diff --git a/Makefile b/Makefile
new file mode 100644
index 0000000000000000000000000000000000000000..8ebc8d55edf504270de78436c3fe7068409472e8
--- /dev/null
+++ b/Makefile
@@ -0,0 +1,9 @@
+
+.PHONY: index.html
+
+
+index: index.html
+
+index.html: index.md
+ pandoc -t html $< > $@
+
diff --git a/README.md b/README.md
index 75a671c7e25ee85ab28c1f567fa196dfd0bb7a8e..de7e29f56fa18a550d03441aa95c0da8886ffd3c 100644
--- a/README.md
+++ b/README.md
@@ -1,2 +1,3 @@
# school-material
+
diff --git a/index.html b/index.html
new file mode 100644
index 0000000000000000000000000000000000000000..fc93023c190561cd1bdb8b3f85696aeda0fb4937
--- /dev/null
+++ b/index.html
@@ -0,0 +1,4 @@
+<h1 id="school-material">school-material</h1>
+<ul>
+<li><a href="monday/">monday excercises</a></li>
+</ul>
diff --git a/index.md b/index.md
new file mode 100644
index 0000000000000000000000000000000000000000..94bab12a0ae336320949c2abe7f3e4dd80a6c2fd
--- /dev/null
+++ b/index.md
@@ -0,0 +1,4 @@
+# school-material
+
+- [monday excercises](monday/)
+
diff --git a/monday/parametric_delay.ipynb b/monday/parametric_delay.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..3fd86279169c35837677e6259c25b03225e22655
--- /dev/null
+++ b/monday/parametric_delay.ipynb
@@ -0,0 +1,211 @@
+{
+ "cells": [
+ {
+ "cell_type": "raw",
+ "metadata": {},
+ "source": [
+ "This file is part of the pyMOR project (http://www.pymor.org).\n",
+ "Copyright 2013-2019 pyMOR developers and contributors. All rights reserved.\n",
+ "License: BSD 2-Clause License (http://opensource.org/licenses/BSD-2-Clause)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import scipy.linalg as spla\n",
+ "import matplotlib as mpl\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "from pymor.basic import *"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Model"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def H(s, mu):\n",
+ " tau = mu['tau']\n",
+ " return np.array([[np.exp(-s) / (tau * s + 1)]])\n",
+ "\n",
+ "def dH(s, mu):\n",
+ " tau = mu['tau']\n",
+ " return np.array([[-(tau * s + tau + 1) * np.exp(-s) / (tau * s + 1) ** 2]])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "f = ProjectionParameterFunctional('tau', ())\n",
+ "parameter_space = CubicParameterSpace(f.parameter_type, 0.01, 1)\n",
+ "\n",
+ "fom = TransferFunction(NumpyVectorSpace(1), NumpyVectorSpace(1),\n",
+ " H, dH,\n",
+ " parameter_space=parameter_space)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Magnitude plot"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "mu_list_short = [0.01, 0.1, 1]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "w = np.logspace(-2, 4, 100)\n",
+ "\n",
+ "fig, ax = plt.subplots()\n",
+ "for mu in mu_list_short:\n",
+ " fom.mag_plot(w, ax=ax, mu=mu, label=fr'$\\tau = {mu}$')\n",
+ "ax.legend()\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "w_list = np.logspace(-2, 4, 100)\n",
+ "mu_list = np.logspace(-2, 0, 50)\n",
+ "\n",
+ "fom_w_mu = np.zeros((len(w_list), len(mu_list)))\n",
+ "for i, mu in enumerate(mu_list):\n",
+ " fom_w_mu[:, i] = spla.norm(fom.freq_resp(w_list, mu=mu), axis=(1, 2))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "fig, ax = plt.subplots()\n",
+ "out = ax.contourf(w_list, mu_list, fom_w_mu.T,\n",
+ " norm=mpl.colors.LogNorm(),\n",
+ " levels=np.logspace(np.log10(fom_w_mu.min()), np.log10(fom_w_mu.max()), 100))\n",
+ "ax.set_xlabel(r'Frequency $\\omega$')\n",
+ "ax.set_ylabel(r'Parameter $\\mu$')\n",
+ "ax.set_xscale('log')\n",
+ "ax.set_yscale('log')\n",
+ "fig.colorbar(out, ticks=np.logspace(-4, 1, 6))\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# TF-IRKA"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "r = 10\n",
+ "roms_tf_irka = []\n",
+ "for mu in mu_list_short:\n",
+ " tf_irka = TFIRKAReductor(fom, mu=mu)\n",
+ " rom = tf_irka.reduce(r, conv_crit='h2', maxit=1000, num_prev=5)\n",
+ " roms_tf_irka.append(rom)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "fig, ax = plt.subplots()\n",
+ "for mu, rom in zip(mu_list_short, roms_tf_irka):\n",
+ " poles = rom.poles()\n",
+ " ax.plot(poles.real, poles.imag, '.', label=fr'$\\tau = {mu}$')\n",
+ "ax.set_title(\"Poles of TF-IRKA's ROMs\")\n",
+ "ax.legend()\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "fig, ax = plt.subplots()\n",
+ "for mu, rom in zip(mu_list_short, roms_tf_irka):\n",
+ " rom.mag_plot(w, ax=ax, label=fr'$\\tau = {mu}$')\n",
+ "ax.set_title(\"Magnitude plot of TF-IRKA's ROMs\")\n",
+ "ax.legend()\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "fig, ax = plt.subplots()\n",
+ "for mu, rom in zip(mu_list_short, roms_tf_irka):\n",
+ " (fom - rom).mag_plot(w, ax=ax, mu=mu, label=fr'$\\tau = {mu}$')\n",
+ "ax.set_title(\"Magnitude plot of error systems\")\n",
+ "ax.legend()\n",
+ "plt.show()"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.6.8"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}