poisson_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",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Test of the Poisson equation with known solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 127\n",
    "A = gallery.poisson((n, n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dimension of matrix A for levels:\n",
      "Level = 0, dimension = (15, 15)\n",
      "Level = 1, dimension = (31, 31)\n",
      "Level = 2, dimension = (63, 63)\n",
      "Level = 3, dimension = (127, 127)\n",
      "\n",
      "Spectral radius = 0.19741190586548468\n"
     ]
    }
   ],
   "source": [
    "linear_gmg = gmg_linear.LinearGMG(A, max_levels=4)\n",
    "print(linear_gmg)\n",
    "print(\"Spectral radius = {}\".format(linear_gmg.compute_rho()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(128,)\n",
      "(127, 127)\n",
      "(16129, 1)\n",
      "(16129, 1)\n",
      "2.05446567233e-11\n",
      "5.02009159216e-05\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d490438>"
      ]
     },
     "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",
    "print(x.shape)\n",
    "xx, yy = np.meshgrid(x[1:], y[1:])\n",
    "print(xx.shape)\n",
    "x_true = np.sin(np.pi * xx) * np.sin(np.pi * yy)\n",
    "rhs = 2 * np.pi**2 * x_true / (n+1)**2\n",
    "plt.imshow(rhs)\n",
    "rhs = rhs.reshape(A.shape, 1)\n",
    "print(rhs.shape)\n",
    "x = linear_gmg.solve(rhs, x0, tol=1e-10)\n",
    "print(x.shape)\n",
    "print(np.linalg.norm(A.dot(x) - rhs))\n",
    "print(np.linalg.norm(x - x_true.reshape(A.shape, 1)) / np.linalg.norm(x_true.reshape(A.shape, 1)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1813a289b0>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d48b4e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogy(linear_gmg.get_gmg_convergence())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x18132dbe10>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1813a447f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(x)\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Study dependance $\\rho$ on dimension in 1D and 2D case and optimize it"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test dims: [7, 15, 31, 63, 127]\n",
      "Current dim = 7\n",
      "Current dim = 15\n",
      "Current dim = 31\n",
      "Current dim = 63\n",
      "Current dim = 127\n"
     ]
    }
   ],
   "source": [
    "num_levels = 2\n",
    "ns = [2**i - 1 for i in range(3, 8)]\n",
    "rhos_linear = []\n",
    "print(\"Test dims: {}\".format(ns))\n",
    "for n in ns:\n",
    "    print(\"Current dim = {}\".format(n))\n",
    "    A = gallery.poisson((n, ))\n",
    "    linear_gmg = gmg_linear.LinearGMG(A, max_levels=num_levels)\n",
    "    rhos_linear.append(linear_gmg.compute_rho())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Spectral radius')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x181ef93b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ns, rhos_linear)\n",
    "plt.xlabel(\"Dimension of the 1D Poisson, $n$\")\n",
    "plt.ylabel(\"Spectral radius\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Current dim = 7\n",
      "Iteration 100/2500\n",
      "Upper bound estimation = 0.05498483747839665\n",
      "Iteration 200/2500\n",
      "Upper bound estimation = 0.04783896219860398\n",
      "Iteration 300/2500\n",
      "Upper bound estimation = 0.040960952236776024\n",
      "Iteration 400/2500\n",
      "Upper bound estimation = 0.03418850451859482\n",
      "Iteration 500/2500\n",
      "Upper bound estimation = 0.02888609477786421\n",
      "Iteration 600/2500\n",
      "Upper bound estimation = 0.026570365794934603\n",
      "Iteration 700/2500\n",
      "Upper bound estimation = 0.0252802789408949\n",
      "Iteration 800/2500\n",
      "Upper bound estimation = 0.024324560172426894\n",
      "Iteration 900/2500\n",
      "Upper bound estimation = 0.02362568536401822\n",
      "Iteration 1000/2500\n",
      "Upper bound estimation = 0.02258014554357622\n",
      "Iteration 1100/2500\n",
      "Upper bound estimation = 0.021899491905042624\n",
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      "Upper bound estimation = 0.02101467405222576\n",
      "Iteration 1300/2500\n",
      "Upper bound estimation = 0.020058076431578895\n",
      "Iteration 1400/2500\n",
      "Upper bound estimation = 0.01926639731764146\n",
      "Iteration 1500/2500\n",
      "Upper bound estimation = 0.018356076534202362\n",
      "Iteration 1600/2500\n",
      "Upper bound estimation = 0.01737234462352419\n",
      "Iteration 1700/2500\n",
      "Upper bound estimation = 0.016713383960763637\n",
      "Iteration 1800/2500\n",
      "Upper bound estimation = 0.01583732337945135\n",
      "Iteration 1900/2500\n",
      "Upper bound estimation = 0.015259499215300938\n",
      "Iteration 2000/2500\n",
      "Upper bound estimation = 0.014386257781141946\n",
      "Iteration 2100/2500\n",
      "Upper bound estimation = 0.013542613996062679\n",
      "Iteration 2200/2500\n",
      "Upper bound estimation = 0.01258515355970757\n",
      "Iteration 2300/2500\n",
      "Upper bound estimation = 0.01190494741270638\n",
      "Iteration 2400/2500\n",
      "Upper bound estimation = 0.010981607239228603\n",
      "Iteration 2500/2500\n",
      "Upper bound estimation = 0.01020077760492154\n",
      "Optimized rho = 0.010187634100419953\n",
      "Current dim = 15\n",
      "Iteration 100/2500\n",
      "Upper bound estimation = 0.055105093170088604\n",
      "Iteration 200/2500\n",
      "Upper bound estimation = 0.04867155874818304\n",
      "Iteration 300/2500\n",
      "Upper bound estimation = 0.04532757818871034\n",
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      "Upper bound estimation = 0.04387647277571088\n",
      "Iteration 500/2500\n",
      "Upper bound estimation = 0.0413419580395707\n",
      "Iteration 600/2500\n",
      "Upper bound estimation = 0.03890634092331192\n",
      "Iteration 700/2500\n",
      "Upper bound estimation = 0.036543110792527554\n",
      "Iteration 800/2500\n",
      "Upper bound estimation = 0.03412096792111098\n",
      "Iteration 900/2500\n",
      "Upper bound estimation = 0.031812138905039616\n",
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      "Upper bound estimation = 0.031023752291009215\n",
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      "Upper bound estimation = 0.029595700230230258\n",
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      "Upper bound estimation = 0.028537111317237615\n",
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      "Upper bound estimation = 0.027572180466853127\n",
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      "Upper bound estimation = 0.026764186354246083\n",
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      "Upper bound estimation = 0.025232879840393938\n",
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      "Upper bound estimation = 0.02315680406749335\n",
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      "Upper bound estimation = 0.02222268608058462\n",
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      "Upper bound estimation = 0.02262975432677643\n",
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      "Upper bound estimation = 0.022806315843117615\n",
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      "Upper bound estimation = 0.021679890477414934\n",
      "Iteration 2100/2500\n",
      "Upper bound estimation = 0.02143918185499661\n",
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      "Upper bound estimation = 0.021033090276397368\n",
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      "Upper bound estimation = 0.020877826173347613\n",
      "Iteration 2400/2500\n",
      "Upper bound estimation = 0.020819663045772208\n",
      "Iteration 2500/2500\n",
      "Upper bound estimation = 0.02059181336970124\n",
      "Optimized rho = 0.01741024415150181\n",
      "Current dim = 31\n",
      "Iteration 100/2500\n",
      "Upper bound estimation = 0.05566587450391064\n",
      "Iteration 200/2500\n",
      "Upper bound estimation = 0.05343587059551577\n",
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      "Upper bound estimation = 0.0500050942454758\n",
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      "Upper bound estimation = 0.046141781323269224\n",
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      "Upper bound estimation = 0.04217849990584061\n",
      "Iteration 600/2500\n",
      "Upper bound estimation = 0.039757100541019504\n",
      "Iteration 700/2500\n",
      "Upper bound estimation = 0.03818054013397824\n",
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      "Upper bound estimation = 0.03727652765726934\n",
      "Iteration 900/2500\n",
      "Upper bound estimation = 0.03631076184144726\n",
      "Iteration 1000/2500\n",
      "Upper bound estimation = 0.03544332534967131\n",
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      "Upper bound estimation = 0.03441541439308166\n",
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      "Upper bound estimation = 0.03347509726523801\n",
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      "Upper bound estimation = 0.03237211246068649\n",
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      "Upper bound estimation = 0.031647773803766224\n",
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      "Upper bound estimation = 0.030144809084157793\n",
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      "Upper bound estimation = 0.02948263096443428\n",
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      "Upper bound estimation = 0.028732773663049913\n",
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      "Upper bound estimation = 0.027896436629772342\n",
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      "Upper bound estimation = 0.02718340051627034\n",
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      "Upper bound estimation = 0.026137832198237003\n",
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      "Upper bound estimation = 0.025334248341013405\n",
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      "Upper bound estimation = 0.024612799615218187\n",
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      "Upper bound estimation = 0.023766130943296097\n",
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      "Upper bound estimation = 0.023194827340469917\n",
      "Iteration 2500/2500\n",
      "Upper bound estimation = 0.022662021116125298\n",
      "Optimized rho = 0.022558664783017546\n",
      "Current dim = 63\n",
      "Iteration 100/2500\n",
      "Upper bound estimation = 0.05917546058905297\n",
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      "Upper bound estimation = 0.05568478629160141\n",
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      "Upper bound estimation = 0.050776539708369\n",
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      "Upper bound estimation = 0.04668260033448929\n",
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      "Upper bound estimation = 0.043979303003655844\n",
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      "Upper bound estimation = 0.04258519908031654\n",
      "Iteration 700/2500\n",
      "Upper bound estimation = 0.04148831475000336\n",
      "Iteration 800/2500\n",
      "Upper bound estimation = 0.040890139927249866\n",
      "Iteration 900/2500\n",
      "Upper bound estimation = 0.04009117694393825\n",
      "Iteration 1000/2500\n",
      "Upper bound estimation = 0.03896125573423408\n",
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      "Upper bound estimation = 0.03816429575753378\n",
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      "Upper bound estimation = 0.03725977311595417\n",
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      "Upper bound estimation = 0.03597163712624054\n",
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      "Upper bound estimation = 0.03508020850462641\n",
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      "Upper bound estimation = 0.03430968959432541\n",
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      "Upper bound estimation = 0.03362475272992238\n",
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      "Upper bound estimation = 0.03271165581607387\n",
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      "Upper bound estimation = 0.03184986644180326\n",
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      "Upper bound estimation = 0.03126138567253965\n",
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      "Upper bound estimation = 0.030186769052946795\n",
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      "Upper bound estimation = 0.02913808030836183\n",
      "Iteration 2200/2500\n",
      "Upper bound estimation = 0.029141845850841078\n",
      "Iteration 2300/2500\n",
      "Upper bound estimation = 0.028490801305214208\n",
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      "Upper bound estimation = 0.02806675273521827\n",
      "Iteration 2500/2500\n",
      "Upper bound estimation = 0.027435031122855606\n",
      "Optimized rho = 0.026694007693062658\n",
      "Current dim = 127\n",
      "Iteration 100/2500\n",
      "Upper bound estimation = 0.06165834671077664\n",
      "Iteration 200/2500\n",
      "Upper bound estimation = 0.057517239529114986\n",
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      "Upper bound estimation = 0.05334599361240447\n",
      "Iteration 400/2500\n",
      "Upper bound estimation = 0.04957208113248327\n",
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      "Upper bound estimation = 0.04712276636586176\n",
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      "Upper bound estimation = 0.045227794949270234\n",
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      "Upper bound estimation = 0.04399299830124899\n",
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      "Upper bound estimation = 0.043214912323280744\n",
      "Iteration 900/2500\n",
      "Upper bound estimation = 0.04187989085049057\n",
      "Iteration 1000/2500\n",
      "Upper bound estimation = 0.04098304409618935\n",
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      "Upper bound estimation = 0.039916801100627675\n",
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      "Upper bound estimation = 0.03885834593695782\n",
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      "Upper bound estimation = 0.03931351435963989\n",
      "Iteration 1400/2500\n",
      "Upper bound estimation = 0.038498876937105485\n",
      "Iteration 1500/2500\n",
      "Upper bound estimation = 0.037594965743324764\n",
      "Iteration 1600/2500\n",
      "Upper bound estimation = 0.03711288492442922\n",
      "Iteration 1700/2500\n",
      "Upper bound estimation = 0.03659746193549578\n",
      "Iteration 1800/2500\n",
      "Upper bound estimation = 0.03598616581137224\n",
      "Iteration 1900/2500\n",
      "Upper bound estimation = 0.035183197780799605\n",
      "Iteration 2000/2500\n",
      "Upper bound estimation = 0.03479767258516046\n",
      "Iteration 2100/2500\n",
      "Upper bound estimation = 0.03400973019437486\n",
      "Iteration 2200/2500\n",
      "Upper bound estimation = 0.03315251677880522\n",
      "Iteration 2300/2500\n",
      "Upper bound estimation = 0.03237335208497482\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 2400/2500\n",
      "Upper bound estimation = 0.03155099083680839\n",
      "Iteration 2500/2500\n",
      "Upper bound estimation = 0.035384012100412816\n",
      "Optimized rho = 0.033789882130446446\n"
     ]
    }
   ],
   "source": [
    "rhos_opt = []\n",
    "K = 20\n",
    "batch_size = 10\n",
    "num_iter = 2500\n",
    "step_size = 5e-5\n",
    "PR_stencil_type = \"3p\"\n",
    "init_point = None\n",
    "convergence = {}\n",
    "opt_par_n = {}\n",
    "conv_time = {}\n",
    "for n in ns:\n",
    "    print(\"Current dim = {}\".format(n))\n",
    "    A = gallery.poisson((n, ))\n",
    "    deep_gmm = dgmg.DeepMG(A, K=K, PR_stencil_type=PR_stencil_type, max_levels=num_levels)\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[n] = opt_par\n",
    "    convergence[n] = deep_gmm.get_optimizer_convergence()\n",
    "    conv_time[n] = 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))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x18136af898>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1813ae7e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ns, rhos_linear, label=\"Linear\")\n",
    "plt.plot(ns, rhos_opt, label=\"DMG\")\n",
    "plt.xlabel(\"Dimension of the 1D Poisson, $n$\")\n",
    "plt.ylabel(\"Spectral radius\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test dims: [7, 15, 31, 63, 127]\n",
      "Current dim = 7\n",
      "Linear spectral radius = 0.16913227029749436\n",
      "AMG spectral radius = 0.09117489460224773\n",
      "Current dim = 15\n",
      "Linear spectral radius = 0.1900485590933702\n",
      "AMG spectral radius = 0.10991720305651478\n",
      "Current dim = 31\n",
      "Linear spectral radius = 0.1956353931532445\n",
      "AMG spectral radius = 0.123741721830234\n",
      "Current dim = 63\n",
      "Linear spectral radius = 0.1970554247753587\n",
      "AMG spectral radius = 0.16366864639939477\n",
      "Current dim = 127\n",
      "Linear spectral radius = 0.1974119058654843\n",
      "AMG spectral radius = 0.26354464738686534\n"
     ]
    }
   ],
   "source": [
    "num_levels = 4\n",
    "ns = [2**i - 1 for i in range(3, 8)]\n",
    "rhos_linear = []\n",
    "rhos_amg = []\n",
    "print(\"Test dims: {}\".format(ns))\n",
    "for n in ns:\n",
    "    print(\"Current dim = {}\".format(n))\n",
    "    A = gallery.poisson((n, n))\n",
    "    linear_gmm = gmg_linear.LinearGMG(A, max_levels=num_levels)\n",
    "    current_rho = linear_gmm.compute_rho()\n",
    "    print(\"Linear spectral radius = {}\".format(current_rho))\n",
    "    rhos_linear.append(current_rho)\n",
    "    amg = classical_amg.ClassicalAMG(A, num_levels)\n",
    "    current_rho = amg.compute_rho()\n",
    "    print(\"AMG spectral radius = {}\".format(current_rho))\n",
    "    rhos_amg.append(current_rho)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1823269eb8>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x151ff64400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ns, rhos_linear, label=\"Linear\")\n",
    "plt.plot(ns, rhos_amg, label=\"AMG\")\n",
    "plt.xlabel(\"Dimension of the 2D Poisson, $n$\")\n",
    "plt.ylabel(\"Spectral radius\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Current dim = 7\n",
      "Dimension of matrix A for levels:\n",
      "Level = 0, dimension = (1, 1)\n",
      "Level = 1, dimension = (3, 3)\n",
      "Level = 2, dimension = (7, 7)\n",
      "\n",
      "Iteration 100/2000\n",
      "Upper bound estimation = 0.17111403439950215\n",
      "Iteration 200/2000\n",
      "Upper bound estimation = 0.16557343973282126\n",
      "Iteration 300/2000\n",
      "Upper bound estimation = 0.15597631003196452\n",
      "Iteration 400/2000\n",
      "Upper bound estimation = 0.15483861396120066\n",
      "Iteration 500/2000\n",
      "Upper bound estimation = 0.1472071303402176\n",
      "Iteration 600/2000\n",
      "Upper bound estimation = 0.1398662123664813\n",
      "Iteration 700/2000\n",
      "Upper bound estimation = 0.13142021528750225\n",
      "Iteration 800/2000\n",
      "Upper bound estimation = 0.12777818121446433\n",
      "Iteration 900/2000\n",
      "Upper bound estimation = 0.1093069922241443\n",
      "Iteration 1000/2000\n",
      "Upper bound estimation = 0.0962772057734996\n",
      "Iteration 1100/2000\n",
      "Upper bound estimation = 0.08633560224228748\n",
      "Iteration 1200/2000\n",
      "Upper bound estimation = 0.07989332371482415\n",
      "Iteration 1300/2000\n",
      "Upper bound estimation = 0.07831868660143992\n",
      "Iteration 1400/2000\n",
      "Upper bound estimation = 0.07502289332985426\n",
      "Iteration 1500/2000\n",
      "Upper bound estimation = 0.07471002986899353\n",
      "Iteration 1600/2000\n",
      "Upper bound estimation = 0.07486883072726937\n",
      "Iteration 1700/2000\n",
      "Upper bound estimation = 0.07496380869125989\n",
      "Iteration 1800/2000\n",
      "Upper bound estimation = 0.07356904073063986\n",
      "Iteration 1900/2000\n",
      "Upper bound estimation = 0.07426628218206456\n",
      "Iteration 2000/2000\n",
      "Upper bound estimation = 0.07385885753312237\n",
      "Optimized rho = 0.06558064966266179\n",
      "Current dim = 15\n",
      "Dimension of matrix A for levels:\n",
      "Level = 0, dimension = (1, 1)\n",
      "Level = 1, dimension = (3, 3)\n",
      "Level = 2, dimension = (7, 7)\n",
      "Level = 3, dimension = (15, 15)\n",
      "\n",
      "Iteration 100/2000\n",
      "Upper bound estimation = 0.19792230480251044\n",
      "Iteration 200/2000\n",
      "Upper bound estimation = 0.19112105750714198\n",
      "Iteration 300/2000\n",
      "Upper bound estimation = 0.18062402765271893\n",
      "Iteration 400/2000\n",
      "Upper bound estimation = 0.17697845281614993\n",
      "Iteration 500/2000\n",
      "Upper bound estimation = 0.17037200607197744\n",
      "Iteration 600/2000\n",
      "Upper bound estimation = 0.16287796106222438\n",
      "Iteration 700/2000\n",
      "Upper bound estimation = 0.15827453660438867\n",
      "Iteration 800/2000\n",
      "Upper bound estimation = 0.154284365134669\n",
      "Iteration 900/2000\n",
      "Upper bound estimation = 0.14800525003801526\n",
      "Iteration 1000/2000\n",
      "Upper bound estimation = 0.14210799893494086\n",
      "Iteration 1100/2000\n",
      "Upper bound estimation = 0.1381091121623713\n",
      "Iteration 1200/2000\n",
      "Upper bound estimation = 0.13496077899675954\n",
      "Iteration 1300/2000\n",
      "Upper bound estimation = 0.12889968189042653\n",
      "Iteration 1400/2000\n",
      "Upper bound estimation = 0.12375152136006541\n",
      "Iteration 1500/2000\n",
      "Upper bound estimation = 0.12349750239337426\n",
      "Iteration 1600/2000\n",
      "Upper bound estimation = 0.12153935294223399\n",
      "Iteration 1700/2000\n",
      "Upper bound estimation = 0.1202756612606245\n",
      "Iteration 1800/2000\n",
      "Upper bound estimation = 0.12061537430843965\n",
      "Iteration 1900/2000\n",
      "Upper bound estimation = 0.11891575563930191\n",
      "Iteration 2000/2000\n",
      "Upper bound estimation = 0.1195469861054928\n",
      "Optimized rho = 0.11249024888895988\n",
      "Current dim = 31\n",
      "Dimension of matrix A for levels:\n",
      "Level = 0, dimension = (3, 3)\n",
      "Level = 1, dimension = (7, 7)\n",
      "Level = 2, dimension = (15, 15)\n",
      "Level = 3, dimension = (31, 31)\n",
      "\n",
      "Iteration 100/2000\n",
      "Upper bound estimation = 0.21332206896910688\n",
      "Iteration 200/2000\n",
      "Upper bound estimation = 0.2064562554401873\n",
      "Iteration 300/2000\n",
      "Upper bound estimation = 0.19813351280456817\n",
      "Iteration 400/2000\n",
      "Upper bound estimation = 0.18996439550072852\n",
      "Iteration 500/2000\n",
      "Upper bound estimation = 0.1845679561385918\n",
      "Iteration 600/2000\n",
      "Upper bound estimation = 0.1835631945677795\n",
      "Iteration 700/2000\n",
      "Upper bound estimation = 0.18065299265489637\n",
      "Iteration 800/2000\n",
      "Upper bound estimation = 0.17856618435143964\n",
      "Iteration 900/2000\n",
      "Upper bound estimation = 0.17521165554017812\n",
      "Iteration 1000/2000\n",
      "Upper bound estimation = 0.17217589545365247\n",
      "Iteration 1100/2000\n",
      "Upper bound estimation = 0.17042084717071124\n",
      "Iteration 1200/2000\n",
      "Upper bound estimation = 0.16615747885900886\n",
      "Iteration 1300/2000\n",
      "Upper bound estimation = 0.16089069781265017\n",
      "Iteration 1400/2000\n",
      "Upper bound estimation = 0.1581129804827372\n",
      "Iteration 1500/2000\n",
      "Upper bound estimation = 0.15280619925589495\n",
      "Iteration 1600/2000\n",
      "Upper bound estimation = 0.1503220414011105\n",
      "Iteration 1700/2000\n",
      "Upper bound estimation = 0.1463285021661347\n",
      "Iteration 1800/2000\n",
      "Upper bound estimation = 0.14474310868187756\n",
      "Iteration 1900/2000\n",
      "Upper bound estimation = 0.14256622401371993\n",
      "Iteration 2000/2000\n",
      "Upper bound estimation = 0.14475624343605584\n",
      "Optimized rho = 0.13044525668375806\n",
      "Current dim = 63\n",
      "Dimension of matrix A for levels:\n",
      "Level = 0, dimension = (7, 7)\n",
      "Level = 1, dimension = (15, 15)\n",
      "Level = 2, dimension = (31, 31)\n",
      "Level = 3, dimension = (63, 63)\n",
      "\n",
      "Iteration 100/2000\n",
      "Upper bound estimation = 0.22974815709053664\n",
      "Iteration 200/2000\n",
      "Upper bound estimation = 0.22195266157635427\n",
      "Iteration 300/2000\n",
      "Upper bound estimation = 0.21434055616028172\n",
      "Iteration 400/2000\n",
      "Upper bound estimation = 0.20905456374801074\n",
      "Iteration 500/2000\n",
      "Upper bound estimation = 0.2029787020493017\n",
      "Iteration 600/2000\n",
      "Upper bound estimation = 0.19832990397833467\n",
      "Iteration 700/2000\n",
      "Upper bound estimation = 0.19198166180298473\n",
      "Iteration 800/2000\n",
      "Upper bound estimation = 0.18563530768932127\n",
      "Iteration 900/2000\n",
      "Upper bound estimation = 0.18016192921806462\n",
      "Iteration 1000/2000\n",
      "Upper bound estimation = 0.17347285159598838\n",
      "Iteration 1100/2000\n",
      "Upper bound estimation = 0.16838079336696674\n",
      "Iteration 1200/2000\n",
      "Upper bound estimation = 0.1627733712819278\n",
      "Iteration 1300/2000\n",
      "Upper bound estimation = 0.158101827946187\n",
      "Iteration 1400/2000\n",
      "Upper bound estimation = 0.15438930798113754\n",
      "Iteration 1500/2000\n",
      "Upper bound estimation = 0.15375628238637318\n",
      "Iteration 1600/2000\n",
      "Upper bound estimation = 0.15453460131669228\n",
      "Iteration 1700/2000\n",
      "Upper bound estimation = 0.1527339425711771\n",
      "Iteration 1800/2000\n",
      "Upper bound estimation = 0.15272452261485644\n",
      "Iteration 1900/2000\n",
      "Upper bound estimation = 0.15269193041013013\n",
      "Iteration 2000/2000\n",
      "Upper bound estimation = 0.15260678946597678\n",
      "Optimized rho = 0.12666717678810785\n",
      "Current dim = 127\n",
      "Dimension of matrix A for levels:\n",
      "Level = 0, dimension = (15, 15)\n",
      "Level = 1, dimension = (31, 31)\n",
      "Level = 2, dimension = (63, 63)\n",
      "Level = 3, dimension = (127, 127)\n",
      "\n",
      "Iteration 100/2000\n",
      "Upper bound estimation = 0.24677928333412671\n",
      "Iteration 200/2000\n",
      "Upper bound estimation = 0.23723826353834626\n",
      "Iteration 300/2000\n",
      "Upper bound estimation = 0.2312724831222658\n",
      "Iteration 400/2000\n",
      "Upper bound estimation = 0.22693586026522722\n",
      "Iteration 500/2000\n",
      "Upper bound estimation = 0.22170623061531194\n",
      "Iteration 600/2000\n",
      "Upper bound estimation = 0.21552855515287797\n",
      "Iteration 700/2000\n",
      "Upper bound estimation = 0.21008796067406255\n",
      "Iteration 800/2000\n",
      "Upper bound estimation = 0.20367373680336248\n",
      "Iteration 900/2000\n",
      "Upper bound estimation = 0.19787930644828222\n",
      "Iteration 1000/2000\n",
      "Upper bound estimation = 0.1924531292675642\n",
      "Iteration 1100/2000\n",
      "Upper bound estimation = 0.1862854242888473\n",
      "Iteration 1200/2000\n",
      "Upper bound estimation = 0.18027099559567086\n",
      "Iteration 1300/2000\n",
      "Upper bound estimation = 0.1762054280961791\n",
      "Iteration 1400/2000\n",
      "Upper bound estimation = 0.3012936677030424\n",
      "Iteration 1500/2000\n",
      "Upper bound estimation = 0.17639539949933838\n",
      "Iteration 1600/2000\n",
      "Upper bound estimation = 0.17511750619500815\n",
      "Iteration 1700/2000\n",
      "Upper bound estimation = 0.173408027183987\n",
      "Iteration 1800/2000\n",
      "Upper bound estimation = 0.17012118213221653\n",
      "Iteration 1900/2000\n",
      "Upper bound estimation = 0.17000325032900407\n",
      "Iteration 2000/2000\n",
      "Upper bound estimation = 0.1696864443178092\n",
      "Optimized rho = 0.12983526097871814\n"
     ]
    }
   ],
   "source": [
    "rhos_opt = []\n",
    "K = 10\n",
    "batch_size = 30\n",
    "num_iter = 2000\n",
    "step_size = 1e-4\n",
    "PR_stencil_type = \"9p\"\n",
    "init_point = None\n",
    "convergence = {}\n",
    "opt_par_n = {}\n",
    "conv_time = {}\n",
    "for n in ns:\n",
    "    print(\"Current dim = {}\".format(n))\n",
    "    A = gallery.poisson((n, n))\n",
    "    gmm = dgmg.DeepMG(A, PR_stencil_type=PR_stencil_type, max_levels=num_levels)\n",
    "    opt_par = gmm.optimize(num_iter=num_iter, step_size=step_size)\n",
    "    opt_par_n[n] = opt_par\n",
    "    convergence[n] = gmm.get_optimizer_convergence()\n",
    "    conv_time[n] = gmm.get_optimization_time()\n",
    "    gmm.update_prd(opt_par)\n",
    "    current_rho = 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": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x182359e390>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1849311be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ns, rhos_linear, label=\"Linear\")\n",
    "plt.plot(ns, rhos_opt, label=\"DMG\")\n",
    "plt.plot(ns, rhos_amg, label=\"AMG\")\n",
    "plt.xlabel(\"Dimension of the 2D Poisson, $n$\")\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
}