n",
      "Freed constraints in eliminator : 0\n",
      "Eliminator terminated.\n",
      "Eliminator - tries                  : 1                 time                   : 0.00            \n",
      "Lin. dep.  - tries                  : 1                 time                   : 0.79            \n",
      "Lin. dep.  - number                 : 1               \n",
      "Presolve terminated. Time: 4.88    \n",
      "Problem\n",
      "  Name                   : Wasserstein     \n",
      "  Objective sense        : min             \n",
      "  Type                   : CONIC (conic optimization problem)\n",
      "  Constraints            : 3691072         \n",
      "  Cones                  : 1229312         \n",
      "  Scalar variables       : 6147345         \n",
      "  Matrix variables       : 0               \n",
      "  Integer variables      : 0               \n",
      "\n",
      "Optimizer  - threads                : 24              \n",
      "Optimizer  - solved problem         : the primal      \n",
      "Optimizer  - Constraints            : 1138\n",
      "Optimizer  - Cones                  : 1229312\n",
      "Optimizer  - Scalar variables       : 3687936           conic                  : 3687936         \n",
      "Optimizer  - Semi-definite variables: 0                 scalarized             : 0               \n",
      "Factor     - setup time             : 1.28              dense det. time        : 0.00            \n",
      "Factor     - ML order time          : 0.01              GP order time          : 0.00            \n",
      "Factor     - nonzeros before factor : 2.79e+05          after factor           : 3.41e+05        \n",
      "Factor     - dense dim.             : 0                 flops                  : 1.17e+08        \n",
      "ITE PFEAS    DFEAS    GFEAS    PRSTATUS   POBJ              DOBJ              MU       TIME  \n",
      "0   6.3e+02  5.1e+02  2.4e+07  0.00e+00   2.213290906e+07   -1.586952925e+06  1.0e+00  10.10 \n",
      "1   2.2e+02  1.8e+02  1.4e+07  -9.87e-01  1.997448375e+07   -3.251324601e+06  3.5e-01  12.82 \n",
      "2   1.4e+02  1.1e+02  1.0e+07  -8.50e-01  1.706335861e+07   -4.132584878e+06  2.2e-01  15.44 \n",
      "3   8.6e+01  6.9e+01  6.1e+06  -5.35e-01  1.255537920e+07   -4.350508351e+06  1.4e-01  17.98 \n",
      "4   3.9e+01  3.1e+01  2.3e+06  -5.91e-02  6.634411697e+06   -3.290271335e+06  6.2e-02  20.60 \n",
      "5   1.6e+01  1.3e+01  6.8e+05  4.56e-01   3.047731323e+06   -1.738035830e+06  2.5e-02  23.20 \n",
      "6   9.2e+00  7.4e+00  3.2e+05  6.93e-01   1.871267186e+06   -1.107832915e+06  1.5e-02  25.98 \n",
      "7   3.8e+00  3.0e+00  9.0e+04  7.82e-01   8.077963925e+05   -5.102524925e+05  5.9e-03  28.62 \n",
      "8   1.0e+00  8.1e-01  1.4e+04  8.51e-01   2.027478294e+05   -1.783065556e+05  1.6e-03  31.46 \n",
      "9   4.2e-01  3.4e-01  4.0e+03  8.87e-01   8.245159686e+04   -8.499836533e+04  6.6e-04  34.22 \n",
      "10  1.2e-01  9.9e-02  6.9e+02  9.00e-01   2.254754497e+04   -2.962276989e+04  2.0e-04  36.82 \n",
      "11  3.6e-02  2.9e-02  1.2e+02  9.02e-01   5.918291547e+03   -1.024285722e+04  5.7e-05  39.36 \n",
      "12  1.1e-02  8.5e-03  2.0e+01  9.00e-01   1.600474776e+03   -3.421335906e+03  1.7e-05  41.97 \n",
      "13  3.3e-03  2.6e-03  3.7e+00  9.03e-01   4.338461931e+02   -1.203269461e+03  5.2e-06  44.63 \n",
      "14  9.2e-04  7.4e-04  5.9e-01  9.15e-01   9.098495781e+01   -3.977520685e+02  1.5e-06  47.24 \n",
      "15  2.5e-04  2.0e-04  8.5e-02  9.22e-01   1.259274659e+00   -1.351784897e+02  3.9e-07  49.97 \n",
      "16  7.1e-05  5.7e-05  1.4e-02  9.31e-01   -1.815269221e+01  -5.892007163e+01  1.1e-07  52.66 \n",
      "17  1.6e-05  1.3e-05  1.6e-03  9.35e-01   -2.349890101e+01  -3.326483992e+01  2.6e-08  55.32 \n",
      "18  3.2e-06  2.6e-06  1.5e-04  9.38e-01   -2.441819572e+01  -2.642396208e+01  5.1e-09  57.91 \n",
      "19  7.5e-07  6.0e-07  1.7e-05  9.44e-01   -2.452957265e+01  -2.501505945e+01  1.2e-09  60.52 \n",
      "20  1.8e-07  1.4e-07  2.0e-06  9.49e-01   -2.454254575e+01  -2.466072167e+01  2.8e-10  63.35 \n",
      "21  3.6e-08  2.9e-08  1.9e-07  9.48e-01   -2.454079867e+01  -2.456580997e+01  5.7e-11  65.94 \n",
      "22  9.3e-09  7.5e-09  2.6e-08  9.50e-01   -2.453852251e+01  -2.454516650e+01  1.5e-11  68.59 \n",
      "23  2.3e-09  1.8e-09  3.3e-09  9.51e-01   -2.453774803e+01  -2.453943434e+01  3.6e-12  71.15 \n",
      "24  7.2e-10  5.0e-10  4.7e-10  9.51e-01   -2.453754481e+01  -2.453801359e+01  9.8e-13  73.75 \n",
      "25  7.1e-10  4.1e-10  3.6e-10  9.54e-01   -2.453752642e+01  -2.453791941e+01  8.1e-13  81.43 \n",
      "26  3.5e-10  9.8e-11  4.3e-11  9.54e-01   -2.453745494e+01  -2.453755111e+01  1.9e-13  88.92 \n",
      "27  7.1e-10  9.8e-11  4.3e-11  9.78e-01   -2.453745493e+01  -2.453755104e+01  1.9e-13  98.60 \n",
      "28  7.4e-10  9.8e-11  4.3e-11  9.79e-01   -2.453745493e+01  -2.453755104e+01  1.9e-13  110.68\n",
      "29  8.4e-10  9.8e-11  4.3e-11  9.79e-01   -2.453745492e+01  -2.453755103e+01  1.9e-13  121.76\n",
      "30  1.1e-09  9.8e-11  4.3e-11  9.83e-01   -2.453745492e+01  -2.453755100e+01  1.9e-13  134.08\n",
      "31  1.1e-09  9.8e-11  4.3e-11  9.79e-01   -2.453745492e+01  -2.453755099e+01  1.9e-13  145.08\n",
      "32  1.1e-09  9.8e-11  4.3e-11  9.77e-01   -2.453745490e+01  -2.453755091e+01  1.9e-13  155.13\n",
      "33  1.4e-09  9.8e-11  4.3e-11  9.78e-01   -2.453745488e+01  -2.453755083e+01  1.9e-13  164.86\n",
      "34  1.4e-09  9.8e-11  4.3e-11  9.79e-01   -2.453745488e+01  -2.453755081e+01  1.9e-13  175.32\n",
      "35  1.4e-09  9.8e-11  4.3e-11  9.77e-01   -2.453745485e+01  -2.453755066e+01  1.9e-13  184.89\n",
      "36  1.4e-09  9.8e-11  4.3e-11  9.77e-01   -2.453745482e+01  -2.453755053e+01  1.9e-13  193.91\n",
      "37  1.4e-09  9.8e-11  4.3e-11  9.80e-01   -2.453745481e+01  -2.453755051e+01  1.9e-13  204.86\n",
      "38  1.4e-09  9.7e-11  4.3e-11  9.84e-01   -2.453745481e+01  -2.453755048e+01  1.9e-13  215.45\n",
      "39  1.4e-09  9.7e-11  4.3e-11  9.79e-01   -2.453745480e+01  -2.453755047e+01  1.9e-13  226.12\n",
      "40  1.4e-09  9.7e-11  4.3e-11  9.79e-01   -2.453745479e+01  -2.453755043e+01  1.9e-13  236.39\n",
      "41  1.4e-09  9.7e-11  4.3e-11  9.80e-01   -2.453745478e+01  -2.453755039e+01  1.9e-13  246.32\n",
      "42  1.4e-09  9.7e-11  4.3e-11  9.82e-01   -2.453745478e+01  -2.453755038e+01  1.9e-13  257.70\n",
      "43  1.4e-09  9.7e-11  4.3e-11  9.77e-01   -2.453745477e+01  -2.453755033e+01  1.9e-13  267.63\n",
      "44  1.4e-09  9.7e-11  4.3e-11  9.80e-01   -2.453745476e+01  -2.453755030e+01  1.9e-13  277.59\n",
      "45  1.4e-09  9.7e-11  4.3e-11  9.79e-01   -2.453745476e+01  -2.453755027e+01  1.9e-13  288.02\n",
      "46  1.4e-09  9.7e-11  4.3e-11  9.78e-01   -2.453745475e+01  -2.453755026e+01  1.9e-13  298.50\n",
      "47  1.4e-09  9.7e-11  4.2e-11  9.78e-01   -2.453745472e+01  -2.453755009e+01  1.9e-13  307.32\n",
      "48  1.4e-09  9.7e-11  4.2e-11  9.80e-01   -2.453745472e+01  -2.453755008e+01  1.9e-13  318.93\n",
      "49  1.4e-09  9.7e-11  4.2e-11  9.79e-01   -2.453745472e+01  -2.453755008e+01  1.9e-13  329.79\n",
      "50  1.4e-09  9.7e-11  4.2e-11  9.79e-01   -2.453745471e+01  -2.453755007e+01  1.9e-13  340.67\n",
      "51  1.4e-09  9.7e-11  4.2e-11  9.78e-01   -2.453745471e+01  -2.453755007e+01  1.9e-13  351.40\n",
      "52  1.4e-09  9.7e-11  4.2e-11  9.85e-01   -2.453745468e+01  -2.453754991e+01  1.9e-13  360.84\n",
      "53  1.4e-09  9.7e-11  4.2e-11  9.86e-01   -2.453745468e+01  -2.453754991e+01  1.9e-13  372.95\n",
      "54  7.9e-10  1.1e-11  1.7e-12  1.00e+00   -2.453743187e+01  -2.453744287e+01  2.1e-14  379.56\n",
      "55  1.2e-09  1.1e-11  1.7e-12  1.00e+00   -2.453743185e+01  -2.453744281e+01  2.1e-14  390.36\n",
      "56  1.2e-09  1.1e-11  1.6e-12  1.00e+00   -2.453743181e+01  -2.453744264e+01  2.1e-14  400.86\n",
      "57  1.4e-09  1.1e-11  1.6e-12  1.00e+00   -2.453743175e+01  -2.453744243e+01  2.0e-14  410.98\n",
      "58  1.4e-09  1.1e-11  1.6e-12  1.00e+00   -2.453743175e+01  -2.453744242e+01  2.0e-14  423.31\n",
      "59  1.4e-09  1.1e-11  1.6e-12  1.00e+00   -2.453743175e+01  -2.453744241e+01  2.0e-14  436.25\n",
      "60  1.4e-09  1.1e-11  1.6e-12  1.00e+00   -2.453743175e+01  -2.453744241e+01  2.0e-14  449.46\n",
      "61  6.7e-10  1.0e-12  4.6e-14  1.00e+00   -2.453742837e+01  -2.453742939e+01  1.8e-15  456.59\n",
      "62  6.3e-10  1.0e-12  4.6e-14  1.00e+00   -2.453742837e+01  -2.453742939e+01  1.8e-15  469.17\n",
      "63  8.4e-10  1.0e-12  4.6e-14  1.00e+00   -2.453742837e+01  -2.453742939e+01  1.8e-15  481.70\n",
      "64  1.0e-09  1.0e-12  4.6e-14  1.00e+00   -2.453742837e+01  -2.453742939e+01  1.8e-15  494.25\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "65  1.1e-09  1.0e-12  4.6e-14  1.00e+00   -2.453742837e+01  -2.453742939e+01  1.8e-15  506.36\n",
      "66  1.3e-09  1.0e-12  4.6e-14  1.00e+00   -2.453742837e+01  -2.453742939e+01  1.8e-15  519.57\n",
      "67  1.2e-09  1.0e-12  4.6e-14  1.00e+00   -2.453742837e+01  -2.453742939e+01  1.8e-15  531.70\n",
      "68  1.2e-09  1.0e-12  4.6e-14  1.00e+00   -2.453742837e+01  -2.453742939e+01  1.8e-15  544.16\n",
      "Optimizer terminated. Time: 558.63  \n",
      "\n",
      "\n",
      "Interior-point solution summary\n",
      "  Problem status  : PRIMAL_AND_DUAL_FEASIBLE\n",
      "  Solution status : OPTIMAL\n",
      "  Primal.  obj: -2.4537428373e+01   nrm: 1e+00    Viol.  con: 1e-07    var: 0e+00    cones: 2e-12  \n",
      "  Dual.    obj: -2.4537429385e+01   nrm: 8e+02    Viol.  con: 0e+00    var: 2e-11    cones: 0e+00  \n",
      "\n",
      "Time Spent to solve problem with Fusion: \n",
      " 592.5434217453003\n",
      "Time Spent in solver: \n",
      " 558.629515171051\n",
      "Objective: \n",
      " -24.53742837253434\n"
     ]
    }
   ],
   "source": [
    "fusion_model = Wasserstein_Fusion()\n",
    "f_bc = fusion_model.Wasserstein_regBaryCenter(train)\n",
    "print('\\nTime Spent to solve problem with Fusion: \\n {0}'.format(fusion_model.time))\n",
    "print('Time Spent in solver: \\n {0}'.format(fusion_model.M.getSolverDoubleInfo(\"optimizerTime\")))\n",
    "print('Objective: \\n {0}'.format(fusion_model.objective))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Problem\n",
      "  Name                   : Wasserstein     \n",
      "  Objective sense        : min             \n",
      "  Type                   : LO (linear optimization problem)\n",
      "  Constraints            : 3136            \n",
      "  Cones                  : 0               \n",
      "  Scalar variables       : 1230097         \n",
      "  Matrix variables       : 0               \n",
      "  Integer variables      : 0               \n",
      "\n",
      "Optimizer started.\n",
      "Presolve started.\n",
      "Linear dependency checker started.\n",
      "Linear dependency checker terminated.\n",
      "Eliminator started.\n",
      "Freed constraints in eliminator : 0\n",
      "Eliminator terminated.\n",
      "Eliminator - tries                  : 1                 time                   : 0.00            \n",
      "Lin. dep.  - tries                  : 1                 time                   : 0.03            \n",
      "Lin. dep.  - number                 : 1               \n",
      "Presolve terminated. Time: 0.96    \n",
      "Problem\n",
      "  Name                   : Wasserstein     \n",
      "  Objective sense        : min             \n",
      "  Type                   : LO (linear optimization problem)\n",
      "  Constraints            : 3136            \n",
      "  Cones                  : 0               \n",
      "  Scalar variables       : 1230097         \n",
      "  Matrix variables       : 0               \n",
      "  Integer variables      : 0               \n",
      "\n",
      "Optimizer  - threads                : 24              \n",
      "Optimizer  - solved problem         : the primal      \n",
      "Optimizer  - Constraints            : 1138\n",
      "Optimizer  - Cones                  : 0\n",
      "Optimizer  - Scalar variables       : 278320            conic                  : 0               \n",
      "Optimizer  - Semi-definite variables: 0                 scalarized             : 0               \n",
      "Factor     - setup time             : 0.11              dense det. time        : 0.00            \n",
      "Factor     - ML order time          : 0.01              GP order time          : 0.00            \n",
      "Factor     - nonzeros before factor : 2.79e+05          after factor           : 3.41e+05        \n",
      "Factor     - dense dim.             : 0                 flops                  : 1.15e+08        \n",
      "ITE PFEAS    DFEAS    GFEAS    PRSTATUS   POBJ              DOBJ              MU       TIME  \n",
      "0   1.8e+04  1.2e+04  5.7e+08  0.00e+00   2.533143200e+07   0.000000000e+00   5.1e+02  1.25  \n",
      "1   1.8e+00  1.2e+00  5.8e+04  -1.00e+00  2.530057802e+07   -1.985024391e+04  5.2e-02  1.32  \n",
      "2   4.0e-03  2.6e-03  1.3e+02  -6.05e-01  6.809717409e+04   -3.693719644e+04  1.1e-04  1.42  \n",
      "3   1.1e-03  7.4e-04  3.7e+01  2.56e+02   1.601417700e+02   -1.716296687e+01  3.3e-05  1.54  \n",
      "4   5.7e-04  3.7e-04  1.8e+01  1.42e+00   7.400571125e+01   -6.338392658e+00  1.6e-05  1.66  \n",
      "5   7.5e-05  4.9e-05  2.4e+00  1.20e+00   9.664295656e+00   -2.705164314e-01  2.2e-06  1.77  \n",
      "6   2.1e-05  1.4e-05  6.8e-01  1.06e+00   3.422966212e+00   6.973656981e-01   6.1e-07  1.87  \n",
      "7   4.1e-06  1.8e-06  1.3e-01  1.02e+00   1.573043800e+00   1.067352406e+00   1.1e-07  1.95  \n",
      "8   8.6e-07  3.7e-07  2.6e-02  1.00e+00   1.225114421e+00   1.119539692e+00   2.4e-08  2.06  \n",
      "9   1.5e-07  6.3e-08  4.5e-03  1.00e+00   1.147377919e+00   1.129274252e+00   4.0e-09  2.15  \n",
      "10  6.3e-09  2.9e-09  1.9e-04  1.00e+00   1.131288555e+00   1.130509098e+00   1.7e-10  2.21  \n",
      "11  7.4e-13  3.7e-13  2.3e-08  1.00e+00   1.130528318e+00   1.130528226e+00   2.0e-14  2.27  \n",
      "12  2.2e-16  6.3e-14  1.5e-12  1.00e+00   1.130528228e+00   1.130528228e+00   2.0e-18  2.31  \n",
      "Basis identification started.\n",
      "Basis identification terminated. Time: 0.07\n",
      "Optimizer terminated. Time: 2.72    \n",
      "\n",
      "\n",
      "Interior-point solution summary\n",
      "  Problem status  : PRIMAL_AND_DUAL_FEASIBLE\n",
      "  Solution status : OPTIMAL\n",
      "  Primal.  obj: 1.1305282283e+00    nrm: 1e+00    Viol.  con: 9e-16    var: 0e+00  \n",
      "  Dual.    obj: 1.1305282283e+00    nrm: 8e+02    Viol.  con: 0e+00    var: 2e-13  \n",
      "\n",
      "Basic solution summary\n",
      "  Problem status  : PRIMAL_AND_DUAL_FEASIBLE\n",
      "  Solution status : OPTIMAL\n",
      "  Primal.  obj: 1.1305282283e+00    nrm: 1e+00    Viol.  con: 2e-17    var: 0e+00  \n",
      "  Dual.    obj: 1.1305282283e+00    nrm: 8e+02    Viol.  con: 0e+00    var: 1e-11  \n",
      "\n",
      "Time Spent to solve non-regularized problem with Fusion: \n",
      " 8.922340393066406\n",
      "Time Spent in solver: \n",
      " 2.7243459224700928\n",
      "The average Wasserstein distance between digits and the barycenter: \n",
      " 1.1305282283356233\n"
     ]
    }
   ],
   "source": [
    "nonReg_model = Wasserstein_Fusion()\n",
    "nonReg = nonReg_model.Wasserstein_BaryCenter(train)\n",
    "print('\\nTime Spent to solve non-regularized problem with Fusion: \\n {0}'.format(nonReg_model.time))\n",
    "print('Time Spent in solver: \\n {0}'.format(nonReg_model.M.getSolverDoubleInfo(\"optimizerTime\")))\n",
    "print('The average Wasserstein distance between digits and the barycenter: \\n {0}'.format(nonReg_model.objective))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1080x576 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15,8))\n",
    "plt.subplot(1,3,1)\n",
    "plt.imshow(np.reshape(f_bc,(28,28)))\n",
    "plt.title('Regularized Barycenter')\n",
    "plt.subplot(1,3,2)\n",
    "plt.imshow(np.reshape(nonReg, (28,28)))\n",
    "plt.title('Non-Regularized Interior Point Barycenter')\n",
    "plt.imshow(np.reshape(nonReg, (28,28)))\n",
    "plt.subplot(1,3,3)\n",
    "plt.title('Non-Regularized Basic Point Barycenter')\n",
    "plt.imshow(np.reshape(nonReg_model.result, (28,28)))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\quad$ The interiror point solution is different than the basic solution, however this is just a coincidence. The interior point solution gives the convex combination of the extreme points if there is infinetly many optimal solutions but this is not always the case in this problem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\quad $ Solving the problem even for just 2 images takes a long time. However, when the output of the iterations are investigated the solver is spending most of the time in earning very little improvements. Since the regularization term is an artificial addition to the problem, it is sensible to test if the approximation with a little loss of accuracy effects the values and images significantly or not, by using \"intpntCoTolRelGap\" parameter. This parameter controls the relative gap termination tolerance of the conic optimizer.\n",
    "In the next problem the parameter is increased from 1.0e-7 to 1.0e-3 in order to terminate Mosek with a little bit less accuracy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Obtaining approximate values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Problem\n",
      "  Name                   : Wasserstein     \n",
      "  Objective sense        : min             \n",
      "  Type                   : CONIC (conic optimization problem)\n",
      "  Constraints            : 3691072         \n",
      "  Cones                  : 1229312         \n",
      "  Scalar variables       : 6147345         \n",
      "  Matrix variables       : 0               \n",
      "  Integer variables      : 0               \n",
      "\n",
      "Optimizer started.\n",
      "Presolve started.\n",
      "Linear dependency checker started.\n",
      "Linear dependency checker terminated.\n",
      "Eliminator started.\n",
      "Freed constraints in eliminator : 0\n",
      "Eliminator terminated.\n",
      "Eliminator - tries                  : 1                 time                   : 0.00            \n",
      "Lin. dep.  - tries                  : 1                 time                   : 0.75            \n",
      "Lin. dep.  - number                 : 1               \n",
      "Presolve terminated. Time: 4.73    \n",
      "Problem\n",
      "  Name                   : Wasserstein     \n",
      "  Objective sense        : min             \n",
      "  Type                   : CONIC (conic optimization problem)\n",
      "  Constraints            : 3691072         \n",
      "  Cones                  : 1229312         \n",
      "  Scalar variables       : 6147345         \n",
      "  Matrix variables       : 0               \n",
      "  Integer variables      : 0               \n",
      "\n",
      "Optimizer  - threads                : 24              \n",
      "Optimizer  - solved problem         : the primal      \n",
      "Optimizer  - Constraints            : 1138\n",
      "Optimizer  - Cones                  : 1229312\n",
      "Optimizer  - Scalar variables       : 3687936           conic                  : 3687936         \n",
      "Optimizer  - Semi-definite variables: 0                 scalarized             : 0               \n",
      "Factor     - setup time             : 1.34              dense det. time        : 0.00            \n",
      "Factor     - ML order time          : 0.01              GP order time          : 0.00            \n",
      "Factor     - nonzeros before factor : 2.79e+05          after factor           : 3.41e+05        \n",
      "Factor     - dense dim.             : 0                 flops                  : 1.17e+08        \n",
      "ITE PFEAS    DFEAS    GFEAS    PRSTATUS   POBJ              DOBJ              MU       TIME  \n",
      "0   6.3e+02  5.1e+02  2.4e+07  0.00e+00   2.213290906e+07   -1.586952925e+06  1.0e+00  9.79  \n",
      "1   2.2e+02  1.8e+02  1.4e+07  -9.87e-01  1.997448375e+07   -3.251324601e+06  3.5e-01  12.58 \n",
      "2   1.4e+02  1.1e+02  1.0e+07  -8.50e-01  1.706335861e+07   -4.132584878e+06  2.2e-01  15.35 \n",
      "3   8.6e+01  6.9e+01  6.1e+06  -5.35e-01  1.255537920e+07   -4.350508351e+06  1.4e-01  18.28 \n",
      "4   3.9e+01  3.1e+01  2.3e+06  -5.91e-02  6.634411697e+06   -3.290271335e+06  6.2e-02  20.98 \n",
      "5   1.6e+01  1.3e+01  6.8e+05  4.56e-01   3.047731323e+06   -1.738035830e+06  2.5e-02  23.66 \n",
      "6   9.2e+00  7.4e+00  3.2e+05  6.93e-01   1.871267186e+06   -1.107832915e+06  1.5e-02  26.15 \n",
      "7   3.8e+00  3.0e+00  9.0e+04  7.82e-01   8.077963925e+05   -5.102524925e+05  5.9e-03  28.85 \n",
      "8   1.0e+00  8.1e-01  1.4e+04  8.51e-01   2.027478294e+05   -1.783065556e+05  1.6e-03  31.64 \n",
      "9   4.2e-01  3.4e-01  4.0e+03  8.87e-01   8.245159686e+04   -8.499836533e+04  6.6e-04  34.18 \n",
      "10  1.2e-01  9.9e-02  6.9e+02  9.00e-01   2.254754497e+04   -2.962276989e+04  2.0e-04  36.94 \n",
      "11  3.6e-02  2.9e-02  1.2e+02  9.02e-01   5.918291547e+03   -1.024285722e+04  5.7e-05  39.48 \n",
      "12  1.1e-02  8.5e-03  2.0e+01  9.00e-01   1.600474776e+03   -3.421335906e+03  1.7e-05  42.19 \n",
      "13  3.3e-03  2.6e-03  3.7e+00  9.03e-01   4.338461931e+02   -1.203269461e+03  5.2e-06  44.90 \n",
      "14  9.2e-04  7.4e-04  5.9e-01  9.15e-01   9.098495781e+01   -3.977520685e+02  1.5e-06  47.40 \n",
      "15  2.5e-04  2.0e-04  8.5e-02  9.22e-01   1.259274659e+00   -1.351784897e+02  3.9e-07  49.96 \n",
      "16  7.1e-05  5.7e-05  1.4e-02  9.31e-01   -1.815269221e+01  -5.892007163e+01  1.1e-07  52.59 \n",
      "17  1.6e-05  1.3e-05  1.6e-03  9.35e-01   -2.349890101e+01  -3.326483992e+01  2.6e-08  55.25 \n",
      "18  3.2e-06  2.6e-06  1.5e-04  9.38e-01   -2.441819572e+01  -2.642396208e+01  5.1e-09  57.85 \n",
      "19  7.5e-07  6.0e-07  1.7e-05  9.44e-01   -2.452957265e+01  -2.501505945e+01  1.2e-09  60.41 \n",
      "20  1.8e-07  1.4e-07  2.0e-06  9.49e-01   -2.454254575e+01  -2.466072167e+01  2.8e-10  62.93 \n",
      "21  3.6e-08  2.9e-08  1.9e-07  9.48e-01   -2.454079867e+01  -2.456580997e+01  5.7e-11  65.49 \n",
      "22  9.3e-09  7.5e-09  2.6e-08  9.50e-01   -2.453852251e+01  -2.454516650e+01  1.5e-11  68.06 \n",
      "23  2.3e-09  1.8e-09  3.3e-09  9.51e-01   -2.453774803e+01  -2.453943434e+01  3.6e-12  70.63 \n",
      "24  7.2e-10  5.0e-10  4.7e-10  9.51e-01   -2.453754481e+01  -2.453801359e+01  9.8e-13  73.16 \n",
      "Optimizer terminated. Time: 75.21   \n",
      "\n",
      "\n",
      "Interior-point solution summary\n",
      "  Problem status  : PRIMAL_AND_DUAL_FEASIBLE\n",
      "  Solution status : OPTIMAL\n",
      "  Primal.  obj: -2.4537544810e+01   nrm: 1e+00    Viol.  con: 1e-08    var: 0e+00    cones: 6e-12  \n",
      "  Dual.    obj: -2.4538013590e+01   nrm: 8e+02    Viol.  con: 0e+00    var: 1e-08    cones: 0e+00  \n",
      "\n",
      "Time Spent to solve problem with Fusion: \n",
      " 109.92306613922119\n",
      "Time Spent in solver: \n",
      " 75.20934391021729\n",
      "Objective: \n",
      " -24.53754480969593\n"
     ]
    }
   ],
   "source": [
    "fusion_model2 = Wasserstein_Fusion()\n",
    "f_bc2 = fusion_model2.Wasserstein_regBaryCenter(train, relgap = \"1.0e-3\")\n",
    "print('\\nTime Spent to solve problem with Fusion: \\n {0}'.format(fusion_model2.time))\n",
    "print('Time Spent in solver: \\n {0}'.format(fusion_model2.M.getSolverDoubleInfo(\"optimizerTime\")))\n",
    "print('Objective: \\n {0}'.format(fusion_model2.objective))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,10))\n",
    "plt.subplot(1,2,1)\n",
    "fus_bc = np.reshape(f_bc,(28,28))\n",
    "plt.imshow(fus_bc)\n",
    "plt.title('Optimal Barycenter')\n",
    "plt.subplot(1,2,2)\n",
    "fus_bc2 = np.reshape(f_bc,(28,28))\n",
    "plt.imshow(fus_bc)\n",
    "plt.title('Approximate Barycenter')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Stats</th>\n",
       "      <td>784.0</td>\n",
       "      <td>-2.565828e-09</td>\n",
       "      <td>8.372986e-09</td>\n",
       "      <td>-2.593707e-08</td>\n",
       "      <td>-8.399538e-09</td>\n",
       "      <td>-3.616124e-09</td>\n",
       "      <td>-4.976524e-10</td>\n",
       "      <td>2.277483e-08</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       count          mean           std           min           25%  \\\n",
       "Stats  784.0 -2.565828e-09  8.372986e-09 -2.593707e-08 -8.399538e-09   \n",
       "\n",
       "                50%           75%           max  \n",
       "Stats -3.616124e-09 -4.976524e-10  2.277483e-08  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "error = pd.Series(f_bc - f_bc2)\n",
    "plt.plot(error)\n",
    "plt.title('Error of Aproximation')\n",
    "plt.xlabel(\"Pixels\")\n",
    "plt.ylabel('Error Values')\n",
    "pd.DataFrame(error.describe(), columns=['Stats']).transpose()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x504 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,7))\n",
    "\n",
    "total_t = [fusion_model.time, fusion_model2.time]\n",
    "solver_t = [fusion_model.M.getSolverDoubleInfo(\"optimizerTime\"), fusion_model2.M.getSolverDoubleInfo(\"optimizerTime\")]\n",
    "#Total time plot\n",
    "plt.subplot(1,2,1)\n",
    "plt.bar(['Optimal', 'Approximation'], height= total_t,\n",
    "        width=0.4, color=(0.3, 0.6, 0.2, 0.5))\n",
    "plt.ylabel(\"Total Time (s)\")\n",
    "plt.title(\"Comparison of Total Time\")\n",
    "\n",
    "#Solver time plot\n",
    "plt.subplot(1,2,2)\n",
    "plt.bar(['Optimal', 'Approximation'], height=solver_t,\n",
    "        width=0.4, color=(0.5, 0.6, 0.9, 0.8))\n",
    "plt.ylabel(\"Solver Time (s)\")\n",
    "plt.title(\"Comparison of Solver Time\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\quad$The two barycenter images that obtained from the optimal solution and approximate solution seem almost identical to each other. In addition statistical description of values of the error between them is presented above with a plot. The mean and the even extreme values are small and indicates that the reduction of time obtained by approximation totally compensates the error."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Modeling the same problem with CVXPY"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "import cvxpy as cp\n",
    "import time\n",
    "class Wasserstein_CVXPY:\n",
    "    \n",
    "    def __init__(self):\n",
    "        self.time = 0.0\n",
    "        self.result = None\n",
    "        self.prob = None\n",
    "\n",
    "    def single_pmf(self, data = None, img=False):\n",
    "        \n",
    "        ''' Takes a image or array of images and extracts the probabilty mass function'''\n",
    "        \n",
    "        if not img:\n",
    "            v=[]\n",
    "            for image in data:\n",
    "                arr = np.asarray(image).ravel(order='K')\n",
    "                v.append(arr/np.sum(arr))\n",
    "        else:\n",
    "            v = np.asarray(data).ravel(order='K')\n",
    "            v = v/np.sum(v)\n",
    "        return v\n",
    "    \n",
    "    def ms_distance(self, m ,n, constant=False):\n",
    "        \n",
    "        ''' Squared Euclidean distance calculation between the pixels '''\n",
    "        \n",
    "        if constant:\n",
    "            d = np.ones((m,m))\n",
    "        else:\n",
    "            d = np.empty((m,m))\n",
    "            coor = []\n",
    "            for i in range(n):\n",
    "                for j in range(n):\n",
    "                    coor.append(np.array([i,j]))\n",
    "            for i in range(m):\n",
    "                for j in range(m):\n",
    "                    d[i][j] = np.linalg.norm(coor[i]-coor[j])**2\n",
    "        return d\n",
    "    \n",
    "    def Wasserstein_Distance(self, bc ,data, img = False):\n",
    "        \n",
    "        ''' Calculation of wasserstein distance between a barycenter and an image by solving \n",
    "            the minimization problem '''\n",
    "    \n",
    "        v = np.array(self.single_pmf(data, img))\n",
    "        n = v.shape[0]\n",
    "        d = self.ms_distance(n,data.shape[1])\n",
    "        \n",
    "        pi = cp.Variable((n,n), nonneg=True)\n",
    "        obj = cp.Minimize((np.ones(n).T @ cp.multiply(d,pi) @ np.ones(n)))\n",
    "        \n",
    "        Cons=[]\n",
    "        Cons.append((np.ones(n) @ pi).T == bc)\n",
    "        Cons.append((pi @ np.ones(n)) == v)\n",
    "        \n",
    "        prob = cp.Problem(obj, constraints= Cons)\n",
    "        \n",
    "        return prob.solve(solver=cp.MOSEK, verbose = True)\n",
    "        \n",
    "    def Wasserstein_BaryCenter(self,data):\n",
    "        \n",
    "        ''' Calculation of wasserstein barycenter of given images by solving the minimization problem '''\n",
    "        \n",
    "        start_time = time.time()\n",
    "        k = data.shape[0]\n",
    "        v = np.array(self.single_pmf(data))\n",
    "        n = v.shape[1]\n",
    "        d = self.ms_distance(n,data.shape[1])\n",
    "        \n",
    "        #Add variables\n",
    "        pi= []\n",
    "        t= []\n",
    "        mu = cp.Variable(n, nonneg = True)\n",
    "        for i in range(k):\n",
    "            pi.append(cp.Variable((n,n), nonneg = True))\n",
    "            t.append(cp.Variable(nonneg = True))\n",
    "            \n",
    "        obj = cp.Minimize(np.sum(t)/k)\n",
    "        \n",
    "        #Add constraints\n",
    "        Cons=[]\n",
    "        for i in range(k):\n",
    "            Cons.append( t[i] >= np.ones(n).T @  cp.multiply(d,pi[i]) @ np.ones(n) ) #Constraint (1)\n",
    "            Cons.append( (np.ones(n) @ pi[i]).T == mu)                               #Constraint (2)\n",
    "            Cons.append( (pi[i] @ np.ones(n)) == v[i])                               #Constraint (3)\n",
    "            \n",
    "        self.prob = cp.Problem(obj, constraints= Cons)\n",
    "        self.result = self.prob.solve(solver=cp.MOSEK,verbose = True)\n",
    "        self.time = time.time() - start_time\n",
    "        \n",
    "        return mu.value\n",
    "    \n",
    "    def Wasserstein_regBaryCenter(self,data, _lambda = None, relgap=\"1.0e-7\"):\n",
    "        \n",
    "        ''' Calculation of wasserstein barycenter of given \n",
    "            images by solving a entropy regularized minimization problem '''\n",
    "        \n",
    "        start_time = time.time()\n",
    "        k = data.shape[0]\n",
    "        v = np.array(self.single_pmf(data))\n",
    "        n = v.shape[1]\n",
    "        d = self.ms_distance(n,data.shape[1])\n",
    "        \n",
    "        if not _lambda:\n",
    "            _lambda = 60/np.median(d.ravel())\n",
    "        \n",
    "        #Add variables\n",
    "        pi= []\n",
    "        t= []\n",
    "        mu = cp.Variable(n, nonneg = True)\n",
    "        for i in range(k):\n",
    "            pi.append(cp.Variable((n,n), nonneg = True))\n",
    "            t.append(cp.Variable(nonneg = True))\n",
    "            \n",
    "        obj = cp.Minimize((np.sum(t) - (1/_lambda)*np.sum(cp.sum(cp.entr(pi[i])) for i in range(k)))/k)\n",
    "        \n",
    "        #Add constraints\n",
    "        Cons=[]\n",
    "        for i in range(k):\n",
    "            Cons.append( t[i] >= (np.ones(n).T @  cp.multiply(d,pi[i]) @ np.ones(n)))#Constraint (1)\n",
    "            Cons.append( (np.ones(n) @ pi[i]).T == mu)                               #Constraint (2)\n",
    "            Cons.append( (pi[i] @ np.ones(n)) == v[i])                               #Constraint (3)\n",
    "            \n",
    "        self.prob = cp.Problem(obj, constraints= Cons)\n",
    "        self.result = self.prob.solve(solver=cp.MOSEK,\n",
    "                                      verbose = True, \n",
    "                                      mosek_params = {\"MSK_DPAR_INTPNT_CO_TOL_REL_GAP\" : relgap })\n",
    "        self.time = time.time() - start_time\n",
    "        \n",
    "        return mu.value\n",
    "    \n",
    "    def reset(self):\n",
    "        self.prob = None\n",
    "        self.result = None\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/yhk/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:116: DeprecationWarning: Calling np.sum(generator) is deprecated, and in the future will give a different result. Use np.sum(np.fromiter(generator)) or the python sum builtin instead.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "Problem\n",
      "  Name                   :                 \n",
      "  Objective sense        : min             \n",
      "  Type                   : CONIC (conic optimization problem)\n",
      "  Constraints            : 4921172         \n",
      "  Cones                  : 1229312         \n",
      "  Scalar variables       : 6147346         \n",
      "  Matrix variables       : 0               \n",
      "  Integer variables      : 0               \n",
      "\n",
      "Optimizer started.\n",
      "Presolve started.\n",
      "Linear dependency checker started.\n",
      "Linear dependency checker terminated.\n",
      "Eliminator started.\n",
      "Freed constraints in eliminator : 0\n",
      "Eliminator terminated.\n",
      "Eliminator - tries                  : 1                 time                   : 0.00            \n",
      "Lin. dep.  - tries                  : 1                 time                   : 0.94            \n",
      "Lin. dep.  - number                 : 1               \n",
      "Presolve terminated. Time: 5.52    \n",
      "Problem\n",
      "  Name                   :                 \n",
      "  Objective sense        : min             \n",
      "  Type                   : CONIC (conic optimization problem)\n",
      "  Constraints            : 4921172         \n",
      "  Cones                  : 1229312         \n",
      "  Scalar variables       : 6147346         \n",
      "  Matrix variables       : 0               \n",
      "  Integer variables      : 0               \n",
      "\n",
      "Optimizer  - threads                : 24              \n",
      "Optimizer  - solved problem         : the primal      \n",
      "Optimizer  - Constraints            : 1138\n",
      "Optimizer  - Cones                  : 1229312\n",
      "Optimizer  - Scalar variables       : 3687936           conic                  : 3687936         \n",
      "Optimizer  - Semi-definite variables: 0                 scalarized             : 0               \n",
      "Factor     - setup time             : 1.32              dense det. time        : 0.00            \n",
      "Factor     - ML order time          : 0.01              GP order time          : 0.00            \n",
      "Factor     - nonzeros before factor : 2.79e+05          after factor           : 3.41e+05        \n",
      "Factor     - dense dim.             : 0                 flops                  : 1.17e+08        \n",
      "ITE PFEAS    DFEAS    GFEAS    PRSTATUS   POBJ              DOBJ              MU       TIME  \n",
      "0   6.3e+02  5.1e+02  2.4e+07  0.00e+00   2.213290906e+07   -1.586952925e+06  1.0e+00  10.80 \n",
      "1   2.2e+02  1.8e+02  1.4e+07  -9.87e-01  1.997448687e+07   -3.251322359e+06  3.5e-01  13.53 \n",
      "2   1.4e+02  1.1e+02  1.0e+07  -8.50e-01  1.706336316e+07   -4.132584664e+06  2.2e-01  16.00 \n",
      "3   8.6e+01  6.9e+01  6.1e+06  -5.35e-01  1.255539057e+07   -4.350508595e+06  1.4e-01  18.47 \n",
      "4   3.9e+01  3.1e+01  2.3e+06  -5.91e-02  6.634396136e+06   -3.290269560e+06  6.2e-02  21.06 \n",
      "5   1.6e+01  1.3e+01  6.8e+05  4.56e-01   3.047707328e+06   -1.738025645e+06  2.5e-02  23.59 \n",
      "6   9.2e+00  7.4e+00  3.2e+05  6.93e-01   1.871307617e+06   -1.107856288e+06  1.5e-02  26.26 \n",
      "7   3.8e+00  3.0e+00  9.0e+04  7.82e-01   8.078374063e+05   -5.102762310e+05  5.9e-03  28.94 \n",
      "8   1.0e+00  8.1e-01  1.4e+04  8.51e-01   2.027566219e+05   -1.783122870e+05  1.6e-03  31.50 \n",
      "9   4.2e-01  3.4e-01  4.0e+03  8.87e-01   8.245390849e+04   -8.500024053e+04  6.6e-04  34.09 \n",
      "10  1.2e-01  9.9e-02  6.9e+02  9.00e-01   2.254812883e+04   -2.962344930e+04  2.0e-04  36.68 \n",
      "11  3.6e-02  2.9e-02  1.2e+02  9.02e-01   5.918677286e+03   -1.024336468e+04  5.7e-05  39.24 \n",
      "12  1.1e-02  8.5e-03  2.0e+01  9.00e-01   1.600641695e+03   -3.421611681e+03  1.7e-05  41.83 \n",
      "13  3.3e-03  2.6e-03  3.7e+00  9.03e-01   4.338561459e+02   -1.203297297e+03  5.2e-06  44.30 \n",
      "14  9.2e-04  7.4e-04  5.9e-01  9.15e-01   9.099180087e+01   -3.977689860e+02  1.5e-06  46.90 \n",
      "15  2.5e-04  2.0e-04  8.5e-02  9.22e-01   1.262938718e+00   -1.351900013e+02  3.9e-07  49.58 \n",
      "16  7.1e-05  5.7e-05  1.4e-02  9.31e-01   -1.815195892e+01  -5.892312187e+01  1.1e-07  52.15 \n",
      "17  1.6e-05  1.3e-05  1.6e-03  9.35e-01   -2.349893678e+01  -3.326489098e+01  2.6e-08  54.74 \n",
      "18  3.2e-06  2.6e-06  1.5e-04  9.38e-01   -2.441820572e+01  -2.642393794e+01  5.1e-09  57.33 \n",
      "19  7.5e-07  6.0e-07  1.7e-05  9.44e-01   -2.452958761e+01  -2.501494965e+01  1.2e-09  59.85 \n",
      "20  1.8e-07  1.4e-07  2.0e-06  9.49e-01   -2.454255453e+01  -2.466070613e+01  2.8e-10  62.42 \n",
      "21  3.6e-08  2.9e-08  1.9e-07  9.48e-01   -2.454079667e+01  -2.456580565e+01  5.7e-11  65.00 \n",
      "22  9.3e-09  7.5e-09  2.6e-08  9.50e-01   -2.453852207e+01  -2.454516536e+01  1.5e-11  67.53 \n",
      "23  2.3e-09  1.8e-09  3.3e-09  9.51e-01   -2.453774797e+01  -2.453943362e+01  3.6e-12  70.11 \n",
      "24  6.9e-10  5.0e-10  4.7e-10  9.51e-01   -2.453754486e+01  -2.453801407e+01  9.8e-13  72.59 \n",
      "Optimizer terminated. Time: 74.99   \n",
      "\n",
      "\n",
      "Interior-point solution summary\n",
      "  Problem status  : PRIMAL_AND_DUAL_FEASIBLE\n",
      "  Solution status : OPTIMAL\n",
      "  Primal.  obj: -2.4537544857e+01   nrm: 4e+00    Viol.  con: 1e-08    var: 0e+00    cones: 6e-12  \n",
      "  Dual.    obj: -2.4538014075e+01   nrm: 8e+02    Viol.  con: 7e-15    var: 1e-08    cones: 0e+00  \n",
      "\n",
      "Time Spent to solve problem with CVXPY: \n",
      " 102.05331134796143\n",
      "Time Spent in solver: \n",
      " 74.98805212974548\n",
      "The average Wasserstein distance between digits and the barycenter: \n",
      " -24.537544856968044\n"
     ]
    }
   ],
   "source": [
    "cvxpy_model = Wasserstein_CVXPY()\n",
    "cvxpy_result = cvxpy_model.Wasserstein_regBaryCenter(train, relgap = 1.0e-3)\n",
    "print('\\nTime Spent to solve problem with CVXPY: \\n {0}'.format(cvxpy_model.time))\n",
    "print('Time Spent in solver: \\n {0}'.format(cvxpy_model.prob.solver_stats.solve_time))\n",
    "print('The average Wasserstein distance between digits and the barycenter: \\n {0}'.format(cvxpy_model.result))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(np.reshape(cvxpy_result.squeeze(), (28,28)))\n",
    "plt.title('Barycenter')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,6))\n",
    "\n",
    "total_t50 = [fusion_model2.time, cvxpy_model.time]\n",
    "solver_t50 = [fusion_model2.M.getSolverDoubleInfo(\"optimizerTime\"), cvxpy_model.prob.solver_stats.solve_time]\n",
    "\n",
    "#Total time plot\n",
    "plt.subplot(1,2,1)\n",
    "plt.bar(['Fusion', 'CVXPY'], height= total_t50,\n",
    "        width=0.4, color=(0.3, 0.6, 0.2, 0.5))\n",
    "plt.ylabel(\"Total Time (s)\")\n",
    "plt.title(\"Comparison of Total Time\")\n",
    "\n",
    "#Solver time plot\n",
    "plt.subplot(1,2,2)\n",
    "plt.bar(['Fusion','CVXPY'], height=solver_t50,\n",
    "        width=0.4, color=(0.5, 0.6, 0.9, 0.8))\n",
    "plt.ylabel(\"Solver Time (s)\")\n",
    "plt.title(\"Comparison of Solver Time\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a rel=\"license\" href=\"http://creativecommons.org/licenses/by/4.0/\"><img alt=\"Creative Commons License\" style=\"border-width:0\" src=\"https://i.creativecommons.org/l/by/4.0/80x15.png\" /></a><br />This work is licensed under a <a rel=\"license\" href=\"http://creativecommons.org/licenses/by/4.0/\">Creative Commons Attribution 4.0 International License</a>. The **MOSEK** logo and name are trademarks of <a href=\"http://mosek.com\">Mosek ApS</a>. The code is provided as-is. Compatibility with future release of **MOSEK** or the `Fusion API` are not guaranteed. For more information contact our [support](mailto:support@mosek.com). "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}