{ "cells": [ { "cell_type": "markdown", "id": "aa870662", "metadata": {}, "source": [ "```{try_on_binder}\n", "```" ] }, { "cell_type": "code", "execution_count": 1, "id": "3f5eafcb", "metadata": { "load": "myst_code_init.py", "tags": [ "remove-cell" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The pymor.discretizers.builtin.gui.jupyter extension is already loaded. To reload it, use:\n", " %reload_ext pymor.discretizers.builtin.gui.jupyter\n" ] } ], "source": [ "from IPython import get_ipython\n", "ip = get_ipython()\n", "if ip is not None:\n", " ip.run_line_magic('load_ext', 'pymor.discretizers.builtin.gui.jupyter')\n", " ip.run_line_magic('matplotlib', 'inline')\n", "\n", "import warnings\n", "warnings.filterwarnings(\"ignore\", category=UserWarning, module='torch')\n", "import pymor.tools.random\n", "pymor.tools.random._default_random_state = None\n" ] }, { "cell_type": "markdown", "id": "c3d87cbe", "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", "## 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_1(t) & = T(0, t),\n", " & t > 0, \\\\\n", " y_2(t) & = T(0.5, t),\n", " & t > 0, \\\\\n", " y_3(t) & = T(1, t),\n", " & t > 0.\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 {meth}`~pymor.models.basic.InstationaryModel.to_lti` method of\n", "{{ InstationaryModel }} to obtain an {{ LTIModel }}).\n", "In particular, we will use the\n", "{meth}`~pymor.models.iosys.LTIModel.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": "afcb3e1a", "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": "9797327a", "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": "1abebe18", "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, 0] = C[1, k] = C[2, -1] = 1\n" ] }, { "cell_type": "markdown", "id": "1c21c3ea", "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": "f2e7f868", "metadata": {}, "outputs": [], "source": [ "fom = LTIModel.from_matrices(A, B, C, E=E)" ] }, { "cell_type": "markdown", "id": "18aa1045", "metadata": {}, "source": [ "We can take a look at the internal representation of the {{ LTIModel }} `fom`." ] }, { "cell_type": "code", "execution_count": 5, "id": "b6ac483e", "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": "cd48acb1", "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", "({class}`~pymor.operators.constructions.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": "3f869900", "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": "6a94584f", "metadata": {}, "source": [ "which gives the dimensions of the underlying system more directly,\n", "together with some of its properties.\n", "\n", "## 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", "{meth}`~pymor.models.transfer_function.TransferFunction.eval_tf` method.\n", "The result is a NumPy array." ] }, { "cell_type": "code", "execution_count": 7, "id": "d430c2be", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[0.5 0.66666667]\n", " [0.625 0.5 ]\n", " [0.5 0.33333333]]\n", "[[0.31606222 0.4999973 ]\n", " [0.39347047 0.30326476]\n", " [0.31606222 0.18394049]]\n", "[[0.37281526-0.21715839j 0.55742226-0.1956196j ]\n", " [0.46483929-0.27336178j 0.36331911-0.23241964j]\n", " [0.37281526-0.21715839j 0.22541935-0.17719566j]]\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": "2159f719", "metadata": {}, "source": [ "Similarly, the derivative of the transfer function can be computed using the\n", "{meth}`~pymor.models.transfer_function.TransferFunction.eval_dtf` method.\n", "The result is again a NumPy array." ] }, { "cell_type": "code", "execution_count": 8, "id": "8a8a6db2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-0.2916625 -0.25926111]\n", " [-0.36718437 -0.3125 ]\n", " [-0.2916625 -0.24073889]]\n", "[[-0.11600655 -0.10808607]\n", " [-0.14598636 -0.12374206]\n", " [-0.11600655 -0.09196959]]\n", "[[-0.10621989+0.18938184j -0.10083093+0.16301232j]\n", " [-0.13365757+0.23848281j -0.11317824+0.20350967j]\n", " [-0.10621989+0.18938184j -0.08260248+0.16036596j]]\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": "95df774d", "metadata": {}, "source": [ "To evaluate the transfer function over a sequence of points on the imaginary\n", "axis,\n", "the {meth}`~pymor.models.transfer_function.TransferFunction.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 sinusiodal, i.e., {math}`\\xi = 0`,\n", "then the output is also sinusiodal.\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 {meth}`~pymor.models.transfer_function.TransferFunction.mag_plot`\n", "method." ] }, { "cell_type": "code", "execution_count": 9, "id": "95cea876", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "w = np.logspace(-2, 8, 300)\n", "_ = fom.transfer_function.mag_plot(w)" ] }, { "cell_type": "markdown", "id": "af7ec546", "metadata": {}, "source": [ "Note that {meth}`~pymor.models.transfer_function.TransferFunction.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": 10, "id": "8d27f8de", "metadata": {}, "outputs": [ { "data": { "image/png": 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0ie2DNf/2VL1xb5p6RrdRUXm1fv7mRk17NVN5JZyoAACnURbCrQTarHr2lhQF2az6am+h/vHFt2ZHAgAAAOBFhneP0Ic/u1QPjO4hm9XQpzvyNPqpL7Tkm4OcZQgAoiyEG+oeFaq51/aVJP0tfbd2HC0xOREAAAAAb+LvZ9EDo3vqw59dqqTEtiqtrNFv3tmi219ar6PFJ82OBwCmoiyEW5o0KEFj+0SrxunSr9/erBqH0+xIAAAAALxMr5hQvTt9uB66+hIF2iz6am+hrpr3pT7ZctTsaABgGspCuCXDMPSnif0UFuinLUeKteDLbLMjAQAAAPBCVouhey/tqk9+cZkGJISr+KRd0xdv0G/e3qyK6hqz4wFAq6MshNuKCgvU73/YR5L09MrdOny8wuREAAAAALxVl4gQvTN9uO4f2U2GIS3JOKTrnv1ae/PLzI4GAK2KshBu7cbUBA3p0l6VdqfmfrDd7DgAAAAAvJjNatGvr+qtN+4dquiwAO3JL9N1z36lDzfnmB0NAFoNZSHc2unpyH4WQ+nb8/TZzjyzIwEAAADwcsO6ddCHP7tUw7p2UHm1QzPe2Ki5H2zjWuoAfAJlIdxez+hQ3T2iiyTpTx/tkJ3/gwYAAADQwiJDA/TaPUN0/8hukqSXv96vqS9/o+IKu8nJAKBlURbCI8y4ors6hPhrX0G5Xl97wOw4AAAAAHyA36lpyc/fnqpgf6u+2luoif/3tb4t4DqGALwXZSE8QligTTPH9pQkzft0j4pP8mkeAAAAgNYxrm+M3v7JcMW3DVJ2Ybmuf+5rrd5baHYsAGgRlIXwGFMGJapndBsVn7TrhVXfmh0HAAAAgA/pExemZT/9gVI7tVNJZY3ufHm93t/EwicAvA9lITyGn9WiX47tJUla+NV+5ZdWmpwIAAAAgC+JDA3QG9PSdHX/WNkdLv38zY168ct9ZscCgGZFWQiPMqZPtFI6ttVJu0PPfbbX7DgAAAAAfEyAn1V/vzlFU4d3llS7COOjH++Qy+UyNxgANBPKQngUwzD0q3G1Zxe+uf6Qcos5uxAAAABA67JYDD18TR/NGt9bkvTCqn16aNlWOZ0UhgA8H2UhPM7wbhEa0rm9qh1OPc+1CwEAAACYwDAM/eTybnriRwNkGNLidQf1m3c2y0FhCMDDURbCI/38yh6SpDfWHeTahQAAAABMM3lwouZNSZbVYmhp5mHNfCtLNQ6n2bEAoNEoC+GRftC9g1I6tlVVjVMvfZltdhwAAAAAPuy65Hg9e3OK/CyG3svK0f+8tYkzDAF4LMpCeCTDMPTTkd0l1Z5dWFppNzkRAAAAAF82vn+s5t+WKpvV0AebcjTrnc1cwxCAR6IshMe6oneUukWGqLSqRm+uP2h2HAAAAAA+bnSfaD1zU4oshrQ087D+8ME2VkkG4HEoC+GxLBZD913WVZK08Kv9qq7huiAAAAAAzDW+f6z+OjlJhiG9uuaAHl++0+xIANAglIXwaBNT4hUZGqDckkp9vOWo2XEAAAAAQNenJOjPE/tLkp7/Yp9e+orrrAPwHJSF8GgBflbdltZJkvTKmv3mhgEAAACAU25J66jfXNVbkvSnj7brw805JicCgPqhLITHuzktUTaroY0HT2jz4RNmxwEAAAAASdJPLu+qO4d1ksslzVyySWv3HTM7EgBcFGUhPF5UaKCu7h8rSVq0er+5YQAAAADgFMMwNOeavhrXN1rVDqemvZqhPXmlZscCgAuiLIRXuHN4Z0nSh5uOqqi82twwAAAAAHCK1WLo6ZtSNKhTO5VW1uieVzJ0nL9ZALgxykJ4hZSO7dQvPkzVDqfe3XDY7DgAAAAAUCfQZtULdwxSYvsgHSyq0PTFmbI7nGbHAoBzoiyE17hpcEdJ0pvrD8rlcpmcBgAAAAD+q32Iv168Y7BC/K1au69Icz/YZnYkADgnykJ4jeuS4xRks+rbgnJlHDhudhwAAAAAOEOvmFDNuylFhiG9vvagFq8/ZHYkADgLZSG8RmigTdcmxUmS3lx30OQ0AAAAAHC2MX2i9atxvSRJf/pop7JZ7wSAm6EshFeZMiRRkvTJ1lyVVdWYnAYAAAAAzjb98m66un+sapwuLdptZZFGAG6FshBeJSWxrbpGhOik3aFPthw1Ow4AAAAAnMUwDD3+o/7q0iFYJ6oNPfj2FjmcXHcdgHugLIRXMQxDNwyMlyS9w6rIAAAAANxUaKBNf78pSTaLS1/tPaZnP9trdiQAkERZCC90/cAEGYa0dl+RDh+vMDsOAAAAAJxTr5hQTe7qlCTNW7lbX+8tNDkRAFAWwgvFtw3SsK4dJEnLNh4xOQ0AAAAAnN+QSJcmp8bL5ZIefGuTjnP9QgAmoyyEV5qYXDsV+YNNXLcQAAAAgHv73YRe6hoZotySSv32X1vkcnH9QgDmoSyEVxrXL0Y2q6FdeaXalVtqdhwAAAAAOK9gfz89c1OKbFZDn2zN1dIMrr8OwDyUhfBK4UE2Xd4zSpL0waYck9MAAAAAwIX1iw/XzDG9JEl/+GCbsgvLTU4EwFdRFsJrXZscJ0l6f1MOp/EDAAAAcHv3XdZVQ7u2V0W1Q/+zJEsOJ3/HAGh9lIXwWqMviVKQzaqDRRXacqTY7DgAAAAAcEFWi6GnJicrNMBPWYdO6KWv9pkdCYAPoiyE1wr299Oo3pGSpBXb8kxOAwAAAAAXF9c2SA/98BJJ0l9X7Na+gjKTEwHwNZSF8Gpj+8RIkv69LdfkJAAAAABQP5MHJerSHhGqqnHq129vZjoygFZFWQivNqpXlPwshvbkl/GJHAAAAACPYBiGHruhv0L8rco4cFyvrtlvdiQAPoSyEF4tPNimYd06SJLStzMVGQAAAIBnSGgXrFkTaqcjP7F8lw4eqzA5EQBfQVkIrze2T7QkaQVlIQAAAAAPcuuQjhratb1O2h16+P2tcrmYjgyg5VEWwuuNOXXdwg0Hjyu/tNLkNAAAAABQPxaLoT9N7C+b1dDnuwq4FjuAVkFZCK8XEx6opMS2crmkT7fnmx0HAAAAAOqte1Qb/fiybpKkuR9sV3lVjcmJAHg7ykL4hP9OReaTOAAAAACeZcYV3ZXYPkhHiys179PdZscB4OUoC+ETxvWtLQtX7z2m0kq7yWkAAAAAoP4CbVY9cm0/SdLCr/drx9ESkxMB8GaUhfAJ3SLbqGtEiKodTv1nV4HZcQAAAACgQUb1jtJVfWPkcLr08HvbWOwEQIuhLIRPMAxDY/vWLnSSzqrIAAAAADzQnGv6KNBm0fr9RfpkK5dYAtAyKAvhM67oHSVJ+nJPgRxOPoUDAAAA4Fni2gbVLXby6Mc7VGl3mJwIgDeiLITPSOnYVm0C/HS8wq5tOcVmxwEAAACABvvx5V0VExaow8dPauHX2WbHAeCFKAvhM2xWi4Z36yBJWrWb6xYCAAAA8DzB/n76zfhekqTnPtur/NJKkxMB8DaUhfApl/WMlCSt2l1ochIAAAAAaJzrkuKVlNhW5dUOPbVit9lxAHgZykL4lMtPlYUbDh5XaaXd5DQAAAAA0HAWi6E5P+wjSVqScUg7jpaYnAiAN6EshE9JbB+szh2CVeN0ac23x8yOAwAAAACNktqpna4eECuXS3ry37vMjgPAi3hkWbh//37dc8896tKli4KCgtStWzc9/PDDqq6uPmO/zZs369JLL1VgYKASExP1xBNPmJQY7qRuKvIerlsIAAAAwHP9cmwvWS2GVu7M1zf7i8yOA8BLeGRZuHPnTjmdTj3//PPatm2b/va3v2n+/Pn67W9/W7dPSUmJxo4dq06dOikzM1P/+7//qz/84Q964YUXTEwOd3BZD65bCABAa2nOD3mXLl2q3r17KzAwUP3799fHH398xv0ul0tz5sxRbGysgoKCNHr0aO3Zs6dFfz4AMFOXiBBNHpQoSXpi+U65XC6TEwHwBh5ZFl511VV6+eWXNXbsWHXt2lXXXnutfvnLX+rdd9+t22fx4sWqrq7WwoUL1bdvX9100036+c9/rqeeesrE5HAHw7p1kM1q6GBRhfYXlpsdBwAAr9ZcH/KuXr1aN998s+655x5t3LhREydO1MSJE7V169a6fZ544gk988wzmj9/vtatW6eQkBCNGzdOlZWsFArAe/3iyh4K8LPom/3H9Z9dzJ4C0HR+ZgdoLsXFxWrfvn3d7TVr1uiyyy6Tv79/3bZx48bpL3/5i44fP6527dqd83mqqqpUVVVVd7ukpPZCsXa7XXY7C2LUx+n3yV3fL3+LNLBjW63LPq7Pd+bqtrSOZkdqVe4+Pr6O8XFfjI17Y3wapzXer6uuukpXXXVV3e2uXbtq165d+sc//qEnn3xS0pkf8vr7+6tv377KysrSU089pfvuu0+S9PTTT+uqq67Sr371K0nSH//4R6Wnp+vZZ5/V/Pnz5XK5NG/ePD300EO67rrrJEmvvvqqoqOjtWzZMt10000t/rMCgBliwgM1dXhnPb9qn5749y5d3jNSFothdiwAHswrysK9e/fq73//e90BpyTl5uaqS5cuZ+wXHR1dd9/5ysLHHntMc+fOPWv7ihUrFBwc3IypvV96errZEc4r0mFIsuqdr7er/bGtF93fG7nz+IDxcWeMjXtjfBqmoqLClNdtzIe8a9as0cyZM894nnHjxmnZsmWSpOzsbOXm5mr06NF194eHhystLU1r1qw5b1nIB8VNR1nv3hgf99Zc43PPDzpq8bqD2nG0RP/acEjXJsU2Rzyfxu+Oe2N8Gqe+75dblYWzZs3SX/7ylwvus2PHDvXu3bvu9pEjR3TVVVdp0qRJmjZtWpMzzJ49+4wD0ZKSEiUmJmrs2LEKCwtr8vP7ArvdrvT0dI0ZM0Y2m83sOOfUKadEH/5jrbLLbRo9dpT8/TxyRn6jeML4+DLGx30xNu6N8Wmc08VYa2rsh7y5ubl12767T25ubt1+333cufY5Fz4obj6U9e6N8XFvzTE+l0cZ+uiQVX/5cLMshzeKkwubB7877o3xaZj6flDsVmXhgw8+qKlTp15wn65du9b9OycnR6NGjdLw4cPPWrgkJiZGeXl5Z2w7fTsmJua8zx8QEKCAgICztttsNv74aCB3fs8GJLZXhxB/HSuv1o68cg3q3P7iD/Iy7jw+YHzcGWPj3hifhmnKe+UOH/I2Bz4objrKevfG+Li35hyfy6pq9PVfv1T+SbucCSn6IWcXNgm/O+6N8Wmc+n5Q7FZlYWRkpCIjI+u175EjRzRq1Cilpqbq5ZdflsVy5plhw4YN0+9+9zvZ7fa6/3DS09PVq1ev805Bhu+wWAwN6dJen2zN1brsIp8sCwEAaIrW/pD3fPt89/7T22JjY8/YJzk5+bwZ+aC4+fCeuTfGx701x/i0s9l076Vd9OSK3frHqmxNHJgoK6cXNhm/O+6N8WmY+r5XHjn38siRIxo5cqQ6duyoJ598UgUFBcrNzT1jisktt9wif39/3XPPPdq2bZuWLFmip59++qxr3cB3De3aQZK0dt8xk5MAAOB5IiMj1bt37wt+nb4G4eljtwt9yLtq1aozrqPz/Q95hw0bppUrV57xuPT0dA0bNkyS1KVLF8XExJyxT0lJidatW1e3DwB4uzuGd1ZYoJ/25pfp4y1HzY4DwEN5ZFmYnp6uvXv3auXKlUpISFBsbGzd12nh4eFasWKFsrOzlZqaqgcffFBz5sypW1EPSOtaezZh5oHjsjucJqcBAMA7NdeHvL/4xS+0fPly/fWvf9XOnTv1hz/8QRkZGZoxY4YkyTAMPfDAA/rTn/6k999/X1u2bNEdd9yhuLg4TZw4sbV/bAAwRVigTfeMqD2r+++f7ZHT6TI5EQBP5FbTkOtr6tSpF532IkkDBgzQl19+2fKB4JF6RoWqbbBNJyrs2nKkWAM7Mj0dAIDmdvpD3r179yohIeGM+1yu2j9iT3/I+9Of/lSpqamKiIg460Pe4cOH64033tBDDz2k3/72t+rRo4eWLVumfv361e3z61//WuXl5brvvvt04sQJjRgxQsuXL1dgYGDr/LAA4Aam/qCzXvxyn3bnlenf23I1vj/XLgTQMB55ZiHQHCwWQ0NOXatw3b4ik9MAAOCdpk6dKpfLdc6v7zr9IW9lZaUOHz6s3/zmN2c916RJk7Rr1y5VVVVp69atmjBhwhn3G4ahRx55RLm5uaqsrNSnn36qnj17tujPBwDuJjzIprt+0FmS9PRKzi4E0HCUhfBpaaeuW7gum+sWAgAAAPAOd4/oojYBftqZW6r/7M43Ow4AD0NZCJ+W1qX2zMKM/cdVw3ULAQAAAHiBtsH+uiWtoyRp/hf7TE4DwNNQFsKnXRIbptBAP5VV1Wj70RKz4wAAAABAs7jrB51lsxpan12kjQePmx0HgAehLIRPs3LdQgAAAABeKDY8SNcmxUuSXljF2YUA6o+yED4vreupspDrFgIAAADwIvdd1lWStHxbrrILy01OA8BTUBbC5w09tcjJ+uwiOVgpDAAAAICX6BUTqit6R8nlkl78krMLAdQPZSF8Xp/YMLUJ8FNJZY12cN1CAAAAAF7k9NmFSzMPq7CsyuQ0ADwBZSF8np/VokGd20mS1mVz3UIAAAAA3iOtS3slJbZVdY1Tr67eb3YcAB6AshCQlNaldipyxn7KQgAAAADewzAM3Xdp7dmFi9cdVFWNw+REANwdZSEgaWDHtpKkDQePy+XiuoUAAAAAvMe4vtGKDQ/UsfJqfbjpqNlxALg5ykJA0oCEtvKzGMorqVJOcaXZcQAAAACg2fhZLbptaCdJ0qLV+zlBAsAFURYCkoL8rbokNkyStOHAcZPTAAAAAEDzunlIR/n7WbTlSLE2HDxhdhwAboyyEDjlu1ORAQAAAMCbtA/x13VJcZJqzy4EgPOhLAROSelYuyLyRj5lAwAAAOCF7hzeWZL0yZajyuXySwDOg7IQOGXgqbJwW06xKu2sEAYAAADAu/SLD9eQzu1V43Rp8boDZscB4KYoC4FTEtsHKaKNv+wOl7blFJsdBwAAAACa3dQfdJYkvbHuoKpqOEkCwNkoC4FTDMOom4q84cAJc8MAAAAAQAsY2ydaMWGBOlZerX9vyzM7DgA3RFkIfEcKi5wAAAAA8GJ+VosmD06UJL257qDJaQC4I8pC4DtOX7dww8HjcrlcJqcBAAAAgOY3ZXCiLIa0Zt8x7SsoMzsOADdDWQh8x4CEcFkthvJKqnSU1cEAAAAAeKH4tkEa2StKkvTPbw6ZnAaAu6EsBL4j2N9Pl8SGSmIqMgAAAADvdcuQjpKktzMPs9AJgDNQFgLfM5BFTgAAAAB4uZG9IhUTFqgiFjoB8D2UhcD3sMgJAAAAAG/nZ7VoCgudADgHykLge06fWbgtp1iVdk7HBwAAAOCdWOgEwLlQFgLf07F9sNqH+MvucGlXbqnZcQAAAACgRcS1DdKoUwudLGGhEwCnUBYC32MYhvrHh0uSNh8pNjkNAAAAALSc01OR3914RDUOp8lpALgDykLgHAYk1JaFWw6fMDcIAAAAALSgkb2i1D7EXwWlVfpyb6HZcQC4AcpC4Bzqziw8zJmFAAAAALyXv59F1yXHSZLezjxschoA7oCyEDiHAQltJUl78st0sppFTgAAAAB4rxtTEyRJ6dvyVFxhNzkNALNRFgLnEB0WoMjQADmcLm0/WmJ2HAAAAABoMX3jwnVJbJiqHU69vznH7DgATEZZCJyDYRgaEM91CwEAAAD4htNnFzIVGQBlIXAe/RNYERkAAACAb7guOU5+FkObDp3Q3vxSs+MAMBFlIXAe/10RmbIQAAAAgHeLaBOgkb2iJElvZx4xOQ0AM1EWAufR79Q05L0FZSqvqjE5DQAAAAC0rNNTkd/dcFgOp8vkNADMQlkInEdUaKBiwwPlcknbcljkBAAAAIB3u6J3lNoG25RfWqW1+46ZHQeASSgLgQvof+rsws0scgIAAADAy/n7WTShf6wk6b0spiIDvoqyELiAuusWssgJAAAAAB9wbVKcJOmTrbmqqnGYnAaAGSgLgQvon9BWEoucAAAAAPANQzq3V0xYoEora/SfXQVmxwFgAspC4AJOT0PeV1iukkq7yWkAAAAAoGVZLIauTa49u/D9rByT0wAwA2UhcAHtQ/yV0C5IkrSVqcgAAAAAfMDpqcif7shTKSdNAD6HshC4iNPXLdzMVGQAAAAAPqBvXJi6RYaoqsapFdvyzI4DoJVRFgIX0e/UVOTtOSUmJwEAAACAlmcYhq5NipckvbeJqciAr6EsBC6iT2yYJGlbDmcWAgAAAPANp69b+PXeQhWWVZmcBkBroiwELqJPXG1ZuK+wXBXVNSanAQAAAICW1yUiREkJ4XI4Xfp4y1Gz4wBoRZSFwEVEhQYqMjRALpe0M7fU7DgAAAAA0CquObXQyUebKQsBX0JZCNTD6anIXLcQAAAAgK+4ql+MJGn9/iLll1aanAZAa6EsBOrh9FTk7UcpCwEAAAD4hoR2wUpKbCuXS/o3qyIDPoOyEKiHvnGnFzmhLAQAAADgOyacOrvwY6YiAz6DshCoh9PTkHceLVGNw2lyGgAAAABoHRP6x0qS1mUfY1VkwEdQFgL10LlDiIL9raqqcWr/sXKz4wAAAABAq0hsH6z+8eFyuqQVTEUGfAJlIVAPFouhS2KZigwAAADA95w+u/DjLUxFBnwBZSFQT6yIDAAAAMAXTehfe93CNfuOqai82uQ0AFoaZSFQT6yIDAAAAMAXdeoQor5xYXI4XVqxLdfsOABaGGUhUE99vjMN2eVymZwGAAAAAFpP3VTkrZSFgLejLATqqVdMqKwWQ0Xl1corYRUwAAAAAL7jdFm4em+hik/aTU4DoCVRFgL1FGizqltkiCRp+9Fik9MAAAAAQOvpEhGiHlFtVON06T+78s2OA6AFURYCDVA3FfkI1y0EAAAA4FvG9o2WJK3YlmdyEgAtibIQaIC+ceGSWOQEAAAAgO8Z26d2VeT/7MpXVY3D5DQAWgplIdAArIgMAAAAwFf1jw9XdFiAyqsdWv3tMbPjAGghlIVAA5yehnzgWIVKK7moLwAAAADfYbEYGtOndipy+namIgPeirIQaIB2If6KDguQJO3OKzM5DQAAAAC0rjGnpiKnb8+T0+kyOQ2AlkBZCDRQr5jaswt35jIVGQAAAIBvGda1g0ID/FRQWqVNh0+YHQdAC6AsBBrokphQSdKu3FKTkwAAAABA6/L3s2hk7yhJ0gqmIgNeibIQaKBep8rCnUcpCwEAAAD4ntPXLVyxLdfkJABaAmUh0EC9vzMN2eXiGh0AAAAAfMvIXpGyWQ19W1Cubwu4ljvgbSgLgQbqFhUiq8VQSWWNcksqzY4DAAAAAK0qLNCmoV07SJI+ZSoy4HUoC4EGCvCzqmtEiCSmIgMAAADwTaMvqZ2K/NnOfJOTAGhulIVAI/SOPT0VmbIQAAAAgO+54tQiJxkHjqv4pN3kNACaE2Uh0Ai9Ty9ykltichIAAAAAaH2J7YPVI6qNHE6XVu0uMDsOgGbk15QHO51OffHFF/ryyy914MABVVRUKDIyUikpKRo9erQSExObKyfgVk6Xhbs4sxAAAACAj7qid5T25Jfp8535uiYpzuw4AJpJo84sPHnypP70pz8pMTFREyZM0CeffKITJ07IarVq7969evjhh9WlSxdNmDBBa9eube7MgOl6nSoL9+aXqbrGaXIaAAAAAGh9o05NRf7P7gI5nC6T0wBoLo06s7Bnz54aNmyYFixYoDFjxshms521z4EDB/TGG2/opptu0u9+9ztNmzatyWEBdxHfNkihAX4qrarRvsIy9Y4JMzsSAAAAALSq1E7tFBbop6LyamUdOqHUTu3MjgSgGTTqzMIVK1borbfe0oQJE85ZFEpSp06dNHv2bO3Zs0dXXHFFk0IC7sYwjLqzC5mKDAAAAMAX2awWXdYzUpL0OasiA16jUWXhJZdcUu99bTabunXr1piXAdxa79jasnDHUcpCAAAAAL7p9KrIn1EWAl6jSQucSNLmzZvPud0wDAUGBqpjx44KCAho6ssAbqfXqanHu1gRGQAAAICPGtkrSoYhbT9aoqPFJxUbHmR2JABN1OSyMDk5WYZhnPd+m82mKVOm6Pnnn1dgYGBTXw5wG5ecmoa8k2nIAAAAAHxU+xB/pSS21YaDJ/T5zgLdktbR7EgAmqhR05C/61//+pd69OihF154QVlZWcrKytILL7ygXr166Y033tBLL72kzz77TA899FBz5AXcRs9TZeHR4koVV9hNTgMAAAAA5mAqMuBdmnxm4Z///Gc9/fTTGjduXN22/v37KyEhQb///e+1fv16hYSE6MEHH9STTz7Z1JcD3EZYoE3xbYN05MRJ7cwtUVrXDmZHAgAAAIBWN6p3lJ5csVtf7y1UVY1DAX5WsyMBaIImn1m4ZcsWderU6aztnTp10pYtWyTVTlU+evRoU18KcDu9T6+InMdUZAAAAAC+qU9smCJDA3TS7lDm/uNmxwHQRE0uC3v37q3HH39c1dXVddvsdrsef/xx9e7dW5J05MgRRUdHN/WlALfTi+sWAgAAAPBxhmHosh6RkqQvdheYnAZAUzW5LHzuuef04YcfKiEhQaNHj9bo0aOVkJCgDz/8UP/4xz8kSfv27dP999/f5LDnUlVVVbfISlZW1hn3bd68WZdeeqkCAwOVmJioJ554okUywHf1jq1dEXnnUVZEBgDgYpp63LZ06VL17t1bgYGB6t+/vz7++OMz7ne5XJozZ45iY2MVFBSk0aNHa8+ePS35IwEATrm8F2Uh4C2aXBYOHz5c2dnZeuSRRzRgwAANGDBAjzzyiLKzszV06FBJ0u23365f/epXTQ57Lr/+9a8VFxd31vaSkhKNHTtWnTp1UmZmpv73f/9Xf/jDH/TCCy+0SA74ptPTkHfnlcnpdJmcBgAA99aU47bVq1fr5ptv1j333KONGzdq4sSJmjhxorZu3Vq3zxNPPKFnnnlG8+fP17p16xQSEqJx48apsrKyVX4+APBll3aPkGHUzrrKK+F/dwFP1uQFTiQpNDRUP/nJT5rjqRrkk08+0YoVK/TOO+/ok08+OeO+xYsXq7q6WgsXLpS/v7/69u2rrKwsPfXUU7rvvvtaPSu8U5eIEPlbLSqrqtGREyeV2D7Y7EgAALilph63Pf3007rqqqvqPoD+4x//qPT0dD377LOaP3++XC6X5s2bp4ceekjXXXedJOnVV19VdHS0li1bpptuuumcuaqqqlRVVVV3u6SkdraA3W6X3W5v9vfBG51+n3i/3BPj4968aXza+BvqHx+mzYdL9PmOXP1oYLzZkZrEm8bGGzE+jVPf96tZysLXXntNzz//vPbt26c1a9aoU6dO+tvf/qauXbvWHaw1t7y8PE2bNk3Lli1TcPDZBc2aNWt02WWXyd/fv27buHHj9Je//EXHjx9Xu3btzvm8HDA2na/90naNDNHO3FJtO3xcMaE2s+NclK+Nj6dhfNwXY+PeGJ/Gaa33qzmO29asWaOZM2ee8bhx48Zp2bJlkqTs7Gzl5uZq9OjRdfeHh4crLS1Na9asOW9Z+Nhjj2nu3LlnbV+xYsU5s+L80tPTzY6AC2B83Ju3jE+sLNosi5as2qKg3E1mx2kW3jI23orxaZiKiop67dfksvAf//iH5syZowceeEB/+tOf5HA4JEnt2rXTvHnzWqQsdLlcmjp1qn7yk59o0KBB2r9//1n75ObmqkuXLmdsO73ISm5u7nnLQg4Ym4+v/NKG1lgkWfT+l5mqyvacqci+Mj6eivFxX4yNe2N8Gqa+B4xN0VzHbbm5uWctmBcdHa3c3Ny6/b77uHPtcy6zZ88+o4QsKSlRYmKixo4dq7CwsPr/oD7MbrcrPT1dY8aMkc3m/h+c+hrGx7152/jEHDyhfy9Yr30V/hp31ShZLYbZkRrN28bG2zA+jXP6hLiLaXJZ+Pe//10LFizQxIkT9fjjj9dtHzRokH75y1826LlmzZqlv/zlLxfcZ8eOHVqxYoVKS0s1e/bsRmW+EA4Ym87XfmmPfJWtb/69RwqP04QJSWbHuShfGx9Pw/i4L8bGvTE+jVPfA8ZzcYfjtuYQEBCggICAs7bbbDb+W2og3jP3xvi4N28Zn9TOHRQW6KfikzXakVeulI7nPknHk3jL2Hgrxqdh6vteNbkszM7OVkpKylnbAwICVF5e3qDnevDBBzV16tQL7tO1a1d99tlnWrNmzVkHdoMGDdKtt96qV155RTExMcrLyzvj/tO3Y2Jizvv8HDA2H195z/rG1/4f4K68Mo/6eX1lfDwV4+O+GBv3xvg0TFPeq9Y+bjvfPt+9//S22NjYM/ZJTk5u8M8HAGg4P6tFI3pE6OMtufpid4FXlIWAL2pyWdilSxdlZWWpU6dOZ2xfvny5LrnkkgY9V2RkpCIjIy+63zPPPKM//elPdbdzcnI0btw4LVmyRGlpaZKkYcOG6Xe/+53sdnvdgXB6erp69ep13inIQGOcXhF5/7EKVdodCrRZTU4EAEDLa+3jtmHDhmnlypV64IEH6p4rPT1dw4YNk1R7TBoTE6OVK1fWlYMlJSVat26dpk+f3hw/MgCgHi7vGamPt+Rq1e4CPTC6p9lxADRCk8vCmTNn6qc//akqKyvlcrm0fv16vfnmm3rsscf04osvNkfGs3Ts2PGM223atJEkdevWTQkJCZKkW265RXPnztU999yj3/zmN9q6dauefvpp/e1vf2uRTPBdUaEBahds0/EKu/bml6lffLjZkQAAcBvNddz2i1/8Qpdffrn++te/6uqrr9Y///lPZWRk6IUXXpAkGYZRdw3tHj16qEuXLvr973+vuLg4TZw4sXV+WACALutZ+0FS1qETOlFRrbbB/hd5BAB30+Sy8N5771VQUJAeeughVVRU6JZbblFcXJyefvrp86461xrCw8O1YsUK/fSnP1VqaqoiIiI0Z84c3XfffaZlgncyDEM9o0O1LrtIu3JLKQsBAGig+hy3DR8+XG+88YYeeugh/fa3v1WPHj20bNky9evXr26fX//61yovL9d9992nEydOaMSIEVq+fLkCAwPN+LEAwCfFhgepZ3Qb7c4r01d7C/XDAXFmRwLQQE0uCyXp1ltv1a233qqKigqVlZUpKiqqOZ623jp37iyX6+xVaAcMGKAvv/yyVbPAN/WOOVUW5pWaHQUAALfWlOO2SZMmadKkSee93zAMPfLII3rkkUeanBMA0HiX9ojU7rwyfb33GGUh4IEszflkwcHBrV4UAu6gV0ztStm7cikLAQAAAPi2Ed0jJElf7y00OQmAxmjUmYUpKSkyDKNe+27YsKExLwF4lF4xtddfoiwEAAAA4OuGdGkvP4uhg0UVOnisQh07BJsdCUADNKos/O5FoisrK/V///d/6tOnT91qdGvXrtW2bdt0//33N0tIwN31jK5dETm3pFLFFXaFB9tMTgQAAAAA5ggJ8FNKx7b6Zv9xff1toTp26HjxBwFwG40qCx9++OG6f9977736+c9/rj/+8Y9n7XPo0KGmpQM8RGigTfFtg3TkxEntyivVkC7tzY4EAAAAAKb5QfeI2rJwb6FuHkJZCHiSJl+zcOnSpbrjjjvO2n7bbbfpnXfeaerTAx6jV0zt2YW7cktMTgIAAAAA5jp93cLV3x6T03n2wlYA3FeTy8KgoCB9/fXXZ23/+uuvFRgY2NSnBzzG6bJwJ9ctBAAAAODjkhLbKsTfqqLyau3ghArAozRqGvJ3PfDAA5o+fbo2bNigIUOGSJLWrVunhQsX6ve//32TAwKeovepsnB3HmUhAAAAAN9ms1o0tGsHrdyZr6/3FqpvXLjZkQDUU5PLwlmzZqlr1656+umn9frrr0uSLrnkEr388suaPHlykwMCnuL0Iic7c0vlcrnqvWI4AAAAAHij4d0jtHJnvr7ae0z3XdbN7DgA6qnJZaEkTZ48mWIQPq9bZBv5WQyVVtboaHGl4toGmR0JAAAAAExz+rqF67OPqarGoQA/q8mJANRHo65Z6HJxcVLg+/z9LOoaGSJJ2sVUZAAAAAA+rmd0G0W0CVCl3amNB0+YHQdAPTWqLOzbt6/++c9/qrq6+oL77dmzR9OnT9fjjz/eqHCApzk9FXkXi5wAAAAA8HGGYWhE9w6SpK/3FpqcBkB9NWoa8t///nf95je/0f33368xY8Zo0KBBiouLU2BgoI4fP67t27frq6++0rZt2zRjxgxNnz69uXMDbql3TKg+3HyUshAAAAAAJP2ge4SWZeXoq72FenBsL7PjAKiHRpWFV155pTIyMvTVV19pyZIlWrx4sQ4cOKCTJ08qIiJCKSkpuuOOO3TrrbeqXbt2zZ0ZcFu9YsIkcWYhAAAAAEi1ZaEkbTp0QiWVdoUF2kxOBOBimrTAyYgRIzRixIjmygJ4vF6npiHvLShTjcMpP2ujZvoDAAAAgFeIaxukrhEh2ldYrrXfHtPYvv/f3p3HR1Xf+x9/n5nMZN9ISMISCGHfV4lRFESEClpxrwubS5Wrt6LWFqtXba16rdpi60JbW7Hq9ae27iCILIqssu97IGwhhITsy2Rmfn9MMhJJIJCQcyZ5PR+PPDJz5syZz8zXMV/e5/v9niSzSwJwBiQZQCNqHxuqMKddFZUe7TtebHY5AAAAAGC66tGFrFsIBAbCQqAR2WyG/yIn25mKDAAAAAA/hIV7jptcCYD6ICwEGln1VOSdhIUAAAAAoPTUONkMaXd2kbLyy8wuB8AZEBYCjax7EiMLAQAAAKBadJhDfdvHSGIqMhAICAuBRtajKizccZSwEAAAAAAk6eLOcZKkpXsICwGra5SwcM+ePXr88cd1yy23KDs7W5L05ZdfasuWLY1xeCCgdKsKCzNzS1RSUWlyNQAAAABgvvSqsHDl3lx5vV6TqwFwOg0OC7/55hv17dtXK1eu1EcffaSioiJJ0oYNG/Tkk082uEAg0MRHBCs+wimvV9p1tMjscgAAAADAdIM7xsphN3ToRKkO5pWaXQ6A02hwWDh9+nT9/ve/1/z58+V0Ov3bR44cqRUrVjT08EBAql63cAfrFgIAAACAwpxB6l+1buFyrooMWFqDw8JNmzbp2muvPWV7QkKCcnJYiwAtU7dE1i0EAAAAgJNdmOqbirxiL2EhYGUNDgtjYmJ05MiRU7avW7dO7dq1a+jhgYDUg5GFAAAAAFBD9bqFy/ceZ91CwMIaHBb+7Gc/069//WtlZWXJMAx5PB4tXbpUv/zlLzVx4sTGqBEION2ToiRJ2wkLAQAAAECSNKiDb93CI/llyswtMbscAHVocFj47LPPqkePHkpOTlZRUZF69eqlSy+9VBdddJEef/zxxqgRCDhdEyIkSTlF5TpeVG5yNQAAAABgvlCnXQOTYyUxFRmwsgaHhU6nU3//+9+1d+9effHFF3rnnXe0fft2vf3227Lb7Y1RIxBwwoOD1KFVmCTWLQQAAACAahemtpLERU4AK2twWFgtOTlZY8eO1fXXX6/i4mLl5eU11qGBgMQVkQEAAACgph8ucpLLuoWARTU4LJw2bZr+8Y9/SJLcbreGDx+uQYMGKTk5WYsXL27o4YGA1b3qisg7GVkIAAAAAJKkQR1j5bTblFVQpn3HWbcQsKIGh4X//ve/1b9/f0nS559/rr1792r79u168MEH9dhjjzW4QCBQVY8s5CInAAAAAOAT4rBrQIcYSaxbCFhVg8PCnJwcJSUlSZLmzJmjm266Sd26ddMdd9yhTZs2NbhAIFD1qAoLd2YVyuNheD0AAAAASFJ61VRk1i0ErKnBYWFiYqK2bt0qt9utuXPn6oorrpAklZSUcIETtGgp8eFy2A0VV7h16ESp2eUAAAAAgCX8sG7hcdYtBCyowWHhlClTdNNNN6lPnz4yDEOjRo2SJK1cuVI9evRocIFAoHLYbercOkISFzkBAAAAgGoDO8TIGWRTdmG59uYUm10OgB9pcFj41FNP6Y033tDPf/5zLV26VMHBwZIku92u6dOnN7hAIJBVT0XewUVOAAAAAECSb93CQaxbCFhWUGMc5IYbbjhl26RJkxrj0EBA61YdFjKyEAAAAAD8LkyN04q9uVqxN1e3pXU0uxwAJ2mUsLC4uFjffPONMjMzVVFRUeOxX/ziF43xEkBA6kFYCAAAAACnSE+N0wzt0vI9vnULDcMwuyQAVRocFq5bt05jx45VSUmJiouL1apVK+Xk5CgsLEwJCQmEhWjRuidFSZL2HCtSRaVHzqAGz/wHAAAAgIA3oEOMgoNsyikq155jxeqSEGF2SQCqNDi5ePDBB3X11VcrLy9PoaGhWrFihfbv36/BgwfrxRdfbIwagYDVNjpEkcFBqvR4lcHCvQAAAAAgSQoOsmtwx1hJ0nLWLQQspcFh4fr16/Xwww/LZrPJbrervLxcycnJ+sMf/qDf/OY3jVEjELAMw/CvW7g9q8DkagAAAADAOi5MjZMkrdhDWAhYSYPDQofDIZvNd5iEhARlZmZKkqKjo3XgwIGGHh4IeN1ZtxAAAAAATlEdFq7M8K1bCMAaGrxm4cCBA/X999+ra9euGj58uJ544gnl5OTo7bffVp8+fRqjRiCgdU/0hYU7jxIWAgAAAEC1/snRVesWVrBuIWAhDR5Z+Oyzz6pNmzaSpGeeeUaxsbGaOnWqjh07pr/97W8NLhAIdN3905AJCwEAAACgWnCQXQM7xEjyjS4EYA0NHlk4ZMgQ/+2EhATNnTu3oYcEmpXqkYUH80pVVF6piOAGf+0AAAAAoFlI6xSnFXtztXJvrm5L62h2OQDUCCMLAZxebLhTCZHBkpiKDAAAAAAnS0ttJYl1CwEraXBYePToUU2YMEFt27ZVUFCQ7HZ7jR8AXOQEAAAAAGozqEOsnHabjhaUa//xErPLAaBGmIY8efJkZWZm6n/+53/Upk0bGYbRGHUBzUqPpEgt2ZVDWAgAAAAAJwlx2NU/OVrf78vTyozjSokPN7skoMVrcFj43XffacmSJRowYEAjlAM0T90SGVkIAAAAALVJ6xTnCwv35urmCzqYXQ7Q4jV4GnJycjLrCgBn0CMpSpK042gh3xcAAAAAOMkP6xbmmlwJAKkRwsIZM2Zo+vTp2rdvXyOUAzRPXRMjZBhSbnGFjhWVm10OAAAAAFjG4I6xCrIZOnSiVAdyWbcQMNs5TUOOjY2tsTZhcXGxOnfurLCwMDkcjhr75uZyZgAIcdiVEheujJxi7cwqUkJkiNklAQAAAIAlhDmD1Ld9tNZlntDKjFwltwozuySgRTunsHDGjBmNXAbQ/HVPjFRGTrG2ZxVoWNd4s8sBAAAAAMtI6xTnCwv3HtcNg9ubXQ7Qop1TWDhp0qTGrgNo9ronRWruliwucgIAAAAAP5KW2kozv9nDuoWABZzzmoUej0fPP/+8Lr74Yl1wwQWaPn26SktLG7M2oFnpnuS7IvLOo4SFAAAAAHCyIR1jZTOkzNwSHcknWwDMdM5h4TPPPKPf/OY3ioiIULt27fTyyy/rvvvua8zagGblh7CwSB4PV0QGAAAAgGqRIQ71aRctSVq5l9GFgJnOOSz817/+pddee03z5s3TJ598os8//1zvvvuuPB5PY9YHNBspceFyBtlU6nIrkyt8AQAAAEANaZ1aSZJWZhw3uRKgZTvnsDAzM1Njx4713x81apQMw9Dhw4cbpTCgubHbDHVNiJAk7WAqMgAAAADUcGFqnCRGFgJmO+ewsLKyUiEhITW2ORwOuVyuBhcFNFfVU5G5yAkAAAAA1DQkpZUMQ9qbU6zsgjKzywFarHO6GrIkeb1eTZ48WcHBwf5tZWVluvfeexUeHu7f9tFHHzWsQqAZ6VEVFm47UmByJQAAAABgLdGhDvVqE6Uthwu0IiNXP+3f1uySgBbpnMPCSZMmnbLt9ttvb1AxQHPXq41vwV7CQgAAAAA4VVqnOG05XKCVe48TFgImOeew8M0332zMOoAWoWcb38jCfcdLVFReqYjgc/4KAgAAAECzk5baSv9cmqGVGaxbCJjlnNcsBHD24iKClRTlW+tzO6MLAQAAAKCGoSm+KyLvzi5STlG5ydUALRNhIdDEerWNkiRtJSwEAAAAgBpiw53+td5XMboQMAVhIdDEerWpCgsPExYCAAAAwI+ldfKNLly597jJlQAtE2Eh0MQYWQgAAAAAdUtLjZMk1i0ETEJYCDSx6pGF27MKVen2mFwNAAAAAFjL0KqRhduzCpVXXGFyNUDLQ1gINLEOrcIU7rSrotKjvTnFZpcDAAAAAJYSHxGsLgkRkqRV+xhdCDQ1wkKgidlshnqybiEAAAAA1OmHdQsJC4GmRlgImIB1CwEAAACgbj+sW8hFToCmRlgImIArIgMAAABA3S6sGlm49UiB8ktdJlcDtCyEhYAJTh5Z6PV6Ta4GAAAAAKwlISpEneLD5fVKq1m3EGhShIWACbolRspuM5RbXKGjBeVmlwMAAAAAluNftzCDsBBoSoSFgAlCHHZ1bh0uSdp6JN/kagAAAADAetJSqy9ywrqFQFMiLARMwrqFAAAAAFC3tE6+i5xsPlygovJKk6sBWg7CQsAkXBEZAAAAAOrWNiZUya1C5fZ4WbcQaEKEhYBJerWJlsTIQgAAAACoS/XoQtYtBJoOYSFgkuqRhfuOl6iwzGVyNQAAAABgPf6LnLBuIdBkCAsBk7QKd6ptdIgkaQujCwEAAADgFBem+kYWbjyYr5IK1i0EmgJhIWCiPu18U5E3H+KKyAAAAADwY+1jQ9U2OkSVHq/W7j9hdjlAi0BYCJioX3tfWLjxIGEhAAAAAPyYYRhKS61et5CpyEBTICwETNS3fYwkRhYCAAAAQF1+WLeQi5wATYGwEDBR36ppyHtzilXARU4AAM3Y7NmzlZaWptDQUMXGxmr8+PE1Hs/MzNS4ceMUFhamhIQEPfLII6qsrLk21eLFizVo0CAFBwerS5cumjVr1imv8+qrryolJUUhISFKS0vTqlWrzuO7AgA0heqRhesPnFCZy21yNUDzR1gImKhVuFPtYkIlMboQANB8/ec//9GECRM0ZcoUbdiwQUuXLtWtt97qf9ztdmvcuHGqqKjQsmXL9NZbb2nWrFl64okn/PtkZGRo3Lhxuuyyy7R+/XpNmzZNd911l+bNm+ff5/3339dDDz2kJ598UmvXrlX//v01ZswYZWdnN+n7BQA0rpS4MCVEBqvC7dHazDyzywGavSCzC2iI2bNn63e/+502btyokJAQDR8+XJ988on/8czMTE2dOlWLFi1SRESEJk2apOeee05BQQH9ttHM9G0XrUMnSrX5UL4u6hxvdjkAADSqyspKPfDAA3rhhRd05513+rf36tXLf/urr77S1q1b9fXXXysxMVEDBgzQ008/rV//+td66qmn5HQ6NXPmTHXq1EkvvfSSJKlnz5767rvv9Kc//UljxoyRJP3xj3/U3XffrSlTpkiSZs6cqdmzZ+uf//ynpk+fXmt95eXlKi8v998vKCiQJLlcLrlcjPqvj+rPic/Lmmgfa6N96u+ClFjN3pSl5buP6YIO0ef99Wgba6N9zk19P6+ATc3+85//6O6779azzz6rkSNHqrKyUps3b/Y/Xn2GOikpScuWLdORI0c0ceJEORwOPfvssyZWDtTUt3205m7J4iInAIBmae3atTp06JBsNpsGDhyorKwsDRgwQC+88IL69OkjSVq+fLn69u2rxMRE//PGjBmjqVOnasuWLRo4cKCWL1+uUaNG1Tj2mDFjNG3aNElSRUWF1qxZo0cffdT/uM1m06hRo7R8+fI663vuuef029/+9pTtX331lcLCwhry1luc+fPnm10CToP2sTba58zCigxJdn25Zre6lO1sstelbayN9jk7JSUl9dovIMPCxjpDXRvOLjccCf/Z6ZkULknadDC/ST4z2sfaaB/rom2sjfY5N03xee3du1eS9NRTT+mPf/yjUlJS9NJLL2nEiBHauXOnWrVqpaysrBpBoST//aysLP/v2vYpKChQaWmp8vLy5Ha7a91n+/btddb36KOP6qGHHvLfLygoUHJyskaPHq2oqKhzf+MtiMvl0vz583XFFVfI4XCYXQ5+hPaxNtqn/rplF+nDvyzTgZIgXT56pIKDzu+qarSNtdE+56Y64zqTgAwLG+sMdW04u9x4SPjrp9glSUHan1uif382R2FN9K2kfayN9rEu2sbaaJ+zU9+zy7WZPn26nn/++dPus23bNnk8HknSY489puuvv16S9Oabb6p9+/b68MMPdc8995xzDY0hODhYwcHBp2x3OBz84+Ms8ZlZG+1jbbTPmfVoG6P4CKdyiiq0NatYQ6uukHy+0TbWRvucnfp+VgEZFjbWGeracHa54Uj4z95ru7/VwRNlatcnTelVV/o6X2gfa6N9rIu2sTba59zU9+xybR5++GFNnjz5tPukpqbqyJEjkmrOAAkODlZqaqoyMzMlSUlJSadctfjo0aP+x6p/V287eZ+oqCiFhobKbrfLbrfXuk/1MQAAgcswDKV1itPsTUe0cu/xJgsLgZbIUmGhFc5Qc3a58fCZ1V+/5BgdPJGlrVnFurR70/yDhvaxNtrHumgba6N9zk5DPqvWrVurdevWZ9xv8ODBCg4O1o4dOzRs2DBJvnB337596tixoyQpPT1dzzzzjLKzs5WQkCDJN0o0KirKHzKmp6drzpw5NY49f/58paenS5KcTqcGDx6sBQsWaPz48ZIkj8ejBQsW6P777z/n9wkAsI601Fa+sDAjV/9tdjFAM2apsLCpz1ADVtG3XYzmbMrSpkNc5AQA0LxERUXp3nvv1ZNPPqnk5GR17NhRL7zwgiTpxhtvlCSNHj1avXr10oQJE/SHP/xBWVlZevzxx3Xffff5T+Lee++9euWVV/SrX/1Kd9xxhxYuXKgPPvhAs2fP9r/WQw89pEmTJmnIkCEaOnSoZsyYoeLiYv/VkQEAgS2tk28W1pr9eXK5PXLYz++6hUBLZamwsKnPUANW0bddtCTfRU4AAGhuXnjhBQUFBWnChAkqLS1VWlqaFi5cqNjYWEmS3W7XF198oalTpyo9PV3h4eGaNGmSfve73/mP0alTJ82ePVsPPvigXn75ZbVv315vvPGGxowZ49/n5ptv1rFjx/TEE0/417SeO3fuKUvTAAACU9eECMWGOZRX4tLGg/ka3DHW7JKAZslSYWF9NdYZasAqqsPCzNwS5Ze4FB3GFDoAQPPhcDj04osv6sUXX6xzn44dO54yzfjHRowYoXXr1p12n/vvv59pxwDQTNlshoZ2aqV5W45qZcZxwkLgPAnYMbsvvPCCfvazn2nChAm64IILtH///lrPUNvtdqWnp+v222/XxIkTa5yhBqwiOsyhDq18V9tmKjIAAAAA1K56KvLKvbkmVwI0XwE5slBqvDPUgFX0bR+tzNwSbTx0QsO6xptdDgAAAABYTlqq7yrIq/flqtLtURDrFgKNjm8VYBH92/umIq/PPGFuIQAAAABgUT2SohQVEqTiCre2HC4wuxygWSIsBCxiUAffFPp1B07I6/WaXA0AAAAAWI+9at1CSVqZcdzkaoDmibAQsIg+7aIVZDN0rLBcB/NKzS4HAAAAACyJdQuB84uwELCIEIddvdtGSfKNLgQAAAAAnKp63cJV+3Ll9jArC2hshIWAhQysmoq8dn+eyZUAAAAAgDX1ahOliOAgFZZVatsR1i0EGhthIWAhAzvESGJkIQAAAADUJchu05AU30CLlRlMRQYaG2EhYCHVFznZejhfZS63ydUAAAAAgDX9sG4hFzkBGhthIWAh7WNDFR/hlMvt1ZbD+WaXAwAAAACWdPK6hR7WLQQaFWEhYCGGYZy0buEJc4sBAAAAAIvq2y5aYU67TpS4tDO70OxygGaFsBCwmB/WLeQiJwAAAABQG4fdpsEdfQMtlu1mKjLQmAgLAYsZxMhCAAAAADiji7vES5KW7ckxuRKgeSEsBCymX/to2Qwpq6BMR/JLzS4HAAAAACzp4s6+sHDF3lxVuj0mVwM0H4SFgMWEOYPUIylKEqMLAQAAAKAuvdpGKSbMoaLySm04yAUigcZCWAhY0KCOMZKkdZmsWwgAAAAAtbHbDKWnxkmSlu1mKjLQWAgLAQsamOxbt3DdgRPmFgIAAAAAFla9buF3hIVAoyEsBCxoUNVVvTYdyleZy21yNQAAAABgTdVh4brMEyqpqDS5GqB5ICwELCglLkzxEcGqqPRoA6MLAQAAAKBWKXFhahcTqgq3R9/vYxknoDEQFgIWZBiG0jq1kiStysg1uRoAAAAAsCbDMHRRZ9YtBBoTYSFgUWmpvrBwJWEhAAAAANRpWFfWLQQaE2EhYFFpnXxnx9bsz5PL7TG5GgAAAACwpvSqkYVbjxQot7jC5GqAwEdYCFhU14QIxYQ5VOpya+PBfLPLAQAAAABLSogMUffESHm90vI9x80uBwh4hIWARdlshoamVE9F5g8eAAAAANTloi6+0YVMRQYajrAQsLC0VN8fPC5yAgAAAAB1G9alet3CY/J6vSZXAwQ2wkLAwqqviLx6X54qWbcQAAAAAGp1YWqcHHZDB3JLte94idnlAAGNsBCwsJ5tohQZEqSi8kptPVJgdjkAAAAAYEnhwUEa0tE32OKbHdkmVwMENsJCwMLsJ69buJepyAAAAABQl+HdW0uSvt3FuoVAQxAWAhaXlspFTgAAAADgTC7t6gsLl+85rvJKt8nVAIGLsBCwuKGdfrjIidvDQr0AAAAAUJuebSLVOjJYpS63Vu/LM7scIGARFgIW16dtlMKddhWUVWpHVqHZ5QAAAACAJRmGoeHdfKMLv9l5zORqgMBFWAhYXJDdpsFV6xau2MtUZAAAAACoy6XVYeEOwkLgXBEWAgHg4s6+qchLdvEHDwAAAADqckmXeBmGtONoobLyy8wuBwhIhIVAAKg+O7Ziby4L9QIAAABAHWLDnerfPkaS9C1TkYFzQlgIBIAeSZFKYKFeAAAAADgj/1RkZmYB54SwEAgAhmHokq6+P3icHQMAAACAulVf5OS7XTmqdHtMrgYIPISFQIC4tFu8JK7qBQAAAACn0799tKJDHcovdWnDwRNmlwMEHMJCIEBc0rW1DEPanlWo7AIW6gUAAACA2gTZbbqkq2+wxYJt2SZXAwQewkIgQLQKd6pvu2hJ0re7ckyuBgAAAACsa1TPREmEhcC5ICwEAsilrFsIAAAAAGc0ontr2W2Gdhwt1IHcErPLAQIKYSEQQKqv6vXd7hx5PF6TqwEAAAAAa4oJc2pwx1hJ0oJtR02uBggshIVAABnYIUYRwUHKLa7Q5sP5ZpcDAAAAAJZ1RfVU5O1MRQbOBmEhEEAcdpsu6hwnianIAAAAAHA6l/dMkCSt2HtchWUuk6sBAgdhIRBgqqcif7uTi5wAAAAAQF1SW0coNT5cLrdXS7hIJFBvhIVAgBleFRauyczTiZIKk6sBAAAAAOuqHl34NesWAvVGWAgEmORWYeqeGCm3x6vFO5iKDAAAAAB1ubxq3cLFO47JzUUigXohLAQC0BW9fH/w5m/l7BgAAAAA1GVIx1hFhzqUW1yhdZl5ZpcDBATCQiAAjaoKC7/ZeUzllW6TqwEAAAAAawqy2zSiu28pp6+3cVVkoD4IC4EA1K9dtBIig1VUXqkVe3PNLgcAAAAALGtU1VTkeVuy5PUyFRk4E8JCIADZbIZ/7Y35W7NMrgYAAAAArOuyHglyBtmUkVOsHUcLzS4HsDzCQiBAje5dfXbsqDws1AsAAAAAtYoIDtLwbr6pyHM2MdgCOBPCQiBAXdw5XpEhQTpWWK7V+1moFwAAAADqMrZvkiRpzqYjJlcCWB9hIRCgnEE2/1WR+YMHAAAAAHW7vGeinHabdmcXaRdTkYHTIiwEAtjYPm0kSXM3ZzEVGQAAAADqEBXi0CVd4yUxFRk4E8JCIIAN6xqviOAgZRWUad0BpiIDAAAAQF2u7OsbbPHlZmZmAadDWAgEsBCHXaN6JkiSPt/AHzwAAAAAqMsVPRMVZDO0PatQe44VmV0OYFmEhUCAu2ZAO0nSFxsPq9LtMbkaAAAAALCm6DCHLu7im4r8Jeu+A3UiLAQC3LCu8WoV7lROUYWW7TludjkAAAAAYFnjqqYis24hUDfCQiDAOew2/x+8T9YfMrkaAAAAALCuK3olym4ztPVIgTJyis0uB7AkwkKgGbhmQFtJ0rzNWSqtcJtcDQAAAABYU2y4U8OqpiJ/vI7BFkBtCAuBZmBwx1gltwpVcYVb87YwnB4AAAAA6nLdIN+675+sOySv12tyNYD1EBYCzYBhGLphULIk6YPVB0yuBgAAAACsa3SvJIU77crMLdGa/XlmlwNYDmEh0ExcP7idDENatue4DuSWmF0OAAAAAFhSqNOuK6vWff/PWqYiAz9GWAg0E+1jw3RxZ9/aG/9ec9DkagAAAADAuq4b6JuKPHvjYZW5WPcdOBlhIdCM3DikvSTpw9UH5Paw9gYAAAAA1ObC1Di1iQ5RQVmlFm3PNrscwFIIC4FmZEzvJMWGOXQ4v4w/eAAAAABQB5vN0Piq0YUfcVVkoAbCQqAZCXHYdeMQ34VO3l6x3+RqAAAAAMC6qqciL9qerdziCpOrAayDsBBoZm4d2kGS9O2uY8o8zoVOAAAAAKA2XRMj1addlCo9Xn2x8bDZ5QCWQVgINDMp8eG6tFtreb3SOysZXQgAAAAAdbluoG/d9/e/PyCvl3XfAYmwEGiWJqV3lCS9typTReWVJlcDAAAAANZ03aB2cgbZtOVwgTYczDe7HMASCAuBZuiy7glKjQ9XYVmlPvj+gNnlAAAAAIAlxYQ5dVW/NpKkd1j3HZBEWAg0SzaboTuGdZIk/XNphtwehtMDAAAAQG1uS/PNzPp8w2Hll7hMrgYwH2Eh0ExdP6i9YsMcOphXqjmbjphdDgAAAABY0qAOMerZJkrllR79Z+1Bs8sBTEdYCDRToU67Jl2UIkl6ddFueRhdCAAAAACnMAxDt6V1kCS9u3I/FzpBi0dYCDRjky9KUURwkLZnFWrB9myzywEAAAAASxo/sJ3CnXbtOVasFXtzzS4HMBVhIdCMxYQ5NaHqysivLNzFGTIAAAAAqEVEcJDGD2wnyTe6EGjJCAuBZu7OYZ0U6rBrw8F8fb2N0YUAAAAAUJvqC53M25Kl7MJyk6sBzENYCDRz8RHBmnJxiiTpxXk7uDIyAAAAANSiV9soXZASK5fbq38tzzS7HMA0hIVAC3DPpZ0VFRKkHUcL9flGrowMAAAAALX5+aWdJUn/9/0BlVWaXAxgEsJCoAWIDnNo6ogukqQ/fr1bFW6TCwIAtCg7d+7UNddco/j4eEVFRWnYsGFatGhRjX0yMzM1btw4hYWFKSEhQY888ogqK2v+K23x4sUaNGiQgoOD1aVLF82aNeuU13r11VeVkpKikJAQpaWladWqVefzrQEAmpnLeySoc+twFZZValm2YXY5gCkIC4EWYsrFKWoXE6oj+WVaeJg/egCApnPVVVepsrJSCxcu1Jo1a9S/f39dddVVysrKkiS53W6NGzdOFRUVWrZsmd566y3NmjVLTzzxhP8YGRkZGjdunC677DKtX79e06ZN01133aV58+b593n//ff10EMP6cknn9TatWvVv39/jRkzRtnZrNkLAKgfm83QPVWjCxcfsami0mNyRUDTIywEWogQh12Pju0hSfr6sE2HT5SaXBEAoCXIycnRrl27NH36dPXr109du3bV//7v/6qkpESbN2+WJH311VfaunWr3nnnHQ0YMEBXXnmlnn76ab366quqqKiQJM2cOVOdOnXSSy+9pJ49e+r+++/XDTfcoD/96U/+1/rjH/+ou+++W1OmTFGvXr00c+ZMhYWF6Z///Kcp7x0AEJiuGdhWCZHByq8w9MUmlnFCyxNkdgEAms64vm00q2OGVu8/od/P2aG/T7rA7JIAAM1cXFycunfvrn/961/+KcR//etflZCQoMGDB0uSli9frr59+yoxMdH/vDFjxmjq1KnasmWLBg4cqOXLl2vUqFE1jj1mzBhNmzZNklRRUaE1a9bo0Ucf9T9us9k0atQoLV++vM76ysvLVV7+wxUvCwoKJEkul0sul6vB778lqP6c+LysifaxNtrHmmySJgxtp5cW7NXfl+zT+P5tZbMxO8tK+O6cm/p+XgEbFu7cuVOPPPKIli5dqoqKCvXr109PP/20LrvsMv8+mZmZmjp1qhYtWqSIiAhNmjRJzz33nIKCAvZtAw1iGIaevKqnrnltmeZvy9bczVn6SZ8ks8sCADRjhmHo66+/1vjx4xUZGSmbzaaEhATNnTtXsbGxkqSsrKwaQaEk//3qqcp17VNQUKDS0lLl5eXJ7XbXus/27dvrrO+5557Tb3/721O2f/XVVwoLCzv7N9yCzZ8/3+wScBq0j7XRPtbTulIKttu1+1ixXnxvrvrEes0uCbXgu3N2SkpK6rVfwKZmV111lbp27aqFCxcqNDRUM2bM0FVXXaU9e/YoKSnJv/ZNUlKSli1bpiNHjmjixIlyOBx69tlnzS4fME2PpEiNbOvV14cMPfnZZl3UJU5RIQ6zywIABJjp06fr+eefP+0+27ZtU/fu3XXfffcpISFBS5YsUWhoqN544w1dffXV+v7779WmTZsmqrh2jz76qB566CH//YKCAiUnJ2v06NGKiooysbLA4XK5NH/+fF1xxRVyOOhTWA3tY220j3W5XC59dWiBFh42tLIwVo/cmibDYHShVfDdOTfVMyjOJCDDwuq1b/7xj3+oX79+kqT//d//1WuvvabNmzcrKSnJv/bN119/rcTERA0YMEBPP/20fv3rX+upp56S0+ms9dhMRWk4hgNbm8vl0ph2Hu0sDVdmbqme/GST/nB9X7PLQhW+P9ZF21gb7XNuGvJ5Pfzww5o8efJp90lNTdXChQv1xRdfKC8vzx++vfbaa5o/f77eeustTZ8+XUlJSadctfjo0aOSpKSkJP/v6m0n7xMVFaXQ0FDZ7XbZ7fZa96k+Rm2Cg4MVHBx8ynaHw8E/Ps4Sn5m10T7WRvtY02VtPFqR49DGQwVatCtXY3ozK8tq+O6cnfp+VgEZFjbW2je1YSpK42E4sHU57dK1bQr151y7Pl5/RDElBzUgjmH1VsL3x7poG2ujfc5Ofaei1KZ169Zq3bp1vV/DZqt5XT2bzSaPx3eFyfT0dD3zzDPKzs5WQkKCJF9bRkVFqVevXv595syZU+MY8+fPV3p6uiTJ6XRq8ODBWrBggcaPHy9J8ng8WrBgge6///5zfp8ZP97jAAAm6ElEQVQAgJYryilNSu+g17/J0IvzdmhUz0TZWbsQLUBAhoWNtfZNbZiK0nAMB7a26va55/orVBG3T69/m6GPDgRr4lXpah8banZ5LR7fH+uibayN9jk39Z2K0hDp6emKjY3VpEmT9MQTTyg0NFR///vflZGRoXHjxkmSRo8erV69emnChAn6wx/+oKysLD3++OO67777/KP+7r33Xr3yyiv61a9+pTvuuEMLFy7UBx98oNmzZ/tf66GHHtKkSZM0ZMgQDR06VDNmzFBxcbGmTJly3t8nAKB5uuviFL278oB2ZRfp0/WHdN2g9maXBJx3lgoLrbD2DVNRGg+fmbU5HA49OLqHlu3N1YaD+Xrgg4368N50BQfZzS4N4vtjZbSNtdE+Z6cpPqv4+HjNnTtXjz32mEaOHCmXy6XevXvr008/Vf/+/SVJdrtdX3zxhaZOnar09HSFh4dr0qRJ+t3vfuc/TqdOnTR79mw9+OCDevnll9W+fXu98cYbGjNmjH+fm2++WceOHdMTTzyhrKwsDRgwQHPnzj3lBDIAAPUVFerQvSM66w9zd+hPX+/UVf3ayhlkO/MTgQBmqbCwqde+AVo6Z5BNr942SFf95TttPJivpz7bomev7cvCvQCARjVkyBDNmzfvtPt07NjxlGnGPzZixAitW7futPvcf//9TDsGADSqyRel6M2l+3Qgt1Tvrz6gCRd2NLsk4LyyVBzeunVr9ejR47Q/Tqez3mvfbNq0SdnZ2f7Hf7z2DQCpfWyY/nTzABmG9N6qA/rHdxlmlwQAAAAAlhHmDNJ/j+wiSfrzgl0qLq80uSLg/LJUWFhfJ699s2HDBu3cuVOPPPJInWvfbNiwQfPmzTtl7RsAPpd1T9BjY3tKkp6Zs01zNh0xuSIAAAAAsI6fXdBBHVqF6Vhhuf68cJfZ5QDnVUCGhdVr3xQVFWnkyJEaMmSIvvvuu1rXvrHb7UpPT9ftt9+uiRMn1lj7BsAP7hzWSbeldZDXKz3w/9bpm53HzC4JAAAAACzBGWTTUz/1zVL8x5IM7c4uNLki4Pyx1JqFZ6Ox1r4B4GMYhn53TR+dKHFp9qYjuuft1fr7xCG6pGtrs0sDAAAAANON7JGoUT0T9PW2bD3x6Ra9e1ca672jWQrIkYUAzg+7zdCfbh6gkT0SVOby6M5ZqzV/61GzywIAAAAAS3jy6t4KDrJp2Z7jms3yTWimCAsB1OAMsun12wfpJ72TVOH26J63V+vtFfvNLgsAAAAATJfcKkz/NcJ3sZPff7GNi52gWSIsBHCK4CC7Xrl1oG4a0l4er/Q/n2zW459sUpnLbXZpAAAAAGCqe4anqkOrMGUVlOmFeTvMLgdodISFAGoVZLfp+ev76Zeju0mS3lmRqfGvLmUhXwAAAAAtWojDrqfH95EkzVq2T0t355hcEdC4CAsB1MkwDN0/sqveumOo4iOc2p5VqKv/slTvrcqU1+s1uzwAAAAAMMXwbq11W1oHSdIvP9yg/FKXyRUBjYewEMAZDe/WWnMeuETDusSr1OXWox9t0o0zl2vr4QKzSwMAAAAAUzw2rqdS4sJ0JL9Mv/1si9nlAI2GsBBAvSREhuhfdwzVb8b2UJjTrtX783TVX5boyU83K6+4wuzyAAAAAKBJhTmD9NJNA2QzpI/WHdKXXB0ZzQRhIYB6s9kM/fzSzlrw8HCN69dGHq/01vL9Gvb8Qv1h7nblEhoCAAAAaEEGd4zV1BGdJUmPfrxJB3JLTK4IaDjCQgBnrU10qF69dZDevStNvdpEqbjCrdcW79Gw5xfquTnbdOhEqdklAgAAAECTeODyburfPlonSly65+01Kq1wm10S0CCEhQDO2cVd4jX7F8P0twmD1atNlEoq3Prrt3t1yfMLde/ba7Ri73EuhAIAAACgWXMG2fT67YMVH+HU1iMFevSjjfw7CAGNsBBAgxiGodG9kzT7F8P0xsQhuqhznDxeae6WLP3sbyt05ctL9N6qTBWXV5pdKgAAAACcF21jfLOvgmyGPll/WP9cus/skoBzRlgIoFEYhqFRvRL1f3dfqHnTLtWtaR0U6rBre1ahHv1ok9KeXaDHPt6kzYfyzS4VAAAAABpdWmqcHh/XU5L07Jxt+nbnMZMrAs4NYSGARtc9KVLPXttXKx69XI+N7alO8eEqKq/UuyszddVfvtPVf/lO/7cyU0WMNgQAAADQjEy6KEXXD2ovt8ere99Zo3WZeWaXBJw1wkIA5010mEN3X5qqhQ8P13t3X6if9m8rp92mTYfy9ZuPN2noM1/r0Y82auPBE6zpAQAAACDgGYah567rq0u6xqukwq0ps77XrqOFZpcFnBXCQgDnnWEYSu8cpz/fMlArfnO5Hh/XU6mtw1VS4dZ7qw7op68s1VV/+U7vrNivwjKX2eUCAAAAwDlzBtk08/bBGpAcoxMlLk34xyodzCsxuyyg3ggLATSpVuFO3XVJqhY8NFzv//xCjR/QVs4gm7YcLtDjn2zW0GcW6Ff/3qB1mXmMNgQAAAAQkMKDg/Tm5AvUJSFCWQVluu2NlTqQS2CIwEBYCMAUhmEoLTVOM342UKt+c7meuKqXuiREqNTl1gerD+ra15bpypeX6F/L9ym/lNGGAAAAAAJLbLh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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "_ = fom.transfer_function.bode_plot(w)" ] }, { "cell_type": "markdown", "id": "cee1e65c", "metadata": {}, "source": [ "## 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", "{meth}`~pymor.models.iosys.LTIModel.poles` method\n", "(assuming the system is minimal)." ] }, { "cell_type": "code", "execution_count": 11, "id": "3eed73f0", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "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": "f6bcebe1", "metadata": {}, "source": [ ":::{note}\n", "\n", "The {meth}`~pymor.models.iosys.LTIModel.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 {meth}`~pymor.models.iosys.LTIModel.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 {meth}`~pymor.models.iosys.LTIModel.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": 12, "id": "5e7fd78e", "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", " [-4.48720858e-17 1.95466800e-15 -3.87392910e-14 ... -1.84179333e-10\n", " 3.10420349e-11 -2.87160762e-12]\n", " [ 3.97648476e-18 -1.92190365e-16 4.26024322e-15 ... -2.24465928e-11\n", " 1.75879252e-12 -8.24288506e-14]\n", " [-1.85127015e-17 7.70480426e-16 -1.45373940e-14 ... 1.65200046e-10\n", " -3.71100064e-11 4.41382006e-12]],\n", " _len=101)" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fom.gramian('c_lrcf')" ] }, { "cell_type": "markdown", "id": "9d973876", "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 {meth}`~pymor.models.iosys.LTIModel.hsv` method can be used to compute them." ] }, { "cell_type": "code", "execution_count": 13, "id": "91cec58d", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "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": "711ff40d", "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 {meth}`~pymor.models.iosys.LTIModel.h2_norm` method of an {{ LTIModel }} can be\n", "used to compute it." ] }, { "cell_type": "code", "execution_count": 14, "id": "55f2acb6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.0377751533822073" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fom.h2_norm()" ] }, { "cell_type": "markdown", "id": "a5e17696", "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 {meth}`~pymor.models.iosys.LTIModel.hinf_norm` method uses a dense solver\n", "from [Slycot]() to compute the\n", "{math}`\\mathcal{H}_\\infty` norm." ] }, { "cell_type": "code", "execution_count": 15, "id": "5b1c837d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.2890705455704852" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fom.hinf_norm()" ] }, { "cell_type": "markdown", "id": "8203c231", "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", "{meth}`~pymor.models.iosys.LTIModel.hankel_norm` relies on the\n", "{meth}`~pymor.models.iosys.LTIModel.hsv` method." ] }, { "cell_type": "code", "execution_count": 16, "id": "e5301f7b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.6221361786735345" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fom.hankel_norm()" ] }, { "cell_type": "markdown", "id": "80876976", "metadata": {}, "source": [ "Download the code:\n", "{download}`tutorial_lti_systems.md`,\n", "{nb-download}`tutorial_lti_systems.ipynb`." ] } ], "metadata": { "jupyter": { "jupytext": { "cell_metadata_filter": "-all", "formats": "ipynb,myst", "main_language": "python", "text_representation": { "extension": ".md", "format_name": "myst", "format_version": "1.3", "jupytext_version": "1.11.2" } } }, "jupytext": { "text_representation": { "format_name": "myst" } }, "kernelspec": { "display_name": "Python 3", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", 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