helmholtz_test.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import dmg.gallery as gallery\n",
    "import dmg.dgmg as dgmg\n",
    "import dmg.gmg_linear as gmg_linear\n",
    "import dmg.classical_amg as classical_amg\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import copy\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 127\n",
    "k = 2\n",
    "A = gallery.helmholtz((n, n), k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.197436002942676"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gmm = gmg_linear.LinearGMG(A, max_levels=3)\n",
    "gmm.compute_rho()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final residual norm = 2.1901206976663828e-11\n",
      "Relative error = 6.295989947258671e-05\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18193f1e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x0 = np.random.randn(A.shape)\n",
    "x = np.linspace(0, 1, num=n+1, endpoint=False)\n",
    "y = np.linspace(0, 1, num=n+1, endpoint=False)\n",
    "xx, yy = np.meshgrid(x[1:], y[1:])\n",
    "x_true = np.sin(np.pi * xx) * np.sin(np.pi * yy)\n",
    "rhs = (2 * np.pi**2 - k**2) * x_true / (n+1)**2\n",
    "plt.imshow(rhs)\n",
    "rhs = rhs.reshape(A.shape, 1)\n",
    "x = gmm.solve(rhs, x0, tol=1e-10)\n",
    "print(\"Final residual norm = {}\".format(np.linalg.norm(A.dot(x) - rhs)))\n",
    "print(\"Relative error = {}\".format(np.linalg.norm(x - x_true.reshape(A.shape, 1)) / \n",
    "                                   np.linalg.norm(x_true.reshape(A.shape, 1))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1817a89f60>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1817abc438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogy(gmm.get_gmg_convergence())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(127, 127)\n"
     ]
    }
   ],
   "source": [
    "x = x.reshape(A.dim)\n",
    "print(x.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x180a276780>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x180a392b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(x)\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Utility functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_rhos(ks, rhos_linear, rhos_amg, rhos_opt=None):\n",
    "    plt.plot(ks, rhos_linear, label=\"Linear\")\n",
    "    plt.plot(ks, rhos_amg, label=\"AMG\")\n",
    "    if rhos_opt:\n",
    "        plt.plot(ks, rhos_opt, label=\"DMG\")\n",
    "    plt.xlabel(\"$k$\")\n",
    "    plt.yscale(\"log\")\n",
    "    plt.ylabel(\"Spectral radius\")\n",
    "    plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1D\n",
    "### Direct optimization for low frequency"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test ks: [5, 10, 15, 20]\n",
      "Current k = 5\n",
      "Current k = 10\n",
      "Current k = 15\n",
      "Current k = 20\n",
      "Linear = [0.08654325241684814, 0.2719690185791753, 0.46640300096455234, 4.9270160971466925]\n",
      "AMG = [0.08255640400751131, 0.08207295353371487, 0.09700057685039515, 0.2620485512858324]\n"
     ]
    }
   ],
   "source": [
    "num_levels = 3\n",
    "n = 63\n",
    "ks = [5 * i for i in range(1, 5)]\n",
    "rhos_linear = []\n",
    "rhos_amg = []\n",
    "print(\"Test ks: {}\".format(ks))\n",
    "for k in ks:\n",
    "    print(\"Current k = {}\".format(k))\n",
    "    A = gallery.helmholtz((n, ), k=k)\n",
    "    linear_gmg = gmg_linear.LinearGMG(A, max_levels=num_levels)\n",
    "    rhos_linear.append(linear_gmg.compute_rho())\n",
    "    amg = classical_amg.ClassicalAMG(A, num_levels)\n",
    "    rhos_amg.append(amg.compute_rho())\n",
    "print(\"Linear = {}\".format(rhos_linear))\n",
    "print(\"AMG = {}\".format(rhos_amg))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18151d4ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_rhos(ks, rhos_linear, rhos_amg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Current k = 5\n",
      "Iteration 100/1000\n",
      "Upper bound estimation = 0.07778162884538245\n",
      "Iteration 200/1000\n",
      "Upper bound estimation = 0.06884513889802542\n",
      "Iteration 300/1000\n",
      "Upper bound estimation = 0.0618750694901742\n",
      "Iteration 400/1000\n",
      "Upper bound estimation = 0.05596635727617811\n",
      "Iteration 500/1000\n",
      "Upper bound estimation = 0.05039791580901554\n",
      "Iteration 600/1000\n",
      "Upper bound estimation = 0.04801261368534604\n",
      "Iteration 700/1000\n",
      "Upper bound estimation = 0.046523769351673315\n",
      "Iteration 800/1000\n",
      "Upper bound estimation = 0.044852275951843185\n",
      "Iteration 900/1000\n",
      "Upper bound estimation = 0.04509872686916643\n",
      "Iteration 1000/1000\n",
      "Upper bound estimation = 0.045880348275049006\n",
      "Optimized rho = 0.04075529144397405\n",
      "Current k = 10\n",
      "Iteration 100/1000\n",
      "Upper bound estimation = 0.05515379240135597\n",
      "Iteration 200/1000\n",
      "Upper bound estimation = 0.049910030073960165\n",
      "Iteration 300/1000\n",
      "Upper bound estimation = 0.048375303591783554\n",
      "Iteration 400/1000\n",
      "Upper bound estimation = 0.04744693150278197\n",
      "Iteration 500/1000\n",
      "Upper bound estimation = 0.04679817744187638\n",
      "Iteration 600/1000\n",
      "Upper bound estimation = 0.04661274077932641\n",
      "Iteration 700/1000\n",
      "Upper bound estimation = 0.046530826045146766\n",
      "Iteration 800/1000\n",
      "Upper bound estimation = 0.04568245253430022\n",
      "Iteration 900/1000\n",
      "Upper bound estimation = 0.04570806676194939\n",
      "Iteration 1000/1000\n",
      "Upper bound estimation = 0.04592765786950658\n",
      "Optimized rho = 0.041735316208712826\n",
      "Current k = 15\n",
      "Iteration 100/1000\n",
      "Upper bound estimation = 0.09577541256211239\n",
      "Iteration 200/1000\n",
      "Upper bound estimation = 0.06612920390436473\n",
      "Iteration 300/1000\n",
      "Upper bound estimation = 0.05758346688342972\n",
      "Iteration 400/1000\n",
      "Upper bound estimation = 0.05362570813569895\n",
      "Iteration 500/1000\n",
      "Upper bound estimation = 0.05043225842862133\n",
      "Iteration 600/1000\n",
      "Upper bound estimation = 0.050318121871707616\n",
      "Iteration 700/1000\n",
      "Upper bound estimation = 0.0494664987742735\n",
      "Iteration 800/1000\n",
      "Upper bound estimation = 0.04920873233649927\n",
      "Iteration 900/1000\n",
      "Upper bound estimation = 0.048856122220746735\n",
      "Iteration 1000/1000\n",
      "Upper bound estimation = 0.04913235028447995\n",
      "Optimized rho = 0.044562800141479036\n",
      "Current k = 20\n",
      "Iteration 100/1000\n",
      "Upper bound estimation = 0.07488197474846148\n",
      "Iteration 200/1000\n",
      "Upper bound estimation = 0.05686055104984252\n",
      "Iteration 300/1000\n",
      "Upper bound estimation = 0.05320202036256843\n",
      "Iteration 400/1000\n",
      "Upper bound estimation = 0.05159382719184363\n",
      "Iteration 500/1000\n",
      "Upper bound estimation = 0.050787184863564955\n",
      "Iteration 600/1000\n",
      "Upper bound estimation = 0.05079872507403149\n",
      "Iteration 700/1000\n",
      "Upper bound estimation = 0.04921280480575144\n",
      "Iteration 800/1000\n",
      "Upper bound estimation = 0.04923271350952451\n",
      "Iteration 900/1000\n",
      "Upper bound estimation = 0.04924003288575395\n",
      "Iteration 1000/1000\n",
      "Upper bound estimation = 0.048493149463895366\n",
      "Optimized rho = 0.04405224028473518\n"
     ]
    }
   ],
   "source": [
    "rhos_opt = []\n",
    "K = 10\n",
    "batch_size = 10\n",
    "num_iter = 1000\n",
    "step_size = 5e-5\n",
    "path2file = \"../data/helmholtz_1d\"\n",
    "PR_stencil_type = \"m3p\"\n",
    "init_point = None\n",
    "convergence = {}\n",
    "opt_par_n = {}\n",
    "conv_time = {}\n",
    "for k in ks:\n",
    "    print(\"Current k = {}\".format(k))\n",
    "    A = gallery.helmholtz((n, ), k=k)\n",
    "    deep_gmm = dgmg.DeepMG(A, K=K, PR_stencil_type=PR_stencil_type, max_levels=num_levels)\n",
    "#     print(deep_gmm)\n",
    "    opt_par = deep_gmm.optimize(num_iter=num_iter, step_size=step_size, batch_size=batch_size, init_point=init_point)\n",
    "    opt_par_n[k] = opt_par\n",
    "    init_point = copy.deepcopy(opt_par)\n",
    "    convergence[k] = deep_gmm.get_optimizer_convergence()\n",
    "    conv_time[k] = deep_gmm.get_optimization_time()\n",
    "    deep_gmm.update_prd(opt_par)\n",
    "    current_rho = deep_gmm.compute_rho()\n",
    "    rhos_opt.append(current_rho)\n",
    "    print(\"Optimized rho = {}\".format(current_rho))\n",
    "if init_point:\n",
    "    init_type = \"random\"\n",
    "else:\n",
    "    init_type = \"linear\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18183630b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_rhos(ks, rhos_linear, rhos_amg, rhos_opt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Show the optimized operators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Current k = 5\n",
      "Damped factor = 0.7094570916262537\n",
      "Nonzero pattern of P matrix from dim 31 to dim 63\n",
      "[[0.51428752 0.98932798 0.5153554 ]\n",
      " [0.50042352 0.98949644 0.50733844]\n",
      " [0.50644909 1.00864944 0.50272012]\n",
      " [0.50428682 0.99330288 0.50099077]\n",
      " [0.50169987 1.00441592 0.50413986]\n",
      " [0.50234101 0.99751115 0.49967102]\n",
      " [0.50077351 0.9984251  0.50100497]\n",
      " [0.50019523 1.00008333 0.50061027]\n",
      " [0.50012131 0.99806279 0.50095183]\n",
      " [0.49989171 0.99990163 0.5006003 ]\n",
      " [0.49908296 0.99733485 0.50235707]\n",
      " [0.5002009  0.99993113 0.50063689]\n",
      " [0.4996625  0.9977037  0.50200633]\n",
      " [0.50131892 0.99961201 0.50037978]\n",
      " [0.50075493 0.99723409 0.50116143]\n",
      " [0.50068602 1.00034077 0.50014214]\n",
      " [0.50048352 0.99853715 0.50043539]\n",
      " [0.50022726 0.99983065 0.50038515]\n",
      " [0.49963107 0.99738672 0.49993221]\n",
      " [0.49902796 1.00072835 0.50005306]\n",
      " [0.50026288 0.99546432 0.50109008]\n",
      " [0.50094255 1.00051773 0.50031785]\n",
      " [0.50147178 0.99537453 0.50118472]\n",
      " [0.50115841 0.99871139 0.50104688]\n",
      " [0.5023738  1.00080766 0.49925363]\n",
      " [0.50321595 0.99816378 0.49690438]\n",
      " [0.50448767 1.0008871  0.49959172]\n",
      " [0.50181464 0.99348926 0.50551793]\n",
      " [0.49905855 1.00266502 0.51245742]\n",
      " [0.50533193 0.9912255  0.50441112]\n",
      " [0.51300423 0.98473851 0.51888034]]\n",
      "Nonzero pattern of R matrix from dim 63 to dim 31\n",
      "[[0.27551393 0.46085285 0.28373831]\n",
      " [0.26525585 0.47540892 0.27875159]\n",
      " [0.2749936  0.47307427 0.28106012]\n",
      " [0.27492363 0.47434177 0.28159773]\n",
      " [0.27607442 0.47109696 0.27910844]\n",
      " [0.27239525 0.47551046 0.27541897]\n",
      " [0.27444666 0.47899915 0.27700125]\n",
      " [0.27468528 0.48196164 0.27610632]\n",
      " [0.27156037 0.47275638 0.27617013]\n",
      " [0.27508222 0.48534393 0.28012246]\n",
      " [0.2785364  0.48101731 0.27675799]\n",
      " [0.27870573 0.48163987 0.27550345]\n",
      " [0.27947584 0.47477384 0.2745572 ]\n",
      " [0.2753939  0.47836989 0.27589993]\n",
      " [0.27840648 0.47789632 0.27576827]\n",
      " [0.27849082 0.48018869 0.27571144]\n",
      " [0.27414116 0.47109731 0.27485313]\n",
      " [0.2777687  0.4824904  0.27825143]\n",
      " [0.27561999 0.4711384  0.27258144]\n",
      " [0.27809257 0.48184858 0.28066246]\n",
      " [0.27199209 0.47434991 0.27331292]\n",
      " [0.27671596 0.48023047 0.27262783]\n",
      " [0.27335498 0.47393382 0.2724286 ]\n",
      " [0.27672714 0.4793637  0.27038325]\n",
      " [0.27158692 0.47104856 0.26938923]\n",
      " [0.27244187 0.47644571 0.27678062]\n",
      " [0.27639209 0.47036111 0.27602737]\n",
      " [0.2826281  0.47100795 0.2725442 ]\n",
      " [0.27910787 0.47025765 0.27250641]\n",
      " [0.27708367 0.47722119 0.26990501]\n",
      " [0.27840054 0.46698442 0.27897166]]\n",
      "Nonzero pattern of P matrix from dim 15 to dim 31\n",
      "[[0.5182579  0.98105424 0.5176181 ]\n",
      " [0.50929813 0.98749093 0.50559502]\n",
      " [0.50768873 0.99437294 0.50365471]\n",
      " [0.50188092 0.99985806 0.49901585]\n",
      " [0.49953772 1.0003481  0.4998948 ]\n",
      " [0.49444216 1.00048481 0.50054868]\n",
      " [0.49881154 1.00080796 0.49966791]\n",
      " [0.49811975 1.00281015 0.49531443]\n",
      " [0.49648877 1.00243071 0.49827846]\n",
      " [0.49524521 1.00105113 0.50149623]\n",
      " [0.49953114 1.00069927 0.50053607]\n",
      " [0.50274584 0.99676896 0.502598  ]\n",
      " [0.50201074 0.9954782  0.50486582]\n",
      " [0.50719644 0.98913272 0.51338352]\n",
      " [0.51433213 0.98429457 0.51594108]]\n",
      "Nonzero pattern of R matrix from dim 31 to dim 15\n",
      "[[0.27251026 0.48030418 0.26543475]\n",
      " [0.25165636 0.49137351 0.25814962]\n",
      " [0.25497935 0.49359379 0.25736128]\n",
      " [0.2565064  0.49216284 0.25518803]\n",
      " [0.2536208  0.49622709 0.25339091]\n",
      " [0.25596892 0.49553935 0.25246317]\n",
      " [0.25263028 0.49656859 0.25398675]\n",
      " [0.25559865 0.49456004 0.2537143 ]\n",
      " [0.25506341 0.49390682 0.25623163]\n",
      " [0.25451296 0.49422286 0.25662938]\n",
      " [0.25488126 0.49228851 0.25836319]\n",
      " [0.25908108 0.49340089 0.25571079]\n",
      " [0.25403175 0.49532947 0.25660175]\n",
      " [0.25729564 0.49204771 0.25874669]\n",
      " [0.26304866 0.48152098 0.27103007]]\n",
      "Current k = 10\n",
      "Damped factor = 0.6957500506910934\n",
      "Nonzero pattern of P matrix from dim 31 to dim 63\n",
      "[[0.5156208  0.98732816 0.51693654]\n",
      " [0.50198671 0.98791519 0.50915045]\n",
      " [0.50823597 1.00687821 0.50442619]\n",
      " [0.5059674  0.99178028 0.50231177]\n",
      " [0.50308673 1.00316485 0.50539836]\n",
      " [0.50361016 0.996002   0.50126014]\n",
      " [0.50254064 0.9966871  0.50303733]\n",
      " [0.50240609 0.99797853 0.50179576]\n",
      " [0.50165018 0.99699513 0.50279992]\n",
      " [0.50093789 0.99897738 0.5011972 ]\n",
      " [0.4954444  0.99726736 0.50389979]\n",
      " [0.50251073 0.99697468 0.50261937]\n",
      " [0.50208779 0.99560616 0.50426158]\n",
      " [0.50352227 0.99703317 0.50286022]\n",
      " [0.50330231 0.99483125 0.50385071]\n",
      " [0.50322969 0.99735721 0.50267334]\n",
      " [0.50307688 0.996578   0.50284783]\n",
      " [0.50263952 0.99701908 0.50273437]\n",
      " [0.50221658 0.99477648 0.50301864]\n",
      " [0.50204527 0.99703342 0.50349552]\n",
      " [0.50353441 0.99291403 0.5026161 ]\n",
      " [0.49410483 1.00276934 0.50019157]\n",
      " [0.50196594 0.99358987 0.50333678]\n",
      " [0.5027113  0.99679093 0.50328747]\n",
      " [0.50433867 0.99909864 0.50079705]\n",
      " [0.50447067 0.99679668 0.4981924 ]\n",
      " [0.50581069 0.999779   0.50078748]\n",
      " [0.50299471 0.99213543 0.50689411]\n",
      " [0.5004829  1.00117144 0.51413768]\n",
      " [0.5071241  0.98973218 0.50579481]\n",
      " [0.51471206 0.98246276 0.51994323]]\n",
      "Nonzero pattern of R matrix from dim 63 to dim 31\n",
      "[[0.27734804 0.46031348 0.28524067]\n",
      " [0.2662037  0.47142127 0.27874542]\n",
      " [0.2730974  0.47672249 0.28097002]\n",
      " [0.27485961 0.47426132 0.28141683]\n",
      " [0.27624912 0.47189965 0.28192162]\n",
      " [0.2742694  0.47513783 0.27754322]\n",
      " [0.27723124 0.47874214 0.28012511]\n",
      " [0.2770632  0.48087138 0.27697324]\n",
      " [0.27378433 0.46671955 0.27482301]\n",
      " [0.28077539 0.48375278 0.28256373]\n",
      " [0.28498476 0.48105302 0.28191735]\n",
      " [0.27896463 0.48126733 0.27717922]\n",
      " [0.27929063 0.4742703  0.27577518]\n",
      " [0.27666077 0.47917856 0.27587197]\n",
      " [0.28121637 0.47689384 0.2772109 ]\n",
      " [0.28165855 0.48055123 0.27956842]\n",
      " [0.27616154 0.46994457 0.27651785]\n",
      " [0.27999056 0.48257979 0.27998784]\n",
      " [0.27626174 0.4712269  0.27334307]\n",
      " [0.28373976 0.47931254 0.28325158]\n",
      " [0.28027197 0.47329714 0.28777924]\n",
      " [0.27605191 0.47768954 0.2862658 ]\n",
      " [0.26625401 0.47046488 0.28111933]\n",
      " [0.27293348 0.47875241 0.27331929]\n",
      " [0.27794472 0.47119993 0.27138538]\n",
      " [0.28046609 0.47446843 0.27959721]\n",
      " [0.28010093 0.47180419 0.27806769]\n",
      " [0.28451345 0.46947993 0.27453116]\n",
      " [0.28146291 0.47457857 0.27328695]\n",
      " [0.27960664 0.47286015 0.27055742]\n",
      " [0.28030755 0.46697706 0.27956438]]\n",
      "Nonzero pattern of P matrix from dim 15 to dim 31\n",
      "[[0.51759669 0.98176025 0.52097876]\n",
      " [0.51103584 0.98841951 0.50508279]\n",
      " [0.50725383 0.99427815 0.50412985]\n",
      " [0.5018345  0.99915706 0.50040187]\n",
      " [0.50007919 1.00159169 0.49792083]\n",
      " [0.4986222  0.99979268 0.50019707]\n",
      " [0.49743513 1.00178888 0.49948736]\n",
      " [0.49783537 1.0020202  0.49678051]\n",
      " [0.49847052 1.00185662 0.49647872]\n",
      " [0.49556998 1.00015733 0.50300712]\n",
      " [0.50256129 1.00466585 0.49253781]\n",
      " [0.49840611 0.99883941 0.50110042]\n",
      " [0.500368   0.99598509 0.50602367]\n",
      " [0.50810914 0.98618392 0.51487063]\n",
      " [0.51999081 0.98527752 0.51255673]]\n",
      "Nonzero pattern of R matrix from dim 31 to dim 15\n",
      "[[0.27714299 0.47543301 0.27021081]\n",
      " [0.25395494 0.49107471 0.25804992]\n",
      " [0.25533786 0.49339469 0.25751166]\n",
      " [0.25710626 0.49208591 0.25289091]\n",
      " [0.25234052 0.49652742 0.25849651]\n",
      " [0.25688106 0.49525408 0.25232045]\n",
      " [0.25194379 0.49742663 0.25298224]\n",
      " [0.25491292 0.49530439 0.25291639]\n",
      " [0.25416993 0.49441735 0.25628814]\n",
      " [0.25530002 0.49284373 0.26054121]\n",
      " [0.25439548 0.49374852 0.25776168]\n",
      " [0.25628342 0.49340016 0.25724022]\n",
      " [0.25527149 0.49389078 0.25825138]\n",
      " [0.25837483 0.49051262 0.26102963]\n",
      " [0.26853509 0.47753312 0.27227679]]\n",
      "Current k = 15\n",
      "Damped factor = 0.6806881010130328\n",
      "Nonzero pattern of P matrix from dim 31 to dim 63\n",
      "[[0.51787589 0.98574209 0.51938993]\n",
      " [0.50345996 0.98635468 0.51045407]\n",
      " [0.51038338 1.00451555 0.50642533]\n",
      " [0.50876171 0.98970612 0.50413603]\n",
      " [0.50620852 1.00038426 0.50554799]\n",
      " [0.50901611 0.98818423 0.49243619]\n",
      " [0.49825831 1.00212656 0.49765248]\n",
      " [0.50035362 0.99948847 0.49954351]\n",
      " [0.50298655 0.99628206 0.50488907]\n",
      " [0.50369082 0.99440429 0.50399108]\n",
      " [0.49964117 0.99461128 0.50676751]\n",
      " [0.50352741 0.99234916 0.50299174]\n",
      " [0.49865237 1.00625009 0.50621686]\n",
      " [0.50797734 0.99396866 0.50273303]\n",
      " [0.50350698 0.99385683 0.50624682]\n",
      " [0.50494238 0.99321804 0.50425667]\n",
      " [0.50406849 0.99781338 0.50144153]\n",
      " [0.50034936 0.996678   0.50084454]\n",
      " [0.50440048 0.99509113 0.51223776]\n",
      " [0.51106427 0.98857023 0.5079849 ]\n",
      " [0.50720458 0.9902504  0.50741756]\n",
      " [0.49693592 0.99813724 0.50247346]\n",
      " [0.50400504 0.99327017 0.50393133]\n",
      " [0.5026664  0.99529061 0.50464453]\n",
      " [0.50626252 0.99608736 0.50651399]\n",
      " [0.5000827  0.9914471  0.5022944 ]\n",
      " [0.5067352  0.99733275 0.50422117]\n",
      " [0.50436582 0.99090255 0.50826634]\n",
      " [0.50167133 0.99939401 0.51610912]\n",
      " [0.50858858 0.98739875 0.50804065]\n",
      " [0.51812135 0.98059162 0.52242282]]\n",
      "Nonzero pattern of R matrix from dim 63 to dim 31\n",
      "[[0.28921402 0.46257374 0.29844055]\n",
      " [0.27447772 0.46623337 0.28139392]\n",
      " [0.2773273  0.48283547 0.28306295]\n",
      " [0.27896124 0.47209237 0.28097132]\n",
      " [0.2731006  0.47178377 0.2835613 ]\n",
      " [0.27812095 0.47993667 0.27338458]\n",
      " [0.2878595  0.47832241 0.28271203]\n",
      " [0.28174657 0.47703491 0.28318792]\n",
      " [0.27856354 0.46698869 0.28006274]\n",
      " [0.2787958  0.48472975 0.27929854]\n",
      " [0.28823876 0.47876159 0.27925551]\n",
      " [0.28502926 0.47745078 0.29113467]\n",
      " [0.28849156 0.48191717 0.28593303]\n",
      " [0.27552619 0.47859659 0.28157779]\n",
      " [0.28198962 0.47753373 0.27801801]\n",
      " [0.28585444 0.47842376 0.27961556]\n",
      " [0.28334049 0.47102101 0.27905647]\n",
      " [0.28406012 0.47921359 0.2830053 ]\n",
      " [0.27987345 0.4731556  0.27746072]\n",
      " [0.29390087 0.47700186 0.29061698]\n",
      " [0.28634342 0.47507335 0.28757431]\n",
      " [0.27546935 0.47606844 0.2878983 ]\n",
      " [0.26822639 0.47267797 0.28558599]\n",
      " [0.27402174 0.47638545 0.27782813]\n",
      " [0.28059294 0.47688891 0.27469685]\n",
      " [0.28056836 0.4739486  0.27169338]\n",
      " [0.28738938 0.47312837 0.28348815]\n",
      " [0.28635046 0.4669768  0.27747904]\n",
      " [0.28280032 0.48023861 0.27583242]\n",
      " [0.28439975 0.46692907 0.28557705]\n",
      " [0.30252948 0.47049353 0.27950176]]\n",
      "Nonzero pattern of P matrix from dim 15 to dim 31\n",
      "[[0.52805231 0.98402278 0.51685259]\n",
      " [0.50529226 0.99270072 0.50227691]\n",
      " [0.49615025 0.99885506 0.51384723]\n",
      " [0.5052061  0.99666495 0.50296061]\n",
      " [0.50044351 1.00138951 0.49787187]\n",
      " [0.50035904 0.99285737 0.51829894]\n",
      " [0.50680497 1.00000846 0.49962528]\n",
      " [0.49853847 0.99963659 0.50052066]\n",
      " [0.50196291 0.99691325 0.50873937]\n",
      " [0.49102466 1.0019945  0.50466625]\n",
      " [0.50447463 1.0028052  0.49421875]\n",
      " [0.50132337 0.99755842 0.50003441]\n",
      " [0.50090033 1.00075751 0.50346065]\n",
      " [0.507156   0.98918752 0.50921855]\n",
      " [0.51739935 0.98297972 0.53152102]]\n",
      "Nonzero pattern of R matrix from dim 31 to dim 15\n",
      "[[0.28393772 0.47010106 0.27453091]\n",
      " [0.25800677 0.48883233 0.25747246]\n",
      " [0.25417006 0.5042914  0.24922001]\n",
      " [0.26121837 0.48896428 0.25559978]\n",
      " [0.25340135 0.49666429 0.25686442]\n",
      " [0.25613426 0.49485729 0.25808356]\n",
      " [0.25713659 0.49754914 0.25206527]\n",
      " [0.25666201 0.4932915  0.2551776 ]\n",
      " [0.25769218 0.4912684  0.25758579]\n",
      " [0.25528007 0.49337306 0.26031978]\n",
      " [0.25631153 0.49152361 0.26014919]\n",
      " [0.25825442 0.49098768 0.2606776 ]\n",
      " [0.25029835 0.48942307 0.26881456]\n",
      " [0.26022863 0.48786043 0.2642377 ]\n",
      " [0.27285478 0.47216162 0.2791491 ]]\n",
      "Current k = 20\n",
      "Damped factor = 0.6609142806771089\n",
      "Nonzero pattern of P matrix from dim 31 to dim 63\n",
      "[[0.51889616 0.98689352 0.52025584]\n",
      " [0.50468884 0.98447783 0.51082821]\n",
      " [0.51523269 0.99972648 0.51018831]\n",
      " [0.51514384 0.98263983 0.50754397]\n",
      " [0.51084693 1.00744076 0.50088565]\n",
      " [0.50613128 0.97813817 0.49406027]\n",
      " [0.50543226 1.00026395 0.50604783]\n",
      " [0.50838623 0.99307749 0.50108605]\n",
      " [0.50821785 0.99334159 0.50825838]\n",
      " [0.51338527 0.98091556 0.5066004 ]\n",
      " [0.50114297 0.99595564 0.51109732]\n",
      " [0.50615996 0.9890209  0.50499532]\n",
      " [0.50622702 1.00060854 0.50473745]\n",
      " [0.50794784 0.99537211 0.4996214 ]\n",
      " [0.5047127  0.99501682 0.50290164]\n",
      " [0.50405587 0.99233694 0.50527062]\n",
      " [0.50487256 0.9946853  0.5047265 ]\n",
      " [0.50508499 0.99189229 0.50419643]\n",
      " [0.50691325 0.99689325 0.50894911]\n",
      " [0.50748971 0.99063255 0.50339005]\n",
      " [0.5024009  0.99419638 0.50440066]\n",
      " [0.50171053 0.99138367 0.49935849]\n",
      " [0.50392381 0.99303858 0.5103315 ]\n",
      " [0.50820735 0.98887859 0.50544138]\n",
      " [0.51008052 0.99398045 0.5090703 ]\n",
      " [0.50226759 0.99163472 0.50513762]\n",
      " [0.50591073 0.99342873 0.50847943]\n",
      " [0.50489864 0.98983059 0.51284438]\n",
      " [0.50222341 0.99686744 0.51800852]\n",
      " [0.51007367 0.98600748 0.51023306]\n",
      " [0.52276481 0.97713626 0.52657736]]\n",
      "Nonzero pattern of R matrix from dim 63 to dim 31\n",
      "[[0.30614355 0.45636876 0.30978899]\n",
      " [0.28247124 0.46007798 0.28643872]\n",
      " [0.28636614 0.48648205 0.28394289]\n",
      " [0.2902964  0.46000606 0.2849403 ]\n",
      " [0.2871567  0.45475668 0.29357659]\n",
      " [0.28323623 0.47298947 0.28269956]\n",
      " [0.29626126 0.47316974 0.29156571]\n",
      " [0.29413976 0.47267486 0.29098334]\n",
      " [0.29271105 0.45546727 0.29171471]\n",
      " [0.29402896 0.47331974 0.29823355]\n",
      " [0.29349753 0.46992545 0.29487984]\n",
      " [0.29651788 0.47289792 0.2895138 ]\n",
      " [0.29700638 0.46551938 0.30192854]\n",
      " [0.28514432 0.47056116 0.2940943 ]\n",
      " [0.28947531 0.45989522 0.28978653]\n",
      " [0.29057626 0.47329152 0.29218269]\n",
      " [0.29339958 0.45287707 0.28933578]\n",
      " [0.29588952 0.47372121 0.29430196]\n",
      " [0.29755047 0.46123971 0.29129435]\n",
      " [0.29987342 0.472057   0.30237176]\n",
      " [0.29308774 0.45856053 0.29560815]\n",
      " [0.29363801 0.46945813 0.29859305]\n",
      " [0.28436782 0.4586085  0.30010429]\n",
      " [0.28345524 0.47111108 0.2855922 ]\n",
      " [0.29450285 0.46908121 0.28331548]\n",
      " [0.2887475  0.46566939 0.27684857]\n",
      " [0.29856827 0.45959383 0.28727512]\n",
      " [0.29285587 0.46117107 0.28313323]\n",
      " [0.294824   0.47423315 0.2902017 ]\n",
      " [0.28960618 0.45977508 0.28933158]\n",
      " [0.31718404 0.46408823 0.31252584]]\n",
      "Nonzero pattern of P matrix from dim 15 to dim 31\n",
      "[[0.53452333 0.98035419 0.51390901]\n",
      " [0.49822982 0.99140668 0.50664795]\n",
      " [0.5004898  0.99252487 0.52204344]\n",
      " [0.50882068 0.99481247 0.50194311]\n",
      " [0.50534365 0.99121945 0.50547945]\n",
      " [0.50679583 0.99359284 0.51246702]\n",
      " [0.49787963 1.00613406 0.50257309]\n",
      " [0.49906965 1.00388794 0.49341586]\n",
      " [0.49920909 1.0000507  0.50895808]\n",
      " [0.49675447 0.99610004 0.51034875]\n",
      " [0.50302549 0.99611002 0.50520798]\n",
      " [0.50409575 0.99516671 0.50201298]\n",
      " [0.49723219 1.00867565 0.49472218]\n",
      " [0.50712096 0.99057043 0.5039484 ]\n",
      " [0.51235229 0.98509795 0.53309323]]\n",
      "Nonzero pattern of R matrix from dim 31 to dim 15\n",
      "[[0.29095017 0.46466974 0.27795294]\n",
      " [0.26213854 0.48691689 0.25605556]\n",
      " [0.26155851 0.49773336 0.25302665]\n",
      " [0.26280662 0.49060636 0.25175069]\n",
      " [0.2532386  0.4898745  0.26263457]\n",
      " [0.25963705 0.49212133 0.25879951]\n",
      " [0.25813861 0.49903175 0.24998749]\n",
      " [0.2581355  0.4916288  0.25712327]\n",
      " [0.25067971 0.49345686 0.26101075]\n",
      " [0.25679562 0.49187134 0.26181457]\n",
      " [0.25598761 0.4979183  0.25151156]\n",
      " [0.26074638 0.48886766 0.26238735]\n",
      " [0.25857945 0.48091431 0.27303496]\n",
      " [0.25591754 0.48347688 0.27135176]\n",
      " [0.27713496 0.46374579 0.29155669]]\n"
     ]
    }
   ],
   "source": [
    "for k in ks:\n",
    "    print(\"Current k = {}\".format(k))\n",
    "    print(\"Damped factor = {}\".format(opt_par_n[k][2]))\n",
    "    init_dim = n\n",
    "    for level in range(len(opt_par_n[k][0]) - 1, -1, -1):\n",
    "        print(\"Nonzero pattern of P matrix from dim {} to dim {}\".format(int((init_dim - 1) / 2), init_dim))\n",
    "        print(\"{}\".format(opt_par_n[k][0][level]))\n",
    "        print(\"Nonzero pattern of R matrix from dim {} to dim {}\".format(init_dim, int((init_dim - 1) / 2)))\n",
    "        print(\"{}\".format(opt_par_n[k][1][level]))\n",
    "        init_dim = int((init_dim - 1) / 2)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Save results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "path2file = path2file + \"_K_\" + str(K) + \"_iter_\" + str(num_iter) + \\\n",
    "        \"_step_\" + str(step_size) + \"_bs_\" + str(batch_size) + \\\n",
    "        \"_krange_\" + str(min(ks)) + \"_\" + str(max(ks)) + \"_N_\" + str(n) + \"_init_type_\" + init_type + \\\n",
    "        \"_stencil_type_\" + PR_stencil_type + \"_num_levels_\" + str(num_levels) + \".npz\"\n",
    "np.savez(path2file, \n",
    "         PRdopt_n=opt_par_n, K=K, step_size=step_size, num_iter=num_iter, N=n, ks=ks, \n",
    "         convergence=convergence, batch_size=batch_size, num_levels=num_levels,\n",
    "         conv_time=conv_time, init_type=init_type, stencil_type=PR_stencil_type)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Homotopy based optimization for high frequency"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test ks: [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]\n",
      "Current k = 100\n",
      "Current k = 200\n",
      "Current k = 300\n",
      "Current k = 400\n",
      "Current k = 500\n",
      "Current k = 600\n",
      "Current k = 700\n",
      "Current k = 800\n",
      "Current k = 900\n",
      "Current k = 1000\n",
      "[0.22783918880769227, 1.1419603624558214, 3.413780700250383, 8.1919945069529376, 30.492265661901001, 28.13936644165765, 37.75437494042059, 1894.0004771693041, 142.72390377337888, 4428.6127300931321]\n",
      "[0.082615396517187911, 0.082526959154125334, 0.082375592232057135, 0.082154410261777056, 0.11681488365224209, 0.2144187848069182, 0.39582858390553105, 0.7583142477205308, 1.555157345523106, 3.5418174473372432]\n"
     ]
    }
   ],
   "source": [
    "num_levels = 3\n",
    "m = 11\n",
    "n = 2**m - 1\n",
    "ks = [100 * i for i in range(1, 11)]\n",
    "rhos_linear = []\n",
    "rhos_amg = []\n",
    "print(\"Test ks: {}\".format(ks))\n",
    "for k in ks:\n",
    "    print(\"Current k = {}\".format(k))\n",
    "    A = gallery.helmholtz((n, ), k=k)\n",
    "    linear_gmg = gmg_linear.LinearGMG(A, max_levels=num_levels)\n",
    "    rhos_linear.append(linear_gmg.compute_rho())\n",
    "    amg = classical_amg.ClassicalAMG(A, num_levels)\n",
    "    rhos_amg.append(amg.compute_rho())\n",
    "print(rhos_linear)\n",
    "print(rhos_amg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1811ec4278>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x181d3c1f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogy(ks, rhos_linear, label=\"Linear\")\n",
    "plt.semilogy(ks, rhos_amg, label=\"AMG\")\n",
    "plt.xlabel(\"$k$\")\n",
    "plt.ylabel(\"Spectral radius\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Current k = 100\n",
      "Max eigenvalue for iteration matrix in init param = 0.22783918880769644\n",
      "Try direct optimization...\n",
      "Upper bound after direct optimization = 0.10424805668467363\n",
      "Direct optimization is successful!\n",
      "Optimized rho = 0.0819385045184356\n",
      "Current k = 200\n",
      "Max eigenvalue for iteration matrix in init param = 0.314931598555673\n",
      "Try direct optimization...\n",
      "Upper bound after direct optimization = 0.10015373074231848\n",
      "Direct optimization is successful!\n",
      "Optimized rho = 0.0799399062626929\n",
      "Current k = 300\n",
      "Max eigenvalue for iteration matrix in init param = 0.6185032002975186\n",
      "Try direct optimization...\n",
      "Upper bound after direct optimization = 0.09021918620884041\n",
      "Direct optimization is successful!\n",
      "Optimized rho = 0.07644832860966443\n",
      "Current k = 400\n",
      "Max eigenvalue for iteration matrix in init param = 0.8059629962539233\n",
      "Try direct optimization...\n",
      "Upper bound after direct optimization = 0.08922631980911921\n",
      "Direct optimization is successful!\n",
      "Optimized rho = 0.07502103424470992\n",
      "Current k = 500\n",
      "Max eigenvalue for iteration matrix in init param = 6.373199205771241\n",
      "Try direct optimization...\n",
      "Upper bound after direct optimization = 1.0818314175919337\n",
      "Direct optimization is failed!\n",
      "Improve init C\n",
      "Upper bound after initial optimization = 0.08717772743370132\n",
      "Start homotopy...\n",
      "Current alpha = 0.1\n",
      "Current eigenvalue upper bound for iteration matrix = 0.7467448240333561\n",
      "Test acceptance = 8.565775296233268\n",
      "Alpha = 0.05\n",
      "Current eigenvalue upper bound for iteration matrix = 0.08670638830246648\n",
      "Test acceptance = 0.9945933537715433\n",
      "New active alpha = 0.05\n",
      "Current alpha = 0.15000000000000002\n",
      "Current eigenvalue upper bound for iteration matrix = 0.11435167148013728\n",
      "Test acceptance = 1.318837904783129\n",
      "New active alpha = 0.15000000000000002\n",
      "Current alpha = 0.25\n",
      "Current eigenvalue upper bound for iteration matrix = 0.08852121238147088\n",
      "Test acceptance = 0.7741138475343309\n",
      "New active alpha = 0.25\n",
      "Current alpha = 0.35\n",
      "Current eigenvalue upper bound for iteration matrix = 0.0844368321612112\n",
      "Test acceptance = 0.953859870302515\n",
      "New active alpha = 0.35\n",
      "Current alpha = 0.44999999999999996\n",
      "Current eigenvalue upper bound for iteration matrix = 0.08731564636502626\n",
      "Test acceptance = 1.0340942942804707\n",
      "New active alpha = 0.44999999999999996\n",
      "Current alpha = 0.5499999999999999\n",
      "Current eigenvalue upper bound for iteration matrix = 0.821912197508729\n",
      "Test acceptance = 9.413114736306195\n",
      "Alpha = 0.49999999999999994\n",
      "Current eigenvalue upper bound for iteration matrix = 0.08477367882997054\n",
      "Test acceptance = 0.9708876055909965\n",
      "New active alpha = 0.49999999999999994\n",
      "Current alpha = 0.6\n",
      "Current eigenvalue upper bound for iteration matrix = 0.0834393323529252\n",
      "Test acceptance = 0.9842598965213999\n",
      "New active alpha = 0.6\n",
      "Current alpha = 0.7\n",
      "Current eigenvalue upper bound for iteration matrix = 0.08429737326631556\n",
      "Test acceptance = 1.0102834105834055\n",
      "New active alpha = 0.7\n",
      "Current alpha = 0.7999999999999999\n",
      "Current eigenvalue upper bound for iteration matrix = 0.08499840083588557\n",
      "Test acceptance = 1.0083161259053148\n",
      "New active alpha = 0.7999999999999999\n",
      "Current alpha = 0.8999999999999999\n",
      "Current eigenvalue upper bound for iteration matrix = 0.0833844266467032\n",
      "Test acceptance = 0.981011711122676\n",
      "New active alpha = 0.8999999999999999\n",
      "Current alpha = 0.9999999999999999\n",
      "Current eigenvalue upper bound for iteration matrix = 0.08370700031775914\n",
      "Test acceptance = 1.0038685121914033\n",
      "New active alpha = 0.9999999999999999\n",
      "Current alpha = 1.0\n",
      "Current eigenvalue upper bound for iteration matrix = 0.08214202329821446\n",
      "Test acceptance = 0.981304108215515\n",
      "New active alpha = 1.0\n",
      "Optimized rho = 0.06537893288167804\n",
      "Current k = 600\n",
      "Max eigenvalue for iteration matrix in init param = 6.244621816355449\n",
      "Try direct optimization...\n",
      "Upper bound after direct optimization = 0.9836951628268438\n",
      "Direct optimization is failed!\n",
      "Improve init C\n",
      "Upper bound after initial optimization = 0.07952667572076023\n",
      "Start homotopy...\n",
      "Current alpha = 0.1\n",
      "Current eigenvalue upper bound for iteration matrix = 0.9432752403077627\n",
      "Test acceptance = 11.861117439635706\n",
      "Alpha = 0.05\n",
      "Current eigenvalue upper bound for iteration matrix = 0.08119945770591686\n",
      "Test acceptance = 1.0210342249313955\n",
      "New active alpha = 0.05\n",
      "Current alpha = 0.15000000000000002\n",
      "Current eigenvalue upper bound for iteration matrix = 0.08358007904074283\n",
      "Test acceptance = 1.0293181925358166\n",
      "New active alpha = 0.15000000000000002\n",
      "Current alpha = 0.25\n",
      "Current eigenvalue upper bound for iteration matrix = 0.08818218404666736\n",
      "Test acceptance = 1.0550622236631428\n",
      "New active alpha = 0.25\n",
      "Current alpha = 0.35\n",
      "Current eigenvalue upper bound for iteration matrix = 0.08363135064807521\n",
      "Test acceptance = 0.9483928250610829\n",
      "New active alpha = 0.35\n",
      "Current alpha = 0.44999999999999996\n",
      "Current eigenvalue upper bound for iteration matrix = 0.08554200009630598\n",
      "Test acceptance = 1.022846091010426\n",
      "New active alpha = 0.44999999999999996\n",
      "Current alpha = 0.5499999999999999\n",
      "Current eigenvalue upper bound for iteration matrix = 0.8950343453248178\n",
      "Test acceptance = 10.463098177704039\n",
      "Alpha = 0.49999999999999994\n",
      "Current eigenvalue upper bound for iteration matrix = 0.08596510968797093\n",
      "Test acceptance = 1.0049462204670057\n",
      "New active alpha = 0.49999999999999994\n",
      "Current alpha = 0.6\n",
      "Current eigenvalue upper bound for iteration matrix = 0.08426322767541894\n",
      "Test acceptance = 0.9802026424589075\n",
      "New active alpha = 0.6\n",
      "Current alpha = 0.7\n",
      "Current eigenvalue upper bound for iteration matrix = 0.08503701397133363\n",
      "Test acceptance = 1.0091829653012498\n",
      "New active alpha = 0.7\n",
      "Current alpha = 0.7999999999999999\n",
      "Current eigenvalue upper bound for iteration matrix = 0.08765654068482268\n",
      "Test acceptance = 1.0308045472336564\n",
      "New active alpha = 0.7999999999999999\n",
      "Current alpha = 0.8999999999999999\n",
      "Current eigenvalue upper bound for iteration matrix = 0.08892698673297163\n",
      "Test acceptance = 1.0144934540905164\n",
      "New active alpha = 0.8999999999999999\n",
      "Current alpha = 0.9999999999999999\n",
      "Current eigenvalue upper bound for iteration matrix = 0.08901910706439072\n",
      "Test acceptance = 1.001035909736779\n",
      "New active alpha = 0.9999999999999999\n",
      "Current alpha = 1.0\n",
      "Current eigenvalue upper bound for iteration matrix = 0.08654674966599742\n",
      "Test acceptance = 0.9722266659380783\n",
      "New active alpha = 1.0\n",
      "Optimized rho = 0.06752607059799012\n",
      "Current k = 700\n",
      "Max eigenvalue for iteration matrix in init param = 4.670569008175677\n",
      "Try direct optimization...\n",
      "Upper bound after direct optimization = 1.1313323947317844\n",
      "Direct optimization is failed!\n",
      "Improve init C\n",
      "Upper bound after initial optimization = 0.08574514207562585\n",
      "Start homotopy...\n",
      "Current alpha = 0.1\n",
      "Current eigenvalue upper bound for iteration matrix = 0.13146229171002624\n",
      "Test acceptance = 1.533174807665239\n",
      "New active alpha = 0.1\n",
      "Current alpha = 0.2\n",
      "Current eigenvalue upper bound for iteration matrix = 0.08902900494073561\n",
      "Test acceptance = 0.6772208500450599\n",
      "New active alpha = 0.2\n",
      "Current alpha = 0.30000000000000004\n",
      "Current eigenvalue upper bound for iteration matrix = 0.7375424300448771\n",
      "Test acceptance = 8.284293759498274\n",
      "Alpha = 0.25\n",
      "Current eigenvalue upper bound for iteration matrix = 0.09437700561859882\n",
      "Test acceptance = 1.060070318447603\n",
      "New active alpha = 0.25\n",
      "Current alpha = 0.35\n",
      "Current eigenvalue upper bound for iteration matrix = 0.09545280645059302\n",
      "Test acceptance = 1.0113989718675942\n",
      "New active alpha = 0.35\n",
      "Current alpha = 0.44999999999999996\n",
      "Current eigenvalue upper bound for iteration matrix = 0.0966140045198076\n",
      "Test acceptance = 1.0121651537801104\n",
      "New active alpha = 0.44999999999999996\n",
      "Current alpha = 0.5499999999999999\n",
      "Current eigenvalue upper bound for iteration matrix = 0.8302208496150074\n",
      "Test acceptance = 8.59317294362638\n",
      "Alpha = 0.49999999999999994\n",
      "Current eigenvalue upper bound for iteration matrix = 0.09357403990373427\n",
      "Test acceptance = 0.9685349486217592\n",
      "New active alpha = 0.49999999999999994\n",
      "Current alpha = 0.6\n",
      "Current eigenvalue upper bound for iteration matrix = 0.09527100039984267\n",
      "Test acceptance = 1.0181349495848868\n",
      "New active alpha = 0.6\n",
      "Current alpha = 0.7\n",
      "Current eigenvalue upper bound for iteration matrix = 0.09921652129435739\n",
      "Test acceptance = 1.0414136607987297\n",
      "New active alpha = 0.7\n",
      "Current alpha = 0.7999999999999999\n",
      "Current eigenvalue upper bound for iteration matrix = 0.10364842242260573\n",
      "Test acceptance = 1.044668983254308\n",
      "New active alpha = 0.7999999999999999\n",
      "Current alpha = 0.8999999999999999\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Current eigenvalue upper bound for iteration matrix = 0.30035969018191333\n",
      "Test acceptance = 2.8978703501849425\n",
      "New active alpha = 0.8999999999999999\n",
      "Current alpha = 0.9999999999999999\n",
      "Current eigenvalue upper bound for iteration matrix = 1.0553630031372847\n",
      "Test acceptance = 3.5136639090888075\n",
      "Alpha = 0.95\n",
      "Current eigenvalue upper bound for iteration matrix = 0.10278066268463106\n",
      "Test acceptance = 0.3421919320211769\n",
      "New active alpha = 0.95\n",
      "Current alpha = 1.0\n",
      "Current eigenvalue upper bound for iteration matrix = 1.233219080669457\n",
      "Test acceptance = 11.998551560748616\n",
      "Alpha = 1.0\n",
      "Current eigenvalue upper bound for iteration matrix = 0.1930572291687288\n",
      "Test acceptance = 1.8783419383186848\n",
      "New active alpha = 1.0\n",
      "Optimized rho = 0.11441530803536362\n",
      "Current k = 800\n",
      "Max eigenvalue for iteration matrix in init param = 7.635494029350327\n",
      "Try direct optimization...\n",
      "Upper bound after direct optimization = 1.199062522395371\n",
      "Direct optimization is failed!\n",
      "Improve init C\n",
      "Upper bound after initial optimization = 0.4367544184353145\n",
      "Start homotopy...\n",
      "Current alpha = 0.1\n",
      "Current eigenvalue upper bound for iteration matrix = 0.10771790974195206\n",
      "Test acceptance = 0.24663267318016982\n",
      "New active alpha = 0.1\n",
      "Current alpha = 0.2\n",
      "Current eigenvalue upper bound for iteration matrix = 0.11368865366497233\n",
      "Test acceptance = 1.0554294447165167\n",
      "New active alpha = 0.2\n",
      "Current alpha = 0.30000000000000004\n",
      "Current eigenvalue upper bound for iteration matrix = 1.1211086224666589\n",
      "Test acceptance = 9.861218215939472\n",
      "Alpha = 0.25\n",
      "Current eigenvalue upper bound for iteration matrix = 0.10953133179126934\n",
      "Test acceptance = 0.9634323941775742\n",
      "New active alpha = 0.25\n",
      "Current alpha = 0.35\n",
      "Current eigenvalue upper bound for iteration matrix = 0.1230375137345056\n",
      "Test acceptance = 1.123308844349438\n",
      "New active alpha = 0.35\n",
      "Current alpha = 0.44999999999999996\n",
      "Current eigenvalue upper bound for iteration matrix = 1.0153025427252937\n",
      "Test acceptance = 8.25197544966771\n",
      "Alpha = 0.39999999999999997\n",
      "Current eigenvalue upper bound for iteration matrix = 0.1138497904746846\n",
      "Test acceptance = 0.9253258377794713\n",
      "New active alpha = 0.39999999999999997\n",
      "Current alpha = 0.5\n",
      "Current eigenvalue upper bound for iteration matrix = 0.11546655499567118\n",
      "Test acceptance = 1.01420085635859\n",
      "New active alpha = 0.5\n",
      "Current alpha = 0.6\n",
      "Current eigenvalue upper bound for iteration matrix = 0.16232453561583135\n",
      "Test acceptance = 1.405814312394761\n",
      "New active alpha = 0.6\n",
      "Current alpha = 0.7\n",
      "Current eigenvalue upper bound for iteration matrix = 0.9075520236137429\n",
      "Test acceptance = 5.590972554892251\n",
      "Alpha = 0.65\n",
      "Current eigenvalue upper bound for iteration matrix = 0.1359244196910261\n",
      "Test acceptance = 0.8373621349067917\n",
      "New active alpha = 0.65\n",
      "Current alpha = 0.75\n",
      "Current eigenvalue upper bound for iteration matrix = 0.12229113552239368\n",
      "Test acceptance = 0.899699522722829\n",
      "New active alpha = 0.75\n",
      "Current alpha = 0.85\n",
      "Current eigenvalue upper bound for iteration matrix = 0.12537739560274327\n",
      "Test acceptance = 1.0252369893137876\n",
      "New active alpha = 0.85\n",
      "Current alpha = 0.95\n",
      "Current eigenvalue upper bound for iteration matrix = 0.15101303220852122\n",
      "Test acceptance = 1.2044677709449647\n",
      "New active alpha = 0.95\n",
      "Current alpha = 1.0\n",
      "Current eigenvalue upper bound for iteration matrix = 0.14013803924301552\n",
      "Test acceptance = 0.9279863942438469\n",
      "New active alpha = 1.0\n",
      "Optimized rho = 0.10649269218813096\n",
      "Current k = 900\n",
      "Max eigenvalue for iteration matrix in init param = 14.999810107110328\n",
      "Try direct optimization...\n",
      "Upper bound after direct optimization = 1.4388176212707466\n",
      "Direct optimization is failed!\n",
      "Improve init C\n",
      "Upper bound after initial optimization = 0.1338175382760996\n",
      "Start homotopy...\n",
      "Current alpha = 0.1\n",
      "Current eigenvalue upper bound for iteration matrix = 0.1350072757776083\n",
      "Test acceptance = 1.0088907441941874\n",
      "New active alpha = 0.1\n",
      "Current alpha = 0.2\n",
      "Current eigenvalue upper bound for iteration matrix = 0.9795928347018574\n",
      "Test acceptance = 7.255852168408307\n",
      "Alpha = 0.15000000000000002\n",
      "Current eigenvalue upper bound for iteration matrix = 0.14012195914306677\n",
      "Test acceptance = 1.0378845016759222\n",
      "New active alpha = 0.15000000000000002\n",
      "Current alpha = 0.25\n",
      "Current eigenvalue upper bound for iteration matrix = 0.42912029430365634\n",
      "Test acceptance = 3.0624771229862526\n",
      "Alpha = 0.2\n",
      "Current eigenvalue upper bound for iteration matrix = 0.9566913827995562\n",
      "Test acceptance = 6.827562136943568\n",
      "Alpha = 0.17500000000000002\n",
      "Current eigenvalue upper bound for iteration matrix = 0.13847668051245052\n",
      "Test acceptance = 0.9882582384611366\n",
      "New active alpha = 0.17500000000000002\n",
      "Current alpha = 0.275\n",
      "Current eigenvalue upper bound for iteration matrix = 0.1363629290640218\n",
      "Test acceptance = 0.9847356866108683\n",
      "New active alpha = 0.275\n",
      "Current alpha = 0.375\n",
      "Current eigenvalue upper bound for iteration matrix = 0.9582593249891752\n",
      "Test acceptance = 7.027271499421053\n",
      "Alpha = 0.325\n",
      "Current eigenvalue upper bound for iteration matrix = 0.1367176562635456\n",
      "Test acceptance = 1.0026013462893368\n",
      "New active alpha = 0.325\n",
      "Current alpha = 0.42500000000000004\n",
      "Current eigenvalue upper bound for iteration matrix = 0.1416404927710314\n",
      "Test acceptance = 1.0360073207954665\n",
      "New active alpha = 0.42500000000000004\n",
      "Current alpha = 0.525\n",
      "Current eigenvalue upper bound for iteration matrix = 0.7306901582349409\n",
      "Test acceptance = 5.1587659993257455\n",
      "Alpha = 0.47500000000000003\n",
      "Current eigenvalue upper bound for iteration matrix = 1.0057974008076047\n",
      "Test acceptance = 7.101058328238973\n",
      "Alpha = 0.45000000000000007\n",
      "Current eigenvalue upper bound for iteration matrix = 0.14334299998149483\n",
      "Test acceptance = 1.0120199187192578\n",
      "New active alpha = 0.45000000000000007\n",
      "Current alpha = 0.55\n",
      "Current eigenvalue upper bound for iteration matrix = 0.1433222850983868\n",
      "Test acceptance = 0.9998554873058977\n",
      "New active alpha = 0.55\n",
      "Current alpha = 0.65\n",
      "Current eigenvalue upper bound for iteration matrix = 0.16255376994915227\n",
      "Test acceptance = 1.134183493080393\n",
      "New active alpha = 0.65\n",
      "Current alpha = 0.75\n",
      "Current eigenvalue upper bound for iteration matrix = 0.9448879348746612\n",
      "Test acceptance = 5.812771584259334\n",
      "Alpha = 0.7000000000000001\n",
      "Current eigenvalue upper bound for iteration matrix = 0.14681233758777415\n",
      "Test acceptance = 0.9031616900284618\n",
      "New active alpha = 0.7000000000000001\n",
      "Current alpha = 0.8\n",
      "Current eigenvalue upper bound for iteration matrix = 0.15241011728654522\n",
      "Test acceptance = 1.0381288098176649\n",
      "New active alpha = 0.8\n",
      "Current alpha = 0.9\n",
      "Current eigenvalue upper bound for iteration matrix = 0.15866076077902244\n",
      "Test acceptance = 1.0410119984405328\n",
      "New active alpha = 0.9\n",
      "Current alpha = 1.0\n",
      "Current eigenvalue upper bound for iteration matrix = 0.16515657976885967\n",
      "Test acceptance = 1.0409415595761853\n",
      "New active alpha = 1.0\n",
      "Optimized rho = 0.12636340346170866\n",
      "Current k = 1000\n",
      "Max eigenvalue for iteration matrix in init param = 21.7406773786819\n",
      "Try direct optimization...\n",
      "Upper bound after direct optimization = 1.5938260101234047\n",
      "Direct optimization is failed!\n",
      "Improve init C\n",
      "Upper bound after initial optimization = 0.2539569175541191\n",
      "Start homotopy...\n",
      "Current alpha = 0.1\n",
      "Current eigenvalue upper bound for iteration matrix = 0.9773505924455579\n",
      "Test acceptance = 3.848489743293884\n",
      "Alpha = 0.05\n",
      "Current eigenvalue upper bound for iteration matrix = 0.15812577419530963\n",
      "Test acceptance = 0.62264802911546\n",
      "New active alpha = 0.05\n",
      "Current alpha = 0.15000000000000002\n",
      "Current eigenvalue upper bound for iteration matrix = 1.0406468225332113\n",
      "Test acceptance = 6.581133454232784\n",
      "Alpha = 0.1\n",
      "Current eigenvalue upper bound for iteration matrix = 1.0519859021224938\n",
      "Test acceptance = 6.652842697377908\n",
      "Alpha = 0.07500000000000001\n",
      "Current eigenvalue upper bound for iteration matrix = 0.15745586504152564\n",
      "Test acceptance = 0.9957634411139291\n",
      "New active alpha = 0.07500000000000001\n",
      "Current alpha = 0.17500000000000002\n",
      "Current eigenvalue upper bound for iteration matrix = 0.17199451626170234\n",
      "Test acceptance = 1.0923347708663786\n",
      "New active alpha = 0.17500000000000002\n",
      "Current alpha = 0.275\n",
      "Current eigenvalue upper bound for iteration matrix = 0.7783869842941109\n",
      "Test acceptance = 4.525650010316246\n",
      "Alpha = 0.22500000000000003\n",
      "Current eigenvalue upper bound for iteration matrix = 0.16780891862465844\n",
      "Test acceptance = 0.9756643541432728\n",
      "New active alpha = 0.22500000000000003\n",
      "Current alpha = 0.32500000000000007\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Current eigenvalue upper bound for iteration matrix = 0.17455409315883125\n",
      "Test acceptance = 1.040195566418373\n",
      "New active alpha = 0.32500000000000007\n",
      "Current alpha = 0.42500000000000004\n",
      "Current eigenvalue upper bound for iteration matrix = 0.8896677865964578\n",
      "Test acceptance = 5.096802776128121\n",
      "Alpha = 0.37500000000000006\n",
      "Current eigenvalue upper bound for iteration matrix = 0.16632498239946938\n",
      "Test acceptance = 0.9528563861755222\n",
      "New active alpha = 0.37500000000000006\n",
      "Current alpha = 0.4750000000000001\n",
      "Current eigenvalue upper bound for iteration matrix = 1.1316876459172445\n",
      "Test acceptance = 6.804074947678184\n",
      "Alpha = 0.42500000000000004\n",
      "Current eigenvalue upper bound for iteration matrix = 0.98396721528071\n",
      "Test acceptance = 5.91593157615659\n",
      "Alpha = 0.4000000000000001\n",
      "Current eigenvalue upper bound for iteration matrix = 0.16868620980997068\n",
      "Test acceptance = 1.0141964687230824\n",
      "New active alpha = 0.4000000000000001\n",
      "Current alpha = 0.5000000000000001\n",
      "Current eigenvalue upper bound for iteration matrix = 1.0079060873576549\n",
      "Test acceptance = 5.975035472627471\n",
      "Alpha = 0.45000000000000007\n",
      "Current eigenvalue upper bound for iteration matrix = 1.105101723615249\n",
      "Test acceptance = 6.55122742315554\n",
      "Alpha = 0.4250000000000001\n",
      "Current eigenvalue upper bound for iteration matrix = 1.1273397033477932\n",
      "Test acceptance = 6.6830578778061955\n",
      "Alpha = 0.4125000000000001\n",
      "Current eigenvalue upper bound for iteration matrix = 0.16348177509204545\n",
      "Test acceptance = 0.9691472425411173\n",
      "New active alpha = 0.4125000000000001\n",
      "Current alpha = 0.5125000000000001\n",
      "Current eigenvalue upper bound for iteration matrix = 1.0589854248288835\n",
      "Test acceptance = 6.477697126989482\n",
      "Alpha = 0.4625000000000001\n",
      "Current eigenvalue upper bound for iteration matrix = 1.106445702430312\n",
      "Test acceptance = 6.768006414215577\n",
      "Alpha = 0.4375000000000001\n",
      "Current eigenvalue upper bound for iteration matrix = 0.1610752882556438\n",
      "Test acceptance = 0.9852797852540643\n",
      "New active alpha = 0.4375000000000001\n",
      "Current alpha = 0.5375000000000001\n",
      "Current eigenvalue upper bound for iteration matrix = 1.1670450425578915\n",
      "Test acceptance = 7.245338842452764\n",
      "Alpha = 0.4875000000000001\n",
      "Current eigenvalue upper bound for iteration matrix = 0.9435593345057504\n",
      "Test acceptance = 5.85787767151607\n",
      "Alpha = 0.46250000000000013\n",
      "Current eigenvalue upper bound for iteration matrix = 0.16337721713721146\n",
      "Test acceptance = 1.0142910120260922\n",
      "New active alpha = 0.46250000000000013\n",
      "Current alpha = 0.5625000000000001\n",
      "Current eigenvalue upper bound for iteration matrix = 0.9301817147757594\n",
      "Test acceptance = 5.693460392305198\n",
      "Alpha = 0.5125000000000002\n",
      "Current eigenvalue upper bound for iteration matrix = 1.1108039202489381\n",
      "Test acceptance = 6.79901359389685\n",
      "Alpha = 0.48750000000000016\n",
      "Current eigenvalue upper bound for iteration matrix = 0.16402033256423384\n",
      "Test acceptance = 1.0039363837767066\n",
      "New active alpha = 0.48750000000000016\n",
      "Current alpha = 0.5875000000000001\n",
      "Current eigenvalue upper bound for iteration matrix = 1.1998830505209823\n",
      "Test acceptance = 7.315453101225012\n",
      "Alpha = 0.5375000000000002\n",
      "Current eigenvalue upper bound for iteration matrix = 0.1658031799202982\n",
      "Test acceptance = 1.0108696728520907\n",
      "New active alpha = 0.5375000000000002\n",
      "Current alpha = 0.6375000000000002\n",
      "Current eigenvalue upper bound for iteration matrix = 0.9984845532358774\n",
      "Test acceptance = 6.022107378856366\n",
      "Alpha = 0.5875000000000002\n",
      "Current eigenvalue upper bound for iteration matrix = 0.16452191710245684\n",
      "Test acceptance = 0.9922723869442235\n",
      "New active alpha = 0.5875000000000002\n",
      "Current alpha = 0.6875000000000002\n",
      "Current eigenvalue upper bound for iteration matrix = 1.1237988573793076\n",
      "Test acceptance = 6.830693911009171\n",
      "Alpha = 0.6375000000000003\n",
      "Current eigenvalue upper bound for iteration matrix = 1.142478972683011\n",
      "Test acceptance = 6.944235715242283\n",
      "Alpha = 0.6125000000000003\n",
      "Current eigenvalue upper bound for iteration matrix = 0.16565848584168544\n",
      "Test acceptance = 1.006908312030675\n",
      "New active alpha = 0.6125000000000003\n",
      "Current alpha = 0.7125000000000002\n",
      "Current eigenvalue upper bound for iteration matrix = 0.9020703110199232\n",
      "Test acceptance = 5.445361319322955\n",
      "Alpha = 0.6625000000000003\n",
      "Current eigenvalue upper bound for iteration matrix = 0.17140697139691538\n",
      "Test acceptance = 1.034700821548759\n",
      "New active alpha = 0.6625000000000003\n",
      "Current alpha = 0.7625000000000003\n",
      "Current eigenvalue upper bound for iteration matrix = 0.8793721857868609\n",
      "Test acceptance = 5.130317504709648\n",
      "Alpha = 0.7125000000000004\n",
      "Current eigenvalue upper bound for iteration matrix = 0.17931480557754254\n",
      "Test acceptance = 1.046134845719405\n",
      "New active alpha = 0.7125000000000004\n",
      "Current alpha = 0.8125000000000003\n",
      "Current eigenvalue upper bound for iteration matrix = 1.1637381073085167\n",
      "Test acceptance = 6.489916454808703\n",
      "Alpha = 0.7625000000000004\n",
      "Current eigenvalue upper bound for iteration matrix = 1.0413191357721518\n",
      "Test acceptance = 5.807212251203908\n",
      "Alpha = 0.7375000000000004\n",
      "Current eigenvalue upper bound for iteration matrix = 0.16918731935478476\n",
      "Test acceptance = 0.9435211934110022\n",
      "New active alpha = 0.7375000000000004\n",
      "Current alpha = 0.8375000000000004\n",
      "Current eigenvalue upper bound for iteration matrix = 0.8212238084826367\n",
      "Test acceptance = 4.853932384616458\n",
      "Alpha = 0.7875000000000004\n",
      "Current eigenvalue upper bound for iteration matrix = 0.6890809427825022\n",
      "Test acceptance = 4.07288764554218\n",
      "Alpha = 0.7625000000000004\n",
      "Current eigenvalue upper bound for iteration matrix = 0.9708979045443258\n",
      "Test acceptance = 5.738597362065645\n",
      "Alpha = 0.7500000000000003\n",
      "Current eigenvalue upper bound for iteration matrix = 0.20774662590921486\n",
      "Test acceptance = 1.2279089632809388\n",
      "New active alpha = 0.7500000000000003\n",
      "Current alpha = 0.8500000000000003\n",
      "Current eigenvalue upper bound for iteration matrix = 0.17440233288145993\n",
      "Test acceptance = 0.839495381059395\n",
      "New active alpha = 0.8500000000000003\n",
      "Current alpha = 0.9500000000000003\n",
      "Current eigenvalue upper bound for iteration matrix = 1.0818850367104307\n",
      "Test acceptance = 6.203386266890022\n",
      "Alpha = 0.9000000000000004\n",
      "Current eigenvalue upper bound for iteration matrix = 0.1710624879541792\n",
      "Test acceptance = 0.9808497691968903\n",
      "New active alpha = 0.9000000000000004\n",
      "Current alpha = 1.0\n",
      "Current eigenvalue upper bound for iteration matrix = 1.1021018768844941\n",
      "Test acceptance = 6.442685886690151\n",
      "Alpha = 0.9500000000000004\n",
      "Current eigenvalue upper bound for iteration matrix = 0.8864425567637273\n",
      "Test acceptance = 5.181980967102325\n",
      "Alpha = 0.9250000000000004\n",
      "Current eigenvalue upper bound for iteration matrix = 0.17295363958118337\n",
      "Test acceptance = 1.0110553263291175\n",
      "New active alpha = 0.9250000000000004\n",
      "Current alpha = 1.0\n",
      "Current eigenvalue upper bound for iteration matrix = 1.0482263019986087\n",
      "Test acceptance = 6.060735723960164\n",
      "Alpha = 0.9750000000000004\n",
      "Current eigenvalue upper bound for iteration matrix = 0.1729274085711232\n",
      "Test acceptance = 0.9998483350213174\n",
      "New active alpha = 0.9750000000000004\n",
      "Current alpha = 1.0\n",
      "Current eigenvalue upper bound for iteration matrix = 0.16868890943639034\n",
      "Test acceptance = 0.9754897203991256\n",
      "New active alpha = 1.0\n",
      "Optimized rho = 0.1437359873819381\n"
     ]
    }
   ],
   "source": [
    "rhos_opt = []\n",
    "K = 10\n",
    "batch_size = 30\n",
    "num_iter = 300\n",
    "adam_step_size = 1e-4\n",
    "PR_stencil_type = \"m3p\"\n",
    "init_point = None\n",
    "\n",
    "homotopy_step_size = 0.1\n",
    "acceptance_limit = 1 + 2\n",
    "homotopy_arg = \"matrix\" # objective\n",
    "acceptance_arg = \"obj_ratio\" # \"rho\" \"objective\"\n",
    "\n",
    "convergence = {}\n",
    "opt_par_n = {}\n",
    "conv_time = {}\n",
    "A_init = gallery.poisson((n,)) * (n + 1)**2\n",
    "for k in ks:\n",
    "    print(\"Current k = {}\".format(k))\n",
    "    A = gallery.helmholtz((n, ), k=k) * (n + 1)**2\n",
    "#     print(\"Init matrix\")\n",
    "#     print(A.get_matrix())\n",
    "    deep_gmm = dgmg.DeepMG(A, K=K, PR_stencil_type=PR_stencil_type, max_levels=num_levels)\n",
    "    opt_par = deep_gmm.homotopy_optimize(A_init=A_init, homotopy_arg=homotopy_arg, \n",
    "                                         homotopy_step_size=homotopy_step_size, acceptance_limit=acceptance_limit, \n",
    "                                         accept_arg=acceptance_arg, init_point=init_point, adam_step_size=adam_step_size, num_iter=num_iter)\n",
    "    A_init = copy.deepcopy(A)\n",
    "    init_point = copy.deepcopy(opt_par)\n",
    "    opt_par_n[k] = opt_par\n",
    "    convergence[k] = deep_gmm.get_optimizer_convergence()\n",
    "    conv_time[k] = deep_gmm.get_optimization_time()\n",
    "    deep_gmm.update_prd(opt_par)\n",
    "    current_rho = deep_gmm.compute_rho()\n",
    "    if current_rho >= 1:\n",
    "        print(\"Optimization failed for k = {}\".format(k))\n",
    "        break\n",
    "    rhos_opt.append(current_rho)\n",
    "    print(\"Optimized rho = {}\".format(current_rho))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1822bdb5f8>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x182ebbdcc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ks, rhos_linear, label=\"Linear\")\n",
    "plt.plot(ks, rhos_opt, label=\"DMG\")\n",
    "plt.plot(ks, rhos_amg, label=\"AMG\")\n",
    "plt.yscale(\"log\")\n",
    "plt.xlabel(\"$k$\")\n",
    "plt.ylabel(\"Spectral radius\")\n",
    "plt.legend()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python (multigrid)",
   "language": "python",
   "name": "multigrid"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}