From b80398627f3b554f502e191f2b82c832a1e98e04 Mon Sep 17 00:00:00 2001 From: Francesco Biscani Date: Wed, 4 Sep 2024 14:36:18 +0200 Subject: [PATCH] Fixes to the TOV equations notebook. --- doc/conf.py | 3 + doc/notebooks/oppenheimer_volkoff.ipynb | 91 ++++++++++++------------- 2 files changed, 48 insertions(+), 46 deletions(-) diff --git a/doc/conf.py b/doc/conf.py index 92440ea8..6b63d735 100644 --- a/doc/conf.py +++ b/doc/conf.py @@ -106,6 +106,9 @@ # NOTE: the sgp4 notebook runs # some benchmarks. "sgp4_propagator*", + # NOTE: high order variational equations + # take too long in debug mode. + "oppenheimer_volkoff*", ] # Force printing traceback to stderr on execution error. diff --git a/doc/notebooks/oppenheimer_volkoff.ipynb b/doc/notebooks/oppenheimer_volkoff.ipynb index df956a34..4ae1cf18 100644 --- a/doc/notebooks/oppenheimer_volkoff.ipynb +++ b/doc/notebooks/oppenheimer_volkoff.ipynb @@ -16,16 +16,16 @@ "In this formulation, the state is:\n", "\n", "$$\n", - "\\mathbf x=[r^2, m/r]=[x_0, x_1]\n", - "$$,\n", + "\\mathbf x=[r^2, m/r]=[x_0, x_1],\n", + "$$\n", "\n", "and the parameters are:\n", "\n", "$$\n", - "\\mathbf p = [\\eta_K, \\eta_\\Gamma]\n", - "$$,\n", + "\\mathbf p = [\\eta_K, \\eta_\\Gamma],\n", + "$$\n", "\n", - " where $K = \\overline K(1+\\eta_K)$ and $\\Gamma = \\overline \\Gamma(1+\\eta_\\Gamma)$ will parameterize the equation of state of a polytrope (a gaseous sphere in hydrodynamic equilibrium).\n", + "where $K = \\overline K(1+\\eta_K)$ and $\\Gamma = \\overline \\Gamma(1+\\eta_\\Gamma)$ will parameterize the equation of state of a polytrope (a gaseous sphere in hydrodynamic equilibrium).\n", "\n", "The equations are then written as:\n", "\n", @@ -34,7 +34,7 @@ "\\begin{array}{ll}\n", "\\frac{dx_0}{dh} &= -\\frac{2x_0 (1-2x_1)}{4\\pi x_0 P(h) + x_1}\\\\\n", "\\frac{dx_1}{dh} &= \\left(2\\pi \\epsilon(h) - \\frac{x_1}{2x_0}\\right) \\frac{dx_0}{dh} \\\\\n", - "\\end{array}\\right.\n", + "\\end{array}\\right. ,\n", "$$\n", "\n", "where an equation of state is needed to define the pressure $P(h)$ and energy density $\\epsilon(h)$ expressions. \n", @@ -42,7 +42,7 @@ "In the case of a relativistic polytrope here studied, the log-entalpy is introduced and defined as:\n", "\n", "$$\n", - "h = \\log{[(\\epsilon+P) / \\rho]}\n", + "h = \\log{[(\\epsilon+P) / \\rho]},\n", "$$\n", "\n", "where $\\rho$ is the (baryonic) mass density (following a [polytropic process](https://en.wikipedia.org/wiki/Polytropic_process)):\n", @@ -51,17 +51,17 @@ "\\begin{array}{l}\n", "\\rho = (\\frac{P}{K})^{1/\\Gamma} \\\\\n", "\\epsilon = \\rho + P / (\\Gamma-1)\n", - "\\end{array}\n", + "\\end{array}.\n", "$$\n", "\n", "Hence, in this case the log-entalpy can be written as:\n", "$$\n", - "h = \\log\\left(1 + \\frac{\\Gamma}{\\Gamma-1} K^{\\frac 1\\Gamma} P^{1-\\frac 1\\Gamma}\\right)\n", + "h = \\log\\left(1 + \\frac{\\Gamma}{\\Gamma-1} K^{\\frac 1\\Gamma} P^{1-\\frac 1\\Gamma}\\right),\n", "$$\n", "\n", "which can be inverted to yield the $P(h)$ form:\n", "$$\n", - "P(h) = K^{-\\frac{1}{\\Gamma-1}}\\left[\\frac{\\Gamma-1}{\\Gamma}\\left(e^h-1\\right)\\right]^{\\frac{\\Gamma}{\\Gamma-1}}\n", + "P(h) = K^{-\\frac{1}{\\Gamma-1}}\\left[\\frac{\\Gamma-1}{\\Gamma}\\left(e^h-1\\right)\\right]^{\\frac{\\Gamma}{\\Gamma-1}}.\n", "$$\n", "\n", "\n", @@ -88,8 +88,8 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# 0 - Preamble \n", - "Let us start introducing common definitions and the reference numerical values we will be using for the parameters $K, \\Gamma$ of the polytrope." + "## 0 - Preamble \n", + "Let us start by introducing common definitions and the reference numerical values we will be using for the parameters $K, \\Gamma$ of the polytrope." ] }, { @@ -131,10 +131,10 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# 1 - Standard Numerical Solution\n", + "## 1 - Standard Numerical Solution\n", "The Tolman–Oppenheimer–Volkoff equations in the Lindblom form are numerically well behaved. \n", "\n", - "We here show a straight forward numerical integration using the Taylor adaptive scheme of *heyoka*." + "We here show a straightforward numerical integration using the Taylor adaptive scheme of *heyoka*." ] }, { @@ -173,7 +173,7 @@ } ], "source": [ - "# Pressure (Change this value to then approximate different part of the M-R curve)\n", + "# Pressure (change this value to then approximate different part of the M-R curve)\n", "P_c = 1e-2\n", "\n", "# Density\n", @@ -233,10 +233,10 @@ "name": "stdout", "output_type": "stream", "text": [ - "Total time to propagate: 0.0002999305725097656\n", + "Total time to propagate: 0.00031447410583496094\n", "Outcome (should be time_limit if all went well): time_limit\n", - "Final value for the stellar radius is: 5.51113483059698\n", - "Final value for the stellar mass is: 1.36846136138855\n" + "Final value for the stellar radius is: 5.511134830596981\n", + "Final value for the stellar mass is: 1.3684613613885503\n" ] } ], @@ -273,7 +273,7 @@ "outputs": [ { "data": { - "image/png": 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", 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", 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" ] @@ -313,7 +313,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# 2 - Variational equations\n", + "## 2 - Variational equations\n", "We seek an analytical expression for the stellar mass and radius, as a function of the variation of the conditions at the stellar center $\\delta h_c$. " ] }, @@ -328,12 +328,12 @@ "\\begin{array}{ll}\n", "\\frac{dx_0}{ds} &= - \\overline h_0 \\frac{2x_0 (1-2x_1)}{4\\pi x_0 P(s) + x_1}\\\\\n", "\\frac{dx_1}{ds} &= \\left(2\\pi \\epsilon(s) - \\frac{x_1}{2x_0}\\right) \\frac{dx_0}{ds} \\\\\n", - "\\end{array}\\right.\n", + "\\end{array}\\right.,\n", "$$\n", "\n", "with:\n", "$$\n", - "P(s) = K^{-\\frac{1}{\\Gamma-1}}\\left[\\frac{\\Gamma-1}{\\Gamma}\\left(e^{\\overline h_0 s}-1\\right)\\right]^{\\frac{\\Gamma}{\\Gamma-1}}\n", + "P(s) = K^{-\\frac{1}{\\Gamma-1}}\\left[\\frac{\\Gamma-1}{\\Gamma}\\left(e^{\\overline h_0 s}-1\\right)\\right]^{\\frac{\\Gamma}{\\Gamma-1}},\n", "$$\n", "\n", "and:\n", @@ -341,9 +341,9 @@ "\\begin{array}{l}\n", "\\rho(s) = \\left(\\frac{P(s)}{K}\\right)^{1/\\Gamma} \\\\\n", "\\epsilon(s) = \\rho + P(s) / (\\Gamma-1)\n", - "\\end{array}\n", + "\\end{array},\n", "$$\n", - "and must be integrated for $s \\in [1, 0]$, which will correspond to $h \\in [\\overline h_0, 0]$" + "and must be integrated for $s \\in [1, 0]$, which will correspond to $h \\in [\\overline h_0, 0]$." ] }, { @@ -383,7 +383,7 @@ "metadata": {}, "outputs": [], "source": [ - "# We augment the dynamics with the variational equations (we use 8th order bu lower orders are good already)\n", + "# We augment the dynamics with the variational equations (we use 8th order but lower orders are good already)\n", "var_sys = hy.var_ode_sys(dyn2, args=[x0, x1, hy.par[2]], order=8)\n", "\n", "# We instantiate the Taylor adaptive integrator for the system of equations augmented with the variational ones\n", @@ -407,7 +407,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Total time to propagate: 11.109041929244995\n", + "Total time to propagate: 13.48798131942749\n", "Outcome: taylor_outcome.time_limit\n", "Final value for the stellar radius is: 5.511134830596981\n", "Final value for the stellar mass is: 1.3684613613885501\n" @@ -443,7 +443,7 @@ "\\begin{array}{l}\n", "R_{\\odot} = \\mathcal P^k_R(\\delta x_{0_0}, \\delta x_{1_0},\\delta h_0) \\\\\n", "M_{\\odot} = \\mathcal P^k_M(\\delta x_{0_0}, \\delta x_{1_0}, \\delta h_0) \n", - "\\end{array}\n", + "\\end{array}.\n", "$$\n", "\n", "Note the underscript $0$ refers to the initial values, not to the star center which would here be indicated using $c$ rather than $0$." @@ -558,10 +558,10 @@ "name": "stdout", "output_type": "stream", "text": [ - "Total time to propagate: 0.00030803680419921875\n", + "Total time to propagate: 0.00030732154846191406\n", "Outcome (should be time_limit if all went well): time_limit\n", - "Final value for the stellar radius is: 4.902082750925565\n", - "Final value for the stellar mass is: 1.1364594040709297\n" + "Final value for the stellar radius is: 4.9020827509255644\n", + "Final value for the stellar mass is: 1.13645940407093\n" ] } ], @@ -600,11 +600,11 @@ "name": "stdout", "output_type": "stream", "text": [ - "Absolute error on mass: -2.613092855319188e-05\n", - "Absolute error on radius: -0.0002199445447912396\n", + "Absolute error on mass: -2.6130928552969834e-05\n", + "Absolute error on radius: -0.00021994454479212777\n", "\n", - "Relative error on mass: -2.2993279354799525e-05\n", - "Relative error on radius: -4.486757077891264e-05\n" + "Relative error on mass: -2.2993279354604138e-05\n", + "Relative error on radius: -4.486757077909383e-05\n" ] } ], @@ -620,7 +620,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# The $M_\\odot$ vs $R_\\odot$ plot" + "## The $M_\\odot$ vs $R_\\odot$ plot" ] }, { @@ -639,7 +639,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Total computation time using the Taylor Map: 0.005026102066040039\n" + "Total computation time using the Taylor Map: 0.0064585208892822266\n" ] } ], @@ -682,7 +682,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Total time using the numerical integrator: 0.09037113189697266\n" + "Total time using the numerical integrator: 0.09951353073120117\n" ] } ], @@ -739,7 +739,7 @@ { "data": { "text/plain": [ - "" + "" ] }, "execution_count": 18, @@ -748,7 +748,7 @@ }, { "data": { - "image/png": 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", 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", 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" ] @@ -761,8 +761,8 @@ "plt.plot(Rstar_gt, Mstar_gt, label = \"Ground truth\")\n", "plt.plot(Rstar, Mstar, c='r', alpha=0.5, label = \"Taylor Map (order 8)\")\n", "\n", - "plt.xlabel(\"$R_{\\odot}$\")\n", - "plt.ylabel(\"$M_{\\odot}$\")\n", + "plt.xlabel(r\"$R_{\\odot}$\")\n", + "plt.ylabel(r\"$M_{\\odot}$\")\n", "plt.legend()" ] }, @@ -781,7 +781,7 @@ ], "metadata": { "kernelspec": { - "display_name": "ns", + "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, @@ -795,10 +795,9 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.11.9" - }, - "orig_nbformat": 4 + "version": "3.12.4" + } }, "nbformat": 4, - "nbformat_minor": 2 + "nbformat_minor": 4 }