lagrange-mulearn.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import gurobipy as gpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Academic license - for non-commercial use only - expires 2022-05-19\n",
      "Using license file /home/malchiodi/.gurobi/gurobi.lic\n"
     ]
    }
   ],
   "source": [
    "model = gpy.Model('mulearn-scaled')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "x1 = model.addVar(name=f'x1', vtype=gpy.GRB.CONTINUOUS, lb=0, ub=1)\n",
    "x2 = model.addVar(name=f'x2', vtype=gpy.GRB.CONTINUOUS, lb=0, ub=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "l0 = 200\n",
    "l1 = -200"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "x1.start = .45\n",
    "x2.start = .55"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "obj = x1**2 +x2**2 + l0 * (x1 + x2 - 1) + l1 * (1 - x1 - x2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "model.setObjective(obj, gpy.GRB.MAXIMIZE)\n",
    "#model.setParam(\"NonConvex\", 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gurobi Optimizer version 9.1.2 build v9.1.2rc0 (linux64)\n",
      "Thread count: 4 physical cores, 8 logical processors, using up to 8 threads\n",
      "Optimize a model with 0 rows, 2 columns and 0 nonzeros\n",
      "Model fingerprint: 0x9d2b64a0\n",
      "Model has 2 quadratic objective terms\n",
      "Coefficient statistics:\n",
      "  Matrix range     [0e+00, 0e+00]\n",
      "  Objective range  [4e+02, 4e+02]\n",
      "  QObjective range [2e+00, 2e+00]\n",
      "  Bounds range     [1e+00, 1e+00]\n",
      "  RHS range        [0e+00, 0e+00]\n",
      "Presolve removed 0 rows and 2 columns\n",
      "Presolve time: 0.02s\n",
      "Presolve: All rows and columns removed\n",
      "\n",
      "Barrier solved model in 0 iterations and 0.02 seconds\n",
      "Optimal objective 4.02000000e+02\n"
     ]
    }
   ],
   "source": [
    "model.update()\n",
    "model.optimize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x1.x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x2.x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "402.0"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.objVal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2022-03-22 14:25:49.149956: W tensorflow/stream_executor/platform/default/dso_loader.cc:59] Could not load dynamic library 'libcudart.so.10.1'; dlerror: libcudart.so.10.1: cannot open shared object file: No such file or directory; LD_LIBRARY_PATH: /home/malchiodi/share/gurobi811/lib:\n",
      "2022-03-22 14:25:49.149975: I tensorflow/stream_executor/cuda/cudart_stub.cc:29] Ignore above cudart dlerror if you do not have a GPU set up on your machine.\n"
     ]
    }
   ],
   "source": [
    "import tensorflow as tf\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Rifacciamo tutto"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Rilassamento lineare del vincolo di = e forma quadratica sviluppata"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# E' QUELLO GIUSTO\n",
    "\n",
    "from tensorflow.keras.optimizers import Adam\n",
    "\n",
    "def solve_problem(Q, q, A, b, C, d,\n",
    "                  max_iter=1000,\n",
    "                  max_gap=1E-4,\n",
    "                  alpha_0=1E-1,\n",
    "                  window_width=30,\n",
    "                  learning_rate=1E-2,\n",
    "                  verbose=False):\n",
    "    '''Solves the lagrangian relaxation for a constrained optimization\n",
    "    problem and returns its result. The structure of the primal problem\n",
    "    is the following\n",
    "    \n",
    "    min x.T Q x + q.T x\n",
    "    subject to\n",
    "    A x = b\n",
    "    C x <= d\n",
    "    \n",
    "    where .T denotes the transposition operator. Optimization takes place\n",
    "    in a iterated two-steps procedure: an outer process devoted to modifying\n",
    "    the values of the lagrange multipliers, and an inner process working on\n",
    "    the primal variables.\n",
    "    \n",
    "    The arguments are as follows, given n as the number of variables of\n",
    "    the primal problem (i.e., the length of x)\n",
    "    \n",
    "    - Q: n x n matrix containing the quadratic coefficients of the cost\n",
    "      function;\n",
    "    - q: vector containing the n linear coefficients of the cost function\n",
    "    - A: s x n matrix containing the coefficients of the = constraints\n",
    "    - b: vector containing the s right members of the = constraints\n",
    "    - C: t x n matrix containing the coefficients of the <= constraings\n",
    "    - d: vector containing the t right members of the <= coefficients\n",
    "    - max_iter: maximum number of iterations of the *outer* optimization\n",
    "      procedure\n",
    "    - max_gap: maximum gap between primal and dual objectives ensuring\n",
    "      premature end of the *outer* optimization procedure\n",
    "    - alpha_0: initial value of the learning rate in the *outer* optimization\n",
    "      procedure\n",
    "    - window_width: width of the moving window on the objective function for\n",
    "      the *inner* optimization process\n",
    "    - verbose: boolean flag triggering verbose output\n",
    "    \n",
    "    returns\n",
    "    '''\n",
    "    \n",
    "    optimizer = Adam(learning_rate=10**-2)\n",
    "\n",
    "    x = tf.Variable(np.random.random(len(q)),\n",
    "                    name='x',\n",
    "                    trainable=True,\n",
    "                    dtype=tf.float32)\n",
    "    Q = tf.constant(np.array(Q), dtype='float32')\n",
    "    q = tf.constant(np.array(q), dtype='float32')\n",
    "    \n",
    "    A = np.array(A)\n",
    "    s = len(A)\n",
    "    C = np.array(C)\n",
    "    b = np.array(b)\n",
    "    d = np.array(d)\n",
    "    \n",
    "    M = np.vstack([A, -A, C])\n",
    "    m = np.hstack([b, -b, d])\n",
    "    lambda_ = tf.constant(np.random.random(len(m)), dtype='float32')\n",
    "    \n",
    "    M = tf.constant(M, dtype='float32')\n",
    "    m = tf.constant(m, dtype='float32')\n",
    "\n",
    "    \n",
    "    def original_objective():\n",
    "        def obj():\n",
    "            return tf.tensordot(tf.linalg.matvec(Q, x), x, axes=1) + \\\n",
    "                   tf.tensordot(q, x, axes=1)\n",
    "        return obj\n",
    "\n",
    "    def lagrangian_objective(lambda_):\n",
    "        def obj():\n",
    "            return tf.tensordot(tf.linalg.matvec(Q, x), x, axes=1) + \\\n",
    "                   tf.tensordot(q, x, axes=1) + \\\n",
    "                   tf.tensordot(lambda_, m - tf.linalg.matvec(M, x), axes=1)\n",
    "        return obj\n",
    "\n",
    "    obj_val = []\n",
    "    lagr_val = []\n",
    "    gap_val = []\n",
    "    gap = max_gap + 1\n",
    "\n",
    "    num_bad_iterations = 0\n",
    "    prev_orig = np.inf\n",
    "\n",
    "    i = 0\n",
    "    \n",
    "    while i < max_iter and (gap<0 or gap > max_gap):\n",
    "        lagr_obj = lagrangian_objective(lambda_)\n",
    "        orig_obj = original_objective()\n",
    "        prev_lagr = 10*3\n",
    "        curr_lagr = 0\n",
    "        vals = []\n",
    "        t = 0\n",
    "        window_width = 30\n",
    "        window = list(np.logspace(1, window_width, window_width))\n",
    "        # this is to ensure a high value for the standard deviation\n",
    "        # of the elements to which the window has been initialized \n",
    "        \n",
    "        while (np.std(window)/abs(np.mean(window)) > 0.001 or t < 100) \\\n",
    "              and t < 1000:\n",
    "            optimizer.minimize(lagr_obj, var_list=x)\n",
    "            prev_lagr = curr_lagr\n",
    "            curr_lagr = lagr_obj().numpy()\n",
    "            vals.append(curr_lagr)\n",
    "            t += 1\n",
    "            window = window[1:]\n",
    "            window.append(curr_lagr)\n",
    "        \n",
    "        curr_orig = orig_obj().numpy()\n",
    "        if curr_orig < prev_orig:\n",
    "            num_bad_iterations += 1\n",
    "\n",
    "        prev_orig = curr_orig\n",
    "\n",
    "        \n",
    "        obj_val.append(curr_orig)\n",
    "        lagr_val.append(curr_lagr)\n",
    "        \n",
    "        subgradient = (m - tf.linalg.matvec(M, x)).numpy()\n",
    "        gap = tf.tensordot(lambda_[:2*s], m[:2*s] - \\\n",
    "              tf.linalg.matvec(M[:2*s], x), axes=1).numpy()\n",
    "        gap_val.append(gap)\n",
    "        \n",
    "        if verbose and i%10 == 0:\n",
    "            print(f'i={i}, dual={lagr_obj().numpy():.3f}, '\n",
    "                  f'prim={orig_obj().numpy():.3f}, gap={gap:.6f}')\n",
    "        \n",
    "        alpha = alpha_0 / num_bad_iterations\n",
    "        lambda_ = tf.maximum(0, lambda_ + alpha * subgradient)\n",
    "\n",
    "        i += 1\n",
    "\n",
    "    return obj_val, lagr_val, x, lambda_, gap_val\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2022-03-22 14:26:16.553431: W tensorflow/stream_executor/platform/default/dso_loader.cc:59] Could not load dynamic library 'libcuda.so.1'; dlerror: libcuda.so.1: cannot open shared object file: No such file or directory; LD_LIBRARY_PATH: /home/malchiodi/share/gurobi811/lib:\n",
      "2022-03-22 14:26:16.553531: W tensorflow/stream_executor/cuda/cuda_driver.cc:312] failed call to cuInit: UNKNOWN ERROR (303)\n",
      "2022-03-22 14:26:16.553580: I tensorflow/stream_executor/cuda/cuda_diagnostics.cc:156] kernel driver does not appear to be running on this host (malchiodi): /proc/driver/nvidia/version does not exist\n",
      "2022-03-22 14:26:16.554414: I tensorflow/core/platform/cpu_feature_guard.cc:142] This TensorFlow binary is optimized with oneAPI Deep Neural Network Library (oneDNN)to use the following CPU instructions in performance-critical operations:  AVX2 FMA\n",
      "To enable them in other operations, rebuild TensorFlow with the appropriate compiler flags.\n",
      "2022-03-22 14:26:16.592241: I tensorflow/core/platform/profile_utils/cpu_utils.cc:104] CPU Frequency: 3399905000 Hz\n",
      "2022-03-22 14:26:16.592463: I tensorflow/compiler/xla/service/service.cc:168] XLA service 0x55c6a1b40b50 initialized for platform Host (this does not guarantee that XLA will be used). Devices:\n",
      "2022-03-22 14:26:16.592478: I tensorflow/compiler/xla/service/service.cc:176]   StreamExecutor device (0): Host, Default Version\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "i=0, dual=1.893, prim=0.094, gap=0.397250\n",
      "i=10, dual=3.144, prim=0.455, gap=0.048821\n",
      "i=20, dual=4.149, prim=0.495, gap=0.005372\n",
      "i=30, dual=5.149, prim=0.499, gap=0.000574\n"
     ]
    }
   ],
   "source": [
    "Q = [[1, 0], [0, 1]]\n",
    "q = [0, 0]\n",
    "A = [[1, 1]]\n",
    "b = [1]\n",
    "C = [[-1, -1], [1, 0], [0, 1], [-1, 0], [0, -1]]\n",
    "d = [-1, 1, 1, 0, 0]\n",
    "\n",
    "obj_val, lagr_val, x, lambda_, gap = solve_problem(Q, q, A, b, C, d, max_gap=10**-4, verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.plot(np.arange(1, len(obj_val)+1), obj_val, label='primal')\n",
    "# plt.plot(np.arange(1, len(lagr_val)+1), lagr_val, label='dual')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.arange(1, len(gap)+1), gap, label='gap')\n",
    "plt.ylim(0, 0.3)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.50239414, 0.49750745], dtype=float32)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4999135"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "obj_val[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.771578e-05"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gap[-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Facciamo una prova passo passo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "xs = np.array([[-2.68412563,  0.31939725],\n",
    "       [-2.71414169, -0.17700123],\n",
    "       [-2.88899057, -0.14494943],\n",
    "       [-2.74534286, -0.31829898],\n",
    "       [-2.72871654,  0.32675451],\n",
    "       [-2.28085963,  0.74133045],\n",
    "       [-2.82053775, -0.08946138],\n",
    "       [-2.62614497,  0.16338496],\n",
    "       [-2.88638273, -0.57831175],\n",
    "       [-2.6727558 , -0.11377425],\n",
    "       [-2.50694709,  0.6450689 ],\n",
    "       [-2.61275523,  0.01472994],\n",
    "       [-2.78610927, -0.235112  ],\n",
    "       [-3.22380374, -0.51139459],\n",
    "       [-2.64475039,  1.17876464],\n",
    "       [-2.38603903,  1.33806233],\n",
    "       [-2.62352788,  0.81067951],\n",
    "       [-2.64829671,  0.31184914],\n",
    "       [-2.19982032,  0.87283904],\n",
    "       [-2.5879864 ,  0.51356031],\n",
    "       [-2.31025622,  0.39134594],\n",
    "       [-2.54370523,  0.43299606],\n",
    "       [-3.21593942,  0.13346807],\n",
    "       [-2.30273318,  0.09870885],\n",
    "       [-2.35575405, -0.03728186],\n",
    "       [-2.50666891, -0.14601688],\n",
    "       [-2.46882007,  0.13095149],\n",
    "       [-2.56231991,  0.36771886],\n",
    "       [-2.63953472,  0.31203998],\n",
    "       [-2.63198939, -0.19696122],\n",
    "       [-2.58739848, -0.20431849],\n",
    "       [-2.4099325 ,  0.41092426],\n",
    "       [-2.64886233,  0.81336382],\n",
    "       [-2.59873675,  1.09314576],\n",
    "       [-2.63692688, -0.12132235],\n",
    "       [-2.86624165,  0.06936447],\n",
    "       [-2.62523805,  0.59937002],\n",
    "       [-2.80068412,  0.26864374],\n",
    "       [-2.98050204, -0.48795834],\n",
    "       [-2.59000631,  0.22904384],\n",
    "       [-2.77010243,  0.26352753],\n",
    "       [-2.84936871, -0.94096057],\n",
    "       [-2.99740655, -0.34192606],\n",
    "       [-2.40561449,  0.18887143],\n",
    "       [-2.20948924,  0.43666314],\n",
    "       [-2.71445143, -0.2502082 ],\n",
    "       [-2.53814826,  0.50377114],\n",
    "       [-2.83946217, -0.22794557],\n",
    "       [-2.54308575,  0.57941002],\n",
    "       [-2.70335978,  0.10770608],\n",
    "       [ 1.28482569,  0.68516047],\n",
    "       [ 0.93248853,  0.31833364],\n",
    "       [ 1.46430232,  0.50426282],\n",
    "       [ 0.18331772, -0.82795901],\n",
    "       [ 1.08810326,  0.07459068],\n",
    "       [ 0.64166908, -0.41824687],\n",
    "       [ 1.09506066,  0.28346827],\n",
    "       [-0.74912267, -1.00489096],\n",
    "       [ 1.04413183,  0.2283619 ],\n",
    "       [-0.0087454 , -0.72308191],\n",
    "       [-0.50784088, -1.26597119],\n",
    "       [ 0.51169856, -0.10398124],\n",
    "       [ 0.26497651, -0.55003646],\n",
    "       [ 0.98493451, -0.12481785],\n",
    "       [-0.17392537, -0.25485421],\n",
    "       [ 0.92786078,  0.46717949],\n",
    "       [ 0.66028376, -0.35296967],\n",
    "       [ 0.23610499, -0.33361077],\n",
    "       [ 0.94473373, -0.54314555],\n",
    "       [ 0.04522698, -0.58383438],\n",
    "       [ 1.11628318, -0.08461685],\n",
    "       [ 0.35788842, -0.06892503],\n",
    "       [ 1.29818388, -0.32778731],\n",
    "       [ 0.92172892, -0.18273779],\n",
    "       [ 0.71485333,  0.14905594],\n",
    "       [ 0.90017437,  0.32850447],\n",
    "       [ 1.33202444,  0.24444088],\n",
    "       [ 1.55780216,  0.26749545],\n",
    "       [ 0.81329065, -0.1633503 ],\n",
    "       [-0.30558378, -0.36826219],\n",
    "       [-0.06812649, -0.70517213],\n",
    "       [-0.18962247, -0.68028676],\n",
    "       [ 0.13642871, -0.31403244],\n",
    "       [ 1.38002644, -0.42095429],\n",
    "       [ 0.58800644, -0.48428742],\n",
    "       [ 0.80685831,  0.19418231],\n",
    "       [ 1.22069088,  0.40761959],\n",
    "       [ 0.81509524, -0.37203706],\n",
    "       [ 0.24595768, -0.2685244 ],\n",
    "       [ 0.16641322, -0.68192672],\n",
    "       [ 0.46480029, -0.67071154],\n",
    "       [ 0.8908152 , -0.03446444],\n",
    "       [ 0.23054802, -0.40438585],\n",
    "       [-0.70453176, -1.01224823],\n",
    "       [ 0.35698149, -0.50491009],\n",
    "       [ 0.33193448, -0.21265468],\n",
    "       [ 0.37621565, -0.29321893],\n",
    "       [ 0.64257601,  0.01773819],\n",
    "       [-0.90646986, -0.75609337],\n",
    "       [ 0.29900084, -0.34889781],\n",
    "       [ 2.53119273, -0.00984911],\n",
    "       [ 1.41523588, -0.57491635],\n",
    "       [ 2.61667602,  0.34390315],\n",
    "       [ 1.97153105, -0.1797279 ],\n",
    "       [ 2.35000592, -0.04026095],\n",
    "       [ 3.39703874,  0.55083667],\n",
    "       [ 0.52123224, -1.19275873],\n",
    "       [ 2.93258707,  0.3555    ],\n",
    "       [ 2.32122882, -0.2438315 ],\n",
    "       [ 2.91675097,  0.78279195],\n",
    "       [ 1.66177415,  0.24222841],\n",
    "       [ 1.80340195, -0.21563762],\n",
    "       [ 2.1655918 ,  0.21627559],\n",
    "       [ 1.34616358, -0.77681835],\n",
    "       [ 1.58592822, -0.53964071],\n",
    "       [ 1.90445637,  0.11925069],\n",
    "       [ 1.94968906,  0.04194326],\n",
    "       [ 3.48705536,  1.17573933],\n",
    "       [ 3.79564542,  0.25732297],\n",
    "       [ 1.30079171, -0.76114964],\n",
    "       [ 2.42781791,  0.37819601],\n",
    "       [ 1.19900111, -0.60609153],\n",
    "       [ 3.49992004,  0.4606741 ],\n",
    "       [ 1.38876613, -0.20439933],\n",
    "       [ 2.2754305 ,  0.33499061],\n",
    "       [ 2.61409047,  0.56090136],\n",
    "       [ 1.25850816, -0.17970479],\n",
    "       [ 1.29113206, -0.11666865],\n",
    "       [ 2.12360872, -0.20972948],\n",
    "       [ 2.38800302,  0.4646398 ],\n",
    "       [ 2.84167278,  0.37526917],\n",
    "       [ 3.23067366,  1.37416509],\n",
    "       [ 2.15943764, -0.21727758],\n",
    "       [ 1.44416124, -0.14341341],\n",
    "       [ 1.78129481, -0.49990168],\n",
    "       [ 3.07649993,  0.68808568],\n",
    "       [ 2.14424331,  0.1400642 ],\n",
    "       [ 1.90509815,  0.04930053],\n",
    "       [ 1.16932634, -0.16499026],\n",
    "       [ 2.10761114,  0.37228787],\n",
    "       [ 2.31415471,  0.18365128],\n",
    "       [ 1.9222678 ,  0.40920347],\n",
    "       [ 1.41523588, -0.57491635],\n",
    "       [ 2.56301338,  0.2778626 ],\n",
    "       [ 2.41874618,  0.3047982 ],\n",
    "       [ 1.94410979,  0.1875323 ],\n",
    "       [ 1.52716661, -0.37531698],\n",
    "       [ 1.76434572,  0.07885885],\n",
    "       [ 1.90094161,  0.11662796],\n",
    "       [ 1.39018886, -0.28266094]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "mus = np.array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "       0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
    "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
    "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
    "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_setosa = xs[:50]\n",
    "y_setosa = mus[:50]\n",
    "x_virginica = xs[50:100]\n",
    "y_virginica = mus[50:100]\n",
    "x_versicolor = xs[100:]\n",
    "y_versicolor = mus[100:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.scatter(*x_versicolor.T, c=y_versicolor)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mulearn.kernel import GaussianKernel\n",
    "\n",
    "k = GaussianKernel()\n",
    "\n",
    "c = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "m = len(xs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "import tensorflow as tf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {},
   "outputs": [],
   "source": [
    "alphas = [tf.Variable(ch, name=f'alpha_{i}', trainable=True, dtype=tf.float32)\n",
    "          for i, ch in enumerate(np.random.uniform(-0.1, 0.1, m))]\n",
    "betas = [tf.Variable(ch, name=f'beta_{i}', trainable=True, dtype=tf.float32)\n",
    "         for i, ch in enumerate(np.random.uniform(-0.1, 0.1, m))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {},
   "outputs": [],
   "source": [
    "gram = np.array([[k.compute(x1, x2) for x2 in xs] for x1 in xs])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = alphas + betas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [],
   "source": [
    "K11 = np.array([[-mu_i * mu_j for mu_j in mus] for mu_i in mus]) * gram\n",
    "K00 = np.array([[-(1-mu_i) * (1 - mu_j) for mu_j in mus] for mu_i in mus]) * gram\n",
    "K01 = np.array([[2 * mu_i * (1-mu_j) for mu_j in mus] for mu_i in mus]) * gram\n",
    "Z = np.zeros((m, m))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [],
   "source": [
    "Q = -np.vstack((np.hstack((K11, K01)), np.hstack((Z, K00))))\n",
    "q = -np.hstack((np.diag(gram) * mus, np.diag(gram) * (1 - mus)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.array([np.hstack((mus, 1-mus))])\n",
    "b = np.array([1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {},
   "outputs": [],
   "source": [
    "C = np.vstack((np.hstack((np.identity(m), np.zeros((m, m)))),\n",
    "               np.hstack((np.zeros((m, m)), -np.identity(m)))))\n",
    "d = np.hstack((np.zeros(m), - c * np.ones(m)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.random.random(2*m)\n",
    "assert(Q.shape == (2*m, 2*m))\n",
    "assert(len(q) == 2*m)\n",
    "assert(type(x @ (Q @ x) + q @ x) is np.float64)\n",
    "\n",
    "assert(A.shape == (1, 2*m))\n",
    "assert(len(b) == 1)\n",
    "assert(type(A@x - b) == np.ndarray)\n",
    "assert(len(A@x - b) == 1)\n",
    "\n",
    "assert(C.shape == (2*m, 2*m))\n",
    "assert(len(d) == 2*m)\n",
    "assert(type(C @ x - d) == np.ndarray)\n",
    "assert(len(C @ x - d) == 2*m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "from tensorflow.keras.optimizers import Adam\n",
    "\n",
    "def solve_lagrange_relaxation(Q, q, A, b, C, d,\n",
    "                  max_iter=1000,\n",
    "                  max_gap=10**-4,\n",
    "                  alpha_0 = 10**-1,\n",
    "                  window_width = 30,\n",
    "                  verbose=False):\n",
    "    \"\"\"Solves the lagrangian relaxation for a constrained optimization\n",
    "    problem and returns its result. The structure of the primal problem\n",
    "    is the following\n",
    "    \n",
    "    min x.T Q x + q.T x\n",
    "    subject to\n",
    "    A x = b\n",
    "    C x <= d\n",
    "    \n",
    "    where .T denotes the transposition operator. Optimization takes place\n",
    "    in a iterated two-steps procedure: an outer process devoted to modifying\n",
    "    the values of the lagrange multipliers, and an inner process working on\n",
    "    the primal variables.\n",
    "    \n",
    "    The arguments are as follows, given n as the number of variables of\n",
    "    the primal problem (i.e., the length of x)\n",
    "    \n",
    "    - Q: n x n matrix containing the quadratic coefficients of the cost\n",
    "    function;\n",
    "    - q: vector containing the n linear coefficients of the cost function\n",
    "    - A: s x n matrix containing the coefficients of the = constraints\n",
    "    - b: vector containing the s right members of the = constraints\n",
    "    - C: t x n matrix containing the coefficients of the <= constraings\n",
    "    - d: vector containing the t right members of the <= coefficients\n",
    "    - max_iter: maximum number of iterations of the *outer* optimization\n",
    "    procedure\n",
    "    - max_gap: maximum gap between primal and dual objectives ensuring\n",
    "    premature end of the *outer* optimization procedure\n",
    "    - alpha_0: initial value of the learning rate in the *outer* optimization\n",
    "    procedure\n",
    "    - window_width: width of the moving window on the objective function for\n",
    "    the *inner* optimization process\n",
    "    - verbose: boolean flag triggering verbose output\n",
    "    \n",
    "    returns\n",
    "    \"\"\"\n",
    "\n",
    "    #TODO add possibility to specify initial values\n",
    "\n",
    "    x = tf.Variable(np.random.random(len(q)),\n",
    "                    name='x',\n",
    "                    trainable=True,\n",
    "                    dtype=tf.float32)\n",
    "    Q = tf.constant(np.array(Q), dtype='float32')\n",
    "    q = tf.constant(np.array(q), dtype='float32')\n",
    "    \n",
    "    A = np.array(A)\n",
    "    s = len(A)\n",
    "    C = np.array(C)\n",
    "    b = np.array(b)\n",
    "    d = np.array(d)\n",
    "    \n",
    "    M = np.vstack([A, -A, C])\n",
    "    m = np.hstack([b, -b, d])\n",
    "    lambda_ = tf.constant(np.random.random(len(m)), dtype='float32')\n",
    "    \n",
    "    M = tf.constant(M, dtype='float32')\n",
    "    m = tf.constant(m, dtype='float32')\n",
    "\n",
    "    \n",
    "    def original_objective():\n",
    "        def obj():\n",
    "            return tf.tensordot(tf.linalg.matvec(Q, x), x, axes=1) + \\\n",
    "                tf.tensordot(q, x, axes=1)\n",
    "        return obj\n",
    "\n",
    "    def lagrangian_objective(lambda_):\n",
    "        def obj():\n",
    "            return tf.tensordot(tf.linalg.matvec(Q, x), x, axes=1) + \\\n",
    "                tf.tensordot(q, x, axes=1) + \\\n",
    "                tf.tensordot(lambda_, m - tf.linalg.matvec(M, x), axes=1)\n",
    "        return obj\n",
    "\n",
    "    obj_val = []\n",
    "    lagr_val = []\n",
    "    gap_val = []\n",
    "    gap = max_gap + 1\n",
    "\n",
    "    num_bad_iterations = 0\n",
    "    prev_orig = np.inf\n",
    "\n",
    "    i = 0\n",
    "    \n",
    "    while i < max_iter and (gap<0 or gap > max_gap):\n",
    "        lagr_obj = lagrangian_objective(lambda_)\n",
    "        orig_obj = original_objective()\n",
    "        prev_lagr = 10*3\n",
    "        curr_lagr = 0\n",
    "        vals = []\n",
    "        t = 0\n",
    "        window_width = 30\n",
    "        window = list(np.logspace(1, window_width, window_width))\n",
    "        # this is to ensure a high value for the standard deviation\n",
    "        # of the elements to which the window has been initialized \n",
    "        \n",
    "        while (np.std(window)/abs(np.mean(window)) > 0.001 or t < 100) \\\n",
    "            and t < 1000:\n",
    "            optimizer.minimize(lagr_obj, var_list=x)\n",
    "            prev_lagr = curr_lagr\n",
    "            curr_lagr = lagr_obj().numpy()\n",
    "            vals.append(curr_lagr)\n",
    "            t += 1\n",
    "            window = window[1:]\n",
    "            window.append(curr_lagr)\n",
    "        \n",
    "        curr_orig = orig_obj().numpy()\n",
    "        if curr_orig < prev_orig:\n",
    "            num_bad_iterations += 1\n",
    "\n",
    "        prev_orig = curr_orig\n",
    "\n",
    "        \n",
    "        obj_val.append(curr_orig)\n",
    "        lagr_val.append(curr_lagr)\n",
    "        \n",
    "        subgradient = (m - tf.linalg.matvec(M, x)).numpy()\n",
    "        gap = tf.tensordot(lambda_[:2*s], m[:2*s] - \\\n",
    "            tf.linalg.matvec(M[:2*s], x), axes=1).numpy()\n",
    "        gap_val.append(gap)\n",
    "        \n",
    "        if verbose and i%10 == 0:\n",
    "            print(f'i={i}, dual={lagr_obj().numpy():.3f}, '\n",
    "                f'prim={orig_obj().numpy():.3f}, '\n",
    "                f'gap={gap:.6f}')\n",
    "        \n",
    "        alpha = alpha_0 / num_bad_iterations\n",
    "        lambda_ = tf.maximum(0, lambda_ + alpha * subgradient)\n",
    "\n",
    "        i += 1\n",
    "\n",
    "    return obj_val, lagr_val, x, lambda_, gap_val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'optimizer' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-28-963def183f2b>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0msol\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msolve_lagrange_relaxation\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mQ\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mq\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mA\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mC\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0md\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mverbose\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m<ipython-input-27-68da92045314>\u001b[0m in \u001b[0;36msolve_lagrange_relaxation\u001b[0;34m(Q, q, A, b, C, d, max_iter, max_gap, alpha_0, window_width, verbose)\u001b[0m\n\u001b[1;32m    105\u001b[0m         \u001b[0;32mwhile\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mwindow\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mabs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmean\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mwindow\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m0.001\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mt\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0;36m100\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;31m \u001b[0m\u001b[0;31m\\\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    106\u001b[0m             \u001b[0;32mand\u001b[0m \u001b[0mt\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0;36m1000\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 107\u001b[0;31m             \u001b[0moptimizer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mminimize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlagr_obj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvar_list\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    108\u001b[0m             \u001b[0mprev_lagr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcurr_lagr\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    109\u001b[0m             \u001b[0mcurr_lagr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlagr_obj\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnumpy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'optimizer' is not defined"
     ]
    }
   ],
   "source": [
    "sol = solve_lagrange_relaxation(Q, q, A, b, C, d, verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mulearn import FuzzyInductor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "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>Sepal length</th>\n",
       "      <th>Sepal width</th>\n",
       "      <th>Petal length</th>\n",
       "      <th>Petal width</th>\n",
       "      <th>Class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Sepal length  Sepal width  Petal length  Petal width   Class\n",
       "0           5.1          3.5           1.4          0.2  Setosa\n",
       "1           4.9          3.0           1.4          0.2  Setosa\n",
       "2           4.7          3.2           1.3          0.2  Setosa\n",
       "3           4.6          3.1           1.5          0.2  Setosa\n",
       "4           5.0          3.6           1.4          0.2  Setosa"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sklearn.datasets as ds\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "iris_X, iris_y = ds.load_iris(return_X_y=True)\n",
    "labels = (\"Setosa\", \"Versicolor\", \"Virginica\")\n",
    "\n",
    "df = pd.DataFrame(iris_X, columns=[\"Sepal length\", \"Sepal width\",\n",
    "                                   \"Petal length\", \"Petal width\"])\n",
    "df['Class'] = iris_y\n",
    "df['Class'] = df['Class'].map(lambda c: labels[c])\n",
    "\n",
    "n = 20\n",
    "filt = list(range(n)) + list(range(50, 50+n)) + list(range(100, 100+n))\n",
    "df = df.iloc[filt]\n",
    "\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "pca_2d = PCA(n_components=2)\n",
    "iris_X_2d = pca_2d.fit_transform(iris_X)\n",
    "\n",
    "iris_versicolor = iris_y.copy()\n",
    "iris_versicolor[iris_versicolor==2] = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "i=0, dual=102.827, prim=242.129, gap=-55.414356\n",
      "i=1, dual=357.986, prim=116.948, gap=323.034851\n",
      "i=2, dual=253.775, prim=46.308, gap=291.154755\n",
      "i=3, dual=100.325, prim=11.752, gap=174.763428\n",
      "i=4, dual=-47.801, prim=5.365, gap=35.609734\n",
      "i=5, dual=-171.988, prim=21.899, gap=-102.683548\n",
      "i=6, dual=-258.151, prim=55.199, gap=-220.886414\n",
      "i=7, dual=-294.699, prim=94.927, gap=-297.112335\n",
      "i=8, dual=-277.160, prim=119.558, gap=-306.029297\n",
      "i=9, dual=-216.890, prim=119.703, gap=-252.049225\n",
      "i=10, dual=-157.622, prim=114.367, gap=-193.186325\n",
      "i=11, dual=-122.937, prim=84.535, gap=-130.854065\n",
      "i=12, dual=-99.620, prim=61.755, gap=-86.653015\n",
      "i=13, dual=-84.435, prim=45.044, gap=-56.396461\n",
      "i=14, dual=-74.877, prim=33.098, gap=-36.320381\n",
      "i=15, dual=-68.864, prim=24.702, gap=-23.322838\n",
      "i=16, dual=-65.050, prim=18.826, gap=-15.028122\n",
      "i=17, dual=-62.515, prim=14.656, gap=-9.747955\n",
      "i=18, dual=-60.734, prim=11.625, gap=-6.371319\n",
      "i=19, dual=-59.380, prim=9.372, gap=-4.202564\n",
      "i=20, dual=-58.285, prim=7.657, gap=-2.798264\n",
      "i=21, dual=-57.270, prim=6.334, gap=-1.884737\n",
      "i=22, dual=-56.282, prim=5.296, gap=-1.283327\n",
      "i=23, dual=-55.285, prim=4.477, gap=-0.883704\n",
      "i=24, dual=-54.259, prim=3.836, gap=-0.616013\n",
      "i=25, dual=-53.223, prim=3.317, gap=-0.429999\n",
      "i=26, dual=-52.210, prim=2.900, gap=-0.298912\n",
      "i=27, dual=-51.305, prim=2.501, gap=-0.189784\n",
      "i=28, dual=-50.460, prim=2.120, gap=-0.096897\n",
      "i=29, dual=-49.669, prim=1.759, gap=-0.015111\n",
      "i=30, dual=-48.924, prim=1.416, gap=0.059783\n",
      "i=31, dual=-48.252, prim=1.090, gap=0.131044\n",
      "i=32, dual=-47.598, prim=0.782, gap=0.201102\n",
      "i=33, dual=-46.964, prim=0.491, gap=0.271690\n",
      "i=34, dual=-46.350, prim=0.215, gap=0.343968\n",
      "i=35, dual=-45.751, prim=-0.045, gap=0.418635\n",
      "i=36, dual=-45.179, prim=-0.291, gap=0.496066\n",
      "i=37, dual=-44.631, prim=-0.523, gap=0.576364\n",
      "i=38, dual=-44.088, prim=-0.741, gap=0.659424\n",
      "i=39, dual=-43.549, prim=-0.946, gap=0.744993\n",
      "i=40, dual=-43.019, prim=-1.139, gap=0.832706\n",
      "i=41, dual=-42.512, prim=-1.319, gap=0.922133\n",
      "i=42, dual=-42.011, prim=-1.489, gap=1.012787\n",
      "i=43, dual=-41.513, prim=-1.647, gap=1.104158\n",
      "i=44, dual=-41.022, prim=-1.794, gap=1.195717\n",
      "i=45, dual=-40.548, prim=-1.932, gap=1.286928\n",
      "i=46, dual=-40.086, prim=-2.060, gap=1.377289\n",
      "i=47, dual=-39.627, prim=-2.178, gap=1.466337\n",
      "i=48, dual=-39.172, prim=-2.288, gap=1.553637\n",
      "i=49, dual=-38.722, prim=-2.389, gap=1.638805\n",
      "i=50, dual=-38.283, prim=-2.482, gap=1.721504\n",
      "i=51, dual=-37.861, prim=-2.568, gap=1.801447\n",
      "i=52, dual=-37.456, prim=-2.646, gap=1.878403\n",
      "i=53, dual=-37.077, prim=-2.718, gap=1.952188\n",
      "i=54, dual=-36.712, prim=-2.783, gap=2.022676\n",
      "i=55, dual=-36.352, prim=-2.842, gap=2.089769\n",
      "i=56, dual=-36.001, prim=-2.895, gap=2.153358\n",
      "i=57, dual=-35.657, prim=-2.943, gap=2.213497\n",
      "i=58, dual=-35.330, prim=-2.986, gap=2.270239\n",
      "i=59, dual=-35.024, prim=-3.024, gap=2.323643\n",
      "i=60, dual=-34.722, prim=-3.058, gap=2.373789\n",
      "i=61, dual=-34.423, prim=-3.087, gap=2.420769\n",
      "i=62, dual=-34.127, prim=-3.113, gap=2.464689\n",
      "i=63, dual=-33.839, prim=-3.135, gap=2.505657\n",
      "i=64, dual=-33.567, prim=-3.153, gap=2.543791\n",
      "i=65, dual=-33.302, prim=-3.168, gap=2.579197\n",
      "i=66, dual=-33.041, prim=-3.180, gap=2.611988\n",
      "i=67, dual=-32.791, prim=-3.188, gap=2.642267\n",
      "i=68, dual=-32.548, prim=-3.194, gap=2.670128\n",
      "i=69, dual=-32.316, prim=-3.198, gap=2.695648\n",
      "i=70, dual=-32.088, prim=-3.198, gap=2.718908\n",
      "i=71, dual=-31.867, prim=-3.197, gap=2.739965\n",
      "i=72, dual=-31.651, prim=-3.192, gap=2.758808\n",
      "i=73, dual=-31.438, prim=-3.184, gap=2.775248\n",
      "i=74, dual=-31.236, prim=-3.173, gap=2.789143\n",
      "i=75, dual=-31.048, prim=-3.159, gap=2.800364\n",
      "i=76, dual=-30.855, prim=-3.142, gap=2.808788\n",
      "i=77, dual=-30.658, prim=-3.122, gap=2.814295\n",
      "i=78, dual=-30.456, prim=-3.098, gap=2.816776\n",
      "i=79, dual=-30.253, prim=-3.071, gap=2.816120\n",
      "i=80, dual=-30.062, prim=-3.042, gap=2.812227\n",
      "i=81, dual=-29.870, prim=-3.009, gap=2.804981\n",
      "i=82, dual=-29.694, prim=-2.972, gap=2.794244\n",
      "i=83, dual=-29.520, prim=-2.933, gap=2.779980\n",
      "i=84, dual=-29.344, prim=-2.891, gap=2.762155\n",
      "i=85, dual=-29.170, prim=-2.845, gap=2.740760\n",
      "i=86, dual=-29.004, prim=-2.797, gap=2.715786\n",
      "i=87, dual=-28.839, prim=-2.745, gap=2.687339\n",
      "i=88, dual=-28.675, prim=-2.691, gap=2.655489\n",
      "i=89, dual=-28.508, prim=-2.635, gap=2.620356\n",
      "i=90, dual=-28.337, prim=-2.576, gap=2.582095\n",
      "i=91, dual=-28.166, prim=-2.516, gap=2.540893\n",
      "i=92, dual=-27.994, prim=-2.453, gap=2.496970\n",
      "i=93, dual=-27.819, prim=-2.389, gap=2.450566\n",
      "i=94, dual=-27.640, prim=-2.323, gap=2.401936\n",
      "i=95, dual=-27.458, prim=-2.257, gap=2.351343\n",
      "i=96, dual=-27.273, prim=-2.190, gap=2.299050\n",
      "i=97, dual=-27.090, prim=-2.122, gap=2.245315\n",
      "i=98, dual=-26.909, prim=-2.053, gap=2.190396\n",
      "i=99, dual=-26.727, prim=-1.985, gap=2.134537\n",
      "i=100, dual=-26.550, prim=-1.917, gap=2.077958\n",
      "i=101, dual=-26.376, prim=-1.849, gap=2.020878\n",
      "i=102, dual=-26.207, prim=-1.781, gap=1.963439\n",
      "i=103, dual=-26.035, prim=-1.714, gap=1.905914\n",
      "i=104, dual=-25.868, prim=-1.648, gap=1.848465\n",
      "i=105, dual=-25.698, prim=-1.582, gap=1.791244\n",
      "i=106, dual=-25.525, prim=-1.518, gap=1.734370\n",
      "i=107, dual=-25.348, prim=-1.455, gap=1.677982\n",
      "i=108, dual=-25.168, prim=-1.392, gap=1.622192\n",
      "i=109, dual=-24.984, prim=-1.331, gap=1.567105\n",
      "i=110, dual=-24.800, prim=-1.271, gap=1.512808\n",
      "i=111, dual=-24.615, prim=-1.213, gap=1.459382\n",
      "i=112, dual=-24.430, prim=-1.156, gap=1.406896\n",
      "i=113, dual=-24.254, prim=-1.100, gap=1.355415\n",
      "i=114, dual=-24.075, prim=-1.045, gap=1.304906\n",
      "i=115, dual=-23.893, prim=-0.992, gap=1.255337\n",
      "i=116, dual=-23.707, prim=-0.940, gap=1.206784\n",
      "i=117, dual=-23.517, prim=-0.889, gap=1.159322\n",
      "i=118, dual=-23.324, prim=-0.839, gap=1.113013\n",
      "i=119, dual=-23.127, prim=-0.791, gap=1.067891\n",
      "i=120, dual=-22.926, prim=-0.744, gap=1.024002\n",
      "i=121, dual=-22.731, prim=-0.699, gap=0.981380\n",
      "i=122, dual=-22.535, prim=-0.655, gap=0.940043\n",
      "i=123, dual=-22.345, prim=-0.613, gap=0.900006\n",
      "i=124, dual=-22.152, prim=-0.571, gap=0.861287\n",
      "i=125, dual=-21.955, prim=-0.531, gap=0.823518\n",
      "i=126, dual=-21.756, prim=-0.492, gap=0.786827\n",
      "i=127, dual=-21.553, prim=-0.454, gap=0.751339\n",
      "i=128, dual=-21.353, prim=-0.417, gap=0.717094\n",
      "i=129, dual=-21.151, prim=-0.382, gap=0.684104\n",
      "i=130, dual=-20.947, prim=-0.348, gap=0.652398\n",
      "i=131, dual=-20.742, prim=-0.315, gap=0.621982\n",
      "i=132, dual=-20.532, prim=-0.284, gap=0.592863\n",
      "i=133, dual=-20.319, prim=-0.253, gap=0.565015\n",
      "i=134, dual=-20.103, prim=-0.225, gap=0.538427\n",
      "i=135, dual=-19.893, prim=-0.197, gap=0.513073\n",
      "i=136, dual=-19.689, prim=-0.170, gap=0.488940\n",
      "i=137, dual=-19.492, prim=-0.145, gap=0.465992\n",
      "i=138, dual=-19.294, prim=-0.121, gap=0.444217\n",
      "i=139, dual=-19.095, prim=-0.098, gap=0.423584\n",
      "i=140, dual=-18.900, prim=-0.076, gap=0.404082\n",
      "i=141, dual=-18.703, prim=-0.055, gap=0.385678\n",
      "i=142, dual=-18.503, prim=-0.035, gap=0.368342\n",
      "i=143, dual=-18.302, prim=-0.016, gap=0.352048\n",
      "i=144, dual=-18.111, prim=0.003, gap=0.336765\n",
      "i=145, dual=-17.921, prim=0.020, gap=0.322453\n",
      "i=146, dual=-17.734, prim=0.036, gap=0.309091\n",
      "i=147, dual=-17.546, prim=0.052, gap=0.296502\n",
      "i=148, dual=-17.354, prim=0.067, gap=0.284810\n",
      "i=149, dual=-17.159, prim=0.081, gap=0.273994\n",
      "i=150, dual=-16.962, prim=0.094, gap=0.264018\n",
      "i=151, dual=-16.761, prim=0.106, gap=0.254843\n",
      "i=152, dual=-16.564, prim=0.118, gap=0.246438\n",
      "i=153, dual=-16.376, prim=0.129, gap=0.238757\n",
      "i=154, dual=-16.191, prim=0.140, gap=0.231756\n",
      "i=155, dual=-16.009, prim=0.150, gap=0.225399\n",
      "i=156, dual=-15.832, prim=0.159, gap=0.219640\n",
      "i=157, dual=-15.657, prim=0.168, gap=0.214431\n",
      "i=158, dual=-15.494, prim=0.176, gap=0.209725\n",
      "i=159, dual=-15.337, prim=0.184, gap=0.205483\n",
      "i=160, dual=-15.183, prim=0.191, gap=0.201645\n",
      "i=161, dual=-15.027, prim=0.198, gap=0.198170\n",
      "i=162, dual=-14.871, prim=0.205, gap=0.195012\n",
      "i=163, dual=-14.715, prim=0.211, gap=0.192125\n",
      "i=164, dual=-14.556, prim=0.217, gap=0.189453\n",
      "i=165, dual=-14.396, prim=0.222, gap=0.186974\n",
      "i=166, dual=-14.233, prim=0.227, gap=0.184641\n",
      "i=167, dual=-14.068, prim=0.232, gap=0.182415\n",
      "i=168, dual=-13.908, prim=0.236, gap=0.180288\n",
      "i=169, dual=-13.751, prim=0.241, gap=0.178209\n",
      "i=170, dual=-13.592, prim=0.244, gap=0.176169\n",
      "i=171, dual=-13.433, prim=0.248, gap=0.173783\n",
      "i=172, dual=-13.283, prim=0.252, gap=0.171280\n",
      "i=173, dual=-13.135, prim=0.255, gap=0.168763\n",
      "i=174, dual=-12.985, prim=0.258, gap=0.166250\n",
      "i=175, dual=-12.833, prim=0.261, gap=0.163742\n",
      "i=176, dual=-12.679, prim=0.263, gap=0.161242\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "i=177, dual=-12.523, prim=0.265, gap=0.158758\n",
      "i=178, dual=-12.366, prim=0.267, gap=0.156319\n",
      "i=179, dual=-12.210, prim=0.268, gap=0.153951\n",
      "i=180, dual=-12.054, prim=0.269, gap=0.151655\n",
      "i=181, dual=-11.896, prim=0.270, gap=0.149477\n",
      "i=182, dual=-11.735, prim=0.271, gap=0.147486\n",
      "i=183, dual=-11.574, prim=0.271, gap=0.145715\n",
      "i=184, dual=-11.410, prim=0.271, gap=0.144255\n",
      "i=185, dual=-11.248, prim=0.270, gap=0.143112\n",
      "i=186, dual=-11.091, prim=0.269, gap=0.142407\n",
      "i=187, dual=-10.940, prim=0.268, gap=0.142267\n",
      "i=188, dual=-10.790, prim=0.265, gap=0.142776\n",
      "i=189, dual=-10.641, prim=0.262, gap=0.144040\n",
      "i=190, dual=-10.493, prim=0.258, gap=0.146106\n",
      "i=191, dual=-10.347, prim=0.254, gap=0.149011\n",
      "i=192, dual=-10.202, prim=0.248, gap=0.152730\n",
      "i=193, dual=-10.059, prim=0.242, gap=0.157201\n",
      "i=194, dual=-9.918, prim=0.235, gap=0.162330\n",
      "i=195, dual=-9.777, prim=0.228, gap=0.167965\n",
      "i=196, dual=-9.638, prim=0.220, gap=0.173953\n",
      "i=197, dual=-9.501, prim=0.212, gap=0.180111\n",
      "i=198, dual=-9.365, prim=0.204, gap=0.186286\n",
      "i=199, dual=-9.231, prim=0.196, gap=0.192350\n",
      "i=200, dual=-9.098, prim=0.189, gap=0.198167\n",
      "i=201, dual=-8.966, prim=0.181, gap=0.203630\n",
      "i=202, dual=-8.837, prim=0.174, gap=0.208670\n",
      "i=203, dual=-8.713, prim=0.167, gap=0.213228\n",
      "i=204, dual=-8.589, prim=0.160, gap=0.217277\n",
      "i=205, dual=-8.473, prim=0.154, gap=0.220807\n",
      "i=206, dual=-8.358, prim=0.148, gap=0.223770\n",
      "i=207, dual=-8.245, prim=0.143, gap=0.226218\n",
      "i=208, dual=-8.132, prim=0.138, gap=0.228139\n",
      "i=209, dual=-8.025, prim=0.133, gap=0.229127\n",
      "i=210, dual=-7.919, prim=0.129, gap=0.229730\n",
      "i=211, dual=-7.814, prim=0.125, gap=0.230057\n",
      "i=212, dual=-7.710, prim=0.122, gap=0.230099\n",
      "i=213, dual=-7.609, prim=0.118, gap=0.229928\n",
      "i=214, dual=-7.515, prim=0.115, gap=0.229514\n",
      "i=215, dual=-7.423, prim=0.111, gap=0.228809\n",
      "i=216, dual=-7.336, prim=0.108, gap=0.228088\n",
      "i=217, dual=-7.250, prim=0.105, gap=0.227238\n",
      "i=218, dual=-7.165, prim=0.101, gap=0.225804\n",
      "i=219, dual=-7.081, prim=0.099, gap=0.223539\n",
      "i=220, dual=-6.997, prim=0.097, gap=0.220295\n",
      "i=221, dual=-6.915, prim=0.096, gap=0.215965\n",
      "i=222, dual=-6.833, prim=0.096, gap=0.210476\n",
      "i=223, dual=-6.753, prim=0.097, gap=0.203805\n",
      "i=224, dual=-6.676, prim=0.098, gap=0.195911\n",
      "i=225, dual=-6.601, prim=0.101, gap=0.186838\n",
      "i=226, dual=-6.529, prim=0.104, gap=0.176576\n",
      "i=227, dual=-6.458, prim=0.108, gap=0.165192\n",
      "i=228, dual=-6.386, prim=0.113, gap=0.152758\n",
      "i=229, dual=-6.315, prim=0.119, gap=0.139397\n",
      "i=230, dual=-6.249, prim=0.125, gap=0.125286\n",
      "i=231, dual=-6.184, prim=0.131, gap=0.110539\n",
      "i=232, dual=-6.119, prim=0.138, gap=0.095255\n",
      "i=233, dual=-6.054, prim=0.145, gap=0.079548\n",
      "i=234, dual=-5.993, prim=0.152, gap=0.063597\n",
      "i=235, dual=-5.931, prim=0.159, gap=0.047550\n",
      "i=236, dual=-5.869, prim=0.166, gap=0.031528\n",
      "i=237, dual=-5.806, prim=0.173, gap=0.015652\n",
      "i=238, dual=-5.742, prim=0.180, gap=0.000033\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "FuzzyInductor(c=1, k=GaussianKernel(sigma=0.3), f=LinearFuzzifier(), solver=TensorFlowSolver(, optimizer=<tensorflow.python.keras.optimizer_v2.adam.Adam object at 0x7fb32b77a160>))"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from mulearn.optimization import TensorFlowSolver\n",
    "from mulearn.fuzzifier import LinearFuzzifier\n",
    "\n",
    "\n",
    "opt = tf.optimizers.Adam(learning_rate=1e-4)\n",
    "\n",
    "fitf = FuzzyInductor(solver=TensorFlowSolver(optimizer=opt),\n",
    "                     k=GaussianKernel(sigma=0.3),\n",
    "                     fuzzifier=LinearFuzzifier())\n",
    "fitf.fit(iris_X_2d, iris_versicolor)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0,\n",
       "       1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1,\n",
       "       1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1,\n",
       "       0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fitf.predict(iris_X_2d, alpha=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris_versicolor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_space = np.linspace(-4, 4, 100)\n",
    "y_space = np.linspace(-2, 2, 100)\n",
    "\n",
    "X, Y = np.meshgrid(x_space, y_space)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "Z = [[fitf.predict([(x, y)])[0] for x in x_space]\n",
    "     for y in y_space]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.cm as cm \n",
    "\n",
    "plt.scatter(*iris_X_2d.T, color=cm.coolwarm(iris_versicolor*255), s=9, alpha=0.7)\n",
    "contours = plt.contour(X, Y, Z, [.5, .6, .7, .8, .9], colors='gray')\n",
    "plt.clabel(contours, inline=True, fontsize=8)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "d82ad741bcea397925f8fc8a41d76633b51eb514db0ee1fc1249c622e214eae3"
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.7.3"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autoclose": false,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}