{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Example: Using DistArray for Gaussian Elimination (L-U decomposition)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Note:** This notebook requires an IPython.parallel cluster to be running. Outside the notebook, run:\n", "\n", "dacluster start -n4\n", "\n", "***" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Gaussian Elimination is an algorithm in Linear Algebra best understood as a series of row operations on the coefficient matrix of a system of linear equations. The method can also be used to calculate the rank, determinant, and inverse of a matrix. The algorithm involves adding multiples of each row to subsequent rows, in order to make the coefficient matrix upper triangular. The resulting system is then solved by back-substitution which is trivial to perform. This algorithm is illustrated in the figure below:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here **i** refers to the index of the pivot row (started at 1). Please note that much of this example notebook is adapted from [Parallel Gaussian Elimination](https://github.com/prashantmital/ge_utpcse/blob/master/Report.pdf) which is a good starting point for gaining a better understanding of Gaussian Elimination from an computational standpoint.\n", "\n", "In this notebook we will demonstrate how to perform GE in *parallel* using the **DistArray API**. The main challenge in parallelizing Gaussian Elimination on a distributed memory machine is that the calculation of each row requires the calculation of all rows that have come before it and therefore concurrency of operations becomes the overriding issue. This bodes well for the client-engine architecture of IPython.parallel (and consequently DistArray) as the client can keep track of *pivot* row, while the row transformations can be pushed out to the engines using custom uFuncs. \n", "\n", "We begin with the imports:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# utility imports\n", "from __future__ import print_function\n", "from pprint import pprint\n", "from matplotlib import pyplot as plt\n", "\n", "# main imports\n", "import numpy as np\n", "import distarray.globalapi as da\n", "from distarray.plotting import plot_array_distribution\n", "\n", "# output goodness\n", "np.set_printoptions(precision=2)\n", "\n", "# display figures inline\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now define the parameter space for our study. We will perform GE on matrices that are *block distributed* in any one or both dimensions, while simultaneously varying the size:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[('n', 'b'), ('b', 'n'), ('b', 'b')]\n" ] } ], "source": [ "distributions = [('n','b'), ('b','n'), ('b','b')]\n", "sizes = [8, 16, 32, 64]\n", "print(distributions)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we create a context and devise a scheme for generating some synthetic data (in this case a matrix) on which to operate:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "context = da.Context()\n", "def synthetic_data_generator(contextobj, datashape=(16, 16), distscheme=('b', 'n')):\n", " \"\"\"Return objective matrix with specified size and distribution.\"\"\"\n", " distribution = da.Distribution(contextobj, shape=datashape, dist=distscheme)\n", " _syndata = np.random.random(datashape)\n", " syndata = contextobj.fromarray(_syndata, distribution=distribution)\n", " return syndata" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order for the Gaussian Elimination operation to be truly parallel, we need to define a uFunc to perform the desired computation:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def parallel_gauss_elim(darray, pivot_row, k, m):\n", " \"\"\"\n", " Perform in-place gaussian elimination locally on all engines.\n", " \n", " Parameters\n", " ---------\n", " darray : DistArray\n", " Handle for the array to be manipulated (global)\n", " pivot_row : numpy.ndarray \n", " Array containing pivot row (global)\n", " k : integer\n", " Pivot row index (global)\n", " m : numpy.ndarray\n", " Vector containing pivoting factors (global)\n", " \"\"\"\n", " import numpy as np\n", " \n", " # retrieve local indices for submatrix that needs to be operated on\n", " n_rows, n_cols = darray.distribution.global_shape \n", " i_slice, j_slice = darray.distribution.local_from_global((slice(k+1, n_rows), \n", " slice(k, n_cols)))\n", " \n", " # limit the slices using actual size of local array\n", " n_rows_local, n_cols_local = darray.ndarray.shape\n", " i_indices, j_indices = (i_slice.indices(n_rows_local), \n", " j_slice.indices(n_cols_local))\n", " \n", " # determine which elements of global pivot row correspond to local entries\n", " _, piv_slice = darray.distribution.global_from_local((slice(0, n_rows_local), \n", " slice(*j_indices)))\n", " \n", " # limit the slice to the size of the global pivot row\n", " piv_indices = piv_slice.indices(n_cols)\n", " \n", " # determine which elements of global pivot factor vector corresponds to local\n", " mul_slice, _ = darray.distribution.global_from_local((slice(*i_indices), \n", " slice(0, n_cols_local)))\n", " \n", " # limit the slice to the size of the global pivot factor vector\n", " mul_indices = mul_slice.indices(n_rows)\n", " \n", " # perform the elimination to create zeros below pivot\n", " if (i_indices[0] == i_indices[1] or j_indices[0] == j_indices[1]):\n", " # computation for the local block is done\n", " return\n", " else:\n", " for i, mul in zip(xrange(*i_indices), xrange(*mul_indices)):\n", " np.subtract(darray.ndarray[i, slice(*j_indices)], \n", " np.multiply(m[mul], pivot_row[slice(*piv_indices)]),\n", " out=darray.ndarray[i, slice(*j_indices)])\n", " return\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We want to use a nice syntax for calling out uFunc hence we *register* it with our context (alternatively, we could have just used Context.apply which has a more obscure call format):" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [], "source": [ "context.register(parallel_gauss_elim)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "All that is left now is to define the high level function that runs on the client and manages the GE operation. Using this function is a way of ensuring synchronicity between the many engines performing this operation. After a pivot row is determined, it is broadcast along with a vector of pivoting factors to the worker engines via the parallel_gauss_elim uFunc. Note how we have actually subverted the need to use canonical MPI constructs (in this case, MPI_Bcast()) by making use of the fact that our uFunc can accept arbitrary arguments. " ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def execute_ge(contextobj, darray):\n", " N = min(darray.shape)\n", " for k in range(N-1):\n", " pivot_factors = (d_array[:, k]/d_array[k, k]).toarray()\n", " contextobj.parallel_gauss_elim(darray, darray[k, :].toarray(), k, pivot_factors)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to enable the reader to better visualize what is happening in this example, we will make the first set of runs with the size fixed at 8, while cycling through the distribution types. We also print out a graphical representation of the distribution of the resulting upper triangular matrices." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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DmxEd/Sxjx7anSJF8ua+8SHHo9RLcWwHuLgeFi8LfWl19/+ZtbMK+qyy0Docn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\ncQSEloEm7WDqSKhZDd74AAoXhEF90x9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BLVtOsGXLCUqW/E/iPHv3vkT9+hM5e/ay25LCSL7xl/JWCSqlDAu4iEwHmgLF\nReQQ8JYxZooTjcfFxdOv3zwWLOhBYGAAkyatY/t2zz/cWTFtWieaNg2jRIl8HDw4gLfeWsK7767g\n228f5Zlnwtm/P4ouXb4DYNu2k3z77Ra2bu1LbGw8ffrM9Wq26tVvZerUDhgDmzefSNwaz4n1lJn1\nArZQHDx4LkfOJkjouunQoRr/939tKFEiH3PnPs769Udp2/Zrx/MEBxdg9epeFCp0C/HxhpdeupMa\nNT7m4sVrieupePG8ievp88838N57LahbtyTGGPbti6J37zmJy5o/vwfx8YbIyGieeOIHr+Ry597V\nNWJEc6pWLU5cnGHPnjO88IJ3P8MA/fvP4+uvHyF37kD27DnLU0/Nvm6aG6RX0O9JdvtXRcTAUIfi\nKKVUguEYY3Ksp1xEzLAszDcMcjSnO/0lplJK+Skt4Eop5ae0gCullJ/SAq6UUn5KC7hSSvkpLeBK\nKeWntIArpZSf0gKulFJ+Sgu4Ukr5KS3gSinlp7SAK6WUn9ICrpRSfkoLuFJK+Slnrge+eZgji1FK\nqUQ1h/s6wQ3PmcvJbtaL+yqlHFZTcvxysuZIFuYrrZeTVUoplUlawJVSyk9pAVdKKT+lBVwppfyU\nFnCllPJTWsCVUspPaQFXSik/pQVcKaX8lBZwpZTyU1rAlVLKT2kBV0opP5VhAReRMiKyRES2iMhm\nEXnR0QQr5sPD1aBtZZj0nqOLvuGzHD0ET90H7W+HDjXhq/+zwz8eBg+EQud69rFivh1+7oydvlFB\neKe/93JdvQLd74BOdaFdDRgzJP1c3vDrj/BIHdtOl/rw569J4z4dYddZx1ow6DG4dtUOX/CdHV47\nELauy36GtNZDgs9HQa0A+74AxFyDN5+CjrXtPKuXZT+DuzefhnuD7d+dYPtGePwu22a/dnDxvB0e\nsSrpfepYG37+xrs5XumW1F6r8vZfd0cPQsMCdp0px2R4MSsRKQmUNMZsEJECwFqggzFmm2t81i9m\nFRcHD1WFzxbBbSHQrSGMnA4Vq2dtednhiyynjtlHtbpw6YItVGNnw4JvIX9B6Dkw+fSXL8G29bB7\ns328/qH3sl2+BHnzQWwsPNkEXvkP/LE49VzecOki5Mtvn++MgJc6ws+74fB+eOZ++Gkb5L4FXu4K\n97aF9j1h73YICIDhveHVUVAjPPs5UlsP4U3sl++wXrB/B3y7FgoXg+kf2y+Of02CMyfh+TbwzWoQ\nh65ztPbx40vqAAAgAElEQVQ3yFcAXn8SZkXYYV0bwqDRUP8emDUFDu+Dfv+EK5ft+gkIsJ+xDjVh\n2XEIDPRODnfvvwKFikDvN5OGDegMAYFQqxH87WXP2tGLWWUowy1wY8wxY8wG1/MLwDagtCOtR6yC\nspUgJAxy5YI23WDJj44s2i+ylChpizfY/xAVqsOJw/Z1al+sefNBeGP7H9Pb8uaz/8Zcs19uhYqm\nncsbEoo32C+3oiXs8wKFICiXLayxsXDlkv3CBahQDcKqOJsj5XooXMy+fn8gDByZfNq926DRffZ5\nsVttEdu8xrks9e9Jeh8SHNxlhwPc2RwWfm+f58lrizfYYl6gsDPFO60cCYyxGyBtuicNWzwbQitA\nxRrOtK8SZaoPXETCgHrAn460fuIwlCyT9Do4NKmA5TRfZzm8325d17nTvp72oe1C+MczEB2VfFqn\ntujSEx9vuwGaBtuiVOn2jHM5bfFseLg6vNAGhri6lwoXg54vQ4uycH9pKFgE7mruvQwp10PFGrZ7\nJzgUqtZOPm3VOrD0J1voI/fB1rVwPNJ72QAq3m7zAPzyHRw7lDQuYpWre+52u5WeE9b+BsWDoWxF\n+/rSBZg8EvoMy5n2bzIeF3BX98lM4CXXlnj25UQh8pQvs1y6YHcxB4+1W+JdX4AF++D7DXBrKXjf\nw11OJwUE2PYXR8La5bBqac7neqADzNkGH82BIU/YYQf3wJcfwC/74dcjdt3992vvZUi5HpbPg89G\nQF+3mw0k7JV0fNoW9q4NYOQAqHO3c1u9afnXZJgxDro0sOsiV+6kcbUawY9b4Nt18O5LcP6cd7MA\nzJsODz6W9PrjYfDkALsnk1N7bzcRj+7IIyK5gO+Br4wxs6+b4ONhSc8bNoNGzTxr/baQ5FsMxw7Z\n/wC+4KssMTHw907wcA9bsACK35Y0vtOz0O9h7+dIS8HCcO+DsGVN8vfVG7lmjIOZn9ov03Fz7ZcE\n2F322Fg4e8rmqHs3FCluxzV/BDashIcedzZLSgnrYds6u3XdqY4dfjzSHruYvsq+b+5buj0aQzmH\nu3RSKl8VJi6wz/fvhOVzr5+mQjUoUxEO7obb63svS2wsLJ4F37kdQN68ChZ9D6MHwfkokADbvdOt\nz/Xzr1oKq5d6L99fUIYFXEQEmARsNcZ8kOpEfYdlrfXbG8CBXbb74LbSMP8be+DQF3yRxRh46xm7\nW/7E35OGnzyaVLwWz4LKta6fz5vOnoLAINuHe+Uy/L4QXhhqD4aVKJl2ruzq1ifpP/bBPfbvFEk6\no6RoCVuwJvzL5rolD/yxyG5ppuTEOkprPbgfnGtVPukg5pXLtsslX35YudD21Veolv0c6Tlz0va3\nx8fDhH/bvSSwn+PgUAgKgiMH7Ge7XGXvZvljkT2Oc5vbIbKpy5OejxtuD4KnVrzBbiC4bySM11uq\nZcSTLfDGQA9gk4isdw0bYozJ/jlkQUHwxkfQu5XtN3zkGd+cgeKrLOv/B//9CqrUTjrt6qV37G7o\n9g22eIWWh7cmJM3TMsyeKhZzzfZ9TvzF+SJx8ii80dMWhfh4ePgJuPMBGPJk2rmctuh7+OkLWwTz\nFYD3Z9jh1epCuydtN0VAAFQPh87PueaZBSNehKhT0OdBqF4PPvk56xnSWg/u3LveTh+H51vbrczg\nUBjxZdbbTs2r3WHNMvvF8kAZ241z6QLM+NiOb94JOvzNPl+3Aia9a9dfUC4YNtEeAHYyR9Rpm6Pf\nP6HjU3ajp233jOdXjtF7Yiqlbkx6GmGG9JeYSinlp7SAK6WUn9ICrpRSfkoLuFJK+Skt4Eop5ae0\ngCullJ/SAq6UUn5KC7hSSvkpLeBKKeWntIArpZSDvH4XMzceXY1QKaWUx2KAAe53MRORhQl3MXOS\nboErpZSDvHoXsxS0gCullJc4fhezFLQLRSmlMmHpSvvIiFfuYpayDb2crFLqhuTHl5N13cXsv8DP\nad4IxwHahaKUUg7y6C5mDtECrpRSzkq4i9l9IrLe9WjtjYa0D1wppRxkjFlBDm0c6xa4Ukr5KS3g\nSinlp7SAK6WUn9ICrpRSfkoLuFJK+Skt4Eop5ae0gCullJ/SAq6UUn4qwwIuInlE5E8R2SAiW0Vk\nhKMJVsyHh6tB28ow6T1HF61ZMunsKejdGjrVhQ41YfbnSeOio2BAZ3i4OrSrAZtcF1f7eBg8EAqd\n69nHivnO5Vm11C6zQ034W7O0s2z8I2nc1x/a4R1qwujXst52XJxtu+/D9vWC76D97VA7ELasTZpu\n5ULo0gA61rb/rlpih1+5DC88mJRlzJCsZ0nw5tNwbzB0rHX9uM9HQa0AOHcm/VxOtp3We3/uDDx1\nHzQqCO/0T76chM9X+9vhH89ATEz2cvkxEQkSkR3ZWUaGv8Q0xlwRkfuMMZdEJAhYISJNXL82yp64\nOHi7H3y2CG4LgW4NoVk7qFg924vWLFkw7SOoVg8GjLDF/KGq8FAPCAqCd1+Ce9rCmJkQGwuXL9p5\nRODJgdBzoLNZoqPg7b4wYQGUDLV5EqSVZdUSWPIT/LAJcuWCMyez3v5XY6FiDbh43r6uXAvGzoLh\nve3fnKDYrTDuv1CiJOzeAr1bweJIO+7pQdCwqS1Szz5gC1yTbPyiuuNT8Hh/eP3J5MOPHoLfF0Lp\ncp7lcqrttN773Hmg/79h92b7cDdmJuQrYJ8P6Azzv4GHe2Q9lx8zxsSKyHYRKWeMOZCVZXjUhWKM\nueR6mhsIBM5kpbHrRKyCspUgJMz+h2vTDZb86MiiNUsW3FoKLkbb5xeioUhxW7zPn4N1v8EjT9tx\nQUFQsHDSfNm8omWq5k2DFp1s8QYoWsL+m16Wb8ZDryF2nYEtYllxLBJ+mwednk362ypUg7Aq109b\nra4tkmAL/pXLtmDnyWuLN9g81cPh+OGs5UlQ/x4oVPT64e8PhIEjPcvldNupvfd580F4Y8h9y/Xj\nEop3TAzEXEt6X29exYAtIvKriMxxPX7ydGaPCriIBIjIBuA4sMQYszWLYZM7cRhKlkl6HRxqh/mC\nZoHOvezW2n2loVMdGDzWDj+8D4reCm8+BY+Gw9BecPlS0nzTPoRH6thd4ugoZ7Ic2JW0K96lAfz0\nZcZZDuyCNcvhsTttl8vmNVlre+QAePl9kEweIlr4PdSon/QFkiA6CpbOgTsfyFqe9Pz6o/18VK2d\n+VxOSO+9lzSuBPtcK2gaDLfkzd4eyV/DP4CHgOHAf4BRrodHPN0CjzfG1AVCgXtFpFnmc6YirTfY\nFzQLfPqO3XJbcgRmbrBdGBfP226Kbeugax/4bh3kzQ+T3rXzdH0BFuyD7zfYLfj3X3YmS2wMbF0H\n4+fBxAUw4V+2QKeXJS4Wos/CtD9sAX6lS+bbXfpfKHYbVK+XuT2L3VtgzGAYOiHF3xELg7pDj5fs\nHpWTLl+y71nf4UnDUmZOK5cTsvreT1wAS49CzFX4carzufyIMWYpsB0oBBTEXoJ2mafzZ+pqhMaY\ncyIyF2gALE0c8fGwpIkaNoNGzTxb4G0hcOxQ0utjh+zWhC/crFlmjIOZn9rnhYpCv3/a52UrQkh5\n2LfDdmMEh0KthnZcy87wmatoFr8taVmdnoV+DzuTpVUXKFLCdkXkyQv174Wdm6Bek+RZWnRKOsgb\nHArNH7HPazW0W9BRp21XkKc2rLT96L/Ng6tXbJfSkCdhxBdpz3MsEv7+CIz4EkLLJx837DkIqwo9\nvHBj8kN74PB+u7cEcDwSutSH6avs+5JeLidk573PfQs07wQRf0L7nnbYqqWweqmTCW94ItIFeB9I\nKNoficirxpjvPJk/wwIuIiWAWGNMlIjkBVpgN/eT9B2WmcxJbm9gt6oO74fbStsDGiOnZ21Z2XWz\nZunWxz4ARg6EPxZDeBM4dRz274AyFaBwMduls3+n7Qf+fRFUut3Oc/Ko3foCWDzLHuxzIsve7fBO\nP3tA99pV+x+950AoEZw8yx+Lk7Lc3wH+/NX2Pe/faftYM1O8Af7+jn0ArF4Gn//n+uLtvpUbHQV9\nHoQB70Hdu5JP939v2i+Af03KXAZPVakFy48nvW5VHr5da9+v9HI5JaP3PuXewKWLdn3cWsrumSz7\nL9zdMml8o2bJN/7GJy8zf1FvAg2NMScARORWYDHgTAEHSgFTRSQA2+XypTFmcRbDpmg9CN74yB4h\nj4uDR57xzVkfmsXq9brtW36kDph4e2CscDE7bsiH8NrjtiiWqQj/nmKHj34Ntm+w3T6h5eEth3bV\nK1SDxq3hkdoQEACdetmDcell6fg0/ONpe6pbrtzwTjpbzZ5K6M5aNAtGvAhRp2xhrF4PPvkZpn9k\nt4THD08qOJ8utFvvn74DFarbvnqAx/onHXzNile7w5pldq/igTJ2b6njU6lPm1aurB40TGj77Cnb\ndt/hdms5rfe+ZZjtfou5Botn27YLF4P+7e0XsjHQuFX21sdfgwDup0uddg3zbGa9J6ZS6obkx/fE\nzESb7wN1gGnYwt0V2GSMGeTJ/HpHHqWU8p1BwCPY27ABTDDGzPJ0Zi3gSinlO/mA2caY70WkKlBN\nRHIZYzw6aV+vhaKUUr7zG3CLiIQAC7A3Q/7c05m1gCullO+I65fujwDjjDGPAjU9nVkLuFJK+ZCI\n3AU8Dsx1DfK4LmsBV0op3/k7MASYZYzZIiIVAY8vHamnESqlbkw3wWmEKdoPAAoYY6I9nUe3wJVS\nykdEZLqIFBKR/MBmYJuIeHQOOGgBV0opX6rh2uLuAPwMhAFPeDqzFnCllPKdIBHJhS3gc1znf3vc\nJ60FXCmlfGcCsB8oACwXkTDgnKcz60FMpdSN6SY7iOnKIECgMSbWk+l1C1wppXxEREqKyCQRSbgb\neHWgp6fzO3ItFFP0BrqbjVLqL+EmqSqfA1OAN1yvdwHfAh5dRF4vZqWUUi5yNivdwdn6qilhjPlG\nRAYDGGNiRMSj7hPQLhSllPKlCyKSeNsoEbmTTBzE1C1wpZTynZeBOUAFEVkJ3Ap09nRmLeBKKeUj\nxpi1ItIUqIrti9nu6bXAQbtQlFLKZ0SkH/b6J5uNMRFAARHp4+n8WsCVUsp3ehljzia8cD1/ztOZ\ntYArpZTvBLiuQgiAiAQCuTydWfvAlVLKdxYAM0RkArYPvDcwP/1ZkmgBV0op33kN22Xyguv1QuAz\nT2fWAq6UUj5ijIkTkcnACteg7caYOE/n1wKulFI+IiLNgKnAAdegsiLS0xizzJP5tYArpZTvjAZa\nGmN2AIhIFWAGEO7JzB6dhSIigSKyXkTmZDlmGuYvgWr3QuXG8N7HTi9ds/hrlh8XQJ3mUK8l1G8N\nv65IGpdWnlf/BdWb2vkeeRbOeXxnwcxZutLmqnk/NHP7zdzTAyG4DtR6wDvtprb8Veuh0YM2T8O2\nsHpD8nkOHoYClWHUJ97J5C6t9RJ2B9R2vZeNHvR+Dj8TlFC8AYwxO8nEhrVH1wMXkYFAfaCgMaZd\ninHGHPY8rbu4OKh6LyyaASEl7Qdw+jioXjlry8sOzXJjZbl4CfLns88jtkHHZ2H3/9LPs3A5PNAE\nAgJg8Dt23ndfdzZX1Dlo3AEWfA2hpeHUGShRzI777U8okB+efAkiFjvbblrLb9YZhvSDVs3g519h\n5DhYMjNpns69IDAQGtWFl593PlOC9NZL+Tth7c9QrGjmlikhzl1n26P2RAxbsnAxq9uzft1yEZkC\nxAFfYc9CeRwIMMY87cn8GW6Bi0go0BZ7ZNTRlblqPVQKg7AykCsXdGtvt7x8QbPcWFkSijfAhYtQ\nomjGeVrca4s3wB31IPKo87mmzYJObW2RgqQiBXDPHVC0sPNtprf8Urcl7WlERUNIqaRxs+dDhXJQ\no4r3MiVIb70AZPO+MX9lzwPbgBeB/sAWks5IyZAnXShjgFeB+KykS8/hY1CmdNLr0FJ2mC9olhsv\ny+z5tkukzRPwf//KXJ7JM6Dt/c5n2rUPzkTBfZ2hQRv4cmbG83jTu6/Dy/+Esg1tF9I7g+3wCxft\n1viwl3MmR3rrRQSad7PDP/06Z/L4AxEJAjYaY0YZYx5xPcYYY656uox0+1pE5CHghDFmvetoqaPk\nBrpiu2ZJnS+zdGhtH7/9CU+8CNuXezbf22Mhd254rKPzmWJiYV0ELP4GLl2Gu9rBneFQuYLzbXni\nmZftl1vHNvDdHPt64QwYNgoG9IJ8eXNm6ze99bJiFpQuCSdPQ4tuUK2S3Zu42RljYkVkh4iUM8Yc\nyHiO62XUWX430E5E2gJ5gEIi8oUx5kn3iYaNSnre7C5odrdnjYeUhENu96A7dMRuUfmCZvF9lnGf\nw6fT7JfG3C+gVLAdfs8dEBsHZ87attPL8/k3MO9XW0iczgXQ5WHbPZA3r33ceyds3Oq7Ar5qAyxq\nY593fgiefTVp+PfzYNDbtmslQCBvHujzN+fa9nS9lC5pp7m1uP2iWbU+9QK+dCUs/d25fH6iGLBF\nRFYBF13DTMpjjWlJt4AbY14HXgdwXfLwlZTFG7K+m9agjt312n8ISgfDNz/ZA1K+oFl8n6XP35IK\nzJ79dstRxG7ZARQvBoULpZ1n/hJ4/xNY9j3kyeOdXNt3Q7837MHUq9fgz/Uw0ONLDzmvUhgs+x2a\n3mXP1Kni+iJZ/kPSNMNHQ8H8zhZv8Gy9XLpshxUsYA9M/7IMhg5MfXnN7k6+8Td8tLN5b1Bvuv51\n39f1eJ8ps+eBO7ozFhQEH/0bWj0GcfHwTDffnGmhWW68LN/Pgy9mQq4ge+bFjHEZ5+n/JlyLsbvp\nAHfVh3EjnM1VrRK0vs+eFhcQAL0eSzpI2L0PLPsDTp+FMg3gn6/CU12dazth+afOJC1/4kjo+wZc\nvWq3sCeOdK69zEhrvew9YE/pBLsX9XhHaNnUNxlvJCKSF3sAsxKwCZicmeuAJy7Hk9MIMwiS5dMI\nlVIqLX/l0whF5FvgGvAb9iy//caYlzLbtP4SUymlcl51Y0wtABGZBKzOykL0euBKKZXzEu88b4zx\n+C70KekWuFJK5bzaInLe7XVet9fGGFPIk4VoAVdKqRxmjAl0YjnahaKUUn5KC7hSSvkpLeBKKeWn\ntIArpZSf0gKulFJ+Sgu4Uko5SEQmi8hxEYnwdltawJVSyllTgNY50ZAWcKWUcpAx5jfgbE60pQVc\nKaX8lP4SUymlMmPVUli91NcpAL2crFLqBuXPl5MVkTBgTsIVB71Fu1CUUspPaQFXSikHich0YCVQ\nRUQOichT3mpL+8CVUspBxpjuOdWWboErpZSf0gKulFJ+Sgu4Ukr5KS3gSinlp7SAK6WUn9ICrpRS\nfkoLuFJK+Skt4Eop5ac8KuAisl9ENonIehFZ5WSA+Uug2r1QuTG897GTS9YsmiVrwu6A2s2hXkto\n9KAd9o+RUKc51G0BD3SBQ67r/yxcDg3a2OkbtIEl/7t+ee3+BrUeyF6mQ4fhvs5w+31Q8374v0lJ\n4z6cDNWb2uGvvZ18voOHoUBlGPWJ99oHu/yAUDiT4iKqqbU/5Ru7Puo0hzY94PSZ7GW7mXl0MSsR\n2QfUN8Zct6qzczGruDioei8smgEhJaFhW5g+DqpXztryskOzaJYE5e+EtT9DsaJJw85fgIIF7PMP\nJ8PGrfDZf2DDZih5m31s2QGtHoPItUnz/TAPvp8HEdth06KsZzp2wj7q1oQLF6F+a5g92Q5750OY\n9yXkygUnT8OtxZPm69wLAgOhUV14+Xnn269e2Rb3XoNgx57r11vK9q9dg1L1YNcKO91rb0O+vDB0\n4PVt+vPFrHJKZrpQHA+4aj1UCoOwMvbD1609/LjA6VY0i2bJvJTbNQnFG2wBK1HMPq9b0xZvgBpV\n4PIViIlJmm7Mp/DmS9cvL7NK3mbbAiiQ3xbOw0fhky9hSD+7PiB58Z49HyqUs7myK7X2jxyzrwcO\nh5FvXD9Pau0HBUHRInDhkl0n0eftl7HKGk8LuAEWicgaEenlVOOHj0GZ0kmvQ0vZYb6gWTRLAhFo\n3s12iXz6ddLwN96Fsg1h6ncwuO/1830/F+rXTiqm/xgJrzxvtzCdtP8QrN8Md4TDzr2w/E+48yFo\n1hnWbLTTXLgII8fBsJedbTtl+z8usO9D7RrJp0mr/YAAGDvcdsOE1Idtu+Hpbs5nvFl4WsAbG2Pq\nAW2AviJyjxONi092OlKnWVJ3M2b532xY/wv8/BV8/Dn89qcd/vZgOLga/tYFBgxLPs+WHTB4BEx4\nz77esBn2HoT2rbK/9e3uwkXo/ByM/afdK4iNg7Pn4I//wvtvQhdXN8mwUTCgl/3y8Fb7AQG2+2b4\nK0njE9pKq/3o8/DiW7BxIRxZB7WqwYgPnct3s/HoaoTGmKOuf0+KyCygEfBbwvhho5KmbXYXNLvb\ns8ZDSsKhI0mvDx2x3+a+oFk0S4JSwfbfW4tDxza26+aeO5LGP9YR2j6R9DryCDzyLHw5FsqXtcP+\nWAdrNtn+9NhYOHEa7n8Ufv0u67liYqB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Yc1v3d7InMfuOgpPRdv/Vb3FjvS1a2ynZpAJ5BsL/lBwTuIjMBVoBpUXkKPCm\nMeYrVzSemJjEsGFLWb78Sby9vZgyJbxArkABe7VJWNhAAgMLkZRkGDHiTurUmUijRuV58skGbNt2\nkvDwQQCMGbOK5cv3MX58G2rWLE1iomH//rMMHpzaezl48EWKFfPDz8+bzp1r0a7dTPbsyV/stWuX\nZfr0LhgDO3acSumNlytXlIULewP2aGH27G2sWLE/X21lJqttdPny9Sz306efdsDPz5sVK+zh/G+/\nRTF0qAt6eTEn7BUUl2PtsMSsCbBklz1p9n+fwaD29oqUbv3tUAZA137wRj97KZ2vH7ybzyOCZJP+\nYodm/upISD6+MM9xEm5UD9sL9vGFNz6HgDQncX/42p68c5WVC2DJDNuWfwB8OC913it9YNNPNpYH\ng+3VH12ftUM48ybaZdp0hy7P5D+OiF/hv7Pg9gapl0eOeNcm5szaql4H2veETnXAx8dup4I+I3+L\nyPEywhwryMdlhOoW5OxlhErpZYQ50l9iKqWUh9IErpRSHkoTuFJKeShN4Eop5aE0gSullIfSBK6U\nUh5KE7hSSnkoTeBKKeWhNIErpZSH0gSulFIeShO4Ukp5KE3gSinloTSBK6WUh9IErpRSHspFD3RQ\nSinP99ax3K8zLh/P68gv7YErpZSH0gSulFIeShO4Ukp5KE3gSinloTSBK6WUh9IErpRSHkoTuFJK\neShN4Eop5aE0gSullIfSBK6UUh5KE7hSSnmoHBO4iASLyBoR2SkiO0TkBVcG0L59DSIjh7F373BG\nj27pyqo9IpYSJQrz7be92LLleX7/fQB16pQF4PbbSxMePihlOn/+NYYPvwOABg3KsX59f7ZuHczi\nxX0ICPBzSSydOtVky5bnCQ8fxKZNz3H//VVT5h08+CJbtw4mPHwQGzYMTCn/4IO27No1lC1bnmfB\ngl4EBhZySSwptodBQx9YsSC17Ivx0LkudK0Pox+H69ds+advQLeG0L0R9H8Qjh/NW5sHdsMTd0GT\nwjDto9Ty40fh2ftt213qwaxPUue93Bt6NLZT+6r2X4D1K6BnM+jawP67cU3eYgI4FwODHrKfr0s9\nWDQtdV7seRjZAx6tDZ3qwLYNtnziOHiwUmps637Ie/tZbZeDe1Lr79EY7iyeum3+/oqNqVtDGNEN\nLl5IX+fxI9A8IH19ymlijMl+AZHyQHljzBYRCQA2A12MMZGO+QbeylPjXl7Cnj3DadNmBtHRsYSF\nPUefPvMJ5T7MAAAgAElEQVTZvTsmT/Xlh7ti+eCDtsTGXuOdd37m9ttLM3Hiw7RtOyPdMiJCdPQo\nWrT4gqioWDZuHMioUctZt+4IzzzTiKpVS/LWW/lIDA7+/r7ExcUDUK/ebSxc2JvQUPuHeODACJo2\n/Tfnzl1Jt06bNtVYteogxhjGj28DwJgxK7NuZMc45wNKTISBbaGwP3R9Ftp2h+hD0P8BWBIJfoXg\npV5wX0fo3BcuX4Sixey6sz+FPVvhL186316ys6fh2GFYvQgCS8IzL9nymBN2qtUI4i5Bz6YwYRFU\nr51+/Q9fhsASMGgs7N4CZcrbad9OGNQeVkXlPiawyfj6NRg53ibzR2rCTyfBxwde7wvNWkG3fpCQ\nAFcuQ7Hi8Pnbdpv0HZW3NtPKaruklZQEDwTB3I1QIdh+gd35IHh5wcev2WVGvpe6/Mge4OUN9Vvc\nWF89wRgj+Q/cOSJiTB5uZiUVualxppVjD9wYc8IYs8Xx+hIQCbjk/lstWgSxb99ZDh8+T0JCEvPm\n7aBz51quqNpjYqlduyxr1hwCYO/eM4SElKBMGf90y7RpU439+88RFRULQGhoadatOwLAypUH6N49\nQwLJo+TkDRAQ4EdMTFy6+ZLJf9GVKw+Q3AnYsCGKSpUCXRILAHM+hXY9oFTZ1LKAQPDxhStxNlFd\njYPbguy85OQNNsGWLJO3dkuVhXrNbDtplSlvkzeAfwBUqw2nM/zFGwPL/wMd+tj3tRrZ9QCq14Gr\nVyA+njwpWwEu2/8DXIqFEqVt8r54AcJ/sckbbFmx4uljcoWstktav62E4Oo2eQPc3dYmb4D6d8CJ\nNF9eqxZBpWp2u6g8ydUYuIiEAI2BDa5oPCgokKNHUw+poqJiCQoqls0aBcddsWzdeoJu3WwCbt48\niCpVit+QBHv3rsecOdtT3u/ceYpOnWoC8NhjdQkOLo6rdO5ci127hrJs2ZO88MKylHJjYOXKpwkL\ne44BA5pkum6/fo1ZuvQP1wRyMhpWL4Zegx0Fjm+P4qWg70vQtjI8UBGKlYC72qSuN+H/oE1lWDId\n+r/mmlgyE30IIiOgwR3pyzf/AqXLQeXqN66zYgHUaQq+2STA7PQYaHvx91eE7g3htQmOWA5CybIw\n9ll4rAm8NdB+wSWb86kdwnijvx1qKUjL5sHDj2c+b+FUe7QE9gt26gcwZFzBxvM/zukE7hg+mQ+M\ncPTE8y2n4ZubyV2xvPfeOkqUKEx4+CCGDWtBRMQJEhNTY/H19ebRR2/nm292ppT167eYIUOaExb2\nHAEBfly/nuiyeBYv3k2dOhN59NE5zJzZNaW8ZcspNGkymQ4dZjF0aAvuuadyuvVef/1erl9PZO7c\n7RmrzJv3X7SH2iKOHqRjmxzZDzP/CT8egtXHbCL47+zU9Ub8DVYegc7PwAcjXRNLRnGX7KH/axNs\nTzytpXMzT2D7dtohhLcm573dL961Pfo1x2D+FvjbUDtslJAAkeHQawh8Ew5FisIUxzBFr8Gw/CAs\n2GJ78B9mMuzhKvHX4afvoN1jN86b/Dfw9UvdNhPHwdMjoYi/644QbkFOPdBBRHyBBcAsY8yiG5dY\nm+Z1iGPKWXT0xXS9x+DgwJRhgpvtZsYyeHBzBg5sgjHw8MOz6d9/ccq8AwdGcODAuZT3HTrUYPPm\n4+mGM/buPcNDD80C7HDKww+HuiyWEyfsd/O6dUfw8fGiVKkinD17JaU8JiaOhQsjadEiKGUYp2/f\nRnTsGMqDD87Ish2nzPsc5n9hX1+6AK/0tq/PxcAvy8Dbx44BN7rbDh8AtOkGW9bDI0+kr+vhx2Fw\nx7y1/a9lqcMeGcXHw4vd4dEn4cEu6eclJMCqhTaJpnUiCl7sBuNnQqWq5ErauAJLwrC/2NeVq0NQ\nVXsCsXwlKFcJ6je389r1gC8dCbz0bal1dR8Awx7Ne/vZbRew+6hO0/RDXmBPtv6yFKasSi3bsRFW\nLoB/jIaL50G84MRRe0SlnJZjAhcRAaYAu4wx/8x8qdZ5anzTpmOEhpaiSpUSHDt2kV696tGnz/w8\n1ZVfNzOWSZPCmDQpDIDAwEL4+noTH5/IgAFN+Omnw1y+fD1l2T596t/Qqy1Txp+YmDhEhLFj72PS\npE0uiaVatZIp5Y0bVwDg7NkrFCnii7e3cOnSdfz9fWnXrjpvv/0TYK/ceeWVu2nVahrXriXkOQ4A\neg+xU0Zjn4VWj8IDnWH3VvjXX+xYcqHC8PtKewIM4PAfUMXxZbZ6MdRqnL+2M/YMjYE3+9sx26de\nvLGO31facfHb0pwiij0PQx6Gke9Do7ucjyezuD4YBb+vgib3QMxJOLQHgqvZYaXywXBoL4Tcbseh\na9S165w+bnveYL9cQuvnvf1kWfWYl86Fjn3Sl637Ab76EKb9ZPdXsuk/p77O6kTrpLdzF+styJke\neEvgSWCbiEQ4ysYYY/JxPZKVmJjEsGFLWb78Sby9vZgyJdwtV6C4M5batcsyfXoXjIEdO06l6437\n+/vSpk01Bg5ckm6dPn3qM3So7W0tWBDJ9OlbXBJL9+51ePrphsTHJ3Lp0nV697ZfYOXLB/Dtt70A\n8PHxYvbsbaxYsR+ATz/tgJ+fNytWPAXAb79FMXTo9y6JJ1O1GkKnp6FXM3tyrHYT6PGcnffPMTap\neXnbE2lvTMpbGzEnoFdze8LQywtmTYAlu+wVJf+dBbc3SL1McMS7cG8H+/qHr29MYHM/g6P7bTJK\nTkhfrMjbCdaBr9svs24NwSTBqA9s8gYY8ym8+oQdxgiuDu98Zcv/8aqNW8T2/t/MxxBOVtvFPwDi\nLtsvsLe/SL/Ou8NtTAPb2vcN74I3Ps97DCqdHC8jzLGCfFxGqG5BubmMUN3a9DLCHOkvMZVSykNp\nAldKKQ+lCVwppTyUJnCllPJQmsCVUspDaQJXSikPpQlcKaU8lCZwpZTyUJrAlVLKQ2kCV0opFyro\np5il5dTdCJVSSjktHhiZ9ilmIrIi+SlmrqQ9cKWUcqGCfIpZRprAlVKqgLj6KWYZ6RCKUkrlwtr1\ndspJQTzF7IY29Hay6qbS28kqZ3nw7WQdTzH7L7As6wfh5J8OoSillAs59xQz19AErpRSrpX8FLP7\nRSTCMT1UEA3pGLhSSrmQMWYdN6lzrD1wpZTyUJrAlVLKQ2kCV0opD6UJXCmlPJQmcKWU8lCawJVS\nykNpAldKKQ+lCVwppTxUjglcRAqLyAYR2SIiu0RkvCsDaN++BpGRw9i7dzijR7d0ZdUaSy5UqhTI\n6tV92bFjCNu3D2H48DsAaNCgHOvX92fr1sEsXtyHgAA/AAoV8mHOnO5s3TqYnTuH8uqr97gumONH\n4dn7oXNd6FIPZn1iyyeOgwcrQY/Gdlr3gy3fvjG1rGsDWPa162IBWL0YujW09fdsChtWp877YryN\ns2t9GP04XL9myy+chQFt4eHbYWA7iD2fvxic3Sa/LLPl8ddh7LN2e3RvBGE/5a/9rGwPg4Y+sGJB\natm6H+DRWtAxFKa8n1r+91fg0dp2W47oBhcvFExMHkJEfERkT77qcOZmViLib4yJExEfYB3wsuPX\nRvm6mZWXl7Bnz3DatJlBdHQsYWHP0afPfHbvjslTfflxq8dSrlwA5csHsHXrCYoW9WPz5ufo0mUe\nM2Z0ZdSo5axbd4RnnmlE1aoleeutNfTt24j27avz+OMLKFzYh127htKq1TSOHs3hj9KZm1nFnLBT\nrUYQd8kmzQmLYPl/oGgx6Dsq/fJXr4BfIfDysut1qQc/nQRv7zxvj3TiLoN/Uft673YY0RWW7YPo\nQ9D/AVgSadt/qRfc1xE694WPRkPJMtBvtE1isedg5Ht5jyG322TuRNgVDn+dAmdPw/Md4OswEBfe\nGyoxEQa2hcL+0PVZaNvdlj1SE75cCbcFQe/m8MFcqF4b1q+AOx+0++nj12wd2W0TD76ZVS7aXAy8\nYIw5nJf1nRpCMcbEOV76Ad7A2bw0llGLFkHs23eWw4fPk5CQxLx5O+jcuZYrqtZYcunkyUts3XoC\ngMuXrxMZGUNQUCChoaVZt+4IACtXHqB799oAHD9+kaJF/fDyEooW9eP69URiY6+5Jpgy5W2iAvAP\ngGq14VS0fZ9Zh6NwEZsUwCbzgOKuS96QmrzBJs+SZezrgEDw8YUrcZCQAFfjbNICWLsEOvW1rzv3\nhdWL8hdDbrfJgUhocb99XaosBJaAHZvyF0NGcz6Fdj1s/cm2b4TKNSAoBHx9oUNvWLPYzru7bep+\nqn8HnIhybTyeqRSwU0RWi8h3jmmJsys7lcBFxEtEtgAngTXGmF15DDadoKDAdD22qKhYgoKKuaJq\njSUfqlQpQePG5dmwIYqdO0/RqVNNAB57rC7BwcUB+PHH/cTGXuP48Zc5dOhFPvxwPRcuXHV9MNGH\nIDICGt5p38/51B6Cv9E//bDE9o2O4YW6MPofro9j1SJ7+D+4A4xxDF8ULwV9X4K2leGBivaL4642\ndt6Zk1CmnH1dupx97yrObJOaDe2XSGIiRB2EXZvhpAsT5sloO7TUa7CjwNEBPRUN5YNTlytXKfWL\nJq2FU+3RinoDeAR4G/g78JFjcoqzPfAkY0wjoBJwn4i0zn2cmdbrimpcQmOxihb1Y/78nowY8QOX\nLl2nX7/FDBnSnLCw5wgIsD1tgCeeaECRIj5UqPB3qlb9Jy+/fDchISVcG0zcJRjZA16bYHudvQbD\n8oOwYAuUrQAfvpS6bP0WsHgn/Ccc3hvh+vHVB7vAd5Hw2Xcw5ilbdmQ/zPwn/HgIVh+DK5fhv7Nv\nXFeElASXX85uk679bPLs1Qw+GAkN73btUcn7L9rhDxHHEYDj/6wzQzST/wa+fvDw466Lx0MZY9YC\nu4FAoBj2FrROn7DI1d0IjTEXROR7oBmwNnVOmpeEOKacRUdfTOnRAQQHBxIVFZubkFxGYwEfHy8W\nLOjJrFnbWLx4NwB7957hoYdmARAaWpqOHUMBuPvuYBYu3E1SkiEmJo5ffz1Cs2YVOXQonyfrksXH\nw4vd4dEnbfIEKH1b6vzuA2DYozeuV60WBFeHI/ugbtO8tz/vc5j/hU1In39vkyNA03vtcMm5GNi5\nCRrdDSVK23ltusGW9fDIE7bXHXPCDn2cPp4+9rzKzTbx9k5/JPJkS6hye/7aT94mAJcuwCu97etz\nMfbkqY+vHUI6cTR1nRNH7RdJskXT4JelMGXVjfVvXAtha/MXo4cRkZ7Ah0By0v5MRF4xxnzjzPrO\nXIVSRkRKOF4XAdoCEemXap1mCnGmXQA2bTpGaGgpqlQpga+vN7161WPJknydlM0zjQWmTOnMrl2n\nmTDh95SyMmX8ARARxo69j3/9y46j7t4dwwMPVAXA39+XO++sRGSki06yGgNv9ofqdeCpF1PLTx9P\nfb1qIYTWt6+jD9mkCnDsMBz+A6qE5i+G3kNgfgR8E27HuJOPinaF239LloGqNWHb73bc3Rj4faWN\nGaB1J1g83b5ePB0e6JK/eHK7Ta5esSdfwZ489PG1X275kbxN5kfADwdsz3/5QTsO/sYkuL8T1G1m\nt3/0IXslzA9f220B9uqUrz6ETxdDocI31t+iNQwdlzrdGsYCzY0xTxtjngaaY4dVnOJMD7wCMF1E\nvLAJf6YxJpOvz9xLTExi2LClLF/+JN7eXkyZEu6Wqz40FmjZsjJPPtmAbdtOEh4+CIDXX19FaGhp\nhg5tDsCCBZFMn74FgMmTNzFlSme2bRuMl5cwdWoEO3eeck0wEb/Cf2fB7Q3spXEAI96FpXNh9xbb\nK65UFd6cbOeFr4Mp79kk5eML4/5tTzC6ysoFsGSGrds/AD6cZ8trNYJOT9thCi8vqN0Eejxn5w14\nDV7qCd9OgYoh8NF/8hdDbrfJmZPw/EMgXrYHPH5m/tp3lo8P/N9nMKi9HX/v1t9egQLw7nCb1Ae2\nte8b3gVvfH5z4vrzEuB0mvdnyMV4mz4TU91c+kxM5axb4zLCD4GGwBxs4u4FbDPGjHZmfX0ij1JK\nuc9ooBv2MWwAk40xC51dWRO4Ukq5jz+wyBizQERqArVExNcYE+/MynovFKWUcp9fgEIiEgQsxz4M\neZqzK2sCV0op9xHHL927AZ8bYx4D6jm7siZwpZRyIxG5C3gC+N5R5HRe1gSulFLu8yIwBlhojNkp\nItWBNc6urCcxlVLKTRw/m/8J7D2ngNPGmBecXV974Eop5SYiMldEAkWkKLADiBQRp64BB03gSinl\nTnWMMbFAF2AZ9l4kTzm7siZwpZRyHx8R8cUm8O8c1387/fN4TeBKKeU+k4FDQADws4iEAE7fC1kT\nuFJKuYkx5hNjTJAxpoMxJgk4DNzv7PqawJVSyk1EpLyITBERxxO6qQ30dXp9V9yN0GTyxCSlMjMu\nyN0RKE/xNnm/y19euOluhD8AXwH/Z4xp4BgPjzDGOPVrTL0OXCmlHORcXjq0+fqOKWOM+VpEXgMw\nxsSLSIKzK+sQilJKuc8lESmd/EZE7iQXJzG1B66UUu7zEvAdUE1E1gNlgR7OrqwJXCml3MQYs1lE\nWgE1sWMxu529FzjoEIpSSrmNiAwDAowxO4wx24EAERni7PqawJVSyn0GGmPOJb9xvH7O2ZU1gSul\nlPt4Oe5CCICIeAO+zq6sY+BKKeU+y4F5IjIZOwY+CPgh+1VSaQJXSin3eRU7ZDLY8X4F8KWzK2sC\nV0opNzHGJIrIVGCdo2i3MSbR2fU1gSullJuISGtgOvYmVgCVRaSv40k9OdIErpRS7vMPoJ0xZg+A\niNwOzAOaOLOyU1ehiIi3iESIyHd5DjMLP6yBWvdBaEt4f6Kra9dYPDGWzlOm8PKJEwzeti2lrFyD\nBvRfv57BW7fSZ/Fi/AICAKj/+OMMCg9Pmd5MSKBc/foFElfFZs14Mz6e2t26pZTd8cILDN62jSHb\nt3PHC6mPMuwxd25KTCMOHGBQeHi+289su7T94AOG7trF81u20GvBAgoFBgLgU6gQ3efMYfDWrQzd\nuZN7Xn013+2XqVmT/uvXM/bKFe4aNSrH2ADq9OjBkB07eDMhgQqNG6eUBzVvnrJ9Bm/dSt2ePfMd\nn4fySU7eAMaYveSiY+3sZYQjgF3k4kkRzkhMhGFj4YfZsGstzF0EkX+4sgWNxRNjifjqK2Y99FC6\nsk5ffsmK0aOZ1LAhkQsX0vKVVwDYPmcOk5s0YXKTJix86inOHTjAye3bXR6TeHnR9v332fdD6gUC\nt9WtS5MBA/iieXMmNWzI7Y88Qslq1QCY36dPSlyRCxYQuWBBvmPIbLvs//FHPq9bl381asSZvXu5\nd8wYAOr17g3ApIYNmdy0KU0HDaJ4cHC+2o87c4Zlw4ez/u9/dyo2gFPbt/N1164c/vnndOUnt2/n\n302bMrlJE2a2a8fDEyciXrfkVc2bReRLEWktIveLyJfAJmdXznGLiUgloCP2zKhLb+24MQJqhEBI\nMPj6Qu/OsHi5K1vQWDwxliPr1nH13Ll0ZaVDQzmyzp7nObByJbW7d79hvfqPP86OefMKJKY7hg9n\n1/z5XD59OqWsTO3aRG/YQMK1a5ikJA7/9FO63nmyuj17sn3u3HzHkNl2ObByJcm3hI7asIHASpUA\nuHj8OH5FiyJeXvgVLUri9etci43NV/txMTEc27yZxPgbf+mdWWwAMXv2cOaPG7/xE65eTYnbp0gR\nrl64gElKyld8Hup5IBJ4ARgO7CT1ipQcOfOV9zHwCuDyrRt9AoIrpr6vVMGWuYPG8ueO5dTOndTs\n1AmAuo89lmlvsm7PnuxwQaLMqFjFitTs3JmwSZNsgSPxnNq+ncr33kuRkiXxLVKE0IcfTkmgyarc\ney+XTp7k3IEDLo8ro8b9+vHH0qWA7Zlfi43l5ePHefHQIdZ/+CFXLzh9k7ubIqh5c4bs2MHQnTtZ\nnmFI5lYgIj7AVmPMR8aYbo7pY2PMNWfryDaBi8gjwCljTAQu7n3b+l1dY95pLJn7s8SyuF8/mg8Z\nwnNhYfgFBJB4/Xq6+UEtWhAfF8fpyEiXt/3QP//JytdeA0BEUjZKzJ49/Pr++zz14488sWwZJyIi\nbuhF1uvTh+1z5rg8pozuff11Eq9fT+npN3jiCXyKFOHvFSrwz6pVufvllykRElLgceRGdFgYn9er\nx+QmTegwYULK+P2twhiTAOwRkSp5rSOnwfK7gU4i0hEoDASKyAxjzNNpFxr3Uerr1ndB67udazyo\nPBxN8wSMo8dsD88dNJY/dyxn9u5NGWMtHRpK6MMPp5tfr3dvlybK5oMH02TgQAAKFy9OD8fQjH+Z\nMtTo0IGk+Hj2fPcdEV99RcRXXwHw4N/+xoUjR1Lq8PL2pnbXrkxu4tQFBXnWqG9fQjt2ZMaDD6aU\nBd99N7sXLsQkJREXE8ORX3+lYrNmnD90KFd1p90Oszt04NLJk64MHbBfhGf37+dqjRr85IKTvR6m\nFLBTRDYClx1lxhjTyZmVs03gxpjXgdc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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = sizes[0]\n", "for scheme in distributions:\n", " d_array = 1000 * synthetic_data_generator(context, datashape=(N,N), distscheme=scheme)\n", " execute_ge(context, d_array)\n", " process_coords = [(0, 0), (1, 0), (2, 0), (3, 0)]\n", " plot_array_distribution(d_array, process_coords, legend=True, \n", " title=str(\"Distribution Scheme = \" + str(scheme)))" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "Now we write a quick routine that runs through all sizes and distributions and records the runtimes. The resulting information is best represented as a plot the data for which is collected in a Dictionary called performance_data. Depending on the contents of your sizes vector, the runtimes may very a great deal on this section." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1 loops, best of 3: 1.15 s per loop\n", "1 loops, best of 3: 2.44 s per loop\n", "1 loops, best of 3: 5.03 s per loop\n", "1 loops, best of 3: 10.3 s per loop\n", "1 loops, best of 3: 1.25 s per loop\n", "1 loops, best of 3: 2.7 s per loop\n", "1 loops, best of 3: 5.73 s per loop\n", "1 loops, best of 3: 11.5 s per loop\n", "1 loops, best of 3: 1.15 s per loop\n", "1 loops, best of 3: 2.38 s per loop\n", "1 loops, best of 3: 4.89 s per loop\n", "1 loops, best of 3: 10.1 s per loop\n" ] }, { "data": { "image/png": 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QEhgILEWPAvoAGCEi8xwiysQADIY4uR92n54bejLzgPaeVi9UncCGgeTPbNP8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\nRPv4ixSBZTNvMdOtPbt4nWKhB3XGzlW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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# create a dictionary of lists\n", "from collections import defaultdict\n", "performance_data = defaultdict(list) \n", " \n", "for scheme in distributions:\n", " for N in sizes:\n", " d_array = 1000 * synthetic_data_generator(context, datashape=(N,N), distscheme=scheme)\n", " _time = %timeit -o execute_ge(context, d_array)\n", " performance_data[scheme].append(_time.best)\n", " plt.plot(sizes, performance_data[scheme], label=str(scheme), linewidth=2)\n", "\n", "plt.legend(loc=4)\n", "plt.xlabel('Problem Size N')\n", "plt.ylabel('Execution Time [seconds]')\n", "plt.title('Gaussian Elimination N vs t')\n", "plt.grid(True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that we observe similar performance from all three distributions with a *block-block* map marginally most efficient. \n", "***" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Application: LU Decomposition\n", "\n", "In this section we will demonstrate how we can, with minimal modification, use the GE approach to perform LU decomposition of a matrix.\n", "\n", "Mathematically, LU-factorization follows naturally from GE operations on any given matrix (with the exception of systems that require partial pivoting - these need some special treatement and in this example we don't concern ourselves with these issues of numerical stability of GE). LU-factorization involves expressing a given matrix as a product of two matrices - one of which is lower triangular ($\\mathbf{L}$), and the other upper triangular ($\\mathbf{U}$):\n", "\n", "$$\\mathbf{A} = \\mathbf{L} \\mathbf{U}$$\n", "\n", "Once we have this factorization, we can make use of it to solve $\\mathbf{A}x=b$:\n", "\n", "$$\\mathbf{A}x = \\mathbf{L}\\mathbf{U}x = b$$\n", "\n", "Which is equivalent to:\n", "\n", "$$\\mathbf{U}x = \\mathbf{L}^{-1}b =:c$$\n", "\n", "Since the cost of matrix inversion is prohibitively high, we find $c = \\mathbf{L}^{-1} b$ through *forward substitution*:\n", "\n", "$$\\mathbf{L}c = b$$\n", "\n", "This is easy to do as $\\mathbf{L}$ is lower triangular. The final step then becomes to perform backward substitution:\n", "\n", "$$\\mathbf{U}x=c$$\n", "\n", "The procedure demonstrated in the preceeding section gives us a method of finding $\\mathbf{U}$, and now we are tasked with computing $\\mathbf{L}$. If the series of elementary row operations that the GE process entails are expressed as a series of matrix transformations on $\\mathbf{A}$ we end up with a series of trivially invertible matrices, which when multiplied give us $\\mathbf{L}$:\n", "\n", "$$\\mathbf{E}_{n} \\mathbf{E}_{n-1} ... \\mathbf{E}_{2} \\mathbf{E}_{1} \\mathbf{A} = \\mathbf{U}$$\n", "$$\\implies \\mathbf{A} = \\mathbf{E}_{1}^{-1} \\mathbf{E}_{2}^{-1} ... \\mathbf{E}_{n-1}^{-1} \\mathbf{E}_{n}^{-1} \\mathbf{U}$$\n", "$$\\implies \\mathbf{E}_{1}^{-1} \\mathbf{E}_{2}^{-1} ... \\mathbf{E}_{n-1}^{-1} \\mathbf{E}_{n}^{-1} =: \\mathbf{L}$$\n", "\n", "It turns out that $\\mathbf{L}$ is basically composed of the **negatives** of the off-diagonal elements in the matrix transformations. \n", "\n", "We now have enough information to write a routine to perform LU-decomposition. Our approach will be to perform the GE in-place on a copy of the objective matrix, and create a new matrix which will be populated with the multiplicative factors. The uFunc for GE will be used by us directly, we need only modify the driver function:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def execute_lu(contextobj, darray):\n", " # create placeholders for lower and upper triangular matrices \n", " uarray = contextobj.fromarray(darray.toarray(), distribution=darray.distribution)\n", " larray = contextobj.fromarray(np.zeros(darray.shape), distribution=darray.distribution)\n", " \n", " N = min(darray.shape)\n", " for k in range(N-1):\n", " pivot_factors = (uarray[:, k]/uarray[k, k]).toarray()\n", " pivot_factors[0:k] = 0.0\n", " # populate lower triangular matrix\n", " larray[:, k] = pivot_factors\n", " contextobj.parallel_gauss_elim(uarray, uarray[k, :].toarray(), k, pivot_factors)\n", " larray[-1, -1] = 1.0\n", " return larray, uarray" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us first test our implementation by checking if we can reproduce our objective matrix $\\mathbf{A}$ by multiplying $\\mathbf{L}$ and $\\mathbf{U}$. For multiplication, we will convert the DistArrays back to NumPy arrays and for comparison of floating point entries we use numpy.allclose() which returns True if all entries are equal within a tolerance. " ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Success: LU == A for distribution scheme = ('n', 'b')\n", "Success: LU == A for distribution scheme = ('b', 'n')\n", "Success: LU == A for distribution scheme = ('b', 'b')\n" ] } ], "source": [ "N = sizes[0]\n", "for scheme in distributions:\n", " d_array = 10 * synthetic_data_generator(context, datashape=(N,N), distscheme=scheme)\n", " L, U = execute_lu(context, d_array)\n", " if (np.allclose(np.dot(L.toarray(), U.toarray()), d_array.toarray())):\n", " print(\"Success: LU == A for distribution scheme = {}\".format(scheme))\n", " else:\n", " print(\"Failure: LU != A for distribution scheme = {}\".format(scheme))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hence we have validated our implementation. Just to confirm that our matrices are actually upper and lower triangular, lets generate a schematic for one $\\mathbf{LU}$ pair:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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wRESaOOfcAhKwAaAtDBERCUUFQ0REQlHBEBGRUFQwREQkFBUMEREJRQVDRERC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\nRK5CYII=\n", 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zzdB2U/mP30eKrcbXqpVIfLxw4MBRatdO5PLLz+TRR4tfMqbkfSDhyggwZcoA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\nbp4//7j2L3rgAUavWsWoFSu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g4//+V+J7N7o3E7hoLRxZQJaqZriPZ+AUjuNMuKdijSc3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\nOIwxxgTl/wPzcdSkkpt8RwAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "process_coords = [(0, 0), (1, 0), (2, 0), (3, 0)]\n", "plot_array_distribution(L, process_coords, legend=True, \n", " title=str(\"Lower Triangular Piece L for Distribution Scheme = \" + str(scheme)))\n", "plot_array_distribution(U, process_coords, legend=True, \n", " title=str(\"Upper Triangular Piece U for Distribution Scheme = \" + str(scheme)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note: the values are not actually perfect integers, they are just displayed as such for the sake of readability.\n", "\n", "***" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.10" } }, "nbformat": 4, "nbformat_minor": 0 }