plots_diffusion.ipynb

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    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import math\n",
    "import matplotlib as mpl\n",
    "from itertools import product\n",
    "import scipy as sp\n",
    "import scipy.interpolate\n",
    "\n",
    "rc_cmufonts = {\n",
    "    \"font.family\": \"normal\",\n",
    "    \"font.serif\": [],\n",
    "    \"font.sans-serif\": [],\n",
    "    \"font.monospace\": [], \n",
    "    }\n",
    "fs = 10\n",
    "font = {'size'   : fs}\n",
    "\n",
    "mpl.rc('font', **font)\n",
    "mpl.rcParams.update(rc_cmufonts)\n",
    "mpl.rcParams['text.usetex'] = True\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.kernel.zmq.pylab import backend_inline\n",
    "cfg = backend_inline.InlineBackend.instance()# InlineBackendConfig.instance()\n",
    "cfg.figure_format = 'svg' # 'png' to switch back\n",
    "\n",
    "sns.set_context('paper', font_scale=1.5)\n",
    "sns.set_style('white')\n",
    "sns.mpl.rcParams['legend.frameon'] = 'False'\n",
    "#sns.rcParams['legend.frameon'] = 'False'\n",
    "palette = sns.color_palette() \n",
    "fig_format = 'pgf'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
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   "source": [
    "def opt_tau_fun(eps, res, dall, tau_all, gamma=2.):   \n",
    "    tau_opt = {}\n",
    "    for d in dall:\n",
    "        for tau in tau_all:    \n",
    "            err_h1 = res[(d, tau, eps, 'h1')]\n",
    "            err_h1_qtt = res[(d, tau, eps, 'h1_qtt')]\n",
    "            if np.abs(err_h1_qtt/err_h1) < gamma:\n",
    "                tau_opt[d] = tau\n",
    "                break\n",
    "            if tau == tau_all[-1]:\n",
    "                raise Exception('WTF?!')            \n",
    "    return tau_opt"
   ]
  },
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   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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   "source": [
    "q = np.load('computations_diffusion.npz')\n",
    "res = q[\"res\"].item()\n",
    "dall = q[\"dall\"]\n",
    "eps_all = q[\"eps_all\"]\n",
    "tau_all = q[\"tau_all\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
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    "err_h1 = np.zeros((len(eps_all), len(dall)))\n",
    "err_h1_qtt = np.zeros((len(eps_all), len(dall)))\n",
    "err_l2 = np.zeros((len(eps_all), len(dall)))\n",
    "mem = np.zeros((len(eps_all), len(dall)))\n",
    "\n",
    "gamma = [2] * 4\n",
    "for i_d, d in enumerate(dall):\n",
    "    for i_eps, eps in enumerate([1e-1, 1e-2, 1e-3, 1e-4]):\n",
    "        tau_opt = opt_tau_fun(eps, res, dall, tau_all, gamma=gamma[i_eps])\n",
    "        err_h1[i_eps, i_d] = res[(d, tau_opt[d], eps, 'h1')]\n",
    "        err_h1_qtt[i_eps, i_d] = res[(d, tau_opt[d], eps, 'h1_qtt')]\n",
    "        err_l2[i_eps, i_d] = res[(d, tau_opt[d], eps, 'l2')]\n",
    "        mem[i_eps, i_d] = res[(d, tau_opt[d], eps, 'memory')]\n",
    "\n",
    "ax = plt.subplot(111)\n",
    "\n",
    "x0 = mem[0, :]   \n",
    "x1 = mem[1, 2:]  \n",
    "x2 = mem[2, 3:]  \n",
    "x3 = mem[3, 5:]  \n",
    "\n",
    "y0 = err_h1_qtt[0, :]\n",
    "y1 = err_h1_qtt[1, 2:]\n",
    "y2 = err_h1_qtt[2, 3:]\n",
    "y3 = err_h1_qtt[3, 5:]\n",
    "\n",
    "\n",
    "fit0 = np.polyfit(np.log(x0), np.log(-np.log(y0)), 1)\n",
    "fit1 = np.polyfit(np.log(x1), np.log(-np.log(y1)), 1)\n",
    "fit2 = np.polyfit(np.log(x2), np.log(-np.log(y2)), 1)\n",
    "fit3 = np.polyfit(np.log(x3), np.log(-np.log(y3)), 1)\n",
    "\n",
    "fit_res0 = np.poly1d(fit0)\n",
    "fit_res1 = np.poly1d(fit1)\n",
    "fit_res2 = np.poly1d(fit2)\n",
    "fit_res3 = np.poly1d(fit3)\n",
    "\n",
    "ax.semilogy(x0, np.exp(-np.exp(fit_res0(np.log(x0)))), '-', color=palette[0],\n",
    "             label='$\\\\delta=10^{-1}$, '+' $\\\\kappa={0:.2f}$'.format(1./fit0[0]))\n",
    "ax.semilogy(x1, np.exp(-np.exp(fit_res1(np.log(x1)))), '-', color=palette[1],\n",
    "             label='$\\\\delta=10^{-2}$, '+' $\\\\kappa={0:.2f}$'.format(1./fit1[0]))\n",
    "ax.semilogy(x2, np.exp(-np.exp(fit_res2(np.log(x2)))), '-',  color=palette[2],\n",
    "             label='$\\\\delta=10^{-3}$, '+' $\\\\kappa={0:.2f}$'.format(1./fit2[0]))\n",
    "ax.semilogy(x3, np.exp(-np.exp(fit_res3(np.log(x3)))), '-', color=palette[5],\n",
    "             label='$\\\\delta=10^{-4}$, '+' $\\\\kappa={0:.2f}$'.format(1./fit3[0]))\n",
    "\n",
    "ax.semilogy(x0, y0, 's', markeredgewidth=1, markeredgecolor=palette[0], markerfacecolor='white', markersize=6)\n",
    "ax.semilogy(x1, y1, 'D', markeredgewidth=1, markeredgecolor=palette[1], markerfacecolor='white', markersize=6)\n",
    "ax.semilogy(x2, y2, 'o', markeredgewidth=1, markeredgecolor=palette[2], markerfacecolor='white', markersize=6)\n",
    "ax.semilogy(x3, y3, 'cv', markeredgewidth=1, markeredgecolor=palette[5], markerfacecolor='white', markersize=6)\n",
    "\n",
    "ax.grid(ls=\":\")\n",
    "ax.set_xlabel('number of QTT parameters $N_l$')\n",
    "ax.set_ylabel('error $\\\\varepsilon_l$') #, $H^1$ error')\n",
    "ax.legend(loc='best', frameon=True)\n",
    "#ax.axes('top').set_visiblee(False)\n",
    "#ax.axis[\"top\"].set_visible(False)\n",
    "\n",
    "#ax.set_frame_on(False)\n",
    "#plt.tick_params(which='major', length=4, direction='in')\n",
    "\n",
    "ax.spines['top'].set_visible(False)\n",
    "ax.spines['right'].set_visible(False)\n",
    "ax.get_xaxis().tick_bottom()\n",
    "ax.get_yaxis().tick_left()\n",
    "\n",
    "plt.savefig('h1_error_qtt.' + fig_format, bbox_inches='tight')"
   ]
  },
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   "cell_type": "code",
   "execution_count": 6,
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   "source": [
    "err_h1 = np.zeros((len(eps_all), len(dall)))\n",
    "err_h1_qtt = np.zeros((len(eps_all), len(dall)))\n",
    "arr_d = np.zeros(len(dall))\n",
    "err_l2 = np.zeros((len(eps_all), len(dall)))\n",
    "mem = np.zeros((len(eps_all), len(dall)))\n",
    "\n",
    "gamma = [2] * 4\n",
    "for i_d, d in enumerate(dall):\n",
    "    arr_d[i_d] = d\n",
    "    for i_eps, eps in enumerate([1e-1, 1e-2, 1e-3, 1e-4]):\n",
    "        tau_opt = opt_tau_fun(eps, res, dall, tau_all, gamma=gamma[i_eps])\n",
    "        err_h1[i_eps, i_d] = res[(d, tau_opt[d], eps, 'h1')]\n",
    "        err_h1_qtt[i_eps, i_d] = res[(d, tau_opt[d], eps, 'h1_qtt')]\n",
    "        err_l2[i_eps, i_d] = res[(d, tau_opt[d], eps, 'l2')]\n",
    "        mem[i_eps, i_d] = res[(d, tau_opt[d], eps, 'memory')]\n",
    "\n",
    "\n",
    "x0 = arr_d[:]   \n",
    "x1 = arr_d[:]  \n",
    "x2 = arr_d[:]  \n",
    "x3 = arr_d[:]  \n",
    "\n",
    "y0 = err_h1_qtt[0, :]\n",
    "y1 = err_h1_qtt[1, :]\n",
    "y2 = err_h1_qtt[2, :]\n",
    "y3 = err_h1_qtt[3, :]\n",
    "\n",
    "ax = plt.subplot(111)\n",
    "\n",
    "fit0 = np.polyfit(x0, -np.log(y0), 1)\n",
    "fit1 = np.polyfit(x1[1:], -np.log(y1[1:]), 1)\n",
    "fit2 = np.polyfit(x2[3:], -np.log(y2[3:]), 1)\n",
    "fit3 = np.polyfit(x3[6:], -np.log(y3[6:]), 1)\n",
    "\n",
    "fit_res0 = np.poly1d(fit0)\n",
    "fit_res1 = np.poly1d(fit1)\n",
    "fit_res2 = np.poly1d(fit2)\n",
    "fit_res3 = np.poly1d(fit3)\n",
    "\n",
    "ax.semilogy(x0, (np.exp(-fit_res0(x0))), '-', color=palette[0],\n",
    "             label='$\\\\delta=10^{-1}$, order'+' $={0:.2f}$'.format((fit0[0]/np.log(2))))\n",
    "ax.semilogy(x1[1:], (np.exp(-fit_res1(x1[1:]))), '-', color=palette[1],\n",
    "             label='$\\\\delta=10^{-2}$, order'+' $={0:.2f}$'.format((fit1[0]/np.log(2))))\n",
    "ax.semilogy(x2[3:], (np.exp(-fit_res2(x2[3:]))), '-',  color=palette[2],\n",
    "             label='$\\\\delta=10^{-3}$, order'+' $={0:.2f}$'.format((fit2[0]/np.log(2))))\n",
    "ax.semilogy(x3[6:], (np.exp(-fit_res3(x3[6:]))), '-', color=palette[5],\n",
    "             label='$\\\\delta=10^{-4}$, order'+' $={0:.2f}$'.format((fit3[0]/np.log(2))))\n",
    "\n",
    "ax.semilogy(x0, y0, 's', markeredgewidth=1, markeredgecolor=palette[0], markerfacecolor='white', markersize=6)\n",
    "ax.semilogy(x1[1:], y1[1:], 'D', markeredgewidth=1, markeredgecolor=palette[1], markerfacecolor='white', markersize=6)\n",
    "ax.semilogy(x2[2:], y2[2:], 'o', markeredgewidth=1, markeredgecolor=palette[2], markerfacecolor='white', markersize=6)\n",
    "ax.semilogy(x3[5:], y3[5:], 'cv', markeredgewidth=1, markeredgecolor=palette[5], markerfacecolor='white', markersize=6)\n",
    "ax.legend(loc='best')\n",
    "\n",
    "ax.grid(ls=\":\")\n",
    "ax.set_xlabel('number of levels $l$')\n",
    "ax.set_ylabel('error $\\\\varepsilon_l$')#$H^1$ error')\n",
    "ax.legend(loc='best', frameon=True)\n",
    "#ax.axes('top').set_visiblee(False)\n",
    "#ax.axis[\"top\"].set_visible(False)\n",
    "\n",
    "#ax.set_frame_on(False)\n",
    "#plt.tick_params(which='major', length=4, direction='in')\n",
    "\n",
    "ax.spines['top'].set_visible(False)\n",
    "ax.spines['right'].set_visible(False)\n",
    "ax.get_xaxis().tick_bottom()\n",
    "ax.get_yaxis().tick_left()\n",
    "ax.set_xlim([8, 21])\n",
    "plt.tight_layout()\n",
    "plt.savefig('h1_error_l.' + fig_format, bbox_inches='tight')"
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   "cell_type": "code",
   "execution_count": 8,
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    "err_h1 = np.zeros((len(eps_all), len(dall)))\n",
    "#err_h1_qtt = np.zeros((len(eps_all), len(dall)))\n",
    "err_l2 = np.zeros((len(eps_all), len(dall)))\n",
    "#mem = np.zeros((len(eps_all), len(dall)))\n",
    "\n",
    "for i_d, d in enumerate(dall):\n",
    "    for i_eps, eps in enumerate([1e-1, 1e-2, 1e-3, 1e-4]):\n",
    "        err_h1[i_eps, i_d] = res[(d, tau_all[0], eps, 'h1')]\n",
    "        err_h1_qtt[i_eps, i_d] = res[(d, tau_all[0], eps, 'h1_qtt')]\n",
    "        err_l2[i_eps, i_d] = res[(d, tau_all[0], eps, 'l2')]\n",
    "        \n",
    "mem = 2**dall \n",
    "\n",
    "ax = plt.subplot(111)\n",
    "\n",
    "x0 = mem[0:]\n",
    "x1 = mem[0:]\n",
    "x2 = mem[2:]\n",
    "x3 = mem[4:]\n",
    "\n",
    "y0 = err_h1[0, 0:]\n",
    "y1 = err_h1[1, 0:]\n",
    "y2 = err_h1[2, 2:]\n",
    "y3 = err_h1[3, 4:]\n",
    "\n",
    "ax.loglog(x0, y0, 's-', color=palette[0], markeredgewidth=1, markeredgecolor=palette[0], markerfacecolor='white', markersize=6, label='$\\\\delta=10^{-1}$')\n",
    "ax.loglog(x1, y1, 'D-', color=palette[1], markeredgewidth=1, markeredgecolor=palette[1], markerfacecolor='white', markersize=6, label='$\\\\delta=10^{-2}$')\n",
    "ax.loglog(x2, y2, 'o-', color=palette[2], markeredgewidth=1, markeredgecolor=palette[2], markerfacecolor='white', markersize=6, label='$\\\\delta=10^{-3}$')\n",
    "ax.loglog(x3, y3, 'cv-', color=palette[5], markeredgewidth=1, markeredgecolor=palette[5], markerfacecolor='white', markersize=6, label='$\\\\delta=10^{-4}$')\n",
    "#ax.loglog(mem, err_h1[1, :])\n",
    "#ax.loglog(mem, err_h1[2, :])\n",
    "#ax.loglog(mem, err_h1[3, :])\n",
    "\n",
    "\n",
    "ax.grid(ls=\":\")\n",
    "ax.set_xlabel('$N_l$, degrees of freedom')\n",
    "ax.set_ylabel('error $\\\\varepsilon_l$')\n",
    "ax.legend(loc='best', frameon=True)\n",
    "\n",
    "ax.spines['top'].set_visible(False)\n",
    "ax.spines['right'].set_visible(False)\n",
    "ax.get_xaxis().tick_bottom()\n",
    "ax.get_yaxis().tick_left()\n",
    "ax.set_xlim([3*1024/8, 1.*10**4 * 1024/8])\n",
    "ax.set_ylim([10**(-6), 0.5])\n",
    "plt.tight_layout()\n",
    "plt.savefig('h1_error_full.' + fig_format, bbox_inches='tight')"
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   "execution_count": 11,
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    "err_h1 = np.zeros((len(eps_all), len(dall)))\n",
    "err_h1_qtt = np.zeros((len(eps_all), len(dall)))\n",
    "err_l2 = np.zeros((len(eps_all), len(dall)))\n",
    "mem = np.zeros((len(eps_all), len(dall)))\n",
    "\n",
    "\n",
    "for i_d, d in enumerate(dall):\n",
    "    for i_eps, eps in enumerate(eps_all):\n",
    "        tau_opt = opt_tau_fun(eps, res, dall, tau_all, gamma=2.5)\n",
    "        err_h1[i_eps, i_d] = res[(d, tau_opt[d], eps, 'h1')]\n",
    "        err_h1_qtt[i_eps, i_d] = res[(d, tau_opt[d], eps, 'h1_qtt')]\n",
    "        err_l2[i_eps, i_d] = res[(d, tau_opt[d], eps, 'l2')]\n",
    "        mem[i_eps, i_d] = res[(d, tau_opt[d], eps, 'memory')]\n",
    " \n",
    "\n",
    "err_h1_interp = []\n",
    "for i_eps, eps in enumerate(eps_all):      \n",
    "    ind = np.argsort(err_h1_qtt[i_eps, :])\n",
    "    err_h1_interp.append(sp.interpolate.interp1d(err_h1_qtt[i_eps, ind], mem[i_eps, ind], kind='linear'))\n",
    "\n",
    "mem_interp = []\n",
    "for i_d, d in enumerate(dall):\n",
    "    ind = np.argsort(mem[i_eps, :])\n",
    "    mem_interp.append(sp.interpolate.interp1d(mem[:, i_d], eps_all))\n",
    "    \n",
    "errors_h1 = [4e-3, 4e-4, 4e-5]\n",
    "\n",
    "mem_plot = np.zeros((len(errors_h1), len(eps_all)))\n",
    "eps_plot = np.zeros((len(errors_h1), len(eps_all)))\n",
    "\n",
    "for i_h1, h1 in enumerate(errors_h1):\n",
    "    for i_eps, eps in enumerate(eps_all): \n",
    "        try:\n",
    "            mem_plot[i_h1, i_eps] = err_h1_interp[i_eps](h1)\n",
    "            eps_plot[i_h1, i_eps] = eps\n",
    "        except:\n",
    "            break\n",
    "\n",
    "xlim = -30   \n",
    "x0 = mem_plot[0, :xlim][mem_plot[0, :xlim]>0]\n",
    "x1 = mem_plot[1, 3:][mem_plot[1, 3:]>0]\n",
    "x2 = mem_plot[2, :][mem_plot[2, :]>0]\n",
    "\n",
    "ind0 = np.argsort(x0)\n",
    "ind1 = np.argsort(x1)\n",
    "ind2 = np.argsort(x2)\n",
    "\n",
    "y0 = eps_plot[0, :xlim][mem_plot[0, :xlim]>0]\n",
    "y1 = eps_plot[1, 3:][mem_plot[1, 3:]>0]\n",
    "y2 = eps_plot[2, :][mem_plot[2, :]>0]\n",
    "\n",
    "x0 = x0[ind0]\n",
    "x1 = x1[ind1]\n",
    "x2 = x2[ind2]\n",
    "\n",
    "y0 = y0[ind0]\n",
    "y1 = y1[ind1]\n",
    "y2 = y2[ind2]\n",
    "\n",
    "y1 = np.delete(y1, 5)\n",
    "x1 = np.delete(x1, 5)\n",
    "\n",
    "y0 = np.delete(y0, 7)\n",
    "x0 = np.delete(x0, 7)\n",
    "\n",
    "\n",
    "\n",
    "fit0 = np.polyfit(np.log(x0), np.log(-np.log(y0)), 1)\n",
    "fit1 = np.polyfit(np.log(x1), np.log(-np.log(y1)), 1)\n",
    "fit2 = np.polyfit(np.log(x2), np.log(-np.log(y2)), 1)\n",
    "#fit3 = np.polyfit(np.log(x3), np.log(-np.log(y3)), 1)\n",
    "\n",
    "fit_res0 = np.poly1d(fit0)\n",
    "fit_res1 = np.poly1d(fit1)\n",
    "fit_res2 = np.poly1d(fit2)\n",
    "#fit_res3 = np.poly1d(fit3)\n",
    "\n",
    "ax = plt.subplot(111)\n",
    "\n",
    "ax.semilogx(np.exp(-np.exp(fit_res0(np.log(x0)))), x0, 'b-', color=palette[0],\n",
    "             label='$\\\\varepsilon=4\\cdot 10^{-2}$, '+' $\\\\kappa={0:.2f}$'.format(1./fit0[0]))\n",
    "ax.semilogx(np.exp(-np.exp(fit_res1(np.log(x1)))), x1, 'g-', color=palette[1],\n",
    "             label='$\\\\varepsilon=4\\cdot 10^{-3}$, '+' $\\\\kappa={0:.2f}$'.format(1./fit1[0]))\n",
    "ax.semilogx(np.exp(-np.exp(fit_res2(np.log(x2)))), x2, 'r-', color=palette[2],\n",
    "             label='$\\\\varepsilon=4\\cdot 10^{-4}$, '+' $\\\\kappa={0:.2f}$'.format(1./fit2[0]))\n",
    "\n",
    "ax.semilogx(y0, x0, 's', markeredgewidth=1, markeredgecolor=palette[0], markerfacecolor='white', markersize=6)\n",
    "ax.semilogx(y1, x1, 'D', markeredgewidth=1, markeredgecolor=palette[1], markerfacecolor='white', markersize=6)\n",
    "ax.semilogx(y2, x2, 'o', markeredgewidth=1, markeredgecolor=palette[2], markerfacecolor='white', markersize=6)\n",
    "\n",
    "ax.grid(ls=\":\")\n",
    "ax.set_ylabel('number of QTT parameters $N_l$')\n",
    "ax.set_xlabel('$\\\\delta$')\n",
    "ax.legend(loc='best', frameon=True)\n",
    "\n",
    "ax.spines['top'].set_visible(False)\n",
    "ax.spines['right'].set_visible(False)\n",
    "ax.get_xaxis().tick_bottom()\n",
    "ax.get_yaxis().tick_left()\n",
    "\n",
    "ax.set_xlim([1e-3, 3e-1])\n",
    "\n",
    "plt.savefig('delta_mem_qtt.' + fig_format, bbox_inches='tight')"
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