From 6038c414ba1d1664db8f7f53a58b0ead9c6ac7c9 Mon Sep 17 00:00:00 2001 From: Liz Munch Date: Fri, 24 Apr 2026 14:20:50 -0400 Subject: [PATCH 1/2] Starting to get branch decomposition to work Co-authored-by: Copilot --- Notebooks_Unused/sandbox_decomposition.ipynb | 197 +++++++++++++++++++ cereeberus/cereeberus/reeb/branchdecomp.py | 86 ++++++++ cereeberus/cereeberus/reeb/reebgraph.py | 60 +++++- doc_source/modules/data/ex_reebgraphs.rst | 2 +- tests/test_reeb_class.py | 32 +++ 5 files changed, 374 insertions(+), 3 deletions(-) create mode 100644 Notebooks_Unused/sandbox_decomposition.ipynb create mode 100644 cereeberus/cereeberus/reeb/branchdecomp.py diff --git a/Notebooks_Unused/sandbox_decomposition.ipynb b/Notebooks_Unused/sandbox_decomposition.ipynb new file mode 100644 index 0000000..2a1434c --- /dev/null +++ b/Notebooks_Unused/sandbox_decomposition.ipynb @@ -0,0 +1,197 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 2, + "id": "8ca81a04", + "metadata": {}, + "outputs": [], + "source": [ + "from cereeberus import ReebGraph \n", + "\n", + "import cereeberus.data.ex_reebgraphs as ex_rg\n", + "import numpy as np" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "81ba67df", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "R = ex_rg.dancing_man()\n", + "R.draw()" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "f9ff166a", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[7, 6, 2, 1, 0]\n" + ] + } + ], + "source": [ + "# Get a path that continues upward in the reeb grpah until it hits a local max \n", + "\n", + "def upward_path(R, v): \n", + " path = [v]\n", + " while R.up_degree(path[-1]) > 0: \n", + " s = next(R.successors(path[-1]))\n", + " path.append(s)\n", + " \n", + " \n", + " return path\n", + "\n", + "v = 7 # I know this is a local min already\n", + "path = upward_path(R, v)\n", + "print(path)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "1c2d8150", + "metadata": {}, + "outputs": [], + "source": [ + "R.remove_path_from(path)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "13eebf46", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "R.draw()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3eba6dd1", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "7" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "R.sorted_vertices()[0]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c2ba646f", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Vertex: 7, f(v) = 1, degree = 0\n", + "Vertex: 5, f(v) = 4, degree = 0\n", + "Vertex: 6, f(v) = 4, degree = 1\n", + "Vertex: 2, f(v) = 5, degree = 2\n", + "Vertex: 3, f(v) = 5, degree = 1\n", + "Vertex: 1, f(v) = 6, degree = 2\n", + "Vertex: 4, f(v) = 6, degree = 1\n", + "Vertex: 0, f(v) = 7, degree = 1\n", + "[[1 7 0 0]\n", + " [4 7 1 1]\n", + " [4 7 2 2]\n", + " [5 7 3 3]\n", + " [5 7 4 4]\n", + " [6 7 5 5]\n", + " [6 6 6 6]\n", + " [7 7 7 7]]\n" + ] + } + ], + "source": [ + "branches = [] \n", + "\n", + "for v in R.sorted_vertices(): \n", + " print(f\"Vertex: {v}, f(v) = {R.f[v]}, degree = {R.down_degree(v)}\")\n", + " \n", + " # get a maximal path upward from v \n", + " path = upward_path(R,v)\n", + " \n", + " start_f = R.f[path[0]]\n", + " end_f = R.f[path[-1]]\n", + " branches.append((start_f, end_f, len(branches), len(branches)))\n", + " \n", + "branches = np.array(branches)\n", + "print(branches)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "bef13a93", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "cereeberus", + "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": "3.12.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/cereeberus/cereeberus/reeb/branchdecomp.py b/cereeberus/cereeberus/reeb/branchdecomp.py new file mode 100644 index 0000000..8ebbf88 --- /dev/null +++ b/cereeberus/cereeberus/reeb/branchdecomp.py @@ -0,0 +1,86 @@ +import numpy as np + + +class BranchDecomp: + """ + This class encodes a branch decmposition of a given Reeb graph. This is a sorted list of intervals (branches), where the endpoints of the intervals have attaching information, either to a previous branch, or to itself (meaning that end of the interval is a local max/min). The Reeb graph can be reconstructed from the data as well. Note that the decomposition is not unique. + + The branches are stored as an n x 4 array, where n is the number of branches. The first two columns are the real-valued endpoints of the branch, and the last two columns are integers giving the attaching information. The attaching information is a tuple of the form (branch_id_low, branch_id_high), where branch_id_low is the ID of the branch that the lower interval endpoint is attached to (can be its own row if it is a local min), and branch_id_high is the ID of the branch that the upper interval endpoint is attached to (can be its own row if it is a local max). + + + """ + def __init__(self): + self.branches = np.empty((0, 4)) + self.paths = [] + + + @staticmethod + def _remove_path_edges(graph, path): + """Remove one edge along each step of the chosen path.""" + for i in range(len(path) - 1): + u, v = path[i], path[i + 1] + if graph.has_edge(u, v): + graph.remove_edge(u, v) + + def decompose(self, reebgraph): + ''' + Decomposes the Reeb graph into branches. + ''' + working = reebgraph.copy() + + self.paths = [] + branch_rows = [] + + # Track endpoint attachments to previously created branches by shared vertex. + endpoint_owner = {} + + while len(working.edges) > 0: + start = self._lowest_available_vertex(working) + if start is None: + break + + path = self._largest_upward_path(working, start) + branch_id = len(self.paths) + start_v = path[0] + end_v = path[-1] + + low_attach = endpoint_owner.get(start_v, branch_id) + high_attach = endpoint_owner.get(end_v, branch_id) + + branch_rows.append( + (working.f[start_v], working.f[end_v], low_attach, high_attach) + ) + self.paths.append(path) + + endpoint_owner.setdefault(start_v, branch_id) + endpoint_owner.setdefault(end_v, branch_id) + + self._remove_path_edges(working, path) + + if len(branch_rows) == 0: + self.branches = np.empty((0, 4)) + else: + self.branches = np.array(branch_rows, dtype=float) + + return self.branches + + def get_branches(self): + ''' + Returns the branches of the Reeb graph. + ''' + return self.branches + + def get_branch(self, branch_id): + ''' + Returns the branch with the given ID. + ''' + if branch_id < 0 or branch_id >= len(self.branches): + raise IndexError("branch_id out of range") + + return self.branches[branch_id] + + def reconstruct(self): + ''' + Reconstructs the Reeb graph from the branches. + ''' + raise NotImplementedError("reconstruct is not implemented yet") \ No newline at end of file diff --git a/cereeberus/cereeberus/reeb/reebgraph.py b/cereeberus/cereeberus/reeb/reebgraph.py index 0cc5f06..a540bec 100644 --- a/cereeberus/cereeberus/reeb/reebgraph.py +++ b/cereeberus/cereeberus/reeb/reebgraph.py @@ -1,8 +1,14 @@ -import networkx as nx -from ..draw import draw +from os import path + import matplotlib.pyplot as plt +import networkx as nx import numpy as np +from ..draw import draw + +# from build.lib.cereeberus.reeb import graph + + class ReebGraph(nx.MultiDiGraph): """ @@ -136,6 +142,27 @@ def number_connected_components(self): """ return nx.number_connected_components(self.to_undirected()) + def get_upward_path(self, start_vertex): + """Return an upward path from the starting vertex by greedy dynamic choice. + + Input: + start_vertex: a vertex in the graph to start from + + Output: + path: a list of vertices representing the upward path + + """ + # Check that the vertex is in the graph + if start_vertex not in self.nodes: + raise ValueError(f"The vertex {start_vertex} is not in the Reeb graph.") + + path = [start_vertex] + while self.up_degree(path[-1]) > 0: + s = next(self.successors(path[-1])) + path.append(s) + + return path + def func_to_vertex_dict(self): """ Get a dictionary mapping function values to all vertices at that height. @@ -426,6 +453,35 @@ def add_edges_from(self, edges, reset_pos=True): if reset_pos: self.set_pos_from_f() + def remove_edges_from(self, edges, reset_pos=True): + """Remove a list of edges from the Reeb graph. + + Parameters: + edges (list): The list of edges to remove. + reset_pos (bool): Optional. If True, will reset the positions of the nodes based on the function values. + """ + for edge in edges: + if self.has_edge(*edge): + super().remove_edge(*edge) + + if reset_pos: + self.set_pos_from_f() + + def remove_path_from(self, path, reset_pos=True): + """Remove a path from the Reeb graph. A path is a list of vertices, and this method will remove one edge along each step of the path. + + Parameters: + path (list): The list of vertices representing the path to remove. + reset_pos (bool): Optional. If True, will reset the positions of the nodes based on the function values. + """ + for i in range(len(path) - 1): + u, v = path[i], path[i + 1] + if self.has_edge(u, v): + self.remove_edge(u, v) + + if reset_pos: + self.set_pos_from_f() + def subdivide_edge(self, u, v, w, f_w): """Subdivide an edge with a new vertex. diff --git a/doc_source/modules/data/ex_reebgraphs.rst b/doc_source/modules/data/ex_reebgraphs.rst index 5cd5992..64ef194 100644 --- a/doc_source/modules/data/ex_reebgraphs.rst +++ b/doc_source/modules/data/ex_reebgraphs.rst @@ -1,7 +1,7 @@ Reeb Graphs ************************************* -This module contains example graphs and data to use for Reeb graph computations. Pictures of these can be seen in `this notebook <../../notebooks/example_reeb_graphs.html>`_ +This module contains example graphs and data to use for Reeb graph computations. Pictures of these can be seen in `this notebook <../../notebooks/example_graphs.ipynb>`_ .. automodule:: cereeberus.data.ex_reebgraphs :members: diff --git a/tests/test_reeb_class.py b/tests/test_reeb_class.py index 24c47eb..2dde923 100644 --- a/tests/test_reeb_class.py +++ b/tests/test_reeb_class.py @@ -113,6 +113,38 @@ def test_add_edge(self): # General check of the Reeb graph self.check_reeb(R) + def test_get_upward_path(self): + # This test makes sure you can get an upward path from a starting vertex. + R = ex_rg.torus(multigraph=True) + + self.assertEqual(R.get_upward_path("a"), ["a", "b", "c", "d"]) + self.assertEqual(R.get_upward_path("d"), ["d"]) + self.assertRaises(ValueError, R.get_upward_path, "chicken") + + def test_remove_edges_from(self): + # This test makes sure you can remove a list of edges from a Reeb graph. + R = ex_rg.torus(multigraph=True) + + self.assertEqual(R.number_of_edges("b", "c"), 2) + + R.remove_edges_from([("b", "c"), ("b", "c"), ("a", "d")]) + + self.assertEqual(R.number_of_edges("b", "c"), 0) + self.assertEqual(R.summary(), {"nodes": 4, "edges": 2}) + self.check_reeb(R) + + def test_remove_path_from(self): + # This test makes sure you can remove one edge along each step of a path. + R = ex_rg.torus(multigraph=True) + + R.remove_path_from(["a", "b", "c", "d"]) + + self.assertFalse(R.has_edge("a", "b")) + self.assertEqual(R.number_of_edges("b", "c"), 1) + self.assertFalse(R.has_edge("c", "d")) + self.assertEqual(R.summary(), {"nodes": 4, "edges": 1}) + self.check_reeb(R) + def test_subdivide_edge(self): # This test makes sure you can subdivide an edge in a Reeb graph. R = ex_rg.juggling_man() From 259da8fe5201dcfb8ea0501467881745d7868f2c Mon Sep 17 00:00:00 2001 From: Liz Munch Date: Thu, 7 May 2026 10:22:03 -0400 Subject: [PATCH 2/2] Added branch decomposition Co-authored-by: Copilot --- .gitignore | 1 + .../lt_losses_0_2_13_15_10.txt | 6 - .../lt_losses_0_2_17_20_1000.txt | 1 - .../lt_losses_0_2_30_32_1.txt | 9 - .../lt_losses_0_2_x_x+2_1.txt | 49 - .../run_exprimetns_loop_line.ipynb | 346 ---- Notebooks_Unused/ilp_basics.ipynb | 224 --- Notebooks_Unused/ilp_different_solvers.ipynb | 193 -- .../integer_linear_programming.ipynb | 214 -- .../integer_linear_programming_diagram.ipynb | 1108 ---------- Notebooks_Unused/juggling_man.ipynb | 204 -- .../linear_optimization_ILP_forms.ipynb | 435 ---- ...ar_optimization_single_parallelogram.ipynb | 1123 ----------- .../linear_optimization_single_triangle.ipynb | 906 --------- Notebooks_Unused/n_search_fail.ipynb | 119 -- .../run_exprimetns_loop_line.ipynb | 797 -------- Notebooks_Unused/sandbox_decomposition.ipynb | 197 -- Notebooks_Unused/sandbox_fixing_LBMs.ipynb | 242 --- .../sandbox_fixing_optimization.ipynb | 100 - Notebooks_Unused/sandbox_liz.ipynb | 1778 ----------------- Notebooks_Unused/torus_line.ipynb | 410 ---- cereeberus/cereeberus/__init__.py | 2 + cereeberus/cereeberus/reeb/__init__.py | 3 +- cereeberus/cereeberus/reeb/branchdecomp.py | 214 +- cereeberus/cereeberus/reeb/reebgraph.py | 41 + doc_source/modules/reeb/branchdecomp.rst | 40 + doc_source/modules/reeb/index.rst | 1 + .../notebooks/branch_decomp_basics.ipynb | 230 +++ doc_source/notebooks/index.rst | 1 + pyproject.toml | 2 +- tests/test_branchdecomp.py | 238 +++ 31 files changed, 762 insertions(+), 8472 deletions(-) delete mode 100644 Notebooks_Unused/experiments/experiments_with_line_torus/lt_losses_0_2_13_15_10.txt delete mode 100644 Notebooks_Unused/experiments/experiments_with_line_torus/lt_losses_0_2_17_20_1000.txt delete mode 100644 Notebooks_Unused/experiments/experiments_with_line_torus/lt_losses_0_2_30_32_1.txt delete mode 100644 Notebooks_Unused/experiments/experiments_with_line_torus/lt_losses_0_2_x_x+2_1.txt delete mode 100644 Notebooks_Unused/experiments/experiments_with_line_torus/run_exprimetns_loop_line.ipynb delete mode 100644 Notebooks_Unused/ilp_basics.ipynb delete mode 100644 Notebooks_Unused/ilp_different_solvers.ipynb delete mode 100644 Notebooks_Unused/integer_linear_programming.ipynb delete mode 100644 Notebooks_Unused/integer_linear_programming_diagram.ipynb delete mode 100644 Notebooks_Unused/juggling_man.ipynb delete mode 100644 Notebooks_Unused/linear_optimization_ILP_forms.ipynb delete mode 100644 Notebooks_Unused/linear_optimization_single_parallelogram.ipynb delete mode 100644 Notebooks_Unused/linear_optimization_single_triangle.ipynb delete mode 100644 Notebooks_Unused/n_search_fail.ipynb delete mode 100644 Notebooks_Unused/run_exprimetns_loop_line.ipynb delete mode 100644 Notebooks_Unused/sandbox_decomposition.ipynb delete mode 100644 Notebooks_Unused/sandbox_fixing_LBMs.ipynb delete mode 100644 Notebooks_Unused/sandbox_fixing_optimization.ipynb delete mode 100644 Notebooks_Unused/sandbox_liz.ipynb delete mode 100644 Notebooks_Unused/torus_line.ipynb create mode 100644 doc_source/modules/reeb/branchdecomp.rst create mode 100644 doc_source/notebooks/branch_decomp_basics.ipynb create mode 100644 tests/test_branchdecomp.py diff --git a/.gitignore b/.gitignore index 351e7f7..1ab7034 100644 --- a/.gitignore +++ b/.gitignore @@ -138,4 +138,5 @@ dmypy.json # Liz's specific sandbox jupyter notebook that probably shouldn't be on the website. doc_source/notebooks/sandbox_liz.ipynb +Notebooks_Unused/ model.lp diff --git a/Notebooks_Unused/experiments/experiments_with_line_torus/lt_losses_0_2_13_15_10.txt b/Notebooks_Unused/experiments/experiments_with_line_torus/lt_losses_0_2_13_15_10.txt deleted file mode 100644 index a1a1e1b..0000000 --- a/Notebooks_Unused/experiments/experiments_with_line_torus/lt_losses_0_2_13_15_10.txt +++ /dev/null @@ -1,6 +0,0 @@ -losses_1: ([4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 3.0], [3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0]) -losses_2: ([2.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0], [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]) -losses_3: ([2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0], [-0.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0]) -losses_4: ([1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], [-0.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0]) -losses_5: ([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]) -losses_6: ([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]) diff --git a/Notebooks_Unused/experiments/experiments_with_line_torus/lt_losses_0_2_17_20_1000.txt b/Notebooks_Unused/experiments/experiments_with_line_torus/lt_losses_0_2_17_20_1000.txt deleted file mode 100644 index 5fd6428..0000000 --- a/Notebooks_Unused/experiments/experiments_with_line_torus/lt_losses_0_2_17_20_1000.txt +++ /dev/null @@ -1 +0,0 @@ -losses_1_1000: ([3.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0], [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]) diff --git a/Notebooks_Unused/experiments/experiments_with_line_torus/lt_losses_0_2_30_32_1.txt b/Notebooks_Unused/experiments/experiments_with_line_torus/lt_losses_0_2_30_32_1.txt deleted file mode 100644 index 089aba9..0000000 --- a/Notebooks_Unused/experiments/experiments_with_line_torus/lt_losses_0_2_30_32_1.txt +++ /dev/null @@ -1,9 +0,0 @@ -losses_1: ([13.0], [12.0]) -losses_2: ([12.0], [10.0]) -losses_3: ([11.0], [8.0]) -losses_4: ([9.0], [6.0]) -losses_5: ([9.0], [4.0]) -losses_6: ([7.0], [2.0]) -losses_7: ([6.0], [-0.0]) -losses_8: ([5.0], [-0.0]) -losses_9: ([5.0], [-0.0]) diff --git a/Notebooks_Unused/experiments/experiments_with_line_torus/lt_losses_0_2_x_x+2_1.txt b/Notebooks_Unused/experiments/experiments_with_line_torus/lt_losses_0_2_x_x+2_1.txt deleted file mode 100644 index d1e8ca7..0000000 --- a/Notebooks_Unused/experiments/experiments_with_line_torus/lt_losses_0_2_x_x+2_1.txt +++ /dev/null @@ -1,49 +0,0 @@ -losses_1: ([13.0], [12.0]) -losses_2: ([12.0], [10.0]) -losses_3: ([11.0], [8.0]) -losses_4: ([0.0], [0.0]) -losses_5: ([0.0], [0.0]) -losses_6: ([1.0], [-0.0]) -losses_7: ([1.0], [-0.0]) -losses_8: ([2.0], [1.0]) -losses_9: ([2.0], [1.0]) -losses_10: ([3.0], [2.0]) -losses_11: ([3.0], [2.0]) -losses_12: ([3.0], [3.0]) -losses_13: ([4.0], [3.0]) -losses_14: ([5.0], [4.0]) -losses_15: ([5.0], [4.0]) -losses_16: ([6.0], [5.0]) -losses_17: ([6.0], [5.0]) -losses_18: ([6.0], [6.0]) -losses_19: ([7.0], [6.0]) -losses_20: ([7.0], [7.0]) -losses_21: ([8.0], [7.0]) -losses_22: ([9.0], [8.0]) -losses_23: ([9.0], [8.0]) -losses_24: ([10.0], [9.0]) -losses_25: ([10.0], [9.0]) -losses_26: ([11.0], [10.0]) -losses_27: ([11.0], [10.0]) -losses_28: ([11.0], [11.0]) -losses_29: ([12.0], [11.0]) -losses_30: ([13.0], [12.0]) -losses_31: ([13.0], [12.0]) -losses_32: ([13.0], [13.0]) -losses_33: ([14.0], [13.0]) -losses_34: ([15.0], [14.0]) -losses_35: ([15.0], [14.0]) -losses_36: ([15.0], [15.0]) -losses_37: ([16.0], [15.0]) -losses_38: ([17.0], [16.0]) -losses_39: ([17.0], [16.0]) -losses_40: ([17.0], [17.0]) -losses_41: ([18.0], [17.0]) -losses_42: ([19.0], [18.0]) -losses_43: ([19.0], [18.0]) -losses_44: ([20.0], [19.0]) -losses_45: ([20.0], [19.0]) -losses_46: ([20.0], [20.0]) -losses_47: ([20.0], [20.0]) -losses_48: ([21.0], [21.0]) -losses_49: ([22.0], [21.0]) diff --git a/Notebooks_Unused/experiments/experiments_with_line_torus/run_exprimetns_loop_line.ipynb b/Notebooks_Unused/experiments/experiments_with_line_torus/run_exprimetns_loop_line.ipynb deleted file mode 100644 index 521795e..0000000 --- a/Notebooks_Unused/experiments/experiments_with_line_torus/run_exprimetns_loop_line.ipynb +++ /dev/null @@ -1,346 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "%reload_ext autoreload\n", - "%autoreload 2" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## This notebook aims to find the the optimized loss function for a line mapper and a loop mapper over multiple iterations. Also the loop size of the mappers are varied to test out the optimization." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Create a loop mapper. Uses the `torus` function from ex_mapergraph.py file.\n", - "Arguments:\n", - "- `a` - int - the height of the bottom most vertex at the very bottom\n", - "- `b` - int - the height where the loop starts\n", - "- `c` - int - the height where the loop ends\n", - "- `d` - int - the height of the top most vertex at the very top\n", - "- `delta` - not needed\n", - "- `seed` - int - the seed for the random number generator\n", - "\n", - "### Create a line mapper. Uses the `line` function from ex_mapergraph.py file.\n", - "Arguments:\n", - "- `a` - int - the height of the bottom most vertex at the very bottom\n", - "- `b` - int - the height of the top most vertex at the very top" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "from cereeberus import Interleave, MapperGraph\n", - "import matplotlib.pyplot as plt\n", - "import math\n", - "from cereeberus.data import ex_mappergraphs" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "torus = ex_mappergraphs.torus(0, 2, 10, 13)\n", - "line = ex_mappergraphs.line(0, 16)\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "myInt = Interleave(torus, line)\n", - "myInt.fit()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## run the iterations for n = 1, 2, 3, 4, 5, 6, 7..." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "a = 0\n", - "b = 2\n", - "c = 13 # loop size is 11\n", - "d = 15\n", - "\n", - "losses_dict = {}\n", - "\n", - "for i in range(1, 7):\n", - " losses_dict[f\"losses_{i}\"] = solver_iter.run_optimization_torus_line(a, b, c, d, i, 10)\n", - "\n", - "# Save to a text file\n", - "with open(\"lt_losses_0_2_13_15_10.txt\", \"w\") as file:\n", - " for key, value in losses_dict.items():\n", - " file.write(f\"{key}: {value}\\n\")\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "\n", - "for i in range(1, 7):\n", - " solver_iter.plot_losses_and_upper_bounds(losses_dict[f\"losses_{i}\"], i)\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Run 1000 iterations for one n value to evaluate the stability of the loss function.\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "a = 0\n", - "b = 2\n", - "c = 17 # loop size is 15\n", - "d = 20\n", - "\n", - "n = 3 # thickening\n", - "\n", - "loss_1_1000 = solver_iter.run_optimization_torus_line(a, b, c, d, n, 10)\n", - "\n", - "# save to a text file\n", - "with open(\"lt_losses_0_2_17_20_1000.txt\", \"w\") as file:\n", - " file.write(f\"losses_1_1000: {loss_1_1000}\\n\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "solver_iter.plot_losses_and_upper_bounds(loss_1_1000, 3)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Relationship between the thickening parameter and the optimized loss function/upper bound" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "a = 0\n", - "b = 2\n", - "c = 30 # loop size is 28\n", - "d = 32\n", - "\n", - "for i in range(1, 10):\n", - " losses_dict[f\"losses_{i}\"] = solver_iter.run_optimization_torus_line(a, b, c, d, i, 1)\n", - "\n", - "# Save to a text file\n", - "with open(\"lt_losses_0_2_30_32_1.txt\", \"w\") as file:\n", - " for key, value in losses_dict.items():\n", - " file.write(f\"{key}: {value}\\n\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "# Plot the results\n", - "\n", - "\n", - "plt.figure(figsize=(20, 5))\n", - "plt.subplot(121)\n", - "\n", - "plt.plot(range(1, 10), [losses_dict[f\"losses_{i}\"][0][0] for i in range(1, 10)], label=\"loss before optimization\")\n", - "plt.plot(range(1, 10), [losses_dict[f\"losses_{i}\"][0][0]+i for i in range(1, 10)], label=\"upper bound before optimization\")\n", - "plt.xlabel(\"thickening parameter n\")\n", - "plt.ylabel(\"value\")\n", - "plt.legend()\n", - "plt.title(\"Losses and upper bounds for different thickening parameters before optimization\")\n", - "plt.subplot(122)\n", - "plt.plot(range(1, 10), [losses_dict[f\"losses_{i}\"][1][0] for i in range(1, 10)], label=\"loss\")\n", - "plt.plot(range(1, 10), [losses_dict[f\"losses_{i}\"][1][0]+i for i in range(1, 10)], label=\"upper bound\")\n", - "plt.xlabel(\"thickening parameter n\")\n", - "plt.ylabel(\"value\")\n", - "plt.legend()\n", - "plt.title(\"Losses and upper bounds for different thickening parameters after optimization\")\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# How does the loss change with change of loop size?" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "a = 0\n", - "b = 2\n", - "\n", - "n =1\n", - "for i in range(4, 50):\n", - " c = i\n", - " d = i+2\n", - " losses_dict[f\"losses_{i}\"] = solver_iter.run_optimization_torus_line(a, b, c, d, n, 1)\n", - "\n", - "# Save to a text file\n", - "with open(\"lt_losses_0_2_x_x+2_1.txt\", \"w\") as file:\n", - " for key, value in losses_dict.items():\n", - " file.write(f\"{key}: {value}\\n\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "# Plot the results\n", - "\n", - "def compute_loss_dict_diff_loopsize(largest_loop, n):\n", - " a = 0\n", - " b = 2\n", - " c = range(4, largest_loop)\n", - " losses_dict = {}\n", - "\n", - " for i in c:\n", - " losses_dict[f\"losses_{i}\"] = solver_iter.run_optimization_torus_line(a, b, i, i+2, n, 1)\n", - "\n", - " return losses_dict\n", - "\n", - "def plot_fig_diff_loopsize(largest_loop, n):\n", - "\n", - " losses_dict = compute_loss_dict_diff_loopsize(largest_loop, n)\n", - "\n", - "\n", - " plt.figure(figsize=(20, 5))\n", - " plt.subplot(121)\n", - " plt.step(range(2, largest_loop-2), [losses_dict[f\"losses_{i}\"][0][0] for i in range(4, largest_loop)], label=\"loss before optimization\")\n", - " plt.step(range(2, largest_loop-2), [losses_dict[f\"losses_{i}\"][0][0]+n for i in range(4, largest_loop)], label=\"upper bound before optimization\")\n", - " plt.xticks(range(2, largest_loop-2))\n", - " plt.yticks(range(int(min([losses_dict[f\"losses_{i}\"][0][0] for i in range(4, largest_loop)])), \n", - " int(max([losses_dict[f\"losses_{i}\"][0][0]+i for i in range(4, largest_loop)])) + 1))\n", - " plt.step(range(2, largest_loop-2), [math.ceil(i/4) for i in range(2, largest_loop-2)], label=\"true interleaving\")\n", - " plt.xlabel(\"loop size\")\n", - " plt.ylabel(\"value\")\n", - " plt.legend()\n", - " plt.title(\"Losses and upper bounds for different loop sizes before optimization\")\n", - " plt.subplot(122)\n", - " plt.step(range(2, largest_loop-2), [losses_dict[f\"losses_{i}\"][1][0] for i in range(4, largest_loop)], label=\"loss\")\n", - " plt.step(range(2, largest_loop-2), [losses_dict[f\"losses_{i}\"][1][0]+n for i in range(4, largest_loop)], label=\"upper bound\")\n", - " plt.xticks(range(2, largest_loop-2))\n", - " plt.yticks(range(int(min([losses_dict[f\"losses_{i}\"][1][0] for i in range(4, largest_loop)])), \n", - " int(max([losses_dict[f\"losses_{i}\"][1][0]+i for i in range(4, largest_loop)])) + 1))\n", - " plt.step(range(2, largest_loop-2), [math.ceil(i/4) for i in range(2,largest_loop-2)], label=\"true interleaving\")\n", - " plt.xlabel(\"loop size\")\n", - " plt.ylabel(\"value\")\n", - " plt.legend()\n", - " plt.title(\"Losses and upper bounds for different loop sizes after optimization\")\n", - " plt.show()\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "plot_fig_diff_loopsize(20, 1)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "plot_fig_diff_loopsize(20,2)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "plot_fig_diff_loopsize(20,3)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### It scales (almost) linearly with the loop size.\n", - "\n", - "## Questions:\n", - "- What is the relationship between the loss function and n value?\n", - "- why does the upper bound go down compared to the true interleaving in certeain situations? (something to do with the ceiling funciton)\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "interleavingenv", - "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": "3.12.3" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/Notebooks_Unused/ilp_basics.ipynb b/Notebooks_Unused/ilp_basics.ipynb deleted file mode 100644 index de0a55b..0000000 --- a/Notebooks_Unused/ilp_basics.ipynb +++ /dev/null @@ -1,224 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 15, - "metadata": {}, - "outputs": [], - "source": [ - "%reload_ext autoreload\n", - "%autoreload 2" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": {}, - "outputs": [], - "source": [ - "from cereeberus import ReebGraph, MapperGraph, Interleave\n", - "import cereeberus.data.ex_mappergraphs as ex_mg\n", - "\n", - "import matplotlib.pyplot as plt\n", - "import numpy as np\n", - "\n", - "import pulp #for ILP optimization" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": {}, - "outputs": [], - "source": [ - "# import the ilp file. Note it is in the same folder as this notebook, we will move it to the correct location later\n", - "\n", - "import cereeberus.distance.ilp as ilp" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Load example MapperGraphs\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Text(0.5, 1.0, 'G')" - ] - }, - "execution_count": 18, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# F = ex_mg.interleave_example_A()\n", - "# G = ex_mg.interleave_example_B()\n", - "F = ex_mg.torus(0, 2, 10, 20, delta = 1, seed = 190)\n", - "G = ex_mg.line(0, 20)\n", - "plt.figure()\n", - "plt.subplot(121)\n", - "F.draw()\n", - "plt.title('F')\n", - "plt.subplot(122)\n", - "G.draw()\n", - "plt.title('G')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Create the interleaving. Change the value of n for different optimizations\n", - "```python" - ] - }, - { - "cell_type": "code", - "execution_count": 32, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "loss before optimization: 1.0\n" - ] - } - ], - "source": [ - "myInt = Interleave(F, G, n = 2, initialize_random_maps=True, seed = 5)\n", - "\n", - "# loss before optimization\n", - "print('loss before optimization: ', myInt.loss())" - ] - }, - { - "cell_type": "code", - "execution_count": 33, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The optimized loss is: -0.0\n", - "Status: Optimal\n" - ] - }, - { - "data": { - "image/png": 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TkVyyqKhIffv21eWXX66nnnpKy5Yt08MPP6zjx4/rkUceOaP8R5I+/fRTLVmyRGlpaZL+zNmuvfZa/f3vf9crr7yiu+++W7///rueeuopjRw5Uh9//HG5ff3zn//UqFGjfI7NmTNH2dnZ3lzOn+/poosu0iOPPKKJEydq9OjR+stf/iJJuuKKK8p8XcMwdN111+mTTz7R7bffroSEBGVnZ2vChAn65Zdf9Pzzz/u0X7Nmjd59913dfffdCg8P14svvqgbbrhBO3fu9P4OApXGAGBpM2fONCQZK1asMPbv32/k5+cb8+bNMxo0aGCEhYUZP//8s/H7778bkoynn376lH317NnT6Nmz5ynbbN682ZBkvPTSSz7H7777bqN+/frGoUOHDMMwjE8//dSQZLz55ps+7ZYtW1bqeNOmTQ1JxrJly0q9Xr169YzU1NRSx2+//XYjJibG+PXXX32ODxkyxHA4HN44DMMwMjIyjFq1ahmrV682FixYYEgypk6desr3aRj/99l26tTJOHr0qPf4U089ZUgyFi9ebBiGYfzxxx/Gueeea9xxxx0+1+/Zs8dwOBw+x0/0uW7dOu+xo0ePGlFRUUaHDh2Mw4cPe48vXbrUkGRMnDjReyw1NdWQZDzwwAM+r1WRz7ssCQkJRlRUlPHbb795j33zzTdGrVq1jNtuu8177OGHHzYkGdddd53P9Xfffbchyfjmm2+8x8r77k58Bnl5ed5jJ34GPv/8c++x7OxsQ5IRFhZm7Nixw3v81VdfNSQZn3zySam4yrN161bD4XAYV199tXH8+HHDMAzj+PHjhsfj8Wn3+++/G40aNTJGjhzpPbZ//35DkvHwww+X6vfk183NzTUkGaNGjfJpd//99xuSjI8//rjUe169erX32L59+wy73W7cd9995b4XAAAMgxwwmDngkSNHjKKiIp9jeXl5ht1uNx555BGf45KMtLQ0n2NpaWll5iWB+mxOdia55NixY73HiouLjX79+hl169Y19u/fbxhGxfKfE5+D3W73ye9O5GzR0dGG2+32Hs/IyCiVC6amphpNmzYt9z1+9tlnRp06dXxyNH+/p3Xr1hmSjJkzZ5bq9+TXXbRokSHJePTRR33a3XjjjYbNZjO2bdvm857r1q3rc+ybb74p8/cEqAxMoQWqiN69e6thw4aKi4vTkCFDVL9+fS1cuFAXXHCBwsLCVLduXa1cudLv6ZTlad26tRISEjR//nzvsaKiIr399tvq37+/d12OBQsWyOFw6Oqrr9avv/7q3Tp16qT69ev7TFOUpObNmys5OdmvGAzD0DvvvKP+/fvLMAyf/pOTk+VyubRhwwZv+0mTJql9+/ZKTU3V3XffrZ49e2rcuHF+v+fRo0f73A296667FBISovfff1+StHz5ch08eFBDhw71iaV27drq0qVLqfd6spycHO3bt0933323z2LA/fr1U9u2bfXee++Vuuauu+7y2a/o513S7t27lZubq+HDhysyMtJ7vGPHjrr66qu977OkE3dWTxg7dqwkldnWX+3atVPXrl29+126dJH051SgJk2alDr+448/+tVvYWGhBg0apPPOO09vvfWW94577dq1vWv+FBcX68CBAzp+/LguvfRSn5+fijjx/tPT032O33fffZJU6rts166d906wJDVs2FBt2rTx+70BAEAOGPgc0G63e0f5FxUV6bffflP9+vXVpk2bM84RpOB9NmeSS44ZM8b7/0+MZjx69KhWrFhxxu/vqquu8hnVeSJnu+GGGxQeHl7quL/5zp49e3TjjTcqISFBr7zyivd4ML6n999/X7Vr1y71c3LffffJMAx98MEHPsd79+7tM8ukY8eOioiIIJeDKZhCC1QRmZmZat26tUJCQtSoUSO1adPG+w+a3W7Xk08+qfvuu0+NGjXS5ZdfrmuvvVa33XabzxQIf91888168MEH9csvv+iCCy7QypUrtW/fPt18883eNlu3bpXL5fIOcT/ZiYc5nNC8eXO/X3///v06ePCgpk+frunTp5+2/7p16+q1115T586dFRoaqpkzZ1bo6acXXnihz379+vUVExPjXbtj69atkv5vzZmTRUREnLL/HTt2SFKZ0yLatm2rNWvW+BwLCQlR48aNfY5V9PP29/UvuugiZWdnl3pQxsmfScuWLVWrVq1S65lURMkinSQ5HA5JUlxcXJnH/f0PkTvuuEPbt2/X559/Xmoqw+zZs/Xss8/qhx9+0LFjx7zHK/LzWNKOHTtUq1YttWrVyud4dHS0zj33XO9nfcLJ71mSzjvvvLP+jywAQM1BDlh+/2eaAxYXF+uFF17QK6+8ory8PJ/18s5mWmSwPpuK5pK1atVSixYtfI61bt1akiyXyx0/flyDBw9WUVGR3n33XZ+nxQbje9qxY4diY2N9Co7SnznxifMlkcvBSijgAVXEZZdd5n0CWVnGjx+v/v37a9GiRcrOztZDDz0kp9Opjz/+WImJiRV6rZtvvlkZGRlasGCBxo8fr3//+99yOBzq27evt01xcbGioqL05ptvltnHiYVxT6jIE7WKi4slSbfccov3oRAnO3mNjuzsbEnSkSNHtHXr1jMu0JwqnjfeeKPMZDjQT+kqebexZAwV+bwDrSIF0fKUtxZNeceNkxYSLssLL7ygt956S3PmzFFCQoLPuTlz5mj48OEaOHCgJkyYoKioKNWuXVtOp9O7ftCZ8vfzOJv3BgCARA54skDkgI8//rgeeughjRw5UlOmTFFkZKRq1aql8ePHe2M4E8H8bKwgGLnchAkT9MUXX2jFihWlbmAH63uqCHI5WAkFPKAaadmype677z7dd9992rp1qxISEvTss89qzpw5FeqnefPmuuyyyzR//nyNGTNG7777rgYOHOhzR6xly5ZasWKFunXrdlbJR1mFkIYNGyo8PFxFRUWlHlRQlm+//VaPPPKIRowYodzcXI0aNUobN2703v07na1bt/o8da2goEC7d+/WNddcI+n/FlWOioryK56TNW3aVNKfCxWfPIpv8+bN3vOncjafd8nXP9kPP/yg888/32f0naRSCfC2bdtUXFzsM20iEEW9s/Hpp5/q/vvv1/jx471P6i3p7bffVosWLfTuu+/6xPrwww/7tKvI+2jatKmKi4u1detW751a6c8Ftw8ePOjXdwkAQKCRA1YsB3z77bfVq1cvzZgxw+f4wYMHdf75559R7FLgPpuTVTSXLC4u1o8//ugddSdJW7ZskSRvLmd2HidJ8+bN09SpUzV16lT17Nmz1Hl/v6eK5nIrVqzQH3/84TMK74cffvCeB6yKNfCAauDQoUM6cuSIz7GWLVsqPDxcHo/njPq8+eabtXbtWr322mv69ddffaZOSPIOdZ8yZUqpa48fP66DBw/69Tr16tUr1bZ27dq64YYb9M4772jTpk2lrtm/f7/3/x87dkzDhw9XbGysXnjhBc2aNUt79+7Vvffe69frS9L06dN9pldmZWXp+PHjSklJkSQlJycrIiJCjz/+uE+7suIpy6WXXqqoqChNmzbN5/v44IMP9P3336tfv36njfFsPu+YmBglJCRo9uzZPu02bdqkDz/80FuoLCkzM9Nn/6WXXpIk72cilf3dVZbdu3dr8ODB6t69u55++uky25y4Y1ryDumXX36pL774wqfdiaf8+vNeTnxWU6dO9Tl+4ul3/nyXAAAECjngmeWAtWvXLjWCasGCBfrll1/8jl0qnTsE6rM52Znkki+//LL3/xuGoZdffll16tTRVVddJali+U8wbNq0SaNGjdItt9yie+65p8w2/n5P5X0fZbnmmmtUVFTk8/lI0vPPPy+bzeaT6wJWwwg8oBrYsmWLrrrqKg0ePFjt2rVTSEiIFi5cqL1792rIkCFn1OfgwYN1//336/7771dkZGSpu6A9e/bUnXfeKafTqdzcXPXp00d16tTR1q1btWDBAr3wwgu68cYbT/s6nTp10ooVK/Tcc88pNjZWzZs3V5cuXfTEE0/ok08+UZcuXXTHHXeoXbt2OnDggDZs2KAVK1bowIEDkqRHH31Uubm5+uijjxQeHq6OHTtq4sSJ+p//+R/deOONZRanTnb06FHv57d582a98sor6t69u6677jpJf65xl5WVpVtvvVWXXHKJhgwZooYNG2rnzp1677331K1bt1JJQEl16tTRk08+qREjRqhnz54aOnSo9u7dqxdeeEHNmjXzK9E828/76aefVkpKirp27arbb79dhw8f1ksvvSSHw6FJkyaVap+Xl6frrrtOffv21RdffKE5c+bor3/9q+Lj471tyvvuKsO4ceO0f/9+/f3vf9e8efN8znXs2FEdO3bUtddeq3fffVeDBg1Sv379lJeXp2nTpqldu3YqKCjwtg8LC1O7du00f/58tW7dWpGRkerQoYM6dOhQ6nXj4+OVmpqq6dOn6+DBg+rZs6e++uorzZ49WwMHDvQZyQkAQLCRA55ZDnjttdd6R+5dccUV2rhxo958881S68adKnbpz3wkOTlZtWvX1pAhQwL22ZysorlkaGioli1bptTUVHXp0kUffPCB3nvvPT344IPeabwVyX+CYcSIEZKkHj16lBopesUVV6hFixZ+f08tW7bUueeeq2nTpik8PFz16tVTly5dypxO3b9/f/Xq1Uv//Oc/9dNPPyk+Pl4ffvihFi9erPHjx/s8sAKwHFOefQvAbzNnzjQkGevWrSu3za+//mqkpaUZbdu2NerVq2c4HA6jS5cuxr///W+fdj179jR69uzp92t369bNkGSMGjWq3DbTp083OnXqZISFhRnh4eHGxRdfbPz97383du3a5W3TtGlTo1+/fmVe/8MPPxg9evQwwsLCDElGamqq99zevXuNtLQ0Iy4uzqhTp44RHR1tXHXVVcb06dMNwzCM9evXGyEhIcbYsWN9+jx+/LjRuXNnIzY21vj999/Ljf3EZ7tq1Spj9OjRxnnnnWfUr1/fGDZsmPH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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Welcome to the CBC MILP Solver \n", - "Version: 2.10.3 \n", - "Build Date: Dec 15 2019 \n", - "\n", - "command line - /Users/ishikaghosh/anaconda3/envs/interleavingenv/lib/python3.13/site-packages/pulp/solverdir/cbc/osx/64/cbc /var/folders/5f/m89pr_zs78n8ffl7t7ndknth0000gn/T/88116d30a2c3417e89a4f2a9ea3fb906-pulp.mps -timeMode elapsed -branch -printingOptions all -solution /var/folders/5f/m89pr_zs78n8ffl7t7ndknth0000gn/T/88116d30a2c3417e89a4f2a9ea3fb906-pulp.sol (default strategy 1)\n", - "At line 2 NAME MODEL\n", - "At line 3 ROWS\n", - "At line 1548 COLUMNS\n", - "At line 4483 RHS\n", - "At line 6027 BOUNDS\n", - "At line 6425 ENDATA\n", - "Problem MODEL has 1543 rows, 397 columns and 2139 elements\n", - "Coin0008I MODEL read with 0 errors\n", - "Option for timeMode changed from cpu to elapsed\n", - "Continuous objective value is 0 - 0.00 seconds\n", - "Cgl0003I 0 fixed, 1 tightened bounds, 0 strengthened rows, 0 substitutions\n", - "Cgl0004I processed model has 24 rows, 8 columns (8 integer (7 of which binary)) and 72 elements\n", - "Cutoff increment increased from 1e-05 to 0.9999\n", - "Cbc0038I Initial state - 0 integers unsatisfied sum - 0\n", - "Cbc0038I Solution found of 0\n", - "Cbc0038I Cleaned solution of 0\n", - "Cbc0038I Before mini branch and bound, 8 integers at bound fixed and 0 continuous\n", - "Cbc0038I Mini branch and bound did not improve solution (0.01 seconds)\n", - "Cbc0038I After 0.01 seconds - Feasibility pump exiting with objective of 0 - took 0.00 seconds\n", - "Cbc0012I Integer solution of -0 found by feasibility pump after 0 iterations and 0 nodes (0.01 seconds)\n", - "Cbc0001I Search completed - best objective -0, took 0 iterations and 0 nodes (0.01 seconds)\n", - "Cbc0035I Maximum depth 0, 0 variables fixed on reduced cost\n", - "Cuts at root node changed objective from 0 to 0\n", - "Probing was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "Gomory was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "Knapsack was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "Clique was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "MixedIntegerRounding2 was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "FlowCover was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "TwoMirCuts was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "ZeroHalf was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "\n", - "Result - Optimal solution found\n", - "\n", - "Objective value: -0.00000000\n", - "Enumerated nodes: 0\n", - "Total iterations: 0\n", - "Time (CPU seconds): 0.01\n", - "Time (Wallclock seconds): 0.01\n", - "\n", - "Option for printingOptions changed from normal to all\n", - "Total time (CPU seconds): 0.01 (Wallclock seconds): 0.02\n", - "\n", - "loss after optimization: -0.0\n" - ] - } - ], - "source": [ - "ilp.solve_ilp(myInt, verbose=True, plot = True)\n", - "loss = ilp.solve_ilp(myInt)[1]\n", - "\n", - "# loss after optimization\n", - "print('loss after optimization: ', loss)" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "interleavingenv", - "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": "3.13.0" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/Notebooks_Unused/ilp_different_solvers.ipynb b/Notebooks_Unused/ilp_different_solvers.ipynb deleted file mode 100644 index 9d7a221..0000000 --- a/Notebooks_Unused/ilp_different_solvers.ipynb +++ /dev/null @@ -1,193 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 16, - "metadata": {}, - "outputs": [], - "source": [ - "%reload_ext autoreload\n", - "%autoreload 2" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": {}, - "outputs": [], - "source": [ - "from cereeberus import ReebGraph, MapperGraph, Interleave\n", - "import cereeberus.data.ex_mappergraphs as ex_mg\n", - "\n", - "import matplotlib.pyplot as plt\n", - "import numpy as np\n", - "import time\n", - "\n", - "import pulp #for ILP optimization\n", - "\n", - "import cereeberus.distance.ilp as ilp # import the ilp file\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Example Mappers" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Text(0.5, 1.0, 'G')" - ] - }, - "execution_count": 18, - "metadata": {}, - "output_type": "execute_result" - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/Users/ishikaghosh/anaconda3/envs/interleavingenv/lib/python3.12/site-packages/IPython/core/events.py:82: UserWarning: Glyph 127 () missing from font(s) DejaVu Sans.\n", - " func(*args, **kwargs)\n", - "/Users/ishikaghosh/anaconda3/envs/interleavingenv/lib/python3.12/site-packages/IPython/core/events.py:82: UserWarning: Glyph 128 (\\x80) missing from font(s) DejaVu Sans.\n", - " func(*args, **kwargs)\n", - "/Users/ishikaghosh/anaconda3/envs/interleavingenv/lib/python3.12/site-packages/IPython/core/events.py:82: UserWarning: Glyph 129 (\\x81) missing from font(s) DejaVu Sans.\n", - " func(*args, **kwargs)\n", - "/Users/ishikaghosh/anaconda3/envs/interleavingenv/lib/python3.12/site-packages/IPython/core/events.py:82: UserWarning: Glyph 130 (\\x82) missing from font(s) DejaVu Sans.\n", - " func(*args, **kwargs)\n", - "/Users/ishikaghosh/anaconda3/envs/interleavingenv/lib/python3.12/site-packages/IPython/core/events.py:82: UserWarning: Glyph 131 (\\x83) missing from font(s) DejaVu Sans.\n", - " func(*args, **kwargs)\n", - "/Users/ishikaghosh/anaconda3/envs/interleavingenv/lib/python3.12/site-packages/IPython/core/pylabtools.py:170: UserWarning: Glyph 127 () missing from font(s) DejaVu Sans.\n", - " fig.canvas.print_figure(bytes_io, **kw)\n", - "/Users/ishikaghosh/anaconda3/envs/interleavingenv/lib/python3.12/site-packages/IPython/core/pylabtools.py:170: UserWarning: Glyph 128 (\\x80) missing from font(s) DejaVu Sans.\n", - " fig.canvas.print_figure(bytes_io, **kw)\n", - "/Users/ishikaghosh/anaconda3/envs/interleavingenv/lib/python3.12/site-packages/IPython/core/pylabtools.py:170: UserWarning: Glyph 129 (\\x81) missing from font(s) DejaVu Sans.\n", - " fig.canvas.print_figure(bytes_io, **kw)\n", - "/Users/ishikaghosh/anaconda3/envs/interleavingenv/lib/python3.12/site-packages/IPython/core/pylabtools.py:170: UserWarning: Glyph 130 (\\x82) missing from font(s) DejaVu Sans.\n", - " fig.canvas.print_figure(bytes_io, **kw)\n", - "/Users/ishikaghosh/anaconda3/envs/interleavingenv/lib/python3.12/site-packages/IPython/core/pylabtools.py:170: UserWarning: Glyph 131 (\\x83) missing from font(s) DejaVu Sans.\n", - " fig.canvas.print_figure(bytes_io, **kw)\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "F = ex_mg.torus(0, 1, 16, 20, delta = 1, seed = 30)\n", - "G = ex_mg.line(0, 20)\n", - "plt.figure()\n", - "plt.subplot(121)\n", - "F.draw()\n", - "plt.title('F')\n", - "plt.subplot(122)\n", - "G.draw()\n", - "plt.title('G')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Create interleaving" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "loss before optimization: 4.0\n" - ] - } - ], - "source": [ - "myInt = Interleave(F, G, n = 3, initialize_random_maps=True, seed = 5)\n", - "\n", - "# loss before optimization\n", - "print('loss before optimization: ', myInt.loss())" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Run optimization for differnet solvers \n", - "## Note the result and the time " - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": {}, - "outputs": [], - "source": [ - "solvers = ['CBC', 'GUROBI', 'GLPK']\n", - "\n", - "results = {}\n", - "for i in range(3):\n", - " start = time.time()\n", - " # optimize the interleave\n", - " ilp_result = ilp.solve_ilp(myInt, solver = solvers[i])\n", - " end = time.time()\n", - " results[solvers[i]] = {'loss': ilp_result[1], 'time': end-start, 'status': ilp_result[2]}" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{'CBC': {'loss': 1.0, 'time': 0.11699414253234863, 'status': 'Optimal'}, 'GUROBI': {'loss': 1.0, 'time': 0.08032798767089844, 'status': 'Optimal'}, 'GLPK': {'loss': 1, 'time': 0.06806826591491699, 'status': 'Optimal'}}\n" - ] - } - ], - "source": [ - "print(results)" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "interleavingenv", - "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": "3.12.3" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/Notebooks_Unused/integer_linear_programming.ipynb b/Notebooks_Unused/integer_linear_programming.ipynb deleted file mode 100644 index 148e4c6..0000000 --- a/Notebooks_Unused/integer_linear_programming.ipynb +++ /dev/null @@ -1,214 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 75, - "metadata": {}, - "outputs": [], - "source": [ - "%reload_ext autoreload\n", - "%autoreload 2" - ] - }, - { - "cell_type": "code", - "execution_count": 76, - "metadata": {}, - "outputs": [], - "source": [ - "from cereeberus import ReebGraph, MapperGraph, Interleave\n", - "import cereeberus.data.ex_mappergraphs as ex_mg\n", - "\n", - "import matplotlib.pyplot as plt\n", - "import numpy as np\n", - "\n", - "import pulp #for ILP optimization" - ] - }, - { - "cell_type": "code", - "execution_count": 77, - "metadata": {}, - "outputs": [], - "source": [ - "# import the ilp file. Note it is in the same folder as this notebook, we will move it to the correct location later\n", - "\n", - "import cereeberus.distance.ilp as ilp" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Load example MapperGraphs\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": 78, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Text(0.5, 1.0, 'G')" - ] - }, - "execution_count": 78, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "F = ex_mg.interleave_example_A()\n", - "G = ex_mg.interleave_example_B()\n", - "# F = ex_mg.torus(0, 2, 10, 20, delta = 1, seed = 190)\n", - "# G = ex_mg.line(0, 20)\n", - "plt.figure()\n", - "plt.subplot(121)\n", - "F.draw()\n", - "plt.title('F')\n", - "plt.subplot(122)\n", - "G.draw()\n", - "plt.title('G')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Create the interleaving" - ] - }, - { - "cell_type": "code", - "execution_count": 79, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "loss before optimization: 4.0\n" - ] - } - ], - "source": [ - "myInt = Interleave(F, G, n = 2, initialize_random_maps=True, seed = 17)\n", - "\n", - "# loss before optimization\n", - "print('loss before optimization: ', myInt.loss())" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### This is a map before the optimization" - ] - }, - { - "cell_type": "code", - "execution_count": 80, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "myInt.phi('0','V').draw()" - ] - }, - { - "cell_type": "code", - "execution_count": 81, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Initial loss is: None\n", - "The optimized loss is: 6.0\n", - "Status: Optimal\n", - "loss after optimization: 6.0\n" - ] - } - ], - "source": [ - "optimized_maps = ilp.solve_ilp(myInt, verbose=True)[0]\n", - "loss = ilp.solve_ilp(myInt)[1]\n", - "\n", - "# loss after optimization\n", - "print('loss after optimization: ', loss)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### This is the same map after the optimization" - ] - }, - { - "cell_type": "code", - "execution_count": 82, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "ilp.solve_ilp(myInt)[0]['Phi_V'].draw()" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "interleavingenv", - "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": "3.12.3" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/Notebooks_Unused/integer_linear_programming_diagram.ipynb b/Notebooks_Unused/integer_linear_programming_diagram.ipynb deleted file mode 100644 index a7483d3..0000000 --- a/Notebooks_Unused/integer_linear_programming_diagram.ipynb +++ /dev/null @@ -1,1108 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 112, - "metadata": {}, - "outputs": [], - "source": [ - "from cereeberus import ReebGraph, MapperGraph, Interleave\n", - "import cereeberus.data.ex_mappergraphs as ex_mg\n", - "\n", - "import matplotlib.pyplot as plt\n", - "import numpy as np\n", - "\n", - "import pulp #for ILP optimization" - ] - }, - { - "cell_type": "code", - "execution_count": 113, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Text(0.5, 1.0, 'M2')" - ] - }, - "execution_count": 113, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Load example MapperGraphs\n", - "\n", - "M1 = ex_mg.interleave_example_A()\n", - "M2 = ex_mg.interleave_example_B()\n", - "# M1 = ex_mg.torus(0, 2, 10, 12, delta = 1, seed = 17)\n", - "# M2 = ex_mg.line(0, 12)\n", - "plt.figure()\n", - "plt.subplot(121)\n", - "M1.draw()\n", - "plt.title('M1')\n", - "plt.subplot(122)\n", - "M2.draw()\n", - "plt.title('M2')" - ] - }, - { - "cell_type": "code", - "execution_count": 114, - "metadata": {}, - "outputs": [], - "source": [ - "# create the interleaving\n", - "myInt = Interleave(M1, M2, n = 2, initialize_random_maps=True, seed=10)" - ] - }, - { - "cell_type": "code", - "execution_count": 115, - "metadata": {}, - "outputs": [], - "source": [ - "# set M1 as F and M2 as G for ease of notation\n", - "F = M1\n", - "G = M2" - ] - }, - { - "cell_type": "code", - "execution_count": 116, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}\n" - ] - } - ], - "source": [ - "# get all the function values \n", - "\n", - "all_func_values = set(F.get_function_values()) | set(G.get_function_values())\n", - "print(all_func_values)" - ] - }, - { - "cell_type": "code", - "execution_count": 117, - "metadata": {}, - "outputs": [], - "source": [ - "# get all the relevant matrices\n", - "\n", - "# distance matrices\n", - "D_GnV = myInt.D('G','n','V')\n", - "\n", - "# initial phi and psi maps\n", - "Phi_0V = myInt.phi('0','V')\n", - "Phi_0E = myInt.phi('0','E')\n", - "\n", - "# boundary matrices\n", - "B_F0_up = myInt.B_up('F', '0')\n", - "B_Gn_up = myInt.B_up('G', 'n')\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# ILPs: Right now we have individual ILPs for each diagrams. Need to figure out how to combine them into one ILP." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## A function to provide the necessary matrices upon request" - ] - }, - { - "cell_type": "code", - "execution_count": 118, - "metadata": {}, - "outputs": [], - "source": [ - "def set_block_matrices(iter, starting_map = 'F', diagram_type = 'parallelogram', obj_type=\"vert\", up_or_down=\"down\", send_all=False):\n", - " \"\"\"\n", - " This function sets the block matrices required for the individual block optimization problems\n", - "\n", - " Parameters\n", - " iter: int\n", - " The function value for which the block matrices are to be set\n", - " \n", - " starting_map: str\n", - " The starting map for the block matrices\n", - " Options are:\n", - " - 'F'\n", - " - 'G'\n", - "\n", - " diagram_type: str\n", - " The type of diagram for which the block matrices are needed. \n", - " Options are:\n", - " - 'edge_vert_parallelogram': Liz's list 1, 2\n", - " - 'parallelogram': Liz's list 3, 4, 5, 6\n", - " - 'triangle': Liz's list 7, 8, 9, 10\n", - " \n", - " obj_type: str\n", - " Wthether the diagram involves an edge or a vertex. Default is 'vert'\n", - " Options are:\n", - " - 'edge'\n", - " - 'vert'\n", - " \n", - " \n", - " up_or_down: str\n", - " The direction of the boundary matrix. This changes some of the indexing. Default is 'down'\n", - " Options are:\n", - " - 'up'\n", - " - 'down'\n", - " \n", - " send_all: bool\n", - " Whether to return all matrices or just the ones needed for a diagram. Default is False\n", - " Options are:\n", - " - True\n", - " - False\n", - " \n", - " Returns\n", - " matrix_dict: dict\n", - " A dictionary containing the block matrices\n", - " \"\"\"\n", - "\n", - " # Distance matrices\n", - " D = {\n", - " # vert\n", - " 'D_F0V': myInt.D('F', '0', 'V'),\n", - " 'D_FnV': myInt.D('F', 'n', 'V'),\n", - " 'D_F2nV': myInt.D('F', '2n', 'V'),\n", - " 'D_G0V': myInt.D('G', '0', 'V'),\n", - " 'D_GnV': myInt.D('G', 'n', 'V'),\n", - " 'D_G2nV': myInt.D('G', '2n', 'V'),\n", - "\n", - " # edge\n", - " 'D_F0E': myInt.D('F', '0', 'E'),\n", - " 'D_FnE': myInt.D('F', 'n', 'E'),\n", - " 'D_F2nE': myInt.D('F', '2n', 'E'),\n", - " 'D_G0E': myInt.D('G', '0', 'E'),\n", - " 'D_GnE': myInt.D('G', 'n', 'E'),\n", - " 'D_G2nE': myInt.D('G', '2n', 'E')}\n", - "\n", - " # Inclusion matrices\n", - " I = {\n", - " # vert\n", - " 'I_F0V': myInt.I('F','0','V'),\n", - " 'I_FnV': myInt.I('F','n','V'),\n", - " 'I_G0V': myInt.I('G','0','V'),\n", - " 'I_GnV': myInt.I('G','n','V'),\n", - "\n", - " # edge\n", - " 'I_F0E': myInt.I('F','0','E'),\n", - " 'I_FnE': myInt.I('F','n','E'),\n", - " 'I_G0E': myInt.I('G','0','E'),\n", - " 'I_GnE': myInt.I('G','n','E')}\n", - " \n", - "\n", - " # Boundary matrices\n", - " #up\n", - " B_up = {\n", - " 'B_F0_up': myInt.B_up('F', '0'),\n", - " 'B_Fn_up': myInt.B_up('F', 'n'),\n", - " 'B_F2n_up': myInt.B_up('F', '2n'),\n", - " 'B_G0_up': myInt.B_up('G', '0'),\n", - " 'B_Gn_up': myInt.B_up('G', 'n'),\n", - " 'B_G2n_up': myInt.B_up('G', '2n')\n", - " }\n", - "\n", - " #down\n", - " B_down = {\n", - " 'B_F0_down': myInt.B_down('F', '0'),\n", - " 'B_Fn_down': myInt.B_down('F', 'n'),\n", - " 'B_F2n_down': myInt.B_down('F', '2n'),\n", - " 'B_G0_down': myInt.B_down('G', '0'),\n", - " 'B_Gn_down': myInt.B_down('G', 'n'),\n", - " 'B_G2n_down': myInt.B_down('G', '2n')\n", - " }\n", - "\n", - " # Initial maps\n", - " # phi\n", - " Phi = {\n", - " 'Phi_0V': myInt.phi('0','V'),\n", - " 'Phi_nV': myInt.phi('n','V'),\n", - " 'Phi_0E': myInt.phi('0','E'),\n", - " 'Phi_nE': myInt.phi('n','E')\n", - " }\n", - " # psi\n", - " Psi = {\n", - " 'Psi_0V': myInt.psi('0','V'),\n", - " 'Psi_nV': myInt.psi('n','V'),\n", - " 'Psi_0E': myInt.psi('0','E'),\n", - " 'Psi_nE': myInt.psi('n','E')\n", - " }\n", - "\n", - " if send_all:\n", - " return D, I, B_up, B_down, Phi, Psi\n", - " else:\n", - " # Decide which diagram and return the appropriate matrices\n", - "\n", - " if diagram_type == 'edge_vert_parallelogram':\n", - " # edge_vert_parallelogram ==> 1,2\n", - " if starting_map == 'F':\n", - " if up_or_down == 'up':\n", - " matrix_dict = {'d':D['D_GnV'][iter+1].get_array(), \n", - " 'map_V':Phi['Phi_0V'][iter+1].get_array(), \n", - " 'map_E':Phi['Phi_0E'][iter].get_array(), \n", - " 'b_0': B_up['B_F0_up'][iter].get_array(), \n", - " 'b_n': B_up['B_Gn_up'][iter].get_array()}\n", - " return matrix_dict\n", - " if up_or_down == 'down':\n", - " matrix_dict = {'d':D['D_GnV'][iter].get_array(),\n", - " 'map_V':Phi['Phi_0V'][iter].get_array(),\n", - " 'map_E':Phi['Phi_0E'][iter].get_array(),\n", - " 'b_0': B_down['B_F0_down'][iter].get_array(),\n", - " 'b_n': B_down['B_Gn_down'][iter].get_array()}\n", - " return matrix_dict\n", - " else:\n", - " raise ValueError('Invalid value for up_or_down')\n", - " if starting_map == 'G':\n", - " if up_or_down == 'up':\n", - " matrix_dict = {'d':D['D_FnV'][iter+1].get_array(),\n", - " 'map_V':Psi['Psi_0V'][iter+1].get_array(),\n", - " 'map_E':Psi['Psi_0E'][iter].get_array(),\n", - " 'b_0': B_up['B_G0_up'][iter].get_array(),\n", - " 'b_n': B_up['B_Fn_up'][iter].get_array()}\n", - " return matrix_dict\n", - " if up_or_down == 'down':\n", - " matrix_dict = {'d':D['D_FnV'][iter].get_array(),\n", - " 'map_V':Psi['Psi_0V'][iter].get_array(),\n", - " 'map_E':Psi['Psi_0E'][iter].get_array(),\n", - " 'b_0': B_down['B_G0_down'][iter].get_array(),\n", - " 'b_n': B_down['B_Fn_down'][iter].get_array()}\n", - " return matrix_dict\n", - " else:\n", - " raise ValueError('Invalid value for up_or_down')\n", - " else:\n", - " raise ValueError('Invalid value for starting_map')\n", - " if diagram_type == 'parallelogram':\n", - " if starting_map == 'F':\n", - " if obj_type == 'vert': #==> 3\n", - " matrix_dict = {'d':D['D_G2nV'][iter].get_array(),\n", - " 'map_0':Phi['Phi_0V'][iter].get_array(),\n", - " 'map_n':Phi['Phi_nV'][iter].get_array(),\n", - " 'i_0': I['I_F0V'][iter].get_array(),\n", - " 'i_n': I['I_GnV'][iter].get_array()}\n", - " return matrix_dict\n", - " if obj_type == 'edge': #==> 4\n", - " matrix_dict = {'d':D['D_G2nE'][iter].get_array(),\n", - " 'map_0':Phi['Phi_0E'][iter].get_array(),\n", - " 'map_n':Phi['Phi_nE'][iter].get_array(),\n", - " 'i_0': I['I_F0E'][iter].get_array(),\n", - " 'i_n': I['I_GnE'][iter].get_array()}\n", - " return matrix_dict\n", - " else: \n", - " raise ValueError('Invalid value for obj_type')\n", - " if starting_map == 'G':\n", - " if obj_type == 'vert': #==> 5\n", - " matrix_dict = {'d':D['D_F2nV'][iter].get_array(),\n", - " 'map_0':Psi['Psi_0V'][iter].get_array(),\n", - " 'map_n':Psi['Psi_nV'][iter].get_array(),\n", - " 'i_0': I['I_G0V'][iter].get_array(),\n", - " 'i_n': I['I_FnV'][iter].get_array()}\n", - " return matrix_dict\n", - " if obj_type == 'edge': #==> 6\n", - " matrix_dict = {'d':D['D_F2nE'][iter].get_array(),\n", - " 'map_0':Psi['Psi_0E'][iter].get_array(),\n", - " 'map_n':Psi['Psi_nE'][iter].get_array(),\n", - " 'i_0': I['I_G0E'][iter].get_array(),\n", - " 'i_n': I['I_FnE'][iter].get_array()}\n", - " return matrix_dict\n", - " else:\n", - " raise ValueError('Invalid value for obj_type')\n", - " else: \n", - " raise ValueError('Invalid value for starting_map')\n", - " if diagram_type == 'triangle':\n", - " if starting_map == 'F':\n", - " if obj_type == 'vert': #==> 7\n", - " matrix_dict = {'d':D['D_F2nV'][iter].get_array(),\n", - " 'map_0':Phi['Phi_0V'][iter].get_array(),\n", - " 'map_n':Psi['Psi_nV'][iter].get_array(),\n", - " 'i_0': I['I_F0V'][iter].get_array(),\n", - " 'i_n': I['I_FnV'][iter].get_array()}\n", - " return matrix_dict\n", - " if obj_type == 'edge': #==> 8\n", - " matrix_dict = {'d':D['D_F2nE'][iter].get_array(),\n", - " 'map_0':Phi['Phi_0E'][iter].get_array(),\n", - " 'map_n':Psi['Psi_nE'][iter].get_array(),\n", - " 'i_0': I['I_F0E'][iter].get_array(),\n", - " 'i_n': I['I_FnE'][iter].get_array()}\n", - " return matrix_dict\n", - " else:\n", - " raise ValueError('Invalid value for obj_type')\n", - " if starting_map == 'G':\n", - " if obj_type == 'vert': #==> 9\n", - " matrix_dict = {'d':D['D_G2nV'][iter].get_array(),\n", - " 'map_0':Psi['Psi_0V'][iter].get_array(),\n", - " 'map_n':Phi['Phi_nV'][iter].get_array(),\n", - " 'i_0': I['I_G0V'][iter].get_array(),\n", - " 'i_n': I['I_GnV'][iter].get_array()}\n", - " return matrix_dict \n", - " if obj_type == 'edge':\n", - " matrix_dict = {'d':D['D_G2nE'][iter].get_array(),\n", - " 'map_0':Psi['Psi_0E'][iter].get_array(),\n", - " 'map_n':Phi['Phi_nE'][iter].get_array(),\n", - " 'i_0': I['I_G0E'][iter].get_array(),\n", - " 'i_n': I['I_GnE'][iter].get_array()}\n", - " return matrix_dict\n", - " else:\n", - " raise ValueError('Invalid value for obj_type')\n", - " else:\n", - " raise ValueError('Invalid value for starting_map')\n", - " else:\n", - " raise ValueError('Invalid value for diagram_type')\n", - "\n", - " " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### ILP for diagram 3, 4, 5, 6" - ] - }, - { - "cell_type": "code", - "execution_count": 119, - "metadata": {}, - "outputs": [], - "source": [ - "def ILP_parallelogram(iter, starting_map, obj_type):\n", - " \"\"\"\n", - " This function runs the ILP for the parallelogram diagrams\n", - "\n", - " Parameters\n", - " iter: int\n", - " The function value for which the block matrices are to be set\n", - " \n", - " starting_map: str\n", - " The starting map for the block matrices\n", - " Options are:\n", - " - 'F'\n", - " - 'G'\n", - "\n", - " \n", - " obj_type: str\n", - " Wthether the diagram involves an edge or a vertex\n", - " Options are:\n", - " - 'edge'\n", - " - 'vert'\n", - " \n", - " Returns\n", - " result: dict\n", - " A dictionary containing the final maps and the loss value\n", - "\n", - " \"\"\"\n", - "\n", - " # set the diagram_type\n", - " diagram_type = 'parallelogram'\n", - "\n", - " # get the block matrices\n", - " d = set_block_matrices(iter, starting_map, diagram_type, obj_type)['d']\n", - " map_0 = set_block_matrices(iter, starting_map, diagram_type, obj_type)['map_0']\n", - " map_n = set_block_matrices(iter, starting_map, diagram_type, obj_type)['map_n']\n", - " i_0 = set_block_matrices(iter, starting_map, diagram_type, obj_type)['i_0']\n", - " i_n = set_block_matrices(iter, starting_map, diagram_type, obj_type)['i_n']\n", - "\n", - "\n", - " # set up the ILP\n", - " prob = pulp.LpProblem(\"Interleave_parallelogram\", pulp.LpMinimize)\n", - "\n", - " # set the parameters to loop over\n", - " shape_m = d.shape[0]\n", - " shape_n = map_n.shape[1]\n", - " shape_o = i_n.shape[1]\n", - " shape_p = map_0.shape[1]\n", - "\n", - " # print('m:',shape_m, 'n:',shape_n, 'o:', shape_o, 'p:',shape_p)\n", - " # print(\"corresponding letters are (i, h), j, l, k\")\n", - "\n", - " # define the decision variables\n", - " map_n_vars = pulp.LpVariable.dicts(\"map_0\", ((h,j) for h in range(shape_m) for j in range(shape_n)), cat='Binary')\n", - " map_0_vars = pulp.LpVariable.dicts(\"map_n\", ((l,k) for l in range(shape_o) for k in range(shape_p)), cat='Binary')\n", - " minmax_var = pulp.LpVariable(\"minmax\", lowBound=0, cat='Continuous')\n", - "\n", - " # define the objective function\n", - " prob += minmax_var\n", - "\n", - " # initialize the constraints\n", - " # for h in range(shape_m):\n", - " # for j in range(shape_n):\n", - " # prob += map_n_vars[h,j] == map_n[h][j]\n", - "\n", - " # for l in range(shape_o):\n", - " # for k in range(shape_p):\n", - " # prob += map_0_vars[l,k] == map_0[l][k]\n", - "\n", - " # define the constraints\n", - "\n", - " # constraint 1: loss is bigger than the absolute difference\n", - " for i in range(shape_m):\n", - " for k in range(shape_p):\n", - " # inner difference\n", - " first_term = pulp.lpSum([map_n_vars[i,j] * i_0[j][k] for j in range(shape_n)])\n", - " second_term = pulp.lpSum([i_n[i][l] * map_0_vars[l,k] for l in range(shape_o)])\n", - "\n", - "\n", - " # total expression\n", - " expression = pulp.lpSum(d[i][h] * (first_term - second_term) for h in range(shape_m))\n", - " \n", - " # expression = pulp.lpSum(d_GnV[i][h] * (pulp.lpSum([phi_0V[h,j] * b_F0_up[j][k] for j in range(shape_n)]) - b_Gn_up[i][l] * phi_0E[l,k] for l in range(shape_o)) for h in range(shape_m))\n", - "\n", - " prob += minmax_var >= expression\n", - " prob += -minmax_var <= expression\n", - "\n", - " # constraint 2: each column sums to 1\n", - " for j in range(shape_n):\n", - " prob += pulp.lpSum([map_n_vars[i,j] for i in range(shape_m)]) == 1\n", - "\n", - " for k in range(shape_p):\n", - " prob += pulp.lpSum([map_0_vars[l,k] for l in range(shape_o)]) == 1\n", - "\n", - " # solve the ILP\n", - " prob.solve(pulp.PULP_CBC_CMD(msg=0))\n", - "\n", - " # get the loss value\n", - " block_loss = prob.objective.value()\n", - "\n", - " # make the phi and psi matrices\n", - " # make the phi and psi matrices\n", - " final_map_n = np.zeros((shape_m, shape_n))\n", - " final_map_0 = np.zeros((shape_o, shape_p))\n", - "\n", - " for h in range(shape_m):\n", - " for j in range(shape_n):\n", - " final_map_n[h,j] = map_n_vars[h,j].value()\n", - "\n", - " for l in range(shape_o):\n", - " for k in range(shape_p):\n", - " final_map_0[l,k] = map_0_vars[l,k].value()\n", - "\n", - " # make a result dictionary\n", - " result = {'map_0': final_map_0, 'map_': final_map_n, 'loss': block_loss}\n", - "\n", - " \n", - " return(result)\n" - ] - }, - { - "cell_type": "code", - "execution_count": 120, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "{'map_0': array([[0.],\n", - " [1.]]),\n", - " 'map_': array([[0.],\n", - " [1.]]),\n", - " 'loss': 0.0}" - ] - }, - "execution_count": 120, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "ILP_parallelogram(iter=5,starting_map='F', obj_type='vert')" - ] - }, - { - "cell_type": "code", - "execution_count": 121, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{('F', 'edge'): [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], ('F', 'vert'): [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], ('G', 'edge'): [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], ('G', 'vert'): [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]}\n", - "[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]\n" - ] - } - ], - "source": [ - "all_func_values = set(F.get_function_values()) | set(G.get_function_values())\n", - "\n", - "para_losses_dict = {}\n", - "for map in ['F', 'G']:\n", - " for obj_type in ['edge', 'vert']:\n", - " losses = []\n", - " for iter in all_func_values:\n", - " losses.append(ILP_parallelogram(iter=iter,starting_map=map, obj_type=obj_type)['loss'])\n", - " \n", - " para_losses_dict[(map, obj_type)] = losses\n", - "\n", - "print(para_losses_dict)\n", - "print(max(para_losses_dict.values()))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### ILP for diagram 1, 2 (each has up or down version)" - ] - }, - { - "cell_type": "code", - "execution_count": 122, - "metadata": {}, - "outputs": [], - "source": [ - "def ILP_edge_vert_parallelogram(iter, starting_map, up_or_down):\n", - " \"\"\"\n", - " This function runs the ILP for the edge_vert_parallelogram diagrams\n", - "\n", - " Parameters\n", - " iter: int\n", - " The function value for which the block matrices are to be set\n", - "\n", - " starting_map: str\n", - " The starting map for the block matrices\n", - " Options are:\n", - " - 'F'\n", - " - 'G'\n", - "\n", - " up_or_down: str\n", - " The direction of the boundary matrix. This changes some of the indexing.\n", - " Options are:\n", - " - 'up'\n", - " - 'down'\n", - "\n", - " Returns\n", - " result: dict\n", - " A dictionary containing the final maps and the loss value\n", - "\n", - " \"\"\"\n", - "\n", - " # set the diagram_type\n", - " diagram_type = 'edge_vert_parallelogram'\n", - "\n", - " # get the block matrices\n", - " d = set_block_matrices(iter, starting_map, diagram_type, up_or_down)['d']\n", - " map_V = set_block_matrices(iter, starting_map, diagram_type, up_or_down)['map_V']\n", - " map_E = set_block_matrices(iter, starting_map, diagram_type, up_or_down)['map_E']\n", - " b_0 = set_block_matrices(iter, starting_map, diagram_type, up_or_down)['b_0']\n", - " b_n = set_block_matrices(iter, starting_map, diagram_type, up_or_down)['b_n']\n", - "\n", - " # set up the ILP problem\n", - " prob = pulp.LpProblem(\"Interleave_edge_vert_parallelogram\", pulp.LpMinimize)\n", - "\n", - " # set the parameters to loop over\n", - " shape_m = d.shape[0]\n", - " shape_n = map_V.shape[1]\n", - " shape_o = b_n.shape[1]\n", - " shape_p = map_E.shape[1]\n", - "\n", - " # print('m:',shape_m, 'n:',shape_n, 'o:', shape_o, 'p:',shape_p)\n", - " # print(\"corresponding letters are (i, h), j, l, k\")\n", - "\n", - " # define the decision variables\n", - " map_V_vars = pulp.LpVariable.dicts(\"map_V\", ((h,j) for h in range(shape_m) for j in range(shape_n)), cat='Binary')\n", - " map_E_vars = pulp.LpVariable.dicts(\"map_E\", ((l,k) for l in range(shape_o) for k in range(shape_p)), cat='Binary')\n", - " minmax_var = pulp.LpVariable(\"minmax\", lowBound=0, cat='Continuous')\n", - "\n", - " # define the objective function\n", - " prob += minmax_var\n", - "\n", - " #initialize the assignment decision variables\n", - " # for h in range(shape_m):\n", - " # for j in range(shape_n):\n", - " # prob += map_V_vars[h,j] == map_V[h][j]\n", - " \n", - " # for l in range(shape_o):\n", - " # for k in range(shape_p):\n", - " # prob += map_E_vars[l,k] == map_E[l][k]\n", - " \n", - " # define the constraints\n", - "\n", - " # constraint 1: loss is bigger than the absolute value of the difference\n", - "\n", - " for i in range(shape_m):\n", - " for k in range(shape_p):\n", - " # inner difference\n", - " first_term = pulp.lpSum([map_V_vars[i,j] * b_0[j][k] for j in range(shape_n)])\n", - " second_term = pulp.lpSum([b_n[i][l] * map_E_vars[l,k] for l in range(shape_o)])\n", - "\n", - " # total expression\n", - " expression = pulp.lpSum(d[i][h] * (first_term - second_term) for h in range(shape_m))\n", - " \n", - " # expression = pulp.lpSum(d_GnV[i][h] * (pulp.lpSum([phi_0V[h,j] * b_F0_up[j][k] for j in range(shape_n)]) - b_Gn_up[i][l] * phi_0E[l,k] for l in range(shape_o)) for h in range(shape_m))\n", - "\n", - " prob += minmax_var >= expression\n", - " prob += -minmax_var <= expression\n", - "\n", - " # constraint 2 : each column sums to 1\n", - " for j in range(shape_n):\n", - " prob += pulp.lpSum(map_V_vars[h,j] for h in range(shape_m)) == 1 \n", - "\n", - " for k in range(shape_p):\n", - " prob += pulp.lpSum(map_E_vars[l, k] for l in range(shape_o)) == 1\n", - "\n", - " # # constraint 3\n", - " # for h in range(shape_m):\n", - " # for j in range(shape_n):\n", - " # prob += phi_0V_vars[h,j] >= 0\n", - "\n", - " # for l in range(shape_o):\n", - " # for k in range(shape_p):\n", - " # prob += phi_0E_vars[l,k] >= 0\n", - "\n", - " # check constraints\n", - " # for constraint in prob.constraints.values():\n", - " # print(constraint)\n", - "\n", - "\n", - " # solve the problem\n", - " prob.solve(pulp.PULP_CBC_CMD(msg=0))\n", - "\n", - " # get the loss value\n", - " block_loss = prob.objective.value()\n", - "\n", - " # make the phi and psi matrices\n", - " final_map_V = np.zeros((shape_m, shape_n))\n", - " final_map_E = np.zeros((shape_o, shape_p))\n", - "\n", - " for h in range(shape_m):\n", - " for j in range(shape_n):\n", - " final_map_V[h,j] = map_V_vars[h,j].value()\n", - "\n", - " for l in range(shape_o):\n", - " for k in range(shape_p):\n", - " final_map_E[l,k] = map_E_vars[l,k].value()\n", - " \n", - " # make a result dictionary\n", - " result = {'map_V': final_map_V, 'map_E': final_map_E, 'loss': block_loss}\n", - " \n", - " return(result)" - ] - }, - { - "cell_type": "code", - "execution_count": 123, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "0.0" - ] - }, - "execution_count": 123, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "\n", - "\n", - "ILP_edge_vert_parallelogram(iter=8,starting_map='G', up_or_down='down')['loss']\n" - ] - }, - { - "cell_type": "code", - "execution_count": 124, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{('F', 'up'): [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], ('F', 'down'): [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], ('G', 'up'): [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], ('G', 'down'): [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]}\n", - "('G', 'up')\n" - ] - } - ], - "source": [ - "# modify the function values to remove the max\n", - "all_func_values = set(F.get_function_values()) | set(G.get_function_values())\n", - "\n", - "\n", - "# store the losses\n", - "mix_losses_dict = {}\n", - "\n", - "for map in ['F', 'G']:\n", - " for up_or_down in ['up', 'down']:\n", - " losses = []\n", - " for iter in all_func_values:\n", - " losses.append(ILP_edge_vert_parallelogram(iter=iter,starting_map='G', up_or_down='down')['loss'])\n", - " \n", - " mix_losses_dict[(map, up_or_down)] = losses\n", - "\n", - "print(mix_losses_dict)\n", - "print(max(mix_losses_dict))\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### ILP for diagram 7, 8, 9, 10" - ] - }, - { - "cell_type": "code", - "execution_count": 125, - "metadata": {}, - "outputs": [], - "source": [ - "def ILP_triangle(iter, starting_map, obj_type):\n", - " \"\"\"\n", - " This function runs the ILP for the triangle diagrams\n", - "\n", - " Parameters\n", - " iter: int\n", - " The function value for which the block matrices are to be set\n", - "\n", - " starting_map: str\n", - " The starting map for the block matrices\n", - " Options are:\n", - " - 'F'\n", - " - 'G'\n", - "\n", - " obj_type: str\n", - " Wthether the diagram involves an edge or a vertex\n", - " Options are:\n", - " - 'edge'\n", - " - 'vert'\n", - "\n", - " Returns\n", - " result: dict\n", - " A dictionary containing the final maps and the loss value\n", - "\n", - " \"\"\"\n", - " \n", - " # set the diagram_type\n", - " diagram_type = 'triangle'\n", - "\n", - " # get the block matrices\n", - " d = set_block_matrices(iter, starting_map, diagram_type, obj_type)['d']\n", - " map_0 = set_block_matrices(iter, starting_map, diagram_type, obj_type)['map_0']\n", - " map_n = set_block_matrices(iter, starting_map, diagram_type, obj_type)['map_n']\n", - " i_0 = set_block_matrices(iter, starting_map, diagram_type, obj_type)['i_0']\n", - " i_n = set_block_matrices(iter, starting_map, diagram_type, obj_type)['i_n']\n", - "\n", - " \n", - " # premultiply the inclusion matrices\n", - " i_n_i_0 = i_n @ i_0\n", - "\n", - " # set up the ILP problem\n", - " prob = pulp.LpProblem(\"Interleave_triangle\", pulp.LpMinimize)\n", - "\n", - " # set the parameters to loop over\n", - " shape_m = d.shape[0]\n", - " shape_n = map_n.shape[1]\n", - " shape_o = map_0.shape[1]\n", - " \n", - "\n", - " # print('m:',shape_m, 'n:',shape_n, 'o:', shape_o, 'p:',shape_p)\n", - " # print(\"corresponding letters are (i, h), j, l, k\")\n", - "\n", - " # define the decision variables\n", - " z =pulp.LpVariable.dicts(\"z\", ((i,j,k) for i in range(shape_m) for j in range(shape_n) for k in range(shape_o)), cat='Binary')\n", - " map_n_vars = pulp.LpVariable.dicts(\"map_n\", ((i,j) for i in range(shape_m) for j in range(shape_n)), cat='Binary')\n", - " map_0_vars = pulp.LpVariable.dicts(\"map_0\", ((j,k) for j in range(shape_n) for k in range(shape_o)), cat='Binary')\n", - " map_mult_vars = pulp.LpVariable.dicts(\"map_mult\", ((i,k) for i in range(shape_m) for k in range(shape_o)), cat='Integer')\n", - " minmax_var = pulp.LpVariable(\"minmax\", lowBound=0, cat='Continuous')\n", - "\n", - "\n", - " # define the objective function\n", - " prob += minmax_var\n", - " \n", - " # #initialize the assignment decision variables\n", - " # for i in range(shape_m):\n", - " # for j in range(shape_n):\n", - " # prob += map_n_vars[i,j] == map_n[i][j]\n", - "\n", - "\n", - " # for j in range(shape_n):\n", - " # for k in range(shape_o):\n", - " # prob += map_0_vars[j,k] == map_0[j][k]\n", - "\n", - " # define the constraints \n", - "\n", - " # constraint 1: loss is bigger than the absolute value of the difference\n", - " for h in range(shape_m):\n", - " prob += minmax_var >= pulp.lpSum(d[i,h] * (i_n_i_0[h,k] - map_mult_vars[h,k]) for i in range(shape_m) for k in range(shape_o))\n", - " prob += -minmax_var <= pulp.lpSum(d[i,h] * (i_n_i_0[h,k] - map_mult_vars[h,k]) for i in range(shape_m) for k in range(shape_o))\n", - " \n", - " # constraint 2: map_mult in terms of z\n", - " for i in range(shape_m):\n", - " for k in range(shape_o):\n", - " prob += map_mult_vars[i,k] == pulp.lpSum(z[i,j,k] for j in range(shape_n))\n", - "\n", - " # constraint 3: z is less than map_n and map_0 and bigger than their sum - 1\n", - " for i in range(shape_m):\n", - " for j in range(shape_n):\n", - " for k in range(shape_o):\n", - " prob += z[i,j,k] <= map_n_vars[i,j]\n", - " prob += z[i,j,k] <= map_0_vars[j,k]\n", - " prob += z[i,j,k] >= map_n_vars[i,j] + map_0_vars[j,k] - 1\n", - "\n", - " # constraint 4: each column sums to 1\n", - " for j in range(shape_n):\n", - " prob += pulp.lpSum(map_n_vars[i,j] for i in range(shape_m)) == 1\n", - "\n", - " for k in range(shape_o):\n", - " prob += pulp.lpSum(map_0_vars[j,k] for j in range(shape_n)) == 1\n", - "\n", - " # solve the problem\n", - " prob.solve(pulp.PULP_CBC_CMD(msg=0))\n", - "\n", - " # get the loss value\n", - " block_loss = prob.objective.value()\n", - "\n", - " # make the phi and psi matrices\n", - " final_map_n = np.zeros((shape_m, shape_n))\n", - " final_map_0 = np.zeros((shape_n, shape_o))\n", - "\n", - " for i in range(shape_m):\n", - " for j in range(shape_n):\n", - " final_map_n[i,j] = map_n_vars[i,j].value()\n", - "\n", - " for j in range(shape_n):\n", - " for k in range(shape_o):\n", - " final_map_0[j,k] = map_0_vars[j,k].value()\n", - "\n", - " # make a result dictionary\n", - " result = {'map_0': final_map_0, 'map_n': final_map_n, 'loss': block_loss}\n", - "\n", - " return(result)" - ] - }, - { - "cell_type": "code", - "execution_count": 126, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "{'map_0': array([[1., 1., 1.]]),\n", - " 'map_n': array([[0.],\n", - " [1.]]),\n", - " 'loss': 3.0}" - ] - }, - "execution_count": 126, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "ILP_triangle(iter=3,starting_map='G', obj_type='edge')" - ] - }, - { - "cell_type": "code", - "execution_count": 127, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{('F', 'edge'): [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], ('F', 'vert'): [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], ('G', 'edge'): [0.0, 3.0, 2.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], ('G', 'vert'): [0.0, 3.0, 2.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]}\n", - "('G', 'vert')\n" - ] - } - ], - "source": [ - "all_func_values = set(F.get_function_values()) | set(G.get_function_values())\n", - "\n", - "tri_losses_dict = {}\n", - "for map in ['F', 'G']:\n", - " for obj_type in ['edge', 'vert']:\n", - " losses = []\n", - " for iter in all_func_values:\n", - " losses.append(ILP_triangle(iter=iter,starting_map=map, obj_type=obj_type)['loss'])\n", - " \n", - " tri_losses_dict[(map, obj_type)] = losses\n", - "\n", - "print(tri_losses_dict)\n", - "print(max(tri_losses_dict))\n", - " " - ] - }, - { - "cell_type": "code", - "execution_count": 128, - "metadata": {}, - "outputs": [], - "source": [ - "def solve_ILP(iter, F, G):\n", - "\n", - " # compute all the losses correspoding to F\n", - " losses_F = {}\n", - "\n", - " # parallelogram\n", - " losses_F['parallelogram_vert'] = ILP_parallelogram(iter=iter,starting_map='F', obj_type='vert')['loss']\n", - " losses_F['parallelogram_edge'] = ILP_parallelogram(iter=iter,starting_map='F', obj_type='edge')['loss']\n", - "\n", - " # triangle\n", - " losses_F['triangle_vert'] = ILP_triangle(iter=iter,starting_map='F', obj_type='vert')['loss']\n", - " losses_F['triangle_edge'] = ILP_triangle(iter=iter,starting_map='F', obj_type='edge')['loss']\n", - "\n", - " # edge_vert_parallelogram\n", - " losses_F['edge_vert_parallelogram_up'] = ILP_edge_vert_parallelogram(iter=iter,starting_map='F', up_or_down='up')['loss']\n", - " losses_F['edge_vert_parallelogram_down'] = ILP_edge_vert_parallelogram(iter=iter,starting_map='F', up_or_down='down')['loss']\n", - "\n", - " # compute all the losses correspoding to G\n", - " losses_G = {}\n", - "\n", - " # parallelogram\n", - " losses_G['parallelogram_vert'] = ILP_parallelogram(iter=iter,starting_map='G', obj_type='vert')['loss']\n", - " losses_G['parallelogram_edge'] = ILP_parallelogram(iter=iter,starting_map='G', obj_type='edge')['loss']\n", - "\n", - " # triangle\n", - " losses_G['triangle_vert'] = ILP_triangle(iter=iter,starting_map='G', obj_type='vert')['loss']\n", - " losses_G['triangle_edge'] = ILP_triangle(iter=iter,starting_map='G', obj_type='edge')['loss']\n", - "\n", - " # edge_vert_parallelogram\n", - " losses_G['edge_vert_parallelogram_up'] = ILP_edge_vert_parallelogram(iter=iter,starting_map='G', up_or_down='up')['loss']\n", - " losses_G['edge_vert_parallelogram_down'] = ILP_edge_vert_parallelogram(iter=iter,starting_map='G', up_or_down='down')['loss']\n", - "\n", - " # compute the maximum loss\n", - " max_loss = max(max(losses_F.values()), max(losses_G.values()))\n", - "\n", - " # get which map is the largest contributor to the maximum loss\n", - " # for key, value in losses_F.items():\n", - " # if value == max_loss:\n", - " # print(f\"for F: {key}\")\n", - " # print(value)\n", - "\n", - " # for key, value in losses_G.items():\n", - " # if value == max_loss:\n", - " # print(f\"for G: {key}\")\n", - " # print(value)\n", - " \n", - " \n", - " print(f\"the max loss is: {max_loss}\")\n", - "\n", - " # return losses_F, losses_G\n" - ] - }, - { - "cell_type": "code", - "execution_count": 129, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "np.float64(4.0)" - ] - }, - "execution_count": 129, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "myInt.loss()" - ] - }, - { - "cell_type": "code", - "execution_count": 133, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "the max loss is: 0.0\n", - "the max loss is: 3.0\n", - "the max loss is: 2.0\n", - "the max loss is: 1.0\n", - "the max loss is: 0.0\n", - "the max loss is: 0.0\n", - "the max loss is: 0.0\n", - "the max loss is: 0.0\n", - "the max loss is: 0.0\n", - "the max loss is: 0.0\n", - "the max loss is: 0.0\n" - ] - } - ], - "source": [ - "for i in range(2,13):\n", - " solve_ILP(i, F, G)" - ] - }, - { - "cell_type": "code", - "execution_count": 134, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{('F', 'up'): [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], ('F', 'down'): [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], ('G', 'up'): [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], ('G', 'down'): [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]}\n", - "{('F', 'edge'): [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], ('F', 'vert'): [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], ('G', 'edge'): [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], ('G', 'vert'): [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]}\n", - "{('F', 'edge'): [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], ('F', 'vert'): [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], ('G', 'edge'): [0.0, 3.0, 2.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], ('G', 'vert'): [0.0, 3.0, 2.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]}\n" - ] - } - ], - "source": [ - "print(mix_losses_dict)\n", - "print(para_losses_dict)\n", - "print(tri_losses_dict)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "interleavingenv", - "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": "3.12.3" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/Notebooks_Unused/juggling_man.ipynb b/Notebooks_Unused/juggling_man.ipynb deleted file mode 100644 index aa88d0e..0000000 --- a/Notebooks_Unused/juggling_man.ipynb +++ /dev/null @@ -1,204 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Juggling Man Example\n", - "\n", - "This is the code used to generate the juggling man Reeb graph drawn on the front page. Maybe not exactly. Gonna want to update to have more examples. " - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "from cereeberus.data import graphs\n", - "from cereeberus import ReebGraph as Reeb\n", - "jm = graphs.juggling_man()\n", - "jm = Reeb(jm)\n", - "jm.plot_reeb()" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "{0: (3, 7),\n", - " 1: (3, 6),\n", - " 2: (1, 5),\n", - " 3: (5, 5),\n", - " 4: (7, 6),\n", - " 5: (0, 4),\n", - " 6: (3, 4),\n", - " 7: (3, 1),\n", - " 8: (6.5, 6.5),\n", - " 9: (2, 6.5),\n", - " 10: (0.75, 5.5)}" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "jm.pos" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "jm.plot_reeb(position = {0: (3, 7),\n", - " 1: (3, 6),\n", - " 2: (1, 5),\n", - " 3: (5, 5),\n", - " 4: (7, 6),\n", - " 5: (0, 4),\n", - " 6: (3, 4),\n", - " 7: (3, 1),\n", - " 8: (6.5, 6.5),\n", - " 9: (4, 6.5),\n", - " 10: (0.75, 5.5)})" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "jm.plot_reeb(position = {0: (3, 7),\n", - " 1: (3, 6),\n", - " 2: (1, 5),\n", - " 3: (5, 5),\n", - " 4: (7, 6),\n", - " 5: (0, 4),\n", - " 6: (3, 4),\n", - " 7: (3, 1),\n", - " 8: (4.5, 6.5),\n", - " 9: (5, 6.5),\n", - " 10: (2, 6.5)})" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [], - "source": [ - "import imageio\n", - "import os\n", - "\n", - "filenames = []\n", - "for j in range(0,30):\n", - " for i in range(0, 3):\n", - " name = 'juggling_men/juggling_man' + str(i) + '.png'\n", - " filenames.append(name)\n", - " filenames.append(name)\n", - " filenames.append(name)\n", - " filenames.append(name)\n", - " filenames.append(name)\n", - " filenames.append(name)\n", - " filenames.append(name)\n", - " filenames.append(name)\n", - " filenames.append(name)\n", - " filenames.append(name)\n", - "\n", - "# filenames" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - ":3: DeprecationWarning: Starting with ImageIO v3 the behavior of this function will switch to that of iio.v3.imread. To keep the current behavior (and make this warning disappear) use `import imageio.v2 as imageio` or call `imageio.v2.imread` directly.\n", - " images.append(imageio.imread(filename))\n" - ] - } - ], - "source": [ - "images = []\n", - "for filename in filenames:\n", - " images.append(imageio.imread(filename))\n", - "imageio.mimsave('./juggling_man.gif', images)" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3.8.8 ('kepler_mapper')", - "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": "3.11.5" - }, - "orig_nbformat": 4, - "vscode": { - "interpreter": { - "hash": "1e77f4eb1f7954f03b3e9a910bed2486f8cb4a1ca8742d30ecdb20c36e3d914b" - } - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/Notebooks_Unused/linear_optimization_ILP_forms.ipynb b/Notebooks_Unused/linear_optimization_ILP_forms.ipynb deleted file mode 100644 index fbe66a0..0000000 --- a/Notebooks_Unused/linear_optimization_ILP_forms.ipynb +++ /dev/null @@ -1,435 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Let's write all the linear constraints for every diagram. We use the diagram list from Liz." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - " Note: Initially, we write down the cosntrainst for the large matrices without using the block structure. Later, we can speed up the computation by using the block structure. Only thing that will change is, we will split the first two diagrams into 4 to accomodate the boundary matrix." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Diagram 1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "![image](/Users/ishikaghosh/Library/CloudStorage/OneDrive-MichiganStateUniversity/Documents/Research/Projects/Interleaving_to_ML/ceREEBerus/doc_source/images/diagram_pictures/Diagram_1.png)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Precomputed matrices:\n", - "- $D_{G^n}^V := [d^n_{g_{ij}}]$ \n", - " - Distance matrix.\n", - " - Block structure. \n", - " - All the entries are non-negative.\n", - " - It is a square matrix. \n", - "- $ B_F := [b_{f_{ij}}]$\n", - " - Boundary Matrix. \n", - " - All the entries are binary.\n", - " - Columns should add up to 2.\n", - " - Usually it doesn't have the block structure, however, we can split it into `up` and `down` boundary matrices to make it block structured.\n", - "- $B_{G^n}^V := [b^n_{g_{ij}}]$\n", - " - Boundary Matrix. \n", - " - All the entries are binary.\n", - " - Columns should add up to 2.\n", - " - Usually it doesn't have the block structure, however, we can split it into `up` and `down` boundary matrices to make it block structured.\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Matrix Variables:\n", - "- $\\varPhi_V := [\\varphi_{v_{ij}}]$\n", - " - assignment from $F$ to $G^n$ on vertices.\n", - " - Block structure. \n", - " - All the entries are binary.\n", - " - Columns should add up to 1.\n", - "- $\\varPhi_E := [\\varphi_{e_{ij}}]$\n", - " - assignment from $F$ to $G^n$ on vertices.\n", - " - Block structure. \n", - " - All the entries are binary.\n", - " - Columns should add up to 1." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We need write down each element as the product and subtraction of matrices.\n", - "\n", - "Let $L := D_{G^n}^V * (\\varPhi_V * B_F - B_{G^n} * \\varPhi_E )$.\n", - "\n", - "* Index summary:\n", - " - $i: 1, 2, \\ldots, m$\n", - " - $j: 1, 2, \\ldots, n$\n", - " - $k: 1, 2, \\ldots, p$\n", - " - $l: 1, 2, \\ldots, o$\n", - " - $h: 1, 2, \\ldots, m$\n", - "\n", - "Then, we have:\n", - "$ \\sum_{h=1}^m d^n_{g_{ih}} * (\\sum_{j=1}^n \\varphi_{v_{hj}} * b_{f_{jk}} - \\sum_{l=1}^o b^n_{g_{il}} * \\varphi_{e_{lk}}) $ for all $i = 1, 2, \\ldots, m$ and all $k = 1, 2, \\dots, p$." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let `m` be the maximum over all absolute valued entries in $L$.\n", - "\n", - "- Objective function: minimize $m$.\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "- Subject to:\n", - " 1. $ m \\geq \\sum_{h=1}^m d^n_{g_{ih}} * (\\sum_{j=1}^n \\varphi_{v_{hj}} * b_{f_{jk}} - \\sum_{l=1}^o b^n_{g_{il}} * \\varphi_{e_{lk}}) = 0$ for all $i = 1, 2, \\ldots, m$ and all $k = 1, 2, \\dots, p$.

\n", - " 2. $ -m \\leq \\sum_{h=1}^m d^n_{g_{ih}} * (\\sum_{j=1}^n \\varphi_{v_{hj}} * b_{f_{jk}} - \\sum_{l=1}^o b^n_{g_{il}} * \\varphi_{e_{lk}}) = 0$ for all $i = 1, 2, \\ldots, m$ and all $k = 1, 2, \\dots, p$.

\n", - " 3. $\\sum_{h=1}^m \\varphi_{v_{hj}} = 1$ for all $j = 1, 2, \\ldots, n$.

\n", - " 4. $\\sum_{l=1}^o \\varphi_{e_{lk}} = 1$ for all $k = 1, 2, \\ldots, p$.

\n", - " 5. $\\varphi_{V_{hj}} \\geq 0$ for all $h = 1, 2, \\ldots, m$ and all $j = 1, 2, \\ldots, n$.

\n", - " 6. $\\varphi_{E_{lk}} \\geq 0$ for all $l = 1, 2, \\ldots, o$ and all $k = 1, 2, \\ldots, p$.

" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "1 and 2 are the absolute value constraints. 3 and 4 makes sure that the columns add up to 1. 5 and 6 makes sure that the entries are non-negative." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Diagram 2" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "![image](/Users/ishikaghosh/Library/CloudStorage/OneDrive-MichiganStateUniversity/Documents/Research/Projects/Interleaving_to_ML/ceREEBerus/doc_source/images/diagram_pictures/Diagram_2.png)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This one is almost identical to the previous one. We only write the ILP formulation." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let $L := D_{F^n}^V * (\\Psi_V * B_G - B_{F^n} * \\Psi_E )$.\n", - "\n", - "* Index summary:\n", - " - $i: 1, 2, \\ldots, m$\n", - " - $j: 1, 2, \\ldots, n$\n", - " - $k: 1, 2, \\ldots, p$\n", - " - $l: 1, 2, \\ldots, o$\n", - " - $h: 1, 2, \\ldots, m$\n", - "\n", - "Then, we have:\n", - "$ \\sum_{h=1}^m d^n_{f_{ih}} * (\\sum_{j=1}^n \\psi_{V_{hj}} * b_{g_{jk}} - \\sum_{l=1}^o b^n_{f_{il}} * \\psi_{E_{lk}}) $ for all $i = 1, 2, \\ldots, m$ and all $k = 1, 2, \\dots, p$." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let `m` be the maximum over all absolute valued entries in $L$.\n", - "\n", - "- Objective function: minimize $m$." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "- Subject to:\n", - " 1. $ m \\geq \\sum_{h=1}^m d^n_{f_{ih}} * (\\sum_{j=1}^n \\psi_{V_{hj}} * b_{g_{jk}} - \\sum_{l=1}^o b^n_{f_{il}} * \\psi_{E_{lk}}) = 0$ for all $i = 1, 2, \\ldots, m$ and all $k = 1, 2, \\dots, p$.

\n", - " 2. $ -m \\leq \\sum_{h=1}^m d^n_{f_{ih}} * (\\sum_{j=1}^n \\psi_{V_{hj}} * b_{g_{jk}} - \\sum_{l=1}^o b^n_{f_{il}} * \\psi_{E_{lk}}) = 0$ for all $i = 1, 2, \\ldots, m$ and all $k = 1, 2, \\dots, p$.

\n", - " 3. $\\sum_{h=1}^m \\psi_{V_{hj}} = 1$ for all $j = 1, 2, \\ldots, m$.

\n", - " 4. $\\sum_{l=1}^o \\psi_{E_{lk}} = 1$ for all $k = 1, 2, \\ldots, p$.

\n", - " 5. $\\psi_{V_{hj}} \\geq 0$ for all $h = 1, 2, \\ldots, m$ and all $j = 1, 2, \\ldots, n$.

\n", - " 6. $\\psi_{E_{lk}} \\geq 0$ for all $l = 1, 2, \\ldots, o$ and all $k = 1, 2, \\ldots, p$.

" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Diagram 3" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "![image](/Users/ishikaghosh/Library/CloudStorage/OneDrive-MichiganStateUniversity/Documents/Research/Projects/Interleaving_to_ML/ceREEBerus/doc_source/images/diagram_pictures/Diagram_3.png)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Precomputed matrices:\n", - "- $D_{G^{2n}}^V := [d^{2n}_{g_{ij}}]$ \n", - " - Distance matrix.\n", - " - Block structure. \n", - " - All the entries are non-negative.\n", - " - It is a square matrix. \n", - "- $ I_F^V := [I_{f_{ij}}]$\n", - " - Inclusion matrix from $F$ to $F^n$.\n", - " - Block structure.\n", - " - All the entries are binary.\n", - "\n", - "- $I_{G^n}^V := [I^n_{g_{ij}}]$\n", - " - Inclusion matrix from $G^n$ to $G^{2n}$.\n", - " - Block structure.\n", - " - All the entries are binary.\n", - " " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Matrix variables:\n", - "- $\\varPhi_V^n := [\\varphi^n_{v_{ij}}]$\n", - " - assignment from $F^n$ to $G^{2n}$ on vertices.\n", - " - Block structure. \n", - " - All the entries are binary.\n", - " - Columns should add up to 1.\n", - "- $\\varPhi_V := [\\varphi_{v_{ij}}]$\n", - " - assignment from $F$ to $G^n$ on vertices.\n", - " - Block structure. \n", - " - All the entries are binary.\n", - " - Columns should add up to 1.\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We need write down each element as the product and subtraction of matrices.\n", - "\n", - "Let $L := D_{G^{2n}}^V * (\\varPhi^n_V * I^V_F - I^V_{G^n} * \\varPhi_V )$.\n", - "\n", - "Then, we have:\n", - "\n", - "$ \\sum_{h=1}^m d^{2n}_{g_{ih}} * (\\sum_{j=1}^n \\varphi^n_{v_{hj}} * I_{f_{jk}} - \\sum_{l=1}^o I^n_{g_{il}} * \\varphi_{v_{lk}})$ for all $i = 1, 2, \\ldots, m$ and all $k = 1, 2, \\dots, p$." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let `m` be the maximum over all absolute valued entries in $L$.\n", - "\n", - "- Objective function: minimize $m$." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "- Subject to:\n", - " 1. $ m \\geq \\sum_{h=1}^m d^{2n}_{g_{ih}} * (\\sum_{j=1}^n \\varphi^n_{v_{hj}} * I_{f_{jk}} - \\sum_{l=1}^o I^n_{g_{il}} * \\varphi_{v_{lk}}) = 0$ for all $i = 1, 2, \\ldots, m$ and all $k = 1, 2, \\dots, p$.

\n", - " 2. $ -m \\leq \\sum_{h=1}^m d^{2n}_{g_{ih}} * (\\sum_{j=1}^n \\varphi^n_{v_{hj}} * I_{f_{jk}} - \\sum_{l=1}^o I^n_{g_{il}} * \\varphi_{v_{lk}}) = 0$ for all $i = 1, 2, \\ldots, m$ and all $k = 1, 2, \\dots, p$.

\n", - " 3. $\\sum_{h=1}^m \\varphi_{v_{hj}} = 1$ for all $j = 1, 2, \\ldots, m$.

\n", - " 4. $\\sum_{l=1}^o \\varphi^n_{v_{lk}} = 1$ for all $k = 1, 2, \\ldots, p$.

\n", - " 5. $\\varphi_{v_{hj}} \\geq 0$ for all $h = 1, 2, \\ldots, m$ and all $j = 1, 2, \\ldots, n$.

\n", - " 6. $\\varphi_{v^n_{lk}} \\geq 0$ for all $l = 1, 2, \\ldots, o$ and all $k = 1, 2, \\ldots, p$.

" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Diagram 7" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "![image](/Users/ishikaghosh/Library/CloudStorage/OneDrive-MichiganStateUniversity/Documents/Research/Projects/Interleaving_to_ML/ceREEBerus/doc_source/images/diagram_pictures/Diagram_7.png)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Precomputed matrices:\n", - "- $D_{F^{2n}}^V := [d^{2n}_{f_{ij}}]$ \n", - " - Distance matrix.\n", - " - Block structure. \n", - " - All the entries are non-negative.\n", - " - It is a square matrix. \n", - "\n", - "- $ I_{F^n}^V := [I^n_{f_{ij}}]$\n", - " - Inclusion matrix from $G$ to $G^n$.\n", - " - Block structure.\n", - " - All the entries are binary.\n", - "\n", - "- $ I_{F}^V := [I_{f_{ij}}]$\n", - " - Inclusion matrix from $G$ to $G^n$.\n", - " - Block structure.\n", - " - All the entries are binary.\n", - "\n", - "We also precompute $I_{f^nf} := I_{F^n}^V * I_{F}^V$." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Matrix variables:\n", - "\n", - "- $\\Psi_V^n := [\\psi^n_{v_{ij}}]$\n", - " - assignment from $G^n$ to $F^{2n}$ on vertices.\n", - " - Block structure. \n", - " - All the entries are binary.\n", - " - Columns should add up to 1.\n", - "\n", - "- $\\varPhi_V := [\\varphi_{v_{ij}}]$\n", - " - assignment from $G$ to $F^n$ on vertices.\n", - " - Block structure. \n", - " - All the entries are binary.\n", - " - Columns should add up to 1." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "* Index summary:\n", - " - $i: 1, 2, \\ldots, m$\n", - " - $j: 1, 2, \\ldots, n$\n", - " - $k: 1, 2, \\ldots, p$\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We need to linearlize the product of variable matrices first. \n", - "\n", - "- Step 1: $\\Psi_V^n\\varPhi_V$
\n", - "\n", - " Let, $C = \\Psi_V^n\\varPhi_V$\\\n", - " Then, $c_{ik} = \\sum_{j=1}^n \\psi^n_{v_{ij}}\\varphi_{v_{jk}}$\\\n", - " We introduce a new *binary* variable `z` which will represent the product of $\\psi^n_{v_{ij}}$ and $\\varphi_{v_{jk}}$.
\n", - "\n", - " We can write the product as following:\n", - " $c_{ik} = \\sum_{j=1}^n z_{ijk}$\n", - "\n", - " While z has the following constraints:\n", - " 1. $z_{ijk} \\leq \\psi^n_{v_{ij}}$\n", - " 2. $z_{ijk} \\leq \\varphi_{v_{jk}}$\n", - " 3. $z_{ijk} \\geq \\psi^n_{v_{ij}} + \\varphi_{v_{jk}} - 1$\n", - "\n", - "\n", - " " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let $L := D_{F^{2n}}^V * (I_{F^n}^V * I_{F}^V - \\Psi_V^n\\varPhi_V)$.\n", - "\n", - "Then, we have:\n", - "\n", - "$ \\sum_{i=1}^m d^{2n}_{f_{ji}} * (I_{{f^nf}_{ik}} - c_{ik})$ for all $k = 1, 2, \\dots, p$." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let `m` be the maximum over all absolute valued entries in $L$.\n", - "\n", - "- Objective function: minimize $m$.\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "- Subject to:\n", - " 1. $ m \\geq \\sum_{i=1}^m d^{2n}_{f_{ij}} * (I_{{f^nf}_{ik}} - c_{ik}) = 0$ for all $k = 1, 2, \\dots, p$.

\n", - " 2. $ -m \\leq \\sum_{i=1}^m d^{2n}_{f_{ij}} * (I_{{f^nf}_{ik}} - c_{ik}) = 0$ for all $k = 1, 2, \\dots, p$.

\n", - " 3. $ c_{ik} = \\sum_{j=1}^n z_{ijk}$ for all $i= 1, 2, \\dots, m$ and $k = 1, 2, \\dots, p$.

\n", - " 4. $ z_{ijk} \\leq \\psi^n_{v_{ij}}$ for all $i= 1, 2, \\dots, m$, $j = 1, 2, \\dots, n$ and $k = 1, 2, \\dots, p$.

\n", - " 5. $ z_{ijk} \\leq \\varphi_{v_{jk}}$ for all $i= 1, 2, \\dots, m$, $j = 1, 2, \\dots, n$ and $k = 1, 2, \\dots, p$.

\n", - " 6. $ z_{ijk} \\geq \\psi^n_{v_{ij}} + \\varphi_{v_{jk}} - 1$ for all $i= 1, 2, \\dots, m$, $j = 1, 2, \\dots, n$ and $k = 1, 2, \\dots, p$.

\n", - " 7. $\\sum_{j=1}^n \\psi^n_{v_{ij}} = 1$ for all $i = 1, 2, \\ldots, m$.

\n", - " 8. $\\sum_{k=1}^p \\varphi_{v_{jk}} = 1$ for all $j = 1, 2, \\ldots, n$.

\n", - " 9. $\\psi^n_{v_{ij}} \\geq 0$ for all $i = 1, 2, \\ldots, m$ and all $j = 1, 2, \\ldots, n$.

\n", - " 10. $\\varphi_{v_{jk}} \\geq 0$ for all $j = 1, 2, \\ldots, n$ and all $k = 1, 2, \\ldots, p$.

" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "1 and 2 are the absolute value constraints. 3 reparametrizes the product of two matrices. 4, 5, and 6 are the constraints for the reparametrized binary variable. 7 and 8 makes sure that the columns add up to 1. 9 and 10 makes sure that the entries are non-negative." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Q. How to combine all the constraints into one ILP? " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "interleavingenv", - "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": "3.13.0" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/Notebooks_Unused/linear_optimization_single_parallelogram.ipynb b/Notebooks_Unused/linear_optimization_single_parallelogram.ipynb deleted file mode 100644 index 686251b..0000000 --- a/Notebooks_Unused/linear_optimization_single_parallelogram.ipynb +++ /dev/null @@ -1,1123 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 20, - "metadata": {}, - "outputs": [], - "source": [ - "from cereeberus import ReebGraph, MapperGraph, Interleave\n", - "import cereeberus.data.ex_mappergraphs as ex_mg\n", - "\n", - "import matplotlib.pyplot as plt\n", - "import numpy as np" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": {}, - "outputs": [], - "source": [ - "# Using PuLP to solve the ILP (Should I use something else?)\n", - "import pulp" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Given two mapper graphs and associated matrices, I am trying to see if the problem can be solved using integer linear programming (ILP).\n", - "\n", - "_Note to self: Fill in the ILP details here._" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Let's create two example mapper graphs." - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Text(0.5, 1.0, 'M_1')" - ] - }, - "execution_count": 22, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "M1 = ex_mg.interleave_example_A()\n", - "M1.draw()\n", - "plt.title('M_1')" - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Text(0.5, 1.0, 'M_2')" - ] - }, - "execution_count": 23, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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5Yb7AoetTcHUdzPXR1BQ8RqRpet80UPQbCT6EEEL0G1NAOmMS3yUz5gmCjOkAKBhpKxBRTs6JCDQkE6H8F1uWXcP2zeUcOXKkP5ss+oCiD7C1iM1mM5GRkTQ2NhIR0dkcbyGEEIOVruuYHVtotH2JxbkXm/MQGg4UAggOyCIsaAIRphlEmmahKCorV65k27ZtREZG8u1vf5ugIEkuNpB05/4tU22FEEKcE4qiEGma3uXHKFdccQWFhYU0NDTw2Wefcc011/RxC0VfkccuQgghBoXAwECuu86b0XTnzp0UFRWd4xaJnjrvez7sniaq7IeosR/BoTUDCiHGaBJM2cQHZWFUpdtOCCEGi8zMTKZMmcKOHTv45JNP+Pa3v01gYCAALs1OjeMoVfZDWN31gE6QIZz4oOEkmIYTZJDVbweK8zL40HQPx5q3sbd+KcXWnQAoqCgnO3o0PICOqhgZGT6H8dGLSQoedQ5bLIQQoqvmzZvHoUOHaGhoYO3atUyak8He+o85ZP785PVdQT05nVfHg34ys2pG6MVMiL6eoaFTUBTp+D+XzrsBp3WOYtaUP0WlvQAFFR2tw/IKBnQ8jAifw+yk/yLYENnTpgshhOgnR48e5Y33/kPw5MMEptX6ruUdOXVPSDaN4aqUnxEVmNpPrb0wdOf+fV6Ffgca1/Bm0UNU2Q8DdBp4eMt4/1gPNX3Ba0fvo8J2oE/bKIQQoveCkixEX7uHgNRagE4DD28Z7z2hwl7AG0XfotC8oU/bKNp33gQf+xpWsqb8T2i4u/RHeDYdDYenmQ+Kf0y5bX8ftFAIIYQ/lFpz+ajkp2gGJz15eqLjwaO7WFn2Bw42rvV/A0Wnzovgo8y6j3UVf+11PToaHt3FxyU/PzlYSQghxEDS7Krh4xO/QNO9Y/d6a035U1TaCnrfMNEtgz74cGl2Vpf/EaWLaXrX/LOIH4xexx+v3dLmfh0Np2ZlfcXf/dlMIYQQvaTrOmsr/oJbc7T7WN1hcbPyH0f554O7+fklX/CD0evY+lFZB7UqrC7/I27N2TeNFm0a9MHHnvoPaXJVdml8R0OFnbUvHCMwpONFjXQ0jjR/RYllt7+aKYQQopeOWbZy3LK9w+t9c4OL1f9XROURKykjO59aq6NR7zxBXsOn/myq6MSgDj403cOeuqW+aVSd+fhPhxg6IZK0seGdllUwsKd+aS9bKIQQwl/21C31pUxoT2R8EL/bOJP/Xj+D636S3cWadfbUf4Sud/4lVvhHt4OPjRs3cu2115KSkoKiKCxdutS3z+Vy8bOf/YycnBxCQ0NJSUnhG9/4BmVlHXV59VyJZRdWT12Xyh7ZXs/eNdXc8PiILpXX8VDU/DVWd0MvWiiEEMIfml01FFt3dNrLbQxUiYjvfvJIs6uCUlteT5snuqnbwYfFYmHChAk899xzrfZZrVZ27drFr371K3bt2sWHH35IQUGBLx2uv5XZ8lHo+BEKgObR+eAPhVxycwopI7qe4U5Hp9IuA5GEEOJc6+tZiAqqzHTsR93OcLpw4UIWLlzY5r7IyEg+++yzFtueffZZLr74YoqLi0lPT+9ZK9tRaS/o0liPTe+coK7MzndemtSt+hVUquyHyAyb1tMmCiGE8IMqxyFUDCczmPYNmfXSf/o8vXpjYyOKohAVFdXmfofDgcPh8L02m81drrvJVUVnU60s9S5W/uMo87+dQVhMYJfrBlBQaHbXdOsYIYQQ/mdx1fhhYm37dDSa3dV9eAZxpj4dcGq32/nZz37GHXfc0W6q1SeffJLIyEjfT1paWpfr987z7tjyvx8hJDKAWXd1vd4z6V04hxBCiL6loeGPvB4dnkOu9/2mz4IPl8vFrbfeiq7rPP/88+2We/zxx2lsbPT9lJSUdPkcJkPHs1aqj1nZvKSUy+5Jo7HaQW2pjdpSG26HhsetU1tqw9Lg6rCOQDW0y+0RQgjRN4LU0C7nc+rxOQxyve8vffLY5VTgcfz4cdavX9/hAjNBQUEEBfVsWft403Cq7IXtPgNsqHKga/DhHwr58A+Frfb/z7yvueyeNG78edszYDQ8xJuG9ahtQggh/CcuaFifjvdQMRAf1NWpuaK3/B58nAo8Dh06xIYNG4iNjfX3KXwSTSPIo/3EMMnZodz/j/Gttq/4+xEcFg83/HwEcenBHZ4jwdS1qblCCCH6ToKpbwMDDU+fn0Oc1u3go7m5mcOHD/teFxUVsWfPHmJiYkhOTubmm29m165dLFu2DI/HQ0VFBQAxMTEEBnZvwGdnMsMu6XAZ5bDoQMbPi2+1/YvXigHa3HeaQmRAMjGBQ/3RVCGEEL0QbxpOmDG+S4NCv3yzBJvZTWOVdzJD/oYaGiu8/z3r7jSCw1vf+gxKgMxs7EfdDj527NjBnDlzfK8fe+wxAO69915+85vf8MknnwAwceLEFsdt2LCB2bNn97ylbQgxRjMi/DIKmzb2aCXbzkyMvgFF6dtnjEIIITqnKgYmRF/Ppup/09nA0/UvFVNfZve9zv2smtzPvEHL5OuSWgUfCiqjIuYRZOh6HijRO90OPmbPno2ut//Bd7SvL0yJu5PCpi+6dcz3Xpvc4X4FlRBDFGMi5/emaUIIIfxoXNQidta9h91jpqMA5L/XzehWvZqmYzuQiivORUBAQC9bKbpiUK/tAhAXlMm0uG+AH0dB62hcmfJTAg0hfqtTCCFE75gM4VyZ9CP8OuVWB3tuBru+LOCf//wnx48f91/dol2DPvgAmBJ7O0NCJnS64FBXTY65jaGhU/xSlxBCCP8ZFn4pE6Ku90tdugaeylhmpn2D8PBw6urqeOWVV1ixYgVOp9Mv5xBtOy+CD4Ni5Noh/0NqSA697QGZGH0jM+K/5Z+GCSGE8LvLE79DTuQ1va4nwJxM01cj2fjFlyxatIiLLroIgO3bt/P8889z9OjRXp9DtE3R+3uQRifMZjORkZE0NjZ2mB+kLR7dxdaa19lR+zagdGndF/BGv4pu5MrUHzI68ioZZCqEEAOcruvkN67gi8r/w6O7uzzp4FQP+bS4e5gQcTPvv/cBR44cwWAwcNttt2EwGPjkk09obGwEYNKkSVx11VWYTKY+ey/ni+7cv8+r4OOUSnshW6pf5Zhlq+8P7exA5NQUXRUj9qNx2Palc9dND5CVldXr9yCEEKJ/mF2VbK1+jYPmdWh4UFBbBSKn7wM6w8Kmc0ncvcSbvNd6t9vN+++/T0FBAaqqcvPNN5OVlcXatWvZvn07AOHh4VxzzTWMGCF5nzpywQcfvrqcFRxq2kilvZBK+0EcHguKohBiiCYpeDRJwaMYET6bz9duYsuWLSQmJvLwww9Lz4cQQgwydo+ZQvMXVNgPUmE7gM3TgK7rBBnCSDKNIjF4JNnhlxEekNDqWI/Hw0cffUR+fj6KonDjjTcybtw4jh8/zieffEJdXR0A48ePZ/78+YSEyGSEtkjw0U1Wq5VnnnkGh8PB9ddfz4QJE/rlvEIIIQYGTdP45JNP2Lt3LwCLFy9m4sSJuFwuNmzYwJYtW9B1ndDQUBYtWsSYMWPOcYsHnu7cv8+LAae9FRISwqxZswBYv349LlfHi80JIYQ4v6iqyuLFi32DTj/++GN27NhBQEAAV111Fffffz/x8fFYLBaWLFnCkiVLaG5uPsetHryk5+Mkt9vNs88+S2NjI/PmzWPGjBm4NTeltlKKLMepc9ahoRGsmhgSkkZm6FAiAvqvfUIIIfqeruusWrWKbdu2ATB//nwuueQSwHuf2LhxI1999RW6rhMcHMy8BVcSnhlOsbWYRpcZHZ1QQwjpoekMDRlKqLHtRzQNzkaOWY5xwlaKXbNjwEBsUAwZoRmkmJIxqn2y7mufkscuPbR3716WLl0K0QrpizLY3LAFh+ZdD8CgGADvH6Z2cvBqVugwrky8gqkxUwblH4oQQojWdF1n3bp1bNq0CYC5c+f6escBysvLeeOzNzkWdpzmFKvvGcKp+4Sma+gnE6GNixjLlYlXMD4qB7fuYVvtNj6rXMcxqzeZmYrqG2fo0b0DZU2qidkJlzE3YTaJpsR+ec/+IMFHD9nddn6z6neUx1eioKArHf9qFBR0dBKDEng460Gywob1U0uFEEL0JV3X2bhxI59//jkAs2bNYs6cOTS7m3nt+Jtsq9uOond+n1BR0dBIMSVj9VhpcDX67h2dHaejsyh5ITekXkeAOvDTvkvw0QMV9kr+t+Cv1DhqO/2jONupP5KbhtzANcmLZLaMEEKcJzZt2sTatWsByJ6ZzVdRW7B5bL4e8L6moJBkSuQnIx8jNii2X87ZUzLgtJsq7ZX8fv8T1Drquh14AGh4u9jeP/EhH5V+3ActFEIIcS7MmDGDBQsWYI9ysCZkPRa3pd8CD/DmJqm0V/G7/U9Q66jtt/P2tQs++HBqTv634Gksbqtf/qA+LvuUzbVb/dAyIYQQA8HISaOomV6Prur+XMO0yzQ0zC4zfy38O27N3f8N6AMX/CjJD058RLWjBqfVSf4bedTkV1Ozvxqn2cmlv5rF8GuyW5Svya/m8PJD1Oyrpv5wHbpH5xtb7/ftV1B49djrjIkYRWRAZH+/HSGEEH6k6zqvHHsNN24aiurZ++Juag/WYKu1YTQZicyMYuzdOaTNSvcd09Z9YvwDEzu9vwA0FDWw429bqdpbiRqgMuTSNKb84GJM0cGcsJXyaflybkhd3J+/gj5xQfd8VNgrWVWxBh0dR4Od3P/sofFYA9HDY9o95sTXJRz+uBBFgfDU8Fb7dXQcHgcfnljahy0XQgjRH/LN+9ndsAcNjebyZlxWF1lXZzP1sUsYf/9EADb8eC2FHx30HdPWfaIr9xdLpYXVj6yg6YSZSd+ezNi7cjjxdQmffW81Hpd3Jswnpcuoc9b33RvuJxd0z8eGqs99I5GD40K4ZcXtBMeGUHOghhXf/KTNY0beOJpx94zHaDKy9c+bMRebW5XR0NhU8zW3pt3S7hxvIYQQA99nlet894khM9IYMiOtxf6Rt4xm+b2fsP/tfEbcMMq7rY37RFfuL3mv7sVtc3H1q9cRlhQGQOyYONZ+bzVHlh1ixA2j0NH5omojNwwZ3L0fF2zPh6ZrfF690TfOwxBoIDi280AhODYYo6nzmM2tu9lat63X7RRCCHFumF1m9jbkdjgeUDWohCaG4mxy+ra1dZ/oyv2leP0xhsxM8wUeACkXpxKRHsGxdUWAt3d9Q/XnDLCJqt12wQYf5fYK7B57n9WvoHK46Uif1S+EEKJvHWk+2uYMSJfNhb3BTtMJM/vf3kfp5hMkT03u1bmsVRbs9XZiR8e12hc3Jp66gjrf60aXedA/erlgH7scsxzr0/o1NA43S/AhhBCD1THLcd8jlzPt/Ps2Cj8qAEBRFdJnD+XiH0/v1bmstTag7R6S4LgQnGYHHqcHQ6A3i+ox6zFig9ofPzLQXbDBR72zoc0/Kn9qdDX0Wd1CCCH6Vr2rHkWBszs/Rt8+lvS5GdhqrBxbewxd09FcvbuXeOzeKbSGwNYPJE4FHB6HG0OgAQWFemdDr853rl2wj136I0mM1oOEZUIIIQYGTddoa2hFZEYUKRenkrUomyv+eiUuq4v1P/6sV+MwDCfHiHicre9NHqd3posh6HR/gab3X6KzvnDBBh/BhuAeZTPtjiA1qE/rF0II0XeCDSFdWi5j6NwMavfXtDn7satCYoMBsNVaW+2z1VgJjAjy9YDo6AQbTD0+10BwwQYfacFD+jT4UFDICBnaZ/ULIYToW2khQ3wrzXbE4/CWcTU7OynZvpCEUEzRJmoP1LTaV7O/mpgRLcd3pIektSo3mFywwcfQ0PTOC/WCgkJmWEafnkMIIUTfyQht+QXSVmdrVUZzaxxZcRhDkIHIzKhenS99TgYnvirBUtns21a+vQxzsZmhV2T6thkUA6nBqb0617l2wQ44DTYEMy5iLPvNB3zjPw4u2Y+zyYm1xtvtdeLLYqxVFgBG3TqGwLBAmsubObryMIAvQs19aQ8AoUlhZC0aDnjHlEyNmdKfb0kIIYQfDQlOJT4onmpHNQBb/rgJl8VF4qQkQuJDsNXaKFp9hMZjjUz5/sUEhHiXvW/rPrHusTXesRsnO9zbur/kfHM8x9cVseY7Kxl121jcVhf5b+YRNTzal4pdRWVS1ESM6uC+fQ/u1vfSvMS57DPn+17nv7kPS/npiLP48+MUf34cgGELsrzBR1kTe/61q0U9p14nXpRE1qLhKCgMC80c9N1iQghxIVMVlSsTr+Dt4nfR0cmYN4zDnxZS8MFBHI12AkIDiB0Vx0XfnUraZad709u6T5RuOtHidVv3l9DEMOb/cxHb/7aN3c/tQA1QSZ2RxpRHL/aN99DQmJc4t4/fed9T9AGWJs1sNhMZGUljYyMRERF9ei5N1/jv/N9xwlrq99kvPx7xQ3Kixvm1TiGEEP3L5rHxs9xfYHaZ+3ySQmdUVIaFZfLL0Y93aSBsf+vO/fuCHfMB3qj24WHf8m+lOoSfCKVxX8OgT38rhBAXumBDMA9k3nfOAw907z3roWEPDMjAo7su6OADYEjIEO7JuMsvdamohLvDiD0Qzbp163j33Xex2VoPUBJCCDF4TIjKYWHS/HPXAB1Q4BLbVBKCEs5dO/zogg8+AOYmzOaO9NsA7yyVnlBQSDIl8fupv+W6BddhMBgoKCjghRdeoLy83J/NFUII0c9uS7uFeQn9P9bi1D0pbl8MZRtKWb9+/XnRq35Bj/k4296GXP599CWa3ZYujwFRUNDRmR1/Gben30qwwZsopqysjCVLltDQ0IDBYGDRokVMmjTpvOguE0KIC5Gu63xZs4k3jr+FS3N1faygRo++6isoRAVE8uCwB2g6YGb16tUAzJw5k7lz5w64+0l37t8SfJzF4rbwSdkyPq/aiF2zY1AMrZLMKCf/p6ExIiyb61OvY2zkmFZ12Ww2li5dSmFhIQATJkzg6quvJiAgoF/eixBCCP+rc9bx0YmP+bp2Cx7djdLGOmEqKjo6uq4TUmVisjaJKZdP5ZPSZRyxHD29/6yxJKfuOSGGEOYmzOaalEW+L7Vbt25l1apVwMAMQCT48AOHx8GO+l0cbj7Mkeaj1Drr0HQNkyGIjJChZIRmMCVmMqnBKR3Wo+s6X331FRs2bEDXdRITE7nllluIjY3tp3cihBCiL1jcFrbV7eBo81EONx/B7G7yBhvGEIaFZpIZmsEwPZN3XnwbgO9+97vExcVRbC1hV/1uiizHOG4pxqE5MCgqsYGxZIVlMSJ8OBdFX0Sg2vqL6pkByIwZM7jiiisGTAAiwccAVFRUxAcffIDFYiEwMJDrr7+e0aNHn+tmCSGE6GPvvPMOBQUFTJw4kcWLF/e6voEagMhU2wEoMzOThx9+mPT0dJxOJ++99x6rV6/G4+l83QAhhBCD16xZswDIzc2loaGh1/VNmzaNhQsXArBp0ybWrl076AahSs9HP/N4PKxbt47NmzcDkJaWxs0339zl91ptN3PQXMqRpkpsHicGRSUlOJpRkalkhMZjVA192XwhhBA98Prrr3P06FGmTJnCokWLKLXVcaCxlGJLDU7NTaBqJD00jlERqQwJielST8a2bdtYuXIlAJdeeinz5s1r97gGp4UDjaUcaqrA4rZjUFTiTRGMikhleHgiAX5I1y6PXQaBAwcO8PHHH+NwOAgNDeWmm24iMzOzzbJ2j4s15Xt59/hmDjV5p+0aFMU3Bcutewc6hRlNXJ82lZvSppEaEtNmXUIIIfpfUVER/37rVUoTdGqGB1PlMANgUFQUvKk8PCev5QlBEdwydDqLh0whKjC0w3q3b9/OihUrgNYBiFvzsKEyn/eOb2ZvgzeVu4qCqrS8dwSpAVyTehE3p08jKzypx+9Rgo9Boq6ujvfee4/KykoURWHOnDnMnDmzReS6vfYIv8ldQrXDjIqC1kmWPVVRQIf7smZzf9Ycv0SzQgghek7XdT4t3clTuR/hUnS6kk5KQcFkCOCx0ddwXerkDntCzgxApk+fzpVXXslBcxn/nfsexyzVXbp3GBQVj65xU9o0vjdyASHGoG69R5DgY1BxuVysWLGCPXv2AJCdnc0NN9yAyWTi2cLVvF60sUt/OGdTgMywBJ6Zch8Jpkj/N1wIIUSn7B4nv9j7Ll9WHehxHTPjR/LExDswGQLbLXNmAKJdMoTV+lHvf3fz3qGiEG+K4Jkp95EZ1r1sqhJ8DEK7d+9mxYoVuN1uIiIjqL80kVV1+3pVp0FRiQ+K4D+XPEK86cL5XQohxEDg8Lj4/s5X2FN3rNtBwJlUFHKi0vnH1PsxGdrPE7Vjxw7+vvtjCtJ6N5HBoCiEGIL49yWPdCsAkdkug9CkSZN44IEHiI6OJtdU3+vAA7zPD6sdZh7b9RpuTWbVCCFEf/rz/k/Y3cvAA7y9F3kNxTyVv7TDcs1pIb0OPAA8uo7V4+DRHS9jdTt6XV9bZEDAAJKUlMTV99zM21ue8y0kdDbb8WpK3/gK6+EKXPXNqEEBmNLjSL5pGlGXZLcq79E1CsxlvHnsK+4ddnnfvwkhhBBsri7kk9Kd3bpm24prKH5hLc35J1CMBqIuziLtwXkERIWgobO8bDfzksczI35kq/M1OK38Yd+HvsGrZ2suKKN2XR7mvcU4KxsxRgQTOiqFId+4DNOQ1kkvPbpOtd3MswWr+OnY3ucmOZv0fAww/ypaD6rS7oAkR2UjHpuD2HnjSH/4SpLvmAHAod++T9WK3e3Xe2gtdY7mvmiyEEKIM2i6xlP7P0ZF6fI121lt5uBP3sBRVs+Qb15O0k3TaNh2hIJfvI3m8vZmKCg8lb/UNyvmTP85so4ml63dPpaKJVuo/6qAiIlDSX9kHvELJ9K0r4T8772M9Vh12+8DnfdLtnKkqaJ3v5A2SM/HAFJpb+SLqgOtcv2fKeri4URdPLzFtsRrJ5P/6MtUfrSNhEWT2jzOo2t8cmIH38ya7c8mCyGEOMvWmsOU2eqBrl+zy979Gs3hYsw/7iMowTtJIHRkMoU/f4eaz3JJWDQJHZ0KeyNbag616P2wuh18cmJnh493Em+8mGE/W4wacDoXVMxlo9n37X9T/t5msn56XZvHGRSVD0q28tMx/u396HbPx8aNG7n22mtJSUlBURSWLl3aYr+u6/z6178mOTmZ4OBg5s2bx6FDh/zV3vPa8tJdXZmB1YpiUAmMi8Btaf/ZnI7OByVbe944IYQQXfLxie0YlPZvr21ds+s3FRB58XBf4AEQOSkTU2oM9V8e9G1TUVhasq1Ffesr87F5nB22KXzMkBaBB4ApNYbgofHYS2rbPc6ja3x6Yhcuzd1h/d3V7eDDYrEwYcIEnnvuuTb3/+lPf+KZZ57hn//8J1u3biU0NJT58+djt9t73djz3d76Yx32epzJY3fiarRiL6un4qNtNO44QsSEoR0eU2lvlEcvQgjRx3bXH2v1aKSja7azpgl3g5XQ7ORWdYWOTMZy5PRjDw2dPfXHW5TJqz/eYbDTHl3XcdVbMEYEd1jOobk40lTZ7fo70u3HLgsXLvTllD+bruv87W9/45e//KVv8ZzXXnuNxMREli5dyu2339671p7n9jee6PKY6JIX11N96nmhqhB96UiGfueqTo87aC7l0jYGKwkhhOi9WkcT9U5Lq+0dXbNddd4vhQExrbOZBsSE4WmyozndqIHeW3ajy0q13exLobCvsaTNcSCdtnVDPq7aJlLvmdVp2QPmUkZFpnb7HO3x65iPoqIiKioqmDdvnm9bZGQk06ZNY/PmzW0GHw6HA4fjdNeT2Wz2Z5MGDbfmodFl63L5xOunEj1zJK7aZuq+PICuaejuzv/4quwX5u9XCCH6Q3U719iOrtma0/tIQw1ofUs+te3M4AOg2nE6+OjJdd1WUkvxc2sIHZ1K3LycDssaFbXd99VTfp3tUlHh7RpKTExssT0xMdG372xPPvkkkZGRvp+0tDR/NmnQ6OrjllOC02KJnJRJ3LwcRvz2VjSbk0O/WdLpyoZaD6JjIYQQXdPeoM+OrtmnggrN1XpcxaltZwYeQIueju5e1111zRz69XsYQoMY/osbUAydhQLdz7LdmXM+1fbxxx+nsbHR91NSUnKum3ROGBUDAUrPV6SNnjkKS2E59tK6DsuFGk09PocQQoiOhRq6tibKmdfsgJgwAFx1rR/XuOqaMYSbWgUfoWesvdKd67rbYqfwV+/httgZ8T+3ERgb3ukxmq4R0sX31VV+DT6Skryr4VVWthyYUllZ6dt3tqCgICIiIlr8XIgURWFYeGLnBdtxqtvO08GMF4DsiJ6vWCiEEKJjQ0JjCezCgp5nXrMD48IxRoZgOVTeqpyloJyQYS3vDQGKgfSQON/rUREpqF2YK6k53Rz6zfvYS+sY8dtbCB4a1+kx4O3Nye7Fardt8WvwkZmZSVJSEuvWrfNtM5vNbN26lenTp/vzVOelcZFpnY5YdjW0jow1t4fadftQg4wEp7f/x2TQFZqOVuB0djwlSwghRM8YFLXFjbqr1+zoGSNp3HYYR/XpsRXm3cewl9YRM2tUi+OzwpMwqqd7ykdHDum0XbpH48iTS7EcKCXr59cTNrrzY8402o+DTaEHA06bm5s5fPiw73VRURF79uwhJiaG9PR0fvCDH/D73/+e7OxsMjMz+dWvfkVKSgrXX3+9P9t9XpqbNK7TXBzHnlmFx+ogPCeNwNhwXPUWajfkYy+pJe3BKzAEt73qoaJDYq3C0m1LWR6wnNGjR5OTk8OwYcNQ1XP+9E0IIc4bVyaP981e7Oo1O/n2S6n/6iAFP3uTxMVT8didVLy/leCMeOKuHO+rW0HhquTxLc43N3Eszx9a02GbSl5cR8OWQ0RNG4672U7N+pbrh8XNHdfmcSoK46OHEhXYeiZOb3Q7+NixYwdz5szxvX7ssccAuPfee3nllVf46U9/isVi4aGHHqKhoYGZM2eyatUqTCYZa9CZKTHDGBIcwwlb++M2Yi4bTc2avVQt343HbEMNDiQ0O4kh988huo21XU7RFVicdBFNdSeor68nNzeX3NxcQkNDGTt2LOPHj/cljhNCCNFz16RO5rnC1bg0T5ev2UHxEYz6010Uv7COEy9/jhJgIHJqFukPXtFivIdBUbgmdXKL8w0Ni2dyTGaHi9hZj1YB0LD1MA1bD7fa317woaFz61D/P7lQ9M6mR/Sz7izJez5aVbaHX+e+59c6DYrKpOgMnpv6AAAnTpwgLy+P/Px8rFarr1xMTAw5OTnk5OQQG9t6oSEhhBBd84+CVbxR9GW3ZzJ2REHhzowZfH/Uolb7dtUd5ZFt//bbuQAMKKSFxvHWjEdbPOZpT3fu3xJ8DDC6rvOjXa+zuaawR0lj2hKkBvDerB+QHBzdYrvH4+Ho0aPk5eVx8OBBXC6Xb19KSgo5OTmMGzeOsLAwv7RDCCEuFHaPizu/+jtltnq/TFNVUUgKjuKdmd/HZGj78fqf8j/mw5JtfpsWq6Lw8vTvdHm8hwQfg1yto4n7Nj9PtcPslwDkDxNu58qznhGezel0cvDgQfLy8jhy5IgvX4iiKAwbNoycnBxGjRpFUJB/p1sJIcT5qsBcxoNb/oVTc/cqIFBRCFCNvDDtoQ4DAavbwYNbX+Boc6Vf7h0/HHU1d2TM6HJ5CT7OA+W2eh7Z+iKV9sYe/dGqKOjAr8bdyDVDJnda/kwWi4V9+/aRl5dHaWmpb7vRaGTUqFHk5OSQlZWFwdDzvCRCCHEhyK0/zvd2vIxTc/coIDAoKoGqkb9P+SYTozM6Ld/gtPLd7f/hSFNFj+4dCqAD38m+qturoEvwcZ5ocFr58/6P+awiD7UbGeZUFBJMkfxm/M1cFDOsV22oq6sjLy+PvLw8amtPr3wYHBzM2LFjycnJIS0tTQaqCiFEO4otNfwmdwn7Gkt8N/fOnCo3JnIIv825haFh8V0+n9Xt4NmCVbxfsrXb947wgGB+Me5GZieO6fL5TpHg4zyzseoA/zm8ngPmUgyKiqbrrQYxGRUVt64RYQzm5qGXcG/m5QQb234u2BO6rlNWVkZeXh779u3DYjk9dz0qKopx48Yxfvx44uO7/g9ECCEuFB5d46OSbbxR9CVltnoUDfQ2shwYFBWPrpEcHMXdGbO4MX1aj1asBe8g1Kd3f0yBqxpFPxn0nPU98dS9I9gQyOIhU7g/ay5RgSE9Op8EH+epg42lfFl9kAONJygwl2P3ODEoKikhMYyNHMLE6AwuTxzTpex6vaFpGkVFReTl5XHgwIEWScuSkpJ8A1Xl8xNCiJaOFhXx9NJXaIhVCR2ZwjFLNS7NTYBqJCMsnrGRaVwcm8XU2CzUHgYdZ3r11VfZV3GU+uQAKo02XPHBuFUdFYV4UwTjotLJiUrnisRxvf7CKsGH6Dcul4uCggLy8vI4fPgwmnb6mWZmZiY5OTmMHj1a8rwIIQSwZs0aNm/ezIQJE/o8+WZjYyN/+9vfADAYDHg8Hr73ve8RExPTJ+frzv27b78ii/NeQEAA48aNY9y4cVitVvLz88nLy6OkpISioiKKiopYvnw5I0aMICcnh+zsbIxG+bMTQlyYCgsLARgxYkSfnysvLw+A5ORkysvLMZlMREdHd3JU/5C7gPCbkJAQpk6dytSpU2loaPANVK2urubAgQMcOHAAk8nE6NGjGT9+PEOHDu23gaoeTeOIuZa8ugpKmhtwaRohxgCyI+PIiU0iKThcBs0KIfzC4XFzsKGKfbUVVNmb8Wg6EYEmUg0myuprCVZVsrKy/HKuSmsTeXUVFDZUY3W7fOMBNV1nT8EurDEGMqMM2BsUJicnDZjrnDx2EX1K13UqKyvJzc1l3759NDU1+fZFRET4BqomJvZ8Rd+OlFoaeevQHt46tIsGpx3wDrAC0NHxnPzzz46M45sjp7A4YyyhAf4bqCuEuHDsr6vk9cKdfFS0D4fmQcE7gBTFGwxoJ683GXogP7vsGuYNycbYg7W17G4Xnx4/wCsF29lf702bruIdUNrihn5GviYd71jT2SlZ3DtyMrOSh6H6ORCRMR9iQNI0jePHj5Obm8uBAwdwOBy+fQkJCb7U7pGRkb0+l1vT+Of+zfwt90t08P2jb8+paW1xplD+fMnVzE71z7cSIcT5z+y08/ud61hyNNc3W6UjKqABo6ISePrSaxkVndDlc31dcYwfb15GubWpW9NoTzEoCh5dZ0r8EP4y/RrSw/33GEaCDzHgud1uCgsLycvL49ChQ3g8Ht++9PR0cnJyGDt2LMHBwd2uu8Zu4b7177KvvrLbx576x/yNERfx68lXYpAVf4UQHdhfX8k3179LrcPa6ZecsxlO9jz8dspV3DXiog7L6rrOn/Z8zj/3b+lR0NH63CpGReEvl17L1UNH96quUyT4EIOKzWbjwIED5OXlcezYMd92VVXJzs4mJyeHESNGEBAQ0GldtXYrN695jZLmBt8jlZ66MXMcf55+jd+7JoUQ54f9dZXc+tkb2D2uXl9vfj15HveNmtrmPl3X+e/ta3j90K5eneNsp65sf5txHddljO11fRJ8iEGrsbHRl9q9svJ0z0VgYCBjxowhJyeHjIwM1DZ6JDRd57bP3mB3TWmvLwSn/HTibL491v/LSQshBrdGh40rlr1Ag8Pmt+vNq3Nv47Lk1lmpXyvYyX/vWOOXc7RFVRQ+XvBNxsUk9aoeCT7EeaGqqso3ULWxsdG3PSwszDdQNSnp9OjtVwp28NsdnwGg2R00Lv8Sx+ESnEdPoFlsxD50E+GXtV7nxrxmM01rt+CqqsMQHkrotByibr4S1RSIUVFZcfUDZEfG9c+bFkIMCj/6+lOWHsvHdriE5q92Yd9/FHdNPWpYCEFZaUTfchUByS2vGx1da1QU4oJDWXvtQ4QHnF7As7ipnquWvYhD87R5XQu+aDS6y93iOlf7wgftN1xVUUOCCBiSSOTVlxEyaRQGRSEzPIblix4gsBdrdknwIc4ruq5TXFxMXl4e+fn52O123764uDhvb8ioEVy1/nUcHjcArup6Sn/4ZwyxUQQkRGM/UNRm8FH3zirMyzYScvE4TGOzcJVW0bRuK6YxWST97D4MisL0xKG8fsUd/fqehRAD156aMm5Y/SoAVX9/E0dhMSHTxhGYloSnsQnzZ1vQ7U6Sf/MIgWne3oTOrjXg7YF4ZMx0fjLxct+5Htn4AWtPHMKj621e14BW1znlrJ5hW94hLJv2ABAyZQxBozJp3rgLV3E58d+/k9Cp41CAX0+5km+OnNLj34skGRPnFUVRGDp0KEOHDmXhwoUcOnSIvLw8CgsLqampYcOGDezf9QWOOKPvIaYxKpwhzz6OMSocx9ETlP/6/1rV6643Y175FaEzJxH/yC2+7QFJcdS99inWXQcIuWg0X1Uco8hcR2ZE32QFFEIMLq8V7vTNaolYOJOg76ainJE8MfSS8ZQ+/gyNn24k/ju3dvlao+k6bx7axaM5MwgyGCm3mvms5JBvcGlb17Xou68mcsGMFte5sJmTWrS3Yel61PAQtCYrMfdcizE2kvDLJlPy6B9p/nI3oVPHAfDywe3cO2Jyv+QCkaH8YlAxGAyMGjWKW265hR//+McsXryYYcOGURBp4MwZ7kqAEWNUeId1OQ4Xg0cj9JLxLbaHTve+tmzJ9Z5TUVhyJNe/b0QIMShZXE4+Pb7fN53WNGJoi8ADvEFFYGoCrjJvDo6uXmsAGp121pUeBuDDo/taLATX1nVNDel86QrN6kCz2DGNzsQYG+k7Tg0KQgn0tl0Hipsb2FF9otP6/EGCDzFoBQUFMXHiRG64/VbMgQp0M1rXXd7pvaf+8Z2iBHpn1TiKSgHw6Drbq0v80GIhxGC3r64Ct9ZxHg9d1/E0NqOGh3pfd/FaA94kiLuqva93VJfgj5ERAUmxoGmokeG4qutxllVR+8rHaDY7EfNn+MqpisKumtIOavIfeewiBr38usoezXg/NRjMUXic4DGnk4o5Co4B4Kk3tziHpusy7VaIC9y+uopO82xYNu3BU28m6uZ5QPeuNW5dY29tGQB7a8t7mc3DSw0xgaJg3ZKL9WQvixoeQuLjD2DKTveVU4B9tRV+OGPnJPgQg16lranzQm0IykwlMCuNxmUbMURHYhozDFdZFbUvfwwGA7rT7Str87iwuJ0tRqELIS48FbYmDIrSbkIxZ1kVta9+QlB2OmGzvInDunOtASi3mPFoGvUOW6/bq1nt2PYdxhgXRdCoTEImjUSzOTGv2kT1394k6VcPeXtG8PbyllobO6nRPyT4EINeb+bYJ3z/TqqffYfaF09OTVNVIhbOwH6wCFd5TYuyWiddrUKI819HWUzdDU1U/e9rqCEm4h+9s8Wsk+5cazy63usMpqdYtueD24MaGkz8wzf7todMHk3pj/9C/ZI1JHzv9Gw+j9Y/E2Al+BCDXlgveiOMMZEk//phXBU1eBqaMCbFYYwKp+S/niQg6fQcfQXY/OVXDElKJjExkdjY2DYTnQkhzm9hAYFthgWa1U7Vn19Bs9pI+tVDGKNbTjXt6rXm1DmMikqgasCpeeiNps+3e+uc3XIKrSEshKARGTgKj7fYHhHYP727EnyIQW90VNcXZWpPQFKc7wLgLK3E09Dk6zIFCHdqbN30NVtPvjYYDMTHx5OYmEhCQoLv/8PCwgbMktVCCP8bHZWI+6yF4zSni8q/vIaroobE//cAgantr9Ld2bVGRSHWrvH6668T6fFQ3YtFtt31ZpyHir0v2roueTzoZ/ToGhWVsb3MctpVEnyIQS81NIKIgCDMLkfnhTuhaxr1b69CCQog/IppABhQmBibwkVxcVRVVVFVVYXT6aSiooKKipaDs0JCQloFJAkJCV1al0YIMfCdnYJc1zSqn30Hx+FiEn54T4sBnB1p61oDoOkaemk1RY0asXEGagJU9B5+ofFN4T052DR87sW+L0fu2kbsBccwjcjwlXfrWq9TrHeVBB9i0FMUhWuGjuHdI3tajP8wr9mMZrXhqfcOSLXtPoinzjuYKuKqS1FDTNS+9im6y03g0GTwaDR/vRfn0RPEPXwzxrgoADzo3HPRTOYNyQa80+gaGhqorKyksrKSqqoqKisrqaurw2q1UlRURFFRUYs2xsTEkJiY2CIwiY6Oll4SIQaZIWGRjIlO4GB9NRo6dW+uwLbrAMGTRqE1W2n+aneL8qcSfnXlWuOlsDh7AqNT0rgoUOPRPS3XdDn7umZetQnLpt1oNifQ8jpn2Z6PITqC4PHZNH+xk8on/0PIlLFodgdNa7eiO91EXnc6m2qQwchlyZl+/o21TYIPcV64a8Qk3jrc8h9944ov8dQ0+F5bt+dj3Z4PQOiMSaghJgIzUjCv+hrL13tBUQjKGkLi4/e3mA6XGBzGnJTTrxVFITo6mujoaEaNGuXb7nK5qK6ubhGQVFZWYrVaqauro66ujgMHDvjKBwQE+HpGTgUmiYmJBAcH+/vXI4Two2+OnMpPtywHwHm8HPDe9G27D7Yqeyr46Mq1xqAozE7N4s7Z1wEwUdf5y+HtHG+u95U5+7rmKq7Adcb5zrzOAUQsnEn07fMJHJpC8xc7qH9vNQBBw4YQ98jNmEZl+s59U2YOEYGdJy3zB1nbRZw3vvX5Ej4vO+K3FSZPeWLaQu4YPrHHxzc3N7cIRk49uvF42h5IFh4e3qKHJDExkbi4OAy9WPBJCNF7uq5jNpspLi/j/j0rqfU4/DQnxUsBPpx/LxPjUgCwWq08sexd3nT1fe6NANXAmmu+RUZ4z5eRkLVdxAXpiWkLueLTf2FxOf1yQTAoChcnpHN71oRe1RMWFkZYWBjDhp1eKlvTNOrq6lo9umloaKCpqYmmpiYOHz7sK6+qKnFxca2CkvDwcHl0I0QfcDgcvn+XZ/7/qYUtp5oUVqYau51ZuT0KCg+NmeYLPPbv38+KFSswWiykJRspDVXpy8n+P5s4u1eBR3dJz4c4r6w9cYiHv/gAHb1XAYhBUYg1hbJ0wb0kh/Tf3+GZF7wzL3oOR9uDaU0mU5sDXIOCJBmaEF3R0ReBtpz6IpCQkMDmIAcfNB5vs1x3GBSF8bHJvD3vLtx2BytWrGD//v0AxMfHc9nCq3hk72oqrM2+NWX8RcX7qOeFy27C0Mv0Ad25f0vwIc47y44f4PubPgY6TgjUnlOBxzvz7hoQK9me6uo9++JYW1vbbuKz6OjoFgFJYmIiMTExkptEXNCam5tb9WR05xFoQkICcXFxGE8uJKfrOn/Zu5Hn8r9GgR594VFRmBCXzMuzb6Xk0BFWrlyJ1WpFURRmzpzJZZddhtFo5ERzI3esfZNyq9lvj5YV4LKUYfzrspsIMvT+QYgEH+KCt7umlB9u+oSS5sYuZwpUUNDRuXJINn+4eCHxwaF93Mrecbvd1NTUtLqYNjW1nW7eaDS2yk2SmJhIaOjAfp9CdNeZg7/P/PdhtVrbLN/W4O+EhARCQkK6dL5lx/bzi22rsLidXQ4MTqVof2D0xTycNZn1q9f4BqQnJiayePFikpOTWxxT77Dy6+1rWHb8QKfry3R2boDv58zikbGXEKD6ZzyZBB9CAHa3ixcObOXVgp3UOawYFbVVciAF70qOHl1ndHQC3x17KYvSRw3qcRRWq7XNb3cul6vN8qGhoa0Ckvj4eN+3OyEGqo6mvbd3a4uNjW3VK+iPae/VNgvP5H3F+0dzsXvcKLreKj+HigKKt92zkjN5dNxMAirqWLVqFTabDVVVmTVrFrNmzepwgPlnJw7x3L5N7K0tx3Dy+tUZg6Jwqti8Idn8YPwsRkf3PkHjmST4EOIMLs3DuhOH2VZVzO6aMoqbG3DrGsEGI6OiExgfk8zc1OG+gV7nI13Xqa+vb/Mi3RZFUYiNjW3V5RwVFTWoAzMxeNlstlZBdWVlZbtB9blK+NfkcvD8xtWsK8ilISIIlykATdcJDwgiJyaJ8bHJLEwfRQxGli9fTkFBAQBJSUksXryYpKSuJ/nKr6tg7YlD5NZVkF9XgcXtQtM1glQjHl3Ho2sYVZXIQBMTY1MYH5vMoqGj+mwcmwQfQogucTqdbXZP22xtr6YZGBjY6oKemJiIydQ/uQHE+c/j8fgeJ575N9ne48S2ljo49TjxXAXKn376Kbt27WLGjBnMmzevxT5d18nNzWXVqlXY7XZUVeXyyy9nxowZg346vUy1FUJ0SWBgIKmpqaSmpvq26bruG5h35sW/uroap9NJSUkJJSUlLeqJiIholcE1NjZ20F9MRd/RdZ2mpqZWf2c1NTXtDqSOiopqFfgOxEUey8u9icdSUlr2pprNZpYtW8ahQ4d8+xcvXkxCgn8ffwwGEnwIIVpQFIXw8HDCw8MZPny4b7vH46G2trZV13djYyNmsxmz2ey7qIL3G2lbuUkulMX3dF2nvLmJfVWVHKqrw+52YVRV0iOiGJeQyLDo6F5PbRwsTk0hP/uRyamcGWcLCgpq9XfTn1PIPZrG0fp69lVVUmxuwK1pmIwBZMfEMC4hkeQwb34dXdc53tjAvqpKihrqcXo8GBWFvXU1RKuKb8Coruvs2bOH1atX43A4MBgMzJ49m0svvXTABU79RR67CCF6xW63t/ks3ul0tlk+ODi4zQGugYG9WL5zALE4nSwtOMCre3ZxuN47psagKKcX9Dr5rT7aZOLOnAncMW48KeHnx7WuuzkzFEVpM0CNiIg4JwFqWZOZt/fl8lbeXupPBkbGk8GBruu+gZ2ZkVEMj40jt7KCSktzu+VSwsK5deRoTEeKKD+53lNqaiqLFy8mPj6+X99bf5AxH0KIc0rXdRobG9vMTdLeJefU4ntn3oQG2+J764qO8LO1q6mz2bqU90FVFFRF4bFLZvCti6b4bmCDgcViafPRnNvtbrN8eHh4q0cmZ+bMOJfcmsaLu7bz9Jav0XS9R/mB2qXrGIHpdhcPzbyM6dOnn7e9HRJ8CCEGJJfL1eZgQovF0mb5s/MvnPr/ruZf6C8eTeO/v1jPW3l7e5x/YXxiEi9ddwMxwQPrvZ3KmXF2z1ZXP7Pu5szob7VWKw988iG5VZV9fq55mVk8s/BqTMa+nXFzrkjwIYQYVAbzt2hN1/nRmhV8UnCw1yn9h0ZFseTmO4g+Bysb9yRnxmDvraqzWbn1/Xc43tDg9wUp26IqChenDOHlxTcSNAB6fPxNgg8hxKB35viBM9e76WjNjbNzk/TH+IHntm/hL5s3+aUug6IwJSWVN2+8FbUP22yz2dpcabmzcTpn/m4H+zgdTde568P32FFW2i+BxymqonDLmHE8ecVV/XbO/iJTbYUQg96pBbzi4uIYO3asb3tHMyeqq6uprq5uUU9fzpw4WFPN37Z83Wk5R8kJGlatwX60CN3lxhgbQ/illxB5+awW5Ty6ztbSE7y9L5e7cnq3mjKczplx9u/KbDa3Wf5Uzoyze5XOxxlKb+XtZWvpCQA0h4PGdZ/jOF6Mo7gYzWoj7s7bCJ821VfecbyYpu07sBcewVVT492oaShBQQSlpRJzw2KCUr1Ta5t378G8YSOuqipQVAKTk4i8YjYhY8eg6Trv5uexaPgIZg3N6O+3PWBI8CGEGFSCgoJIS0sjLS3Nt+3U4ntn32RrampwOBwUFxdTXFzcop6oqKhWQUl3F9/77RfrOy1jPVhA5QsvETQklairrkQJCsRdU4unobHdY5748nMWjxxNWBd7FnqSMyMyMrLN938h5GZpcjh48qsvfK89zRYaVn+GITqKwJQU7IePtDqmYd0GHEXHUIODQdMITE3BVVOD7nKhBJnQmryzXho3fkXdB0sJHjOa6GsWobvdNG/bQeULL5Fw/72ETshBVRR+uWEtG+59oE97uAYyCT6EEIOeoihERkYSGRlJdna2b3tH2TIbGhpoaGjwpbcG7zf/tga4hoWFtTrn4bpa3zfn9mh2OzVvvEPI2NEk3PcNlC4GNna3m6UH93P3+Imt9jmdzlaPTDrLmXH2+0lISLigs9IuLTiA/YzxRMbICNL+59cYIyJwFJdQ9pe/tzomcs7luMaPo+b1t31BhKuqmtKn/oIaFETwqBEAmDd+RWB6GokP3e/rLQq/5GKKf/0/NG/bQeiEHDRdp8TcyKbi4xds74ffgw+Px8NvfvMb3njjDSoqKkhJSeGb3/wmv/zlL8+7bjshxMBmMBh83+rPdGqdkLPHPLhcLsrLy30ZKk8JDQ1tdQN/51BBp4t6Ne/YhaepieirF6KoKprDgRIQ0KUg5M28vSxIGdKqN6e+vr7N8m3lzEhISCAyMlKuvWd5O29vi9eK0YixkzEKpswM6j76hKChaYROyEHXNAyREQQkJeKqPD1TRrc7MMTHt/idqyYTalAgyhnryhgUhXfycyX48JennnqK559/nldffZWxY8eyY8cO7rvvPiIjI3n00Uf9fTohhOi24OBgMjIyyMjI8G07c/G9M3sW6urqsFgsFBUVUXQyURTA8vBgPMaOH1HYCg+hmEx4Ghs58Z9XcFVVowQGEjZ1MjE3XIfaziJnOlBQU83fn3uuzYt0WFhYq0cmAyVnxkBndbkoqK3p9swkzW7HUVxC+Mzp1H26AvOXm9AdDlAVAs5YDM40PAvL3lwaN35FyNgx6G435o1fodnsRFw+01fOo+tsLyv107safPz+l/r111+zePFirr76agAyMjJ4++232bZtm79PJYQQfqMoCjExMcTExDB69GjfdpfL1WqAa1lFBXWGznsv3NU1oHmo/PfLhF8yjehrFmE/fOTkzchGwr13d9QgGgMDyIlrvWjaQM2ZMRgcqKnq0ZRoV00t6DqWXXtQVAMx112Ns6ycpk2bcZWVYz1wkJDRo4i9aTEei4W6D5ZS98FSANTQUJK++zCmzIwWddZYrdRYrcRdgJ+n34OPSy+9lBdeeIHCwkJGjBjB3r17+eqrr/jrX//aZnmHw4HD4fC9bm8UthBCnAsBAQGtFt+rs1p54d/Pd3qs5nCiO12Ez5hO7E3XA3i77N1umr7egmvhfAIS2k+zPf+mG7l6xKhevwdxWmVzc4+O00/epzSLleQffg81OJi6T1cQNDQdZ3UNDavXEjJ6FEpgIAEJ8RijIgkZOxrN7qDx8y+peulVkh/9LgHxcWe1p+mCDD78nuP1//2//8ftt9/OqFGjCAgIYNKkSfzgBz/grrvuarP8k08+6RsoFhkZ2WIEuxBCDERtzx9pTQnwfr8LvWhii+2hkycBYD92vMPjB1QSpvNET3N6nBqvYYyNwRgTTeW//oNqMpHwwL2E5ozFUVyC7vFQ9fJruOvrib/rdkInTiD8kotJ/t630d0e6pev9Ft7Bju/Bx/vvfceb775Jm+99Ra7du3i1Vdf5X//93959dVX2yz/+OOP09jY6Ps5e6luIYQYaMICu5Ye2xAZ6f3/8PCW20++1qy2Do8PHcRJvAaq8MCe5XcxRHoHpKqhoVT+899oNhtJ3/4WxshIDGFh4PHgLK/AdqCAkHFjWx4bGoJpWCb2o8da1dvV6dTnG78/dvnJT37i6/0AyMnJ4fjx4zz55JPce++9rcoHBQX12zLJQgjhDyZjAGkRkZSY28/VARCUNgR7QSGexkZITPBt9zR6jzOEhXZ4/Oi482/l03NtVFxc54XaYIyMRA0Pw1lahmJQSfrOwwSeHGjqMZtRAoxopzLEtpFbRfd4Wm0PMhgYGhnVo/YMdn7v+bBara2S9BgMhnYT3QghxGA0MSkZQydTWEMnebOUNm1pOeC+afM2UFVM2VntHhtlMpEY2jq/iOidxNAwonqQ40TXNNTAQPB4iJp3hW/wqKfZgiUvH1P2cAIT4kFRsOze22I9HHdDA/ajRQQOSWlR5+j4BAzn6Qq3nfF7z8e1117LH/7wB9LT0xk7diy7d+/mr3/9K/fff7+/TyWEEOfMwuEj+LTwYIdlgoakEjbtYpq3bqNK0zBlDcN++AiWPblEzpuL8eRjmbMZFIXrRoyS/Bx9QFEUrh0xirfy9rYYb2He+BUem93XK2Xdtx/3ySy0kZfNoH7lGty1dWA0Ur9mLY4TJ1ACArAfOozuchF9zSIMYWGEXXIxzZu3UvHcPwkdn4PmcGD+6mt0l4vIeXNPtwO4Jntkv773gcTvwcc//vEPfvWrX/Gd73yHqqoqUlJSePjhh/n1r3/t71MJIcQ5M29YFrHBIdTarB2Wi7vtJozRUTRv244ldx/G6GhibriOyNmXtXuMR9e5K2ein1ssTrk6bSiv5+5psa1xwxe4604ncLPm5mHNzQMgbMpFOEtP5uQ4mRnVmruvxfGn1nWJu+VGglKSadqyjbpl3gGmQelDiL/7DoKHn+7pCjAYuGl0y7EhFxJZ1VYIIXrojdw9/PrzdX6t06AozBs2nOevvs6v9QpvaoeNGzeyZcsW1gUHUhJgQD8HvUsK8NDkqfxsRvsB6GDUnfv3hfmwSQgh/ODOnAlMTUntdOxHVylAaEAgv5tzhV/qE166rrNnzx6effZZvv76azRN447EZEIDA+nv0MOgKAyNiuIH0y7t5zMPLJKLVwghekhVFP46fxHXv/MmDXZbr3I2KHjHIzy9YBHxIR3PghFdd+LECVauXElZWRkAMTExzJ8/n+zsbEYcL+LBT5eCrvdLThVVUQg0GHl24bUEXeCp8OWxixBC9NKRulru/HAJdTZrjwKQUz0nzyy8hoXDR/i7eRekpqYm1q5dS25uLgCBgYFcfvnlTJs2DYPh9Jo8Kw8X8ujKZUDfJvwyKApBRiOvXn8Tk5NTOz9gEOrO/VuCDyGE8IMqSzM/X/cZ648dBV2HLj6KUYChUdE8fdVCJiQl920jLwBut5vNmzfz5Zdf4nK5AJg4cSJXXHEFYWFtT13eW1HOD9es5HhDfdd7QLr4GSt4M9VOSkrmf69aSGZUdFfPMOhI8CGEEOeArus899kaXtq3lwajAYOioLXRpW9UVdyaRmxwCN+cOIlvTZpywXfD95au6xQUFLBmzRrq672zVoYMGcKCBQtarMvTHofbzb937+CVPbuptVl9n9GZlJM/GqDqOpqitFkOTn/GQyIieHjyxdw+Nue8z+nRnfu3/LULIYQfBRQd47omGxmXXEx9ZAR7Kyo4WFuN3e3GqKoMjYxiYlIy01KHMCdjGAFnPAIQPVNVVcXq1as5evQoAOHh4cybN4+cnJwu50oJMhr57tRLeOiiqWw4dpStpSfYU1HO8cYG3JqGyWhkVGw8SlUVoVU1XDl+AjETx7OppJi9FeUcqa/D6fEQaDAwPCaWCYlJzEgbyqVp6aiSr6UVCT6EEMJPSkpKqKioIMBo5NZZlxNyAa5W2p9sNhuff/4527dvR9d1DAYD06dPZ9asWQT2cM2UAIOBq7KyuSoru9W+kpISXnrpJVRV5fLLLiMqKopZ6Rm9fBcXJgk+hBDCT7Zu3Qp417SSwKPvaJrGzp072bBhAzabd3G+UaNGcdVVVxEd3XdjKjZu3AjAhAkTiIqK6rPzXAgk+BBCiC7QdZ2yBjP5ZVUcqa7D4XITYDQwNCaKsSkJRAWoHDhwAIBp06ad49aeWw6Xm4LKGvLLKqlpsqDpEBEcxMikOMYkJxIV0v21VU45duwYq1atorKyEoD4+HgWLFjAsGHDetXmqqZm8ksrOVRZi9XlwqiqpERFMDYlgaz4WCoryjl8+DCKojBr1qxenUtI8CGEEB1qsjv4aHc+b2zZQ0ndydVoVQXlZHqqU4MNwwOMDPUEMDs9icTExHPW3nMpv6ySt7buZdnegzg9HhTwDbLUdB3t5PyGS4alcfclk5g9MrPLgzAbGhr47LPP2L9/PwAmk4k5c+YwZcqUVouZdpXd5WZFXgGvb97NwYpqwDsl9tQ4kVOfbVhQIDlhRmJ0hVkTJ/Rp78qFQoIPIYRox6p9hfz3x2tpsjtabPdoOpw1h6XJ5WYfQRQUm4nYvJu7pk1EVS+MgYaNNjtPrvicj/ccwKAqJ38/3t9QWzNBthedYMvREsYkJ/DHm+aTndj+MvdOp5NNmzbx9ddf43a7URSFyZMnM2fOnF492tp6tIT/98EqKszNnPkxeXTdO432DM0OJ1scDnTCiFNDWeh2Eyizk3pFptoKIcRZnG4Pv/xoDZ/mHvTlaeiuqRmpPHfXYsJNQf5u3oCSX1bJw68tpd5q8/VsdNWpHqRfXzuXW6bktNin6zr5+fl89tlnmM1mADIyMliwYEGvepZ0Xefpzzbx4pfbUU9Ohe4OBciKj+HFe28kKTK8x+04H0meDyGE6CGXx8P3317G54VHz/4C3C2qojAyKY7X7r+FsPM0AMkvreSe/yzB4XZ3+yZ+tl9dM5c7p00AoLy8nFWrVlFcXAxAZGQkV111FaNHj+7y1Nm26LrO75dv4K2te3vVVoOqEB8exjsP3U5iRNuJyy5EkudDCCF66G9rN/F5wdFer/Wh6ToFFTX87IPVPHvntb26aQ5E9VYbD772kV8CD4D/WbaelLBgzEcOsnv3bgACAgKYOXMm06dPJyAgoNfneHtbbq8DD/A+dqtuauaR15fy3iN3SK6WHpDgQwghTtpdXMbLX+3EWlZMY+52rMcO42qsxxAcQnDqUOJnLyQwNsFXvmHXZhr37cRZW4Vmt2EMiyRkaBaxl80nMCoGTddZf/AIK/IKuHr8qHP4zvzvD8s20Giz43bYqd28AXvpcWxlxWh2G0nX3k7UhItblC/75G3Mudtb1RMYm8Cwb/8/FOBH7y5jodpEgOKdrjxv3jy/9YCX1DXwp1VfYOviZ3vw94+1W1dI5gjS73qEgxXVvPTVTh6+/OJ2y4q2SfAhhBB4u+R/9+l6FEWh7uv1WE8UETF6AkEJKbibm6jf8RVF//4rGfd9n6AE7xos9spSAqJiCRsxDoMpGFdDHQ27t9B8eD8ZD/6YgPBIFOB/lm3gyjHDz5tBiruOl7I8rwAAt9VC7ZdrMEZEY0pMwXr8SLvHKQYjSdfc2mKbGhQMeMfVWHUoDY3lt7ddR3p6ul/b/OfVX+LWtC5/tsmL72xVh728hPptXxI67PTif8+u38yNF40lPlxWIu6O8+NfghBC9FJeaaVvumX0tMtJueFuFMPpS2TE2IkU/evP1H69jpTr7wYgaeHNreoJHzmOY/95GnPuDmJnXIGOdzbI6vxDXDthdL+8l7725tY9vlktxrAIhv/gNxjDIrCVlXD8pafbP1BVicyZ0kHNCgVuA8ldWIulOyrNzaw7cARN17v82bbVTm9gpRAx9iLfNk3X+WDnPh6ZfWHndumu83uVGyGE6KIPdu7DcHLOZUhaZoubE0BgTDyB8Uk4aqo6rCcgMgYAj8Pm26YqCu9uz/Nzi88N88lA6tR0WtVoxBjW9Ucjuqbhcdjb3V9vtbOx8Fhvm9nCx7v3+/67p5+t5nbTdDCXkKHDCIiIOr1d13lne65f23shkJ4PIYQAthWd8N1Q26LrOh5LE0HxSa32eawWdF3D1dhA7ZdrAAjNOL02iKbr5JVW4NG0Qb+yaX5ZVYe/p47oLheFf/45usuJagomYuxFJFxxDWrg6dlARlVlT0kZV4zO8leT2VlcSuu1hc9oVwef7SmWw/vR7DYixk1uta/S3Ex1k0UevXSDBB9CiAuezenieF19h2XM+3bibmok7vIFrfYd/vtv0T1uAAzBoSTMv4HQYSNblHG6PRytruswodZgkF9W2aP8GMawcGIunYMpaQjoOs1HDtKwcxOOyjLSv/EdFNU7Y8StaeSdqPRrm3NPVHQ4bbqjz/Z0mV0oBiPhoye0uT+/rJLZI3uX4v1CIsGHEOKCV9Ns6fDm5KippHLVhwQPySBy/NRW+4fc8SC6242zppLGfTvRnc4266lqsgz64KPK3Nyj4CNh7jUtXkeMnURgTDw1n6+g6UAuEWMn+faVN5r90lYATdNpsLb/mKezzxbA47DTfHg/ocNHYzAFt1mmytzsl/ZeKAZ3/58QQviBp4MbqbvZzIl3/o0aZCLlpntR2nhsEpqRTdjw0cRcMpvUG++l5svV1G//svV52kg1Pth09Lvqrphpl4GiYCkqbHmOHj7WaUtHQVJXPluApgO56G43EeMuanM/+Pf3ciGQ4EMIccELD2o7A6nHbqPk7RfxOGyk3fEQAeGRndYVGBOHKWkIjft2tdoXFhTY67aea/58D2pAIIbgUDw2a4vt/kxJbzSoBLaRBKw7n615307UIBNh2WPbLXM+fLb9SYIPIcQFLyY0mKjglsu8a24XJ979D866atJu+1aHgxHPprlcaG3M6BgxyB+5AIxMim9zsbie8DjseKwWjCGnB2oaVZWxqf5dFTg7MbbF6+58tu4mM9bjhwkfNR61gzwtI5Pi/dbeC4EEH0KIC56iKIwfkoR6MgW6rmmUffgattJjpN70DYKHZLQ6Rtc8rb6xA9hKj+OoKseUnNZi+5DoiPNijZexKd0PDDS3q83ptbVffQbohGadzv7q0TTGpiS0KtsbE9KSfdOou/LZnsm8fzfoepuzXE4JNBgYFhfjzyaf92TAqRBCAAvGjWDjoWMAVK39mObCfMKyx+KxWWnM29GibGTOFDSnk8PP/I6IMRMJik9CCQjEUV1O497tqCYTcbOu9JVXFYWrc86P9OrpMZEMT4jlSFWtb/Jq/fYv8djtuJsbAWg+lI/b7P3v6Kkz8dhtHPv3X7yDTE+mMLccLcBy+AChWaMIGznOV7+iKFwxyn/TbAHmj832renSlc/2TOZ9OzGGRxCS0XabDKrClWOGYzTId/nukOBDCCGAhTkj+cOKz7E4nNgrygDvTbT5UH6rspE5U1ADAoiaNA3rscM0HcxFc7kwhkcQMXYSsTOvJDDq9DdhXde5ZWpOq3oGI0VRuOeSifz3J+t822q3fI678fRU5eaDeTQf9CZVi8iZjMEUTNjwMViOFtKYuwM0jYCYOOLnLCLmkjkoivfGbVAV5o7KIsHPK8VOzRjC0NgoimsbuvTZnuKorcJefoLoaZf72ng2j6b7VuMVXafo+sAaotudJXmFEMKfXty4jb9+tsmvdaqKwvUTx/CHG6/ya73nks3pYsHTL1HdbO316r9nUhWF9x65o0ePdjqzPLeAHy9Z4dc6DarCRempvHr/zefdqsU90Z37t/QTCSHESffNmMLo5Hjf+IDeUhWF6NBgfrbwMr/UNxDous7B/H2Md9T5NfBQgAcvm9ongQfAgrHDGRcTjuLHVhtVlSduvEoCjx6Q4EMIIU4yGlT+cuvVhAYG0tv4Q8EbfDx929VEnDWTZrByOp0sXbqUTz75hDjdyczYEL/UqyoKk9JT+E4fLc7mdDpZsmQJwxvLCEbv9WcL3s/3DzdcxZDozqdfi9Yk+BBCiDNkxkXzxIJLMep6j78lGxSFAIOB/7t7MVMzhvi5hedGVVUVL774Irm5uSiKwty5c/nXow/ywEzvGIme3s8VBSamJfOve64nsIOprD1lNpt5+eWXKSgoINSo8uerZ5EcGYGhh70VqqKgAL+/4SquHn9+DCI+F2TAqRBCnKGxsZFd6z9jvsFGfnAcR5sdKNDlMEQBhiXE8KebFjIqefDnftB1nT179rBixQrcbjfh4eHcdNNNDB06FIAfz5/FqKR4fvvpOmwuV5ezkxpOpmi/f8YUvjd3OkEB/r8dlZWV8c4779DU1ERISAi33347aWlpTBqfw++XbWBFXkG3UsWrikJCRBhP3TSfizPTOj9AtEsGnAohxEkul4uXX36Z8vJykpKSuO+++1i+7xAvfrmdopp6DKqKpmmtAhGjquLWNBLCQ7n30ou4Z/okAtrIqjnYOJ1Oli9fTm6ud8n4rKwsbrjhBkJDW6/eWt1k4bkNm1m6ez9OtwfDyd/JmXx5VHSdmdkZfHfOJUxIS+6Tth84cICPPvoIl8tFfHw8d9xxB9HR0S3KbDh4hOc/30peaSUG1RuEnH1HPPXZRgQHccfFE3hw1lRCJZtpm7pz/5bgQwgh8N4QP/74Y/bu3UtwcDAPPfQQUVFRvn07jpey6dBx8korKKyswen2YDSoZMRGMyEtmYszhzArOwNDO+uDDDZVVVUsWbKEmpoaFEVhzpw5zJw5s9PBlU12B6vzD7G3pJw9JeXUNlvRdI2woCDGpSYyLjWR+WOzSYuJ6pN267rOpk2bWLfOOxU4KyuLm2++GZOp/XE3+8uq2HDwCPtKK9lfUY3d6cKgqqRGRzBhSDKTh6ZwxeisPnksdD6R4EMIIbpp69atrFq1CkVRuPvuuxk27MJcHl3XdXbv3s3KlSvbfMwykHk8HpYtW8aePXsAmDp1KgsWLEA9TwLCga47928J44QQF7xjx46xevVqAK688soLNvDozmOWgcZqtfLee+9x/PhxFEVh/vz5TJvWN7NnRO9J8CGEOK/YnW4OlVZzsLiKGrMFXYfwkCBGDIlndFoCEaEtu98bGhpYsmQJuq6Tk5PDJZdcco5a3jP1TVb2F1dxqLQai82JqiokRoczOj2B4SlxBBi7NvaksrKS999/v9uPWXpL13Uq6ps4UFzF0fJaHE43RoPKkPgoRqcnMDQxutNHWbW1tbz11lvU1dURGBjIzTffTHZ2dp+2W/SOBB9CiPPC/uMVvPfFXlZuO4jLo6Eo+G5amqb7ZjRMG5XO7bMnMjMnE83j4b333sNqtZKUlMS11147KBJGudwe1u8+zDuf72bv0XIAVFXxDeh0e7wDPU2BRq69ZCy3Xj6erJS2V9Q9V49ZLHYny7ce4O0Nuzle6U3NblAV3+//1HuICgvmlsvGc+PMHBKjw1vVU1RUxHvvvYfdbicyMpI77riDxMS+SVQm/EfGfAghBjWzxc6f3tvAim0HMahKp1M9VVVB03RGpyVweZqR8qMHCQkJ4cEHH/QNMB3I8o9V8MuXV3G8qr5L00RP/U5umz2RR6+fSXBQgG/fuXrM8vneI/zu9TU0Wrwr3XZ2E1IVBVVV+K/FM7jriot8QeWuXbtYvnw5mqaRmprK7bffTliYf9eFEV0nA06FEBeE/GMVPPrcUhot9i7najhFVbzf+idG2vnVI3eSkZHRN430o9c+28EzH30Firc3pztURSExOoznvncjGUkxrR6zzJ07lxkzZvRpz4/bo/HEW+tY+vU+FIVW01q7YnxmMk9/+zp2bNnE119/DcC4ceO47rrrCAgI6ORo0Zck+BBCnPfyj1Xw4NNLcLo83Q48TtMBhZ/feQU3zxrvz+b53YsrtvD8p5t7VYdBVQgLDuIni3LYvfmLfn3M4tE0fv6flazdVdir1VUMqkKUycDFYXUEqnDZZZcxe/bsQfG47Hwns12EEOe1+iYr//XsRzjdvQk84FRS8CffWkdmUgyTswdmKvR1uw71OvAA7/LvTVY7T3y4lTmxbkaNGM7111/fL7NZXli+hc92Ffa6Ho+mU2d1sdMTwlP3XcWECbKc/WAkwYcQYtD54zsbaLI5aKo4Tl3BdprLDuNsqsdgCiE0YSjJFy/EFJUAgK5r1BXsoKEoD1tNKR6HlcDwGKKHTyJhwmxUYwCKovDrV1bx/q/vbTEmYiCob7LyP29+hgK4XQ6q9mzAUnUca1UxHoeN9Nm3Ezvq4naP1z0eDr7/v9jrK0m55FoSJ87B6lFojs7mzjvv6JcegwPFlfxn5TYsVcWdfl6+dusaNfs3U7t/M/aGKlRjIMGxKaReupiQuFSqHEaKmg1I6DE4SeYVIcSgsvPQCT7bVYim6VTtWU9DUS7hqdmkzrieuNHTaS4/SsH7f8VW550ForldFH/+Dm57M3FjpntvXgnplO9YxZEVL6Dr3pkwlfXNvLFu5zl+d639a/kWLHYnOuC2WajYuQZ7fRXBsSldOr5635c4m+rP2qqwsaCSooo6v7e3LU+9uwFFoUuf1ynFG97lxKaPCI4fwpCZN5I0+SoCw6Jx25p9Zf53yefYHK5+eQ/Cv6TnQwgxqLz7+R7fDI748Zcz9Iq7UQ2nL2VRWRM5uOTPVO5eR8YVd6OoBrKv/x5hSZm+MnFjphMYHk3FjtU0lR4iYsgINF3n3c/38M35UwfMuiwWu5OPv873zeAJCI1g3Dd+Q0BIBNaqEgo+fLrD4122Jip2riFx0lzKt69qsU9VFd7fmMtPb5vTZ+0HKDxRTe7J6cBd+bwA6g/voa5wO5nzv0lUZvtjcawOF6u2H+SGmTl9+h6E//VJz0dpaSl33303sbGxBAcHk5OTw44dO/riVEKIC0ijxc76PYd9N+OwpMwWNzIAU1Q8pugk7PVVAKgGY4vA45SoTO8Ny1Ff6dtW12Rj8/7jfdX8bvtsVyEOl9v3WjUYCQjp+kD8si3LCYpKIDp7cqt9Hk3n46/zcXk8fmlrez7+Oh+D6n2005XPC6Aq93NCEtKJyhyPrmt4XI4261YUeP/L3L5rvOgzfu/5qK+vZ8aMGcyZM4eVK1cSHx/PoUOHWq0mKIQQ3ZV/vKLTKaa6ruO2NWGKTuqwnMvaBIDBdHqwpUFVyT1azmU5AyO9eu6Rcgyqiues1WG7wlJ5nLrC7YxY/D1ODaw9m83poqi8jhFD4nvZ0vbtOnyiw9wrZ39eHqcda1UJcWMvpWzrcqr3fYXmchAYHkPKtGuIHj7xjGO9PStOl5vAAOnIH0z8/mk99dRTpKWl8fLLL/u2ZWa2/tYhhBDddeB4lS9JWHvqD+3EZWkkeeqCDuuq2rMBNdBERPpo3zZN09h/rMJv7e2t3KKyHgUeuq5zYtNHRGdNJDQpA4e5/bEd+4sr+yz4cHk8HCmr7bDM2Z+Xw1wD6NQf2YOiqKRccg2GQBPVeV9ybO3rGAKDWnxmHk3ncFkNY4Z2HGyKgcXvj10++eQTpkyZwi233EJCQgKTJk3ixRdfbLe8w+HAbDa3+BFCiLZUNTT7Uoi3xV5fSclXHxKamEHMiKntlqvYtZam0kJSpl2NMSjYt10Hyuub/NnkXqlutPTouLqC7djqykm55JoOyxlVleqG5g7L9EZjs92XJr0tbX1emssJgMduYdiC+4kfO4OY7MkMv/bbGE0hVOxa26qeqoae/Z7EueP34OPo0aM8//zzZGdns3r1ar797W/z6KOP8uqrr7ZZ/sknnyQyMtL3k5aW5u8mCSHOE5qutZuL22U1c2TlvzEEmsi86l6UdhYjqz+8m/JtK4kdNY34sTNa7e9JT0Nf6W4WU/A+tijbupzECXMIDOvkcbdCp+noe6OjHCztfV6qwTvVOTA8htDE04nPDAFBRAwdi7WqGF1rOU5lIH1momv8HnxomsZFF13EE088waRJk3jooYd48MEH+ec//9lm+ccff5zGxkbfT0lJib+bJIQ4T4QFB7U5fMHjsHFk+Yt4HDayFj1EQGhkm8ebSwo4vv4tIoaOJu2ym9ssEx4c5M8m90qoKbDbx1Tt3YCuuYnKmojDXIfDXIfL0gB4f08Ocx2axzuIVdN0wnpwjq5qr/0dfV4Bod4BtcaQ1ovIGYPD0DWPr3fklL58D6Jv+H3MR3JyMmPGjGmxbfTo0XzwwQdtlg8KCiIoaOD8YxdCDFzZqXGtuvE1t4sjq/6Do7Ga4dc8QnBM28/+LZXHKVr9MiHxaWRe+Q0UtfV0WqOqMjp94KyIOiotgZpGS7eyuDqbGvA4bBx870+t9lXuXkvl7rWMvPlHhMSlouk62X042DTUFEhCVBhVZzza6ezzCgiNxBgSjsvS2Ko+l9WMYjCiBra8Z/TlgFnRN/wefMyYMYOCgoIW2woLC/t83QAhxPlvzFmBga5pHFv7GpbKYwybfz+hSRltHmevr+TIyn8TGB7DsEXfQjW2/U3ZrWmMTk9oc9+5MDYjkU35RZ0v+3qG+JxZRGaOa7HNbWumZOMSYkZOJTJjHEHhMb59o9P69v3mZCazYc9hNF3v8ucVnTWR6rwvMZcUEJE20vceGo/tIzw1G0U53WkfFxFCdHhIn74H4X9+Dz5++MMfcumll/LEE09w6623sm3bNl544QVeeOEFf59KCHGBGZoYTUZiNMcr69GB0s0f03gsn4ihY/E4rNQVtswnFDNiCh6nncPL/4XHYSVxwmzMx/e3KBMUEee7CaqqwuXjs/rp3XTuiknZrdZ0qd73JR6H3dcz0Hg83/ff8eNmEhI/hJD4lmvUnJrtYopO8uU3UVWFi4anEhFq6tP3MO+ibNbtPgR07fMCSJw0j/ojeyla8woJ4y/HEBhMzf6v0TUPyRcv8pU3qArzp47q0/aLvuH34GPq1Kl89NFHPP744/zud78jMzOTv/3tb9x1113+PpUQ4gKjKAp3zJnEH99ZD4CtpgwA8/F8zMfzW5WPGTEFt92Kq7kBgLKty9soM5XQpAwMqsLcSdnERfb9ImtdNSw5lknDU9l7pMz36KVqz+c4m0+nS28syqOxKA+A6OzJGM6YvdMRTdO5bfZEv7f5bHMnDicy1ESjxd6lzwsgICScEdd/j9LNn1CVtxFd8xCamMHQK+4iJC7VV96j6QN+NWLRNkXXe7UkpN91Z0leIcSFx+ZwccNvXun2WIjOqIrCWz+/a8CNH9h2sJhH/t72mLmeMqgKGYkxvP2LuzEa+n6Jr7fW7+J/l3zh1zoNqsIVk7L547eu9mu9oue6c/+WheWEEINKcFAAv713vl8DDwX41qJpAy7wALh4VDo3zczpML9Jd+k6/P6+Bf0SeADcNnsiY4cmtJNntfsUxTvz6We3z/VTjaK/SfAhhBh0po1K54EF7S8j3x2qojApO9Vv9fWFH9x0GcNSYn1rpPTWj2+5nJF9PND0TFaLhXHBDQQoGkp3Rs+2QcH7mT1x/yKiw7r2iEkMPBJ8CCEGpfuunMTYmN7djBUFJg5P4e/fuZ4A48BYybYtoaZA/vX9m8hMjqWn8cepjpNHb5jJ7XMm+a9xnairq+Oll17C3lDDVWkQEWLqcRBlUBVUVeXPD13L9DEyg3Iwk+BDCDHoeDwe3n//fbICGpmZBCFBAd26oamqgqLAN6+ayv9978YeJfPqb9HhIfznsZsZEe29bHfn9q2qCpGhwTz9yHV886r20877W0VFBS+99BINDQ1ER0fzw0fu591ffYNpo9KB0wFRVygKpCVE8+pPb2f2hIEzI0n0jCwDKIQYdFavXk1RURFBQYH84v47UU2h/GvZFpZt2Y/L7UFtYyXYU2MmdF1n+uihPHLNdMZmDK7FyPbs3MHIwAZSkkOpDxnC7iPlqKoCeutU5kaDitujERwUwA0zxvHgokuI7ONptWcqLi7mrbfewuFwkJiYyN13301YWBgA//ivG1i1vYCXVm3jSHkthpOLBZ79QObUe4iNCOHOuZO4a+5FsnrteUJmuwghBpXt27ezYsUKAG677TZGjTqd56HJ5mDtzkLyiirIKyqntsmKpmmEBQcxdmgiY4YmceXkbFJi206/PpDV1dXx/PPP43a7ueGGGxg/fjxFFXWs332Y/cWVHDheicXhxKCqJEaFMS4ziQnDUrhiUjbBQQH92tbCwkKWLFmC2+0mPT2dO+64A5OpdeCj6zq5R8vZlH+M/GMVHCqtweF2E2BQSYuPYlxmMlOyhzBjXGa/DY4VPded+7cEH0KIQaOoqIjXX38dXdeZO3cus2bNOtdN6he6rvPmm29y5MgRMjMzueeee1D8OPvFn3Jzc1m6dCm6rpOdnc0tt9xCQED/Bj/i3OjO/Vv6r4QQg0JdXR1LlixB13VycnKYOXPmuW5Sv8nPz+fIkSMYDAauvvrqARt4bN26lVWrVgEwfvx4rrvuOgyGgTuQV5w7EnwIIfqdxeqgsKiKQ0VVNDbZUICoyBBGDEskOyOe4LMGgDocDt5++21sNhupqalce+21A/YG3FUej8bx0joKjlZSVtmA260RbAogY0gso4YnER8ThqIo2O123w191qxZxMbG9kl73G4PRSdqKThSSWWNGY9HJ9gUwLD0OEZlJREb3X7mV13X+fzzz9m4cSMAF198MQsWLBj0n5HoOxJ8CCH6ha7rbN97nA9W7ubrnUfQde8gUPXkLBWPpqHr3umUs6eP4MaFkxg/KhVd1/nggw+oqakhPDyc2267bVB341dUm/l4zV4+XrMXc7MdAINBRcH7O/Jo3ifhGUNiufnqi9CtxVgsFmJjY5kxY4bf23OivJ6PVu/h07V5WG3OFu3RdB3tZHtGDEvklkWTmDtjFEGBp28duq6zcuVKtm/fDsDs2bO57LLLJPAQHZIxH0KIPldW2cATz65iz/4TGFTFd4Ntz6kyM6dmcfGoQPL27sBoNHLfffeRkpLST632L7dH462l2/jPu1+jn3FTb4+ieDORBho1xgxx8qP/uovMzEy/tcfhdPPye1/z5tJtqErnn4miKOi6TlJ8BL/83kImjk3D4/GwdOlS9u3bB8CiRYuYOrX/pvKKgUUGnAohBowvth7it39bjsft6fQGdzZVUVAVjQkZdh689wbGjRvX+UEDUH2jhR//4UMKjlT24GgdULhxwUS+f/9cDH6Y9VFRbeax3y2hpLye7t4B1JPTYu+54WJCKebIkSOoqsr1119PTk5Or9smBi8ZcCqEGBDWf13Af//1U4Bu3+TgZLe/DruPhWDzhPu5df2jvtHKt3/xDmWVDT2swfv44sNVe7BYnfziewt9j6p6oqLazCOPv0V9o6Vnn8nJAPL1j7aRHudiTJqR22+/jeHDh/e4TeLCIxOnhRB94tCxKn779DLQexZ4nKag6/D4Ux9RXtXor+b1C03T+eWfP6a8sqHTxyxdsXrjft5cuq3Hx7tcHn76xIfUN1q63QvVluKaAIaMmCGBh+g26fkQQvid2+3hf/6+Ah0w15VQVbyDxuojOKx1GANDCY9JZ+iYBQSHn15FtqmumKrjO2iqL8baWI6ua8y48c+Ad1Cjy+XhiWdX8cxvbx00gxk/Wr2HvQdKAfC4HZQWfk5TXTHN9SW4XTaGT76VxKEtx0hUFG2lumQXtqYq3C4bgaYIIuOySBt9JabQGP79ziZmTMliWHpct9vz2odbKCqu6fJncmjHO1QV72xVT3BYPBdd9VMA3li6hwVzLiIpXh6Ti66Tng8hhN99ujaPo8U1aJpOaeEGakvziEoYTub4xSRlTsNcc5Q96/+GpbHCd0x9xUEqj20DFIJCW08n9Wg6u/NL2Lj1UD++k55rtjj4v9e+8L12OSyUHFyLramKkMj2B81aGkoxhUSTOmI2WRNvJD7tIuorD7J3wzM4bI2g6/z9pfXdbk9VbROvvr8FHbr8mQAoqpHsKbe3+MnIueb0+3J5+OcbG7vdHnFhk54PIYRf6brOkuU7fbM1UrIvY8TFd6Kqpy83cUMmsHvtXyktXM+IqXcCkDRsOqkj52AwBHBkz0dUNFe3qltVFZas2MXll4zot/fTU6u+yMfpcvteB5oimLroVwSaImiqLyF3wzNtHpc16cZW22JTxrF3w9+pLt7JkJFz2ZlXTHFZHekpMV1uz6ef5fr+u6ufCYCiqCSkT263Xo+ms+HrAh69bw4xUe3nAhHiTNLzIYTwq/2HKiguOz2LIiI2o8VNDrzd9iERiVibqnzbAk3hGAwd5+/QNJ09+Sd6MXiz/3y8Zm+LsS6qwUigqWePJoJCogFwu07mBVEVlq/b1+XjdV3n4zV7feNOuvqZnD5e85277fph1Rf7u9weIaTnQwjhV/sKSlEVpdUqq2fSdR2XvZmQiMSenaOwnJTEqB62sO9ZbU6OldT2qg6Xw4Ku6zhs9ZQcWAtAVLx3YKdH08k9eKLLdVXWNFHXaO2wTHufieZxseWTX6J5XBgDgolLm0jGuKsxGINOF1JgX0FZl9sjhAQfQgi/KjhaiaJAq/XRz1BdsgunvZH0MVd1u36jQaXgSAVXzRrd80b2sUNFVR29/S7ZvvL36Jr3sY0xMITMCYuJSjz9uKnwaBWapndp2m3B0c7zi7T1mQSYIkgdMZuwKG+m2YbKg1Qc3YylsZycWY+gqN51WzRNJ79Qgg/RdRJ8CCH8qrLa3OE0TmtTFUf3LCU8ZigJQ6d0u35N06mpa+5NE/tctR/aN2bGA+geN9amSqqLd6O5nS32O5xurDYnYaFB7dRwWk1tk28MTlva+0wyxi1qUS4+bSKmsHiK96+ipjSP+LSJvn31nfSsCHEmGfMhhPCrjgIPp93Mga//gyHAxMhp96Ao3b8E6eh+yVHRlzRN63UdUfHDiU4aRWr25YycdjclBz6j/MimHp3H+/tqu4eku59JSvZlgEJDVctZR7qmM8ASZosBTIIPIYRfhYUG0VYaDrfLxv5N/8HtsjN2xrcICo7sUf2qqhIaHNh5wXMoNKTz3ojuCA6LIzQqleqSXb5tCmAydW2BvbCQoDYDg558JgZDAAFBIbhdLXs6goICBk3+FXHuSfAhhPCr7IwEVLXlpUXzuDjw9cvYmqsZPf2+Hg80Be+3/eEZCb1tZp/KGhrfeaFu0jyuFjNOUpOiCAzo2pPzrIzW7enpZ+J22XE5rAQEtpxWO7yNcwjRHgk+hBB+NSorEY/n9OMAXdco2PYGTXXHGTntHiJiM3pVv67DyKyeBy/9ITEunPAujMU4m655cDtbj51oqivGYq4gLHoI4J1qO3ZE11f3HZYW12JBuq58JmcHO6ecOLgW0IlOHOnbZjCojMlO7nJ7hJABp0IIv5o6IQNTkBG7wztToyj3U+rK9xOdNAa309oqXfepBFZ2az3VJ/c113unkZYc9E4xDQqJ9pWLiQwZ8Dc6RVG4YsYoPl2b22J8SvmRTbhdNpw2MwD15ftx2rzr1SRnzQAdtq/8A3FDJhASkYjBEIjFXEHV8e0YA0ykjZoHeMdwzLm064nWAgIMzJyaxVfbDuPR9C59Jk57E3vW/434IRMJDvf2NDVUFlBfeZCoxJHEpIz1lfd4NOZMH/iJ38TAIcGHEMKvQoIDWTRnHB+v2YtH07E0eqdg1lfsp76idSKqU0GFw1JH8f7VLfadeh0RN4yE9MmoisKNCydh9MOy8n3t+vkTWbpmb4ttpYe+wGGt972uLdtHbZk3WVh82kUEBkeQmHExjTVHqC3NQ/O4CAyOIG7IJNJGXYEp1JvRNC46lOkXDetWe25aMIkvtngHiXblMzEGBBOTNJqGqkNUFe9A13WCw2IZOnYhKdmX+wamKgpkDIll3Miu98QIoegDbHiy2WwmMjKSxsZGIiJkoSIhBqOyygbu/v7LOF0ev9WpKN6BnG//4wGiI0P8Vm9fevyPS/l65xG/z875ycNXsviqCd06Rtd1vvPLt9lfWO739vzhJ9cNipT3om915/498L8+CCEGnZTEKL7zjcv9Wqeue2+6gyXwAPjxw1diMgW0OfunJwyqwqSxaVx35fhuH6soCr/4r4WtBgP3hqoqzJk+QgIP0W0SfAgh+sSNCyYx6+Lhfpl+qQDXXTmeK2aM6n3D+lFsdCi//v7VgNJOlo2uM6gKkREh/PLRhT3+nQ5JjuZn3+5+Vtn22pMcH8mPHprnl/rEhUWCDyFEn1BVhd8+dg2XTu7e2IS2LJwzlh89ODhvcjOmZPHbx65BVZUupUJvi6JAVGQIz/7PbSTG9e5x9ILZY/nJw1eerLdn7VFVhaSESP7xP7cRFTF4eqLEwCHBhxCizwQGGPnDTxfz8F2zMBjUbt18DapCYKCRxx68gse/u6DFVNHBZu6lI/m/P9xJSkJktx7BnCobF+bmh9+YSHpKjF/as/iqCTz965vx5mrr+vgP9WSDrpw5mhefupuE2HC/tEdceGTAqRCiXxwtruH3Ty+hsLgZBQVFVXxLvJ9iUL2r4RpUlStmjOL+2y4lNSnq3DS4DzgcLt7+dAfvL99Fg9mG0aDi9rRMka4o3pu8R9PJGhrPJTnRVB7fjckUxHe+8x2/XRfz8vJ4b8mHFNeaqGgMxmJzYjCoLXK0eNujoCre6b1jspO575bpTPdDb5Y4/3Tn/i1TbYUQ/SI1MZzh8fUkhrrJGHkpFbUO9h8qx9xsR1UgMjyYsSNSGJ2dxNxLR56X3flBQQF88+bp3H39xWzaeZQ9+SXsP1ROaUUDHo9GUKCRrIwERmclMn1yFmOyk9B1nZdeqqK0tJRly5Zxxx139HocjcvlYu3atRgN8MBt05l2yaV8ue0wuQdOkF9YTkWNGc2jYTIFMCIzkVFZicy8eDjZAzyzrBg8JPgQQvSLffv24XK5GJIcx0N3X3FBrwNiNBq4fFo2l0/L7rSsoigsXryYf/3rXxw6dIi8vDzGj+/+bJczff31175vqdOnTycgwMi8maOYN3NwDegVg9fgfYgqhBhUdu3yLoo2adKkCzrw6In4+Hguv9w7dXnlypU0Nzf3uC6z2cymTd7VcefNm0dAQNcWpxPCn6TnQwjhF5ZmO4cLKzhcWEmT2QYKREWHkj0yibAIhbKyMlRVZcKE7iXHEl6XXnop+/fvp6KiguXLl3Prrbf6griGegsFB8rYvaOI0hP1WJodBAcHkJQSxYSLMhg9NpW4+HAURWH9+vW4XC7S0tIYO3ZsJ2cVom9I8CGE6DFN09m57ShL39/O9s2H0XVQzphSqnk0dB1UFWITFS69fCghIeffWI7+YDAYWLx4MS+++CIHDx4kN3cf9dUq7725mUMFFe0e98kH3nVbUlKjueqa0RQc3ovBCPPnz5ceKHHOyGwXIUSPlJ2o48+//5R9uSWobcxcaUXRQVeYcflIvv+TRUTHhHZcXrRpw4YNLP90I4V5BmyW7h8fEKgz/7qhfP+xb/i/ceKCJunVhRB96ov1+/nW3f/iQL539dlOAw8A3fste/NXhdx3+/+Ru/t4XzbxvFVVGsTeLQZslp59b3Q5FZa9X8xzT6/u2ucmRB+Q4EMI0S3r1+zj97/8EJfLg8fT/ZuX5tGxWZ387AdvsXfXMf838Dz2xstf8u//W3/yVe8emSxdsp2/PPGpBCDinJDgQwjRZYUHy3nqdx97X/TinqVpOppH41c/eY+qykb/NO489+WGA7z64hd+rXPNilzef3uLX+sUoitkwKkQoktcLg9//O1SABqbT1BetYd681FsjgYCjCFEhg8hK20eocFxLY6zWKsoPLaShqZiFMVAXPQIRmQsJDAgFKfTxV+fXM6TT/c+cdb5rKHewtN/XA6A2+Og8NgKahuO4HCaAR2jMZiYyGG+37+ua5RX76Gqbj9NlnJcbhumwChcbgsut5XsofMZmjITgJf/tYFpM7IZmhHXQQuE8C/p+RBCdMmyj3ZyorgWTdM5XvolVXX5xERmMTJjEamJU2gwH2db7vM0Wyt9x9gdjezI/w9Wex1Z6fMYmjKDmvpCdu1/BU1z4/F4Z8ts2XToHL6zge/1l76kudkOgMtlpaxqFw6nmaBA79oq0REZLX7/Hs3F/iMf4XJZGZI4lZEZizAYAnG5rQCcOc9A03T++fc1/f+mxAVNgg8hRKd0Xeej97b5nrSkp8xg5kU/YmTm1aQmTmHYkNlMGfstdF3jWOlG33HHSjfi0VxMHnsf6cnTyRxyOTkjbqPZWkFZ9W7Au0Lq0iXbz8G7GhysFgerl+3hVLwQFBjOhJF3MXfar5kw8k4A4qNHtfj9q4qBKeMeZGrOQ2QOmU18zChs9lqiIzK9ddrrfPVrms6OrUcpO1HX6txC9JU+Dz7++Mc/oigKP/jBD/r6VEKIPpKfW0J5WYNvnEdUeDqq2vKpbUhwLKEhCVhsNb5tVXX5xEWPwBQU5dsWG5VFiCmWqtp9gPfmt2t7kYz9aMfGDQdwONy+16pqJD5mVIe/f1U1EhWe7tt36PhnhATH+R61OF0tM6SqBoVVy/b24bsQoqU+DT62b9/Ov/71r16vQyCEOLfy8074Eoe1R9d1nK5mAozeJGJ2hxmny0JEaGqrshFhQ2iylLfYdiC/1H8NPo905XcPrX//pzQ2naC8ejcjMhbidHkfuxgNgS3KaB6dfbkl/mu0EJ3os+CjubmZu+66ixdffJHo6Oi+Oo0Qoh8cOljeaZmKmr04nGYS48YB4HQ1AfjGJZwpKDAcl9uGpnm/0RsMKocOtp+l80J2cF9pl6bDnv37B29AUnBsOYmx44gKT6e0yvt4K8TUenDpoYJyBljOSXEe67Pg47vf/S5XX3018+bN67Ccw+HAbDa3+BFCDCyVFY0d3gAttmoOFi0jMiyNlPhJAHg0FwCqYmhVXlWMLcrouk5Ntfzbb0tNTVOnZRzOpla/f4Dy6t00WyvJHjqfohNf0NhUDIDB0HoxObvNhd3m8l/DhehAnwQf77zzDrt27eLJJ5/stOyTTz5JZGSk7yctLa0vmiSE6IWOAg+Hs4k9B17HaDAxfuTtKIr3smJQvTc4Tfe0rk93tyjT2TkuZF35vRSXb271+3e77Rwu/oyhKTNoaCrmSMk6EmLHdViPpml+abMQnfF78FFSUsL3v/993nzzTUwmU6flH3/8cRobG30/JSXy3FGIgSYs/P+3d6fRUZ1ngsf/997aVEIqUUK7QAgtCAyIxWCxiNWErTE0dMbuOLHHcac7GfAEx33idreT053pHqedTnLaHSc5jif2ODZjbBNiIIDNKjB7EASxChCrtSIJldBS273zQUZGSKUFlYRUen7n6IOq3nvvo2tc96l3ed62/1/2+Ro5fvYdfP5GJox6Cqvly/0cLOam4Ra3p/U3d7enFrMprHnSpKIq2MOtPRB5/2e3WwK+5/O7AdB1T6v7f7V4P7rux2pxcOrCRwyOTCU5bjIAXl8DDY3VzcNe0LTqyGpr3SMiRE8IevJx7NgxysvLmThxIiaTCZPJRF5eHq+99homkwm/v+W3IKvVSmRkZIsfIUTfkp4Zj6a1/Ljw615OnHuX+sZKsrO+ziB7bIv3bdZIzKZwXHWtJ5K6bt9gkD2h+Xfdr5OWHtczwfdzGSMT2nzdr3u5cGUbAEMTpra6/42eGnz+Bs4VfQzoVLuKyD/zFtC0BHr/8Z9R11DR3D5pqBOTqfUQmRA9IegVTufNm0dBQUGL15555hmysrJ48cUX0TT5xy1Ef5MxMh6//8suecPQKSj8gJrb18ke+WSLZZ13i40eTUnFCRrdNdisDgCqai5R31jJsIRpd50PMrLie/aP6KcyRyVwaH8hd88FvXP/7xR0s9uiWx03JCqT8srTmExhpA97FE2z4PHWca5oIwkxE4hxZhFmbVoMoGoKox5qvSpJiJ4S9OQjIiKCMWNajiuGh4cTHR3d6nUhRP8wOScNs0XD62nquSy8so2b1ecYMngkXl89JRUnWrRPiBkPQGrSLMorT3Ps9G8ZmjAVv+7m6uf7GWSPIzF2YnP7ITERAb/hD3S5s7Na7emSf/otqmuvYLNE0ei5xfXSw1RUnwcg2pFOfMw4Cq9uw697SY2fBYDf78Hv9wCgaRZinaObz6f7DWbOGdVLf5EQsreLEKITwgfZ+MqicWzbfAK/36C2vmnp7c3q89z84qF3tzvJh83qYNJD36TwyjYuXvsU9Yu9XTJSFn0530NRWLby4VbDOqLJsOFDSM+M4WLhl0Mkt243zY1r9NwCoLaumNq6YgAqqs4QHZWO29NUtO3ite2tzllT23Ju3ZCYCB7OSeuJ8IVoU68kH3v27OmNywghetBXn5zKJ1tOgt/Pww892+njBtnjmDj66QDvGmgmcMa58fv9Mix7j2vXrrFr1y5skaXAl/dmXs4/d3jso1P/V6ev89TfzJTkT/Qq+dcmhOiUpGQnz357TpDPqpD+kJ+Dh/bx5ptvUloqhcYASkpKeO+993jrrbe4evUq0bEa4ybFEPyNfw2SU8KZM1+GXETvUow+VtLO5XLhcDioqamRlS9C9DF+v84PX/yAo4cuYQShLsfSFZOYNT+Rbdu20djYiKqqzJgxg9zcXEymgTcqXFFRwZ49ezhz5gzQNCQ1YcIEZs2ahUmzsubb/5crl8sxglCOQ1HAbDHIztFJSHSycuVKEhMTu39iMWB15fktyYcQoks8bh///NKH/OnwJbrz6bHosfGs+f4SVFXh9u3bbNmyhbNnzwIQExPDsmXLSEoaGCswqqurycvL4+TJk80lzseOHcvs2bNxOp3N7W5V1/H9//keV4rKu3XvFQWc0YP43j/NY/+BHbhcLlRVZe7cuUybNg0l+F0sYgCQ5EMI0aN8Pj/rfneAd367F2haLdEZmqZgMml8+7vzWbJsYquH3JkzZ9iyZQt1dXUoikJOTg5z5szBbA7N4le1tbXs3buX/Pz85uqiWVlZzJ49m7i4tuueNNR7eOP1HWzekH/f150+cyTf/f4iBjsH0dDQwKZNm5oTvxEjRrB8+XIiIlrvySNEeyT5EEL0iqKLZbzz5l4OfFYIRtM36nvLgWuaiq7raJrGnPkP8fTfzCQuISrgOevr6/nkk084efIkAE6nk8cee4yUlJSe/FN6VX19Pfv37+fIkSP4fE1VRkeMGMHcuXM73dtz4tgV3vk/eRSc6HxV6NS0GL7+zExy52S1SPwMw+D48eNs3boVn8+H3W5n2bJlZGZmdu0PEwOaJB9CiF5VUe5i766znD9bzLkzxdx2NaCoCo4oO6MeSiJrdBKz5o0i0mHv+GRfKCwsZPPmzdTWNpVnnzx5MvPmzcNq7b9l2N1uN4cOHeLgwYO43U2l0ZOTk5k7dy6pqan3dc5rV26yd9cZDh+4yNXLN3G7vRiGgaIomC0mkpIHM2VqOtNnjSRrdPuJTUVFBevXr6esrKl42ZQpU5g/f/6AnH8juk6SDyFESGhsbGT79u3k5zcNMTgcDpYuXUpaWv+qSeH1ejl69CifffYZDQ0NAMTFxTF37lwyMjL61BwLn8/Hjh07OHz4MNAU58qVK4mJiXnAkYm+TpIPIURIKSoqYtOmTdy6dQuA8ePHs2DBgk5tXvkg+f1+jh8/zt69e5t7cKKjo5kzZw6jR4/uU0nHvS5cuMAf/vAH6uvrMZlMLFy4kIkTW8/TEeIOST6EECHH4/Gwc+dOjhw5AjRt5bBkyRJGjhzZ5XNVltVwoeA6V8+X0tjgQdNU4pKdpI9NZlh6HFo3N1jTdZ2CggL27NnTnDA5HA5mzZpFdnY2qto/Sizdvn2bDRs2UFRUBMCoUaNYunQpYWFhnTreMAxKr1dyseAGN4rKcTd6m4aChseQPjaZxOFD+s29EB2T5EMIEbKuXbvGxo0bqaysBGDMmDEsWrQIu739+SSNDR7yNubz8dv7uHy2qRS5qqlffJM38PuaVpuER9pY9NfTWPL1acQPbb1hW3sMw+DcuXPs3r2bioqmcujh4eHk5uYyadKkfjl3wjAMDh48yM6dO9F1ncjISFasWNHuBODamnq2f3iEjW/vo+xGFdA08Zh77rUzLpKlT81g4eM5RA2R1TX9nSQfQoiQ5vV62bNnDwcPHsQwDOx2O4sXLw44lHH8s/P89IW1VJa5UBSFjj72VE0BA55YPZ8nVs/HbGk/aTAMg0uXLrF7926Ki5sSG5vNxvTp05kyZQoWi+X+/9g+ori4mPXr11NVVYWiKOTm5jJr1qwWPReGYbD743xef/lDGuo8GBjQwRNGURUsFhPfenkZi5+UGiP9mSQfQogB4fPPP2fjxo2Ul5cDTTUyFi9e3FyjQtd1fvvjzax/YzeqqrRaBtwRRYGUzHj+9Z1vEx3naLPNnf1Xrl69CoDZbCYnJ4dp06b1+TkpXeXxeNi6dSsnTpwAYOjQoaxYsYKoqCg8jV5+8r33+GzLn1EU7qsI2sTcTP7pV89gHxRa922gkORDCDFg+P1+9u3bx759+9B1HZvNxoIFCxg3bhyv/2A9W9470K3zq5rKkHgHP9/wXZyxXyYgJSUl7Nq1i4sXLwKgaRqTJ09mxowZhIeHd+uafd2pU6fYvHkzbrcbq9XKwgWL+PBnBzm+v7BbZfdVVSFj3DB+vPY72Oz9d0n1QCXJhxBiwCkrK+Pjjz+mpKQEAG95BMf+2PkCXO1RNZW00Un8fMN3qaquCrj/ykD6zKqurub3v/89N27c4PLBesrOezocYukMVVWYsTibl34RaCdk0VdJ8iGEGJB0XefAgQNs/Xgnx9ffancDtjpvNRduHaTaXYxXbyRMiyAhfCSpkZPQ1LbLuT+yNBU15la7+68MJLqu886vP2LdqwcDtqlsvM7RsvVtvpcT/zhR1oQ233v5188wfeG4oMQpekdXnt/9b+q1EEIEcGdX3K1vnARuBWzX4KvlYOn7mBQLKRHZmFUbt9wlXKw5hMtTzsTYx9o87sgfLzPx8UjGjh/d7v4rA4WiKOxffwlFVTocbkmJGI/D0vJ+2U1RAc4Lr//gIx6Z9xAmc/eWPYu+SZIPIURIKf+8muP7LrY74bG47iw+3c0jCf+NCEvTctqhEWMxMCiuO4vX34hZaz3p0TBgeFQ2jz++oqfC71cKDl/ixqXyTrUdbE0iPjyjU20NA6orajm887T0foQoqe4ihAgpO9YfpaPVmj7dA4BVa1kbxKqFAwqKEuDbtgGfbTodhChDwyfrDqNqnX+M+HQPentjYXdRVYWta7s3WVj0XdLzIYQIKaePFnVYx8NpS+ay60+cqtxOelQOZjWMW+5irteeJCViPKYAcz4Aym5UUVN1G4dzULBD73cKDl9E93cumSio/BS/4UVBYbA1iZGDc3FYAw9b6brBmfwrzZvkidAiyYcQImQYhsH5P1/rsMZETNhwMhxTueQ6SnlJUfPrIyKnkDl4WofXuVhwg0mzsrobbr92u6aBiuJbHbZT0YizpxMTlopFtXHbW8Vl1zEOl31ATvzjRFpiAx7bcNtN6fVKEoYNCWLkoi+Q5EMIETL8Pp06V0On2oaZInFak4izp2PWwqiov0yR6whWzU5K5Ph2j71ZVhOEaPu3yvLO3YPBtkQG2xKbf48ljTh7BvtL3qWwej8Px/1l+9cprZHkIwRJ8iGECBmdHQIoqTvPqaqdzEx8GpupqRpqvD0dMCi89RkJ4SOxaIE3T+vsdUJZd+5BuDmK2LARlNVfwjB0FCXwvBHd36eqQYggkQmnQoiQYbaa0Ewdf6xdqz1JpCWmOfG4I9Y+Ar/hw+WpaPd4Kf/d/XsQZorAwI/f8LZ/nQipdBqKJPkQQoQMRVEYlhHfYTu3v77NSal3VmIYtP+tfsSoxHbfHwhikwYTFn7/iUG9rwZV0dCUwJvuqZrCsPSO/3uK/keSDyFESBk1IaVp+/Z2hJujcHkqqPNWt3i9pO48oBBhDjzHwGozkzQiJhih9muKopA+NrnDZc0ef32r11yeCsrrixhiS2l3JUvyiFgstsArj0T/JXM+hBAhZcbibLasDVzuGyA1chI3G65wuPRDhkVkY9FslNdf5mbjFZIHjcFmansZraapzFic3WIb+YFs5pIJFBy61G6bExVb0FQTUdZELGoYt71V3LhdgKaYyBw8I+Bxiqow+7GJwQ5Z9BHyf5AQIqRkT8sgflg0tPON3GlL5pEvlnlev/1nzlblUe+rISNqGqOdcwMe5/fr/MU3Aj8wB5q5fzmpw56JWHsaHn8DV1z5nKnaTWl9IXH2dKYmfI1B5sB74ijAgsdzghyx6Cuk50MIEVJUVeUbzy/kJ8+/1267KGs8D8ct7/R5NU1lbE4aI8cP62aEocM+yMZf/e0c/t9/fRqwtsrwyAkMj5zQpfOqqsLiJ6fhjJXNRUOV9HwIIULOnOWTmDxnVJdKf7dLAZNF4/lX/1qqbd7jidXzSU6LC9q9VlUFZ5yDb/7D0qCcT/RNknwIIUKOoiis+fcniI6NDNpD8YX/+BqxSYODcq5QYraY+MfXn8ZqM6Oq3UvMFEVBM2v84+tPd2sljej7JPkQQoQkZ2wkP/ngOaLjHPedgKiqgqIovPAfXyN3yfjgBhhCho9M4JW1/wNbuLXDlUaBqJqK2WLiR2/9LaMmDg9ugKLPkeRDCBGy4oY6+a/N32vell3p4jfzCGcYr65bxaMrJ/dEeCFlZPYwfvHHF8iamNL0Qhc7QVKzEnht0/OMn5YR/OBEn6MYHW3/2MtcLhcOh4OamhoiI2WykRAiOA58UsD7v9jOhYLrqJqKoRutCo1pJg2/z0/YIAvONIW0KVE8/8IabDapaNpZuq7zybrDfPTrXRRfvYlmUvH7dbjnSaOZVPw+nZiEKFZ8azZLn5qBZtIeTNAiKLry/JbkQwgxoFwouM7hHacpPHmNorPFuOs9aCaVuKHRZE1IYczkEUyZN5rfvPkGlZWV5ObmMndu4OW3om2GYXDy4EXy952n8M/XuHqhFK/bh8mskZwey8jsFMZPy2DizJFSNyVESPIhhBDddPbsWT744APMZjPPPfccERERHR8kxADWlee3pJtCCNGGrKwskpOT8Xq95OXlPehwhAgpUmRMCCHaoCgKjz76KG+//Tb5+fnk5OQwZMgQam66KDxWxOWTV6mrqUfVVIYkOUmfOILUscOwWGUvEiE6IsmHEEIEkJKSQmZmJufOnufN//0O5cduUbDvLNC0NFRVFQzA7/ODARabhflPzWLZqgWkjk15sMEL0YfJnA8hhGjHkZ3H+Lev/Zz6CjeqpqD72//IvLOK4y/+bj7fevUb2CPCeilSIR4smfMhhBBBsOG1Lfxg4as0VHoAOkw8APw+HYAtv9nJs6PXcOX09R6NUYj+SJIPIYRow7pXP+aXa95C9+sYetc7iHVdp6r0FmtyX5YERIh7SPIhhBD3OLjpT7z5D+92+zy6X6ehtpGXFv4rda76IEQmRGiQCadCCHEXV1UtP332lyiq0maPx2njKCVcDXj8DJZgU76c56H7dapKqvnN93/Hml//XY/ELER/I8mHEELcZe2//Z7a6rqAQy1JjMBJbKvXz5JPGOEtEo87dN3gj2/sYOl3FpCWPTzYIQvR78iwixBCfKGx3s2WN3eg+/WAbaKUaBKUlBY/YYSj4yeeoQGP00wqm375SU+ELUS/E/Tk45VXXmHy5MlEREQQGxvL8uXLOX/+fLAvI4QQQbd/wxEaahu7fFwp1wCIZ1jANn6fzqe/y8PT6Lnv+IQIFUFPPvLy8li1ahWHDh1i+/bteL1evvKVr1BXVxfsSwkhRFCdPnAezdy1nVV1Q6eMGziIJkwJb7ett9FL0cnA80WEGCiCPudj27ZtLX5/++23iY2N5dixY8ycOTPYlxNCiKA5d+QCfq+/S8dUUooXDwnt9HrcoShw4VgRWVMy7jdEIUJCj084rampAcDpdLb5vtvtxu12N//ucrl6OiQhhGjTzRuVXT6mlOsoKMSS3GFbzaRx8/Oq+wlNiJDSoxNOdV1nzZo1TJ8+nTFjxrTZ5pVXXsHhcDT/DB0aeMKWEEL0pPYmmrbFZ/iooJho4rEo1h65hhChqEeTj1WrVnHq1Cnef//9gG1eeuklampqmn+uX5dKgEKIB8Me2bV9WCr4/ItVLh0PuUDTklt7pP1+QhMipPTYsMvq1avZvHkze/fuJTk5cHek1WrFau3cNwYhhOhJmZPSKLt6s9O9E6VcQ8NEDAmdaq/7dUZky263QgS958MwDFavXs2GDRvYtWsXqampwb6EEEL0iIxJaZ1u6zHcVFFODIloSue/x2VOGnE/oQkRUoKefKxatYp3332XtWvXEhERQWlpKaWlpTQ0NAT7UkIIEVQzVkzpdK9HGdcxMDq1ygVAVRVGTc1kcFxUNyIUIjQEPfn41a9+RU1NDbNnzyYhIaH5Z926dcG+lBBCBFVSegITHx2LqnX80VjKNSxYcRLXqXPrusHy1Yu6G6IQISHocz4Mo+tbTwshRF/xjR9+lfydBR22m6zM7fQ5VU0lMS2O3JWPdCc0IUKG7O0ihBB3GTNjFMtXL0JRlaCd09ANXnznOcwWc9DOKUR/JsmHEELc49lXniR9fGqnhl8641v//nWpairEXST5EEKIe9jsVn786cukZQ+/7x4QRWk67r//6Am++vePBTM8Ifo9ST6EEKINkc4Ifpr3LyxbtRCgS70gqqYyaHA4P/zo73ny5ZU9FaIQ/ZYkH0IIEUBYuI1V//lNfpb3I8bNGg00JRZqG70hmlkDBWzhVh77zgLeOvef5K6QCaZCtEUx+tjyFJfLhcPhoKamhsjIyAcdjhBCNLtRWMy+9YcpPHaJwmOXaHA1oGgq0YmDGf1IJqOmZjLzr3IIG9S1Mu1ChIKuPL8l+RBCCCFEt3Xl+S3DLkIIIYToVZJ8CCGEEKJX9diutvfrziiQy+V6wJEIIYQQorPuPLc7M5ujzyUftbW1AAwdOvQBRyKEEEKIrqqtrcXhcLTbps9NONV1neLiYiIiIpqL9AghhBCibzMMg9raWhITE1HV9md19LnkQwghhBChTSacCiGEEKJXSfIhhBBCiF4lyYcQQgghepUkH0IIIYToVZJ8CCGEEKJXSfIhhBBCiF4lyYcQQgghetX/BxuiY3i4Rx//AAAAAElFTkSuQmCC", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "M2 = ex_mg.interleave_example_B()\n", - "M2.draw()\n", - "plt.title('M_2')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Create an interleaving and to generate all the relevant matrices.\n", - "\n", - "Then, we can try to solve the problem using ILP." - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "metadata": {}, - "outputs": [], - "source": [ - "myInt = Interleave(M1, M2, initialize_random_maps=True, seed=10)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Let's get all the matrices for diagram: Parallelogram with top vertices of the boundary matrices (indexed by 1)." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "First we need the distance matrix $D^V_{G^n}$." - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "D = myInt.D('G', 'n', 'V')\n", - "D.draw(colorbar=True)\n", - "D.shape()\n", - "print(D.get_all_block_indices())" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We need the boundary matrices $B_{F_\\text{up}}$ and $B_{G^n_\\text{up}}$." - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "B_F = myInt.B_up('F', '0')\n", - "B_F.draw()\n", - "B_F.shape()\n", - "print(B_F.get_all_block_indices())" - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(32, 32)" - ] - }, - "execution_count": 27, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "B_G_n = myInt.B_up('G', 'n')\n", - "B_G_n.draw()\n", - "B_G_n.shape()\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We also need the initial phi vertex and edge matrices $\\varphi_V$ and $\\varphi_E$." - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(32, 25)" - ] - }, - "execution_count": 28, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "Phi_V = myInt.phi('0','V') \n", - "Phi_V.draw()\n", - "Phi_V.shape()" - ] - }, - { - "cell_type": "code", - "execution_count": 29, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(32, 26)" - ] - }, - "execution_count": 29, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "Phi_E = myInt.phi('0','E')\n", - "Phi_E.draw()\n", - "Phi_E.shape()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Let's set up the ILP problem." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Before we set up the variables and constraints, let's set up the dimensions of the matrices. Also save the function values." - ] - }, - { - "cell_type": "code", - "execution_count": 30, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "D.shape: (32, 32)\n", - "B_F.shape: (25, 26)\n", - "B_G_n.shape: (32, 32)\n", - "Phi_V.shape: (32, 25)\n", - "Phi_E.shape: (32, 26)\n" - ] - } - ], - "source": [ - "# Print the shape of the matrices\n", - "print('D.shape:', D.shape())\n", - "print('B_F.shape:', B_F.shape())\n", - "print('B_G_n.shape:', B_G_n.shape())\n", - "print('Phi_V.shape:', Phi_V.shape())\n", - "print('Phi_E.shape:', Phi_E.shape())" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Initialize the ILP" - ] - }, - { - "cell_type": "code", - "execution_count": 31, - "metadata": {}, - "outputs": [], - "source": [ - "prob = pulp.LpProblem(\"ParallelogramILP\", pulp.LpMinimize)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Matrix parameters" - ] - }, - { - "cell_type": "code", - "execution_count": 32, - "metadata": {}, - "outputs": [], - "source": [ - "# convert everything to numpy arrays\n", - "D_mat = D.to_labeled_matrix().get_array()\n", - "B_F_mat = B_F.to_labeled_matrix().get_array()\n", - "B_G_n_mat = B_G_n.to_labeled_matrix().get_array()\n", - "Phi_V_mat = Phi_V.to_labeled_matrix().get_array()\n", - "Phi_E_mat = Phi_E.to_labeled_matrix().get_array() \n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Let's set up the dimensions\n", - " There has to be a more sophisticated way of choosing the dimensions. " - ] - }, - { - "cell_type": "code", - "execution_count": 33, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "m: 32 n: 25 o: 32 p: 26\n", - "corresponding letters are (i, h), j, l, k\n" - ] - } - ], - "source": [ - "m = D_mat.shape[0] # same as D_mat.shape[1] as D is square also Phi_V_mat.shape[0] and B_G_n_mat.shape[0]\n", - "n = Phi_V_mat.shape[1] # same as B_F_mat.shape[0]\n", - "o = B_G_n_mat.shape[1] # same as Phi_E_mat.shape[0]\n", - "p = B_F_mat.shape[1] # same as Phi_E_mat.shape[1]\n", - "print('m:', m, 'n:', n,'o:', o,'p:', p)\n", - "print(\"corresponding letters are (i, h), j, l, k\")\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Define the decision variables" - ] - }, - { - "cell_type": "code", - "execution_count": 34, - "metadata": {}, - "outputs": [], - "source": [ - "phi_v_vars = pulp.LpVariable.dicts(\"phi_v\", ((h,j) for h in range(m) for j in range(n)), lowBound=0, cat=\"Integer\")\n", - "phi_e_vars = pulp.LpVariable.dicts(\"phi_e\", ((l,k) for l in range(o) for k in range(p)), lowBound=0, cat=\"Integer\")\n", - "minmax_var = pulp.LpVariable(\"m\", lowBound=0, upBound=None, cat=\"Integer\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Objective function" - ] - }, - { - "cell_type": "code", - "execution_count": 35, - "metadata": {}, - "outputs": [], - "source": [ - "prob += minmax_var" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Initialize the Assignment Decision Variables\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": 36, - "metadata": {}, - "outputs": [], - "source": [ - "for h in range(m):\n", - " for j in range(n):\n", - " prob += phi_v_vars[h,j] == Phi_V_mat[h][j]\n", - "\n", - "for l in range(o):\n", - " for k in range(p):\n", - " prob += phi_e_vars[l,k] == Phi_E_mat[l][k]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Constraints\n", - "1. $ m \\geq \\sum_{h=1}^m d^n_{g_{ih}} * (\\sum_{j=1}^n \\varphi_{v_{hj}} * b_{f_{jk}} - \\sum_{l=1}^o b^n_{g_{il}} * \\varphi_{e_{lk}})$ for all $i = 1, 2, \\ldots, m$ and all $k = 1, 2, \\dots, p$.

\n", - "2. $ -m \\leq \\sum_{h=1}^m d^n_{g_{ih}} * (\\sum_{j=1}^n \\varphi_{v_{hj}} * b_{f_{jk}} - \\sum_{l=1}^o b^n_{g_{il}} * \\varphi_{e_{lk}})$ for all $i = 1, 2, \\ldots, m$ and all $k = 1, 2, \\dots, p$.

" - ] - }, - { - "cell_type": "code", - "execution_count": 37, - "metadata": {}, - "outputs": [], - "source": [ - "for i in range(m):\n", - " for k in range(p):\n", - " expression = pulp.lpSum([D_mat[i][h] * (pulp.lpSum([phi_v_vars[h,j] * B_F_mat[j][k] for j in range(n)]) - B_G_n_mat[i][l] * phi_e_vars[l,k]) for h in range(m) for l in range(o)])\n", - "\n", - " prob += minmax_var >= expression\n", - " prob += -minmax_var <= expression" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Constraints\n", - "\n", - "These ones ensure that the $\\psi$ and $\\phi$ represnent valid assignment. This condition says that the sum of each coulmn should add to 1.\n", - "\n", - "1. $ \\sum_{h=1}^{m} \\varphi_{V_{hj}} = 1$ for each $j$.\n", - "2. $ \\sum_{l=1}^{o} \\varphi_{E_{lk}} = 1$ for each $k$." - ] - }, - { - "cell_type": "code", - "execution_count": 38, - "metadata": {}, - "outputs": [], - "source": [ - "for h in range(m):\n", - " prob += pulp.lpSum(phi_v_vars[h,j] for j in range(n)) == 1 \n", - "\n", - "for l in range(o):\n", - " prob += pulp.lpSum(phi_e_vars[l, k] for k in range(p)) == 1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Constraints\n", - "\n", - "These constraints ensure that the $\\phi_V$ and $\\phi_E$ are non-negative.\n", - "\n", - "1. $ \\varphi_{V_{hj}} \\geq 0$ for each $h$ and $j$.\n", - "2. $ \\varphi_{E_{lk}} \\geq 0$ for each $l$ and $k$." - ] - }, - { - "cell_type": "code", - "execution_count": 39, - "metadata": {}, - "outputs": [], - "source": [ - "for h in range(m):\n", - " for j in range(n):\n", - " prob += phi_v_vars[h,j] >= 0\n", - "\n", - "for l in range(o):\n", - " for k in range(p):\n", - " prob += phi_e_vars[l,k] >= 0" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Solve the ILP" - ] - }, - { - "cell_type": "code", - "execution_count": 40, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Welcome to the CBC MILP Solver \n", - "Version: 2.10.3 \n", - "Build Date: Dec 15 2019 \n", - "\n", - "command line - /Users/ishikaghosh/anaconda3/envs/interleavingenv/lib/python3.13/site-packages/pulp/solverdir/cbc/osx/64/cbc /var/folders/5f/m89pr_zs78n8ffl7t7ndknth0000gn/T/d7b5133e4e614f389f5687dee17396c2-pulp.mps -timeMode elapsed -branch -printingOptions all -solution /var/folders/5f/m89pr_zs78n8ffl7t7ndknth0000gn/T/d7b5133e4e614f389f5687dee17396c2-pulp.sol (default strategy 1)\n", - "At line 2 NAME MODEL\n", - "At line 3 ROWS\n", - "At line 4997 COLUMNS\n", - "At line 18673 RHS\n", - "At line 23666 BOUNDS\n", - "At line 25300 ENDATA\n", - "Problem MODEL has 4992 rows, 1633 columns and 10408 elements\n", - "Coin0008I MODEL read with 0 errors\n", - "Option for timeMode changed from cpu to elapsed\n", - "Problem is infeasible - 0.00 seconds\n", - "Option for printingOptions changed from normal to all\n", - "Total time (CPU seconds): 0.02 (Wallclock seconds): 0.04\n", - "\n" - ] - }, - { - "data": { - "text/plain": [ - "-1" - ] - }, - "execution_count": 40, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "prob.solve()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Output the solution" - ] - }, - { - "cell_type": "code", - "execution_count": 41, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Objective value (minimization over the maximum of the absolute values of the matrix) = 186.0\n" - ] - } - ], - "source": [ - "print(f\"Objective value (minimization over the maximum of the absolute values of the matrix) = {pulp.value(prob.objective)}\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Put all the optimized values of the phi and psi matrix back to matrix form and output it." - ] - }, - { - "cell_type": "code", - "execution_count": 42, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(array([[ True, True, True, True, True, True, True, True, True,\n", - " True, True, True, True, True, True, True, True, True,\n", - " True, True, True, True, True, True, True, True],\n", - " [False, True, True, True, True, True, True, True, True,\n", - " True, True, True, True, True, True, True, True, True,\n", - " True, True, True, True, True, True, True, True],\n", - " [ True, True, True, True, True, True, True, True, True,\n", - " True, True, True, True, True, True, True, True, True,\n", - " True, True, True, True, True, True, True, True],\n", - " [ True, True, True, True, True, True, True, True, True,\n", - " True, True, True, True, 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True, True, True, True, True, True,\n", - " True, True, True, True, True, True, True, True, True,\n", - " True, True, True, True, True, True, True],\n", - " [ True, True, True, True, True, True, True, True, True,\n", - " True, True, True, True, True, True, True, True, True,\n", - " True, True, True, True, True, True, True],\n", - " [ True, True, True, True, True, True, True, True, True,\n", - " True, True, True, True, True, True, True, True, True,\n", - " True, True, True, True, True, True, True],\n", - " [ True, True, True, True, True, True, True, True, True,\n", - " True, True, True, True, True, True, True, True, False,\n", - " False, False, False, True, True, True, True],\n", - " [ True, True, True, True, True, True, True, True, True,\n", - " True, True, True, True, True, True, True, True, True,\n", - " True, True, True, True, True, True, True],\n", - " [ True, True, True, True, True, True, True, True, True,\n", - " True, True, True, True, True, True, True, True, True,\n", - " True, True, True, True, False, True, True],\n", - " [ True, True, True, True, True, True, True, True, True,\n", - " True, True, True, True, True, True, True, True, True,\n", - " True, True, True, False, True, True, True],\n", - " [ True, True, True, True, True, True, True, True, True,\n", - " True, True, True, True, True, True, True, True, True,\n", - " True, True, True, True, True, True, True],\n", - " [ True, True, True, True, True, True, True, True, True,\n", - " True, True, True, True, True, True, True, True, True,\n", - " True, True, True, True, True, False, True],\n", - " [ True, True, True, True, True, True, True, True, True,\n", - " True, True, True, True, True, True, True, True, True,\n", - " True, True, True, True, True, True, True],\n", - " [ True, True, True, True, True, True, True, True, True,\n", - " True, True, True, True, True, True, True, True, True,\n", - " True, True, True, True, True, True, True]]))" - ] - }, - "execution_count": 42, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "final_phi_v = np.zeros((m,n))\n", - "final_phi_e = np.zeros((o,p))\n", - "\n", - "for h in range(m):\n", - " for j in range(n):\n", - " final_phi_v[h,j] = pulp.value(phi_v_vars[h,j])\n", - "\n", - "for l in range(o):\n", - " for k in range(p):\n", - " final_phi_e[l,k] = pulp.value(phi_e_vars[l,k])\n", - "\n", - "# are they all zero?\n", - "final_phi_e == np.zeros((o,p)), final_phi_v == np.zeros((m,n))" - ] - }, - { - "cell_type": "code", - "execution_count": 43, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 43, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.matshow(final_phi_v)\n", - "plt.title('final_phi_v')\n", - "plt.colorbar()" - ] - }, - { - "cell_type": "code", - "execution_count": 44, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 44, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.matshow(final_phi_e)\n", - "plt.title('final_phi_e')\n", - "plt.colorbar()\n" - ] - }, - { - "cell_type": "code", - "execution_count": 45, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "final_phi_v column sum: [1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", - " 0. 0.]\n" - ] - } - ], - "source": [ - "# check that the column sum adds to one\n", - "\n", - "print(\"final_phi_v column sum:\", np.sum(final_phi_e, axis=0))\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Attempt 2: ILP using the parallelogram and triangle functions. Preferably, by block." - ] - }, - { - "cell_type": "code", - "execution_count": 46, - "metadata": {}, - "outputs": [], - "source": [ - "from cereeberus import ReebGraph, MapperGraph, Interleave\n", - "import cereeberus.data.ex_mappergraphs as ex_mg\n", - "\n", - "import matplotlib.pyplot as plt\n", - "import numpy as np" - ] - }, - { - "cell_type": "code", - "execution_count": 47, - "metadata": {}, - "outputs": [], - "source": [ - "import pulp" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Let's create two example mapper graphs." - ] - }, - { - "cell_type": "code", - "execution_count": 48, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Text(0.5, 1.0, 'M_1')" - ] - }, - "execution_count": 48, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "M1 = ex_mg.interleave_example_A()\n", - "M1.draw()\n", - "plt.title('M_1')" - ] - }, - { - "cell_type": "code", - "execution_count": 49, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Text(0.5, 1.0, 'M_2')" - ] - }, - "execution_count": 49, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "M2 = ex_mg.interleave_example_B()\n", - "M2.draw()\n", - "plt.title('M_2')" - ] - }, - { - "cell_type": "code", - "execution_count": 50, - "metadata": {}, - "outputs": [], - "source": [ - "myInt = Interleave(M1, M2, initialize_random_maps=True, seed=190)" - ] - }, - { - "cell_type": "code", - "execution_count": 51, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "loss for block 2 = 6.0\n", - "loss for block 3 = 5.0\n", - "loss for block 4 = 5.0\n", - "loss for block 5 = 3.0\n", - "loss for block 6 = 2.0\n", - "loss for block 7 = 3.0\n", - "loss for block 8 = 3.0\n", - "loss for block 9 = 2.0\n", - "loss for block 10 = 1.0\n", - "loss for block 11 = 2.0\n", - "loss for block 12 = 3.0\n", - "loss for block 13 = 4.0\n", - "loss for block 14 = 2.0\n" - ] - } - ], - "source": [ - "for i in range(2,15):\n", - " loss = myInt.loss_each_block(i)\n", - " print(f\"loss for block {i} = {loss}\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Let's create an ILP for each function value over all the diagrams." - ] - }, - { - "cell_type": "code", - "execution_count": 52, - "metadata": {}, - "outputs": [], - "source": [ - "prob = pulp.LpProblem(\"Minimize_Loss\", pulp.LpMinimize)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "interleavingenv", - "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": "3.13.0" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/Notebooks_Unused/linear_optimization_single_triangle.ipynb b/Notebooks_Unused/linear_optimization_single_triangle.ipynb deleted file mode 100644 index ef20de9..0000000 --- a/Notebooks_Unused/linear_optimization_single_triangle.ipynb +++ /dev/null @@ -1,906 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 28, - "metadata": {}, - "outputs": [], - "source": [ - "from cereeberus import ReebGraph, MapperGraph, Interleave\n", - "import cereeberus.data.ex_mappergraphs as ex_mg\n", - "\n", - "import matplotlib.pyplot as plt\n", - "import numpy as np" - ] - }, - { - "cell_type": "code", - "execution_count": 29, - "metadata": {}, - "outputs": [], - "source": [ - "# Using PuLP to solve the ILP (Should I use something else?)\n", - "import pulp" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Given two mapper graphs and associated matrices, I am trying to see if the problem can be solved using integer linear programming (ILP).\n", - "\n", - "_Note to self: Fill in the ILP details here._" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Let's create two example mapper graphs." - ] - }, - { - "cell_type": "code", - "execution_count": 30, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Text(0.5, 1.0, 'T')" - ] - }, - "execution_count": 30, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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0eHQTELAJK/ZU/AFCqFPnRMTwQURE1I+cxg9Q31k8rEct/RGwo6Q1ExebD6tW50TD8EFERNQHIQSy6t9xSd0SZGQ3vOeSuicCTrUlIiLqQ0XbWZit5U6Vbaxqx4d/uYhzB+vQ0miFKciAhGX+uPXHcdDqe/+dL6CgtDULFmsVvHXBajd93Btyz8eBAwewYcMGhIWFQZIkvPfeez1eF0LgiSeeQGhoKIxGI9auXYuCggK12ktERDQqKtpyITlxmzRXd+BPd55E1odVSFsfjFt/Eod5nwvBhZMN6Gy3D3huZdtZtZo7oQw5fLS0tCA1NRXPPPNMn6//9re/xV/+8hc899xzOHbsGDw8PHDdddehvb19xI0lIiIaLdXt+U6V2/bHQlhqO/Dwy3Nxy6Y4LL0rHDd8ewY2bVsMo1f/DxhkaFDl5DUmmyE/dlm/fj3Wr1/f52tCCPz5z3/GT3/6U2zcuBEA8PLLLyM4OBjvvfce7r777l7ndHR0oKOjw/G9xWIZapOIiIhU12StHnSgqaIInNlbg6TVAYhM9u71+kBLqgsItNjqRtzOiUjVAaeXLl1CZWUl1q5d6zhmMpmwcOFCHDlypM9zNm/eDJPJ5PiKiIhQs0lERETDomDgRyYA0FLfifZmO0Jneg7jCgJCqDeLZiJRNXxUVlYCAIKDew6eCQ4Odrz2WZs2bYLZbHZ8lZSUqNkkIiKiYXHTeLm0fgkydLLRpdcYr8Z8tovBYIDBYBjrZhAREfUQYJiBkpasAXtAPPz0cPPUoKKwecj1K1AQ6DZjJE2csFTt+QgJCQEAVFX1XDa2qqrK8RoREdFEEOwWN+ijF1mWkLImELkf1aI4p/eYxYFXMRUIcosbYSsnJlXDx/Tp0xESEoK9e/c6jlksFhw7dgyLFy9W81JEREQuFekxDxpJP2i5G787A15+evztSxl4d3M+Dr9Zhh3PXMRvNhxFW5Ot3/M8tP4IdotXs8kTxpAfuzQ3N6OwsNDx/aVLl5CdnQ0/Pz9ERkbikUcewS9/+UvExsZi+vTpePzxxxEWFoabb75ZzXYTERG5lEHjgUTTOuQ0bh9w1otPsBu++8Z8bP/LBWRsq0R7sx2mYANmLfeH3k3T5zkSJMz22QhZ6vv1yW7I4ePkyZNYvXq14/tHH30UAHDffffhX//6F374wx+ipaUFX/va19DY2Ihly5Zhx44dcHNzU6/VRERELiaEgHtVChTtBxgsI/iGueHe3yQ5WbMEveyJFN8bR9zGiUoS42xbPYvFApPJBLPZDG/v3nOmiYiIXK25uRlbt25Ffn4+9LFlcE+/qGr9N4Q9gVjvFarWOdaGcv8e89kuRERE44UQAjk5Odi+fbtjZe7OgjD4xwm0e16GwMj/Xk/x2TDpgsdQMXwQERGha/uQDz74AOfOnXMc02q12LBhAxKTE/BB2S9wueXYiK6RZFqP1cHfGmlTJzyGDyIimvLOnj2Lbdu2oa2tzXEsMDAQd955JwICAgAAG8KfxMm613G09mV0LY7u3OqkEjTQSFosD/oGUnxuGnDJ9amC4YOIiKas1tZWbN++Hbm5uT2Oz5kzBzfccAN0Op3jmCxpsCDgXsR4LsaR2pdwqfnwlVekXkFEggYCCmRoEOe9CosD7oe3nutddWP4ICKiKen8+fPYtm0bWlpaHMd0Oh1uvPFGpKam9ntegFsMNoT/As3WWuQ37Ud1ez4q286j3d4ESZJg1JgQ4jYLIcYExHqvhFFjGoV3M7EwfBAR0ZTS1taGDz/8EGfOnOlxPDAwEHfccQcCAwOdqsdTF4B0v9td0cRJj+GDiIimjPz8fGzduhXNzT33YpkzZw7Wr18PvX7wFU1p5Bg+iIho3LELO8raynG5pQh1HXWwww5FKNBAAwUKJEmCBhr4G/wR7RGFacYwaAZYCay9vR07d+5EdnY2AECSJAghoNVqceONN2LOnDmj88YIAMMHERGNI1Xt1fioej/21xxAm71r5okEqc/1Na4+7ia7YVXQClwTtArBbsE9yhUWFmLLli1oampyHBNCICAgAHfccQeCgoJc+I6oLwwfREQ05qyKFVvKt2Fr+QeQIEG5avZIfwt7XX28XWnHrso92Fm5GzeF3oCN0zZAsSrYuXMnsrKyAHQNJrVarQCA1NRU3HDDDXzMMkYYPoiIaEzVd9bj93l/QnlbOQT6DxuD6Q4s2yq240j1UQQfC0BbTVfvSXfw0Gq1uOGGGzBnzhyutzGGGD6IiGjM1Hc24Kmzm9HY2ajCwuVdBARqrXVoSG7EjKwo2M12WK1WBAQE4Pbbb0dwcPDglZBLyWPdACIimppsig1/yv8fNHY29njM0pfCbQV4eeELaC5vGrCcgwzYDXZcTiqBAgUpKSl48MEHGTzGCfZ8EBHRmPiwcieKW0tcdwEJ6PSyIviGUNwy9xY+ZhlH2PNBRESjrrHTjHfL3nf9hSTguHISjdZG11+LnMbwQUREo+5A7UEowrmN2UZKQODjmoOjci1yDh+7EBHRqPuoev+wZrVY26w48cejKD5QjLbaVug99fCN9UP6Q/PgnxDQ5zkCAvuq92Nj2AY+ehknGD6IiGhUNXY2or6zYVjnZj+XibIjpUi4YxZM033RYW5H9akqmC+b+w0fAGC2mtFgbYSf3ne4zSYVMXwQEdGoutxSNOxzK09WIHZjPOZ9Z+GnB7/o7HUvM3yMExzzQUREo6rBOrxeDwDQeehQm1uD1prWoV+3s3HY1yV1MXwQEdGoGslA0+T7ZqPxYgP++7k38MEDW5D9fCaayiyDnvfZJdtpbDF8EBHRqDJq3Id9bvjSCNzyzh2Y/71FcA9wx9lXc7DlnndRdnjg9UIEBIyy27CvS+pi+CAiolEV4R4+ovPdA9yRcPssrP7dWtzy7h0weBtw+sVTTlw3YkTXJfUwfBAR0agKdQuBBpphnWttsfb43uhnhDHQHYp14EcqGkmDacawYV2T1MfZLkRENCqampqQnZ2NrKwsuEUa0BLSOuQ/gbd/dSui10yHb6wftEYdKk6Uo+5sLeZ9Z0G/58iQMdc3HVqZt7zxgv8niIjIZRRFwYULF5CZmYm8vDwI0bWwWIDODy1hQ5+xEnP9TNTm1qD4oyIIIeAV7o2FP1yM+Ntm9d8GKFgTtHrY74HUx/BBRESqM5vNyMrKQlZWFiyWT2ejREREID09HbNmzcIfL/4P8psKnJqFMvOmWMy8KXbI7ZAhY6bnDMR7xQ35XHIdhg8iIlKF3W5HQUEBMjMzUVBQ4DhuNBoxe/ZspKenIygoyHH8qzEPYNPpx126x4tGkvFgzFe4rPo4w/BBREQj0tDQgMzMTGRnZ6O5udlxPDo62tHLodX2vt0E6AOw0r4ce6R9XQdckA++PP0BBLkFql8xjQjDBxERDZnNZsP58+eRmZmJS5cuOY57eHggNTUV6enp8Pf37/f8hoYGvP/++ygqKkJAuB9qk+shQRrWZnOf1V3PA9H3YUnAohHXR+pj+CAiIqfV1tYiMzMTp06dQmvrpwNGZ8yYgfT0dMTHx0Oj6X8arRACGRkZ2LVrF6xWK3Q6He5JvQvusR54/tILaOhsGFEAkSDBR++Dr8V8BYne/Q9CpbHF8EFERAOyWq04e/YsMjMzUVxc7Dju5eWFtLQ0pKWlwcfHZ9B6zGYztm7digsXLgAAIiMjcfPNN8PXt2uzt80pT2FbxXbsq/oILfZWaCQN7MI+aL3d5dw17lgTtBo3hd0ANw1XMx3PJNE972mcsFgsMJlMMJvN8Pb2HuvmEBFNWVVVVcjIyMCZM2fQ3t4OAJAkCbGxsUhPT0dsbCxkefCFOoQQOHXqFHbs2IGOjg5otVpcc801WLRoUZ8DQa2KFZkN2chvyseFlouo7aiFVbEBAPSyDp1K10JjOlmLAEMAYjxiEO8Vi3TfNOhknYqfAA3FUO7f7PkgIiKHzs5O5OTkIDMzE2VlZY7jJpMJ6enpmDNnzpD+MGxubsbWrVuRn58PAJg2bRpuvvlmBAQE9HuOTtZhof98LPSfP/w3QuMawwcR0RQnhEBFRQUyMjKQk5ODzs5OAIAsy0hISEB6ejpiYmKGPF01JycH27dvR1tbG2RZxqpVq7B06VKnektocmP4ICIaI4pQUNxSi/OWcpS01sGq2OGm0WG6RyASTNMQ4ubj0vUp2tvbcebMGZzMzMAFcwXMHgKtgQIGdyMiQ8Iwf0YK5gTNQLCbaUjtaG1txfbt25GbmwsACAkJwc0334zg4GBXvRWaYBg+iIhGWU27Be+WHMd/S46hobMFQNdiWBIAAcB+ZdGtCHd/3BW1BDdMS4OnVp0BlEIIlJSUIDMzEyfzz+CiXyeKw+zojOp6XQMZktSKc9ZCbD+XD5wDojwCcFfUEqwPS4OH1jBg/Xl5edi6dStaWlogSRKWL1+OFStWDDgDhqYeDjglIholdqHgjaLDeCZvJ+xCgeLElFIJgJfOiJ8k3YLVIcnDvnZraytOnz6NzMxMVNdU42KoHXnhdkACxCCdGt0vm3TueDzlNiwP6j2Ftb29HTt27MCpU11b2wcGBuLmm29GWBh3kp0qhnL/ZvggIhoFFmsbvpfxMk41Fg353O4ekRunpeMnSbdAKzvXiyCEwOXLl5GZmYlz587BbrejUytwMt6GBg9lyCuKdi/edUv4fPwg8XOOdhQWFmLLli1oamoCACxZsgSrV6/uc1VTmrw424WIaBxpsrbhG8eex8WWqmGd3/0X4vayTLRY2/HrOfcMGECam5sdW9fX19c7jvuGBWJ3VCPMV6aqDr0dXS15r/QEmm3t+EnCzdi7ew8yMzMBAH5+fti4cSMiIyOHVT9NHQwfREQuJITA46fewMXmqj4fs5S9ehDl/z6EOa9/BzqT+8B1Afi4+iz+WbgH/y/uuh6vKYqCixcvOrauV5SucSN6vR4pKSlIS0vDr8o+RG1Dq1OPewZrx+7KM6jMuYjIC13rbyxYsABr1qyBXq8fUd00NTB8EBG50AflWThcm69afQLASxcPYFVwEhJN4bBYLI6t681ms6NceHg40tPTkZSUBL1ej3dLjuNk/UXV2gEAZ/xbEN7ki/uvvx3Tp09XtW6a3Bg+iIhcpN1uxR/PbXOM2VCLBODJjDexsSoUBQUF6B665+bm5ti6/uppra22Dvz5/HYVW/BpO8rmeDF40JAxfBARucieitNotrWrXq8CgYudtThRaoZJyIiKinJsXa/T9V5efEd5NtrsncO6lr29Exq3vh+lCAk4bS7GhaYqzPDiGh7kPIYPIiIXebfk+LC2ie+oMiNv02uQ9VrEb/48dL4evcpIArCmBOKheXcPuFT5p+0YvPele/xJ8nMPovz1T2A+eRGGIBOSnvlyv+doJBlbSk/iu7NudOKdEXVRfY1bu92Oxx9/HNOnT4fRaMSMGTPw1FNPYZzN6CUicimbYsc5S9mQg0d7eQPO//BVaIwGxD99b5/BA+jqdaj1tA8aPNrtVhQ0VQ6pFYW/fhdKhxXh961E4PrUAcvahYLshstDqJ3IBT0fTz/9NJ599lm89NJLSEpKwsmTJ/HAAw/AZDLh29/+ttqXIyIaly42V8F2ZaVSZ7WV1CFv02vQ+3sh7pd3QetlHLD85ZYadCo26OX+f5UXNFUMeXaLe0wQZjy20enyhU2VsCl2p9cfIVI9fBw+fBgbN27EjTd2dcFFR0fjP//5D44fP95n+Y6ODnR0dDi+t1gsajeJiGjUVbcP7XdZW1ENLmx+D25hvoh78i5oPAZexhzo6nVo6GxBsJup3zK1Q2wHAATdkDak8lZhR5OtDb56zyFfi6Ym1R+7LFmyBHv37nVsn3zq1CkcOnQI69ev77P85s2bYTKZHF8RERFqN4mIaNQNtbeh4OdvQ2PUI+6XdzsVPBzXGaR3xT6MeTb6EJ8hn2Pno3UaAtXDx49+9CPcfffdSEhIgE6nQ1paGh555BHce++9fZbftGkTzGaz46ukpETtJhERjToPjfMBAgB8l8ajo6IRdR/lDu06g2w4N9R2AICsH3qn+HCuQ1OX6o9d3nzzTfz73//Ga6+9hqSkJGRnZ+ORRx5BWFgY7rvvvl7lDQYDDAb+oyWiyWWmV8iQykd85RpIGhlFz+yExqiH/+qkQc/x13vCWzfwuJDYIbZjOELcfGDUcmVTcp7q4eMHP/iBo/cDAFJSUlBUVITNmzf3GT6IiCaT7i3rc3NzYbTJaNM5OehUAqK/vR72tk5c+sM2yEY9fBfF9ltchoQkn8EfUwe4ecNX74GGzhZn38KQyJCQ7EQ7iK6mevhobW2FLPd8mqPRaBz7DBARTTZCCJSWliI3Nxdnz5517O4aGiHhUujgW9Z3k2QJMT/YgMK2Tlz49buIe/JOeM+J7rOsAoG1ISlO1bsudDbeLj7qknEZCgTWhCSrXi9NbqqHjw0bNuBXv/oVIiMjkZSUhKysLPzxj3/El7/c/yI1REQTjRACZWVljsBx9Uw9g8GAhIQEXBMbju+VvDOkemWtBjN/cgvyH38TBU/+F/G/vhueCdN6lfPSuuEaJ276iqJgVpOXywaE+uo9sDIo0SV10+QlCZVX/2pqasLjjz+Od999F9XV1QgLC8M999yDJ554wqndDi0WC0wmE8xmM7y9vdVsGhHRiAghUF5e7ggcV2/kptfrkZCQgMTERMyYMQNabdffdk+cfhO7yk+NeCfZz/pO/HrcO335gGUKCwuxe/duVFdXI2OmFVV+itO9MM76/qwNuDNqsbqV0oQ0lPu36uFjpBg+iGg86Q4cZ8+eRW5ubq/AER8fj8TERMycOdMROK5m7mzFHQf/CLO1bcirnfZFI8mI9wrF/y3+JjRS3xMWq6qqsHv3bly4cAFA14Zz6csX4TetH6PZ1q5KDNJIMpJNEfjHwgch99MOmlqGcv/m3i5ERJ8hhEBFRYWjh6OxsdHxmk6nQ3x8PJKSkjBjxow+N3K7mknvjl/NuQffPvkiFDGy+CFDgofWgKdS7+4zeDQ1NWHfvn3Izs4G0DXebsGCBVi+fDmMRiM8a0Lx3YyXgBHGII0kwVtnxC9m38ngQcPCng8iInQFjsrKSkfgaGhocLym0+kQFxeHpKQkzJw5c9DA0ZeD1efxWNa/ISBgH+Ky60BXT4On1g3PLvhqr2m8nZ2d+OSTT3DkyBFYrVYAQFJSEtasWQNfX98eZT+qysWPs/8DIcSwHgVpJBneOiOeW/AgpnsGDfl8mrz42IWIyAlCCFRVVTkCR319veM1rVbrCByxsbHDChyflWcpxxOn38Tl5mqnb/vdu9Eu9J+Jn6bc1mMpdUVRkJ2djY8++gjNzc0AgIiICFx77bUDrhZ91lyKJ069iZLWOqf7QLp3510SEIefJN+KQDf+fqaeGD6IiPohhEB1dbUjcNTV1Tle02q1iI2NdQQOZwbJD5VVseE/lw/j9aJPUNvRBK0k99qATgIgSzLsQkG0RyDuj1mF9WFzIEmfjha9ejApAPj6+mLt2rWYNWtWj3L96VRseO3SIbxedBj1nc2DtmOGZzDuj1mFdaGznaqfph6GDyKiqwghUFNTg9zcXOTm5vYZOBITExEXF+eSwNEXm2LHkdp8ZNRfQk5jCUpaa2FT7DBodIjxDEaSKRyLA+OQ6hPV42bf12DSlStXYv78+dBohr6rrE2x45OaPGTUX0KuuQSlrXWOdsz0CkGiKRxLAuKR4hPB0EEDYvggIgJ6BI7a2lrHcY1G0yNwTIQtHj47mFSWZSxYsAArVqyA0TjwEutEo4GzXYhoyqqpqXFMi62pqXEc12g0mDlzJhITExEfHz8hAgfQNZj08OHDOHz48KCDSYkmCoYPIhqSZmsHcuurcLahCvUdrZAgwddgRLJfCBJ9g+GhG/0Nxmprax1jOLrHQABdvQNXBw43t4F3gB2q/j6LJL8QJI3ws+hrMGl4eDjWrVs34GBSoomA4YOIBiWEwOGqIrycl4E9pQVQICBDgnxlDIBdCAgIaCQJ10XE44txc7EwyLVjBOrq6hyBo6qqynFclmXMmDEDiYmJSEhIUD1wCCFwpKoIL+dnYHfJwJ/FuvA4fCl+LhYGRQ7psxjpYFKi8Y5jPohoQGUtZvzwyAc4XFUEjSQNukeI5srsiFVhM/CbhesR7O6lWlvq6+sdgaOystJxXJZlxMTEICkpCfHx8S4bA1HeYsFjRz/AocrLjvc5kO7Pa2VoDH6z6AaEDPJZ9DeYdN68eX2unko0nnDAKRGpYk9pAb596H10KrYhb0ymkSS4aXT4+4pbsCI0ZthtaGhocASOiooKx3FJkhyBIyEhweWDLveVFeJbh95Dh314n4VBo8Xfl9+ClWEzer3OwaQ0GTB8ENGI7SrJxzcPvAMxgqW4u9aJkPB/q+7o86bbn4aGBseg0c8GjunTpzsCh7u7+zBbNjS7SwvwjQP/hRjB8ujdn8XzK2/H6mkzAfQ9mDQxMRFr1qyBn5+fOo0nGiUMH0Q0IgXmWty4/f9gUwZegLvpQAbq/vlfTPvTD6AL7HvmhQRAL2uw86YHEeXV/+yMxsZGR+AoLy//9PwrgaN7DIeHh8cw39XwXDDXYf32/4NNsY94QzYJgE7WYPsNX4b5QjEHk9Kkwqm2RDRsNkXBdz/ZMuJN0LoJADah4PtHtuGNa7/gGJgJAGaz2RE4ysrKHMclSUJ0dDQSExMxa9asUQ8c3eyKgu8e3gJFDGcXlN4Euj7fL773Aq693AYZHExKUxPDBxH18N+LZ5DbUDV4QQCey9LgsWg2JN3Av0rsQuBkTSk+KDqHFb7TcPbsWZw9exalpaU9yl0dODw9PYf9HtTy7qUcnKmvHLzgECgQqNDaUeprwFfnd61MysGkNNXwXzwROQgh8ML5E47NzAYjyTIkvXNbqksAfnvwA2RebO1xPCoqComJiUhMTBwXgeNqL+adgAxpWLu/DkQCUDMzCIsXL1a1XqKJguGDiBzONlQh31wzeMErnBnz0U0AKJVtMOuAlNBIR+Dw8lJvKq6azjVU42xD9eAFAbTnXUb9qx+gs7QKWl9vmG5cDltjE8zv7kP0q7/uVV4AONNQhQJzLWJNASq3nGj8Y/ggIoeMmjKnez2GK23j9fhi0kIXXkEdmTWlTn0WnSWVqHr6RcheHvC5ZQ2g2NHwzl5oTIP34mTWlDF80JTE8EFEDjn1lY4t1F1BK8kobDW7pG61namvhKaPbeY/q/HtPYAQCH38a9AG+AAA3Ocno3zTXwY8TyvJOFNfgbuQqlaTiSYM5x7WEtGUUNFqcVnwAAC7UFDV1uSy+tVU2do0aPAQioK2MwVwn5voCB4AoJ8WBGNK7IDn2oSCqrZmNZpKNOEwfBCRw2A325ESwJBXBx0rzoQwu6UFotMKbYh/r9d0oYM/TrErrv28icYrhg8icvDWuUGC69aa0EgSPLWjv+vtcHjp3SC7+rMYgx2AicYDhg8ickj0DYLswnWuhABm+Qa77gIqmuUThMHW/NJ4e0DS62CrrOv1mrWidsBzBSbOZ0GkNoYPInJI9gtx6WMRBQIpfiEuq19NKU58FpIsw5gSi9aMs7DVNjqOd5ZVo+1MwYDnKkIgeYJ8FkRq42wXInJYEhIND60eLbZOl9TvqzdibmC4S+pW26LgSHjpDGiydgxYzue2NWg7nY+Kp/4J77ULIRQFll1HoAsPgrW4/9VRTXo3LAjiPi40NbHng4gcjFod7p6ZCo0L9hiRJQn3xqVBr9GoXrcruGl1uHvmnEE/C31kKIIfewAabw80/HcPmj/OgO+ta+A+N7HfczSShHtj02DQ8O8/mpr4L5+IevhywgL8uyALdrtt8MJK12MJSR747xgJgLtWhy/FzVWhhaPngYR5eDU/E21264Dl3BKmI+yph3oca/jvnj7LSgAMGi3ui5+nVjOJJhz2fBBRD6HuXrjDw7lHI/ZGCyBJkD2NA5YTAJ6cfx0CjeNr75bBhLp744l5a1Wts+uzWIegCfZZEKmJ4YOIHDo6OvDGG29AzsxHdJO934mmdnMTLLuPoGnvcRhmRkA29D9lVAJwe0wKbo5OckmbXUkIgbByC6Y32bum6oyQBOCW6GTcOj1l5I0jmsAYPogIANDQ0IAXXngBeXl50Go0+P2im3BdRHyfZTvLatDwnx3QBvsj4Ou3D1jv56KTsHnhDZBcMI7ElYQQ2L17Nz766CMsr7JjnrH3QmJDdVPULPx28Y0T7rMgUpskxPhabtBiscBkMsFsNsPb23usm0M0JVy+fBlvvvkm2tra4Onpibvuugvh4eGwKwr+9/xx/D77YwgIp6fhaiQJGknGj9JW4774eZAn2M1WURRs3boV2dnZAIB169ZhwcKFeCHvBH6X/TEUoQz5s3gsbRXuj58/4T4LImcN5f7N8EE0xWVkZGD79u1QFAWhoaG4++67e/3sFZpr8afTB7GjJA8QgCT1XiZdI0lQRNd/b4hMwHdTlyPay28034oqbDYb3nnnHZw7dw6SJGHDhg1IS0tzvH7BUoc/nTqAHSV5EAN+FgJy92cxewWme0+8z4JoKBg+iGhQdrsdO3fuxIkTJwAAycnJ+NznPgedTtfvOTVtzdhWdA6n6yqQXVeOxo42SJIEH70RaQFhmO0fihujZiHAzWO03oaqOjs78cYbb+DixYvQaDS47bbbMGvWrD7LDvRZzAkIQ+oE/yyIhorhg4gG1NbWhrfeeguXLl0CAKxevRrLly+f0mMR2tra8O9//xtlZWXQ6XS4++67ERMTM9bNIpowhnL/5jofRFNMTU0N/vOf/6ChoQE6nQ633norEhISxrpZY6qpqQmvvPIKampqYDQa8fnPfx7h4RNjJVaiiYjhg2iCaOnsRG5NNc7WVKO+rQ2SBPi6GZEYGISkwCB46AffIbWgoABvv/02Ojs74ePjg7vvvhvBwRN/czNzezvOVFfhfG0NLB0dkCQg0N0DyUHBmBUQCIO2/1919fX1eOWVV9DY2AgvLy984QtfQFBQ0Ci2nmjqYfggGseEEDhaWoJXTmdj18VCxyDG7hkTdkWBQNcAx2tjZuKLs+dgUXhEr8cnQggcPnwYe/Z0rboZFRWFO+64Ax4eE3c8gl1RsO/SRbx8OguflBQDQJ+fjV6jwcb4BHxhdhpSgnoGraqqKrz66qtobm6Gr68vvvjFL8LX13e03wrRlMMxH0TjVHmTBZv27sLB4iJoJGnQqZ3dZVZERuM3a9chxNMLQNfsja1bt+L06dMAgPT0dNxwww3QTJA9VvpSUFeHR3dtR25N9ZA+m1sSEvHEitUwubmhpKQEr732Gtrb2xEcHIwvfOEL8PTkqqNEw8UBp0QT3EeXL+Jb27ehw24b8hb3GkmCQavFM+s3IN0/AG+++SZKS0shSRKuv/56zJ8/f0IPLH0z9wx++tEeCOH8uiPdZEmCr5sRv0ifj+ydu2C1WhEREYF77rkHRuPAS8QT0cAYPogmsL0XL+DrH7wPIQSG+8MpoetGu94m4G9phpubG+64444JP3vj32dO4fGP+t6wzVkyAFkIXNfUhoXR03HnnXdC78R4GSIa2FDu31xenWgcudhQj/+3fcugwaPp2Alc+s73Ya2r7/N1ga4xD9tlAdnfD1/96lcnfPA4WlqCJ0YYPABAAWAH8JHJE9ffcjODB9EYYPggGifsioJHd30IZQQ9Hj1IEiBJyAzwhc8EH0TZ0tmJ7+36ULXHRUKS0AGBpw5+rEp9RDQ0DB9E48R7eedwuqrSqXEMnvPnIur3m6H1GzhUKABOVVdha/55lVo5Nv436ySqWpqhqPiU2C4Etuafx4nyUtXqJCLnMHwQjRP/ys50etMxSZYh63RO9QTIkoR/ZWeOtHljxmq345XT2aoGj24aScLLp7JVr5eIBsbwQTQOnK+tQW5NtdM32MHGfFxNEQKnq6uQX1c70maOiQNFl1Hf1jZgmYYPd+LSd76PzqpqVL/4Mi7/8Cco2vQE6v77HhSrtd/z7EJgR2E+zO3tajebiAbgkvBRVlaGL3zhC/D394fRaERKSgpOnjzpiksRTQqZFeVw9eTXrIpyF1/BNTIqyqGVnftVVf3iKxA2G/w23ABjYgIsBw6h7o23BzzHLgTOVFep0VQicpLqK5w2NDRg6dKlWL16NT788EMEBgaioKCAqwYSDSCnugoaSYZNKC6pXyvLOF1dhbtcUrtrnaqqgF1x7nPR+fsh+MEHAADey5ei1s0NTYcOw7R6JfTTwvo8R5Yk5FRXYVlklGptJqKBqR4+nn76aURERODFF190HJs+fXq/5Ts6OtDR0eH43mKxqN0konGvsrnZZcEDAGyKguqWZpfV70oVTU1Oz/7xWr6kx/feK5ah6dBhtJ49P2D4qJqgnw3RRKX6Y5ctW7Zg3rx5uOOOOxAUFIS0tDQ8//zz/ZbfvHkzTCaT4ysiIkLtJhGNe64MHo5rKONqPUGnDWUVU11gQM/vA/wBSYKtfuCxMc72rBCROlQPHxcvXsSzzz6L2NhY7Ny5E9/85jfx7W9/Gy+99FKf5Tdt2gSz2ez4KikpUbtJROOeyWBw6ehvWZLgNUEX0/IyGFx+DU+9669BRJ9S/bGLoiiYN28efv3rXwMA0tLSkJOTg+eeew733Xdfr/IGgwGGUfjlQjSeJQQEYkdhAeDC3Q4SAgJdVrcrJQcGIb+uFjYneiesNbXQ+ft/+n1tHSAEtH5+/Z5jUxTMCpyYnw3RRKX6H1uhoaFITEzscWzWrFkoLi5W+1JEk0ZyYPCQN0kbCkWIXtvJTxQpwSFOPxZpOni4x/eWA4cAAMbEhAHPS56gnw3RRKV6+Fi6dCny8vJ6HMvPz0dUFEeSE/VnXkgo3F24xb23wYAF08JdVr8rrZ0+w+ll1a119ah6/gVYDn6C6ldeQ9Ohw/CYmwZDP4NNJQAz/fwRbfJRr8FENCjVw8d3v/tdHD16FL/+9a9RWFiI1157Df/85z/x0EMPqX0pogmvs7MTR48exT/+/ndMb2mD5KJVPD+fnAqDVvWnrKMi2NMT182YCY0TASTo/i8AWi3qt25H29lz8F6+FAH33NlveQHg/tQ01faMISLnqP7baP78+Xj33XexadMmPPnkk5g+fTr+/Oc/495771X7UkQTVkdHB44fP46jR4+itbUVALDA2wuFGgkdTjxi8Fo4H14L5w9aTgJg0GpxX2raSJs8pv7fvIXYeaFw0HIaT08EP/Alp+qUJQnBHp64OSFx8MJEpCqX/Cl000034aabbnJF1UQTWmtrK44dO4bjx4+j/cqS3j4+Pli2bBlSU1MRn3cOP9q7S7XrCQA/X3kNgj09VatzLCQFBeP/zVuIZ04cVWfHX3SNg/nDuvVw1+lUqpGInDUx+2GJJpjm5mYcOXIEJ06cgPXKXiMBAQFYvnw5kpOTIV9ZPvyOxGQcLinG1vzzI77JSgA2xs/CbbOSRljT+PDwgkU4VlaCjIpyVTaZ+9aCRVgUznWFiMYCwweRC5nNZnzyySfIysqCzWYDAISEhGD58uWYNWtWr7EGkiThd9deD5tQsL0gf0TXvjE2Hk+vvW7SjGfQazT4v8/dii+//w4yKsqGFc4kdPUGfS19Hh5ZuGSw4kTkIpIQLpzfNwwWiwUmkwlmsxne3t5j3RyiYamvr8ehQ4dw6tQpKFfGcISHh2P58uWIjY0dNBDYFQUvZmfid4cPQhHC6Wm4GkmCLEn44dIVeGBOOuRJEjyu1mGz4c/HDuOfGScgAXB2bVKNJMGo0+HJVWuxMT5h0oQyovFiKPdvhg8iFdXU1ODQoUM4c+YMun+0oqOjsWLFCkRHRw/5hnexoR5/OnoYOwrzoQgBWZJ6BRGNJDleu35mHL67aAlifPtfVGuyyK4ox6NvvY7LQukKWVc+h6tpZRl2RYFeo8Gts5LwnYWLEeQxsce/EI1XQ7l/87ELkQoqKipw8OBBnDt3znFs5syZWL58OSIjI4ddb4yvH/66/ibUtLZge0EeTlVWIruqAo3t7ZAAmNzckBYShtnBwbghNh6B7h4qvJuJwau1DSsbmrDIzYCI1auQW1uD09WVaOrohCxJCHR3x5yQUKSFhGJ9bDy8uZIy0bjB8EE0AiUlJTh48CAKCgocx2bNmoVly5YhLKzvha2GI9DdA/elpgOpqlU54WVkZAAAlqXMxg0LFo1xa4hoKBg+iIZICIHLly/j4MGDuHTpEoCugaLJyclYtmwZgoKCxriFk19TUxPOnz8PAJg3b94Yt4aIhorhgya8tk4rzlfW4Gx5NepaWiEEYHJ3Q2JoIGaFBsHLTZ3udiEECgsLceDAAZSWlgIAZFlGamoqli1bBr8BNi+joVEUgeKGRuSWVeNyXQOsNjsMOi2mB/giKSwIF05nQwiByMhIhj2iCYjhgyYkIQSyisvx2rFT2JlbAJuiQJIAjdS1XoYiBBQhIEnAyrjpuHfhHCyZEQVZHvoMByEEzp07h4MHD6KyshIAoNFokJ6ejqVLl8JkMqn63qayuuZWvJ2Rg9eOZaO6qQVA16BRoGuKbPcGc54yMBN6rEvhcyiiiYizXWjCqW1uwc+37MXecxegkSXYlYH/CXeXmRs1DZtvXYcIPx+nrqMoCnJycnDo0CHU1NQAAHQ6HebNm4fFixfDy8trpG+FrhBC4I0Tp/H0jgPotNmdWESs63UPgwE/23ANbprNqbNEY41TbWnSOn6pFA+/tgWtHZ1D3oJeI0vQyDJ+e9v1uC45rt9ydrsdp06dwqFDh9DQ0AAAMBgMWLhwIRYuXAh3d/cRvQfqqaWjE9/+z1YcvlA85HO7Fw27LikWT992PQw6duYSjRVOtaVJ6filEnz1pXdgV8Swlte2KwKKYsd33/gAv1MEbpwd3+N1q9WKrKwsfPLJJ7BYLAAAd3d3LFq0CPPnz4ebm5sq74M+1dppxZf/9V/klFUN6/zufwW7zxaiuf19/P0LN0Ov1ajXQCJyCYYPmhAqzE34xqvv9xk8aj7egbqDuzDz0SehdR94ASmBrr+Wf/j2h5ge4IvEsCB0dHTg5MmTOHLkCFpausYZeHp6YsmSJZg7dy70er2L3hX99N1dyCmrGvFeLYoQOHyxGE9/+DEe33CNSq0jIldh+KBxTwiBn767C502myobigkAsgT84K3teHR2FDJOnEBbWxsAwGQyYdmyZZgzZw60Wv54uNKu3AJ8mDOy/WuuJgTw2vFTuC45Fgumc8M4ovGMv11p3Nt3/uKwxgMMxK4IXKytxwv7yxEnW+Hv749ly5YhJSUFGg277V3NZlfw1LZ9jjEbapElCT/fshcffPs+DkAlGscYPmjce/VoFjR97GmihguSO3506xokJSU5trUn19t3/gJqm1tVr1cRApdqG3DichkWTA9XvX4iUgfDB41r5Y0WHL1Y4lRZpb0N5Xu2ojnvDADAKz4Fwetvg6zrb8yGBLNdwOrtx+Axyt46eQZyHxvBfVZ7ZSlqPtqOtpJLEELAOC0KgavWwxge3e85GlnC2xlnGD6IxjH+xqVxLbukwumyZe+8DKWzHYHX3AivWakwnz6B2gM7BzxHlqQhXYNGTgiBrJKKQYNHR00lil76GzqqyuG3+BoELL8W1sY6FL/yd7SVFfV7nl0ROHm5TO1mE5GK2PNB41pueRW0sgzblZUtB+IWPA2hG+52fG9va4U5+ziC1mzo9xwJGPY0Txqe0gYzWjo6By1Xs387oNgRed+3oPf1BwCYUubj4rObUb13K6K+9HC/51aYm2Bpa4e3kdOjicYj9nzQuFZtaXF6hovP3CU9vnePjIG9rQX2jvZ+z7ELgQpz04jaSENTZWketIxQFLRczIdnfIojeACA1ssb3snpaCu5NOD/VwCO5dmJaPxh+KBxze5Ej0c3nbdvj+9lNyMAQGkbeGDjUK5BI+dMmLS3NkNYO6H3C+z1mj4gGBACNkvjwNcZZNl9Iho7DB80rnm5GSA7O2Wyn03jBrsFqbXrLTnHwzA6i7Z5uHFxOKLxiuGDxrW4kACX9kxoZRmzQrkl+2iaGeg/aKDUuHtC0unRWV/T67XO2mpAkqD19un3fHe9DmEmbvxHNF4xfNC4Fhvgo+oiVJ9lUxQkhTF8jCaDTouYQN8By0iyDI+YODTn5aCzsd5x3NbcBEtuJowR06Ex9D2YVAKQFBbMRcaIxjHOdqFxRwiB4uJiZGVl4UxOLoxwQxskdN1W1GXQarA8Nlr1emlgN6Qk4G/7jgw4/iNw1Q1ouZiP4pf+Cp+5SyHJMhozj0DYbAPOYBIA1qf0v2sxEY09hg8aN5qbm3Hq1ClkZWWhrq7OcTzVS4djTXbVe0A0soSb05LgyTEfo+72ucn4274jA5YxBIYg6r6HUbPvA9Qf3tu1yFhYJMJuvhfGaVH9nuem0+JzqbPUbjIRqUgSwgVrVo+AxWKByWSC2WyGt7f3WDeHXExRFFy4cAGZmZnIz8+HcmV8h06nQ3JyMtLT0+Hh64/1//MvWNraVQ0geo0GW771JUT5+6hYKznrqa378PqJ06psFthNAvDNVQvxrTVLBi1LROoayv2bPR80JhobG5GVlYXs7GxYLBbH8fDwcKSlpSEpKQkGw6c9Ek9uXIvvvL5N1TY8um4Zg8cYenTdMuw7fwHVTc6v5TIQjSQhOsAXX1+5UIXWEZErMXzQqLHZbMjLy0NmZiYuXrzoOG40GjF79mykp6cjKKjvwZ/rkmJxz4LZ+M/x0yNuhyxJWBEXjS8uShtxXTR8HgY9/nT3TbjvhbdgsysjCiCyJMFNp8Uf77oRei13JSYa7xg+yOWqq6uRmZmJ06dPo62tzXE8JiYGaWlpSEhIgFY7+D/Fn954DTptCv6bmTPstkgAlsVG4c933QS5n3VBaPTMiQjFP794C77+yruwKQrsw1gYTCNLMOp0eOH+2xAXHOCCVhKR2jjmg1yis7MTOTk5yMrKQmlpqeO4l5cX5syZg7S0NPj6Djzdsi9CCLxx4jSe3nEAVrvd6ZuV5krQeHj1Ynx1+XxoNZxlPp4UVtfhsbd34GxFtdPnSOia2ZIeGYbf3HYdIvx8XNU8InLCUO7fDB+kGiEEysrKkJmZidzcXHR2dm0eJssy4uLikJ6ejhkzZqiyfX1Zgxl/3XcEH5zOg11RIMtyr8XINJLkGKC6OiEG375mCeJC+JfxeGWzK3jteDZe/CQDlebmfjcU7D4e6eeDryyfh9vTk9mLRTQOMHzQqGptbcXp06eRlZWF6upP/3L18/NDeno6UlNT4enp6ZJrN7S2YUdOPs6UVuJUSQXqW9sghIC30Q2p4aFImhaM9clxCPZ2zfVJfYoi8MmFIhy9UIzTZZW4WFOP5pZWyBBIighDenQEls6MwoLp4VxIjGgcYfgglxNC4NKlS8jMzMT58+dht9sBAFqtFomJiUhPT0dkZCRvDqSKP/3pT7BYLHjwwQcRFhY21s0hoj5wqi25jMViQXZ2NrKystDY2Og4HhoairS0NKSkpMDNre9lr4mGS6/v2iSuo6NjjFtCRGpg+JgAbHYFFyvqcK64GhX1FtjtCowGHWaE+SMxKhiBJtc+UrDb7cjPz0dWVhYKCwvR3VlmMBiQkpKC9PR0hIaGurQNNDU1tXXgfHE1zjdKqGky4N8f52BmkRmzIoIQFxEIo1431k0komFg+BjHSmoa8faB03j30Bk0t3cN3uyepSGEcMz0iA8PxN2r03DdvHi46dX7X1pXV4fMzEycOnUKLS0tjuNRUVFIS0tDYmIidDr+8id1KYrAkbOX8fr+bBzOvQyB7l199Lhw4gKU44UQomvg6bVz43DnqlSkxvBRDNFEwjEf41Cn1Ybntx/DiztPAFLXL+OByBKgCCDY1xNP3nc95sdHDPvaVqsVZ8+eRVZWFoqKihzHPTw8kJqaivT0dPj7+w+7fqKBFFc34mcv7cCpixXQyNKgU6m7y1yTNhM/vnsN/LzdR6mlRPRZHHA6gVU1NOGhv76DS5X1GOr/GVmSoAiBB66bj4c3Lh3SYM+KigpkZmbizJkzjufqkiRh5syZSE9PR2xsLDQarhxJrrPzZB6eeGknlGEsNqaRJbi76fHnb25E2sxpLmohEQ2E4WOCqmpowv2/fR21lpZhrfR4tbtWpuKHd60eMIC0t7fjzJkzyMrKQkVFheO4j48P0tLSMGfOnCn3/4DGxvbj5/DTF3c4Fg4bDlmSoNHI+Pu3b8Xc2HA1m0dETuBslwnIarfjO39/X5XgAQBvfHwK00P9cefK1B7HhRAoLi5GZmYmzp49C5vNBgDQaDRISEhAeno6pk+fzimyNGrOFlXiiX/tBDD84AGga28Yu4LvPPMe3vn5/Qjy4douROMVw8c48dKuk8gvrVG1zj/992MsTYrGtAATmpubcerUKWRlZaGurs5RJjAwEOnp6Zg9ezbc3fm8nEZXp9XW1eMxki6PqyhCoMNqw5Ov7MJfH76FIZponGL4GAdqzS3457ajqtdrsyv45cvbsWqajPz8fChXlqrW6XRITk5Geno6pk2bxl/QNGbeOnAaRdUNQx7fNBC7InD4bBEO5VzC8pQY9SomItUwfIwD732SM6LtxPtjVwSOFVTA1NgMo0YgPDwcaWlpSEpKgsFgUP16REOhKAL/+ShLlR6Pz9LIEl7fn83wQTROMXyMA28fPO1U+GgqK0TZ0S1or6+EzsOE4DmrYW2xoDJjF9K+8cc+z5EASIEz8M27rkVQUJDKLScavqwLZSivswxYpuLEDlRm7ELiPZtQmbEH5stnIAD4TE9BxLLbIOv0fZ5nVwSOni1CVUMTgn29XNB6IhoJl+8r/pvf/AaSJOGRRx5x9aUmpJrGZlQ3Ng9arrW2FBe2/xP29laEzrsO/gkLUXlyF8yXcwY+UZLQKnsweNC4c/piOWQnH/ld2v0y7NZ2hC68Eb4xqajPO4GKjJ0DniMA5FyqVKGlRKQ2l/Z8nDhxAv/4xz8we/ZsV15mQjtbXOVUuYoTOyFJMuJu/hZ0HiYAgO+MVJx94+kBzxMCyLnMX8A0/uRedu7fPgAYA6YhatXdju9tHa2oO38c0xZt6PccjSzjbHEV1qTHjqidRKQ+l/V8NDc3495778Xzzz8PX1/ffst1dHTAYrH0+JpKaswtg5YRioKmsnyYopMdwQMADKZAeEfMGvT8huY2jLPlXIhQ2dDk9FingMQlPb73DImBvb0F9s72Ac4SqHGiV5GIRp/LwsdDDz2EG2+8EWvXrh2w3ObNm2EymRxfERHDXxp8IlIUgcE6nm1tzRA2KwymgF6v9XWsL2qsHUKkpu7ZV87Qe/b8A0ZjMAIA7B2t/Z4jBGBn6CYal1wSPl5//XVkZmZi8+bNg5bdtGkTzGaz46ukpMQVTRq3PNz0rhjs34Neq3FsSEc0Xni5uzldtr/p4ANlC1mW4OnW94BUIhpbqo/5KCkpwXe+8x3s3r0bbm6D/3IxGAxTetpn7LTBey60Rk9IGi06zLW9Xuvr2HCuQTTa4sMDkVVYBpvd+R6QobDZFcSGB7qkbiIaGdX/HM7IyEB1dTXS09Oh1Wqh1Wrx8ccf4y9/+Qu0Wi3sdrval5zQYkL9odMOvGGbJMvwCo+D+XIOrC1mx/EOcw0sJecGPFcjy0ieHqpKW4nUlBgV7LLg4bhGJGd5EY1Hqvd8rFmzBmfOnOlx7IEHHkBCQgIee+wx7oz6GVqNjGvmzMCezIIBx2WEzrsO+SV5yH/vrwhIXAIhFNTmHILRNxRtdWX9nmdXFKxN42h/Gn+WJkVDp9XAanPNHyTBvp6Ij2D4IBqPVA8fXl5eSE5O7nHMw8MD/v7+vY5T10ZvC6N9sfPkwCM/3AMjMOPGr6HsyBZUnPgQOk8fhM6/Hu2N1Whv7HvKogQgIsgH6bHcYpzGHy93N9y4cBa2HslVfUC0JEm4a9UcaGSOdSIaj7jC6RiqrKzEzp07cenSZfjr3FFv1WCguS9e02KRcPv3ehy7uOMF6D18+iwvAHxzwxLu3ULj1n3XzsO2o2fR3xrrofOvR+j863sd909YAP+EBX2eI0mAycMNty5NUbOpRKSiUQkf+/fvH43LTBhNTU3Yt28fsrOzAQBarQZfW5uMP+wpQKe1/y5oxdYJWfvp6P32xhpYis/BL25er7IaWcLylBismxunevuJ1BIV7IuHNy7Fn985qFqdQgA/+8K18PZwfjYNEY0u9nyMIqvViiNHjuDQoUOwWq0AgOTkZKxZswY+Pj7wCp2OH7/wYb/n5772K/jHz4feyx+dzQ2ozT0MSdYgaM41PcppZAnBvl746efXsteDxr1716TjRF4JjpwtUmWDxbtXzcHK1BkqtIyIXIXhYxQIIZCTk4O9e/fCbO6arTJt2jRcd911PRZVu35+AtqtNjz16m5IkHr9IvaOSEBDQRasbU2QNFp4BEchbMGNcPP5dDqhfCV4PP/oHfDzdh+dN0g0AhpZxu++tgHf/8cWHDlbNKJ1b25bloLv37FKraYRkYtIYpytu22xWGAymWA2m+Ht7T3WzRmx0tJS7Ny5E6WlpQAAb29vrF27FsnJyf32SpzML8Hj/9qBmsYWp/8SlKWusHLdvHg8dtdq+HgaVXsPRKPBarfjxR0n8M8PjkKSnF+VVyNL0Gk1+N7tK3HrshT29hGNkaHcvxk+XMRsNmPPnj3IyenadVan02HZsmVYvHgxdDrdoOe3tnfixZ0n8NaBU7C0dkCrkXutiSBJXaHDrggkRQXjqzcsxMrZ7G6miS2/tAbPbTuCj09f6DogRK+B2BpZgqIIaDUyrp+fgG9sWIxQv4n7+4JoMmD4GEOdnZ04dOgQjhw5ApvNBgCYM2cOrrnmGnh5eQ29PqsN+09fQFZhOc5cqkB5nQV2RYFRr0N8eCASo4KxMnUGErieAU0ylfVNeO6tD5Fx/jJaJSPskgaSJMHXy4iU6aFIiQ7BtXPjYeLAUqJxYSj3b475UIkQAtnZ2di3bx+am7t20oyKisJ1112H0NDhrzCq12mxbm481s2NV6upRBNCiJ8X4r3tkHzacN11K7Bo0aKxbhIRqYThQwWXL1/Gzp07UVlZCQDw9fXFtddei4SEBD5/JhqB7p+pkQR4Ihp/Jn34sDS3I/9iFQouV6O5pQMSAD9fD8TFBCM2KhAGw+DjL/pTX1+P3bt34/z58wC6NslbsWIFFixYAK120n+0RKoRQqCi2oy8i1UoKqtHR4cNEhTkFbXA211CUFDwWDeRiFQ0Ke+QdruCI5mX8N8PM3HyVNfUPVmSIMtdvRB2RYEQgE4rY82yWbj1+jlIjHX+L6v29nYcOHAAx44dg6IokCQJc+fOxapVq+Dh4eGid0U0+Via2/HhRzl4e3sWKqq7pqFrNDIkdAUSu9I1nuPub72IW69Pw4a1KfDz4c8Y0UQ36QacFpXW4am/fIjzFyohXxkRPxCN3DVbZO2yBHz3q2tg8up/iqqiKMjIyMD+/fvR2toKAJgxYwbWrVuHoCAO+CRylhACuw+dxx/+uRutbZ2A6G+B9U/JkgStToNv3bcKG9elOv6YIKLxYcrOdvlwfy6e/vvOK38xDe1tybIELw8Dfvvj25AU17sXpLCwELt27UJNTQ0AICAgAOvWrUNsLHeMJRqKTqsNv/zLh9h3OA+S1LUc+lDNmx2FX/9wI9yN+sELE9GomJLhY9ueM/jNsztHdG35ymJF//OLO5EcFwYAqKmpwa5du1BYWAgAMBqNWLVqFebOnQuNRjOi6xFNNVarHT/6zbs4furysEJHN1mWEB8TjP/5+Z0MIETjxJQLH6fPl+Ghn/5n0F9mTfUluHT6fbSYy6HYrUi95hF4+vTcbl6WJXgY9fjfp+/BqazjOHnyJIQQkGUZCxYswIoVK2A0cvVQouH48//tw38/zBxR8OgmyxJWLorDU9/bMPLKiGjEptQ6H+0dVjz1P9shSRIGylGKYkfe8Vcgy1pMn/05yBod3Nx9+ygn0NLage/89AWkRLYBAOLj43HttdfC39/fZe+DaLLLyi3B29szVatPUQQ+OpyH/UvisWoxd28mmkgmfPh464NMVNZYBgweANDeUoeO1gbMSLsdIdMXDlhWEUBlo4zkGf64754bMX36dDWbTDTlCCHw+3/udmoQ+FBIEvCH5/dg2fwZ0Gr5GJRoopDHugEjYbcreHt75qDBAwCsHV2rjmr1zj0ykWUJHZppDB5EKjh9rgxFpfWqBg+ga7Bqg7kVB08UqlovEbnWhO75OHm6CHUNLYOWKzj5OqqLMwAAecdeQR4A74AYpKz4Zr/nKIrAJycuosHcCl8Tt6YnGomte89Ao5Fgt/cMH8Vnd6Hk/G6kX/tDlJzfjfqKc5BkDUKmL0Jk4nXobDPj4ql3Ya65AFmjw7S4VZgWu7JHHbIsYcuu01i9mFsQEE0UEzp8nDlf5linYyDB0xdBbzShNG8fQmcsg6dvOPSGwTd5U4TA+cJKLJ4bo1aTiaak7NySXsHjannHX4XRKwhRyevRUHkepXl7odW7o+rSUZgCZyIq+QbUlGTh8plt8PSNgCng059JRRHIyS+HEILbGRBNEBP6scu5C1VQnHjk4u0fDZ+grgFp3gHTERQ5Fz7Bgw9Q08gS8i5WjbidRFNZc0sHKmssA5bx9I1A/IJ7ERqzBLMW3w+90YTLZ7YhKGo+ZqTditCYJUhc/GXIGh2qLx/vdX5buxVllY0uegdEpLYJHT6qaiyqTNnrlyShpr7ZhRcgmvzqGgb/GQqO/nQQuCTJ8PQJByAQHL3AcVyrN8LoGYj2lvo+6+DPKtHEMaHDh11RXH4NZRSuQTSZObPasMHdp8f3Wp0bZFkLnaHnPi4anRts1rY+61B7MCsRuc6EDh9eHm4uvwZXTyQaGQ/3wX+GJKmPX0V9HQPQ3y4wHvxZJZowJvSA07iYIORdrILd7preCbtdQVnROezebUN0dDQiIyNhMBhcci2iyUIIgfr6ehQXF6OkpARFRUXQyAJ2xXWDQWVJwvQILgJINFFM6PCRMCME7+085dJr2NtrcfhwDQ4fPgxJkhASEoKoqCjHF5dap6nObrejoqLCETaKi4sduz538za6oaHFdYuARYT5wmDQuax+IlLXhA4fS+fFODXVdjgkCQgJ9Ma9d61FUVERioqK0NDQgIqKClRUVODo0aMAgODg4B5hxMPDY5CaiSa2trY2lJaWOsJGWVkZbDZbjzIajQZhYWGIjIxEREQEZhVY8JcXP3ZJe2RJwtplCS6pm4hcY0KHD1+TB1YvicdHh/NcEkDu2jAPc+bMwZw5cwB0bZrTHUSKiopQW1uLqqoqVFVV4fjxrul/AQEBiIqKQnR0NKKiouDlNfh6IkTjlRACjY2Njh6NkpISVFdX9ypnNBodQSMiIgJhYWHQaj/99RIR2Yl/vvYJ2jtsvc4dMQnYsHa2+vUSkctM+F1tLxbX4IHvvaxq+JAlCb4+7vjPX78y4IDT5ubmHmGkr1/Kfn5+jl6R6OhomEwm1dpJpDZFUVBZWdkjbDQ1NfUq5+fn5wgbkZGR8Pf3H3SBrxfePIwX3zys6vR4WZbwuWtn4/tfu1a9SoloWIZy/57w4QMA/vXWEfzf65/0MwZ+eP74+O1YMCd6SOe0traiuLgYly9fRlFRESorK3uV8fHx6fGYxtfXl6sy0pjp6OhAaWmpI2yUlpbCarX2KCPLMkJDQx1BIyIiAp6enkO+ltVqx5d/8DKKytTZ40WWJPj7euDff/kyZ6URjQNTLnzYbHY8+tTbyD5bqsovtXtvXoBvfnHFiOtpb29HcXGxo2ekvLy81yZ4Xl5ejkc0UVFRTv0FSTRcFoulx8DQqqqqXv8mDQaD4/FJZGQkpk2bBp1OncGcl0pq8fVNr6G9wzqin1VJkqDVyPjrk3chOT5MlbYR0chMufABAK1tnXhs87vIPlsyrG5dCV2rB9x501x86/5VLgkAHR0djqmHRUVFKCsr67WImYeHR4/HNIGBgQwjNCyKoqCmpqZH2DCbzb3K+fj49AgbQUFBLv03d76wEt/5xZtob7cO63GpRpag0Wrw2023YN7sKBe0kIiGY0qGD6CrW/fFt47glXeOQZKcX/FQI0vQ67X47lfWYP3qpFG72VutVpSWljoe05SWlsJut/coYzQaezymCQ4OhixP6LXhyEWsVivKysocYaOkpAQdHR09ynRPF7/6EcpQf87UUF7ViF//bQeyz5YO+dzY6UF4/Ns3ICYywAUtI6LhmrLho9v5C5V44Y3DOJxxEbIkAX0EEY1GhmJXoNVqcN3KRHzlriUI9B/bmSk2mw1lZWWOnpGSkpJez98NBgOioqIQGRmJ6OhohIaGMoxMUc3NzT0GhlZUVPTqSdPr9QgPD+/xCGW8LJSnKALb9+Xg1feOo7SiARqN3OeCgd3Hg/y9cPfn5uHW9WnQavhvnmi8mfLho1tFtRkfHcnH+cJKnCusRHNrB2Spa4puUlwoEmNDcc3S+FFZpn047HY7ysvLHWGkuLgYnZ2dPcro9XpEREQ4HtOEhYVBo3HdYk40NoQQqK2t7RE26ut7b7Dm5eXVYxbKROgpE0IgK7cEJ04V4WxBBS6V1MFqtUGr1SAyzBeJsaFIT4nEgtRoaBg6iMYtho9JqnsaZPdjmuLiYrS3t/coo9VqHWEkKioK4eHhPdZboInBZrOhvLy8R9hoa+u9oVpQUJAjaERGRsJkMnGMEBGNCYaPKUIIgaqqqh5rjXx2WWuNRoPw8HDHY5rw8HDo9ZyWON60trY6xmkUFxejvLy81/gfrVaLadOm9VjMy81tfPbaEdHUw/AxRQkhUFNT0yOMNDc39ygjyzLCwsIcj2kiIiLGzRiAgbS2dKAwvxKF+VWwmFsBCTCZ3DEzLgQz40JgdGLn1PFCCIGGhgYUFxc7ejVqa2t7lfPw8OgxMDQ0NJSP1Iho3GL4IACf7i56+fJlx+JnFoulRxlJkhAaGup4TBMZGTluNssTQiA74zLe/+9JHDmYD0URkCQJsqbrsYJiFxBCQJYlLF0Zj423zcPstKhx99jBbrejsrKyx5TXlpaWXuUCAgJ6PELhAnRENJEwfFCfuvfp6O4VuXz5MhobG3uV694sr3vxM3d391Fva3WlGb//9VZknbzc7yyIq3WXmb9oBh7ddCMCAsfu3057e3uPjddKS0v73Xjt6p6NsficiYjUwvBBTjObzT0e09TV1fUqExgY2GPhs+EsrT0URz8pwC8ffwc2qw12+9D+ecoaCQa9Do//6jbMXzTDRS38lBACZrO5x8DQqqqqXuWMRmOPhbw+u/EaEdFEx/BBw9bU1NQjjNTU1PQq4+/v3yOMqPn/6fCBPPzix29DCDHsDcgkqWtsy5O/vRMLFs9UrW1A14yjqqqqHmHjs4+yAMDX17fHlNeAgAA+QiGiSY3hg1TT0tLSY7O8vv6q9/Hx6bE/jY+Pz7ButEWXa/GN+56H3WbvFTwulOzDpdKPsGLej6DXeQxalyQBWp0Gz7/6dUwL9xtyW7p1dnb22njts2utyLKMkJCQHmHD1b1DRETjzVDu3+z3pQF5eHhg1qxZmDVrFgCgra2tx2Z5FRUVaGxsRHZ2NrKzswEA3t7eiI6Odkzv9fPzGzSM2G0Knv7Fe1CU4fd4XE2IrgGpv31qC/707H2QZefCUFNTU49ZKJWVlQNuvBYREYFp06Zx+jIR0RAwfNCQGI1GxMfHIz4+HsCnm+V194yUl5fDYrHg9OnTOH36NADA09Ozx2Oavh5B7N5xGgV5laq21W5XcPZMKfbvycU165J7vd49NfnqWSh9DcA1mUw9ejUCAwPH/aqhRETjGcMHjYjBYMDMmTMxc2bX2IruxxTdPSOlpaVobm5Gbm4ucnNzAQDu7u49NssLCgrCu28ehyRBlV6Pq8myhHffPI5r1iXDarWivLy8x8Zrn10hVpIkBAcH95iFYjKZ1G0UEdEUx/BBqtLr9YiJiUFMTAyArmXCrw4jJSUlaG1txblz53Du3DkAgLXDgIuFtoGqdbDaWnH+0lbUNRZClmSEBKRiZtQ6aGRdn+UVReD82XL88Q/PoaW1ptfGazqdrsfGa+Hh4RNi0TUioolM9fCxefNmvPPOOzh//jyMRiOWLFmCp59+2tFNT1OLVqtFdHQ0oqOjAXy6WV73Y5qSkhJUFHcCkK58DexM/htwM/hgZuS1MDeVoKTyKKy2NiTH3j7AWQIF56sREi7g6enZ4xFKSEgIH6EQEY0y1cPHxx9/jIceegjz58+HzWbDj3/8Y6xbtw5nz56Fh8fgsxRoctNoNI6BmsuXL4eiKPjl42/hUl4hFGXwZy5uBl/MSbgXABARshBajQGlVccRFbYMXh4hfZ4jyxKCAqbj29++cdgzcYiISD2qh48dO3b0+P5f//oXgoKCkJGRgRUrVvQq39HRgY6ODsf3fa2ZQJOXLMtoa7U7FTyArsDR4/vQRSitOo66xvx+w4eiAFD08PX1HWlziYhIBS7vbzabzQAAP7++11rYvHkzTCaT4ysiIsLVTaJxZrCl06/m7ubf43ujwQ+AhLaOxoGvoTh/DSIici2Xhg9FUfDII49g6dKlSE7uPdURADZt2gSz2ez4KikpcWWTaBzy9HQb/qMQJ06TZQkeHhxESkQ0Xrh0tstDDz2EnJwcHDp0qN8yBoOBswumuOkzg/DJwTwI++BlW9vrYHT79PFJW3s9AAGjwWfA82JmBo+skUREpBqX9Xw8/PDD2LZtGz766COEh4e76jI0CcQlhEFxcgO5kspjPb+vOAoA8PeJ7fccRRGITQgdfgOJiEhVqvd8CCHwrW99C++++y7279+P6dOnq30JmmTmzI2Cu7sera2dg5Zt72hA9vlX4e8TC3NTCSprTyEkYDa8PPoPF17eRiTP5lgiIqLxQvWej4ceegivvvoqXnvtNXh5eaGyshKVlZVoa2tT+1I0SRgMOtywMd2p/VdSYu+ELGlRWLwbtQ35CA9ZiFkzbu63vCxLuOnmdOj1XE+PiGi8UH1X2/4GDr744ou4//77Bz2fu9pOTTXVFtx/19/R2eHcSqdOkQCjUY9/vfH/4OfPXWaJiFxpTHe1VTnL0BQghMDFS+cQFWtFQY6KC4AJ4Fvfu57Bg4honGFfNI2p9vZ2bNmyBefOnUNQGGDvNOFSQfOIN5iTJGDNdSlYe32KOg0lIiLVcFMLGjMVFRX45z//iXPnzkGWZaxffz3+9vzDWLYqYcR1r1qbhO//eAOXUiciGofY80GjTgiBjIwM7NixA3a7HSaTCXfccQemTZsGAPjJk7finTeO4YXnPoIQAnYnp+FqNBJkWcZX/98a3HzHfKcGsBIR0ehj+KBR1dHRgW3btiEnJwcAEBcXh5tvvhlGo9FRRqORccfnF2Phkli8/L8f4+D+8xACkGT0Wg9E1kgQSteslhXXzMKXvroS4RF9L+VPRETjg+qzXUaKs10mr6qqKrz11luoq6uDJElYu3YtFi9ePOijkfq6Zny89yzyzpXjfG45LJY2SBLg7W1EQtI0xCeGYeU1ifD1467JRERjZUxnuxB9lhAC2dnZ2L59O2w2G7y9vXH77bc7vYmgn78nbrlzgYtbSUREo4Xhg1yqs7MT27dvx6lTpwAAM2fOxC233AJ3d/cxbhkREY0Vhg/qpcXShsKcUlw8W4YmcysgSfDx98TM5HDEJE6Dm1HvVD01NTV46623UFNTA0mSsHr1aixbtowzUIiIpjiGDwIAKIqCzAN52PLSIZzcfw5CCEhy1+wRAFDsCoQQ0GhlLL9xDjZ8aRkS5/a/b8+pU6fwwQcfwGq1wtPTE7fddhuio6NH6d0QEdF4xgGnhPKiWvzhe6/h7MlLkDUyFLsyYHmNRobdrmDp9bPx8C9vh0+Al+M1q9WKDz/8EFlZWQCAmJgY3HLLLfD05CqjRESTGQecktMObMvC77/3GhRbV+AYLHgAgP1KmSO7c3DqcAF+9r9fQfKCGairq8Nbb72FqqoqAMDKlSuxYsUKR+8JERERwPAxpX30fgZ++8irXd8Mo/9LsStobW7Hj7/wHL7yi3U4e/kkOjs74eHhgVtvvRUxMTHqNpiIiCYFho8pquBMCX7/3X8PK3RcTVEEhNWGfz6+Ham3eiMucTpuu+02eHl5DX4yERFNSQwfU1Bnhw2/e+TVrt3XRpo+AAgBCDvQkGvAFzd/ERqNZuSNJCKiSYsP46eg7f/+BKUXq50a3+E0AVzOrcHJ/efVq5OIiCYlho8pRlEUvPfiARX6O3qTNTK2/OuAC2omIqLJhI9dppizJy+hqqTeqbLttmYUNB5GTdtlWJUOeOhMiPaei3DPpD7LK3YFmQfzUVPRiMBQHxVbTUREkwnDxxRzNuMyZFmCogzc99Fhb8HRytcBSIj0SoVeY0Rt22Xk1O2GTelAtHd6v+eez7qMwNA56jaciIgmDT52mWIKTpc4V67xMAQEloR+HjN9FiLSazbSgz6HEPc4FDYehV2x9XmeRiuj8Eypmk0mIqJJhuFjiqkpbxi010MIgcrWQgQau5ZP77S3Ob4CjFGwiU5YOqv7OReoqzKr3m4iIpo8+NhlirE7McOlU2mDTelAaXMOSptz+inT2vfJQjh1DSIimroYPqYYT2+jE6W6ekbCPBIQ5pHYZwkvfUCfxyVZgrun23CbR0REUwDDxxQTkzQNZ45fgN3Wf++EXjZCI+khhECAMXJI9St2BTGzwkbaTCIimsQ45mOKiU2JGDB4AIAkyQhxn4nK1kI0ddb2er3T3s8jF3SN+ZiZEjHidhIR0eTFno8pZt7KWdAZtLB29D1bpVuc71LUtZfgaOXrCPdMhqfOH1alHZbOatS1F2NNxDf7PC8gxISZyeGuaDoREU0S7PmYYjxNRqy5ZR40moH/1xs0Hlgceg+meSahqvUCztZ/hKKmLFiVdsT5LOvzHEmSsOG+5YPWTUREUxt7PqagG7+0GLveOjZoOYPGHYl+q5Hot3rQspIkwcvHHevvWaRGE4mIaBLjn6hTzIULF/D+h28hPN2gar1CCHznN3fBy8dD1XqJiGjyYc/HFGGz2bB3714cPXoUAJCyYhpMWoGcY5cgBll0zBkbvrQMS65LGXE9REQ0+TF8TAHV1dV45513UFVVBQCYN28e1q1bB+VBgae+/iIyD5yHGEH+WH/PInzj57eo1FoiIprsGD4mMSEEjh8/jj179sBms8Hd3R0bN25EXFxcVwEd8PP//SrefHYv/v0/OwF0rdPhDFkjQ6fT4GtP3Iz19yyGJEmuehtERDTJSEKM5G9e9VksFphMJpjNZnh7e491cyas5uZmvP/++ygsLAQAzJw5Exs3boSnp2ef5S+dK8crf9qBo3u6llOXJKlXENFoZSh2BRqtBqs2puMLj1yP4HA/174RIiKaEIZy/2b4mITy8/Px/vvvo7W1FRqNBuvWrcP8+fOd6p2oqWjEoQ+ykX+6BHnZRWgyt0GWAZOfJxLSohE/JxLLb5wDb18OLCUiok8N5f7Nxy6TiNVqxa5du3Dy5EkAQHBwMG699VYEBQU5XUdgqA9u+eoqF7WQiIiI4WPSqKiowDvvvIPa2q7l0BctWoQ1a9ZAq+X/YiIiGl94ZxoDiqKg/EIV8k9eQFlBBawdVhiMBoTHhyFubgxCpgc5PYBTCIHDhw9j3759UBQFnp6euPnmmzFjxgwXvwsiIqLhYfgYRQ3VZnz4v3ux5e87UFfeAADQaDWQpK4Q0b3hW3B0IG5+eD3W3b8K3n5e/dZnsVjw3nvv4dKlSwCAhIQEbNiwAe7u7q5/M0RERMPEAaejQAiBbf/YjX987yV0dlgHX9RLAiRIMHq54dvPPIhrPr+sV09Ibm4utm3bhvb2duh0Olx//fVIS0vjlFciIhoTHHA6jrQ2teHJ23+PjN2nnT9JAAICbU3t+M0X/4LD7x/HYy9/C3o3PTo6OrBjxw5kZ2cDAMLCwnDrrbfC39/fNW+AiIhIZQwfLtTW0o7H1j2J/JMXh3V+d6fUwXeOocXcim88+0Vs2bYFDQ1dj2yWL1+OlStXQqPRqNZmIiIiV2P4cKE/fvVZ5J+86PSqof0RikDmntN44vO/wYz1oTCZTLjlllsQFRWlUkuJiIhGD3e1dZGD7xzD/jcOjzh4dBMCqDheB385GN/4xjcYPIiIaMJi+HABm9WGvz78v6oP/pRkCRmvnYPBYFC1XiIiotHE8OECR7ZmoKGyEWpPJBKKQGleOU4fOKtqvURERKOJYz5cYPvzeyBr5H4fubSJFhQhD/WoRjtaoYEWvghELGbDKA28Z4pGK+PD/92L1JVJrmg6ERGRy7ms5+OZZ55BdHQ03NzcsHDhQhw/ftxVlxpXhBDI/eT8gGM9LGhAI+oQjAjEYw6mIQb1qEYGPoZd2Aas325TcObgObWbTURENGpcEj7eeOMNPProo/jZz36GzMxMpKam4rrrrkN1dbUrLjeuVFysQltz+4BlAhCKRdK1mCElYZoUg5lSMtKwDO1oRTXKBr1GdXEtmhtb1GoyERHRqHJJ+PjjH/+IBx98EA888AASExPx3HPPwd3dHS+88EKvsh0dHbBYLD2+JrLasvpBy2ikT9flUISCTtEBIzyhhQ4WNDh1nbrywa9DREQ0Hqk+5qOzsxMZGRnYtGmT45gsy1i7di2OHDnSq/zmzZvxi1/8Qu1mjBlnptbahR2XcR7luIwOtPV4zYaBH7sM5TpERETjkeo9H7W1tbDb7QgODu5xPDg4GJWVlb3Kb9q0CWaz2fFVUlKidpNGlYdp8E3d8pCFSziHYIQjBYuQhuVIw3LooAfg3AwZd29uHkdERBPTmM92MRgMk2rdishZ0yDLEpQBNo+rRhlCEY04KdVxzC7ssMHq1DWMnm4IigwYcVuJiIjGguo9HwEBAdBoNKiqqupxvKqqCiEhIWpfbtwxGA2ISJg2YBkJEj7bw1GCQggnej0kCYidG8Pda4mIaMJSPXzo9XrMnTsXe/fudRxTFAV79+7F4sWL1b7cuLTqrqWQ5f7DQQBCUYli5IlslIqLyBUnUILCK49dBiYArLpziYqtJSIiGl0ume3y6KOP4vnnn8dLL72Ec+fO4Zvf/CZaWlrwwAMPuOJy4876r67p6qLoRxxSEYIoVKIYBTiNTrQjHSugceIpmMFNjzVfWKFmc4mIiEaVS8Z83HXXXaipqcETTzyByspKzJkzBzt27Og1CHWy8g/1xU1fvxbbntvV59gPnaRHEub1Or4MNwxYryRJuOP7n4O7l1G1thIREY02Sai9AckIWSwWmEwmmM1meHt7j3Vzhq2tuQ1fTvwu6ssboCgjnxYra2RExIfh2czfQqfXqdBCIiIi9Qzl/s2N5VzE6GnE428+Co1OhjTA+A9nyBoZBnc9fvrGowweREQ04TF8uFDiojj86oMfQ6fXQdYM76OWtTKMnm743Z6fITopQuUWEhERjT6GDxdLuyYFfz/5G8TMjgKG0gFypWziojg8m/FbxM+f6ZL2ERERjTaGj1EQlRiBvx3bjG/+8X4ERvgDADQ6Te+CEqDRdh0PmxGC7/7j6/jD/l8gNGZqDNQlIqKpgQNOR5miKMjYdQpZe8/g/IlClJwvh81qg86gQ3RSOOLnzcTcdalIXZXEhcSIiGjCGMr9m+GDiIiIRoyzXYiIiGjcYvggIiKiUTXmu9p+VvdTIIvFMsYtISIiImd137edGc0x7sJHU1MTACAigmtaEBERTTRNTU0wmUwDlhl3A04VRUF5eTm8vLw424OIiGiCEEKgqakJYWFhkOWBR3WMu/BBREREkxsHnBIREdGoYvggIiKiUcXwQURERKOK4YOIiIhGFcMHERERjSqGDyIiIhpVDB9EREQ0qv4/iIh28StxnSEAAAAASUVORK5CYII=", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "T = ex_mg.torus(0, 2, 10, 12, delta = 1, seed = 17)\n", - "T.draw()\n", - "plt.title('T')" - ] - }, - { - "cell_type": "code", - "execution_count": 31, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Text(0.5, 1.0, 'L')" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "L = ex_mg.line(0, 12)\n", - "L.draw()\n", - "plt.title('L')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Create an interleaving and to generate all the relevant matrices.\n", - "\n", - "Then, we can try to solve the problem using ILP." - ] - }, - { - "cell_type": "code", - "execution_count": 32, - "metadata": {}, - "outputs": [], - "source": [ - "myInt = Interleave(T, L, initialize_random_maps=True, seed=0)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Let's get all the matrices. Diagram: Vertex triangle F_G_F." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Inclusion matrices to define the maps $F \\to F_n \\to F_{2n}$ and $G \\to G_n \\to G_{2n}$. Can be accessed by `Interleave.I`. \n", - "\n", - "For vertex triangle from $F$ to $G$, we need $I^V_{F^n}$ and $I^V_{F}$" - ] - }, - { - "cell_type": "code", - "execution_count": 33, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Inclusion matrices \n", - "\n", - "I_F_0 = myInt.I('F', '0', 'V')\n", - "I_F_0.draw()" - ] - }, - { - "cell_type": "code", - "execution_count": 34, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "I_F_n = myInt.I('F', 'n', 'V')\n", - "I_F_n.draw()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Multiply $I^V_{F^n}$ with $I^V_{F}$ and denote it by $I$. Is the multiplication method correct? " - ] - }, - { - "cell_type": "code", - "execution_count": 35, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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WLYWFhZleDgDgxoyHUHp6uqKiogrvx8fHS5Li4uI0Z84c08sBANyY8RDq2rWrKlmzVgBAJcVnQgAA2xBCAADb2H6K9vUs2rdTATUrlpHdQtuYKQYA4BLshAAAtiGEAAC2IYQAALYhhAAAtiGEAAC2MR5CiYmJ6tChg2rWrKm6deuqT58+2rt3r+llAAAewHgIrV69WsOHD9emTZu0YsUK5eXlKSYmRjk5OaaXAgC4OePfE1q2bFmR+3PmzFHdunW1bds23XvvvaaXAwC4MZd/WTUzM1OSVKtWrRJ/TntvAPBeLj0xoaCgQKNGjdI999yjO+64o8QxtPcGAO/l0hAaPny4du3apY8++ui6Y2jvDQDey2Vvxz3//PP69NNPtWbNGtWvX/+642jvDQDey3gIWZalF154QYsWLVJaWpoiIiJMLwEA8BDGQ2j48OGaN2+elixZopo1a+rUqVOSpMDAQPn5+ZleDgDgxox/JpSUlKTMzEx17dpVISEhhbcFCxaYXgoA4OZc8nYcAABlwbXjAAC2qbSdVfve3lI+jmoVmiP1xHYzxYgurQDgCuyEAAC2IYQAALYhhAAAtiGEAAC2IYQAALZxyZdVW7VqpYCAAAUEBKhz5876/PPPTS8DAPAAxkOofv36mjp1qrZt26b09HTdf//9io2N1ddff216KQCAmzP+PaFevXoVuT9lyhQlJSVp06ZNatGihenlAABuzKVfVs3Pz9fHH3+snJwcde7cucQxdFYFAO/lkhMTdu7cqRo1asjpdOrZZ5/VokWL1Lx58xLH0lkVALyXS0KoWbNm2r59uzZv3qznnntOcXFx2r17d4lj6awKAN7LJW/HVa9eXU2aNJEktWvXTlu3btUbb7yhd955p9hYOqsCgPf6Rb4nVFBQUORzHwAAJBfshCZMmKAePXooLCxMFy9e1Lx585SWlqbU1FTTSwEA3JzxEDpz5oyGDBmikydPKjAwUK1atVJqaqoefPBB00sBANyc8RBKTk42PSUAwENx7TgAgG0IIQCAbSpte28TTLbkNtUqnDbhAPBv7IQAALYhhAAAtiGEAAC2IYQAALYhhAAAtnF5CE2dOlUOh0OjRo1y9VIAADfj0hDaunWr3nnnHbVq1cqVywAA3JTLQig7O1uDBg3Se++9p9tuu81VywAA3JjLQmj48OHq2bOnoqOjSx2Xm5urrKysIjcAgHdwyRUTPvroI2VkZGjr1q03HJuYmKiXXnrJFWUAACo54zuhY8eOaeTIkfrrX/8qX1/fG46nvTcAeC/jO6Ft27bpzJkzuvPOOwuP5efna82aNXr77beVm5urqlWrFv6M9t4A4L2Mh9ADDzygnTt3Fjk2bNgwRUZGaty4cUUCCADg3YyHUM2aNXXHHXcUOebv76+goKBixwEA3o0rJgAAbPOL9BNKS0v7JZYBALgZdkIAANt4dGdVk0x1RDXVodUkur0CsAs7IQCAbQghAIBtCCEAgG0IIQCAbQghAIBtjIfQpEmT5HA4itwiIyNNLwMA8AAuOUW7RYsW+uKLL/69iA9nggMAinNJOvj4+Cg4ONgVUwMAPIhLPhPav3+/QkND1ahRIw0aNEhHjx697lg6qwKA9zIeQp06ddKcOXO0bNkyJSUl6fDhw/rNb36jixcvljg+MTFRgYGBhbcGDRqYLgkAUEk5LMuyXLnAhQsXFB4erunTp+vJJ58s9vPc3Fzl5uYW3s/KylKDBg3UVbHycVRzZWm24LI9ADzdFStPaVqizMxMBQQElDrW5WcM3Hrrrbr99tt14MCBEn9OZ1UA8F4u/55Qdna2Dh48qJCQEFcvBQBwM8ZDaMyYMVq9erW++eYbbdiwQX379lXVqlU1cOBA00sBANyc8bfjvv32Ww0cOFDfffed6tSpoy5dumjTpk2qU6eO6aUAAG7OeAh99NFHpqcEAHgorh0HALANIQQAsA0XdfuFVcbv5PDdJQB2YScEALANIQQAsA0hBACwDSEEALANIQQAsI1LQuj48eP63e9+p6CgIPn5+ally5ZKT093xVIAADdm/BTt77//Xvfcc4+ioqL0+eefq06dOtq/f79uu+0200sBANyc8RCaNm2aGjRooPfff7/wWEREhOllAAAewPjbcUuXLlX79u3Vv39/1a1bV23bttV777133fG09wYA72U8hA4dOqSkpCQ1bdpUqampeu655zRixAilpKSUOJ723gDgvYy3965evbrat2+vDRs2FB4bMWKEtm7dqo0bNxYb723tvSsjLtsDwKTytPc2vhMKCQlR8+bNixz79a9/raNHj5Y43ul0KiAgoMgNAOAdjIfQPffco7179xY5tm/fPoWHh5teCgDg5oyH0OjRo7Vp0yb9+c9/1oEDBzRv3jy9++67Gj58uOmlAABuzngIdejQQYsWLdL8+fN1xx13aPLkyZoxY4YGDRpkeikAgJtzST+hhx56SA899JArpgYAeBCuHQcAsA2dVVEpT4c2edp4ZXx+AH7CTggAYBtCCABgG0IIAGAbQggAYBtCCABgG+Mh1LBhQzkcjmI3rpgAAPg546dob926Vfn5+YX3d+3apQcffFD9+/c3vRQAwM0ZD6E6deoUuT916lQ1btxY9913n+mlAABuzqVfVr18+bI+/PBDxcfHy+FwlDimpH5CAADv4NITExYvXqwLFy5o6NCh1x1DZ1UA8F4uDaHk5GT16NFDoaGh1x0zYcIEZWZmFt6OHTvmypIAAJWIy96OO3LkiL744gstXLiw1HFOp1NOp9NVZQAAKjGX7YTef/991a1bVz179nTVEgAAN+eSECooKND777+vuLg4+fhwoW4AQMlcEkJffPGFjh49qieeeMIV0wMAPIRLtikxMTGyLMsVUwMAPAjXjgMA2IYQAgDYhrMGUCmZbMltqlU4bcIB89gJAQBsQwgBAGxDCAEAbEMIAQBsQwgBAGxjPITy8/OVkJCgiIgI+fn5qXHjxpo8eTJfXgUAFGP8FO1p06YpKSlJKSkpatGihdLT0zVs2DAFBgZqxIgRppcDALgx4yG0YcMGxcbGFl49u2HDhpo/f762bNlieikAgJsz/nbc3XffrZUrV2rfvn2SpK+++krr1q1Tjx49Shyfm5urrKysIjcAgHcwvhMaP368srKyFBkZqapVqyo/P19TpkzRoEGDShyfmJiol156yXQZAAA3YHwn9Le//U1//etfNW/ePGVkZCglJUWvvvqqUlJSShxPe28A8F7Gd0Jjx47V+PHj9dhjj0mSWrZsqSNHjigxMVFxcXHFxtPeGwC8l/Gd0KVLl1SlStFpq1atqoKCAtNLAQDcnPGdUK9evTRlyhSFhYWpRYsW+vLLLzV9+nS6rAIAijEeQm+99ZYSEhL0n//5nzpz5oxCQ0P1H//xH5o4caLppQAAbs54CNWsWVMzZszQjBkzTE8NAPAwXDsOAGAbOqvC45nqiGqqQ6tEl1bgKnZCAADbEEIAANsQQgAA2xBCAADbEEIAANu4JIQuXryoUaNGKTw8XH5+frr77ru1detWVywFAHBjLgmhp556SitWrNAHH3ygnTt3KiYmRtHR0Tp+/LgrlgMAuCnjIfTDDz/ok08+0csvv6x7771XTZo00aRJk9SkSRMlJSWZXg4A4MaMf1n1ypUrys/Pl6+vb5Hjfn5+WrduXbHxubm5ys3NLbxPZ1UA8B7Gd0I1a9ZU586dNXnyZJ04cUL5+fn68MMPtXHjRp08ebLY+MTERAUGBhbeGjRoYLokAEAl5ZLPhD744ANZlqVf/epXcjqdevPNNzVw4MBifYYkOqsCgDdzybXjGjdurNWrVysnJ0dZWVkKCQnRgAED1KhRo2Jj6awKAN7Lpd8T8vf3V0hIiL7//nulpqYqNjbWlcsBANyMS3ZCqampsixLzZo104EDBzR27FhFRkZq2LBhrlgOAOCmXLITyszM1PDhwxUZGakhQ4aoS5cuSk1NVbVq1VyxHADATblkJ/Too4/q0UcfdcXUAAAPwrXjAAC2IYQAALahvTdQRiZbcptqFU6bcLg7dkIAANsQQgAA2xBCAADbEEIAANsQQgAA25Q7hNasWaNevXopNDRUDodDixcvLvJzy7I0ceJEhYSEyM/PT9HR0dq/f7+pegEAHqTcIZSTk6PWrVtr5syZJf785Zdf1ptvvqlZs2Zp8+bN8vf3V7du3fTjjz9WuFgAgGcp9/eEevTooR49epT4M8uyNGPGDP33f/934RWz586dq3r16mnx4sV67LHHKlYtAMCjGP1M6PDhwzp16pSio6MLjwUGBqpTp07auHFjiY/Jzc1VVlZWkRsAwDsYDaFTp05JkurVq1fkeL169Qp/9nO09wYA72X72XG09wYA72U0hIKDgyVJp0+fLnL89OnThT/7OafTqYCAgCI3AIB3MBpCERERCg4O1sqVKwuPZWVlafPmzercubPJpQAAHqDcZ8dlZ2frwIEDhfcPHz6s7du3q1atWgoLC9OoUaP0P//zP2ratKkiIiKUkJCg0NBQ9enTx2TdAAAPUO4QSk9PV1RUVOH9+Ph4SVJcXJzmzJmjF198UTk5OXrmmWd04cIFdenSRcuWLZOvr6+5qgEAHsFhWZZldxHXysrKUmBgoLoqVj6OanaXA7gE/YTgya5YeUrTEmVmZt7wc37bz44DAHgvOqsCNjC1gzG1o5LYVcEe7IQAALYhhAAAtiGEAAC2IYQAALYhhAAAtjHeWXXhwoWKiYlRUFCQHA6Htm/fbqhUAICnMd5ZNScnR126dNG0adMqXBwAwLMZ7awqSYMHD5YkffPNNzddFADAO9j+ZdXc3Fzl5uYW3qezKgB4D9tPTKCzKgB4L9tDiM6qAOC9bH87zul0yul02l0GAMAGtu+EAADey3hn1fPnz+vo0aM6ceKEJGnv3r2SpODgYAUHBxsqGwDgCcq9E0pPT1fbtm3Vtm1bST91Vm3btq0mTpwoSVq6dKnatm2rnj17SpIee+wxtW3bVrNmzTJYNgDAE5R7J9S1a1eV1ox16NChGjp0aEVqAgB4CT4TAgDYhhACANjG9lO0Adw8ky25TbUKp004yoOdEADANoQQAMA2hBAAwDaEEADANoQQAMA2Rtt75+Xlady4cWrZsqX8/f0VGhqqIUOGFF7CBwCAaxlt733p0iVlZGQoISFBGRkZWrhwofbu3avevXsbKRYA4FmMtvcODAzUihUrihx7++231bFjRx09elRhYWE3VyUAwCO5/MuqmZmZcjgcuvXWW0v8Oe29AcB7ufTEhB9//FHjxo3TwIEDFRAQUOIY2nsDgPdyWQjl5eXp0UcflWVZSkpKuu442nsDgPdyydtxVwPoyJEj+uc//3ndXZBEe28A8GbGQ+hqAO3fv1+rVq1SUFCQ6SUAAB7CaHvvkJAQPfLII8rIyNCnn36q/Px8nTp1SpJUq1YtVa9e3VzlAAC3V+4QSk9PV1RUVOH9+Ph4SVJcXJwmTZqkpUuXSpLatGlT5HGrVq1S165db75SAIDHMd7eu7SfAQBwLa4dBwCwDZ1VAUgy1xHVVIdWk+j2WnmxEwIA2IYQAgDYhhACANiGEAIA2IYQAgDYxmhnVUmaNGmSIiMj5e/vr9tuu03R0dHavHmzqXoBAB7EaGdVSbr99tv19ttva+fOnVq3bp0aNmyomJgYnT17tsLFAgA8i9HOqpL0+OOPF7k/ffp0JScna8eOHXrggQfKXyEAwGO59Muqly9f1rvvvqvAwEC1bt26xDF0VgUA7+WSExM+/fRT1ahRQ76+vnr99de1YsUK1a5du8SxdFYFAO/lkhCKiorS9u3btWHDBnXv3l2PPvqozpw5U+JYOqsCgPdySQj5+/urSZMmuuuuu5ScnCwfHx8lJyeXONbpdCogIKDIDQDgHX6R7wkVFBQU+dwHAADJcGfVoKAgTZkyRb1791ZISIjOnTunmTNn6vjx4+rfv7/RwgEA7s9oZ9VZs2bpX//6l1JSUnTu3DkFBQWpQ4cOWrt2rVq0aGGuagCARzDeWXXhwoUVKggA4D24dhwAwDaEEADANrT3BmBUZWylTcvxyoudEADANoQQAMA2hBAAwDaEEADANoQQAMA2xtt7X+vZZ5+Vw+HQjBkzKlAiAMBTGW/vfdWiRYu0adMmhYaG3nRxAADPZry9tyQdP35cL7zwglJTU9WzZ89Sx9JZFQC8l/HPhAoKCjR48GCNHTu2TBctpbMqAHgv4yE0bdo0+fj4aMSIEWUaT2dVAPBeRi/bs23bNr3xxhvKyMiQw+Eo02OcTqecTqfJMgAAbsLoTmjt2rU6c+aMwsLC5OPjIx8fHx05ckS///3v1bBhQ5NLAQA8gNGd0ODBgxUdHV3kWLdu3TR48GANGzbM5FIAAA9gtL13WFiYgoKCioyvVq2agoOD1axZs4pXCwDwKEbbe8+ZM8dYYQAAz2e8vffPffPNN+VdAgDgJbh2HADANnRWBeDxKmMXU5PdXivj8ysrdkIAANsQQgAA2xBCAADbEEIAANsQQgAA2xjvrDp06FA5HI4it+7du5uqFwDgQVzSWbV79+46efJk4W3+/PkVKhIA4Jlc0lnV6XQqODj4posCAHgHl3wmlJaWprp166pZs2Z67rnn9N133113bG5urrKysorcAADewXgIde/eXXPnztXKlSs1bdo0rV69Wj169FB+fn6J42nvDQDey/hlex577LHC/9+yZUu1atVKjRs3Vlpamh544IFi4ydMmFB4JW5JysrKIogAwEu4/BTtRo0aqXbt2kV6EF3L6XQqICCgyA0A4B1cHkLffvutvvvuO4WEhLh6KQCAmzHaWbVWrVp66aWX9PDDDys4OFgHDx7Uiy++qCZNmqhbt25GCwcAuD+jnVWTkpK0Y8cOpaSk6MKFCwoNDVVMTIwmT54sp9NprmoAgEcw3lk1NTW1QgUBALwH144DANiGEAIA2Ib23gBgA5MtuU21CrejTTg7IQCAbQghAIBtCCEAgG0IIQCAbQghAIBtjLf3lqQ9e/aod+/eCgwMlL+/vzp06KCjR4+aqBcA4EGMt/c+ePCgunTposjISKWlpWnHjh1KSEiQr69vhYsFAHgW4+29/+u//ku//e1v9fLLLxcea9y48XXH5+bmKjc3t/A+nVUBwHsY/UyooKBA//jHP3T77berW7duqlu3rjp16lTiW3ZX0VkVALyX0RA6c+aMsrOzNXXqVHXv3l3Lly9X37591a9fP61evbrEx0yYMEGZmZmFt2PHjpksCQBQiRm9bE9BQYEkKTY2VqNHj5YktWnTRhs2bNCsWbN03333FXuM0+mkzQMAeCmjO6HatWvLx8dHzZs3L3L817/+NWfHAQCKMRpC1atXV4cOHbR3794ix/ft26fw8HCTSwEAPIDR9t5hYWEaO3asBgwYoHvvvVdRUVFatmyZ/u///k9paWkm6wYAeACj7b3nzJmjvn37atasWUpMTNSIESPUrFkzffLJJ+rSpYu5qgEAHsFhldar2wZZWVkKDAxUV8XKx1HN7nIAoNKrbP2Erlh5StMSZWZmKiAgoNSxXDsOAGAbOqsCgJsztYMxtaPKulig224v21h2QgAA2xBCAADbEEIAANsQQgAA2xBCAADbGO+s6nA4Sry98sorpmoGAHgI451VT548WeQ2e/ZsORwOPfzwwxUuFgDgWYx3Vg0ODi5yf8mSJYqKilKjRo3KXx0AwKO59Muqp0+f1j/+8Q+lpKRcdwztvQHAe7n0xISUlBTVrFlT/fr1u+4Y2nsDgPdyaQjNnj1bgwYNkq+v73XH0N4bALyXy96OW7t2rfbu3asFCxaUOo723gDgvVy2E0pOTla7du3UunVrVy0BAHBzxjurSj+dXPDxxx/rtddeM1cpAMDjGO+sKkkfffSRLMvSwIEDzVQJAPBIdFYFAEgy3U/oEJ1VAQCVGyEEALAN7b0BAJLMtQm/YuVJOlSmseyEAAC2IYQAALYhhAAAtiGEAAC2IYQAALYx3t47Oztbzz//vOrXry8/Pz81b95cs2bNMlUvAMCDGG/vHR8fr2XLlunDDz/Unj17NGrUKD3//PNaunRphYsFAHgW4+29N2zYoLi4OHXt2lWS9Mwzz+idd97Rli1b1Lt372Lj6awKAN7L+GdCd999t5YuXarjx4/LsiytWrVK+/btU0xMTInj6awKAN7LeAi99dZbat68uerXr6/q1aure/fumjlzpu69994Sx9NZFQC8l/HL9rz11lvatGmTli5dqvDwcK1Zs0bDhw9XaGiooqOji42nsyoAeC+jIfTDDz/oD3/4gxYtWqSePXtKklq1aqXt27fr1VdfLTGEAADey+jbcXl5ecrLy1OVKkWnrVq1qgoKCkwuBQDwAMbbe993330aO3as/Pz8FB4ertWrV2vu3LmaPn260cIBAO6v3J1V09LSirT3vupqe+9Tp05pwoQJWr58uc6fP6/w8HA988wzGj16tBwOxw3np7MqALi3K1ae0rSkTJ1Vae8NADCqPCHEteMAALYhhAAAtiGEAAC2IYQAALYhhAAAtiGEAAC2IYQAALYx3ln19OnTGjp0qEJDQ3XLLbeoe/fu2r9/v6l6AQAexGhnVcuy1KdPHx06dEhLlizRl19+qfDwcEVHRysnJ8dIwQAAz2G0s+r+/fu1adMm7dq1Sy1atJAkJSUlKTg4WPPnz9dTTz1VsWoBAB7F6GdCV9t0+/r6/nuBKlXkdDq1bt266z4mKyuryA0A4B2MhlBkZKTCwsI0YcIEff/997p8+bKmTZumb7/9VidPnizxMbT3BgDvZTSEqlWrpoULF2rfvn2qVauWbrnlFq1atUo9evQo1mPoKtp7A4D3Mt7eu127dtq+fbsyMzN1+fJl1alTR506dVL79u1LHE97bwDwXi77nlBgYKDq1Kmj/fv3Kz09XbGxsa5aCgDgpox3Vv34449Vp04dhYWFaefOnRo5cqT69OmjmJgYo4UDANxfuUMoPT29SGfV+Ph4Sf/urHry5EnFx8fr9OnTCgkJ0ZAhQ5SQkGCuYgCAx6CzKgDAKDqrAgDcgvGz4yrq6sbsivKkSrVHAwCUxRXlSfr33+elqXQhdPHiRUnSOn1mcyUAgIq4ePGiAgMDSx1T6T4TKigo0IkTJ1SzZk05HI7rjsvKylKDBg107NixG77nWBpT81ATNXl6TZ783KjJ7FyWZenixYsKDQ297oUKrqp0O6EqVaqofv36ZR4fEBBQ4V+qyXlMzkVNv+w8Jufy5Jo8+bmZnMvba7rRDugqTkwAANiGEAIA2MZtQ8jpdOqPf/xjha87Z2oeaqImT6/Jk58bNdkzl1QJT0wAAHgPt90JAQDcHyEEALANIQQAsA0hBACwDSEEALANIQQAsA0hBACwDSEEALDN/wPhlxxFs+t2KQAAAABJRU5ErkJggg==", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# multiply two matrices\n", - "I = I_F_n @ I_F_0\n", - "I.draw()\n", - "\n", - "# We also keep a labeled matrix representation of the inclusion matrix\n", - "I_mat = I.to_labeled_matrix().get_array()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Store the distance matrix too. We need $D^V_{F^{2n}}$. Can be summoned by `Interleave.D`." - ] - }, - { - "cell_type": "code", - "execution_count": 63, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "D = myInt.D('F', '2n', 'V')\n", - "D.draw(colorbar=True)\n", - "\n", - "# We also keep a labeled matrix representation of the distance matrix\n", - "D_mat = D.to_labeled_matrix().get_array()\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's also store a $\\varphi_V$ and $\\psi_V^n$ matrices. These two are variable matrices in the ILP. Can be summoned by `Interleave.phi` and `Interleave.psi`." - ] - }, - { - "cell_type": "code", - "execution_count": 37, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "phi = myInt.phi('0', 'V')\n", - "phi.draw(colorbar=True)\n", - "\n", - "# We also keep a labeled matrix representation of the phi matrix\n", - "phi_mat = phi.to_labeled_matrix().get_array()\n" - ] - }, - { - "cell_type": "code", - "execution_count": 38, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "psi_n = myInt.psi('n', 'V')\n", - "psi_n.draw(colorbar=True)\n", - "\n", - "# We also keep a labeled matrix representation of the psi matrix\n", - "psi_n_mat = psi_n.to_labeled_matrix().get_array()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Before we set an ILP, let's check the dimension and function values of the matrices. Also, if everything lines up, we will try to solve it by block level." - ] - }, - { - "cell_type": "code", - "execution_count": 39, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Shape of inclusion matrix product I_F_n @ I_F_0: (20, 20)\n", - "Shape of distance matrix D: (20, 20)\n", - "Shape of phi matrix: (15, 20)\n", - "Shape of psi matrix: (20, 15)\n" - ] - } - ], - "source": [ - "# Print shapes of the matrices\n", - "print(f\"Shape of inclusion matrix product I_F_n @ I_F_0: {I.shape()}\")\n", - "print(f\"Shape of distance matrix D: {D.shape()}\")\n", - "print(f\"Shape of phi matrix: {phi.shape()}\")\n", - "print(f\"Shape of psi matrix: {psi_n.shape()}\")" - ] - }, - { - "cell_type": "code", - "execution_count": 40, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Function values of inclusion matrix product I_F_n @ I_F_0: [-2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]\n", - "Function values of distance matrix D: [-2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]\n", - "Function values of phi matrix: [-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]\n", - "Function values of psi matrix: [-2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]\n" - ] - } - ], - "source": [ - "# print the function values (block indices) of the matrices\n", - "print(f\"Function values of inclusion matrix product I_F_n @ I_F_0: {I.get_all_block_indices()}\")\n", - "print(f\"Function values of distance matrix D: {D.get_all_block_indices()}\")\n", - "print(f\"Function values of phi matrix: {phi.get_all_block_indices()}\")\n", - "print(f\"Function values of psi matrix: {psi_n.get_all_block_indices()}\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Attempt to set up the ILP." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Initialize the ILP\n" - ] - }, - { - "cell_type": "code", - "execution_count": 41, - "metadata": {}, - "outputs": [], - "source": [ - "prob = pulp.LpProblem(\"Triangle_ILP\", pulp.LpMinimize)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Matrix Parameters\n" - ] - }, - { - "cell_type": "code", - "execution_count": 64, - "metadata": {}, - "outputs": [], - "source": [ - "# D_mat\n", - "# I_mat\n", - "# phi_mat\n", - "# psi_n_mat" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Let's clear up the dimension problem\n" - ] - }, - { - "cell_type": "code", - "execution_count": 42, - "metadata": {}, - "outputs": [], - "source": [ - "m = 20 # Number of rows in $\\psi_n$\n", - "n = 15 # Number of columns in $\\phi_n$ or Numbe of rows in $\\phi$\n", - "p = 20 # Number of columns in $\\phi$\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### define the decision variables\n" - ] - }, - { - "cell_type": "code", - "execution_count": 43, - "metadata": {}, - "outputs": [], - "source": [ - "z = pulp.LpVariable.dicts(\"z\", ((i, j, k) for i in range(m) for j in range(n) for k in range(p)), cat='Binary')\n", - "psi_vars = pulp.LpVariable.dicts(\"psi\", ((i, j) for i in range(m) for j in range(n)), lowBound=0, cat='Integer')\n", - "phi_vars = pulp.LpVariable.dicts(\"phi\", ((j, k) for j in range(n) for k in range(p)), lowBound=0, cat='Integer')\n", - "psi_phi = pulp.LpVariable.dicts(\"psi_phi\", ((i, k) for i in range(m) for k in range(p)), lowBound=0, cat='Integer')\n", - "minmax_var = pulp.LpVariable(\"m\", lowBound=0, cat='Continuous')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Objective function" - ] - }, - { - "cell_type": "code", - "execution_count": 44, - "metadata": {}, - "outputs": [], - "source": [ - "prob += minmax_var" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Initialize the assignment decision variables\n" - ] - }, - { - "cell_type": "code", - "execution_count": 45, - "metadata": {}, - "outputs": [], - "source": [ - "for i in range(n):\n", - " for j in range(p):\n", - " prob += phi_vars[i,j] == phi_mat[i][j]\n", - "\n", - "for j in range(m):\n", - " for k in range(n):\n", - " prob += psi_vars[j,k] == psi_n_mat[j,k]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Constraints\n", - "1. $m \\geq \\sum_{i=1}^{m} d_{ik}(I_{ik}-C_{ik})$ for each $k$. \n", - "2. $-m \\leq \\sum_{i=1}^{m} d_{ik}(I_{ik}-C_{ik})$ for each $k$.\\\n", - " This is probably wrong. Check the other notebook.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 46, - "metadata": {}, - "outputs": [], - "source": [ - "for i in range(m):\n", - " prob += minmax_var >= pulp.lpSum(D_mat[i][k] *(I_mat[i][k] - psi_phi[i,k]) for k in range(p))\n", - " prob += -minmax_var <= pulp.lpSum(D_mat[i][k] *(I_mat[i][k] - psi_phi[i,k]) for k in range(p))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Constraints\n", - "\n", - "$C_{ik} = \\sum_{j=1}^{n} z_{ijk}$ for each $i$ and $k$." - ] - }, - { - "cell_type": "code", - "execution_count": 47, - "metadata": {}, - "outputs": [], - "source": [ - "for i in range(m):\n", - " for k in range(p):\n", - " prob += psi_phi[i,k] == pulp.lpSum(z[i, j, k] for j in range(n))\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Constraints\n", - "\n", - "1. $z_{ijk} \\leq \\psi_{ij}$ for each $i$, $j$ and $k$.\n", - "2. $z_{ijk} \\leq \\phi_{jk}$ for each $i$, $j$ and $k$" - ] - }, - { - "cell_type": "code", - "execution_count": 48, - "metadata": {}, - "outputs": [], - "source": [ - "for i in range(m):\n", - " for j in range(n):\n", - " for k in range(p):\n", - " prob += z[i, j, k] <= psi_n_mat[i, j] \n", - " prob += z[i, j, k] <= phi_mat[j, k]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Constraints\n", - "\n", - "$z_{ijk} \\geq \\psi_{ij} + \\phi_{jk} - 1$ for each $i$, $j$ and $k$." - ] - }, - { - "cell_type": "code", - "execution_count": 49, - "metadata": {}, - "outputs": [], - "source": [ - "for i in range(m):\n", - " for j in range(n):\n", - " for k in range(p):\n", - " prob += z[i, j, k] >= psi_n_mat[i, j] + phi_mat[j, k] - 1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Constraints\n", - "\n", - "These ones ensure that the $\\psi$ and $\\phi$ represnent valid assignment. This condition says that the sum of each coulmn should add to 1.\n", - "\n", - "1. $ \\sum_{i=1}^{m} \\psi_{ij} = 1$ for each $j$.\n", - "2. $ \\sum_{j=1}^{m} \\varphi{jk} = 1$ for each $k$." - ] - }, - { - "cell_type": "code", - "execution_count": 50, - "metadata": {}, - "outputs": [], - "source": [ - "for i in range(m):\n", - " prob += pulp.lpSum(psi_vars[i,j] for j in range(n)) == 1 \n", - "\n", - "for j in range(n):\n", - " prob += pulp.lpSum(phi_vars[j,k] for k in range(p)) == 1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Constraints\n", - "\n", - "These constraints ensure that the $\\psi$ and $\\phi$ are non-negative.\n", - "\n", - "1. $ \\psi_{ij} \\geq 0$ for each $i$ and $j$.\n", - "2. $ \\varphi_{jk} \\geq 0$ for each $j$ and $k$." - ] - }, - { - "cell_type": "code", - "execution_count": 51, - "metadata": {}, - "outputs": [], - "source": [ - "for i in range(m):\n", - " for j in range(n):\n", - " prob += psi_vars[i,j] >= 0\n", - "\n", - "for j in range(n):\n", - " for k in range(p):\n", - " prob += phi_vars[j,k] >= 0" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Solve the ILP" - ] - }, - { - "cell_type": "code", - "execution_count": 52, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Welcome to the CBC MILP Solver \n", - "Version: 2.10.3 \n", - "Build Date: Dec 15 2019 \n", - "\n", - "command line - /Users/ishikaghosh/anaconda3/envs/interleavingenv/lib/python3.13/site-packages/pulp/solverdir/cbc/osx/64/cbc /var/folders/5f/m89pr_zs78n8ffl7t7ndknth0000gn/T/1b991050110041639468f0d4162baf85-pulp.mps -timeMode elapsed -branch -printingOptions all -solution /var/folders/5f/m89pr_zs78n8ffl7t7ndknth0000gn/T/1b991050110041639468f0d4162baf85-pulp.sol (default strategy 1)\n", - "At line 2 NAME MODEL\n", - "At line 3 ROWS\n", - "At line 19680 COLUMNS\n", - "At line 59934 RHS\n", - "At line 79610 BOUNDS\n", - "At line 86611 ENDATA\n", - "Problem MODEL has 19675 rows, 7001 columns and 26252 elements\n", - "Coin0008I MODEL read with 0 errors\n", - "Option for timeMode changed from cpu to elapsed\n", - "Problem is infeasible - 0.92 seconds\n", - "Option for printingOptions changed from normal to all\n", - "Total time (CPU seconds): 0.97 (Wallclock seconds): 1.02\n", - "\n" - ] - }, - { - "data": { - "text/plain": [ - "-1" - ] - }, - "execution_count": 52, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "prob.solve()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Output the solution" - ] - }, - { - "cell_type": "code", - "execution_count": 53, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Objective value (minimization over the maximum of the absolute values of the matrix) = 2.0\n" - ] - } - ], - "source": [ - "print(f\"Objective value (minimization over the maximum of the absolute values of the matrix) = {pulp.value(prob.objective)}\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Put all the optimized values of the phi and psi matrix back to matrix form and output it." - ] - }, - { - "cell_type": "code", - "execution_count": 54, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Psi_n = [[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", - " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", - " [0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", - " [0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", - " [0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", - " [0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", - " [0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", - " [0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]\n", - " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", - " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", - " [0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n", - " [0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n", - " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", - " [0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]\n", - " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n", - " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n", - " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n", - " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]\n", - " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n", - " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]]\n", - "Phi = [[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", - " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", - " [0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", - " [0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", - " [0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", - " [0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", - " [0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", - " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", - " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]\n", - " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n", - " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n", - " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n", - " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]\n", - " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n", - " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]]\n" - ] - } - ], - "source": [ - "Psi_n = np.zeros((m, n))\n", - "Phi = np.zeros((n, p))\n", - "\n", - "for i in range(m):\n", - " for j in range(n):\n", - " Psi_n[i,j] = pulp.value(psi_vars[i,j])\n", - "\n", - "for j in range(n):\n", - " for k in range(p):\n", - " Phi[j,k] = pulp.value(phi_vars[j,k])\n", - "\n", - "print(f\"Psi_n = {Psi_n}\")\n", - "print(f\"Phi = {Phi}\")\n" - ] - }, - { - "cell_type": "code", - "execution_count": 55, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 55, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.matshow(Psi_n)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As the initial matrices are not equal to final matrices, we can say that ILP is at least doing something." - ] - }, - { - "cell_type": "code", - "execution_count": 56, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 56, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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SEh8AQFLiAwBISnwAAEmJDwAgqbK81Rb6It+9cmzK/R04Ec4F9HSufAAASYkPACAp8QEAJCU+AICkxAcAkJT4AACSEh8AQFLiAwBISnwAAEmJDwAgKfEBACQlPgCApMQHAJCU+AAAkhIfAEBS4gMASEp8AABJiQ8AICnxAQAkJT4AgKTEBwCQlPgAAJISHwBAUrWVHgDoW5ryk8q+xto928u+Rop/B/RWrnwAAEmJDwAgKfEBACQlPgCApMQHAJCU+AAAkhIfAEBS4gMASCrz+Dh8+HAsWrQoxo0bF4MHD47TTz89brvttiiVSlkvBQBUocw/4XTp0qWxfPnyWLVqVYwfPz62bNkSc+bMibq6upg3b17WywEAVSbz+Hj++edj5syZcemll0ZExNixY+Phhx+OF154IeulAIAqlPmfXT7/+c/HunXr4qWXXoqIiD//+c/x3HPPRXNz8xGPLxaLUSgUum0AQO+V+ZWPm266KQqFQpx11lnRv3//OHz4cNxxxx0xa9asIx7f0tISt956a9ZjAAA9VOZXPh577LF48MEH46GHHopt27bFqlWr4he/+EWsWrXqiMcvXLgwOjo6ura2trasRwIAepDMr3xcf/31cdNNN8WVV14ZERETJkyIV155JVpaWmL27NnvOz6Xy0Uul8t6DACgh8r8ysdbb70V/fp1f9j+/ftHZ2dn1ksBAFUo8ysfM2bMiDvuuCPGjBkT48ePjz/96U9x1113xbe//e2slwIAqlDm8XHPPffEokWL4gc/+EHs27cv8vl8fO9734vFixdnvRQAUIUyj4+hQ4dGa2trtLa2Zv3QAEAv4LtdAICkxAcAkJT4AACSEh8AQFLiAwBIKvN3uwBUWlN+UqVH+NjW7tle9jV6w++J6uTKBwCQlPgAAJISHwBAUuIDAEhKfAAASYkPACAp8QEAJCU+AICkxAcAkJT4AACSEh8AQFLiAwBISnwAAEmJDwAgKfEBACQlPgCApMQHAJCU+AAAkhIfAEBS4gMASEp8AABJiQ8AICnxAQAkJT4AgKRqKz0AAO/XlJ9U6REysXbP9rKv0Vt+V32JKx8AQFLiAwBISnwAAEmJDwAgKfEBACQlPgCApMQHAJCU+AAAkjru+NiwYUPMmDEj8vl81NTUxOrVq7vdXyqVYvHixTF69OgYPHhwNDY2xs6dO7OaFwCocscdHwcPHoyJEyfGsmXLjnj/nXfeGXfffXesWLEiNm/eHEOGDImmpqZ4++23P/awAED1O+6PV29ubo7m5uYj3lcqlaK1tTVuvvnmmDlzZkREPPDAA1FfXx+rV6+OK6+88uNNCwBUvUxf87F79+5ob2+PxsbGrn11dXUxderU2Lhx4xF/plgsRqFQ6LYBAL1XpvHR3t4eERH19fXd9tfX13fd999aWlqirq6ua2toaMhyJACgh6n4u10WLlwYHR0dXVtbW1ulRwIAyijT+Bg1alREROzdu7fb/r1793bd999yuVwMGzas2wYA9F6Zxse4ceNi1KhRsW7duq59hUIhNm/eHBdccEGWSwEAVeq43+1y4MCB2LVrV9ft3bt3x/bt22P48OExZsyYmD9/ftx+++1xxhlnxLhx42LRokWRz+fj8ssvz3JuAKBKHXd8bNmyJaZPn951e8GCBRERMXv27Fi5cmXccMMNcfDgwfjud78b//73v+MLX/hCrFmzJgYNGpTd1ABA1aoplUqlSg/xnwqFQtTV1cW0mBm1NQMqPQ4AH8PaPdvLvkZTflLZ1+DDvVs6FOvjiejo6PjQ129W/N0uAEDfIj4AgKTEBwCQlPgAAJISHwBAUsf9VlsAOFa95Z0o5X7XTm/5PR0rVz4AgKTEBwCQlPgAAJISHwBAUuIDAEhKfAAASYkPACAp8QEAJCU+AICkxAcAkJT4AACSEh8AQFLiAwBISnwAAEmJDwAgKfEBACQlPgCApMQHAJCU+AAAkhIfAEBS4gMASEp8AABJiQ8AICnxAQAkVVvpAQCgp2vKTyrr46/ds72sjx9R/n/D8XDlAwBISnwAAEmJDwAgKfEBACQlPgCApMQHAJCU+AAAkjru+NiwYUPMmDEj8vl81NTUxOrVq7vuO3ToUNx4440xYcKEGDJkSOTz+fjmN78Ze/bsyXJmAKCKHXd8HDx4MCZOnBjLli17331vvfVWbNu2LRYtWhTbtm2L3/72t7Fjx4748pe/nMmwAED1O+5POG1ubo7m5uYj3ldXVxdPP/10t3333ntvTJkyJV599dUYM2bMR5sSAOg1yv7x6h0dHVFTUxMnnHDCEe8vFotRLBa7bhcKhXKPBABUUFlfcPr222/HjTfeGFdddVUMGzbsiMe0tLREXV1d19bQ0FDOkQCACitbfBw6dCi+/vWvR6lUiuXLl3/gcQsXLoyOjo6ura2trVwjAQA9QFn+7PJeeLzyyivxhz/84QOvekRE5HK5yOVy5RgDAOiBMo+P98Jj586d8cwzz8SIESOyXgIAqGLHHR8HDhyIXbt2dd3evXt3bN++PYYPHx6jR4+Or371q7Ft27Z46qmn4vDhw9He3h4REcOHD4+BAwdmNzkAUJWOOz62bNkS06dP77q9YMGCiIiYPXt23HLLLfHkk09GRMSkSZO6/dwzzzwT06ZN++iTAgC9wnHHx7Rp06JUKn3g/Ue7DwDAd7sAAEmJDwAgKfEBACQlPgCApMQHAJBU2b9YDgA4uqb8pLKvsXbP9rI+fmF/Z5z46WM71pUPACAp8QEAJCU+AICkxAcAkJT4AACSEh8AQFLiAwBISnwAAEmJDwAgKfEBACQlPgCApMQHAJCU+AAAkhIfAEBS4gMASEp8AABJiQ8AICnxAQAkJT4AgKTEBwCQlPgAAJISHwBAUuIDAEhKfAAASdVWegAAoPya8pPK+vjvlg5FxN+O6VhXPgCApMQHAJCU+AAAkhIfAEBS4gMASEp8AABJiQ8AICnxAQAkddzxsWHDhpgxY0bk8/moqamJ1atXf+Cx3//+96OmpiZaW1s/xogAQG9y3PFx8ODBmDhxYixbtuyoxz3++OOxadOmyOfzH3k4AKD3Oe6PV29ubo7m5uajHvP666/HddddF2vXro1LL730Iw8HAPQ+mX+3S2dnZ1x99dVx/fXXx/jx4z/0+GKxGMViset2oVDIeiQAoAfJ/AWnS5cujdra2pg3b94xHd/S0hJ1dXVdW0NDQ9YjAQA9SKbxsXXr1vjlL38ZK1eujJqammP6mYULF0ZHR0fX1tbWluVIAEAPk2l8/PGPf4x9+/bFmDFjora2Nmpra+OVV16Jn/zkJzF27Ngj/kwul4thw4Z12wCA3ivT13xcffXV0djY2G1fU1NTXH311TFnzpwslwIAqtRxx8eBAwdi165dXbd3794d27dvj+HDh8eYMWNixIgR3Y4fMGBAjBo1Ks4888yPPy0AUPWOOz62bNkS06dP77q9YMGCiIiYPXt2rFy5MrPBAIDe6bjjY9q0aVEqlY75+L///e/HuwQA0Iv5bhcAICnxAQAkJT4AgKTEBwCQVObf7fJxvfdi1nfjUMSxv64VAKigd+NQRMQxvSmlx8XH/v37IyLiufjfCk8CAByv/fv3R11d3VGPqSkdz/tmE+js7Iw9e/bE0KFDj/n7YQqFQjQ0NERbW5uPZ+8DnO++xfnuW5zv6lUqlWL//v2Rz+ejX7+jv6qjx1356NevX5xyyikf6Wd9N0zf4nz3Lc533+J8V6cPu+LxHi84BQCSEh8AQFK9Ij5yuVwsWbIkcrlcpUchAee7b3G++xbnu2/ocS84BQB6t15x5QMAqB7iAwBISnwAAEmJDwAgKfEBACQlPgCApMQHAJCU+AAAkvq/ma8M9GTuV98AAAAASUVORK5CYII=", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.matshow(Phi)" - ] - }, - { - "cell_type": "code", - "execution_count": 57, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(False, True)" - ] - }, - "execution_count": 57, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# did phi and psi_n change?\n", - "np.allclose(phi_mat, Phi), np.allclose(psi_n_mat, Psi_n)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Implement the algorithm at the block level." - ] - }, - { - "cell_type": "code", - "execution_count": 62, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "D function values: [-2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]\n", - "Phi function values: [-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]\n", - "Psi function values: [-2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]\n", - "I function values: [-2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]\n" - ] - } - ], - "source": [ - "# get all indices of the matrices\n", - "\n", - "print(f\"D function values: {D.get_all_block_indices()}\")\n", - "print(f\"Phi function values: {phi.get_all_block_indices()}\")\n", - "print(f\"Psi function values: {psi_n.get_all_block_indices()}\")\n", - "print(f\"I function values: {I.get_all_block_indices()}\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "interleavingenv", - "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": "3.13.0" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/Notebooks_Unused/n_search_fail.ipynb b/Notebooks_Unused/n_search_fail.ipynb deleted file mode 100644 index d95cb3e..0000000 --- a/Notebooks_Unused/n_search_fail.ipynb +++ /dev/null @@ -1,119 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "id": "47f4a073", - "metadata": {}, - "outputs": [], - "source": [ - "%reload_ext autoreload\n", - "%autoreload 2" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "282a714d", - "metadata": {}, - "outputs": [], - "source": [ - "from cereeberus import Interleave, MapperGraph, ReebGraph\n", - "\n", - "import cereeberus.data.ex_reebgraphs as ex_rg\n", - "import cereeberus.data.ex_mappergraphs as ex_mg" - ] - }, - { - "cell_type": "markdown", - "id": "e191f088", - "metadata": {}, - "source": [ - "# Create torus and line mappers of mismatched heights" - ] - }, - { - "cell_type": "markdown", - "id": "d1a6c618", - "metadata": {}, - "source": [ - "### It works when the difference is 1" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "6c6b8ae9", - "metadata": {}, - "outputs": [], - "source": [ - "line = ex_mg.line(a=0, b= 16)\n", - "torus = ex_mg.torus(a=0, b =2, c = 13, d = 17)\n", - "myInt = Interleave(torus, line)\n", - "result = myInt.fit()\n", - "dist_result = myInt.dist_fit() # dist_fit function optimizes with the distance matrix\n", - "print(f\"Interleaving distance: {result}\")\n", - "print(f\"Interleaving distance (with dist_fit): {dist_result}\")" - ] - }, - { - "cell_type": "markdown", - "id": "30459cf0", - "metadata": {}, - "source": [ - "### But fails when the difference is more than 1" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "ee3dea41", - "metadata": {}, - "outputs": [], - "source": [ - "line = ex_mg.line(a =0, b= 16)\n", - "torus = ex_mg.torus(a=0, b =2, c = 13, d = 18)\n", - "myInt = Interleave(torus, line)\n", - "result = myInt.fit()\n", - "dist_result = myInt.dist_fit() # dist_fit function optimizes with the distance matrix\n", - "print(f\"Interleaving distance: {result}\")\n", - "print(f\"Interleaving distance (with dist_fit): {dist_result}\")" - ] - }, - { - "cell_type": "markdown", - "id": "b442c31a", - "metadata": {}, - "source": [ - "I checked the code and I think the problem is in the boundary matrix computation. Which affects the edge-vertex parallelogram checks. Tried fixing, but haven't figured it out yet." - ] - }, - { - "cell_type": "markdown", - "id": "c17be785", - "metadata": {}, - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "interleavingenv", - "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": "3.12.3" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/Notebooks_Unused/run_exprimetns_loop_line.ipynb b/Notebooks_Unused/run_exprimetns_loop_line.ipynb deleted file mode 100644 index 0d47efc..0000000 --- a/Notebooks_Unused/run_exprimetns_loop_line.ipynb +++ /dev/null @@ -1,797 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "%reload_ext autoreload\n", - "%autoreload 2" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "from cereeberus import ReebGraph, MapperGraph, Interleave\n", - "import cereeberus.data.ex_mappergraphs as ex_mg\n", - "import cereeberus.distance.ilp_torus_line as ilp_tl\n", - "import cereeberus.distance.ilp as ilp\n", - "\n", - "import matplotlib.pyplot as plt\n", - "import math" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# section hyperlink\n", - "[Section 3: Go here!!](#section_3)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## This notebook aims to find the the optimized loss function for a line mapper and a loop mapper over multiple iterations. Also the loop size of the mappers are varied to test out the optimization." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Section 1: Line and Loop Mapper Visualization\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Text(0.5, 1.0, 'Torus Mapper')" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# display the line and loop mapppers from ex_mappergraphs.py\n", - "\n", - "\n", - "M1 = ex_mg.line(0,10, seed=10)\n", - "M2 = ex_mg.torus(0,2,8,10, seed=10)\n", - "\n", - "# plot these two mappers as subplots\n", - "fig, axs = plt.subplots(1,2, figsize=(10,5))\n", - "\n", - "M1.draw(ax = axs[0])\n", - "axs[0].set_title('Line Mapper')\n", - "\n", - "M2.draw(ax = axs[1])\n", - "axs[1].set_title('Torus Mapper')\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Section 2: Loss Function Optimization with ILP for different loop sizes and thicknesses\n", - "\n", - "### We will try to find the optimized loss function for the line and loop mapper over different values of n." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "running for n=4\n", - "running for n=5\n", - "running for n=6\n", - "running for n=7\n", - "running for n=8\n", - "running for n=9\n", - "running for n=10\n", - "running for n=11\n", - "running for n=12\n", - "running for n=13\n", - "running for n=14\n", - "running for n=15\n", - "running for n=16\n", - "running for n=17\n", - "running for n=18\n", - "running for n=19\n", - "running for n=20\n", - "running for n=21\n", - "running for n=22\n" - ] - } - ], - "source": [ - "best_loss_dict = {}\n", - "for n in range(4, 23): # corresponds to loop sizes of 1 to 19\n", - " a, b, c, d = 0, 2, n, n+2\n", - "\n", - " print (f\"running for n={n}\")\n", - "\n", - " line = ex_mg.line(a,d, seed=10)\n", - " torus = ex_mg.torus(a,b,c,d, seed=10)\n", - "\n", - " losses_before, losses_after = ilp_tl.run_optimization_multi_n(line, torus, range(1,n//4+1))\n", - "\n", - " ub_before, ub_after = [num + i for i, num in enumerate(losses_before, start=1)], [num + i for i, num in enumerate(losses_after, start=1)]\n", - "\n", - "\n", - " # plt.plot(range(1,n//2), ub_before, label=f'Before n={n}')\n", - " # plt.plot(range(1,n//2), ub_after, label=f'After n={n}')\n", - "\n", - " best_loss_dict[n] = min(ub_after)\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Text(0, 0.5, 'Distance (Optimized or True)')" - ] - }, - "execution_count": 6, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "c_val = list(best_loss_dict.keys())\n", - "loop_size = [i-3 for i in c_val] # loop size is c - b - 1\n", - "\n", - "upper_bounds = list(best_loss_dict.values())\n", - "\n", - "# true interleaving \n", - "true_int = [math.ceil(i/4) for i in loop_size]\n", - "plt.figure(figsize=(10,5))\n", - "plt.scatter(loop_size, upper_bounds, color='green')\n", - "plt.step(loop_size, true_int, color='lightblue')\n", - "plt.xticks(range(1,21))\n", - "plt.legend(['Upper bounds', 'True interleaving'])\n", - "plt.xlabel('Loop size')\n", - "plt.ylabel('Distance (Optimized or True)')\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Section 3: See how the assignment change for different values of n\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "loss before optimization: 7.0\n", - "loss after optimization: 6.0\n" - ] - }, - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "line = ex_mg.line(0,20, seed=10)\n", - "torus = ex_mg.torus(0,2,18, 20, seed=10) # loop size is 15\n", - "\n", - "# create an interleaving object\n", - "myInt = Interleave(torus, line, n = 1, initialize_random_maps= True, seed=1)\n", - "\n", - "# optimize the interleaving\n", - "maps, loss = ilp.solve_ilp(myInt)\n", - "\n", - "# make subplots\n", - "fig, axs = plt.subplots(1,2, figsize=(15,5))\n", - "\n", - "# psi map before optimization\n", - "myInt.psi('0', 'V').draw(ax = axs[0])\n", - "\n", - "# psi map after optimization\n", - "maps['Psi_0_V'].draw(ax = axs[1])\n", - "\n", - "\n", - "\n", - "print(f\"loss before optimization: {myInt.loss()}\")\n", - "print(f\"loss after optimization: {loss}\")\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### checking if the loss is computed correctly when we pass the correct maps to the interleaving object" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "loss before optimization: 5.0 and loss after optimization: 4.0\n" - ] - } - ], - "source": [ - "line = ex_mg.line(0,16, seed=10)\n", - "torus = ex_mg.torus(0,2,14,16, seed=10) # loop size is 11\n", - "\n", - "# create an interleaving object\n", - "myInt = Interleave(torus, line, n = 1, initialize_random_maps= True, seed=1)\n", - "\n", - "# optimize the interleaving\n", - "maps, loss = ilp.solve_ilp(myInt)\n", - "\n", - "print(f\"loss before optimization: {myInt.loss()} and loss after optimization: {loss}\")\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Plot to check if the maps are correct" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "\n", - "\n", - "\n" - ] - }, - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 9, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", 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NmzbhvffeU/razJkzsWTJEq319eTJEwwZMgR169ZVms9qypQpZdbV9N/yn3/+wfr163H16lWIRCI0a9YMY8eOhYODQ5l11q9fj88//xzXr18HADRu3BjTpk3DuHHjyqyjrZ9rIiIiXdDVuE6mOo3vZDjOU85YxnsyhjTu44T0f27evIm3334bly9flucaAv7/24Kynv2OiYlBvXr1EBISonD9u+++w/379/Hhhx8CAPz8/BReT05ORnFxsfwbtrS0NJibm6N9+/Y4evSo0r527NiBUaNGYeTIkfj+++9x5coVeHl54euvv8a+ffvwyy+/qP2+4+LicOvWLRw6dAi///67wmt+fn44f/68PE5BEHD9+nWYm5ujadOmuHbtGkQiEU6cOIHmzZsDAObNm4f58+fDx8cHrq6upb5t2bVrl9oxNmjQAP7+/pg/fz5eeeUVleuV92Fcq1YtbNq0Cf369VO4Pn36dGzdulXtLcfLi/Hbb7/FxIkTYW1tDScnJ4V/E5FIhJs3byptU9N/y3PnzqFXr16wtrbG66+/DkEQcO7cOTx9+hSHDh1Cu3btStX55JNP8Pnnn2Py5Mno1KkTACApKQmrVq3C1KlT8dlnnyntS/Yz8vz581I/yy/3IxKJyvy5JiIi0jZdj+tkqsv4Tqa6jvNUidUYxnsyBjfuE0gQBEHo16+fEBgYKNy7d0+wtbUVrly5Ihw/flx4/fXXhcTExDLreXh4CL///nup66dOnRI8PT2V1lm2bJnQv39/4eHDh/JrDx8+FAIDA4WlS5eW2Vfbtm2FDRs2CIIgCLa2tsKNGzcEQRCECxcuCPXq1VMoe/HiRaG4uLjsN6yCzz//XBg0aJAgkUjk1yQSifDOO+8IK1asEAoKCoTAwEAhICBA/rqLi4uwcePGSvX7b3PnzhWCg4MFLy8vterFxsYKc+fOFTp37lzqtV9//VVwcHAQEhIS5NfCw8MFNzc34erVq1qNsV69ekJ0dLTa/39o+m/ZtWtXITg4WCgqKpJfKyoqEoKCgoQ333xTaR0nJydhy5Ytpa5v2bJFcHJyKrMvTX+WiYiIdKkqx3Uypjy+k6mu4zxVYjWG8Z6MoY37OCH9HycnJ+HixYuCIAiCvb298OeffwqCIAi//fab0LZt2zLricVi4ebNm6Wu37hxQxCLxUrruLm5CX/88Uep65cvXxZcXV3L7Mva2lrIyMgQBEHxA0tZX2ZmZsJff/0lCIIgNGjQQHjw4EGZ7ZbFzc1NSE1NLXX9jz/+ENzc3ARBEITk5GSFH1xHR0chPT1d7b704YcffhBq164tnD17Vvjvf/8ruLm5CdeuXdN6P7Vr19bo30TTf0srKyulH7apqamCtbW10jq1atUS0tLSSl2/du2a4ODgUGZfmv4sExER6VJVjutkTHl8J8NxXtmMYbwnY2jjPqZ9+Z/i4mL57lV16tRBTk4OgBfbLV+7dq3Meu7u7qUehQCA33//HW5ubkrr5OXl4a+//ip1/d69e3j8+HGZfbm6uiI9Pb3U9RMnTsDLy0vhWq1atZCRkQEAyMzMLPU8uiokEgnu3btX6vr9+/eRl5cn7+fldRnjxo3T6o5lygwaNEje/6BBg8o9Ro8ejcWLF0MikZRqZ9iwYYiOjkbXrl3x888/IyEhAU2aNNF6vEFBQdi2bZva9TT9t7S3t0dWVlap69nZ2bCzs1Na57333sPq1atLXV+7di1GjhxZZl+a/iwTERHpUlWO62RMeXwnw3Fe2YxhvCdjaOM+C41rmpiWLVvi0qVL8PLyQseOHbF48WJYWlpi7dq1pT4MXjZu3DhMmzYNRUVF8Pf3B/BiYfIHH3yA999/X2mdt99+G2PGjMGyZcvwxhtvAABOnTqFmTNnYtCgQWX2NWHCBEydOhXfffcdRCIRcnJykJSUhBkzZmDOnDkKZQcPHozu3bvLn0X38fGBubm50nbLeqY9MDAQISEhWLZsGTp06ACRSIQzZ85gxowZGDhwIADgzJkzsLa2li9yLikpwdq1a3HkyBG0bt261ILulxc4R0RE4NNPP4WNjU2Fi6Rfrufg4CB/vr6iRdtSqRSrV6/GiRMn0KhRI6VlnJ2d4e3tja+//rpUf9pYvF1cXIzFixfj4MGDFf6bvOzZs2cq/1u+bOjQoRg7diyWLl2Kzp07y9eBzJw5E8OHDy8z/vXr1+PQoUMKP5PZ2dkYPXq0wr/Dy/1q+rNMRESkS1U5rpMxtfGdbPL28hjA1MZ5L8eqKmMf78kY0riPmxr9z8GDB1FQUIBBgwbh5s2b6NevH/788084OTlh27Zt8g+lfxMEAR999BFWrlwp/ybJysoKH374YakPEZknT55gxowZ+O6771BUVAQAsLCwwNixY7FkyRLY2NiUGeesWbPw+eef49mzZwAAsViMGTNm4NNPPy1V9sCBA0hPT8eUKVMwf/78Mr8tmTp1qtLr+fn5mD59OjZu3Ijnz5/L4wwKCsLnn38OGxsbpKSkIDQ0VKXcSP9e4Ozn54ddu3ahVq1apTYFKK+euq5cuYIOHTrg9ddfV6n8y/2VF5eqMWr63jStV1hYiJkzZ+Kbb76R//9Wo0YN/Pe//8XChQshFovV6qu8fivzs0xERKQrVTmukzG18R0AtG3bVuMxgjGM816OVdO6qrRhKOM9Vfosr39djfs4IS3Hw4cPUbt2bZXy8uTn5+Pq1auwtrZG48aNy/0hkCkoKMCNGzcgCAIaNWqk8v+JT548wZUrV1BSUoLmzZtXOBkcM2YMVq5cWeHt+7Lk5+fj5s2bEAQBDRs2NOhkx8oUFxfjjz/+QJs2bfQdSpV68uSJws9XzZo1ddaXpj/LREREVUXX4zoZju+qVnUd58lU5XhPRtvjPk5IiYiIiIiISC+4qRERERERERHpBSekREREREREpBeckJZBKpUiKioKUqlU5/Wqsq+qrmcMMWpazxhi1LReVcdIRESkS/r4u2YMf+8rU08fffI9ar+evvp8GdeQliEvLw8ODg6QSCSwt7fXab2q7Kuq6xlDjJrWM4YYNa1X1TESERHpkj7+rhnD3/vK1DOmWPkeDa/Pl/EOKREREREREekFJ6RERERERESkFxb6DkCfSkpKkJOTAzs7u1I5qfLy8hT+V1Wa1KvKvqq6njHEqGk9Y4hR03q66EsQBDx+/Bhubm4wM+N3YUREpF2GMq7TV598j9qvp48+TeU9qjPuq9ZrSG/fvg13d3d9h0FUrWRnZ+PVV1/VdxhERGRiOK4jMjyqjPuq9R1SOzs7AC/+obgBC5Fu5eXlwd3dXf57R0REpE2yvy+3znvC3la9J3HM6l3QRUhE1ZY6475qPSGVPc5hb2/PCSlRFfn3Y1RERETaIB/X2ZrB3k7NCSnHgUQ6ocq4T28Lub7++ms0aNAAVlZWaN++PY4fP652G9HR0ejcuTNq1qyJWrVqaT9IIiIiIipXYmIi+vfvDzc3N4hEIuzevVvtNjIzMzF27Fg0aNAA1tbWaNiwIebOnYvCwkLtB0xEBkUvE9Jt27Zh2rRpmDVrFi5cuIA333wTffr0QVZWllrtFBYWYsiQIfjvf/+ro0iJiIiIqDwFBQVo06YNVq1apXEbf/75J0pKSrBmzRqkpqbi888/xzfffIOPP/5Yi5ESkSHSy6ZGHTt2RLt27bB69Wr5tWbNmmHgwIGIiYlRu724uDhMmzYN//zzj1r1tJXMlYgqxt83IiLTJxKJsGvXLgwcOLDSbS1ZsgSrV6/GzZs3VSov+zvzKM1L/Ud2Xa5rEiIRlUGdcV+VryEtLCxEcnIyPvroI4XrAQEBOHnypE77lkqlkEql8nNNtkUmIiIiIt2TSCRwdHQs83WO64hMQ5U/svvgwQMUFxejXr16Ctfr1auH3NxcnfYdExMDBwcH+cGtwYmIiIgMz40bN/Dll19i4sSJZZbhuI7INOhtU6N/77gkCILOd9+MjIyERCKRH9nZ2Trtj4iIiIjUk5OTg969e2PIkCEYN25cmeU4riMyDVX+yG6dOnVgbm5e6m7ovXv3St011TaxWAyxWKzTPoiIiIhIMzk5OfDz80OnTp2wdu3acstyXEdkGqr8DqmlpSXat2+Pw4cPK1w/fPgwOnfuXNXhEBEREZEBuHPnDnx9fdGuXTvExsbCzExvD/IRURWq8jukABAREYFRo0bBx8dH/g1YVlZWuesElMnKysLDhw+RlZWF4uJipKSkAAAaNWoEW1tbHURORERERC/Lz89Henq6/DwjIwMpKSlwdHRE/fr1VWojJycHvr6+qF+/PpYuXYr79+/LX3NxcdF6zERkOPQyIR06dCj+/vtvzJ8/H3fv3kXLli3xyy+/wMPDQ14mKioKcXFxyMzMLLOdOXPmYMOGDfJzb29vAMCxY8fg6+urq/CJiIiI6H/OnTsHPz8/+XlERAQAICgoCHFxcQAqHtcdOnQI6enpSE9Px6uvvqrwmh4yFBJRFdJLHlJVBAcHA4D8g0wXmBeRqOrw942IqPqqynEd85AS6Z9B5yFVVUJCAhITE6ukr5K/vFHyhB9cRERERLpQleM6s3oXYKbmF58luY01749jQqJKMdgJaUZGhr5DICIiIiIt4LiOiMrC7cuIiIiIiIhIL/QyIU1MTET//v3h5uYGkUiE3bt3q91GZmYmxo4diwYNGsDa2hoNGzbE3LlzUVhYqP2AiYiIiIiISOv0MiEtKChAmzZtsGrVKo3b+PPPP1FSUoI1a9YgNTUVn3/+Ob755ht8/PHHWoyUiIiIiMoTExODDh06wM7ODs7Ozhg4cCCuXbumdjsDBgxA/fr1YWVlBVdXV4waNQo5OTk6iJiIDIle1pD26dMHffr0qVQbvXv3Ru/eveXnXl5euHbtGlavXo2lS5dWNkQiIiIiUkFCQgLCwsLQoUMHPH/+HLNmzUJAQACuXLkCGxsbldvx8/PDxx9/DFdXV9y5cwczZszAO++8g5MnT+oweiLSN4Pd1EgTEokEjo6OZb4ulUohlUrl53l5eVURFhEREZHJOnDggMJ5bGwsnJ2dkZycjG7duqnczvTp0+X/7eHhgY8++ggDBw5EUVERatSoobV4iciwmMymRjdu3MCXX36JiRMnllkmJiYGDg4O8sPd3b0KIyQiIiIyfRKJBADKvUlQkYcPH2Lz5s3o3LlzmZNRqVSKvLw8hYOIjI9JTEhzcnLQu3dvDBkyBOPGjSuzXGRkJCQSifzIzs6uwiiJiIiITJsgCIiIiEDXrl3RsmVLtet/+OGHsLGxgZOTE7KysrBnz54yy/JGA5FpMPoJaU5ODvz8/NCpUyesXbu23LJisRj29vYKBxERERFpR3h4OC5duoQffvhBo/ozZ87EhQsXcOjQIZibm2P06NEQBEFpWd5oIDINRr2G9M6dO/Dz80P79u0RGxsLMzOjn18TERERGaXJkydj7969SExMxKuvvqpRG3Xq1EGdOnXQpEkTNGvWDO7u7jh16hQ6depUqqxYLIZYLK5s2ESkZ3qZkObn5yM9PV1+npGRgZSUFDg6OqJ+/foqtZGTkwNfX1/Ur18fS5cuxf379+Wvubi4aD1mIiIiIipNEARMnjwZu3btQnx8PBo0aKC1dgEobEhJRKZHLxPSc+fOwc/PT34eEREBAAgKCkJcXBwAICoqCnFxccjMzFTaxqFDh5Ceno709PRS38KV9WgHEREREWlXWFgYtmzZgj179sDOzg65ubkAAAcHB1hbW6vUxpkzZ3DmzBl07doVtWvXxs2bNzFnzhw0bNhQ6d1RIjIdIsFAZ2/BwcEAIJ+g6kJeXh4cHBwgkUjUXk9akttY7f7MXK6rXYfIVFTm942IiAyXSCRSej02NlY+nqvoRsPly5cxdepUXLx4EQUFBXB1dUXv3r0xe/ZsvPLKKyrFUdXjOhmO74hKU+f30WDXkCYkJCAxMVHfYRARERFROVS5t5GZmQlfX98yX2/VqhWOHj2qxajUU5lJpaaTWU5kiV4w2AlpRkaGvkMgIiIiIi3gjQYiKovBTkiJiIiIyDTwRgMRlUUveVJiYmLQoUMH2NnZwdnZGQMHDsS1a9fUbmfAgAGoX78+rKys4OrqilGjRiEnJ0cHERMREREREZG26WVCmpCQgLCwMJw6dQqHDx/G8+fPERAQgIKCArXa8fPzw48//ohr165hx44duHHjBt555x0dRU1ERERE/7Z69Wq0bt0a9vb2sLe3R6dOnfDrr79q3J5UKkXbtm0hEomQkpKivUCJyCDp5ZHdAwcOKJzHxsbC2dkZycnJ6Natm8rtTJ8+Xf7fHh4e+OijjzBw4EAUFRWhRo0aWouXiIiIiJR79dVXsXDhQjRq1AgAsGHDBgQGBuLChQto0aKF2u198MEHcHNzw8WLF7UdKhEZIINYQyqRSAAAjo6OGrfx8OFDbN68GZ07dy5zMiqVShWSK+fl5WncHxEREREB/fv3VziPjo7G6tWrcerUKbUnpL/++isOHTqEHTt2VOouKxEZD708svsyQRAQERGBrl27omXLlmrX//DDD2FjYwMnJydkZWVhz549ZZaNiYmBg4OD/HB3d69M6ERERET0kuLiYmzduhUFBQXo1KmTWnX/+usvhIaG4vvvv0fNmjUrLC+VSpGXl6dwEJHx0fuENDw8HJcuXcIPP/ygUf2ZM2fiwoULOHToEMzNzTF69Ogy82FFRkZCIpHIj+zs7MqETkREREQALl++DFtbW4jFYkycOBG7du1C8+bNVa4vCAKCg4MxceJE+Pj4qFSHNxqITINeH9mdPHky9u7di8TERLz66qsatVGnTh3UqVMHTZo0QbNmzeDu7o5Tp04p/VZOLBZDLBZXNmwiIiIieslrr72GlJQU/PPPP9ixYweCgoKQkJCg8qT0yy+/RF5eHiIjI1XuMzIyEhEREfLzvLw8TkqJjJBeJqSCIGDy5MnYtWsX4uPj0aBBA621C0BhnSgRERER6ZalpaV8UyMfHx+cPXsWX3zxBdasWaNS/aNHj+LUqVOlbhz4+Phg5MiR2LBhQ6k6vNFAZBr0MiENCwvDli1bsGfPHtjZ2SE3NxcA4ODgAGtra5XaOHPmDM6cOYOuXbuidu3auHnzJubMmYOGDRuqvWaBiIiIiLRHEAS1bhCsXLkSn332mfw8JycHvXr1wrZt29CxY0ddhEhEBkIvE9LVq1cDAHx9fRWux8bGIjg4GAAQFRWFuLg4ZGZmKm3D2toaO3fuxNy5c1FQUABXV1f07t0bW7du5bdlRERERFXk448/Rp8+feDu7o7Hjx9j69atiI+PL5Xmrzz169dXOLe1tQUANGzYUONlXURkHPT2yG5FMjMzS01YX9aqVSscPXpUi1Gpx8zlutp1SnIbV1lfRERERFXhr7/+wqhRo3D37l04ODigdevWOHDgAHr27CkvU9GNBiKqvgwiD6kyCQkJSExM1HcYRERERFSO9evXV1imohsN/+bp6anSDQwiMn4GOyHNyMjQdwhEREREpAWmfKNB0yfZepoN0aje4ZLtGtUjMlR6yUO6evVqtG7dGvb29rC3t0enTp3w66+/atyeVCpF27ZtIRKJkJKSor1AiYiIiKjSMjIymJKFiJTSy4T01VdfxcKFC3Hu3DmcO3cO/v7+CAwMRGpqqkbtffDBB3Bzc9NylERERERERKRLepmQ9u/fH//5z3/QpEkTNGnSBNHR0bC1tcWpU6fUbuvXX3/FoUOHsHTpUh1ESkRERESqiomJgUgkwrRp09Su6+npCZFIpHB89NFH2g+SiAyK3teQFhcXY/v27SgoKFA7f+hff/2F0NBQ7N69GzVr1qywvFQqVciJlZeXp3a8RERERFTa2bNnsXbtWrRu3VrjNubPn4/Q0FD5uSz9CxGZLr3cIQWAy5cvw9bWFmKxGBMnTsSuXbvQvHlzlesLgoDg4GBMnDgRPj4+KtWJiYmBg4OD/OBaBiIiIqLKy8/Px8iRI7Fu3TrUrl1b43bs7Ozg4uIiPzghJTJ9epuQvvbaa0hJScGpU6fw3//+F0FBQbhy5YrK9b/88kvk5eUhMjJS5TqRkZGQSCTyIzs7W5PQiYiIiOglYWFh6Nu3L3r06FGpdhYtWgQnJye0bdsW0dHRKCwsLLOsVCpFXl6ewkFExkdvj+xaWlqiUaNGAAAfHx+cPXsWX3zxBdasWaNS/aNHj+LUqVMQi8UK1318fDBy5Ehs2LChVB2xWFyqPBERERFpbuvWrTh//jzOnj1bqXamTp2Kdu3aoXbt2jhz5gwiIyORkZGBb7/9Vmn5mJgYzJs3r1J9EpH+6X0NqYwgCArrOyuycuVKfPbZZ/LznJwc9OrVC9u2bUPHjh11ESIRERERvSQ7OxtTp07FoUOHYGVlVam2pk+fLv/v1q1bo3bt2njnnXfkd03/LTIyEhEREfLzvLw8LsciMkJ6mZB+/PHH6NOnD9zd3fH48WNs3boV8fHxOHDggMpt1K9fX+FctsagYcOGePXVV7UaLxERERGVlpycjHv37qF9+/bya8XFxUhMTMSqVasglUphbm6uUdtvvPEGACA9PV3phJRPvhGZBr1MSP/66y+MGjUKd+/ehYODA1q3bo0DBw6gZ8+e8jJRUVGIi4tDZmamPkIkIiIiogq89dZbuHz5ssK1MWPGoGnTpvjwww81nowCwIULFwAArq6ulYqRiAybXiak69evr7BMZmYmfH19VW7T09MTgiBUIioiIiIiUoednR1atmypcM3GxgZOTk6lrpcnKSkJp06dgp+fHxwcHHD27FlMnz4dAwYMKPVUHBGZFoNZQ/pvCQkJSExM1HcYWmXmcl2jeiW5jau0PyIiIiJtqujJN7FYjG3btmHevHmQSqXw8PBAaGgoPvjgg6oNlIiqnMFOSDMyMvQdAhERERGpKT4+vtS1ip58a9euHU6dOqW7oIjIYBnshJSIiIiITIMpPvlWWQdzUvQdApFBMNN3ADExMRCJRJg2bZradT09PSESiRSOjz76SPtBEhEREZHGMjIymJKFiJTS6x3Ss2fPYu3atWjdurXGbcyfPx+hoaHyc1n6FyIiIiIiIjJsertDmp+fj5EjR2LdunWoXbu2xu3Y2dnBxcVFfnBCSkRERKQflXnyDQD279+Pjh07wtraGnXq1MGgQYO0GyARGRy9TUjDwsLQt29f9OjRo1LtLFq0CE5OTmjbti2io6NRWFhYZlmpVIq8vDyFg4iIiIgqr7JPvu3YsQOjRo3CmDFjcPHiRfz+++8YMWKElqMkIkOjl0d2t27divPnz+Ps2bOVamfq1Klo164dateujTNnziAyMhIZGRn49ttvlZaPiYnBvHnzKtUnERERESl6+cm3zz77TO36z58/x9SpU7FkyRKMHTtWfv21117TZphEZICq/A5pdnY2pk6dik2bNsHKyqpSbU2fPh3du3dH69atMW7cOHzzzTdYv349/v77b6XlIyMjIZFI5Ed2dnal+iciIiKiyj/5dv78edy5cwdmZmbw9vaGq6sr+vTpg9TU1DLr8Mk3ItNQ5RPS5ORk3Lt3D+3bt4eFhQUsLCyQkJCAlStXwsLCAsXFxRq3/cYbbwAA0tPTlb4uFothb2+vcBARERGR5mRPvsXExGjcxs2bNwEAUVFRmD17Nvbt24fatWuje/fuePjwodI6MTExcHBwkB/cxZfIOFX5hPStt97C5cuXkZKSIj98fHwwcuRIpKSkwNzcXOO2L1y4AABwdXXVVrhEREREVAZtPflWUlICAJg1axYGDx6M9u3bIzY2FiKRCNu3b1dah0++EZmGKl9Damdnh5YtWypcs7GxgZOTU6nr5UlKSsKpU6fg5+cHBwcHnD17FtOnT8eAAQNQv359bYdNRERERP/y8pNvMsXFxUhMTMSqVasglUpVutkgu5nQvHlz+TWxWAwvLy9kZWUprSMWiyEWiyv5DohI3/S2y25FoqKi4OnpWebrYrEY27Ztg6+vL5o3b445c+YgNDQUP/zwQ9UFSURERFSNaevJt/bt20MsFuPatWvya0VFRcjMzISHh4euwiciA6CXXXb/LT4+vtS1zMxM+Pr6llmnXbt2OHXqlO6CIiIiIqJyaevJN3t7e0ycOBFz586Fu7s7PDw8sGTJEgDAkCFDtBozERkWg5iQKpOQkIDExER9h2EQerm11aje4RLtxkFERESkiaioKMTFxSEzM7PMMkuWLIGFhQVGjRqFp0+fomPHjjh69Chq165ddYESUZUz2AlpRkaGvkMgIiIiIjVp8uQbANSoUQNLly7F0qVLdRMYERkkg52QEhEREZFp4JNvpZm5XNeoXk8zzR9hPlyifMdiIn3S+6ZGMTExEIlEmDZtmkb19+/fj44dO8La2hp16tTBoEGDtBsgEREREVVKRkYG84QSkVJ6vUN69uxZrF27Fq1bt9ao/o4dOxAaGooFCxbA398fgiDg8uXLWo6SiIiIiIiIdEFvE9L8/HyMHDkS69atw2effaZ2/efPn2Pq1KlYsmQJxo4dK7/+2muvaTNMIiIiIiIi0hG9PbIbFhaGvn37okePHhrVP3/+PO7cuQMzMzN4e3vD1dUVffr0QWpqapl1pFIp8vLyFA4iIiIi0lxUVBREIpHC4eLiolYb8fHxpdqQHWfPntVR5ERkCPQyId26dSvOnz+PmJgYjdu4efMmgBcfgrNnz8a+fftQu3ZtdO/eHQ8fPlRaJyYmBg4ODvKDaxmIiIiIKq9Fixa4e/eu/FB3CVXnzp0V6t+9exfjxo2Dp6cnfHx8dBQ1ERmCKp+QZmdnY+rUqdi0aROsrKw0bqek5EWSzVmzZmHw4MFo3749YmNjIRKJsH278h3EIiMjIZFI5Ed2drbG/RMRERHRCxYWFnBxcZEfdevWVau+paWlQn0nJyfs3bsXISEhEIlEOoqaiAxBla8hTU5Oxr1799C+fXv5teLiYiQmJmLVqlWQSqUwNzevsB1XV1cAQPPmzeXXxGIxvLy8kJWVpbSOWCyGWCyu5DsgIiIiopddv34dbm5uEIvF6NixIxYsWAAvLy+N29u7dy8ePHiA4ODgMstIpVJIpVL5OZdiERmnKr9D+tZbb+Hy5ctISUmRHz4+Phg5ciRSUlJUmowCQPv27SEWi3Ht2jX5taKiImRmZsLDw0NX4RMRERHRSzp27IiNGzfi4MGDWLduHXJzc9G5c2f8/fffGre5fv169OrVq9zlVVyKRWQaqvwOqZ2dHVq2bKlwzcbGBk5OTqWul8fe3h4TJ07E3Llz4e7uDg8PDyxZsgQAMGSI5gmDiYiIiEh1ffr0kf93q1at0KlTJzRs2BAbNmxARESE2u3dvn0bBw8exI8//lhuucjISIX28/LyOCklMkJ6zUNanqioKMTFxSEzM7PMMkuWLIGFhQVGjRqFp0+fomPHjjh69Chq165ddYESERERkZyNjQ1atWqF69eva1Q/NjYWTk5OGDBgQLnluBSLyDQYxIQ0Pj6+1LXMzEz4+vqWW69GjRpYunQpli5dqpvADMThEuWbNFWkJLexRvXMXDT7A0JEREQklUpx9epVvPnmm2rXFQQBsbGxGD16NGrUqKGD6IjI0BjEhFSZhIQEJCYm6jsMIiIiIirHjBkz0L9/f9SvXx/37t3DZ599hry8PAQFBand1tGjR5GRkYGxY8fqIFIiMkR6yUOqioyMDK4DICIiIjJwt2/fxvDhw/Haa69h0KBBsLS0xKlTpxQ2mYyKioKnp2eFba1fvx6dO3dGs2bNdBgxERkSg71DSkRERESGb+vWrRWWUWUpFgBs2bJFCxERkTHRy4Q0KioK8+bNU7hWr1495ObmqtxGfHw8/Pz8lL525swZdOjQoVIxEhEREZF2cCmW9hzMSdF3CERapbc7pC1atMCRI0fk56rmH5Xp3Lkz7t69q3Dtk08+wZEjR+Dj46OVGImIiIio8jIyMvQdAhEZKL1NSC0sLODi4qJxfUtLS4X6RUVF2Lt3L8LDwyESibQRIhEREREREemQ3jY1un79Otzc3NCgQQMMGzYMN2/erFR7e/fuxYMHDxAcHFxmGalUiry8PIWDiIiIiCrnzp07eO+99+Dk5ISaNWuibdu2SE5OVquNtLQ0BAYGok6dOrC3t0eXLl1w7NgxHUVMRIZCLxPSjh07YuPGjTh48CDWrVuH3NxcdO7cGX///bfGba5fvx69evUqd2femJgYODg4yA/u4ktERERUOY8ePUKXLl1Qo0YN/Prrr7hy5QqWLVuGWrVqqdVO37598fz5cxw9ehTJyclo27Yt+vXrp9YeI0RkfESCIAj6DqKgoAANGzbEBx98gIiICLXr3759Gx4eHvjxxx8xePDgMstJpVJIpVL5eV5eHtzd3SGRSGBvb69R7IasJLexRvXMXK5rORKiF79vDg4OJvv7RkRUXX300Uf4/fffcfz4cY3bePDgAerWrYvExES8+eabAIDHjx/D3t4eR44cwVtvvVVhG9Xl74ym4zuAYzyqOur8PhpEHlIbGxu0atUK169r9ksSGxsLJycnDBgwoNxyYrEY9vb2CgcRERERaW7v3r3w8fHBkCFD4OzsDG9vb6xbt06tNpycnNCsWTNs3LgRBQUFeP78OdasWYN69eqhffv2SutwKRaRaTCICalUKsXVq1fh6uqqdl1BEBAbG4vRo0ejRo0aOoiOiIiIiMpy8+ZNrF69Go0bN8bBgwcxceJETJkyBRs3blS5DZFIhMOHD+PChQuws7ODlZUVPv/8cxw4cKDMR3+5FIvINOhlQjpjxgwkJCQgIyMDp0+fxjvvvIO8vDwEBQWp3dbRo0eRkZGBsWPH6iBSIiIiIipPSUkJ2rVrhwULFsDb2xsTJkxAaGgoVq9erXIbgiBg0qRJcHZ2xvHjx3HmzBkEBgaiX79+pdL8yURGRkIikciP7Oxsbb0lIqpCepmQ3r59G8OHD8drr72GQYMGwdLSEqdOnYKHh4e8TFRUFDw9PStsa/369ejcuTOaNWumw4iJiIiISBlXV1c0b95c4VqzZs2QlZWlchtHjx7Fvn37sHXrVnTp0gXt2rXD119/DWtra2zYsEFpHS7FIjINeslDunXr1grLZGZmwtfXt8JyW7Zs0UJEpqmXW1uN6h0u0W4cREREZLq6dOmCa9euKVxLS0tTuNFQkSdPngAAzMwU75WYmZmhpIQDEyJTppcJqSoSEhKQmJio7zCIiIiIqBzTp09H586dsWDBArz77rs4c+YM1q5di7Vr16rcRqdOnVC7dm0EBQVhzpw5sLa2xrp165CRkYG+ffvqMHoi0jeD2NRImYyMDC5OJyIiIjJwHTp0wK5du/DDDz+gZcuW+PTTT7FixQqMHDlSXqaipVh16tTBgQMHkJ+fD39/f/j4+ODEiRPYs2cP2rRpUwXvgoj0RW8T0jt37uC9996Dk5MTatasibZt2yI5OVmtNtLS0hAYGIg6derA3t4eXbp0wbFjx3QUMREREREp069fP1y+fBnPnj3D1atXERoaqvC6KkuxfHx8cPDgQfz999/Iy8tDUlIS+vTpo8OoicgQ6OWR3UePHqFLly7w8/PDr7/+CmdnZ9y4caPMbb3L0rdvXzRp0gRHjx6FtbU1VqxYgX79+uHGjRtwcXHRTfBEREREpBYuxdIeM5frGtftaTZEo3qHS7Zr3CdRRfQyIV20aBHc3d0RGxsrv6bKjrove/DgAdLT0/Hdd9+hdevWAICFCxfi66+/RmpqKiekRERERAYiIyND3yEQkYHSyyO7e/fuhY+PD4YMGQJnZ2d4e3tj3bp1arXh5OSEZs2aYePGjSgoKMDz58+xZs0a1KtXD+3bt1daRyqVIi8vT+EgIiIiIiIi/dDLhPTmzZtYvXo1GjdujIMHD2LixImYMmUKNm7cqHIbIpEIhw8fxoULF2BnZwcrKyt8/vnnOHDgQJmP/sbExMDBwUF+cNMkIiIiosrx9PSESCQqdYSFhanVzvnz59GzZ0/UqlULTk5OGD9+PPLz83UUNREZCr1MSEtKStCuXTssWLAA3t7emDBhAkJDQ7F69WqV2xAEAZMmTYKzszOOHz+OM2fOIDAwEP369cPdu3eV1omMjIREIpEf2dnZ2npLRERERNXS2bNncffuXflx+PBhAMCQIaqvV8zJyUGPHj3QqFEjnD59GgcOHEBqaiqCg4N1FDURGQq9rCF1dXVF8+bNFa41a9YMO3bsULmNo0ePYt++fXj06BHs7e0BAF9//TUOHz6MDRs24KOPPipVRywWQywWVy54IiIiIpKrW7euwvnChQvRsGFDdO/eXeU29u3bhxo1auCrr76CmdmL+yVfffUVvL29kZ6ejkaNGmk1ZiIyHHq5Q9qlSxdcu3ZN4VpaWho8PDxUbuPJkycAIP/QkjEzM0NJSUnlgyQiIiIitRQWFmLTpk0ICQmBSCRSuZ5UKoWlpaXCuM7a2hoAcOLEiTLrcG8QIuOnlwnp9OnTcerUKSxYsADp6enYsmUL1q5dq9Zag06dOqF27doICgrCxYsXkZaWhpkzZyIjIwN9+/bVYfREREREpMzu3bvxzz//qP2orb+/P3Jzc7FkyRIUFhbi0aNH+PjjjwGgzKVY3BuEyDToZULaoUMH7Nq1Cz/88ANatmyJTz/9FCtWrMDIkSPlZaKiospNBVOnTh0cOHAA+fn58Pf3h4+PD06cOIE9e/agTZs2VfAuiIiIiOhl69evR58+feDm5qZWvRYtWmDDhg1YtmwZatasCRcXF3h5eaFevXowNzdXWod7gxCZBr2sIQWAfv36oV+/fmW+npmZCV9f33Lb8PHxwcGDB7UcGRERERGp69atWzhy5Ah27typUf0RI0ZgxIgR+Ouvv2BjYwORSITly5ejQYMGSstzbxAi06C3CWlFEhISkJiYqO8wjNrhku0a1etppvqueJXti4iIiExDbGwsnJ2dK710ql69egCA7777DlZWVujZs6c2wiMiA2WwE9KMjAx9h0BEREREKigpKUFsbCyCgoJgYaHZ8HLVqlXo3LkzbG1tcfjwYcycORMLFy4sM788EZkGvawhJSIiIiLTceTIEWRlZSEkJETp6xXtDQIAZ86cQc+ePdGqVSusXbsWa9aswZQpU3QQLREZEr1MSD09PSESiUod6uyyCwDnz59Hz549UatWLTg5OWH8+PHIz8/XUdREREREpExAQAAEQUCTJk2Uvq7K3iAbN27E33//DalUiosXL2LUqFE6iJSIDI1eHtk9e/YsiouL5ed//PEHevbsiSFDVF+7mJOTgx49emDo0KFYtWoV8vLyMG3aNAQHB+Onn37SRdhEREREpAHuDWIYDuak6DsEolL0MiGtW7euwvnChQvRsGFDdO/eXeU29u3bhxo1auCrr76SJ1H+6quv4O3tjfT0dDRq1EirMRMRERGRZrg3CBGVRe9rSAsLC7Fp0yaEhIRAJBKpXE8qlcLS0lI+GQUAa2trAMCJEyfKrJOXl6dwEBERERERkX7ofUK6e/du/PPPPwgODlarnr+/P3Jzc7FkyRIUFhbi0aNH+PjjjwEAd+/eVVonJiYGDg4O8sPd3b2y4RMRERGZrOfPn2P27Nlo0KABrK2t4eXlhfnz56OkpEStdqKjo9G5c2fUrFmzzF1zs7Ky0L9/f9jY2KBOnTqYMmUKCgsLtfAuiMiQ6X1Cun79evTp0wdubm5q1WvRogU2bNiAZcuWoWbNmnBxcYGXlxfq1asHc3NzpXUiIyMhkUjkR3Z2tjbeAhEREZFJWrRoEb755husWrUKV69exeLFi7FkyRJ8+eWXarVTWFiIIUOG4L///a/S14uLi9G3b18UFBTgxIkT2Lp1K3bs2IH3339fG2+DiAyYXvOQ3rp1C0eOHMHOnTs1qj9ixAiMGDECf/31F2xsbCASibB8+XI0aNBAaXmxWAyxWFyZkImIiIiqjaSkJAQGBqJv374AXmRK+OGHH3Du3Dm12pk3bx4AIC4uTunrhw4dwpUrV5CdnS2/SbFs2TIEBwcjOjoa9vb2mr8JIjJoer1DGhsbC2dnZ/mHnKbq1asHW1tbbNu2DVZWVujZs6eWIiQiIiKqvrp27YrffvsNaWlpAICLFy/ixIkT+M9//qPVfpKSktCyZUuFJ+Z69eoFqVSK5ORkpXW4NwiRadDbHdKSkhLExsYiKCgIFhaahbFq1Sp07twZtra2OHz4MGbOnImFCxeWuTaBiIiIiFT34YcfQiKRoGnTpjA3N0dxcTGio6MxfPhwrfaTm5uLevXqKVyrXbs2LC0tkZubq7ROTEyM/M4rERkvvd0hPXLkCLKyshASEqL09aioKHh6epbbxpkzZ9CzZ0+0atUKa9euxZo1azBlyhQdREtERERU/Wzbtg2bNm3Cli1bcP78eWzYsAFLly7Fhg0btN6XsmwLgiCUmYWBe4MQmQa93SENCAiAIAhlvp6ZmQlfX99y29i4caOWoyIiIiIimZkzZ+Kjjz7CsGHDAACtWrXCrVu3EBMTg6CgIK314+LigtOnTytce/ToEYqKikrdOZXh3iBEpkGvmxqVJyEhAYmJifoOo1o6mJOi7xCIiIjIADx58kQh5zsAmJubq532pSKdOnVCdHQ07t69C1dXVwAvNjoSi8Vo3769VvsiIsNisBPSjIwMfYdAREREVK31798f0dHRqF+/Plq0aIELFy5g+fLlZS65KktWVhYePnyIrKwsFBcXIyUlBQDQqFEj2NraIiAgAM2bN8eoUaOwZMkSPHz4EDNmzEBoaCh32CUycQY7ISUiIiIi/fryyy/xySefYNKkSbh37x7c3NwwYcIEzJkzR14mKioKcXFxyMzMLLOdOXPmKKw79fb2BgAcO3YMvr6+MDc3x/79+zFp0iR06dIF1tbWGDFiBJYuXaqz90ZEhkHrmxo9f/4cs2fPRoMGDWBtbQ0vLy/Mnz9f7Uc7oqOj0blzZ9SsWbPMXXOzsrLQv39/2NjYoE6dOpgyZQoKCwu18C6IiIiIyM7ODitWrMCtW7fw9OlT3LhxA5999hksLS3lZVTZ9yMuLg6CIJQ6Xq5Xv3597Nu3D0+ePMHff/+NL7/8kmtEiaoBrd8hXbRoEb755hts2LABLVq0wLlz5zBmzBg4ODhg6tSpKrdTWFiIIUOGoFOnTli/fn2p14uLi9G3b1/UrVsXJ06cwN9//42goCAIgoAvv/xSm2+JiIiIiMrAfT+Mh5nLdY3q9TQbolG9wyXbNapH1YvWJ6RJSUkIDAxE3759AQCenp744YcfcO7cObXakeWViouLU/r6oUOHcOXKFWRnZ8uTKC9btgzBwcGIjo7megMiIiKiKsB9P4ioMrT+yG7Xrl3x22+/IS0tDQBw8eJFnDhxAv/5z3+02k9SUhJatmwpn4wCQK9evSCVSpGcnKy0jlQqRV5ensJBRERERERE+qH1O6QffvghJBIJmjZtCnNzcxQXFyM6OhrDhw/Xaj+5ubml8lLVrl0blpaWyM3NVVonJiZGfueViIiIiIiI9Evrd0i3bduGTZs2YcuWLTh//jw2bNiApUuXKuyspi0ikajUNUEQlF4HgMjISEgkEvmRnZ2t9ZiIiIiITMXjx48xbdo0eHh4wNraGp07d8bZs2fVbkeVzSqnTp2K9u3bQywWo23btpULnIiMhtbvkM6cORMfffQRhg0bBgBo1aoVbt26hZiYGAQFBWmtHxcXF5w+fVrh2qNHj1BUVFTqzqmMWCzmbm1EREREKho3bhz++OMPfP/993Bzc8OmTZvQo0cPXLlyBa+88orK7VS0WSXw4qZCSEgITp8+jUuXLmnrLRCRgdP6HdInT57AzEyxWXNzc7XTvlSkU6dO+OOPP3D37l35tUOHDkEsFqN9+/Za7YuIiIiounn69Cl27NiBxYsXo1u3bmjUqBGioqLQoEEDrF69Wq225s2bh+nTp6NVq1Zlllm5ciXCwsLg5eVV2dCJyIho/Q5p//79ER0djfr166NFixa4cOECli9fjpCQELXaycrKwsOHD5GVlYXi4mKkpKQAABo1agRbW1sEBASgefPmGDVqFJYsWYKHDx9ixowZCA0N5Q67RERERJX0/PlzFBcXw8rKSuG6tbU1Tpw4oaeo/p9UKoVUKpWfc7NKIuOk9TukX375Jd555x1MmjQJzZo1w4wZMzBhwgR8+umn8jJRUVHw9PQst505c+bA29sbc+fORX5+Pry9veHt7S1PH2Nubo79+/fDysoKXbp0wbvvvouBAwdi6dKl2n5LRERERNWOnZ0dOnXqhE8//RQ5OTkoLi7Gpk2bcPr0aYUn1PQlJiYGDg4O8sPd3V3fIRGRBrR+h9TOzg4rVqzAihUryiyTmZkJX1/fctuJi4srMwepTP369bFv3z71g6RyaZI0uSS3cZX1RURERFXj+++/R0hICF555RWYm5ujXbt2GDFiBM6fP6/v0BAZGYmIiAj5eV5eHielREZI6xNSVSQkJCAxMVEfXRMRERGRiho2bIiEhAQUFBQgLy8Prq6uGDp0KBo0aKDv0LhZJZGJ0MuENCMjQx/dEhEREZEGbGxsYGNjg0ePHuHgwYNYvHixvkMiIhOhlwkpERERERm+gwcPQhAEvPbaa0hPT8fMmTPx2muvYcyYMWq1U9FmlQCQnp6O/Px85Obm4unTp/IyzZs3h6WlpTbfFhEZEK1vasQEykRERESmQSKRICwsDE2bNsXo0aPRtWtXHDp0CDVq1JCX0cZmlcCLnKfe3t5Ys2YN0tLS5GVycnJ09faIyABo/Q4pEygTERERmYZ3330X7777brlltLVZZXx8vHrBEZFJ0OqEVJZAec+ePejWrRuAF9+a7d69G6tXr8Znn32mclvz5s0DgHI/vFauXAkAuH//PiekRERERHrAzSpN38GcFH2HQCZMqxNSJlAmIiIiql64WSURVYZW15AygTIRERERERGpSuubGn3//fcQBAGvvPIKxGIxVq5ciREjRsDc3FzbXaktMjISEolEfmRnZ+s7JCIiIiK9SExMRP/+/eHm5gaRSITdu3eXKiMIAqKiouDm5gZra2v4+voiNTVV7b4q2ogyPj4egYGBcHV1hY2NDdq2bYvNmzdr8K6IyNhofUIqS6Ccn5+P7OxsnDlzBkVFRQaTQNne3l7hICIiIqqOCgoK0KZNG6xatarMMosXL8by5cuxatUqnD17Fi4uLujZsyceP36sVl+yjSiHDh2q9PWTJ0+idevW2LFjBy5duoSQkBCMHj0aP//8s1r9EJHx0VkeUiZQJiIiIjJcffr0QZ8+fcp8XRAErFixArNmzcKgQYMAABs2bEC9evWwZcsWTJgwQeW+KtqI8uOPP1Y4nzJlCg4ePIhdu3ahf//+KvdDRMZH6xNSJlAmIiIiMn4ZGRnIzc1FQECA/JpYLEb37t1x8uRJtSakmpBIJGjWrFmZr3OzSiLToPUJqUQiQWRkJG7fvg1HR0cMHjwY0dHRpRIox8XFITMzs8x25syZgw0bNsjPvb29AQDHjh2T57oaN24cEhISSpXJyMioMEEzEREREZUtNzcXAFCvXj2F6/Xq1cOtW7d02vdPP/2Es2fPYs2aNWWWiYmJkacJJCLjpfUJKRMoV0+93NpqVO9wiXbjICIiIu0SiUQK54IglLqmTfHx8QgODsa6devQokWLMstFRkYiIiJCfp6Xl8cMCkRGSGdrSMvDBMpEREREhs3FxQXAizulrq6u8uv37t0rdddUWxISEtC/f38sX74co0ePLresWCyGWCzWSRxEVHW0vsuuKjIyMvgNFhEREZEBa9CgAVxcXHD48GH5tcLCQiQkJKBz585a7y8+Ph59+/bFwoULMX78eK23T0SGSa0JKfNVEREREZmG/Px8pKSkyDeFzMjIQEpKCrKysgC8eFR32rRpWLBgAXbt2oU//vgDwcHBqFmzJkaMGKFWX+np6UhJSVHYiDIlJQWFhYUA/n8yOmXKFAwePBi5ubnIzc3Fw4cPtfqeicjwqDUhZb4qIiIiItNw7tw5eHt7yzeFjIiIgLe3N+bMmSMv88EHH2DatGmYNGkSfHx8cOfOHRw6dAh2dnbyMsHBwRXuDTJu3Dh4e3tjzZo1SEtLk/ebk5MD4MXeIU+ePEFMTAxcXV3lhyzdDBGZLpEgCIJGFUUi7Nq1CwMHDpRfEwQBbm5umDZtGj788EMAL7bkrlevHhYtWqTR9uBRUVHYvXu3/Nu78vTt2xf16tXDd999p1LbeXl5cHBwgEQigb29vdqx0f/raTZEo3qHS7ZrORIyVPx9IyIyTb6+vvD19UVUVJRe4+DfGd0pyW2sUT0zl+tajoSMhTq/j1rd1Ij5qoiIiIiqj8ePH+PGjRvYt2+fvkMhHdJ0YskbFqQKrW5qVF6+KtlruiLLVzVmzJgyy8TExMDBwUF+cGMlIiIiIs3Z2dkhOzsbtra2+g6FiIyUTnbZNeR8VRKJRH5kZ2frLCYiIiIiIiIqn1YnpC/nq3qZIeWrsre3VziIiIiIqiNVsifs3LkTvXr1Qp06dSASiVTa00OZirInXLt2DX5+fqhXrx6srKzg5eWF2bNno6ioSKP+iMh4aHVCynxVRERERMZBlewJBQUF6NKlCxYuXFipvirKnlCjRg2MHj0ahw4dwrVr17BixQqsW7cOc+fOrVS/RGT41NrUKD8/H+np6fJzWb4qR0dH1K9fXyFfVePGjdG4cWMsWLBA43xV+fn5CvmqAKB58+awtLSUT0anTp0qz1cFAJaWlnB0dFSrLyIiIqLqpk+fPujTp0+5ZUaNGgUAyMzMrFRfK1euBADcv38fly5dKvW6l5cXvLy85OceHh6Ij4/H8ePHK9UvERk+tSak586dg5+fn/w8IiICABAUFIS4uDgAL/JVPX36FJMmTcKjR4/QsWNHpfmqMjMzER8fX2Zf48aNQ0JCgvxcliMrIyMDnp6eCvmqYmJi5OW6d+9ebrtEREREZNjS09Nx4MCBcvOQMnsCkWlQa0Lq6+uLitKWikQiREVFlZuLKjMzs8IEyhVNKuPi4uSTYCIiIiIyfp07d8b58+chlUoxfvx4zJ8/v8yyMTExmDdvXhVGR0S6oNU8pKpgvirTpGm+KCZaJiIiIplt27bh8ePHuHjxImbOnImlS5figw8+UFo2MjJS/rQe8OIOKVP6ERmfKp+QyvJVERERERG9TDahbN68OYqLizF+/Hi8//77MDc3L1VWLBZDLBZXdYhEpGU6yUNKRERERFQZgiCgqKiowuViRGTc1JqQMl8VERERkWnIz89HSkqKfKwmy56QlZUlL/Pw4UOkpKTgypUrAF6Mv1JSUkrlnK9Ienq6vJ4se0JKSgoKCwsBAJs3b8aPP/6Iq1ev4ubNm9i+fTsiIyMxdOhQWFhU+QN9RFSF1PoNl+WrGjNmDAYPHlxmmS5dumDIkCEIDQ3VODBZvqrTp08r3R5clq+qXbt2qFWrFi5evIjQ0FCUlJRgwYIFGvdLREREVB2okj1h7969GDNmjLzMsGHDAABz586Vb2CpjewJFhYWWLRoEdLS0iAIAjw8PBAWFobp06dr460SkQFTa0LKfFVEREREpkGV7AnBwcEIDg4ut4w2sicMHToUQ4cOLbcMEZkmk3kGgvmqiIiIiKoWsydQeQ7mpOg7BDICRr+pUefOnWFlZYXGjRvjzTffrDBflYODg/zg1uBEREREmpNlT7C1tdV3KERkpIx+Qrpt2zacP38eW7Zswf79+7F06dIyy0ZGRkIikcgPpp8hIiIiIiLSH6OfkLq7u6N58+YYPnw4Fi5ciKioKBQXFystKxaLYW9vr3AQERERVUcVZU8oKirChx9+iFatWsHGxgZubm4YPXo0cnJy1O6rouwJL0tPT4ednR1q1aqldj9EZHyMfkL6MuarIiIiIlKNLHvCqlWrlL7+5MkTnD9/Hp988gnOnz+PnTt3Ii0tDQMGDFC7L1n2hIo2LioqKsLw4cPx5ptvqt0HERkntTY1ys/PR3p6uvxclq/K0dER9evXB/AiX1VWVpb827Nr164BAFxcXODi4qJyX+np6cjPz1fIVwUAzZs3h6WlJTZv3owaNWqgVatWEIvFSE5OZr4qIiIiIhVVlD3BwcEBhw8fVrj25Zdf4vXXX0dWVpZ87KeKirInyMyePRtNmzbFW2+9hZMnT6rcPhEZL7VmbsxXRURERFR9SSQSiEQinTxOe/ToUWzfvh0pKSnYuXNnheWZPYHINKg1IWW+KiIiIqLq6dmzZ/joo48wYsQIre/D8ffffyM4OBibNm1Sue2YmBjMmzdPq3EQUdWr8mdbma+KXtbLra1G9Q6XaDcOIiIiKltRURGGDRuGkpISfP3111pvPzQ0FCNGjEC3bt1UrhMZGSl/Wg94cYeUKf2IjE+VT0hl+aqIiIiIyPAVFRXh3XffRUZGBo4ePaqTLAVHjx7F3r175en7BEFASUkJLCwssHbtWoSEhJSqIxaLIRaLtR4LEVUt7v5DRERERErJJqPXr1/HsWPH4OTkpJN+kpKSFNL27dmzB4sWLcLJkyfxyiuv6KRPIjIMaqV9Yb4qIiIiItOQn5+PlJQUeSYDWfaErKwsAMDz58/xzjvv4Ny5c9i8eTOKi4uRm5uL3NxcFBYWqtVXeno6UlJSFLInpKSkyNtp1qwZWrZsKT9eeeUVmJmZoWXLlqhdu7ZW3zcRGRa1JqTMV0VERERkGs6dOwdvb295JoOIiAh4e3tjzpw5AIDbt29j7969uH37Ntq2bQtXV1f58XJKluDg4Ao3qxw3bhy8vb2xZs0apKWlyfvV5KYFEZkWtR7ZZb4qIiIiItNQUfYET0/PCrMrANrJnvBvqmRtICLToPM1pMxXRURERGSamD2BymPmcl2jej3Nhmjc5+GS7RrXJf1Q65FddVVFvqq4uDi18lU5ODjID24NTkRERKQ5WfYEW1tbfYdCREZKZxNSQ81XJZFI5AfTzxAREREREemPTiakL+erOnz4sM7yVS1duhQWFhawsLDA2LFjIZFIYGFhge+++05pHbFYDHt7e4WDiIiIiIiI9EPrE9KX81UdOXJEp/mqZFuGp6SkYP78+bCzs0NKSgrefvttnfRJREREZCoqSucHAFFRUWjatClsbGxQu3Zt9OjRA6dPn1a7r4rS+WVmZkIkEpU6Dhw4oME7IyJjotamRvn5+UhPT5efy/JVOTo6on79+vJ8VefPn8e+ffvk+aoAwNHREZaWlir3lZ6ejvz8fIV8VQDQvHlzWFpaolmzZgrlz507J89XRURERETlk6XzGzNmDAYPHqy0TJMmTbBq1Sp4eXnh6dOn+PzzzxEQEID09HTUrVtX5b5k6fxOnz5dbvaEI0eOoEWLFvJzR0dH1d8QERkltSak586dg5+fn/w8IiICABAUFIS4uDh5vioApb79OnbsmHxL8ODgYGRmZpa7Bfi4ceOQkJAgP5flyMrIyICnp6c6YRMRERHRv1SUzg8ARowYoXC+fPlyrF+/HpcuXcJbb72lcl+qpvNzcnKCi4uLyu0SkfFTa0LKfFWkbZpuza3pduDcCpyIiEgzhYWFWLt2LRwcHNCmTRud9DFgwAA8e/YMjRs3xvTp0/HOO++UWZbp/IhMg07Tvigjy1c1Y8aMqu6aiIiIiNS0b98+2NrawsrKCp9//jkOHz6MOnXqaLUPW1tbLF++HD/99BN++eUXvPXWWxg6dCg2bdpUZh2m8yMyDWrdIdUGWb4qIiIiIjJ8fn5+SElJwYMHD7Bu3Tq8++67OH36NJydnbXWR506dTB9+nT5uY+PDx49eoTFixfjvffeU1onMjJSvnwMeHGHlJNSIuNT5XdIiYiIiMh42NjYoFGjRnjjjTewfv16WFhYYP369Trv94033sD169fLfJ3p/IhMg1oTUm4PTkRERFS9CYKgsHZTVy5cuABXV1ed90NE+qXWI7vcHpyIiIjINFSUzq+goADR0dEYMGAAXF1d8ffff+Prr7/G7du3MWSIepsLVpTOb8OGDahRowa8vb1hZmaGn3/+GStXrsSiRYu0+ZaJyACpNSHl9uBEREREpqGidH7m5ub4888/sWHDBjx48ABOTk7o0KEDjh8/rnAzQFvp/D777DPcunUL5ubmaNKkCb777rsy148SkenQ6aZG3B6ciIiIyDBVlM7PysoKO3furLAdbaTzCwoKQlBQUIV9EZHp0cmEdN++fRg2bBiePHkCV1dXnW4P3qVLF5iZmWHv3r0YOnQoNmzYUOa3aTExMZg3b55W4yAiIiKqrmTp/Pbt26fvUMiEHMxJ0XcIVIV0MiHl9uBEREREpo/p/IiosnSS9oXbgxMREREREVFFqiQPKbcHJyIiIjIsqqTze9mECRMgEomwYsUKtfuqKJ0f8GK8uHTpUjRp0gRisRju7u5YsGCB2n0RkXFR65Fdbg9OREREZBpUSecns3v3bpw+fRpubm4a9aVKOr+pU6fi0KFDWLp0KVq1agWJRIIHDx5o1B8RGQ+1JqTcHpyIiIjINKiSzg8A7ty5g/DwcBw8eBB9+/bVqK+K0vldvXoVq1evxh9//IHXXntNoz6IyDipNSHl9uBkKLj7GhERke6VlJRg1KhRmDlzpsLNBW37+eef4eXlhX379qF3794QBAE9evTA4sWL4ejoqLQO0/kRmYYqWUP6Mtn24DNmzKjqromIiIhIDYsWLYKFhQWmTJmi035u3ryJW7duYfv27di4cSPi4uKQnJxcbn75mJgYODg4yA9mTiAyTjpJ+1Iebg9OREREZPiSk5PxxRdf4Pz58xCJRDrtq6SkBFKpFBs3bkSTJk0AAOvXr0f79u1x7do1pY/xMp0fkWlQ6w4pd2MjIiIiqh6OHz+Oe/fuoX79+rCwsICFhQVu3bqF999/X76fh7a4urrCwsJCPhkFgGbNmgEAsrKylNZhOj8i06DWHVLuxkZERERUPYwaNQo9evRQuNarVy+MGjUKY8aM0WpfXbp0wfPnz3Hjxg00bNgQAJCWlgYA8PDw0GpfRGRY1JqQcjc2IiIiItNQUTo/JycnODk5KdSpUaMGXFxc1B57VZTOr0ePHmjXrh1CQkKwYsUKlJSUICwsDD179lS4a0pEpkfrmxrpYze2Bg0awNPTE+PGjcPDhw/LrCOVSpGXl6dwEBEREVVH586dg7e3tzy1XkREBLy9vTFnzhy12gkODq4we8K4cePg7e2NNWvWIC0tTd5vTk4OAMhzytepUwfdunVD37590axZM2zdulWj90ZExkPrmxrpaze24uJiTJ8+He+88w6OHj2qtE5MTAzmzZun07iIiIiIjEFF6fyUyczMVHqtsun8AMDNzQ07duxQKx4iMn5anZByNzYiIiKi6kOWzm/fvn36DoVMiJnLdY3r9jQbolG9wyXbNe6TKkerj+xyNzYiIiKi6kOWzs/W1lbfoRCRkdLqHVLuxkZERERERESqUusOaX5+PlJSUuQ7o8l2Y5PdkXRyckLLli0VjsrsxpaSkqKwG1tKSgoKCwsBQGE3tgsXLiA5ORkTJkzgbmxEREREKlAlv3xwcDBEIpHC8cYbb6jdV0X55aOiokr1IxKJYGNjo8E7IyJjotYd0nPnzsHPz09+LluPGRQUhLi4OJXbCQ4ORmZmZrkL3MeNG4eEhAT5uWwHuIyMDHh6esp3Y5s8eTK6desGGxsb9OnTB8uWLVPnLRERERFVS6rml+/duzdiY2Pl55aWlmr3VVF++RkzZmDixIkK19566y106NBB7b6IyLioNSHlbmxEREREpkHV/PJisRguLi6V6qui/PK2trYK61AvXryIK1eu4JtvvqlUv0Rk+LSe9qUi3I2NtEHT3ddKchtXWV9ERESmID4+Hs7OzqhVqxa6d++O6OhoODs767TPb7/9Fk2aNMGbb75ZZhmpVAqpVCo/Z355IuOk1V12VcHd2IiIiIiMQ58+fbB582YcPXoUy5Ytw9mzZ+Hv768wEdQ2qVSKzZs3Y+zYseWWi4mJgYODg/xgKj8i41Tld0iJiIiIyDgMHTpU/t8tW7aEj48PPDw8sH//fgwaNEgnfe7cuROPHz/G6NGjyy3H/PJEpkGtO6TcjY2IiIio+nJ1dYWHhweuX9fdcpZvv/0W/fr1q3DdKvPLE5kGtSakst3YVq1aVW653r174+7du/Ljl19+UTsw2W5sL38z97IZM2Yo9HH37l00b94cQ4YMUbsvIiIiIqrY33//jezsbLi6uuqk/YyMDBw7dqzCx3WJyHSo9cgud2MjIiIiMg35+flIT0+Xn8vyyzs6OqJ+/frIz89HVFQUBg8eDFdXV2RmZuLjjz9GnTp18Pbbb6vVV3p6OvLz8xXyywNA8+bNFdLIfPfdd3B1dVVpvElEpkEna0i5GxsRERGRYasov7y5uTkuX76MjRs34p9//oGrqyv8/Pywbds22NnZyetpI788AJSUlCAuLg7BwcEwNzfX4jslIkOm9Qlpnz59MGTIEHh4eCAjIwOffPIJ/P39kZycDLFYrO3uAPz/bmwfffRRueViYmIwb948ncRAREREZEwqyi9vbW2NgwcPVtiOtvLLm5mZITs7u8JyRGRatD4h5W5sRERERNUD88uToTmYk6LvEEhNOk/7Ymi7senqLi0RERFRdSPLL09EpCmdT0iraje2vXv36qR9IiIiIiIi0g21JqTcjY2IiIiIiIi0Ra08pOfOnYO3t7d8Z7SIiAh4e3tjzpw5ACDfjS0wMBBNmjRBUFAQmjRpgqSkpFK7sVW0+H3cuHHw9vbGmjVrkJaWJu83JydHXoa7sRERERFpJjExEf3794ebmxtEIhF2796ttNzVq1cxYMAAODg4wM7ODm+88QaysrLU6mvq1Klo3749xGIx2rZtq7TMwYMH8cYbb8DOzg5169bF4MGDkZGRoea7IiJjo9YdUu7GRkRERGQaCgoK0KZNG4wZMwaDBw9WWubGjRvo2rUrxo4di3nz5sHBwQFXr16FlZWVWn0JgoCQkBCcPn1aaX75mzdvIjAwEBEREdi8eTMkEgmmT5+OQYMG4cKFCxq9PyIyDjpfQ/pv3I2N9KmXW1u16xwu0X4cRERE+tanT58KlzzNmjUL//nPf7B48WL5NS8vL7X7WrlyJQDg/v37Siek58+fR3FxMT777DOYmb14gG/GjBkIDAxEUVERatSoUaoO88sTmQa1HtnVBtlubLa2tlXdNRERERGpqKSkBPv370eTJk3Qq1cvODs7o2PHjmU+2lsZPj4+MDc3R2xsLIqLiyGRSPD9998jICBA6WQUeJFf3sHBQX4wlR+RcaryCSkRERERGb579+4hPz8fCxcuRO/evXHo0CG8/fbbGDRoEBISErTal6enJw4dOoSPP/4YYrEYtWrVwu3bt7F169Yy60RGRkIikcgPLuMiMk5qTUi5+J2IiIioeigpebFmJTAwENOnT0fbtm3x0UcfoV+/fvjmm2+02ldubi7GjRuHoKAgnD17FgkJCbC0tMQ777xT5v4lYrEY9vb2CgcRGR+1JqSyxe+rVq0qs4xs8XvTpk0RHx+Pixcv4pNPPtF48fvQoUOVvi5b/O7v74+UlBQcPHgQDx48wKBBg9Tqh4iIiIhKq1OnDiwsLNC8eXOF682aNVP7RkNFvvrqK9jb22Px4sXw9vZGt27dsGnTJvz22284ffq0VvsiIsOi1qZGxr74nYiIiIhUY2lpiQ4dOuDatWsK19PS0uDh4aHVvp48eVIqhZ/sXHanlohMk1bXkBr64nepVIq8vDyFg4iIiKg6ys/PR0pKClJSUgAAGRkZSElJUbj7OXPmTGzbtg3r1q1Deno6Vq1ahZ9//hmTJk1Sq6/09HSkpKQgNzcXT58+lfdbWFgIAOjbty/Onj2L+fPn4/r16zh//jzGjBkDDw8PeHt7a+09E5Hh0eqE1NAXv3M3NiIiIqIXzp07B29vb/mELyIiAt7e3pgzZ468zNtvv41vvvkGixcvRqtWrfDtt99ix44d6Nq1q7xMcHBwhfnlx40bB29vb6xZswZpaWnyfnNycgAA/v7+2LJlC3bv3g1vb2/07t0bYrEYBw4cgLW1tfbfPBEZDJFQ1krxiiqKRNi1axcGDhwov5aTk4NXXnkFw4cPx5YtW+TXBwwYABsbG/zwww9q9xMVFYXdu3fLv72Tyc3NRbdu3TBw4EAMHz4cjx8/xpw5c2BhYYHDhw9DJBKVaktZvip3d3dIJBIuhK8mepoNUbvO4ZLtOoik+snLy4ODgwN/34iITIyvry98fX0RFRWl1zj4d4YqQ5MxIsBxYlnU+X1Uaw1pRcpb/H7ixAltdqWw+F1m06ZNcHd3x+nTp/HGG2+UqiMWiyEWi7UaBxEREVF19fjxY9y4cQP79u3TdyhEZKS0OiHl4nciIiKi6sPOzo75P4moUtSakObn5yM9PV1+Llv87ujoiPr16wN4sfh96NCh6NatG/z8/HDgwAH8/PPPiI+PVyuw9PR05OfnKyx+B4DmzZvD0tISffv2xeeff4758+fLH9n9+OOPufidiIiIiIjISKi1qREXvxMRERGZhsTERPTv3x9ubm4QiURKsyKIRCKlx5IlS9Tqa+rUqWjfvj3EYjHatm2rtMyPP/6Itm3bombNmvDw8FC7DyIyTmrdIfX19YUqeyCFhIQgJCSkzNczMzMrnJCqckd12LBhGDZsWIXliGQ0WXjORe5ERGSKCgoK0KZNG4wZMwaDBw9WWubu3bsK57/++ivGjh1bZvmyCIKAkJAQnD59Wml++V9//RUjR47El19+iYCAAFy9ehXjxo2DtbU1wsPD1eqLiIyLVteQqoKL34mIiIj0r0+fPujTp0+5ZVxcXBTO9+zZAz8/P3h5eanV18qVKwEA9+/fVzoh/f777zFw4EBMnDgRAODl5YUPP/wQixYtQlhYmNLsCURkGqp8QsrF70RERETG56+//sL+/fuxYcMGrbctlUpRs2ZNhWvW1ta4ffs2bt26BU9PT6V1/p3Oj4iMj1prSImIiIioetqwYQPs7OwwaNAgrbfdq1cv7Ny5E7/99htKSkqQlpaGFStWACj92LBMTEwMHBwc5Ie7u7vW4yIi3VNrQsrF70RERETV03fffYeRI0fCyspK622HhoYiPDwc/fr1g6WlJd544w35PiH/TvMnExkZCYlEIj/4BB6RcVJrQipb/L5q1aoyy9y9e1fh+O677yASiTRe/D506FClr8sWv0+cOBF//PEHvv76ayxfvrzc2IiIiIhIfcePH8e1a9cwbtw4nbQvEomwaNEi5Ofn49atW8jNzcXrr78OAEof1wUAsVgMe3t7hYOIjI9aa0i5+J2IiIio+lm/fj3at2+PNm3a6LQfc3NzvPLKKwCAH374AZ06dYKzs7NO+yQi/dLppkZc/E5ERERkmPLz85Geni4/z8jIQEpKChwdHVG/fn359by8PGzfvh3Lli3TuK/09HTk5+cjNzcXT58+RUpKCgCgefPmsLS0xIMHD/DTTz/B19cXz549Q2xsLLZv346EhASN+yQi46DTTY24+J2IiIjIMJ07dw7e3t7w9vYGAERERMDb2xtz5sxRKLd161YIgoDhw4crbSc4OLjC/PLjxo2Dt7c31qxZg7S0NHm/OTk58jIbNmyAj48PunTpgtTUVMTHx8sf2yUi06XTO6S6Xvx+48YN9OvXD0VFRbC3t8fUqVMRFRVV7uL3iIgI+XleXh4npURERFQt+fr6QhCECsuNHz8e48ePL/P1zMzMCiek8fHx5b5ep04dJCUlVRgLEZkenU1IZYvft23bppP2ZYvfFyxYgNzcXNStWxe//fYbgPIXv4vFYp3EQ0RERFTdPH78GDdu3MC+ffv0HQpRpRzMSdF3CNWWziakXPxOREREZNrs7OyYboWIKkWtCSkXvxMREREREZG2qLWpERe/ExEREZmGxMRE9O/fH25ubhCJRNi9e3epMvn5+QgPD8err74Ka2trNGvWDKtXr1arn4sXL2L48OFwd3eXt/HFF1+UKnf58mV0794d1tbWeOWVVzB//nyV1rgSkXFT6w4pF79TdcQ1BUREZIoKCgrQpk0bjBkzBoMHD1ZaZvr06Th27Bg2bdoET09PHDp0CJMmTYKbmxsCAwNV6ic5ORl169bFpk2b4O7ujpMnT2L8+PEwNzdHeHg4gBdP1/Xs2RN+fn44e/Ys0tLSEBwcDBsbG7z//vtae89EZHh0usuuMlz8TkRERKR/ffr0QZ8+fcotk5SUhKCgIPmNhPHjx2PNmjU4d+6cyhPSkJAQhXMvLy8kJSVh586d8gnp5s2b8ezZM8TFxUEsFqNly5ZIS0vD8uXLERERAZFIpP4bJCKjoNM8pMrIFr/b2tpWdddEREREpIauXbti7969uHPnDgRBwLFjx5CWloZevXpVql2JRAJHR0f5eVJSErp3766QDaFXr17IyclBZmam0jakUiny8vIUDiIyPmpNSLnWgIiIiKj6WLlyJZo3b45XX30VlpaW6N27N77++mt07dpV4zaTkpLw448/YsKECfJrubm5qFevnkI52Xlubq7SdmJiYuDg4CA/mFueyDip9cgu1xoQERERVR8rV67EqVOnsHfvXnh4eCAxMRGTJk2Cq6srevTooXZ7qampCAwMxJw5c9CzZ0+F1/79WK7sJkNZj+tGRkYiIiJCfp6Xl8dJKZERUmtCyrUGRERERNXD06dP8fHHH2PXrl3o27cvAKB169ZISUnB0qVL1Z6QXrlyBf7+/ggNDcXs2bMVXnNxcSl1J/TevXsAUOrOqYxYLFZ4xJeIjJPW15ByrQERERGR8SsqKkJRURHMzBSHi+bm5igpKVGrrdTUVPj5+SEoKAjR0dGlXu/UqRMSExNRWFgov3bo0CG4ubnB09NTo/iJyDhofULKtQZEREREhi8/Px8pKSlISUkBAGRkZCAlJQVZWVkAAHt7e3Tv3h0zZ85EfHw8MjIyEBcXh40bN+Ltt99WuR/ZZLRnz56IiIhAbm4ucnNzcf/+fXmZESNGQCwWIzg4GH/88Qd27dqFBQsW8Kk3ompAJxNS2VqD5ORkLFu2DJMmTcKRI0c0ak/baw0kEon8yM7O1igmIiIiImN37tw5eHt7w9vbGwAQEREBb29vzJkzR15m69at6NChA0aOHInmzZtj4cKFiI6OxsSJE+VlgoODy80vv337dty/fx+bN2+Gq6ur/OjQoYO8jIODAw4fPozbt2/Dx8cHkyZNQkREhMIaUSIyTVrNQ8q1BkRERETGwdfXt8LsBC4uLoiNjS23TGZmZrkT0qioKERFRVUYT6tWrZCYmFhhOSIyLVqdkGp7rYG/v3+5aw0+/vhjFBYWwtLSEgDXGhARERFVpcePH+PGjRvYt2+fvkMhqhQzl+sa1etpNkTjPg+XbNe4rilR65FdrjUgIiIiIhk7OztkZ2fD1tZW36EQkZFS6w7puXPn4OfnJz+XPdcfFBSEuLg4AC/WGkRGRmLkyJF4+PAhPDw8lK41yMzMRHx8vNJ+Xl5rsHnzZvl1Dw8P+Q66srUGYWFh8PHxQe3atbnWgIiIiIiIyIiodYdUttbg34dsMgr8/1qDO3fu4OnTp/jzzz9L3bVUZa2Bsn7+nc5Fttbg2bNnuHv3LubOncu7o0REREQqSExMRP/+/eHm5gaRSITdu3eXKvPXX38hODgYbm5uqFmzJnr37o3r19V7tPHixYsYPnw43N3dYW1tjWbNmuGLL75QKPPs2TMEBwejVatWsLCwwMCBAyvxzojImGh1DakquNaAjI2mawpKchtXaX9ERETqKCgoQJs2bTBmzBgMHjy41OuCIGDgwIGoUaMG9uzZA3t7eyxfvhw9evTAlStXYGNjo1I/ycnJqFu3LjZt2gR3d3ecPHkS48ePh7m5OcLDwwEAxcXFsLa2xpQpU7Bjxw6tvk8iMmxVPiGVrTUgIiIiIv3p06cP+vTpU+br169fx6lTp/DHH3+gRYsWAICvv/4azs7O+OGHHzBu3DiV+gkJCVE49/LyQlJSEnbu3CmfkNrY2GD16tUAgN9//x3//POPBu+IiIyR1vOQEhEREZHxk0qlAAArKyv5NXNzc1haWuLEiROValsikcDR0bHS8eXl5SkcRGR81JqQcq0BERERUfXQtGlTeHh4IDIyEo8ePUJhYSEWLlyI3Nxc3L17V+N2k5KS8OOPP2LChAmVii8mJgYODg7yw93dvVLtEZF+qDUhla01WLVqldLXZWsNbt68iT179uDChQvw8PBAjx49UFBQoHI/L681SE1NxaxZsxAZGanQ78trDXr06KHO2yAiIiKiCtSoUQM7duxAWloaHB0dUbNmTcTHx6NPnz4wNzfXqM3U1FQEBgZizpw56NmzZ6Xii4yMhEQikR9cEkZknNRaQ8q1BkRERETVR/v27ZGSkgKJRILCwkLUrVsXHTt2hI+Pj9ptXblyBf7+/ggNDcXs2bMrHZtYLIZYLK50O0SkX1pdQ8q1BkRERESmx8HBAXXr1sX169dx7tw5BAYGqlU/NTUVfn5+CAoKQnR0tI6iJCJjpNVddl9ea7BmzRrY2Nhg+fLlWltrsH///krFFxMTg3nz5lWqDSIiIiJTkJ+fj/T0dPl5RkYGUlJS4OjoiPr16wMAtm/fjrp166J+/fq4fPkypk6dioEDByIgIEDlfmST0YCAAERERCA3NxfAi5sWdevWlZe7cuUKCgsL8fDhQzx+/BgpKSkAgLZt21b+zRKRwdLqhFS21mDs2LFwdHSEubk5evToUe5jvhXR9lqDiIgI+XleXh4XwBMREVG1dO7cOfj5+cnPZWOkoKAgxMXFAQDu3r2LiIgI/PXXX3B1dcXo0aPxySefKLQTHByMzMxMxMfHK+1n+/btuH//PjZv3ozNmzfLr3t4eCAzM1N+/p///Ae3bt2Sn3t7ewN4sUcJEZkurech5VoDIiIiIsPn6+tb4WRvypQpmDJlSrllMjMz4evrW+brUVFRiIqKqjCelyenRFR9aH1CKuPg4AAA8rUGn376qVr1U1NT4e/vz7UGRERERAbq8ePHuHHjBvbt26fvUIj04mBOir5DMHpqTUi51oCIiIiIZOzs7JhuhYgqRa0JKdcaEBERERERkbaIBD3M3nx9feHr66vSegJdysvLg4ODAyQSCezt7fUaC5mektzGGtUzc7mu5UgMA3/fiIhIl/h3hvRB0/EeYLpjPkC930et5iFVhWytwYwZM6q6a6Iq1cutrUYHERFRVYiJiUGHDh1gZ2cHZ2dnDBw4ENeuXVMoIwgCoqKi4ObmBmtra/j6+iI1NVWtfi5evIjhw4fD3d0d1tbWaNasGb744guFMvHx8QgMDISrqytsbGzQtm1bhafkiMh0VfmEVLbWwNbWtqq7JiIiIqL/SUhIQFhYGE6dOoXDhw/j+fPnCAgIQEFBgbzM4sWLsXz5cqxatQpnz56Fi4sLevbsicePH6vcT3JyMurWrYtNmzYhNTUVs2bNQmRkJFatWiUvc/LkSbRu3Ro7duzApUuXEBISgtGjR+Pnn3/W6nsmIsOjl0d2DQUf7SBd6mk2RKN6h0u2azkSw8DfNyIiw3b//n04OzsjISEB3bp1gyAIcHNzw7Rp0/Dhhx8CAKRSKerVq4dFixZhwoQJGvcVFhaGq1ev4ujRo2WW6du3L+rVq4fvvvtO6etSqRRSqVR+Lssvz78zVJX4yK5yOntkl492EBEREZkmiUQCAHB0dATwIptCbm6uQqYEsViM7t274+TJk5XuS9aPpmViYmLg4OAgP9zd3SsVExHph1oTUj7aQURERGR6BEFAREQEunbtipYtWwKAPO1evXr1FMrWq1dP/pomkpKS8OOPP5Z7h/Wnn37C2bNnMWbMmDLLREZGQiKRyA+mnyEyTmqlfTlw4IDCeWxsLJydnZGcnCx/tGPFihWYNWsWBg0aBADYsGED6tWrhy1btqj8aEdISIjCuZeXF5KSkrBz506Eh4cDAD7++GOFMlOmTMHBgwexa9cu9O/fX523RURERFSthYeH49KlSzhx4kSp10QikcK5IAilrqkqNTUVgYGBmDNnDnr27Km0THx8PIKDg7Fu3Tq0aNGizLbEYjHEYrFGcRCR4ajUpkbG9miHVCpFXl6ewkFERERUnU2ePBl79+7FsWPH8Oqrr8qvu7i4AECpu6H37t0rdddUFVeuXIG/vz9CQ0Mxe/ZspWUSEhLQv39/LF++HKNHj1a7DyIyPhpPSI3x0Q6uNSAiIiJ6QRAEhIeHY+fOnTh69CgaNGig8HqDBg3g4uKCw4cPy68VFhYiISEBnTt3Vquv1NRU+Pn5ISgoCNHR0UrLxMfHo2/fvli4cCHGjx+v/hsiIqOk1iO7LzPGRzsiIyMREREhP5ftxkZERERU3YSFhWHLli3Ys2cP7Ozs5DcPHBwcYG1tDZFIhGnTpmHBggVo3LgxGjdujAULFqBmzZoYMWKEyv3IJqMBAQGIiIiQ92Nubo66desC+P/J6NSpUzF48GB5GUtLywqfkCMi46bRHVJjfbRDLBbD3t5e4SAiIiKqjlavXg2JRAJfX1+4urrKj23btsnLfPDBB5g2bRomTZoEHx8f3LlzB4cOHYKdnZ28THBwMHx9fcvsZ/v27bh//z42b96s0E+HDh3kZeLi4vDkyRPExMQolJHtSUJEpkutPKSCIGDy5MnYtWsX4uPj0bhx41Kvu7m5Yfr06fjggw8AvHi0w9nZWe18VampqfD390dQUBAWL16stEx8fDz69euHRYsWISwsTOW2ZZgXkXSJeUgV8feNiMg0+fr6wtfXF1FRUXqNg39nyNiY8lhRnd9HtR7Z5aMdRERERCTz+PFj3LhxA/v27dN3KERkpNR6ZJePdhARERGRjJ2dHbKzs2Fra6vvUIjISKn1yK628NEOorKZ6uMb/H0jIiJd4t8ZMjamOuYD1Pt9rFQeUk3IHu2YMWNGVXdNRERERP8TExODDh06wM7ODs7Ozhg4cCCuXbumUGbnzp3o1asX6tSpA5FIhJSUFLX7uXjxIoYPHw53d3dYW1ujWbNm+OKLLxTKXLt2DX5+fqhXrx6srKzg5eWF2bNno6ioqDJvkYiMgMZpXzQle7SDiIiIiPQnISEBYWFh6NChA54/f45Zs2YhICAAV65cgY2NDQCgoKAAXbp0wZAhQxAaGqpRP8nJyahbty42bdoEd3d3nDx5EuPHj4e5uTnCw8MBADVq1MDo0aPRrl071KpVCxcvXkRoaChKSkqwYMECrb1nIjI8VT4hJSIiIiL9O3DggMJ5bGwsnJ2dkZycjG7dugEARo0aBQDIzMzUuJ+QkBCFcy8vLyQlJWHnzp3yCamXlxe8vLzkZTw8PBAfH4/jx49r3C8RGQe1Htnlox1EREREpkkikQBAlWQrkEgk5faTnp6OAwcOoHv37mWWkUqlyMvLUziIyPioNSGVPdpx6tQpHD58GM+fP0dAQAAKCgrkZWSPdixcuFDjoF5+tCM1NRWzZs1CZGQkVq1aJS8je7Tj0KFDuHbtGlasWIF169Zh7ty5GvdLREREVB0JgoCIiAh07doVLVu21GlfSUlJ+PHHH5Xmp+/cuTOsrKzQuHFjvPnmm5g/f36Z7cTExMDBwUF+uLu76zJsItIRtR7Z5aMdRERERKYnPDwcly5dwokTJ3TaT2pqKgIDAzFnzhz07Nmz1Ovbtm3D48ePcfHiRcycORNLly7FBx98oLStyMhIREREyM/z8vI4KSUyQpVaQ2qIj3aUl4dUKpVCKpXKz/loBxEREVV3kydPxt69e5GYmIhXX31VZ/1cuXIF/v7+CA0NxezZs5WWkU0omzdvjuLiYowfPx7vv/8+zM3NS5UVi8UQi8U6i5eIqobGaV/4aAcRERGR8RIEAeHh4di5cyeOHj2KBg0a6Kyv1NRU+Pn5ISgoCNHR0SrHV1RUBEEQdBYXEemfxndI+WgHERERkfEKCwvDli1bsGfPHtjZ2SE3NxcA4ODgAGtrawDAw4cPkZWVhZycHACQb2bp4uICFxcXlfqRTUYDAgIQEREh78fc3Bx169YFAGzevBk1atRAq1atIBaLkZycjMjISAwdOhQWFkwKQWTKNPoN56MdRERERMZt9erVAABfX1+F67GxsQgODgYA7N27F2PGjJG/NmzYMADA3LlzERUVBQAIDg5GZmYm4uPjlfazfft23L9/H5s3b8bmzZvl1z08POR7jlhYWGDRokVIS0uDIAjw8PBAWFgYpk+fXvk3SkQGTa0JqSAImDx5Mnbt2oX4+HidP9rh7+/PRzuIiIiIdECV8VJwcLB8clqWzMzMUpPal0VFRcknr2UZOnQohg4dWmE8RGR61JqQ8tEOIiIiIpJ5/Pgxbty4gX379uk7FCKjczAnRd8hGAS1Zm58tIOIiIiIZOzs7JCdna3vMIjIiIkEPTzf6uvrC19f3wof39C1vLw8ODg4QCKRwN7eXq+xEMmU5DbWqJ6Zy3UtR6Jd/H0jIiJd4t8ZMjamOuYD1Pt91Djti6Zkj3bMmDGjqrsmIiIiov+JiYlBhw4dYGdnB2dnZwwcOFC+1AoAioqK8OGHH6JVq1awsbGBm5sbRo8eLV+WpaqLFy9i+PDhcHd3h7W1NZo1a4YvvvhCocy1a9fg5+eHevXqwcrKCl5eXpg9ezaKioq08l6JyHBV+WJLPtpBREREpH8JCQkICwtDhw4d8Pz5c8yaNQsBAQG4cuUKbGxs8OTJE5w/fx6ffPIJ2rRpg0ePHmHatGkYMGAAzp07p3I/ycnJqFu3LjZt2gR3d3ecPHkS48ePh7m5OcLDwwEANWrUwOjRo9GuXTvUqlULFy9eRGhoKEpKSrBgwQJd/RMQkQFQ65HdmJgY7Ny5E3/++Sesra3RuXNnLFq0CK+99hqAF9+kzZ49G7/88gtu3rwJBwcH9OjRAwsXLoSbm5vKQV28eBELFy7EiRMn8ODBA3h6emLixImYOnWqvMy1a9cwceJEXLlyBRKJBG5ubhgxYgTmzp2LGjVqqNQPH+0gQ2Sqj2/w942IyLDdv38fzs7OSEhIQLdu3ZSWOXv2LF5//XXcunUL9evX17ivsLAwXL16FUePHi2zTEREBM6ePYvjx4+r1Cb/zpCxMdUxH6De76Nad0j5TRoRERGRaZJIJAAAR0fHcsuIRCLUqlWr0n2V1096ejoOHDiAQYMGlVlGKpVCKpXKz/Py8ioVExHpR6U2NeI3aUTaZ6rflvH3jYjIcAmCgMDAQDx69KjMcdSzZ8/QtWtXNG3aFJs2bdK4r6SkJHTv3h379+9Hz549FV7r3Lkzzp8/D6lUivHjx2P16tUwM1O+5UlUVBTmzZtX6jr/zpCxMNUxH1CFmxoZ4jdp3bt3L7OMVCpFXl6ewkFERERU3YWHh+PSpUv44YcflL5eVFSEYcOGoaSkBF9//bXG/aSmpiIwMBBz5swpNRkFgG3btuH8+fPYsmUL9u/fj6VLl5bZVmRkJCQSifzgHiVExknjTY0EQUBERAS6du2Kli1bKi3z7NkzfPTRRxgxYkSlvqlKSkrCjz/+iP3795d67d/fpM2fP7/MdmJiYpR+k0ZERERUXU2ePBl79+5FYmIiXn311VKvFxUV4d1330VGRgaOHj2q8ZjuypUr8Pf3R2hoKGbPnq20jLu7OwCgefPmKC4uxvjx4/H+++/D3Ny8VFmxWAyxWKxRLERkODS+Q8pv0oiIiIiMlyAICA8Px86dO3H06FE0aNCgVBnZZPT69es4cuQInJycNOorNTUVfn5+CAoKQnR0tMrxFRUVoRKry4jICGh0h5TfpBEREREZt7CwMGzZsgV79uyBnZ0dcnNzAQAODg6wtrbG8+fP8c477+D8+fPYt28fiouL5WUcHR1haWmpUj+yyWhAQAAiIiLkbZibm6Nu3boAgM2bN6NGjRpo1aoVxGIxkpOTERkZiaFDh8LCosqzFBJRFVLrN1wQBEyePBm7du1CfHx8hd+kHTt2rFLfpPn7+/ObNCIiIiIdWL16NQDA19dX4XpsbCyCg4Nx+/Zt7N27FwDQtm1bhTLHjh2T1wsODkZmZibi4+OV9rN9+3bcv38fmzdvxubNm+XXPTw8kJmZCQCwsLDAokWLkJaWBkEQ4OHhgbCwMEyfPr3S75OIDJtaE1J+k0ZERERkGir6At/T01OlL/kzMzNLTWpfFhUVhaioqHLbGDp0KIYOHVphX0RketSaufGbNCIiIiKSefz4MW7cuIF9+/bpOxQio6Np+hZTSxdTqTykmvL19YWvr2+F35bpGvMikiEytQ8ZGf6+ERGRLvHvDFUXxjBWVOf3scqfbeU3aUTlq8pvywx9EktEREREpk3jtC+asrOzQ3Z2Nmxtbau6ayIiIiL6n5iYGHTo0AF2dnZwdnbGwIEDce3aNYUyUVFRaNq0KWxsbFC7dm306NEDp0+fVqufixcvYvjw4XB3d4e1tTWaNWuGL774oszy6enpsLOzQ61atTR5W0RkZKp8QkpERERE+peQkICwsDCcOnUKhw8fxvPnzxEQEICCggJ5mSZNmmDVqlW4fPkyTpw4AU9PTwQEBOD+/fsq95OcnIy6deti06ZNSE1NxaxZsxAZGYlVq1aVKltUVIThw4fjzTff1Mp7JCLDp9aElN+kEREREZmGAwcOIDg4GC1atECbNm0QGxuLrKwsJCcny8uMGDECPXr0gJeXF1q0aIHly5cjLy8Ply5dUrmfkJAQrFy5Et27d4eXlxfee+89jBkzBjt37ixVdvbs2WjatCneffddrbxHIjJ8ak1I+U0aERERkWmSSCQAXqTqU6awsBBr166Fg4MD2rRpU+m+/t3P0aNHsX37dnz11VcqtSGVSpGXl6dwEJHxUWtTowMHDiicx8bGwtnZGcnJyejWrRuAF9+kvWz58uVYv349Ll26hLfeekulfkJCQhTOvby8kJSUhJ07dyI8PFzhNdk3aW+99RZOnjypztshIiIiIrzISRoREYGuXbuiZcuWCq/t27cPw4YNw5MnT+Dq6orDhw+jTp06GveVlJSEH3/8Efv375df+/vvvxEcHIxNmzapvENuTEwM5s2bp3EcRGQYKrWGlN+kERERERm/8PBwXLp0CT/88EOp1/z8/JCSkoKTJ0+id+/eePfdd3Hv3j2N+klNTUVgYCDmzJmDnj17yq+HhoZixIgR8hscqoiMjIREIpEf2dnZGsVERPql8YS0om/SbG1tYWVlhc8//1xr36RNmDBBfk32TVpcXJxa36Q5ODjID3d3d41jIiIiIjIFkydPxt69e3Hs2DG8+uqrpV63sbFBo0aN8MYbb2D9+vWwsLDA+vXr1e7nypUr8Pf3R2hoKGbPnq3w2tGjR7F06VJYWFjAwsICY8eOhUQigYWFBb777jul7YnFYtjb2yscRGR8NM5DKvsm7cSJE6Vek32T9uDBA6xbtw7vvvsuTp8+DWdnZ7X70fY3aREREfLzvLw8TkqJiIioWhIEAZMnT8auXbsQHx+PBg0aqFxPKpWq1Vdqair8/f0RFBSE6OjoUq8nJSWhuLhYfr5nzx4sWrQIJ0+exCuvvKJWX0RkXDSakMq+SUtMTCz3mzTZt2mNGzfG+vXrERkZqVY/FX2TtnfvXixduhTAiw/HkpISWFhYYO3ataXWoQIvvkkTi8VqxUBERERkisLCwrBlyxbs2bMHdnZ2yM3NBQA4ODjA2toaBQUFiI6OxoABA+Dq6oq///4bX3/9NW7fvo0hQ4ao3E9qair8/PwQEBCAiIgIeT/m5uaoW7cuAKBZs2YKdc6dOwczM7NST+ERkelRa0LKb9KIiIiITMPq1asBAL6+vgrXY2NjERwcDHNzc/z555/YsGEDHjx4ACcnJ3To0AHHjx9HixYt5OWDg4ORmZmJ+Ph4pf1s374d9+/fx+bNm7F582b5dQ8PD2RmZmr7bRGRkVFrQspv0oiIiIhMgyAI5b5uZWWlNFfov2VmZpaa1L4sKioKUVFRasUWHByM4OBgteoQkXFSa0LKb9KIiIiISObx48e4ceMG9u3bp+9QiKoNM5frGtUryW1c5X2qQiRU9PWYDvj6+sLX11ftb8u0LS8vDw4ODpBIJNyZjYyeJh8yuvxw+Tf+vhERkS7x7wxR+apyQqrO76PGu+xqit+kEemGJpNLTT+YqnIiS0RERESmq8onpHZ2dkxcTERERERERDDTdwBEREREVPViYmLQoUMH2NnZwdnZGQMHDsS1a9fKLD9hwgSIRCKsWLFCrX4uXryI4cOHw93dHdbW1mjWrBm++OILhTKZmZkQiUSljgMHDmjy1ojIiKg1IeUHFxEREZFpSEhIQFhYGE6dOoXDhw/j+fPnCAgIQEFBQamyu3fvxunTp+Hm5qZ2P8nJyahbty42bdqE1NRUzJo1C5GRkVi1alWpskeOHMHdu3flh7+/v0bvjYiMh1qP7Mo+uDp06IDnz59j1qxZCAgIwJUrV2BjY6NQVlsfXO7u7jh58iTGjx8Pc3NzhIeHK5Q9cuSIwg6+jo6OavdHREREVN38+0v82NhYODs7Izk5Gd26dZNfv3PnDsLDw3Hw4EH07dtX7X5CQkIUzr28vJCUlISdO3eWGtc5OTnBxcVFpXalUqlCnvu8vDy1YyMi/VNrQmrsH1xEREREpJxEIgGg+OV+SUkJRo0ahZkzZyrcANBGX8puIgwYMADPnj1D48aNMX36dLzzzjtlthETE4N58+ZpLSYi0o9KrSE1lA8uZ2dndOnSBT/99FO5bUilUuTl5SkcRERERNWdIAiIiIhA165d0bJlS/n1RYsWwcLCAlOmTNFaX0lJSfjxxx8xYcIE+TVbW1ssX74cP/30E3755Re89dZbGDp0KDZt2lRmO5GRkZBIJPKDm2YSGSeNd9nVxwfX/v375ddkH1xdunSBmZkZ9u7di6FDh2LDhg147733lLbDb9KIiIiISgsPD8elS5dw4sQJ+bXk5GR88cUXOH/+PEQikVb6SU1NRWBgIObMmYOePXvKr9epUwfTp0+Xn/v4+ODRo0dYvHhxmeM6sVgMsVislbiISH80npAa4wdXZGQkIiIi5Od5eXlwd3fXSpxERERExmjy5MnYu3cvEhMT8eqrr8qvHz9+HPfu3UP9+vXl14qLi/H+++9jxYoVyMzMVKufK1euwN/fH6GhoZg9e3aF5d944w18++23avVBRMZHo0d2ZR9cx44dK/ODy8LCAhYWFrh16xbef/99eHp6qt2PJh9c169fL/N1sVgMe3t7hYOIiIioOhIEAeHh4di5cyeOHj2KBg0aKLw+atQoXLp0CSkpKfLDzc0NM2fOxMGDB9XqKzU1FX5+fggKCkJ0dLRKdS5cuABXV1e1+iEi46PWHVJBEDB58mTs2rUL8fHxSj+4evTooXCtV69eGDVqFMaMGaNWYKmpqfD39+cHFxEREZEOhIWFYcuWLdizZw/s7OyQm5sLAHBwcIC1tTWcnJzg5OSkUKdGjRpwcXHBa6+9pnI/ssloQEAAIiIi5P2Ym5ujbt26AIANGzagRo0a8Pb2hpmZGX7++WesXLkSixYt0tK7JSJDpdaElB9cRERERKZh9erVAABfX1+F67GxsQgODla5neDgYGRmZiI+Pl7p69v/r737j6my/P84/kLMI8PjsYZnUp6ddH3PgtFyGeUWwYEp4SpBVzP/CWYhbYguZn8YmrQiWukfbm7+kYoz8edmxo/mdEMwFm6NHBUiNhJjUyb98Jyjc2dD7u8fn3HPk2Dehx/nAM/Hdm/e97mu+33df9wX78v7vq/r+HH19fWpurpa1dXV5nG32x3y2u+nn36qq1evKjY2Vh6PR/v27Rv2MywAk4elASkdFwAAwORgGIblOkN9N9rd3X1fbniv8vJylZeXP/C8+fn5ys/Pt9weAA9v2rzhP238LwO9/2etfGDgocvGGOH0RiPk9Xrl9Xr/s3Maa36/Xw6HQz6fj+9JAQusdkqS5A8M6FHP79xvADCJBAIBJScnq6OjQ7NmzYpoW8jrgLFjNfezkveFPctuuAKBgLq6ulRXVzfeoQEAADCK7HY7638CGJFxH5DScQEAAAAApDCXfQEAAMDEVllZqdTUVNntdjmdTuXl5amzszOkTEFBgWJiYkK2JUuWWIrT1tamNWvWyOVyKS4uTklJSdq5c+d95QzD0Pbt2+XxeGSz2eRyufTZZ5+N6BoBRD9LA1I6LgAAgMmhqalJxcXFOn/+vM6cOaP+/n5lZ2fr9u3bIeVycnJ0/fp1c/vuu+8sxWltbdXcuXN18OBBtbe3q6ysTJs3b9auXbtCym3cuFF79uzR9u3bdenSJdXW1uqFF14Y8XUCiG6WXtkd7LhSU1PV39+vsrIyZWdn6+LFi4qPjzfL5eTkqKqqytyfMWOGpUbd23G5XC798MMPWrdunWJjY7V+/Xqz3MaNG3X69Glt375dzzzzjHw+n/78809LsQAAAKaiU6dOhexXVVXJ6XSqtbVV6enp5nGbzaZ58+aFHWft2rUh+wsXLlRLS4tOnDhh5nUdHR3avXu3fv31V0tLBQKY+CwNSOm4AAAAJiefzydJeuyxx0KONzY2yul0as6cOcrIyFBFRYWcTueIY90bp7a2VgsXLlRdXZ1ycnJkGIaWLl2qL7744r72DAoGgwoGg+a+3+8fUZsARMaIviH9r47L4/GosLBQN27cGEkYM9ZwHdeCBQv05JNP6t1339Xff/897DmCwaD8fn/IBgAAMNUZhqHS0lKlpaUpJSXFPL58+XJVV1eroaFBO3bs0I8//qisrKyQgaBVLS0tOnbsmIqKisxjv//+u65evarjx4/rwIED2r9/v1pbW/XGG28Me57Kyko5HA5zc7lcYbcJQOSEvQ6pYRjKzc3VP//8o++//948fvToUc2aNUtut1tXrlzR1q1b1d/fr9bWVtlstrAa2dLSooyMDNXX12vZsmWSpPfee0/79+/XokWL9OWXX+ru3bt6//339eijj6qhoWHI85SXl+vjjz++7zjrVQHWsA4pAEwuxcXFqq+vV3Nzs+bPnz9suevXr8vtduvIkSNatWqV5Tjt7e3KzMzUhg0btGXLFvP4unXr9NVXX6mzs1Mej0eS9NNPP2nx4sW6dOnSkG/DDfWE1OVy8XcGGANRuQ7p+vXr9fPPP6u5uTnk+OrVq81/p6Sk6Pnnn5fb7VZ9fX3YHVdubq4++ugjczAqSQMDAwoGgzpw4IDZce3du1eLFy9WZ2fnkB3X5s2bVVpaau4PdlwAAABTVUlJiWpqanTu3LkHDkYlKTExUW63W7/99pvlOBcvXlRWVpYKCwtDBqOD550+fbqZ00lSUlKSJOmPP/4YMq+z2WxhP+wAED3CemV3sOM6e/Zs1HZcQ7HZbJo9e3bIBgAAMBUZhqH169frxIkTamho0IIFC/6zzl9//aWenh4lJiZaijX4ZDQ/P18VFRX3/f7SSy+pv79fXV1d5rHLly9Lktxut6VYACYWSwNSOi4AAIDJobi4WAcPHtShQ4dkt9vV29ur3t5e3blzR5J069Ytbdq0SS0tLeru7lZjY6Nef/11JSQkaOXKlQ8dZzCnW7ZsmUpLS804fX19ZpmlS5fqueee09q1a3XhwgW1traqqKhIy5YtC3n4AGDysTQgpeMCAACYHHbv3i2fzyev16vExERzO3r0qCQpNjZWv/zyi3Jzc+XxeJSfny+Px6OWlhbZ7XbzPAUFBfJ6vcPGOX78uPr6+lRdXR0SJzU11Swzbdo01dbWKiEhQenp6Xr11VeVlJSkI0eOjNn1A4gOliY1iomJGfJ4VVWVCgoKdOfOHeXl5enChQu6efOmEhMTlZmZqU8++STkW82CggJzwDqU4SYfcrvd6u7uNvevXbumkpISnT59WvHx8Vq+fLl27Ngx7PTg/+b3++VwOPj4HbCISY0AAIO8Xq+8Xq/Ky8sj2g7yOmDsjOWkRmHPsjsSdFzA1MP9BgCTTyAQUHJysjo6OjRr1qyItoW/M0D0sHI/hj3LbrgCgYC6urpUV1c33qEBAAAwiux2u3p6eiLdDAAT2LgPSOm4AAAAAACSxUmNKisrlZqaKrvdLqfTqby8PHV2dt5XrqOjQytWrJDD4ZDdbteSJUuGXYplKG1tbVqzZo1cLpfi4uKUlJSknTt3hpQpLy9XTEzMfVt8fLyVSwIAAJiSyOsARANLA9KmpiYVFxfr/PnzOnPmjPr7+5Wdna3bt2+bZbq6upSWlqann35ajY2Namtr09atWzVz5syHjtPa2qq5c+fq4MGDam9vV1lZmTZv3qxdu3aZZTZt2qTr16+HbMnJyXrzzTetXBIAAMCURF4HIBqMaFKjvr4+OZ1ONTU1KT09XZL01ltv6ZFHHtHXX389ao2U/rfkTEdHhxoaGob8va2tTYsWLdK5c+f08ssvP9Q5+fgdGD/cbwAQ3cjrAIwWK/ejpSek/+bz+STJXGZlYGBA9fX18ng8euWVV+R0OvXiiy/q5MmTIwljxnrQci579uyRx+N5YKcVDAbl9/tDNgAAAJDXAYiMsAekhmGotLRUaWlpSklJkSTduHFDt27d0ueff66cnBydPn1aK1eu1KpVq9TU1BR2I1taWnTs2DEVFRUN+XswGFR1dbXeeeedB56nsrJSDofD3O5dGxUAAGCqIq8DEClhv7JbXFys+vp6NTc3a/78+ZKka9eu6YknntCaNWt06NAhs+yKFSsUHx+vw4cPW47T3t6uzMxMbdiwQVu2bBmyzOHDh/X222+rp6dH8+bNG/ZcwWBQwWDQ3Pf7/XK5XLzaAYwDXqUCgOhFXgdgNI35OqQlJSWqqanRuXPnzE5LkhISEjR9+nQlJyeHlE9KSlJzc7PlOBcvXlRWVpYKCwuH7bSk/73W8dprrz2w05Ikm80mm81muR0AAACTFXkdgEiyNCA1DEMlJSX65ptv1NjYqAULFoT8PmP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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, axs = plt.subplots(1,2, figsize=(15,5))\n", - "\n", - "# psi map before optimization (vertex)\n", - "myInt.psi('0', 'V').draw(ax = axs[0], filltype='nan')\n", - "\n", - "# psi map after optimization (vertex)\n", - "maps['Psi_0_V'].draw(ax = axs[1], filltype='nan')\n", - "\n", - "fig, axs = plt.subplots(1,2, figsize=(15,5))\n", - "\n", - "# psi map before optimization (edge)\n", - "myInt.psi('0', 'E').draw(ax = axs[0], filltype='nan')\n", - "\n", - "# psi map after optimization (edge)\n", - "maps['Psi_0_E'].draw(ax = axs[1], filltype='nan')\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### put these maps to create a new interleaving object and draw an empty map" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n" - ] - }, - { - "data": { - "image/png": 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b3JdhOiLtUuQjTJ06ddC8eXMAQOfOnZGQkIDPPvsMX375Zal9GaYj0q5quQ9EkiSjeQ4iqhmEn4G8//77CAgIQJMmTfDo0SNs2bIFsbGxpR51SETaJ7yA3LlzB8HBwcjIyIC9vT3at2+PPXv2oE+fPqK7IiIzE760ZVXJXdqyOnEZTarJKvM3yCwMEcnGAkJEsileQMLDw6HT6TBz5kyluyKiaqZoAUlISMCaNWvQvn17JbshIjNRrIDk5ORg9OjR+Oqrr/DSSy8p1Q0RmZFiBWTKlCno378/evfuXe5+eXl5yM7ONnoRkTYociv7li1bcOrUKSQkJLxw3/DwcHz44YdKDIOIFCb8DCQtLQ0zZszApk2bULdu3RfuzzAdkXYJPwNJTExEZmYmOnXqVLKtsLAQR44cwapVq5CXlwcLC4uS9ximI9Iu4QXk9ddfR3JystG2cePGwdPTE3PnzjUqHkSkbcILiK2tLdq2bWu0zcbGBg4ODqW2E5G28U5UIpJN0WeiFouNja2ObqpNda2CxwAeqR3PQIhINhYQIpJNeAEJCwuDTqczerm4uIjuhohUQJE5EC8vLxw4cKDka166JaqZFCkglpaWPOsg+gtQZA4kJSUFBoMBHh4eGDFiBK5evVrmvgzTEWmX8ALSrVs3REdHY+/evfjqq69w+/Zt9OjRA/fv3ze5P1emI9IuxR+qnJubi2bNmuHdd99FaGhoqfdNrY3bpEkTVT9UWQ7eB0JaUZmHKit+I5mNjQ3atWuHlJQUk+8zTEekXYrfB5KXl4cLFy5Ar9cr3RURVTPhBWT27NmIi4vDtWvXcOLECQwZMgTZ2dkICQkR3RURmZnwjzDp6ekYOXIk7t27h0aNGqF79+6Ij4+Hm5ub6K6IyMyEF5AtW7aIPiQRqRSzMEQkGwsIEcnGAkJEsilSQG7evIm33noLDg4OqFevHjp27IjExEQluiIiMxI+ifrw4UO88sor8PPzw08//QQnJydcuXIFDRo0EN0VEZmZ8ALyySefoEmTJli/fn3JNnd39zL3N3UrOxFpg/CPMDt37kTnzp0xdOhQODk5wdvbG1999VWZ+zNMR6RdwgvI1atXERERgRYtWmDv3r2YNGkSpk+fjujoaJP7c2U6Iu0S/hGmqKgInTt3xqJFiwAA3t7eOHfuHCIiIjBmzJhS+zNMR6Rdws9A9Ho92rRpY7StdevWSE1NFd0VEZmZ8ALyyiuv4OLFi0bbLl26xCwMUQ0kvIDMmjUL8fHxWLRoES5fvozNmzdjzZo1mDJliuiuiMjMFHki2a5du/Dee+8hJSUFHh4eCA0NxTvvvFOhtpV5GlJNx6eYkTmY/Ylkb7zxBt544w0lDk1EKsIsDBHJxgJCRLIJLyDu7u6llrbU6XScRCWqgYTPgSQkJKCwsLDk67Nnz6JPnz4YOrTyE4JEpG7CC0ijRo2Mvl68eDGaNWuGXr16ie6KiMxM0XVh8vPzsWnTJoSGhkKn05nch2lcIu1SdBJ1+/bt+P333zF27Ngy92Eal0i7FC0ga9euRUBAAAwGQ5n7MI1LpF2KfYS5ceMGDhw4gK1bt5a7H9O4RNql2BnI+vXr4eTkhP79+yvVBRGZmSIFpKioCOvXr0dISAgsLRVfv5uIzESRAnLgwAGkpqbi7bffVuLwRKQSipwe+Pv7Q4GQLxGpDLMwRCQbCwgRySa8gDx9+hT//ve/4eHhAWtrazRt2hQfffQRioqKRHdFRGamyMJSkZGRiIqKgpeXF06ePIlx48bB3t4eM2bMEN0dEZmR8ALyyy+/IDAwsOT+D3d3d3zzzTc4efKk6K6IyMyEf4Tx8fHBwYMHcenSJQDAmTNncOzYMfzjH/8wuX9eXh6ys7ONXkSkDcLPQObOnYusrCx4enrCwsIChYWFWLhwIUaOHGly//DwcHz44Yeih0FE1UD4GUhMTAw2bdqEzZs349SpU4iKisKnn36KqKgok/szTEekXcLPQObMmYN58+ZhxIgRAIB27drhxo0bCA8PR0hISKn9GaYj0i7hZyCPHz9GrVrGh7WwsOBlXKIaSPgZyIABA7Bw4UK4urrCy8sLp0+fxvLly5mLIaqBhBeQL774AgsWLMDkyZORmZkJg8GAiRMn4oMPPhDdFRGZmSJLW1YFl7asGjnLYQJcEpP+X2X+BpmFISLZWECISDZFCsijR48wc+ZMuLm5wdraGj169EBCQoISXRGRGSlSQCZMmID9+/dj48aNSE5Ohr+/P3r37o2bN28q0R0RmYnwAvLkyRN8//33WLJkCXr27InmzZsjLCwMHh4eiIiIEN0dEZmR8Mu4T58+RWFhIerWrWu03draGseOHSu1P1emI9Iu4Wcgtra2ePnll/Hxxx/j1q1bKCwsxKZNm3DixAlkZGSU2p8r0xFplyJzIBs3boQkSfjb3/4GKysrfP755xg1ahQsLCxK7cswHZF2KfJU9mbNmiEuLg65ubnIzs6GXq/H8OHD4eHhUWpfhumItEvR+0BsbGyg1+vx8OFD7N27F4GBgUp2R0TVTJEzkL1790KSJLRq1QqXL1/GnDlz0KpVK4wbN06J7ojITBQ5A8nKysKUKVPg6emJMWPGwMfHB/v27UPt2rWV6I6IzESRM5Bhw4Zh2LBhShyaiFSEWRgiko0FhIhkq3QBOXLkCAYMGACDwQCdToft27cbvS9JEsLCwmAwGGBtbQ1fX1+cO3dO1HiJSEUqXUByc3PRoUMHrFq1yuT7S5YswfLly7Fq1SokJCTAxcUFffr0waNHj6o8WCJSl0pPogYEBCAgIMDke5IkYeXKlZg/fz4GDx4MAIiKioKzszM2b96MiRMnVm20RKQqQudArl27htu3b8Pf379km5WVFXr16oXjx4+bbMOV6Yi0S2gBuX37NgDA2dnZaLuzs3PJe89jmI5IuxS5CqPT6Yy+liSp1LZiDNMRaZfQG8lcXFwA/HkmotfrS7ZnZmaWOispxjAdkXYJPQPx8PCAi4sL9u/fX7ItPz8fcXFx6NGjh8iuiEgFKn0GkpOTg8uXL5d8fe3aNSQlJaFhw4ZwdXXFzJkzsWjRIrRo0QItWrTAokWLUK9ePYwaNUrowInI/CpdQE6ePAk/P7+Sr0NDQwEAISEh2LBhA9599108efIEkydPxsOHD9GtWzfs27cPtra24kZNRKrAlekIgLwV7biaXc3ElemIqFqwgBCRbCwgRCSb8DTu1q1b0bdvXzg6OkKn0yEpKUnQUIlIbYSncXNzc/HKK69g8eLFVR4cEamb0DQuAAQHBwMArl+/XqHjcWU6Iu0y+xwIw3RE2mX2AsIwHZF2KfJU9spgmI5Iu8x+BkJE2sUCQkSyCU/jPnjwAKmpqbh16xYA4OLFiwD+fFZI8fNCiKhmqPQZyMmTJ+Ht7Q1vb28Af6Zxvb298cEHHwAAdu7cCW9vb/Tv3x8AMGLECHh7eyMyMlLgsIlIDZjGJQBM49L/YxqXiKoFCwgRySY0TFdQUIC5c+eiXbt2sLGxgcFgwJgxY0omVImoZhEapnv8+DFOnTqFBQsW4NSpU9i6dSsuXbqEgQMHChksEamL0DCdvb290RPZAeCLL75A165dkZqaCldXV3mjJCJVUvxW9qysLOh0OjRo0MDk+0zjEmmXopOof/zxB+bNm4dRo0aVeTmIaVwi7VKsgBQUFGDEiBEoKirC6tWry9yPaVwi7VLkI0xBQQGGDRuGa9eu4dChQ+XejMI0LpF2CS8gxcUjJSUFhw8fhoODg+guiEglhIbpDAYDhgwZglOnTmHXrl0oLCzE7du3AQANGzZEnTp1xI2ciMxO6NKWYWFh2LlzJwCgY8eORu0OHz4MX19f+SMlItVhmI5kYwCvZmKYjoiqBQsIEckmfGW6sLAweHp6wsbGBi+99BJ69+6NEydOiBovEamI8JXpWrZsiVWrViE5ORnHjh2Du7s7/P39cffu3SoPlojUpUqTqDqdDtu2bUNQUFCZ+xRPyBw4cACvv/76C4/JSVTt4CRqzVSZv0FFw3T5+flYs2YN7O3t0aFDB5P7MExHpF2KTKLu2rUL9evXR926dbFixQrs378fjo6OJvdlmI5IuxQpIH5+fkhKSsLx48fRr18/DBs2DJmZmSb3ZZiOSLsUKSA2NjZo3rw5unfvjrVr18LS0hJr1641ua+VlRXs7OyMXkSkDdVyH4gkSUbzHERUMwgN0zk4OGDhwoUYOHAg9Ho97t+/j9WrVyM9PR1Dh1Z+xp6I1E1omC4yMhK//fYboqKicO/ePTg4OKBLly44evQovLy8xI2aiFSh0gXE19cX5d06snXr1ioNiIi0g1kYIpKNBYSIZBMepnvWxIkTodPpsHLlyioMkYjUSniYrtj27dtx4sQJGAwG2YMjInUTujJdsZs3b2Lq1KnYu3cv+vfvL3twRKRuwsN0RUVFCA4Oxpw5cyp06ZZhOiLtEj6J+sknn8DS0hLTp0+v0P4M0xFpl9ACkpiYiM8++wwbNmyATqerUBuG6Yi0S2gBOXr0KDIzM+Hq6gpLS0tYWlrixo0b+Ne//gV3d3eTbRimI9IuoXMgwcHB6N27t9G2vn37Ijg4GOPGjRPZFRGpgNAwnaura6mlLGvXrg0XFxe0atWq6qMlIlURGqbbsGGDsIERkfpxZTqqVnwQs/pxZToiqhYsIEQkm/Aw3dixY6HT6Yxe3bt3FzVeIlIRRcJ0/fr1Q0ZGRsnrxx9/rNIgiUidFAnTWVlZwcXFRfagiEgbFJkDiY2NhZOTE1q2bIl33nmnzDVhgD/DdNnZ2UYvItIG4QUkICAAX3/9NQ4dOoRly5YhISEBr732WpnLOjBMR6Rdii+unZGRATc3N2zZsgWDBw8u9b6pOH+TJk14H0gNxftA1E81i2sDgF6vh5ubG1JSUky+b2VlBSsrK6WHQUQKUPw+kPv37yMtLQ16vV7proiomgkN0zVs2BBhYWF48803odfrcf36dbz//vtwdHTEoEGDhA6ciMxPaJguIiICycnJiI6Oxu+//w69Xg8/Pz/ExMTA1tZW3KiJSBWEr0y3d+/eKg2IiLSDWRgiko0FhIhkYwEhItkUWdrywoULGDhwIOzt7WFra4vu3bsjNTVVxHiJSEWEp3GvXLkCHx8feHp6IjY2FmfOnMGCBQtQt27dKg+WiNRFeBp3/vz5+Mc//oElS5aUbGvatGmZ+3NlOiLtEjoHUlRUhN27d6Nly5bo27cvnJyc0K1bN5Mfc4oxTEekXUILSGZmJnJycrB48WL069cP+/btw6BBgzB48GDExcWZbMOV6Yi0S2iYrqioCAAQGBiIWbNmAQA6duyI48ePIzIyEr169SrVhmE6Iu0Segbi6OgIS0tLtGnTxmh769ateRWGqAYSWkDq1KmDLl264OLFi0bbL126BDc3N5FdEZEKCF/acs6cORg+fDh69uwJPz8/7NmzBz/88ANiY2NFjpuIVED40paDBg1CZGQkwsPDMX36dLRq1Qrff/89fHx8xI2aiFSBS1uS6sl5DCLARyHKxaUtiahasIAQkWzCw3TPL2tZ/Fq6dKmoMRORSggP0z27pGVGRgbWrVsHnU6HN998s8qDJSJ1ER6me35Jyx07dsDPz6/cQB0RaZOi68LcuXMHu3fvRlRUVJn7MI1LpF2KTqJGRUXB1tbW5Ip0xZjGJdIuRQvIunXrMHr06HIfJsQ0LpF2KfYR5ujRo7h48SJiYmLK3Y9pXCLtUuwMZO3atejUqRM6dOigVBdEZGbCw3TAnxOh3377LZYtWyZupESkOsLDdACwZcsWSJKEkSNHihklEakSw3SkegzTVS+G6YioWrCAEJFswsN0OTk5mDp1Kho3bgxra2u0bt0aERERosZLRCoiPEw3a9Ys7NmzB5s2bcKFCxcwa9YsTJs2DTt27KjyYIlIXYSH6X755ReEhITA19cXAPA///M/+PLLL3Hy5EkEBgbKHigRqY/wORAfHx/s3LkTN2/ehCRJOHz4MC5duoS+ffua3D8vLw/Z2dlGLyLSBuEF5PPPP0ebNm3QuHFj1KlTB/369cPq1avLfKgyw3RE2qVIAYmPj8fOnTuRmJiIZcuWYfLkyThw4IDJ/RmmI9IuoWG6J0+e4P3338e2bdvQv39/AED79u2RlJSETz/9FL179y7VhmE6Iu0SegZSUFCAgoIC1KplfFgLC4uSdXOJqOYQHqbr1asX5syZA2tra7i5uSEuLg7R0dFYvny50IETkfkJD9Nt2bIF7733HkaPHo0HDx7Azc0NCxcuxKRJk8SNmohUgWE6qrHkhPAYwGOYjoiqCQsIEckmPEx3584djB07FgaDAfXq1UO/fv2QkpIiarxEpCJCw3SSJCEoKAhXr17Fjh07cPr0abi5uaF3797Izc0VMmAiUg+hYbqUlBTEx8fj7Nmz8PLyAgCsXr0aTk5O+OabbzBhwoSqjZaIVEXoHEjxCnPPrgNjYWGBOnXq4NixY2W2YZiOSJuEFhBPT0+4ubnhvffew8OHD5Gfn4/Fixfj9u3byMjIMNmGYToi7RJaQGrXro3vv/8ely5dQsOGDVGvXj3ExsYiICAAFhYWJtswTEekXcJXpuvUqROSkpKQlZWF/Px8NGrUCN26dUPnzp1N7s8wHZF2KXYfiL29PRo1aoSUlBQ+jYyohhIepvv222/RqFEjuLq6Ijk5GTNmzEBQUBD8/f2FDpyIzE94mC4jIwOhoaG4c+cO9Ho9xowZgwULFogbMRGpBsN0VGMxTCcPw3REVC1YQIhItkoVkPDwcHTp0gW2trZwcnJCUFAQLl68aLSPJEkICwuDwWCAtbU1fH19ce7cOaGDJiJ1qFQBiYuLw5QpUxAfH4/9+/fj6dOn8Pf3NwrKLVmyBMuXL8eqVauQkJAAFxcX9OnTB48ePRI+eCIyrypNot69exdOTk6Ii4tDz549IUkSDAYDZs6ciblz5wL4M+vi7OyMTz75BBMnTnzhMTmJSqJwElWeaptEzcrKAgA0bNgQwJ/3hNy+fdvong8rKyv06tULx48fN3kMhumItEt2AZEkCaGhofDx8UHbtm0BALdv3wYAODs7G+3r7Oxc8t7zGKYj0i7ZBWTq1Kn49ddf8c0335R6T6fTGX0tSVKpbcUYpiPSLllhumnTpmHnzp04cuQIGjduXLLdxcUFwJ9nInq9vmR7ZmZmqbOSYgzTEWlXpc5AJEnC1KlTsXXrVhw6dAgeHh5G73t4eMDFxQX79+8v2Zafn4+4uDj06NFDzIiJSDUqdQYyZcoUbN68GTt27ICtrW3JvIa9vT2sra2h0+kwc+ZMLFq0CC1atECLFi2waNEi1KtXD6NGjVLkGyAi86lUAYmIiAAA+Pr6Gm1fv349xo4dCwB499138eTJE0yePBkPHz5Et27dsG/fPtja2goZMBGpB8N0RM/gvSMM0xFRNWEBISLZWECISDbhadytW7eib9++cHR0hE6nQ1JSksjxEpGKCE/j5ubm4pVXXsHixYuFD5aI1KVSl3H37Nlj9PX69evh5OSExMRE9OzZEwAQHBwMALh+/XqFjpmXl1eyoh0AhumINERoGlcOhumItEtoGlcOhumItEv2ynTFadyyFs2uKIbpiLRLaBqXiP5aKlVAJEnCtGnTsG3bNsTGxpZK4xLRX4vQNC4APHjwAKmpqbh16xYAlNwn4uLiUvK8ECKqGSo1iRoREYGsrCz4+vpCr9eXvGJiYkr22blzJ7y9vdG/f38AwIgRI+Dt7Y3IyEixIycis6v0R5gXGTt2bEm0n4hqNmZhiEg2FhAikk1omK6goABz585Fu3btYGNjA4PBgDFjxpRMqBJRzSI0TPf48WOcOnUKCxYswKlTp7B161ZcunQJAwcOVGTwRGReQpe2NCUhIQFdu3bFjRs34Orq+sJj8pGGZE58pGHl/gZl38oOVCxMl5WVBZ1OhwYNGph8n2lcIu1SNEz3xx9/YN68eRg1alSZlYxpXCLtUmRpS+DPCdURI0agqKgIq1evLvM4TOMSaZciYbqCggIMGzYM165dw6FDh8r9HMU0LpF2CQ/TFRePlJQUHD58GA4ODsIGS0TqIjRM9/TpUwwZMgSnTp3Crl27UFhYWLJPw4YNUadOHfHfARGZTaUu4+p0OpPbi5e2vH79epkR/8OHD5daEtMUXsYlc+JlXAUv476o1ri7u1cocEekVnKKwV+56DALQ0SysYAQkWzCV6YLCwuDp6cnbGxs8NJLL6F37944ceKE0EETkToIX5muZcuWWLVqFZKTk3Hs2DG4u7vD398fd+/eFT54IjIvxcN0xTO6Bw4cwOuvv/7CY/IqDGlNTZtEVU2YLj8/H2vWrIG9vT06dOhgch+G6Yi0S5Ew3a5du1C/fn3UrVsXK1aswP79++Ho6GjyOAzTEWmXImE6Pz8/JCUl4fjx4+jXrx+GDRuGzMxMk8dhmI5Iu2QVkOIw3eHDh02G6WxsbNC8eXN0794da9euhaWlJdauXWvyWFZWVrCzszN6EZE2VMvKdJIkGc1zEFHNIDRMl5ubi4ULF2LgwIHQ6/W4f/8+Vq9ejfT0dAwdWvmZaiJSt0oVkIiICAAoFYorDtNZWFjgt99+Q1RUFO7duwcHBwd06dIFR48ehZeXl7BBE5E6VOk+ECXwPhD6K1DzvSOV+RtkFoaIZGMBISLZhIfpnjVx4kTodDqsXLmyquMkIhUSHqYrtn37dpw4cQIGg0HYYIlIXSp1FWbPnj1GX69fvx5OTk5ITEw0CtPdvHkTU6dOxd69e9G/f38xIyUi1REepisqKkJwcDDmzJlToUu3DNMRaZfwMN0nn3wCS0tLTJ8+vULHYZiOSLuEhukSExPx2WefYcOGDWU+wf15DNMRaZfQMN3Ro0eRmZkJV1dXWFpawtLSEjdu3MC//vUvuLu7mzwWw3RE2iU0TBccHIzevXsbbevbty+Cg4Mxbty4qo+WiFRFaJjOwcGh1FKWtWvXhouLC1q1aiVu1ESkCpX6CBMREYGsrCz4+vpCr9eXvGJiYpQaHxGpmNCV6Uy5fv16pdsQ1XTVtQKe3L4qilkYIpKNBYSIZBMephs7dix0Op3Rq3v37kIHTUTqoEiYrl+/fsjIyCh5/fjjj0IHTUTqoEiYzsrKCi4uLmJGSESqVaU5kLJWpouNjYWTkxNatmyJd955p8w1YYA/w3TZ2dlGLyLSBuFhuoCAAHz99dc4dOgQli1bhoSEBLz22mtlLuvAMB2Rdsl+qPKUKVOwe/duHDt2zOTiUsUyMjLg5uaGLVu2YPDgwaXeNxXnb9KkCR+qTPSc6roPRPHFtYvDdEeOHCm3eACAXq+Hm5sbUlJSTL5vZWUFKysrOcMgIjNTfGW6+/fvIy0tDXq9XvYgiUidKjUHMmXKFGzatAmbN28uCdPdvn0bT548AQDk5ORg9uzZ+OWXX3D9+nXExsZiwIABcHR0xKBBgxT5BojIfISvTJecnIzo6Gj8/vvv0Ov18PPzQ0xMDGxtbYUNmojUQWiYztraGnv37q3SgIhIO6r0UGUiqj5yU7WVvXrzVCqo8L4M0xGRbCwgRCSbIktbXrhwAQMHDoS9vT1sbW3RvXt3pKamChs0EamD8DTulStX4OPjA09PT8TGxuLMmTNYsGAB6tatK3zwRGResm9lB4C7d+/CyckJcXFxJWncESNGoHbt2ti4cWOFjsFb2YmUJWcSNRY7KvQ3KDSNW1RUhN27d6Nly5bo27cvnJyc0K1bN2zfvr3MYzBMR6RdQtO4mZmZyMnJweLFi9GvXz/s27cPgwYNwuDBgxEXF2fyOFyZjki7ZN8HUry05bFjx0q2FRUVAQACAwMxa9YsAEDHjh1x/PhxREZGolevXqWOwzAdkXYJXdrS0dERlpaWaNOmjdH+rVu35lUYohpIaBq3Tp066NKlS6lLu5cuXYKbm1vVR0tEqiJ0aUsAmDNnDoYPH46ePXvCz88Pe/bswQ8//IDY2Fjhgyci86rUZVydTmdye3Eat9i6desQHh6O9PR0tGrVCh9++CECAwMr1EdlnoZERC+m5GXcKt0HogQWECLzqszfILMwRCQbCwgRySY8TPf8spbFr6VLlwodOBGZn/Aw3bNLWmZkZGDdunXQ6XR48803hQ+eiMxLeJjueUFBQXj06BEOHjxYoWNyEpXIvBRfF6ZYWUtbFrtz5w52796NqKioMo9hKo1LRNogfGnLZ0VFRcHW1tbkinTFmMYl0i5Fl7b09PREnz598MUXX5R5HD4PhEhdVLG05dGjR3Hx4kXExMSUeyymcYm0S7GlLdeuXYtOnTqhQ4cOVR4kEamT8DAd8Ocp0Lfffotly5aJHS0RqYrQpS2LbdmyBZIkYeTIkZUeUPGUDK/GEJlH8d9eRaZHVRemS09P55UYIhVIS0src46zmOoKSFFREW7dugVbW9tSjw8ovkKTlpZW4Ss01dVG7ePjz6F626h9fOW1kSQJjx49gsFgQK1a5d/pobq1cWvVqvXCqmdnZ1fpS7zV1aY6+1Jzm+rsS81tqrMvkW3s7e0r1J5pXCKSjQWEiGTTVAGxsrLCf/7zn0rdeFZdbdQ+Pv4cqreN2scn93t6nuomUYlIOzR1BkJE6sICQkSysYAQkWwsIEQkGwsIEcnGAkJEsrGAEJFsLCBEJNv/AksxgsBa9pyoAAAAAElFTkSuQmCC", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "newInt = Interleave(torus, line, n = 1, initialize_random_maps= False)\n", - "\n", - "newInt.psi('0', 'V').draw(filltype='nan')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Put the correct maps to the interleaving object and draw the map" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "\n" - ] - }, - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 11, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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tLdX+9Sk9PR3W1tbo1q0bDh8+XK6vH374ARMnTsSrr76Kr7/+GhcvXkSLFi2wZs0axMXF4aeffjL+B6CHv78/zpw5o41REARcvnwZ1tbWaNu2LdLS0iCRSHDs2DH4+fnptOUHhi5jPzAAw3+Wp0+fxpAhQ2Bvb49nn30WgiDg9OnTuH//Pg4ePIhnnnmmwr4M/cB49Dvy4MGDcr/Hj/cjkUj0/k4b8wFFREQkFkvI/wDxc8CYmBhcvXoVBw8exC+//KJzzNj878MPP8SiRYvQvXt3uLu7l/sj8K5duwyKETBu8pTKBsONGzfGli1b8OKLL+qUz5kzB99++61Ry3ZUFuN///tfvPnmm7C3t4ezs7POz0QikeDKlSvlzmfsz9HY/G/BggX49NNPMWPGDPTu3RsAcOLECURHR2PWrFn46KOP9LaraQ6ol1DHvfjii0JQUJCQl5cnNGrUSLh48aJw9OhR4dlnnxUSExMrbOft7S388ssv5cpPnjwp+Pj4VNhuxYoVwvDhw4U7d+5oy+7cuSMEBQUJy5cv19umS5cuQmxsrCAIgtCoUSMhMzNTEARBOHv2rNCsWTOduufOnRNKS0srfsHV8OmnnwqjRo0SVCqVtkylUgkvv/yysGrVKqGoqEgICgoSAgICdNpFRkYKVlZWwrPPPisEBQUJI0eO1NnqArlcLvz444/lymfPni24ubmJ3t/69esFa2troVGjRoK3t7fg4+Oj3Xx9fStsZ8zPsl+/fkJISIhQUlKiLSspKRGCg4OF5557rsK+5s+fLzg4OAjvvfeesGfPHmHPnj3Ce++9JzRq1EiYN2+e3jbG/B7XpD8iIiIxWUL+JwjVzwHNmf+5ubkJmzdvrlHf//TBBx8IISEhQosWLardZtOmTcIHH3wg9OnTp9yx//3vf4JcLheUSqW2bPr06YKHh4dw6dIl0WNs1qyZsHjxYoP+TYz9ORqb/zk7Owvbtm0rV75t2zbB2dm5wnY1yQErUucHjM7OzsK5c+cEQRAER0dH4ffffxcEQRB+/vlnoUuXLhW2k0qlwpUrV8qVZ2ZmClKptMJ2Hh4ewm+//Vau/MKFC4K7u7veNvb29kJWVpYgCLofFvr6srKyEv78809BEATB19dXuHXrVoWxVBZjampqufLffvtN8PDwEARBEJKTk8v9MpniA0NspvjAqIwxHxiCYNzP0s7OTu9rSE1NFezt7StsZ8wHhjG/xzXpj4iISEyWkP8JQvVzQHPmf05OTkJGRobB/dW2b775RmjSpImQlJQk/Otf/xI8PDyEtLQ0k/TVpEkTg38mxv4cjc3/GjduLKSnp5crT0tLE+RyeYXtapIDVsSmetchzae0tFQ721DTpk1x48YNtGnTBt7e3khLS6uwnaenJ3755Rf4+vrqlP/yyy/w8PCosJ1arcaff/6J9u3b65Tn5eWhoKBAbxt3d3dkZGTAx8dHp/zYsWNo0aKFTlnjxo2RlZUFV1dXZGdnl7uVsTpUKhXy8vLK3W6an58PtVqt7eef9/sXFxejT58+BvdXHaNGjUJMTAwcHR0xatSoSus2atQI7du3x5tvvlnu3u2hQ4fiyy+/xMiRI3Hw4EFs3LgRe/bswZEjR9C6dWvR4y4uLsbYsWNhZWXYCjPG/CwdHR2Rk5ODtm3b6pRfu3YNMpmswnalpaXo3r17ufJu3brhwYMHetsY83tck/6IiIjEZAn5H1D9HNCc+d+UKVOwbds2LFiwwOA+q8PQHLBDhw6YNm1auRxw3LhxuHv3Lvr16wcXFxcolUq0bNnSJDEHBwdj+/bteP/996vdxtifo7H532uvvYa1a9eWe85w3bp1ePXVVytsV5McsCJ1fsDYoUMHnD9/Hi1atEDPnj3x8ccfw9bWFuvWrSs3GHvclClTMHv2bJSUlGDgwIEAHj5z9u9//xtvv/12he1eeuklTJ48GStWrECvXr0AACdPnsTcuXMrfBNMmzYNs2bNwsaNGyGRSHDjxg2cOHEC77zzDhYuXKhTd/To0RgwYID23ufu3btXuBCpvvunASAoKAihoaFYsWIFevToAYlEgl9//RXvvPMORo4cCQD49ddfyw2wTPmBIZfLtfdyV/UAr0ajwZdffolffvkFe/fuLXe8rn9gAMb9LMeOHYvXX38dy5cvR58+fbTPGcydOxfjx4+vsJ0xHxjG/B7XpD8iIiIxWUL+B1Q/B6zt/O/xiU/Kysqwbt06HDp0CJ06dSo3X8Pj3/fh4eH4z3/+AwcHhyonT3nUztAccO3atTh27FiFuZ2rqyu6du2KNWvWVBhjdVU0qUtpaSk+/vhjHDhwoMqfySN///13tX+OjzM2/wMezilx8OBBnd/Ja9euYdKkSTo/h8f7rkkOWJE6P+nNgQMHUFRUhFGjRuHKlSt48cUX8fvvv8PZ2Rnbt2/Xfhj8kyAIeO+997B69WrtX1rs7Ozw7rvvlhvEPe7evXt45513sHHjRpSUlAAAbGxs8Prrr+OTTz6Bg4OD3nbz5s3Dp59+ir///hsAIJVK8c477+A///lPubr79+9HRkYGZs6ciUWLFlX414VZs2bpLS8sLMScOXOwefNm7RUfGxsbBAcH49NPP4WDgwNSUlIAAJs3b9a2KysrQ2xsLDp16mSSDwxDXLx4ET169EBRUVGF5//+++/RtWtXnSUvxP7AmDlzJjZv3ozOnTsb9OafNWsWNm/eXK2f5SPFxcWYO3cuvvzyS+2/W4MGDfCvf/0LS5cuhVQq1dvXjBkzsHnzZnh6eur9wHi870f9Gvp7/PjP8sGDB4iJiYGXl5fe/j7//HO9cRIREYnFUvI/oPo5YG3mf3PmzKkw3sf9c+ITf39/7Nq1C40bNy43KVBl7QzxKAd89tlnjY7RmHaPM+a1GfvzMDb/M/Z11uR3ucI+6vqAUZ87d+6gSZMm1Zrqv7CwEJcuXYK9vT1atWpV4T/KPxUVFSEzMxOCIKBly5bV+uHeu3cPFy9eRFlZGfz8/KpcuHPy5MlYvXp1pZejK1NYWIgrV65AEAQ8/fTTevsz9pfN1B8YpaWl+O2339C5c+caxWhMu8cZ+9pq8jO5d++ezu9Ww4YNK6xbVV9V9Vvd32MxfpZERESmVFfzP8CwHLA28r+67PEcsD4xNP+rKWN/l/WxyAEjERERERERmZ5hM30QERERERFRvcEBIxEREREREellUQNGjUaDyMhIaDSaJ66dJcRobDtLiNHYdpYQo7HtjO2LiIhIbJbwvWlsO0uI0dh2lhCjse0sIcaatHucRT3DqFarIZfLoVKp4Ojo+ES1s4QYjW1nCTEa284SYjS2nbF9ERERic0SvjeNbWcJMRrbzhJiNLadJcRYk3aPs6grjERERERERFR7OGAkIiIiIiIivWzMHcA/lZWV4caNG5DJZOXW2VGr1Tr/rS5LaGcJMRrbzhJiNLadJcRobLvK2giCgIKCAnh4eMDKin93IiKimmMOWHdjNLadJcRobDtLiLGydobkcnXuGcbr16/D09PT3GEQUTVcu3YNzZs3N3cYRET0BGAOSFT7qpPL1bkrjDKZDMDD4DnRBlHdpFar4enpqX2/EhER1RRzQKLaY0guV+cGjI9uQXB0dOSHBVEd989bhoiIiIzFHJCo9lUnlzPZw0dr1qyBr68v7Ozs0K1bNxw9etRUXRERERFRDYiRty1evBh9+vRBw4YN0bhxY/GDJCKzMMmAcfv27Zg9ezbmzZuHs2fP4rnnnkNgYCBycnJM0R0RERERGUmsvK24uBhjxozBv/71LxNFSkTmYJJJb3r27IlnnnkGa9eu1Za1a9cOI0eORFRUVKVtuVg4Ud3H9ykR0ZOjJnmbPjExMZg9ezb++usvg9rxu4Wo9hjyfhP9CmNxcTGSk5MREBCgUx4QEIDjx4+Xq6/RaKBWq3U2IiIiIjI9Q/M2MTEHJLIMog8Yb926hdLSUjRr1kynvFmzZsjNzS1XPyoqCnK5XLtxOmUiIiKi2mFo3iYm5oBElsFkk978c8YdQRD0zsITEREBlUql3a5du2aqkIiIiIhIj+rmbWJiDkhkGURfVqNp06awtrYu91epvLy8cn+9AgCpVAqpVCp2GERERERUBUPzNjExBySyDKJfYbS1tUW3bt0QHx+vUx4fH48+ffqI3R0RERERGYl5GxFVRfQrjAAQHh6OiRMnonv37ujduzfWrVuHnJwcvPnmm6bojoiIiIiMJFbelpOTgzt37iAnJwelpaVISUkBALRs2RKNGjUyQeREVBtMMmAcO3Ysbt++jUWLFuHmzZvo0KEDfvrpJ3h7e5uiOyIiIiIyUnXytsjISMTExCA7O7vC8yxcuBCxsbHa/a5duwIAjhw5AoVCYarwicjETLIOY01wDR6iuo/vUyKi+iUkJATAwzUWTYXfLUS1x5D3m0muMIqh7M+uKLtn2COWVm6XTRQNERERUf2lVCqRmJhYK30xBySqW+rsgJGIiIiI6oasrCxzh0BEZmKydRiJiIiIiIjIsok+YExMTMTw4cPh4eEBiUSC3bt3i90FEREREYlEjNwtOzsbr7/+Onx9fWFvb4+nn34aH3zwAYqLi8UPmIhqlegDxqKiInTu3BnR0dFin5qIiIiIRCZG7vb777+jrKwMX331FVJTU/Hpp5/iyy+/xPvvvy9ipERkDqI/wxgYGIjAwECxT0tEREREJiBG7jZ06FAMHTpUu9+iRQukpaVh7dq1WL58eU1DJCIzMvukNxqNBhqNRruvVqvNGA0RERERiUGlUsHJyanC48wBiSyD2Se9iYqKglwu126enp7mDomIiIiIaiAzMxOff/453nzzzQrrMAcksgxmHzBGRERApVJpt2vXrpk7JCIiIiIy0o0bNzB06FCMGTMGU6ZMqbAec0Aiy2D2W1KlUimkUqm5wyAiIiKiGrpx4wb8/f3Ru3dvrFu3rtK6zAGJLIPZrzASERERkeX7448/oFAo8Mwzz2DTpk2wsmKaSfQkEP0KY2FhITIyMrT7WVlZSElJgZOTE7y8vMTujoiIiIhqQIzc7caNG1AoFPDy8sLy5cuRn5+vPebm5iZ6zERUe0QfMJ4+fRr+/v7a/fDwcABAcHAwYmJixO6OiIiIiGqgOrlbZGQkYmJikJ2drfccBw8eREZGBjIyMtC8eXOdY4IgmCRuIqodEqGOvYvVajXkcjlUKhUcHR0NaluW28qoPq3cLhvVjqi+qsn7lIiILE9ISAgAmPSP/8wBiWqPIe83s096Q0RERER1m1KpRGJiornDICIz4ICRiIiIiCqVlZVl7hCIyEw4fRURERERERHpJfqAMSoqCj169IBMJoOrqytGjhyJtLQ0sbshIiIiIhGIlbuNGDECXl5esLOzg7u7OyZOnIgbN26YIGIiqk2iDxiVSiXCwsJw8uRJxMfH48GDBwgICEBRUZHYXRERERFRDYmVu/n7++O7775DWloafvjhB2RmZuLll182UdREVFtMPktqfn4+XF1doVQq0b9//yrrc4YsorqPs6QSET25DM3dKrJ3716MHDkSGo0GDRo0qLI+c0Ci2lOnZklVqVQAACcnJ73HNRoNNBqNdl+tVps6JCIiIiKqQFW5W3XcuXMHW7duRZ8+fSocLDIHJLIMJp30RhAEhIeHo1+/fujQoYPeOlFRUZDL5drN09PTlCERERERUQWqk7tV5t1334WDgwOcnZ2Rk5ODPXv2VFiXOSCRZTDpLalhYWHYt28fjh07hubNm+uto++vS56enrwdgagO4y2pRERPpurkbpW5desW7ty5g6tXr+LDDz+EXC5HXFwcJBJJubrMAYnMp07ckjpjxgzs3bsXiYmJlX7gSKVSSKVSU4VBRERERNVQ3dytMk2bNkXTpk3RunVrtGvXDp6enjh58iR69+5dri5zQCLLIPqAURAEzJgxA7t27UJCQgJ8fX3F7oKIiIiIRGKq3O3RTWyPX0UkIssj+oAxLCwM27Ztw549eyCTyZCbmwsAkMvlsLe3F7s7IiIiIqoBMXK3X3/9Fb/++iv69euHJk2a4MqVK1i4cCGefvppvVcXichyiD7pzdq1a6FSqaBQKODu7q7dtm/fLnZXRERERFRD1cndIiMj4ePjU+E57O3tsXPnTjz//PNo06YNQkND0aFDByiVSt52SmThTHJLqrkY++CyMQ9K8yFpIiIiehJUJ3fLzs6GQqGo8HjHjh1x+PBhEaMyDHNAItMx+TqMRERERGTZlEolEhMTzR0GEZkBB4xEREREVKmsrCxzh0BEZmKSZxg7deoER0dHODo6onfv3vjf//4ndjdEREREJAKxczeNRoMuXbpAIpEgJSVFvECJyCxEHzA2b94cS5cuxenTp3H69GkMHDgQQUFBSE1NFbsrIiIiIqohsXO3f//73/Dw8BA5SiIyF9EHjMOHD8cLL7yA1q1bo3Xr1li8eDEaNWqEkydPit0VEREREdWQmLnb//73Pxw8eBDLly83QaREZA4mfYaxtLQUO3bsQFFRUYVr8Gg0Gp0FXdVqtSlDIiIiIqIKVCd3q8iff/6JqVOnYvfu3WjYsGGV9ZkDElkG0a8wAsCFCxfQqFEjSKVSvPnmm9i1axf8/Pz01o2KioJcLtdunp6epgiJiIiIiCpgSO6mjyAICAkJwZtvvonu3btXqw1zQCLLYJIBY5s2bZCSkoKTJ0/iX//6F4KDg3Hx4kW9dSMiIqBSqbTbtWvXTBESEREREVXAkNxNn88//xxqtRoRERHVbsMckMgySITqrNZaQ4MGDcLTTz+Nr776qsq6arUacrkcKpUKjo6Opg4NABdtJTKUOd6nRERUewzJ3QBg5MiR+PHHHyGRSLRlpaWlsLa2xquvvorY2Ngqz8EckKj2GPJ+q5V1GAVB0LlHnYiIiIjqLkNzt9WrV+Ojjz7S7t+4cQNDhgzB9u3b0bNnT1OESES1RPQB4/vvv4/AwEB4enqioKAA3377LRISErB//36xuyIiIiKiGhIjd/Py8tLZb9SoEQDg6aefRvPmzUWNl4hql+gDxj///BMTJ07EzZs3IZfL0alTJ+zfvx+DBw8WuysiIiIiqqHq5G6RkZGIiYlBdna2+QIlIrMQfcC4YcMGsU9JRERERCZSndwtOzsbCoWi2uf08fFBLUyTQUS1oFaeYazrjHl42ZiHpI3ti4iIiMiclEolEhMTzR2G6IzJywZbjTGqr/iyHUa1IzI3DhiJiIiIqFJZWVnmDoGIzMQk6zASERERERGR5TP5gDEqKgoSiQSzZ882dVdEREREVAM1ydt8fHwgkUh0tvfee0/8IImoVpn0ltSkpCSsW7cOnTp1MmU3RERERFRDYuRtixYtwtSpU7X7j5bXICLLZbIrjIWFhXj11Vexfv16NGnSxFTdEBEREVENiZW3yWQyuLm5aTcOGIksn8kGjGFhYRg2bBgGDRpUaT2NRgO1Wq2zEREREVHtqW7eVpVly5bB2dkZXbp0weLFi1FcXFxhXeaARJbBJLekfvvttzhz5gySkpKqrBsVFYUPP/zQFGEQERERURUMydsqM2vWLDzzzDNo0qQJfv31V0RERCArKwv//e9/9dZnDkhkGUQfMF67dg2zZs3CwYMHYWdnV2X9iIgIhIeHa/fVajU8PT3FDouIiIiI/sHQvK0yc+bM0f5/p06d0KRJE7z88svaq47/xByQyDKIPmBMTk5GXl4eunXrpi0rLS1FYmIioqOjodFoYG1trT0mlUohlUrFDoOIiIiIqmBo3maIXr16AQAyMjL0DhiZAxJZBtEHjM8//zwuXLigUzZ58mS0bdsW7777rtEfOkREREQkLlPmbWfPngUAuLu71yhGIjIv0QeMMpkMHTp00ClzcHCAs7NzuXIiIiIiMh+x8rYTJ07g5MmT8Pf3h1wuR1JSEubMmYMRI0bAy8tL7LCJqBaZbJZUIiIiInoyREZGwsfHp8LjUqkU27dvh0KhgJ+fHxYuXIipU6fim2++qb0gicgkTDJL6j8lJCTURjdEREREVEP68rbs7GwoFIoK2zzzzDM4efKk6YIiIrOplQHjk8jK7bJR7QZbjTGqXXzZDqPaEREREdWUUqlEYmKiucOoEw7cSDF3CES1igNGIiIiIqpUVlaWuUMgIjPhM4xERERERESkl+gDxsjISEgkEp3Nzc1N7G6IiIiISGRRUVGQSCSYPXu2Ue337duHnj17wt7eHk2bNsWoUaPEDZCIap1Jbklt3749Dh06pN3n2otEREREdVtSUhLWrVuHTp06GdX+hx9+wNSpU7FkyRIMHDgQgiCUW+ORiCyPSQaMNjY2vKpIREREZCEKCwvx6quvYv369fjoo48Mbv/gwQPMmjULn3zyCV5//XVteZs2bcQMk4jMwCTPMF6+fBkeHh7w9fXFuHHjcOXKlQrrajQaqNVqnY2IiIiIak9YWBiGDRuGQYMGGdX+zJkz+OOPP2BlZYWuXbvC3d0dgYGBSE1NrbANc0AiyyD6gLFnz57YvHkzDhw4gPXr1yM3Nxd9+vTB7du39daPioqCXC7Xbp6enmKHREREREQV+Pbbb3HmzBlERUUZfY5HFwciIyMxf/58xMXFoUmTJhgwYADu3Lmjtw1zQCLLIPqAMTAwEKNHj0bHjh0xaNAg7Nu3DwAQGxurt35ERARUKpV2u3btmtghEREREZEe165dw6xZs7BlyxbY2dkZfZ6ysjIAwLx58zB69Gh069YNmzZtgkQiwY4d+teSZg5IZBlMvg6jg4MDOnbsiMuX9S90L5VKIZVKTR0GEREREf1DcnIy8vLy0K1bN21ZaWkpEhMTER0dDY1GU63JC93d3QEAfn5+2jKpVIoWLVogJydHbxvmgESWweTrMGo0Gly6dEn7QUJEREREdcPzzz+PCxcuICUlRbt1794dr776KlJSUqo90323bt0glUqRlpamLSspKUF2dja8vb1NFT4R1QLRrzC+8847GD58OLy8vJCXl4ePPvoIarUawcHBYndFRERERDUgk8nQoUMHnTIHBwc4OzuXK6+Mo6Mj3nzzTXzwwQfw9PSEt7c3PvnkEwDAmDFjRI2ZiGqX6APG69evY/z48bh16xZcXFzQq1cvnDx5kn9dIiIiIrJQkZGRiImJQXZ2doV1PvnkE9jY2GDixIm4f/8+evbsicOHD6NJkya1FygRiU4iCIJg7iAep1arIZfLoVKp4OjoaO5wRFeW28qodlZu+p8BJTKHJ/19SkREukJCQgAAMTExJuvjSf9uGWxl3JXW+DL9kwYR1YQh7zeTT3pDRERERJZNqVQiMTHR3GEQkRlwwEhERERElcrKyjJ3CERkJiafJZWIiIiIiIgsk0kGjH/88Qdee+01ODs7o2HDhujSpQuSk5NN0RURERER1UBkZCQkEonO5ubmZtA5EhISyp3j0ZaUlGSiyImoNoh+S+rdu3fRt29f+Pv743//+x9cXV2RmZmJxo0bi90VEREREYmgffv2OHTokHa/uusvPtKnTx/cvHlTp2zBggU4dOgQunfvLkqMRGQeog8Yly1bBk9PT2zatElb5uPjI3Y3RERERCQSGxsbg68qPs7W1lanfUlJCfbu3Yvp06dDIpGIESIRmYnot6Tu3bsX3bt3x5gxY+Dq6oquXbti/fr1FdbXaDRQq9U6GxERERHVnsuXL8PDwwO+vr4YN24crly5UqPz7d27F7du3dIux6EPc0AiyyD6gPHKlStYu3YtWrVqhQMHDuDNN9/EzJkzsXnzZr31o6KiIJfLtZunp6fYIRERERFRBXr27InNmzfjwIEDWL9+PXJzc9GnTx/cvn3b6HNu2LABQ4YMqTSvYw5IZBkkgiAIYp7Q1tYW3bt3x/Hjx7VlM2fORFJSEk6cOFGuvkajgUaj0e6r1Wp4eno+sYu2luW2MqqdldtlkSMhMt6TvrgyEVF9VlRUhKeffhr//ve/ER4ebnD769evw9vbG9999x1Gjx5dYb36lgMOthpjVLv4sh0iR0JkWC4n+jOM7u7u8PPz0ylr164dfvjhB731pVIppFKp2GEQERERkREcHBzQsWNHXL5s3B+rN23aBGdnZ4wYMaLSeswBiSyD6Lek9u3bF2lpaTpl6enp8Pb2FrsrIiIiIhKZRqPBpUuX4O7ubnBbQRCwadMmTJo0CQ0aNDBBdERU20QfMM6ZMwcnT57EkiVLkJGRgW3btmHdunUICwsTuysiIiIiqqF33nkHSqUSWVlZOHXqFF5++WWo1WoEBwcbfK7Dhw8jKysLr7/+ugkiJSJzEH3A2KNHD+zatQvffPMNOnTogP/85z9YtWoVXn31VbG7IiIiIqIaun79OsaPH482bdpg1KhRsLW1xcmTJ3XuDouMjKzWMmkbNmxAnz590K5dOxNGTES1SfRJb2qKk2noxwelqS7h+5SIqH55tDxGTEyMyfp40r9bOPEh1SVmnfSGiIiIiJ4sSqUSiYmJ5g6DiMyAA0YiIiIiqlRWVpa5QyAiMxH9GUYfHx9IJJJyGye9ISIiIqqb/vjjD7z22mtwdnZGw4YN0aVLFyQnJxt0jvT0dAQFBaFp06ZwdHRE3759ceTIERNFTES1RfQBY1JSEm7evKnd4uPjAQBjxhj3DB4RERERmc7du3fRt29fNGjQAP/73/9w8eJFrFixAo0bNzboPMOGDcODBw9w+PBhJCcno0uXLnjxxReRm5trmsCJqFaIfkuqi4uLzv7SpUvx9NNPY8CAAWJ3RUREREQ1tGzZMnh6emLTpk3asurMiPq4W7duISMjAxs3bkSnTp0APMwB16xZg9TUVLi5uYkZMhHVItGvMD6uuLgYW7ZsQWhoKCQSid46Go0GarVaZyMiIiKi2rF37150794dY8aMgaurK7p27Yr169cbdA5nZ2e0a9cOmzdvRlFRER48eICvvvoKzZo1Q7du3fS2YQ5IZBlMOmDcvXs3/vrrL+1UzPpERUVBLpdrN09PT1OGRERERESPuXLlCtauXYtWrVrhwIEDePPNNzFz5kxs3ry52ueQSCSIj4/H2bNnIZPJYGdnh08//RT79++v8NZW5oBElsGk6zAOGTIEtra2+PHHHyuso9FooNFotPtqtRqenp5P7Bo8xuI6jFSXPOlrZRER1Se2trbo3r07jh8/ri2bOXMmkpKScOLEiWqdQxAEjBw5EiUlJZg3bx7s7e3x3//+F3v37kVSUhLc3d3LtalvOSDXYaS6pE6sw3j16lUcOnQIO3furLSeVCqFVCo1VRhEREREVAl3d3f4+fnplLVr1w4//PBDtc9x+PBhxMXF4e7du9rkc82aNYiPj0dsbCzee++9cm2YAxJZBpPdkrpp0ya4urpi2LBhpuqCiIiIiGqob9++SEtL0ylLT0+Ht7d3tc9x7949AICVlW5qaWVlhbKyspoHSURmY5IBY1lZGTZt2oTg4GDY2JjsIiYRERER1dCcOXNw8uRJLFmyBBkZGdi2bRvWrVtn0BravXv3RpMmTRAcHIxz584hPT0dc+fORVZWFi8eEFk4kwwYDx06hJycHISGhpri9EREREQkkh49emDXrl345ptv0KFDB/znP//BqlWr8Oqrr2rrREZGVrrURtOmTbF//34UFhZi4MCB6N69O44dO4Y9e/agc+fOtfAqiMhUTHL5LyAgACacS4eIiIiIRPTiiy/ixRdfrPB4dnY2FApFpefo3r07Dhw4IHJkRGRuvF/UQhy4kWLuEIiIiKieUiqVSExMNHcYFs3Y2U45Uz6ZGweMRERERFSprKwsc4dARGZisllSiYiIiIiIyLKJPmB88OAB5s+fD19fX9jb26NFixZYtGgRp1QmIiIiqoN8fHwgkUjKbYbMkgoAZ86cweDBg9G4cWM4OzvjjTfeQGFhoYmiJqLaIvqAcdmyZfjyyy8RHR2NS5cu4eOPP8Ynn3yCzz//XOyuiIiIiKiGkpKScPPmTe0WHx8PABgzpvrPzt24cQODBg1Cy5YtcerUKezfvx+pqakICQkxUdREVFtEf4bxxIkTCAoK0q654+Pjg2+++QanT58WuysiIiIiqiEXFxed/aVLl+Lpp5/GgAEDqn2OuLg4NGjQAF988QWsrB5ej/jiiy/QtWtXZGRkoGXLlqLGTES1R/QrjP369cPPP/+M9PR0AMC5c+dw7NgxvPDCC3rrazQaqNVqnY2IiIiIal9xcTG2bNmC0NBQSCSSarfTaDSwtbXVDhYBwN7eHgBw7NixCtswBySq+0QfML777rsYP3482rZtiwYNGqBr166YPXs2xo8fr7d+VFQU5HK5dvP09BQ7JCIiIiKqht27d+Ovv/4y+FbSgQMHIjc3F5988gmKi4tx9+5dvP/++wCAmzdv6m3DHJDIMog+YNy+fTu2bNmCbdu24cyZM4iNjcXy5csRGxurt35ERARUKpV2u3btmtghEREREVE1bNiwAYGBgfDw8DCoXfv27REbG4sVK1agYcOGcHNzQ4sWLdCsWTNYW1vrbcMckMgyiP4M49y5c/Hee+9h3LhxAICOHTvi6tWriIqKQnBwcLn6UqkUUqlU7DCIiIiIyABXr17FoUOHsHPnTqPaT5gwARMmTMCff/4JBwcHSCQSrFy5Er6+vnrrMwcksgyiDxjv3bunc/86AFhbW3NZDSIiIqI6bNOmTXB1ddVOXGisZs2aAQA2btwIOzs7DB48WIzwiMhMRB8wDh8+HIsXL4aXlxfat2+Ps2fPYuXKlQgNDRW7KyIiIiISQVlZGTZt2oTg4GDY2BiXHkZHR6NPnz5o1KgR4uPjMXfuXCxduhSNGzcWN1giqlWiDxg///xzLFiwAG+99Rby8vLg4eGBadOmYeHChWJ3RUREREQiOHToEHJycir8A39kZCRiYmKQnZ1d4Tl+/fVXfPDBBygsLETbtm3x1VdfYeLEiSaKmIhqi+gDRplMhlWrVmHVqlVin5qIiIiITCAgIACCIFR4PDs7GwqFotJzbN68WeSoiKguEH3ASKZh5XbZqHaDrcYY3Ca+bIdRfREREdGTSalUIjEx0dxh1EsHbqSYOwSq5zhgJCIiIqJKZWVlmTsEIjIT0ddhJCIiIiIioieDSQaMBQUFmD17Nry9vWFvb48+ffogKSnJFF0RERERUQUePHiA+fPnw9fXF/b29mjRogUWLVpk8HJnixcvRp8+fdCwYcMKZz3NycnB8OHD4eDggKZNm2LmzJkoLi4W4VUQkTmZ5JbUKVOm4LfffsPXX38NDw8PbNmyBYMGDcLFixfx1FNPmaJLIiIiIvqHZcuW4csvv0RsbCzat2+P06dPY/LkyZDL5Zg1a1a1z1NcXIwxY8agd+/e2LBhQ7njpaWlGDZsGFxcXHDs2DHcvn0bwcHBEAQBn3/+uZgviYhqmegDxvv37+OHH37Anj170L9/fwAPp2LevXs31q5di48++kjsLomIiIhIjxMnTiAoKAjDhg0DAPj4+OCbb77B6dOnDTrPhx9+CACIiYnRe/zgwYO4ePEirl27Bg8PDwDAihUrEBISgsWLF8PR0dH4F0FEZiX6LakPHjxAaWkp7OzsdMrt7e1x7NixcvU1Gg3UarXORkREREQ1169fP/z8889IT08HAJw7dw7Hjh3DCy+8IGo/J06cQIcOHbSDRQAYMmQINBoNkpOT9bZhDkhkGUQfMMpkMvTu3Rv/+c9/cOPGDZSWlmLLli04deoUbt68Wa5+VFQU5HK5dvP09BQ7JCIiIqJ66d1338X48ePRtm1bNGjQAF27dsXs2bMxfvx4UfvJzc1Fs2bNdMqaNGkCW1tb5Obm6m3DHJDIMphk0puvv/4agiDgqaeeglQqxerVqzFhwgRYW1uXqxsREQGVSqXdrl27ZoqQiIiIiOqd7du3Y8uWLdi2bRvOnDmD2NhYLF++HLGxsaL3JZFIypUJgqC3HGAOSGQpTDLpzdNPPw2lUomioiKo1Wq4u7tj7Nix8PX1LVdXKpVCKpWaIgwiIiKiem3u3Ll47733MG7cOABAx44dcfXqVURFRSE4OFi0ftzc3HDq1Cmdsrt376KkpKTclcdHmAMSWQaTrsPo4OAAd3d33L17FwcOHEBQUJApuyMiIiKix9y7dw9WVrrpnrW1tcHLalSld+/e+O2333QePzp48CCkUim6desmal9EVLtMcoXxwIEDEAQBbdq0QUZGBubOnYs2bdpg8uTJpuiOiIiIiPQYPnw4Fi9eDC8vL7Rv3x5nz57FypUrERoaatB5cnJycOfOHeTk5KC0tBQpKSkAgJYtW6JRo0YICAiAn58fJk6ciE8++QR37tzBO++8g6lTp3KGVCILZ5IBo0qlQkREBK5fvw4nJyeMHj0aixcvRoMGDUzRHRERERHp8fnnn2PBggV46623kJeXBw8PD0ybNg0LFy7U1omMjERMTAyys7MrPM/ChQt1nnvs2rUrAODIkSNQKBSwtrbGvn378NZbb6Fv376wt7fHhAkTsHz5cpO9NiKqHRJBEARzB/E4tVoNuVwOlUrFv0iJoCy3lcFtrNwumyASepLwfUpE9OQICQkBUPEai7WF3y3iGmw1xqh28WU7RI6E6iJD3m8mucJIRERERJZBqVQiMTHR3GEQUR3FASMRERFRPZaVlWXuEIioDjPpLKlERERERERkuQweMCYmJmL48OHw8PCARCLB7t27dY4LgoDIyEh4eHjA3t4eCoUCqampYsVLRERERNVUUFCA2bNnw9vbG/b29ujTpw+SkpIMPs/ixYvRp08fNGzYEI0bN9ZbZ9asWejWrRukUim6dOlSs8CJqM4weMBYVFSEzp07Izo6Wu/xjz/+GCtXrkR0dDSSkpLg5uaGwYMHo6CgoMbBEhEREVH1TZkyBfHx8fj6669x4cIFBAQEYNCgQfjjjz8MOk9xcTHGjBmDf/3rXxXWEQQBoaGhGDt2bE3DJqI6xOBnGAMDAxEYGKj3mCAIWLVqFebNm4dRo0YBAGJjY9GsWTNs27YN06ZNq1m0RERERFQt9+/fxw8//IA9e/agf//+AB4uobF7926sXbsWH330UbXP9eGHHwKofCbV1atXAwDy8/Nx/vx54wMnojpF1GcYs7KykJubi4CAAG2ZVCrFgAEDcPz4cb1tNBoN1Gq1zkZERERENfPgwQOUlpbCzs5Op9ze3h7Hjh0zU1T/hzkgkWUQdcCYm5sLAGjWrJlOebNmzbTH/ikqKgpyuVy7eXp6ihkSERERUb0kk8nQu3dv/Oc//8GNGzdQWlqKLVu24NSpU7h586a5w2MOSGQhTDJLqkQi0dkXBKFc2SMRERFQqVTa7dq1a6YIiYiIiKje+frrryEIAp566ilIpVKsXr0aEyZMgLW1tblDYw5IZCFEXYfRzc0NwMMrje7u7tryvLy8clcdH5FKpZBKpWKGQUREREQAnn76aSiVShQVFUGtVsPd3R1jx46Fr6+vuUNjDkhkIUS9wujr6ws3NzfEx8dry4qLi6FUKtGnTx8xuyIiIiKianJwcIC7uzvu3r2LAwcOICgoyNwhEZGFMPgKY2FhITIyMrT7WVlZSElJgZOTE7y8vDB79mwsWbIErVq1QqtWrbBkyRI0bNgQEyZMEDVwIiIiIqrcgQMHIAgC2rRpg4yMDMydOxdt2rTB5MmTDTpPTk4O7ty5g5ycHJSWliIlJQUA0LJlSzRq1AgAkJGRgcLCQuTm5uL+/fvaOn5+frC1tRXzZRFRLTJ4wHj69Gn4+/tr98PDwwEAwcHBiImJwb///W/cv38fb731Fu7evYuePXvi4MGDkMlk4kVNRERERFVSqVSIiIjA9evX4eTkhNGjR2Px4sVo0KCBtk5kZCRiYmKQnZ1d4XkWLlyI2NhY7X7Xrl0BAEeOHIFCoQDwcM1HpVJZrk5WVhZ8fHzEe1FEVKskgiAI5g7icWq1GnK5HCqVCo6OjuYOp14abDXGqHbxZTtEjoTqKr5PiYieHCEhIQAqX2OxNvC7RVxlua2MamfldlnkSKguMuT9JuqkN0RERERkWZRKJRITE80dBhHVURwwEhEREdVjWVlZ5g6BiOowg2dJTUxMxPDhw+Hh4QGJRILdu3frHN+5cyeGDBmCpk2bQiKRaB94JiIiIiLxVJWTAQ/Xwo6MjISHhwfs7e2hUCiQmppqcF+zZs1Ct27dIJVK0aVLl3LHExISEBQUBHd3dzg4OKBLly7YunWrEa+KiOoagweMRUVF6Ny5M6Kjoys83rdvXyxdurTGwRERERGRflXlZADw8ccfY+XKlYiOjkZSUhLc3NwwePBgFBQUGNSXIAgIDQ3F2LFj9R4/fvw4OnXqhB9++AHnz59HaGgoJk2ahB9//NGgfoio7jH4ltTAwEAEBgZWeHzixIkAUOlMW0RERERUM1XlZIIgYNWqVZg3bx5GjRoFAIiNjUWzZs2wbds2TJs2rdp9rV69GgCQn5+P8+fPlzv+/vvv6+zPnDkTBw4cwK5duzB8+PBq90NEdY/BVxjFptFooFardTYiIiIiqpmsrCzk5uYiICBAWyaVSjFgwAAcP37c5P2rVCo4OTlVeJw5IJFlMPuAMSoqCnK5XLt5enqaOyQiIiIii5ebmwsAaNasmU55s2bNtMdM5fvvv0dSUhImT55cYR3mgESWwewDxoiICKhUKu127do1c4dERERE9MSQSCQ6+4IglCsTU0JCAkJCQrB+/Xq0b9++wnrMAYksg9mX1ZBKpZBKpeYOg4iIiOiJ4ubmBuDhlUZ3d3dteV5eXrmrjmJRKpUYPnw4Vq5ciUmTJlValzkgkWUw+xVGIiIiIhKfr68v3NzcEB8fry0rLi6GUqlEnz59RO8vISEBw4YNw9KlS/HGG2+Ifn4iMg+DrzAWFhYiIyNDu5+VlYWUlBQ4OTnBy8sLd+7cQU5ODm7cuAEASEtLA/Dwr1yP/tJFRERERDVTVU4mkUgwe/ZsLFmyBK1atUKrVq2wZMkSNGzYEBMmTDCor4yMDBQWFiI3Nxf379/XrrPt5+cHW1tb7WBx1qxZGD16tPYZSVtb20onviGiuk8iCIJgSIOEhAT4+/uXKw8ODkZMTAxiYmL0PuD8wQcfIDIyssrzq9VqyOVyqFQqODo6GhIaiWSw1Rij2sWX7RA5Eqqr+D4lIjK/qnIy4OHzih9++CG++uor3L17Fz179sQXX3yBDh06aOuHhIQgOzsbCQkJFfalUCigVCrLlWdlZcHHxwchISGIjY0td3zAgAGVnvdx/G4RV1luK6PaWbldFjkSqosMeb8ZPGA0NX5YmB8HjFQVvk+JiJ4cCoUCCoWiWn/YNyV+t4iLA0aqjCHvN7NPekN1z4EbKeYOgYiIiGpBQUEBMjMzERcXZ+5QSGTGDvyMuXDAiwZPNg4YiYiIiOopmUzG5SyIqFKcJZWIiIiIiIj0MnjAmJiYiOHDh8PDwwMSiQS7d+/WHispKcG7776Ljh07wsHBAR4eHpg0aZJ2xlQiIiIiEkdlOdkjO3fuxJAhQ9C0aVNIJBLt7KaGmjVrFrp16wapVIouXbqUO56WlgZ/f380a9YMdnZ2aNGiBebPn4+SkhKj+iOiusPgAWNRURE6d+6M6Ojocsfu3buHM2fOYMGCBThz5gx27tyJ9PR0jBgxQpRgiYiIiOihynKyx+v07dsXS5curVFfgiAgNDQUY8eO1Xu8QYMGmDRpEg4ePIi0tDSsWrUK69evxwcffFCjfonI/Ax+hjEwMBCBgYF6j8nlcp3FYQHg888/x7PPPoucnBx4eXkZFyURERER6agsJ3tk4sSJAIDs7Owa9bV69WoAQH5+Ps6fP1/ueIsWLdCiRQvtvre3NxISEnD06NEa9UtE5mfySW9UKhUkEgkaN26s97hGo4FGo9Huq9VqU4dERERERCaUkZGB/fv3Y9SoURXWYQ5IZBlMOunN33//jffeew8TJkyocH2PqKgoyOVy7ebp6WnKkIiIiIjIRPr06QM7Ozu0atUKzz33HBYtWlRhXeaARJbBZAPGkpISjBs3DmVlZVizZk2F9SIiIqBSqbQbp3YmIiIiskzbt2/HmTNnsG3bNuzbtw/Lly+vsC5zQCLLYJJbUktKSvDKK68gKysLhw8frvDqIgBIpVJIpVJThEFEREREtejRVUI/Pz+UlpbijTfewNtvvw1ra+tydZkDElkG0QeMjwaLly9fxpEjR+Ds7Cx2F0RERERUxwmCgJKSEgiCYO5QiKgGDB4wFhYWIiMjQ7uflZWFlJQUODk5wcPDAy+//DLOnDmDuLg4lJaWIjc3FwDg5OQEW1tb8SInIiIiqscqy8kezUx/584d5OTkaNfETktLAwC4ubnBzc2t2n1lZGSgsLAQubm5uH//vnY9Rz8/P9ja2mLr1q1o0KABOnbsCKlUiuTkZERERGDs2LGwsTH5HItEZEIGv4NPnz4Nf39/7X54eDgAIDg4GJGRkdi7dy8AlFvU9ciRI1AoFMZHSkRERERaleVkMTExAIC9e/di8uTJ2jrjxo0DAHzwwQeIjIwEAISEhCA7OxsJCQkV9jVlyhQolUrtfteuXQE8HKT6+PjAxsYGy5YtQ3p6OgRBgLe3N8LCwjBnzhwxXioRmZFEqGP3CajVasjlcqhUqkqffSTTKcttZVQ7K7fLIkdCdRXfp0RETw6FQgGFQqEdQJoLv1vqhsFWYwxuE1+2wwSRkCkZ8n7jPQJUjrEDP2M+YAB+yBAREZlLQUEBMjMzERcXZ+5QqI44cCPF3CFQHcMBIxEREVE9JZPJuJwFEVXKZOswEhERERERkWUzeMCYmJiI4cOHw8PDAxKJBLt379Y5HhkZibZt28LBwQFNmjTBoEGDcOrUKbHiJSIiIiJUnZOVlJTg3XffRceOHeHg4AAPDw9MmjRJO2OqIWbNmoVu3bpBKpWWm9jwnzIyMiCTydC4cWOD+yGiusfgAWNRURE6d+6M6Ohovcdbt26N6OhoXLhwAceOHYOPjw8CAgKQn59f42CJiIiI6KGqcrJ79+7hzJkzWLBgAc6cOYOdO3ciPT0dI0aMMLgvQRAQGhqKsWPHVlqvpKQE48ePx3PPPWdwH0RUNxn8DGNgYCACAwMrPD5hwgSd/ZUrV2LDhg04f/48nn/+ecMjJCIiIqJyqsrJ5HI54uPjdco+//xzPPvss8jJydGu1Vgdq1evBgDk5+fj/PnzFdabP38+2rZti+effx7Hjx+v9vmJqO4y6aQ3xcXFWLduHeRyOTp37qy3jkajgUaj0e6r1WpThkRERERUb6lUKkgkEpPcLnr48GHs2LEDKSkp2LlzZ5X1mQMSWQaTTHoTFxeHRo0awc7ODp9++ini4+PRtGlTvXWjoqIgl8u1m6enpylCIiIiIqrX/v77b7z33nuYMGGC6Osc3r59GyEhIYiJian2uZkDElkGkwwY/f39kZKSguPHj2Po0KF45ZVXkJeXp7duREQEVCqVduPUzkRERETiKikpwbhx41BWVoY1a9aIfv6pU6diwoQJ6N+/f7XbMAcksgwmGTA6ODigZcuW6NWrFzZs2AAbGxts2LBBb12pVApHR0edjYiIiIjEUVJSgldeeQVZWVmIj483Sa51+PBhLF++HDY2NrCxscHrr78OlUoFGxsbbNy4UW8b5oBElsGkzzA+IgiCzj3qRERERGR6jwaLly9fxpEjR+Ds7GySfk6cOIHS0lLt/p49e7Bs2TIcP34cTz31lEn6JKLaYfCAsbCwEBkZGdr9rKwspKSkwMnJCc7Ozli8eDFGjBgBd3d33L59G2vWrMH169cxZswYUQMnIiIiqs8qy8m8vLzw4MEDvPzyyzhz5gzi4uJQWlqK3NxcAICTkxNsbW2r3VdGRgYKCwuRm5uL+/fvIyUlBQDg5+cHW1tbtGvXTqf+6dOnYWVlhQ4dOtT8hRKRWRk8YDx9+jT8/f21++Hh4QCA4OBgfPnll/j9998RGxuLW7duwdnZGT169MDRo0fRvn178aImIiIiqucqy8liYmJw/fp17N27FwDQpUsXnbZHjhyBQqEAAISEhCA7OxsJCQkV9jVlyhQolUrtfteuXQE8HKT6+PjU/MUQUZ0lEQRBMHcQj1Or1ZDL5VCpVLyX3cKU5bYyqp2V22WRIyFT4/uUiOjJoVAooFAoEBkZadY4+N1iuQZbGXcnYXzZDpEjoeoy5P1WK88wEhEREVHdU1BQgMzMTMTFxZk7FCKqozhgJCIiIqqnZDIZl7MgokqZZFkNIiIiIiIisnwGDxgTExMxfPhweHh4QCKRYPfu3RXWnTZtGiQSCVatWlWDEImIiIjon6qTk0VGRqJt27ZwcHBAkyZNMGjQIJw6dcrgvmbNmoVu3bpBKpWWm0AHALKzsyGRSMpt+/fvN+KVEVFdYvCAsaioCJ07d0Z0dHSl9Xbv3o1Tp07Bw8PD6OCIiIiISL/q5GStW7dGdHQ0Lly4gGPHjsHHxwcBAQHIz883qC9BEBAaGoqxY8dWWu/QoUO4efOmdhs4cKBB/RBR3WPwM4yBgYEIDAystM4ff/yB6dOn48CBAxg2bJjRwRERERGRftXJySZMmKCzv3LlSmzYsAHnz5/H888/X+2+Vq9eDQDIz8/H+fPnK6zn7OwMNze3ap+XiOo+0Z9hLCsrw8SJEzF37txqrb2o0WigVqt1NiIiIiISV3FxMdatWwe5XI7OnTubpI8RI0bA1dUVffv2xffff19pXeaARJZB9AHjsmXLYGNjg5kzZ1arflRUFORyuXbz9PQUOyQiIiKieisuLg6NGjWCnZ0dPv30U8THx6Np06ai9tGoUSOsXLkS33//PX766Sc8//zzGDt2LLZs2VJhG+aARJZB1GU1kpOT8dlnn+HMmTOQSCTVahMREYHw8HDtvlqt5gcGERERkUj8/f2RkpKCW7duYf369XjllVdw6tQpuLq6itZH06ZNMWfOHO1+9+7dcffuXXz88cd47bXX9LZhDkhkGUS9wnj06FHk5eXBy8sLNjY2sLGxwdWrV/H222/Dx8dHbxupVApHR0edjYiIiIjE4eDggJYtW6JXr17YsGEDbGxssGHDBpP326tXL1y+fLnC48wBiSyDqFcYJ06ciEGDBumUDRkyBBMnTsTkyZPF7IqIiIiIjCAIAjQajcn7OXv2LNzd3U3eDxGZlsEDxsLCQmRkZGj3s7KykJKSAicnJ3h5ecHZ2VmnfoMGDeDm5oY2bdrUPFoiIiIiAlB1TlZUVITFixdjxIgRcHd3x+3bt7FmzRpcv34dY8aMMaivjIwMFBYWIjc3F/fv30dKSgoAwM/PD7a2toiNjUWDBg3QtWtXWFlZ4ccff8Tq1auxbNkyMV8yEZmBwQPG06dPw9/fX7v/6N7z4OBgxMTEiBYYEREREVWsqpzM2toav//+O2JjY3Hr1i04OzujR48eOHr0qM5M9iEhIcjOzkZCQkKFfU2ZMgVKpVK737VrVwAPB6mPHjv66KOPcPXqVVhbW6N169bYuHFjhc8vEpHlkAiCIJg7iMep1WrI5XKoVCrey15PDLYy7K+cj8SX7RA5Eqouvk+JiJ4cCoUCCoUCkZGRZo2D3y2Wqyy3lVHtrNwqfsaVTMuQ95uozzASERERkeUoKChAZmYm4uLizB0KEdVRHDASERER1VMymQzXrl0zdxhEVIcZvKxGYmIihg8fDg8PD0gkEuzevVvneEhICCQSic7Wq1cvseIlIiIiIlSdk/3TtGnTIJFIsGrVKoP7mjVrFrp16wapVIouXbrorSMIApYvX47WrVtDKpXC09MTS5YsMbgvIqpbDL7CWFRUhM6dO2Py5MkYPXq03jpDhw7Fpk2btPu2trbGR0hERERE5VQnJ3tk9+7dOHXqFDw8PIzqSxAEhIaG4tSpUzh//rzeOrNmzcLBgwexfPlydOzYESqVCrdu3TKqPyKqOwweMAYGBiIwMLDSOlKpFG5ubkYHRURERESVq05OBgB//PEHpk+fjgMHDmDYsGFG9bV69WoAQH5+vt4B46VLl7B27Vr89ttvXEqN6Alj8C2p1ZGQkABXV1e0bt0aU6dORV5eXoV1NRoN1Gq1zkZERERENVdWVoaJEydi7ty5OktpiO3HH39EixYtEBcXB19fX/j4+GDKlCm4c+dOhW2YAxJZBtEHjIGBgdi6dSsOHz6MFStWICkpCQMHDoRGo9FbPyoqCnK5XLt5enqKHRIRERFRvbRs2TLY2Nhg5syZJu3nypUruHr1Knbs2IHNmzcjJiYGycnJePnllytswxyQyDKIPkvq2LFjtf/foUMHdO/eHd7e3ti3bx9GjRpVrn5ERIR2oVng4Zog/MAgIiIiqpnk5GR89tlnOHPmDCQSiUn7Kisrg0ajwebNm9G6dWsAwIYNG9CtWzekpaXpvU2VOSCRZTDJLamPc3d3h7e3Ny5f1r8wp1QqhaOjo85GRERERDVz9OhR5OXlwcvLCzY2NrCxscHVq1fx9ttvw8fHR9S+3N3dYWNjox0sAkC7du0AADk5OXrbMAcksgwmX4fx9u3buHbtGtzd3U3dFRERERH9fxMnTsSgQYN0yoYMGYKJEydi8uTJovbVt29fPHjwAJmZmXj66acBAOnp6QAAb29vUfsiotpl8ICxsLAQGRkZ2v2srCykpKTAyckJTk5OiIyMxOjRo+Hu7o7s7Gy8//77aNq0KV566SVRAyciIiKqzyrLyby8vODs7AxnZ2edNg0aNICbm5vBM5lmZGSgsLAQubm5uH//PlJSUgAAfn5+sLW1xaBBg/DMM88gNDQUq1atQllZGcLCwjB48GCdq45EZHkMHjCePn0a/v7+2v1H954HBwdj7dq1uHDhAjZv3oy//voL7u7u8Pf3x/bt2yGTycSLmoiIiKieqywni4mJqfZ5QkJCkJ2djYSEhArrTJkyBUqlUrvftWtXAA8HqT4+PrCyssKPP/6IGTNmoH///nBwcEBgYCBWrFhh2IsiojrH4AGjQqGAIAgVHj9w4ECNAiIiIiKiqlWVk+mTnZ2tt0yhUFTarrLB5CMeHh744YcfDIqHiOo+kz/DSFSVAzdSzB0CERFRvVRQUIDMzEzExcWZOxSyYFZu+ie3rMpgqzFGtYsv22FUOzIOB4xERERE9ZRMJsO1a9fMHQYR1WEmX1aDiIiIiIiILJPBA8bExEQMHz4cHh4ekEgk2L17d7k6ly5dwogRIyCXyyGTydCrV68K1+AhIiIiIsNVJycLCQmBRCLR2Xr16mVwX7NmzUK3bt0glUrRpUuXcscjIyPL9SORSODg4GDEKyOiusTgAWNRURE6d+6M6OhovcczMzPRr18/tG3bFgkJCTh37hwWLFgAOzu7GgdLRERERA9VlZM9MnToUNy8eVO7/fTTTwb3JQgCQkNDMXbsWL3H33nnHZ0+bt68CT8/P4wZY9wzakRUdxj8DGNgYCACAwMrPD5v3jy88MIL+Pjjj7VlLVq0MC46IiIiItKrqpzsEalUCjc3txr1tXr1agBAfn4+zp8/X+54o0aN0KhRI+3+uXPncPHiRXz55Zc16peIzE/UZxjLysqwb98+tG7dGkOGDIGrqyt69uyp9xaJRzQaDdRqtc5GREREROJISEiAq6srWrdujalTpyIvL8/kff73v/9F69at8dxzz1VYhzkgkWUQdcCYl5eHwsJCLF26FEOHDsXBgwfx0ksvYdSoUTqLvT4uKioKcrlcu3l6eooZEhEREVG9FRgYiK1bt+Lw4cNYsWIFkpKSMHDgQGg0GpP1qdFosHXrVrz++uuV1mMOSGQZRF1Wo6ysDAAQFBSEOXPmAAC6dOmC48eP48svv8SAAQPKtYmIiEB4eLh2X61W8wODiIiISASPP3PYoUMHdO/eHd7e3ti3bx9GjRplkj537tyJgoICTJo0qdJ6zAGJLIOoA8amTZvCxsYGfn5+OuXt2rXDsWPH9LaRSqWQSqVihkFEREREeri7u8Pb2xuXLxu30Hp1/Pe//8WLL75Y5XOTzAGJLIOoA0ZbW1v06NEDaWlpOuXp6enw9vYWsysiIiIiMtDt27dx7do1uLu7m+T8WVlZOHLkCPbu3WuS8xNR7TN4wFhYWIiMjAztflZWFlJSUuDk5AQvLy/MnTsXY8eORf/+/eHv74/9+/fjxx9/REJCgphxExEREdVrVeVkhYWFiIyMxOjRo+Hu7o7s7Gy8//77aNq0KV566SWD+srIyEBhYSFyc3Nx//59pKSkAAD8/Pxga2urrbdx40a4u7tXa/ZWIrIMBg8YT58+DX9/f+3+o3vPg4ODERMTg5deeglffvkloqKiMHPmTLRp0wY//PAD+vXrJ17URERERPVcVTmZtbU1Lly4gM2bN+Ovv/6Cu7s7/P39sX37dshkMm27kJAQZGdnV/rH/SlTpuhMYNi1a1cADwepPj4+AB7OZRETE4OQkBBYW1uL+EqJyJwMHjAqFAoIglBpndDQUISGhhodFBERERFVrqqczN7eHgcOHKjyPNnZ2VAoFJXWqc6dYlZWVrh27VqV9YjIsoj6DCORMazcjHvwfrDVGIPbxJftMKovIiKiJ1FBQQEyMzMRFxdn7lCoHjpwI8XcIVA1cMBIREREVE/JZDJeFSSiSlmZOwAiIiIiIiKqmwweMCYmJmL48OHw8PCARCLB7t27dY5LJBK92yeffCJWzERERET1XlU52SOXLl3CiBEjIJfLIZPJ0KtXL+Tk5BjU16xZs9CtWzdIpVJ06dJFb50DBw6gV69ekMlkcHFxwejRo5GVlWXgqyKiusbgAWNRURE6d+6M6Ohovcdv3ryps23cuBESiQSjR4+ucbBERERE9FBVORkAZGZmol+/fmjbti0SEhJw7tw5LFiwAHZ2dgb1JQgCQkNDMXbsWL3Hr1y5gqCgIAwcOBApKSk4cOAAbt26hVGjRhnUDxHVPQY/wxgYGFjp2jpubm46+3v27IG/vz9atGhheHREREREpFdVORkAzJs3Dy+88AI+/vhjbZkxOdnq1asBAPn5+Th//ny542fOnEFpaSk++ugjWFk9vB7xzjvvICgoCCUlJWjQoIHBfRJR3WDSZxj//PNP7Nu3D6+//nqFdTQaDdRqtc5GRERERDVTVlaGffv2oXXr1hgyZAhcXV3Rs2fPCm9drYnu3bvD2toamzZtQmlpKVQqFb7++msEBARUOFhkDkhkGUw6YIyNjYVMJqv0doSoqCjI5XLt5unpacqQiIiIiOqFvLw8FBYWYunSpRg6dCgOHjyIl156CaNGjYJSqRS1Lx8fHxw8eBDvv/8+pFIpGjdujOvXr+Pbb7+tsA1zQCLLYNIB48aNG/Hqq69Wep98REQEVCqVduPUzkREREQ1V1ZWBgAICgrCnDlz0KVLF7z33nt48cUX8eWXX4raV25uLqZMmYLg4GAkJSVBqVTC1tYWL7/8MgRB0NuGOSCRZTDZOoxHjx5FWloatm/fXmk9qVQKqVRqqjCIiIiI6qWmTZvCxsYGfn5+OuXt2rXDsWPHRO3riy++gKOjo86zklu2bIGnpydOnTqFXr16lWvDHJDIMpjsCuOGDRvQrVs3dO7c2VRdEBEREVEFbG1t0aNHD6SlpemUp6enw9vbW9S+7t27B2tra52yR/uPrnQSkWUy+ApjYWEhMjIytPtZWVlISUmBk5MTvLy8AABqtRo7duzAihUrxIuUiIiIiLSqk5PNnTsXY8eORf/+/eHv74/9+/fjxx9/REJCgkF9ZWRkoLCwELm5ubh//z5SUlIAAH5+frC1tcWwYcPw6aefYtGiRRg/fjwKCgrw/vvvw9vbG127dhXrJRORGUiEim4sr0BCQgL8/f3LlQcHByMmJgYAsG7dOsyePRs3b96EXC43KCC1Wg25XA6VSgVHR0eD2lL9MthqjMFt4st2mCCS+ofvUyIi86tOTgY8nFMiKioK169fR5s2bfDhhx8iKChIezwkJATZ2dmVDiIVCoXeiXKysrLg4+MDAPj222/x8ccfIz09HQ0bNkTv3r2xbNkytG3btlqvh98t9U9Zbiuj2lm5XRY5kvrHkPebwQNGU+OHBVWXMR8y/IARB9+nRERPDoVCAYVCgcjISLPGwe8Wqi5jLhoAvHDwOEPebyab9IaIiIiI6raCggJkZmYiLi7O3KEQUR3FASMRERFRPSWTybicBRFVyqTrMBIREREREZHlMnjAmJiYiOHDh8PDwwMSiQS7d+/WOV5YWIjp06ejefPmsLe3R7t27bB27Vqx4iUiIiIiVJ2TAYBEItG7ffLJJwb1NWvWLHTr1g1SqRRdunTRW+e7775Dly5d0LBhQ3h7exvcBxHVTQYPGIuKitC5c2dER0frPT5nzhzs378fW7ZswaVLlzBnzhzMmDEDe/bsqXGwRERERPRQVTkZANy8eVNn27hxIyQSCUaPHm1QX4IgIDQ0FGPHjtV7/H//+x9effVVvPnmm/jtt9+wZs0arFy5stLYiMgyGPwMY2BgIAIDAys8fuLECQQHB0OhUAAA3njjDXz11Vc4ffq0zhTORERERGS8qnIyAHBzc9PZ37NnD/z9/dGiRQuD+lq9ejUAID8/H+fPny93/Ouvv8bIkSPx5ptvAgBatGiBd999F8uWLUNYWBgkEolB/RFR3SH6M4z9+vXD3r178ccff0AQBBw5cgTp6ekYMmSI3voajQZqtVpnIyIiIiJx/fnnn9i3bx9ef/110c+t0WhgZ2enU2Zvb4/r16/j6tWrFbZhDkhU94k+YFy9ejX8/PzQvHlz2NraYujQoVizZg369eunt35UVBTkcrl28/T0FDskIiIionovNjYWMpkMo0aNEv3cQ4YMwc6dO/Hzzz+jrKwM6enpWLVqFYCHt8XqwxyQyDKYZMB48uRJ7N27F8nJyVixYgXeeustHDp0SG/9iIgIqFQq7capnYmIiIjEt3HjRrz66qvlrgSKYerUqZg+fTpefPFF2NraolevXhg3bhwAwNraWm8b5oBElkHUdRjv37+P999/H7t27cKwYcMAAJ06dUJKSgqWL1+OQYMGlWsjlUohlUrFDIOIiIiIHnP06FGkpaVh+/btJjm/RCLBsmXLsGTJEuTm5sLFxQU///wzAMDHx0dvG+aARJZB1AFjSUkJSkpKYGWle+HS2toaZWVlYnZFRERERNW0YcMGdOvWDZ07dzZpP9bW1njqqacAAN988w169+4NV1dXk/ZJRKZl8ICxsLAQGRkZ2v2srCykpKTAyckJXl5eGDBgAObOnQt7e3t4e3tDqVRi8+bNWLlypaiBExEREdVnVeVkj6jVauzYsQMrVqwwuq+MjAwUFhYiNzcX9+/fR0pKCgDAz88Ptra2uHXrFr7//nsoFAr8/fff2LRpE3bs2AGlUml0n0RUNxg8YDx9+jT8/f21++Hh4QCA4OBgxMTE4Ntvv0VERAReffVV3LlzB97e3li8eLF2mmUiIiIiqrmqcrJHvv32WwiCgPHjx+s9T0hICLKzs5GQkFBhX1OmTNEZ/HXt2hXAw0Hqo1tOY2Nj8c4770AQBPTu3RsJCQl49tlnjXx1RFRXSARBEMwdxOPUajXkcjlUKhUcHR3NHQ49YQZbjTGqXXzZDpEjsWx8nxIRPTkUCgUUCgUiIyPNGge/W6i6ynJbGdXOyu2yyJFYLkPeb6I+w0hERERElqOgoACZmZmIi4szdyhEVEdxwEhERERUT8lkMi5nQUSVMngdxsTERAwfPhweHh6QSCTYvXu3zvE///wTISEh8PDwQMOGDTF06FBcvszLv0RERERiqionAx5OjDN9+nQ0b94c9vb2aNeuHdauXWtQP+fOncP48ePh6empPcdnn31Wrt6FCxcwYMAA2Nvb46mnnsKiRYtQx558IiIjGDxgLCoqQufOnREdHV3umCAIGDlyJK5cuYI9e/bg7Nmz8Pb2xqBBg1BUVCRKwERERERUeU72yJw5c7B//35s2bIFly5dwpw5czBjxgzs2bOn2v0kJyfDxcUFW7ZsQWpqKubNm4eIiAidftVqNQYPHgwPDw8kJSXh888/x/LlyzlLPtETwOBbUgMDAxEYGKj32OXLl3Hy5En89ttvaN++PQBgzZo1cHV1xTfffIMpU6bULFoiIiIiAlB5TvbIiRMnEBwcDIVCAQB444038NVXX+H06dMICgqqVj+hoaE6+y1atMCJEyewc+dOTJ8+HQCwdetW/P3334iJiYFUKkWHDh2Qnp6OlStXIjw8HBKJxPAXSER1gsFXGCuj0WgAAHZ2dtoya2tr2Nra4tixYxW2UavVOhsRERER1Vy/fv2wd+9e/PHHHxAEAUeOHEF6ejqGDBlSo/OqVCo4OTlp90+cOIEBAwZAKpVqy4YMGYIbN24gOztb7zmYAxJZBlEHjG3btoW3tzciIiJw9+5dFBcXY+nSpcjNzcXNmzf1tomKioJcLtdunp6eYoZEREREVG+tXr0afn5+aN68OWxtbTF06FCsWbMG/fr1M/qcJ06cwHfffYdp06Zpy3Jzc9GsWTOdeo/2c3Nz9Z6HOSCRZRB1wNigQQP88MMPSE9Ph5OTExo2bIiEhAQEBgbC2tpab5uIiAioVCrtxpm6iIiIiMSxevVqnDx5Env37kVycjJWrFiBt956C4cOHTLqfKmpqQgKCsLChQsxePBgnWP/vO300YQ3Fd2OyhyQyDKIvqxGt27dkJKSApVKheLiYri4uKBnz57o3r273vpSqVTn9gUiIiIiqrn79+/j/fffx65duzBs2DAAQKdOnZCSkoLly5dj0KBBBp3v4sWLGDhwIKZOnYr58+frHHNzcyt3JTEvLw8Ayl15fIQ5IJFlEPUK4+PkcjlcXFxw+fJlgx6sJiIiIqKaKykpQUlJCaysdNM9a2trlJWVGXSu1NRU+Pv7Izg4GIsXLy53vHfv3khMTERxcbG27ODBg/Dw8ICPj49R8RNR3WDwFcbCwkJkZGRo97OyspCSkgInJyd4eXlhx44dcHFxgZeXFy5cuIBZs2Zh5MiRCAgIEDVwIiIiovqsqpzM0dERAwYMwNy5c2Fvbw9vb28olUps3rzZoOUuHg0WAwICEB4err2SaG1tDRcXFwDAhAkT8OGHHyIkJATvv/8+Ll++jCVLlmDhwoWcIZXIwhk8YDx9+jT8/f21++Hh4QCA4OBgxMTE4ObNmwgPD8eff/4Jd3d3TJo0CQsWLBAvYiIiIiKqMicDgG+//RYRERF49dVXcefOHXh7e2Px4sV48803te1CQkKQnZ2NhIQEvf3s2LED+fn52Lp1K7Zu3aot9/b21s6AKpfLER8fj7CwMHTv3h1NmjRBeHi4NiYislwS4dETyXWEWq2GXC6HSqWCo6OjucOhJ8xgqzFGtYsv2yFyJJaN71MioieHQqGAQqFAZGSkWePgdwtVV1luK6PaWbldFjkSy2XI+030SW+I6rIDN1LMHQIREVGdUVBQgMzMTMTFxZk7FKJqM3bgxwsHxuGAkYiIiKiekslkXM6CiCplsllSiYiIiIiIyLIZNGCMiopCjx49IJPJ4OrqipEjRyItLU2njiAIiIyMhIeHB+zt7aFQKJCamipq0ERERET1XWJiIoYPHw4PDw9IJBLs3r27XJ0///wTISEh8PDwQMOGDTF06FBcvmzY7Xznzp3D+PHj4enpCXt7e7Rr1w6fffaZTp2///4bISEh6NixI2xsbDBy5MgavDIiqksMGjAqlUqEhYXh5MmTiI+Px4MHDxAQEICioiJtnY8//hgrV65EdHQ0kpKS4ObmhsGDB6OgoED04ImIiIjqq6KiInTu3BnR0dF6jwuCgJEjR+LKlSvYs2cPzp49C29vbwwaNEgnd6tKcnIyXFxcsGXLFqSmpmLevHmIiIjQ6be0tBT29vaYOXMmBg0aVOPXRkR1R41mSc3Pz4erqyuUSiX69+8PQRDg4eGB2bNn49133wUAaDQaNGvWDMuWLcO0adOqPCdnyCJT4qxa4uD7lIiobpFIJNi1a5fOlb309HS0adMGv/32G9q3bw/g4cDO1dUVy5Ytw5QpU4zuLywsDJcuXcLhw4fLHQsJCcFff/2l94pnZfjdQqbGSW/+jyHvtxo9w6hSqQAATk5OAB4uGJubm4uAgABtHalUigEDBuD48eN6z6HRaKBWq3U2IiIiIqoZjUYDALCzs9OWWVtbw9bWFseOHavRuVUqlTb/q0l8zAGJ6j6jB4yCICA8PBz9+vVDhw4dAAC5ubkAgGbNmunUbdasmfbYP0VFRUEul2s3T09PY0MiIiIiov+vbdu28Pb2RkREBO7evYvi4mIsXboUubm5uHnzptHnPXHiBL777rtq3TlWGeaARJbB6AHj9OnTcf78eXzzzTfljkkkEp19QRDKlT0SEREBlUql3Ti1MxEREVHNNWjQAD/88APS09Ph5OSEhg0bIiEhAYGBgbC2tjbqnKmpqQgKCsLChQsxePDgGsXHHJDIMhi1DuOMGTOwd+9eJCYmonnz5tpyNzc3AA+vNLq7u2vL8/Lyyl11fEQqlUIqlRoTBhERERFVolu3bkhJSYFKpUJxcTFcXFzQs2dPdO/e3eBzXbx4EQMHDsTUqVMxf/78GsfGHJDIMhh0hVEQBEyfPh07d+7E4cOH4evrq3Pc19cXbm5uiI+P15YVFxdDqVSiT58+4kRMRERERAaRy+VwcXHB5cuXcfr0aQQFBRnUPjU1Ff7+/ggODsbixYtNFCUR1UUGXWEMCwvDtm3bsGfPHshkMu1ziXK5HPb29pBIJJg9ezaWLFmCVq1aoVWrVliyZAkaNmyICRMmmOQFEBEREdVHhYWFyMjI0O5nZWUhJSUFTk5O8PLyAgDs2LEDLi4u8PLywoULFzBr1iyMHDlSZ4LCqjwaLAYEBCA8PFyb/1lbW8PFxUVb7+LFiyguLsadO3dQUFCAlJQUAECXLl1q/mKJyGwMGjCuXbsWAKBQKHTKN23ahJCQEADAv//9b9y/fx9vvfUW7t69i549e+LgwYOQyWSiBExEREREwOnTp+Hv76/dDw8PBwAEBwcjJiYGAHDz5k2Eh4fjzz//hLu7OyZNmoQFCxbonCckJATZ2dlISEjQ28+OHTuQn5+PrVu3YuvWrdpyb29vZGdna/dfeOEFXL16VbvftWtXAA/vUCMiy1WjdRhNgWvwkClxHUZx8H1KRPTkUCgUUCgUiIyMNGsc/G4hU+M6jP/HkPebUZPeEFkqYwd+/IAhIqInUUFBATIzMxEXF2fuUIhM7sCNFHOHYJE4YCQiIiKqp2QyGZezIKJKGb0OIxERERERET3ZDBowRkVFoUePHpDJZHB1dcXIkSORlpamU2fnzp0YMmQImjZtColEop0hi4iIiIjEU528TBAEREZGwsPDA/b29lAoFEhNTTWon3PnzmH8+PHw9PSEvb092rVrh88++0ynTkJCAoKCguDu7g4HBwd06dJFZ4IcIrJcBg0YlUolwsLCcPLkScTHx+PBgwcICAhAUVGRtk5RURH69u2LpUuXih4sERERET1Unbzs448/xsqVKxEdHY2kpCS4ublh8ODBKCgoqHY/ycnJcHFxwZYtW5Camop58+YhIiIC0dHR2jrHjx9Hp06d8MMPP+D8+fMIDQ3FpEmT8OOPP4r6momo9tVoltT8/Hy4urpCqVSif//+Oseys7Ph6+uLs2fPGrT+DmfIorqIk97o4vuUiKju+WdeJggCPDw8MHv2bLz77rsAAI1Gg2bNmmHZsmWYNm2a0X2FhYXh0qVLOHz4cIV1hg0bhmbNmmHjxo3VOie/W8jUOFv+/zHk/VajZxhVKhUAwMnJyehzaDQaqNVqnY2IiIiIDPPPvCwrKwu5ubkICAjQ1pFKpRgwYACOHz9e476qyv+qqsMckMgyGD1gFAQB4eHh6NevHzp06GB0AFFRUZDL5drN09PT6HMRERER1Uf68rLc3FwAQLNmzXTqNmvWTHvMGCdOnMB3331X6RXK77//HklJSZg8eXKFdZgDElkGoweM06dPx/nz5/HNN9/UKICIiAioVCrtxqmdiYiIiAxTWV4mkUh09gVBKFdWXampqQgKCsLChQsxePBgvXUSEhIQEhKC9evXo3379hWeizkgkWUwah3GGTNmYO/evUhMTETz5s1rFIBUKoVUKq3ROYiIiIjqq4ryMjc3NwAPrzS6u7try/Py8spddayOixcvYuDAgZg6dSrmz5+vt45SqcTw4cOxcuVKTJo0qdLzMQcksgwGXWEUBAHTp0/Hzp07cfjwYfj6+poqLiIiIiKqRFV5ma+vL9zc3BAfH68tKy4uhlKpRJ8+fQzqKzU1Ff7+/ggODsbixYv11klISMCwYcOwdOlSvPHGG4a/ICKqkwy6whgWFoZt27Zhz549kMlk2vvf5XI57O3tAQB37txBTk4Obty4AQDa9YDc3Ny0f+kiIiIiopqpKi+TSCSYPXs2lixZglatWqFVq1ZYsmQJGjZsiAkTJlS7n0eDxYCAAISHh2v7sba2houLC4D/GyzOmjULo0eP1taxtbWt0eSIRGR+Bi2rUdH97ps2bUJISAgAICYmRu8Dzh988AEiIyOr7INTKlNdxGU1dPF9SkRkftXJywRBwIcffoivvvoKd+/eRc+ePfHFF1/oTFgYEhKC7OxsJCQk6D1fZGQkPvzww3Ll3t7eyM7O1p4jNja2XJ0BAwZUeN5/4ncLmRqX1fg/hrzfarQOoynww4LqIn7A6OL7lIjoyaFQKKBQKKr1h31T4ncL1VVP4oUDQ95vRk16Q0RERESWr6CgAJmZmYiLizN3KERUR3HASERERFRPyWQyLmdBRJUyeh1GIiIiIiIierIZNGCMiopCjx49IJPJ4OrqipEjR2pnQQWAkpISvPvuu+jYsSMcHBzg4eGBSZMmaWdMJSIiIiJxVJWXAcDOnTsxZMgQNG3aFBKJBCkpKQb3c+7cOYwfPx6enp6wt7dHu3bt8Nlnn+nUSUtLg7+/P5o1awY7Ozu0aNEC8+fPR0lJSU1eIhHVAQYNGJVKJcLCwnDy5EnEx8fjwYMHCAgIQFFREQDg3r17OHPmDBYsWIAzZ85g586dSE9Px4gRI0wSPBEREVF9VVVeBgBFRUXo27cvli5danQ/ycnJcHFxwZYtW5Camop58+YhIiIC0dHR2joNGjTApEmTcPDgQaSlpWHVqlVYv349Pvjggxq9RiIyvxrNkpqfnw9XV1colUr0799fb52kpCQ8++yzuHr1Kry8vKo8J2fIorqIs6Tq4vuUiKjuqSwvy87Ohq+vL86ePYsuXbrUuK+wsDBcunQJhw8frrBOeHg4kpKScPTo0Wqdk98tVFdxltQaUKlUAFDpgqwqlQoSiQSNGzfWe1yj0UCj0Wj31Wp1TUIiIiIiqpeqk5eJ2Vdl/WRkZGD//v0YNWpUhXWYAxJZBqMnvREEAeHh4ejXr5/O4q+P+/vvv/Hee+9hwoQJFY5co6KiIJfLtZunp6exIRERERHVS9XJy8Ry4sQJfPfdd5g2bVq5Y3369IGdnR1atWqF5557DosWLarwPMwBiSyD0QPG6dOn4/z58/jmm2/0Hi8pKcG4ceNQVlaGNWvWVHieiIgIqFQq7capnYmIiIgMU1VeJpbU1FQEBQVh4cKFGDx4cLnj27dvx5kzZ7Bt2zbs27cPy5cvr/BczAGJLINRt6TOmDEDe/fuRWJiIpo3b17ueElJCV555RVkZWXh8OHDld4XK5VKIZVKjQmDiIiIqN6rKi8Ty8WLFzFw4EBMnToV8+fP11vn0VVCPz8/lJaW4o033sDbb78Na2vrcnWZAxJZBoMGjIIgYMaMGdi1axcSEhLg6+tbrs6jweLly5dx5MgRODs7ixYsERERET1UnbxMLKmpqRg4cCCCg4OxePHiasdXUlKCGsyvSER1gEEDxrCwMGzbtg179uyBTCZDbm4uAEAul8Pe3h4PHjzAyy+/jDNnziAuLg6lpaXaOk5OTrC1tRX/FRARERHVQ1XlZQBw584d5OTkaNfEfrROo5ubG9zc3KrVT2pqKvz9/REQEIDw8HBtP9bW1nBxcQEAbN26FQ0aNEDHjh0hlUqRnJyMiIgIjB07FjY2NZpjkYjMzKBlNSQSid7yTZs2ISQkRDtlsz5HjhyBQqGosg9OqUx1EZfV0MX3KRGR+VWVlwFATEwMJk+eXK7OBx98gMjISADQ5nAJCQl6zxcZGYkPP/ywXLm3tzeys7MBPHx28eOPP0Z6ejoEQYC3tzdee+01zJkzB3Z2dtV6Pfxuobqqvi+rUaN1GE2BHxb0JHlSB5p8nxIRPTkUCgUUCoV2AGku/G6huupJzOdqbR1GIiIiIrJcBQUFyMzMRFxcnLlDIaI6igNGIiIionpKJpNxOQsiqpRB6zBGRUWhR48ekMlkcHV1xciRI7UPTz8SGRmJtm3bwsHBAU2aNMGgQYNw6tQpUYMmIiIiqu+qystKSkrw7rvvomPHjnBwcICHhwcmTZqknQCnus6dO4fx48fD09MT9vb2aNeuHT777DOdOmlpafD390ezZs1gZ2eHFi1aYP78+SgpKRHltRKR+Rg0YFQqlQgLC8PJkycRHx+PBw8eICAgAEVFRdo6rVu3RnR0NC5cuIBjx47Bx8cHAQEByM/PFz14IiIiovqqqrzs3r17OHPmDBYsWIAzZ85g586dSE9Px4gRIwzqJzk5GS4uLtiyZQtSU1Mxb948REREIDo6WlunQYMGmDRpEg4ePIi0tDSsWrUK69evxwcffCDqayai2lejSW/y8/Ph6uoKpVKJ/v37663z6IHKQ4cO4fnnn6/ynHzgmZ4kT+JD0gDfp0REdVF18rKkpCQ8++yzuHr1Kry8vIzuKywsDJcuXcLhw4crrBMeHo6kpCQcPXq0WufkdwvVVU9iPldrk96oVCoAD9dY1Ke4uBjr1q2DXC5H586d9dbRaDTQaDTafbVaXZOQiIiIiOqlqvKyR3UkEgkaN25c474q6ycjIwP79+/HqFGjKqzDHJDIMhh0S+rjBEFAeHg4+vXrhw4dOugci4uLQ6NGjWBnZ4dPP/0U8fHxaNq0qd7zREVFQS6XazdPT09jQyIiIiKqlyrLyx75+++/8d5772HChAk1uoJ34sQJfPfdd5g2bVq5Y3369IGdnR1atWqF5557DosWLarwPMwBiSyD0QPG6dOn4/z58/jmm2/KHfP390dKSgqOHz+OoUOH4pVXXkFeXp7e80REREClUmk3ztRFREREZJjK8jLg4QQ448aNQ1lZGdasWWN0P6mpqQgKCsLChQsxePDgcse3b9+OM2fOYNu2bdi3bx+WL19e4bmYAxJZBqNuSZ0xYwb27t2LxMRENG/evNxxBwcHtGzZEi1btkSvXr3QqlUrbNiwAREREeXqSqVSSKVSY8IgIiIiqveqystKSkrwyiuvICsrC4cPHzb66uLFixcxcOBATJ06FfPnz9db59FVQj8/P5SWluKNN97A22+/DWtr63J1mQMSWQaDBoyCIGDGjBnYtWsXEhIS4OvrW+12j9+jTkREREQ1U5287NFg8fLlyzhy5AicnZ2N6is1NRUDBw5EcHAwFi9eXO34SkpKUIP5FYmoDjBowBgWFoZt27Zhz549kMlkyM3NBQDI5XLY29ujqKgIixcvxogRI+Du7o7bt29jzZo1uH79OsaMGWOSF0BERERUH1WVlz148AAvv/wyzpw5g7i4OJSWlmrrODk5wdbWtlr9pKamwt/fHwEBAQgPD9eew9raGi4uLgCArVu3okGDBujYsSOkUimSk5MRERGBsWPHwsamRnMsEpGZGfQOXrt2LQBAoVDolG/atAkhISGwtrbG77//jtjYWNy6dQvOzs7o0aMHjh49ivbt24sWNBEREVF9V1Vedv36dezduxcA0KVLF506R44c0bYLCQlBdnY2EhIS9PazY8cO5OfnY+vWrdi6dau23NvbG9nZ2QAAGxsbLFu2DOnp6RAEAd7e3ggLC8OcOXNq/DqJyLxqtA6jKXANHnqSPInr9gB8nxIRPUkUCgUUCgUiIyPNGge/W6iuehLzuVpbh5GIKmfsB4UxH0x1+UOJiIjqpoKCAmRmZiIuLs7coRDVWfU9n+OAkYiIiKiekslkXM6CiCpl9DqMRERERERE9GQzaMAYFRWFHj16QCaTwdXVFSNHjkRaWlqF9adNmwaJRIJVq1bVNE4iIiIiekx18rLIyEi0bdsWDg4OaNKkCQYNGoRTp04Z1M+5c+cwfvx4eHp6wt7eHu3atcNnn31WYf2MjAzIZDI0btzYmJdFRHWMQQNGpVKJsLAwnDx5EvHx8Xjw4AECAgJQVFRUru7u3btx6tQpeHh4iBYsERERET1UnbysdevWiI6OxoULF3Ds2DH4+PggICAA+fn51e4nOTkZLi4u2LJlC1JTUzFv3jxEREQgOjq6XN2SkhKMHz8ezz33nCivkYjMr0azpObn58PV1RVKpRL9+/fXlv/xxx/o2bMnDhw4gGHDhmH27NmYPXt2tc7JGbKI6v5D0nyfEhHVPRXlZY979Pl96NAhPP/880b3FRYWhkuXLuHw4cM65e+++y5u3LiB559/HrNnz8Zff/1V7XPyu4WeNHU5n6u1WVJVKhWAh4u/PlJWVoaJEydi7ty51Vp7UaPRQKPRaPfVanVNQiIiIiKql/TlZY8rLi7GunXrIJfL0blz5xr39c9+Dh8+jB07diAlJQU7d+6s8hzMAYksg9GT3giCgPDwcPTr1w8dOnTQli9btgw2NjaYOXNmtc4TFRUFuVyu3Tw9PY0NiYiIiKheqigvA4C4uDg0atQIdnZ2+PTTTxEfH4+mTZsa3deJEyfw3XffYdq0adqy27dvIyQkBDExMdW+OsgckMgyGD1gnD59Os6fP49vvvlGW5acnIzPPvsMMTExkEgk1TpPREQEVCqVduPUzkRERESG0ZeXPeLv74+UlBQcP34cQ4cOxSuvvIK8vDyj+klNTUVQUBAWLlyIwYMHa8unTp2KCRMmVHgrrD7MAYksg1HPMM6YMQO7d+9GYmIifH19teWrVq1CeHg4rKz+bxxaWloKKysreHp6Ijs7u8pz8/51orp9zzvA9ykRUV1SUV5WkVatWiE0NBQREREG9XPx4kX4+/tjypQpWLx4sc6xxo0bo7CwULsvCALKyspgbW2NdevWITQ0tMrz87uFnjR1OZ8z2TOMgiBgxowZ2LVrFxISEsp9KE2cOBGDBg3SKRsyZAgmTpyIyZMnG9IVEREREVWiqryssnaPPztYHampqRg4cCCCg4PLDRaBh7eplpaWavf37NmDZcuW4fjx43jqqacM6ouI6haDBoxhYWHYtm0b9uzZA5lMhtzcXACAXC6Hvb09nJ2d4ezsrNOmQYMGcHNzQ5s2bcSLmoiIiKieqyovKyoqwuLFizFixAi4u7vj9u3bWLNmDa5fv44xY8ZUu5/U1FT4+/sjICAA4eHh2n6sra3h4uICAGjXrp1Om9OnT8PKyqrc85REZHkMeoZx7dq1UKlUUCgUcHd3127bt283VXxEREREpEdVeZm1tTV+//13jB49Gq1bt8aLL76I/Px8HD16VGcm+5CQECgUigr72bFjB/Lz87F161adfnr06GHql0hEdUCN1mE0Bd6/TlS373kH+D4lInqSKBQKKBQKREZGmjUOfrfQk6Yu53O1tg4jEZmGMR8WxnwoGdsXERE9GQoKCpCZmYm4uDhzh0L0xHlS8jkOGImIiIjqKZlMxuUsiKhSRq/DSERERERERE82gwaMUVFR6NGjB2QyGVxdXTFy5EikpaXp1AkJCYFEItHZevXqJWrQRERERPVddfKyx02bNg0SiQSrVq0yqJ9z585h/Pjx8PT0hL29Pdq1a4fPPvtMp052dna5/E8ikWD//v3GvDQiqkMMuiVVqVQiLCwMPXr0wIMHDzBv3jwEBATg4sWLcHBw0NYbOnQoNm3apN23tbUVL2IiIiIiqnZeBgC7d+/GqVOn4OHhYXA/ycnJcHFxwZYtW+Dp6Ynjx4/jjTfegLW1NaZPn65T99ChQzozsDo5ORn34oiozjBowPjPvxJt2rQJrq6uSE5ORv/+/bXlUqkUbm5u4kRIREREROVUNy/7448/MH36dBw4cADDhg0zuJ/Q0FCd/RYtWuDEiRPYuXNnuQGjs7Mzc0CiJ0yNnmFUqVQAyv/1KCEhAa6urmjdujWmTp2KvLy8Cs+h0WigVqt1NiIiIiIyjL68rKysDBMnTsTcuXN1rvyJ0Ze+q4cjRoyAq6sr+vbti++//77SczAHJLIMRg8YBUFAeHg4+vXrhw4dOmjLAwMDsXXrVhw+fBgrVqxAUlISBg4cCI1Go/c8UVFRkMvl2s3T09PYkIiIiIjqpYrysmXLlsHGxgYzZ84Ura8TJ07gu+++w7Rp07RljRo1wsqVK/H999/jp59+wvPPP4+xY8diy5YtFZ6HOSCRZZAIgiAY0zAsLAz79u3DsWPH0Lx58wrr3bx5E97e3vj2228xatSocsc1Go3OYFKtVsPT05OLthIZqDbX7eHiykREdYu+vCw5ORnDhg3DmTNntM8u+vj4YPbs2Zg9e7ZR/aSmpsLf3x8zZ87E/PnzK607Y8YMKJVKnD9/Xu9x5oBE5dVWPmdILmfUFcYZM2Zg7969OHLkSKWDRQBwd3eHt7c3Ll/W/yKkUikcHR11NiIiIiKqnorysqNHjyIvLw9eXl6wsbGBjY0Nrl69irfffhs+Pj4G93Px4kUMHDgQU6dOrXKwCAC9evWqMP8DmAMSWQqDJr0RBAEzZszArl27kJCQAF9f3yrb3L59G9euXYO7u7vRQRIRERGRrqrysokTJ2LQoEE6ZUOGDMHEiRMxefJkg/pKTU3FwIEDERwcjMWLF1erzdmzZ5n/ET0BDBowhoWFYdu2bdizZw9kMhlyc3MBAHK5HPb29igsLERkZCRGjx4Nd3d3ZGdn4/3330fTpk3x0ksvmeQFEBEREdVHVeVlzs7OcHZ21mnToEEDuLm5oU2bNtXu59FtqAEBAQgPD9f2Y21tDRcXFwBAbGwsGjRogK5du8LKygo//vgjVq9ejWXLlon0aonIXAwaMK5duxYAoFAodMo3bdqEkJAQWFtb48KFC9i8eTP++usvuLu7w9/fH9u3b4dMJhMtaCIiIqL6rqq8rLpCQkKQnZ2NhIQEvcd37NiB/Px8bN26FVu3btWWe3t7Izs7W7v/0Ucf4erVq7C2tkbr1q2xceNGvPbaa9WOg4jqJqMnvTEVTqZBVLuMebhaXVCGJq2v8H1KRPQEUCgUUCgUiIyMNGsczAGJjGdoPmdILmfQFUYiIiIienIUFBQgMzMTcXFx5g6FiOooDhiJiIiI6imZTIZr166ZOwwiqsOMWlaDiIiIiIiInnwGDRijoqLQo0cPyGQyuLq6YuTIkUhLSytX79KlSxgxYgTkcjlkMhl69eqFnJwc0YImIiIiqu+qk5eFhIRAIpHobL169TKon3PnzmH8+PHw9PSEvb092rVrh88++6xcPUEQsHz5crRu3RpSqRSenp5YsmRJjV4jEZmfQbekKpVKhIWFoUePHnjw4AHmzZuHgIAAXLx4EQ4ODgCAzMxM9OvXD6+//jo+/PBDyOVyXLp0CXZ2diZ5AURERET1UXXyMgAYOnQoNm3apN23tbU1qJ/k5GS4uLhgy5Yt8PT0xPHjx/HGG2/A2toa06dP19abNWsWDh48iOXLl6Njx45QqVS4detWzV8oEZlVjWZJzc/Ph6urK5RKJfr37w8AGDduHBo0aICvv/7aqHNyhiyi2sVZUomIngz68rKQkBD89ddf2L17t6h9hYWF4dKlSzh8+DCAh3eXderUCb/99ptBazw+jjkgkfFMOUtqjZ5hVKlUAAAnJycAQFlZGfbt24fWrVtjyJAhcHV1Rc+ePSv9kNJoNFCr1TobERERERnmn3nZIwkJCXB1dUXr1q0xdepU5OXlidLX4/38+OOPaNGiBeLi4uDr6wsfHx9MmTIFd+7cqfAczAGJLIPRA0ZBEBAeHo5+/fqhQ4cOAIC8vDwUFhZi6dKlGDp0KA4ePIiXXnoJo0aNglKp1HueqKgoyOVy7ebp6WlsSERERET1kr68DAACAwOxdetWHD58GCtWrEBSUhIGDhwIjUZjdF8nTpzAd999h2nTpmnLrly5gqtXr2LHjh3YvHkzYmJikJycjJdffrnC8zAHJLIMRt+SGhYWhn379uHYsWNo3rw5AODGjRt46qmnMH78eGzbtk1bd8SIEXBwcMA333xT7jwajUbnQ0utVsPT05O3IxDVEt6SSkRk+fTlZfrcvHkT3t7e+PbbbzFq1CiD+0lNTYW/vz9mzpyJ+fPna8vfeOMNrF+/HmlpaWjdujUA4MyZM+jWrRt+//13vbepMgckEo8pb0k1ah3GGTNmYO/evUhMTNT5UGratClsbGzg5+enU79du3Y4duyY3nNJpVJIpVJjwiAiIiKq9yrKy/Rxd3eHt7c3Ll++bHA/Fy9exMCBAzF16lSdweKj89rY2GgHi8DD/A8AcnJy9A4YmQMSWQaDbkkVBAHTp0/Hzp07cfjwYfj6+uoct7W1RY8ePcpN6Zyeng5vb++aR0tEREREAKrOy/S5ffs2rl27Bnd3d4P6enRlMTg4GIsXLy53vG/fvnjw4AEyMzO1Zenp6QDAHJDIwhl0hTEsLAzbtm3Dnj17/l97dxMSVfvGcfynViZymgiVrETamEpRFFILk1HSisJXwtyoFNFiMEJy0RuNizCKoCgowowoNZOofAEpKjXBNi0kTAokyVDLTTq2GIjxWfxp+Ps0Y87RdM7j9wNnMc59nfuaxXGua+7zIsMwNDIyIkmy2WyKiIiQJFVUVKiwsFBpaWlKT09XW1ubmpub1d7ePufJAwAALFZ/qssmJibkdDpVUFCg2NhYDQwM6NSpU4qKilJeXt6M5/nVLGZlZam8vNw7T1hYmKKjoyVJu3bt0tatW3Xo0CFduXJFHo9HDodDmZmZU1YdAVhPQCuMN27c0NjYmOx2u2JjY71bQ0ODd0xeXp5u3rypixcvatOmTaqurtajR4+Umpo658kDAAAsVn+qy8LCwvTu3Tvl5OQoISFBJSUlSkhIUHd3twzD8O6ntLRUdrvd7zyNjY0aHR1VbW3tlHlSUlK8Y0JDQ9Xc3KyoqCilpaVp3759SkpK0oMHD/7a5wcwP2b1HMa/gWfwAMGP4xQA/jvsdrvsdrucTueC5sF3CzB/AjneTN30BgAAANbncrnU39+vlpaWhU4FQJCiYQQAAFikDMPQ4ODgQqcBIIgFdA1jVVWVUlJSZBiGYmJilJub+9sdUUNCQnxuly5dmtPEAQAAFrOZ1GWS1NfXp+zsbNlsNhmGoR07dujz588znqenp0dFRUWKi4tTRESEkpKSdPXq1SljnE6nz/ovMjJy1p8TwMIKqGHs6OiQw+HQmzdv9Pz5c/38+VNZWVn68eOHd8zw8PCUraamRiEhISooKJjz5AEAABarmdRl/f39Sk1NVWJiotrb29XT06OzZ89q+fLlM57n7du3io6O1v3799Xb26vTp0/r5MmTun79unfMiRMnfqsBk5OTdeDAgTn9zADm36xuejM6OqqYmBh1dHQoLS3N55jc3Fy5XC69ePFiRvvkgmcg+HGcAkDw8VWXHTx4UEuXLtW9e/fmdC6Hw6G+vj69fPnS5/s9PT3asmWLOjs7tXPnzhntk+8WYP4EcrwFtML4b2NjY5KkVatW+Xz/69evam1t1eHDh/3uw+12a3x8fMoGAACAwPy7LvN4PGptbVVCQoJ2796tmJgYbd++XU+ePJmTufzVf5JUXV2thISEaZtFakDAGkw3jJOTkyovL1dqaqo2btzoc8zdu3dlGIby8/P97qeqqko2m827xcXFmU0JAABgUfJVl3379k0TExO6cOGC9uzZo2fPnikvL0/5+fnq6OgwPVd3d7cePnyoo0eP+nzf7XartrZ22gUDiRoQsArTp6Q6HA61traqq6tL69at8zkmMTFRmZmZunbtmt/9uN1uud1u7+vx8XHFxcVxOgIQxDhtCACCi6+6bGhoSGvXrlVRUZHq6uq8Y7OzsxUZGan6+vqA5+nt7VV6erqOHTumM2fO+BxTX1+v4uJiDQ4OavXq1X73RQ0ILJy//hzGsrIyNTU1qbOz02+z+Pr1a3348EENDQ3T7is8PFzh4eFm0gAAAFj0/NVlUVFRWrJkiZKTk6eMT0pKUldXV8DzvH//XhkZGTpy5IjfZlH63+mo+/fvn7ZZlKgBAasIqGGcnJxUWVmZHj9+rPb2dq1fv97v2Nu3b2vbtm3avHnzrJMEAADAVH+qy5YtW6aUlJTfHrXx8eNHxcfHBzRXb2+vMjIyVFJSovPnz/sd9+nTJ7169UpNTU0B7R9A8AqoYXQ4HKqrq9PTp09lGIZGRkYkSTabTREREd5x4+Pjamxs1OXLl+c2WwAAAEiaWV1WUVGhwsJCpaWlKT09XW1tbWpublZ7e/uM5/l1GmpWVpbKy8u984SFhSk6OnrK2JqaGsXGxmrv3r1z8yEBLLiArmEMCQnx+fc7d+6otLTU+/rWrVs6fvy4hoeHZbPZAkqIa6OA4MdxCgALb6Z1WU1NjaqqqvTlyxdt2LBBlZWVysnJ8b5fWlqqgYEBv02k0+lUZWXlb3+Pj4/XwMCA97XH41F8fLyKi4unXYX0h+8WYP4EcrzN6jmMf8PY2JhWrlypwcFB/lkAQerXjQm+f/8e8I9CAIDgYrfbZbfb5XQ6FzQPakBg/gRSy5m66c3f5HK5JIlbKwMW4HK5aBgBwMJcLpf6+/vV0tKy0KlQAwILYCa1XNCtMHo8Hg0NDckwjN9OtfjVCQf6y5MV4qyQo9k4K+RoNs4KOZqNmy5mcnJSLpdLa9asUWio6ce5AgDgRQ0YvDmajbNCjmbjrJDjdHGB1HJBt8IYGhrq91Edv6xYscLUqQpWiLNCjmbjrJCj2Tgr5Gg2zl8MK4sAgLlEDRj8OZqNs0KOZuOskKO/uJnWciwNAAAAAAB8omEEAAAAAPhkqYYxPDxc586dU3h4+H8uzgo5mo2zQo5m46yQo9k4s3MBADDXrPC9aTbOCjmajbNCjmbjrJDjbOL+X9Dd9AYAAAAAEBwstcIIAAAAAJg/NIwAAAAAAJ9oGAEAAAAAPtEwAgAAAAB8omEEAAAAAPhEwwgAAAAA8ImGEQAAAADgEw0jAAAAAMCnfwAmcWP4geXn6gAAAABJRU5ErkJggg==", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "phi_dict = {'0': {'V': maps['Phi_0_V'], 'E': maps['Phi_0_E']}, 'n': {'V': maps['Phi_n_V'], 'E': maps['Phi_n_E']}}\n", - "psi_dict = {'0': {'V': maps['Psi_0_V'], 'E': maps['Psi_0_E']}, 'n': {'V': maps['Psi_n_V'], 'E': maps['Psi_n_E']}}\n", - "\n", - "newInt.set_interleaving_maps(phi_dict, psi_dict)\n", - "\n", - "# plot psi vertex and edge maps as subplots\n", - "\n", - "fig, axs = plt.subplots(1,2, figsize=(15,5))\n", - "\n", - "newInt.psi('0', 'V').draw(ax = axs[0],filltype='nan')\n", - "newInt.psi('0', 'E').draw(ax = axs[1],filltype='nan')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### compute the loss for the whole matrices" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 4.0, 0.0]\n" - ] - }, - { - "data": { - "text/plain": [ - "4.0" - ] - }, - "execution_count": 12, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "newInt.loss(verbose=True)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We see that the loss is 4 for the triangles F-G-F (vertex and edge). These are the torus-line-torus maps\n", - "\n", - "### Now compute loss by block to see how that is changing" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[0.0, 0.0, 0.0, 0.0, 1.0, 2.0, 3.0, 4.0, 4.0, 3.0, 2.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0]\n" - ] - }, - { - "data": { - "text/plain": [ - "4.0" - ] - }, - "execution_count": 13, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "newInt.loss_by_block(verbose=True)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "See that the loss increases inside the loop of the torus and it is maximum at the middle of the loop\n", - "\n", - "### Let's check how the triangle loss looks like in terms of matrix multiplication" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "trianlge_loss_vertex = newInt.triangle(start_graph='F', obj_type='V', draw=True, returntype='dist', func_val=8)\n", - "# max value is at 8 for vertex" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "taingle_loss_edge = newInt.triangle(start_graph='F', obj_type='E', draw=True, returntype='dist', func_val=8)\n", - "# max value is at 7 or 8 for edge" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### The individual matrices are computed correctly.Then? \n", - "\n", - "Interleaving distance is 3. Hence the Loss should have been 2. But it is double. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Relationship between the thickening parameter and the optimized loss function/upper bound" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": {}, - "outputs": [ - { - "ename": "NameError", - "evalue": "name 'solver_iter' is not defined", - "output_type": "error", - "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", - "Cell \u001b[0;32mIn[16], line 7\u001b[0m\n\u001b[1;32m 4\u001b[0m d \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m32\u001b[39m\n\u001b[1;32m 6\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(\u001b[38;5;241m1\u001b[39m, \u001b[38;5;241m10\u001b[39m):\n\u001b[0;32m----> 7\u001b[0m losses_dict[\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mlosses_\u001b[39m\u001b[38;5;132;01m{\u001b[39;00mi\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m\"\u001b[39m] \u001b[38;5;241m=\u001b[39m \u001b[43msolver_iter\u001b[49m\u001b[38;5;241m.\u001b[39mrun_optimization_torus_line(a, b, c, d, i, \u001b[38;5;241m1\u001b[39m)\n\u001b[1;32m 9\u001b[0m \u001b[38;5;66;03m# Save to a text file\u001b[39;00m\n\u001b[1;32m 10\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m \u001b[38;5;28mopen\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mlt_losses_0_2_30_32_1.txt\u001b[39m\u001b[38;5;124m\"\u001b[39m, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mw\u001b[39m\u001b[38;5;124m\"\u001b[39m) \u001b[38;5;28;01mas\u001b[39;00m file:\n", - "\u001b[0;31mNameError\u001b[0m: name 'solver_iter' is not defined" - ] - } - ], - "source": [ - "a = 0\n", - "b = 2\n", - "c = 30 # loop size is 28\n", - "d = 32\n", - "\n", - "for i in range(1, 10):\n", - " losses_dict[f\"losses_{i}\"] = solver_iter.run_optimization_torus_line(a, b, c, d, i, 1)\n", - "\n", - "# Save to a text file\n", - "with open(\"lt_losses_0_2_30_32_1.txt\", \"w\") as file:\n", - " for key, value in losses_dict.items():\n", - " file.write(f\"{key}: {value}\\n\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Plot the results\n", - "\n", - "\n", - "plt.figure(figsize=(20, 5))\n", - "plt.subplot(121)\n", - "\n", - "plt.plot(range(1, 10), [losses_dict[f\"losses_{i}\"][0][0] for i in range(1, 10)], label=\"loss before optimization\")\n", - "plt.plot(range(1, 10), [losses_dict[f\"losses_{i}\"][0][0]+i for i in range(1, 10)], label=\"upper bound before optimization\")\n", - "\n", - "plt.axhline(y = 7, color = 'k', linestyle = '-')\n", - "plt.xlabel(\"thickening parameter n\")\n", - "plt.ylabel(\"value\")\n", - "plt.legend()\n", - "plt.title(\"Losses and upper bounds for different thickening parameters before optimization\")\n", - "plt.subplot(122)\n", - "plt.plot(range(1, 10), [losses_dict[f\"losses_{i}\"][1][0] for i in range(1, 10)], label=\"loss\")\n", - "plt.plot(range(1, 10), [losses_dict[f\"losses_{i}\"][1][0]+i for i in range(1, 10)], label=\"upper bound\")\n", - "plt.axhline(y = 7, color = 'k', linestyle = '-')\n", - "plt.xlabel(\"thickening parameter n\")\n", - "plt.ylabel(\"value\")\n", - "plt.legend()\n", - "plt.title(\"Losses and upper bounds for different thickening parameters after optimization\")\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# How does the loss change with change of loop size?" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [ - { - "ename": "KeyboardInterrupt", - "evalue": "", - "output_type": "error", - "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)", - "File \u001b[0;32m~/anaconda3/envs/interleavingenv/lib/python3.12/site-packages/networkx/drawing/layout.py:480\u001b[0m, in \u001b[0;36mspring_layout\u001b[0;34m(G, k, pos, fixed, iterations, threshold, weight, scale, center, dim, seed)\u001b[0m\n\u001b[1;32m 479\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mlen\u001b[39m(G) \u001b[38;5;241m<\u001b[39m \u001b[38;5;241m500\u001b[39m: \u001b[38;5;66;03m# sparse solver for large graphs\u001b[39;00m\n\u001b[0;32m--> 480\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m\n\u001b[1;32m 481\u001b[0m A \u001b[38;5;241m=\u001b[39m nx\u001b[38;5;241m.\u001b[39mto_scipy_sparse_array(G, weight\u001b[38;5;241m=\u001b[39mweight, dtype\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n", - "\u001b[0;31mValueError\u001b[0m: ", - "\nDuring handling of the above exception, another exception occurred:\n", - "\u001b[0;31mKeyboardInterrupt\u001b[0m Traceback (most recent call last)", - "Cell \u001b[0;32mIn[9], line 8\u001b[0m\n\u001b[1;32m 6\u001b[0m c \u001b[38;5;241m=\u001b[39m i\n\u001b[1;32m 7\u001b[0m d \u001b[38;5;241m=\u001b[39m i\u001b[38;5;241m+\u001b[39m\u001b[38;5;241m2\u001b[39m\n\u001b[0;32m----> 8\u001b[0m losses_dict[\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mlosses_\u001b[39m\u001b[38;5;132;01m{\u001b[39;00mi\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m\"\u001b[39m] \u001b[38;5;241m=\u001b[39m \u001b[43msolver_iter\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun_optimization_torus_line\u001b[49m\u001b[43m(\u001b[49m\u001b[43ma\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mb\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mc\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43md\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mn\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m 10\u001b[0m \u001b[38;5;66;03m# Save to a text file\u001b[39;00m\n\u001b[1;32m 11\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m \u001b[38;5;28mopen\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mlt_losses_0_2_x_x+2_1.txt\u001b[39m\u001b[38;5;124m\"\u001b[39m, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mw\u001b[39m\u001b[38;5;124m\"\u001b[39m) \u001b[38;5;28;01mas\u001b[39;00m file:\n", - "File \u001b[0;32m~/Library/CloudStorage/OneDrive-MichiganStateUniversity/Documents/Research/Projects/Interleaving_to_ML/ceREEBerus/cereeberus/cereeberus/distance/ilp_solver_iterations.py:41\u001b[0m, in \u001b[0;36mrun_optimization_torus_line\u001b[0;34m(a, b, c, d, n, num_iter)\u001b[0m\n\u001b[1;32m 38\u001b[0m M2 \u001b[38;5;241m=\u001b[39m ex_mg\u001b[38;5;241m.\u001b[39mtorus(a,b,c,d, seed\u001b[38;5;241m=\u001b[39mloop_seed)\n\u001b[1;32m 40\u001b[0m \u001b[38;5;66;03m# generate an interleaving of the two mapper graphs\u001b[39;00m\n\u001b[0;32m---> 41\u001b[0m myInt \u001b[38;5;241m=\u001b[39m \u001b[43mInterleave\u001b[49m\u001b[43m(\u001b[49m\u001b[43mM1\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mM2\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mn\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43m \u001b[49m\u001b[43mn\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43minitialize_random_maps\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43;01mTrue\u001b[39;49;00m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mseed\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43m \u001b[49m\u001b[43mloop_seed\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 43\u001b[0m \u001b[38;5;66;03m# calculate the loss before optimization\u001b[39;00m\n\u001b[1;32m 44\u001b[0m loss_before \u001b[38;5;241m=\u001b[39m myInt\u001b[38;5;241m.\u001b[39mloss()\n", - "File \u001b[0;32m~/Library/CloudStorage/OneDrive-MichiganStateUniversity/Documents/Research/Projects/Interleaving_to_ML/ceREEBerus/cereeberus/cereeberus/distance/interleave.py:190\u001b[0m, in \u001b[0;36mInterleave.__init__\u001b[0;34m(self, F, G, n, initialize_random_maps, seed)\u001b[0m\n\u001b[1;32m 188\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(\u001b[38;5;28mlen\u001b[39m(vert_set)):\n\u001b[1;32m 189\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m j \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(i\u001b[38;5;241m+\u001b[39m\u001b[38;5;241m1\u001b[39m, \u001b[38;5;28mlen\u001b[39m(vert_set)):\n\u001b[0;32m--> 190\u001b[0m D_i[i, j] \u001b[38;5;241m=\u001b[39m \u001b[43mM\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mthickening_distance\u001b[49m\u001b[43m(\u001b[49m\u001b[43mvert_set\u001b[49m\u001b[43m[\u001b[49m\u001b[43mi\u001b[49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mvert_set\u001b[49m\u001b[43m[\u001b[49m\u001b[43mj\u001b[49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 191\u001b[0m D_i[j, i] \u001b[38;5;241m=\u001b[39m D_i[i, j]\n\u001b[1;32m 192\u001b[0m block_D[f_i] \u001b[38;5;241m=\u001b[39m LM( rows \u001b[38;5;241m=\u001b[39m vert_set, cols \u001b[38;5;241m=\u001b[39m vert_set,array \u001b[38;5;241m=\u001b[39m D_i)\n", - "File \u001b[0;32m~/Library/CloudStorage/OneDrive-MichiganStateUniversity/Documents/Research/Projects/Interleaving_to_ML/ceREEBerus/cereeberus/cereeberus/reeb/reebgraph.py:235\u001b[0m, in \u001b[0;36mReebGraph.thickening_distance\u001b[0;34m(self, u, v)\u001b[0m\n\u001b[1;32m 233\u001b[0m \u001b[38;5;66;03m# For each difference, build the slice and see if the two vertices are in the same connected component\u001b[39;00m\n\u001b[1;32m 234\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m n \u001b[38;5;129;01min\u001b[39;00m diff:\n\u001b[0;32m--> 235\u001b[0m S \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mslice\u001b[49m\u001b[43m(\u001b[49m\u001b[43ma\u001b[49m\u001b[38;5;241;43m-\u001b[39;49m\u001b[43mn\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43ma\u001b[49m\u001b[38;5;241;43m+\u001b[39;49m\u001b[43mn\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mtype\u001b[39;49m\u001b[43m \u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mclosed\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m 236\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[1;32m 237\u001b[0m nx\u001b[38;5;241m.\u001b[39mshortest_path(S\u001b[38;5;241m.\u001b[39mto_undirected(), u, v)\n", - "File \u001b[0;32m~/Library/CloudStorage/OneDrive-MichiganStateUniversity/Documents/Research/Projects/Interleaving_to_ML/ceREEBerus/cereeberus/cereeberus/reeb/reebgraph.py:589\u001b[0m, in \u001b[0;36mReebGraph.slice\u001b[0;34m(self, a, b, type, verbose)\u001b[0m\n\u001b[1;32m 586\u001b[0m H \u001b[38;5;241m=\u001b[39m ReebGraph()\n\u001b[1;32m 588\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m v \u001b[38;5;129;01min\u001b[39;00m v_list:\n\u001b[0;32m--> 589\u001b[0m \u001b[43mH\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43madd_node\u001b[49m\u001b[43m(\u001b[49m\u001b[43mv\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mf\u001b[49m\u001b[43m[\u001b[49m\u001b[43mv\u001b[49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 591\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m e \u001b[38;5;129;01min\u001b[39;00m e_dict:\n\u001b[1;32m 592\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m e[\u001b[38;5;241m0\u001b[39m] \u001b[38;5;129;01min\u001b[39;00m v_list \u001b[38;5;129;01mand\u001b[39;00m e[\u001b[38;5;241m1\u001b[39m] \u001b[38;5;129;01min\u001b[39;00m v_list:\n\u001b[1;32m 593\u001b[0m \u001b[38;5;66;03m# The edge is entirely in the set, so both vertices are already there\u001b[39;00m\n", - "File \u001b[0;32m~/Library/CloudStorage/OneDrive-MichiganStateUniversity/Documents/Research/Projects/Interleaving_to_ML/ceREEBerus/cereeberus/cereeberus/reeb/reebgraph.py:311\u001b[0m, in \u001b[0;36mReebGraph.add_node\u001b[0;34m(self, vertex, f_vertex, reset_pos)\u001b[0m\n\u001b[1;32m 308\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mf[vertex] \u001b[38;5;241m=\u001b[39m f_vertex\n\u001b[1;32m 310\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m reset_pos:\n\u001b[0;32m--> 311\u001b[0m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mset_pos_from_f\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n", - "File \u001b[0;32m~/Library/CloudStorage/OneDrive-MichiganStateUniversity/Documents/Research/Projects/Interleaving_to_ML/ceREEBerus/cereeberus/cereeberus/reeb/reebgraph.py:490\u001b[0m, in \u001b[0;36mReebGraph.set_pos_from_f\u001b[0;34m(self, seed, verbose)\u001b[0m\n\u001b[1;32m 488\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpos_f \u001b[38;5;241m=\u001b[39m {}\n\u001b[1;32m 489\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m--> 490\u001b[0m pos \u001b[38;5;241m=\u001b[39m \u001b[43mnx\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mspring_layout\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mseed\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43m \u001b[49m\u001b[43mseed\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 491\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpos \u001b[38;5;241m=\u001b[39m pos\n\u001b[1;32m 493\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpos_f \u001b[38;5;241m=\u001b[39m {}\n", - "File \u001b[0;32m compilation 4:4\u001b[0m, in \u001b[0;36margmap_spring_layout_1\u001b[0;34m(G, k, pos, fixed, iterations, threshold, weight, scale, center, dim, seed)\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mcollections\u001b[39;00m\n\u001b[1;32m 3\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mgzip\u001b[39;00m\n\u001b[0;32m----> 4\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01minspect\u001b[39;00m\n\u001b[1;32m 5\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mitertools\u001b[39;00m\n\u001b[1;32m 6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mre\u001b[39;00m\n", - "File \u001b[0;32m~/anaconda3/envs/interleavingenv/lib/python3.12/site-packages/networkx/drawing/layout.py:495\u001b[0m, in \u001b[0;36mspring_layout\u001b[0;34m(G, k, pos, fixed, iterations, threshold, weight, scale, center, dim, seed)\u001b[0m\n\u001b[1;32m 493\u001b[0m nnodes, _ \u001b[38;5;241m=\u001b[39m A\u001b[38;5;241m.\u001b[39mshape\n\u001b[1;32m 494\u001b[0m k \u001b[38;5;241m=\u001b[39m dom_size \u001b[38;5;241m/\u001b[39m np\u001b[38;5;241m.\u001b[39msqrt(nnodes)\n\u001b[0;32m--> 495\u001b[0m pos \u001b[38;5;241m=\u001b[39m \u001b[43m_fruchterman_reingold\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m 496\u001b[0m \u001b[43m \u001b[49m\u001b[43mA\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mk\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mpos_arr\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mfixed\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43miterations\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mthreshold\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdim\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mseed\u001b[49m\n\u001b[1;32m 497\u001b[0m \u001b[43m \u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 498\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m fixed \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m \u001b[38;5;129;01mand\u001b[39;00m scale \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m 499\u001b[0m pos \u001b[38;5;241m=\u001b[39m rescale_layout(pos, scale\u001b[38;5;241m=\u001b[39mscale) \u001b[38;5;241m+\u001b[39m center\n", - "File \u001b[0;32m compilation 12:4\u001b[0m, in \u001b[0;36margmap__fruchterman_reingold_9\u001b[0;34m(A, k, pos, fixed, iterations, threshold, dim, seed)\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mcollections\u001b[39;00m\n\u001b[1;32m 3\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mgzip\u001b[39;00m\n\u001b[0;32m----> 4\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01minspect\u001b[39;00m\n\u001b[1;32m 5\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mitertools\u001b[39;00m\n\u001b[1;32m 6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mre\u001b[39;00m\n", - "File \u001b[0;32m~/anaconda3/envs/interleavingenv/lib/python3.12/site-packages/networkx/drawing/layout.py:551\u001b[0m, in \u001b[0;36m_fruchterman_reingold\u001b[0;34m(A, k, pos, fixed, iterations, threshold, dim, seed)\u001b[0m\n\u001b[1;32m 549\u001b[0m np\u001b[38;5;241m.\u001b[39mclip(distance, \u001b[38;5;241m0.01\u001b[39m, \u001b[38;5;28;01mNone\u001b[39;00m, out\u001b[38;5;241m=\u001b[39mdistance)\n\u001b[1;32m 550\u001b[0m \u001b[38;5;66;03m# displacement \"force\"\u001b[39;00m\n\u001b[0;32m--> 551\u001b[0m displacement \u001b[38;5;241m=\u001b[39m \u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43meinsum\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m 552\u001b[0m \u001b[43m \u001b[49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43mijk,ij->ik\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdelta\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m(\u001b[49m\u001b[43mk\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43m \u001b[49m\u001b[43mk\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m/\u001b[39;49m\u001b[43m \u001b[49m\u001b[43mdistance\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m2\u001b[39;49m\u001b[43m \u001b[49m\u001b[38;5;241;43m-\u001b[39;49m\u001b[43m \u001b[49m\u001b[43mA\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43m \u001b[49m\u001b[43mdistance\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m/\u001b[39;49m\u001b[43m \u001b[49m\u001b[43mk\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 553\u001b[0m \u001b[43m\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 554\u001b[0m \u001b[38;5;66;03m# update positions\u001b[39;00m\n\u001b[1;32m 555\u001b[0m length \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mlinalg\u001b[38;5;241m.\u001b[39mnorm(displacement, axis\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m)\n", - "File \u001b[0;32m~/anaconda3/envs/interleavingenv/lib/python3.12/site-packages/numpy/core/einsumfunc.py:1001\u001b[0m, in \u001b[0;36m_einsum_dispatcher\u001b[0;34m(out, optimize, *operands, **kwargs)\u001b[0m\n\u001b[1;32m 997\u001b[0m path \u001b[38;5;241m=\u001b[39m [\u001b[38;5;124m'\u001b[39m\u001b[38;5;124meinsum_path\u001b[39m\u001b[38;5;124m'\u001b[39m] \u001b[38;5;241m+\u001b[39m path\n\u001b[1;32m 998\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m (path, path_print)\n\u001b[0;32m-> 1001\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21m_einsum_dispatcher\u001b[39m(\u001b[38;5;241m*\u001b[39moperands, out\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m, optimize\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs):\n\u001b[1;32m 1002\u001b[0m \u001b[38;5;66;03m# Arguably we dispatch on more arguments than we really should; see note in\u001b[39;00m\n\u001b[1;32m 1003\u001b[0m \u001b[38;5;66;03m# _einsum_path_dispatcher for why.\u001b[39;00m\n\u001b[1;32m 1004\u001b[0m \u001b[38;5;28;01myield from\u001b[39;00m operands\n\u001b[1;32m 1005\u001b[0m \u001b[38;5;28;01myield\u001b[39;00m out\n", - "\u001b[0;31mKeyboardInterrupt\u001b[0m: " - ] - } - ], - "source": [ - "a = 0\n", - "b = 2\n", - "\n", - "n =1\n", - "for i in range(4, 50):\n", - " c = i\n", - " d = i+2\n", - " losses_dict[f\"losses_{i}\"] = solver_iter.run_optimization_torus_line(a, b, c, d, n, 1)\n", - "\n", - "# Save to a text file\n", - "with open(\"lt_losses_0_2_x_x+2_1.txt\", \"w\") as file:\n", - " for key, value in losses_dict.items():\n", - " file.write(f\"{key}: {value}\\n\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "# Plot the results\n", - "\n", - "def compute_loss_dict_diff_loopsize(largest_loop, n):\n", - " a = 0\n", - " b = 2\n", - " c = range(4, largest_loop)\n", - " losses_dict = {}\n", - "\n", - " for i in c:\n", - " losses_dict[f\"losses_{i}\"] = solver_iter.run_optimization_torus_line(a, b, i, i+2, n, 1)\n", - "\n", - " return losses_dict\n", - "\n", - "def plot_fig_diff_loopsize(largest_loop, n):\n", - "\n", - " losses_dict = compute_loss_dict_diff_loopsize(largest_loop, n)\n", - "\n", - "\n", - " plt.figure(figsize=(20, 5))\n", - " plt.subplot(121)\n", - " plt.step(range(2, largest_loop-2), [losses_dict[f\"losses_{i}\"][0][0] for i in range(4, largest_loop)], label=\"loss before optimization\")\n", - " plt.step(range(2, largest_loop-2), [losses_dict[f\"losses_{i}\"][0][0]+n for i in range(4, largest_loop)], label=\"upper bound before optimization\")\n", - " plt.xticks(range(2, largest_loop-2))\n", - " plt.yticks(range(int(min([losses_dict[f\"losses_{i}\"][0][0] for i in range(4, largest_loop)])), \n", - " int(max([losses_dict[f\"losses_{i}\"][0][0]+i for i in range(4, largest_loop)])) + 1))\n", - " plt.step(range(2, largest_loop-2), [math.ceil(i/4) for i in range(2, largest_loop-2)], label=\"true interleaving\")\n", - " plt.xlabel(\"loop size\")\n", - " plt.ylabel(\"value\")\n", - " plt.legend()\n", - " plt.title(\"Losses and upper bounds for different loop sizes before optimization\")\n", - " plt.subplot(122)\n", - " plt.step(range(2, largest_loop-2), [losses_dict[f\"losses_{i}\"][1][0] for i in range(4, largest_loop)], label=\"loss\")\n", - " plt.step(range(2, largest_loop-2), [losses_dict[f\"losses_{i}\"][1][0]+n for i in range(4, largest_loop)], label=\"upper bound\")\n", - " plt.xticks(range(2, largest_loop-2))\n", - " plt.yticks(range(int(min([losses_dict[f\"losses_{i}\"][1][0] for i in range(4, largest_loop)])), \n", - " int(max([losses_dict[f\"losses_{i}\"][1][0]+i for i in range(4, largest_loop)])) + 1))\n", - " plt.step(range(2, largest_loop-2), [math.ceil(i/4) for i in range(2,largest_loop-2)], label=\"true interleaving\")\n", - " plt.xlabel(\"loop size\")\n", - " plt.ylabel(\"value\")\n", - " plt.legend()\n", - " plt.title(\"Losses and upper bounds for different loop sizes after optimization\")\n", - " plt.show()\n" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "interleavingenv", - "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": "3.12.3" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/Notebooks_Unused/sandbox_decomposition.ipynb b/Notebooks_Unused/sandbox_decomposition.ipynb deleted file mode 100644 index 2a1434c..0000000 --- a/Notebooks_Unused/sandbox_decomposition.ipynb +++ /dev/null @@ -1,197 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 2, - "id": "8ca81a04", - "metadata": {}, - "outputs": [], - "source": [ - "from cereeberus import ReebGraph \n", - "\n", - "import cereeberus.data.ex_reebgraphs as ex_rg\n", - "import numpy as np" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "81ba67df", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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Jc/eLON2t6m+hLXddjihZ2vcPkhLj34JlZWVlJrFaRzO+/PJLE+xYEhISaoMMzc9wOlmLEGhvHo9H9u7dK59++mltI8mePXvKvHnz5LLLLjNfrznzB9lX8Harn0vPKf3jp8ii3r8URzOufPwdsSCwAGyiyZRaeq1v6jExMXLjjTdKXO8KWZ3xkFR7q/xe8rjeC1ScEuGIkiXpj0pqp5EtOq7KykoTXGiQoSMa+rVFFxLUyhINMvTkFRHBICbQljQbQc8dH3/8sWRnZ5vb9M179uzZZpHPulOY2sjqk6z/koMFH7TqOfvFTZFre/9cIpz+d+hUBBZAG54YPvvsM3OlYfV70aopnaZQeZWn5IPMRyW7/FCz990jZqjMT31IukSl2XKsOnKh0yQ6XaKBhgZBlqioKBk8eLAZzdDuuvo1gMA5c+aMCSi0q7XSC5Irr7xSLr/8cp9Bvp5v9uW/JetznjSBhr8XLLoystLp1IndbjWl8c1FYAG0AX1jXr16tZl2UNqZdsGCBRedFPQEsC//bdl5/lUpqsr2uaiQdbvmU4zvulRGdV7UohOAv0OvmvB58OBBE2QUFRXVfk+Pf8CAAWYkQ4MNHdkAYI/8/HxzIaJTH8rlcpmqSw0qOnXyr0KjoPKMbDn7ghwpXGvOGTq62TDIqOnYWZNAfln8dJmSfKd0j275wqEEFkAbXG28+uqr5iShb8QLFy40re6bWuPjZOluySjZZUYwzlecFLe3ymRnd43uY0Yo0uPGS59O45o199laehWkeSE6kqFbXl5e7fc0B6Nfv34myNDRDBpyAS2/ENmwYYNs3bpV3O6aIECnO2bNmmUSrFu0z+oCOVK0VrLLDktW+RdmdWV9Pce4EkwPjB4xQ2RQwlUSH9m91X82AgsggHbv3i3vvvuumVrQKQ+d+tApkFCgJ6WcnJzaIEM/r6tPnz61yZ/WdA8A36qrq2X79u2mQqu8vKZ3jQbrmpipvWeCBYEFEKATxHvvvSe7du0yX2suwg033BDSUwXnzp2rzcnQUY26NJiyemV07976KyIglHi9Xtm/f7+sWbPGjGxa/WU0oBg4cGDQlX0TWAA20xODTn3oFIjS4UudEw22k0NraJlZ3YZcdfvraWBhBRlaJhdOvxegoePHj8tHH31kuuMqnULUc8bYsWODtsSbwAKwkZZrvv7662aOVEcnbrrpJpPcGM5KSkpqG3JpVrsmg1p0ikSnS3Q1ZBpyIZzk5OSYSo+jR4/WVlvpAp7axC7YK60ILAAb6BW5ttXVTel8qOZTsNhXfTpvbDXk0hNq3YZceqVWtyGXZsADoUarqrTSY8+ePea8oaMSEyZMkKuuukri4uIkFBBYADb06tdF93S0Qk2cOFHmz59PEyk/WhLr70xHMjTYsNoSW3X6VkMuHfGhIReCnf5/a/vtzZs31wbUw4YNkzlz5oTcQoAEFkAr6Lyo5lNoToG++S1atEjGjBnD77SZtKSubkMuDdYsOiysya9WQ67o6Gh+vwiq/21N4l67dm3t/3V6erpJzNSPoYjAAmgBHcLUk4VWfuiJQ2vLb731VrM6KOxpyGUFGdZ6CEqnR+o25PK3SRDQHucI/f/VPIrz58+b27p27Spz5841QbIjhJOWCSyAFgzha28KnSNVOmS/ZMkSM3wP+0/OOipk9cqwTtBKT8x1G3LpomlAR5CRkSEffvihnDp1ynytAfDMmTNNx91wyB0qZBEywH/aaVKnPrKysswbmy4ApJncoXz10ZGCDF3e3QoyrIWYLDqsbCV/trQ7IdDaXi6ffPKJ+f9UkZGRMnXqVJk2bVpYTeEVElgA/tEEQ03S1MoGvQLRUlJrmWK0PR29sKZLrCtDi/bHsHplaKMhINAl1ZpDsXPnThMA64WG9qHQfhThOJJWSGABND3nrycNXZlUab+FpUuXSmJiIr+6DnQisxpynThx4qKGXNZIhnYAZXQJdqmsrJQtW7aYag/9XGnuj1Z6pKSkhO0vupDAAvBNs7hXrlxZu1yxLlN89dVXh8U8abA35NJA49ixY/UacmlfkboNuYK1syHal/5PaY6V9qMoLi42t2nQqpUe/fu3fFXQUEFgAfig611oPoW+SHSudPHixWaFQQQPnbbSRlxWQy5NvLVoMyJrJEOTQAkW0RQdCdP/I6300Hwfq3usjlCMGDGC0bALCCyAS5w8duzYIe+//765MtHmNdpFM5yHNkOBBhU6gqHTJTqicamGXBpoaDmrBpJAXVqdpGt66Noe1v/MjBkzZNKkSTRwa4DAAmjw5vP222/L3r17zdd6NXv99deHVUZ3uDXk0iBDp08sGlRoIy7929OQC1oJpquO6uqjSke2Jk+eLFdccUVIr1bcGgQWQJ1SMZ360MWBNMFPG9loqRjJfqFNR6W074BVxtqwIZdW/miQoSMaNOQKH7qQ4Pr162X79u0mEFWjR482lR46/QHfCCwAETMHv3r1ajM8rnPvN998s5l3R/hNg+ly91aQocFmw4ZcOl2iG1VBoUnX8di6dats2LDB5OgoDS71QkMTNNE0AgtIuF+t6jCnlotZTZa0lDQca8/huyGXBp7aFK0urSqxemXQkCs0/t46BaqVHrr2j9IW/RpQaN4NI5f+I7BA2NJ5dS0l1bl2pfOmWi5GdQB8zbVbQYZOndSlb0B1G3LxJhRctJxcEzOt4FFHo3TKQ6c+KEluPgILhCV9Y1ixYoUUFRWZZD1N0NRyMcAf+n9jNeTSKoG6Dbm0isgqY01NTSXI6MC0LbwGFFotpDRJW5My9SKDyqCWI7BAWNE3gG3btpkFgnQaRLsyaikpbZ/RmiZqdRtyWYl+1pWvNZKh02xc/XacNz6d8rAWEtS/i5aNavkoCbqtR2CBsKEtd996663asjHtvnjddddRSgrbaPKvNlDSkYyGDbn0DcsaydDujEy5tT1NxtSkTE3O1CRNpSOVupigLmkOexBYICycPXvWlJJqMp5enWguhQ53MheOQNGgQufurV4ZVoWBNeRuNeQaOHAgw+4BpqNI2vRu3bp1poxU9enTx5wHNAkX9iKwQMg7ePCgvPHGG2bEIj4+3lR96EkFaMs3Ns3FsJI/Gzbk0uDCasilHR1h39Snvv51KXNNvlU6/amVHrpYGBcWgUFggZClORTa03/z5s3m6759+5r+FBpcAO35f6nLvFu9MqzSxroNuXQkQ0c0tKcKWkZXudXETF3zR+nvUis9xo0bR65LgBFYICTpioOvvfaaObko7aCpVykkz6GjXVFriaMVZOiUnUWvpjUYtvIyaMjlH53u1BEKnX6yRoSmTZtmtqioqAD9JVEXgQVCzsmTJ00pqQYXeiJZsmSJOTEDHV3dhlzaAbSu3r1711aYkGh4MX29a6XH7t27TcCmgdn48eNl5syZjFK2MQILhAw9mWzZssUMf+rnWkKqpaQ6pwoEm/z8/NqRjIYNuXSlXSvI0M/DOVdAc6c2bdpkNqsKR6eRdISS1377ILBAyJT5aSnpgQMHzNejRo2SRYsWMfSJkGnIpUP7GmRop9i6Dbl09MKaLtFRjXAJMjRXZdeuXbJ27draZFj9+bXSQ6eQ0H4ILNBu3F6PHC/OkS8KMyWz9LxUez0S64qSy+JTZFhSb0mOTvTrJKnDx1pKqvPTmkMxf/580+wmXE6wCC9aLmk15Pryyy8vashlBRla+dReOUUFlaVyqPC0HC3KkuLqcnGKQ7pFJ8jQxFQZmNBTol2RLd63BlX682sehZWTomu1zJkzx/Sm4XXf/ggs0OYyS/NkVcY2sxVW19SURzhqToDeCwGHGhDfQ27tO03m9xojsRGXTrrSEQotJdUhUF04TEtJtcMhEC4jdRpcWA25dFqgbkMunRKwGnJFREQE9FiqPW75LPeQrDixWXac/8rcpgGF07y2veZ1ra/vKGeELOg1Vm7uO0WGJKY26zm0mkanOjWPSsXGxspVV10lEydOpOFYB0JggTajJ54Xvlonfzq2xlx11JxmfNPxBr1Ht6h4+fmom2Vq8uDa7+lVmp5gtIOe0uWstZSU8jyEK+0kWbchl9UIymrIpX0brIZcdldHfFmUJY/sfdWMUGgw0dRr2+VwmkBjce/xcv/QayUhMrbR+58/f96MUGhPCqVB0pQpU2T69On0/eiACCzQJs5WFMn9O56Xo0VnmjjlXMwhDvGKV27tM00eGLZQSopLTNWHldCmJxdtyUspKfBN4K2l1laFiVZMWPRN2WrIpcFGaxty6cjj7w6+WfO8F0Yb/aVBSJeoOHls4ndl8CVGL3QdFu2WqV0zNadCjR071vSjoPy24yKwQMCdqyiS7295SrLK85t94mloZtJgSd6YK6UlpeYqTEtJ9SoMwKXp6GDdhlxabWLRYNxqyKVbc0f8XjmxSf7zi7db9at3OhwS7YyUpyffUzs1olObWuG1ceNGM92jNBjSSg9doh4dG4EFAkoDiXu2Pi0HC061OqiwDD3hkmne3qaUlHp+oHlBhi4VrlMKOpKhic8WTXrUhE8dydAgIykpqdF9bT17VH604zlbfv0aXCRFdpJXpt8vx784avpR6JuT6tmzp6n00AAIwYHAAgH1v8c3yu8PvXPJ7xUfzpRzn+yTws9PSmV2gUQkxkrc0FRJu2OGxKR187lPp9chL069TwZ2bl7iF4D6tKrCGslo2JArNTW1tldGt271X49a6XHLZ7+X8xXFl8ynKDuRK6df3CClX2ZJVV6xOKMjJaZPd+l102TpPGXQpV/X4pD+RbEy9GBNlYsGNjrFqaXjVHoEFwILBO6fq6pMFn66XCo9NcsTN/Tlv78uxQdPSZcrh0qn/ilSlVci2W/tFE9ZpQz7/Z3SqV+yz8SvSd0GyOMTv8dfD7CJTpHoKIYGGVbVhUWbcFllrDoV8eTRj0witq8kzfxtX0r2mzskflhvieqaIO6KKsnbeFiK92dI3x9dIykLx/k8jplH42TJhFly+eWXB7ySBYFBYIGAeen4Bnns0Ls+kzWLDp6SuEG9xBnpqr2t/PR52X/vn6TLFUNlwM+ua3T/r8/4B0nr5HtkA0DLaLKnBhm6aUMuK3FSJXbtLKsHnZMyufQFgy9et0cO/Pg58VZWy6hn/o/PUYs5KSPl1+O/zZ8uDAKLZnVZ+cUvfmGGrupuJNiFn9dPbmv0+wnD0+oFFSqmd1eJ7Zss5RnnmpyTfevUTluOE0B9ugKw9oa4/fbb5ac//alJktaeGDqCcNjb/KBCOVxOieqeKNUlNcmYl6IjIGtyD0hJte/7IHQ0ezxqxIgRZsnq2h0wpBVWiqrK5GTpNys1Nie5TKdEYvs2vr6Hx+uVz/NrVi4FEDjahGrMmDFm0wZc/779FXEWHhKPo+nCcXd5pXgqqsVdUiH5W49KwY5j0nVG4wsCapL34cLTMr4ryZqhrtmBhQYSms2L8HSoMLNFjzv36QGpOlckvb9zZdPPUXC6dhVDAIGnjbXOuEr9CipUxjNrJPfd3TVfOB3SZdoQ6fvDqxt9jE6HfFGQSWARBpodWGh7Wc0q1uYrU6dOleXLl5tSJl+0VtmqV1ZWqRGC09mK5v/9yjLOyck/fihxw3pL97mjmrx/qbtSyt1VPtt9A7BfTnmB3/ftsWSSdLliiFSdK5bzn30hXo9HvNWeJqc5c1tw/kDwaVaOxeTJk+X555+X999/X5544gmT/HPllVeaFfp80cBDkz2sjfUegpu7zuqL/qg6XyxHf/6quOKiZeA/32DmY/16HrGnNwYA/7ib0Ts3Nr2bJI3rby4UBv/yFlPxdfQXK+qtznoxh3hs6nmDEAosFixYYBaDGj16tFlp8t133zWlTLoCpS/Lli0zGaTWZrVrRnCKi4j2+77VJeVy5F9fNR8H/9utEtUtwa/H6ZBpjLPlqyQCaL74Zry2G9Jqr5IjZ0z1ly/avr855w8Er1YVE3fu3Nn0pNdV+HzR9sy6ITQMSvAvv8ZTWS1Hf/GaOdEMWf6tJpM26+rTqbtEOOtXlQAIrKGJveVEydkWddLV17vSZE5fdL+DEnq16hgRgiMWl6qJPnbsmPTqxT9LuOgd21XiXNFN1rUfW75aSr44LQMeXiLxw9L83r/DI+I5mWcWI9u3b1+9/BwAgTMsqbepympMVX7JRbd5qt1y7pP94oyOkNg+3ZsMXhD6mjVioXXPixcvlr59+0pmZqY88sgj4nK55NvfpulJuNBKjbk9R8nbp3f5zIPIeOYTyd9yVDpPHijVxeVyds3+et/vPnukz/17nSI9zoocLDho1j3Q/y9dS0A7A2q9fadOnWz/mQCIzEwZLv/1xaXb9FuOP/6+uEsrJGFUupna1BJyrfjS/jTpd88RV2yUz+nNAQk9pVdsZ37VYaBZgYWupKdBxLlz5yQ5OVmuuOIKs1Kdfo7woCMIfXNcjSZXln6VYz7mb/3SbA01Flj0iEmSh5beJkcOHTYtiPV/TSuRdNOgRoNaazElllcG7NMjtrNcmTJUNuQc8tnSW3tVnP3wc8l5Z7e4C8vEGRslcYN6Stpds6SLj7VClO7v1r5TKSEPEw5v42m87dYSFB2L2+2W3bt3y9q1a6WkpES2Da6Us5294rW51cS/jLxRrkubaD7Xf826iyllZWXVu29aWlrtOgeshgq0nq5W/L3N/9OM+pCm6WiFXjC8cuUDEuMiKTuY+fv+zUowaJS+uR8+fNh0W9XRA6Vv4g+PmCoPZ78tZe5KW36DugDZxK6XyeLeE2pv0xEKHQ3TbcaMGZKXl2cCDF3nQKuLdARNNz02XUDJWrFR709zLaD5HJlFMig7So6kVGp1qC10tOIXo5cSVIQRRizgk75pf/TRR7UrImp+w1VXXSUTJkwwuQ9rsw/KP+1+sdVXNxpUdImKkxem3ifJMf6NYmnvFGvFxuPHj9ern9fAxwoytJkbQQbQOF2M7JNPPpFNmzaJ2+GV3WOdkhtV4XNKpDnuGThHvj9wDn+CEMDqpmgxHZlYs2aNSZ602rhPmTJFpk+fbjqu1vVB5ufyyN6aPiYtOQlpUNE1Kl6evPxuSY9r2YqmpaWlcuTIERNkaJWSTttYdLjOmi7RDrFOZ6sKoYCQo9V9K1euNAG60o7Kk2dMlwf3/FX252eY/hPNpYMd+qjvXjZT7h00j+A+RBBYoNk0d2L9+vWyY8eO2uWUx44dK7NmzWp0Pm1v3gl5ZO8KySzL8/sk5BCHua9moj80Yol0jY63LblUEz11NEODjaqqqtrv6YiLFWT079/fjLoA4UxHI7W0W4MLXS/k+uuvl+HDh5vvaVv9p49+LC8e/8zkSfh74aAXC7GuKHloxPVyda8xAf4J0JYILOA3ffPV6p4NGzaYVQ7VwIEDZe7cuSZ3wR96Evrr1+vl1RObpaCqVCIcTqlu0GhHgwldL0Ab5QxJSJXvDZgps3qMCNjVjP5cX331lRnJ0DyR8vLy2u9p0zYtX9VAQ3/WyEiSyhA+dOpw69atZqpTLyK6d+8ut956q/nY0L78k/LM0U9ky7mjJsBQDYMMDSb0dR3tjJRFvcfL9wfOlm7R/nXaRfAgsECT9ITy+eefy6efflq73os2O9OAQntHtESVp1o+yzkku/O+lgP5p+R06Xmp9rol2hUpgxN6yfCkNLkiZaj52JZ0euTEiRO1yZ96hWbRqZ5BgwaZIEM7yTac7gFCiV48vPnmm3LgwAHz9YgRI+S6664zIxaNOVV6TtZkHZAvCk7JwcJTUlJdYQINDSBGdk6XUZ37yOyeIyU+gtdPqCKwQKNXK9qGXaspcnJqek5oCdHs2bNl1KhRIT8fqj+/VpVYQYaud2PRHIy6Dbni4uLa9VgBO2n5tq7tlJuba/7Xr776arn88stD/jUPexBY4JLOnDljhj91ZVqlV+e6Qq2eXPTKPdxokKH9MaxeGXritejJVhM+rYZcGnwBwUqTsd944w0zYpGQkCA333yz+f8G/EVggXr0qlwrPXT9DaWJixpMaFARGxvLb+sCvZKzylg1CKurd+/etcmf3bq1rIIFaGs6Daijk5pHpfr16yc33XSTxMfbkzCN8FHoZ4Ms+liEuLKyMvnss89k27ZttWWYOt2h0x66Oi0aD8as6RKrl4clJSWltleGfs5QMjoizZ167bXXav9/p02bJnPmzKHsGi1CYBHmqqurTTChQYVVDaEllpqYqU2j0Dya7Fm3IZdVjms15LJGMnRUgyADHYEmK2tQYZWSLlmyxPyPAi1FYBGmNGdApzt02kOHq5ReUWtAoWWVvOnZMwpkNeTSJNi6Dbl07toKMnTBNBpyoT3OAZs3bzbTH/q5vv5vueUWpu/QagQWYUgTMjUx08oN0Dc5bW41ZswY3uACRBPh6jbksvqAWA25tLLEasgVjsmxaFvaIE5LSa2uuTrtuWjRoiZLSQF/EFiEES0Z1YBCr56VnkR0SXttw03jp7adfqrbkEtHNuo25NIeGVZDLk70CETi8SuvvGJa8utI2TXXXCMTJ05klBK2IbAIkz+yNrfSJlc65KknE10gTBcKo/9C+9IcDJ3j1ivHSzXk0uBCRzJoyAU77N+/34xUaLdZzdZfunSppKW1bRM6hL5CqkJCe7hz48aNZh5Vr5KV9vfXSg/KIDseDfp0pVirV0bDhlw6TWI15KIEEM2h+T0ffvihSdRW+r+kpaRcWCAQCCxC9CSyc+dOWbdunVnRU6Wnp8u8efPMRwRHkJGdnV0bZOjwdV2a8Gklf9KQC02d5LXqQ7vIKp3+1JwqEoYRKAQWIfZmpG9Cn3zyiZw/f97cpiMTWumhV7lUegQv7fRplbFmZmbW+56WBVu9MhiJQsNEbV3qXFck1vydG264wZwLgEAisAgR2thGEzN1KF3pEKfmUIwfP55lv0OMlgdbDbk0P6Ou5OTk2iBDV5wlmAzfi4xNmzaZiwz9XP8XtJRUe6kAgUZgEQJXsnry0DcZpdUdU6dONZ3z9AoFoU2TPbWyRAMNvTqt25CrS5cutdMlmqBHkBEetNGdrvVhnRO0jPzaa6+l8gtthsAiiN9QNIdCcyn0ikTfNMaNGyczZ840fSkQfrRsVXtlWA25rIRdRUOu8KB5OboqqU6F6jo/CxYsMKOWBJVoSwQWQUYbK2mVhw5zWk2WtBRR8yh0GByw/k80uNCrVh3RqNuQSxeTsxpy6dLvNOQKDXv37pW33nrLBJSa0KulpNo6HmhrBBZBQoe4d+/eLWvXrq3tdaBJe1rpoasQAr7oG41Ok1h5GXUbcmkDLqsh16BBg2jIFaR/3w8++EB27Nhhvh4wYIDceOONpqMr0B4ILDo4nebQ4W3t52+VHOpqo7ry4IgRIxjiRLMDVE30tRpy6aqWFh06r9uQS0c20PETeVesWCGnT582X8+YMcMkbVNKivZEYNGB6clCKz2szH890euJQ9vvMnwNO4JW/R+zemXk5eXVfk/fmHQkTIMMHc2gIVfHo23htZRUe9XExMSYUQoddQLaG4FFB6QneF11VNvvWleSup6HNrbREwgQiCBD15Kxggz9vK4+ffrUVpjoiBna92+1YcMG06ZfP+/Zs6cpJdUqIKAjILDoQPTKY/369bJ9+/baskEtFdMueXRXRFvSBaqsnAxrmN3Sq1ev2l4Z3bt35w/TxqWkq1atMivkKq0EW7hwISOY6FAILDoAXRBo69at5ipE1/dQmq2viZl6NQK09zy+1fVT8zP0KtmigYUVZOj/KmWNgZOVlWVKSXVEU0cxNaDQUlKgoyGwaEd6gtYSMZ320D+E0g55GlBoZjfQ0WhraKshl87x123IpVMk1nSJrklDkGGfPXv2yDvvvGMqQPT3rKWkWhUGdEQEFu3k2LFjJjFTG9ooXcJYVx0dNWoUGd0ImmF5HZLX0QytXKrbkEuTPa0gQxdM0ytsNJ/+Tt977z3ZtWuX+VqTM3W9Dyp20JERWLTDcKaWjmpgobTttiZlTp48mZa7COrpPG3IpSMZGmxYU3pKE46thlw6EkdFk3/y8/NNKam16Jx21dWqMEaC0NERWLThPLVmcX/++ee15XyTJk0yJwoa2SCUuN3ueg25NCm5bkMuveq2GnKxns2laZD2+uuvm2ZmOjqhpaTaYwQIBgQWbTBcrEmZW7ZsMSdcpY2tdNqDlQYRLg25rCDDyiVSOj2iIxhWQy4C7Jq8K60M0w67SvMoNJ+CEl8EEwKLANEgQstG9SRhtVDWuWZNzKR/P8L1TVOH9a1eGbpQlkWH9+s25ArHhfT0PKGjFDpaoSZMmCDXXHMNU0cIOgQWATh5HjhwwFR6WJ0MtSRPAwod+mV+FKh5nWiLeivIsJKYLVpVYiV/hkPjpzNnzphSUs2r0BwUXeZ87Nix7X1YQIsQWNhIW29/+OGHtclWmhmvCVfaxIbe/YBvOnphTZecOnWq3ve0P4bVKyMUV/DVio93333XjHJqEKVdNOlfg2AWFoFFRXW1HDqbK/tzcySnpFj0J0mIjpJh3VNkZEqKdI5p3WJLeuWllR5WN7zIyEiZPn26TJ06ldUigRa89q2GXBqsN2zIZY1kaAfQ9hoB1PPIvuxsOXzurJRVV4nL4ZTeiYkyMqWHDOraTSKcTr8qaTSg0B4VSvNMtJSUtv0IdiEdWOzPyZYX9+6R1Ye/kEq3W/QU5Lrwgvd4vWZT09LS5Y4x42R2/wF+nRAsujKkJlnpcub669GTnM6L6uqCLNoEtJ5WlNRtyGUlQCs9P9RtyBXoUcHy6ip568hheWHPLjl4tmalYZfDURvcVF9oFpYQFSXfGjla/m7kGOnrY10VnSbVUlKdAtHHa9t+LTtnqhShICQDi8KKcvm39Wtl5RcHzAvf3cShW/cZ1j1Z/mv+QhnSrfH1D7RGf9OmTbJ582Zz1aH0BKdLmbN2AhC4CittxGU15LJeeyouLq42yNAkULsbcm3OOCn/8NF7klVcLE5xiEeaPqfoPX44cbLcN2myREdE1H5Pj12TNPXn0UqYm266ybTwB0JFyAUWOkpx15uvy/mystoRCX9ZVx+/mjnHXHE0pFdLOjqhoxTa2lilpaWZxExd/RFA29CgQpvM6UiGjmg0bMil0wpWQy6dmmwpPe39x6YN8uTObeJ0OJp9TtGxjIFdu8nz198kPeLiZN26daZSTGl1mJaSssAgQk1IBRYaVHxr5StSXl3d7BNAQ7+4araZHlH6o+vJS/ModNVHpT0odIRCT14MXwLtRwP+48ePy8GDB83r1Ar6lQYVVkMuDTaa05BLX/e/WLdG/rq3JgeipfSCJblTnNweGSO5Xx83t02cOFHmz59PKSlCUsgEFvnlZTL3r89Jfnl5q4MKy4s3LJU+DqdZ00Ob/CgdutQcCs2lYP0DoOM15MrIyKitMNHzh0VfrzrloBcD2mK8qYZcGlA8svYTW47L4RXp4nbL9WVVcv3ixTJ69MUjokCoCJnA4oEP3pG3jxy+ZD5F2dEvJev/PXnJx/V64EcS06/vRbfrsGe8wymLzhWIDqRqbfmUKVNMtQdZ20DHp6csTY60emVYo411G3LpSIZuDc8xJwvyZf6LL0iF+5uF1S6lIuOU5L//oZR/9bV4q6ololtXSZg2RZKuuvKS9/8/o8bKP82aY9NPCHRM/r5/f5N51AHtOpMpbxw+1OT9EmdcIdF90uvdFtn90omaOupR5KmW/TFR8r2hw03WdmvLXgG0HQ0etCW2btpC/+zZs2a6REcydDFAXc9EN109VHOlrORPneZcvmG9VHu+qUC5lNJDhyX76T9LdFpv6Xz1PHFER0n12XPizv9mlKShZw/slbsunyLJcXEB+ImB4NKhA4u/7N3tV/VHzID+Ejd2jN/79TocciIpQRYsWiRRLPsMBHWQoc21dBpTNy33tKZLdOpEm3LppnlUnVKS5cOqskbrPjzl5XL2xZel04hhkvK9O8ThZ6mrXrC8enCf3Ddpim0/GxCsWlUg/uijj5oX9v333y92K6yokHePHmkyqKh7QvDWqYVvSkFlhXx6/KtWHCGAjkY7XE6bNk3uuusuefDBB2XhwoXSv39/c57aWpiv8yiNPr54xy5xFxVJl2sXmKDCU1Eh3gt9LJoKLP62r2aFYyDctXjEQhfieuqppwKWrKSVIFZjmqbkvvSqeLUszemUmMv6S9frF100NdKQNszafSZT5g8YZNMRA+hIdMGzSZMmmU0bct2x8lWRvG/yMS6l7MhRccTEiLugQE49+7xU5eSKIypK4idNkK43XCfORkpctRdGbkkJ0yEIey0asSguLpbbbrtNnnnmmYAtJKSBhSZaNsYRESGdxoySbjdeLynf/550WXiNVJ45I2ce/6NUnDrd6GM1aPk8O8vmowbQEWmlyNdlpU20vxKpzj0r4nFL9p+ek9ihQyTlrjslYcrlUrRxs5x96ZUmn2dfTv1F14Bw1KLA4r777jOr9M2dO7fJ+2qDG80krbv5I6ukuMnAIqZ/P+lx4YUfN2qEdJ43W1If+LFpX5P31rtNPkdmUZFfxwIguOlURV55WdP3q6gUb2WVxE+aKN1uWiJxeuFy0xJTEVKya48ZwWhMdkmxjUcNhElg8fLLL5tV+5YvX+7X/fV+Wp5ibdr739+69ZaITO4unUaNMKWoTc2Nur0tew4AwcXfHjiOyJrZ4bjx9Zc2j5tQ01Sv/PiJRh/vbuF5CwjbwEKzrH/yk5/I3/72N797PixbtszUvFqb7sMfCc3opNdQhC4Q5HaLt7Ky8eeIavlzAAgemlPlTwWYKymp5mNCQv3bL3ztKW181COecwrQvMBi586dkpOTI+PHjzeNpXTTHvmPP/64+bzuCoUWbbWrfSLqbv4Y2i3Z7+TNhqrOnTNXHpp05YuWsY7q0aNF+wcQfAY3sQihik5PMx81ebMu62tXfON9KoYlJ7fqGIGwCyx0DY19+/bJnj17ajftja+JnPq5na2w/XnTdxdfPJ9ZcTpTSvcflNghQxqtQdeh0ZHJBBZAuBjXs5cZuWhM3LiafjhFW7bVu71o87aaqrNBA3w+VkdEBnTpatPRAmFSbqrlWyNHjqx3my5r3K1bt4tub630xCRzhXH03Fmfmdw5z/9VHJGRJonTGR8vVVnZUrR5izijIqXL4oWN7l/r2uddNtDWYwbQcS0YOLjJhce022b85MuleOs2yfF4JGbAZVL+5TEp2bNXkubOlogLUyUNuRxOuWbAoCYDFyAcdNjOm/rG/90x4+ThNR/5vE+nUSOlZOcuKfh0vWmQ5YqPl06jR0mXa642SZyNTYPM6T9AejWYRwUQuib3TpN+nTvLifz8RstOu996k0R06SzF27ZLyd79EtGli+lhkTRzRqOJ4LePrp/wCYSrDr0IWVlVlcx78TnTeMaulU2VlrGuuvU2GZXCVAgQTt46ckh+8v47tu5TL1QmpvaWl268xVwQAaHK3/fvDj1uFxsZKf85b4GtQYW+7H8w4XKCCiAMLRo0ROb2H2CCAbtEOF3yH/OuIagAgiGwUJPT0uUnk6faNlIxvleq/OhyFgoCwpGOKPxmztXSMz7BluBC9/C7efMlLfHSuRdAOOrwgYX68eVTzSiDaumpQB83tmcv+fN1N0p0RIdNLQEQYN07dZKXb75VerUiuNCLFH3ko3Pny+LBQ20/RiCYOYPlKuNn06+UP8xfKPFRUc06Geh99d53j58of7thaasabwEIDb0TEuWNb90uCwcNMV83tXxAXXrfHnHx8rcbb5Glw+2thgNCQYdO3rwUXT3wsW2bZeXB/VLpdovL6byokZZ1ktAf7co+/eT+KdPMaAUANPTJV8fkv7dvkb3ZWeZCxOMV8TaoG4m4cJ5Jio421R86ghrXSAM+IBT5+/4ddIGFpaiiQt798ojsyTpjlj/PLS01SZ46ojGmR0/TYEvr1vskdbb1+AGEpgM52fLx18dkX3a2fH7mtBSVlUuEyykDklNMc61JqWky97IBTKUibBWGemABAIGyf/9+WblypfTv31/uuOMOftGAhEi5KQAACC4EFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAgMACAAB0PIxYAAAA2xBYAAAA2xBYAAAA2xBYAAAA2xBYAAAA2xBYAAAA2xBYAAAA2xBYAAAA2xBYAAAA2xBYAAAA2xBYAAAA2xBYAAAA2xBYAAAA2xBYAAAA2xBYAACA9gksnnjiCRk9erQkJiaaberUqfLee+/ZdzQAACB8Aou0tDR59NFHZefOnbJjxw6ZPXu2XH/99XLgwIHAHSEAAAgaEc258+LFi+t9/etf/9qMYmzZskVGjBhh97EBAIBQDizqcrvdsmLFCikpKTFTIr5UVFSYzVJYWNjSpwQAAKGWvLlv3z6Jj4+X6Oho+cEPfiCrVq2S4cOH+7z/8uXLJSkpqXZLT09v7TEDAIBQCSyGDBkie/bska1bt8q9994rd955pxw8eNDn/ZctWyYFBQW1W0ZGRmuPGQAAhMpUSFRUlAwcONB8PmHCBNm+fbs89thj8tRTT13y/jqyoRsAAAh9re5j4fF46uVQAACA8NWsEQud1liwYIH06dNHioqK5KWXXpK1a9fKBx98ELgjBAAAoRlY5OTkyB133CFnzpwxiZjaLEuDinnz5gXuCAEAQGgGFs8++2zgjgQAAAQ91goBAAC2IbAAAAC2IbAAAAC2IbAAAAC2IbAAAAC2IbAAAAC2IbAAAAC2IbAAAAC2IbAAAAC2IbAAAAC2IbAAAAC2IbAAAAC2IbAAAAC2IbAAAAC2IbAAAAC2IbAAAAC2IbAAAAC2IbAAAAC2IbAAAAAEFgAAoONhxAIAANiGwAIAANiGwAIAANiGwAIAANiGwAIAANiGwAIAANiGwAIAANiGwAIAANiGwAIAANiGwAIAANiGwAIAANiGwAIAANiGwAIAANiGwAIAANiGwAIAANiGwAIAANiGwAIAANiGwAIAANiGwAIAANiGwAIAANiGwAIAANiGwAIAANiGwAIAANiGwAIAANiGwAIAALRPYLF8+XKZNGmSJCQkSEpKiixZskQOHz5s39EAAIDwCSzWrVsn9913n2zZskU++ugjqaqqkquvvlpKSkoCd4QAACBoRDTnzu+//369r59//nkzcrFz506ZMWOG3ccGAABCObBoqKCgwHzs2rWrz/tUVFSYzVJYWNiapwQAAKGYvOnxeOT++++X6dOny8iRIxvNy0hKSqrd0tPTW/qUAAAgVAMLzbXYv3+/vPzyy43eb9myZWZkw9oyMjJa+pQAACAUp0L+/u//Xt5++21Zv369pKWlNXrf6OhoswEAgNDXrMDC6/XKj370I1m1apWsXbtW+vfvH7gjAwAAoR1Y6PTHSy+9JG+88YbpZZGVlWVu19yJ2NjYQB0jAAAIxRyLJ554wuRJzJw5U3r16lW7vfLKK4E7QgAAELpTIQAAAL6wVggAALANgQUAALANgQUAALANgQUAALANgQUAALANgQUAALANgQUAALANgQUAALANgQUAACCwAAAAHQ8jFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYEFgAAwDYR9u0KAILb2czzcnTnV7L1k+1yYne2FHatlPfdn8rgCZdJ3+Fp4opwtfchAh0egQWAsFZRViGfvrxJVv/3u3Jsz3Fzm9PlEK/XK6ccZ2XvG0fMbXFJnWTh9+fIoh9cLakDerbzUQMdl8Orr542VFhYKElJSVJQUCCJiYlt+dQAUM/uNfvkd9/9o5w9dU4cTod4PY2fDp0upwk4/m7ZjXLbv94kkVGR/EYRNgr9fP8mxwJA2NHg4E8PvSg/m/srOZ95vua2JoIK5XF7zP1e+s3rcu+Ef5Kzp8+1wdECwYXAAkDYBRX/70fPyiu/e8N87fEjoLjUPk4dPi0/nvbPBBdAAwQWAMLKW098KG/+zwet3o+72iPnz+TJvyx+VNzVbluODQgFJG8CCBtnvsqWp376gs/vH/BulzNywuf3r5BrJcYRWy+4OPb5cXn1P96Uby+7wfbjBYIRgQWAsPHUP/6l0dGF3nKZdJWUi27/QnZJrMTVCypqeUVeeOQVueauWdKlR2e7DxkIOkyFAAgLuafOyaY3tptRBl86O7pJL0ffepsGFB5xS09J9/k4j8cj7z27JkBHDoR4YLF+/XpZvHixpKamisPhkNWrVwfmyADARh/9ZZ05ZzVXlpw0H3tKH5/30UqRt5/8sFXHB4RtYFFSUiJjxoyRP/7xj4E5IgAIgAMbD/lVUlqXx+uRbDklSdJNYh1xTY6InM/Ka+VRAmGYY7FgwQKzAUAwObTtS1Mm2hznJEuqpFJ6NTJaUZe2A5987YQWHiEQGgKevFlRUWG2up27AKAtud1uKTxX1OzHZUmGOMQhKZLm1/3PZTJiAQQ8eXP58uWmBai1paf7ToACgEBo7hSIqvZWS65kSjfpKVGO6KYf4NAAxndiKBAuAh5YLFu2zPQVt7aMjIxAPyUA1BMRGSGR0c0boM2V0xeqQfybBtGy004JlyhHBcJMwKdCoqOjzQYA7anfyD4mB6I51SAuiZBk6eX3Yy4b07eFRweEDvpYAAgLQy8fJK4Il1/3rfRWyHnJkWRJFZfDv+uvyJhI6TO0dyuPEgjDwKK4uFj27NljNvX111+bz0+erKn1BoCOaMbNU/xe0yNbMsQrXr+rQTRgufLGyX4HLkAoa3ZgsWPHDhk3bpzZ1IMPPmg+//nPfx6I4wMAW4yZOUJSB/YUf3pk6TRIlERLV+nh1741YLnuh9e0/iCBcMyxmDlzZrNrwQGgvWnXze/+6lvym7/7Q5P3neSY7fd+XRFOGXnFMBk+dXArjxAIDeRYAAgbM2+dJlOvmyhOl9PWipOf/vmHLWoXDoQiAgsAYUPf/B94+geSnNbNjDS0foci//DsD6Vnv4tXRAXCFYEFgLDSJSVJ/nPtL6V7WrcWj1zo4zRI+Yc//VBmfWu67ccIBDMCCwBhp0ffZPmf7b81lSLK6fR/GsPhdEj33l3lP9Y8Itd8b1YAjxIITgQWAMJSYrcE+ef/fUB+ufpnMmjCAHObM8JpAoeGXJE1ZaTxXeLk2w/dIH868HsZc9WINj9mIBg4vG1c4qGLkOmaIdreOzExsS2fGgB8+nL317L5zR1yeMcxObbnaykvrRCXyyk9+qXIsMmDZNSVw2Tq9ZMkKjqS3yLCUqGf798Bb+kNAMFg4Lj+ZgPQOkyFAAAA2xBYAAAA27T5VIiV0qFzNQAAIDhY79tNpWa2eWBRVFRkPqanp7f1UwMAABvexzWJs8NUhXg8HsnMzJSEhARa4AIAECQ0XNCgIjU1VZxOZ8cJLAAAQOgieRMAANiGwAIAANiGwAIAANiGwAIAANiGwAIAANiGwAIAANiGwAIAAIhd/n+L3QapFjonIgAAAABJRU5ErkJggg==", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "R = ex_rg.dancing_man()\n", - "R.draw()" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "f9ff166a", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[7, 6, 2, 1, 0]\n" - ] - } - ], - "source": [ - "# Get a path that continues upward in the reeb grpah until it hits a local max \n", - "\n", - "def upward_path(R, v): \n", - " path = [v]\n", - " while R.up_degree(path[-1]) > 0: \n", - " s = next(R.successors(path[-1]))\n", - " path.append(s)\n", - " \n", - " \n", - " return path\n", - "\n", - "v = 7 # I know this is a local min already\n", - "path = upward_path(R, v)\n", - "print(path)" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "1c2d8150", - "metadata": {}, - "outputs": [], - "source": [ - "R.remove_path_from(path)" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "13eebf46", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "R.draw()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "3eba6dd1", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "7" - ] - }, - "execution_count": 24, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "R.sorted_vertices()[0]" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "c2ba646f", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Vertex: 7, f(v) = 1, degree = 0\n", - "Vertex: 5, f(v) = 4, degree = 0\n", - "Vertex: 6, f(v) = 4, degree = 1\n", - "Vertex: 2, f(v) = 5, degree = 2\n", - "Vertex: 3, f(v) = 5, degree = 1\n", - "Vertex: 1, f(v) = 6, degree = 2\n", - "Vertex: 4, f(v) = 6, degree = 1\n", - "Vertex: 0, f(v) = 7, degree = 1\n", - "[[1 7 0 0]\n", - " [4 7 1 1]\n", - " [4 7 2 2]\n", - " [5 7 3 3]\n", - " [5 7 4 4]\n", - " [6 7 5 5]\n", - " [6 6 6 6]\n", - " [7 7 7 7]]\n" - ] - } - ], - "source": [ - "branches = [] \n", - "\n", - "for v in R.sorted_vertices(): \n", - " print(f\"Vertex: {v}, f(v) = {R.f[v]}, degree = {R.down_degree(v)}\")\n", - " \n", - " # get a maximal path upward from v \n", - " path = upward_path(R,v)\n", - " \n", - " start_f = R.f[path[0]]\n", - " end_f = R.f[path[-1]]\n", - " branches.append((start_f, end_f, len(branches), len(branches)))\n", - " \n", - "branches = np.array(branches)\n", - "print(branches)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "bef13a93", - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "cereeberus", - "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": "3.12.12" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/Notebooks_Unused/sandbox_fixing_LBMs.ipynb b/Notebooks_Unused/sandbox_fixing_LBMs.ipynb deleted file mode 100644 index 6d950ab..0000000 --- a/Notebooks_Unused/sandbox_fixing_LBMs.ipynb +++ /dev/null @@ -1,242 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "\n", - "import networkx as nx\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "import pandas as pd \n", - "from scipy.linalg import block_diag\n", - "\n", - "from cereeberus import EmbeddedGraph, ReebGraph\n", - "import cereeberus.data.ex_mappergraphs as ex_mg\n", - "import cereeberus.data.ex_reebgraphs as ex_rg\n", - "# from cereeberus.data.ex_mergetrees import randomMergeTree\n", - "\n", - "from cereeberus.distance.interleave import Interleave\n", - "from cereeberus.distance.labeled_blocks import LabeledBlockMatrix as LBM \n", - "from cereeberus.distance.labeled_blocks import LabeledMatrix as LM\n", - "from cereeberus.compute.unionfind import UnionFind" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "Mat1 = LM([[0, 1, 2], [-3, -4, -5]], ['u', 'v'], ['a', 'b', 'c'])\n", - "\n", - "# 3 x 3\n", - "Mat2 = LM([[0, 1], [1, 0], [0,0]], ['a', 'b', 'c'], ['x', 'y', 'z'])\n", - "\n", - "# 2 x 2\n", - "Mat4 = LM([[0, 1], [1, 0]], ['a', 'b'], ['x', 'y'])\n", - "\n", - "# 3 x 3\n", - "Mat5 =LM([[0, 1], [1, 0], [3,-2]], ['a', 'c', 'b'], ['x', 'y', 'z']) \n", - "\n", - "# 2 x 2 \n", - "Mat6 = LM([[0, 1], [1, 0]], ['u', 'v'], ['x', 'y'])\n", - "Mat7 = LM([[0, 1], [1, 0]], ['a','b'], ['u', 'v'])" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "cols_dict = {1: ['a','b'], 2: ['c','d','e']}\n", - "rows_dict = {0: ['u'], 1: ['v','w'], 2: ['x']}\n", - "map_dict = {'a': 'v', 'b':'v', 'c': 'x', 'd':'x', 'e':'x'}\n", - "lbm = LBM(map_dict, rows_dict, cols_dict)\n", - "\n", - "# A second example with rows and columns switched\n", - "cols_dict = {0: ['u'], 1: ['v','w'], 2: ['x']}\n", - "rows_dict = {0: ['x','y'], 1: ['z','a','b'], 2: ['c'], 3: ['d','e']}\n", - "map_dict = {'u': 'y', 'v':'z', 'w': 'b', 'x':'c'}\n", - "lbm2 = LBM(map_dict, rows_dict, cols_dict)" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "LabeledBlockMatrix(matrices={0: LabeledMatrix(\n", - "array=\n", - "[[0.]\n", - " [1.]], \n", - "rows=['x', 'y'], \n", - "cols=['u']), 1: LabeledMatrix(\n", - "array=\n", - "[[1. 0.]\n", - " [0. 0.]\n", - " [0. 1.]], \n", - "rows=['z', 'a', 'b'], \n", - "cols=['v', 'w']), 2: LabeledMatrix(\n", - "array=\n", - "[[1.]], \n", - "rows=['c'], \n", - "cols=['x']), 3: LabeledMatrix(\n", - "array=\n", - "[], \n", - "rows=['d', 'e'], \n", - "cols=[])})" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "lbm2" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "1.0" - ] - }, - "execution_count": 5, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "lbm2.max()" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "1.0" - ] - }, - "execution_count": 6, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "lbm.max()" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n" - ] - }, - { - "data": { - "image/png": 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", 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "lbm.draw()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "base", - "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": "3.12.7" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/Notebooks_Unused/sandbox_fixing_optimization.ipynb b/Notebooks_Unused/sandbox_fixing_optimization.ipynb deleted file mode 100644 index 8f6cc54..0000000 --- a/Notebooks_Unused/sandbox_fixing_optimization.ipynb +++ /dev/null @@ -1,100 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": null, - "id": "3d7c8bc8", - "metadata": {}, - "outputs": [], - "source": [ - "%reload_ext autoreload\n", - "%autoreload 2" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "a632ce73", - "metadata": {}, - "outputs": [], - "source": [ - "from cereeberus import Interleave, MapperGraph, Assignment\n", - "import cereeberus.data.ex_mappergraphs as ex_mg\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "import networkx as nx" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "44844a7b", - "metadata": {}, - "outputs": [], - "source": [ - "mg1 = ex_mg.line(0, 20)\n", - "mg2 = ex_mg.torus(0, 2, 17, 18)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "0657e22b", - "metadata": {}, - "outputs": [], - "source": [ - "myInt = Interleave(mg1, mg2)\n", - "myInt.fit(verbose=True)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "6a5a4786", - "metadata": {}, - "outputs": [], - "source": [ - "from cereeberus import ReebGraph\n", - "import numpy as np" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "88cb17ae", - "metadata": {}, - "outputs": [], - "source": [ - "# Example point cloud (you can replace this with your own)\n", - "points = np.random.rand(500, 3) # 500 points in 3D\n", - "\n", - "# Define a scalar function on these points — say, height (z-coordinate)\n", - "values = points[:, 2]\n", - "\n", - "# Build and compute the Reeb graph\n", - "rg = ReebGraph()\n" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "interleavingenv", - "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": "3.12.3" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/Notebooks_Unused/sandbox_liz.ipynb b/Notebooks_Unused/sandbox_liz.ipynb deleted file mode 100644 index 840c30c..0000000 --- a/Notebooks_Unused/sandbox_liz.ipynb +++ /dev/null @@ -1,1778 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Sandbox for testing purposes" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "%reload_ext autoreload\n", - "%autoreload 2" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [], - "source": [ - "import networkx as nx\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "import pandas as pd \n", - "from scipy.linalg import block_diag\n", - "\n", - "from cereeberus import EmbeddedGraph, ReebGraph\n", - "import cereeberus.data.ex_mappergraphs as ex_mg\n", - "import cereeberus.data.ex_reebgraphs as ex_rg\n", - "import cereeberus.data.ex_graphs as ex_g\n", - "# from cereeberus.data.ex_mergetrees import randomMergeTree\n", - "\n", - "import cereeberus.distance.ilp as ilp\n", - "import pulp\n", - "\n", - "\n", - "from cereeberus.distance.interleave import Interleave, Assignment\n", - "\n", - "\n", - "from cereeberus.distance.labeled_blocks import LabeledBlockMatrix as LBM \n", - "from cereeberus.distance.labeled_blocks import LabeledMatrix as LM\n", - "from cereeberus.compute.unionfind import UnionFind" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "ename": "AttributeError", - "evalue": "module 'pulp' has no attribute 'CBC_CMD'", - "output_type": "error", - "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mAttributeError\u001b[0m Traceback (most recent call last)", - "Cell \u001b[0;32mIn[9], line 8\u001b[0m\n\u001b[1;32m 6\u001b[0m L \u001b[38;5;241m=\u001b[39m ex_mg\u001b[38;5;241m.\u001b[39mline(\u001b[38;5;241m0\u001b[39m, \u001b[38;5;241m4\u001b[39m\u001b[38;5;241m+\u001b[39mh)\n\u001b[1;32m 7\u001b[0m myAssgn_TL \u001b[38;5;241m=\u001b[39m Assignment(L,T, n \u001b[38;5;241m=\u001b[39m n)\n\u001b[0;32m----> 8\u001b[0m myAssgn_TL\u001b[38;5;241m.\u001b[39moptimize(pulp_solver \u001b[38;5;241m=\u001b[39m pulp\u001b[38;5;241m.\u001b[39mCBC_CMD(msg\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0\u001b[39m))\n", - "\u001b[0;31mAttributeError\u001b[0m: module 'pulp' has no attribute 'CBC_CMD'" - ] - } - ], - "source": [ - "h = 16 # height of the torus \n", - "n = 3 \n", - "# Correct interleaving distance should be ceiling of h/4\n", - "true_interleaving = np.ceil(h/4)\n", - "T = ex_mg.torus(0, 2, 2+h, 4+h, delta = 1, seed = 17)\n", - "L = ex_mg.line(0, 4+h)\n", - "myAssgn_TL = Assignment(L,T, n = n)\n", - "myAssgn_TL.optimize(pulp_solver = pulp.CBC_CMD(msg=0))\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "test\n", - "maybe this?\n" - ] - } - ], - "source": [ - "from IPython.utils import io\n", - "\n", - "with io.capture_output() as captured:\n", - " print('Hello, world!')\n", - "\n", - "print('test')\n", - "print('maybe this?')" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [], - "source": [ - "import sys\n", - "import os\n", - "def _blockPrint():\n", - " sys.stdout = open(os.devnull, 'w')\n", - "\n", - "# Restore Printing\n", - "def _enablePrint():\n", - " sys.stdout = sys.__stdout__\n" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "This should print\n", - "This should print again\n", - "This will print normally again\n", - "Welcome to the CBC MILP Solver \n", - "Version: 2.10.3 \n", - "Build Date: Dec 15 2019 \n", - "\n", - "command line - /opt/anaconda3/lib/python3.12/site-packages/pulp/solverdir/cbc/osx/64/cbc /var/folders/lm/dn75vz_d72b1cntn3ncjj10c0000gn/T/20041d82c4b641849bea0a80a04ab2f5-pulp.mps -timeMode elapsed -branch -printingOptions all -solution /var/folders/lm/dn75vz_d72b1cntn3ncjj10c0000gn/T/20041d82c4b641849bea0a80a04ab2f5-pulp.sol (default strategy 1)\n", - "At line 2 NAME MODEL\n", - "At line 3 ROWS\n", - "At line 1648 COLUMNS\n", - "At line 5522 RHS\n", - "At line 7166 BOUNDS\n", - "At line 7763 ENDATA\n", - "Problem MODEL has 1643 rows, 596 columns and 2680 elements\n", - "Coin0008I MODEL read with 0 errors\n", - "Option for timeMode changed from cpu to elapsed\n", - "Continuous objective value is 0 - 0.00 seconds\n", - "Cgl0003I 0 fixed, 9 tightened bounds, 2 strengthened rows, 0 substitutions\n", - "Cgl0003I 0 fixed, 0 tightened bounds, 11 strengthened rows, 0 substitutions\n", - "Cgl0003I 0 fixed, 0 tightened bounds, 11 strengthened rows, 0 substitutions\n", - "Cgl0003I 0 fixed, 0 tightened bounds, 3 strengthened rows, 0 substitutions\n", - "Cgl0003I 0 fixed, 0 tightened bounds, 3 strengthened rows, 0 substitutions\n", - "Cgl0004I processed model has 43 rows, 22 columns (22 integer (18 of which binary)) and 120 elements\n", - "Cutoff increment increased from 1e-05 to 0.9999\n", - "Cbc0038I Initial state - 0 integers unsatisfied sum - 6.66134e-15\n", - "Cbc0038I Solution found of 1\n", - "Cbc0038I Cleaned solution of 1\n", - "Cbc0038I Before mini branch and bound, 22 integers at bound fixed and 0 continuous of which 3 were internal integer and 0 internal continuous\n", - "Cbc0038I Mini branch and bound did not improve solution (0.02 seconds)\n", - "Cbc0038I After 0.02 seconds - Feasibility pump exiting with objective of 1 - took 0.00 seconds\n", - "Cbc0012I Integer solution of 1 found by feasibility pump after 0 iterations and 0 nodes (0.02 seconds)\n", - "Cbc0001I Search completed - best objective 1, took 0 iterations and 0 nodes (0.02 seconds)\n", - "Cbc0035I Maximum depth 0, 0 variables fixed on reduced cost\n", - "Cuts at root node changed objective from 1 to 1\n", - "Probing was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "Gomory was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "Knapsack was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "Clique was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "MixedIntegerRounding2 was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "FlowCover was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "TwoMirCuts was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "ZeroHalf was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "\n", - "Result - Optimal solution found\n", - "\n", - "Objective value: 1.00000000\n", - "Enumerated nodes: 0\n", - "Total iterations: 0\n", - "Time (CPU seconds): 0.01\n", - "Time (Wallclock seconds): 0.02\n", - "\n", - "Option for printingOptions changed from normal to all\n", - "Total time (CPU seconds): 0.01 (Wallclock seconds): 0.03\n", - "\n", - "Welcome to the CBC MILP Solver \n", - "Version: 2.10.3 \n", - "Build Date: Dec 15 2019 \n", - "\n", - "command line - /opt/anaconda3/lib/python3.12/site-packages/pulp/solverdir/cbc/osx/64/cbc /var/folders/lm/dn75vz_d72b1cntn3ncjj10c0000gn/T/68327286bf474d45bf6fbad9c7353672-pulp.mps -timeMode elapsed -branch -printingOptions all -solution /var/folders/lm/dn75vz_d72b1cntn3ncjj10c0000gn/T/68327286bf474d45bf6fbad9c7353672-pulp.sol (default strategy 1)\n", - "At line 2 NAME MODEL\n", - "At line 3 ROWS\n", - "At line 1648 COLUMNS\n", - "At line 5522 RHS\n", - "At line 7166 BOUNDS\n", - "At line 7763 ENDATA\n", - "Problem MODEL has 1643 rows, 596 columns and 2680 elements\n", - "Coin0008I MODEL read with 0 errors\n", - "Option for timeMode changed from cpu to elapsed\n", - "Continuous objective value is 0 - 0.00 seconds\n", - "Cgl0003I 0 fixed, 9 tightened bounds, 2 strengthened rows, 0 substitutions\n", - "Cgl0003I 0 fixed, 0 tightened bounds, 11 strengthened rows, 0 substitutions\n", - "Cgl0003I 0 fixed, 0 tightened bounds, 11 strengthened rows, 0 substitutions\n", - "Cgl0003I 0 fixed, 0 tightened bounds, 3 strengthened rows, 0 substitutions\n", - "Cgl0003I 0 fixed, 0 tightened bounds, 3 strengthened rows, 0 substitutions\n", - "Cgl0004I processed model has 43 rows, 22 columns (22 integer (18 of which binary)) and 120 elements\n", - "Cutoff increment increased from 1e-05 to 0.9999\n", - "Cbc0038I Initial state - 0 integers unsatisfied sum - 6.66134e-15\n", - "Cbc0038I Solution found of 1\n", - "Cbc0038I Cleaned solution of 1\n", - "Cbc0038I Before mini branch and bound, 22 integers at bound fixed and 0 continuous of which 3 were internal integer and 0 internal continuous\n", - "Cbc0038I Mini branch and bound did not improve solution (0.03 seconds)\n", - "Cbc0038I After 0.03 seconds - Feasibility pump exiting with objective of 1 - took 0.00 seconds\n", - "Cbc0012I Integer solution of 1 found by feasibility pump after 0 iterations and 0 nodes (0.03 seconds)\n", - "Cbc0001I Search completed - best objective 1, took 0 iterations and 0 nodes (0.03 seconds)\n", - "Cbc0035I Maximum depth 0, 0 variables fixed on reduced cost\n", - "Cuts at root node changed objective from 1 to 1\n", - "Probing was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "Gomory was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "Knapsack was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "Clique was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "MixedIntegerRounding2 was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "FlowCover was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "TwoMirCuts was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "ZeroHalf was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "\n", - "Result - Optimal solution found\n", - "\n", - "Objective value: 1.00000000\n", - "Enumerated nodes: 0\n", - "Total iterations: 0\n", - "Time (CPU seconds): 0.01\n", - "Time (Wallclock seconds): 0.03\n", - "\n", - "Option for printingOptions changed from normal to all\n", - "Total time (CPU seconds): 0.01 (Wallclock seconds): 0.04\n", - "\n", - "Welcome to the CBC MILP Solver \n", - "Version: 2.10.3 \n", - "Build Date: Dec 15 2019 \n", - "\n", - "command line - /opt/anaconda3/lib/python3.12/site-packages/pulp/solverdir/cbc/osx/64/cbc /var/folders/lm/dn75vz_d72b1cntn3ncjj10c0000gn/T/01885074d39645589b6bf77c8089094a-pulp.mps -timeMode elapsed -branch -printingOptions all -solution /var/folders/lm/dn75vz_d72b1cntn3ncjj10c0000gn/T/01885074d39645589b6bf77c8089094a-pulp.sol (default strategy 1)\n", - "At line 2 NAME MODEL\n", - "At line 3 ROWS\n", - "At line 1648 COLUMNS\n", - "At line 5522 RHS\n", - "At line 7166 BOUNDS\n", - "At line 7763 ENDATA\n", - "Problem MODEL has 1643 rows, 596 columns and 2680 elements\n", - "Coin0008I MODEL read with 0 errors\n", - "Option for timeMode changed from cpu to elapsed\n", - "Continuous objective value is 0 - 0.00 seconds\n", - "Cgl0003I 0 fixed, 9 tightened bounds, 2 strengthened rows, 0 substitutions\n", - "Cgl0003I 0 fixed, 0 tightened bounds, 11 strengthened rows, 0 substitutions\n", - "Cgl0003I 0 fixed, 0 tightened bounds, 11 strengthened rows, 0 substitutions\n", - "Cgl0003I 0 fixed, 0 tightened bounds, 3 strengthened rows, 0 substitutions\n", - "Cgl0003I 0 fixed, 0 tightened bounds, 3 strengthened rows, 0 substitutions\n", - "Cgl0004I processed model has 43 rows, 22 columns (22 integer (18 of which binary)) and 120 elements\n", - "Cutoff increment increased from 1e-05 to 0.9999\n", - "Cbc0038I Initial state - 0 integers unsatisfied sum - 6.66134e-15\n", - "Cbc0038I Solution found of 1\n", - "Cbc0038I Cleaned solution of 1\n", - "Cbc0038I Before mini branch and bound, 22 integers at bound fixed and 0 continuous of which 3 were internal integer and 0 internal continuous\n", - "Cbc0038I Mini branch and bound did not improve solution (0.03 seconds)\n", - "Cbc0038I After 0.03 seconds - Feasibility pump exiting with objective of 1 - took 0.00 seconds\n", - "Cbc0012I Integer solution of 1 found by feasibility pump after 0 iterations and 0 nodes (0.03 seconds)\n", - "Cbc0001I Search completed - best objective 1, took 0 iterations and 0 nodes (0.03 seconds)\n", - "Cbc0035I Maximum depth 0, 0 variables fixed on reduced cost\n", - "Cuts at root node changed objective from 1 to 1\n", - "Probing was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "Gomory was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "Knapsack was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "Clique was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "MixedIntegerRounding2 was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "FlowCover was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "TwoMirCuts was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "ZeroHalf was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "\n", - "Result - Optimal solution found\n", - "\n", - "Objective value: 1.00000000\n", - "Enumerated nodes: 0\n", - "Total iterations: 0\n", - "Time (CPU seconds): 0.01\n", - "Time (Wallclock seconds): 0.03\n", - "\n", - "Option for printingOptions changed from normal to all\n", - "Total time (CPU seconds): 0.01 (Wallclock seconds): 0.05\n", - "\n", - "testing bueller\n" - ] - } - ], - "source": [ - "print('This should print')\n", - "_blockPrint()\n", - "\n", - "print('This should not print')\n", - "_enablePrint()\n", - "print('This should print again')" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [], - "source": [ - "import os, sys\n", - "\n", - "class HiddenPrints:\n", - " def __enter__(self):\n", - " self._original_stdout = sys.stdout\n", - " sys.stdout = open(os.devnull, 'w')\n", - "\n", - " def __exit__(self, exc_type, exc_val, exc_tb):\n", - " sys.stdout.close()\n", - " sys.stdout = self._original_stdout\n", - " \n", - "with HiddenPrints():\n", - " # Code that prints a lot\n", - " print(\"This will not print\")\n", - "\n", - "print(\"This will print normally again\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [], - "source": [ - "\n", - "Loss = myAssgn_TL.loss(verbose = True)\n", - "print('Loss = ', Loss)\n", - "print('n = ', n)\n", - "print(\"\\nComputed distance Loss = \", Loss + n)\n", - "print(\"True interleaving distance = \", true_interleaving)" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [], - "source": [ - "myInt = Interleave(L, T)\n", - "# myInt.phi()" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [], - "source": [ - "search_data = myInt.fit(verbose=True)" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "{1: 3.0, 2: 2.0, 4: -0.0, 3: 1.0}" - ] - }, - "execution_count": 8, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "search_data" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "4" - ] - }, - "execution_count": 9, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "myInt.n" - ] - }, - { - "cell_type": "code", - "execution_count": 49, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Welcome to the CBC MILP Solver \n", - "Version: 2.10.3 \n", - "Build Date: Dec 15 2019 \n", - "\n", - "command line - /opt/anaconda3/lib/python3.12/site-packages/pulp/solverdir/cbc/osx/64/cbc /var/folders/lm/dn75vz_d72b1cntn3ncjj10c0000gn/T/dbf45bac007d4e5a9602c884a58cd109-pulp.mps -timeMode elapsed -branch -printingOptions all -solution /var/folders/lm/dn75vz_d72b1cntn3ncjj10c0000gn/T/dbf45bac007d4e5a9602c884a58cd109-pulp.sol (default strategy 1)\n", - "At line 2 NAME MODEL\n", - "At line 3 ROWS\n", - "At line 1648 COLUMNS\n", - "At line 5522 RHS\n", - "At line 7166 BOUNDS\n", - "At line 7763 ENDATA\n", - "Problem MODEL has 1643 rows, 596 columns and 2680 elements\n", - "Coin0008I MODEL read with 0 errors\n", - "Option for timeMode changed from cpu to elapsed\n", - "Continuous objective value is 0 - 0.00 seconds\n", - "Cgl0003I 0 fixed, 9 tightened bounds, 2 strengthened rows, 0 substitutions\n", - "Cgl0003I 0 fixed, 0 tightened bounds, 11 strengthened rows, 0 substitutions\n", - "Cgl0003I 0 fixed, 0 tightened bounds, 11 strengthened rows, 0 substitutions\n", - "Cgl0003I 0 fixed, 0 tightened bounds, 3 strengthened rows, 0 substitutions\n", - "Cgl0003I 0 fixed, 0 tightened bounds, 3 strengthened rows, 0 substitutions\n", - "Cgl0004I processed model has 43 rows, 22 columns (22 integer (18 of which binary)) and 120 elements\n", - "Cutoff increment increased from 1e-05 to 0.9999\n", - "Cbc0038I Initial state - 0 integers unsatisfied sum - 6.66134e-15\n", - "Cbc0038I Solution found of 1\n", - "Cbc0038I Cleaned solution of 1\n", - "Cbc0038I Before mini branch and bound, 22 integers at bound fixed and 0 continuous of which 3 were internal integer and 0 internal continuous\n", - "Cbc0038I Mini branch and bound did not improve solution (0.01 seconds)\n", - "Cbc0038I After 0.01 seconds - Feasibility pump exiting with objective of 1 - took 0.00 seconds\n", - "Cbc0012I Integer solution of 1 found by feasibility pump after 0 iterations and 0 nodes (0.01 seconds)\n", - "Cbc0001I Search completed - best objective 1, took 0 iterations and 0 nodes (0.01 seconds)\n", - "Cbc0035I Maximum depth 0, 0 variables fixed on reduced cost\n", - "Cuts at root node changed objective from 1 to 1\n", - "Probing was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "Gomory was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "Knapsack was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "Clique was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "MixedIntegerRounding2 was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "FlowCover was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "TwoMirCuts was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "ZeroHalf was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "\n", - "Result - Optimal solution found\n", - "\n", - "Objective value: 1.00000000\n", - "Enumerated nodes: 0\n", - "Total iterations: 0\n", - "Time (CPU seconds): 0.01\n", - "Time (Wallclock seconds): 0.01\n", - "\n", - "Option for printingOptions changed from normal to all\n", - "Total time (CPU seconds): 0.01 (Wallclock seconds): 0.02\n", - "\n", - "The optimized loss is: 1.0\n", - "Status: Optimal\n" - ] - } - ], - "source": [ - "# map_dict, loss_val = ilp.solve_ilp(myAssgn_TL);\n", - "out = ilp.solve_ilp(myAssgn_TL, verbose = True)" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "out[0]['phi_0_V'].draw(filltype = 'nan')" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "[-2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "M = myAssgn_TL.get_interleaving_map('phi', 'n', 'V')\n", - "\n", - "M.get_all_block_indices()" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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"outputs": [ - { - "data": { - "text/plain": [ - "dict_keys(['Phi_0_V', 'Phi_0_E', 'Phi_n_V', 'Phi_n_E', 'Psi_0_V', 'Psi_0_E', 'Psi_n_V', 'Psi_n_E'])" - ] - }, - "execution_count": 7, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "map_dict.keys()" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 14, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, ax = plt.subplots(1, 2, figsize=(12, 6))\n", - "map_dict['Phi_0_E'].draw(ax[0],)\n", - "myAssgn_TL.phi('0', 'E').draw(ax[1],)\n" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "4.0" - ] - }, - "execution_count": 22, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "F = ex_mg.line(0,10)\n", - "G = ex_mg.torus(0,1,9,10)\n", - "\n", - "\n", - "myInt = Assignment(F, G, n = 0, initialize_random_maps=True, seed = 17)\n", - "\n", - "myInt.loss()\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Welcome to the CBC MILP Solver \n", - "Version: 2.10.3 \n", - "Build Date: Dec 15 2019 \n", - "\n", - "command line - /opt/anaconda3/lib/python3.12/site-packages/pulp/solverdir/cbc/osx/64/cbc /var/folders/lm/dn75vz_d72b1cntn3ncjj10c0000gn/T/8cd2befe8aff4df88df018a8d9ac4de6-pulp.mps -timeMode elapsed -branch -printingOptions all -solution /var/folders/lm/dn75vz_d72b1cntn3ncjj10c0000gn/T/8cd2befe8aff4df88df018a8d9ac4de6-pulp.sol (default strategy 1)\n", - "At line 2 NAME MODEL\n", - "At line 3 ROWS\n", - "At line 992 COLUMNS\n", - "At line 3566 RHS\n", - "At line 4554 BOUNDS\n", - "At line 4931 ENDATA\n", - "Problem MODEL has 987 rows, 376 columns and 1820 elements\n", - "Coin0008I MODEL read with 0 errors\n", - "Option for timeMode changed from cpu to elapsed\n", - "Continuous objective value is 0 - 0.00 seconds\n", - "Cgl0003I 0 fixed, 17 tightened bounds, 4 strengthened rows, 0 substitutions\n", - "Cgl0003I 0 fixed, 0 tightened bounds, 17 strengthened rows, 0 substitutions\n", - "Cgl0003I 0 fixed, 0 tightened bounds, 17 strengthened rows, 0 substitutions\n", - "Cgl0003I 0 fixed, 0 tightened bounds, 6 strengthened rows, 0 substitutions\n", - "Cgl0003I 0 fixed, 0 tightened bounds, 4 strengthened rows, 0 substitutions\n", - "Cgl0003I 0 fixed, 0 tightened bounds, 1 strengthened rows, 0 substitutions\n", - "Cgl0004I processed model has 75 rows, 34 columns (34 integer (22 of which binary)) and 192 elements\n", - "Cutoff increment increased from 1e-05 to 0.9999\n", - "Cbc0038I Initial state - 23 integers unsatisfied sum - 11.25\n", - "Cbc0038I Pass 1: suminf. 0.50000 (1) obj. 2 iterations 36\n", - "Cbc0038I Solution found of 2\n", - "Cbc0038I Branch and bound needed to clear up 1 general integers\n", - "Cbc0038I Full problem 75 rows 34 columns, reduced to 0 rows 0 columns\n", - "Cbc0038I Cleaned solution of 2\n", - "Cbc0038I Before mini branch and bound, 0 integers at bound fixed and 0 continuous\n", - "Cbc0038I Full problem 75 rows 34 columns, reduced to 75 rows 34 columns\n", - "Cbc0038I Mini branch and bound did not improve solution (0.01 seconds)\n", - "Cbc0038I Round again with cutoff of 1.00009\n", - "Cbc0038I Reduced cost fixing fixed 1 variables on major pass 2\n", - "Cbc0038I Pass 2: suminf. 3.10000 (14) obj. 1 iterations 14\n", - "Cbc0038I Pass 3: suminf. 5.43056 (17) obj. 1 iterations 19\n", - "Cbc0038I Pass 4: suminf. 5.37500 (17) obj. 1 iterations 4\n", - "Cbc0038I Pass 5: suminf. 3.60000 (15) obj. 1 iterations 18\n", - "Cbc0038I Pass 6: suminf. 3.10000 (14) obj. 1 iterations 3\n", - "Cbc0038I Pass 7: suminf. 4.90000 (19) obj. 1 iterations 6\n", - "Cbc0038I Pass 8: suminf. 3.60000 (15) obj. 1 iterations 4\n", - "Cbc0038I Pass 9: suminf. 3.88750 (15) obj. 1 iterations 6\n", - "Cbc0038I Pass 10: suminf. 3.98750 (15) obj. 1 iterations 9\n", - "Cbc0038I Pass 11: suminf. 7.19167 (21) obj. 1 iterations 14\n", - "Cbc0038I Pass 12: suminf. 4.80417 (17) obj. 1 iterations 9\n", - "Cbc0038I Pass 13: suminf. 3.60000 (15) obj. 1 iterations 4\n", - "Cbc0038I Pass 14: suminf. 4.81667 (16) obj. 1 iterations 9\n", - "Cbc0038I Pass 15: suminf. 6.52188 (19) obj. 1 iterations 11\n", - "Cbc0038I Pass 16: suminf. 4.05417 (15) obj. 1 iterations 9\n", - "Cbc0038I Pass 17: suminf. 3.10000 (14) obj. 1 iterations 3\n", - "Cbc0038I Pass 18: suminf. 5.43056 (17) obj. 1 iterations 19\n", - "Cbc0038I Pass 19: suminf. 5.37500 (17) obj. 1 iterations 4\n", - "Cbc0038I Pass 20: suminf. 3.10000 (14) obj. 1 iterations 15\n", - "Cbc0038I Pass 21: suminf. 5.73854 (15) obj. 1 iterations 9\n", - "Cbc0038I Pass 22: suminf. 3.28750 (14) obj. 1 iterations 9\n", - "Cbc0038I Pass 23: suminf. 3.10000 (14) obj. 1 iterations 1\n", - "Cbc0038I Pass 24: suminf. 5.43056 (17) obj. 1 iterations 19\n", - "Cbc0038I Pass 25: suminf. 5.37500 (17) obj. 1 iterations 4\n", - "Cbc0038I Pass 26: suminf. 3.90000 (17) obj. 1 iterations 19\n", - "Cbc0038I Pass 27: suminf. 3.60000 (15) obj. 1 iterations 3\n", - "Cbc0038I Pass 28: suminf. 3.10000 (14) obj. 1 iterations 1\n", - "Cbc0038I Pass 29: suminf. 5.43056 (17) obj. 1 iterations 19\n", - "Cbc0038I Pass 30: suminf. 5.37500 (17) obj. 1 iterations 4\n", - "Cbc0038I Pass 31: suminf. 3.28750 (14) obj. 1 iterations 14\n", - "Cbc0038I No solution found this major pass\n", - "Cbc0038I Before mini branch and bound, 7 integers at bound fixed and 0 continuous of which 6 were internal integer and 0 internal continuous\n", - "Cbc0038I Mini branch and bound did not improve solution (0.04 seconds)\n", - "Cbc0038I After 0.04 seconds - Feasibility pump exiting with objective of 2 - took 0.03 seconds\n", - "Cbc0012I Integer solution of 2 found by feasibility pump after 0 iterations and 0 nodes (0.04 seconds)\n", - "Cbc0006I The LP relaxation is infeasible or too expensive\n", - "Cbc0013I At root node, 0 cuts changed objective from 1 to 1 in 1 passes\n", - "Cbc0014I Cut generator 0 (Probing) - 1 row cuts average 0.0 elements, 2 column cuts (2 active) in 0.000 seconds - new frequency is 1\n", - "Cbc0014I Cut generator 1 (Gomory) - 0 row cuts average 0.0 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is -100\n", - "Cbc0014I Cut generator 2 (Knapsack) - 0 row cuts average 0.0 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is -100\n", - "Cbc0014I Cut generator 3 (Clique) - 0 row cuts average 0.0 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is -100\n", - "Cbc0014I Cut generator 4 (MixedIntegerRounding2) - 0 row cuts average 0.0 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is -100\n", - "Cbc0014I Cut generator 5 (FlowCover) - 0 row cuts average 0.0 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is -100\n", - "Cbc0014I Cut generator 6 (TwoMirCuts) - 0 row cuts average 0.0 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is -100\n", - "Cbc0014I Cut generator 7 (ZeroHalf) - 0 row cuts average 0.0 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is -100\n", - "Cbc0001I Search completed - best objective 2, took 0 iterations and 0 nodes (0.04 seconds)\n", - "Cbc0035I Maximum depth 0, 0 variables fixed on reduced cost\n", - "Cuts at root node changed objective from 1 to 1\n", - "Probing was tried 1 times and created 3 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "Gomory was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "Knapsack was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "Clique was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "MixedIntegerRounding2 was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "FlowCover was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "TwoMirCuts was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "ZeroHalf was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "\n", - "Result - Optimal solution found\n", - "\n", - "Objective value: 2.00000000\n", - "Enumerated nodes: 0\n", - "Total iterations: 0\n", - "Time (CPU seconds): 0.04\n", - "Time (Wallclock seconds): 0.04\n", - "\n", - "Option for printingOptions changed from normal to all\n", - "Total time (CPU seconds): 0.04 (Wallclock seconds): 0.04\n", - "\n" - ] - }, - { - "data": { - "text/plain": [ - "2.0" - ] - }, - "execution_count": 24, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "myInt.optimize()" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "2.0" - ] - }, - "execution_count": 5, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "myInt.loss()" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(
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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "myInt.draw_all_phi()" - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "6.0" - ] - }, - "execution_count": 25, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "F = ex_mg.interleave_example_A()\n", - "G = ex_mg.interleave_example_B()\n", - "\n", - "\n", - "myInt = Assignment(F, G, n = 1, initialize_random_maps=True, seed = 17)\n", - "\n", - "myInt.loss()\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Welcome to the CBC MILP Solver \n", - "Version: 2.10.3 \n", - "Build Date: Dec 15 2019 \n", - "\n", - "command line - /opt/anaconda3/lib/python3.12/site-packages/pulp/solverdir/cbc/osx/64/cbc /var/folders/lm/dn75vz_d72b1cntn3ncjj10c0000gn/T/8423cd8c162b414e8aa48938bd65a2b1-pulp.mps -timeMode elapsed -branch -printingOptions all -solution /var/folders/lm/dn75vz_d72b1cntn3ncjj10c0000gn/T/8423cd8c162b414e8aa48938bd65a2b1-pulp.sol (default strategy 1)\n", - "At line 2 NAME MODEL\n", - "At line 3 ROWS\n", - "At line 2812 COLUMNS\n", - "At line 11778 RHS\n", - "At line 14586 BOUNDS\n", - "At line 15713 ENDATA\n", - "Problem MODEL has 2807 rows, 1126 columns and 6712 elements\n", - "Coin0008I MODEL read with 0 errors\n", - "Option for timeMode changed from cpu to elapsed\n", - "Continuous objective value is 0.46875 - 0.01 seconds\n", - "Cgl0003I 0 fixed, 33 tightened bounds, 514 strengthened rows, 0 substitutions\n", - "Cgl0003I 0 fixed, 0 tightened bounds, 221 strengthened rows, 0 substitutions\n", - "Cgl0003I 0 fixed, 0 tightened bounds, 72 strengthened rows, 0 substitutions\n", - "Cgl0003I 0 fixed, 0 tightened bounds, 11 strengthened rows, 0 substitutions\n", - "Cgl0004I processed model has 1123 rows, 574 columns (574 integer (543 of which binary)) and 3646 elements\n", - "Cutoff increment increased from 1e-05 to 0.9999\n", - "Cbc0045I 1 integer variables out of 574 objects (574 integer) have cost of 1 - high priority\n", - "Cbc0045I branch on satisfied Y create fake objective Y random cost Y\n", - "Cbc0038I Initial state - 160 integers unsatisfied sum - 54.3293\n", - "Cbc0038I Pass 1: suminf. 16.41667 (37) obj. 6 iterations 266\n", - "Cbc0038I Pass 2: suminf. 16.41667 (37) obj. 6 iterations 24\n", - "Cbc0038I Pass 3: suminf. 12.16667 (28) obj. 6 iterations 10\n", - "Cbc0038I Pass 4: suminf. 12.16667 (28) obj. 6 iterations 2\n", - "Cbc0038I Pass 5: suminf. 8.50000 (17) obj. 6 iterations 32\n", - "Cbc0038I Pass 6: suminf. 2.50000 (5) obj. 6 iterations 23\n", - "Cbc0038I Solution found of 6\n", - "Cbc0038I Branch and bound needed to clear up 5 general integers\n", - "Cbc0038I Full problem 1123 rows 574 columns, reduced to 0 rows 0 columns\n", - "Cbc0038I Cleaned solution of 6\n", - "Cbc0038I Before mini branch and bound, 387 integers at bound fixed and 0 continuous of which 5 were internal integer and 0 internal continuous\n", - "Cbc0038I Full problem 1123 rows 574 columns, reduced to 300 rows 136 columns\n", - "Cbc0038I Mini branch and bound improved solution from 6 to 3 (0.09 seconds)\n", - "Cbc0038I Round again with cutoff of 1.90009\n", - "Cbc0038I Reduced cost fixing fixed 1 variables on major pass 2\n", - "Cbc0038I Pass 7: suminf. 40.47051 (141) obj. 1 iterations 140\n", - "Cbc0038I Pass 8: suminf. 18.12523 (107) obj. 1.90009 iterations 107\n", - "Cbc0038I Pass 9: suminf. 14.50020 (97) obj. 1.90009 iterations 47\n", - "Cbc0038I Pass 10: suminf. 14.17392 (95) obj. 1.90009 iterations 6\n", - "Cbc0038I Pass 11: suminf. 13.98147 (99) obj. 1.90009 iterations 16\n", - "Cbc0038I Pass 12: suminf. 13.91109 (102) obj. 1.90009 iterations 10\n", - "Cbc0038I Pass 13: suminf. 16.84353 (107) obj. 1.90009 iterations 49\n", - "Cbc0038I Pass 14: suminf. 12.82392 (104) obj. 1.90009 iterations 43\n", - "Cbc0038I Pass 15: suminf. 11.98850 (107) obj. 1.90009 iterations 10\n", - "Cbc0038I Pass 16: suminf. 17.66807 (105) obj. 1.90009 iterations 62\n", - "Cbc0038I Pass 17: suminf. 12.52380 (100) obj. 1.90009 iterations 47\n", - "Cbc0038I Pass 18: suminf. 11.53158 (101) obj. 1.90009 iterations 12\n", - "Cbc0038I Pass 19: suminf. 13.28375 (102) obj. 1.90009 iterations 31\n", - "Cbc0038I Pass 20: suminf. 11.53158 (101) obj. 1.90009 iterations 36\n", - "Cbc0038I Pass 21: suminf. 13.28375 (102) obj. 1.90009 iterations 35\n", - "Cbc0038I Pass 22: suminf. 25.87956 (150) obj. 1.90009 iterations 176\n", - "Cbc0038I Pass 23: suminf. 15.70806 (116) obj. 1.90009 iterations 120\n", - "Cbc0038I Pass 24: suminf. 15.70806 (116) obj. 1.90009 iterations 2\n", - "Cbc0038I Pass 25: suminf. 14.10207 (109) obj. 1.90009 iterations 15\n", - "Cbc0038I Pass 26: suminf. 11.73213 (102) obj. 1.90009 iterations 5\n", - "Cbc0038I Pass 27: suminf. 11.28209 (100) obj. 1.90009 iterations 1\n", - "Cbc0038I Pass 28: suminf. 12.13822 (92) obj. 1.90009 iterations 23\n", - "Cbc0038I Pass 29: suminf. 11.63751 (92) obj. 1.90009 iterations 12\n", - "Cbc0038I Pass 30: suminf. 11.28209 (100) obj. 1.90009 iterations 5\n", - "Cbc0038I Pass 31: suminf. 14.96519 (100) obj. 1.90009 iterations 54\n", - "Cbc0038I Pass 32: suminf. 12.69136 (101) obj. 1.90009 iterations 36\n", - "Cbc0038I Pass 33: suminf. 11.67210 (101) obj. 1.90009 iterations 8\n", - "Cbc0038I Pass 34: suminf. 15.46766 (110) obj. 1.90009 iterations 66\n", - "Cbc0038I Pass 35: suminf. 12.51652 (106) obj. 1.90009 iterations 39\n", - "Cbc0038I Pass 36: suminf. 11.59227 (106) obj. 1.90009 iterations 11\n", - "Cbc0038I Pass 37: suminf. 17.05531 (108) obj. 1.90009 iterations 54\n", - "Cbc0038I Pass 38: suminf. 12.83320 (108) obj. 1.90009 iterations 38\n", - "Cbc0038I Pass 39: suminf. 11.81394 (108) obj. 1.90009 iterations 7\n", - "Cbc0038I Pass 40: suminf. 15.11176 (111) obj. 1.90009 iterations 25\n", 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"Cbc0038I Pass 81: suminf. 11.87399 (106) obj. 1.90009 iterations 25\n", - "Cbc0038I Pass 82: suminf. 11.10724 (105) obj. 1.90009 iterations 13\n", - "Cbc0038I Pass 83: suminf. 11.91766 (96) obj. 1.90009 iterations 24\n", - "Cbc0038I Pass 84: suminf. 11.42225 (105) obj. 1.90009 iterations 18\n", - "Cbc0038I Pass 85: suminf. 11.10724 (105) obj. 1.90009 iterations 11\n", - "Cbc0038I Pass 86: suminf. 11.91766 (96) obj. 1.90009 iterations 28\n", - "Cbc0038I Pass 87: suminf. 11.42225 (105) obj. 1.90009 iterations 20\n", - "Cbc0038I Pass 88: suminf. 11.10724 (105) obj. 1.90009 iterations 12\n", - "Cbc0038I Pass 89: suminf. 14.31190 (102) obj. 1.90009 iterations 37\n", - "Cbc0038I Pass 90: suminf. 12.15401 (107) obj. 1.90009 iterations 27\n", - "Cbc0038I Pass 91: suminf. 11.49725 (106) obj. 1.90009 iterations 12\n", - "Cbc0038I Pass 92: suminf. 14.28693 (101) obj. 1.90009 iterations 36\n", - "Cbc0038I Pass 93: suminf. 11.87399 (106) obj. 1.90009 iterations 26\n", - "Cbc0038I Pass 94: suminf. 11.10724 (105) obj. 1.90009 iterations 10\n", - "Cbc0038I Pass 95: suminf. 11.96343 (96) obj. 1.90009 iterations 25\n", - "Cbc0038I Pass 96: suminf. 11.42225 (105) obj. 1.90009 iterations 17\n", - "Cbc0038I Pass 97: suminf. 11.10724 (105) obj. 1.90009 iterations 6\n", - "Cbc0038I Pass 98: suminf. 15.44269 (110) obj. 1.90009 iterations 54\n", - "Cbc0038I Pass 99: suminf. 12.62896 (106) obj. 1.90009 iterations 42\n", - "Cbc0038I Pass 100: suminf. 11.23221 (106) obj. 1.90009 iterations 9\n", - "Cbc0038I Pass 101: suminf. 15.63024 (110) obj. 1.90009 iterations 46\n", - "Cbc0038I Pass 102: suminf. 12.22067 (105) obj. 1.90009 iterations 29\n", - "Cbc0038I Pass 103: suminf. 11.10724 (105) obj. 1.90009 iterations 8\n", - "Cbc0038I Pass 104: suminf. 14.07192 (101) obj. 1.90009 iterations 28\n", - "Cbc0038I Pass 105: suminf. 12.15401 (107) obj. 1.90009 iterations 24\n", - "Cbc0038I Pass 106: suminf. 24.32913 (140) obj. 1.90009 iterations 146\n", - "Cbc0038I No solution found this major pass\n", - "Cbc0038I Before mini branch and bound, 276 integers at bound fixed and 0 continuous of which 2 were internal integer and 0 internal continuous\n", - "Cbc0038I Full problem 1123 rows 574 columns, reduced to 598 rows 274 columns - 84 fixed gives 191, 100 - ok now\n", - "Cbc0038I Mini branch and bound did not improve solution (0.20 seconds)\n", - "Cbc0038I After 0.20 seconds - Feasibility pump exiting with objective of 3 - took 0.14 seconds\n", - "Cbc0012I Integer solution of 3 found by feasibility pump after 0 iterations and 0 nodes (0.20 seconds)\n", - "Cbc0038I Full problem 1123 rows 574 columns, reduced to 263 rows 120 columns\n", - "Cbc0006I The LP relaxation is infeasible or too expensive\n", - "Cbc0013I At root node, 0 cuts changed objective from 1 to 1 in 1 passes\n", - "Cbc0014I Cut generator 0 (Probing) - 1 row cuts average 0.0 elements, 2 column cuts (2 active) in 0.000 seconds - new frequency is 1\n", - "Cbc0014I Cut generator 1 (Gomory) - 0 row cuts average 0.0 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is -100\n", - "Cbc0014I Cut generator 2 (Knapsack) - 0 row cuts average 0.0 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is -100\n", - "Cbc0014I Cut generator 3 (Clique) - 0 row cuts average 0.0 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is -100\n", - "Cbc0014I Cut generator 4 (MixedIntegerRounding2) - 0 row cuts average 0.0 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is -100\n", - "Cbc0014I Cut generator 5 (FlowCover) - 0 row cuts average 0.0 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is -100\n", - "Cbc0014I Cut generator 6 (TwoMirCuts) - 0 row cuts average 0.0 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is -100\n", - "Cbc0014I Cut generator 7 (ZeroHalf) - 0 row cuts average 0.0 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is -100\n", - "Cbc0001I Search completed - best objective 3, took 0 iterations and 0 nodes (0.21 seconds)\n", - "Cbc0035I Maximum depth 0, 0 variables fixed on reduced cost\n", - "Cuts at root node changed objective from 1 to 1\n", - "Probing was tried 1 times and created 3 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "Gomory was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "Knapsack was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "Clique was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "MixedIntegerRounding2 was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "FlowCover was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "TwoMirCuts was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "ZeroHalf was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "\n", - "Result - Optimal solution found\n", - "\n", - "Objective value: 3.00000000\n", - "Enumerated nodes: 0\n", - "Total iterations: 0\n", - "Time (CPU seconds): 0.21\n", - "Time (Wallclock seconds): 0.22\n", - "\n", - "Option for printingOptions changed from normal to all\n", - "Total time (CPU seconds): 0.21 (Wallclock seconds): 0.23\n", - "\n" - ] - } - ], - "source": [ - "map_dict, loss_val = ilp.solve_ilp(myInt);" - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "dict_keys(['V', 'E'])" - ] - }, - "execution_count": 27, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "myInt.phi_['0'].keys()" - ] - }, - { - "cell_type": "code", - "execution_count": 29, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "map_dict['phi_0_E'].draw()" - ] - }, - { - "cell_type": "code", - "execution_count": 31, - "metadata": {}, - "outputs": [ - { - "ename": "TypeError", - "evalue": "Interleave.__init__() got an unexpected keyword argument 'n'", - "output_type": "error", - "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)", - "Cell \u001b[0;32mIn[31], line 5\u001b[0m\n\u001b[1;32m 1\u001b[0m F \u001b[38;5;241m=\u001b[39m ex_mg\u001b[38;5;241m.\u001b[39minterleave_example_A()\n\u001b[1;32m 2\u001b[0m G \u001b[38;5;241m=\u001b[39m ex_mg\u001b[38;5;241m.\u001b[39minterleave_example_B()\n\u001b[0;32m----> 5\u001b[0m myInt \u001b[38;5;241m=\u001b[39m Interleave(F, G, n \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m1\u001b[39m, initialize_random_maps\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m, seed \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m17\u001b[39m)\n\u001b[1;32m 7\u001b[0m myInt\u001b[38;5;241m.\u001b[39mloss()\n", - "\u001b[0;31mTypeError\u001b[0m: Interleave.__init__() got an unexpected keyword argument 'n'" - ] - } - ], - "source": [ - "F = ex_mg.interleave_example_A()\n", - "G = ex_mg.interleave_example_B()\n", - "\n", - "\n", - "myInt = Interleave(F, G, n = 1, initialize_random_maps=True, seed = 17)\n", - "\n", - "myInt.loss()\n" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Unexpected exception formatting exception. Falling back to standard exception\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Traceback (most recent call last):\n", - " File \"/opt/anaconda3/lib/python3.11/site-packages/IPython/core/interactiveshell.py\", line 3508, in run_code\n", - " exec(code_obj, self.user_global_ns, self.user_ns)\n", - " File \"/var/folders/j9/kbv0jxbn7458fwg4nvr4rlkm0000gn/T/ipykernel_49302/3716933441.py\", line 1, in \n", - " ilp.solve_ilp(myInt, verbose = True)\n", - " File \"/Users/lizliz/Library/CloudStorage/Dropbox/Math/Code/ceREEBerus/cereeberus/cereeberus/distance/ilp.py\", line 248, in solve_ilp\n", - " first_term = pulp.lpSum([map_V_vars[i,j] * bou_0[j][k] for j in range(shape_n_mix)])\n", - " ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n", - " File \"/Users/lizliz/Library/CloudStorage/Dropbox/Math/Code/ceREEBerus/cereeberus/cereeberus/distance/ilp.py\", line 248, in \n", - " first_term = pulp.lpSum([map_V_vars[i,j] * bou_0[j][k] for j in range(shape_n_mix)])\n", - " ~~~~~~~~~~^^^^^\n", - "KeyError: (0, 0)\n", - "\n", - "During handling of the above exception, another exception occurred:\n", - "\n", - "Traceback (most recent call last):\n", - " File \"/opt/anaconda3/lib/python3.11/site-packages/IPython/core/interactiveshell.py\", line 2105, in showtraceback\n", - " stb = self.InteractiveTB.structured_traceback(\n", - " ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n", - " File \"/opt/anaconda3/lib/python3.11/site-packages/IPython/core/ultratb.py\", line 1396, in structured_traceback\n", - " return FormattedTB.structured_traceback(\n", - " ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n", - " File \"/opt/anaconda3/lib/python3.11/site-packages/IPython/core/ultratb.py\", line 1287, in structured_traceback\n", - " return VerboseTB.structured_traceback(\n", - " ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n", - " File \"/opt/anaconda3/lib/python3.11/site-packages/IPython/core/ultratb.py\", line 1140, in structured_traceback\n", - " formatted_exception = self.format_exception_as_a_whole(etype, evalue, etb, number_of_lines_of_context,\n", - " ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n", - " File \"/opt/anaconda3/lib/python3.11/site-packages/IPython/core/ultratb.py\", line 1055, in format_exception_as_a_whole\n", - " frames.append(self.format_record(record))\n", - " ^^^^^^^^^^^^^^^^^^^^^^^^^^\n", - " File \"/opt/anaconda3/lib/python3.11/site-packages/IPython/core/ultratb.py\", line 955, in format_record\n", - " frame_info.lines, Colors, self.has_colors, lvals\n", - " ^^^^^^^^^^^^^^^^\n", - " File \"/opt/anaconda3/lib/python3.11/site-packages/IPython/core/ultratb.py\", line 778, in lines\n", - " return self._sd.lines\n", - " ^^^^^^^^^^^^^^\n", - " File \"/opt/anaconda3/lib/python3.11/site-packages/stack_data/utils.py\", line 145, in cached_property_wrapper\n", - " value = obj.__dict__[self.func.__name__] = self.func(obj)\n", - " ^^^^^^^^^^^^^^\n", - " File \"/opt/anaconda3/lib/python3.11/site-packages/stack_data/core.py\", line 698, in lines\n", - " pieces = self.included_pieces\n", - " ^^^^^^^^^^^^^^^^^^^^\n", - " File \"/opt/anaconda3/lib/python3.11/site-packages/stack_data/utils.py\", line 145, in cached_property_wrapper\n", - " value = obj.__dict__[self.func.__name__] = self.func(obj)\n", - " ^^^^^^^^^^^^^^\n", - " File \"/opt/anaconda3/lib/python3.11/site-packages/stack_data/core.py\", line 649, in included_pieces\n", - " pos = scope_pieces.index(self.executing_piece)\n", - " ^^^^^^^^^^^^^^^^^^^^\n", - " File \"/opt/anaconda3/lib/python3.11/site-packages/stack_data/utils.py\", line 145, in cached_property_wrapper\n", - " value = obj.__dict__[self.func.__name__] = self.func(obj)\n", - " ^^^^^^^^^^^^^^\n", - " File \"/opt/anaconda3/lib/python3.11/site-packages/stack_data/core.py\", line 628, in executing_piece\n", - " return only(\n", - " ^^^^^\n", - " File \"/opt/anaconda3/lib/python3.11/site-packages/executing/executing.py\", line 164, in only\n", - " raise NotOneValueFound('Expected one value, found 0')\n", - "executing.executing.NotOneValueFound: Expected one value, found 0\n" - ] - } - ], - "source": [ - "ilp.solve_ilp(myInt, verbose = True)" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "1.0" - ] - }, - "execution_count": 5, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "F = ex_mg.line(0,10)\n", - "G = ex_mg.torus(0,1,3,10)\n", - "\n", - "\n", - "myInt = Interleave(F, G, n = 0, initialize_random_maps=True, seed = 17)\n", - "\n", - "myInt.loss()\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "E" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "base", - "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": "3.12.7" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/Notebooks_Unused/torus_line.ipynb b/Notebooks_Unused/torus_line.ipynb deleted file mode 100644 index ab77d37..0000000 --- a/Notebooks_Unused/torus_line.ipynb +++ /dev/null @@ -1,410 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "# Note this code isn't on the main branch, need the `smoo` branch of cereeberus until I get this stuff onto the main branch.\n", - "from cereeberus import ReebGraph, MapperGraph, Interleave\n", - "import cereeberus.data.ex_mappergraphs as ex_mg\n", - "from cereeberus.compute.draw import line_loop_index\n", - "\n", - "import matplotlib.pyplot as plt\n", - "import matplotlib as mpl\n", - "from matplotlib import cm\n", - "import matplotlib.colors as clr\n", - "\n", - "from matplotlib.colors import ListedColormap, LinearSegmentedColormap\n", - "import networkx as nx\n", - "import numpy as np\n", - "import pandas as pd\n", - "\n", - "# Note this code isn't on the main branch, need the `smoo` branch of cereeberus until I get this stuff onto the main branch.\n", - "from cereeberus import ReebGraph, MapperGraph, Interleave\n", - "import cereeberus.data.ex_mappergraphs as ex_mg\n", - "from cereeberus.compute.draw import line_loop_index\n", - "\n", - "import matplotlib.pyplot as plt\n", - "import matplotlib as mpl\n", - "from matplotlib import cm\n", - "import matplotlib.colors as clr\n", - "\n", - "from matplotlib.colors import ListedColormap, LinearSegmentedColormap\n", - "import networkx as nx\n", - "import numpy as np\n", - "import pandas as pd\n", - "\n", - "\n", - "%load_ext autoreload\n", - "%autoreload 2" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "cmap_binary = ListedColormap([\"#B87BBC\", \"black\",])\n", - "cmap_binary_2 = ListedColormap(['#743B75','#26B0E7','#F3A61B','#D94E3D'])\n", - "cmap_linear = clr.LinearSegmentedColormap.from_list('custom blue', ['#B87BBC','#26B0E7',], N=256)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Testing torus/line" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "h = 5\n", - "T = ex_mg.torus(0,2, 2+h, 4+h, delta = 1)\n", - "L = ex_mg.line(0, 4+h)\n", - "\n", - "myInt = Interleave(T, L, n=1, initialize_random_maps=True, seed = 0 )\n", - "myInt.draw_all_graphs(cmap = cmap_linear, figsize = (10,7), cpx = 1);" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - " Dgm Type Req A Req B Loss\n", - "0 Edge-Vertex phi up 0.0\n", - "1 Edge-Vertex phi down 0.0\n", - "2 Edge-Vertex psi up 0.0\n", - "3 Edge-Vertex psi down 1.0\n", - "4 Thickening phi V 0.0\n", - "5 Thickening phi E 0.0\n", - "6 Thickening psi V 0.0\n", - "7 Thickening psi E 1.0\n", - "8 Triangle V F 0.0\n", - "9 Triangle V G 0.0\n", - "10 Triangle E F 1.0\n", - "11 Triangle E G 0.0\n", - "\n", - "Loss: 1.0\n", - "Interleaving distance bound: 1 + 1.0 = 2.0\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "myIntT = Interleave(T, L, n=1, initialize_random_maps=True, seed = 0 )\n", - "myIntT.loss(verbose = True)\n", - "myIntT.draw_all_psi(filltype = 'nan', cmap = cmap_binary, figsize = (10,7));" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - " Dgm Type Req A Req B Loss\n", - "0 Edge-Vertex phi up 0.0\n", - "1 Edge-Vertex phi down 0.0\n", - "2 Edge-Vertex psi up 0.0\n", - "3 Edge-Vertex psi down 0.0\n", - "4 Thickening phi V 0.0\n", - "5 Thickening phi E 0.0\n", - "6 Thickening psi V 0.0\n", - "7 Thickening psi E 0.0\n", - "8 Triangle V F 0.0\n", - "9 Triangle V G 0.0\n", - "10 Triangle E F 1.0\n", - "11 Triangle E G 0.0\n", - "\n", - "Loss: 1.0\n", - "Interleaving distance bound: 1 + 1.0 = 2.0\n" - ] - }, - { - "data": { - "text/plain": [ - "1.0" - ] - }, - "execution_count": 5, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "myIntT.set_single_assignment('f',6,'psi', '0','V')\n", - "myIntT.set_single_assignment('g',8,'psi', '0','V')\n", - "myIntT.set_single_assignment(('f','g'), (6,8),'psi', '0','E')\n", - "myIntT.set_single_assignment(('g','h'), (8,9),'psi', '0','E')\n", - "myIntT.draw_all_psi(filltype = 'nan', cmap = cmap_binary, figsize = (10,7));\n", - "\n", - "myIntT.loss(verbose = True)" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mapping to (6, 7, 0)\n", - " Dgm Type Req A Req B Loss\n", - "0 Edge-Vertex phi up 0.0\n", - "1 Edge-Vertex phi down 0.0\n", - "2 Edge-Vertex psi up 1.0\n", - "3 Edge-Vertex psi down 0.0\n", - "4 Thickening phi V 0.0\n", - "5 Thickening phi E 0.0\n", - "6 Thickening psi V 0.0\n", - "7 Thickening psi E 1.0\n", - "8 Triangle V F 0.0\n", - "9 Triangle V G 0.0\n", - "10 Triangle E F 1.0\n", - "11 Triangle E G 0.0\n", - "\n", - "Loss: 1.0\n", - "Interleaving distance bound: 1 + 1.0 = 2.0\n", - "Mapping to (6, 7, 1)\n", - " Dgm Type Req A Req B Loss\n", - "0 Edge-Vertex phi up 0.0\n", - "1 Edge-Vertex phi down 0.0\n", - "2 Edge-Vertex psi up 1.0\n", - "3 Edge-Vertex psi down 0.0\n", - "4 Thickening phi V 0.0\n", - "5 Thickening phi E 0.0\n", - "6 Thickening psi V 0.0\n", - "7 Thickening psi E 1.0\n", - "8 Triangle V F 0.0\n", - "9 Triangle V G 0.0\n", - "10 Triangle E F 1.0\n", - "11 Triangle E G 0.0\n", - "\n", - "Loss: 1.0\n", - "Interleaving distance bound: 1 + 1.0 = 2.0\n" - ] - } - ], - "source": [ - "for label in (0,1):\n", - " print(f\"Mapping to {6,7, label}\")\n", - "\n", - " myIntT.set_single_assignment((5,6,0), (6,7,label), 'psi', 'n','E')\n", - " myInt.loss(verbose = True)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [], - "source": [ - "myIntL = Interleave(L,T, n=1, initialize_random_maps=True, seed = 0 )\n", - "# myIntL.loss(verbose = True)\n", - "# myIntL.draw_all_phi(filltype = 'nan', cmap = cmap_binary, figsize = (10,7));" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - " Dgm Type Req A Req B Loss\n", - "0 Edge-Vertex phi up 0.0\n", - "1 Edge-Vertex phi down 0.0\n", - "2 Edge-Vertex psi up 0.0\n", - "3 Edge-Vertex psi down 0.0\n", - "4 Thickening phi V 0.0\n", - "5 Thickening phi E 0.0\n", - "6 Thickening psi V 0.0\n", - "7 Thickening psi E 0.0\n", - "8 Triangle V F 0.0\n", - "9 Triangle V G 0.0\n", - "10 Triangle E F 0.0\n", - "11 Triangle E G 1.0\n", - "\n", - "Loss: 1.0\n", - "Interleaving distance bound: 1 + 1.0 = 2.0\n" - ] - }, - { - "data": { - "text/plain": [ - "1.0" - ] - }, - "execution_count": 8, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "myIntL.set_single_assignment('f',6,'phi', '0','V')\n", - "myIntL.set_single_assignment('g',8,'phi', '0','V')\n", - "myIntL.set_single_assignment(('e','f'), (4,6),'phi', '0','E')\n", - "myIntL.set_single_assignment(('f','g'), (6,8),'phi', '0','E')\n", - "myIntL.set_single_assignment(('g','h'), (8,9),'phi', '0','E')\n", - "myIntL.draw_all_phi(filltype = 'nan', cmap = cmap_binary, figsize = (10,7));\n", - "\n", - "myIntL.loss(verbose = True)" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mapping to (6, 7, 0)\n", - " Dgm Type Req A Req B Loss\n", - "0 Edge-Vertex phi up 0.0\n", - "1 Edge-Vertex phi down 0.0\n", - "2 Edge-Vertex psi up 0.0\n", - "3 Edge-Vertex psi down 0.0\n", - "4 Thickening phi V 0.0\n", - "5 Thickening phi E 1.0\n", - "6 Thickening psi V 0.0\n", - "7 Thickening psi E 0.0\n", - "8 Triangle V F 0.0\n", - "9 Triangle V G 0.0\n", - "10 Triangle E F 0.0\n", - "11 Triangle E G 1.0\n", - "\n", - "Loss: 1.0\n", - "Interleaving distance bound: 1 + 1.0 = 2.0\n", - "Mapping to (6, 7, 1)\n", - " Dgm Type Req A Req B Loss\n", - "0 Edge-Vertex phi up 0.0\n", - "1 Edge-Vertex phi down 0.0\n", - "2 Edge-Vertex psi up 0.0\n", - "3 Edge-Vertex psi down 0.0\n", - "4 Thickening phi V 0.0\n", - "5 Thickening phi E 0.0\n", - "6 Thickening psi V 0.0\n", - "7 Thickening psi E 0.0\n", - "8 Triangle V F 0.0\n", - "9 Triangle V G 0.0\n", - "10 Triangle E F 0.0\n", - "11 Triangle E G 1.0\n", - "\n", - "Loss: 1.0\n", - "Interleaving distance bound: 1 + 1.0 = 2.0\n" - ] - } - ], - "source": [ - "for label in (0,1):\n", - " print(f\"Mapping to {6,7, label}\")\n", - "\n", - " myIntL.set_single_assignment((5,6,0), (6,7,label), 'phi', 'n','E')\n", - " myIntL.loss(verbose = True)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "base", - "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": "3.11.7" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/cereeberus/cereeberus/__init__.py b/cereeberus/cereeberus/__init__.py index a21c3bb..c3f911d 100644 --- a/cereeberus/cereeberus/__init__.py +++ b/cereeberus/cereeberus/__init__.py @@ -1,5 +1,6 @@ __all__ = [ "ReebGraph", + "BranchDecomp", "LowerStar", "computeReeb", "computeMapper", @@ -15,6 +16,7 @@ ] from .reeb.reebgraph import ReebGraph +from .reeb.branchdecomp import BranchDecomp from .reeb.merge import MergeTree from .reeb.mapper import MapperGraph from .reeb.embeddedgraph import EmbeddedGraph diff --git a/cereeberus/cereeberus/reeb/__init__.py b/cereeberus/cereeberus/reeb/__init__.py index 12afaf8..726ca43 100644 --- a/cereeberus/cereeberus/reeb/__init__.py +++ b/cereeberus/cereeberus/reeb/__init__.py @@ -1,7 +1,8 @@ -__all__ = ["reebgraph", "merge", "mapper", "embeddedgraph", "lowerstar"] +__all__ = ["reebgraph", "merge", "mapper", "embeddedgraph", "lowerstar", "branchdecomp"] from .reebgraph import * from .merge import * from .mapper import * from .embeddedgraph import * from .lowerstar import * +from .branchdecomp import * diff --git a/cereeberus/cereeberus/reeb/branchdecomp.py b/cereeberus/cereeberus/reeb/branchdecomp.py index 8ebbf88..b33bb63 100644 --- a/cereeberus/cereeberus/reeb/branchdecomp.py +++ b/cereeberus/cereeberus/reeb/branchdecomp.py @@ -1,19 +1,103 @@ import numpy as np +import matplotlib.pyplot as plt class BranchDecomp: """ - This class encodes a branch decmposition of a given Reeb graph. This is a sorted list of intervals (branches), where the endpoints of the intervals have attaching information, either to a previous branch, or to itself (meaning that end of the interval is a local max/min). The Reeb graph can be reconstructed from the data as well. Note that the decomposition is not unique. - - The branches are stored as an n x 4 array, where n is the number of branches. The first two columns are the real-valued endpoints of the branch, and the last two columns are integers giving the attaching information. The attaching information is a tuple of the form (branch_id_low, branch_id_high), where branch_id_low is the ID of the branch that the lower interval endpoint is attached to (can be its own row if it is a local min), and branch_id_high is the ID of the branch that the upper interval endpoint is attached to (can be its own row if it is a local max). - - + A branch decomposition of a Reeb graph. + + A branch decomposition breaks a Reeb graph into a collection of non-overlapping + upward paths called *branches*. Each branch is a path that travels strictly upward + in function value, starting at either a local minimum or a saddle point (where a + previous branch split off) and ending at either a local maximum or another saddle + point. The decomposition is built greedily and is not unique. + + **Algorithm:** Branches are extracted one at a time by repeatedly finding the + unprocessed vertex with the lowest function value that still has outgoing edges, + then greedily following successors upward until a local maximum is reached. The + edges along that path are removed from a working copy of the graph, and the + process repeats until no edges remain. Isolated vertices (no edges) are added last + as degenerate branches. + + **Branch storage (``self.branches``):** An ``n x 4`` numpy array where each row + represents one branch in the order they were extracted: + + - Column 0 (``f_low``): function value of the lower endpoint. + - Column 1 (``f_high``): function value of the upper endpoint. Equal to ``f_low`` + for degenerate (isolated vertex) branches. + - Column 2 (``low_attach``): index of the branch that owns the lower endpoint + vertex. If the lower endpoint is a local minimum, this is the branch's own index. + - Column 3 (``high_attach``): index of the branch that owns the upper endpoint + vertex. If the upper endpoint is a local maximum, this is the branch's own index. + Otherwise it points to the earlier branch whose path passes through that vertex. + + Because branches are extracted in order, attachment indices always satisfy + ``low_attach <= branch_id`` and ``high_attach <= branch_id``. + + **Path storage (``self.paths``):** A list of lists, in the same order as + ``self.branches``. Each entry is the ordered list of vertex names (from the + original ReebGraph) that make up the branch path. + + **Reconstruction:** The original Reeb graph can be recovered exactly from the + stored paths and function values via :meth:`reconstruct`. + + Example:: + + import cereeberus.data.ex_reebgraphs as ex_rg + from cereeberus.reeb.branchdecomp import BranchDecomp + + R = ex_rg.dancing_man() + bd = BranchDecomp() + bd.decompose(R) + bd.draw() + R2 = bd.reconstruct() """ def __init__(self): self.branches = np.empty((0, 4)) self.paths = [] + @staticmethod + def _lowest_available_vertex(graph): + """ + Find the vertex with the lowest function value that still has outgoing edges. + + Parameters: + graph: ReebGraph object + + Returns: + The vertex with lowest function value and out_degree > 0, or None if no such vertex exists. + """ + available_vertices = [v for v in graph.nodes if graph.up_degree(v) > 0] + + if not available_vertices: + return None + + return min(available_vertices, key=lambda v: graph.f[v]) + + @staticmethod + def _largest_upward_path(graph, start_vertex): + """ + Greedily follow upward edges from a starting vertex until reaching a local maximum. + + Parameters: + graph: ReebGraph object + start_vertex: vertex to start from + + Returns: + A list of vertices representing the upward path from start to a local max. + """ + path = [start_vertex] + current = start_vertex + + while graph.up_degree(current) > 0: + # Pick any successor arbitrarily + next_vertex = next(graph.successors(current)) + path.append(next_vertex) + current = next_vertex + + return path + @staticmethod def _remove_path_edges(graph, path): """Remove one edge along each step of the chosen path.""" @@ -28,6 +112,7 @@ def decompose(self, reebgraph): ''' working = reebgraph.copy() + self._f = reebgraph.f.copy() self.paths = [] branch_rows = [] @@ -52,11 +137,19 @@ def decompose(self, reebgraph): ) self.paths.append(path) - endpoint_owner.setdefault(start_v, branch_id) - endpoint_owner.setdefault(end_v, branch_id) + for v in path: + endpoint_owner.setdefault(v, branch_id) self._remove_path_edges(working, path) + # Handle any remaining isolated vertices (never part of any path) as degenerate branches + for v in working.nodes: + if v not in endpoint_owner: + branch_id = len(self.paths) + f_v = working.f[v] + branch_rows.append((f_v, f_v, branch_id, branch_id)) + self.paths.append([v]) + if len(branch_rows) == 0: self.branches = np.empty((0, 4)) else: @@ -79,8 +172,111 @@ def get_branch(self, branch_id): return self.branches[branch_id] + def get_branch_path(self, branch_id): + ''' + Returns the list of vertices constituting the path for the given branch ID. + + Parameters: + branch_id (int): The ID of the branch. + + Returns: + list: The list of vertices in the path for the given branch. + ''' + if branch_id < 0 or branch_id >= len(self.paths): + raise IndexError("branch_id out of range") + + return self.paths[branch_id] + def reconstruct(self): ''' - Reconstructs the Reeb graph from the branches. + Reconstructs the Reeb graph from the branch decomposition stored in self.paths and self._f. + + Returns: + ReebGraph: The reconstructed Reeb graph. + ''' + from .reebgraph import ReebGraph + + if not self.paths: + return ReebGraph() + + R = ReebGraph() + + # Add all unique vertices across all paths + seen = set() + for path in self.paths: + for v in path: + if v not in seen: + R.add_node(v, self._f[v], reset_pos=False) + seen.add(v) + + # Add one edge per step in each path + for path in self.paths: + for i in range(len(path) - 1): + R.add_edge(path[i], path[i + 1], reset_pos=False) + + R.set_pos_from_f() + return R + + def draw(self, ax=None, figsize=(12, 8)): + ''' + Draw the branch decomposition with branches ordered left to right. + + Each branch is drawn as a vertical line at its proper function values. + Endpoint labels show the branch attachment information: + - Lower endpoint labeled with low_attach branch ID + - Upper endpoint labeled with high_attach branch ID + + Parameters: + ax: matplotlib axis object. If None, creates a new figure. + figsize: tuple of figure size (width, height) + + Returns: + ax: the matplotlib axis object ''' - raise NotImplementedError("reconstruct is not implemented yet") \ No newline at end of file + if len(self.branches) == 0: + print("No branches to draw.") + return + + if ax is None: + fig, ax = plt.subplots(figsize=figsize) + + n_branches = len(self.branches) + + # Evenly space branches horizontally + x_positions = np.linspace(0, n_branches - 1, n_branches) + + # Darker colors + purple = '#6B4C7A' # Darker purple + green = '#5A8C5A' # Darker green + + # Draw each branch as a vertical line + for i, (f_low, f_high, low_attach, high_attach) in enumerate(self.branches): + x = x_positions[i] + + # Draw the branch line (black) + ax.plot([x, x], [f_low, f_high], 'k-', linewidth=2.5) + + # Draw points at endpoints + ax.plot(x, f_low, 'o', color=purple, markersize=10) # Lower endpoint + ax.plot(x, f_high, 'o', color=green, markersize=10) # Upper endpoint + + # Label lower endpoint with attachment info + ax.text(x - 0.12, f_low, f'B{int(low_attach)}', fontsize=12, + ha='right', va='center', color=purple, fontweight='bold') + + # Label upper endpoint with attachment info + ax.text(x - 0.12, f_high, f'B{int(high_attach)}', fontsize=12, + ha='right', va='center', color=green, fontweight='bold') + + ax.set_xlabel('Branch (ordered left to right)', fontsize=14, fontweight='bold') + ax.set_ylabel('Function Value', fontsize=14, fontweight='bold') + ax.set_title('Branch Decomposition of Reeb Graph', fontsize=16, fontweight='bold') + ax.grid(True, alpha=0.3) + ax.set_xticks(x_positions) + ax.set_xticklabels([f'B{i}' for i in range(n_branches)], fontsize=12) + ax.tick_params(axis='y', labelsize=12) + + # Add padding on left side to accommodate labels + ax.set_xlim(-0.5, n_branches - 0.5) + + return ax \ No newline at end of file diff --git a/cereeberus/cereeberus/reeb/reebgraph.py b/cereeberus/cereeberus/reeb/reebgraph.py index a540bec..cd16834 100644 --- a/cereeberus/cereeberus/reeb/reebgraph.py +++ b/cereeberus/cereeberus/reeb/reebgraph.py @@ -70,6 +70,47 @@ def summary(self): """ return {"nodes": len(self.nodes), "edges": len(self.edges)} + def copy(self): + """Create a deep copy of the Reeb graph. + + Returns: + ReebGraph + A new ReebGraph object with the same nodes, edges, and function values. + """ + # Create a new ReebGraph with copies of the nodes and edges + H = ReebGraph() + + # Copy the function values dictionary + H.f = self.f.copy() + + # Copy all nodes and edges from the parent MultiDiGraph + for v in self.nodes(): + H.add_node(v, self.f[v], reset_pos=False) + + for u, v, key in self.edges(keys=True): + super(ReebGraph, H).add_edge(u, v, key) + + # Copy position information if it exists + if hasattr(self, 'pos_f') and self.pos_f: + H.pos_f = self.pos_f.copy() + if hasattr(self, 'pos') and self.pos: + H.pos = self.pos.copy() + + return H + + def branch_decomp(self): + """Compute and return the branch decomposition of the Reeb graph. + + Returns: + BranchDecomp + A :class:`~cereeberus.reeb.branchdecomp.BranchDecomp` object whose + ``decompose`` method has already been called on this graph. + """ + from .branchdecomp import BranchDecomp + bd = BranchDecomp() + bd.decompose(self) + return bd + # -----------------# # Methods for getting info about the Reeb graph and its nodes # -----------------# diff --git a/doc_source/modules/reeb/branchdecomp.rst b/doc_source/modules/reeb/branchdecomp.rst new file mode 100644 index 0000000..ca2f9fe --- /dev/null +++ b/doc_source/modules/reeb/branchdecomp.rst @@ -0,0 +1,40 @@ +BranchDecomp class +================== + +The ``BranchDecomp`` class computes and stores a branch decomposition of a Reeb graph. + +For a worked example, see the :doc:`branch decomposition tutorial `. + +This implementation and tutorial are based in part on the branch decomposition and +unsmoothing perspective developed in Samira Jabry's thesis: *Unsmoothing of Reeb +Graphs*, Saint Louis University, 2025. Available via ProQuest at +https://www.proquest.com/dissertations-theses/unsmoothing-reeb-graphs/docview/3231769569/se-2. + +A branch decomposition breaks a Reeb graph into a collection of non-overlapping upward paths called *branches*. Each branch travels strictly upward in function value, starting at either a local minimum or a saddle point and ending at either a local maximum or another saddle point. The decomposition also records how branch endpoints attach to previously-computed branches, allowing the original Reeb graph to be fully reconstructed. + +The decomposition can be computed either directly via this class, or via the convenience method on the Reeb graph:: + + import cereeberus + import cereeberus.data.ex_reebgraphs as ex_rg + from cereeberus.reeb.branchdecomp import BranchDecomp + + R = ex_rg.dancing_man() + + # Option 1: via the ReebGraph method + bd = R.branch_decomp() + + # Option 2: directly + bd = BranchDecomp() + bd.decompose(R) + + # Visualise the decomposition alongside the original graph + import matplotlib.pyplot as plt + fig, axes = plt.subplots(1, 2, figsize=(14, 6)) + R.draw(ax=axes[0]) + bd.draw(ax=axes[1]) + + # Reconstruct the original graph + R2 = bd.reconstruct() + +.. automodule:: cereeberus.reeb.branchdecomp + :members: diff --git a/doc_source/modules/reeb/index.rst b/doc_source/modules/reeb/index.rst index cd0d3ed..18fc172 100644 --- a/doc_source/modules/reeb/index.rst +++ b/doc_source/modules/reeb/index.rst @@ -12,4 +12,5 @@ The module `cereeberus.reeb` contains classes for both the Reeb graph and merge embedgraph.rst mappergraph.rst lowerstar.rst + branchdecomp.rst diff --git a/doc_source/notebooks/branch_decomp_basics.ipynb b/doc_source/notebooks/branch_decomp_basics.ipynb new file mode 100644 index 0000000..d6118b2 --- /dev/null +++ b/doc_source/notebooks/branch_decomp_basics.ipynb @@ -0,0 +1,230 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "b4dd7036", + "metadata": {}, + "source": [ + "# Tutorial: Branch Decomposition of a Reeb Graph" + ] + }, + { + "cell_type": "markdown", + "id": "8696deda", + "metadata": {}, + "source": [ + "A **branch decomposition** breaks a Reeb graph into a collection of non-overlapping upward paths called *branches*. Each branch travels strictly upward in function value, starting at either a local minimum or a saddle point and ending at either a local maximum or another saddle point.\n", + "\n", + "Each branch stores:\n", + "- The function values at its two endpoints (`f_low`, `f_high`)\n", + "- Attachment information: which earlier branch each endpoint belongs to (pointing to itself if it is a local min/max)\n", + "\n", + "This tutorial follows the branch decomposition viewpoint developed in Samira Jabry's thesis, *Unsmoothing of Reeb Graphs*, Saint Louis University, 2025:\n", + "https://www.proquest.com/dissertations-theses/unsmoothing-reeb-graphs/docview/3231769569/se-2\n", + "\n", + "For the API and class reference, see the [branch decomposition documentation page](../modules/reeb/branchdecomp.html)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "462d6378", + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "from cereeberus import ReebGraph\n", + "import cereeberus.data.ex_reebgraphs as ex_rg\n", + "from cereeberus.reeb.branchdecomp import BranchDecomp" + ] + }, + { + "cell_type": "markdown", + "id": "6783161d", + "metadata": {}, + "source": [ + "## A simple example: the dancing man\n", + "\n", + "We'll start with the `dancing_man` example graph, which is a connected Reeb graph with several saddle points." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3cc2507f", + "metadata": {}, + "outputs": [], + "source": [ + "R = ex_rg.dancing_man()\n", + "\n", + "fig, axes = plt.subplots(1, 2, figsize=(14, 6))\n", + "R.draw(ax=axes[0])\n", + "axes[0].set_title('Reeb Graph', fontsize=14, fontweight='bold')\n", + "\n", + "bd = R.branch_decomp()\n", + "bd.draw(ax=axes[1])\n", + "\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "b0f9031f", + "metadata": {}, + "source": [ + "The branch decomposition diagram shows each branch as a vertical line positioned at its function values. Labels next to each endpoint indicate which branch that endpoint is attached to:\n", + "\n", + "- **Purple (lower endpoint)**: the branch ID whose path contains this vertex\n", + "- **Green (upper endpoint)**: the branch ID whose path contains this vertex\n", + "\n", + "When a label matches the branch's own ID, that endpoint is a local min or max (no other branch claims it)." + ] + }, + { + "cell_type": "markdown", + "id": "813632e0", + "metadata": {}, + "source": [ + "## Inspecting the branches\n", + "\n", + "The branches are stored as an $n \\times 4$ numpy array. Each row is one branch:\n", + "\n", + "| Column | Meaning |\n", + "|--------|---------|\n", + "| 0 | `f_low` — function value of the lower endpoint |\n", + "| 1 | `f_high` — function value of the upper endpoint |\n", + "| 2 | `low_attach` — branch ID owning the lower endpoint |\n", + "| 3 | `high_attach` — branch ID owning the upper endpoint |" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9184fe25", + "metadata": {}, + "outputs": [], + "source": [ + "print(\"Branches (f_low, f_high, low_attach, high_attach):\")\n", + "print(bd.branches)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "aead1647", + "metadata": {}, + "outputs": [], + "source": [ + "# You can also inspect individual branches and their vertex paths\n", + "for i in range(len(bd.branches)):\n", + " print(f\"Branch {i}: f=[{bd.branches[i,0]}, {bd.branches[i,1]}] \"\n", + " f\"attaches=({int(bd.branches[i,2])}, {int(bd.branches[i,3])}) \"\n", + " f\"path={bd.get_branch_path(i)}\")" + ] + }, + { + "cell_type": "markdown", + "id": "69d80062", + "metadata": {}, + "source": [ + "## Reconstructing the Reeb graph\n", + "\n", + "Once you have a branch decomposition, you can reconstruct the original Reeb graph exactly from it using `reconstruct()`." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ea7fd61d", + "metadata": {}, + "outputs": [], + "source": [ + "R2 = bd.reconstruct()\n", + "\n", + "fig, axes = plt.subplots(1, 2, figsize=(12, 5))\n", + "R.draw(ax=axes[0])\n", + "axes[0].set_title('Original', fontsize=13, fontweight='bold')\n", + "R2.draw(ax=axes[1])\n", + "axes[1].set_title('Reconstructed', fontsize=13, fontweight='bold')\n", + "plt.tight_layout()\n", + "plt.show()\n", + "\n", + "print(f\"Original: {R}\")\n", + "print(f\"Reconstructed: {R2}\")" + ] + }, + { + "cell_type": "markdown", + "id": "0cb9074c", + "metadata": {}, + "source": [ + "## Handling isolated vertices: the juggling man\n", + "\n", + "The `juggling_man` graph has isolated vertices (vertices with no edges), representing disconnected components. These are handled as **degenerate branches** where `f_low == f_high` and both attachment IDs point to the branch itself." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b22dd894", + "metadata": {}, + "outputs": [], + "source": [ + "J = ex_rg.juggling_man()\n", + "\n", + "fig, axes = plt.subplots(1, 2, figsize=(16, 6))\n", + "J.draw(ax=axes[0])\n", + "axes[0].set_title('Juggling Man Reeb Graph', fontsize=14, fontweight='bold')\n", + "\n", + "bd_j = J.branch_decomp()\n", + "bd_j.draw(ax=axes[1])\n", + "\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "514266b4", + "metadata": {}, + "outputs": [], + "source": [ + "# Identify the degenerate branches (isolated vertices)\n", + "print(\"Degenerate branches (isolated vertices):\")\n", + "for i, (f_low, f_high, low_a, high_a) in enumerate(bd_j.branches):\n", + " if f_low == f_high:\n", + " print(f\" Branch {i}: vertex={bd_j.get_branch_path(i)}, f={f_low}, \"\n", + " f\"attaches=({int(low_a)}, {int(high_a)})\")" + ] + }, + { + "cell_type": "markdown", + "id": "f1867367", + "metadata": {}, + "source": [ + "## Summary\n", + "\n", + "The `BranchDecomp` class provides:\n", + "\n", + "- `decompose(R)` — compute the decomposition from a `ReebGraph`\n", + "- `branches` — the $n \\times 4$ array of branch data\n", + "- `get_branch(i)` — return row $i$ of the branches array\n", + "- `get_branch_path(i)` — return the list of vertices in branch $i$\n", + "- `reconstruct()` — rebuild the original `ReebGraph` from the stored paths\n", + "- `draw()` — visualise the decomposition\n", + "\n", + "You can also call `R.branch_decomp()` directly on any `ReebGraph` or `MapperGraph` as a shortcut." + ] + } + ], + "metadata": { + "language_info": { + "name": "python" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/doc_source/notebooks/index.rst b/doc_source/notebooks/index.rst index d6e487d..6d5268a 100644 --- a/doc_source/notebooks/index.rst +++ b/doc_source/notebooks/index.rst @@ -15,3 +15,4 @@ This section is for adding example jupyter notebooks. interleaving_basics.ipynb compute_reeb.ipynb compute_mapper.ipynb + branch_decomp_basics.ipynb diff --git a/pyproject.toml b/pyproject.toml index ea0c6e1..83575fd 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -4,7 +4,7 @@ build-backend = "setuptools.build_meta" [project] name = "cereeberus" -version = "0.1.14" +version = "0.1.15" authors = [ { name="Liz Munch", email="muncheli@msu.edu" }, ] diff --git a/tests/test_branchdecomp.py b/tests/test_branchdecomp.py new file mode 100644 index 0000000..b457efb --- /dev/null +++ b/tests/test_branchdecomp.py @@ -0,0 +1,238 @@ +import unittest +import numpy as np + +from cereeberus.data import ex_reebgraphs as ex_rg +from cereeberus import ReebGraph +from cereeberus.reeb.branchdecomp import BranchDecomp + + +class TestBranchDecomp(unittest.TestCase): + + def check_decomp(self, R, bd): + """General validity checks on a BranchDecomp given the original ReebGraph.""" + n = len(bd.branches) + + # branches and paths have the same length + self.assertEqual(n, len(bd.paths)) + + # Each branch row has 4 columns + self.assertEqual(bd.branches.shape, (n, 4)) + + for i in range(n): + f_low, f_high, low_attach, high_attach = bd.branches[i] + + # f_low <= f_high + self.assertLessEqual(f_low, f_high) + + # attachment IDs are valid branch indices + self.assertGreaterEqual(int(low_attach), 0) + self.assertLess(int(low_attach), n) + self.assertGreaterEqual(int(high_attach), 0) + self.assertLess(int(high_attach), n) + + # A branch can only attach to a previous branch or itself + self.assertLessEqual(int(low_attach), i) + self.assertLessEqual(int(high_attach), i) + + # Path vertices are all in the original graph + for v in bd.paths[i]: + self.assertIn(v, R.nodes) + + # Every edge in the original graph is covered by exactly one path + edge_count = {} + for path in bd.paths: + for j in range(len(path) - 1): + edge = (path[j], path[j + 1]) + edge_count[edge] = edge_count.get(edge, 0) + 1 + + for u, v, _ in R.edges: + # Edges are directed low -> high + self.assertIn((u, v), edge_count, + msg=f"Edge ({u},{v}) not covered by any branch path") + + # Every vertex appears in at least one path + all_path_verts = {v for path in bd.paths for v in path} + for v in R.nodes: + self.assertIn(v, all_path_verts, + msg=f"Vertex {v} not in any branch path") + + def test_dancing_man(self): + R = ex_rg.dancing_man() + bd = BranchDecomp() + bd.decompose(R) + self.check_decomp(R, bd) + + def test_juggling_man_isolated_vertices(self): + """juggling_man has isolated vertices; they should become degenerate branches.""" + R = ex_rg.juggling_man() + bd = BranchDecomp() + bd.decompose(R) + self.check_decomp(R, bd) + + # Find the isolated vertices in the original graph + isolates = {v for v in R.nodes if R.up_degree(v) == 0 and R.down_degree(v) == 0} + self.assertGreater(len(isolates), 0, "juggling_man should have isolated vertices") + + # Each isolate must appear as a degenerate branch (f_low == f_high) + isolate_path_verts = set() + for i, path in enumerate(bd.paths): + if len(path) == 1: + f_low, f_high, _, _ = bd.branches[i] + self.assertEqual(f_low, f_high, + msg=f"Single-vertex path for branch {i} should have f_low == f_high") + isolate_path_verts.add(path[0]) + + for v in isolates: + self.assertIn(v, isolate_path_verts, + msg=f"Isolated vertex {v} should have a degenerate branch") + + def test_degenerate_branch_self_attaches(self): + """Degenerate branches (isolated vertices) should attach to themselves.""" + R = ex_rg.juggling_man() + bd = BranchDecomp() + bd.decompose(R) + + isolates = {v for v in R.nodes if R.up_degree(v) == 0 and R.down_degree(v) == 0} + + for i, path in enumerate(bd.paths): + if len(path) == 1 and path[0] in isolates: + f_low, f_high, low_attach, high_attach = bd.branches[i] + self.assertEqual(int(low_attach), i, + msg=f"Degenerate branch {i} low_attach should be itself") + self.assertEqual(int(high_attach), i, + msg=f"Degenerate branch {i} high_attach should be itself") + + def test_get_branch(self): + R = ex_rg.dancing_man() + bd = BranchDecomp() + bd.decompose(R) + + for i in range(len(bd.branches)): + branch = bd.get_branch(i) + self.assertEqual(len(branch), 4) + np.testing.assert_array_equal(branch, bd.branches[i]) + + self.assertRaises(IndexError, bd.get_branch, -1) + self.assertRaises(IndexError, bd.get_branch, len(bd.branches)) + + def test_get_branch_path(self): + R = ex_rg.dancing_man() + bd = BranchDecomp() + bd.decompose(R) + + for i in range(len(bd.paths)): + path = bd.get_branch_path(i) + self.assertIsInstance(path, list) + self.assertGreater(len(path), 0) + self.assertEqual(path, bd.paths[i]) + + self.assertRaises(IndexError, bd.get_branch_path, -1) + self.assertRaises(IndexError, bd.get_branch_path, len(bd.paths)) + + def test_original_graph_unchanged(self): + """decompose should not modify the original ReebGraph.""" + R = ex_rg.dancing_man() + nodes_before = set(R.nodes) + edges_before = set(R.edges) + f_before = R.f.copy() + + bd = BranchDecomp() + bd.decompose(R) + + self.assertEqual(set(R.nodes), nodes_before) + self.assertEqual(set(R.edges), edges_before) + self.assertEqual(R.f, f_before) + + def test_reebgraph_branch_decomp(self): + """ReebGraph.branch_decomp should return a populated BranchDecomp.""" + R = ex_rg.dancing_man() + bd = R.branch_decomp() + + self.assertIsInstance(bd, BranchDecomp) + self.check_decomp(R, bd) + + def test_reebgraph_copy(self): + """ReebGraph.copy should preserve nodes, multiedges, f-values, and positions.""" + R = ex_rg.dancing_man() + R.add_edge(6, 3) + + nodes_before = set(R.nodes) + edges_before = list(R.edges(keys=True)) + f_before = R.f.copy() + pos_before = R.pos.copy() + pos_f_before = R.pos_f.copy() + + R_copy = R.copy() + + self.assertIsInstance(R_copy, ReebGraph) + self.assertIsNot(R_copy, R) + self.assertEqual(set(R_copy.nodes), nodes_before) + self.assertEqual(list(R_copy.edges(keys=True)), edges_before) + self.assertEqual(R_copy.f, f_before) + self.assertEqual(R_copy.pos, pos_before) + self.assertEqual(R_copy.pos_f, pos_f_before) + + # Mutating the copy should not affect the original. + R_copy.add_node("copy_only", 10, reset_pos=False) + self.assertNotIn("copy_only", R.nodes) + self.assertIn("copy_only", R_copy.nodes) + + def test_empty_graph(self): + """An empty Reeb graph should produce an empty decomposition.""" + R = ReebGraph() + bd = BranchDecomp() + bd.decompose(R) + + self.assertEqual(len(bd.branches), 0) + self.assertEqual(len(bd.paths), 0) + + def test_path_function_values_match_branches(self): + """The f-values at path endpoints should match what's stored in branches.""" + R = ex_rg.dancing_man() + bd = BranchDecomp() + bd.decompose(R) + + for i, (f_low, f_high, _, _) in enumerate(bd.branches): + path = bd.paths[i] + self.assertAlmostEqual(R.f[path[0]], f_low) + self.assertAlmostEqual(R.f[path[-1]], f_high) + + def test_reconstruct(self): + """Reconstructed graph should have the same nodes, edges, and f-values as the original.""" + for make_graph in [ex_rg.dancing_man, ex_rg.juggling_man]: + R = make_graph() + bd = BranchDecomp() + bd.decompose(R) + R2 = bd.reconstruct() + + # Same node set + self.assertEqual(set(R.nodes), set(R2.nodes), + msg=f"Node sets differ for {make_graph.__name__}") + + # Same f-values + for v in R.nodes: + self.assertEqual(R.f[v], R2.f[v], + msg=f"f-value mismatch for vertex {v} in {make_graph.__name__}") + + # Same number of edges + self.assertEqual(len(R.edges), len(R2.edges), + msg=f"Edge count differs for {make_graph.__name__}") + + # Reconstructed graph passes the standard Reeb graph structural checks + self.assertEqual(set(R2.nodes), set(R2.f.keys())) + self.assertEqual(set(R2.nodes), set(R2.pos_f.keys())) + for edge in R2.edges: + v1, v2 = edge[:2] + self.assertGreater(R2.f[v2], R2.f[v1]) + + def test_reconstruct_empty(self): + """Reconstructing from an empty decomposition returns an empty ReebGraph.""" + bd = BranchDecomp() + bd.decompose(ReebGraph()) + R2 = bd.reconstruct() + self.assertEqual(len(R2.nodes), 0) + self.assertEqual(len(R2.edges), 0) + + +if __name__ == "__main__": + unittest.main()