{ "cells": [ { "cell_type": "code", "execution_count": 28, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "text/plain": [ "{'scroll': True,\n", " 'start_slideshow_at': 'selected',\n", " 'theme': 'sky',\n", " 'transition': 'zoom'}" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from traitlets.config.manager import BaseJSONConfigManager\n", "import jupyter_core\n", "#path = \"/home/damian/miniconda3/envs/rise_latest/etc/jupyter/nbconfig\"\n", "path = \"/Users/i.oseledets/anaconda2/envs/teaching/etc/jupyter/nbconfig\"\n", "cm = BaseJSONConfigManager(config_dir=path)\n", "cm.update(\"livereveal\", {\n", " \"theme\": \"sky\",\n", " \"transition\": \"zoom\",\n", " \"start_slideshow_at\": \"selected\",\n", " \"scroll\": True\n", "})\n" ] }, { "cell_type": "markdown", "metadata": { "code_folding": [ 1 ], "slideshow": { "slide_type": "slide" } }, "source": [ "# Lecture 4: Matrix rank, low-rank approximation, SVD" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Previous lecture\n", "\n", "- Peak performance of algorithms\n", "- Complexity of matrix multiplication algorithms\n", "- Idea of blocking (why it is good?)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Todays lecture\n", "- Matrix rank\n", "- Skeleton decomposition\n", "- Low-rank approximation\n", "- Singular Value Decomposition (SVD)\n", "- Applications of SVD" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Matrix and linear spaces\n", "A matrix can be considered as a sequence of vectors, its columns:\n", "$$\n", " A = [a_1, \\ldots, a_m], \n", "$$\n", "where $a_m \\in \\mathbb{C}^{n\\times 1}$. \n", "A matrix-by-vector product is equivalent to taking a linear combination of those columns \n", "$$\n", " y = Ax, \\quad \\Longleftrightarrow y = a_1 x_1 + a_2 x_2 + \\ldots +a_m x_m.\n", "$$\n", "\n", "This is a special case of **block matrix notation** (columns are also blocks) that we have already seen (blocking to fit cache memory, Strassen algorithm)." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Linear dependence\n", "\n", "The key point is the concept of linear dependence between vectors.\n", "\n", "Vectors $a_i$ are called **linearly dependent**, if there exist non-zero (simultaneously) coefficients $x_i$ such that \n", "$$\\sum_i a_i x_i = 0,$$\n", "\n", "or in the matrix form\n", "\n", "$$\n", " Ax = 0, \\quad \\Vert x \\Vert \\ne 0.\n", "$$\n", "\n", "In this case, we say that the matrix $A$ has a non-trivial **nullspace** (or **kernel**) denoted by $N(A)$ (or $\\text{ker}(A)$).\n", "\n", "Vectors that are not linearly dependent are called **linearly independent**." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Linear (vector) space\n", "A **linear space** spanned by vectors $\\{a_1, \\ldots, a_m\\}$ is defined as all possible vectors of the form \n", "\n", "$$\n", " \\mathcal{L}(a_1, \\ldots, a_m) = \\left\\{y: y = \\sum_{i=1}^m a_i x_i, \\, \\forall x_i, \\, i=1,\\dots, n \\right\\}, \n", "$$\n", "\n", "In the matrix form, the linear space is a set of all $y$ such that \n", "\n", "$$y = A x.$$\n", "\n", "This set is also called the **range** (or **image**) of the matrix, denoted by $\\text{range}(A)$ (or $\\text{im}(A)$) respectively.\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Dimension of a linear space\n", "\n", "The dimension of a linear space $\\text{im}(A)$ denoted by $\\text{dim}\\, \\text{im} (A)$ is the minimal number of vectors required to represent each vector from $\\text{im} (A)$.\n", "\n", "The dimension of $\\text{im}(A)$ has a direct connection to the matrix rank.\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Matrix rank\n", "\n", "Rank of a matrix $A$ is a maximal number of linearly independent *columns* in a matrix $A$, \n", "or the **dimension of its column space** $= \\text{dim} \\, \\text{im}(A)$. \n", "\n", "You can also use linear combination of *rows* to define the rank,
i.e. formally there are two ranks: column rank and row rank of a matrix." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "** Theorem** \n", "The dimension of the column space of the matrix is equal to the dimension of the row space of the matrix.\n", "\n", "[Proof](https://ocw.mit.edu/courses/mathematics/18-701-algebra-i-fall-2010/study-materials/MIT18_701F10_rrk_crk.pdf)\n", "\n", "In the matrix form this fact can be written as $\\mathrm{dim}\\ \\mathrm{im} (A) = \\mathrm{dim}\\ \\mathrm{im} (A^\\top)$.\n", "\n", "Thus, there is a single rank!" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Full-rank matrix\n", "\n", "A matrix $A \\in \\mathbb{R}^{m \\times n}$ is called of **full-rank**, if $\\mathrm{rank}(A) = \\min(m, n)$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Suppose, we have a linear space, spanned by $n$ vectors. \n", "Let these vector be random with elements from standard normal distribution $\\mathcal{N}(0, 1)$.\n", "\n", "**Q**: What is the probability of the fact that this subspace has dimension $m < n$?\n", "\n", "**A**: Random matrix has full rank with probability 1." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Dimensionality reduction\n", "\n", "A lot of data from real-world applications are high dimensional, for instance images (e.g. $512\\times 512$ pixels), texts, graphs.
\n", "However, working with high-dimensional data is not an easy task.
\n", "Is it possible to reduce the dimensionality, preserving important relations between objects such as distance?\n", "\n", "**Johnson–Lindenstrauss lemma** \n", "\n", "Let $N\\gg 1$. Given $0 < \\epsilon < 1$, a set of $m$ points in $\\mathbb{R}^N$ and $n > \\frac{8 \\log m}{\\epsilon^2}$ (we want $n\\ll N$).\n", "\n", "Then there exists linear map $f$ from $\\mathbb{R}^N \\rightarrow \\mathbb{R}^n$ the following inequality holds:\n", "\n", "$$(1 - \\epsilon) \\Vert u - v \\Vert^2 \\leq \\Vert f(u) - f(v) \\Vert^2 \\leq (1 + \\epsilon) \\Vert u - v \\Vert^2.$$\n", "\n", "\n", "This theorem states that there exists a map from high- to a low-dimensional space so that distances between points in these spaces are almost the same.\n", "\n", "It is not very practical due to the dependence on $\\epsilon$.\n", "\n", "\n", "This lemma does not give a recipe how to construct $f$, but guarantees that $f$ exists." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Skeleton decomposition\n", "\n", "A very useful representation for computation of the matrix rank is the **skeleton decomposition** and is closely related to the rank. \n", "This decompositions explains, why and how matrices of low rank can be compressed.\n", "\n", "It can be graphically represented as follows: \n", "\n", "or in the matrix form\n", "\n", "$$\n", " A = C \\widehat{A}^{-1} R,\n", "$$\n", "\n", "where $C$ are some $r=\\mathrm{rank}(A)$ columns of $A$, $R$ are some $r$ rows of $A$ and $\\widehat{A}$ is the **nonsingular** submatrix on the intersection." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Remark\n", "\n", "We have not yet formally defined the inverse, so just a reminder:\n", "\n", "An inverse of the matrix $P$ is the matrix $Q = P^{-1}$ such that \n", "$ P Q = QP = I$. \n", "If the matrix is square and has full rank then the inverse exists." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Proof for the skeleton decomposition\n", "* Let $C\\in \\mathbb{C}^{n\\times r}$ be the $r$ columns based on the nonsingular submatrix $\\widehat{A}$. Therefore they are linearly independent. \n", "* Take any other column $a_i$ of $A$. Then $a_i$ can be represented as a linear combination of the columns of $C$, i.e. $a_i = C x$. \n", "\n", "* $a_i = C x$ are $n$ equations. We take $r$ of those corresponding to the rows that contain $\\widehat{A}$ and get the equation \n", "$$\\widehat{r} = \\widehat{A} x \\quad \\Longrightarrow \\quad x = \\widehat{A}^{-1} \\widehat r$$ \n", "Thus, $a_i = C\\widehat{A}^{-1} \\widehat r$ for every $i$ and $$A = [a_1,\\dots, a_m] = C\\widehat{A}^{-1} R.$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### A closer look on the skeleton decomposition\n", "Any rank-$r$ matrix can be written in the form\n", "\n", "$$A = C \\widehat{A}^{-1} R,$$\n", "\n", "where $C$ is $n \\times r$, $R$ is $r \\times m$ and $\\widehat{A}$ is $r \\times r$, or \n", "\n", "$$\n", " A = U V,\n", "$$\n", "where $U$ and $V$ are not unique, e.g. $U = C \\widehat{A}^{-1}$, $V=R$.\n", "\n", "The form $A = U V$ is standard for skeleton decomposition.\n", "\n", "Thus, every rank-$r$ matrix can be written as a product of a \"skinny\" (\"tall\") matrix $U$ by a \"fat\" (\"short\") matrix $V$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "In the index form, it is \n", "$$\n", " a_{ij} = \\sum_{\\alpha=1}^r u_{i \\alpha} v_{\\alpha j}.\n", "$$\n", "For rank 1, we have\n", "$$\n", " a_{ij} = u_i v_j,\n", "$$\n", "i.e. it is a separation of indices and rank-$r$ is a sum of rank-$1$ matrices!" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Storage\n", "It is interesting to note, that for the rank-$r$ matrix \n", "$$A = U V$$\n", "only $U$ and $V$ can be stored, which gives us $(n+m) r$ parameters, so it can be used for compression. We can also compute matrix-by-vector $Ax$ product much faster:\n", "\n", "* Multiplication $y = Vx$ costs $\\mathcal{O}(mr)$ flops.\n", "* Multiplication $z = Uy$ costs $\\mathcal{O}(nr)$ flops.\n", "\n", "The same works for addition, elementwise multiplication, etc.\n", "For addition:\n", "\n", "$$\n", " A_1 + A_2 = U_1 V_1 + U_2 V_2 = [U_1|U_2] [V_1^\\top|V_2^\\top]^\\top\n", "$$" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "49.9 ms ± 2.37 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n", "123 µs ± 413 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n" ] } ], "source": [ "#A fast matrix-by-vector product demo\n", "import numpy as np\n", "n = 10000\n", "r = 10\n", "u = np.random.randn(n, r)\n", "v = np.random.randn(n, r)\n", "a = u.dot(v.T)\n", "x = np.random.randn(n)\n", "%timeit a@x\n", "%timeit u@(v.T@x)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Computing matrix rank\n", "We can also try to compute the matrix rank using the built-in ```np.linalg.matrix_rank``` function" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Rank of the matrix: 1\n", "Rank of the matrix: 50\n" ] } ], "source": [ "#Computing matrix rank\n", "import numpy as np\n", "n = 50 \n", "a = np.ones((n, n))\n", "print('Rank of the matrix:', np.linalg.matrix_rank(a))\n", "b = a + 1e-5 * np.random.randn(n, n)\n", "print('Rank of the matrix:', np.linalg.matrix_rank(b, tol=1e-8))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ " So, small perturbations might crucially affect the rank. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Instability of the matrix rank\n", "For any rank-$r$ matrix $A$ with $r < \\min(m, n)$ there is a matrix $B$ such that its rank is equal to $\\min(m, n)$ and\n", "\n", "$$\n", " \\Vert A - B \\Vert = \\epsilon.\n", "$$\n", "\n", "**Q**: So, does this mean that numerically matrix rank has no meaning? (I.e., small perturbations lead to full rank!)
\n", "**A**: No. We should find a matrix $B$ such that $\\|A-B\\| = \\epsilon$ and $B$ has minimal rank. So we can only compute rank with given accuracy $\\epsilon$.\n", "One of the approaches to compute matrix rank $r$ is SVD." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Low rank approximation\n", "\n", "The important problem in many applications is to find low-rank approximation of the given matrix with given accurcacy $\\epsilon$ or rank $r$.
\n", "Examples:\n", "* principal component analysis\n", "* factor analysis\n", "* least squares\n", "* latent semantic analysis\n", "\n", "These problems can be solved by SVD." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Singular value decomposition\n", "To compute low-rank approximation, we need to compute **singular value decomposition** (SVD).\n", "\n", "**Theorem** Any matrix $A\\in \\mathbb{C}^{n\\times m}$ can be written as a product of three matrices: \n", "\n", "$$\n", " A = U \\Sigma V^*,\n", "$$\n", "\n", "where $U$ is an $n \\times K$ unitary matrix, $V$ is an $m \\times K$ unitary matrix, $K = \\min(m, n)$,
$\\Sigma$ is a diagonal matrix with non-negative elements $\\sigma_1 \\geq \\ldots, \\geq \\sigma_K$ on the diagonal.
\n", "Moreover, if $\\text{rank}(A) = r$, then $\\sigma_{r+1} = \\dots = \\sigma_K = 0$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Proof\n", "* Matrix $A^*A$ is Hermitian, hence diagonalizable in unitary basis (will be discussed further in the course).\n", "* $A^*A\\geq0$ (non-negative definite), so eigenvalues are non-negative.\n", "Therefore, there exists unitary matrix $V = [v_1, \\dots, v_n]$ such that\n", "\n", "$$\n", " V^* A^* A V = \\text{diag}(\\sigma_1^2,\\dots, \\sigma_n^2), \\quad \\sigma_1\\geq \\sigma_2\\geq \\dots \\geq \\sigma_n.\n", "$$\n", "\n", "Let $\\sigma_i = 0$ for $i>r$, where $r$ is some integer.
\n", "Let $V_r= [v_1, \\dots, v_r]$, $\\Sigma_r = \\text{diag}(\\sigma_1, \\dots,\\sigma_r)$. Hence\n", "\n", "$$\n", " V^*_r A^* A V_r = \\Sigma_r^2 \\quad \\Longrightarrow \\quad (\\Sigma_r^{-1} V_r^* A^*) (A V_r\\Sigma_r^{-1} ) = I.\n", "$$\n", "\n", "As a result, matrix $U_r = A V_r\\Sigma_r^{-1}$ satisfies $U_r^* U_r = I$ and hence has orthogonal columns.
\n", "Let us add to $U_r$ any orthogonal columns that are orthogonal to columns in $U_r$ and denote this matrix as $U$.\n", "Then\n", "\n", "$$\n", " AV = U \\begin{bmatrix} \\Sigma_r & 0 \\\\ 0 & 0 \\end{bmatrix}\\quad \\Longrightarrow \\quad U^* A V = \\begin{bmatrix}\\Sigma_r & 0 \\\\ 0 & 0 \\end{bmatrix}.\n", "$$\n", "\n", "Since multiplication by non-singular matrices does not change rank of $A$, we have $r = \\text{rank}(A)$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "**Corollary 1**: $A = \\displaystyle{\\sum_{\\alpha=1}^r} \\sigma_\\alpha u_\\alpha v_\\alpha^*$ or elementwise $a_{ij} = \\displaystyle{\\sum_{\\alpha=1}^r} \\sigma_\\alpha u_{i\\alpha} \\overline{v}_{j\\alpha}$\n", "\n", "**Corollary 2**: $$\\text{ker}(A) = \\mathcal{L}\\{v_{r+1},\\dots,v_n\\}$$\n", "$$\\text{im}(A) = \\mathcal{L}\\{u_{1},\\dots,u_r\\}$$\n", "$$\\text{ker}(A^*) = \\mathcal{L}\\{u_{r+1},\\dots,u_n\\}$$\n", "$$\\text{im}(A^*) = \\mathcal{L}\\{v_{1},\\dots,v_r\\}$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Eckart-Young theorem\n", "\n", "The best low-rank approximation can be computed by SVD.\n", "\n", "**Theorem:** Let $r < \\text{rank}(A)$, $A_r = U_r \\Sigma_r V_r^*$. Then\n", "\n", "$$\n", " \\min_{\\text{rank}(B)=r} \\|A - B\\|_2 = \\|A - A_r\\|_2 = \\sigma_{r+1}.\n", "$$\n", "\n", "The same holds for $\\|\\cdot\\|_F$, but $\\|A - A_r\\|_F = \\sqrt{\\sigma_{r+1}^2 + \\dots + \\sigma_{\\min (n,m)}^2}$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Proof \n", "Since $\\text{rank} (B) = r$, it holds $\\text{dim}~\\text{ker}~B = n-r$. \n", "\n", "\n", "Hence there exists $z\\not=0$ such that $z\\in \\text{ker}(B) \\cap \\mathcal{L}(v_1,\\dots,v_{r+1})$ (as $\\text{dim}\\{v_1,\\dots,v_{r+1}\\} = r+1$).\n", "\n", "Fix $\\|z\\| = 1$. Therefore,\n", "$$\n", " \\|A-B\\|_2^2 \\geq \\|(A-B)z\\|_2^2 = \\|Az\\|_2^2 = \\| U\\Sigma V^* z\\|_2= \\|\\Sigma V^* z\\|_2 = \\sum_{i=1}^{n} \\sigma_i^2 (v_i^*z)^2 =\\sum_{i=1}^{r+1} \\sigma_i^2 (v_i^*z)^2 \\geq \\sigma_{r+1}^2\\sum_{i=1}^{r+1} (v_i^*z)^2 = \\sigma_{r+1}^2\n", "$$\n", "as $\\sigma_1\\geq \\dots \\geq \\sigma_{r+1}$ and $$\\sum_{i=1}^{r+1} (v_i^*z)^2 = \\|Vz\\|_2^2 = \\|z\\|_2^2 = 1.$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Main result on low-rank approximation\n", "\n", "**Corollary:** computation of the best rank-$r$ approximation is equivalent to setting $\\sigma_{r+1}= 0, \\ldots, \\sigma_K = 0$. The error \n", "\n", "$$\n", " \\min_{A_r} \\Vert A - A_r \\Vert_2 = \\sigma_{r+1}, \\quad \\min_{A_r} \\Vert A - A_r \\Vert_F = \\sqrt{\\sigma_{r+1}^2 + \\dots + \\sigma_{K}^2}\n", "$$\n", "\n", "that is why it is important to look at the decay of the singular values." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Computing SVD\n", "\n", "Algorithms for the computation of the SVD are tricky and will be discussed later.\n", "\n", "But for numerics, we can use numpy already!\n", "\n", "Let us go back to the previous example" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Rank of the matrix: 1\n", "Rank of the matrix: 50\n" ] } ], "source": [ "#Computing matrix rank\n", "import numpy as np\n", "n = 50 \n", "a = np.ones((n, n))\n", "print('Rank of the matrix:', np.linalg.matrix_rank(a))\n", "b = a + 1e-5 * np.random.randn(n, n)\n", "print('Rank of the matrix:', np.linalg.matrix_rank(b))" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2.83450541212e-06\n", "2.83450541214e-06\n" ] } ], "source": [ "u, s, v = np.linalg.svd(b)\n", "print(s[1]/s[0])\n", "r = 1\n", "u1 = u[:, :r]\n", "s1 = s[:r]\n", "v1 = v[:r, :]\n", "a1 = u1.dot(np.diag(s1).dot(v1))\n", "print(np.linalg.norm(b - a1, 2)/s[0])" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Separation of variables for 2D functions\n", "\n", "We can use SVD to compute approximations of **function-related** matrices, i.e. the matrices of the form \n", "\n", "$$a_{ij} = f(x_i, y_j),$$\n", "\n", "where $f$ is a certain function, and $x_i, \\quad i = 1, \\ldots, n$ and $y_j, \\quad j = 1, \\ldots, m$ are some **one-dimensional grids**." ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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TTbS2drvdtGvXjmX7fPzlkzXsK6p8PEe3lg14YHQPjm/moaCggFAoZIxqIvnB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\nb7zxBuPHj49nlWmllVZajtaIrs2ZfdtwLh/QFoA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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "sns.set_style(\"whitegrid\")\n", "sns.set_context(\"talk\")\n", "# plt.xkcd()\n", "n = 1000\n", "a = [[1.0/(i+j+1) for i in range(n)] for j in range(n)] #Hilbert matrix \n", "a = np.array(a)\n", "u, s, v = np.linalg.svd(a)\n", "fig, ax = plt.subplots(1, 1)\n", "ax.semilogy(s[:30]/s[0])\n", "#We have very good low-rank approximation of it!" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Now we can do something more interesting, like function approximation" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3.61306030826e-10\n" ] }, { "data": { "text/plain": [ "[]" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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OgDcXJ0+eRFpaWsC7KCOFvpdN9raV10VRRHl5uercU1IOFE8dD3LiOA52ux08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\n2qoUT3JZyKTuL2kzDKNJAGTyVQqcPp5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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "n = 128\n", "t = np.linspace(0, 5, n)\n", "x, y = np.meshgrid(t, t)\n", "f = 1.0 / (x + y + 0.5) # test your own function. Check 1.0 / (x - y + 0.5)\n", "u, s, v = np.linalg.svd(f, full_matrices=False)\n", "r = 10\n", "u = u[:, :r]\n", "s = s[:r]\n", "v = v[:r, :] # Mind the transpose here!\n", "fappr = u.dot(np.diag(s).dot(v))\n", "er = np.linalg.norm(fappr - f, 'fro') / np.linalg.norm(f, 'fro')\n", "print(er)\n", "plt.semilogy(s/s[0])" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "And do some 3D plotting" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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kJiYiKysLFy9edFt+6dIl3HDDDXR0+AoaSPr3dpbGz84IKnfffTe6d++O5557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\ngiDQ2tpKS0uLviio1eLJj6b6MNMI3e12IwgC4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A8PI0mSXos1Vw1FUfSlrdkaCVM7cpre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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D\n", "# plt.xkcd()\n", "fig = plt.figure(figsize=(10, 5))\n", "ax = fig.add_subplot(121, projection='3d')\n", "ax.plot_surface(x, y, f)\n", "ax.set_title('Original function')\n", "ax = fig.add_subplot(122, projection='3d')\n", "ax.plot_surface(x, y, fappr - f)\n", "ax.set_title('Approximation error with rank=%d, err=%3.1e' % (r, er))\n", "fig.subplots_adjust()\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Singular values of a random Gaussian matrix\n", "\n", "What is the singular value decay of a random matrix?" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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PtWcu5lBPjId3HOHlQ708uusoHQMJ+oZ0HnyljQdfaSPk93HyonqOn1vLohmV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\nPVXY8Fc3dwJbu8mn0+mCawBOag9uheLsDSjOpQ9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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "# plt.xkcd()\n", "n = 1000\n", "a = np.random.randn(n, n)\n", "u, s, v = np.linalg.svd(a)\n", "plt.semilogy(s/s[0])" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Linear factor analysis & low-rank\n", "Consider a linear factor model, \n", "\n", "$$y = Ax, $$ where $y$ is a vector of length $n$, and $x$ is a vector of length $r$. \n", "The data is organized as samples: we observe vectors \n", "$$y_1, \\ldots, y_T,$$\n", "but do not know matrix $A$,\n", "then the factor model can be written as \n", "$$\n", " Y = AX,\n", "$$\n", "where $Y$ is $n \\times T$, $A$ is $n \\times r$ and $X$ is $r \\times T$. This is exactly a rank-$r$ model: it tells us that the vectors lie in a small subspace! \n", "We also can use SVD to recover this subspace (but not the independent components). Principal component analysis can be done by SVD!" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Applications of SVD\n", "\n", "SVD is extremely important in computational science and engineering.\n", "\n", "It has many names: Principal component analysis, Proper Orthogonal Decomposition, Empirical Orthogonal Functions\n", "\n", "We will consider:\n", "\n", "1. Latent semantic analysis\n", "2. Collaborative filtering\n", "3. Data compression" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Application 1: Latent semantic analysis\n", "One of the most famous application is Latent semantic indexing, see, for example, \n", "[Deerwester, Scott C., et al. \"Indexing by latent semantic analysis.\" (1990)](http://lsa.colorado.edu/papers/JASIS.lsi.90.pdf) \n", "\n", "The problem setup: we have a set of text documents $D_1, \\ldots, D_N.$ We want to solve the search problem: i.e., we have a query as a set of words, and we want to find the best documents. \n", "Our data is processed as follows: for each document we create a list of words contained in the document, and count the frequencies of each word. This is called the **bag of words** model (i.e., the document is unordered set of words). " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Term-document matrix\n", "This is how the term-document matrix $A$ is obtained. Its row size is **the size of the dictionary**. \n", "Its column size is **the number of documents**. An element $A_{ij}$ the frequency of occurence of the $i$-th word in the $j$-document.\n", "\n", "To do the search, we can just multiply a term-documnt matrix by a **search vector**, i.e. a list of words." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "**The problem**: The document will be returned only if there is an exact word match. However, we might search for \"Samuel Clemens\", and hope to get the results for \"Mark Twain\" as well. But there might be no exact match! \n", "How the SVD can help?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Idea of LSI\n", "Compute **low-rank approximation** $A_r$ of the term-document matrix $A$. \n", "$$A \\approx A_r,$$\n", "and **we do not care about the approximation error** (i.e., we do not require it to be small). \n", "The matrix $A_r$ can be then used to do queries. \n", "\n", "We project the documents to **low-dimensional subspace**, given a query $q$ the projection is \n", "$$q_r = \\Sigma^{-1}_r U^{\\top}_r q$$\n", "Now we can compute the similarity between $d_r$ and other projected documents \n", "$$\\widehat{d}_i = \\Sigma^{-1}_r U^{\\top}_r d_i,$$\n", "and compute the **cosine** of the angles between the query and the projected document." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Demo\n", "Now we can test a demo database" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " 0 1 2 3 4 5 6 7 8\n", "human 1.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0\n", "interface 1.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0\n", "computer 1.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n", "user 0.0 1.0 1.0 0.0 1.0 0.0 0.0 0.0 0.0\n", "system 0.0 1.0 1.0 1.0 0.0 0.0 0.0 0.0 0.0\n", "response 0.0 1.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0\n", "time 0.0 1.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0\n", "EPS 0.0 0.0 1.0 1.0 0.0 0.0 0.0 0.0 0.0\n", "survey 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0\n", "trees 0.0 0.0 0.0 0.0 0.0 1.0 1.0 1.0 0.0\n", "graph 0.0 0.0 0.0 0.0 0.0 0.0 1.0 1.0 1.0\n", "minors 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 1.0" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "import pandas as pd\n", "import re #Regular expressions\n", "rows = ['human', 'interface', 'computer', 'user', 'system', 'response', 'time', 'EPS', 'survey', 'trees', 'graph', 'minors']\n", "nterms = len(rows)\n", "docs = []\n", "docs += ['Human machine interface for Lab ABC computer applications']\n", "docs += ['A survey of user opinions of computer system response time']\n", "docs += ['The EPS user interfaces management system']\n", "docs += ['System and human system engineering testing of EPS']\n", "docs += ['Relation of user-perceived response time on user management']\n", "docs += ['The generation of random, binary, unordered trees']\n", "docs += ['The intersection graph of paths in trees']\n", "docs += ['Graph minors IV: Width of trees and well-quasi-ordering']\n", "docs += ['Graph minors: A survey']\n", "ndocs = len(docs)\n", "term_doc = np.zeros((nterms, ndocs))\n", "for i in range(nterms):\n", " for j in range(ndocs):\n", " if re.search(rows[i], docs[j], re.IGNORECASE):\n", " term_doc[i, j] = 1\n", "#Use pandas to plot \n", "pd.DataFrame(data=term_doc,index=rows)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Now we can compare the results between ordinary matvec and low-rank matvec." ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "There query is: Human computer interaction, the scores are:\n" ] }, { "data": { "text/html": [ "
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No SVDSVD
Human machine interface for Lab ABC computer applications2.00.316794
A survey of user opinions of computer system response time1.01.011276
The EPS user interfaces management system0.00.663677
System and human system engineering testing of EPS1.00.405542
Relation of user-perceived response time on user management0.00.554066
The generation of random, binary, unordered trees0.0-0.035325
The intersection graph of paths in trees0.0-0.065210
Graph minors IV: Width of trees and well-quasi-ordering0.0-0.082587
Graph minors: A survey0.00.055939
\n", "
" ], "text/plain": [ " No SVD SVD\n", "Human machine interface for Lab ABC computer ap... 2.0 0.316794\n", "A survey of user opinions of computer system re... 1.0 1.011276\n", "The EPS user interfaces management system 0.0 0.663677\n", "System and human system engineering testing of EPS 1.0 0.405542\n", "Relation of user-perceived response time on use... 0.0 0.554066\n", "The generation of random, binary, unordered trees 0.0 -0.035325\n", "The intersection graph of paths in trees 0.0 -0.065210\n", "Graph minors IV: Width of trees and well-quasi-... 0.0 -0.082587\n", "Graph minors: A survey 0.0 0.055939" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "query = 'Human computer interaction'\n", "qv = np.zeros((nterms))\n", "for i in range(nterms):\n", " if re.search(rows[i], query, re.IGNORECASE):\n", " qv[i] = 1\n", "res1 = qv.dot(term_doc) #Non-compressed search result\n", "\n", "u, s, v = np.linalg.svd(term_doc)\n", "r = 2\n", "u = u[:, :r]\n", "s = s[:r]\n", "v = v[:r, :] #Numpy transposes\n", "appr1 = u.dot(np.diag(s)).dot(v)\n", "res2 = qv.dot(appr1)\n", "res_all = np.vstack((res1, res2)).T #To make two columns\n", "print('There query is: {}, the scores are:'.format(query))\n", "pd.DataFrame(res_all, index=docs, columns=['No SVD', 'SVD'])" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Application 2: Collaborative filtering\n", "\n", "Another important (and similar) application comes from **recommender systems**. \n", "\n", "Suppose you have a **user-product matrix**: each user puts a rating for a particular product.\n", "\n", "The matrix is then **the number of users times the number of products**. The goal is to recommend additional products to be bought for a particular user. \n", "\n", "The scheme is the same: we compute the SVD, and the recommendation for each user is just a column of the approximated matrix.\n", "\n", "We will do this demo tomorrow :)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Application 3: Dense matrix compression\n", "\n", "Dense matrices typically require $N^2$ elements to be stored. For $N \\sim 10^4 - 10^5$ the memory requirements. A low rank approximation can reduces this number of $\\mathcal{O}(Nr)$" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "text/plain": [ "Text(0.5,1,'Singular values decay for a Hilbert matrix')" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Q803CPEKI6cE4zhNCbDF5539CiLuF+SaKYfj1119F3759xeLFi+WjKSZ5zhJC\nrDB8er0Q4kohxK8m0a4UQtwugstKgzgghOhrEndXoXmQ14RKIcQo5Zu/GMK3CSE6BsOGCiFKRfQ4\nKIS4Q2ibTp4lFE9zBXuEEE8LIYqVZxVCiBOEEEeJcM/8ciHEyGA+fy80z2qJvSLcG3qFEOIjEQ63\nyTMjqnNv/k0IMSaYdzMcEEIMEUK8Yni+SwhxtGgcXSeEECLZY6g7LGj7+/RH2++mHG0/nCVoY8Q2\nNE/Llmgt7YPB9z1oe+JUoO31MgjoDsxxu9384Q9/oKSkhOHDh1NaWsr//vc/Lr30UukcVQR0Dl4j\ngt+vR9v2uw3aBFUp2j4zMh03mtdvXjBPa4JXv2A+13F4E6/laEska0KbIM0lwfjleLgNrbWbr6Sz\nOviuMZ2f0bZdzkbbjvwotKWxK9H2djoUzIsPradyEtpeNZVoSzN/UNJNQZtU7BF8dzPaXJC+AY8J\nOqHxLwfYEqQlBW1vGumd1RUYiebx+ivaBLbquWUNxpGPVpbLObxnT1rw2+5o/P8RbZ6jAPjI7XZz\n3nnnsXPnTgYMGMDLL7+MxWIpQSvXEsLhQJOTDLTVR3LZpT3Im9wgvSuAZcE85KDJXwCtnEqr4YUl\nGHd/tP2lNgXz2xetHJeZ5KkLWnlUBcNVXmeh7RVlDeYnBegd5NHqYLypaOXoRCu3CjQP+85oQ0H/\nMeTXguaQVxCkbTPairIqtPKR6S1Hq2cE7wej7dNVjjaBqzq4tQ7S7Avyp0yhqyz4zIdWl9qh1b3V\naPI/Am2124FgvC2C7+xEk/MuwFC08tkZpNMX5FU5mnwMRivXsuD3vmD+DwXpzUfzfncHvzNdndYA\nEBDfQ0kZHN68LQ1NqM0qWaxgCabZFq0AO6NVxpZoCq9VMNwVvDKDlwutsrjQBMMZ/LWCNjn5+eef\ns3nzZpxOJ8OGDWPAAOnJjzd4qZvrWYK0ysuKebn50XjjCcbhU+KrQKtQh9AEtTj4Wxp8Ljf8Kw++\nUxr83Rf876ZhzsBNReN3NpoCSkMbEsnk8E6jGcErK/g8G63ipQafp6HxPwWN73aqn9gTym8geAnD\npb4nd/+UZWBT7kPw4osvYrfbOe+88+Qqrt/QlIgHrTwOKVep8vsbmhHdG/xfGsxXQ8KKxtsOaEa9\nFRqPszjMd3mgUKryrAUa/1W+V8sjBUbZMpPvAJqM+9F4WMlhWT4QvORZFgfR+CbDJG/L0GS6sZSw\nhAVNnqUeyQr+bx28l7KeFrxvh1YvspQwBzXrAyNUGW/NYd0Z94ahitDVE1VorZ9SNCIr0SpcSfBZ\nBZqiqyC0MstdTluiCbIsGFfL3IpYAAAgAElEQVTweXrwas1hB6pERwCtkklFdRCtEu5H47vkcyWa\nEZGtfXvwcqIJeQs05d0STZFIQ5DDYcWTRCg8aAe+FAWvcjQZlwpPGntp3P0clvdUDjdMZINFKvKW\naAonB61MstHKJIMjvEqpCaASjW8laPzcj8bbEg47Hh4I/u4LPnej8TQQ/HWg8VkqcCnfmWgy3RaN\nl9IAZAbfyUHTOY15wNZPaD0aiHPDYEFrAVuFEDV6GDZFBAIBAoEAXq8Xn8+H1WrVn3s8HioqKvB6\nvfj9ft35RV7yW3mFFl84rFYrFosl7LLZbNhsNqxWa8h/u92O1WoNuWS43W7X34s3ngNh/PP5fCF8\nDgQCIf/l++ozNUyGy7jlZURGRobuVFdeXk5lZaXOW2N5mF0OhwO73Y7D4dD535QhhMDn8+H3+/F6\nvTqPhRCmvDb+qrytia9GeVZl1SjTNfHXZrPFjTz7/X6drx6PR+etz+fD5/OFyankoeS/kZfBSfpK\nNCMFcW4YHIBHCMFPP/2ExWIJEwCjUjNTbsaKKeORz1TUpJwl09WCkQUoC1FVQkIIPS9OpxO73R6i\nkGUe5TO1AhiVNhx2HpO/skhrmmSSwqTmVSpLo1JUw+R/6TGq8lXlrfpc3qv5NxoqNf8qz1U6jIIu\nearmU82jsRwCgUCYwVNpMMunfKbeq2VREx0WiyWkEhoNjhmfVSWp0ijlSC6RVA2FKteqLKnyU10D\nwQgjr82MotG4yjzKy+fz6flxOBw4HA5TXqo8V3+r46+Rp6rxMBqY6i4pH0ZjpPJQ5lvNk8pTVV7U\nvAKmRtto6NT0VWOpKvfq8i6E0Mve6XTq+ZSNB1VGzWRZ8lDlp8ViqeLweSZNxjBkornuH4fW9Z2H\ntsyspqZwBtowRqrKdFVJqIKtCoPRqhoVfXUtFLMWd3Uta6Owy8ohK3J1lfJI4+DBg+zevbuu696r\nheSZka+S/8YwY2vQyGe1ohthNIry12iMJL/VVrWxYRCvPR0VsgGitsRVfkvlovLerNdZXU/T2ACR\n8qr+qjIvy0AqJtnQOdJ83r9/Pzt37qzT9hS1Qcqnqj+MusQo68YWuMpjI4wyrPZSzHSFmS5RDVes\neFtWVsaOHTvIy8sLMwyN7eDWHm3VRYbybCLaiU4Tqd44lKGtAvmhsrKS7du307t3b3XfoTpBVjBl\nD5pmDSGEenpWxFCHPpoyDh06xLZt2+jTp0/tL8cJZE9N3d8HNI/msrIyuQa+2cNisUS8WaMR0sgZ\nedqUUFxcrG+lEitYrdZqGwiNPVj5NJCxZs0abrnlFh566CHpkToBzdGnJrhB2xbBbAuGuqC8vJw1\na9bUOk7fXGCz2apt1TRXVFVVJQS9Xq+XHTt2JAStkHiybLFY6jSnWB/YbDa5AWNYF6QxDUML4EKv\n18vdd9/NHXfcwdChQ3n88cdleG37nPhAs3qRbmilTvomApL0Nl8kEq2QpDdWcQbjC7MDjWkY8kFz\nbz/mmGNo3bo1p556Kj/99JMMP6mW772QNAz1QZLe5otEohWS9MYqzqZoGDJBGwdu2bIlELYqpba1\n0xb5TaTdK5leoghXkt7mi0SiFZL0xirOoO4MswNHYvI5BzgbbV3sZ2hOZ6A50JyC5j25k6Are1ZW\nlr69rcxsHZEm34/WMCTKOGVqaip9+/Zt0pNssUQilW8i0QqaLBcUFDR5n45Y4UiUr6I7w5RurA1D\nFtoeM72C92Voe4iMBKZj0gvo2rUrGzduxOfzUVhYSOfOnWXQEuO7BrSoJbxWpKSk0LZt27hawmhc\nA1/TEjn5q14OhyOu6I0GKSkp9O3bt7YjIOsNye9Ilt0a/QpiBYfDQdu2beNeUVa3BLQ6nqr8jHfa\na4LL5WLQoEERyYwZL2urE6phiFZKj0bbArfX+vXrKS8vZ9CgQRlop4ENFkLo5wP37t1b34Y3PT2d\niy++mGuuuYZAIKDvgY/my1ATWhof1McL+qmFG3hv2a+8OnlorUdpxgKqI4u6Htrj8YR5Lapr0qtT\nPtGiJi9Ro7+AmQepXN7XlI2M1WrF6XSGObup96ovQE3OXEafgFjAuLZd5b/RcVD1FVD9YSTsdrva\nqGoUGB0PVc9nMz6aeT5Hw9uaPKCNvgBG3wFV7psqJF/lr/R8lj5cqg4xejsbMXjwYJMUDiNWPYax\nwEcAu3fv5s9//jPjx4+X7taDAR566CEWLVrEiBEjeOGFF7jgggu47rrrADjrrLM466yz1Pi2AM/V\nkqbq+4D0gjbzrlSFwW63k52dzeLN+9hZXMkbS7Zz+++74/V6QxQihHbfzDyHq1MeRm9hWWhmBSSF\nUlUI8qAeo3elmedzTV7D1bVmq/N2Vh17jF6a1VVaWRmlwjJ6b5t5tdbmhWv0bjW2IFXHRaMzl3GL\ni9qcuYweo6rnq1Fp1+T9LOMz0iFpgOo9n418Vj3mVc95lQ7V81zlt5nns5kMVZdPM89nVckYeat6\nPks5UmE0ZMb8GhsfdfEsN5Pv6rye1TpoDDNzYjV6xBvlWZVrM56q+axOhtX0jY0Woye/qldUyEaP\nzKfT6SQtLS1MTo1e0NU414ZVkFgZhkcAPv74Y/7+97+HEbF582beeecdvvzyS9q0acNFF13E2Wef\nzYUXXigPaCkEugVffxq4n9p3PMw0PujRo4dpq1BeqoU9tlsOP2w9yNcb9nLTSZ3ZuHFjvYk2eoIa\n/zscDtLS0sJaeo21R0tVVRUbN24kNze33r0k47YDqhI2KulAIIDb7Q7bdiOWPR7jthCy8qampta4\nJYrRozdeYGyNG5Wd5H1FRYXOczNFXV+YNUaMns8ulyvEu1/dBuNI8biyspL169eTl5eHy+WKKA7V\ni7w2z+eKioowD+hooDaUVPk1M5jqJXVJjJ1Lj5hh6Ajw3nvv8eSTT4adSbx48WIGDBign9LVo0cP\nunTpwvfff8/YsWMB/ga8Us80M+GwVbZYLGRnZ9f541GeA8z8cjOF+8o55LNTUFBQo2u7Was9nhQL\naLyqx7nPIYiVt3N1Y8fV8Vz+RjI2X1VVxaZNm+jZs2eDDBceSVgsFl1xmClCr9fLwYMHadWqVVgZ\nGVvXtW3fYNYjbYoIBAJR5a86L/K6oKZ5JmPPTv5GM79UVVXFmjVr6NOnT8yMgpJP2XrQH8TKMKwG\nTpSHuxsNw+7du0OObgTtgO09e/bI29DAuiEb6jevoKKgczZpThsVHj+Lt+zngiGNOz7bEFCNaGNB\nGpiGgOy5NGXlFitIz+fs7Oww/lYzfBDXaGxZluk2pCxHquuqgxJf2NYRsZrGvwnt9CZTuN3usP2I\nXC6XutdJJMtGdMMQyWoEp93KgE5aD2PNriN5vk/TgRxWaM6rN1QkEr2JRCsk6Y0FFN3pNobFKpUf\n0I4VfMssMCsrS+6BpKOkpESeZAWRnbyWA5H3GAB6tNXO3dm6vzyi7+MNjd3KamgkEr2JRCsk6Y1V\nnMH4wsaXG8Tc9u/fn82bN+vE+Xw+tm3bRs+ePeUrhRFE2waiMwxdW2mGYfPesoi+jzckK1PzRSLR\nCkl6YxVnML6whT4NYhgGDx7Mvn37+PTTTxFC8Pbbb5OamiqXs/qBxRFE2wKim4DKbaf5yO04UEmF\nJzZb+DZlJCtT80Ui0QpJemMBRXcesTmGEGRlZZGefvh45IyMDKZPn86zzz7LoEGD+Oc//8mzzz4r\nVwO8iXbGan3RGiKfYwDo2fawK8TGoubfa5DjlIlSmRKJ3kSiFZL0xgKK7gzrMcR6S4w1APfee6/6\n7A7gpuHDh7edP38+Xq9XdcfeCNwSYVptQGNYpIahdbqdrFQHhyq9rC8qZUDnui93jUdEw6t4RCLR\nm0i0QpLeGMcZNscba85OQ/NH2I7mvfwP4HFgIPC8xWIpDRqFvcBMYHjwf31hJej57PP5Il4y5vf7\n6ZKjnYG9q7g2f7r4hzyLN1GQSPQmEq2QpDdWcQZ1Z7ExLNacrcD8gJ1dwJ+Ba9A20ov2fMkMgns7\nBQKBiA2Dz+ejfZaLlTsPsbs4+iMvmzqSrazmi0SiFZL0xirOoO48ZAxraM4KojcKAO3kn2gsqdfr\npWO25l+x61Cyx9DckEj0JhKtkKQ3xnGGzfHGq8nNkX+iNQxtM7WtEvaWhvl4NDskK1PzRSLRCkl6\nYxxnszEM+pInv98f8VCSx+PhqCxt35mdCTDHEA2v4hGJRG8i0QpJemMc5wFjWLwahjT5JxpLWlVV\nReeWWlSlVT4OVYQt521WSLaymi8SiVZI0hvjOJufYfD7/RFPyng8Hn1VEjT/rTGimaiPRyQSvYlE\nKyTpjQUU3VlhDItXw6CfxRBNF8vv99My1UZGimaJC/c1b8OQ7H43XyQSrZCkN8ZxNps5Bv28Z6/X\nG/F+6l6vFyEEXVtrvYYtzdgwSHoj4VU8IpHoTSRaIUlvrKDEucsYFq+GoZX84/P5ImKYeqKYHE76\n9UBYj6rZQNKbKOOyiURvItEKSXpjBUV3FhnD4tUwdAD0o/ciYZjXq000W61WuuRoi5y2NWPDIOlN\nlFZWItGbSLRCkt5YQNGdlUCpMVwahnjbiao9HB4ji2RjKXlIkNVqpVtwKKk5zzFIehOllZVI9CYS\nrZCkNxZQdGfYdhhw2DDE5oT2hkNriHx+QX4rz1/t3kbbZfVAuYeD5ZGdidzUIelNlAm7RKI3kWiF\nJL2xijOoO/eZhcfrUFILiG4DPbmG12KxcEybw9tvb2qmh/ao9CYCEoneRKIVkvTGKs6g7jTdxDRe\nDUMaRNdjUCetW6Y7aZmm/S/c2zyHkyKdpI9XJBK9iUQrJOmNBRTduccsPF4NQwoQ8cQzhPc25HBS\nc12yGk3vKh6RSPQmEq2QpDcWUHRnjXMM8QYXRO/cFmIYWmsrkzb91jyHkpIOQc0XiUQrJOmNcZxN\n2jC0A34HDAPq0mdyQGwNgzz/eUNR2MqtZoFkZWq+SCRaIUlvjOM8aBbe2IbBATyHNs61EFgMeIBT\navnOBtHtk2TceyS3vWYYdhysoNztiyjOpozk3jLNF4lEKyTpjQUU3Rl2rCc0vmH4O/Bnj8fDkiVL\n2LJli3z+OdCjhu90wxDNqiT127yjNMMgBKzb0/x6Dclx2eaLRKIVkvTGAjXtkwQNaxhaAecAfwxe\nVwC3BAIBrrzyStatW8fTTz/Nxx9/LN//Uw1xWSE6w2C0wm0yUshJdwKwvhkahmQrq/kikWiFJL2x\ngKI7TXsMDeU62An4gaDHsory8nImTJjAmDFjKCgoYO7cuYwdOxagew3xWSC2cwwWi4X8ozL5dtM+\nVu4MOwI17pEcl22+SCRaIUlvjOM0XYbZUIZhHNB+06ZNrFu3Tn+YkZHBSSedxJgxY/jggw948cUX\nefDBB2Xw2Bris4C262A0cwxGh5GCztl8u2kfy3eYTtTHNczobc5IJHoTiVZI0hsLKLrTbxYeC8Pg\nAnzBS4UVbS7AG/yP1+ulvPywgVKt4Mknn0xWVhbTpk3jtddegzrs3ySEiJhhZt/265QFwMaiUqq8\nflyO5tMqiYZX8YhEojeRaIUkvTGO03QPoGgMQzbwT7RlpmXAA8CTwIjg/5FohmEd8DFwMC8vr2Ve\nXl5IJHv27GHZsmWceeaZnHTSSTz66KMyKLW2DAQCgYh6DHK7beO3fTtqhsEXEKzbU0pB5+x6x90U\nIYSgX79+CdP9rq58myMSiVaJQYMGIUS8be8WGY5U+Sq6M6aGIRV4E/i9x+PBZrO1sNlsj6ONV/0f\naAQFvet6A72Bz4LfSIXfDvhbdnY2r732GmVlZaxbt44xY8bINL6rB3H1QiAQID09PcxrukOWi1bp\nTvaXe1i581CTNAxCCAKBAIFAQBcas0oiWxgWi0W/5LfyvjkjNzeXtLS02l+MAJLfxjKQz6srD7lp\no/obi7x06dKF1NRa21FxAZWXdZFxlZ/N1Tjm5+eTkpIS8fcqL+Vu1IrujNlQ0nBgDtDr4MGDnHvu\nuTz33HP07t3bQtAovPDCC8yePRuPx8OIESN49NFHycjIGAPMAl5X4urmcrkunzNnDkuWLCE/P59+\n/frJsIfrQrDFYsHtdmOz2eq8BbfNZqN3795hzy0WC307ZvH1hr2s2FEMw46uNa66QhpKuQ+63+/H\n5/Ph8Xjw+Xz4fD5d4ft8Pj28OuUTLaxWq84zeVmtVux2e0hlM4ap9w6Ho0kaGIvFQosWcvnxYUMq\n+a7ee73ekHKRYcZLDYtVGajGwsh/yWe73a5fDodD/5WybrVaadOmTUzyEy2kjPt8Pp2vXq8Xr9dr\nykcj3+WBNJFC7kBqJtsqP1UZttlsOl9jZaxjCYvFQmpqqn6Km9fr1fnr8Xh03srnqoyqh5FJDBgw\nALvdrg4lxcQwZKI5oqVv3ryZv/zlL+zcuTPkha+//prXXnuNDz74gJycHK677jqeeuop7r33XoDr\ngfeV168DXGlpaX8cPXq0Gs2lwPzaMiOt3sqVK3Xi1Uom/6vCoFY8tWJarVacTicDu2Tz9Ya9/PJr\nsS7YRsWsKnkz5aEqIFmIPp/PVOilUKr5crlcep6lsBrzKi+1Z6DCLM/yuVkeVUVpFC55Vddqk3x1\nOBx6vswqoLG1bLzUONX8GluQMq/SoKq0qIq+NkVusVhClIKqUKTRM8qTyndjy9+MDkmDlFeVBtXo\nq3yWl6pcjfIj82402qosqXQZZai6fKq8VpW1+qvyVpaBqphUGA2ZMb/GxocZb81kpLr6aOShWgeN\nYUa5UMtb5a2Rv2ojtLq8quVu5KuavrHRIuufmn/5q0LqK5lPp9NJWlpamJzKfKn8l7IYyx7DACB9\n9erVTJo0SVf6Kj788EPGjRtHx44dAZgyZQrXXHMN99xzD1ar9UQ0b2dv8PUKYAJwF1CAdpLQ4uDz\nWiGJ6927d0hL29gqkZdqYY0VE8DlctG3Q2sANu8tp7zKw8Z1a6pNXxV0M4PkcDhIS0sLa+mpV0O0\nUNxuN+vWraNXr164XK6I4lCFWvJOrWyqkg4EArjd7pBej1nrJRqoxkhVNqmpqWHlYOwVqQ2DeIGx\nNW5UdpL3FRUVOs/NFHV9YdYYUS+73Y7L5cLhcIRdR6IF7na7WbVqFfn5+VEPFQohwno3xgaSlOeK\nioowHRMN1IaSKr9mBlO9nE6n/j8aKIbBdIyqvoahBKB9+/YsWLCA1q1bM23atJAXNm7cyIknnqjf\n9+jRg9LSUoqKijjqqKMcaMdybjPEuzV4RYT6Cojf76eyslK3sGprNKdMs1n+gGDjvir69OkDENY6\naIrdzuogK0AsuunRCmR1Y8dmRkNtiddnbN7j8VBYWMjRRx8dsSFsarBYLLriUGnyeDzs2bOHjh07\nVrs1s7F1bWwQGdMx65E2FcRy0ln2uiLZ0rqmeSZjz07+RjK/5Ha72bRpEz169DhSsmwaaX0Nwwrg\n+1atWh1X3QtlZWVkZmbq9/K/skw1vZ5pxhxer5f169fTp08fXC5XSBerfZaNdpkpFJW4WfFrMYOP\nbtnIuY0dmkIlb4iTtwKBAGVlzXOXXCMCgQB79+6lbdu21Sq45rjYoLHpkekfaVkWQlBVVXUkk8gw\ne1jfaXyBtgz1zOpecDgceDyHV0C53W4AdVY9plTGWkAsFgt9O2jLVlfvMvUWTyKJJJKIewR1Zyuz\nsEjWd3nQJoYrzQK7d+/Ovn2HjxHdu3cvNpuN1q1by0emmzZFimi6ltV927+Ttkx12TbTHWnjFomy\n9lsikehNJFohSW8M48w0C1MNQ0xSPu6441i4cKFOyMKFCxk4cKBcZ70RaPIbER3XPQeAwn3lFJUc\n0W5cEkkkkURjwnQoKeZ7JZ133nnMnTuXq666ig4dOvDxxx/z0ksvyeC5sU5PWY9bZ9T2fkHnbBw2\nC16/4IetBxjbv0M0WWx0NPZ4bEMjkehNJFohSW8sEdSdLczConEVLAaYPn06nTp1ks9+bNGiBfPm\nzWPcuHHk5eUxb948CgoKALYD06qJq74IQPRMq6575nLYdK/nHwoPRJVGU0Ky+918kUi0QpLeaKHo\nTtMlndH0GKYBj40aNUrevw9cAjyfkpIy8ayzzlLfXQ5cQDXHyEWAAGBVHaHqA6MDihkGdMrmh60H\nm8UW3HWhtzkhkehNJFohSW8s4w3GqQ4lWQhOKURjGB4HPgKOAX4DlqF50V0C3I92PKcdWAUsohoP\nuwih9xiiMQw1oX+wx7B6Vwk+fwC7LX73YUl2v5svEolWSNIby3iDutN0PX60cwzrgpcRm4PXkYIP\ncEJklrQuVrh/cKdVty/Auj2l+s6r8YhkK6v5IpFohSS9sUQwzrDD06Dxz3yOFB5A91quLySza9ou\n4OhWabTO0I76XLIlpitsGxx1obc5IZHoTSRaIUlvrKDozk6m4TFNreHgBo1pkTBMbs9bk1GxWCwc\n30PzvViyJb4noOtCb3NCItGbSLRCkt5YQdGdrc3C494wHAkHNwm5HcZP2w82C0FsDjTUB4lEbyLR\nCkl6o4WiO03HyOPVMJRDdENJdeltSMNwoNzDrwdNHb3jAnWlt7kgkehNJFohSW+soOjONILztSHh\nMU2t4aAbhkgZVpdve7bLwG7VxvhW74rvZavR8CoekUj0JhKtkKT3CMQZti1G0jDUgBS7jV7tNcfA\nX35NGoZ4QiLRm0i0QpLeIxBnszEMxRAdw2w2W52+HdhF82f4eXt8b6hXV3qbCxKJ3kSiFZL0xgIG\n3Rm2ZDVeDcNB0BgW6UlKVqu1Tt8O7KzNM6z49RA+f/wKY13pbS5IJHoTiVZI0hsLGHRn2KHh8WoY\nKuHIDyUBFAR7DBUeP4X7ymt5u+ki2f1uvkgkWiFJ7xGIs11YeExTazhUQuR+DFD3FU1dW6Xjcmhs\nWrenNKK0mgIiXcEVr0gkehOJVkjSGwsYdGeyxyBR129tVgs922oT0BuK4tswJFtZzROJRCsk6T0C\ncYbtlxSvhqECorOk9WF2z3baBoTr47zHkKxMzROJRCsk6Y1VnIrubDarkkqgYSafAXLbaT2GTb/F\n7wHzyQm75otEohWS9MYCBt0ZdopbvBqGMmiY5aoAucEew9b95VR541Mgk0v8mi8SiVZI0hsLGHRn\n2Clu8WoYdAe3aHoMdWV23lFaTysg4nc4Kdn9br5IJFohSW+s4lR0Z9h+SU3BMHQDXkI7OcgLPA20\nquWb/RDdUJLNZsPn89Xp3faZLrJSHUD8Gob60NsckEj0JhKtkKQ3VnEqurPJTT73AbYAk4P3duAv\nwFogu4bv9gA4HA68Xm9ECdfnW4vFom+NsT5OVyZFw6t4RCLRm0i0QpLeIxBnkxtKegXgiy++4Prr\nr+fKK69kzZo1oK2rnVrDd6UAdrs9qh6DEKLOq5qOaavNM2zeG58T0PWlN96RSPQmEq2QpDcWMOjO\nsMnnaI/2rCtSgP8DLjcGlJSU8PrrrzN79mz27NnDu+++S35+PsBxNcQXk030APx+P3Z77Wzo3jod\ngC1749P7ub70xjsSid5EohWS9MYqTkV3phnDG4qrkzAxCgDLly+nT58+zJo1C6fTyZQpU2TQkBri\ni5lhqOv33YKGYWdxJV5/AIetsTtb9UN96Y13JBK9iUQrJOmNVZxKfGHnMTSUYegJ8NZbb/Hpp5/q\nD3v37k1+fj5ffPEFjz76KKtXr+b+++/nscceA9hWQ3wewG+1Wm2BQAAhhH42al1hs9mAujO7a9Aw\n+AOCXw9W6oYiXlBfeuMdiURvItEKSXpjAWkYgrrTZgyPxjBYgEuA0UARMAPYgTZsdCFwLJol+gXY\nDDBhwgQmTJgQEsl///tfRo4cSUFBAQUFBcydO1cG9aohbQGUWyyWTEmgZF5dId+v6xxFp5apWCwg\nhObPEG+GISUlhX79+iVE1xvqX77xjESiFcDlcjFo0KDGzkaD4UiUr8VioSbdGY2WuBX4h3J/JnA2\nMB/INby7D/gI6MThGfBjAAYNGsTs2bMpLy9nw4YNdOnSRX6zvpb0S4FMueyqvobBarWSlpZW5wmd\nFLuNozJd7DpUxY4DFfVKK5YQQhAIBHRrX92klOxByaMBLRaLzqNIeljxBrvdTu/evUlNTY153JLf\nxjKQz6srD1kZ1d9YwGaz0aFDh3rXgaYIlZd1kXGVn3LIpbnBbrfTv3//iBt1Rl7a7XZdH1SnOyNJ\nKR24B7hDCMHjjz/OlClTyMrK6gMsBXI2btzIv/71L9xuN2eddRZDhgxpDRwP5AF7lbiWZmdnD735\n5pu57777cDqd3H///TLszVryUQJ0lMT5fD5sNludK5vNZiMvL6/uVAOdctLYdagqovOfhRD4/X4C\ngQB+v1/Ps8fjwefz4fP5dIXv8/n08OqUT7SwWq3YbLaQy2q1YrfbQyqbMUy9dzgcTdbAWCwW0tPT\nTfku+ez3+/F6vSHhMsx4qWGxKgPVWBj5L/lst9v1y+Fw6L+qrFutVo466qiY5CkaSF77fD6dr16v\nF6/Xa8pHI9/9fn9UvJXKzky2VX6qMmyz2XS+xtJYxxIWiwW73a7zVf56PB6dt/K5KqOSn0ae9u7d\nm/T09Br9wOprGFzA/4CBfr+fRx55hNdff51JkyaRlZUFkLN582YuvvhiJk+ejMvlYsqUKcyYMYPh\nw4e3QluC+lclvgnAxiFDhjBkSMhc8xfAc7XkpRQOO2ps376dsrKykEom/6vCoFY8tWLKS97D4Va3\nEAKbzUbnlmksLTzAjgMVVFVVUVFRYao8VAWkFqaZ0EuhVPPlcrn0PMs8meVVFWSjQBuNidqaNcuj\nqiiNwiWv6lptkq8Oh0PPl1kFNLaWjZcap5pfYwtS5lUaVJUWVdHXpsgtFkuIUlAVijR6RnlS+W5s\n+ZvRIWkAQvJj7PWpfJaXqlyN8iPzbjTaqiypdBllqLp8qrxWlbX6q/JWloGqmFQYDZkxv8bGhxlv\nzWTEKNvGumdWB41hRjYPsEQAACAASURBVLlQy1vlrZG/Mr9mPFXzWZ0Mq+mrfFbrn5p/+avCarXi\ndDr1fDqdTtLS0sLkVOZLza/L5QJCnNzCJi/qaxhOAAbu2LGDW2+91dTp4qWXXuK0007j6quvBsDr\n9fLcc88xfPhwgPGEGoZNQGtgCvA7tF1T3wdeBWpz9QtZmdSlSxfcbrdpq1BeqoU1Vsza0KpVKzq2\n1IYldhVXUlFRwdatW8OMkPrf4XCQlpYW1tJTr4Zsoaxdu5a2bdvSqlVtjuXhUIVa8k6tbKqSDgQC\nelmoRieWPR7VGKnKJjU1NawcjL0itWEQLzC2xo3KTvK+oqJC57mZoq4vzBoj6mW323G5XDgcjrDr\nSLbAV65cSfv27WnTJuwogTpDCBHWuzE2kKQ8y0ag2hCJBmpDSZVfM4OpXk6nU/8fLZSVSWHE1Ncw\nZAEUFRUxbtw4xo0bx+DBg0NeWLZsGTfccIN+P3z4cJ555hl8Ph92u7034EDb+kJiP/D34FUfhBiG\n1NTUeo8nV1ZW6oWhtuTMFJjVaqXDb3sA2FlcRcuWLcnJyalnlhsXUuAjgRTgaAWyurFjM56rLfFI\nxuY3b95MZmYmLVuGefzHHeRwglTERhQVFZGRkUF6eviiCGPruqYGkVkPuinCYrFErZxlr8vhcNT7\n25rmmYw9O/kbzfzS+vXrycrKon37sOOZI4ZiGMIa4fU1DIsBMWTIEMuQIUOorAwfa9+/f39IRWzZ\nsiVer5eysjKys7OtaHt/769numbYB9Htl7R161YyMzPp2LFjnRSe7DHsK3Pj9gVwOeJrsi8aXsUK\n6iT4kYbH48Hj8TRIWo2NAwcO4PP5TA2DcRimOaCxZVnys6FkWfZeYomahpLqO42/GzgL+G91Lxi9\n8+R/pUsbKwn9TcbfEPslAXTMPtwj2VVc/wnoxkZyj5nmi0SiFZL0xgKK7ozaMAB8gmYcTNGqVStK\nSkr0++LiYqxWKy1a6Ps0lZh+WH/ok8/ReD/X59sOIYahKqI0GxPJ7YqbLxKJVkjSGwsoujMmhqFG\nDB48mBUrVuj3K1euJDc3V47jbUHzWo4FDkH0W2/Xh9kuh41W6Zr3+O5D8ddjiMaIxiMSid5EohWS\n9MYqzlgNJdWKsWPH8vbbb7No0SJWrFjB888/z8SJE2XwwhgmdRCiO6wnEqPSMmgYiivirxvb2OOy\nDY1EojeRaIUkvbGAojujXq4qEZARn3TSSTidh/dgGjFiBPfddx/PPvssHo+HiRMnct5558ngaRGm\nZ4Z9oI29RXqIRSTzE9nBA3sOVsTfpGY08zHxiESiN5FohSS9sYCiO2O2V1IV8GNKSsqQWbNmyWeb\n0A7ZmXfGGWfYzjjjDOM3k6h9m4v64CCgewRGgki+bZuZAsDeUndEaTYmouFVPCKR6E0kWiFJb4zj\njOkmeuOB24GuwE7gcTTjcAyagTg5+N5y4Bng5yjSMoMXop9jqPdQUprWO4rHHkOy+918kUi0QpLe\nGMcZNqUQjWHYAVxn8nwrcGMU8dYVVtDWE0d7JkN9NpVrlRHsMZTFn2GIhN54RiLRm0i0QpLeWKAm\n3RnP2xH6QGNYpNssSAbXx7C0aaEZhv1l8TeUFAm98YxEojeRaIUkvbGAojvD7EA8GwYbxOYUt/oY\nlkyX1skqrvDG3ZmzkdAbz0gkehOJVkjSG6s4g7ozbI4hng2DA0J34qwvIrHCnYLbYpS5fZRUxtfk\nV7KV1XyRSLRCkt5Yxdkcewx2iI1hqM/3HbMPn5u9M862xYiE3nhGItGbSLRCkt5YxdkcDYPuPBGt\nYagPWmc4kZ8VlcbXthiJMEmnIpHoTSRaIUlvrBDUnWGRx71hiAXD6mNY7Darvi3Gvjj0ZYDEaWVJ\nJBK9iUQrJOmNBorulH/0yFXDEG8mOHx/4XoiUqOSnRaf22IkW1nNF4lEKyTpPdKI5x5D1KfkRGp9\nW6bF57YYydZV80Ui0QpJeo804tkwtKj9lSODw97P8dVjSCKJJJIwQZhLdTwbhlSIjSdgfb9PT9F8\nGcrd8bVcVSLZDW++SCRaIUlvNFB0Z7MyDGm1v1IzZPesvszOCU4+HyiPz6GkRKlMiURvItEKSXpj\njCN/HkMDohVE12OIdNyuVUZwVVKcbYuRHJdtvkgkWiFJb6ziDOrOsDHxeDYMR0FsDEO9ewxxuiop\n2cpqvkgkWiFJb6zibI6GoQ00jmFIdWpbi1R44muOIVmZmi8SiVZI0hurOJujYWgPjdRjCM4xlFT5\n8PrjZ6+WZGVqvkgkWiFJb6ziDMYXtoVDNOcxxApWYBQwGCgDPgZ+rcN3bUDbVEruPFhfyA2p6vt9\nVvB4T4CSSq9+RkNTR6T0xisSid5EohWS9MYqzmB8YZu+NbZhaAl8ChynPPs/tAOAZtbwXSqQARpx\n0fQYLBZLvb/PSDnMtnK3n1YZESXf4IiU3nhFItGbSLRCkt5YQNGdYatoGtvczgaOKyoq4pVXXmHB\nggXSMs4ATqnhu47yjxAiqh5DJIxOcx42DGVx5MsQjRGNRyQSvYlEKyTpjQUU3VluDGtIwzAIeAB4\nLHi9DpxbXl7OVVddRbdu3di5cyfTp0+X799UQ1wd5B+/34/NFnbORJ0Q6bdyjgHia8lqNLyKRyQS\nvYlEKyTpjXGcJcawhhpK6gN8B4QNxq9du5YBAwYwatQoRo4cybhx47jhhhsAzqghvvbyT7RzDJF8\n67RbyXTZKanyxdV+SdHwKh6RSPQmEq2QpDfGcZYZwxrKMJwKpCxZsoRvvvlGf9i6dWtOPfVUNmzY\ngNvtZseOHRQWFtYlvtbyj8/ni6rHYLdHxoKsNAclVT4OVcaPL0M09MYjEoneRKIVkvTGAoruPGgM\nizalVKA/UAxs4PB+3g4gF23big0Euyrdu3cnLe3wThYpKSl06tSJc889l6uvvpqePXvSq1evuqTb\nUv5pjKEk0DbS23GgMq6c3Nq1a0fbtm0bOxsNhkQabkgkWgE6dOiQUN7PR3go6ZAxLBrD0AP4CugU\nvH8NuAy4Bvgbodtivw9sa9u27dFGxVRWVobL5WLOnDkcOHCAW2+9VQbV1HXQ1wFFY0mtVisulyui\nb+WS1YYeShJCEAgECAQCCCH0ywg5USVXMsjLarXGZOPBeEC7du2OyHCD5LexDOTz6spD8l/9jRVa\ntGhBenrUR5Q0OlRe1kXGVX4256GlDh06RGwYjLy0Wq3YbDZVd8ZsjqEL8AHQacuWLbRv3560tLRL\n0dbDTgHYvn07paWl9OrVC7vd/gdgCXAOWm8CtBPYvk1PT2fBggWsWLGCTZs2yfkFgLdqSF/vdgQC\nAex2O36/v96VrVOnTrW/VA3kKW77y+pmGIQQ+P1+AoEAfr8fv9+Pz+fD4/Hg8/nw+Xy6wvf5fHp4\ndconWkjhUC+r1Yrdbg+pbMYw9d7hcDRpA5OSkmLKd8lnv9+P1+sNCZdhxksNi1UZqMbCyH/JZ7vd\nrl8Oh0P/tdlsIbxv2bJlDSk1DCSvfT6fzlev14vX6zXlo5Hvfr8/Kt5aLBadj0bZVvmpyrDNZtP5\nGmtjHUvYbDadr/LX4/HovJXPVRmV/DTytFOnTrRr107XncRojuEy4AXAsXHjRi666CLefPNNevfu\nDTDF5/Nx6623snz5clq0aEFVVRVz5syhY8eOw4DjgeeUuO61WCx/mzFjBrt37yYnJ0dtwT9ZQx5C\nhpKcTic7duxg//79IZVM/leFQa14asWUl7yH0AO41ctut+unuB2s8FBZWcmhQ4dMFZBamGZCL4VS\nzZfL5dLzLPNklldVkI0Cbcyz2po1y6OqKI3CJa/qWm2Srw6HQ8+XWQU0tpaNlxqnml9jC1LmVRpU\nlRZV0demyC0WS4hSUBWKNHpGeVL5bmz5m9EhaQBC8mPs9al8lpeqXI3yI/NuNNqqLKl0GWWounyq\nvFaVtfqr8laWgaqYVBgNmTG/xsaHGW/NZMQo28a6Z1YHjWFGuVDLW+Wtkb8yv2Y8VfNZnQyr6at8\nVuufmn/5q8JqteJ0OvV8Op1O0tLSwuRU5kvNb0qKtgZI6k60qYDQcjOtMdWjPTBHCMGCBQt44IEH\nKCsLNTYffvgh69atY/78+bhcLu69917+8Y9/yGWoVxBqGB4GhMViebBDB30F6jfApZhMiCjQh5J8\nPh8Oh4N27dqRnZ1t2iqUl2phjRWzPsjOzqZ9lmbAikqq8Hq97N+/P8wgORwO0tLSwlp66tWQLZQN\nGzaQnZ0d0TyDKtSSd2plU5V0IBDA7XaH9Hqqa71ECtUYqcomNTU1rByMvSK1YRAvMLbGjcpO8r6i\nokLnuZmiri/MGiPqZbfbcblcOByOsOtItsDXrFlDTk4O7du3r/3laiCECOvdGBtIUp4rKipCevN+\nf9gRBvWC2lBS5dfMYKqX0+nU/0cLqTuBImNYfQ1DL4Bly5bxzDPP8PTTTzNlypSQFz7//HPGjh1L\namoqABdddBEXXnghXq8Xh8MxEG3CWrpgB4CHgH+gOa0dxGQixASZKnFSIcg064rKykpdsagtOTMF\nZmwdtCvZDUBRiZvMzEz69OlTr7QbA5WVlREPOUgBjlYgqxs7ro7n8jeSsfkNGzbQunVrMjMza3+5\nicNiseiKw2xebM+ePWRmZoYs7pAwtq5rahCZ9aCbIrxeb9SyKHtdQeVYL9Q0z2Ts2cnfaOaX1qxZ\nQ5s2bcjIiN02C1J3EoNVSTsB+vTpwyeffGJaMNu2beO0007T7zt27IjX62XPnj107tzZguacttnw\nmRfYWo986Md6RjNbv3btWrp27UpOTk6942iToVXOQ5Veqrx+XI6mvyKkKaxckQamIVBWVkbr1v/f\n3pnHSVGde//b1ftszMaugiKIoAiouEQNGBc0ilu8GvK6hORNYlyv0Zjo1U9ibuKKccmNuUmuxjUq\nua9eTDQmBjF6AyjihggiCAFkZ5ile6a7q+q8f5w+NdXVPQvd1TM90/X7fM6nu+pUnz6/p57zPGc/\njT0/OAjw+eefW90JTgzGrSP6W5eVPPsqDx0dHX26wE0N4/dWaz4F/ks113Ohvb09w6up74mEtUI4\nv2lAmbC0P18FUZ49X2GrriSAbc1ZmxOWHArlO9BQTnzLiSt4fN2CzXZmtRiUY9iXjt9vYtuSwolI\nJEI8Hreu1RiErZsnawQ8D1hWOZVK5TVdNZWS6w/yaUYCjKrtdAxbB4BjKJTvQEM58S0nruDxdTPd\ntO3c6YzLd+LvVnJs1QowadIktm7d2vng1q2Ew2E14GnmykQeCEOnJ81n/nKh29hWhALURKRD2taS\nUxQlBW+b4sGLcuIKHl83YLOdKfrioJ7jjz+ehQsX0t4ujeVzzz3HSSedpLzde0C8u9/3EhHo3Osj\nn/5TNaugEGGPrpM9WluaSt8xuMF3IKGc+JYTV/D4ugGb7czZg+P6ZiNz5syxZiY1NDSwZ88efve7\n36noR1z6mygUvh0GFDZ4NLo2ysdbW9iyd+A4hnLply0nvuXEFTy+bqXZ1fgCFOYYtgAH/+Uvf6G+\n3tr94tFgMPj1hx9+mHXr1hGLxZg4caJaRLEEef6CGwhCxnSrfYau6xmL2fLBfnVy3GTzAGgxuMF3\nIKGc+JYTV/D4upVmV1NVobCupO8DrcOHDycYDKaQ+yN9E3mOwp5x48YxZcoU5RQeA84A3NpYKABY\n22DkA9M0C17kNJAcgxt8BxLKiW85cQWPrxuw2c6cXfuFtBieR57PPAy5pFqdAvRz5LGcU5A1+9V0\nv4o5H/ih/3ZWVdjPNsZgmAK/VrqK2t/zvvsa5cS3nLiCx9flNLNOb4PCxxhSpBe9OZAElheYdo9Q\nnjQfuCHsMQ3SMSQNk8/3trN/ffbiolKBV5gGL8qJK3h83YDNduY8N2BAd9IVenpboU2zsQ2d2xxv\n3O3GZKviwTsjd/CinLiCx9etNLuznQPeMeQrsHzXP9gRDfkZXiN3KtywO2eLrGTgBt+BhHLiW05c\nwePrBmy2M2dTZEBLtz/Oe3biwEbZali/s7Qdg3dG7uBFOXEFj29fpDlQpSug8OmqbvTbHdgo94L6\nbJcbO30UD27xHSgoJ77lxBU8vm6lmbadObtcBqpjMKHwFoMbwh43VLYYPt1Z2o7BLb4DBeXEt5y4\ngsfXrTTTtjPnjJkB7RgKna7qRvNs3FDZYtjc1E5HqrDDO4oJt/gOFJQT33LiCh5ft9JM286cXS4D\nVbquOIZ8u6HsOCjdYhCitGcmucV3oKCc+JYTV/D4upVm2nZ6g892uOWF96+roDIkZfvR5705fK5/\n4NWyBi/KiSt4fN2AzXYOqhaDDwrzpG4tGtE0H5NHDQHgg82l7RjKqV+2nPiWE1fw+LqVZtp25jwP\neaA6BqCw09vcHNA5Yn/pGN7btNeV9NyG23xLHeXEt5y4gsfXLdhs56AafAak0PJZ4KYO63areaZa\nDJ9sb8U09+UwvL6B23xLHeXEt5y4gsfXzXTTtjOcK36gStcHhTsGt5aZTxxZDUA8abCpqfQGoN3m\nW+ooJ77lxBU8vm6mm06znhxrGQaqYwAKdwxu4aDGKmtn1Y+3trqathtwm2+po5z4lhNX8Pi6mW7a\ndkaAkDO+rB2DW144FNCYNLIGKM1xBq+WNXhRTlzB4+tmurY0K53x/eUYNGAomU2YSroYIe/i9yXj\nGAAmj5KOYc22FtfSdAteYRq8KCeu4PF1M11bmkOc8XbH0FdttKOBTcAO4BPg34C2dIgjD/b5Qg9p\n+CD/3VWLIezxw+U4w9odpbc1hleYBi/KiSt4fN2Cw3bWpD+tG33dYpgNvAWMamtrAzgY+AlQ2d7e\nTjKZBDgEeBM4tpt0rHwXIjA3hX3wMLk1xpa97cSTumvpuolyKUwK5cS3nLiCx9flNLOmrBZzXfko\nMruGzkYe+8nf//53nnrqKf7zP/8TgDvuuIOtW7fS1tbGaaedxsUXXwzwI6QjcR3F8MKHjqhOpy0H\noI8cU+da2oXCq2UNXpQTV/D4Fgl94hiGAC8Bx+eKfPTRR1myZAmmaQLQ1NREc3MzDz74ILquc845\n5yjHcHpv/qxUFGRYTYTGqjC72hKs2tpSUo7BgwcPHpyw2c6hzrhidCVdABzf3NzMP//5Tyts3boV\ngNmzZ3PnnXdaD9fV1VnXa9eupb6+XkV9XoS8FRWHptczfLy19AagPXjw4KELZA0+F6PF0Ajw7rvv\n8te//tW6OWLECK6++mpGjhzJnj17sn60Zs0abr31Vu69915165He/Fm+M5OKgUkja3hj7S5We47B\ngwcPJQ7HWoYM9NYxBIDbgTOBJuDfgb8BI4HrkLOIosCHwNuAOXPmTG3mzJm9Svytt97ivvvu44EH\nHmD06NHqdnetGbOH+F7B7cUjE2wzk0rJYYXDYaZMmVJWWxVDeS2GKheukUiEI488smz4KhSZb7Xz\nRm8shQ+4F7jWdu9o5MDwn+ic6gQwHbgM+AOwjczBZwFsRg4qW9i1axfXX3891157LR999BEff/wx\np5xyCsA3gVu6yJNOerVePgZY0zQqKytdN9zjh8uZSa0dOttaOhg5pLfLMnoPtamWaZoIIazghOLm\n8/msoKaoqTBYEQqFmDBhAuFwzm1gCoaSt/MdqPtdvQ+fz4emaRmfhSIYDHLAAQcMGqdvl2VvdNwu\nz8G4f1IoFGLSpElEIlmV+l7DLku/32/pnc12Zo0x9KRNo4EHgfNTqRRXX301P/zhDxkzZkwl8AbA\n66+/ziOPPEJbWxtnnHEG8+bNQ9O0rwBHAisc6VUDP4pGo1x44YUAtLW1MW/ePFpbW2ltbbW/3GA3\n+UoCIUUwkUjg9/szSHeHUCjExIkTe3xuX3HwsCp8Pjkzac221gzHIITAMAxM08QwDAzDQNd1kskk\nuq6j67pl8HVdt+K7Mj6FQtM0S2YqaJpGIBDIKGzOOPt1MBgsSQejaRrV1WqWWKcjVXK3X6dSqYz3\nouKcwR7n1juwOwun/JWcA4GAFYLBoPWpdN3v9zN0aFa57hcoHdd13ZJrKpUilUrllKNT7oZhFCRb\nJY9cum2Xp12H/X6/JVe3nLWb0DSNaDSKEMKSpZJvMpm0ZKvu23VUydMu06lTp+ayk43O/+3OMUSA\n/wXGtLW1cdNNN/Haa6/xve99z3pg5cqV3HDDDdxxxx00NDRw88034/f7+frXvw5wI/BVR5qtwIvR\naPTs00+Xk47Gjh3LvHnzcv3/U93krR2o0jQN0zRZvXo1ui7XDtgLmfpuVwZ7wbMXTBXUNZDhWZ0h\nlxGpra3lwIZK1u+K8eHmZiYOMWlqarJeWi6lV0ppz1ckErHyrPKUK692RXYqdK48q/tOI6kUShVk\np3Kp0FWtTck1GAxa+cpVAJ21ZWewp2nPr7MGqfKqHKqdi93Q92TIfT5fhlGwGxTl9Jz6ZJe7s+af\ni4fiAGTkx9nqs8tZBbtxdeqPyrvTadt1yc7LqUNd5dMua7uxtn/aZavegd0w2ZHLkdnz66x85JJt\nLh3pqjw6ZajyqGTZnT7b37ddtk752iuhXeXV/t6dcrX/v7PSosqfPf/q0w5N0wiFQlY+Q6EQFRUV\nWXqq8qXyq2ybsp3p66wtMbpzDNOBMZ999hmXX345M2bMyGquPv3005xxxhmq64drr72Wu+++WzmG\nM5DdUM5SeRFyTcNoYB0wjOxR8bXIbqquEAOGKnITJkywDEWuWqEKdg/rLJj5wK7oSnmmj6lj/a4Y\n727ay+UzRmAYRlZNzx76ooZiGAYrV67koIMOoqampucf5IBdqZXs7IXNbqRN0ySRSGS0enLVXgqB\n3RnZjU00Gs2qGDhbRfaKwUCBszbuNHZK9vF43JJ5LkO9r8hVGbGHQCBAJBIhGAxmhWLUwA3D4L33\n3mP8+PF567KCECKrdeOsICl9jsfjGa15wyjsfHd7Rcmuv7kcpj2EQiHreyFQtjONfRp81kAqxl13\n3cWxxx7Lyy+/nPHARx99xKWXXmpdH3HEEWzZsoWmpibq6uqGAMORYw12tAPP7TOTTMShk1w0um99\n+UIIYrGYVTN31kZzGbBctfZcSj9ppNxddc22Vqqrq60ujf6EpmmWQucLpcCFKmRXfcddyVx97kvf\nvBCCTz75hFGjRpWE/N2Az+ezDIe9v1kIwaZNmxg+fHiX5cBZu+6uQpSrBV1KUDXeQh0edLa6gsHu\neq1zo7txJmfLTn3mM74khGDVqlXst99+VFVV7XM+u4LDMdQ647tzDG8Bu8aOHds4duzYnA/s3buX\n2trONIcMkRX/5uZm6urqQA5MOx2DG0hBFrlew+fz8cknnzB27Fjq6+sto+cG1MykLXvbaUvoVIX7\nf1DQPvjc33BT1t39RywWI5VKFfV/SgE+n49du3ZRVVXVpWMYTJMNSkWXlTz7QpdV69tNOGxnVu2p\nu2H8JLI76cddPWDvC4ZOL24TVrE2DUrm+v99QSG/7Q6HjOiU8ZptpXM2Q7H4lirKiW85cQWPbxHS\nzOpK6ml+1ybk9NJkrshRo0bR1NRkXavv6dYCyDUPxUDJOoah1WEaKuW5F55j6D+UE99y4goe3yKk\nuc+OoVscffTRLFu2zLpetmwZhxxyiOoL20zxHEMCStMxAIxL77S6bmfpbMHtFabBi3LiCh7fIqTp\nrmM4//zzee211/jFL37BH/7wB+bPn893v/tdFf1iIWn3gDbIf4yh0N/2hPFpx/BpCZ3NUEy+pYhy\n4ltOXMHjW4Q0s0bfe+sYOgC+853v2De5i40ZM4YFCxbQ3NzMihUruPPOO5k9ezbImUd3F5b1brEb\n5FiGWr+wrwgEAq4P6CiMG1p6jqGYfEsR5cS3nLiCx9cNOGxnlmPo7ZSZ/wdcftVVV6nr95G7qP7x\noIMOmnjLLRk7V7QB5wMb8shvb9EEhQmsEKfSE9TWGKU0M6mYfEsR5cS3nLiCx9cNOGxn3o7h28Bi\nYBywHXgGWWufgnQQp6TT+hB4HNhZSKZ7gb1Qui2GiSM6F96s2VYah/Z4tazBi3LiCh5fN+CwnVk9\nR711DEngsRz3U0gn8UxeucsfMSjMMahFX8XA0Oow9ZUh9sSSfLqjNBxDMfmWIsqJbzlxBY+vG3DY\nzqxFLgN1O8JWKN3BZ4BxQ+X2I2u3l8Y4gzdgN3hRTlzB49sXaQ5Ux7ATZBOrkK6kYtY61AroT0pk\nALrYfEsN5cS3nLiCx7cv0hyojmEHlLZjOLBRthg27IoV7T/2BV5hGrwoJ67g8e2LNAeqY9gCcsvq\nZDLnouweEQqFSKVSRVsoc1C6K2lzU5yk3v/N3mLzLTWUE99y4goeXzfgsJ1ZCQ9Ux7AHJLlCWgxA\n0WY3HNgop6yaAv65p/9bDcXmW2ooJ77lxBU8vm7AYTuzaq4D1THEAKFpWt6nPqmN/oqlXPvVRQlo\ncrB//c7+dwzF5ltqKCe+5cQVPL5uwGE7s7YhHqiOwQRa1b7mpegYgn6N/esrAPjnnnhR/mNf4BWm\nwYty4goeXzfgsJ2DxjFAevWz3+/PS2DqwI9iKteYBukYPiuBAei+4FtKKCe+5cQVPL5uwWY7B5Vj\n+BxkX1k+B7Koox2LeZjL2AY5AF0qLYZi8y0llBPfcuIKHl+3YLOdCWfcQHYM1pTVfASmjkos5rS3\nA9JdSRt3979j6Au+pYRy4ltOXMHj6xZstjOrKTKQHcNOyL/FUOhvewPlGLbsbUc3+n/KarH5lhrK\niW85cQWPr8tpDppZSWDbLynfvrdib8alBp8NU7C1uaNo/9NbeJuPDV6UE1fw+LoBm+3MWgw2kB1D\nHCS5QvZLKq5j6DycfVNT/3cnFZtvqaGc+JYTV/D4ugGb7RxUXUltUFiLoZDf9gYVoQD16fOftzS1\nF+1/eoti8y01lBPfcuIKHl+X0xw0K58BdChs58FCWhu9xeha2WrYsrc0HEM57UpZTnzLiSt4fN1A\nd7azP44WqwVuhIVnmwAAIABJREFUAcYCf0ZOOz3NlhcDWAQs7CGdFBTWxOqL7XtH1Ub4cEszW/f2\n/xiDt13x4EU5cQWPr1tppm1n1nkMfe0YhiCdwTHp66908dy1wMXAs92kZUDhx3sWuzk6rDoCwI7W\n/ncMXvN78KKcuILH1w3YbGe/OobDgQ8AtmzZwhtvvMHFF18MwPPPP8/KlSsBmDx5Mueffz7AmXTv\nGAIg5/iW6mE9AA1VcoxhTyy/XWDdhFfLGrwoJ67g8XUDNtvZJ47Bh6zxn07mIdNfAnjnnXe47bbb\nOOqoo6yIBQsWcPPNN6NpGjU11nnJe3v4HwGFz0oqtnINrQ4DsKM1a3Fhn8MrTIMX5cQVPL5uwGY7\ns/xAMRzD5cDPu4pcuXIlN954I6+99hoAuq7T0dHB6tWriUajnH766erRPT38jw8KP96z2M3Rhkrp\nGHa3JRFC4PNlOec+gzfFb/CinLiCx9etNNO20++MK4ZjOBbg0Ucf5fXXX7duTp06leuuu47LLruM\nDz74wLq/Y8cOqquraWho4O2332bp0qX85Cc/ATkg/eOe/qxQxyCEKKrBbkx3JSUNk9aETk0k2MMv\nioe+4FtKKCe+5cQVPL5upZm2nWFn3L44hiOB44BNwMt0rpY7HDgK6XWWAxsBLrvsMi699NIeEx01\nahSPPfYYADNnzmT27Nkq6vgefuqHwjyp2s7WNE3ru9sYXhOxvu9o6ehXx1BTU8Nhhx3Wb//f1+iL\n91sqKCeuAEOGDGHq1Kn9nY0+QzHer812KsdgrWforWOYCzxJ5yDFk8B1wGPAlx3PvgW8o2nakTnS\nSQIh+43333+f//7v/+b222/n888/p7GxUUVt6CFPYej0pPnA7/cTiUSKWpjUGAPIcYaDh1UXlJ4Q\nAtM0MU3TqkHk4q9qFT6fLyMEg/3nmPoaFRUVHHbYYda2xW5Bydv5DtT9rt6Hz+ez9sFXn24hHA4z\nbNiwAX/cpV2WvdFxuzzdfs+lhMrKSqZPn56XzuSSZSgUstvOfe5K8iGdwiOA73/+538488wzCQaD\nXwMOAY5uaWlh8eLFmKbJF7/4Rerq6mYAy5CG21mVnw68FQqFaGhoAGDKlCn88Y9/5Morr8QwDH78\nY6v36Pc95K0SsA6bUIqzL4KrqKhg8uTJvX4+H0SCfiJBjY6USUt7ilQqha7rGIaBruskk0l0XUfX\ndcvg2+O7Mj6FQtM0/H5/RtA0jUAgkFHYnHH262AwWNLNeJVPJVfDMDAMI+M6lUpZ9+xxzmCPc+sd\n2J2FU/5KzoFAwArBYND6VFsxK4RCIfbff39X8pUvhBCW3iq5plJS53PJ0Sn3fE9jVPD5fJYcnbpt\nl6ddh/1+vyVXt521m/D5fJZc1WcymbRkq+7bdVTJ0ylTTdOYNm2a/aCerNpid44hBDwDnAfw1FNP\ncfvtt3PqqacSDAZ9wNGff/45F110EUceeSSmaXLPPffw3HPPMXr06GOAi4AnHGmuAVITJ04MTpw4\n0SJ8yy23OP/7n8CdPciqWv1eEV+xYkVGIVPf7cpgL3j2gqmCulZpA1mGWQm9K+NhN0CjR49mSDRI\nRyrB3niK9evX09bWZpFQSmnPVyQSsfKs8pQrr3ZFdip0rjyr+848KoVSBdmpXCp0VWtTcg0Gg1a+\nchVAZ23ZGexp2vPrrEGqvCqHaudiN/Q9GXLVglKytxsU5fSc+mSXu7Pmn4uH4gBk5MfZ6rPLWQW7\ncdV1PYOHyrvTadt1yc7LqUNd5dMua7uxtn/aZavegd0w2eF0ZM78OisfuWSbS0e6Ko9OGao8Kll2\np8/2922XrVO+Kr+5ZGrPZ1c6bP9/Z6VFlT97/tWnHZqmEQqFrHyGQiEqKiqy9FTly5lfRznbJ8cw\nEzhvz5493HvvvSxatCjrgYcffpjjjz+eu+66C4Af/vCH/PKXv+SnP/0pyJaG0zG0ABcAP0CugP4z\nsBS4DVCd3/cA/55+tjvU2cn5fD7GjRuXs1aogt3DOgtmPrArei6HpAxlVTjAdhK0duiMPWIsQIZy\n9RU6OjpYu3YtEyZMIBzOGm/qFnalVrKzFza7kTZNk0QikdHq6ar2ki/szshubKLRaNZ7cLaK7BWD\ngQJnbdxp7JTs4/G4JfNchnpfkasyYg+BQIBIJEIwGMwKxayBt7e3s2bNGg499FAikUjPP8gBIURW\n68ZZQVL6HI/HM1rzhc4QsleU7Pqby2Hag6rIuNH1bXMM+9SVtB/Am2++SSgU4oknnuCss87KeOB/\n//d/ufnmm63r2bNnc+utt6rLo8iNF9PBjgXdEegCtVk3arNudQtlwMLhcM5+TTty1dp7q/QNlWHW\n7YyxJ57cZ4PsNpLJZF7GWSlwoQrZVd9xVzJXn/n0zScSCdauXcvBBx+ct/EoFajDWpQhdiKVStHU\n1ERDQ0PWO3LWrrurEOVqQZciClnYak9DObF9RXfjTM6WnfosZHypo6ODVatWMWnSpD6ZXGB3DM6c\nrgI4++yzmTNnDjt27MiIFEKwbds2hg0bZt1rbGxk+/btmKaJpmmNyE36irUKpaHQBJLJJKtWrWLy\n5MlFNRzVESnm1o7yOVikKygH0xcQQpBI9P/Cwr6AYRhs2rSJmpqaLPk6u2E8FA4lz76cAdaXEwu6\nG8ZfBtzTlUKpJlU02nnmgDKutiPoijkFZkihCfSVoGsr5ESspnj/OoaBPmNlX1FOfMuJK3h8XcY+\nnccggO8Do3JFBoNBotEora2t1r2WlhZCoRChUAjk1NRiVtfqAVcWfBS7NqVaDG0dpXFGbbnVHsuJ\nbzlxBY9vIbDZzqwaa0ETf6dMmcJnn31mXX/22WeMHz9eXW4oJO0e4MMFx6D6KIutXOGAFHNS79+9\nXfqKb6mgnPiWE1fw+LoBm+3MqsAX5BhOPvlknnjiCVpaWmhtbeWJJ57g7LPPVtFvFJJ2D6gjPT5i\nmmbewlLNs2IvjImGZD9kPNW/e7v0Fd9SQTnxLSeu4PF1AzbbmeUYer0lhqZp1NfXZ9ybO3cun332\nGbNmzcI0Tc466ywuueQSFf2LAvLcE6zl0UKIvIXVV7WOULrF0JHsX8fg1bIGL8qJK3h83YDNdmYd\nL9kbx7ADaGpsbKxbsmSJurcJeDwUCt3y4x//mFtuucW53cKPgPcKznnXsGYkGYZRsGModq2jNioH\nn9dsb+U3f1/PWUeMZOSQaA+/ch99xbdUUE58y4kreHzdgM12xpxxvfkXA3ma2rvATuBt4GvArcCF\nwHK1Ag95EM9cerEraoGwmi6Fthj6Yirf6ZOHW3sm/fSlj5l5z+J+OQO6r/iWCsqJbyAQoK6uriy4\nQnm9WygOX5vtzDpFrLddSX9JByf+kA4R5Cymvpo0bk1VLWTw2Y0ZTb1BQ1WYl645kTte+pj/9+4W\nErrJC+9u4cpZBxf9v+0ohK9umLSnDNpTBi3tOu1Jg7aETiyhE0vqdKQMkrpJyhB06Aa6IdANk5Qp\nMG1T7fw+HwG/RjigEdB8VIQDVIX9VIYCVIUD1ESDVIUDVEUCDIkGCfrzryH11fvNF7phsjuWZG88\nRTyp056WYTxpkNANOlLye8ow0Q0TwwTdNNFtMtV8PjQfBP0aQb9GYNM6QgGNgF8j5PcRDQWoCPqp\nCPkJBTSiIT91FSEqw1Lefq105dMdCqkQAiR0g91tSfbEkul3kKQtoRNPGHSkDHRTkDJMTAECgQ8f\nAc2HX/MRCmgE/T7CAT/VkQCV4QCVoQC1FVJ3I0F5vyLk3ur6Yuhyd4PPbp3H0NcHGleqL+nFdHkl\nUqhy7QuGVoe576KpVEUCPL5kI799Yz3jh1UxfUwdNZGgNQ5RTNTU1DBx4kQMU9DcnqIpnmRbcwe7\nY0m2Nbezuy3JztYELR06O9sS7GpNEEtKJ5DopxlVkaBGVThIbUWQmkiA6kiQaNDPkGiQYTVhhkSD\nNFSFiAYDVEcCDKsOS6MXCVBRJfkWG6YpaOlIpR2lQVsiRVvCoLUjRUu7bsm5uT3FtpYOtrd0sKMl\nQXs/T0YAqAz5GVodpq4yREXIT1U4QG00JA1bOMDQ6jC10SDVkQCNVWEqQn4q0kYwEuz77b0TukFb\nh07cF6Vi5DiWrNtNLKGT0E1iSZ2Wdvke4kmDXa0J4kmDeMqgOZ4knpQVm9YOneb24q8pCgU0KkJ+\nhlWHGV4ToSocoK4yRG00yNDqMCOHRKgKB4mGNCLBtFyjQYZEg2gOh11VVcXYsWNdzZ/NdsadcX15\n5rObqFJfCnEMhYxP5ItvnXQQC5Zvpime4ltPvGPdr47IwlYZkjXlqnCAgN9HKOAnqPkI+jXCQY2A\npqH5QNN81lJ1UwhShiBpmHSklb8tXVjak7IGpApFPKnTkXLPyPs1H5VpYxEM+AhqGuGgn6Bf1rAC\nfplfHz4EAtOElGmS1E10Q6QLsU5bQidlZC/i6UiZdKQS7GrLrzFaGfJTHUk7lqh0LqGAhl+TrZZQ\nuuUS9Gv40zIVgGEKjHStMambJA2Ttg6d1g6dDl3KNJYwiCXlPcN0bwFSRchPJOgnnK7hh/waAb8P\nv6ZZtVYlU1PI1kPSEKR0E8OUeiBbGYJYUhrJrvIXSxrEdsfZsDvLNvSIoN9HRShANF1DrorIVojM\nt2ypSB3W8Pt8GTorUFt1gCGknA1TkNRlizORki2m5nbZmkroJs3xFK2J4qwFqknnvSoia/x+Teqy\npnXK2TAFuimk7pomCd2ktUPqbq6p6Eld6s7eeIpPtrfl+Nfc8PkglG5VV4UDRNP6EPRrhPwaI4ZE\nuP2cydbC2Xxhs51ZYwwD1TFYhxoUOvjc145hv7oKFnznOG5/cRVvbeg8vbQ1bXT6A1XhAMNrwjRW\nhRmWrtkMrQ4zrDpMdSRAOOBPK6is2dREgkTTtctwwL39dJK6NASxhG7V6lrTNfG9cfm9pUO2YJrb\nU+xo7WBve4o9sWSXrZpY0iCWNNjW0teNWilX6fBDDK8JU1cRsmqPI4ZEqAwHaKwKUV8ZoiIYIBKS\nBT8feba3t5NMJhkyJPeGAMq5xZNSlm1pGbd2pNjRkmBvPGnVplV8W0JnZ2tCvpOkjnPxbcqQLU/Z\nEspHQu4goPmIBP1EQ7IlWRkOEA1qDK2OUJk2qqrSFQn5qQr7GVoVSbeUgtRXhAgU0GUJkDJMmuJJ\n2RWlSznuiSWJJXS2tyTY0dpBLKHTFE+xN55ke0uC7S0dOXVWCEjo0vG0dGETDhlRzfHjGpgwvJrK\ncH5m3GY79zrjBqpjsKar6rpOIJAfDV3X++XgmsNGD+G57xzHjpYOtrfIgrc7lqClXdaImttTxBOy\nbzmZrvmlDKkoKcNEpPs9TVPWLnw+CKRrwJGgn2jQT1W6ZlwRlAWjIizvq9poXUVIGqqacL90CeRC\nKKAxtDqccbjRvqAjZbCzNWG1mNqThlU498STliFUrZVEujWgWgaGKWuwmib77v2aT8o1qBH2a1SG\nA9REpaOMBDUqQgEqw9JR1leGrP7m6kiQiqA/qzugmNi1axft7e1dOoZQunVUFQ4wrHrf9wUzTMGe\nWFK2lJLK6MkWaDxppB247OZJGukWalLpsMA0BQKR4Vx8PjVG4ku3MDWCAanHSpdro7ISEg5o1ESD\nNFbJ7sNIUCMckN1gpaC/Qb8m5bqP53DZx+7ak4blOJRjaOvQrRZTUjd54G9rAbjnlTUAXDB9P+b/\nyxF55dlmO3c74waqYxiqvhiGkfdGVoX81g0Mq4kwrKbvdv3cunUruq6z//4j++w/+xKRoJ/96yus\n682bNzMmAvvtd0A/5qpvUGxd9mu+vB12MbBhwwaShkGkflx/Z6UgBPwa1X6N6vSRv2O62Bp0x44d\nhMNhTp00nP/zX8vYm953LRrKv6Vj05nmrHzlnWr/ok59GciOoa8Rj8fLim8ikSgbvuWmy+XGt7W1\nlXg8zmFjx/L6DbP4zRvrWb+rjWtOHt/zj7vAYHQMVrXQMIy8zzjQdV1t+FcW8Pg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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "# plt.xkcd()\n", "n = 256\n", "a = [[1.0/(i + j + 0.5) for i in range(n)] for j in range(n)]\n", "a = np.array(a)\n", "u, s, v = np.linalg.svd(a)\n", "plt.semilogy(s/s[0])\n", "plt.title('Singular values decay for a Hilbert matrix')" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## A more realistic example\n", "We can try to test on a more realistic matrix, since solving linear systems with Hilbert matrix has little practical sense. Instead, we solve a linear system with a matrix\n", "$$A_{ij} = \\frac{1}{i - j + \\frac{1}{2}},$$\n", "which corresponds to an integral equation\n", "$$\n", " \\int \\frac{q(y)dy}{x - y } = f(x).\n", "$$\n", "In real life, the equation \n", "\n", "$$\n", " \\int_{\\Omega} \\frac{q(y)dy}{\\Vert x - y\\Vert } = f(x),\n", "$$\n", "\n", "is solved, where $\\Omega$ is a surface in 3D. This is used, for example, in modelling integral circuits.\n", "Let us see what happens with the singular values." ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "text/plain": [ "2.6645352591003757e-15" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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iov2G1TpqgVc1TbsxPz+fRx99lHHjxuH1eo0T8vLymDNnDi6Xi/T0dJYtW2Yo\njqKiInN6AZCRQdOmTbnmmmsYOHAgv/zyC9XV1ZZzbr/9dq688kpGjRrFgAED2L59O4sWLeKOO+4g\nMzOTYcOGMXPmTMaOHct5551HTU0N8+fPZ9SoUSo62ArsRHqJS30+35AHHniA22+/nZ07d9KuXTsW\nLlxoiSRyc3O54IILmDJlChdeeCFZWVm8/fbbZGRkMGHCBED2ISxdupT8/HwGDhzI1q1bWb58OS+8\n8ALt2rUjJyeHRx99lIKCAmOYeFZWFtu3b7dEgiNHjuQf//gHWVlZamJlEDnRdL+YPHkyl112Gfn5\n+QwYMIAtW7awbNky7r77biN1uh+sBU7Oy8vjmWee4aGHHqJVq1Z88sknRjrTJFNdkBMew8g1Bl++\n99572blzJ1dccQW9evWibdu2bNmyhW+//ZbTTz/dGEU5YMAA/vWvf3HjjTfSt29fNm3axKeffkpW\nVpYxCvXss88mJSWFyy+/nN/97nf8+OOPFgcE4LbbbmPChAlcfvnl5ObmsmrVKvbs2WPpRzoQ5Ofn\nc9ddd3Huueeqel+L7GdpYTotQ3/ehOKLL75gwoQJdO3alUWLFtGmTRtjIuzFF1/MwoULGTNmDMOH\nD8fhcPDmm29y5plnMnBg7OIGgIz2W6vI6tprr+WKK65QTs1goG4PdT/o1asXzZo1484772T48OEU\nFxezaNEi2rdvb9QZ8ub885//ZP369ZYsSV146aWXWLVqFXPmzMHj8TB58mTef/997rrrLl588UWc\nTuc05BqAvxxq2fcH5wMPPPCA6fcfG+pGRwCrgCFNmzZtdfHFF3P88ccjhCAcDtOhQwduvvlmbrjh\nBmMggMPh4LjjjuOUU04BpEfbu3dvi/JzuVycdNJJtGvXDofDwdChQ+nTpw8ej4cLL7yQiy66iFdf\nfZXLL7+c7Oxs2rdvT9++fSkqKsLv93PzzTczZMgQWrRoYcy5MN+nf//+NG3alIKCAmpraxk7diyT\nJ0/G5/PRrl07mjVrhsvlomfPnqpzcinxBXk3cG27du1IT08nPz9f5fAXAl369+9PZmamcZ8xY8ZY\n7tO8eXNcLhennHIKbdq0wefzcd555xEIBCgqKuLcc8/ltttuIzk5mdzcXJKSksjOziY/Px9N0ygo\nKKBZs2bccccdRkewz+dj+PDhOJ1Ofv31V8LhMJdffjnXXXedUvhTiCqVr4HxOTk5nv79+7Njxw6q\nqqq488476d27NyeccAIdO3ZE0zTy8vI49dRTKSgooKKigry8PP74xz+qNBopKSnk5+fj8/nYtGkT\nrVq14sEHH6Rnz544HA7OO+9dCkgMAAAgAElEQVQ8hBBs3rwZt9vNlClTGD58OCkpKXTu3NnI1Tdt\n2tQYyqvPuVnAvpFRHtDX4XDQqVMnunbtCsjUVX5+Pi6Xi82bN5Odnc0f/vAHBg8ebJGt//u//1Md\n1vOR864UdgHjc3Nztfbt27NlyxbKysoYPHgwU6dOJT09nTZt2qg00lpghf6/74GOXq+35/Dhwznl\nlFMIhUJUVlZy/PHHM3nyZCZNmmREFq1ateLMM8+ksLCQ7du306VLFx588EE6d+5Meno6Xbt2JTU1\nlcGDB1NdXU1paSnnn38+N910E2lpaeTm5uLxeGjdujXDhw+noqKC7du307NnTx555BEjvepyucjN\nzbUMHHI6nXTr1s28YgXZ2dn8+9//5rbbbqNTp04gU34fIQeBqK0caXQ1n89Hnz591HVfR64ecBlw\nvMvlokePHnTu3BmQ7a5Pnz40a9YMVV+qDzg5OZmpU6cSCoUoKCjg/PPP57777jP6cjwejzFEX/WR\njhkzhltvvdVwSJ1OJyeeeCIdOnQAOUesTWZmZmqXLl0QQtChQwf1TGuRqztcBzRX7c7cF5iUlETv\n3r2Nfjg1TDs3N5e0tDSGDBlCVVUVBQUFNG3alHvvvZezzjoLt9ttyHmfPn0QQhhZjHj3cTqd5OTk\n0LFjR7799ltGjRrFmWeeaakzIQQtW7akSZMmGrK9riHxeAA4poZ2I+Qih7NF3agWcghsZT3n7BJC\n7DOm9D//+Y8x1FPhtddeE926dbMM925AVIu6F5nUhBDzY85fLYTwCiH+JA5gxnYMqvZz/Fex78Kv\nCnuFEOOEXCg0Hvwi/qKMpwshttdzz7CQC2/WVbb/Crkg5Ot1HN8mhNhcz/Ut2LBhg8jJyREbN25U\nuy6IU+b+QohQzF/vFUK8V8dldwkh1sbsKxPxF8y9TtQzu19HWAiRG/M/h5CrRlTX8Z9aIcR9Qog+\non6+DxSbhL7qwQGgWMRfAFcIIYey9+vXT62eEhJCtBTx5T12RYRiIcRx+rEbDqbw+8F/hFx49FkR\nvw2FxL6rk4SFEOcKIYaI+HUwWMhyxq7sUS32XdVkj74lElVCiDtF3TrBL4QYGacsZUKuCtJgQ7vN\nb3qFY+dtr12QHbadkWF9CXJo4nzkOktdkDPWk5BrSzmRs4vLkV7NNmQ43QvpaZ24Zs0axo4dy7Bh\nwzj11FPZsWMHr7zyChdffLFacPU74Gzkygi5yP64Pchl6h3IdZ08MfdJQ85q74RcA+sH5JL4LZC5\n7wiQjkzFLaH+2c/JyAUwOyI96/n6vUGuMabuE0B60JXItfWq9Pukme7zM3LlhTzkWls79fOD+rVf\n158hl+jadMU6B3ORa2WBnMB4HnKNvDDSK/yvzm9dzzAWmaP2IeWxQC/jCmS/SAZyZFgfZH/JZuTy\n/ObIojuyHtSafav0MgeRM+AHI9foK0VyLpDycsHGjRt58cUX+fjjj+nevTtPP/00yDXYOiCHXcfi\nVOT6ai69fMtN+y9CrndYihzR9gaynkcgZbAa6SXXlfpor/ORo3OxFslzS2Q9LqZumchE1k1X/fxK\n5Pp3bxGVi1Sdp1769y3I9pCJ5H8Vcp20C5GTTdOQ9V+OrM9f9Weq0o9fgFz3bCtypOEKZH9VZ/2c\nhcgRZecgR/lNBlquWLGCd999lyVLlnDTTTdxzTXXgFzDbVQdz5asH2sXc12FgUjZjCDXcmyBrL9y\npOypV8usQ7avNsgRuT5924rstP/JdM22yNUuTkTK0XqkLG9GrvvWR+fkA6KyeByy/toh1yScj8wC\ngKzPC5BTG2qRdbkF2U6VzMzXn2EE0bUA30S2yzP159qtl9ODHJm6EZlBOR8pgxqy/tchZWCxfn4/\n5OKoafrxTUiZehfZjrN0jpvpHC9CrlXZEBBgfe04HB1jlIpsoAIpZFUc+fdquJCVkqp/piErozlS\nUKcCKd999x1z585lx44dpKenM2jQIIYOHarSTiGkUauLQ0F0FE3sq961ev4XQfIRQjYC9VmL5KoE\nKeiVSAGuRBqDEv0cdV6Zvr8MaZAriPJ+pKEhuc5GNoS2yMbWFGlsmunHlXJI1zcfcr6MD6lM1KK2\nsQNxFNcR0yaQPKpjmunTgaw73+7du5k6dSqtW7fm9ttvN9J/JgSQC1qaufXr+6uR/KqtwvS5G6nI\n9+jfK/RyHSkkIfnOQCqtZOQQ8nT904fkPFU/no6U/wyi7SIJybdL3xwkQGd8+eWXPPvss+Tm5ppT\n6euRfO1FOhR7kDJdgZTzYqLcVurn1cS5fGODAynnXfWtI9IQZupbBpJrL1YZd+r/PRTOlfxHkLoj\niJTXIFJmlc5QeqMQufTSNqSx3aHvO+BRVfuBC6uubzTGKIxVmexFCp4ipkrfVM64Sj9WTvRlVQ7k\nAzpN311ElVkSsnEphdcCqfBS9M06weh/BxFkg1bKsQTJ/26kkCplqoS1Gsm5UvAakj/1sjIXsjG1\nJMpzJpJ/pfxS9X0HNxHk2EMAGXEW6lslUqaLiCrbcqIrOUeIyrZP//QSld8m+tZc/0whyr8yJsc6\n/ER1g3LU9uq/lXzvRvKrjJxyyswKWilvJ9IQJCE5TCLKd3OkcW9C1IinIeVeGRXVNpRhcfHbzj5F\nkBz5kXJZgXTIypF8qj69UiTXxfr+Mv37XGRGQI0AzUFmBRqFMdLQvUNhGsn0W0EkEiESiRAMBgkG\ng4RCIUKhEJFIhHA4TDgcJhQKEQ6HiUQiljyp+q/arNWwLxwOB5qm7bM5nU6cTicOh8Py3eVy4XA4\nLJs67nK5jPN+a5wD+/CnhosrnhX/Zm5j95mPqeNOp5Ps7GySkpIIh8OUlpZaRigpKD41TbN8N9dH\nvM3tduNyuXC73Qb/jRlCCEN+lYyr+WfxuI79NHNrln0zvF4vLVu2xOv1EgwGKSkpoba2dh/ulEzX\nx6/T6fzNyLPSD8FgkEAgYHBr1iHxZFXxXxefCko2wao7lB4wy6+ZV4fDYcipOlcdbwBueyEHRDQK\nY+QGAkIIVq9eXSc5ZkUaT6HGKgN1HbXPjPoMgqposzAooVGCY1Z8QgijLB6PB5fLZTECqoxqn9mI\nxBoKiE5KU5+qaurr/FMCbC6rUtCxith8TH3XNM1QjqqsZm7N+9XveErYzHU8zs3PEdu4FKd1GfHY\neohEIvsYWfMzxCunuRHGln1/z6Hm+CjEGrl4PJsVs/kZlRyFw2GD11j+zfVgdizqKms8JRHLdTxD\nHGvQVRnNzpUqj9vtxu12x+XSzHmssotX5lhOzQYr1qjVtSn5iDWAZg5Vuc1lMnNqlhdzWSE6XaMu\nTpXsmg2vuX3FtsnYsgshjLr3eDxGOc2GQJUrniwrDven42K3WGfBrA/Mei5euZWuUOUzy0OsPjbr\ni3jl1p/tdOQ74xqFMUpFhnAOM1lmxWRuTGbSYr2HWONSl+cQL7KoK4KIbWCqQSrlUZciaCwoKioi\nJSWlzvWy4gmj2TDEHosnyPG8tHjeWqwhNntpZgNo9s7qckYOJaLbsmULGRkZ8fqAjgqU02OOOMx8\nK4Vm5j5edF2fZ2xWYEpezZ9mmVd1oJSNcq4as3zHQsmnWX/E6pJYWY+NNMwcxyJWhs3RWDxdEU+X\nNHCkkRBUVFTg8/nM60ganCgnJdYJNn+PdX7jZYBOOeUUNE3LQw74EXD0J71WAp8AZ23YsIHs7Gya\nNGly0At3KgQCAaPCbcCOHTvIzs6u0xiZ00rHOsrLy/H5fI3GGCkv09zgjyRKSkrwer0HvYZbY4Yy\nrAfLqa03rCgoKCA7O9tYtBWihtjr9Vom1B8KTEtZWdbvawxJ6zIAt9t9UMtXxMOmTZvqXXvufw2J\n4PRYgc2FFYWFhXH7w/4XYesNKxq6rWzdulWtINLojFENyBm/B7EeW1wk4hrHEmw+orC5sMLmIwqb\nCysamg/T9Zub9zcGYwTYxqghYPMRhc2FFTYfUdhcWHEEjZFl8c1GY4wcDkedrzM4ktc4lmDzEYXN\nhRU2H1HYXFjR0HyYrp9i3n+0BzCAPs/INkaJh9frJRw+0otZNE7YsmGFzUcUNhdWHEFjpEbPaECj\neO24BokhQA1LPdYghKA6EMYfihAMRwiEIoQiAn8oTJU/jD8YPRaOxA5J9bF+7S4cmobbqeF2OnA5\nNFxOB26nhsvhIM3nIiPZTZLbicvZaILlhCJRDSwUjlATDFMbjFATCBMIhwmEBLWhMMGQ5D8UEcan\nEILYKnE5NDwuB0keJx6n/PS5nLhdsn7SfW48roath8aqgAOhCFX+EJX+EDXBcFTWg2FCEUEgHCEU\ntg69dmgaLqfkVPGZ5nWT4nWS4nXhddU/FSAlJaVRcnG4EEIQDEvOqv0h/KEItcEw1YEwwXCEYFgQ\nEVJWXU6NzBQPnbPTaNKkieV9YImGSfYsabrGoLm9IAt4OF58IBRhXZmDQCiNwg17yUzxkOJxkZ7k\nItnjwu08+nOChBCU14Yorgqwu7yWSr3RVdSGKKoMsKu8hpKqICXVAWqDYSr8IcprgpTVBAmGj8wS\ncskeJ6leF8keJ01TPPhcTrxuB16Xg1Svm/QkFykeF5kpHlJ98nuy10lWqpdUr4s0n4smSe5GY9SC\nYdkAXamZ+NzpfLO1hCp/mPLaINWBMDXBMDWBEKXVQXZX+KmsDVEdDFOt141qwP6QND41wSMTaXpc\n0igle5w0SZKKNSPJQ1aal6YpHrLTvDRJctOqiY/MFA8t0n0kew587kpSUhJ+v3//Jx4CagJh9lb6\nKSyvZW+lnz0Vfir8IXaX+9lb6afKH6I2GKEqEDI4La8JUhMMN4ice1wO0rwuUnXZTPO5SPW6yEjy\nkJ7kIk3nOb1wG1lpXjKS3TRL8ZLslW3B5z76Q74jEUF1MExFbdDQF7sraimtDlJYXsuuslr2VPqp\nqA2xt9JPWXWQ6mA4jnNaPzKS3Yw4pQ23DujQQE9i0fWWeQWNwRilgyzg/pbEqQ/PfrCBvy2v+71P\nTodGisdJRrKHNJ9UmpkpHl3xSu/J7XTgcTlI9jjxup149d8Oh4ZDb+MRAeFIhGBIGNFJZa304qoD\nYWqDsnFV1IaoDoSoDsiGVh2QCrA22DAemEMDl8OBwyE9RaWSIgIiQnpAB9LQqwPyOQAKiqr3c3Z8\naBpkJntI9jp1h8CtN3639Fp9brwuB163Q48IZLTmdjpw6uV3OjQ0JO8RAWEhiESE4dHVBsMEwhH8\nwQhlNdKAF1UFqKwNUuUPU+mXjdIfOjoer6aBU9NkXWjyN4DQ62N/dREIRdhbeXDGwunQSHY7yUz1\n6PLtJSPJTYpXKuFUr9OQcZfTgcfp5NvS7bicmiEz0pgJhICgHpHUhiLUBqRz5A+FqQmE8QcjVAZC\n+IMyOq8JhinV66CituE6vzVNRpaaXl6hy0Z9SjcQilAUkmU7FCjjleJ1keSWTlqaV2YT0nXj5nFG\n9YfH6cClZyFU/at6lxGzlNtAOEJFrXRG/aGwEbVU+UOU1QQpqgpQ5Q8Z8nwkUFodZOanBfxaUsNz\nl52KuwGcSpOuTzLvbwzGqAkcfmR0SrsMstO8FFcFCMURzHBERiXlDdhQDhZOh0aaLxpptEj3kZni\npqke1SmvOCPZQ0ay2zCYbqcUeI/LQbLXSZLbGVdo1Az/pCRZ50JIAxoKywYR0kP4itogpdVB3UMN\nyQYQCFFSHTRSgCpSq6iVx4t1pVMTkJGE2Y8QAoqqAhRVHSkmDx5JbicpXic+t5Nk3UC2SPeS7nPj\n04+let0kuR143U58uuFM8bpI8TrxuuT/PC5ZD16XTLk5HRouh4bDUX+EEokIPRKI6NGZnoYKRSiv\nCVKhK6SaQJiymiBVgRClVUH2VPopqgqwt8JPSXXAcBxAyniFP0TFEVJcBwKP00FWmpc0n4usNK/8\nrkcbSrn7PE7SffK7UvopenTucmq4HTL15nLoTkodyx8FdEdFRbWVuiIvqwlS5Q9RURukvFZ+VvpD\nlFQFqfAHqawNURUIU1odpKjKT6xPrAxGY0O6z0VGsoySWzTx0SLNR6rPRVaqh4xkD8keqRs8LoeR\nrvS6nSS7ow6g4jQQjrCtuIZZn29h5qcFvPdTIY8vWccfzj8x4eU26XqLMTraywGBfF9N++rqagoK\nCjjxxEN/eLWEiuZyU1IVpDqgN2i9sVfUyt+VevqruCpgpAr8IdkXEwjLnLX6rfphlH1zaNKIeFwO\nnJqGV29ASXrFJ+mKK12PAlI8LtJ9MvpK87nITveSmeKlRbqXJHfDLglSXFxMQUEBp556aoPdA6QS\nLKryy/SXilIqA1QHQlTqKbHK2hClunKtqA0aUU1tMExQN4yKa8W3ECL6jge90bgcMmXo1Y2ASmdl\nJLtpnuol3acrMq+L5ike0pPc+NzSWKgUYqrX1WjSiIcDIaTxKa4MUKinfasDYYqrApTrnrXZsFUH\nQgRDenSpR/e1oTBhve8gIkAg0JDevNOh4TMZ4lSfVGgqk5DscZHkcZDikcYlI9lN02TpVDVP9dCi\niY80b+NfUsjv91NbW0uTJk2IRATltZK7Gj2bsadCyrbKdJRUS0estDpAeU2I8togwXDEcCZUP5eS\nZyXDToeGU+/f8rqiRiLd5zJ4TvZIZyfNJ+U5xSONtorO0nxuUn0umia7SfYkPpYQQvDAW2t58bMt\nuJ0a39w3iFRvYu9j0vU/I1+jAY1kAEMmyFfgHu7Ir6qqKjZs2MCpp55Kyybxl8D5X4LT6TTWlGpI\nheB0aGSn+Rr1SwrKysrYsGEd7U49tdErxwOFpmmk+9yk+9wc3zxl/38wIRgMUltbS2pq6jHDx6Gi\ntrbW0BsOh6ZnIjxHu1hHBZqmMfnczrz8+RaCYcHnG4vIO7HF/v94EDDpeovQHm33MAldhSVqaDdw\nTI6MORTYfERhc2FFbW0t69evt/nAlo1YpPucdGmZDsB3v5Ym/PpxhnbL/Qm/08GhjfpiG6PEw+Yj\nCpsLK2w+orC5sCISidC9tTRGa3eUJ/z6Jl1v6TM6UGPUHDgD+U71/cWv2cj3s59C9I1+daG1+hL7\nzphDgUo32EIlYfMRhc2FFTYfUdhcWCGE4KQ2cnX777eXJfz6Jl1vWf57f8aoNfAm8jXgHwNf699v\nj/Pf1sAC5CuUVwLfAL8C4+u5fss4BTxkxL6U7n8dNh9R2FxYYfMRhc2FFebIaHeFnCeWSJh0vcWG\n1GeMMpFGZURNTQ1r1qxh48aNCCHSgb8Aj5vOzQBWABdWVVWxevVqCgoKQEZJ/wGur+MezevYf0j4\nX++IjYXNRxQ2F1bYfERhc2GFpmmc0DzJmBv3QwNER/FQ32i6PwAdv//+e2644QY6duzIrl276NCh\nA08//TQej+c24AXgZ2Aq0Hnt2rVcd911tG/fnoKCAgYMGMCDDz6Ipml/Af4LFMXco2mDPJUNGzZs\n2DhkOEWIVuk+dpTVsrOs9ojcs77IKB/g/vvvZ/z48bz00ku8/fbbbNmyhbfffludMxg5hP5qgGnT\npnHllVfyyiuvsHDhQpYvX87HH38Mcg2ii+LcIzXOvkOGHWZbYfMRhc2FFTYfUdhcWCGEIBwOk+SR\nyyBVBxpswq+F+PqMUZIQgnvuuYeLLpJ2xOPxkJmZSVmZEbYlA52A5oWFhaxdu5b8/HwAMjMzGThw\nIMuWLVPn9o1zj2PnnceNEE6nk8zMTGO00P8yPB4PJ5xwAh7P/+b8ERs2DhQOhwOnM7qqS7wVbRIE\ny4XrS9PdrWnas7m5uUkAn3zyCYsXL6asrIzhw4erczagj4jbtm0bSUlJZGZmGhdo3bo1n3/+ufp5\nXJx7GGm6RHgnmqbhcjX+Gd8gnzcSiRCJRIyJqfE4UM+i3kEfb6sLHo+HDh0absHD3xKcTidNmjSx\n7FN8x9aB2l9XfWiahsPhsHz+1uB0OmnevHmDrXJv5vJAZNzM55F2njRNw+12N/p6jMdlPE7r0xUH\n8oxerxev14vLKc8NhRM7ytBUXssqB/VJ4ktAEHgZ4JtvvqGsrIxQKMS2bduU0ekPLAa5xENqqjXr\nlpqaal4ZON6SCMYf1CoBqqCHIhg+n4+ePXse9P8OBiqEjUQihMNhwuEwoVCIQCBgLEekjEwoFDKO\n16XwDhfKizFvDocDl8tlaeCxx8y/f0sN0cy7+XcwGLTUizoWu5mPJaoOzAYqln/Fs8vlMjb1qhO3\n243T2bBLQtUFj8dD+/bt4x5TMq7WNlT8BoPBuDzG8h4Ohw+LW03TDB5jZdvMp1mGnU6nwevBOgg+\nn4+TTz75kMt7MBBCGLyqz0AgYHCr9ptlVPGZCHlVxl5xFI9bt9tNRkYGXpdM0wVCEQIBucis4vdw\nOdDrxzJMry5jpAHzgBFqx6RJkwB46qmneOCBB3jzzTcBbgZ2AiQnJ1NVZV0Zs7Ky0likE4j3gox0\ncwEdDgehUIjvvvvO0rDVd7MAmhu7WRmYiVakmYduxm7xFFessVGGRQlKPKFQDcFcLp/PZ5RZlSle\nWc2NJ7YR1eUFKeUcW0azco4VaLXV5Z0qXt1ut1GueI0+Niqoy/MyOxfxPGVVVmXEzc9iNi77Mx7K\ns1Xcm5WYMrSx8mTmPTbCifcc6hkAS3lio1szz2ozK/RY+VFlj3UUzLJkfq5YGaqrnGauzQbC/Gnm\nVtWBWRmaEWs8Y8sb6/DE4zaejNTVHmM5NLfB2GPxIgOzgTKXycyvKm88Ts3lrEuGzfePdZRU+zOX\nX32a4XA48Hg8Rjk9Hg/Jycn7yKnZeMTjcn9lrUseYp3mQCBAeXk5brdc0xGgJhhm586d7N271yhz\nrA42f48nC2pfSkqKoesBy8iIuoxRKjDC7/fz0ksvcckllxhRT48ePZg9e7b53EcAunTpQm1tLcXF\nxUaqbvv27Rx//PHqvB1x7mOsZqaspdPppFOnTnG9X7WZPYlYZXAoMDeueEbQ7XaTnJy8j0dr3hpj\nZBEIBKioqCAzM9MirLGerbmBmw1DJBLB7/dbortEemmAxQCaFVxSUtI+9RAb/Zmdkf2hpqaGX3/9\nlY4dO+J0Hr3308RGHbEKVnFfXV1tcB7POBws4jlA5s3lcuHz+XC73ftsjT0VaY42Yg2B+XskEqG6\nutqigA93PUyzc2aW33hG2rx5PB7je2ODcpgchs6QXS5ZWVmGzJp1guIzEAjE1ddKV7jdbk4++WRz\nZGQZGVGXMaoBKjweT9rcuXNxuVyMHz+eUCjEggULOO200wAoLy9n48aNnHzyyaSlpdGzZ09ee+01\nrr/+eoqKili2bBnTp09X1/wszn2MAQyqgA6Hg4yMjEMiURGk3pexv3xqbFRyrKG2tpaCggKaNm1q\n8aAS0Qjq6guoi3P1ebT6WoLBIOXl5Ue9rlW/plL+B4PYKKI+JyxepsCMQCBAWVkZzZs3P+qcHC5U\ndOl272/Bl31hjg5UJiWe7mgMMnykUF1djd8ffZWGpnHI/AIWeVW/D8YYhYDXNU276i9/+QuTJ09m\n6dKlFBUV0aJFC5588kkAfvjhB8aPH8+aNWtISkpi2rRpTJo0iffff59ff/2VCy64gL59+wJUIOcZ\nxcJojZFI5LArtrKy0lh991gUkoPF4fS/7Q/KqP1W0JBcHCkcaAf0gaCmpoatW7fSvHlC553/5qBp\nmq03YqCMh3on1+GOXzA7/2DR9ZYr1zeA4U5gQK9evdotW7aMTZs2kZqaynHHHWdUWG5uLp999pnh\n4XXv3p13332Xn376iaysLFq1aqWudTMQb/lXY20iUx7xkKEsry1QEjYfUdhcWGHzEYXNhRWKj+jb\nrRM7tNuk64Pm/fVp/z1AP2Cu1+ulW7dutG3bFk3TKoH7gWc8Hk9Q748oB+4AXlF5Qd0QbQPGAi/W\ncQ/DGEUikYQYI3tOTRQ2H1HYXFhh8xGFzYUVKnJJsA2yXF/n2/Ie+P1NMtiBNCbXAp2BKuTcIpXr\nuxP5gqRS077f6+eW6OfWF+QZabpQKHTYaZ9QKNRg8yZ+i7D5iMLmwgqbjyhsLqwIhUK43W78ITm4\nw+dObDrepOstkZG5BuqLUcuRK3bHokbfzCgGVh1guYzp8JFI5LCNke3hWGHzEYXNhRU2H1HYXFih\nIiNNNwmCxIZIJl1vGcp4tGvAMIaJ8E5sD8cKm48obC6ssPmIwubCilBIJrnUCgzBUGKNkYnvA+4z\nOhKwjVEDwuYjCpsLK2w+orC5sEINc2+oAR0mvi19RkfbGBkIh8OHnaZLxDWOJdh8RGFzYYXNRxQ2\nF1aEw+GYpdkSf/3GmKYzYEdGiYfNRxQ2F1bYfERhc2GFiozUCgzhBK/aXRffjcYYhcPhhAzttj2c\nKGw+orC5sMLmIwqbCyuMAQwNNO3KpOstS5A0KmNkp+kSC5uPKGwurLD5iMLmwgplLAIhOSvH40qs\nmTDx7TXvP9rGyJiDFAwGD3ntI5Czeg/3GscSbD6isLmwwuYjCpsLKxQfmqbhdKj3GSU2TWfi2/Km\ny6NtjIzRFGqi1aFCrQ5r534lbD6isLmwwuYjCpsLKxQfDoeDJH2ya23o8FY2j4VJ1zeqyMgPGEuO\nH45ABINyyLrt4UjYfERhc2GFzUcUNhdWKD4cDoexJl0iu45idH2K+djRNkZBiOYQD2dcuzFRy/Zw\nAJsPM2wurLD5iMLmwgrFh8PhoMovI6JUX+K4idH1SeZjR9sYheDw+4vUNX5rrzVoSNh8RGFzYYXN\nRxQ2F1YoPjRNM4Z0uxyJi41idH2j6jMKQ2IXSbWXgZew+YjC5sIKm48obC6sMPNRE5SRkdeVOEMd\no+stIdfRNkYRSExkdLgDII412HxEYXNhhc1HFDYXVpj5qA7IlF2KN3Fpuhhdb7E/R9sYCeCwBy9A\nYqKrYwk2H1HYXFhh8xGFzYUVZj4C4cTPM4rR9RbiG40xsie8JhY2H1HYXFhh8xGFzYUVZj7U/CJ3\nAvuM6uP7aBujCNjGqBE6IYIAACAASURBVCFg8xGFzYUVNh9R2FxYYeYjqEdGLmdiI6NGb4zsdekS\nC5uPKGwurLD5iMLmwgozH7VBaYx87sQao7p0faMxRokYTWcLVRQ2H1HYXFhh8xGFzYUVZj5qG2A0\nXYyut6wzdLSNkQaJMUa2h2OFzUcUNhdW2HxEYXNhhZmPkJpn5GywPqOQ+djRNkYOsPuMGgI2H1HY\nXFhh8xGFzYUVio+I6R1GzgTOwYrhu1G96VUDjIX5DgfqHRw2JGw+orC5sMLmIwqbCysUH8GI8UIF\n3AkcwBCj66vVbogao6NVGw6QBTxcgUjENY4l2HxEYXNhhc1HFDYXVig+TLbIeJVEIq+vo9Z8TBmj\nxL6w4sDhBmmNDycyEkIkJLo6VmDzEYXNhRU2H1HYXFhh5sNsn4VInHmI0fVB87GjXQsuOHxjFNHN\nuC1UEjYfUdhcWGHzEYXNhRVmPhJof/a5h4nvuJHR0YIXDj9UVpbbDrclbD6isLmwwuYjCpsLK8x8\nmFNz4UjiLFOMrq8yHzvaxigJ7Mgo0bD5iMLmwgqbjyhsLqww8+E2DecOJtAYxej6GvOxo10LHkhM\nnxHYQqVg8xGFzYUVNh9R2FxYYeZD0zTjPUahcKS+vx0UYnR9pfnYMVELiexgOxZg8xGFzYUVNh9R\n2FxYEcuHGtIdTKAxikGx+ccxYYwU7NyvFTYfUdhcWGHzEYXNhRWKD5Wq84cazBiVm38cqDFyAe2B\nLBpoTpItEDZs2LDReODR16QLJNgYmXR9tXn//oxRG+Bl5HjwAmA3sAWYFPNfDXgUKEPOWTJvJcAf\n2Y8RS0TIbIfdVth8RGFzYYXNRxQ2F1YoPrz6S/USHRmZ+D7gyKg1sAq4LBKJsHPnTioqKgDaAk8D\nz5vOzQXuBtLjXCcDuA84Kc6xBov/bNiwYcPGoSPZIyOjmkC4oW5RZP5RnzGaDrT58ssvOffccxk/\nfjx5eXnccMMNVFdXA0wE8vRzzwJ49dVX6dKli2V777331PU6xrmHYYwOxzuxU3xW2HxEYXNhhc1H\nFDYXVsTyYRijYGKNkUnXV5j312WMfMCISCTCrbfeyo033siSJUv48MMPKS0t5YUXXlDn5eufpwD8\n9NNPXHXVVaxcudLYzjrrLHXu9jj3CUHihMIOt62w+YjC5sIKm48obC6sUHz43NIYVScwMorR9Qc0\n6TUb8JaXl3P22WczfPhwWTifjzPOOIOffvpJnddO/zSMUW5uLtnZ2cbm9XpB9iV9Hec+hjFKRGRk\nC5WEy+UiOzvbXhofyUX79u3xeDxHuyiNAnZbicLmwgqn00mzZs2MeUCpXhcAVf5QfX87KMToess8\nI1cd/9kFrM3IyOj+0EMPGTuDwSDLli1j8ODBatdWZBR1YigUYv369cybN48//OEPpKamcvXVV3Pp\npZeiaZoTORhiW8x9EmaMfD7fbyrsFkIQiUSIRCLGAoXxOFDPpGlanVssnE4nbdu2bfBn+C3A6XTS\nvHnzuMcU37F1oPbXVR+aphkTA9XnbwUOh4OMjAxcrrqafmJg5vJAZNzM55GahKppGl6v9zdTf/G4\njMdpfbqivmd1uVwcf/zxxu80n5SRitpgHf84eMToessKDHVJZAAYAEwAHgb5OtqpU6cCcNVVV6nz\nXkEO+Xbu3r2brKwszj//fP7yl7+wevVqpkyZQlZWFoMHD04FxgMPxtzHeEohBH6/H6fTidPpPCgB\ncbvddO/e/YDPPxwIIQiHw0QiEcLhMOFwmFAoRCAQIBQKEQqFDCMTCoWM43UpvMOFw+EwOFObw+HA\n5XJZGnjsMfNvt9vd6Buk2Xgr3s2/g8GgpV7UsdjNfCxRdWA2ULH8K55dLpexud1u4/NgZf1w4XK5\n6NSpU73nKBkPhUIGr8FgkGAwGJfHWN7D4fBhO5eKx1jZNvNplmGn02nweqAOgtvtpkePHodczkOB\nEMLgVX0GAgGDW7XfLKOKz0TIqzL2iqN43LrdblJTU0nVjVGlP6rXFL+Hy4EOS5quPveoGDgNoKqq\niilTprB3715mzJhBcnIywAzgJ+AEgNatW7N8+XLjz7/73e8YOXIkS5YsUZFUrzj3qAW1Sqxg/fr1\nBALy5X/mhq2+mwXQ3NjNysBMtCLNHI7HbvEUV6yxUYZFCUo8oVANwVwun89nlFmVKV5ZzY0nthHV\n5QUp5RxbRrNyjhVotdXlnSpe3W63Ua54jT42KqjL8zJ7QfE8ZVVWZcTNz2I2LvszHpqmWRSRWYkp\nQxsrT2beYyOceM+hngGwlCc2ujXzrDazQo+VH1X2WEfBLEvm54qVobrKaebabCDMn2ZuVR2YlaEZ\nscYztryxDk88buPJSF3tMZZDcxuMPRYvMjAbKHOZzPyaHd+6ymqu91hezfePdZRU+zOXX32a4XA4\n8Hg8Rjk9Hg/Jycn7yKnZeMTjcn9lrUseYp3mQCBAeXk5wWCQJkluAIqrApSVlVFQUGCUOVYHm7/H\nk4X09HTju6m+9lpkLE7bVrgfuLC4uJgJEyaQnZ3Nyy+/TEpKijo+Xt8A2LVrFxs2bODMM880LpCa\nmsru3bsN3uPcw6+IjEQinHDCCQYp8bxftZk9iVhlcCgwN654RtDtdpOcnLyPR2veGlNkIYRgz549\nZGRk7NNXYm5IijtzAzcbhkgkgt/vt0R3ifTSAIsBNCu4pKSkfeohNvozOyP1cbFlyxaaNWumnKij\nitioI1bBKu6rq6sNzuMZh4NFPAfIvLlcLnw+H263e5+tsacizdFGrCEwf49EIlRXV1sUcDh8eJ3z\nZufMLL/xjLR583g8xvfGAiEEJSUlpKen43K5aL51MwAl1UEyMjLo1q2bIbNmnaD4DAQCcfW1EILu\n3bsbXSkmWd5lvn9dxigbuCMSiTBp0iQ6dOjAY489tk+euaqqioqKClq2bMnu3bu57rrrWLJkCW3b\ntqW6upqlS5dy9dVXq9PXxrlPAKIedFJS0iGTWFtbayjeWG/AjHjRSWNuaIeKbdu24fF49jFG5tD8\ncFBXX0BdnKvPo9HXUlRUREZGRqMwRpqmGcrK5/Md1H9jo4j6nLB4mQJ1jbKyMpKTk4+ZQR0qunS7\n3Qf1P9U1oP73/9t78zg7qjrh+1t36yXp9JLQQSAkmWCAJCQEQgBlU3YFJSMogxqG+AIqIrjMIMvM\nqz7OCPggCCMOoCCLyqLvKC+Co+w8Qgi72HSCSQjJhCVk7e70crfz/FH31Dmnum4n3bc6t7v5fT+f\n+tx7q+rWPfW9p86vzqlTpwa6FlPtPLyreOONN5gxYwZNTU1BB4bO3jzJZHLIx0/YY+lzjlL5rykX\njD4K1Dz11FO88MILTJgwwe6izUEHHcSPf/xjHnzwQb773e+qV1991Zs7dy6LFy/mzDPP5LDDDuOV\nV15hzpw5fOpTuvc3t0f8TjcQrroNGs/zaG9vZ9q0abS0tAx5O2MFHWwrPZve0W+MpLO6cuwKF7uK\nHV2A3tltrF69Wo4VfBevvfaauCgRPlYmlJrptvVkUWroz5yzv2eV9Z3h9coFox6AuXPn8rvf/a7f\nQl2DOe644zjwwAODX7rkkkv49Kc/zapVqzj//POZOXOmXvS/gBURvxMEo0oLizi2MZYQHwZx4SI+\nDOLCxfbR2lADQK6g2Lw9y8TxNXFuf2t4Wblg9Cfgqebm5iObm5vLbri5uZnS8hzwW+DD06dP32P6\n9Ol6lXfxe9D9pMwmekIJHDKSqVzEh0FcuIgPg7hwsX3s3miakTd09sUdjHrDy8oFo27gaPwhfMZH\nLC8CrwN7lZavxq92pYB5+N29NwJLCbULhugMJXDIJJNJyVQW4sMgLlzEh0FcuNg+muvNNcWt3fHc\na2SV9f3upB2oN50CVu1g2+HlefyRFqJGW4iiE3wBlfZqSSQSFW9jLCE+DOLCRXwYxIWL7aM2nSST\nTJAtFGO78dUq6/tVUuzu1tUYEyO4z0ia6eJFfBjEhYv4MIgLl7CP5nF+J4aNXQM1cA1p+339lsXy\nC0OnB4ilt1OlPfLGGuLDIC5cxIdBXLiEfUye4F83eq+zX+wYElZZ3xNeNiKCkdSM4kd8GMSFi/gw\niAuXsI/GoHv38F8zqnYwiuU+I70NyVQG8WEQFy7iwyAuXMI+9GCpHTFdM7LK+n43KVY7GHWAdGAY\nDsSHQVy4iA+DuHAJ+9A96rZsj+eakVXWj7hg1AXStXs4EB8GceEiPgziwiXsQ99btLk79g4M/WJP\ntYPRdojn7ESq2y7iwyAuXMSHQVy4lL1mFON9RiO1ZrQJ4mmmSyaT5PPxPZFwtCM+DOLCRXwYxIVL\n2MfEcX4z3YbOvlh6HVpl/YTwsmoHo3fAfxZQLldZ5I1jG2MJ8WEQFy7iwyAuXMI+dNfurr48ffnK\na5DW9hvDy6odjDrBf3BXHDWjOJ+zM9oRHwZx4SI+DOLCJexjQp0ZpKcjhu7dVlnf73kU1Q5GwTWj\nOO4zAqRnTAnxYRAXLuLDIC5cwj7s8ek2xdCjzirr+z3Ma8wFI7kY6SM+DOLCRXwYxIVL2Mcka6Tu\nOLp3W2V9vyepVjsYZYGCTmAlVWX9oDfJVD7iwyAuXMSHQVy4hH1kUglq036YiGMUBqusTxOqHVU7\nGCmgWz/Ct5IMoSVKddtHfBjEhYv4MIgLlygfcQ4JFCrrnR511Q5GUBqfrtLu3dL26yI+DOLCRXwY\nxIVLlI+J4/ymunc74hks1Srrm5zfjmXrldELEoziRnwYxIWL+DCIC5coH3s1+5d33trab6DtITGS\ng1EOKg9GnufFcvPsWEF8GMSFi/gwiAuXKB8fKD1+/J2Ofk8KHxLW9sfZ80dCMALkMRLDgfgwiAsX\n8WEQFy5hH62lG1/fjSkYletRJ8FoDCM+DOLCRXwYxIVL2EfcNSNr++Od+bFsvTL8h1vEND6dVLcN\n4sMgLlzEh0FcuIR96JG7t3bnyBcqD9rW9ltLszwYGcHIA3+YCBmfLl7Eh0FcuIgPg7hwCftoKnXt\nBujsrXxQWausH3EdGDIQz3NFpLrtIj4M4sJFfBjEhUu5p71CPE98tcr6EddMFwSjOJrpJFMZxIdB\nXLiID4O4cAn7GFdjglF3tvLmTKusb7Dnj4RgVAfxPGBP2n5dxIdBXLiID4O4cAn7yCRNmMjG8BgJ\nq6yf5MyveMuV4VHqa55Opyt+yFUc153GEuLDIC5cxIdBXLiEfdSkTZiI65lGpbJ+N3t+tYNRM6XH\nz6ZSqViCkTy10SA+DOLCRXwYxIVL2EfaqhnlYuhNZ22/xZ5f7WAUVNOka3f8iA+DuHARHwZx4RL2\nkUp4wftCMdZHj4+oERgm6jee58X2TCN5aqOP+DCICxfxYRAXLmEfnmeCUTEGR1ZZn7HnVzsYBdW0\nRCJRcWbQ0qRnjI/4MIgLF/FhEBcuYR92uZywAtNQscr6IT/PKA2kdriWT81ObrsxSEiMT3uVMxwf\n8WEQFy7iwyAuXMI+bC0xxKKyjx7fUcCoBb4FrMB/KmsOeBn4fyK+mwEuB9bgPxYiB/wBOHiA7Qdt\nhp7nSc0oZsSHQVy4iA+DuHAJ+8hb14mSicqjkVXWO810A9V0MvjB5GiAfD6vhxefB9xSmr8Yf2y5\nFHA/cCJANpslnU4nPM87sTTvWODRiN8I7sCNMxjJGY6P+DCICxfxYRAXLmEfxZib6ayy3ok/A9WM\nvgkc/dZbb7FkyRIOP/xwDj30UC6++GI6OjoAPgecUVr3y8CJGzdu5POf/zyHHXYYhx56KPfcc4/e\n1u2EqmQlnDtw4wpGgo/4MIgLF/FhEBcuYR92d+50Mh5XpbI+ac8bKBidDXD55Zez11578cwzz/DE\nE0/Q2dnJNddco9f5XOn1qwBXXHEF06ZN47nnnuPnP/85V155Je3t7QB7AadF/EbQtTvODCFnOC7i\nwyAuXMSHQVy4aB/2EED1mZ3tNlAeq6x3Cv1ywcgDPlgoFBg/fjznnnsuqVSKcePGceqpp/Liiy/q\n9WYAewAzOjo6eOyxxzjvvPNIJpPMmjWLj370o9x///163WMifme3iHlDRs5wXFKpFC0tLcEFyfcz\nmUyGffbZh0wms+OV3wfIsWIQFy7JZJJx48YFXnpzJhjVpZPlvlYx5cKcAp5LJpMLb7jhBmfBU089\nxQc/+EH98R1gOsCqVatIp9Pstddewbp/93d/x8svv6w/To/4neahJz2aVKryyL0rUEpRLBYpFoso\npYIpjM4QnueVncqRTqeZPj1K+/uPZDJJY2OjMy9oEw/9B6YXUfT/4XkeiUTCeR1tJBIJJk2aRDI5\nPIWL7XJn8rjtsxonT+l0escrVZkol1FOByordiavZjIZ9ttvv+CzXTOqrUIwAr9Z7SvAZXrGHXfc\nwVNPPcWvf/1rPes+Std9Ojs7aWxsdHa2sbGR7du364/O3bYl6sMzom602llqa2uZN2/eoL83GJRS\nFAoFisUihUKBQqFAPp8nm82Sz+fJ5/NBkMnn88HycgVepSQSCZLJpDMlEglSqZRzgIeX2Z/T6fSI\nL1Dt4K29259zuZzzv+hl4cleFtd/YAeosH/tOZVKBVM6nQ5ek8lkVdxnMhmmTp0auUzn8Xw+H3jN\n5XLkcrlIj2HvhUKhIreljlKRedv2aefhZDIZeB3sCUJtbS1z584dcnoHg1Iq8Kpfs9ls4FbPt/Oo\n9hlHftXBXjuKcqvzpfZsP8NoQm2sJ/vOsBcDbfltoBt8gddffz133303t956K3vvvTfAi8BtlJrf\n0uk0fX19zgZ6e3uprQ36LfRE/EaNfqOUCnpZvPTSS86Brd/bGdA+2O3CwBatz7Ds3iHhKargCgcb\nHVh0RonKFPpAsNNVW1sbpFmnKSqt9sETPojKnQXpwjmcRrtwDmdoPZU7O9Ve0+l0kK6ogz5cKyh3\n5mX3kIw6U9Zp1UHc3hc7uOwoeHie5xREdiGmA204P9newzWcqP3Q+wA46QnXbm3PerIL9HD+0WkP\nnyjYecner3AeKpdO27UdIOxX263+D+zC0CYcPMPpDZ/wRLmNyiPljsewQ/sYDC+LqhnYAcpOk+1X\npzfKqZ3OcnnY/v3wiZI+/uz061ebRCJBJpMJ0pnJZKivr++XT+3gEeVyR2ktlx/CJ83ZbJaOjo4g\nD6TTaXoyk43bYp6XXnq1Xxlsv4/KC3oaP358UNYziGC0CPhePp/niiuu4KWXXuLuu++2z6YOwr+f\nCIAZM2bQ2dnpBKCNGzcyeXKwI+9F/EZDeIbnecyYMSPy7FdP9plEuDAYCvbBFRUE0+k09fX1/c5o\n7Wkk1izy+Tzbtm2jubnZuZEtfGZrH+B2YCgWi/T19Tm1uzjP0gAnANoFXF1dXb//IVz7s09GdkRf\nXx9r165l2rRpVW2SCdc6wgWsdt/d3R04jwoOgyXqBMieUqkUtbW1pNPpftNIb4q0axvhQGC/LxaL\ndHd3OwVwHONh2oFCu4wK0vaUyWSC9yONQqFAb28v9fV+w9XD7RsAvyddJpNm7733dsoE7TObzUaW\n17qsSCQSzJ8/3/4pJ1OXC0ZJ4FqAK6+8kuXLl/OrX/2KlhZnkNXgh5PJJK2trUyfPp0//elPnHrq\nqWSzWR599FEuvPBCvfrzEb8TBCMdLT3Po6mpKWLVHaMF6eEmdtSeGq6VjDX6+vpYs2YNDQ0NwYV7\nu2peCeWuBZRzrl+rda0ln8/T0dFR9R5TnucFhZXVarBThGsRA52ERbUU2OTzebZs2UJLS8uILBAH\ng65dDuUkw64d2CdsYa8jIQ/vKnp7e1m+fDkHHHAAmUyG7qzfTFeX9suNiRMn7mALLnZ+1Z9L3pzn\ndpQLRgcCU9etW8ddd93F7rvvzjnnnBMsbG1t5ZZbbmHp0qWcc845vPzyy9TV1fH1r3+dyy67jJdf\nfpm2tjZaW1s56aST9Nd+E/E7dXaCK/1je3p6WLFiBXPnzpVeU1R2/W1H6KA2WhhOF7uKnb0AvTP0\n9vaydu1ampqaRtX/GDee5znlxmjoyDDchI+VbT1+zGisH5ob++Rfb7+0bee5HeWCkQcwbtw4brrp\npn4La2r8Sz377bcfN998c1Dwn3DCCey///48+eSTHH744RxzzDG6d9vVwJsRvxPsXRzBaCwUOHEi\nPgziwkV8GMSFS9iH7tpdm4rnpGWw14xeAZ5oaWk5+uijjy670ZaWFqzljwF7TJkyZd/Pfvaz9mrX\nYPXICxH8vgSj+BEfBnHhIj4M4sIl7GNjVxaAiePjaW0abM0oBxwHLCD0ND6LFfg3rbbgD47ajl+j\n+giwP7AVeAJYN0C6glBbLBYrvr9At0nKTZ4+4sMgLlzEh0FcuIR9bOzye0nv1jC4a5wDbb+07Z0K\nRnrFpTvY7qrQZwU8Upp2BicYxVEzirNdfbQjPgziwkV8GMSFS9hHT+mm1/qYbngtV9ZX+1Qg2Dul\nVCw1I8lQBvFhEBcu4sMgLlzCPnQHhgl18dzwapX1TtfuagejYI8LhULFvXri2MZYQnwYxIWL+DCI\nC5ewj45ePxg11MbT09DavtOBodrBKCCua0bS7msQHwZx4SI+DOLCJexjU8wdGMr5tudUtZ6az+dj\nqRmNloFSdwXiwyAuXMSHQVy4hH281+l3YGiNqQODVdaPqGa6AGmmix/xYRAXLuLDIC5cbB/5QjF4\n7Hh9Jh5H5XxXOxgFkTGOs5M4aldjCfFhEBcu4sMgLlxsH315U3nJpOIJF1ZZv9OPHd8VBBew5JpR\n/IgPg7hwER8GceFi+7AfOZ5JxuPI2r5zEara/0BWvykUCrEEIznDMYgPg7hwER8GceFi++jNmWBU\nk46vZjQSg1HwCIp8Pl/xIIW5XE4uRFqID4O4cBEfBnHhYvvQ3bohvq7dVlnvbLDawSh4Gl8+n4/l\nmpFkKoP4MIgLF/FhEBcuto9OKxjF9ZRXa/s19vxqB6NO/UZ608WP+DCICxfxYRAXLraPbN480ykd\n0zUja/sjqgNDh35TaYbQD3CSTOUjPgziwkV8GMSFS9hH3nrCcCoRz62oVlnvSB8xwajSdttczq9O\nysOxfMSHQVy4iA+DuHAJ+9CDpGaSCVIx1YzKlfXVDkadYKJxJb3pZBh4F/FhEBcu4sMgLlzCPvR9\nRjUx3WM0UFlf7X+gAKbfeSUj5xYKfgSXTOUjPgziwkV8GMSFS9iHvs8olYyniW6gsr7a/0AC4uu8\nAEjbbwnxYRAXLuLDIC5cwj70UEBxNdGFyvoRNTZdEeLr1u15npzhlBAfBnHhIj4M4sIl7CMbczNd\nqKzP2cuq/Q9kId7RF+QhWT7iwyAuXMSHQVy4hH305vyaUl1MT3kNlfVZe1m1g1EO5B6j4UB8GMSF\ni/gwiAuXsI9scM1oWJrpdDBSUP1g1APxjA0lmcpFfBjEhYv4MIgLl7CPor5mFNM9RqGyfkTVjIJg\nFEcznVS1DeLDIC5cxIdBXLiEfZRiETHFonBZ32cvq3Yw2g7xZIhK71Maa4gPg7hwER8GceES9qF7\n0yVirBlZZX23vaza/0Ia5FlGw4H4MIgLF/FhEBcuYR9K+cEoGVPtMbT9TnuZnlutemoG4uvaLW2/\nBvFhEBcu4sMgLlzCPoqlYJSIKRiFyvoee1m1TwnqIb6akWQqg/gwiAsX8WEQFy5hH16pnqJQ5b4y\n6O3v6JpRPL80eJogvq7dUt02iA+DuHARHwZx4RL2oa8VFYrxhIhQWT+irhmNh/iCkTwgyyA+DOLC\nRXwYxIVL2Ie+VjRMwajLXlbtYNQI8TTTyRmOi/gwiAsX8WEQFy5hH3qA1FxhWJrpttvLqv0vNEM8\nZydy85qL+DCICxfxYRAXLmEfekw6PRJDHNu3yvpee1m1g1E9xPOUV7kQaRAfBnHhIj4M4sIlykd9\nxg8c+iF7lRIq6yO7du+I3YDfA9uANuC4iHVOBx4Gng1NfwROK7PdNPgSKrnpVfeFl+q2j/gwiAsX\n8WEQFy5RPsbX+sGoozcX+Z2h/IZV1m+yl+1M21g98GvgqNLnWcDtwF6YXngzgHspf7/SscDfAW+G\n5scajGRYDx/xYRAXLuLDIC5conw01PghYntfnmJRVTwSQ6is32ov29EpwRHAC8BRGzZs4JhjjqG7\nuxtgD0pNbCWOB7yHH36YM844w5mWLVumf+fAiO2nIhI4aLREwUd8GMSFi/gwiAuXKB9N9WnAH6Mu\njtpRqKx3unYPVDOaDjwOJFetWsUFF1zA22+/XW7dAwGWLVvGBz7wAT75yU8GC6ZNm6bfbov4ntSM\nhgHxYRAXLuLDIC5cony0jMsE7zdvz9JUn+n3vcH+xlDGpjsSSD755JN85jOf4cQTTxzoNw4EaG9v\n59hjj3Wm1tZWgDzwTMT3MhEJHDSSqVwSiQStra2k0+lqJ6XqJBIJpk6dSm1tbbWTMiKQY8UgLlw8\nz2PixIlOz+YJtaYM6ezNV/wbQ60Z9QHsueeePPDAAyQSCf7zP/8zar0kMFcpRXt7O8uXL+f++++n\noaGBxYsXc9BBB4F/oSpDaPgH/ftxjNpdW1s7qi5E6p4rxWIRpVQwhdFePM8rO4VJJpNMmTJl2Pdh\nNJBMJpk0aVLkMu07/B/o+eX+D/1YZvt1NNHU1DTsN3raLncmj9s+d+VxXFNTM2rKjSiXUU4HKisG\nyqupVMpuyQKgodbkkzia6UJl/Rbn9wf43h+BLTNmzGgG2LBhQ7n1pgN169evp7Ozk3w+z5IlS3jx\nxRdZvHgxv/zlL5k7d+5k4B+BG0LfDfr4eZ5HX18fyWRy0I8BzmQyzJ49e6fXrwSlFIVCgWKxSKFQ\noFAokM/nyWaz5PN58vl8EGTy+XywvFyBVymJRCJwpqdEIkEqlXIO8PAy+3M6nR7xBaodvLV3+3Mu\nl3P+F70sPNnL4voP7AAV9q89p1KpYEqn08Hrrn7kdSaTYcaMGQOuo/N4Pp8PvOZyOXK5XKTHsPdC\noVCRW8/zAo/hNhPdCQAAIABJREFUvG37tPNwMpkMvO7sCUImk2HOnDlDTudQUEoFXvVrNpsN3Or5\ndh7VPuPIrzrYa0dRbnW+TCaTNDY2UpdO0pMr0Nmbj2WAAuu/WWfPHygYbcHvOXcu8N0B1usCvwa1\ndOlSmpubAfjwhz/MmjVrdDAC+BD9g5HDX//61+C9fWDr93YGtA92uzCwRWtpeuejziiiCq5wsNGB\nRWeUqEyhDwQ7XbW1tUGadZqi0mofPOGDqNxZkC6cw2m0C+dwhtZTubNT7TWdTgfpijrow7WCcmde\nnuc56Q2fKeu06iBu74sdXHYUPDzPcwoiuxDTgTacn2zv4RpO1H7ofQCc9IRrt7ZnPdkFejj/6LSH\nTxTsvGTvVzgPlUun7doOEPar7Vb/B3ZhaBMOnuH0hk94otxG5ZFyx2PYoX0MhpdF1QzsAGWnyfZr\nn/iWS6v9v4e92r8fPlHSx5+dfv1qk0gkyGQyQTozmQz19fX98qkdPKJc7iit5fJD+KQ5m83S0dER\n5IF99tmH5vo0PdsKbN6eZeXKlWzfvr1fGWy/j8oLTU1N4cO2AGx28li/I9vlHeCnRAejy4Az8bts\nB9HdZu+996a9vV1/bBzohzzPY//993fkhM++9GSfSYQLg6FgH1xRQTCdTlNfX9/vjNaeRlLNIp/P\ns3nzZlpaWvo1x9gHknZnH+B2YCgWi/T19Tm1uzjP0gAnANoFXF1dXb//IVz7s09GypHL5Vi/fj2T\nJ08mk6ns4mschGsd4QJWu+/u7g6cRwWHwRJ1AmRPqVSK2tpa0ul0v2mkN0XatY1wILDfF4tFuru7\n+5UxlWCfnNn5NypI21MmkwnejxTy+TwdHR00NjYG6VJK0TI+w1vbetm8Pctec/eip6fHKRO0z2w2\nG1leK6U4+OCDg98p5aXNhAborqTh+DL7w3PPPceFF17IU089xfjx41FKsWzZMj70oQ/pVVbuaIP1\n9fU7WiUSXWjW1NREng3YRNVORvKBNhTy+Tzr1q1jwoQJ/YKRXTWvhHLXAso516+7+lpLoVBg06ZN\n7L777sP+WzuD53lBYTXYThXhWsRAJ2FRLQXg++js7KShoWFEFYSVoGuXg+2wUywWyWazZDKZyBaI\ncA1Wv47m64UDkc/neeONN5g9e3aQNzzPY/cJdfx1fQdvb+uhvr5+0OV0mRPXLeEZFV3F/N3vfsf3\nv//9wtKlS5OHHXYY8+bN4wtf+AInn3wyS5cuZfPmzSxevFivft+OEjzUPzabzfLaa68xe/Zs6TW1\ni9BBTdh17OgC9M6Qy+VYtWqVU+C8X8lms7S1tUm5sQN2a/BbFDZ2ZYf0/ahLD57nbQ2vtzPBqBug\noaGB733ve87Zx5w5c7j00kuT4Lcp//SnP+Whhx5i5cqVnHDCCZxyyim6aeQ+4KmIbReJcXy8uJqO\nxgriwyAuXMSHQVy4hH1MnuAH6ne29UatPlTWh2fsTDDaBvy6rq7u9DPOOEPP+y1w8IwZM6bYPXNS\nqRSnnnpq+Ps/By4os+08MdxrNJaqynEgPgziwkV8GMSFSzkfE0s3vm7tGVrNKEyprN8Unr+zzXSf\nBW4F9sQfX+4x/Ke0Hof/gLzlwJ/xu3mfCOyNf2/R74C/DbDdLJCpNFOEe5K83xEfBnHhIj4M4sKl\nnI8JdX5r2Nbuyu8zssr67eFlOxuMssBDoXkbgbtD81YDPxlE2nqA8YlEoqL+63oHK+1xNFYQHwZx\n4SI+DOLCpZwPPSRQZ2+eXKFIOjn0KytWWd/Zb9mQtxoP28EkcKjoICaZykd8GMSFi/gwiAuXcj6a\nrfHoKq0dWWV9v7GFqh2MukGCUdyID4O4cBEfBnHhUs7HxPEmGL3XGR7RbfC/Udp+vxu87GBUjYbT\nHFQejHSXV8lUPuLDIC5cxIdBXLiU89HaUEs66Tfh/c+W7qiv7jRWWd/Tb1lFW66cLLjDxgyVOLYx\nlhAfBnHhIj4M4sIlykcy4dHaUOre3VFZ925r+xKM3i+ID4O4cBEfBnHhUs7Hbg01wNBvfI3Yfr+L\nT9UORn0gwWg4EB8GceEiPgziwqWcD/0oia4Kn2k0koNRF1R+zSiubYwlxIdBXLiID4O4cCnnoz7j\nDx3Vk6ssGFnb7zcWVbWD0SbwR77N5yvbyVQqVfEIvGMJ8WEQFy7iwyAuXMr5GF/j3/ha6dNerbJ+\nQnhZtYPRFognQ8QR0MYS4sMgLlzEh0FcuJTzoZvpKg1GVlk/4oLRVpCa0XAgPgziwkV8GMSFSzkf\n42r8VrXtfbHVjMaFl1U7GG0HP4FxXDOSTGUQHwZx4SI+DOLCpZyPlnF+b7pN2yvrTWeV9TX9frui\nLVdOJ0gHhuFAfBjEhYv4MIgLl3I+WsbpwVIrC0bW9vs9+bvaweg98KuGcTTTSduvQXwYxIWL+DCI\nC5dyPuoz/jWj7mxltUhr+xPDy6odjDaABKPhQHwYxIWL+DCIC5dyPnQHhr58kd7c0AOStf09w8uq\nHYzWA6TTabLZyqp/mUyGXC4nN7CVEB8GceEiPgziwqWcj7q0uS2oLzf0Zk2rrN89vKzawWgz+AmM\no2YEyMXIEuLDIC5cxIdBXLiU81GTsoJRfuiurLJ+xF0z2g4o3YOjkrOTZNKXJZnKR3wYxIWL+DCI\nC5dyPuoyJhj1VNBMZ5X19YQe7lrtYFQE+hKJRMVjREmmchEfBnHhIj4M4sKlnI9MyoSKbL6yZ89Z\nZX2Ds2zIW42PHvAlVJIh9IOhJFP5iA+DuHARHwZx4VLORzrhBe9zhcqur1ll/WTntyvaajx0g9+W\nmMsN/ZG2yWQSz/Mq2sZYQnwYxIWL+DCIC5dyPtJJEypyhcruy7LK+lZ7/kgIRgXwL5xVkiE8z5Nu\nmhbiwyAuXMSHQVy4lPORSpqaUb7Cm4Stsl73qPNgZASjIlReM4prG2MJ8WEQFy7iwyAuXKJ8JK1m\nugorRvb2nRtfR0IwSkHl14xABj0MIz4M4sJFfBjEhUuUj4RnglGxwnuyrLJ+vPMbFW01HmpABksd\nDsSHQVy4iA+DuHDZkQ87MA0Fq6x37jUaCcGoFuKpGcWxjbGE+DCICxfxYRAXLsPtw9q+80yjagcj\nD6iDeEbPjaN2NZYQHwZx4SI+DOLCJcpHnKMlWWV9vTM/vp8YEi2UrhnFUVWW4eBdxIdBXLiID4O4\ncInykbM+250Zhrr9kVgzatJv4nr0uFS3DeLDIC5cxIdBXLhE+ShYN7qmk5UFI6usH1EdGILI6Hme\nPGAvZsSHQVy4iA+DuHAZ7pqRVdaPqGa6oJ95XL3pJFMZxIdBXLiID4O4cInyYX9MJSoLG1ZZP6Rg\nlAKuAl4FngSOL7PeCcC9wCvA08B38a8LlSMYDiKuR49LddsgPgziwkV8GMSFS5SPgtWDocKKUdkO\nDKno1R084IfAhda83+LXanqteVcCl4S+ezhwDvARYGXEtoN+5nEFI6UUSim8CvvCjwXEh0FcuIgP\ng7hwifLRZz02wn620VC3XyrrBzVq9xTgv4ALs9ks5513HmvWrAE/os2w1lsEXJLNZrn66qs57bTT\nWLJkCS+88ALAXsDdZX6r1k5gHB0YAKlylxAfBnHhIj4M4sIlykd31pTN9rONhoJV1u90B4Za4M/A\nJ7u6urjooot44oknyo3h9C2Aq666ira2Nq666ipOPPFEzj//fN5++22Ag4FjI743zk5gpY/+1VFc\nMpWP+DCICxfxYRAXLlE+uvrMwKkNtTvToFYeq6xPO/MH+M5BwJTVq1dz8skn09jYGDySNkQTsLC3\nt5d7772Xb37zm+y777585jOfYf78+fzmN7/R650U8d0gMlb6cD29DUCeZ18inU7T0jLQJbv3D7W1\nteyzzz7BWd/7HTlWDOLCJZVKMW7cOGdeT6lm5HlQk6qsA4NV1mec3x3oO+BX2X74wx9yyCGH8MAD\nD0Stty/AypUrKRQKzJkzJ1gwd+5c2tranPVCBBew4ghGiUSCVCo1KjKVUopisUixWAzaZ6PSrQ8U\nz/PKTuWoqalh+vTpw7YPo4lUKkVjozMUVuA7/B/o+eX+D8/zgidW6tfRRiqVYtKkScHD1OLGdrkz\nedz2OVxpKkcikSCdTo/4ciPKZZTTgcqKncmrtbW17Lfffs68fNH/jXQM+d0q6534M1Aweg7YMHXq\n1NapU6cOtO1GgK1bt9LY2OgktLGxkY6ODv1xQsR36yISOOQLiXV1dcybN2/Q3xsMSikKhQLFYpFC\noUChUCCfz5PNZsnn8+Tz+SDI5PP5YHm5Aq9SEokEyWTSmXRQtg/w8DL7czqdHvEFqh28tXf7cy6X\nc/4XvSw82cvi+g/sABX2rz2nUqlgSqfTwat+mNmupqamhnLHtc7j+Xw+8JrL5cjlcpEew94LhUJF\nbj3PCzyG87bt087DyWQy8DrYE4S6ujrmzp075PQOBqVU4FW/ZrPZwK2eb+dR7TOO/KqDvXYU5Vbn\nS/uzftR4pTe8glPWO80UAwWjLH5T3RL8LtrlUBDdG65QKNhNe1G9E+oj5vHiiy86B7Z+b2dA+2C3\nCwNbtD7Dsqvh4Smq4AoHGx1YdEaJyhT6QLDTVVtbG6RZpykqrfbBEz6Iyp0F6cI5nEa7cA5naD2V\nOzvVXtPpdJCuqIM+XCsod+YVPsEInynrtOogbu+LHVx2FDw8z3MKIrsQ04E2nJ9s7+EaTtR+6H0A\nnPSEa7e2Zz3ZBXo4/+i0h08U7Lxk71c4D5VLp+3aDhD2q+1W/wd2YWgTDp7h9IZPeKLcRuWRcsdj\n2KF9DIaXRdUM7ABlp8n2q9Mb5dROZ7k8bP9++ERJH392+vWrTSKRIJPJBOnMZDLU19f3y6d28Ihy\nuaO0lssP4ZPmbDZLR0eHExAbGhrY0l0DQFN9hs7OTt544w2nrLPfR+UFPY0f7/RZcPNY2SU+64H/\nBVxBqH0POBW4Hr/bNnvssQcdHR0UCoWgXX7r1q32NYvNEduPvKAxY8aMyLNfPdlnEuHCYCjYB1dU\nEEyn09TX1/c7o7WnkVizyOfzbNu2jaampuA/sQ8k7c4+wO3AUCwW6evrc2p3cZ6lAU4AtAu4urq6\nfv9DuPZnn4zsiGw2y5tvvsnUqVPJZMJZedcRrnWEC1jtvru7O3AeFRwGS9QJkD2lUilqa2tJp9P9\nppHeFGnXNsKBwH5fLBbp7u52CuA4evDagUK7jArS9pTJZIL3I41CoUBvby91dXV4nkehUOBP69cA\n0FiXJpPJsPvuu/drBcpms5HltV1WHHzwwWV/t5JuEd+3P0ydOpWJEyeybNkyDj/8cACeeeYZTj31\nVL3KXyK2ERkmm5qaombvEH0w2/3kB2pPDddKxhq5XI41a9Ywe/bsINPbVfNKKHctoJxz/Vqtay2F\nQoGOjo6q95jSj3XWhf9gCNciBjoJi2opsMnn82zZsoXm5uZyHZNGDbp2mU6nd7xyCLt2oFtSosqO\nkZCHdxXZbJbly5cze/bsoHWns9fvTddQm6KmpobW1tYdbMVg59cQzoyKcuErr7zCF7/4xdxjjz2W\nrq2tZfHixfzLv/wLX/nKV3j55ZfZuHEjixYt0qvfH7GJ4JpRHDecZbNZXnvtNebMmUNNTU1F2xpL\nDMcBo4PaaGM0Fx47ewF6Z8jlcqxdu5YJEyaM+mBUCZ7nSblRBjuv9ZZueq1ND/6Yt0/+wSnrhxSM\neoHMl7/8ZaercEtLC6effnpQKJ177rlMmzaNRx99lNbWVn71q1/pNsL/Al6K2G5wahhHMNKRdzQX\nOHEiPgziwkV8GMSFS5SPvrwORpX3dKw0GP0aWPLlL39Zf24H6qdMmTL1G9/4RlA39jyPE044gRNO\nOMH+7hPAP5bZbtCZvVgsVpwZdLV6V3cNHamID4O4cBEfBnHhEuVDN9ONq6m8Fm2V9UMKRl8CHsMf\nAuhd/MFQa4DT8TshvFmaNwE/8OwPbAUeAR4I/6hFcM1IKVVxZpAzHBfxYRAXLuL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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import numpy as np\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "# plt.xkcd()\n", "n = 256\n", "a = [[1.0/(i - j + 0.5) for i in range(n)] for j in range(n)]\n", "a = np.array(a)\n", "u, s, v = np.linalg.svd(a)\n", "plt.plot(s)\n", "plt.title('Singular values decay for a Cauchy-Hilbert matrix')\n", "plt.tight_layout()\n", "s[5] - np.pi" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "What to do? \n", "\n", "The idea is to break the matrix intro blocks \n", "\n", "$$\n", " A = \\begin{bmatrix}\n", " A_{11} & A_{12} \\\\\n", " A_{21} & A_{22}\n", " \\end{bmatrix}\n", "$$\n", "\n", "and the blocks $A_{12}$ and $A_{21}$ will be of low-rank! Let us try that.." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Block-low rank matrices\n", "\n", "Surprisingly many matrices in PDEs can be well approximated by block-low-rank (other names: hierarchical, mosaic-skeleton) matrices.\n", "\n", "They have linear storage, but algorithms are not very **simple**" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Take home message\n", "- Matrix rank definition\n", "- Skeleton approximation and dyadic representation of a rank-$r$ matrix\n", "- Singular value decomposition and Eckart-Young theorem\n", "- Three applications of SVD" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Next lecture\n", "- Linear systems\n", "- Inverse matrix\n", "- Condition number\n", "- Linear least squares\n", "- Pseudoinverse" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Next lecture\n", "- Think of course projects" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "##### Questions?" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true, "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "from IPython.core.display import HTML\n", "def css_styling():\n", " styles = open(\"./styles/custom.css\", \"r\").read()\n", " return HTML(styles)\n", "css_styling()" ] } ], "metadata": { "anaconda-cloud": {}, "celltoolbar": "Slideshow", "kernelspec": { "display_name": "Python [conda env:p3]", "language": "python", "name": "conda-env-p3-py" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.0" }, "latex_envs": { "LaTeX_envs_menu_present": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": false, "user_envs_cfg": false }, "nav_menu": {}, "toc": { "navigate_menu": true, "number_sections": false, "sideBar": true, "threshold": 6, "toc_cell": false, "toc_section_display": "block", "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 1 }