interior.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return x\n",
    "\n",
    "\n",
    "def grad(x):\n",
    "    return np.array([1])\n",
    "\n",
    "\n",
    "def hess(x):\n",
    "    return np.array([0])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def puntoInterior(x0, lam0, A, b, Ae, be, alpha=0.2, sigma=0.2):\n",
    "    k = 0\n",
    "    n = x0.shape[0]\n",
    "\n",
    "    if type(Ae) != type(None):\n",
    "        A = np.concatenate((A, Ae))\n",
    "        b = np.concatenate((b, be))\n",
    "\n",
    "    m = A.shape[0]\n",
    "\n",
    "    y = A.dot(x0)-b\n",
    "    print(\"k, lamdas, x, y, error\")\n",
    "\n",
    "    for i in range(0, 1000):\n",
    "\n",
    "        rd = grad(x0) - np.dot(A.T, lam0)\n",
    "        mu = np.dot(y.T, lam0)/m\n",
    "        # print(rd, mu)\n",
    "\n",
    "        # llenar Y\n",
    "        Y = np.zeros((m, m))\n",
    "        for i in range(len(Y)):\n",
    "            Y[i, i] = y[i]\n",
    "        # llenar Lamda\n",
    "        L = np.zeros((m, m))\n",
    "        for i in range(len(L)):\n",
    "            L[i, i] = lam0[i]\n",
    "        # valores de rb\n",
    "        e = np.ones((m))\n",
    "        aux = np.dot(np.linalg.inv(L), e)\n",
    "        rb = y.T-sigma*mu*aux\n",
    "        # print(rb)\n",
    "\n",
    "        F = np.array([rd])\n",
    "        F = np.append(-F, -rb)\n",
    "        # print(F)\n",
    "\n",
    "        mA = np.concatenate((hess(x0), -A.T), axis=1)\n",
    "        # print(mA)\n",
    "        mB = np.array([A])\n",
    "        c = np.dot(np.linalg.inv(L), Y)\n",
    "        mB = np.concatenate((A, c), axis=1)\n",
    "        sistema = np.vstack((mA, mB))\n",
    "\n",
    "        # print(sistema)\n",
    "        deltas = np.linalg.solve(sistema, F)\n",
    "        # actualizar alphas\n",
    "        # print(f\"nueuvo alpha : {calcularAlpha(A, x0, b, deltas, lam0)}\")\n",
    "        # alpha = calcularAlpha(A, x0, b, deltas, lam0)\n",
    "\n",
    "        x0 = x0 + alpha*deltas[:n]\n",
    "        lam0 = lam0 + alpha*deltas[n:]\n",
    "        y = A.dot(x0) - b\n",
    "        mDelta = np.linalg.norm(deltas)\n",
    "        print(k, lam0, x0, y, mDelta)\n",
    "        k += 1\n",
    "        if (mDelta < 1e-6):\n",
    "            return x0\n",
    "\n",
    "\n",
    "def calcularAlpha(A, x, b, deltas, lam):\n",
    "    m = A.shape[0]\n",
    "    n = x.shape[0]\n",
    "\n",
    "    dx = deltas[:n]\n",
    "    dl = deltas[n:]\n",
    "\n",
    "    num = b - A*x\n",
    "    den = A.dot(dx)\n",
    "\n",
    "    t1 = np.dot(num.T, num)\n",
    "    t2 = np.dot(den, den)\n",
    "    print(t1, t2)\n",
    "    tx = t1/t2\n",
    "\n",
    "    num1 = dl.dot(lam)\n",
    "    den1 = dl.dot(dl)\n",
    "    tl = -num1/den1\n",
    "    print(tl)\n",
    "    t = tx if tx < tl else tl\n",
    "    if t > 1:\n",
    "        return 1\n",
    "    else:\n",
    "        return t\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "k, lamdas, x, y, error\n"
     ]
    },
    {
     "ename": "ValueError",
     "evalue": "setting an array element with a sequence.",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;31mTypeError\u001b[0m: only size-1 arrays can be converted to Python scalars",
      "\nThe above exception was the direct cause of the following exception:\n",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "Cell \u001b[1;32mIn [5], line 7\u001b[0m\n\u001b[0;32m      4\u001b[0m x0 \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39marray([\u001b[39m0.8\u001b[39m])\n\u001b[0;32m      5\u001b[0m lam0 \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39marray([\u001b[39m0.1\u001b[39m, \u001b[39m0.1\u001b[39m])\n\u001b[1;32m----> 7\u001b[0m puntoInterior(x0,lam0,A,b)\n",
      "Cell \u001b[1;32mIn [4], line 18\u001b[0m, in \u001b[0;36mpuntoInterior\u001b[1;34m(x0, lam0, A, b, alpha, sigma)\u001b[0m\n\u001b[0;32m     16\u001b[0m Y \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39mzeros((m, m))\n\u001b[0;32m     17\u001b[0m \u001b[39mfor\u001b[39;00m i \u001b[39min\u001b[39;00m \u001b[39mrange\u001b[39m(\u001b[39mlen\u001b[39m(Y)):\n\u001b[1;32m---> 18\u001b[0m     Y[i, i] \u001b[39m=\u001b[39m y[i]\n\u001b[0;32m     19\u001b[0m \u001b[39m# llenar Lamda\u001b[39;00m\n\u001b[0;32m     20\u001b[0m L \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39mzeros((m, m))\n",
      "\u001b[1;31mValueError\u001b[0m: setting an array element with a sequence."
     ]
    }
   ],
   "source": [
    "A = np.array([[1], [-1]])\n",
    "b = np.array([[0], [-1]])\n",
    "\n",
    "x0 = np.array([0.8])\n",
    "lam0 = np.array([0.1, 0.1])\n",
    "\n",
    "puntoInterior(x0,lam0,A,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 4]\n",
      "k, lamdas, x, y, error\n",
      "0 [0.10210526 0.02157895] [1.93263158 3.84526316] [1.77789474 0.02      ] 1.86108269801862\n",
      "1 [ 0.10318794 -0.01327934] [1.91123568 3.6878389 ] [1.59907458 0.13463246] 1.62654398782299\n",
      "2 [0.1019376  0.02865221] [1.96591392 3.50844683] [1.47436075 0.42338101] 1.9217451354384716\n",
      "3 [0.10225574 0.02009906] [1.96745794 3.37079894] [1.33825688 0.56411695] 1.3792238018782577\n",
      "4 [0.10234579 0.01586788] [1.97264374 3.24510028] [1.21774402 0.70018719] 1.2587674865770342\n",
      "5 [0.10228096 0.01336278] [1.97875253 3.13125157] [1.1100041  0.82625349] 1.1404002003623468\n",
      "6 [0.10208539 0.01167339] [1.98487229 3.02843328] [1.01330557 0.9413113 ] 1.0301429098541153\n",
      "7 [0.10176684 0.0104277 ] [1.99066803 2.9356784 ] [0.92634643 1.04565767] 0.9294467749231058\n",
      "8 [0.10132722 0.00945002] [1.99601347 2.85203489] [0.84804835 1.13999205] 0.8382099492791062\n",
      "9 [0.10076644 0.00864759] [2.00086816 2.77661244] [0.77748061 1.22512389] 0.7558486508203095\n",
      "10 [0.10008393 0.0079671 ] [2.0052303  2.70859445] [0.71382475 1.30186615] 0.6816453450276898\n",
      "11 [0.09927944 0.00737578] [2.00911626 2.64723846] [0.65635472 1.37099406] 0.6148703734633457\n",
      "12 [0.09835341 0.00685244] [2.01255104 2.59187243] [0.60442346 1.43322965] 0.5548266735525066\n",
      "13 [0.09730724 0.00638272] [2.01556342 2.54188968] [0.5574531  1.48923716] 0.5008657408362722\n",
      "14 [0.09614334 0.00595656] [2.01818347 2.49674342] [0.5149269  1.53962352] 0.45239198160188543\n",
      "15 [0.09486523 0.0055667 ] [2.0204412  2.45594147] [0.47638267 1.58494093] 0.40886215665876974\n",
      "16 [0.09347751 0.00520771] [2.02236582 2.41904114] [0.44140697 1.62569051] 0.3697827422768453\n",
      "17 [0.09198579 0.00487547] [2.0239854  2.38564465] [0.40963005 1.66232614] 0.33470647188360425\n",
      "18 [0.0903966  0.00456676] [2.02532662 2.35539475] [0.38072137 1.69525848] 0.3032286462602846\n",
      "19 [0.0887173  0.00427902] [2.02641474 2.32797082] [0.35438556 1.72485867] 0.2749834903303634\n",
      "20 [0.0869559  0.00401019] [2.02727355 2.30308523] [0.33035878 1.75146187] 0.2496406861930913\n",
      "21 [0.08512094 0.00375855] [2.02792538 2.28048013] [0.30840551 1.77537062] 0.226902138475446\n",
      "22 [0.08322132 0.00352265] [2.02839111 2.25992442] [0.28831553 1.7968578 ] 0.20649899081432188\n",
      "23 [0.08126614 0.00330129] [2.02869025 2.24121107] [0.26990132 1.81616942] 0.18818889325342542\n",
      "24 [0.07926458 0.00309339] [2.02884091 2.22415468] [0.25299559 1.83352714] 0.17175351070421438\n",
      "25 [0.07722571 0.00289803] [2.02885993 2.20858925] [0.23744917 1.84913061] 0.15699625791319546\n",
      "26 [0.07515843 0.00271439] [2.02876284 2.19436617] [0.22312901 1.86315951] 0.14374024429473334\n",
      "27 [0.07307133 0.00254172] [2.02856398 2.18135246] [0.20991644 1.8757755 ] 0.13182641132579834\n",
      "28 [0.0709726  0.00237936] [2.02827651 2.16942908] [0.19770559 1.88712394] 0.12111184532676716\n",
      "29 [0.06886997 0.0022267 ] [2.02791248 2.15848948] [0.18640196 1.89733548] 0.11146824904193184\n",
      "30 [0.06677066 0.00208317] [2.02748288 2.1484383 ] [0.17592118 1.90652746] 0.10278055631273258\n",
      "31 [0.06468133 0.00194825] [2.0269977  2.13919017] [0.16618787 1.91480522] 0.09494567521199553\n",
      "32 [0.06260806 0.00182146] [2.02646598 2.13066864] [0.15713462 1.92226332] 0.08787134621967066\n",
      "33 [0.06055637 0.00170234] [2.02589589 2.12280522] [0.14870111 1.92898656] 0.0814751033229828\n",
      "34 [0.05853117 0.00159045] [2.02529476 2.11553856] [0.14083332 1.93505095] 0.07568332727100432\n",
      "35 [0.05653682 0.00148541] [2.02466915 2.10881365] [0.13348279 1.94052465] 0.07043038155786975\n",
      "36 [0.05457711 0.00138683] [2.02402491 2.10258113] [0.12660603 1.94546868] 0.06565782300186208\n",
      "37 [0.05265531 0.00129435] [2.02336723 2.09679673] [0.12016396 1.94993773] 0.061313679984252696\n",
      "38 [0.0507742  0.00120762] [2.02270071 2.09142068] [0.11412139 1.95398074] 0.05735179247473116\n",
      "39 [0.04893608 0.00112633] [2.02202937 2.08641723] [0.10844661 1.95764151] 0.05373120887388761\n",
      "40 [0.04714282 0.00105016] [2.02135676 2.08175426] [0.10311101 1.96095926] 0.05041563543591298\n",
      "41 [0.04539589 0.00097882] [2.02068593 2.07740281] [0.09808874 1.96396905] 0.04737293459893807\n",
      "42 [0.0436964  0.00091204] [2.02001954 2.07333683] [0.09335637 1.96670226] 0.044574668961026444\n",
      "43 [0.04204514 0.00084954] [2.01935989 2.0695328 ] [0.08889268 1.96918698] 0.04199568792049181\n",
      "44 [0.04044258 0.00079109] [2.0187089 2.0659695] [0.08467839 1.97144829] 0.03961375417871764\n",
      "45 [0.03888894 0.00073644] [2.01806821 2.06262776] [0.08069597 1.97350867] 0.03740920741191509\n",
      "46 [0.0373842  0.00068536] [2.01743921 2.05949023] [0.07692944 1.9753882 ] 0.03536466248311392\n",
      "47 [0.03592814 0.00063764] [2.01682303 2.05654119] [0.07336421 1.97710486] 0.033464739610669224\n",
      "48 [0.03452037 0.00059308] [2.01622056 2.05376639] [0.06998696 1.97867473] 0.03169582395272132\n",
      "49 [0.03316032 0.00055148] [2.01563255 2.05115291] [0.06678546 1.9801122 ] 0.030045852120671363\n",
      "50 [0.03184729 0.00051266] [2.01505956 2.04868897] [0.06374853 1.98143015] 0.028504123205855873\n",
      "51 [0.03058049 0.00047646] [2.014502   2.04636387] [0.06086587 1.98264012] 0.027061131994875302\n",
      "52 [0.02935902 0.0004427 ] [2.01396015 2.04416786] [0.058128   1.98375244] 0.025708422159814823\n",
      "53 [0.0281819  0.00041123] [2.01343419 2.04209201] [0.0555262  1.98477636] 0.024438457337048077\n",
      "54 [0.02704808 0.00038191] [2.0129242  2.04012819] [0.05305239 1.9857202 ] 0.023244508148373987\n",
      "55 [0.02595649 0.00035459] [2.01243017 2.03826894] [0.05069911 1.98659139] 0.022120553366324253\n",
      "56 [0.02490599 0.00032916] [2.01195202 2.03650744] [0.04845946 1.9873966 ] 0.021061193577158185\n",
      "57 [0.02389542 0.00030549] [2.01148962 2.03483739] [0.04632701 1.98814185] 0.020061575846320224\n",
      "58 [0.02292363 0.00028345] [2.01104277 2.03325304] [0.04429581 1.98883251] 0.019117328038602024\n",
      "59 [0.02198941 0.00026296] [2.01061125 2.03174906] [0.04236031 1.98947343] 0.018224501586330454\n",
      "60 [0.02109159 0.00024389] [2.01019477 2.03032057] [0.04051534 1.99006896] 0.01737952163169281\n",
      "61 [0.02022899 0.00022617] [2.00979304 2.02896304] [0.03875608 1.99062304] 0.01657914359255616\n",
      "62 [0.01940042 0.00020969] [2.00940573 2.02767228] [0.03707802 1.99113919] 0.015820415314198418\n",
      "63 [0.01860473 0.00019438] [2.00903251 2.02644442] [0.03547693 1.9916206 ] 0.015100644071985126\n",
      "64 [0.01784077 0.00018016] [2.00867301 2.02527586] [0.03394888 1.99207016] 0.014417367782375378\n",
      "65 [0.01710741 0.00016695] [2.00832686 2.02416327] [0.03249014 1.99249046] 0.013768329862094635\n",
      "66 [0.01640355 0.00015468] [2.00799369 2.02310354] [0.03109724 1.99288385] 0.013151457248439406\n",
      "67 [0.0157281  0.00014329] [2.00767312 2.02209378] [0.0297669  1.99325246] 0.012564841158189297\n",
      "68 [0.01508001 0.00013272] [2.00736476 2.02113129] [0.02849605 1.99359824] 0.012006720219205192\n",
      "69 [0.01445824 0.00012291] [2.00706823 2.02021355] [0.02728177 1.99392291] 0.011475465658269913\n",
      "70 [0.01386181 0.0001138 ] [2.00678314 2.0193382 ] [0.02612135 1.99422808] 0.010969568271800897\n",
      "71 [0.01328973 0.00010536] [2.00650913 2.01850306] [0.02501218 1.9945152 ] 0.010487626943473683\n",
      "72 [1.27410609e-02 9.75307552e-05] [2.00624581 2.01770604] [0.02395184 1.99478557] 0.010028338505176797\n",
      "73 [1.22148911e-02 9.02703755e-05] [2.00599281 2.01694521] [0.02293802 1.99504041] 0.009590488765711067\n",
      "74 [1.17103342e-02 8.35395741e-05] [2.00574978 2.01621875] [0.02196853 1.9952808 ] 0.009172944555786143\n",
      "75 [1.12265345e-02 7.73008464e-05] [2.00551635 2.01552495] [0.0210413  1.99550776] 0.008774646658671103\n",
      "76 [1.07626654e-02 7.15192273e-05] [2.00529219 2.0148622 ] [0.02015439 1.99572219] 0.008394603513751988\n",
      "77 [1.03179290e-02 6.61621309e-05] [2.00507696 2.01422898] [0.01930594 1.99592494] 0.008031885595652443\n",
      "78 [9.89155573e-03 6.11992000e-05] [2.00487032 2.01362386] [0.01849418 1.99611677] 0.007685620384790949\n",
      "79 [9.48280376e-03 5.66021638e-05] [2.00467195 2.01304549] [0.01771745 1.99629841] 0.007354987856637903\n",
      "80 [9.09095845e-03 5.23447028e-05] [2.00448155 2.0124926 ] [0.01697415 1.99647049] 0.007039216426691019\n",
      "81 [8.71533175e-03 4.84023228e-05] [2.0042988  2.01196398] [0.01626278 1.99663362] 0.006737579296597544\n",
      "82 [8.35526155e-03 4.47522350e-05] [2.00412342 2.01145848] [0.01558191 1.99678836] 0.006449391154067179\n",
      "83 [8.01011098e-03 4.13732440e-05] [2.00395513 2.01097504] [0.01493016 1.99693522] 0.00617400518543141\n",
      "84 [7.67926769e-03 3.82456420e-05] [2.00379364 2.01051262] [0.01430626 1.99707466] 0.00591081036505582\n",
      "85 [7.36214316e-03 3.53511098e-05] [2.00363869 2.01007026] [0.01370895 1.99720713] 0.005659228990410958\n",
      "86 [7.05817195e-03 3.26726233e-05] [2.00349004 2.00964703] [0.01313707 1.99733304] 0.005418714435587102\n",
      "87 [6.76681093e-03 3.01943662e-05] [2.00334741 2.00924207] [0.01258948 1.99745276] 0.005188749099456037\n",
      "88 [6.48753862e-03 2.79016482e-05] [2.00321059 2.00885454] [0.01206514 1.99756665] 0.004968842527652295\n",
      "89 [6.21985437e-03 2.57808281e-05] [2.00307934 2.00848367] [0.01156301 1.99767502] 0.004758529690106217\n",
      "90 [5.96327772e-03 2.38192418e-05] [2.00295344 2.00812869] [0.01108213 1.99777819] 0.004557369398074717\n",
      "91 [5.71734760e-03 2.20051352e-05] [2.00283267 2.0077889 ] [0.01062157 1.99787645] 0.004364942846546712\n",
      "92 [5.48162172e-03 2.03276010e-05] [2.00271683 2.00746362] [0.01018045 1.99797005] 0.004180852269566772\n",
      "93 [5.25567579e-03 1.87765199e-05] [2.00260572 2.00715221] [0.00975793 1.99805924] 0.004004719697476454\n",
      "94 [5.03910290e-03 1.73425057e-05] [2.00249915 2.00685404] [0.0093532  1.99814426] 0.003836185806333671\n",
      "95 [4.83151287e-03 1.60168541e-05] [2.00239694 2.00656855] [0.00896549 1.99822533] 0.0036749088508813864\n",
      "96 [4.63253157e-03 1.47914943e-05] [2.00229891 2.00629517] [0.00859407 1.99830264] 0.0035205636733940155\n",
      "97 [4.44180033e-03 1.36589445e-05] [2.00220488 2.00603337] [0.00823825 1.9983764 ] 0.0033728407815775147\n",
      "98 [4.25897531e-03 1.26122704e-05] [2.00211471 2.00578264] [0.00789735 1.99844678] 0.003231445489440073\n",
      "99 [4.08372695e-03 1.16450459e-05] [2.00202823 2.0055425 ] [0.00757073 1.99851395] 0.0030960971156917733\n",
      "100 [3.91573937e-03 1.07513169e-05] [2.00194528 2.00531249] [0.00725778 1.99857808] 0.002966528234810723\n",
      "101 [3.75470982e-03 9.92556797e-06] [2.00186574 2.00509218] [0.00695792 1.9986393 ] 0.0028424839764107134\n",
      "102 [3.60034819e-03 9.16269023e-06] [2.00178945 2.00488114] [0.00667059 1.99869777] 0.0027237213689862982\n",
      "103 [3.45237647e-03 8.45795255e-06] [2.00171629 2.00467897] [0.00639526 1.99875362] 0.0026100087245086107\n",
      "104 [3.31052823e-03 7.80697409e-06] [2.00164613 2.00448529] [0.00613142 1.99880698] 0.002501125060684529\n",
      "105 [3.17454822e-03 7.20569901e-06] [2.00157884 2.00429973] [0.00587857 1.99885796] 0.002396859558006425\n",
      "106 [3.04419183e-03 6.65037285e-06] [2.00151431 2.00412195] [0.00563626 1.99890668] 0.002297011048979546\n",
      "107 [2.91922471e-03 6.13752064e-06] [2.00145243 2.00395162] [0.00540404 1.99895324] 0.002201387537175125\n",
      "108 [2.79942232e-03 5.66392649e-06] [2.00139308 2.0037884 ] [0.00518148 1.99899775] 0.002109805743950727\n",
      "109 [2.68456951e-03 5.22661469e-06] [2.00133616 2.00363202] [0.00496818 1.99904031] 0.0020220906808928085\n",
      "110 [2.57446018e-03 4.82283208e-06] [2.00128158 2.00348216] [0.00476373 1.999081  ] 0.001938075246191846\n",
      "111 [2.46889685e-03 4.45003171e-06] [2.00122923 2.00333855] [0.00456778 1.99911991] 0.0018575998433256297\n",
      "112 [2.36769030e-03 4.10585772e-06] [2.00117903 2.00320093] [0.00437996 1.99915712] 0.0017805120205587638\n",
      "113 [2.27065928e-03 3.78813120e-06] [2.00113088 2.00306905] [0.00419993 1.99919271] 0.0017066661298908963\n",
      "114 [2.17763012e-03 3.49483712e-06] [2.00108471 2.00294265] [0.00402736 1.99922676] 0.001635923004199151\n",
      "115 [2.08843644e-03 3.22411225e-06] [2.00104042 2.00282151] [0.00386194 1.99925934] 0.0015681496514226931\n",
      "116 [2.00291882e-03 2.97423386e-06] [2.00099796 2.00270541] [0.00370336 1.9992905 ] 0.0015032189647204903\n",
      "117 [1.92092453e-03 2.74360931e-06] [2.00095723 2.00259413] [0.00355136 1.99932033] 0.0014410094476260855\n",
      "118 [1.84230726e-03 2.53076634e-06] [2.00091817 2.00248747] [0.00340564 1.99934886] 0.001381404953289573\n",
      "119 [1.76692681e-03 2.33434416e-06] [2.00088071 2.00238523] [0.00326594 1.99937618] 0.0013242944369661947\n",
      "120 [1.69464885e-03 2.15308505e-06] [2.00084478 2.00228724] [0.00313202 1.99940232] 0.0012695717209758306\n",
      "121 [1.62534468e-03 1.98582672e-06] [2.00081032 2.0021933 ] [0.00300362 1.99942734] 0.0012171352714077542\n",
      "122 [1.55889101e-03 1.83149514e-06] [2.00077727 2.00210326] [0.00288053 1.99945129] 0.0011668879859015918\n",
      "123 [1.49516968e-03 1.68909792e-06] [2.00074558 2.00201694] [0.00276252 1.99947422] 0.001118736991876788\n",
      "124 [1.43406749e-03 1.55771818e-06] [2.00071518 2.00193419] [0.00264938 1.99949617] 0.0010725934546310636\n",
      "125 [1.37547597e-03 1.43650887e-06] [2.00068603 2.00185487] [0.0025409  1.99951719] 0.0010283723947597915\n",
      "126 [1.31929118e-03 1.32468754e-06] [2.00065807 2.00177882] [0.00243689 1.99953731] 0.0009859925143923427\n",
      "127 [1.26541353e-03 1.22153144e-06] [2.00063125 2.00170591] [0.00233716 1.99955658] 0.0009453760317690946\n",
      "128 [1.21374759e-03 1.12637300e-06] [2.00060553 2.00163602] [0.00224155 1.99957504] 0.0009064485237122614\n",
      "129 [1.16420191e-03 1.03859572e-06] [2.00058086 2.00156901] [0.00214986 1.99959271] 0.0008691387755764525\n",
      "130 [1.11668886e-03 9.57630239e-07] [2.0005572  2.00150476] [0.00206195 1.99960964] 0.0008333786382870969\n",
      "131 [1.07112447e-03 8.82950805e-07] [2.0005345  2.00144316] [1.97766000e-03 1.99962585e+00] 0.0007991028920963042\n",
      "132 [1.02742825e-03 8.14071958e-07] [2.00051274 2.0013841 ] [1.89683202e-03 1.99964137e+00] 0.0007662491167172315\n",
      "133 [9.85523096e-04 7.50545469e-07] [2.00049186 2.00132747] [1.81932614e-03 1.99965625e+00] 0.0007347575675048443\n",
      "134 [9.45335093e-04 6.91957510e-07] [2.00047183 2.00127317] [1.74500469e-03 1.99967050e+00] 0.0007045710573811543\n",
      "135 [9.06793413e-04 6.37926041e-07] [2.00045263 2.00122111] [1.67373579e-03 1.99968414e+00] 0.0006756348442184656\n",
      "136 [8.69830173e-04 5.88098388e-07] [2.0004342  2.00117119] [1.60539307e-03 1.99969722e+00] 0.0006478965234030452\n",
      "137 [8.34380314e-04 5.42149003e-07] [2.00041653 2.00112332] [1.53985545e-03 1.99970975e+00] 0.0006213059253278713\n",
      "138 [8.00381483e-04 4.99777397e-07] [2.00039958 2.00107742] [1.47700694e-03 1.99972175e+00] 0.0005958150175715607\n",
      "139 [7.67773916e-04 4.60706225e-07] [2.00038333 2.00103341] [1.41673636e-03 1.99973325e+00] 0.0005713778115298667\n",
      "140 [7.36500335e-04 4.24679518e-07] [2.00036773 2.0009912 ] [1.35893722e-03 1.99974426e+00] 0.0005479502732892523\n",
      "141 [7.06505837e-04 3.91461048e-07] [2.00035278 2.00095073] [1.30350744e-03 1.99975482e+00] 0.0005254902385359471\n",
      "142 [6.77737799e-04 3.60832816e-07] [2.00033843 2.00091192] [1.25034922e-03 1.99976494e+00] 0.0005039573313037681\n",
      "143 [6.50145781e-04 3.32593656e-07] [2.00032467 2.0008747 ] [1.19936883e-03 1.99977463e+00] 0.0004833128863799931\n",
      "144 [6.23681434e-04 3.06557944e-07] [2.00031147 2.00083901] [1.15047645e-03 1.99978392e+00] 0.00046351987519623744\n",
      "145 [5.98298411e-04 2.82554406e-07] [2.0002988  2.00080478] [1.10358600e-03 1.99979282e+00] 0.0004445428350357515\n",
      "146 [5.73952287e-04 2.60425015e-07] [2.00028666 2.00077196] [1.05861497e-03 1.99980135e+00] 0.00042634780140331533\n",
      "147 [5.50600476e-04 2.40023973e-07] [2.00027501 2.00074048] [1.01548430e-03 1.99980953e+00] 0.0004089022434100577\n",
      "148 [5.28202154e-04 2.21216772e-07] [2.00026383 2.00071029] [9.74118220e-04 1.99981737e+00] 0.00039217500202915335\n",
      "149 [5.06718186e-04 2.03879323e-07] [2.00025311 2.00068134] [9.34444083e-04 1.99982488e+00] 0.00037613623109165396\n",
      "150 [4.86111054e-04 1.87897156e-07] [2.00024282 2.00065357] [8.96392280e-04 1.99983208e+00] 0.0003607573408941173\n",
      "151 [4.66344792e-04 1.73164678e-07] [2.00023296 2.00062694] [8.59896082e-04 1.99983898e+00] 0.0003460109442975187\n",
      "152 [4.47384919e-04 1.59584486e-07] [2.00022349 2.0006014 ] [8.24891530e-04 1.99984559e+00] 0.0003318708052016025\n",
      "153 [4.29198379e-04 1.47066739e-07] [2.00021442 2.0005769 ] [7.91317316e-04 1.99985193e+00] 0.00031831178928838584\n",
      "154 [4.11753480e-04 1.35528572e-07] [2.00020571 2.00055341] [7.59114673e-04 1.99985801e+00] 0.0003053098169271207\n",
      "155 [3.95019837e-04 1.24893557e-07] [2.00019735 2.00053087] [7.28227267e-04 1.99986384e+00] 0.00029284181814569774\n",
      "156 [3.78968319e-04 1.15091207e-07] [2.00018934 2.00050926] [6.98601097e-04 1.99986942e+00] 0.00028088568957204316\n",
      "157 [3.63570995e-04 1.06056515e-07] [2.00018165 2.00048853] [6.70184394e-04 1.99987477e+00] 0.00026942025325657736\n",
      "158 [3.48801086e-04 9.77295309e-08] [2.00017428 2.00046865] [6.42927531e-04 1.99987991e+00] 0.0002584252172918649\n",
      "159 [3.34632916e-04 9.00549691e-08] [2.0001672  2.00044958] [6.16782933e-04 1.99988483e+00] 0.0002478811381464866\n",
      "160 [3.21041866e-04 8.29818483e-08] [2.00016042 2.00043129] [5.91704991e-04 1.99988955e+00] 0.00023776938463721317\n",
      "161 [3.08004330e-04 7.64631571e-08] [2.00015391 2.00041374] [5.67649977e-04 1.99989407e+00] 0.00022807210346550985\n",
      "162 [2.95497676e-04 7.04555467e-08] [2.00014766 2.00039692] [5.4457597e-04 1.9998984e+00] 0.00021877218624853024\n",
      "163 [2.83500198e-04 6.49190466e-08] [2.00014167 2.00038077] [5.22442778e-04 1.99990256e+00] 0.00020985323797624082\n",
      "164 [2.71991087e-04 5.98168022e-08] [2.00013592 2.00036529] [5.01211868e-04 1.99990655e+00] 0.00020129954683456298\n",
      "165 [2.60950387e-04 5.51148334e-08] [2.00013041 2.00035044] [4.80846294e-04 1.99991037e+00] 0.00019309605532826884\n",
      "166 [2.50358964e-04 5.07818106e-08] [2.00012512 2.0003362 ] [4.61310633e-04 1.99991404e+00] 0.00018522833265258767\n",
      "167 [2.40198467e-04 4.67888495e-08] [2.00012004 2.00032253] [4.42570921e-04 1.99991755e+00] 0.00017768254825170326\n",
      "168 [2.30451301e-04 4.31093204e-08] [2.00011517 2.00030942] [4.24594593e-04 1.99992092e+00] 0.0001704454465152657\n",
      "169 [2.21100592e-04 3.97186732e-08] [2.0001105  2.00029685] [4.07350424e-04 1.99992415e+00] 0.00016350432256335572\n",
      "170 [2.12130159e-04 3.65942752e-08] [2.00010602 2.00028479] [3.90808475e-04 1.99992725e+00] 0.00015684699906770596\n",
      "171 [2.03524484e-04 3.37152625e-08] [2.00010172 2.00027322] [3.74940037e-04 1.99993022e+00] 0.00015046180406904654\n",
      "172 [1.95268687e-04 3.10624016e-08] [2.00009759 2.00026212] [3.59717582e-04 1.99993307e+00] 0.00014433754974168818\n",
      "173 [1.87348496e-04 2.86179626e-08] [2.00009364 2.00025148] [3.45114714e-04 1.99993580e+00] 0.00013846351206699554\n",
      "174 [1.79750225e-04 2.63656025e-08] [2.00008984 2.00024126] [3.31106120e-04 1.99993842e+00] 0.0001328294113760749\n",
      "175 [1.72460748e-04 2.42902563e-08] [2.0000862  2.00023147] [3.17667528e-04 1.99994093e+00] 0.00012742539371988636\n",
      "176 [1.65467479e-04 2.23780380e-08] [2.00008271 2.00022207] [3.04775662e-04 1.99994334e+00] 0.00012224201303643714\n",
      "177 [1.58758345e-04 2.06161482e-08] [2.00007935 2.00021306] [2.92408202e-04 1.99994565e+00] 0.00011727021407493618\n",
      "178 [1.52321766e-04 1.89927895e-08] [2.00007614 2.00020441] [2.80543743e-04 1.99994787e+00] 0.00011250131604721593\n",
      "179 [1.46146640e-04 1.74970884e-08] [2.00007305 2.00019611] [2.69161760e-04 1.99994999e+00] 0.00010792699697382358\n",
      "180 [1.40222316e-04 1.61190230e-08] [2.00007009 2.00018815] [2.58242567e-04 1.99995203e+00] 0.00010353927869435465\n",
      "181 [1.34538580e-04 1.48493564e-08] [2.00006725 2.00018052] [2.47767287e-04 1.99995398e+00] 9.933051251334726e-05\n",
      "182 [1.29085635e-04 1.36795755e-08] [2.00006453 2.00017319] [2.37717816e-04 1.99995586e+00] 9.529336545444344e-05\n",
      "183 [1.23854085e-04 1.26018346e-08] [2.00006191 2.00016617] [2.28076790e-04 1.99995766e+00] 9.14208070970021e-05\n",
      "184 [1.18834918e-04 1.16089028e-08] [2.0000594  2.00015943] [2.18827561e-04 1.99995938e+00] 8.770609696870432e-05\n",
      "185 [1.14019490e-04 1.06941164e-08] [2.000057   2.00015296] [2.09954157e-04 1.99996103e+00] 8.414277247077277e-05\n",
      "186 [1.09399510e-04 9.85133408e-09] [2.00005469 2.00014675] [2.01441263e-04 1.99996262e+00] 8.07246373139489e-05\n",
      "187 [1.04967026e-04 9.07489645e-09] [2.00005247 2.0001408 ] [1.93274191e-04 1.99996414e+00] 7.744575044044639e-05\n",
      "188 [1.00714411e-04 8.35958806e-09] [2.00005035 2.00013509] [1.85438853e-04 1.99996560e+00] 7.430041541587645e-05\n",
      "189 [9.66343487e-05 7.70060271e-09] [2.00004831 2.00012961] [1.77921738e-04 1.99996700e+00] 7.128317026408431e-05\n",
      "190 [9.27198216e-05 7.09351147e-09] [2.00004635 2.00012436] [1.70709886e-04 1.99996834e+00] 6.838877773290296e-05\n",
      "191 [8.89640987e-05 6.53423308e-09] [2.00004447 2.00011932] [1.63790868e-04 1.99996963e+00] 6.561221596735444e-05\n",
      "192 [8.53607236e-05 6.01900671e-09] [2.00004267 2.00011448] [1.57152763e-04 1.99997086e+00] 6.294866957620884e-05\n",
      "193 [8.19035031e-05 5.54436688e-09] [2.00004094 2.00010984] [1.50784137e-04 1.99997205e+00] 6.039352107111082e-05\n",
      "194 [7.85864967e-05 5.10712032e-09] [2.00003929 2.00010539] [1.44674024e-04 1.99997319e+00] 5.794234266790041e-05\n",
      "195 [7.54040061e-05 4.70432459e-09] [2.0000377  2.00010112] [1.38811904e-04 1.99997428e+00] 5.559088842979034e-05\n",
      "196 [7.23505652e-05 4.33326846e-09] [2.00003617 2.00009702] [1.33187688e-04 1.99997532e+00] 5.3335086739490173e-05\n",
      "197 [6.94209309e-05 3.99145375e-09] [2.00003471 2.00009309] [1.27791699e-04 1.99997632e+00] 5.117103308781074e-05\n",
      "198 [6.66100734e-05 3.67657861e-09] [2.0000333  2.00008931] [1.22614654e-04 1.99997729e+00] 4.909498316209105e-05\n",
      "199 [6.39131681e-05 3.38652216e-09] [2.00003195 2.0000857 ] [1.17647649e-04 1.99997821e+00] 4.710334622531198e-05\n",
      "200 [6.13255868e-05 3.11933024e-09] [2.00003066 2.00008222] [1.12882145e-04 1.99997909e+00] 4.519267877182757e-05\n",
      "201 [5.88428898e-05 2.87320238e-09] [2.00002942 2.00007889] [1.08309948e-04 1.99997994e+00] 4.3359678444966815e-05\n",
      "202 [5.64608183e-05 2.64647966e-09] [2.00002823 2.0000757 ] [1.03923202e-04 1.99998076e+00] 4.1601178212894044e-05\n",
      "203 [5.41752868e-05 2.43763369e-09] [2.00002708 2.00007263] [9.97143685e-05 1.99998154e+00] 3.991414078382128e-05\n",
      "204 [5.19823761e-05 2.24525626e-09] [2.00002599 2.00006969] [9.56762178e-05 1.99998229e+00] 3.8295653255563594e-05\n",
      "205 [4.98783265e-05 2.06805000e-09] [2.00002494 2.00006687] [9.18018142e-05 1.99998301e+00] 3.6742921987152716e-05\n",
      "206 [4.78595313e-05 1.90481958e-09] [2.00002393 2.00006416] [8.80845049e-05 1.99998370e+00] 3.5253267685315065e-05\n",
      "207 [4.59225305e-05 1.75446378e-09] [2.00002296 2.00006156] [8.45179082e-05 1.99998436e+00] 3.3824120692265915e-05\n",
      "208 [4.40640051e-05 1.61596802e-09] [2.00002203 2.00005907] [8.10959022e-05 1.99998499e+00] 3.2453016473243074e-05\n",
      "209 [4.22807707e-05 1.48839759e-09] [2.00002114 2.00005667] [7.78126146e-05 1.99998560e+00] 3.1137591288862616e-05\n",
      "210 [4.05697727e-05 1.37089137e-09] [2.00002028 2.00005438] [7.46624120e-05 1.99998619e+00] 2.9875578048327962e-05\n",
      "211 [3.89280806e-05 1.26265606e-09] [2.00001946 2.00005218] [7.16398905e-05 1.99998675e+00] 2.866480233359073e-05\n",
      "212 [3.73528831e-05 1.16296078e-09] [2.00001867 2.00005006] [6.87398662e-05 1.99998728e+00] 2.750317859020462e-05\n",
      "213 [3.58414832e-05 1.07113225e-09] [2.00001792 2.00004804] [6.59573662e-05 1.99998780e+00] 2.6388706474529948e-05\n",
      "214 [3.43912933e-05 9.86550207e-10] [2.00001719 2.00004609] [6.32876199e-05 1.99998830e+00] 2.531946735322879e-05\n",
      "215 [3.29998313e-05 9.08643234e-10] [2.0000165  2.00004423] [6.07260509e-05 1.99998877e+00] 2.4293620946644793e-05\n",
      "216 [3.16647157e-05 8.36884939e-10] [2.00001583 2.00004244] [5.82682690e-05 1.99998923e+00] 2.3309402113456573e-05\n",
      "217 [3.03836618e-05 7.70790403e-10] [2.00001519 2.00004072] [5.59100626e-05 1.99998966e+00] 2.2365117764734318e-05\n",
      "218 [2.91544779e-05 7.09912911e-10] [2.00001458 2.00003907] [5.36473912e-05 1.99999008e+00] 2.1459143908965923e-05\n",
      "219 [2.79750611e-05 6.53840953e-10] [2.00001399 2.00003749] [5.14763790e-05 1.99999048e+00] 2.0589922818073095e-05\n",
      "220 [2.6843394e-05 6.0219545e-10] [2.00001342 2.00003597] [4.93933073e-05 1.99999087e+00] 1.9755960308970124e-05\n",
      "221 [2.57575412e-05 5.54627198e-10] [2.00001288 2.00003452] [4.73946091e-05 1.99999124e+00] 1.8955823140857647e-05\n",
      "222 [2.47156457e-05 5.10814522e-10] [2.00001236 2.00003312] [4.54768620e-05 1.99999159e+00] 1.818813651599097e-05\n",
      "223 [2.37159261e-05 4.70461101e-10] [2.00001186 2.00003178] [4.36367829e-05 1.99999194e+00] 1.7451581686696744e-05\n",
      "224 [2.27566732e-05 4.33293980e-10] [2.00001138 2.00003049] [4.18712220e-05 1.99999226e+00] 1.6744893659145597e-05\n",
      "225 [2.18362473e-05 3.99061721e-10] [2.00001092 2.00002926] [4.01771577e-05 1.99999258e+00] 1.6066858992877325e-05\n",
      "226 [2.09530750e-05 3.67532714e-10] [2.00001048 2.00002808] [3.85516910e-05 1.99999288e+00] 1.541631369017524e-05\n",
      "227 [2.01056470e-05 3.38493613e-10] [2.00001005 2.00002694] [3.69920406e-05 1.99999317e+00] 1.4792141173842456e-05\n",
      "228 [1.92925151e-05 3.11747899e-10] [2.00000965 2.00002585] [3.54955383e-05 1.99999344e+00] 1.419327034603082e-05\n",
      "229 [1.85122900e-05 2.87114549e-10] [2.00000926 2.0000248 ] [3.40596244e-05 1.99999371e+00] 1.3618673728848551e-05\n",
      "230 [1.77636387e-05 2.64426821e-10] [2.00000888 2.0000238 ] [3.26818428e-05 1.99999396e+00] 1.3067365680496094e-05\n",
      "231 [1.70452822e-05 2.43531126e-10] [2.00000852 2.00002284] [3.13598374e-05 1.99999421e+00] 1.2538400686067078e-05\n",
      "232 [1.63559935e-05 2.24285990e-10] [2.00000818 2.00002191] [3.00913477e-05 1.99999444e+00] 1.2030871715659578e-05\n",
      "233 [1.56945953e-05 2.06561102e-10] [2.00000785 2.00002103] [2.88742049e-05 1.99999467e+00] 1.154390865386755e-05\n",
      "234 [1.50599581e-05 1.90236431e-10] [2.00000753 2.00002018] [2.77063283e-05 1.99999488e+00] 1.1076676791030965e-05\n",
      "235 [1.44509981e-05 1.75201419e-10] [2.00000723 2.00001936] [2.65857217e-05 1.99999509e+00] 1.062837537746635e-05\n",
      "236 [1.38666756e-05 1.61354229e-10] [2.00000693 2.00001858] [2.55104698e-05 1.99999529e+00] 1.0198236236721511e-05\n",
      "237 [1.33059929e-05 1.48601065e-10] [2.00000665 2.00001783] [2.44787351e-05 1.99999548e+00] 9.78552243604618e-06\n",
      "238 [1.27679928e-05 1.36855528e-10] [2.00000638 2.0000171 ] [2.34887546e-05 1.99999566e+00] 9.38952701114785e-06\n",
      "239 [1.22517571e-05 1.26038043e-10] [2.00000613 2.00001641] [2.25388368e-05 1.99999584e+00] 9.009571743338317e-06\n",
      "240 [1.17564044e-05 1.16075313e-10] [2.00000588 2.00001575] [2.16273591e-05 1.99999601e+00] 8.645005987396496e-06\n",
      "241 [1.12810895e-05 1.06899828e-10] [2.00000564 2.00001511] [2.07527643e-05 1.99999617e+00] 8.295205546302692e-06\n",
      "242 [1.08250011e-05 9.84494065e-11] [2.00000541 2.0000145 ] [1.99135587e-05 1.99999632e+00] 7.95957159352041e-06\n",
      "243 [1.0387361e-05 9.0666776e-11] [2.00000519 2.00001391] [1.91083090e-05 1.99999647e+00] 7.63752963778121e-06\n",
      "244 [9.96742231e-06 8.34991860e-11] [2.00000498 2.00001335] [1.83356400e-05 1.99999662e+00] 7.328528531434465e-06\n",
      "245 [9.56446868e-06 7.68980504e-11] [2.00000478 2.00001281] [1.75942324e-05 1.99999675e+00] 7.032039519403573e-06\n",
      "246 [9.17781261e-06 7.08186196e-11] [2.00000459 2.00001229] [1.68828203e-05 1.99999688e+00] 6.747555325811611e-06\n",
      "247 [8.80679448e-06 6.52196774e-11] [2.0000044 2.0000118] [1.62001893e-05 1.99999701e+00] 6.47458928111163e-06\n",
      "248 [8.45078143e-06 6.00632622e-11] [2.00000423 2.00001132] [1.55451739e-05 1.99999713e+00] 6.2126744798927135e-06\n",
      "249 [8.10916620e-06 5.53144104e-11] [2.00000405 2.00001086] [1.49166561e-05 1.99999725e+00] 5.961362978478273e-06\n",
      "250 [7.78136615e-06 5.09409195e-11] [2.00000389 2.00001042] [1.43135632e-05 1.99999736e+00] 5.7202250206705464e-06\n",
      "251 [7.46682225e-06 4.69131301e-11] [2.00000373 2.00001   ] [1.37348659e-05 1.99999747e+00] 5.488848299464391e-06\n",
      "252 [7.16499808e-06 4.32037256e-11] [2.00000358 2.0000096 ] [1.31795766e-05 1.99999757e+00] 5.2668372451805066e-06\n",
      "253 [6.87537897e-06 3.97875470e-11] [2.00000344 2.00000921] [1.26467478e-05 1.99999767e+00] 5.0538123448544315e-06\n",
      "254 [6.59747110e-06 3.66414223e-11] [2.0000033  2.00000884] [1.21354705e-05 1.99999776e+00] 4.849409489416216e-06\n",
      "255 [6.33080063e-06 3.37440102e-11] [2.00000317 2.00000848] [1.16448722e-05 1.99999785e+00] 4.653279345755117e-06\n",
      "256 [6.07491291e-06 3.10756550e-11] [2.00000304 2.00000814] [1.11741160e-05 1.99999794e+00] 4.465086756806376e-06\n",
      "257 [5.8293717e-06 2.8618254e-11] [2.00000291 2.00000781] [1.07223989e-05 1.99999802e+00] 4.28451016406704e-06\n",
      "258 [5.59375845e-06 2.63551346e-11] [2.0000028  2.00000749] [1.02889504e-05 1.99999810e+00] 4.11124105571325e-06\n",
      "259 [5.36767151e-06 2.42709412e-11] [2.00000268 2.00000719] [9.87303112e-06 1.99999818e+00] 3.944983434711691e-06\n",
      "260 [5.15072553e-06 2.23515318e-11] [2.00000258 2.0000069 ] [9.47393179e-06 1.99999825e+00] 3.7854533115277305e-06\n",
      "261 [4.94255074e-06 2.05838815e-11] [2.00000247 2.00000662] [9.09097177e-06 1.99999832e+00] 3.632378214121715e-06\n",
      "262 [4.74279234e-06 1.89559946e-11] [2.00000237 2.00000635] [8.72349799e-06 1.99999839e+00] 3.4854967219496165e-06\n",
      "263 [4.55110990e-06 1.74568233e-11] [2.00000228 2.0000061 ] [8.37088385e-06 1.99999846e+00] 3.3445580156888567e-06\n",
      "264 [4.36717677e-06 1.60761929e-11] [2.00000218 2.00000585] [8.03252814e-06 1.99999852e+00] 3.2093214461623737e-06\n",
      "265 [4.19067952e-06 1.48047325e-11] [2.0000021  2.00000561] [7.70785395e-06 1.99999858e+00] 3.0795561216382237e-06\n",
      "266 [4.0213174e-06 1.3633812e-11] [2.00000201 2.00000539] [7.39630778e-06 1.99999864e+00] 2.955040512058562e-06\n",
      "267 [3.85880183e-06 1.25554832e-11] [2.00000193 2.00000517] [7.09735850e-06 1.99999869e+00] 2.8355620674459935e-06\n",
      "268 [3.70285593e-06 1.15624259e-11] [2.00000185 2.00000496] [6.81049653e-06 1.99999874e+00] 2.7209168538088895e-06\n",
      "269 [3.55321400e-06 1.06478988e-11] [2.00000178 2.00000476] [6.53523288e-06 1.99999879e+00] 2.6109092038983795e-06\n",
      "270 [3.40962110e-06 9.80569314e-12] [2.0000017  2.00000457] [6.27109837e-06 1.99999884e+00] 2.5053513803255575e-06\n",
      "271 [3.27183262e-06 9.03009094e-12] [2.00000164 2.00000438] [6.01764283e-06 1.99999889e+00] 2.4040632546260068e-06\n",
      "272 [3.13961383e-06 8.31582621e-12] [2.00000157 2.0000042 ] [5.77443429e-06 1.99999893e+00] 2.306871998035037e-06\n",
      "273 [3.01273950e-06 7.65804919e-12] [2.00000151 2.00000403] [5.54105828e-06 1.99999898e+00] 2.2136117845221952e-06\n",
      "274 [2.89099353e-06 7.05229347e-12] [2.00000145 2.00000387] [5.31711710e-06 1.99999902e+00] 2.124123507871997e-06\n",
      "275 [2.77416854e-06 6.49444571e-12] [2.00000139 2.00000372] [5.10222916e-06 1.99999906e+00] 2.0382545079397435e-06\n",
      "276 [2.66206556e-06 5.98071773e-12] [2.00000133 2.00000357] [4.89602829e-06 1.99999910e+00] 1.955858309432617e-06\n",
      "277 [2.55449366e-06 5.50762079e-12] [2.00000128 2.00000342] [4.69816315e-06 1.99999913e+00] 1.8767943704427838e-06\n",
      "278 [2.45126963e-06 5.07194199e-12] [2.00000123 2.00000328] [4.50829664e-06 1.99999917e+00] 1.800927843334551e-06\n",
      "279 [2.35221768e-06 4.67072240e-12] [2.00000118 2.00000315] [4.32610526e-06 1.99999920e+00] 1.72812934155495e-06\n",
      "280 [2.25716912e-06 4.30123704e-12] [2.00000113 2.00000302] [4.15127865e-06 1.99999923e+00] 1.6582747194290778e-06\n",
      "281 [2.16596211e-06 3.96097634e-12] [2.00000108 2.0000029 ] [3.98351897e-06 1.99999927e+00] 1.5912448596197201e-06\n",
      "282 [2.07844132e-06 3.64762919e-12] [2.00000104 2.00000278] [3.82254044e-06 1.99999930e+00] 1.526925469093133e-06\n",
      "283 [1.99445773e-06 3.35906715e-12] [2.000001   2.00000267] [3.66806886e-06 1.99999932e+00] 1.4652068823806737e-06\n",
      "284 [1.91386834e-06 3.09333012e-12] [2.00000096 2.00000256] [3.51984111e-06 1.99999935e+00] 1.405983875787363e-06\n",
      "285 [1.83653592e-06 2.84861294e-12] [2.00000092 2.00000246] [3.37760471e-06 1.99999938e+00] 1.3491554855755967e-06\n",
      "286 [1.76232882e-06 2.62325321e-12] [2.00000088 2.00000236] [3.24111742e-06 1.99999940e+00] 1.2946248369514185e-06\n",
      "287 [1.69112069e-06 2.41571997e-12] [2.00000085 2.00000226] [3.11014677e-06 1.99999943e+00] 1.242298976620928e-06\n",
      "288 [1.62279030e-06 2.22460332e-12] [2.00000081 2.00000217] [2.98446970e-06 1.99999945e+00] 1.192088714583409e-06\n",
      "289 [1.55722131e-06 2.04860485e-12] [2.00000078 2.00000209] [2.86387220e-06 1.99999947e+00] 1.1439084717744624e-06\n",
      "290 [1.49430211e-06 1.88652881e-12] [2.00000075 2.000002  ] [2.74814889e-06 1.99999949e+00] 1.0976761338193255e-06\n",
      "291 [1.43392557e-06 1.73727402e-12] [2.00000072 2.00000192] [2.63710271e-06 1.99999951e+00] 1.0533129100620345e-06\n",
      "292 [1.37598893e-06 1.59982639e-12] [2.00000069 2.00000184] [2.53054456e-06 1.99999953e+00] 1.0107431990640321e-06\n",
      "293 [1.32039355e-06 1.47325201e-12] [2.00000066 2.00000177] [2.42829300e-06 1.99999955e+00] 9.69894459741777e-07\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([2.00000066, 2.00000177])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def f(x):\n",
    "    return (x[0]-2)**2+(x[1]-2)**2\n",
    "\n",
    "\n",
    "def grad(x):\n",
    "    return np.array([2*(x[0]-2), 2*(x[1]-2)])\n",
    "\n",
    "\n",
    "def hess(x):\n",
    "    return np.array([[2, 0], [0, 2]])\n",
    "\n",
    "\n",
    "A = np.array([\n",
    "    [1, 1],\n",
    "    [2, -1]\n",
    "])\n",
    "\n",
    "b = np.array([4, 0])\n",
    "x0 = np.array([2, 4])\n",
    "lam0 = np.array([.1, .1])\n",
    "\n",
    "print(grad(x0))\n",
    "puntoInterior(x0, lam0, A, b, 0.1, 0.2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "k, lamdas, x, y, error\n",
      "0 [ 0.09419806  0.10613856  0.10037337  0.10072298 -0.00778251 -0.11524705\n",
      " -0.06336032 -0.06650681] [0.79221749 0.68475295 0.73663968 0.73349319] [0.79221749 0.68475295 0.73663968 0.73349319 0.20778251 0.31524705\n",
      " 0.26336032 0.26650681] 2.3706061913102503\n",
      "1 [ 0.08720674  0.11453296  0.09981635  0.10038989  0.00242384 -0.02263652\n",
      " -0.01466743 -0.01578237] [0.70439606 0.50413989 0.6044964  0.60027843] [0.70439606 0.50413989 0.6044964  0.60027843 0.29560394 0.49586011\n",
      " 0.3955036  0.39972157] 1.4940407633226016\n",
      "2 [ 0.08013354  0.12602383  0.09906142  0.09995551  0.00502749 -0.00944044\n",
      " -0.00507804 -0.00569898] [0.63309966 0.36221239 0.49904665 0.49363548] [0.63309966 0.36221239 0.49904665 0.49363548 0.36690034 0.63778761\n",
      " 0.50095335 0.50636452] 1.0985938337489867\n",
      "3 [ 0.07282493  0.14269496  0.09784628  0.09912938  0.00576547 -0.00442514\n",
      " -0.00135569 -0.00176623] [0.5757995  0.24921624 0.41472436 0.40827   ] [0.5757995  0.24921624 0.41472436 0.40827    0.4242005  0.75078376\n",
      " 0.58527564 0.59173   ] 0.8780300778728984\n",
      "4 [ 6.54479851e-02  1.68677086e-01  9.60659237e-02  9.78232697e-02\n",
      "  5.82209642e-03 -1.97328089e-03  4.02905459e-04  1.07958859e-04] [0.52966528 0.15945554 0.34728858 0.33985523] [0.52966528 0.15945554 0.34728858 0.33985523 0.47033472 0.84054446\n",
      " 0.65271142 0.66014477] 0.7099384006139914\n",
      "5 [ 0.0581968   0.21378178  0.09363259  0.09599241  0.00557291 -0.00064184\n",
      "  0.0012817   0.00105886] [0.49231532 0.0887668  0.29337218 0.28486831] [0.49231532 0.0887668  0.29337218 0.28486831 0.50768468 0.9112332\n",
      " 0.70662782 0.71513169] 0.6004634710663523\n",
      "6 [5.12758712e-02 3.07047717e-01 9.04606285e-02 9.36891745e-02\n",
      " 5.16786860e-03 1.08106847e-04 1.69978078e-03 1.52461811e-03] [0.46153682 0.03477475 0.25031531 0.24026923] [0.46153682 0.03477475 0.25031531 0.24026923 0.53846318 0.96522525\n",
      " 0.74968469 0.75973077] 0.6416452906760096\n",
      "7 [4.49780518e-02 5.66808252e-01 8.64178391e-02 9.13951949e-02\n",
      " 4.65939348e-03 5.21930857e-04 1.84799460e-03 1.70235577e-03] [ 4.34187133e-01 -2.18258714e-04  2.16127200e-01  2.02624896e-01] [ 4.34187133e-01 -2.18258714e-04  2.16127200e-01  2.02624896e-01\n",
      "  5.65812867e-01  1.00021826e+00  7.83872800e-01  7.97375104e-01] 1.342532380854869\n",
      "8 [3.99529631e-02 1.42948198e+00 8.11474083e-02 9.13612560e-02\n",
      " 4.02204180e-03 7.30789371e-04 1.81518086e-03 1.67515730e-03] [0.4028136  0.00070949 0.18970283 0.16559798] [4.02813595e-01 7.09492526e-04 1.89702831e-01 1.65597975e-01\n",
      " 5.97186405e-01 9.99290507e-01 8.10297169e-01 8.34402025e-01] 4.322365805897846\n",
      "9 [3.50897665e-02 2.09601871e+00 7.53949365e-02 9.09078061e-02\n",
      " 3.49951329e-03 8.52771900e-04 1.73561882e-03 1.60255527e-03] [0.37799443 0.00042436 0.16851473 0.13623543] [3.77994432e-01 4.24364303e-04 1.68514725e-01 1.36235431e-01\n",
      " 6.22005568e-01 9.99575636e-01 8.31485275e-01 8.63764569e-01] 3.3401183624745547\n",
      "10 [3.05198357e-02 2.63215903e+00 6.92423192e-02 9.00739667e-02\n",
      " 3.04993537e-03 9.07738683e-04 1.62429228e-03 1.49947780e-03] [3.58050150e-01 3.38527638e-04 1.51554354e-01 1.12718466e-01] [3.58050150e-01 3.38527638e-04 1.51554354e-01 1.12718466e-01\n",
      " 6.41949850e-01 9.99661472e-01 8.48445646e-01 8.87281534e-01] 2.6867479664074674\n",
      "11 [2.63101702e-02 3.06117811e+00 6.28536059e-02 8.87833549e-02\n",
      " 2.66025362e-03 9.16407308e-04 1.49760666e-03 1.38214230e-03] [3.42058679e-01 2.87904325e-04 1.37973645e-01 9.39014179e-02] [3.42058679e-01 2.87904325e-04 1.37973645e-01 9.39014179e-02\n",
      " 6.57941321e-01 9.99712096e-01 8.62026355e-01 9.06098582e-01] 2.1500697606137367\n",
      "12 [2.25028924e-02 3.40416209e+00 5.64004308e-02 8.69749416e-02\n",
      " 2.32033669e-03 8.93636479e-04 1.36537900e-03 1.25987348e-03] [3.29245638e-01 2.50496128e-04 1.27098192e-01 7.88415533e-02] [3.29245638e-01 2.50496128e-04 1.27098192e-01 7.88415533e-02\n",
      " 6.70754362e-01 9.99749504e-01 8.72901808e-01 9.21158447e-01] 1.7190609413724847\n",
      "13 [1.91148835e-02 3.67822890e+00 5.00507107e-02 8.46013369e-02\n",
      " 2.02271304e-03 8.50363450e-04 1.23384998e-03 1.13844561e-03] [3.18986463e-01 2.20018441e-04 1.18389162e-01 6.67821989e-02] [3.18986463e-01 2.20018441e-04 1.18389162e-01 6.67821989e-02\n",
      " 6.81013537e-01 9.99779982e-01 8.81610838e-01 9.33217801e-01] 1.3738331090177307\n",
      "14 [1.61420416e-02 3.89712635e+00 4.39541593e-02 8.16355263e-02\n",
      " 1.76163044e-03 7.94593064e-04 1.10696855e-03 1.02144559e-03] [3.10779129e-01 1.93995637e-04 1.11415686e-01 5.71179306e-02] [3.10779129e-01 1.93995637e-04 1.11415686e-01 5.71179306e-02\n",
      " 6.89220871e-01 9.99806004e-01 8.88584314e-01 9.42882069e-01] 1.0975015488672897\n",
      "15 [1.35646282e-02 4.07187009e+00 3.82313171e-02 7.80776321e-02\n",
      " 1.53246583e-03 7.32115078e-04 9.87152307e-04 9.11039733e-04] [3.04220131e-01 1.71244353e-04 1.05833002e-01 4.93650447e-02] [3.04220131e-01 1.71244353e-04 1.05833002e-01 4.93650447e-02\n",
      " 6.95779869e-01 9.99828756e-01 8.94166998e-01 9.50634955e-01] 0.8763818316026339\n",
      "16 [1.13525580e-02 4.21128232e+00 3.29677923e-02 7.39597429e-02\n",
      " 1.33137094e-03 6.67048018e-04 8.75775362e-04 8.08445213e-04] [2.98984931e-01 1.51112634e-04 1.01365052e-01 4.31375939e-02] [2.98984931e-01 1.51112634e-04 1.01365052e-01 4.31375939e-02\n",
      " 7.01015069e-01 9.99848887e-01 8.98634948e-01 9.56862406e-01] 0.699491654017189\n",
      "17 [9.46998768e-03 4.32242950e+00 2.82137202e-02 6.93473718e-02\n",
      " 1.15505639e-03 6.02255234e-04 7.73495266e-04 7.14235535e-04] [2.94812286e-01 1.33195779e-04 9.77906171e-02 3.81280568e-02] [2.94812286e-01 1.33195779e-04 9.77906171e-02 3.81280568e-02\n",
      " 7.05187714e-01 9.99866804e-01 9.02209383e-01 9.61871943e-01] 0.5580423923146627\n",
      "18 [7.87891877e-03 4.41097379e+00 2.39873210e-02 6.43367147e-02\n",
      " 1.00065729e-03 5.39663670e-04 6.80478684e-04 6.28546263e-04] [2.91491724e-01 1.17214443e-04 9.49322972e-02 3.40917382e-02] [2.91491724e-01 1.17214443e-04 9.49322972e-02 3.40917382e-02\n",
      " 7.08508276e-01 9.99882786e-01 9.05067703e-01 9.65908262e-01] 0.44500350590465837\n",
      "19 [6.54178512e-03 4.48145378e+00 2.02809409e-02 5.90477744e-02\n",
      " 8.65647072e-04 4.80507774e-04 5.96560508e-04 5.51217666e-04] [2.88853581e-01 1.02957177e-04 9.26477442e-02 3.08341565e-02] [2.88853581e-01 1.02957177e-04 9.26477442e-02 3.08341565e-02\n",
      " 7.11146419e-01 9.99897043e-01 9.07352256e-01 9.69165843e-01] 0.3547447261700696\n",
      "20 [5.42314387e-03 4.53750813e+00 1.70680007e-02 5.36143606e-02\n",
      " 7.47780425e-04 4.25515645e-04 5.21357566e-04 4.81895680e-04] [2.86761066e-01 9.02515983e-05 9.08226946e-02 2.82008374e-02] [2.86761066e-01 9.02515983e-05 9.08226946e-02 2.82008374e-02\n",
      " 7.13238934e-01 9.99909748e-01 9.09177305e-01 9.71799163e-01] 0.282748010341357\n",
      "21 [4.49065026e-03 4.58205370e+00 1.43096597e-02 4.81726553e-02\n",
      " 6.45053662e-04 3.75050489e-04 4.54350397e-04 4.20104312e-04] [2.85103948e-01 7.89493319e-05 8.93654213e-02 2.60690640e-02] [2.85103948e-01 7.89493319e-05 8.93654213e-02 2.60690640e-02\n",
      " 7.14896052e-01 9.99921051e-01 9.10634579e-01 9.73930936e-01] 0.22537934013070027\n",
      "22 [3.71550465e-03 4.61742760e+00 1.19604808e-02 4.28502343e-02\n",
      " 5.55675706e-04 3.29217552e-04 3.94942068e-04 3.65297792e-04] [2.83793508e-01 6.89179913e-05 8.82023070e-02 2.43412361e-02] [2.83793508e-01 6.89179913e-05 8.82023070e-02 2.43412361e-02\n",
      " 7.16206492e-01 9.99931082e-01 9.11797693e-01 9.75658764e-01] 0.1797103460216439\n",
      "23 [3.07253724e-03 4.64550069e+00 9.97280683e-03 3.77571576e-02\n",
      " 4.78045483e-04 2.87944393e-04 3.42500194e-04 3.16898035e-04] [2.82758477e-01 6.00368718e-05 8.72743015e-02 2.29395595e-02] [2.82758477e-01 6.00368718e-05 8.72743015e-02 2.29395595e-02\n",
      " 7.17241523e-01 9.99939963e-01 9.12725699e-01 9.77060440e-01] 0.14337992656812595\n",
      "24 [2.54006283e-03 4.66776873e+00 8.29985503e-03 3.29801227e-02\n",
      " 4.10733286e-04 2.51040638e-04 2.96386523e-04 2.74321233e-04] [2.81941759e-01 5.21946537e-05 8.65340776e-02 2.18018336e-02] [2.81941759e-01 5.21946537e-05 8.65340776e-02 2.18018336e-02\n",
      " 7.18058241e-01 9.99947805e-01 9.13465922e-01 9.78198166e-01] 0.11448660522155378\n",
      "25 [2.09960382e-03 4.68542575e+00 6.89770203e-03 2.85799622e-02\n",
      " 3.52464663e-04 2.18242022e-04 2.55977321e-04 2.36996323e-04] [2.81297746e-01 4.52881889e-05 8.59437411e-02 2.08781401e-02] [2.81297746e-01 4.52881889e-05 8.59437411e-02 2.08781401e-02\n",
      " 7.18702254e-01 9.99954712e-01 9.14056259e-01 9.79121860e-01] 0.09150354781659462\n",
      "26 [1.73555009e-03 4.69942336e+00 5.72639811e-03 2.45921431e-02\n",
      " 3.02106012e-04 1.89242428e-04 2.20676904e-04 2.04377397e-04] [2.80790127e-01 3.92218578e-05 8.54729827e-02 2.01282590e-02] [2.80790127e-01 3.92218578e-05 8.54729827e-02 2.01282590e-02\n",
      " 7.19209873e-01 9.99960778e-01 9.14527017e-01 9.79871741e-01] 0.07320988790106563\n",
      "27 [1.43480113e-03 4.71051870e+00 4.75044811e-03 2.10295256e-02\n",
      " 2.58651449e-04 1.63716850e-04 1.89926135e-04 1.75951554e-04] [2.80390083e-01 3.39072115e-05 8.50975848e-02 1.95196627e-02] [2.80390083e-01 3.39072115e-05 8.50975848e-02 1.95196627e-02\n",
      " 7.19609917e-01 9.99966093e-01 9.14902415e-01 9.80480337e-01] 0.05863393429623342\n",
      "28 [1.18641855e-03 4.71931335e+00 3.93886499e-03 1.78864845e-02\n",
      " 2.21210682e-04 1.41337501e-04 1.63207214e-04 1.51243413e-04] [2.80074806e-01 2.92627371e-05 8.47982152e-02 1.90259607e-02] [2.80074806e-01 2.92627371e-05 8.47982152e-02 1.90259607e-02\n",
      " 7.19925194e-01 9.99970737e-01 9.15201785e-01 9.80974039e-01] 0.04700554491153861\n",
      "29 [9.81304688e-04 4.72628465e+00 3.26495728e-03 1.51435505e-02\n",
      " 1.88997776e-04 1.21784804e-04 1.40045815e-04 1.29817168e-04] [2.79826290e-01 2.52136558e-05 8.45594530e-02 1.86256901e-02] [2.79826290e-01 2.52136558e-05 8.45594530e-02 1.86256901e-02\n",
      " 7.20173710e-01 9.99974786e-01 9.15440547e-01 9.81374310e-01] 0.037716151190446454\n",
      "30 [8.11914991e-04 4.73181104e+00 2.70596839e-03 1.27719102e-02\n",
      " 1.61320731e-04 1.04754597e-04 1.20011312e-04 1.11276892e-04] [2.79630346e-01 2.16917085e-05 8.43690042e-02 1.83013685e-02] [2.79630346e-01 2.16917085e-05 8.43690042e-02 1.83013685e-02\n",
      " 7.20369654e-01 9.99978308e-01 9.15630996e-01 9.81698631e-01] 0.030285548358921256\n",
      "31 [6.72006394e-04 4.73619239e+00 2.24264897e-03 1.07373384e-02\n",
      " 1.37571821e-04 8.99625400e-05 1.02715698e-04 9.52656141e-05] [2.79475803e-01 1.86349078e-05 8.42170714e-02 1.80387461e-02] [2.79475803e-01 1.86349078e-05 8.42170714e-02 1.80387461e-02\n",
      " 7.20524197e-01 9.99981365e-01 9.15782929e-01 9.81961254e-01] 0.024334762549788388\n",
      "32 [5.56420873e-04 4.73966620e+00 1.85881479e-03 9.00335361e-03\n",
      " 1.17218686e-04 7.71465032e-05 8.78116255e-05 8.14635797e-05] [2.79353875e-01 1.59872488e-05 8.40958480e-02 1.78262074e-02] [2.79353875e-01 1.59872488e-05 8.40958480e-02 1.78262074e-02\n",
      " 7.20646125e-01 9.99984013e-01 9.15904152e-01 9.82173793e-01] 0.019564278541932448\n",
      "33 [4.60901499e-04 4.74242056e+00 1.54092167e-03 7.53355849e-03\n",
      " 9.97961282e-05 6.60675140e-05 7.49898882e-05 6.95859820e-05] [2.79257654e-01 1.36983828e-05 8.39991136e-02 1.76542894e-02] [2.79257654e-01 1.36983828e-05 8.39991136e-02 1.76542894e-02\n",
      " 7.20742346e-01 9.99986302e-01 9.16000886e-01 9.82345711e-01] 0.015736839622601355\n",
      "34 [3.81937541e-04 4.74460450e+00 1.27767495e-03 6.29323666e-03\n",
      " 8.48985984e-05 5.65096890e-05 6.39765888e-05 5.93803972e-05] [2.79181702e-01 1.17232613e-05 8.39219118e-02 1.75152892e-02] [2.79181702e-01 1.17232613e-05 8.39219118e-02 1.75152892e-02\n",
      " 7.20818298e-01 9.99988277e-01 9.16078088e-01 9.82484711e-01] 0.01266400936381513\n",
      "35 [3.16634903e-04 4.74633605e+00 1.05968107e-03 5.25033277e-03\n",
      " 7.21733508e-05 4.82794829e-05 5.45301664e-05 5.06240820e-05] [2.79121742e-01 1.00217591e-05 8.38602920e-02 1.74029437e-02] [2.79121742e-01 1.00217591e-05 8.38602920e-02 1.74029437e-02\n",
      " 7.20878258e-01 9.99989978e-01 9.16139708e-01 9.82597056e-01] 0.010195734557254284\n",
      "36 [2.62608308e-04 4.74770879e+00 8.79143197e-04 4.37595861e-03\n",
      " 6.13142286e-05 4.12044928e-05 4.64384081e-05 4.31212516e-05] [2.79074405e-01 8.55828636e-06 8.38111050e-02 1.73121659e-02] [2.79074405e-01 8.55828636e-06 8.38111050e-02 1.73121659e-02\n",
      " 7.20925595e-01 9.99991442e-01 9.16188895e-01 9.82687834e-01] 0.008212248803343635\n",
      "37 [2.17891907e-04 4.74879689e+00 7.29599319e-04 3.64455908e-03\n",
      " 5.20560533e-05 3.51319961e-05 3.95155354e-05 3.67004200e-05] [2.79037035e-01 7.30140062e-06 8.37718398e-02 1.72388291e-02] [2.79037035e-01 7.30140062e-06 8.37718398e-02 1.72388291e-02\n",
      " 7.20962965e-01 9.99992699e-01 9.16228160e-01 9.82761171e-01] 0.006617776766664988\n",
      "38 [1.80865366e-04 4.74965918e+00 6.05699376e-04 3.03385043e-03\n",
      " 4.41695820e-05 2.99273513e-05 3.35994229e-05 3.12118589e-05] [2.79007539e-01 6.22342430e-06 8.37404935e-02 1.71795887e-02] [2.79007539e-01 6.22342430e-06 8.37404935e-02 1.71795887e-02\n",
      " 7.20992461e-01 9.99993777e-01 9.16259507e-01 9.82820411e-01] 0.005335615978814169\n",
      "39 [1.50192866e-04 4.75034233e+00 5.03017112e-04 2.52461855e-03\n",
      " 3.74569967e-05 2.54723547e-05 2.85489900e-05 2.65252121e-05] [2.78984264e-01 5.30007622e-06 8.37154684e-02 1.71317371e-02] [2.78984264e-01 5.30007622e-06 8.37154684e-02 1.71317371e-02\n",
      " 7.21015736e-01 9.99994700e-01 9.16284532e-01 9.82868263e-01] 0.004304273395095664\n",
      "40 [1.24772844e-04 4.75088338e+00 4.17892255e-04 2.10044149e-03\n",
      " 3.17478857e-05 2.16636161e-05 2.42417861e-05 2.25272832e-05] [2.78965904e-01 4.51012111e-06 8.36954896e-02 1.70930838e-02] [2.78965904e-01 4.51012111e-06 8.36954896e-02 1.70930838e-02\n",
      " 7.21034096e-01 9.99995490e-01 9.16304510e-01 9.82906916e-01] 0.003474413753436469\n",
      "41 [1.03696604e-04 4.75131170e+00 3.47298740e-04 1.74738047e-03\n",
      " 2.68956798e-05 1.84109984e-05 2.05717802e-05 1.91200097e-05] [2.78951428e-01 3.83504067e-06 8.36795396e-02 1.70618582e-02] [2.78951428e-01 3.83504067e-06 8.36795396e-02 1.70618582e-02\n",
      " 7.21048572e-01 9.99996165e-01 9.16320460e-01 9.82938142e-01] 0.0028064374272031185\n",
      "42 [8.62142637e-05 4.75165064e+00 2.88735069e-04 1.45366855e-03\n",
      " 2.27745030e-05 1.56361481e-05 1.74473557e-05 1.62186234e-05] [2.78940021e-01 3.25872864e-06 8.36668064e-02 1.70366296e-02] [2.78940021e-01 3.25872864e-06 8.36668064e-02 1.70366296e-02\n",
      " 7.21059979e-01 9.99996741e-01 9.16333194e-01 9.82963370e-01] 0.0022685503488878178\n",
      "43 [7.17067440e-05 4.75191871e+00 2.40133312e-04 1.20941443e-03\n",
      " 1.92764005e-05 1.32711327e-05 1.47895057e-05 1.37499925e-05] [2.78931039e-01 2.76721058e-06 8.36566415e-02 1.70162425e-02] [2.78931039e-01 2.76721058e-06 8.36566415e-02 1.70162425e-02\n",
      " 7.21068961e-01 9.99997233e-01 9.16343359e-01 9.82983758e-01] 0.0018352214680007826\n",
      "44 [5.96627300e-05 4.75213059e+00 1.99783740e-04 1.00633095e-03\n",
      " 1.63089064e-05 1.12571935e-05 1.25302195e-05 1.16511386e-05] [2.78923970e-01 2.34838878e-06 8.36485273e-02 1.69997642e-02] [2.78923970e-01 2.34838878e-06 8.36485273e-02 1.69997642e-02\n",
      " 7.21076030e-01 9.99997652e-01 9.16351473e-01 9.83000236e-01] 0.0014859473386593365\n",
      "45 [4.96597208e-05 4.75229797e+00 1.66272491e-04 8.37492809e-04\n",
      " 1.37929160e-05 9.54361458e-06 1.06110480e-05 9.86791716e-06] [2.78918414e-01 1.99181176e-06 8.36420505e-02 1.69864420e-02] [2.78918414e-01 1.99181176e-06 8.36420505e-02 1.69864420e-02\n",
      " 7.21081586e-01 9.99998008e-01 9.16357949e-01 9.83013558e-01] 0.0012042613086085258\n",
      "46 [4.13484416e-05 4.75243008e+00 1.38430056e-04 6.97124094e-04\n",
      " 1.16608311e-05 8.08670625e-06 8.98183538e-06 8.35384953e-06] [2.78914049e-01 1.68846732e-06 8.36368812e-02 1.69756681e-02] [2.78914049e-01 1.68846732e-06 8.36368812e-02 1.69756681e-02\n",
      " 7.21085951e-01 9.99998312e-01 9.16363119e-01 9.83024332e-01] 0.0009769382082910588\n",
      "47 [3.44400170e-05 4.75253429e+00 1.15288752e-04 5.80414722e-04\n",
      " 9.85494621e-06 6.84889757e-06 7.59960213e-06 7.06909368e-06] [2.78910626e-01 1.43059787e-06 8.36327556e-02 1.69669525e-02] [2.78910626e-01 1.43059787e-06 8.36327556e-02 1.69669525e-02\n",
      " 7.21089374e-01 9.99998569e-01 9.16367244e-01 9.83033047e-01] 0.0007933556779086019\n",
      "48 [2.86954136e-05 4.75261641e+00 9.60476111e-05 4.83363343e-04\n",
      " 8.32604858e-06 5.79793102e-06 6.42756514e-06 5.97954090e-06] [2.78907943e-01 1.21153653e-06 8.36294634e-02 1.69598995e-02] [2.78907943e-01 1.21153653e-06 8.36294634e-02 1.69598995e-02\n",
      " 7.21092057e-01 9.99998788e-01 9.16370537e-01 9.83040100e-01] 0.000644981191614827\n",
      "49 [2.39167469e-05 4.75268107e+00 8.00434152e-05 4.02644026e-04\n",
      " 7.03220606e-06 4.90615147e-06 5.43428164e-06 5.05602575e-06] [2.78905844e-01 1.02556221e-06 8.36268365e-02 1.69541899e-02] [2.78905844e-01 1.02556221e-06 8.36268365e-02 1.69541899e-02\n",
      " 7.21094156e-01 9.99998974e-01 9.16373163e-01 9.83045810e-01] 0.0005249600410889392\n",
      "50 [1.99401210e-05 4.75273192e+00 6.67267918e-05 3.35493771e-04\n",
      " 5.93772015e-06 4.14988131e-06 4.59290313e-06 4.27363730e-06] [2.78904204e-01 8.67772219e-07 8.36247407e-02 1.69495660e-02] [2.78904204e-01 8.67772219e-07 8.36247407e-02 1.69495660e-02\n",
      " 7.21095796e-01 9.99999132e-01 9.16375259e-01 9.83050434e-01] 0.00042778444489643627\n",
      "51 [1.66297277e-05 4.75277187e+00 5.56424888e-05 2.79618044e-04\n",
      " 5.01222316e-06 3.50887328e-06 3.88052726e-06 3.61112033e-06] [2.78902925e-01 7.33970479e-07 8.36230689e-02 1.69458198e-02] [2.78902925e-01 7.33970479e-07 8.36230689e-02 1.69458198e-02\n",
      " 7.21097075e-01 9.99999266e-01 9.16376931e-01 9.83054180e-01] 0.00034902785466163407\n",
      "52 [1.38729813e-05 4.75280322e+00 4.64130956e-05 2.33111729e-04\n",
      " 4.22990112e-06 2.96583309e-06 3.27763609e-06 3.05035612e-06] [2.78901929e-01 6.20569894e-07 8.36217354e-02 1.69427834e-02] [2.78901929e-01 6.20569894e-07 8.36217354e-02 1.69427834e-02\n",
      " 7.21098071e-01 9.99999379e-01 9.16378265e-01 9.83057217e-01] 0.0002851316528404766\n",
      "53 [1.15765053e-05 4.75282779e+00 3.87256035e-05 1.94393154e-04\n",
      " 3.56882593e-06 2.50600420e-06 2.76761041e-06 2.57591324e-06] [2.78901156e-01 5.24507295e-07 8.36206719e-02 1.69403214e-02] [2.78901156e-01 5.24507295e-07 8.36206719e-02 1.69403214e-02\n",
      " 7.21098844e-01 9.99999475e-01 9.16379328e-01 9.83059679e-01] 0.00023323394381057468\n",
      "54 [9.66282076e-06 4.75284701e+00 3.23203095e-05 1.62149145e-04\n",
      " 3.01038235e-06 2.11680758e-06 2.33631066e-06 2.17465981e-06] [2.78900557e-01 4.43169552e-07 8.36198239e-02 1.69383240e-02] [2.78900557e-01 4.43169552e-07 8.36198239e-02 1.69383240e-02\n",
      " 7.21099443e-01 9.99999557e-01 9.16380176e-01 9.83061676e-01] 0.0001910321555809373\n",
      "55 [8.06761156e-06 4.75286203e+00 2.69816489e-05 1.35289340e-04\n",
      " 2.53877695e-06 1.78752997e-06 1.97171600e-06 1.83542936e-06] [2.78900093e-01 3.74329537e-07 8.36191479e-02 1.69367029e-02] [2.78900093e-01 3.74329537e-07 8.36191479e-02 1.69367029e-02\n",
      " 7.21099907e-01 9.99999626e-01 9.16380852e-01 9.83063297e-01] 0.00015667279158540072\n",
      "56 [6.73746555e-06 4.75287374e+00 2.25306210e-05 1.12908231e-04\n",
      " 2.14061787e-06 1.50905470e-06 1.66361394e-06 1.54873340e-06] [2.78899736e-01 3.16090751e-07 8.36186090e-02 1.69353866e-02] [2.78899736e-01 3.16090751e-07 8.36186090e-02 1.69353866e-02\n",
      " 7.21100264e-01 9.99999684e-01 9.16381391e-01 9.83064613e-01] 0.00012866297790612582\n",
      "57 [5.62800734e-06 4.75288285e+00 1.88185269e-05 9.42536740e-05\n",
      " 1.80455561e-06 1.27362973e-06 1.40333404e-06 1.30651470e-06] [2.78899462e-01 2.66839549e-07 8.36181796e-02 1.69343172e-02] [2.78899462e-01 2.66839549e-07 8.36181796e-02 1.69343172e-02\n",
      " 7.21100538e-01 9.99999733e-01 9.16381820e-01 9.83065683e-01] 0.00010579950266297011\n",
      "58 [4.70235443e-06 4.75288993e+00 1.57217914e-05 7.87007571e-05\n",
      " 1.52097626e-06 1.07466811e-06 1.18351947e-06 1.10193557e-06] [2.78899252e-01 2.25203987e-07 8.36178374e-02 1.69334479e-02] [2.78899252e-01 2.25203987e-07 8.36178374e-02 1.69334479e-02\n",
      " 7.21100748e-01 9.99999775e-01 9.16382163e-01 9.83066552e-01] 8.711189041340804e-05\n",
      "59 [3.92983985e-06 4.75289541e+00 1.31376775e-05 6.57301403e-05\n",
      " 1.28173989e-06 9.06576597e-07 9.97931599e-07 9.29196663e-07] [2.78899093e-01 1.90018437e-07 8.36175648e-02 1.69327410e-02] [2.78899093e-01 1.90018437e-07 8.36175648e-02 1.69327410e-02\n",
      " 7.21100907e-01 9.99999810e-01 9.16382435e-01 9.83067259e-01] 7.181673521442883e-05\n",
      "60 [3.28495487e-06 4.75289964e+00 1.09807404e-05 5.49100942e-05\n",
      " 1.07995749e-06 7.64608701e-07 8.41282840e-07 7.83381965e-07] [2.78898972e-01 1.60293206e-07 8.36173478e-02 1.69321658e-02] [2.78898972e-01 1.60293206e-07 8.36173478e-02 1.69321658e-02\n",
      " 7.21101028e-01 9.99999840e-01 9.16382652e-01 9.83067834e-01] 5.9281063420989384e-05\n",
      "61 [2.74647342e-06 4.75290290e+00 9.17989048e-06 4.58816115e-05\n",
      " 9.09801157e-07 6.44738832e-07 7.09093889e-07 6.60326363e-07] [2.78898881e-01 1.35188501e-07 8.36171749e-02 1.69316976e-02] [2.78898881e-01 1.35188501e-07 8.36171749e-02 1.69316976e-02\n",
      " 7.21101119e-01 9.99999865e-01 9.16382825e-01 9.83068302e-01] 4.8992937397755956e-05\n",
      "62 [2.29672661e-06 4.75290540e+00 7.67595982e-06 3.83460642e-05\n",
      " 7.66342520e-07 5.43554661e-07 5.97571955e-07 5.56502621e-07] [2.78898812e-01 1.13992129e-07 8.36170373e-02 1.69313161e-02] [2.78898812e-01 1.13992129e-07 8.36170373e-02 1.69313161e-02\n",
      " 7.21101188e-01 9.99999886e-01 9.16382963e-01 9.83068684e-01] 4.05378648870537e-05\n",
      "63 [1.92100144e-06 4.75290732e+00 6.41968570e-06 3.20549701e-05\n",
      " 6.45415392e-07 4.58165165e-07 5.03506944e-07 4.68925027e-07] [2.78898762e-01 9.61004338e-08 8.36169278e-02 1.69310053e-02] [2.78898762e-01 9.61004338e-08 8.36169278e-02 1.69310053e-02\n",
      " 7.21101238e-01 9.99999904e-01 9.16383072e-01 9.83068995e-01] 3.357986281745902e-05\n",
      "64 [1.60704203e-06 4.75290877e+00 5.37003822e-06 2.68015062e-05\n",
      " 5.43499093e-07 3.86122149e-07 4.24183055e-07 3.95067314e-07] [2.78898725e-01 8.10020101e-08 8.36168407e-02 1.69307518e-02] [2.78898725e-01 8.10020101e-08 8.36168407e-02 1.69307518e-02\n",
      " 7.21101275e-01 9.99999919e-01 9.16383159e-01 9.83069248e-01] 2.7846252363280085e-05\n",
      "65 [1.34463593e-06 4.75290987e+00 4.49283301e-06 2.24134695e-05\n",
      " 4.57619386e-07 3.25353341e-07 3.57303557e-07 3.32792799e-07] [2.78898698e-01 6.82638115e-08 8.36167714e-02 1.69305449e-02] [2.78898698e-01 6.82638115e-08 8.36167714e-02 1.69305449e-02\n",
      " 7.21101302e-01 9.99999932e-01 9.16383229e-01 9.83069455e-01] 2.311544511706102e-05\n",
      "66 [1.12527067e-06 4.75291070e+00 3.75957987e-06 1.87474365e-05\n",
      " 3.85264413e-07 2.74105401e-07 3.00926830e-07 2.80294969e-07] [2.78898679e-01 5.75193042e-08 8.36167163e-02 1.69303761e-02] [2.78898679e-01 5.75193042e-08 8.36167163e-02 1.69303761e-02\n",
      " 7.21101321e-01 9.99999942e-01 9.16383284e-01 9.83069624e-01] 1.9207127119309536e-05\n",
      "67 [9.41848541e-07 4.75291132e+00 3.14652682e-06 1.56839164e-05\n",
      " 3.24313417e-07 2.30895416e-07 2.53412018e-07 2.36046998e-07] [2.78898666e-01 4.84583803e-08 8.36166725e-02 1.69302381e-02] [2.78898666e-01 4.84583803e-08 8.36166725e-02 1.69302381e-02\n",
      " 7.21101334e-01 9.99999952e-01 9.16383328e-01 9.83069762e-01] 1.5974365340921198e-05\n",
      "68 [7.88449713e-07 4.75291177e+00 2.63386605e-06 1.31233266e-05\n",
      " 2.72976323e-07 1.94469655e-07 2.13372884e-07 1.98758865e-07] [2.78898657e-01 4.08187731e-08 8.36166377e-02 1.69301254e-02] [2.78898657e-01 4.08187731e-08 8.36166377e-02 1.69301254e-02\n",
      " 7.21101343e-01 9.99999959e-01 9.16383362e-01 9.83069875e-01] 1.329725570130982e-05\n",
      "69 [6.60135307e-07 4.75291211e+00 2.20507413e-06 1.09826508e-05\n",
      " 2.29742556e-07 1.63768516e-07 1.79638656e-07 1.67340960e-07] [2.78898651e-01 3.43787575e-08 8.36166101e-02 1.69300332e-02] [2.78898651e-01 3.43787575e-08 8.36166101e-02 1.69300332e-02\n",
      " 7.21101349e-01 9.99999966e-01 9.16383390e-01 9.83069967e-01] 1.1077807489162755e-05\n",
      "70 [5.52783695e-07 4.75291235e+00 1.84636347e-06 9.19266298e-06\n",
      " 1.93337706e-07 1.37896759e-07 1.51220820e-07 1.40873221e-07] [2.78898648e-01 2.89509476e-08 8.36165881e-02 1.69299577e-02] [2.78898648e-01 2.89509476e-08 8.36165881e-02 1.69299577e-02\n",
      " 7.21101352e-01 9.99999971e-01 9.16383412e-01 9.83070042e-01] 9.235819784212263e-06\n",
      "71 [4.62954333e-07 4.75291252e+00 1.54622620e-06 7.69561997e-06\n",
      " 1.62686841e-07 1.16098243e-07 1.27284970e-07 1.18578959e-07] [2.78898646e-01 2.43770295e-08 8.36165707e-02 1.69298960e-02] [2.78898646e-01 2.43770295e-08 8.36165707e-02 1.69298960e-02\n",
      " 7.21101354e-01 9.99999976e-01 9.16383429e-01 9.83070104e-01] 7.705554132903978e-06\n",
      "72 [3.87774462e-07 4.75291264e+00 1.29505467e-06 6.44334314e-06\n",
      " 1.36883481e-07 9.77344975e-08 1.07126960e-07 9.98026897e-08] [2.78898645e-01 2.05232919e-08 8.36165569e-02 1.69298453e-02] [2.78898645e-01 2.05232919e-08 8.36165569e-02 1.69298453e-02\n",
      " 7.21101355e-01 9.99999979e-01 9.16383443e-01 9.83070155e-01] 6.433046715666763e-06\n",
      "73 [3.24844807e-07 4.75291272e+00 1.08482562e-06 5.39562333e-06\n",
      " 1.15163353e-07 8.22665567e-08 9.01527153e-08 8.39913518e-08] [2.78898646e-01 1.72768351e-08 8.36165460e-02 1.69298039e-02] [2.78898646e-01 1.72768351e-08 8.36165460e-02 1.69298039e-02\n",
      " 7.21101354e-01 9.99999983e-01 9.16383454e-01 9.83070196e-01] 5.3739344431489796e-06\n",
      "74 [2.72161045e-07 4.75291277e+00 9.08837256e-07 4.51889376e-06\n",
      " 9.68822003e-08 6.92395709e-08 7.58611364e-08 7.06784102e-08] [2.78898646e-01 1.45423576e-08 8.36165373e-02 1.69297698e-02] [2.78898646e-01 1.45423576e-08 8.36165373e-02 1.69297698e-02\n",
      " 7.21101354e-01 9.99999985e-01 9.16383463e-01 9.83070230e-01] 4.491694409211002e-06\n",
      "75 [2.28048403e-07 4.75291280e+00 7.61490268e-07 3.78512559e-06\n",
      " 8.14970353e-08 5.82697703e-08 6.38296393e-08 5.94704048e-08] [2.78898648e-01 1.22394333e-08 8.36165305e-02 1.69297419e-02] [2.78898648e-01 1.22394333e-08 8.36165305e-02 1.69297419e-02\n",
      " 7.21101352e-01 9.99999988e-01 9.16383470e-01 9.83070258e-01] 3.7562161057439723e-06\n",
      "76 [1.91107160e-07 4.75291281e+00 6.38105394e-07 3.17090846e-06\n",
      " 6.85502994e-08 4.90334318e-08 5.37019250e-08 5.00355726e-08] [2.78898649e-01 1.03002064e-08 8.36165250e-02 1.69297190e-02] [2.78898649e-01 1.03002064e-08 8.36165250e-02 1.69297190e-02\n",
      " 7.21101351e-01 9.99999990e-01 9.16383475e-01 9.83070281e-01] 3.142641805104906e-06\n",
      "77 [1.60167215e-07 4.75291281e+00 5.34771380e-07 2.65668487e-06\n",
      " 5.76564835e-08 4.12575426e-08 4.51776395e-08 4.20942272e-08] [2.78898650e-01 8.66743938e-09 8.36165207e-02 1.69297001e-02] [2.78898650e-01 8.66743938e-09 8.36165207e-02 1.69297001e-02\n",
      " 7.21101350e-01 9.99999991e-01 9.16383479e-01 9.83070300e-01] 2.630423301830569e-06\n",
      "78 [1.34250221e-07 4.75291281e+00 4.48218234e-07 2.22611229e-06\n",
      " 4.84908318e-08 3.47119037e-08 3.80036353e-08 3.54106280e-08] [2.78898652e-01 7.29286188e-09 8.36165173e-02 1.69296846e-02] [2.78898652e-01 7.29286188e-09 8.36165173e-02 1.69296846e-02\n",
      " 7.21101348e-01 9.99999993e-01 9.16383483e-01 9.83070315e-01] 2.20255343901119e-06\n",
      "79 [1.12537995e-07 4.75291280e+00 3.75711534e-07 1.86553163e-06\n",
      " 4.07798072e-08 2.92024536e-08 3.19665882e-08 2.97861094e-08] [2.78898653e-01 6.13577424e-09 8.36165147e-02 1.69296719e-02] [2.78898653e-01 6.13577424e-09 8.36165147e-02 1.69296719e-02\n",
      " 7.21101347e-01 9.99999994e-01 9.16383485e-01 9.83070328e-01] 1.8449390259001122e-06\n",
      "80 [9.43461627e-08 4.75291279e+00 3.14964261e-07 1.56352422e-06\n",
      " 3.42930450e-08 2.45656245e-08 2.68867618e-08 2.50532774e-08] [2.78898654e-01 5.16186658e-09 8.36165125e-02 1.69296614e-02] [2.78898654e-01 5.16186658e-09 8.36165125e-02 1.69296614e-02\n",
      " 7.21101346e-01 9.99999995e-01 9.16383487e-01 9.83070339e-01] 1.5458883033046944e-06\n",
      "81 [7.91021744e-08 4.75291278e+00 2.64063235e-07 1.31054233e-06\n",
      " 2.88365633e-08 2.06635755e-08 2.26127421e-08 2.10711095e-08] [2.78898656e-01 4.34222090e-09 8.36165109e-02 1.69296527e-02] [2.78898656e-01 4.34222090e-09 8.36165109e-02 1.69296527e-02\n",
      " 7.21101344e-01 9.99999996e-01 9.16383489e-01 9.83070347e-01] 1.2956913512369787e-06\n",
      "82 [6.63269447e-08 4.75291276e+00 2.21407722e-07 1.09860105e-06\n",
      " 2.42470376e-08 1.73801641e-08 1.90169931e-08 1.77208172e-08] [2.78898657e-01 3.65246794e-09 8.36165096e-02 1.69296456e-02] [2.78898657e-01 3.65246794e-09 8.36165096e-02 1.69296456e-02\n",
      " 7.21101343e-01 9.99999996e-01 9.16383490e-01 9.83070354e-01] 1.0862760310244181e-06\n",
      "83 [5.56195282e-08 4.75291275e+00 1.85658169e-07 9.21021213e-07\n",
      " 2.03869711e-08 1.46175464e-08 1.59921060e-08 1.49023547e-08] [2.78898658e-01 3.07207498e-09 8.36165085e-02 1.69296397e-02] [2.78898658e-01 3.07207498e-09 8.36165085e-02 1.69296397e-02\n",
      " 7.21101342e-01 9.99999997e-01 9.16383491e-01 9.83070360e-01] 9.109254145337884e-07\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([2.78898658e-01, 3.07207498e-09, 8.36165085e-02, 1.69296397e-02])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G = np.array([[16, 8, 4, 12],\n",
    "              [8, 29, 3, 16],\n",
    "              [4, 3, 102, 21],\n",
    "              [12, 16, 21, 53]\n",
    "              ])\n",
    "\n",
    "d = np.array([5, -2, 10, 6])\n",
    "\n",
    "\n",
    "def f(x):\n",
    "    return 0.5*np.dot(x, np.dot(G, x)) - d.dot(x)\n",
    "\n",
    "\n",
    "def grad(x):\n",
    "    return G.dot(x)-d\n",
    "\n",
    "\n",
    "def hess(x):\n",
    "    return G\n",
    "\n",
    "\n",
    "A = np.array([\n",
    "    [1., 0., 0., 0.],\n",
    "    [0., 1., 0., 0.],\n",
    "    [0., 0., 1., 0.],\n",
    "    [0., 0., 0., 1.],\n",
    "    [-1., 0., 0., 0.],\n",
    "    [0., -1., 0., 0.],\n",
    "    [0., 0., -1., 0.],\n",
    "    [0., 0., 0., -1.]\n",
    "])\n",
    "b = np.array(\n",
    "    [0, 0, 0, 0, -1, -1, -1, -1]\n",
    ")\n",
    "\n",
    "# b = np.array([4, 0])\n",
    "x0 = np.array([0.9, 0.9, 0.9, 0.9])\n",
    "lam0 = np.array([0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1])\n",
    "\n",
    "f(x0)\n",
    "\n",
    "# print(grad(x0))\n",
    "puntoInterior(x0, lam0, A, b, 0.2, 0.2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "array() missing required argument 'object' (pos 0)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[1;32mIn [12], line 19\u001b[0m\n\u001b[0;32m     13\u001b[0m Ae \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39marray([\n\u001b[0;32m     14\u001b[0m     [\u001b[39m3\u001b[39m, \u001b[39m1\u001b[39m],\n\u001b[0;32m     15\u001b[0m     [\u001b[39m1\u001b[39m, \u001b[39m3\u001b[39m]\n\u001b[0;32m     16\u001b[0m ])\n\u001b[0;32m     17\u001b[0m be \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39marray([\u001b[39m3\u001b[39m, \u001b[39m3\u001b[39m])\n\u001b[1;32m---> 19\u001b[0m A \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39;49marray()\n\u001b[0;32m     20\u001b[0m b \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39marray()\n\u001b[0;32m     22\u001b[0m x0 \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39marray([\u001b[39m1\u001b[39m,\u001b[39m2\u001b[39m])\n",
      "\u001b[1;31mTypeError\u001b[0m: array() missing required argument 'object' (pos 0)"
     ]
    }
   ],
   "source": [
    "def f(x):\n",
    "    return 2*x[0]**2 +3*x[1]**2\n",
    "\n",
    "def grad(x):\n",
    "    return np.array([4*x[0], 3*x[1]])\n",
    "\n",
    "def hess(x):\n",
    "    return np.array([\n",
    "        [4,0],\n",
    "        [0,6]\n",
    "    ])\n",
    "\n",
    "Ae = np.array([\n",
    "    [3, 1],\n",
    "    [1, 3]\n",
    "])\n",
    "be = np.array([3, 3])\n",
    "\n",
    "A = np.array([[],[]])\n",
    "b = np.array([])\n",
    "\n",
    "x0 = np.array([1,2])\n",
    "\n",
    "lam0 = np.array([0])\n",
    "puntoInterior(x0=x0,lam0=lam0,A=A, b=b, Ae=Ae, be=be)"
   ]
  }
 ],
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