{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Adaptive step size ODE filters\n",
"\n",
"\n",
"In ProbNum the step size adaptation scheme from [Schober et al., 2019](https://arxiv.org/pdf/1610.05261.pdf) is implemented.\n",
"\n",
"In this notebook we demonstrate how for the KF-IBM(1) Combo, they work quite well (which is what is claimed in the paper) but also, how it doesn't quite generalize to other filters."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"# Make inline plots vector graphics instead of raster graphics\n",
"%matplotlib inline\n",
"from IPython.display import set_matplotlib_formats\n",
"set_matplotlib_formats('pdf', 'svg')\n",
"\n",
"# Plotting\n",
"import matplotlib.pyplot as plt\n",
"plt.style.use('../../probnum.mplstyle')"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"from probnum import random_variables as rvs\n",
"from probnum.diffeq import IVP, lotkavolterra, probsolve_ivp"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### IBM(1) with KF\n",
"\n",
"We start by showing how solving an IVP with adaptive steps works."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"application/pdf": 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\n",
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