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Sr:adding files for chapter 9
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‎.ipynb_checkpoints/Chapter 9-checkpoint.ipynb‎

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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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"collapsed": true
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},
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"outputs": [],
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"source": [
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"# Example 9.6.7\n",
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"from vec import *\n",
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"from mat import *\n",
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"from matutil import *\n",
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"from vecutil import *\n",
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"from GF2 import one\n",
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"from orthogonalization import *\n",
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"from orthonormalization import *\n",
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"import independence\n",
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"from QR import *"
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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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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[Vec({0, 1, 2, 3},{0: -4, 1: 3, 2: 1, 3: -2}), Vec({0, 1, 2, 3},{0: 0.5333333333333332, 1: 0.10000000000000009, 2: 2.3666666666666667, 3: 0.2666666666666666}), Vec({0, 1, 2, 3},{0: 0.41899441340782123, 1: 0.3910614525139665, 2: -0.07821229050279327, 3: -0.29050279329608936}), Vec({0, 1, 2, 3},{0: -1.1102230246251565e-16, 1: 0.33333333333333315, 2: -0.06666666666666665, 3: 0.46666666666666673}), Vec({0, 1, 2, 3},{0: 5.5511151231257815e-18, 1: -4.163336342344337e-17, 2: -1.9255430583342559e-16, 3: 0.0}), Vec({0, 1, 2, 3},{0: 2.1094237467877978e-16, 1: 2.220446049250313e-16, 2: -1.3877787807814457e-17, 3: -2.220446049250313e-16})]\n",
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"\n",
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" 0 1 2 3\n",
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"-----------------\n",
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" -120 -30 -90 -60\n"
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]
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}
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],
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"source": [
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"L = [list2vec(v) for v in [[8,-2,2], [0,3,3], [1,0,0], [0,1,0], [0,0,1]]]\n",
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"\n",
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"Lstar = orthogonalize(L)\n",
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"\n",
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"#print(Lstar)\n",
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"# Problem 9.11.1\n",
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"\n",
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"U1 = [list2vec(v) for v in [[0,0,3,2],[1,2,-3,-1],[1,2,0,1],[3,1,0,-1],[-1,-2,3,1]]]\n",
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"Lstar = orthogonalize(U1)\n",
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"\n",
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"#print(Lstar[1])\n",
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"\n",
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"\n",
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"#independence.is_independent(U1) \n",
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"\n",
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"U2 = [list2vec(v) for v in [[3,0,1],[1,0,0],[1,0,1]]]\n",
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"Lstar = orthogonalize(U2)\n",
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"#print(Lstar[2])\n",
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"\n",
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"U3 = [list2vec(v) for v in [[-4,3,1,-2],[-2,2,3,-1],[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]]\n",
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"Lstar = orthogonalize(U3)\n",
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"print(Lstar)\n",
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"\n",
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"\n",
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"# Problem 9.11.3\n",
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"\n",
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"#A = [list2vec(v) for v in [[-4,0],[-1,4],[-3,0],[-2,-1]]]\n",
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"\n",
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"A = [list2vec(v) for v in [[-4,-1,-3,-2],[0,4,0,-1],[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]]\n",
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"\n",
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"Basis = orthogonalize(A)\n",
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"print((Basis[0]*Basis[0]) *Basis[0])\n"
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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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"collapsed": false,
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"scrolled": false
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},
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"outputs": [],
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"source": [
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"# Problem 9.11.9\n",
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"D = {'a','b','c','d'}\n",
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"L = [Vec(D, {'a':4,'b':3,'c':1,'d':2}), Vec(D, {'a':8,'b':9,'c':-5,'d':-5}), Vec(D, {'a':10,'b':1,'c':-1,'d':5})]\n",
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"for v in orthonormalize(L): print(v)\n",
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"\n",
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"# Problem 9.11.10 \n",
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" \n",
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"# U2 = [list2vec(v) for v in [[0.73, 0.55, 0.18, 0.37], [0.19, 0.40, -0.57, -0.69], [0.53, -0.65, -0.51, 0.18]]]\n",
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"# #Lstar = orthogonalize(U2)\n",
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"\n",
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"# U3 = 1\n",
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"\n",
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"L = [list2vec(v) for v in [[4,3,1,2],[8,9,-5,-5],[10,1,-1,5]]]\n",
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"\n",
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"print(coldict2mat(L))\n",
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"\n",
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"#Qlist_unormalized = aug_orthogonalize(L)[0]\n",
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"#Rlist1 = aug_orthogonalize(L)[1]\n",
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"# print(coldict2mat(Qlist[1]))\n",
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"\n",
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"# print(mat2rowdict(coldict2mat(Qlist[1])))\n",
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"\n",
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"# print(Qlist[0]*Qlist[0])\n",
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"\n",
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"# print(2*mat2rowdict(coldict2mat(RList))[0])\n",
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"\n",
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"Qlist,Rlist = aug_orthonormalize(L)\n",
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"print(coldict2mat(Qlist))\n",
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"\n",
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"print(coldict2mat(Rlist))\n",
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"\n",
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"\n",
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"print(coldict2mat(Qlist)*coldict2mat(Rlist))\n",
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"\n",
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"# problem 9.11.12\n",
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"L = [list2vec(v) for v in [[6,2,3],[6,0,3]]]\n",
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"print(coldict2mat(L))\n",
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"\n",
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"Qlist,Rlist = aug_orthonormalize(L)\n",
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"print(coldict2mat(Qlist))\n",
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"\n",
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"print(coldict2mat(Rlist))\n",
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"print(coldict2mat(Qlist)*coldict2mat(Rlist))\n",
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"\n",
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"# problem 9.11.12\n",
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"L = [list2vec(v) for v in [[2,2,1],[3,1,1]]]\n",
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"print(coldict2mat(L))\n",
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"\n",
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"Qlist,Rlist = aug_orthonormalize(L)\n",
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"print(coldict2mat(Qlist))\n",
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"\n",
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"print(coldict2mat(Rlist))\n"
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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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"collapsed": false
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},
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"outputs": [],
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"source": [
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"A=Mat(({'a','b','c'},{'A','B'}), {('a','A'):-1, ('a','B'):2, ('b','A'):5, ('b','B'):3,('c','A'):1, ('c','B'):-2})\n",
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"\n",
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"print(A)\n",
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"Q= factor(A)\n",
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"\n",
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"print(Q)"
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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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"collapsed": false
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},
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"outputs": [],
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"source": [
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"# Problem 9.11.10 \n",
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" \n",
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"# U2 = [list2vec(v) for v in [[0.73, 0.55, 0.18, 0.37], [0.19, 0.40, -0.57, -0.69], [0.53, -0.65, -0.51, 0.18]]]\n",
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"# #Lstar = orthogonalize(U2)\n",
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"\n",
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"# U3 = 1\n",
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"\n",
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"L = [list2vec(v) for v in [[4,3,1,2],[8,9,-5,-5],[10,1,-1,5]]]\n",
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"\n",
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"print(coldict2mat(L))\n",
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"\n",
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"#Qlist_unormalized = aug_orthogonalize(L)[0]\n",
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"#Rlist1 = aug_orthogonalize(L)[1]\n",
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"# print(coldict2mat(Qlist[1]))\n",
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"\n",
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"# print(mat2rowdict(coldict2mat(Qlist[1])))\n",
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"\n",
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"# print(Qlist[0]*Qlist[0])\n",
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"\n",
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"# print(2*mat2rowdict(coldict2mat(RList))[0])\n",
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"\n",
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"Qlist,Rlist = aug_orthonormalize(L)\n",
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"print(coldict2mat(Qlist))\n",
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"\n",
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"print(Qlist)\n",
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"\n",
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"print(mat2coldict(rowdict2mat(Rlist)))\n",
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"dict2list(mat2coldict(rowdict2mat(Rlist)),range(len(Qlist)))\n"
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]
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}
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],
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