{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Hamiltonian Monte Carlo algorithm\n", "\n", "In this notebook, I shall implement Hamiltonian Monte Carlo algorithm (HMC), a MCMC algorithm using Hamiltonian dynamics to propose a point, which is distant from the current point yet with low rejection probability.\n", "\n", "The formulation in this notebook is based on Neal \"MCMC using Hamiltonian dynamics\" https://arxiv.org/abs/1206.1901" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import random \n", "from matplotlib import pyplot as plt\n", "\n", "%matplotlib inline\n", "plt.rcParams['axes.labelsize'] = 14\n", "plt.rcParams['xtick.labelsize'] = 12\n", "plt.rcParams['ytick.labelsize'] = 12" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 1 Theory\n", "\n", "## 1.1 Setting\n", "\n", "* Let us assume that the variable of interest resides in $\\mathbb{R}^d$, with $d \\in \\mathbb{N}$ being the dimension. \n", "* Let $\\pi_Q$ be a probability distribution over $\\mathbb{R}^d$, from which we want to sample. It is assumed that $\\pi_Q$ can be expressed as $\\pi_Q = \\frac{1}{Z_Q} \\tilde{\\pi}_Q$ with constant $Z_Q$ and a unnormalized distribution $\\tilde{\\pi}_Q$, where $\\tilde{\\pi}_Q$ can be evaluated easily.\n", "* Let us define $U(q) := - \\log \\tilde{\\pi}_Q(q)$, and assume that it is differentiable with respect to $q$.\n", "* For simplicity, we shall assume that the $\\pi_Q$ is everywhere non-zero, so that $U$ is defined everywhere on $Q$. (If there exists a region on which $\\pi_Q = 0$ holds, then ergodicity might break. In my intuition, assuming that the region $\\left\\{ q \\in \\mathbb{R}^d | \\pi_Q(q) > 0 \\right\\}$ is singly connected may suffices, but I have not verified it.)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1.2 Introducing the momentum variable\n", "\n", "Let us introduce \n", "\n", "* an auxiliary variable, which shall be called \"momentum\", $p \\in \\mathbb{R}^d$, and\n", "* a probability distribution $\\pi_P(p) \\propto e^{-K(p)}$ over $\\mathbb{R}^d$, where $K$ is even in the sense that $K(p) = K(-p)$ holds for all $p \\in \\mathbb{R}^d$. (Later, we take $K(p) = \\frac{1}{2} p^T p$.) It is assumeed that $\\pi_P$ can be easily sampled. \n", "\n", "Let us define the Hamiltonian $H$ by $H(q,p) = K(p) + U(q)$.\n", "\n", "Under these definitions, consider sampling from the joint probability distribution $\\pi_{Q, P}(q, p) = \\pi_Q(q) \\pi_P(p)$. \n", "It is clear that marginalizing the distribution with respect to $p$ will immediately give us $\\pi_Q$, our target distribution. Put differently, if we sample from the joint distribution and simply dispose $p$ components, then we get samples of $q$ which follows $\\pi_Q$.\n", "\n", "Also, it should be noted that $\\pi_{Q, P}(q, p) \\propto \\exp[-H(q, p)] =: \\tilde{\\pi}_{Q, P}(q, p)$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1.3 Recap of Metropolis-Hastings algorithm\n", "\n", "The idea of HMC is to use a deterministic dynamics to propose the next point in Metropolis-Hastings algorithm.\n", "Thus, here we quickly go through Metropolis-Hastings algorithm applied to the current problem.\n", "\n", "In the Metroopolis-Hastings algorithm, a single update step (which shall be called Metropolis-Hastings update) proceeds as follows (denote the current point by $(q_{\\rm current}, p_{\\rm current})$): \n", "1. a point $(q_{\\rm tmp}, p_{\\rm tmp})$ is proposed according to a given proposal distribution $\\rho(q_{\\rm tmp}, p_{\\rm tmp} | q_{\\rm current}, p_{\\rm current})$.\n", "2. The next point $(q_{\\rm next}, p_{\\rm next})$ is determined by\n", "\n", "$$\n", "\\begin{align}\n", " (q_{\\rm next}, p_{\\rm next}) = \\begin{cases}\n", " (q_{\\rm tmp}, p_{\\rm tmp}) & (\\mbox{ with probability } A((q_{\\rm tmp}, p_{\\rm tmp}), (q_{\\rm current}, p_{\\rm current} )) \\ )\\\\\n", " (q_{\\rm current}, p_{\\rm current}) & (\\mbox{ with probability } 1 - A((q_{\\rm tmp}, p_{\\rm tmp}), (q_{\\rm current}, p_{\\rm current}) ) \\ )\n", " \\end{cases}\n", "\\end{align}\n", "$$\n", "\n", "where \n", "\n", "$$\n", "\\begin{align}\n", " A((q', p')| (q, p) ) := \\min \\left( 1, \\frac{\\tilde{\\pi}_{Q, P}(q', p')}{\\tilde{\\pi}_{Q, P}(q, p)} \\cdot \\frac{\\rho(q, p| q', p')}{\\rho(q', p' | q, p)} \\right)\n", "\\end{align}\n", "$$\n", "\n", "In the former case, we say the proposed point $(q_{\\rm tmp}, p_{\\rm tmp})$ is accepted, while in the latter case it is said to be rejected.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1.4 Metropolis-Hastings update with deterministic transitions\n", "\n", "Let us consider a deterministic transition defined by $f : \\mathbb{R}^d \\times \\mathbb{R}^d \\rightarrow \\mathbb{R}^d \\times \\mathbb{R}^d $ as our proposal distribution:\n", "\n", "$$\n", "\\begin{align}\n", " \\rho(q, p | q', p') = \\delta((q, p) - f(q', p')), \n", "\\end{align}\n", "$$\n", "where $\\delta$ stands for the delta fucnction. (NOTE : Here all the mathematical subtleties related to the delta function are neglected.)\n", "\n", "Assuming\n", "1. $f$ is invertible and $f^{-1} = f$, and\n", "2. $f$ has unit Jacobian, \n", "\n", "it can be shown that, \n", "\n", "$$\n", "\\begin{align}\n", " A((q', p')| (q, p) ) := \\min \\left( 1, \\frac{\\tilde{\\pi}_{Q, P}(q', p')}{\\tilde{\\pi}_{Q, P}(q, p)} \\right)\n", "\\end{align}\n", "$$\n", "\n", "holds(Again, I have not verified it in mathematically rigorous way.) \n", "\n", "Thus, if we can find a mapping $f$ that satisfies the properties shown above, we can use it to propose candidate points, without being bothered by the ratio of proposal distribution. Also, if $f$ approximately conserves $\\tilde{\\pi}(q, p)$, then we can realize a low rejection rate." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1.5 Hamiltonian dynamics\n", "\n", "It turns out that Hamiltonian dynamics defined by \n", "$$\n", "\\begin{align}\n", " \\frac{dq(t)}{dt} = \\left. \\frac{\\partial H(q, p)}{\\partial p} \\right|_{q=q(t), p=p(t)} \\\\\n", " \\frac{dp(t)}{dt} = - \\left. \\frac{\\partial H(q, p)}{\\partial q}\\right|_{q=q(t), p=p(t)} \n", "\\end{align}\n", "$$\n", "fits perfectly with our purpose. Here, it should be understood as follows: starting from an arbitrarily chosen current point, denoted by $(q_0, p_0)$, follow the time evolution defined by the differential equation for an arbitrary time interval, say, $s$, which gives us a point $(q(s), p(s))$. This mapping from $(q_0, p_0)$ to $(q(s), p(s))$ is expressed as $T_s$.\n", "\n", "The mapping $R \\circ T_s$, where $R$ stands for momentum inversion $R : (q, p) \\mapsto (q, -p)$, satisfies the following properties: \n", "1. Both $R$ and $T_s$ have unit Jacobian, and hence $R \\circ T_s$ also has unit Jacobian.\n", "2. $(R \\circ T_s)^{-1} = R \\circ T_s$ \n", "3. Both $R$ and $T_s$ conserves the value of Hamiltonian, and hence $H((R \\circ T_s)(q,p)) = H(q, p)$\n", "\n", "Thus, with this mapping, we can use the formula shown in the end of the previous section to perform Metropolis-Hastings update.\n", "However, there remain two problems:\n", "\n", "1. The mapping $T_s$ cannot be obtained exactly, and we must resort to numerical integration. \n", "2. Because $T_s$ conserves the value of $H$, it breaks ergodicity. (Its numerically approximated version may break the exact conservation, but if $H$ changes very slowly, then convergence toward stationary distribution can also be slow.) \n", "\n", "The latter problem is solved by interleaving the Metropolis-Hastings update (by Hamiltonian dynamics) with sampling the momentum $p$ from $\\pi_P$. It can be easily shown that this update leaves the probability distribution $\\pi_{Q, P}$ invariant.\n", "\n", "As to the former problem, we shall see in the next subsection how to integrate the differential equation numerically while exactly maintaining some desirable properties of the original Hamiltonian dynamics. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1.6 Leapfrog method\n", "\n", "Let us define $f_{\\delta} : \\mathbb{R}^d \\times \\mathbb{R}^d \\rightarrow \\mathbb{R}^d \\times \\mathbb{R}^d$, $g_{\\delta} : \\mathbb{R}^d \\times \\mathbb{R}^d \\rightarrow \\mathbb{R}^d \\times \\mathbb{R}^d$ and $h_{\\delta} : \\mathbb{R}^d \\times \\mathbb{R}^d \\rightarrow \\mathbb{R}^d \\times \\mathbb{R}^d$ for $\\delta \\in \\mathbb{R}$ by \n", "$$\n", "\\begin{align}\n", " f_{\\delta} \\begin{pmatrix}\n", " q \\\\\n", " p\n", " \\end{pmatrix}\n", " = \\begin{pmatrix}\n", " q \\\\\n", " p - \\frac{\\delta}{2} \\frac{\\partial U}{\\partial q}\n", " \\end{pmatrix}, \\\n", " g_{\\delta} \\begin{pmatrix}\n", " q \\\\\n", " p\n", " \\end{pmatrix}\n", " = \\begin{pmatrix}\n", " q + \\delta \\frac{\\partial K}{\\partial p} \\\\\n", " p\n", " \\end{pmatrix}, \\\n", " h_{\\delta} = f_{\\delta} \\circ g_{\\delta} \\circ f_{\\delta}\n", "\\end{align}\n", "$$\n", "\n", "Let us denote a discretized time step by $\\varepsilon > 0$. \n", "Then, a single update of leapfrog method can be expressed by $h_{\\varepsilon}$. ($f_{\\varepsilon}$ corresponds to update (11.64) and (11.66) of PRML, while $g_{\\varepsilon}$ corresponds to update (11.65).). \n", "\n", "Assuming that we want to integrate the equation of motion over time interval $\\varepsilon L$, with $L \\in \\mathbb{N}$, the approximate dynamics can be expressed by $h_{\\varepsilon}^{L}$.\n", "\n", "It can be shown that \n", "1. $h_{\\varepsilon}$ and $h_{\\varepsilon}^{L}$ have unit Jacobian, and that\n", "2. $(R \\circ h_{\\varepsilon}^{L})^{-1} = R \\circ h_{\\varepsilon}^{L}$\n", "\n", "Thus, instead of $R \\circ T_s$, we can use $R \\circ h_{\\varepsilon}^{L}$ for the Metropolis-Hastings update. It should be noted, however, that now the value of Hamiltonian conserves only approximately, resulting in non-zero rejection probability." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1.7 HMC algorithm\n", "\n", "With everything described so far in mind, a HMC update consists of the following two steps: \n", "\n", "input : $q_{\\rm current}, p_{\\rm current}$\n", "\n", "1. $p_{\\rm current} \\leftarrow$ value randomly sampled from $\\pi_P$\n", "2. Sample $(q,p)$ by Hamiltonian dynamics as follows:\n", " 1. $(q_{\\rm proposed}, p_{\\rm proposed}) \\leftarrow h_{\\varepsilon}^{L} (q_{\\rm current}, p_{\\rm current}) $, i.e., the point obtained by leapfrog update starting from $(q_{\\rm current}, p_{\\rm current})$, with step size $\\varepsilon$ and the number of steps $L$.\n", " 2. $p_{\\rm proposed} \\leftarrow - p_{\\rm proposed}$ \n", " 3. With probability $\\min\\left\\{ 1, \\exp\\left[ H(q_{\\rm current}, p_{\\rm current}) - H(q_{\\rm proposed}, p_{\\rm proposed}) \\right] \\right\\}$, accept $(q_{\\rm proposed}, p_{\\rm proposed})$, i.e., let $(q_{\\rm current}, p_{\\rm current}) \\leftarrow (q_{\\rm proposed}, p_{\\rm proposed})$\n", " \n", "\n", "NOTE : The operation 2-B is unnecessary in practice, because of the fact that $K(p) = K(-p)$ and that in the next update we choose a new $p$ at random without any reference to the current value of $p$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 2 Code and experiment 1 : numerical solutions of Hamiltonian equation of motion \n", "\n", "Before delving into implementing HMC, we shall first take a look on leapfrog method itself as a way for integrating Hamiltonian equation of motion." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.1 Stability and numerical error in trajectory\n", "\n", "Here we shall compare the behavior of leapfrog method with the two methods shown below:\n", "\n", "Euler method\n", "$$\n", "\\begin{align}\n", " h_{\\varepsilon}^{\\rm E}\n", " \\begin{pmatrix}\n", " q \\\\\n", " p\n", " \\end{pmatrix} =\n", " \\begin{pmatrix}\n", " q + \\varepsilon \\frac{\\partial K}{\\partial p} \\\\\n", " p - \\varepsilon \\frac{\\partial U}{\\partial q}\n", " \\end{pmatrix}\n", "\\end{align}\n", "$$\n", "\n", "Modified Euler method\n", "$$\n", "\\begin{align}\n", " f_{\\varepsilon}^{\\rm ME}\n", " \\begin{pmatrix}\n", " q \\\\\n", " p\n", " \\end{pmatrix} =\n", " \\begin{pmatrix}\n", " q \\\\\n", " p - \\varepsilon \\frac{\\partial U}{\\partial q}\n", " \\end{pmatrix}, \\\n", " g_{\\varepsilon}^{\\rm ME} \n", " \\begin{pmatrix}\n", " q \\\\\n", " p\n", " \\end{pmatrix} =\n", " \\begin{pmatrix}\n", " q + \\varepsilon \\frac{\\partial K}{\\partial p} \\\\\n", " p \n", " \\end{pmatrix}, \\\n", " h_{\\varepsilon}^{\\rm ME} = g_{\\varepsilon}^{\\rm ME} \\circ f_{\\varepsilon}^{\\rm ME}\n", "\\end{align}\n", "$$\n", "\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def integrate_eqm(q_initial, p_initial, grad_U, epsilon, L, method=\"leapfrog\"):\n", "\n", " q_trajectory = np.zeros((L+1, len(q_initial)), dtype=q_initial.dtype)\n", " p_trajectory = np.zeros((L+1, len(p_initial)), dtype=p_initial.dtype)\n", " q_trajectory[0] = q_initial\n", " p_trajectory[0] = p_initial\n", "\n", " q = q_initial\n", " p = p_initial\n", " \n", " for i in range(1, L + 1):\n", " if method == \"euler\":\n", " p_tmp = p.copy()\n", " p = p - epsilon * grad_U(q)\n", " q = q + epsilon * p_tmp\n", " elif method == \"modified_euler\":\n", " p = p - epsilon * grad_U(q)\n", " q = q + epsilon * p\n", " elif method == \"leapfrog\":\n", " p = p - epsilon / 2 * grad_U(q) # f__{\\varepsilon}\n", " q = q + epsilon * p # g_{\\varepsilon}\n", " p = p - epsilon / 2 * grad_U(q) # f_{\\varepsilon}\n", " else:\n", " raise Exception\n", "\n", " q_trajectory[i] = q\n", " p_trajectory[i] = p\n", "\n", " return q_trajectory, p_trajectory" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here, we consider a simple problem of $H(q, p) = \\frac{1}{2} q^2 + \\frac{1}{2} p^2$, where $q, p \\in \\mathbb{R}$, whose equation of motion is exactly solvable." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# U(q) = \\frac{1}{2} q^2\n", "def grad_U(q):\n", " return q\n", "\n", "q_initial = np.array([0.0])\n", "p_initial = np.array([1.0])\n", "\n", "q_exact = np.cos(np.linspace(0, 2*np.pi, 101))\n", "p_exact = np.sin(np.linspace(0, 2*np.pi, 101))" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def solve_and_plot_trajectory(ax, q_initial, p_initial, q_exact, p_exact, grad_U, epsilon, L, method):\n", " q_trajectory, p_trajectory = integrate_eqm(q_initial, p_initial, grad_U, epsilon, L, method=method)\n", " ax.plot(q_trajectory[:, 0], p_trajectory[:, 0], 'o-')\n", " ax.plot(q_exact, p_exact, '--', color='k')\n", " ax.axis(\"equal\")\n", " ax.set_title(f\"{method} : stepsize = {epsilon}\")" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(2, 3, figsize=(18, 12))\n", "\n", "L = 20\n", "for ax, epsilon, method in zip(\n", " axes.flatten(),\n", " [0.3, 0.3, 0.3, 1.2, 1.2, 1.2],\n", " [\"euler\", \"modified_euler\", \"leapfrog\", \"euler\", \"modified_euler\", \"leapfrog\"]\n", "):\n", " solve_and_plot_trajectory(ax, q_initial, p_initial, q_exact, p_exact, grad_U, epsilon, L, method)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the figure, shown in dashed curves are exact solutions, while shown in solid curves are numerical solutions.\n", "It can be seen that\n", "\n", "* In Euler method, the trajectory diverges to infinity (At least for this example, it can be analytically proved that the method gives rise to diverging trajectories for any $\\varepsilon > 0$.)\n", "* Modified Euler and leapfrog method seem to be return stable trajectories, but the latter performs better than the former. It can be shown that, for a single step, as $\\varepsilon \\rightarrow 0$, modified Euler method has $\\mathcal{O}(\\varepsilon^2)$ error, while leapfrog method has $\\mathcal{O}(\\varepsilon^3)$.\n", "\n", "However, it should be noted that, when step size is too large, leapfrog method can generate trajectories far from the exact solution, as in the following example (In the next subsection, it will be illustrated that in some cases, Hamiltonian grows indefinitely.):" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(1, 3, figsize=(18, 6))\n", "\n", "L = 20\n", "method = \"leapfrog\"\n", "for ax, epsilon in zip(\n", " axes.flatten(),\n", " [1.99, 2.0, 2.01],\n", "):\n", " solve_and_plot_trajectory(ax, q_initial, p_initial, q_exact, p_exact, grad_U, epsilon, L, method)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.2 Violation of Hamiltonian conservation\n", "\n", "Although leapfrog method performs better than other methods shown above, it is not without numerically error. \n", "In HMC, this numerical error shows itself as non-zero rejection probability resulting from the violation of energy conservation, which are illustrated below." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def solve_and_plot_energy(ax, q_initial, p_initial, grad_U, epsilon, L, method):\n", " q_trajectory, p_trajectory = integrate_eqm(q_initial, p_initial, grad_U, epsilon, L, method=method)\n", " ax.plot(np.linspace(0, epsilon * L, L + 1), 0.5 * ((q_trajectory**2).sum(axis=1) + (p_trajectory**2).sum(axis=1)), 'o-', label=f\"epsilon={epsilon}\")\n", " E0 = 0.5 * ((q_initial**2).sum() + (p_initial**2).sum())\n", " ax.plot([0, epsilon * L], [E0, E0], '--', color='k')" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(10, 6))\n", "ax = fig.add_subplot(111)\n", "for epsilon, L in zip([0.2, 0.4, 0.8], [40, 20, 10]):\n", " solve_and_plot_energy(ax, q_initial, p_initial, grad_U, epsilon, L, method=\"leapfrog\")\n", "\n", "ax.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It can be seen that as the step size grows, so does the numerical fluctuation of Hamiltonian. \n", "When the stepsize is too large, Hamiltonian may indefinitely grow as follows, which makes acceptance probability in HMC extremely low:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "epsilon = 2.01\n", "L = 50\n", "\n", "q_trajectory, p_trajectory = integrate_eqm(q_initial, p_initial, grad_U, epsilon, L, method=method)\n", "E = 0.5 * ((q_trajectory**2).sum(axis=1) + (p_trajectory**2).sum(axis=1))\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(10, 6))\n", "axes[0].plot(q_trajectory[:, 0], p_trajectory[:, 0], 'o-')\n", "axes[0].set_title(\"trajectory\")\n", "axes[1].plot(np.linspace(0, epsilon * L, len(E)), E, 'o-')\n", "axes[1].set_title(\"energy\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 3 Code and experiment 2 : HMC sampling" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3.1 Leapfrog method\n", "\n", "In HMC, where we do not need the trajectory of $p$, the successive application of $h_{\\varepsilon}$ can be simplified as follows:\n", "$$\n", "\\begin{align}\n", " h_{\\varepsilon} \\circ h_{\\varepsilon} = f_{\\varepsilon} \\circ g_{\\varepsilon} \\circ f_{\\varepsilon}^{2} \\circ g_{\\varepsilon} \\circ f_{\\varepsilon}\n", "\\end{align}\n", "$$\n", "$$\n", "\\begin{align}\n", " f_{\\varepsilon}^{2}\n", " \\begin{pmatrix}\n", " q \\\\\n", " p\n", " \\end{pmatrix}\n", " = \\begin{pmatrix}\n", " q \\\\\n", " p - \\varepsilon \\frac{\\partial U}{\\partial q}\n", " \\end{pmatrix}\n", "\\end{align}\n", "$$\n", "\n", "More concretely, \n", "$$\n", "\\begin{align}\n", " h_{\\varepsilon}^{L} = f_{\\varepsilon} \\circ g_{\\varepsilon} \\circ \\left( f_{\\varepsilon}^{2} \\circ g_{\\varepsilon} \\right)^{L-1} \\circ f_{\\varepsilon}\n", "\\end{align}\n", "$$" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "def leapfrog(q_initial, p_initial, grad_U, epsilon, L):\n", " '''\n", " This is a function for integrating Hamiltonian equation of motion using leapfrog method.\n", " It only returns the value obtained at the end of trajectory.\n", " \n", " Parameters\n", " ----------\n", " q_initial : 1D numpy array\n", " 1D numpy array representing the initial value of the position variable q.\n", " p_initial : 1D numpy array\n", " 1D numpy array representing the initial value of the momentum variable p.\n", " len(p_initial) == len(q_initial) must holds\n", " grad_U : function\n", " A function, given position variable q, that returns the gradient of potential energy U.\n", " epsilon : float\n", " A positive real number representing the time step size\n", " L : int\n", " A positive integer representing the number of time steps\n", " \n", " Returns\n", " ----------\n", " q : 1D numpy array\n", " 1D numpy array representing the final value of the position variable.\n", " p : 1D numpy array\n", " 1D numpy array representing the final value of the momentum variable.\n", " '''\n", " \n", " q = q_initial\n", " p = p_initial\n", " \n", " p = p - epsilon / 2 * grad_U(q) # f__{\\varepsilon}\n", " for i in range(1, L):\n", " q = q + epsilon * p # g_{\\varepsilon}\n", " p = p - epsilon * grad_U(q) # f_{\\varepsilon}^{2}\n", " \n", " q = q + epsilon * p # g_{\\varepsilon}\n", " p = p - epsilon / 2 * grad_U(q) # f__{\\varepsilon}\n", " \n", " return q, p" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true, "source_hidden": true } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# for test\n", "\n", "def grad_U(q):\n", " return q\n", "\n", "q_initial = np.array([0.0])\n", "p_initial = np.array([1.0])\n", "epsilon = 0.2\n", "L = 30\n", "\n", "q_trajectory = np.zeros((L+1, len(q_initial)))\n", "p_trajectory = np.zeros((L+1, len(p_initial)))\n", "\n", "q = q_initial\n", "p = p_initial\n", "q_trajectory[0] = q\n", "p_trajectory[0] = p\n", "\n", "for l in range(1, L+1):\n", " q, p = leapfrog(q, p, grad_U, epsilon, 1)\n", " q_trajectory[l] = q\n", " p_trajectory[l] = p\n", "\n", "\n", "plt.plot(q_trajectory[:, 0], p_trajectory[:, 0], 'o-')\n", "q_exact = np.cos(np.linspace(0, 2*np.pi, 101))\n", "p_exact = np.sin(np.linspace(0, 2*np.pi, 101))\n", "plt.plot(q_exact, p_exact, \"k--\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3.2 Sampler\n", "\n", "With leapfrog method implemented above, the implementation of HMC is straightforward." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "class HMCsampler:\n", " def __init__(self, dim, U, grad_U):\n", " self.dim = dim\n", " self.U = U\n", " self.grad_U = grad_U\n", " \n", " def _hamiltonian(self, q, p):\n", " return 0.5 * (p * p).sum() + U(q)\n", " \n", " def _update(self, q_current, epsilon, L):\n", " '''\n", " A method for performing a single HMC update. \n", " \n", " Parameters\n", " ----------\n", " q_current: 1D array\n", " 1D array representing the current value of the variable q.\n", " epsilon : float\n", " A positive real number representing the time step size\n", " L : int\n", " A positive integer representing the number of time steps\n", " \n", " Returns\n", " ----------\n", " q : 1D array\n", " '''\n", " # randomly sample momentum from \\pi_{P}\n", " p_current = np.random.normal(size=self.dim) \n", " \n", " # generate a proposal point by leapfrog method\n", " q_proposed, p_proposed = leapfrog(q_current, p_current, self.grad_U, epsilon, L)\n", " \n", " # determine accept/reject\n", " tmprand = np.random.random()\n", " if tmprand < np.exp(self._hamiltonian(q_current, p_current) - self._hamiltonian(q_proposed, p_proposed)):\n", " return q_proposed # accept\n", " else:\n", " return q_current # reject\n", "\n", " \n", " def sample(self, q_initial, n_samples, epsilon, L):\n", " '''\n", " A method for performing HMC sampling. \n", " \n", " Parameters\n", " ----------\n", " q_initial : 1D array\n", " 1D array representing the initial value of the variable q.\n", " n_samples : int\n", " An integer reprensenting the number of samples required.\n", " epsilon : float\n", " A positive real number representing the time step size\n", " L : int\n", " A positive integer representing the number of time steps\n", " \n", " Returns\n", " ----------\n", " Q : 2D array\n", " (n_samples, len(q_initial)) array storing samples\n", " '''\n", " \n", " Q = np.zeros((n_samples, self.dim))\n", " q_current = q_initial\n", " for i in range(n_samples):\n", " q_current = self._update(q_current, epsilon, L)\n", " Q[i] = q_current\n", " return Q" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3.3 Experiment \n", "\n", "### 3.3.1 1D gaussian distribution\n", "\n", "As a first set of experiments on HMC sampler, we shall sample from one dimensional gaussian distribution with zero mean and unit variance." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "def U(q):\n", " return 0.5 * ((q**2).sum())\n", "\n", "def grad_U(q):\n", " return q\n", "\n", "hmc_1dgaussian = HMCsampler(dim=1, U=U, grad_U=grad_U)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "def sample_hmc_1dgaussian(hmc, q_initial, n_samples, epsilon, L, idx_start=0):\n", " # get the samples\n", " samples = hmc.sample(\n", " q_initial=q_initial,\n", " n_samples=n_samples,\n", " epsilon=epsilon,\n", " L=L\n", " )\n", " \n", " print(f\"sample mean : \", np.mean(samples[idx_start:, 0]))\n", " print(f\"sample variance : \", np.var(samples[idx_start:, 0]))\n", "\n", " fig, axes = plt.subplots(1, 2, figsize=(12,4))\n", " # plot histogram\n", " ax = axes[0]\n", " ax.hist(samples, bins=np.arange(-3, 3, 0.2), density=True, label=\"Normalized histogram\")\n", " xx = np.linspace(-3, 3, 100)\n", " ax.plot(xx, np.exp(-0.5*xx*xx)/(np.sqrt(2*np.pi)), label=\"probability density function\")\n", " # plot time series of q\n", " axes[1].plot(samples[:, 0], '.')" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sample mean : -0.016955330591120615\n", "sample variance : 0.9775082145312359\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sample_hmc_1dgaussian(hmc_1dgaussian, q_initial=np.array([1.0]), n_samples=500, epsilon=0.3, L=13, idx_start=10)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sample mean : 0.026514017628016955\n", "sample variance : 0.9036613947255572\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# neglecting samples obtained in early stage, it seems that HMC still works when it was started from a tail\n", "sample_hmc_1dgaussian(hmc_1dgaussian, q_initial=np.array([15.0]), n_samples=500, epsilon=0.3, L=13, idx_start=10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The figures indicate that the sample obtained approximately follow the distribution form which we want to sample. \n", "\n", "However, if we choose inappropriate values of $\\varepsilon$ and $L$, then the results get odd." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sample mean : -0.14759803956986964\n", "sample variance : 0.7669510004374782\n" ] }, { "data": { "image/png": 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hWJIkSblnKJYkSVLuGYolSZKUe4ZiSZIk5Z6hWJIkSblnKJYkSVLuGYolSZKUe4ZiSZIk5Z6hWJIkSblnKJYkSVLuNVW6AEn7Zvr5Nw3aZuXX3jEMlUiSVLs8UixJkqTcMxRLkiQp9wzFkiRJyj1DsSRJknLPUCxJdSQiJkbEDRGxNSJWRcSZu2k7PyK6IqKzaJkxnPVKUrVw9glJqi8XAzuBKcDRwE0RsSSltHSA9tellD48bNVJUpXySLEk1YmIGAOcAVyYUupMKd0J/AT4SGUrk6TqZyiWpPoxC9iVUlpetG0JMHs3j3lnRGyIiKUR8YmBGkXEvIhYFBGLOjo6ylWvJFUNh09IFeAFNzREWoDNfbZtAsYO0H4hcAnwDPB64EcR8VxK6dq+DVNKlxTa0t7enspWsSRVCY8US1KNiIhbIyINsNwJdAKtfR7WCmzp7/lSSg+llNamlLpTSncD3wbeO7S9kKTq5JFiSaoRKaWTdnd/YUxxU0TMTCk9Utg8BxjoJLuX/BNA7H2FklS7PFIsSXUipbQVuB74UkSMiYjjgNOBK/trHxGnR8SEyLwO+GvgxuGrWJKqh6FYkurLJ4HRwLPAtcAneqdji4gTIqKzqO0HgUfJhldcAVyUUrp8mOuVpKrg8AlJqiMppQ3Auwe47w6yk/F61z80XHVJUrXzSLEkSZJyr6RQXOplQ71kqCRJkmpRqcMn9uSyoV4yVJIkSTVl0CPFXjZUkiRJ9a6U4RN7etlQLxkqSZKkmlJKKN6Ty4YuBF4FtAHnAv8QEf2e3ZxSuiSl1J5Sam9ra9uDkiVJkqTyKiUUl3zZUC8ZKkmSpFpUSiheTuGyoUXbSr1sqJcMlSRJUtUbNBTvyWVDvWSoJEmSalGpF+/o97KhXjJUkiRJ9aCkeYoHumyolwyVJElSPSj14h1Sddn2HKx/DJ5bBZvWwOa18Pw6eH49bN8EO5+Hruch9bzwmKZmGLEfjGyB/SZmy5j9YdzBvLHhKValKaxJbXTTWLl+SZKkijAUq7qlBOsfhbW/h6eWwNP3Q8cy6Hzmxe1GtsCYybDfZBg1HloPzAJwQ9MLz7NrO3Rtg52dsGEFrLkXtq6D1M0VI7NmO1ITK9IBLEuH8GDPdJam6dzfM4NO9hvefkuSpGFlKFZ16enOgu+K22HV3fDE/8C2Ddl9jc0wZTa84hRomwWTZsL4qTD+EBg1bu/+ve5dsOUp3nfRQqY3PM2h8RSHxpPMbVjO6Y13ZyWlYFk6hEU9s2DpTpj+RhgzqUwdliRJ1cBQrMrr7IBHfw2P/Bc8fgts25htn/QKeOXbYerr4aC5MHkWNI4o77/d2ATjD+HedBj3dh/2orsmsJkjG1bwmoZHeE08wp823gk//HV258uOgplvhZmnwEHt2fNIkqSa5V9yVcb6x+Dhn8EffpYNYyBBy5QsBM84CaafAK0HVLTEjbRye88cbu+ZA0ATu3j0rw6AFbfBo7+BO78Fd/wLjJ6Y1X3YO+DQN8OIURWtW5Ik7TlDsYbPxpWw9AZ48PpsiARkR1xP+jzMOjW73VDqLIHDbxdNcMjrsuWNn81O9nvsN7Ds5/CHn8J9V8HIsfDK0+CI98ChJ0PTyEqXLUmSSmAo1tB6fkMWhO9fCE/ck207qB3e+o9w+LuyMcG1avT4LPwe8R7YtRNW3g5Lf5wF5AcWwugJcPi74agPwNRjILy4oyRJ1cpQrPLr3gWP/TfcdzUs+wV074S2w+Dkf4AjzoAJ0ytdYfk1jYRXvCVb3vHNbGz0/QthyQ9g8f+FCS+Ho8+EOR+s7Q8CkiTVKUOxymZ6PAW/ng/3XQudT8N+k+C1H8uC4MuOys+R0qaR2XCQWafCji2FoRXXwC3/CLd8FWacxDsajuRXPXPZSZlPHJQkSXvFUKx9MpIu3tZwLx9s/A3HNj4EdzVkszK8+iPZz7yPqW0emx0hPvpM2LgqC8f3Xc3FI29hQ2rhR91v5Afdb+KxdFClK5UkKdcMxdorL4+n+FDjb3hv421MjE5W97Txz13v57Of+2J24Qy91IRp8KbPw4l/x0cvuIgPNN7COY2/5Nymn/O7nsO4etdbuLnntR49liSpAgzFKlkTuzilYTFnNf6a4xuX0pUa+a+euVzbfTJ39cwm0cBnDcSDa2j841Rvk9nEextv40ONv+FfR/4b69NYfth9Itd2v7nSVUqSlCuGYg3uudWw+HLubv4P9o/nWJMm889d72dh90l0ML7S1dW0dYzju93v4nvdf8LxDQ9yVuN/87HGn/OXTT+DK34K7X+eTfFW7ouWSDm2eNVGvnvbYzy0dhM7untobmqktbmJzdu72NHdA9DvtoG21/O2fX38+NEj+fPjXs6Zr/cEY1U/Q7H619OdXWFu0WXwyK8ggiU9R3N198nc3jOHHqp3PuFalGjgjp6juKPnKPZnI+9vvJXPrPstLPwItLwMXvPRbBl/SKVLlWra4lUb+cD37mZXz4u3P9lP2/627Unbetm2L49ft2Unf3/DAwAGY1U9k41ebNOTcOtF8H+OhGs/CE/dn12o4n/dz7ldn+HWnlcbiIfYs0zg37r/FP7mfvjQdXDAUXD7P8O3j4JrPgDLbs6mvZO0x+55fP1LArGG3i8efKrSJUiD8kixsoD16K9g8eXwyC8h9WSXKz7tIpj1tqKv7u+vaJm509AIr3xbtmxcBf/vCvj9lbD8Zmg9CF794WyWD0klO2bGJJoaMBgPs9OOOKDSJUiDMhTn2YYVWcj6/dXZvMItU+D4T2VBa+LLK12dik2YBidfCCedn4XixQvgtq/DbV9nwYijuK77JH7dM5cud2lpt+ZOm8B1Hz/WMcWOKZZewr+gebNzKzx0YxaEV90JUTSv8KxTPaGr2jWOgFe9M1ueWw2/v4pZt36f7zR+mw2phRu7j+OH3SfyUJpe6UqlqjV32gS+/9H2SpchqcoYivOgpxtW3pFdcvihn0DXVpg4A958Icz5EIzzwhE1afxUeNPfc/wvj+SEhgd4X+NtnNn43/xZ0y95qGca13cfz43dx9LBhEpXKklS1TMU16uU4On74f6F8OCPYMtT0DwOjnxvFoSnHpOfyy7XuR4auK1nDrf1zGEcnbyz8bec0XgHF4y4ms83XcNdPUfA75/Lji6Paq10uZIkVSVDcT1JCZ59CJbeAA9eDxseg4YRMPMUOPKr2Xy3I0ZXukoNoU20cFX3KVzVfQozYi2nN97Fuxvughs/CT/7FLziLXDEe7KhMs1jK12uJFWFa363msvufJzntncB1TWuu1xjwkc2NfCB1051fPduGIprXU8PrP09/OEn8IefZkE4GmD6CXDcX8Or3gX7Tax0laqAx9OBfGvX+/gW72XlX02BpddnH5iW3QSNzdkMI4e/C2aeCmMmVbpcSaqIa363+o9zKRerprmiyzXP9JI1zhm9O4biWrRzK6y4PZuFYNnN2cwRDU3w8jfCsefBYX8CLftXukpVjYBDXpstb/1HeOKe7APUH34Ky3+RfYg65Jjsm4RZp8LkWQ6tkZQbeZtD+RcPPmUoHoChuBb09MCzS+GxW+Cx38Cqu6B7J4xsyb4OP+wd2U+PCGswDQ0w7dhsOfWr2bcMy36RLb+6MFvGTYWZb4EZb8o+aI32Ut6S6tdpRxzAHY+sq3QZw8Y5owdmKK5GKcG65dmMESvvzJatHdl9bYfB6+Zl06hNfQM0jaxsrapdEXDQa7Llzf8bNq3JLun9yH9lJ2guuiw7inzA0TD9+CwgH/J6T9archFxHnAOcCRwbUrpnEHafwr4HLAf8J/AJ1JKO4a4TKlq9B41dUyxDMXVYEdndsTuyUXwxP/A6ntg24bsvrEHZmM/Z5yULa0HVq5O1bdxB0P7n2VLdxesWQSP3wIr7oB7vgN3/2sWkqfMzoZbHPxaOLg9m97P4RbVZC3wFeBUYLdn1kbEqcD5wJsLj7sB+GJhm5QbZ77esChD8fDbthGeeQiefgCeug/W3gfrlmWXVgaYeCgc9vYsdEw/Dia83MCh4dc4Aqa9IVveBOx8HtYUPrCt/i0suRbu/X7WdtR4OPDo7IjyAXNgyhEw6dDsMtUadiml6wEioh04eJDmZwOXppSWFh7zZeBqDMWScshQPBRSyoY7rH8U1j2SDYXoeBiefRg2r3mhXcuULEgc/q7sqNtBcx0XrOo0cr8Xvq2A7IIwHQ9nR5OfXJx9wPvtxdCTffVI0yhoe2U23KftMJg8EybNzC4f3tRcmT6oP7OBG4vWlwBTImJSSml9ccOImAfMA5g61SNqkuqPoXhvpATPr4fNT8KmJ2HTE9kld59bDRtXwIaVsHPLC+2bRmVn9E87NvvqecoR2c9WB7urRjU0Fl7Ls2Hu2dm2XTugYxk8sxSeeRCe/UM2Hv7+64oeGNkwjQnTs2X8VBh3SLat9cBscS7t4dQCbCpa7709FnhRKE4pXQJcAtDe3p6GpTpJGkYlheKImAhcCrwVWAd8PqV0TT/tAvga8LHCpv8Azk8pVfcbaHcXbN8M25/Lhjdsey4Lvds2wNZ12VHfreug85kXlu6dL36OplHZH/eJL4epx2Y/J83MvkYeP9WvklX/mprhgKOypdj2zdm3Jusfy35uXAEbV2Yn9HU+89LnGTUexr4s+yalZX8Y0wZjJsPoibDfpOzblFHjs1kxRo3LZmHJyRCjiLgVOHGAu+9KKR2/h0/ZCRSfOdl7e0s/bSWprpV6pPhiYCcwBTgauCkilvSOQysyD3g3MAdIwK+AFcB3y1NukZV3wvZNWTjdtRO6d2RHqnbtgF3bCz+3QVdh2bkVup7Pfu7szE5u29mZ/cHetW3gfycaYL/J2R/llv1h0itg7BRoPSg7qjX2wCz0jpmcmz/M0h4Z1frCLBd9dW3PZr3YvAY2r82+fdnydLZ0PgNr7s0+kO7sHPj5oyG7Ol9zaxaQm1tg5BgYMSYb9jGidxkFTaOz8N40Kpu5pWkUNI58YTngqKo+mTWldFKZn3Ip2fv1wsL6HOCZvkMnJCkPBg3FETEGOAM4IqXUCdwZET8BPsJLT8Y4G/hGSmlN4bHfAM5lKELxT/8G1j+yu8qzr2FHjM7+EI4Ynf2hHDkGWl4Gk1qyP6CjWqF5XPbzj0efxhcdkRrnUV5pqIwYBZNfkS2707UNnt9Q+AZn4wvf6mzflH2w3bG58EF3C+zYkp0Y2NkBXVuz4N21LftQ3DvmeSDv+Q846n3l618FREQT2Xt7I9AYEaOAXSmlXf00vwJYEBFXk80+cQGwYLhqlaRqEoONbIiIV5N9Lbdf0bbPACemlN7Zp+0m4K0ppd8V1tuBW1JKY/t53j+etAG8Eli2F/VPJhvOUWuse3hZ9/Cq1bph72qfllJqG4pi9kZEzAe+0GfzF1NK8yNiKvAQcHhKaXWh/afJ5ikeDfwI+MvB5imOiA5g1V6UV8uvjVLUc//sW+2q5/7tbd/6fd8uJRSfAPwwpfSyom3nAmf1/SovIrqB2SmlhwvrM4HlQMNQjCuOiEUppfZyP+9Qs+7hZd3Dq1brhtquvRbU+++3nvtn32pXPfev3H1rKKFN3xMxKKz3dyJGfydtdFb9iXaSJEnKtVJC8XKgqXDUt9ccshM0+uo9aWOwdpIkSVLVGDQUp5S2AtcDX4qIMRFxHHA6cGU/za8APh0RB0XEgcDfMrQnbVwyhM89lKx7eFn38KrVuqG2a68F9f77ref+2bfaVc/9K2vfBh1TDH+cp/gy4BSyCd3PTyldUxhv/IuUUkuhXQAX8eJ5ij/n8AlJkiRVs5JCsSRJklTPShlTLEmSJNU1Q7EkSZJyr+ZDcURcFRFPRcTmiFgeER8b/FGVFRHNEXFpRKyKiC0RcV9EnFbpukoVEedFxKKI2BERCypdz0AiYmJE3BARWwu/6zMrXVMpauX321ctv65r8X2kltTqvthrd/tkRJwcEQ9HxPMRcUtETCu6rzkiLiu8rp4uXCilqgy239ZB/wbct2u9b70iYmZEbI+Iq4q2nVn4P90aET8unBvWe19N7I8RcWuhX52FZVnRfUPSv5oPxcA/AdNTSq3Au4CvRMTcCtc0mCbgCeBEYBzZpVUXRsT0Cta0J9YCXyTEBI8AAASZSURBVCE7+bKaXQzsBKYAZwHfiYjZlS2pJLXy++2rll/Xtfg+UktqdV/s1e8+GRGTyWZnuhCYCCwCritqMh+YCUwD3gT8XUS8bRjq3RMD7rd10r9+9+066Vuvi4F7e1cK+9b3gI+Q7XPPA//ep32t7I/npZRaCssrYYj7l1Kqm4XsctFPAe+vdC17Ufv9wBmVrmMPa/4KsKDSdQxQ25jCTjGraNuVwNcqXVs9/H73oA+1+Lqu2feRalzqYV8sqvtF+yQwD7i7T1+3AYcV1tcCby26/8vADyrdjxL6eT9wRr31r3jfrpe+AR8EFpKF+KsK274KXFPU5tDCPji2lvZH4FbgY/1sH7L+1cORYiLi3yPieeBhshf8zytc0h6JiCnALLzQSTnNAnallJYXbVsCVOun4bpTa6/rWn8fqWL1vC/OJusL8Md5/R8DZkfEBOCA4vupgX732W/ron8D7Ns137eIaAW+BPQd2tG3b49RCIrU3v74TxGxLiLuioiTCtuGrH91EYpTSp8k+4RwAtnXITsqW1HpImIEcDVweUrp4UrXU0dagM19tm0ie51oiNXi67qW30eqXD3viy1kfSnW27eWovW+91WlfvbbuujfAPt2PfTty8ClKaU1fbYP1rda2R8/B8wADiK7SMdPI+JQhrB/VR2KC4Os0wDLncVtU0rdKaU7gYOBT1Sm4kypdUdEA9lh/Z3AeRUruMie/M6rXCfQ2mdbK7ClArXkSjW+rktVTe8jdaSe98Xd9a2zaL3vfVVngP22bvrXz75d032LiKOBtwDf6ufuwfpWE/tjSul3KaUtKaUdKaXLgbuAtzOE/Wvat5KHVkrppL14WBPZ+JKKKaXuiAjgUrKB4G9PKXUNdV2l2MvfeTVaDjRFxMyU0iOFbXOoka/ya1W1vq73QsXfR+pIPe+LS4Gze1ciYgzZ62ZpSmljRDxF1tdfFZpUZb93s9/WRf/66N23a71vJwHTgdXZfx8tQGNEHA7cTFYvABExA2gm2xd7qN39MQFBVuvQ9K/SA6n3cRD2/mSDzFuARuBUYCvwrkrXVkLt3wXuAVoqXcte1N4EjCI7q/fKwu2mStfVT50/AK4lG3h/HNlXKLMrXVe9/H4HqL3mXte1/D5SK0ut7otF9fe7TwJthb6cUdh2EXBP0eO+BtwGTAAOIxvP+rZK96ef/vW739Z6/3a3b9dB3/YDXla0/Avwn4V+zSYbQnBCYZ+7iqKTBGthfwTGF/6/eve1swr/d7OGsn8V7/g+/tLaCi/a5wq/oAeAcytdVwl1TyP7xLOd7FB/73JWpWsrsf75hfqLl/mVrqufOicCPy7sSKuBMytdUz39fvupuyZf17X6PlJLS63ui0X1D7hPkn2F/TDZzAW3kk3/1fu4ZrJp3DYDzwCfrnRf+unbbvfbWu7fYPt2LfdtgNfoVUXrZxb2ta3AjcDEovuqfn8s/N/dSzbs4TmyD22nDHX/ovAEkiRJUm5V9Yl2kiRJ0nAwFEuSJCn3DMWSJEnKPUOxJEmScs9QLEmSpNwzFEuSJCn3DMWSJEnKPUOxJEmScu//A6MVyp4EaoSgAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# too large epsilon, which makes Hamiltonian grows indefinitely, resulting in extremely low acceptance probability\n", "\n", "sample_hmc_1dgaussian(hmc_1dgaussian, q_initial=np.array([1.0]), n_samples=500, epsilon=2.01, L=13, idx_start=10)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sample mean : 1.7765263115643308\n", "sample variance : 0.20363048455146832\n" ] }, { "data": { "image/png": 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3Pdfpmh33fqUXdmKMMSZdXQ1Sy8ePYO22ffHL+UEhElGiEO9JXD5+BK9t34fGYmb34J23Y0WmOkv0t8yzBcbGGGOMMTmqK0FqdUOIR9btAJwgeP65ZVxcPi6hxrhoWAELV9cRjQXFAgkH76Cts4S/93FX9cfMswXGxhhjjDE5yg1S3dKHA4dSN6hxg2gAFOp2f8LF5eP49oUnxdfc/+L2+JoAcPbJo7l1+sR2B+8y0VmiP/Y0TquPsYgcLSK/FZHPRKRBROamWDdERB4QkT0i8pGIPCsi7RrFG2OMMcaYnqssLeKGaRNQnBrhB16pZ+mGxqRr3SA6AESB17bv45rF6xNGM3v7DBfkB9oFxd7n9fc+7qqu9DTurTHS6WaM78dpID8WOAN4TkQ2qap//OjfA9Nw2v3sx5mS9Atgdma2a4wxxhhjvOp2f5JweU3t7vj4Zi8303vfC1t5bfu+lJna2ZOLkdj/ZiuD69YWL5hZ3q4dnL/uuDdLLjoNjEXkSJyelhWq+inwqog8A1wL3OZbfgLw36q6J3bfJ4CfZ3bLxhhjjDHGNaNifMKBuhkV41OurSwt4tbpE3ljx0ftaoT9AejsycVZ2W91Q4irF62jJaIEA3DlmSUJt3n3cMO0Cfy+7oN4qUi2Sy7SyRhPBFpVdavnuk3A+UnWPgT8m4gcC3wMXAOs6fEujTHGGGNMXHVDiBU1TWzfc4DDrVEuPeNYmj8LM6NifNJssVdlaRELZpbHh3wk6zZxuCXKipqmrASgK2qaCMfaxLVGYcmGRp54Y2d8mIh3Dw+8Uh+/n5D9MdLpBMbDgU981+0HCpOs3QbsBN4HIsBm4JZkDyoi84H5ACUlHf8DGmOMMcYYh5txDXt6EG9q2s9PLjut06DYvb87wGPdu80ATBpXyPsfHyIQEKKxgR/Lq5uYk4VyimRN2N1+yQtnVZAXdDpe+JWOGsbP/uqMrB7QS+fw3afACN91I4ADSdbeDwwBRgFHAitJkTFW1UWqOkVVp4wZMyb9HRtjjDHGDGLr65sTBnO4/MM7Orq/d4DH7U9v5uoH1/P4641otO1xIxGnbCHTZk8uJhhoHx5HVandtR/UCcz9r3D+eSdmvWtFOoHxViBPRE72XHc64D94B87BvEdU9SNVPYxz8O4sERnd860aY4wxxpiqslHkB9sHlh3VFvvv741Lo0q8fEEV8gKSVqeI7qosLeLuWRXk+YLjvGAAwQnW/S4+dWxa2fCe6rSUQlU/E5GVwEIRmYcT/M4CvpBk+RvAdSLyEnAQ+Btgl6ruS7LWGGOMMcZ0UWVpEcvmT+OBl9/lrV37GVqQxzfOPiHtwLGytIiLThnL82/tiV8XDAiokp8XSNopItPmTi1h0rhCVtQ08eTGnUQiTlReOCSvXalFQV6Am88/MSv78Eu3XdvfAA8De4Fm4FuqWici5wJrVHV4bN33gH/HqTUuAGqByzK7ZWOMMcYYs3bbh/HuDZPGFXZpvPJN55/IS1v20hJR8oPCXV+roHbXfgSn3rg3Bm1Ulhaxvr6ZaNQpnWiJKIvW1uNNGAtweaXTHeP+F7dnfXR0WoGxqn4EXJrk+rU4h/Pcy804nSiMMcYYY0yW+KfGrahpYmVNU6e9fr3B87L50+K/AyxcXUc49li9NZ7ZP7lPfUHxkPwAI4bkceWv1hFVzXof47Qm3xljjDHGmP7DPzVOoN14ZT+3R/DPnt/CNYvXA8Sn1yUbz9wb3NZx4qufCIpTbrFgZjmLX32P1qjGa6GzuTcLjI0xJseIyBAReUhEGkTkgIi8KSIzUqy9XkSqReQTEWkSkZ+KSJ7n9pdE5M8i8mnsZ0vvvRJjTE/MnlzMVWeVsGReFbMnF3c6XnllTROHW5IHv10Zz5xpoYPhhExxQODuS0/jny47jdDBMBHfYbyiYQVZ20u6NcbGGGP6jzycnvHnA43AJcCTInKaqu7wrR0G3ApsAMYAz+CcB7nXs+YWVV2c7U0bYzIj2YQ6d9xzqhrj6oYQT23cGW+BFgwmBr+d3T+b3C4b4YgSjAXF7kHCqrJRDMlPLLVYuLoua3XQljE2xpgco6qfqepdqrpDVaOquhp4D6hMsvaXqrpWVcOq+j6wBDi7t/dsjMmcVGUPlaVFfPvCkwDnoFp1Qyh+n5U1TfHex+6Btt4Mfjvl1lL4aircgP2ck0cTEBLGQmeDZYyNMSbHichYYCLJ+8v7nZdk3T0ici+wBfihqr6U5DlsWqkx/YRb9tDSGm1X9uDPJi+ZVwWQkC3OzwswZ3JxwmO69zvcEiUYEBbOquiVvsEQG1gSm3QXiU3AA+JdMmZPLubW6RN5Y8dHhFucdZt2fkx1Qyjjwb1ljI0xJoeJSD5OFvhRVX2nk7XfAKYA/+K5+vtAGXAcsAh4VkTaNQy1aaXG9B9uFvW7X5qU0KGhuiHEfS9sjWeTD7c4HSbW1zfHh2akyhb7p+EtWFWbkHHOpqqyUQmT8CJR5Y6nN7N0QyNLNjRy9YPOQcEFM8tBIKLw/Ft7uPrB9RnfowXGxhiTo0QkAPwaCAO3dLL2UuAeYIZ36JKqblDVA6p6WFUfBV7DqVk2xvRTyfoVuxnfV7fti/cBVmB5dRNFwwriB+uG5LfPFkP74DSq2qudKRbGJuEFxBk24j1v55ZO1O3an/T6TLJSCmOMyUEiIsBDwFjgElVt6WDtXwIPAl9R1c2dPLRCu8FTxph+IlmphLfdmn+YcmskSuhgmAUzy1lTu5sZFeOTlh+4wemCVbXxfsG92ZnCnYS3vr6ZomEF3PVMLeFYTbRbLvKrl99NuE8gIBnfowXGxhiTm34JnAJMV9VDqRaJyBdxSi0uU9XXfbcdBUwFXgZagStxapD/PlubNsb0TLKDd5WlRe0GZbgCImzbc4BnNu1CFd7Y8VHKjg7e4LS3O1OAE5y7z+mOi3ZrjAFe2rI3vjYgcPesiozv0QJjY4zJMSJSCtwEHAY+kLZT3DcBa4G3gFNVtRG4AxgJ/M6zbq2qzgDygR8DnwMiwDvApaq6tZdeijGmi6rKRpEXdA7eeVuuuXXHD7z8Ln96Zy/RqBIMCDM/P56n39wVv//hlrZgOhlvcNqX/Pu4/8XtCXXSV51VkpXDgRYYG2NMjlHVBjoudxjuWXthB4/zIXBmBrdmjOkN7jQM9RdOwNptH8aD4oWzKlhTuzvhdhF6tUQiU/ydOJLVSWeCBcbGGGOMMTnC7TChON0bvNlfb52xqhI6GGZGxXjWbouft2X+uWX9IiPcVb01gMQCY2OMMcaYHNFRD+NUt1186lj2fvJnrjwzO+UHvcVbXpGsM0cmWGBsjDHGGNPLuhvYdZQ5rSwtSug+ASR0sJg0rjDjr6MvpOrMkQkWGBtjjDHG9KKeBnapDshVN4RYuLqOcGuUN3Z8xJzJxUk7WOS6VJ05MsEGfBhjjDHG9CJ3ylxUIdySuSEV/oBRIT7Yw192kcvckpFsvC7LGBtjjDHG9KKiYQXxXsNRYNueA2ndr7Pyi2SdG+ZMLu6zvsTZks2DeBYYG2OMMcb0orpd+xMuP/3mLs46YVSHB+OWbmjkjqc3E1XIDwrL5k9rFxCmChgHSkDsytbBO7BSCmOMMcaYXnPv795m6YbGdtf7+w17VTeEuOPpzUTUmdkejigP+MYjuypLi/j2hScldG+4/8XtVDeEMrL/vubWZ//s+S1cs3h9xl+XZYyNMcYYY3rBvb97mwdeqU96m9tFIpmVNU1EfLM8/vTOXqobQh1mTJduaGTBqlqiqhnv3tBXsnnwDixjbIwxxhiTUUs3NHLtQxsSMsPVDSF+lSQoPr14JD+57LSUZRTVDSGe2riz3fWq2uGhveqGEAtW1dIaVeeQX2vmDvn1pWwevAPLGBtjjDHGZMzSDY384LebAeIT5+ZOLWFFTRP+Ac43n1fGbZec0uHjra9vpsWXLhacbhMdBYXr65uJRNvuFxAZEF0psj0BzwJjY4wxxpgMeeKNxPrhNbW7mTu1BPGtO2tCUadBMTgZ0mBAaI0FuQKcc/Jobp0+scOg0Nv5AmDeOSfkfBmFK1Uf50ywUgpjjDHGmAyobgi16zgxo2I81Q0hFKebhJvt/f6MjoNi99AcwMJZFeQFhIDAkPxAp0ExQOhgOB6MB4DCofnde1GDjGWMjTHGGGMyYH19M57qBS4+dSyTxhXGp9zlBYS5U0uYPbk4oWuEvywg2WS8J26a1qXygaqyUQzJb+tpPBDKKHqDBcbGGJNjRGQI8J/AdOBo4F3gH1V1TYr13wG+DwwDlgPfUtXDsdsmAP8FTAUagVtU9YUsvwRjBqSqslHkBYSWiJIfFG4+/8TELgoRRaFdAHy4JUowICycVcHcqSXtOi+sqGniuKOGdqmmNtu1uAOVBcbGGJN78oCdwPk4wewlwJMicpqq7vAuFJEvA7cBXwR2Ab8FfhS7DmAZsC72GJcAy0XkZFX9sBdehzEDjwigsf9tC5bDsaB4eXUTc2IZ4/X1zfy5JQpAa1RZsKqWSeMKEybYBQPC8uomWiPRLrdcy2Yt7kBlNcbGGJNjVPUzVb1LVXeoalRVVwPvAZVJll8PPKSqdaoaAu4GbgAQkYnAZOBOVT2kqiuAzcCcXnkhxgwQbj3wyhongFUgEmnrsXvFlOPja1s9bdOKhhUkPE5rVFn4bB0ra5pYMLOc735pEldMOZ7WSGLfXpM9aWWMReRo4CHgS8A+nK/slqZYOxm4D+eP7WfAT1T13zKzXWOMMX4iMhaYCNQlubkcWOW5vAkYKyKjYrfVq+oB3+3lSZ5jPjAfoKQk9dhaYwYbbz1wXkDICwaIRBLresuPHRlfH6UtIHYPyHm7R2xq2s+mpv3kB4XH508DYEVNk9UK95J0SynuB8LAWOAM4DkR2aSqCX+ERWQ08HvgOzh1bAVAcea2a4wxxktE8oElwKOq+k6SJcMB7zF59/fCJLe5tx/nfxBVXQQsApgyZYq/Hasxg9bKmiYOt8SyxFHlyrOO57ijhlI0rCCe3Q0dDBMQiCoExLkMbQfkwi1RiN3uaokov3r5XUYXDuG8k8cwpnBIwqE9kx2dBsYiciTO12oVqvop8KqIPANcS1uNmuu7wH+r6pLY5cPA2xncrzHGmBgRCQC/xklc3JJi2afACM9l9/cDSW5zbz+AMaZT7lQ6N54NBgPMmezkA71dJRbMLI/XDHuzvt4DcgcOtbQbF/38W3viv+cHhdmTLdeYbenUGE8EWlV1q+e6pF+1AVXARyLyPyKyV0SeFZGk37mJyHwR2SgiGz/80M54GGNMV4iI4JS4jQXmqGpLiqV1wOmey6cDe1S1OXZbmYgU+m5PVpJhBqlk442NY319c8Lgjcsr2w7VebtKhA6GWTKviu9+aVK7w3OVpUVUlY2ibvcnHT5XS0RZWdOUzZdjSK+UYjjg/9faj/M1nF8xTm3xxTgHOH6Kc+L5bP9C+1rOGGN65JfAKcB0VT3UwbrHgEdEZAlOV4rbgUcAVHWriLwJ3CkitwMzgM9jh+9yXrLeuN2RaryxcbjdI8ItUQIBYcSQPO5/cTtFwwraZYhTdYhwa5Td7hRAvOzCz4Kl7EsnMO7KV22HgN+q6hsAIvIjYJ+IjFRVfx2bMcaYbhCRUuAmnHK1D0Tiw2ZvAtYCbwGnqmqjqv5eRH4KvAgMBVYAd3oe7iqcQDmE0/rtcmvVltuSDYfobnC8pnZ3u8sWGLepLC1iwcxyFqyqpTWqPPBKPYIznW7BzHJqd+1HgC0fHEj5QWV9fTOHfUHx/HPLeGTdjnjtMkBBUOJlGiZ70gmMtwJ5sb6W22LXpfqq7f9I/EBjH26MMSbDVLUB4tNekxnuW/9z4OcpHmsHcEGm9mb6nhtoKRBuaWsZ1h0zKsbHM8XuZZModDBMxJPeVSDcGuXFLXt58Z29RKJO/+KAkPSDSlXZKIIBiZdkgDO+2a09LhpWQOhg2IZ09JJOA2NV/UxEVgILRWQeTleKWcAXkiz/L2CFiPw7TuB8B/CqZYuNGRgm3PZcWut23PuVLO/EGJNK0bCCeFbK2xqsO9zs8Jra3cyoGG/Z4iSqykYREIj4UoF/igXFLm8fYn+N8cJZFSxYVUtUlYJOSi9MdqXbri85LKEAACAASURBVO1vgIeBvUAzzjjROhE5F1ijqsMBVPVPIvID4Dmc0aOvAnMzv21jjDEmN2Sq3jddqVqDddfcqSUWEKfg/ttWlhbx+o5Q/PqyMcPZvvfThLUCKfsQz51awqRxhfH/nwDc/+J2yxL3gbQCY1X9CLg0yfVraf+V3S9xDoUYY4wxg1om633T5R0nnMmBENUNIVbUNCEw6Pvpuu+FO6rZGewhRCJKflD4xtknxOuOXeecPJpbp09M+b65GeK++P+MaZNuxtgYY4wxXeRt2xVuiXLfC1s7DI4ywdsb1ztkojvP6WZEDxxq4cG19fFygaeqm1h24+AM2NzA1XswriWiTD91LGccf1RCltdbHpHuv7u/1VtPasRN11lgbIwxxmRJVdko8gJCOKJEgde27+ONHR9lPQtYWVrElg8OJARmXX3OZAGga7AGbNUNIe57YSvh1mi7TgMvb/2Qm88/Mf6e+Msj0n2vspXxN+lJZ8CHMcYYY7qrrZ1eQhYwm6obQtwR+yo/qk6XhK4+p5u5TNZeKi8ogy5gcz8ovLptX7x+O+jpDROJtH+P3eEd6+ubqW4IkQ63BdwXThrNgpnlg+7DR1+zjLExxhiTJevrm2mNRBOuCwaznwVcWdOU0BFBpOuBrHd4RdR32xVTjh90AZv3g0IAOO24kQzJC1Dd+DGqmjS725164eqGEAtX1xFujfLGjo+YNK5w0L3XfckCY2NMn0in9Zu1fTO5zltK4Ypq9lv8+5/hi587psvBlbdW+cChFha/+l68LGMwDprwljiIwOb398en0wUDkjS72516Yasx7lsWGBtjjDFZUllaxBVTjmfJhsb4dZGIZj3YmTO5mOUbd9IS65Jw8/kndutxvL10Ly4f16tt53oq023y3A8KK2qaeOKNnQkfcKJRTdoWrzv1wlZj3LcsMDbGGGOyaPbkYp7auDOeNe6NYKeytIhl86dlLDDs7V7MPZWplmf+111ZWtSuTAVS/5t6s+7pvnfduY/JHAuMjTHGmCxyg1S3B3D5sSN71EKtM95g7tsXnkR1Q6hHwyJysa9uJsoRkr1ugCfeaMv+BwSmnzKWmzzdKPy6M8HOpt71HQuMjTHGmCzxBqk/uey0rAeZ/sdfMLM8fpCruy3b3PZkuVTzmolyBG9wfbglyoqaJgBaPScRLzplLIuum5KpbZt+wAJjY4wxJguSBcEra5rifYGzEWT6M6Vrand3O6j19zEOSO+UgWSC2/JsTe1uZlSM79Z77D04qcDy6iYumDgmYc0xhUMytGPTX1gfY2OMMSYLEqbetUZjh7Ya4x0jstG2rWhYAQGReBA7o2I8BXkBgt0Iav3tyc6O9dXtSk/evuK2PHtt+z4Wrq7r1n7dg5Nuq+JIJMrowiEU5AUQoCAvwOxB2J1joLOMsTHG5BgRuQW4ATgNWKaqN6RY9wDwdc9V+UBYVQtjt78EVAGtsdvfV9VJ2dn14FM0rCDeziuqsH3PgYSv4c+fOCbjZRQLV9cRiWq8fVh3p69B+3KEGRXje1SW0Zsy1fJs9uRiVtQ0xd+DOZOLmTO52A7GDWAWGBuT49LpB2wGnF3Aj4EvA0NTLVLVm4Gb3csi8gi0m9Vwi6ouzsIeB73QwTAC8Yzr4dbEtz7TX8N7M7yqbe3DenKQa/bkYiT2v7nUXzdTLc/8HSIAC4oHOAuMjTEmx6jqSgARmQKk9V2uiBwJzAFmZnFrxqOqbBRD8tuCsyvPLOHtD5yMazAglB87MuPPl6n+t/766NmTi3Oqv242Wp5t+eBAzmTMTfdZYGyMMYPDHOBD4BXf9feIyL3AFuCHqvpSb29soEoVnC1YVUskqixYVQvA3KklWX2+7kiWHf72hSfFB1xI5w/Ra1L1WM5EyzPvB4SACFHVnMiYm+6zwNgYYwaH64HHVBPmEX8feAsIA1cBz4rIGar6rv/OIjIfmA9QUpKZQG4w8AdnoYNhIlGny0FrVLn96c1Az4Njf+9i/21uMDt7cnF8Px0N7egoO7yypil+mLCvs6bZbn/n/YCAKoGAIGi/z5ib7rPA2BhjBjgRKQEuAG70Xq+qGzwXHxWRq4FLgF/4H0NVFwGLAKZMmaL+2016qspGEQwIrbFTeVF1MsiTxhV2OaBbuqGRNbW7KR8/gkfW7SDcGiUvIFwx5fh4AFzdEOLqReviU/cef2Mnd8+qYNK4wg4DylTZ5/5WZ5zt/Xg/IAQDwgWTjmFM4ZCEDxhmYLF2bcYYM/BdC7ymqvWdrFPoV9+S5yx32py/TVhlaRHzzjkh4bpIVOOT8NK1dEMjP/jtZtZu28cDr9RzuCXWFi6iLN3QyDWL18czwi2Rts8xkViW+p/XvM2fW9payfmfP1U22Q0Uu9P+LRtS7SfV+99V7geEK88qIQr84a09PLVxZwZ2bvoryxgb009ZtwmTiojk4fz9DgJBETkCaFXV1hR3uQ74Z99jHAVMBV7Gadd2JXAe8PfZ2vdg0dnX+4VD8+PdKgCCAUkaYHZU6rCmdnfCZYk9oMYe182eVpWNIj8o8YwxOFnq13eEEi4XDSuIP1/RsIKUh8yycaitJ5LtJ5PlFe57su/AYVpj72E4oqyoaerz126ywwJjY4zJPbcDd3oufx34kYg8jFMzfKqqNgKIyDSczhVP+R4jH6fl2+eACPAOcKmqbs3y3ge8ZKOE/VnXIfkBwi1RROCLnzum3WO4JRAtESU/KCybPy3hMWZUjGfttn3xy/PPLeOTw60sr24iEmmrC64sLWLZ/Gk88PK7vPD2HjRFEUztrv3xYLizQ2aZONSWSf79JAxWaYly3wtbuXX6xC7v2Rtg+79Gsa9VBi4rpTDGmByjqnepqvh+7lLVRlUd7gbFsbXrVPVIVT3ge4wPVfVMVS1U1aNUtUpV/9D7ryb3dPY1vXewhwJPbdyZsNbNcl41tYRgMMALb++Jlz64/nnN2/FRxG6G0mvu1BJ+ctlpnHvyaH5y2WlcXD4OgAsmjuGiU8YyxzORrbK0iAevm8JN55Yl3W8wIAjEg8loVAmIdFgukalShWxwyysCOE27X9u+r937mw5vgK3a9j7ZxLuBzTLGxhhjTJqqG0Jc/eD6eLeGZTe2/5reHazhao1o0qzr+vpmWiPtD44t3dCYUOoAyTOUc6eWMHdqSbsDdgABIaFrRHVDiHVJ6pgDQvwwnnfC24KZ5YQOhpOWS2S7E0R3+MtOlsyr4r4XtvLa9n3dPpjn78zR0XtiBg4LjI0xxpg0ua3KwMmwrkxSa1pVNooCT11vXjB5DXGqlmjJ6odTZSirG0Lc98LWhAN2QEIwCCQNnKefMpabzj8xvv90a4f7W2eKZIE6wPFHDyMvGEgoLenKY66vb7ZgeBCywNgYY4xJk79EN1XfuvMnHcMfYzW9qepRUx1k89cP33RuWdKs7YqaJpZXO1le/z4CnjIIf2cKgKvOckox/Ptxs8v3v7g9ZTDY3ybgraxp4nBLNH7ocEVNU/wDTECg4riRXHlmSdqBrfutgDuh8O5ZFRYUDyIWGBtjjDFpmjO5mOUbd8YPxc3xZXLd7KUbqEFbO7ZkwVWyg2zusI81tbuZUTG+3fCPZM8BcNKYI5laNoryY0e2y3J6O1MU5AXa7du1dEMjd8Qm8xWkKBXpT50pqhtCPLVxZ9v7IMK+A4fb6qUV/q9pP1v21HXaK9rNEm/a+XH8WwG3vV13+kyb3GSBsTHGGJMmt8tDsqDQLWsIezK4Qvf6/br1w8m4pQz+LHFj6BD/nGTwhLvnZNPvvKobQtzx9Gbc5HKqUhH3MXsrUOyobd36+ub4sBRwAtmXtuwlLxiIZ9K97etS7bmjDhRRhV+9/C6nH39Un38QMNlngbExxhiTplRBmj+LGxDaTaHLFG8pAxAPZCOR1MFfqkDWnZ43o2K8M67aF2339YjDjg76VTeEeP/jQwlBMDjB8ZVnHQ/Qrn1dKt666WTtuv74zl5eeHtPvzlsaLLHAmNjjDEmDR0Fad4sbgA4+6TR3eqdmw5vKcOBQy0sfvU9oqpdzky70/MA1m7bx6VnHEtQ2gLtvCSlIl4dZXIzJdVBP++/RUCcA4puj+Zg0CkVqSwtYs7k4rT26K+bvmHaBB5cW+8EygLaQV9nM7CkFRiLyNHAQ8CXgH3AP6rq0g7WFwCbgEJVtWZ/xhhjcl5H3RjcwCrcEiUQEGZUjM9q8OQ+9jWL19MaVQICN0yb0KXn9He/WPXmrvhM8DMnFPH9GaekfLylGxpZsKqWqGpWs6ipDvr5ewy7BLi8si1D7/3g4r3sl6xu+uLycQmTAPvLYUOTXelmjO8HwsBY4AzgORHZpKp1Kdb/A/AhUNjzLRpjjDF9r6psVPxr+2AwMUCqLC1iwcxyp0Y3qtz1TG1GDmx1Vl97uMUpp4gqLH71PS4uH5f2c/q7X6jnf6sbQqyMDRVJ1hFjwaraeG1vOItZ1FQH/bwfREQgEBCiUSdrXnHsyHhXDSDtnsv+chPv5UnjCvvFYUOTfZ0GxiJyJDAHqFDVT4FXReQZ4FrgtiTrT8AZT/pd4MHMbteYNLSG4dM9zk/LwbbrjxgJw8fBkaMhEOy7/RljcpebnkwyW/mlLXvbDq7FptX1JIhKVbrhBstFwwoIBiQeoEY1dfeLZNzDfYteeZcdzQcTbouokxX2Dglxra9vJuI58BaQ5H2a3dfQ04AyWX10ZWkRN0ybwKJYuUMQpwVd4ZC8hEz2nMnFafdcdlvgJTug2N/GYJvsSSdjPBFoVdWtnus2AeenWP8L4AfAoY4eVETmA/MBSkqSn7w1plPRKOx+E957GXa9Cbs3Qei9ju8TyIMxp8D40+G4v4ATL4KjT+id/RpjcpbbAUFJbMHmBlQvvL0nYX2q/sVdeT5/UAeJGdB555wQrzEu6Gb3CyAhA+xK1c2hqmwUQ/IDHI5la+edc0LKLheZmpDnD7CrG0Kx1+3c7v67LH71vYRMtkJaPZf90wMff2Mnd8+qSNkZxAxc6QTGw4FPfNftJ0mZhIhcBgRV9bcickFHD6qqi4BFAFOmTOnrg68ml6hCw2uwaRlsfR4+2+tcf1SpE+x+/koYMd7JDg8Z3nafQyEni7x/J3xQC1vXwJu/cW4fPREmXQJnXANjJvbN6zLG9GvJ6l3dWttILDBzBQOSclpdZ7wZYf/z+YPlwqH5PHFT8vZx6T7XwtV1RKJKXkCYd84JfHK4tcNuDm7ZiJuZfWTdjqQlHJmakOcPsBfMLGdN7e52WWuBhOA+IM7hwTmTi+OZ4FT8Q1AiUeUO6188KKUTGH8KjPBdNwI44L0iVnLxU+CSzGzNGJ9DH8PGh6HmMScrXFAIJ18ME7/sZH2Hj+na46nCR/Ww7Q+w7b9h3X/Aa/dB8Vlw5jehYg4E87PzWowxOcdf7wrJM615AWFhN6el+YPAG6ZNoG73JwmH+fzBck++5vd204iqUjg0n9suOaXTbg6hg2GinXRqKBpWQEAE6HrHjGR7jCqEW6Lt3nP3/W5s/izhfm4m262XDsem4iXLXFeVjUoYggJOOUlPy2FM7kknMN4K5InIyaq6LXbd6YD/4N3JwARgrYgAFAAjReQDoEpVd2Rkx2bw+XSvE7S+8TCED0DpOXDBbXDK16BgWPcfVwRGnej8VN3sPM+mx+F/fw2/vQn+9E/whb+FyddC/tDMvR5jTM7yBqH3v7i9XVB8VifdHPy82eHQwTC7Pj6UEAS6ZRIb6pup27Wf2ZOLMzp1rmhYQbwcIarOZf/rTCbx8JvE7+d9XW4mOhgQFsws7/ZevZl6EWn3ns875wQmjStkwara+HUCFA51EhudZa7df4O7vlbBw6+9x/a9nyY8jhlcOg2MVfUzEVkJLBSReThdKWYBX/AtrQWO91z+AvAfwGScDhXGdE34M1h3P7x6H7QeglMvhXO+A+M/n53nG34MnP13MO0W2PY8vPpzWPMP8D//DhctgIrLIZCs9bvxm3Dbc329BWOyzh8MAry+I8SWDw6kFQSmGgoSCAgaUUSIZ2XDEWXJhkYef72Ri04Zy03nn5iRTGboYBgnp+v0Xw4dDKd1P385xcLViSOXvZloVU37cVM9l/thoGhYAbc/vRlvbFy3+xMKh+YnlFYEA20HAlO1fIPkZRp3PdvWmq275TAmd6X7X/m/AYYCe4FlwLdUtU5EzhWRTwFUtVVVP3B/gI+AaOxyJCu7NwOTKvzfU/CLSnjxn+Cki+Dbb8AV/5W9oNgrEIBJfwnf+G+47hkYdjSsvBEevBCaNmb/+Y3phIjcIiIbReSwiDzSwbobRCQiIp96fi7w3D5BRF4UkYMi8o6ITO+N/Q8E1Q2hdn2AXamu9/OPdo4qtEY03vBCYkGyV0Th+bf2cOWidVQ3hLq7/Tj3IF1QoCC/a+UOycopvI9bkOc8rgg8X/cBSzc0As57d/+L29Pev/fg3dypJcw/tyzh9hkV4+OvI0D7UhY3sP7ulyYl7bDhzSaHDoZZdmMV3/vyJJbdaBPuBqO0+hir6kfApUmuX4tzOC/ZfV4C7KOW6ZrQDlj9XXj3j3DsZLjiESip6pu9iEDZ+XDjS7D5KXjhTlg8Hc6aDxfdAUOsTbfpM7uAHwNfxkladGSdqp6T4rZlwDqcsyGXAMtjZXOD8lu+jtp1+de5md5kZlSMT+v5qspGkRdIrGuVgKDqHOTTqFJx3Eg2Ne1vd9/WDLSDg9R9gtPdf6pMrPu4D7z8Ln94aw+bmvazqWkzr7/XzO8276YlouQHhWXzp3X4nN6MrnfEdsmoI+OjrN3OER29Drc0xA3K3TXJXoO1ZhvcbCS06R9U4Y3F8PwdTo/hGT+FM+f1j37DgQCcfiVMmgF/XAivL4J3noNL/9MJnI3pZaq6EkBEptDNBISITMQpdfuSqh4CVojIrTh96x/I1F5zRXVDiCsXraM1FqQ+Vd2UMmPoz/S644gDAvPPLUu7xVdlaRFXTDmeJbFMqgBf/NwxrN32YTxQu/LMEt7eXZsQPLv2HTjcrdeabB/dCQQ7C6orS4v4c0viF8ZPv7kr/ns6vZ4TDt5FlKUbGnlq406umHJ8u5HbqV6Hm3H2js/2to/LZM22yX0WGJu+d2APrPo2bP8DnDQdvvpvMLIfftlwxAj4yr/A5/8Knv4WPPY1px75ogWQN6Svd2dMKn8hIvtwytt+Ddyjqq1AOVCvqt4OQ5ti17cz0HvPr6xpigfF0P6QljebXH7syIRMbzAgXBnLZHY1sCo/dmT8dwVOHH0kYwqHJGSt63btjwfPXi9t/ZDqhlCfBnOdBaPl40ckTNfz6+xwm5vRdeuwlbYAOVWHCf8+vHXcLu+0vnTHRpvBwQJj07e2/9Gp3w1/Bpf8i5Mlln5+Dvj4s+CmV5zs9rr/cIaLXPGo093CmP7lFaACaMAJeJ8AWoF7cMrg/N/R7weOS/ZAA733vP8FBTyHt/zDH/KDwl8cfxSv73BqZDWqHHvU0G4FVKGDYQLi1BcLJGQ03YNfs2N9eMOe4BAgEsneKOaecHs7u6/j0jOO5ZlNu1B13jvFKQVJ53Bbwqhtzz9SquEjfv7svss7rS+Tg0hM7rPA2PSNaBRe+Sm8dC8cc4pTSzxmUl/vKn0FR8LMn8PJX4Knb4ZFF8Clv4RTZvb1zoyJU9V6z8XNIrIQ+AecwDitHvWDxZzJxSzfuJNwRAkK3O05vLW+vjmhlKElomz0HBwLBrvfo9ffiixZb2B/V4aFq+s6neTWV6obQglBbLg1ysljC3nq5i8k9H/uSulC6GC43fAUNL3eyP6Ms8s7rW99fXP89nBL//ywYXqPBcam9x36GFZ8E7a/AKdfDV/5ec/6EfelSX/pZI+fvB6euAbOvtUpregPtdHGtKe0fXtdB5SJSKGnnOJ0YGmf7KwPefvYhg6G4wHb0g2NrKndTfn4EQSFhIyl2xlMgMsru15C4fIGvW4NbLKBGN6v/CeNK+w3NbH+Uc0raprwl0O7r+P9jw+xsqaJ2ZOL+faFJ7U7CJeK98NDMCBcMOkYxhQOSat0xX1/73thK69u2xdvi+f2OAan7V68MwjJ2/CZwcMCY9O79m2DZVdBqAFm/itU/nX/L53ozFEl8I3fw+9vcybn7X0b5ix2apKNyQIRycP5+x0EgiJyBNAaqx32rpsB1KjqHhH5HHAH8BSAqm4VkTeBO0XkdmAG8Hmcw3eDhrcGNRhr8wVw42Mb+cNbewBYu20fl55xLM9u2kVUIRiAQCAQH5k8p4e9bitLi9jywQH+9Q9b0xqI0V+6JiQrQUj213zLBwe465m2A4RPVTfxjS9M4MG19URj5RWpulO4gfeCmeXU7trPkxt38oe39pAfTH/kdmVpEbdOn8gbOz5Kmmn3lrMEJP1ezmZgssDY9J7tf4Sn/toZs3z9s1A6ra93lDl5Q5xAf2w5/O7/ddq6zX0cji7r/L7GdN3twJ2ey18HfiQiDwNvAaeqaiNwEfCIiAwH9gC/AX7iud9VwCNACGgELh9srdq8X6O3RpU7nt5MMBgg3JrYiq35szBP9qAcoCPVDaGEMcfRHg7E6C3+Uc33vbCVGRXjCQYkPmxDFRa98i4tnjRyuDXKA6+0Vfmk6k7hD7zPO3lM/IBkOh0tvDrqPtFR2zkz+FhgbHpH9aOw+jtOPfHVy5ws60B05jwYPRGevM4Jjq9+Ao4/s693ZQYYVb0LuCvFzcM9674HfK+Dx9kBXJC5neWeqrJRBANtY4YjCtHW9v2JZ1SMb5epzVTWdn19c8LUNu/BsP7MOxY6Cry2fR9v7PiIG885gcWvvkck6vRjbmg+2O7wm1+yTLN/+MaeT/7c6X060lGmffbk4k77V5vBwebbmuxShT/eDc/+HZx4oVNyMFCDYtcJ58E3X3AGgDw6E95+tq93ZIxJobK0iHnnnJDydhG4+bz0exN3R0dT2/ozNwt79smj46UIh1uifHK4lSdumsY5sevdcdPjRiRva5mqLMI7Pc/t6VyQF0AgoWtHV/in7rlZ6cdfd9q/GWMZY5M9kRZ45m9h0zKYfD185WdOGcVgMPokmPdHp576iWvhkv8Pzrqxr3dljEmicGh+PLCDxNZtARIPamVDLg+ZcOt3N8Q6dyiwvLqJOZOL29X1/t1FE+MdNdI5RJfsfenJwcNkNdEra5ripTTptH8zA58FxiY7wp/BUzfAtufhwtvhvO/l/iG7rjpytFNLvfyb8Lvvwad74cIfDL73wZh+LlVLL4FeqzntLwfqusOd4Ld0QyNKW3/lb194Uo8CW3/HC/e5uvs++WuiFz5bR93uT+L/5j1pu2cGDguMTeYd/AiWXgnvb4SZ98GUv+7rHfWd/KHwV4/B6r93+jZ/9qGTObd2bsb0G25mckVNE8urm4hEnIzmFd2cZjfYVDeEUJwPEW6nDjfATFaXnc77mY2hG/6a6P9r2t821puetd0zA4cFxiazDuyBX18GzducaXCnfq2vd9T3gnnwtf+AI8fAq/8Kf94PsxcNnrISY/opf0aysrSIOZOL44M0cqEzRF/zBrB5AeGqs0oy8mHCm9093BLtUgeKVLw9jV/bvi+hF/WQ/J633TMDgwXGJnM+boTHZsGBD2Duk85hO+MQgel3wRFHwQt3QstBZ9pf/tA+3pgxg1OqjKQbfHmDPcscp+YNYFsjSu37bVPGk7VfS7fdXVXZKPIC0q5uORPB8YyK8ax7txlVJSBw0Sljuen8E+3f1wAWGJtMaX4XHv0ahA/Adavg+LP6ekf90zm3Ot0qnvt/YMkVcPXjMGR45/czxmSUvxWY99BVQi1qRFm6welYkImv8zuSrKa2v6sqG0VerO9zFNjUtJ9NTft5qrqJZTe2vV/+zDIitEZSl0lUlhZxwaRjeD42ZMWtW85Ez+i7nqlNaM/3p3f2csGkY3LmPTfZZe3aTM/tfQf+awa0HoLrV1tQ3Jkzv+mUUjT8D/xmjlNaYYzpVW5GUoBgILFvsFuL6h6T9XYsyBY3cPzZ81u4ZvH6eDuxnKDtuxT736+EDyIRpcX3ocSvuiHES1v2xi9n6mDcipqm+AQ+V2tUWbCqNrfec5M1FhibnvlgMzxyifP7Db+D8Z/v2/3kis//FVz+sHNA8bFLnQOLxpje5XaI8XWKcWtRr57q9M0NACJC0bCCrG0lWQY7F6yvb45nX7383TwSehIHhfzY78GAsOvjQ+2CUu/jZvJgXKqeQFHVnHnPTXZZYGy6b9f/wiMzIe8I+Os1cMzn+npHuaX8UrjyN7CnFh77Gnxmf5SN6S0ra5poaY0mtBfzqiwt4ieXncZdXy0nEBCiqixcXZe1rKJ/mEWutA3z7rsgKJw1oYjTi0dy11fL23WjWDKviu9+aRLL5k9j2Y1VXHlWCYiw7PXGdlly7+Nm8mDc7MnF5AUTw2N3YEiuvOcmu6zG2HRPU7XTfWLoSKdXb9GEvt5Rbpo0wxmR/fg18OhXnfrs4WP6elf9xoTbnut0zY57v9ILOzEDSXVDiCc27kyrf23oYJioatJa5EzK1SEf3n0XDStg4eo6wq1RtuypY9K4wg5bta2vb6Y10tZX+L4XtnLr9Inxddl4PypLi3hi/jRW1DQhQPmxIwkdDOfUe26yywJj03U734DfzIZhRztB8UAf8ZxtJ013DuEtu9oZIX3dM1A4tq93ZcyAtbKmiVZPnekZxSPjGWN/cORmLt3pbdnMKubqkA933/e/uD3lgcZk/H2FX9u+jzd2fJTQISRbH0Jy8X02vcNKKUzXNG5wMsVHjnZqii0ozowTL4RrnnJa3j0602l5Z4zJiOqGEPe/uD3+Vb2/Ira68eOUh968JQDZ7kqR67paDuK+t2efPDo+kjuX6qvNwGQZY5O+hnWw5HIoHOdkikcc29c7GlhOOBeuWe60cXvkKxzDd9iL/UfYmK7wtzxL1q94zuRilm/cSUvEcYMVuQAAHd9JREFU6WOrnZRKWIYxPd0pf6gsLeLW6RN5Y8dHtLRGEw7j2Xtu+oJljE16drzmtBYrHA83PGdBcbZMOBu+vgIOfMDjBXczFutWYdoTkVtEZKOIHBaRRzpYd72IVIvIJyLSJCI/FZE8z+0vicifReTT2M+WXnkBWZKs5VlCT2JP4Lts/jS+9+VJ3H3paR1mOf3ZZtOxytIivn3hSV0Kat2A+sqzSlBg6YZGrn4wx1rWmQHDMsamc++thaV/BSOLnT7FVv+aXaXT4OsrGfPQLB4vuJurw7fzAXZa2iTYBfwY+DLQ0fjEYcCtwAZgDPAM8D3gXs+aW1R1cZb22auStTwrGlYQH/0bVeIt17xZ4EnjCpNmOd1A+3CLk8lcOKuCuVOtfCwbKkuLnE4hsdrvcGuUlRkYA21MV1nG2HSs/mXnq/2jSpxMsQXFvaNkKteHv89o+YQnCu7mWPb19Y5MP6KqK1X1aaDDYkxV/aWqrlXVsKq+DywBzu6VTfYBt8bV23c4dDAc710rQO2u9gN1UmU519c3c7jFaelmQyCy78MDhxMut++ObEz2WcbYpPbui06nhKIJTk2xtRHrVTU6kWvD/8hjBffEM8fvY/8Gfum0dANr6xZzHlDnu+4eEbkX2AL8UFVfSnZHEZkPzAcoKemfWdPK0iIWzCxnwaraeN/hBTPLyQ8K4YiiwBNvNFL3/n6uPLOk0+xvVdkoggGJD5pwh0BYFjNz3HKXomEFCZPuALbvOWC1xqbXWcbYJLf9BVh2FRxdBjestqC4j7ypJ/H18A8YKZ/xxJC7KZa9nd/JmCRE5BvAFOBfPFd/HygDjgMWAc+KyInJ7q+qi1R1iqpOGTOm//49qNu1n0hU471x19Tu5oJJx8SzxpEobGrazw9+u5l7f/d2h49VWVrEwlkV5AWEgNgQiEzz1oQvWFXbboLe6ztCXLVonWXpTa+yjLFpb+vz8MQ1MGYSXLsKjrT/EPSl/9MTmRv+IUsKfsITscxxo1pJi0mfiFwK3ANMV9V4XY6qbvAse1RErgYuAX7Ry1vMiKUbGnn89cb4V/Bub9y8gDOCONwaTVi/aG09JaOO7HDAw9ypJSlrkE3PeGvCVdU/mRuAlohl6U3vSitjLCJHi8hvReQzEWkQkbkp1v2DiNSKyAEReU9E/iGz2zVZ985z8PhcOOZUZ9CEBcX9Qp2ewNXh2xnKYZ4ouJsy2dXXWzI5QkT+EngQ+Kqqbu5kuQJJwpP+r7ohxIJVtUR8halRhUhUubyymItPHdvutgWralP2MHZ1p9OC6Zy3JlwB1fZBSX5QLEtvelW6pRT3A2FgLHAN8EsRKU+yToDrgCLgL4FbROSqTGzU9ILalfDkdTD+dGc08bCj+3pHxuNtLeWq8B3k0coTBXczUXb29ZZMHxGRPBE5AggCQRE5wtuGzbPuizgH7uao6uu+244SkS+79xWRa3BqkH/fG6/Bqyst0VKtXVnTlPBVfDBW+uC2YZszuZgHr5vCzeeVERDnP1Z5AWk37tn0Hv+ADwVE4OJTx3J68Ui+dOpYHp8/zT6QmF7VaSmFiBwJzAEqVPVT4FUReQa4FrjNu1ZVf+q5uEVEVuGcgH48c1s2WbHpCXj6Zji+Cq55EoYU9vWOTBJb9XiuCt/B0oJ/4vGCu7k2/APqdEJfb8v0vtuBOz2Xvw78SEQeBt7i/2/vzsOcqs4Hjn/fJJNhGZZh3wRkVQZFgSpVUXGpYhVUqlLQUhV37fNoRaktSMGK+qv1qb/SClXcEGUHC65VUFSgMvxEGIrgoDMOIJsjw4BMknvP74+bDJmQYcI4MzfJvJ/nyQO59yS8J7knvDk5C/QxxhQCE4BmwBty5HfqlcaYoUAGzpJvJwEWsBm40hizpW6q4Ii3AUdliVBlZXMLipnzaWGFsrcM7sbFOe2OGgIx/rKTy49nN/IzeWlenWz3rOIb0CWboX3bsyp/X3g4hTCkdxtdFk+5JpExxr2AUMyH5XrgvGM9SJxP4cHA9ErOJ/0M53pj7UxYep+z89ovXwN/Y7cjUseQbzpybWAir/gfZbb/EW4MPMA608vtsFQdMsZMAiZVcjorqtyQYzzHHuAnNRpYNcRbe7iyxLiysqu37cOqOHyYvJ0lXJzTjkHdWpb3BEeeN5E1jFXdyC0oZvLSvPLefst2VhPp3a6Jvh/KFYkkxllAScyx/UBVXYqTcIZqPB/vpDFmBs4saAYOHKjLFbrl46fh3QnQ8xK49kXIONZeASpZFJh2XFc2gVn+R3nZP5WxwftZZccb3aRUcouMM02k17aysoO6tSxfki3i4y/3smbbPhAhZDk9zBMvz6H4UKB8feNIMqwJmHsiX3YiDFV/QVKqNiWSGJcCTWOONQUOVPYAEbkbZ6zxYGNMWWXllIuMgRVT4YPHIecquGoG+PxuR6WOw3Zac21gIrP8U3kh4wnuDP6G9+wBboel1HGJjDNNpNc2UnbBuqIKMwQjWzwvWFdE3vb9bNi+3+lVtgzgrF8cCNrO5DzbuR9Zfu1YQzdU7Yt82QkEbWyc90WHtSg3JZIYbwF8ItLTGLM1fKwfRy8SD5SvlTkeONcYU1QzYaoaZdvw1oPwnxlw+vVwxdPg8bodlaqGPWRzXWACL/ofZ3rGU4wL3sYie7DbYSlVqxauKyIQslmwrqg8sY3cIuOQgyFnG2cDhCwDQoXJeYkM3VC1L/qLUWxPvlJuqDIxNsYcFJGFwGQRGQucBgwHzootG57V/CgwxBizraaDVTXACsKi22HjfDjrHrh4CnEXj1Qp43uaMCrwe2Zk/IWn/P+gebCU562hboelVEKOZ/IdHD3O+JkP8jkctBjatz2jzuxcIdE68EOQf67cVr4UWDTtmUweOpxFJZNEN/i4E5gJ7Ab2AXcYY/JEZDDwpjEmMtnjEaAl8GnUDOhZxpjbazBmVV1lpc5ybPnvwUWT4Jx73Y5I1ZCDNOSm4Dj+yjQezniZllLCn0PXkqJL0qp65Hgm3+UWFLP9+x/weT1Ylo0IvLtpFwArt+5lxRe7ue287uWPv276qqPWNRbgoj5tOe2E5tozqZQ6SkKJsTHmO+DKOMdXUnEG9Ik1F5qqUaW74ZVr4NsNztCJAWPcjkjVsDL83BX8DVPM89ztW0JbivldaCwh3eBSJbFEJ99F9yz7PMLIMzqz5qvv+HJ3aXmZdzbt4sOte8p7jK2YLYYj44pvj0qelVIqmv6PWR/sy4dZI+DAtzByNvS+1O2IVC2x8PJQ6Ga+NS24L2M+rWU/dwV/w0F0tRGVnOJNvpu9ppA3N+4sHx4BFXuWIxPovt5betTzRXqdB3VrSWaGM6nL4xHGnnMiTRpmaC+xUuqYNDFOdwWfOFs8iwfG/AtOcH3ZUlXrhKetq9lFNn/yPcc8/2RuCtzPt+hYSpWcoseYPvbGf3nmQ2eKysqtewEYdWZnBnVric/r9CyLR8gLrzwRITjTJSK9zsez2oVSSkVoYpzOPp8HS+6E5l2c3exadHM7IlWH5lhD2GlaMC3jaRZnTuTmwDjdJU8lndyC4vLkFWDGyorztt/cuJPe7ZqwYF0RtjHlq0x8XrTf2UIYZ+1bAI8IEy/PibuRh1JKJUIT43Rk284axR8+AV3OhutmQaMWbkelXPCh3Y9rAg8z0/8E8/x/5N7gnbxt668GKjnMXlPIxCUbsY3B7/Mwon8nYoYFk9O+KaOfXU1Z0Cb6lMHZQapzy0YUfncI24AxhuJDAaBiwq3JsVIqUR63A1A1rKwU5t7gJMWnXw83LNKkuJ7bbDozvGwKW0wnpvuf4h7vQkA3m1Tuyi0oZuKSjYRsg20gELLZfaDiflDn9mxF3s4SAiH7qCvWI+DP8HDrud3x+zx4o4ZRRCbqPfnOF4x+djW5BcV1VzGlVErTHuN08t02mHMD7N4El0yFQXfoGsUKOLIRyNSMZ/ltxnxO8hTyQPA2nZSnXBO7aoSI0KZJZvnQCAE+yd9XPtFOcJLhC09uy/m921TYCKJ3uyYVeoenLf8y4SXglFIqmibG6eKLt2DhrU4iPHoe9LjI7YhUkinDz33BO/iv3Znxvlfp5d/ObcF72WY6uB2aqocGdWtJhlcIhBcaFoEmmT68HsE2BqHiTnWIkzB/uHUPt53XHXCSazh6LHGiS8AppVQsTYxTnRWCDx6DD/8H2p3ijCfO7up2VCppCf+0LmejOZG/ZTzNEv8EHgzewhv2ILcDU/XMgC7ZXDPwBGavKcQAlmWYsXIbxjg9wxVm1eHsXGdweoAXrCtifq6zLbTXI0wZ3rd8WbfIc+uKFEqp6tAxxqmsZCe8NMxJik8bDTe/q0mxSsgqO4fLyx7lS9ORv/ufZopvJpkE3A5LJUhE7haRtSJSJiIvVFH2XhH5VkRKRGSmiGRGnesqIstF5JCIbBaRWv2pKbegmIcWbeD3izaQW1BMTodmeD1SngPb5sifth2nLjjjiPceKCMQcgpYtmHCko1HjSMe0CWbu4b00KRYKXVctMc4VW15GxbfAcEf4Mpn4LRfuh2RSjE7acm1gYnc75vDbb5lDPBs5Z7g3eSbjm6Hpqq2A3gEuAQqHyguIpcA44ELwo9ZBPwxfAzgVWAVcFn4Nl9Eehpj9tR0wLkFxfxyxqryoROv/qcQr0ewbIOI0yN8JG7weT2EQjY2TkLs9QrXDTyBq/t3YsG6ogrPbdtGxxErpWqE9hinmsBBWHovzL4WmrSHWz/QpFhVWxAfU0OjuTEwjrbyHcv8D/Er79voqhXJzRiz0BizGNhXRdExwHPGmDxjTDEwBfg1gIj0AvoDDxtjfjDGLAA2ACNqI+aF64rKk2JweoWDljOxDgPeqHnCHo8w6YocRp7ZGV/4hAe4un8nBnTJZkT/Tvii/vfSccRKqZqiiXEq+eY/MP1cWPs8nHUP3PI+tO7ldlQqDSy3T+fSssdZZfdhcsaLvJTxGB3Y63ZY6sfLAdZH3V8PtBWRluFz24wxB2LO58R7IhG5NTx8Y+2ePcfXoZxbUMy8td/EPSc4y65deHJbIrmxsZ31iDs2b4gdXpXCCvcKgzNMYs5tZzHqzM6MPrMzr94ySHuLlVI1QodSpILAQXj/EVj9D2jWCca8Diee63ZUKs3soTk3Bh/gevvf/M43m7czH2RqaBSvWkMw+h06VWUB+6PuR/7eJM65yPm4Y2mMMTOAGQADBw48rp8UVm/bV2GFicj2zT6PcE14eAQ4K05EVpLIbuRn4479+LweLOvo1SV0VzulVG3QxDjZbX0Xlv0Wvi+An4yFiyZBZhO3o1JpS5hlXcwKux+P+/7JoxnPMcz7Cb8P3qRjj1NTKdA06n7k7wfinIucP0ANG9StJT7PkaXZoscLRye3kZUkshv5mbw0j0DIxucRRp7RmZwOzSr0GCulVG3QbqBkVbID5v4KXvkFeP3w62Xw8yc1KVZ1osi0YXTwIcYHx3KyFPCmfzzjfK/RgLKqH6ySSR7QL+p+P2CXMWZf+Fw3EWkScz6vpoOILM0WPVSiQ/OGRyW4kZUkig8FyjfosGzD7gNlTFyyUXeyU0rVOk2Mk03gEHzwBPzvAGfliQv+AHd8DF3PcTsyVe8Ir1kXcEHZk7xun81dvtd5L/N+hnk+QSfnuUtEfCLSAPACXhFpICLxfgF8CbhZRPqISHPgD8ALAMaYLcBnwMPhx18FnAosqI2Yr+7ficyMI1s3ZzfyM235l3GT3MgGHV4Br0d4f/PuCltHR3qOlVKqpulQimRhW7BhHrw3BUqKoM9wuHiyrkucprqOX+Z2CAnbRzPuD97OnND5TMx4iaf9f+PX9ls8GhzFWnOS2+HVV38AHo66fz3wRxGZCWwC+hhjCo0xb4nIE8BynGXdFsQ8biROolwMFAK/qI2l2qDiphvRQyX8Pg+vjK04eS667I7vf2D2msLycx4RXYFCKVVrNDF2mzGweZkzuW7Pf6F9P7h6BnQ92+3IlKrgU3MSwwKPMMK7knG+OczPnMxyqx9/Dl1Hnunqdnj1ijFmEjCpktNZMWX/Avylkuf5Gji/5iI7tsiEuWnLvywfKhEM9wDHG1YxoEs2uQXFLFhXRCBo4/EIk4f31THGSqlao4mxW2wbNi91dq379nNo2QOueQFOHg4eHeGikpPBw3zrPJZagxjjfYc7fK+zLPMh3rEG8LfQlXxuursdokoBkcl4Qcvg9Ry7B1i3d1ZK1SVNjOta8DBsmAurpsGezdCiOwyfBqeOBK++HSo1HCaT6dYVvGpdwI3et7jR9xavZ05gpdWXZ62f84F9KiBVPo+qfyI9wOWj1KXq60SXZlNK1RXNxOrK/iLIfRHWzoRDe6HtKTDiOci5Cjxet6NTqlpKaMxfrRE8a13G9d5/c5PvTV70Ps5WuyMvWJew2Dqbg5XvWKzqmdyCYkY/u5qyoF2eGFtW/KEUSinlBk2Ma5MVdNYhXvcibH3HGU/c61L46Z3QdXBCPSVKpYKDNGS6dQUzraH83LOam31v8KeMmTzke4Ul1lnMtYbwmemO9iLXb6u37SMQOpIUC7qds1IquWhiXNOMge25zgoTG+bBoX3QuA2ccy/0HwPZXdyOUKlaE8THYvscFgfO5jTJZ5T3Pa7yfswo33Ly7fYstAaz1B5EgWnndqjKBZFl2IIhG2/UrnfaW6yUShaaGNcEKwiFq+GLN2DT685ya95M6D0U+o2EHheBN8PtKJWqQ8JnpgefhXowJXQDQ71ruNr7EeMy5jKOueTZXXjTOoN/2wPYbE5Ae5LrB51Ip5RKdpoYV9f3hbBtBeS/D1++D2X7nR3qelwEF05wkuIGzdyOUinXHaARc60hzLWG0IG9XOr9lMu8a7g/Yx73M4/tpiUrrNNYaZ/CKrsP+yuuNqbSjE6kU0olM02ME2HbsO9L+Ga10zNc8AkUf+Wcy2oHfa5wxg53O1+3bFbqGHbQipnWUGZaQ2lNMUO8n3Gh5/8Y7v2Y0b73sI2wyXThU7s3n9q9ybV7sYsWboetlFKqntDEOFYo4CTBuzY66wvvXA87PoOyEud8o5bQ+adw5u1OIty6t06iU6oa9pBd3pPsI8Spso3Bng2c4dnMSO9ybvS9DcAu05zP7e7kmS5ssruwyXRhu2mF0R3tlVJK1bCEEmMRaQE8B/wM2Av8zhgzO045AR4DxoYPPQuMN8aY2LKusoJQst0ZDvHdNue2Lx/2bnH+NJZTzpsJbU6GU66BjgOg00Bo1UsTYaVqWAgf60wv1lm9wAIfIfrK1/Tz5Ds3yedCzzo8Puej5JDJJN+0J9904GvTjq/tdhSaNnxjWrOXZpo0K6WUqpZEe4ynAQGgLXAasExE1htj8mLK3QpcCfQDDPAu8BXwTM2Eewy2BYf3ww/FzkoQh/bBwb1QugtKd8OBnc6tZIfzp7GPPNbrh+yuTtJ78jCnF7htX2jVUyfNKeWCED5n8p7VA8LfUxtymN5SxEmeQnrIdnrKdgZ6tjCMVeUJM0CZyWCnacEustlpWrDbZLPHNIP1B6BRK2jUwvnlp2G2M/RJv+gqpZQKqzIxFpHGwAigrzGmFPhIRF4HbgDGxxQfAzxpjCkKP/ZJ4BZqIzF+80H4aqUzxOFwSXioQyUd0w2aQVZbaNIeTjwPmnZwlk1r3hmyT4RmnXSTDaWS3A80OJIsR/ET5ATZzQmym06ylxNkN+3lO9pKMf1lK609+2koAVh01I9cIF7n86FBU8hsCmfcCv1vqKMaKaWUSjaJ9Bj3AkLGmC1Rx9YD58UpmxM+F10up/rhHUNmE6eXN/IfWsNsaNjc+bNRyyO3rLaQ0aBWQlBKuS9ABvmmI/mmYyUlDI05TN6404/8knRoHxz+3vmF6fB+58v14f3gb1SnsSullEouiSTGWUBJzLH9QLzlF7LC56LLZYmIxI4zFpFbcYZeAJSKyBeJhVxBK5wxz6lG465bGnfdS7rY5fFESs2rbtz1auee3NzcvSJSUI2HJt11UcPSuX7pXDdI7/qlc92gevWr9DM7kcS4FGgac6wpcCCBsk2B0niT74wxM4AZCfz7lRKRtcaYgT/mOdygcdctjbvupWrsqRp3XTPGtK7O49L99U3n+qVz3SC965fOdYOar18iU7e3AD4R6Rl1rB8QO/GO8LF+CZRTSimllFIqqVSZGBtjDgILgcki0lhEzgaGAy/HKf4ScJ+IdBSRDsBvgRdqMF6llFJKKaVqRaKLfd4JNAR2A68Cdxhj8kRksIiURpWbDvwL2ABsBJaFj9WWHzUUw0Uad93SuOteqsaeqnGninR/fdO5fulcN0jv+qVz3aCG6yfJtveGUkoppZRSbtDtoZRSSimllEITY6WUUkoppYA0SIxFZJaI7BSREhHZIiJj3Y4pESKSKSLPiUiBiBwQkc9EZKjbcSVCRO4WkbUiUiYiL7gdT2VEpIWILBKRg+HXeZTbMSUiVV7fWCl+Tafk50iqSNW2GHGsNikiF4rIZhE5JCLLRaRL1LlMEZkZvq6+FZH76jz4KlTVbtOgfpW27VSvW4SI9BSRwyIyK+rYqPB7elBEFotIi6hzKdEeRWRFuF6l4dsXUedqrX4pnxgDU4GuxpimwDDgEREZ4HJMifAB3+DsINgM+AMwV0S6uhhTonYAjwAz3Q6kCtOAANAWGA38Q0RqZyfGmpUqr2+sVL6mU/VzJFWkaluMiNsmRaQVzqpNE4AWwFpgTlSRSUBPnM0EhgAPiMildRDv8ai03aZJ/eK27TSpW8Q04NPInXDbmg7cgNPmDgF/jymfKu3xbmNMVvjWG+qgfsaYtLkBvYGdwLVux1LN+D8HRrgdx3HE+wjwgttxVBJb43DD6BV17GXgMbdjS4fX9zjqkFLXdDjmlP4cSbZbOrTFqLgrtEmc3Vs/ianrD8BJ4fs7gJ9FnZ8CvOZ2PRKo5+fAiHSrX3TbTpe6ASOBuTiJ/KzwsUeB2VFluofbYJNUao/ACmBsnOO1Wr906DFGRP4uIoeAzTgX/Rsuh3TcRKQt0AvdEKWm9AJCxpgtUcfWA8n6rTjtpNo1nQ6fI0kqndtiDk5dgPJ1//OBHBHJBtpHnycF6h3TbtOifpW07ZSvm4g0BSYDscM8YuuWTzhZJPXa41QR2SsiH4vI+eFjtVq/tEiMjTF34nxTGIzz00iZuxEdHxHJAF4BXjTGbHY7njSRBZTEHNuPc52oWpaK13Sqf44ksXRui1k4dYkWqVtW1P3Yc0kpTrtNi/pV0rbToW5TgOeMMUUxx6uqW6q0xweBbkBHnLWK/yUi3anl+iV1YhweeG0quX0UXdYYYxljPgI6AXe4E/ERicYuIh6cbv4AcLdrAYcdz2ue5EqBpjHHmgIHXIilXkm2a/p4JNvnSJpI57Z4rLqVRt2PPZd0Kmm3aVO/OG07pesmIqcBFwFPxTldVd1Soj0aY9YYYw4YY8qMMS8CHwOXUcv181U/5NpnjDm/Gg/z4Yw3cVUisYuIAM/hDBC/zBgTrO24qlLN1zwZbQF8ItLTGLM1fKwfKfKzfqpKxmu6mpLicyRNpHNbzAPGRO6ISGOc6ybPGFMsIjtx6vpuuEhS1vsY7TYt6hcj0rZTvW7nA12BQuftIwvwikgf4C2ceAEQkW5AJk5btEnd9mgAwYm19urn9uDqHzkwuw3OwPMswAtcAhwEhrkdW4LxPwOsBrLcjuU44/YBDXBm+74c/rvP7bjixPkazhbmjYGzcX5OyXE7rnR5fSuJPeWu6VT/HEmFW6q2xaj447ZJoHW4LiPCxx4HVkc97jHgAyAbOAlnfOulbtcnTv3itttUr9+x2nYa1K0R0C7q9mdgfrheOTjDCQaH29wsoiYOpkJ7BJqH369IWxsdfu961Xb9XK/8j3zhWocv3O/DL9IG4Ba340ow9i44334O43T9R26j3Y4tgdgnhWOPvk1yO644cbYAFocbUyEwyu2Y0un1jRN3Sl7Tqfw5kiq3VG2LUfFX2iZxfs7ejLOiwQqcpcEij8vEWeKtBNgF3Od2XeLU7ZjtNpXrV1XbTuW6VXKNzoq6Pyrc1g4CS4AWUeeSvj2G37tPcYZAfI/zxe3iuqifhJ9EKaWUUkqpei2pJ98ppZRSSilVVzQxVkoppZRSCk2MlVJKKaWUAjQxVkoppZRSCtDEWCmllFJKKUATY6WUUkoppQBNjJVSSimllAI0MVZKKaWUUgrQxFgppZRSSikA/h+xUPza2m30sgAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Case where $\\varepsilon L$ is the period of the trajectory determined by Hamiltonian\n", "# In such case, the proposed point is expected to be close from the current point, which results in random-walk-like behavior.\n", "sample_hmc_1dgaussian(hmc_1dgaussian, q_initial=np.array([1.0]), n_samples=500, epsilon=2*np.pi/13, L=13, idx_start=10)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sample mean : -0.00028602897036381135\n", "sample variance : 0.9892399961614358\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Case where $\\varepsilon L$ is the half of the period of the trajectory determined by Hamiltonian\n", "# The point hops between two peaks.\n", "sample_hmc_1dgaussian(hmc_1dgaussian, q_initial=np.array([1.0]), n_samples=500, epsilon=2*np.pi/(13*2), L=13, idx_start=10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.3.2 1D gamma distribution\n", "\n", "Here gamma distribution is considered. \n", "$$\n", "\\begin{align}\n", " \\pi(q) = \\frac{1}{\\Gamma(k) \\theta^k} q^{k-1} e^{-\\frac{q}{\\theta}}, \n", "\\end{align}\n", "$$\n", "which has mean $k \\theta$ and variance $k \\theta^2$.\n", "\n", "In the following, parameters $k = 3$ and $\\theta = 1$ are used." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "def U(q):\n", " assert len(q) == 1\n", " if q[0] <= 0:\n", " return np.float(\"inf\")\n", " else:\n", " return -2 * np.log(q[0]) + q[0]\n", "\n", "def grad_U(q):\n", " return 1 - 2/q\n", "\n", "hmc_1dgamma = HMCsampler(dim=1, U=U, grad_U=grad_U)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "def sample_hmc_1dgamma(hmc, q_initial, n_samples, epsilon, L, idx_start=0):\n", " # get the samples\n", " samples = hmc.sample(\n", " q_initial=q_initial,\n", " n_samples=n_samples,\n", " epsilon=epsilon,\n", " L=L\n", " )\n", " \n", " print(f\"sample mean : \", np.mean(samples[idx_start:, 0]))\n", " print(f\"sample variance : \", np.var(samples[idx_start:, 0]))\n", "\n", " fig, axes = plt.subplots(1, 2, figsize=(12,4))\n", " # plot histogram\n", " ax = axes[0]\n", " ax.hist(samples, bins=np.arange(0, 10, 0.2), density=True, label=\"Normalized histogram\")\n", " xx = np.linspace(0, 10, 100)\n", " ax.plot(xx, 0.5*xx**2*np.exp(-xx), label=\"probability density function\")\n", " # plot time series of q\n", " axes[1].plot(samples[:, 0], '.')" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sample mean : 2.9953845634540177\n", "sample variance : 3.2318418091581966\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sample_hmc_1dgamma(hmc_1dgamma, q_initial=np.array([1.0]), n_samples=1000, epsilon=0.1, L=50, idx_start=10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.3.3 2D Gaussian distribution\n", "\n", "$$\n", "\\begin{align}\n", " \\pi(q) &= \\frac{1}{2\\pi \\sqrt{\\det \\Sigma}} \\exp \\left( - \\frac{1}{2} q^T \\Sigma^{-1} q \\right) \\\\\n", " \\Sigma &= \\frac{1}{2} \\begin{pmatrix}\n", " 26 & 24 \\\\\n", " 24 & 26\n", " \\end{pmatrix}, \\\\\n", " \\Sigma^{-1} &= \\frac{1}{2} \\begin{pmatrix}\n", " 1.04 & -0.96 \\\\\n", " -0.96 & 1.04\n", " \\end{pmatrix}\n", "\\end{align}\n", "$$" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "S = 0.5 * np.array([[26.0, 24.0],[24.0, 26.0]])\n", "Sinv = 0.5 * np.array([[1.04, -0.96],[-0.96, 1.04]])" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "def U(q):\n", " return 0.5 * q @ Sinv @ q\n", "\n", "def grad_U(q):\n", " return Sinv @ q\n", "\n", "hmc_2dgaussian = HMCsampler(dim=2, U=U, grad_U=grad_U)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "def sample_hmc_2dgaussian(hmc, q_initial, n_samples, epsilon, L, idx_start=0):\n", " # get the samples\n", " samples = hmc.sample(\n", " q_initial=q_initial,\n", " n_samples=n_samples,\n", " epsilon=epsilon,\n", " L=L\n", " )\n", " \n", " print(f\"sample mean : {np.mean(samples[idx_start:], axis=0)}\")\n", " print(f\"sample covariance : \\n {np.cov(samples[idx_start:], rowvar=False)}\")\n", " \n", " # contour plot of the density function\n", " xx = np.linspace(-15.0, 15.0, 100)\n", " yy = np.linspace(-15.0, 15.0, 101)\n", " XX, YY = np.meshgrid(xx, yy)\n", " Z = np.exp( -0.25*( Sinv[0, 0]*XX*XX + 2*Sinv[0, 1]*XX*YY + Sinv[1, 1]*YY*YY ))/(2*np.pi*10)\n", "\n", "\n", " fig, axes = plt.subplots(1, 3, figsize=(18, 6))\n", " ax = axes[0]\n", " ax.plot(samples[:,0], samples[:,1],'.')\n", " ax.contour(XX, YY, Z)\n", " axes[1].plot(samples[:, 0], '.')\n", " axes[2].plot(samples[:, 1], '.')\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sample mean : [0.07129976 0.03718861]\n", "sample covariance : \n", " [[10.75489208 9.8896402 ]\n", " [ 9.8896402 10.82490231]]\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sample_hmc_2dgaussian(hmc_2dgaussian, q_initial=np.array([0.0, 0.0]), n_samples=1000, epsilon=0.3, L=40) # setting L = 50 will generate a peculiar result" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sample mean : [0.57971157 0.58000071]\n", "sample covariance : \n", " [[12.24096243 12.12037847]\n", " [12.12037847 12.29749392]]\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# An example HMC sampler performs badly.\n", "sample_hmc_2dgaussian(hmc_2dgaussian, q_initial=np.array([0.0, 0.0]), n_samples=1000, epsilon=np.pi/10, L=10)" ] } ], "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": "3.8.2" } }, "nbformat": 4, "nbformat_minor": 4 }