{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Figure 5\n", "This notebook recreates Figure 5 in Rein & Tamayo 2016. The figure illustrates the accuracy of second order variational equations compared to finite differences. \n", "\n", "When using finite differences to calculate approximations to a derivative, the *finite difference* needs to be fine tuned. It has to be small enough to stay in the linear regime, but large enough to avoid floating point rounding issues. As we will see, there is only a small range in which finite differences give accurate approximations to the local derivative. The problem is significantly exaggerated for second order derivates. Even for fine tuned values of the finite differences (which is in general not possible to do), one cannot achieve an accuracy better than $10^{-6}$ with finite differences.\n", "\n", "When variational equations are used to calculate derivatives, none of the problems exits. There is no small parameter that needs to be fine tuned. Variational equations *just work*. Better yet, because we use the high accuracy IAS15 integrator, the derivates are accurate to machine precision in all cases.\n", "\n", "We start by import the REBOUND, numpy and matplotlib packages. " ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import rebound\n", "import numpy as np\n", "%matplotlib inline\n", "import matplotlib\n", "import matplotlib.pyplot as plt\n", "from matplotlib.colors import LogNorm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We recreate the same problem as for Figures 3 and 4. Two planets are orbiting one star. We sample the radial velocity of the star at random intervals." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [], "source": [ "sample_times = np.array([0.,0.1,0.3,1.2,1.5,1.9,2.3,2.8,3.3,9.5,11.5,12.5,15.6,16.7,20.])\n", "def generatedata(x):\n", " a, e = x\n", " sim = rebound.Simulation()\n", " sim.add(m=1.)\n", " sim.add(primary=sim.particles[0],m=1e-3, a=a, e=e)\n", " sim.add(primary=sim.particles[0],m=1e-3, a=1.3,f=1.4)\n", " sim.move_to_com()\n", " samples = np.zeros((len(sample_times)))\n", " for i,t in enumerate(sample_times):\n", " sim.integrate(t)\n", " samples[i] = sim.particles[0].vx\n", " return samples\n", "x_true = (1.0,0.2500)\n", "samples_true = generatedata(x_true)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following function calculates a goodness of fit, the $\\chi^2$ amd the derivates of $\\chi^2$ with respect to the inner planet's initial semi-major axis and eccentricity. We use the variational equation approach in the following function." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def chi2_derivatives(x):\n", " a, e = x\n", " sim = rebound.Simulation()\n", " sim.add(m=1.)\n", " sim.add(primary=sim.particles[0],m=1e-3, a=a, e=e)\n", " sim.add(primary=sim.particles[0],m=1e-3, a=1.3,f=1.4)\n", " \n", " var_da = sim.add_variation()\n", " var_dda = sim.add_variation(order=2,first_order=var_da)\n", " var_de = sim.add_variation()\n", " var_dde = sim.add_variation(order=2,first_order=var_de)\n", " var_da_de = sim.add_variation(order=2,first_order=var_da,first_order_2=var_de)\n", " var_da.vary(1,\"a\")\n", " var_de.vary(1,\"e\")\n", " var_dda.vary(1,\"a\")\n", " var_dde.vary(1,\"e\")\n", " var_da_de.vary(1,\"a\",\"e\")\n", "\n", " sim.move_to_com()\n", " \n", " l = 0.\n", " d = np.zeros((2))\n", " dd = np.zeros((2,2))\n", " \n", " for i, t in enumerate(sample_times):\n", " sim.integrate(t)\n", " rvobs = samples_true[i]\n", " rv = sim.particles[0].vx\n", " l += (rv-rvobs)*(rv-rvobs)\n", " d[0] += 2. * var_da.particles[0].vx*(rv-rvobs)\n", " d[1] += 2. * var_de.particles[0].vx*(rv-rvobs)\n", " dd[0][0] += 2. * var_dda.particles[0].vx*(rv-rvobs)\n", " dd[0][0] += 2. * var_da.particles[0].vx*var_da.particles[0].vx\n", " dd[1][0] += 2. * var_da_de.particles[0].vx*(rv-rvobs)\n", " dd[1][0] += 2. * var_da.particles[0].vx*var_de.particles[0].vx\n", " dd[1][1] += 2. * var_dde.particles[0].vx*(rv-rvobs)\n", " dd[1][1] += 2. * var_de.particles[0].vx*var_de.particles[0].vx\n", "\n", " dd[0][1] = dd[1][0]\n", " \n", " return l, d, dd" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following function calculates the same as `chi2_derivatives`, but uses the finite difference approach. " ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def chi2_derivatives_finite_differences(x, d=(1e-6,1e-6)):\n", " a, e = x\n", " d_a, d_e = d\n", " sim = rebound.Simulation()\n", " sim.add(m=1.)\n", " sim.add(primary=sim.particles[0],m=1e-3, a=a, e=e)\n", " sim.add(primary=sim.particles[0],m=1e-3, a=1.3,f=1.4)\n", " sim.move_to_com()\n", " \n", " sim_a = rebound.Simulation()\n", " sim_a.add(m=1.)\n", " sim_a.add(primary=sim_a.particles[0],m=1e-3, a=a+d_a, e=e)\n", " sim_a.add(primary=sim_a.particles[0],m=1e-3, a=1.3,f=1.4)\n", " sim_a.move_to_com()\n", "\n", " sim_e = rebound.Simulation()\n", " sim_e.add(m=1.)\n", " sim_e.add(primary=sim_e.particles[0],m=1e-3, a=a, e=e+d_e)\n", " sim_e.add(primary=sim_e.particles[0],m=1e-3, a=1.3,f=1.4)\n", " sim_e.move_to_com()\n", "\n", " sim_aa = rebound.Simulation()\n", " sim_aa.add(m=1.)\n", " sim_aa.add(primary=sim_aa.particles[0],m=1e-3, a=a-d_a, e=e)\n", " sim_aa.add(primary=sim_aa.particles[0],m=1e-3, a=1.3,f=1.4)\n", " sim_aa.move_to_com()\n", "\n", " sim_ee = rebound.Simulation()\n", " sim_ee.add(m=1.)\n", " sim_ee.add(primary=sim_ee.particles[0],m=1e-3, a=a, e=e-d_e)\n", " sim_ee.add(primary=sim_ee.particles[0],m=1e-3, a=1.3,f=1.4)\n", " sim_ee.move_to_com()\n", "\n", " sim_ea1 = rebound.Simulation()\n", " sim_ea1.add(m=1.)\n", " sim_ea1.add(primary=sim_ea1.particles[0],m=1e-3, a=a+d_a, e=e-d_e)\n", " sim_ea1.add(primary=sim_ea1.particles[0],m=1e-3, a=1.3,f=1.4)\n", " sim_ea1.move_to_com()\n", "\n", " sim_ea2 = rebound.Simulation()\n", " sim_ea2.add(m=1.)\n", " sim_ea2.add(primary=sim_ea2.particles[0],m=1e-3, a=a-d_a, e=e+d_e)\n", " sim_ea2.add(primary=sim_ea2.particles[0],m=1e-3, a=1.3,f=1.4)\n", " sim_ea2.move_to_com()\n", "\n", " sim_ea3 = rebound.Simulation()\n", " sim_ea3.add(m=1.)\n", " sim_ea3.add(primary=sim_ea3.particles[0],m=1e-3, a=a+d_a, e=e+d_e)\n", " sim_ea3.add(primary=sim_ea3.particles[0],m=1e-3, a=1.3,f=1.4)\n", " sim_ea3.move_to_com()\n", "\n", " sim_ea4 = rebound.Simulation()\n", " sim_ea4.add(m=1.)\n", " sim_ea4.add(primary=sim_ea4.particles[0],m=1e-3, a=a-d_a, e=e-d_e)\n", " sim_ea4.add(primary=sim_ea4.particles[0],m=1e-3, a=1.3,f=1.4)\n", " sim_ea4.move_to_com()\n", " \n", " d = np.zeros((2))\n", " dd = np.zeros((2,2))\n", "\n", " for i, t in enumerate(sample_times):\n", " sim.integrate(t)\n", " sim_a.integrate(t)\n", " sim_e.integrate(t)\n", " sim_aa.integrate(t)\n", " sim_ee.integrate(t)\n", " sim_ea1.integrate(t)\n", " sim_ea2.integrate(t)\n", " sim_ea3.integrate(t)\n", " sim_ea4.integrate(t)\n", "\n", " rvobs = samples_true[i]\n", " rv = sim.particles[0].vx\n", " \n", " rv_da = (sim_a.particles[0].vx-sim.particles[0].vx)/d_a\n", " rv_de = (sim_e.particles[0].vx-sim.particles[0].vx)/d_e\n", " \n", " rv_da_de = (sim_ea3.particles[0].vx-sim_ea1.particles[0].vx-sim_ea2.particles[0].vx+sim_ea4.particles[0].vx)/(4.*d_e*d_a)\n", " rv_daa = (sim_a.particles[0].vx-2.*sim.particles[0].vx+sim_aa.particles[0].vx)/(d_a*d_a)\n", " rv_dee = (sim_e.particles[0].vx-2.*sim.particles[0].vx+sim_ee.particles[0].vx)/(d_e*d_e)\n", " \n", " dd[0][0] += 2. * rv_daa*(rv-rvobs)\n", " dd[0][0] += 2. * rv_da*rv_da\n", " dd[1][0] += 2. * rv_da_de*(rv-rvobs)\n", " dd[1][0] += 2. * rv_da*rv_de\n", " dd[1][1] += 2. * rv_dee*(rv-rvobs)\n", " dd[1][1] += 2. * rv_de*rv_de\n", " \n", " d[0] += 2. * rv_da*(rv-rvobs)\n", " d[1] += 2. * rv_de*(rv-rvobs)\n", " \n", " dd[0][1] = dd[1][0]\n", " \n", " return d,dd" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now test both approaches for a given set of inital conditions, $a=0.951, e=0.12$. We vary the finite difference parameters $\\delta a$ and $\\delta e$ on a 50x50 grid (this may take a few minutes to run, depending on the speed of your computer)." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [], "source": [ "N=50\n", "grid_a = np.logspace(-16.,-1.5,N)\n", "grid_e = np.logspace(-16.,-1.5,N)\n", "d_var = chi2_derivatives((0.951,0.12))[1]\n", "dd_var = chi2_derivatives((0.951,0.12))[2]\n", "d_sha = np.zeros((N,N,2))\n", "dd_sha = np.zeros((N,N,3))\n", "for i, a in enumerate(grid_a):\n", " for j, e in enumerate(grid_e):\n", " res = chi2_derivatives_finite_differences((0.951,0.12),d=(a,e))\n", " resabs = np.abs((res[0]-d_var))\n", " #print((\"%e %e %e %e\") %(a,e,resabs[0]/np.abs(d_var[0]), resabs[1]/np.abs(d_var[1])))\n", " d_sha[i][j][0] = resabs[0]/np.abs(d_var[0])\n", " d_sha[i][j][1] = resabs[1]/np.abs(d_var[1])\n", " dd_sha[i][j][0] = np.abs((res[1][0][0]-dd_var[0][0])/dd_var[0][0])\n", " dd_sha[i][j][1] = np.abs((res[1][1][1]-dd_var[1][1])/dd_var[1][1])\n", " dd_sha[i][j][2] = np.abs((res[1][0][1]-dd_var[0][1])/dd_var[0][1])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now create a series of plots that show the relative error of the finite difference method for both 1st and 2nd order derivatives of $\\chi^2$." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/rein/rebound/venv/lib/python3.4/site-packages/matplotlib/image.py:375: UserWarning: Images are not supported on non-linear axes.\n", " warnings.warn(\"Images are not supported on non-linear axes.\")\n" ] }, { "data": { "image/png": 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twDOVxDZF92X45xT3x0s7oNjRsFvpI1WAge+U2VcSaa+ARFcjIvOBE4E3VfXA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qzS5Qa9YEbLnH8mDcnDIUgkF/iykQX9Zc6/bNsogSRFf8NWoU6c70cYiVIzjnpkqccpqY38/k6w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\ni0PFH4RxY3gYvvzlxuO23z5U2S9bFp6zSO7w7neHxOaZk+7LLSIiIsDIK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PZSROoGBwcZ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\nAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(22,4))\n", "ax = plt.subplot(131)\n", "extent = [min(grid_a),max(grid_a)]\n", "#ax.set_xlim(extent[0],extent[1])\n", "ax.set_xlabel(\"$\\delta a$\")\n", "ax.set_ylim(1e-8,1e1)\n", "ax.set_xscale(\"log\")\n", "ax.set_yscale(\"log\")\n", "ax.set_ylabel(\"relative error\")\n", "ax.plot(grid_a, d_sha[:,0,0],label=\"first derivative\")\n", "ax.plot(grid_a, dd_sha[:,0,0],\"--\",label=\"second derivative\")\n", "legend = plt.legend(loc=2)\n", "ax = plt.gca().add_artist(legend)\n", "\n", "ax = plt.subplot(132)\n", "extent = [min(grid_a),max(grid_a)]\n", "#ax.set_xlim(extent[0],extent[1])\n", "ax.set_xlabel(\"$\\delta e$\")\n", "ax.set_ylim(1e-8,1e1)\n", "ax.set_xscale(\"log\")\n", "ax.set_yscale(\"log\")\n", "ax.set_ylabel(\"relative error\")\n", "ax.plot(grid_e, d_sha[0,:,1])\n", "ax.plot(grid_e, dd_sha[0,:,1]+2.*grid_e,\"--\")\n", "\n", "ax = plt.subplot(133)\n", "extent = [min(grid_a),max(grid_a),min(grid_e),max(grid_e)]\n", "#ax.set_xlim(extent[0],extent[1])\n", "ax.set_ylabel(\"$\\delta e$\")\n", "ax.set_xlabel(\"$\\delta a$\")\n", "ax.set_xscale(\"log\")\n", "ax.set_yscale(\"log\")\n", "import matplotlib.ticker as plticker\n", "loc = plticker.LogLocator(numticks=10) \n", "ax.xaxis.set_major_locator(loc)\n", "ax.yaxis.set_major_locator(loc)\n", "im = ax.imshow((dd_sha[:,:,2]), vmax=1e1, vmin=1e-6, cmap=\"viridis_r\", origin=\"lower\",norm=LogNorm(),aspect='auto', extent=extent) #interpolation=\"none\",\n", "cb = plt.colorbar(im, ax=ax)\n", "cb.set_label(\"relative error of second derivative (cross term)\")\n", "\n", "plt.savefig('paper_test4.pdf',bbox_inches='tight')" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "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": "3.4.2" } }, "nbformat": 4, "nbformat_minor": 0 }