{ "cells": [ { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "Ir_CtXQrjWtT" }, "source": [ "# Strum-Liouville System" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "OR505Iq-jWtV" }, "source": [ "## Introduction" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "dcaCxsBopTPd" }, "source": [ "Let $K$ be a bounded function on $y \\in [-\\frac\\pi2, \\frac\\pi2]$. We want to find the eigenvalue and eigenfunction to the following Strum-Liouville System with Dirichlet Boundary condition:\n", "$\n", "\\newcommand{\\pth}[1]{\\left(#1\\right)}\n", "\\newcommand{\\d}{\\mathrm{d}}\n", "\\newcommand{\\dfr}[2]{\\frac{\\d #1}{\\d #2}}\n", "$\n", "\\begin{align}\n", "\\tag{1}\n", "-\\phi'' (y) + K (y) \\phi (y) = \\lambda \\phi (y), \\qquad \\phi \\pth{-\\frac\\pi2} = \\phi \\pth{\\frac\\pi2} = 0.\n", "\\end{align}\n", "We want to use power method. First, we introduce the Boundary Value Problem solver operator. Given a function $f$, we solve the following Boundary Value Problem\n", "\\begin{align}\n", "\\tag{2}\n", "-\\phi'' (y) + K (y) \\phi (y) = f (y), \\qquad \\phi \\pth{-\\frac\\pi2} = \\phi \\pth{\\frac\\pi2} = 0.\n", "\\end{align}\n", "Let $$T _K = \\pth{-\\dfr{^2}{y ^2} + K} ^{-1}: f \\mapsto \\phi$$ be the operator that maps the source function to the solution of (2). With an initial guess on eigenvalue $\\mu _0$ and eigenfunction $f _0$, we run the following iteration.\n", "\\begin{align}\n", "\\tag{3}\n", "\\phi _k = T _{K - \\mu _0} f _k, \\qquad \\mu _{k + 1} = \\frac{\\|f _k\\| _{L^2}}{\\|\\phi _k\\| _{L^2}}, \\qquad f _{k + 1} = \\frac{\\phi _k}{\\|\\phi _k\\| _{L^2}}.\n", "\\end{align}\n", "As it goes, $\\mu _k ^{-1}$ should converge to the largest eigenvalue of $T _{K - \\mu _0}$, $\\mu _k$ should converge to the smallest eigenvalue of $-\\dfr{^2}{y^2} + (K - \\mu _0)$, thus $\\mu _k + \\mu _0$ will converge to the eigenvalue closest to $\\mu _0$, and we can return $\\mu _k + \\mu _0$ to be the eigenvalue, and $\\phi _k$ to be the eigenfunction." ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "Vox0ikMbjWtc" }, "source": [ "## BVP Solver" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "colab": {}, "colab_type": "code", "id": "Xp05kR8g42oy" }, "outputs": [], "source": [ "import numpy as np\n", "from numpy import cos, exp, pi, sqrt, floor, ceil, log, arctan\n", "from numpy.linalg import norm\n", "import matplotlib.pyplot as plt\n", "from scipy.integrate import solve_bvp" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "LUtEAfmBjWtf" }, "source": [ "Now we realize the operator $T _K$. We write a function `BVP_solver`. It should take two arguments $K$ and $f$, both functions, and return a function $\\phi$." ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "q1idYDMS9YA-" }, "source": [ "Define the initial mesh with 5 nodes. Use 0 as initial guess." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "colab": {}, "colab_type": "code", "id": "otkaySli9qD6" }, "outputs": [], "source": [ "initial_mesh = np.linspace(-pi / 2, pi / 2, 5)\n", "initial_func = np.zeros((2, initial_mesh.size))" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "HWtjtZQJ9wJi" }, "source": [ "Now we program the BVP solver. Convert the equation into first order system with Dirichlet boundary conditions.\n", "\\begin{align}\n", " \\tag{4}\n", " \\dfr{}{y} \\begin{pmatrix}\n", " \\phi \\\\\n", " \\phi'\n", " \\end{pmatrix} = \\begin{pmatrix}\n", " 0 & 1 \\\\\n", " K & 0\n", " \\end{pmatrix} \\begin{pmatrix}\n", " \\phi \\\\\n", " \\phi'\n", " \\end{pmatrix} + \\begin{pmatrix}\n", " 0 \\\\\n", " -f\n", " \\end{pmatrix}.\n", "\\end{align}\n", "Then use `solve_bvp` function from `scipy` library." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "colab": {}, "colab_type": "code", "id": "gc7VT9u4gYtU" }, "outputs": [], "source": [ "EPSILON = 1e-10\n", "\n", "def BVP_solver(K, f):\n", " fun = lambda y, phi: np.vstack((phi[1], K(y) * phi[0] - f(y)))\n", " bc = lambda ya, yb: np.array([ya[0], yb[0]])\n", " sol = solve_bvp(fun, bc, initial_mesh, initial_func, tol=EPSILON).sol\n", " sol.c = sol.c[:,:,0] # sol = (phi, phi') is an interpolation polynomial, and sol.c is a tensor of coefficients. This takes the first argument phi.\n", " \n", " return sol" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "pUF5XcUQjWtk" }, "source": [ "Let's try a test run." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 300 }, "colab_type": "code", "id": "_mtgMjIHjWtk", "outputId": "f946bd10-0be8-40f5-f3bc-219e6f48ac06" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 26.5 ms, sys: 5.32 ms, total: 31.8 ms\n", "Wall time: 30.5 ms\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%%time\n", "\n", "def graph(fun):\n", " y_plot = np.linspace(-pi / 2, pi / 2, 100)\n", " phi_plot = [fun(y) for y in y_plot]\n", " plt.plot(y_plot, phi_plot)\n", " \n", "test_f = lambda _: 1\n", "test_K = lambda _: 0\n", "test_sol = BVP_solver(test_K, test_f)\n", "graph(test_sol)" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "4lvXeEOnjWtl" }, "source": [ "## Iteration" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "9lYLzkZJjWtm" }, "source": [ "Now we build the iteration. We need to realize several functions. First, the $L^2$ norm of a function can be approximated by" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "colab": {}, "colab_type": "code", "id": "rIKuF39UjWtm" }, "outputs": [], "source": [ "def L2_norm(phi):\n", " y_sample = np.linspace(-pi / 2, pi / 2, 100)\n", " phi_sample = [phi(y) for y in y_sample]\n", " if phi_sample[31] > 0:\n", " sign = 1\n", " else:\n", " sign = -1\n", " return norm(phi_sample) * sqrt(pi / 100) * sign" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "nGyrR1mcjWtn" }, "source": [ "Let's try a test run." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 52 }, "colab_type": "code", "id": "si5yZNpPjWtn", "outputId": "70c766a2-a1b4-4991-fc21-94fddf182aa5" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.9952021753076212\n", "1.9558236269704938\n" ] } ], "source": [ "print(L2_norm(lambda y: pow(y, 2)))\n", "print(np.math.sqrt(np.math.pow(pi, 5) / 80))" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "mqHfLSdujWtp" }, "source": [ "We now realize algorithm (3). Function `eigen` takes three arguments, which are multiplier $K$, initial guess $\\mu _0$ and $f _0$. It returns a tuple, (eigenvalue, eigenfunction, number of iteration)." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "colab": {}, "colab_type": "code", "id": "ga07EVlvjWtp" }, "outputs": [], "source": [ "MAX_ITERATION = 100\n", "\n", "def eigen(K, mu_0 = -3, f = exp):\n", " K_mu_0 = lambda y: K(y) - mu_0\n", " old_mu = np.inf\n", " i = 0\n", " for i in range(MAX_ITERATION):\n", " phi = BVP_solver(K_mu_0, f)\n", " mu_k = L2_norm(f) / L2_norm(phi)\n", " f = phi\n", " f.c = f.c / L2_norm(phi) # phi is an interpolation polynomial, so we scale the coefficient matrix c.\n", " if abs(mu_k - old_mu) < EPSILON:\n", " break\n", " old_mu = mu_k\n", " return (mu_k + mu_0, f, i)" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "XGD8_v5hjWtr" }, "source": [ "Let's do a test run to confirm the accuracy is satisfactory." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 69 }, "colab_type": "code", "id": "9gkQBOcAjWtr", "outputId": "9e07724b-0a38-4a52-a259-d47ee5999501" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(4.000000000018323, , 10)\n", "CPU times: user 220 ms, sys: 4.08 ms, total: 224 ms\n", "Wall time: 223 ms\n" ] } ], "source": [ "%%time\n", "\n", "test_K = lambda _: 0\n", "test_mu_0 = 5\n", "test_f_0 = exp\n", "print(eigen(test_K, test_mu_0, test_f_0))" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "H13o7yKHjWts" }, "source": [ "# Reighley-Kuo Equation" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "DliIDIX2j9ip" }, "source": [ "## Setup of the Equation" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "15s-_UYhkAQa" }, "source": [ "We want to find the smallest eigenvalue to the Strum-Liouville System with Dirichlet Boundary condition\n", "$$\n", "-\\phi''-\\frac{\\beta - U''}{U - c}\\phi = \\lambda \\phi, \\qquad \\phi \\pth{\\pm\\frac\\pi2} = 0.\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "eGxA_XMM5dS0" }, "source": [ "In our case, \n", "$$U(y) = \\cos ^2 (y), \\qquad U''(y) = 2 - 4 \\cos ^2 (y).$$" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "colab": {}, "colab_type": "code", "id": "t_zHVfrbkDuX" }, "outputs": [], "source": [ "U = lambda y: cos(y) * cos(y)\n", "Upp = lambda y: 2 - 4 * U(y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Comparing to the model in our article, the domain is rescaled from $[-1, 1]$ to $[-\\pi/2, \\pi/2]$, for computational simplicity. Therefore, some results here differ from the article by a factor of $\\pi/2$ or $\\pi^2/4$." ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "6owZZUN0u5Ql" }, "source": [ "We first define the coefficient function\n", "$$\n", "K_{\\beta,c}(y) = -\\frac{\\beta - U''(y)}{U(y) - c}.\n", "$$" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "colab": {}, "colab_type": "code", "id": "8Hfomk5N5O3m" }, "outputs": [], "source": [ "def K(beta, c):\n", " return lambda y: -(beta - Upp(y)) / (U(y) - c)" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "L_XNtJNPjWtu" }, "source": [ "Let's find the eigenvalue of the case $\\beta = -1.8$, $c = 1.1$ for exammple." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 317 }, "colab_type": "code", "id": "6eYdebb9jWtv", "outputId": "5d43c16f-4ee5-476b-c64f-29b3d36e9f07" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(-0.5288820708571951, , 14)\n", "CPU times: user 344 ms, sys: 3.56 ms, total: 348 ms\n", "Wall time: 346 ms\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%%time\n", "\n", "test_sol = eigen(K(-1.8,1.1), mu_0=0)\n", "print(test_sol)\n", "graph(test_sol[1])" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "0eoJtHkAjWtw" }, "source": [ "Now we define $\\lambda _1 (\\beta, c)$ to be the principal eigenvalue of $K _{\\beta, c}$. Because the eigenvalues are greater than $-3$, we can use default $\\mu _0 = -3$ to find smallest eigenvalue." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "colab": {}, "colab_type": "code", "id": "VeZGYtM7jWtw" }, "outputs": [], "source": [ "def lambda1(beta, c, mu_0 = -3, f = exp):\n", " res = eigen(K(beta, c), mu_0, f)\n", " if res[2] < MAX_ITERATION - 1:\n", " return (res[0], res[1])\n", " else:\n", " res = eigen(K(beta, c), mu_0 * 1.01, f)\n", " if res[2] < MAX_ITERATION - 1:\n", " return (res[0], res[1])\n", " else:\n", " return (np.nan, exp)" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "Px5Xnfbujxd-" }, "source": [ "A test run." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 34 }, "colab_type": "code", "id": "ysPsT1Vab2cG", "outputId": "a902f9b4-c05f-4167-da12-743a50a7cc9b" }, "outputs": [ { "data": { "text/plain": [ "(-0.5385420390101288, )" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lambda1(-3, 2, mu_0=-2)" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "btjiSvrAjz4i" }, "source": [ "## Eigenvalue Plot" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "ivuJzxaXjtBt" }, "source": [ "We want to compute the eigenvalue and eigenvector for $\\beta \\in (\\beta _1, \\beta _2)$ and $c \\in (c _1, c _2)$. The following function will take arguments `beta_sample` and `c_sample`, then return the eigenvalue and eigenfunction matrix, and does a contourplot of eigenvalues. The idea is the following. Because when the system is regular, the eigenvalues are analytic in $\\beta$ and $c$, so once we found the eigenvalue and eigenfunction at one grid, we can use them as initial guess for the eigenvalues nearby, which can speed up the computation. In the following, we use a linear combinition of the previous two eigenvalues. \n" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "sBkqrsAim0YC" }, "source": [ "Linear extrapolation: $y _0 = f (x _0)$, $y _1 = f(x _1)$, so\n", "$$\n", " y _2 = \\frac{y _1 - y _0}{x _1 - x _0} (x _2 - x _1) + y _1 = \\frac{x _2 - x _1}{x _0 - x _1} y _0 + \\frac{x _2 - x _0}{x _1 - x _0} y _1 := a _0 y _0 + a _1 y _1.\n", "$$" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "colab": {}, "colab_type": "code", "id": "WGY1PtE9oaDn" }, "outputs": [], "source": [ "def linearExtrapolate(x0, x1, x2, y0, y1):\n", " a0 = (x2 - x1) / (x0 - x1)\n", " a1 = (x2 - x0) / (x1 - x0)\n", " return a0 * y0 + a1 * y1" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "# This is a library that enable it to show a progress bar for our long calculation. \n", "# Each of the calculateEigen procedure takes about one hour in my case.\n", "\n", "try:\n", " import progressbar\n", "except:\n", " from pip._internal import main as pipmain\n", " pipmain(['install', 'progressbar2'])\n", " import progressbar" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "colab": {}, "colab_type": "code", "id": "-aKRd8KLhjC7" }, "outputs": [], "source": [ "def calculateEigen(beta_sample, c_sample, mu_0 = -3, f = exp):\n", "\n", " beta_size = len(beta_sample)\n", " c_size = len(c_sample)\n", " evMat = np.full((beta_size, c_size), np.nan)\n", " efMat = np.full((beta_size, c_size), exp)\n", "\n", " for i in progressbar.progressbar(range(beta_size)):\n", " beta = beta_sample[i]\n", " for j in range(c_size):\n", " c = c_sample[j]\n", " if i == 0:\n", " if j == 0:\n", " (evMat[i, j], efMat[i, j]) = lambda1(beta, c, mu_0, f)\n", " elif j == 1:\n", " (evMat[i, j], efMat[i, j]) = lambda1(beta, c, evMat[i, j - 1], efMat[i, j - 1])\n", " else:\n", " evTest = linearExtrapolate(c_sample[j - 2], c_sample[j - 1], c_sample[j], evMat[i, j - 2], evMat[i, j - 1])\n", " (evMat[i, j], efMat[i, j]) = lambda1(beta, c, evTest, efMat[i, j - 1])\n", " elif i == 1:\n", " (evMat[i, j], efMat[i, j]) = lambda1(beta, c, evMat[i - 1, j], efMat[i - 1, j])\n", " else:\n", " evTest = linearExtrapolate(beta_sample[i - 2], beta_sample[i - 1], beta_sample[i], evMat[i - 2, j], evMat[i - 1, j])\n", " (evMat[i, j], efMat[i, j]) = lambda1(beta, c, evTest, efMat[i - 1, j])\n", " if np.isnan(evMat[i, j]):\n", " (evMat[i, j], efMat[i, j]) = lambda1(beta, c, evTest * 1.01, efMat[i, j - 1])\n", " \n", " betaMat, cMat = np.meshgrid(beta_sample, c_sample)\n", " return (betaMat, cMat, evMat, efMat)\n", "\n", "def eigenPlot(result, minEigen = np.nan, maxEigen = np.nan, level_increment = 1, figure_size=(12, 6), label=False):\n", " plt.figure(figsize=figure_size)\n", " if np.isnan(minEigen):\n", " minEigen = floor(np.array(result[2]).min() / level_increment) * level_increment\n", " if np.isnan(maxEigen):\n", " maxEigen = ceil(np.array(result[2]).max() / level_increment) * level_increment\n", " number_of_levels = int(round((maxEigen - minEigen) / level_increment + 1))\n", " CS = plt.contour(result[0], result[1], result[2].T, levels = np.linspace(minEigen, maxEigen, number_of_levels), manual=label)\n", " plt.clabel(CS, inline=1, fontsize=10, colors='k')" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "ANSkHvPytWJl" }, "source": [ "Now draw the eigenvalue in the region $-3 < \\beta < 3$, $1 < c < 2$. Since as $c \\to 1 ^+$, the system becomes singular, we need to add more sample grids near $c = 1$. Here we use exponential." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 400 }, "colab_type": "code", "id": "SeBjOER9lTCp", "outputId": "93537843-2854-4908-9819-f1f306abd3d3", "scrolled": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100% (601 of 601) |######################| Elapsed Time: 1:25:01 Time: 1:25:01\n", "/Users/jincheng/opt/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:38: UserWarning: The following kwargs were not used by contour: 'manual'\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "beta_sample = np.linspace(-3, 3, 601)\n", "c_sample = [1 + exp(-0.08 * x) for x in range(100)]\n", "res1 = calculateEigen(beta_sample, c_sample)\n", "eigenPlot(res1, minEigen = -3, maxEigen = 10)" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "uNG-iOM4uzlL" }, "source": [ "For the region $-3 < \\beta < 3$, $-1 < c < 0$, again because as $c \\to 0 ^-$, the system becomes singular, we use exponential samples." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 385 }, "colab_type": "code", "id": "72Bf2lgMvBc0", "outputId": "cce667ce-8541-46ac-e599-a7dfe025ce75", "scrolled": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100% (601 of 601) |######################| Elapsed Time: 1:25:11 Time: 1:25:11\n", "/Users/jincheng/opt/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:38: UserWarning: The following kwargs were not used by contour: 'manual'\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "beta_sample = np.linspace(-3, 3, 601)\n", "c_sample = [-exp(-0.08 * x) for x in range(100)]\n", "res0 = calculateEigen(beta_sample, c_sample)\n", "eigenPlot(res0, minEigen = -3, maxEigen = 10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can patch them together by doing a transform $\\tilde c = \\frac1{c - 1/2}$. In this way we may have a better view of the shape of the eigenvalues." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100% (601 of 601) |######################| Elapsed Time: 1:25:02 Time: 1:25:02\n", "100% (601 of 601) |######################| Elapsed Time: 1:22:29 Time: 1:22:29\n" ] } ], "source": [ "beta_sample = np.linspace(-3, 3, 601)\n", "c_tilde_sample_negative = [-2 + 2 * exp(-0.08 * x) for x in range(1, 100)]\n", "c_tilde_sample_positive = [2 - 2 * exp(-0.08 * x) for x in range(1, 100)]\n", "c_sample_negative = [1/2 + 1 / x for x in c_tilde_sample_negative]\n", "c_sample_positive = [1/2 + 1 / x for x in c_tilde_sample_positive]\n", "restilde_negative = calculateEigen(beta_sample, c_sample_negative, mu_0 = -1)\n", "restilde_positive = calculateEigen(beta_sample, c_sample_positive, mu_0 = -1)\n", "c_tilde_sample_negative.reverse()\n", "c_tilde_sample = c_tilde_sample_negative + c_tilde_sample_positive\n", "restilde_neg = restilde_negative[2].T.tolist()\n", "restilde_neg.reverse()\n", "restilde_pos = restilde_positive[2].T.tolist()\n", "res_mat = restilde_neg + restilde_pos\n", "bMat, cMat = np.meshgrid(beta_sample, c_tilde_sample)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(12, 6))\n", "CS = plt.contour(bMat, cMat, res_mat, levels = range(-4, 8))\n", "plt.clabel(CS, inline=1, fontsize=10, colors='k')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Apparently there is a saddle point at $(-1, 0)$ that python contourplot cannot draw numerically. This corresponds to the system at $\\beta = -1$, $c = \\infty$. Since in general" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\frac{\\partial \\lambda _1}{\\partial \\tilde c} \n", "= \\frac{\\partial \\lambda _1}{\\partial c} \\frac{\\d c}{\\d \\tilde c}\n", "= - \\int _{-\\frac\\pi2} ^{\\frac\\pi2} \\frac{\\beta - U''}{(U - c) ^2} |\\phi| ^2 \\d y \n", "\\cdot \\left(-\\frac1{(c - 1/2)^2}\\right) ^{-1}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here $\\phi$ is the corresponding normalized eigenfunction. See equation (3.18) of the article for derivation. When $c \\to \\infty$, $\\tilde c \\to 0$, $\\phi \\to C \\cos (y)$, $\\lambda _1 \\to 1$. Therefore the above partial derivative vanishes at $\\beta$ that" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\int _{-\\frac\\pi2} ^{\\frac\\pi2} (\\beta - U'') \\cos ^2 (y) \\d y = 0.\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With $U'' = 2 - 4 \\cos (y) ^2$, one easily concludes the saddle point is $\\beta = -1$." ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "q_Drv8sfvlHR" }, "source": [ "To take a closer look at $c = 0$, we test $\\beta \\in (0.392, 0.408)$, $\\beta \\in (0.992, 1.008)$, and $\\beta \\in (1.592, 1.608)$." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 228 }, "colab_type": "code", "id": "rZbHpuRnv8Kw", "outputId": "f62f76d9-a555-4080-b6c1-3cf4374c5de0" }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100% (400 of 400) |######################| Elapsed Time: 0:47:54 Time: 0:47:54\n", "/Users/jincheng/opt/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:38: UserWarning: The following kwargs were not used by contour: 'manual'\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "beta_sample = np.linspace(0.392, 0.408, 400)\n", "c_sample = [-0.005 * exp(-0.08 * x) for x in range(100)]\n", "res04 = calculateEigen(beta_sample, c_sample, mu_0 = -0.5)\n", "eigenPlot(res04, level_increment = 0.004, figure_size = (10, 3))" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100% (400 of 400) |######################| Elapsed Time: 0:43:03 Time: 0:43:03\n", "/Users/jincheng/opt/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:38: UserWarning: The following kwargs were not used by contour: 'manual'\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "beta_sample = np.linspace(0.992, 1.008, 400)\n", "c_sample = [-0.005 * exp(-0.08 * x) for x in range(100)]\n", "res10 = calculateEigen(beta_sample, c_sample, mu_0 = -1.2)\n", "eigenPlot(res10, level_increment = 0.004, figure_size = (10, 3))" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 34 }, "colab_type": "code", "id": "hRZMwcxixN4J", "outputId": "5db3534c-f1ee-42d2-e3b8-fb2445938e51" }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100% (400 of 400) |######################| Elapsed Time: 0:42:50 Time: 0:42:50\n", "/Users/jincheng/opt/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:38: UserWarning: The following kwargs were not used by contour: 'manual'\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "beta_sample = np.linspace(1.592, 1.608, 400)\n", "c_sample = [-0.005 * exp(-0.08 * x) for x in range(100)]\n", "res16 = calculateEigen(beta_sample, c_sample, mu_0 = -2.0)\n", "eigenPlot(res16, level_increment = 0.004, figure_size = (10, 3))" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "Xb7UhkMikGBz" }, "source": [ "# Instability Boundary" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "fkjDnMECX9zo" }, "source": [ "## Rough Graph" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "FkXGkIxakXBB" }, "source": [ "For each $\\beta \\in (-2, 2)$, we need to find $c$ that minimize $\\lambda _1 (\\beta, c)$. The negative part of the minimum will be denoted by $\\Lambda _\\beta$. " ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "colab": {}, "colab_type": "code", "id": "-RYEh5U6kJl9" }, "outputs": [], "source": [ "beta_sample = np.linspace(-3, 3, 601)\n", "Lambda0 = [min(res0[2][i, :]) for i in range(len(beta_sample))]\n", "Lambda1 = [min(res1[2][i, :]) for i in range(len(beta_sample))]\n", "Lambda_Min = [min(Lambda0[i], Lambda1[i]) for i in range(len(beta_sample))]\n", "Lambda_beta = [max(-Lambda_Min[i], 0) for i in range(len(beta_sample))]" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 282 }, "colab_type": "code", "id": "aSYFja1vTBbs", "outputId": "f20cd786-672a-4a7b-ec15-9b8617795e27" }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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76ibwdNlvb7e35cQW3tzwJkmZSbSv0Z4XbnyBusF1zS7LZbnUd/q+EznkF5fSpEYQXp4eNA5tzO5Tu80uSzhK1hHrSJMLJuiExBibDscOMoYMesjYYmd2Mv8kE+InMPfAXKoHVGdCtwn0iuolbZRycqkg/2z1Qb7bdAg/b09a1q6CR2g0u/Nmczwni+qBctPKLZ3bhCFhDhzZbDx2boJOk0EQ0VQm6LiAEksJ3yZ+y0fbPqKwtJARzUbw92Z/lzaKjbhUkI+9uSEd61djc2om8amnSUqsgm/tUjpN+oL6ga1pEx1CXEwIcdGhRIb4yU95V6Q1pCecn115YpfxeI2W0PNfxpV3NemluZL44/G8ufFN9mXuo2Otjjzf9nligmPMLsutKK3LtezJdYmLi9Px8fHlPk56bha9fuxCi8DbIbMvW9POkFtYAkBEkA9tokNoEx1KXHQITWoG4e0pv3Y7Ja3h6JbzbZNT+wFl7FcZO9B4k00YXE56XjoTNk9g/oH51AyoybPtnqVH7R5ygVUOSqnNWuu4ix93qSvyi4VXDqZJ1Vg8vQ7y5e03UmrRJB3PYXPqaeJTM4lPyWTBzuMA+Hl70qJ2MHHRocTFhNA6OoQgX1mtzjSWUji0wbhZmTAXsg+D8jR2im//mDG7MrC62VWK61BsKeabhG/4aNtHlFhKeKT5Izzc7GH8vPzMLs1tuXSQA7SJaMN3id9RWFqIj6cPTWoG0aRmEA/cFAPAsax8oxWTYrRjPl6RTOnvGqWgUUSgtGMcqbQYDq48v4PO2XTw9DHW7+7+IjTqB/6yobYrW39sPW9veJvkrGS6RHbh+bbPy6QeB3D5II+LiOOrPV+xI2MHbau3/cvnawT7MaC5HwOa1wTgbGEJ2w6d+SPYZ287yswNxiYV4YE+xMVIO8amivOtsyvnWHfQyQLvAGNWZexAaNAbfALNrlKU06GcQ7y76V2WHVpGZOVIPujxAd1qdzO7rArD5YO8bfW2eCkvVh9Zfckgv1iAjxcd61ejY31jXY1rbce0iQmhdVQIwX7SjrmqwhzrDjpzjdmV53bQadTfuFlZrzt4y6/Z7iCvOI/pO6czY/cMPD08eaL1EwxtMlSWzXAwl77Zec7Dix4mszCTnwZdck+LMjueVUB86mniUzLZnJrJnmPZlFqMdkzD8EDaxIQQF220Y2qHSjsGgLzTxuzKPXOMPSxLCyEgDBoPMK6863SRHXTcyLmdeiZtnkR6fjoD6w7kyTZPEu4vm0vbk1ve7Dync63OvLf5PY6fPU71gPLfIKse7MuA5jX/1I7ZfuiMccWemsncbUf5xtqOCQv0IS46xNprD+WGitSOyTlhrCSYMBdSVhmzK4MijaVgmwyC2jfKDjpuaPfJ3by18S22Z2ynadWmTOg+gRZhLcwuq0JzjyCPNIJ81ZFV3NXwLpsfP8DHiw71q9HhgnbM3hM5xKdmsjnFaMks3GW0Y3y9PWhZu4r7tmPOHDo/QSdtPaAhtC7c9LgR3jVbywQdN3Uy/ySTt0xm9v7ZhPqG8lrH1xhUb5Ds1OME3KK1orWm7499aRjSkA96fmCz45aFW7djTu6HhNl/3v4soql1jPcgCI+V8HZjxaXFzEyYydQdUyksLeSB2AcY2XwklStVNru0CsetWytKKbrV7sYPe3/gbPFZArwDHF6DW7VjtDZmVCbMNXreGQnG47XaQK9XjQCvWs/cGoVDrDy8knc2vUNqdipdI7vydNzTMivTCblFkAP0junNN4nfsPLwSvrV6Wd2OWVux7SIrPLHePbWUSEE+zu4HWOxWGdXzjHCO/Ogsf1ZVAfo+1+IHSDbn1UgB7MO8s6md1h9ZDUxQTF83OtjOtXqZHZZ4jLcorUCYNEWev1fL1qEtWBi94k2Pba9nMgu+GM8++bUTHYfNdoxAA0jKv8xnj0uJoSoUH/bt2MspZC69vzGw9lHwMPLWL+7ySBodAtUDrPtOYVTyynKYer2qXyT8A2+Xr6MajGKIY2H4C0jjpyCW7dWADyUB72ie/HTvp/IK85ziVXVIoJ8uaV5DW5pXgOAvKILJytlMm/7Ub7deL4d0ybKOgu1PO2YkiLr7MrZkLgA8k6Cl6+x/VnPf0HDPuAXYssvU7iAEksJP+37iSnbppBZkMntDW5nTKsxsmO9i3CbIAfoHd2bbxO/ZdmhZQyoO8DscsrMv5IXHepVo0O9y7djft19He2YojxIXmrdu/JXKMyCSpWN0I4dZIS4j9y4qqjWHl3L+E3j2X9mP63DW/NRr4+4oeoNZpclysAmrRWl1OfAACBda930as+3R2sFjPZK/5/6UzuwNp/2/tTmx3cG19qOaVvTi9oZq1AJc4ztz4rzjCvtRrcYNyvrdgNvX1O/FmGug1kHeS/+PVYcXkGtyrV4Ku4p2eTBydm7tfIl8CHwlY2Od108lAeD6g1i6vapHMs9Ro3KNcwsxy4u147ZnJJJwoFUvHbMpMrW9UR47ESpErI8QzlS/Ra8m91KdKubqeTjY/JXIMyWVZjFx9s/ZlbiLHy8fBjbZiz3xd6Hj6d8b7gqmwS51nqlUirGFscqr8H1B/Px9o+ZnTybUS1GmV2O3fkXZNDh1Dw6HJ4LR1cDpRQHR7Kv2hCW6Hb8kF6DtORCSAafectoUbvKHzdQ20SFOn50jDBNsaWYWYmz+Hj7x+QW53JHgzsY3XK09MHdgM1GrViDfN7lWitKqZHASICoqKg2qampNjnvpfx90d85nHuYBbcvcM9ZZ5kp5zdhOLQR0FC1gTHSJHYQ1Gjxpwk6V2rHNAiv/KcVH6Or2mF0jDCV1poVh1fwXvx7pGSncFONm3i67dM0DGlodmmijC7XWnFYkF/IXj3yc+Ymz+XF1S/yeZ/Pr2lFRJdw+iDs/gn2zIZj243Hqjc3gjt2IIQ3vuZDXdiOiU/NZEtaJjkFxs5K1Sr70Ca6yh8bcDSrFYyXM01WEmWSdDqJ8fHj2XBsAzFBMTzT9hk61+osP6xdlNsPP7xQr+hevLnhTX7Y+4NrB3luOmz/zgjwc1PjI9vCza8Z4R1a57oOe/HoGItFszc954/lBeJTT7No9wkAgv286dYojB6Nw+nWMFxaMS7iZP5JPtz6IT/v/5nK3pV5vt3z3N3obrw95N/PHbllkPt5+TG4/mBmJc3i6bynCfN3oUktWsPhTbBxGuz+BSzFULOVEd433GqXvSs9PBSNqwfRuHoQ97ePBiA9u4CNKaf5PTGD35PSmb3tKJ4einYxoQxsUZP+zapTxV/WnHY2haWF/G/P//h056cUlhQypPEQRrUYRbBPsNmlCTuy1fDDb4FuQDXgBPCK1vqzyz3f3q0VgLTsNAb8PIBHWjzC6Jaj7Xoum9AaDq6A5W9D2jrwCYKWQyDuYQgzt5dZatFsP3yGpQknWLjrOAcyzuLtqejaMJzBLWvSKzYCv0qyXK2ZtNYsTl3MxM0TOZJ7hG6R3RgXN446wdf3W5twTnbvkZeFI4IcYPTS0ew6uYvf7vzNuXcsSV0HS/4Nh9ZDYE3o9CS0vM8pJ+lordl9NJs5248yZ9tRjmcXEOjrxe2tanHvjVE0rh5kdokVzu6Tu3ln0ztsSd9Cg5AGPNv2WdrXaG92WcIOKmSQrz26lkd+e4Q3Or3BoHqD7H6+Mss6DL/9C3b9CIE1oPNT0OoBl5moY7Fo1h88xfebDrFg13GKSiy0iqrCve2iGNC8Bv6V3LJz5zSO5h7l/a3vM//AfEJ9QxnTagy31b8NT9nMw21VyCDXWnPr7Fvx8fRh1oBZznOnvrQE1n0Ay/8LaOjwD+MqvJLjl9+1lcyzRfy09Qjfbkxjf3ougb5e3NsuimEdYqhVRfbntKXsomym75zOzD0zUUoxtMlQhjcdLuuDVwAVMsgBftr3E6+sfcV5luE8sRt+eQyObTP2s+zzJoREm12VzWit2ZSSyYx1KfxqXaa3b9PqDO9YhzbRshhXeRSXFvP93u+Zun0qWYVZDKw3kDGtxthke0PhGipskBeXFtP/5/7UCKjBjL4zzLsqt1hgzST4/U1jR/lb3oUmt7r1zjpHzuTz1doUvtmYRk5BCS1rV+HhTnXo36wGnh7u+3XbmtaaZWnLmLhlIqnZqdxY/UbGxY2jSdUmZpcmHKzCBjnAt4nf8uaGN82bIJSbDj8/Yuwu32Qw3DIBAqo5vg6TnC0s4ccth/l89UFSTuURU9WfUV3rcVvrWvh4ST/3SnZk7ODd+HfZmr6VesH1GBc3Tib0VGAVOsgLSgro+2NfGoQ0cPyqiAdXwY8PQ0EW9H0b2jzo1lfhV2KxaBbvOcGU3/ez80gW1YN8GdGlLve2qy03Ri9yKOcQ7295n19TfqWqb1VGtxrNbfVvw8tDXqeKrEIHOcCXu77kvc3v8VW/r2gV3sr+J9QaNk2Hhc8Z+1ve9SVEyBrPYLQKVu07yZTf97Ph4GlC/L0Z3rEOQzvEEOxXsWceZhVmMW3HNL5J/AYv5cWDTR/kwRseNGUfWuF8KnyQ5xXnccvPtxAVGMWXfb+076+mJUWw8FnY/AU06AN3TAdfGV99KfEpp5ny+35+T8qgso8XQ2+KZkTnuoQEOPG4fzsoKi3iu8Tv+GTHJ+QU5XBr/VsZ3XI0EQERZpcmnEiFD3KAWYmzeH3D60zpOYUukV3sc5KCbJh1vzFLs9NY6PEyyLjeq9p9NIuPfk9mwa5jBFTyYnjHGB7uVNft13Y5NyNz0uZJHM49TIeaHRjXZhyNQhuZXZpwQhLkGOsxD/5lMP5e/nw/8HvbL3GbcwJm3gnpe2DQB8YUe1EmScdzmLx0Lwt2HifQ14uHO9VheKc6BPm6X6BvTd/Ku/HvsiNjBw1CGvBUm6foWKuj2WUJJyZBbrXgwAKeW/Ucb3V+y7b7ep5Khv/dboxQuftraNDLdseugPYczWby0r0s2n2CIF8vRnSuy4MdYwh0g0BPy05j0pZJ/Jb6G2F+YYxpNYZB9QbJjExxVRLkVhZt4d7593Iq/xRzbp2Dv7d/+Q96ch98OQBKi+C+/4PIv7zO4jrtOpLFpCX7WJJwgir+3ozoXJdhHWKo7ON6ozcyCzL5ZMcnzEqchbenNw81fYhhTYbZ5ntQVAgS5BfYmr6VoQuHMqrFqPKvjJixF2YMBF0Kw+ZCeKxtihR/suPwGSYt2ceyxHRCAyrxWLd63N8+Gl9v57+KLSgpYGbCTD7b+RlnS85ye4PbGd1yNNX8Ks5cAmEbEuQXeXblsyxLW8acW+dQs3LN6ztIxl6YMcAYajhsbpl26RHXZ2taJu8uTmLN/lPUDPbliV4NuKN1pFPuYlRqKWVO8hymbJvCibwTdInswtjWY6kfUt/s0oSLkiC/yPGzxxn480A6R3ZmQrcJZT9AZip83gcspfDgPAiTUQaOtGb/Sd5ZlMT2Q2eoGxbAUzc3ol/T6ng4wdR/rTWrjqxi4uaJ7D+zn2bVmjG2zVjX3q1KOIXLBbnzXcY4SPWA6oxoPoLfUn9j+aHlZfvLuRnw9W1QnAdDZ0uIm6Bj/Wr88lgHpt7fBk+lGP3NFgZNWc3ypHTMuDg5Z2fGToYvGs7opaMpKi3i3a7vMrP/TAlxYVcV9oocjAW17p53N7nFufwy+Jdrmz1XmGPc2MxIgqG/QJQs4G+2Uovml61HmLhkL4cz82lXJ5Tn+jaiTXSow2pIy05j8pbJLE5dTKhvKKNajOLOhnfKHpnCpqS1chnb0rcxdOFQ7ou9j+faPXflJ5cUwsy7IGU13PstNOzjmCLFNSkqsfDdpjTeX7qfk7mF9GwcztN9GhFbw36zak/ln2Lq9qn8sPcHvD29GXbDMJlSL+xGgvwKXl//Ot8nfc/M/jNpFtbs0k/SGn4aCTu/h1unQst7HVukuGZ5RSV8sSaFT1Ykk1NYwqAWNRnbqyEx1WwXrnnFeczYM4Mvd31JYWkhdzS4g0dbPiojUYRdSZBfQU5RDoN/GUywTzCzBsy69P6eq96Dpf+BHv+ELs84vkhRZll5xUxdmcwXaw5SUqq5p21tnujVgPDA699Kr9hSzM/7fuajbR9xquAUvaJ68Y/W/5BNjoVDSJBfxYpDK3h82eM8dMNDjIsb9+dPJs6H71ce/mEAABieSURBVIZA0zuNBbAq6DK0rio9u4APlu3n241peHt6MKJzHUZ0qVumWaJaa5amLWXylsmkZKfQOrw1Y9uMpWV4SztWLsSfSZBfg1fXvcqPe3/k8z6fE1fd+lod3wWf9TZGpjy0ALxl/0lXlXLyLO8uTmLejmOEBlRiTI/6DLkx6qqbW2w5sYUJmyewPWM7dYPr8mTrJ+lWu5ts7iAczq5BrpTqC0wGPIHpWuu3r/R8Zw3yvOI87px7J6WWUn4c9COVLaXwSVcozoeRyyGohtklChvYcfgMby9MZG3yKWqH+vHUzY0Y1KLmX8agHzhzgIlbJrL80HLC/cJ5rOVjDK4/WDZ3EKaxW5ArpTyBvcDNwGFgE3Cv1nrP5f6OswY5GKNYhv06jAF1B/DGkTSjrfLgfIi+yezShA2d29zi7YWJ7DmWTZMaQTzXrzFdGlQjIz+Dj7Z9xM/7f8bfy5/hTYdzf5P78fOS38aEuS4X5La4tGgH7NdaH7Ce6DtgMHDZIHdmLcNb8vdmf2fajmkU554lomU/1Ml1cHKd2aUJO+jZEWLSc9lw8DQj5pZQI0ST670BC6UMaTyEkc1HEuIbYnaZQlyRLYK8FnDogj8fBm68+ElKqZHASICoqCgbnNZ+Hq3ajkNnJ7GpcjC5OXvRCUlmlyTsTAWDf6DmdCkUZ8bSoer93FO3MyG+Mh5cOD9bBPml7vj8pV+jtZ4GTAOjtWKD89pHYQ5eP43gHfzhoWXgJ1djFUlOQTGfrjzAp6sO0mv3Cu5tF8WYnvXLNWRRCHuzxVorh4HaF/w5Ejhqg+Oa49cX4Ewa3DZNQrwCCvT1ZlzvRqx4tht/a1ebbzam0W38cib8tpecgmKzyxPikmwR5JuABkqpOkqpSsDfgDk2OK7jJc6HrV9Dpyfl5mYFFx7oy+u3NuO3sV3o3iic95fuo9v45Xy55iBFJRazyxPiT8od5FrrEuBxYBGQAHyvtd5d3uM6XG4GzPkHRDSDbi+aXY1wEnXDKjPlvtb8MrojDSMC+ffcPfScsJzZ245gsThvh1BULDIh6Jzv7oN9i2HkCohoYnY1wglprVlpHbKYcCybG2oG8Xy/xnRuEGZ2aaKCkPXIryRhLiTOg24vSIiLy1JK0bVhGPPHdGLSPS3Jyi/mgc82ct/09ew8nGV2eaICkyvygmyY0g78qxqzNz1l/WhxbQpLSpm5Po0Plu0jM6+YQS1q8kyfRtQOlc2UhX3IFfnlLP0P5ByHge9LiIsy8fHyZHinOqx4tjuju9dj0e7j9HxvBW/M38OZvCKzyxMVSMUO8kMbYdN0uPERiGxjdjXCRQX5evNMn8Ysf6Ybg1vWZPrqg3Qdv5xPVx6gsKTU7PJEBVBxWyuWUvikC+RnwugN4BNobj3CbSQcy+bthYms2JtBZIgfz/RpxMDmf12US4iyktbKxbbMgBO7oM8bEuLCpmJrBDFjeDv+9/CNBPl688R32xg8ZQ1rk0+aXZpwUxUzyPMzYelrEN0RmtxqdjXCTXVqUI15Yzox4e4WnMotZMinGxj+5Sb2nsgxuzThZipmkK94xwjzvm/Lbj/Crjw8FLe3jmTZ0914vl9jNqWcpu+klTz/4w7SswvMLk+4iYoX5KeSYeM0aD0UajQ3uxpRQfh6ezKqaz1WPNOdYR1i+HHLYbpa13DJLSwxuzzh4ipekP/+BnhWgu4vmV2JqIBCAyrxysAbWDKuKz0an1/D5X/rUykplTVcxPWpWEF+bDvs+hHaPwaBEWZXIyqw6KoBTLmvNT8/1oE61fz55y+76D1pJYt3H8eMkWTCtVWsIF/6H2Np2o7/MLsSIQBoFRXC94/cxLQHjHkMI7/ezD3T1rPt0BmTKxOupOIEecoa2L8EOo0D32CzqxHiD0opet9QnUVPduG1W5tyICOXW6es4fFvtpB2Ks/s8oQLqDhBvvIdCAiHdiPMrkSIS/L29OCB9tEsf6Y7/+hRn6UJ6fScsJz/zJUp/+LKKkaQH9oEB5ZDhzHgLTuhC+dW2ceLcb0bsfyZbtzeKpIv1xpT/j9bLZtaiEurGEG+6l2jNx433OxKhLhmEUG+/PfO5ix4ojPNI4N5bd4eek9cwSK5ISou4v5BfmwH7P0V2o8Gn8pmVyNEmTWuHsRXw9vxxUNt8fL04BHrDVFZA12c4/5BvmYS+ARJb1y4NKUU3RuF8+sTnXnt1qYkp+cy8MPVjPt+G8ey8s0uT5jMvYM8+yjsmW3M4vSrYnY1QpSbl/WG6O/PdGNU13rM236M7u8uZ8LiJM7KDNEKy72DfNNnxnK1cjUu3EyQrzfP92vM0qe60is2gveX7afbu8v5ftMhSmVT6ArHfYO8uAA2fwGN+kNIjNnVCGEXtUP9+XBIa358tAORIX48++MOBnywmjX7ZcncisR9g3zn/0HeKWg/yuxKhLC7NtEh/PRoBz64txXZ+cXcN30DD3+5if3puWaXJhygXEGulLpLKbVbKWVRSv1l1wrTaA0bP4HwJhDT2exqhHAIpRQDW9Rk6VNdea5vYzYcPE2fSSt5ZfYuTp+VCUXurLxX5LuA24GVNqjFdo5tg+M7jXHjst64qGB8vT15tFs9lj/TjXvb1ebr9al0Hf8701Ymyx6ibqpcQa61TtBaJ9mqGJvZOhM8faDZnWZXIoRpqlX24fVbm/Hrk11oEx3CmwsS6TVhBQt2HpMJRW7GYT1ypdRIpVS8Uio+IyPDficqLjD647EDjNmcQlRwDSMC+fKhdnw1vB3+3l48NnMLd3+yTiYUuZGrBrlSaolSatcl3gaX5URa62la6zitdVxYWNj1V3w1SQug4Ay0vM9+5xDCBXVpGMaCJzrz5m3NOJBxlkFTVvPsD9tJz5Et51yd19WeoLXu5YhCbGbbTAiKhLrdzK5ECKfj6aEYcmMUA1rU4IOl+/hybQoLdh7n8R71eahjDD5enmaXKK6Dew0/zD4Kycug5b3gId+QQlxOkK83L93ShMVju9K+bihvL0yk98SVsiCXiyrv8MPblFKHgZuA+UqpRbYp6zrtmQ3aAs3vMbUMIVxFnWoBTB/Wlq+Gt6OSdUGu+z/bQNLxHLNLE2WgzPjpGxcXp+Pj421/4M/6QGEOPLbW9scWws0Vl1qYuT6ViUv2kVNQzH03RjP25oaEBlQyuzRhpZTarLX+y5wd92mtZB+FQ+vhhlvNrkQIl+Tt6cGDHeuw/OluPNA+mm82ptFt/O98seYgxaWyoYUzc58g3zPHeN9EglyI8ggJqMSrg5uy8InOtKhdhVfn7qHf5FUsT0o3uzRxGe4T5AlzISwWwhqaXYkQbqFhRCBfDW/H9KFxlJRaePCLTQz/chMHMmT9FmfjHkFekAVp66BRP7MrEcKtKKXo1SSCRWO78GL/xmw6eJreE1fy+rw9ZOUXm12esHKPIE9eBroUGvQ2uxIh3JKPlycju9Rj2dPduLNNJJ+tOUj3d5fzzYY0Wf/cCbhHkO/7DXyDIbKt2ZUI4dbCAn14+47mzH28E/XDK/PizzsZPGU1m1MzzS6tQnP9ILdYjCCv1xM8rzpRVQhhA01rBTNrZHs+uLcVJ3OKuOPjtTz1vUz3N4vrB/nxHXA2XdoqQjjYheufP9qtHnO2H6HHuyuYvuqADFd0MNcP8pTVxvu6Xc2tQ4gKKsDHi+f6NmbRk12Iiwnh9fkJ9J+8SrabcyDXD/LUtRBSB4Jqml2JEBVa3bDKfPFgW6YPjaOgpJT7pm/gsZmbOXIm3+zS3J5rB7nFAmlrIaaj2ZUIITg/XPG3sV0Zd3NDliWm0/O95Xy4bB8FxbI7kb24dpBnJEB+JkRLkAvhTHy9PflHzwYsGdeV7o3CeXfxXnpPXMnShBNml+aWXDvIU62LY0V3MLcOIcQlRYb48/H9bfjfwzdSycuDh2fE89AXGzl48qzZpbkVFw/yNcYmElWiza5ECHEFnRpUY+ETnfnnLbFsSsmkz8SVvPNrInlFJWaX5hZcO8iPbIbabUEpsysRQlyFt6cHf+9cl2VPdWVAixp8tDyZnu+tYKFsBl1urhvk+WfgTBpUb252JUKIMggP8mXC3S35YdRNVPGvxKMzt/DQl5tIPSXtluvlukF+fKfxvoYEuRCuKC4mlLmPd+TlAU3YdPA0N09cyeQlMrrlerhwkO8w3ssVuRAuy8vTg4c71WHpU93o3SSCiUv20m/yKlbuzTC7NJfiwkG+EypXh8rhZlcihCin6sG+fDikNV8/3A6AoZ9vZPQ3WzieJWu3XAvXDfJjO6B6M7OrEELYUOcGYfz6ZGeeurkhS/acoOd7y5m+6gAlsnbLFblmkBcXwMkk6Y8L4YZ8vDwZ07MBv43tSrs6obw+P4EBH6wmPuW02aU5LdcM8owEsJTIFbkQbiyqqj+fP9iWqfe3ITu/mDunruPZH7Zz+myR2aU5nXIFuVJqvFIqUSm1Qyn1s1Kqiq0Ku6KMJON9+A0OOZ0QwhxKKfo2rc5v47rySNe6/LTlCD3eW86sTWky9vwC5b0i/w1oqrVuDuwFXih/SdfgVDIoDwiJccjphBDmCvDx4oV+sSx4ojMNIwJ57sed/G3aepJlI2ignEGutV6stT43x3Y9EFn+kq7B6QMQXBu8KjnkdEII59AwIpDvRrTnv3c0I/F4Dv0mrWLykn0UllTssee27JEPBxZe7pNKqZFKqXilVHxGRjnHiJ5OhtC65TuGEMIleXgo7mkbxZJxXenbtDoTl+yl/+RVbDxYcW+GXjXIlVJLlFK7LvE2+ILnvASUADMvdxyt9TStdZzWOi4sLOz6K9YaTh2AqvWu/xhCCJcXFujD+/e24suH2lJYYuHuT9bxwk87ycovNrs0h7vqbsVa615X+rxSahgwAOipHXH3oeAMFGYZuwIJISq8bo3CWTy2C5OW7GP6qgMsSTjBKwObcEuzGqgKsqBeeUet9AWeAwZprfNsU9JVZB813svWbkIIK/9KXrzYP5Y5j3eiepAvj3+zlYdnxHM40zGxZLby9sg/BAKB35RS25RSU21Q05XlHDPeS5ALIS7StFYwPz/WgZcHNGH9gVP0nriSz1YfpNTi3kMVr9pauRKtdX1bFXLNsq1BHljd4acWQji/cwtx9bkhgn/N3s1r8/bwy9YjvHNnc2JrBJldnl243szOc1fkgTXMrUMI4dQiQ/z5bFgcHw5pxbGsfAZ9uJpJS/ZSVOJ+67a4ZpD7VwUvH7MrEUI4OaUUA5rXZPHYrtzSrAaTluxj0Ier2Xk4y+zSbMr1gjz7mFyNCyHKJDSgEpP+1orpQ+PIzCvi1o/W8N9fE91mEwvXC/KcY9IfF0Jcl15NIlg8tit3to7k4+XJ3PL+KjanZppdVrm5XpAXZoNfiNlVCCFcVLCfN/+9szlfDW9HQbGFO6eu5bV5e8gvct2rc9cL8qKzUCnA7CqEEC6uS8MwFo3twv03RvPZ6oP0nbySdcmnzC7rurhokFc2uwohhBuo7OPFa7c25buR7QG499P1/Gv2LvKKSq7yN52LawW5xWIEube/2ZUIIdxI+7pV+fWJLgzvWIev1qXSf7Jr9c5dK8hL8gEtrRUhhM35VfLkXwOb8M2IGyku1dw1dS3jFyW6xLhz1wryorPGewlyIYSddKhXjV+f7MwdrSOZ8nsyg6esIfF4ttllXZGLBbl1NxDpkQsh7CjQ15vxd7Xg06FxZOQUMOiDNUxdkey0a7a4WJDLFbkQwnFubhLBoie70KNxOG8vTOSeT9aReuqs2WX9hQS5EEJcQdXKPnx8f2sm3tOCpBM59Ju8im82ONfmzy4W5NJaEUI4nlKK21pFsujJLrSOCuHFn3cy6n+byTxbZHZpgMsFuVyRCyHMU7OKH18Nb8dL/WNZlphOv8mrnGISkQS5EEKUgYeHYkSXuvz0aEf8KnkyZPp6xi9KpLjUvGGKLhrk0loRQpirWWQw88Z04q42xjDFu6auI+2UOVvLuViQn+uRyxW5EMJ8AT5evHNnCz4c0orkjFz6v7+Kn7cedngdLhbkeYACbz+zKxFCiD8MaF6ThU90pnH1QMbO2s7T/7fdoaspuliQWxfMUsrsSoQQ4k8iQ/z5bmR7/tGjPj9uOcxtH60hOSPXIed2rSD39oPQGLOrEEKIS/Ly9GBc70Z88WBbTmQXMOiD1czbcdTu51XlGdSulHoNGAxYgHTgQa31VauOi4vT8fHx131eIYRwdkfP5PP4N1vYknaGYTdF8+Itsfh4eZbrmEqpzVrruIsfL+8V+XitdXOtdUtgHvCvch5PCCHcQs0qfsx65CYe7lSHGetSuXvqOg5n2mdUS7mCXGt94ZJgAYDzzFkVQgiTeXt68PKAJky9vw0HMs5yy/ur2XDA9hOIvMp7AKXUG8BQIAvoXu6KhBDCzfRtWp3YGoH885dd1A61/cY4V+2RK6WWAJfatv4lrfXsC573AuCrtX7lMscZCYwEiIqKapOamnrdRQshREV0uR55uW52XnSCaGC+1rrp1Z4rNzuFEKLs7HKzUynV4II/DgISy3M8IYQQZVfeHvnbSqlGGMMPU4FR5S9JCCFEWZQryLXWd9iqECGEENfHtWZ2CiGE+AsJciGEcHES5EII4eIkyIUQwsXZbBx5mU6qVAbGKJfrUQ04acNybEXqKjtnrU3qKhupq2zKU1e01jrs4gdNCfLyUErFX2pAvNmkrrJz1tqkrrKRusrGHnVJa0UIIVycBLkQQrg4VwzyaWYXcBlSV9k5a21SV9lIXWVj87pcrkcuhBDiz1zxilwIIcQFJMiFEMLFOX2QK6XGK6USlVI7lFI/K6WqXOZ5fZVSSUqp/Uqp5x1Q111Kqd1KKYtS6rJDiZRSKUqpnUqpbUopuy/CXoa6HPp6Wc8ZqpT6TSm1z/o+5DLPK7W+XtuUUnPsVMsVv36llI9Sapb18xuUUjH2qOM6a3tQKZVxwWv0dwfU9LlSKl0ptesyn1dKqfetNe9QSrW2d03XWFc3pVTWBa+VQ/YVVkrVVkr9rpRKsP5/fOISz7Hda6a1duo3oDfgZf34v8B/L/EcTyAZqAtUArYDTexcVyzQCFgOxF3heSlANQe+Xlety4zXy3red4DnrR8/f6l/S+vncu1cx1W/fuAxYKr1478Bsxz073cttT0IfOio7ynrObsArYFdl/l8f2AhoID2wAYnqasbMM+Rr5X1vDWA1taPA4G9l/h3tNlr5vRX5FrrxVrrEusf1wORl3haO2C/1vqA1roI+A4YbOe6ErTWSfY8x/W4xroc/npZDQZmWD+eAdzqgHNeyrV8/RfW+gPQUymlnKQ2h9NarwROX+Epg4GvtGE9UEUpVcMJ6jKF1vqY1nqL9eMcIAGoddHTbPaaOX2QX2Q4xk+wi9UCDl3w58P89UUziwYWK6U2W/ctdQZmvV4RWutjYHyjA+GXeZ6vUipeKbVeKWWPsL+Wr/+P51gvJLKAqnao5XpqA7jD+uv4D0qp2g6o62qc+f/gTUqp7UqphUqpGxx9cmtbrhWw4aJP2ew1K+8OQTZxLRs8K6VeAkqAmZc6xCUeK/e4ymvdePoqOmqtjyqlwoHflFKJ1qsIM+uyy+sFV66tDIeJsr5mdYFlSqmdWutkW9RndS1fv91eo6u4lvPOBb7VWhcqpUZh/ObQw+6VXZlZr9fVbMFYnyRXKdUf+AVocJW/YzNKqcrAj8CTWuvsiz99ib9yXa+ZUwS51rrXlT6vlBoGDAB6amtz6SKHgQuvSiKBo/au6xqPcdT6Pl0p9TPGr87lCnIb1GWX1wuuXJtS6oRSqobW+pj1V8j0yxzj3Gt2QCm1HONqxpZBfi1f/7nnHFZKeQHBOOZX+KvWprU+dcEfP8W4d2Q2u31PlceF4am1XqCU+kgpVU1rbffFtJRS3hghPlNr/dMlnmKz18zpWytKqb7Ac8AgrXXeZZ62CWiglKqjlKqEcXPKLqMdykIpFaCUCjz3McaN20veXXcws16vOcAw68fDgL/89qCUClFK+Vg/rgZ0BPbYuI5r+fovrPVOYNllLiJs7aq1XdRHHYTRfzXbHGCodSRGeyDrXBvNTEqp6ufubSil2mFk3qkr/y2bnFcBnwEJWusJl3ma7V4zR9/NvY67v/sx+kjbrG/nRhLUBBZcdAd4L8aV20sOqOs2jJ+ohcAJYNHFdWGMPNhufdvtLHWZ8XpZz1kVWArss74PtT4eB0y3ftwB2Gl9zXYCD9uplr98/cB/MC4YAHyB/7N+/20E6jriNbrG2t6yfj9tB34HGjugpm+BY0Cx9fvrYYzN1kdZP6+AKdaad3KFkVwOruvxC16r9UAHB9XVCaNNsuOC7Opvr9dMpugLIYSLc/rWihBCiCuTIBdCCBcnQS6EEC5OglwIIVycBLkQQrg4CXIhhHBxEuRCCOHi/h8uvS2qhwKT0gAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(beta_sample[100:500], Lambda0[100:500])\n", "plt.plot(beta_sample[100:500], Lambda1[100:500])\n", "plt.plot(beta_sample[100:500], Lambda_beta[100:500])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot for $\\alpha = \\sqrt{\\Lambda _\\beta}$." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "colab": {}, "colab_type": "code", "id": "WLxnjqkBXU0I" }, "outputs": [], "source": [ "alpha = [sqrt(Lambda_beta[i]) for i in range(len(beta_sample))]" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 282 }, "colab_type": "code", "id": "acmkwjzoXw8C", "outputId": "ba8a80f9-0874-4ecb-b5ef-3c5d3175c330" }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(beta_sample[100:500], alpha[100:500])" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "yNCgXk2VYBZ-" }, "source": [ "## Detailed Calculation" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "_wv0tm4WYM7M" }, "source": [ "For each $\\beta$, we will calculate $\\Lambda _\\beta$ with more accuracy now. We will use a simple optimization method. We first consider $\\beta \\in \\pth{-2, 0}$." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "def minimize(f, left, right, ev_left = np.nan, ev_right = np.nan):\n", " \n", " gamma = (sqrt(5) - 1) / 2\n", " if np.isnan(ev_left):\n", " ev_left = f(left)\n", " if np.isnan(ev_right):\n", " ev_right = f(right)\n", " center_left = right - (right - left) * gamma\n", " ev_center_left = f(center_left)\n", " center_right = left + (right - left) * gamma\n", " ev_center_right = f(center_right)\n", "\n", " while abs(right - left) > EPSILON:\n", " if ev_center_left < ev_center_right:\n", " (right, ev_right) = (center_right, ev_center_right)\n", " (center_right, ev_center_right) = (center_left, ev_center_left)\n", " center_left = right - (right - left) * gamma\n", " ev_center_left = f(center_left)\n", " else:\n", " (left, ev_left) = (center_left, ev_center_left)\n", " (center_left, ev_center_left) = (center_right, ev_center_right)\n", " center_right = left + (right - left) * gamma\n", " ev_center_right = f(center_right)\n", " \n", " final_point = [left, center_left, center_right, right]\n", " final_value = [ev_left, ev_center_left, ev_center_right, ev_right]\n", " j = np.argmin(final_value)\n", " return (final_point[j], final_value[j])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now use minimize function to refine `Lambda_Min` in $\\beta \\in (-2, 0)$ and $(0, 2)$ respectively." ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 249 }, "colab_type": "code", "id": "lRJuLnYYX1Qa", "outputId": "43a88dfb-8ba2-40b3-e570-ecef87dff1ef", "scrolled": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100% (40 of 40) |########################| Elapsed Time: 0:03:00 Time: 0:03:00\n" ] } ], "source": [ "c_star = np.zeros_like(beta_sample)\n", "c_sample = [1 + exp(-0.08 * x) for x in range(100)]\n", "\n", "for i in progressbar.progressbar(range(100, 140)):\n", "\n", " # find min element\n", " beta = beta_sample[i]\n", " j = np.argmin(res1[2][i, :])\n", " mu_0 = res1[2][i, j]\n", " phi = res1[3][i, j]\n", "\n", " if j == 0:\n", " j += 1\n", " if j == len(c_sample) - 1:\n", " j -= 1\n", " \n", " # use minimize function\n", " func = lambda c: lambda1(beta, c, mu_0, phi)[0]\n", " (c_star[i], Lambda_Min[i]) = minimize(func, c_sample[j - 1], c_sample[j + 1])" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100% (200 of 200) |######################| Elapsed Time: 0:19:07 Time: 0:19:07\n" ] } ], "source": [ "c_sample = [-exp(-0.08 * x) for x in range(100)]\n", "c_sample += [0]\n", "\n", "for i in progressbar.progressbar(range(300, 500)):\n", "\n", " # find min element\n", " beta = beta_sample[i]\n", " j = np.argmin(res0[2][i, :])\n", " mu_0 = res0[2][i, j]\n", " phi = res0[3][i, j]\n", "\n", " if j == 0:\n", " j += 1\n", " \n", " # use minimize function\n", " func = lambda c: lambda1(beta, c, mu_0, phi)[0]\n", " (c_star[i], Lambda_Min[i]) = minimize(func, c_sample[j - 1], c_sample[j + 1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Take a look at the plot of $c^*$." ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(beta_sample[100:140], c_star[100:140])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For $\\beta > 0$, $c ^*$ is small but not always zero." ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 285 }, "colab_type": "code", "id": "_C3Bdci9sffs", "outputId": "e24fe6a8-8572-4191-b7db-2640d03977b6" }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(beta_sample[300:], c_star[300:])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now compare the value of our results and the hypothesis of Kuo." ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 629 }, "colab_type": "code", "id": "heMTHrZ0shvD", "outputId": "d3a136a7-6308-48eb-ece8-0165818f440b", "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "Lambda_beta = [max(-Lambda_Min[i], 0) for i in range(len(beta_sample))]\n", "alpha = [sqrt(Lambda_beta[i]) for i in range(len(beta_sample))]\n", "plt.plot(beta_sample[100:500], alpha[100:500])\n", "\n", "hypothesis = np.zeros_like(beta_sample)\n", "for i in range(300, 500):\n", " hypothesis[i] = 2 * sqrt(1 - pow(sqrt(-beta_sample[i] / 4 + 9 / 16) + 1 / 4, 2))\n", "\n", "plt.plot(beta_sample[100:500], hypothesis[100:500])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The difference for $0 < \\beta < 2$ is the following." ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 164 }, "colab_type": "code", "id": "354FJHl3ss7e", "outputId": "0b83dbf6-eb6b-4cf1-b197-7d123fed0d9e" }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(beta_sample[300:500], alpha[300:500] - hypothesis[300:500])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calculate $\\beta _-$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The question to find $\\beta$ can be thought as the following general problem. For a continuous function $f = f(x, y)$, which is continuous in $(x, y)$, monotonously increasing in $x$, single-humped in $y$ (which means for a fixed $x$, $f (x, \\cdot)$ is monotone on both sides of the criticle point), we want to find" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "x _- = \\max\\left\\{x \\in [x _1, x _2]: \\min _{y \\in [y _1, y _2]} f(x, y) \\le 0\\right\\}. \n", "$$" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [], "source": [ "EPSILON = 1e-7\n", "\n", "def maxmin(f, x1, x2, y1, y2):\n", " \n", " # Initial x_step_size and y_step_size is a quarter the length\n", " x_step_size = (x2 - x1) / 4\n", " y_step_size = (y2 - y1) / 4\n", " \n", " bar_max_value = max(log(x_step_size / EPSILON * EPSILON), log(y_step_size / EPSILON))\n", " bar = progressbar.ProgressBar(max_value = bar_max_value)\n", " \n", " while y_step_size > EPSILON or x_step_size > EPSILON * EPSILON:\n", " \n", " # First, we take 5 sample on the left edge. Find the minimal one.\n", " y_list = np.linspace(y1, y2, 5)\n", " f_list = [f(x1, y_list[i]) for i in range(1, 4)]\n", " i = np.argmin(f_list)\n", " yc = y_list[i + 1]\n", " \n", " # Second, we go from (x1, yc) to right, until we cross the contour.\n", " # We quarter the x_step_size every iteration\n", " if x_step_size > EPSILON * EPSILON:\n", " x_step_size /= 4\n", " while (f(x1, yc) < 0):\n", " x1 += x_step_size\n", " \n", " x1 -= x_step_size\n", " \n", " # Finally, we shrink the y-window. Go from (x1, yc) up or down until we cross the contour.\n", " y_step_size = (y2 - y1) / 8\n", " y1 = yc\n", " y2 = yc\n", " while (f(x1, y1) < 0):\n", " y1 -= y_step_size\n", " while (f(x1, y2) < 0):\n", " y2 += y_step_size\n", " bar.update(bar_max_value - max(log(x_step_size / EPSILON * EPSILON), log(y_step_size / EPSILON), 0))\n", " \n", " return x1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's run a test. For $f(x, y) = \\sin x - 0.5 + y ^2 + e^{x+y}$, the maximum for a fixed $x$ is obtained when" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "0 = \\frac{\\partial f}{\\partial y} = 2y + e^{x + y}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Therefore this point should be" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([-0.19864597, -0.30282083])" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from scipy.optimize import fsolve\n", "\n", "func = lambda x: [np.sin(x[0]) - 0.5 + x[1] * x[1] + exp(x[0] + x[1]), 2 * x[1] + exp (x[0] + x[1])]\n", "fsolve(func, [0, 0])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our maxmin function gives" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "\r", "N/A% (0 of 15.424948470398375) | | Elapsed Time: 0:00:00 ETA: --:--:--" ] }, { "data": { "text/plain": [ "-0.19864596889513564" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "func = lambda x, y: np.sin(x) - 0.5 + y * y + exp(x + y)\n", "maxmin(func, -1, 1, -1, 1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's apply this function on our lambda1 function." ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100% (14.721750953984929 of 14.721750953984929) || Elapsed Time: 0:04:54 ETA: 00:00:00" ] } ], "source": [ "func = lambda b, c: lambda1(b, c, mu_0 = 0)[0]\n", "beta_minus = maxmin(func, -1.7, -1.5, 1.01, 2)" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-1.6489545393735134" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "beta_minus" ] } ], "metadata": { "colab": { "collapsed_sections": [], "name": "Sturm-Liouville Stystem 1108.ipynb", "provenance": [] }, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.4" } }, "nbformat": 4, "nbformat_minor": 1 }