From 8e841729fe8ad2c31b7514bbd99e9dfee1a55628 Mon Sep 17 00:00:00 2001
From: Bas Nijholt <basnijholt@gmail.com>
Date: Thu, 12 Sep 2019 17:22:00 +0200
Subject: [PATCH] start new figure
---
figures.ipynb | 132 ++++++++++++++++++++++++++++++++++++++++++--------
1 file changed, 113 insertions(+), 19 deletions(-)
diff --git a/figures.ipynb b/figures.ipynb
index 49bdf4d..53ccedf 100644
--- a/figures.ipynb
+++ b/figures.ipynb
@@ -57,7 +57,7 @@
"source": [
"np.random.seed(1)\n",
"xs = np.array([0.1, 0.3, 0.35, 0.45])\n",
- "f = lambda x: x**3\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",
@@ -70,7 +70,7 @@
"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",
+ " xytext=(xs[0] + 0.05, ys[0] - 0.05),\n",
" arrowprops=dict(arrowstyle=\"->\"),\n",
" ha=\"center\",\n",
" zorder=10,\n",
@@ -85,10 +85,12 @@
" arrowprops=dict(arrowstyle=\"->\"),\n",
" ha=\"center\",\n",
" )\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",
+ "ax.scatter(\n",
+ " xs_means, ys_means, c=\"red\", s=300 * losses, zorder=8, label=\"candidate points\"\n",
+ ")\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",
@@ -113,18 +115,26 @@
"source": [
"import adaptive\n",
"\n",
+ "\n",
"def f(x, offset=0.123):\n",
" a = 0.02\n",
- " return x + a**2 / (a**2 + (x - offset)**2)\n",
+ " return x + a ** 2 / (a ** 2 + (x - offset) ** 2)\n",
+ "\n",
"\n",
"def g(x):\n",
- " return np.tanh(x*40)\n",
+ " return np.tanh(x * 40)\n",
+ "\n",
"\n",
"def h(x):\n",
- " return np.sin(100*x) * np.exp(-x**2 / 0.1**2)\n",
+ " return np.sin(100 * x) * np.exp(-x ** 2 / 0.1 ** 2)\n",
+ "\n",
"\n",
- "funcs = [dict(function=f, bounds=(-1, 1), title=\"peak\"), dict(function=g, bounds=(-1, 1), title=\"tanh\"), dict(function=h, bounds=(-0.3, 0.3), title=\"wave packet\")]\n",
- "fig, axs = plt.subplots(2, len(funcs), figsize=(fig_width, 1.5*fig_height))\n",
+ "funcs = [\n",
+ " dict(function=f, bounds=(-1, 1), title=\"peak\"),\n",
+ " dict(function=g, bounds=(-1, 1), title=\"tanh\"),\n",
+ " dict(function=h, bounds=(-0.3, 0.3), title=\"wave packet\"),\n",
+ "]\n",
+ "fig, axs = plt.subplots(2, len(funcs), figsize=(fig_width, 1.5 * fig_height))\n",
"n_points = 50\n",
"for i, ax in enumerate(axs.T.flatten()):\n",
" ax.xaxis.set_ticks([])\n",
@@ -132,24 +142,108 @@
" if i % 2 == 0:\n",
" d = funcs[i // 2]\n",
" # homogeneous\n",
- " xs = np.linspace(*d['bounds'], n_points)\n",
- " ys = d['function'](xs)\n",
+ " xs = np.linspace(*d[\"bounds\"], n_points)\n",
+ " ys = d[\"function\"](xs)\n",
" ax.set_title(rf\"\\textrm{{{d['title']}}}\")\n",
" else:\n",
" d = funcs[(i - 1) // 2]\n",
" loss = adaptive.learner.learner1D.curvature_loss_function()\n",
- " learner = adaptive.Learner1D(d['function'], bounds=d['bounds'], loss_per_interval=loss)\n",
+ " learner = adaptive.Learner1D(\n",
+ " d[\"function\"], bounds=d[\"bounds\"], loss_per_interval=loss\n",
+ " )\n",
" adaptive.runner.simple(learner, goal=lambda l: l.npoints >= n_points)\n",
" # adaptive\n",
" xs, ys = zip(*sorted(learner.data.items()))\n",
- " xs_dense = np.linspace(*d['bounds'], 1000)\n",
- " ax.plot(xs_dense, d['function'](xs_dense), c='red', alpha=0.3, lw=0.5)\n",
- " ax.scatter(xs, ys, s=0.5, c='k')\n",
- " \n",
- "axs[0][0].set_ylabel(r'$\\textrm{homogeneous}$')\n",
- "axs[1][0].set_ylabel(r'$\\textrm{adaptive}$')\n",
- "plt.savefig(\"figures/adaptive_vs_grid.pdf\", bbox_inches=\"tight\", transparent=True)\n"
+ " xs_dense = np.linspace(*d[\"bounds\"], 1000)\n",
+ " ax.plot(xs_dense, d[\"function\"](xs_dense), c=\"red\", alpha=0.3, lw=0.5)\n",
+ " ax.scatter(xs, ys, s=0.5, c=\"k\")\n",
+ "\n",
+ "axs[0][0].set_ylabel(r\"$\\textrm{homogeneous}$\")\n",
+ "axs[1][0].set_ylabel(r\"$\\textrm{adaptive}$\")\n",
+ "plt.savefig(\"figures/adaptive_vs_grid.pdf\", bbox_inches=\"tight\", transparent=True)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Fig 3. "
]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import itertools\n",
+ "import adaptive\n",
+ "import holoviews.plotting.mpl\n",
+ "import matplotlib.tri as mtri\n",
+ "\n",
+ "\n",
+ "def f(xy, offset=0.123):\n",
+ " a = 0.1\n",
+ " x, y = xy\n",
+ " return x * y + a ** 2 / (a ** 2 + (x - offset) ** 2 + (y - offset) ** 2)\n",
+ "\n",
+ "\n",
+ "def g(xy):\n",
+ " x, y = xy\n",
+ " return np.tanh(x * 40) * np.tanh(y * 40)\n",
+ "\n",
+ "\n",
+ "def h(xy):\n",
+ " x, y = xy\n",
+ " return np.sin(100 * x * y) * np.exp(-x ** 2 / 0.1 ** 2 - y ** 2 / 0.4 ** 2)\n",
+ "\n",
+ "\n",
+ "funcs = [\n",
+ " dict(function=f, bounds=[(-1, 1), (-1, 1)], title=\"peak\"),\n",
+ " dict(function=g, bounds=[(-1, 1), (-1, 1)], title=\"tanh\"),\n",
+ " dict(function=h, bounds=[(-0.3, 0.3), (-0.3, 0.3)], title=\"wave packet\"),\n",
+ "]\n",
+ "fig, axs = plt.subplots(2, len(funcs), figsize=(fig_width, 1.5 * fig_height))\n",
+ "\n",
+ "plt.subplots_adjust(hspace=-0.1, wspace=0.1)\n",
+ "n_points = 50\n",
+ "for i, ax in enumerate(axs.T.flatten()):\n",
+ " ax.xaxis.set_ticks([])\n",
+ " ax.yaxis.set_ticks([])\n",
+ " if i % 2 == 0:\n",
+ " d = funcs[i // 2]\n",
+ " # homogeneous\n",
+ " ax.set_title(rf\"\\textrm{{{d['title']}}}\")\n",
+ " x, y = d[\"bounds\"]\n",
+ " xs = np.linspace(*x, n_points)\n",
+ " ys = np.linspace(*y, n_points)\n",
+ " data = {xy: d[\"function\"](xy) for xy in itertools.product(xs, ys)}\n",
+ " learner = adaptive.Learner2D(d[\"function\"], bounds=d[\"bounds\"])\n",
+ " learner.data = data\n",
+ " else:\n",
+ " # adaptive\n",
+ " d = funcs[(i - 1) // 2]\n",
+ " learner = adaptive.Learner2D(d[\"function\"], bounds=d[\"bounds\"])\n",
+ " adaptive.runner.simple(learner, goal=lambda l: l.npoints >= n_points ** 2)\n",
+ " tri = learner.ip().tri\n",
+ " triang = mtri.Triangulation(*tri.points.T, triangles=tri.vertices)\n",
+ " # ax.triplot(triang, c=\"w\", lw=0.2, alpha=0.8)\n",
+ " values = np.array(list(learner.data.values()))\n",
+ " ax.imshow(learner.plot().Image.I.data, extent=(-0.5, 0.5, -0.5, 0.5))\n",
+ " ax.set_xticks([])\n",
+ " ax.set_yticks([])\n",
+ "\n",
+ "axs[0][0].set_ylabel(r\"$\\textrm{homogeneous}$\")\n",
+ "axs[1][0].set_ylabel(r\"$\\textrm{adaptive}$\")\n",
+ "plt.savefig(\"figures/adaptive_2D.pdf\", bbox_inches=\"tight\", transparent=True)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
}
],
"metadata": {
--
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