{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "edd55666",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy\n",
    "from sympy import Symbol, Integer, Piecewise, Catalan, N, Min, Sum, lambdify, pi, sqrt, exp, log, acos, asin, besselk\n",
    "from fractions import Fraction\n",
    "import matplotlib.pyplot as plt\n",
    "import sys\n",
    "from IPython.display import display"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e52d53a",
   "metadata": {},
   "source": [
    "# Outline\n",
    "\n",
    "We follow the outline of the paper:\n",
    "\n",
    "  - In Section 3 we treat the truncated Coulomb case, giving details on the proof of Proposition 3.8 and the code to produce Figure 1.\n",
    "  - In Section 4 we treat the Yukawa case, detailing the proof of Lemma 4.6 and the code to produce Figures 2 and 3."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02dd5e2f",
   "metadata": {},
   "source": [
    "# 3. Truncated Coulomb potential"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a2ffae0",
   "metadata": {},
   "source": [
    "## Proof of Proposition 3.8"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64b0a621",
   "metadata": {},
   "source": [
    "We check that  the fact $\\rho^{3,\\mathrm{ball}}_{R_{1,\\kappa}}<\\rho^{3,\\mathrm{cyl}}_{R_{1,\\kappa}}$ for $\\kappa=11/10$ using symbolic computation (SymPy library).\n",
    "\n",
    "First, we define\n",
    "$$\n",
    "f_{1,11/10}(\\lambda) = \\frac{60}{11}\\lambda + 6\\pi\\left(\\frac{11}{10}\\right)^{2}\n",
    "\\left( \\frac{\\lambda^3}{15} -\\frac{\\lambda}{3}+\\dfrac1{3}\\right)\n",
    "$$\n",
    "as in eq. (34) in the proof of Proposition 3.8."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e77d77ef",
   "metadata": {},
   "outputs": [],
   "source": [
    "kappa = Fraction(\"11/10\")\n",
    "\n",
    "x = Symbol('x')\n",
    "sigma_K_11_10_sympy = lambda x: Fraction(\"60/11\")*x+6*pi*Fraction(\"11/10\")**2*(Fraction(\"1/3\")+x**3*Fraction(\"1/15\")-x*Fraction(\"1/3\"))\n",
    "sigma_K_11_10_numpy = lambdify(x, sigma_K_11_10_sympy(x), 'numpy')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "67152ce3",
   "metadata": {},
   "source": [
    "Then we define\n",
    "$$\n",
    "\\lambda_{*,11/10,1}\n",
    "= \\left[\\frac{5}{\\pi}\\left(\\frac{\\pi}{3}-\\left(\\frac{10}{11}\\right)^3\\right)\\right]^{1/2}\n",
    "$$\n",
    "and\n",
    "$$\n",
    "\\rho^{3,\\mathrm{ball}}_{R_{1,11/10}}=\\sigma_{1,11/10}(\\lambda_{*,11/10,1})\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "81eef043",
   "metadata": {},
   "outputs": [],
   "source": [
    "lmbstar = sqrt(5/pi*(pi*Fraction(\"1/3\")-Fraction(\"10/11\")**3))\n",
    "rho_ball = sigma_K_11_10_sympy(lmbstar)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "565fdfb9",
   "metadata": {},
   "source": [
    "An upper bound of $\\rho^{3,\\mathrm{cyl}}_{R_{1,11/10}}$ is\n",
    "$$\n",
    "\\sigma^{3,\\mathrm{cyl}}_{R_{1,11/10}}(11/20) = \\frac{40}{11}+\\left(\\frac{11}{5}\\right)^2\\left(\\frac{\\pi}{2} -\\frac{17}{12} +\\frac{C}{2}\\right)\n",
    "$$\n",
    "where $C$ is the Catalan constant (see Lemma 3.5)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "447cc3e3",
   "metadata": {},
   "outputs": [],
   "source": [
    "rho_cyl_upper_bound = Fraction(\"40/11\")+Fraction(\"11/5\")**2*(pi*Fraction(\"1/2\")-Fraction(\"17/12\")+Catalan*Fraction(\"1/2\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c6d7551",
   "metadata": {},
   "source": [
    "Finally, we ask SymPy the truth value of $\\sigma^{3,\\mathrm{cyl}}_{R_{1,11/10}}(11/20) < \\rho^{3,\\mathrm{ball}}_{R_{1,11/10}}$. SymPy evaluates the expressions with a accuracy which is sufficient for determining the truth value of the comparison."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "1b123b0a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For kappa= 11/10 we find:\n",
      "\n",
      "rho^ball= "
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{363 \\pi \\left(- \\frac{\\sqrt{5} \\sqrt{- \\frac{1000}{1331} + \\frac{\\pi}{3}}}{3 \\sqrt{\\pi}} + \\frac{\\sqrt{5} \\left(- \\frac{1000}{1331} + \\frac{\\pi}{3}\\right)^{\\frac{3}{2}}}{3 \\pi^{\\frac{3}{2}}} + \\frac{1}{3}\\right)}{50} + \\frac{60 \\sqrt{5} \\sqrt{- \\frac{1000}{1331} + \\frac{\\pi}{3}}}{11 \\sqrt{\\pi}}$"
      ],
      "text/plain": [
       "363*pi*(-sqrt(5)*sqrt(-1000/1331 + pi/3)/(3*sqrt(pi)) + sqrt(5)*(-1000/1331 + pi/3)**(3/2)/(3*pi**(3/2)) + 1/3)/50 + 60*sqrt(5)*sqrt(-1000/1331 + pi/3)/(11*sqrt(pi))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "rho^{cyl}< sigma(kappa/2)= \n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{10627}{3300} + \\frac{121 G}{50} + \\frac{121 \\pi}{50}$"
      ],
      "text/plain": [
       "-10627/3300 + 121*Catalan/50 + 121*pi/50"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(G is the Catalan number C)\n",
      "\n",
      "For the assertion rho^cyl < sigma(kappa/2), SymPy returns:  True\n",
      "\n",
      "The 10 first digits in the decimal representation are:\n",
      "rho^ball  ~=  6.619922674\n",
      "sigma(kappa/2) ~= 6.598987929\n"
     ]
    }
   ],
   "source": [
    "print(\"For kappa=\", kappa, \"we find:\\n\")\n",
    "print('rho^ball=', end=\" \")\n",
    "display(rho_ball)\n",
    "print()\n",
    "print(\"rho^{cyl}< sigma(kappa/2)= \")\n",
    "display(rho_cyl_upper_bound)\n",
    "print(\"(G is the Catalan number C)\\n\")\n",
    "\n",
    "print('For the assertion rho^cyl < sigma(kappa/2), SymPy returns: ', rho_cyl_upper_bound < rho_ball)\n",
    "\n",
    "print()\n",
    "print('The 10 first digits in the decimal representation are:')\n",
    "print('rho^ball  ~= ', rho_ball.evalf(n=10, strict=True))\n",
    "print(\"sigma(kappa/2) ~=\", rho_cyl_upper_bound.evalf(n=10, strict=True))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "37d0482d",
   "metadata": {},
   "source": [
    "## Producing Figure 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2a696cf",
   "metadata": {},
   "source": [
    "## Computation of $\\rho^{3,\\mathrm{ball}}_{R_{1,\\kappa}}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9831b778",
   "metadata": {},
   "source": [
    "The function `rho_ball_tC` below computes $\\rho^{3,\\mathrm{ball}}_{R_{1,\\kappa}}$ for a given $\\kappa$, according to Proposition 3.3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "6ee62763",
   "metadata": {},
   "outputs": [],
   "source": [
    "def rho_ball_tC(K):\n",
    "    r''' Computes e^{3,ball}_{R_{1,K}}, for a fixed K, to machine precision.\n",
    "         See Proposition 3.3.\n",
    "       \n",
    "         Returns (val_opt, r_opt), where\n",
    "         val_opt: the computed minimum\n",
    "         r_opt: the computer minimizer\n",
    "    '''\n",
    "\n",
    "    Kmin = (3/np.pi)**(1/3)\n",
    "    Kmax = (15/(2*np.pi))**(1/3)\n",
    "    riesz_ball_dim3 = 32/15*np.pi**2\n",
    "    \n",
    "    f = lambda l : 6*l/K+6*np.pi*K**2*(l**3/15-l/3+1/3)\n",
    "    if K <= Kmin:\n",
    "        return (f(0),np.inf)\n",
    "    elif K >= Kmax:\n",
    "        r_opt = (4*np.pi/(2*riesz_ball_dim3))**(1/3)\n",
    "        return (3*3/(2*r_opt), r_opt)\n",
    "    else:\n",
    "        l_star = np.sqrt(5/np.pi*(np.pi/3-1/K**3))\n",
    "        return (f(l_star),K/(2*l_star))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e71aa38f",
   "metadata": {},
   "source": [
    "We define `sigma_cyl_tC` below which computes $\\sigma^{3,\\mathrm{cyl}}_{R_{1,\\kappa}}(l)$ given $\\kappa$ and $l$, following Proposition 3.4. It uses Simpson's quadrature formula to compute the integral in equation (23) of the paper. This function is only used to produce Figure 1, that is, to illustrate that $\\rho^{3,\\mathrm{ball}}_{R_{1,\\kappa}}<\\rho^{3,\\mathrm{cyl}}_{R_{1,\\kappa}}$ likely holds for an interval around $\\kappa=11/10$.\n",
    "\n",
    "We also introduce the auxiliary functions\n",
    "  - `xlogx(x) = x*log(x)` which is stable for small values of $x$ and returns $0$ for $x=0$\n",
    "  - `log1p(x= log(1+x)` which is accurate also for x so small that `1 + x == 1` in floating-point accuracy.\n",
    "  - `quad_simpson(f,a,b,n)` which uses Simpson's quadrature formula with `n` subintervals to estimate $\\int_a^b f(t)\\,dt$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "48dc969e",
   "metadata": {},
   "outputs": [],
   "source": [
    "xlogx = lambda x : scipy.special.xlogy(x,x)\n",
    "log1p = np.log1p\n",
    "\n",
    "def quad_simpson(f,a,b,n):\n",
    "    r\"\"\" Compute \\int_a^b f using Simpson quadrature method with n subintervals.\"\"\"\n",
    "    \n",
    "    h = (b-a)/n\n",
    "    X = np.linspace(a,b,n+1)\n",
    "    fX = np.array([f(x) for x in X])\n",
    "    Xmil = (X[:-1]+X[1:])/2\n",
    "    fXmil = np.array([f(x) for x in Xmil]) # we can use fXmil = f(Xmil) if f accepts numpy arrays\n",
    "    \n",
    "    return h/6*(fX[1:]+fX[:-1]+4*fXmil).sum()\n",
    "\n",
    "def sigma_cyl_tC(K,l,quad_method=\"simpson\", N=2**6):\n",
    "    r''' Computes f_{R_{1,K}}^{3,cyl}(l) given K and l, i.e. the energy-per-mass\n",
    "         of the infinite cylinder of radius l, for the truncated Coulomb potential.\n",
    "    \n",
    "         It involves numerical evaluation of a 1D integral.\n",
    "        \n",
    "         quad_method: quadrature method to be used, which can be specified to \"simpson\".\n",
    "         N: number of sub_intervals used when quad_method is simpson\n",
    "        \n",
    "         If quad_method in not \"simpson\", scipy default quadrature method is used.\n",
    "    '''\n",
    "    \n",
    "    lmbd = K/(2*l)\n",
    "    \n",
    "    if quad_method == \"simpson\":\n",
    "        quad_func = lambda f,a,b: quad_simpson(f,a,b,N)\n",
    "    else:\n",
    "        quad_func = lambda f,a,b: scipy.integrate.quad(f,a,b)[0]\n",
    "        \n",
    "    def g(ell):\n",
    "        # Notice x^3 arctanh(sqrt(1-x^2)) = x^3*log(1+sqrt(1-x^2))-x**3*log(x)\n",
    "        # Using the functions np.log1p(x)=log(1+x) and scipy.special.xlogy(x,x)=x*log(x),\n",
    "        # we have an expression which is stable even for small x.\n",
    "        if ell<1:\n",
    "            return 4*np.pi/3*(ell-np.arcsin(ell)+2*ell*(1-np.sqrt(1-ell**2))+ell**3*log1p(np.sqrt(1-ell**2))-ell**2*xlogx(ell))\n",
    "        else:\n",
    "            return 4*np.pi*(ell-np.pi/6)\n",
    "    \n",
    "    integrand1 = lambda r: g(np.sqrt(1-r**2)/lmbd)\n",
    "    integrand2 = lambda r: g(np.sqrt(l**2-r**2)*2/K)\n",
    "    \n",
    "    if lmbd == 1:\n",
    "        I_cyl_tC = K**4*np.pi*(np.pi/2-17/12+1/2*float(sympy.Catalan))\n",
    "    elif lmbd > 1:\n",
    "        I_cyl_tC = 2*K**2*l**2*lmbd*quad_func(integrand1,0,1)\n",
    "    else:\n",
    "        I_cyl_tC = 2*K**2*l**2*lmbd*quad_func(integrand1,0,lmbd)+K**3*quad_func(integrand2,K/2,l)\n",
    "\n",
    "    return 2/l+I_cyl_tC/(np.pi*l**2)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "abe54699",
   "metadata": {},
   "source": [
    "Below, we plot $\\rho^{3,\\mathrm{ball}}_{R_{1,\\kappa}}$ and an upper bound of $\\rho^{3,\\mathrm{cyl}}_{R_{1,\\kappa}}$ for varying $\\kappa$. An upper bound is obtained by computing $\\sigma^{3,\\mathrm{cyl}}_{R_{1,\\kappa}}(l(\\kappa))$ for an adequate $l(\\kappa)$. We use SciPy's optimization tools to find an adequate $l(\\kappa)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "861e127c",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Plot rho^{ball}_{R_{1,K}} and Plot rho^{cyl}_{R_{1,K}} for a range of K\n",
    "\n",
    "nK = 70\n",
    "vK = np.linspace(0.96,1.15,nK)\n",
    "\n",
    "l_cyl_hint = 1./2\n",
    "vrho_ball = np.zeros_like(vK)\n",
    "vrho_cyl = np.zeros_like(vK)\n",
    "i = nK-1\n",
    "while True:\n",
    "    K = vK[i]\n",
    "    \n",
    "    vrho_ball[i], r_ball_opt = rho_ball_tC(K)\n",
    "    \n",
    "    res_opt = scipy.optimize.minimize(lambda l:  sigma_cyl_tC(K,l,quad_method=\"scipy\"),\n",
    "                                      l_cyl_hint, constraints=[scipy.optimize.LinearConstraint(np.ones(1), lb=0)])\n",
    "    vrho_cyl[i] = res_opt.fun\n",
    "    l_cyl_hint = res_opt.x[0]\n",
    "    \n",
    "    i -= 1\n",
    "    if i < 0:\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "6df4b15d-1cf2-43cf-8a0f-da465a735fb5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot energy-per-mass\n",
    "plt.figure(1)\n",
    "plt.rcParams.update({'mathtext.fontset': \"cm\", \"font.family\": \"serif\"})\n",
    "plt.plot(vK, vrho_ball, '-', linewidth=1.2,label='$\\\\rho^{\\\\mathrm{ball}}_{\\\\mathcal{R}_{1,\\\\kappa}}$')\n",
    "plt.plot(vK, vrho_cyl, '-',linewidth=1.2,label='$\\\\rho^{\\\\mathrm{cyl}}_{\\\\mathcal{R}_{1,\\\\kappa}} \\\\mathrm{(upper~bound)}$')\n",
    "plt.title(\"Energy/mass ratios for truncated\\n Coulomb potential\", fontsize=16, pad=12)\n",
    "plt.xlabel(\"$\\\\kappa$\",fontsize=20)\n",
    "plt.ylabel(\"Energy/mass ratio\", fontsize=16)\n",
    "plt.legend(loc=\"lower right\", fontsize=16)\n",
    "plt.savefig(\"energy-per-mass_trunc_coulomb.pdf\",bbox_inches='tight')\n",
    "\n",
    "plt.show()\n",
    "\n",
    "# Plot relative improvement\n",
    "plt.figure()\n",
    "plt.plot(vK, vrho_cyl/vrho_ball-1, '-', linewidth=1.2, \n",
    "         label=\"$\\\\frac{\\\\rho^{\\\\mathrm{cyl}}_{\\\\mathcal{R}_{1,\\\\kappa}}}{\\\\rho^{\\\\mathrm{ball}}_{\\\\mathcal{R}_{1,\\\\kappa}}}-1$\")\n",
    "plt.plot(vK, np.zeros_like(vK), 'k', linewidth=0.8, linestyle=\"dashed\" )\n",
    "Kmin = (3/np.pi)**(1/3)\n",
    "vy = np.linspace(-4e-3,1.5e-3,100)\n",
    "plt.plot(np.full_like(vy,Kmin), vy, linewidth=1.2, linestyle=\"dashed\")\n",
    "\n",
    "plt.title(\"Relative energy/mass ratios, balls vs cylinders\\n for truncated Coulomb potential\", fontsize=16 ,pad=14)\n",
    "plt.xlabel(\"$\\\\kappa$\", fontsize=20, math_fontfamily='cm')\n",
    "plt.ylabel(\"Relative difference\",fontsize=16)\n",
    "plt.legend(fontsize=20,loc='upper center')\n",
    "\n",
    "plt.savefig(\"relative_diff_trunc_coulomb.pdf\",bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64e42ff4",
   "metadata": {},
   "source": [
    "# 4. Yukawa potential"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca1f57bb",
   "metadata": {},
   "source": [
    "This section is related to the proof of Lemma 4.6 as well as Figures 2 and 3."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a5be0dd",
   "metadata": {},
   "source": [
    "## Proof of Lemma 4.6"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83c9dce7",
   "metadata": {},
   "source": [
    "We want to establish\n",
    "$$\n",
    "\\rho^{3,\\mathrm{cyl}}_{1,0.56} < \\rho^{3,\\mathrm{ball}}_{1,0.56}.\n",
    "$$\n",
    "\n",
    "First, we set $\\kappa=0.56$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "8cf5bcc0",
   "metadata": {},
   "outputs": [],
   "source": [
    "kappa = Fraction(\"0.56\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2caa12c",
   "metadata": {},
   "source": [
    "### Estimation of $\\rho^{3,\\mathrm{ball}}_{Y_{1,0.56}}$ from below"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b19f091c",
   "metadata": {},
   "source": [
    "According to Proposition 4.4, we have\n",
    "$$\n",
    "\\rho^{3,\\mathrm{ball}}_{Y_{1,\\kappa}} = \\inf f_{\\kappa}(l)\n",
    "$$\n",
    "where\n",
    "$$\n",
    "f_\\kappa(l)= \\frac{6l}{K}+4\\pi K^2(1-3l(1-4l^2)-3l(4l^2+4l+1)e^{-1/l}\n",
    "$$\n",
    "\n",
    "We first look for an approximation of the minimizer $l_{\\mathrm{opt}}(\\kappa)$.\n",
    "\n",
    "For this, we define the functions $f_\\kappa$, $f_\\kappa'$ and $f_\\kappa''$, as in the proof of Proposition 4.4.\n",
    "\n",
    "For numerical computations only, we introduce the auxiliary function:\n",
    "  - `invx_p_exp_minvx(x)` which computes $\\frac{e^{-1/x}}{x^p}$ in a stable way even for small and large values of $x$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9d3ba45b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Definition of f_K, f_K' and f_K'', working with sympy (symbolic) and numpy (numeric).\n",
    "\n",
    "# Definition of f_K, f_K' and f_K'', working with sympy (symbolic) or numpy (numeric).\n",
    "fK_sympy = lambda K,l : 6*l/K+4*pi*K**2*(1-3*l*(1-4*l**2)-3*l*exp(-1/l)*(4*l**2+4*l+1))\n",
    "fK_p_sympy = lambda K,l : 6/K-12*pi*K**2*(1-12*l**2+exp(-1/l)/l*(12*l**3+12*l**2+5*l+1))\n",
    "fK_pp_sympy = lambda K,l : 12*pi*K**2*(24*l-exp(-1/l)/l**3*(24*l**4+24*l**3+12*l**2+4*l+1))\n",
    "\n",
    "# We don't use lambdify because sympy would automatically replace exp(-1/x-p*log(x)) by e^{-1/x}/x^p,\n",
    "# which is not numerically stable for x small.\n",
    "def invx_p_exp_m_invx(p,x):\n",
    "    \"\"\" Compute e^{-1/t} / t^p if t > 0 and 0 otherwise, in a numerically stable way for t small or large.\n",
    "        t : scalar\n",
    "        p : exponent\n",
    "    \"\"\"\n",
    "    if x <= 0:\n",
    "        return 0.\n",
    "    else:\n",
    "        return np.exp(-1/x-p*np.log(x))\n",
    "\n",
    "fK_numpy = lambda K,l : 6*l/K+4*np.pi*K**2*(1-3*l*(1-4*l**2)-3*l*invx_p_exp_m_invx(0,l)*(4*l**2+4*l+1))\n",
    "fK_p_numpy = lambda K,l : 6/K-12*np.pi*K**2*(1-12*l**2+invx_p_exp_m_invx(1,l)*(12*l**3+12*l**2+5*l+1))\n",
    "fK_pp_numpy = lambda K,l : 12*np.pi*K**2*(24*l-invx_p_exp_m_invx(3,l)*(24*l**4+24*l**3+12*l**2+4*l+1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9f0f3a6",
   "metadata": {},
   "source": [
    "Then, we define the function `rho_ball_Y` which evaluates *numerically* $\\rho^{3,\\mathrm{ball}}_{1,\\kappa}$ for a given $\\kappa$. We use Newton method to find the unique zero of $f_K'$ to machine precision, when the minimizer belongs to $(0,+\\infty)$.\n",
    "\n",
    "This function is used to get a first estimate of $l_{\\mathrm{opt}}(\\kappa)$ for $\\kappa=0.56$, and to produce Figure 3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "95534186",
   "metadata": {},
   "outputs": [],
   "source": [
    "def newton(f,Df,x0,max_iter=200, armijo_improv=0.9):\n",
    "    r\"\"\" Newton method to find a zero of f in (0,\\infty), starting from x0.\"\"\"\n",
    "    x = x0\n",
    "    value = f(x)\n",
    "    i = 1\n",
    "    while True:\n",
    "        prev_x, prev_value = x, value\n",
    "        d = -f(x)/Df(x)\n",
    "        t = 1\n",
    "        while True:\n",
    "            x = prev_x+t*d\n",
    "            # Once x is close to the minimizer, t=1 should work (Newton)\n",
    "            # Before that, we reduce t as much as needed to decrease |f| by a given factor (armijo criterion)\n",
    "            value = f(x)\n",
    "            if x>=0 and np.abs(value) <= np.abs(prev_value)*0.9:\n",
    "                break\n",
    "            else:\n",
    "                t /= 2\n",
    "        i += 1\n",
    "        \n",
    "        if np.isclose(prev_x,x,atol=1e-18) or i >= max_iter:\n",
    "            break\n",
    "    return (x,i < max_iter)\n",
    "\n",
    "def rho_ball_Y(K, use_scipy_optimizer=False):\n",
    "    r''' Computes rho^{3,ball}_{Y_{1,K}}, for a fixed K, to machine precision.\n",
    "         Setting f_K(l)= \\frac{6l}{K}+4\\pi K^2(1-3l(1-4l^2)-3l(4l^2+4l+1)rho^{-1/l} and l=K/(2R),\n",
    "         \n",
    "         If use_scipy_optimize is False (the default), we use Newton method to find the zero of f_K'.\n",
    "         Otherwise, we use scipy optimizer as a black box.\n",
    "         \n",
    "         Returns (val_opt, r_opt, success), where\n",
    "         val_opt: the computed minimum\n",
    "         l_opt: the computed minimizer\n",
    "         success: a boolean indicating if machine precision was reached\n",
    "    '''\n",
    "\n",
    "    if K <= (2*np.pi)**(-1/3):\n",
    "        # The minimizer is 0, and the minimum is 4\\pi^2\n",
    "        return (4*np.pi*K**2, 0, True)\n",
    "\n",
    "    # We use Newton method on fK_p\n",
    "    R_init = 15/(16*np.pi)**(1/3) # We take the optimal radius in the classical Coulomb case as initial guess\n",
    "    l_init = K/(2*R_init)\n",
    "    \n",
    "    if use_scipy_optimizer:\n",
    "        # Scipy may use one of BFGS, L-BFGS-B, SLSQP method.\n",
    "        res = scipy.optimize.minimize(lambda l: (fK_numpy(K,l), fK_p_numpy(K,l)),\n",
    "                                      l_init,\n",
    "                                      jac=True,\n",
    "                                      tol=1e-18,\n",
    "                                      constraints=[scipy.optimize.LinearConstraint(np.ones(1), lb=0)])\n",
    "        return (res.fun, l_res.x[0], res.success)\n",
    "    else:\n",
    "        l_opt,success = newton(lambda l: fK_p_numpy(K,l), lambda l: fK_pp_numpy(K,l),l_init)\n",
    "        \n",
    "        return (fK_numpy(K,l_opt), l_opt, success)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "48013969",
   "metadata": {},
   "source": [
    "We observe numerically that $l_{\\mathrm{opt}}(0.56)\\simeq 0.08848204538567361$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "b77f30fa",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "l(0.56) ~= 0.08848204538567361\n"
     ]
    }
   ],
   "source": [
    "rho_ball_opt, l_ball_opt, success = rho_ball_Y(np.float64(kappa))\n",
    "assert success\n",
    "print(\"l(\"+ f'{kappa:.2f}' + \") ~= \" + f'{l_ball_opt}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0befcd90",
   "metadata": {},
   "source": [
    "We check with SympPy that $l_{\\mathrm{opt}}(0.56) \\in (\\alpha,\\beta)$, where $\\alpha=8.84\\times 10^{-2}$ and $\\beta=\\alpha+10^{-4}$, since $f_\\kappa$ is stricly convex and\n",
    "\n",
    "$$\n",
    "f_\\kappa'\\alpha)f_\\kappa'(\\beta) < 0.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "a16e913a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The assertion f_K'(alpha)*f_K'(beta)<0 is:  True\n"
     ]
    }
   ],
   "source": [
    "alpha = Fraction('8.84e-2')\n",
    "beta = alpha+Fraction('1e-4')\n",
    "\n",
    "print(\"The assertion f_K'(alpha)*f_K'(beta)<0 is: \", fK_p_sympy(kappa,alpha)*fK_p_sympy(kappa,beta)<0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e495b9de",
   "metadata": {},
   "source": [
    "By the convexity of $f_\\kappa$, we have\n",
    "\n",
    "$$\n",
    "f_\\kappa(l_{\\mathrm{opt}}(\\kappa)) \\geq \\min(T_\\alpha(\\beta),T_\\beta(\\beta))\n",
    "$$\n",
    "\n",
    "where $T_\\alpha$ and $T_\\beta$ are respectively the tangent lines of $f_\\kappa$ at $\\alpha$ and $\\beta$.\n",
    "\n",
    "Below, we ask SymPy to evaluate this minimum to a precision of $10^{-10}$, to get the lower bound\n",
    "\n",
    "$$\n",
    "\\rho^{3,\\mathrm{ball}}_{1,0.56} \\geq 3.875503068.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "45715477",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "By SymPy, we have\n",
      "\n",
      "rho_ball >= \n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{147 \\pi \\left(\\frac{6031501583}{345312500 e^{\\frac{2500}{221}}} + \\frac{1415977}{1562500}\\right)}{390625} + \\frac{531}{560} + \\frac{784 \\pi \\left(\\frac{2902694083}{3906250000} - \\frac{1434626583}{3906250000 e^{\\frac{2500}{221}}}\\right)}{625}$"
      ],
      "text/plain": [
       "-147*pi*(6031501583*exp(-2500/221)/345312500 + 1415977/1562500)/390625 + 531/560 + 784*pi*(2902694083/3906250000 - 1434626583*exp(-2500/221)/3906250000)/625"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ">= 3.875503068\n"
     ]
    }
   ],
   "source": [
    "Talpha = lambda x : fK_sympy(kappa,alpha)+fK_p_sympy(kappa,alpha)*(x-alpha)\n",
    "Tbeta = lambda x : fK_sympy(kappa,beta)+fK_p_sympy(kappa,beta)*(x-beta)\n",
    "\n",
    "eball_Y_lbound = Min(Talpha(beta),Tbeta(alpha))\n",
    "\n",
    "print(\"By SymPy, we have\\n\")\n",
    "print(\"rho_ball >= \")\n",
    "display(eball_Y_lbound)\n",
    "print(\">=\", N(eball_Y_lbound,10,strict=True))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aaea116e",
   "metadata": {},
   "source": [
    "### Estimation of $\\rho^{3,\\mathrm{cyl}}_{Y_{1,0.56}}$ from above"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "019aed29",
   "metadata": {},
   "source": [
    "By definition of $\\rho^{3,\\mathrm{cyl}}_{Y_{1,0.56}}$, we have\n",
    "$$\n",
    "\\rho^{3,\\mathrm{cyl}}_{Y_{1,0.56}} \\leq \\sigma^{3,\\mathrm{cyl}}_{Y_{1,0.56}}(l)\n",
    "$$\n",
    "for any $l$.\n",
    "By Proposition 4.5, we have\n",
    "$$\n",
    "\\sigma^{3,\\mathrm{cyl}}_{Y_{1,0.56}}(l) = \\frac{2}{l}+\\frac{8}{l^2} \\mathcal{J}_\\kappa(l)\n",
    "$$\n",
    "where\n",
    "$$\n",
    "\\mathcal{J}_{\\kappa}(l) = \\int_0^{2l} sK_0(s/\\kappa)I(s)\\,ds.\n",
    "$$\n",
    "Here $K_0$ is the zero-th modified Bessel function of the second kind, and\n",
    "\n",
    "$$\n",
    "I(s) = \\frac{l(2l-s)}{2}\\arccos\\left(\\frac{s}{2l}\\right)+ls\\arcsin\\left(\\sqrt{\\frac{2l-s}{4l}}\\right)\n",
    "-\\frac{s}{4}\\sqrt{(2l)^2-s^2}.\n",
    "$$\n",
    "\n",
    "Using the motonocity of $I$ and $K_0$ by equation (51), for any positive integer $N$, setting $h=2l/N$ we have the upper bound\n",
    "\n",
    "$$\n",
    "\\mathcal{J}_\\kappa \n",
    "\\leq \\frac{\\sqrt{2}}{3}I(0)\\sqrt{\\pi\\kappa}|h|^{3/2}+\\sum_{k=1}^{N-1}\n",
    "\\frac{|h|^2}{2}\\left(k+\\frac{1}{2}\\right)I(kh)K_0\\left(\\frac{kh}{\\kappa}\\right).\n",
    "$$\n",
    "\n",
    "We define this symbolic upper bound with SymPy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "8f724f57",
   "metadata": {},
   "outputs": [],
   "source": [
    "k = Symbol('k')\n",
    "\n",
    "I_sympy = lambda s: l*(2*l-s)/2*acos(s/(2*l))+l*s*asin(sqrt((2*l-s)/(4*l)))-(s/4)*sqrt((2*l)**2-s**2)\n",
    "K0_sympy = lambda s: besselk(Integer(0), s)\n",
    "JK_upper_bound = lambda l,N,h: kappa*h*I_sympy(Integer(0))+Sum(I_sympy(h*k)*K0_sympy(h*k/kappa)*h**2*(k+Fraction(\"1/2\")), (k, 1, N))\n",
    "\n",
    "sigma_cyl_upperbound = lambda l,N: 2/l+8/l**2*JK_upper_bound(l,N,2*l/N)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bacb3661",
   "metadata": {},
   "source": [
    "Then we choose $l=2.09$, $N=20000$, and ask SymPy to evaluate the bound to the precision $10^{-10}$, which gives\n",
    "\n",
    "$$\n",
    "\\rho^{3,\\mathrm{cyl}}_{Y_{1,0.56}} \\leq \\sigma^{3,\\mathrm{cyl}}_{Y_{1,0.56}}(2.09) \\leq 3.875452115\n",
    "$$\n",
    "\n",
    "Since $\\rho^{3,\\mathrm{ball}}_{1,0.56} \\geq 3.875503068$, this implies\n",
    "\n",
    "$$\n",
    "\\rho^{3,\\mathrm{cyl}}_{Y_{1,0.56}} < \\rho^{3,\\mathrm{ball}}_{1,0.56}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "77643aeb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "We have e_cyl <= sigma_cyl(2.09) <=\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{80000 \\sum_{k=1}^{20000} \\frac{43681 \\left(k + \\frac{1}{2}\\right) \\left(- \\frac{209 k \\sqrt{\\frac{43681}{2500} - \\frac{43681 k^{2}}{1000000000000}}}{4000000} + \\frac{43681 k \\operatorname{asin}{\\left(\\sqrt{\\frac{1}{2} - \\frac{k}{40000}} \\right)}}{100000000} + \\left(\\frac{43681}{10000} - \\frac{43681 k}{200000000}\\right) \\operatorname{acos}{\\left(\\frac{k}{20000} \\right)}\\right) K_{0}\\left(\\frac{209 k}{560000}\\right)}{1000000000000}}{43681} + \\frac{1463 \\pi}{3125000} + \\frac{200}{209}$"
      ],
      "text/plain": [
       "80000*Sum(43681*(k + 1/2)*(-209*k*sqrt(43681/2500 - 43681*k**2/1000000000000)/4000000 + 43681*k*asin(sqrt(1/2 - k/40000))/100000000 + (43681/10000 - 43681*k/200000000)*acos(k/20000))*besselk(0, 209*k/560000)/1000000000000, (k, 1, 20000))/43681 + 1463*pi/3125000 + 200/209"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<=  3.875452114 +1e-10\n"
     ]
    }
   ],
   "source": [
    "N_ = Integer(20000)\n",
    "l = Fraction(\"2.09\")\n",
    "\n",
    "print(\"We have e_cyl <= sigma_cyl(2.09) <=\")\n",
    "display(sigma_cyl_upperbound(l,N_))\n",
    "\n",
    "# Set evaluate_sum to True to evaluate the sum. Caution: this takes a few minutes!\n",
    "evaluate_sum = False\n",
    "if evaluate_sum:\n",
    "    print(\"<= \", N(sigma_cyl_upperbound(l,N_).doit(),10), \"+1e-10\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dedc4a36",
   "metadata": {},
   "source": [
    "## Producing Figures 2 and 3"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ad1c8e2",
   "metadata": {},
   "source": [
    "The function below `sigma_cyl_Y` computes numerically $\\sigma^{3,\\mathrm{cyl}}_{Y_{1,\\kappa}}(l)$ for given $\\kappa$ and $l$, according to Proposition 4.5. We use Simpson's quadrature formula to compute the integral of\n",
    "\n",
    "$$\n",
    "F^{\\mathrm{reg}}_\\kappa(s) = F_\\kappa(s)- G_\\kappa^{(1)} (s)- G_\\kappa^{(2)} (s),\n",
    "$$\n",
    "\n",
    "where\n",
    "\n",
    "$$\n",
    "G_{\\kappa}^{(1)}=-\\log(s/\\kappa)\\left[\n",
    "\\kappa I(0)\\left(\\frac{s}{\\kappa}\\right)\n",
    "+\\kappa^2I'(0)\\left(\\frac{s}{\\kappa}\\right)^2\\right]\n",
    "$$\n",
    "\n",
    "and\n",
    "\n",
    "$$\n",
    "G_\\kappa^{(2)} = \\frac{4}{3}l^{3/2}K_0\\left(\\frac{2l}{K}\\right)(2l-s)^{3/2}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "4624c8c8",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigma_cyl_Y(K,l,quad_method=\"simpson\", N=2**6):\n",
    "    r''' Computes f_{Y_{1,K}}^{3,cyl}(l) given K and l.\n",
    "    \n",
    "         It involves numerical evaluation of a 1D integral.\n",
    "        \n",
    "         quad_method: quadrature method to be used, which can be specified to \"simpson\".\n",
    "         N: number of sub_intervals used when quad_method is simpson\n",
    "        \n",
    "         If quad_method in not \"simpson\", scipy default quadrature method is used.\n",
    "    '''\n",
    "    \n",
    "    K0 = lambda s: scipy.special.kn(0,s)\n",
    "    I = lambda s : l*(2*l-s)/2*np.arccos(s/(2*l))+l*s*np.arcsin(np.sqrt((2*l-s)/(4*l)))-(s/4)*np.sqrt((2*l)**2-s**2)\n",
    "    F = lambda s: s*K0(s/K)*I(s) if s>0 else 0\n",
    "    I0 = l**2*np.pi/2\n",
    "    Ip0 = -l\n",
    "    G1 = lambda s : -scipy.special.xlogy(s/K,s/K)*(K*I0+K**2*Ip0*(s/K))\n",
    "    G2 = lambda s : 4/3*l**(3/2)*K0(2*l/K)*(2*l-s)**(3/2)\n",
    "    F_reg = lambda s : F(s)-G1(s)-G2(s)\n",
    "    \n",
    "    intG1 = l**2*I0*(1-2*np.log(2*l/K))+8/9*l**3*Ip0*(1-3*np.log(2*l/K))\n",
    "    intG2 = 32*np.sqrt(2)/15*l**4*K0(2*l/K)\n",
    "    \n",
    "    if quad_method == \"simpson\":\n",
    "        quad_func = lambda f,a,b: quad_simpson(f,a,b,N)\n",
    "    else:\n",
    "        quad_func = lambda f,a,b: scipy.integrate.quad(f,a,b)[0]\n",
    "        \n",
    "    JK = quad_func(lambda s: F_reg(s),0,2*l)+intG1+intG2\n",
    "    \n",
    "    return 2/l+8/(l**2)*JK\n",
    "\n",
    "assert np.isclose(sigma_cyl_Y(0.56,2.09,quad_method=\"simpson\",N=2**10),sigma_cyl_Y(0.56,2.09,quad_method=\"scipy\"),atol=1e-8)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40bda2e1",
   "metadata": {},
   "source": [
    "From the discussion at the end of our paper, we should find an error $e(h) \\sim |h|^{7/2}$ for the integration of $F_\\kappa^{\\mathrm{reg}}$, where $h=1/N$ and $N$ is the number of subintervals. In fact, we observe $e(h) \\sim |h|^4$ due to the small prefactor $sK_0(s/\\kappa)\\simeq 10^{-3}$ in $s=2l$ and the fact that machine precision is reached for $|h|\\simeq 10^{-3}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "6fa34b6b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Convergence of the numerical integration for sigma_cyl_Y(0.56, 2.09)\n",
    "\n",
    "vi = np.arange(8)\n",
    "vN = 2**(vi+4)\n",
    "vh = 1/vN.astype(np.float64)\n",
    "vcyl = np.zeros_like(vh)\n",
    "\n",
    "K = 0.56\n",
    "l = 2.09\n",
    "\n",
    "for (i,N) in enumerate(vN):\n",
    "    vcyl[i] = sigma_cyl_Y(K,l,quad_method=\"simpson\", N=N)\n",
    "\n",
    "precise_value = sigma_cyl_Y(l,K,quad_method=\"simpson\", N=vN[-1]*8)\n",
    "\n",
    "verror = np.abs(vcyl[1:]-vcyl[:-1])\n",
    "vh = vh[:-1]\n",
    "\n",
    "plt.figure(0)\n",
    "plt.rcParams.update({'mathtext.fontset': \"cm\", \"font.family\": \"serif\"})\n",
    "plt.loglog(vh, (vh/vh[-1])**4*verror[-1], '--', label='$|h|^4$')\n",
    "plt.loglog(vh,verror, 'kx', label='$e(h)$')\n",
    "\n",
    "plt.legend(fontsize=16)\n",
    "plt.xlabel('$h$',fontsize=16)\n",
    "plt.ylabel('$e(h)$',fontsize=16)\n",
    "plt.title(\"Convergence rate for the integration of $F_\\\\kappa^{\\\\mathrm{reg}}$\",fontsize=15, pad=14)\n",
    "\n",
    "plt.savefig(\"cv_numerical_integration_yukawa.pdf\",bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4ca7234",
   "metadata": {},
   "source": [
    "Eventually, we compute and plot $\\rho^{3,\\mathrm{ball}}_{Y_{1,\\kappa}}$ and $\\rho^{3,\\mathrm{cyl}}_{Y_{1,\\kappa}}$ for an interval of $\\kappa$ around $0.56$. We use the bound\n",
    "\n",
    "$$\n",
    "\\rho^{3,\\mathrm{cyl}}_{Y_{1,\\kappa}} \\leq \\sigma^{3,\\mathrm{cyl}}_{Y_{1,\\kappa}}(l(\\kappa)),\n",
    "$$\n",
    "\n",
    "where adequate $l(\\kappa)$ are obtained by minimizing $l\\mapsto \\sigma^{3,\\mathrm{cyl}}_{Y_{1,\\kappa}}(l)$ with SciPy's library."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "68aed6ff",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Plot rho^{ball}_{Y_{1,K}} and Plot rho^{cyl}_{Y_{1,K}} for a range of K\n",
    "\n",
    "nK = 81\n",
    "vK = np.linspace(0.56-0.019,0.56+0.03,nK)[::-1]\n",
    "Kmin = (2*np.pi)**(-1/3)\n",
    "l_cyl_hint = 1./3\n",
    "vrho_ball = np.zeros_like(vK)\n",
    "vrho_cyl = np.zeros_like(vK)\n",
    "i = 0\n",
    "while True:\n",
    "    K = vK[i]\n",
    "    \n",
    "    vrho_ball[i], r_ball_opt, success = rho_ball_Y(K)\n",
    "    \n",
    "    res_opt = scipy.optimize.minimize(lambda l:  sigma_cyl_Y(K,l,quad_method=\"scipy\"),\n",
    "                                      l_cyl_hint, tol=1e-13, constraints=[scipy.optimize.LinearConstraint(np.ones(1), lb=0)])\n",
    "    vrho_cyl[i] = res_opt.fun\n",
    "    l_cyl_hint = res_opt.x[0]\n",
    "    \n",
    "    i += 1\n",
    "    if i >= nK:\n",
    "        break\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "5e7d9ac2-80d7-4ed0-be18-1fff1f777de5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot energy-per-mass\n",
    "plt.figure(1)\n",
    "plt.rcParams.update({'mathtext.fontset': \"cm\", \"font.family\": \"serif\"})\n",
    "plt.plot(vK, vrho_ball, '-', linewidth=.8,label='$\\\\rho^{\\\\mathrm{ball}}_{\\\\mathcal{Y}_{1,\\\\kappa}}$')\n",
    "plt.plot(vK, vrho_cyl, '-',linewidth=.8,label='$\\\\rho^{\\\\mathrm{cyl}}_{\\\\mathcal{Y}_{1,\\\\kappa}}$ $\\\\mathrm{(upper~bound)}$')\n",
    "plt.title(\"Energy/mass ratios with Yukawa potential\",fontsize=15, pad=12)\n",
    "plt.xlabel(\"$\\\\kappa$\",fontsize=19)\n",
    "plt.ylabel(\"Energy/mass\",fontsize=14)\n",
    "plt.legend(fontsize=16)\n",
    "\n",
    "plt.savefig(\"energy-per-mass_yukawa.pdf\",bbox_inches='tight')\n",
    "\n",
    "plt.show()\n",
    "\n",
    "# Plot relative improvement\n",
    "plt.figure()\n",
    "plt.rcParams.update({'mathtext.fontset': \"cm\", \"font.family\": \"serif\"})\n",
    "\n",
    "plt.plot(vK, vrho_cyl/vrho_ball-1, '-', linewidth=1, \n",
    "         label=\"$\\\\frac{\\\\rho^{\\\\mathrm{cyl}}_{\\\\mathcal{Y}_{1,\\\\kappa}}}{\\\\rho^{\\\\mathrm{ball}}_{\\\\mathcal{Y}_{1,\\\\kappa}}}-1$\")\n",
    "plt.plot(vK, np.zeros_like(vK), 'k', linewidth=1, linestyle=\"dashed\" )\n",
    "vy = np.linspace(-7e-4,2.5e-4,100)\n",
    "plt.plot(np.full_like(vy,Kmin), vy, linewidth=1.1, linestyle=\"dashed\")\n",
    "\n",
    "plt.title(\"Relative energy/mass ratios, balls vs cylinders\\n for the Yukawa potential\", pad=14, fontsize=15)\n",
    "plt.xlabel(\"$\\\\kappa$\", fontsize=20, math_fontfamily='cm')\n",
    "plt.ylabel(\"Relative difference\",fontsize=14)\n",
    "plt.legend(fontsize=19,loc='upper center')\n",
    "\n",
    "plt.savefig(\"relative_diff_yukawa.pdf\",bbox_inches='tight')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.12.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}