{ "cells": [ { "cell_type": "markdown", "id": "ba50d1af", "metadata": {}, "source": [] }, { "cell_type": "code", "execution_count": 1, "id": "c91e58ff", "metadata": { "load": "myst_code_init.py", "tags": [ "remove-cell" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Loading pyMOR defaults from file /builds/pymor/pymor/docs/source/pymor_defaults.py\n" ] } ], "source": [ "import warnings\n", "\n", "import matplotlib as mpl\n", "from IPython import get_ipython\n", "\n", "import pymor.tools.random\n", "\n", "ip = get_ipython()\n", "if ip is not None:\n", " ip.run_line_magic('matplotlib', 'inline')\n", "\n", "warnings.filterwarnings('ignore', category=UserWarning, module='torch')\n", "\n", "pymor.tools.random._default_random_state = None\n", "\n", "mpl.rcParams['figure.facecolor'] = (1.0, 1.0, 1.0, 0.0)\n" ] }, { "cell_type": "markdown", "id": "1fd4bf43", "metadata": {}, "source": [ "# Tutorial: Linear time-invariant systems\n", "\n", "In this tutorial,\n", "we discuss finite-dimensional, continuous-time, linear time-invariant (LTI)\n", "systems of the form\n", "\n", "```{math}\n", "\\begin{align}\n", " E \\dot{x}(t) & = A x(t) + B u(t), \\\\\n", " y(t) & = C x(t) + D u(t).\n", "\\end{align}\n", "```\n", "\n", "where\n", "{math}`u` is the input,\n", "{math}`x` the state, and\n", "{math}`y` the output of the system,\n", "and {math}`A, B, C, D, E` are matrices of appropriate dimensions\n", "(more details can be found in {cite}`A05`).\n", "In pyMOR, these models are captured by `LTIModels`,\n", "which contain the matrices {math}`A, B, C, D, E` as `Operators`.\n", "We start by building an `LTIModel` and then demonstrate some of its properties,\n", "using a discretized heat equation as the example.\n", "\n", "We focus on a non-parametric example,\n", "but parametric LTI systems can be handled similarly\n", "by constructing {math}`A, B, C, D, E` as parametric `Operators` and\n", "passing `parameter_values` via the `mu` argument to the methods of the\n", "`LTIModel`.\n", "\n", "::: {note}\n", "\n", "Discrete-time LTI systems can be constructed by passing positive values for the\n", "`sampling_time` to any constructor of an `LTIModel`.\n", "\n", ":::\n", "\n", "## Building a model\n", "\n", "We consider the following one-dimensional heat equation over {math}`(0, 1)` with\n", "two inputs {math}`u_1, u_2` and three outputs {math}`y_1, y_2, y_2`:\n", "\n", "```{math}\n", "\\begin{align}\n", " \\partial_t T(\\xi, t) & = \\partial_{\\xi \\xi} T(\\xi, t) + u_1(t),\n", " & 0 < \\xi < 1,\\ t > 0, \\\\\n", " -\\partial_\\xi T(0, t) & = -T(0, t) + u_2(t),\n", " & t > 0, \\\\\n", " \\partial_\\xi T(1, t) & = -T(1, t),\n", " & t > 0, \\\\\n", " y_k(t) & = 3 \\int_{\\frac{k - 1}{3}}^{\\frac{k}{3}} T(\\xi, t) \\, \\mathrm{d}\\xi,\n", " & t > 0,\\ k = 1, 2, 3.\n", "\\end{align}\n", "```\n", "\n", "There are many ways of building an `LTIModel`.\n", "Here, we show how to build one from custom matrices,\n", "instead of using a discretizer as in {doc}`tutorial_builtin_discretizer`\n", "(and the `to_lti` method of\n", "`InstationaryModel` to obtain an `LTIModel`).\n", "In particular, we will use the\n", "`from_matrices` method of `LTIModel`,\n", "which instantiates an `LTIModel` from NumPy or SciPy matrices.\n", "\n", "First, we do the necessary imports and some matplotlib style choices." ] }, { "cell_type": "code", "execution_count": 2, "id": "22552cd0", "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import scipy.sparse as sps\n", "from pymor.models.iosys import LTIModel\n", "\n", "plt.rcParams['axes.grid'] = True" ] }, { "cell_type": "markdown", "id": "8857cb53", "metadata": {}, "source": [ "Next, we can assemble the matrices based on a centered finite difference\n", "approximation using standard methods of NumPy and SciPy." ] }, { "cell_type": "code", "execution_count": 3, "id": "6c11f0c1", "metadata": { "load": "heat_equation.py" }, "outputs": [], "source": [ "import numpy as np\n", "import scipy.sparse as sps\n", "\n", "k = 50\n", "n = 2 * k + 1\n", "\n", "E = sps.eye(n, format='lil')\n", "E[0, 0] = E[-1, -1] = 0.5\n", "E = E.tocsc()\n", "\n", "d0 = n * [-2 * (n - 1)**2]\n", "d1 = (n - 1) * [(n - 1)**2]\n", "A = sps.diags([d1, d0, d1], [-1, 0, 1], format='lil')\n", "A[0, 0] = A[-1, -1] = -n * (n - 1)\n", "A = A.tocsc()\n", "\n", "B = np.zeros((n, 2))\n", "B[:, 0] = 1\n", "B[0, 0] = B[-1, 0] = 0.5\n", "B[0, 1] = n - 1\n", "\n", "C = np.zeros((3, n))\n", "C[0, :n//3] = C[1, n//3:2*n//3] = C[2, 2*n//3:] = 1\n", "C /= C.sum(axis=1)[:, np.newaxis]\n" ] }, { "cell_type": "markdown", "id": "c2a877e4", "metadata": {}, "source": [ "Then, we can create an `LTIModel` from NumPy and SciPy matrices `A`, `B`, `C`,\n", "`E`." ] }, { "cell_type": "code", "execution_count": 4, "id": "993a05fc", "metadata": {}, "outputs": [], "source": [ "fom = LTIModel.from_matrices(A, B, C, E=E)" ] }, { "cell_type": "markdown", "id": "5c0356a9", "metadata": {}, "source": [ "We can take a look at the internal representation of the `LTIModel` `fom`." ] }, { "cell_type": "code", "execution_count": 5, "id": "284b8ba9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "LTIModel(\n", " NumpyMatrixOperator(<101x101 sparse, 301 nnz>, source_id='STATE', range_id='STATE'),\n", " NumpyMatrixOperator(<101x2 dense>, range_id='STATE'),\n", " NumpyMatrixOperator(<3x101 dense>, source_id='STATE'),\n", " D=ZeroOperator(NumpyVectorSpace(3), NumpyVectorSpace(2)),\n", " E=NumpyMatrixOperator(<101x101 sparse, 101 nnz>, source_id='STATE', range_id='STATE'),\n", " presets={})" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fom" ] }, { "cell_type": "markdown", "id": "a97f75ec", "metadata": {}, "source": [ "From this, we see that the matrices were wrapped in `NumpyMatrixOperators`,\n", "while the default value was chosen for the {math}`D` matrix\n", "(`ZeroOperator`).\n", "The operators in an `LTIModel` can be accessed via its attributes, e.g.,\n", "`fom.A` is the `Operator` representing the {math}`A` matrix.\n", "\n", "We can also see some basic information from `fom`'s string representation" ] }, { "cell_type": "code", "execution_count": 6, "id": "687d0be8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "LTIModel\n", " class: LTIModel\n", " number of equations: 101\n", " number of inputs: 2\n", " number of outputs: 3\n", " continuous-time\n", " linear time-invariant\n", " solution_space: NumpyVectorSpace(101, id='STATE')\n" ] } ], "source": [ "print(fom)" ] }, { "cell_type": "markdown", "id": "76cda8d0", "metadata": {}, "source": [ "which gives the dimensions of the underlying system more directly,\n", "together with some of its properties.\n", "\n", "## Time-domain simulation\n", "\n", "The `solve` and `output` methods can be used to respectively compute the\n", "solution and output trajectories.\n", "For this, it is necessary to set the final time and the time-stepper.\n", "This could have been done in the `from_matrices` call.\n", "Instead of creating a new model using `from_matrices`,\n", "we can redefine `fom` using its `with_` method." ] }, { "cell_type": "code", "execution_count": 7, "id": "6f87fd6a", "metadata": {}, "outputs": [], "source": [ "from pymor.algorithms.timestepping import ImplicitEulerTimeStepper\n", "fom = fom.with_(T=4, time_stepper=ImplicitEulerTimeStepper(200))" ] }, { "cell_type": "markdown", "id": "a06eadbd", "metadata": {}, "source": [ "With this done, we can compute the output for some given input and plot it." ] }, { "cell_type": "code", "execution_count": 8, "id": "317f938e", "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "722d60b530a047e0a965d35b064120e6", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Accordion(children=(HTML(value='', layout=Layout(height='16em', width='100%')),), titles=('Log Output',))" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "Y = fom.output(input='[sin(4 * t[0]), sin(6 * t[0])]')\n", "fig, ax = plt.subplots()\n", "for i, y in enumerate(Y.T):\n", " ax.plot(np.linspace(0, fom.T, fom.time_stepper.nt + 1), y, label=f'$y_{i+1}(t)$')\n", "_ = ax.set(xlabel='$t$', ylabel='$y(t)$', title='Output')\n", "_ = ax.legend()" ] }, { "cell_type": "markdown", "id": "25ba6283", "metadata": {}, "source": [ "Additionally, there are the `impulse_resp` and `step_resp` methods for computing\n", "the impulse and step responses, respectively.\n", "\n", "Impulse response for continuous-time LTI systems is given by\n", "\n", "```{math}\n", "h(t) = C e^{t E^{-1} A} E^{-1} B + D \\delta(t),\n", "```\n", "\n", "where {math}`\\delta` is the Dirac function.\n", "\n", "For computations, we ignore the {math}`D` term and compute the first part by\n", "integrating the ODE system\n", "\n", "```{math}\n", "E \\dot{x}_i(t) = A x_i(t),\\ x_i(0) = E^{-1} B e_i\n", "```\n", "\n", "for canonical basis vectors {math}`e_i` to get the {math}`i`-th column of\n", "{math}`h_i(t) = C x_i(t)`." ] }, { "cell_type": "code", "execution_count": 9, "id": "f40de364", "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "d1127ce0529e4ce78eba06bc4574065e", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Accordion(children=(HTML(value='', layout=Layout(height='16em', width='100%')),), titles=('Log Output',))" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "y_impulse = fom.impulse_resp()\n", "fig, ax = plt.subplots(fom.dim_output, fom.dim_input, sharex=True, constrained_layout=True)\n", "for i in range(fom.dim_output):\n", " for j in range(fom.dim_input):\n", " ax[i, j].plot(np.linspace(0, fom.T, y_impulse.shape[0]), y_impulse[:, i, j])\n", "for i in range(fom.dim_output):\n", " ax[i, 0].set_title(f'Output {i + 1}', loc='left', rotation='vertical', x=-0.2, y=0.2)\n", "for j in range(fom.dim_input):\n", " ax[0, j].set_title(f'Input {j + 1}')\n", " ax[-1, j].set_xlabel('Time')\n", "_ = fig.suptitle('Impulse response')" ] }, { "cell_type": "markdown", "id": "d7312c7f", "metadata": {}, "source": [ "Step response for continuous-time LTI systems is the output corresponding to the\n", "zero initial condition and inputs {math}`u_i(t) = e_i`." ] }, { "cell_type": "code", "execution_count": 10, "id": "d7676f3a", "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "c7727358496a4f0ca535e329ae0295eb", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Accordion(children=(HTML(value='', layout=Layout(height='16em', width='100%')),), titles=('Log Output',))" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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FUiAcceyvC1Je20h5TSPltUHKaxqprA9SVR+iqj5EdcPB11UNIarqg1RHt+uC4XRXgWy/jyy/4fcZfjNCoUbyc3PJ8vvw+4wsX/Q9n0XL+Q7sO/Q5ut8f3TbD5zN8Bj4zzA6+9hnR7eg+n2GxcrRfpq1zmoER2/ZeR//z3ie6P/qeGYTDYVYuX96ZP+abgLudc/fhxXEdcC5wNfCTFspfjXdV8iTnXDC6b3NnBiiZJ+xgb00jtcEG9tcFqawPsb8u6L2OPg5sR9u0mgYvWaxpDFHbGE5BcpcaWdH2KeD3EfB7bZH32siKbsfaiarK/QzoX0SW34fPDrZvsfdjr/0+rw3zWwvvN9vv9xFt76JtD7G26NB2KbbP5/OSu5baK7NmbVW0vEUPiLWRB8/ftHz0fd/BcwFEwmHeXbW8c372nXJWkV6gIRRmV0Udm6tgweoS9tWGKKlsoLSqnn01jeyraaSiNsi+2kb21wVJxSyE2Vk+8rL99AlEH9kHn3Oj+/Jir5uUywn4yPb7yM7yGtHsLO+R4/cRyDr4XnbT103KB/xeUhYTDAZ5+umnOeec0zKuw7p/+1udcu7o1cZjgNti+5xzETNbCJzYymEfBhYBvzWz84E9wKPA7c65930LMbMcIKfJrgLw6hUMBpsXb1GsXLzle4veVu+GUISSynr2VDWwt6bRe1R77VZsu6za21dRlwWvv5CSz80N+MjPziIv209+tp+8nKxoO+UjJ8trq3KyfOQG/ORkea9zAj5ys5pu+6NlvHbqQHLoNy8x9B1MEANNEsgs36HtWFuCwSDFxcXMmzcr49o433aXcHsQDyWUkpGcc+yraWR7eV30UXvgeWdFPaVV9ZTXxv5HyoJV8d0WKcjNon9eNv3zs+mfF6BfnwAFuVn0zfGeY4/Ydt+cLApzA/SNvs7O0ji5XmwQ4AdKmu0vAaa1cswE4AzgEeAcYBLwOyAAfK+F8rcAtzbfuWDBAvLy8hIKtri4OKHyvUVPqHfEQWUj7G2AikajogHKo88VjUZFI1QFE7+t2cfv6JMFffyQl9X0NfTJct6zH/pkQY7fkeODHH/04YNsP3gX3Brb/zAHBKOPumb1i+6qe99BqdcTft+dId5619bWxn1OJZTSaznn2FPdwIbSGjaWVbOhtIZNZdVsiyaO9cFIu+cI+I2+/ghjhhQxtDCXIYU5DCnIZVDfHAbkByjKy2ZAfjb987IpygsQ8CshlJTy4fWf/Ez0iuQyMxuJN6inpYTyNrw+mjEFwPb58+cnNG2Qd+VmXsZduelO9Y5EHDv317Npbw1b99WxdW8tW/fVsmVfLdvK6+Jqv7KzfAwpyGFQ32wG5mczqK/XXg3Mj23nUJjjY9XS1/jw2WeSm5PdBTXrHrrb77urJFrvysrKuM+thFJ6hT1VDazeVcmaXZWsK6liw54aNpZWU9UQavUYMxhakMuo/n2ijzxG9e/D8KI+DC3MYWhBLvkBeOaZZzjnnOMzqtGRTlEGhIGhzfYPBXa3cswuINjs9vYaYJiZZTvnDrkU5JxrABpi27Hbf4FAIOF/v8kc0xt0db2dc+yurGddSTXvlVTx7u4q1pVWs76kiprG1vtW+33GiKJcRvTrw4iiPgzrl8uIfrkM7xd9XdSH/nmBdm8BB4NBNq+A3Jxs/b4zSLz1TuRno4RSehTnvG/tb20tZ9WOygNJ5J6qhhbL+wxGD8hjwqB8Jg7uy4TBfRkzIJY45pKT5W/z83pLfypJP+dco5ktA+YCTwKYmS+6fWcrh70KXGpmPudc7JLUFGBX82RSuj/nHNvL61i5fT8rd1Tw9vb9rNqxn8r6lr/4BvzG2IH5jBuYx9iB+YyNPQ/IY2T/ProjIt2KEkrp1uoaw7y9Yz9vbS3nza3lvLW1gtIWkkczGD8on+nDC5k2tIBJQ7zkcezAPHIDbSeNIl3oDuABM1sKLMGbNigfiI36fhDY4Zy7JVr+98AXgP8zs98Ak4FvAL/u4rglCfXBMG9trWDJpn0s21rO29srmvTNPsjvM8YNzGPqsAImDylg6rACpgzty9iB+UoapcdQQindSmMowvJtFby6vozXNpSxfFsFwfChw6ezfMZhIwqZObIfh40o5LDhhUwdVkBetv45S/fmnHvczAYD38eb2Hw5cLZzLjZQZwzemIRY+W1mdhbwS2Al3jyU/wfc3pVxS3yqG0K8sXkfSzZ5j5Xb399+BfzGtGGFzBzVjyNG9mPGyH5MHtq33bslIt2d/gJLWjnneK+0mufXlvLqhr28sWnf++ZkHFKQw6wx/Tl6TBGzxvZnxoh+9MlW4ys9k3PuTlq5xe2cm9PCvkXACZ0cliQhEnGs3lXJS+/t4cV397BsSzmhZvMxDi3MYfb4gRw3rj9HjS5i6rACJY/SKymhlC4XDEd4Y9M+Fq4pZeGaErbuO3RagoH52Zw4cSAnTxrESRMHMmZAXtxzi4mIdKaGUJhX15fx7Krd/G/tHsqqD+2CM2ZAHsePH8Ds8QM4fvxARg/oo/ZLMoISSukSoXCE1zbs5akVO3nund2HdELPzvJx4oSBfGDKYE6aOJCpQwsOrB4gIpJutY0hnl+7h2ff2c3za0upbjJ7RF62n5MmDuS0KYP5wJTBjB2Yn8ZIRdJHCaV0GuccS7eU86/lO3n67V3srTk4KHVgfjZnTBvC3OlDOXXyIPJz9E9RRLqPcMTx+sa9PPHmDp5ZtYvaJlP4DC3M4ezDhzH/8GEcO66/bmGLoIRSOkFZdQN/X7adx9/YxsaymgP7B+Rnc87MYZx3xAiOHTcAv65Cikg3s3lvDU8s382Tb+1g1/76A/tHD+jDOTOGc/aMYRw5qkh3UUSa6ZSE0syuB/6fc25CZ5xfuh/nHK+u38tjS7ayYPXuAyMb87P9nD1jOOcdOZyTJw3SFBgi0u2EI47/ri3l96t9rF306oH9hblZfOjIEXx01khmjemvvpAibeisK5RFwNhOOrd0Iw2hMP9cvpM/vbyRdSXVB/YfObqITxw3mvOOHKHb2SLSLVXUNvLnN7bx8Otb2F5eB/gwgzlTBnPRsaM5Y9oQzWMrEqe4/9Kb2ZgEzluUeCjSk1TUNvLI4q3c/9rmA6vU9M3J4sJZI7nkuDEcNiK+dYNFRLpaaVU997y8iYdf33JgecOiPgFmFTXwzUs+wMSh/dIcoUjPk8ilo82Aa69QlCVQVnqQ8tpG7lu0gQde23ygk/qwwlyuPmUcl8weQ2Fu5q2JKiI9w/byWv7w4kYeX7qNxpA3f/y0YQVcfcp4PnjYYP5X/BxjBuSlOUqRnimRhLIBWA08GkfZucBZSUUk3VJlXZCnt/r4xh0vU9PgJZLThhXw2dMmcO7MEWRnqW+kiHRPJZX1/Grhe/x16bYDE4/PGlPEF86YxOlTh2BmBIPvXxJRROKXSEL5JtDXOfeL9gqaWS5KKHuFxlCEh17fwq//u479dT4gzPThhdw0bwpnTh+iTuoi0m1V1gf5w4sbuOeVTdQHvSuSJ08ayPWnT+LECQPVfomkUCIJ5RLgC2aW75yraaesRR/SQznnKF5dwm3PrGVTdOqfYX0c3zz/KM49YqSmzBCRbisccTy2ZCu/WPAu5bXelcdjxvbn6x+cxnHjBqQ5OpHeKZGE8vfAciCeTnK/Bh5KJiBJv01lNXz7yVW8sr4MgEF9c/jy3Inklazk7MOHKpkUkW7rza3lfOefq1i1oxKAiYPzufnsacw/bKiuSIp0orgTSufcOmBdnGUrgcpkg5L0aAiFueuFjfz2hfU0hiJkZ/n49Knj+dycSeT4HE8/vTLdIYqItGh/bZAfPb2avyzdDkBBThY3zZ/CFSeMJUvz34p0Ok0QKAAs3byPm/++ko17vNvbp04exA8vmHFgXVp1WBeR7qp4dQnf/MfblEanMPvYMaP42tnTGFyQk+bIRDKHEsoM1xAK86uF7/GHFzcQcd7t7e+cdxjnHTFct4dEpFsrr2nku0+9wz+X7wRgwuB8fvrRIzhW/SRFupwSygy2ZlclX358OWt3VwHw0Vmj+M55h9Gvj+aSFJHu7bUNZdz45+WUVjXgM/j0Bybw5TOnaGUbkTRRQpmBnHM8vHgrP3hqNY3hCAPys/nxR2Zy9oxh6Q5NRKRNoXCEXy18j9++sB7nvEE3v/j4URw1uijdoYlktG6XUJrZ9cBXgWHACuCLzrklcRx3CfAY8E/n3AWdGmQPVtMQ4pYn3uZfK7xbRHOnDeEnHz1CfY1EpNvbWVHHFx97i2VbygG45LjRfOe8w8jL7nZ/ykQyTlL/F0bX9d7jnKtr5f0+wGDn3NYEz3sxcAdwHbAYuBF4zsymOudK2zhuHPBz4OVEPi/TrCup4nMPL2PDnhr8PuOWD07jmlPGq6+kiHR7izfu5fOPvMnemkYKcrL48YUzOe/IEekOS0Sikp1LYRPwkTbe/3C0TKJuAu52zt3nnFuNl1jWAle3doCZ+YFHgFuBjUl8ZkZYuLqEC377Khv21DCsMJfHP3MC1546QcmkiHRrzjkeen0Ll/1pMXtrGjlseCFP33CqkkmRbibZ+wTtZSEBIJLQCc2ygWOA22L7nHMRM1sInNjGod8BSp1z95jZqXF8Tg7Q9P5uAXjT4sQzNU6sTE+ZRsc5x32vbeEnz63DOThxwgB++fEjGJifnVAdelq9U0X1Vr3jKS+dozEU4dZ/reKxJdsAOO/IEfz0o0fQJ1sDb0S6m7gTSjMrBIqa7BoYvfXdXBFwCbArwVgGAX6gpNn+EmBaKzGdAlwDHJXA59yCdzXzEAsWLCAvLy/ukxQXFyfwkekRjsBfN/lYVOpdiD5pSISPDS5l8YsLkz5nT6h3Z1C9M0u89a6tre3kSDJXdUOIzz28jJffK8MMvnb2ND77Ad1VEemuErlC+WW8q4EADvhV9NESA76VdFRxMLMCvOUdP+2cK0vg0Nvw+mnGFADb58+fT2FhYbsHB4NBiouLmTdvHoFA951ep7YxxBceW8Gi0r34DL5+9lSuOnFM0o1xT6l3qqneqndbKiu1IFhn2FPVwNX3v8HbO/bTJ+Dnt5cdzRnThqY7LBFpQyIJ5QKgGi9Z/CneiOo3m5VxQA2wzDm3NMFYyoAw0LzVGArsbqH8RGAc8FSTJMkHYGYhYKpzbkPzg5xzDUBDbDt2bCAQSOgPZ6Llu9L+2iCfeuBN3txaQZ+AnzsvPZq501PTGHfnencm1TuzxFvvZH42msmibVv21nDlvUvYsreWAfnZ3HvVcZoSSKQHSGQt70XAIgAzyweecM69napAnHONZrYMmAs8Gf0cX3T7zhYOWQvMbLbvh3hXHG8AtqUqtp6ktKqeK+9ZwtrdVfTrE+C+Tx3HrDH90x2WiKCZLNrzXkkVn7h7MWXVDYwe0IcHrz6e8YPy0x2WiMQhqUE5zrnvpTqQqDuAB8xsKbAEr7HNB+4DMLMHgR3OuVucc/XAqqYHm1lFNL5D9meK7eW1XPanxWzZW8vgghweumY204a1fxtfRLrMgZksAMzsOuBcvJksftLSAc1msjiVQ/uy9xpNk8npwwt54OrjGFKQm+6wRCROyc5D+Z32S+Gccz9I5LzOucfNbDDwfbzbQcuBs51zsYE6Y0hw9Him2L2/nkvvXszWfbWMHtCHR645gTED4x9kJCKdqytmsujoLBaxsk2fu8J7pdVcce9S9tY0Mn1YAQ9cNYv+uf4ujUEzG6jemaAzZ7JIdtqg77bxnsPrZ+mAhBJKAOfcnbR8ixvn3Jx2jr0q0c/rDUqr6rn07tfZuq+WMQPyePyzJzC8X590hyUih+qKmSxSMosFdN0I/9218JvVfqqDxqh8xxWjyln0QvIzUXSUZjbILKp32xKZySLZW97vmxA92t9xLHA98AHgg8mcWxKzt7qBy+5ezMayGkYW9eHRTx+vZFKkF0hyJosOzWIBXTvCf2dFHR//4xKqgw0cNryAB646lqK89AwC08wGqncm6MyZLFK2AKpzLoK3Os5XzOwR4DfApak6v7xfZX2QK+5Zwnul1QwtzOHRTx/PqP66zS3STXX6TBapmsUi2WMSUV7TyNUPvklJVQNThvblkWtPoH9+dqd9Xrw0s0FmUb3bLxevZJdebM9LwDmddG7BW0Hicw8vY/WuSgb1zeaRa09g7ECNhhTprpxzjUBsJgvgkJksFrVwSGwmi6OaPP4FPB993WNnsqgPhrn2waVs2FPD8H65PHD17G6RTIpI8lJ2hbKZY9HgmU7jnOPrT6zk1fV7ycv2c/+nZjNpSN90hyUi7cv4mSxC4QhfePQtlm0ppzA3iweunq1uOiK9QLKjvK9s5a0ivP6TFwJ/SjImaccvi9fxxJs78PuM3142ixkj+6U7JBGJg2aygB89vYaFa0rIyfJxz1XHMWVoQbpDEpEUSPYK5f1tvFeGN5/a95M8t7ThL29s49f/Ww/Ajy6YwelTh6Q5IhFJRCbPZPGXpdu479XNAPzq4qM4btyA9AYkIimTbEI5voV9Dih3zlV1IB5pw7It5XzzSW9xoi+eMYlLZo9Jc0QiIvFZtqWcb/3Du1P/5TOn8MGZw9MckYikUrLTBm1JdSDSttLKej738DKCYcc5M4dx07wp6Q5JRCQue6oa+NzDy2gMR/jgjGF88YxJ6Q5JRFKsQ4NyzGwG3mjucdFdm4FnUrnGt3gjuj//yJuUVjUweUhffvqxI2kyjYiISLcVjji+/PjyA+3Xzy86Ep9P7ZdIb5PsoJwc4A/AFXir4sQ6kfuA26LzUF4bnSZDOuiH/1nN0i3lFORk8YcrjqFvTmcNzhcRSa3fPb+eV9aX0Sfg53eXzSJf7ZdIr5TsPJS3A1cCvwemA7l468dOB+4CLgd+mooAM90Tb27nwUVeD4NfXXIUEwZreiAR6RmWbNrHLxeuA+AHF8xgskZ0i/RayX5VvBx4yDn3hWb73wWuN7PCaJkbOxBbxttcVsO3n/Q6sX9p7mTmTm++wIaISPdU3RDipr8sJ+Lgwlkj+dgxo9Idkoh0omSvUAaA19t4/zU6b9L0jBAMR7jhz29R0xhm9vgB3DB3crpDEhGJ24/+s5rt5XWMLOrD9z58eLrDEZFOlmxC+RxwVhvvnw0sSPLcgjd5+Yrt+ynMzeJXFx+FX53YRaSHeH5tKY8t8VaG/PlFR1KQm3lrJYtkmmSvIn4b+IuZPQH8Flgf3T8ZuB4YC1xsZofMWuuc25dsoJnktQ1l/P7FDQD85KNHMKJIy5KJSM9QVR/k60+sBODqk8dz4sSBaY5IRLpCsgnlmujzTOD8Zu/FLqWtbuE4f5KflzEqahu56fEVOAcXHzuaczT5r4j0IHcUr6OksoGxA/O4+eyp6Q5HRLpIsgnl9/FWxpEU++F/1rC7sp7xg/L5znmHpTscEZG4rdqxnwde2wzAD86fQW5A1xBEMkWyK+V8N8VxCPDSuj38bdl2zODnFx2h+dpEpMcIRxzf/MfbRBycd+QIPjBlcLpDEpEulNSgHDO718yOb+P92WZ2b/JhZZ6ahhC3POEtMPTJE8dxzNgB7RwhItJ9/HXpNlZs309BThbfPnd6usMRkS6W7Cjvq4CJbbw/HvhkkufOSD977l12VHhTbHz1LPU7EpGeo7YxxB3F3gTmN5w5mSGFuWmOSES6WrIJZXtGAHWddO5eZ9mWfTywaDMAt104U7e6RaRHueflTZRWNTBmQB5Xnjgu3eGISBrEnbmY2fkcOqL7M2Z2ZgtFi4AzgTc6FlpmaAxF+Nrf38Y5+Ngxo9TvSER6lLLqBu6KTnP21bOmkp3VWdcpRKQ7S+RS2GHARdHXDjgeOKZZGQfUAC8BN3U4ugzwwGubWV9azaC+2XxL/Y5EpIf59X/fo6YxzJGj+nGupjkTyVhxJ5TOuduA2wDMLAJc45x7tLMCywSlVfX833/fA+Dms6dRlJed5ohEROK3e389jy3ZCsDXPzgdn1b0EslYyU4bpHsaKfDTZ9+luiHEkaP68bFZo9IdjohIQv708kaCYcfs8QO0Io5IhlNimCZvbS3nb8u2A/DdDx+ub/Yi0qOU1zTyaPTq5OfntDXph4hkgqSuUEZvebe7Uo5zTssktCAScXz3X+8A3kCco8f0T3NEIiKJuf+1zdQ2hjl8RCGnaTChSMZL5dKLfmAccAHwLvDvZE5sZtcDXwWGASuALzrnlrRS9tPAlcCM6K5lwDdaK99d/O3N7azYvp++OVla61ZEepzqhhD3R5dY/PycSZjpDotIpkv50otmNhx4HViX6HnN7GLgDuA6YDFwI/CcmU11zpW2cMgc4DHgNaAe+BqwwMwOd87tSPTzu0JdY5hfLHgXgC/NncSQAk0ALCI9yxNvbmd/XZAJg/I5e8awdIcjIt1AyvtQOud2AXcB307i8JuAu51z9znnVuMllrXA1a181mXOud8555Y759YC1+LVaW5y0Xe+BxZtpqSygZFFffjkSePSHY6ISEKcczy62Os7eeWJY/Gr/7eIkPwt7/bU4C2/GDczy8ab1/K22D7nXMTMFgInxnmaPCAA7Gvjc3KAnCa7CgCCwSDBYLDdD4iViadsc5V1QX7/wnoAbjhjIj4XIRiMJHyedOhIvXsy1Vv1jqd8Inp6t57l2ypYu7uKnCwfHzlas1OIiCflCaWZzQC+ROK3vAfh9cMsaba/BJgW5zluB3YCC9socwtwa/OdCxYsIC8vL86PgeLi4rjLxvx7q4/9dT6G9XEEdi7n6V3LEz5HuiVT795A9c4s8da7trY2ofP2hm49sXknzz1iOP3yAukIQUS6oWRHeW+i5VHeRUA/vNvUFyQdVRLM7OvAJcAc51x9G0Vvw2vQYwqA7fPnz6ewsLDdzwkGgxQXFzNv3jwCgfgb09KqBr7+y5eBCLd+5GjOnD4k7mO7g2Tr3dOp3qp3WyorKxP9iAPdegDM7DrgXLxuPT9pXtg5d1nTbTO7FvgoXreeBxP98I6qrA/y1IpdAFw6e0xXf7yIdGPJXqF8kfcnlA4oBzYAf3bOtXrbuRVlQBgY2mz/UGB3Wwea2VeArwNnOudWtlXWOdcANDQ5FoBAIJDQH85Ey9/10rvUBSMcPaaIs2eO6LGjIhOtd2+hemeWeOudyM+mK7r1dLRLT6xs0+emnli6lbpgmEmD8zliRN9e1SVC3TxU70zQmd16kh3lfVUyx7VzzkYzW4b3zftJADOLDbC5s7XjzOxm4JvAWc65pamOKxW27q09cJvoa2dP67HJpIh0SFd060lJlx5o+bb/n1b6AWNmfiXPPPNMQufrKdTNI7Oo3m1LpFtPh/pQmlk+UAhUOeeqO3KuqDuAB8xsKbAEr39RPhC7PfQgsMM5d0t0+2t4c2JeCmw2s9j8FdUpiicl7nz+PUIRxwemDOaECVqeTEQSF2e3ng516YHWb/tv3lvD9kWv4vcZX7tkLgPzs5OrSDelbh6qdybozG49CSeUZjYOuBmv38+oJvt3AE8BP3fObUr0vADOucfNbDBekjgMWA6c7ZyLfaMfAzQdFv05IBv4W7NTfQ/4bjIxpNqOijqeeNPrO3/jmZPTHI2IpFGnd+tJVZeelo559p09AJw8aRDDivITOldPom4emUX1br9cvBJKKM3sfOAhoC+wGS+BrML7FnwEXoJ3pZld7pz7ZyLnjnHO3Ukrt7idc3OabY9L5jO60h9f3EAo4jhxwkBmaYlFkYzV07v1/HulNxjnQ0cMT1cIItKNxZ1QmtlhwOPARuCzzrmXWyhzKt6k5n82s2Oik5NnrD1VDfz5jW0AfOGMSWmORkS6gR7ZrWdTWQ3vllQR8BtnHaaVcUTk/RJZKecbeLdsTmkpmQSI7j8V2IvXOTyj3fPKJhpCEY4aXcRJE9V3UiTTOeceB76ClyQuB47i/d16ml4CbNqtZ1eTx1e6JmLPf9d44R0/fqDmnhSRFiVyy/t04E/tTQfknNtnZvcC13Qosh5uf22Qh1/fAsAXTp+kkd0iAvTMbj0LownlGdN61vy5ItJ1ErlCORCv32Q8NkXLZ6z7X9tMdUOIacMK1AiLSI+1vzbIG5vLAThzevPxRCIinkQSyjLiX597fLR8RqppCHHfa95A98+fPgmfT1cnRaRnenn9HsIRx6QhfRkzMLG5LEUkcySSUL4AXGNmA9oqFH3/mmj5jPT3N7dTURtk7MA8zp2pEZEi0nO9tmEvAKdOHpTmSESkO0skofwx3m3sl8zspJYKRPe/GC13W0tlertIxHHfq5sBuPrk8fh1dVJEerDX1ns3m06eqIRSRFoX96Ac59xqM7sUeBB42cw2Ays4dB7K8UA9cLlz7p3Uh9v9/W9tKZvKaijMzeJjx4xq/wARkW5qR0Udm/fW4vcZx09o8+aUiGS4hCY2d849YWbL8VbK+RBwQZO3dwF/An7mnFufqgB7mntf9fpOfmL2GPJzOrSypYhIWsWuTs4c2Y+CXE0XJCKtSzjjcc5tBK4DMLNCvKuTVc65+Bd87KVW76zktQ178fuMT540Lt3hiIh0yJJN3ixxJ2oeXRFpR4cuoUWTyIxPJGPuj47s/uCMYYwo6pPmaEREOuatbRUAHKNlY0WkHYkMypE27K8N8s/lOwH41Mnj0huMiEgH7a8Lsr7UW93x6DFF6Q1GRLo9JZQp8tdl22gIRZg+vJBZ+jYvIj3cyu37ARg7MI+BfXPSHI2IdHdKKFMgEnE8sngrAJefMEbLLIpIjxe73a0vyCISDyWUKfDahr1sKquhb04WFxw1Mt3hiIh02PJt3hXKWbrdLSJxUEKZAg+/vgWAC2eN1FRBItIrrNldBcCMkf3SHImI9ARKKDuopLKe4jUlAFx+wtg0RyMi0nGVjVBW3YgZTB1WkO5wRKQHUELZQX9/czvhiOOYsf2ZMlQNr4j0fDtrvX7g4wfmk5etuy4i0j4llB3gnOOvS7cDcPGxo9McjYhIauys9Z6nDdeXZBGJjxLKDli6pZxNZTXkZfs594jh6Q5HRCQldtZ4VyinDStMcyQi0lMooeyAv7yxDYAPHTFcg3FEpNeI3fKePlwJpYjERwllkqobQvzn7V0AfFy3u0WklwiGI+yu815P04AcEYmTEsokPbOqhNrGMBMG5XPMWE38KyK9w86KesLOyMnyMbKoT7rDEZEeQgllkp6Mrtv9sWNHaWUcEek1Nu+tAWDsgDx8PrVtIhIfJZRJKG+AJZvLAbQyjoj0Kpv3ekO8xw7MS3MkItKTKKFMwptl3rf22eMHMEK3hESkF9kSTSjHKaEUkQR0u4TSzK43s81mVm9mi81sdjvlLzKztdHyb5vZOZ0d47Iy78emq5Mikqju3sZtVkIpIknoVgmlmV0M3AF8D5gFrACeM7MhrZQ/CXgMuAc4GngSeNLMZnRWjO+VVLOj1gj4jXNmDuusjxGRXqgntHG65S0iyehWCSVwE3C3c+4+59xq4DqgFri6lfI3AM86537mnFvjnPs28Cbwhc4K8KmV3lRBH5g8iKK87M76GBHpnbp1G9cYirCjwpszSFcoRSQR3WY2bjPLBo4Bbovtc85FzGwhcGIrh52I922/qeeAC9r4nBwgp8muAoBgMEgwGGwzRucc/4omlOccPrjd8r1JrK6ZVGdQvVXv+MrHoyvauI60bwCb9tQQcZDtc/TP9WXU71//5lXvTNCZbVy3SSiBQYAfKGm2vwSY1soxw1op39a96FuAW5vvXLBgAXl5bX8j31wFOyqyyPE5IttW8vTOlW2W742Ki4vTHUJaqN6ZJd5619bWJnLarmjjkm7fAFaVG+BncC4sXLiw3fK9kf7NZxbVu22JtHHdKaHsKrdx6Df+AmD7/PnzKSxse5mxSMRx9DFlPPvKUs49ex6BQKAz4+xWgsEgxcXFzJunemcC1Tu+eldWVnZBVAlJun0DOKGmkSM37WX58uX63WcI1Vv1bksibVx3SijLgDAwtNn+ocDuVo7ZnWB5nHMNQENsOzYpeSAQiOuHe+KkwZSvc3GX721U78yierdfLgGd3sZ1tH0bWhTgrBnZhLe+pd99hlG9M0tntHHdZlCOc64RWAbMje0zM190e1Erhy1qWj5qXhvlRUTSQm2ciPRm3ekKJXi3ah4ws6XAEuBGIB+4D8DMHgR2OOduiZb/P+BFM/t/wH+AS4Bjgc90cdwiIvFQGycivVK3Siidc4+b2WDg+3idzpcDZzvnYp3SxwCRJuVfM7NLgR8CPwbeAy5wzq1K9LPj7ScQDAapra2lsrIyoy6Tq96qdyZItN6J9qFMVxuXSJz63avemUD1Tn0bZ865jsTW45nZSGB7uuMQkR5tlHNuR7qDaE7tm4ikSLttnBJKr9f6CKAqzkMK8BroUQkc0xuo3qp3Jkim3gXATtcNG9Mk2jfQ7171zgyqd4rbuG51yzsdoj+guK8sxEZNAlXOuW43Z0hnUb1V70yQZL277c8n0fYN9LtH9c4Iqnfq27huM8pbRERERHomJZQiIiIi0iFKKBPXAHyPJpMHZwjVO7Oo3pkrU38GqndmUb1TLOMH5YiIiIhIx+gKpYiIiIh0iBJKEREREekQJZQiIiIi0iFKKEVERESkQ5RQioiIiEiHZPxKOUkuTSYiEtPbll4UEWlKSy/GaQTeupYiIskaRYJLHHYRtW8ikgrttnFKKKPf3Ldt20ZhYWG7hYPBIAsWLGD+/PkEAoFOD667UL1V70yQaL0rKysZPXo0dN8rgAm1b6DfveqdGVTv1LdxSiijCgsL404o8/LyKCwszLh/hKq36t3b9dZ6x9u+Qe/9GbRH9Va9M0Fn1luDckRERESkQ3SFUqQXcs4RDDsaQmEaQhFCYUcwHIk+Dr4ORRzBUIRg9DkUidAYdjQ0BllWYlQs2UYEIxR2NIYjhCOOcMQRcd5z2DkiEUc4wvv2hSLR91yzY5qUPbjPNdkHLloH57yyrqV9TbYdB8vFnmm+D7yy0dcHztv8HGE/55yTpl+ciCTEOa+taQxFaAhFos/hA9te++e1daGIIxRtAxuDQZbuMRre2okzIxj22p9gtJ0LNXntvecdF4o0bQe9NiPS9LVzRCJNXjsOtG+u+esmZSKRll6//7yxOsfas6ZtG0Tbz+btXdP2ExiS3TltXLdLKM3seuCrwDBgBfBF59ySNsoXAT8CLgQGAFuAG51zT3d+tCLJCYUj1DSGqW0MUdMQpqYhRE1jiNqGMDXRfbWNIaobQtQ2eu83hCLUB8OHPDc02a4Peg1p7DnS4THHfti4JhXV7VF8lu4IRHqPYDhCVX2IyrogNY0h6hrD1DSGqWv02rbaxnB0n/fegX1Brx2si7ZxzRPFptvJt3V+WL8qldXtEYKdlPl1q4TSzC4G7gCuAxYDNwLPmdlU51xpC+WzgWKgFPgY3giksUBFF4UsGcw5R21jmLLqBsqqG6mobWR/XfB9j8o6rzFtuq8uGO7SWAN+I8vnI+A3An4fAb+PLL+RHX32tn1kR8tl+WDf3j2MGDaMnIDfe99nZPl9+H3gN8PnM/xm+H0HXx/cx6HvNyvn93Fg3yHvm+Ez7z2LPhPbhgP7vNcHy3jPAHZImdh73mkMn897blreZ965fAahUIgXX3ihS383It2dc47K+hD7ahrZV9PAvprggef9dUEq64MHksaq+iCV9SHvuS7U5W1dls/IyfKRneUjJ8tPdla0jfP58PvMawv9PnwG+8v3MnTwYLKz/NH3vDIHyvuNgM/wR9tOf7QNzPK9v73y+Vp+7W/STvl93uv3HWte23TgdbNtvw+atlVN2zbgkHbQDpTzjrFm7WcoFOKVF1/onJ99p5w1eTcBdzvn7gMws+uAc4GrgZ+0UP5qvKuSJznngtF9m9v6ADPLAXKa7CoAr6NqMBhs+aAmYmXiKdubZFK9wxFHaVUDu/fXs21fDa/sMt557l3K60LsrW6krKaBfdWNlNU0Uh+MdOizsnxGfo6f/Ows8rL95EVf52f7ycvOim77ycv2k5PlJzfga/LsIyfgJyfLR2608cwJ+A6WyfIdaFgt1vLEKRgMUlxczLx5h2dYh3VjYG78/84z4f8H6b3qg2F2lteyoRL+8/ZuymqClFTWU1LZQFl1QzSBbKS8tpFguGO3PPKz/eTneO1cn2gb1yfatuVlZ3mvA9HtWLmAVyY3mhg2TxRzDjy87ewsLyGMRzAY5Omnn+acc47JsDYuSFFO++WS0W0SyujVxmOA22L7nHMRM1sInNjKYR8GFgG/NbPzgT3Ao8DtzrnWvhbdAtzafOeCBQvIy8uLO97i4uK4y/YmvaHeoQjsbYA99cbeeqhoMMoboaLRKG+AykaI0LRR8sPmLa2eL+BzFAQgPwv6ZDnysiDPD32yIC+63Se6Ly/L0ScL+vghxw9ZPoB2kpIIUP/+3S66ux7Yn+gPIU694fedjHjrXVtb28mRiCSvqj7Itn11bCuvZdu+WraX17FtXy07KuooqaynvDbW9mTBOyvbPV9+tp8BfbMZkJ/DgLwAA/Jz6NcnQGGfLApzAxTkZlHYJ/qcG6Bf9HXfnCyy/BoD3Nt1m4QSGAT4gZJm+0uAaa0cMwE4A3gEOAeYBPwOCADfa+WY2/Buq8cUANvnz58f97RB3pWbeRn3raYn1TsScWyrqOO9kmo27a1h6746tu6tZcu+Wnburz8waKM1fp8xtCCHYYU5RGrLOWzCaAYX5DKobw6D+mYzMD+bgdHn/Jzu9L9RavS033eqJFrvysrKLohKpHXBcIQte2tYX1rDhj3VbCitZsOearbuq22SMLYuJ8tHX3+Y8cP6M7woj2GFOQwt9Nq6AfnZhzxyA/4uqJH0VD39L6EPr//kZ6JXJJeZ2Ui8QT0tJpTOuQagIbYduxUYCAQS+sOZaPneorvV2zlHSWUD75ZUsW53lfccfbR1Ozo/28/YgfmMGZDHiKI+jCjKZXi/PgwvymVEvz4MLsjB77Mmt0Uy69ZvTHf7fXeVeOudiT8bSQ/nHNvL63hn535W76xk7e4q1u+pZuveWkJtjEoZkJ/N6P59GDUgj9H986JtXi7D+uUyrDCXvCx45plnOOec2fr3LB3SnRLKMiAMDG22fyiwu5VjdgHBZre31wDDzCzbOdeY+jAlncqqG1i5vYIV2/bz9o79rNxeQVl1y7/m7Cwfkwb3ZdKQvowbmMfYgfmMG5THmAH5DOqbnXC/QhGRrhBLHpdtKWfl9v2s3uUlkZX1oRbL52f7mTikL5MG92XikL5MHJzP2IH5jB6QR9927qCoH7CkSrdJKJ1zjWa2DJgLPAlgZr7o9p2tHPYqcKmZ+ZxzsctRU4BdSiZ7Pucc60urWbxpH4s37ePNLeXsqKh7XzmfwfhB+UwdVsCUoQVMHVrA1GEFjBmQp347ItLtNYTCrNpRyZtbylm2pZxlW8vZU9XwvnIBvzFlaAGHjyhk+vBCJg8pYOKQfIYV5uoLsqRdt0koo+4AHjCzpcASvGmD8oHYqO8HgR3OuVui5X8PfAH4PzP7DTAZ+Abw6y6OW1LAOce6kmpe21DGkk37WLJpH3tr3v+9YMLgfI4cVcQRo/pxxKgiDh9RqL49ItJjRCKOd3ZW8sr6Ml5dX8Ybm/fREDq0i07Abxw2oh9Hjy7isBGFHD7CSyCzs/QlWbqnbpVQOuceN7PBwPfxJjZfDpztnIsN1BmDN+Y1Vn6bmZ0F/BJYiTcP5f8Bt3dl3JK8qvogr64v44V39/Diuj3s2n/ocOacLB+zxvTn+AkDOG7cAGaO6kdhrvr5iEjPUlJZz//WlvLKe2W8uqGMimYDZgbmZzNrbH+OiT5mjuynL8rSo3SrhBLAOXcnrdzids7NaWHfIuCETg5LUqiksp7n3tnNs6t2s2TTvkM6lOdk+Zg9fgAnTBjI8eO9BDInS42qiPQszjneK62meHUJC97ZzYrth07u1TcnixMmDOSUSQM5ZfIgJg7uq9vW0qN1u4RSeqedFXU8/fYunl21m2Vbyw+ZtmfCoHxOmzqYOVOHcPz4AfpWLiI91vrSav65fAdPrdjJ5r0H5yk1g6NGFzFnyhBOmTyII0f1Ux9v6VWUUEqnqW0M8eyq3fxt2XYWbdx7SBI5a0wRH5wxnPmHD2XswPz0BSki0kEllfX8a/lO/rliB6t2HJybNDvLx8kTBzL/8GHMnT6EIQW5aYxSpHMllFBGly28DJiON83P35xzG1oodybwDefcGSmJUnoM5xxLt5Tz+BvbeObtXdQ0HpzRafb4AZw7czhnHT6MYf3UsIpIzxWOOF5at4dHFm/hf2tLifXcyfIZH5gymPOPGsHc6UPbnbZHpLeI+1+6mfUDXsNLJmN+YGY/B77VZNoe8OaOPC01IUpPUB8M88/lO7j/tS2s2XXwG/rYgXl8dNYoPnL0SEYPiH9pSxGR7qi0qp6/vLGNx5ZsO2Qas2PG9ueCo0Zw7hEjGJCfncYIRdIjka9O3wYmAp8E/gEMB74GfB040swucs5pYdsMs6OijgcXbebxN7YdGLWYG/Dx4SNHcNGxozl2bH91NBeRHu+9kir+8NJG/rl8B8GwdzmyX58AHztmFJ+YPYZJQ/qmOUKR9EokofwQ8Hvn3EPR7feAa83sf8CfgP+Z2TnOuX2pDlK6ny17a/jd8xv4+5vbD4zSHtW/D1ecMJaLjxtNUZ6+oYtIz7d08z7uenEDC9eUHth39JgiLj9+LOceMVyDCEWiEkkoRwNvN9/pnHvUzLYB/wReMbOzUxWcdD/rS6v54ytb+OfyHQf6DJ0wYQBXnzyeudOH4vfpaqSI9HyvbSjjl8XreGNzOeCN0p5/2FA+e9pEZo3pn+boRLqfRBLK3XgTi7+Pc+5lMzsdeBZvOcSHUxCbdCPbymt5YJ2Pt15/7cBo7TlTB/PFMyZxzNgB6Q1OpAcxs+uBr+It3rAC+KJzbkkcx10CPAb80zl3QacGmcGWb6vgV//bwKvr9wKQ7ffxkaNH8pnTJjBxsG5ri7QmkYTyDeAC4LstvemcW2FmpwALgJs7HJl0C+U1jfzmf+t56PXNBMPenGnzDxvKF8+YzMxR/dIcnUjPYmYX4y0xex2wGG952efMbKpzrrSN48YBPwde7oIwM9KWvbX8aa2Ptxd5uX3Ab3xi9hiuP30SQws1K4VIexJJKP8C/MHMPuCce6mlAs65DWZ2EvAcMDMVAUp6hMIRHli0hV8tXEdVfQiAqf0i3H7pSRw1dmCaoxPpsW4C7nbO3QdgZtcB5wJXAz9p6QAz8wOPALcCpwJFrZ08OrVbTpNdBQDBYJBgMNjyQc3EysVbvqerbgjx+xc3ct9rWwiGffgMPnL0CL4wZyKj+vcBevfPItN+3zGqd2LtQTziTiidc08AT8RRrgQ4Ku4IpNt5Y/M+vv3kKtburgJg+vBCvjp/ElXrlnD4iMI0RyfSM5lZNnAMcFtsn3MuYmYLgRPbOPQ7QKlz7h4zO7Wdj7kFL/E8xIIFC8jLS2zaruLi4oTK9zTOwdIy419bfFQGvb7f0/pF+Mi4CMNytrJy0VZWpjnGrtTbf9+tUb3bVlsb/+Q9mnFVDiivaeRHT6/hb8u2A1CUF+Dms6Zx8XGjiYRDPL0uzQGK9GyDAD9Q0mx/CTCtpQOi3YiuIf4v6bfh3VKPKQC2z58/n8LC+L4MBoNBiouLmTdvHoFAIM6P7Vm2ldfynX+t4ZVoP8mxA/L42vyJNG5+i/nze2+9W5IJv++WqN7x1buysrLdMjFKKAWABe/s5hv/WEVZdQMAn5g9mq+eNe3ABL2RcFtHi0iqmVkB8BDwaedcWTzHOOcagIYm5wAgEAgk/EczmWO6u3DEce8rm7ijeB11wTDZWT5umDuZT586AXNhnt7yVq+sdzxU78wSb70T+dkoocxwFbWNfO+p1fzjrR0ATBrSl59+7AhNiyGSemVAGG8lsaaG4s2i0dxEYBzwVJPFAXwAZhYCpra09K20bNu+Wr78+HKWbvGmATphwgB+/JGZTIiO3A4G9a1ZpCOUUGaw1zfu5YY/v0VJZQM+g898YCI3njlZE/WKdALnXKOZLQPmAk8CmJkvun1nC4es5f2DG3+Idxv7BmBbpwXbizjn+MdbO/jOP9+huiFE35wsvnXudC4+brRW8RJJISWUGSgccdz5v/X833/XEXEwYVA+P//4kboqKdL57gAeMLOlwBK8aYPygdio7weBHc65W5xz9cCqpgebWQWAc+6Q/dKyqvog3/jHKp5asROAY8f255cXH8XoAYkNUBKR9iWVUJrZGGCPc66ulff7AIOdc1s7EpykXmllPTf8eTmLNnqd0T86axTfP/9w8nP03UKksznnHjezwcD38SY2Xw6cHZ0dA7zFIyJpCq9Xea+kis8+vIyNe2rw+4wb507mc3MmkuX3pTs0kV4p2SxiE3AF8Ggr7384+p7unXYjy7dV8JkHl1Ja1UBetp8fXjCDC2eNSndYIhnFOXcnLd/ixjk3p51jr+qEkHqdf6/cyc1/W0ltY5jh/XL57WWzdAdGpJMlm1C21/EkgL5ldytPvLmdrz/xNo2hCJOH9OWuK47RMmIi0quEI46fPLOGu1/eBMBJEwfy608czaC+Oe0cKSIdFXdCaWaFHLpCw8Dore/mioBLgF0dikxSIhxx3P7sWv740kYA5h02lF9efBR9dYtbRHqR2sYQN/55OQtWe70HrjttIl+ZP0W3uEW6SCJZxZfxVmwAcMCvoo+WGPCtpKOSlKgPhrnhz2/x3DteA/vFMybx5TOn4PNpZKOI9B6lVfVc+8BSVm7fT7bfx88uOoLzjxqZ7rBEMkoiCeUCoBovWfwp8BjwZrMyDqgBljnnlqYkQknK/rogn35gKUs27yPb7+MXHz+S844cke6wRERSan1pFZ+89w12VNTRPy/AH688luPGDUh3WCIZJ5G1vBcBiwDMLB94wjn3dmcFJskrqaznk/cuYe3uKgpysrj7k8dywoSB6Q5LRCSlVu3Yz5X3LmFfTSPjB+Vz71XHMX5QfrrDEslISXUucc59r7OSSTO73sw2m1m9mS02s9lxHneJmTkze7Iz4uoptu2r5aO/f421u6sYXJDD4589UcmkiPQ6y7aU84m7X2dfTSNHjOrH3z93kpJJkTRKdh7K77RfCuec+0GC570Yb+Lf64DFeJP+PmdmU51zpW0cNw74OfByIp/X22zbV8slf3ydHRV1jB+Uz4NXz9YEviLS6yzasJdrHniD2sYwx43rzz1XHUdhbuatxyzSnSQ71Pe7bbzn8PpZOiChhBK4CbjbORdbNeI64FzgauAnLR1gZn7gEeBW4FQOHYmeMZomkxMG5fPnz5zAkMLcdIclIpJSr60v41P3v0FDKMIpkwbxxyuPIS9bs1aIpFtS/xc65953qzy6Ju1Y4HrgA8AHEzmnmWUDxwC3NfmciJktBE5s49DvAKXOuXvM7NQ4PicHaDopWQFAMBgkGAy2G2esTDxlu8q28louv2cpO/fXM35gHg9dfSz9+/hTGmN3rHdXUL1V73jKS9dYtqWcax9cSkMowtxpQ/jtZbPIDWj9DJHuIGVf65xzEbwVdL5iZo8AvwEuTeAUg/BW1ilptr8EmNbSAWZ2CnANcFQCn3ML3tXMQyxYsIC8vPhvDxcXFyfwkZ1nfyP8apWffQ3GkFzHp8ZVsvTl/3ba53WXenc11TuzxFvv2traTo5EYt7ZuZ+r7ltCbWOYUycP4neXzyInS8mkSHfRWfcJXgJu76RzA2BmBcBDwKedc2UJHHobXj/NmAJg+/z58yksLGz34GAwSHFxMfPmzSMQSG+fnar6IJfes5R9DVWMGdCHx66dzZCCzlkRojvVuyup3qp3WyorK7sgKllfWs2V9yyhqj7EceP684crjlEyKdLNdFZCeSyJL71YBoSBoc32DwV2t1B+IjAOeMrswETdPgAzCwFTnXMbmh/knGsAGmLbsWMDgUBCfzgTLZ9q9cEwn39sBWt3VzGobw4PX3MCI7tgAE66650uqndmibfemfiz6Wq799dzxT2L2VvTyIyRhdxz1XHqMynSDSU7yvvKVt4qwus/eSHwp0TO6ZxrNLNlwFzgyejn+KLbd7ZwyFpgZrN9P8S74ngDsC2Rz+9JwhHHTX9Zzusb99E3J4v7P3UcYwZqNLeI9C41DSGueeANdu2vZ+LgfB68+niN5hbpppL9mnd/G++V4Y3I/n4S570DeMDMlgJL8KYNygdio74fBHY4525xztUDq5oebGYVAM65Q/b3Nj9+eg1Pv72bbL+PP15xDDNG9kt3SCIiKRWOOG7481u8s7OSgfnZ3P+p2QzIz053WCLSimQTyvEt7HNAuXOuKtlgnHOPm9lgvGR0GLAcONs5FxuoM4bEb6X3Kn9duo17XtkEwC8+fiQnTRqU5ohERFLvh/9ZzcI1peRk+bj7k8dqTl2Rbi7ZaYO2pDqQJue+k5ZvceOcm9POsVd1QkjdxrIt5XzzH97F1xvmTtba3CLSKz20aDP3vboZgDs+fhSzxvRPb0Ai0q4O9Ww2sxnAOXiDYwA2A89oje/U272/nuseXkZjOMJZhw/lhrmT0x2SiEjKLduyj+89tRqAr541lXOPGJ7miEQkHskOyskB/gBcgbcqTuw2tA+4LToP5bXOucaURJnh6oNhPvPQUvZUNTBtWAF3fPwofD5r/0ARkR6krLqBzz/yJqGI40NHDOfzcyamOyQRidP7VryJ0+3AlcDvgelALt7qM9OBu4DLgZ+mIkCBH/x7NSu376d/XoC7rzyW/BxNmSEivUsoHOGLj75FSWUDk4b05faPHkGTKeFEpJtLNjO5HHjIOfeFZvvfBa43s8JomRs7EJsA/1m5i0cWb8UM/u+So9UxXUR6pTuK17Fo417ysv3cdfksfXEW6WGSvUIZAF5v4/3X6LxJ0zPGtn21fP3vKwH43GkT+cCUwWmOSEQk9f67poTfveCtQ3H7R49g0pCCNEckIolKNqF8DjirjffPBhYkeW4BGkMRvvDYW1Q1hDhmbH9umjcl3SGJiKTcnqoGbv6b98X5qpPGafYKkR4q2auI3wb+YmZPAL8F1kf3TwauB8YCF5vZgKYHOef2JRtopvnZc2tZsa2Cfn0C/PoTR5PlTzb3FxHpnpxzfP3vK9lb08i0YQXccs60dIckIklKNqFcE32eCZzf7L1YL+rVLRznT/LzMsqiDXu5+2Vv8vKffuwIRhb1SXNEIiKp99iSbfx3bSnZfh+/uuQocrL0J0Kkp0o2ofw+3so4kmI1DSFu/vsKAD4xewxnHT4szRGJiKTeprIafvDvg/NNThtWmOaIRKQjkl0p57spjkOibn92Ldv21TGyqA/f0O0fEemFQuEIX358OXXBMCdOGMg1p7S0mq+I9CRJdcwzs3vN7Pg23p9tZvcmH1Zmem1DGQ8u8la1vP2jR1CQG0hzRCIiqXfvq5tYvq2CgtwsfvHxI7VQg0gvkOxIj6uAtpYwGA98MslzZ6SahtCBkY6XHj+GUyYPSnNEIiKpt21fLb8sfg+Ab507nRHqIy7SK3TW0OERQF0nnbtX+umza9leHrvVPT3d4YiIpJxzjm89uYq6YJgTJgzg48eOTndIIpIicfehNLPzOXRE92fM7MwWihYBZwJvdCy0zPH29v08+PrBW919tUKEiPRC/1qxkxfX7SE7y8ePPzJTSyuK9CKJZC6HARdFXzvgeOCYZmUcUAO8BNzU4egyQCTi+NY/V+EcnH/UCN3qFpFeqaK2ke8/5Y3q/uLpk5gwuG+aIxKRVIr7lrdz7jbnXIFzrgBvrslrYttNHoXOueHOuQ8559Z1Xti9x5/f2MaKbRX0zcnim7rVLdLrmdn1ZrbZzOrNbLGZzW6j7KfN7GUzK48+FrZVvjv78dNr2FvTyOQhffnsaW11wReRniipPpTOOZ9z7tFUB5Np9tU08tPn1gLw5XlTGFKYm+aIRKQzmdnFwB3A94BZwArgOTMb0sohc4DHgNOBE4FtwAIzG9n50abO8m0V/GXpdgBuu3Am2Vla+Uukt9H/1Wn002fXUlEbZNqwAj554th0hyMine8m4G7n3H3OudXAdUAtcHVLhZ1zlznnfuecW+6cWwtci9duz+2yiDvIOcf3n3oHgI/OGsWx4wa0c4SI9ERJjf4wswhxrJTjnNM6Wq14a2s5f35jGwA/uGCG1uoW6eXMLBuv3/ltsX3OuYiZLcS7+hiPPCAA7GvlM3KAnCa7CgCCwSDBYDCuD4iVi7d8e55auYs3t1bQJ+Djy3MnpOy8qZbqevcUqrfqHU/5eKRy6UU/MA64AHgX+HeS5+71nHP88D/ecugXzhrJcfrGLpIJBuG1kyXN9pcA8S6LdTuwE1jYyvu3ALc237lgwQLy8vLi/AhPcXFxQuVb0hiGHy33A8bpw4Ise+V/HT5nZ0tFvXsi1TuzxFvv2trauM+Z8qUXzWw48DqgQTmtWLC6hGVbyskN+Pja2VpeUUTaZ2ZfBy4B5jjn6lspdhteH82YAmD7/PnzKSyMb63sYDBIcXEx8+bNIxDo2Gpddz6/gYrGDYzol8vtnzqZ3ED3vWmVynr3JKq36t2WysrKuM+d8gkPnXO7zOwu4Nt4ncmliWA4wu3PeANxrj1lAkM1EEckU5QBYWBos/1Dgd1tHWhmXwG+DpzpnFvZWjnnXAPQ0OQ4AAKBQMJ/NJM5pqnd++v548ubAbjlnOkU5PWMtq6j9e6pVO/MEm+9E/nZdFbHvRq85Relmcff2MbGshoG5Gfz2dMmpDscEekizrlGYBlNBtSYWWyAzaLWjjOzm/G+oJ/tnFva2XGmys8XvEtdMMwxY/vzoSOGpzscEelkKU8ozWwG8CWSvOXdm+doq2kI8auF3hq2N8ydTEFu5n0rEslwdwCfNrNPmtl04PdAPnAfgJk9aGYHBu2Y2deAH+CNAt9sZsOij249K/j60mqeeNObJuhb507XijgiGSDZUd6baHmUdxHQD28ajAuSOG9sjrbrgMXAjXhztE11zpW2cMgcvNvqrwH1wNfw5mg73Dm3I9HP72x3v7yRsuoGxg7M4xOzx6Q7HBHpYs65x81sMN7AxmHAcrwrj7GBOmOASJNDPgdkA39rdqrvAd/t1GA74FcL1xFxcOb0oRw9pn+6wxGRLpBsH8oXeX9C6YByYAPwZ+dci9NatOPAHG0AZnYdcC7et/OfNC/snLus6baZXQt8FO8W0oNJfH6nKatu4I8vbQTg5rOmaWJfkQzlnLsTuLOV9+Y02x7XBSGl1Jpdlfx75S4Abpo3Jc3RiEhXSXaU91UpjqNL5miLfk6H5mlLdu6qu15YT21jmCNGFjJv2sAeN/eV5uxSvTNBZ87Rlil+scDr7fShI4Zz2Ij4RpaLSM/XoVHeZpYPFAJVzrnqDsbSFXO0QYrmaUtk7qrqIDz4pjcX2wkF5TzzzDNxH9vdaM6uzKJ6ty2ROdoywfJtFSxcU4LP4MYzdXVSJJMknFCa2TjgZrxb0aOa7N8BPAX83Dm3KVUBJhBXPHO0QQfnaUtm7qqfL3iPxsgmZowo5CuXHt8jO6hrzi7VOxN05hxtmeAXC94F4MJZo5g0pFuPGxKRFEsooTSz84GHgL7AZrwEsgovKTsCrwP5lWZ2uXPunwnG0ulztEHq5mmLt3x5TSMPL94KwA1nTiE7Ozvuz+iONGdXZlG92y8nnjc27+Pl98rI8hk3zJ2c7nBEpIvFPTLEzA4DHge2A6c55yY45y5wzl0RfZ4AnAZsBf4cLR+33jpH2z2vbKKmMcxhwws5c/qQdIcjItIpfvv8egAuOnY0owcktsyjiPR8iQw1/gbeVcRTnHMvt1Qguv9UYC9eX8VE9ao52vbXBrn/tc0AfGnu5B55q1tEpD2rd1bywrt78BlcpwUbRDJSIre8Twf+1N50QM65fWZ2L3BNosH0tjna7nl1E9UNIaYNK2D+Yc3v5IuI9A5/eGkDAOfMHM7YgflpjkZE0iGRhHIgXr/JeGyKlk9Yb5mjraYhxP2vemOTvjR3Mj6frk6KSO+zdW8tT63YCcB1p01MczQiki6J3PIuI/71ucdHy2esvy7dRmV9iPGD8jn78GHpDkdEpFPc/fJGIg4+MGUwM0b2S3c4IpImiSSULwDXmNmAtgpF378mWj4jhSOOe1/dDMDVp4zX1UkR6ZXKqhv4y9JtgPpOimS6RBLKH+Pdxn7JzE5qqUB0/4vRcre1VCYTFK/ezdZ9tRTlBfjYrFHtHyAi0gPd/+pmGkIRjhxdxIkTkurlJCK9RNx9KJ1zq83sUrw1sl82s83ACg6dh3I8UA9c7px7J/Xh9gx/etnrO3n58WPpk+1PczQiIqlX0xDiwUWbAfjcaRM1i4VIhktoYnPn3BNmthxvpZwPARc0eXsX8CfgZ8659akKsKd5a2s5S7eUk+33ceWJY9MdjohIp3jize0H+olrFgsRSXjpRefcRuA6ADMrxLs6WeWc0xpkwJ9e8a5OfvioEQwpzE1zNCIiqeecOzDH7idPHKt+4iKSeELZVDSJVCIZtW1fLc+8vQuAa06Jd0C8iEjP8sr6MjbsqSE/289Hj1E/cRFJbFCOtOPBRZuJODh18iCmDy9MdzgiIp3igejVyYuOHU1BrtYzFxEllClTHwzzl6XbAfjUyePSG4yISCfZureW/64tBVA/cRE5QAllijz99i721wUZWdSH06YMSXc4IiKd4sFFm3EOTpsymAmD+6Y7HBHpJpRQpsgji7cCcOnxY/Crg7qI9EI1DSEej05kftVJ49IbjIh0K0ooU2DNrkqWbSkny2dcdKw6qItI7/SPt3ZQVR9i3MA8TpsyON3hiEg3ooQyBR6NXp086/BhDCnQVEEi0vs45w5MZH7lieM0VZCIHEIJZQfVNIT4x1s7AO92t4hIb/T6xn2sK6kmL9vPx3QnRkSaUULZQU+t2El1g7dahNayFZHe6qHXNwNwwdEjKdRUQSLSjBLKDjowGGf2GN0CEpFeadf+Op57pwTQVEEi0jIllB2wcnsFb+/YT7bfp9UiRKTXemzxVsIRx+zxA5g2TIs2iMj7KaHsgL9Ep884e8YwBuRnpzkaEZHUawxFeHSJ19bp6qSItEYJZZIagmGeWuGt262pgkSkt3r2nd2UVTcwpCCHsw4flu5wRKSbUkKZpP+9u4f9dUGG98vlpImD0h2OiEineCg6VdAnZo8h4NefDBFpmVqHJD3x1k4APnL0SK2MIyK90uqdlbyx2Vu0QdOiiUhblFAmobIRXl6/F0CDcUSk17rnlU2At2jD0EIt2iAirVNCmYSlZUY44jh6TBETB/dNdzgiIim3vbyOJ5d7izZce+r4NEcjIt1dt0sozex6M9tsZvVmttjMZrdT/iIzWxst/7aZndOZ8TnnWFLq/dg+pquTIpKg7t7Gxdz10kbCEcepkwdx9Jj+XfGRItKDdauE0swuBu4AvgfMAlYAz5nZkFbKnwQ8BtwDHA08CTxpZjM6K8bVu6rYVWdkZ/n40BEjOutjRKQX6gltHMDmKvjLMu/q5BfPmNyZHyUivUS3SiiBm4C7nXP3OedWA9cBtcDVrZS/AXjWOfcz59wa59y3gTeBL3RWgH+PDsaZN20I/fpo+TERSUi3b+N27a/n0Q1+nIMLZ41k9vgBnfVRItKLZKU7gBgzywaOAW6L7XPORcxsIXBiK4ediPdtv6nngAva+JwcIKfJrgKAYDBIMBhsM8bGUOTA3JPnzRzSbvneJFbXTKozqN6qd3zl49EVbVxH2jeApVvK+cJjy9lbZwzMz+Zr8ydnzL8B/ZtXvTNBZ7Zx3SahBAYBfqCk2f4SYForxwxrpXxbs+/eAtzafOeCBQvIy8trM8AtVVBd76cwALWb3uTpzW0W75WKi4vTHUJaqN6ZJd5619bWJnLarmjjkm7fADZUQnmtn5F5cM2UWl5/cWG7x/Q2+jefWVTvtiXSxnWnhLKr3Mah3/gLgO3z58+nsLD9NWo/XlXL40+/wNnz5xEIZM4t72AwSHFxMfPmqd6ZQPWOr96VlZVdEFVCOtS+AcxcW0LFe8s492z97jOB6q16tyWRNq47JZRlQBgY2mz/UGB3K8fsTrA8zrkGoCG2beZNSh4IBOL64Q4syGNcQfzlexvVO7Oo3u2XS0Cnt3Edbd8A5kwbytMb9bvPNKp3ZumMNq7bDMpxzjUCy4C5sX1m5otuL2rlsEVNy0fNa6O8iEhaqI0Tkd6sO12hBO9WzQNmthRYAtwI5AP3AZjZg8AO59wt0fL/B7xoZv8P+A9wCXAs8JlEPzjey7rBYJDa2loqKysz6luN6q16Z4JE653ELe+0tHGJxKnfveqdCVTvTmjjnHPd6oE3HcYWvNs2i4Hjm7z3AnB/s/IXAe9Gy68Czknw80YCTg899NCjA4+R3bGNQ+2bHnrokZpHu22cRRudjGVeJ6MRQFWchxQA24FRCRzTG6jeqncmSKbeBcBO1w0b0yTaN9DvXvXODKp3itu47nbLu8tFf0A74i0f6+QOVDnnut0Qz86ieqvemSDJenfbn0+i7Rvod4/qnRFU79S3cd1mUI6IiIiI9ExKKEVERESkQ5RQJq4B+B5N5nrLEKp3ZlG9M1em/gxU78yieqdYxg/KEREREZGO0RVKEREREekQJZQiIiIi0iFKKEVERESkQ5RQioiIiEiHKKEUERERkQ5RQikiIiIiHaKEUkREREQ6RAmliIiIiHSIEkoRkS5kZteb2WYzqzezxWY2O87jLjEzZ2ZPdnKIIiIJy0p3AOlmZgaMAKrSHYuI9EgFwE4Xx7JjZnYxcAdwHbAYuBF4zsymOudK2zhuHPBz4OVEAlP7JiIpEFcbl/FLL5rZSGB7uuMQkR5tlHNuR3uFzGwx8IZz7gvRbR+wDfiNc+4nrRzjB14C7gVOBYqccxfEE5TaNxFJkXbbuIy/Qkn0m/u2bdsoLCxst3AwGGTBggXMnz+fQCDQ6cF1F6q36p0JEq13ZWUlo0ePhjiuAJpZNnAMcFtsn3MuYmYLgRPbOPQ7QKlz7h4zO7Wdz8gBcprv37RpEwUFBe2FCHg/g+eff57TTz894373qrfq3dslWu+qqirGjx8PcbRxSiijCgsL404o8/LyKCwszLh/hKq36t3bdXK9BwF+oKTZ/hJgWksHmNkpwDXAUXF+xi3Arc13Llq0iLy8vLgDzcvLY/HixXGX7y1U78yierevtrY27vMqoRQR6YbMrAB4CPi0c64szsNuw+ujGVMAbJ8/f35cX5jBS6qLi4uZN29exn2ZUL1V794u0XpXVlbGfW4llCJygHOOUMRRHwzTEIbKuiDW6AhFIoQjjlDYec+R2HPk0O3woftjj4iDiHNEnMMdeE10u+n7XgyRSNP34yjvmpWPOBwHt53ztp0DR3RfdJvYtoNwJMKO7T7O6ZwfbxkQBoY22z8U2N1C+YnAOOApb2wNEJ2Zw8xCwFTn3IamBzjnGoCG2HbsuEAgkPAfzWSO6Q1U78zStN7OOYJhr/0KRduzUDhCMOIIhx3BSIRQ2BEMRw60c8Fw03Yu+ohAONpWhSMH275I0+2IIxxrtyKx97y2KHzgPN773v4m5aMN2MH2sUm75pq1fdF6xdrRcCRCTamPc+L8fSfyb0IJpUg34pyjIRShrjFMXTD6aDz0uT4Yprbx0O2GUITGUOTAczDsPTc2f46912Q79joYjhA5ZIxeFix5Pl0/irTxH0zeUso512hmy4C5wJNwYFDOXODOFg5ZC8xstu+HeFcdb8AbzCPSq4QjjtrGELWNXjtX0xCiLhh9bgxTE233GqLt3sG279B2sCEYpjEcoSH4/ve8di9Mfb2fbyz7L8GIlzge2v71XiPzOqeNU0IpkkINoTDlNUHKaxspr2mksj5IVX2IqvoQ1Q0hquqDVDeEqKwPUV1/cLsqul3dGKI7TrzgM8jy+fD7jCyf4fdHn3126P4mj6bbPos+fOAzw8zwGdH9NNs2rMl77yvva7u8Ndk2OPC+AUT3edsH91v0uEg4zHvr3u3MH+UdwANmthRYgjdtUD5wnxeePQjscM7d4pyrB1Y1PdjMKgCcc4fsF+kOQuEI5bVB9tcFqawPUlkXpLI+FH0OUlkXet/+moZY8ug9N4QiXRixQTjcdgmDQKyN8xsBv4+saPuW5feRFW0LfdakrfN5bZG/Wbvn93ltmf9AWxYt16SN9Mo0PfbQMi21dbG2zBd97Ys2ak3bP1+TNm7nps5p45RQirQhEnFUNsLqXZXsqwtTWllPaWUDe2savaSxNkh5TSP7ahqpqG2kprHtxikR2X4ffbL99An46ZPtJzfgp0/AR152lvc629vuE/CTE/CT7feRneUjEH3OzvKR4/cRyDKy/f4D+wJ+IyfLd2BfwG/ee37fgQQxEgmxcMECzj3nbHKzs/H5OucbbXcTDAZ5umZtp53fOfe4mQ0Gvg8MA5YDZzvnYgN1xgBd+RdVpE3VDSF276+ntLKePdUN7Iu2d2XVjeyr8bb31jSyt7qR/XXBlH2uzyA/O4s+2X7yc7LoE/CTn+OnT3YWeQE/OQEfOVk+crK8diwn1uZl+Zu89h1oGw+W99o+c2FefeVl5p4+h9ycAIFo+xfwRZNE/8Evy71JZ7ZxSiglYznn2FfTyPbyOraX17Gjopbt5XXsrKijtKqB0soG9lQ3EI5kwbLX4z6v32f0zwtQlJdNvz4BCnKz6JuTRUGu97ogJ4u+ud5235wsCnMPbufn+L2EMctHlj99C1kFg5Dth4DflzHJZFdxzt1Jy7e4cc7NaefYqzohJMlQ9cEwm/fU8E65UbFkG3uqg+yurKeksp5d++sp2V9PVUMooXOaQWFugMI+Wd5z09d9Dt0uiLZ9edlZ5Gd7X5JjSWROlo8mfYdTLhgMsiEPxg7My8i+o51BCaX0apGIY0dFHRvLathQWs2mshq2ldeyI5pE1gXbv6JoOAb2zWFIQS5DCnMYUpDDoL45DMjPpigvmwH5AfrnZXuP/GwKcrKUhIlIt1DbGGJDaQ3r91SxdW8dW/fVsm1fLVv31bK7sj5ayg9r17R6joKcLIb2y2VQ32wG5ucwsG82A/KzGZifzcBoWxh73a9PoNdd1ZP4KKGUXiEccWzeW8OaXZWsK6lmw55qNpRWs3lvDfXB1u8gmsGQghxG9c9jVP8+jOrfh+H9+jCs0Ese+/fx88bL/+O8c+foW6yIdFtV9UHWlVTxXkk160urea/Ue95RUdfmcfnZfoqyQkwdPYQR0fZvaGEuw/vlMrQwl2H9cumbo1RB2qd/JdLjNIYirN5Vyaod+1m9q5I1uypZu6uq1auN2X4fYwfmMXFwXyYMzmfMgLwDCeTwolxysvytflYwGMSvL9si0o2U1zSyaud+Vu2oZNXO/byzYz+b97Y+AfWgvtlMHNyXcQPzGTMwj9ED8hgTffQNwDPPPMM55xytL83SIUoopdvbtb+ON7dU8NbWct7cWs6qnZU0tjASMDfgY+qwQqYNLWDSEC95nDi4L6P690lrf0QRkWSFI451JVUs3VLOss37WLa1nG37Wr7qOLxfLpOG9GXyEK8NnDy0L5MG96V/fnar5w8GUzeQRjKbEkrpdnbtr+PV9Xt5bX0ZizbuZdf++veV6Z8XYOaoIg4fUcj04YUcNryQ8YPy1XdHRHq0cMTx9o79vPLeHpZsLuetLeUtDowZNzCPw0f2Y8aIfswYWcjhI/oxoI3EUaSzKaGUtKusD/LKe2W8ur6M1zbsZVNZzSHv+33GtGEFHD2miFlj+nP0mP6MG5jXqSMARUS6yvbyWl55r4yX3yvjlfVl75t+Jy/bz9Fjijhm7ACOHdufI0cX0a+Pbk9L96KEUtJi695aFq4p4b9rS1i8cR+hJksU+Axmjiri5IkDOWniIGaNLSIvW/9URaR3iEQcb22rYME7uyleU8LGPYd+iS7IzeKkiQM5ccJAjh03gGnDCtRtR7o9/ZWWLrNxTzVPrdjF02/v4t2SqkPemzg4nw9MGcxJEwdx/IQBFObq27eI9B6hcIRFG/fy7KrdFK8uobTqwJLr+H3G0aOLOHXyYE6ZPIgjR/VTAik9jhJK6VQ7K+r498qd/GvFTlbtqDyw3+8zjhvXnzOnD+XM6UMZNyg/jVGKiKSec453dlbyxJs7+NeKnZRVH0wiC3KyOGP6EOYfNoxTpwzSl2jp8ZRQSso1hiIsXFPCY0u28sr6sgNrU/t9ximTBnHekSM4c/oQivLUgVxEep89VQ38bdl2nnhzO++VVh/YPyA/m7MOH8ZZhw/lpImDyM7SVUjpPRJKKM1sJvA5oAhY6Jy718yygB8DlwH9gDeArzvnFqc4VunmNpXV8Oc3tvL3Zdspq248sH/2+AGcd+QIzpkxjIF9c9IYoYhI53DOsXRLOQ8t2sIzq3YRDHvfpLOzfMybPpSPHD2S06YOJqBb2dJLxZ1QmtnhwOtAAKgFLjazsUAf4Argf9HXc4H/mdls59w7qQ9ZuhPnHK9v3MfdL2/kf2tLD+wfUpDDRceO4uJjxzBmYF4aIxQR6Tz1wTB/f3M7Dy3awtrdB/uGHz2miIuPHc0HZw7XiGzJCIlcofwusBM4GdgD/Am4EVgDTHfOVQCY2ThgKXALcHnKIpVuJRSO8PSq3dz90kbe3rEf8JYxnDNlMJ+YPYYzpg1Rp3IR6bUq64M8/PoW7n1l04E7MrkBH+cfOZIrThzLjJH90hyhSNdKJKE8Afidc64UwMx+CXwKuC+WTAI45zab2b3AJ1IZqHQPjaEIf31zK799fv2BNWJzAz4uOmY0V58ynvEaXCMivVhZdQP3vbqJB1/bcmDC8ZFFffjUyeO46JjR9MvT1UjJTIkklIOB3U22Y683tlB2HTAk2aCk+wmFI7xeavzs/15he4W3cs3A/Gw+edI4Lj9hrFZoEJFebX9dkLte3MB9r26iPugt/TppSF8+P2ci5x05Qn0jJeMlklDuBQY12Q4C7wKVLZTtD1S1sF96GOccxatLuO3pNWza6wfqGdQ3h8/Pmcilx48hN+BPd4giIp2mPhjm/tc28/sXNhxYwebIUf34/OmTmDd9KD4t9yoCJJZQvg0cHdtwzu0HprdS9ihgQ/JhSXewasd+fvSfNSzauBeA/CzHF+ZO5aqTJ9AnW4mkiPRezjn+8/YufvyfNezc792VmTK0LzefNY2504do6VeRZhJJKO8CZrZXyMwG4430/l2yQUl6VdQ28pNn1vL40m045017cc1JYxlX/x4XnjKOgK5Kikgv9u7uKr77r3cOfJke0S+Xm+ZP5SNHj8SvK5IiLYo7oXTOPQk8GUe5PcCw5EOSdHHO8Y+3dvCj/6xhb403avHDR47g5rOnMrRvgKeffi/NEYqIdJ7GMPzk2Xe5f9FWwhFHTpaPz82ZyHWnTVT3HpF2aKUcAWDL3hpueeJtXtvgfSOfPKQvP/rITGaPHwBAMBhMZ3giIp1q8aZ93L7CT1nDFgDOPnwY3zx3OqMHaB5dkXgoocxwzjkeW7KNH/5nNbWNYXKyfHxp7mQ+feoELQsmIr1edUOI255ewyOLtwLGsMIcfnzhTM6YNjTdoYn0KEooM1hpZT03/30lL7y7B4Djxw/gZx87UivbiEhGWLGtgi/9+S227K0F4KShEe689mQGFPRJc2QiPY8Sygz1/NpSbvrLcsprg2Rn+bj5rKlcffJ4TYEhIr1eJOL4w0sb+cWCdwlFHCP65fKTCw+nfO1iCnL1Z1EkGd3unqaZXW9mm82s3swWm9nsOI+7xMycmT3ZySH2aKFwhJ8+u5ZP3f8G5bVBDh9RyL+/eArXnjpByaSI9Hpl1Q1cee8Sbn92LaGI45yZw3jmhg9w4oSB6Q5NpEdL6quYmY0B9jjn6lp5vw8w2Dm3NcHzXgzcAVwHLMZbK/w5M5saW/KxlePGAT8HXk7k8zJNaVU9X3rsLV7fuA+AK08cyzfPnU5OlkYvikjv9/b2/Xz2oaXs3F9Pn4CfW887jIuPG42ZaeChSAcle4VyE/CRNt7/cLRMom4C7nbO3eecW42XWNYCV7d2gJn5gUeAW2l5GUgBVm6v4EO/foXXN+4jP9vPbz5xNN8/f4aSSRHJCH9ftp2P3vUaO/fXM35QPv/6wslcMnuMJigXSZFkO4u0939gAIgkdEKzbOAY4LbYPudcxMwWAie2ceh3gFLn3D1mdmocn5MD5DTZVQDetDjxfEONlelJ32affaeEr/79beqDESYNzue3nziKCYPzE6pDT6x3Kqjeqnc85aX7CkccP/zPau57dTMAc6cN4Y6Lj6Jfn0B6AxPpZeJOKM2sEChqsmtg9NZ3c0XAJcCuBGMZBPiBkmb7S4BprcR0CnAN3lKP8boF72rmIRYsWEBeXvyjm4uLixP4yPRwDhbuNP691bsKOb0owlXj9rP2jRdZm+Q5e0K9O4PqnVnirXdtbW0nRyIdUR8Mc8Of3+K5d7w/K186YxI3njlF/cVFOkEiVyi/jHc1EMABv4o+WmLAt5KOKg5mVgA8BHzaOVeWwKG34fXTjCkAts+fP5/CwsJ2Dw4GgxQXFzNv3jwCge77DTcUjvCdp9bw7607ALjyhDHccvYUsvzJ9XLoKfVONdVb9W5LZWVlF0QlydhX08i1D7zBm1sryPb7+MXHj+S8I0ekOyyRXiuRhHIBUI2XLP4UeAx4s1kZB9QAy5xzSxOMpQwIA81nkx0K7G6h/ERgHPBUkz4wPgAzCwFTnXMbmh/knGsAGmLbsWMDgUBCfzgTLd+VGkJhvvzXlTz7zm58Bt/78OFcceK4lJy7O9e7M6nemSXeemfiz6Yn2Lavlk/eu4SNZTUU5mZx95XHcrxGcYt0qkTW8l4ELAIws3zgCefc26kKxDnXaGbLgLlE1ww3M190+84WDlkLzGy274d4VxxvALalKraepKYhxHUPL+Pl98rI9vv49SeO5uwZWlpdRDLDxj3VXHr3YnZX1jOyqA/3f+o4Jg8tSHdYIr1eUoNynHPfS3UgUXcAD5jZUmAJ3rRB+cB9AGb2ILDDOXeLc64eWNX0YDOriMZ3yP5Msb8uyFX3LeGtrRXkZfu5+8pjOXnSoHSHJSLSJdaXVvGJuxezp6qByUP68vC1xzO0MDfdYYlkhGTnofxO+6VwzrkfJHJe59zjZjYY+D4wDFgOnO2ciw3UGUOCo8czRVV9kCvvXcKKbRX06xPg/k8dx9Fj+qc7LBGRLrF2dyWX3b2YvTWNTBtWwMPXHs+gvjntHygiKZHstEHfbeM9h9fP0gEJJZQAzrk7afkWN865Oe0ce1Win9cb1DSE+NR9b7BiWwX98wI8+ukTmD68/QFGIiK9wdrdlXzij68fWP3r4WuOp39+drrDEskoSQ35dc75mj/wktOJwC+BpcCQFMYprahrDHPNA2+wdEs5hblZPHTN8UomRSRjbNlbwxX3LKG8NsgRo/rx6LUnKJkUSYOUreXtnIs45zY5574CvAf8JlXnlpY1hiJ89uFlvL5xH31zsnjg6tnMGNkv3WGJiHSJ0sp6rrhnCXuqGpg2rICHrj6efnkaeS+SDilLKJt5CTink84tgHOOr/99JS+t20Netp/71GdSRDLI/togV9yzhK37ahkzII8Hr56tZFIkjToroTwWDZ7pVL9YsI4n3tqB32f87rJZHDduQLpDEhHpEvXBMFc/8AbvllQxuCCHh685niEazS2SVsmO8r6ylbeKgA8AFwJ/SjImacdjS7Zy5/PrAfjxR2YwZ6q6q4pIZnDOcfPfVrLsQL/x2YwZGP+yuSLSOZId5X1/G++VAT/Bm/pHUuz5d0v51pPeNJtfOmMSFx/X0nLqIiK902/+t55/rdhJls+464pjmDZMgxBFuoNkE8rxLexzQLlzrqoD8Ugb1pdW88VH3yIccXx01ii+PG9KukMSEeky/1m5izuK1wHwgwtmcNJELdwg0l0ku1LOllQHIm2rqg/y2YeWUt0QYva4Adx24UyarGEuItKrrdxewf/763IArjllPJ+YrbszIt1JslcoATCzGXijucdFd20GnknlGt8CkYjjK39dwYY9NQwrzOW3l80iO6uzxlOJiHQv+2oa+exDy6gPRjh96mC+cc70dIckIs0kOygnB/gDcAXeqjixEd0+4DYzewS41jnXmJIoM9zvX9zAc++UkO338fvLZzG4QMuJiUhmiEQcNz6+nF3765kwOJ9ff+Jo/D7dnRHpbpK9zHU7cCXwe2A6kAvkRF/fBVwO/DQVAWa6l9bt4ecL3gXge+cfrrkmRXo4M7vezDabWb2ZLTaz2W2U/bSZvWxm5dHHwrbK90a/e2E9L63bQ27Ax+8um0VBruaaFOmOkk0oLwcecs59wTn3rnMu5JwLR19fDzwSLSMdsKeqgZv+shzn4BOzR6vPkEgPZ2YXA3cA3wNmASuA58ystbm/5gCPAacDJwLbgAVmNrLzo02/1zaUHRyEc/4MjegW6caSTSgDwOttvP8aHeyfmem8udZWUFbdyNShBdx63uHpDklEOu4m4G7n3H3OudXAdUAtcHVLhZ1zlznnfuecW+6cWwtci9duz+2yiNOktLKeLz22nIiDi44ZxUXHjk53SCLShmSTvueAs/BuebfkbGBBkucW4IHXNvP8u3vIzvLx608cTW7An+6QRKQDzCwbOAa4LbbPORcxs4V4Vx/jkYf3hX5fK5+Rg9f9KKYAIBgMEgwG4/qAWLl4y3cG5xz/7y/LKatuYOrQvnz7nKmdHk93qHc6qN6qdzzl45FsQvlt4C9m9gTwW2B9dP9k4HpgLHCxmR2yHqBzrsVGUA61ZlclP35mLQDfPGc6U4cVpDkiEUmBQYAfKGm2vwSYFuc5bgd2Agtbef8W4NbmOxcsWEBeXmKryRQXFydUPpVe2W28vMlPwBwXDqvg+YXPddlnp7Pe6aR6Z5Z4611bWxv3OZNNKNdEn2cC5zd7Lzb8bnULx+kyWzvqg2G+9NhbNIYinDFtCFeeODbdIYlIN2BmXwcuAeY45+pbKXYbXh/NmAJg+/z58yksjK//YTAYpLi4mHnz5hEIdP0AmM17a/j6bxcBEW7+4DSu6qI2MN31ThfVW/VuS2VlZdznTjah/D7eyjiSYr9cuI73SqsZ1DeHn37sCE1eLtJ7lAFhYGiz/UOB3W0daGZfAb4OnOmcW9laOedcA9DQ5DgAAoFAwn80kzmmo0LhCDc/8Q51wQgnTRzINadMxNfFUwSlo97dgeqdWeKtdyI/m2RXyvluMsdJ21Zur+DulzYCcNuFMxnUV/NNivQWzrlGM1uGN6DmSQAziw2wubO148zsZuCbwFnOuaVdEGra/OGljby1tYKCnCx+dtGRXZ5MikjykhrlbWb3mtnxbbw/28zuTT6szBMMR7j5byuJODjvyBHMO6z5RQwR6QXuAD5tZp80s+l4AxvzgfsAzOxBMzswaMfMvgb8AG8U+GYzGxZ99E1D7J1qza5KfrXQmyLoe+cfzsiiPmmOSEQSkey0QVcBE9t4fzzwySTPnZH+8OIG1u6uon9egFvPOyzd4YhIJ3DOPQ58Ba/b0HLgKOBs51xsoM4YYHiTQz4HZAN/A3Y1eXylayLuGpGI45Yn3iYYdsw/bCgfOTojptkU6VU6a67IEUBdJ52711lfWsWv/+sNlL/1vMN1q1ukF3PO3Ukrt7idc3OabY/rgpDS7pHFW1i+rYK+OVl8//wZ6jsu0gPFnVCa2fkcOqL7M2Z2ZgtFi4AzgTc6FlpmiEQcX/v72zSGI5w+dTDnHzUi3SGJiHSZksp6fvqst7zszWdPZVi/3DRHJCLJSOQK5WHARdHXDjgeb5LephxQA7yEtyKEtOOJt3awbEs5+dl+fvSRmfpmLiIZ5XtPvUNVQ4gjRxdx2fGaJk2kp4o7oXTO3UZ0hQcziwDXOOce7azAMkFVfZCfRCcw/9LcyYxQJ3QRySD/XVPC02/vxu8zbvvITPwa1S3SYyU7bVCyg3mkid/8bz1l1Q1MGJTPp04en+5wRES6TH0wzHf++Q4A154ynsNGxDfxuoh0T0oM02R9aTX3vrIJgG+fdxjZWfpViEjm+ONLG9lRUceIfrnccObkdIcjIh2U1BXK6C3vdlfKcc5pqcUWOOf4/r9XE4o45k4bwulTh6Q7JBGRLrN7fz2/f2EDAF8/Zzp52Z014YiIdJVULr3oB8YBFwDvAv9O5sRmdj3wVWAYsAL4onNuSStlPw1cCcyI7loGfKO18t3Ff9eU8tK6PWT7fXz7Q5pzUkQyy+3PrqUuGOaYsf0574jh7R8gIt1eypdeNLPhwOvAukTPa2YX460kcR2wGLgReM7MpjrnSls4ZA7wGPAaUA98DVhgZoc753Yk+vldIRSO8OOn1wBwzanjGTcoP80RiYh0nTe3lvOPt7zm+TsfOkwzW4j0EinvuOec2wXcBXw7icNvAu52zt3nnFuNl1jW4i071tJnXeac+51zbrlzbi1wLV6d5iYXfef727LtbCyrYUB+Np+f09ZiQyIivYtzju8/tRqAj84axZGji9IbkIikTGd1XKnBW34xbmaWjTev5YF1bJ1zETNbCJwY52nygACwr43PyQGaLkVTABAMBgkGg+1+QKxMPGWbqw+G+WV0rdrrPjCeXH9y50mHjtS7J1O9Ve94ykt8/rl8J8u3VZCX7efms6emOxwRSaGUJ5RmNgP4Eonf8h6E1w+zpNn+EmBanOe4HdgJLGyjzC3Arc13LliwgLy8vDg/BoqLi+MuG/O/nUZJpZ+ibMeAfe/w9NPvJHyOdEum3r2B6p1Z4q13bW1tJ0fSezSEwvzsOW9FnM/PmcjQQq2II9KbJDvKexMtj/IuAvrh3aa+IOmokmBmXwcuAeY45+rbKHobXj/NmAJg+/z58yksbH8etGAwSHFxMfPmzSMQCMQdX1V9kFvveAUI8rVzZ3D+rJFxH9sdJFvvnk71Vr3bUllZ2QVR9Q6PvL6VHRV1DC3M4ZpTJqQ7HBFJsWSvUL7I+xNKB5QDG4A/O+dave3cijIgDAxttn8osLutA83sK8DXgTOdcyvbKuucawAamhwLQCAQSOgPZ6Ll73t+IxV1QSYN6ctFx44hy98z551MtN69heqdWeKtdyb+bJJR3RDit8+vB+CGuVPok60Z5UR6m2RHeV+V4jhwzjWa2TK8ATVPAphZbIDNna0dZ2Y3A98EznLOLU11XKmwp6qBe6KTmH9l/pQem0yKiCTjnpc3sbemkXED87jo2FHpDkdEOkGH+lCaWT5QCFQ556pTEM8dwANmthRYgjdtUD5wX/TzHgR2OOduiW5/DW9OzEuBzWY2LHqe6hTFkxJ/eHEDtY1hjhzVj7MOH9b+ASIivcS+mkbufnkjAP9v/lQC+kIt0isl/H+2mY0zs9+Z2RagEtgO7DezrWb2WzNLelFq59zjwFfwksTlwFHA2c652ECdMUDTWXA/B2QDfwN2NXl8JdkYUq28ppFHFm8F4MZ5UzTnmohklN89v57qhhCHjyjk3JmaxFykt0roCqWZnQ88BPQFNgNPAVV4A1uOwEvwrjSzy51z/0wmIOfcnbRyi9s5N6fZ9rhkPqMr3ffqJuqCYQ4fUcicKYPTHY6ISJfZWVHHg69vAeDms6fh8+kLtUhvFXdCaWaHAY8DG4HPOudebqHMqXiTmv/ZzI6JTk6esarqg9z/2mYArj99kq5OikhGufP59TSGIhw/fgAfmDwo3eGISCdK5Jb3N/BGYp/SUjIJEN1/KrAXb77HjPbQ61uorA8xcXA+Z6vvpIhkkB0Vdfx16TYAblJ3H5FeL5GE8nTgnvamA4q+fy9wRkcC6+nqGsPc87I3svvzcybpVo+IZJS7XthAMOw4YcIAjp8wMN3hiEgnSyShHIjXbzIem6LlM9bjb2xlb00jo/r34cNHjUh3OCIiXWbX/joef8O7OnnD3ClpjkZEukIiCWUZ8a/PPT5aPiM1hiL88SVvmozPnjZR02SISEa564UNNIYjzB4/gBMnZvS1BZGMkUim8wJwjZkNaKtQ9P1rouUz0n/e3snO/fUMLsjhomM0ia+IZI6Synoei16dvHHu5DRHIyJdJZGE8sd4t7FfMrOTWioQ3f9itNxtHQ+v53HOHVgV55MnjiU3oCXGRCRz/P6FDTSGIhw3rr+uTopkkLinDXLOrTazS4EHgZfNbDOwgkPnoRwP1AOXO+feSX243d8bm8tZtaOSnCwflx4/Nt3hiIh0mdLKeh5b4i3k8KW5kzWyWySDJDSxuXPuCTNbDtwMfAi4oMnbu4A/AT9zzq1PVYA9zT2veH0nL5w1igH52WmORkSk6/zhpY00hCLMGlPEKZM076RIJkl4LW/n3EbgOgAzK8S7OlnlnKtMcWw9zta9tSxY7a0Sec0p49IbjIhIF9pT1cAji71VcW44U/NOimSahBPKpqJJZMYnkjH3v7YZ5+C0KYOZNKQg3eGIiHSZP760gfpghKNGF2lVHJEMpPlsUqSuMczflnkjG686eVx6gxER6UJl1Q089Hrs6qT6TopkIiWUKfLUip1U1ocYMyCP0yYPTnc4IiJd5u6XNlIfjHDkqH7MmaL2TyQTKaFMkdi388uOH6NlFkUkY5RVN/DgIl2dFMl0SihTYMW2Ct7esZ/sLB8XHTs63eGIiHSZP7y4gbpgmCNHF3H61CHpDkdE0kQJZQrErk6eO3O4pgoSkYxRWlV/oP37sq5OimQ0JZQdtL82yFMrdgJw+QmayFxEMsddL3h9J48eU8Rp6jspktGUUHbQv1bsoCEUYdqwAmaNKUp3OCIiXaK0sv7AvJNf1ryTIhlPCWUHPb7Umyro48eOVoMqIhnjdy9soCEU4dix/TlV806KZDwllB3wzs79rNpRScBvXHD0yHSHIyLSJXbvr+fR6JrdX56nq5MiooSyQ/5/e/ceI1dZxnH8+3RZIC0tFXvTSkytQVSU2hbEC0XFcpMIKIjhHy/xCiQQjcFrtEgC0djUQOMfxkAlYpTEVBAVUcRrRUtvIIJguJXS1nLrltqy2z7+MbOybra7szsz5wxzvp/kZHbevtN53tnJr0/PnHPmxrWbATjldXM8GUdSZXzj1vt4fmA/x887grfOf2nZ5UjqADaUE7R3YD+rNzwOwHmLX1FyNZJUjA2PPcNP1tWy70tnvNa9k5IAG8oJu/2+7Tyzu5850w7lRL8ZR1IFZCaX3/x3AN63cC7HHjm93IIkdQwbygn6yfrapYLev2guPX4zjqQKuGnjFtY9+gyTD+7hstOOLrscSR3EhnICdvXDHx98EoBz3uTH3ZK639PPPc8Vt/wDgAvfMZ/Z0w4tuSJJncSGcgI2PBkM7E+OmTuNV886rOxyJKmtMpOv3vR3/t23l/kzp/CxE19VdkmSOowN5QSs3VF72c5e4KWCJHW/6//yCDdt3MKkgG99YAGH9vaUXZKkDtNxDWVEXBQRD0fEnoi4MyKOH2P+eRFxX33+3RFxRjvr2/z0f3ioL4iAM9/48nY+laQu1OkZN9wv73mCZTffC8Blpx3NAk/EkTSCjmooI+J8YDmwDFgIbARujYhZB5j/VuCHwPeANwGrgdURcUy7avzZpicAOGHeEcw53GOIJDXuxZBxg/YO7Ofq3zzAhT9Yx779yfsWzuUTS/yoW9LIDiq7gGE+A3w3M68FiIhPAe8BPgpcNcL8S4BfZuY36/e/EhFLgYuBT430BBFxCHDIkKGpAP39/fT3949aXGby0421hvKM188cc343GVxrldYMrtt1NzZ/HNqacc3kG8D9W/tYteYR7n1oEl9Zfwc79wwAcN6iuXz9va9jYGCgwWW++Pied91V0M6Mi8ycUFGtFhEHA7uBczNz9ZDxVcD0zDxrhMc8CizPzBVDxpYBZ2fmsQd4nq8BXx0+fsMNNzB58uRRa3z8OfjGpoPoieSKxfuY3GntuKRC7d69mwsuuADg8MzcOdrcIjKumXwDeODZ4Jp7Xzg+8vDe5L2v3M+iGYnXL5eqZzwZ10kt0QygB9g2bHwbcKALns05wPw5ozzPldQ+cho0Fdh8yimnMG3atFELfG7vAC+Z9wR/WHcPZ52+lN7e3lHnd5P+/n5uu+02li513VXguhtb986do+brcEVk3ITzDWB7315y5iPseOxfnLlkMcfNm1GZ6+z6nnfdVdDOjOukhrIQmbkX2Dt4f/Brw3p7e8d8caf39nLu4iOZvP3uhuZ3I9ddLa577HmdpJl8A5h7RC+Xvvsofv7zBzlh/syOW18RfM9Xi+see16jOumknB3APmD2sPHZwNYDPGbrOOdLUlnMOEldq2Maysx8HrgLOHlwLCIm1e+vOcDD1gydX7d0lPmSVAozTlI367SPvJcDqyJiLfBX4FJgCjB4RuT3gccz8wv1+d8GfhcRnwVuAT4ILAY+Md4nbvQ4gf7+fnbv3s3OnTsrtZvcdbvuKhjvusd5DCWUlHHjqdPfveuuAtfdhozLzI7aqF0O4xFqxwHdCbx5yJ/dAVw3bP55wP31+fcAZ4zz+eYC6ebm5tbENrcTMw7zzc3NrTXbmBnXMZcNKkvUjlp/OdDX4EOmApuBV4zjMd3AdbvuKpjIuqcCW7IDw3QC+Qb+7l13NbjuFmdcp33kXbj6C/R4o/PjhYux9Y11TaZu4rpddxVMcN0d+/qMN9/A3z2uuxJcd+szrmNOypEkSdKLkw2lJEmSmmJDOX57gWUMuXhwRbjuanHd1VXV18B1V4vrbrHKn5QjSZKk5riHUpIkSU2xoZQkSVJTbCglSZLUFBtKSZIkNcWGchwi4qKIeDgi9kTEnRFxfNk1tVtELImImyNiS0RkRJxddk1FiIgvRMTfIqIvIrZHxOqIeE3ZdbVbRHw6IjZFxM76tiYiTi+7riJFxOfr7/UVZddSNDOuGhlnvlU336B9GWdD2aCIOB9YTu10+4XARuDWiJhVamHtN4XaWi8qu5CCnQSsBE4AlgK9wK8iYkqpVbXfZuDzwCJgMXA78NOIeH2pVRUkIo4DPglsKruWoplxlco4862C+QbtzTgvG9SgiLgT+FtmXly/Pwl4DLg6M68qtbiCREQC52Tm6rJrKVpEzAS2Aydl5u/LrqdIEfEU8LnM/F7ZtbRTRBwGrAMuBL4MbMjMS0stqkBmXHUzznzr/nyD9meceygbEBEHU/sfza8HxzJzf/3+W8qqS4U6vH77VKlVFCgieiLig9T24Kwpu54CrARuycxfjzmzy5hxlWe+VUNbM+6gdvylXWgG0ANsGza+DTi6+HJUpPqemhXAnzLznpLLabuIeAO1gD0U2EVtj8295VbVXvV/WBYCx5VdS0nMuIoy37o/36CYjLOhlMa2EjgGeHvZhRTkfmABtb0W5wKrIuKkbg3diDgS+DawNDP3lF2PVDDzrYvzDYrLOBvKxuwA9gGzh43PBrYWX46KEhHXAGcCSzJzc9n1FCEznwcerN+9q34Q9yXUDuTuRouAWcC6iBgc6wGWRMTFwCGZua+s4gpixlWQ+VaJfIOCMs5jKBtQfwPeBZw8OFb/mOBkqnPsRaVEzTXAOcC7MvOhsmsq0STgkLKLaKPfAG+gttdicFsL/ABYUIFm0oyrGPPt/3R7vkFBGeceysYtp7ZrfC3wV+BSagfzXltmUe1WPyvs1UOG5kXEAuCpzHy0nKoKsRK4ADgL6IuIOfXxZzPzP+WV1V4RcSXwC+BRYCq11+AdwKklltVWmdkH/N+xYxHxHPBkFY4pG8KMq6lCxplvFck3KC7jbCgblJk/ql9a4XJgDrABOC0zhx/E3m0WA78dcn95/XYV8OHCqynOp+u3dwwb/whwXaGVFGsW8H3gZcCz1K5Vdmpm3lZqVWo7M+5/qpBx5pv51nJeh1KSJElN8RhKSZIkNcWGUpIkSU2xoZQkSVJTbCglSZLUFBtKSZIkNcWGUpIkSU2xoZQkSVJTbCglSZLUFBtKVV5EXBcRq8uuQ5LawYxTEfzqRXW1iBjrq6CWAZcAUUA5ktRSZpw6hQ2lut3Lhvx8PrXvKX7NkLFdmbmr2JIkqWXMOHUEP/JWV8vMrYMb8Gxt6IWxzNw1/OOgiLgjIq6OiBUR8XREbIuIj0fElIi4NiL6IuLBiDh96HNFxDER8YuI2FV/zPURMaPgJUuqEDNOncKGUhrZh4AdwPHA1cB3gBuBPwMLgV8B10fEZICImA7cDqwHFgOnAbOBHxdduCQ1wIxTS9lQSiPbmJlXZOYDwJXAHmBHZn63PnY58FLgjfX5FwPrM/OLmXlfZq4HPgq8MyKOKmMBkjQKM04t5TGU0sg2Df6Qmfsi4kng7iF/vq1+O6t+eyy1YB3pWKX5wD/bUqUkTYwZp5ayoZRG1j/sfg4dy8yMCHhhL/9hwM3AZSP8XU+0o0BJaoIZp5ayoZRaYx3wfuDhzBwouxhJajEzTqPyGEqpNVYCRwA/jIjjImJ+RJxaP2Oyp+ziJKlJZpxGZUMptUBmbgHeBvRQOzvybmAF8Aywv7TCJKkFzDiNJTLHusi+JEmSdGDuoZQkSVJTbCglSZLUFBtKSZIkNcWGUpIkSU2xoZQkSVJTbCglSZLUFBtKSZIkNcWGUpIkSU2xoZQkSVJTbCglSZLUFBtKSZIkNeW/0H6BaCrlY3EAAAAASUVORK5CYII=", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "y_step = fom.step_resp()\n", "fig, ax = plt.subplots(fom.dim_output, fom.dim_input, sharex=True, constrained_layout=True)\n", "for i in range(fom.dim_output):\n", " for j in range(fom.dim_input):\n", " ax[i, j].plot(np.linspace(0, fom.T, y_step.shape[0]), y_step[:, i, j])\n", "for i in range(fom.dim_output):\n", " ax[i, 0].set_title(f'Output {i + 1}', loc='left', rotation='vertical', x=-0.2, y=0.2)\n", "for j in range(fom.dim_input):\n", " ax[0, j].set_title(f'Input {j + 1}')\n", " ax[-1, j].set_xlabel('Time')\n", "_ = fig.suptitle('Step response')" ] }, { "cell_type": "markdown", "id": "039b30c5", "metadata": {}, "source": [ "## Transfer function evaluation\n", "\n", "The transfer function {math}`H` is the function such that\n", "{math}`Y(s) = H(s) U(s)`,\n", "where {math}`U` and {math}`Y` are respectively the Laplace transforms of\n", "the input {math}`u` and the output {math}`y`,\n", "assuming zero initial condition ({math}`x(0) = 0`).\n", "The expression for {math}`H` can be found by applying the Laplace transform\n", "to the system equations to obtain\n", "\n", "```{math}\n", "\\begin{align}\n", " s E X(s) & = A X(s) + B U(s), \\\\\n", " Y(s) & = C X(s) + D U(s).\n", "\\end{align}\n", "```\n", "\n", "using that {math}`s X(s)` is the Laplace transform of {math}`\\dot{x}(t)`.\n", "Eliminating {math}`X(s)` leads to\n", "\n", "```{math}\n", "Y(s) = \\left( C (s E - A)^{-1} B + D \\right) U(s),\n", "```\n", "\n", "i.e., {math}`H(s) = C (s E - A)^{-1} B + D`.\n", "Note that {math}`H` is a matrix-valued rational function\n", "(each component is a rational function).\n", "\n", "The transfer function of a given `LTIModel` is stored as the attribute\n", "`transfer_function`.\n", "It can be evaluated using its\n", "`eval_tf` method.\n", "The result is a NumPy array." ] }, { "cell_type": "code", "execution_count": 11, "id": "6bbb3898", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[0.56266667 0.61333333]\n", " [0.620175 0.50166667]\n", " [0.564075 0.38833333]]\n", "[[0.35516035 0.42800414]\n", " [0.39053974 0.30625375]\n", " [0.35602872 0.21798312]]\n", "[[0.41916591-0.24498821j 0.49022668-0.21786001j]\n", " [0.46133002-0.27112399j 0.36609293-0.23081817j]\n", " [0.42019995-0.24562591j 0.26612665-0.20191321j]]\n" ] } ], "source": [ "print(fom.transfer_function.eval_tf(0))\n", "print(fom.transfer_function.eval_tf(1))\n", "print(fom.transfer_function.eval_tf(1j))" ] }, { "cell_type": "markdown", "id": "d5451641", "metadata": {}, "source": [ "Similarly, the derivative of the transfer function can be computed using the\n", "`eval_dtf` method.\n", "The result is again a NumPy array." ] }, { "cell_type": "code", "execution_count": 12, "id": "f9490ca2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-0.32905051 -0.28965578]\n", " [-0.36417571 -0.31024153]\n", " [-0.32990749 -0.27380581]]\n", "[[-0.13086074 -0.11936496]\n", " [-0.14479475 -0.12300531]\n", " [-0.1312008 -0.10527819]]\n", "[[-0.1198173 +0.21367653j -0.11093146+0.18362116j]\n", " [-0.13256763+0.23652374j -0.11255455+0.20186916j]\n", " [-0.12012849+0.21423385j -0.09488566+0.18167128j]]\n" ] } ], "source": [ "print(fom.transfer_function.eval_dtf(0))\n", "print(fom.transfer_function.eval_dtf(1))\n", "print(fom.transfer_function.eval_dtf(1j))" ] }, { "cell_type": "markdown", "id": "d0231e0c", "metadata": {}, "source": [ "To evaluate the transfer function over a sequence of points on the imaginary\n", "axis,\n", "the `freq_resp` method\n", "can be used.\n", "A typical use case is plotting the transfer function,\n", "which is discussed in the next section.\n", "\n", "## Magnitude and Bode plots\n", "\n", "It is known that if the input is chosen as\n", "{math}`u(t) = a e^{\\xi t} \\sin(\\omega t + \\varphi) e_j`\n", "(where {math}`e_j` is the {math}`j`-th canonical vector),\n", "then\n", "\n", "```{math}\n", "\\lim_{t \\to \\infty}\n", "\\left(\n", " y_i(t)\n", " - a \\lvert H_{ij}(\\xi + \\boldsymbol{\\imath} \\omega) \\rvert e^{\\xi t}\n", " \\sin(\\omega t + \\varphi + \\arg(H_{ij}(\\xi + \\boldsymbol{\\imath} \\omega)))\n", "\\right)\n", "= 0.\n", "```\n", "\n", "In words, if the input is a pure exponential,\n", "the frequency is preserved in the output,\n", "the amplitude is multiplied by the amplitude of the transfer function, and\n", "the phase is shifted by the argument of the transfer function.\n", "In particular, if the input is sinusoidal, i.e., {math}`\\xi = 0`,\n", "then the output is also sinusoidal.\n", "\n", "It is of interest to plot the transfer function over the imaginary axis to\n", "visualize how the LTI system responds to each frequency in the input.\n", "Since the transfer function is complex-valued (and matrix-valued),\n", "there are multiple ways to plot it.\n", "\n", "One way is the \"magnitude plot\", a visualization of the mapping\n", "{math}`\\omega \\mapsto \\lVert H(\\boldsymbol{\\imath} \\omega) \\rVert`,\n", "using the `mag_plot`\n", "method." ] }, { "cell_type": "code", "execution_count": 13, "id": "c87951fb", "metadata": {}, "outputs": [ { "data": { "image/png": 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azBxwonPuzWrzJgNTnXOXBl77gBXAA865281sP+Ba59yJgffvBaY4517YxTZuAm4Mnv/CCy+QkbHrB1qKSMOs3w6vLfWxYKu//HRp6hjTvYI99NdOROqhqKiIMWPGAOQ45/JrWjZui5CZpQJFwClB5WgC0Mw5d3zgZOl5wEhgKzAN2M85t4kQdrFHaOXGjRvJzs4O6/dTVlbGxIkTGTVqFCkputlcpGicoyMc4+yc47/TV/PP9xdQUFxOSpJx7RG9OHefzvh0h+od9DMdHRrn6IjUOOfn59OqVSuoRRGK9UNjNWkFJAHrguavA3oDOOfKzexq4DP850PdsasSFFi+BNhxTa+Z/5dvSkpKxP4iRHLd8guNc3Q0dJzP2LsrI3u35frXZ/HZgg388/0FfLVkM/8+dSBtstLDmDT+6Wc6OjTO0RHuca7Luhr9QXjn3NvOuV7OuR7OuUe9ziMiNWuX04Qnxw7n7yf0Jy3ZxxcLN3D0vV/yxcINXkcTkUYonovQRqACaBs0vy2wNvpxRCRczIyz9+nCO5cdQO89sthUWMq5T03hvo8XUVkZH4fzRSQ+xG0Rcs6V4j/n57CqeYGTpQ8DvvUql4iET6+2Wbw5bn/OGNEZ5+Cejxdy3oSpbCkq9TqaiDQSMV2EzKypmeWaWW5gVrfA686B13cDF5rZuWbWB3gI/yX3TzVwu+PMbC4wpSHrEZGGS09J4raTBnDnKQNJS/YxacEGfvvg1yxaV+B1NBFpBGK6CAHDgOmBCfzFZzpwC4Bz7mXgmsDrPCAXOMo5F3wCdZ0458Y75/rivzO1iMSAU4d14vU/7EfH5k34aXMRJ/7nGz6bX+fbhYmI7CSmi5BzbpJzzkJMY6st86BzrotzLs05t7dzbrKHkUUkgvq1z+GtcfszolsLtpWUc96EqTz+5Y96PIeI1FtMFyERkWAtm6bx3Pl7c/rwTjgHt747j5vfmUuFTqIWkXpQERKRuJOa7OO2kwbwl2P6APD0N8u45LlpepK9iNSZipCIxCUz48KD9mT8mCGkJvv4aO46xjz+na4oE5E6URESkbj2m4HteP6CvclpksL0n7Zw2iPfsi6/2OtYIhInVIRC0OXzIvFleNcWvHrxvrTNTmPhum2c/NA3LNtY6HUsEYkDKkIh6PJ5kfjTq20Wr128H11bZrDy5+2c8vC3LFirew2JSM1UhESk0ejUIoNXL96PPu2y2bithNMf/ZY5q7d6HUtEYpiKkIg0Kq2z0njxwr0Z2DGHn4vKGPPYZGas2OJ1LBGJUSpCItLoNMtI5bkL9mZI52Zs3V7GWY9PJk9lSERCUBESkUYpOz2FZ87fmxHdWlBQUs45T0xm9iodJhORnakIiUij1TQtmafGDmdYl+bkF5dz1hOTmb823+tYIhJDVIRC0OXzIo1HZloyT/1uOIM6NWNLURlnPjaZxet1NZmI+KkIhaDL50Ual6z0FJ753Qj6tc9mU2EpYx6bzFLdZ0hEUBESkQSRk5HCs+fvTe89slhfUMKYx75jxeYir2OJiMdUhEQkYbTI9F9N1r11Jmu2FnPGY9+xest2r2OJiIdUhEQkobRqmsYLF+6z4w7UZz8xmZ8L9aBWkUSlIiQiCadtdjrPX7gP7XLSWbKhkLFPT6WwpNzrWCLiARUhEUlIHZo14dnzR9AsI4UZK7Zw8XPTKC2v9DqWiESZipCIJKwebbJ4auxwMlKT+HLRRq5+dQaVlc7rWCISRSpCIpLQBnduzsNnDSUlyXhnxmpufmcOzqkMiSQKFaEQdENFkcRyUK/W/PvUQZjBhG+X88Cni72OJCJRoiIUgm6oKJJ4js/twE3H9QPg7okLee675R4nEpFoUBESEQk4d7+uXH5YTwBueGs2E+eu8ziRiESaipCISDVXHd6T04d3otLBZS/+QN6KLV5HEpEIUhESEanGzPj7Cf05uFdrissqOf/pqSzfpOeSiTRWKkIiIkFSknyMP3PIjoe0jn1qKpt192mRRklFSEQkhKZpyTw1djgdmjVh6cZCLpgwleKyCq9jiUiYqQiJiOxCm+x0Jpw3nOz0ZH74aQtXvDSdCt1wUaRRURESEalBjzZZPH7ucFKTfHw4Zx1//99cryOJSBipCImI7MaIbi2467RBADz9zTKe/nqpx4lEJFxUhEREauG4Qe257qjeANzyv7l8Ol/3GBJpDFSEQtAjNkQklIsP3pPRw/z3GLr0henMXZ3vdSQRaSAVoRD0iA0RCcXMuPXE/uzXvSVFpRWcP2Eq6/KLvY4lIg2gIiQiUgcpST4eOnMo3VtnsmZrMedPmEpRabnXsUSknlSERETqKCcjhafGjqBFZiqzV+Vz+Yt5uqxeJE6pCImI1EPnlhk8ds5QUpN9fDxvHbe9N8/rSCJSDypCIiL1NLRLC/59qv+y+se/Wspz3y33OJGI1JWKkIhIA/x2UHuuHtULgBvfnsPnCzd4nEhE6kJFSESkgS49tAcnDelARaXj0ud/YMHaAq8jiUgtqQiJiDSQmXHbSQMY0a0FBSXlnPf0VDYUlHgdS0RqQUVIRCQM0pKTeOSsoXRrlcmqLdu54Jnv2V6qp9WLxDoVIRGRMGmemcqTY4fTLCOFGSu2cPWreVTqsnqRmKYiJCISRt1aZfLIWUNJSTLem7WWOz9a4HUkEamBilAIetaYiDTE3nu25PaTBgLw0KQlvDJ1hceJRGRXVIRC0LPGRKShTh7akcsP7QHA9W/M4pslGz1OJCKhqAiJiETIVaN6cdyg9pRXOi5+dhqL12/zOpKIBFEREhGJEDPjzlMGMqRzM/KL/ZfVby4s9TqWiFSjIiQiEkHpKUk8ds4wOrVowk+bi7jome8pKddl9SKxQkVIRCTCWjZN48lzh5OVnsz3y3/mutdm4pwuqxeJBSpCIiJR0LNtFg+dOZQkn/Fm3mru/2Sx15FEBBUhEZGoOaBnK249oT8A93y8kLfyVnmcSERUhEREouiMEZ35/UF7AnDtqzP5ftlmjxOJJDYVIRGRKLvuqN4c0bctpRWVXPTsNJZvKvQ6kkjCUhESEYkyn8+49/RcBnTIYXNhKec9PZWtRWVexxJJSCpCIiIeyEhN5vFzh9EuJ50lGwq55PlplFVUeh1LJOGoCImIeKRtdjpPnDuczNQkvlmyib++MVuX1YtEmYqQiIiH+rbP5oExg/EZvPz9Ch754kevI4kkFBUhERGPHdq7LTcc2xeA29+fzwez13icSCRxqAiJiMSAsft349x9uwBw5ct5zFixxdtAIglCRUhEJEb87di+jNyrNcVllVzwzPes2rLd60gijZ6KUAhmNs7M5gJTvM4iIokjOcnHA2cMpvceWWwoKOH8p6dSUKzL6kUiSUUoBOfceOdcX2CE11lEJLFkpafwxNjhtM5KY/7aAi57cTrluqxeJGJUhEREYkyHZk14/JxhpKf4mLRgA3//31yvI4k0WipCIiIxaFCnZtw7OheACd8u5+mvl3obSKSRUhESEYlRR/Vvx5+P7g3ALf+by6fz13mcSKTxURESEYlhvz9oT0YP60Slg8temM68NQVeRxJpVFSERERimJlx64n92a97SwpLK7jouR/YWup1KpHGQ0VIRCTGpST5eOjMoXRvncna/BIem59EUWm517FEGgUVIRGROJCTkcKTY4fTPCOFFYXGNa/NprJSD2gVaSgVIRGRONGlZSYPjcklyRwT563nXx/M9zqSSNxTERIRiSNDuzRnTHf/DRYf+eJHXpzyk8eJROKbipCISJwZ1tpx+SHdAfjbm7P5atFGjxOJxC8VIRGROHTpIXty4uAOlFc6Lnl+GovW6bJ6kfpQERIRiUNmxu0nD2B41+YUFJdz3oSpbNxW4nUskbijIiQiEqfSkpN45OxhdG6RwYrN27nome8pLqvwOpZIXFEREhGJYy0yU3ly7HCy05P54actXPvaTJzTZfUitaUiJCIS53q0acrDZw0l2We8M2M193y8yOtIInFDRUhEpBHYr0cr/nnSAADu/2QRr/+w0uNEIvFBRUhEpJE4bVgnLhnpv6z+uv/OZPKPmzxOJBL7VIRERBqRa4/Yi6P770FZheP3z01j2cZCryOJxDQVIRGRRsTnM+4+LZdBHXPYUlTGeU9PZUuRHlcvsisqQiIijUyT1CQeO3cYHZo14ceNhVz83DRKyyu9jiUSk1SEREQaoTZZ6TwxdhhN05L57sfNXP/GLF1WLxKCilAIZjbOzOYCU7zOIiJSX733yObBMYPxGbw2bSX/mbTE60giMUdFKATn3HjnXF9ghNdZREQaYuRebbj5t/0AuPPDBbw7c43HiURii4qQiEgjd/a+Xfnd/l0B+OMreUz/6WdvA4nEEBUhEZEE8Nff9OWw3m0oKa/kwme+Z8XmIq8jicQEFSERkQSQ5DPuP2Mwfdtls3FbKedPmEp+cZnXsUQ8pyIkIpIgMtOSeWLsMNpkpbFw3TbGPf8D5RW6rF4Sm4qQiEgCaZfThCfOHU6TlCS+XLSRG9+eo8vqJaGpCImIJJgBHXO49/RczOD5yT/x5NfLvI4k4hkVIRGRBHRkvz24/ug+ANz67lw+nrvO40Qi3lAREhFJUBcc2I0zRnTGObj8penMXrXV60giUaciJCKSoMyMW47vx4E9W1FUWsH5E6aydmux17FEokpFSEQkgaUk+XhwzBB6tmnKuvwSzp8wlcKScq9jiUSNipCISILLaZLCk2OH0zIzlTmr87nipTwqKnUlmSQGFSEREaFTiwwePWcYqck+Pp63jtvem+d1JJGoUBESEREAhnZpzl2nDgLg8a+W8tx3yz1OJBJ5KkIiIrLDcYPac80RvQC48e05fL5wg8eJRCJLRUhERHYy7pAenDSkAxWVjkuf/4EFawu8jiQSMSpCIiKyEzPjtpMGMKJbCwpKyjnv6alsKCjxOpZIRKgIiYjIr6QlJ/HIWUPp2jKDVVu2c+Ez31NcVuF1LJGwUxESEZGQmmem8uTY4TTLSCFvxRaufW2mHtAqjY6KkIiI7NKerZvy8FlDSfYZ78xYzaNf/Oh1JJGwUhESEZEa7bNnS248ri8A//pgvq4kk0ZFRUhERHbrrH26MHpYJyodXPbCDyzbWOh1JJGwUBESEZHdMjNuOaEfgzs3I7+4nIue/V7PJJNGQUVIRERqJS05iYfPGkqbrDQWrtvG1a/M0MnTEvdUhEREpNbaZqfz8NlDSU3y8cGctYz/bLHXkUQapMFFyMzSwxFERETiw5DOzbnl+H4A3DVxIZ/MW+dxIpH6q1cRMjOfmf3NzFYB28xsz8D8v5vZ+WFNKCIiMef0EZ05e58uOAdXvpTH4vXbvI4kUi/13SP0V2As8CegtNr82cAFDcwkIiJx4G/H9mVEV/9jOC569nvyi8u8jiRSZ/UtQucAFznnngeq33N9BtC7walERCTmpSb7GH/mENrlpPPjhkKueimPykqdPC3xpb5FqAMQ6gw5H5BS/zgiIhJPWmel8cjZQ0lN9vHJ/PXc+/FCryOJ1El9i9Bc4MAQ808Bptc/joiIxJuBHZtx24kDALj/08V8MHuNx4lEai+5np+7BZhgZh3wl6mTzGwv/IfMjg1XOBERiQ8nD+3InNX5PPn1Uv74ygy6tWrKXntkeR1LZLfqtUfIOfcWcBxwOFCIvxj1AY5zzk0MXzwREYkX1x/Tm/26t6SotIKLnv2erUU6eVpiX73vI+Sc+9I5N8o518Y5l+GcO8A591E4w4WLmb1hZj+b2WteZxERaaySk3w8OGYIHZs3YfmmIi598QcqdPK0xLhEubP0ffgP24mISAS1yEzl0bOHkZ7i48tFG7njw/leRxKpUa2LUGCPyubaTJEMXB/OuUlAgdc5REQSQd/22dx5yiAAHvn8R96esdrjRCK7Vpc9QlcCVwWmWwPzPgRuCkwfBub9vS4BzOwgM3vHzFabmTOzE0IsM87MlplZsZlNNrMRddmGiIhE13GD2nPxwd0B+NNrM5izeqvHiURCq3URcs5NqJqA/YEbnHNnOOfuD0xnADcAB9cxQyb+GzGOC/WmmY0G7gZuBoYElv3QzNpUWybPzGaHmNrXMYuIiITJtUfuxUG9WlNcVslFz0xjc2Hp7j8kEmX1vXz+SOC6EPM/AG6vy4qcc+8D7wOYWahF/gg85px7KrDMxcBvgPOqtuWcy63LNnfFzNKAtGqzsgDKysooKwvv1Q9V6wv3emVnGufo0DhHT7yN9d2n9Oekh7/jp83b+cNz3/PUuUNJTor901PjbZzjVaTGuS7rM+fqfka/mS0H7nfO3RU0/2rgcudclzqv1P95B5zonHsz8DoVKAJOqZoXmD8BaOacO74O6x4JXOqcO6WGZW4Cbgye/8ILL5CRkVHbTYmISDVriuDuWUmUVhoHt6vkpK6VXkeSRq6oqIgxY8YA5Djn8mtatr57hG4EHg+Ui8mBeXsDRwEX1nOdobQCkoB1QfPXUYdnmpnZx8AgINPMVgKnOue+DbHobfgPw1XJAlYeccQRZGdn1yn47pSVlTFx4kRGjRpFSoqeShIpGufo0DhHT7yOdcc+67j0pRl8vsbHb/YdyImDY/vMhXgd53gTqXHOz6+x++ykXkXIOfe0mc0DLgdOCsyeBxzgnJu86096wzl3eC2XKwFKql5XHapLSUmJ2F+ESK5bfqFxjg6Nc/TE21gfm9uRhesLuf/Txfz17bns1S6HQZ2aeR1rt+JtnONVuMe5LutqyA0VJzvnznTODQlMZ0agBG3E/3T7tkHz2wJrw7wtERGJoCsP78XhfdpQWl7J75+dxoaCkt1/SCTC6lWEzKxzTVO4wjnnSoFpwGHVtu0LvA51aEtERGKUz2fcMzqX7q0zWZtfzB+en0Zpuc4XEm/Vd4/QMmBpDVOtmVlTM8s1s9zArG6B11WF6m7gQjM718z6AA/hv+T+qXpmFxERj2Slp/DoOcPISktm6rKfueV/c7yOJAmuvkVoMP57+lRNewMXAwuBU+u4rmHA9MAE/uIzHf+DXHHOvQxcE3idB+QCRznngk+gDpvADRznAlMitQ0RkUTVvXVT7jsjFzN47rufeHHKT15HkgRW35OlZ4SY/b2ZrQauBV6vw7omASFvIFRtmQeBB+uSsSGcc+OB8WaWDeh2qCIiYXZo77ZcPaoX//5oITe8NZtebZsytEsLr2NJAgr3Xa0WAMPDvE4REWmExh3Sg6P770FZhePi535gXX6x15EkAdX3ZOnsoCnHzHrjfwbZovBGFBGRxsjM+Pepg9irbRYbCkr4/bPTKCmv8DqWJJj67hHaAvxcbdoMzAX2BS4JSzIREWn0MtOSefScoWSnJ5O3Ygs3va2TpyW66luEDgEOrTaNBPoC3Xdxx2YREZGQurTM5MExQzCDF6es4I3pK72OJAmkvkXIAV875z4PTF865+YDmNlB4YvnDV01JiISXQf1as3lh/YE4PrXZ7N4fYHHiSRR1LcIfQaEOr0/J/BeXHPOjXfO9QVGeJ1FRCRRXH5YT/bv0ZLtZRX84fkfKCot9zqSJID6FiHDv1coWEugsP5xREQkUSX5jHtHD6Z1VhoL123jhrd0vpBEXp3uI2RmVfcHcsDTZlb9QTFJwEDgmzBlExGRBNM6K437Tx/MmY9/x2vTVjKiWwtOG9bJ61jSiNV1j9DWwGRAQbXXW/E/BPVR4KxwBhQRkcSyb/eW/HFULwBueGs2C9bqfCGJnDrtEXLO/Q7AzJYB/3bO6TCYiIiE3R9G9mDKsp/5YuEG/vD8NN6+9AAy0+r1MASRGtXrHCHn3M0qQSIiEik+n3HPaYPYIzudJRsK+csbs3Au1KmpIg1T6yJkZj+YWfPA19MDr0NOkYsrIiKJomXTNB4YM5gkn/Fm3mpemrrC60jSCNVlP+NbQNXJ0W+GP0rsMLNxwDjC/yw2ERGpg+FdW3DNEXvxrw/mc+PbcxjYMYd+7XO8jiWNSK2LkHPu5lBfN0Z6+ryISOz4/UF7MmXpJj5bsIFxz//AO5cdQFZ6itexpJFo0B4PM0s1s45m1rn6FK5wIiIiPp9x92m5tM9JZ9mmIv78us4XkvCp79Pne5nZl8B2YDmwNDAtC/wpIiISNs0zU3nwzCEk+4x3Z67hue+Wex1JGon67hF6CqgEjgWGAkMC0+DAnyIiImE1pHNz/nx0bwD+/r95zFqpMxek4epbhHKB3zvn3nfO5TnnZlSfwphPRERkh/MP6Maovm0prahk3As/kF9c5nUkiXP1LUJzgVbhDCIiIrI7Zsa/TxlEx+ZN+GlzEX96dabOF5IGqW8Rug64w8xGmllLM8uuPoUzoIiISHU5GSmMHzOElCTjgzlreerrZV5HkjhW3yL0MbAP8AmwHvg5MG0J/CkiIhIxgzo14y/H9AHgtvfnkbdii7eBJG7V98Eth4Q1RYzRDRVFRGLfuft1Zcqyzbw3ay3jnv+Bdy8/gGYZqV7HkjhTryLknPs83EFiiW6oKCIS+8yM208eyJzV+SzfVMQ1r87ksXOGYmZeR5M4Ut/7CA3cxTTAzHqaWVq4g4qIiATLTvefL5Sa5OPjeet4/Evdyk7qpr6HfvKA6SGmPGA+sNXMJphZehgyioiI7FL/Djn87bi+APzrg/lMW77Z40QST+pbhE4EFgEX4b+nUG7g6wXAGOB84FDg1gYnFBER2Y2z9u7McYPaU17puPSF6WwuLPU6ksSJ+hahvwBXOOeecM7NCkxPAFcBVzvnngcuw1+YREREIsrMuO2kAezZKpM1W4v54yt5VFbq/kKye/UtQgPwP2Ms2PLAe+A/TNaunusXERGpk6ZpyYw/cwhpyT4mLdjAw18s8TqSxIH6FqH5wJ/NbMd1imaWAvw58B5AB2Bdw+KJiIjUXp922dz8234A3PXRQqYs1flCUrP6FqFx+B+4utLMPjazj4GVgXmXBJbZE/hPwyOKiIjU3ujhnThxcAcqKh2XvfgDG7eVeB1JYli9ipBz7hugG3ADMDMw3QB0c859F1jmWefcneEKKiIiUhtmxq0n9Kd760zW5Zdw1cs6X0h2rd53TnbOFTjnHnbO/TEwPeKcKwhnOK+Y2TgzmwtM8TqLiIjUXWZaMg+dNZT0FB9fLtrI+M8Wex1JYlSDHiFhZn3N7Cgz+231KVzhvOKcG++c6wuM8DqLiIjUT6+2Wdx6gv/6nXs+Xsg3SzZ6nEhiUb0esWFmewJv4L9CzAFV9zOv2veY1PBoIiIiDXPK0I5M/nETr05byeUv5vHeFQfQJkv3+pVf1HeP0H3AUqANUAT0Aw4CvgdGhiWZiIhIGNxyfH/2apvFxm0lXPFiHhU6X0iqqW8R2he4wTm3EagEKp1zXwH/B9wfrnAiIiIN1SQ1ifFnDiEjNYlvf9zE/Z8s8jqSxJD6FqEkoOrE6I1A+8DXy4G9GhpKREQknHq0aco/T/SfL/TAp4uYtvxnjxNJrKhvEZoNDAp8PRn4k5ntj/8S+h/DEUxERCScThjcgRMHd6DSwVUv57GtpNzrSBID6luEbq322Rvx31PoS+AY4Iow5BIREQm7m4/vR4dmTfhpcxG3vDPH6zgSA+p7Q8UPnXOvB75e5JzrDbQC2jjnPglnQBERkXDJTk/h7tMGYQavfL+SD2av9TqSeKxOl8+b2ZO1WAbn3Hn1jyQiIhI5e+/Zkt8f1J2HP1/C/70+kyGdm9EmW5fUJ6q67hEaCxwCNAOa1zCJiIjErD+O6kXfdtn8XFTGta/NxDldUp+o6lqEHgJy8J8T9BlwvnPuxOAp7ClFRETCKDXZx32n55KW7OPzhRt49rvlXkcSj9SpCDnnxgHtgDuA44AVZvaKmR1pZlbzp0VERGJHz7ZZ/N/RvQH4x7vzWLy+UTwuU+qozidLO+dKnHMvOudGAX2BOcB/gGVm1jTcAb2gh66KiCSGc/btykG9WlNSXsmVL+dRWl7pdSSJsgY9dBX/XaWrnjXWaJ4vpoeuiogkBp/PuPOUgTTLSGH2qnzu/Xih15EkyupchMwszczOMLOJwEL8D169FOjsnNsW7oAiIiKR1DY7ndtP8t91+qHPlzBl6WaPE0k01akImdl/gDXAn4H/AZ2cc6c6595zzml/ooiIxKWj+rfjlKEdcYG7ThcUl3kdSaKkTvcRAi4GfsL/GI2DgYNDnSPtnDup4dFERESi58bj+jJ56SZWbN7O39+dz8gmXieSaKjrobFn8F82vwXYWsMkIiISV7LSU7jntFx8Bm/krWH6Jl0MnQjqtEfIOTc2QjlEREQ8N6xrC/4wsgcPfraYV5b4OD+/mE4tU7yOJRHU0KvGREREGpUrDu/JgA7ZFFUY170+m8pK3XW6MVMREhERqSYlyce/Tx5Ais/xzZLNPP3NMq8jSQSpCImIiATZs3UmJ3TxXwx9+wfzWbBWd51urFSEREREQti/rePgXq0oDdx1uqS8wutIEgEqQiIiIiGYwW0n9KNFZirz1uRz90e663RjpCIkIiKyC62z0nbcdfrRL3/k2yWbPE4k4aYiJCIiUoMj+u3B6cM74Rxc/UoeW7frrtONiYqQiIjIbvzt2L50aZnB6q3F3PDWbK/jSBipCImIiOxGZloy94zOJclnvJW3mrfyVnkdScJERSgEMxtnZnOBKV5nERGR2DCkc3MuPaQHAH99czartmz3OJGEg4pQCM658c65vsAIr7OIiEjsuPTQHuR2akZBcTnXvDJDd51uBFSEREREaiklycc9o3NpkpLEtz9u4omvlnodSRpIRUhERKQOurXK5Ibj+gJw54cLmLs63+NE0hAqQiIiInV0+vBOHN6nLaUVlVz58nSKy3TX6XilIiQiIlJHZsbtJw+gVdNUFq7bxp0fLvA6ktSTipCIiEg9tGqaxh2nDATgia+W8tWijR4nkvpQERIREamnQ3u35cy9OwNwzasz2FJU6nEiqSsVIRERkQb4y2/6sGerTNbmF/OXN2bjnC6pjycqQiIiIg2QkZrMvafnkuwz3p21hjem667T8URFSEREpIEGdmzGFYf1BODGt+awYnORx4mktlSEREREwuCSkd0Z2qU5BSXlXP2q7jodL1SEREREwiA5ycc9p+WSkZrElKWbeeqbZV5HklpQERIREQmTzi0z+Mtv+gBwxwfzWbx+m8eJZHdUhERERMJozIjOHNizFSXllVz96gzKKyq9jiQ1UBESEREJIzPjjlMGkpWezIwVW3jkix+9jiQ1UBESEREJs3Y5TbjpuH4A3PvxQuat0YNZY5WKkIiISAScNKQDo/q2pazC8cdXZlBarkNksUhFSEREJALMjH+eOIDmGSnMW5PPg58u8jqShKAiJCIiEiGts9K49YQBAIyftIQZK7Z4G0h+RUVIREQkgn4zsB3HDWpPRaXj6ldnUFxW4XUkqUZFSEREJMJu+W0/WmelsXj9Nu6euNDrOFKNipCIiEiENc9M5bYT/YfIHvvyR6Yu2+xxIqmiIiQiIhIFh/dty6lDO+IcXPPqDIpKy72OJKgIhWRm48xsLjDF6ywiItJ4/O24vrTPSWf5piJuf3++13EEFaGQnHPjnXN9gRFeZxERkcYjOz2FO04ZBMAz3y7n68UbPU4kKkIiIiJRdEDPVpy9TxcA/vTaTPKLyzxOlNhUhERERKLsz0f3pnOLDFZt2c6t/5vrdZyEpiIkIiISZZlpyfz71EGYwSvfr+STeeu8jpSwVIREREQ8MKJbCy44oBsAf359Fj8XlnqcKDGpCImIiHjk6iP2onvrTDYUlHDj23O8jpOQVIREREQ8kp6SxF2n5ZLkM96esZr3Zq3xOlLCURESERHxUG6nZvxhZHcA/vrmbDYUlHicKLGoCImIiHjsskN70qddNpsLS/nLG7NwznkdKWGoCImIiHgsNdnHXacOIiXJ+GjuOt6YvsrrSAlDRUhERCQG9G2fzZWH9wLgxrfnsGbrdo8TJQYVIRERkRjx+4P2ZFCnZhQUl3Pdf3WILBpUhERERGJEcpL/EFlaso8vFm7gxSkrvI7U6KkIiYiIxJAebZpy7ZF7AfCPd+eyYnORx4kaNxUhERGRGHPe/t0Y0bUFhaUVXPPqDCordYgsUlSEREREYozPZ9x56kAyUpOYvHQzT3+zzOtIjZaKkIiISAzq0jKT64/pA8C/PpjPkg3bPE7UOKkIiYiIxKgz9+7MgT1bUVJeyTWvzqC8otLrSI2OipCIiEiMMjP+dfJAstKSmf7TFh798kevIzU6KkIiIiIxrH2zJtz4234A3DtxEfPX5nucqHFRERIREYlxJw/pwOF92lBaUcnVr8ygtFyHyMJFRUhERCTGmRn/PGkAzTJSmLM6nwc/W+x1pEZDRUhERCQOtMlK59YT+gMw/rPFzFq51eNEjYOKkIiISJw4dmB7fjOwHRWVjqteyWN7aYXXkeKeipCIiEgc+fvx/Wmdlcbi9du47f15XseJeypCIiIicaRFZip3nToIgGe+Xc4n89Z5nCi+qQiJiIjEmYN6teb8A7oB8KfXZrKhoMTjRPFLRUhERCQOXXvkXvTeI4tNhaVc+9oMnNODWetDRUhERCQOpackcf8Zg0lN9jFpwQae+Xa515HikoqQiIhInOrVNovrj+4NwD/fm8fCdQUeJ4o/KkIiIiJx7Nz9unJwr9aUlFdy+YvTKSnXJfV1oSIkIiISx8yMO08dSMvMVOavLeDODxZ4HSmuqAiJiIjEuTZZ6dxxykAAHv9qKV8u2uBxovjR6IuQmXUys0lmNtfMZprZqV5nEhERCbfD+rTl7H26AHD1KzPYXFjqcaL40OiLEFAOXOmc6wscAdxrZpkeZxIREQm764/pQ482TVlfUMJ1/52pS+prodEXIefcGudcXuDrtcBGoIWnoURERCKgSWoS952eS0qSMXHuOl6ausLrSDHP8yJkZgeZ2TtmttrMnJmdEGKZcWa2zMyKzWyymY2o57aGAknOOf1kiIhIo9SvfQ5/OtJ/Sf0t78xlyYZtHieKbcleBwAygRnAk8DrwW+a2WjgbuBiYDJwJfChme3lnFsfWCaP0N/LEc651YFlWgDPABfuKoiZpQFp1WZlAZSVlVFWVlbX76tGVesL93plZxrn6NA4R4/GOjrifZzP2bsjn81fxzc/buaKF6fz8oUjSE32fN/Hr0RqnOuyPoul44dm5oATnXNvVps3GZjqnLs08NoHrAAecM7dXsv1pgETgcecc8/WsNxNwI3B81944QUyMjLq8J2IiIh4a0sJ/GtmEkXlxuHtKzmuS6XXkaKmqKiIMWPGAOQ45/JrWjami5CZpQJFwClB5WgC0Mw5d3wt1mnAC8AC59xNu1k21B6hlRs3biQ7O7tu38xulJWVMXHiREaNGkVKSkpY1y2/0DhHh8Y5ejTW0dFYxvmjuesY9+IMzODZ3w1j726xdYpspMY5Pz+fVq1aQS2KUCwcGqtJKyAJWBc0fx3Qu5br2B8YDcysdv7R2c65WcELOudKgB2P8PV3KEhJSYnYX4RIrlt+oXGODo1z9GisoyPex/k3gzryxaLNvPz9Cv7039m8f8VB5GTE3vcT7nGuy7pi74BhmDnnvnLO+ZxzudWmX5UgERGRxuiG4/rStWUGq7cWc/2bs3RJfZBYL0IbgQqgbdD8tsDa6McRERGJL5lpydx3+mCSfca7M9fw+g+rvI4UU2K6CDnnSoFpwGFV8wInSx8GfOtVLhERkXgyqFMzrhrVC4Ab3prN8k2FHieKHZ4XITNrama5ZpYbmNUt8Lpz4PXdwIVmdq6Z9QEewn/J/VMRzDTOzOYCUyK1DRERkWi6+ODujOjagsLSCq58OY/yisS5iqwmnhchYBgwPTCBv/hMB24BcM69DFwTeJ0H5AJHOeeCT6AOG+fc+MAjOep140YREZFYk+Qz7h49iKz0ZKb/tIUHPl3sdaSY4HkRcs5Ncs5ZiGlstWUedM51cc6lOef2ds5N9jCyiIhIXOrYPIN/nDgAgAc+XcS05Zs9TuQ9z4uQiIiIRM9vB7XnpMEdqHRwxUt5FBTH592zw0VFSEREJMHcfHw/OrVowsqft3PjW3O8juMpFSEREZEEk5Wewr2jc/EZvD59FW/lJe4l9SpCIiIiCWholxZcdmhPAP765mxW/lzkcSJvqAiFoMvnRUQkEVx2aA8Gd25GQXE5f3xlBhWViXfXaRWhEHT5vIiIJILkJB/3js4lMzWJKUs38/DnS7yOFHUqQiIiIgmsS8tMbj6+PwD3TFzIjBVbvA0UZSpCIiIiCe7kIR34zcB2lFc6rnw5j8KScq8jRY2KkIiISIIzM/55wgDa5aSzdGMhf//fXK8jRY2KkIiIiJCTkcLdp+ViBi9NXcEHs9d4HSkqVIREREQEgH27t+Tig7sD8OfXZ7F2a7HHiSJPRUhERER2uOrwXgzokMOWojKufjWPykZ+Sb2KUAi6j5CIiCSq1GQf956eS5OUJL5evIknvlrqdaSIUhEKQfcREhGRRNa9dVNuOK4vAHd8OJ85q7d6nChyVIRERETkV04f3okj+ralrMJxxUt5bC+t8DpSRKgIiYiIyK+YGbefPJA2WWksXr+N296f53WkiFAREhERkZBaZKZy12mDAHjm2+V8Mm+dx4nCT0VIREREdunAnq05/4BuAPzptZlsKCjxOFF4qQiJiIhIja49ci9675HFpsJSrn1tBs41nkvqVYRERESkRukpSdx/xmDSkn1MWrCBZ75d7nWksFERCkH3ERIREdlZr7ZZXH9MHwD+8d48Fq4r8DhReKgIhaD7CImIiPzaOft24ZC9WlNaXsnlL06nuCz+L6lXERIREZFaMTPuOGUQLTNTmb+2gDs/XOB1pAZTERIREZFaa52Vxp2nDgTgia+W8sXCDR4nahgVIREREamTQ3u35Zx9uwBw9asz2FxY6nGi+lMREhERkTq7/pg+9GjTlA0FJVz335lxe0m9ipCIiIjUWXpKEvednktqko+Jc9fx0tQVXkeqFxUhERERqZd+7XP401F7AXDLO3NZsmGbx4nqTkVIRERE6u28/btxQI9WbC+r4MqX8igtr/Q6Up2oCImIiEi9+XzGv08dRLOMFGat2so9Hy/0OlKdqAiJiIhIg+yRk87tJ/kvqX/48yV8u2STx4lqT0UoBD1iQ0REpG6O6r8Hpw/vhHPwx1fy2FpU5nWkWlERCkGP2BAREam7vx3bl26tMlmztZjr35gVF5fUqwiJiIhIWGSmJXPv6FySfca7s9bw3x9WeR1pt1SEREREJGwGdWrGVaN6AXDjW7NZvqnQ40Q1UxESERGRsLr44O6M6NaCwtIKrnw5j/KK2L2kXkVIREREwirJZ9wzOpes9GSm/7SFBz5d7HWkXVIREhERkbDr0KwJ/zxxAAAPfLqIacs3e5woNBUhERERiYjjBrXnpCEdqHRwxUt5FBTH3iX1KkIiIiISMTf/th+dWjRh5c/bufGtOV7H+RUVIREREYmYrPQU7h2di8/g9emreCsvti6pVxESERGRiBrapQWXHdoTgL++OZuVPxd5nOgXKkIiIiIScZcd2oPBnZtRUFzOH1+eQUVlbNx1WkUoBD1rTEREJLySk3zcN3owmalJTFm2mYc/X+J1JEBFKCQ9a0xERCT8OrfM4Jbj+wNwz8SFzFi51eNEKkIiIiISRScN6cCxA9tRXum4+tVZlFR4m0dFSERERKLGzPjHCQNon5PO8s1FvL7M2yqiIiQiIiJRlZORwt2jczGDKRuMZR4+mDXZsy2LiIhIwtpnz5b85ei9KFoxh64tMz3LoT1CIiIi4olz9+1Cl6beZlAREhERkYSlIiQiIiIJS0VIREREEpaKkIiIiCQsFSERERFJWCpCIiIikrBUhERERCRhqQiJiIhIwlIREhERkYSlIiQiIiIJS0UoBDMbZ2ZzgSleZxEREZHIUREKwTk33jnXFxjhdRYRERGJHBUhERERSVjJXgeIB/n5+WFfZ1lZGUVFReTn55OSkhL29Yufxjk6NM7Ro7GODo1zdERqnOvy77Y558K24cbGzDoAK73OISIiIvXS0Tm3qqYFVIRqYGYGtAcKArOmEPq8oVDzdzcvC3/J6lht/ZG0q+yR+Hxtlq1pGY1z+JYN1ziHmu/lOIfKE8nP7m75+r5fm5/p4Nf6mdbvjoZ+PlHGOQtY7XZTdHRorAaBwdvRJM2s0jn3q/1toebvbp6/YwFQEGqd4bar7JH4fG2WrWkZjXPsjXOo+V6Oc005I/HZ3S1f3/dr8zMd4nXVl/qZruV7+t1R92UbyTjXan06Wbpuxtdhfm3nRUtDt12Xz9dm2ZqW0TiHb9lwjXOo+V6Oc0O3X9fP7m75+r5fm5/feB7nun5evzui8/lEHudf0aExj5hZNrAVyInW/0EnIo1zdGico0djHR0a5+iIhXHWHiHvlAA3B/6UyNE4R4fGOXo01tGhcY4Oz8dZe4REREQkYWmPkIiIiCQsFSERERFJWCpCIiIikrBUhERERCRhqQiJiIhIwlIRinFm1snMJpnZXDObaWanep2pMTOzN8zsZzN7zessjYmZHWtmC8xskZld4HWexko/v5Gn38nRYWbNzOx7M8szs9lmdmHEtqXL52ObmbUD2jrn8sxsD2Aa0Ms5V+hxtEbJzEbifz7Nuc65U7xN0ziYWTIwFzgE/43TpgH7Oec2eRqsEdLPb+Tpd3J0mFkSkOacKzKzTGA2MCwSvze0RyjGOefWOOfyAl+vBTYCLTwN1Yg55yYRvYeGJooRwBzn3Crn3DbgfeAIjzM1Svr5jTz9To4O51yFc64o8DINsMAUdipCDWRmB5nZO2a22sycmZ0QYplxZrbMzIrNbLKZ1esJw2Y2FEhyzq1oaO54FM2xll+EYdzbU+3hxYGvO0Q4dtzRz3d0hHOcE/13ck3CMc6Bw2Mz8D+d/k7n3MZIZFURarhMYAYwLtSbZjYauBv/LcSHBJb90MzaVFum6hho8NS+2jItgGeAiyL4vcS6qIy1/EqDx11qReMcHWEZZ/1O3q0Gj7NzbotzbhDQDRhjZm0jktQ5pylME+CAE4LmTQYerPbah///iP9ch/WmAV8AZ3v9PcbKFKmxDnxuJPCa199jLE71GXdgP+CNau/fC4zx+nuJ5akhP9/6+Y38OOt3cnTGOWj5/wCnRCKf9ghFkJmlAkOBj6vmOecqA6/3reU6DHga+NQ592wEYjYK4RhrqbtajvsUoL+ZdTCzpsDRwIfRzhrP9PMdHbUZZ/1ObrhajnNbM8sKfJ0DHAQsiEQeFaHIagUkAeuC5q8D9qjlOvYHRgMnBA7r5JnZgDBmbCzCMdaY2cfAq8AxZrbSzPSPTM12O+7OuXLgauAzIA+4y+mKsbqq1c+3fn4brDbjrN/JDVebce4CfBk4R+hL4AHn3KxIhEmOxEolfJxzX6HCGjXOucO9ztAYOefeBt72Okdjp5/fyNPv5Ohwzk0BcqOxLf3HjKyNQAUQfIJXW2Bt9OM0ahprb2jco0PjHB0a5+iIqXFWEYog51wp/pttHVY1z8x8gdffepWrMdJYe0PjHh0a5+jQOEdHrI2zDo01UODkzx7VZnUzs1xgs3PuJ/yXB04ws+/xnzR6Jf7LCp+KctS4p7H2hsY9OjTO0aFxjo64GmevL6uL9wn/paouxPR0tWUuBZYDJfgvGdzb69zxOGmsNe6NedI4a5wb0xRP46xnjYmIiEjC0jlCIiIikrBUhERERCRhqQiJiIhIwlIREhERkYSlIiQiIiIJS0VIREREEpaKkIiIiCQsFSERERFJWCpCIiIikrBUhEREGsDMUs1ssZntF6H1TzKze+v52VZmtt7MOoY5lkijoSIkIjuY2dNm5kJMPXb/6YR1MbDUOfdNNDdqZp+Z2QU1LeOc2wg8A9wcnVQi8UdFSESCfQC0C5qWBi9kZqlRzhVzzMzwPzjyid0slxLm7bYA9gfeqcXiTwFnBj4jIkFUhEQkWIlzbm3QVBE4RPOgmd1rZhuBDwHMrL+ZvW9m28xsnZk9a2atqlZmZplm9kzg/TVmdnXw4Z7AXqcTqocwsy1mNrba605m9kpg/mYze8vMulZ7/2kze9PMrglsZ5OZja9eQswszcz+ZWYrzKwkcEjrfPNbbGbXBGXI3c0esaFAd+Ddap/pGvjMaDP73MyK8ReRlmb2opmtMrMiM5tlZmcEbe9XY7WL7f4G+ME5t87MmpvZ82a2wcy2m9kiM/td1YLOuTnAauDEXaxLJKGpCIlIXZwLlOLfG3GxmTUDPgWmA8OAo4C2wCvVPnMncDBwPHAEMBIYUpeNBsrMh0ABcGBg+9uAD4L2TB2Cv5gcEsg6NjBVeQY4A7gc6AP8HtjmnHPAk8Dv2NnvgC+cc4t3Ee1AYKFzriDEe7cD9wW28yGQDkzDX2L6A48Cz5rZiGqfqe1Y/RZ4K/D134G+wNGBbV0CbAxafkogq4gESfY6gIjEnGPNbFu11+87504NfL3IOfenqjfM7K/AdOfc9dXmnQesMLNe+PdEnA+c5Zz7JPD+ucDKOmYajf9/3C4IlBYCez224C8LHwWW+xm41DlXAcw3s3eBw4DHAnlOA0Y55z4OLP9jtW08DdxiZiOcc1MC5WsMsNNeoiBdAt9jKPc6514Pmvfval8/YGZHBjJNMbOm1GKszCwNf+G8KTCrM/7/Bt8HXi8LkWU1MLiG70MkYakIiUiwz/DvVahSWO3raUHLDgIOCSpOVboDTYBUYHLVTOfcZjNbUMdMg4AeQIH/tJwd0gPbqTInUIKqrAEGBL7OBSqAz0NtwDm3OlCczsO/B+U4IA14tYZcTYDiXbz3ffUXZpYEXI+/+HTAPy5pQFFgke7UbqwOBdYHDnkBPAT818yG4C+Eb4Y4cXs7kFHD9yGSsFSERCRYYQ2HggqDXjfFf8LudSGWXYO/vNSGAyxoXvUTjJviL2Fnhvjshmpfl4VYb9UpANtrkeNx/IerrsJ/WOxl51xRDctv5JeiFSx4rK4FrgCuBGYF3r8Xf/mpi98Cb1e9cM69b2ZdgGOAUcAnZjbeOVd9T1YLdh4nEQnQOUIi0hA/AP2AZc65xUFTIbAEfznZu+oDZtYc6BW0ng34r06rWqYnO+/B+AHoiX9PSPB2ttYy6yz8v/MOrmGZ9/AXlEvwH356cjfrnA70tqDdVLuwP/CWc+4559wM/Iflqo/DbscqsJ3j+OX8IACccxuccxOcc2fhL1oXBW27fyCriARRERKRhhiPf2/Di2Y23My6m9mRZvaUmSU557bhv7T8TjM71Mz64z8XpzJoPZ8Cl5rZYDMbBjzMznt3nse/9+UtMzvQzLqZ2Ugzu99qebNA59wyYALwpJmdUG0dp1VbpiKQ7zb850N9u5vVfoZ/b1W/WkRYBIwys/3MrA/wCP4Ty6u2XZuxGoq/IH5VNcPMbjGz482sh5n1A44F5lV7PyPwuY8QkV9RERKRenPOrca/pyMJ/z+0s/Af7tnCL/+AXwt8if8Q2sf4/xEPPtfoamBFYLkX8J9UvOOQVODw1EHAT8Dr+P+hfwL/OUL5dYh8CfAa8B9gPvAYkBm0zBP4D1c9tbuVOec2AW8Q+pBdsFvx79n6EJgErAXeDFpmd2N1PPCec6682rxS/MVtJvAF/vOgTg/6zE/OuS9rkVEk4VjgAgwRkagxs0lAnnPuSo+j/IqZHQh8AnRyzq2rxfIDgYlA98BenUhmmwnc6px7ZbcL//KZ74D7nXMvRC6ZSPzSHiEREXbcbLEj/svSX61NCQJwzs3Ef7J4twjGq7qT93+B9+vwmVb496C9GKlcIvFOe4REJOpicY+Q+e9i/QSQB/zWObfK00AiEhUqQiIiIpKwdGhMREREEpaKkIiIiCQsFSERERFJWCpCIiIikrBUhERERCRhqQiJiIhIwlIREhERkYSlIiQiIiIJ6/8BMf1hEoZj4VwAAAAASUVORK5CYII=", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "w = (1e-2, 1e3)\n", "_ = fom.transfer_function.mag_plot(w)" ] }, { "cell_type": "markdown", "id": "021bba9c", "metadata": {}, "source": [ "Note that `mag_plot`\n", "computes the Frobenius norm of {math}`H(\\boldsymbol{\\imath} \\omega)` by default,\n", "just as `scipy.linalg.norm`.\n", "Likewise, the choice of the norm {math}`\\lVert \\cdot \\rVert` can be controlled\n", "using the `ord` parameter.\n", "\n", "Another visualization is the Bode plot,\n", "which shows the magnitude and phase of each component of the transfer function.\n", "More specifically,\n", "{math}`\\omega \\mapsto \\lvert H_{ij}(\\boldsymbol{\\imath} \\omega) \\rvert`\n", "is in subplot {math}`(2 i - 1, j)` and\n", "{math}`\\omega \\mapsto \\arg(H_{ij}(\\boldsymbol{\\imath} \\omega))`\n", "is in subplot {math}`(2 i, j)`." ] }, { "cell_type": "code", "execution_count": 14, "id": "591dc489", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axs = plt.subplots(6, 2, figsize=(8, 10), sharex=True, constrained_layout=True)\n", "_ = fom.transfer_function.bode_plot(w, ax=axs)" ] }, { "cell_type": "markdown", "id": "97b3e851", "metadata": {}, "source": [ "To restrict which inputs and outputs are plotted by `bode_plot`,\n", "its parameters `input_indices` and `output_indices` can be used.\n", "The following restricts the plot to the second input {math}`u_2` and the first output {math}`y_1`." ] }, { "cell_type": "code", "execution_count": 15, "id": "a08c38e2", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axs = plt.subplots(2, 1, figsize=(8, 10), sharex=True, constrained_layout=True)\n", "_ = fom.transfer_function.bode_plot(w, ax=axs, input_indices=[1], output_indices=[0])" ] }, { "cell_type": "markdown", "id": "8be4cabb", "metadata": {}, "source": [ "Note the change in the `axs` shape compared to the first call to `bode_plot`.\n", "\n", "## System poles\n", "\n", "The poles of an LTI system are the poles of its transfer function.\n", "From the form of the transfer function\n", "it follows that the poles are eigenvalues of {math}`E^{-1} A`,\n", "assuming that {math}`E` is invertible.\n", "Conversely, the eigenvalues of {math}`E^{-1} A` are the poles of the system\n", "in the generic case\n", "(more precisely, if the system is minimal, i.e., controllable and observable;\n", "see {cite}`A05`).\n", "\n", "The poles of an `LTIModel` can be obtained using its\n", "`poles` method\n", "(assuming the system is minimal)." ] }, { "cell_type": "code", "execution_count": 16, "id": "b9033577", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "poles = fom.poles()\n", "fig, ax = plt.subplots()\n", "ax.plot(poles.real, poles.imag, '.')\n", "_ = ax.set_title('Poles')" ] }, { "cell_type": "markdown", "id": "55569627", "metadata": {}, "source": [ ":::{note}\n", "\n", "The `poles` method uses a dense\n", "eigenvalue solver,\n", "which is applicable only up to medium-sized problems.\n", "\n", ":::\n", "\n", "## System Gramians\n", "\n", "The controllability and observability Gramians of an asymptotically stable\n", "system with invertible {math}`E` are respectively\n", "\n", "```{math}\n", "\\begin{align*}\n", " P & =\n", " \\int_0^\\infty\n", " e^{t E^{-1} A} E^{-1} B\n", " B^{\\operatorname{T}} E^{-\\!\\operatorname{T}}\n", " e^{t A^{\\operatorname{T}} E^{-\\!\\operatorname{T}}}\n", " \\operatorname{d}\\!t, \\text{ and} \\\\\n", " E^{\\operatorname{T}} Q E & =\n", " \\int_0^\\infty\n", " e^{t A^{\\operatorname{T}} E^{-\\!\\operatorname{T}}}\n", " C^{\\operatorname{T}} C\n", " e^{t E^{-1} A}\n", " \\operatorname{d}\\!t.\n", "\\end{align*}\n", "```\n", "\n", "From this,\n", "it is clear that {math}`P` and {math}`Q` are symmetric positive semidefinite.\n", "Furthermore,\n", "it can be shown that {math}`P` and {math}`Q` are solutions to Lyapunov equation\n", "\n", "```{math}\n", "\\begin{align*}\n", " A P E^{\\operatorname{T}}\n", " + E P A^{\\operatorname{T}}\n", " + B B^{\\operatorname{T}}\n", " & = 0, \\\\\n", " A^{\\operatorname{T}} Q E\n", " + E^{\\operatorname{T}} Q A\n", " + C^{\\operatorname{T}} C\n", " & = 0.\n", "\\end{align*}\n", "```\n", "\n", "The Gramians can be used to quantify how much does the input influence the state\n", "(controllability) and state the output (observability).\n", "This is used to motivate the balanced truncation method\n", "(see {doc}`tutorial_bt`).\n", "Also, they can be used to compute the {math}`\\mathcal{H}_2` norm (see below).\n", "\n", "To find the \"Gramians\" {math}`P` and {math}`Q` of an `LTIModel`,\n", "the `gramian` method can be used.\n", "Although solutions to Lyapunov equations are generally dense matrices,\n", "they can be often be very well approximated by a low-rank matrix.\n", "With `gramian`,\n", "it is possible to compute the dense solution or only the low-rank Cholesky\n", "factor.\n", "For example, the following computes the low-rank Cholesky factor of the\n", "controllability Gramian as a `VectorArray`:" ] }, { "cell_type": "code", "execution_count": 17, "id": "bb0d5f9b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "NumpyVectorArray(\n", " NumpyVectorSpace(101, id='STATE'),\n", " [[-9.67050759e-01 -9.49603788e-01 -9.37818152e-01 ... -5.08356138e-01\n", " -5.03442167e-01 -4.98481264e-01]\n", " [-1.13133419e+00 -9.59580542e-01 -8.43810516e-01 ... 1.94699113e-01\n", " 1.92880555e-01 1.91000976e-01]\n", " [ 9.08538963e-01 4.58145972e-01 2.24375612e-01 ... 9.25753046e-02\n", " 9.17614570e-02 9.08841977e-02]\n", " ...\n", " [ 3.51003655e-17 -1.46991338e-15 2.80238240e-14 ... -2.17255529e-10\n", " 4.81820026e-11 -5.62679055e-12]\n", " [-3.56111613e-18 1.67661586e-16 -3.59568481e-15 ... -5.01115974e-11\n", " 1.11501400e-11 -1.27118577e-12]\n", " [ 2.25015197e-18 -1.18139105e-16 2.79146870e-15 ... -5.84341985e-12\n", " 2.57132302e-12 -4.13133686e-13]],\n", " _len=101)" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fom.gramian('c_lrcf')" ] }, { "cell_type": "markdown", "id": "d9f47cdb", "metadata": {}, "source": [ "## Hankel singular values\n", "\n", "The Hankel singular values of an LTI system are\n", "{math}`\\sigma_i = \\sqrt{\\lambda_i(E^{\\operatorname{T}} Q E P)}`,\n", "where {math}`\\lambda_i` is the {math}`i`-th eigenvalue.\n", "\n", "Plotting the Hankel singular values shows us how well an LTI system can be\n", "approximated by a reduced-order model.\n", "The `hsv` method can be used to compute them." ] }, { "cell_type": "code", "execution_count": 18, "id": "aa50dac4", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "hsv = fom.hsv()\n", "fig, ax = plt.subplots()\n", "ax.semilogy(range(1, len(hsv) + 1), hsv, '.-')\n", "_ = ax.set_title('Hankel singular values')" ] }, { "cell_type": "markdown", "id": "6cfeee5b", "metadata": {}, "source": [ "As expected for a heat equation, the Hankel singular values decay rapidly.\n", "\n", "## System norms\n", "\n", "There are various system norms,\n", "used for quantifying the sensitivity of system's outputs to its inputs.\n", "pyMOR currently has methods for computing:\n", "the {math}`\\mathcal{H}_2` norm,\n", "the {math}`\\mathcal{H}_\\infty` norm, and\n", "the Hankel (semi)norm.\n", "\n", "The {math}`\\mathcal{H}_2` norm is\n", "(if {math}`E` is invertible,\n", "{math}`E^{-1} A` has eigenvalues in the open left half plane, and\n", "{math}`D` is zero)\n", "\n", "```{math}\n", "\\lVert H \\rVert_{\\mathcal{H}_2}\n", "=\n", "\\left(\n", " \\frac{1}{2 \\pi}\n", " \\int_{-\\infty}^{\\infty}\n", " \\lVert H(\\boldsymbol{\\imath} \\omega) \\rVert_{\\operatorname{F}}^2\n", " \\operatorname{d}\\!\\omega\n", "\\right)^{\\frac{1}{2}}.\n", "```\n", "\n", "It can be shown that\n", "\n", "```{math}\n", "\\lVert y \\rVert_{\\mathcal{L}_\\infty}\n", "\\leqslant\n", "\\lVert H \\rVert_{\\mathcal{H}_2}\n", "\\lVert u \\rVert_{\\mathcal{L}_2}.\n", "```\n", "\n", "Additionally, for systems with a single input or a single output\n", "(i.e., {math}`u(t) \\in \\mathbb{R}` or {math}`y(t) \\in \\mathbb{R}`),\n", "\n", "```{math}\n", "\\lVert H \\rVert_{\\mathcal{H}_2}\n", "=\n", "\\sup_{u \\neq 0}\n", "\\frac{\\lVert y \\rVert_{\\mathcal{L}_\\infty}}{\\lVert u \\rVert_{\\mathcal{L}_2}}.\n", "```\n", "\n", "The computation of the {math}`\\mathcal{H}_2` norm is based on the system\n", "Gramians\n", "\n", "```{math}\n", "\\lVert H \\rVert_{\\mathcal{H}_2}^2\n", "= \\operatorname{tr}\\!\\left(C P C^{\\operatorname{T}}\\right)\n", "= \\operatorname{tr}\\!\\left(B^{\\operatorname{T}} Q B\\right).\n", "```\n", "\n", "The `h2_norm` method of an `LTIModel` can be\n", "used to compute it." ] }, { "cell_type": "code", "execution_count": 19, "id": "abebb1da", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.3148819640649632" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fom.h2_norm()" ] }, { "cell_type": "markdown", "id": "3f70b372", "metadata": {}, "source": [ "The {math}`\\mathcal{H}_\\infty` norm is\n", "(if {math}`E` is invertible and\n", "{math}`E^{-1} A` has eigenvalues in the open left half plane)\n", "\n", "```{math}\n", "\\lVert H \\rVert_{\\mathcal{H}_\\infty}\n", "= \\sup_{\\omega \\in \\mathbb{R}}\n", "\\lVert H(\\boldsymbol{\\imath} \\omega) \\rVert_2.\n", "```\n", "\n", "It is always true that\n", "\n", "```{math}\n", "\\lVert H \\rVert_{\\mathcal{H}_\\infty}\n", "=\n", "\\sup_{u \\neq 0}\n", "\\frac{\\lVert y \\rVert_{\\mathcal{L}_2}}{\\lVert u \\rVert_{\\mathcal{L}_2}},\n", "```\n", "\n", "and, in particular,\n", "\n", "```{math}\n", "\\lVert y \\rVert_{\\mathcal{L}_2}\n", "\\leqslant\n", "\\lVert H \\rVert_{\\mathcal{H}_\\infty}\n", "\\lVert u \\rVert_{\\mathcal{L}_2}.\n", "```\n", "\n", "The `hinf_norm` method uses a dense solver\n", "from [Slycot]() to compute the\n", "{math}`\\mathcal{H}_\\infty` norm." ] }, { "cell_type": "code", "execution_count": 20, "id": "eae888a1", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.3351147226114526" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fom.hinf_norm()" ] }, { "cell_type": "markdown", "id": "f106de01", "metadata": {}, "source": [ "The Hankel norm is\n", "(if {math}`E` is invertible and\n", "{math}`E^{-1} A` has eigenvalues in the open left half plane)\n", "\n", "```{math}\n", "\\lVert H \\rVert_{\\operatorname{H}}\n", "= \\sigma_1,\n", "```\n", "\n", "i.e., the largest Hankel singular value.\n", "Since it is independent of {math}`D`,\n", "the \"Hankel norm\" is only a seminorm in general.\n", "\n", "It can be shown that the Hankel norm is the norm of the Hankel operator\n", "{math}`\\mathcal{H} \\colon \\mathcal{L}_2(-\\infty, 0) \\to \\mathcal{L}_2(0, \\infty)`\n", "mapping past inputs {math}`u_-` to future outputs {math}`y_+`\n", "\n", "```{math}\n", "y_+(t)\n", "= \\mathcal{H}(u_-)(t)\n", "= \\int_{-\\infty}^0 h(t - \\tau) u_-(\\tau) \\operatorname{d}\\!\\tau,\n", "```\n", "\n", "where {math}`h` is the impulse response\n", "{math}`h(t) = C e^{t E^{-1} A} E^{-1} B + D \\delta(t)`\n", "(i.e., {math}`H` is the Laplace transform of {math}`h`).\n", "Thus,\n", "\n", "```{math}\n", "\\lVert H \\rVert_{\\operatorname{H}}\n", "=\n", "\\sup_{u_- \\neq 0}\n", "\\frac{\\lVert y_+ \\rVert_{\\mathcal{L}_2}}{\\lVert u_- \\rVert_{\\mathcal{L}_2}},\n", "```\n", "\n", "The computation of the Hankel norm in\n", "`hankel_norm` relies on the\n", "`hsv` method." ] }, { "cell_type": "code", "execution_count": 21, "id": "f8f2a251", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.6648253696498123" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fom.hankel_norm()" ] }, { "cell_type": "markdown", "id": "a70c87a3", "metadata": {}, "source": [ "Download the code:\n", "{download}`tutorial_lti_systems.md`,\n", "{nb-download}`tutorial_lti_systems.ipynb`." ] } ], "metadata": { "jupytext": { "text_representation": { "extension": ".md", "format_name": "myst", "format_version": 0.13, "jupytext_version": "1.16.2" } }, "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.4" }, "source_map": [ 12, 17, 22, 90, 97, 102, 106, 111, 113, 117, 119, 129, 131, 145, 148, 152, 159, 182, 194, 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00:02 LTIModel: Computing output of LTIModel for {input: StepFunction(2, 0, 0.0)(0) = [1.0, 0.0]} ...
00:02 LTIModel: Computing output of LTIModel for {input: StepFunction(2, 1, 0.0)(0) = [0.0, 1.0]} ...
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