From 9f42b003c018dabbfd6ca072245c6a46ee2484a6 Mon Sep 17 00:00:00 2001
From: Bas Nijholt <basnijholt@gmail.com>
Date: Mon, 16 Sep 2019 17:25:38 +0200
Subject: [PATCH] add algo description figure
---
figures.ipynb | 147 +++++++++++++++++++++++++++++++++++++++++++++++++-
1 file changed, 146 insertions(+), 1 deletion(-)
diff --git a/figures.ipynb b/figures.ipynb
index 0ec8695..733b3d7 100644
--- a/figures.ipynb
+++ b/figures.ipynb
@@ -14,7 +14,7 @@
"import matplotlib.pyplot as plt\n",
"\n",
"%matplotlib inline\n",
- "%config InlineBackend.figure_format = 'svg'\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",
@@ -322,6 +322,151 @@
"plt.plot(np.cumsum(times))"
]
},
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Algo explaination"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "fig, axs = plt.subplots(1, 1, figsize=(fig_width, 3 * fig_height))\n",
+ "\n",
+ "def f(x, offset=0.123):\n",
+ " a = 0.2\n",
+ " return a ** 2 / (a ** 2 + (x - offset) ** 2)\n",
+ "\n",
+ "learner = adaptive.Learner1D(\n",
+ " f, (0, 2),\n",
+ " loss_per_interval=adaptive.learner.learner1D.curvature_loss_function()\n",
+ ")\n",
+ "learner._recompute_losses_factor = 0.1\n",
+ "xs_dense = np.linspace(*learner.bounds, 400)\n",
+ "ys_dense = f(xs_dense)\n",
+ "step = 0.4\n",
+ "\n",
+ "for i in range(11):\n",
+ " offset = -i * step\n",
+ "\n",
+ " x = learner.ask(1)[0][0]\n",
+ " y = f(x)\n",
+ " learner.tell(x, y)\n",
+ " xs, ys = map(np.array, zip(*sorted(learner.data.items())))\n",
+ " ys = ys + offset\n",
+ " if i >= 1:\n",
+ " axs.plot(xs_dense, ys_dense + offset, c=\"k\", alpha=0.3, zorder=0)\n",
+ " axs.plot(xs, ys, zorder=1, c=\"k\")\n",
+ " axs.scatter(xs, ys, alpha=1, zorder=2, c=\"k\")\n",
+ " (x_left, x_right), loss = list(learner.losses.items())[0] # it's a ItemSortedDict\n",
+ " (y_left, y_right) = [\n",
+ " learner.data[x_left] + offset,\n",
+ " learner.data[x_right] + offset,\n",
+ " ]\n",
+ " axs.scatter([x_left, x_right], [y_left, y_right], c=\"r\", s=10, zorder=3)\n",
+ " x_mid = np.mean((x_left, x_right))\n",
+ " y_mid = np.interp(x_mid, (x_left, x_right), (y_left, y_right))\n",
+ " axs.scatter(x_mid, y_mid, zorder=4, marker=\"x\", c=\"green\")\n",
+ "\n",
+ "axs.text(\n",
+ " -0.1,\n",
+ " 0.5,\n",
+ " (r\"$\\mathrm{time}$\" + \"\\n\" + \"$\\longleftarrow$\"),\n",
+ " transform=axs.transAxes,\n",
+ " horizontalalignment=\"center\",\n",
+ " verticalalignment=\"center\",\n",
+ " rotation=90,\n",
+ " fontsize=18,\n",
+ ")\n",
+ "\n",
+ "\n",
+ "# legend\n",
+ "\n",
+ "import matplotlib.patches as mpatches\n",
+ "import matplotlib.lines as mlines\n",
+ "class LargestInterval:\n",
+ " pass\n",
+ "\n",
+ "\n",
+ "class Interval:\n",
+ " pass\n",
+ "\n",
+ "\n",
+ "class Function:\n",
+ " pass\n",
+ "\n",
+ "\n",
+ "class IntervalHandler:\n",
+ " def __init__(self, with_inner=True, length=20, *args, **kwargs):\n",
+ " super().__init__(*args, **kwargs)\n",
+ " self.with_inner = with_inner\n",
+ " self.length = length\n",
+ "\n",
+ " def legend_artist(self, legend, orig_handle, fontsize, handlebox):\n",
+ " x0, y0 = handlebox.xdescent, handlebox.ydescent\n",
+ " offsets = [0, self.length]\n",
+ " line = mlines.Line2D((0, offsets[-1]), (0, 0), zorder=0, c=\"k\")\n",
+ " handlebox.add_artist(line)\n",
+ "\n",
+ " for offset in offsets:\n",
+ " circle1 = mpatches.Circle(\n",
+ " [x0 + offset, y0], 4, facecolor=\"k\", lw=3, zorder=1\n",
+ " )\n",
+ " handlebox.add_artist(circle1)\n",
+ " if self.with_inner:\n",
+ " circle2 = mpatches.Circle(\n",
+ " [x0 + offset, y0], 3, facecolor=\"red\", lw=3, zorder=1\n",
+ " )\n",
+ " handlebox.add_artist(circle2)\n",
+ "\n",
+ "\n",
+ "class FunctionHandler:\n",
+ " def __init__(self, xs, ys, *args, **kwargs):\n",
+ " super().__init__(*args, **kwargs)\n",
+ " self.xs = xs / xs.ptp() * 20\n",
+ " self.ys = ys - ys.mean()\n",
+ "\n",
+ " def legend_artist(self, legend, orig_handle, fontsize, handlebox):\n",
+ " x0, y0 = handlebox.xdescent, handlebox.ydescent\n",
+ "\n",
+ " line = mlines.Line2D(self.xs, self.ys * 10, zorder=0, c=\"k\", alpha=0.3)\n",
+ "\n",
+ " handlebox.add_artist(line)\n",
+ "\n",
+ "\n",
+ "plt.legend(\n",
+ " [\n",
+ " Function(),\n",
+ " mlines.Line2D([], [], marker=\"o\", lw=0, c=\"k\"),\n",
+ " LargestInterval(),\n",
+ " Interval(),\n",
+ " mlines.Line2D([], [], marker=\"x\", lw=0, c=\"green\"),\n",
+ " ],\n",
+ " [\n",
+ " \"original function\",\n",
+ " \"known point\",\n",
+ " \"interval\",\n",
+ " \"largest interval\",\n",
+ " \"next candidate point\",\n",
+ " ],\n",
+ " handler_map={\n",
+ " LargestInterval: IntervalHandler(False),\n",
+ " Interval: IntervalHandler(True),\n",
+ " Function: FunctionHandler(xs, ys),\n",
+ " },\n",
+ " bbox_to_anchor=(0.25, 0.9, 1.0, 0.0),\n",
+ " ncol=1,\n",
+ ")\n",
+ "\n",
+ "axs.axis(\"off\")\n",
+ "plt.savefig(\"figures/algo.pdf\", bbox_inches=\"tight\", transparent=True)\n",
+ "plt.show()"
+ ]
+ },
{
"cell_type": "code",
"execution_count": null,
--
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