From f2a9cc32eeea4cf666be01c606fd1775603c56f4 Mon Sep 17 00:00:00 2001 From: Enzo Busseti Date: Mon, 1 Jul 2024 01:59:09 +0400 Subject: [PATCH] more experiments; scaling objective terms does not help; dynamic diag scaling of hessian around cg loop saves about 50% total iters --- experiments/CG convergence.ipynb | 328 +- .../DiagonalScalingCGAndScalingTerms.ipynb | 4150 +++++++++++++++++ 2 files changed, 4351 insertions(+), 127 deletions(-) create mode 100644 experiments/DiagonalScalingCGAndScalingTerms.ipynb diff --git a/experiments/CG convergence.ipynb b/experiments/CG convergence.ipynb index 9bf52c0..78011bd 100644 --- a/experiments/CG convergence.ipynb +++ b/experiments/CG convergence.ipynb @@ -58,7 +58,7 @@ }, { "cell_type": "code", - "execution_count": 97, + "execution_count": 3, "id": "4cf3532d", "metadata": {}, "outputs": [], @@ -174,113 +174,27 @@ }, { "cell_type": "code", - "execution_count": 718, + "execution_count": 4, "id": "4df79fd5", "metadata": { "scrolled": true }, "outputs": [ { - "name": "stdout", + "name": "stderr", "output_type": "stream", "text": [ - "===============================================================================\n", - " CVXPY \n", - " v1.5.1 \n", - "===============================================================================\n", - "(CVXPY) Jun 30 06:14:38 PM: Your problem has 170 variables, 175 constraints, and 0 parameters.\n", - "(CVXPY) Jun 30 06:14:38 PM: It is compliant with the following grammars: DCP, DQCP\n", - "(CVXPY) Jun 30 06:14:38 PM: (If you need to solve this problem multiple times, but with different data, consider using parameters.)\n", - "(CVXPY) Jun 30 06:14:38 PM: CVXPY will first compile your problem; then, it will invoke a numerical solver to obtain a solution.\n", - "(CVXPY) Jun 30 06:14:38 PM: Your problem is compiled with the CPP canonicalization backend.\n", - "-------------------------------------------------------------------------------\n", - " Compilation \n", - "-------------------------------------------------------------------------------\n", - "(CVXPY) Jun 30 06:14:38 PM: Compiling problem (target solver=GLPK).\n", - "(CVXPY) Jun 30 06:14:38 PM: Reduction chain: Dcp2Cone -> CvxAttr2Constr -> ConeMatrixStuffing -> GLPK\n", - "(CVXPY) Jun 30 06:14:38 PM: Applying reduction Dcp2Cone\n", - "(CVXPY) Jun 30 06:14:38 PM: Applying reduction CvxAttr2Constr\n", - "(CVXPY) Jun 30 06:14:38 PM: Applying reduction ConeMatrixStuffing\n", - "(CVXPY) Jun 30 06:14:38 PM: Applying reduction GLPK\n", - "(CVXPY) Jun 30 06:14:38 PM: Finished problem compilation (took 1.856e-02 seconds).\n", - "-------------------------------------------------------------------------------\n", - " Numerical solver \n", - "-------------------------------------------------------------------------------\n", - "(CVXPY) Jun 30 06:14:38 PM: Invoking solver GLPK to obtain a solution.\n", - "\n", - "ECOS 2.0.10 - (C) embotech GmbH, Zurich Switzerland, 2012-15. Web: www.embotech.com/ECOS\n", - "\n", - "It pcost dcost gap pres dres k/t mu step sigma IR | BT\n", - " 0 +2.796e-15 -4.250e+01 +2e+03 7e-01 4e-01 1e+00 2e+00 --- --- 1 1 - | - - \n", - " 1 +2.431e+01 +1.393e+01 +9e+02 3e-01 1e-01 1e+00 1e+00 0.6757 2e-01 1 1 1 | 0 0\n", - " 2 +2.818e+01 +2.371e+01 +5e+02 1e-01 4e-02 5e-01 5e-01 0.9551 5e-01 1 1 1 | 0 0\n", - " 3 +3.392e+01 +3.169e+01 +3e+02 5e-02 2e-02 2e-01 3e-01 0.6023 2e-01 1 1 1 | 0 0\n", - " 4 +3.568e+01 +3.389e+01 +2e+02 4e-02 2e-02 2e-01 2e-01 0.3509 4e-01 1 1 1 | 0 0\n", - " 5 +3.873e+01 +3.762e+01 +1e+02 2e-02 9e-03 1e-01 1e-01 0.4375 1e-01 1 1 1 | 0 0\n", - " 6 +3.993e+01 +3.917e+01 +8e+01 2e-02 5e-03 4e-02 1e-01 0.7327 5e-01 1 1 1 | 0 0\n", - " 7 +4.201e+01 +4.162e+01 +4e+01 8e-03 3e-03 2e-02 5e-02 0.5206 9e-02 1 1 1 | 0 0\n", - " 8 +4.295e+01 +4.273e+01 +2e+01 4e-03 1e-------------------------------------------------------------------------------\n", - " Summary \n", - "-------------------------------------------------------------------------------\n", - "(CVXPY) Jun 30 06:14:38 PM: Problem status: optimal\n", - "-03 1e-02 3e-02 0.5909 2e-01 1 1 1 | 0 0\n", - " 9 +4.380e+01 +4.374e+01 +7e+00 1e-03 4e-04 2e-03 8e-03 0.9362 3e-01 1 1 1 | 0 0\n", - "10 +4.416e+01 +4.414e+01 +2e+00 3e-04 1e-04 4e-04 2e-03 0.8013 7e-02 1 1 1 | 0 0\n", - "11 +4.427e+01 +4.427e+01 +3e-01 4e-05 1e-05 6e-05 3e-04 0.8955 4e-02 1 1 1 | 0 0\n", - "12 +4.428e+01 +4.428e+01 +7e-02 1e-05 3e-06 1e-05 8e-05 0.8943 2e-01 1 1 1 | 0 0\n", - "13 +4.428e+01 +4.428e+01 +2e-02 3e-06 1e-06 4e-06 2e-05 0.9890 3e-01 1 1 1 | 0 0\n", - "14 +4.429e+01 +4.429e+01 +4e-04 7e-08 2e-08 9e-08 5e-07 0.9801 2e-03 1 1 1 | 0 0\n", - "15 +4.429e+01 +4.429e+01 +1e-05 2e-09 7e-10 3e-09 2e-08 0.9690 5e-04 1 1 1 | 0 0\n", - "16 -nan +nan -nan -nan -nan -nan -nan 0.9890 1e-04 0 0 0 | 0 0\n", - "Reached NAN dead end, recovering best iterate (15) and stopping.\n", - "\n", - "Close to OPTIMAL (within feastol=2.1e-09, reltol=3.1e-07, abstol=1.4e-05).\n", - "Runtime: 0.079745 seconds.\n", - "\n", - "\n", - "ECOS 2.0.10 - (C) embotech GmbH, Zurich Switzerland, 2012-15. Web: www.embotech.com/ECOS\n", - "\n", - "It pcost dcost gap pres dres k/t mu step sigma IR | BT\n", - " 0 +2.796e-15 -4.250e+01 +2e+03 7e-01 4e-01 1e+00 2e+00 --- --- 1 1 - | - - \n", - " 1 +2.431e+01 +1.393e+01 +9e+02 3e-01 1e-01 1e+00 1e+00 0.6757 2e-01 1 1 1 | 0 0\n", - " 2 +2.818e+01 +2.371e+01 +5e+02 1e-01 4e-02 5e-01 5e-01 0.9551 5e-01 1 1 1 | 0 0\n", - " 3 +3.392e+01 +3.169e+01 +3e+02 5e-02 2e-02 2e-01 3e-01 0.6023 2e-01 1 1 1 | 0 0\n", - " 4 +3.568e+01 +3.389e+01 +2e+02 4e-02 2e-02 2e-01 2e-01 0.3509 4e-01 1 1 1 | 0 0\n", - " 5 +3.873e+01 +3.762e+01 +1e+02 2e-02 9e-03 1e-01 1e-01 0.4375 1e-01 1 1 1 | 0 0\n", - " 6 +3.993e+01 +3.917e+01 +8e+01 2e-02 5e-03 4e-02 1e-01 0.7327 5e-01 1 1 1 | 0 0\n", - " 7 +4.201e+01 +4.162e+01 +4e+01 8e-03 3e-03 2e-02 5e-02 0.5206 9e-02 1 1 1 | 0 0\n", - " 8 +4.295e+01 +4.273e+01 +2e+01 4e-03 1e-03 1e-02 3e-02 0.5909 2(CVXPY) Jun 30 06:14:38 PM: Optimal value: 4.429e+01\n", - "e-01 1 1 1 | 0 0\n", - " 9 +4.380e+01 +4.374e+01 +7e+00 1e-03 4e-04 2e-03 8e-03 0.9362 3e-01 1 1 1 | 0 0\n", - "10 +4.416e+01 +4.414e+01 +2e+00 3e-04 1e-04 4e-04 2e-03 0.8013 7e-02 1 1 1 | 0 0\n", - "11 +4.427e+01 +4.427e+01 +3e-01 4e-05 1e-05 6e-05 3e-04 0.8955 4e-02 1 1 1 | 0 0\n", - "12 +4.428e+01 +4.428e+01 +7e-02 1e-05 3e-06 1e-05 8e-05 0.8943 2e-01 1 1 1 | 0 0\n", - "13 +4.428e+01 +4.428e+01 +2e-02 3e-06 1e-06 4e-06 2e-05 0.9890 3e-01 1 1 1 | 0 0\n", - "14 +4.429e+01 +4.429e+01 +4e-04 7e-08 2e-08 9e-08 5e-07 0.9801 2e-03 1 1 1 | 0 0\n", - "15 +4.429e+01 +4.429e+01 +1e-05 2e-09 7e-10 3e-09 2e-08 0.9690 5e-04 1 1 1 | 0 0\n", - "16 -nan +nan -nan -nan -nan -nan -nan 0.9890 1e-04 0 0 0 | 0 0\n", - "Reached NAN dead end, recovering best iterate (15) and stopping.\n", - "\n", - "Close to OPTIMAL (within feastol=2.1e-09, reltol=3.1e-07, abstol=1.4e-05).\n", - "Runtime: 0.087315 seconds.\n", - "\n", - "GLPK Simplex Optimizer 5.0\n", - "877 rows, 521 columns, 63602 non-zeros\n", - " 0: obj = 0.000000000e+00 inf = 1.501e+02 (186)\n", - " 684: obj = 1.095693126e+02 inf = 5.235e-14 (0) 5\n", - "* 1148: obj = 4.428640698e+01 inf = 0.000e+00 (0) 4\n", - "OPTIMAL LP SOLUTION FOUND\n", - "(CVXPY) Jun 30 06:14:38 PM: Compilation took 1.856e-02 seconds\n", - "(CVXPY) Jun 30 06:14:38 PM: Solver (including time spent in interface) took 1.336e-01 seconds\n" + "/home/enzo/repos/project_euromir/experiments/../env/lib/python3.11/site-packages/cvxpy/problems/problem.py:1407: UserWarning: Solution may be inaccurate. Try another solver, adjusting the solver settings, or solve with verbose=True for more information.\n", + " warnings.warn(\n" ] }, { "data": { "text/plain": [ - "2.7755575615628914e-16" + "6.521699014161442e-09" ] }, - "execution_count": 718, + "execution_count": 4, "metadata": {}, "output_type": "execute_result" } @@ -301,7 +215,7 @@ }, { "cell_type": "code", - "execution_count": 99, + "execution_count": 5, "id": "a83ea724", "metadata": {}, "outputs": [ @@ -311,7 +225,7 @@ "1795.977318834588" ] }, - "execution_count": 99, + "execution_count": 5, "metadata": {}, "output_type": "execute_result" } @@ -323,7 +237,7 @@ }, { "cell_type": "code", - "execution_count": 100, + "execution_count": 6, "id": "443067c3", "metadata": {}, "outputs": [], @@ -333,17 +247,17 @@ }, { "cell_type": "code", - "execution_count": 101, + "execution_count": 7, "id": "9aadf4cc", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "[]" + "[]" ] }, - "execution_count": 101, + "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, @@ -375,16 +289,6 @@ "plt.plot(np.linalg.eigh(H)[0])" ] }, - { - "cell_type": "code", - "execution_count": null, - "id": "098870ad", - "metadata": {}, - "outputs": [], - "source": [ - "optimal_point = xy" - ] - }, { "cell_type": "markdown", "id": "dc632887", @@ -395,7 +299,7 @@ }, { "cell_type": "code", - "execution_count": 565, + "execution_count": 8, "id": "1bdfca03", "metadata": {}, "outputs": [ @@ -403,13 +307,13 @@ "name": "stdout", "output_type": "stream", "text": [ - "6.525929617483746e-10\n", - "6.522278456272828e-10\n" + "1795.9773188345885\n", + "29.31652539415214\n" ] }, { "data": { - "image/png": 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", + "image/png": 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/+4ZONnlU+HCWBvWJDdp1AQCwgq78fvs8MjN16tTzPl5gzpw5mjNnjq+nDmu9YqN0ssbDJGAAAIIs5J7N1Fn5+flKS0tTZmamKddvvdXE8mwAAILLMmHGzNVMEsuzAQAwi2XCjNl4PhMAAOawTJgJldtMhBkAAILLMmHG7NtMhBkAAMxhmTBjttYww5OzAQAILsKMn/TiydkAAJiCMOMn3qXZPJ8JAICgskyYMXsCMEuzAQAwh2XCDBOAAQDoniwTZsxGmAEAwByEGT9pDTO1p5rlafHp2Z0AAKALCDN+0hpmJKn2FKMzAAAEi2XCjNkTgKPsEYqLtkviVhMAAMFkmTBj9gRgieXZAACYwTJhJhSwPBsAgOAjzPgRK5oAAAg+wowfEWYAAAg+wowfEWYAAAg+y4QZs1czSV89bJInZwMAEDyWCTOsZgIAoHuyTJgJBdxmAgAg+AgzfsTSbAAAgo8w40eMzAAAEHyEGT8izAAAEHyEGT9qDTOsZgIAIHgIM37UKzZaklTb0KzG5haTqwEAoHsgzPhRrx5RuuAfe818vL/G5GoAAOgeLBNmQmHTvIgIm8an9pEkbfniiGl1AADQnVgmzITCpnmSNGFIb0nSli+OmloHAADdhWXCTKiYcPHpkZn39xxVk4d5MwAABBphxs+G9ovXBbFROtHo0Ud7mTcDAECgEWb8jHkzAAAEF2EmAL6aN0OYAQAg0AgzAfDVvJljzJsBACDACDMB0Dpv5mQT82YAAAg0wkwAMG8GAIDgIcwECPNmAAAIjpANMydOnNDgwYP10EMPmV1KpzBvBgCA4AjZMPP4449r/PjxZpfRacybAQAgOEIyzOzatUuffvqprr/+erNL6TTmzQAAEBw+h5nCwkJNmzZNycnJstlsWrt2bbs2y5YtU2pqqmJiYuRyubRp0yafrvHQQw8pLy/P19JCDvNmAAAIPJ/DTH19vTIyMrR06dKzfr569WrNnTtXCxcuVElJiSZPnqycnBxVVFR427hcLqWnp7d77d+/X//7v/+roUOHaujQoZ3/ViGCeTMAAARepK9/kJOTo5ycnHN+vnjxYt19992aNWuWJOmpp57SunXrtHz5cu9oS3Fx8Tn/fsuWLXrxxRf18ssvq66uTk1NTUpISNC///u/n7V9Q0ODGhoavO/dbrevXylgWufNHDvRpI/21sg1+AKzSwIAwHL8OmemsbFRxcXFys7ObnM8OztbRUVFHTpHXl6eKisrtWfPHv3qV7/SPffcc84g09re6XR6XykpKV36Dv7EvBkAAALPr2GmurpaHo9HSUlJbY4nJSXp4MGD/ryU14IFC1RTU+N9VVZWBuQ6ncW8GQAAAsvn20wdYbPZ2rw3DKPdsY646667ztvG4XDI4XAoPz9f+fn58ng8Pl8nkM6cNxNlD8kFZAAAhC2//rImJibKbre3G4WpqqpqN1rjb7m5uSorK9O2bdsCeh1fsd8MAACB5dcwEx0dLZfLpYKCgjbHCwoKNHHiRH9eKmwwbwYAgMDyOczU1dWptLRUpaWlkqTy8nKVlpZ6l17Pnz9fK1eu1LPPPqsdO3Zo3rx5qqio0OzZs/1a+Jny8/OVlpamzMzMgF6nM5g3AwBA4NgMwzB8+YMNGzYoKyur3fGZM2dq1apVkk5vmrdo0SIdOHBA6enpWrJkiaZMmeKXgs/H7XbL6XSqpqZGCQkJQbnm+Xx2sFbXPlWoHlF2ffSzbObNAABwhq78fvscZkJdKIaZlhZD4x5/S0frG/XKvRPZbwYAgDN05ffbMkMEoXyb6fS8GW41AQAQCJYJM6G6mqnVhCFMAgYAIBAsE2ZCXWuYeX/PMTU285wmAAD8xTJhJpRvM0nSpf16qndctE42ebR933GzywEAwDIsE2ZC/TZT23kzR02uBgAA67BMmAkHzJsBAMD/CDNBxLwZAAD8jzATRMybAQDA/ywTZkJ9ArDEvBkAAALBMmEm1CcAt2LeDAAA/mWZMBMumDcDAIB/EWaC7OvzZkorj5tdDgAAYY8wE2QRETZNuiRRkrT+syqTqwEAIPxZJsyEwwTgVlcN7ydJWv8pYQYAgK6yTJgJlwnAknTl0L6KsEmfHqzVvuMnzS4HAICwZpkwE04uiIvWmEEXSGJ0BgCAriLMmIRbTQAA+AdhxiRZw06HmXc/r9apJo/J1QAAEL4IMyYZMSBeA5wxOtXUos1soAcAQKdZJsyE02omSbLZbJo6jFtNAAB0lWXCTDitZmrVOm/m7U+rZBiGydUAABCeLBNmwtEVl/RRdGSE9h47qV1VdWaXAwBAWCLMmCg2OlKX/+NZTW9zqwkAgE4hzJjs67eaAACA7wgzJmsNM8VfHlPNiSaTqwEAIPwQZkyW0jtWl/TrKU+LocJdh80uBwCAsEOYCQHsBgwAQOcRZkJA627AG3YelqeFJdoAAPjCMmEm3DbN+7pxF12g+JhIHa1v1Id7j5tdDgAAYcUyYSYcN81rFWWP0JRL+0riVhMAAL6yTJgJd1ks0QYAoFMIMyFi6rC+stmkT/a7dch9yuxyAAAIG4SZEJHY06FRA3tJ4lYTAAC+IMyEkKv+sarp74QZAAA6jDATQlr3m3l3d7Uamj0mVwMAQHggzISQy5IT1DfeoRONHr33xVGzywEAICwQZkJIRIRNWcNOL9FmVRMAAB1DmAkxVw1PkiSt/6xKhsFuwAAAnE9IhpnIyEiNHj1ao0eP1qxZs8wuJ6gmXZqoKLtNXx45oS+q680uBwCAkBdpdgFn06tXL5WWlppdhil6OiI1PrWP3tldrfWfVunivj3NLgkAgJAWkiMz3R27AQMA0HE+h5nCwkJNmzZNycnJstlsWrt2bbs2y5YtU2pqqmJiYuRyubRp0yafruF2u+VyuTRp0iRt3LjR1xLDXusS7a3lR1V7qsnkagAACG0+h5n6+nplZGRo6dKlZ/189erVmjt3rhYuXKiSkhJNnjxZOTk5qqio8LZxuVxKT09v99q/f78kac+ePSouLtZvfvMb3XnnnXK73Z38euEpNTFOqYlxam4xtP6zw2aXAwBASLMZXVgyY7PZtGbNGk2fPt17bPz48Ro7dqyWL1/uPTZixAhNnz5deXl5Pl8jJydH//Ef/6Fx48ad9fOGhgY1NDR437vdbqWkpKimpkYJCQk+Xy9U/Oebn+nXb+/Wpf166m8PTlaknTuCAADrcrvdcjqdnfr99usvZGNjo4qLi5Wdnd3meHZ2toqKijp0jmPHjnnDyd69e1VWVqYhQ4acs31eXp6cTqf3lZKS0vkvEEJmTR6iXrFR2lVVp5eL95pdDgAAIcuvYaa6uloej0dJSUltjiclJengwYMdOseOHTs0btw4ZWRk6MYbb9R//dd/qXfv3udsv2DBAtXU1HhflZWVXfoOocLZI0oPXHWpJGlxwU7VNzSbXBEAAKEpIEuzbTZbm/eGYbQ7di4TJ07U9u3bO3wth8Mhh8Oh/Px85efny+OxzjON7pgwWP+9eY++PHJCKwq/0LxrhppdEgAAIcevIzOJiYmy2+3tRmGqqqrajdb4W25ursrKyrRt27aAXieYoiMj9Mi1wyVJKwq/UJX7lMkVAQAQevwaZqKjo+VyuVRQUNDmeEFBgSZOnOjPS3Ub14/srzGDeulkk0dL3tppdjkAAIQcn8NMXV2dSktLvTv0lpeXq7S01Lv0ev78+Vq5cqWeffZZ7dixQ/PmzVNFRYVmz57t18LPlJ+fr7S0NGVmZgb0OsFms9m08PoRkqTV2yq181CtyRUBABBafF6avWHDBmVlZbU7PnPmTK1atUrS6U3zFi1apAMHDig9PV1LlizRlClT/FLw+XRlaVcom/2HYr3xyUFdNbyfnr3LWoENAICu/H53aZ+ZUGTVMFNeXa9rFm9Uc4uhF2aN18RLEs0uCQAAvwmZfWbMZNXbTK1SE+N0+/hBkqTHX9+hlhZLZVAAADqNkZkwcqSuQVN/uUG1Dc1acmuGbhoz0OySAADwC0Zmuok+PR26N+tiSdKv1u3UqSbr7KkDAEBnEWbCzA+uSFWyM0b7jp/UqqI9ZpcDAIDpLBNmrD5nplVMlF3/lj1MkpT/9m4drW80uSIAAMxlmTBjxR2Az+WmMRcqbUCCahua9fTfd5ldDgAAprJMmOlOIiJsWnjD6Y30nt/ypfZU15tcEQAA5iHMhKkrLknU1GF91dxi6MHVpTxVGwDQbVkmzHSXOTNf99Npl6lXbJQ+rDyuf/3D+6xuAgB0S+wzE+ZKK4/r9me2qL7Ro+y0JC27fawi7ZbJqACAboJ9Zrqx0Sm99MzMcYqOjNCbZYf0yCsfsTswAKBbIcxYwMSLE5X//bGyR9j06gf79NhfymSxATcAAM6JMGMR16Ql6Ve3jJIkrSraoyVvsWQbANA9WCbMdMcJwGe6acxAPfbPl0mSnv77Lq3c9IXJFQEAEHhMALagpW/v0q/e3ClJWvSdUfpuZorJFQEA8M2YAIw2crMu0b9OGSJJevTVj/S37QdMrggAgMAhzFiQzWbTgpzh+l5miloM6YEXS7Rx52GzywIAICAIMxZls9n0+E0jdcOoAWryGLrnv9/Xuk8Oml0WAAB+R5ixMHuETUu+O1rXXdZfjZ4W3ft8sV56v9LssgAA8CvLhBlWM51ddGSEln5/jL47bqBaDOmRP33EKicAgKWwmqmbMAxDeX/7VCsKTweZ3KyL9VD2MNlsNpMrAwCA1UzoAJvNph9fP0I/um64JCl//edauPZjeXj0AQAgzBFmupl7p16sJ24aKZtNeuG9Cj3wYokam1vMLgsAgE4jzHRD3x8/SL++bYyi7Db99aMDmvX793WisdnssgAA6BTCTDd146hkrZyZqR5RdhXuPKw7Vr6n4ycazS4LAACfEWa6sSuH9tXzs8bL2SNKH1Qc1y2/2azy6nqzywIAwCeEmW7ONfgCvfTDy9Uv3qFdVXX69q/f0Vtlh8wuCwCADiPMQMP6x+vP90/SuMEXqLahWbN+/77+883PWOkEAAgLlgkzbJrXNUkJMXrhngm6a+JFkqRfv71bdz23VcfqmUcDAAhtbJqHdtaW7NOjr36kU00turBXD/12hkvpFzrNLgsAYGFsmge/mj7mQq2Zc4UG94nVvuMndfPyIp7pBAAIWYQZnNWIAQl67b5J+qcR/dTY3KJH/vSRFry6XQ3NHrNLAwCgDcIMzsnZI0orZozTQ9lDZbNJ/7O1Qt/97RZVuU+ZXRoAAF6EGXyjiAib7rvqUq36P99Sr9gofVh5XDctK9LOQ7VmlwYAgCTCDDroyqF99VruJA3pG6d9x0/qO8uK9M6uarPLAgCAMIOOG9QnVq/eO1Hfuqi3ahuadddzW5kYDAAwHWEGPukVG60/zPqW/nl0sppbDD3yp4+0+M3PZLEV/gCAMEKYgc8ckXY9deto3X/VJZKkp9/erfkvfchKJwCAKUIyzJSXlysrK0tpaWkaOXKk6ut5+GGosdls+rfsYfp/3xkpe4RNa0r26c7fbVXNiSazSwMAdDMhGWbuuusuPfbYYyorK9PGjRvlcDjMLgnncGvmID13V6Z6OiL1XvlR3bz8XVUePWF2WQCAbiTkwswnn3yiqKgoTZ48WZLUu3dvRUZGmlwVvsmUoX31p3svV7IzRp8frtdNy97Vx/tqzC4LANBN+BxmCgsLNW3aNCUnJ8tms2nt2rXt2ixbtkypqamKiYmRy+XSpk2bOnz+Xbt2qWfPnvr2t7+tsWPH6oknnvC1RJhgeP8Ercm9QpclJ6i6rlF3/O497TjgNrssAEA34HOYqa+vV0ZGhpYuXXrWz1evXq25c+dq4cKFKikp0eTJk5WTk6OKigpvG5fLpfT09Hav/fv3q6mpSZs2bVJ+fr42b96sgoICFRQUdP4bImiSEmL04r9O0OiUXjp+okl3rHxPu9hcDwAQYF16arbNZtOaNWs0ffp077Hx48dr7NixWr58uffYiBEjNH36dOXl5Z33nJs3b9bPf/5zvfHGG5KkX/7yl5Kkhx9++KztGxoa1NDQ4H3vdruVkpLCU7NNVHOySbev3KKP97mV2NOh1T+coIv79jS7LABACAuZp2Y3NjaquLhY2dnZbY5nZ2erqKioQ+fIzMzUoUOHdOzYMbW0tKiwsFAjRow4Z/u8vDw5nU7vKyUlpUvfAV3n7BGl5+8er+H941Vd16DvP7NFe6pZkQYACAy/hpnq6mp5PB4lJSW1OZ6UlKSDBw926ByRkZF64oknNGXKFI0aNUqXXnqpbrzxxnO2X7BggWpqaryvykp2pA0FvWKj9cdZ43Vpv5465D4daFjlBAAIhICsZrLZbG3eG4bR7tg3ycnJ0fbt2/Xxxx9r8eLF39jW4XAoISFBf/jDHzRhwgRdffXVnaoZ/tenp0N/vGe8hvSN0/6aU7rtmS3af/yk2WUBACzGr2EmMTFRdru93ShMVVVVu9Eaf8vNzVVZWZm2bdsW0OvAN/3iY/Q/90zQRX1itffYSd32zBYdrDlldlkAAAvxa5iJjo6Wy+Vqt/qooKBAEydO9OelEEaSEmL0wj0TlNK7h748ckLfX7lFVbUEGgCAf/gcZurq6lRaWqrS0lJJpx89UFpa6l16PX/+fK1cuVLPPvusduzYoXnz5qmiokKzZ8/2a+Fnys/PV1pamjIzMwN6HXROcq8eemHWBCU7Y/TF4Xrd/sx7qq5rOP8fAgBwHj4vzd6wYYOysrLaHZ85c6ZWrVol6fSmeYsWLdKBAweUnp6uJUuWaMqUKX4p+Hy6srQLgfflkXp997ebdcjdoIv6xOq5//MtpSbGmV0WAMBkXfn97tI+M6GIMBP6vjhcpxm/26p9x0+qV2yUVswYp2+l9ja7LACAiUJmnxkzcZspfAzp21Nrc69QxkCnd6fg/y3dZ3ZZAIAwxcgMTHOy0aO5q0u07pNDkqT51wzV/Vdd4tMyfgCANTAyg7DUI9qu5be79K9ThkiSFhfs1EMvf6TG5haTKwMAhBPCDEwVEWHTj68foV9MT5c9wqZXPtirO599TzUnmswuDQAQJiwTZpgzE97umDBYv5s5Tj0dkdryxVHdvPxdVRzh8QcAgPNjzgxCyo4Dbv1g1TYdqDmlPnHRembmOI0ddIHZZQEAAow5M7CMEQMStDb3Cl2WnKAj9Y26e9U2Hn8AAPhGhBmEnKSEGL30w8uVfmGCjp1o0tzVJfK0WGoAEQDgR5YJM8yZsZY4R6Se/t4YxUbbteWLo1q+YbfZJQEAQhRzZhDS/lS8Vw+9/KHsETa99MMJcg1mp2AAsCLmzMCyvjP2Qk0fnSxPi6EH/qdUNSdZsg0AaIswg5Bms9n0H9PTNah3rPYdP6kfv7pdFhtMBAB0EWEGIS8+JkpP3zZGkRE2/XX7Ab30fqXZJQEAQohlwgwTgK1tdEovPXTtMEnST1/7RLurak2uCAAQKpgAjLDR0mJo5nNbtWlXtYb3j9fa3CsUE2U3uywAgB8wARjdQkSETf/53Qz1iYvWpwdr9eTfPjW7JABACCDMIKz0i4/Rr76bIUlaVbRHb5UdMrkiAIDZCDMIO1nD+mnWpFRJ0sN/+pDHHQBAN0eYQVh6+Lph3scdzFtdynJtAOjGLBNmWM3UvTgi7Xr6e2PUI8quzV8c0cadh80uCQBgEsuEmdzcXJWVlWnbtm1ml4IgGdK3p24fP0iStGz95yZXAwAwi2XCDLqnWZOHKNoeoa17jmrbnqNmlwMAMAFhBmGtvzNG33FdKElatp4nawNAd0SYQdj74ZSLFWGT1n92WJ/srzG7HABAkBFmEPYuSozTjaOSJUnLNzB3BgC6G8IMLOHeqRdLkv66/YC+OFxncjUAgGAizMASRgxI0NXD+8kwpN9u/MLscgAAQUSYgWXMyTo9OvNqyV4dqDlpcjUAgGCxTJhh0zy4BvfW+NTeavIYeqaw3OxyAABBYjMstg98Vx4hjvBXuPOw7nx2q3pE2fXuo1epd1y02SUBADqgK7/flhmZASRp8qWJSr8wQSebPFr1LqMzANAdEGZgKTabTblTL5EkrSrao9pTTSZXBAAINMIMLOfay/prSN84uU8164X3KswuBwAQYIQZWE5EhE33Xnl6ZdMzm8p1qsljckUAgEAizMCSpo+5UBf26qHquga9XLzX7HIAAAFEmIElRdkjdM/kVEnSbzd+rmZPi8kVAQAChTADy7o1c5D6xEVr77GT+vNH+80uBwAQIIQZWFaPaLt+MOn06Myy9Z+rpcVSWyoBAP4h5MLMZ599ptGjR3tfPXr00Nq1a80uC2HqjgmDFe+I1K6qOr3yAXNnAMCKQi7MDBs2TKWlpSotLdU777yjuLg4XXPNNWaXhTDl7BGl3KtO7zvzi7/u0OHaBpMrAgD4W8iFma977bXXdPXVVysuLs7sUhDGZk1K1WXJCao52aTH/lJmdjkAAD/zOcwUFhZq2rRpSk5Ols1mO+stoGXLlik1NVUxMTFyuVzatGlTp4p76aWXdOutt3bqb4FWkfYIPXnzKEXYpD9/uF9vf3rI7JIAAH7kc5ipr69XRkaGli5detbPV69erblz52rhwoUqKSnR5MmTlZOTo4qKr3ZidblcSk9Pb/fav/+rFSdut1vvvvuurr/++k58LaCtkQOdmjV5iCTpJ2s+Vl1Ds8kVAQD8pUtPzbbZbFqzZo2mT5/uPTZ+/HiNHTtWy5cv9x4bMWKEpk+frry8vA6f+w9/+IPWrVun559//hvbNTQ0qKHhq3kQbrdbKSkpPDUb7Zxs9OjapwpVcfSE7pp4kX727cvMLgkA8A8h89TsxsZGFRcXKzs7u83x7OxsFRUV+XSujt5iysvLk9Pp9L5SUlJ8ug66jx7Rdj1+U7ok6b8379EHFcdMrggA4A9+DTPV1dXyeDxKSkpqczwpKUkHDx7s8Hlqamq0detWXXvttedtu2DBAtXU1HhflZWVPteN7mPypX31nbEDZRjSo698pMZmdgYGgHAXkNVMNputzXvDMNod+yZOp1OHDh1SdHT0eds6HA4lJCS0eQHf5Cc3jFCfuGjtPFSn32z83OxyAABd5Ncwk5iYKLvd3m4Upqqqqt1ojb/l5+crLS1NmZmZAb0Owt8FcdH692lpkqSlb+/W7qo6kysCAHSFX8NMdHS0XC6XCgoK2hwvKCjQxIkT/XmpdnJzc1VWVqZt27YF9Dqwhm9nJCtrWF81elq04NWPeNQBAIQxn8NMXV2dd4deSSovL1dpaal36fX8+fO1cuVKPfvss9qxY4fmzZuniooKzZ4926+Fn4mRGfjCZrPpFzeNVGy0Xdv2HNMLWyvO/0cAgJDk89LsDRs2KCsrq93xmTNnatWqVZJOb5q3aNEiHThwQOnp6VqyZImmTJnil4LPpytLu9D9PPduuX7+5zLFOyJVMP9K9XfGmF0SAHRLXfn97tI+M6GIMANfeFoMfWd5kUorj+uatCStmOHyabI6AMA/QmafGTNxmwmdYY+w6cnvjFRkhE0FZYe07hMedQAA4YaRGUDSL9d9qvz1n2twn1gVzLtS0ZGWyfkAEBYYmQG6aM7US9Q33qEvj5zQ7zfvMbscAIAPCDOApDhHpP7tmqGSpF+/vVvHTzSaXBEAoKMsE2aYM4OuumVciob3j1fNySY9/ffdZpcDAOgg5swAX1O487DufHarouw2Fcy7UhclxpldEgB0C8yZAfxkytC+unJoXzV5DD35t0/NLgcA0AGEGeAMC28YoQib9MYnB7W1/KjZ5QAAzsMyYYY5M/CXoUnx+t63BkmSHv9rGc9tAoAQx5wZ4CwO1zZo6i/Xq77Ro//63mj98+gLzS4JACyNOTOAn/WNd2hO1iWSpEVvfKZTTR6TKwIAnAthBjiHuyelKtkZo33HT+p375SbXQ4A4BwIM8A5xETZ9fB1wyRJyzd8ruq6BpMrAgCcjWXCDBOAEQj/nHGhRg10qq6hWUsKdppdDgDgLJgADJzHe18c0a0rtijCJq2bO0WXJsWbXRIAWA4TgIEAGj+kj7LTktRiSE+8vsPscgAAZ4g0uwAgHCy4foTe/rRK6z87rEf+9KHiHPynA6D7Sk2M052XX2R2GV78HxnogNTEOM24fLCee3ePXnp/r9nlAICpJl7chzADhKNHrh2ufvExqmtoMrsUADDVoN6xZpfQhmXCTH5+vvLz8+XxsLkZAqNHtF33Tr3Y7DIAAGdgNRMAADAdq5kAAEC3RZgBAABhjTADAADCGmEGAACENcIMAAAIa4QZAAAQ1ggzAAAgrBFmAABAWLNMmMnPz1daWpoyMzPNLgUAAAQROwADAADTsQMwAADotggzAAAgrFnmqdmtWu+aud1ukysBAAAd1fq73ZnZL5YLM7W1tZKklJQUkysBAAC+qq2tldPp9OlvLDcBuKWlRfv371d8fLxsNpvfzut2u5WSkqLKykomFgcB/R1c9Hdw0d/BRX8HV2f72zAM1dbWKjk5WRERvs2CsdzITEREhAYOHBiw8yckJPAfQxDR38FFfwcX/R1c9Hdwdaa/fR2RacUEYAAAENYIMwAAIKwRZjrI4XDopz/9qRwOh9mldAv0d3DR38FFfwcX/R1cZvS35SYAAwCA7oWRGQAAENYIMwAAIKwRZgAAQFgjzAAAgLBGmOmgZcuWKTU1VTExMXK5XNq0aZPZJYWdvLw8ZWZmKj4+Xv369dP06dP12WeftWljGIZ+9rOfKTk5WT169NDUqVP1ySeftGnT0NCg+++/X4mJiYqLi9O3v/1t7d27N5hfJSzl5eXJZrNp7ty53mP0t3/t27dPd9xxh/r06aPY2FiNHj1axcXF3s/pb/9pbm7WT37yE6WmpqpHjx4aMmSIHnvsMbW0tHjb0N+dV1hYqGnTpik5OVk2m01r165t87m/+vbYsWOaMWOGnE6nnE6nZsyYoePHj/tesIHzevHFF42oqCjjmWeeMcrKyowHH3zQiIuLM7788kuzSwsr1157rfHcc88ZH3/8sVFaWmrccMMNxqBBg4y6ujpvmyeffNKIj483XnnlFWP79u3GrbfeagwYMMBwu93eNrNnzzYuvPBCo6CgwPjggw+MrKwsIyMjw2hubjbja4WFrVu3GhdddJExatQo48EHH/Qep7/95+jRo8bgwYONu+66y3jvvfeM8vJy46233jJ2797tbUN/+88vfvELo0+fPsZf/vIXo7y83Hj55ZeNnj17Gk899ZS3Df3dea+//rqxcOFC45VXXjEkGWvWrGnzub/69rrrrjPS09ONoqIio6ioyEhPTzduvPFGn+slzHTAt771LWP27Nltjg0fPtx49NFHTarIGqqqqgxJxsaNGw3DMIyWlhajf//+xpNPPultc+rUKcPpdBq/+c1vDMMwjOPHjxtRUVHGiy++6G2zb98+IyIiwnjjjTeC+wXCRG1trXHppZcaBQUFxpVXXukNM/S3f/3oRz8yJk2adM7P6W//uuGGG4wf/OAHbY7dfPPNxh133GEYBv3tT2eGGX/1bVlZmSHJ2LJli7fN5s2bDUnGp59+6lON3GY6j8bGRhUXFys7O7vN8ezsbBUVFZlUlTXU1NRIknr37i1JKi8v18GDB9v0tcPh0JVXXunt6+LiYjU1NbVpk5ycrPT0dP55nENubq5uuOEG/dM//VOb4/S3f7322msaN26cbrnlFvXr109jxozRM8884/2c/vavSZMm6e9//7t27twpSfrwww/1zjvv6Prrr5dEfweSv/p28+bNcjqdGj9+vLfNhAkT5HQ6fe5/yz1o0t+qq6vl8XiUlJTU5nhSUpIOHjxoUlXhzzAMzZ8/X5MmTVJ6erokefvzbH395ZdfettER0frggsuaNeGfx7tvfjii/rggw+0bdu2dp/R3/71xRdfaPny5Zo/f75+/OMfa+vWrXrggQfkcDh055130t9+9qMf/Ug1NTUaPny47Ha7PB6PHn/8cd12222S+Pc7kPzVtwcPHlS/fv3anb9fv34+9z9hpoNsNlub94ZhtDuGjrvvvvv00Ucf6Z133mn3WWf6mn8e7VVWVurBBx/Um2++qZiYmHO2o7/9o6WlRePGjdMTTzwhSRozZow++eQTLV++XHfeeae3Hf3tH6tXr9bzzz+vF154QZdddplKS0s1d+5cJScna+bMmd529Hfg+KNvz9a+M/3PbabzSExMlN1ub5cSq6qq2qVSdMz999+v1157TevXr9fAgQO9x/v37y9J39jX/fv3V2Njo44dO3bONjituLhYVVVVcrlcioyMVGRkpDZu3Kinn35akZGR3v6iv/1jwIABSktLa3NsxIgRqqiokMS/3/728MMP69FHH9X3vvc9jRw5UjNmzNC8efOUl5cnif4OJH/1bf/+/XXo0KF25z98+LDP/U+YOY/o6Gi5XC4VFBS0OV5QUKCJEyeaVFV4MgxD9913n1599VW9/fbbSk1NbfN5amqq+vfv36avGxsbtXHjRm9fu1wuRUVFtWlz4MABffzxx/zzOMPVV1+t7du3q7S01PsaN26cbr/9dpWWlmrIkCH0tx9dccUV7bYa2LlzpwYPHiyJf7/97cSJE4qIaPsTZrfbvUuz6e/A8VffXn755aqpqdHWrVu9bd577z3V1NT43v8+TRfuplqXZv/ud78zysrKjLlz5xpxcXHGnj17zC4trNx7772G0+k0NmzYYBw4cMD7OnHihLfNk08+aTidTuPVV181tm/fbtx2221nXe43cOBA46233jI++OAD46qrrmIpZQd9fTWTYdDf/rR161YjMjLSePzxx41du3YZf/zjH43Y2Fjj+eef97ahv/1n5syZxoUXXuhdmv3qq68aiYmJxiOPPOJtQ393Xm1trVFSUmKUlJQYkozFixcbJSUl3i1J/NW31113nTFq1Chj8+bNxubNm42RI0eyNDuQ8vPzjcGDBxvR0dHG2LFjvcuJ0XGSzvp67rnnvG1aWlqMn/70p0b//v0Nh8NhTJkyxdi+fXub85w8edK47777jN69exs9evQwbrzxRqOioiLI3yY8nRlm6G//+vOf/2ykp6cbDofDGD58uLFixYo2n9Pf/uN2u40HH3zQGDRokBETE2MMGTLEWLhwodHQ0OBtQ3933vr168/6/+uZM2cahuG/vj1y5Ihx++23G/Hx8UZ8fLxx++23G8eOHfO5XpthGIaPI0wAAAAhgzkzAAAgrBFmAABAWCPMAACAsEaYAQAAYY0wAwAAwhphBgAAhDXCDAAACGuEGQAAENYIMwAAIKwRZgAAQFgjzAAAgLBGmAEAAGHt/wM+RF6K8AoXzAAAAABJRU5ErkJggg==", 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", + "image/png": 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", "text/plain": [ "
" ] @@ -513,6 +417,69 @@ "print(separated_loss(xy))" ] }, + { + "cell_type": "markdown", + "id": "3f701343", + "metadata": {}, + "source": [ + "# Scaling of columns? " + ] + }, + { + "cell_type": "code", + "execution_count": 209, + "id": "6385ca55", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(2271, 1398)\n" + ] + }, + { + "data": { + "text/plain": [ + "(array([147., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n", + " 0., 0., 0., 0., 0., 0., 0., 0., 5., 149., 1.,\n", + " 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 39.,\n", + " 0., 4., 471., 0., 0., 0., 0., 15., 0., 0., 0.,\n", + " 0., 142., 0., 0., 0., 425.]),\n", + " array([0. , 0.02828491, 0.05656982, 0.08485473, 0.11313964,\n", + " 0.14142455, 0.16970946, 0.19799437, 0.22627928, 0.25456418,\n", + " 0.28284909, 0.311134 , 0.33941891, 0.36770382, 0.39598873,\n", + " 0.42427364, 0.45255855, 0.48084346, 0.50912837, 0.53741328,\n", + " 0.56569819, 0.5939831 , 0.62226801, 0.65055292, 0.67883783,\n", + " 0.70712274, 0.73540764, 0.76369255, 0.79197746, 0.82026237,\n", + " 0.84854728, 0.87683219, 0.9051171 , 0.93340201, 0.96168692,\n", + " 0.98997183, 1.01825674, 1.04654165, 1.07482656, 1.10311147,\n", + " 1.13139638, 1.15968129, 1.1879662 , 1.2162511 , 1.24453601,\n", + " 1.27282092, 1.30110583, 1.32939074, 1.35767565, 1.38596056,\n", + " 1.41424547]),\n", + " )" + ] + }, + "execution_count": 209, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "print(Dresidual(xy).shape)\n", + "plt.hist(np.linalg.norm(Dresidual(xy).todense(), axis=0), bins=50)" + ] + }, { "cell_type": "markdown", "id": "20f9b808", @@ -722,7 +689,7 @@ }, { "cell_type": "code", - "execution_count": 119, + "execution_count": 13, "id": "597f8f66", "metadata": {}, "outputs": [], @@ -733,7 +700,7 @@ }, { "cell_type": "code", - "execution_count": 460, + "execution_count": 174, "id": "80b39e69", "metadata": {}, "outputs": [ @@ -741,14 +708,14 @@ "name": "stdout", "output_type": "stream", "text": [ - "1.5202885446733455e-08\n" + "1.873018098622551e-06\n" ] }, { "data": { - "image/png": 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", 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", 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" + "
" ] }, "metadata": {}, @@ -764,7 +731,7 @@ "residualnorms = []\n", "# len_direction = []\n", "best_losses = []\n", - "# unit_step_losses = []\n", + "unit_step_losses = [separated_loss(xy)]\n", "def get_best_loss_direction(xy, direction):\n", " return np.min([separated_loss(xy + step * direction) for step in steps])\n", "\n", @@ -773,17 +740,21 @@ " return xy + (steps[which]) * direction\n", "\n", "EXPONENT = .5\n", + "FREQ_CHECK = 1\n", "\n", - "for i in range(1, 1000):\n", + "for i in range(1, 100):\n", " cg_solution = sp.sparse.linalg.cg(H, -grad, atol=0., rtol=0., maxiter=i)[0]\n", " residualnorms.append(np.linalg.norm(H @ cg_solution + grad))\n", " # len_direction.append(np.linalg.norm(cg_solution))\n", + " \n", " best_losses.append(get_best_loss_direction(xy, cg_solution))\n", " if np.linalg.norm(H @ cg_solution + grad) < (np.linalg.norm(grad)**(1+EXPONENT)):\n", + " pass\n", + " #break\n", + " unit_step_losses.append(separated_loss(xy + cg_solution))\n", + " if (i % FREQ_CHECK == 0) and (unit_step_losses[-1] > unit_step_losses[-1 - FREQ_CHECK]):\n", " break\n", - " # unit_step_losses.append(separated_loss(xy + cg_solution))\n", - "\n", - "fig, axes = plt.subplots(2, figsize=(8,9))\n", + "fig, axes = plt.subplots(3, figsize=(8,12))\n", "\n", "plt.sca(axes[0])\n", "plt.plot(np.array(residualnorms)/np.linalg.norm(grad), label='||r||/||g||')\n", @@ -805,14 +776,117 @@ "plt.legend()\n", "plt.title(\"BEST NEXT LOSS ASSUMING GOOD LINE SEARCH DIVIDED BY CURRENT\")\n", "\n", - "# plt.figure()\n", - "# plt.plot(unit_step_losses)\n", - "# plt.title(\"UNIT STEP NEXT LOSS\")\n", + "plt.sca(axes[2])\n", + "plt.plot(unit_step_losses, '.-')\n", + "plt.yscale('log')\n", + "plt.title(\"UNIT STEP NEXT LOSS\")\n", "\n", "xy = get_next_point(xy, cg_solution)\n", "print(separated_loss(xy))" ] }, + { + "cell_type": "markdown", + "id": "ff4bc69b", + "metadata": {}, + "source": [ + "## Same code as above, without plots, iterated " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "13fdce8d", + "metadata": {}, + "outputs": [], + "source": [ + "np.random.seed(0)\n", + "xy = np.random.randn(n+m)\n", + "tot_losses = [separated_loss(xy)]\n", + "tot_matmuls = [0]" + ] + }, + { + "cell_type": "code", + "execution_count": 230, + "id": "efb65904", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "for k in range(2000):\n", + "\n", + "\n", + " H = separated_hessian(xy)\n", + " grad = separated_grad(xy)\n", + " steps = np.logspace(-10,0,100)\n", + " #residualnorms = []\n", + " # len_direction = []\n", + " #best_losses = []\n", + " unit_step_losses = [separated_loss(xy)]\n", + "# def get_best_loss_direction(xy, direction):\n", + "# return np.min([separated_loss(xy + step * direction) for step in steps])\n", + "\n", + " def get_next_point(xy, direction):\n", + " which = np.argmin([separated_loss(xy + step * direction) for step in steps])\n", + " return xy + (steps[which]) * direction\n", + "\n", + " EXPONENT = .5\n", + " FREQ_CHECK = 1\n", + "\n", + " for i in range(1, 100):\n", + " cg_solution = sp.sparse.linalg.cg(H, -grad, atol=0., rtol=0., maxiter=i)[0]\n", + " #residualnorms.append(np.linalg.norm(H @ cg_solution + grad))\n", + " # len_direction.append(np.linalg.norm(cg_solution))\n", + "\n", + " #best_losses.append(get_best_loss_direction(xy, cg_solution))\n", + " #if np.linalg.norm(H @ cg_solution + grad) < (np.linalg.norm(grad)**(1+EXPONENT)):\n", + " # pass\n", + " #break\n", + " unit_step_losses.append(separated_loss(xy + cg_solution))\n", + " if (i % FREQ_CHECK == 0) and (unit_step_losses[-1] > unit_step_losses[-1 - FREQ_CHECK]):\n", + " break\n", + " #print('BROKE AT CGITER', i)\n", + " xy = get_next_point(xy, cg_solution)\n", + " # print(separated_loss(xy))\n", + " tot_losses.append(separated_loss(xy))\n", + " tot_matmuls.append(tot_matmuls[-1] + i)\n", + " \n", + "plt.plot(tot_matmuls, tot_losses)\n", + "plt.yscale('log')" + ] + }, + { + "cell_type": "code", + "execution_count": 224, + "id": "871e3471", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "-3.2358056269255684e-06" + ] + }, + "execution_count": 224, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(np.log10(tot_losses[-1] / tot_losses[0]) / tot_matmuls[-1])" + ] + }, { "cell_type": "markdown", "id": "9e8bb8f4", diff --git a/experiments/DiagonalScalingCGAndScalingTerms.ipynb b/experiments/DiagonalScalingCGAndScalingTerms.ipynb new file mode 100644 index 0000000..7ae8d99 --- /dev/null +++ b/experiments/DiagonalScalingCGAndScalingTerms.ipynb @@ -0,0 +1,4150 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "3a422525", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "['/usr/lib/python311.zip',\n", + " '/usr/lib/python3.11',\n", + " '/usr/lib/python3.11/lib-dynload',\n", + " '',\n", + " '/usr/local/lib/python3.11/dist-packages',\n", + " '/usr/lib/python3/dist-packages',\n", + " '../env/lib/python3.11/site-packages',\n", + " '..']" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import sys\n", + "sys.path.append('../env/lib/python3.11/site-packages')\n", + "sys.path.append('..')\n", + "sys.path" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "5cfe40e3", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "LOADING LIBRARY /home/enzo/repos/project_euromir/experiments/../project_euromir/libproject_euromir.so\n" + ] + } + ], + "source": [ + "import cvxpy as cp\n", + "import numpy as np\n", + "import scipy as sp\n", + "import matplotlib.pyplot as plt\n", + "from project_euromir import equilibrate\n", + "from project_euromir.loss_no_hsde import (_densify)\n", + "\n", + "# %matplotlib tk" + ] + }, + { + "cell_type": "code", + "execution_count": 168, + "id": "4cf3532d", + "metadata": {}, + "outputs": [], + "source": [ + "MASTER_SEED = 120\n", + "np.random.seed(MASTER_SEED)\n", + "\n", + "m, n = 81, 70\n", + "x = cp.Variable(n)\n", + "A = np.random.randn(m, n)\n", + "b = np.random.randn(m)\n", + "objective = cp.norm1(A @ x - b)\n", + "d = np.random.randn(n, 5)\n", + "constraints = [cp.abs(x) <= .75, x @ d == 2.,]\n", + "program = cp.Problem(cp.Minimize(objective), constraints)\n", + "\n", + "data = program.get_problem_data('SCS')[0]\n", + "matrix=data['A']\n", + "b=data['b']\n", + "c=data['c']\n", + "zero=data['dims'].zero\n", + "nonneg=data['dims'].nonneg\n", + "m = len(b)\n", + "n = len(c)\n", + "\n", + "QR = False\n", + "if not QR:\n", + " d, e, sigma, rho, matrix_transf, b_transf, c_transf = \\\n", + " equilibrate.hsde_ruiz_equilibration(\n", + " matrix, b, c, dimensions={\n", + " 'zero': zero, 'nonneg': nonneg, 'second_order': ()},\n", + " max_iters=1000)\n", + "else:\n", + " q, r = np.linalg.qr(np.vstack([matrix.todense(), c.reshape((1, n))]))\n", + " matrix_transf = q[:-1].A\n", + " c_transf = q[-1].A1\n", + " sigma = np.linalg.norm(b) / np.mean(np.linalg.norm(matrix_transf, axis=1))\n", + " b_transf = b/sigma\n", + "\n", + "\n", + "workspace = {\n", + " 'SCALE_GAP': 1,\n", + " 'SCALE_Y_ERROR':1,\n", + " 'SCALE_S_ERROR':1\n", + "}\n", + "\n", + "\n", + "\n", + "# variable is xy\n", + "def loss_gradient(xy, m, n, zero, matrix, b, c, workspace):\n", + " \"\"\"Function for LBFGS loop, used in line search as well.\"\"\"\n", + " \n", + " # preallocate some variables\n", + " s_error = np.empty(m, dtype=float)\n", + " gradient = np.empty(n+m, dtype=float)\n", + "\n", + " x = xy[:n]\n", + " y = xy[n:]\n", + "\n", + " # zero cone dual variable is unconstrained\n", + " y_error = np.minimum(y[zero:], 0.)\n", + " \n", + " y_error *= workspace['SCALE_Y_ERROR']\n", + "\n", + " # this must be all zeros\n", + " dual_residual = matrix.T @ y + c\n", + "\n", + " # slacks\n", + " s = -matrix @ x + b\n", + "\n", + " # slacks for zero cone must be zero\n", + " s_error[:zero] = s[:zero]\n", + " s_error[zero:] = np.minimum(s[zero:], 0.)\n", + " \n", + " s_error *= workspace['SCALE_S_ERROR']\n", + "\n", + " # duality gap\n", + " gap = (c.T @ x + b.T @ y) * workspace['SCALE_GAP']\n", + "\n", + " # loss\n", + " loss = np.linalg.norm(y_error)**2\n", + " loss += np.linalg.norm(dual_residual)**2\n", + " loss += np.linalg.norm(s_error)**2\n", + " loss += gap**2\n", + "\n", + " # dual residual sqnorm\n", + " gradient[n:] = 2 * (matrix @ dual_residual)\n", + "\n", + " # s_error sqnorm\n", + " gradient[:n] = -2 * (matrix.T @ s_error) * workspace['SCALE_S_ERROR']\n", + "\n", + " # y_error sqnorm\n", + " gradient[n+zero:] += 2 * y_error * workspace['SCALE_Y_ERROR']\n", + "\n", + " # gap sq\n", + " gradient[:n] += (2 * gap) * c * workspace['SCALE_GAP']\n", + " gradient[n:] += (2 * gap) * b * workspace['SCALE_GAP']\n", + "\n", + " return loss, gradient\n", + "\n", + "\n", + "# these functions should be unpacked inside newton-cg\n", + "def separated_loss(xy):\n", + " return loss_gradient(\n", + " xy, m=m, n=n, zero=zero, matrix=matrix_transf, b=b_transf, c=c_transf, workspace=workspace)[0]\n", + "\n", + "def separated_grad(xy):\n", + " return np.copy(loss_gradient(\n", + " xy, m=m, n=n, zero=zero, matrix=matrix_transf, b=b_transf, c=c_transf, workspace=workspace)[1])\n", + "\n", + " \n", + "def hessian(xy, m, n, zero, matrix, b, c, workspace, regularizer = 0.):\n", + " \"\"\"Hessian to use inside LBFGS loop.\"\"\"\n", + "\n", + " x = xy[:n]\n", + " y = xy[n:]\n", + "\n", + " # zero cone dual variable is unconstrained\n", + " y_error = np.minimum(y[zero:], 0.)\n", + "\n", + " # this must be all zeros\n", + " dual_residual = matrix.T @ y + c\n", + "\n", + " # slacks\n", + " s = -matrix @ x + b\n", + "\n", + " # slacks for zero cone must be zero\n", + " s_error = np.empty_like(s)\n", + " s_error[:zero] = s[:zero]\n", + " s_error[zero:] = np.minimum(s[zero:], 0.)\n", + "\n", + " def _matvec(dxdy):\n", + " result = np.empty_like(dxdy)\n", + " dx = dxdy[:n]\n", + " dy = dxdy[n:]\n", + "\n", + " # dual residual sqnorm\n", + " result[n:] = 2 * (matrix @ (matrix.T @ dy))\n", + "\n", + " # s_error sqnorm\n", + " s_mask = np.ones(m, dtype=float)\n", + " s_mask[zero:] = s_error[zero:] < 0.\n", + " result[:n] = 2 * (matrix.T @ (s_mask * (matrix @ dx))) * workspace['SCALE_S_ERROR']**2\n", + "\n", + " # y_error sqnorm\n", + " y_mask = np.ones(m-zero, dtype=float)\n", + " y_mask[:] = y_error < 0.\n", + " result[n+zero:] += 2 * y_mask * dy[zero:] * workspace['SCALE_Y_ERROR']**2\n", + "\n", + " # gap\n", + " constants = np.concatenate([c, b])\n", + " result[:] += constants * (2 * (constants @ dxdy)) * workspace['SCALE_GAP']**2\n", + "\n", + " return result + regularizer * dxdy\n", + "\n", + " return sp.sparse.linalg.LinearOperator(\n", + " shape=(len(xy), len(xy)),\n", + " matvec=_matvec\n", + " ) \n", + " \n", + " \n", + " \n", + "def separated_hessian(xy):\n", + " return hessian(\n", + " xy, m=m, n=n, zero=zero, matrix=matrix_transf, b=b_transf, c=c_transf,\n", + " workspace=workspace, regularizer=0.)\n", + "\n", + "def dense_hessian(xy):\n", + " return _densify(hessian(\n", + " xy, m=m, n=n, zero=zero, matrix=matrix_transf, b=b_transf, c=c_transf,\n", + " workspace=workspace, regularizer=0.))#1e-10))" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "id": "6ac5a38a", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "CHECKING GRADIENT\n", + "1.1724365045916606e-05\n", + "1.4708677824213562e-05\n", + "1.356375594335425e-05\n", + "1.3029475131428598e-05\n", + "1.2998648437408286e-05\n", + "1.4532331228614665e-05\n", + "1.1140564338501662e-05\n", + "1.5727084315158747e-05\n", + "1.8864156580795226e-05\n", + "1.709211564807148e-05\n", + "\n", + "CHECKING HESSIAN\n", + "2.8590053261115433e-06\n", + "3.132560438339349e-06\n", + "3.7776133379945417e-06\n", + "2.8287560745035742e-06\n", + "2.867783614950541e-06\n", + "2.4329890720593626e-06\n", + "3.6404848958377982e-06\n", + "2.196805546070164e-06\n", + "3.3536047656012005e-06\n", + "3.8459510121365754e-06\n" + ] + } + ], + "source": [ + "workspace['SCALE_GAP'] = 1\n", + "workspace['SCALE_Y_ERROR'] = 1\n", + "workspace['SCALE_S_ERROR'] = 1\n", + "\n", + "\n", + "print('\\nCHECKING GRADIENT')\n", + "for i in range(10):\n", + " print(sp.optimize.check_grad(separated_loss, separated_grad, np.random.randn(n+m)))#, epsilon=1e-8))\n", + " \n", + "print('\\nCHECKING HESSIAN')\n", + "for i in range(10):\n", + " print(sp.optimize.check_grad(separated_grad, dense_hessian, np.random.randn(n+m)))" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "4cb9856b", + "metadata": {}, + "outputs": [], + "source": [ + "def line_search(xy, direction): # can be made much smarter, I understand enough dcsrch now\n", + " current_loss = separated_loss(xy)\n", + " for i in range(200):\n", + " proposed = xy + direction * 0.5**i\n", + " if separated_loss(proposed) < current_loss:\n", + " break\n", + " return proposed" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "665cc1dc", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CONVERGED IN ITERS 145\n", + "FINAL LOSS: 1.6975878157515966e-32\n" + ] + }, + { + "data": { + 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "np.random.seed(0)\n", + "xy = np.random.randn(n+m)\n", + "\n", + "losses = []\n", + "\n", + "for i in range(350):\n", + " # print(i)\n", + " current_loss = separated_loss(xy)\n", + " losses.append(current_loss)\n", + " if current_loss < 1e-30:\n", + " print('CONVERGED IN ITERS', i)\n", + " break\n", + " current_grad = separated_grad(xy)\n", + " direction = np.linalg.lstsq(dense_hessian(xy), -current_grad, rcond=None)[0]\n", + " xy = line_search(xy, direction)\n", + "\n", + "plt.plot(np.arange(len(losses)), losses, label=f'DENSE SOLVE')\n", + "print('FINAL LOSS:', losses[-1])\n", + "plt.legend()\n", + "plt.yscale('log')\n", + "plt.show()\n", + " # print('FINAL LOSS:', losses[-1])\n" + ] + }, + { + "cell_type": "markdown", + "id": "6de50e28", + "metadata": {}, + "source": [ + "### Bunch of experiments with 81x71, 2zero, .75 constraints " + ] + }, + { + "cell_type": "markdown", + "id": "5c61a792", + "metadata": {}, + "source": [ + "- no scaling: 110 iters, 7.7e-31\n", + "\n", + "#### upscaling gap\n", + "\n", + "- scale gap = 2; 102 iters, 2e-32\n", + "- scale gap = 5; 95 iters, 2e-32\n", + "- scale gap = 10; 101 iters, 9e-31\n", + "- scale gap = 20; 76 iters, 8e-31\n", + "- scale gap = 50; 141 iters, 7e-31, ~90 1e-27\n", + "- scale gap = 100; 99 iters, ~60 1e-25\n", + "- scale gap = 200; ~100 1e-26\n", + "\n", + "#### downscaling gap\n", + "doesn't seem to help\n", + ".1 154 iters\n", + "\n", + "\n", + "\n", + "#### scale y\n", + "upscaling doesn't seem to help, quite clear it makes slower\n", + "downscaling also, seems slower anyway, sadly\n", + "\n", + "\n", + "\n", + "#### scale s\n", + "upscaling makes slower, seems very sensitive?\n", + "scale 100, ~175 iters\n", + "scale .1, 168 iters\n", + "scale .01, 221 iters\n", + "\n", + "\n", + "\n", + "#### scale y and s same\n", + "upscaling 10; 216 iters\n", + "downscale .1; 108 iters\n", + "downscale .01; 117 iters\n", + "downscale 0.001; gets stuck at 1e-14 loss;\n", + "\n", + "\n", + "#### upscale gap, downscale cones\n", + "10 gap, 0.1 cones = 118; \n", + "\n", + "## So, it seems only gap helps a bit\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "b0654bf9", + "metadata": {}, + "source": [ + "### Run many tests " + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "dcf4b017", + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'SCALE_GAP': 0.01, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 1}\n", + "iters 249\n", + "{'SCALE_GAP': 0.010974987654930561, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 1}\n", + "iters 195\n", + "{'SCALE_GAP': 0.012045035402587823, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 1}\n", + "iters 235\n", + "{'SCALE_GAP': 0.013219411484660288, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 1}\n", + "iters 175\n", + "{'SCALE_GAP': 0.014508287784959394, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 1}\n", + "iters 248\n", + "{'SCALE_GAP': 0.015922827933410922, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 1}\n", + "iters 200\n", + "{'SCALE_GAP': 0.01747528400007684, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 1}\n", + "iters 222\n", + "{'SCALE_GAP': 0.019179102616724886, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 1}\n", + "iters 154\n", + "{'SCALE_GAP': 0.02104904144512021, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 1}\n", + "iters 194\n", + "{'SCALE_GAP': 0.023101297000831605, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 1}\n", + "iters 189\n", + "{'SCALE_GAP': 0.025353644939701114, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 1}\n", + "iters 233\n", + "{'SCALE_GAP': 0.027825594022071243, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 1}\n", + "iters 139\n", + "{'SCALE_GAP': 0.030538555088334154, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 1}\n", + "iters 216\n", + "{'SCALE_GAP': 0.033516026509388425, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 1}\n", + "iters 181\n", + "{'SCALE_GAP': 0.03678379771828634, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 1}\n", + "iters 216\n", + 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jUe3/LfVe+D0uxJJpRGJJtAR98j6xRDbqHtDnoGSP0xEK4I5L34+/ffwPAABFAe7asLwso+yoabIolkij3pfnzoQQQsgMgS+18xC0CGsTLZ5QvVemzZpHjbO7eEwVFFOlY3V3Njtm48ffV5ZBFshNt6VRlhBCyGyAAiUP2RaPhUAJeOVCQfOosZjsyclBMY0ZHx7OGmL93vJaW+m0mjO+TKMsIYSQ2QAFSh5EBSWiEyBGgaKJCnMcvvCg+DMtnnxJsodHsgLFKvDNDpF4UvpY/JkwOabJEkIImQ1QoORBeFDyV1AyAiVWuMXTVJcJaiskUCzyVOwgRI/XraApoD0OKyiEEEJmAxQoeQia9vGk06oc6W2q88ox4omEvRZPNJFCUucP0bd4JsusoAiB0ljnhc8tKihMkyWEEDLzoUDJgzmobSyWhBhQatJ5UKKmFk9MbjPWPl8IHe1YWfGgr6CUK1CygskjW0qFKih94Sh27h8sGAhn5z6EEEJItSl7F89sJ+tB0QSIGOf1e1yo87p1HhRTi8c0ZuzzuORI8lgsgVC91opxwoMiJnga67xIZKoz+aZ4fvJCL77y6B6oBaL1H3mhFxuL3IcQQgiZClhByYN5ikfvPwFgQ6BkJ3PMWSiRWBIjE9nx4GiiPN+IyGVprPNIk6xVBaUvHMVXtuyRFSCraP2+cFSKk3z3IYQQQqYKCpQ8mKd4cgVKbk4KoIu61wkUcxbKkRHjRb98k2zWE+MrIFB6BiMwx+eJaH3DffLE7xNCCCFTDQVKHupNUzx2KiiqquaMGQO6UePMsQ6ZBEr5HpRsBcVXYMy4uzUIxXSbOVrfzn0IIYSQqYICJQ8NfmMQW16BojO+6sVBXYEKipjgcbs0SVCuB2VU50ER25OtKigdoQDO0SXXuhUlJ1q/IxTA6u45Be9DCCGETBU0yeZBCBDhGxk1CZSAaPHoxEVM5yURywIBoMHvNRxLGGQXtdSjZzBScQ5KU8CTHTPOY5JdOKcez/ccR2vQh1/81fmWwqOl3i/Pa/NfnEtxQgghZNpgBSUPsoJiavE0mSoo+jFjUQlxuxR43dmGiTTJmjwoJ89rAFBBiyearaAU8qAA2QC5aCKVV3gMT8QBaMFvFCeEEEKmEwqUPAgTbCSeQjqt2vKgyAkejwuKkhUoch9PpiUjWjynzNcESvljxpkKis6Dkk+giC3LkXgqb5ibECiMyyeEEDLdUKDkoUEXsBZNpPJO8eh39Zhj7gWNJpPsYVlBCcrjl4M+ByVrkrU+1qSu/aQfcdYznLmdcfmEEEKmGwqUPNR5Xch4WBGJJe21eOLWAqVB1+JJpNI4OjoJQFdBKdODMqqroBTKQQGMwkVUSvSoqooRVlAIIYTUCBQoeVAUJRvWFk/lmGStWzwi5t74bW30Z4Pa+sOTSKtawuzCOdoIbyyZRjptTiopjsxBCdjwoOgqKMcjuQJlPJZEIqVmzof7fAghhEwvFCgF0Geh5GvxRG20eBp0SbKivbOgOSA3Jus/txTGdDko/swUT76oe70R16rFo78tnkxDNae2EUIIIVMIBUoBgrrKRz6TbETX4olZxNwD2THjscmkNMh2NtcZRpFLbfMkUmlZvSlligewbvHob0urQLKMig4hhBDiFBQoBRBG2UgsKf0e2RwUTVxMJrLtGauYe/1xzBUUl0uR3pFSjbJiZBkoniQrzlMwbNHiMbd9nDbKcksyIYSQUmBQWwFElWRgLIZURoQIgSL8KYAmLoJ+T34Pis4kKyooC5rrM/d1I5ZMl5yFIlJkA143vG5XwSRZIFvdAbLTOnrMbZ9YMo2gv6RTysvmXb3YuGUP0tySTAghxCasoBRAVD5EsJrP7ZLio87rgog6Ea0WITL8BSooRzIVhAVztCA0UW2JxkurWOhTZAEUr6Dobi/W4tGO44xRti8cleIE4JZkQggh9qBAKYAwwh4Z0caCmwJeGcCmKIoUF2Kjsaig5LR4dCbZg8e17cCdzXXafcW4cpkVlMY6raLjK2CSTadVQ2XFqsVjvs2pFk/PYARmOwu3JBNCCCkGBUoBhElWvNoPBYwdMSFgRAUlKk2yxm+rPvStNyNQFupaPPrPtctoNDvBA0Bnks09jrmqYtXiMd/mVBZKd2tQ5skIuCWZEEJIMShQChDMVDf6wloFRfhPBOYsFDnF4zFWUPwel9zNk1YBRQHaQ5kKSkbMlOpBkRkoooJSoMVjPvaIjRaPUxWUjlAAmzaskO8rALckE0IIKQoFSgFEBUVM3jTlFSiixWM9ZqwoiqGK0tZYJwVFdhqoVIFirKAUSpI1ixaroLZqeVAA4Kqzu6RAu3LlAhpkCSGEFIUCpQAiSE1c9M0VlICpgiLHjH1GgQJkvSJA1n8C6E2yFXpQCggUs/gZnUwiafKqDEdMLZ6Ec2PG+pRar5s/coQQQorDq0UBgn6j58QsUIKmNFlhkhXVDD36CsqCOVn/RbkeFPMUj6ygWJhkRUjbnPrs+YvgOYFo+4jJpFieRNpyGBzPVmfyJd0SQggheihQCqDPOgGKV1DytXiA7CQPoIW0yWOUbZI1eVDc+XNQhHCq93nQlDkPc0vneOb91gYt/MTJCsrQeEz+n5uSCSGE2IECpQDFKig5HpSkCGqzaPEYKig6gSI8KCW2eMZ0m4yBwibZmMxncaEl6ANgnNqZTKSkiGlr0gSKk5WOQZ1A4aZkQgghdqBAKUDQ5CXJb5LNVFDi1lH3gLmCYuFBKbXFEzN6UAqZZKVw8rjRXJ8RKDqjrKimeFwK5gZFBcU5kyxbPIQQQkqFUfcFKF5BMeagZLcZF/GgNFfuQcmfg5LfJFvndcmvQd/iEVM9zfU+KXScrHQMGlo8zgkfQgghs5eSKiibNm3C6tWr0djYiPnz5+OKK67AW2+9ZbiPqqq488470dnZiUAggLVr1+L111833CcWi+Gmm25Ca2srgsEgLr/8chw6dKjyr8ZhxBSPIF+LJ1pkzBgwVlDcuuQymSRbctR9xoMSME3xpNJQVWN0q/685li0eMQenjn1XhnT76RXZEhfQWGLhxBCiA1KEijbt2/HjTfeiOeeew5bt25FMpnEunXrEIlE5H2+/e1v4zvf+Q7uvfde7Nq1C+3t7fjYxz6GsbExeZ+bb74Zjz76KB555BHs2LED4+Pj+OQnP4lUqrZeXReroAhxETFN8VgJlAPHst+jdd/djs27erVjeMvLQRmdtK6gALltlJjuvOaIFs9EbotnTtAnI/OrVkFhi4cQQogNSmrx/PrXvza8f//992P+/Pl46aWXcMEFF0BVVXzve9/DHXfcgQ0bNgAAHnjgAbS1teHhhx/GX/zFXyAcDuO+++7Dj3/8Y1x88cUAgAcffBBdXV148skncckll+Q8biwWQyyWvciNjo6W/IWWQ32RKR7zmHG+qPu+cBS/feOofF8szLtg2byyPCiqqsoKinkXD6CJC78uzVaErvk9LjlqbPCgZP6vVVDyt4rKZZBTPIQQQkqkIpNsOBwGALS0tAAAenp60N/fj3Xr1sn7+P1+fOQjH8HOnTsBAC+99BISiYThPp2dnVi+fLm8j5lNmzYhFArJt66urkpO2zbFTLIBm0myPYMRmPblyYV5db7Sg9piybQMPmsyJckCuSJAX9mxavEMyxaP3oPiXDWLLR5CCCGlUrZAUVUVt9xyC84//3wsX74cANDf3w8AaGtrM9y3ra1Nfqy/vx8+nw9z5szJex8zGzduRDgclm8HDx4s97RLwuN2yWqI26XkCJZ6U4snlqfFU2hhXjkVFJGBoijZKo6iKNmNxjkCJVvZES2ekXwtniqYZI85XEHpC0exc/+gXOJICCFk9lH2FM+XvvQlvPbaa9ixY0fOxxTFeDVWVTXnNjOF7uP3++H3+8s91YoI+jyYTMQRCnhzzq9eV/1IpVXprzCPGYuFeV/ZshcpVYVbUeTCvP0DmjelFA+K9J/4PXDplI/P40I8lc4VKLLF40ZzpsVzPE+LZzym3depSkcsmZKZLUBxD0pfOIqewQi6W4OWCwUfeaEXGx/dA1UFXAqwacMK7vYhhJBZSFkC5aabbsLPf/5zPPPMM1i4cKG8vb29HYBWJeno6JC3DwwMyKpKe3s74vE4hoeHDVWUgYEBnHfeeWV9EdUk6PdgKBLP8Z8A+jHjpEFgWI0ZX716ES5YNg8HBiewpLVeXnwDPu2+pVRQzP4Tgc/jAmK5IkBG8OuC2kYsWjzN9T4kUlq1w6kWj769ox03v0DZvKsXG7fsQTqP+OgLR6U4AYxeHm5HJoSQ2UVJLR5VVfGlL30JW7ZswbZt29Dd3W34eHd3N9rb27F161Z5Wzwex/bt26X4OOuss+D1eg336evrw969e2tSoIgqidl/ov9YNJ4yChRP7hQPoFVSPnTyXMPFtK6MZYHmCR6BnMAxxdQLsVHnyU7xjEQTSKe1K71o97ToPChOVVCEQBHFp3zH7QtHpTgBsuJD38bpGYzANEEtvTyEEEJmFyVVUG688UY8/PDD+NnPfobGxkbpGQmFQggEAlAUBTfffDPuuusuLF26FEuXLsVdd92F+vp6fPazn5X3vf7663Hrrbdi7ty5aGlpwW233YYVK1bIqZ5aQgSsWVdQsh4Ukdbqc7sMbZdilONBMWegCOQEjmlcW2+SFS2eVFrF2GQSoXqv3MMzJ+hFX9hZD4qY4JnX4MfAWAyJPC2ensGIFCcCIT6EoOtuDUIBDIZj4eUhhBAyuyhJoPzgBz8AAKxdu9Zw+/3334/rrrsOAPDlL38Z0WgUX/ziFzE8PIwPfvCD+O1vf4vGxkZ5/+9+97vweDy46qqrEI1G8dGPfhQ//OEP4XZbVx6mExGqph/jFdTrxoxFBcSqvVMIuYunJJOscQ+PIF+Gid4k6/e4EfS5EYmnMDwRR6jei5FItsXjtElWCJSO5gAGxmJIq0AylYbH9P20Iz46QgFcsLQV2/cNyo8LLw8hhJDZRUkCxZxQaoWiKLjzzjtx55135r1PXV0d7rnnHtxzzz2lPPyUs3lXL57vOQ4AePIPR7F5V6/BEyEqKPFUGpGYJhqsQtoKISooiZRqeeG2oqAHBYXHjAFNiETiUQxPxLEgFcBY5ty1Fo+zSbJiD8+C5jq8mhm+ilt8naL9tXP/EID84mNhS33ma3HhqdvWUpwQQsgshcsC8yA8EXrMnoiAbuxYtElKFSj6+09aiAKrkVrzJmNBPoGiD2oDtFYOoI0XixFjRdFaRj6Hc1BkBUUnJPKJn8VzgwCA0zqasOP2Cy2nc8ZjInMmjdaG6ZnsIoQQUn24LDAPdjwRPrcLbpeCVFrF8UylwGqTcSH0AWvReMqwVDDfVMtovgpKnhaPOZ9Fxt1HEnKaJxTwwu1SHF8WOJQRKG1NfrgUzfyaT6CI290uJW9lRFSqAC0PZi5FCiGEzEpYQclDoXA1gaIoss0zLCsopX1LFUWx3MdTaKpFVlACRn2Zb9Gfecuyfh+PyEBpydxWrRZPa4O/qL9FVG30IsTMuO5j4Wgi7/0IIYTMbChQ8iDC1dyZ+dh8ngghUIYyF3p/iRUUQLfRWCdQClVw8npQRJJsTg5KdswYQHYfj67FI6Z7qmWSndvgz3t+AvGYYwUESiSW/R5RoBBCyOyFLZ4C5AtX06NN8sRki6dUDwqgGzXWZaGICo5epCgAlrTWyykecw5KvgyTbFBb1iQLaAFt+j08hY5RLtkKig8+jxtAMu+xhUAZn7RXQRmhQCGEkFkLKyhFsApX0yMqKMIkGyixxQNkWy/6Coqo4OjxeVyo87ilB6XJ5hSP2SSbTZONG/bwANksFSdMsum0iuORbA5KMfETS2S3QqfM5aMM4yYPCiGEkNkJBUqFSA9KpIIKikWLBwCuOrsL3owRZn6jH7FkGj/Yvl96UPImySbzB7UBMOzj0e/hMRwjUXkFZXgiLitA+kWExVo8gFGI6InQg0IIIScEFCgVEsiEtYnle/li7gseQ5hk47nCIpG5wn/tstMAAA/sPCC3A5s9KDJJtkBQGwDdRuOEYQ+PdgztXGJFlvrZYUgnfrxuV95tywK9QLEyyqbSKiZ03yP9PiFCCCGzCwqUCqn3Gk2ypU7xaJ9jXUERFQK3S8EnVnTgnCUtiCWz24qjCeNFXFY/dOJCVVV54RePI1o8wxPx7B6ezG16EWEnmK8Qg2NZgyyQvwUl0Fd+rCookbjxNlZQCCFk9kKBUiH1fu2iLy6Wdb4KTLJ5BEoo4IWiKPjyx081fPxT9/4em3f1yvetBIC+KiE8IKLFMxxJyMqPaPH4dQIrXyvGLqLS09rgM5xfvgmheJEWj7mqwgoKIYTMXihQKqTeJEjKavH4cqd4AKNAAYAFc4xGXfPGX0uBovOSmIPa4qk0joxMAtC1eHTBcZWOGotNxrKCYnPMGLCe5DELFFZQCCFk9kKBUiFiYaCgkjFj88JAcQEWW4t7BiM5nyuyUQDrCoUIaXO7FHgzAqHe55b37R/VBIq5xQNUbpTVbzLWn1+xKR7A2oMyHjN+fzjFQwghsxcKlAoxR9uXN2ZcuMUjdu4US7e1SoHNhrRlz0tRFNnSEYi2j6IoRadt7CIrKEFji8eOSdYqrM1cVRmJxis6P0IIIbULBUqFBP2mFk8lY8Zx44Xb3OIplm5rJQDMI8YC0eYRNAey7/vlqHFlWSiigtLaaK6g5B5Xb+YF8lVQtNtEG4otHkIImb0wSbZCAg62eAqZZAWF0m39Fh4PUUHRe0sAo0Bp9HukeAA0o+xYrPIKymAku4cn3/kJzLcV8qAsaA7g3cEIBQohhMxiKFAqpN5rrqCUXpTK50EZtRAogFZJsUq2LTTFk1NBCWaP2Rw05alkWkUVe1DkmHHxFo/ZkDsezz9mvGCOJlAmE2lMJlJliUJCCCG1DVs8FeJEi6fO5hRPMbIm2exxZAXFdF7NugqKud3jxMJAVVUxFLFvkjWLIasKikjQbWuqk14cGmUJIWR2QoFSIU62eCaT9ioo+bDadWNOkRW0FBAoTiwMjMRT0v8iKygWQXICc4vHyoMibmvwe+T3hG0eQgiZnVCgVEhODopD24yBSioo+jHjzCZjkwelWTfFY57osarElIpo79T73HIUu3AFxfhYhYLa9AKFG40JIWR2QoFSIeYx47I8KD7tc/LloNgWKBYm1JisoOSf4mmuQgVFtHdE9QQozYMyZtXiEQKlTldBYZosIYTMSihQKiToN7Z4zILFDkVzUEqsoMQtKijmhFsRzGb+P6AzydoUKH3hKHbuH5SJtgBwbMw4wZPv/ATmxzLv3QGyFZSg34NQRlSxxUMIIbMTTvFUiKMtnkorKBYtnlgeD4pTLZ7Nu3qxccsepFXApQCbNqzA1asXZSsoQZ1AKTBmnNPisRwz1u7T4HezxUMIIbMcVlAqJODoLh6juVUIDbsVlIJJsgVaPOadxXZbPH3hqBQngHE30GCmgjKvURcAZ6OCIqZzzLH22m2ZCorPg1BA09asoBBCyOyEAqVCcnJQfGVE3Xtyc1DEBI+iaEFqdrCe4rE2yT711oD8/9d//rrlVuRiLZ6ewYgUJwKxG0hUUEpt8Yh203gsV3iM6zwoIvmWY8aEEDI7oUCpEI/bJS+8imJctmcXWUFJpKCq2hU/u4fHC5d5AU8erHboiDaNvoLSF47ib3/5hnxfNW1F9tsUKEvm1ufcpijAktZ6GXM/N2hhkrVq8WTOUwiUyUQayTyjx4Ypngnu4yGEkNkIBYoDCB9KnccNRbEnJvQI8ZBKq0ikjALFrv8EyIqjVFqVF3dZQdEJlEKVD8C+SfbZ/cdzbgt43fC4XLLFI/bwAJDblK2OGzdVUICs50QwrjfJMgeFEEJmNRQoDiDaPOWMGAPGyR9hlC1LoOjaOHEpUHJNssW2ItsxyQ6MTuIbv3gdAPCXHzkJP/7COThlfgMm4il8/ed7MVjIJFugxdNY55X308fdq6oqKyiNfg9C9RQohBAym6FAcYD6jEeknBFjAPC6FbgzimGyAoGi95kIEWA1ZlxsK3Ixk+yRkQn85YO7MTqZxIoFIdy27lR8eNk8fO/qM+FxKXhiTz/ePRbJ3DtbqrET1ObzuNBQp30/9ZM80URKVn2CDGojhJBZD8eMHUC2eMoUKIqiIOB1YzyWlGmy5QgUj9sFl6JN00iBInfxGLVooa3IhUyym3f14vaf7pGy46Pvnw9PpuKxfEEIX1x7Mv7vtnfk/T/3r8/L0ePCHpSsmbfB78HxSNyQJiv+ryja91t8X2iSJYSQ2QkrKA4gKifmhXylYA5rG41qF2S7I8YCs7iI5QlqA7RKyodOnpuzGdlqXBnIjhXr7Sv3/O4dQ0DbZ85aaPgc/eixnTFjv8ctw+/0AkX4UYI+DxRFkTku4WhCGosJIYTMHihQHEBcUMv1oADZuPtKPChAbhhavhyUQuSb4ilmrgWAQyNRmBH38bmthY/2WCn52GKsOmIQKNkJHiD7fUmkVEzEy98ZRAghpDahQHEAMSZcrgdF/7mTFbR4AMAnJnAy0zv5kmQLH8Nl+FxBd2sQ5hklvblW3CefAbdgi0dOG7kQ9Gtfg96DInbziI8FvG543doDWRllreL3CSGEzBxKFijPPPMMLrvsMnR2dkJRFDz22GOGjyuKYvn2f/7P/5H3Wbt2bc7Hr7nmmoq/mOmiXreNuNwLojnuPruHpzSbkN9jrqBkWyflHkPQEQrgypUL5Ptmc624Tz4Drp2gNr/HjYY6TZSNF6igKIqCUCasbcS0MHDzrl6c961t+Oy/PI8139pmCKEjhBAyMyjZJBuJRHDGGWfgv/23/4ZPf/rTOR/v6+szvP+rX/0K119/fc59b7jhBvyv//W/5PuBgNEHMZM4PKy1OF4+OII139omTaGlkOtBKa+CYvZ5TCZLr6AIL42oauh5f0cT8PJhrDl5Lv7+qjNy/CtAfgNuIYESN5hkMxUUvUCJZzNQBKGAB4PjMUMFpS8cxe1b9kA1xe9fsGye5bkSQgipTUoWKOvXr8f69evzfry9vd3w/s9+9jNceOGFOOmkkwy319fX59w3H7FYDLFYTL4/OjpawhlXl75wFM++mw0sK/eCmN3HU2mLxygChMgoxYNSaKmfEA1LWoMFv76OUCDn4/rjqqpqCLXTe1AaLDwo46YKCgA01/sARAwCpWcwArNnVnhgKFAIIWTmUFUPytGjR/H444/j+uuvz/nYQw89hNbWVpx++um47bbbMDY2lvc4mzZtQigUkm9dXV3VPO2S6BmM5CzbMxtH7SA9KBlhUbFASaUyxyungpI/qE2/D6dU9EFyIjFXoB8zFlWSMb1AmcwVKNk02WzcfXdrMOdxzT4ZQgghtU9VBcoDDzyAxsZGbNiwwXD75z73OfzkJz/B008/ja9+9av46U9/mnMfPRs3bkQ4HJZvBw8erOZpl0SxVFa7OGaSFXHyCVMOSikeFNMx9EgviK90geK3SLoVGDwo/tygtkjMqsWTmybbEQrg5HlZkWLlkyGEEFL7VDWo7d/+7d/wuc99DnV1dYbbb7jhBvn/5cuXY+nSpTj77LOxe/durFq1Kuc4fr8ffr8/5/ZaQJhCv7JlL1KqWvYFsU63MDCeTEsvSskeFK+xjTKpm44p5xhmxi2Egl30ixTjyTSge0pli8frQoNq1eJJ5Txuvn084hy9bgXPfPlCihNCCJmBVE2g/Nd//RfeeustbN68ueh9V61aBa/Xi3379lkKlFqnUCqrXfRTPPoLbmNdmRWUZNogMErLQclvko1U0OJxuRR4XAqSaTXHKCvHjD0uGftvaPHEtO9JY12uQNFP8YxNJnB0VPMrJVIq2hqN4pgQQsjMoGoC5b777sNZZ52FM844o+h9X3/9dSQSCXR0dFTrdKqOlSm0FAK6UWUhUBrrPPJibRe9SXZSJzCskmSLHaOgB6WMCoo4djKeyhUouhaPP/MlRyyTZLNfh1UFpWcwAj2TyRTqy2hHEUIImV5K/ss9Pj6Od97J7lrp6enBK6+8gpaWFixapI3Wjo6O4j/+4z9w991353z+/v378dBDD+HSSy9Fa2sr3njjDdx6661YuXIl1qxZU8GXMrMRUzyTugpKqe0dIBvUFk+mZdCaS4EMNbNDoUh6q1ZLaefnwkQ8JU28Av0UjxBIVrt4goYpnlyBsv/YuOG40TgFCiGEzERK/sv94osv4sILL5Tv33LLLQCAa6+9Fj/84Q8BAI888ghUVcUf//Ef53y+z+fD7373O/zDP/wDxsfH0dXVhU984hP4+te/Dre7/CTWmY4+B6XcDBTA2OKZ1I0Y60d6ix6jwLLAbGBaec+V/vz0yBwUr0sKCquoe6sWj0GgDBgrKBPxFOaWdaaEEEKmk5IFytq1a4suZ/vzP/9z/Pmf/7nlx7q6urB9+/ZSH3bWo2/xjE6WL1CkwTWZliPG+ukZW8fIVGGSaRWptGpoM2UFSunnBuQPaxOCxefOTvGMTRauoFgKFHMFJcE9PYQQMhPhLp4aQb8sUMbcl2iQBfRhaKmyQtoA0ziwSUiMxYw7cUo+vyICxe/NBrXFkmkkMkbfSlo8hBBCZh4UKDWCzEFJpBCeqKCC4smtoJQqUPSBanqjbCKVlsKibJNsnpTaWCJb7dGLEFGxMe/iAYAmXQUlnVaRTKVlQJ74fnLTMSGEzEwoUGqEOosx41B9OSZZ/RRPeS0ej0uR4XP6SofeE1KuSTafAVc/xePzuOT9xqVA0b4WqyRZVdUqO4eGo4in0vB7XDgpE9Y2yRYPIYTMSChQaoQ6izFjp0yy/hIrKIqiWBplhSfE73HB6y7vR8eqxZNMpZFMq/LYQFaIjMeSiCVTsuKiF0Z+j1tWSkajCbw7qLV3uluDCGaMtqVUUPrCUezcP1j2RmpCCCHOwfnLGiHb4klnPSiVmmQz1YO6EisogHbxn0ykDQJFbBQut70D6HcFZY+r/784/4Y6D4YicURiSVk9AYw5KIAm4qKJFEYmEnKC5+T5DTIm365JdvOuXmzcsgdpVRvLLmcjNSGEEOdgBaVGCPgsWjyVVFBSWXFRqgcFyFYy9B4Uq304ZZ+fTvjoE2vFx0UFZGwyKR+3zuuCx1S50U/yCIPsyfMadFNRSRSjLxyV4gTIbqRmJYUQQqYPCpQawSpJttKgNllBKWEPT/Y4uUKi0pA2/XH1LR5RQfG4FClARJR+JJbSpdfmfj9C9VYCJYh6n32TbM9gRIoTQTkbqQkhhDgHBUqNYGmSLUugWLR4Kqig6IWEaJs0ViRQsgJKICoo+umhrAcloRMouV+H3McTjWP/sUyLZ16DoSJVDKc2UhNCCHEOCpQaIaDzVgyOa8vuKhEosWRKNxlTTgUlszDQYoqn3AwUwHrMOGYRKKcPayu0QVl8j94bmsDxSByAJjj0FaliiI3UAgUoayM1IYQQ56BAqRH0RtZESus3VJqDEnO6guKEB8XiuPoRY4F4jEgsVdD70pz5Hr3cOwwA6AzVIej3yBaPXZPsp85cIP//8eXtNMgSQsg0Q4FSI3jcLlldEOj3zthFPyUzWSWTbDnnZT6uUaBkKig6r4x4jPFYIvu4BSoorx4KA9AmeACgrgQPCgAcHqEhlhBCagkKlBpCb2YN+txlZY343RYelLJaPBmBkrCooFSwHdhqzFg8hr7FIx5jPJaS+SuWLZ6MSVYInpPnaQKl3ltaBeXwcFag6LcoE0IImR4oUGoIvQ+lnPYOkCdJtqwKSsbMmnK4xeO21+JpqMsGtUUKTA+Zv08iQVaaZG1WUI7oKiiMxyeEkOmHAqWGCOiERDkhbYBxPHjSojJhF9niSeS2eJwIaotZtXgMJlm3fEwREGfVWjILFFFBCcgkWXvVEH2LJ8IKCiGETDsUKDWE3itSbgXFrxvjjZW5LFA7Tm4rRuSgNFTgQSlkkjWOGWtf//hkMtvisWgt5RMo2RZPOudzrNC3eCI2RQ0hhJDqQYFSQzjf4qnAJOu18qBo+SyOtHhSVi0enQclU0HRWjz5x5ub633Zz/G50dbkB6Bv8dgTG4f0LZ4YWzyEEDLdUKDUEAEHKiiyhZKqMEnWIpI+u1G4ghwUKaCyIsDKg9Jo8KDkby3pv08nz2+AomiJa6UEtQFGDworKIQQMv1QoNQQjggUiyke/YXfLsJYq690RJyc4jEkyeaOGYsWTySWDWqzai016W7raKqT/y8lqC2VVtEfnpTvTybSSKbstYYIIYRUBwqUGqLOwRYPAIzpluyVipVJtpBQKPW4dls8Y7HCSbI/3X1I/v+3bxzF5l29AJANarMhUI6OTiKZVg1x9xM2Ky+EEEKqAwVKDWGooNSXa5LNPqWjUSFQSq+gWHlFxp2Y4rE5Ztzoz+abjEwkLB9XbCEWqMhuIRYtnolECqpq2gRoQrR3OpsDcGdUCn0ohBAyvVCg1BCGMeO6ylo8ADA2qV3Y68pq8RhNsum0KvNBnI+6zx0z1htiB8a09ou5tVRoC7H4Xqqq0UdjhRgxXtAcQDAjbOhDIYSQ6YUCpYZwYorH5VLgdWtVgJiMuq/cJKu/YDuegyLyWnTn6XG75HmL3UTmHJRCW4j1Yq9Ym+dQZsR4wZyAbgcQBQohhEwnFCg1RJ0DQW0Acnb6VGKSFUJCtHc8LqWs4DfzuelbR+L/PrfxPM1CyFy5EVuI3ZnJHbeiyC3E+t1GxfwkooKysDkgvSsRtngIIWRaKf+lMHEcJ6Z4AK1KEdFVDSoyyWbaL/qNwmKUt9xzA8xTPLkVFEATKIPjcfm+VQ7K1asX4YJl83BgcAJLWuvREQrIjwV8bsSj6aIVFOFBWTAnIEWR3QRaQggh1YECpYYI6C7QlQgUrWKSyL5fjknWJCRkimwF7R2r4wLWHhTAWDHxupW8laCOUMAgTAQBrxvhaKKoQBEpsp3NAdT7svkrhBBCpg+2eGoIJzwogHHUGCi3gmJs8TixhwcoliSbv8VTzuPW2whrU1XVaJLNVGm4MJAQQqYXCpQaQnhQfG4XhiKxso+jFyiKkutJKeUYQjzIfTgVpMjqj2s9Zpzb4hGUMzkkR40LtGtGJhJSjHQ20yRLCCG1AgVKDfHigWEAWnVhzbe2ydCxUtELEr/HVZZnxG+KpI8UCEsr6dxsJskCxkC4cioowtMzWaCCIqonrQ0+1HndssVDkywhhEwvFCg1Ql84igeff0++n1azoWOloq+glBPSBuhNssYxY6daPMm0inQmxCRfiydYYYsnW0EpLlAWNGselqCNqgshhJDqQ4FSI/QMRmAOPBWhY6Wib5WUE9IGWJlkHRIounMTPhQhUMzemcZKWzxeGwJFl4ECAPWixUOBQggh0woFSo1QKHSsVIwVlPKeYrNJdnzS2RYPkBUocRtTPJWYZO20eEQFRWxqZtQ9IYRMLxQoNUKh0LFS0V/oywlp0x/DnIPiVIsHyFZn7JlkS/867LR49Ht4AHDMmBBCaoSSBcozzzyDyy67DJ2dnVAUBY899pjh49dddx0URTG8nXvuuYb7xGIx3HTTTWhtbUUwGMTll1+OQ4cO4UTn6tWLsOP2C/GTG87FjtsvxNWrF5V1HGcqKNkWj6qqMgel0gqKoig5CwPtjRmXPnYd8GqfX2jMOMeDwjFjQgipCUq+ekUiEZxxxhm49957897n4x//OPr6+uTbE088Yfj4zTffjEcffRSPPPIIduzYgfHxcXzyk59EKsWLQkcogA+dPLesyonAMMVTtklW+7y0qhlaZQWlrvJsP7O/xd4UT+lfh8xBKcGDIhYS0oNCCCHTS8lXm/Xr12P9+vUF7+P3+9He3m75sXA4jPvuuw8//vGPcfHFFwMAHnzwQXR1deHJJ5/EJZdckvM5sVgMsVg2F2R0dLTU0z6h0Fciyp3i0VdhYsm0ziRbWQ6KPHYs1yRbrRyUfAIlGk9hKKJF6S9srjc8DnNQCCFkeqmKB+Xpp5/G/PnzsWzZMtxwww0YGBiQH3vppZeQSCSwbt06eVtnZyeWL1+OnTt3Wh5v06ZNCIVC8q2rq6sapz1rMLR4ylzsZzCz6gSKqDBUgr7Fo6qqrTHjiqZ48rR4jmRGuIM+N5oC2vG5LJAQQmoDxwXK+vXr8dBDD2Hbtm24++67sWvXLlx00UWyAtLf3w+fz4c5c+YYPq+trQ39/f2Wx9y4cSPC4bB8O3jwoNOnPavQi4tyWzxulwJPZqwolkw5ZpLVn18smTZE3ptbPI26Fk9jGa2lbAXFuhqib++IMDsuCySEkNrA8WWBV199tfz/8uXLcfbZZ2Px4sV4/PHHsWHDhryfp6pq3sRTv98Pv9/v9KnOWpyooABayyUZTyGeTFfNgxLTJcqaI/kNFZQyKjfFdvGYDbKAPgeFFRRCCJlOqj5m3NHRgcWLF2Pfvn0AgPb2dsTjcQwPDxvuNzAwgLa2tmqfzgmB/kJfrgcFyFZfYsk0xhyKugeMCwP1kfeFPCiFskzyUVckqM1skAWySbLxZBoJXXWHEELI1FJ1gTI0NISDBw+io6MDAHDWWWfB6/Vi69at8j59fX3Yu3cvzjvvvGqfzgmBvlVS7pgxkBUSsUS6Ki0efQXFZ7Ez6PHXjsj/3/TIyyXvJio2xWPOQNE+J/v1MayNEEKmj5KvNuPj43jnnXfk+z09PXjllVfQ0tKClpYW3Hnnnfj0pz+Njo4OHDhwAF/5ylfQ2tqKK6+8EgAQCoVw/fXX49Zbb8XcuXPR0tKC2267DStWrJBTPaQynKugaMcJRxPIrM1xpoKiFygJ6xTZvnAU//OxvfJ9NbOb6IJl82yPYBdr8RyyaPH4PC743C7EU2lE4kmE6kvPXyGEEFI5JV9tXnzxRVx44YXy/VtuuQUAcO211+IHP/gB9uzZgx/96EcYGRlBR0cHLrzwQmzevBmNjY3yc7773e/C4/HgqquuQjQaxUc/+lH88Ic/hNtd+QgrMSfJVuZBAYChiGZwVhSgvgLBYz5uPJXKO8HTMxiRokggdhPZFShCnOWroPQOaXuOAqYqU73fjfhEmqPGhBAyjZQsUNauXQvVvNVOx29+85uix6irq8M999yDe+65p9SHJzZwYpux/jjHM1khQZ8HLvPCoHKO685t8ZiFlNhNpBcppe4mEu0aK4Hy8PPvoX90EgDwlw/uxqYNK2Ryb9DnwchEgkZZQgiZRriLZxbixJgxkK1qSIHiQEgbkKfFY6piOLGbSJ+DohfV5vZROtM+6hO5KHJhICsohBAyXTg+ZkymH0OSbAUtHlHpEGmrThhkAWMOSr4WD6DtJrpg2TwcGJzAktb6kuP/RQ5KKq0ikVLh82hip1j7iAsDCSFk+qFAmYU4sYtH+9xMi2fcYYFiMWbsyyOkOkKBsvcSBXRfezSeko/R3RqEomjGW4G+fcSFgYQQMv2wxTMLcTKoDQCOT4gWj7MVlEIeFKceR6Th6id5OkIBfGbVQvm+uX3EhYGEEDL9sIIyC3HOJGv2oFRDoFiPGTtFwOfG2GQyJ7p+aVsDAGDNyXPx91edYajSiK+TOSiEEDJ9sIIyC3FKoPhNUzyNVa2gVGfEXLR5zFkowldzantTTgtJ5KfQg0IIIdMHBcosxBjUVoFJNiMkhh1u8fh1HpR8UzxOkS9NdjgjUFqCuUFsXBhICCHTDwXKLEQvSiqpTIgKiupgiiwwdR4UIP8+nuNSoOQuoaz3cWEgIYRMNxQosxCfLpF3dDJe9nHM4qahGjkoVW7x5Iu7P16ggiKmeJgkSwgh0wcFyizk16/3y/9f/U/PlbxkT2Ae/XV6zDiWqr5JNl+abKEKiqgURWiSJYSQaYMCZZbRF47iW7/6g3zfnJJaCmbR4FyLR6tQxJPZHJRqt3hKqaCIqgs9KIQQMn1QoMwyCqWklopZNDidJDsVHpSs2MgKlEQqjdFJTXxYVlDoQSGEkGmHAmWWIZbs6Sl1yZ6gehUU/S6ejEBxYEuyFWLMeFJXQRFTSYoChAIWFRR6UAghZNqhQJllOLFkT5Bjkq1zPup+KoLaAGO7RrR35tT74LbYzizHjClQCCFk2mCS7Cyk0iV7gmqZZP1T2OIJyByUtLwtK1ByqycAx4wJIaQWoECZpVSyZE8wJS2eao8ZS5NsbgVlroX/BDCOGauqCkXJrbIQQgipLmzxkLxUbczYY9HiqVKSbMDCJCtSZOdYTPAAWSGWTKuIp9KW9yGEEFJdKFBIXsxVjaDPoaA2d65JVh/P7yQBi6j7oQIZKEC26gJwYSAhhEwXFCgkL/qqRp3XBY9DIkJUUGLJtKxQVH0XTyK3gjI36LP8HI/bJdtbXBhICCHTAwUKyYu+quFUewfQe1BS2THjam8ztqigzMkjUAD9wkBWUAghZDqgQCF50Vc1HBUoUzpmnCs0RA5KvgoKoMtCsUiT7QtHsXP/YFnpvIQQQuzBKR6SF30FxakJHiDfmPHUBbUNjRevoIg0WbMHZfOuXmzcsgdpFXApwKYNK3D16kVOnzYhhJzwsIJC8qJPd3VSoIgWT1rNVjaq7UEptYIivl69B6UvHJXiBKhszxEhhJDCUKCQvOjbLtXwoADA2GQi57GcxJwkq6pqNqitUIvHIoHWyT1HhBBCCkOBQvLiq5JA8epaR+KCb85ccYpsi0drJY3HkkiktAdtqS/e4tGnyXa3BnPuV+6eI0IIIYWhQCF50Vc1nGzxeFwKzOGsVUuSzVRC4qk0kqm0rJ4EvG5ZXbH8PIuFgR2hABbOyabzVrLniBBCSGFokiV5MY4ZOycgFEWBz+2SBlmgei2eOp2PJppI6ULa8ldPgPwLA4VgeV9bI+7/wuq84qQvHEXPYATdrUEKGEIIKQMKFJIXRVHg87gQT6YdraAAWktnKgSK3+OCS9FaSdF4Soa0FRMoVgsDxyYTGJ7QPDNQkFd4PPz8e7jjsb1QOelDCCFlwxYPKYgQDk56UPTHBQC3S3EspdaMoijZsLYSKihBC5PswePZaZ3RaMLy8/rCUdzxqCZOAE76EEJIuVCgkIJ4XJpZJJVSi9yzNPTto2pVTwT6sDa7FZTsmHG2gtJ7PDutMzZpHYHfMxiB+TvFSR9CCCkdChSSl827emVL41u/fhObd/U6dmz91E61BYo+C+W4bYGS+ZyYvoKiEyixJFLmmWNokz4m/y8nfQghpAwoUIglIpRMoMLZVoVRoFRngkegT5O1K1CyHpSsQNFXUABg3KKK0hEK4JzuFvm+SwEnfQghpAxKFijPPPMMLrvsMnR2dkJRFDz22GPyY4lEAn/zN3+DFStWIBgMorOzE5///Odx5MgRwzHWrl0LRVEMb9dcc03FXwxxjmqHkukFSrUyUASBMioownMTydPiAYDRSWsfSmujX/7/3//iQzTIEkJIGZR8ZYhEIjjjjDNw77335nxsYmICu3fvxle/+lXs3r0bW7Zswdtvv43LL78857433HAD+vr65Ns//dM/lfcVkKrQ3RqEy9SrcLJVMaUeFJ1J9ngm5n5OgZA2INsW0ldQDg7bEyh6A23Sog1ECCGkOCWPZqxfvx7r16+3/FgoFMLWrVsNt91zzz0455xz0Nvbi0WLsq8k6+vr0d7eXurDkymiIxTApg0r8JUte5FSVcdDyQwtnirt4REIsRGNJ2UFZW6DPZOsWBaYTqs4lJniqfe5MRFPYTRqbZQN6wQKp3cIIaQ8qp6DEg6HoSgKmpubDbc/9NBDePDBB9HW1ob169fj61//OhobGy2PEYvFEIvF5Pujo6PVPGWS4erVi3DBsnk4MDiBJa31jvoofDrfSbU9KHVSoGRbPMUqKEHZ4tFEyNGxScRTaXhcCpbOb8Crh8J5Kyh6gXJkZLLi8yeEkBORqgqUyclJ3H777fjsZz+LpqYmefvnPvc5dHd3o729HXv37sXGjRvx6quv5lRfBJs2bcI3vvGNap4qyUNHKFAVg+dUtnjqMy2e0cmkHA8utMkYyOagROJJqKqK3iGtvbNgTgDNGXGTLwvFKFBYQSGEkHKomkBJJBK45pprkE6n8f3vf9/wsRtuuEH+f/ny5Vi6dCnOPvts7N69G6tWrco51saNG3HLLbfI90dHR9HV1VWtUydTgH8axowPD2tiwaUAoYC38OdkKihpFYgl09Igu6ilHk2Zz7XKQkmnVYNwoUAhhJDyqIpASSQSuOqqq9DT04Nt27YZqidWrFq1Cl6vF/v27bMUKH6/H36/3+IzyUxlKseMRYvncEYszKn3wWV2AJuo1+3wicSSMgOlq6Ve5pxYtXjG40nD9FNfmC0eQggpB8dfugpxsm/fPjz55JOYO3du0c95/fXXkUgk0NHR4fTpkBrF0OKptknWq+lwKVCKtHcAwOVSspM8sZSsoHTNqUdjnVZBsTLJhieMouUwKyiE2KIvHMXO/YM0lhNJyRWU8fFxvPPOO/L9np4evPLKK2hpaUFnZyc+85nPYPfu3fjlL3+JVCqF/v5+AEBLSwt8Ph/279+Phx56CJdeeilaW1vxxhtv4NZbb8XKlSuxZs0a574yUtMYclCqtIdHEPBpxxdioVgGiqDe58FEPIVIPImDmfbQopZ6vHc8AsC6giL8Jw1+D8ZjmudlPJZ0fJcRIbOJzbt6sXHLHqS5YJPoKPnK8OKLL2LlypVYuXIlAOCWW27BypUr8bWvfQ2HDh3Cz3/+cxw6dAhnnnkmOjo65NvOnTsBAD6fD7/73e9wySWX4NRTT8Vf/dVfYd26dXjyySfhdle31E9qh6kcMxa7eOKZ7cktRSZ4BDLuPp40elDqhAclV6AI0dIeqkNTnfa4fayiEJIXkVqd5oJNYqLkl3Vr166FquYPnyr0MQDo6urC9u3bS31YMsuYjqh7QUuRDBRBMCNsjo3FcWxMG3Nf1FKPnqFMBcWixSMMsqGAFx6XgtH+MRweiWJpm/UIPSEnOoVSq7ki4sSGu3jItDClY8Y+k0ApsYLyVv8YAKCpzoNQvReNmcpIoRZPKOBFZ7P2x5VGWULywwWbJB8UKGRamNIKilmglOBBAYA3+7VgwK4W7Q+maPEUEygdoToAHDUmpBAdoQBW6xZsOp1aTWYudO6RacE/lR4Uc4vHpkARxtY/9GkCZVFGoIQC2u1WOSh6gTIvszSQabKEFEYEJ/rcLjz91x9BZzOrJ4QVFDJN+KYhqE1gv4Kifd57OoMsoKugRBM5nishUJoCXnQ2axUUmv0IKcxwZolnPJVGQ13hEEVy4kCBQqYFvQfFN0XbjAV2BYrYxyM0iGjxiByUtApE4inD54QzxtmmOg86MyVqtngIKcyILj9oYJQVR6JBgUKmhZngQREmWYGooNR5XfC6NVufeR+PlUn2SHiy6HQbIScyeoFydDRW4J7kRIIChUwLU9viMVqtSjXJCoRAURRFl4Vi9KHoBUpbUx0URctfGcpsUSaE5CJaPABwlBUUkoEChUwLUzlmrG/x1PvcqPPaq9gEdZUXRYGsiADIO2qsz0HxeVyY16AZZfvKNMoy/pvMdqLxFGKZEEWAFRSShVM8ZFowJslWeVmgbkpojs0MFCC70RgAOkMBwzmLjcZ5Wzz12sc7mgMYGIvhSDiKFQtDJZ0347/JiYC+egKwgkKysIJCpoWpbPEoiiKrKHNtpsgCMOzP6WoxZjJYZaGoqmpo8QDAgubyslAY/01OFMwCZWCMAoVoUKCQacE/hQIFyI4Ml1RB0bV4hP9E0GSRhTIRTyGVURRCoIiwqVLTZAvFfxMymzBvAJ9JLR62YKsLWzxkWvDpFkNWe4oHgPSdzLVpkAWyY8ZArkBp9Oe2eET1xOvOVmyEb+VwiRWU7tZgzm2M/yazkeGMQPF5XIgn0zOmxcMWbPVhBYVMC/oWT7VzUADIseBSHiuom+IRpliBqKCM6ioo+vaOomiP15mJuy91o3FHKCCj8gHtDyDjv8lsRLR4ls5vAAAMjMZqfiyfLdipgQKFTAtT6UHZvKsXB4YmMv8/iM27em193tNvDcj/3/mLNwyfp0+TFehTZAUdZS4MjMSShleS/99Hl/LVGZmVjGQEyqmZjd/xVNqQi1KLsAU7NVCgkGlBL1BGotXLCBGvdAQq7L3S6QtH8fe/fSv7eaZXSEKEjOWpoAhE3P3R0UkkU9lRymK8dihs+AM4XON/sAkpF/GzPa/JLzOKjta4Uba7NQjFtIKZLVjnoUAh08Kv9vTJ/3/q3t/brmqUSrmvdIp9nlUOipVAaQ364XUrSKvA0TH75r/dvcMAAI9L+yv43lDE9ucSMpMQ1ZI59T7MzyzYrHWjbEcogE+vXCjfV8AWbDWgQCFTTl84irue+IN8v5r92+7WIFxlvNIp9nlWLZ5RC4Hicinyj1Ypo8Yv944AAC5YNg8A8N4QS8dkdiJaPM2Z9GVgZmSh1Pmyl89LlrezBVsFKFDIlDOV/duOUACbNqyAO1OPdSuKrVc6xT5PBrVZtHiaTNtYhdnVrkBRVRUvZyooV65cAAA4ODwhR5jLgeOQtQWfjyzCJNtc70Nbk1ZBmQkLA/ccCsv/D42XVvHh828PjhmTKUdUJ/TX22r2b69evQgXLJuHA4MTWNJab7sMW+jzsjkohVs8QHbU+IjNuPuDx6MYisThdSu4+P1t8LldiKfSODISlRuVS4HjkLUFnw8j2RaPvoJS2y2eeDKNP/SNyfd7j9t/ccXn3z6soJApp9yqRqWP+aGT55b8GPk+r1G2eJJyJDK/QMmMGtt8tfTyQa16cnpnCAGfW6bYlvJHUMBxyNqCz0cuooIyJ+jD/BnS4nn76BjiqbRco3F0NIbJRKro5/H5Lw1WUMi0UG5Vo1Zoyphk46k0Ysk06rzuvAIl60Gx90d393uaQFm5qBkAsGRuEPuPRXBgKII1p7SWdJ6F2mkz7Xs+G+DzYSSdzq6HaK73ok2YZEswlE8Hrx4aAQCcvbgFrx4cwVgsiUPDEzhlfmPBz+PzXxqsoJBpo9yqRi0Q9HmkiVaYY0ctclAAYEFzaSbZlw+OAABWLZoDAFg0V2vrlGOULdckTKoDnw8jY5NJecFuDvhki8dJD0o1/B7Cf/KBhSHZdrVT4exuDUKxuH372wPY+Q49KWYoUAgpA5dLybZ5MkbZvBWUTIun93ik6B+gyUQKbxwZBWCsoADljRp3hAK4Zd2p8n2OQ04vHaEA/veVKwy3feNTp8+Y58Ppi71o7wR9bvg8rqxAGYshXYEpXLB5Vy/WfGsbPvsvz2PNt7Y5FmfwmkGgaM/dwePFvycdoQBO72zKuf3/bX8Xn/1XZ89xNkCBQkiZmLNQwlFNqJgFyrP7hwAA47FU0T9Aew6HkUyrmN/ol5WXSiooAHDeyXPl/5e01tOQN81c/P42w/snzcvdu1SLVONir5/gAYDWBh8UBUilVQxFKgtwrJbfYzKRwttHNYPsioXNck+XXY/YRFzzqnzl0vfhsS9+yFBRoSfFCAUKIWWiz0JRVTWbg1KfFSh94Sj+9pdvyPeL/QHS+0/EPp9sBWWirB0lI7p19u8NTSASSxa4N6k2x0z+it+/MzhNZ2Kfal3s5QRPUPud8bhdaG0QYW2VtXmqFWfwh75RJNMq5gZ96AzVlSRQJhMpHMhUQq9YuQATiTTMv9GMzM9CgUJImegXBk4m0ohnouz1FZRS/0iKgLaVGf8JoHlY3C4F0UQq5+Jmh+FIdhQ6rQJv9I2WfAziHMfGzQJlaJrOxD7VutiLNRdz6rNbxmUWSoVx99Xy++w5rLV3ViwMQVEU6UE5aEOg7Ds6jrQKtAR9mNfgtzxHl4IT1pNkhgKFkDIRFZSxyYT0n7hdCoI+t7xPKX8kVVWVEferdALF53HJUeUDZbR5hieMpfLXdAFTZOoRIlNs733t0Ij8+alVrMydTlzshXjWi/q2Ru1nvT9c2SSPiDPQ44T/SvpPFoQAwFBBKVbhfLNfe3FwalsjFEXJiVwAgEtXdMwYT1K1oUAhpEz0WSh6g6yi+2Mj/gDpRco3r7T+I/nKwREMjMXgVoAVmT9+gkqMsuLcxGntyYxIkulBVAZWLAzhpHlBpFXguXdru4rSEQqgtSFb5XDKbC3aj/oKipNZKFevXiS9Yqd3NjnivxITPCsWNgMAFswJQFE0b0kx38yb/Zp35X0d2XHkq1cvwo7bL8Tnz10MAOgvcfP5bIYChZAyybZ4EnkneADtD9D2v16L+kyo07K2hpz7bN7Viw3f3wkASKnAz189bPi4eJVWjlFWVFA+kPmD+tphVlCmE1FBmdfox/mZXJudNe5D6QtHcWw8e/E9o6vZkYv9sC5FVuBUiwfQclaE50q/2LNcJuJJ7BvQRMYHFmovIvweN9ozoqpYm+ctIVDajXkpHaEA/vuFJwMAXnxvmCIlAwUKIWWiN8mG82SgCLpagvjoae0AgG1vDhg+JgyI+uKw2YAoKigHyqigiIvABUu1i+G7xyKGiH4ytUiB0uDHeSdrz8mOGhcowicjLsSvHwljIl652do8xQPA0bj78Xg2Z+XYWKwsk7meN46MIq0C8xv98jwB2M5CERWUU9tzR407QgGsykQL/HpvX87HT0QoUAgpEyFGxiaTukWB+cOZL3qftpl425vHDLfbMSAunlvaKKMeUUY/aV5Qji7vYRVl2hACZX5THT500ly4FGD/sUhNv2oWFZ4rVy3AwjkBJFIqXug5XvFxxe+NmOIBshUUJ1o8+m3jk4k0IvHicfSF0Oef6Flkwyg7NB7D4HgMimJdRQU0/wkAPLGnv6LznC1QoBBSJvoclEItHsFHls2HomhjivrqSHdrEEoRI+1iUUEZLL2CIkY5m+t98g/rHhplpw0xxTOvwY9QvVf6jaZ73DhfCJuqqrLC8+FTWrEmU/Vx4nxlBSWg86A0OldBMZuPByuM0JcTPAuaDbfbGTUW7Z1FLfWo91m/kFmfESi73js+IzY6V5uSBcozzzyDyy67DJ2dnVAUBY899pjh46qq4s4770RnZycCgQDWrl2L119/3XCfWCyGm266Ca2trQgGg7j88stx6NChir4QQqYaqxZPIYHSEvRhZVczAGObpyMUQPfcbFiX1fJE8QdwdDJpyDWxQ3ZbrA8rMgKFPpTpQ+9BASD3K02nQCkUwvbOwDgGxmLwe1xYtXgO1iwV51u5sVdM8TQbPCiaQBmKxJDIjO6Xy2jU2IYyj3iXymsZg3m+CkohgSLbO2359/UsaA7gzK5mqCrw69dZRSlZoEQiEZxxxhm49957LT/+7W9/G9/5zndw7733YteuXWhvb8fHPvYxjI1lV1PffPPNePTRR/HII49gx44dGB8fxyc/+UmkUpWV3wiZSvQ5KKM2BAoAXPS++QCAp3QC5fUjYbw7GIFLAe7945XYcfuFOQbEgM8tS9+ljhrLbbH1Xnwg88rPqoJSjZ0lxMhkIoWxzGoEIVCEUXbHO4MVeyTKoVgImxBOq5e0oM7rlsnEb/SNYqjCC77VFM/coA9ulwJVBQYrPL6TFZSxyQT2H9MqmOK5E9iJu89nkDXziUwV5fHX6EMpWaCsX78e3/zmN7Fhw4acj6mqiu9973u44447sGHDBixfvhwPPPAAJiYm8PDDDwMAwuEw7rvvPtx99924+OKLsXLlSjz44IPYs2cPnnzyycq/IkKmCH0Oil2BcmFGoPz+nSG5nv3fdhwAoPWfP3lGZ97RzcV5Ro0LCYtYMiWjtZsDPtlO6D0+YajEVGtnCTEiqic+j0v6lVYtngO/x4WBsRh++tKhggKxGiKymAdqR6ZSIio9rQ1+eZHdub/8Kko8mfWE6AWKy6VgvthqXGGbxzy5U0kF5Z5t78j/X37vDsPviDDJ9oWjiCetqz5vHs1vkNWzfoVmpn++5zh+tafvhH7B4KgHpaenB/39/Vi3bp28ze/34yMf+Qh27tRGKF966SUkEgnDfTo7O7F8+XJ5HzOxWAyjo6OGN0Kmm6Y8OSiFOK2jCe1NdYgmUnju3SEMjE3iF68eAQBcf353wc9dYrGTp5iwEO0dl6J5ZkL1Xnkc0U+vVow5yWVAN8Ej8nLqvG55gbvtP1/LKxCrJSKtQ9i0NNNkKo3nMxktotKj///O/eW3pUSKrPjZ1ONUFsqoQxWUvnAU//LMu/J98+/IvAY/6rwupFXrreXptIq35QRP4QrKwjn1WDhHe5Hy3x/afUK/YHBUoPT3az2ztjbjMqy2tjb5sf7+fvh8PsyZMyfvfcxs2rQJoVBIvnV1dTl52oSUhWjxRBMpDGYCmooJFEVRZBXlqTcH8OBzvYin0li5qNkQb2/FYtOosR1hoTfIujJpcSJgSkwkVCvGfDZSaQUjO8GTbRH0haPYPzAu37d6HqspIjtCAazubjHcdt2abnSEAnjtcBhjsSRCAS9O023hXXNK5ePR4mczFPDKn01Bu8hCcVig6LNcSqFnMFJwZ46iKAV9KL3HJxBNpODzuOQLhHz0haM4PJx9Xk/kFwxVmeJRTCMJqqrm3Gam0H02btyIcDgs3w4ePOjYuRJSLg3+7Ku+w8PaH6ViAgXI+lCe/MMAHnruPQDFqyeAbtQ4U0HpOVZcWGRzJrLnJSK6hQ/loIWnxYkY89mGExUM/QSPoNjFT9ynmiKyMfOzLALTXug5DlVV8ft9mgA57+S5cOtExDndLfC4FBw8HpU/j6UyHMn1nwicykKRY8yZr6ucXVaAVmUyY/4dKSRQhEF2WVsDPO7Cl107Pw8nCo4KlPZ2rXdmroQMDAzIqkp7ezvi8TiGh4fz3seM3+9HU1OT4Y2Q6cbjdsm9O4OZV2b5gtr0rDllLnweFw6PRDEUiaO9qQ4fP7296OctbhEVFO0PlVU8uvmPppUJUUzy7DkcxshEHH+/9W3DMZyKMZ9NOFXBME/wAPb2NdkZRa+Eo5nU1q9c+n4EfW7sORzGr/b2ywrJGl17BwCCfo/cF/X7Mts8wxO5EzyCNqdaPBlD8snztNyRck235qh/q0m7hXPyZ6G8JSd4il+7qrXkcCbiqEDp7u5Ge3s7tm7dKm+Lx+PYvn07zjvvPADAWWedBa/Xa7hPX18f9u7dK+9DyEzBLEjsVFDqfR5ZDQG0P8I/3V18zH5R5nMGx2P4910H8X91pj1A6+Wb/2jKi4DuvE7vbIKiAIdHorjl31/FsbEYTpnfgL++5FQAwOolcxyJMZ9NOFXBOJYRAnqBYl5qZ/U8doQC+NQZnQXvUwmiUvH+jib82YdPAgB8+9dvyuWV55sECgCcd4o2zVNum8dKPAukSbbC3BJRQalUoKTTqhxZ/r/XnGk5aVeogvLWUc03WWyCB7D383CiULJAGR8fxyuvvIJXXnkFgGaMfeWVV9Db2wtFUXDzzTfjrrvuwqOPPoq9e/fiuuuuQ319PT772c8CAEKhEK6//nrceuut+N3vfoeXX34Zf/Inf4IVK1bg4osvdvSLI6TaCKOsIGTxatBMXziKd45mPQcq7L0aDwW8Umh8+aevAQCuO2+JbNl841On5/zRtIoSb6zz4qRMyXrbmwNQAHz7Mx+Qr4jL7dPPZqxf1aLkV7VWFRRA29d0esbj8c0rllsKRP3nfPfqMx0TkclUWl6425rq8Gcf7sacei8ODE0gkVLR3lRnENQCIVq2vzUgW5ylMBLN+qPMiAqKUx6Uk+drP+/lxt0fHZtEPJWG26Xk3TYs02Qtvhdv2jTICq5evQgnz9PO+e6rnHuuZxolC5QXX3wRK1euxMqVKwEAt9xyC1auXImvfe1rAIAvf/nLuPnmm/HFL34RZ599Ng4fPozf/va3aGzMPjHf/e53ccUVV+Cqq67CmjVrUF9fj1/84hdwu92Wj0lIrSKMsoD2SqchT0KknnJ7zJt39co/6oBWCfnqJ09DV+biEU/m/uENWyxj087b+P6+o2NycuDwcBRpc7ngBKcjFMD/+Ngyw23CSFoK0iTbWJfzsaXztVf54aj1jht9/o2TcSmD43GoKuB2KZgb9KGxzit3BAFA/+gk/v3FXN/f25mx2fFYCud/+6mSPTlW/iiBECiHhicqMoeKCspJrdr3NpZMYzxW+g4hkW+yoDmQ10OyyOQRE0wmUjIB2k4FRdCZWUuRLBBWN9uzi0oWKGvXroWqqjlvP/zhDwFoBtk777wTfX19mJycxPbt27F8+XLDMerq6nDPPfdgaGgIExMT+MUvfsHJHDIjadRVUJosphGsKKfHLDwQev7QN4qBsUm0NeZ/tSlD2oLZV6l94She6R2R74sKDqDC7VIQT6XlOCzJor9oA1rCaqnkq6AA+XNuBPrbKw0w0yN8HvMb/XC5FPSFo/iVaVmd1VTR/3xsr3xfLcOTMxKxFs9Adnx5PJaqaMxW5KC0h+py/GKlINo2okpiRdecbNqzeGEAaD8naVX7Oq2e93wIEZvvd/FEyC7iLh5CKkC/HNDc7smH6DG7M65HK8OdGSsPRFoFDgxOFFyuZmVEzFfBOTQ8KbfVHiqjZD/bCWdyO+Y1+qEowPa3j+GdgbEin5VFVdXsFI+lQMnNuRGk06rB21DORTYfUqBknns7fhsnPDlW7UdAEz9/+8s35PuVjNnq84laM9/zciZ5xPdeJMZaEfC55fOqf66ezYitJa3BotOsesQoutX5nijZRRQohFSAvlVixyAruHr1Iuy4/UL85IZzLQ13ZgpVXQqNZI5YLGMrdCzR5jk0PLv+0DmByO14X3sjPvZ+beLwvkwKsB3C0QQSKe2Kop8IERSqoAyMxTCZyJb6K42Y1yOMqG2Zi6vdqaJKJ030O6L0OGVIjiVT8nvWVOeVo93lVJ8OSoFS+Ovryvz+CIGyeVcv7nriTQDAK70jJVU5hFF4YCz3hceJkl1EgUJIBeirJqUIFECrpHzo5Lm2fAyFqi7ildZRiz9kwxYelELHEn+AWUHJRR8sJnJrtuw+JPM8iiFeCYcCXvg9uX47EeDVNzop1yAIzKLFyRaPaA0KoWunwifuIzRKOaPpIknW3OKxEj+uMgzJYupGySTVtlYgUOy0ePQf/699x/Db1/tw+0/3yGqlXTO8QLZ4LF54nCijyMUdfYSQvOgjuksVKKVy9epFuGDZPBwYnMCS1np5MWhvyv+HTJ8ka+dYooJSaOnZiUo4mm2XndPdguULmrD38Cj+6Zn9uGDZPHS3BgteoAekQdbah9AS9KHB78F4LIlDwxM4ZX7WUCnaPh6XgmRarUqLp02Xbpvv50PP1asXYSSSwKZfv4kPnTy35EkTIZ7Nk29C/Hxly16kMm7g5npfyb9fwn/S4PfA5VLQ2qj9DlTS4ikmUMQiyEd2HcQju3KNxaLKYUfIiRceVh6UjlAA1563BPf//gCA2ZtdxAoKIRWgb/HYCWmrFKuqi/AOjMeShgkFVVWzWRPB3HOzOpYImzo0wgqKGb2fQVEUfGGNVkX5f9vftWVULGSQBbQBA+FDMZfqxXoDMYrsaItnVMTvGyeL7FT4FmdesZsrPsUw/GxajBmLFui/XXs22hr9OB6J4//85q2SHsO8H2teg/b1lVpBicZT8rkrJFD6wlFs020pt6KUKoe+xWM1Gr1UJ2DP6GqelaPIFCiEVEAlLR6naPB7ZOy+fpJnPJZEMtOotroIWEEPSn7Mfp6zFxt3JxUzKhYTKIDOKGsK+xLvr8o8pjYa7Mys8VFTi6cUQpnvxYhp500xIvGU9OPk+9nsCAVw0fvb8O0/OgMA8MOdB/CbvX22x2pFBor4Hc1WUEqrPol2Z2Odp+DvuJX5HIBsxdgxw+sRLZ7JRBpjFqPR+qWE+46OITULowHY4iGkAvQ5KNMlUACtHDx+LImjozGclEnNFO0dv8eFOq+9jCHhQTkyEkUqrRr2r5zoiIuwaEkcsthaW6iEb7WHx0w+o6x4/6zFc3D/7w8gntIuWnYnxwohWgj6Fo9dxHSYeSlfMYRvx+9xIeAr/LP5kWXzcNXZC/HvLx7CXzy4G4B20d+0YUXBqoG5giI8KMdKrKDICZ459QWncIQvRK8T3IqCLV/8ECbi6bytsnwEfG40+j0YiyUxMBrLea6P6ERaJJ7Cu8fGsbTNfs7KTIAVFEIqoLEGKigAslkoOqPscIESev7j+OFxKUikVMvpgROZEdPagFL349ipoAijrDGUTcV7mZbPqW2Nslo26EBWTSyZwvGMWGizCI8rhhAoIxOJkio62SV+9n42Rfy+wM5YrdjDI15EiO97qd83u/6TfObiM7rm2DbDm5nXlH+S54hJIIvt5GZmcpgbKyiEVEDTFJpkC2GVhTJSYBlbPjxuFzqa63DweBQHj0dnnemuEkZN0ewdoQBuXXcq/j7jjXAX2ZliR6AsyiyE7NVVUIYnEhiLJaEoWoVrboMP47EkhiJxnDSvsq9JnJPP7Srp50Qg2l3JtIpIPGXY8F2IQimyVlj5RooZTkdzPCjZKR5VVW1nkkiBYhH3b8aOubgU5jf68e6xSJ4sFO13XZi19xwO49NnLTTcZ/OuXpmXYqfqVGuwgkJIBeiNscl0/kjqamOVhVJOBQUAFjbPrFHjqXqFOBLNFXx//uGT5KjtYzeuKfjHX7wKtoq5F4jqy6HhqIw4FwbZ9qY61Hnd2XFZByooWYOsv6QQMUGd1wVfJvpdeHTsUGiTsRXlbHPO8aBkvm+xpLWnIx9ioq1YBoqglPiAYuTb6pxOq1KgXHKatgn9tUMjhvvMhjA3ChRCKuDXe/vl/2/e/Mq0xU3Pt/hDJoOwLCZ4CjGTjLKPvNCL8zZVP+47nc5OnegrZT6PCwsz6aLRRGGBaqeC0tZYB7/HhWRaxZER7bkUu12EgVaEvA3azF8phDkDpVQURZGenJEJ+z6UQhM8VnSEAvgfFy+V79sxnJo9KAGfu6z22EGbLZ5qICd5TBECQ5E44sk0FAX42OlaaODrR0YNe3tmQ5gbBQohZdIXjuJrP6tsH4lTiBbPgEUFJRQorYIyU8La+sJRbHw0G4RVzVeI4/Gk/GNvbuUtKbJDBwDiybSsGhQSKC6XIi+EonIi/hWPM9fBCkq/RQZKqQhPTilG2eFI/k3G+bjmHK06pQB45stri7YqRA6KvsopxZ3NHBlVVW17UKpBvn084md8XoMfy+Y3otHvQSyZxj7dfqju1iDMNbFyNnBPJxQohJRJLb1CkaXgMYsKSonegplSQekZjORs9a3W918sf6vz5k5EiQuX1Q4dwVBEu8B4XIq8oOfDPMkjjrtIVlDKT0Q1I1s8ZRhkBdIoW4JAyZciWwghDFUADTaml8wVFEA3yWNT3A2OxxFNpKAoQGdz+d+jcpmfxyQrqmudzQG4XAqWLwgBAPbojLLtTXU5KxW+cH7pG7inEwoUQsqkluKmxQTG0dFsqFOpZXSBCGs7WOMVlO7WYM5t1fr+yxRZi2qUqGwcKFBBERfE1gZ/0Y3X5qWB75kqKOKiM+RAmmylLR5Al4VSUoundAO33+NGfWYkOWzjsUTUvT4KQE7y2BR3onrS0VRnuZ6g2syTYW3G8xUTPEI0fWChJlBeOzwi77NvYBzHxuPwuhSce1ILAGd+ZqYSChRCyqScrcTVQrzSmkyk5XhlqUZEgaig9I1MGnratUZ7U11Ohka1vv+FLqhCUPQezy/ohECZb6OVYh41lhWUlipUUMYqb/GICoWoitgh3ybjYgixPWzDkFuogmL3e2d3SWC1EJWtY6PWLZ7OzM/6ioW5FZTHX+sDAHzk1Hn460veBwB4Ym8fxiZLy6yZTjhmTEgFOD1WWC51XjdCAS/C0QQGRicRCnizyaclXgTamurgdWtZKEfHYljQXPhr6gtH0TMYKbqLxmkODUcRjWcj1gNeF65YuaAqjyUuvlbrDERL5sBg/gqKeAVcKKTNfLz3hiIYm0xgKGOGFUJobjBTQXHAJCtaPJVUUIRos1PVMD9uqWG4oYAXh0eittpJ0oNSV36LZzoNskBW0I7FkojGU1KQixZPR+Z38wMLmgEAf+gbQzyZhs/jwq/2agJl/fIOrFrUjJPmBfHusQie2NM3Y0aNWUEhpEKcHCushGwWivbH12qTsR3cLgWdmT98hwpUBQAtZ2HNt6o/RWOFCKZavqAJ8xr9iCbSeKHneFUeyxzSpkdcvEYnk3lHbe1M8Aj0FRnhp2lt8MlQwNYyA8essFoUWCriexK26UHZvKsXf+gbBQDcvuW1kn5mssFwhcVZOq3m5KAA5bd4pkugNPo9qPNql2m9D+WIrKBowrKrJYBQwIt4Ko23j47hnYExvH10HF63gotPa4OiKPijs7oAAP/x4qEp/irKhwKFkFmCOTOh3DI6oNtqXMAoOxU5C4UyTkS//YyFzbjwVC2xrNiytnIfK2yRgSII+NzyAn8gj1G2FIGyoDkAj0tBLJnGCwc0waW/QLYGs6+qS13Sp2cinpTbd82LAkuhuYQxY/EzIyh18k20eIqJoYhu6spqiueYTS9GKSFt1UBRFMtJnj6dSVbcT/pQDoXxxB4t/uD8U1qlQNuwagFcCvDie8PoKVDtqyUoUAiZJYg/ZEfHNO+IuPiUWkEB7IW1VXuKqVh1RvTbP7AwhIveNx8A8FSZAqXYY4Wjhcdi8+3QEZQiUDxulxSIz7x9DEDWIAtopk8RjlZJm0eMpAe82s6XcgnVi4WBxc+l0p8ZkbkixpTzIZ4vn2kPVanVp+n2oAC5WSiJVFp6hzp0k0UrxCTP4RE8sUdr71y6okN+vK2pDhcs04T8f750sPon7gAUKITMEvRZKPpXmOVE8He1FB81ts5ZcGaKplh1Jp1WpUBZsaAZ5y+dB69bwYGhCbx7bDzfYct6LACWIW16lpgmb8zYWRSoZ1FGkDz37lDm/ez3VFEUzJWTPOW3efTtnXJSZAWixWOnglLp5FuzTUOunOAxjSPP0y0MLLY7KJZMoS/zPeqaM40CxTRqrE3qaesJRDUNyE7ybH3jKN7sH4PHpeBjp7UZjiXaPP++6xB27Kv9/TwUKITMEvQtHuE/aazzwOMu/ddcjBoXqqB0hAIyfwHQArScmqLZd3S84CvtA0MRjMWS8HtcWNrWgAa/B+d0a6OUpbZ57LyqFxfffAJlcZFR41KmeICs4Ikl05n3jSPVc2XgWAUCRZ5TZfkeoRI8KB2hAP7qo6Ulwuqxa8jNTvAYK0OighW3EXd/eDgKVdUqTOY8kanE3OIRBtn2UJ1hZH3FwmYA2RC6Nae05lT8Pvr++Qh43Tg2HsOf3Df1vrFSoUAhZJagXxhYbgaKwG5Ym/4CuaS13rHpgKffyhUZ+lfaew5r1ZPTOpvgzQiwi96nvVq0EiiF/CV2KkFWe3j0mLNL9KhqdjP0vAZ7YsBsylxs8kBk9/HkVhLs7iZyIgMF0IkGmybZ1Us0IblwTh123H5hST8zzTbHjK1SZAFt2k3E3Reb5BH+q0Ut9RVVmCplnqnFI0eMTcFxnaE6OeEFAOedPDfnWMMTcYNvqdb381CgEDJLmK9bGFjuBI9AVFD6wvmzUPrCUfSFJ+FStMmfnsEJ2bOvhDeOjOJHz75nuM1cnRETPB/QVXCED+WFnuOGrIdHXujFeQX8JR2hAD6YCbICtK2v5lf1YTnFYy34snH3uV//eCyJycyeHrsLJc0Vk8XmCkqmtD8YMV5kN+8q/LXqkS0eG76YQojvyUQ8hViyuGlXiNquOaWPpWdbPHYrKLk///Ns+lB6a8B/Aug8KBmRK1NkTd87RVEMlZ6/+/WbOc9/z2AE5sZWLe/noUAhZJYgXgkPjE1WNMEDaH8UfW4XUrqtqWZe7h0BALyvvQlnLZoDAHjKovJRColUGn/9n68imVZxyelt+Mp6LWDqpHlBwyvtrEG2Wd7W3RpEd2sQybSKHfsGAQD7jo7h9i17ZN5GvleM+jyV//mJ9+e8qheeh3wVFOERGRyPYdzUOnhg5wH5/4u/s91WSV1fvWms8+QIzdbGTItHV0ERXppiX6vAiQwUcX6iwGCninI8Y+ydW0bbRPw8F2vxmDcZ67G7j2e6M1AE4oXHMdniERUUo0DpC0fx9tGs/8rq+a+l9Gs7UKAQMksQBsBESpVjhOVWUFwuBQuKtHle7h0GAKxa3IwLM9WLSsd873h0D14/Mormei/+9orluGp1FzwuBfuPRaT5NZVWsfdIdoJHz4WnaufxyK5ePPPWMfzpfS/kPI75FWM8mcYf+sbk+1ZbiQu9Ige0C2FLprzeq6ui9IWjuHvr2/J9uyX1hTpTZmdzXU6LQZgjh3QVlFInZEQFxa4vJh8ul5L1odgwyoq4dX07wi5zbO79scpAEWTD2qyFt+Dt/rHMMaY3z1RUUMTzJX52OkwtHjvVkY5QAP/7yhXyfatqYS1BgULILMHncck/+m9l/riWW0EB9D4U6wucqKCs7Joj2yvP7h8yVCPsIsZ8/z0TInXJ6W2Y31iH5nofzjulFQDwq71atsO7x8YxEU+h3ufGSfMaDMcRrw63vz2Iz9//gtzWq8f8ivHto2OI69pYZvEwmUjJFk2ogODLLg3MGmXLXWj4s1cOy/+/1T+eU3WRFRSdB6jUqSphumyvsIIC2G+9AFlRNdfmRJOekC6oLW1WYzrEuocmC3GRDWvLX0HZvKsXT2dGvL/3u33TaiQVAmV4IoF4Mo3DeVo8dqsjf3zOImnC/u7VZ9Z0qiwFCiGzCFGuzwqU8iooQFag7Nw/lHPRjifTeC1jVF21eA6WtTVgQXMAsWQaO/cPlvQ45jFfAPjPFw/Jx7x0eTsAyGwHmSDbGYJb9xe5LxzFv/2+J+f4N390qbxwW00avabbXwIA/aaWlqieuF1KwbwQ8w4doLyFhuYwMyC36iI8KPrlbx2hAFZ3Z700SoFXx6qq6saMKxcopVRQhDAop8UjHietouAUTqGKV7F9PJWGyTnNnHofvG7tJ/jYeExnkjU+r6XsBlva1gjAvrF5uqBAIWQWISZ5Dmf61OVO8QBZr8CjLx/OMVz+oW8U8WQazfVeLJmrTTmIKsrvHBnzhawyrDu9HW6XgtePjOK9oYic4Flhau9YHQcAPnjSXPzdpz8AQMt3Mb9i3JNJpH1fu/ZH2+y50Y8YF5rmEEbW3uPZCorb9JLWzlitnVZNvovsRDx70b5mdVfeV8fjsSQmMpWuSls8gD6szU6LJ1NBCZb+uHY3Ghf2oBTex1PtAMJScbkU2b59bygifx7NLR5A2w224/YL8ZMbzi04ISWE87vHajtRlgKFkFmE+dVwuRWUvnAUv339qHzf7J3YnfGfrOxqlhdtfZprsRAsPd2tQZiv+/oqQ0vQJ0cmH9/Th9cOjQDI9Z8UKnFfcno7FAXoPR7NuaiLCsq607VKjbmCIpcuFgm8E6PA+gvZbzJtqdM6mopeNOx8HQLR4jkeiSOVuZpOJlKycgZk2xxWCINsY50H9b7KPRbZsLbiabIi/bbcbBE7G43tTPEcGIyUPXY+1czL/F6/elD7WW30eyzFF2BvN5gQKPlye2oFChRCZhHm0K1yKyjFDHfCf7IqM70DAB86eS7qvC70hSfxpu5CWYyOUACXLs9GcltVGdZnPv6LV/vw+hFt0dyKBaGc4+QrcYfqvTg1U9bepVsoqL+or8ukbg5FjFkR8mJXROxlKyhZgfJ4pi11xcpO2wsl7ZTqW+p9UBRNOIoL9Vv9Y0ikss+amPawwqkMFEEpWSjHZYunvMpNyIbfJV8OCgC8khHX+wcjecfOz1qc/bkuNUyuGggfyisHtXO3qp6UghAotb6TZ3rtyYQQRzFvpS23giJexetL3fpXkbKCohModV43zju5FdveHMC2Nwfw/o4m24/n82ivla46ayH+x7plOReDS05vw1d/tlduwW30e3KyQgCtxH3Bsnk4MDiBJa31huOc092CN/vH8MKB41if2VHyZv8YkmkVc4M+nN7ZBL/HhVgyjaOjk1JwjBSZ4BEID8qRcBSTiRTGJpNyu/J6nQCzQ6GvA9D29cyp9+F4JI7B8RhaG/zSEzQ36MNQJC4XylkhdrlUssVYj924+8lESnpHWsqY4gHsbTTOV0HpC0fxg+375fuiMnjBsnmG77FYTfA3Hz8VV6xcMO1TLkKgiAqK2X9SKkKgHBqOIp5My9+/WqM2z4oQUhZtjc5UUMSreH2r4fb170NHKICBsUkcGo5CUYAzukxjvpk2z89eOWwonxdLN309Mzb88RXtlheDuQ1+nKsLU1va1mCI+Tafu1W1QiSYvqCroOzJtItWLAxBURT5h1/vQ8mGtBUWKC1BHxr8HqiqNvn0m9f7kVaBMxaGygr7KlaqFxNbwigrvhaxf+Xo2CQSeUL2ZAZKozMVlCabcffC1+R1K2iqK+/1sfiZLiSG8u3iseMvOTo6ifeGJqAowOfOXTzt4gTIxt2LqbRKz2l+ox/1PjdSaRUHC6yzmG4cFyhLliyBoig5bzfeeCMA4Lrrrsv52Lnnnuv0aRByQuKUBwXQXsX//vaLsKxNG+UVZfNXMu2dZfMb0Wi6AEQyr47fPjqONd/ahvt/34P7f99TcFPwZCKF/Rmz3mkdRsGjR79o7+XekZJHP8Wunj/0jcqvxZxIK0Zu9T6UbEhbYbGnKIoh8v5Xe7X2zvoVpVVP7GI2yoqvZe2p8+F1K1DVbHaGmWwGilMtHnsm2WwGSvkLCrOjxtaPFU+mEc206MwVFDv+HiFgT+toyuvzmGrMRuYFFbZ4FEWRFcieGjbKOi5Qdu3ahb6+Pvm2detWAMAf/dEfyft8/OMfN9zniSeecPo0CDkh0ZfsPS5F7h0pl45QADdfvAwA8NDzvZhMpLBb+E8WNxvu2xeO4tu/flO+n1aBb/ziDXzjF28U3BT89tExpNIqWoK+vC2HvnAUP3/1iHxfRemjn21NdVg8tx5pFXjpPa1FlZ0Ias58vXWZx9MJlCKLAvUIgbK7dxjP7tc2EV9aYnvHLnN1iajReAr7BrQguzO7mtGe+TqO5GnziEj+gNeZS0CzHDMubJIdlBko5U+XFdtoPKpbc9BgqtJYVQb/95VGf8muA5pAERW3WmC+aR2BE1Wd7nmFjbJ2dzpVE8c9KPPmzTO8/61vfQsnn3wyPvKRj8jb/H4/2tvbnX5oQk545jb4pXekud7nyJKzdae1YUFzAIdHonjs5cMyQXZl1xzD/fKN+ZoRJXXxR1aYXk/vbMp7voVK86X8sT5nSQveG5rArp7jOLd7Lt4+qhlkxUSQuLD36/4oh4ssCtQjfCsPPd+LtAosX9AkY/CdRl9BeaNvFKm0inmNfrQ1+dEZCuDg8ajlxWXzrl6Z+Pu9J/ehPVRXcVhXs82E16EKDbL6x8o3Ziyer8Y6T86YN6BVBj/YPRcf++52JFKqYV0CkK2gfLC7lgSKsWJSqUkWALozP6vvWhhlH37+Pdzx6F6o0MIPN21YMS2BblX1oMTjcTz44IP4whe+YPjD8/TTT2P+/PlYtmwZbrjhBgwMFM5NiMViGB0dNbwRQnJxuxQ5RllJe0ePx+3CdectAQD8644e2UpYuajZcD+r8rkCFC2pv5ERKKcVMNU6tUNEBJm90HMcb/SFkVa1V6eiNdaR8aAc0XtQbJpkgaxRVlRdLq1SewfIjssOjcek/+QDC4xeGnMFJSeEDM6EkDUXabsIjmcqKK1lGmS1xyo8ZlwoA0WwpDWIC5ZqL6b1+6NGJuJ4KyNaz66lCkpOi8eBCooYNTYJlL5wFHc8tldO8U3nxuOqCpTHHnsMIyMjuO666+Rt69evx0MPPYRt27bh7rvvxq5du3DRRRchFsu/WXLTpk0IhULyraurq5qnTciMRlxs3UpubHu5XH1OF4I+N94ZGEc0kULQ78bJpph5q/HYb316BTZtWGHIlTCPbL6Rmcw5rTO/QCklJbMQ4lXxa4fCeKFHqwTp81Q6rDwoE/YrKItajJNF1WrvAFmT7OB4XE7wiPC6zmbR4jE+/9UKIQtlNhqPTiYKRtCLCkq5EzxA8Vh9u4LSan/UiweGoaracsp5FW55dpK5QZ8hK0hU+ipBtHjMo8blrmeoBlUdM77vvvuwfv16dHZ2ytuuvvpq+f/ly5fj7LPPxuLFi/H4449jw4YNlsfZuHEjbrnlFvn+6OgoRQoheRBZGG9ljKpOlGeb6rw4o6sZOzO+ikgshf946WDOcfONx3Y0BfD5+19AndeFK1culPdPpVU5Onx6AYFS6NilsKilHvMb/RgYi+HhF94DAKxY0Cw/3m7lQcl4HcRFuBCvZVJpBc/3DGGJRdy9E+hbPGLzrhBb4ntjFqgiFE9/AXIihEyIAVUFxiaTeTNjBh1p8RTeaFxoD48eESz4cu8whiNxzAn6pP+klto7gFbFnBv0y5Fyv8dd8TFFi6cvPIloPIVAJqG3nPUM1aJqFZT33nsPTz75JP7sz/6s4P06OjqwePFi7Nu3L+99/H4/mpqaDG+EkFz6wlF5wQecK8/2haN47t0hw235jms1Hnv+0la0BH2YTKTxaqYdAWjR3RPxFOq8LnS3NuQcy86xS0FRFDnNc/C4du6GCkpGoAyOxxBPaiO6disofeEo/u5Xbxpuq2ZpXBhNDx6fwDuZTc/LM9NIogVw2NTi6QgFcNXZWYHoVAiZz+OSEfT5zKuAflFg+RUUsdE4X4vHbgWlszmA97U3Iq0C2zOLAZ/vqT2DrEB83eUm8OYcL+iTP9N6o2xTnRduXbVmOoPqqiZQ7r//fsyfPx+f+MQnCt5vaGgIBw8eREdH9UqhhJwoWCVDOlGerbQ14HIpMq5+x77sMkHR3jm1vcnS0FgNzjG9Ol6uS6RtCfpkaNXR0Umk0irGMq/Ii+WgTPUOF1FBGZ5IQFU1cSXMlMJEaSWOxA6ci98/31b0vl3shLWJFk8lF9mQLrXWqp1kx4Mi0O+PmognsTfTKjP/jEw3m3f1yimtN/vHHNuuLEeNdX83XjhwHClVqyb+5IYPOvozUipVESjpdBr3338/rr32Wng82TLb+Pg4brvtNjz77LM4cOAAnn76aVx22WVobW3FlVdeWY1TIeSEwikzaTWOu+aUVgDA79/JChT9BM9Uob/4tDX6DV4DRVEMo8ajOp+DVWy6nmp97/PRamqT6KP/hUl2ZCJhWCAIaBk1APDhpfMcfVVsZ2FgJYsC5eMU2Wg8WoKpWQiU7W8NYNeBYSTTKjpDdVg4Z/r27pixs926XE6yiLzfmfn9XLtsHj50cuu0BtVVRaA8+eST6O3txRe+8AXD7W63G3v27MGnPvUpLFu2DNdeey2WLVuGZ599Fo2NjdU4FUJOKJwyk1bjuOdnBMorB0cwnrmw2JngcRqxRwgAjo7Fcl6NirC2vnBUXmwb/B543YX/XFbre5+PgM+NoC/rRdC3qprqvDIDxzzJ886ANqWydH7xllopFFsYqKqqXBRYiUm22EbjQnt4zKxcNAfN9V6MTibxT5kI/FqrnlSzMrfEQqDseEdr5Z6X+X2dTqpikl23bp3lNtNAIIDf/OY31XhIQkgGJ8yk1ThuV0s9FrXUo/f4BF7oGcJF72uzNcHjJH3hKO54NPfVqH4XS0coO8mzqEUYZO2NbFfre5+PuQ1+RDIG2RWmPI+OUB32DYyjLxzFKRkxMplIyWWGp7Q5K1DE92g0TwUlEk8hlvH1VOJBAbS4+4l4FMMT8ZycmVLGwt0uBWuXzcNjrxyRBvDVNSZQiu3FqvTYQFagDI7HpIdNtGSnE+7iIWQWUqmZtFrHXXOK8KEMYWBsEsfGYnApwPvbp0ag2Hk12i4nYCZlBaWUTJlqfe+t0O+zMW93zmahZFsB+4+NZ0L8vIbVAU5QLAtFtHfqfW7U+yp7bVxoo7Hcw1Nkikcgxo0FtTbBU83KnDkLRaQfv7+jKaeFOB1wmzEhZMpYc0orfvLCQezcP4gLlmkl5O7WoBxxrDZ2Xo3qKyijZQiUqWLzrl7sPZKd2Nr6Rr/BzJjNQsm2eN7JGC2Xzm9wJGVYT6hImmx2xLjyKZRCG41LqaAA2QWGghcPDOOU+bVlOahWZU60eIYicYSjCekPW1MD1ROAFRRCyBRy3smaKHmzf0yOdp7WmX9BoNPYeTWaNclGS9rDM5XYMU52WmSh7MsYZKtxAW4OFN4y7IRBVlBoo7H0oNiY4ukLR/G3v3zDcNsdj05PamoxqlGZa/B75J6fnsEI/iszYbdm6fT7TwBWUAghU0hL0IfTOprwRt8o/n3XQQBTO8EDFH812qFv8UiB4kz2hFPY2U3UYRF3v69KBllAtyMnTw6KMMg6keNRaKNxKRUUp3Y8zWSWtAYxMBbD9reO4fBIFF63gnNqJAeGFRRCyJRyfubVWSSeAjC1EzyCQq9GRZrssfEYBjOv+mutxWNnpFm2eCwqKMvaqlFByeaTWHHcgQke82OZQ+FUVc3moNgQKFM9Gl6LiFHjn7ygTbOt7JqDYIVb0J2CAoUQMqWsMY0vOuFJcJK5QR+8bgWqCrntuFhI21Rjp1UlWjxHRqJQVRWxZEomhi51eIIH0BlX87R4hNirJOZekG+j8XgsKSsi0YwALsRUj4bXIsKH0j+qVdrMv5/TSW3IJELICcPqJXPgVoDMyiBcds+OaVvnboXLpaA9VIeDx6N4sz8jUGqsggIUb1WJStBkIo2RiQSOjk0irQKNdVnfgZMUM8mKFNm5TlRQ8mw0fuj5bKbNRXc/bevnaqpHw2sN8+6d85fWhkEWYAWFEDLFhKMJKU6A6V3nno+OJu0ilfUz1FaVR1CoVVXndUu/x5FwVCbILmtrdHyCBzAu8bPKwRJ7eJwYX7XaaNwXjuLvfp3dhVTKz9VUjobXGifpBErA68IHTHk60wkFCiFkSqnWviAnMa+zr7UpHrt0hLJG2XeOVs8gC2RFQzyVRjSR214ZcnTMOHejcc9gBGZdVGs/V7WIWJAIANFEGlt2H5rGszFCgUIImVJmgjGxwyRQarHFY4dO3dJAsWzulCoJlHqfG97MGlwro6zMQXFkzDh3o3F3axDmulCt/VzVGn3hKL72s72G22qpmkmBQgiZUmaCMdFcQZmpAkV8Tw+PZAXK0ipM8ADaosV8Rtl0WpViwokKitVG445QQG7nBWrz56rWmOoN3KVCkywhZMqpdWOi+Xyaa9SDUowFmSyU3qEJGWe+rAoTPIJQwIvB8XiOQAlHE0hlroQiZK3SxwGyG41DAS8SqTT6RrVX/n//R2dgzSknpqekFKq558cJWEEhhEwLtWxM1Ld4fB4X6rwz809lR6bF89y7Q0imVTT4PXJbczWQ3hBTPokwyIYCXvg8lX8vrTYav9k3hslEGk11HmxYuaAmf65qjVqvZrKCQgghJvQCJRTwVmXqZSoQCwOHMxfxU6qwg0dPc54Wj5N7eATmjcYvHxwGAJy5aA5cZpMTyUstVzMpUAghxMTcBj88LgXJtFpzIW2l0Gm62FRrgkeg94boERM8rQ4YZOVjBbw4PBKVo8a739MEyqpFzY49xolCRyhQU8JEMDPrloQQUkXcLgVtmVbITDXIAsC8Rk1oCaoRca9HLgw0C5SISJF1roJi3mj88sERAMDKRXMcewwyvVCgEEKIBaLNk0qjZsYuS0UvtADglCoaZIH8cfeiguLEHh6BfqPx4HgM7w1pkydndjU79hhkeqFAIYQQC+KpNABgd+8w1nxrGzbv6i3yGbWJyEIBgFBddbv6+TYaZysoDrZ4dBuNX+kdAaB5bGZqqB7JhQKFEEJM9IWj2HMoLN+vxTh+uyQyQgsAPvP/nq2q0GquL1xBaXWyxaPbaCwMsitZPZlVUKAQQoiJnsEIzNtkainAyi594ShePTh1QktUL46MRA2PMeRgiqxAv9F493sjAIBVi+k/mU1QoBBCiImZEMdvh6kWWrsOaJWMA0MThrbYYFVMsr7MseN49dAIAGAlJ3hmFRQohBBiotYDrOwylUKrLxzFD55+R76vr9ZkKyjOt3hefm8YE/EUGvweLJ1f3SklMrUwB4UQQiyo5QAruwih9ZUte5FS1aoKrXx7XfYPjMtcFCdNsqKCMhZLAgDO6ArBzYC2WQUFCiGE5KFWA6xKYaqEltVeF5eS9aW4FDgaejfHlE+zsov+k9kGWzyEEDLLmYq9R+a2GADMb/RLwdIS9DsaQR8yCZRVi5sdOzapDVhBIYQQ4giiWvPawRH8zU/3oH80hm8+/gYAZ0eMAeTknZzJCsqsgwKFEEKIY4i2WDIN3PjwbjnZ01DndvRx/B436rwuTCbS6JoTcDSlltQGbPEQQghxnE98oAPLO5vk+y8eGHE0JG7zrl5MJrQQuoPD0Rmb9EvyQ4FCCCHEcfrCUbzRN2q4zamQuL5wFBu37KnKsUntQIFCCCHEcfKNHTsRElfNY5PagQKFEEKI41QzJG62JP2SwlCgEEIIcZxqpvHOlqRfUhhFVVXzqoaKuPPOO/GNb3zDcFtbWxv6+/sBAKqq4hvf+Ab++Z//GcPDw/jgBz+If/zHf8Tpp59u+zFGR0cRCoUQDofR1NRU/BMIIYRMC33haNVC4qp5bFIdSrl+V2XM+PTTT8eTTz4p33e7s+Nl3/72t/Gd73wHP/zhD7Fs2TJ885vfxMc+9jG89dZbaGzkHgVCCJlNVDONdzYk/ZL8VKXF4/F40N7eLt/mzZsHQKuefO9738Mdd9yBDRs2YPny5XjggQcwMTGBhx9+uBqnQgghhJAZSFUEyr59+9DZ2Ynu7m5cc801ePfddwEAPT096O/vx7p16+R9/X4/PvKRj2Dnzp15jxeLxTA6Omp4I4QQQsjsxXGB8sEPfhA/+tGP8Jvf/Ab/8i//gv7+fpx33nkYGhqSPpS2tjbD5+g9KlZs2rQJoVBIvnV1dTl92oQQQgipIRwXKOvXr8enP/1prFixAhdffDEef/xxAMADDzwg76MoxvkwVVVzbtOzceNGhMNh+Xbw4EGnT5sQQgghNUTVx4yDwSBWrFiBffv2ob29HQByqiUDAwM5VRU9fr8fTU1NhjdCCCGEzF6qLlBisRj+8Ic/oKOjA93d3Whvb8fWrVvlx+PxOLZv347zzjuv2qdCCCGEkBmC42PGt912Gy677DIsWrQIAwMD+OY3v4nR0VFce+21UBQFN998M+666y4sXboUS5cuxV133YX6+np89rOfdfpUCCGEEDJDcVygHDp0CH/8x3+MwcFBzJs3D+eeey6ee+45LF68GADw5S9/GdFoFF/84hdlUNtvf/tbZqAQQgghROJ4kuxUwCRZQgghZOZRyvWbu3gIIYQQUnNQoBBCCCGk5qjKLp5qI7pSTJQlhBBCZg7ium3HXTIjBcrY2BgAMFGWEEIImYGMjY0hFAoVvM+MNMmm02kcOXIEjY2NhgTa1atXY9euXZafk+9j5ttHR0fR1dWFgwcPTrsBt9DXM5XHK+Xz7Ny3nOcp38esbputz+FMeP4KfZy/g3wOp4MT8Tms5WuhqqoYGxtDZ2cnXK7CLpMZWUFxuVxYuHBhzu1utzvvNzLfx/LdXguJtYW+nqk8XimfZ+e+5TxP+T5W6P6z7TmcCc9foY/zd5DP4XRwIj6HtX4tLFY5Ecwqk+yNN95Y8scKfc504/S5lXu8Uj7Pzn3LeZ7yfayWnz/A2fObCc9foY/zd5DP4XRwIj6Hs+VaOCNbPNWEGSszHz6HMxs+fzMfPoczn1p4DmdVBcUJ/H4/vv71r8Pv90/3qZAy4XM4s+HzN/PhczjzqYXnkBUUQgghhNQcrKAQQgghpOagQCGEEEJIzUGBQgghhJCagwKFEEIIITUHBQohhBBCag4KlDI5ePAg1q5di9NOOw0f+MAH8B//8R/TfUqkDK688krMmTMHn/nMZ6b7VIhNfvnLX+LUU0/F0qVL8a//+q/TfTqkDPh7N3OZymsfx4zLpK+vD0ePHsWZZ56JgYEBrFq1Cm+99RaCweB0nxopgaeeegrj4+N44IEH8J//+Z/TfTqkCMlkEqeddhqeeuopNDU1YdWqVXj++efR0tIy3adGSoC/dzOXqbz2sYJSJh0dHTjzzDMBAPPnz0dLSwuOHz8+vSdFSubCCy9EY2PjdJ8GsckLL7yA008/HQsWLEBjYyMuvfRS/OY3v5nu0yIlwt+7mctUXvtmrUB55plncNlll6GzsxOKouCxxx7Luc/3v/99dHd3o66uDmeddRb+67/+q6zHevHFF5FOp9HV1VXhWRM9U/kckqmh0uf0yJEjWLBggXx/4cKFOHz48FScOsnA38uZjZPPX7WvfbNWoEQiEZxxxhm49957LT++efNm3Hzzzbjjjjvw8ssv48Mf/jDWr1+P3t5eeZ+zzjoLy5cvz3k7cuSIvM/Q0BA+//nP45//+Z+r/jWdaEzVc0imjkqfU6uOtKIoVT1nYsSJ30syfTj1/E3JtU89AQCgPvroo4bbzjnnHPUv//IvDbe9733vU2+//Xbbx52cnFQ//OEPqz/60Y+cOE1SgGo9h6qqqk899ZT66U9/utJTJCVSznP6+9//Xr3iiivkx/7qr/5Kfeihh6p+rsSaSn4v+Xs3/ZT7/E3VtW/WVlAKEY/H8dJLL2HdunWG29etW4edO3faOoaqqrjuuutw0UUX4U//9E+rcZqkAE48h6S2sPOcnnPOOdi7dy8OHz6MsbExPPHEE7jkkkum43SJBfy9nNnYef6m8tp3QgqUwcFBpFIptLW1GW5va2tDf3+/rWP8/ve/x+bNm/HYY4/hzDPPxJlnnok9e/ZU43SJBU48hwBwySWX4I/+6I/wxBNPYOHChdi1a5fTp0psYuc59Xg8uPvuu3HhhRdi5cqV+Ou//mvMnTt3Ok6XWGD395K/d7WJnedvKq99nqocdYZg7l2rqmq7n33++ecjnU5X47RICVTyHALgBEgNUuw5vfzyy3H55ZdP9WmREij2HPL3rrYp9PxN5bXvhKygtLa2wu1257zSHhgYyFGOpDbhczj74HM68+FzOLOptefvhBQoPp8PZ511FrZu3Wq4fevWrTjvvPOm6axIKfA5nH3wOZ358Dmc2dTa8zdrWzzj4+N455135Ps9PT145ZVX0NLSgkWLFuGWW27Bn/7pn+Lss8/Ghz70IfzzP/8zent78Zd/+ZfTeNZED5/D2Qef05kPn8OZzYx6/qo6IzSNPPXUUyqAnLdrr71W3ucf//Ef1cWLF6s+n09dtWqVun379uk7YZIDn8PZB5/TmQ+fw5nNTHr+uIuHEEIIITXHCelBIYQQQkhtQ4FCCCGEkJqDAoUQQgghNQcFCiGEEEJqDgoUQgghhNQcFCiEEEIIqTkoUAghhBBSc1CgEEIIIaTmoEAhhBBCSM1BgUIIIYSQmoMChRBCCCE1BwUKIYQQQmqO/x9MxLx04x9NOwAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def get_convergence_iters():\n", + " print(workspace)\n", + " np.random.seed(0)\n", + " xy = np.random.randn(n+m)\n", + " losses = []\n", + " for i in range(350):\n", + " # print(i)\n", + " current_loss = separated_loss(xy)\n", + " losses.append(current_loss)\n", + " if current_loss < 1e-25:\n", + " print('iters', i)\n", + " break\n", + " current_grad = separated_grad(xy)\n", + " direction = np.linalg.lstsq(dense_hessian(xy), -current_grad, rcond=None)[0]\n", + " xy = line_search(xy, direction)\n", + "\n", + " return i\n", + "\n", + "niters_at_gap = []\n", + "gaps = np.logspace(-2, 2, 100)\n", + "for gap in gaps:\n", + " workspace['SCALE_GAP'] = gap\n", + " niters_at_gap.append(get_convergence_iters())\n", + " \n", + "plt.plot(gaps, niters_at_gap, '.-')\n", + "plt.xscale('log')" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "id": "281d45cc", + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 0.01, 'SCALE_S_ERROR': 1}\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 0.010974987654930561, 'SCALE_S_ERROR': 1}\n", + "iters 146\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 0.012045035402587823, 'SCALE_S_ERROR': 1}\n", + "iters 173\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 0.013219411484660288, 'SCALE_S_ERROR': 1}\n", + "iters 164\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 0.014508287784959394, 'SCALE_S_ERROR': 1}\n", + "iters 128\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 0.015922827933410922, 'SCALE_S_ERROR': 1}\n", + "iters 191\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 0.01747528400007684, 'SCALE_S_ERROR': 1}\n", + "iters 90\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 0.019179102616724886, 'SCALE_S_ERROR': 1}\n", + "iters 150\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 0.02104904144512021, 'SCALE_S_ERROR': 1}\n", + "iters 134\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 0.023101297000831605, 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "workspace['SCALE_GAP'] = 1\n", + "workspace['SCALE_Y_ERROR'] = 1\n", + "workspace['SCALE_S_ERROR'] = 1\n", + "\n", + "\n", + "niters = []\n", + "tests = np.logspace(-2, 2, 100)\n", + "for test in tests:\n", + " workspace['SCALE_Y_ERROR'] = test\n", + " niters.append(get_convergence_iters())\n", + " \n", + "plt.plot(tests, niters, '.-')\n", + "plt.xscale('log')" + ] + }, + { + "cell_type": "code", + "execution_count": 79, + "id": "d5afb81d", + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.01}\n", + "iters 142\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.010974987654930561}\n", + "iters 103\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.012045035402587823}\n", + "iters 121\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.013219411484660288}\n", + "iters 157\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.014508287784959394}\n", + "iters 111\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.015922827933410922}\n", + "iters 87\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.01747528400007684}\n", + "iters 109\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.019179102616724886}\n", + "iters 84\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.02104904144512021}\n", + "iters 77\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.023101297000831605}\n", + "iters 88\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.025353644939701114}\n", + "iters 139\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.027825594022071243}\n", + "iters 86\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.030538555088334154}\n", + "iters 89\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.033516026509388425}\n", + "iters 152\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.03678379771828634}\n", + "iters 85\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.040370172585965536}\n", + "iters 116\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.044306214575838825}\n", + "iters 66\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.04862601580065353}\n", + "iters 154\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.0533669923120631}\n", + "iters 110\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.05857020818056667}\n", + "iters 70\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.06428073117284322}\n", + "iters 140\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.07054802310718646}\n", + "iters 138\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.0774263682681127}\n", + "iters 108\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.08497534359086446}\n", + "iters 82\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.093260334688322}\n", + "iters 76\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.10235310218990264}\n", + "iters 68\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.11233240329780277}\n", + "iters 70\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.12328467394420665}\n", + "iters 97\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.13530477745798075}\n", + "iters 84\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.1484968262254465}\n", + "iters 94\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.16297508346206444}\n", + "iters 84\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.1788649529057435}\n", + "iters 67\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 0.19630406500402714}\n", + "iters 127\n", + "{'SCALE_GAP': 1, 'SCALE_Y_ERROR': 1, 'SCALE_S_ERROR': 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "workspace['SCALE_GAP'] = 1\n", + "workspace['SCALE_Y_ERROR'] = 1\n", + "workspace['SCALE_S_ERROR'] = 1\n", + "\n", + "\n", + "niters = []\n", + "tests = np.logspace(-2, 2, 100)\n", + "for test in tests:\n", + " workspace['SCALE_S_ERROR'] = test\n", + " niters.append(get_convergence_iters())\n", + " \n", + "plt.plot(tests, niters, '.-')\n", + "plt.xscale('log')" + ] + }, + { + "cell_type": "markdown", + "id": "0b540a0d", + "metadata": {}, + "source": [ + "# PLAYING WITH SCALING FOR CG " + ] + }, + { + "cell_type": "code", + "execution_count": 87, + "id": "4df79fd5", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "3.3306690738754696e-16" + ] + }, + "execution_count": 87, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "workspace['SCALE_GAP'] = 1\n", + "workspace['SCALE_Y_ERROR'] = 1\n", + "workspace['SCALE_S_ERROR'] = 1\n", + "\n", + "program.solve(# verbose=True,\n", + " # ECOS/CVXOPT\n", + " # solver='ECOS', abstol=1e-16, reltol=1e-16, feastol=1e-16,\n", + " # CLARABEL\n", + " solver='CLARABEL', tol_feas = 1.0e-16, tol_gap_abs = 1.0e-16, tol_gap_rel=1e-16,\n", + " # solver='GLPK', verbose=True, # CVXPY intf does not work?\n", + " # SCS\n", + " # solver = 'SCS', eps=1e-16, max_iters=1000000\n", + " )#, eps=1e-16, max_iters=1000000)\n", + "\n", + "np.max(constraints[0].violation())" + ] + }, + { + "cell_type": "code", + "execution_count": 88, + "id": "a83ea724", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "228.0845811666564" + ] + }, + "execution_count": 88, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "xy = np.random.randn(m+n)\n", + "separated_loss(xy)" + ] + }, + { + "cell_type": "code", + "execution_count": 89, + "id": "443067c3", + "metadata": {}, + "outputs": [], + "source": [ + "grad = separated_grad(xy)" + ] + }, + { + "cell_type": "code", + "execution_count": 91, + "id": "9aadf4cc", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 91, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "H = dense_hessian(xy)\n", + "plt.imshow(H)\n", + "plt.figure()\n", + "plt.plot(np.linalg.eigh(H)[0])\n", + "plt.plot(np.diag(H))" + ] + }, + { + "cell_type": "code", + "execution_count": 97, + "id": "dc8355e1", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([-2.64534563e-15, -1.93715081e-15, -1.39773241e-15, -4.79652069e-16,\n", + " -4.16299924e-16, -3.96463581e-16, 7.88985573e-17, 3.43543554e-16,\n", + " 4.58736699e-16, 5.04928738e-16, 1.07736215e-15, 1.46206343e-15,\n", + " 1.69839275e-15, 2.84310696e-02, 3.97224002e-02, 4.02273528e-02,\n", + " 7.21882298e-02, 7.34128179e-02, 1.40868621e-01, 1.62372830e-01,\n", + " 1.82807137e-01, 2.12717059e-01, 2.32433918e-01, 3.10323278e-01,\n", + " 3.74419197e-01, 5.17282258e-01, 5.22458399e-01, 5.47932742e-01,\n", + " 5.85599805e-01, 5.94376874e-01, 6.29116950e-01, 6.56254554e-01,\n", + " 6.58698411e-01, 6.83849254e-01, 6.92873292e-01, 7.21790030e-01,\n", + " 7.29226922e-01, 7.55590796e-01, 7.65366873e-01, 7.82809956e-01,\n", + " 8.11091454e-01, 8.39603380e-01, 8.55290554e-01, 8.81718452e-01,\n", + " 9.49245705e-01, 1.11404895e+00, 1.19992693e+00, 1.22815041e+00,\n", + " 1.28745015e+00, 1.32409224e+00, 1.39616133e+00, 1.41408402e+00,\n", + " 1.46323023e+00, 1.52794008e+00, 1.56604818e+00, 1.57569970e+00,\n", + " 1.61827889e+00, 1.62310849e+00, 1.63147564e+00, 1.66968816e+00,\n", + " 1.68604068e+00, 1.77885136e+00, 1.79849117e+00, 1.82714850e+00,\n", + " 1.84801919e+00, 1.84966458e+00, 1.88704469e+00, 1.95932739e+00,\n", + " 1.99036205e+00, 2.07161920e+00, 2.15023755e+00, 2.22505729e+00,\n", + " 2.25072742e+00, 2.33659497e+00, 2.43095652e+00, 2.57542502e+00,\n", + " 2.73397628e+00, 2.98479458e+00, 2.99583823e+00, 3.13462200e+00,\n", + " 3.26899652e+00, 3.30247292e+00, 3.32117283e+00, 3.32303986e+00,\n", + " 3.32310040e+00, 3.32335597e+00, 3.32657287e+00, 3.35851353e+00,\n", + " 3.37181365e+00, 3.37289682e+00, 3.38347951e+00, 3.39925214e+00,\n", + " 3.42314705e+00, 3.44434459e+00, 3.58702827e+00, 3.60015398e+00,\n", + " 3.83355769e+00, 3.87245892e+00, 3.95829995e+00, 4.02457278e+00,\n", + " 4.17966821e+00, 4.32519093e+00, 4.35457523e+00, 4.37374405e+00,\n", + " 4.38911204e+00, 4.40281566e+00, 4.51777194e+00, 4.55625396e+00,\n", + " 4.58957277e+00, 4.61165038e+00, 4.62983791e+00, 4.63887007e+00,\n", + " 4.65687516e+00, 4.67534993e+00, 4.69036940e+00, 4.69275479e+00,\n", + " 4.73806894e+00, 4.74116479e+00, 4.75847527e+00, 4.80405380e+00,\n", + " 4.87267934e+00, 4.91161344e+00, 4.99339746e+00, 5.15047673e+00,\n", + " 5.20754745e+00, 5.28702403e+00, 5.28753948e+00, 5.31993372e+00,\n", + " 5.32357048e+00, 5.32792929e+00, 5.32999602e+00, 5.33456854e+00,\n", + " 5.39412631e+00, 5.45927775e+00, 5.56653337e+00, 5.73617742e+00,\n", + " 6.32104607e+00, 6.74336158e+00, 8.37518771e+00])" + ] + }, + "execution_count": 97, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "eival" + ] + }, + { + "cell_type": "markdown", + "id": "5cf99a3b", + "metadata": {}, + "source": [ + "# CG ITER SCALED " + ] + }, + { + "cell_type": "code", + "execution_count": 169, + "id": "4ac10786", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "iters 212\n", + "iters 181\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "MINICOUNTER = 0\n", + "\n", + "workspace['SCALE_GAP'] = 1\n", + "workspace['SCALE_Y_ERROR'] = 1\n", + "workspace['SCALE_S_ERROR'] = 1\n", + "\n", + "def denser_count(dense):\n", + " global MINICOUNTER\n", + " MINICOUNTER = 0\n", + " def matvec(x):\n", + " global MINICOUNTER\n", + " MINICOUNTER += 1\n", + " return dense @ x\n", + " return sp.sparse.linalg.LinearOperator(shape=dense.shape, matvec=matvec)\n", + "\n", + "\n", + "def get_scaler(H): # just to see how much we gain with perfect scaling\n", + " # H sqrt\n", + " eival, eivec = np.linalg.eigh(H)\n", + " Hsqrt = np.diag(np.sqrt(np.maximum(eival, 0.))) @ eivec.T\n", + " assert np.linalg.norm(Hsqrt.T @ Hsqrt - H) < 1e-12\n", + " column_norms = np.linalg.norm(Hsqrt, axis=0)\n", + " scaler = np.minimum(1 / column_norms, 10)\n", + " return scaler\n", + "\n", + "def cg_iter_scaled(H, grad, **kwargs):\n", + " scaler = get_scaler(H)\n", + " H_scaled = np.diag(scaler) @ H @ np.diag(scaler)\n", + " grad_scaled = np.diag(scaler) @ grad\n", + " result = sp.sparse.linalg.cg(denser_count(H_scaled), -grad_scaled, **kwargs)[0]\n", + " return result * scaler\n", + "\n", + "\n", + "def cg_iter_scaled_precond(H, grad, **kwargs):\n", + " scaler = get_scaler(H)\n", + " result = sp.sparse.linalg.cg(denser_count(H), -grad, M = np.diag(scaler**2), **kwargs)[0]\n", + " return result\n", + "\n", + "\n", + "\n", + "def cg_iter_unscaled(H, grad, **kwargs):\n", + " result = sp.sparse.linalg.cg(denser_count(H), -grad, **kwargs)[0]\n", + " return result\n", + "\n", + "\n", + "np.random.seed(0)\n", + "xy = np.random.randn(n+m)\n", + "\n", + "# kwargs = {'rtol':0., 'maxiter':20}\n", + "LEN = 500\n", + "CONVERGENCE = 1e-30\n", + "losses = [separated_loss(xy)]\n", + "used_iters = [0] \n", + "for i in range(LEN):\n", + " g = separated_grad(xy)\n", + " direction = cg_iter_unscaled(dense_hessian(xy), g, rtol=min(0.5, np.linalg.norm(g)**.5))\n", + " xy = line_search(xy, direction)\n", + " current_loss = separated_loss(xy)\n", + " losses.append(current_loss)\n", + " used_iters.append(used_iters[-1] + MINICOUNTER)\n", + "\n", + " if current_loss < CONVERGENCE:\n", + " print('iters', i)\n", + " break\n", + "\n", + "plt.plot(used_iters, losses, label='unscaled')\n", + "\n", + "##\n", + "## SCALED\n", + "##\n", + "\n", + "np.random.seed(0)\n", + "xy = np.random.randn(n+m)\n", + "\n", + "losses = [separated_loss(xy)]\n", + "used_iters = [0] \n", + "\n", + "for i in range(LEN):\n", + " \n", + " g = separated_grad(xy)\n", + " direction = cg_iter_scaled(dense_hessian(xy), g, rtol=min(0.5, np.linalg.norm(g)**.5))\n", + " xy = line_search(xy, direction)\n", + " current_loss = separated_loss(xy)\n", + " losses.append(current_loss)\n", + " used_iters.append(used_iters[-1] + MINICOUNTER)\n", + "\n", + " if current_loss < CONVERGENCE:\n", + " print('iters', i)\n", + " break\n", + "\n", + "plt.plot(used_iters, losses, label='scaled')\n", + "\n", + "\n", + "##\n", + "## SCIPY CG PRECOND\n", + "##\n", + "\n", + "np.random.seed(0)\n", + "xy = np.random.randn(n+m)\n", + "\n", + "losses = [separated_loss(xy)]\n", + "used_iters = [0] \n", + "\n", + "for i in range(LEN):\n", + " \n", + " g = separated_grad(xy)\n", + " direction = cg_iter_scaled_precond(dense_hessian(xy), g, rtol=min(0.5, np.linalg.norm(g)**.5))\n", + " xy = line_search(xy, direction)\n", + " current_loss = separated_loss(xy)\n", + " losses.append(current_loss)\n", + " used_iters.append(used_iters[-1] + MINICOUNTER)\n", + "\n", + " if current_loss < CONVERGENCE:\n", + " print('iters', i)\n", + " break\n", + "\n", + "plt.plot(used_iters, losses, label='precond')\n", + "\n", + "\n", + "plt.legend()\n", + "plt.yscale('log')" + ] + }, + { + "cell_type": "code", + "execution_count": 110, + "id": "03bda526", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 110, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# H sqrt\n", + "eival, eivec = np.linalg.eigh(H)\n", + "Hsqrt = np.diag(np.sqrt(np.maximum(eival, 0.))) @ eivec.T\n", + "\n", + "assert np.linalg.norm(Hsqrt.T @ Hsqrt - H) < 1e-12\n", + "\n", + "column_norms = np.linalg.norm(Hsqrt, axis=0)\n", + "scaler = np.minimum(1 / column_norms, 10)\n", + "\n", + "H_scaled = np.diag(scaler) @ H @ np.diag(scaler)\n", + "\n", + "\n", + "plt.imshow(H_scaled)\n", + "plt.figure()\n", + "plt.plot(np.linalg.eigh(H_scaled)[0])\n", + "plt.plot(np.diag(H_scaled))\n" + ] + }, + { + "cell_type": "code", + "execution_count": 112, + "id": "d05255fa", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n", + " 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n", + " 1., 1., 1., 0., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n", + " 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n", + " 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n", + " 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n", + " 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n", + " 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n", + " 1., 1., 1.])" + ] + }, + "execution_count": 112, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.diag(H_scaled)" + ] + }, + { + "cell_type": "code", + "execution_count": 120, + "id": "d8fe92ee", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "5.018999362014234" + ] + }, + "execution_count": 120, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.linalg.norm(grad_scaled)**.5" + ] + }, + { + "cell_type": "code", + "execution_count": 125, + "id": "e0ca992a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(array([ 1.60933555e-01, -3.68086261e-01, -3.68086261e-01, -3.68086261e-01,\n", + " -3.68086261e-01, 3.87528268e+00, -3.68086261e-01, 7.18100118e-01,\n", + " -1.51524365e-01, -3.68086261e-01, 5.06885322e+00, 1.05350006e+00,\n", + " -3.68086261e-01, 8.63836453e-01, 2.62153354e+00, -3.68086261e-01,\n", + " -1.72881486e-01, 1.79673816e+00, -2.73485553e-01, -3.68086261e-01,\n", + " -2.31446531e-01, -7.49199411e-01, -4.50359006e-01, 7.44705065e-02,\n", + " 1.29792804e+00, 1.50500383e-01, -2.86747834e-01, 1.62356509e-02,\n", + " 2.02944684e-01, -7.69043584e-01, 1.74021853e+00, 1.19984877e+00,\n", + " 1.89401545e-01, 8.79076871e-01, -1.70585171e+00, -7.75193709e-01,\n", + " -3.47082633e-03, 0.00000000e+00, -2.31602212e+00, 6.33687383e-01,\n", + " 2.80039554e+00, -2.26861295e-01, 1.01516409e+00, 6.59303977e-01,\n", + " 1.26476687e+00, 7.69412303e-02, -3.32599565e-01, 6.74294218e-01,\n", + " -2.88958646e+00, 2.80098618e-01, 9.92488775e-01, 3.09916668e+00,\n", + " -6.78468660e-02, 4.18165027e+00, 1.09612274e+00, 5.50048581e-01,\n", + " 1.40795133e+00, -2.23071891e+00, -1.14038467e+00, -1.57201603e+00,\n", + " 1.91979818e+00, -1.32924594e+00, -1.86335772e-01, -7.68109168e-01,\n", + " -1.52681985e+00, 1.95902084e+00, 9.95548027e-01, -7.80816749e-01,\n", + " 5.50308006e+00, -1.92995419e+00, -4.93042844e-01, 1.51997732e-01,\n", + " -2.65036211e-01, 2.08147627e+00, 8.46694254e-01, -1.27896092e+00,\n", + " -1.47343234e+00, -3.49288627e+00, 1.60727932e-01, 1.37635414e+00,\n", + " 1.10053270e+00, 2.16919916e+00, 1.96133614e-01, -7.09518991e-01,\n", + " 1.31298680e-01, -1.12927252e+00, 6.32311042e-01, 8.46626184e-01,\n", + " 1.20758765e+00, 3.43085498e+00, 3.17242822e+00, 2.38932010e+00,\n", + " -1.57889704e+00, -1.06888640e+00, -1.86964871e+00, 2.55869436e+00,\n", + " 3.90592081e+00, 1.29432646e+00, -4.11604063e-01, -2.09319360e-02,\n", + " -1.28365239e+00, 1.35179959e-01, -2.38306619e+00, 4.25121475e-01,\n", + " 1.88930732e+00, 3.36857129e+00, 1.73100690e+00, -2.43670804e-01,\n", + " 1.77887038e+00, -1.39969569e+00, -1.75243841e+00, 4.77144592e+00,\n", + " -1.16448285e+00, 4.54856365e+00, 4.22855065e-01, -1.93167071e+00,\n", + " 7.28225288e-01, 2.52359439e+00, 1.19069771e+00, 4.60149405e-01,\n", + " 3.57453941e-01, 4.53013021e-01, 1.78109848e-01, -4.55844786e-01,\n", + " 2.41704749e+00, 5.60903260e-01, -2.14637024e+00, 7.87282520e-01,\n", + " 8.36584108e-01, -4.13254726e-01, 5.11759498e+00, -7.59273890e-01,\n", + " 1.28936080e+00, -2.31970192e-01, -1.36212090e-01, -1.33348096e+00,\n", + " 5.35337240e-01, 1.38713249e+00, -1.93459642e+00]),\n", + " 0)" + ] + }, + "execution_count": 125, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "grad = separated_grad(xy)\n", + "grad_scaled = np.diag(scaler) @ grad\n", + "\n", + "sp.sparse.linalg.cg(H_scaled, -grad_scaled, rtol=1e-4, maxiter=30)" + ] + }, + { + "cell_type": "code", + "execution_count": 127, + "id": "6846bdeb", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(array([ 1.21817136e-02, -9.06710153e-01, -8.06204948e-01, -9.76043741e-01,\n", + " -8.34277921e-01, 2.09440783e+00, -9.02546860e-01, 5.16186435e-01,\n", + " -1.37450678e-01, -8.48458593e-01, 2.73990657e+00, 5.68955111e-01,\n", + " -9.48147216e-01, 4.66545650e-01, 1.41682317e+00, -1.30904385e+00,\n", + " -1.81280154e-01, 9.70940241e-01, -2.95159870e-01, -8.95261025e-01,\n", + " -1.83930146e-01, -5.73847826e-01, -4.53085677e-01, 1.26898900e-02,\n", + " 9.31239230e-01, 8.75530068e-02, -3.42115087e-02, -3.54067380e-01,\n", + " 1.15699711e-01, -4.55362334e-01, 1.40551335e+00, 1.08938766e+00,\n", + " 1.09140069e-01, 1.12240400e+00, -1.35550892e+00, -4.65588918e-01,\n", + " -1.49162266e-03, 0.00000000e+00, -1.71327624e+00, 7.35651695e-01,\n", + " 2.20065700e+00, -3.67829624e-03, 6.82462741e-01, 5.17307177e-01,\n", + " 9.78046585e-01, -8.63137668e-02, -5.52037379e-01, 5.02614821e-01,\n", + " -2.12595284e+00, 3.03528973e-01, 7.93343821e-01, 2.18830023e+00,\n", + " -4.46788261e-02, 2.09087633e+00, 5.46645051e-01, 2.75415761e-01,\n", + " 7.01896202e-01, -1.57722251e+00, -8.11373334e-01, -1.11383772e+00,\n", + " 9.59441218e-01, -9.41686310e-01, -1.33726354e-01, -5.39381055e-01,\n", + " -1.07133954e+00, 9.79217060e-01, 4.97113223e-01, -5.49165379e-01,\n", + " 2.75133885e+00, -1.36477928e+00, -3.48012494e-01, 7.60949777e-02,\n", + " -1.82041857e-01, 1.03903708e+00, 4.22861452e-01, -9.02546494e-01,\n", + " -1.04156228e+00, -2.46594028e+00, 8.03642157e-02, 6.90804519e-01,\n", + " 5.51431353e-01, 1.08463426e+00, 9.87384872e-02, -4.99869344e-01,\n", + " 6.34065939e-02, -8.07194087e-01, 3.16256056e-01, 4.23814610e-01,\n", + " 6.01514825e-01, 1.71626023e+00, 1.58610012e+00, 1.19437769e+00,\n", + " -1.11632660e+00, -7.61248690e-01, -1.32346041e+00, 1.27953534e+00,\n", + " 1.95320643e+00, 6.46501483e-01, -2.93804876e-01, -4.30769299e-01,\n", + " -9.07644598e-01, -3.44799271e-01, -1.68248049e+00, 2.13377105e-01,\n", + " 9.44975978e-01, 1.68695158e+00, 8.65226297e-01, -1.72831665e-01,\n", + " 8.85107622e-01, -9.87206639e-01, -1.24096275e+00, 2.38466164e+00,\n", + " -8.21753259e-01, 2.27429819e+00, -1.19278751e-01, -1.36369711e+00,\n", + " 7.59425174e-02, 1.26186484e+00, 5.95313771e-01, 2.30030679e-01,\n", + " 1.79365573e-01, 2.27025026e-01, 8.84298804e-02, -3.36740608e-01,\n", + " 1.20901177e+00, 2.80286845e-01, -1.51766466e+00, 3.94484893e-01,\n", + " 4.17012579e-01, -8.45636778e-01, 2.55989939e+00, -1.12711373e+00,\n", + " 6.45890359e-01, -1.63441970e-01, -9.61450667e-02, -9.40218300e-01,\n", + " 2.67486915e-01, 6.92564826e-01, -1.38159852e+00]),\n", + " 30)" + ] + }, + "execution_count": 127, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sp.sparse.linalg.cg(H, -grad, rtol=1e-4, maxiter=30)" + ] + }, + { + "cell_type": "markdown", + "id": "dc632887", + "metadata": {}, + "source": [ + "### USING LSQR INSTEAD " + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "1bdfca03", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1795.9773188345885\n", + "29.31652539415214\n" + ] + }, + { + "data": { + "image/png": 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", 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kBwKMDYMjMN0EGAAAHEWAsYHbqAEASA4EGBu8Ho8k1sAAAOA0AowN1hRSLwEGAAAnEWBsOH0XEo8SAADASQQYG9gHBgCA5ECAsYEAAwBAciDA2MBGdgAAJAcCjA1sZAcAQHIgwNjARnYAACQHAowNbGQHAEByIMDYYE0hsQYGAABHEWBsYAQGAIDkQICxgTUwAAAkBwKMDewDAwBAciDA2OBLOfUwRwIMAACOIsDYwEZ2AAAkBwKMDWxkBwBAciDA2MBdSAAAJAcCjA1nTiEZYxxuDQAAFy8CjA2DAUZiHQwAAE4iwNgwuAZGYhoJAAAnEWBsIMAAAJAcCDA2uN0upXpcktiNFwAAJxFgbOJWagAAnEeAscmXemo3XhbxAgDgGAKMTYzAAADgvKgCzPr165Wbm6u0tDQFAgHt3r37rHVbW1t1zz336KqrrpLb7VZZWdmw9bZv366ZM2fK5/Np5syZ+vnPfx5N00YcT6QGAMB5tgNMTU2NysrKVFlZqaamJhUVFWnevHlqaWkZtn53d7cmTJigyspKXXPNNcPWaWhoUElJiRYtWqT33ntPixYt0l/+5V/qnXfesdu8EcduvAAAOM9lbG4pe/311+u6665TdXW1VZaXl6cFCxaoqqrqnOfedNNNuvbaa7Vu3bqw8pKSEgWDQf3bv/2bVXbrrbdq3LhxevnllyNqVzAYlN/vV1dXl9LT0yO/IJvm/3i3PmgN6h+/91V948sTRuxzAAC4GET7/W1rBKanp0eNjY0qLi4OKy8uLlZ9fb2dtwrT0NAw5D3nzp17zvfs7u5WMBgMOxKBERgAAJxnK8B0dHQoFAopMzMzrDwzM1NtbW1RN6Ktrc32e1ZVVcnv91tHdnZ21J9vBwEGAADnRbWI1+Vyhf1tjBlSNtLvuXLlSnV1dVnHkSNHYvr8SPmsBzqGEvJ5AABgqBQ7lTMyMuTxeIaMjLS3tw8ZQbEjKyvL9nv6fD75fL6oPzNag7dRd/cyAgMAgFNsjcB4vV4FAgHV1dWFldfV1WnOnDlRN6KwsHDIe+7cuTOm9xwp1hQSG9kBAOAYWyMwklRRUaFFixapoKBAhYWF2rhxo1paWlRaWippYGrn6NGjeumll6xzmpubJUknTpzQsWPH1NzcLK/Xq5kzZ0qSli9frq9//ev6+7//e/3Zn/2Z/uVf/kVvvPGG3n777ThcYnz5WAMDAIDjbAeYkpISdXZ2avXq1WptbVV+fr5qa2uVk5MjaWDjuj/eE2b27NnW742Njdq6datycnJ06NAhSdKcOXO0bds2rVq1So8++qiuvPJK1dTU6Prrr4/h0kYGG9kBAOA82/vAJKtE7QOz6p/36af/2aLl3/oTlX/7yyP2OQAAXAwSsg8MJK+HhzkCAOA0AoxN7AMDAIDzCDA2EWAAAHAeAcYm7kICAMB5BBibBjeyYw0MAADOIcDYdPo2ah4lAACAUwgwNrEGBgAA5xFgbPKxkR0AAI4jwNjECAwAAM4jwNjEIl4AAJxHgLGJERgAAJxHgLGJAAMAgPMIMDZZG9kxhQQAgGMIMDZZD3NkBAYAAMcQYGxiCgkAAOcRYGzysg8MAACOI8DYxAgMAADOI8DYdOYiXmOMw60BAODiRICxaXAERuJOJAAAnEKAsWlwJ16JaSQAAJxCgLGJAAMAgPMIMDa53S6lelySmEICAMApBJgoWA90ZAQGAABHEGCiwK3UAAA4iwATBTazAwDAWQSYKBBgAABwFgEmCr4UHugIAICTCDBRsBbxchcSAACOIMBEgUW8AAA4iwATBQIMAADOIsBE4fQDHUMOtwQAgIsTASYKbGQHAICzCDBRYAoJAABnEWCiwD4wAAA4K6oAs379euXm5iotLU2BQEC7d+8+Z/1du3YpEAgoLS1N06dP14YNG4bUWbduna666iqNGTNG2dnZKi8v1x/+8IdomjfiuI0aAABn2Q4wNTU1KisrU2VlpZqamlRUVKR58+appaVl2PoHDx7U/PnzVVRUpKamJj3yyCN68MEHtX37dqvOz372M61YsUKPPfaY9u/fr82bN6umpkYrV66M/spGkDUC00uAAQDACSl2T1i7dq2WLFmipUuXShoYOXn99ddVXV2tqqqqIfU3bNigqVOnat26dZKkvLw87d27V88++6zuvPNOSVJDQ4NuuOEG3XPPPZKkadOm6e6779aePXuiva4RZe3EywgMAACOsDUC09PTo8bGRhUXF4eVFxcXq76+fthzGhoahtSfO3eu9u7dq97eXknSjTfeqMbGRiuwfPzxx6qtrdVtt9121rZ0d3crGAyGHYnCIl4AAJxlawSmo6NDoVBImZmZYeWZmZlqa2sb9py2trZh6/f19amjo0OTJk3SXXfdpWPHjunGG2+UMUZ9fX26//77tWLFirO2paqqSk888YSd5scNAQYAAGdFtYjX5XKF/W2MGVJ2vvpnlr/11lt66qmntH79er377rvasWOHfvGLX+jJJ58863uuXLlSXV1d1nHkyJFoLiUqPgIMAACOsjUCk5GRIY/HM2S0pb29fcgoy6CsrKxh66ekpGj8+PGSpEcffVSLFi2y1tVcffXV+v3vf6/vf//7qqyslNs9NGf5fD75fD47zY8b7kICAMBZtkZgvF6vAoGA6urqwsrr6uo0Z86cYc8pLCwcUn/nzp0qKChQamqqJOnkyZNDQorH45ExxhqtSSZMIQEA4CzbU0gVFRV68cUXtWXLFu3fv1/l5eVqaWlRaWmppIGpncWLF1v1S0tLdfjwYVVUVGj//v3asmWLNm/erIceesiqc/vtt6u6ulrbtm3TwYMHVVdXp0cffVR33HGHPB5PHC4zvtjIDgAAZ9m+jbqkpESdnZ1avXq1WltblZ+fr9raWuXk5EiSWltbw/aEyc3NVW1trcrLy/XCCy9o8uTJeu6556xbqCVp1apVcrlcWrVqlY4ePaoJEybo9ttv11NPPRWHS4w/ppAAAHCWyyTjHE0UgsGg/H6/urq6lJ6ePqKf9a/vfaIfvNykr02/XNu+XziinwUAwIUs2u9vnoUUBaaQAABwFgEmCtxGDQCAswgwUeAuJAAAnEWAiYI1AsMiXgAAHEGAiYL31K3djMAAAOAMAkwUmEICAMBZBJgoEGAAAHAWASYK1m3UrIEBAMARBJgoWDvx9vUn5bOaAAC40BFgojA4AiNJvSECDAAAiUaAiYLvjADT3RdysCUAAFycCDBRGJxCkljICwCAEwgwUXC7XUr1uCSxmR0AAE4gwETpzIW8AAAgsQgwUWIvGAAAnEOAiZK1FwwBBgCAhCPARMnLAx0BAHAMASZKrIEBAMA5BJgoeVN4IjUAAE4hwESJRbwAADiHABMln4dFvAAAOIUAEyVf6uAiXh4lAABAohFgosQiXgAAnEOAiRJrYAAAcA4BJkpsZAcAgHMIMFGyppDYyA4AgIQjwESJKSQAAJxDgIkSAQYAAOcQYKJEgAEAwDkEmCixkR0AAM4hwESJERgAAJxDgImSb/BhjtyFBABAwhFgosQIDAAAziHARImN7AAAcA4BJkpsZAcAgHOiCjDr169Xbm6u0tLSFAgEtHv37nPW37VrlwKBgNLS0jR9+nRt2LBhSJ3PP/9cy5Yt06RJk5SWlqa8vDzV1tZG07yEOD2FxNOoAQBINNsBpqamRmVlZaqsrFRTU5OKioo0b948tbS0DFv/4MGDmj9/voqKitTU1KRHHnlEDz74oLZv327V6enp0be//W0dOnRIr7zyij788ENt2rRJU6ZMif7KRhhrYAAAcE6K3RPWrl2rJUuWaOnSpZKkdevW6fXXX1d1dbWqqqqG1N+wYYOmTp2qdevWSZLy8vK0d+9ePfvss7rzzjslSVu2bNGnn36q+vp6paamSpJycnKivaaEsAIMU0gAACScrRGYnp4eNTY2qri4OKy8uLhY9fX1w57T0NAwpP7cuXO1d+9e9fb2SpJeffVVFRYWatmyZcrMzFR+fr7WrFmjUOjs0zPd3d0KBoNhRyINbmTHCAwAAIlnK8B0dHQoFAopMzMzrDwzM1NtbW3DntPW1jZs/b6+PnV0dEiSPv74Y73yyisKhUKqra3VqlWr9A//8A966qmnztqWqqoq+f1+68jOzrZzKTHjLiQAAJwT1SJel8sV9rcxZkjZ+eqfWd7f36+JEydq48aNCgQCuuuuu1RZWanq6uqzvufKlSvV1dVlHUeOHInmUqLGGhgAAJxjaw1MRkaGPB7PkNGW9vb2IaMsg7Kysoatn5KSovHjx0uSJk2apNTUVHk8HqtOXl6e2tra1NPTI6/XO+R9fT6ffD6fnebHlbUTLwEGAICEszUC4/V6FQgEVFdXF1ZeV1enOXPmDHtOYWHhkPo7d+5UQUGBtWD3hhtu0EcffaT+/tNh4MCBA5o0adKw4SUZMAIDAIBzbE8hVVRU6MUXX9SWLVu0f/9+lZeXq6WlRaWlpZIGpnYWL15s1S8tLdXhw4dVUVGh/fv3a8uWLdq8ebMeeughq87999+vzs5OLV++XAcOHNAvf/lLrVmzRsuWLYvDJY4Maw0MdyEBAJBwtm+jLikpUWdnp1avXq3W1lbl5+ertrbWuu25tbU1bE+Y3Nxc1dbWqry8XC+88IImT56s5557zrqFWpKys7O1c+dOlZeXa9asWZoyZYqWL1+uhx9+OA6XODK8Z9yFdL41QAAAIL5cZnBF7SgXDAbl9/vV1dWl9PT0Ef+8ri96dc0TOyVJB344zxqRAQAAkYv2+5tv3Sj5zggsbGYHAEBiEWCiNDiFJLGQFwCARCPARMntdinFPbDuhQADAEBiEWBicHo3Xp5IDQBAIhFgYuBjLxgAABxBgIkBz0MCAMAZBJgYWLvxchcSAAAJRYCJwZmb2QEAgMQhwMTAywMdAQBwBAEmBjzQEQAAZxBgYuDzsAYGAAAnEGBiwAgMAADOIMDEgAADAIAzCDAxGLwLiZ14AQBILAJMDHypbGQHAIATCDAx8LKIFwAARxBgYsAaGAAAnEGAiQEBBgAAZxBgYkCAAQDAGQSYGLCRHQAAziDAxIARGAAAnEGAiQEBBgAAZxBgYmBtZMcUEgAACUWAiYE3xSNJ6u4lwAAAkEgEmBj4UljECwCAEwgwMTi9BoZnIQEAkEgEmBiwiBcAAGcQYGLgZQoJAABHEGBiYG1kxwgMAAAJRYCJAVNIAAA4gwATAwIMAADOIMDEgDUwAAA4gwATA2snXkZgAABIKAJMDAZHYAgwAAAkVlQBZv369crNzVVaWpoCgYB27959zvq7du1SIBBQWlqapk+frg0bNpy17rZt2+RyubRgwYJompZQvlOPEujp65cxxuHWAABw8bAdYGpqalRWVqbKyko1NTWpqKhI8+bNU0tLy7D1Dx48qPnz56uoqEhNTU165JFH9OCDD2r79u1D6h4+fFgPPfSQioqK7F+JAwZHYCSpN0SAAQAgUWwHmLVr12rJkiVaunSp8vLytG7dOmVnZ6u6unrY+hs2bNDUqVO1bt065eXlaenSpfre976nZ599NqxeKBTSwoUL9cQTT2j69OnRXU2C+c4IMCzkBQAgcWwFmJ6eHjU2Nqq4uDisvLi4WPX19cOe09DQMKT+3LlztXfvXvX29lplq1ev1oQJE7RkyZKI2tLd3a1gMBh2JNrgIl6JW6kBAEgkWwGmo6NDoVBImZmZYeWZmZlqa2sb9py2trZh6/f19amjo0OS9Otf/1qbN2/Wpk2bIm5LVVWV/H6/dWRnZ9u5lLhwu11KcbskEWAAAEikqBbxulyusL+NMUPKzld/sPz48eO69957tWnTJmVkZETchpUrV6qrq8s6jhw5YuMK4ofN7AAASLwUO5UzMjLk8XiGjLa0t7cPGWUZlJWVNWz9lJQUjR8/Xu+//74OHTqk22+/3Xq9v38gDKSkpOjDDz/UlVdeOeR9fT6ffD6fneaPCG+KWyd7QuoJhZxuCgAAFw1bIzBer1eBQEB1dXVh5XV1dZozZ86w5xQWFg6pv3PnThUUFCg1NVUzZszQvn371NzcbB133HGHbr75ZjU3NzsyNWQHm9kBAJB4tkZgJKmiokKLFi1SQUGBCgsLtXHjRrW0tKi0tFTSwNTO0aNH9dJLL0mSSktL9fzzz6uiokJ//dd/rYaGBm3evFkvv/yyJCktLU35+flhn/GlL31JkoaUJyOmkAAASDzbAaakpESdnZ1avXq1WltblZ+fr9raWuXk5EiSWltbw/aEyc3NVW1trcrLy/XCCy9o8uTJeu6553TnnXfG7yocxG68AAAknstcIFvIBoNB+f1+dXV1KT09PWGfO+/Hu7W/NaiXvvdVff3LExL2uQAAXAii/f7mWUgxYgoJAIDEI8DEyHdqES878QIAkDgEmBgxAgMAQOIRYGJEgAEAIPEIMDGy9oFhCgkAgIQhwMSIERgAABKPABMjAgwAAIlHgIkRAQYAgMQjwMTo9LOQeJgjAACJQoCJkS+VERgAABKNABMjNrIDACDxCDAxYg0MAACJR4CJEQEGAIDEI8DEiI3sAABIPAJMjLwpHkmMwAAAkEgEmBgxhQQAQOIRYGJEgAEAIPEIMDHychs1AAAJR4CJ0eBGduzECwBA4hBgYmRtZMcUEgAACUOAiRFrYAAASDwCTIwIMAAAJB4BJkZWgGERLwAACUOAiZG1Ey8jMAAAJAwBJkZMIQEAkHgEmBidOYVkjHG4NQAAXBwIMDHyeQaehWSM1NdPgAEAIBEIMDEaHIGRmEYCACBRCDAxOjPAsJAXAIDEIMDEyON2KcXtksQIDAAAiUKAiQPuRAIAILEIMHFw+k4kHugIAEAiEGDigM3sAABILAJMHDCFBABAYhFg4oAAAwBAYkUVYNavX6/c3FylpaUpEAho9+7d56y/a9cuBQIBpaWlafr06dqwYUPY65s2bVJRUZHGjRuncePG6ZZbbtGePXuiaZojBqeQeKAjAACJYTvA1NTUqKysTJWVlWpqalJRUZHmzZunlpaWYesfPHhQ8+fPV1FRkZqamvTII4/owQcf1Pbt2606b731lu6++269+eabamho0NSpU1VcXKyjR49Gf2UJ5GMEBgCAhHIZmw/wuf7663XdddepurraKsvLy9OCBQtUVVU1pP7DDz+sV199Vfv377fKSktL9d5776mhoWHYzwiFQho3bpyef/55LV68OKJ2BYNB+f1+dXV1KT093c4lxewvNtTrN4c+U/XC6zTv6kkJ/WwAAEazaL+/bY3A9PT0qLGxUcXFxWHlxcXFqq+vH/achoaGIfXnzp2rvXv3qre3d9hzTp48qd7eXl1++eVnbUt3d7eCwWDY4RRfysDzkLgLCQCAxLAVYDo6OhQKhZSZmRlWnpmZqba2tmHPaWtrG7Z+X1+fOjo6hj1nxYoVmjJlim655ZaztqWqqkp+v986srOz7VxKXLGIFwCAxIpqEa/L5Qr72xgzpOx89Ycrl6RnnnlGL7/8snbs2KG0tLSzvufKlSvV1dVlHUeOHLFzCXFl7QPDIl4AABIixU7ljIwMeTyeIaMt7e3tQ0ZZBmVlZQ1bPyUlRePHjw8rf/bZZ7VmzRq98cYbmjVr1jnb4vP55PP57DR/xDACAwBAYtkagfF6vQoEAqqrqwsrr6ur05w5c4Y9p7CwcEj9nTt3qqCgQKmpqVbZj370Iz355JN67bXXVFBQYKdZjiPAAACQWLankCoqKvTiiy9qy5Yt2r9/v8rLy9XS0qLS0lJJA1M7Z945VFpaqsOHD6uiokL79+/Xli1btHnzZj300ENWnWeeeUarVq3Sli1bNG3aNLW1tamtrU0nTpyIwyWOvMEAs/fQp2rt+sLh1gAAcOGzNYUkSSUlJers7NTq1avV2tqq/Px81dbWKicnR5LU2toatidMbm6uamtrVV5erhdeeEGTJ0/Wc889pzvvvNOqs379evX09Oi73/1u2Gc99thjevzxx6O8tMSZnnGpJOnf/7tdb/39m5r7p5laXDhN1+defs61QQAAIDq294FJVk7uA9Pfb7Tzgzb9Y/1hNXzcaZXPyBqr++ZM04Jrp2iM15PQNgEAMBpE+/1NgImzD9uO6x8bDunn7x7VF70hSVJ6WopKvpKtRV+bpqnjL3GsbbHoC/XrD3396u4Nqbuv/9QRUndvv/5wRlnPqfKes/0d6leo36g3ZBTq71dfyKi3f+D3gTKj3lN1+vqN+sJ+N+rrP32+MUb9Ruo/9dMYo5Ax6u83MqfKjaQz/4UPlJwuuyD+8QNAgtR8/2uaPXVcXN+TAJMkAWZQ18le/VPjEb3UcFgtn56UJLlc0pfGpGpMqkdjvB5d4k059XPgGJOaoku8HnncLpkzvnyNzKmfg1+8Rv394V/cg7+HzKkv9n5ZX+Z9/QPBYPDo6+9XyMgKEINBofdUQAgrO/Wz/4L4VwIAiMWO/2+OriPAxFeyBZhB/f1Gbx1o1/+rP6z/OHDM6ebEhdfjli/FLV+qW74Uj3wpbnlT3PKleuTzDJafKkvxDNQ/VZbqcSvF41aK26UUj2vgp9t96nf36bJTdTxul1I9Lnncp845dZ7bNVDf5ZLcLpfc7lM/XQP7C7ldLrk0UCYNhMc/Nlg23DolVi4BwFDjL/Nau8/HS7Tf37YX8cIet9ulb87I1DdnZKrzRLc+/X2PvugN6WRPSF/0DPw82dNnlZ3sCam/38jlOvUleuqL2Pqylct6zX3qC9596kvcdeoL3OM+/ftACBj48nefCgCeM356TgWIVI/rj4LF6bJUt2sgqKS65fW45Xbz9Q4AcBYBJoHGX+bT+MuSY/M9AABGs6geJQAAAOAkAgwAABh1CDAAAGDUIcAAAIBRhwADAABGHQIMAAAYdQgwAABg1CHAAACAUYcAAwAARh0CDAAAGHUIMAAAYNQhwAAAgFGHAAMAAEadC+Zp1MYYSVIwGHS4JQAAIFKD39uD3+ORumACzPHjxyVJ2dnZDrcEAADYdfz4cfn9/ojru4zdyJOk+vv79cknn2js2LFyuVxxe99gMKjs7GwdOXJE6enpcXtfDI/+Tiz6O7Ho78SivxMr2v42xuj48eOaPHmy3O7IV7ZcMCMwbrdbV1xxxYi9f3p6Ov8DSCD6O7Ho78SivxOL/k6saPrbzsjLIBbxAgCAUYcAAwAARh0CzHn4fD499thj8vl8TjflokB/Jxb9nVj0d2LR34mV6P6+YBbxAgCAiwcjMAAAYNQhwAAAgFGHAAMAAEYdAgwAABh1CDDnsH79euXm5iotLU2BQEC7d+92ukmjUlVVlb7yla9o7NixmjhxohYsWKAPP/wwrI4xRo8//rgmT56sMWPG6KabbtL7778fVqe7u1s/+MEPlJGRoUsvvVR33HGH/vd//zeRlzLqVFVVyeVyqayszCqjr+Pv6NGjuvfeezV+/Hhdcskluvbaa9XY2Gi9Tp/HT19fn1atWqXc3FyNGTNG06dP1+rVq9Xf32/Vob+j9x//8R+6/fbbNXnyZLlcLv3zP/9z2Ovx6tvPPvtMixYtkt/vl9/v16JFi/T555/ba6zBsLZt22ZSU1PNpk2bzAcffGCWL19uLr30UnP48GGnmzbqzJ071/zkJz8xv/3tb01zc7O57bbbzNSpU82JEyesOk8//bQZO3as2b59u9m3b58pKSkxkyZNMsFg0KpTWlpqpkyZYurq6sy7775rbr75ZnPNNdeYvr4+Jy4r6e3Zs8dMmzbNzJo1yyxfvtwqp6/j69NPPzU5OTnmr/7qr8w777xjDh48aN544w3z0UcfWXXo8/j54Q9/aMaPH29+8YtfmIMHD5p/+qd/MpdddplZt26dVYf+jl5tba2prKw027dvN5LMz3/+87DX49W3t956q8nPzzf19fWmvr7e5Ofnm+985zu22kqAOYuvfvWrprS0NKxsxowZZsWKFQ616MLR3t5uJJldu3YZY4zp7+83WVlZ5umnn7bq/OEPfzB+v99s2LDBGGPM559/blJTU822bdusOkePHjVut9u89tprib2AUeD48ePmT/7kT0xdXZ35xje+YQUY+jr+Hn74YXPjjTee9XX6PL5uu+02873vfS+s7M///M/Nvffea4yhv+PpjwNMvPr2gw8+MJLMf/7nf1p1GhoajCTz3//93xG3jymkYfT09KixsVHFxcVh5cXFxaqvr3eoVReOrq4uSdLll18uSTp48KDa2trC+tvn8+kb3/iG1d+NjY3q7e0NqzN58mTl5+fz32QYy5Yt02233aZbbrklrJy+jr9XX31VBQUF+ou/+AtNnDhRs2fP1qZNm6zX6fP4uvHGG/Xv//7vOnDggCTpvffe09tvv6358+dLor9HUrz6tqGhQX6/X9dff71V52tf+5r8fr+t/r9gHuYYTx0dHQqFQsrMzAwrz8zMVFtbm0OtujAYY1RRUaEbb7xR+fn5kmT16XD9ffjwYauO1+vVuHHjhtThv0m4bdu26d1339VvfvObIa/R1/H38ccfq7q6WhUVFXrkkUe0Z88ePfjgg/L5fFq8eDF9HmcPP/ywurq6NGPGDHk8HoVCIT311FO6++67JfFvfCTFq2/b2to0ceLEIe8/ceJEW/1PgDkHl8sV9rcxZkgZ7HnggQf0X//1X3r77beHvBZNf/PfJNyRI0e0fPly7dy5U2lpaWetR1/HT39/vwoKCrRmzRpJ0uzZs/X++++rurpaixcvturR5/FRU1Ojn/70p9q6dav+9E//VM3NzSorK9PkyZN13333WfXo75ETj74drr7d/mcKaRgZGRnyeDxDkmB7e/uQ5InI/eAHP9Crr76qN998U1dccYVVnpWVJUnn7O+srCz19PTos88+O2sdDAzftre3KxAIKCUlRSkpKdq1a5eee+45paSkWH1FX8fPpEmTNHPmzLCyvLw8tbS0SOLfd7z9zd/8jVasWKG77rpLV199tRYtWqTy8nJVVVVJor9HUrz6NisrS//3f/835P2PHTtmq/8JMMPwer0KBAKqq6sLK6+rq9OcOXMcatXoZYzRAw88oB07duhXv/qVcnNzw17Pzc1VVlZWWH/39PRo165dVn8HAgGlpqaG1WltbdVvf/tb/puc4Vvf+pb27dun5uZm6ygoKNDChQvV3Nys6dOn09dxdsMNNwzZFuDAgQPKycmRxL/veDt58qTc7vCvLo/HY91GTX+PnHj1bWFhobq6urRnzx6rzjvvvKOuri57/R/5euSLy+Bt1Js3bzYffPCBKSsrM5deeqk5dOiQ000bde6//37j9/vNW2+9ZVpbW63j5MmTVp2nn37a+P1+s2PHDrNv3z5z9913D3tr3hVXXGHeeOMN8+6775pvfvOb3PYYgTPvQjKGvo63PXv2mJSUFPPUU0+Z3/3ud+ZnP/uZueSSS8xPf/pTqw59Hj/33XefmTJlinUb9Y4dO0xGRob527/9W6sO/R2948ePm6amJtPU1GQkmbVr15qmpiZrC5F49e2tt95qZs2aZRoaGkxDQ4O5+uqruY06nl544QWTk5NjvF6vue6666zbfmGPpGGPn/zkJ1ad/v5+89hjj5msrCzj8/nM17/+dbNv376w9/niiy/MAw88YC6//HIzZswY853vfMe0tLQk+GpGnz8OMPR1/P3rv/6ryc/PNz6fz8yYMcNs3Lgx7HX6PH6CwaBZvny5mTp1qklLSzPTp083lZWVpru726pDf0fvzTffHPb/r++77z5jTPz6trOz0yxcuNCMHTvWjB071ixcuNB89tlnttrqMsaYKEaSAAAAHMMaGAAAMOoQYAAAwKhDgAEAAKMOAQYAAIw6BBgAADDqEGAAAMCoQ4ABAACjDgEGAACMOgQYAAAw6hBgAADAqEOAAQAAow4BBgAAjDr/P0Hlz4b55QoWAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def residual(xy):\n", + " x, y = xy[:n], xy[n:]\n", + " \n", + " y_error = np.minimum(y[zero:], 0.)\n", + "\n", + " dual_residual = matrix_transf.T @ y + c_transf\n", + "\n", + " s = -matrix_transf @ x + b_transf\n", + " \n", + " s[zero:] = np.minimum(s[zero:], 0.)\n", + "\n", + " gap = c_transf.T @ x + b_transf.T @ y\n", + "\n", + " return np.concatenate([y_error, dual_residual, s, [gap]])\n", + "\n", + "def Dresidual(xy):\n", + " \n", + " x, y = xy[:n], xy[n:]\n", + " \n", + " y_active = np.zeros(m, dtype=float)\n", + " y_active[zero:] = y[zero:]<=0\n", + " \n", + " s = -matrix_transf @ x + b_transf\n", + " \n", + " s_active = np.ones(m, dtype=float)\n", + " s_active[zero:] = s[zero:]<=0\n", + " \n", + " return sp.sparse.bmat([\n", + " [None, sp.sparse.diags(y_active).tocsc()[zero:]],\n", + " [None, matrix_transf.T],\n", + " [- sp.sparse.diags(s_active) @ matrix_transf, None],\n", + " [c_transf.reshape(1,n), b_transf.reshape(1,m)]\n", + " ])\n", + "# dual_residual = matrix_transf.T @ y + c_transf\n", + "\n", + "# s = -matrix_transf @ x + b_transf\n", + " \n", + "# s[zero:] = np.minimum(s[zero:], 0.)\n", + "\n", + "# gap = c_transf.T @ x + b_transf.T @ y\n", + "\n", + "\n", + "print(np.linalg.norm(residual(xy))**2,)\n", + "\n", + "#plt.imshow(Dresidual(xy).todense()[:])\n", + "def get_best_loss_direction(xy, direction):\n", + " return np.min([separated_loss(xy + step * direction) for step in steps])\n", + "\n", + "def get_next_point(xy, direction):\n", + " which = np.argmin([separated_loss(xy + step * direction) for step in steps])\n", + " return xy + (steps[which]) * direction\n", + "steps = np.logspace(-10,0,100)\n", + "\n", + "H = separated_hessian(xy)\n", + "grad = separated_grad(xy)\n", + "steps = np.logspace(-10,0,100)\n", + "\n", + "EXPONENT = 0.25\n", + "\n", + "TOL=1e-6\n", + "DAMP=0#1e-4\n", + "iters = np.arange(1,1000,20)\n", + "losses = []\n", + "residualnorms=[]\n", + "for iterlim in iters:\n", + " direction = sp.sparse.linalg.lsmr(Dresidual(xy), -residual(xy), atol=TOL, btol=TOL, damp=DAMP,\n", + " maxiter=iterlim)[0]\n", + " #direction = sp.sparse.linalg.lsqr(Dresidual(xy), -residual(xy), atol=0., btol=0., iter_lim=iterlim)[0]\n", + " losses.append(get_best_loss_direction(xy, direction))\n", + " residualnorms.append(np.linalg.norm(H @ direction + grad))\n", + " # if np.linalg.norm(H @ direction + grad) < (np.linalg.norm(grad)**(1+EXPONENT)):\n", + " # break\n", + " \n", + " \n", + "plt.plot(iters[:len(losses)], \n", + " np.array(residualnorms)/(np.linalg.norm(grad)**(1+EXPONENT)), label=f'||r||*||g||^-({1+EXPONENT})')\n", + "plt.yscale('log')\n", + "plt.figure()\n", + "plt.plot(iters[:len(losses)],np.array(losses)/(np.linalg.norm(residual(xy))**2))\n", + "\n", + "xy = get_next_point(xy, direction)\n", + "print(separated_loss(xy))" + ] + }, + { + "cell_type": "markdown", + "id": "3f701343", + "metadata": {}, + "source": [ + "# Scaling of columns? " + ] + }, + { + "cell_type": "code", + "execution_count": 209, + "id": "6385ca55", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(2271, 1398)\n" + ] + }, + { + "data": { + "text/plain": [ + "(array([147., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n", + " 0., 0., 0., 0., 0., 0., 0., 0., 5., 149., 1.,\n", + " 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 39.,\n", + " 0., 4., 471., 0., 0., 0., 0., 15., 0., 0., 0.,\n", + " 0., 142., 0., 0., 0., 425.]),\n", + " array([0. , 0.02828491, 0.05656982, 0.08485473, 0.11313964,\n", + " 0.14142455, 0.16970946, 0.19799437, 0.22627928, 0.25456418,\n", + " 0.28284909, 0.311134 , 0.33941891, 0.36770382, 0.39598873,\n", + " 0.42427364, 0.45255855, 0.48084346, 0.50912837, 0.53741328,\n", + " 0.56569819, 0.5939831 , 0.62226801, 0.65055292, 0.67883783,\n", + " 0.70712274, 0.73540764, 0.76369255, 0.79197746, 0.82026237,\n", + " 0.84854728, 0.87683219, 0.9051171 , 0.93340201, 0.96168692,\n", + " 0.98997183, 1.01825674, 1.04654165, 1.07482656, 1.10311147,\n", + " 1.13139638, 1.15968129, 1.1879662 , 1.2162511 , 1.24453601,\n", + " 1.27282092, 1.30110583, 1.32939074, 1.35767565, 1.38596056,\n", + " 1.41424547]),\n", + " )" + ] + }, + "execution_count": 209, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "print(Dresidual(xy).shape)\n", + "plt.hist(np.linalg.norm(Dresidual(xy).todense(), axis=0), bins=50)" + ] + }, + { + "cell_type": "markdown", + "id": "20f9b808", + "metadata": {}, + "source": [ + "## MINI SOLVER " + ] + }, + { + "cell_type": "code", + "execution_count": 579, + "id": "a8b01f6d", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "7.819071330021671e-16" + ] + }, + "execution_count": 579, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.linalg.norm(separated_grad(xy))" + ] + }, + { + "cell_type": "code", + "execution_count": 715, + "id": "73badb8a", + "metadata": {}, + "outputs": [], + "source": [ + "np.random.seed(0)\n", + "xy = np.random.randn(n+m)\n", + "TOTITERS = 0" + ] + }, + { + "cell_type": "code", + "execution_count": 716, + "id": "8438cc40", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "iters 574 loss 27.83195265972278\n", + "iters 1312 loss 2.884542891256059\n", + "iters 1836 loss 0.6416850697554278\n", + "iters 3026 loss 0.3530810469418572\n", + "iters 3983 loss 0.2538035491703633\n", + "iters 4573 loss 0.14165754389851112\n", + "iters 5358 loss 0.08916730032290011\n", + "iters 6217 loss 0.08335596285313752\n", + "iters 7047 loss 0.0738648207906936\n", + "iters 7797 loss 0.03213948703751669\n", + "iters 8770 loss 0.028159432043503064\n", + "iters 9352 loss 0.010275255112950014\n", + "iters 10237 loss 0.00927747135369286\n", + "iters 11144 loss 0.006781680801958021\n", + "iters 11900 loss 0.004062769980356029\n", + "iters 12971 loss 0.003739825394414027\n", + "iters 13768 loss 0.0023586480261149766\n", + "iters 15169 loss 0.0023579293494375188\n", + "iters 16288 loss 0.0019166356548574444\n", + "iters 17294 loss 0.0017803944719270172\n", + "iters 18210 loss 0.0010421196530086732\n", + "iters 19616 loss 0.0010312547814803035\n", + "iters 21231 loss 0.0010309371610243117\n", + "iters 22861 loss 0.001030583195545363\n", + "iters 24431 loss 0.0010062432587785832\n", + "iters 25648 loss 0.0008681469097759874\n", + "iters 26644 loss 0.0007549318656194022\n", + "iters 27665 loss 0.0006460182098109562\n", + "iters 28946 loss 0.000623474945721827\n", + "iters 30018 loss 0.000480286753402478\n", + "iters 31216 loss 0.0004756780128140519\n", + "iters 32623 loss 0.00047019328130473194\n", + "iters 33759 loss 0.0003961818411778967\n", + "iters 34998 loss 0.00037098599279038115\n", + "iters 36223 loss 0.00035276695496022127\n", + "iters 37661 loss 0.0003439159883418181\n", + "iters 38924 loss 0.00031152190820110654\n", + "iters 40209 loss 0.00030211526187534307\n", + "iters 41448 loss 0.0002763485281438899\n", + "iters 42614 loss 0.00023099385891931794\n", + "iters 44068 loss 0.00021980253078724072\n", + "iters 45387 loss 0.00021487374690829755\n", + "iters 46752 loss 0.00020943124378992154\n", + "iters 47974 loss 0.00016553363533558773\n", + "iters 49349 loss 0.00016491340647126906\n", + "iters 50828 loss 0.0001639761874969347\n", + "iters 52269 loss 0.00015262294258455513\n", + "iters 53768 loss 0.00014860073275797957\n", + "iters 55053 loss 0.00012723072717317984\n", + "iters 56352 loss 0.00012702941176135753\n", + "iters 57843 loss 0.00012649625011643348\n", + "iters 59335 loss 0.00012626564432794855\n", + "iters 60700 loss 0.00011874249504995292\n", + "iters 62168 loss 0.00011616183871411972\n", + "iters 63483 loss 0.00010867932417266075\n", + "iters 64833 loss 9.934946860689878e-05\n", + "iters 66145 loss 9.732733104929122e-05\n", + "iters 67494 loss 9.142604022570204e-05\n", + "iters 68961 loss 9.076267369663076e-05\n", + "iters 70530 loss 9.066179087090549e-05\n", + "iters 72098 loss 9.064717580394984e-05\n", + "iters 73579 loss 8.715825324441766e-05\n", + "iters 75005 loss 8.634062288342079e-05\n", + "iters 76304 loss 7.448076493874197e-05\n", + "iters 77514 loss 7.378932120906498e-05\n", + "iters 78783 loss 7.143254137099781e-05\n", + "iters 80132 loss 6.699434953878056e-05\n", + "iters 81557 loss 6.438553921665864e-05\n", + "iters 83081 loss 6.243488458221998e-05\n", + "iters 84630 loss 6.137358512475096e-05\n", + "iters 86237 loss 6.110672596368715e-05\n", + "iters 87870 loss 6.097145784488719e-05\n", + "iters 89377 loss 4.976970466914789e-05\n", + "iters 90882 loss 4.958748564104349e-05\n", + "iters 92395 loss 4.950228981277284e-05\n", + "iters 93980 loss 4.9479443639699675e-05\n", + "iters 95491 loss 4.726459055962389e-05\n", + "iters 96958 loss 4.6541255169847844e-05\n", + "iters 98546 loss 4.640576456274344e-05\n", + "iters 100080 loss 4.611618356451744e-05\n", + "iters 101558 loss 4.3348498400970484e-05\n", + "iters 103055 loss 4.165198789605964e-05\n", + "iters 104588 loss 4.0616685481051755e-05\n", + "iters 106159 loss 4.048694165108817e-05\n", + "iters 107746 loss 4.023690468898971e-05\n", + "iters 109294 loss 3.980685622116898e-05\n", + "iters 110822 loss 3.9074661640362885e-05\n", + "iters 112428 loss 3.7420756014224874e-05\n", + "iters 113982 loss 3.6280529541493986e-05\n", + "iters 115488 loss 3.4637298116876936e-05\n", + "iters 117067 loss 3.256211190639637e-05\n", + "iters 118706 loss 3.252617102603743e-05\n", + "iters 120258 loss 3.2453490659720254e-05\n", + "iters 121754 loss 2.9532991393664534e-05\n", + "iters 123398 loss 2.9412144043696122e-05\n", + "iters 124978 loss 2.8700476344581536e-05\n", + "iters 126469 loss 2.6865476372964754e-05\n", + "iters 127979 loss 2.4870239651360155e-05\n", + "iters 129530 loss 2.3980109004745484e-05\n", + "iters 131002 loss 2.3205857059332256e-05\n" + ] + } + ], + "source": [ + "TOL=1e-2\n", + "DAMP=1e-4\n", + "\n", + "\n", + "for i in range(1,101):\n", + " \n", + "# global iter_used\n", + "# iter_used = 0\n", + " \n", + "# D = Dresidual(xy)\n", + "# def matvec(var):\n", + "# global iter_used\n", + "# iter_used += 1\n", + "# return D @ var\n", + "# def rmatvec(var):\n", + "# global iter_used\n", + "# iter_used += 1\n", + "# return D.T @ var\n", + "# wrapped = sp.sparse.linalg.LinearOperator(shape=D.shape,\n", + "# matvec=matvec,\n", + "# rmatvec=rmatvec,)\n", + " \n", + " TOL = 1e-12 #max(separated_loss(xy)**0.5, 1e-8)\n", + " result = sp.sparse.linalg.lsmr(\n", + " #wrapped, \n", + " Dresidual(xy),\n", + " -residual(xy), \n", + " atol=0.,\n", + " btol=TOL,#np.linalg.norm(separated_grad(xy))**.5, \n", + " damp=DAMP,#1e-3,\n", + " maxiter=10000)\n", + " # print('iters', result[2])\n", + " #print('iters', iter_used)\n", + " direction = result[0]\n", + " xy = get_next_point(xy, direction)\n", + " # xy += direction\n", + " TOTITERS += result[2] #iter_used\n", + " print('iters', TOTITERS, 'loss', separated_loss(xy))\n", + " if separated_loss(xy) < 1e-25:\n", + " break" + ] + }, + { + "cell_type": "markdown", + "id": "ce3d2686", + "metadata": {}, + "source": [ + "# DEPENDENCE ON NUMBER OF CG ITERS " + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "597f8f66", + "metadata": {}, + "outputs": [], + "source": [ + "np.random.seed(0)\n", + "xy = np.random.randn(n+m)" + ] + }, + { + "cell_type": "code", + "execution_count": 174, + "id": "80b39e69", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.873018098622551e-06\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "H = separated_hessian(xy)\n", + "grad = separated_grad(xy)\n", + "steps = np.logspace(-10,0,100)\n", + "\n", + "residualnorms = []\n", + "# len_direction = []\n", + "best_losses = []\n", + "unit_step_losses = [separated_loss(xy)]\n", + "def get_best_loss_direction(xy, direction):\n", + " return np.min([separated_loss(xy + step * direction) for step in steps])\n", + "\n", + "def get_next_point(xy, direction):\n", + " which = np.argmin([separated_loss(xy + step * direction) for step in steps])\n", + " return xy + (steps[which]) * direction\n", + "\n", + "EXPONENT = .5\n", + "FREQ_CHECK = 1\n", + "\n", + "for i in range(1, 100):\n", + " cg_solution = sp.sparse.linalg.cg(H, -grad, atol=0., rtol=0., maxiter=i)[0]\n", + " residualnorms.append(np.linalg.norm(H @ cg_solution + grad))\n", + " # len_direction.append(np.linalg.norm(cg_solution))\n", + " \n", + " best_losses.append(get_best_loss_direction(xy, cg_solution))\n", + " if np.linalg.norm(H @ cg_solution + grad) < (np.linalg.norm(grad)**(1+EXPONENT)):\n", + " pass\n", + " #break\n", + " unit_step_losses.append(separated_loss(xy + cg_solution))\n", + " if (i % FREQ_CHECK == 0) and (unit_step_losses[-1] > unit_step_losses[-1 - FREQ_CHECK]):\n", + " break\n", + "fig, axes = plt.subplots(3, figsize=(8,12))\n", + "\n", + "plt.sca(axes[0])\n", + "plt.plot(np.array(residualnorms)/np.linalg.norm(grad), label='||r||/||g||')\n", + "plt.plot(np.array(residualnorms)/(np.linalg.norm(grad)**(1+EXPONENT)), label=f'||r||*||g||^-({1+EXPONENT})')\n", + "# plt.plot(np.array(residualnorms)/(np.linalg.norm(grad)**1.3), label='||r||*||g||^-1.3')\n", + "# plt.plot(np.array(residualnorms)/(np.linalg.norm(grad)**1.5), label='||r||*||g||^-1.5')\n", + "plt.hlines(1, xmin=0, xmax=len(residualnorms), label='one')\n", + "plt.yscale('log')\n", + "plt.legend()\n", + "plt.title('CG RESIDUAL BY N CG ITERS')\n", + "\n", + "# plt.figure()\n", + "# plt.plot(np.array(len_direction) / np.linalg.norm(grad))\n", + "# plt.title('LENGHT OF THE DIRECTION DIV BY GRAD LEN')\n", + "\n", + "plt.sca(axes[1])\n", + "plt.plot((best_losses) / separated_loss(xy), label='BEST NEXT LOSS GAIN')\n", + "plt.yscale('log')\n", + "plt.legend()\n", + "plt.title(\"BEST NEXT LOSS ASSUMING GOOD LINE SEARCH DIVIDED BY CURRENT\")\n", + "\n", + "plt.sca(axes[2])\n", + "plt.plot(unit_step_losses, '.-')\n", + "plt.yscale('log')\n", + "plt.title(\"UNIT STEP NEXT LOSS\")\n", + "\n", + "xy = get_next_point(xy, cg_solution)\n", + "print(separated_loss(xy))" + ] + }, + { + "cell_type": "markdown", + "id": "ff4bc69b", + "metadata": {}, + "source": [ + "## Same code as above, without plots, iterated " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "13fdce8d", + "metadata": {}, + "outputs": [], + "source": [ + "np.random.seed(0)\n", + "xy = np.random.randn(n+m)\n", + "tot_losses = [separated_loss(xy)]\n", + "tot_matmuls = [0]" + ] + }, + { + "cell_type": "code", + "execution_count": 230, + "id": "efb65904", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "for k in range(2000):\n", + "\n", + "\n", + " H = separated_hessian(xy)\n", + " grad = separated_grad(xy)\n", + " steps = np.logspace(-10,0,100)\n", + " #residualnorms = []\n", + " # len_direction = []\n", + " #best_losses = []\n", + " unit_step_losses = [separated_loss(xy)]\n", + "# def get_best_loss_direction(xy, direction):\n", + "# return np.min([separated_loss(xy + step * direction) for step in steps])\n", + "\n", + " def get_next_point(xy, direction):\n", + " which = np.argmin([separated_loss(xy + step * direction) for step in steps])\n", + " return xy + (steps[which]) * direction\n", + "\n", + " EXPONENT = .5\n", + " FREQ_CHECK = 1\n", + "\n", + " for i in range(1, 100):\n", + " cg_solution = sp.sparse.linalg.cg(H, -grad, atol=0., rtol=0., maxiter=i)[0]\n", + " #residualnorms.append(np.linalg.norm(H @ cg_solution + grad))\n", + " # len_direction.append(np.linalg.norm(cg_solution))\n", + "\n", + " #best_losses.append(get_best_loss_direction(xy, cg_solution))\n", + " #if np.linalg.norm(H @ cg_solution + grad) < (np.linalg.norm(grad)**(1+EXPONENT)):\n", + " # pass\n", + " #break\n", + " unit_step_losses.append(separated_loss(xy + cg_solution))\n", + " if (i % FREQ_CHECK == 0) and (unit_step_losses[-1] > unit_step_losses[-1 - FREQ_CHECK]):\n", + " break\n", + " #print('BROKE AT CGITER', i)\n", + " xy = get_next_point(xy, cg_solution)\n", + " # print(separated_loss(xy))\n", + " tot_losses.append(separated_loss(xy))\n", + " tot_matmuls.append(tot_matmuls[-1] + i)\n", + " \n", + "plt.plot(tot_matmuls, tot_losses)\n", + "plt.yscale('log')" + ] + }, + { + "cell_type": "code", + "execution_count": 224, + "id": "871e3471", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "-3.2358056269255684e-06" + ] + }, + "execution_count": 224, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(np.log10(tot_losses[-1] / tot_losses[0]) / tot_matmuls[-1])" + ] + }, + { + "cell_type": "markdown", + "id": "9e8bb8f4", + "metadata": {}, + "source": [ + "# Line search research " + ] + }, + { + "cell_type": "code", + "execution_count": 343, + "id": "d84bed00", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.0004052682826740908 -4.066879161035486e-07 2.0408981730941382e-07\n", + "0.0005017514736412268\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "current_point = xy\n", + "current_loss = separated_loss(xy)\n", + "current_direction = cg_solution\n", + "current_gradient = separated_grad(xy)\n", + "assert current_direction @ current_gradient < 0\n", + "\n", + "losses_on_line = [separated_loss(current_point + cg_solution * step) for step in steps]\n", + "plt.plot(steps, losses_on_line)\n", + "\n", + "test_step_len = 1\n", + "loss_test_step = separated_loss(current_point + current_direction*test_step_len)\n", + "\n", + "current_loss, loss_step_1\n", + "\n", + "c = current_loss\n", + "b = current_direction @ current_gradient\n", + "# a * (1**2) + b * 1 + c = loss_step_1\n", + "def get_a(loss_at_step, step_len):\n", + " return (loss_at_step - c - b * step_len)/(step_len**2)\n", + "\n", + "a = get_a(loss_test_step, test_step_len)\n", + "\n", + "vertex = -b / (2 * a)\n", + "\n", + "print(a, b, c)\n", + "quad_approx = lambda x: a * x**2 + b * x + c\n", + "plt.plot(steps, [quad_approx(x) for x in steps])\n", + "plt.yscale('log')\n", + "\n", + "print(vertex)" + ] + }, + { + "cell_type": "code", + "execution_count": 349, + "id": "c775b1f7", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.0 -7.527354584959345e-05\n", + "2.0408981730941382e-07 2.0167405033450724e-07\n" + ] + }, + { + "data": { + "image/png": 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t8eT47XE4EhFZuXKlREREiF6vl9jYWMnOznY+N2fOHJk8ebJL/Y4dO2TMmDGi1+slMjJSVq9e3WSdGzZskKFDh4pOp5Po6GjJzMz0aLvV1dXy6KOPSmhoqOj1egkJCZGZM2fK/v37nTUlJSUyadIk6dOnj+j1ehk0aJDMnz9fLl261OL3znBERETdxZ+2HZOIRZ/I5Jc/F7PVrnQ7t8WT47fH1znq7nidIyIi6g4ummow5Y87UG21Y9XjsZg+snOfftJm1zkiIiKi7uHPWcdRbbUjdkBvTBsRrHQ77YrhiIiIiFwcv1iJ/ztwFgCw9KGufcFHdxiOiIiIyMXyzYVwCDB1eDDiIvoo3U67YzgiIiIipz0nK/DFsW+hVauwaFq00u0oguGIiIiIAAAOh+D3m2sv+Pj4uAGICvRRuCNlMBwRERERAOBf+edx9IIJvQxazL9/sNLtKIbhiIiIiFBjteN/PzsOAEidMggBPQ0Kd6QchiMiIiLCO3uKcf5qNUL8vPDkf0Up3Y6iGI6IiIi6uSvXLVj5xUkAwLOJQ+Gl0yjckbIYjoiIiLq51z4/gcoaG4aF+OLRMf2VbkdxDEdERETd2JlL1/H+3jMAgCXTo6FRd68LPrrDcERERNSNvbz1GKx2waQhfZEwuK/S7XQIDEdERETdVO6ZK/j0cClUKmBxN73gozsMR0RERN2QiOAPdRd8/EFsGIaFNP9L9d0JwxEREVE39NnRMuSeuQIvnRrPJg5Vup0OheGIiIiom7HaHXhp6zEAwM/+ayCC/bwU7qhjYTgiIiLqZj7cV4KiiusI8NFj3uSBSrfT4TAcERERdSOmGiv+8p8TAIC0B4egl5dO4Y46HoYjIiKibmTNjlO4fN2CgX19MPs74Uq30yExHBEREXUTF65WI2NXEQAgfWo0dBrGAHe4V4iIiLqJP207DrPNgbGRffBgTJDS7XRYDEdERETdQMEFEz7KOwcAWPLQMKhU/JmQm2E4IiIi6gaWbymECDDj7hCMDu+tdDsdGsMRERFRF5d9/FvsPFEBnUaFF5L4MyG3wnBERETUhdkdguV1PxPyxIRIDAjwVrijjo/hiIiIqAvLPHgO35RVwtdLi6fvu0vpdjoFhiMiIqIuqtpix5+21f5MyFP33YXe3nqFO+ocGI6IiIi6qIxdp3HRZEb/3j3wxIRIpdvpNBiOiIiIuqCKa2asyT4NAHhh6lB46TQKd9R5MBwRERF1QX/ZfgLXzDaM7O+H794dqnQ7nUqrwtGqVasQFRUFLy8vxMXFYefOnc3WZ2dnIy4uDl5eXhg4cCDWrFnTpCYzMxMxMTEwGAyIiYnBpk2bPN7ur3/9a0RHR8PHxwf+/v544IEHsG/fPpcas9mMp59+GoGBgfDx8cHMmTNx7ty5VuwFIiKijunUt9fw4f4SAMCS6cOgVvOCj57wOBytX78eaWlpWLp0KfLy8pCQkIBp06ahpKTEbX1RURGmT5+OhIQE5OXlYcmSJZg/fz4yMzOdNTk5OUhOTkZKSgry8/ORkpKCWbNmuQSblmx3yJAheP3113H48GHs2rULkZGRSExMxLfffuusSUtLw6ZNm7Bu3Trs2rUL165dw4wZM2C32z3dFURERB3SS1u+gd0huD+6HyYMClC6nc5HPDR27FhJTU11GYuOjpb09HS39S+88IJER0e7jM2bN0/Gjx/vfDxr1iyZOnWqS01SUpLMnj271dsVETEajQJAtm/fLiIiV69eFZ1OJ+vWrXPWnD9/XtRqtWzduvWm63G3TqPR2KJ6IiKi9rTv9CWJWPSJRKV/IsfLTEq302F4cvz2aObIYrEgNzcXiYmJLuOJiYnYs2eP29fk5OQ0qU9KSsKBAwdgtVqbralfZ2u2a7FY8Oabb8LPzw+jRo0CAOTm5sJqtbqsJzQ0FCNGjLjpeoiIiDoLEcEf6i74mPydARgc1EvhjjonrSfFFRUVsNvtCApy/SXfoKAglJWVuX1NWVmZ23qbzYaKigqEhITctKZ+nZ5s95NPPsHs2bNRVVWFkJAQZGVlITAw0NmLXq+Hv79/i/s3m80wm83OxyaTyW0dERGR0j49XIpDZ6/CW6/BggcHK91Op9WqE7Ib/5KviDT7677u6huPt2SdLam59957cejQIezZswdTp07FrFmzUF5e3uz7aa7/5cuXw8/Pz7mEh4c3uy4iIiIlmG12vLy19oKPP580EP16eSncUeflUTgKDAyERqNpMstSXl7eZFanXnBwsNt6rVaLgICAZmvq1+nJdn18fHDXXXdh/PjxyMjIgFarRUZGhnM7FosFV65caXH/ixcvhtFodC5nz551W0dERKSk9/eWoORyFfr2MmBuwkCl2+nUPApHer0ecXFxyMrKchnPysrCxIkT3b5mwoQJTeq3bduG+Ph46HS6Zmvq19ma7dYTEefHYnFxcdDpdC7rKS0txZEjR266HoPBAF9fX5eFiIioIzFWWfHaf04AABY+OAQ+Bo/OmqHGPD3be926daLT6SQjI0MKCgokLS1NfHx8pLi4WERE0tPTJSUlxVl/+vRp8fb2lgULFkhBQYFkZGSITqeTjRs3Omt2794tGo1GVqxYIYWFhbJixQrRarWyd+/eFm/32rVrsnjxYsnJyZHi4mLJzc2VJ598UgwGgxw5csS5ntTUVAkLC5Pt27fLwYMH5b777pNRo0aJzWZr0fvnt9WIiKij+f2nBRKx6BN54E87xGqzK91Oh+TJ8dvjcCQisnLlSomIiBC9Xi+xsbGSnZ3tfG7OnDkyefJkl/odO3bImDFjRK/XS2RkpKxevbrJOjds2CBDhw4VnU4n0dHRkpmZ6dF2q6ur5dFHH5XQ0FDR6/USEhIiM2fOlP3797uso7q6Wp566inp06eP9OjRQ2bMmCElJSUtfu8MR0RE1JGUXLoug5dslohFn8h/CsuUbqfD8uT4rRKpOzuaWsRkMsHPzw9Go5EfsRERkeKeWZeHfx26gAkDA/Dh3HHNfkGqO/Pk+M3fViMiIuqkvj53Ff86dAFA7c+EMBjdGQxHREREnZA0uODjI6NDMTLMT+GOug6GIyIiok7o82/Ksff0Zei1ajyXNFTpdroUhiMiIqJOxmZ3YPmWbwAAP5kYiTB/b4U76loYjoiIiDqZ/ztwDifLr6G3tw6/uPcupdvpchiOiIiIOpHrZhteyToOAHj6vsHw66FTuKOuh+GIiIioE3nzy9OouGZGRIA3UsZHKN1Ol8RwRERE1EmUm2rw5penAQAvJEVDr+VhvC1wrxIREXUSf95+HNVWO8YM6I3pI4OVbqfLYjgiIiLqBI5frMT6r84CAJbygo9tiuGIiIioE1ix5Rs4BEgaHoT4yD5Kt9OlMRwRERF1cHtOVeDzb8qhVauwaGq00u10eQxHREREHZjDceNnQh4bNwAD+/ZUuKOuj+GIiIioA/s4/wKOnDehp0GLZ+4frHQ73QLDERERUQdVY7Xjj58dAwD895RBCOhpULij7oHhiIiIqIP6x55inL9ajWBfL/z0niil2+k2GI6IiIg6oCvXLXj9i5MAgGcTh6CHXqNwR90HwxEREVEH9NfPT6Kyxobo4F74XmyY0u10KwxHREREHcyZS9fx3t5iAMCS6cOgUfOCj+2J4YiIiKiDeXnrMVjtgoTBgZg0pK/S7XQ7DEdEREQdyMGSK/j0cClUqtpZI2p/DEdEREQdhIjgD5/WXvDx+7FhGBbiq3BH3RPDERERUQfx2dGLOHDmCrx0ajybOETpdrothiMiIqIOwGp34KWt3wAAnvyvKIT49VC4o+6L4YiIiKgDWLu/BEUV1xHgo0fq5EFKt9OtMRwREREprLLGir9sPwEAeOaBwejlpVO4o+6N4YiIiEhha7JP4dJ1CwYG+uCHYwco3U63x3BERESkoFJjNf6+swgA8MLUaOg0PDQrjf8FiIiIFPSnbcdhtjkQH+GPpOFBSrdDYDgiIiJSTMEFEzIPngMALHloGFQq/kxIR8BwREREpJDlWwohAjw0MgSxA/yVbofqtCocrVq1ClFRUfDy8kJcXBx27tzZbH12djbi4uLg5eWFgQMHYs2aNU1qMjMzERMTA4PBgJiYGGzatMmj7VqtVixatAgjR46Ej48PQkND8cQTT+DChQsu65gyZQpUKpXLMnv27NbsBiIiolb78vi32HmiAjqNCi9MHap0O9SAx+Fo/fr1SEtLw9KlS5GXl4eEhARMmzYNJSUlbuuLioowffp0JCQkIC8vD0uWLMH8+fORmZnprMnJyUFycjJSUlKQn5+PlJQUzJo1C/v27WvxdquqqnDw4EH86le/wsGDB/HRRx/h+PHjmDlzZpOe5s6di9LSUufyxhtveLobiIiIWs3uEPxhc+3PhPxofAQiAnwU7ogaUomIePKCcePGITY2FqtXr3aODRs2DI888giWL1/epH7RokX4+OOPUVhY6BxLTU1Ffn4+cnJyAADJyckwmUzYsmWLs2bq1Knw9/fH2rVrW7VdAPjqq68wduxYnDlzBgMG1H41csqUKRg9ejReffVVT962k8lkgp+fH4xGI3x9+Zs3RETkuQ0HzuL5jV+jl5cWXz5/L/x99Eq31OV5cvz2aObIYrEgNzcXiYmJLuOJiYnYs2eP29fk5OQ0qU9KSsKBAwdgtVqbralfZ2u2CwBGoxEqlQq9e/d2Gf/ggw8QGBiI4cOH47nnnkNlZeVN12E2m2EymVwWIiKi1qq22PGnbccBAP/fvXcxGHVAWk+KKyoqYLfbERTk+lXDoKAglJWVuX1NWVmZ23qbzYaKigqEhITctKZ+na3Zbk1NDdLT0/HYY4+5JMTHH38cUVFRCA4OxpEjR7B48WLk5+cjKyvL7XqWL1+OZcuWuX2OiIjIU2/tLkKZqQb9e/fAjydGKt0OueFROKrX+KuGItLs1w/d1Tceb8k6W7pdq9WK2bNnw+FwYNWqVS7PzZ0713l/xIgRGDx4MOLj43Hw4EHExsY2WdfixYuxcOFC52OTyYTw8HC375OIiKg5FdfMWL3jFADg+aSh8NJpFO6I3PEoHAUGBkKj0TSZrSkvL28yq1MvODjYbb1Wq0VAQECzNfXr9GS7VqsVs2bNQlFRET7//PNbfq4YGxsLnU6HEydOuA1HBoMBBoOh2XUQERG1xGv/OYFrZhtG9PfFzFGhSrdDN+HROUd6vR5xcXFNPoLKysrCxIkT3b5mwoQJTeq3bduG+Ph46HS6Zmvq19nS7dYHoxMnTmD79u3O8NWco0ePwmq1IiQk5Ja1RERErXX622v4cF/tN6yXTB8GtZoXfOywxEPr1q0TnU4nGRkZUlBQIGlpaeLj4yPFxcUiIpKeni4pKSnO+tOnT4u3t7csWLBACgoKJCMjQ3Q6nWzcuNFZs3v3btFoNLJixQopLCyUFStWiFarlb1797Z4u1arVWbOnClhYWFy6NAhKS0tdS5ms1lERE6ePCnLli2Tr776SoqKiuTTTz+V6OhoGTNmjNhstha9f6PRKADEaDR6uuuIiKgb+/m7X0nEok/kJ2/vV7qVbsmT47fH4UhEZOXKlRIRESF6vV5iY2MlOzvb+dycOXNk8uTJLvU7duyQMWPGiF6vl8jISFm9enWTdW7YsEGGDh0qOp1OoqOjJTMz06PtFhUVCQC3yxdffCEiIiUlJTJp0iTp06eP6PV6GTRokMyfP18uXbrU4vfOcERERJ7aX3RJIhZ9IlHpn8jxMpPS7XRLnhy/Pb7OUXfH6xwREZEnRATfW70HeSVX8cOx4Vj+vbuVbqlbarPrHBEREZFnNh8uQ17JVXjrNVjwwBCl26EWYDgiIiJqI2abHS9t/QYAMDdhIPr5eincEbUEwxEREVEbeX9vCUouV6FvLwN+Pmmg0u1QCzEcERERtQFjtRV//fwEAGDBA0PgY2jVdZdJAQxHREREbWDVFydxtcqKu/r1xKz4MKXbIQ8wHBEREd1h565U4e09xQCAxdOiodXwcNuZ8L8WERHRHfa/nx2DxebA+IF9cF90P6XbIQ8xHBEREd1Bh88Z8c9DFwAAS6fHNPvD7NQxMRwRERHdISKCP2wuBAA8PDoUI8P8FO6IWoPhiIiI6A754lg5ck5fgl6jxnOJQ5Vuh1qJ4YiIiOgOsNkdWL659oKPP74nEuF9vBXuiFqL4YiIiOgO2JB7DifKr8Gvhw7/35S7lG6HbgPDERER0W26brbhlazjAICn77sLft46hTui28FwREREdJv+tvM0vq00I7xPD6RMiFC6HbpNDEdERES3obyyBm9+eRoA8EJSNAxajcId0e1iOCIiIroNf846gSqLHaPCe2PG3SFKt0N3AMMRERFRK524WIn1X5UAAJZOH8YLPnYRDEdERESttGLLN3AI8GBMEMZG9VG6HbpDGI6IiIhaIefUJfznm3Jo1CqkT4tWuh26gxiOiIiIPORw3PiZkB+ODcegvj0V7ojuJIYjIiIiD/376ws4fN4IH70Gz9w/ROl26A5jOCIiIvJAjdWOl7ceAwCkTh6Evr0MCndEdxrDERERkQfezSnG+avVCPI14GcJA5Vuh9oAwxEREVELXa2y4PXPTwIAnn1wKHroecHHrojhiIiIqIX++vlJmGpsiA7uhe/HhSndDrURhiMiIqIWOHPpOt7NKQYALJ4+DBo1L/jYVTEcERERtcDLnx2D1S5IGByIyUP6Kt0OtSGGIyIiolvIK7mCT78uhUoFLJ42TOl2qI0xHBERETVD5MYFH783Jgwxob4Kd0RtjeGIiIioGdsKLuKr4iswaNV4LokXfOwOWhWOVq1ahaioKHh5eSEuLg47d+5stj47OxtxcXHw8vLCwIEDsWbNmiY1mZmZiImJgcFgQExMDDZt2uTRdq1WKxYtWoSRI0fCx8cHoaGheOKJJ3DhwgWXdZjNZjz99NMIDAyEj48PZs6ciXPnzrVmNxARURdntTvw0pZvAABP/lcUQvx6KNwRtQePw9H69euRlpaGpUuXIi8vDwkJCZg2bRpKSkrc1hcVFWH69OlISEhAXl4elixZgvnz5yMzM9NZk5OTg+TkZKSkpCA/Px8pKSmYNWsW9u3b1+LtVlVV4eDBg/jVr36FgwcP4qOPPsLx48cxc+ZMl37S0tKwadMmrFu3Drt27cK1a9cwY8YM2O12T3cFERF1cev2l+B0xXX08dEjdcogpduh9iIeGjt2rKSmprqMRUdHS3p6utv6F154QaKjo13G5s2bJ+PHj3c+njVrlkydOtWlJikpSWbPnt3q7YqI7N+/XwDImTNnRETk6tWrotPpZN26dc6a8+fPi1qtlq1bt950PQ0ZjUYBIEajsUX1RETUOZmqLRL7m20SsegTeWd3kdLt0G3y5Pjt0cyRxWJBbm4uEhMTXcYTExOxZ88et6/JyclpUp+UlIQDBw7AarU2W1O/ztZsFwCMRiNUKhV69+4NAMjNzYXVanVZT2hoKEaMGNHseoiIqPtZ+cUpXLpuQVSgDx4bN0DpdqgdaT0prqiogN1uR1BQkMt4UFAQysrK3L6mrKzMbb3NZkNFRQVCQkJuWlO/ztZst6amBunp6Xjsscfg6+vr7EWv18Pf37/F6zGbzTCbzc7HJpPJbR0REXUdGw6cxZrsUwCARVOHQqfh95e6k1b911apXK8KKiJNxm5V33i8Jets6XatVitmz54Nh8OBVatWNfNObt3/8uXL4efn51zCw8NvuT4iIuq8PjtahkWZXwOoPQk7aXiwwh1Re/MoHAUGBkKj0TSZZSkvL28yq1MvODjYbb1Wq0VAQECzNfXr9GS7VqsVs2bNQlFREbKyspyzRvXbsVgsuHLlSov7X7x4MYxGo3M5e/as2zoiIur8dp+swNMf5sEhwP+LC8MvHxrW7D/+qWvyKBzp9XrExcUhKyvLZTwrKwsTJ050+5oJEyY0qd+2bRvi4+Oh0+maralfZ0u3Wx+MTpw4ge3btzvDV724uDjodDqX9ZSWluLIkSM37d9gMMDX19dlISKirufQ2auY++4BWOwOJA0PwvLvjWQw6q48Pdt73bp1otPpJCMjQwoKCiQtLU18fHykuLhYRETS09MlJSXFWX/69Gnx9vaWBQsWSEFBgWRkZIhOp5ONGzc6a3bv3i0ajUZWrFghhYWFsmLFCtFqtbJ3794Wb9dqtcrMmTMlLCxMDh06JKWlpc7FbDY715OamiphYWGyfft2OXjwoNx3330yatQosdlsLXr//LYaEVHXc7zMJKOWfSYRiz6Rx/6WI9WWlh0TqPPw5PjtcTgSEVm5cqVERESIXq+X2NhYyc7Odj43Z84cmTx5skv9jh07ZMyYMaLX6yUyMlJWr17dZJ0bNmyQoUOHik6nk+joaMnMzPRou0VFRQLA7fLFF18466qrq+Wpp56SPn36SI8ePWTGjBlSUlLS4vfOcERE1LWUXLouY3+fJRGLPpGZr++Syhqr0i1RG/Dk+K0SqTs7mlrEZDLBz88PRqORH7EREXVy5ZU1mLUmB8WXqjC4X0/837wJ8PfRK90WtQFPjt/8biIREXVLxmornsjYj+JLVQjz74H3nhzHYEQAGI6IiKgbqrLY8NN3vsI3ZZUI7GnA+0+OQ7Cfl9JtUQfBcERERN2KxebAf79/ELlnrsDXS4v3nhyLyEAfpduiDoThiIiIug27Q7Dw/w4h+/i38NKp8fZPvoNhITx/lFwxHBERUbcgIvjVv47gk69LodOo8EZKPOIi+ijdFnVADEdERNQt/PGzY/hwXwlUKuDPyaMxeUhfpVuiDorhiIiIurw3sk9h1Y7aH5L9/SMjMePuUIU7oo6M4YiIiLq0dftLsHzLNwCARVOj8di4AQp3RB0dwxEREXVZmw+XYsmmwwCAeZMH4r+nDFK4I+oMGI6IiKhL2nniWzyzLg8OAWZ/JxzpU6OVbok6CYYjIiLqcnLPXMHP382F1S54aGQIfv/oSKhUKqXbok6C4YiIiLqUb8pM+Ok7X6HaakfC4EC8kjwKGjWDEbUcwxEREXUZJZeqkJKxH8ZqK2IH9MYbKXEwaDVKt0WdDMMRERF1CRdNNXg8Yy++rTQjOrgX3v7xWHjrtUq3RZ0QwxEREXV6V6sseCJjP85ersaAPt5496dj4eetU7ot6qQYjoiIqFO7brbhJ+98hWMXK9GvlwHvPzkO/Xy9lG6LOjGGIyIi6rTMNjtS389FXslV+PXQ4b0nx2FAgLfSbVEnx3BERESdkt0hSFt3CDtPVMBbr8HbP/kOhgb3Urot6gIYjoiIqNMRESz56DC2HCmDXqPGmynxiB3gr3Rb1EUwHBERUaciIli+5RusP3AWahXw2g9H478GByrdFnUhDEdERNSprM4+hTe/PA0AWPG9uzF1RIjCHVFXw3BERESdxgf7zuDlrccAAL98aBhmfSdc4Y6oK2I4IiKiTuHf+Rfwy38eAQA8de9d+FnCQIU7oq6K4YiIiDq8HcfKsWD9IYgAPxo/AM8mDlG6JerCGI6IiKhDO1B8Ganv58LmEMwcFYrfzBwBlYo/JEtth+GIiIg6rIILJvzkna9QY3Xg3qF98adZo6BWMxhR22I4IiKiDqmo4jqeeGs/Kmts+E6kP1Y9Hgedhoctanv8U0ZERB1OmbEGP/r7PlRcMyMmxBd/n/Md9NBrlG6LugmGIyIi6lAuX7fgRxn7cP5qNaICffCPn46FXw+d0m1RN8JwREREHcY1sw0/eXs/TpZfQ7CvF957ciz69jIo3RZ1MwxHRETUIdRY7fj5uweQf84If28d3v/ZWIT5eyvdFnVDrQpHq1atQlRUFLy8vBAXF4edO3c2W5+dnY24uDh4eXlh4MCBWLNmTZOazMxMxMTEwGAwICYmBps2bfJ4ux999BGSkpIQGBgIlUqFQ4cONVnHlClToFKpXJbZs2d7tgOIiOiOstkdmL82D3tOXYKPXoN//HQs7urXS+m2qJvyOBytX78eaWlpWLp0KfLy8pCQkIBp06ahpKTEbX1RURGmT5+OhIQE5OXlYcmSJZg/fz4yMzOdNTk5OUhOTkZKSgry8/ORkpKCWbNmYd++fR5t9/r167jnnnuwYsWKZt/D3LlzUVpa6lzeeOMNT3cDERHdIQ6HIP2jw9hWcBF6rRp/mxOPu8N6K90WdWMqERFPXjBu3DjExsZi9erVzrFhw4bhkUcewfLly5vUL1q0CB9//DEKCwudY6mpqcjPz0dOTg4AIDk5GSaTCVu2bHHWTJ06Ff7+/li7dq3H2y0uLkZUVBTy8vIwevRol+emTJmC0aNH49VXX/XkbTuZTCb4+fnBaDTC19e3VesgIqJaIoLfflKIt3YXQaNWYfXjsUgcHqx0W9QFeXL89mjmyGKxIDc3F4mJiS7jiYmJ2LNnj9vX5OTkNKlPSkrCgQMHYLVam62pX2drttucDz74AIGBgRg+fDiee+45VFZW3rTWbDbDZDK5LEREdGe8/vlJvLW7CADw8vfvZjCiDkHrSXFFRQXsdjuCgoJcxoOCglBWVub2NWVlZW7rbTYbKioqEBISctOa+nW2Zrs38/jjjyMqKgrBwcE4cuQIFi9ejPz8fGRlZbmtX758OZYtW+bRNoiI6NbezSnGn7KOAwD+Z0YMvh8XpnBHRLU8Ckf1Gv+mjYg0+zs37uobj7dknZ5u1525c+c6748YMQKDBw9GfHw8Dh48iNjY2Cb1ixcvxsKFC52PTSYTwsPDPdomERG5+mfeefzPv44CAJ65fzB++l9RCndEdINHH6sFBgZCo9E0ma0pLy9vMqtTLzg42G29VqtFQEBAszX162zNdlsqNjYWOp0OJ06ccPu8wWCAr6+vy0JERK33n8KLeHZDPgDgxxMjkfbAYIU7InLlUTjS6/WIi4tr8hFUVlYWJk6c6PY1EyZMaFK/bds2xMfHQ6fTNVtTv87WbLeljh49CqvVipCQkNtaDxER3dq+05fwiw8Owu4QPDqmP/5nRozHnwAQtTWPP1ZbuHAhUlJSEB8fjwkTJuDNN99ESUkJUlNTAdR+DHX+/Hm8++67AGq/mfb6669j4cKFmDt3LnJycpCRkeH8FhoAPPPMM5g0aRJeeuklPPzww/jXv/6F7du3Y9euXS3eLgBcvnwZJSUluHDhAgDg2LFjAGpnpoKDg3Hq1Cl88MEHmD59OgIDA1FQUIBnn30WY8aMwT333NOK3UdERC115LwRP/vHAZhtDjwwrB9e/sHdUKsZjKgDklZYuXKlREREiF6vl9jYWMnOznY+N2fOHJk8ebJL/Y4dO2TMmDGi1+slMjJSVq9e3WSdGzZskKFDh4pOp5Po6GjJzMz0aLsiIm+//bYAaLK8+OKLIiJSUlIikyZNkj59+oher5dBgwbJ/Pnz5dKlSy1+70ajUQCI0Whs8WuIiLq7k+WVEvubbRKx6BOZtWaPVFtsSrdE3Ywnx2+Pr3PU3fE6R0REnrlwtRo/WL0HF4w1GNHfF2vnjkcvL/6QLLWvNrvOERERkScuXTPjRxn7cMFYg4F9ffCPn4xlMKIOj+GIiIjaRGWNFXPe3o/T315HqJ8X3n9yHAJ6GpRui+iWGI6IiOiOq7Ha8bN/HMCR8yYE+Ojx3s/GIbR3D6XbImoRhiMiIrqjrHYHnvrwIPYVXUYvgxb/+OlYDOrbU+m2iFqM4YiIiO4Yh0Pwwsavsb2wHAatGn+fE48R/f2UbovIIwxHRER0R4gIfvNJATblnYdWrcLqH8Vi3MAApdsi8hjDERER3RGvbj+Bd/YUQ6UC/jRrFO6Lvr2fdyJSCsMRERHdtrd2FeEv/6n9jcplM4fj4dH9Fe6IqPUYjoiI6LZk5p7Dbz4pAAA8++AQPDEhUtmGiG4TwxEREbXatqNleCHzawDAk/8Vhafuu0vhjohuH8MRERG1yp5TFXhqbR7sDsEP4sKwdPowqFT8IVnq/BiOiIjIY1+fu4q5/zgAi82BxJggrPjeSKjVDEbUNTAcERGRR06WV2LOW/tx3WLHxEEBeO2HY6DV8HBCXQf/NBMRUYudu1KFH/19P65UWTEqzA9vPhEPL51G6baI7iiGIyIiapFvK81IydiPMlMNBvfriXd+MhY9DVql2yK64xiOiIjolozVVsx5az+KKq6jf+8eeO/JcfD30SvdFlGbYDgiIqJmVVvs+Nk/vkJBqQmBPQ344GfjEOznpXRbRG2G4YiIiG7KYnPgvz/IxVfFV9DLS4t3fzoWkYE+SrdF1KYYjoiIyC27Q/DshnzsOPYtvHRqvP3j7yAm1FfptojaHMMRERE1ISJ48eMj+Hf+Beg0Kqz5URziI/so3RZRu2A4IiKiJv607Tje31sClQp4ZdZoTBnaT+mWiNoNwxEREbn425en8foXJwEAv3tkBL47KlThjojaF8MRERE5/d9XZ/H7zYUAgBemDsXj4yIU7oio/TEcERERAGDrkVKkf/Q1AGDepIH478mDFO6ISBkMR0REhF0nKjB/7SE4BEiOD0f6tGioVPwhWeqeGI6IiLq5vJIr+Pl7B2CxOzB9ZDD+8L2RDEbUrTEcERF1Y8fKKvHjt79ClcWOhMGB+HPyaGjUDEbUvTEcERF1U2cvVyElYx+M1VaMGdAba34UB4NWo3RbRIpjOCIi6obKTTV4/O/7UF5pxtCgXnj7x9+Bj0GrdFtEHQLDERFRN2OssuKJt/aj5HIVBvTxxntPjkVvb73SbRF1GK0KR6tWrUJUVBS8vLwQFxeHnTt3NlufnZ2NuLg4eHl5YeDAgVizZk2TmszMTMTExMBgMCAmJgabNm3yeLsfffQRkpKSEBgYCJVKhUOHDjVZh9lsxtNPP43AwED4+Phg5syZOHfunGc7gIiokzpxsRKP/X0vvimrRL9eBrz/5Dj08/VSui2iDsXjcLR+/XqkpaVh6dKlyMvLQ0JCAqZNm4aSkhK39UVFRZg+fToSEhKQl5eHJUuWYP78+cjMzHTW5OTkIDk5GSkpKcjPz0dKSgpmzZqFffv2ebTd69ev45577sGKFStu2n9aWho2bdqEdevWYdeuXbh27RpmzJgBu93u6a4gIuo0bHYHVu84hYde24WjF0zw99bhvSfHYUCAt9KtEXU4KhERT14wbtw4xMbGYvXq1c6xYcOG4ZFHHsHy5cub1C9atAgff/wxCgsLnWOpqanIz89HTk4OACA5ORkmkwlbtmxx1kydOhX+/v5Yu3atx9stLi5GVFQU8vLyMHr0aOe40WhE37598d577yE5ORkAcOHCBYSHh2Pz5s1ISkq65fs3mUzw8/OD0WiEry9/nZqIOr4TFyvx3IZ85J8zAgDui+6HPzw6EsF+nDGi7sOT47dHM0cWiwW5ublITEx0GU9MTMSePXvcviYnJ6dJfVJSEg4cOACr1dpsTf06W7Ndd3Jzc2G1Wl3WExoaihEjRni0HiKizsBmd2DVjpN46LVdyD9nRC8vLf73/41Cxpx4BiOiZnj01YSKigrY7XYEBQW5jAcFBaGsrMzta8rKytzW22w2VFRUICQk5KY19etszXZv1oter4e/v3+L12M2m2E2m52PTSZTi7dHRKSU4xcr8Txni4hapVXf22x85VQRafZqqu7qG4+3ZJ2ebrelmlvP8uXLsWzZstveBhFRe7DZHXjjy9P4y/YTsNgd8PXS4sXvDsf3YvvzqtdELeTRx2qBgYHQaDRNZlnKy8ubzOrUCw4Odluv1WoREBDQbE39Oluz3Zv1YrFYcOXKlRavZ/HixTAajc7l7NmzLd4eEVF7On6xEt9bvQd//OwYLHYH7o/uh6yFk/H9uDAGIyIPeBSO9Ho94uLikJWV5TKelZWFiRMnun3NhAkTmtRv27YN8fHx0Ol0zdbUr7M123UnLi4OOp3OZT2lpaU4cuTITddjMBjg6+vrshARdSQ2uwMrvziJGa/twtfnjPD10uKVWaPw9znxCOLX9Ik85vHHagsXLkRKSgri4+MxYcIEvPnmmygpKUFqaiqA2pmW8+fP49133wVQ+820119/HQsXLsTcuXORk5ODjIwM57fQAOCZZ57BpEmT8NJLL+Hhhx/Gv/71L2zfvh27du1q8XYB4PLlyygpKcGFCxcAAMeOHQNQO2MUHBwMPz8/PPnkk3j22WcREBCAPn364LnnnsPIkSPxwAMPtGL3EREp61hZJZ7fmI+v684tuj+6H/7wvZEMRUS3Q1ph5cqVEhERIXq9XmJjYyU7O9v53Jw5c2Ty5Mku9Tt27JAxY8aIXq+XyMhIWb16dZN1btiwQYYOHSo6nU6io6MlMzPTo+2KiLz99tsCoMny4osvOmuqq6vlqaeekj59+kiPHj1kxowZUlJS0uL3bjQaBYAYjcYWv4aI6E6z2uzy+ucnZPCSzRKx6BMZ+eJWycw9Kw6HQ+nWiDokT47fHl/nqLvjdY6ISGnHymqvW3T4fO1s0QPDar+JxitdE92cJ8dv/sogEVEnYbM7sCb7FP7ynxOw2gV+PXT49cwYPDKa30QjupMYjoiIOoFvykx4fsPXDWaLgvCHR0dwtoioDTAcERF1YFa7A280mi1aNnM4Hh4dytkiojbCcERE1EF9U2bCcxvyceR87ZX5OVtE1D4YjoiIOhir3YE1O07htc85W0SkBIYjIqIOpLDUhOc33pgtejAmCL9/dAT69eJsEVF7YTgiIuoArHYHVu84hb/WzRb19q6dLZo5irNFRO2N4YiISGGFpbXnFh29UDtblBgThN9xtohIMQxHREQK4WwRUcfEcEREpICCC7XnFnG2iKjjYTgiImpHVrsDq76onS2yOThbRNQRMRwREbWTggu15xYVlNbOFiUND8LvHhmJvr0MCndGRA0xHBERtTGr3YGVX5zE65+fhM0h8PfWYdnDI/Ddu0M4W0TUATEcERG1oaMXjHh+w9ecLSLqRBiOiIjagMXmwKodrrNFv3l4BGZwtoiow2M4IiK6w45eMOK5DV+jsG62aOrwYPz2kRGcLSLqJBiOiIjuEIut9tyilV9wtoioM2M4IiK6AxrPFk0bUTtbFNiTs0VEnQ3DERHRbWg8W9THR4/fPDwcD43kbBFRZ8VwRETUSpwtIuqaGI6IiDxksTnw+hcnsarBbNFvHx6Bh+4OUbo1IroDGI6IiDxw5LwRz23IxzdllQCA6SOD8ZuHOVtE1JUwHBERtYDF5sDrn5/Aqh2nOFtE1MUxHBER3ULj2aKHRobgNw8PRwBni4i6JIYjIqKbqJ8tWrnjFOwOQYCPHr/hbBFRl8dwRETkRpPZortD8JuZnC0i6g4YjoiIGjDb7Hj985NY1WC26LePjMD0kZwtIuouGI6IiOocPlc7W3TsImeLiLozhiMi6vbOXq7C33aexgf7SjhbREQMR0TUfR0+Z8QbX57C5sOlcEjt2Iy7Q7CMs0VE3RrDERF1KyKCnScq8MaXp7D75CXn+KQhfZE6aSAm3hWoYHdE1BGoW/OiVatWISoqCl5eXoiLi8POnTubrc/OzkZcXBy8vLwwcOBArFmzpklNZmYmYmJiYDAYEBMTg02bNnm8XRHBr3/9a4SGhqJHjx6YMmUKjh496lIzZcoUqFQql2X27Nmt2AtE1JnY7A7869B5TH9tF554az92n7wEjVqFR0aHYvP8BLz707EMRkQEoBXhaP369UhLS8PSpUuRl5eHhIQETJs2DSUlJW7ri4qKMH36dCQkJCAvLw9LlizB/PnzkZmZ6azJyclBcnIyUlJSkJ+fj5SUFMyaNQv79u3zaLsvv/wyXnnlFbz++uv46quvEBwcjAcffBCVlZUuPc2dOxelpaXO5Y033vB0NxBRJ1FlseHt3UWY/McdeGbdIRSWmtBDp8FP7olE9vNT8OrsMYgJ9VW6TSLqQFQiIp68YNy4cYiNjcXq1audY8OGDcMjjzyC5cuXN6lftGgRPv74YxQWFjrHUlNTkZ+fj5ycHABAcnIyTCYTtmzZ4qyZOnUq/P39sXbt2hZtV0QQGhqKtLQ0LFq0CABgNpsRFBSEl156CfPmzQNQO3M0evRovPrqq568bSeTyQQ/Pz8YjUb4+vIvVKKOquKaGe/uKca7e8/gapUVABDgo8dP7onEj8ZHoLe3XuEOiag9eXL89mjmyGKxIDc3F4mJiS7jiYmJ2LNnj9vX5OTkNKlPSkrCgQMHYLVam62pX2dLtltUVISysjKXGoPBgMmTJzfp7YMPPkBgYCCGDx+O5557rsnMUkNmsxkmk8llIaKOq7jiOpZuOox7VnyO1z4/iatVVkQGeOP3j47A7vT78NR9gxmMiKhZHp2QXVFRAbvdjqCgIJfxoKAglJWVuX1NWVmZ23qbzYaKigqEhITctKZ+nS3Zbv2tu5ozZ844Hz/++OOIiopCcHAwjhw5gsWLFyM/Px9ZWVlu+1++fDmWLVvm9jki6jjyz17FG1+ewpYjZaifDx8V5ofUyYOQODwYGrVK2QaJqNNo1bfVVCrXv2REpMnYreobj7dknXeiZu7cuc77I0aMwODBgxEfH4+DBw8iNja2Se+LFy/GwoULnY9NJhPCw8Obvkkiancigh3Hv8Ub2aew9/Rl5/i9Q/ti3uRBGBfVp9m/m4iI3PEoHAUGBkKj0TSZJSovL28yY1MvODjYbb1Wq0VAQECzNfXrbMl2g4ODAdTOIIWEhLitcSc2NhY6nQ4nTpxwG44MBgMMBl7vhKgjsdod+Hf+BbyRfdp5NWutWoWZo0Px80kDER3M8wGJqPU8OudIr9cjLi6uyUdQWVlZmDhxotvXTJgwoUn9tm3bEB8fD51O12xN/Tpbst36j8oa1lgsFmRnZ9+0NwA4evQorFarS6Aioo7pmtmGv+88jckvf4GF/1f7Mx8+eg3mJkThyxfuxSuzRjMYEdHtEw+tW7dOdDqdZGRkSEFBgaSlpYmPj48UFxeLiEh6erqkpKQ460+fPi3e3t6yYMECKSgokIyMDNHpdLJx40Znze7du0Wj0ciKFSuksLBQVqxYIVqtVvbu3dvi7YqIrFixQvz8/OSjjz6Sw4cPyw9/+EMJCQkRk8kkIiInT56UZcuWyVdffSVFRUXy6aefSnR0tIwZM0ZsNluL3r/RaBQAYjQaPd11RNRKF03V8tKWQhn54laJWPSJRCz6ROJ+myUrvzghV6ssSrdHRJ2AJ8dvj8ORiMjKlSslIiJC9Hq9xMbGSnZ2tvO5OXPmyOTJk13qd+zYIWPGjBG9Xi+RkZGyevXqJuvcsGGDDB06VHQ6nURHR0tmZqZH2xURcTgc8uKLL0pwcLAYDAaZNGmSHD582Pl8SUmJTJo0Sfr06SN6vV4GDRok8+fPl0uXLrX4vTMcEbWfk+WVkp6ZL4OXbHaGonv/+IWs3XdGqi0t+wcNEZGIZ8dvj69z1N3xOkdEbe9gyRW8kX0K2wouOr95FjugN+ZNHoQHhwVBzW+eEZGHPDl+87fViKhDcDgEn39Tjje/PI39xTe+efbAsCCkTh6I+Mg+CnZHRN0JwxERKcpss+Nfhy7gzS9P42T5NQCATqPCo2P64+eTBuKufr0U7pCIuhuGIyJShKnGirX7SvDW7iJcNJkBAL0MWjw2fgB+ek8Ugny9FO6QiLorhiMialcXTTV4a3cRPtxbgkqzDQAQ5GvAT++Jwg/HDYCvl07hDomou2M4IqJ2cbK8Em9+eRqb8s7Daq89y3pwv574+aSBeHh0f+i1Hl12jYiozTAcEVGbOlB8GWuyT2N74UXn2NjIPpg3eSDuHdqP3zwjog6H4YiI7jiHQ5BVeBFvZJ/CwZKrAACVCkiMCcLPJw1CXIS/sg0SETWD4YiI7pirVRZsPlyGv+86jdPfXgcA6DVqfD+uP36WMBCD+vZUuEMioltjOCKi21JuqsFnBRfx2ZEy5Jy+BLuj9nwiXy8tfjQ+Aj++JxL9evGbZ0TUeTAcEZHHSi5VYevRUmw9Uub82KxedHAv/CAuDLPHDkBPA/+KIaLOh39zEdEtiQiOX7yGrUfKsPVoGQpLTS7PjxnQG1OHByNpeDAiA30U6pKI6M5gOCIitxwOQf65q9h6tAyfHSlD8aUq53MatQrjB/bB1OHBeDAmGMF+/NiMiLoOhiMicrLZHdhffBmfHSnDZ0cvosxU43xOr1Vj0uBAJA0PxgPDguDvo1ewUyKitsNwRNTN1Vjt2H2yAluPlGF74UVcqbI6n/PRa3DfsCAkDQ/ClKH9eA4REXUL/JuOqBu6ZrZhx7FybD1Shi++Kcd1i935nL+3Dg/GBGHqiGBMHBQIL51GwU6JiNofwxFRN3HlugVZhRex7WgZvjxRAYvN4Xwu2NcLScODkDQiGGMj+0Cr4U95EFH3xXBE1IWVGWuwraAMW4+UYV/RZec1iAAgMsAbU0eEYOqIYNzd348/40FEVIfhiKiLKa64js+O1n7lPq/RNYiGhfhi6vBgTB0RjCFBPaFSMRARETXGcETUyYkIvimrxNYjZfjsaBm+Kat0eT4uwt95DaIBAd4KdUlE1AwRwFoN1FwFqq8C4gCCRyjWDsMRUScjIjh3pRr5567i4Jmr+M83F3Gm0TWIJgwMQNKIYCTGBCHIl9cgIqJ2IAJYrtWGm5qrQI2x7r7xRuipMQLVVxo8bnBrt9xYV78Y4Bc57f0OnBiOiDo4Y5UVh85dRf7ZuuXcVVRcs7jUGLRqTBrSt+4aRP3Q25vXICIiDzlnb4xulqs3ud8wABkBsd9iI7eg0gBefoBX79t/P7eB4YioA6mx2lFYasIhZxAyoqjiepM6rVqFYSG+GB3eG+MHBmDK0L7w4TWIiLo3uw0wm2qXGlNtWGlyv1HocY7V3Tqst97OrWj0teHGyw/o0bvR/brgUz/e+NbQC+gA50Lyb1MihTgcgtMV15F/9mptGDp3FYWlJljt0qQ2MsAbo8J7Y3R4b4wK742YEF9ef4ioK7GZAXNlXWCpvBFqnLeVgNnYaKzRrbXpP6RaxTl74wd4+Ta439v11hl26sd8a291PTpEwLkdDEdE7aTcVOMMQYfOXsXXZ42oNNua1AX46DEqvDdGhfXG6AG9cXd/P/5UB1FHJALYauqCS12gcd5vbqxhCKqrsVtuvb2W0va4EWwMvq4hx9Aw7Pi5H9P7dPpwc7sYjojawDWzDYfPGZFfd67QobNXUWqsaVLnpVNjZH8/ZxAaFdYbYf49+BV7orYiAliu1544bL4GWCrrbusem00Nnqt77LxfH2au3Qg9t3uOTWP6XrUfLXn51t4afBvd92s03iD8GOpuNbo721M3xHBEdBscDsHFyhoUVVzH6W+v4+tzV5F/1ogT5ZVwNPp0TK0ChgT1wqiw3s6PyIYE9eTVqImaY7fVBhPLtRuhxnK9dqkPLfVj5krXGnNlo6BTd4umH13fNn0vwNCzNqwYejVYGj/u2TTk1IchfU9AzY/LOwKGI6JbcDgEpaYaFFdcR/Gl6zhzqcrlvrnBz3A01L93D4wKr5sVCu+NEf39eNI0dV0Oe20gsVbdCC+W67XnwViqGty/2XLN/WO7uY0aVtWGEr1P3W3PGwHGeb+n67jzOd8GQacXoPMB1PxHTlfCv6mJANgdggtXq3HmUhWKLl3HmYrrKL5UheJL11Fyucrld8ga06pVCO/jjcgAbwwP9as9XyjcD/168fpC1IE4HICtuvar2pbrtbfWqrowU3XjfuPH9fedwafqRuCxVtWFmKo2DDF11NraYKLvWRtKdN514aU+xPi4Pq/v2Sj49Gz6en58TTfBcETdhsXmQJmxpm7G5zqKKqpw5lLtDNDZy9Ww2G8egHSa+gDkg4gAb0QF+iAiwAdRAT4I7e3Fj8ao9ZyhpeZGeHEuVbUn/FqrGo1XN6itcq1veOsMOXX17UGlrg0gOu+6wOLd4LH3jdBSH2acdT1v1Ot8XAOOvieg5ZcSqP0wHFGnJyK4WmVFmakGZaYaXDTW3ZrMuGiqQZmxBhdNNbh0vflvg+g1aoT36YHIAB9EBvogMsC77tYHIX4MQF2eCOCw1YYRm7kuUJjrHtct1ppGj+trqhu8pqZB0LnVbfWd/ZZSS2m9akOJzrv2a9f1gURf99h53/tGqGk4pvdxM153q/XijAx1eq0KR6tWrcIf//hHlJaWYvjw4Xj11VeRkJBw0/rs7GwsXLgQR48eRWhoKF544QWkpqa61GRmZuJXv/oVTp06hUGDBuH3v/89Hn30UY+2KyJYtmwZ3nzzTVy5cgXjxo3DypUrMXz4cGeN2WzGc889h7Vr16K6uhr3338/Vq1ahbCwsNbsCmpDIoJKsw2Xr1nw7TWzM+SUGWtwsdLcIATV3PS8n8b0WjUG1M0ANQw/EQHeCO3dAxr+Mn37EwHs1tqPZWyWultzbWhwuW34vKU2hNTX1i9uH9c0CDkNn288Xl37e05K0uhrv4ata7zUhY76+zqv2jDS8Pkmt143gk79mN67dv08P4aoWR6Ho/Xr1yMtLQ2rVq3CPffcgzfeeAPTpk1DQUEBBgwY0KS+qKgI06dPx9y5c/H+++9j9+7d+MUvfoG+ffvi+9//PgAgJycHycnJ+O1vf4tHH30UmzZtwqxZs7Br1y6MGzeuxdt9+eWX8corr+Cdd97BkCFD8Lvf/Q4PPvggjh07hl69egEA0tLS8O9//xvr1q1DQEAAnn32WcyYMQO5ubnQaPgtgbZUY7Xj8nULLl+34EqV5cb96xZcrrLgynWrc6z2sQW2xl/5akYfHz369TIg2M8Lwb5eCPL1ct7v52tAsK8X+vjou8/X5B2O2qvd2i214cNhu8X9usfOW6ub8ebu1y02SzNjjQJO/VhHpNHXBhKtoTZQaA21gUPrdSOouDzXo8F4fY1XXdhpfNvDtb7+Pr+pRNQhqETEo+80jhs3DrGxsVi9erVzbNiwYXjkkUewfPnyJvWLFi3Cxx9/jMLCQudYamoq8vPzkZNT+6NyycnJMJlM2LJli7Nm6tSp8Pf3x9q1a1u0XRFBaGgo0tLSsGjRIgC1s0RBQUF46aWXMG/ePBiNRvTt2xfvvfcekpOTAQAXLlxAeHg4Nm/ejKSkpFu+f5PJBD8/PxiNRvj6+nqy6zodEUGN1YEqiw3VVjuqLXZU1S3VVhuqLHZcN9tQWWODqcaGyhorKl1uXe83d05Pc3z0GgT0rA03QX5eCKoLQA3DT99ehqZXjBapnQlw2GuvReJy22jcYbsx5rA1GK+vsbl5ztbotbZGi931sb3hc9Ybz9cHFIe9LsxYG7zGWjfW4HV2W4O6xo8bvEbpWZDWUqlrg4JGXxs6NIba8000hrowYmgQXOpuGz7X8DXaHjdqnEHHy02NoUHYqVsfZ1eIuhRPjt8ezRxZLBbk5uYiPT3dZTwxMRF79uxx+5qcnBwkJia6jCUlJSEjIwNWqxU6nQ45OTlYsGBBk5pXX321xdstKipCWVmZy7YMBgMmT56MPXv2YN68ecjNzYXVanWpCQ0NxYgRI7Bnz54WhaO2cuniOZzY+GuXsYYTHA0jrKrxNTpEnCPS4H9EHLX5QAQiAkfdrfO+Q+AQh/PW4XDA4ah9naNurH57KgjUdbequi2pIfCFwA+AGg6oAKjgcNbdqBeo1QKVWqBRCfQaQK8GdGpAp6m91aoAnVqgVQm0akCjckCrAtQQqKUuzFQLUOUALjQIOGKvnSFx3q8LM+LovOGgLWn0gFoHaLQN7utq72v0N8Y1+trxJs/XjWsNruNq7Y3QUr80rnEZM7jWNww/nD0hIoV5FI4qKipgt9sRFBTkMh4UFISysjK3rykrK3Nbb7PZUFFRgZCQkJvW1K+zJdutv3VXc+bMGWeNXq+Hv79/i/s3m80wm29M+5tMJrd1t6vKdAnjv93QJutulbb8R7MAsNctd+A3DltPVXsgVmlqD+5qTYPHdWMqTe0Mglrb4HHD+oY1uht1zppGjzW6Bo8b1Gsa1upqn68PJ87nG913hpcGjxsGmsYhSK3hibJERC3QqhOyG5+zISLNnsfhrr7xeEvWeadqGmuuZvny5Vi2bFmzr78Tevbuh5z+P2lRrQoCgcp5nBOo0GBPQqWqfa72VgUVVFCpVVCrVFCrVdCo1VCr1VCrau9rNHW3ajW0GjU0GjU0ag20GjX0Wg10mtp6qNQAVLUHWFVdelKp6sbUDRZVg9oGY0DdAVp9k6VuXc6aRrXqhrV1z9WHGZWb1zmDjto12DhvGRSIiKgpj8JRYGAgNBpNk1mW8vLyJjM29YKDg93Wa7VaBAQENFtTv86WbDc4OBhA7exQSEjITWssFguuXLniMntUXl6OiRMnuu1/8eLFWLhwofOxyWRCeHi429rb4d83BBPmvnrH10tERESe8ejDE71ej7i4OGRlZbmMZ2Vl3TRcTJgwoUn9tm3bEB8fD51O12xN/Tpbst2oqCgEBwe71FgsFmRnZztr4uLioNPpXGpKS0tx5MiRm/ZvMBjg6+vrshAREVEXJh5at26d6HQ6ycjIkIKCAklLSxMfHx8pLi4WEZH09HRJSUlx1p8+fVq8vb1lwYIFUlBQIBkZGaLT6WTjxo3Omt27d4tGo5EVK1ZIYWGhrFixQrRarezdu7fF2xURWbFihfj5+clHH30khw8flh/+8IcSEhIiJpPJWZOamiphYWGyfft2OXjwoNx3330yatQosdlsLXr/RqNRAIjRaPR01xEREZFCPDl+exyORERWrlwpERERotfrJTY2VrKzs53PzZkzRyZPnuxSv2PHDhkzZozo9XqJjIyU1atXN1nnhg0bZOjQoaLT6SQ6OloyMzM92q6IiMPhkBdffFGCg4PFYDDIpEmT5PDhwy411dXV8tRTT0mfPn2kR48eMmPGDCkpKWnxe2c4IiIi6nw8OX57fJ2j7q47XeeIiIioq/Dk+M2rnBERERE1wHBERERE1ADDEREREVEDDEdEREREDTAcERERETXAcERERETUAMMRERERUQMMR0REREQNMBwRERERNaBVuoHOpv6C4iaTSeFOiIiIqKXqj9st+WEQhiMPVVZWAgDCw8MV7oSIiIg8VVlZCT8/v2Zr+NtqHnI4HLhw4QJ69eoFlUp1R9dtMpkQHh6Os2fP8nfb2hD3c/vgfm4f3M/th/u6fbTVfhYRVFZWIjQ0FGp182cVcebIQ2q1GmFhYW26DV9fX/4frx1wP7cP7uf2wf3cfriv20db7OdbzRjV4wnZRERERA0wHBERERE1wHDUgRgMBrz44oswGAxKt9KlcT+3D+7n9sH93H64r9tHR9jPPCGbiIiIqAHOHBERERE1wHBERERE1ADDEREREVEDDEdEREREDTActbNVq1YhKioKXl5eiIuLw86dO5utz87ORlxcHLy8vDBw4ECsWbOmnTrt3DzZzx999BEefPBB9O3bF76+vpgwYQI+++yzduy28/L0z3O93bt3Q6vVYvTo0W3bYBfh6X42m81YunQpIiIiYDAYMGjQILz11lvt1G3n5el+/uCDDzBq1Ch4e3sjJCQEP/nJT3Dp0qV26rZz+vLLL/Hd734XoaGhUKlU+Oc//3nL1yhyHBRqN+vWrROdTid/+9vfpKCgQJ555hnx8fGRM2fOuK0/ffq0eHt7yzPPPCMFBQXyt7/9TXQ6nWzcuLGdO+9cPN3PzzzzjLz00kuyf/9+OX78uCxevFh0Op0cPHiwnTvvXDzdz/WuXr0qAwcOlMTERBk1alT7NNuJtWY/z5w5U8aNGydZWVlSVFQk+/btk927d7dj152Pp/t5586dolar5S9/+YucPn1adu7cKcOHD5dHHnmknTvvXDZv3ixLly6VzMxMASCbNm1qtl6p4yDDUTsaO3aspKamuoxFR0dLenq62/oXXnhBoqOjXcbmzZsn48ePb7MeuwJP97M7MTExsmzZsjvdWpfS2v2cnJwsv/zlL+XFF19kOGoBT/fzli1bxM/PTy5dutQe7XUZnu7nP/7xjzJw4ECXsddee03CwsLarMeupiXhSKnjID9WaycWiwW5ublITEx0GU9MTMSePXvcviYnJ6dJfVJSEg4cOACr1dpmvXZmrdnPjTkcDlRWVqJPnz5t0WKX0Nr9/Pbbb+PUqVN48cUX27rFLqE1+/njjz9GfHw8Xn75ZfTv3x9DhgzBc889h+rq6vZouVNqzX6eOHEizp07h82bN0NEcPHiRWzcuBEPPfRQe7TcbSh1HOQPz7aTiooK2O12BAUFuYwHBQWhrKzM7WvKysrc1ttsNlRUVCAkJKTN+u2sWrOfG/vTn/6E69evY9asWW3RYpfQmv184sQJpKenY+fOndBq+VdPS7RmP58+fRq7du2Cl5cXNm3ahIqKCvziF7/A5cuXed7RTbRmP0+cOBEffPABkpOTUVNTA5vNhpkzZ+Kvf/1re7TcbSh1HOTMUTtTqVQuj0Wkydit6t2NkytP93O9tWvX4te//jXWr1+Pfv36tVV7XUZL97Pdbsdjjz2GZcuWYciQIe3VXpfhyZ9nh8MBlUqFDz74AGPHjsX06dPxyiuv4J133uHs0S14sp8LCgowf/58/M///A9yc3OxdetWFBUVITU1tT1a7VaUOA7yn2/tJDAwEBqNpsm/QsrLy5uk4nrBwcFu67VaLQICAtqs186sNfu53vr16/Hkk09iw4YNeOCBB9qyzU7P0/1cWVmJAwcOIC8vD0899RSA2oO4iECr1WLbtm2477772qX3zqQ1f55DQkLQv39/+Pn5OceGDRsGEcG5c+cwePDgNu25M2rNfl6+fDnuuecePP/88wCAu+++Gz4+PkhISMDvfvc7zuzfIUodBzlz1E70ej3i4uKQlZXlMp6VlYWJEye6fc2ECROa1G/btg3x8fHQ6XRt1mtn1pr9DNTOGP34xz/Ghx9+yHMGWsDT/ezr64vDhw/j0KFDziU1NRVDhw7FoUOHMG7cuPZqvVNpzZ/ne+65BxcuXMC1a9ecY8ePH4darUZYWFib9ttZtWY/V1VVQa12PYRqNBoAN2Y26PYpdhxs09O9yUX9V0UzMjKkoKBA0tLSxMfHR4qLi0VEJD09XVJSUpz19V9hXLBggRQUFEhGRga/yt8Cnu7nDz/8ULRaraxcuVJKS0udy9WrV5V6C52Cp/u5MX5brWU83c+VlZUSFhYmP/jBD+To0aOSnZ0tgwcPlp/97GdKvYVOwdP9/Pbbb4tWq5VVq1bJqVOnZNeuXRIfHy9jx45V6i10CpWVlZKXlyd5eXkCQF555RXJy8tzXjKhoxwHGY7a2cqVKyUiIkL0er3ExsZKdna287k5c+bI5MmTXep37NghY8aMEb1eL5GRkbJ69ep27rhz8mQ/T548WQA0WebMmdP+jXcynv55bojhqOU83c+FhYXywAMPSI8ePSQsLEwWLlwoVVVV7dx15+Ppfn7ttdckJiZGevToISEhIfL444/LuXPn2rnrzuWLL75o9u/bjnIcVIlw/o+IiIioHs85IiIiImqA4YiIiIioAYYjIiIiogYYjoiIiIgaYDgiIiIiaoDhiIiIiKgBhiMiIiKiBhiOiIiIiBpgOCIiIiJqgOGIiIiIqAGGIyIiIqIGGI6IiIiIGvj/AQNzL3u4RE+nAAAAAElFTkSuQmCC", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def fit_cubspline(x_left, loss_left, grad_left, x_right, loss_right, grad_right):\n", + " # a * x^3 + b * x^2 + c * x + d\n", + " assert grad_left < 0\n", + " assert grad_right > 0\n", + " assert x_left < x_right\n", + " matrix = [\n", + " [x_left**3, x_left**2, x_left, 1.],\n", + " [x_right**3, x_right**2, x_right, 1.],\n", + " [3 * x_left**2, 2 * x_left, 1., 0.],\n", + " [3 * x_right**2, 2 * x_right, 1., 0.],\n", + " ]\n", + " rhs = [loss_left, loss_right, grad_left, grad_right]\n", + " return np.linalg.solve(matrix, rhs)\n", + "\n", + "current_point = xy\n", + "current_loss = separated_loss(xy)\n", + "current_direction = cg_solution\n", + "current_gradient = separated_grad(xy)\n", + "\n", + "\n", + "LEFT_STEP = 0\n", + "left_point = xy + current_direction * LEFT_STEP\n", + "left_loss = separated_loss(left_point)\n", + "left_grad = separated_grad(left_point)\n", + "\n", + "RIGHT_STEP = 0.01187731700475939\n", + "right_point = xy + current_direction * RIGHT_STEP\n", + "right_loss = separated_loss(right_point)\n", + "right_grad = separated_grad(right_point)\n", + "\n", + "\n", + "\n", + "a,b,c,d = fit_cubspline(x_left=LEFT_STEP, loss_left=left_loss, grad_left=current_direction@left_grad,\n", + " x_right=RIGHT_STEP, loss_right=right_loss, grad_right=current_direction@right_grad)\n", + "\n", + "my_spline = lambda x: a * x**3 + b * x**2 + c * x + d\n", + "\n", + "xs = np.linspace(0,1)\n", + "plt.plot(steps, losses_on_line)\n", + "plt.plot(xs, [my_spline(x) for x in xs])\n", + "# plt.yscale('log')\n", + "\n", + "print((current_direction@left_grad) / (current_direction@current_gradient),\n", + " (current_direction@right_grad) / (current_direction@current_gradient))\n", + "print(left_loss, right_loss)\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 347, + "id": "a66067ac", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(0.01187731700475939, -52.433477785125454)" + ] + }, + "execution_count": 347, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def get_roots_spline(a,b,c,d):\n", + " # 3 * a * x^2 + 2 * b * x + c == 0 \n", + " tmp = np.sqrt((2*b)**2 - 4 * (3 * a * c))\n", + " # x = (-b ± √ (b2 - 4ac) )/2a\n", + " return (- 2 * b + tmp)/(6*a), (- 2 * b - tmp)/(6*a)\n", + "\n", + "get_roots_spline(a,b,c,d) " + ] + }, + { + "cell_type": "code", + "execution_count": 372, + "id": "6e11c200", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.0003117785215677139\n" + ] + }, + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x, y = xy[:n], xy[n:]\n", + "s = b_transf - matrix_transf @ x\n", + "\n", + "plt.plot(x, label='x')\n", + "plt.figure()\n", + "plt.plot(y, label='y', alpha=.5)\n", + "plt.plot(s, label='s', alpha=.5)\n", + "print(y.T @ s)" + ] + }, + { + "cell_type": "markdown", + "id": "46f66f47", + "metadata": {}, + "source": [ + "# MINI NEWTON_CG " + ] + }, + { + "cell_type": "code", + "execution_count": 104, + "id": "14f9942c", + "metadata": {}, + "outputs": [], + "source": [ + "def line_search(xy, direction): # can be made much smarter, I understand enough dcsrch now\n", + " current_loss = separated_loss(xy)\n", + " for i in range(100):\n", + " proposed = xy + direction * 0.5**i\n", + " if separated_loss(proposed) < current_loss:\n", + " break\n", + " return proposed" + ] + }, + { + "cell_type": "code", + "execution_count": 105, + "id": "50aba4e8", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FINAL LOSS: 5.013207684135979e-08\n", + "FINAL LOSS: 2.2336614022752972e-08\n", + "FINAL LOSS: 7.103871419007735e-09\n", + "FINAL LOSS: 2.2960431230258557e-09\n", + "FINAL LOSS: 4.934056476386888e-10\n", + "FINAL LOSS: 5.522459784737324e-10\n", + "FINAL LOSS: 1.2209644570790878e-09\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "for CG_ITERS in [2,5,10,20,50,100,200]:\n", + " \n", + " np.random.seed(0)\n", + " xy = np.random.randn(n+m)\n", + "\n", + " losses = []\n", + "\n", + " for i in range(100000//CG_ITERS):\n", + " current_loss = separated_loss(xy)\n", + " losses.append(current_loss)\n", + " current_grad = separated_grad(xy)\n", + " direction = sp.sparse.linalg.cg(\n", + " separated_hessian(xy), -current_grad, atol=0., rtol=0., maxiter=CG_ITERS)[0]\n", + " xy = line_search(xy, direction)\n", + "\n", + " plt.plot(np.arange(len(losses)) * CG_ITERS, losses, label=f'CG_ITERS = {CG_ITERS}')\n", + " print('FINAL LOSS:', losses[-1])\n", + "plt.legend()\n", + "plt.yscale('log')\n", + "plt.show()\n", + " # print('FINAL LOSS:', losses[-1])\n" + ] + }, + { + "cell_type": "markdown", + "id": "2b76b68d", + "metadata": {}, + "source": [ + "# USING SOME TERMINATION RULE " + ] + }, + { + "cell_type": "code", + "execution_count": 106, + "id": "dfe4c076", + "metadata": {}, + "outputs": [], + "source": [ + "def run_with_term_rule(xy, MAXHESSIAN, cg_termination_rule):\n", + " \n", + " losses = [separated_loss(xy)]\n", + " cg_used_iters = [0]\n", + " USED_ITERS = 0\n", + " \n", + " for i in range(1000):\n", + " if USED_ITERS > MAXHESSIAN:\n", + " break\n", + " def iter_counter(_):\n", + " nonlocal USED_ITERS\n", + " USED_ITERS += 1\n", + " direction = sp.sparse.linalg.cg(\n", + " separated_hessian(xy), -separated_grad(xy), **cg_termination_rule(xy),\n", + " callback=iter_counter)[0]\n", + "\n", + " xy = line_search(xy, direction)\n", + " \n", + " losses.append(separated_loss(xy))\n", + " cg_used_iters.append(int(USED_ITERS))\n", + " if losses[-1] < 1e-25:\n", + " break\n", + " \n", + " \n", + " plt.plot(cg_used_iters, losses)\n", + " print('FINAL LOSS:', losses[-1])\n", + " plt.yscale('log')\n", + " return xy\n" + ] + }, + { + "cell_type": "markdown", + "id": "6ef93ef0", + "metadata": {}, + "source": [ + "# FIX SEED " + ] + }, + { + "cell_type": "code", + "execution_count": 107, + "id": "2eed485c", + "metadata": {}, + "outputs": [], + "source": [ + "SEED = 0\n", + "MAXITERS = 1000000" + ] + }, + { + "cell_type": "code", + "execution_count": 108, + "id": "52691a96", + "metadata": {}, + "outputs": [], + "source": [ + "# np.random.seed(SEED)\n", + "# xy = np.random.randn(n+m)\n", + "\n", + "# solution = run_with_term_rule(\n", + "# xy, MAXHESSIAN=MAXITERS,\n", + "# cg_termination_rule= lambda x: {'maxiter':200})" + ] + }, + { + "cell_type": "markdown", + "id": "260df638", + "metadata": {}, + "source": [ + "### Nocedal " + ] + }, + { + "cell_type": "code", + "execution_count": 109, + "id": "ac59d535", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FINAL LOSS: 7.246752968237809e-26\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "np.random.seed(SEED) # this was run with 1000 Ruiz iters\n", + "xy = np.random.randn(n+m)\n", + "\n", + "solution = run_with_term_rule(\n", + " xy, MAXHESSIAN=MAXITERS,\n", + " cg_termination_rule=lambda xy: {'rtol':min(0.5, np.linalg.norm(separated_grad(xy)) ** 0.5)})" + ] + }, + { + "cell_type": "code", + "execution_count": 92, + "id": "39643cce", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FINAL LOSS: 5.624313078551257e-30\n" + ] + }, + { + "data": { + "image/png": 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jleaK1Q3jEpWdMZICYwDAsBW0UNPQ0KBjx44F3peVlam0tFTJycnKzMxUQUGBFi1apOnTpysnJ0fr169XeXm5li1bFqwuRLWHbpmgf97ikTGSz290sva8Ttae15HKzutIPexO10O3pGtMokMOm00Ou1VOu1WuuBhZrTy5GAAQvYJ2S/eOHTuUm5vbZfvixYu1YcMGSe0P3/vRj36kyspKZWVl6d/+7d90xx13BOP0VxUuTxQeiOZWn3x+o/rmNp2sPa/TnmYdKD+nmsYWvf/ZWZ2sPX/F301w2PTc127W16eHX7E0AABXEvXLJPRHNISaq3n/sxq9+n65PqioVX1zq7xtfrW0+dV2SQ3O7deNVporTnk3j1NqklNJsTFyxcVoVIIjhD0HAKB7hJpuDIdQcyXlNU2648fbe2zz1UnJmv+VCcq9YazGuajLAQCEB0JNN4ZzqJGkk7XndbymUadqm7W3rEYfVNSpvrlVnuY2NXjbAu1ibBZ9acwITR6fpMlpSRrnilVygkPuiaPktNtC+AkAAMMRoaYbwz3U9ORU7Xm9/G6Z3i87qw9P1HXbJsZm0ThXrEbFO+SwWZV741jddeNYxdgsShnh1Mh4pq8AAMFHqOkGoebqjDH66JRHVXXNKq2o1fGzTTpd16zPaxpVXe+94u857FZ9f+4NWjzzGsXYhuTRRwCAYYJQ0w1CTf/5/UZVnmadrD2v+uZWffZFo17bWy7P+Vadabi4uvgIp103pyXpB1+7WTeN5xoDAAaOUNMNQs3g8PuN/v294/rf73wSCDjjkmL1327L1LzsNBbjBAAMCKGmG4SaweXzG5VW1Krg9VIdr2mSJNmsFo1LipUzxiqn3aZJKfFadNs1unFcokbGx/Rp3S8AwPBEqOkGoWZofFHv1ca/lOv9srPa9cmZK7aLd9iU4LTLeeGJxw67TXExVo2Kd2j0CIcSnHYlOu3KzhipiaPjFeewyxUXoxHOIV2DFQAQYoSabhBqhl7F2SbVNLbI2+rT+Vaf3v6wUtuPVneqw+mrBIdNMXar7FaLMpPjdd3YEYqNsclhs8pqtSgp1q7kBKdsVslutWr29Skay3pYABCxCDXdINSEj+ZWn6rqmnW+1Sdvm1/eVp9afH41tfh0rrFFZxq8amrx6bTHq4Mna1VZ1xx4OnJfTZ84Sr//7sxB+BQAgKHQl7/fjOVjyMXG2HRNSt8LiOubW1XT0KI2v5G3zaejVfXtgedCOPIbo9qmVp1rapUxRv/1cbX2HT+npb/ap0vLdzp+THDaNWFknB78ygRdN3ZEcD4cACBkGKlB1Hrk57v1l8/PXbVdXIxNT+ffqMzR8bJZLLJaLLJapFRXrK4ZnSAbq5sDQMgw/dQNQs3wc9rTrJ1Hv5Dvwlf80m+6Uftq59s/rtb7ZWeveIwYm0WuuBhNmeDSvyyYovGuuMHuNgDgEoSabhBq0B2f3+jnOz/Vto+q5DNGPn/7k5Xb/EYnz53X+VZfoG3KCIf++99+WfdNGc+yEAAwRAg13SDUoK98F56kXFXXrP+x+ZCOVHoC+zKT4zUuKVZJcTFyxcXIGWOV1SLZLBZZLBbZrO1TWCPjHbpu7AiNSXRqhNOuBKddsXarLBaLYmOsioux8bweAOgBoaYbhBoMxPkWn15977je2H9CH1fVB+24VosCz+SJsVtlkWS1WGSx6EJtT/vPFotFl0afGLtV0yeOUkIvntuTFGvXdWNHyBUXoxibVTeNT6JOCEDEINR0g1CDYDnb2KK/nq5XTUOL6s63qu58q1p9fvn8RsYY+YyR37QvIVFd79Wx6gada2pRo7dNDd42tfpC+7/co1/NUOGCqSHtAwD0Frd0A4MoOcGh264d3e/f9/uNjCRvm08Nze1BpyPsmI5AZIz8xsiY9gJn32X/9qiqO6/Dpzy6WjwyRjrT4NWnXzTofKtPJ86d12/2VujuG1P1N5NT+/0ZACAcEWqAIWa9MPUT77Ar3mHX2CE89z+/fVgv7SrT028e1ObxiUofFT+EZweAwWUNdQcADJ3v5d2g68eO0JkGr+5Zs0trdxzTloOVqjvfGuquAcCAUVMDDDMVZ5u0YmOpSo5ffDDhuKRY/XHFbG5VBxB2+vL3m5EaYJjJSI7X64/naNUDN+tvbkrVmESnqjzN+ue3j4S6awAwIIzUAMPcvs/P6pEX98gYafb1KYqNsSnRadeI2PaaH5tVmjAyXo9+NYNn6gAYctz9BKDXpl+TrG/dNlG/2nNcuz4502Pbv7s1c4h6BQB9R6gBoGfvm6wZk5J1vsWnVp9Rg7f1wu3mPp2qPa8/flSlf9lyRLk3jmH9KwBhi1ADQA67VfdPTet2n89v9PDPd+tAea2e3XRIv1w8nWkoAGGJQmEAPbJZLfrRQ1PlsFn1zsfVeqv0VKi7BADdItQAuKrrUxP15F3XSZJ++B8fadOBE9pxtFrNl6xiDgChFpbTT/Pnz9eOHTt099136/e//32v9wEYPMvmfElbDlXpSKVH/33jB5KkRKddt31ptK4fO0IJTvuFRTgvLMZpvfhzx2yVRdKXxozo8jwci0WalJKg2BjbEH8qANEkLG/p3r59uxoaGvSrX/2qS3DpaV9PuKUbGLhj1fUq3PKxmtt8+uyLRlXWNQft2O6Jo/T64zmsIA6gk4i/pTs3N1c7duzo8z4Ag+u6sYn65WMzJLUvzHmg4pw+PFGnz75oVEubX/4Lq5SbC4tytq9cfvH3vW1+Han0qNXn73Tcc00tKjl+Ti+/W6als68dyo8EIIr0OdQUFxfrxz/+sUpKSlRZWalNmzbpwQcf7NRm7dq1+vGPf6zKykrdfPPNWrNmjWbPnh2sPgMIA1arRe6JyXJPTB7wsX6zt1wr3zyof932V00YGafcG8cyFQWgz/ocahobG5Wdna1vf/vbeuihh7rs37hxo1asWKG1a9fq9ttv14svvqj8/HwdPnxYmZntD+5yu93yer1dfnfbtm1KS+v+tlIA0esbMzL0VulJvffZWX331/sVY7PomtEJSh8Vp8TYGCXGtj/hOMZqba/TsVoC9TsWi6VT3Y4kOe3WLr8f77BxKzoQ5focavLz85Wfn3/F/atXr9aSJUu0dOlSSdKaNWu0detWrVu3ToWFhZKkkpKSfna397xeb6fg5PF4Bv2cAPrHYrHo5//NrRfeOab/PFSlk7Xn9Ul1gz6pbgjiOSSHzSqLRbLIEtjWEXNsVovuyRqnp/NvUnICC3sCkSioNTUtLS0qKSnR008/3Wl7Xl6edu/eHcxTXVVhYaF++MMfDuk5AfTfyHiH/sf9k/XsfTfpZO15HatuULXHK09zq+qb29TgbZPPb+Q3HS/JGCO/X/Jddr9DQ3ObPq9pL2Tu+D1j2mt6evL6vhMqOnxaf3drpnJvGKuR8Y5Od3Bd+t+Ony3SxWR0gdVi0egEByNDwBALaqg5c+aMfD6fUlNTO21PTU1VVVVVr48zd+5c7d+/X42NjUpPT9emTZs0Y8aMq+671MqVK1VQUBB47/F4lJGR0c9PBmCoWCwWpY+KV/qo+KAczxij5la/6ptb1eLzdypcNkYyat9w8tx5rfr/Duvjqnr9bPun+tn2Twd03uyMkfqX+Vm6Oc01oOMA6L1Bufvp8n+dGGP69C+WrVu39mvfpZxOp5xOZ6/PCSA6WSwWxTlsinP0XHg8cXSC/uPJWdpysFLbDp/W3rKzavX55fdfvJvLfyEEBUaJLvz3cn4jfVBRq6+98K7uvnGs/uamVN08IUmTUhIU7wjLm06BqBDU/7tSUlJks9m6jMpUV1d3Gb0BgHATY7PqgWkT9MC0CQM6zmlPs1b9x2G9fSEgbTt8OrDPYbNqRKxdibF2xcW0Fy9b1F7fM+u6FH3/nht5Vg/QT0ENNQ6HQ263W0VFRZo/f35ge1FRkR544IFgngoAwlZqUqx+9s1btPxUnYoOn9afPzmjY180qLapfQrsbGOLzja2dPm9j055NMJp15N3Xx+CXgORr8+hpqGhQceOHQu8LysrU2lpqZKTk5WZmamCggItWrRI06dPV05OjtavX6/y8nItW7YsqB0HgHB3c5pLN6e5tOJvvixJqr9Q9Nxe+Nyq8y3+wHTWR6fq9KM/HtW//emv+uqkZN167egQ9x6IPH0ONfv27VNubm7gfUcx7uLFi7VhwwYtXLhQNTU1WrVqlSorK5WVlaUtW7Zo4sSJwes1AESg9mfmxHS7784vj9Gn1Y16Y/8JLf3VPv3f+Tfq776aKStTUUCvheXaT4OBtZ8AhLtGb5u+9f/uVcnxc5La18MqXDBFX05NDHHPgNDpy99vQg0AhBGf3+iVPZ/rJ1uPqrHFJ7vVoi+nJspqbX9oYMdTlAPPzVF7kfE4V5yeufdGjXfFhfojAEFFqOkGoQZAJDlVe17/862P9Kcjp6/e+IKp6S69/ngO62YhqhBqukGoARBpjDH66JRHNY0t8rc/KVD+S1ZBNxfatPiMnnvrkM41tWrBLRP0Tw9m8TwcRI2+/P3mWw8AYcpisShrQu+eSDw6waFFv3xfb+4/qTf3n1TKCIeS4mI0wtm+mOcIp112q7V9GstyyYKg6lj+4eKyD5PGJGjJrEly2hnxQWQh1ABAFLj9uhQ9v2CqCv/ziM41tepMQ4vONHR9Fk5vHT/TpOcfmsL6VYgohBoAiBJfn5Ghr8/IUF1Tq07UNqmhuU2NLW1q8PrUGFjYs/25OJ0WBQ1MaUkN3lat2/GpNu6r0E3jE/XY7ZNC/bGAXiPUAECUccXHyBXf/4U0XXEx+pctH+t/vX1E16cm6vbrUoLYO2DwWEPdAQBAePnO7Gs1/ysT5PMb/R+v7Vd5TVOouwT0CqEGANCJxWJR4YIpyk53qbapVUtf+YsOnayT3z8sbpZFBOOWbgBAt6rqmvW1F/6s6nqvJGlUfIzSRsYpKTZGdlvnAuLuCoov3eKKi9H/nDdZKSOcg9llRCFu6QYADNg4V6xeWfJV/WTrUe3+tEbnmlp1rqm138cbPzJWK/NvCmIPgc4YqQEAXFVLm19HKj0629Qiz/nW9ocBXnD5X5HL33/6RYPW7vhUYxKd2vP0XbLbqHxA7zFSAwAIKofdquyMkf363ZY2vzb+pUJf1Hu1869f6O6bUoPbOeAC4jIAYFA57FbN/8oESdLr+ypC3BtEM0INAGDQPTI9Q5L0X0eqdabBG+LeIFoRagAAg+6GcYnKTnepzW+0bsenBBsMCmpqAABD4pHpGfrgRJ1++ecy/fLPZUpNcirBaVeCw644h03xDptiLhQRX3o7eMfd4pYLWwPvL9k+eoRD38q5RteNHTFEnwbhiFADABgSj0xPV/nZJhX/9Qt9XFWv0x6vpOCN2Pz7e8c1b2qaFtwyQe6Jo5QYGxO0YyMycEs3AGDI1Ta1qOLseTW1tKmpxaemFp8aWzoW3WxvY9T+w8X3F1zYYC55++6xM9p2+HTg+FaLdO2YEZowMk6pSU457TbZrBbZrRbZbBbZLBZd+rxAiy5/mGDn/nZ5tOAlDS7f1/V3L44w3fHlMZrWz7vIhqu+/P0m1AAAosJHp+r0q92f673Pzqr8bHiuV+WKi9H7z9yt2BhbqLsSMXhODQBg2Lk5zaUfPZwtqX2Jh2PVDTpVe16nPc1q9Rv5/H61+Y18PqO2q6xjdfm/9y9v3eWBg11adG2z9aMqnWlo0Z+OnNb9U9N69ZnQN4QaAEDUGeeK1ThXbKi70cnI+Bj9bPun+n3JCULNIOGWbgAAhsBDt6RLkor/+oWqPc0h7k10ItQAADAErh0zQrdkjpTfSJtLT4a6O1GJUAMAwBB5yN0+WvNGyckudTsYOEINAABD5P6paXLYrTp6ul4fnfKEujtRh1ADAMAQccXF6G8nt69S/vuSEyHuTfQJy1Azf/58jRo1Sg8//HCXfXa7XdOmTdO0adO0dOnSEPQOAID+e/jCFNRbpSfV0uYPcW+iS1iGmqeeekqvvPJKt/tGjhyp0tJSlZaW6he/+MUQ9wwAgIGZfV2KxiQ6da6pVduPVoe6O1ElLENNbm6uEhMTQ90NAACCzm6zav5XJkiS3mAKKqj6HGqKi4s1b948paWlyWKxaPPmzV3arF27VpMmTVJsbKzcbrd27doVjL5Kan9cstvt1qxZs7Rz586gHRcAgKHS8cya7UerdbaxJcS9iR59fqJwY2OjsrOz9e1vf1sPPfRQl/0bN27UihUrtHbtWt1+++168cUXlZ+fr8OHDyszM1OS5Ha75fV2XZl127ZtSkvr+SmLn3/+udLS0nTo0CHdd999OnjwIGs5AQAiyg3jEpU1IUmHTnr09Rf36I7rx+im8YlKHxWvMYkO2a1W2W2WwH9jrNZuF+LsLafdKkt/fjHC9DnU5OfnKz8//4r7V69erSVLlgSKeNesWaOtW7dq3bp1KiwslCSVlJT0s7sKhJ6srCxNnjxZf/3rXzV9+vQu7bxeb6fg5PFw6xwAIHx8Z/a1WrGxVMeqG3SsumFQzzV5fJI2fHuGxiaF19IRwRbUmpqWlhaVlJQoLy+v0/a8vDzt3r17wMc/d+5cIKicOHFChw8f1rXXXttt28LCQrlcrsArIyNjwOcHACBYHpg2QXuf+Ru98Hdf0bdyJmr29Sm6NiVBrrgYjXDa5bRbZbcGZ3TlcKVHi1/+izzNrUE5XrgK6oKWZ86ckc/nU2pqaqftqampqqqq6vVx5s6dq/3796uxsVHp6enatGmTZsyYoSNHjujxxx+X1do+jPbTn/5UycnJ3R5j5cqVKigoCLz3eDwEGwBAWBmT6NT9U9N6XODSGCOfv31lcd9VVhfvTmXdeX1j/fs6UunR0g379PezrlHayDjFxdhksUgWi0UWtf/XapEsujjF1bG/JyMcdrniY/rcr8EwKKt0X34BjDF9msvbunVrt9tnzpypgwcP9uoYTqdTTqez1+cEACAcWSyW9voaW/9+/7qxidrw7Rn6xvr3tPfzs9r7+dmg9s9utejVpbfqtmtHB/W4/epLMA+WkpIim83WZVSmurq6y+gNAAAYGlkTXPr10lv1iz+Xqfxskyprz6vF55cx7QMPRur6s4yutjxVq8+vNr/RoZN10RdqHA6H3G63ioqKNH/+/MD2oqIiPfDAA8E8FQAA6IPsjJH6349+JajH/D9/94F+X3JCbf2YFhsMfQ41DQ0NOnbsWOB9WVmZSktLlZycrMzMTBUUFGjRokWaPn26cnJytH79epWXl2vZsmVB7TgAAAitjkLm/tT6DIY+h5p9+/YpNzc38L6jGHfx4sXasGGDFi5cqJqaGq1atUqVlZXKysrSli1bNHHixOD1GgAAhJztQqhp80VoqJkzZ47MVSbZli9fruXLl/e7UwAAIPzF2NqfDOPzh8fCnGG59hMAAAh/HSM1rWEy/USoAQAA/RJuNTWEGgAA0C/hVlNDqAEAAP1iv1BT00ZNDQAAiGQd00/h8pwaQg0AAOiXjuknH9NPAAAgksXYGKkBAABRwGalpgYAAEQBamoAAEBUoKYGAABEhYs1NUw/AQCACHaxpoaRGgAAEMFYJgEAAEQF+4Xpp1Yf008AACCCMVIDAACiAjU1AAAgKnRMPzFSAwAAIlrH9FMrz6kBAACRLPDwPZ5TAwAAIpmdmhoAABANOmpq2ph+AgAAkYxbugEAQFSwWVn7CQAARIEY24WaGqafAABAJLs4UkOoAQAAEYyaGgAAEBXsHdNP1NQAAIBI1jFSQ01ND+bPn69Ro0bp4Ycf7rLvJz/5iW6++WZlZWXp1VdfDUHvAACA1LmmxpjQB5uwDDVPPfWUXnnllS7bDx48qNdee00lJSXat2+f1q1bp9ra2qHvIAAACIzUSFI4lNWEZajJzc1VYmJil+1HjhzRzJkzFRsbq9jYWE2bNk1//OMfQ9BDAADQUVMjSa2+0NfV9DnUFBcXa968eUpLS5PFYtHmzZu7tFm7dq0mTZqk2NhYud1u7dq1Kxh9VVZWlrZv367a2lrV1tbqnXfe0cmTJ4NybAAA0DeXjtSEwx1Q9r7+QmNjo7Kzs/Xtb39bDz30UJf9Gzdu1IoVK7R27VrdfvvtevHFF5Wfn6/Dhw8rMzNTkuR2u+X1erv87rZt25SWlnbFc0+ePFlPPfWU7rrrLrlcLs2YMUN2e/cfwev1djqHx+Pp60cFAAA9sF0SasLhWTV9DjX5+fnKz8+/4v7Vq1dryZIlWrp0qSRpzZo12rp1q9atW6fCwkJJUklJST+7Kz3++ON6/PHHJUlLly7Vdddd1227wsJC/fCHP+z3eQAAQM8uHalpi8Tpp560tLSopKREeXl5nbbn5eVp9+7dQTlHdXW1JOno0aPau3ev5s6d2227lStXqq6uLvCqqKgIyvkBAEA7i8USGK2JyOmnnpw5c0Y+n0+pqamdtqempqqqqqrXx5k7d67279+vxsZGpaena9OmTZoxY4Yk6cEHH1Rtba0SEhL08ssvX3H6yel0yul09v/DAACAq7JZLfL5TWROP/WGxWLp9N4Y02VbT7Zu3XrFfcEa8QEAAANnt1rUovAYqQnq9FNKSopsNluXUZnq6uouozcAACDyddTVROQt3T1xOBxyu90qKirqtL2oqEgzZ84M5qkAAEAY6HhWTTiM1PR5+qmhoUHHjh0LvC8rK1NpaamSk5OVmZmpgoICLVq0SNOnT1dOTo7Wr1+v8vJyLVu2LKgdBwAAoXfpUgmh1udQs2/fPuXm5gbeFxQUSJIWL16sDRs2aOHChaqpqdGqVatUWVmprKwsbdmyRRMnTgxerwEAQFiICaNFLfscaubMmXPVRauWL1+u5cuX97tTAAAgMthsHSM1UVZTAwAAhhe7NXxqagg1AACg3y7e/USoAQAAESycnihMqAEAAP1mp6YGAABEAxs1NQAAIBrEUFMDAACiATU1AAAgKlBTAwAAokLHc2rC4YnChBoAANBvdqafAABANAinBS0JNQAAoN+oqQEAAFGBmhoAABAVqKkBAABRgZoaAAAQFey2juknamoAAEAEszNSAwAAogHLJAAAgKgQc+GW7lZu6QYAAJHMduGWbh+3dAMAgEhGTQ0AAIgKF2/pZvoJAABEsI6aGgqFAQBARLOxTAIAAIgGLJMAAACigj1wSzehBgAARLCLIzUUCndRUVGhOXPmaPLkyZo6dap+97vfBfbV19drxowZmjZtmqZMmaKXXnophD0FAADhVFNjD3UHLme327VmzRpNmzZN1dXVuuWWW3TvvfcqISFB8fHx2rlzp+Lj49XU1KSsrCwtWLBAo0ePDnW3AQAYljqmn8LhOTVhF2rGjx+v8ePHS5LGjh2r5ORknT17VgkJCbLZbIqPj5ckNTc3y+fzyZjQX0QAAIariH74XnFxsebNm6e0tDRZLBZt3ry5S5u1a9dq0qRJio2Nldvt1q5du/rVuX379snv9ysjIyOwrba2VtnZ2UpPT9f3v/99paSk9OvYAABg4GyRXFPT2Nio7OxsvfDCC93u37hxo1asWKFnn31WBw4c0OzZs5Wfn6/y8vJAG7fbraysrC6vU6dOBdrU1NToW9/6ltavX9/p+CNHjtQHH3ygsrIyvfbaazp9+nRfPwIAAAgS+4WamtZIrKnJz89Xfn7+FfevXr1aS5Ys0dKlSyVJa9as0datW7Vu3ToVFhZKkkpKSno8h9fr1fz587Vy5UrNnDmz2zapqamaOnWqiouL9cgjj3R7DK/XG3jv8Xiu+tkAAEDf2KP1icItLS0qKSlRXl5ep+15eXnavXt3r45hjNFjjz2mu+66S4sWLeq07/Tp04Fw4vF4VFxcrBtuuKHb4xQWFsrlcgVel05hAQCA4IjompqenDlzRj6fT6mpqZ22p6amqqqqqlfHePfdd7Vx40Zt3rxZ06ZN07Rp03Tw4EFJ0okTJ3THHXcoOztbs2bN0hNPPKGpU6d2e5yVK1eqrq4u8KqoqBjYhwMAAF2EU03NoNz9ZLFYOr03xnTZdiWzZs2S/woXxu12q7S0tFfHcTqdcjqdvWoLAAD6J8YWPs+pCepITUpKimw2W5dRmerq6i6jNwAAIPLZonX6yeFwyO12q6ioqNP2oqKiKxb8AgCAyBVOC1r2efqpoaFBx44dC7wvKytTaWmpkpOTlZmZqYKCAi1atEjTp09XTk6O1q9fr/Lyci1btiyoHQcAAKHXMVLT6ovAmpp9+/YpNzc38L6goECStHjxYm3YsEELFy5UTU2NVq1apcrKSmVlZWnLli2aOHFi8HoNAADCQkdNTUSO1MyZM+eqSxMsX75cy5cv73enAABAZIjamhoAADC8BJ5TEwbTT4QaAADQb/aOW7oZqQEAAJEsnO5+ItQAAIB+o6YGAABEhY4FLampAQAAEc1ubY8SfiP5QzxaQ6gBAAD91jH9JEm+qzzyZbARagAAQL/ZLwk1oV7UklADAAD6raOmRpLa/KGtqyHUAACAfuuoqZFCf1s3oQYAAPTbJbNPamX6CQAARCqLxaIYW3g8gI9QAwAABuTiA/ioqQEAABGso66GkRoAABDROkZqqKkBAAARjZoaAAAQFaipAQAAUaGjpoYnCgMAgIgWWKmb6ScAABDJOqafqKkBAAARrWNRyzYfNTUAACCCBWpqGKkBAACRzM4t3QAAIBpcvKWbUAMAACIYNTUAACAqUFMDAACiAjU1V1BRUaE5c+Zo8uTJmjp1qn73u98F9h09elTTpk0LvOLi4rR58+bQdRYAAFyyoGVop5/sIT17N+x2u9asWaNp06apurpat9xyi+69914lJCTohhtuUGlpqSSpoaFB11xzjf72b/82tB0GAGCY65h+CvVITdiFmvHjx2v8+PGSpLFjxyo5OVlnz55VQkJCp3Z/+MMfdPfdd3fZDgAAhpY9Uu9+Ki4u1rx585SWliaLxdLt9M/atWs1adIkxcbGyu12a9euXf3q3L59++T3+5WRkdFl3+uvv66FCxf267gAACB4bLYIvfupsbFR2dnZeuGFF7rdv3HjRq1YsULPPvusDhw4oNmzZys/P1/l5eWBNm63W1lZWV1ep06dCrSpqanRt771La1fv77LOTwej959913de++9fe0+AAAIspgwGanp8/RTfn6+8vPzr7h/9erVWrJkiZYuXSpJWrNmjbZu3ap169apsLBQklRSUtLjObxer+bPn6+VK1dq5syZXfa/9dZbmjt3rmJjY3s8htfrDbz3eDw9nhMAAPSPLUxqaoJ691NLS4tKSkqUl5fXaXteXp52797dq2MYY/TYY4/prrvu0qJFi7pt05upp8LCQrlcrsCruyksAAAwcBFbU9OTM2fOyOfzKTU1tdP21NRUVVVV9eoY7777rjZu3KjNmzcHbt0+ePBgYH9dXZ327t2ruXPn9niclStXqq6uLvCqqKjo+wcCAABXdbGmJsKmn3rDYrF0em+M6bLtSmbNmiW//8qFRi6XS6dPn77qcZxOp5xOZ6/OCQAA+q+jpsbXw9/voRDUkZqUlBTZbLYuozLV1dVdRm8AAEB0sEXjMgkOh0Nut1tFRUWdthcVFXVb8AsAACJfxzIJoQ41fZ5+amho0LFjxwLvy8rKVFpaquTkZGVmZqqgoECLFi3S9OnTlZOTo/Xr16u8vFzLli0LascBAEB4uLhKd4SFmn379ik3NzfwvqCgQJK0ePFibdiwQQsXLlRNTY1WrVqlyspKZWVlacuWLZo4cWLweg0AAMKGPUxqavocaubMmSNjek5iy5cv1/Lly/vdKQAAEDk6ampao6mmBgAADD8dNTW+EE8/EWoAAMCAROXD9wAAwPBjC5OaGkINAAAYkI6RGmpqAABARLPbLixoSU0NAACIZNTUAACAqGALhBpqagAAQASL6Zh+YqQGAABEMluYLJNAqAEAAANiZ/oJAABEAxuFwgAAIBpQUwMAAKICNTUAACAqUFMDAACiQscThampAQAAEe3igpahDTX2kJ4dAABEvPGuWC2f8yUlJzhC2g9CDQAAGJC0kXH6/j03hrobTD8BAIDoQKgBAABRgVADAACiAqEGAABEBUINAACICoQaAAAQFQg1AAAgKhBqAABAVCDUAACAqECoAQAAUYFQAwAAogKhBgAARAVCDQAAiArDZpVuY4wkyePxhLgnAACgtzr+bnf8He/JsAk19fX1kqSMjIwQ9wQAAPRVfX29XC5Xj20spjfRJwr4/X6dOnVKiYmJslgsQT22x+NRRkaGKioqlJSUFNRjRxOuU+9xrXqH69R7XKve4Tr1zlBeJ2OM6uvrlZaWJqu156qZYTNSY7ValZ6ePqjnSEpK4n+CXuA69R7Xqne4Tr3HteodrlPvDNV1utoITQcKhQEAQFQg1AAAgKhAqAkCp9Op5557Tk6nM9RdCWtcp97jWvUO16n3uFa9w3XqnXC9TsOmUBgAAEQ3RmoAAEBUINQAAICoQKgBAABRgVADAACiAqFmgNauXatJkyYpNjZWbrdbu3btCnWXguYHP/iBLBZLp9e4ceMC+40x+sEPfqC0tDTFxcVpzpw5+uijjzodw+v16sknn1RKSooSEhL0ta99TSdOnOjU5ty5c1q0aJFcLpdcLpcWLVqk2traTm3Ky8s1b948JSQkKCUlRU899ZRaWloG7bNfTXFxsebNm6e0tDRZLBZt3ry50/5wuzYHDx7UnXfeqbi4OE2YMEGrVq3q1ToqA3W16/TYY491+Y7ddtttndoMh+tUWFioGTNmKDExUWPHjtWDDz6oo0ePdmrDd6p314nvVLt169Zp6tSpgYfj5eTk6D//8z8D+6P2+2TQb7/97W9NTEyMeemll8zhw4fNP/7jP5qEhARz/PjxUHctKJ577jlz8803m8rKysCruro6sP/55583iYmJ5o033jAHDx40CxcuNOPHjzcejyfQZtmyZWbChAmmqKjI7N+/3+Tm5prs7GzT1tYWaHPPPfeYrKwss3v3brN7926TlZVl7r///sD+trY2k5WVZXJzc83+/ftNUVGRSUtLM0888cTQXIhubNmyxTz77LPmjTfeMJLMpk2bOu0Pp2tTV1dnUlNTzTe+8Q1z8OBB88Ybb5jExETzk5/8ZPAu0AVXu06LFy8299xzT6fvWE1NTac2w+E6zZ0717z88svm0KFDprS01Nx3330mMzPTNDQ0BNrwnerddeI71e4Pf/iDefvtt83Ro0fN0aNHzTPPPGNiYmLMoUOHjDHR+30i1AzAV7/6VbNs2bJO22688Ubz9NNPh6hHwfXcc8+Z7Ozsbvf5/X4zbtw48/zzzwe2NTc3G5fLZX7+858bY4ypra01MTEx5re//W2gzcmTJ43VajV//OMfjTHGHD582Egy7733XqDNnj17jCTz8ccfG2Pa/zBarVZz8uTJQJvf/OY3xul0mrq6uqB93v66/I91uF2btWvXGpfLZZqbmwNtCgsLTVpamvH7/UG8Ej27Uqh54IEHrvg7w/E6GWNMdXW1kWR27txpjOE7dSWXXydj+E71ZNSoUeYXv/hFVH+fmH7qp5aWFpWUlCgvL6/T9ry8PO3evTtEvQq+Tz75RGlpaZo0aZK+8Y1v6LPPPpMklZWVqaqqqtPndzqduvPOOwOfv6SkRK2trZ3apKWlKSsrK9Bmz549crlcuvXWWwNtbrvtNrlcrk5tsrKylJaWFmgzd+5ceb1elZSUDN6H76dwuzZ79uzRnXfe2ekhWXPnztWpU6f0+eefB/8C9NGOHTs0duxYffnLX9Z3vvMdVVdXB/YN1+tUV1cnSUpOTpbEd+pKLr9OHfhOdebz+fTb3/5WjY2NysnJiervE6Gmn86cOSOfz6fU1NRO21NTU1VVVRWiXgXXrbfeqldeeUVbt27VSy+9pKqqKs2cOVM1NTWBz9jT56+qqpLD4dCoUaN6bDN27Ngu5x47dmynNpefZ9SoUXI4HGF5rcPt2nTXpuN9qK9ffn6+fv3rX+udd97Rv/7rv+ovf/mL7rrrLnm93kD/htt1MsaooKBAs2bNUlZWVqfz8526qLvrJPGdutTBgwc1YsQIOZ1OLVu2TJs2bdLkyZOj+vs0bFbpHiwWi6XTe2NMl22RKj8/P/DzlClTlJOToy996Uv61a9+FSi868/nv7xNd+370ybchNO16a4vV/rdobRw4cLAz1lZWZo+fbomTpyot99+WwsWLLji70XzdXriiSf04Ycf6s9//nOXfXynLrrSdeI7ddENN9yg0tJS1dbW6o033tDixYu1c+fOHvsW6d8nRmr6KSUlRTabrUuKrK6u7pI4o0VCQoKmTJmiTz75JHAXVE+ff9y4cWppadG5c+d6bHP69Oku5/riiy86tbn8POfOnVNra2tYXutwuzbdtekYjg+36zd+/HhNnDhRn3zyiaThd52efPJJ/eEPf9D27duVnp4e2M53qrMrXafuDOfvlMPh0HXXXafp06ersLBQ2dnZ+ulPfxrV3ydCTT85HA653W4VFRV12l5UVKSZM2eGqFeDy+v16siRIxo/frwmTZqkcePGdfr8LS0t2rlzZ+Dzu91uxcTEdGpTWVmpQ4cOBdrk5OSorq5Oe/fuDbR5//33VVdX16nNoUOHVFlZGWizbds2OZ1Oud3uQf3M/RFu1yYnJ0fFxcWdbqHctm2b0tLSdM011wT/AgxATU2NKioqNH78eEnD5zoZY/TEE0/ozTff1DvvvKNJkyZ12s93qt3VrlN3hut3qjvGGHm93uj+PvWprBiddNzS/ctf/tIcPnzYrFixwiQkJJjPP/881F0Liu9973tmx44d5rPPPjPvvfeeuf/++01iYmLg8z3//PPG5XKZN9980xw8eNA8+uij3d4SmJ6ebv70pz+Z/fv3m7vuuqvbWwKnTp1q9uzZY/bs2WOmTJnS7S2Bd999t9m/f7/505/+ZNLT00N6S3d9fb05cOCAOXDggJFkVq9ebQ4cOBC4nT+crk1tba1JTU01jz76qDl48KB58803TVJS0pDcVtrTdaqvrzff+973zO7du01ZWZnZvn27ycnJMRMmTBh21+m73/2ucblcZseOHZ1uRW5qagq04Tt19evEd+qilStXmuLiYlNWVmY+/PBD88wzzxir1Wq2bdtmjIne7xOhZoB+9rOfmYkTJxqHw2FuueWWTrcWRrqO5xbExMSYtLQ0s2DBAvPRRx8F9vv9fvPcc8+ZcePGGafTae644w5z8ODBTsc4f/68eeKJJ0xycrKJi4sz999/vykvL+/Upqamxnzzm980iYmJJjEx0Xzzm980586d69Tm+PHj5r777jNxcXEmOTnZPPHEE51u/xtq27dvN5K6vBYvXmyMCb9r8+GHH5rZs2cbp9Npxo0bZ37wgx8MyS2lPV2npqYmk5eXZ8aMGWNiYmJMZmamWbx4cZdrMByuU3fXSJJ5+eWXA234Tl39OvGduujv//7vA3+bxowZY+6+++5AoDEmer9PFmOG4NGGAAAAg4yaGgAAEBUINQAAICoQagAAQFQg1AAAgKhAqAEAAFGBUAMAAKICoQYAAEQFQg0AAIgKhBoAABAVCDUAACAqEGoAAEBUINQAAICo8P8DS3lnv7n7Qh8AAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "np.random.seed(SEED) # this was run with 100 Ruiz iters\n", + "xy = np.random.randn(n+m)\n", + "\n", + "solution = run_with_term_rule(\n", + " xy, MAXHESSIAN=MAXITERS,\n", + " cg_termination_rule=lambda xy: {'rtol':min(0.5, np.linalg.norm(separated_grad(xy)) ** 0.5)})" + ] + }, + { + "cell_type": "markdown", + "id": "df36dd23", + "metadata": {}, + "source": [ + "### With different powers" + ] + }, + { + "cell_type": "code", + "execution_count": 93, + "id": "4fa96702", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FINAL LOSS: 9.964404118963978e-26\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "np.random.seed(SEED)\n", + "xy = np.random.randn(n+m)\n", + "\n", + "solution = run_with_term_rule(\n", + " xy, MAXHESSIAN=MAXITERS,\n", + " cg_termination_rule=lambda xy: {'rtol':min(0.5, np.linalg.norm(separated_grad(xy)) ** 0.25)})" + ] + }, + { + "cell_type": "code", + "execution_count": 94, + "id": "b66c3c07", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FINAL LOSS: 1.2870836166383337e-29\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "np.random.seed(SEED)\n", + "xy = np.random.randn(n+m)\n", + "\n", + "solution = run_with_term_rule(\n", + " xy, MAXHESSIAN=MAXITERS,\n", + " cg_termination_rule=lambda xy: {'rtol':min(0.5, np.linalg.norm(separated_grad(xy)) ** 0.75)})" + ] + }, + { + "cell_type": "code", + "execution_count": 95, + "id": "72401742", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FINAL LOSS: 7.334390622227785e-26\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "np.random.seed(SEED)\n", + "xy = np.random.randn(n+m)\n", + "\n", + "solution = run_with_term_rule(\n", + " xy, MAXHESSIAN=MAXITERS,\n", + " cg_termination_rule=lambda xy: {'rtol':min(0.5, np.linalg.norm(separated_grad(xy)) ** 1)})" + ] + }, + { + "cell_type": "markdown", + "id": "72ac2cb0", + "metadata": {}, + "source": [ + "# FOR COMPARISON: LBFGS " + ] + }, + { + "cell_type": "code", + "execution_count": 96, + "id": "880df8c0", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "np.random.seed(SEED)\n", + "xy = np.random.randn(n+m)\n", + "def fun(xy):\n", + " return separated_loss(xy), separated_grad(xy)\n", + "\n", + "all_losses = []\n", + "def callback(xy):\n", + " all_losses.append(separated_loss(xy))\n", + "\n", + "sp.optimize.fmin_l_bfgs_b(\n", + " fun,\n", + " x0=xy,\n", + " factr=0.,\n", + " pgtol=0.,\n", + " m=10,\n", + " maxiter=MAXITERS*2,\n", + " maxfun=np.inf,\n", + " callback=callback,\n", + ")\n", + "\n", + "plt.plot(np.arange(len(all_losses))/2., all_losses)\n", + "plt.yscale('log')" + ] + }, + { + "cell_type": "markdown", + "id": "26210e17", + "metadata": {}, + "source": [ + "# FOR COMPARISON: DENSE SOLVE " + ] + }, + { + "cell_type": "code", + "execution_count": 116, + "id": "c05cf8a4", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "3a049f18e9ae4943b600145730f6767c", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + " 0%| | 0/1000 [00:00" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "np.random.seed(0)\n", + "xy = np.random.randn(n+m)\n", + "\n", + "losses = []\n", + "\n", + "for i in range(1000):\n", + " print(i)\n", + " current_loss = separated_loss(xy)\n", + " losses.append(current_loss)\n", + " current_grad = separated_grad(xy)\n", + " direction = np.linalg.lstsq(dense_hessian(xy), -current_grad, rcond=None)[0]\n", + " xy = line_search(xy, direction)\n", + "\n", + "plt.plot(np.arange(len(losses)), losses, label=f'DENSE SOLVE')\n", + "print('FINAL LOSS:', losses[-1])\n", + "plt.legend()\n", + "plt.yscale('log')\n", + "plt.show()\n", + " # print('FINAL LOSS:', losses[-1])\n" + ] + }, + { + "cell_type": "code", + "execution_count": 717, + "id": "7a03d2e1", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "559200.0" + ] + }, + "execution_count": 717, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "800 * len(xy)/2" + ] + }, + { + "cell_type": "markdown", + "id": "fe7cd6b1", + "metadata": {}, + "source": [ + "# END " + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "63ee4417", + "metadata": {}, + "outputs": [ + { + "ename": "Exception", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mException\u001b[0m Traceback (most recent call last)", + "Cell \u001b[0;32mIn[20], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mException\u001b[39;00m\n", + "\u001b[0;31mException\u001b[0m: " + ] + } + ], + "source": [ + "raise Exception" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e7571cb2", + "metadata": {}, + "outputs": [], + "source": [ + "fixed_rule = lambda x: {'maxiter':200}\n", + "np.random.seed(0)\n", + "xy = np.random.randn(n+m)\n", + "\n", + "solution = run_with_term_rule(xy, MAXHESSIAN=40000, cg_termination_rule=fixed_rule)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "59c63663", + "metadata": {}, + "outputs": [], + "source": [ + "xs = np.linspace(0,1)\n", + "losses = []\n", + "for step in xs:\n", + " losses.append(separated_loss(xy + step * cg_solution))\n", + " \n", + "plt.plot(xs, losses)\n", + "print(np.min(losses))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0b4aaf75", + "metadata": {}, + "outputs": [], + "source": [ + "plt.imshow(matrix_transf)\n", + "plt.colorbar()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "36a431e2", + "metadata": {}, + "outputs": [], + "source": [ + "# system = sp.sparse.bmat([[None, matrix_transf.T], [matrix_transf, None]]).todense()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "78196dee", + "metadata": {}, + "outputs": [], + "source": [ + "plt.imshow(matrix_transf.T @ matrix_transf)\n", + "plt.colorbar()\n", + "plt.figure()\n", + "plt.plot(np.linalg.eigh(matrix_transf.T @ matrix_transf)[0])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "893985dc", + "metadata": {}, + "outputs": [], + "source": [ + "plt.imshow(matrix_transf @ matrix_transf.T)\n", + "plt.colorbar()\n", + "plt.figure()\n", + "plt.plot(np.linalg.eigh(matrix_transf @ matrix_transf.T)[0])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "dcaf4e89", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.9" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}