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dpsanders/quiver_error.ipynb

Created April 26, 2018 19:59
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quiver_error.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Problema para graficar soluciones de intervalos negativos usando \n",
"`DifferentialEquations.jl`"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Para este ejemplo usamos el sistema descrito por la matriz\n",
"$$A = \\begin{pmatrix} 1 & 1 \\\\ 4 & -2 \\end{pmatrix}. $$"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"using DifferentialEquations, Plots"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Quiver2D (generic function with 1 method)"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function Quiver2D(X, Y, dx, dy; graph = true, scale = 1, multiplot = false)\n",
" \n",
" DX = []\n",
" DY = []\n",
" PX = []\n",
" PY = []\n",
"\n",
" for i in X\n",
" for j in Y\n",
" push!(DX, dx(i,j)*scale)\n",
" push!(DY, dy(i,j)*scale)\n",
" push!(PX, i)\n",
" push!(PY, j)\n",
" end\n",
" end\n",
" \n",
" if graph == true\n",
" if multiplot == false\n",
" return quiver(PX, PY, quiver = (DX, DY), xlims = (X[1],X[end]), ylims = (Y[1],Y[end]), color = \"#D8D8D8\")\n",
" else\n",
" return quiver!(PX, PY, quiver = (DX, DY), xlims = (X[1],X[end]), ylims = (Y[1],Y[end]), color = \"#D8D8D8\")\n",
" end\n",
" else\n",
" return PX, PY, DX, DY\n",
" end \n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
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"source": [
"X = linspace(-5,5,20)\n",
"Y = linspace(-5,5,20)\n",
"dx(x,y) = x + y\n",
"dy(x,y) = 4*x -2*y\n",
"\n",
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{
"cell_type": "code",
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"metadata": {},
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{
"data": {
"text/plain": [
"AMatrix (generic function with 1 method)"
]
},
"execution_count": 11,
"metadata": {},
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}
],
"source": [
"function AMatrix(du,u,p,t)\n",
" du[1] = u[1] + u[2]\n",
" du[2] = 4*u[1] -2*u[2]\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2×2 Array{Int64,2}:\n",
" 1 1\n",
" 4 -2"
]
},
"execution_count": 12,
"metadata": {},
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}
],
"source": [
"A = [1 1; 4 -2]"
]
},
{
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},
"execution_count": 13,
"metadata": {},
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}
],
"source": [
"# En este caso todo funciona bien\n",
"\n",
"E = eigvecs(A)\n",
"u0 = 0.1*E[:,1]\n",
"tspan = (0.0,2.0)\n",
"\n",
"S = solve(ODEProblem(AMatrix, u0, tspan))\n",
"Quiver2D(X, Y, dx, dy, scale = 1/10)\n",
"plot!(S, vars = (1,2), xlims = (-5,5), ylims = (-5,5)) \n"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
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" 309.82,193.78 309.82,193.78 309.82,193.781 309.821,193.781 309.821,193.781 309.822,193.781 309.822,193.782 309.822,193.782 309.823,193.782 309.823,193.782 \n",
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" 309.827,193.785 309.827,193.785 309.827,193.785 309.828,193.785 309.828,193.786 309.828,193.786 309.829,193.786 309.829,193.786 309.829,193.786 309.83,193.787 \n",
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" \n",
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]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"E = eigvecs(A)\n",
"u0 = 0.1 * E[:,1]\n",
"tspan = (0.0,-2.0) # En este caso el intervalo temporal está \"invertido\"\n",
"\n",
"S = solve(ODEProblem(AMatrix, u0, tspan))\n",
"Quiver2D(X, Y, dx, dy, scale = 1/10)\n",
"plot!(S, vars = (1,2), xlims = (-5,5), ylims = (-5,5)) "
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 0.6.2",
"language": "julia",
"name": "julia-0.6"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "0.6.2"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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