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ShfitedPowGMRES
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Now algo 1 works, I hope

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pull/1/head
Luca Lombardo 2 years ago
parent 74522d86d9
commit 6651a16f28
2 changed files with 74 additions and 55 deletions
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8
README.md
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@ -1 +1,9 @@
# ShfitedPowGMRES # ShfitedPowGMRES
```bash
mkdir data && cd data
wget https://snap.stanford.edu/data/web-BerkStan.txt.gz
wget https://snap.stanford.edu/data/web-Stanford.txt.gz
gunzip web-Stanford.txt.gz
gunzip web-BerkStan.txt.gz
```

119
src/filtering.ipynb
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@ -2,14 +2,17 @@
"cells": [ "cells": [
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 1, "execution_count": null,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
"import numpy as np\n", "import numpy as np\n",
"import networkx as nx\n", "import networkx as nx\n",
"import time\n",
"import math\n",
"import scipy as sp\n", "import scipy as sp\n",
"import scipy.sparse" "from scipy.sparse import *\n",
"from scipy.sparse.linalg import norm"
] ]
}, },
{ {
@ -21,7 +24,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 2, "execution_count": null,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -39,7 +42,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 3, "execution_count": null,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -71,12 +74,12 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 4, "execution_count": null,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
"n = G1.number_of_nodes()\n", "n = G2.number_of_nodes()\n",
"P = create_matrix(G1) " "P = create_matrix(G2) "
] ]
}, },
{ {
@ -88,11 +91,13 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 5, "execution_count": null,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
"# define d as a nx1 sparse matrix, where n is the number of nodes in the graph. The vector is filled with d(i) = 1 if the i row of the matrix P is filled with zeros, other wise is 0\n", "# define d as a nx1 sparse matrix, where n is the number of nodes in the graph. The vector is filled with d(i) = 1 if the i row of the matrix P is filled with zeros, other wise is 0\n",
"\n",
"# d is the vector of dangling nodes\n",
"d = sp.sparse.lil_matrix((n,1))\n", "d = sp.sparse.lil_matrix((n,1))\n",
"for i in range(n):\n", "for i in range(n):\n",
" if P[i].sum() == 0:\n", " if P[i].sum() == 0:\n",
@ -108,7 +113,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 6, "execution_count": null,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -129,7 +134,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 7, "execution_count": null,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -140,7 +145,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 8, "execution_count": null,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -152,7 +157,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 9, "execution_count": null,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -175,70 +180,76 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 10, "execution_count": null,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
"a = [0.85, 0.9, 0.95, 0.99]\n", "# list of alpha values, from 0.85 to 0.99 with step 0.01\n",
"tau = 10**-8\n", "a = []\n",
"max_mv = 1000\n", "for i in range(85,100):\n",
"\n", " a.append(i/100)\n",
"# this should return mv (the number of iteration needed for the convergence), and two vector of lenght len(a) called x and r. Where x is the vector of the pagerank and r is the residual vector\n",
"\n", "\n",
"tau = 10**-6\n",
"max_mv = 100\n",
"\n", "\n",
"# this should return mv (the number of iteration needed for the convergence), and two vector called x and r. Where x is the vector of the pagerank and r is the residual vector\n",
"\n", "\n",
"def Algorithm1(Pt, v, tau, max_mv, a: list):\n", "def Algorithm1(Pt, v, tau, max_mv, a: list):\n",
" u = Pt.dot(v) - v\n", " # take time of the performance\n",
" mv = 1\n", " start_time = time.time()\n",
" for i in range(len(a)):\n", "\n",
" r = sp.sparse.lil_matrix((len(a),1))\n", "\n",
" r[i] = a[i]*u\n", " u = Pt.dot(v) - v \n",
" mv = 1 # number of iteration\n",
" r = sp.sparse.lil_matrix((n,1)) \n",
" Res = sp.sparse.lil_matrix((len(a),1))\n", " Res = sp.sparse.lil_matrix((len(a),1))\n",
" Res[i] = np.linalg.norm(r[i])\n", " x = sp.sparse.lil_matrix((n,1)) \n",
"\n",
" for i in range(len(a)):\n",
" r = a[i]*(u) \n",
" normed_r = norm(r)\n",
" Res[i] = normed_r \n",
"\n", "\n",
" if Res[i] > tau:\n", " if Res[i] > tau:\n",
" x = sp.sparse.lil_matrix((len(a),1))\n", " x = r + v \n",
" x[i] = r[i] + v\n", "\n",
" \n", " print(\"STARTING THE WHILE LOOP\\n\")\n",
"\n",
" # take the maximum value of the sparse matrix Res\n",
"\n",
"\n",
" while max(Res) > tau and mv < max_mv:\n", " while max(Res) > tau and mv < max_mv:\n",
" u = Pt.dot(u)\n", " u = Pt*u # should it be the same u of the beginning?\n",
" mv += 1\n", " mv += 1 \n",
" print(\"mv = \", mv)\n",
" print(\"max(Res) = \", max(Res))\n",
"\n", "\n",
" for i in range(len(a)):\n", " for i in range(len(a)):\n",
" if Res[i] >= tau:\n", " if Res[i] >= tau: \n",
" r = sp.sparse.lil_matrix((len(a),1))\n", " r = (a[i]**(mv+1))*(u)\n",
" r[i] = a[i]*u\n", " Res[i] = norm(r)\n",
" Res = sp.sparse.lil_matrix((len(a),1))\n",
" Res[i] = np.linalg.norm(r[i])\n",
"\n", "\n",
" if Res[i] > tau:\n", " if Res[i] > tau:\n",
" x = sp.sparse.lil_matrix((len(a),1))\n", " x = r + x\n",
" x[i] = r[i] + x[i]\n", "\n",
" print(\"\\nEND OF THE WHILE LOOP\\n\")\n",
"\n",
" if mv == max_mv:\n",
" print(\"The algorithm didn't converge in \", max_mv, \" iterations\")\n",
" else:\n",
" print(\"The algorithm converged in \", mv, \" iterations\")\n",
"\n",
" print(\"\\nThe execution time is %s seconds\" % (time.time() - start_time))\n",
" \n",
" return mv, x, r " " return mv, x, r "
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 11, "execution_count": null,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [],
{
"ename": "ValueError",
"evalue": "shape mismatch in assignment",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m/tmp/ipykernel_128897/741213869.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;31m# launch the algorithm\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mmv\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mAlgorithm1\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mPt\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mv\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtau\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmax_mv\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[0;32m/tmp/ipykernel_128897/1942976890.py\u001b[0m in \u001b[0;36mAlgorithm1\u001b[0;34m(Pt, v, tau, max_mv, a)\u001b[0m\n\u001b[1;32m 12\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 13\u001b[0m \u001b[0mr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msparse\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlil_matrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 14\u001b[0;31m \u001b[0mr\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mu\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 15\u001b[0m \u001b[0mRes\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msparse\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlil_matrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 16\u001b[0m \u001b[0mRes\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinalg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnorm\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mr\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m/usr/lib/python3/dist-packages/scipy/sparse/_lil.py\u001b[0m in \u001b[0;36m__setitem__\u001b[0;34m(self, key, x)\u001b[0m\n\u001b[1;32m 330\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_set_intXint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkey\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 331\u001b[0m \u001b[0;31m# Everything else takes the normal path.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 332\u001b[0;31m \u001b[0mIndexMixin\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__setitem__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkey\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 333\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 334\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_mul_scalar\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m/usr/lib/python3/dist-packages/scipy/sparse/_index.py\u001b[0m in \u001b[0;36m__setitem__\u001b[0;34m(self, key, x)\u001b[0m\n\u001b[1;32m 130\u001b[0m if not ((broadcast_row or x.shape[0] == i.shape[0]) and\n\u001b[1;32m 131\u001b[0m (broadcast_col or x.shape[1] == i.shape[1])):\n\u001b[0;32m--> 132\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'shape mismatch in assignment'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 133\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m0\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 134\u001b[0m \u001b[0;32mreturn\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;31mValueError\u001b[0m: shape mismatch in assignment"
]
}
],
"source": [ "source": [
"# launch the algorithm\n",
"mv, x, r = Algorithm1(Pt, v, tau, max_mv, a)" "mv, x, r = Algorithm1(Pt, v, tau, max_mv, a)"
] ]
}, },

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