{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "3a9a45cb-54bb-44dc-b5f0-652702d3c9c8", "metadata": {}, "outputs": [], "source": [ "using LinearAlgebra" ] }, { "cell_type": "code", "execution_count": 2, "id": "0f09a7b7-79c3-46dc-86e9-b73fa107b699", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "7.3" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lambda=4.5\n", "mu=7.3" ] }, { "cell_type": "code", "execution_count": 3, "id": "d19d6515-b98c-45f2-aa5a-a7883e4c6125", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "28×28 Tridiagonal{Float64, Vector{Float64}}:\n", " -4.5 4.5 ⋅ ⋅ ⋅ ⋅ … ⋅ ⋅ ⋅ ⋅ ⋅ \n", " 7.3 -11.8 4.5 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ \n", " ⋅ 7.3 -11.8 4.5 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ \n", " ⋅ ⋅ 7.3 -11.8 4.5 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ \n", " ⋅ ⋅ ⋅ 7.3 -11.8 4.5 ⋅ ⋅ ⋅ ⋅ ⋅ \n", " ⋅ ⋅ ⋅ ⋅ 7.3 -11.8 … ⋅ ⋅ ⋅ ⋅ ⋅ \n", " ⋅ ⋅ ⋅ ⋅ ⋅ 7.3 ⋅ ⋅ ⋅ ⋅ ⋅ \n", " ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ \n", " ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ \n", " ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ \n", " ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ … ⋅ ⋅ ⋅ ⋅ ⋅ \n", " ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ \n", " ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ \n", " ⋮ ⋮ ⋱ ⋮ \n", " ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ \n", " ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ \n", " ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ \n", " ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ \n", " ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ … ⋅ ⋅ ⋅ ⋅ ⋅ \n", " ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ \n", " ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 4.5 ⋅ ⋅ ⋅ ⋅ \n", " ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ -11.8 4.5 ⋅ ⋅ ⋅ \n", " ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 7.3 -11.8 4.5 ⋅ ⋅ \n", " ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ … ⋅ 7.3 -11.8 4.5 ⋅ \n", " ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 7.3 -11.8 4.5\n", " ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 7.3 -7.3" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a1=mu*ones(27)\n", "a3=lambda*ones(27)\n", "a2=[-lambda,-(mu+lambda)ones(26)...,-mu]\n", "A=Tridiagonal(a1,a2,a3)" ] }, { "cell_type": "code", "execution_count": 4, "id": "331ed594-29d8-462d-92ad-44839c90dc73", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "28-element Vector{Float64}:\n", " -23.190907067935594\n", " -22.97558296560806\n", " -22.61971942326365\n", " -22.127791631424344\n", " -21.505985867495507\n", " -20.762121699738803\n", " -19.90555365166377\n", " -18.947053563467282\n", " -17.8986751298931\n", " -16.77360231802679\n", " -15.58598357125999\n", " -14.350753884405758\n", " -13.0834469874733\n", " ⋮\n", " -8.014016428740039\n", " -6.8263976819732415\n", " -5.701324870106908\n", " -4.652946436532733\n", " -3.6944463483362258\n", " -2.837878300261149\n", " -2.094014132504443\n", " -1.4722083685756537\n", " -0.9802805767363099\n", " -0.6244170343919467\n", " -0.4090929320643733\n", " -7.277919910922247e-16" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eigvals(A')" ] }, { "cell_type": "code", "execution_count": 5, "id": "c399efd1-cbd4-4dd0-83e0-71c108f9dd6c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "28-element Vector{Float64}:\n", " 0.7874031705869717\n", " 0.4853855161152557\n", " 0.29921024966008897\n", " 0.18444467444800003\n", " 0.1136987719199999\n", " 0.07008828406027452\n", " 0.043205106612497934\n", " 0.02663328489811484\n", " 0.016417778361851525\n", " 0.010120548305251028\n", " 0.006238694160771468\n", " 0.0038457703730780442\n", " 0.002370680366965653\n", " ⋮\n", " 0.000342319483090002\n", " 0.0002110188594388131\n", " 0.00013008011883233636\n", " 8.018637462276119e-5\n", " 4.9429956959409885e-5\n", " 3.0470521413098395e-5\n", " 1.8783198131294333e-5\n", " 1.1578683779713957e-5\n", " 7.1375447956952334e-6\n", " 4.39985638096156e-6\n", " 2.7122402345887854e-6\n", " 1.6719289118143017e-6" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "K28=eigvecs(A')[:,28]" ] }, { "cell_type": "code", "execution_count": 6, "id": "8d5381b2-04bb-4264-93a3-423f289890ff", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "28-element Vector{Float64}:\n", " 0.3835621458845425\n", " 0.23644241869595048\n", " 0.14575217590846254\n", " 0.08984723172439471\n", " 0.055385279830106264\n", " 0.03414161085417539\n", " 0.021046198471751928\n", " 0.01297368398943596\n", " 0.007997476431844043\n", " 0.0049299512251093835\n", " 0.0030390110291771567\n", " 0.0018733629631912726\n", " 0.0011548127855287378\n", " ⋮\n", " 0.0001667516723538337\n", " 0.00010279212679334747\n", " 6.336500966722519e-5\n", " 3.906062239764748e-5\n", " 2.4078465861648048e-5\n", " 1.4842889914599362e-5\n", " 9.149726659651564e-6\n", " 5.6402424615016065e-6\n", " 3.476861791327425e-6\n", " 2.143270967282712e-6\n", " 1.3211944317645632e-6\n", " 8.144349237301792e-7" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Pe=K28/sum(K28)" ] }, { "cell_type": "code", "execution_count": 7, "id": "6554db57-c936-4cba-9e06-a539c94876cb", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.0" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sum(Pe)" ] }, { "cell_type": "code", "execution_count": 8, "id": "be4da203-b39e-4847-be92-7abe30d07ced", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.3835621458845425" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Pe[1]" ] }, { "cell_type": "code", "execution_count": 9, "id": "fc4076ef-10fe-455c-96fb-1d01faad10aa", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.6164378541154575" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "1-Pe[1]" ] }, { "cell_type": "code", "execution_count": null, "id": "86ac2c91-f879-49dd-be96-ed9555d3bb5a", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Julia 1.10", "language": "julia", "name": "julia-1.10" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.10.10" } }, "nbformat": 4, "nbformat_minor": 5 }