commit 1d9d6d8a7d80be6cd48a39b585318d5930eabdda
parent 932be1ec2d05eef485dd743aa432055816ce8dd7
Author: miksa <milutin@popovic.xyz>
Date: Mon, 23 May 2022 07:06:54 +0200
foo
Diffstat:
6 files changed, 354 insertions(+), 0 deletions(-)
diff --git a/app_pde/refs/A Modern Introduction to the Mathematical Theory of Water Waves.pdf b/app_pde/refs/A Modern Introduction to the Mathematical Theory of Water Waves.pdf
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diff --git a/app_pde/refs/Atmospheric and Oceanic Fluid Dynamics.pdf b/app_pde/refs/Atmospheric and Oceanic Fluid Dynamics.pdf
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diff --git a/app_pde/refs/On the Homogeneous Model of Wind-Driven Ocean Circulation.pdf b/app_pde/refs/On the Homogeneous Model of Wind-Driven Ocean Circulation.pdf
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diff --git a/app_pde/refs/ScaleDependentModels-annurev-fluid-121108-145537.pdf b/app_pde/refs/ScaleDependentModels-annurev-fluid-121108-145537.pdf
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diff --git a/num_ana/prog/.ipynb_checkpoints/prb10_p-checkpoint.ipynb b/num_ana/prog/.ipynb_checkpoints/prb10_p-checkpoint.ipynb
@@ -0,0 +1,177 @@
+{
+ "cells": [
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "id": "e8c4b067",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 59,
+ "id": "35139a3d",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def lanczos_alg(A: np.ndarray, b: np.array, N: int=None) -> np.ndarray:\n",
+ " if N == None:\n",
+ " N = A.shape[0]\n",
+ " v_1 = b/np.linalg.norm(b)\n",
+ " V = np.zeros([A.shape[0], N])\n",
+ " \n",
+ " V[:,0] = v_1\n",
+ " w̃_j = A @ V[:,0]\n",
+ " α_j = np.conjugate(w̃_j) @ V[:,0]\n",
+ " w_j = w̃_j - α_j*V[:,0]\n",
+ " \n",
+ " ritz = [np.conjugate(V[:,0]) @ A @ V[:,0]]\n",
+ " for j in range(1, N):\n",
+ " if (β_j:=np.linalg.norm(w_j)) != 0:\n",
+ " V[:,j] = w_j/β_j\n",
+ " else:\n",
+ " break\n",
+ " w̃_j = A @ V[:,j]\n",
+ " α_j = np.conjugate(w̃_j) @ V[:,j]\n",
+ " w_j = w̃_j - α_j*V[:,j] - β_j * V[:,j-1]\n",
+ " \n",
+ " ritz.append(np.conjugate(V[:,j]) @ A @ V[:,j])\n",
+ " return V, ritz"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 73,
+ "id": "aa9ac15b",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[[ 0.57900658 -0.32435077 -0.56269734 0.49286881 -0.42996386 -0.82840343\n",
+ " 0.29946173 0.19799369 0.44790496 0.62677608 0.30550101 0.55964456\n",
+ " -0.44827518 -0.65545559 0.49439402 0.35355848 0.44829467 0.65322912\n",
+ " 0.4691473 0.38546294 -0.45234048 -0.65328039 -0.29575937 0.3119645\n",
+ " 0.62324105 0.65328105 -0.41041207 -0.5310114 -0.35045076 -0.65327485\n",
+ " 0.44828037 0.57780436 0.19626784 0.65314259 -0.44838273 0.18210056\n",
+ " -0.62814265 -0.60853106 0.44940642 0.75811541 0.39629793 -0.21773652\n",
+ " -0.46989337 -0.65860905 0.63005841 -0.30019911 -0.28132012 0.48236852\n",
+ " -0.62832911 -0.5187234 -0.32163515 0.29769028 0.73425597 -0.47967195\n",
+ " -0.37704813 -0.43765746 -0.66045568 -0.40777599 -0.45326236 0.44812517\n",
+ " 0.65380112 -0.30669785 -0.6051936 -0.3358828 -0.65334514 -0.02324727\n",
+ " 0.45896652 0.60195637 0.65303739 -0.45292671 0.23926742 0.55576214\n",
+ " -0.65478006 0.4482482 0.31696558 0.52987942 0.64640066 -0.44829888\n",
+ " 0.38549514 0.44541757 -0.67232128 0.4483082 0.46400403 0.38569858\n",
+ " -0.66016044 -0.4473534 0.54359334 -0.61275386 -0.39239591 -0.41840701\n",
+ " -0.54758134 0.15479221 -0.82132777 -0.0401838 0.32731399 -0.62451906\n",
+ " 0.64802289 0.2879372 -0.45982671 0.5518971 ]\n",
+ " [ 0.58805175 -0.05423688 -0.06798499 -0.80413403 -0.5455362 0.01059911\n",
+ " -0.83007415 0.11512958 0.54666835 0.26787692 0.09236427 -0.78794957\n",
+ " -0.54682618 -0.26728689 -0.78877515 -0.08586063 0.54683546 0.27063279\n",
+ " -0.284458 -0.74509647 -0.53914128 -0.27059833 0.05982443 0.73244018\n",
+ " -0.62187536 0.27059779 -0.57079841 0.30321086 0.71346104 -0.27059759\n",
+ " 0.54686975 -0.77908366 0.14408408 0.27049265 -0.54687059 -0.57656055\n",
+ " 0.52268989 -0.3078303 0.54736985 -0.34213788 0.43095611 -0.81346418\n",
+ " 0.18839992 -0.24489227 0.33655805 0.62300199 0.66228768 0.08814893\n",
+ " -0.60383867 0.38361569 0.6931433 0.47604162 0.38162238 0.30471331\n",
+ " 0.73136448 -0.5423859 -0.27941799 0.17456422 0.77353787 0.54552404\n",
+ " 0.2712379 0.00992259 0.67047551 -0.69075046 -0.27060662 0.04018302\n",
+ " 0.60116859 -0.7507227 0.27091894 -0.54786238 0.06259372 -0.78982004\n",
+ " -0.2685389 0.5468414 -0.0277812 -0.78831559 0.28062614 -0.54683543\n",
+ " -0.13969699 -0.79016108 -0.23895029 0.54683931 -0.27550642 -0.7469929\n",
+ " -0.25977012 -0.54645887 -0.44674577 -0.35911728 0.56980911 -0.58887229\n",
+ " 0.46580066 -0.34670594 -0.33969343 -0.73988723 -0.62453819 -0.33669113\n",
+ " 0.27858351 -0.64728847 -0.53769625 -0.45259002]\n",
+ " [ 0.30509728 0.93431284 -0.07857044 0.16673885 -0.55200807 0.19652033\n",
+ " 0.25878826 -0.76791633 0.5469731 -0.20466397 -0.78185586 0.21825329\n",
+ " -0.54684481 0.26920035 0.36451884 -0.70399848 0.54683972 -0.27053318\n",
+ " -0.58773768 0.52572562 -0.55225742 0.2705957 0.75410176 0.40915197\n",
+ " 0.43669568 -0.27059837 -0.58485955 0.50059999 -0.57802549 0.27060699\n",
+ " 0.54682743 0.14591815 -0.77885009 -0.27039935 -0.54680038 0.71500562\n",
+ " 0.36081765 0.24502887 0.54638668 -0.49172198 -0.10982104 -0.0510733\n",
+ " -0.86228786 0.29659175 0.32148198 0.62758918 -0.64406094 -0.42645651\n",
+ " -0.4363783 0.50865706 -0.60743461 0.59215986 -0.14697125 0.57280492\n",
+ " -0.5473977 -0.55114273 0.26170673 0.65832555 -0.44016397 0.54770734\n",
+ " -0.26996275 0.73353648 -0.39697567 -0.48077268 0.27054053 0.92054875\n",
+ " 0.24150568 0.14500457 -0.27062647 -0.53278517 -0.77219061 0.21652209\n",
+ " 0.27014777 0.5469465 -0.72882184 0.30754943 -0.27401056 -0.54683426\n",
+ " -0.6772041 0.42098046 0.25523824 0.54683146 -0.59400045 0.52829137\n",
+ " 0.26196833 -0.54721502 -0.44984181 0.35763158 -0.64622441 -0.50213147\n",
+ " 0.42716543 -0.4564788 -0.40350926 0.66808463 -0.62051456 -0.33380815\n",
+ " -0.29503483 0.64535901 -0.53733834 -0.46604763]\n",
+ " [ 0.47524959 -0.13752981 0.82010757 0.28748383 -0.46131163 0.52441889\n",
+ " 0.39284631 0.59820414 0.4487263 -0.70250008 0.53557389 0.13527362\n",
+ " -0.44832047 0.6530443 0.02311554 0.60992662 0.44829587 -0.65334631\n",
+ " 0.59459976 -0.14093311 -0.44690773 0.65328343 -0.58333349 0.44587465\n",
+ " 0.18476611 -0.65328189 -0.40458672 -0.61277215 0.18451055 0.6532846\n",
+ " 0.44828334 0.19462443 0.57802357 -0.65354623 -0.44821293 -0.3509762\n",
+ " -0.44949161 0.68912358 0.44708132 0.25770561 -0.80322109 -0.53689696\n",
+ " -0.01285863 0.64675747 0.62161436 -0.3576043 0.25965269 -0.76005606\n",
+ " -0.22395394 -0.57011668 0.21708613 0.57802385 -0.5418782 -0.59072763\n",
+ " 0.15263178 -0.45881933 0.64593611 -0.60815586 0.04947804 0.44900337\n",
+ " -0.65275892 -0.606434 -0.16313681 -0.42297067 0.65323809 -0.38785937\n",
+ " 0.60796469 0.23029901 -0.65338075 -0.45917771 0.58528181 0.14293683\n",
+ " 0.65281706 0.44820483 0.60628356 0.05656569 -0.65447183 -0.44829835\n",
+ " 0.6109606 0.00491072 0.65248778 0.44828772 0.59662378 -0.11893881\n",
+ " 0.65427844 -0.44923642 0.55006076 0.60635562 0.32208235 -0.47542505\n",
+ " -0.54837407 -0.80464991 0.21727711 -0.06793428 0.34318986 -0.62063447\n",
+ " -0.64452464 -0.28569487 -0.45903121 0.52284938]]\n",
+ "\n",
+ "\n",
+ "[[ 10.36 2.58 -0. ... -0.08 -10.67 -0.05]\n",
+ " [ 2.58 1.94 1.05 ... 0.31 -3.03 -0.68]\n",
+ " [ -0. 1.05 2.91 ... -0.3 -0.39 0.11]\n",
+ " ...\n",
+ " [ -0.08 0.31 -0.3 ... 0.59 0. 0. ]\n",
+ " [-10.67 -3.03 -0.39 ... 0. 11.09 0.21]\n",
+ " [ -0.05 -0.68 0.11 ... 0. 0.21 0.91]]\n",
+ "\n",
+ "\n",
+ "[ 3.41 0.59 11.09 0.91]\n",
+ "[11.1 3.41 0.9 0.59]\n"
+ ]
+ }
+ ],
+ "source": [
+ "A = np.array([[4, 3, 2, 1],\n",
+ " [3, 4, 3 ,2], \n",
+ " [2, 3, 4, 3], \n",
+ " [1, 2, 3, 4]])\n",
+ "b = np.random.rand(4)\n",
+ "V, ritz = lanczos_alg(A, b, N = 100)\n",
+ "\n",
+ "print(V)\n",
+ "print('\\n')\n",
+ "print(np.round(np.conjugate(V).T @ A @ V, 2))\n",
+ "print('\\n')\n",
+ "print(np.round(ritz, 2)[-4:])\n",
+ "print(np.round(np.linalg.eig(A)[0], 2))"
+ ]
+ }
+ ],
+ "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": "3.10.4"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/num_ana/prog/prb10_p.ipynb b/num_ana/prog/prb10_p.ipynb
@@ -0,0 +1,177 @@
+{
+ "cells": [
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "id": "e8c4b067",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 59,
+ "id": "35139a3d",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def lanczos_alg(A: np.ndarray, b: np.array, N: int=None) -> np.ndarray:\n",
+ " if N == None:\n",
+ " N = A.shape[0]\n",
+ " v_1 = b/np.linalg.norm(b)\n",
+ " V = np.zeros([A.shape[0], N])\n",
+ " \n",
+ " V[:,0] = v_1\n",
+ " w̃_j = A @ V[:,0]\n",
+ " α_j = np.conjugate(w̃_j) @ V[:,0]\n",
+ " w_j = w̃_j - α_j*V[:,0]\n",
+ " \n",
+ " ritz = [np.conjugate(V[:,0]) @ A @ V[:,0]]\n",
+ " for j in range(1, N):\n",
+ " if (β_j:=np.linalg.norm(w_j)) != 0:\n",
+ " V[:,j] = w_j/β_j\n",
+ " else:\n",
+ " break\n",
+ " w̃_j = A @ V[:,j]\n",
+ " α_j = np.conjugate(w̃_j) @ V[:,j]\n",
+ " w_j = w̃_j - α_j*V[:,j] - β_j * V[:,j-1]\n",
+ " \n",
+ " ritz.append(np.conjugate(V[:,j]) @ A @ V[:,j])\n",
+ " return V, ritz"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 73,
+ "id": "aa9ac15b",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[[ 0.57900658 -0.32435077 -0.56269734 0.49286881 -0.42996386 -0.82840343\n",
+ " 0.29946173 0.19799369 0.44790496 0.62677608 0.30550101 0.55964456\n",
+ " -0.44827518 -0.65545559 0.49439402 0.35355848 0.44829467 0.65322912\n",
+ " 0.4691473 0.38546294 -0.45234048 -0.65328039 -0.29575937 0.3119645\n",
+ " 0.62324105 0.65328105 -0.41041207 -0.5310114 -0.35045076 -0.65327485\n",
+ " 0.44828037 0.57780436 0.19626784 0.65314259 -0.44838273 0.18210056\n",
+ " -0.62814265 -0.60853106 0.44940642 0.75811541 0.39629793 -0.21773652\n",
+ " -0.46989337 -0.65860905 0.63005841 -0.30019911 -0.28132012 0.48236852\n",
+ " -0.62832911 -0.5187234 -0.32163515 0.29769028 0.73425597 -0.47967195\n",
+ " -0.37704813 -0.43765746 -0.66045568 -0.40777599 -0.45326236 0.44812517\n",
+ " 0.65380112 -0.30669785 -0.6051936 -0.3358828 -0.65334514 -0.02324727\n",
+ " 0.45896652 0.60195637 0.65303739 -0.45292671 0.23926742 0.55576214\n",
+ " -0.65478006 0.4482482 0.31696558 0.52987942 0.64640066 -0.44829888\n",
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+ " 0.64802289 0.2879372 -0.45982671 0.5518971 ]\n",
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+ " -0.284458 -0.74509647 -0.53914128 -0.27059833 0.05982443 0.73244018\n",
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+ " 0.2712379 0.00992259 0.67047551 -0.69075046 -0.27060662 0.04018302\n",
+ " 0.60116859 -0.7507227 0.27091894 -0.54786238 0.06259372 -0.78982004\n",
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+ " 0.42716543 -0.4564788 -0.40350926 0.66808463 -0.62051456 -0.33380815\n",
+ " -0.29503483 0.64535901 -0.53733834 -0.46604763]\n",
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+ " 0.18476611 -0.65328189 -0.40458672 -0.61277215 0.18451055 0.6532846\n",
+ " 0.44828334 0.19462443 0.57802357 -0.65354623 -0.44821293 -0.3509762\n",
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+ " 0.60796469 0.23029901 -0.65338075 -0.45917771 0.58528181 0.14293683\n",
+ " 0.65281706 0.44820483 0.60628356 0.05656569 -0.65447183 -0.44829835\n",
+ " 0.6109606 0.00491072 0.65248778 0.44828772 0.59662378 -0.11893881\n",
+ " 0.65427844 -0.44923642 0.55006076 0.60635562 0.32208235 -0.47542505\n",
+ " -0.54837407 -0.80464991 0.21727711 -0.06793428 0.34318986 -0.62063447\n",
+ " -0.64452464 -0.28569487 -0.45903121 0.52284938]]\n",
+ "\n",
+ "\n",
+ "[[ 10.36 2.58 -0. ... -0.08 -10.67 -0.05]\n",
+ " [ 2.58 1.94 1.05 ... 0.31 -3.03 -0.68]\n",
+ " [ -0. 1.05 2.91 ... -0.3 -0.39 0.11]\n",
+ " ...\n",
+ " [ -0.08 0.31 -0.3 ... 0.59 0. 0. ]\n",
+ " [-10.67 -3.03 -0.39 ... 0. 11.09 0.21]\n",
+ " [ -0.05 -0.68 0.11 ... 0. 0.21 0.91]]\n",
+ "\n",
+ "\n",
+ "[ 3.41 0.59 11.09 0.91]\n",
+ "[11.1 3.41 0.9 0.59]\n"
+ ]
+ }
+ ],
+ "source": [
+ "A = np.array([[4, 3, 2, 1],\n",
+ " [3, 4, 3 ,2], \n",
+ " [2, 3, 4, 3], \n",
+ " [1, 2, 3, 4]])\n",
+ "b = np.random.rand(4)\n",
+ "V, ritz = lanczos_alg(A, b, N = 100)\n",
+ "\n",
+ "print(V)\n",
+ "print('\\n')\n",
+ "print(np.round(np.conjugate(V).T @ A @ V, 2))\n",
+ "print('\\n')\n",
+ "print(np.round(ritz, 2)[-4:])\n",
+ "print(np.round(np.linalg.eig(A)[0], 2))"
+ ]
+ }
+ ],
+ "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": "3.10.4"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
