{
 "cells": [
  {
   "cell_type": "markdown",
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   "source": [
    "# The UKF exposed: How it works, when it works and when it's better to sample"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Sebastian Bitzer](http://sbitzer.eu) (sebastian.bitzer@tu-dresden.de)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Abstract\n",
    "\n",
    "Among nonlinear, Bayesian filters the Unscented Kalman Filter (UKF) promises to be computationally more efficient than a particle filter and more accurate than an Extended Kalman Filter. It, therefore, is a good candidate for many practical filtering applications in which the uncertainty of the filter estimates needs to be tracked, too. The approximation employed by the UKF is usually formalised with 3 free parameters, but, apart from very general hints about their purpose, users are left in the dark about the practical effects they have. I here go through the theory behind the UKF to review its parameters in more detail. I show that the UKF effectively has only 2 parameters. I then investigate the accuracy of the UKF with different parameter settings and show that the typically suggested parameter values lead to bad approximations compared to other parameter settings, when model functions are strongly nonlinear within the range covered by the current state distribution. I further show that, for the tested model, the accuracy of the UKF approximation deterioates in higher dimensions such that random sampling becomes computationally more efficient and more accurate in high dimensions ($D>10$). I conclude with a new suggestion for default UKF parameter values and discuss possible causes of my findings in comparison to sampling."
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "[Bayesian filters](http://www.cambridge.org/sarkka) infer the likely positions of a dynamically changing, but unobserved hidden state given some noisy observations and a probabilistic model which defines how the hidden state changes and relates to observations. The best known of these filters is the [Kalman filter](https://en.wikipedia.org/wiki/Kalman_filter) which is defined for linear models with Gaussian noise where it is exact, i.e., if the observations are really generated by the assumed Gaussian linear model, the Kalman filter computes the true posterior density over the hidden state. For nonlinear models, even under the assumption of Gaussian generative noise, the true posterior over the hidden state becomes non-Gaussian and probably multimodal. Yet, you can try to approximate the true posterior with, for example, a Gaussian to still apply the Kalman filter framework in principle. One such approach is the [Extended Kalman Filter (EKF)](https://en.wikipedia.org/wiki/Extended_Kalman_filter) (see also [Särkkä2013, chapter 5](http://www.cambridge.org/sarkka), [free pdf](http://users.aalto.fi/~ssarkka/pub/cup_book_online_20131111.pdf)) where the nonlinear model functions are locally linearised to be able to still apply the standard Kalman filter updates locally in each step. This has, however, been shown to be an inaccurate approximation for many nonlinear models.\n",
    "\n",
    "Another approach to probabilistic filtering is to sample from the state distribution and then to propagate the samples through the model functions to approximate the resulting distributions without making any assumptions of their form. This is known under the name of [sequential monte carlo or particle filtering](https://en.wikipedia.org/wiki/Particle_filter) and has become a very popular method. However, it requires considerable amount of computation time, if approximations are to be made exact and the hidden state has many dimensions (the higher the dimension, the more samples you need to approximate the underlying distribution reliably).\n",
    "\n",
    "To overcome the limitations of the EKF without spending the resources necessary for a particle filter the [Unscented Kalman Filter (UKF)](http://dx.doi.org/10.1109/JPROC.2003.823141) has been proposed. The UKF represents a state distribution with a small set of very special samples which is called the *sigma points*. These sigma points are propagated through the model functions and then are used to approximate the predictive distributions of the model which are needed to apply standard Kalman filter updates. The trick with the sigma points is that they are chosen such that a very small number of them leads to a better approximation of the predictive distributions than what would be achieved with the linearisation of the EKF. In the 2000s other Gaussian filters based on specially chosen samples have been proposed such as the Gauss-Hermite Kalman filter, or the Cubature Kalman Filter (see [Särkkä2013, chapter 6](http://www.cambridge.org/sarkka)). I do not address them here directly, but it can, for example, been shown that the Cubature Kalman Filter corresponds to a UKF with a particular choice of paramter values ([Särkkä2013, chapter 6](http://www.cambridge.org/sarkka)).\n",
    "\n",
    "Typical descriptions of the UKF provide instructions for generating a standard set of sigma points given some parameter values, but lack an explanation for what the parameters actually do, or why certain values may be a good choice and others not and when this is the case. I here reiterate the theory behind the UKF with a focus on the interpretation of the UKF parameters. Different parameterisations will define alternative filters via different sigma point selection rules which I call sigma point sets. I then investigate the quality of the approximations implemented by the different sigma point sets to identify useful parameter values depending on \n",
    "1. the nonlinearity of the model functions\n",
    "2. the uncertainty in hidden states\n",
    "3. the dimensionality of the hidden state and \n",
    "4. the Gaussianity of the hidden state distribution. \n",
    "\n",
    "The conclusions I can draw from my results are limited by my choice of model that I use in my simulations. Nevertheless, I believe that some of my observations are sufficiently general to apply to a wider range of models. In particular, I show that the standard parameter settings for the UKF fail, when the hidden state is very uncertain and covers several complicated nonlinearities in the model functions. In this situation, simpler parameterisations, for example, those equivalent to a Cubature Kalman Filter, provide more accurate approximations. I further find for the tested model that the approximations made by the UKF get considerably worse when the dimensionality of the hidden state increases. This leads to the surprising result that approximations made with only very few random samples are more accurate in high dimensions than the approximations resulting from the carefully selected sigma points, even for the most accurate sigma point set.\n",
    "\n",
    "This document is structured as follows: I start with explaining the theory behind the main UKF approximation which is called the Unscented Transform (UT) and derive the different sigma point sets. I use 5 distinct sigma point sets which partially overlap in the sense that you can sometimes transform one sigma point set into another by changing parameter values. I then introduce the accuracy measure and the probabilistic model I use in the experiments together with their Python implementations. After the implementations of the 5 sigma point sets, I evaluate their accuracy in a series of simulations in which I vary the setup as itemised above. I close with my conclusions."
   ]
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    "collapsed": false
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   "source": [
    "## The Theory of the Unscented Transform\n",
    "\n",
    "The core approximation that the UKF uses is the Unscented Transform (UT). Apparently the UT has been developed by [Uhlmann](http://bengal.missouri.edu/~uhlmannj/public_html/) & [Julier](http://www0.cs.ucl.ac.uk/people/S.Julier.html) in the 1990s, but most of the material used here comes from their [2004 review](http://dx.doi.org/10.1109/JPROC.2003.823141). The mindset behind the UT is clearly an engineering one where computational efficiency is traded off against the accuracy of the solution. Although a similar tradeoff may be achieved in a particle filter by varying the number of used particles, the UT tries to improve upon the efficiency of random particles by choosing a minimum number of particular particles, the sigma points, that can be analytically shown to guarantee a desired level of accuracy. \n",
    "\n",
    "In the following I will provide the theoretical background for the UT and will define four increasingly complex instantiations of UT (sigma point sets) as I go along. I will also point out a gap in the argument which supposedly guarantees a desired level of accuracy of the UT."
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem definition\n",
    "\n",
    "I define a multidimensional random variable ${\\bf r} \\in {\\mathcal R}^D$ (a vector of random variables) that is transformed through some nonlinear function ${\\bf h}({\\bf r}) = {\\bf o}$ which makes it to the transformed random variable ${\\bf o} \\in {\\mathcal R}^d$. Knowing something about the probability density $p({\\bf r})$ I would then like to approximate the transformed density $p({\\bf o})$. To be precise, I only want to approximate the mean $\\bar{\\bf o}$ and covariance $\\Sigma_o$, because these are the only two entities that I need in a Kalman filter. [Julier and Uhlmann (2004)](http://dx.doi.org/10.1109/JPROC.2003.823141) have shown that the more I know about $p({\\bf r})$ the better my approximation of $\\bar{\\bf o}$ and $\\Sigma_o$ will be.\n",
    "\n",
    "Notice that, just because I concentrate on mean and covariance, I do not need to assume a Gaussian approximation in the UT. For example, assume that $\\bf r$ and $\\bf o$ live in the same space, I could then generate sigma points from a given mean and covariance of $\\bf r$, project them through $\\bf h$, estimate the resulting mean and covariance and then generate sigma points from the estimated mean and covariance, all without making any more assumptions about the underlying distributions. Practically, however, there is no advantage of leaving the particular approximation unspecified, because the accuracy of the approximation of mean and covariance of $\\bf o$ also depends on the higher moments of $\\bf r$, as I reiterate from [Julier and Uhlmann (2004)](http://dx.doi.org/10.1109/JPROC.2003.823141) next."
   ]
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   "source": [
    "### Taylor series approximation of  mean and covariance\n",
    "\n",
    "I can represent the transformation function $\\bf h$ with a [Taylor series](https://en.wikipedia.org/wiki/Taylor_series) around the mean of $p({\\bf r})$, ${\\bf \\bar{r}}$. I choose the mean, because it is one of the most informative points about the density $p({\\bf r})$, and, more importantly, this allows me to formulate the approximation in terms of [central moments](https://en.wikipedia.org/wiki/Moment_%28mathematics%29) of the distribution $p({\\bf r})$.\n",
    "\n",
    "$$\n",
    "{\\bf o} = {\\bf h}({\\bf r}) = {\\bf h}({\\bf \\bar{r}}) + {\\bf D}_{\\bf e}{\\bf h} + \\frac{1}{2!}{\\bf D}_{\\bf e}^2{\\bf h} + \\frac{1}{3!}{\\bf D}_{\\bf e}^3{\\bf h} + \\dots\n",
    "$$\n",
    "\n",
    "where ${\\bf e} = {\\bf r} - {\\bf \\bar{r}}$ and I have copied the notation of [Julier and Uhlmann (2004)](http://dx.doi.org/10.1109/JPROC.2003.823141) for [multidimensional Taylor series](https://en.wikipedia.org/wiki/Taylor_series#Taylor_series_in_several_variables) in which ${\\bf D}_{\\bf e}^i{\\bf h}$ is shorthand for the higher order polynomial terms including partial derivatives:\n",
    "\n",
    "$$\n",
    "{\\bf D}_{\\bf e}^i{\\bf h} = \\left.\\left( \\sum_{j=1}^D e_j \\frac{\\partial}{\\partial r_j} \\right)^i {\\bf h}({\\bf r})\\right|_{{\\bf r}=\\bar{{\\bf r}}}\n",
    "$$\n",
    "\n",
    "Notice how this translates into other forms to write these terms, e.g., for the second order term:\n",
    "\n",
    "$$\n",
    "{\\bf D}_{\\bf e}^2{\\bf h} = \\left.\\left( \\sum_{j=1}^D e_j \\left. \\frac{\\partial}{\\partial r_j} \\right)^2 {\\bf h}({\\bf r})\\right|_{{\\bf r}=\\bar{{\\bf r}}} = \\sum_{j=1}^D\\sum_{k=1}^D e_j e_k \\frac{\\partial^2}{\\partial r_j \\partial r_k} {\\bf h}({\\bf r}) \\right|_{{\\bf r}=\\bar{{\\bf r}}} \n",
    "$$\n",
    "\n",
    "To get the mean of $p({\\bf o})$ I can simply apply the corresponding expectation to the above formula such that\n",
    "\n",
    "$$\n",
    "{\\bf \\bar{o}} = E[{\\bf o}] = E[{\\bf h}({\\bf \\bar{r}})] + E[{\\bf D}_{\\bf e}{\\bf h}] + \\frac{1}{2!}E[{\\bf D}_{\\bf e}^2{\\bf h}] + \\dots\n",
    "$$\n",
    "\n",
    "where the expectation is over the original random variable $\\bf r$. If I want to approximate the mean, I can cut the higher order terms of the Taylor series as usual. For example, you can linearise which gives\n",
    "\n",
    "$$\n",
    "\\bar{\\bf o} \\approx {\\bf h}({\\bf \\bar{r}}) + \\sum_{j=1}^D E[e_j]\\frac{\\partial}{\\partial r_j}\\left. {\\bf h}({\\bf r})\\right|_{{\\bf r}=\\bar{\\bf r}} = {\\bf h}(\\bar{\\bf r}),\n",
    "$$\n",
    "\n",
    "because the first [central moments](https://en.wikipedia.org/wiki/Moment_%28mathematics%29) $E[e_j]$ are 0. This is interesting, because it means that the gradient of ${\\bf h}$ is irrelevant for determining the mean $\\bar{{\\bf o}}$. Obviously, higher order central moments such as the covariances need not be 0. Therefore, the quality of the approximation depends on how much the higher order moments contribute to the estimated mean $\\bar{\\bf o}$ which also depends on the corresponding partial derivatives of the nonlinear transformation ${\\bf h}({\\bf r})$ around the mean $\\bar{\\bf r}$. For example, when the covariance between two of the random variables, $E[e_je_k]$, increases, the linear approximation of the mean $\\bar{\\bf o}$ above should get worse. Note that $j$ could be equal to $k$, i.e., the more uncertainty about a random variable $r_j$ there is, the worse is the approximation of $\\bar{\\bf o}$. Similarly, if the mean $\\bar{\\bf r}$ moves into a region where the local curvature of ${\\bf h}$ increases, the approximation gets worse. Similar arguments hold for higher order moments (skewness, kurtosis) and higher order partial derivatives (whatever you want to call them - I don't have intuitions about them).\n",
    "\n",
    "The covariance of $\\bf o$ is\n",
    "\n",
    "$$\n",
    "\\Sigma_o = E\\left[ ({\\bf o} - \\bar{\\bf o})({\\bf o} - \\bar{\\bf o})^T \\right] = \\sum_{i_1=1}^\\infty \\sum_{i_2=1}^\\infty \\frac{E\\left[ {\\bf D}_{\\bf e}^{i_1}{\\bf h}({\\bf D}_{\\bf e}^{i_2}{\\bf h})^T  \\right] - E[{\\bf D}_{\\bf e}^{i_1}{\\bf h}]E[{\\bf D}_{\\bf e}^{i_2}{\\bf h}]^T}{i_1!i_2!}\n",
    "$$\n",
    "\n",
    "which simplifies to\n",
    "\n",
    "$$\n",
    "\\Sigma_o \\approx E\\left[ {\\bf D}_{\\bf e}{\\bf h}({\\bf D}_{\\bf e}{\\bf h})^T  \\right] = {\\bf J}(\\bar{\\bf r})\\Sigma_r{\\bf J}^T(\\bar{\\bf r})\n",
    "$$\n",
    "\n",
    "for a linear approximation where ${\\bf J}(\\bar{\\bf r})$ is the [Jacobian matrix](https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant) of $\\bf h$ evaluated at $\\bar{\\bf r}$. The covariance, therefore, depends on the gradients of $\\bf h$ as well as the covariance of $\\bf r$ plus all the higher order terms. [Julier and Uhlmann (2004)](http://dx.doi.org/10.1109/JPROC.2003.823141) further note that for symmetric distributions all terms where $i_1 + i_2$ is odd are 0, because these terms contain odd central moments which are 0 for symmetric distributions. In any case, the general formula shows that for an approximation of the covariance of $\\bf o$ with order $m$ where $\\max(i_1,i_2)=m$ you need to know central moments of the distribution of $\\bf r$ whose order is larger than $m$.\n",
    "\n",
    "The point of the excercise is that we now understand better why simple linearisation, as it is done in the Extended Kalman Filter, fails in many situations, especially, when uncertainty is high which leads to bad approximation of the mean $\\bar{\\bf o}$. It is also clear now that it is tricky to make better than linear approximations of the covariance $\\Sigma_o$, because for that we immediately need to know about high order ($\\geq 3$) central moments of $p({\\bf r})$ and high order partial derivatives of $\\bf h$. In principle, the unscented transform is designed to at least capture a few more higher order moments than a linearisation would do, as I describe next."
   ]
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   "source": [
    "### Is it really enough to capture as many as possible moments?\n",
    "\n",
    "The main idea of the UT is to select an as small as possible set of _sigma points_ ${\\bf S} = [{\\bf s}_1, \\dots, {\\bf s}_N]$, which represents as many as possible moments of $p({\\bf r})$. Then, to project the sigma points through $\\bf h$ and approximate the transformed mean $\\bar{\\bf o}$ and covariance $\\Sigma_o$ with the mean $\\hat{\\bf o}$ and covariance $\\widehat{\\Sigma}_o$ of the sigma points. The rest is hope, because I have not seen an analytical argument which would, for example, guarantee that this procedure actually corresponds to using the higher order terms of the Taylor series defined above. The Taylor series formulation just provides an intuitive motivation for why I should want that the used sigma points capture many higher moments of $p({\\bf r})$. Although [Julier and Uhlmann (2004)](http://dx.doi.org/10.1109/JPROC.2003.823141) state that\n",
    "\n",
    ">  Any set of sigma points that encodes the mean and covariance correctly, including the set in (11), calculates the projected mean and covariance correctly to the second order (see Appendixes I and II).\n",
    "\n",
    "they don't actually show this in the referred appendices. I miss the connection from projected sigma points to higher order partial derivatives of $\\bf h$ that occur in the higher order Taylor series terms. Do I overlook some basic property about points projected through a nonlinear function that would guarantee that? If yes, great! If not, we're back to hope. I have also not seen a numerical check of Julier and Uhlmann's above statement where somebody would have to have gone through computing 4th order partial derivatives and moments to analytically approximate the covariance $\\Sigma_o$ and check whether the UT approximation is equally close to the true $\\Sigma_o$ (perhaps approximated by a large number of random samples). Also, which criterion would you use to say that the approximation from the UT is at least as good as the 2nd order Taylor series approximation? This is all more practical to do for the approximated mean $\\hat{\\bf o}$, but I defer doing that to some unspecified point in the future. So, for now I'm going to believe Julier and Uhlmann and follow them in the hope that I only need to care about how many higher moments a specific set of sigma points captures and the rest is taken care of by simply projecting the sigma points through the nonlinear function $\\bf h$."
   ]
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   "metadata": {},
   "source": [
    "### What it means to capture a moment\n",
    "Formally, _capturing_ the moment of a distribution $p({\\bf r})$ with a set of sigma points ${\\bf S} = [{\\bf s}_1, \\dots, {\\bf s}_N]$ means that I can reconstruct the value of the moment from the sigma points. In general, I define an arbitrary moment of a $D$-dimensional variable ${\\bf r} = [r_1, \\dots, r_D]^T$ as \n",
    "\n",
    "$$\n",
    "m(r_{i_1}, \\dots, r_{i_M}) = E[r_{i_1} \\dots r_{i_M}] = \\int p({\\bf r})r_{i_1} \\dots r_{i_M} d{\\bf r}\n",
    "$$\n",
    "\n",
    "where $M$ is the order of the moment and the indices $i_1, \\dots, i_M$ select the particular elements of $\\bf r$ that contribute to the moment. For example, the third moment in the second element of $\\bf r$, i.e., $m(r_2^3)$ is defined as $i_1=i_2=i_3=2$. To use central moments I replace $\\bf r$ with ${\\bf e} = {\\bf r} - E[{\\bf r}] = {\\bf r} - \\bar{\\bf r}$. For example, the covariance between $r_1$ and $r_2$ is defined as $\\Sigma_{12} = m(e_1, e_2)$.\n",
    "\n",
    "In the unscented transform [Julier and Uhlmann (2004)](http://dx.doi.org/10.1109/JPROC.2003.823141) suggested that moments should be reconstructed from sigma points using\n",
    "\n",
    "$$\n",
    "m(r_{i_1}, \\dots, r_{i_M}) \\approx \\hat{m}(r_{i_1}, \\dots, r_{i_M}) = \\sum_{n=1}^N w_n s_{i_1n} \\dots s_{i_Mn}\n",
    "$$\n",
    "\n",
    "where $s_{i_1n}$ is the $i_1$-th element of the $n$-th sample and $w_n$ is a weight associated with the $n$-th sigma point. This is a very general formulation which also includes the case in which you approximate the moment of the underlying distribution with the corresponding moment of the set of sigma points. For example, the sample covariance simply is\n",
    "\n",
    "$$\n",
    "\\widehat{\\Sigma}_{i_1i_2} = \\hat{m}(e_{i_1}, e_{i_2}) = \\frac{1}{N}\\sum_{n=1}^N \\hat{e}_{i_1n}\\hat{e}_{i_2n}\n",
    "$$\n",
    "\n",
    "where $w_n = 1/N$ and $\\hat{e}_{in} = s_{in} - \\bar{r}_i$."
   ]
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   "source": [
    "### Capturing mean and covariance (min set)\n",
    "\n",
    "The whole point of the UT is to construct sigma point sets with as few as possible sigma points which still capture as many as possible moments. By trying to capture higher moments I may get an approximation that is better than the linear one used by the EKF and by using as few as possible sigma points I may be computationally more efficient than a particle filter. So how can I make sigma point sets which capture the _given_ moments of a distribution?\n",
    "\n",
    "In the context of Kalman filters I mostly concentrate on mean and covariance. So let's start with these. Capturing the mean alone is super easy. I only need one sigma point for that which is \n",
    "\n",
    "$$\n",
    "{\\bf s}_0 = \\bar{\\bf r}\n",
    "$$\n",
    "\n",
    "with $w_0 = 1$. \n",
    "\n",
    "For the covariance of a $D$-dimensional random variable I need at least $D$ sigma points. To see that I need some linear algebra and I need to remember that \n",
    "\n",
    "$$\n",
    "\\widehat{\\Sigma}_{ij} = \\frac{1}{N}\\sum_{n=1}^N \\hat{e}_{in} \\hat{e}_{jn} = \\frac{1}{N}\\left[\\sum_{n=1}^N \\hat{\\bf e}_n\\hat{\\bf e}_n^T\\right]_{ij}.\n",
    "$$\n",
    "\n",
    "If I let $\\widehat{\\bf E} = [\\hat{\\bf e}_1, \\dots, \\hat{\\bf e}_N]$,\n",
    "\n",
    "$$\n",
    "\\widehat{\\Sigma} = \\frac{1}{N}\\sum_{n=1}^N \\hat{\\bf e}_n\\hat{\\bf e}_n^T = \\frac{1}{N}\\widehat{\\bf E}\\widehat{\\bf E}^T.\n",
    "$$\n",
    "\n",
    "I want that $\\widehat{\\Sigma} = \\Sigma$ where $\\Sigma$ is the given covariance matrix which, as I know, is positive definite. This means that I can decompose $\\Sigma$ using the [Cholesky decomposition](https://en.wikipedia.org/wiki/Cholesky_decomposition) such that\n",
    "\n",
    "$$\n",
    "\\Sigma = {\\bf L}{\\bf L}^T\n",
    "$$\n",
    "\n",
    "where ${\\bf L} = [{\\bf l}_1, \\dots, {\\bf l}_D] \\in \\mathcal{R}^{D\\times D}$ is a lower triangular matrix. Well, this has the same form as $\\widehat{\\Sigma}$ above. So I can set $\\hat{\\bf e}_i = \\sqrt{D}{\\bf l}_i$ to make $\\widehat{\\Sigma} = \\Sigma$. Consequently, I need at least $N=D$ sigma points which need to be\n",
    "\n",
    "$$\n",
    "{\\bf s}_n = \\bar{\\bf r} + \\sqrt{D}{\\bf l}_n \\qquad n \\in {1, \\dots, D}.\n",
    "$$\n",
    "\n",
    "By construction, with $w_n = 1/D$, these sigma points, thus, capture the covariance $\\Sigma$. At the same time the construction shows that $D$ is the samllest number of sigma points that can capture all components of the covariance. Together with the mean I therefore need at least $D+1$ sigma points to capture the first two moments of $p({\\bf r})$ resulting in the following set of sigma points which I call the _min set_:\n",
    "\n",
    "\\begin{align}\n",
    "{\\bf s}_0 &= \\bar{\\bf r}\\\\\n",
    "{\\bf s}_n &= \\bar{\\bf r} + \\sqrt{D}{\\bf l}_n \\qquad n \\in {1, \\dots, D}\\\\\n",
    "w_0^m &= 1 \\quad w_n^m = 0\\\\\n",
    "w_0^c &= 0 \\quad w_n^c = \\frac{1}{D}\n",
    "\\end{align}\n",
    "\n",
    "where I had to use different weights for reconstructing the mean ($w^m$) and reconstructing the covariance ($w^c$). I can use a common set of weights with a symmetric set of sigma points, as described next."
   ]
  },
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   "source": [
    "### Capturing symmetric distributions (base set)\n",
    "\n",
    "For symmetric distributions there is a very simple way to capture many higher moments, because all odd central moments of symmetric distributions are 0, i.e.,\n",
    "\n",
    "$$\n",
    "m(e_{i_1}, \\dots, e_{i_M}) = 0\n",
    "$$\n",
    "\n",
    "when $M$ is odd. This is because there is an equal amount of mass on the left and on the right of the mean which cancels when you integrate over all values. I can capture this property by choosing a symmetric set of sigma points. Of course, I don't want to loose the representation of the covariance which is why I choose the following set of sigma points which I call the _base set_:\n",
    "\n",
    "\\begin{align}\n",
    "{\\bf s}_n &= \\bar{\\bf r} + \\sqrt{D}{\\bf l}_n \\quad n \\in {1, \\dots, D}\\\\\n",
    "{\\bf s}_{n+D} &= \\bar{\\bf r} - \\sqrt{D}{\\bf l}_n\\\\\n",
    "w_j &= \\frac{1}{2D} = \\frac{1}{N} \\quad j\\in 1, \\dots, N\n",
    "\\end{align}\n",
    "\n",
    "When I subtract the mean from these sigma points and sum over them, I get 0 as long as the sign is preserved, i.e.,\n",
    "\n",
    "$$\n",
    "\\hat{m}(\\hat{e}_{i_1}, \\dots, \\hat{e}_{i_M}) = 0\n",
    "$$\n",
    "\n",
    "when $M$ is odd. Also, the symmetry means that sigma points ${\\bf s}_1, \\dots, {\\bf s}_{2D}$ average to $\\bar{\\bf r}$ which is the same as the weighted sum of sigma points with $w_j = 1/2D$.\n",
    "\n",
    "Note that this set of sigma points, when embedded in a [Gaussian filter](https://doi.org/10.1109/TSP.2006.875389), also implements the [Cubature Kalman Filter](https://doi.org/10.1109/TAC.2009.2019800) as shown by [Simo Särkkä](http://users.aalto.fi/~ssarkka/) in his book on [Bayesian Filtering and Smooting](http://www.cambridge.org/sarkka) (also available as [pdf on his website](http://users.aalto.fi/~ssarkka/pub/cup_book_online_20131111.pdf), see chapter 6)."
   ]
  },
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   "source": [
    "### Capturing higher order moments (Gauss set)\n",
    "\n",
    "It is really tedious to think about higher moments of arbitrary multivariate distributions. Therefore, I will stick with a distribution that is simple and well-known: the [multivariate Gaussian](https://en.wikipedia.org/wiki/Multivariate_normal_distribution). For the Gaussian, mean and covariance are the [sufficient statistic](https://en.wikipedia.org/wiki/Sufficient_statistic) of the distribution, i.e., these parameters are sufficient to completely specify the distribution. As a result, higher (central) moments of the distribution can be formulated in terms of the covariances. A particular formula is defined by [Isserli's theorem](https://en.wikipedia.org/wiki/Isserlis'_theorem) which, for 4th order moments (aka. [kurtosis](https://en.wikipedia.org/wiki/Kurtosis)), prescribes\n",
    "\n",
    "$$\n",
    "m(e_{i_1}, e_{i_2}, e_{i_3}, e_{i_4}) = \\Sigma_{i_1i_2}\\Sigma_{i_3i_4} + \\Sigma_{i_1i_3}\\Sigma_{i_2i_4} + \\Sigma_{i_1i_4}\\Sigma_{i_2i_3}.\n",
    "$$\n",
    "\n",
    "Hang on. If the mean and covariance is everything there is to know about the Gaussian, why should I care about capturing higher moments, if I approximate all densities in my model with Gaussians? I gave an intuitive reason when discussing the Taylor approximation above. The problem is that the nonlinear function may add strange distortions to the probability distribution and by trying to capture as many as possible properties of the distribution explicitly in the sigma points we may get a better approximation of the introduced distortions. Below I will test this assumption numerically by comparing a set of sigma points that was specified to capture higher order moments with the base set and a set of sigma points that was randomly chosen.\n",
    "\n",
    "[Julier and Uhlmann (2004)](http://dx.doi.org/10.1109/JPROC.2003.823141) presented a set of sigma points which can capture 4th order moments, but the set consists of $2D^2 + 1$ sigma points and is quite complicated to construct. As an alternative they extended the base set above and introduced additional parameters which may be tuned such that the difference in 4th (and perhaps higher) order moments is minimised.\n",
    "\n",
    "__Partially capturing kurtosis.__ The equation for the 4th Gaussian moments above suggests a considerable simplification when the Gaussian is isotropic, i.e., $\\Sigma$ is diagonal. Then, the only nonzero moments are (the order of the arguments of $m$ doesn't matter):\n",
    "\n",
    "$$\n",
    "m(e_{i_1}, e_{i_1}, e_{i_2}, e_{i_2}) = \\Sigma_{i_1i_1}\\Sigma_{i_2i_2}\n",
    "$$\n",
    "\n",
    "and \n",
    "\n",
    "$$\n",
    "m(e_i, e_i, e_i, e_i) = 3\\Sigma_{ii}^2.\n",
    "$$\n",
    "\n",
    "In comparison, the sample moments $\\hat{m}$ for the base set and diagonal covariance are\n",
    "\n",
    "$$\n",
    "\\hat{m}(\\hat{e}_{i_1}, \\hat{e}_{i_2}, \\hat{e}_{i_3}, \\hat{e}_{i_4}) = \\sum_{n=1}^{2D}w_n a_n^4 l_{i_1n}l_{i_2n}l_{i_3n}l_{i_4n} = \\left\\{ \n",
    "\\begin{array}{cl} \n",
    "D\\Sigma_{ii}^2 & i=i_1=i_2=i_3=i_4\\\\\n",
    "0 & \\mathrm{else}\n",
    "\\end{array}\\right.\n",
    "$$\n",
    "\n",
    "where $w_n = 1/2D$ and $a_n = \\sqrt{D}$. Because I want to keep the construction of sigma points from the square root of $\\Sigma$ ($\\bf L$), I cannot capture $m(e_{i_1}^2, e_{i_2}^2)$, but [Julier and Uhlmann (2004)](http://dx.doi.org/10.1109/JPROC.2003.823141) came up with a way to capture $m(e_i^4)$ without affecting the reconstructions for mean and covariance. They did this by introducing one extra sigma point ${\\bf s}_0$ and adjusting sigma points ($a_n$) and weights $w_n$ resulting in what I call the _Gauss set_:\n",
    "\n",
    "\\begin{align}\n",
    "\\kappa &\\in \\mathcal{R}^+\\\\\n",
    "{\\bf s}_0 &= \\bar{\\bf r}\\\\\n",
    "{\\bf s}_n &= \\bar{\\bf r} + a_n{\\bf l}_n\\\\\n",
    "{\\bf s}_{n+D} &= \\bar{\\bf r} - a_n{\\bf l}_n \\qquad n \\in 1,\\dots,D\\\\\n",
    "w_0 &= 1 - \\frac{D}{\\kappa}\\\\\n",
    "w_j &= \\frac{1 - w_0}{2D} = \\frac{1}{2\\kappa} \\qquad j\\in 1,\\dots, 2D\\\\\n",
    "a_n &= \\sqrt{\\frac{D}{1 - w_0}} = \\sqrt{\\kappa}.\n",
    "\\end{align}\n",
    "\n",
    "There are several things to recognise: i) The mean is still captured, but this is not done by simply averaging the sigma points. Instead, ${\\bf s}_0$, which is the actual mean, contributes with weight $w_0$ to the computation of the mean whereas all other sigma points contribute $1-w_0 = D/\\kappa$. The new parameter $\\kappa$, therefore, controls this new mixture of sigma points, but note that $w_0$ becomes negative for $\\kappa < D$. This mixing is obviously unimportant as long as we just consider capturing the mean of $p({\\bf r})$, but it may have an effect when we estimate $\\hat{\\bf o}$ after nonlinear transformation of the sigma points. ii) The covariance is still captured, because ${\\bf s}_0 - \\bar{\\bf r} = {\\bf 0}$ and the contribution of $w_0$ cancels between $w_n$ and $a_n$. Again, however, notice that $a_n$ grew with $D$ in the base set whereas here it is fixed to $\\sqrt{\\kappa}$. This may have very different impacts after nonlinear transformation. iii) I can easily recover the base set by setting $\\kappa = D$. Finally, iv) I see that some of the 4th moments are captured for $\\kappa=3$, i.e., $\\hat{m}(\\hat{e}_i^4) = 3\\Sigma_{ii}^2$. \n",
    "\n",
    "In summary, this new set of sigma points introduced some changes to the construction of the sigma points which on their own may already have positive effects on the estimation of mean and covariance after nonlinear transformation. Intuitively, introducing an explicit sigma point for the mean and weighting it strongly after nonlinear transformation may have a stabilizing effect on the estimate of the mean. Similarly, fixing the dispersion of sigma points (irrespective of scaling due to the covariances) instead of using greater dispersion in higher dimensions may also result in more stable results, because the nonlinearity is approximated by the sigma points more locally, i.e., only in the area prescribed by the covariance. Whether the kurtosis is captured or not, may then not be that important anymore. This is underlined by the fact that anyway most 4th-order moments of the Gaussian are not captured by this sigma point set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Nonnegative weights (mean set)\n",
    "\n",
    "As I mentioned above, the Gauss set uses negative weight $w_0$ for $\\kappa < D$. This negative weight can lead to instabilities when estimating the transformed covariance matrix $\\Sigma_o$, i.e., $\\Sigma_o$ may then not be positive definite anymore (as seen in my results below). I can prevent negative $w_0$ by increasing $\\kappa$ with $D$, as it is already the case for the base set where $\\kappa = D$ and the 0th sigma point ${\\bf s}_0$ for the mean is removed. It is not necessary, however, to remove the focus on the mean from the sigma point set. Instead, I can use the weight $w_0$ as parameter and constrain it to be in $[0, 1)$ which gives the following sigma point set derived from the Gauss set:\n",
    "\n",
    "\\begin{align}\n",
    "w_0 &\\in [0, 1)\\\\\n",
    "{\\bf s}_0 &= \\bar{\\bf r}\\\\\n",
    "{\\bf s}_n &= \\bar{\\bf r} + \\sqrt{\\frac{D}{1 - w_0}}{\\bf l}_n\\\\\n",
    "{\\bf s}_{n+D} &= \\bar{\\bf r} - \\sqrt{\\frac{D}{1 - w_0}}{\\bf l}_n \\qquad n \\in 1,\\dots,D\\\\\n",
    "w_j &= \\frac{1 - w_0}{2D} \\qquad j\\in 1,\\dots, 2D.\\\\\n",
    "\\end{align}\n",
    "\n",
    "This sigma point set, which I call the _mean set_, ensures that all weights are in $[0, 1)$ and sum to 1, but it assigns a given, potentially high weight to the (transformed) mean of the source distribution. By default I will set $w_0 = 1/3$, because for $D=2$ this setting recovers the Gauss set. From $D=3$, however, the Gauss set with $\\kappa=3$ cannot be turned into the mean set with $w_0 > 0$. The Gauss and mean sets, therefore only differ by the constraints defined for their free parameters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mitigating the effects of uncaptured moments (scaled set)\n",
    "\n",
    "[Julier and Uhlmann (2004)](http://dx.doi.org/10.1109/JPROC.2003.823141) point out that it may, on average, be worse to approximate a moment with some more or less arbitrary value than approximating the moment with 0. Consequently, they introduced an additional parameter $\\alpha$ which reduces the scale of approximated higher moments $\\hat{m}(\\hat{e}_{i_1}, \\dots, \\hat{e}_{i_M})$ in the Taylor expansion of the nonlinear transformation. \n",
    "\n",
    "Of all the extensions they suggested I'm probably most skeptical about this one. Even though they gave an intuitive motivation for why you should capture many higher moments, I am sufficiently uncertain about the effect of capturing higher moments _after nonlinear transformation_ of sigma points that I'm willing to ignore potential problems with higher moments as long as the sigma point set makes sense in terms of which parts of the space defined by the distribution $p({\\bf r})$ it covers. For completeness and to get clear about the effect of $\\alpha$ on sigma points I explain the extension in the following.\n",
    "\n",
    "To manipulate the influence of higher moments on the nonlinear transform [Julier (2002)](http://dx.doi.org/10.1109/ACC.2002.1025369) introduced the auxiliary transform\n",
    "\n",
    "$$\n",
    "\\tilde{\\bf h}({\\bf r}) = \\frac{ {\\bf h}\\left(\\bar{\\bf r} + \\alpha({\\bf r} - \\bar{\\bf r})\\right) - {\\bf h}(\\bar{\\bf r}) }{\\mu} + {\\bf h}(\\bar{\\bf r})\n",
    "$$\n",
    "\n",
    "which is equal to $\\bf h$ for $\\alpha=\\mu=1$ and for $\\alpha < 1, \\mu < 1$ pulls transformed points $\\tilde{\\bf h}({\\bf r})$ closer to the transformed mean ${\\bf h}(\\bar{\\bf r})$. The auxiliary transform has the Taylor series\n",
    "\n",
    "$$\n",
    "\\tilde{\\bf o} = {\\bf h}({\\bf \\bar{r}}) + \\frac{\\alpha}{\\mu}{\\bf D}_{\\bf e}{\\bf h} + \\frac{\\alpha^2}{\\mu2!}{\\bf D}_{\\bf e}^2{\\bf h} + \\frac{\\alpha^3}{\\mu3!}{\\bf D}_{\\bf e}^3{\\bf h} + \\dots\n",
    "$$\n",
    "\n",
    "The mean and covariance of $\\tilde{\\bf o}$ are then\n",
    "\n",
    "\\begin{align}\n",
    "E[\\tilde{\\bf o}] &= {\\bf h}({\\bf \\bar{r}}) + \\frac{\\alpha^2}{\\mu2!}E[{\\bf D}_{\\bf e}^2{\\bf h}] + \\frac{\\alpha^3}{\\mu3!}E[{\\bf D}_{\\bf e}^3{\\bf h}] + \\dots\\\\\n",
    "E\\left[ (\\tilde{\\bf o} - E[\\tilde{\\bf o}])(\\tilde{\\bf o} - E[\\tilde{\\bf o}])^T \\right] &= \\frac{\\alpha^2}{\\mu^2}E\\left[ {\\bf D}_{\\bf e}{\\bf h}({\\bf D}_{\\bf e}{\\bf h})^T  \\right] + \\dots\n",
    "\\end{align}\n",
    "\n",
    "where $\\dots$ stands for the higher order terms. For $\\mu = \\alpha^2$ I can therefore recover the original mean and covariance correctly up to the second order while higher order terms are scaled (out) by $\\alpha$:\n",
    "\n",
    "\\begin{align}\n",
    "\\bar{\\bf o} &\\approx E[\\tilde{\\bf o}]\\\\\n",
    "\\Sigma_o &\\approx \\alpha^2 E\\left[ (\\tilde{\\bf o} - E[\\tilde{\\bf o}])(\\tilde{\\bf o} - E[\\tilde{\\bf o}])^T \\right].\n",
    "\\end{align}\n",
    "\n",
    "Note that I had to multiply the covariance of $\\tilde{\\bf o}$ by $\\alpha^2=\\mu$ to recover the original covariance $\\Sigma_o$ and I made the relation approximate, because I ignored higher order terms. Anyway, this shows that the auxiliary transform $\\tilde{\\bf h}$ has two desired properties: i) The contriubtion of the first two moments of $p({\\bf r})$ is the same as in the original transform ${\\bf h}$. ii) The contribution of higher moments is scaled by $\\alpha$ such that choosing $\\alpha \\rightarrow 0$ reduces the contriubtion of higher moments considerably.\n",
    "\n",
    "The detour via the auxiliary transform is not really desired, because it doubles the number of necessary function evaluations of ${\\bf h}$. Therefore, [Julier (2002)](http://dx.doi.org/10.1109/ACC.2002.1025369) (originally) and [Julier and Uhlmann (2004)](http://dx.doi.org/10.1109/JPROC.2003.823141) suggested to scale sigma points in an equivalent way, i.e.,\n",
    "\n",
    "$$\n",
    "{\\bf s}'_n = \\bar{\\bf r} + \\alpha({\\bf s}_n - \\bar{\\bf r})\n",
    "$$\n",
    "\n",
    "which, for $\\alpha=1$, recovers the original sigma point and for $\\alpha<1$ moves the sigma point closer to the mean of $p({\\bf r})$. I can reformulate this scaling of sigma points as another function to be able to compare this function to $\\tilde{\\bf h}$:\n",
    "\n",
    "$$\n",
    "{\\bf h}'({\\bf r}) = {\\bf h}(\\bar{\\bf r} + \\alpha({\\bf r} - \\bar{\\bf r})).\n",
    "$$\n",
    "\n",
    "${\\bf h}'$ and $\\tilde{\\bf h}$ have almost the same derivatives. To be precise\n",
    "\n",
    "$$\n",
    "\\frac{\\partial \\tilde{\\bf h}}{\\partial r_j} = \\frac{1}{\\mu}\\frac{\\partial {\\bf h}'}{\\partial r_j}.\n",
    "$$\n",
    "\n",
    "Therefore, the Taylor series of ${\\bf o}'$ is \n",
    "\n",
    "$$\n",
    "{\\bf o}' = {\\bf h}({\\bf \\bar{r}}) + \\alpha{\\bf D}_{\\bf e}{\\bf h} + \\frac{\\alpha^2}{2!}{\\bf D}_{\\bf e}^2{\\bf h} + \\frac{\\alpha^3}{3!}{\\bf D}_{\\bf e}^3{\\bf h} + \\dots\n",
    "$$\n",
    "\n",
    "which means that the scaled sigma points, for equal $\\alpha$, remove the influence of higher moments more rigorously than $\\tilde{\\bf h}$. Further, it means that $\\alpha$ in the scaled sigma points already affects the first and second order terms of the Taylor series which potentially introduces large distortions in the estimates of mean and covariance from the scaled sigma points. How could I remove these distortions of the lower order terms? [Julier (2002)](http://dx.doi.org/10.1109/ACC.2002.1025369) suggested an adaptation of the weights with which mean and covariance are estimated such that the estimates produced by transforming standard sigma points $\\bf s$ through $\\tilde{\\bf h}$ give the same result as transforming the scaled sigma points ${\\bf s}'$ through $\\bf h$.\n",
    "\n",
    "__First, I will consider the mean__ approximated by $\\bf s$ and $\\tilde{\\bf h}$:\n",
    "\n",
    "\\begin{align}\n",
    "\\bar{\\bf o} &\\approx \\sum_{j=0}^N w_j \\tilde{\\bf h}({\\bf s}_j)\\\\\n",
    "&= \\sum_{j=0}^N w_j \\left[ \\frac{ {\\bf h}\\left(\\bar{\\bf r} + \\alpha({\\bf s}_j - \\bar{\\bf r})\\right) - {\\bf h}(\\bar{\\bf r}) }{\\mu} + {\\bf h}(\\bar{\\bf r}) \\right]\\\\\n",
    "&= \\left[\\sum_{j=0}^N w_j \\frac{\\mu-1}{\\mu}{\\bf h}(\\bar{\\bf r})\\right] + \\left[ \\sum_{j=0}^N \\frac{w_j}{\\mu} {\\bf h}\\left(\\bar{\\bf r} + \\alpha({\\bf s}_j - \\bar{\\bf r})\\right) \\right]\\\\\n",
    "&= \\frac{w_0 + \\mu-1}{\\mu}{\\bf h}(\\bar{\\bf r}) + \\sum_{j=1}^N \\frac{w_j}{\\mu} {\\bf h}\\left(\\bar{\\bf r} + \\alpha({\\bf s}_j - \\bar{\\bf r})\\right).\n",
    "\\end{align}\n",
    "\n",
    "In the last step I have used that $\\sum_{j=0}^N w_j=1$ and that ${\\bf s}_0 = \\bar{\\bf r}$. It is easy to see now that this has the same structure as reconstructing the mean from the scaled sigma points:\n",
    "\n",
    "\\begin{align}\n",
    "\\bar{\\bf o} &\\approx \\sum_{j=0}^N \\bar{w}'_j {\\bf h}({\\bf s}'_j)\\\\\n",
    "&= \\sum_{j=0}^N \\bar{w}'_j {\\bf h}(\\bar{\\bf r} + \\alpha({\\bf s}_j - \\bar{\\bf r}))\\\\\n",
    "&= \\bar{w}'_0 {\\bf h}(\\bar{\\bf r}) + \\sum_{j=1}^N \\bar{w}'_j {\\bf h}(\\bar{\\bf r} + \\alpha({\\bf s}_j - \\bar{\\bf r}))\n",
    "\\end{align}\n",
    "\n",
    "meaning that\n",
    "\n",
    "\\begin{align}\n",
    "\\bar{w}'_0 &= \\frac{w_0 + \\mu-1}{\\mu}\\\\\n",
    "\\bar{w}'_j &= \\frac{w_j}{\\mu} \\qquad j \\in 1, \\dots, N.\n",
    "\\end{align}\n",
    "\n",
    "__I can use a similar argument for the covariance__, which can be approximated from the original sigma points $\\bf s$ projected through $\\tilde{\\bf h}$ by:\n",
    "\n",
    "\\begin{align}\n",
    "\\Sigma_o &\\approx \\mu \\sum_{j=0}^N w_j \\left( \\tilde{\\bf h}({\\bf s}_j) - \\bar{\\bf o}\\right)\\left( \\tilde{\\bf h}({\\bf s}_j) - \\bar{\\bf o}\\right)^T.\\\\\n",
    "\\end{align}\n",
    "\n",
    "By using the same decomposition of $\\tilde{\\bf h}$ as above the individual components of the outer product become\n",
    "\n",
    "\\begin{align}\n",
    "\\tilde{\\bf h}({\\bf s}_j) - \\bar{\\bf o} &= \\frac{1}{\\mu}{\\bf h}({\\bf s}'_j) + \\frac{\\mu - 1}{\\mu}{\\bf h}(\\bar{\\bf r}) - \\frac{\\mu - 1 + 1}{\\mu}\\bar{\\bf o}\\\\\n",
    "&= \\frac{1}{\\mu}\\left( {\\bf h}({\\bf s}'_j) - \\bar{\\bf o} + (\\mu -1)({\\bf h}(\\bar{\\bf r}) - \\bar{\\bf o}) \\right).\n",
    "\\end{align}\n",
    "\n",
    "Plugging this back into the equation for the covariance yields\n",
    "\n",
    "\\begin{align}\n",
    "\\Sigma_o &\\approx \\mu \\sum_{j=0}^N \\frac{w_j}{\\mu^2} \\left( {\\bf h}({\\bf s}'_j) - \\bar{\\bf o} + (\\mu -1)({\\bf h}(\\bar{\\bf r}) - \\bar{\\bf o})\\right)\\left( {\\bf h}({\\bf s}'_j) - \\bar{\\bf o} + (\\mu -1)({\\bf h}(\\bar{\\bf r}) - \\bar{\\bf o})\\right)^T\\\\\n",
    "&= \\frac{1}{\\mu} \\sum_{j=0}^N w_j \\left( ({\\bf h}({\\bf s}'_j) - \\bar{\\bf o})({\\bf h}({\\bf s}'_j) - \\bar{\\bf o})^T + (\\mu -1)({\\bf h}({\\bf s}'_j) - \\bar{\\bf o})({\\bf h}(\\bar{\\bf r}) - \\bar{\\bf o})^T\\right.\\\\\n",
    "&\\left. \\qquad + (\\mu -1)({\\bf h}(\\bar{\\bf r}) - \\bar{\\bf o})({\\bf h}({\\bf s}'_j) - \\bar{\\bf o})^T + (\\mu -1)^2({\\bf h}(\\bar{\\bf r}) - \\bar{\\bf o})({\\bf h}(\\bar{\\bf r}) - \\bar{\\bf o})^T\\right).\n",
    "\\end{align}\n",
    "\n",
    "I can simplify the individual components of the sum:\n",
    "\n",
    "\\begin{align}\n",
    "\\sum_{j=0}^N w_j (\\mu -1)({\\bf h}({\\bf s}'_j) - \\bar{\\bf o})({\\bf h}(\\bar{\\bf r}) - \\bar{\\bf o})^T &= (\\mu - 1)\\left[ \\sum_{j=0}^N w_j({\\bf h}({\\bf s}'_j) - \\bar{\\bf o}) \\right] ({\\bf h}(\\bar{\\bf r}) - \\bar{\\bf o})^T\\\\\n",
    "&= -(\\mu - 1)^2 \\left({\\bf h}(\\bar{\\bf r}) - \\bar{\\bf o}\\right)\\left({\\bf h}(\\bar{\\bf r}) - \\bar{\\bf o}\\right)^T\n",
    "\\end{align}\n",
    "\n",
    "where\n",
    "\n",
    "\\begin{align}\n",
    "\\sum_{j=0}^N w_j({\\bf h}({\\bf s}'_j) - \\bar{\\bf o}) &= w_0 \\left({\\bf h}(\\bar{\\bf r}) - \\bar{\\bf o}\\right) + \\sum_{j=1}^N w_j ({\\bf h}({\\bf s}'_j) - \\bar{\\bf o})\\\\\n",
    "&= (w'_0\\mu + 1 - \\mu)\\left({\\bf h}(\\bar{\\bf r}) - \\bar{\\bf o}\\right) + \\mu \\sum_{j=1}^N w'_j ({\\bf h}({\\bf s}'_j) - \\bar{\\bf o})\\\\\n",
    "&= (1 - \\mu) \\left({\\bf h}(\\bar{\\bf r}) - \\bar{\\bf o}\\right) + \\mu \\sum_{j=0}^N w'_j ({\\bf h}({\\bf s}'_j) - \\bar{\\bf o})\\\\\n",
    "&= (1 - \\mu) \\left({\\bf h}(\\bar{\\bf r}) - \\bar{\\bf o}\\right)\n",
    "\\end{align}\n",
    "\n",
    "because ${\\bf s}'_0 = \\bar{\\bf r}$, $\\sum_{j=0}^N w'_j = 1$ and $\\sum_{j=0}^N w'_j{\\bf h}({\\bf s}'_j) = \\bar{\\bf o}$. Also, the first part of the covariance sum simplifies to:\n",
    "\n",
    "\\begin{align}\n",
    "\\sum_{j=0}^N w_j ({\\bf h}({\\bf s}'_j) - \\bar{\\bf o})({\\bf h}({\\bf s}'_j) - \\bar{\\bf o})^T &= (1 - \\mu)\\left({\\bf h}(\\bar{\\bf r}) - \\bar{\\bf o}\\right)\\left({\\bf h}(\\bar{\\bf r}) - \\bar{\\bf o}\\right)^T + \\mu \\sum_{j=0}^N w'_j ({\\bf h}({\\bf s}'_j) - \\bar{\\bf o})({\\bf h}({\\bf s}'_j) - \\bar{\\bf o})^T\\\\\n",
    "&= (1 - \\mu)\\left({\\bf h}(\\bar{\\bf r}) - \\bar{\\bf o}\\right)\\left({\\bf h}(\\bar{\\bf r}) - \\bar{\\bf o}\\right)^T + \\mu \\Sigma'_o\n",
    "\\end{align}\n",
    "\n",
    "Putting everything back together, I have\n",
    "\n",
    "\\begin{align}\n",
    "\\Sigma_o &\\approx \\frac{1}{\\mu} \\left( (1-\\mu -2(\\mu - 1)^2 + (\\mu - 1)^2)\\left({\\bf h}(\\bar{\\bf r}) - \\bar{\\bf o}\\right)\\left({\\bf h}(\\bar{\\bf r}) - \\bar{\\bf o}\\right)^T + \\mu \\Sigma'_o  \\right)\\\\\n",
    "&= (1 - \\mu)\\left({\\bf h}(\\bar{\\bf r}) - \\bar{\\bf o}\\right)\\left({\\bf h}(\\bar{\\bf r}) - \\bar{\\bf o}\\right)^T + \\sum_{j=0}^N w'_j ({\\bf h}({\\bf s}'_j) - \\bar{\\bf o})({\\bf h}({\\bf s}'_j) - \\bar{\\bf o})^T\\\\\n",
    "&= \\sum_{j=0}^N w''_j ({\\bf h}({\\bf s}'_j) - \\bar{\\bf o})({\\bf h}({\\bf s}'_j) - \\bar{\\bf o})^T\n",
    "\\end{align}\n",
    "\n",
    "with\n",
    "\n",
    "\\begin{align}\n",
    "w''_0 &= w'_0 + 1 - \\mu\\\\\n",
    "w''_j &= w'_j \\quad j \\in 1,\\dots, N.\n",
    "\\end{align}\n",
    "\n",
    "[Julier (2002)](http://dx.doi.org/10.1109/ACC.2002.1025369) further suggested additional correction of the covariance for better approximation of higher order terms in the Taylor series. I will skip the derivation here. The simple outcome is an additional parameter $\\beta$ added to the 0th covariance weight such that\n",
    "\n",
    "$$\n",
    "w''_0 = w'_0 + 1 - \\mu + \\beta.\n",
    "$$\n",
    "\n",
    "__Scaled set.__ Combining all derivations in this section, I can now define the _scaled set_ of sigma points. I take the mean set as basis and use $\\mu = \\alpha^2$, as suggested above.\n",
    "\n",
    "\\begin{align}\n",
    "\\kappa &\\in \\mathcal{R}^+\\\\\n",
    "\\alpha &\\in \\mathcal{R}^+\\\\\n",
    "\\beta &\\in \\mathcal{R}\\\\\n",
    "{\\bf s}_0 &= \\bar{\\bf r}\\\\\n",
    "{\\bf s}_n &= \\bar{\\bf r} + \\alpha\\sqrt{\\kappa}{\\bf l}_n\\\\\n",
    "{\\bf s}_{n+D} &= \\bar{\\bf r} - \\alpha\\sqrt{\\kappa}{\\bf l}_n \\qquad n \\in 1,\\dots,D\\\\\n",
    "w_0^m &= \\frac{\\alpha^2\\kappa - D}{\\alpha^2\\kappa}\\\\\n",
    "w_0^c &= w_0^m + 1 - \\alpha^2 + \\beta\\\\\n",
    "w_j &= \\frac{1}{2\\alpha^2\\kappa} \\qquad j\\in 1,\\dots, 2D.\n",
    "\\end{align}\n",
    "\n",
    "This is the set of sigma points and reconstruction weights typically associated with the UKF. For example, Wan and van der Merwe defined the unscented transform using this set in [their chapter about the UKF](http://doi.org/10.1002/0471221546.ch7) in a book on [Kalman filtering and Neural Networks (2001)](http://doi.org/10.1002/0471221546), although they used a parameter $\\kappa'$ with $\\kappa = \\kappa' + D$ for unknown reasons. \n",
    "\n",
    "The scaled set is overparameterised: $\\kappa$ always occurs together with $\\alpha^2$ except in $w_0^c$ where $\\alpha^2$ occurs together with $\\beta$. This means that for any change of $\\alpha$ to $\\alpha^*$ I can find $\\kappa^* = \\alpha^2\\kappa / \\alpha^{*2}$ and $\\beta^* = \\alpha^{*2} - \\alpha^2 + \\beta$ which produce exactly the same approximated mean $\\bar{\\bf o}$ and covariance $\\Sigma_o$ that I got when using the old combination of $\\alpha, \\beta$ and $\\kappa$. So I should remove one of the parameters and $\\kappa$ appears to be a good candidate, because it just scales $\\alpha^2$. \n",
    "\n",
    "Why did I have $\\kappa$ in the first place? This parameter is a remnant of the Gauss set where [Julier and Uhlmann (2004)](http://dx.doi.org/10.1109/JPROC.2003.823141) optimised it to capture the 4th moment $\\hat{m}(\\hat{e}_i^4)$ of Gaussian distributions by setting $\\kappa=3$. In contrast, the scaled set was motivated by removing the contribution of higher order moments from the estimates of $\\bar{\\bf o}$ and $\\Sigma_o$ by choosing small $0 < \\alpha \\ll 1$. These two choices contradict each other. So [Julier (2002)](http://dx.doi.org/10.1109/ACC.2002.1025369) introduced $\\beta$ to compensate for the loss of captured higher moments in $\\bf r$-space in the reconstructed covariance in $\\bf o$-space. I cannot follow his derivation (repeated in [Julier and Uhlmann, 2004](http://dx.doi.org/10.1109/JPROC.2003.823141)), but the outcome is that $\\beta$ should be 2 for Gaussians. I found another argument for deriving a value for $\\beta$ when $\\kappa$ is removed, i.e., $\\kappa^*=1$: Note that I can recover the Gauss set for $\\kappa=3, \\alpha=1$ and $\\beta=0$. Thus, to maintain the same estimates of $\\bar{\\bf o}$ and $\\Sigma_o$ when changing $\\kappa$ to 1 I can set $\\alpha^{*2}=3$ and $\\beta^*=2$, reproducing Julier's optimal value of $\\beta$ for Gaussians.\n",
    "\n",
    "Irrespective of the choice of $\\beta$ it appears to be a much bigger, more impactful decision to concentrate sigma points around the mean (by using $\\alpha\\ll 1$) instead of spreading them out according to the covariance of ${\\bf r}$ as in the Gauss set with $\\alpha=1$, $\\kappa=3$ and $\\beta=0$. Anyway, it should be clear now that you can easily traverse between sigma point sets by choosing appropriate values of the parameters $\\alpha, \\beta$ and $\\gamma$. The following overview figure visualises the relations between sigma point sets. The most complex sigma point set, the scaled set, is at the top, the simplest, the min set, at the bottom. The min set cannot be reached by adapting parameters of the scaled set.\n",
    "\n",
    "<img src=\"SigmaPointSets.svg?dummy=1043\" width=\"300px\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluating the Unscented Transform\n",
    "\n",
    "Now that I know the UT and have a good grasp of what the parameters of the UT do I will evaluate the performance of the UT. I have a few hypotheses about the performance of the different sigma point sets. Clearly, the base and mean sets should outperform the min set, because they use almost twice as many sigma points which are also better spread around the mean. If [Julier and Uhlmann's (2004)](http://dx.doi.org/10.1109/JPROC.2003.823141) arguments are correct, then the mean set should also outperform the base set when $p({\\bf r})$ is Gaussian. I'm skeptical about the benefits of the scaled set, but can imagine that there are situations (mostly when $\\bf h$ changes quickly) in which it performs better than the mean set. I will evaluate performance based on ground truth as estimated from random sampling with many samples. For comparison I will also try to estimate the number of random samples needed to reach the performance of the different sigma point sets on average. My experiments will be based on one particular probabilistic model, because I have noticed through work with the model that the UKF had issues with it.\n",
    "\n",
    "This section is organised as follows: First, I will define the performance measure I use. A description of the probabilistic model follows. Subsequently, I will explain and perform the evaluations. All subsections contain the relevant implementations of the described concepts and procedures in Python. For preparation I first import the necessary Python modules and load a module (file) with auxiliary functions, mostly used for plotting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# general imports and initialisation of matplotlib\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy import linalg\n",
    "\n",
    "# use pandas for printing of tables\n",
    "import pandas\n",
    "pandas.set_option('display.precision', 5)\n",
    "\n",
    "# auxiliary functions used here, but outsourced for more clarity\n",
    "import UKF_aux as aux"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Performance measure\n",
    "\n",
    "I will evaluate the accuracy of approximations using a [Wasserstein distance](https://en.wikipedia.org/wiki/Wasserstein_metric), sometimes also called earth mover's distance, between the true distribution $p({\\bf o})$ and the approximating distribution $\\hat{p}({\\bf o})$, i.e., I will use $W(p, \\hat{p})$. The idea behind this distance is that it tries to quantify how much work you would need to do to make the distributions equal by moving probability mass from one to the other.\n",
    "\n",
    "To keep things simple I will assume that $p({\\bf o})$ and $\\hat{p}({\\bf o})$ are multivariate Gaussian distributions, because for this case the Wasserstein distance can be computed using a particularly simple formula depending only on true mean $\\bar{\\bf o}$, true covariance $\\Sigma_o$, approximated mean $\\hat{\\bf o}$ and approximated covariance $\\widehat{\\Sigma}_o$ (see [Djalil Chafai's](http://djalil.chafai.net/) [blog post](http://djalil.chafai.net/blog/2010/04/30/wasserstein-distance-between-two-gaussians/)):\n",
    "\n",
    "$$\n",
    "W(p, \\hat{p})^2 = \\|\\hat{\\bf o} - \\bar{\\bf o}\\|^2 + \\left\\|\\widehat{\\Sigma}_o^{\\frac{1}{2}} - \\Sigma_o^{\\frac{1}{2}}\\right\\|^2_{Fro}\n",
    "$$\n",
    "\n",
    "where $\\|\\cdot\\|_{Fro}$ is the [Frobenius norm](https://en.wikipedia.org/wiki/Matrix_norm#Frobenius_norm) of a matrix and I use the [Cholesky decomposition](https://en.wikipedia.org/wiki/Cholesky_decomposition) to compute the matrix square roots $\\Sigma^\\frac{1}{2}$. \n",
    "\n",
    "The true distribution $p({\\bf o})$ will rarely be Gaussian, but I can estimate its mean and covariance by sampling from $p({\\bf r})$, projecting the samples through $\\bf h$ and computing sample mean and covariance from them. It is clear that the Wasserstein distance for Gaussians defined above will only approximate the proper Wasserstein distance between the general distributions, but at least it tells me how well the first two moments of the distributions match which is particularly interesting in the context of (Kalman) filtering. Alternatively, I could try to estimate a distance from samples directly. The [Maximum Mean Discrepancy (MMD)](http://dl.acm.org/citation.cfm?id=2503308.2188410) may be a good candidate for that, but I don't currently see the necessity to introduce this extra complexity for the points I make here.\n",
    "\n",
    "Here is the implementation of the Wasserstein distance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def WassDist(mean, Sigma, mean2, Sigma2):\n",
    "    # ensure that means are 1D arrays\n",
    "    mean = mean.squeeze()\n",
    "    mean2 = mean2.squeeze()\n",
    "    \n",
    "    # check that covariances are positive definite\n",
    "    # by computing matrix square roots\n",
    "    try:\n",
    "        SC  = linalg.cholesky(Sigma);\n",
    "        SC2 = linalg.cholesky(Sigma2);\n",
    "    except linalg.LinAlgError:\n",
    "        return np.nan\n",
    "    else:    \n",
    "        return np.sqrt(linalg.norm(mean - mean2, ord=2) ** 2 + \n",
    "                       linalg.norm(SC - SC2, ord='fro') ** 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Probabilistic model\n",
    "\n",
    "In the following I will use a particular probabilistic model as a testbed for the UKF. This model is what we called the [Bayesian Attractor Model](http://dx.doi.org/10.1371/journal.pcbi.1004442) before and consists of a Hopfield dynamics $\\bf f$ with an interpolating observation function $\\bf g$. Both functions are nonlinear, mainly due to embedded sigmoid functions which limit the [range](https://en.wikipedia.org/wiki/Image_%28mathematics%29) of the model functions. In particular, I define the dynamics $\\dot{\\bf z}$ in continuous time as\n",
    "\n",
    "$$\n",
    "\\dot{\\bf z} = k\\left({\\bf L\\sigma(z)} + b^{lin}(g\\bf{1} - \\bf{z}) \\right)\n",
    "$$\n",
    "\n",
    "where $\\bf L$ implements competition between elements of $\\bf z$ and $\\bf \\sigma$ is a sigmoid. See the [paper](http://dx.doi.org/10.1371/journal.pcbi.1004442) for details. Here is an illustration of the phase space of the Hopfield dynamics in two dimensions:\n",
    "\n",
    "<img src=\"HopfieldDynamics.svg\" width=\"400px\"/>\n",
    "\n",
    "The dynamics has one saddle point between two fixed points and the further the state moves away from the saddle point the larger the dynamics pulls the state back towards the saddle and eventually one of the fixed points. Therefore, without defining hard limits for the positions the state $\\bf z$ can be in, the $\\bf z$ will typically stay in the displayed region.\n",
    "\n",
    "I define the observation function ${\\bf x} = {\\bf g}({\\bf z})$ as\n",
    "\n",
    "$$\n",
    "{\\bf g}({\\bf z}) = {\\bf M\\sigma}({\\bf z})\n",
    "$$\n",
    "\n",
    "where ${\\bf M} = [-{\\bf m}, {\\bf m}]$ contains opposing column vectors ${\\bf m}$ such that the values $\\sigma_i({\\bf z}) \\in [0, 1]$ effectively interpolate between $-{\\bf m}$ and ${\\bf m}$ while I obviously take ${\\bf z} \\in \\mathcal R^2$. Again, $\\bf z$ enters nonlinearly, because its effect is bounded by the used sigmoid function.\n",
    "\n",
    "So far I did not account for noise. To complete the probabilistic model I assume additive Gaussian noise, or rather, a quadratic Wiener noise process for the dynamics such that, now in discretised time, the model predictions at time step $t$ are:\n",
    "\n",
    "$$\n",
    "{\\bf z}_t = {\\bf z}_{t-dt} + k\\left({\\bf L\\sigma}({\\bf z}_{t-dt}) + b^{lin}(g{\\bf 1} - {\\bf z}_{t-dt}) \\right)dt + q\\cdot dt\\cdot {\\bf w}\n",
    "$$\n",
    "\n",
    "where ${\\bf w} \\sim N({\\bf 0}, {\\bf I})$ is isotropic, normal noise and\n",
    "\n",
    "$$\n",
    "{\\bf x}_t = {\\bf M\\sigma}({\\bf z}_t) + r\\cdot {\\bf v}\n",
    "$$\n",
    "\n",
    "with ${\\bf v} \\sim N({\\bf 0}, {\\bf I})$. The parameters $q$ and $r$ determine the amount of assumed noise in dynamics and observations and will become important below.\n",
    "\n",
    "A note about the underlying noise process: Typically you would use Wiener process noise for which $\\bf w$ would be multiplied by $\\sqrt{dt}$ instead of $dt$, i.e., in a Wiener process the variance of the state increases linearly with $dt$, but here the variance increases quadratically with $dt$. I originally used this, because it simplified my implementation of the UKF. I, thus, stick with it mostly for historical reasons. Practically it means that uncertainty about the state $\\bf z$ rises very quickly in the generative model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Implementation\n",
    "\n",
    "The following python code implements the above equations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# implement probabilistic model as object to have parameters in one place\n",
    "# and be able to automatically update parameters in response to changes of \n",
    "# other parameters\n",
    "class BAttM(object):\n",
    "    \"\"\"Basic implementation of the Bayesian Attractor Model.\"\"\"\n",
    "\n",
    "    def __init__(self):\n",
    "        \"\"\"Initialise parameters (a 2D case).\"\"\"\n",
    "\n",
    "        # dimensionality of state space\n",
    "        self._nd = 2\n",
    "        # dimensionality of observations\n",
    "        self.nD = 2\n",
    "\n",
    "        # dynamics: parameters\n",
    "        self.inhib = 1.7;\n",
    "        self.hopk = 100.0;\n",
    "        self.hopg = 10.0;\n",
    "        self.leak = self.inhib / (2 * self.hopg);\n",
    "        self.hopslope = 1;\n",
    "        self.hopL = ( -self.inhib * np.ones((self.nd, self.nd)) +\n",
    "                      self.inhib * np.eye(self.nd) );\n",
    "\n",
    "        # observations: parameters\n",
    "        self.oslope = .7\n",
    "        self.oshift = self.hopg / 2\n",
    "        self.set_standard_oM()\n",
    "\n",
    "        # noise / uncertainties as standard deviations\n",
    "        self.q = 0.0 # dynamics uncertainty\n",
    "        self.r = 0.0 # observation uncertainty\n",
    "\n",
    "\n",
    "    def set_standard_oM(self):\n",
    "        \"\"\"Distributes observation prototypes around the unit circle.\"\"\"\n",
    "\n",
    "        rho = np.linspace(0, 2*np.pi, self.nd, endpoint=False)\n",
    "        self.oM = np.vstack( (np.cos(rho), np.sin(rho)) )\n",
    "\n",
    "\n",
    "    @property\n",
    "    def nd(self):\n",
    "        \"\"\"Getter for dimensionality of state space.\"\"\"\n",
    "        return self._nd\n",
    "\n",
    "\n",
    "    @nd.setter\n",
    "    def nd(self, nd):\n",
    "        \"\"\"Setter for dimensionality of state space.\n",
    "\n",
    "        Changing the dimensionality of state space will also update the\n",
    "        connection matrix between state variables and the observation\n",
    "        prototypes.\n",
    "        \"\"\"\n",
    "\n",
    "        self._nd = nd\n",
    "\n",
    "        # update connection matrix\n",
    "        self.hopL = ( -self.inhib * np.ones((nd, nd)) +\n",
    "                      self.inhib * np.eye(nd) );\n",
    "\n",
    "        # update observation prototypes\n",
    "        self.set_standard_oM()\n",
    "\n",
    "\n",
    "    def dynfun(self, Z):\n",
    "        \"\"\"Dynamics function.\"\"\"\n",
    "\n",
    "        sigz = 1 / ( 1 + np.exp( -self.hopslope * (Z - self.hopg) ) )\n",
    "        dZ = self.hopk * (self.hopL.dot(sigz) + self.leak * (self.hopg - Z))\n",
    "        if self.q > 0:\n",
    "            dZ = dZ + self.q * np.random.normal(size=dZ.shape)\n",
    "\n",
    "        return dZ\n",
    "\n",
    "\n",
    "    def obsfun(self, Z):\n",
    "        \"\"\"Observation function.\"\"\"\n",
    "\n",
    "        alpha = 1 / ( 1 + np.exp( -self.oslope * (Z - self.oshift) ) )\n",
    "        X = self.oM.dot(alpha)\n",
    "        if self.r > 0:\n",
    "            X = X + self.r * np.random.normal(size=X.shape)\n",
    "\n",
    "        return X\n",
    "    \n",
    "    \n",
    "    def findSaddle(self):\n",
    "        \"\"\"Estimates location of the saddle point of the Hopfield dynamics.\"\"\"\n",
    "\n",
    "        oldq = self.q\n",
    "        self.q = 0\n",
    "\n",
    "        z = np.ones((self.nd))\n",
    "\n",
    "        zold = z - 1\n",
    "        while linalg.norm(z - zold) > 1e-7:\n",
    "            zold = z\n",
    "            z = z + 0.01 * self.dynfun(z)\n",
    "\n",
    "        self.q = oldq\n",
    "\n",
    "        return z"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example trajectories\n",
    "\n",
    "For better understanding I will now plot a few example trajectories of the state and observations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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x0tmYzz9J49xr0ZXbo52W6Em8KTKOTsQ1Swu6E088keeff75l4t148c47S8lS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\nuHEjgwcP3udt67aVEbA5ycq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QQggR56SgE0IIIYSIc1LQCSGEEELEOSnohBBCCCHinBR0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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f32ccc9dcd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# instantiate BAttM\n",
    "bam = BAttM()\n",
    "\n",
    "# noise\n",
    "bam.q = 1\n",
    "bam.r = 0.05\n",
    "\n",
    "# starting points: one at origin, one close to saddle, \n",
    "# one beyond saddle, but biased towards one fixed point\n",
    "z0 = np.vstack((np.zeros((bam.nd)), bam.findSaddle(), [10, 15])).T\n",
    "n0 = z0.shape[1]\n",
    "\n",
    "# evolve discretised dynamics for a couple of time steps\n",
    "nt = 30\n",
    "dt = 0.05\n",
    "T = np.arange(nt) * dt\n",
    "X = np.zeros((bam.nD, nt, n0))\n",
    "Z = np.zeros((bam.nd, nt, n0))\n",
    "Z[:, 0, :] = z0\n",
    "for i0 in range(n0):\n",
    "    for t in range(1, nt):\n",
    "        Z[:, t, i0] = Z[:, t-1, i0] + dt * bam.dynfun(Z[:, t-1, i0])\n",
    "    \n",
    "    # compute observations\n",
    "    X[:, :, i0] = bam.obsfun(Z[:, :, i0])\n",
    "\n",
    "# plot\n",
    "axes = aux.plottr(Z, X, T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The trajectories follow the dynamics that I expected from the phase space plot: When started from the origin (left), the dynamics moves the state to the saddle point, but, because of the noise, the state leaves the saddle and randomly moves into one of the two fixed points which are at $[10, 0]^T$ and $[0, 10]^T$ for the parameters defined above. Obviously, starting from the saddle (middle) simply skips the initial part of the trajectory, but otherwise behaves the same. Finally, when started from a position closer to one of the fixed points (right), the state will immediate move to the respective fixed point."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementations of UT with different sigma point sets\n",
    "\n",
    "#### Min set\n",
    "\n",
    "The min set will provide the basic structure. Note that weights are recomputed anytime the dimensionality $D$ is changed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class UT(object):\n",
    "    \"\"\"Implements the Unscented Transform (min set).\"\"\"\n",
    "\n",
    "    _name = 'min set'\n",
    "\n",
    "    def __init__(self, D):\n",
    "        \"\"\"Initialise weights.\"\"\"\n",
    "\n",
    "        # dimensionality in original space, will compute weights\n",
    "        self.D = D\n",
    "\n",
    "\n",
    "    @property\n",
    "    def D(self):\n",
    "        return self._D\n",
    "\n",
    "\n",
    "    @D.setter\n",
    "    def D(self, D):\n",
    "        self._D = D\n",
    "\n",
    "        self.setWeights()\n",
    "\n",
    "\n",
    "    @property\n",
    "    def N(self):\n",
    "        \"\"\"Number of sigma points.\"\"\"\n",
    "\n",
    "        return self.D + 1\n",
    "\n",
    "\n",
    "    def setWeights(self):\n",
    "        # weights for reconstructing the mean\n",
    "        self.wm = np.hstack((1.0, np.zeros((self.D))))\n",
    "\n",
    "        # weights for reconstructing the covariance\n",
    "        self.wc = np.hstack((0.0, np.ones((self.D)) / self.D))\n",
    "\n",
    "\n",
    "    def constructSigmaPoints(self, mean, cov):\n",
    "        \"\"\"Construct sigma points.\"\"\"\n",
    "\n",
    "        SP = mean[:, None].repeat(self.N, axis=1)\n",
    "        SP[:, 1:] = SP[:, 1:] + np.sqrt(self.D) * linalg.cholesky(cov)\n",
    "\n",
    "        return SP\n",
    "\n",
    "\n",
    "    def performUT(self, mean, cov, trfun):\n",
    "        \"\"\"Performs the unscented transform.\"\"\"\n",
    "\n",
    "        # construct sigma points\n",
    "        SP = self.constructSigmaPoints(mean, cov)\n",
    "\n",
    "        # transform sigma points\n",
    "        SP_tr = trfun(SP)\n",
    "\n",
    "        # reconstruct mean and covariance from transformed sigma points\n",
    "        return self.reconstruct(SP_tr)\n",
    "\n",
    "\n",
    "    def performUTforUKF(self, mean, cov, dynfun, obsfun):\n",
    "        \"\"\"Performs the unscented transform twice for use within UKF.\"\"\"\n",
    "\n",
    "        # construct sigma points\n",
    "        SP = self.constructSigmaPoints(mean, cov)\n",
    "\n",
    "        # transform through dynamics function\n",
    "        SPdyn = dynfun(SP)\n",
    "\n",
    "        # reconstruct mean\n",
    "        meandyn = SPdyn.dot(self.wm)\n",
    "\n",
    "        # error between sigma points and mean\n",
    "        errdyn = SPdyn - meandyn[:, None]\n",
    "\n",
    "        # reconstruct covariance from errors\n",
    "        covdyn = errdyn.dot((self.wc * errdyn).T)\n",
    "\n",
    "        # same procedure with transform through observation function\n",
    "        SPobs = obsfun(SPdyn)\n",
    "        meanobs = SPobs.dot(self.wm)\n",
    "        errobs = SPobs - meanobs[:, None]\n",
    "        covobs = errobs.dot((self.wc * errobs).T)\n",
    "\n",
    "        # compute cross-covariance between dynamic states and observations\n",
    "        xcov = errdyn.dot((self.wc * errobs).T)\n",
    "\n",
    "        return meandyn, covdyn, meanobs, covobs, xcov\n",
    "\n",
    "\n",
    "    def reconstruct(self, S):\n",
    "        \"\"\"Reconstruct mean and covariance from sigma points.\n",
    "\n",
    "        (D, N) = shape(S) where D is the dimensionality of the sigma points\n",
    "                          and N is their number\n",
    "        \"\"\"\n",
    "        mean = S.dot(self.wm)\n",
    "\n",
    "        Sm = S - mean[:, None]\n",
    "        cov = Sm.dot((self.wc * Sm).T)\n",
    "\n",
    "        return mean, cov\n",
    "\n",
    "\n",
    "    def printparams(self):\n",
    "        return ''\n",
    "\n",
    "\n",
    "    def __str__(self):\n",
    "        desc = 'Unscented Transform (%s with %d sigma points)' % (\n",
    "            self._name, self.N)\n",
    "\n",
    "        parstr = self.printparams()\n",
    "\n",
    "        if len(parstr) > 0:\n",
    "            desc = desc + '\\n' + parstr\n",
    "\n",
    "        return desc\n",
    "    \n",
    "ut_min = UT(bam.nd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Base set\n",
    "\n",
    "The base set only differs in the selection of sigma points and weights."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class UT_base(UT):\n",
    "    \"\"\"Implements the Unscented Transform (base set).\"\"\"\n",
    "\n",
    "    _name = 'base set'\n",
    "\n",
    "    @property\n",
    "    def N(self):\n",
    "        \"\"\"Number of sigma points.\"\"\"\n",
    "\n",
    "        return self.D * 2\n",
    "\n",
    "\n",
    "    def setWeights(self):\n",
    "        self.wm = np.ones((self.N)) / self.N\n",
    "        self.wc = self.wm\n",
    "\n",
    "\n",
    "    def constructSigmaPoints(self, mean, cov):\n",
    "        SP = mean[:, None].repeat(self.N, axis=1)\n",
    "        L = np.sqrt(self.D) * linalg.cholesky(cov)\n",
    "        SP[:, :self.D] = SP[:, :self.D] + L\n",
    "        SP[:, self.D:] = SP[:, self.D:] - L\n",
    "\n",
    "        return SP\n",
    "    \n",
    "ut_base = UT_base(bam.nd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Gauss and scaled sets\n",
    "\n",
    "For the full UT, as usually used, I introduce the three parameters $\\kappa$, $\\alpha$ and $\\beta$ where $\\kappa$ should actually always be $\\kappa=1$, as argued above. $\\beta=2$ is a standard choice such that the Gauss set is recovered by setting $\\alpha=\\sqrt{3}$ while the scaled set corresponds to the UT with $\\alpha \\ll 1$, e.g., $\\alpha=0.01$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class UT_scaled(UT):\n",
    "    \"\"\"Implements the Unscented Transform (Gauss and scaled sets).\"\"\"\n",
    "\n",
    "    _name = 'scaled set'\n",
    "\n",
    "    def __init__(self, D):\n",
    "        \"\"\"Initialise parameters and weights.\"\"\"\n",
    "\n",
    "        # these default parameters implement the Gauss set\n",
    "        self._alpha = np.sqrt(3)\n",
    "        self._kappa = 1.0\n",
    "        self._beta = 2.0\n",
    "\n",
    "        # dimensionality in original space, will compute weights\n",
    "        self.D = D\n",
    "\n",
    "\n",
    "    @property\n",
    "    def name(self):\n",
    "        if np.allclose([np.sqrt(3), 1.0, 2.0],\n",
    "                       [self.alpha, self.kappa, self.beta]):\n",
    "            return 'Gauss set'\n",
    "        else:\n",
    "            return self._name\n",
    "\n",
    "\n",
    "    @property\n",
    "    def N(self):\n",
    "        \"\"\"Number of sigma points.\"\"\"\n",
    "\n",
    "        return self.D * 2 + 1\n",
    "\n",
    "\n",
    "    @property\n",
    "    def alpha(self):\n",
    "        \"\"\"Scale parameter.\"\"\"\n",
    "\n",
    "        return self._alpha\n",
    "\n",
    "\n",
    "    @alpha.setter\n",
    "    def alpha(self, alpha):\n",
    "        self._alpha = float(alpha)\n",
    "\n",
    "        self.setWeights()\n",
    "\n",
    "\n",
    "    @property\n",
    "    def kappa(self):\n",
    "        \"\"\"Another scale parameter.\"\"\"\n",
    "\n",
    "        return self._kappa\n",
    "\n",
    "\n",
    "    @kappa.setter\n",
    "    def kappa(self, kappa):\n",
    "        self._kappa = float(kappa)\n",
    "\n",
    "        self.setWeights()\n",
    "\n",
    "\n",
    "    @property\n",
    "    def beta(self):\n",
    "        \"\"\"Scale correction parameter.\"\"\"\n",
    "\n",
    "        return self._beta\n",
    "\n",
    "\n",
    "    @beta.setter\n",
    "    def beta(self, beta):\n",
    "        self._beta = float(beta)\n",
    "\n",
    "        self.setWeights()\n",
    "\n",
    "\n",
    "    def setWeights(self):\n",
    "        a2k = self.alpha**2 * self.kappa\n",
    "        self.wm = np.ones((self.N)) / (2 * a2k)\n",
    "        self.wc = np.copy(self.wm)\n",
    "\n",
    "        self.wm[0] = (a2k - self.D) / a2k\n",
    "        self.wc[0] = self.wm[0] + 1 - self.alpha**2 + self.beta\n",
    "\n",
    "\n",
    "    def constructSigmaPoints(self, mean, cov):\n",
    "        SP = mean[:, None].repeat(self.N, axis=1)\n",
    "        L = self.alpha * np.sqrt(self.kappa) * linalg.cholesky(cov)\n",
    "        SP[:, 1:self.D+1] = SP[:, 1:self.D+1] + L\n",
    "        SP[:, self.D+1:] = SP[:, self.D+1:] - L\n",
    "\n",
    "        return SP\n",
    "\n",
    "\n",
    "    def printparams(self):\n",
    "        return 'alpha = %5.3f\\nbeta  = %5.3f\\nkappa = %5.3f' % (self.alpha,\n",
    "                                                                self.beta,\n",
    "                                                                self.kappa)\n",
    "    \n",
    "ut_gauss = UT_scaled(bam.nd)\n",
    "ut_scaled = UT_scaled(bam.nd)\n",
    "ut_scaled.alpha = 0.01"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Mean set\n",
    "\n",
    "The mean set holds $w_0$ constant by increasing the scale of the sigma points with the dimensionality. My standard choice of $w_0 = 1/3$ implements the Gauss set in two dimensions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class UT_mean(UT):\n",
    "    \"\"\"Implements the Unscented Transform (mean set).\"\"\"\n",
    "\n",
    "    _name = 'mean set'\n",
    "\n",
    "\n",
    "    def __init__(self, D):\n",
    "        \"\"\"Initialise parameters and weights.\"\"\"\n",
    "\n",
    "        # this default value implements a Gauss set in 2D\n",
    "        self._w0 = 1.0 / 3.0\n",
    "\n",
    "        # dimensionality in original space, will compute weights\n",
    "        self.D = D\n",
    "\n",
    "\n",
    "    @property\n",
    "    def D(self):\n",
    "        return self._D\n",
    "\n",
    "\n",
    "    @D.setter\n",
    "    def D(self, D):\n",
    "        self._D = D\n",
    "        self._kappa = D / (1 - self.w0)\n",
    "\n",
    "        self.setWeights()\n",
    "\n",
    "\n",
    "    @property\n",
    "    def N(self):\n",
    "        return 2 * self.D + 1\n",
    "\n",
    "\n",
    "    @property\n",
    "    def w0(self):\n",
    "        return self._w0\n",
    "\n",
    "\n",
    "    @w0.setter\n",
    "    def w0(self, w0):\n",
    "        self._w0 = w0\n",
    "        self._kappa = self.D / (1 - w0)\n",
    "\n",
    "        self.setWeights()\n",
    "\n",
    "\n",
    "    def setWeights(self):\n",
    "        self.wm = np.r_[self.w0, np.ones(2 * self.D) / (2 * self._kappa)]\n",
    "        self.wc = self.wm\n",
    "\n",
    "\n",
    "    def constructSigmaPoints(self, mean, cov):\n",
    "        SP = mean[:, None].repeat(self.N, axis=1)\n",
    "        L = np.sqrt(self._kappa) * linalg.cholesky(cov)\n",
    "        SP[:, 1:self.D+1] = SP[:, 1:self.D+1] + L\n",
    "        SP[:, self.D+1:] = SP[:, self.D+1:] - L\n",
    "        \n",
    "        return SP\n",
    "\n",
    "\n",
    "    def printparams(self):\n",
    "        return 'w0 = %5.3f with kappa = %5.3f' % (self.w0, self._kappa)\n",
    "    \n",
    "\n",
    "ut_mean = UT_mean(bam.nd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Naive Sampling\n",
    "\n",
    "For comparison I will use naive sampling. For that I will assume Gaussian distributions. I only need a function which takes mean, covariance, transform function and the number of samples as input and returns estimates of the transformed mean and covariance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def naiveSamplingEstimate(mean, cov, trfun, N=None):\n",
    "    # if no covariance, mean contains samples\n",
    "    if cov is None:\n",
    "        S = mean\n",
    "    # else sample from Gaussian using numpy\n",
    "    else:\n",
    "        S = np.random.multivariate_normal(mean, cov, int(N)).T\n",
    "\n",
    "    # project through transform function\n",
    "    Str = trfun(S)\n",
    "\n",
    "    # estimate transformed mean\n",
    "    meantr = np.mean(Str, 1)\n",
    "\n",
    "    # estimate transformed covariance\n",
    "    covtr = np.cov(Str)\n",
    "\n",
    "    return meantr, covtr, Str"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I can now verify that sampling and my performance measure $W$ work. I do this by applying the naive sampling estimate without transformation. When I increase the number of samples, the Wasserstein distance $W$ between true and estimated distributions should decrease.\n",
    "\n",
    "As test case I use the following mean and covariance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.  2.  3.  4.]\n"
     ]
    }
   ],
   "source": [
    "mean = np.arange(1, 5, dtype=float)\n",
    "print mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  0.  0.  0.]\n",
      " [ 0.  2.  0.  0.]\n",
      " [ 0.  0.  3.  0.]\n",
      " [ 0.  0.  0.  4.]]\n"
     ]
    }
   ],
   "source": [
    "cov = np.diag(mean)\n",
    "print cov"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "I will use an exponential increase in the number of samples and will repeat each estimate 20 times to estimate the variability induced by different samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "nsample = 10 ** np.arange(1, 6)\n",
    "nrep = 20\n",
    "Dis = np.zeros((nrep, nsample.size))\n",
    "for i in range(nsample.size):\n",
    "    for rep in range(nrep):\n",
    "        meantr, covtr, _ = naiveSamplingEstimate(mean, cov, lambda x: x, nsample[i])\n",
    "        Dis[rep, i] = WassDist(mean, cov, meantr, covtr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is a plot of the relationship between $W$ and the number of samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f32ac28ac50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Dismean = Dis.mean(axis=0)\n",
    "Perc = np.percentile(Dis, [5, 95], axis=0)\n",
    "plt.errorbar(nsample, Dismean, np.c_[Dismean - Perc[0, :], Perc[1, :] - Dismean].T)\n",
    "plt.gca().set_xscale('log')\n",
    "plt.gca().set_yscale('log')\n",
    "plt.gca().set_xlabel('number of samples')\n",
    "plt.gca().set_ylabel('$W$')\n",
    "plt.gca().set_xlim([nsample[0]-3, 2*nsample[-1]]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$W$ nicely tends to 0 as I increase the number of samples. It even appears to be a roughly linear relationship. So my sampling procedure and the performance measure work as intended."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Experiments\n",
    "\n",
    "I'm interested in the accuracy of the UT depending on\n",
    "- the nonlinearity of $\\bf h$\n",
    "- the amount of uncertainty, i.e., the variances of $p({\\bf r})$\n",
    "- the dimensionality of ${\\bf r}$ and ${\\bf o}$\n",
    "\n",
    "Although these dependencies may interact I will investigate them in isolation to keep the complexity of the corresponding experiments low. Further, I wish to quanitfy \n",
    "- the computational efficiency of the UT compared to naive sampling\n",
    "- the benefit of taking Gaussianity of $p({\\bf r})$ into account\n",
    "\n",
    "In the following I will go through these points in turn and will end in a demonstration of using different sigma point sets inside the Unscented Kalman Filter."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Effects of nonlinearity\n",
    "\n",
    "I will here investigate how the nonlinearity of $\\bf h$ affects the accuracy of the UT variants. \n",
    "\n",
    "It is hard to pin down an intuitive measure of nonlinearity, i.e., when is a function more or less nonlinear? I shall not attempt this here. Instead, I note that the observation and dynamics functions of the probabilistc model defined above are locally more linear for some inputs than for others. This is because their nonlinearity results from a sigmoid function which is locally linear around its inflection point and constant for very small and very large values, as shown in the following figure (red line)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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5REVMUZ3tcPIImkwrPGrtLUE62oLMLpRefLi9cXryNrheIiEvYora+Rba8rVy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\nQl4IIWKYhLwQQsQwCXkhhIhh/x8V57yFXN6SEQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f32ac050790>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sigmoid = lambda x, shift, slope: 1.0 / (1.0 + np.exp(-slope * (x - shift)))\n",
    "xx = np.linspace(-10.0, 10.0, 1000)\n",
    "plt.plot(xx, sigmoid(xx, 0, 1),                    # standard sigmoid\n",
    "         xx, sigmoid(xx, bam.hopg, 1),             # dynamics function sigmoid\n",
    "         xx, sigmoid(xx, bam.oshift, bam.oslope)); # observation function sigmoid\n",
    "plt.gca().set_ylim([-0.01, 1.01]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the dynamics function, the inflection point of the sigmoid is moved to the value of `hopg` which is 10 (cf. blue line). This means that the dynamics is roughly linear at its stable fixed points, because there one state variable $z_i=10$ while the others are 0 which is mapped to a constant value (0). In contrast, the saddle point ($\\approx [7.9, 7.9]^T$) resides in a nonlinear part of the dynamics, because the corresponding sigmoid has a large curvature between 6 and 9.\n",
    "\n",
    "In the observation function, the inflection point of the sigmoid is at `hopg/2` and its slope has been decreased such that the extent of the approximately linear region is slightly stretched (cf. violet line). Therefore, both, the stable fixed points and the saddle point of the dynamics, lie in the nonlinear region of the observation function, but it could still be argued that the saddle point lies in a more nonlinear region, because of greater curvature around this region. The point at [`hopg/2`, `hopg/2`$]^T$, on the other hand, should lie in more or less linear regions of the observation and dynamics functions.\n",
    "\n",
    "Based on these considerations I choose the following points around which I want to investigate the performance of the UT:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  5.           7.87196527  10.        ]\n",
      " [  5.           7.87196527   0.        ]]\n"
     ]
    }
   ],
   "source": [
    "Z = np.vstack((np.ones(bam.nd) * bam.oshift,             # point in linear region\n",
    "               bam.findSaddle(),                         # saddle point of dynamics\n",
    "               np.hstack((bam.hopg, np.zeros(bam.nd-1))) # a stable fixed point\n",
    "              )).T\n",
    "print Z"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I further choose a moderate variance around these points to (mostly) stay within the linear, or nonlinear regions, respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  0.]\n",
      " [ 0.  1.]]\n"
     ]
    }
   ],
   "source": [
    "C = np.eye(bam.nd)\n",
    "print C"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As first step, I estimate the true transformed distributions by sampling and projecting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "num = Z.shape[1]\n",
    "nsample = 10000\n",
    "\n",
    "# set noise after transformation to 0 to concentrate\n",
    "# on the effects of transformation\n",
    "bam.r = 0.0\n",
    "bam.q = 0.0\n",
    "\n",
    "# make full dynamics function\n",
    "# (model function is only the continuous change dz/dt)\n",
    "dynfun = lambda x: x + dt * bam.dynfun(x)\n",
    "\n",
    "# initialise output arrays\n",
    "meantrue = np.zeros((bam.nd, num, 2))\n",
    "covtrue = np.zeros((bam.nd, bam.nd, num, 2))\n",
    "Strue = np.zeros((bam.nd, nsample, num, 2))\n",
    "for i in range(num):\n",
    "    meantrue[:, i, 0], covtrue[:, :, i, 0], Strue[:, :, i, 0] = \\\n",
    "        naiveSamplingEstimate(Z[:, i], C, bam.obsfun, nsample)\n",
    "    meantrue[:, i, 1], covtrue[:, :, i, 1], Strue[:, :, i, 1] = \\\n",
    "        naiveSamplingEstimate(Z[:, i], C, dynfun, nsample)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is a visualisation of the result. The top row of panels shows the distributions transformed through the observation function and the bottom row shows the distributions transformed through the dynamics function. For the observation function I plot histograms, because the transformed distribution is effectively only one-dimensional. For the dynamics function I plot 500 sample points in 2D. All panels are augmented by a visualisation of the Gaussian densities with the mean and covariance estimated from the samples (black lines). For the observation function this shows the values of the corresponding probability density function. For the dynamics function I plot an ellipse which encloses 90% of the probability mass of the Gaussian."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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K7NmzB6mpqVV6PI3GGDfGkf6quxn0xo0b4qOPPhKnTp0St27dEocOHRKDBw8WLi4u4s6d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\nIiLKUyzUiIiIiPLU/wdo3C4HKNXWSwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f32ac292d90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "funlabels = ['observation function', 'dynamics function']\n",
    "pointlabels = ['[5, 5]', 'saddle point', 'stable fixed point']\n",
    "aux.plotSamples(Strue, meantrue, covtrue, \n",
    "                ylabels=funlabels, titles=pointlabels);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot confirms some of my considerations of the effect of nonlinearity from above: For the dynamics function the distribution centred at the saddle point transforms to a distribution that is clearly non-Gaussian indicating strong nonlinearity in the transformation whereas the Gaussian approximation is better for the other two test points, at least visually. For the observation function it appears that the Gaussian density fits the histogram density of the samples reasonably well for the point $[5, 5]^T$, but there are larger differences for the saddle and stable fixed points. Overall, however, the Gaussians appear to approximate these 1D distributions well.\n",
    "\n",
    "I will now repeat my analysis of naive sampling from above to determine how accurately I can reconstruct the true mean and covariance with a given number of samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of samples: [  4   6  10  18  34  66 130 258 514]\n"
     ]
    },
    {
     "data": {
      "image/png": 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FLxxadVfQO3nyJK1bt7ZzaRomTdOqfZ+EqEj7YA9aeVj/kJL57kRjU2+PWd9+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\nEEKIIPb/A+A+paSmgwV4AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f32abe117d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nsample = 2 + bam.nd ** np.arange(1, 10)\n",
    "print 'number of samples: ' + nsample.__str__()\n",
    "nrep = 20\n",
    "desDis = np.array([10.0, 1.0, 0.1, 0.01]);\n",
    "trfuns = (bam.obsfun, dynfun)\n",
    "\n",
    "estN = aux.plotSamplingDis(Z, C, meantrue, covtrue, nsample, nrep, trfuns, \n",
    "                           desDis, funlabels, pointlabels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot shows how $W$ decreases, i.e., how the accuracy of the estimated mean and covariance increase, as I increase the number of samples. The different lines in each panel represent the Wasserstein distance after transformation of the corresponding test points through the observation function (left) and the dynamics function (right). When transforming through the observation function the performance is worst for point $[5, 5]^T$ and best for the stable fixed point. The performance of the sampling approximation, therefore, appears to depend on the spread of the transformed distribution with larger spread leading to worse approximations. The same picture holds for the dynamics function where the point $[5, 5]^T$ has the smallest spread of the transformed distribution and sampling performs best compared to the other test points. The plot also clearly shows that the Wasserstein distance strongly depends on the intrinsic dimensionality of the distributions: The distributions transformed through the observation function are effectively one-dimensional and have overall lower Wasserstein distances than the two-dimensional distributions resulting from transformation through the dynamics function.\n",
    "\n",
    "Using linear interpolation I have also estimated the number of samples you need to reach a given average accuracy. These are helpful later to judge the efficiency of the UT approximations. For the observation function the numbers of samples are:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "       [5, 5]  saddle point  stable fixed point\n",
      "10.00       4             4                   4\n",
      "1.00        4             4                   4\n",
      "0.10        7             4                   4\n",
      "0.01      496           191                  23\n"
     ]
    }
   ],
   "source": [
    "print pandas.DataFrame(estN[:, :, 0].round(), desDis, pointlabels).to_string()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The table shows that I need less then 10 random samples to achieve an average accuracy of $W=0.1$ for all test points. The next step to $W=0.01$, however, requires considerably more samples where the numbers reflect the differences discussed for the plots above, especially, they show that you need many more samples (NaN means more than 514) to reach high performance (low $W$) for the point [5, 5]^T than for the other test points.\n",
    "\n",
    "For the dynamics function the numbers of samples are:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "       [5, 5]  saddle point  stable fixed point\n",
      "10.00       4             4                   4\n",
      "1.00        4             5                   5\n",
      "0.10      111           486                 395\n",
      "0.01      NaN           NaN                 NaN\n"
     ]
    }
   ],
   "source": [
    "print pandas.DataFrame(estN[:, :, 1].round(), desDis, pointlabels).to_string()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, the numbers follow the findings from above, as expected, and particularly show that I need only very few samples to reach mediocre accuracy, but need about 100 times more samples to reduce the distance by one order of magnitude for wide transformed distributions.\n",
    "\n",
    "So how do the different UT variants perform in these cases? Here I compute the KL-based performance measure for them:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "UTs = (ut_min, ut_base, ut_gauss, ut_scaled)\n",
    "nut = len(UTs)\n",
    "meanUT = np.zeros((bam.nd, num, nut, 2))\n",
    "covUT = np.zeros((bam.nd, bam.nd, num, nut, 2))\n",
    "Dis = np.zeros((num, nut, 2))\n",
    "for uti, ut in enumerate(UTs):\n",
    "    for i in range(num):\n",
    "        meanUT[:, i, uti, 0], covUT[:, :, i, uti, 0] = \\\n",
    "            ut.performUT(Z[:, i], C, bam.obsfun)\n",
    "        meanUT[:, i, uti, 1], covUT[:, :, i, uti, 1] = \\\n",
    "            ut.performUT(Z[:, i], C, dynfun)\n",
    "        Dis[i, uti, 0] = WassDist(meantrue[:, i, 0], covtrue[:, :, i, 0],\n",
    "                                  meanUT[:, i, uti, 0], covUT[:, :, i, uti, 0])\n",
    "        Dis[i, uti, 1] = WassDist(meantrue[:, i, 1], covtrue[:, :, i, 1],\n",
    "                                  meanUT[:, i, uti, 1], covUT[:, :, i, uti, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, I look at the performance on the observation function (in terms of $W$):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                    UT min  UT base  UT Gauss  UT scaled\n",
      "[5, 5]              0.0041   0.0041    0.0039     0.0225\n",
      "saddle point        0.0455   0.0029    0.0049     0.0133\n",
      "stable fixed point  0.0146   0.0057    0.0023     0.0042\n"
     ]
    }
   ],
   "source": [
    "utlabels = ('UT min', 'UT base', 'UT Gauss', 'UT scaled')\n",
    "print pandas.DataFrame(Dis[:, :, 0], pointlabels, utlabels).to_string()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The table shows that the UT with the mean set consistently produces an excellent approximation of the true mean and covariance ($W<0.01$) irrespective of the underlying test point and it only uses $2*D+1=5$ points for that. To achieve comparable performance with random samples I would have needed over 500 samples at the point $[5, 5]^T$. The other sigma point sets performed worse than the mean set. As expected, the min set is typically worst. The base set also outperforms the scaled set on 2 test points and outperforms the mean set at the saddle point. Because the Wasserstein distances are generally low, however, I don't want to overinterpret these differences.\n",
    "\n",
    "For the dynamics function the distances $W$ are:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                    UT min  UT base  UT Gauss  UT scaled\n",
      "[5, 5]              0.0780   0.0288    0.0081     0.0726\n",
      "saddle point        0.6257   0.2509    0.0978     0.3111\n",
      "stable fixed point  0.0801   0.0793    0.0617     0.3652\n"
     ]
    }
   ],
   "source": [
    "print pandas.DataFrame(Dis[:, :, 1], pointlabels, utlabels).to_string()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, the mean set performs best for all test points and particularly so in the nonlinear region around the saddle point. The distances increased by an order of magnitude for the saddle point which I expected based on the dependence of the distance on the dimensionality of the distribution. In the nonlinear region of the dynamics function (saddle point) the UT performs worst across all sigma point sets. Strangely, the scaled set is equally bad at the stable fixed point whereas even the min set performs reasonably well there.\n",
    "\n",
    "Here are the corresponding plots of the transformed distributions, but this time with the UT approximations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Ddu/u6tpMMbn5vyG/4JSMU3hk6wLe2f028UTs8BWcJEnStyADNEmSDiglJYWB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\nN/ux35c03AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f32ac050150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fun = 1\n",
    "ax = aux.plotSamples(Strue[:, :, :, fun], \n",
    "                     meantrue[:, :, fun], covtrue[:, :, :, fun], \n",
    "                     meanUT=meanUT[:, :, 1:, fun], covUT=covUT[:, :, :, 1:, fun], \n",
    "                     titles=pointlabels, ylabels=funlabels[fun], \n",
    "                     utlabels=utlabels[1:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the saddle point, I see that the ellipse of the mean set (blue) is very close to the true ellipse estimated from many samples (black). Whereas the base set (red) leads to a narrower distribution, the scaled set (green) leads to a wider distribution. Overall, however, the plot shows that distances below 0.5 give reasonably good approximations of the underlying mean and covariance of the true distribution in two dimensions.\n",
    "\n",
    "In conclusion, the results presented here indicate that the mean set produces the best approximations both in linear and nonlinear regions of the transformation function. The small variances of the source distribution $p({\\bf r})$ used here, however, meant that the transformation functions produced only moderate nonlinearities such that all UT approximations captured the transformed mean and covariance with an acceptable accuracy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Effects of large uncertainty\n",
    "\n",
    "Increasing the uncertainty in $p({\\bf r})$ means that the distribution spreads over larger parts of the domain of the transformation function $\\bf h$. For both, the observation and the dynamics functions defined above, this means that the source distribution $p({\\bf r})$ maps through larger nonlinearities. I consequently expect that the UT approximations get worse with increasing uncertainty and that the differences between the sigma point sets become more salient.\n",
    "\n",
    "I will test this now using the following standard deviations in $p({\\bf r})$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "stdsr = np.array([2.0, 4.0, 8.0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I can simply repeat the analysis from above by replacing different test points with different uncertainties. I will use $[5, 5]^T$ as the test point, because this showed originally no nonlinearities and lead to very good approximations. So here are the estimates of the true mean and covariance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "testp = 0\n",
    "num = stdsr.size\n",
    "nsample = 10000\n",
    "\n",
    "meantrue = np.zeros((bam.nd, num, 2))\n",
    "covtrue = np.zeros((bam.nd, bam.nd, num, 2))\n",
    "Strue = np.zeros((bam.nd, nsample, num, 2))\n",
    "for i in range(num):\n",
    "    C = stdsr[i]**2 * np.eye(bam.nd)\n",
    "    meantrue[:, i, 0], covtrue[:, :, i, 0], Strue[:, :, i, 0] = \\\n",
    "        naiveSamplingEstimate(Z[:, testp], C, bam.obsfun, nsample)\n",
    "    meantrue[:, i, 1], covtrue[:, :, i, 1], Strue[:, :, i, 1] = \\\n",
    "        naiveSamplingEstimate(Z[:, testp], C, dynfun, nsample)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The transformed distributions look like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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CC7Zjx45h+vTpKF++vGpbgwYN8PXXX7NgIyIiItIhwdN6ZGVlQS6X59kml8vx+vVrrYci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FAoFIT8x6mnnsqNN94ovOQUFHY3kiRx4oknUiqVePfddymXy7S0tKDRaJAkCa/Xy+joqNCq6uvr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\nAYGORI21/Fl6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f32a3639dd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "stdlabels = ['std=%d' % y for y in stdsr]\n",
    "ax = aux.plotSamples(Strue, meantrue, covtrue, \n",
    "                     ylabels=funlabels, titles=stdlabels, nplot=1000);\n",
    "ax[1, 0].set(ylim=(-25, 35), xlim=(-15, 22));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot clearly shows that with increasing uncertainty the transformed distributions depart more and more from Gaussianity. The observation function leads eventually to a distribution with three separate modes and the distribution resulting from the dynamics function also exhibits an increasingly complex shape.\n",
    "\n",
    "I can compute the UT approximations as before:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "meanUT = np.zeros((bam.nd, num, nut, 2))\n",
    "covUT = np.zeros((bam.nd, bam.nd, num, nut, 2))\n",
    "Dis = np.zeros((num, nut, 2))\n",
    "for uti, ut in enumerate(UTs):\n",
    "    for i in range(num):\n",
    "        C = stdsr[i]**2 * np.eye(bam.nd)\n",
    "        meanUT[:, i, uti, 0], covUT[:, :, i, uti, 0] = \\\n",
    "            ut.performUT(Z[:, testp], C, bam.obsfun)\n",
    "        meanUT[:, i, uti, 1], covUT[:, :, i, uti, 1] = \\\n",
    "            ut.performUT(Z[:, testp], C, dynfun)\n",
    "        Dis[i, uti, 0] = WassDist(meantrue[:, i, 0], covtrue[:, :, i, 0],\n",
    "                                  meanUT[:, i, uti, 0], covUT[:, :, i, uti, 0])\n",
    "        Dis[i, uti, 1] = WassDist(meantrue[:, i, 1], covtrue[:, :, i, 1],\n",
    "                                  meanUT[:, i, uti, 1], covUT[:, :, i, uti, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "leading to the following divergences for the observation function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "       UT min  UT base  UT Gauss  UT scaled\n",
      "std=2  0.0155   0.0155    0.0224     0.1312\n",
      "std=4  0.0229   0.0229    0.1023     0.4857\n",
      "std=8  0.1080   0.1080    0.1993     1.3719\n"
     ]
    }
   ],
   "source": [
    "print pandas.DataFrame(Dis[:, :, 0], stdlabels, utlabels).to_string()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here it is the base set and, to my surprise, the min set which produce the best approximations. The Gauss set tends to overconcentrate probability mass around the mean and consequently underestimates the tails and extra modes of the transformed distribution $p({\\bf o})$. Overall, however, the Gauss set at least gives a reasonable approximation also for `std=8`. The scaled set, however, completely overestimates the variance of the distribution for `std=4` and `std=8`, as shown in the following plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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WIhNCCCFERUjCdoNTFIUVfycwulN9XB0qPj/cZS4OOu7r0oAvd19EUZRaiFAI\ndUpJSSE2NrbET06OtOkUQtiGDOtxgzsYk0NqbjH9AryqvI/QNp78ejiF/Rey6dKs4o9UhagLcnJy\nyMjIKLXcbDbz+eefl1j2yCOP4Orqaq3QhBDCQhK2G5iiKHwXkciYrg2w01V99gKdVsPYbg34NiKR\nzk0NaDQyE4K4cWRkZBAeHl5q+fjx420QjRBClE0SthvY0fhc8o1mujcvXSumKAoRERH89ddfxMbG\n4urqSps2bQgJCcHO7tJ/Cw8PD0ttQld/N77Zl8ihuBw6+Bmseh5CCCHEzU7asN3A1vyTzIj2Pmiv\nqhGLiopi1KhRPPPMM+Tn59O1a1ecnJxYuHAhAwYMYM6cOYSHh5d4TKTVaBjRvh4//ZNs7dMQQggh\nbnpSw3aDOpuSz4W0Ambd1azE8vXr1/Pcc88xY8YMxowZY6lNS0hIoKioiISEBLZu3UpcXBwTJ04s\nse3tLd35NiKR08n5tKjnZLVzEUIIIW52UsN2g1oXmcpdQd7Y6/69xWvWrGHWrFmsXLmSBx980JKs\nXalRo0aMHDmSpKQkFixYUKJnqL1Oy11tvVgXmWqVcxBCCCHEJZKw3YByC03sOpNJ3wBPy7I9e/bw\nyiuv8M0339ChQ4drbq/X67n77rs5fvw4ixYtKvFeaIAXf5/NJKdQZj8QQgghrEUSthvQ9ugM2vsZ\n8HS2ByAxMZEpU6awePFiAgICKrQPvV7P22+/zVdffcW2bdssyz2c7OjYxMC2kzIxvBBCCGEtkrDd\nYBRFYX1UKgPbelleP/fcc4wZM4ZevXpVal8+Pj4sWbKE6dOnk5r672PQgW29WX8sTQbSFUIIIaxE\nErYbzJmUAgqNZoJ9XQD47rvvSE5O5qmnniqxnpKdjfL5FyiPPIrSO5T6949h4o5d3BF9Cscio2W9\n2267jbCwMP773/9alrVt5IxJUTiVnG+VcxJCCCFudpKw3WC2nkynV2tPNBoN6enpzJs3j4ULF6LX\n6y3rFPxvNaawkeQeP07KPSOI/+hD4j/6kD8DWuORl8cTW7fR8UKMZf3nnnuOvXv3Wh6NajQaerf2\nZKs8FhVCCCGsQhK2G0ixSeGvUxn0buUBwLvvvsvgwYMJCgoCQCkuRlnwDtqvv+HT9u1Y6OzE0ogI\nPl21CqOjI2d9fPi1/a2s7NGN7mfO4r5sOUpxMc7Ozrz22mvMmTOH4uJiAHq18mDn6UyMJrPNzlcI\nIYS4WUhmCGuqAAAgAElEQVTCdgM5GJONr4cDDd0diI6O5ueff2bGjBkAKGYzvPY6nD1H8lvzSHQr\nf07QJDc3Pgu5DbuLF2HuayhmM/3796devXqsWrUKgPoGPU08HTlwIdsq5yaEEELczKyWsC1dupRH\nH32UZ599ttx1PvvsM5588klmzJjB2bNnrRXaDWNbdAa9rqhdmzx5Ml5e/z/p++IlEBsH776D4uJy\n3X0V2duTOvMFuJgAi95Ho9Hw4osvsnDhQvLzL7Vd69Xag23RpSfNFkIIIUTNslrC1qdPH1588cVy\n3z9w4ACJiYl88MEHPPbYY3z66afWCu2GUGA0809sNj2au3PixAl27drFhAkTAFA2bIBt2+Ddd9A4\nOlZ8pw4O8O5C2LUb5Y91dOrUiY4dO7Jy5UoAuvu7cTguh3yjjMkmhBBC1CarJWyBgYG4XKNmJyIi\nwjLsRKtWrcjNzS0xl6W4tgMXsmlV3xl3JzsWLVrE5MmTcXFxQYmJgQULYd6baNzdK71fjcEAb74O\n776HcuECTz75JMuWLaOwsBCDox0BDZzZf14eiwohhBC1STVt2NLS0vD29ra89vb2Ji0tzYYR1S07\nz2QQ0sKds2fPsmPHDh566CFysrIofHE2GfeEEefiQmxsLLGxsZhMlasR07RuDY9Oglf+S7ugINq0\nacMPP/wAQM8WHuw4nVkbpySEEEKI/6eahA2QgVirqMBo5lBsDt393QgPD2fs2LG4uLhQ9L/VJCUm\n8kHiRcLDwy0/l3t6Vsq9I0Gngx/XMG3aND788EPMZjPd/N04EpdDXpE8FhVCCCFqS+nZv23Ey8ur\nxGj6qamp/zaYv0JkZCSRkZGW16NHj8ZgMFglxqrS6/W1GuPBEykE+rrhqFNYs2YNe/bswaWgANM3\n3/J9h1tBoymxvuaq1+XR6XQl4ja98Tp54x+i708/4unpye7du7nrrrto5+dGZJKR0ECPGj2vq9X2\ndawpl3vSAgQFBVmGVaktUiaqR6fTWX4v1LmQq/ehSOfMulNFpDs2waUoBb0537KuWuIGdV3Ha1FD\nmbianZ2dqq6dmu7llWWiIuuqJW6oO9exKmVCNQlbly5dWL9+PSEhIZw8eRIXFxc8PEonAGWdWHa2\nuttQGQyGWo1xW1QSXZo4s2zZMvr164erqys5b84jt3cvksyla74qWpNpMplKxt2gAcrQIeS++x4P\nPvggH374ISEhIXRu4sK2qCS6+lWiQ0MV1PZ1rAkGg6HMD4faJGWiekwmE7n2Xlx0DaTAzh3XomQc\nirPRaCDT0Zc4t1txLUqhQc7x0mXCxtR0HcujljJxteLiYlVdOzXdy8o0m5EyUb5rXceqlAmrPRJd\ntGgRL7/8MvHx8UydOpUtW7awceNGNm7cCECnTp2oX78+06ZN45NPPuGRRx6xVmh1WrFJ4UBMNp38\nXFi5ciUTJ05EOXsWtm4je9S9NX/ACQ/B9r8YHhxMZGQkp06domszA//EZssguqLOKSo2s+ZYHuc9\nuuNZEEtg8h80y9xHw9zjDGyhxz9jD4HJ63ApSuGMZwjro/MxmaXphri5mDQ6CnUupOSZUajYExpR\n86xWwzZ9+vTrriNJWuVFJuTSyF3P4X078fb2pn379ijPzYDx41BcXau1b71eT2xsbKnlPg/cj8Mn\nnzJmzBi+/PJLXnvtNZp6OXIkLpdOTdVRFS3E9eQWmpi//jw6s5nWKZuxU4rKXE+nmKiXdxr3gniO\npwxl4aYLTA9tgt5OVU2AhahRJo2OdKdmpDk1o1BnwM5cwLL9BWTWH4qzMQ3vvDO4F8bbOsybivzF\nqeP2nM2ku78bK1euZPz48ShRURAVBaNHVXvf2dnZJTorXP5J6d0Lok8xoWs3fvzxR/Lz8+nm78ae\nc1k1cEZC1L7cQhNzfjtDUy8HJnZ2KTdZu5LenM/j3VzRaODNdecoKpYaZXFjOnyxiOM+A8jR16NR\n9lGCkn4jMGUDs+9wpm3yWrzyz5Ls0ppo71DisqrQiU1UiSRsdZiiKOw9n0UzpwL27t1Lly5dyP9w\nKRlDhxKXnFzp4TsqSu/iQsawoRj+9z8CAgL4+uuvaVffjn3nszBLT1+hckaTmbc2nCewoQuTQnzR\nVrATDoC9TsMzfZvi6mDHB3/Gyv93cUMxmRU+2RHHT1H5NMvYi3/GHgxFyWj598uJTinGsyCOlmlb\n8ck7zZI9OWyMkiG4rEEStjrsXGoBDjot29f9SN++fdn08ccU/3OIpfFxVR++owKys7P5MDYG45Gj\ntNXZ8fHHH+NgysVFr+NMSn6tHFOImqAoCh9tj8NFr+Ph2xpVuMf0lXRaDU/28SMjz8g3exNrIUoh\nrK+o2MzbG84Tl1HEjNvdcDWmXnN9DeCVf56nbzOw5p9kvtuXKENz1TJJ2OqwiAvZdGpqYPX//seQ\nIUMIOXWav29pTnElumRXlUmnY3eLWxidn096ejoXLlygc1MDETLrgVCxLSfSOZ2cz1OhTdBpq954\nWm+n5fkBzdgWncGBC/J/XtRtJrPCe5tjsNNpmD2oGU72FS8b9V11vDmiBbvPZrLmUEotRikkYavD\n9p/PwpAfj729Pe3q16dFcgoHmjax2vEPNm3CLalphDRvztq1a+nSzMB++fASKhWTXsCKPRd5tl9T\nHO2r/6fPzcmO6aFNWLI1lrRcYw1EKIRtfLIjnoJiM9NDm2Cvq3zZ8HCyY87g5mw4lsqWE+m1EKEA\nSdjqrMz8YmIzCtmzbhX33Xcfrmv/4LBfYwrt7a0WQ5GdHf808WOCkzPr1q2jdX0nLmYWyoeXUB2T\nWWHJ1lge6NKApl41N15gkK8L/QI9Wb4jXh4HiTppY1QaxxJyeb5/0yola5d5u9jz0iB/VvydwOlk\naRpTGyRhq6MOxGQT1NCJP9b+xj0DB+K8eQt7mvtbPY69zf3pkZqGt4MDB/dH0N7PwMEYqWUT6rL2\naCr2Oi0D2paePaW6RnWqT3xGIbvPSC9pUbecTs7n670XeX5AU5z01W9K4+fpyGN3NGbBxvPkFMp0\nhTVNErY66sCFbByyLnDrrbdSf/8BioKDyHR2tnocWU5OnPHx4dmAAH744Qc6y2NRoTIpOUZWH0zi\n8V6NK9UjtKLsdVqe6NWY8F3xMqeuqDOKis28vyWGiT198fOsuVrnnre407mpG5/ukDHaapokbHWQ\nyaxwKDaHo1vXEDZiBPzwIzl33WWzeCL8m3J7Ugq///47bevpORKXQ7FJHg8JdVi5J4GBbb3wdXeo\ntWO0aehCxyYGVh9IqrVjCFGTvotIpImXA3e0dK/xfT/YvSHRyXn8fSazxvd9M6twwhYfH8///vc/\nli1bxurVq4mPl+zZVk4l5+PhqGX31g0MadIUiospahdss3jOe3lhZ2/HPc38ObRvJ/Xd9EQn5dks\nHiEui7qYy7GEPO7pUL/WjzW2WwM2n0gnPqOw1o8lRHWcSs5j68kMHru9cZWGtrkeB3st03r7sXxn\nPLnyaLTGVChhi4iIYNasWcTHx2MwGIiLi2PWrFns27evtuMTZTgYk41rQQIhISE4//EHjLwHaqHQ\nVZhGQ+5dA3nY3Z1ffvmFjtKOTaiAoih8uTuBsd0a1Eiv0OvxdLZnePt6rNxzsdaPJURVmRWF5X/F\nM657Q9ydam92yoCGLnRt5sY3+2SswppSob9i3377LTNmzOCpp55izJgxPPXUUzz//PN89913tR2f\nKMPBmGxO793AyH79YOcuGHy3rUMir1cvmiVc5MDmLbRtoOdgbI6tQxI3uX3nsyksVrizlYfVjjk4\n2JvopDypYRaqtSkqHZ1WQ+/WtV8uxnVrwK4zmTKgeg2pUMKWlpZGYGBgiWVt2rQhNfXaIyGLmpdd\nUExsWgGHt/1KaFER3H47Gjc3W4eF4uKCtncvpjRrRuyRXSRkFpKRL3PMCdswmRW+2XeRMV0b1EpH\ng/I42GkZ1bm+1CoIVcorMvFdRCKP3V65KdmqyuBox/1d6vP5rgQZ9qYGVChha9asGb/++qvltaIo\n/Pbbb/j7+9dWXKIch2Jz8CCTO3rehv6P9TBsqK1D+tewYQxT4LdffibY15XDUssmbGTXmUwc7bR0\naWaw+rH7tvHiYlYRkfG5Vj+2ENfy0z/JdGziSnMfJ6sds1+AF5n5xTJ6QA2oUMI2adIkNm/ezGOP\nPcasWbOYPHkymzdvZtKkSbUdn7jKodgcUo7vYWznzpCXB5072Tqkf3XsgKujIxk7dxHUwIFDsVJA\nhfWZFYXVB5IY3blBrTSovh47nYaRHeux+qD0GBXqkZprZN2xNB7o2sCqx9VpNYzv3pCVey5iMkst\nW3VUqMWhn58f7733HtHR0aSnp+Pp6UmrVq2ws6u9BouiNEVROHghi6gdv9HTox8MGYxGq56RWTQa\nDboRw3l05UpSLxzmUGYTFEWxyYemuHntPZeFXqelYxNXm8XQq5UHq/YnEZ2UR6v61h8fUYirrT6Q\nRL8AT3xc9VY/dpdmBn4+lMz2Uxn0ae1p9ePfKCr8aW9nZ0dgYCA9e/YkMDBQkjUbiMsoJL+ggJ5t\nm2P351ZVdDYoZdAgbi8y8vf6n7HTaYhJlyEOhPUoisIPB5K5t1M9m35RsNdpCWtfj//JuGxCBZKy\ni9h5OpMR7evZ5PgajYb7uzbgf/uTpJatGtRTPSOu61BcDsWJx3moZSu45RY0vr62DqkUTcMGaNu0\nge1/0a6RM4ekHZuwoqPxuRQUm+nqb/uOOKEBnpxKyic2vcDWoYib3A8HkhgQ6IVbLQ7jcT3Bvq74\nuNqz9aRMDl9VkrDVIfvPZXBm3yY6JyWps3bt/+lHDGeMhwd2meelHZuwqp8PJTPsVh+r9gwtj4Od\nlruCvPjlcIqtQxE3seTsInafzWJ4ex9bh8J9nRuw+mCy1LJVkSRsdUSxSSEyPpcOHhrsD/4DfUNt\nHVL5QvvQ3mQmdvuvRF3Mw2gy2zoicRO4kFbAmZQCellx3LXrGdjWm91nMknPM9o6FHGT+uVwCv0C\nPDE42r4ZU5CvC17OduyWKauqRBK2OiI6OQ8lL5WH6nmS1/5W4jIyiI2NtfyYTOqZ/kPj4oKxWzcc\n/9yEr7uek4kyaKKofb8eSeGuIC/0dur5s+buZMftLT1YF5lm61DETSgzv5ht0RkMaWf72rXLwjrU\n48d/kmVctipQz182cU0Hz2eSeGw37S8m8mtRIeHh4SV+iovVNUityz1hDHVwpL4uh8Nx0o5N1K7s\ngmL+PpPJwLbe1duRouBUVIR3Tg728fE4GKtfMzY42JuNUWlS0yysbu3RVG67xR0vF3tbh2LRuakB\nRYEDMn1hpVmtjvSff/7hiy++wGw2ExoayogRI0q8n5WVxeLFi8nIyMBsNjN06FB69+5trfBUb9eJ\nizQpSsY5Pp5TLUJsHU4per2e2NjYfxc08aOFVkvm/i2kMcLqY/+Im8vG4+l083er0tyImvx8OlyI\noXViEs3S0tAoCrkOetyOn2R6cjJGnY5zPt6caNAAqpDA+Xk60tTLkV2nM+klQxoIKyk0mll/LJU3\nh7ewdSglaDQaRnTw4ZdDKXRuavvOQXWJVRI2s9lMeHg4L7/8Ml5eXsyaNYsuXbrg5+dnWWfdunU0\nb96cMWPGkJWVxfTp07njjjvQ6XTWCFHV8o0mEnLhP64K+d27YVLhNcnOzuarr74qsayvpwc+m9aw\nt/ld5BWZcNarL25R95nMCusiU3lhQLNKbadkZ8OKlTRc/QNtXJyJbNSIte2CyHFwAI2G8ePHs3LF\nCtzzC2iekkKHmFgaTnoMZfw4uP8+NI6OFT7W3cHe/HAwSRI2YTVbo9Np08AZXw8HW4dSSs9b3Fm5\n5yJnU/KtOutCXWeVR6KnTp2iYcOG1K9fHzs7O0JCQoiIiCixjqenJ3l5lyZMzs/Px2AwSLL2/47F\n55J/8TQ9kpPIv+N2W4dTYaeaN2egsZDGrsg0PaLWRJzPwsvZjhb1KvaHX1EUlHXr4d5RkJZG0sIF\nfN+1C0f9GpPj6AhX9jDVaMh0duKfpk34ukc3Ut54DY4fh3tHo+zcVeEYOzc1kJVfLJPCC6swKwq/\nHUll2K3qabt2JXudlruDvPntiPSgrgyrJGxpaWl4e//btsTLy4u0tJKNcPv27UtsbCyTJ09mxowZ\nTJgwwRqh1QlbDp3DOfEkjhnpFAYHV3t/iqJQ7GIkzy+XrNaZZASnsy57LVmtM8nzy8XoakSh+g1C\nL/h400jvgGNspLRjE7Vm/bE07gqqWNs1JTcXXpwNX3wJ772H5uWXMNWvX+FjFfv5oZk/D16ZA2+/\njTJvPkpR0XW302k19G/rzYZj0vlA1L6DMdno7TS0beRi61DK1T/Qi73nskjLlR7UFaWaTgdr1qzB\n39+fZcuW8fbbbxMeHk5+vvQuBDgUm80IXQ70CYVq1DqaHExkt8xkecZHpHVJocirEI1Jgz7Tnob2\njdCYNBR5FZLeOYXk3hfZkbcdk2PVOzMoGg3J7YKpt2sdR+IlYRM172JWEWdS8rntFvfrrqvExMDD\nE8FggBVfoGkbWOXjarp2ga+/gvR0mDwFJSX1utuEtvHk77OZ5Baqp0e3uDGtPZrKkGCfas/2oS8u\npllqKu1jYul+5ixuv68lKC4e34wMtObqdaIxONoR0sKDjVHyJaairNKGzcvLi9TUf/+gpaam4uXl\nVWKdkydPEhYWBmB5fBofH0+LFiUbTEZGRhIZGWl5PXr0aAwGQy1GX316vb7KMWblG8k12zPs4mmc\nn5hb7mPisgrm5WVmezPZLbPI983FKd6ZkW73seH3DSXW7dC7I0dOH7W8NhqKKOpXRHJIIk4Jzhii\n3dAaddc91tUMYWH0nf0ye7ONFGsd8HSp+jx21bmO1rRq1SrL70FBQQQFBdXq8W62MnGl7w+ep39Q\nfXw8r52wmY4dI2/yVBwen4r+gftLvHe5TCmKQnZ2NtnZ2RQWFrJt2zYSEhJwc3PDxcXFsq4lboMB\nZemHFH24lKLHJuMS/gnapk3LjcFggK63ePH3hXxGdGpUjbP+l5SJspVVJq5mZ2enqmtXU/cyNj2f\nsykFvD7Sr0pD3ChZWbiuX8+EnbtpmJVFopuBNGcXCuztsUtKIuBiIt45OXjm5XHOxxvntkG4jh+H\nxr7yPVHv7daEmauP8dCdt2Cvq5n6IzWViWs166pKmbBKwtaiRQsuXrxIUlISXl5e7Nq1i6eeeqrE\nOr6+vhw5coSAgAAyMjKIj4+nQYPSPQvLOrHsbHV3DzYYDFWOcW3EWcxxx3HNzSGvTWtMCQllrlfW\nmDaKopDfKI+swAwcLzpR76+G6Ip01O98/UdA9tl6Ql36EfN7HDktskm+IxHDcXec4p3LPVZZitsG\n0sjBHp+iZP4+mcjtLas+qGl1rqO1GAyGMj8catPNViYuM5rMrDuSyOvDbrnmvpTISHj6WZj5Aqnd\nupIRFfXvPoxG/vrrLzZt2kR8fDw6nQ43NzccHBwoLCzk5MmTZGZmYmdnh5+fH+3bt6dBgwZotVd8\nuDz0IIrBlZxx42HpUjTNyk/aQlsZ+GRHPKEtXWpkrlMpE2WryAdgcXGxqq5dTd3LH/bGE9rGk8L8\nXCozk7OSkwMrVsKPP2IfHMzOli044+NdopNb/fHj+WHlSgAci4y0TkrEf+1asleshAkPwfBhaCox\nz7iPI/i669l0OK5anw1XUlOZuNb4qFUpE1ZJ2HQ6HRMnTuSNN96wDOvh5+fHxo0bAejfvz9hYWEs\nXbqUGTNmYDabGTduHK6urtYIT9W2/HOWHgVJaEL7oKnE41CzzszanN/IbpmFZ4QP+qyq1WzpinS4\nR3ngHOdMRvs0Cn0KKVKu32bHQqsl+dZbaXDsb460bVVjhVKIfeez8fNwoPE1esEpJ07AM8/Cyy+h\nueN2MmJjLeMWHjt2jCNHjtCqVSsaN25Mjx49SvzNGT9+PCtXrkRRFDIzMzl//jzvvfceH3zwAf/5\nz38YMWKEJXHT3HMPip0dPPEflI8/QuPXuMx4ghq5UGxWOJmYR5uG6m1fJOqmAqOZrSczWDiyZYW3\nURQFNmyARR/AbT3gyy9JV8xEh4df+1h6ew77+dH1kUdonJEBHy6FH35AmTUTTbt2FT7+oP/vfCCf\nDddntXHYOnbsSMeOHUss69+/v+V3Nzc3Zs6caa1w6oxz2VoeSoyG8VMqvI3JsZi0Tqn44IXPrvpo\nTdWvarbP0uOzsz6ZQRl8k/kVGkctuoKK/fdpOOYBer76Lt/Fjrj+ykJU0KaoNPoFlD9MhhIXD9Of\ngednoLmid/X58+fZtWsXXl5eDBw4kOnTp5cakuZKGo0GDw8PPDw8mDhxImfOnGHBggV89tlnvPnm\nm9x6662X1hs2DKWgEJ58EuWzcDQepT+ANBoNfQO82HQ8XRI2UeN2nM4gsKEz9QwV+4Ku5OTAvPkQ\nHQ1vz/830bpyTM0K0AQHoyz9EDZuhOdmoNx7L0x8uEKVDF2bufHpznjOpxXQzKviQ+XcjFTT6UCU\nFpuShUljT2DKBWh/a4W2MboaSemRjFOCM4NcBtdIsnaZxqzF/YgnQQ7BpNyWhNG1Yr173G6/nbbZ\nSWTn5JOUXYnaOSHKkZxdxKnkfHqU09lAycqC6U/DhIfQ9O0LXHpM/Oqrr7Jr1y7uuOMOBg4ciI9P\n5YY90Gg09OrVi19++YUHH3yQ8ePH8+6771pmGtGMHgWhofDMcygFBWXuo09rD/4+m0l+kXQ+EDVr\n/bG0Cs/2oZy/ABMud8L5slK1YmXRaDRoBgyAr1bCgQPw9LOXxjq8Djudhn4BXtKDugIkYVOxn7Yd\nwi/tHHahvSv0TcXoVkRa12QMJ91wPWuokTYyV9OgoatTN9yOe5DWLZkit+snYBqtlvhWLWiUGM1R\nGY9N1IAtJ9K5o6U7DmU0qlZMJpj9EvTojua+S+1ETp06xZAhQ9DpdNx7770lBu2uCq1Wy+jRo1m3\nbh179+5l7Nix/w5V9PhUaNAA5r9VZttOT2d7gnxd2XFaJsAWNedUch7ZBcW097t+UyLl4EF47DEY\nNxbNzBcqNQj09Wjq1YPFH0DTJjBxEsrFxOtu0y/Ak79OZVBglOnbrkUSNhXbdyaFO1LOXPrGfh3J\nxcmkdUnB7ZgHzvG1/6jFKcEZ96OepHdJqVBNm3tYGMEn93FExmMT1WRWFLacSCe0jVfZKyz9GIpN\n8NSTAOzcuZN77rmHyZMnM3v2bOyr0JutPI0aNeLrr7/m1ltvZfDgwZw+fRqNVgtzXoKTJ+H7VWVu\n17eNJ1tOpNdYHEJsOJZGvwAvdNprf1FXdu6EF2bBq6+iGTG8VmLR2Nmhee5ZGDEcHn0M5dz5a65f\nz6AnoKEzO05n1Eo8NwpJ2FRKURSyNB50j4uCTh2vuW6xUzGrs1fhFuWBU6KzlSIExyQn3I55kNY1\nmXTTtT98mg0fRpf4KP45m1Zuj1IhKiIyPhdnvY5bfErXCijb/7rUgHreG2js7Pjtt9+YOnUqH330\nEWPGjKmVeHQ6HbNnz+bJJ5/k3nvv5dChQ2icnGDBAvj8c5SjR0tt06mpgcTsImLTy35sKkRl5BeZ\n2H0mk77XaNMJXJqdY+5r8O47aLp3q/W4NGPHwKOPXOqMExNzzXUHBHqxScZkuyZJ2FRqx/6jOOjs\nadql7TW7SZvtzaR1SaG7Uw+cEqyXrF3mdNEZ11Nu/JC1CrN9+W1yNHZ2ZLnaY87LIyFL2rGJqrtU\nu+ZZ6pG/cjER3ngDXn8VjYcHP//8My+//DLffPMNISEhtR7XAw88wPz583nwwQc5ePAgmsa+MHMm\nzH7pUpu6K+i0Gnq19ODPk1KjIKpvx+lMgnxd8XQuv/ZY2b8f5r4KCxegqYEZcypKM2wYTHoEHv/P\nNR+PdmxiICXXyPk0+RJTHknYVOr3v6MISjmNJrRPuesoGoX0jqk4JjvSybGzFaMrySXGlVb61qR1\nSkXRlKw90+v1xMbGEhsbS+Ft3WkRc5SIM9cfFV6IsuQVmdh3Pos7W5XsgamYTPDKf+H++9G0b8/a\ntWv573//y9dff02wFT+cBg4cyDvvvMNDDz3EkSNH0PTpDbffDvNKt2fr08aTbSfTMZmlxllUz6bj\n1+kxferUpSnZ3ny92p0LqkITNgLuvw+eml7qy8tlOq2G0DaeUst2DZKwqdTpiwV0jT8OXbuWu05W\nYAYakwbD8etPy1Pb7nTujdaoJattyRqD7OxswsPDCQ8PZ2t2Nh1jIjlw4qKNohR13a4zmQT7uuLu\ndFWt8zffgmKGB8ezc+dOZs6cycqVK2nbtq3VY+zfvz/z5s3joYce4ty5czDtP3D6FKwvObtIUy9H\nvFzsORQr7TpF1Z1PLSA110jHJmWP7q8kJ18a3ubZZ9F06WLl6P6lGTsGenSHGS+gGMtu99y3jRd/\nncqgqFg6H5RFEjYVSk1NRePlT9uGzsQlJVlqqGJjYy0jJ+c1zqXQuxCPQ15oqPneoJWl0WjwOOxF\noVcheX5l9wTV6PXkXzzBqdRiaccmqmTryQz6tL6qdu3U6UsjtL/yCieio5k6dSoff/yxVWvWrjZ4\n8GCefvppxo4dS3peHrw6F959DyUpqcR6fVp7si1aOh+Iqtt8Io3Q1p5ldjZQCgrguedh5D1oBvQv\nY2sre+pJMLjC2wvK/Axo4KbH39uJfefLroW72UnCpkK/bN6FCwpOHQMstVOXf4qLizG6GskOyMTz\noDfaYvXcQm2xFq8D3mS3ycRoKLud2jlnHY4FuVxIr8ykKUJAYtalRvqdmv5bk6AUF8Orr8HUKaQ6\n6JkwYQJz586lZ8+eNoz0kvHjxzNkyBAmTZpEUfPmcO/IUo9GQ1q4s/9CtkwIL6rEaDKzPTqD0Dal\nH4cqinJpUFy/xpemjVIBjVYLc/8Lh4/A6h/KXKdvgCebj8uXmLKo59NeWOw6dI4OCccp6tih1HtF\nSvZOPj0AACAASURBVBHpHVMxHHfHPqfmhieoKXa59hii3EnvkIZZV7paO611K4Jjj3EkOqmMrYUo\n37bodEJauJecJPrbb8HFBePgu3n00UcZOXIkYWFhtgvyKi+88AJeXl7Mnj0bHp4ACQklHo26OdkR\n7OvK7rMyJpuovIjz2TT1cqShexnTs/24Bk5GX5qWrRbG5KwqjYsLvPM2fPJpmT2ou/m7cSo5n5Qc\n6Zx2NUnYVMZkMlFY5ESgvhDFyanU+3/mbkGfqcc5Tr3T2jjHu6DP0JMVWLoHnJOHB44XT7DvwGkb\nRCbqKkVR2HYyg96t/61JUGLj4MuVMPtFXnv9ddzc3Hj22WdrNY4rO9Fc+ZOTU3Y7NK1Wy6JFi4iI\niOCbVavg5ZfgvUUoGf+WjT6tPdgqY7KJKtj8/z2mr6ZERcGy5TB/Xo0OiltTNE2awKyZMGs2SkbJ\nLysOdlpCWrhLD+oyWG0uUVEx+/cfoNgviI7NMrj6oWFB/XzOG8/idkz9k+S6HfMgJSSRk4UnSr2n\ndy7mVLEzJrNy3UEehQA4mZSPVquhZb1LX2IURYG33oYHx/PTvr1s2bKFtWvXWiZjry3Z2dllzjs6\ndepUMjJKfsB4eHjg6uqKq6srn376Kffccw/BK1dya/9+8MFimPMycGlMtqXb40jKLqJ+BeeAFCIt\n18jJxDxm9GtaYrmSm3tppo8Zz6Fp1rScrW1P06f3pRkX3ngD5e23StQC9g3wZOGmGO7tWE9VtYO2\nJjVsKvPH5t24F+Xh07tkGxyT3kRmUDp3uw5RVbu18mhNWjwOe7Exdz0mfcn2OQ363YFnXibn4uUb\nlKiYbSfTubOVx79/vDdugpQUznTvxpw5c1i2bBnu7rbrLX1lb+jLP1cmcC1btuT111/n8ccfJ3vs\nGNizF+XAQQDsdVp63uLO9mgpD6LitkVn0KO5Gw72V30eLFgIHTui6d/PNoFVxn+egPiE/2PvvMOi\nuPM//pptLCxLB2lSBBXEhr2X2FJN1TTLqblcYnKJxvRLVfO7S2xpl6KxpJjkTCyp9l4TjR0rSlc6\nC7uwfef3B4oii4ICCzKv59nngZnvzL53dmbnM5/vp5RP315GTIA7KrnA8ewyFwlrnDT+O38zIze1\niLjS8wg+lW8+Je10uJ/zIFzZ0kXKao9K50YHdSeKE4oQuRRo3a5XLwKzjrFv60EXqpNoKljtDnad\nLWZAbLlnWSwthQ8+wPrcVJ785z95/vnnXZoRWlNGjhxJ//79eWn6dJg6pTxT7kLT+IGtfdh6Widl\nT0vUCFEU2XyyiMFXTIeKGzbCkcMw7TkXKasdgkoF78yETz8rb0Z/cbkgMLitL5ulUIFKSAZbI+L8\n+fPIfaNIbFX5IjQGl2HVWtGedn29tdrSx70vdo0NU6ixYplSqURtyedIuhRoLXFtDmQYCPNxo4XX\nhenChYugew/eXbOali1bMm7cONcKrAVvvvkmJ0+eZHlRIfj7w7IfAGjbwgObQ+RsvlTlXeLaJOcZ\nsTtE4lpc6m4j5ueXt0N7600Ej4bvenO9CFGR8Pjf4a23Kh5gAAbE+rAnpVhqCH8ZksHWCDAYDGRm\nZrL8x+UUhsbRIj6souaaQ2mnJF6HzxFfBEfTm8tXCAq8j/hREqerNDUa2TWWFM9QrJZrN46XaN5s\nO62r6GwgpqbCL7+yt1cPVq1axaxZs5pUjIu7uzsfffQR02fMIHvMo7B4CWJ+AYJQ3qpKqskmURM2\nnSxiYJtLIQKiKML//QfuvtslnQxumAfuB3cP+PpSfKifRknbYI2UQX0ZksHWCNDpdCxcuJDDa3eg\nNer4/vefKmqulcQVo872QKVzkrbdRFAVq3A/50FJ3KULb9Bdt+Klz+P0tr9cqEyisVNqtnMwU0+f\nVhe8y/Pex/zwQzz9xhvMnj0bPz8/1wq8DhISEnjyySf555zZiLffBp99BsCA1j7sOFMstaqSuCoX\nQwQuz5hm7To4dw7+/pjrhN0AgkwGr/8Lln6LmJJSsXxwGx+2npIeYi4iGWyNBLvdTqBvNAH6rIpl\nadZULP5mtKe8XKisbvA87YXV14w5oHzKJzg4GI/cZP7cc8LFyiQaM3tSyltRadUKxJ27IDOLt5KO\nMmjQIAYPrr7PbmPn8ccfx2Kx8K27GrbvQDx5klAfNwI0So5kSa2qJKpnX5qeSD91RUaxWFgI894v\nr7emrJvanDabjcLCQlJTU0lKSuLgwYPs37+fpUuXcvz4cVJTUykqKsLhqLvpSiEkBP7xOMyYWd4b\nGOge6cXZfJNUk+0CUlmPRkL2+fMERg5GLs8DQJSJrDesxeuYDzJ707erZXYZXsd8KG5XhFUsnwb1\nDVCSbNMgOhzlT1gSElewPVnH8Hj/8tiW9z/gyJBb2PzlEjZs2OBqaTeEXC5n3rx53H333dz67LP4\nz5mH+PmnDLiQfNC5mr6QEhJbThVV9q7NfR9uvw0h4fr75jocDg4cOMD69evZuXMnSUlJqNVqvL29\n0Wg0qFQqZDIZxcXF5OXlUVpaSnFxMWVlZezbt48hQ4YwdOhQOnTocGMhCvffB+vXl3dBeHA0KoWM\n3hcyqO9LDLr+/d4kSAZbI0GRms7ZjrHEFqagAAyt9ATLW1Caa7zmtk0FdZ47xvAy9pTtRpmppH3n\naP6XEkDWpq0Q17qibpWEBJTXmTqTZ6TrrVpYuQK7nx9/X7KE92a9h1bb9A2amJgYnn76aZ5at47v\n5UrYto1+3fvwv305mK2OquUaJJo9xUYbSedLmXJLebUAcdduOHIEvv/2uvaXlZXF0qVL+eGHH9Bq\ntQwfPpyXXnqJ4OBgli5dWmX82LFj+frrryv+t1gsJCYmkpSUxJNPPokgCIwaNYpHHnmEwMDAWusR\nZDLEV1+Bxx5HHDgQIbgFg9v48N+tWdzbWarJJv0iNBLC5T5ojUUosGFzt1EaaWCIpgnU0aklXse9\n+bNkD59/9zkH9u7BrTCLTd//WqVulYTE9mQdPaO9UZnK4IuFzHd3o3ef3gwcONDV0uqMxx57jBKD\ngS0dO8CHH+OtEmgd5CE1v5Zwyo5kHd0ivHBXycsbu7/7Hrz8EoKTrjhX4/jx4zz55JMMHz4cg8HA\nl19+yaZNm3j55Zfp168f6hp2R1CpVPTq1Ys333yTHTt28NFHH5GZmcnAgQOZNm0aZ8+erfVnFKKi\n4MHRMHs2UJ5B7XCIJOfdPM6L60Uy2BoBWVlZeIe3Q2vNB6AkXodniide8qZXxuNayE0Kerj3oiRe\nhyATsOYnY1TV/klM4uZne7KuvPbal19R2LYNC7Zu5Y033qjx9hezry9/2e2Nq8m6QqFg9uzZPPPd\nt1j8/WDFSvq39mFbsvTwIlGVLad0DGp7odPNosWQ0A6hd68ab5+ZmclTTz3FQw89RKdOndizZw/T\np0+nXbvrn069iCAIJCYmMmvWLHbs2EFISAgjR47kpZdeIje3lr2jx4+DlBTEbdvLM6jb+LBFalXV\ncAbbwYMHmTJlCs888wyrVq1yOiYpKYkXX3yRadOm8dZbbzWUNJeTtHYt6eEJICvBFGjE5mlDk9r0\np3yqo6u6GzYPG+YgE6KjiOQWbfCvphejRPMks8hEUZmNdspSxBUr+WfSUV5//fVaZYVezL6+/GW7\nrM5TYyEhIYGHHnqIOVYLLFpMzyAFx86Xojc1Pq0SriOjyERRmZUOoZ7l5W1WrCwvwFwDzGYzc+fO\nZcSIEbRq1Ypdu3bxxBNP1FtogZ+fH88//zzbt29Ho9EwZMgQFixYUOPrT1Cp4MUXYc4cRJOJAa19\n2XlGh9XevGuyNYjB5nA4WLhwIa+++ipz585l586dZGZmVhpTWlrKwoULeemll5gzZw7PPdc0KjXX\nBeKuP0gNjMLDlk9JfDFex7ybZM21miIX5Hgf86EkTke4L6T6tSQ6O9/VsiQaEduTi+kX4418wUIO\nRUYgBgVx7733ulpWvTF16lR+Pn6cnMhI3Jd9T2JLLbvOSvWnJC6x9VR5PUKZALw3GyZNRKhBnNhf\nf/3F8OHDOXLkCOvWrWPatGloNJr6Fwz4+vryxhtvsHLlStatW8fdd9/NiRM1qwwg9OwB7dvD4iUE\ne6kI83HjQEbzfrBvEIMtOTmZ4OBggoKCUCgU9O3bl3379lUas2PHDnr27Im/vz8AXl5Nv5RFTTAa\njXgp/dCaCjBFFqMoVaDOr108QlPErUCNwqBEbGtClp8K1pv/M0vUDFEU2Z6so7+mDPvmzTz15x+8\n8847N3XAsYeHBzNnzuSpI4cQ/7eM/kFytku9RSUu4BBFtp7WMbC1L2zaBEVFMOqBq25js9l47733\nmDhxItOmTWPx4sWEhYU1kOLKxMbGsmzZMh555BFGjRrFF198UbOSIM8+A8tXIGZkMLC1L1uaeU22\nBjHYCgsLKwwxKHeXFhYWVhpz/vx5DAYDb7/9Ni+//DLbtm1rCGkuZ++atZS07IBSno2hlR6v4zdf\n3Fp1eJ3wwRBtwG5NISugFbKCAldLkmgEnM41IpcJtPpmAas8Ndw7fjytWrVytax6Z+jQoXjHxXEw\nJJjOa78nQ2cmVy/Vn5KApHOleKnlRGiA9z+EF55HUFRf5OHcuXOMGjWqolTHyJEjG05sNQiCwKOP\nPsovv/zCqlWrGD9+PEVFVzfAhKAgGDcW5s6jT4w3h7MMGMyNKw61IWk0SQd2u52UlBReeeUV/vWv\nf7F8+XLOnz/valn1Tv6KFRyM6ogi4jgeWR4oyuqm8GFTQFGmwCPTA/9O5/gzOA73vXtdLUmiEbAt\nWUc/LwuWAwf4KCebp59+2tWSGozp06fz7IEDyH7/nV5BCnackaZFJcprrw1sU56AQ6eOCF0Sqx27\ne/du7rzzTgYPHszSpUsJCmpc9cuioqJYuXIlMTEx3HbbbRw9evTqGzz8EKRnoNm3h07hnuw803w9\nzw1Sh83Pz4+Cy7wnBQUFVYKH/f390Wq1qFQqVCoV8fHxpKWlERISUmlcUlISSUlJFf+PHj260ddk\nUqlUTjWKoojP2QwKhsrxCSzCc1twpfXOpoCqmxa60bG1GVeXujzPeGEckI1OL2DYuZeIqVOr1VPd\ncWxsLFu2rOLvhIQEEhIS6vX9bqZrwu4Q2XW2hP/b/x0fGct4Z/bs677hyOXyKstqc+46ozbnuVwu\nr/X3EB8fz6P/fJrVv/3O4MMbWVA2nPH9q/cuSteEc5xdE1eiUCga1bGr7rs0We3sTdPzeDtPhB+X\no1m1Alk1uhctWsQ777zD/PnzGTJkyHVrcXbtXG3s9RzHOXPm0LdvXx555BHmzp171RhV679ewfzv\nd7n1/SUsO5DDAz2jqh3bmK6Jqx3H67kmGsRgi4mJITs7m9zcXPz8/Ni1axfPPvtspTHdu3dn0aJF\nOBwOrFYrp0+f5s4776yyL2cfTK/X16v+G0Wr1TrVeOrAAYSQNvhF7cYj2QuZrbLDUxSr9hR0tqwu\nxtZmXF3qktlkeJ72whi2hWSjkvCsLIRq4herO46NCa1W6/TmUJ/cTNfEwQw9gZhRH/6DpOgonu/b\n97o/i7MSHrU5d51Rm/Pcbrdfl/a//e1v3PXVV/y8+kdK/tafo6l5RPo7r4slXRPOqckN0GazNapj\nV913ue20jtZB7qjen4U4ehSlGg1cMc7hcDB9+nQ2bdrEypUriY6OvqHPVpvyN9d7ngMMGzaMb7/9\nlgkTJnDixAmeeuop5w9FXboghoYQt2kFGY5ETmcVEOylcrrPxnRNXO04Xs810SBTonK5nIkTJ/LO\nO+8wdepU+vTpQ3h4OOvXr2f9+vUAhIWF0alTJ55//nleffVVhgwZQnh4eEPIa1Aurw2VtGABm3u3\nQuFWikdGw2TtNEY8MjUolEbWdQ+DHTtdLUfChWw7raP3kc28k5/HG9On39SJBtWhVqt58e23WWQ2\n0vf8UakmWzNn6+kiBiqL4WgSjB1TZb3JZOLJJ5/k6NGj/Pzzz0RHR7tA5fXTvn17fv75Z37++Wde\neeWV6o2cqVNQfPUV/cLdm21D+AZrTZWYmEhiYuV592HDhlX6f+TIkY0iOLI+uVgbCqDHvr1kj3Jn\nkHIop8U/XazMdQiigOZkAPld8jD/tgH17be5WpKECzBbHew9U8iwQ5tIGjWqWSQaVMfQoUP5dvFi\nXtjzC++HJPBojxbImqHx2twpLLVyKqeMF7Z8CE9PRriiA4HBYGDChAn4+vryzTff1LhDQWMjJCSE\n5cuXM2nSJJ544gk+/vhj3NzcKo0RoqIQRwxn4P51zAsfxOiuQc3uga7RJB00N2ylpZgGtcRu96Sb\nV6yr5bgc73ywW7Wscc8qb7ki0ezYm1pMq9yzLMg/x7NTalYQtDGjUqmqdFrIzMzEUIMi0YIg8K/p\n0/kxNQm1rpAT2WUNoFiisbHjjI6e8hLc5AIMH15pXVFREQ8++CDR0dF8+umnTdZYu4hWq63oUzph\nwgSMRietqP7+GDHrVyK3WTmZ0/yuCclgcxFeqafZdGsAYkpb5DLpa5AhoMhMYOMQb4x/bHe1HAkX\nsG3PGeKOb6fnC8/j6enpajk3jF6vr9JpoTY9c2NjYxFG3kX3E9vZtudMPauVaIxsOVHIgA3fwdQp\nlbxJhYWFPPjgg/To0YN33323VkkCjRk3Nzc+/fRT/P39GTNmDKWlpZXWC97eCBP+xsCUvWxthnUK\nJUvBRcjb2bEXBeBZZHW1lEZD95AYzLm+rM9c7WopEg1MSamZJJ2DQ3knGNXAAeqNmWeef56kpK3s\nzjI2+7Y8zY20AhOGIj0JLb0QOnSoWF5YWMjo0aMZPHgwb7zxxk03LahQKPjggw+Iiopi7NixVYw2\nHrifASe2s/NkQbO7JiSDzQXY5WYyB/hTWHALnpZaNsW9iekZG0hhwS1sDdVRVCa1qmpObPt5J9EZ\nR7hv+pvIJI9zBd7e3rSb+AhBhVkc2HTA1XIkGpDNh7IYcHw7sqcmVyy76FkbMmQIL7/88k1nrF1E\nJpMxa9YsWrVqxfjx4ytNjwpKJYF/H0dkfjp7zzYvL5v0y+gCzC3OEX7QClYNbvbmNw9fHcHeahR2\nD6KOwvK9n9U43keiaSPabGw7o0c0ptOjZ09Xy2l0PDJ2LNbUfWzYdbpWJUgkmi52h8j2E4UMjPFC\nCA0FoKSkhEcffZQBAwbUqbF2eeWCi6/alPW4kVjNqyGTyXjvvfcIDQ1lwoQJmC6PbR40kEHFp9m6\n89QNvUdTo8GyRCXKKbAVYIwRKPgpFm2U5F27HL1ej1yXRkpGMGKHFNK+/4x/PPTETRHPJFE9Z5Yu\nJ8uzJTPHTnK1lEaJQqFgxMPD+PqEByVbd+A9qL+rJUnUM4f+PIl/cS7hT5eHBxiNRsaPH0+XLl14\n7bXX6tSzdnnlgouMGVO1fEh16PV6vvnmmyrLJ02adMO/3TKZjHnz5jF58mQmT57M/PnzUSgUCIJA\n74eGsXh7GbpCPT5+jaNQbn0jedgamM3FG+i/PpfM0K5ozZLBdiVBMj3J/u24ZX0e+jZSW56bHdFq\nZdfuZIJNWURHRrhaTqPltmGD8SxKY/N36yUvWzNgy9bjDAxTIWi1WK1WHn/8cVq2bMmMGTNu2mnQ\n6pDL5Xz00UdYLBaee+65iqbxHp3a082Sy84ft7hWYAMiGWwNyFnDGTIMZ2m9tZBSrzA8LXmultTo\n0NoKUIS2JXa3AYfWTIYlw9WSJOqRrM/nsy2qG4+MHnTd+3A2pVPbaZ2mwPBB7dkVlIBh7VpXS5Go\nRwy7/mC/Jpx+9/bD4XDw3HPPIZfLmTNnTrON71SpVCxYsID09HRmzJhR8dAy8Jb2bCmQI+YXXGMP\nNwfN89t3AaIosjJjBZ226NkYmoDaVoJclDJEr0Qu2lAY81npHUX3bWVsKtkgeRRuUkSzmZzV27B6\n+dAlOuC693NxSufKl81mq0O1rueuPnGkBbci/eMvpGviJkV0ONj941ba+wh4a92ZMWMGGRkZfPrp\npyiVSlfLcynu7u4sWbKErVu38tlnnwHQsWMkRb6BpC/6zsXqGgbJYGsgjhYfRW8tYchvpzkZ1xOt\nOcfVkhotfo5CdgfEcPvGdEwOI0d0h10tSaIeOP7eLNbE9GJ414hmN81zPbgpZPSI8WFnYBw5y35w\ntZwmj91ur5dg+RtizRq2hHRkUN/WfP7552zZsoXFixfj7u7uOk2NCB8fH7755hsWLVrEypUrkcsE\nBrQLYku2iJiS4lJtN5q8UROkpIN6wmAwVBTIlMkEfsj+H73zI7CYrOhbxNFSL6XoV4ePLZ9zMd0w\nH1vDMH08qzJX0N6nw7U3lGgyWAwGfH79jRMT/8uEOD9Xy2kyjOgYwvunhnPrx68jjnrA1XKaNCUl\nJXz55ZdVltdFsPz1IJpMZH/5A1nDp5J9ZBsLFizgp59+wtfXt8G1NGZCQ0P5+uuvefDBBwkKCuKW\nDl1580RfHv34ExRzZrlM140mb9QEycNWT1w+TfPBbx9QlFeEefZydodFY1O442Ftns1ra4K7TYdS\n483Pai86bU/DXe7BnvzdrpYlUYfseuFFtkd3JjTIi1Bvt2tvcBPhrAxCTb067UI0CL6BnPHw5/SC\nL+pZqURDYvlmKVs6D6W1r503XvsXS5YsISwszNWyGiVxcXF88sknTJ48mdLcNPz9PTmsExH339yO\nEMlgq2dEmYihdQnaE150KdKR1v8OPM15SBNA1SMAnuZcfvOOwGPXHu4Nv49fs37GYre4WppEHVCS\nl0f4ps2cun08A1v7uFpOg+OsZVVN21XJBIGBbXzZfft4lIuXYL/J4vSaK6KuGNPCxWxs0Z6fP32b\nDz74gPbt27taVqOmb9++vP7664wbN47uYW5sHjQKPvzopo7vlAy2eqaspQGFQUnoWSOi3UZpVGe0\nFil+7Vr42gswx3bDZLMRk2Uj3KMlG7LWu1qWRB3wx8svkxESxkm7ln4xzc9gu1EGtfHhjF8bjDI5\nO6fPcLUcibpg8WKODL2X3NxzTB5zH4MHD3a1oibBAw88wKhRo/jy3ec5YPXEgBzbTZxFLRls9YhD\n4cAQo0d7yovI06fZIpeTapBL9ddqgNaSgyaiA7s8PWHDRu4Jv5dfUn/CaJM6QzRVDAYD+3fupNPB\nw5wc8wyxvnJKCrKlbha1JNxXjb9GSfLEKXgv+wHTlb0WJZoUYtY5xF9/490yDS1lBYwfP87VkpoU\n06ZNIzI0CHvuSXaMegLT3HmI1puzAoNksNUjpVF63PLVKEuUdM4vYF98D7zdBFQO47U3buYoHWZU\n9lIWmhSwfgMh7qF0Dkhk7fmb9+npZken07HnhRc55e7OmlyRkhPbazUdKHGJwW18SY7qjkOjYdsb\nb7hajsSN8Omn/B7YAnNgW2ZMHuVqNU0OQRCYM2cOpad28l2aEVlkJKxY6WpZ9YJksNUTBruB0shS\nPE97EaQrxmGzURrXizh/uaulNRl8rXkURSVidjjg2HHubzWK7blbKbZIN/imyMkDBxhltrCz9wBM\nCi+05mxXS2r0OCsVYDAY6Bfrzf4MPeqXXqb1lm0U5Epe+6aIePw4Zdt38LlnBN1jA/HzbF4JOHWF\nWq1mwX9eothkZ1XHnrBoMeJN6LmXDLZ6Yod+Gx5ZHiiMCqKSk1mPiNkrgrgAyWCrKV6WHALie7Nb\n44F+5UoK0wvpoO7I/059L02jNTFEUSRjzlxOemlJbdEBH2MmMhyultXocVYUWKfToVUr6BDqSUrb\nvuDvz+aXXna1VIlaIooiurdnME9fQuthY7grMdTVkpo0LYKCGNzWj3l/pFAY1xa+rtrftKkjGWz1\nQK4plyTTUTzPaEEU6ZSXz6HIGCxyDZHe0iGvKR7WInDz4sO0c9jXrWP+55+T8lMaB3UHOJOf7Gp5\nErVgw6pV3F1axl9dEilyj8TPmHZd+2mI4pRNhcFtfVl3LA//V1+mx+EjJJ844WpJErXg/PLlFJ4+\nTeLs/1JsEegeLdVbu1Ee7NeG0K63MnbXLhw//Ih4k3meJeuhHvgpcyU9NL2QWeWE6HSYrFaMHfrj\naclFLpMKetQUAZG2gUqyQhMwIRCu0yGzytCkeLK5ZJOr5UnUEIvFQvp/3qW4fQKZ/tHIRBvutuub\n1nbmcbrZWlDVlC4ttWQVmTAk9kYIC2OH5GVrMhQXFmJ8bzaZ99xNvnskg9r4SveGOiDE243WIT50\nGfssy+027J986mpJdYpksNUxqYYUkvXJ9NT0AiAm+Sxr7DbsfrF4STE7taZdoILg9v3ZpJCTkHUO\nAE2qlixLJmcNZ1ysTqIm/G/+fEYh4DZ5MoXuUfga06Q6hHWAQi4wJD6AzSeLCHrjNUacO8+uLVtc\nLUviGtjtdpaNG4/Mx4fer7zC1tM6bmkredfqils7BKGO7cOuNq0pW7cO8dQpV0uqMySDrQ4pb/C+\nnDvD7kIlUyGIIh3zcjkYGoreLUjqH3odxPnLUQa34XtdCQnnzyM4HAgOgQHaQazIWH5TF0m8GdDp\ndFgWLsI+cAClgS0oUYfga8q45nbOpj6b8/RndYxoH8TmU0UounRFaB3LgTffwuGQYgMbM7NnzODe\n/ALCZ73LX+kGQr1VhPlIyQZ1Rf82/pzKNTLt/+bwlUJBxk3keW4wg+3gwYNMmTKFZ555hlWrVlU7\nLjk5mYceeog//vijoaTVGUnFR9FZi+kT2BeAlgUF5FltiJ0GoLbpUTrMLlbY9NCoBNxtejL8oihS\nqogqKASgk0dnSm0GqTF8I2fBu+/yoNodn2nPceCcBY0lv0bXgbOpz+Y8/Vkd0YEafD2UHMo00OKN\n13nIZGbFt9+6WpZENaxYsQK/1WvQ9uuLslMnNpwoZGi81Eu3LlEr5fSL8WZ3upF7vlyCIyOTw/MX\nuFpWndAgBpvD4WDhwoW8+uqrzJ07l507d5KZmel03NKlS+ncuXOT85w4RAcrMpZzb8v7kQvlVb0+\nIQAAIABJREFUmaCtz6bwu80KQW2l6dAbwNuSTXjiLWyUy2h/rnxaVCbIuDf8flZmLscuSl6XxobB\nYGDXrl20WL2GskEDybJa2Z1hxs+Y6mppjRJn/UVr6lEcGufLhhOFCHFxCJ07kzXvfcrKygtMV+ep\nlLKsG57Dhw/z0ZtvMsHdA9XUqeTqLZzONdK7lberpd10DI33Y8OJIkIiozD/fRJun88n5UzTD6FR\nNMSbJCcnExwcTFBQEFDeA2zfvn2Eh4dXGrd69Wp69erFmSZ4YPfk78ZD7k4nn07lC6xW2uflMz8k\nGItbCFE6qXn59eJlOo86ohffrf+cB8uM/N6+/CbWwacj67PXsTtvF/2C+rtYpcTl6HQ6Zj//PEvc\n3JgvQMGSZRSGDSdKCgtwil6v55tvqpYhGDNmzDW37Rfjw9d/ZFNstOH78otMeGQMX7z/Ac+8+kqF\np/JKJk2ahKenZ51ol7g2eXl5PPbYY/zYpy/ydu0QwkLZtDeH/rHeuCmkyKS6plWAO95qBYcyDSQ+\n/jg5v63mq/F/Y/Ka1U36vG+QM6WwsBB/f/+K//38/CgsLKwyZt++fQwfPhwor17cVLDYzfyS9RP3\nRTxQodtt/35O2qy4t++BKAiobSUuVtl0cbPrUcgEstwDyNR40PpCqrYgCNzf8gF+yfoZk93kYpXN\nk+o8OH/++ScPlxrZHxVFqZsbhR6RdA2RI9C4POciIjbRhkNpx662YfOwYdNYsXpaybflY9NYsXnY\nsLvZcSgdjdKbq3GT0z3Si62nixCio5EP6I9y2TKysrJcLU2C8izpxx9/nCeHDaNlSipM+Bt2h8iG\nk4UMj/e/5vYS18eweD/WHS9EEARa/N9M/iHCi08/3aRjPBvEw1YTlixZwiOPPIIgCIii2KSmRDfk\nbCDasxWtPGMqltl//Y1frVZkIQl4m85JWXE3gAB4m88T2X0Ea09sYGjmuYp1UZ7RtNG2YUP2Ou4M\nG+k6kc0UZx4ch8PB2U2b+Njdnc9iY3Ego0gdQY8wBWuc7OPidODl1EVygdlhxuplweZux+5uw6G2\n84v+Jwp65OJQOcpfSgcfFM5FHCAiOGQIDsAhIAA/6Veg61IMMhFRJiLKReYVzkYcLiKzyspfZjky\ni4wtpZsojdQjNyqQG+XIyxr2p3VYvB+fbsvirg4BeDz7DON27GTmjBk89dpr9fJ+BoPBaUsxHx+f\nJu3BqA/eeOMNfLy9Ga8rhscmIXh58VdqCYGeKiL91Q2mo7rvrL4SeZxd1w15fvSP9eabP7MpKLXi\n3749moED6L97Nx988AFTp05tEA11TYP8qvj5+VFQUFDxf0FBAX5+lQMtz549y/vvvw+UTw8cPHgQ\nhUJBt27dKo1LSkoiKSmp4v/Ro0ej1WrrUf3VKTbr2JSzkendZqD1KNchlpTgffwEJ8PDUKpDCdUf\nqRjvzHNYnTexIcfWZpwrPoOX6Rya6K58t+VrHtNoKS4rq/jeH40bw2t7/8Wt0bfj6+b69Phly5ZV\n/J2QkEBCQkK9vp8rrwm5vGrnjpMnT/KUA/5sHYNJpaRYHYLaVkKgxrk3wWAw8PXXX1daNnbsWKdj\nnZ0jVqxYfMxYvazYPC++bHxa9DFiB8oNKKMCuUlOrKo1ucl5yCzyCqNr3KPjqrz/RQ1f/1p5+Zgx\nY/j6269wKEUcKjsOlQO7mx2PWA9sGhvmADN293JP3adF/8XS3YLCoESpV6DQq1DqlTd8Tcjl8orv\nV6VSodVq6eHpyec7zpNeAu3btoX77qXD999z7Ngxp/u9fB/Xw/nz551OtT7++OOEhIRUWd4Yrokr\nqe6Y3+ixuZzFixfzxx9/sGnGTGQffoRm3FgEpZKNJzO4u0topfe5+F3WF9V9Z86utdrMcFU31tl1\nXd35UZdcPI5aYFBcANvPljK2T0scr7zMg/fcx8hvv6Nr167ccccddfq+zn4Lr3Ycr+eaaBCDLSYm\nhuzsbHJzc/Hz82PXrl08++yzlcZ8/PHHFX9/8skndO3atYqxBs4/mF6vrx/hNeD71O/o4dcTD7um\nQodj1U/sslkJbJdIrtwDjeWSserMc1idN7Ehx9ZmnCs+g8ZaAD5adEpPTvh4E7ltO/o2bQBQ405v\n/z58d3IpY6PHO/8wDYRWq3V6c6hPXHlNXPl0brFYMB04QLewlsyNjgag0D0aP2MKohjldB+1OUfs\nDjtWrQWLrwWrtwWLj4WPCz5AiBdQ6JUo9UrUOe4oDErGPTCOpauXVto+vm87/ircX6P3qg7BIUNu\nBrn50g90D/denDp2qfuGiMjIh0fywx8/YNNasfhaKI0sxaaxsajoC0rbl6LSuaHUqVAYFLW6Jux2\ne8X3q9VqK/4e0tabVX9lEundEib8jftW/cTf332PmP79qtw4Lt/H9VCdV8bZfhvLNXEl1Z5jN3hs\nLrJ3716mT5/Oyh9+gNfewPHMPzGYTOTklnAiW89zQ8Iqvc/l32V9UN13Vpvrr6bbV7e8ro7t1bj8\nOA5ureX/VqdxV4I3cq0W4f77+PL4cQY99RTBwcG0uXAPqQucHd+rHcfruSYaJIZNLpczceJE3nnn\nHaZOnUqfPn0IDw9n/fr1rF+/viEk1AvnyrI4ULifO8LurLTc8L9lrFMqEFrE4WXObnRxO02R8mnR\nbKJ73sYvdjuazVsqrb8t9HYOFx0is6xq9rFE9VTXXPx62f/XX7zu649+9ChscjlmuQaTwgtv0/nr\n2p+IiMXbgqFVCYXd8vio6AOKOhdi9bKg0qnwPejHM35TCdjdAp+jfmjStLgVqJGb5S6NgxUQ8JZ7\no85X45mixeeIH4E7WxC8IZRbPW9HWaLC4memqGs+OUPOs7LkRwxReqxaC+I1fi8uzyg9depUxd/d\nQ1XsTSvBYLYj+PmheuRhxppMnD59uoE+tcRFzp07xxNPPMG8efNodfAQtAiCfuXlntYeK2BQax8p\n2aABiPZ3J8BTyb60CzHk48fhd+Yscx97jAkTJjidIm7MNFigRWJiIomJiZWWDRs2zOnYyZMnN4Sk\nG2Z5xo/cGno7GoWmYpmYkYGQkYFm2DDOq8MIKDvrQoU3F17mcxhievDjlu94VQQxNQ0hKhIAD4UH\nd4TdxY/py3i27dQmlbTiSpzFoD355JPXFZ+k0+kITEmhZXAI+sGD4PvvKfCIxteYXqtG73a1jUOm\ngxQlFmD2MyE3y1EVqPHI8OSRNo+y4vcVlcZfLKPTFBAcAiGKEDTpnpBevszuZiduZDvOaTZSFFGK\nqHCgKnDDLV9NqaO0yj6qyyidNGkSXSO0bD5ZxF0dAxDGjmHA/5bx4b6/sERFoVKp6vvjSQBGo5HH\nLhgEt3TrBqMehE/+iyAIWGwONp0s4v/uibn2jiTqhFvb+bE6qZCe0d4IGg3ik08wdOUqtt9yC089\n9RRfffWV0+nMxkijSTpoahzVHSHPlMvA1k9VWu745VdWlZXRb/jtHD6iRCvVX6sztOZcbN7dsKu1\nZLZPIPL332HykxXr+wf2Z0vOJo7oDtPRt5MLlTZtqjMInBlyF6cBRFFkz65dLPUPZHN8HN0UChzI\nKHSPpHXBlqu+nyiWe9FMQUbMQSbsajsZ1nTcctR4HfOpNPXoIfO48Q/YyJCb5cS7teOvpPKpWpva\nhiXAhDnIxELdfBy9HbjluqPOVaPQK6vdj0qloktgGd8dzqGzrxFBEHAfPYp/ffUVMw4coGfPng31\nkZo0NxIsL4oiL730EpGRkTz11FMwew7ccgtCbLmBtvNsMa0C3An1ljobNBR9YrxZsiebLJ25vKPE\nHbfDDz/wZq/ePHzyJP/+9795rZbJOc4SOBqiC4tksF0HdoeNH9OX8UDEaBQyxaUvz+HAZ/kKdvn5\nMAh/tObkWnkWJK6ODAde5hxiet/BSksOT//yKzl33A4Xno58fHx4IGI0P6T/j3beCShk0ul9kbrI\nEHNmyF2sE5aens4AowllkDcngoPpBujU4XhYdbjZq3qJREQsfhZMLcr4TPcJxo5G1DnueCf5oNSp\nuHPMSL45V9VobA4oTAoUmZ54ZHrycLuHWbJnMaYWJoq6lMfCbindhMXbgrJYiXBZ/rler2fzym8o\n8R/CB99sRWvJY8yDD9L6u+/xST6Drm1bfHx8qn1fKfOzHGfneU3r1s2fP5+TJ0+Wd/M5cxbWb4Bl\n/6tYvyapgPsTg+pcs0T1KOUyhrT1ZU1SAZP6hiLIZIjTpiF79V98tuBz7nzgAdq1a8d9991X4306\nm5moSc3EG0W6o10HW3O34qvyo4NPR+DSlxedn09vvZ78yJYcyLbgY5LqINU13qYsTDE9WbT4eUYH\nBbN51izOBgYC5T+q7cM7sDlnE1tyNzM02PmUe3OkugKqdfEjY7PZ+GvXLjb6BfBzQjxcmI4u8Igm\nqPRS42VRFLH4mDGGGDEFlyGzyFFnuzPa60FW/7b6hnXcjMgFOW6FatwK1YjHvbFprSiGKdB1LASZ\niDrbHffzHihKyj1vAuBflkKBRyu0ljxQKtncLo7pdjtjd+1ixG23IQhCtaVUlixZUkXD1TyrEpfY\nunUrn332Gb/++itqtRrmzisv4+FT3sngVE4ZJUYbXSNcV9WguTKinR/TlifzSPcWuKvkCJ06IiYm\n4vvTzyxcuJDRo0cTExNDp06Ne2ZGMthqicGqZ/W535gSN61KnFSn1HS+KSkmqvVw0nUOYi3SdGhd\n42XOIcO7Ky1aRrNZJScxPbPCYLvIAxGjmXP8PXr498RL6eUipc2HQ4cO8Q8fX/L8/Mi4UK4no8SO\nVa7Gy3wem8aKMbSMBbrPKO1QivqcB/5/BKIoKzcy/HtLxUNrgoCAUq+in8cAUranYdNaMQYbKUos\nAIfA7rJd2NQ2fE3pZGvjscjcATgWEkKvMykMyM0hLS2NqKioq3pLr6Q2Y5srZ86c4ZlnnmH+/PmE\nhYUhbtoEhYVw370VY347ms9t7f2Ry5pvfK2zBwWofy9uoFZFhzANm04VcUf7gPKFzzwNj4wh7q67\nmDVrFpMmTeK3336jRYsW9abjRpEMtlryc9ZPdPPvQZhHWKXl7hYLMbm57PbxJt6nFbF+cuRZ0lNo\nXSPDjtacQ+Swh/hu5Wfcb7XjbrFgvCygOsQ9hJ7+vfgpcxVjo8e5UO3Nz7lz5ziXlMS4oGCWxLet\nWL4904Cf93YKYnOxq224n/fgbu29rPttfaVpPInr46LxptSr0J72wupjwTBIT37fXJR6Jb4Fuykw\nRVwYLLChXTwvlJUxZPfuKi0BJW6M4uJiJk6cyAsvvEDPnj0RTSZ4/0N48w0ERfkttrDUyoEMA4/3\nC7vG3m5urpYwU9/T7ne0D+C/WzO5LcEfmSAgBAUhjnkU5s3j1jmzOX78OJMmTeLHH38s95A2QqS8\n4lqQUZrOgcL93Bl2V5V1HbLOsd1uI6RtW4rU4XQObhpZJ00RH1MmYosEktLTOR4YQMfMqlPPd4Td\nxRHdIdIMqQ0vsBnx4Ycf8nZ4BEfDw8n31GD2M1HYSUdmwEJUnll4ntYStCUErxM+tFAES8ZaPSAg\noNK5McxzBC02h+CRpsHN9wyOnttZrV+NxdtCmr8vOf7+POXrx4EDB1wt+abBZrMxefJkBgwYcMnr\nuORLaJ+A0LVLxbi1xwrpG+ONxk26L7iK+GAP1EoZ+9MvqwP3yMOQmoq4cydTpkwhLCyMF198sdF2\nWpIMthoiiiLfp33HyPB7KpXxuLCSjqmpfFNSQlh0G8qUvsQHSBdmfeFlzibHKCM8Jo5fZAJd0jPg\nigvMQ+HB3eH38n3atzhEKfGjPkhNTUWRkUE3lYOfbwslb0AOJe10WMpCaFkwEb+Dvqjz3RFEyUhr\nKASHgHuOBwH7fDEfGkFpmRe6zgXk981l2R1R3KeWk3f8BGlpaa6WelMwc+ZM7HY7b775JgBiejr8\nuBymXCoMb7Y6WHusgLs6BLhKpgTlXQfu6hDAL4fzLy1TqWDaNJg9FywW3n//fU6dOsWnn37qQqXV\nIxlsNeSPgt3YRCt9A/tVWac6eRLRZCYvMgK9JgIvczYquXSTqi9kOGgXKCeix+3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8KVif1VfNIFsQqdL6jmJBnlEfTS9MLD9LNH3ioVn8fH8cd9+3koZhgvH0hm/fr1XRPoNThQkkz8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\nKi/yfEZhu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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f32abee1450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fun = 0\n",
    "ax = aux.plotSamples(Strue[:, :, :, fun], meantrue[:, :, fun], covtrue[:, :, :, fun], \n",
    "                     meanUT=meanUT[:, :, 1:, fun], covUT=covUT[:, :, :, 1:, fun], \n",
    "                     titles=stdlabels, ylabels=funlabels[fun], \n",
    "                     utlabels=utlabels[1:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I explain the overestimation of the variance by the scaled set with its locality: The scaled set estimates the spread of the transformed distribution only locally around the point $[5, 5]^T$ where the observation function has a sizeable linear slope. The sigmoid in the observation function, however, limits the spread of the transformed distribution which is never accounted for by the scaled set.\n",
    "\n",
    "For the dynamics function the Gauss set again provides the best approximation across all standard deviations of the source distribution $p({\\bf r})$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "       UT min  UT base  UT Gauss  UT scaled\n",
      "std=2  0.5349   0.2055    0.1751     0.5954\n",
      "std=4  2.5973   1.9808    1.0708     2.3574\n",
      "std=8  4.9868   1.7744    1.2085     5.1237\n"
     ]
    }
   ],
   "source": [
    "print pandas.DataFrame(Dis[:, :, 1], stdlabels, utlabels).to_string()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The base set has a striking lapse for `std=4`. The large distance results from underestimation of the spread of the transformed distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Y/VqpVIpoNEo6nWbPnj00NTUB3YsQcnJy0Gg0pFIpmpqaqKurY1NqA5+kP+Zi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\n9dRTueSSS97Tl8P7gePV+T4M69b5z1KpFNlsFqPRSCaToVQqoVKpcJv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irNSz6akHWbp0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\nEEKIQUiSNCGEEEKIQej/AdK5ldo1S8sXAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f32a3c89ad0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fun = 1\n",
    "ax = aux.plotSamples(Strue[:, :, :, fun], \n",
    "                     meantrue[:, :, fun], covtrue[:, :, :, fun], \n",
    "                     meanUT=meanUT[:, :, 1:, fun], covUT=covUT[:, :, :, 1:, fun], \n",
    "                     titles=stdlabels, ylabels=funlabels[fun], \n",
    "                     utlabels=utlabels[1:])\n",
    "ax[0, 0].set(xlim=(-15, 22), ylim=(-25, 35));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I don't quite understand why this happens. It at least gets the mean roughly right and the spread along the major direction of variance is also captured.\n",
    "\n",
    "The scaled set again suffers from its locality: The spread of the sigma points around the test point $[5, 5]^T$ is apparently, even for the largest standard deviation, so low that the specific effect of the dynamics (the pull towards the stable fixed points) does not enter the approximation such that the approximated covariance remains roughly isotropic.\n",
    "\n",
    "The following code repeats all analysis steps for another test point (preset to the stable fixed point here). The overall results are the same as for point $[5, 5]^T$: The base and Gauss sets produce comparably good approximations with slight advantages for the Gauss set whereas the scaled set performs considerably worse for uncertain source distributions, i.e., when $p({\\bf r})$ has large (co)variances."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test point: \n",
      "[ 10.   0.]\n",
      "\n",
      "observation function:\n",
      "       UT min  UT base  UT Gauss  UT scaled\n",
      "std=2  0.0657   0.0347    0.0096     0.0313\n",
      "std=4  0.2435   0.0548    0.0364     0.0263\n",
      "std=8  0.5119   0.0532    0.1948     0.7547\n",
      "\n",
      "dynamics function:\n",
      "       UT min  UT base  UT Gauss  UT scaled\n",
      "std=2  0.2217   0.2167    0.3492     1.6702\n",
      "std=4  0.3886   0.3583    0.7558     5.2867\n",
      "std=8  3.6379   1.3800    1.1463    12.5987\n"
     ]
    },
    {
     "data": {
      "image/png": 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I1IVzRU4oOYeeYdtevp3UsDRycnKIKItkZ0cLRRs24NNtURERaSWmjrAdawuq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BYpFouKTm8ul2MyFmNwbg/t8TgrXnqJZKsbrznLtGTjsaEcK/02jFpxu2u3qC3cH7qP73z6u5x3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\nTU0kEglFJ1WlUjF92KF0jYww9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YIT+GbXJ4RiaZaubJc61yKRCJlMRtoJqLCzvA9l9kwq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\n/g/JUtw5cPckgAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f32ac00e1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "testp = 2\n",
    "print 'test point: \\n' + Z[:, testp].__str__() + '\\n'\n",
    "\n",
    "meantrue = np.zeros((bam.nd, num, 2))\n",
    "covtrue = np.zeros((bam.nd, bam.nd, num, 2))\n",
    "Strue = np.zeros((bam.nd, nsample, num, 2))\n",
    "for i in range(num):\n",
    "    C = stdsr[i]**2 * np.eye(bam.nd)\n",
    "    meantrue[:, i, 0], covtrue[:, :, i, 0], Strue[:, :, i, 0] = \\\n",
    "        naiveSamplingEstimate(Z[:, testp], C, bam.obsfun, nsample)\n",
    "    meantrue[:, i, 1], covtrue[:, :, i, 1], Strue[:, :, i, 1] = \\\n",
    "        naiveSamplingEstimate(Z[:, testp], C, dynfun, nsample)\n",
    "        \n",
    "meanUT = np.zeros((bam.nd, num, nut, 2))\n",
    "covUT = np.zeros((bam.nd, bam.nd, num, nut, 2))\n",
    "Dis = np.zeros((num, nut, 2))\n",
    "for uti, ut in enumerate(UTs):\n",
    "    for i in range(num):\n",
    "        C = stdsr[i]**2 * np.eye(bam.nd)\n",
    "        meanUT[:, i, uti, 0], covUT[:, :, i, uti, 0] = \\\n",
    "            ut.performUT(Z[:, testp], C, bam.obsfun)\n",
    "        meanUT[:, i, uti, 1], covUT[:, :, i, uti, 1] = \\\n",
    "            ut.performUT(Z[:, testp], C, dynfun)\n",
    "        Dis[i, uti, 0] = WassDist(meantrue[:, i, 0], covtrue[:, :, i, 0],\n",
    "                                  meanUT[:, i, uti, 0], covUT[:, :, i, uti, 0])\n",
    "        Dis[i, uti, 1] = WassDist(meantrue[:, i, 1], covtrue[:, :, i, 1],\n",
    "                                  meanUT[:, i, uti, 1], covUT[:, :, i, uti, 1])\n",
    "\n",
    "print 'observation function:'\n",
    "print pandas.DataFrame(Dis[:, :, 0], stdlabels, utlabels).to_string()\n",
    "print ''\n",
    "print 'dynamics function:'\n",
    "print pandas.DataFrame(Dis[:, :, 1], stdlabels, utlabels).to_string()\n",
    "\n",
    "ax = aux.plotSamples(Strue[:, :, :, :], \n",
    "                     meantrue[:, :, :], covtrue[:, :, :, :], \n",
    "                     meanUT=meanUT[:, :, 1:, :], covUT=covUT[:, :, :, 1:, :], \n",
    "                     titles=stdlabels, ylabels=funlabels, \n",
    "                     utlabels=utlabels[1:])\n",
    "ax[1, 0].set(xlim=(-15, 22), ylim=(-25, 35));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Effects of the dimensionalities of $\\bf r$ and $\\bf o$\n",
    "\n",
    "I can easily increase the dimensionality of the Bayesian attractor model without changing the main properties of its dynamics. For each added dimension a new stable fixed point will appear on the corresponding coordinate axis in state space, e.g., at $[0, 0, 10]^T$ for three dimensions. Additionally, the observation function becomes truly two-dimensional for larger dimensionality of the dynamics, because I map the stable fixed points to equally spaced points around the unit circle. Consequently, the observation function becomes considerably more nonlinear as the dimensionality increases. At the same time, however, the transformed distribution resembles more and more a circular Gaussian, because each dimension adds a term in a sum of random variables in the observation function.\n",
    "\n",
    "Below I generate results for a combination of test point and spread of the source distribution (`std`) for increasing dimensionality (`nds`). The preselected values are a stable fixed point as test point and large spread of `std=8`. I chose those values, because they reveal problems of the scaled set. Some other settings and results are discussed below, but you should explore the behaviour of the UTs in response to different settings for yourself.\n",
    "\n",
    "The code below generates the tables with the Wasserstein distances $W$ for the observation and dynamics functions as well as two plots. The first plot visualises the results for the observation function as above just that the distributions are now in 2D. The second plot shows the true and approximated distributions for the dynamics function, but only for one of the dimensionalities. This plot visualises the high-dimensional distribution by showing all distinct 2D-slices of the distribution.\n",
    "\n",
    "Notice that I now explicitly include the mean set into the list of UTs, because the Gauss and mean sets differ for $D \\neq 2$. Also notice that the Gauss and base sets are equal for $D = 3$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test point: stable fixed point\n",
      "std = 8.0\n",
      "\n",
      "observation function:\n",
      "       UT min  UT base  UT Gauss  UT scaled  UT mean\n",
      "nd=3   0.5494   0.2117    0.2117     0.8564   0.3274\n",
      "nd=5   0.5196   0.3758    0.2069     0.7729   0.4920\n",
      "nd=11  0.5886   0.6982    0.1787     0.7231   0.8171\n",
      "nd=16  0.7626   0.9422    0.1854     0.7439   1.0628\n",
      "\n",
      "dynamics function:\n",
      "        UT min  UT base  UT Gauss  UT scaled  UT mean\n",
      "nd=3    6.1882   3.5534    3.5534    20.0922   3.0181\n",
      "nd=5   10.6469   6.1692   12.1514    33.2995   6.7308\n",
      "nd=11  30.3231  22.7785       NaN    71.5892  26.0426\n",
      "nd=16  54.7164  45.2402       NaN   103.5120  49.8152\n"
     ]
    },
    {
     "data": {
      "image/png": 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Kx+MhEAgwNDREIBAgGAwSi8WQJInGxkZCoRCiKOJyuejt7cVqtdLT04MkSfT3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\n/h/39+aN1wvPwgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f32ac2af1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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SkcFRejt7lX64rRJGPT09iKLI2NgYPp9P8cpptVolQaLlbavX63R3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QKXy8UnU+Kf0GJqs9nQ6XQYCTOZTPj5z3++pA7euhUSsxk3PfVLVDx9qJpM0HTLGBN7eDOvRbRn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UIBq9VKMBhkcnISvV5PTU0NZqOR8qub0b6+hREchOpXk7fXELW4CVrcIJUxLP8zEqDacRoW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\nkY/WU3xuOKK2vMTjd91FdGZGrE60220ymYy4eVpfX0er1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SzLVCoVgWdQR05+v59bb72V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weL30m4pk6zby5TyZq1MQgm3V7UQiESYmJtDr9UQiEZaXl6nX6+v5dh1DgjchhBDiImIy\nmXC5XMTjK1uCuVxOC9xa58NmZmZ45plnSKVSuN1ukskk09PTmM1mNm3ahM/no1qtasV39+zZg7Er\nyPevSGKpWgmkdlE3OKhUKvj9fux2OxMTEzSbTa0V1uLiIqVSiXw+T0dHB263m2azqQVYZrOZSqVC\nPp+nq6uLjo4OTCYTRqORcrnM0NAQsJIB29nZSTKZpFgsUq1WaWtrY3Fxkbm5OQDq9ToDAwPaGTin\n00k6nabmtZJXDCyNLFCJVjA+a8agN2Cz2VAUhWazicfj0ebi9/tpa2vTVt3WiwRvQgghxAWoVqsd\nNzNSURTcbjddXV0YjUay2awWjFUqlZVaaBMTWv/PaDRKNBpFp9MxOzurba+63W4KhQL9/f1YbRa+\nt2UJU7nGSGI7tnKcSG3lXFosFtMyRGOxGC6Xi/7+frxeL+VyGavVSrVaxWKxYLPZ8Hq9uN1uFGWl\ngXyrb6rX69Vqt7USB+bm5jAYDNjtduLxOCaTiZGREWKxGIqiYLPZCIVCWqZqX18fbrebeDyOwWCA\nYBsM/waz3kzo7jDt/natbMjOnTu1Pw8NDTE4OMjQ0NCGKBUiCQtCCCHEKSgUCtx///3MzMwc09NU\nURQ++clPruPMXup4NdyO1ir5MTk5qWWStoKpSCSCqqrU63VqtZrWkzSfz2MwGGg0GthsNnK5HAcP\nHuTSyy7lOftzlBQDH/ineR7+sAOXQ8/+sEKy1KRcLqPT6ajVarhcLjo6Okin0+h0OsxmM7VajYGB\nAYrFIrFYjMXFRQKBAF6vl0wmo5X7WF5eplwu09nZqW29BoNB7Szc0NCQttXp8Xio1+tEo1Hcbjcd\nHR08//zzNJtNfD4fpVKJptrkl8FxdAYre2o38J3Jfbz1LW/Vas05nU4uv/xyLfg0Go0rAd8GsDFm\nIYQQQmxw//AP/4Cqqlx99dXHbJtttEK9R9dwA7QabkfPuVarodfrufzyy1e2D2s1isUikUiESqVC\nMBjUGtX7fD50Oh35fB6Xy0VXVxezs7PE43HC4TDdt3YSbYTZsrgdveUITEyQbG/Hh4MXYjWu6e0h\nnU7TbDbp6upiYmJCK7uhKApbt24llUoRjUZJp9OUSiWq1SputxuPx6OtDhqNRgqFArOzs2zfvp1E\nIsH8/Lx27i2fz6PX68lkMnR1dbG4uIjdbmdgYACTycTo6CiPPfYYTqcTr8/L47r9VOwVaod/h2dy\nj2kBYyqVIhQK4XK5cLlcGAwGstmslrG6EUjwJoQQQpyCyclJ7rrrrnU/77RaqqqSTqeZnp4ml8vh\ndrupVqvEYjG8Xu8xNdcURSGbzaLT6dizZw+5XI5YLKbVbLNcZqbYUeDK+d3YLXYWuzoJzM4xYzRi\nrOsIO/tJpcLaFmw6ncZgMBCJRGg2mwSDQWZmZggGgzSbTUqlEgDlcpmuri4MBgMmk0krbWIymdDr\nV/qRtlb0bDYbxWKRUqlEvV7XSoxs375dK9DbOkN3yy23EI1FebT5a2pqlb7DmwjpHMwcfI6hoSHt\nPFw4HMZutxMKhbDb7Xi9Xi3bdCOQM29CCCHEKdi6dStLS0vrPY2TMhqN+P1+rbis3+8/JuCsVqta\nRinA1NQU1WqV7u5uIpEIVquVtrY2APR6PRaLRVuFSyaTJBKJlU4H3gKdrwuwdX4b6XCafD5PZKCf\n7qUlqtUqXfo0SdXJQqKATqejUCgwMTFBMBjE4XBgNpsJBAI0Gg2q1SpOp1O7LRAIYLPZCAQCZLNZ\n6vW6FlT29vZqnQ4CgYDWQkuv19NoNFAUhU2bNmE2m4nH41piRDKZZP9j+3m0/muylix7sr+Fw9WN\nr5Bi6sgLDA4OAivJDT09PVogaLFYqFarGyrbVFbehBBCiFPwZ3/2Z3zuc59jeHgYj8ejbUsqisJb\n3/rWdZ7dsXw+n1Y49sUrha2WV/l8nnq9jsvl0rIvFUWh0WgwOztLIBDAZDIB0Gg0qNVq5HI5kskk\nlk4Lh9rHeO72A7z+j28lVomRy+Uw7tmD/4Gf0ud0YgoEqNWrxEpbMGefwWw2MzIyomWD4iWZsQAA\nIABJREFU6vV6stkswWBQSyDwer10dnZqnRiKxSLhcJhms0lHx0r3BqPRiNfrpdlsMjMzA8DmzZu1\nwr+tOR85cgSTyYTJZGJiYgKrzcpM2xRpNc310Ruw/f/t3XmUXPV16PtvDafmuarH6kmt7tbQAiED\nkhgMNraxn3Mdg42VBy/Jxb4ZjExsTPC1n5043Bv7gh+LFa0EAb6JLxhIABEDMYNxcs08CxBCak20\neu7q7uqa5/m8P9p1Lg2S6NaA1PL+rMVa1dWndp3q+kOb3++391bsJPXQmIny61gMv9+vtUIB2Ldv\nHw6Hg5aWFtLptBb3VCArb0IIIcQC3H///Vqj2qmpKaanp5menmZqaupk39ohKYpyyC3e+pxOVVUp\nlUq4XC78fj+FQgG3261Vc9arO4vFIrlcDpvNRnNzM42djQy07qJ1PEhkYO7cWXt7O+effz6DU1PM\nfmwdG0dGCQQCnOnJM1KwE+xeSU9PDz6fj0wmQy6X05JIVVWxWCwkk0ni8bi2pTo6Osr+/fsxm81U\nq1Vti7Q+VisSiRAMBlm9ejWlUgmbzUZnZyfZbJbp6WmKxSKTk5Ok02nsDjtDvkEyrgzL9nWTjmbm\netWlytgzUT75yU9is9kIh8NaoYTL5UKn0zEwMIDT6aRYLJJIJE7CN/lBsvImhBBCLMArr7zCli1b\nTolWEcciEokQCoWw2WzalmogEKClpYVIJILVasXtdpNMJhkfH0dVVfx+/1yiZVDZ1bQT/6wf25Qd\nh8OBXq/HYDAQDofp6+tjrwof/6ef8b9bmmnp7WWVx85LUwY+11lldHSUXC6ntR1paGjAbDYzPDxM\ntVqlUqng9/vJ5/PE43HMZjPm347cAvB4PExOTpLNZrUqWLvdzszMDDqdjlwuRzKZJBwOEwwG515r\ntxHripAjR/dADw2BBpqamgAYLjtZObyDC79woTYGzGg0otfrUVWVYrGovU8+nyccDmtFFCeTrLwJ\nIYQQC9DY2HjKtIo4WvWtz3pbkHoT3nQ6TUNDA62trfj9fm1uabVa1dqD5At53nK8gTGnsFZdR0ND\ng1bFqtfrURSFPXv28G42w2xvD+eFppiZmaE5s5fpmofXD0aZmZkhEAiQzWZpa2ujtbVV6xXn9Xqx\n2WwYDAZisRjt7e3aFIb6NnWhUCCbzVKtVjGZTFQqFQqFAuFwGJvNxtTUlLaSmE6nWda9jPHGMcbU\nMb5g/CIbztqA3W5ndHSUPYNjTOGgMTmC1WqloaEBj8fDxMQEbW1tmM1mVFUlGAxiMpmYmZnRJkOc\nbIYbb7zxxpN9E0IIIcSprlAosG3bNkwmE6lUSmteGw6HaWxsXFCMY51LajabKZVKR/36Wq2mtdRQ\nFAWHw0FHRwfFYlEbVeV0OjEajdrWIcz1invb8BZJXZK1kXVEZ6PYbDbGxsZwuVwEg0FCoRDZbJZA\nIEDC5Wbdv/8HsQsvYCw0QYNVZbeuh15bBofVTCAQoFAoEAqFaG1t1bZn3W43er0el8tFNBqlra0N\nnU7H4OCgVnEaCARwOBzazNT6DNJoNIrH49Ea/rrcLnYqO5gxTNE72IehYsTlcmnn13bFFZoPHsDb\noGdSr8NkMuHxeEin01pbk+XLl1MsFonH41qy+N65psfjOzmaofZL+38hhBBCiI/Ir3/9a2Du7Nv7\nbd269aO+naOiKIq2Berz+QgEAgQCAYxGo9bUt56IVioVMpkMy5cv543UdmaM05wxshaM4PV6SafT\nuFwuxsbGOOecc6jVagQCgbnK0bVnMrFvH90PbiN6+WWEZydosrs5oKyky5ogkYgTiUSw2WwcPHgQ\nv99PW1sbe/bsIRAIaGOxzGazttJVKpWwWq10dHSwc+dObcj87OwstVpNOxtnMBioVCsMOt8lrAvT\ntquTqq5G0pBEp9PN9avzeDmYs/KtoUeZ3PQZgr+thq0ndjabjfHxcW1UVy6X0ypgT4XV15N/B0II\nIcQSsFQStIWoV1TW+7nVq1MrlQpGoxFFUbRD+u9mDvBm6g0+U70U1TW39Vqr1SiVStjtdsbGxtDr\n9axYsYLp6Wmtka7uS5fTf8utuF98ifRZaznXneTprJ+3kk4Mo2/T0tJCqVTCbDbj8XjYuXPn3Kgt\nq5UdO3agKAqxWAxFUWhqamJycpKmpiamp6e1VcLx8XF0Op3W/02n0+EP+Hld9xpJU5yzRj9GXsnj\n8/mwWq3aduuv92dwzUZoarYwptNh0OtpaGggFAppjXptNhuJRAJVVWlra6NUKrFixYqTft4N5Myb\nEEII8TujXC4TjUap1WrUajWtXxrMbemOj48zPDxMLBabG381uZt7xu/mk1xCaiJNPB6npaVFO9jf\n3d3NwMAAxWKR6elpbWUvlUrx7ugoI1/7Kp/cPUBDqUQxn+U800H2JU0Umj+G1Woln8+Ty+WIxWI0\nNjaSSqWYnJzE5/NRLBapVqu43W7sdjvd3d3zGvTGYjGtQjYej5NIJGhobGCH+U2SpjgX5T5Jq7+V\n1atX09LSQigUIhaLUVacjOvb+O6uxxhftYpIJML4+Lg2mcFsNlOr1bDb7bhcLhoaGmhubqa5uRm3\n232Sv8E5svImhBBCHMZ1113Hli1bALjmmmsOe90dd9zxgecGBgYYGBjQft60adNRnW96L5PJdEwx\nisUiRqMRq9UKzPWoUxQFk8lENpvFYrEAkEgkKOlLPJL+V84snEV0MIbdbsdkMrFz507a29sJBoN0\ndXXR3d3NO++8w4YNG9i9ezcGg0Gr5hxExXHpp/nkv/8Hv/j0p/AE7XzKOsHTqXaqWR0d1hSxWBQA\nl8tFpVIhlUoRDAYxGo1aH7p0Oo1OpyMej2u92FKpFH6/n+Hh4bkihYCfZ4tPk9Vl+Sz/FzMzM5jN\nZpxOJ2NjYzidTkbGxnkt5OOcyDt43Bb+w2ig9ttmvNFoFJfLhdvtxmq1auf56oUUgUAAr9f7gXFo\nx/qdAGzbtk173N/fT39//xGv16n1LoNCCCGEmGfv3r2sWrUKYF4i9n4f9o9tXSgUOqb7cTqdx1z0\nkMvlmJycpFgsUiqVcDgceL1ebf4oQKFc4N9KD9NUbaFhfG5FrH4ov97Ut1Qqoaoqzz33HAcOHODL\nX/4yTqdTa/HR2dlJLpdjKhRi4wsvEswX+JeN69HbbKw482z+Zb8RSynKKt0IrY0BrS1HrVajUqlo\nZ+90Oh179uzB4XBgs9mIRqO0tLTgcrlIpVKEQiFq1BjvGqVoLLAhfT6KqpBOp8nlcrS1zc1WDU1N\n8Wapi0w8yf2v3MPeG77Nu9ksExMT+Hw+bY6py+VifHyc5uZmVFUlEAiwatUqrWXI8f5OWltbF/0a\nSd6EEEKIj8ipkLwpikI8Hmd8fHzeDFOfz0csFiObzfJc7RlypRxr4+uw2+xUKhVmZ2eJRqNa/7R0\nOq399w//8A9cd911+P1+rFYrLpdL25Y1m80Y9HpWbnsIT6HAy1/+EhWTicaWNp44WGO6ZGGdYYiV\nLQ6q1Sow10i4UqloY61WrFihnT+LxWJ4vV4sFgtGoxFVr/Ky5UUqlTLrEufQ3tKurbSFQiEKhQLn\nbjiPO1+aYTqWYuueR4k0N5C67IvA3PSIeDyOoihavzq3243BYMBoNNLa2sq6deu01crj/Z1I8iaE\nEEIcRw888AA6nW7eKKxD+YM/+IMFxTvZyVs9OSsUCnOTB+x2YO5zLVu2jGKxyBMHH2d75jXOnd6A\nxWglmUzS3d1NLpfTti69Xq929qxYLPL4449TKBT4whe+gNVqpbOzk3K5zPbt2zGZTPT19ZFNp1n9\n2BP4IxFevOz3Kblc9PT08PJgnFdSAVqrk6yxJ2kKzMUOh8MUCgU8Hg8ej0erQDUajdRqNVRVxRVw\n8bLtRZSSwjn59Rj1c7/L5XLMzs5it9spmby8mm5kauQA35t4mtXxOPv+8ttMTE9rI7mMRiPlcpn9\n+/djs9no6+tj3759rF69mq6uLjo6Ok7Yd3I0yZv0eRNCCCEO47nnniOfz5PP50kmk/zmN7/RxkeN\njIzw8ssv43a72bhx44Lincw+b+VymVAopJ0lg7mkTa/Xay0+dkzs4N+zv2Lt9Dp0BT3JZFJbhSoU\nClpvuPoWq8lkolQq0dvbyxNPPMHy5cvp6OggHo8zNDSkDZavVqvY7HYGPG5M2SwXPPMsamsrg5Uy\nxmKCNkOMwbyDvbV2iqUK5nKSUiGnzSutT4Goj+9yOBzo7Tpecb1IQA3QO7uCaCRKY2Pj/0kyUxmG\nDMvYXWnj4G/u5a9ye9kQj/PcpiuYSia16Q7pdForntDr9fT09Gifqa+vj+bm5hP2nYD0eRNCCCGO\nq2984xva4y1btvCtb31rXqL22muv8corr5yMWzsmqqpiNptpa2vT+pbtOTjAE7nHOCt3Nh69l3A2\nTKVSwe12UyqV8Hg8VKtVpqenKRQKOJ1OhoeHsVqtWCwWLrvsMu6//36ampqwWq2Uy2USiQROpxOb\nzTY32cHnY9/55xHtXsZFT/4KS2MjE5uu4MDEBBfY8xhcZd6K29hbW8EyS4JALYKSz6CqKg0NDVSr\nVYrFIkWlwJuBN+iodLGitJKkIUlLSwujo2PEygoJaztj9l4s+Wn23P11/ufKHlYlUvzvy79ISqfD\nYjYDcwUcVquVYrFIZ2cndrud2dlZLBYLhUJB6313qo1Ek1YhQgghxALs2LGD9evXz3vu7LPPZseO\nHSfpjhanvnql0+nm+qH99nyaoijU1BpP5h5nhWkF6xvXU6vVCAaD9PT0kEgkqFQqDA8PYzKZtIrU\n+qioRCJBJBJh1apVtLe38+ijj2I2m1m+fDkAFosFm82mDaXX6XSYzj6bX1z+RRSjgQ3/sJWLsjk6\ng0Gc+iLnWCb4T75xLIqRfXTxH9V1PJ9p5zcHc7x6MMZIOcOLnpfwR1txhrqZKNgYqgR4IWzjhdqZ\n7NSvplIu4z74GJmffoenPE6C+QKvfvU/U/F6sVqt2vir+tZsS0sLDoeDZcuWsWbNGtxuN36/H1VV\n57VTOVXItqkQQgixAK+++iqVSoXe3l7tuaeeeopoNMpnPvOZBcU42eOx6jM87Xb7vOrJJ6ceJ1qK\ncqn5c5hMJhwOB01NTVqbjlqthsFgIB6P09raitVqJZfL0dzcTKFQ0EZLtba28sILLxAOhzn//PNp\naGgA5qY2RCIRqtWqFmv5qlW8YbcRMptZu28/y55+BpPdRjEYJDwToi+g0K3EcCb20+z3EC4YmVEK\nJLpfIzu5kanZDYyXHEzGixhNZgyVHJ26aVbpx3n9wf/J5YP7+LbDyUtnrGHgExdjcrlwuVyYTCbK\n5TK5XI7Gxkai0SjJZJLOzk50Oh2RSITZ2Vlgrg2ITqfD6/VqjY2P93dyNNumUrAghBBCLMDw8DC3\n3HIL1WpVq8w0GAzccMMNdHd3LyjGyS5YOFSMd+I7+ZeR+/j+mr/GylxFZTqdJhKJoNPpSCaThMNh\nRkdHURSF5cuXk0wmsdvtlMtl7Qza7t27tcHyt912G2vWrOGP/uiPsFgsRCIRQqEQBoMBs9lMNpul\npaUFn8+nzVs17d/PildfoykaI7luHZPBVnKrVxMp5JmZmcHZ5+B1+6t0TXQTyDVgMpmwWq2MjIzQ\n0NBAdzDI7KP/hvnZZ7nAZGZ0RR8Dn7iYvNGIyWSiu7ubmZkZCoUCfX192lxak8mE1+slGAzOrUL+\ndnpENDp3hq6pqemI26ZSbSqEEEKcwiqVCgcOHNAqLvv6+hY16/JUS95mC7P8f3tu4uu9m1nu7Jl3\nXT6fByCZTPL888+TzWbxer1MTEzQ2NiozUdVFIVsNouiKExPTwNzK1Z33XUXiqJw2WWX0dXVhcVi\nIRQKkUqlaGxsJJPJYDAY6OrqYmhoiHK5TGNjI6bJEL0zM7j37cc/NUXU6+X181t45uPwyYFmes1d\nZEplqpFZLNEYgXKZytg4vqkpdlcqzH5sHYXzNlIymfD5fFpRhdlsRlEUgsEgwWCQdDrNnj17tGTN\nbDbT2Niojb/S6XS0tbUdtkXI8fpOJHkTQgghTmGnUvJWqpW4Zc/NnBe4gI/7LwLQEpdYLMbMzAww\nN4R+79695HI5kskkqVSKpqYmxsbGADjzzDMZGxvD6/Vit9sZGhrC4XAwPj7Oq6++yq5du7j44ov5\nyle+oiV6Y2NjGAwGVFWlqamJYrFIKpXCarVSKBRob2+fO282OUmiNMBwf5bLf6XSNZbDUCxh0QFe\nHzGLmd/s3cuboUkc55zDxy+/HIvFojUVVlVVS97qkxPWrl2L3+8nkUgQi8UYGBjAYrHQ0NCATqfD\n4/FQq9UIBAILKlSQ5E0IIYQ4jZ0qyVsqleLe4Z9TrpW5zPslotG5EVWBQACn08muXbtIJpMA2hzT\n/fv3Y7fb8fv97Nu3D4vFgsPh0BKjmZkZOjs7tbYqqVSKQCBAKBTioYceIpPJcMUVV7B+/XqSySTT\n09N0dHRoK3qhUIhSqURbWxuVSoVcLsewfYjZhhl6h1aiS82thI2MjDA0NMTo6Ch79+7l/PPP12Ia\njUYuuugiDh48SLVaJRaLUSqVaG1tpVwu09raitvtxmazabNYk8kkiqKgKApGo5FVq1bh9XoXPID+\nZCRv0ipECCGE+B3z4uwLDGeH+Mve7xAam0JVVarVKjMzM5hMJtLpNKqqotPpiEajWo81g8GA2+0m\nGAxSLpcxmUxkMhlSqRQWi4VsNovVaqW9vZ1UKsXU1BR2u50bbriB7du389RTT/Gzn/2M1atXs2HD\nBmAuOTSbzQSDQQwGA1arlaHhIabbpogqEXrfXYlT52RgdICHH36YgwcP0tHRwRlnnMGVV16Jy+Vi\neHgYVVVxOp3aebz6RAZFUeamPBgMOBwOUqkUuVyOYrFINpvV5qM2Nzfj9/tJJpN4vd6T/A0dmSRv\nQgghxO+QkfQwv5x4lL9c9V8xG+baftQTML1ej8/nIxAIaD3O6o128/k8JpOJ/fv3EwgEyOfz2pD7\nUCiExWJBr9fT3d3Nrl27yOfz+Hw+stksRqOR3t5eWlpaUFWV/fv388ILLzA4OKit4Lnd7rl5pkYw\nXqJHN6vj3TsP8ujwLzEajZx11lmsWbOGq6++mjVr1lCpVJiensbn8zExMUEwGMRmszE6Okp/fz+5\nXI6WlhZtlJbZbCafz5PJZHA4HPh8PsLhMACdnZ00NDSg1+tZChuSsm0qhBBCfERO9rZpqVbi5j3/\ng882f44Ngblmw7Ozs+zZs0dbSQPo6OigUCgQj8cxGo0kk0ksFgvJZJJMJoPNZkOv1+PxeMjn84TD\nYVRVpbGxkWKxSCgUwuv1kk6nsdls2O129Ho9kUiEfD6vFQF4vV4mJyfJ5XI4HA72j+8nsyGFqWDC\n+KoJn9tHc3MzLpeLxsZGre9arVZj9erVWK1W9u3bh8vlYmJiQtu6tdvtuN1u4vE4FouFZcuWUS6X\nmZiYIB6P43A4aGlpwWQyoSgKJpOJQqEAsOCzbsfrO5FtUyGEEEIc1iPjv6DD0cF6/wbtOY/HQzAY\nJBwOUywWgbmErlQqUSwWMZvN2hD4es+zTCZD8rcjpnK5HGazGavVSjwe10ZajY2NEQwG6ezs1Oap\nWq1WrbWIy+VCr9fjcrno7u7G1Kiwp38XXaku3LNe1GUqHR0dzMzMaAnW3r17yWQymM1mhoeHCQaD\n5HI5bWyWz+ejWCwSj8e1c3P1Pm71xrwtLS2Uy2UMBgMrV66kUqmgKIrWiHehZ91OJknehBBCiN8B\ne5IDvB3fwU823kKt8H823RRFwePxMDk5CYDBYGD6t0Pb62Ot7HY7ZrMZr9dLpVLBZrPR2trKjh07\nMBqN2jSFaDRKNpvF4/HQ2dmJ1+vFZrMxMjJCOBzGarVitVpxu920t7eTSCTo7Oxkf3ofb+ff4jzl\nfFJjGWrUaO9oJxwO097ejk6no1QqYTAYsNlsWK1W7VyeoiiMj49jt9vJZrNkMhl8Ph/lcploNIrR\naMRut5NKpSiXy1gsFq1Zr9lsRqfTLanEDSR5E0IIIU6IgYEBBgYGtJ83bdp0VN3038tkMh1VjHQ5\nzb077+Hr/Zvx2n2UlPkTAex2OyaTienpacLhMA0NDaiqyujoKE6nk0QiQSKRwOPxYDQatRmn9RWx\nTCZDNBrFbrdjMBiYmZmho6ODYrGI0WikqalJOyPn9/txOBxMT0+TTCaZ8Uyz2/sOPaMr6FnWx5Bn\niEwmQyQSwel0YjQaMRqN5HI52tvb2bt3L9Vqld7eXsbHx4nFYlgsFvx+Px6Ph1wuh6IoWsFF/Vxe\nfURXfWXQ7/drhQ31alu/309jYyM6ne6EfyfvtW3bNu1xf38//f39R7xezrwJIYQQH5GTceZNVVX+\ncfCneE1evtL5B4eNUS6XKRaLTE9Pk81mOXjwoLbClUgkCAQCWkWn2WxmfHxcO1dW315VFIVqtYrZ\nbCaVSuFwOGhvb6dQKFCtVimXy7hcLkqlEslUkiH/IOOMc9bsx1jesFzrFzc+Po6qqvT09JDJZPB4\nPHi9Xvbt26dVxtYrS2OxGFarlVKpxMaNG1FVlXg8Tjqdxuv1ksvlqFQqdHd309bWpiVa9cRz9+7d\nWpGCTqdj2bJli1qBkzNvQgghhDiu3ohtJ5QP8dXl/+UDv6tvF9bHYQHa4HmXy4XRaCSfz+NyudDp\ndFrbjWw2S3t7O1NTU7hcLiqVCpVKBYPBQKFQwOPxoNPpyOVyqKqKqqoYDAaq1Sq5XI6yWmanfwe5\nao710Q00eZqJRCJ4vV7K5bK2wqeqqjbWKhwOz1WjAqlUSiuEqM9e7ejoYHh4mGq1qvV1m5mZ4Ywz\nzsBqtWozWU8HkrwJIYQQp6lUOcW20QfY3PcXKPr5q0mxWEwbFl+tVjGZTKiqqk04cDgcHDhwgEAg\nQKlUwmQy0dbWRjweJxqNUq1WaWtrI5vNksvlKJVKdHR04HK5OHDgAKqq0tbWpg13D4VCmM1mioYi\nr7tewVVzs2qsn4aWRqxWK8VikVKpxMTEBFarFYvFgs1m48CBA+h0OhobG7VtVKfTicvlIp1Os3z5\ncqrVKsVikXK5TDqdJpvNsnz5cgKBAEajEa/Xe8jEzWQyzWuLEggElsS5N0nehBBCiNOQqqrcP/LP\nnN9wIcscy+b9rlwuE4lEtFWxaDRKS0uL9nuj0UhzczNGo5FEIgHMVaVWKhXtHJ/H49FmvBqNRnp6\neli2bBmzs7P09/eTz+cpFAqEQiH0ej0AcWK87XuL9lwH5zsupNxdZnR0VDsrl06ntRW+QCBAOp3G\nYDCQTCZJJpP09vbS19eHz+fTChQikQjhcJjJyUkSiQQWiwWdTkexWGTlypU4HA7MZvMh/0Y6nQ6f\nzzdvK3UpkORNCCGEOA29GXuDqfwUX1v+J0e8zmAw4HQ6tUP67119qk9WqBscHJxbPSsWmZ2dxefz\n0dTUpBUHGAwGMpkMBw4c0AoFFEXB4XAwVD7IW/Y3OKeynj7bCtwuN++++67WMHd0dBSXy4Xdbmdm\nZgZVVSmV5gorrFYr+XyeUqnE0NAQBoMBj8dDOp3Wmu6uXLkSnU5HPp/H7/ejKArRaJT9+/fjdDrp\n6urSqlBhfqK2VJK2OknehBBCiNNMqpxi29gDXNN77Qe2SwFtZau+XdjV1XXY1af6z/XeaM3NzRgM\nBm2aQr03nN/v11bC6o18y+UyFquFHbq3GLYf5DP6z7G6ZTU2m41kMkmlUsFut1OtVunq6kJRFEKh\nEB/72Me01iKJRIJKpcLy5cvJZrNa9Wv9/lVVpVarYTAYOPvss4nFYlSrVa3qtVqtzlW1zsxQq9WI\nxWLAXGLqcDhO2HdwIknyJoQQQpxm/m3iUc71rf/Adul7LXa7sJ7wZbNZ7XF9K9VonEsnRkZG0Ov1\ntLa2kslkKOvLvOF9nbJa5kr7H9Ld3I3H48Hj8WhbnKOjo8DcVAefz6c1741GoyQSCRoaGiiVSlr/\ntnQ6rY3e0ul0WqVorVbD6/VqvegmJyfnjbqqVqvE43HtuUgkQnNz89H9gU8ySd6EEEKI08hkboJ3\n4m/z38780Ydeu9jtQp9vblxVNpslnU4zPDwMzK1i1RNBv98/N9VASTLQ+A4rLCv5uPViOto6tKIB\nvV6Poih0dXXR1NQEQD6fZ2pqimq1SqFQoK2tDUVRMBqNWvuO+vk5h8NBJpPB6/XOW0mrfx5FUfD5\nfBQKBaLRKE6nk6amJu383lInyZsQQghxGvnF2EN8vvX3sBltJyR+vVVIfcsS0Brq1hO3qD/C29Y3\n+bTtUnqVPnSqTlude7/6ebaZmRn0er02+aCtrY3W1lbi8TgAbrebUqmEXq/HYDCg0+lwu93ambz3\nJ6L1lcX6yqCiKBgMhnmVpSaTSTtXt5RI8iaEEEKcJgYSu4mWolzUePFJeX+Hx8EvY48yUhvm6x3f\nQJ+aqzI9UguOWCxGNBolHA7jcDi0c2hGo1ErmEgmk9qqWaFQwOFwaEUJR6Ioyrxr3r9VvJhJCqcS\nSd6EEEKI00BVrfKv49u4vP0KDPoT+8/7+wseAoEAyVqCn+6/kyZLE9/r/wEWg4Wy/8gzQ+stS2Bu\nu3V2dhaz2Uxra+u818RiMVRVnbcq19DQQCaTOap7X+okeRNCCCFOAy/NvojT6GKtZ+1H8n7vXcXa\nl93HPQN38bnWz3NJ06e0Fa2FJkr1tiAWiwWr1UqtVjvsdTC3KrdUV82OB/3JvgEhhBBCHJt8Nc/j\nk49xRcdXPtKkxmA08NTMk/zz8D38ee81fKr504t6//oKXq1WI5PJYLVamZyc5MCBA4TD4XnX6HQ6\ndDrdkpmCcCLJypsQQgixxP069BSrXavpsHd+ZO+ZKqe4e+h/Ua6V+X/7/wq3yf3hLzoEn8+nNfMN\nhUIATE9PUywW0el0NDQ0LMkpCCeSrLwJIYQQS1i8FOeF8HN8sf2yj+w934nv5Ef3VfeUAAANfElE\nQVS7/zsdtg6uW3n9USdudVarVRtGHw6HtQQtEonMm4ggidscWXkTQgghlrCXZl/gbP+5eE2+E/5e\nhWqBB/fezzuRnfxZz5/T4+w9brEDgQDRaJShoSGy2SwOhwODwXDc4p9OJHkTQgghToCBgQFtiDvA\npk2btK2/o2UymebFqKk1Xom8zPVrb1hw7PfHWKh3k+9yx56trPSt4ubzbjmmPnKHuod0Ok0ikaC3\nt5d4PE6hUCAQCOD1eg95ju5oP8epGGPbtm3a4/7+fvr7+494vSRvQgghxAlwqH+E0+n0McV0Op3z\nYuxO7MJhdOAnsODY74/xYcq1Mr8KPcEL4ef5v7v+Hz7R+QnS6TRpPhjjUEPfF3oP+XxeO+dWrVbR\n6/XaWKzj8TlO1RhOp5NNmzYt6jWSvAkhhBBL1IuzL3Bhw0UnLP5odpSfD91FwBzgB2t+iMfkOey1\nsVhsXt83n29x27hWq5Wuri7efPNNarUaTU1NpFKpBTXj/V0jyZsQQgixBCVLSQ6k9nN199eOe+xy\nrcyTocd5MfwCV3RsYr1/wxFbgNSb7b5/XNZik66WlhZ6e3u1hrzi0CR5E0IIIZagPckBVrpXYTFY\njmvcg+lB/nnkPgLmAH+15oe4j7DatlAL3U5VFIXW1tZ5K3iy6vZBkrwJIYQQS9BgZpBeZ99xixcp\nzvLI+MMMZQ7ypfYvc45v/YIb7h5qXFY96Vrsdqr0dPtwkrwJIYQQS9DB9Ltc3PiJY46Tq+T4VegJ\nXp59iUuaP81/XnY1JoN50XEOlXQdbjv1w0jSdmSSvAkhhBBLUKKcJGAOHPXrq7UKz88+z5OTj3Om\n9yx+eMaNx7xFKknXR0OSNyGEEGIJqtTKKPrFJ0uqqvJOfCe/GP9XfCYf31p5PW22thNwh0feThVH\nT5I3IYQQYgmyGCykyin8Zv+Crq+pNQaSu3nm3aeJF2J8pWMT/e41J3yQvZxhO/4keRNCCCGWoDWe\nM9gRe5NPt1x6xOtixSgvzb7Iy5GXcCseLu34LGsdZ2HQyeippUqSNyGEEGIJuqTpU/z9/i14TF7W\nes/StlBrao3p/BSDmUF2xt9mJDPMuf71fKPvm7TZ2o7LVIHFONbmveKDJHkTQgghlqAOeydf793M\nI+MP888j9+Iz+amoZdLlNDajnR5nD+v9G/jz3msw6U9Ow9ujrTYVRybJmxBCCLFE9Th7+c7q75Iq\np0iVkxh1CjajDZfiOtm3Jk4gSd6EEEKIJc6luE7JhE2qTU8MSd6EEEIIccJItenxp1PrG9FCCCGE\nOG4GBgYYGBjQft60adMxFwqYTCZKpdJJjXEq3MPpFMPpdLJt2zbt5/7+fvr7+4/4GknehBBCiI9I\nKBQ6ptcfj0rRY41xKtzD6RSjtbV10a/RH/W7CSGEEEKIj5wkb0IIIYQQS4gkb0IIIYQQS4gkb0II\nIYQQS4gkb0IIIYQQS4gkb0IIIYQQS4gkb0IIIYQQS4j0eRNCCCGEWEJk5U0IIYT4CLy3i/5SjnEq\n3MPpFONoXi/JmxBCCCHEEiLJmxBCCCHEEmK48cYbbzzZNyGEEEL8LmhsbDwtYpwK93A6xVjs66Vg\nQQghhBBiCZFtUyGEEEKIJUSSNyGEEEKIJcR4sm9ACCGEOF1t27aNp59+GpfLBcCVV17JunXrAHjk\nkUd45pln0Ov1fPWrX2Xt2rVHjPXYY49x33338bOf/QyHw7GoGA888ABvvvkmAE6nk82bNxMIBBYV\n49577+Wtt97CaDTS1NTE5s2bsdlsi4rxyiuv8NBDDzE5OclNN91Ed3e39rvF/D3efvtt7r77bmq1\nGpdccgmXXXbZEf92t99+Ozt27MDlcnHrrbcCkMlk+Lu/+zsikQgNDQ18+9vfxm63HzZGJBJh69at\nJJNJdDodn/rUp/j85z+/qDilUokbb7yRcrlMpVLh3HPP5aqrrlr0vaAKIYQQ4oTYtm2b+thjj33g\n+fHxcfWGG25Qy+WyOjMzo1577bVqtVo9bJzZ2Vn1Rz/6kbp582Y1nU4vOkYul9MeP/nkk+odd9yx\n6Bg7d+7Ufnffffep991336JjTExMqJOTk+qNN96oHjx48Kj+HtVqVb322mvVmZkZtVwuqzfccIM6\nPj5+2L+dqqrqnj171KGhIfX666/Xnrv33nvVRx99VFVVVX3kkUe0z3M48XhcHR4eVlVVVfP5vPrN\nb35THR8fX3ScQqGgqqqqVioV9fvf/766d+/eRceQbVMhhBDiBFIPURe4fft2LrjgAoxGI42NjTQ3\nNzM4OHjYGPfccw9/+Id/eNQxrFar9rhQKOB0Ohcd48wzz0Svn0sbent7iUaji44RDAZpbW09pr/H\n4OAgzc3NNDY2YjQaueCCC3jjjTcOeW3dqlWrPrCS9cYbb3DxxRcD8IlPfILt27cfMYbH46GrqwsA\ni8VCMBgkFostOo7ZbAagUqlQq9Ww2+2LjiHbpkIIIcQJ9NRTT/H888/T3d3NH//xH2O324nH4/T2\n9mrX+P1+YrHYIV+/fft2fD4fnZ2d855fTAyA+++/n+effx6TycRNN910VDHqnn76aS688MJjinG0\nnyUWi+H3+7WffT7fERPfw0kmk3g8HgDcbjfJZHLBrw2Hw4yMjNDb27voOLVaje9+97vMzMxw6aWX\n0t7evugYkrwJIYQQx+Bv//ZvSSQSH3j+yiuv5NJLL+WKK64A4MEHH+See+7hmmuu+cC1O3bs4J13\n3uGhhx76QIxHH32UH/zgB9pzh1rJ+7AY55xzDldeeaUW7+6772bz5s2LjgHw8MMPYzQateTtaGIs\nhE6nW/C1x2ox71UoFLj11lu5+uqr561oLjSOXq/nlltuIZfL8eMf/5jdu3cvOoYkb0IIIcQx+Ou/\n/usFXXfJJZfwk5/8BJhbLapvOwJ0dHSwadOmeatPAGNjY4TDYb7zne8Ac6tO3/ve9/jxj3+84Bjv\nd+GFF2orb4uN8eyzz7Jjx455n/lo7+O93h8jGo3i8/mO+dojcbvdJBIJPB4P8Xgct9v9oa+pVCrc\neuutXHTRRaxfv/6o4wDYbDbWrVvH0NDQomPImTchhBDiBInH49rj119/nY6ODgDOOeccXnrpJSqV\nCuFwmOnpaXp6ej7w+o6ODv7xH/+RrVu3snXrVnw+Hz/5yU/weDwLjgEwNTWlPd6+fbt2dmsxMd5+\n+21++ctf8p3vfAeTyaQ9v5gYh7OYGMuXL2d6eppwOEylUuHll19e1Iree9/z2WefBeC5557j3HPP\nPeL1qqpy5513EgwG+b3f+72jipNKpchms8Bc5emuXbtYtmzZou9FJiwIIYQQJ8htt93GyMgIOp2O\nhoYG/uzP/kw72/Twww/zzDPPYDAYuPrqqznrrLM+NN61117LzTffrLUKWWiMW2+9lVAohF6vp6mp\niT/90z/VVncWGuOb3/wmlUpFe+++vj7+5E/+ZFExXn/9de666y5SqRQ2m41ly5bx/e9/f9F/jx07\ndsxrFXL55Zcf8e+2ZcsW9u7dSyqVwuPxsGnTJs4999xFtefYt28ff/M3f0NHR4e2tXnVVVfR09Oz\n4DhjY2Ns3bqVWq2GqqpcdNFF/P7v//6iW4VI8iaEEEIIsYTItqkQQgghxBIiyZsQQgghxBIiyZsQ\nQgghxBIiyZsQQgghxBIiyZsQQgghxBIiyZsQQgghxBIiyZsQQgghjtnWrVt54IEHANi7dy/XXXfd\nSb6j05eMxxJCCCHEMdPpdFrz2lWrVrFly5bjEjccDvMXf/EXmM1m7bnLLruML33pS8cl/lIkyZsQ\nQgghjosT2ff/5z//+Uc6rP5UJsmbEEIIIRZteHiYO++8k+npadatWzfvdwMDA9x2223ccccdAHzj\nG9/gs5/9LM8//zzhcJjzzjuPK6+8kttvv539+/fT09PD9ddff8SRUKqqSvL2W3LmTQghhBCLUqlU\nuOWWW7j44ou566672LhxI6+99toRk6vXX3+dH/7wh2zZsoW33nqLm266iauuuop/+qd/QlVVfvWr\nXx3xPTdv3sw111zD7bffTjqdPt4faUmR5E0IIYQQi3LgwAGq1Sqf//zn0ev1bNy4kZ6eniO+5nOf\n+xwulwufz8fKlSvp7e2lq6sLRVFYv349w8PDh3ydy+Xipptu4vbbb+fmm2+mUCjw93//9yfiYy0Z\nkrwJIYQQYlHi8Tg+n2/ec4FA4Iiv8Xg82mOTyTTvZ0VRKBQKh3ydxWKhu7sbvV6P2+3ma1/7Gu+8\n885hr/9dIMmbEEIIIRbF6/USi8XmPReJRBYV41iLG05kccSpTpI3IYQQQixKX18fBoOBJ598kkql\nwmuvvcbg4OAJea/BwUFCoRC1Wo10Os1dd91Ff38/Vqv1hLzfUiDVpkIIIYRYFKPRyA033MBPf/pT\nHnzwQdatW8eGDRsWFeO9xQ3v7RH3fjMzM9x///0kk0lsNhtnnnkm3/rWt47p/pc6nfq7vO4ohBBC\nCLHEyLapEEIIIcQSIsmbEEIIIcQSIsmbEEIIIcQSIsmbEEIIIcQSIsmbEEIIIcQSIsmbEEIIIcQS\nIsmbEEIIIcQSIsmbEEIIIcQSIsmbEEIIIcQS8v8DzbFTfNBtURYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f32a3bb2490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# different dimensionalities of the dynamics\n",
    "nds = [3, 5, 11, 16]\n",
    "num = len(nds)\n",
    "\n",
    "# select test point (0: 5*ones, 1: saddle, 2: stable FP)\n",
    "testp = 2\n",
    "print 'test point: ' + pointlabels[testp]\n",
    "\n",
    "# spread of source samples (standard deviation)\n",
    "std = 8.0\n",
    "print 'std = %3.1f' % (std, ) + '\\n'\n",
    "\n",
    "# how strongly should the mean be weighted in the mean set (default: 1/3)?\n",
    "ut_mean.w0 = 1/3.0\n",
    "\n",
    "UTs = (ut_min, ut_base, ut_gauss, ut_scaled, ut_mean)\n",
    "nut = len(UTs)\n",
    "utlabels = ('UT min', 'UT base', 'UT Gauss', 'UT scaled', 'UT mean')\n",
    "\n",
    "meantrueobs = np.zeros((bam.nD, num))\n",
    "covtrueobs = np.zeros((bam.nD, bam.nD, num))\n",
    "Strueobs = np.zeros((bam.nD, nsample, num))\n",
    "meantruedyn = []\n",
    "covtruedyn = []\n",
    "Struedyn = []\n",
    "meanUTobs = np.zeros((bam.nD, num, nut))\n",
    "covUTobs = np.zeros((bam.nD, bam.nD, num, nut))\n",
    "meanUTdyn = []\n",
    "covUTdyn = []\n",
    "Dis = np.zeros((num, nut, 2))\n",
    "Z = []\n",
    "C = []\n",
    "for ndi, nd in enumerate(nds):\n",
    "    # set dimensionality of dynamics\n",
    "    bam.nd = nd\n",
    "\n",
    "    # create test point\n",
    "    if testp == 0:\n",
    "        Z.append(5.0 * np.ones(nd))\n",
    "    elif testp == 1:\n",
    "        Z.append(bam.findSaddle())\n",
    "    else:\n",
    "        Z.append(np.r_[bam.hopg, np.zeros(nd-1)])\n",
    "    \n",
    "    C.append(std**2 * np.eye(nd))\n",
    "    \n",
    "    dynfun = lambda x: x + dt * bam.dynfun(x)\n",
    "    \n",
    "    meantrueobs[:, ndi], covtrueobs[:, :, ndi], Strueobs[:, :, ndi] = \\\n",
    "        naiveSamplingEstimate(Z[ndi], C[ndi], bam.obsfun, nsample)\n",
    "    mt, ct, St = naiveSamplingEstimate(Z[ndi], C[ndi], dynfun, nsample)\n",
    "    \n",
    "    meantruedyn.append(mt)\n",
    "    covtruedyn.append(ct)\n",
    "    Struedyn.append(St)\n",
    "    \n",
    "    mtUT = np.zeros((nd, nut))\n",
    "    ctUT = np.zeros((nd, nd, nut))\n",
    "    for uti, ut in enumerate(UTs):\n",
    "        ut.D = nd\n",
    "        meanUTobs[:, ndi, uti], covUTobs[:, :, ndi, uti] = ut.performUT(Z[ndi], C[ndi], \n",
    "                                                                        bam.obsfun)\n",
    "        mtUT[:, uti], ctUT[:, :, uti] = ut.performUT(Z[ndi], C[ndi], dynfun)\n",
    "        \n",
    "        Dis[ndi, uti, 0] = WassDist(meantrueobs[:, ndi], covtrueobs[:, :, ndi],\n",
    "                                    meanUTobs[:, ndi, uti], covUTobs[:, :, ndi, uti])\n",
    "        Dis[ndi, uti, 1] = WassDist(mt, ct, mtUT[:, uti], ctUT[:, :, uti])\n",
    "        \n",
    "    meanUTdyn.append(mtUT)\n",
    "    covUTdyn.append(ctUT)\n",
    "\n",
    "ndlabels = ['nd=%d' %(y, ) for y in nds]\n",
    "\n",
    "print 'observation function:'\n",
    "print pandas.DataFrame(Dis[:, :, 0], ndlabels, utlabels).to_string()\n",
    "ax = aux.plotSamples(Strueobs, \n",
    "                     meantrueobs, covtrueobs, \n",
    "                     meanUT=meanUTobs[:, :, 1:], covUT=covUTobs[:, :, :, 1:], \n",
    "                     titles=ndlabels, ylabels=funlabels[0], \n",
    "                     utlabels=utlabels[1:])\n",
    "ax[0, 0].set_ylim([-7, 3]);\n",
    "\n",
    "print '\\ndynamics function:'\n",
    "print pandas.DataFrame(Dis[:, :, 1], ndlabels, utlabels).to_string()\n",
    "\n",
    "ndi = 1\n",
    "utinds = np.array([1, 4, 3])\n",
    "utl = [utlabels[i] for i in utinds]\n",
    "axes = aux.plotHDSamples(Struedyn[ndi], meantruedyn[ndi], covtruedyn[ndi], \n",
    "                  title=ndlabels[ndi], meanUT=meanUTdyn[ndi][:, utinds], \n",
    "                  covUT=covUTdyn[ndi][:, :, utinds], utlabels=utl)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Results for the stable fixed point.__ For the observation function I observe that the transformed distributions are reasonably well approximated by all but the scaled set which underestimates the spread of the transformed distribution in one dimension irrespective of the dimensionality. Mean and base sets, however, also tend to underestimate the spread of the transformed distribution which becomes more severe as the dimensionality increases. The Gauss set works exceptionally well, even as the dimensionality of the source distribution, $p({\\bf r})$, increases. \n",
    "\n",
    "Unfortunately, the Gauss set fails completely when the dimensionality of the transformed distribution, $p({\\bf o})$, increases, as it is the case when transforming through the dynamics function. This is because of the negative weight of the 0th sigma point (the mean) which leads to approximated covariance matrices that are not positive definite (producing $W$ = `NaN`). I do not show the Gauss set in the slice plot above. Instead, the plot shows the poor performance of the scaled set which severely underestimates the spread of the transformed distribution in the dimension of the one state variable that is not 0 in the stable fixed point (`dim 1` here). Note, though, that this underestimation is due to severe overestimation of the spread along the other dimensions. The other sigma point sets perform much better, but slightly underestimate the spread of the transformed distribution. \n",
    "\n",
    "__Results for the saddle point.__ Whereas the scaled set continues to overestimate the spread of the transformed distribution, the other sigma point sets considerably underestimate it at the saddle point. Overall, however, the Wasserstein distances show that the base and mean sets clearly outperform the scaled set with slight advantages for the base set over the mean set.\n",
    "\n",
    "__Results for the point $[5, \\dots, 5]^T$.__ Due to the similarity of this test point and the saddle point the base and mean sets perform very similar for the point $[5, \\dots, 5]^T$ (underestimation of spread and increase of distances with dimensionality). The scaled set performs best among the three test points for this point, because it only slightly overestimates the spread of the transformed distribution here (dynamics function). The Wasserstein distances identify the base set as the one with the highest accuracy across dimensionalities, except for `nd=11` where the scaled set gives the lowest distance, but only for the dynamics function. In combination of the results for observation and dynamics function the base set gives the best results.\n",
    "\n",
    "__The best sigma point set.__ Provided that the main idea behind the scaled set is to stabilise the performance of the UT for unknown nonlinearities I was surprised by the strongly varying performance of the scaled set for the different test points, i.e., nonlinearities. This variability is large for large uncertainty in the source distribution, $p({\\bf r})$. For smaller uncertainty, i.e., more local nonlinearities, the scaled set performs reasonably well for all test points, but is usually outperformed by the mean set. Overall, the base and mean sets performed best when all test points and uncertainty settings are taken into account. As the mean set is equal to the Gauss set in two dimensions and the Gauss set clearly performs best in two dimensions I favor the mean set overall, although the base set appeared to be more robust in high dimensions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Computational efficiency\n",
    "\n",
    "Seeing that the UT is not perfect in higher dimensions, I am now interested in how much computational efficiency I gain from using the UT as compared to naive sampling. I will therefore estimate the number of samples needed to reliably achieve Wasserstein distances $W$ that are at least as low as those of the mean set. I will say that a divergence is achieved reliably, when a fraction $\\gamma$ of repetitions has equal or better divergence than the mean set. The following function estimates the number of samples for which this criterion is fulfilled:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# function that estimates the smallest number of samples that gives a desired gamma\n",
    "def estimateNsample(mean, cov, trfun, trmean, trcov, DisUT, gamma, nsample=10, nrep=100):\n",
    "    gammaest = -np.inf\n",
    "    while gammaest < gamma or np.isnan(gammaest):\n",
    "        Dis = np.zeros(nrep)\n",
    "\n",
    "        for rep in range(nrep):\n",
    "            # for small number of samples it can happen that the \n",
    "            # estimated covariance matrix is singular so here I repeat sampling\n",
    "            # until the covariance matrix can be inverted in KLGauss\n",
    "            singular = True\n",
    "            while singular:\n",
    "                means, covs, _ = naiveSamplingEstimate(mean, cov, trfun, nsample)\n",
    "\n",
    "                try: \n",
    "                    Dis[rep] = WassDist(trmean, trcov, means, covs)\n",
    "                except linalg.LinAlgError:\n",
    "                    pass\n",
    "                else:\n",
    "                    singular = False\n",
    "                \n",
    "        gammaest = (Dis < DisUT).sum() / float(nrep)\n",
    "        \n",
    "        nsample += 1\n",
    "        \n",
    "    return nsample - 1, np.mean(Dis)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I will now estimate the number of samples needed to reliably achieve the distances computed above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test point: stable fixed point\n",
      "UT: mean set\n",
      "\n",
      "estimated number of samples:\n",
      "       obs  dyn  UT\n",
      "nd=3    16   55   7\n",
      "nd=5    12   35  11\n",
      "nd=11   11   12  23\n",
      "nd=16   16   17  33\n",
      "\n",
      "corresponding mean Wasserstein distances:\n",
      "          obs  UT obs      dyn   UT dyn\n",
      "nd=3   0.2145  0.3274   2.2431   3.0181\n",
      "nd=5   0.3328  0.4920   5.3006   6.7308\n",
      "nd=11  0.5494  0.8171  22.0171  26.0426\n",
      "nd=16  0.4953  1.0628  26.6638  49.8152\n"
     ]
    }
   ],
   "source": [
    "print 'test point: ' + pointlabels[testp]\n",
    "\n",
    "# fraction of repetitions that need to give better divergence\n",
    "gamma = 0.9\n",
    "\n",
    "# select the mean set for comparison\n",
    "uti = 4\n",
    "print \"UT: \" + UTs[uti]._name + '\\n'\n",
    "\n",
    "Distmp = np.copy(Dis)\n",
    "\n",
    "# uncomment this to check the increase of samples for fixed divergence\n",
    "# KLstmp[:, uti, :] = np.ones((num, 2))\n",
    "\n",
    "Nsamples = np.zeros((num, 3))\n",
    "Dismeans = np.zeros((num, 2))\n",
    "for ndi, nd in enumerate(nds):\n",
    "    # set dimensionality of dynamics\n",
    "    bam.nd = nd\n",
    "    dynfun = lambda x: x + dt * bam.dynfun(x)\n",
    "\n",
    "    Nsamples[ndi, 0], Dismeans[ndi, 0] = estimateNsample(Z[ndi], C[ndi], bam.obsfun, \n",
    "                                                        meantrueobs[:, ndi], \n",
    "                                                        covtrueobs[:, :, ndi], \n",
    "                                                        Distmp[ndi, uti, 0], \n",
    "                                                        gamma, nsample=nd)\n",
    "    Nsamples[ndi, 1], Dismeans[ndi, 1] = estimateNsample(Z[ndi], C[ndi], dynfun, \n",
    "                                                        meantruedyn[ndi], \n",
    "                                                        covtruedyn[ndi], Distmp[ndi, uti, 1], \n",
    "                                                        gamma, nsample=nd)\n",
    "    UTs[uti].D = nd\n",
    "    Nsamples[ndi, 2] = UTs[uti].N\n",
    "\n",
    "print \"estimated number of samples:\"\n",
    "print pandas.DataFrame(Nsamples, ndlabels, ['obs', 'dyn', 'UT']).to_string()\n",
    "\n",
    "print \"\\n\" + \"corresponding mean Wasserstein distances:\"\n",
    "print pandas.DataFrame(np.c_[Dismeans[:, 0], Distmp[:, uti, 0], Dismeans[:, 1], Distmp[:, uti, 1]], \n",
    "                       ndlabels, ['obs', 'UT obs', 'dyn', 'UT dyn']).to_string()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The estimated numbers of samples are surprisingly low! I expected that the number of necessary samples raises very quickly with the dimensionality of the source distribution. Instead the necessary number of samples decreases with increasing dimensionality! \n",
    "\n",
    "Furthermore, my criterion to reach the performance of the UT 90% of the time actually means that the average Wasserstein distance achieved by naive sampling with the estimated number of samples is lower than that of the UT. In other words, most of the time ($\\rightarrow 90\\%$) when using the estimated number of samples the naive sampling estimate performs better than the UT. I illustrate this with the following plot which shows the estimated distributions for UT and naive sampling for one particular draw of samples (regenerate the plot to see how the estimated distribution varies between draws of samples):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W = 5.1497\n"
     ]
    },
    {
     "data": {
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m+Z6l0+kQBEH2AFU9S6+08Pr9ftRqNdFoFIvFgtvtprOzc1HKSk0ob6Io8pGPfISOjg5y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\nu7LYEX+/UtJo9GE+oEkOoaqq8gA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wkB0bo5JKYb3+Nj6XsfGP//RPfPnv/5Ibrr+OG2+8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McPtSKKonBMq5Hv7cPzzL9z+PBhMpkMqqoyPz9v9BNN08iV69hNrLt+Yzr3rwiCIGwef/zH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\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DrVQqEAQBfr9fayuSTqehKAqsVitqtRq6u7shSRJmZ2dxzTXXIBqNwmw2I5VKQVEU9Pb2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\nqIX8fxgMQ2zJdluwAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f32a1b76ad0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ndi = 1\n",
    "\n",
    "bam.nd = nds[ndi]\n",
    "dynfun = lambda x: x + dt * bam.dynfun(x)\n",
    "\n",
    "means, covs, Samples = naiveSamplingEstimate(Z[ndi], C[ndi], dynfun, Nsamples[ndi, 1])\n",
    "\n",
    "print \"W = %6.4f\" % (WassDist(meantruedyn[ndi], covtruedyn[ndi], means, covs),)\n",
    "\n",
    "meanEst = np.c_[meanUTdyn[ndi][:, uti], means]\n",
    "covEst = np.concatenate((covUTdyn[ndi][:, :, uti][:, :, None], covs[:, :, None]), axis=2)\n",
    "estlabels = [utlabels[uti], 'naive']\n",
    "\n",
    "axes = aux.plotHDSamples(Struedyn[ndi], meantruedyn[ndi], covtruedyn[ndi], \n",
    "                  title=ndlabels[ndi], meanUT=meanEst, \n",
    "                  covUT=covEst, utlabels=estlabels, S2=Samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So sampling appears to outperform the UT in high dimensions in the sense that for `nd` $\\geq11$ you need fewer random samples than the number of sigma points to, on average, better approximate the transformed mean and covariance. In few dimensions, however, you need considerably more random samples to reliably achieve the accuracy of the UT. This result is caused by a relative drop in accuracy of the UT in higher dimensions (cf. underestimation of variance). The accuracy of naive sampling also drops in higher dimensions, but apparently not as heavily. The following plot shows the accuracy of naive sampling for a fixed number of 17 samples and increasing dimensionality in comparison to the accuracy of the mean set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test point: stable fixed point\n",
      "UT: mean set\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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Ll6K4uBju7u6wtbWV70ms/xyGhob4888/YWBggMGDByMgIABCoRB//PEHdHV1FWI3lA8h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\n5mBV+AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f32a149bb50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print 'test point: ' + pointlabels[testp]\n",
    "print \"UT: \" + UTs[uti]._name + '\\n'\n",
    "\n",
    "ns = 17\n",
    "nrep = 100\n",
    "DisS = np.zeros((nrep, num, 2))\n",
    "for ndi, nd in enumerate(nds):\n",
    "    # set dimensionality of dynamics\n",
    "    bam.nd = nd\n",
    "    dynfun = lambda x: x + dt * bam.dynfun(x)\n",
    "    \n",
    "    for rep in range(nrep):\n",
    "        means, covs, _ = naiveSamplingEstimate(Z[ndi], C[ndi], bam.obsfun, ns)\n",
    "        DisS[rep, ndi, 0] = WassDist(meantrueobs[:, ndi], covtrueobs[:, :, ndi], means, covs)\n",
    "        \n",
    "        means, covs, _ = naiveSamplingEstimate(Z[ndi], C[ndi], dynfun, ns)\n",
    "        DisS[rep, ndi, 1] = WassDist(meantruedyn[ndi], covtruedyn[ndi], means, covs)\n",
    "        \n",
    "Dismean = DisS.mean(axis=0)\n",
    "Perc = np.percentile(DisS, [5, 95], axis=0)\n",
    "\n",
    "fig, axes = plt.subplots(1, 2, figsize=(10.0, 5.0), sharex='all')\n",
    "\n",
    "for fi, ax in enumerate(axes):\n",
    "    ax.errorbar(nds, Dismean[:, fi], np.c_[Dismean[:, fi] - Perc[0, :, fi], \n",
    "                                           Perc[1, :, fi] - Dismean[:, fi]].T,\n",
    "                label='sampling')\n",
    "    ax.plot(nds, Dis[:, uti, fi], label='mean set')\n",
    "    ax.set(xlabel='number of dimensions', ylabel='$W$', xlim=[1, nds[-1]+1],\n",
    "           title=funlabels[fi])\n",
    "    \n",
    "    ax.legend(loc='upper left');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Altogether, the above results demonstrate that, compared to naive sampling, I do not gain as much computational efficiency as I thought from the UT. Instead of saving orders of magnitude of computation time I am, perhaps, only up to 5-times faster with the UT than with naive sampling (in low dimensions). In some circumstances naive sampling actually produces more accurate approximations of nonlinearly transformed mean and covariance with fewer numbers of samples than the UT. My results also suggest that, when I want to achieve consistently lower distances, i.e., better accuracy, than with UT I can use naive sampling with about 50 samples (for up to 11 dimensions tested here). This number, however, only applies to the difficult situation in which the source distribution is very wide and covers several complicated nonlinear regions of the transform function, i.e., where the UT approximation is not perfectly accurate. At this point it is also worth remembering that the accuracy, as quantified by the Wasserstein distance between Gaussians, may not be the accuracy you may be interested in, because it ignores higher-order moments of the distributions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Gaussianity assumptions\n",
    "\n",
    "The Gauss set explicitly captures one of the fourth moments of Gaussian distributions. At the same time, it often produces the lowest divergences in the situations tested above, at least when the dimensionality is low. So, does the theory work? Does the advantage of the Gauss set come from capturing some fourth moments of the source distribution $p({\\bf r})$? So far I have only used Gaussian $p({\\bf r})$. I will, therefore, investigate two things:\n",
    "\n",
    "1. Does the Gauss set perform best when its free parameter is set to $\\kappa=3$?\n",
    "2. Will the Gauss set loose its advantage when $p({\\bf r})$ becomes non-Gaussian?\n",
    "\n",
    "I will run the experiments in two dimensions again, because the Gauss set performs particularly well there (and particularly badly in higher dimensions). The results from above already suggest that 1. will not hold in all conditions, but let me look at this more diligently."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Benefits of $\\kappa=3$.__ In two dimensions the Gauss set is equal to the mean set and because I find the interpretation of $w_0$ more intuitive, I will use the mean set for the experiments. As a reminder: For $w_0=0$ I recover the base set and for $w_0=1/3$ I recover the Gauss set. This means that, when I vary $w_0\\in [0,1)$, the performance should be best for $w_0=1/3$, if capturing 4th moments of the source distribution $p({\\bf r})$ helps in approximating the mean and covariance of the transformed distribution $p({\\bf o})$. The following experiment tests this assumption:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test point: stable fixed point\n"
     ]
    },
    {
     "data": {
      "image/png": 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Vv1A2i1OVrrFqb4AT55pU6YqaelU6yaJWP6XY1Je4T2qyKk3D4zWQUHjnnGqb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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f32a130d610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# set dimensionality\n",
    "nd = 2\n",
    "bam.nd = nd\n",
    "dynfun = lambda x: x + dt * bam.dynfun(x)\n",
    "ut_mean.D = nd\n",
    "\n",
    "# select test point (0: 5*ones, 1: saddle, 2: stable FP)\n",
    "testp = 2\n",
    "print 'test point: ' + pointlabels[testp]\n",
    "if testp == 0:\n",
    "    Z = 5.0 * np.ones(nd)\n",
    "elif testp == 1:\n",
    "    Z = bam.findSaddle()\n",
    "else:\n",
    "    Z = np.r_[bam.hopg, np.zeros(nd-1)]\n",
    "\n",
    "# select values of w0 to test\n",
    "W0 = np.linspace(0, 1, 51)\n",
    "W0 = W0[:-1]\n",
    "nut = W0.size    \n",
    "\n",
    "# select stds to test\n",
    "stds = np.logspace(-1, 1, 50)\n",
    "num = stds.size\n",
    "\n",
    "Dis = np.zeros((num, nut, 2))\n",
    "for stdi, std in enumerate(stds):\n",
    "    # set spread of source distribution\n",
    "    C = std**2 * np.eye(nd)\n",
    "\n",
    "    # estimate true transformed mean and cov\n",
    "    meantrue = np.zeros((nd, 2))\n",
    "    covtrue = np.zeros((nd, nd, 2))\n",
    "    Strue = np.zeros((bam.nd, nsample, 2))\n",
    "    meantrue[:, 0], covtrue[:, :, 0], Strue[:, :, 0] = \\\n",
    "        naiveSamplingEstimate(Z, C, bam.obsfun, nsample)\n",
    "    meantrue[:, 1], covtrue[:, :, 1], Strue[:, :, 1] = \\\n",
    "        naiveSamplingEstimate(Z, C, dynfun, nsample)\n",
    "\n",
    "    for w0i, w0 in enumerate(W0):\n",
    "        ut_mean.w0 = w0\n",
    "        meanUT, covUT = ut_mean.performUT(Z, C, bam.obsfun)\n",
    "        Dis[stdi, w0i, 0] = WassDist(meantrue[:, 0], covtrue[:, :, 0], meanUT, covUT)\n",
    "        \n",
    "        meanUT, covUT = ut_mean.performUT(Z, C, dynfun)\n",
    "        Dis[stdi, w0i, 1] = WassDist(meantrue[:, 1], covtrue[:, :, 1], meanUT, covUT)\n",
    "        \n",
    "ax = aux.plotKLcontours(W0, np.log10(stds), Dis, titles=funlabels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The generated figure shows the Wasserstein distance $W$ depending on $w_0$ (x-axis) and on the spread of the source distribution (`std` in log10-scale on the y-axis) for the observation (left) and the dynamics (right) functions. I have marked $w_0=1/3$ by a vertical, grey line. Lighter blues indicate lower distance (in log10-scale), but I have limited the color scaling such that $W\\leq 0.001$ is white and $W\\geq 10$ is the darkest blue. The light gray dots indicate for each tested spread (`std`) the $w_0$ with the lowest $W$.\n",
    "\n",
    "The figure shows that the UT with mean set reaches distances around and below 0.001 for a wide range of values of $w_0$ if the spread of the source distribution is low (`std`$<0.4\\approx 10^{-0.4}$). In other words, for tight source distributions the UT with mean set performs very well irrespective of the precise setting of $w_0$. For medium spread of the source distribution (`0.4 < std < 3`) it appears that the distances are indeed lowest for $w_0 \\approx 1/3$, although the best values of $w_0$ seem to be slightly shifted from 1/3. The following plot confirms this for `std` $\\approx 1$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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VZYm/tby9vamoqLA8Pnv2bJOPDQsL4/Tp05d97mqvyWAw4ObmRmZmpmVbVlaWVdIXojNw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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f32a0f01b90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "std = 10 ** 0.0\n",
    "stdi = np.abs(std - stds).argmin()\n",
    "ax = plt.axes()\n",
    "ax.plot(W0, Dis[stdi, :, :])\n",
    "ax.set(yscale='log', title='std = %5.2f' % (stds[stdi],), \n",
    "       xlabel='$w_0$', ylabel='$W$')\n",
    "ax.legend(funlabels, loc='upper left');\n",
    "ax.plot(np.ones(2)/3, ax.get_ylim(), color='0.4');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For both, the observation and dynamics function, the divergence has a minimum at $w_0$ that is close to but unequal from 1/3 (tested with the stable fixed point at `std=0.95`). I would, however, still say that the performance for $w_0=0$ is good with $W\\leq 0.07$ such that the qualitative difference in performance between the found minima and other (small) values of $w_0$ is small. It is, therefore, more interesting to check the dependence of performance on $w_0$ in situations where the distances are higher overall. This is the case for larger spreads of the source distribution. For example, for `std=6.25`, the stable fixed point and the dynamics function $W\\approx 1.0$ at $w_0=1/3$, but the minimum is at $w_0=0$ with $W\\approx 0.6$ (check by setting `std = 10 ** 0.8` in the code above). The blue-colored contour plot above also shows that $w_0=0$ should be preferred over $w_0=1/3$ for the dynamics function and intermediate `std`s, because this value leads to lower distances. This relationship, however, reverses for large spreads above `std=7`. Then, $w_0\\geq 1/3$ should be preferred for the dynamics function. For large spreads of the source distribution the distances for the observation function show exactly the opposite trend: there, $w_0\\rightarrow 0$ produces the smallest distances. With some variation I observed similar effects for all three test points.\n",
    "\n",
    "The results for large spreads of the source distribution worry me, because they suggest contradictory consequences for setting $w_0$ depending on the nonlinear transform function. This fact demonstrates that simply capturing some moments of the source distribution with the sigma points is not sufficient to optimise the accuracy of the UT approximation. Instead, the specific form of the transform function, which enters the Taylor series of mean and covariance in the form of partial derivatives, also matters to a large degree. There is, however, a different interpretation of these results that is compatible with the original idea of the UT: It could be argued that a wider source distribution increases the contribution of higher order terms in the Taylor series, because a large region of the transform function is used to compute the transformed mean and covariance. This means in turn that the wider the source distribution the less important it becomes to capture the 4th moments relative to capturing higher moments. So the performance differences that I observe for different values of $w_0$ and different transform functions may simply reflect the different higher order partial derivatives of the transform functions. Optimal values of $w_0\\neq 1/3$ may in this interpretation just imply that the resulting sigma points by accident better capture relevant higher moments.\n",
    "\n",
    "So how should I set $w_0$, if I don't know much about my transform function, but do know that I will have large spread in my source distributions? My observations suggest that $w_0\\approx 1/3$ may be a good compromise. I can actually quantify that by determining the $w_0$ that leads to the lowest sum of $W$ (will be stongly influenced by large values) or the lowest median $W$ over the two transform functions and all values of `std`: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "best w0 (median): 0.38\n",
      "best w0 (sum): 0.02\n"
     ]
    }
   ],
   "source": [
    "Dispool = Dis.transpose((0, 2, 1)).reshape((2 * num, nut))\n",
    "print 'best w0 (median): %4.2f' % (W0[np.median(Dispool, axis=0).argmin()], )\n",
    "print 'best w0 (sum): %4.2f' % (W0[np.sum(Dispool, axis=0).argmin()], )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because I chose `std` logarithmically there are many more low values than the large values that I'm interested in, but I can look at values above a certain `std` too:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "best w0 (median): 0.00\n",
      "best w0 (sum): 0.00\n"
     ]
    }
   ],
   "source": [
    "inds = stds > 3.0\n",
    "ninds = inds.sum()\n",
    "Dispool = Dis[inds, :, :].transpose((0, 2, 1)).reshape((2 * ninds, nut))\n",
    "print 'best w0 (median): %4.2f' % (W0[np.median(Dispool, axis=0).argmin()], )\n",
    "print 'best w0 (sum): %4.2f' % (W0[np.sum(Dispool, axis=0).argmin()], )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These values of $w_0$ are specific to the chosen test point, but they don't differ that much for the other test points such that $0\\leq w_0 \\leq 1/3$ appears to be a sensible range with a tendency towards lower values for large spreads of the source distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Non-Gaussian distributions.__ The above results suggest that at least for some spreads of the source distribution the Gauss set indeed performs close to optimally, but is this really because the Gauss set captures some 4th moments of the underlying Gaussian distribution? I can test this by contrasting a Gaussian source distribution and a non-Gaussian source distribution with the same mean and covariance. The Gauss set should produce better approximations of the transformed distribution for the Gaussian source distribution. \n",
    "\n",
    "I will use the dynamics function at the saddle point for this experiment, because the resulting transformed distributions are non-Gaussian even for intermediate spreads of the source distribution and the means of source and transformed distributions should be the same. Consequently, I can use the distributions resulting from transforming a Gaussian through the dynamics function as non-Gaussian source distributions for my experiment. As a reminder, here is the non-Gaussian distribution for `std=0.5` of the original Gaussian source distribution (also check out other values):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test point: saddle point\n",
      "std =  0.50\n",
      "covariance of transformed distribution:\n",
      "[[ 0.27334685 -0.24303746]\n",
      " [-0.24303746  0.27597767]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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66qsOTsJERIcPHyae5+nKlStERLR8+XLq3LkzqdVqcnJyopiYGAdZW7ZsIYlE\nUqudq1evpoCAAJJIJBQUFOSwk4OobufCQ4cO1dp1d2t7iIh+/fVX4nme0tLShHNnz56lMWPGkE6n\nI4VCQcHBwTRjxgwqKioSyqxZs4a8vb1JoVDQ4MGDadu2bWyXXzNRWVlJM2bMICcnJ3JycqIZM2bQ\nwoULa91vd7pPysvL6ZlnniGdTkcGg4GWLVtGU6dOddjlFxMTQ1OmTKG///3v5OLiQhqNhqZNmybs\n8CQimjx5ci3n5127dlHv3r1JqVSSVqulyMhIWr58eb39+vjjjykgIIDEYjEFBAQQUd16RHTjnoyO\njiaFQkEBAQH0/vvv19pUUpce3Ny/3NxceuSRR8jHx4dkMhl5eXnR9OnTqayszKH/Nzul26+bMGEC\nOTs7k0KhoJiYGPrjjz+Ez+vStduN063jTUQUHx/vsBuYiOjDDz+kyMhIksvlpNPpqFevXrRhwwbh\n88LCQnr88cdJpVKRm5sbLVq0iCZNmsSc0lsIi8VCXl5e9MUXXzic/+WXX+jRRx8lDw8PkkgkpNPp\nKDY2ljZs2OCwEWHx4sXk7u5OKpWKRo4cSZ9++mmt3+Zvv/2WwsPDSaFQUN++fWnfvn3E87zglP7B\nBx/QQw89RFqtltRqNUVFRdHu3buJ6MZGoqeeeooCAgJILpeTwWCgCRMmUHZ2tlD/rfry+eefU0hI\nCMnlcnrwwQcpMTGRxGIxbdu2jYhuOKXX9XwMDg6mZcuWCccmk4m0Wi0dOHDgXoe5TcAR3f61af36\n9Th58iS0Wi3eeustAEBFRQXefvttFBQUwM3NDXPnzr2tzw6DwWAwGO2dlStX4vDhw3+pNCsN4T//\n+Q9Wr16NM2fO3O+mtAj1+lDFxsZi0aJFDud27dqFLl26YM2aNejcuTN27drVIEG37oJpTlpSVkvL\na6+yWlpeS/ftfreBfZdtT1ZLy2M6cffMnTsX586dq9d3ra327W5l1dTUYOXKlfjXv/7VIvKag8bK\nqtegCg8PrzX79Pvvv2PAgAEAbiRPbajzY2sehLYkr73Kaml57OHRfuS1V1ktLY/pxN2jUCiQlZVV\nb7iKttq3u5UlEomQnJyMYcOGtYi85qBJDaq6KC0tFbY/Ojk5CVsiGQwGg8FgMP6q3FPYBJbNnMFg\nMBgMBgOo1ykduBE1e9WqVYJT+pw5c/Dqq6/C2dkZxcXFWLZsGd55551a1yUlJTlMlz3++ONN3HQG\n497YuXP2IBq2AAAgAElEQVSn8P+IiAiHbcTNAdMJRmuH6QSD4UhjdKLRBtX27duhVqsxduxY7Nq1\nC0ajEU8//XSDGnZz5NjmRKPRCBFi25u89iqrpeV5eXm1iJw7wXSCyWot8phOtB957VVWS8trrE7U\nG9jznXfeQXJyMsrKyjBz5kw8/vjjGDt2LN5++20cOnRICJvAYDAYDAaD8VemXoNqzpw5dZ6/XQ4g\nBoPBYDAYjL8iLJcfg8FgMBgMxj3CDCoGg8FgMBiMe4QZVAwGg8FgMBj3CDOoGAwGg8FgMO4RZlAx\nGAwGg8Fg3CPMoGIwGAxGm8JiscBisdzvZjAYDtQbNoHBYDAYjNZEUVERCgoKAACurq7Q6/X3uUUM\nxg3YDBWDwWAw2gQWiwUFBQUgIhARCgoK2EwVo9XADCoGg8FgMBiMe4QZVAxGO4L5ljDaMxKJBK6u\nruA4DhzHwdXVFRKJpMHX2/XDYrGgurq6GVvK+CvCfKgYjHYC8y1h/BXQ6/XQaDQA0ChjqqioCHl5\neTAajVAoFNBqtVCpVExPGE0GM6gYjHbAzb4lAFBQUACNRtOoBw6D0VZo7H1tsViQkZGBsrIyFBcX\nw2KxwN/fH0qlkukJo8lgBhWDwWAw2jVWqxXl5eUgIpSWloLneVitVhQWFsJqtQoGlX25nBlYjLuB\nGVQMRjvA7lty85Lf3TwUKisrAQAKhaJJ28dg3E/EYjFcXFxQWFgItVoNpVIJq9UKjUYDsfjGY/B2\nS+bMyGI0FGZQMRjthLv1LbGTmZmJ9PR0AEBAQAB8fX2btH0Mxv1CIpHAy8sLcrkc7u7uMBqN0Ol0\ncHZ2hkQiue2SeXl5eYv4JVZWVuKdd97Bb7/9Br1ej8DAQMTFxaFXr17gOK5ZZDKaHmZQ3QR7E2G0\nde723q2srER6ejpqamoAAOnp6XBzcxNmqm7dOdiUOkJE7KHBaHZufuEAAJVKBbPZfNvyVqu1xfwS\n//3vf+PixYv4xz/+gdLSUly6dAkLFiyAQqHA9OnT8fDDD0MqlTa5XEbTwsIm/B9FRUVIT09Heno6\nioqK7ndzGIxWQ1FRETIyMnDx4kWcPXsWqampuH79+j3X++mnn+LBBx9E586d8dRTT+GDDz6A0Whs\nghYzGHUjkUiEP5lM5nD+1nAM9qXAO2GxWFBZWXlP4Up+/fVXzJo1C3369MGIESMwZ84c/PTTT/j7\n3/+OnTt3onfv3ti0aRMLidLKYQYVWPRdBkOhUCAgIAAikQgikQgBAQFQKBQOulFYWIiCggJcvXoV\n58+fR35+/l0/SIgIy5cvx0cffYSDBw9i8uTJOHXqFHr37o133nkHZWVlzdBLBuP26PV6BAQEICAg\nAHq9vkExr4qKinDx4kUcP34cZ8+eveuXcWdn51r3PM/ziIuLw44dO/Dxxx/j4MGDGD58OE6cOHHX\nfWQ0L2zJj8FgAAB8fX3h5uYG4PZO6eXl5XByckJlZSUuX76M6upqaDQa+Pv7N8p/q6amBtXV1QgO\nDoZarcaQIUMwZMgQpKam4t1330V0dDTi4+MxY8YMtgTPaDFuvdfq80u0WCzCS4bNZkNpaSny8vKE\nZUGLxQKr1QqxWHzHe9jf3x9paWkYPHhwnZ9HRETgk08+we7duxEfH4+BAwdi4cKFLIZWK+OuZ6j2\n7t2L+fPnY/78+di7d29TtqnFudfouwxGe0GhUDgYUzfrhqurK1QqFXieh1arxbVr14QHyeXLl5GR\nkYHU1FRcvXoVubm5qKiouK0csViMiIgInDlzxuF8cHAw3n33XXzzzTf47bffMGLEiFplGIyWxL5E\n2BiKiopw9uxZHD9+HBcuXMDVq1frXc4eOHAgvvzyS8Ffqy44jsOYMWNw6NAhyOVyDBw4EDt27Kj3\nGkbLInr11VdfbexFmZmZ+PTTT/HPf/4Tw4YNw44dOxAaGgq1Wl3vdeXl5XfbzkYhk8nqdTasC3vk\nXJ1Od8d+3Iz9LcRisUAkEjW2qY3mbvrWFmS1tLybnVPvJ61ZJ+zYdcPFxQUuLi4QiUSoqqoCx3Hg\n+RvvZGazGWKxGLm5uSgqKsKRI0eQlpYGkUgkjPWt+pGTk4M///yzzrdynU6HcePGQaVSYc6cOSgq\nKkKPHj3qfLAxnWgamE40DpFIBI7jUFNTg6qqKmi1Wvj4+EAmkyErKwuFhYUoKytDXl4eLl++jKKi\nIkilUuHF/WZ98PPzw6ZNm9CpUyf4+Pjcsd0DBw5EdHQ0Vq9ejR9//BF9+/aFSqVqsr41BqYT/+Ou\nZqiuXr2KkJAQSKVS8DyPTp064fjx43dTVauisW8i9vXzX3/99Z7WzxmM1o5dN1xdXREUFISQkBB4\nenqC53loNBq4uLigpKQEHMfh3LlzMJlMyM3NxdGjR3H27FmcP38eeXl5Dv5Wzz33HPbs2YOcnJw6\nZXIch0cffRQHDhxAdnY24uLi8Ouvv7ZUlxmMO6LX6xEaGoqoqCg88MADDktwNptNCLtgNBqRl5eH\n8+fP4/jx4zh58iSysrIEH0Se5zFlyhRs3ry5wbK7dOmC3bt3Izw8HEOHDsWBAweao4uMRnBXM1Qc\nx+Hrr79Gv379QET473//C4VCgW7dutV7XVt582gIFosFubm5yMvLA8dxMJlM4DgOzs7OwpuHxWKB\nzWZr0pkr9ubRNLC38btHJBJBqVRCp9PB09MTXl5ekEgkgi9JRUUFysvLhVAIbm5uuHr1KlJSUlBV\nVQWe5yEWi6HValFUVITffvsNAwcOvK08pVKJUaNGwcfHB/PmzUNJSQl69eolzI4xnWgamE7cHSKR\nCBKJRPidt2/sMBqNKC8vh81mg1QqhUQiQWlpKQoKClBcXIzi4mIYjUYUFxdDLBajU6dOeO211zBq\n1Cg4OTk1WHa/fv3QtWtX/P3vf0dWVhaio6OhVCqZTjQBLTJD5e3tjTFjxuD111/HypUrERAQwOLI\n/B/25T8WhoHR3pFIJFAoFJBIJHBzc0OnTp3g6emJ8PBwKBQKqNVqPPDAA8jOzkZhYSEA4MKFC9iz\nZw+OHDmC9PR0TJkyBV999RWuXbt2R3lDhw7F999/j1OnTuGxxx677cwWg3G/0ev16NatGx588EG4\nurpCLpeDiISZqtzcXBiNRpSWlgIAUlJSkJOTg0ceeQQrV65stLxevXph3759yM3NxZgxY5CWltbU\nXWI0AI6awKPtk08+gaurK4YMGSKcS0pKQlJSknD8+OOPt9ibh1QqbXYLloiQn5+P7OxslJSUQKFQ\nwNXVFVarFcCN5UC1Wg2JRAKO4xAUFOQQ9+RuaYm+3Q9ZLS1Po9Fg586dwnFERAQiIiKaVeZfQSfM\nZjOMRiPy8/ORn5+PiooKFBYWwmg0oqqqCoWFhZDL5VAqlfD09ETHjh3x8ccf4/r161i7di2cnJzu\nOKNrs9nw7rvvYu3atXj//fcxatQophNNANOJpsdqteLKlSvIyspCQUEB0tPTUVhYCJlMBr1eDzc3\nN6hUKly6dAkuLi7geR7Lly/H66+/jkceeUTwuWooRISNGzdi1apVWL16NR599NFm7N0NmE78j7s2\nqEpLS+Hk5ISCggKsWLECK1asgFKprPeaq1ev3o2oRmNPGdASWCwWSCQSVFZWIjs7G0SEmpoaXLhw\nAVqtFs7OztBoNAgICBCuqc9PKzc3F3v27EFBQQHMZjMiIyMRHR0tbGdvyb61pKyWlufl5dUicu5E\ne9QJ4EYU6oKCAtTU1OD69eu4cuUKLl++LCyNy+VyYenQYDBg3rx5iI+Px+DBg+Hm5tagjSHHjh1D\nQkICnn32WSQkJAhLgM0J04nmpz3qREFBAQoLC5GamirEdbOnwTl9+jS0Wi3Kysqg1+uRnp6OXbt2\nYevWrXBzc4NOp2t0bs20tDRMnDgRI0aMwKJFi5p1wxTTif9xVz5UAPDPf/4T33zzDX755Rc8++yz\n8Pb2vuM1bW1tvCHYdzFVV1ejuLgYAJCfnw+tVgubzQaLxQJfX19YLBZcvXoVJSUlsNlsguEFQGjr\n/v378fTTT0On0wlvLgcPHsTrr7+OL774Avn5+ejcuXOLhXRga+PNT3vUCQCQy+WC74hOp4NSqYRc\nLgfP87DZbJBIJJDL5aiuroZYLIaPjw/Wr18Pd3d3mEwmWK1WEJGDb8qt+Pj4YOzYsXj//fexZ88e\nxMbGNntSZ6YTzU971AmlUgkvLy9hA4d9hqqkpETwK5RIJDCZTNDpdEhNTUVWVhZcXV1RWFgIIoJS\nqWywYeTn54eRI0fio48+wu7duzFo0CDI5fJm6RvTif/RJEt+DaU9vnkAN6Yg7Q6IRUVFyM3Nhclk\ngkajgV6vh4+PD7KyssDzPCoqKlBVVYWCggLwPI8OHTqgqqoKADB9+nRs3boVDz74oEP9VqsVZ8+e\nxY4dO/DNN9/g4YcfxowZMxxmvZoD9ubR/LRXnahLnsVigclkgtFoxKlTp5CVlSW8bOTn52P37t2o\nrq7GM888A7VaDZvNBm9vbwQGBgoztHUhl8vx0ksvYd++fdi4cSMeeOCBFu1Xc8J0ovm4X9+lxWJB\naWkpsrKykJeXB7FYjJKSEgA3cmoWFBSA4zisX78eCxcuFFLgBAUFoUOHDlCpVBCJRPU6rttlWa1W\nLF++HPv378eWLVvQsWPHZutXS9GadeKuZ6juhvb45lFUVIS8vDxcv34dSqUSer0excXFqKmpQU1N\nDSwWC4gI165dg9FohMlkwqVLlyAWi2E0GpGZmQmxWIzz588jJSUFs2fPFmau7G8jPM/D09MTcXFx\neO6553D27FksXLgQZ86cQefOneHs7NwsfWNvHs1Pe9SJ28kTiUSQy+XQaDQQi8Uwm83C7if7/3/5\n5RdoNBphBtdoNEKlUqGmpua2EacVCgWio6NhMBgwa9Ys6PV6dO7cucX61ZwwnWg+7td3aV/qdnV1\nha+vL7y9veHr6wuJRAKr1QqbzQbgxqzWwYMHYTAYANwwtkpLS1FYWIicnByYzWa4urrWK4vnecTG\nxkKj0WDWrFkICgpCcHBws/SrpWjNOsEMqnvAvownFouFBJlOTk4wm81QqVRQqVSoqKiAWq2GSCRC\nTk4O1Go1TCYTLBYLzGYzqquroVQqkZGRgevXryMkJAQpKSnCWN36ENHr9ejRowcmTZqEnJwczJ8/\nH2VlZejWrVuTZyNnitL8tDedaKg8nU4HHx8feHt7QyaTCQ7tPj4++Prrr9GpUycYDAbhAcJxHKqr\nq1FRUQGdTlenrNDQUAwePBhLlixBamoqYmJimtyvqrWNY1PCdKJl5dnDLUilUigUCvA8j6KiIvA8\nDx8fH3h5eeHHH3+ETCaDj48PKisrQUTw8vJCeXk58vLyhLrsy+u3kxUREYHevXtjzpw5MBqN6Nmz\nZ5PtzL/f49ictEjYBMbtEYvFkMlkyMvLQ15eHrRaLYAby4Kenp7w8PBAUFAQxGIxlEolQkJChDeT\n8vJylJWVoaysDKmpqTh8+DCOHTuGzMzMWgloVSoVXnjhBfz444/IyclBbGwsfvzxx/vRZQbjrrCH\nVggICEBUVBT69euHuLg4REZG4vDhwygsLATP85DL5Thx4gSOHj2KwsJCpKWlobS0tM6kzCEhIfjm\nm2+QmpqK6dOno7Ky8j70jMFoPG5ubujSpQs6d+4MvV4PX19fxMfH4/DhwygoKIBer4e7uzuOHTuG\nixcvAgAyMjJw6dIlJCcn3zFUQrdu3fDtt9/i4MGDmDFjBkwmU0t06y8FM6jugbpyAAJAVVUV3Nzc\n4O7uLkzfisVi6HQ65OXlwWw2o3fv3hg0aBCUSiUKCgrQsWNH5OTkID09HUQkrKlbrVb8/vvvSE1N\nRX5+Pqqrqx3a4OnpibVr1+Ktt97Cq6++iunTp6OgoKBlB4LBuEcUCgXCw8MRGRmJhQsXoqysDJcu\nXYKzszOys7MF/6sTJ06gpKQEaWlpSEtLw7Vr12o9GLRaLf7zn/9AqVTiiSeeYHHgGG0G+zJgeHg4\nIiIi8OijjyIhIQE//PADXFxckJmZibKyMlgsFmRnZ6OqqgrXr19HRkYGUlJScPHiRZSWlgp+ubfi\n7u6Ozz//HCqVCuPHj2fPiiaGGVT3iF6vR1BQEAICAhzSDtij5arVavj4+ECr1SI3NxcWiwVKpRIW\ni0XIHejq6gqFQgFPT0+UlJRAJpNBp9PB29sbRUVF4DgOFy9exJEjR3D69GlcvXq11pt3v379sH//\nfvj7+2PIkCH46aefWngkGIx7x8nJCV26dMHatWuxf/9+VFZWCrO5dh+s7OxsIelseno6jh07Vsto\nkkqlWLNmDXr16oUxY8YgMzPzPvWIwWgc9jRPCoUCer0eL7zwAtzc3LB7926IRCK4urpCLBbDarVC\nLpfj8uXLyM7OhkKhQEZGBk6cOIFTp04hPz+/zvplMhnefvttxMTEYMyYMUhPT2/hHrZfmA9VE6BU\nKoWAnvaEmZWVlcKsldlsFuKPcBwHIoJKpYKzszNMJhOUSiVsNpsQxyouLg5yuRyXLl2CRqMRnHNl\nMhkyMjKQl5cnjOXNOz0kEgn69euHiIgIzJs3D7m5uejdu7ewS6SxsLXx5qe96sS9yvP09ISfnx/+\n9a9/YdKkSSgtLQXHcXBzc0NGRgaISAiua5djD81gh+M49OvXDxzHYf78+YiOjoa7u/t97Vdrlsd0\nonXK4zgOgwYNwsqVK9GvXz/h5SIsLExI96TT6VBVVYWrV68Kqxg2mw0mk0lYNr+1zj59+kAqlWLO\nnDno1asXPDw8WrRfd0tr1glmUDWDPIVCIcw+yWQyXLt2DaWlpVCpVCgrK4NCoYC/vz+cnJwEZ1uZ\nTAZPT09s3LgRbm5uKC8vh5eXF3ieh9FohNVqhclkQnl5OTQaDSorK1FeXg6e54VttHZ8fX3x2GOP\n4bPPPsPGjRvRu3dvh9mzu+1Xc9OaFaW5+KvoxN3QsWNH5OXlYe/evUJ8tqtXr4LjOIhEImH2lud5\nWK1WlJaWwmQyCUFB7TrRrVs3dOjQAQkJCQgPD4e/v/997Vdrlcd0ovXKUyqVCA8Px6uvvop58+bB\n398f1dXVggEVGBiItLQ0ODk5IS8vD4WFhXByckJqaqrgn1tXFoKuXbsiMDAQ8fHxCA0NRWBgYIv2\n625ozTrBDKpmkmdf8rPZbCgpKYFUKkVlZSW0Wi1CQkKEN2V7So6KigoUFxfj7NmzEIlEUKlU4DgO\nOp0OFRUVEIvFKC0thY+PD3Jzc8FxHBQKBdLT04Vt5zd/+QqFAqNHjwYR4f/9v/93V1vJW8M4Nhfs\n4dE25PXp0wc7d+5EZWUlBg8eDLVaDZ7nUVlZKeyOMhqNqKioEHYLchwnOK2rVCoAN5zVu3fvjlmz\nZkGn0911WIW2Oo4NgelE65bn5+eH4uJibNu2Dc888wxycnIglUqF0Dyurq7IzMyEzWYTdp7bN0jZ\nQ/hYLJZa33NQUBCioqLw/PPPw9nZmT0nboIZVGhdX7B9CdBisQjpNuw/+hUVFTh//jwqKytRXFwM\nm80GuVyO77//Hn379gUAeHh4oKioCBKJBAaDAfn5+VCr1cjPz4fRaISHhweSkpKQn58Pm80GlUol\nbJ/lOA5du3bFoEGDsHTpUqSkpKB///4NjrbbmsaxqWEPj7Yhzx5HZ+HChejUqRN69+4NpVIJlUoF\niUQiJJfV6/WCn1RJSQlyc3NRWVkJs9ksJHD29vZGXFwc/vGPf9z11vG2Oo4NgelE65fXu3dvfP31\n1zh//jx69+4NhUIhPF8MBgMqKiogkUjg5OQk/L+goABlZWXC5g27m8nN4Xi8vLwQFxeHBQsWoLy8\nHL169WqwbrTFcWwoLGxCK0Sv1wupeexZx4uKioScTna/KpPJBF9fXygUCly7dg3h4eEoLi6GSqUS\not7q9XpUVlZCoVDAZrMhPT0dCoUCNTU1OHfuHJKSkpCSkuKwpTw0NBTffPMNsrOz8eSTT7JdT4w2\nhZubG95//33Mnz8fGRkZ8PLyQocOHaDX6+Hv7w8PDw9kZmYKP7SXL19GcXExysvLUV1djaSkJMHY\nCg4Oxtdff429e/fipZdeEnwfGYy2gEgkwnvvvYf9+/fjt99+g0KhgIuLC7y8vCCRSNCzZ094enpC\nKpUiICBASMRsj/N25coVnDt3DhcuXKi1UcOuG99//z0WLFjAdOMuYAZVCyEWi4XZKrPZjJycHOTl\n5cHZ2RlSqVRwshWJRBg+fDj27t0Ls9ksRE3XaDQwm80wGAzgOA4ymQxubm6w2WxQKBTIyspCaWkp\nSkpKcObMGZw+fdphS6xWq8WWLVvw4IMPYuTIkUhOTr5fQ8FgNJoePXpg7ty5mDZtGkwmE9zc3BAZ\nGYmQkBCoVCooFAr4+PjAZDJBKpVCJpMhJSUFFy5cAABkZWWhoqICwI2t41988QWysrIwdepUFquK\n0abQ6XTYvHkzVq9eDaPRiK5duyI4OBhqtRoVFRXw9PSEl5cXDAYDAgIChGePPdxCTk4OUlNTUVpa\niszMTIf732Aw4IsvvkB2djbTjbuALfm1kLybd//l5+dDo9FAIpHgypUrkMvlkMvlUCqV4DgOLi4u\nOHXqFGw2G7p37w6lUomysjJBjqenp5DCICQkRDCOnJ2dheXBwsJCmM1mYQcIcGP5pF+/ftDr9Zg1\naxYCAwPrTUPQGsexqWDLG21PXmRkJE6dOoUdO3Zg9OjRwtJGcHAwlEolKioqIJVKIZVKcf36dSgU\nChQUFECtVsPf3x8mk0kIw6BSqTB69Gj8/PPP+OCDDzB06FAolcr70q/WIo/pRNuR5+bmBh8fHyxY\nsADjx4+Hi4sLnJ2dYTAYhLA8wA1ndru/ocViQVFREbRaLaxWK4qKilBYWIjS0lJYrVbhOSGVSvHw\nww8jMTERGzduxLBhw+pNOt6Wx/FOMB8qtN4vWKFQCGUVCgUKCwshlUrh4uIChUIBkUgEi8UCvV6P\nyMhIrFu3Do899hiys7OhVqtRWVkJo9EIhUIBhUIBDw8PYdegRqNBTk6O8FlZWZmQdqOyshIuLi5C\nO8LDwxEdHY05c+bAZDLd1pektY5jU8AeHm1PHsdxGDhwIHbt2oVjx45h8ODB4DgOarUaTk5OgqEk\nl8tRVFSEiooK+Pr64tq1a7hy5QoqKytx7do15OTkQCKRQK/XY9iwYcjOzsayZcswcODAO+bFbA/j\neDuYTrQteaGhobh+/To+/PBDjBs3TohfZU97VlNT4+Czq1AoUF5eDq1WC57nkZeXB6vVipqaGmFj\nkz1NmkgkwrBhw5CZmYnly5dj0KBBt9WNtj6O9cEMKrTeL7ioqAj5+fmoqakR8vhptVooFAqIxWIE\nBwfD398fXl5eCA0NRU5ODg4cOICHHnoIWVlZQjDQq1evwmg0CjsHOY5DWVkZ3N3d4eXlhfz8fEil\nUnh4eODEiRPIzs6GWCyGk5OT4Ijo4eGBMWPGYPXq1UhKSkJsbGytvGetdRybAvbwaJvyRCIRhg4d\ninXr1iE/Px+9e/cWZDk7O0Ov16O6uhpWqxUymUyYqbVvMZfL5ZBKpTCbzZDJZFCr1ejbty/EYjHm\nzp2Lnj171huPp72MY10wnWh78qKjo7F7924kJSUhJiZGOO/i4gKpVAq9Xg+z2Yzi4mLU1NQgLCxM\nSLLs5OQEtVqN69evC6F70tPTodFoBGf3fv36ged5zJ8/H/3794ebm1uL9Ks+WrNOMIOqheTZEykT\nkZDvz8vLCwCEAKBarVZ4yxCJRPDz88Obb74JDw8PyGQylJeXw9XVFTzPQ6/XIy8vT0hp4+TkBG9v\nb5w7d05YCvzjjz8AAGq1GikpKbDZbMIMmP382LFjsXXrVhw4cABDhgxxCALaGsexqWAPj7YrTyqV\nYujQoViyZAkUCgW6d+8uyLo5krRarRbScJjNZvA8Dzc3NxQWFsJoNAo7bV1dXdG1a1cEBAQgPj4e\n4eHhCAgIaPF+3W95TCfanjye5zFw4EC8/vrr0Gq1iIiIEGRZrVaIRCK4ublBo9FAqVRCJpMJEdhr\namqEDUrFxcVC4uXCwkJhphe4sdTu4eGBF154Af369YPBYGj2ftVHa9YJZlC1kDx7PKqb8fLygk6n\ng06nE4IR2rFYLCgoKIBYLMaOHTvQt29f4W3D3d0d5eXlKCwsFFLZ8DyP5ORkh63kKpUKer0eFRUV\nqKqqglQqFaK124O8yWQyjB49Gnv37sUnn3yC4cOHQyaTNbhfTUlrVpTm4q+sE/eCSqVCbGwsZs+e\njZCQEPj6+jp8rtPphDhUFRUVsFqt6NSpE0pLS1FcXCwshdhfMkQiESIiIhAVFYWEhAQEBQUhKCio\nxft1P+UxnWib8hQKBfr164cXXngBnTt3hp+fXy1ZGo0GRqMR5eXlqKyshMlkgqurK/Lz81FeXg4X\nFxfk5uaiqqpK8LEqLy8X/KrCwsLg7e2N559/Hn379nUwqtrLONYFM6jQOr/gulLS3LxefSs2m00I\n5Hn27FlkZGRgxIgRkMlk0Ov1uHz5MqRSqZCKw57GprKyElarVdg2m5WVheLiYgQEBMBqtSIvLw9G\noxFmsxlSqRRKpRJisRgjR47EyZMn8e6772LYsGFQqVStchybCvbwaPvydDodoqKiMG3aNGG7+M04\nOTnB2dkZWq0WHTp0gM1mQ2FhIUQiEcxmM/Ly8qDX62Gz2ZCXl4fKykqEhYWhb9++SEhIgL+/P0JC\nQlq8X/dLHtOJtivPxcUFkZGRmDlzJmJiYuDt7V1Llk6ng1arRVVVFa5cuSIEkLZarSgpKYFer4dI\nJEJqaiqqq6uh0WhgMpkEoyo0NBS+vr5ISEhAdHS0sDTensbxVphBhdb7Bd+ckubWGalbsRtgNpsN\nnTt3xieffAJ/f38MGDAAROQQIdce2M3d3R3Z2dlwcnJCYGAgzp8/D6VSCTc3N5hMJiGwqFQqRXFx\nMVx9swsAACAASURBVJydnVFVVQWNRgOe5zFo0CDk5+dj6dKliIuLg8FgaJXj2BSwh0f7kOfp6YkH\nHngA8fHxGDJkiPDjb0cikcDFxQWlpaWQSqUoKytDVVUVjEYjfHx8IBKJcOHCBUgkEtTU1KCiogI+\nPj4YMmQIZs2aBW9vb4SGhrZ4v+6HPKYTbVtehw4d4OXlhblz52LcuHHCSsPNSKVSIXSPPQOHl5eX\n4FN47do11NTUwNnZGUlJSaiurkZlZaVgPIWEhCAwMBAJCQno1asXPD0929043kyLGVRfffUVNm3a\nhB9++AEXLlzAQw89dMcI3ExRcNsZqbqwG2AdOnRAly5dsGTJEkydOhVSqRQmkwllZWWwWq0wGAy4\nfv06ysrK8OCDD4KIoFAoYLFYYDQahTdyIoJSqURRURHkcjmqqqqQkpICq9UKd3d3cByH6OhoiEQi\nzJ8/H0OHDm3RH9nWrCjNBdOJeyciIgJSqRQLFy7E6NGjhXQzN+Pi4oLKykohEblcLodGo0FycrKQ\n1qm4uBhOTk4oLS1F586dERsbixdeeAHu7u4IDw9v8X61tDymE21fXlhYGGpqarBs2TKMHTu2TqNK\npVKBiFBVVYXq6moolUq4u7vDbDajoKAAAQEBSE9PFz4rKCiATCYTdooHBwcjODgYM2fORI8ePRAQ\nENDuxtFOixhU+fn52Lp1K958800MHz4cv/76KywWyx2TjjJFaTwikQilpaXgOA5GoxEff/wxnnji\nCVgsFiFhsslkgouLC3x9fYUdTTabDRqNRshrptVqIRaLkZubK8w8ZWVlwdnZGRaLRcgbCNxwQnR2\ndsbzzz+P2NhYh5ALzUlrVpTmgulE08gKDQ1FSUkJ3nrrLYwbN05Iv3Qzdr9BuVwOrVaLzMxMWCwW\nVFdXg4jg7OwMnudBRKipqYGfnx8GDx6M2bNnQ6/XIyIiol2PI9OJ9iGve/fuSE9Px+bNmzFmzJg6\nX+CdnZ0hl8thsVhw8eJFcByH4OBguLm5IS8vDyaTCQaDAf+/vTsPj7K8Gj/+nT0zmSUzmawkkA0I\nRBQUWRQVFUGpQLWvoKBvwbVsikgFfX+0KlYBFRfEpW51qVarRWprtb4ufa1dVMQFZBEIIQtZJpmZ\nbDOT2X5/cM1TIhAkyUwWzue6elXCTM5zQw5zP/dz3+cEg0GamprQarX4fD7sdjsajYbCwkKGDh3K\n/PnzGTt27GEb1eOpN+dEpyZU0WiUDz/8kHPOOQeNRsP//d//cfLJJysNf49GEuXogsEgkUjksB/+\nQ08Hjhgxgk2bNlFfX4/ZbMbtdpOUlEQ4HMZoNFJbW4vP5yMpKYlIJKI8zos1yqytrcVqtZKens6+\nffuw2Wy43W4CgQAqlYr6+nplH8pJJ51EVlYWCxcuTNikqjcnSrxITnRfrPHjx/Pll1/yu9/9jmnT\nph3xg8RkMmGz2WhrO9iFILanRKVSkZWVhVqtpra2Fq/Xi1arxWQycemll7JkyRJsNhunnXZav/1z\nlJzoH/FUKhVTp07lrbfe4sMPP+Siiy46Yp1Bs9lMRkYGOTk5WK1WmpubCQQC2Gy2djfnmZmZeDwe\nIpFIu5pW+fn5DB8+nGuvvZZRo0aRk5MT97FB786JTk2o9Ho9Op2Oe+65h7/85S/k5uYyffr0Y75P\nEuXIGhoaqKqqwuPxKD+sMYeeDlSr1YwbN44777yTk046CYfDQTAYZOjQoVRUVABQXV1NfX09gwYN\norS0lOrqanJycmhpaVE26VZWVjJw4EBcLhc6nY7W1lZcLpdSeyS2UjV69GhsNhs33ngj5513Xtwn\nVb05UeJFcqL7YsUKf27atIl//OMfTJ48+YgfJBqNBrvdTktLC8FgUHm0XlNTQ3V1NcnJyQSDQfx+\nP36/n8zMTC655BKWLl2KyWRSjqYncmyJIDnRf+IlJSVxzjnn8NRTT7F//34mTJhwxNdpNBrMZjNG\no5FAIIBarUar1dLU1EQ4HMZgMGAwGCgrK8Pr9SpV2GPdPfLy8hgzZgzXXHMNo0aNIjc3N+5j6805\n0akJVXV1Nc899xz3338/l156KR9//DGRSIRBgwZ1+D5JlMMdugIFB6uaW61W5e76+6cDCwoKSEtL\nY+3atVx88cVKI8yKigpqa2uVwoXNzc1KOQWDwYBarVYeg1gsFgwGA3q9nkAgoNS+ivV6crvdZGdn\nYzAYKCwsJDU1lSVLljBp0iSlhlU89OZEiRfJie6NpVarufDCC3n88cepqqrizDPPPOr70tPTCYfD\nhEIhqqurUavVqNVqpRyJzWbDYrEQjUbJzc1l6tSpLFu2DK1Wy8iRIxM+tniTnOg/8QwGA5FIhClT\npnDnnXei1+s55ZRTjvp6nU6HSqUiGo3i9XrZtWsXoVAItVqtdOpobm7G7XaTlpamvM5utzN06FDl\n8d/o0aMZMGBA3MfWW3NCe+yXHG7v3r0MHTpUCTZ27Fh27tzJWWedpbxm27ZtbNu2Tfn1zJkzE5aw\ner0+of84dCVeIBDAaDQqEyqVSqWULIiJLc3G7qYvvfRSpV3G888/T3V1Nbm5ucrju6KiIjwej3IX\n3tDQoHxQ6HQ68vLylLuStrY26urqgIN1sSorK/H5fNhsNk4++WQsFgvz5s1Dq9Uye/Zs/vSnP1FQ\nUND1P7QjSPTf22uvvab8d0lJSdxXHiQnEhPLYrHwxhtvMGnSJPLy8rj66quP+t6TTjpJaRgbCoXQ\narWEw2G0Wi01NTUYDAa8Xi/Nzc0MGzaMd999l8mTJ2M2m5k3b17CxxZvkhP9I14slsViYePGjVx4\n4YXk5+dz0UUXHfU9ZrMZh8OBSqXiwIED1NfXY7VasVqtNDU1EY1GCQaDlJeXAyinBEeMGMFFF13E\nU089xbXXXsvvf/97TjvttLiPLVGOJydU0dgn+XHYt28f69ev595770Wn07FhwwaKioq48MILO3xf\nVVXV8YbqFIvFkrC7nO6I19DQgMvlAsDpdB5xFSj2GqPRqPRpWrZsGQDXX3+9slzr9XqVeiL19fXK\n12IJodPpGDJkCLt27UKn02EwGGhublZWsrKzs9myZQtOp5Phw4e3S4wXX3yRDRs2sGnTpmPul+uM\nRP69xarU9zTJifjFKi0t5dJLL2XNmjVMnjy5w++xY8cO6uvrlQ+LxsZGotGo8pg8Vm7k3HPPZc+e\nPVx22WUsW7aMyy+/PC5jipGciJ8TKSe++OIL5s6dywsvvHDM1dWGhgYqKirYvXs3BoOBlJQUtm/f\njtfrJTs7G7VajclkUtqm5eTkKD877733HsuWLeO3v/0tJ510UkLGFk/HmxOdeuQXq1/0zDPP8N57\n72G325k5c+ZhveC+T5Zyj+xY9am+37amqamJ5uZmxo0bx8svv0xzczOFhYVYrVZOOukkzGYz9fX1\nGI1GTCYTzc3NeL1ekpOTycnJUZrE6nQ63G43qamppKen4/F4qKurU053NDc3Y7fblbuBU045hdbW\nVlavXn3UI7ld0ZuXcuNFciJ+sex2O+PGjeNnP/sZp59+eoePIpxOJ36/n4yMDNxuNy6Xi4KCAhob\nG/F6vUpzcjh4bPz888/n5ptvxm63x3UVR3Iifk6knMjKyqKwsJDFixdz4YUXdtgEPNaaJj09HaPR\nSHV1tVJWJxQKARAKhQgEArS2tmI0GrFYLOh0OgoLC8nLy2PhwoWcc845R+z9191ji6eE1aEqLi5m\nypQpTJkyhTFjxhxzMgWSKB3pqD7VoRvTYwUII5EIoVAIp9PJb37zG4YNG8bQoUNJS0tj//79tLa2\nolar8Xg8aLVajEYjer2evLw8Zam2ubmZrKwsVCoV5eXlyoeJ3+/HaDQqx2S9Xq+yIX3MmDHs3LmT\nZ599lhkzZrTr/ddVvTlR4kVyIr6xMjMzGTZsGPPnz2f8+PEdNj5OTU2lqalJadlUW1ur1HsLBAIM\nHDiQyspK/H4/RUVFXHDBBSxZsoS0tDSlTlUix9bdJCf6T7wjxSosLMRgMPD//t//Y9q0aUes1xYT\nq6Jus9nQ6XS4XC6lllskElH+19LSwoEDBzAYDMpTi8GDB5OVlRW3w0y9OSekUnofiHfoxnSdTofN\nZlPuHMLhMMOHD+fhhx9m5MiR5OXlUVZWhk6nUyqiGwwGTCYTJpOJ1tZW6urqiEQi2Gw2rFYrer0e\nr9eLy+UiNzdXqWsVa6qclJSE1+tV7lImTpzIBx98wDvvvMPUqVN/0GT6h+jNiRIvkhPxj5Wfn09h\nYSELFixgwoQJHT6uttvtJCUloVKpqKysxO12AwdvasxmM6mpqYTDYcLhMHa7nYsuuogbb7yRrKws\niouLEz627iQ50X/iHS3WyJEj8Xg83HvvvUybNq3difIj0Wg0GI1GGhoalNP9SUlJNDU1UV1djdVq\nVT5XIpEIycnJ6HQ6iouLlcNMF1xwwWEdDOIxtniQCRX9M1FijwUzMjLQ6/Xo9XpCoZByEikjI4OH\nH36YqVOnolKpqKioIBQKYTabqa6uxu12Y7fblb1UscKfOp1OqUkVq6Cbk5OD1+ulvLwck8mk7CWJ\nvUetVnPBBRfw29/+lq1bt3Luuece8Xj68erNiRIvkhOJiXXoo4jvN3f9vtgHBoDL5SIcDjNw4EC0\nWi319fXKCdpAIEBhYSETJ05k8eLF5ObmMmTIkISPrbtITvSfeB3FGjduHFVVVdx///1cfPHFx5xU\nxUrr1NTUoNVqcblcBINBLBYLBw4cIBwOK58lsceANpuN4cOHY7VaueWWW7jwwgux2WxxH1t3kwkV\n/TdRNBoNJpOJtrY25fFgW1sbFouF8ePHY7PZWLlyJWeccQZGoxGbzcb+/fuV1arW1lZlL0hLS4vS\nGNloNGI0GmlpaSEpKQmfz0dtba2yZytW2M3lcqFWq7Hb7Wi1WqZMmcK6detobGxk7NixXR5fb06U\neJGcSFyswYMHk5OTw6JFi465vyMlJYVwOKxUVY+1bCovL1cK8MZWjYcNG8aECRNYuHAhBQUFFBUV\nJXxs3UFyov/E6yiWSqViwoQJ7Nu3j0ceeYRp06Z1uB82tp/WYrFQW1ur3NB7vV5lMmUymSgvL6eu\nrg6DwYDdbken0zFixAgMBgPLly9n6tSp3fIz1ptzQiZUfSzeobFiq1YpKSm43W7UajWNjY288sor\nTJ8+HZ1OR0tLCx6Ph7a2NtLT03E4HEpbgVj7Ab1eT0tLC42NjUQiEWpqajCZTNjtdkwmE5WVldTX\n1ysta1JSUtDr9SQlJTF58mRuv/120tPTu/zIozcnSrxITiQ21pAhQ5T9HcfqABD7+Y/l1+7du9Hp\ndMoHidFopKKiApVKxfDhwznzzDNZsGABJSUlx6zJF4+xdZXkRP+Jd6xYKpWKs88+m507d/LYY48x\nffr0I7ZrgoOPuxsaGpSSIn6/H41GQygUUto1lZWVYbValWK5FoulXSuzYDDIr371q6M2be7OsXUn\nmVBxYiVKrPHxtm3bCIfDFBcXU1ZWxjvvvMPIkSOxWq3AwYKHqampSqFOs9lMRUUFpaWlpKSkUFNT\no7SfcTgcyib2QCBAY2MjFouFffv2EQqFaGtrIzk5GaPRiNlsZvz48SxcuJCzzz67Sz2denOixIvk\nROJjFRcX43Q6WbJkCeeff36HxWqTk5NRq9W43W7C4TBut1t57O31epWCuCaTiSFDhnDqqacyf/58\nzjrrrG7pbyY5ET8nek6oVCrOPfdcvvzyS5555hmmTZuGTqc77HWx1djW1lb0ej0GgwGLxYLT6cTj\n8RAKhZQK6k6nU6mkXl9fr+xXHD16NN999x3PPffcUfsLdufYusvx5kT37CYWCRMIBAgGgx2+Zt68\neaSkpPDCCy+gUqlIT0+noKCA1NRUpUny3r17lVNM1dXVyumnWKKoVCplMpaWlqbUyTIYDOzatYvd\nu3cr13HSSSdx9913c80111BfXx/H0QvRPX7yk5+wfPlyZs2axd69ezt8rc1mw+FwMGjQINLT00lN\nTUWv1yuHRAKBALt376a0tJSxY8dyzz338NOf/lSpaSVEb6VSqVi9ejWDBg1i7ty5SmmQ73M4HOTl\n5TF48GBOOeUUioqK8Pl8pKWlYTQaycjIwOfzKa2aPv30U7777jt27dqlxLnzzjuxWCzccsstdKL8\nZZ8gE6o+pKGhgT179lBaWkpDQ4Py9VijyljphcLCQtasWUNVVRWPPfYY4XCYmpoaqqqq2Lt3Lx6P\nB6PRiE6nw2w2Kyc4Tj75ZEaMGEFLS4typ1JQUIBKpUKr1ZKTk4PL5aK5uZlIJEJZWZlyDTNmzODH\nP/4xN9xwwzEnfEL0BjNnzmTZsmXMmjWL0tLSDl87bNgwMjMzGT58OG1tbaSmpiqdCDIzMwmFQpSV\nlVFaWsrFF1/MwoULmTNnTrs8FaI3UqvV3H///aSnp3PdddcRCASO+LpYizKdTofJZMJisSgrTdu3\nbycvLw+v18unn35KVlYWbrebyspKDhw4ABxc6Xr00UfZt28fa9asSdj4EkkmVH1EMBjE5XIRjUaJ\nRqPKSYvY/wYOHMiYMWMYM2YMWVlZNDc3s2bNGmpra/n1r3+N2WxGo9Hgcrnwer3KxkKDwcCQIUPw\n+/3s3buXhoYGhgwZQm5uLs3NzUqB0FGjRlFVVYXP5yM/P5+tW7ficrnafRDdeuutGI1GEvgUWYgu\nueKKK1iyZAmXXXYZu3fv7vC1hYWF2Gw2Ro4cSSAQwOl00tLSwpdffondbicQCHDgwAF8Ph9XX301\nU6ZMYd68eUe96xeit9BoNDz00EOYTCZuuOGGH/RILRqNYjQaycrKIj8/n+rqatra2lCr1cqTlNhB\njthNttFo5De/+Q1vvfUWL774YryHlXAyoeqjVCoVHo+H0tJSZcUqdlovxmQysXr1asrKynjxxReJ\nRCIAysZap9NJUVERbW1tlJeX09raisfjoaysDJfLRXZ2ttK2JhAIMGzYMNLT03G5XAQCASorK/F6\nvcqkSqPRsGHDBj7++GNeeeWVHvlzEeJ4zZkzh5///OfMmjVLeURxNCNHjsTpdJKZmcnOnTsJBAJo\nNBoqKyuxWCxUVFQoK7e33XYbAwcOZNGiRYTD4UQMRYhO02q1bNiwAa1W2+FKVUxycjJWq5VgMKh0\nIdBqtRQUFFBfX09mZiYNDQ189dVX7Z5mpKam8tJLL7Fu3Tree++9uI4p0WRC1UfodDplb5NKpcJu\nt+N2uw9bsfr+ay0WC48//jh79uzh5ZdfVvZ/xDbWxop8JicnEwgEcLvdyqrXvn37KCkpYfDgwVRV\nVVFdXU1ycjIej0dpT1NbW4vH41Huwq1WK88++yz33HMPW7du7ck/MiF+sFmzZnH77bdz+eWXs337\n9qO+TqvVkp2drRzs0Gg0pKamsnv3bvbs2UNKSgrl5eWUlpaiVqt54IEHaG5uZuXKlf1234joP3Q6\nHY8//jgGg4Frr70Wv99/1Nc5nU7UarVSG7GwsBCLxUI0GqWgoEDZo2swGNi3bx87d+5U3p+fn88z\nzzzD0qVL+fLLLxM1vLiTCVUf4nA4KCwsJD8//5hF0hwOB/n5+eTl5VFSUsIbb7xBVVUVr7zyCjk5\nOUQiEdRqNdFoFJPJhM1mIxQK4XA4CAQC6HQ6amtr2bVrF5WVlUSjUXw+H62trRQVFaFWq0lOTmbv\n3r2UlZW1uwMpKiril7/8JYsWLZLHHaLP+MlPfsIvf/lLZs+efcybgeLiYsaMGYPT6aS6uhqn00lt\nbS1lZWWo1WpaWlqUmj1PP/00n332GY8++miCRiJE5+l0Oh577DEsFgtXX331MTeqFxcXY7FYaG5u\nJi0tDbPZrNRqi0QihMNhPB4P5eXl7SZVp556Kg888ABXX311u8+PvkwmVH2MwWBQNgYeumLldDoP\nO/Iaex0cbP766quv8tVXX7Fu3TqGDh1KamoqKSkpGAwGjEYjgwYNUjYclpWVKcdTY6eV1Gq10j+w\nra2NvXv3EggEKC8vZ//+/e26xP/kJz+hpKSEVatWJe4PR4gumjFjBqtWrWLOnDl8/fXXHb62uLiY\nwsJCHA4HwWBQqfsWjUZpbW3F6/UqNXlefPFFXnrpJX7/+98naCRCdJ5Wq+WRRx4hNTW1w9N/sYNN\nsbpTra2tSjeOjIyMdpOrxsZG6urqqKmpUd4/efJkbrzxRq688sp+cYBDJlR9SDAYbPdcO7YKlZ+f\n32EtnRir1cqGDRv48ssvWb58OW1tbWRlZZGVlYXBYKC5uRmv10taWhoGgwG1Wk0kEsHpdGK1WgkE\nAtjtdurq6tBqtQSDQaUJc3V1tZIwcHCP1z333MP777/f756Ti/7t4osvZu3atVx55ZV88cUXR32d\nTqdj0KBB5OXloVKpSE5OJi8vj2+++YaqqiqCwSBerxc42KT5pZde4le/+hV/+9vfEjUUITpNq9Xy\n0EMPkZmZyVVXXUVLS8sRXxe7oS8sLMTpdJKdnY3dbqe6uprs7GysVit79uyhurqampoa5UYjZu7c\nuVx44YUdTtz6CplQ9RENDQ2UlpayZ8+edjP5Q1ehjiU2IVu7di2tra2sXLmSxsZGgsEgdXV1ZGRk\nYLfbKS8vZ+jQodhsNqVYW2trK7m5uQBUV1djMBjIysrCbDZjNptxOBz4/X7q6+uVZLHZbKxfv55b\nb72V2tra7v9DESJOpkyZwgMPPMDcuXP57LPPjvq6tLQ0CgoKGD16NCaTie+++05p+bRjxw5qamqU\nfB08eDBPPfUUixcv5ptvvknUUIToNI1Gw7p16xg0aBBXXXUVzc3NR31tZmYmRUVFSs/LkpISDAYD\n+/fvV27Ya2pqlBv3Q912223k5uayePHiPn2AQyZUfcDRSiZ0lsFg4K677iIrK4tbb70Vr9fLoEGD\nqKysxOfzkZycTF1dHQ6HA7PZTDgcRqvV0tjYSFVVldIo2W63M2LECHJyclCr1WzevJkdO3ZQUVGh\nxBozZgyzZ8/m5ptvlk25ok+54IILeOSRR7jmmms6XFXKzs4mKSkJi8VCamoqTU1NpKSk0NTUxO7d\nu6mrq1Py9fTTT2fNmjXMnTuX/fv3J2ooQnSaRqPhvvvuo6ioiDlz5nRYyd7pdBKJRPD5fOzdu5ek\npCQKCgoIBoOo1ep2N96HUqvVrFu3Do/Hw5133hnvIcWNTKhOIIfuu9JqtaxZs4Zx48Zx0003sWfP\nHpxOJykpKfj9frRardLTr6GhgWg0qtSt0mg0qNVq/H4/DQ0NBINB9u7dS11dHR6Ph+3bt7dbul2y\nZAn19fW8/vrrPTh6IY7fxIkTefrpp7nxxhs73P80cOBABg0axODBg0lNTcXv95OUlKTciBx6k3HR\nRRexePFiKfwp+gy1Ws3q1asZPnw4V1xxBR6P56ivtdvtDB48GI1Gg9/vJyUlBbvdTnp6OjabjYaG\nBhoaGtrtuYWDN/pPP/00H3zwAa+++mq8hxQX0suvD8Q7tLO9TqcjJSUFs9ncqe8Va6gMKOUP1Go1\nTz31lLLaBJCbm0taWhr19fWYzWZMJhMajYZgMIjVaqW6uhq/308oFMLr9SqTLL1ej9FoxG63K32Q\nNBoNI0aMYOnSpcycObNdraxD9eYeTfEiOdH7Yw0YMIBJkyaxbNkyfD4fp512GiqVqt1rdDodra2t\nyglZlUpFdXU1VqtVKa/g9/uV07kjR46kpqaG9evXc8kllxz1sb3kRPxIThwflUrF+eefz+7du1mz\nZg0XXHABVqu1XazYZ1VbWxt6vZ6srCyqq6vJzc1FpVLR1NTE/v37lZOxsQlXTFJSEhMmTGDRokWc\nccYZSku0eI/taKQ5Mv0zUWIToVjNj66IRCJKO4Cmpiby8vLIzc3l4YcfZuLEiYwePZpQKITFYiEp\nKQmz2azsswoEAiQlJSkdx7VaLQaDAbvdjlarRa1WYzAYUKlUpKWlKa0JMjMzqaio4KOPPmLy5MlH\nvK7enCjxIjnRN2KlpqYybdo0Vq9ezbfffsu5556LWt1+gd9ut9PU1ITL5cLtdpORkcGePXuor6/H\nbrcTiURwOBxKTkyYMIF//etfbNy4kYsvvviw75eoscVITvSfePGKpVKpmDhxIoFAgJ///OdMmDCB\nnJycdrGMRiM2mw2z2UxbWxvRaJTq6mp8Ph91dXVKqR6fz4fNZsNisbS7oUhNTSU/P5+lS5dyySWX\nkJycnJCxHUlCJlRVVVWsWrWK9957j/fee4+XXnoJg8HA4MGDO3yfJErXaDQaTCZTl2NFIhFlydZg\nMOD3+xkxYgTjxo1jxYoVWK1WzjnnHDIzM1GpVITDYaLRKKmpqUrRz7y8PILBII2NjeTm5iqPEvV6\nPW63G7fbTX5+PklJSUrc0047jZUrV3LmmWcqXcgP1ZsTJV4kJ/pOLLPZzJw5c3j66ad55513mDx5\n8mErS06nk3A4TCAQ4LvvvkOn09HY2EhzczMZGRkEAgHlRG7sjv/1119n69atnHvuuT02NpCc6E/x\n4h1r9OjRZGRksHDhQk499VSysrLa/X7ssypW6DMajZKVlYXL5SIpKUk5QX7oftxDDR48GI/Hw5NP\nPsmll16q3IQkYmyHOt6c6NQequzsbNauXcvatWtZvXo1BoOBMWPGdOZbiR4Q20sFB384S0pKKCoq\nYsqUKfzxj3/kd7/7HStWrFBOKMU2GW7ZskU59XfoqcCamhoaGxv56quv+Pbbb5U7isrKynZ7RGw2\nGz//+c/5xS9+IRvURZ9ktVp54YUXSE5OZubMmUfcA5WVlUVhYSFWq5WWlhZsNhuNjY1UVlYqk6sY\nvV7PE088wfvvv8+bb76ZyKEI0SUzZszg8ccfZ+7cuWzatOmIr9HpdAwYMACLxYLP56O4uBhA2V/4\n3XffUVtbe8RyCcuWLSM5OblPbVLv8qb0b775hoyMDOUDWvQNh1ZSP7Tqem5uLps2bcLr9XLFgffA\ncgAAIABJREFUFVcopzH27dun9Cyrr6/H7XazdetWbDYbVquVHTt2KNXWy8rKKCgooKKigt27d7c7\nkXj55ZfT2NjIBx98kPAxC9Ed9Ho9jzzyCGeccQYzZsw4rMqzzWbDYDBw8sknk5GRgc/nY+jQobhc\nLr777rt2hQ1jr//1r3/NypUr2bFjRyKHIkSXnHnmmbz11lusWrWKJ5988oiv0el0ZGRk4HK5aGtr\nU/ZTVVZWUl5eTnV1NdXV1Ye9T61Ws379ej766KM+s0m9yxOqTz75hAkTJnTHtYgE0+l0NDU1tWuw\nDAebXj722GOcfvrpzJ8/n+3bt2M0GklJScHhcFBXV6c84quurlYq4rrdbqxWK5mZmUSjUcrLy/n8\n88+VSutwcCl4wYIFPPHEEz01bCG6TKVScdttt3HNNddwySWXHFZVPT8/H4vFwqhRoxg2bJiyinvg\nwAH2799/WF22kpISfvGLX3DttdfS2NiYyKEI0SUlJSVs2rSJ3/3ud9xxxx1EIpHDXmO328nNzVUe\n1VVVVWEwGEhPT8flchEIBI64SmWz2Xj22We5++67+0TPvy5NqEKhEJs3b2b8+PHddT0igTqqb9XS\n0sJVV13F5ZdfzooVK9i6dSt2u52ioiJlL0heXh5qtZrGxkacTic2mw2TyURWVhb79u2jvr6epKQk\nysvL2yXL9OnTKS0tPWZrDyF6u7lz53LPPfdw5ZVX8uGHH7b7veHDh5OSkqLkSyAQIC0tjaqqKpqb\nmw+rJXfZZZdx9tlnS8020ecMGDCAjRs38vXXX7NgwYJ2HT3g4M17dna2Uvh52LBhSiuznJwc3G73\nUfv5DRkyhPvuu48bbrihw3INvYEq2oXM/eyzz/jrX//K//zP/xz2e9u2bWPbtm3Kr2fOnJmwzYZ6\nvT6hmw0TGa87YwUCAfbs2aP8461SqSgsLARg69atNDc3U19fT2NjIxs2bMBoNDJnzhwlAYxGo7Iy\n5ff7SU9PV9rRtLa2Eg6HsVqtpKSkMGbMGOx2u3LcfP369WzevJnf/OY3cRnbsVgsFl577TXl1yUl\nJZSUlMQ1puRE/43173//mzlz5nDnnXcyZ84c5et1dXVs2bKFqqoqAoEAFRUVOBwORo4cSWpqKiUl\nJe023AYCAS666CKmTZvGzTffLDkRR5IT3R/L7/dz/fXX43K5ePnll9uVRPD5fHz66ae43W68Xi/R\naJSGhgb0ej2DBw+mtbWVU045hfz8/MPKkgAsX76cyspKXn311S4Vtj4ex5sTXZpQPfTQQ4wcOZKJ\nEyf+oNd/v5BXvFgsloQlZaLjdXeshoYGXC4XcPCEksPhUH7wk5KSqKysJDk5mVAoxOuvv86//vUv\nLrvsMs455xwsFgtZWVk0NDTg9/upqqrCaDSi1WrRaDRK8+RRo0ZhsVjIzs5WTjg1NTUxbtw43nvv\nPbKzs+Myto7EYvY0yYn+E2v37t1ceeWVzJo1iyVLligfCjt27KC2tpavv/4ajUajnGgaNWoUAwYM\nOKymXFVVFT/60Y945JFHmDp1quREnEhOxCdWOBzmjjvu4B//+Acvvvhiu5+rhoYGysvL2bt3L16v\nF51Oh1arJRAI4HQ6yc3Npbi4+Ih12QKBANOnT+fqq69m1qxZCRnb8eZEp+tQ+f1+nnvuOa6//vof\n3EtOjsP2vlix+lZ2u73dP+wej4dQKITJZKK1tZW2tjZOO+00srKyePnll2lsbCQvL4/k5GQyMzPJ\nzs5GpVJRX1+P3+/H7XajVqvR6XRUVFRgMBgIh8NKHR6DwcDWrVtRq9WcdNJJcRlbR+SIeP+J11ti\nORwOpk+fzn333cc333yj1KpyOp20tbURDofR6XT4fD4sFgtWq5VQKHTYkXGLxUJJSQk33XQTs2bN\n+sH/vnaV5ET/ideTsdRqNeeeey6tra2sWLGCs88+Wzm0FqtRFVudamlpIRAIoNFoaG1tpbGxsd0p\n9ENptVrOOOMMFi5cyMSJE0lLS4v72BJSNgEOHnt85plnjlr1WvQd32+wrNPpyMvLIzMzk1AoxMCB\nAykuLiYSiZCVlcXdd9+t1CLbsWMHDQ0NaDQa2traCIVCqNVqWltb0Wq11NXV4ff7iUaj1NfXEwqF\nlDjjx4/nn//8Z08MWYi4SE9P54033qCiooJrrrmG1tZWAPLy8sjLy6OtrQ2LxUJLSwuffPIJdXV1\nR2w4e9ZZZ3HFFVdw/fXXH3GTrxC9mUqlYv78+dx2221cdtllfPTRR8rvGY1GMjMzSU5OxmazKRvS\nPR5Ph6f+AAoLC7n77rtZvHgxfr8/QaP54aSXnziiWFmFjIwMDAYDer2eaDTKwIEDcTqdXH311Vx+\n+eWsXLmShx9+mKamJtRqNSaTSVm+BTCZTAwZMoRIJILFYkGr1SoxzjjjDJlQiX7HbDbz/PPPY7fb\nmTlzJjU1Neh0OhwOB8XFxfj9fsrKyvB6vezcufOop/puvvlmAoEAjz76aIJHIET3uOSSS3jqqadY\nunQpjz/+uLJfN9aFw2g0MnDgQJqbm5UcqaysxOfzHXWf1OzZs8nPz2ft2rWJHMoPIhMqcVRms5mM\njAxlL0isano4HCY9PV1pHKvVapk8eTIffPABWq2WaDRKcnIyQ4YMYdy4caSlpWE2mzGbzXi9XuX7\nFxYWHrWomxB9mU6n48EHH+T8889n6tSp/Pvf/yY7O1vpgxnLpdra2iOe+IODjzieeeYZnn76abZu\n3doDoxCi68aOHctbb73Fpk2bWLx4MT6fD6PRSHFxMeFwmEgkQklJCVqtlmAwSEpKCuFw+KjfT6VS\nsWbNGjZt2sQnn3ySwJEcm0yoxFGpVCplpWrQoEEMHToUlUqFWq1WlmxTU1NZuXIlTz31FO+++y53\n3nkn+/bto6WlBbfbTUtLi5IcdXV17Nq1i7q6OuBg2Y1IJNKuPY0Q/YVKpeLmm2/m/vvv54YbbuDJ\nJ58kKyuLk08+GZ1Oh0ajYejQoVRUVCiPBr9vwIAB3H777Sxbtqzd43Ih+pJYWQU4uGpVWVnJwIED\nOffccykuLkav12O1WjGZTHg8HjZv3tzu9Of3ORwOVq9ezfLlyw8r0dCTpDlyH4vXE7E0Gg1er5fW\n1lZsNhsDBgygra2NSCRCIBCgrKwMg8HABRdcgMFg4C9/+Qvvvvuu8pgwGAwSjUapqKhQupA7HA62\nbt3K3//+d6655pqEj0024PafeL09Vn5+Pj/60Y+47777+Pe//83ZZ5+NTqcjPT0dv99PXV0dVqsV\njUZz2J7UWI/UP//5z9TV1cW1xZfkRP+J1xtj6XQ6LrroIlpaWli2bBkjR44kOTmZPXv2EAqF0Gq1\nuFwuamtriUajBAIBMjMzj5gTbW1tFBYW8ve//53y8nLGjRsXl7ElbFO6OHHECoDGHvc1NjYqjyhc\nLhehUIjGxkaampqYMWMG69ev56abbmLLli2sWbOGl19+mY0bNyqPOhoaGvjmm29Yvnw51113XQ+P\nToj4y83NZePGjdhsNm688UYikYhykxKJRPjHP/5BVVXVER/9qVQq1q5dy+OPP86ePXt64OqF6B4q\nlYqf/exnrFu3juuvv54XXngBlUqFyWSiubmZxsZGHA4HgUCA5uZm5WnG0dx11108/fTT7N+/P0Ej\n6JisUPWxeD0RKxKJtKtQG3sUGPuhN5vNBINBVCoVFosFnU7HoEGDyMzMVJZzd+3axf/+7//y17/+\nlddff50PPviAn/70p8ybN0/ZoyUrVPEjOdHzsbRaLRdccAHJycmsXLmSrKwsTCYTANFolJaWFsxm\nc7syCrF4sf6Ajz76KDNnzjxi4cOukpzoP/F6e6y8vDzOP/98Vq9eTUVFBaNGjcJms5GZmUl9fT1W\nq5WBAwcqE6xDt4UcGi9WeuS3v/0tl1xySbeOC2SFSsRBrC6ISqVCpVKRmppKWloaeXl5DB8+HI1G\ng9/vR61W09bWRkpKCjU1NWg0GpKTkzn55JO5/fbbueuuu7j//vv517/+xeeff861114blw8GIXqz\nWbNm8cILL/CnP/2Jt99+W6nF09jY2OEhjblz5xIMBvnDH/6Q4CsWovsNGTJEqUK+YsUKysrKyMnJ\noaCgAIPBwGeffUZZWZlSePpobrjhBkpLS/nrX/+aiMvukEyoxA8S25yen5+vVDvX6XSkpKRgsVgo\nKCjA6XQqxTzr6+tRq9Wkp6cTiUTw+/2kpaWRn5+fkIJsQvRmo0eP5sUXX0Sr1fLcc8+xf/9+1Go1\nlZWVR73b12g0LF++nEceeaTDU1BC9BU5OTn8+te/ZtGiRdxzzz288cYbHDhwgD179uD3+2lsbGT/\n/v0dTqoMBgN33303d9xxR48f3JAJlfjBvl8ANCbWXFmtVqPVamlpaUGr1eL1elGpVKSlpeF0OsnK\nysJoNBIKhRLWi0mI3qqoqIhly5Zx9tln84c//IG3336bxsbGo574A5gwYQIpKSn86U9/SuCVChE/\ner2e2bNns3HjRt555x1effVVZVtJZmYmra2t7Nq1q8PPjFg19p5epZIJlTimYDB41B/m7z8OtNvt\ntLS0KI8F9Xo9BQUFmEwmtFotSUlJVFVVUVZWRm1tbYJHIkTvodPpyM7OZuLEifz0pz+ltraWJ554\ngi1bthw131QqFUuWLOHhhx+WCuqiXxkyZAhvvvkmOTk5vPTSS9TV1dHU1ITP56OpqanDGw2Aa6+9\nlmeeeSZBV3tksim9j8VLZCy9Xk91dTVVVVV4PB5UKtURWw0d2g/Q7/ezd+9egsEgaWlp2O12CgsL\nsdvtWCwWvF4vTU1N7Ny5kwMHDqDX65VNuLIpPX4kJ3pnLJPJRCQSUaqop6am8uCDD+J2uxkzZgzJ\nycmHxcvLy+Oll16iuLiYnJycbrsWyYn+E6+vxopGo8q2khdeeAG3201mZiZqtZq0tDTlcMaR4hUU\nFPDAAw9wxhlnkJ6e3i3XI5vSRaccaRWqra0Nl8ulPNJzuVwdrlQBuN1uzGYz0WgUr9dLRkaG8qgw\nVkW9tLRU6e23ZcsWWakSJyydTkdGRgaBQIC0tDQyMjJYunQpO3fuZNKkSbz66quH7QtRqVSMGzeO\nLVu29NBVCxEfsebJgwYN4tZbbyUcDrNu3To++eQTysvLO3zsp9PpmDdvHs8991wCr7g9mVAJGhoa\nKC0tpbS0lIaGhi5/v1jLmvT0dGw2m/J1nU6H1WpFq9Xi9/uVI+MNDQ2yp0qcsKxWKzabjfLychwO\nB1qtlunTp7No0SKeffZZzjnnHF599dV2OZKfn09paWkPXrUQ8ZGTk8OwYcNIS0tj4sSJzJgxg3/+\n85/cdtttfPXVVx2+d+LEiT16o6E99ktEfxYr2hlrWulyuZRaUnq9HqfTqZywcDqdR9yUHhPbT+Vy\nudBqtUd8fXp6OoMHD+azzz4jGo0yePDgDr+nEP1drEGsx+PB4/FQXV2NWq1m+PDhvPLKK3z++ec8\n9NBDrF27lrFjx1JUVMRbb73F9ddf39OXLkS30+l02O12tFotGRkZGAwG0tPTqampYe7cuVx22WXM\nnTuXQYMGHfbe/Px8ysrKiEQiqNWJXy+SCZU4qthJi9hz5B8y8TnW64PBIBqNhhEjRtDS0qLUHrHb\n7e0KGgpxIhk4cCBtbW289dZbhEIhLBYLpaWlNDU1MX78eMaPH8/u3bv54osv2LNnDzfddBMzZszo\n6csWIi4cDgcZGRm4XC4ikQiDBw9m5MiRXH755bz//vv86Ec/Yty4cVx33XWMGTNGqWfo8/nQ6XQy\noRI949BVJTjyKtTxriAd6/XRaBSTyURDQwMmkwmDwYDL5SIzM/P4Ll6IfiRW662qqoqkpCQGDBiA\nXq9Xfr+oqIiioqIevEIhEkOn05GZmUkgEKCpqYn6+nqla8dVV13FjTfeyGuvvcYtt9yCTqejpKSE\nrKws/v73vzNjxgy02p6Z2siEShz3KlRXxCZwsQRRq9W4XC5sNpvy2FGIE5HFYiE3Nxez2Ux5eTlu\nt5uqqiqGDBnS05cmRMLZbDZ0Op3yudDW1kZTUxOVlZU4HA7mzp3Lf//3f/PVV1+xe/duKioqWLx4\nMVOmTOmxa5YJlQDiP5E6lMPhwGg0tjtFqNfrpQ2NOKHpdDpycnLYu3cvBoMBn8/H559/js1mIyMj\no6cvT4iEMhqN2O12KisrcbvdSn3DQ1szqdVqRo0axahRo3rwSv9DTvmJHqHVatHr9WRlZZGdnY3B\nYOjpSxKixyUnJ6PT6QgEAsrXPB6PnIIVJySHw4FarSYSiSilfYLBYELrhx2PTq9QtbS08MQTT1BR\nUQHA/PnzZWlaHCb2QXCkfVmpqanK3q3U1FT0en2vTRQhEsFsNlNcXMznn39ONBplyJAhaDSanr4s\nIXqEyWTCarWi0+kYMGAAarWaQCBAdXU14XBY6SvbW3R6QvXcc88xatQobrnlFsLhcLs7KiHgYH2p\nQze7f/+H//t7t+SRnxBQXFyM3W7H4/Gg1+sxm81SWkSckGIbzkOhEJWVlUQiEVpbW6murkar1Sol\nfnqLTj3ya21tZceOHZx33nnAwS7osSKNQkD7+lYdVVk/WsNlIU5kGRkZpKamAlBfX98tBXeF6Isc\nDgennnoq6enpaLVa3G43u3bt6pWLOJ1aoaqtrcVqtfLYY49RVlZGfn4+8+bNk30wQhEKhZQVJzm9\nJ8TxCQaD7N+/H7/fTzQaJRAI9Lq7cSESJXZoye/3Awf3Gvr9fjweD2lpaT18df/RqRWqcDhMaWkp\nkydPZs2aNSQlJfHmm29297WJPqqhoYHy8nKampqU0gjHqrIuhPiPUChEc3Mz0WiU6upq9u7dS319\nfU9flhA9wmg0UlRUhMPhwGq1kp+fTzQaxe1296oDG51aoUpNTcXhcChF5saNG3fYhGrbtm1s27ZN\n+fXMmTMT1s1cr9cntHN6IuP19liBQICWlhaSkpJISkoiFApRUFCA2Ww+5h6pRP+9vfbaa8p/l5SU\nUFJSEtd4khMS63jiZGVlsWvXLpKSkkhLS8Pn86HX6+P6JEByon/E64+xhgwZQiAQwO12s2PHDjQa\nDaeeeirJycm9Jic6NaFKSUnB6XRSVVVFdnY2X3/9NTk5Oe1ec6TATU1NnQl33CwWS8JiJTpeb48V\nDAbx+XzKYz6VSkUwGKS5uTku8TrLYrEwc+bMhMSKkZyQWMfDbrfjdDoJBoPs27ePyspK4GC/sniQ\nnOg/8fpjrGAwiFarpaKigkgkAkB5eTmFhYUYjca4xDzenOj0Kb958+axfv16QqEQGRkZLFiwoLPf\nSvQjP6SVjRDi2JxOJyqVir/97W9oNBqSk5MpLy8nMzMzbh8gQvRWOp0Oq9VKUlIS0WhUeQrSm3R6\nQpWXl8e9997bndci+olEtrIRoj9zOBw4HA5aW1upqqpCq9WSm5sbt1UqIXqz9PR0Ro4cydatW/H7\n/djtdnw+X6+5wZDWMyIuZCIlRNeZzWYGDRrEJ598glqtJjMzU1apxAmtsLCQQCCgbCtxuVy95gSs\nTKiEEKKXik2iYqeaVCqVFMAVJ7xIJNIuH0KhUK+YUEkvPyGE6MWMRiO5ublEo1Fqa2sB2jWIFeJE\notfrcTqdqNVqgsEgXq+Xffv29Yrit7JCJYQQvVxWVhYejwez2YzBYOhVjzmESCSVSoXD4cBoNLJt\n2zaamppoamrC5/P1eE7IhEr0CsFgsFe2EhCiN/B6vdTW1uL1ejEajWRmZvb0JQnR4zweDx6PBzhY\ncLynH/3JhEr0uFgTZaPRSHJycq/rIC5ETwoGg0qjZAC/349WK/90C2EwGJQ9hb2h9Z1kpYi7WGuA\nI905HKmJck8v2wrR28TyIyMjA5VKpUyuhDhRabVazGYzavXBreAmk6nHbzRkQiXiKrb6BAcLFcrq\nkxDHR6fTkZqaSiAQoL6+HovFQnp6utx0iBOaTqdj0KBB1NTUoFKpcDqdPX1JMqES8XPo6hMcuV7I\noZXVY0khHxRCtBcrlhsKhdBqtZIjQvCfvPB4PNTV1VFXV0dGRkaP3bjLhEr0uFhSJCcn09bW1tOX\nI0SvpNPpZCIlxBGUl5fj9XoBevS0n9ShEnETW32KFV/raPVJp9P1ik2FQggh+o5QKERTUxPRaJRw\nOIzX6yUUCvXItcgKlYgr6esnhBAiXrRaLampqVRUVNDa2kpaWhotLS090ppJJlQi7mQiJYQQIh50\nOh0ZGRk0NjZitVqx2Wy43W5sNlvCP3tkQiWEEEKIPislJYW0tDTlAFTs/xNN9lAJIYQQos+KlRaJ\n6anT4rJCJYQQQog+rTfs15UJlRBC9FEddSEQ4kTT03kgEyohhOiDpAuBEL1LpydUCxcuxGg0olar\n0Wg03Hvvvd15XUK0I3fiQvzHD+lCIMSJqqc+L7q0QnXHHXdgNpu761qEOCK5ExdCCPFD9OTnRZdO\n+fXU0URx4jj0TjwajeJyuZS7DyFOVMfThUCIE0VPf150eoVKpVKxatUq1Go1kyZNYtKkSd15XUII\nITrQG041CSH+o9MTqlWrVmG322lsbGTVqlUMGDCAYcOGdee1CaHciR+6hCsfHkIcJLkgxH98//PC\nbrcnNL4q2g3P7X7/+9+TlJTEtGnTlK9t27aNbdu2Kb+eOXMmTU1NXQ31g+j1etra2hISK9Hx+mus\njuJFo1Hl63q9HpVK1eVYFouF1157Tfl1SUkJJSUlXf6+HZGckFi9OZ7kRP+J119j/ZB40WiUQCBA\nQ0MDHo8HgNTUVNLT04/7s+N4c6JTE6pAIEAkEsFoNOL3+/nVr37Ff/3Xf3HKKad0+L6qqqrjDdUp\nFoslYUmZ6Hj9NVai42VnZyckzrFITkis3hJPcqL/xOuvsX5ovGAwSGlpqbLPW6VSkZ+ff9wruseb\nE5165Of1ernvvvsAiEQiTJgw4ZiTKSGEEEKI/qpTE6r09HRlQiWEEEII0Vv01N5bqZQuhBBCiH6l\nJ07ByoRKCCGEEP1Ook/BdqmwpxBCCCGEkAmVEEIIIUSXyYRKCCGEEKKLZEIlhBBCiH4rGAwmpKef\nbEoXQgghRL/U0NDQrnyCw+GIWyxZoRJCCCFEvxMMBnG5XESjUaLRKC6XK64rVTKhEkIIIYToIplQ\nCSGEEKLfiVVMV6lUqFSquFdMlz1UQgjRj8QeaSS6qKEQvVEiK6bLhEoIIfqJRG7AFaKvSNTNhTzy\nE0KIfiDRG3CFEO3JhEoIIYQQootkQiWEEP1AojfgCiHakz1UQgjRTyRyA64QfVE8D23IhEoIIfoR\nmUgJcWTxPrQhj/yEEEII0a8l4tCGTKiEEEIIIbqoSxOqSCTCrbfeyurVq7vreoQQQgghulUiDm10\naQ/V22+/TU5ODj6fr7uuRwghhBCi28X70EanV6jq6+vZsmUL5513HtFotDuvSQghhBCi2+l0urgd\n3Oj0hOr555/nyiuvRK2WbVhCCCGEOLF16pHf5s2bsVqt5Ofns23btiO+Ztu2be1+b+bMmcpSW7zp\n9fqExUp0vP4aqyfivfbaa8p/l5SUUFJSEtd4khMSq7fHk5zoH/H6a6yeiHc8OaGKduJ53csvv8zH\nH3+MWq0mGAzi8/kYO3YsixYt6vB9VVVVxxuqUywWC01NTQmJleh4/TVWouNlZ2cnJM6xSE5IrN4S\nT3Ki/8Trr7ESHe94c6JTK1SzZ89m9uzZAHz77bf88Y9/POZkSgghhBCiv+qWDVAqlao7vo0QQggh\nRJ/U5dYzw4cPZ/jw4d1xLUIIIYQQfZIc0RNCCCGE6CKZUAkhhBBCdJFMqIQQQgghukgmVEIIIYQQ\nXSQTKiGEEEKILpIJlRBCCCFEF8mESgghhBCii2RCJYQQQgjRRTKhEkIIIYToIplQCSGEEEJ0kUyo\nhBBCCCG6SCZUQgghhBBdJBMqIYQQQogukgmVEEIIIUQXyYRKCCGEEKKLZEIlhBBCCNFFMqESQggh\nhOgimVAJIYQQQnSRtjNvamtr44477iAYDBIKhTj99NOZPXt2d1+bEEIIIUSf0KkJlV6v55e//CUG\ng4FwOMwvfvELduzYQXFxcXdfnxBCCCFEr9fpR34GgwGAUChEJBLBbDZ320UJIYQQQvQlnVqhAohE\nIixfvpyamhomT55MTk5Od16XEEIIIUSf0ekVKrVazX333ccTTzzB9u3b2bZtW3delxBCCCFEn6GK\nRqPRrn6T119/Hb1ez/Tp05Wvbdu2rd0ka+bMmV0NI0S3eu2115T/LikpoaSkJK7xJCdEbyc5IUR7\nx5UT0U7wer3R5ubmaDQajQYCgegvfvGL6Ndff93he1599dXOhOqURMZKdLz+GivR8RI9tp6+Bvm7\n7HuxEh1PcqL/xOuvsRId73hjdWoPlcfjYcOGDUQiEaLRKGeffTYjRozozLcSQgghhOjzOjWhGjhw\nIGvWrOnuaxFCCCGE6JM0d9xxxx2JCpaenp6oUAmNleh4/TVWouMlemw9fQ3yd9n3YiU6nuRE/4nX\nX2MlOt7xxOqWTelCCCGEECcy6eUnhBBCCNFFMqESQgghhOiiTldKPx6RSIQVK1bgcDhYsWJFXGMt\nXLgQo9GIWq1Go9Fw7733xi1WS0sLTzzxBBUVFQDMnz+fIUOGxCVWVVUVDz30kPLrmpoaZs2axdSp\nU+MSb+PGjXz88ceoVCoGDhzIggUL0Ol0cYn19ttv8/777wNw/vnnd/uYHnvsMbZs2YLVauWBBx4A\noLm5mQcffBCXy0VaWho333wzycnJ3Rq3I5ITXSc50XmSE5IT3UFy4nviUbvh+956663oww8/HF29\nenXcYy1YsCDa1NQU9zjRaDS6fv366Pvvvx+NRqPRUCgUbWlpSUjccDgcve6666J1dXVx+f41NTXR\nhQsXRtva2qLRaDS6bt266IcffhiXWGVlZdGlS5dGA4FANBwOR++6667ogQMHujXGt9/ghRlMAAAD\n+0lEQVR+G927d2906dKlytdefPHF6JtvvhmNRqPRjRs3Rl966aVujXkskhPdS3Li+EhOSE50leTE\n4eL+yK++vp4tW7Zw3nnnEU3Q/vdExGltbWXHjh2cd955AGg0GkwmU9zjAnzzzTdkZGTgdDrj8v1N\nJhMajYZAIEA4HCYQCOBwOOISq6qqisGDB6PX61Gr1QwfPpxPP/20W2MMGzbssLuKzz//nHPOOQeA\niRMn8tlnn3VrzI5ITnQ/yYnjIzkhOdFVkhOHi/sjv+eff54rr7wSn88X71AAqFQqVq1ahVqtZtKk\nSUyaNCkucWpra7FarTz22GOUlZWRn5/PvHnzMBgMcYl3qE8++YQJEybE7fubzWamTZvGggUL0Ov1\nnHLKKZx88slxiZWbm8srr7xCc3MzOp2OL774gqKiorjEOpTX6yUlJQUAm82G1+uNe8wYyYnuJznR\ndZIT3U9yonv0lZyI6wrV5s2bsVqt5OfnJ+yuY9WqVaxdu5bbb7+dd999l+3bt8clTjgcprS0lMmT\nJ7NmzRqSkpJ488034xLrUKFQiM2bNzN+/Pi4xaiurubPf/4zGzZs4Mknn8Tv9/Pxxx/HJdaAAQOY\nMWMGd999N/fccw/5+fmoVKq4xDqaRMaTnOh+khPdT3Kie0hOdI++khNxXaHauXMnmzdvZsuWLQSD\nQXw+H48++iiLFi2KW0y73Q6A1WplzJgx7N69m2HDhnV7nNTUVBwOhzJLHjduXEISZcuWLRQUFGC1\nWuMWY+/evQwdOhSLxQLA2LFj2blzJ2eddVZc4p133nnKkvjLL78ctyXqQ9lsNjweDykpKbjdbmw2\nW9xjguREPEhOdA/JCcmJ4yE5cbi4rlDNnj2bxx9/nA0bNrBkyRJKSkrimiSBQEBZMvb7/Xz99dcM\nHDgwLrFSUlJwOp1UVVUB8PXXX5OTkxOXWIf65JNPOPPMM+MaIzs7m++++462tjai0WjcxxZbRnW5\nXHz22WdxXaaOGT16NB999BEAf/vb3zj99NPjHhMkJ+JBcqJ7SE50P8mJ7tMXciIhZRNi4r1E5/V6\nue+++4CDR3AnTJjAKaecErd48+bNY/369YRCITIyMliwYEHcYsHB5P/mm2+44YYb4honLy+Ps88+\nmxUrVqBSqcjPz4/bHgOAdevW0dTUhEaj4Zprrun2TZsPPfQQ27dvp7Gxkfnz5zNz5kx+/OMf8+CD\nD/Lhhx8qx2F7guRE10hOdI7khOREV0lOHE5azwghhBBCdJFUShdCCCGE6CKZUAkhhBBCdJFMqIQQ\nQgghukgmVEIIIYQQXSQTKiGEEEKILpIJlRBCCCFEF8mESgghhBCii2RCJYQQQgjRRf8fPJc8USAd\nV9sAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f32a34e6390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# select test point (0: 5*ones, 1: saddle, 2: stable FP)\n",
    "testp = 1\n",
    "print 'test point: ' + pointlabels[testp]\n",
    "if testp == 0:\n",
    "    Z = 5.0 * np.ones(nd)\n",
    "elif testp == 1:\n",
    "    Z = bam.findSaddle()\n",
    "else:\n",
    "    Z = np.r_[bam.hopg, np.zeros(nd-1)]\n",
    "\n",
    "# spread of source distribution\n",
    "std = 0.5\n",
    "C = std**2 * np.eye(nd)\n",
    "print 'std = %5.2f' % (std, )\n",
    "\n",
    "# get non-Gaussian by transforming through dynamics function\n",
    "meantrue = np.zeros((nd, 3))\n",
    "covtrue = np.zeros((nd, nd, 3))\n",
    "Strue = np.zeros((nd, nsample, 3))\n",
    "meantrue[:, 0], covtrue[:, :, 0], Strue[:, :, 0] = \\\n",
    "    naiveSamplingEstimate(Z, C, dynfun, nsample)\n",
    "\n",
    "# transform again to see how non-Gaussian distribution changes\n",
    "meantrue[:, 1], covtrue[:, :, 1], Strue[:, :, 1] = \\\n",
    "    naiveSamplingEstimate(Strue[:, :, 0], None, dynfun)\n",
    "    \n",
    "# transform Gaussian with mean and cov of transformed distribution\n",
    "meantrue[:, 2], covtrue[:, :, 2], Strue[:, :, 2] = \\\n",
    "    naiveSamplingEstimate(meantrue[:, 0], covtrue[:, :, 0], dynfun, nsample)\n",
    "\n",
    "# plot everything\n",
    "aux.plotSamples(Strue, meantrue, covtrue,\n",
    "                titles=['transformed', 'double transformed', \n",
    "                        'double transformed\\n(Gaussian)'], ylabels=[''])\n",
    "print 'covariance of transformed distribution:'\n",
    "print covtrue[:, :, 0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Additionally to the transformed distribution I also show the distribution resulting from transforming the transformed distribution which I call the double transformed distribution. This distributions looks less noisy, because the dynamics function concentrates points on a trajectory between the stable fixed points and the saddle point (see also the slope field plot for the dynamics function above). Whereas the double transformed distribution is stretched more than the transformed distribution for `std=0.5`, for large spreads, e.g., `std=10`, the double transformed distribution is more condensed. This is because the dynamics function implements a pull towards the stable fixed points which spreads points out that are close to the saddle point, but contracts points that are beyond the stable fixed points. Further, I show in the third panel the distribution resulting from transforming a Gaussian with the same mean and covariance as the transformed distribution. This distribution is strikingly similar to the true double transformed distribution. It just appears to be slightly more spread out. Even for other spreads of the source distribution the true and Gaussian double transformed distributions are very similar. I guess, what you can learn from this is that the mean and covariance are usually already good descriptors of the true distributions. This further means that I cannot expect large differences in the performance of the UT when I compare the UT against naive sampling with Gaussian and non-Gaussian source distributions.\n",
    "\n",
    "I will now generate non-Gaussian source distributions with increasing spreads. These non-Gaussian distributions will have very different covariances from the Gaussian source distributions that I used before, because the two state variables are anti-correlated such that the covariance is better represented by an elongated ellipse instead of a circle. Also, the variances will be lower than those previously tested. For example, a Gaussian with `std=8` transforms to a distribution with a standard deviation of indiviudal variables of about 5.9. To reach standard deviations of 10 I, thus, use `std` up to 16 for the initial Gaussian."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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888/9odlaOJK6vEWDs+OHEt2n6CKEY7RsYAnmqDot7RBcsi1oNZFW2LC5yTfQ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\nKNMQ1JTTSWwvlnUQ10faaB5K3EK7SUrTdcvDBTnScrnjOcxo2ZekbTS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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f32a175f850>"
      ]
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   "source": [
    "# select stds to test\n",
    "stds = np.logspace(np.log10(0.5), np.log10(16), 50)\n",
    "num = stds.size\n",
    "\n",
    "# dimensions: stds, w0, dist\n",
    "stdstr = np.zeros(num)\n",
    "Dis = np.zeros((num, nut, 2))\n",
    "for stdi, std in enumerate(stds):\n",
    "    # set spread of initial source distribution\n",
    "    C = std**2 * np.eye(nd)\n",
    "\n",
    "    # get non-Gaussian source distribution\n",
    "    meantrue = np.zeros((nd, 2))\n",
    "    covtrue = np.zeros((nd, nd, 2))\n",
    "    Strue = np.zeros((nd, nsample, 2))\n",
    "    mean0, cov0, S0 = naiveSamplingEstimate(Z, C, dynfun, nsample)\n",
    "    \n",
    "    stdstr[stdi] = np.sqrt(cov0[0, 0])\n",
    "    \n",
    "    # transform by assuming Gaussian source with corresponding mean and cov\n",
    "    meantrue[:, 0], covtrue[:, :, 0], Strue[:, :, 0] = \\\n",
    "        naiveSamplingEstimate(mean0, cov0, dynfun, nsample)\n",
    "    \n",
    "    # transform true non-Gaussian distribution\n",
    "    meantrue[:, 1], covtrue[:, :, 1], Strue[:, :, 1] = \\\n",
    "        naiveSamplingEstimate(S0, None, dynfun)\n",
    "\n",
    "    for w0i, w0 in enumerate(W0):\n",
    "        # use UT to approximate double transformed distribution\n",
    "        ut_mean.w0 = w0\n",
    "        meanUT, covUT = ut_mean.performUT(mean0, cov0, dynfun)\n",
    "        \n",
    "        # compute KL for Gaussian source\n",
    "        Dis[stdi, w0i, 0] = WassDist(meantrue[:, 0], covtrue[:, :, 0], meanUT, covUT)\n",
    "        \n",
    "        # compute KL for non-Gaussian source with same mean and cov\n",
    "        Dis[stdi, w0i, 1] = WassDist(meantrue[:, 1], covtrue[:, :, 1], meanUT, covUT)\n",
    "\n",
    "ax = aux.plotKLcontours(W0, np.log10(stdstr), Dis, titles=['Gaussian', 'non-Gaussian'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first to note from these plots is that they show less variation in color, i.e., Wasserstein distances, than the previous contour plots. This is mainly because the lowest distance achieved here is $W \\approx 10^{-1.8}$ whereas above it was $W\\approx 10^{-3}$. \n",
    "\n",
    "Overall, the shades of blue are similar between the Gaussian and non-Gaussian source distributions, but for intermediate spreads (`2 < std < 4`) it indeed appears that $w_0=1/3$ gives higher accuracy for the Gaussian distribution, although it's rarely exactly $w_0=1/3$ that gives the lowest distance. For small and large spreads, $w_0=1/3$ appears to be a reasonable compromise for both Gaussian and non-Gaussian source distributions.\n",
    "\n",
    "In conclusion, there is something about $w_0\\approx 1/3$ that ensures reasonably good UT approximations when compared to other settings of $w_0$. It may, therefore, well be that capturing some 4th moments improves the UT approximation, but I cannot draw definite conclusions from these results, because they only rely on a single transform function. Also, I should mention that, for example, at the point $[5, 5]^T$ larger values of $w_0\\approx 0.5$ give lowest distances for a wide range of source distribution spreads, no matter whether Gaussian or non-Gaussian source distributions are transformed. Note that this finding contrasts to my results above where I found that $w_0$ should best be small, perhaps around $w_0=0.2$, across all test points. The difference to the results here is that the source distribution here has no isometric covariance anymore, but is already aligned to the principle domain of the transform function. In light of the new variation in the best values for $w_0$ depending on the source distribution and the transform function $w_0=1/3$ may be a good compromise after all, although the particular type of transform function may have a larger influence on that than the Gaussianity of the source distribution."
   ]
  },
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   "metadata": {
    "collapsed": true
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   "source": [
    "## Conclusion\n",
    "\n",
    "In the present document I have reviewed the theory behind the approximation employed by the UKF - the Unscented Transform (UT). In this process I have highlighted a gap in previous claims about the accuracy of the approximation. In particular, I have argued that previously stated guarantees ignore contributions of the nonlinear transform functions. Indeed, my experiments showed that the accuracy of the UT varies even when only the transform function changes (see results across different test points, but also results across different widths of the source distribution, because I could have equivalently scaled the transform function to get the same effects). The practical impact of this is rather small, though, because the previous 'guarantees' were already vague: Depending on the type of transform function and state distribution, the accuracy of the UT is also driven by higher order terms in the underlying Taylor series that are not captured by the UT. It remains unclear whether the observed variance in the accuracy of the UT is because the UT does not properly account for the properties of the transform function in low-order terms, or does not account for high-order terms at all.\n",
    "\n",
    "In my review of the UT I have defined 5 increasingly complex sigma point sets. Whereas previous theory suggested that the most complex, the scaled set, should be most accurate on average, it is consistently outperformed by the base, Gauss and mean sets in my experiments. I explain the poor accuracy of the scaled set with its locality: sigma points are chosen to lie very close to the mean of the state distribution which implies that nonlinear effects away from the mean cannot be accounted for although the spread of the state distribution may require it. Given these results I strongly discourage the use of small $\\alpha$, as typically suggested in descriptions of the UKF (as, e.g., in [Wan and van der Merwe (2001)](http://doi.org/10.1002/0471221546.ch7), or on [Wikipedia](https://en.wikipedia.org/wiki/Kalman_filter#Unscented_Kalman_filter)) and suggest to stick with the base or mean sets in which $\\alpha$ is implicitly set to 1 (see overview figure over sigma point sets at the end of the theory section).\n",
    "\n",
    "The base set has no free parameters and spreads sigma points out according to the spread of the state distribution and the square root of the dimensionality of the state space. The mean set is a generalisation of the base set in which sigma points can be spread further depending on the single, free parameter $w_0 \\in [0, 1)$ (larger $w_0$, larger spread). Because with $w_0 = 0$ I recover the base set, I was able to investigate the benefits of the added complexity more quantitatively. My analysis showed large variability in values of $w_0$ that lead to the greatest accuracy depending on the particular transform function (see contour plots in Gaussianity assumptions section). Overall, I saw that the previously suggested value of $w_0 = 1/3$ appears to be a good compromise when suitable, problem-specific values of $w_0$ are unknown. Perhaps a slightly lower value of $w_0 = 0.2$ may be good, but it will really depend on the problem at hand. The base set with $w_0 = 0$ actually may also be a reasonable choice in many situations. It has the additional, small advantage that it uses one sigma point less than the mean set.\n",
    "\n",
    "My most surprising result is that the UT lost against purely random sampling in terms of accuracy as well as computational efficiency when the state distribution was high-dimensional. This was because the UT approximation became quite inaccurate in high dimensions while the performance of random sampling dropped slower with increasing dimensionality, i.e., the curse of dimensionality persisted, but appeared to be worse for the UT than for random sampling. I currently have no good explanation for this result. A colleague ([Dimitrije Markovic](https://dimarkov.github.io/)) pointed out that this may be due to the larger number of interactions between the increasing number of state variables in my model functions (each transformed variable depends on an increasing number of source variables). In the future I may try the experiment with other transform functions with fewer interactions between variables, but I guess you would always want some interaction between variables in your model. Otherwise, you could just have separate models. An alternative explanation for the relatively poor performance of the UT in high dimensions may be based on sampling theory: Drawing random samples from the source distribution may lead to transformed samples that are closer to being independent draws from the transformed distribution than the transformed sigma points. Thus, the transformed samples from naive sampling may actually contain more information in high dimensions than the transformed sigma points that were deterministically chosen. But why is this only the case in high dimensions?\n",
    "\n",
    "The number of random samples needed to achieve reasonable accuracy in low dimensions and better accuracy than the UT in high dimensions was only about 50 for my model. To reliably achieve the accuracy of the UT in 11 dimensions I even only needed the minimum 11 or 12 samples. Given these numbers, using random sampling with 50 samples to ensure a certain level of accuracy across models may be better than employing the UT, if you can afford to run 50 samples. I should point out, however, that the UT with mean set gave consistently high accuracy in two dimensions which could only be reached with more than 50 random samples while the UT only uses 5 sigma points. Then again, random samples, when not only used to compute transformed mean and covariance, allow you to approximate higher order moments or multiple modes of the distribution. The UT may be extended to capture higher order moments of the state distribution, too (see [Julier and Uhlmann, 2004](http://dx.doi.org/10.1109/JPROC.2003.823141)), but the construction of sigma points becomes very complex such that the advantage in computational efficiency of the UT over random sampling may further decrease.\n",
    "\n",
    "The largest caveat to my results is that they rely on only one model. Notice, however, that I evaluated the UT for two transform functions defined by this model. I further emulated different transform functions by investigating different regions of my model functions and by scaling the region which is covered by the state distribution which is equivalent to scaling the transform functions, i.e., including more nonlinearities in the transformations. The nonlinearities used in the tested transformations are based on sigmoids which leads to edge effects, as particularly seen in the observation function in 2D (see section Effects of large uncertainty). Perhaps other nonlinearities, such as sinusoids, would lead to slightly different results, but I believe that the overall findings, that the scaled set should be avoided and that $w_0 \\leq 1/3$ may be a reasonable setting for many problems, will hold up. To directly test this for your model is, of course, better and I have here demonstrated a procedure that could be followed to do this."
   ]
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