hard_margin.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import cvxpy as cp\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from data import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X[0,:], X[1,:], 'r.')\n",
    "plt.plot(Y[0,:], Y[1,:], 'b.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "lambd = cp.Variable(shape=(100,))\n",
    "M = np.concatenate((X, -Y), axis=1)\n",
    "D = M.T @ M + np.eye(M.shape[1]) * 1e-5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(100, 100)\n",
      "(50, 100)\n",
      "True\n",
      "[4.65163889e+05+0.00000000e+00j 1.79169939e+04+0.00000000e+00j\n",
      " 1.69909549e+04+0.00000000e+00j 1.57166879e+04+0.00000000e+00j\n",
      " 1.43997251e+04+0.00000000e+00j 1.35757548e+04+0.00000000e+00j\n",
      " 1.30565373e+04+0.00000000e+00j 1.19165148e+04+0.00000000e+00j\n",
      " 1.13666783e+04+0.00000000e+00j 9.88722032e+03+0.00000000e+00j\n",
      " 9.26269188e+03+0.00000000e+00j 8.80752462e+03+0.00000000e+00j\n",
      " 8.45444283e+03+0.00000000e+00j 7.72338328e+03+0.00000000e+00j\n",
      " 7.41493888e+03+0.00000000e+00j 7.12076940e+03+0.00000000e+00j\n",
      " 6.69014491e+03+0.00000000e+00j 6.07341083e+03+0.00000000e+00j\n",
      " 6.01646665e+03+0.00000000e+00j 4.87088920e+03+0.00000000e+00j\n",
      " 4.30635469e+03+0.00000000e+00j 4.14601749e+03+0.00000000e+00j\n",
      " 3.77978747e+03+0.00000000e+00j 3.61164935e+03+0.00000000e+00j\n",
      " 3.47551210e+03+0.00000000e+00j 2.61349331e+03+0.00000000e+00j\n",
      " 2.78817208e+03+0.00000000e+00j 2.85608407e+03+0.00000000e+00j\n",
      " 2.37172532e+03+0.00000000e+00j 2.23614107e+03+0.00000000e+00j\n",
      " 2.12842523e+03+0.00000000e+00j 1.97674260e+03+0.00000000e+00j\n",
      " 1.87253644e+03+0.00000000e+00j 1.68353327e+03+0.00000000e+00j\n",
      " 1.35142169e+03+0.00000000e+00j 1.53712507e+03+0.00000000e+00j\n",
      " 1.17192111e+03+0.00000000e+00j 1.05430685e+03+0.00000000e+00j\n",
      " 1.51438683e+03+0.00000000e+00j 1.06859351e+03+0.00000000e+00j\n",
      " 6.40201591e+02+0.00000000e+00j 7.82386107e+02+0.00000000e+00j\n",
      " 5.91221808e+02+0.00000000e+00j 5.26830420e+02+0.00000000e+00j\n",
      " 3.56082242e+02+0.00000000e+00j 3.04571296e+02+0.00000000e+00j\n",
      " 4.66851425e+02+0.00000000e+00j 2.13198389e+02+0.00000000e+00j\n",
      " 1.37925839e+02+0.00000000e+00j 2.00393086e+02+0.00000000e+00j\n",
      " 1.00000132e-05+9.69048860e-14j 1.00000132e-05-9.69048860e-14j\n",
      " 9.99998646e-06+6.88222926e-13j 9.99998646e-06-6.88222926e-13j\n",
      " 9.99998642e-06+0.00000000e+00j 1.00000109e-05+0.00000000e+00j\n",
      " 1.00000098e-05+2.64775215e-13j 1.00000098e-05-2.64775215e-13j\n",
      " 1.00000101e-05+0.00000000e+00j 9.99998898e-06+0.00000000e+00j\n",
      " 9.99998975e-06+0.00000000e+00j 9.99999101e-06+0.00000000e+00j\n",
      " 1.00000079e-05+0.00000000e+00j 1.00000075e-05+0.00000000e+00j\n",
      " 1.00000067e-05+4.74557592e-14j 1.00000067e-05-4.74557592e-14j\n",
      " 9.99999199e-06+0.00000000e+00j 9.99999247e-06+0.00000000e+00j\n",
      " 9.99999282e-06+0.00000000e+00j 1.00000059e-05+2.88450408e-13j\n",
      " 1.00000059e-05-2.88450408e-13j 1.00000052e-05+0.00000000e+00j\n",
      " 9.99999329e-06+0.00000000e+00j 1.00000044e-05+0.00000000e+00j\n",
      " 9.99999718e-06+2.86322868e-12j 9.99999718e-06-2.86322868e-12j\n",
      " 9.99999383e-06+0.00000000e+00j 1.00000040e-05+0.00000000e+00j\n",
      " 1.00000037e-05+0.00000000e+00j 9.99999471e-06+8.76165122e-13j\n",
      " 9.99999471e-06-8.76165122e-13j 1.00000031e-05+1.47488194e-13j\n",
      " 1.00000031e-05-1.47488194e-13j 9.99999484e-06+0.00000000e+00j\n",
      " 1.00000024e-05+1.65351086e-13j 1.00000024e-05-1.65351086e-13j\n",
      " 9.99999533e-06+2.38633421e-13j 9.99999533e-06-2.38633421e-13j\n",
      " 1.00000014e-05+0.00000000e+00j 1.00000006e-05+1.77001560e-13j\n",
      " 1.00000006e-05-1.77001560e-13j 1.00000001e-05+0.00000000e+00j\n",
      " 9.99999653e-06+0.00000000e+00j 9.99999671e-06+0.00000000e+00j\n",
      " 9.99999862e-06+7.57093427e-13j 9.99999862e-06-7.57093427e-13j\n",
      " 9.99999792e-06+3.74256083e-13j 9.99999792e-06-3.74256083e-13j\n",
      " 9.99999914e-06+0.00000000e+00j 9.99999823e-06+0.00000000e+00j]\n"
     ]
    }
   ],
   "source": [
    "print(D.shape)\n",
    "print(M.shape)\n",
    "print(np.all(np.linalg.eigvals(D) >= 0))\n",
    "print(np.linalg.eigvals(D))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.0001475478535173157"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "objective = cp.Minimize(-cp.sum(lambd) + 0.5*cp.quad_form(lambd, D))\n",
    "constraints= [lambd >= 0, cp.sum(lambd[0:50] - lambd[50:100]) == 0]\n",
    "problem = cp.Problem(objective, constraints)\n",
    "problem.solve(solver=cp.ECOS, verbose=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.28851177e-10, 2.45541944e-10, 1.52547187e-09, 2.10612339e-10,\n",
       "       1.37043194e-05, 2.32301016e-10, 1.96794667e-10, 1.10820066e-10,\n",
       "       2.08023963e-10, 1.82758960e-10, 1.02517796e-10, 2.15059696e-10,\n",
       "       2.71199928e-10, 2.27191918e-08, 2.44192897e-10, 3.23942786e-10,\n",
       "       2.25839225e-10, 1.71233251e-10, 7.21986831e-10, 1.79760431e-10,\n",
       "       2.14916157e-10, 3.92368325e-09, 2.13651725e-10, 2.61796295e-10,\n",
       "       4.76121867e-10, 2.55849367e-10, 2.46912443e-10, 5.94278306e-05,\n",
       "       2.93692671e-05, 9.64864524e-11, 2.00341009e-10, 1.99466242e-05,\n",
       "       3.72717771e-10, 3.00465969e-10, 1.03512178e-10, 2.50418930e-05,\n",
       "       5.62467954e-10, 6.64381992e-10, 5.34733237e-10, 2.54787166e-10,\n",
       "       4.51111704e-10, 1.35683445e-10, 3.36916372e-10, 1.02757342e-09,\n",
       "       1.23625654e-10, 2.01496371e-10, 2.69548534e-10, 1.97143662e-10,\n",
       "       1.83503264e-10, 1.83024474e-10, 1.82334831e-10, 2.18752155e-10,\n",
       "       1.68916381e-10, 8.91956917e-10, 5.66183210e-09, 1.37987623e-09,\n",
       "       3.94502100e-10, 6.36374939e-10, 2.39387858e-10, 2.33943251e-10,\n",
       "       3.69932807e-05, 2.29096736e-10, 1.03420124e-05, 3.56143999e-09,\n",
       "       1.27088268e-10, 1.62549982e-10, 3.85268337e-10, 2.00585103e-10,\n",
       "       1.20231443e-05, 1.08912491e-10, 3.80845385e-10, 2.84366695e-10,\n",
       "       1.28010536e-10, 5.33350352e-10, 1.94274509e-10, 4.15268045e-10,\n",
       "       1.24909448e-10, 1.57545371e-09, 2.20381305e-10, 2.39334888e-09,\n",
       "       9.21776945e-11, 1.58874486e-10, 2.70759800e-10, 1.18087247e-10,\n",
       "       2.36864499e-10, 2.06759096e-10, 2.08842763e-10, 3.62676201e-05,\n",
       "       5.70071626e-10, 3.18347686e-10, 6.17229883e-10, 5.18755774e-05,\n",
       "       2.50078327e-10, 5.15285501e-10, 2.27815106e-10, 1.86750912e-10,\n",
       "       5.45205674e-10, 1.93462595e-10, 2.45138123e-09, 1.15206053e-10])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lambd.value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "w = np.sum(np.multiply(lambd.value,M), axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(50, 1)\n",
      "(50, 1)\n"
     ]
    }
   ],
   "source": [
    "print(w.shape)\n",
    "print(M[:, 23].shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "index = np.argmax(lambd.value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "b = 1 - (w.T@M[:,index])[0,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.02383312584157904"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "i1 = 0\n",
    "i2 = 28\n",
    "plt.plot(X[i1,:], X[i2,:], 'r.')\n",
    "plt.plot(Y[i1,:], Y[i2,:], 'b.')\n",
    "x = np.linspace(-10, 0, 100)\n",
    "y = -(w[i1, 0]*x + b)/w[i2, 0]\n",
    "plt.plot(x, y)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "35eeb062e26c9701e83ea6659403bee76c3934b635ee6a9209e92f796c1714bb"
  },
  "kernelspec": {
   "display_name": "Python 3.9.12 ('EE5606_venv')",
   "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": "3.9.12"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}