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Harmonic distance restraints are not Gaussian
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Harmonic distance restraints are not Gaussian\n",
"## Change of variables\n",
"\n",
"It is often overlooked that a sampling algorithm and a specific parameterization of the representation (set of sampled variables) are intricately linked, though this is clear upon further reflection. When using a Markov chain based sampling algorithm such as Molecular Dynamics or Markov Chain Monte Carlo, each proposed point is only based on the previous one. Moreover, to ensure proper behavior (namely, convergence to a target distribution), we generally want to satisfy detailed balance. The easiest way to satisfy this is to propose moves that would be as likely to be accepted in the forward direction as in the backward direction, namely, reversible moves. The simplest reversible move for a real-valued parameter is to draw a perturbation from a normal distribution. Of course, this implicitly means that our parameterization matters. Sampling a parameter from a normal distribution is *very* different from sampling its inverse!\n",
"\n",
"The mathematical explanation for this is drawn from change of variables in mathematics. Namely, if $x=\\phi(y)$, then $dx = \\phi'(y) dy$. The $\\phi'(y)$ term accounts for te rescaling of different parts of parameter space that happens upon transformation.\n",
"\n",
"Consider the lowly harmonic restraint:\n",
"\n",
"$$f(r) = \\frac{1}{2} k (r-r_0)^2$$\n",
"\n",
"The harmonic is often thought of as Gaussian, due to its similarity to a Gaussian potential\n",
"\n",
"$$g(r) = -\\log \\mathcal{N}(r_0, \\frac{1}{\\sqrt{k}}) = \\frac{1}{2}\\log(2\\pi) - \\frac{1}{2}\\log k + \\frac{1}{2} k (r-r_0)^2$$\n",
"\n",
"Clearly, if $k$ is constant, then the first two terms are constant and have no effect on the score; the usual argument concludes that the harmonic is Gaussian. And this is true, assuming that $r$ is actually the variable being sampled! However, in most cases, $r \\equiv r(X_1,X_2)$ is the distance between two particles with coordinate vectors $X_1$ and $X_2$, and these coordinate vectors are the actual sampled variables!\n",
"\n",
"It is well known in statistics that a modification to a probability density function is necessary when changing variables. For the physicists, this corresponds to change of variables coming from the differential change during u-substitution.\n",
"\n",
"If we start with the \"harmonic\" restraint when sampling in Cartesian coordinates, what is the effective restraint on the distance? Without loss of generality, we fix one of the particles. We then begin by writing\n",
"\n",
"$$ p(X_1) \\propto \\exp \\left(-\\frac{1}{2} k (r(X_1, X_2)-r_0)^2\\right).$$\n",
"\n",
"We then introduct a change of variables $Y = X_1 - X_2$. Since $dY = dX_1$, no change of variables is necessary for this linear transformation:\n",
"\n",
"$$p(Y) \\propto \\exp \\left(-\\frac{1}{2} k (r(Y)-r_0)^2\\right).$$\n",
"\n",
"We then change variables to spherical coordinates. Namely, $Y=(x,y,z) = (r\\sin\\theta\\cos\\phi, r\\sin\\theta\\sin\\phi, r\\cos\\theta)$, where $r$ is exactly the same as the $r$ we've been using above. What factor is needed for this change of variables? We will not show it here, but for multivariate change of variables, we need the absolute value of the determinant of the Jacobian matrix of the transformation. Namely, $dY = dx dy dz = r^2 \\sin\\theta dr d\\theta d\\phi$.\n",
"\n",
"We're only interested in $r$, so we integrate out the directional terms:\n",
"\n",
"$$p(r) = \\int_0^{2\\pi} \\int_0^{\\pi} p(r,\\phi,\\theta) r^2 \\sin\\theta d\\theta d\\phi \\propto \\exp \\left(-\\frac{1}{2} k (r-r_0)^2\\right) r^2$$\n",
"\n",
"Lastly, the effective distance restraint is\n",
"\n",
"$$f(r) = -\\log p(r) = \\frac{1}{2} k (r-r_0)^2 - 2\\log r.$$\n",
"\n",
"Therefore, any time we put a harmonic restraint on a distance but sample coordinates, we are effectively sampling using this distance restraint. $2\\log r$ approaches 0 when the relative difference between $r$ and $r_0$ is low, which occurs when $r$ is close to $r_0$ or when both are high in value. If $k$ is sufficiently high that $r$ fluctuates only very narrowly about $r_0$, then and only then will the effective distance restraint behave harmonicly.\n",
"\n",
"We demonstrate this with a trivial simulation in IMP."
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import scipy.stats\n",
"import matplotlib\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"import IMP\n",
"import IMP.algebra\n",
"import IMP.core\n",
"\n",
"sns.set_style(\"white\")\n",
"matplotlib.rcParams.update({\"axes.labelsize\": 18})\n"
]
},
{
"cell_type": "code",
"execution_count": 73,
"metadata": {},
"outputs": [],
"source": [
"# Constants\n",
"center = IMP.algebra.Vector3D(0, 0, 0)\n",
"mean = 1.5\n",
"k = 1000.\n",
"move_size = .15#2.5\n",
"nwarmup = 1000\n",
"nsample = 10000\n",
"nskip = 10\n",
"\n",
"def get_harmonic_sample(center, mean, k, nwarmup, nsample, nskip, move_size):\n",
"\n",
" # Setup system\n",
" mdl = IMP.Model()\n",
" p = IMP.Particle(mdl)\n",
" d = IMP.core.XYZ.setup_particle(p)\n",
" d.set_coordinates_are_optimized(True)\n",
"\n",
" # Setup scoring function\n",
" h = IMP.core.Harmonic(mean, k)\n",
" ss = IMP.core.DistanceToSingletonScore(h, center)\n",
" r = IMP.core.SingletonRestraint(mdl, ss, d)\n",
" sf = IMP.core.RestraintsScoringFunction(r)\n",
"\n",
" # Setup sampler\n",
" mover = IMP.core.NormalMover(mdl, d.get_particle_index(), move_size)\n",
" mc = IMP.core.MonteCarlo(mdl)\n",
" mc.set_scoring_function(sf)\n",
" mc.set_movers([mover])\n",
" mc.set_return_best(False)\n",
"\n",
" # Randomize initial configuration\n",
" d.set_coordinates(\n",
" 10 * IMP.algebra.get_random_vector_in(IMP.algebra.get_unit_sphere_3d())\n",
" )\n",
"\n",
" # Sample\n",
" coords = np.empty((3, nsample), dtype=np.double)\n",
" mc.optimize(nwarmup)\n",
" mover.reset_statistics()\n",
" for i in range(nsample):\n",
" mc.optimize(nskip)\n",
" coords[:, i] = d.get_coordinates()\n",
" \n",
" print(mover.get_number_of_accepted() / mover.get_number_of_proposed())\n",
" \n",
" return coords\n",
"\n",
"def plot_results(center, mean, k, nwarmup, nsample, nskip, move_size, fn=None):\n",
" coords = get_harmonic_sample(center, mean, k, nwarmup, nsample, nskip, move_size)\n",
" dists = np.linalg.norm(coords - np.array(center)[:, np.newaxis], axis=0)\n",
" std = k**(-.5)\n",
" dist_range = np.r_[np.linspace(dists.min(), dists.max(), 1000), mean]\n",
" a, b = (0 - mean) / std, np.inf\n",
" pdist = scipy.stats.truncnorm.pdf(dist_range, a, b, mean, k**(-.5))\n",
" pdist_corrected = pdist * dist_range**2\n",
" pdist_corrected /= scipy.integrate.trapz(pdist_corrected[:-1], dist_range[:-1])\n",
"\n",
" fig = plt.figure(figsize=(8, 5))\n",
" ax = fig.add_subplot(111)\n",
" \n",
" ax.plot(\n",
" dist_range[:-1],\n",
" pdist[:-1],\n",
" c='k',\n",
"# alpha=.5,\n",
" linewidth=2,\n",
" label=r'True Harmonic ($\\frac{1}{2} k (r-r_0)^2$)',\n",
" )\n",
" line, = ax.plot(\n",
" dist_range[:-1],\n",
" pdist_corrected[:-1],\n",
"# alpha=.5,\n",
" linewidth=2,\n",
" label=r'True \"Harmonic\" ($\\frac{1}{2} k (r-r_0)^2 - 2 \\log r$ )',\n",
" )\n",
" sns.distplot(\n",
" dists,\n",
" ax=ax,\n",
" kde=False,\n",
" color=line.get_color(),\n",
" norm_hist=True,\n",
" label=r'Simulated \"Harmonic\" ($\\frac{1}{2} k (r(X)-r_0)^2$'\n",
" )\n",
" ax.vlines(mean, 0, [pdist[-1]], color='k', linestyle='--', label=r'$r_0$')\n",
"# plt.axvline(mean, c='k', linestyle='--')\n",
" ax.legend()\n",
" ax.set_xlabel(\"Distance\")\n",
" ax.set_ylabel(\"Density\")\n",
" # plt.xlim(0, None)\n",
" fig.tight_layout()\n",
" sns.despine()\n",
" \n",
" if fn is not None:\n",
" fig.savefig(fn)\n",
" plt.show()\n"
]
},
{
"cell_type": "code",
"execution_count": 76,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.2527\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 576x360 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"k = 1\n",
"move_size = 2.5\n",
"plot_results(center, mean, k, nwarmup, nsample, nskip, move_size, fn=\"effective_harmonic.png\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Why is this not a problem?\n",
"\n",
"Take molecular force fields for example. In the process of parameterizing a force field, care is generally taken that small molecules sampled using MD according to the force field have expected ensemble properties. Therefore, the \"harmonic\" terms themselves are parameterized such that the correct target distribution is achieved. Moreover, the stiffness constants seen in force fields are generally quite large. Very narrow pseudoharmonics are barely distinguishable from true harmonics when little density is near the origin:"
]
},
{
"cell_type": "code",
"execution_count": 80,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.25351\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x360 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"k = 1000\n",
"move_size = .15 # Adjusted for efficient MCMC sampling\n",
"plot_results(center, mean, k, nwarmup, nsample, nskip, move_size, fn=\"effective_harmonic_stiff.png\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Why is this a problem?\n",
"\n",
"In integrative modeling in particular, it is not uncommon to introduct distance restraints between two bodies to reflect prior information that the two bodies co-localize in space. It is always important when designing a new restraint that it genuinely reflects the information available to us. If we have performed the highly recommended practice of testing our restraints on toy systems using various assumed modes to be sure they behave properly, then we probably already noticed the the \"harmonic\" restraint is not truly harmonic; if we use it, then it must be because we feel that it accurately reflects our available information. However, if we simply co-opt the harmonic restraint by analogy to a Gaussian and proceed without model checking, then we may be surprised at the sub-optimal results"
]
},
{
"cell_type": "code",
"execution_count": 84,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/usr/local/lib/python3.7/site-packages/ipykernel_launcher.py:4: RuntimeWarning: divide by zero encountered in log\n",
" after removing the cwd from sys.path.\n"
]
},
{
"data": {
"image/png": 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F5I8ryYFFd8LRH6HnX82j9ZxsOwCw+Wgu936wBYC5dyfTrZlzzcfktyngReSPOZECC0dA8UkYOAs63l6t4ZbtyGDiop00qRPCu6MvpWlMmEWFyllOBbzNZuPRRx8lIyODyspKHnjgAVq0aMHkyZPx8fEhMTGRadOm4VuN7+wiUoukLIQVf4HQeuYBHXFdnB7KMAxeWXWAf39zgO4JdZk5oouO13MRpwJ++fLlREdH8+KLL5Kfn88tt9xC69atGT9+PMnJyUydOpVVq1bRt29fq+sVkZpUZTuzeWkmNO0Fg96D8Finh6uwVzHp450s3ZHJbUlNeG5gBx3S4UJOBXz//v3p168fYH439vPzIzU1lW7dugHQu3dv1q5dq4AX8WTFp8wlkMfWQvdx0Pcp8HN+Vje3pJL75mxh89E8/nZtS8Zd1UJ93F3MqW+dYWFhhIeHU1xczEMPPcT48eMxDOPcb1ZYWBhFRUWWFioiNShtM7zZGzK2wcC3of+z1Qr3g6eKueU/a0lJL+C1YZ158OpEhXsNcPrfRidOnGDUqFHcfPPNDBgw4Ffz7SUlJURGqimQiEfa+j68fz34BcLdX0PHwdUa7rv9p7j1P2spqbCz4J7uDNAyyBrjVMBnZ2czZswYJk6cyKBBgwBo27YtGzduBGD16tV07drVuipFxPVsZbD8z+bD1Ka94N7voWEHp4czDIM3fzjEmPc3c1HdUJY9eDldLq5jWbny+5z6N9fMmTMpLCxkxowZzJgxA4DHHnuMZ555hpdffpmEhIRzc/Qi4gFyDsFHd8LJXdBrAlz1mNPNwsBsOzB5sfkw9YYOjXhxcEdCA7Uqu6b5GIZhuOviAwcOZMmSJe66vIgApH4Cy/5szrHf+ha0vLZaw2UVlHPvnC3sTC9gQt+WPHi1HqZa7Y9mp76lilyo7JXmEshNb0KTS80lkNEXVWvIbcfzuG/OVkor7Lw1sgvXtmtoUbHiDAW8yIUo75jZvz1jK3T/E/R5Evyrt9no463pPLpkFw2jgpk7NplWDZ3vTyPWUMCLXGj2fwGf3A+GA26fA21vqtZwtioHz3+xj3fWHOGy5vX4z/Ak6oRpZ2ptoIAXuVBU2WDVU7DuVWjYEW6fDXWr15b3VFE5D87fzqYjuYy+rCmP3dCGAD/tTK0tFPAiF4Lcw/DxWMjcBl3ugv7PQ0BwtYbccjSXP83bRmG5jX8NuYRbOzexqFixigJexNvt/Ag+/avZ1nfwbGh3S7WGMwyD2euO8sxne4mrE8LsMd1o00gbG2sjBbyIt6oogs/+BjsXQnwPs8VvNVfJlFbaeXTJLpbuyKRPm/q8dHsnokJ0IHZtpYAX8UYZ22DxWPMg7CsmQ++J1eolA3A0u4T7525l/8ki/nZtS/50ZQudmVrLKeBFvInDAetfMx+mhjeE0Z/BxZdVe9iv95zkrx/twM/Xh/fv6sYVLZ1vGSw1RwEv4i0KT8DSB+Dwd9DmJrjpVQipXu+XSruD6V+aSyDbx0Xyxh1duKhuqEUFi6sp4EW8we7F5oNUewUMeAWS7oRqtgdIyy3lwQXbSUnL584eF/PoDW0I8ne+P43UPAW8iCcryzMfpO7+GOK6wq1vQkyLag+7MjWLiYtSMAyYcUcS13doZEGxUtMU8CKe6tC3sHQclJyCqx6Hng9X+0Fqpd3Bc1/s5b21R+nYJIrXhyURX09TMp5KAS/iaSpL4ZtpsOktiGkFw+ZD487VHvZ4TikPLtjGzvQCRl/WlEeub60pGQ+ngBfxJBlbYcm9kHPQbBJ2zVQICKn2sJ/vOsGkxTvxAWaO6EL/9uoC6Q0U8CKewFYOP0yHta9ARCMYtRwSrqj2sCUVdp5ckcpHW9K55KJoXh/WWatkvIgCXqS2S9sEy8ZB9k/QeQRc+w8Iia72sDvS8hm/cDvHckt58KoW/KVPohqFeRkFvEhtVVkK3z4DG2ZAVBMYsQRaXFPtYascBjN/OMS/vv6JBpHBLLynO8kJ9SwoWGobBbxIbXR0DSx7EPKOQNex0PdJCKr+ARoZ+WU8/OEONh3J5caOjfjHrR3US8aLKeBFapOKYvjmCdg8C+o0hTs/hWa9LBl6RUomj36yC8OAl2+/hFs7x+msVC+ngBepLX76Cj6bAAVp5gqZqx+HwLBqD1tQauOJFal8sj2DzvHRvDKks9a2XyAU8CLuVngCvpwMe5ZCbGsYsxLiky0Z+vv9p5i0eCc5xZWM75PIg1e1wF8PUi8YCngRd3FUwZZ3zc6P9gq4egpc9lC1D78GKK6w84/P9rBgUxotG4Tz9qhL6dAkyoKixZMo4EXcIWsXrBgPGVsg4Sq44SWo19ySodcfymHixylk5pdx/xXNebhvonakXqAU8CI1qbIEvn8e1v/HbOU78G3oMKjanR8ByiqrmP7lPt5fd5RmMWEsuv8yulxcvXbB4tkU8CI1wTBg7wpY+RgUHDfb+fZ5AkLrWjL8lqO5TPx4J0eySxh9WVMm9W9NSKDu2i90CngRVzv9E3zxd/Mgjvrt4K4vLDllCaCo3MYLX+5nzoZjxEWHMP+eZC5rHmPJ2OL5FPAirlJRBD+8YO5EDQiD614wNy1Vs6XvWd/uO8ljn+wmq7Ccuy5vyt+ubUVYkP5Ky8/0p0HEaoYBuxbBV1OgOAs6j4RrpkG4NeeY5hRX8NSne1i2I5OWDcL5zx2XkRSvuXb5vxTwIlbK2gWf/x2OrzN7tA+dB026WjK0YRgs3ZHBUyv2UFxhZ3yfRP50ZQsC/bWuXX6bAl7ECkVZZmOw7XPN1TEDXjXv3H2tCd/jOaVMWbabH346Tef4aKbf1pGWDarfm0a8mwJepDoqS2H967Dm31BVabYYuGKiGfIWqLBX8dYPh3n9u4P4+/owbUBbRvVoip+vesjI76tWwKekpPDPf/6TOXPmcOzYMSZPnoyPjw+JiYlMmzYNX4vuXkRqHYcDdn5o7kItyoQ2A6DPk5ZtVgJYcyCbqct2czi7hBs6NGLKjW1pGBVs2fji/ZwO+FmzZrF8+XJCQszjwp577jnGjx9PcnIyU6dOZdWqVfTt29eyQkVqjSM/wlePwYkUc5590DuWLXsEOFVYztOf7WVFSiYX1wvl/bsu5cpW9S0bXy4cTt9ix8fH89prr537PDU1lW7dugHQu3dv1q1bV/3qRGqTk3tgwTCYfSOU5MDAWXD3t5aFu73KwXtrj3D1Sz+wMjWL8X0SWTm+t8JdnOb0HXy/fv1IT08/97lhGOd6S4eFhVFUVFT96kRqg7yj8N1z5pRMUITZFKzHOEsOuz5r/aEcnlyRyr6sInolxvDUze1pFlP9VsFyYbPsIesv59tLSkqIjIy0amgR9yg6CatfhK3vg68fXPZn6PmwZe0FANJyS3n28718sTuLuOgQZtyRxHXtG+ogDrGEZQHftm1bNm7cSHJyMqtXr6Z79+5WDS1Ss8ryYd2rsOENs41v0ki4YhJENrbsEiUVdt74/hBv/XgYPx8fJvRtyT29EwgOUP8YsY5lAT9p0iSmTJnCyy+/TEJCAv369bNqaJGaUVEEm2bB2legPB/a3wZXPWbpyhiHw2BZSgbPf7GPk4UV3NKpMZOua02jKOume0TOqlbAN2nShI8++giAZs2aMXfuXEuKEqlR5YWw6S1zPXtZHrToC9dMgUaXWHqZrcdyeeazvWw/nk/HJlHMuCOJLhdbN90j8t+00UkuXOWFsPFNM9jL8yHxWnMqxqLWAmcdOl3MC1/uY2XqSWIjgnhxUEduS2qCrzYriYsp4OXCU15wJtj/YwZ7y/5wxd8hroullzlVVM4r3xxg4eY0gv19mdC3JWN7NSM0UH/tpGboT5pcOEpyYNObsHGmGfKtrjeDvXFnSy9TXGFn1urDzPrxMJV2ByOS4/nzNYnEhAdZeh2R36OAF++Xd8ychtk2B+xl0PpGM9gtnmOvsFfx4eY0Xl11gOziSm7o0IiJ/VrRVOvZxU0U8OK9snbD2n/D7iXg4wsdh8DlD0FsK0svY6ty8PHWdF7/9iAZ+WV0a1aXWaNa01k92sXNFPDiXQwDjq01uzse/BoCw6H7A2aXx6g4Sy9lr3KwdEcmr646wPHcUi65KJrnBnagV2KMNipJraCAF+9gr4DUT8z59cztEBZrthS4dKxlrXvPcjgMVuzM5JVVBzh8uoR2jSN5586uXN26voJdahUFvHi24lOw5V3Y/A6UnIKYlnDDy9BpuKW9YgCqHAaf7zrBa98e4KeTxbRqEMHMEV3o166Bgl1qJQW8eKbMHebd+u7F5kEbLfpC9/sh4WrLTlE6q9LuYOn2DN744RBHsktoHhvGq8M6c2OHRlrLLrWaAl48h70C9q4w79aPr4OAMEi6E5Lvg5hEyy9XVlnFh5uP89bqw2QWlNOucSRv3JHEte0a6kQl8QgKeKn9cg+bHR23z4PSbIiOh2ufMc88DYm2/HKF5TbmbjjGOz8eIaekkkub1uHZgR24omWspmLEoyjgpXaqssH+z2HLe3D4O/Dxg1bXQZe7oLn10zAAmfllzF53lPmbjlNUbueKlrGMu6oF3ZqpX4x4JgW81C65h8079e1zoPgkRMbBlY+aLXstbNf7SzvT83n7xyN8tusEANe1b8h9vZvToUmUS64nUlMU8OJ+FUWQuhR2zDfn1vExG391HQOJfc3DNixW5TD4Zu9J3vnxCJuO5hIR5M+Yy5ty52VNaVIn1PLribiDAl7cw+GAoz+aob53OdhKoV4LuGaqueM0qolLLltQamPR1jTmbDjGsZxS4qJDmHJjW27v2oSI4ACXXFPEXRTwUrNO74ddiyBlIRSkQVCUGeid7jDb9LroIeau9ALmbDjK8pRMym0OkuKj+Xu/1vRr1wB/P+vn80VqAwW8uF7uEUhdYvaEObnb7AvT/Gro8wS0vsHyDUlnlduqWJGSydwNx0hJLyAkwI9bOzdhRPd42jXW/Lp4PwW8uEZhptk6YPdiyNhqvndRMlz3ArS9GSIauuzS+7IKWbQlnY+3plNQZqN5bBhPDGjLwC5NiNQ0jFxAFPBinfzjsO8zczPSsXWAYbbk7fsUtLvVXL/uIgVlNpanZLJoSxo70wsI8PPh2rYNGdH9Yron1NX6dbkgKeDFeYYBp/bCvk/NUM/aab4f2waufMQ8tDqmhcsu73AYrDuUw0db0vgyNYtKu4PWDSOYemNbbukcR92wQJddW8QTKODl/DiqIH0L7FsBez+FvCPm+026mXfqrW+Ees1ddnnDMNhzopDlKZl8mnKCjPwyIoP9GXrpRdze9SLaNY7U3brIGQp4+X0lOXBoFRz4Cg6ugrJc8A2AZr3NAzRaXe/SOXWAo9klLE/JZHlKJgdPFePn60PvxBj+3r8V/do1JDjA+rXyIp5OAS//l8Nh9lQ/+LUZ6hnbAANCY8wNSIl9zY9g165Eycwv44vdWSxPySQlLR+Abk3r8swt7bm+QyNNwYj8DgW8mPKOwuEf4MhqOPy92dQLH3Nt+pWPQGIfaNTZJT1gfungqWJWpmaxMjWLnekFALRrHMkj17XmxksaExftmiWVIt5IAX+hKsqCIz/Cke/NUM8/br4f3gBaXGP2V29+NYTVc2kZhmGwK6OAlalZfLk7i0OnSwC45KLoc9MvzWPDXVqDiLdSwF8oCjLg+Ho4vsEM9Oz95vvBUdC0F1z2kDmnHtPSZbtJzyost7HmQDbf7z/FDz+d5mRhBX6+PiQ3q8uoHk25tl0DGkXpTl2kuhTw3shRZS5fPL4e0jaaoV6QZv5cQBjEd4fOd5iB3rCjS5p5/ZJhGOw9UcT3P53i+32n2Xo8jyqHQUSwP70TY7myVSx92jSgjubURSylgPcGpbnmQ9GMbZC2AdI2QUWh+XPhDc1A7zHOfG3QAfxc+9tuGAbHckpZfziH9YdyWH84h9NFFQC0bRTJfb0TuLJVfZLio9UHRsSFFPCeprIETqSYYZ65zXw9uxYdoH5bc4NRfA+IT4boi10+5WIYBul5Zaw/nMOGM4F+oqAcgNiIIHok1KNnYgxXtoylfmSwS2sRkZ8p4GuzimI4tcfcIZqx3Qz00/vAcJg/H9kE4jpD0iiIS4JGnVxyhN1/K7dVsSujgO3AePgfAAAMD0lEQVTH89h2LJ9tx/M4deYOvV5YIN0T6tG9eT16JNSjeWyYNh6JuInHBvypwnKiQwMJ9PeCf+IbhjlHnrXb7LaYtct8zT0CGObXhNQ1Q7zNAGicZP44vL7LS7NXOTh0uoTUzAJ2ppuhvudEIbYqs674uqH0aF6PpPg6dE+oR2L9cHx1ILVIreCRAb8zPZ+bXl9LgJ8PLepH0KZRBG0bRdLmzEet3gBjKztzV342zHfDyVSoKPj5a+o0g4btoeNQ87VBe7NRl4vvhEsr7ezLKiI1s5A9mQWkZhayL6uISrv5L4bgAF86NolmbM8EkuKj6Rxfh9iIIJfWJCLO88iA7xAXxRt3JJGSXsDeE4WsOZDNkm0Z536+QWQQLeqHkxATTkJsGAmx4STEhBEXHVJzd5eGYbbMPXdHnmr+OOfgz1MsAWHQoB10uM0M8YYdzDn0INet+zYMg+ziSg6dLubgKfPj0OliDp0qJvPMvDlAVEgA7RpHcmePi2nXOIq2jSNJiAnTQ1ERD2JpwDscDp544gn2799PYGAgzzzzDBdffLGVlwDAx8eH6zo04roOjc69l11cwb4TRew9UcjeE4UcOl3M0u0ZFFXYz31NkL8vzWLCiK8bSlydEOKiz3yc+XHdsEDn5ott5ebc+Lk78jMfZXk/f010vLmCpd2tZ8K8PUQ3dcnO0OIKO+l5paTnlpGeV0panvmanldGWm4pheU//5qEBvrRPDacbs3q0qJ+OC0bRNAuLorGUcGaOxfxcJYG/DfffENlZSUffvghO3bs4Pnnn+eNN96w8hL/U0x4ED0Tg+iZGHPuvbN3q4dPF3M4u8R8PV3CkewS1hzMprSy6ldjBAf40jgqhJjwIGIiAqkXFkRMeBD1wgPN98IDifIppU5BKuG5uwnK3oPPyd2QfQCMM2MFhJp34W1uMu/IG7QzP5zs22IYBqWVVRSU2Sgst1FQaqOw3E5+aSWniio4XVTB6eIKTheeeS2qoPgX39TO/n9dVCeUJnVCSIqvQ0JsGM1jw2lRP5yGkcGaMxfxUpYG/NatW+nVqxcAnTp1Yvfu3VYOf958fHyIjQgiNiKI5IRfb7k3DIOCMhvpeWVk5peRkV9GRl4ZJwrLyS6qYH9WEYXFWVxU/hOX+B4izPcwdX0OkeCbdW6MdCOGAzTlqP+tpAU2Jy0wgdzAxvg7Agg87UtQni+BB3wJ8DuMYZiPSw3DOPvYFAyochhU2Ksotzkot1dR8YvXMlsVhWU27A6D/yUiyJ/YiCBiIoJo1ziS2Igg6kcE06ROCBfVNUO9nrP/MhERj2ZpwBcXFxMe/vP8sZ+fH3a7HX//2jfV7+PjQ3RoINGhgbSPO3N3bSuH9M1wbC0cXQNlmyHInJe2hTWkoE4H9kUN40RYG44HtSLHEUpRuY2icjslFXYcdgehVQ4q7A6Kyu3k2B1UVjmwVTnwOXNNH4AzWesD+Pr4EBzgR3CAL+FB/tQL8yUowI9gf/O9qJAAIkMCzNfgM68h/kSHBBITEUhoYO37tRWR2sHSdAgPD6ekpOTc5w6Ho1aG+68UZcFPX8L+L8wuivZy81Dohh2g61i4+DKI60JAZCNigBigtZtLFhH5IyxN36SkJL777juuv/56duzYQcuWLa0c3jrlBZC6FHbMN7f2g/kQNOlOs4NifPca2TAkIuJKlgZ83759Wbt2LUOHDsUwDJ599lkrh6++U/tg3auwe7F5px7TCq6eYp5IVL+Ny9eZi4jUJEsD3tfXl6eeesrKIa1xah+sehL2f26ucuk0HDqPMHeEKtRFxEvV8gnyaqoohm+fgU1vQWA4XDEZut3r8kMsRERqA+8N+Mwd8PEYyD0MXUbD1Y9DWMzv/mciIt7COwN+zzJYfLd5SPToT6FpT3dXJCJS47wv4HfMh2XjoMmlMGwhhNZ1d0UiIm7hXQF/6FtY9qB5xuiwBRAY5u6KRETcxntaAxZlmXPusa1hyFyFu4hc8Lwj4A0DPn3Y7LV++2wIjnR3RSIibucdAX/4O3ON+1WPQkyiu6sREakVPD/gDQO+e9Y8nzT5fndXIyJSa3h+wJ9IMTtAXv4X8NfxcSIiZ3l+wO+YB35B0HGwuysREalVPDvgHVVm47DWN0BIHXdXIyJSq3h2wJ/YAaU5ZjdIERH5Fc8O+MPfm68JV7qxCBGR2smzAz5zO9RNgPBYd1ciIlLreHbAn9gJDTu6uwoRkVrJcwO+vADyj0EjBbyIyG/x3IDPO2q+1tPOVRGR3+K5AV+Yab5Gxrm3DhGRWspzA74g3XyNUsCLiPwWzw34wkzw9YcwraAREfktHhzwGRDRGHz93F2JiEit5LkBX5QFEQ3cXYWISK3luQFfUQTBUe6uQkSk1vLsgA+KcHcVIiK1lgJeRMRLeXjA6+xVEZH/xTMD3uEAWwkEhru7EhGRWsvf3QU4xdcX+jwBrQe4uxIRkVrLMwMeoOfD7q5ARKRW88wpGhER+V0KeBERL1WtgP/666+ZMGHCuc937NjB4MGDGTp0KK+//nq1ixMREec5HfDPPPMML730Eg6H49x706ZN46WXXmLBggWkpKSwZ88eS4oUEZHz53TAJyUl8cQTT5z7vLi4mMrKSuLj4/Hx8aFnz56sW7fOihpFRMQJv7uKZtGiRcyePftX7z377LNcf/31bNy48dx7xcXFhIf/vC49LCyMtLQ0C0sVEZHz8bsBP3jwYAYPHvy7A4WHh1NSUnLu85KSEiIjtdNURMRdLFtFEx4eTkBAAMePH8cwDNasWUPXrl2tGl5ERM6TpRudnnzySf72t79RVVVFz549ueSSS/6/X5+RkcHAgQOtLEFExOtlZGT8oa/zMQzDcHEtIiLiBtroJCLipRTwIiJeSgEvIuKlFPAiIl5KAS8i4qU8LuAdDgdTp05lyJAhjBw5kmPHjrm7JJez2WxMnDiR4cOHM2jQIFatWuXukmpETk4OV1xxBYcOHXJ3KTXmzTffZMiQIQwcOJBFixa5uxyXstlsTJgwgaFDhzJ8+HCv/31OSUlh5MiRABw7doxhw4YxfPhwpk2b9queXlbyuID/5ptvqKys5MMPP2TChAk8//zz7i7J5ZYvX050dDTz58/n7bff5umnn3Z3SS5ns9mYOnUqwcHB7i6lxmzcuJHt27ezYMEC5syZQ1ZWlrtLcqkffvgBu93OwoULGTduHP/+97/dXZLLzJo1i8cff5yKigoAnnvuOcaPH8/8+fMxDMNlN20eF/Bbt26lV69eAHTq1Indu3e7uSLX69+/P3/5y18AMAwDPz8/N1fketOnT2fo0KHUr1/f3aXUmDVr1tCyZUvGjRvH/fffz5VXXunuklyqWbNmVFVV4XA4KC4uxt/fcw+Y+z3x8fG89tpr5z5PTU2lW7duAPTu3dtljRk97lf0v5ua+fn5YbfbvfoPR1hYGGD+vz/00EOMHz/ezRW51pIlS6hbty69evXirbfecnc5NSYvL4/MzExmzpxJeno6DzzwAF9++SU+Pj7uLs0lQkNDycjI4LrrriMvL4+ZM2e6uySX6devH+np6ec+Nwzj3O9rWFgYRUVFLrmux93B/3dTM4fD4dXhftaJEycYNWoUN998MwMGePdh44sXL2bdunWMHDmSvXv3MmnSJE6fPu3uslwuOjqanj17EhgYSEJCAkFBQeTm5rq7LJd5//336dmzJytXrmTZsmVMnjz53BSGt/P1/Tl6XdmY0eMCPikpidWrVwPmCVItW7Z0c0Wul52dzZgxY5g4cSKDBg1ydzkuN2/ePObOncucOXNo06YN06dPJzY21t1luVyXLl348ccfMQyDkydPUlZWRnR0tLvLcpnIyEgiIiIAiIqKwm63U1VV5eaqakbbtm3PtVtfvXq1yxozetytb9++fVm7di1Dhw7FMAyeffZZd5fkcjNnzqSwsJAZM2YwY8YMwHxocyE9gLwQXHXVVWzevJlBgwZhGAZTp0716ucto0eP5tFHH2X48OHYbDYefvhhQkND3V1WjZg0aRJTpkzh5ZdfJiEhgX79+rnkOmo2JiLipTxuikZERP4YBbyIiJdSwIuIeCkFvIiIl1LAi4h4KQW8iIiXUsCLiHgpBbyIiJf6f5nDYEHC8kIXAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"r = np.linspace(0, 10, 1001)\n",
"score = .5 * 1 * (r - 1.5)**2\n",
"plt.plot(r, score)\n",
"score += 2 * np.log(r)\n",
"plt.plot(r, score)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"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": "3.7.4"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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