{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Adaptive step size ODE filters\n",
"\n",
"\n",
"In `probnum`, we implement the step size adaptation scheme from Schober et al., 2019:\n",
"\n",
"https://arxiv.org/pdf/1610.05261.pdf\n",
"\n",
"We show how for the KF-IBM(1) Combo, they work very well (which is what they write in their paper) but also, how it doesn't quite generalise 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": 2,
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"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",
"image/svg+xml": [
"\n",
"\n",
"\n",
"\n"
],
"text/plain": [
"