MonteCarlo.ipynb

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   "cell_type": "markdown",
   "id": "91b928f5",
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   "source": [
    "# Monte Carlo\n",
    "\n",
    "Now that you have written your own MD code, you have a recipe for evaluating thermodynamic properties of systems in the microcanonical ensemble. We used MD simulations to sample configurations from that ensemble and, since they all had the same probability, we took their arithmetic mean to calculate ensemble averages. But what would you do if you wanted to sample the canonical ensemble? You would have to evaluate Eq.[](ensemble_av_NVT), in which each configuration has a different weight. Effectively, this also means evaluating very **high-dimensional integrals**, since $\\textbf x$ is of dimension $6N$ where $N$ is the number of atoms. Here, we will learn about the difficulties of calculating such integrals and of an ingenious algorithm to overcome them."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5a6cdb6",
   "metadata": {},
   "source": [
    "## Evaluation of high-dimensional integrals\n",
    "\n",
    "As we have seen, the expectation values we encounter in statistical mechanics are of the form \n",
    "\n",
    "$$\n",
    "A = \\langle a \\rangle_f = \\int f(\\textbf x) \\, a(\\textbf{x}) \\, \\mathrm{d} \\textbf{x},\n",
    "$$(expval)\n",
    "\n",
    "where \n",
    "\n",
    "$$\n",
    "f(\\textbf x) = \\frac{1}{\\mathcal Z} \\mathcal{F}(\\mathcal{H} (\\textbf{x}))\n",
    "$$\n",
    "is a positive, normalized phase space probability density. From now, we will consider the canonical ensemble, for which $\\mathcal{F}(\\mathcal{H} (\\textbf{x})) = e^{-\\beta \\mathcal H (\\textbf x)}$.\n",
    "\n",
    "How could we evaluate these expectation values in practice? One way is to sample $a(\\textbf{x}_j)$ on a multi-dimensional grid, multiplying each one of the samples by its probability and doing the integration by quadrature,\n",
    "\n",
    "$$\n",
    "A_M = \\sum_{j=1}^{N_g} f(\\textbf{x}_j) a(\\textbf{x}_j) \\Delta \\textbf x = \\frac{ \\sum_{j=1}^{N_g} e^{-\\beta \\mathcal{H}(\\textbf{x}_j)}\\, a(\\textbf{x}_j)}{ \\sum_{j=1}^{N_g} e^{-\\beta \\mathcal{H} (\\textbf{x}_j) }}.\n",
    "$$ (quad)\n",
    "\n",
    "However, this is very, very expensive and the algorithm scales exponentially with the particles. Why? Because we need to evaluate a $6N$ dimensional integral on a grid. \n",
    "\n",
    "Admittedly, if the property we are interested in does not depend on the momenta, i.e. $a(\\textbf{x}_j) = a(\\textbf{r}_j)$, then the integration over $\\textbf p$ can be done analytically to obtain,\n",
    "\n",
    "$$\n",
    "A_M = \\frac{ \\sum_{j=1}^{N_g} e^{-\\beta U(\\textbf{r}_j)}\\, a(\\textbf{r}_j)}{ \\sum_{j=1}^{N_g} e^{-\\beta U(\\textbf{r}_j) }}.\n",
    "$$ (config_part)\n",
    "\n",
    "Nevertheless, we remain with a $3N$ dimensional integral. To evaluate it, even if we divide each spatial dimension for every particle into only 10 grid points, we would need to sum over $N_g = 10^{3N}$ points to evaluate the integral. This is completely prohibitive already for a very small number of particles. Monte Carlo is a clever way to evaluate such integrals without resorting to quadrature. Moreover, Monte Carlo is a conceptually different approach for sampling equilibrium distribution functions that does not rely on the dynamics in time of the system to generate the configurations (like MD).\n",
    "\n",
    "## Uniform random sampling\n",
    "\n",
    "A solution to this problem was invented by [Ulam](https://en.wikipedia.org/wiki/Stanislaw_Ulam) and [Metropolis](https://en.wikipedia.org/wiki/Nicholas_Metropolis) in 1949. Their ingenious idea was to use random numbers to evaluate multidimensional integrals instead of a quadrature on a grid. They showed that using their approach, it is possible to evaluate integrals using a much smaller number of samples than the exponentially growing number of grid points. Their idea was to choose a known reference volume in space that bounds the (irregular volume) we wish to calculate. Then, we sample random points uniformly distributed in the reference volume. We count the number of samples that lie within the irregular volume we wish to calculate. The ratio of this number to the total number of samples, multiplied by the reference volume is an estimate of the irregular volume,\n",
    "\n",
    "$$\n",
    "\n",
    "V = \\frac{\\tau_{in}}{\\tau_{tot}} V_0\n",
    "\n",
    "$$(MCint)\n",
    "\n",
    "For example, to evaluate the area of a two-dimensional disk with radius $R=1$ in the first quadrant, we need to solve the integral\n",
    "\n",
    "$$\n",
    "\n",
    "\\int_0^1 \\int_0^{\\sqrt{1-x^2}} \\mathrm{d} x  \\mathrm{d} y = \\frac{\\pi}{4}.\n",
    "\n",
    "$$(disk)\n",
    "Instead, we choose a reference square of unit side length that bounds the unit circle and evaluate the integral numerically using MC uniform sampling. Below we demonstrate this method and evaluate the area/volume of a ball in two and three dimensions, using both quadrature and Monte Carlo uniform sampling. To treat the two methods on equal footing, we make sure to use the same number of function evaluations and compare the obtained accuracy. We show that for two dimensions, quadrature is more accurate than MC sampling. But already for three dimensions, MC is more accurate by an order of magnitude. MC is also much faster than quadrature for three dimensions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6486207a",
   "metadata": {},
   "outputs": [],
   "source": [
    "#imports \n",
    "import numpy as np\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "import time\n",
    "from scipy import integrate, special\n",
    "\n",
    "#Radius of unit sphere\n",
    "R = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "3bd0c720",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.7854453780175082, 6.043574189984469e-06, {'neval': 1888215})"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#2D quadrature\n",
    "func = lambda x,y: x**2 + y**2 <= R**2\n",
    "integrate.nquad(func, [[0,R], [0,R]], full_output=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "6c34a29c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.5236018744846193, 0.0001344051879086777, {'neval': 1839958785})"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#3D quadrature\n",
    "func = lambda x,y,z: x**2 + y**2 + z**2 <= R**2\n",
    "integrate.nquad(func, [[0,R], [0,R], [0,R]], full_output=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "2612a5a5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean = 0.7857092923494083\n",
      "BSE = 0.00016751888217729133\n",
      "Expected = 0.7853981633974483\n",
      "neval = 1888220\n"
     ]
    }
   ],
   "source": [
    "#2D MC uniform sampling\n",
    "d = 2\n",
    "\n",
    "Nsamples = 188822\n",
    "M=10\n",
    "\n",
    "rng = np.random.default_rng()\n",
    "\n",
    "res = np.array([])\n",
    "for seed in range(M):\n",
    "\n",
    "    #generate random samples\n",
    "    p = rng.uniform(0,R, size= (d,Nsamples))\n",
    "    \n",
    "    #count how many are inside the n-ball\n",
    "    inside = ((p**2).sum(axis=0) <= R**2).sum()\n",
    "    V0 = R**d\n",
    "    res = np.append(res, inside/Nsamples*V0)\n",
    "    \n",
    "print(\"Mean = \" + str(res.mean()) ) \n",
    "print(\"BSE = \" + str(res.std()/np.sqrt(M)) )\n",
    "\n",
    "#volume of d-ball in first quadrant\n",
    "voln = math.pi**(d/2) * R**d / special.gamma(d/2 + 1) / 2**d\n",
    "print( \"Expected = \" +  str(voln) )\n",
    "\n",
    "print(\"neval = \" + str(Nsamples*M) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "67a48c09",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fcad2524eb0>]"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1200x1200 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(1, figsize=(8,8), dpi=150)\n",
    "plt.xlabel(r\"$x$\")\n",
    "plt.ylabel(r\"$y$\")\n",
    "\n",
    "lessp = p[:,0:-1:100]\n",
    "idx = lessp[0,:]**2 + lessp[1,:]**2 <= R**2\n",
    "\n",
    "plt.plot(lessp[0,:],lessp[1,:],'.')\n",
    "plt.plot(lessp[0,idx],lessp[1,idx],'.')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "a83d4135",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean = 0.5236000046501041\n",
      "BSE = 1.139280597847283e-05\n",
      "Expected = 0.5235987755982989\n",
      "neval = 1839958790\n"
     ]
    }
   ],
   "source": [
    "#3D MC uniform sampling\n",
    "d = 3\n",
    "\n",
    "Nsamples = 183995879\n",
    "M=10\n",
    "\n",
    "rng = np.random.default_rng()\n",
    "    \n",
    "res = np.array([])\n",
    "for seed in range(M):\n",
    "\n",
    "    #generate random samples\n",
    "    p = rng.uniform(0,R, size= (d,Nsamples))\n",
    "    \n",
    "    #count how many are inside the n-ball\n",
    "    inside = ((p**2).sum(axis=0) <= R**2).sum()\n",
    "    V0 = R**d\n",
    "    res = np.append(res, inside/Nsamples*V0)\n",
    "    \n",
    "print(\"Mean = \" + str(res.mean()) ) \n",
    "print(\"BSE = \" + str(res.std()/np.sqrt(M)) )\n",
    "\n",
    "#volume of d-ball in first quadrant\n",
    "voln = math.pi**(d/2) * R**d / special.gamma(d/2 + 1) / 2**d\n",
    "print( \"Expected = \" +  str(voln) )\n",
    "\n",
    "print(\"neval = \" + str(Nsamples*M) )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fdab2f96",
   "metadata": {},
   "source": [
    "## The Central Limit Theorem\n",
    "\n",
    "We have just established that random (uniform) sampling could be very helpful for evaluating multi-dimensional integrals, in comparison to numerical quadrature. But there are situations in which uniform sampling could be highly wasteful too. For example, when $f(\\textbf x)$ is localized in a small volume in the $3N$ dimensional space. In that case, many of our uniform samples will not be counted when evaluating the integral. \n",
    "\n",
    "Note that this is not the case for the example of the n-ball above. For the n-ball, the volume grows like $\\sim R^d$ where $d$ is the number of spatial dimensions. We sample uniformly in an $d$-dimensional cube, whose volume also scales the same. This means that the ratio of the two volumes does not depend on $d$. \n",
    "\n",
    "For the problematic, localized case, can we do better than uniform sampling? Yes! If we know how to generate samples that are already distributed according to $f(\\textbf x)$.\n",
    "\n",
    "At this point, we will *assume* that we have an algorithm for obtaining a set of $M$ **independent** samples (configurations of the system) $\\textbf x_1 ,..., \\textbf x_M$ that are all **identically distributed** according to $f(\\textbf x)$ with some mean $\\langle a \\rangle_f$ and variance $\\sigma^2 = \\langle a^2 \\rangle_f - \\langle a \\rangle_f^2$. This is by no means a trivial task. It is straightforward only for simple distributions and the form of Monte Carlo that we will study next was designed to address exactly this problem. But, for now, we will simply assume such an algorithm exists. If that is the case, we can then evaluate $a(\\textbf{x}_j)$ for each sample. \n",
    "\n",
    "The central limit theorem (CLT) ensures that if we consider the simple arithmetic mean of the samples as a random variable,\n",
    "\n",
    "$$\n",
    "A_M = \\frac{1}{M} \\sum_{j=1}^{M} a(\\textbf{x}_j).\n",
    "$$ (mean)\n",
    "It will be normally distributed with the same mean $ \\langle a \\rangle_f $ as the samples $ \\textbf{x}_j $ and a variance \n",
    "\n",
    "$$\n",
    "\\sigma^2_M = \\frac{\\sigma^2}{M}\n",
    "$$\n",
    "\n",
    "In other words, the CLT guarantees that the arithmetic mean of the samples converges to the ensemble average of $A$ in the limit $M \\to \\infty$, because its variance from the mean decays like $M^{-1}$. Note that the CLT does not assume a specific form of the distribution $f(\\textbf{x})$. This is very powerful, it means that even when our sampling algorithm (dynamic or not) provides samples from a nonuniform distribution, the arithmetic mean will still converge to the true expectation value. An important outcome is that we can use the simple arithmetic mean of the samples to calculate expectation values for the canonical ensemble, just like in the NVE ensemble, as long as we can generate samples from the desired distribution.\n",
    "\n",
    "However, that is exactly where things get tricky! We know how to generate random samples only from relatively simple probability distributions (Gaussian, uniform, exponential, see others [here](https://numpy.org/doc/1.16/reference/routines.random.html)). \n",
    "\n",
    "There are two solutions to this problem: 1) Use a different distribution, $h(\\textbf x)$, that is simple enough to be sampled directly and resembles $f(\\textbf x)$ better than a uniform distribution. 2) Generate samples consecutively (and not altogether at random as we did above) in a process that is sure to converge to the distribution $f(\\textbf x)$. The first solution is called **importance sampling**, which we describe first. The second solution, called the **Metropolis Monte Carlo** or **Markov Chain Monte Carlo**, will be discussed in the next section.\n",
    "\n",
    "## Importance Sampling\n",
    "\n",
    "We can use the CLT even if we do not know how to sample from $f(\\textbf x)$ directly, but know how to sample a different distribution, $h(\\textbf x)$, that has much more substantial overlap with $f(\\textbf x)$ than the uniform distribution. Since $h(\\textbf x)$ is a positive, normalized probability density, we rewrite Eq. [](expval) as\n",
    "\n",
    "$$\n",
    "A = \\langle a \\rangle_f = \\int h(\\textbf x) \\, \\frac{f(\\textbf x)}{h(\\textbf x)} \\, a(\\textbf{x}) \\, \\mathrm{d} \\textbf{x} = \\langle a(\\textbf x) w (\\textbf x) \\rangle_h,\n",
    "$$(reweight)\n",
    "where $w(\\textbf x) = f(\\textbf x) / h(\\textbf x)$ is the weight we need associate with every configuration sampled from $h(\\textbf x)$ to obtain the expectation value we are really interested in, Eq. [](expval). As a result, this procedure is also often called **reweighting**.\n",
    "\n",
    "Below we show an example from the book by Tuckerman that uses importance sampling to evaluate the integral\n",
    "\n",
    "$$\n",
    "\\int_0^1 e^{-x} \\, \\mathrm{d}x = 1 - \\frac{1}{e} = 0.632120558829.\n",
    "$$\n",
    "\n",
    "If we sample $x$ uniformly, we get a good estimate of the mean after 1000 random samples.\n",
    "But the error is an order of magnitude smaller if we use importance sampling with \n",
    "\n",
    "$$\n",
    "h(x) = \\frac{1 - ax}{1-\\frac{a}{2}},\n",
    "$$\n",
    "while choosing $a$ to have the higest similarity between $h(x)$ and $e^{-x}$. The similarity is measured using a function called the [Kullback-Leibler (KL) divergence](https://towardsdatascience.com/kl-divergence-python-example-b87069e4b810), the optimal value is found to be $a=0.64$. \n",
    "\n",
    "```{admonition} Active learning\n",
    ":class: tip\n",
    "Show that $h(x)$ given above is a positive and normalized probability density in the range [0,1].\n",
    "```\n",
    "\n",
    "```{admonition} Solution\n",
    ":class: dropdown\n",
    "\n",
    "$$\n",
    "\\int_0^1 \\frac{1 - ax}{1-\\frac{a}{2}} \\, \\mathrm{d}x = \\frac{x - \\frac{ax^2}{2}}{1-\\frac{a}{2}} \\bigg| _0^1 = 1\n",
    "$$\n",
    "\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "d4825cc4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "KL divergence h(x) = -0.011662666832944757\n",
      "KL divergence uniform = 4.133335709606822\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'f(x)')"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1200x1200 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Ng=100; a=0.64\n",
    "\n",
    "plt.figure(figsize=(8,8), dpi=150)\n",
    "xg = np.linspace(0,1,Ng)\n",
    "\n",
    "p = np.exp( -xg ) / np.trapz( x=xg, y=np.exp(-xg) )\n",
    "q = ( 1 - a*xg )/( 1 - a/2 ) \n",
    "q2 = np.ones(Ng)\n",
    "\n",
    "print( \"KL divergence h(x) = \" + str( np.sum( special.rel_entr(q,p) ) ) )\n",
    "print( \"KL divergence uniform = \" + str( np.sum( special.rel_entr(q2,p) ) ) )\n",
    "\n",
    "plt.plot( xg, p, label = r\"$e^{-x}$\" )\n",
    "plt.plot( xg, q, label = r\"$h(x)$\" )\n",
    "plt.plot( xg, q2, label = \"uniform\" )\n",
    "plt.legend()\n",
    "plt.xlabel(r\"x\")\n",
    "plt.ylabel(r\"f(x)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dbadbe06",
   "metadata": {},
   "source": [
    "How do we sample from $h(x)$? If we have $\\xi$, which is sampled from a uniform distribution between $[0,1]$, other distributions $h(x)$ in the same range can be obtained *if* we can solve the inverse equation\n",
    "\n",
    "$$\n",
    "\n",
    "\\int_0^x h(x') \\, \\mathrm{d} x' = \\xi.\n",
    "\n",
    "$$(inverse)\n",
    "\n",
    "The solution $x$ will be then distributed according to $h(x)$. We see below that for a simple linear distribution this becomes a second-order root search problem. For more complicated distributions, the resulting equations are too difficult to solve.\n",
    "\n",
    "```{admonition} Active learning\n",
    ":class: tip\n",
    "Show that the solution of the above inverse equation is  \n",
    "\n",
    "$$\n",
    "x = \\frac{1 - \\sqrt{1 - 2 a (1-\\frac{a}{2}) \\xi}}{a}\n",
    "$$\n",
    "\n",
    "```\n",
    "\n",
    "```{admonition} Solution\n",
    ":class: dropdown\n",
    "\n",
    "The integral leads to \n",
    "\n",
    "$$\n",
    "\\int_0^x \\frac{1 - ax'}{1-\\frac{a}{2}} \\, \\mathrm{d}x' = \\frac{x - \\frac{ax^2}{2}}{1-\\frac{a}{2}} = \\xi\n",
    "\n",
    "$$\n",
    "\n",
    "Which can be rearranged as a second order equation\n",
    "\n",
    "$$\n",
    "- \\frac{ax^2}{2} + x - \\xi (1-\\frac{a}{2}) = 0,\n",
    "$$\n",
    "\n",
    "whose solution is the expression given above. **Bonus:** What happened to the other root?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f2fdac09",
   "metadata": {},
   "source": [
    "The advantage of importance sampling can be also seen in the figure below, showing the value of the estimator, $e^{-x}$ or $e^{-x}/h(x)$, for the generated random samples. It is clear that the standard deviation of the latter is much smaller. Note that if we would have chosen $a=1$, the sampling would actually be worse that for the case of uniform sampling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "abec69d0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "uniform mean = 0.6322484133201973\n",
      "uniform BSE = 0.0002341326057815266\n",
      "IS mean = 0.6321353195266276\n",
      "IS BSE = 2.5306811085860125e-05\n",
      "expected = 0.632120558829\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Estimator')"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1200x1200 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def sampleh(p, a=1):\n",
    "    \n",
    "    newp = ( 1 - np.sqrt(1 - ( 1 - a/2 ) * 2 * a * p) ) / a\n",
    "    h = (1 - a * newp) / ( 1 - a/2 )\n",
    "    #plt.hist(p[1,:-1:100], bins=20)\n",
    "    return newp,h\n",
    "\n",
    "Nsamples = 100000\n",
    "M=10\n",
    "\n",
    "res = np.array([])\n",
    "res_IS = np.array([])\n",
    "for seed in range(M):\n",
    "\n",
    "    rng = np.random.default_rng()\n",
    "\n",
    "    #generate random samples\n",
    "    p = rng.uniform(0,R, size= Nsamples)\n",
    "    expp = np.exp(-p)\n",
    "    \n",
    "    #append result for this realization\n",
    "    res = np.append(res, np.mean(expp))\n",
    "    \n",
    "    #Sample from h instead\n",
    "    newp, h = sampleh(p, a=0.64)\n",
    "    \n",
    "    #Evaluate new estimator e^-x/h(x)\n",
    "    expp_h = np.exp(-newp)/h\n",
    "    \n",
    "    #append result for this realization\n",
    "    res_IS = np.append(res_IS, np.mean(expp_h))\n",
    "\n",
    "print(\"uniform mean = \" + str(res.mean()) ) \n",
    "print(\"uniform BSE = \" + str(res.std()/np.sqrt(M)) )\n",
    "\n",
    "print(\"IS mean = \" + str(res_IS.mean()) ) \n",
    "print(\"IS BSE = \" + str(res_IS.std()/np.sqrt(M)) )\n",
    "\n",
    "print(\"expected = 0.632120558829\")\n",
    "\n",
    "plt.figure(figsize=(8,8), dpi=150)\n",
    "plt.plot(expp)\n",
    "plt.plot(expp_h)\n",
    "plt.xlabel(r\"Sample\")\n",
    "plt.ylabel(r\"Estimator\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4381eaed",
   "metadata": {},
   "source": [
    "Finally, we note that importance sampling is useful not only when we do not know how to sample $f(\\textbf x)$. For example, when $a(\\textbf x)$ is highly oscillatory, with both negative and positive contributions, such that its expectation value results from the near-cancellation of the positive and negative terms. We do not go into detail here, but a judicious choice of $h(\\textbf x)$ could significantly improve convergence in such difficult cases. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "864828fc",
   "metadata": {},
   "source": [
    "## Metropolis Monte Carlo and detailed balance\n",
    "\n",
    "We already saw that if we have a way to sample $f(\\textbf x)$, we can easily obtain expectation values using importance sampling MC. But it is an unfortunate fact that we have efficient algorithms to sample directly only relatively simple distributions, such as exponential, Gaussian, uniform, etc. \n",
    "\n",
    "In a seminal paper in 1953, [Arianna](https://en.wikipedia.org/wiki/Arianna_W._Rosenbluth) and [Marshall](https://en.wikipedia.org/wiki/Marshall_Rosenbluth) Rosenbluth, [Augusta](https://en.wikipedia.org/wiki/Augusta_H._Teller) and [Edward](https://en.wikipedia.org/wiki/Edward_Teller) Teller, and [Nicholas Metropolis](https://en.wikipedia.org/wiki/Nicholas_Metropolis) (sans spouse) developed an algorithm that, instead of obtaining random samples from $f(\\textbf x)$ at once, creates a sequential samples $\\textbf{x}_1, \\textbf{x}_2, ...$ that converge to the correct $f(\\textbf x)$, for an arbitrary distribution function! The importance of this result truly could not be overstated. It is perhaps one of the greatest results of the previous century. \n",
    "\n",
    "The idea at the core of the algorithm is that we need to specify a rule to generate the next sample $\\textbf{x}_{i+1}$ from the current sample $\\textbf{x}_i$. A sequence of samples that is generated based on information solely from the previous step is called a **Markov chain**. We denote the probability of obtaining a sample $\\textbf x$ from some other sample $\\textbf y$ as $R(\\textbf x | \\textbf y)$. For this probability to be a valid rule for generating a Markov chain, it must satisfy a condition called **detailed balance**,\n",
    "\n",
    "$$\n",
    "R(\\textbf x | \\textbf y) f(\\textbf y) = R(\\textbf y | \\textbf x) f(\\textbf x)\n",
    "$$(detailed_balance)\n",
    "\n",
    "where $R(\\textbf x | \\textbf y) f(\\textbf y)$ is called the *a priori* probability of moving from $\\textbf y$ to $\\textbf x$, which is just the probability to move from $\\textbf y$ to $\\textbf x$, given that the system was already in $\\textbf y$. Detailed balance is important, because it guarantees that the Markov chain is microscopically reversible, which can be shown to be an important property of thermodynamic equilibrium. It effectively ensures that if, during the Markov chain, we reach the distribution $f(\\textbf x)$, it will be stationary.\n",
    "\n",
    "After a move is generated, we must decide whether to accept it or not. \n",
    "\n",
    "The Metropolis MC algorithm states a rule for proposing **moves**, which we denote as $T(\\textbf x | \\textbf y)$, which has to be normalized, \n",
    "\n",
    "$$\n",
    "\\int T(\\textbf x | \\textbf y) \\, \\mathrm{d}x = 1,\n",
    "$$(Tnorm)\n",
    "\n",
    "and a probability that the move is accepted, which is denoted as $A(\\textbf x | \\textbf y)$. Then the probability to move from $\\textbf y$ to $\\textbf x$ is given by the product of the probability of suggesting such a move, times the acceptance probability, i.e.\n",
    "\n",
    "$$\n",
    "R(\\textbf x | \\textbf y) = T(\\textbf x | \\textbf y) A(\\textbf x | \\textbf y).\n",
    "$$\n",
    "\n",
    "Inserting this equation into the detailed balance conditions, Eq. [](detailed_balance) we get\n",
    "\n",
    "$$\n",
    "A(\\textbf x | \\textbf y) = r(\\textbf x | \\textbf y) A(\\textbf y | \\textbf x),\n",
    "$$\n",
    "where \n",
    "\n",
    "$$\n",
    "r(\\textbf x | \\textbf y) = \\frac{T(\\textbf y | \\textbf x) f(\\textbf x)}{T(\\textbf x | \\textbf y) f(\\textbf y)}.\n",
    "$$(ratio)\n",
    "\n",
    "Now, suppose $A(\\textbf x | \\textbf y)=1$ and the move from $\\textbf y$ to $\\textbf x$ is favorable, then $A(\\textbf y | \\textbf x) < 1$ and therefore $r(\\textbf x | \\textbf y) > 1$. However, if $A(\\textbf x | \\textbf y)<1$, then $A(\\textbf y | \\textbf x) = 1$ is favorable and so $r(\\textbf x | \\textbf y) < 1$. We can summarize these findings as\n",
    "\n",
    "$$\n",
    "A(\\textbf x | \\textbf y) = \\min \\left[ 1,r(\\textbf x | \\textbf y) \\right] .\n",
    "$$(acc_crit)\n",
    "\n",
    "Now all the ingredients for Metropolis MC are ready! Given that the system is at some configuration $\\textbf{x}_k$, we define a probability $T(\\textbf{x}_{k+1} | \\textbf{x}_k)$ and suggest a new trial configuration $\\textbf{x}_{k+1}$. Next, based on $\\textbf{x}_{k+1}$ and $\\textbf{x}_k)$, and the probability we want to sample, $f(\\textbf{x}_k)$, we evaluate the ratio $r(\\textbf{x}_{k+1} | \\textbf{x}_k)$ using Eq.[](ratio). Finally, we accept or reject the move based on the criterion in Eq. [](acc_crit). The final step is done in practice in the following way: If $r(\\textbf{x}_{k+1} | \\textbf{x}_k) \\ge 1$ the move is accepted. If it is smaller than 1, the step is accepted with probability $r(\\textbf{x}_{k+1} | \\textbf{x}_k)$, i.e., a random number $\\xi$ is sampled from a uniform distribution between $[0,1]$. If $r(\\textbf{x}_k | \\textbf{x}_{k+1}) \\gt \\xi $, the move is accepted. Otherwise, the move is rejected. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ad21649",
   "metadata": {},
   "source": [
    "## MC moves and acceptance ratio\n",
    "\n",
    "A simple, but rather useful, MC move is a translation with uniform probability from $\\textbf{y}$ to any point $\\textbf x$ within a box of side length $2\\Delta$ centered around y. The volume of the box is denoted by $V_{\\Delta}$. The trial probability, our rule for making moves, is then given by\n",
    "\n",
    "$$\n",
    "T(\\textbf x | \\textbf y) = \n",
    "\\begin{cases}\n",
    "    \\frac{1}{V_{\\Delta}},& \\text{if } x \\in V_{\\Delta} \\\\\n",
    "    0,              & \\text{otherwise}\n",
    "\\end{cases}.\n",
    "$$\n",
    "\n",
    "This probability is properly normalized, and it is also symmetric, i.e. $T(\\textbf x | \\textbf y) = T(\\textbf y | \\textbf x) $. As a result, the acceptance criterion of Eq.[](acc_crit) becomes\n",
    "\n",
    "$$\n",
    "A(\\textbf x | \\textbf y) = \\min \\left[ 1, \\frac{f(\\textbf x)}{f(\\textbf y)} \\right].\n",
    "$$\n",
    "\n",
    "Now, if we wish to sample the canonical ensemble, the probability is $f(\\textbf{r}) \\propto e^{- \\beta U(\\textbf{r}) }$, giving an acceptance probability\n",
    "\n",
    "$$\n",
    "A(\\textbf x | \\textbf y) = \\min \\left[ 1, e^{-\\beta \\left( U(\\textbf x) - U(\\textbf y) \\right)} \\right].\n",
    "$$(acc_canonical)\n",
    "\n",
    "This means that if the new proposed step has a lower potential energy, the move is accepted. If the potential energy of the new configuration is high, though, it is accepted with a probability that is the ratio of Boltzmann factors.\n",
    "\n",
    "A point of emphasis here is that the probability of accepting a new move in the canonical ensemble is that the new energy would not be very different than the previous energy. Since the energy is an extensive quantity, changing randomly the positions of all of the particles at once, would result in a massive energy change. Thus, we cannot move all particles together, like in MD simulations. The solution to this problem is to select randomly a single atom $i$ to move, and change its coordinates in the following manner:\n",
    "\n",
    "$$\n",
    "\n",
    "\\textbf{r}_i^{k+1} = \\textbf{r}_i^k + \\zeta \\Delta,\n",
    "\n",
    "$$(translation)\n",
    "\n",
    "where $\\zeta$ is a vector of three independent uniform random numbers in the range $[-1,1]$. Repeating this process $N$ times, where $N$ is the number of atoms in the system, is called a **MC pass**. Notice that this does not necessarily mean that all atoms have been moved since we choose the atoms randomly.\n",
    "\n",
    "Two final comments are in order: First, when we need to evaluate the difference in potential energies after moving a single particle at random, we do not need to compute all of the potential energy from scratch. That is very expensive, and we should update only the interactions of the chosen particle. Second, that the parameter $\\Delta$ has an important effect on the percentage of MC steps that will be accepted, which is called the **acceptance ratio**. If $\\Delta$ is too large, the change in potential energy will be large, and many moves will be rejected. If it is too small, all moves might be accepted but we will not explore all of phase space efficiently. Therefore, a rule of thumb is to use an acceptance ratio between $20 \\% - 50 \\%$.\n",
    "\n",
    "## Demo - sampling 1D arbitrary distributions \n",
    "\n",
    "In the demo below, we use Metropolis MC to sample from a bimodal probability distribution that would not have been simple to sample otherwise. Already in this 1D example, we see the utility of the MC approach!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "b0569e7e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.59865\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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JDN+UdWNtG3741hHfsVULS5Ge4vCdZ3pBOmqau3H8TB8OnbzgexkAYNG0fL8HsqIo03ct+TXqWnv86ha4HYrKkmz87O5Zvnomyu4Tw5hNgt2GQZcbGckJWD6v2PccV5fmItlhw6DTHdRBzpuSE3SewHc5sBN1uz0Dmf/81TK/dxAAnC530CDnuWVzAAAfHevComn5mHdNrq8/eG1fG+o7enFNbipOXrji608C9fbL5xf73unA9+/7rx1SvSeLZ0U+bToJEb+uklVVVWL//v0j/v7ZvquY9/M/AwDeeOJGvxuv1CHWtfbgwZeGBcOmx6ojMuKta+3BfS98AsAzDdzy+I2GrrN680HfA+l9QCPF7H/ZgakT0vHjr8/k0T8TMab9aDsGh9xY9ZVrsWbxl/yOed/V7NREX6dNAF5/Qvm9+dKPt2PWpEwUZaf4DZYIQJJjeLa+sbYNW/a14bPTvXC7RdBM3ghGB1he1m5rxLpdzb7thWV5EEDQgNMIRFQnhKgKXdLiMwC5+A/8Ubx6vsB9mx5THtWbiXyaKgQMq1Yi3enLSbDbMHtSJnf+TEQR0stKCip377v6/IdNfvvV3hu7jVAxOQs/vmsmCjKSfarXsgnpfu+1XN0Z7juv1J/owTvT2dHQ6TfTjxaWFgAjWQc20h/SCHJVioNVKwzj0/9rmVzl74ndRrreG7laVI1ovPNa6KljpLC0F1C8In/Y/v2R+XE/uo5jLSFjEbyPmNIMwIv8PXl4QYnqe8OPq35MEQBE9DsiOktE9SrHFxHRRVnO4KfNuG4oRBw/CjbpQY+Gq1c4kNYbyTAm4bVFks70MEUhYv7wY6sPs1RA/wbgtwBe1SjzsRDiLpOup4t4HrmS5PfmFgL2sHIiMczoR88MgDEfU2YAQohdAIKdchlVfG5qcSykGCba6O3/49l7cTQRTRvAAiI6TETbiag8GheM50fEO9KJZzUVw0QLwVOAmBAtL6ADAEqEEJeIaAmArQDKlAoS0UoAKwGguDi8BCTuOA4H7dF1Cp4BMIwM7v6jS1RmAEKIXiHEJenzNgAOIspTKbteCFElhKjKz8+PRvViAz/pDBMETwCiS1QEABEVkOROQkTzpOtqB+2wOGwDYJhg9HoBacHvlH5MUQER0SYAiwDkEVE7gH8B4AAAIcQ6AN8E8AQRuQBcAbBMRMGKE88PAtsAGCaY0xfNSfLO7sv6MEUACCEeDHH8t/C4iUaVeO5cvSOdeBZSXuL5PjKjH3mY8dfr2vGtqskhF0eOhvdmNMArgWPE8AwgvuFxFBNp5LGxhqRonUx0sLQAiOdRwrANII4ryTBRYCQxfhhzsLYAiHUFNPDqKOO5jgwTDeTqnvtvCK3+AYC/NZ3jDHUmYGkBEM9Y1QtoY20bHn6l1i+zGsPoZVKWvhy6fz3WhYdermEhECaWDgcd1+oVtZRFoxh5prOPj58DgBEntRjNmBFffqxi0+m9I6CcwctzzEIvVYSxtACI44XAsv4/jitpkO31p4O2x5oA2N10Dn//sidZeYKN8LO7Z42Je2CW0DPivallL2DnBX1YWgDEMzbb6HED1cviWYW+kb93e6yxs+GM77PLLfD02/WYXpBu6ZlAXWsPlq3fA+eQQKLdhk0rI5NKNQj29Q8bi9sA4rd3HRrypLg+1H4hthUxEflI95mlsw2PfOtae/D8h02jWq+bkeI/phpNbo17TpzDrz84Zvj+v3mgHc4hz7s2OOTGmwfaR1wHI1360JB71NzbeMXSM4B4HV3Xtfbg8uAQAOCJP9RhQ4SSz5uJ0Sn+SDr/B17cA5dbwGEnbF65IO7viRK9V1x+20TQdGvcWNuG7fWnw0oCPhK8181NS0T35UGUF2b4kpM//2ETNkn3X8/vHvia1Z+6iLrWnhH9fmapgBh9WFsAyD6P9IGMBPJRi3NI2ZAVL1xxDmHbp6exee9JuIVAYoINGx41X2C9eaAdLslo4xwSePNAe9zeEy2uK8r023YL4Ghnn2JnGiujufy6XuSqu8EhgTcOtOPcpQE8/oc62Aiav/t9c4uwqbbN974dOXURD71cM6LnRCsWUKBn2ZDKAM/pcmPT3jYQELNcu6MFS6uAGk71+j7Hk8tYdWkuEhNssFN8J4XfWNuG/sEhnO93wuUWcIthzwsvZqltAt9lMydv0VQtzSjMCNr3u93N2HPiHO5/cQ9++f5R37OoZDSPBm8cOBmyDAHYss9Tzi2AQacbz8nUQ09sqEPFz97H6s0HUVmSjdmThgWf9zl540C74fuuNQMIvD9K6rW12xoxJIDeqy6s29WMtdsadV97LGLpGcCnMv26mstYLKgsycaGR6vj3lVQqUOSC6y61h489HINBpxuJDk8I8SRct/cIt8IzyZtm0Fdaw8efKkGgy43kh0jn72E4+XS1HUZP/2PzzDkneFIz6JZRnOjdWs9d1nzuMNOuHduEd79tMO3zw3PLGFfy3mUjU/DkVN9AICthzxlMlIcfuew2wiv7TN31hh4vwCg74rTb3tHQ2fQNs8C1LH0DGB2kf+oJJ5G2pUl2Xjylqlx2/kDwR3ShPREvxe5prkbA043BIABl7ZBLtQo/Ghnn++zW7Yd6nuBxwMXotU0d2PQ5TG4D4aoo1bdl633jN4fXL8HP3rriOHZRO9VT0dFGBaiy+cX4ybpmVwyu8BP/ROqXfJy96/bg1+8dxQPvLhHV73O9zuD9q1aWOr77B2ET5YSr0/MTPYdc7rcaDx9ye+7HzSewcnz/X77ctISfbPGQaf++64VxXP5/GI8evMUv33rdjX73ZM7ywv8jgduM/5Yegbw3M6jvs8CwJrXD2Pn9xfFrD6jjeXzi/HzP32GAZcbLrdA5ZQcP4GVnZoIKbEZSADvB4y+vNS1nMcD62vgFgI2AsonZuKBG4r9Orwt+/w7tuc/PI7pBel4cH0NBofcSEqwYaPMWL6xtg1b9rXh0/aLAIAkhw3/sGCKz5DpHSlWl+Z6qwiH3Zi6bfXmg/joWBcmZibLvFwENtS24Y/7T+JbVZNx79wiXUJ87uQsdFzoREVxFuZPycFzHxzD4lmFmF6Ygb81d2Nu8fA59pw4h4ektQSJCcrt8t67X39wDEOSt4PLLfDiX0/g8a9cqzkjsFPwGpm+gWHjtVe1kppoBwBkpznQcfEqAE8HnZeWiM6+AV/5ywNDuDTgLwA6e4ePuyE9KzoIZQNOT3YE7ZOvN7m9vADrdjUjLdGOh6tLePQfAksLgJM9V/22T4SY+jLBpCTaMejyeCwdahseXda19vgZEt0ADkudcSDPvn/UZ+B1C0+5w+2e77rdbuxoOIMvAn6bUxeu4p/e+BSDQ8Oj9+c+OIbVt01DzYlz+MX7x/zKO13uoOn/9vrTmF6QjpREO/oHh/DrZRW6Z1yrNx/0qTcuKIyYvYLgjQPtmuqN1EQ7fvz1mXAOufHukU64XG6/zvwmBYG09dApXwet1i5vh9fa7d/x7jrWhb8e64JzyK2oelm9+SCc7uB6bpYJYO8MxatCbegYnp253AJnZZ0/ENpeYyOgp38wRCkPobyA5l2TE7TPO1Ota+3Bg+v3AACuOt24nUf/IbGkAFjxSi32tpxHop0wIHMVuDYvLYa1Gp2cuzT84nZcHMDqzQfx3LI5eEOnr/fG2jbsaT6veOx3u5vR1KUulJvODqsaBIZ10HaFXsJut+FOafTnpbwwA/e/uMenezfCR8e6dJXz6vOPdvZhe/1pVEzO8jtelJ2C5fOL8eqeFgDAkY5ev+OfdgwLzbXbGrGjoROTsoZVLo6E4HbJVXPzS3PQKlO/XHUN9+5Kdq8Pj55VbMeQTCh4hcZ/3linWFZBfmiSaMDRIdQMYE6xv6D9yd/NxPSCdDz/YRP+evQsBqX3fUiIuLH5xTOWswGseKUWu46fw1Wn26/zL8tPY/WPQZQ8KD5oPIO12xrxzqFTus6h5dly1TlkuE5OlxsDruAu6PqiTL/p/jNLZ6P53GW/zt9IgLpF0/Tlo3Yk2HD8TB9++NYRfHz8HP73X5oUy/3+b18o7u+76lG9vPxxM9btakZLdz/+dsIjMCdnp2DDo9VYs2QGZk/0eBctKM3xU53dNFUxtTYAj1DMTk30syUsuEa5vLzjrSzJxj2/3Y2OiwOKZY1ixAAcKpPXs+997re9v+U8vrXuE/zivaPY2+Jv/4gnm1+8YooAIKLfEdFZIqpXOU5E9BsiaiKiT4lorhnXVWJvi/Jokzt/4wSqHgDA7RZYt6sZlwb0dd5ani1K+txQEBHyxgXrk/e19Ph18G3dl/GXz8/4lWkNMFSqUdfag7IJ6b5tm0af9PRd5Xj7UIfq8RNnL2FjbRuaz2lfW64z9zIpOwWVJdm474W/+WYO+1p6dBugry/KxL+8U+/nevqTu8sVy8rnSGu3Naqq8+wjiL7wB2n2oydS7Ot12i6qbx70H3i8/9kZxZhfCTbw6F8HZqmA/g2elI+vqhxfDKBM+psP4AXpv+nMm5KDXQGuYszIqJichZYAHXO/kgJZgY21bVg+32Po/dXOo36qJC+JCcbHH0o6aC+/2z2sJpGrTLwQhhcE1rX2eBY79Q3gQv8gBlxuPHBDMaYXpGPZ+j1wyWaPWhqkQyd7NHXgQwJBi670sveL86j++Qd+BleXW+C///EwxiUn4IEbipGWZFf9/j7ZiHjA6fHL/y9fLQt53Zc+blZtk9LiK6+RXY2thzpweXAIOz/zCORAQ/aTG4ZVTUdO9frUjEqkJNgBDNtk4nSx/6jBrJzAu4hoikaRuwG8KiWCryGiLCIqFEKYvvLle7dNYwFgEv2DxlU0XuSGyisq53nghmKfMdgIah2ylj0BAFq6+/Hg+j1YNH08PvjsTJAu+3D7EWQkJ/g8fvTVJXJdkFvAr/P34nVmONx+BJUlWbrOJeDJt3u+L7Qx1kDzfecOhbfz97JlX5vv+fjoqL+9Rcv+8sQtU/HjrcOKBrXfyuWOr9X/8Uq0bACTAMjndu3SPtMJJxAV409z16XQhVTwqn5Wbz7oi3skp6IoMyZhkgeHhEdtoHK896pL5Ygybx3QZwuJFHWtF3SXdbrc+LhJn3E70jR0eEb68rhYXvLT1F1GH5yn/5l57Pf7Rly/sUK0vICUNIeKopuIVgJYCQDFxcY7CJ4SmoeaqkUP9R0XsfLV/fjL58peJ4faL1pimb7R0XIsIfL4418evBLrqsDlFth6qAMfKjwfnb1XFb5hHKUFb4w/0RIA7QAmy7aLAChazoQQ6wGsB4CqqirDr1e7TkMfE5rLA8ZGw3L0eNy8tj90TBrGPFZ+uRRnegfQrtODKxpcVJhxKXl5MZEhWiqgdwCskLyBqgFcjIT+HwA+PaXsvcAYRx7gKxLwCC26nDh3GbuOKc/I4okEuznd0sIydRdZxoMpMwAi2gRgEYA8ImoH8C8AHAAghFgHYBuAJQCaAPQD+E9mXFeJRdPyfSs4GYYZJtAQG6+UTwyOqOrl3v/zN13nsAF49ZGIOBpaCrO8gB4McVwAeNKMa4Xi/GV9S86Z0NQHrFplmGiwdI56JFi9M3xWIunDciuBd6u4gBpZBcp4mKUxEmOYSPGRSrgKAEgwsBAtXvJ/xDOWEwA2lWWbgdEmmdBM4dhJTAz4W5P6Op5/vLlU9VggnC84NJYTAHddpxx6YCSrTsc6egOiMYyZmOUFxLGAQmO5XvHhBVMU9+9v1R9DhfFwXYS9gBhGiWtyU1WPbdqrbyZvJ44FpAfLCQC1aZ8QPCU0ynweQTExoCArRfXYFZ0RZIeEJzIwo43lBIBa5iECTwmNcvxMX+hCDGMynRfUVyo7DKwR2HX8nCVWm0cSywmAhg5lN7GfL53NU0KDHDp5IdZVYMYgWmG7x6cnGTqXUkhzZhjLCYADKnr+tm5OB2kU1xB7UzPRJz1ZfXnSmYvG4gQ5tJI5MNYTAGdUAkm9uKuZjcAGOceL6pgYoOUFdMWgh1AXP8OaWE4ATB0/TnG/ABuBjTJZwxjHMJFCLX8EYLzDYk82bSwnAOYWq+v5+65w8DEjnNIwxjFMpEhNVM9yppUBTYk2jg6sieUEwGaNEMMNpzm2jRH0pn9kGDNxauTgfGh+iaFzdfAgRhPLCYALGiGGtRKUM8HkpBpP2s4w4TKoMfAozlFfJKYEu35rYzkBoIbdhpikIBzN3F81OXQhhjEZm0av9NN3PzN0rtM8A9DEcgIgTUV/aCN2BzMKq8yYWJCosdjLaJygpi52/9bCcgLg4WplHaFzSHBIaIOUF3I4aCb6ODXWn9gNjuOyWY2pieUEQK9GHtvt9RHJQmlZ0lP45WGij5bvgZaHkBIvffuGMGtjbSwnALQGCGwENkYtr5tg4gwjKqBEO3H4lxCYIgCI6E4iOkpETUS0RuH4IiK6SESHpL+nzbiuEuUTlRd+pCTY2AhskNovzse6CgzjR06acrBHJQaHBK/+D0HYAoCI7ACeB7AYwEwADxLRTIWiHwshKqS/n4V7XTXqVYLBXXG5+WEwiMvN6wCY+GJCRrKh8v+6naOBamHGDGAegCYhRLMQYhDAZgB3m3DeEdGkEcL4zQPtUazJ6Meh5Y/HMDEg06BdqunspQjVxBqY8YZPAiBfftsu7QtkAREdJqLtRFRuwnUV0QpfcLZvIFKXtSRXTUrNxzBG0MreWt9hzDVZLTYY40E97qp+lOyugWu5DwAoEUJcIqIlALYCKFM8GdFKACsBoLjYuM5+UKPTMhpLnGGY6CPUI0HgvMHonlqxwRhzZgDtAORLRosAdMgLCCF6hRCXpM/bADiIKE/pZEKI9UKIKiFEVX5+vuHKaCV/v3dukeHzMQwTXYxk/QrFHvZk08SMO70PQBkRXUNEiQCWAXhHXoCICog8S3GJaJ503Yj8MhnJyjpCAieJZpjRQEaKumLC6EKwJC19EhO+ABBCuAB8F8B7ABoBvCaEaCCiVUS0Sir2TQD1RHQYwG8ALBNCa6I3ctRmAALglcAGSXHwy8NEHy1ff6NG4KkT0sOtjqUxwwbgVetsC9i3Tvb5twB+a8a1QrGgNBeH25VdQbfXn+a1AAbITUtE+wVjKfgYJlyuaiwF1goToURGkildnGWx3BCvTyMURK6BRSQMkK6iTmOYSKKl5bmskS1MCQ5oqI3lBIBaUngA6Ob8oIZoOceRFJnok5So3i1p5IpRhAMaamM5AdDcrd5p8cNgDKMJuBnGDMxcgPjXY12mncuKWE4AODX0hyd4RGsITqHAxAIzH7tjZ9UjAzAWFACk0aKzvWzQNEI2h4NmRjmR8TW0DpYTAEVZ6jlDH7iBPYCMcEnDoM4wkSLRoR7z3+g6gAQbT2O1sJwAmJChHu6BXUCNMTjEwycm+jg0Om2jT2SKwQQyYw3LCQCtYHAcDpph4p/uS+pBGx0GV/am8zoATSwnALQWirzB4aANwbNnJt64fpJywic1eC2LNpYTAL1X1fXWh9p4BmAEM4NyMYxetHz9jUb3dBpdODDGsNwb7tTQWxsNJTvWGZfE+lMm+mhNPD9oPGPoXDmpPAPQwnICIFUjgNk9FUp5ahg1+g0uu2cYM3BpjNo7Lxpz5c5M5fAvWlhOAGipLdYsmRHFmox+UjTc8RgmUgxq2PEGDAaDu9jPs34tLCcAtEYP7AVkDNafMrFA66nTSvikRItGaBjGggLgkoYR+MW/nohiTUY/yZxMg4kBaRozz1SDs1IXr2XRZEy94c1dl2JdhVFF3jjOocxEn8k56qv5jVJs4rmsiPUEgIYLwTX546JXDwtgNPkGw5hBl8ZCMC0vPyUuXHGGWx1LYzkBYNcIYXnL9PFRrMnoJ4cT6DAxQMv0NGQwulvF5KzwKmNxTBEARHQnER0loiYiWqNwnIjoN9LxT4lorhnXVUJrqXgPewQYok/DnsIwkSJXw3d/yOCslF2ZtQlbABCRHcDzABYDmAngQSKaGVBsMYAy6W8lgBfCva4aGcnqsT+y2SfYEG3n+2NdBWYM0qLx3F3RyPehBNv9tDFjBjAPQJMQolkIMQhgM4C7A8rcDeBV4aEGQBYRFZpw7SC0Rvk8AzDGVRePnpjoo6XnNxqfiu1+2pghACYBOCnbbpf2GS1jCoMu9Yenjw1ChrBxSjAmzkjXmOErwXY/bcwQAEq9RGAvrKeMpyDRSiLaT0T7u7rMzefZcLrX1PNZnYmZKbGuAsP4YTRJEc/6tTFDALQDmCzbLgLQMYIyAAAhxHohRJUQoio/P99wZbI1DEiLZ0VE62RZeALAxIIkjbRfLoOeydWluWHWxtqYIQD2ASgjomuIKBHAMgDvBJR5B8AKyRuoGsBFIcRpE64dBHuum8cZzqHMxABevBs9whYAQggXgO8CeA9AI4DXhBANRLSKiFZJxbYBaAbQBOAlAN8J97pqaOn5f7e7OVKXtSSZnEyDiQGTstRVj0aNwDXN3WHWxtqYki9NCLENnk5evm+d7LMA8KQZ1woFEQEqi0WuGJ0/jnEmZCajs099VSbDRII5xVmqx7JTHOju1+/Mwa7f2lhuJbBWLMHywowo1mP0s4D1p0wM2HVc3fnD6Erg+o6L4VbH0lhOAGgtI3/8K9dGryIWoPkch9Jloo9b4yXWSvmqBKeB1cZyAsDOmcxNg1dRMrEgQSOci8EJgOEMYmMNywmAJI2MYG8eaI9iTUY/pbyKkokByRrvsNHx3dTx/AxrYTkBoJUR7CwbNA2xiFdRMjFgxsRM0871T4s5DawWlhMAWkYiVg4ZY/0uzqDGRB+t8A1G1ggQgMqS7PArZGEsJwC08gHkp3OGKyOc5GigTAzYelBdVWukw+KMpqGx3C1Kcqg3qdzEqeVYgA3qTCyo71CP2WUz0GMZjBw9JrGcANCCA0MZg6OBMrFgwKkehtzGgxJTsZwAsGsMEXhVoDH4ZWNigZaaf2aBscWcda28DkAL6wkAjT6LZwDGKMlJjXUVmDGIlq//qQtXDJ3rxb+yI4MWlhMA3ZfVO3kODWsMzqfKxAKtGcB5g4M4Xs2ujeUEgNYMgDFG92VeN8FEH61XWBg07JbmpYVVF6tjPQGgYQPg0LDGSHHYY10FZgyiZXoymiqA439pYzkBoLUQjFVAxjhvIOwuw5hFlkZWPyNuoExoLHc7jQaLYtTRisrIMJHCoRELKMegJx/P+rWxnADQ4g0OBmcIXgbAxIIEDR3QZYOOCTzr1yYsAUBEOUS0k4iOS/8VA28QUQsRHSGiQ0S0P5xrhiIjWT3JGfdnxihmN1AmBpy6oB7C+YpBAXC0sy/c6liacGcAawD8WQhRBuDP0rYatwghKoQQVWFeU5PLA+oJI+6dWxTJS1uOislZsa4Cw/iRlmjMMWHLvrYI1cQahCsA7gbwe+nz7wHcE+b5wkYrHDRjjF3H1FPzMUykGJek3sk7Db7fSRwRTpNw784EIcRpAJD+q8VxFQDeJ6I6IloZ5jW10dDzsA3AGBwMjokFWkZgt0EvjzO9vJZFC3WFuQQRfQCgQOHQjwxc5yYhRAcRjQewk4g+F0LsUrneSgArAaC4uNjAJTzYiTCk4i3M3ZkxrslLQ9clDp/BRJeMFHU30AnpSWjXsBEEwosZtQkpAIQQt6kdI6IzRFQohDhNRIUAzqqco0P6f5aI3gIwD4CiABBCrAewHgCqqqoM63NcGhkj0pNCNpeRwco0JhZo5fHNG2dMANw2Y4IZVbIs4aqA3gHwbenztwG8HViAiNKIKN37GcAdAOrDvK4qWp1Ww2n1OONMMD28EIyJAQND6vEemrouGTpXQUZyuNWxNOEKgLUAbiei4wBul7ZBRBOJaJtUZgKA3UR0GMBeAH8SQuwI87qqJGoEA1o8qzBSl7UkHEeFiQUpGobbydnGXJO3HjoVbnUsTVg6ESFEN4BbFfZ3AFgifW4GcH041zGCzWYDhoJ9he0ELJ9v3KYwllk0fTze/+xMrKvBjDGSE9W7pfz0JDQa8O3nHCDaWM5HarxK3l8OEWGc+o6Lsa4CMwZJ1PA++/SUsWcyXWNhKGNBATC9IF1xP6cHNQ57TTExQePBWzQt39CpBlz85mthOQFw8ny/4v5UjWTxjDLlEzNjXQVmDKJluH14wRRD58rUcCllLCgAzvQqu4gRRzYzDKfQZGJBm8ogDjCe4lHrXIwFBYDa0u9BDdcyRhmOpMjEAq2Ab2oDPDXuLFdaw8p4sZwAUEtiorW8nFGmskQxuCvDRBStwdoDN+j35LMBWLNkhgk1si6W6xWdKg9PBq8CNszabY2xrgIzBtFYzG8IdvwLjeUEgJq7Z9cljglilB0NnbGuAjMG0TLXGQnvzAIgNJYTACkq8cLNGlWMJTghDBMLUhzq4aAncGgHU7GcAFhRXaK4n71AjcP5VJlYoPYOA8DjX7k2ijWxPpbrFtWMPk43sLGWswMZYZCnTUwM6NTw9DHimKAVF4zxYDkBoMX2+tOxrsKoIn8cx1Fhos8Hjerxp+pae3SfJyeNn99QWE4AaD0gHA3UGBXF7AbKRJ/cNOV4XoAxtWT3ZV7IGArLCQC1tI9ZKQkcDdQgZw0uumEYM5imEs8LMLY40c35wUNiOQHQdEY5VGyyhmcBo4yRRTcMYxbHVd5ho9g4p3VILCcATl24orh/Mrs0Gmb5/GLcPJXDQTDRpaVbPX6PERXQkFsYshmMRSwnANRk/prFvCR8JHBCDSae6LuiP00pgV2ZQ2E5AVCYlRK079Yv5XNcmxFQ19qDbfW8GpiJLlqd0h4DHbrdbuOAhiEISwAQ0beIqIGI3ERUpVHuTiI6SkRNRLQmnGuGYtqEYANSSd64SF7SstQ0d7MhjYk6WnF7jawE/mZlEQ/8QhDuDKAewL0AdqkVICI7gOcBLAYwE8CDRDQzzOuqcu/cIiQELACpmMyJTUZCdWkux1Nh4gq9K4EddsJ9c4siXJvRT1gCQAjRKIQ4GqLYPABNQohmIcQggM0A7g7nulpUlmRjy8oFfvs4sxXDjB5SVHJ6APpXAv/0G7N49K+DaNgAJgE4Kdtul/ZFjMAf/t1POyJ5OcsSbQMae+3FhlULS1E2Pn7UpP/j78rDPkd9h7Hk8WOVkAKAiD4gonqFP72jeKXXWlWzQEQriWg/Ee3v6urSeQlt/r+dxzkO0AioLs2FPUSvTASYEXIl0W7Dshsmh38ixjDFuWn4xbeuj3U1fGiFbNHr1vl6XTu7gOogpAAQQtwmhJil8Pe2zmu0A5C/2UUAVIfkQoj1QogqIURVfn6+zkv4o9TZcxwg41SWZGPJLO2UekKYk3jbOeTG3i/Oh32e0UJh5rAx80saK1+jwQ/fOoL3GuLn/dAK2VLT3K3q6i1naMjNLqA6iIYKaB+AMiK6hogSASwD8E4kL/iTd+qD9nEcoMihlobTCAJAU9dl37bDTkgNY/X27EkZhr+jlk86EiyQuSeatfJVCb2Ts9frlEOoyImkis5uA64vysQzS2drhmypLs1FksMWctbpSGAXUD2E6wa6lIjaASwA8Cciek/aP5GItgGAEMIF4LsA3gPQCOA1IURDeNXWRimMMccBMk5daw+2K6wDmBEwYk0w0DPoLfm9r5YhNSC5j0Onrumeion4yTdmIdlgh56mkkxopGjVtvvycIa6SETdtkmqOb25sAecWs6XHm6dMSHcaqmSlezA29+9OeR7WlmSjQ2PVuOpO6YjT4r2GSjsH5pfjA2PVrMRWAfhegG9JYQoEkIkCSEmCCG+Ju3vEEIskZXbJoSYJoS4Vgjx83ArHYqirGTNbUYfNc3dcAfk2HTYCf9z6Wzf9jNLZ+PGa/WNtAozkvD6Ezf6tr9clocSlRAdv/rgGM4FRHN06uwpuy8PejqKx6rx3742HQvL8nR970qITjDBRli1sBTJDpsuQZaU4F9q8ewCn5DRingpZ2KmvnKB3DZjAp66YzrWLJ4OALg2Lw1fLsvDqoWl+LLC/agoztI8n42AVV+5Fs8snY2p+WmYlB284DKQ1ET93YuRWWRlSTaqS3N90T4/7+zzzU7sNsK9c9n/Xy+WWwkMALvX3IqirGQQPJ3/7jW3xrpKo5Lq0tygjm7RNP9V1cvnF+teK3C6dwB/2NPi21592zT86oEKxem80vozvbMHr7qvsiQbT94yVXf9puRqx4u68dpcrFkyAxserUZJiLIAcNXlf+X368/AIc1KlswuRGKCR5AETqDkhvd/kkKYhJr9BCY/+aLrEp68ZSrKpIWRhVkp+MMj87FmyQysvm2a714SebyAinPSVM/tsBP+uOpGVJZkY/n8Ynzw/UX4u9mhVao//no5nlk6G18uywu6t+MCZlsCxmL9y/X7riExnAtcCNb9G8CSAgDwCIEv1n6dO/8wqCzJRn66/wj0s9O9QeWM2FfkyT4eerkGAPDaqhvx3742HTeFmEncXTFR9Zi8//s/Hx43VD+CpwN9eMEUzXJ7W86jrrUHlSXZWLnQeGpCtxBwujyzjOuKMrHpsWr84GvT8cdVN2LVwlIUZCRh3pRsvPb48DqWX77vWWYjn/0EquCKspKDfqfjXZdVO9TKkmxMkMp/95apWLNkBsonBttMkqSbmpEcbOTf0RA6RMjy+cVYPr8Yf3hkPn55fwWSZXlZ/z4g7aONjLkdy20BDjvBkSB9Zt2/ISwrABhzuKfCf8nGwrJgz6zl84t1GwiLc1J9ZZ0uj6eGd6T+1B3TkWgnX4ccqK54btkcrFpYqjhSl2uH2i9cxc1r/+xXP+9I9Jmls33nGJfkGYU+9uVSbFq5AD39g5qzDG99vecMzDil9N2KouFFiDaCT6X21sFTvnZXlmRjzZIZqPnhbXht1Y349QfHfN9pOx8c3Xb76oW4p2IislIduKdiInavuRUpiQlB5dQ61LrWHpzp89ggXtzVjLrWHkVPpAHppnZfHsRDL9f4CZQ7y/29wyqKMpGT6i8o5OUrS7Lx9F3D/v3/tqcFqxaWIsFGsBGQaLDjltsCNq1cgE2PeT6z7t8YwU8Nw8jw5lh+afcXGHIL1aX4N0/Nw67j5xSP2QCkJtlx24wJeHjBFDz0cg2cLnfQaK2yJBubVi5ATXM3qktzfS/ylDV/AuDpUNYsmYE1S2bg9l9+hOMyr6FATl3wT2bjHY3K23Xzv/4Flwau4OEFJb5w4UkOG64q2AIIwaPL+yuLsG5Xs2/77oqJKJuQjtrmbnx66iIWTcvHvGtycaj9CACPkPLaGf7f7Z8jPdmhaPTc2xLaHfa5ZXP8tmdNzEDT2Uu+bRt5Rsn9g66g79Y0d/vUYi7JXVIpfSJheMGOXFgDnvt38OQF1Equu4fagxdePfRyjV+H3NM/bNNxutxIT3Fgy+PBv7deKkuy/b7DHb9xeAbAhGTNkhm+/MANASssvaM8LT07EfDEoql4btkcv5Gb0mhNPiqWnx+A3yh05/cXoSw/DTYCyvLTggz9k0Zg+PfWLTs1WOVxXVFmUH3XLJnhm02sWliK55bNwZO3TMWrj8zHoafvwHPL5miuP1E7Nm9KTtC+6SHWCgSmP5w9KVO1Q5TbdhKkiJkfHT0bVE7uhaWkWkkM4WUlnzF5r5sUoKoJ/L2Z6MIzACYkda09ONPrURk89dphXLwyPKr0jvIWzyrExwEzAK+BU2mkr/eFr2nullQnwaPQnd9f5FfWO1MI1/B/QRZznuDRMT/9d+WKdfbOSNRQui/yY0q8+sh8rHilFntbzmNKbho+7+zTlrAK1wnM5nbyfL/PflFZko3sVAfO9zvxjesLUVmSjRSFNRdfv64Qr+1vR25aItavqApqv1bblGZMlSXZ2PhY9YhH/Iz5sABgQuLvceH2G7l6O+Unb5mKH77lUXX84PZpeHbnMeSlJ+IfbrwmrJe9ujQXiQk2RZWRGt+5pUzXubsveYTaz/6jAS99+wYAUlulztYG4KayPKy+bdqI6+9V8WyvP+3r8L2ftXzeX31kPgDgN38+js87+3BUtlhs7bbGIKETeB3v9okuj1qo9Xy/T1gf7ezzuV2+XncKc4tz8PCCKXj7UIefnCnM9Lh6XhkcwtHOvqB7oNa28sIMpKc4FH93I8KfiTwsAJiQeD0uvJ3w4lmF2NdyXrVTvnvOJDy78xiSEux48papYV3bq5YJNWqUh//wCiKtDnb15oM+ffzOxrNYvfkgnls2J6it4XT+XgLtD0YWJfZeDfaP99odlIRA4LkvXXX5dPleYR1oHN5efxrL5xfjuqJMHJbp8rcePAUA6HcOqd7TcNrGxB4WAExIlDrh6QXpITvl3itOn9oh3OuHOkegPt3bqanx0bEuxW29AidaLJ5ViH+vaQ0yTO9o6NRUPXlZcG0ekhxNfsI6OzXRT3XjHb0/cEMxDksGawC+NQteQt1TZvTBAoDRhZLHhVrnuO2IpzPuveoK8gSJFIH66FC+/4um5WProQ6/bS/xpKbwCqS12xuxr0XdDTPU9+UCzdu2QHWRkkrHO/IHOJ6WFSEhIhCIxCSqqqrE/v37Y10NRgd1rT2474VPAHgMv0J41A52Ap66Y3rYqiA9bKxt06Vf97J680F8dKwLi6blB7lVxiNrtzViR0Mn7iwv0DX6NwOj95SJPURUJ4RQTdHrV5YFAGMGK1/dj/c/G17la6NhTxBenMMw0cOIAGAVEGMKZ3r9F16V5qVh6dyiuNCjMwyjDAsAxhQCDYj/eHMpqwwYJs5hAcCYgpofOsMw8QsLAMY0lPzQGYaJXzgWEMMwzBiFBQDDMMwYJdycwN8iogYichORqtsREbUQ0REiOkRE7NfJMAwTB4RrA6gHcC+AF3WUvUUIoRw6kGEYhok6YQkAIUQjABDpzdbKMAzDxAvRsgEIAO8TUR0RrYzSNRmGYRgNQs4AiOgDAEqRp34khHhb53VuEkJ0ENF4ADuJ6HMhxC6V660E4BUSl4joqM5rBJIHYKypnLjN1mestRfgNhulRG9BU2IBEdFHAH4ghAhp4CWinwC4JIR4NuwLa19nv954GFaB22x9xlp7AW5zJIm4CoiI0ogo3fsZwB3wGI8ZhmGYGBKuG+hSImoHsADAn4joPWn/RCLaJhWbAGA3ER0GsBfAn4QQO8K5LsMwDBM+4XoBvQXgLYX9HQCWSJ+bAVwfznVGyPoYXDPWcJutz1hrL8BtjhhxnQ+AYRiGiRwcCoJhGGaMYjkBQER3EtFRImoiojWxro8RiGgyEX1IRI1SiI3vSftziGgnER2X/mfLvvPPUluPEtHXZPsrpfAbTUT0G5JW6xFREhFtkfbXEtGUqDdUASKyE9FBInpX2rZ0m4koi4heJ6LPpd97wRho83+Vnut6ItpERMlWazMR/Y6IzhJRvWxfVNpIRN+WrnGciL6tq8JCCMv8AbADOAGgFEAigMMAZsa6XgbqXwhgrvQ5HcAxADMB/C8Aa6T9awD8q/R5ptTGJADXSG23S8f2wmOcJwDbASyW9n8HwDrp8zIAW2LdbqkuTwHYCOBdadvSbQbwewCPSp8TAWRZuc0AJgH4AkCKtP0agH+wWpsBLAQwF0C9bF/E2wggB0Cz9D9b+pwdsr6xfhFMvvkLALwn2/5nAP8c63qF0Z63AdwO4CiAQmlfIYCjSu0D8J50DwoBfC7b/yCAF+VlpM8J8Cw2oRi3swjAnwF8FcMCwLJtBpABT2dIAfut3OZJAE5KHVQCgHfhcQm3XJsBTIG/AIh4G+VlpGMvAngwVF2tpgLyPmRe2qV9ow5pajcHQC2ACUKI0wAg/R8vFVNr7yTpc+B+v+8IIVwALgLIjUgj9PMcgP8OwC3bZ+U2lwLoAvB/JbXXy+RZI2PZNgshTgF4FkAbgNMALgoh3oeF2ywjGm0cUd9nNQGgFJVu1Lk5EdE4AG8AWC2E6NUqqrBPaOzX+k5MIKK7AJwVQtTp/YrCvlHVZnhGbnMBvCCEmAPgMjyqATVGfZslvffd8Kg6JgJII6K/1/qKwr5R1WYdmNnGEbXdagKgHcBk2XYRgI4Y1WVEEJEDns5/gxDiTWn3GSIqlI4XAjgr7Vdrb7v0OXC/33eIKAFAJoDz5rdENzcB+AYRtQDYDOCrRPTvsHab2wG0CyFqpe3X4REIVm7zbQC+EEJ0CSGcAN4EcCOs3WYv0WjjiPo+qwmAfQDKiOgaIkqEx0jyTozrpBvJ0v8KgEYhxK9kh94B4LXqfxse24B3/zLJM+AaAGUA9krTzD4iqpbOuSLgO95zfRPAX4SkNIwFQoh/FkIUCSGmwPN7/UUI8fewdps7AZwkounSrlsBfAYLtxke1U81EaVKdb0VQCOs3WYv0WjjewDuIKJsabZ1h7RPm2gbSKJggFkCj/fMCXgilsa8TgbqfjM807ZPARyS/pbAo+P7M4Dj0v8c2Xd+JLX1KCRPAWl/FTwxl04A+C2GF/0lA/gjgCZ4PA1KY91uWZ0XYdgIbOk2A6gAsF/6rbfC47lh9Tb/FMDnUn3/AI/3i6XaDGATPDYOJzyj8kei1UYA/yjtbwLwn/TUl1cCMwzDjFGspgJiGIZhdMICgGEYZozCAoBhGGaMwgKAYRhmjMICgGEYZozCAoBhGGaMwgKAYRhmjMICgGEYZozy/wNW/6Uw8LkpnQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Generic probability distribution\n",
    "def evalf(x):\n",
    "    mu1 = 2\n",
    "    sigma1 = 0.1\n",
    "    g1 = np.exp(-0.5*(x-mu1)**2/(sigma1**2))/np.sqrt(2*math.pi)/sigma1\n",
    "    \n",
    "    mu2 = 0\n",
    "    sigma2 = 0.5\n",
    "    g2 = np.exp(-0.5*(x-mu2)**4/(sigma2**2))/np.sqrt(2*math.pi)/sigma2\n",
    "    \n",
    "    return (g1+g2)/2.2162802142575204 #evaluated normalization with trapz\n",
    "    \n",
    "#number of MC steps\n",
    "Nsteps = 100000\n",
    "\n",
    "#maximal step size\n",
    "delta = 0.5\n",
    "\n",
    "rng = np.random.default_rng()\n",
    "\n",
    "#initial position\n",
    "xn = 1\n",
    "\n",
    "x = np.array([])\n",
    "\n",
    "x = np.append(x, xn)\n",
    "\n",
    "#for acceptance ratio\n",
    "accept = 0\n",
    "\n",
    "for step in range(Nsteps):\n",
    "\n",
    "    xnp1 = xn + delta * np.random.uniform(low=-1.0, high=1.0)\n",
    "\n",
    "    ratio = np.divide(evalf(xnp1),evalf(xn))\n",
    "       \n",
    "    xsi = np.random.uniform()\n",
    "    \n",
    "    if ratio < xsi:\n",
    "        x = np.append(x, xn)\n",
    "    else:\n",
    "        x = np.append(x, xnp1)\n",
    "        xn = xnp1\n",
    "        accept += 1\n",
    "\n",
    "plt.hist(x[100:], bins=100, density=True)\n",
    "xg = np.linspace(-3,3,1000)\n",
    "plt.plot(xg, evalf(xg))\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(x,'.-')\n",
    "print(accept/Nsteps)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c7631702",
   "metadata": {},
   "source": [
    "## Sampling other distributions\n",
    "\n",
    "We have seen how to generate configurations according to an arbitrary probability density function using the Metropolis algorithm. We also saw in Eq.[](acc_canonical) the expression for the acceptance probability for the canonical ensemble. But the great merit of MC simulations is that it is usually much easier to extend them to other ensembles than MD simulations (although that is also possible!).\n",
    "\n",
    "For example, if we are interested in the isothermal-isobaric ensemble, in which the number of particles $N$, the pressure $P$, and the temperature $T$ are fixed (the $NPT$ ensemble), we can do so rather easily. There are only two changes that need to be made to the algorithm that samples from the canonical ensemble: First, we need a move to change the volume of the system,  \n",
    "\n",
    "$$\n",
    "\n",
    "V^{k+1} = V^k + \\zeta \\Delta_V,\n",
    "\n",
    "$$(volume)\n",
    "where $\\zeta$ is a random variable just like in Eq.[](translation), and $\\Delta_V$ is the maximal allowed change in volume.\n",
    "\n",
    "Secondly, each time the volume changes, the particle coordinates must be scaled accordingly by \n",
    "\n",
    "$$\n",
    "\n",
    "\\textbf{r}_i^{k+1} = \\textbf{r}_i^k \\left( \\frac{V^{k+1}}{V^k} \\right)^{\\frac{1}{3}},\n",
    "$$(scale)\n",
    "and the potential energy needs to be re-evaluated.\n",
    "\n",
    "Finally, since in this ensemble $f(\\textbf x,V) \\propto V^N e^{-\\beta ( U(\\textbf x) + PV) }$ the volume moves are accepted with probability\n",
    "\n",
    "$$\n",
    "A(\\textbf x, V' | \\textbf y, V) = \\min \\left[ 1, e^{-\\beta \\left( H(\\textbf x, V') - H(\\textbf y, V) \\right)} \\right],\n",
    "$$(acc_NPT)\n",
    "where \n",
    "\n",
    "$$\n",
    "H(\\textbf x, V) = U(\\textbf x) + P V - \\frac{N}{\\beta} \\ln(V).\n",
    "$$(enthalpy)\n",
    "\n",
    "Much more elaborate MC moves can be designed. As long as they obey detailed balance, they are legitimate and can be used to sample various distributions. One interesting example is the case where the potential energy has many local minima separated by high barriers. In that case, standard MC translation moves will not work anymore and the system will be trapped in one of the local minima. One solution to this problem is called **parallel tempering** or **replica exchange**, in which several replicas of the system are simulated using standard MC simulations but at increasing temperatures. \n",
    "\n",
    "We are interested in sampling the system at the lowest temperature but systems are higher temperatures will cross the energy barriers more easily. Therefore, every several MC passes, a pair of neighboring replicas are chosen and a move is attempted to switch their particle coordinates. For example, if before the move the system at temperature $\\beta$ was in configuration $\\textbf x$ while the system in temperature $\\beta'$ was in configuration $\\textbf y$, one can show that in that the acceptance probability should be \n",
    "\n",
    "$$\n",
    "A(\\textbf x, \\beta'; \\textbf y, \\beta | \\textbf x, \\beta; \\textbf y, \\beta') = \\min \\left[ 1, e^{\\delta} \\right],\n",
    "$$(acc_REMC)\n",
    "where $\\delta = \\left( \\beta' - \\beta \\right) \\left[ U(\\textbf y) - U(\\textbf x) \\right]$.\n",
    "\n",
    "In one of the final projects, you will implement such a replica exchange MC simulation and compare it with alternative algorithms to overcome high energy barriers that are based on MD simulations."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7aa58a65",
   "metadata": {},
   "source": [
    "## Proof that $f(x)$ is a stationary point of Metropolis MC\n",
    "\n",
    "We follow the proof that is presented in the Book by Tuckerman. \n",
    "At every iteration of the Markov chain/Metropolis algorithm, the points $\\textbf{x}_k$ are distributed according to some function $\\pi_k(\\textbf x)$. We wish to show that if the algorithm reached a point in which $\\pi_k(\\textbf x) = f(\\textbf x)$, all following steps will be distributed according to $f(\\textbf x)$. In other words, we wish to show that $f(x)$ is a stationary point of the Metropolis algorithm.\n",
    "\n",
    "We will use induction to prove that is the case. We will assume that at some *arbitrary* MC step $k$, $\\pi_k(\\textbf x) = f(\\textbf x)$, then we will derive the expression for $\\pi_{k+1}(\\textbf x)$, the distribution in the next MC step, and we will show that it is also equal to $f(\\textbf x)$. \n",
    "\n",
    "The probability to be at point $\\textbf x$ at step $k+1$, $\\pi_{k+1}(\\textbf x)$, has two contributions: First, from moves that started in other points $\\textbf y$, proposed $\\textbf x$ as a new configuration and were accepted. The term is given by the probability to be at $\\textbf y$ in the previous step, $\\pi_{k}(\\textbf y)$, times the probability that $\\textbf x$ will be proposed as the next move if we are at $\\textbf y$, $T(\\textbf x | \\textbf y)$, times the probability that the move will be accepted, $A(\\textbf x | \\textbf y)$. The final expression for this first contribution is then given by integrating over all the possible initial $\\textbf y$,\n",
    "\n",
    "$$\n",
    "\n",
    "\\int A(\\textbf x | \\textbf y) T(\\textbf x | \\textbf y) \\pi_{k}(\\textbf y) \\mathrm{d} \\textbf y.\n",
    "\n",
    "$$\n",
    "\n",
    "The second contribution includes moves that started at $\\textbf x$, proposed some new step $\\textbf y$, and were rejected. This term is equal to the probability to be at $\\textbf x$ in the previous step, $\\pi_{k}(\\textbf x)$, time the probability that $\\textbf y$ will be proposed as the next step, $T(\\textbf y | \\textbf x)$, times the probability that the move will be rejected, $1 - A(\\textbf y | \\textbf x)$. The final expression is given by integrating over all possible moves $\\textbf y$,\n",
    "\n",
    "\n",
    "$$\n",
    "\n",
    "\\int \\left( 1 - A(\\textbf y | \\textbf x) \\right) T(\\textbf y | \\textbf x) \\pi_{k}(\\textbf x) \\mathrm{d} \\textbf y.\n",
    "\n",
    "$$\n",
    "\n",
    "Combining these two contributions, we get\n",
    "\n",
    "$$\n",
    "\\pi_{k+1}(\\textbf x)=\n",
    "\\int A(\\textbf x | \\textbf y) T(\\textbf x | \\textbf y) \\pi_{k}(\\textbf y) \\mathrm{d} \\textbf y + \n",
    "\\int \\left( 1 - A(\\textbf y | \\textbf x) \\right) T(\\textbf y | \\textbf x) \\pi_{k}(\\textbf x) \\mathrm{d} \\textbf y.\n",
    "$$(prob_kp1)\n",
    "\n",
    "Now, we assume that $\\pi_k(\\textbf x) = f(\\textbf x)$ and rearrange Eq.[](prob_kp1) to get\n",
    "\n",
    "$$\n",
    "\\pi_{k+1}(\\textbf x)=\n",
    "\\int \\left( A(\\textbf x | \\textbf y) T(\\textbf x | \\textbf y) f(\\textbf y) -  A(\\textbf y | \\textbf x) T(\\textbf y | \\textbf x) f(\\textbf x) \\right) \\mathrm{d} \\textbf y + \n",
    "\\int T(\\textbf y | \\textbf x) f(\\textbf x) \\mathrm{d} \\textbf y.\n",
    "$$\n",
    "\n",
    "The first integral vanishes due to detailed balance, Eq.[](detailed_balance), and in the second term we can take $f(\\textbf x)$ out of the integral. Finally, since $T(\\textbf y | \\textbf x)$ is normalized (see Eq. [](Tnorm)), we get\n",
    "\n",
    "$$\n",
    "\\pi_{k+1}(\\textbf x)= f(\\textbf x),\n",
    "$$\n",
    "which completes the proof.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2f3c0fa",
   "metadata": {},
   "source": [
    "## Combining MD and MC for canonical time correlation functions\n",
    "\n",
    "In the last section of the MD chapter, we discussed how to evaluate various observables. \n",
    "We looked at properties like the kinetic energy (Eq. [](Kinetic_p)), potential energy (e.g., Eq. [](LJ)), and also at structural properties like the density (see Eq.[](density_est)). In your first numerical exercise, you even evaluated spatial correlations by looking at the [radial distribution function](https://en.wikipedia.org/wiki/Radial_distribution_function) (AKA pair correlation function).\n",
    "The same estimators can be used in MC simulations to evaluate expectation values in the canonical ensemble. You will do just that in your second numerical exercise!\n",
    "\n",
    "But we also mentioned special observables, called equilibrium time-correlation functions, that were defined in Eq.[](t-corfun). You might recall that their special importance came from the [fluctuation dissipation theorem](https://en.wikipedia.org/wiki/Fluctuation-dissipation_theorem) which states that the response of a system to a small time-dependent perturbation, driving the system out of equilibrium, is determined by equilibrium time-correlation functions. In other words, the response, as measured by transport properties (diffusion, thermal/electric conductivity, reaction rate, etc.), is determined by the fluctuations of equilibrium time correlation functions. \n",
    "\n",
    "Of the methods we have discussed in the course, time correlation functions can only be evaluated by doing MD simulations. The reason we cannot evaluate them using MC simulations is that the steps in the Metropolis algorithm are determined by a random process - they store no information about the dynamics in time of the system. \n",
    "\n",
    "On the other hand, our MD simulations only allowed us to evaluate expectation values in the microcanonical ensemble. But most transport properties are measured in experiments at constant temperature, not energy! To the rescue comes the combination of MC and MD. \n",
    "\n",
    "To evaluate time correlation functions in the canonical ensemble, we can perform one long MC simulation, which will converge to sampling configurations from the Boltzmann distribution. Once it is converged, we can take a sample every few hundred steps and, from each one, generate regular MD trajectories at constant energies to determine the time correlation function for this particular energy. Taking the average over all of the trajectories (initial conditions) will give the desired time correlation functions in the canonical ensemble. In your second exercise you will do this to evaluate the self-diffusion coefficient of Argon at various temperatures.\n",
    "\n",
    "## Error estimation\n",
    "\n",
    "Finally, assuming we have managed to evaluate some expectation values, how accurate are they? What is the **statistical uncertainty** of our results? An estimate of the statistical error can be obtained by using [**the central limit theorem**](https://en.wikipedia.org/wiki/Central_limit_theorem) again. Loosely speaking, it states that, under certain conditions, the means of samples of independent random variables are normally distributed. This is true even if the original variables are not normally distributed. \n",
    "\n",
    "Practically, it means that if we have some property $A$ which is not normally distributed, as is often the case in MD/MC simulations, if we sample it many times, divide the samples into $M$ equal blocks, and then evaluate the mean for each block, $\\langle A \\rangle_m$ where $m=1,...,M$ - those means follow a normal distribution. Why is it important? Because if we know that the means are normally distributed, we can evaluate the **standard error** on the averages from,\n",
    "\n",
    "$$\n",
    "\\epsilon_A = \\frac{\\sigma_A}{\\sqrt{M}},\n",
    "$$(error)\n",
    "where $\\sigma_A^2$ is the variance between the means of the different blocks,\n",
    "\n",
    "$$\n",
    "\\sigma_A^2 = \\frac{\\sum_{m=1}^M \\left[ \\langle A \\rangle_m - \\langle A \\rangle \\right]^2 }{M-1},\n",
    "$$(std)\n",
    "and $\\langle A \\rangle$ is the average from the entire simulation data, as in Eq. [](av_sim). As we said previously, this analysis can be used in any ensemble, because the means always distribute normally.\n",
    "\n",
    "The only question that remains is - how do we choose the number of blocks $M$? For this analysis to be valid, the different blocks have to generate statistically independent samples of the means. How do we know that the  blocks are spaced enough so that this is the case? It turns out, that the autocorrelation function of the observable is the answer. The autocorrelation function starts from a value of $\\langle A^2 \\rangle$ and decays towards zero. The time it takes to decay it called the **autocorrelation time** and it effectively determines how long it takes for the system to forget all past correlations so that new samples are independent from the initial ones. Thus, we need to choose the block length to be larger that the autocorrelation time.\n",
    "\n",
    "Evaluating time correlation functions is quite expensive, so we do not want to do this for every property (although it is a more rigorous approach).\n",
    "How do we evaluate if our samples are correlated or not in practice? We start with very small blocks (very large $M$), containing only a few steps each. In this case, many of our block means are highly correlated. Our estimate of the error on the average of the observable from Eq. [](error) will be very small because we are assuming all of them are statistically independent, which is not true. Then, we increase the block size (decrease $M$) and re-calculate the error on the mean. It will increase a little. We repeat this procedure until our estimate of the error on the average has reached a plateau. Then, our estimate of the number of independent samples of the mean during the simulation is equal to the number of blocks we have used. The procedure to determine the statistical uncertainty according to Eq. [](error) is then reliable.\n",
    "\n",
    "We note that this analysis is required if we want to evaluate the statistical error on expectation values that were evaluated in a single simulation. If we have enough time and computational power, we can always resort to doing several independent simulations, by sampling different initial conditions, and simply treat each simulation as an independent block in the error analysis.\n"
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