From ca7a7cc50cbf2698a6be219f14b705fb9ce1050e Mon Sep 17 00:00:00 2001
From: Bas Nijholt <basnijholt@gmail.com>
Date: Mon, 23 Sep 2019 12:41:14 +0200
Subject: [PATCH] add 2D line loss
---
figures.ipynb | 153 ++++++++++++++++++++++++++++++++++++--------------
1 file changed, 112 insertions(+), 41 deletions(-)
diff --git a/figures.ipynb b/figures.ipynb
index eee3291..37a3a6b 100644
--- a/figures.ipynb
+++ b/figures.ipynb
@@ -1,5 +1,19 @@
{
"cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Adaptive paper figures"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## imports and function definitions"
+ ]
+ },
{
"cell_type": "code",
"execution_count": null,
@@ -101,8 +115,9 @@
"\n",
"def phase_diagram(xy, fname):\n",
" ip, _ = phase_diagram_setup(fname)\n",
- " return np.round(ip(xy))\n",
- "\n",
+ " zs = ip(xy)\n",
+ " return np.round(zs)\n",
+ " \n",
"\n",
"def density(x, eps=0):\n",
" e = [0.8, 0.2]\n",
@@ -127,14 +142,15 @@
"\n",
"\n",
"funcs_2D = [\n",
- " dict(function=ring, bounds=[(-1, 1), (-1, 1)], npoints=33),\n",
+ " dict(function=ring, bounds=[(-1, 1), (-1, 1)], npoints=33, title=\"ring\"),\n",
" dict(\n",
- " function=phase_diagram,\n",
+ " function=functools.partial(phase_diagram, fname=\"phase_diagram.pickle\"),\n",
" bounds=phase_diagram_setup(\"phase_diagram.pickle\")[1],\n",
" npoints=100,\n",
" fname=\"phase_diagram.pickle\",\n",
+ " title=\"PD\",\n",
" ),\n",
- " dict(function=level_crossing, bounds=[(-1, 1), (-3, 3)], npoints=50),\n",
+ " dict(function=level_crossing, bounds=[(-1, 1), (-3, 3)], npoints=50, title=\"LC\"),\n",
"]"
]
},
@@ -142,7 +158,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "# loss_1D"
+ "## Interval and loss"
]
},
{
@@ -200,7 +216,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "# adaptive_vs_grid"
+ "## Learner1D vs grid"
]
},
{
@@ -245,7 +261,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "# adaptive_2D"
+ "## Learner2D vs grid"
]
},
{
@@ -337,7 +353,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "# Algo explaination"
+ "## Algorithm explaination: Learner1D step-by-step"
]
},
{
@@ -494,7 +510,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "# Line loss"
+ "## Line loss visualization"
]
},
{
@@ -573,7 +589,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "# Line loss error"
+ "## Line loss L1-error(N)"
]
},
{
@@ -582,52 +598,104 @@
"metadata": {},
"outputs": [],
"source": [
- "import scipy\n",
+ "from adaptive import Learner1D, LearnerND\n",
+ "from scipy import interpolate\n",
+ "\n",
"\n",
- "def err(xs, ys, xs_rand):\n",
- " ip = scipy.interpolate.interp1d(xs, ys)\n",
+ "def err_1D(xs, ys, xs_rand, f):\n",
+ " ip = interpolate.interp1d(xs, ys)\n",
" abserr = np.abs(ip(xs_rand) - f(xs_rand))\n",
" return np.average(abserr ** 2) ** 0.5\n",
"\n",
"\n",
- "def get_err(learner, N, bounds):\n",
- " xs_rand = np.random.uniform(*bounds, size=100_000)\n",
+ "def get_err_1D(learner, N):\n",
+ " xs_rand = np.random.uniform(*learner.bounds, size=100_000)\n",
"\n",
- " xs = np.linspace(*bounds, N)\n",
+ " xs = np.linspace(*learner.bounds, N)\n",
" ys = f(xs)\n",
- " err_lin = err(xs, ys, xs_rand)\n",
+ " err_lin = err_1D(xs, ys, xs_rand, learner.function)\n",
"\n",
" xs, ys = zip(*learner.data.items())\n",
" xs, ys = xs[:N], ys[:N]\n",
- " ip = scipy.interpolate.interp1d(xs, ys)\n",
- " err_learner = err(xs, ys, xs_rand)\n",
+ " ip = interpolate.interp1d(xs, ys)\n",
+ " err_learner = err_1D(xs, ys, xs_rand, learner.function)\n",
" return err_lin, err_learner\n",
"\n",
+ "def err_2D(zs, zs_rand):\n",
+ " abserr = np.abs(zs - zs_rand)\n",
+ " return np.average(abserr ** 2) ** 0.5\n",
"\n",
- "N_max = 10000\n",
- "Ns = np.geomspace(4, N_max, 100).astype(int)\n",
- "loss = adaptive.learner.learner1D.curvature_loss_function()\n",
+ "def get_err_2D(learner, N):\n",
+ " xys_rand = np.vstack(\n",
+ " [\n",
+ " np.random.uniform(*learner.bounds[0], size=int(100_000**0.5)),\n",
+ " np.random.uniform(*learner.bounds[1], size=int(100_000**0.5)),\n",
+ " ]\n",
+ " )\n",
"\n",
- "fig, ax = plt.subplots(1, 1, figsize=(fig_width, fig_height))\n",
+ " xys_hom = np.array(\n",
+ " [\n",
+ " (x, y)\n",
+ " for x in np.linspace(*learner.bounds[0], int(N**0.5))\n",
+ " for y in np.linspace(*learner.bounds[1], int(N**0.5))\n",
+ " ]\n",
+ " )\n",
"\n",
- "for i, d in enumerate(funcs_1D):\n",
- " f = d[\"function\"]\n",
- " bounds = d[\"bounds\"]\n",
- " learner = adaptive.Learner1D(f, bounds, loss_per_interval=loss)\n",
- " adaptive.runner.simple(learner, goal=lambda l: l.npoints >= N_max)\n",
- " errs = [get_err(learner, N, bounds) for N in Ns]\n",
- " err_hom, err_adaptive = zip(*errs)\n",
- " color = f\"C{i}\"\n",
- " label = \"abc\"[i]\n",
- " ax.loglog(Ns, err_hom, ls=\"--\", c=color)\n",
- " ax.loglog(Ns, err_adaptive, label=f\"$\\mathrm{{({label})}}$ {d['title']}\", c=color)\n",
- "\n",
- " d[\"err_hom\"] = err_hom\n",
- " d[\"err_adaptive\"] = err_adaptive\n",
+ " try:\n",
+ " # Vectorized\n",
+ " zs_hom = f(xys_hom.T)\n",
+ " zs_rand = f(xys_rand)\n",
+ " except:\n",
+ " # Non-vectorized\n",
+ " zs_hom = np.array([f(xy) for xy in xys_hom])\n",
+ " zs_rand = np.array([f(xy) for xy in xys_rand.T])\n",
+ "\n",
+ " ip = interpolate.LinearNDInterpolator(xys_hom, zs_hom)\n",
+ " zs = ip(xys_rand.T)\n",
+ " err_lin = err_2D(zs, zs_rand)\n",
+ "\n",
+ " ip = interpolate.LinearNDInterpolator(learner.points[:len(xys_hom)], learner.values[:len(xys_hom)])\n",
+ " zs = ip(xys_rand.T)\n",
+ " err_learner = err_2D(zs, zs_rand)\n",
+ "\n",
+ " return err_lin, err_learner\n",
+ "\n",
+ "N_max = 10000\n",
+ "Ns = np.geomspace(4, N_max, 20).astype(int)\n",
+ "\n",
+ "fig, axs = plt.subplots(2, 1, figsize=(fig_width, 1.6 * fig_height))\n",
+ "\n",
+ "loss_1D = adaptive.learner.learner1D.curvature_loss_function()\n",
+ "loss_2D = adaptive.learner.learnerND.curvature_loss_function()\n",
+ "\n",
+ "for ax, funcs, loss, Learner, get_err in zip(\n",
+ " axs,\n",
+ " [funcs_1D, funcs_2D],\n",
+ " [loss_1D, loss_2D],\n",
+ " [Learner1D, LearnerND],\n",
+ " [get_err_1D, get_err_2D],\n",
+ "):\n",
+ " ax.set_xlabel(\"$N$\")\n",
+ " ax.set_ylabel(r\"$\\text{Err}_{1}(\\tilde{f})$\")\n",
+ "\n",
+ " for i, d in enumerate(funcs):\n",
+ " f = d[\"function\"]\n",
+ " bounds = d[\"bounds\"]\n",
+ " learner = Learner(f, bounds, loss)\n",
+ " adaptive.runner.simple(learner, goal=lambda l: l.npoints >= N_max)\n",
+ " errs = [get_err(learner, N) for N in Ns]\n",
+ " err_hom, err_adaptive = zip(*errs)\n",
+ " color = f\"C{i}\"\n",
+ " label = \"abc\"[i]\n",
+ " ax.loglog(Ns, err_hom, ls=\"--\", c=color)\n",
+ " ax.loglog(\n",
+ " Ns, err_adaptive, label=f\"$\\mathrm{{({label})}}$ {d['title']}\", c=color\n",
+ " )\n",
+ "\n",
+ " d[\"err_hom\"] = err_hom\n",
+ " d[\"err_adaptive\"] = err_adaptive\n",
"\n",
"plt.legend()\n",
- "ax.set_xlabel(\"$N$\")\n",
- "ax.set_ylabel(r\"$\\text{Err}_{1}(\\tilde{f})$\")\n",
"plt.savefig(\"figures/line_loss_error.pdf\", bbox_inches=\"tight\", transparent=True)\n",
"plt.show()"
]
@@ -640,6 +708,9 @@
"source": [
"# Error reduction\n",
"for d in funcs_1D:\n",
+ " print(d[\"err_hom\"][-1] / d[\"err_adaptive\"][-1])\n",
+ "\n",
+ "for d in funcs_2D:\n",
" print(d[\"err_hom\"][-1] / d[\"err_adaptive\"][-1])"
]
},
@@ -647,7 +718,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "# Iso surface"
+ "## iso-line plots"
]
},
{
--
GitLab