commit 3f3537af772ff2fb6fcb07a2b88f0c757dc1ffb5
parent 9ae6dd03cde73e87788f86a561b7c25935e43517
Author: miksa234 <milutin@popovic.xyz>
Date: Mon, 28 Mar 2022 08:17:22 +0200
foo
Diffstat:
10 files changed, 3072 insertions(+), 15 deletions(-)
diff --git a/num_ana/build/prb2.aux b/num_ana/build/prb2.aux
@@ -0,0 +1,39 @@
+\relax
+\providecommand\zref@newlabel[2]{}
+\providecommand\hyper@newdestlabel[2]{}
+\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
+\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
+\global\let\oldcontentsline\contentsline
+\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
+\global\let\oldnewlabel\newlabel
+\gdef\newlabel#1#2{\newlabelxx{#1}#2}
+\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
+\AtEndDocument{\ifx\hyper@anchor\@undefined
+\let\contentsline\oldcontentsline
+\let\newlabel\oldnewlabel
+\fi}
+\fi}
+\global\let\hyper@last\relax
+\gdef\HyperFirstAtBeginDocument#1{#1}
+\providecommand\HyField@AuxAddToFields[1]{}
+\providecommand\HyField@AuxAddToCoFields[2]{}
+\@writefile{toc}{\contentsline {section}{\numberline {1}Sheet 2}{1}{section.1}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Problem 1}{1}{subsection.1.1}\protected@file@percent }
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+\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.1.2}}{2}{subsubsection.1.1.2}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.1.3}}{2}{subsubsection.1.1.3}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Problem 2}{3}{subsection.1.2}\protected@file@percent }
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+\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.2.2}}{3}{subsubsection.1.2.2}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsection}{\numberline {1.3}Problem 3}{4}{subsection.1.3}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.3.1}}{4}{subsubsection.1.3.1}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.3.2}}{4}{subsubsection.1.3.2}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.3.3}}{4}{subsubsection.1.3.3}\protected@file@percent }
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+\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.4.1}}{5}{subsubsection.1.4.1}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.4.2}}{5}{subsubsection.1.4.2}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.4.3}}{5}{subsubsection.1.4.3}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsection}{\numberline {1.5}Problem 5}{6}{subsection.1.5}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.5.1}}{6}{subsubsection.1.5.1}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.5.2}}{6}{subsubsection.1.5.2}\protected@file@percent }
+\gdef \@abspage@last{6}
diff --git a/num_ana/build/prb2.fdb_latexmk b/num_ana/build/prb2.fdb_latexmk
@@ -0,0 +1,257 @@
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+\T1/mlmr/m/n/10 We can show that all the eigen-val-ues of $\OML/mlmm/m/it/10 P[]$ \T1/mlmr/m/n/10 are in $\OT1/mlmr/m/n/10 [0\OML/mlmm/m/it/10 ; \OT1/mlmr/m/n/10 4]$ \T1/mlmr/m/n/10 be-cause $\OML/mlmm/m/it/10 P[]$ \T1/mlmr/m/n/10 is the fi-nite dif-fer-enece/laplacian
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diff --git a/num_ana/build/prb2.out b/num_ana/build/prb2.out
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diff --git a/num_ana/build/prb2.pdf b/num_ana/build/prb2.pdf
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diff --git a/num_ana/build/prb2.toc b/num_ana/build/prb2.toc
@@ -0,0 +1,19 @@
+\contentsline {section}{\numberline {1}Sheet 2}{1}{section.1}%
+\contentsline {subsection}{\numberline {1.1}Problem 1}{1}{subsection.1.1}%
+\contentsline {subsubsection}{\numberline {1.1.1}}{1}{subsubsection.1.1.1}%
+\contentsline {subsubsection}{\numberline {1.1.2}}{2}{subsubsection.1.1.2}%
+\contentsline {subsubsection}{\numberline {1.1.3}}{2}{subsubsection.1.1.3}%
+\contentsline {subsection}{\numberline {1.2}Problem 2}{3}{subsection.1.2}%
+\contentsline {subsubsection}{\numberline {1.2.1}}{3}{subsubsection.1.2.1}%
+\contentsline {subsubsection}{\numberline {1.2.2}}{3}{subsubsection.1.2.2}%
+\contentsline {subsection}{\numberline {1.3}Problem 3}{4}{subsection.1.3}%
+\contentsline {subsubsection}{\numberline {1.3.1}}{4}{subsubsection.1.3.1}%
+\contentsline {subsubsection}{\numberline {1.3.2}}{4}{subsubsection.1.3.2}%
+\contentsline {subsubsection}{\numberline {1.3.3}}{4}{subsubsection.1.3.3}%
+\contentsline {subsection}{\numberline {1.4}Problem 4}{5}{subsection.1.4}%
+\contentsline {subsubsection}{\numberline {1.4.1}}{5}{subsubsection.1.4.1}%
+\contentsline {subsubsection}{\numberline {1.4.2}}{5}{subsubsection.1.4.2}%
+\contentsline {subsubsection}{\numberline {1.4.3}}{5}{subsubsection.1.4.3}%
+\contentsline {subsection}{\numberline {1.5}Problem 5}{6}{subsection.1.5}%
+\contentsline {subsubsection}{\numberline {1.5.1}}{6}{subsubsection.1.5.1}%
+\contentsline {subsubsection}{\numberline {1.5.2}}{6}{subsubsection.1.5.2}%
diff --git a/num_ana/prog/.ipynb_checkpoints/prb2_p-checkpoint.ipynb b/num_ana/prog/.ipynb_checkpoints/prb2_p-checkpoint.ipynb
@@ -0,0 +1,185 @@
+{
+ "cells": [
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "id": "517aef32",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import matplotlib.pyplot as plt"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "85da4812",
+ "metadata": {},
+ "source": [
+ "# Sheet 2, Exercise 3"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "id": "e14c738f",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def gauss_siedel(A, b, k):\n",
+ " n, m = Q.shape\n",
+ " D = np.reshape([Q[i][j] if i==j else 0 for i in range(n) for j in range(n)], (n ,n))\n",
+ " L = np.reshape([Q[i][j] if i>j else 0 for i in range(n) for j in range(n)], (n ,n))\n",
+ " U = np.reshape([Q[i][j] if i<j else 0 for i in range(n) for j in range(n)], (n ,n))\n",
+ "\n",
+ " x = np.random.rand(n)\n",
+ " for i in range(k):\n",
+ " x = np.linalg.inv(D)@(b - (L + U)@x)\n",
+ " return x\n",
+ "\n",
+ "def poisson_mat(n, m=None):\n",
+ " return 2 * np.eye(n, m) + (-1) * np.eye(n, m, k=1) + (-1) * np.eye(n, m, k=-1)\n",
+ "\n",
+ "# test\n",
+ "for n in range(5, 20):\n",
+ " Q = poisson_mat(n)\n",
+ " b = np.ones(n)\n",
+ " x = gauss_siedel(Q, b, k=1000)\n",
+ " np.testing.assert_allclose(Q@x, b, rtol=1e-5, err_msg=f'GS failed at dim - {n}')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "51428a2b",
+ "metadata": {},
+ "source": [
+ "# Sheet 2, Exercise 5"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "id": "caef181e",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "1\t44.76606865271526\n",
+ "2\t59.35975010638207\n",
+ "3\t22.760834328149066\n",
+ "4\t35.62184004487846\n",
+ "5\t15.344146462132612\n",
+ "6\t25.450588757787237\n",
+ "7\t11.636387156050118\n",
+ "8\t19.801556558635152\n",
+ "9\t9.412478177542988\n",
+ "10\t16.208077941288785\n",
+ "11\t7.930495393514105\n",
+ "12\t13.721435287552058\n",
+ "13\t6.872470144914724\n",
+ "14\t11.898893608722659\n",
+ "15\t6.079418049762978\n",
+ "16\t10.506063704904786\n",
+ "17\t5.463014409761165\n",
+ "18\t9.407246486889383\n",
+ "19\t4.970264368579988\n",
+ "20\t8.518437685556936\n",
+ "21\t4.567443892886474\n",
+ "22\t7.784851843354031\n",
+ "23\t4.2320702628688585\n",
+ "24\t7.1692347898822\n",
+ "25\t3.948578490221603\n",
+ "26\t6.645370572800227\n",
+ "27\t3.705850699860457\n",
+ "28\t6.194275175956779\n",
+ "29\t3.495733758960119\n",
+ "Max. and Min. Singular value are far apart from each other for uneaven p\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ "<Figure size 504x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "def neumann_polynomial_preconditioner(n, p):\n",
+ " Q = poisson_mat(n)\n",
+ " D = np.reshape([Q[i][j] if i==j else 0 for i in range(n) for j in range(n)], (n ,n))\n",
+ " N = D - Q\n",
+ " C_p = np.zeros([n, n])\n",
+ " for k in range(p+1):\n",
+ " C_p += np.linalg.matrix_power(N @ np.linalg.inv(D), k)\n",
+ " return np.linalg.inv(D) @ C_p\n",
+ " \n",
+ " \n",
+ "n = 20\n",
+ "Q = poisson_mat(n)\n",
+ "P = np.arange(1, 30)\n",
+ "cond_2 = []\n",
+ "for p in P:\n",
+ " C_p = neumann_polynomial_preconditioner(n, p)\n",
+ " cond_2.append(np.linalg.cond(C_p @ Q, p=2))\n",
+ " print(p, cond_2[p-1], sep='\\t')\n",
+ " \n",
+ "plt.figure(figsize=[7, 4])\n",
+ "plt.scatter(P, cond_2)\n",
+ "print(\"Max. and Min. Singular value are far apart from each other for uneaven p\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "73ce1ef6",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "53064abd",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "26476d82",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "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": "3.10.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/num_ana/prog/prb2_p.ipynb b/num_ana/prog/prb2_p.ipynb
@@ -21,7 +21,7 @@
},
{
"cell_type": "code",
- "execution_count": 53,
+ "execution_count": 2,
"id": "e14c738f",
"metadata": {},
"outputs": [],
@@ -58,7 +58,7 @@
},
{
"cell_type": "code",
- "execution_count": 60,
+ "execution_count": 6,
"id": "caef181e",
"metadata": {},
"outputs": [
@@ -66,21 +66,41 @@
"name": "stdout",
"output_type": "stream",
"text": [
- "1\t31706.88589269506\n",
- "2\t534.147900485917\n",
- "3\t31706.885892666996\n",
- "4\t890.0968016459952\n",
- "5\t31706.885892699214\n",
- "6\t1245.8213126008322\n",
- "7\t31706.885892666185\n",
- "8\t1601.2319940002324\n",
- "9\t31706.88589270954\n",
+ "1\t44.76606865271526\n",
+ "2\t59.35975010638207\n",
+ "3\t22.760834328149066\n",
+ "4\t35.62184004487846\n",
+ "5\t15.344146462132612\n",
+ "6\t25.450588757787237\n",
+ "7\t11.636387156050118\n",
+ "8\t19.801556558635152\n",
+ "9\t9.412478177542988\n",
+ "10\t16.208077941288785\n",
+ "11\t7.930495393514105\n",
+ "12\t13.721435287552058\n",
+ "13\t6.872470144914724\n",
+ "14\t11.898893608722659\n",
+ "15\t6.079418049762978\n",
+ "16\t10.506063704904786\n",
+ "17\t5.463014409761165\n",
+ "18\t9.407246486889383\n",
+ "19\t4.970264368579988\n",
+ "20\t8.518437685556936\n",
+ "21\t4.567443892886474\n",
+ "22\t7.784851843354031\n",
+ "23\t4.2320702628688585\n",
+ "24\t7.1692347898822\n",
+ "25\t3.948578490221603\n",
+ "26\t6.645370572800227\n",
+ "27\t3.705850699860457\n",
+ "28\t6.194275175956779\n",
+ "29\t3.495733758960119\n",
"Max. and Min. Singular value are far apart from each other for uneaven p\n"
]
},
{
"data": {
- "image/png": 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\n",
+ "image/png": "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\n",
"text/plain": [
"<Figure size 504x288 with 1 Axes>"
]
@@ -95,7 +115,7 @@
"def neumann_polynomial_preconditioner(n, p):\n",
" Q = poisson_mat(n)\n",
" D = np.reshape([Q[i][j] if i==j else 0 for i in range(n) for j in range(n)], (n ,n))\n",
- " N = Q - D\n",
+ " N = D - Q\n",
" C_p = np.zeros([n, n])\n",
" for k in range(p+1):\n",
" C_p += np.linalg.matrix_power(N @ np.linalg.inv(D), k)\n",
@@ -104,7 +124,7 @@
" \n",
"n = 20\n",
"Q = poisson_mat(n)\n",
- "P = np.arange(1, 10)\n",
+ "P = np.arange(1, 30)\n",
"cond_2 = []\n",
"for p in P:\n",
" C_p = neumann_polynomial_preconditioner(n, p)\n",
@@ -143,7 +163,7 @@
],
"metadata": {
"kernelspec": {
- "display_name": "Python 3",
+ "display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
diff --git a/num_ana/prog/prb2_p.pdf b/num_ana/prog/prb2_p.pdf
Binary files differ.
