From 846a781a138c785b9bf5ccb2e20d1826ec9e3d93 Mon Sep 17 00:00:00 2001
From: Bas Nijholt <basnijholt@gmail.com>
Date: Wed, 11 Sep 2019 13:44:05 +0200
Subject: [PATCH] add another comparison figure
---
figures.ipynb | 100 ++++++--------------------------------------------
paper.md | 4 ++
2 files changed, 16 insertions(+), 88 deletions(-)
diff --git a/figures.ipynb b/figures.ipynb
index 799e8c6..49bdf4d 100644
--- a/figures.ipynb
+++ b/figures.ipynb
@@ -111,15 +111,8 @@
"metadata": {},
"outputs": [],
"source": [
- "import adaptive"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
+ "import adaptive\n",
+ "\n",
"def f(x, offset=0.123):\n",
" a = 0.02\n",
" return x + a**2 / (a**2 + (x - offset)**2)\n",
@@ -130,102 +123,33 @@
"def h(x):\n",
" return np.sin(100*x) * np.exp(-x**2 / 0.1**2)\n",
"\n",
- "funcs = [dict(function=f, bounds=(-1, 1)), dict(function=g, bounds=(-1, 1)), dict(function=h, bounds=(-0.3, 0.3))]\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",
"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",
" 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, loss_per_interval=loss)\n",
+ " learner = adaptive.Learner1D(d['function'], bounds=d['bounds'], loss_per_interval=loss)\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.plot(xs, ys, c='k', alpha=0.3, lw=0.3)\n",
- " ax.scatter(xs, ys, s=0.5, c='k')"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": []
- },
- {
- "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"
+ " 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"
]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": []
}
],
"metadata": {
diff --git a/paper.md b/paper.md
index d066a98..684493d 100755
--- a/paper.md
+++ b/paper.md
@@ -53,6 +53,10 @@ Each candidate point has a loss $L$ indicated by the size of the red dots.
The candidate point with the largest loss will be chosen, which in this case is the one with $L_{1,2}$.
](figures/loss_1D.pdf){#fig:loss_1D}
+{#fig:adaptive_vs_grid}
+
#### We provide a reference implementation, the Adaptive package, and demonstrate its performance.
We provide a reference implementation, the open-source Python package called Adaptive[@Nijholt2019a], which has previously been used in several scientific publications[@vuik2018reproducing; @laeven2019enhanced; @bommer2019spin; @melo2019supercurrent].
It has algorithms for $f \colon \R^N \to \R^M$, where $N, M \in \mathbb{Z}^+$ but which work best when $N$ is small; integration in $\R$; and the averaging of stochastic functions.
--
GitLab