add figure

figures.ipynb

+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib\n",
+    "\n",
+    "matplotlib.use(\"agg\")\n",
+    "\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "%matplotlib inline\n",
+    "%config InlineBackend.figure_format = 'svg'\n",
+    "\n",
+    "golden_mean = (np.sqrt(5) - 1) / 2  # Aesthetic ratio\n",
+    "fig_width_pt = 246.0  # Columnwidth\n",
+    "inches_per_pt = 1 / 72.27  # Convert pt to inches\n",
+    "fig_width = fig_width_pt * inches_per_pt\n",
+    "fig_height = fig_width * golden_mean  # height in inches\n",
+    "fig_size = [fig_width, fig_height]\n",
+    "\n",
+    "params = {\n",
+    "    \"backend\": \"ps\",\n",
+    "    \"axes.labelsize\": 13,\n",
+    "    \"font.size\": 13,\n",
+    "    \"legend.fontsize\": 10,\n",
+    "    \"xtick.labelsize\": 10,\n",
+    "    \"ytick.labelsize\": 10,\n",
+    "    \"text.usetex\": True,\n",
+    "    \"figure.figsize\": fig_size,\n",
+    "    \"font.family\": \"serif\",\n",
+    "    \"font.serif\": \"Computer Modern Roman\",\n",
+    "    \"legend.frameon\": True,\n",
+    "    \"savefig.dpi\": 300,\n",
+    "}\n",
+    "\n",
+    "plt.rcParams.update(params)\n",
+    "plt.rc(\"text.latex\", preamble=[r\"\\usepackage{xfrac}\", r\"\\usepackage{siunitx}\"])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "np.random.seed(1)\n",
+    "xs = np.sort(np.random.uniform(-1, 1, 3))\n",
+    "errs = np.abs(np.random.randn(3))\n",
+    "ys = xs ** 3\n",
+    "means = lambda x: np.convolve(x, np.ones(2) / 2, mode=\"valid\")\n",
+    "xs_means = means(xs)\n",
+    "ys_means = means(ys)\n",
+    "\n",
+    "fig, ax = plt.subplots()\n",
+    "plt.scatter(xs, ys, c=\"k\")\n",
+    "ax.errorbar(xs, ys, errs, capsize=5, c=\"k\")\n",
+    "ax.annotate(\n",
+    "    s=r\"$L_{1,2} = \\sqrt{\\Delta x^2 + \\Delta \\bar{y}^2}$\",\n",
+    "    xy=(np.mean([xs[0], xs[1], xs[1]]), np.mean([ys[0], ys[1], ys[1]])),\n",
+    "    xytext=(xs_means[0], ys_means[0] + 1),\n",
+    "    arrowprops=dict(arrowstyle=\"->\"),\n",
+    "    ha=\"center\",\n",
+    ")\n",
+    "\n",
+    "for i, (x, y, err) in enumerate(zip(xs, ys, errs)):\n",
+    "    err_str = fr'${{\\sigma}}_{{\\bar {{y}}_{i+1}}}$'\n",
+    "    ax.annotate(\n",
+    "        s=err_str,\n",
+    "        xy=(x, y + err / 2),\n",
+    "        xytext=(x + 0.1, y + err + 0.5),\n",
+    "        arrowprops=dict(arrowstyle=\"->\"),\n",
+    "        ha=\"center\",\n",
+    "    )\n",
+    "\n",
+    "    ax.annotate(\n",
+    "        s=fr\"$x_{i+1}, \\bar{{y}}_{i+1}$\",\n",
+    "        xy=(x, y),\n",
+    "        xytext=(x + 0.1, y - 0.5),\n",
+    "        arrowprops=dict(arrowstyle=\"->\"),\n",
+    "        ha=\"center\",\n",
+    "    )\n",
+    "\n",
+    "\n",
+    "ax.scatter(xs, ys, c=\"green\", s=5, zorder=5, label=\"more seeds\")\n",
+    "ax.scatter(xs_means, ys_means, c=\"red\", s=5, zorder=5, label=\"new point\")\n",
+    "ax.legend()\n",
+    "\n",
+    "ax.text(\n",
+    "    x=0.5,\n",
+    "    y=0.0,\n",
+    "    s=(\n",
+    "        r\"$\\textrm{if}\\; \\max{(L_{i,i+1})} > \\textrm{average\\_priority} \\cdot \\max{\\sigma_{\\bar{y}_{i}}} \\rightarrow,\\;\\textrm{add new point}$\"\n",
+    "        \"\\n\"\n",
+    "        r\"$\\textrm{if}\\; \\max{(L_{i,i+1})} < \\textrm{average\\_priority} \\cdot \\max{\\sigma_{\\bar{y}_{i}}} \\rightarrow,\\;\\textrm{add new seeds}$\"\n",
+    "    ),\n",
+    "    horizontalalignment=\"center\",\n",
+    "    verticalalignment=\"center\",\n",
+    "    transform=ax.transAxes,\n",
+    ")\n",
+    "ax.set_title(\"AverageLearner1D\")\n",
+    "ax.axis(\"off\")\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "np.random.seed(1)\n",
+    "xs = np.array([0.1, 0.3, 0.35, 0.45])\n",
+    "f = lambda x: x**3\n",
+    "ys = f(xs)\n",
+    "means = lambda x: np.convolve(x, np.ones(2) / 2, mode=\"valid\")\n",
+    "xs_means = means(xs)\n",
+    "ys_means = means(ys)\n",
+    "\n",
+    "fig, ax = plt.subplots(figsize=fig_size)\n",
+    "ax.scatter(xs, ys, c=\"k\")\n",
+    "ax.plot(xs, ys, c=\"k\")\n",
+    "# ax.scatter()\n",
+    "ax.annotate(\n",
+    "    s=r\"$L_{1,2} = \\sqrt{\\Delta x^2 + \\Delta y^2}$\",\n",
+    "    xy=(np.mean([xs[0], xs[1]]), np.mean([ys[0], ys[1]])),\n",
+    "    xytext=(xs[0]+0.05, ys[0] - 0.05),\n",
+    "    arrowprops=dict(arrowstyle=\"->\"),\n",
+    "    ha=\"center\",\n",
+    "    zorder=10,\n",
+    ")\n",
+    "\n",
+    "for i, (x, y) in enumerate(zip(xs, ys)):\n",
+    "    sign = [1, -1][i % 2]\n",
+    "    ax.annotate(\n",
+    "        s=fr\"$x_{i+1}, y_{i+1}$\",\n",
+    "        xy=(x, y),\n",
+    "        xytext=(x + 0.01, y + sign * 0.04),\n",
+    "        arrowprops=dict(arrowstyle=\"->\"),\n",
+    "        ha=\"center\",\n",
+    "    )\n",
+    "    \n",
+    "ax.scatter(xs, ys, c=\"green\", s=5, zorder=5, label=\"existing data\")\n",
+    "losses = np.hypot(xs[1:] - xs[:-1], ys[1:] - ys[:-1])\n",
+    "ax.scatter(xs_means, ys_means, c=\"red\", s=300*losses, zorder=8, label=\"candidate points\")\n",
+    "xs_dense = np.linspace(xs[0], xs[-1], 400)\n",
+    "ax.plot(xs_dense, f(xs_dense), alpha=0.3, zorder=7, label=\"function\")\n",
+    "\n",
+    "ax.legend()\n",
+    "ax.axis(\"off\")\n",
+    "plt.savefig(\"figures/loss_1D.pdf\", bbox_inches=\"tight\", transparent=True)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import adaptive\n",
+    "adaptive.notebook_extension()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def f(x, offset=0.12312):\n",
+    "    a = 0.01\n",
+    "    return x + a**2 / (a**2 + (x - offset)**2)\n",
+    "\n",
+    "learner = adaptive.Learner1D(f, bounds=(-1, 1))\n",
+    "adaptive.runner.simple(learner, goal=lambda l: l.npoints > 100)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs, ys = zip(*learner.data.items())"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "fig, ax = plt.subplots()\n",
+    "for i in range(1, len(xs)):\n",
+    "    if i % 10 != 0:\n",
+    "        continue\n",
+    "    alpha = np.linspace(0.2, 1, 101)[i]\n",
+    "    offset = i / len(xs)\n",
+    "    xs_part, ys_part = xs[:i], ys[:i]\n",
+    "    xs_part, ys_part = zip(*sorted(zip(xs_part, ys_part)))\n",
+    "    ax.plot(xs_part, offset + np.array(ys_part), alpha=alpha, c='grey', lw=0.5)\n",
+    "\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "xs_part, ys_part"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "language_info": {
+   "name": "python",
+   "pygments_lexer": "ipython3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}