created a testing notebook for each algo
Luca Lombardo
2 years ago
parent
1c3c69b775
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da82dcfa14
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import networkx as nx\n",
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"import time\n",
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"import math\n",
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"import pandas as pd\n",
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"import scipy as sp\n",
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"import plotly.express as px\n",
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"import plotly.graph_objs as go\n",
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"from scipy.sparse import *\n",
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"from scipy import linalg\n",
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"from scipy.sparse.linalg import norm\n",
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"from scipy.optimize import least_squares"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Algorithm 2 testing"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"def Arnoldi(A, v, m): # defined ad algorithm 2 in the paper\n",
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" beta = norm(v)\n",
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" print(\"A\")\n",
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" v = v/beta\n",
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" print(\"B\")\n",
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" h = sp.sparse.lil_matrix((m,m))\n",
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" print(\"C\")\n",
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"\n",
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" for j in range(m):\n",
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" w = A.dot(v)\n",
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" print(\"D\")\n",
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" for i in range(j):\n",
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" h[i,j] = v.T.dot(w)\n",
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" print(\"E\")\n",
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" w = w - h[i,j]*v[i]\n",
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" print(\"F\")\n",
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"\n",
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" h[j+1,j] = norm(w)\n",
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" print(\"G\")\n",
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"\n",
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" if h[j+1,j] == 0:\n",
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" print(\"The algorithm didn't converge\")\n",
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" m = j\n",
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" v[m+1] = 0\n",
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" break\n",
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" else:\n",
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" print(\"H\")\n",
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" v[j+1] = w**h[j+1,j] # THIS IS WRONG, I DON'T KNOW HOW TO FIX IT. ERROR \" matrix is not square\"\n",
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" print(\"I\")\n",
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"\n",
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" return v, h, m, beta, j"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Creating a small test case"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"A = sp.sparse.rand(100,100, density=0.5, format='lil')\n",
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"v = sp.sparse.rand(100,1, density=0.5, format='lil')\n",
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"m = 100"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"v, h, m, beta, j = Arnoldi(A, v, m)"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3.10.6 64-bit",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.10.6"
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},
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"orig_nbformat": 4,
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"vscode": {
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"interpreter": {
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"hash": "916dbcbb3f70747c44a77c7bcd40155683ae19c65e1c03b4aa3499c5328201f1"
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}
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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@ -0,0 +1,174 @@
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import networkx as nx\n",
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"import time\n",
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"import math\n",
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"import pandas as pd\n",
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"import scipy as sp\n",
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"import plotly.express as px\n",
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"import plotly.graph_objs as go\n",
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"from scipy.sparse import *\n",
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"from scipy import linalg\n",
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"from scipy.sparse.linalg import norm\n",
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"from scipy.optimize import least_squares"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"This function is needed in the algorithm. Note that this is a NON-functioning version, for now it's just a place holder. When algo2_testing will be completed, this will be updated and I'll work on algo4_testing."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"def Arnoldi(A, v, m): # defined ad algorithm 2 in the paper\n",
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" beta = norm(v)\n",
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" print(\"A\")\n",
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" v = v/beta\n",
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" print(\"B\")\n",
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" h = sp.sparse.lil_matrix((m,m))\n",
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" print(\"C\")\n",
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"\n",
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" for j in range(m):\n",
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" w = A.dot(v)\n",
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" print(\"D\")\n",
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" for i in range(j):\n",
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" h[i,j] = v.T.dot(w)\n",
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" print(\"E\")\n",
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" w = w - h[i,j]*v[i]\n",
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" print(\"F\")\n",
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"\n",
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" h[j+1,j] = norm(w)\n",
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" print(\"G\")\n",
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"\n",
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" if h[j+1,j] == 0:\n",
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" print(\"The algorithm didn't converge\")\n",
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" m = j\n",
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" v[m+1] = 0\n",
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" break\n",
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" else:\n",
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" print(\"H\")\n",
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" v[j+1] = w**h[j+1,j] # THIS IS WRONG, I DON'T KNOW HOW TO FIX IT. ERROR \" matrix is not square\"\n",
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" print(\"I\")\n",
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"\n",
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" return v, h, m, beta, j"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Algorithm 4 testing\n",
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"\n",
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"Still a complete mess. Conceptually and technically wrong. I'll work on it when algo2_testing will be completed."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"def Algo4(Pt, v, m, a: list, tau, maxit: int, x):\n",
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" \n",
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" iter = 1\n",
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" mv = 0\n",
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" e1 = sp.sparse.lil_matrix((1,n))\n",
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" e1[0,0] = 1\n",
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" x = sp.sparse.lil_matrix((len(a),1))\n",
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" I = sp.sparse.eye(n, n, format='lil')\n",
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" res = sp.sparse.lil_matrix((len(a),1))\n",
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" r = sp.sparse.lil_matrix((n,1))\n",
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" y = sp.sparse.lil_matrix((n,1))\n",
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"\n",
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" for i in range(len(a)): # I don't think that this is what was intended in the pseudocode... \n",
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" r = ((1-a[i])**a[i])*v - ((1**a[i])*I - Pt).dot(x)\n",
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" res[i] = a[i]*norm(r)\n",
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"\n",
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" def Find_k(res, maxit):\n",
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" k = 0\n",
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" for i in range(len(a)):\n",
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" if res[i] == max(res):\n",
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" k = i\n",
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" break\n",
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" return k\n",
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"\n",
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" def Find_gamma(res, a, k):\n",
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" gamma = sp.sparse.lil_matrix((len(a),1))\n",
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" for i in range(len(a)):\n",
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" if i != k:\n",
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" gamma[i] = (res[i]*a[k])/(res[k]*a[i])\n",
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" else:\n",
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" gamma[i] = 0\n",
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" return gamma\n",
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"\n",
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"\n",
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" while max(res) > tau and iter < maxit:\n",
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" k = Find_k(res, maxit)\n",
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" gamma = Find_gamma(res, a, k)\n",
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" v, h, m, beta, j = Arnoldi((1**a[k])*I - Pt, r, m)\n",
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" Hbar = sp.sparse.lil_matrix((m+1,m))\n",
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" Hbar[0:m,0:m] = h\n",
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" Hbar[m+1,0:m] = e1\n",
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"\n",
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" mv += j\n",
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"\n",
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" y = sp.sparse.linalg.least_squares(Hbar, beta*e1)\n",
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" res[k] = a[k]*norm(beta*e1 - Hbar*y)\n",
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" x[k] = x[k] + v*y[k]\n",
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"\n",
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" for i in range(len(a)):\n",
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" if i != k:\n",
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" if res[i] >= tau:\n",
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" Hbar[i] = Hbar[k] + ((1-a[i])/a[i] - (1-a[k])/a[k])*I\n",
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" z = beta*e1 - Hbar*y\n",
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" y = sp.sparse.linalg.solve(Hbar, gamma*beta*e1)\n",
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" x = x + v*y\n",
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" res[i] = a[i]**a[k]*gamma[i]*res[k]\n",
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" \n",
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" iter += 1\n",
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" \n",
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" return x, res, mv\n"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3.10.6 64-bit",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.10.6"
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},
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"orig_nbformat": 4,
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"vscode": {
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"interpreter": {
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"hash": "916dbcbb3f70747c44a77c7bcd40155683ae19c65e1c03b4aa3499c5328201f1"
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}
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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