From 8a5e4b130e3c98d57fdc11ac62426652c9579f13 Mon Sep 17 00:00:00 2001 From: Michael Lange Date: Fri, 12 May 2017 15:41:56 +0100 Subject: [PATCH 01/12] CFD: Add tutorial notebook for linear 2D convection example All of this is based on Lorena Barba's "CFD Python: 12 steps to Navier-Stokes" tutorial: http://lorenabarba.com/blog/cfd-python-12-steps-to-navier-stokes/ We also sanity check the intermediate results and run the tutorial notebook collection through travis. --- .travis.yml | 1 + examples/cfd/__init__.py | 1 + examples/cfd/test_01_convection.ipynb | 506 ++++++++++++++++++++++++++ examples/cfd/tools.py | 46 +++ 4 files changed, 554 insertions(+) create mode 100644 examples/cfd/__init__.py create mode 100644 examples/cfd/test_01_convection.ipynb create mode 100644 examples/cfd/tools.py diff --git a/.travis.yml b/.travis.yml index e0ddb849c6..e4b1c19ecc 100644 --- a/.travis.yml +++ b/.travis.yml @@ -56,4 +56,5 @@ script: - python examples/seismic/acoustic/acoustic_example.py - py.test -vs examples/seismic/tutorials - py.test -vs examples/diffusion/example_diffusion.py + - py.test -vs examples/cfd - if [[ $DEVITO_ARCH == 'gcc-5' ]]; then ./docs/deploy.sh; fi diff --git a/examples/cfd/__init__.py b/examples/cfd/__init__.py new file mode 100644 index 0000000000..8b2ff9678b --- /dev/null +++ b/examples/cfd/__init__.py @@ -0,0 +1 @@ +from .tools import * # noqa diff --git a/examples/cfd/test_01_convection.ipynb b/examples/cfd/test_01_convection.ipynb new file mode 100644 index 0000000000..cdab463777 --- /dev/null +++ b/examples/cfd/test_01_convection.ipynb @@ -0,0 +1,506 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Devito CFD Tutorial series\n", + "\n", + "The following series of notebook tutorials will demonstrate the use of Devito and it's SymPy-based API to solve a set of classic examples from Computational Fluid Dynamics (CFD). The tutorials are based on the excellent tutorial series _CFD Python: 12 steps to Navier-Stokes_ by Lorena Barba and focus on the implementation with Devito rather than pure CFD or finite difference theory. For a refresher on how to implement 2D finite difference solvers for CFD problems, please see the original tutorial series here:
\n", + "http://lorenabarba.com/blog/cfd-python-12-steps-to-navier-stokes/" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Example 1: Linear convection in 2D\n", + "\n", + "Lets start with a simple 2D convection example - step 5 in the original blog. This will already allow us to demonstrate a lot about the use of Devito's symbolic data objects and how to use them to build a simple operator directly from the symbolic notation of the equation. The governing equation we will implement in this tutorial is:\n", + "\n", + "$$\\frac{\\partial u}{\\partial t}+c\\frac{\\partial u}{\\partial x} + c\\frac{\\partial u}{\\partial y} = 0$$\n", + "\n", + "In order to implement this equation we first discretize it using forward differences in time and backward differences in space. Just as the original tutorial, we will use $u_{i,j}^n$ to denote a finite difference stencil point with $i$ and $j$ denoting spatial indices and $n$ denoting the time index. So, after re-arragning the discretized equation for the forward stencil point in time we get \n", + "\n", + "$$u_{i,j}^{n+1} = u_{i,j}^n-c \\frac{\\Delta t}{\\Delta x}(u_{i,j}^n-u_{i-1,j}^n)-c \\frac{\\Delta t}{\\Delta y}(u_{i,j}^n-u_{i,j-1}^n)$$\n", + "\n", + "Using this, we can start deriving the computational stencil for this equation. Let's first look at the original _pure Python_ implmenentation of the linear convection flow - but first we import our tools and define some parameters:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "scrolled": true + }, + "outputs": [], + "source": [ + "from examples.cfd import plot_field, init_hat\n", + "import numpy as np\n", + "%matplotlib inline\n", + "\n", + "# Some variable declarations\n", + "nx = 81\n", + "ny = 81\n", + "nt = 100\n", + "c = 1.\n", + "dx = 2. / (nx - 1)\n", + "dy = 2. / (ny - 1)\n", + "sigma = .2\n", + "dt = sigma * dx" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**A small note on style:** Throughout this tutorial series we will use utility functions to plot the various 2D functions and data sets we deal with. These are all taken from the original tutorial series, but have been slightly modified for our purposes. One of the differences readers might find is that the original series uses _(y, x)_ indexing for 2d data arrays, whereas many of the examples have been adapted to use _(x, y)_ notation in our tutorials.\n", + "\n", + "So, let's start by creating a simple 2D function and initialising it with a \"hat function\". We will use that initialisation function a lot, so it comes from our utility scripts:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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NBn0YocVA1yJJkkLVz1X0WS0UCvr6uFrtuaIa6GphkCMKDjsh2BPnIHOBdpZW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\n+QjPTeQHBjrylnHTxcaNG9Hf3w9N0zBjxgx9JO/II48cM7J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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Create field and assign initial conditions\n", + "u = np.empty((nx, ny))\n", + "init_hat(field=u, dx=dx, dy=dy, value=2.)\n", + "\n", + "# Plot initial condition\n", + "plot_field(u)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can repeat the _pure NumPy_ solve from the original tutorial, where we use NumPy array operations to speed up the computation. Note that we skip the derivation of the stencil used to implement our convection equation, as we are going to walk though this process using the Devito API later in this tutorial." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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vfe1rccUVV0yfc++99+Lxxx/HD3/4Q3zta1/Db/7mb+LBBx/M74BTQoKOSEyUilU2WzSL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\nC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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Repeat initialisation, so we can re-run the cell\n", + "init_hat(field=u, dx=dx, dy=dy, value=2.)\n", + "\n", + "for n in range(nt + 1):\n", + " # Copy previous result into a new buffer\n", + " un = u.copy()\n", + " \n", + " # Update the new result with a 3-point stencil\n", + " u[1:, 1:] = (un[1:, 1:] - (c * dt / dx * (un[1:, 1:] - un[1:, :-1])) -\n", + " (c * dt / dy * (un[1:, 1:] - un[:-1, 1:])))\n", + "\n", + " # Apply boundary conditions\n", + " u[0, :] = 1.\n", + " u[-1, :] = 1.\n", + " u[:, 0] = 1.\n", + " u[:, -1] = 1.\n", + "\n", + "plot_field(u)\n", + "\n", + "# A small sanity check for auto-testing\n", + "assert (u[45:55, 45:55] > 1.8).all()\n", + "u_ref = u.copy()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Hooray, the wave moved! Now, this little example is already very concise from a notational point of view and it teaches us quite a few key points about how to perform finite difference stencil computation via NumPy:\n", + "* Due to the backward differencing scheme in space (more later) we use only three stencil point in this example: $u^{n}_{i, j}$, $u^{n}_{i-1, j}$ and $u^{n}_{i, j-1}$. These can be identified in the code through the array indices and correspond to `un[1:, 1:]`, `un[:-1, 1:]` and `un[1:, :-1]` respectively. \n", + "* Two buffers for array data are used throughout: `un[...]` is read from, while `u[...]` is updated, where the line `un = u.copy()` performs a deep copy of the field to switch buffers between timesteps. Note that in some other finite difference tutorials the cost of this copy operation is sometimes amortised by using two pre-allocated buffers and switching the indices of them explicitly. \n", + "* The final four lines within the loop code show us how to implmement simple Dirichlet boundary condition by simply setting a value on the outermost rows and columns of our cartesian grid." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Devito implementation\n", + "Now we want to re-create the above example via a Devito operator. To do this, we can start by defining our function `u` as a symbolic function object of type `devito.TimeData`. The core thing to note here is that this is one of Devito's symbolic data objects, which have a dual role in the creation of finite difference solvers:\n", + "* They behave symbolically like `sympy.Function` objects, so that we can construct derivatives and use them in symbolic expressions, thus inheriting all the power of automated symbolic manipulation that SymPy provides.\n", + "* They act as containers for user data by providing a `.data` property that wraps automatically allocated memory space in a neat NumPy array.\n", + "\n", + "The particular `TimeData` type that we will declare our variable $u$ as in this case is aware of the fact that we will want to implement a timestepping algorithm with it. So the object `u` it will declare two buffers of shape `(nx, ny)` for us and present them as `u.data[0]` and `u.data[1]`. Let's fill the initial buffer with some data and look at it:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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NBn0YocVA1yJJkkLVz1X0WS0UCvr6uFrtuaIa6GphkCMKDjsh2BPnIHOBdpZW\nqVarBh2Lu9tjoGuQVdmSMPT3NPdZzWQy6OrqqvumD1sgdcoqiNabXiaqR5Zl7lwk37GGXjUWFW4O\nA12Lgh7h0jQNxWJRb8/VaJ/VoI+/Wcbjdjq9TFSPcZ2TeY1Tu1wsKTiNrgFrJOiVy+WqGnrGOnpR\n+4BiN8q7Z88eFhWugYGuCcYwEVQgMvZZTSQS6O3tbarPalQDHQB9obEIcvWml4nq6enpcTwqAtRu\nUUTklU6toccRutoY6FrkdyByu89qFAOduIg6XSdI1IhGOgtomoZcLtcWF0u3MODa8/q58bqGnl/s\nnqfh4WEGuhoY6JoQxAiduT2Xm31WoxLoxIYPsUYumUyip6eHFw/yhTnoxeNxlEolpNNpxxfLeDzO\n12sHC+pcG7WgV2sN3aGHHur5/UcVA12LRC9XryiKgkKhgEql4kl7riiM0Fnt3C2Xy7w4UijUu1gq\nilLVK7SdF7NTfWH6f24k6InNf+YPKH6+dgcHBzlCVwMDXRP8KHhobhbf09PjSSmAMJ1czIxBzrxz\nt1KpBH14RDVZXSydrs+L6mJ2gFOu7cAu6BlDnpcfUjjl2hwGuhaJE65bJzFRdsOvZvFhHKGrFeSE\nMB43UT311ueJ0bywTH2Ru6Iedo0bggQvSqvYPU+Dg4Pc5VoDA10T3O62YNdn1Y83vjj2MJxorGrp\n2ZVgYaCjoLn5+mtl16KxvErQ72HqPG7X0Kv1vhoaGmKgq4GBzgXNhgtj/TRN0wIphBuGC4AxyMXj\ncce19BjoKGhev39qrXESo3mdUmy2HYThg7NfWgl6wN714+bR6OHhYXaKqIGBzgWNBjrjbk0g+Ppp\nbk4ZN0IEuUKhgK6uLmSzWce19DrlpEhkRZKkhttHWTWD9+J91EmhpVH8EFp/NFpRlKrX7gMPPID7\n7rsP06dPR6VSwZo1a3DMMcdg2rRpDVV6WLRoEdasWYO+vj709/db/sy6devwla98BZVKBfvvvz+e\nfvrplh6r3xjommA+WTnd6WqeUgw6yAl+T1+au1s0UxSZU65E1Tq12GzU8Lm1Jj50ANCvjwBwwQUX\n4OSTT8arr76K73//+7jvvvvw6quv4i9/+QumT5+OY489Fj/4wQ/qPq8LFy7E5ZdfjgULFlh+f2ho\nCF/+8pfx3//935gyZQp27tzp7gP0AQOdC+qFC/NIVKPtubzmVzhyI8gJDHREzjgtTcG2ZxQG5hHe\nnp4ezJnkByCMAAAgAElEQVQzB7Nnz8aDDz6INWvWAABGRkbw2muv4c0333T02pw3bx4GBgZsv//Q\nQw/hnHPOwZQpUwAA++23X4uPxH8MdE1wuinC2J6r1QDjJa/DkTHItdKmjIjc00pZFQa95tj1KKX6\nVFWteu56e3tx8skn4+STT3bl9rds2YJKpYKPfOQjGB0dxZIlS3DBBRe4ctt+4VXVBeZA5HZ7Lq95\nFejM/WbdfB44QkfkvkbantlN2/J9Sa2o1SVi3Lhxnt2vLMt44YUX8NRTTyGXy+GUU07BKaecgsMP\nP9yz+3QbA50LJEnST3SFQsGT9lxecjsc+RFoGeiI/NPI+jwAyOfzbHtmgRtG6qsV6Lzc4Tp16lTs\nv//+SKVSSKVSmD9/Pl566aVIBTqO/TbB/GIT5UeGhoYgSRLGjx+PTCYTiTAHuBeOVFVFPp/H0NAQ\nNE3DuHHjkM1mI/M8EFFjxLRtIpFAd3e3vpC9p6cH3d3d+oaxcrmMXC6HXC6HQqGAUqmkt5PqpA9m\nnfRYm1Ur0LXaJUKMNFs566yz8Otf/xqKoiCfz+O5557DjBkzWro/v3GErkmi/VSxWES5XNaDXBTX\nR7Qa6Iwjcn6NTHKEjih8xHtSjOZ1WtszJ9rxMfmh1UB3/vnnY926ddi1axcOPvhgLFu2TL92L168\nGNOnT8ff/u3f4thjj0U8HsfixYsxc+ZMFx+B9xjomjQ6OopyuYxUKoXe3l59iiGKmg1HQQQ5gYEu\n/A65N46BS5SgD4MCYBVa2PaMnLDbONJqoHvooYfq/szSpUuxdOnSpu8jaAx0TUqlUujp6YEkSZGf\nNhBrAJ0yrxUMYmQyiECnKAoKhYKv90nU7jqp7RnX0NVn9xzt2bOHbb/qYKBrUiKR0ENQ1EeLnB6/\noij6FHN3d3coppj9OEGaHzcReY9tzzqT3Tl9eHgYkyZNCuCIooOBrknGF1yYGtw3q1agC2OQ8+N5\nDuPjJgozP86BYW57Vk+UrxFBGxoa4ghdHQx0Loj6G9Tu+MUUY6VSCWWg8aoHrXFKOYyPm4iqRaHt\nWZRncfzk5S7XdsdA5xKxPT+KJTrMU65hD3JeYZAjai9hbHsW9QEArzHQNY+BrklO239FgTh2Y5AT\nmz7CHGjcrJ/HIEfUOdj2LJxqnc855VofA51LohzoxMlreHgYqVQKmUwmEicqt+vnMcgRtSbKa8Tc\naHtWa9o2ys+N36yep5GREU9bf7UDBromtcMInSzLKBQKkGUZADBhwoRInXDcqp/HIEdEdtxYnxfF\npThBqBV6NU3j81gHA51LohTojEEunU4jk8lgcHAw6MPyXJCFkImovdRbnydKq4gRPaFUKnHa1oZd\noIvKtTVoDHRNiuIInTnIZbPZSJ9MnD7nDHJE5Be79XmyLOutpjq17Vmr+JzUxkDnErHLNYxEz1lF\nUZBKpSyDnFclQLxUL9AxyFGjovYeCBs+f9aM07bJZFL/OtueVbN7/ciyzHO3Awx0Lmm0fZYfKpUK\nCoUCVFW1DXJCFEYYrVgds6qqKJVKKBaLSCQSDHLkWC6X44gJ+aaT2p45UatLxPjx4wM4omhhoGtS\nWKdcxdC+CHLpdBrJZLLuGz4sx98I82PSNA3FYpFBjpqWyWSq1kDVGjER02VETjQyetmpbc/snqPB\nwUHWoHOAga4FxhAUdCBqNsgJQR9/M4wt1xjkyA3GERNje6lahWgLhULkL6Ru4ZSrPTfOr1Fue9YK\nFhV2hoHOJUEFIk3T9KlVTdMaDnJCFAMd8P76QAY58pLViEm5XIaiKEgkEvqFtFwud+z6J6rPi///\nKLQ9c4ojdK1hoGtBkCN0xiAHAKlUqqkgJ0Qp0BlH5GKxGHp7e8d8aiXymrgAWo2Y2F1IvW4rReHl\n9/k1jG3P6hFh04wjdM7wKugSv3a5moNcOp1GIpFo+U0XhUCnaRpKpRIKhQK6urqQSqWgaRrDHIWK\n3YXUeBG1Wv9kXuTOoNd+wvB/Gua2Zxyhaw2vhC0wvvC8DkReBTnzfYSROciJEblSqYRKpRL04RE5\nIi6ERk7LVhh324YZ19BFk9dtz1o1PDyMqVOnun677YaBzmVun9A0TUO5XEaxWATgTZADwjlCJ4Jc\nsVhEPB63nFoN2zFTtH3gu/di/T9e4tv9OVn/pCiKfiFtl92MnchuOjHM3Gp75vT1WWuEbp999nHl\nMbUzBjqXiBe+W4FOBDmxg66npwddXV2enbjDFOjMQS6bzVpOq/IiRm4rzs4HfQgAqqfFEokEgPCM\nllBzwnJ+dUOjbc+cfhCxu35yDZ0zDHQt8KIWnTnIZTIZT4OcEIbCyE6DnBCmEErktUZGSxRF4Whe\nCLX7c9/K+rx4PG57Ph8aGsLEiRP9ehiRxUDnIhGKmimdYQwzIsiJT+Z+CDIcWYVYJ4+dgY6ouYuo\nV7XJuIbOXqeeq+qtzzOuHwWAfD6PWCyG119/Hb/61a8wc+ZM5PN5dopwgIGuBeYTVywWa/hNG3SQ\nE4IIR80GOSKqjS2lwonP5/vMr1FN05DL5ZDJZPQPHtu3b8dTTz2FzZs349BDD8UxxxyDWbNm6b9O\nOeWUugMoixYtwpo1a9DX14f+/n7bn9u4cSNOOeUU/PjHP8bZZ5/t6mP1CwOdixoJRY1OL3rNz0Dn\nVpDjCB1RY1ppKcW+tuQlMborXqOzZs3CjTfeCAA4/fTT8bOf/QyvvPIKXnnlFWzatAkPP/ww1q1b\nV/d2Fy5ciMsvvxwLFiyw/RlVVfH1r38dH//4x916OIFgoGtBM2vozCU4gg5ygh/hyO31gQx0RO6o\n11KqXl/bRnYydipOR9dm9/yIc/wBBxyAU089FaeeempDtztv3jwMDAzU/Jnbb78d5557LjZu3NjQ\nbYdN8EmijdQKGMbuBsZaamHhZTjycqMHAx2RNxrtayvez7FYDJVKhdO2JjxXtcar19Gf//xnPPro\no3jqqaewYcMGT+7DL+FJFG3AKhSZG8eHLcgJXgQ6czHknp4eV2voidvhJ18i/9TahCHqZRpH9FhS\n5X2d+JidsjuPl8tlT9dWX3nllbjhhhuqridRFb5kESFWU66i9IeqqvoauSg0jncz0PnR1QLgyZEo\nLIyjeebaebU2YVjttm1HUQ4JfgmqBt3zzz+Pz33uc9A0DTt37sTatWuRSCRw5plnenafXmGga5Ex\nCMViMZTLZeTzeZRKpUgEObNWRrv8CnJGbhZzJvcdcm8cA5coQR8G+cT8Xmy2r227bsJol8fhp6Gh\noZZLlogRZCv/+7//q/954cKF+OQnPxnJMAcw0LlGrCWRZRmxWCxyQa6VThdBBDkiiq5O6GtLjanV\n9quVEbrzzz8f69atw65du3DwwQdj2bJlKJfLkCQJixcvrvrZqL+mGOhapGmaPiLX1dWFWCyGbDYb\n9GE1pdFp1zAEOT93uqqqqj9WInJXO/e15SxCfbUCXStdIh566CHHP/uDH/yg6fsJAwa6Fo2OjkKS\nJIwbNw4AMDIyEvARNc9pONI0DbIsI5/f2/cylUohmUwGcsLyI9CJIFcul9Hd3e3pfRFRNSd9bRVF\nQblcDm1fW66hq0/835mxj6tzDHQt6u3t1d+sYnogymodvwhyhUIBqqoinU4HFuTMx+UFVVVRLBZR\nKpWQTCYxfvx4yxMOEe3l10hUo31tAYzZgOH3aF7Q58moGhwcxL777hv0YUQCA12LYrGYfsIQo0VR\nHV6vNdolplbDFOQAb06S5lIzUVsPSdSpmm0Ob2535vZ5Jeof9P1gd90cHh7GtGnTAjii6GGgc1Er\nGwvCwOqYwxrkBLfLrTDIkVNRfZ93mrD0teVrpbZaZUtaWUPXSRjoWtRM+6+wMh572IOc4MbzbW7H\nFtbiz0Tknlp9bcVInl1JFWO7szCeF6MoqDp07YRXLZdFPdDJsoxSqQRVVZFKpdDd3d22JyxzSzIG\nOaLWtMOopZNpW1mWa27CsBoNjPrzEpTBwUHss88+QR9GJPDq1aJ2GaGTZRmVSgWapiGdTkcmyDXz\nfItyK/l8Xu8t62VrGSKKNqfTtsa+tsZwpyhKJK8LfuIIXesY6FwWtUAndq0qiqKvF0mlUkEflmON\nPN9e95Ylos7idBOGCHS5XM6y3Vmnn4NqncOLxSLS6bSPRxNdDHQuM/ZzDTMR5GRZRjqdRjabRalU\n0nfsRomTQCdG5AB2sqDaxAgLXx+N49Si9WheqVSCpmlIJBId39fWinjd2D1mlotyhoGuReYXYCwW\nC/UInVWQE48haqOLQP1jjsrmDgqPfD4fqS4EFA0itFltwhDtzjqpr60TUbseBY2BzmVhDUXGIJdK\npaqCnBDWY6/FbkTUOJXMIEeNyGQyjroQRGEknsJPkqQxm7GM07bGkGe1CUPsto2yeiO7UX98fmGg\na5FVKArTiV5RFBQKBVQqFdsgJ0Q10BmPWVEU5PN5yxFIIifOmbAIAPCfQ9V9Hc0L4I3roljOgmqx\na2tlxzhtawx7TjdhRG1E2S7QFYvFSK3pDhoDnQuMoSIsocgc5DKZTN03d1iOvRmNBFciJ84ef/GY\nr/3n0A/0KTPx4S2ZTNYtZ2GcMmtXxnMgVXPrvOp0E0aY+9pasQt0g4ODGD9+fABHFE0MdC4LOhQ1\nE+SEoI+9GaK/7PDwMLq7u9lvlTxlFfKA2qN5iqJAlmWui+pwXv0fN9sJIwqbMFiypDEMdC4wj9AF\nMeVqDnI9PT0NB5soBTpVVVEoFFAqlSBJEoMcBarWaJ6ocehkXZSbraYoPII4r9p1wjAvG/C7r62V\nWiN0DHTOMdC5zO9drsYg1+oIVRQCnaqqKBaLKJVKSCaTyGQyKBaLDHMUOrVG86zWRdm1mgriAkvu\nC8v/m10nC+NuW7tNGF4tHWBRYXcw0LnMr1CkKAqKxSLK5bLrU41hrCWlaRqKxSKKxSKSySTGjRuH\neDwOWZZ9P5YXvvUPOP5bd/p+v9Qe6q3NA+pfYMM4XRbG8wY542Ta1m7pgBuvw1qBbuLEiU3dZidi\noHOB8YUoAp1XJzcvg5w43jCdmI1BLpFI6EFOiMKoIlE9jazNs6tZxg4E4RWmc2ojjNO2VksHxEYg\nu5IqjbwO7aZcJ02a5PrjalcMdC7z6k0r1ox5EeSMwnLS0TQNpVIJhUIBXV1d6O3tHVOrCWCgo/Zm\nN5pnVGvxuznkhWU0r9O00zmqkU0YiqI4Gs2rNUJ31FFHef6Y2gUDnQvsCvS6ceL0K8gJQQckTdNQ\nLpdRKBQQj8dtgxxRp3IyZQvYL373qpRFVEeh/NLuz43TkipWo8riA4j5NcQp18bwSukBsdO1leBl\nDHLJZNK3XZxBBTpjkIvFYshkMvoQfy1BB1CiMGimnEqjoyjUnE4+PzkdzRMzMqVSCdu3b8dtt92G\no48+Gnv27OEH+gbwmXKBm/1czbs4/S7H4XdA0jRN77cK7G271NXV1fCFhKMDRGM1sgHDSWHadmgz\nFRQ+b+8zj+aJzj6SJKG3txdHHnkkNm/ejN/97nf42c9+hgMOOACzZs3Csccei2OPPRZnnnlm3Q4S\nixYtwpo1a9DX14f+/v4x33/ooYdwww03QJIkZLNZ3HXXXZg1a5Ynj9cvDHQeaCYUBR3kBL8CnSgI\nnM/nAQDpdBqJRKLhk14YN3IQhVmzo3l2baYY8mrr5BE6p8T5W5Ik9PX14bLLLgMAfOpTn8JLL72E\nd999F/39/Xj55ZexatUqnHnmmXVvc+HChbj88suxYMECy+9PmzYN//M//4Px48fjsccew6WXXor1\n69e7+rj8xkDngUZCkTnImXdx+s2PQCdG5FRVRTqdRjKZbOmCwIsJUeuaGc0ztjoT78NyudwRrc4a\nwefBXq3rTalUQk9PD4444ggcccQROOeccxzf7rx58zAwMGD7/Q984ANVf962bZvj2w4rBjoX2G2K\nqCVsQU7wMtDJsoxCoQBFUVwJcgLX0RF5o5HRvEqloi94Z6uz9/Hc5Iz5NeFnb+B7770Xp59+uuf3\n4zUGOg/UChhhDXKCF+FIURTk83l9nUQ2m3X1TcpAR+Qvq6D3413/jlgspq9tYquz97XzY2tVveUy\nXj93Tz/9NFauXIlnn33W0/vxAwOdC6xG6Mz9XFVVRalUsi2QGxZuhiNzf1m3gxxFwyH3xjFwiRL0\nYZDHPrvvYsuvd3qrM37YrM0u0PnxvPX392Px4sV47LHH2qI8CgOdS4xBKBaLQVH2XsDqdToIG6sw\n2ihjN4tUKoVMJuPpSZkjdETh1a6tzhoRteP1k12gKxQK6Onpafm27a4Nb7/9Ns455xz86Ec/wmGH\nHdbS/YQFA50HRCgqFAqRCXJCK+HI7yLIgp+BTkyZE1Hz7EKeVb2yqLc644fN5gwODmLChAlN//vz\nzz8f69atw65du3DwwQdj2bJlKJfLkCQJixcvxre//W3s3r0b//AP/wBN05BIJLBhwwYXH4H/GOhc\nYuzhWqlUIMsyYrFYZIKcENWSK16fNI0jrclk0tP7IupErRRHDnurszAcQ1jZjdC1Gugeeuihmt+/\n5557cM899zR9+2HEQOcSTdP0ETlxUslms0EfVsMaCXTmkBNUePXyZGnsKRulkVaidhHWVmdOcYSu\nNq8CXSdioHPJ6OgoVFVFb28vJEnCyMhI0IfUFCeBLmzrAr2YcmVP2c71vw/PxrTPbw76MKiGqLU6\n4widPbtANzQ0xEDXIF6hXNLb26tvJhAnjyiqFY6Mo1VdXV2hCTluBjpjKzJJkix7yn4i/QXgax90\n5f6IyD1hbHXGEbrmMNA1LvircZswvumj3o7KfALqlNEqEeQ0TbNsRfaJ9BcCPDoiaoZXrc4aObdH\n8TrgFxGkzYaGhjB16tQAjii62u+qHBBzoBOjRlF7IxuP1xjkYrGY5WhVGLQ6QlevgwWDHFH7abXV\nmTnk2U3ZRvE64KdaU66zZs0K4Iiii4HOI1GtjSaOWxRBBoBMJoOurq7QnpSarZ1nLHxs18GCYY6o\nczQzmqcoSs1WZwx0tdldJznl2jgGOpc00881bDRNgyzLAIBisWg57RhWjTzXxnp5doWPGeSISKg1\nmidmLWq1OhNf65RWZ43ipgh3MNB5JGqBTqwfEyNd2Ww2MuU5nJ4YjfXy7AofM8gRkRO1iiMb1xjn\n83n9753Q6qxRtaZc26Edl58Y6DziRgstP1itHxsaGgr6sBpSLzw7KbPCIEdErbKbsv3xrn8f08+2\nnVudNYJlS9zDQOcS8wtSrJ0IKxHkZFkes34saqOLdsdrLrPCIEdEQfjsvovHfK1dW501otZ1RpZl\nduVpEAOdR8IaiowbAVKplOVGgLAeu1Pm3blWZVYY5IgoSO3c6qxR5mOO8vUnSAx0Lgl7KFIUBcVi\nseZGACFsx16PsY+uLMvI5/MAYF8UmIgopKLe6qwR9XYAh/GYw4yBzkXGIBSWNXTGHZ12GwHMohjo\nVFXFyMgIVFVFT08PiwITUduIWqszp+wCHUu9NIeBziNBhyLjjs5kMukoyAlBH3sjFEVBPp+HpmlI\nJpPo7u5mCRIi6ghhbHXmhpGREWSz2aAPI3IY6DwS1AidcUdnMpm03AhQTxQCnXEtYHd3t74m0IhB\njog6TRhanTlVa4fr+PHjXb+/dsdA5yJjEPJ7l6uT0hxOhTnQWU0hS5Kkd7UAGOSIiMz8anXWCJYs\ncRcDnUf8CkXm0hxWOzobFZb1f0bmkUfjFLJ4nhnkiIicq1Uc2aiRVmeNjObZBbo9e/awqHATGOhc\nZHxheh3ojKU54vG4K0FOCNMInTGw2o08frLngoCOjoiovdSasnXa6swc8hodzeMIXXMY6DxiLKXh\n5toDc401q9IcrQpDoHMSWDkiR0TkD6etzowhr16rM1FmxWx4eJiBrgkMdC4yj9C5SdM0vd8qsLfG\nWldXl2c7koIKdMbHKUkSa8kREYVUvdE8oVarMzGAEIvF8PLLL+Ooo47C0NAQDj30UL8eRttgoPOQ\nWIvWSpN7c7HcdDo9psaa24Latl6pVGo+TgY5IqLwc7o2L5/P67toR0dHcdlll+H1119HX18fDjnk\nELz++us47rjjcNxxx2HKlCmOrk2LFi3CmjVr0NfXh/7+fsufWbJkCdauXYtMJoP7778fs2fPbu6B\nhoyzwmTUlFZ3ulYqFYyMjCCXyyGVSmHcuHFIJpOeBy6/p1xlWa77OBnmiIii6+zxF+u/BNGjNplM\nYuLEifjtb3+LrVu34qMf/ShOPfVUDA4O4rbbbsOJJ56I/fbbD1u2bKl7PwsXLsTjjz9u+/21a9fi\njTfewJ/+9Cfcfffd+NKXvuTK4wsDjtC5yK32X7Iso1AoQFEUpNNpX0KckV+BzlhLLp1OW/aVZZAj\nImpPVmvMk8kkCoUCPv/5z+OII47Qv75jxw7ss88+dW9z3rx5GBgYsP3+6tWrsWDBAgDA3LlzMTQ0\nhB07dqCvr6/JRxEeDHQeajQYiSAny7JtwPGD14HOWEvOrq8sgxwRUXuxKm5sV4fOXLbErcC1bds2\nHHTQQfrfp0yZgm3btjHQUbVmR+iMI1WpVCqwICd4tUPX2I7Mrq8sgxwRUXsxBznB7hozPDzsWacI\nq2tyGNqduYGBzkP1Ap2iKCgWizVHqoLgxQ7deu3IGOTa2yH3xjFwiRL0YRCRz2qFOTuqqrpWV9Vs\n6tSpeOedd/S/b926FZMnT/bkvvzGQOciqxE6q44LVu2rrGrxBEmE0VbCnbmLBYMcEVFnsAtyZuZr\njBvLfcQMk5UzzzwTK1aswHnnnYf169djwoQJbTHdCjDQeSoWi0FR3h+VME45mttXhU0r6+jMxY9Z\nFJiIqHM4CXP1BgyaHUw4//zzsW7dOuzatQsHH3wwli1bhnK5DEmSsHjxYpxxxhn45S9/icMPPxyZ\nTAYrV65s6n7CiIHOZcYgZFyLVm/KMWyaCXRWxY9ZFJiIqDM4HZUD7Efi7LpHOPXQQw/V/Zk77rij\n6dsPMwY6j8myjMHBQds+pGHVzA7dfD4PVVXR09NjWfyYYY6IqP00EuSM7Ha4jhs3rtVD6kgMdC4T\n6+bE2jEAllOOYec00DmpmccgR0TUnpoNc7VKlni1w7XdRStlRECpVEIul0M8HkdPTw+KxWLkwhzg\nbIduvVIrDHJERO2p2SAn1Ap0EyZMaOm2O1X0kkYEiLVjohFxFNkFOic7dBnkiIjaV6thrhYGuuYx\n0LkslUrpO1tb7eUaJHOgM2/sYJAjIuosbgY5jtC5j4HOB253XPCL2KEr1gPabexgkCMiam9uj8rZ\nXRf37Nkzpu0XOcNA5zLjC1SSJFcK9AZFlmUMDQ0hHo+zlhwRUQfyanpV0zTL8iTDw8OYNGmSJ/fZ\n7hjoPOZ1o3u3iVpypVIJAJDNZllLjoiow3i5Tq6WoaEhjtA1iYHOZVbtv6IS6CqVCvL5PAAgmUxC\nVVWGOSKiDuNHmOMaOvcx0HnMrp9rmFjVkjOO0gEMckRE7c7PUTkGOvcx0LnM/AIN805XYy25dDpd\nVUtOjCwyyBERtT+/p1hrBTpOuTaHgc5jYZxyNdaSS6VSyGQyY95Ynx63MKCjIwren7/2QQDA5Bt+\nG/CREHkrqLVydkZGRtj6q0kMdB4LU6BTVRXFYhGlUolFgYmIOljQQc5uhE7TtMj0PA8bBjqXhXFT\nBIsCEzWGI3PUzv5j223I5XKIxWKIxWKIx+OIxWJ6qS2v2V0Tg75WRh0DnQeMIS7ITREsCkzUmGmf\n3xz0IRB5RozKiaLxqqpCURRUKhWoqqrXhhMBT/xyO+SJ0Tm7241i3dYwYKDzWCwWQ6VS8fU+NU1D\nuVxGoVBALBZjUWAiBxjmqJ39dM+9+p9FmIrFYlXXBlVV9V/GoGcMd8bRPLfJsszp1hYw0HnAPELn\n1zCyKApcKBQAAJlMZkwdOYBhjsiIQY7a2Y93/Ts0TYOiKHqfcRHoRKgTRGgzEiN54lepVIKqqvq/\nNY7mOZ2ytVs/Nzw8jPHjx7f4iDsXA53H/Ap0Isipqoqenh4kEokxbxgGOaL3MchRu/v58Eo9ZIkp\nVfG7ccoVeH8zgrhuiGAnSRLi8XjVyFmtKVvzdK3VaJ5doBscHGQNuhYw0HnA3M/Vy0BnVRSYQY7I\nHoMctbtV730fqqpidHQUAPSQJYKZCFlifbcYfTMGPmNNUvNontMp23K5rK/LM07Z2q0rZ1Hh1jDQ\necyrQGcsCpxKpaqKAgsMckTVGOaona0e/WHV38VImphuFR2AVFWtCnfxeLxqVscc7kQAUxRFD2jN\nTNkqigJZlvXbKxQKiMfjeP755zF58mTs2bOHga4FDHQeE4HOboi5UcaiwKwlR+QMgxy1O3OYA6pH\n0ozrqY0hT4ykic0P5qAnri9uTNmKYyiVSvrPq6qKlStXYt26dSgUCjjggAMwMjKC2bNnY/bs2Zgx\nYwaSyWTdx//YY4/hyiuvhKqqWLRoEb72ta9Vff+dd97BhRdeiMHBQaiqiuXLl+P0009v4pkOL6nO\n6BGLwjRBfAoRdu/ejQkTJowJXo3QNA2FQgGlUgnJZBLpdJpBLiDKqSdgx4ndQR9G6PU9X6r6+8Al\niu/HwCBH7c4qyDXDGNCMv4yBzLwBwmrK1pwprKZsS6USJEkaE9TuuusubN++HZMmTcLmzZuxefNm\nvPnmm/jFL36B0047zfbYVVXFkUceiSeffBKTJ0/GSSedhFWrVmH69On6z3zxi1/E8ccfjy9+8Yt4\n7bXXcMYZZ+DNN9905bnzme3IEEfofNBKP1fWkgsX5dQTAOwNKwx14cYwR+3OrTAH1N78YBzJE9Ou\nxpDX6JStGA0Uvwvlchnz5s3D2WefrX8tn8/XHQzZsGEDjjjiCBxyyCEAgM997nNYvXp1VaCLxWIY\nHh4GsHfzxZQpU1p8xsKHgc4DbnSLMNaSi8fjrCUXEvEnN+mhjsKJQY7anZtBrha7KVvzmjixLs84\nZZKEzUsAACAASURBVGsc0TP+m1KpBEVREIvF9H8vrpHvvvsuPvjBD1YdQ09PT93j3LZtGw466CD9\n71OnTsWGDRuqfua6667Dxz72Mdx2223I5/N44oknWnlqQomBzgeNBDpRS058KmEtufCJP7kJADD5\nyeqvi4buFAwGOWp3fgW5esS0q3GQwTxlW6lUqqZsJUnSCwdns9mq3a6yLOPRRx/F2rVr8fnPf77h\n47G6vpoHVh5++GEsXLgQX/nKV7B+/Xp84QtfwKuvvtrwfYUZA50Hmh2hE0EOAGvJRZBV/0+GvPcd\ncm/ck3V0DHLUCcIS5uzYTdmKjXyyLOujcrt27cIFF1yAo48+GkcccQTWrFmD6dOnY/PmzRg3blzD\n9z116lS8/fbb+t+3bt2KyZMnV/3Mfffdh8cffxwA8IEPfADFYhE7d+7Efvvt1+QjDh8GOh/UC3Sy\nLCOfz0NVVdaSazMMed5imKN2F/YgV4uok5pIJJDJZPTrWnd3N6666ir88pe/xMMPP4ydO3fiueee\nw3PPPafvbl24cCF6e3sd3c9JJ52E119/HQMDAzjwwAOxatUqPPzww1U/c8ghh+CJJ57AhRdeiNde\new2lUqmtwhzAQOcL424gI2MtuXQ6je7ubga5DsCQ1zoGOeoEUQ1zYlROdC4yr//+85//jO9///uY\nM2cOfv3rXyOdTiOfz+OVV17Biy++iBdffLGhnq7xeBx33HEHPvaxj+llS2bMmIHrrrsOJ510Ej7x\niU/gX//1X3HppZfi5ptvRiwWww9/GM3nthaWLfFIqfR+yYZCoQBN0/TFncZacqlUCqlUikGOxoh6\nyDOXLQFaL13CIEedIKpBTqwBLxaLSCaTYwYpZFnG3XffjdWrV+OWW27BiSeeGODRRhbLlvjNOM0q\nRuhUVUWxWESpVGJRYKqLI3nvY5CjThHVMGcclctkMmNG2H7/+99j6dKlOO200/D0009bbvaj1jDQ\n+USWZQwNDSGZTDLIUdM6MeQxzFEniGqQEyW2xECFeQ14uVzGTTfdhGeffRZ33nknZs6cGeDRtjcG\nOo+IUTlRFBgAiwKTJ9o15DHIUSeIapAD3l8HDmDMqJymaXjxxRfxta99DZ/97Gfxq1/9qqF1cdQ4\nBjqPlEol5HI5xGIxpNNplEolvpjJN1EOeQxy1CmiGuZEByPRU9w8KpfP57F8+XK89tpr+NGPfoRp\n06YFeLSdg5siPDIyMgJJkpBIJKAoCkZGRjBhwgTbn+dIHQXBy5DXzKYIhjnqBFENcsD7pUjEYIVx\n+ZCmafjNb36D//f//h+++MUv4qKLLmqphzlZ4qYIv6XTaSjK3ouXk8LCawoPjPkaQx55LSwjeQxy\n1CmiGuY0TUOxWESlUkEqlRpT+H54eBj/9E//hN27d+PRRx/FgQceGODRdiaO0HlElmU90Gmahj17\n9mDixIljypM0iiGPgtBMyHMyQscgR50iqkEOeH9ULh6PI5VKjRmV+9WvfoXvfOc7uOaaa/CZz3ym\n5esc1cQROr8ZX9Buvrg5kkdBcHskj0GOOkWUg5xxVC6dTo8pNbJr1y58/etfRzwex2OPPYZ99903\noCMlgCN0nlEUBbIs63/fs2ePZbkSrzDkURCMIc9qhA4A4k9u8utwiAIV5TBXqVT0tl3m4veapuE/\n//M/cdttt2HZsmU4/fTTOSrnH9snmoHOI6qqolKp6H8fHBxENpsd0wLFTwx5FATl1BMAMMhR54hy\nkBMF8BVFQTqdHnPNevfdd7F06VIceOCBuP766zFu3DjPjmXr1q1YsGABtm/fjng8jksvvRRLliwZ\n83NLlizB2rVrkclkcP/992P27NmeHVMIMND5zRzohoaG0NPTE7rq2Ax5RETuiWqYq9e2S1VVPPDA\nA1i5ciW+973vYf78+Z6Pym3fvh3bt2/H7NmzMTo6ihNOOAGrV6/G9OnT9Z9Zu3Yt7rjjDvzXf/0X\nnnvuOVxxxRVYv369p8cVMK6h85v5hR6LxerudPWbqqp4ZOfdY3rKMuQRETUmqkEOqN+2680338TV\nV1+N4447DuvWrUM6nfbluCZNmoRJkyYBALLZLGbMmIFt27ZVBbrVq1djwYIFAIC5c+diaGgIO3bs\nQF9fny/HGCYMdD5xUrrEL2Khq/gkZlzbp2kaVo/+EKqqAth73JIk4azshUEeMhFRaP3oz7cjl8sh\nHo/rv6JQf83YtiuZTKKnp6dqMEJRFNx99934+c9/jltuuQUnnXRSYMf61ltvYfPmzZg7d27V17dt\n24aDDjpI//uUKVOwbds2BjryThgCnajuLRa6GluRaZoGVVXHBDnh58MrUSwWIcuyXhn8U70XBfEw\niIhCYfXoD/Vzp6IoUBQFpVJJP48aA148Hh9zXg1SrbZdAPDaa69h6dKl+Ju/+Rs8/fTTSCaTQRwm\nAGB0dBTnnnsubr31VmSz2arvWV1Xw/Ic+42BziPmF1SQgU6sjcjn84jFYujt7dUXuoqTkaZp0DRt\nzAnH2OIlmUyit7dX/77VFANH8oio3RnPfZIk6YFNEOdTEfLK5TIURYGmaWNCXiwW8zWA1GvbVS6X\nccstt+CZZ57BHXfcgaOPPtq3Y7MiyzLOPfdcXHDBBTjrrLPGfH/q1Kl455139L9v3boVkydP9vMQ\nQ4OBzkPGECdJkv6pzU9i67mmafqmDONxiZOMJEljikWKofiuri5ks1lHUwgMeUTUzpyslRMfjGOx\nWNVGOONInizL+mieXyFPURT9g73VOf3FF1/EV7/6VXzmM5/BE088EYr+4xdffDFmzpyJK664wvL7\nZ555JlasWIHzzjsP69evx4QJEzpyuhXgLldPlctlPTiVSiVUKpUxw8VeEW9csfXc+CnMOL0qvmb8\nnizLKBaLiMViSKVSnrypGfKIKEq82vRgHMkTv1RVRSwWs5yybfY+xKicVduuQqGA5cuX45VXXsGK\nFStw2GGHufXwWvKb3/wG8+fPx6xZs/SQ/N3vfhcDAwOQJAmLFy8GAFx22WV47LHHkMlksHLlShx/\n/PEBH7mnWLYkCJVKRR+VE6Ndvb29nt6n2K1k3rkK1F8nJ4KcpmmW9Ye8pGka1+QRUSj5vYPVGPKM\no3rGkCf+XG/mpF7brt/+9rf45je/icWLF2PhwoWR2MzR4RjogmAMdGLq06sijJqmoVAooFQqobu7\nu+qNWy/IKYqiF5K0+vQWFIY8IgpSmEqRmDdfiF/GNXzmkbxabbtGRkZw3XXX4b333sPtt9/esevO\nIoiBLgjGQCfLMnK5HMaPH+/qfZh3rqbTacc7V1VV1aeCrRbHhhGnaonID2EKc3aM53hjyBPX9Vgs\nhu7ubhSLRX0nq6ZpeOKJJ/Av//IvWLp0KT772c+G/rxPVRjogiDLMhRFAbB3FGxkZAQTJkxw5bbF\npgUxlG6cIm1k52oikUB3d3ekh9kZ8ojILVEIcnbEkhtFUfQyI4qiYPny5bjnnnswc+ZMAHvLqSxf\nvhwf/OAHQ9e9iOpioAuCMdCpqorBwUHss88+Ld+uKEECoKqdmNXOVXOQM+5cNa+naCcMeUTUiCgH\nOWPbrkQiUbV2Wnx/1apV+OlPf4qDDjoIuVwOL7zwAgYGBjBz5kx87nOfw9KlSwN8BNQAtv4KgvEN\nZdyY0Ozwtljc6mTnqjHMGXeuSpJkWUSy3bB8ChE5FeUwZ2zb1dPTM2Yz2/bt27F06VL09fVh1apV\nVct+RkdH0d/frw88ULRxhM5DotaQsGfPnqo2W06pqop8Pq8vbjU2TW5k52oqlUJXVxfXSxgw5BF1\nrigHOXPbLuN1Adh73XjggQewcuVK3HDDDfjwhz/Mc3974AhdEFrtFqGqKorFor5z1dxzNYo7V8OG\nI3lEnSnKYa5e26633noLV111FY499lisW7cO6XQ6iMMkn3GEzkOqqqJSqeh/HxoaQiaTqVvfzbhz\nNZlMIp1OOw5yUdy5GgUMeUTtIcpBzjgqZ3V+VxQF99xzD372s5/h5ptvxsknnxzg0ZJHOEIXBvVG\n6Mw7V8eNGzemBInTnatOW3WRMxzJI4q2KAc5oH7brj/84Q+4+uqr8ZGPfARPP/20vsuVOgdH6Dwk\nApowMjKir3Uwa2Xnqtjd1O47V8NGPO+SJOn1/xjyiMInymGuXtuuSqWCW265BU8//TRWrFiBo48+\nOsCjJR9whC4MYrHYmBE6WZaRz+f1HUrGN6to/2IMcnY7V612N5E3xPpEVVXHbDThSB5ReEQ5yAHv\nVzawG5XbvHkzvvrVr+Kcc87Bk08+2fbVC6g2jtB5rFQq6X/O5/P6aI5Y1Mqdq9Hh5vpEhjwib0U5\nzGmaVrNtV6FQwPXXX4+XX34ZK1aswGGHHRbQkVIAWFg4KOVyWR+VE7WCJEnSF7Wm02nHQU5RFJRK\nJciyzJ2rPjIuRPayswZDHlHrohzkgPf7fnd1dVVdH4C956Lf/e53+MY3voFLL70UF198MZfYdB4G\nuqCIQKdpGkZHR/XRnWZ3rlrVGyJvGKe1Y7EYUqmU71MaDHlEzkU5zIkyVbIsWy6hGRkZwbe+9S3s\n2LEDt99+O6ZMmRLQkVLAGOiCUi6XUSwWUSgUIEkSYrEYent7AXRez9UoqbVOLkiapuFTvRcFfRhE\noRLlIOekbdeTTz6Jb3/727j66qtx3nnnheJcRIFhoAvKrl27oKoq0um0vi5CBDonO1fj8XggI0Od\nKop1/BjyqFNFOcgB1W270un0mFG53bt349prrwUA3HTTTdh///09PZ5FixZhzZo16OvrQ39//5jv\nP/PMMzjrrLMwbdo0AMDZZ5+Nb37zm54eE43BQBeUUqmkhzZZlpHL5ZDJZKp6utrtXBUjQ+Q9v9bJ\n+YVTtdTuohzmjB/arZbRaJqG1atX4+abb8Z1112Hv/u7v/Plg+Wzzz6LbDaLBQsW2Aa6f/u3f8Mv\nfvELz4+FbLFsSVDi8bg+EifKkIyOjiIej1f9Ep/UuHPVX+Z1clZtdKKI5VOoXUU5yAH123Zt374d\n11xzDfbff3888cQTGD9+vG/HNm/ePAwMDNT8mUbaV5K/GOg8JkKc2PDQ29urf01RFJTLZf178Xgc\nyWQy0iNDUSJOrCJEm0sDtBuGPIq6R3bejUqlgng8HrnzZL22Xaqq4sEHH8R9992HG264AX/9138d\nyg/169evx5w5czB58mTceOONmDlzZtCHRP+Hgc5jl1xyCf7yl7/g+OOPxwknnIATTjgB++23H/bs\n2YMbbrgBn/70pzFnzhx0dXVBVdWqkGcexYvFYqF8g0eNcTdZVNbJeYUhj6Lg58Mrqz4EK4oCAGPO\nkeb1yGFhHJWzKhA8MDCAq666CscccwzWrVuHnp6eIA6zrhNOOAEDAwPo6enB2rVr8alPfQpbtmwJ\n+rDo/3ANncc0TcPOnTuxceNGbNiwARs2bMCrr76KoaEhzJ8/HxdccAHmz5+PbDY7Zg2FoiiQZVk/\nkQFjT2BR+5QaJPOuYfNuMrLHkEdBsJteNS5hMf4CwhXy6rXtUhQF9957L37yk5/g5ptvxsknnxz4\nOWlgYACf/OQnLdfQmR166KHYtGkT9tlnHx+OjP4P19AFRZIk7L///vj4xz+O3bt3Y+XKlZgzZw4u\nv/xy7N69Gxs3bsTdd9+NXC6Hww8/XB/JmzVrFpLJZNWmCDGCV+tTKtfejSXWyRUKBcTj8bZZJ+cn\njuSR32qtlRMhLRaLVfW9Ni9nsTpHxmIxX2Y76rXt+uMf/4irr74aH/7wh7Fu3Tokk0lPj8cp8Txa\n2bFjB/r6+gAAGzZsgKZpDHMhwhE6n7zwwgv48pe/jBtvvBHz5s0b831FUbBlyxY899xz2LhxI15+\n+WWoqoqjjz4ac+bMwYknnoijjjqqKoiIN55xFE9RFMRiMctPqZ3IuE7OqiwAuYshj1rl9qYH4wdh\n8UvTNM+WtJjbdpk/ZFcqFdx666146qmncMcdd+CYY45p+T7dcv7552PdunXYtWsX+vr6sGzZMpTL\nZUiShMWLF2PFihW46667kEgkkE6ncfPNN2Pu3LlBH3anYdmSMDCWKnHys+VyGf39/fp07ZYtW5BK\npXDcccfpI3kHH3xw1Sc/UazYfAIzhryurq62X49nXCfHNmn+Mk4zdXd347P7Lg76kCgi/NrB6lXI\nM7btSqVSY0blXnrpJVxzzTU4++yzsWTJEn7ApGYw0LUD0T5s06ZN2LhxIzZu3Ih33nkHEyZM0Efx\nxKYLq/V4xl/tuunCGCbYJs1fxqltuwuawJE8MgpDKRJjyBN/dnqeNH6ATKfTY3bMF4tFXH/99Xjp\npZewYsUKHH744X4+NGovDHTtStM07Nq1Sx/F27hxI3bu3IkpU6boo3hz5syx3XQhfsmyrH9C7erq\nCsWC4kaYu2sYe+WS99yY2mbI60xhCHN2nHwYFlOsyWTSsm3X+vXr8Y1vfAMXX3wxLrnkEp6XqFUM\ndJ1E0zS88847+nq8F154AblcDocddhiOP/54nHjiifqmC3MdJCe7xsJ2QhKFgblOzn/G9UJelIBh\nyGtfYQ5ytRgrEJTLZX0DQTwex6uvvor+/n4cf/zx+Ku/+issX74c7777Lm6//XZMnTo14COnNsFA\n1+nEpgtROqWRTRfm8imSJFWN4gW16YLr5IJjHBGtN73qNoa8aItqkBOs2nYBe8+xv/vd7/CDH/wA\nmzdvxptvvokpU6bgox/9KE488UQcf/zxmDVrFlKpVMCPgCKOgY6qmTddbNy4EVu2bEF3dzeOPfZY\nvQhyM5suvA55XCcXLGOR1LD0G2bIi4aohzlVVZHP5wEA6XR6TPmjPXv24Nprr4WiKPjOd76Dd999\nFy+88AI2bdqETZs2YWhoCG+99VYAR05thIGO6tM0DblcTt90sWHDhqpNFyLk7b///mPWiaiqWjWK\n58WmiyBHhWjvxaxUKqFSqURiRJQhLzyiHuTqte3SNA2/+MUvcNNNN+Gf/umf8IlPfMLyvSHLcig+\nAFGkMdBRc8ybLp5//nm89957mDx5sr4eb/bs2ejt7W14Z62oz+QkFIh1ckB4RoU6hTFIJxIJdHd3\nRzJIa5qGT/VeFPRhdJyohznjiLTVqNz27dtxzTXXYN9998X3vvc9TJgwIYjDpM7BQEfuEZsuxHq8\nF198EaOjo/qmC9HpwjwV2symC66TC5YxSFtdzKKOo3jeiXqQq9e2S1VVPPzww7jnnntw/fXX4yMf\n+QjPTeQHBjrylnHTxcaNG9Hf3w9N0zBjxgx9JO/II48cM7JmDnmyLEOSJL0cgKIoluUAyFudHKQZ\n8loT9SAHVLftsiqB9Pbbb+Oqq67CjBkz8O1vfxs9PT0BHSl1IAY68pdYc/Lyyy9XdboQmy5EyDNv\nupBlGW+88QYmTZqkf11VVbYz84lxrVAikWCQ/j8Mec5EPcwZy/BYfZBRFAX33XcffvzjH+Omm27C\n3Llz+f4gvzHQUfDMmy42btyIt99+G+PHj8ecOXMwceJEPPDAA5gyZQoeeeQRfTTPvLNWlmU95BnL\np7RDp4sgiVEJSZLacnrVbQx574t6kAP2vv7z+bzthqstW7bgqquuwvz583Httdfq5UqIfMZA55XH\nHnsMV155JVRVxaJFi/C1r32t6vvlchkLFizApk2bsN9+++GRRx7BwQcfHNDRho+maXjhhRdwxRVX\n4NVXX8Vpp52GgYGBMZ0umtl0wZDnjLltkbmZODnXiSEv6mFO0zQUCgXbtl2VSgW33XYbnnjiCdxx\nxx2YNWtWQEdKBICBzhuqquLII4/Ek08+icmTJ+Okk07CqlWrMH36dP1n7rrrLrz88su488478cgj\nj+DnP/85Vq1aFeBRh8uNN96I66+/HldddRWuuuoqpNPpqk0XotPF6Ogopk2bppdOsdp0YVUEGQh/\np4ugGKdXWc/PO+0a8qIe5IC9Ya1QKNguL+jv78fSpUvx6U9/GldccQV311MYMNB5Yf369Vi2bBnW\nrl0LALj++ushSVLVKN3HP/5xLFu2DHPnzoWiKJg0aRLee++9oA45dJ599llMmzYNkydPrvlzqqqO\n6XShKApmzpzZ0KYLq5DXiSNSogxJLBZDKpXi9KrPoh7yoh7mVFVFoVCAqqqW7QKLxSJuuOEGvPji\ni1ixYgWOOOKIgI6UaAzbixU/brRg27ZtOOigg/S/T506FRs2bLD9mXg8jgkTJmD37t3YZ599fD3W\nsJo3b56jn4vFYpg+fTqmT5+OBQsWAABKpRJeeeUVbNiwAXfeeSf++Mc/IplMVnW6OOSQQ5BIJPRp\nFNHOTIzilUol5PP5jtl0YbyQiUXf5B+x6P5Hf759TIHaKIS8qAc5c9uunp6eMaP8zz33HP7xH/8R\nCxcuxPLlyzmiT5HBQNcCq9FNcwgw/4ymaW0ZFILQ3d2tB7e///u/1zddvPDCC9i4cSP++Z//uWrT\nhfjZAw44AMlkUr8d86aLSqVS1c5MbLyI8no8c7s084WMvCem97q6upDNZscEBauwFJaQF/UgB1R/\nmMlkMmNGpUdHR7Fs2TJs27YNP/3pTzF16tSAjpSoOQx0LZg6dSrefvtt/e9bt24dM3V40EEH4Z13\n3sHkyZOhKAqGh4cxceJEvw+1I0iShGw2i/nz52P+/PkA9gaZ3bt366VT/uM//gPvvfceJk2apAc8\nsenCeII3brqQZRmlUimSmy7EaGStIEHeMgaJnp6ehtZhhSHkRT3MOWnb9fTTT2PZsmW48sor8fnP\nf97z98iiRYuwZs0a9PX1ob+/3/JnlixZgrVr1yKTyeD+++/H7NmzPT0mij6uoWuBoig46qij8OST\nT+LAAw/EySefjIcffhgzZszQf+bOO+/EK6+8gjvvvBOrVq3Co48+yk0RAdM0DVu3bq3qdDEyMvL/\n27v3oKjO8w/g311YFVgNYMMqLoIky8UGRWDFa6exMY4NAjpmpLTijI7UtkQsaoKXDDFObCLEWrOM\npWNLbZ2I1YnFSth0BkuCSdmFGK/VCURdkUTpqKARZWH3/P7wd073hqCBvcj3M+OMC2eGd12EZ9/z\nfp8H0dHRUrJ20qRJvYYubAs9QRDsdvHEW7XeUORZLBbcv3+/13NCNLjcGToZjCLP1ws5oO+xXbdu\n3cKmTZtgNpuxc+dOhIWFuWVdx48fh1KpRE5OjsuCrrq6GjqdDlVVVTAYDMjPz0d9fb1b1kZej6GI\nwaLX65Gfny+1LSksLERRURG0Wi3S0tLQ1dWFpUuX4osvvsDo0aNRUVGBqKgoTy+bHFitVjQ1NcFg\nMEiTLiwWC+Lj46WdvNjY2McKXbg7WWvbHNXVjgQNPm/o6fddijxfL+Zsjxj0tit39OhRlJSUYPPm\nzUhPT3f7/xGTyYQFCxa4LOhWrVqF559/HkuWLAEAxMfHo7a2FiqVyq1rJK/Ego7oUZnNZil0YTQa\n7UIXYrI2MjLSrlgTQxeO7VNkMpndLt5ghC5sD3z31hyVBldfkwY8ra8i79CtPV61y/w4+hrbdf36\ndaxfvx4hISEoLi5GcHCwR9b5sIJuwYIF2LBhA2bMmAEAeOGFF7B9+3YkJSW5e5nkfZhyJXpUw4YN\nQ1JSEpKSkrBq1Sqn0MXWrVthMpkwatQoTJkyBSkpKVLowjFZ+7DQxUAUeeKtJUEQHvmcFn13tsW0\nQqFwaoTtLXo7k3fo1h5YLBaYzWav2GV+HH0V01arFRUVFfjDH/6A3/zmN5gzZ45XvkZA/wJ3RI74\nU5+onx4WumhsbITBYLALXdhOuhg1apRT6MJqtUq7eGaz+bFCF7y96nm2ZxV9sZgWizzH1j7iGxBf\nKPLEXTk/Pz+XwZ+WlhYUFBQgNjYW//rXvxAUFOShlfaPWq1GS0uL9NhV4I7IkW/95CHyMjKZDKNH\nj8a8efMwb948APahi08++QQ7d+7EnTt3MGHCBOk8nhi6sJ0H2VeyVrxlKxZstjtCTK+6X1/ntHyV\neLtVLpc/tMjr6emBTCbzmvOirsZ2WSwWlJeXo6KiAjt27EBqaqrXvEbiv6kr6enpKC0txZIlS1Bf\nX4/g4GCen6M+8QwdkRuIoQvbSRc9PT2Ij4+XdvLi4uL6FboQ/8/KZDIMHz4cCoWCxZyb9XVOayhw\nPEpge160tzchA6mvsV1ffvkl1q5di5kzZ2LTpk12b548LTs7G7W1tbhx4wZUKhW2bNkCs9kMmUyG\n3NxcAEBeXh70ej2CgoJQXl7O83MkYiiCyNvYhi4aGhpw4cIFDBs2DAkJCdJOXlRUlFQstLW1oba2\nFvPmzZMaI4u3bcVfoo7tU2hgWa1W3L9/v9dB7kNdb0XeQJ4XFV8Di8Xish1Pd3c3dDodPvroI+h0\nOkyaNGkgnhqRt2BBR+6j1+uxZs0aqZWL7WxbANi7dy/Wr18vdWLPy8vD8uXLPbFUryIIAjo7O3Hi\nxAmpyDOZTFAqlVAqlairq8PixYtRUlLilKwd7F+iQ51j6MHVjhC5NlDfn/15Dc6cOYN169YhPT0d\nv/71r33uPON3ce7cORw+fBhz585FamoqsrKy2PP0ycSUK7mH1WpFXl4eampqEB4eDq1Wi4yMDMTF\nxdldl5WVhV27dnlold5JJpMhKCgIs2fPxuzZswEAdXV1+OUvfwk/Pz+sXLkS//nPfzB37lyoVCq7\nSRe9hS7E83hi6EIul9vt4nn7pAtvYNuc1tXIKHo421uwokdNfvc1tuv+/fvYvn07Tpw4gT/96U/Q\naDTufpoed+fOHSgUCgiCgObmZiiVSk8vidyMBR0NKKPRCI1Gg8jISAAPCrfKykqngq6PnWEC8M47\n70Cn0+Hdd9/Fyy+/LBVegiCgtbXVZejCdtLFiBEj4OfnJ92efVLGmbkLE8SD51GKPJlMBkEQ4O/v\nj4CAAKcGwUajERs3bsSyZcuwbdu2IXmeEQCmTZuG3/72t3jttdewb98+qYcdDR0s6GhAtba2iuAC\nJgAAETxJREFUIiIiQnqsVqthNBqdrvvggw9QV1eHmJgY7Nixg4OwXcjOzsavfvUrp3faMpkMarUa\narUaixYtAmAfujh8+DDeeOMNWCwWxMXFSTt5YujC9jaUbRNk8XYW4L3tKdxFPHDP+bfu41jkWSwW\ndHZ2AnjQE1LcpcvJycHXX3+NSZMmob29HXfu3MG+ffvwzDPPeHL5XkFsx/Lvf/8bq1ev9vBqyN1Y\n0NGA6k9DzPT0dGRnZ0OhUKCsrAzLli1DTU2Nu5boM2wL477I5XLExsYiNjYWS5cuBfCgKDl79iwM\nBgPKyspw4cIFKBQKu0kXUVFRTkWe7S6Jqx5kg5lc9DTbW3u+2FPuSdBXO5h9+/bh4MGDqKqqQmdn\nJ9rb25GQkIDvf//7SElJwbx585CZmenBZ+A548ePx8GDB1FTU4PS0lJPL4fcjD+taECp1WpcuXJF\neuyqIWZISIj095UrVzqFJmhgKBQKTJkyBVOmTJEmXYihi4aGBrz11lu4fPmyNOlC3MlTqVROky4E\nQZCaIIsJwycpdCEIAsxmM7q6ujBs2DAEBgb67HPxZeKunFwud7kz2t7ejk2bNuHevXsoLy9HWFgY\nAODu3bs4deoUGhsb8d///tcTS/e4PXv24Ic//CHCw8ORkZHh6eWQBzDlSgPKYrEgNjYWNTU1GDt2\nLKZOnYr9+/cjPj5euubatWsYM2YMAODw4cMoLi7GZ5995qklD2mCIODWrVvSpIvGxka0tbVBpVJJ\n5/GSkpIwatQop7NLD0suirt4vnAeT+wpJ5PJEBAQwNCDB9juyrka2yUIAqqqqlBcXIyNGzciMzPT\n67+v3K2mpgadnZ1oampCXl6edHaWnjhsW0Luo9frkZ+fL7UtKSwsRFFREbRaLdLS0rBx40YcOXIE\nCoUCoaGh2L17N2JiYjy9bPp/tqGLhoYGfP7557hz5w6ioqLsJl04to2wDV2If7w5dNHX7E9yD9ux\nXSNGjHDalWtra8Orr76KUaNGobi42G6Hn2gIYkFHRI/ParWiubkZBoMBDQ0NOH36NLq7u6VJFykp\nKS4nXTgma8VJF66aILurmGJPOe/Q19guq9WKAwcOoKysDNu2bcOPfvQjvk5ELOiIaKCJoQtxJ+/8\n+fN2oYvk5GRMmDDBacfF1a1awD3JWvEMoNVqdTllgNzDNkXs2IoEeHD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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from devito import TimeData\n", + "\n", + "u = TimeData(name='u', shape=(nx, ny))\n", + "init_hat(field=u.data[0], dx=dx, dy=dy, value=2.)\n", + "\n", + "plot_field(u.data[0])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Nice. Now we can look at deriving our 3-point stencil using the symbolic capabilities given to our function $u$ by SymPy. For this we will first construct our derivative terms in space and time. For the forward derivative in time we can easily use Devito's shorthand notation `u.dt` to denote the first derivative in time and `u.dxl` and `u.dyl` to denote the space derivatives. Note that the `l` means were using the \"left\" or backward difference here to adhere to the discretization used in the original tutorials.\n", + "\n", + "From the resulting terms we can then create a `sympy.Equation` object that contains the fully discretised equation, but from a neat high-level notation, as shown below." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Eq(-u(t, x, y)/s + u(t + s, x, y)/s + 2.0*u(t, x, y)/h - 1.0*u(t, x, y - h)/h - 1.0*u(t, x - h, y)/h, 0)\n" + ] + } + ], + "source": [ + "from sympy import Eq\n", + "\n", + "eq = Eq(u.dt + c*u.dxl + c*u.dyl)\n", + "\n", + "print(eq)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The above step resulted in a fully discretised version of our equation, which includes place-holder symbols for the spacing in time (`s`) and space (`h`). These symbols are based on an internal convention and will later be replaced when we build an operator.\n", + "\n", + "But before we can build an operator, we first need to change our discretised expression so that we are updating the forward stencil point in our timestepping scheme - Devito provides another short-hand notation for this: `u.forward`. For the actual symoblic reordering, SymPy comes to the rescue with the `solve` utility that we can use to re-organise our equation." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(h*u(t, x, y) - 2.0*s*u(t, x, y) + s*u(t, x, y - h) + s*u(t, x - h, y))/h\n" + ] + } + ], + "source": [ + "from sympy import solve\n", + "\n", + "stencil = solve(eq, u.forward)[0]\n", + "\n", + "print(stencil)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The careful reader will note that this is now the equivalent symbolic expression to the RHS term of the NumPy code we showed earlier - only with `dx` and `dy` denoted as `h` and `dt` denoted as `s`, while `u(t, x, y)`, `u(t, x - h, y)` and `u(t, x, y - h)` denote the equivalent of $u^{n}_{i, j}$, $u^{n}_{i-1, j}$ and $u^{n}_{i, j-1}$ respectively. \n", + "\n", + "We can now use this stencil expression to create an operator to apply to our data object:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "DSE: extract_time_invariants [flops: 5, elapsed: 0.00] >>\n", + " eliminate_inter_stencil_redundancies [flops: 5, elapsed: 0.00] >>\n", + " eliminate_intra_stencil_redundancies [flops: 5, elapsed: 0.00] >>\n", + " factorize [flops: 4, elapsed: 0.01] >>\n", + " finalize [flops: 4, elapsed: 0.00]\n", + " [Total elapsed: 0.02 s]\n", + "DLE: analyze [elapsed: 0.01] >>\n", + " avoid_denormals [elapsed: 0.00] >>\n", + " loop_fission [elapsed: 0.00] >>\n", + " create_elemental_functions [elapsed: 0.00] >>\n", + " loop_blocking [elapsed: 0.02] >>\n", + " simdize [elapsed: 1.10]\n", + " [Total elapsed: 1.13 s]\n", + "CustomCompiler: compiled /tmp/devito-1000/6aaf870464b3b177e4afd85a712be00325a70519.c [0.23 s]\n", + "=========================================================================================\n", + "Section main<101,80,80> with OI=0.49 computed in 0.000 s [Perf: 6.06 GFlops/s]\n", + "=========================================================================================\n" + ] + }, + { + "data": { + "image/png": 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XcM0119ifuf/++/GDH/wATz75JL72ta/hN3/zN/Hwww9nd8AJIUFHxCZMxirrLZpGS6oy\nwh8r6+og+rkQ2ZVH7ENCr7yU7aG0SLyE79LSElqtFn7jN35j6vXRaBTKQnf06FEcPXrU3ta1116L\nM2fOTAm6z372szh58iQA4Oabb0a328X6+jqOHDmS5JAygwQdEQm+gTOrwxWl9EhSymih44Vc1u25\nklC280q4EyYg3TCM2B0CwkDWp3DQOQrGay51u12sra3NvN5oNCLv48c//jG+/e1v4+abb556/cyZ\nM7jkkkvs348dO4YzZ86QoCPKTZiM1SilR+JSFkHHrJPsfIks5IBwC0tZzj3hDh+Qzicghe0QQBY9\nQiS63S5WV1cTb2d3dxdvfvOb8aEPfWgmY9btfify3CdBR/jCP82HLT2yyAVw+fZckiShUqmgVquh\nXq8XPbRIkIVlcQjbIYCEXnrQ9RUer563nU4ncUFhXdfx5je/GW9729vw+te/fub948eP49lnn7V/\nf+6553DxxRcn2meWLOaqSwQSpvQIX26jWq3mUjdNVCuRW3uuSqWCfr9fyht3GcdMpEsSoWeaJhRF\ngWEYJPSIRHiJ306n4+pyjcI73vEOXHfddXjPe97j+v6tt96KD3/4w3jLW96Chx9+GGtra8K6WwES\ndIQDPj7Oq/RIkeU2RBN0lmVhNBp5FkYWbbxelGWcRPGEEXqqqtqWe7LozUIWuvBEjaELy1e/+lV8\n6lOfwvXXX4+bbroJkiThj//4j/H0009DkiScOnUKr33ta/H5z38eV1xxBdrtNu65554kh5I5JOgI\nAOFKj7CM1SLLbYgiPHg3c17tuQhCZHihp+s6FEVBtVol1y2RCZ1OB4cOHYr9/Ve+8pV2Yp8fd999\nd+x95A2tQAsOS3Twy1hd9NIjPM4OF0FuZlEEaFrM07EQ+UAxerOQhS48XudqZ2cHl19+eQEjEhcS\ndAsIu5HyrVXyLD2ShKIEkrM9V5F9VrMgzHkt+m9PlIcwgoWEHhEGP5dr0qSIeYME3QLBlx7p9/uQ\nZRmNRsO39Eir1UKlUhHmhilJ0lR/v6zhW5XFiRecNwsdQWTNIgg9stCFw+/eSYJuFhJ0C4BXxiqw\nb3XhXYmLXnoEmE78ELU9V1YYhgFVVaEoivBN4InFIQ2hx/9OlAevLFcSdNMs7oq9APhlrDLLUdlc\niVlbvJyJH+12O5GYyduimATDMNDr9eyAdr4JvCzL9k9d10noEcIQReix/wPwtOjlMafJQhcOv/OU\nNMt1HiFBN4eEyVhlMXLj8Tj30iNJyELQsfNVhj6rWaDrui3eWq0W2u02NE2zj58vRcHHXjKBV9Si\nSIiLCIIlrNBzdsChOS0OfvNoNBqh2WzmPCKxIUE3R7CnUF7IOePjmCuRWVlWVlZKIeQYaQo6Jk6G\nwyEsy8qkPZfIMXRMxDKLXK1WQ6PRmBkvaxnF5gnreuFcFEnoEWVABKEnguAtA0H3zjKtXXlAgq7k\nsJtQmNIjTLiwjFVVVRfygnBm8GbRc1ZkmFvZMAzbGjkcDgO/5xSnTOh5NYHnhR6bm84FUVGU0p53\nUYU6o7Z7AwCgKoW/zWuWDnXpkayGJDReQg+APZfZ3KaHl/xwO4+iX3tFQYKupPAZq0GlR1hfUV64\naJpWyosiicXLmcGbh5ATyULHRL2bW9lNrMXFS+jxIo+fu2XLUOQRbYxW7yWocwJOkWSY2LMwIfjh\nTZFkNPs3AQCG7X/LZpAlxCuRIq6V2qs/KTGNnyWTRPMsJOhKBktkYAG+bFI7hZyzHZWz9IhIQiMK\nccbNCzlFUWbac80zzvjALNzKYXFbFOepFEWR2EJuT8wp0vR5dhNzTOjx78uQoVmTkI3K7gn7fX3p\ndLTxLIhLMYqV2plgxCeqkThxx2sejUYjO/SD2IcEXUnwKj3CT3ZnFwO/dlRlFXRR4NtzFVWKpajz\nLJKQ82MRao5lidV7CQBAkSTomLi1K1BgWNOZ1QZmM6150WfChGYZkLF/DmVIMGHZ+5GWv5v6+OeV\nIKHHwj3IdRuPTqeD1dXVoochHCToBMev9AgjTumRsgq6MOOOImznjbiJHs7yKkVbWNIQeiw+b14X\nRKv3Emgw0ZD2r/UKwpccYqJPkWRo1kQMMgHHhB0TdVVJAXZPQLMMEnYJ4BOMqtWqfV+iBCN3/LpE\nUMmSWRZjlSshbhmrzsWNL34btfTIPAo60zQxHA6FqqmX13nmhRyQTas2EWrq+Qk9Z3weK7Myjwui\n2rsWAGwxN9oTZFV4z7W6R3LE2NIATLtlTVgzom6w97lqCGtd0Q8EouM8P3Fdt/M2r514xRp2Oh0S\ndC6QoBMMthj5ZazyrrR6vZ6o+G1Zb7z8uJ0WyrLU1EsDp5BLM9GjTHNjURbE3s7VqO+5SscOt2o1\nIOlhvBcbB+yLO+amBSZuV6eo47/D0GBC27ka7ZXvRz8AIhKLMq+9IAtdNEjQCQBzI7GLEgguPZI0\nJorPtirThc6PNYmFMi+ystClLeT4cfJzo+zM04K41b0KNUmyhVydi4ELEnNOxpY+464FMJURyyxy\nyp6lToEEY88CWJVk9EnUxSbpfXee5nUcqI+rOyToCiRs6ZGsSm2UedHe3d2123MtUp/VRa+hlxZp\nLIh5nvOt7lUYWxJqe7vkxVzPNFCT+IzVCS2f+nPannBjrlpe2A32rHLM5WrAchV1AEjUCca8CT0v\n4dvpdHD06NECRiQ2JOgKIGzGKp+h6VZ6JCllEnS8qxkAFEUpRXuutM4xX1NQlmW0Wq3U5wMRvYYe\nAPtvkpXYY2JueU+p9UxAlfZdpTWPfTFhxqTeko/AG1mGi7XOchV1XdPAqqygZwHLEvBs5xpcsva4\n/T3e0ku4k7dnJInQY9/lS6zkhZ/L9eqrr85tHGWBBF2OhMlYzTtDU3RBx1yLo9HILr9hGAbq9fpC\nLBhOIZeFsAfKJe6LwK2GnmEYGA6HqFarmZVWeXL7JWhLEzHX21NmdSne32l3T+CploVleTZZaGQZ\ndpYrgxd15839eLquaQCQ0Nv7+Eb3KhxefSLWuBYNka6zOEIvz7JBfoKOXK6zkKDLASbk/DJW45Qe\nSYrIi7hf1uZoNBJ23E7inmOnq12EYsgiz5ciYFZ15wNXmjX02pKOHasGmKrr+07rnDPwwJmTrO79\n/XqmMSPqBrb7dXorm4aJaoCIHFmLEfKQJiI/kIYVesxSnYXQ87vXUFKEOyToMsSt9IhzcvMN0huN\nRq6B/SLeUPzalTHmWViIKOSIaKRVLHm9d91EzHHEtc650TMnAm5ZVmwxBwAjy5wRdW4osGBAQlWy\noFkSHt++HtcceDS18RHiUYTQc/vczs4OWehcIEGXMlEyVpkb0dlXMy9EEkZuQsbLtSjSuMMSFDPj\nbE9WRFcLIluChB5r56frOp4avhxVaSLmViR361zPUnDIJRmC4WWdc7JpmGg5vsxE3Xlj8h3Nknyt\ndFXJQhsaHt++HletPiLkw6IolK2yQBiChB77GcVa7XeeyOXqDq0YKRE2Y5XPUMyi+GsURBBGljXb\nd3aeLFJBf1sm5IbDYWHtyQAx5sKi4hR6j56/AVXJu4DzeXNyfVQlE1umtyXtkBy+CPTAlNCSp//+\nZw0JNZ9CxcC+lY7RlrTQ+yTmHyb0nISxVvN1Rp0WvfF4TL1cXSBBl5AwGatZlh5JQpGLOJ/FGzX5\no2ziw63en1PIitaerGzneF549PwN6JkNHFQGAKatc32rgn6EPwkv9sKIO17UdczJIqxCRm3P1udl\npXteX7L/f1jp44nuDbik9nD4gS4Y82ihi0qYsAS2po7HY5imiU996lN44IEHcM0110CSJHzzm9/E\nddddh6WlJY+9uHPHHXfgvvvuw5EjR3D69OmZ93d2dvBrv/ZreOaZZ2AYBn7nd34Hb3/725Mcbm5I\nATdtuqN74JbowP8EZkuPNBoNoaxPrEhxq9XKbZ/OLN5msxk5+aPf70NRFDQajYxGmS7b29t2bCQv\n5KrVKhqNhhBCjiWgrKys2L+zp2UGa6eV53wRGdZqrt1up7bN/755sy3mAEDjkg0a0n6WqZ8Fzw22\nnYPytAVtbM0Ki5Zs2YIOgC3o9vc9WRbO6PvHbe45fFVr/3svv+Drkca4KBiGgfF4TNdRALquQ9M0\nNJtNWJaFM2fO4Fvf+hYee+wx/P3f/z3a7Ta+//3v48ILL8R1112Hl770pfjABz4QKJYfeughLC0t\n4eTJk66C7v3vfz92dnbw/ve/H5ubm7j66quxvr4uxH16D88DFGaEZYEXcoPBwBZqPHzGarVaFaKn\nqBuSlF9vziKyeEWBnWfeIina8YexyC26VSFr/vvmzVO/axlkjjJ3rVPY8TyvN9Di3uetdAxezLmx\npgwTjHK+IQtdOPjzJEkSjh8/juPHj+N1r3sdvvzlL+Ohhx6CYRj40Y9+hO9973t45plnQp3XW265\nBU8//bTn+5IkodfrAQB6vR4OHTokkpjzpRyjFATDMKCqExcIMxfziyCrSyVyKyqePNxqWZyTMrkD\nWYxIr9cTUsgRYvCFc/8OK9xlcd5oYVke2b/z1rmouAnD82YV7RjbPGtM3FuyQ+DJe51ga5IB1VLQ\nMZr40sbP4ucP/3O8QRMLj5fwHQ6HtnVTURRcccUVuOKKK1Lb77vf/W7ceuutuPjii7G7u4u//du/\nTW3bWUOCLgLO+DgmLFjGatlaUWUpjPg+q2mfkzIIOt61LEkS2u02arVa8BeJhWRF3rdonTf8XXEb\nxhIuruwk3ueW2cAhTjQCQMecBJoPzOqMlS5oXEQ4yEKXjE6nk2kNugceeAA33XQTvvSlL+EHP/gB\nfvEXfxGnT5+OHKtXBOKrDoHgxRwL3ByPx+j3+6hWq1hbW0Oz2SyFmAOyEUaapqHX66HX60FRlEzO\niciCzjRNDAYDdLtdWJaFlZUV1y4DoiHyOZ13/v6F18y8tuwQWowz+mQhe15f8fwXhpE1eZbfMr3j\nUAdmtHhfZrWrcW3JHt58WaRtEATDr49rloLunnvuwRvf+EYAwItf/GJcdtllePzxxwO+JQZkoYsA\nW/RY6RHW725lZaWUT1xp9hllBZKLrKtXJLxFzhkjSGKJ8ONY9bzv+1tGNMsAL+rCWPKYpY5Z5/y2\nyVy/JuQZt6uTljTGwKpDVVXhmr4XCVnowsHWVydpCDqWTevGi170IvzjP/4jXvnKV2J9fR1PPPEE\nLr/88kT7ywsSdBGwLAs7Ozt2BwMm7sp6cSYVGnx7Lsuy0Gw2c6mrJ5JAYpmOLNlD9LjJpIhy3kUg\njYX57194DY5VgS1jGYeUnv36GX2/aGojQW23Z/csekcVf2G3ZTaguBQ1GJhVdMxm5P2yWDpg/z7h\nbPruLCZb1vsokS9J237ddtttePDBB7G1tYVLL70Ud911l72Onzp1Cu973/vw9re/HSdOnAAAfPCD\nH8TBgwfTGn6mkKCLgCRJWF5ethdsvhtEGUnSZ5QvkJx3XT0RBF0UISfCeKMiy/LM3KYFN12+cO7f\noSFXsGUsT71+RjuIZY8s0VrM5IizxsTCdlTZsd2tPB2zhUNyP3A7I6via6VjyRFMzLWkMb668wt2\ncoRf0/dFEXpkoQuH13lKKujuvfde3/cvuugiPPDAA7G3XyQk6CKiKIq9ODuzXMtGVKEhUoHkos47\nX36lDJnMYXHOhTLP67LQM5po7CUeMOucn5hLgx9oh3Gssu363pbZnhF1LGavLY8Dt/2kehQAYO6V\nyVKtCo5Vp/cVthfoIgo9Yho/QXf8+PECRiQ+5V+JcmYem8QHHQMrhtvtdqFpGtrtNlZWVgprW1bE\nPg3DQL/ft13uq6uroTN3yzhP/GJMiOR88Mcnp34/ox3EGW3WrZPE3Wp43N55d66TLbPNfc7dCuK0\n8D2pHrXFHE9N0nFGm+zrr597s+9YmdCrVquo1+toNptot9tot9uo1+tQFAWmaUJVVQwGA/T7fQwG\nA4zHY2iaBsMwSjNfyUIXDj9BR31c3SELXQLYQl3WCzRozM5OF6I0jM9TIJWttmBS+N6ylmVBUZSp\nLN2yLJqic1l9w7bO5UWfS3o4ox+wLXUdM7gcSd+su1rpvq9eBNkReyfDsq10AGxRFwfeose67ITp\nA+rV8J2tXsWNAAAgAElEQVQoP0ldrvNM8atzyXBa6MqOW59RZ3su0Yrh5l0QOWkdvbJY6CzLQqfT\nQaVSQavVsl1ebNFkMXX9fp8WzQR88McncRmXUDriyoP4uVvjxs95cUY/4CrStsz21Ji8eFI9Eml/\nnz77y3jj0eSxSWH6gIos9MpqAMgTP0MJCTpvSNAlxE0QlQlebDgD/UUTcnmQZUFkEeEtcgCwvLyM\nSqViN8bm//6WZaHf76PZbNqLpq7rFOsUkcvqG+gaLTTkLta1VaxyvVvdeGo8cWdWHYJOlvYfEl5c\nW481Fi/LW9Bnvzs+ZgtME9KMlY5Rk3Soey7aDX3Z9TNpUXahR8xCLtdokKCLiHOCsWzAsi76kiTN\n9FkV3a2YhcXLKeTa7XZqN3URLXR8gouiKFhaWkKv1wvlUncrlBwlqF1RlIVeMLt7HRfWtVXPz/xo\nfCGqXIHeIH7gsJb9RG0j1Pd6RhM9o4mj1c7U6x2jjTXFPevVuS83nG7XlqxiYNbwwR+fxH/6if8n\n1NjSIqzQ4x9O2Of5kIO0Hk7KbADIC79zRBY6b0jQJUTExTos7AbW7/dLFR+W5jlnBZFZ27Y0hZyI\nsJIzw+EQsiyj3W6jWq3a5zPuYhMme9EwDHvOLapl5GPPvcn3/R+NLwy1Hd4658aTe1a9K+tnAUzH\nzwVxVgu3WKpWJXU3cJ74CT3KuBUXXdepjaIHJOgSUkZBx4sYViS5Xg9/wxeFJE+6/DloNpuZdrYQ\nYY54CTmG89jTtE7GDWpn1pF5XjB5d+umj0vS6W4NCxN2F1fdS5Uwzmproax0j44uQUtWZ74f1u26\nWvF3L4tA1qVVyEIXjNc5Kvo+Kjok6CLitvCVYZJ5tefq94OLiYpGkpuhpmkYjUYwDGMhWpQFCbki\nCHKBsQSMebOMfPDHJ3HQ4477o/FhLCvu/VvT4Gn1Aryotjn1Ws+Y7gARZJn7oRrOesgQye2aBmkJ\nvTKsF0UTJHrLdN3nCQm6hIgu6FjbndFoBNM0Z9pziT5+L6Imo7AWZUX0mpUkKfeOIlkKuawsDElc\nYM5YJxE5WJl9ePrR+LDrZ6PEzznRLPdEJjdRF4SblW5g1mwrXdndrmkQVuipqmrfB1js6iKFG0TB\nz0JH58kbEnQRKYuFju+zCgCNRsO1ELCo4w8izLidVsm8es0WiZuQq1QqoY45SCQXdd78FkxmzRM9\nc5FZ515QV3FRrZtoW0Hxc054gRck6jb1ZVxQ6U291jHaeEY9hKUAC6Kb2/XR/qSi/9Wts/ZrZXC7\npoHbvDVNE4PBALVarRTzVjR6vR6WlpaKHoawkKBLSBHWFz/4BZ3Fx/m15yqroPNDNCGXxzl2CvhW\nq1VYW7a8kCRpJis3KD7PzSqS1zl6QZ3Oaj2vtz0+mS1PqxfgoEcGa1o8OpgIOVmyYFoSvj84Cs1S\ncHlzkn1bVrdrUthcizpvF03o+dWgW131zg5fdEjQRcStbIlhxHePpIWzz2pYy4xogjQsbiIpyL08\njziFXJH9dUVAxMzFD/74JMbm5FY7NCbZeT8cHsZadd9S5Rc/Fzchwo9n1EO4tLY19RpLynBa6Z5R\nD81838vtyoScFz8cHrZFHbEP1dCbhooKx4MEXUKKtnCxPqusPVfUWKmixx8Xftxh3ctFkcU5zkLI\nlXUuhCFOnJPTmhd3sexoLTSV/czQHw7d4+byxk3U+bFrNHzdro/2j4dyB3f14FZj80rUGLAoQk9V\n1akaemXOFGcPWk62t7epqLAPJOhiwC98RS2CfJ/VarVqV/iPSpkXcbYAL5J1Ki+L3DyfQx43oRfW\nKsJ/Nqvz9Vj/IlTkaQ+Ashendm37+ZnPOxMivBIkGF6izi2Wzg8WK2daUqCoe2G8iovq3YV1u6aB\niJboPCALnT8k6BKStyBKu89qGQUdW0TDxgkWTRrnmFyr+RHWKsLao/n1tv2Dp/7DlHUuDE8NvMuD\nKFzSwWP9i6fecxN4YfGqgefmbmUwt+t3+sd8s3JZHF1VMqBZCmqybou6RSPrLM2sa+jlhdd52tnZ\nIUHnAwm6GBRhoXO250qzz2pZBB1L+GAxcrVaDa1Wa65FDUvwGAwm8VZZCrkwczlquZh5win0FEXB\neDye6m3rXCx5nh0ewAW1STICHz8HAI/1j9r/r0rxYlof618MY6/uG59V6mTXaEz9/ox6yLVYsJvI\nc7pdv9M/BmBiCYxaauWJ3eAWYvNGUffasgk9vxi6yy67LPP9lxUSdAlhvVyzwjAMDIdDaJqWSXuu\nMljo3DJ3VVUtTU/QOOdYtExdwhuvxfKt//YHuHyvwgIv5pw8N/K2ODjdrWH5/mAiEItIQAjjdgWA\n5eoI//GJd+FPrvqLHEYlDiJdw1GEHkv+c/ZlzjMRo9PpkIXOBxJ0Mcij4KGzWXyr1cqkz6pINxcn\nfjXVNE0reniZwRdBJiFXXi5f2sKm2gbgXp6EWahalXFmY3i8fxGuab8Q+LlnRwdxSeP8zGuHaru+\n2waAmhw+C5e5XRnbajGlWwh/vIQeL/JY2EEWGbfkco0HCbqEMBN0WoKOld3Iq1m8iBa6MMVxRRy3\nF2HHKoKQK8s5LQObPmIlC3ejgem5ou6VSgkSdVvqxIzoJuq21KUZUbdrNPDcaDbT0M/tyuLoGDVZ\nt8e3SJQ9XIFPCGJkUVrF6zx1Oh3KcvVh8a6oFHBOtKTiwqvPah4XPhu7CDcat1p6XiVYyiToghBB\nyAFiW2tFxG/+/cZ3/iNkj9P5w91DWKq6J0rEjZ8LglnTjje2M9l+EhbR7TpPpF1Dz++66na7JOh8\nIEGXAnHFBZ+5aFlWIYu5CIs4L+QURQldS68sgs5rfrBkh6KFnBduY5knIZ0GXn8v2SHMWPycn5gL\nQkH2551Z6Z4dHfT8zJP9C9FU/EMeosTRLZLbVYQH57xIIvSASfy4MxFjZ2eHOkX4kH5Q1gISdZFj\nAmZnZwfD4RDNZhOrq6uo1+uFWWaKWKRZUeROpwNN07C0tITl5eVQYq7MN0Vd19Hr9bC7u4tarVbo\n394JibVs+OHuIfxw17sESF482fcuicJwijnmkuUZGvvX6CK6TuNC1xds0VapVFCr1ewY8Xa7jUaj\nYcftMWPHRz7yEbzsZS/DyZMnoWka7rvvPjz55JOROzTdcccdOHLkCE6cOOH5mQcffBA33XQTXvrS\nl+JVr3pVouMsAilggtHsc4Fl/TB2d3dRrVZRr9d9v+d0KTYaDSFqiXU6HSwvL6dWBiUIZ3eLZrMZ\nuSjyeDy2RaDoWJaF7e1trKysYDgcwjAMNBoNYUQco9froV6v243DNU2bGd9gMEC9Xs9troiMruvQ\nNA3NZnPq9bf+2x9gpTbC2cEyjrYmxXl31P1SIbyFzpkQwbtcvQoKe+EVQ8fDhNiV7XMA3MWaGyyO\njheEvJWOT4xgcXROC93p7f26eYYp44rVTQBAT2vgye0L8OWf/d1QYykz4/EYkiShVqsVPRRhMQwD\n4/EYrdako8hgMMD3v/99fPe738Vf/dVf4ZJLLsF3v/tdnDt3Dtdccw1OnDiBj3/844H30oceeghL\nS0s4efIkTp8+PfN+t9vFz/zMz+Af/uEfcOzYMWxubuKCCy7I5BgT4nmg9GiVAkEWLibkhsNhrPZc\nWZOXhc4p5OJ2twDK5frT9cli1+v10Gw2c4uPJIphpTap08bEnIg82b/QFnVOzo5WcLSxM/WaW3JE\nWHghx/NU9wJb1B1quZd0IRYPp1u61Wrhpptuwo033ohPfepTuO+++wBM7qePPfYYfvSjH4W6n95y\nyy14+umnPd+/99578aY3vQnHjk1qKwoq5nwhQReDsEkRfHuupAImS7IWR7yQS9KmrGywRBcm6NKu\nIZglJDiTwVvnnukdwFp9GPidJAkRYaxzTp7sX4iDjgLHQZ/nGRpV31g6LyHH893zR3HpcgcHQ5yf\necCrRykRjGmaU+dueXkZL3vZy/Cyl70sle0/8cQT0DQNr3rVq7C7u4s777wTb3vb21LZdl7M/6qa\nA05BlHZ7rqzJStA5+82meR5EttDxQo5Z5La3t4UXSSKf07Lw1n/7Aww82mgVDR/3FoSblc4P1axM\nuV2/07ko0tgIguHXJWJlZSWz/eq6jn/913/Fl770JfT7fbziFa/AK17xClxxxRWZ7TNtSNClgCRJ\ndsbOcDjMpD1XlqS9kOchaEUUH3xXD2fpmXlpmSXieRcZp3XOL8P18e60BUzmYuYkj4zRl655t/gK\nw4/7B/ET7fPBH8QkDpC5k/145PwxKLK/tVGRTRimjLqi45neGi5d7uCN3/rP+PRP/pdQYykr83AP\nyBo/QZdlhuvx48dx+PBhNBoNNBoN/NzP/RweeeSRUgk6sv3GwDnZWPmRbrcLSZKwurqKdrtdCjEH\npLdIm6aJwWCAbrcLy7KwsrKCpaWl0pyHuBiGgd3dXezs7EBRFKytraHZbNKNe8H4lYf/dwz0iRVM\nNSp4phdcL+vx7SP2vzh8p3MU3+kcxfe2jwZ/2AGfqME4O1px/f+P+95lTHjijAMAzo+bwR+aA+hh\nKBg/QZe0SwQrmeLG61//evzzP/8zDMPAYDDA1772NVx77bWJ9pc3ZKGLCWs/NRqNoKqqLeTKGB+R\nVNDxFrm8LJMiWIqcFjm/rh4ijDeIMoxxnnim5704yTEKDDAxdd2BaFa7KFY6J3wc3enzF6MSMw5w\nV61jqTbGeDye6g86jw9F83hMeZBU0N1222148MEHsbW1hUsvvRR33XWXvXafOnUK11xzDX75l38Z\nJ06cgKIoOHXqFK677roUjyB7SNDFZHd3F6qqotFoYHl5GYPBoJRiDoi/kBch5BhFio8oQo4gnDzV\nmdSjqynR6miF5fT5STLCNWvuWaxuJBF1afJLX/+/8YWfuhOmadoJBG7dBOh6m1+8EkeSCrp77703\n8DPvfe978d73vjf2PoqGBF1MWDFESZJgGEapLRssBjAszljBIiyTRQg6p5BrtVqhj7tM1i/mctA0\nbWohVRSlNMeQNy//0v+JtVbw55iYSxPLchc3j3cutEVdmIQI3sXKvzYy9pcJrzi6xzvT8X+GKYeO\no+M51Orbdf34bgKsLqJT6DFrXpJG8HlCMXTBeJ2j7e1tavsVAAm6mFSrVVsElWmxdiPs+A3DsF3M\n9XpdCBdzHjdIEY87C/h6ifV63S4tw9rz6LpuW2X5hbRMC2pWrLX2Ex/O9Zbt3/mEiB9vH0Sj5l7m\no5qRtY4JrRctB/dwfWGwjIti1M5zirmo1BUdY6OCrUF7qh6dJElQFGXG6m9ZFgzDSK0RPCEWXvf0\nnZ0dHD0aL0ZzUSBBFxN+wonU4D4ufoJOREGTx3lO87hFFv28xbVSqWB1dRWSJNnxJYqi2IWwh8Oh\nLebYgqqqKrnHANQU3fM9PzEXhFeGaxR+0LkAL17btH93S4iIi6pXUKtMjl235NhxdACwNQju6ypJ\n0kwdy6D+oM4HkKLmZZnXiKLpdrtkoQuABF0KlP0C9Ro/72IURcjxZFUKhBc4Ih53WvAxkPV6HfV6\n3V7wvMQnWwjdFlSne4z1Wlwkax5vnQOAzriJzkCMDE6nqAvL+VELBxv7BYh5t+uT24dTG1+9omOs\nV/BTX/y/8M1f/N8ifdevEXyQ2zYvoSfqA51oZJnlOu+QoEsJZrEoY4kOp/VIdCGXFVkKOZEsdM5k\nFnacg0H4rgFO3NxjQVYTtxioMgo9Fj93rjdbUNhLzPklRMTJcA1LkKhzul2f78cv5Bo3ji5N/Ny2\nvNBTVdUOocn6AaSMczxPSNDFhwRdTMK2/yoDbOxJgv6LIM36eYtgkXO2YHNmJac9h5NYTcoW7C6K\nFU63gudtGu7WHbWB9X56HTFYHF1exH0AWRRLc1H43X/I5RoMCbqUKLOgYzevnZ2dUpXhSLt+XpZC\nrsj5wSc7iNCKLshqYhiG72KqKEoprHnr28uo173j6tLAK8OVRzemz/PGYAmHW7tTr21zhX3dkiOc\nblcAGGkVNKqT4+Pj6JLSbnh308gSvwcQXuix5KCobluKnwuP23nq9XqZtv6aB0jQxWQeLHTO5vFr\na2uluuGkVT9vni1yrJeuoihYXl6eiX0TiTBWE13XfZMw8v47vupf/sL19ShiLqsMVz+e6a7h0tWO\n72f83K1Pd7wtJUGJEU9vTLpO2GLUknDhwUnf2CRxdFmRRnxeGUNxisBP9FqWRecxAHHv7iWjTILO\n2Ty+3W6j0/G/uc8Di1II2bIsqKqK4XAIWZaxtLQUSsiFqUeY9zwPu5iyGKiiXWPjcQXr41lXZNwM\n1ywYasFz4YVBeu5UHibmnJw7vwJTl3DgYN/1fREJY2nmLXqM8XhMblsPvARdWdbWoiFBF5MyWuic\nQo5vHl9Gwp7zIoVcnrCewsPhEJIkod1u2+VG4iDy3IgaA1XWkipplCzxIoyVjsfN7RoES4xwE3KS\nZE2sdJIFhHAdlwWvucmsy6wYvVtIwby3PUsKnRN/SNClBMtyFRHWc9YwDDQaDVchl1UJkCwJEnQi\nCbksBT8v5ACg2WyiWq2W6m+ZBnFdY241ysLw01/8MOp1oL/TQHtltnuCF84MV81QsL61796U5P15\n4iboLrkguEhwWJ7prmG5MY70Hd7dGiaOzssq50SuWNg+38aBg/3C4uiygp+btVrNfp09hDBrXpFl\nVUTAaw3SdX0uH8LThgRdSkRtn5UHbJE3TdNTyDHKYGF0w23MpmnasWMiJAEwsji/7G9sWVZiIVfW\nORBEko4DYSwmUcQcAKiGgvPnl/bHxws4Ofj8P7u5L6iOH8ouVGK738SB9nDqtfOjEP3NsB9H9+zm\ngchWxu3zbdRamlBxdFmxSJngYfDrErG6ulrAiMoFCbqYiOpyZaZ9JuSazSZqtVrgBS/K+KPgPKag\nshxFkvb51XUdg8Eg0t84KmWz2EYlqOMAL/LcLCbOpIf+dhOVVnCsHC/mksKLu4sOdWfed2a4unGu\nu4wLVx1ZrbvhhFvYsRHRrqckDyFljs/zOkedTodq0IWABF0C+EW6aEEUV8gxih5/HNiYRRZyPGmc\nX/Y3Zu7zer2e+027bPMkCrzFhBd7TovJT3/xw9DHk3puYS10WxsTt6qkpGPJd5YseX5jsuBdfDg7\nq91GdwmNerBofX5jzbY2WpaUaSxgWUjjugl6CBG57VkSqKhwOEjQpURRgoiPn2JutzjWmjIKOmA/\nPlBkIQckD+bliz7nmdDifGIu6zxJipfFhOG0zjmtd0zMzWw3hIs1Ks9vrHmKOq8MVzcrHeDudnXi\njKPb3A5vgXQmRsgVC6YuYbxTR30lWmxfGcjimk2jrIooQo8sdMkgQZeAIi10zkD4RqORyO1WpoWa\nt8jJsix8fbUkOLt3ZFn02TmfyzQn8kYfVAFlcm762/5dIvrd/LtIPL+xBsuQcOTwTu77ZlimlFiw\nXv+ZD+PRN/yvKY2oWPK+loLKqhTR9iwIJjadkIUuHPO5ChZAXlmuWWU0lmHx5jseVCoVNBoNWJZV\nCjEX9fwuSjuyMnL9/+teTNjJ7uYkDk2qxruu0nBTrm+s+Iq64Xg/45JZ6bzi5za6E8vbaFz1dLtu\nbC5DUlJwLVZMjHfqtmieF4q2gLExiNr2jCx0yRB/JRSYPF1ReZSmEFXQOYUcs8iNx2NomjgFW4OI\nWjOPhJzAMKFhuF9/47H7rTWt+LkoBIm6IMK4XYGJmCPKSdZtz5Kys7OD48ePp77deYMEXcqknRnI\nqv6PRpPA66xqjIlooQvTukq0MXsR9PcSoR2ZiHOgrGi9WvCHHKQZT2c5hOb6xgpW1oKLAp/rLqPi\n0opsu+/vNh5xsXmWIc1Y6ZIkRsyL29XLnSgyabU9C7te+VnoDh4MV89wkSFBlxJ8zFEaYsvZvqnV\naqFSqeQSP1U0TiHn1bpKBPdFFNzOb1kydBki1lsUDX2zAdTzPUeWGXwt7HRaoUSdG7ruPyd3ttqQ\nKvGO2SsxAsDEAjonbldR7q9pELXtWVi3rdf6STF04SBBl4AsatE5hVy73c5UyDFEWKjDCjmGSCI0\nCLcbF3Mjl0HIERO84udYhqu+2YCVg5hzliwJ9R1DRndrCauHdiN/Vx3UUGvtd2/wi6Ob2mcKiRHz\nRNkeQqOSJD5PURTP+3m328WBA1TXMAgSdCnCRFGchZkXM0zIJenDGZUixZGbiA1z7GUSdMD+jS3I\njVwUZTufRSN1qrCWJ+U69EEVGES77kUUOmq/ChVVtCJ0v9jZamcyFqliwtJlYCDG9ZGURb22guLz\n+LZnADAYDCDLMp566il88YtfxHXXXYfBYECdIkJQLoe+YDiftmRZjnzRMpdbt9uFqqpot9tYWVnJ\nVcwBxSzmTNx0u12Mx+PCjj0vTNO0/85LS0tCiTkiAhFcgHEzXLOkuzXJVuUzXNPA0pMtJ9Z6A9bZ\nhut7N/zXjybatijMu4UuCkzkVatV1Ot1NBp7hbrbbbtg+tmzZ3H33XfjK1/5Ci677DL87M/+LN71\nrnfhL//yL/HQQw/BMGbjPZ3ccccdOHLkCE6cOOH7uW984xuoVCr49Kc/ncrxFQEJuhSJIop4Iadp\nGpaWlgoVM3kKurSEXBksSsz62O/3YVmWfaxlEHK0+Exz/Sf/GsDEMsdb5wBEts4FkXVnBSbqvBjs\nNLj/TxIi1MG0AByNva9XZ1IG4O4mNtabMNabsNb39idbsM42IJ+r+46PmD9Y/Bxz215//fX4kz/5\nE3zuc5/DiRMn8Pjjj+MP//APcfXVV+Nb3/oWfv/3fz/UPer222/HAw884PsZ0zTxe7/3e/iVX/mV\ntA6nEMRfVQQmTgydswRHUJxYXuQhjtKODxRZ0LkVfmbxckQ5kQwJ6BV/rYpEXHersT6dNctyIuzf\nZUA+V4dxUAPqBuYhDWfeeyMnxev8sHv8hRdeiFe/+tV49atfHWm7t9xyC55++mnfz/z5n/853vzm\nN+Mb3/hGpG2LBt2dUsRPYPDZjHwtNVHIUhxlmeghoqBztmKrVqt2oWCRCTMHRBbRRaFsVWE0gyVH\nVjXonBmubtYxN9StBmqHwsfKxcWZGOEUc4sCXTfJyEoMP//88/jMZz6DL33pS/j617+eyT7yQhxF\nMQe4LXbOshSiCTlGFgu100rVarVSraHHtiPKk6+u6xgMBjBNc6anrgjjI+Jz/Sf/GhJm/4bKVjyL\nq7xeh8UHvMgW+KvPeSUyb6VyJN5DgWW4R9fwok7tTx/LYKfhmxyhbjWB+nQMk6XLvuVLooo55XwV\nRnuyvRv+60fxyB3vjPR90aD7gDde93FVVTP1bPz2b/82PvCBD0ytJ2VFPGVRItxcrqz0h2madjZj\nGcpSpCno8uhqAYhzc9R1HcPhEIZhoNFo2AG9Tsp8oyBmYWKOt875lSyR15PHhRnrTds1KR3J3rrG\n4ucYzvIlGCszoo7hLDBsrTcgYV+chqXSUaCvBQe/iwxd+8EUVYPum9/8Jt761rfCsixsbm7i/vvv\nR7Vaxa233prZPrOCBF1CeCEkyzJUVcVgMMB4PC6FkHOSxNqVl5DjSbOYc1QMw8BwOISmaWg2m1ha\nWvIchyji0w9+LluWZRcFZZXey3AMWSGFdGO6UVmfCD+Luw1YEdLRvASQnUhgScCFEcXdeH8Aebhe\n7bGGQbYAl0LJZgi3tugs8jUUl263m7hkCSuR4sYPf/hD+/+33347Xve615VSzAEk6FLDNE2oqgpd\n1yHLcumEXJJOF0UIuSLhhVyj0UC73U7c2kYU+HhHdgMcj8dTdaRYcdCsGnSXAVkNd9xMzGXOuT3B\nFFXY7eF0t9r0KgCfzcs+vxXBdcplsPrhlhgh7Wk4ZqVTVRWKoiz03JtX/Np+JbHQ3XbbbXjwwQex\ntbWFSy+9FHfddRdUVYUkSTh16tTUZ8s+p0jQJcSyLNsiV6lUIMsylpb8SwKISlS3qwhCLs8gfZbY\noKoq6vV6pH6rZbhR6Ppk4R4Oh2g2m1MhBKzSu67rdlxo0r6NZeHGj3wUiFiyrb5ehVlEDbpzDeDQ\nOPr3RgrQCOfWdJYv8SWKZc4Dq2pB0iTIQxk//cn/hn/51f85UjspERD9QU4E/ARdki4R9957b+jP\nfvzjH4+9HxEgQZeQ3d1dSJKElZUVAECv1yt4RPEJK46YO24wmPSFbDQaUwkAeZKHoEsi5JyIeGPn\nYwABYGVlBZIk2QLvTWt3AAA+3f24LfJardZMg25VVV0X2nlx2VZ3ZGgr/m4/aSyj1inWMi9tTGL1\nrMMxhF0KsMQI+Vw9kms5LGzuOdtJqarq+pDBRF6R849i6IJhfzsn1Mc1PCToErK8vGxfrKZplv7C\n9Rs/E3LD4dA1k7MosjrnpmliNBphPB6jVqslEnKAeFY6Zwxgu91Gp9Oxx/mG5bdPff6Nq++Y2can\nux/37duo67rnQls2ax4Tc7VtGXrbfc55iTkrL43H6U1pox5a1MkjGRjJMNe4/qy9PTesh9vVxicx\nQjJn4wUlK3piBABUexK05cl592snxT9kaJpmP6gwV21R1rwyzXWR6HQ6OHToUNHDKAUk6BIiy7J9\nw2DWIhGtMGHws3Yx16pIQg7I5ibpLDWTVjykKDXceIsjHwPIj+3fN38t1LbcRB4wEXo8TmsKS7hw\nNucWwZrCc+NHPgplJEEZSYHWucaGAjNOyFySnq4BykjaqMM8qPl+JirydhVmw/9cxO30YMfR7SVG\n8HF0RghPb9zm8LzYy2L+iXDdi47Xurmzs4PLL7+8gBGVDxJ0KZIksUAE3MYsqpBjpF1uJQshJwph\nLI4nj92Zyr78rHmsphS/0PKLLG/Ncy60RVPbnj5frGRJbDEXkTgdwSrnqtAv5ETdOLkfVB7JnqKu\ncq4Gq+IyUFNKJl73+MkPfQzfes9vhP58FGtelvNPhPkrMn5lS5LE0C0SJOgSEqf9l6jwYxddyDHS\nODfUKQwAACAASURBVN/OdmxZFX8uam6EEaphLXJJ8LPm8eebF3lu1pQ8rXmVvmS7S5mY492tylBG\ndVe868LJjKjzQO5Up92ujCC3qwNJl9xFXUxYYkS1J8Vy17rhZs0Dws2/eYoNFYWi6tDNEyToUqbs\ngk7XdYzHY5im6Vskdx5wtiQTtYtHXPjjUxTF9fjyEHJBRInNMwzD1ZrijI9KY86+/P/4GNCK912/\nDNc0atDFIayo80Pe9jBD7sXRVc7N+kXd4uhEJozb1i82lP3jKavXRgQ6nQ4OHjxY9DBKwfysXgUx\nLxY6XdehaZrdf7QsQi7O+WblVgaDgd1bNsvWMs5957EP/viWlpaEFHJ+RInNYyLPaU1xE3lR5rQe\nQsyVwTrHUzlXhb46ncAgj6bFh9ypwnSLNOhNz6EZt+s4fHhC3MQIowYoavDn0ias29Yr09swjFKu\nC3lCFrrkkKBLmbIJOr5kBVsAG43ktaPyIsr5zrq3bBB57IcJOcD9+EQXckF4WfN4gmKjoljzmLtV\ncknibGxIMBazz7wrtc104ggb67LdzFYygdGFs9d31Di6rAibhMEEXb/fT/ygMY/43cNHoxGaTbrQ\nwkCCLmX4Yqwiw4Scrut226rxeGxn7JaJMIKOFzpFdbLIUuyzuoBeMY9lF3J+hLXm8SKPt+bFKU7b\n2Ag/d4ooWcKQXcLeahsVqIf94+FqXRnqavT7mKzBFnWucXQ+iRHNs+5+2cY5aSLsuMoVlWHkoeWG\nmzVvPB7DsixUq9VUHjTmDWad8zrmJOWiFgkSdAlxTkBZloW20LkJOXYMZbMuAsFjLktyR1wMw8Bg\nMLD/nk5X+TwLuSDiWvMMw8AvfOhvAuPnUrHOZViyxI8wom7mO13v+ntJ8BJyThpb06KubDDR5paE\n4RU2IHJJnzwo23pUNCToUkZUUcQLuUaj4dpIXtSx++FlEeVdyaIIuTTPr2EYGI1Gdi05t7/nIos5\nL8ImYPDxc7UOoC3v/+5mnRO1ZImTsD1ovaj0pSlRx+Loapv+ZkivxIiwYs7+/DqgHgCMBvDK//wx\nfPW/FO92TYokSTMxrmFK+pS1QLcbQUkjZT++vCBBlxA3USSSy9XZSN5t4WeUVdDxY3ZarPyOt4zw\nteS82pCRkIuGq8v2D38G1R6gphyL3TwrTQsbx9x0Gt2GF2V3L6ltVKAvz26/sjsZYFi3qzOpIizN\nF2Qg4NLkCws7CZO0Igpeba284N22biV9gpIwyua29RJ0o9GoVDHdRUOCLgV4USGKKHIKOdYNwA9R\nxh6HKMK1KJKcX76WnFdRYBJy6fD8f5qIOWBineOpDKJvr3l2fx5GLd/RfGH6C6Oj6Qq82pYM9VCy\nbVYcmb58HJ0bzRfkYG+xBDsxApgWdrXtiZWuTKR1Xw2bhCFyX1s3vARdp9PB6upqASMqJyToUqZo\nURRHyDGKHnscWH/ZnZ0dT4tVmeGLHhdZFHiRYe7Wxhagh4ybmxJxKSZFNDgX5ehIftdqrRvvmnIm\nRjTXkwkJqwJIOqCMEm2mELISUXE7YZQhCYNKlkSDBF0KOC10RbhcnUKu1WpFFjZlEnSsH+l4PIYk\nSaUQclFLrJShKPA84laiJAr1rXjfi5rjwIvG4dH4162flc7N7ToTR6cCZog+q80XJCClS7Tamwjt\nssTRFXFf9eqE4ZXtnVdfWzf8LHQk6MJDgi5l8s5y5YVcUgtVGQSdsx9pu93GaDQSXsyFha+VJ0mS\na9FjEnLZce63fsb19UYIkdY8N/npWpQ3Y5rPTxZDXti5lSyJg591rnY+4WJvITCOzg1zb+UqUxyd\nKBYwr04Wfp1Y3LJt04SKCqcDCbqUyUsU8VmOabsaRWxT44whY65HXU9p1cqBsCVWWLeOeSsKXFbc\nxJyzZAkTc06yqkHnlfHaPCt5Wuv8MlyZlY4lRCTFGUfXiONq3YujY/FzzgQJZqUjkhPGbWsYBnRd\nzyQJw0/QHThQsoDJAiFBlwL8RGSLdlaiKEshx8YrkqALaixfBqtiEEElVkjIiYFX/Fx9O+YGM7rE\nmmclyAYwjBhj5yXm3IST0+3qR+t5acZqGbf1F7AfRwdMklTK4HYV6Z4aBd5tyzwFbn1tvUqqRHHb\nerlcjx49mvpxzSsk6FImq4uWxYxlIeR4RLnp8MkAlUrFNYYMKJegc8ZX8u5yrxIrJObyY/sdr4AR\nIhaMp3kunxp0cWiuS76iTnb0RJXHgFkPv33e3eoVR+dluUwLycixE0cCynKPCkOUJAzDMEJZ8/ws\ndFdffXXmxzQvkKBLAa8CvWmIo7yEHKNogRQmGaDs8H9Tr0xkEnL5o7Vnr1evRvDKEKj1Mh5QCgSJ\nurCk5t40kVpihFlJL04wD0R5WM6KsCVV+CQMFpPHLHzOdZNcrtGYr5VSEJglJonw4hd9r7pjWVCU\noOOFnCzLrskAbhQtQKOiaZrv35SEXPHUdgB1JeAzHmLOLyEiag26tGiuSxiHXBOj1HirDPyTEkJb\n52ImRpSFMt2f0iasNY95ZMbjMc6ePYs/+7M/w0te8hJsb2/P3QN9lsxHamDBpNnP1TRNDAYDdLtd\nAMDq6ira7XZuWZx5CyQm5HZ2djAajdBut7G8vBxKzDm3IyqWZWE4HGIwmFSlXVlZmfmb/vvmr5GY\nK5Dtd7wCwETMMRrbHk3kN8Wda17EjvNLAF/+RXYpBROqldnerTVIDP/Cuz4aelxFMe8Wuigw61y1\nWrX7T7daLfv+f9VVV+Hb3/42vvrVr+Lnf/7ncdlll+HWW2/F+973Pvzd3/0dRqPgQoR33HEHjhw5\nghMnTri+f++99+KGG27AjTfeiFtuuQWPPvpo2oeZOyR9MyCOKHKW4yiqrlpego4VBGYixy2rMwwi\nJnIw2FPnaDSCoihotVrQNG3KJUEiThyqfQumIkE2vE1GWYm5uAkCACZuTA438QQAjU1gdIH3ZlgX\nDN5KV+UskbzbteYiEPk4usZm8LDD0Fq37I4RTABKJjA8yCWiJawbmDUiP2yKArt/S5KEI0eO4N3v\nfjcA4A1veAMeeeQRvPDCCzh9+jQeffRR/M3f/A1uvfXWwG3efvvt+K3f+i2cPHnS9f3LL78cX/nK\nV7C6uoovfOELeOc734mHH3441ePKGxJ0GRBFFDmFnFsngDzJQ9Cx8hymabpmdUZFRCGnaRoGgwFk\nWcbS0hIqlQpUdT8gi4SceJjK/jxys84xMWfUw823vEuW+H5nT/QEibpcCBFH11r3P8jmeWtK1OlN\nse4BTkS7R4mE33ozHo/RarVw5ZVX4sorr8Sb3vSm0Nu95ZZb8PTTT3u+//KXv3zq/2fOnAm9bVEh\nQZcCXkkRfogm5BhZCrqg8hxxESmOjgk5AGi326hUKvYxSpKEX73wPxQ5PMIF5m6NQ+wM1wLX98Zm\niBjBkLF0zjg6WZ12W4eGM4oGiTlGa8PC6MD+ifyFd30U//gX74yx82wR5d4kOs61gO++lDUf+9jH\n8JrXvCbz/WQNCboM8BMYogo5RhbiyDAMDAYD6LruWZ4jCSIIOuY+9rI6kkWufPBZr9X+4i3KVZfE\nj2pvvwacF3xRYb6siGz4J414CjlWYFjaq1/HFRhubE+LOlEhC503QeEyWZ+7f/qnf8I999yDhx56\nKNP95AEJuhRws9A5+7mapmnHU3k1WReBNMWRs79s2kJOBJxilQX4MkjIlZ/mlgW9UfQo0qWxBYwO\nZbPdKLACw61z0e85ljIRjK0NE+qyLKzbteiHTdHxEnR5nLfTp0/j1KlT+MIXvjAX5VFI0KUEL4Rk\nWYZhTIJWgjodiIabGI0K383Cq85amhRhoQsjVknMic/4dS8DsB8/19g2oa7Em6tu1icmVGaSHhy/\n8+8PjuQjTHhRxxIieMKUb4nNXhxd85yV2P1sVvY38Jpf/2vc/9/+l2QbzIB5e5BNEy9BNxwO0Wol\na9bLatu58cwzz+BNb3oTPvnJT+LFL35xov2IAgm6DGCiaDgclkbIMZKIo7yLIDPyFHS8y9zrGEnI\nlQd1efqa5MVccyvenLJFXMzL3c31GFbkeWW4pkl1AGjcOhtUj86LZgyrnBe13sRKp7XFq8RFFrp4\ndDodrK2txf7+bbfdhgcffBBbW1u49NJLcdddd0FVVUiShFOnTuGP/uiPcP78ebzrXe+CZVmoVqv4\n+te/nuIR5A8JupTge7hqmgZd1yHLcmmEHKOsJVeyvmnyllYqCjw/hHGlhvlM65w5lSUbhTAlS3iR\nJ1mcwAthTPcr6xHkenVa6fwSHnh3q1ccHaO1YUUr1eIRR8fcrgBQGU7O0Xg8TqVhfJqIMAZR8bLQ\nJRV09957r+/7H/3oR/HRj4pfvzAKJOhSghWPZTXHWLmKshFF0DlFTlHiNcubJd9T1svSSkKunIxe\nfzNqO5O5PjogTblbKx51S50lS2Rt4qZ1knXJEibwBoejz31Zm/7dzd0albDbkA2gcd5xf0mpU4Ss\nWzArEt5w6hP4//761+0WU0kaxqcBWej8yUrQLSIk6FJid3cXpmlieXkZkiSh1ytBo0cXwgg60eIC\ns3C5hukpS0JufnATZVl8B0CqJUuYe3dwYfyNVoaA3oz2Hafbtd4BjHrw95qblt31gSVEpIFZkSDr\nk3OhtWU0GhOzapKG8WlCFjpvvARdt9slQRcREnQpsby8bCcTsJtHGfETR7y1qlKpuIqcIkhT0DGX\n+XA4hCRJrj1lScjNN80tMzAWq3XOjF+DLgOYsBsdiiccnOU/qpzFLW5yBO92zYtqf/K3e+PqO+zX\nPt39eGDDeFVVYVnWjMBTFCWxGCMLXTxI0EWn+NV4TuAvepHbUYXBeQMKY62aB5iQsyzLtRUZCbn5\nYfT6m2FUp6/NMNmtrXPuD2px4+fSprkxuXaHEVyxlVE4wRGrYPAekuHdGzf8RhAYR2fUJVT7JoZv\nuBnNz3wNAKbEHc+nux+f+t1pzVNVFaZpzljzmMiLcm8v4zqQF0xIO+l2uzh+/HgBIyov87cqF4RT\n0DGrUdkuZH68vJCTZdnVWiUCSS10QR0sSMgtBs0tf6t6a8OAUYue7JOWWzEKzQ0rkqgD/Iv0uok5\n5natdya/K2Nvt2tz07LjCiUTttvVJqU4OoYyCvaQuAm9IGueruuu1jwWN+1VT61s60Ce+Llcr7/+\n+gJGVF5I0GWECN0L4sDGzYogA7MtrEQjbu08vpacVwcLEnPzh/ZLPxX5O60NwTvAY797AqN91oqV\nNJEnceLoWhvGfj9bg7maK1NxdHGJY80zDAO6rs9Y85jII0Hnj9c6SS7X6JCgS4k4/VxFw7Is6Pqk\nr89oNHJ1O4pKlHPN18vzKnxMQm5+MZr7Fpjajg51Zfo26IyfY2IujnUuiETWuxBTvrUxLeqcGa5O\nGtvWTCavH9WA7FZZA+rdvZ6cLuVLwtI65yGoFQkwLDQ3NIwP7P8djYYM83/8HyB/+V/j7dCBnzWP\neS14a55hGHaWLf8aE3milFMRBUqKSAcSdBlRNkHH4seYpWtpaak09fPC3hipKDDBYPFzTMzVOzr0\n9ux8r/XchYRfsH/WJUui0tqIX+KEUd3dyyBdmt5GvWtB82m51dwypzo5MFzdrh64WUdZHJ39uyyh\nvq1D1iyoq5O/qd5UUAu3i1h4iTxZlqdijAeDgf07L/SYNc8p8hZN6Pm5XOehHVeekKDLiDRaaOWB\nW/xYt9steliRCBLPYcqskJBbDJi7tbYzsUQzQecm5hqbGsx6yla5Atfq1oaF0dr0ANwSIuodE+O1\neMftF0cXiCOObkrI7SVEBGE6El3StNKFwctl+3dbH5kSecyaZxiGXU6FWfOcIm/erXlUtiQ9SNCl\nhHNCstgJUWFCjjWV5+PHymZd9Bqvs8wKCTlCMoFK35iyDnlZ54hZqrvWjJXOi6AkE4Yzjq51zkgk\nfGtdHUbaQjwh/9OhUzOvMWseDy/ynNY8N5FXdqHnt87ouo5aLUsb6/xBgi4jRBVFYZrKizr2sDiz\nc6koMAFMrHPOxIF6R5/5XGMzINDMgV/JkiIyXP1obZgYHA4WO1GsdNWhv9uVdXAAguPo7Fi5EFmv\nttt1L47OkiVI5uS+pYxNGHV54nZ9+Q3Aw4+EOpY8iVtOhbfmOUVeWa15zjGXef0pEhJ0KSG6KDIM\nA6PRyDcRgCHa2IPg++jquo7BYBKpTUWBCTfsTgUBBqTU3a0Z4jwW2ScpN6yoC4IlOzhRxkDzvAGj\n5i8snHF0gZnEEdyusmah2tehtSsw6wrK85cMV04FwJTI4615Rbc6i0JQBrCIYxYZEnQpwgshUWLo\n+IxOr0QAJ2UUdKZpotfrwTRNtFotKgpMzFAZGjDq/q5VZeguKsJkuLbOTSx7lszVcnSuRz7rU/9o\nhNtxjMtT1va/1NowoS7PDoY1uAf2rXQsIYIRxe0alizKwpgVGdW+DnmsQ37JVTC++0Tq+8iLJNa8\nIlqdhcVL0FGpl3iQoMuIokURn9FZq9VCCTlG0WOPgmEYGAwGsCwLtVoN9XqdSpAQM1g/e5OnmGPx\nc/XzKvRmtFi65roGi8vi5MVcVNpnZ92/kUReRGo9y1XU8TjFXNDrXvBuVx5eyM2I34RuVx7tgqVS\nWenCEqc4ctatztKg1+thaWmp6GGUDhJ0GVGUhY7P6KzVaq6JAEGUQdDxsYD1et2OCeQhIUc4qexq\n0FaqqO5o0Jf23fH182robdTPR4uxs4mxTjpF3uBIerdsRQ1WTF5CzOnS5ePomucNe/tublcWR9fc\n0IEEAtgP5nYFALO+WMucCK3OwuKX4bq6upr6/uadxZrpGcMLobyzXMOU5giLyILOzYUsSZLd1QIg\nIUdMo1x/DZgs0lZmC8iFFXONjTEAwFKKs/W01veOxEpH3DW3TAwPRT+eat+cKcAcC9OKJupCxtHZ\nm6/IkHUTylCDfOJaGKcfizzEeSGvVmdRoJIl6UKCLiPyEkXO0hxuGZ1RESX+j8dpeeRdyOw8k5Aj\n3NDXmpA0ExVtf07z1rkwMDHnxHKxXuWFLe4ADA/Hv+b9RF11YAGwMF4JFm/VoYXKMNx9o7kx616O\n0wYMAOqb+w9zYDHMhgVtZbYgnvKSq2B87ynAEuv+VhR+xZF5orQ6i2LN8xJ029vbVFQ4BiToUoSf\nmFkLOr40h6IoqQg5hkgWOl6welkeX9d6W0GjI0SncuWLYQx1WBUPwdIZw2zudxZgsAzX+uZEyJnV\n6NaoPEuWtM5NBNLgwopvhqsXzS0TWivagMNY6Xi3K3PfNjcnYw3VKcLHK8z+NpYkQXK5X1V3xjBa\nE+HO3K4y036STKLOAz+XbdhWZ06RF9WaRxa6eJCgywi+lEaasQfOGmtupTmSIoKgCyNYySJHBGGs\ntjzf48WcE3lsotqbxMrFEXOZ4rg0+RZYrXM6Rodmj4nPcI1Dfce0rXT1nfhCiIm5KSK6XZmQC4Oy\nM/msZBgwW5MitZWrLof+xA8noo6HBJ4vYVud8SIvqNUZK7PiZGdnhwRdDEjQpYjTQpcmlmXZ/VaB\nSY21SqWSWUZSUYKOP05JkqiWHBGbypUvhgG4WueqHX9RwMScE7/4uSQZrmnS3JiMfXjY+0FvkhAx\nTX3bwPhA/I4Z9e2JWDMa2QjguofbG+CsdJIEWBYsRYJkWEBFBvSJUJMHKiTNgFWvovKiS2A8+9z+\n902LBF4Mgqx5DL9WZ8yAIMsyHn30UVx99dXodru47LLL8jqMuYEEXYawWLQkTe6dxXKbzeZMjbW0\nKSptXdM03+MkIUeEQVIUKMcv9n5f916o61sTn5xZS7kVWAGXVHND8xV1QUzi5/bhrXT2ZyK4XRtb\ne67Wvc4azsLCgHscnZ+QC4ulKJAMzhddr0KqVGHZrzn81CTmEhE2Nm8wGNhZtLu7u3j3u9+Np556\nCkeOHMGLXvQiPPXUU7jhhhtwww034NixY6HWpjvuuAP33Xcfjhw5gtOnT7t+5s4778T999+PdruN\nT3ziE7jxxhvjHahgSAGWGDECqUoCCxZldLtd25IWB2apMk0TzWYTtVotF7Gl6zr6/X5uaeOsr6xh\nGJ7HSWKOCELiHpyUy38CxmoL8nAMY7kJZXcEY2lS1oYXdLzLVRnsW+V4Qce7XJ0WOr8adFPCJM3L\n1sflCmCmDpukWxhdMC3s3Cx08nhyXpiVzinovNDasm2dA9wtdNUeV29O4c8ZP4DJ6/x5i+JetePo\nuDVNMizbQscEnaQZwFgDLBPmxhawd89m4s5y1rEjcZc6rIQKi43m10hVVfG7v/u7uPTSS7G7u4tH\nHnkEjzzyCDRNw7/8y7/gqquu8t32Qw89hKWlJZw8edJV0N1///24++678bnPfQ5f+9rX8J73vAcP\nP/xwugeYLZ53E7LQpUha7b/CCJwsySuGjq8l12w2XfvKkpAjwjAl5o5fDIzHkIcKIElTYk7pDWE2\nJ9mPYcScH0VmuEalsanNiDoeJuaA6K7Xan9a8CgjM7HbNYqQYzjdrjZ7btcZK12jDvnwIVjdHixV\n5VZJY1bUEZngFmNeq9UwHA7xq7/6q7jyyivt19fX13Hw4MHAbd5yyy14+umnPd//7Gc/i5MnTwIA\nbr75ZnS7Xayvr+PIkSMxj0IcSNBlSFRhxIScruueAicPshZ0fC05r76yJOSIMPBCTlIUyBcdAWo1\nWBFcppXOEFbN/VYYNyEirwzXMNY5RpCo4/GyzlV3dWhL0ZYNVoiZnUvJsHzdrnHEXBSsqjIRb2MN\n0A1I9UmyhAUAur43pzhrHcXWpYZbcWOvOnTOsiVpCa4zZ87gkksusX8/duwYzpw5Q4KOmCauhY63\nVDUajcKEHCOrDF2+HZlXX1kSckQo9hZZy7QgVyuTnwfWAE2fWGdq09mtSm+STMSsc8BEyKVJfWPA\njW9y3YwON1PdR9IgmMamBm0l+LYvj027dEsQta4WuWWa57a2shVz0mAMq8XVp9tLuLLvcrIMS9M5\npZx+j9lFxCnkGF5rzM7OTmYhP25rsgjtztKABF2GBAk6wzAwGo18LVVFkEWGblA7MhJyRCgc1hJJ\nUSZirt0CFAWocPMqo2uptjURbnwsmNe+GhsT0Wj5jGV8uOH5XhbUz6sYH6z5fqYyNIChAXVt36JX\n3dXtn04rXWVoTIk65naN0iatvjnyPU9hUTp7wtp0xNTtFUuXdvqT35uNiZVu7zNSvebbPtZOoODn\nIFnrAvETc16YpplaXVUnx48fx7PPPmv//txzz+Hii72TqMoECboUcbPQuXVccGtf5VaLp0iYGE0i\n7pxdLEjIEYngFlLmapWqFUiVCqR2C9A0oKLAWnbUnnNZOOTxvtDwcrfyVM8PgJjXaJBIqW+MZl7L\nWuTxoo6Pn0sTZTS9XVkzXd2uk/Eks8xVOoPZF2VpIupYTJ0sT0RdpTJJhOjtCbvanrjVJnPC8uiS\nI3FJL5ZBlrsgvIScE+cak0a4D/MwuXHrrbfiwx/+MN7ylrfg4Ycfxtra2ly4WwESdJkiyzIM7sLn\nXY7O9lWikSSOzln8mIoCE4lwEXLs/1KlMrHMadqexUWFJE8+Yy01IO2OYLUnLjZJNaCoe9a1hnss\nGZ8QUdkeeHaYmLLOZUAeIi+Mpa7W0aasdAxmpat194Wx00pX60x65AYlmdQ3RgCLqbOsyFa6GTHn\nTIrw/KIC6AawVyoJ1eqUdY5PlOAFHMXVBRNGzAUZDOIaE2677TY8+OCD2NrawqWXXoq77roLqqpC\nkiScOnUKr33ta/H5z38eV1xxBdrtNu65555Y+xEREnQpwwshPhYtyOUoGnEEnVvxYyoKTMTGxb06\n9bM6EXNStWKLOTT3Y9ak3VlRFISsGpD7ey2lPMRc8LizEXv1jZFdmsMtNs8vIcJzm+dVaO14ywBz\nwSahthX9b8Rwtco5CbLSMRe9rgOaBkvXAcOYPCQA00Jtbz5Ksrn3ljX7mQUnrFUO8LbEeXWPCMu9\n994b+Jm777479vZFhgRdxui6jk6n49mHVFTiZOgOBgOYpolWq+Va/JjEHBEaH6scsCfmKpXJT2Ai\n5lxg1rkwyJ0+UPW4JQpmSWexeQAwviBZ4kV9e4zxAS5ZZDjtTqx1tMglWph1DpiIZGal492u9Y0B\nLHZeDcu20gURSsiFtdLZG50IPKlSmeSdaJNsV7YFidWqM63ZkiZsri6wsIsi5Hi8MlxXVlaSDmkh\nIUGXMixujsWOAXB1OYpOWEFHRYGJVHFa5WTJXiglRZn8X1H2LSzVyr7YYta58Rio7wsUqbcnAPZe\n492t0mAMaZAwszKnRCa3BvQAUN+c3GfUg8EuWdmnS0ZUKrsajKZ/coQXtfPeGcZ+btdQYs5JkJVu\nrAL1GixVg1SrTjKlq5V9UTfes9iywsSsADLVqgMQX8z5lSzJq6j9vFEulVECxuMx+v0+FEVBq9XC\naDQqnZgDwmXoBpVaISFHRIYXb3vYVrlaDZZhQKrXJ9aUZmOyCDfqsMYqpGYzUMzxSDv9yaLO8LLO\nJTmcHLPWa5uTY1UvaAV8ch9ZnYgUp5XOSWVXg740G0unDPUZUdc4t1cixiN2rrYx2I+ZM81QVrpY\nQs5ppdvdS4JgSQ/8e3sWXkvdiwnU9JmsVok7HFNzcTdL8kJZ6eIKOcb/3965h0dR3/v/PbvZJJts\nIIAQCEEQDSQoEhICXpBWj2itCMhBQU4JFQraXxFoAAXFInoUEASERMpRG205JVSPGA6YeGokFlSy\n4SaXYkGFAJGbEHLd7GVmfn8k32FmdvaSy14m+byeJw/szuzud5Pdmfe8Pzdvgi4+Pr5Vz91R0Z/S\n0AEsd4wNItYjngSdPxW6JOSI1sAEnCiIUlsSzhTRKOaMxkZXxWhUibnoRjEnR9CuRJTaVnjBW/5c\noAsiWgsTds745oVioyrt4KM9nxI8iTp/kIdd/UHu0rVIzDFqvPytmeAzGgBeaPyssfy5ps9a/L4B\nEwAAIABJREFU4+3G7fKcOTeXrgMJOaD1Ys4bJOhaDgm6NiY6OlqqbDUYDEEZoRUI1IJOXdhBQo5o\nc2TNgjmjUXJEOKNR6ikmNjV6lUSfLHdOtDVIXf9hswFRGhWcdfUBceIkQtVHUnXhyPEiIq/Uw9HN\nf7cOACKqG+DqpAzdGhu8Fz9ouXQen/9aUxGEzI1TuHTyfStlYqy5v1cm5OQunTrkKsebqGu6UOAM\nnLLCVV0w0QFEXVsKOXLo2h4SdEGgrScuBAtWocvyAT0VdpCQI1qNvAhCnjcX0egIiTwvFUBwkZEQ\nnU5wTf3DOHM0RJusWtKmys9y8YCLtaaQHfL8TYUIg4IIT/lzvmBNkB3dYvzOn9MSddK2Jpcuola7\nYXBEjXYxBACYrtRB9FUU1iT0jC115bQcOa0CCSbqtLa5XNd70fGCQsAxZ64jhlzb2pXzdF6srKx0\nG/tF+AcJujZG/gHlOK5NGvSGCpfLhaqqKhiNRuolRwQWdiLkDFIYS3JLgOvVrBynEHNwuSQxx8kd\nOS13zhseXDvuWm2jeyO/T164YfDxvW763vNdLM1bTxsTebkWri5Kt47lzzUXLTHXHJfOF5piThR9\nu3TewqsMDQEn2h3uDqfB0Cjq2N/eV8j1+gPbnagLVHhVFEXN9iTV1dXo2bNnQF6zvUOCLsAEetB9\nW8N6ydmbwgwWi4V6yRGBx0PPOYiNYTDwvNJRa2ojoXbZxIam8Jj8BG3yI++ruvb6/w0Gj+Of3BrK\nekMmQIyVtR53C5bYi6hsFEpqYae5b5NL5yvcqnhMjXvrGObSGWuaRDfPX3fpNMKuxqomMedLKMtp\nppBTuLns2CwPwzbtyxkMEB0a7XB8tSlpJ6IukHly3qiqqiKHroWQoGtjtMZ/6UXQOZ1O1Dd1TY+M\njIQgCCTmiMCjDrcC7tWuERGN4S/I3DoZosMhnZy5SNlnVv75lT+uwQ5YIq5XPoawP6SW2AukyIuo\nrNcUdZxDKd4iqhs0x6IZ6psmQMQoXVDO7oQY1bKiCQDXxZwn1C6dP0JO/vB6jVYpcsdOQ9RphVtF\nQfQ8+qsdCDkgOGKOcujaHhJ0AcbTPNdwQquXnNylA0jIEQFEJt7kISz5bU5DzImCADQ5KJw/Lhyj\ntr5xQoA/Ys7oxZFrjovUTNQiT4iP9byzRkGEt+0AYLpcC76z7ypYQ3UDBA/5dP4ScbUOoknWhkbD\npTNUN4ktdoIXRO+/32aIOdFmk4pqNNEQdVL7EmmfpoIdl7PpZvuscg2mK0eCru0hQdfGqD+g4Vzp\nKu8lZzabFb3kmLNIQo4ICqrcOcUm2W1RnozeJLbkYo65c6KtoWmSRNPtepvb82oSBgUQWhiuyQSM\nKEJohYPHNRVHGKtsfok6j2uqd0guHRuX1hKXThJz/tBcISe9COdT1Inytjeq/ZmQ8/x4/YdZgx1i\n9SboKOTaMkjQBZhwDLnKe8lFR0cjNjbW7Yv1aKcnQ7Q6okOhkZMmD2cpCiPkgkzlnEm5TqpQGAuz\nKR4b0cLwagvz5wKBQebgCZ2b15pEjjdRxzXlz8ldOhZu9RdD0zxdzslrunQG1viZCWl5WFXt0tW2\noh8d4FHUycP1ivvlnyVV3pzmlAidirpQ5cp5oqamhkZ/tRASdAEmnASdIAhoaGiA3W6npsBE2KM1\nLQJAo5hjRRFGoyTmlKLNz0NbS8OtYYShqV+b0MVLWNYLxiobBLN3V81T6NVQ7y6G/HXpJDHnC3lP\nOT8Q1W1rFC96XdQpCh7kRRNaLUnYc3ty+UjINRtPDp0oirqZeR5ukKBrY8KxKIKaAhNhi6xdidsm\nmTOnmKPZzHmk15sQN4UFI7QdLbGhAVxM4zaxvl7ZnoQR1xTqrKu7/v9goj6WyASGobLuuoPUuWlt\nfubvGqptEDp5D78aqhsAjQkanM0B0exeIMHVNgAyYSd36aSRbOzELQjaLl2NMtTsTdR5FXLy/bQq\nVwGA5z0KtvZWBPHnivWoq6uDwWCAwWCA0WiEwWCQWm0FGk/nxFCfK/UOCboAIBdxoSyKoKbAhG4Q\nBU1Rp3Dp1EnyKgdPclYMnDL0Kv/Mc5yy2lF+YWM0QKz34RrV1F5/jRoPrUg4LjRiT76Eqsa1iXFK\n8cp5EcNyUcdptCvhHE6IEZ7nvSr2bQq1wu70KOrckIs6oHGqhxoPos4fMcda2mjS5Ph6KnaQpkTo\nHObKsabxgiCA53k4nU4IgiD1hmMCj/20tchj7pyn59Vj39ZwgARdgDEYDHA6fSTUtjGiKMLhcMBm\ns8FgMFBTYEK3KJwRUXaQ5wyA0HQSNhohCtphMq+FEF4KIDTduebgSewBQRV7bG6t2Mm/cCwrUBAj\ntUOmXL0dYkyU4jag7dJ5XJM81MrGbKmprfMrxOq3K+dJzLk8fG4MnJsrp9lM2FdPujDiw8p3pP8z\nMWUwGBTnBkEQpB+50JOLO7mb19a4XC4Kt7YCEnQBQO3QBctGZk2BbU0HudjYWLc+cgCJOSJM8RB+\ndXPmvIktb60uvJ2AmpMv19p2JVpiL8Aij6uu8yzqNHLGuLp6iLHaoWm1qJPubxJ1kjvHkLt0rLDB\nU2FKTa126FVO0/2tcuU8CDnAc3hVr/lzf7vyXxBFETzPS3PGmaBjoo7BRJsc5uSxH7vdDkEQpMfK\n3Tx/Q7ae8ueqq6vRuXPnVr7jjgsJugATLEHHhJwgCIiJiYHJZHL7wpCQI3SBaui5+4lUVgVr4CC6\nlPsrtqkqFaWmw4Fy51rqWvgj8rzkzzVuVwkLdbFCZU3T8/pw65oiCnJRx6n6sjFnTg1nczQ+Xqsv\noLxK1cVfF3XMpWMhVk/5dOxtsZC5D2GtKea8CDlAW8zpVcgBwLbqPElksZAq+1cecgWuFyOw8wYT\ndhzHwWg0KpwzbyFbdbhWy83zJOiuXbtGPehaAQm6AKCe5xpIQafVFJiEHNEu8CGsvDl3nra5NYwF\n3IQBK4wIOWqRZ2lZFav78zYVGvgSdvDu1KHBDkR7yKlTizq7j7QTf0Os8vxHD82HA+7K6UDI5V/+\nIwRBQG1t42eIiSwmzJjIYvndzH2TCz55T1K1m+dvyNbhcEh5efKQrae8cmoq3DpI0AWYQAk6eVPg\n6OhoRVNgBgk5Qtd4OXG65cZ5E3/N7B8neAnlcQYDOHPrJie0mFpVU93WCs+qGiDGd2Nhrq7ev3m4\nQKPI04I17ZU7o3KXDlD1oFO6dIr5q3Jkoo6EHFBQ+77iNnPSWLiVTQASBEEh7oxGoyKqoxZ3TIDx\nPC8JtJaEbHmeh8vlkp7PZrPBaDRi3759SExMRGVlJQm6VkCCLsAwQefJYm4u8qbA1EuO6JD4E4aV\nR1o1Wm1ItCAfzqO4AMD5IZDaBFFsbJ3CiI113y6H9yBG6m1KUadVwOXiG3/kQpaJp+a4dIB7JWtt\nvef8xaZ9vf2+Af+qV90e087y5AB3MQconTR5PrVc5DEnjRU/qIUeO7+0RciWrcFut0v7C4KAvLw8\nlJSUwGazoUePHqipqUFaWhrS0tKQmpqKyEjfBTdFRUWYN28eBEHAjBkz8Nxzzym2nz17FtOmTcO1\na9cgCAKWL1+Ohx56qAW/6fCF8+Ee6b9OOwSwqxDG1atXER8f7ya8moMoirDZbLDb7YiMjITZbCYh\nR3RcPLhubqFWPx8H4Hp+nceHtvz72+ZCz1s+nSXGt6DTCnnFmD0LOgYTdVoiyuEAtE68Wq/Ffpfs\neeSiTnbhKzbYPYZiPfaTY7SFmNOpkGsJcoEm/5ELMnUBhFbIVq0ptEK2drsdHMe5CbWNGzfiwoUL\n6NmzJw4dOoRDhw7h1KlT2L59O0aPHu1x7YIgYMCAASguLkZiYiIyMzORn5+PlJQUaZ+nnnoK6enp\neOqpp3D8+HH88pe/xKlTp9rkdxdkPB7kyKELAq2Z50q95AhCAw8nWpH30qrER+hVM7+OPdSH2POF\nIveLPWeg3DxWfBDbjOd3uYDqGqULByjFHADYGq6LPi3xphZ1TLBp/f48OWusipVt99FQWLne5odX\nARJzgPfiB7mTx8KucpHX3JAtcwPZvwyHw4GRI0diwoQJ0n319fU+zRCr1Yrk5GT07dsXADB58mQU\nFBQoBJ3BYEB1dTWAxuKL3r17t/I3Fn6QoAsAbTEtQt5Lzmg0Ui85gvATkec9iDfee186b7hcHsMV\nnB/hIC08iTyx3uZd7PmqdmXUNfWU43lwngob1LDwpj95gnLxJnfLtJw6h1Mh6sS6euXfghckl04K\nscpP4jJRJ9o9uHYdOFcuUHgK2apz4lhenjxkK3f05I+x2+3geR4Gg0F6PDtHnj9/HnfddZdiDTF+\n5IpWVFSgT58+0u2kpCRYrVbFPkuXLsUDDzyA9evXo76+Hp999llrfjVhCQm6INAcQcd6ybGrEuol\nRxDNxIsT582l8ST2fIVxtUJ/rRV5crHXFk6e2NQShIuN8WscmFhbBy5aQ9SpQ7Kewp4Oh7vQbBJ1\nTLCJPO8m6hS/S1W+HRvd1nij6bk5joRcCGBhV7nJoA7ZOp1ORciW4zipcbDFYlFUu7pcLnz88cco\nLCzEE0880ez1aJ1f1cbKli1b8OSTT+L3v/899u7di1/96lc4duxYs18rnCFBFwBa6tAxIQeAeskR\nREvxdGL2FXL1cPLnDM0/THrK72qJ0FM7ea2pshXr6gFRVIpET7lmDY3CS1PYyfdzON1C0ix8zami\nCmJtnWIyhFzUKQSbVrWrp9fWal3SQYoewglPIVtWyOdyuSRX7sqVK5g6dSpuvfVWJCcnY8eOHUhJ\nScGhQ4fQqVOnZr92UlISzpw5I90+d+4cEhMTFfu8++67+PTTTwEAd9xxBxoaGvDTTz/hhhtuaOE7\nDj+oKCIAsHApo7a2FiaTCVFR2tVgLpcL9fX1EASBeskRRDBpZhNhJh5aHLpVP18LnTyGKAgwmK+L\nM8FmU9x2EzbqhPUYc6PIAsA1VatqiqGmaRKcqqJVnncoF3WK++UuDjsuqn9/WqKShVg9CU7VhAtp\nNBe5cmEDa3hvMpkQHR0tndfsdjtKSkrwySef4ODBg/jpp59w6dIlpKSkSNWtTz75JOLi4vx6HZ7n\nMXDgQBQXF6NXr14YPnw4tmzZgtTUVGmfhx9+GI8//jimTZuG48ePY/To0Th37lxA3neAoaKIUCKv\nBpIj7yVnNpsRFRVFQo4ggkkz3Dy5E+TRzWum0GuNkyeyCkNV3zz5bV/PI8p620lFCCbPpwW2j1rY\nAdedOnVxiehygYuIUL5X2QxX+f2sklgSa1rum8aoMqD9CTlAv2KOuXJscpE6//vHH3/EH//4Rwwd\nOhS7d++G2WxGfX09jh49ioMHD+LgwYPNmulqNBqRk5ODBx54QGpbkpqaiqVLlyIzMxNjxozB6tWr\nMXPmTKxduxYGgwHvv6/P3603yKELEHZZ+MBms0EURSm5U95LLjo6WnHlwiAhRxDhRUtduUC5eaKv\nXDi1GxcVpVFQoXwOuSiSRJuGgBJ5Hpwqt1eU5dexbaIq504KrzLXTau4QatnnoHzKOQan9BD1bNO\nQ6x6FXIsB7yhoQGRkZFuJoXL5cKmTZtQUFCAdevWYdiwYSFcrW4hhy7YyPPmmEMnCAIaGhpgt9up\nKTBB6IyWunJaj2uJyFM4XBEtyOuTXWRykZE+iyMkN061VvZ+mFjjTCY34SY6nW6CT3qsXFTKixsA\nZehV5pJ6FHPNEXJhLuIYehVzclcuNjbWzWH75z//iQULFmD06NHYtWuXZrEf0TrIoQsQbIYdAEnE\nCYJATYEJogPQEsHWGidPFERlYYI/VfVNooc9TlOwyp6H5cJ5qxRWwJw29SQIl8sth050urSriTmD\n59fTEGh6deQA/Qo5ljPOjAp1DrjD4cCaNWuwZ88e5OTkYNCgQSFcbbuAHLpgw1w51hQYADUFJogO\nQktcuZY6eUzEqHPXOC+5cPKWItLj1MJLJQo9hknlIVL2HPL7ZD3mJAeOvVejUXLf2PtQFjc07Sd3\n6+RhYXleo05dOb0KOeB6HjgAN1dOFEUcPHgQzz33HB5//HH8/e9/b1ZeHNF8SNAFCLvdjrq6OhgM\nBpjNZtjtdvowE0QHJpgiD9CoAvUm8EQBcMnEj1ZIV72WiAj3fDdPM2N5oTHvTuXCaYVSRUF0F2JN\nt9WizaMjJ3tMOKNXMccmGLGZ4mpXrr6+HsuXL8fx48fxl7/8Bf379w/hajsOFHINEDU1NeA4DiaT\nCTzPo6amBvHx8R73J6eOIAigeaFXydVqzsWiKICLMClue3peQCYEVYJO67XVAlQqglDfb+CaFR71\nKtz8eHy4oVchBzQWNthsNsmskKcPiaKIL7/8Ei+++CKeeuop/PrXv27VDHNCE48hVxJ0AcLlcoFv\nOogJgoCqqip06dKlWc9BIo8gCEBbsHkTOR4FngexoxBlHkKXPvfxhCi4t4GRr6Npm5bo87YevaJX\nMSeKIhoaGuB0OhEdHe3W+L66uhp/+MMfcPXqVWzYsAG9evUK4WrbNSTogo1c0ImiiMrKSnTp0sWt\nPUlzIZFHEASAZjVF5oxG/0WQN/Hl7bU1RJq/r9neHDgt9CrkgOuunNFoRHR0tJsr9/e//x2vvvoq\nFi5ciMcee6zV5znCK1QUEWzkH+i2/HDvsG12u49EHkF0QPwVWvCQi6fOZ5NElXbRgcfX5gxua/G3\ncMFr6NXba+oIPQs5uStnNpvdWo1cuXIFixYtgtFoRFFREbp16xailRIAOXQBg+d5uGQ9lSorKzX7\nzgUKEnkEQQBo9ngz70/lSQRe394st00LnQo3LfQs5jyN7QIahd5HH32E9evXY9myZXjooYfIlQse\n5NAFG/WHm7UxCZagIyePIAgA7gLJn5Cq1n7wHRptltvm7zp0iJ6FHGuAz/O85tiu8+fPY8GCBejV\nqxeKi4vRqVOngK3l3LlzyMrKwoULF2A0GjFz5kzMmTPHbb85c+agsLAQsbGxeO+995CWlhawNYUz\nJOiChHxyRKggkUcQhN/CyZsQbIu8unYk4OToVcypx3aZzWaFMSEIAjZv3oy8vDy8/vrrGDVqVMBd\nuYiICKxZswZpaWmora1FRkYGHnjgAaSkpEj7FBYW4vvvv8fJkydRWlqKp59+Gnv37g3ousIVEnQB\nQv1BNxgMIRd0agRBwNafNrnNlCWRRxCEG74EWGu36xy9CjnA99iuU6dOYf78+RgyZAhKSkpgNpuD\nsq6ePXuiZ8+eAACLxYLU1FRUVFQoBF1BQQGysrIAACNGjEBVVRUuXryIhISEoKwxnCBBFyTCwaFj\nsERXdiUmz+0TRREFte9DaJrzyHEcOI7DOMu0UC6ZIAgibPnLjxtQV1cHo9Eo/eih/5p8bFdkZCRi\nYmIUZgTP89i0aRO2bduGdevWITMzM2RrPX36NA4dOoQRI0Yo7q+oqECfPn2k271790ZFRQUJOiJw\nhIOgY929WaKrfBSZKIoQBMFNyDG2VeehoaEBLpdL6gw+Pu7XoXgbBEEQYUFB7fvSsZPnefA8L83t\nBqAQeEaj0e24Gkq8je0CgOPHj2PBggW47777sGvXLkRGRoZimQCA2tpaTJw4EW+++SYsFotim9Z5\nNVx+x8GGBF2A0CqKCJWgY7kR9fX1MBgMiIuLkxJd2cFIFEWIouh2wJGPeImMjERcXJy0XSvEQE4e\nQRDtHfmxj+M4SbAx2PGUiTyHwwGe5yGKopvIMxgMQRUgvsZ2ORwOrFu3Dl988QVycnJw6623Bm1t\nWrhcLkycOBFTp07FuHHj3LYnJSXh7Nmz0u1z584hMTExmEsMG0jQBRC5iGNVrsGGlZ6LooiYmBip\nuzdbFzvIcBzn1iySWfERERGwWCx+hRBI5BEE0Z7xJ1eOXRgbDAZF7za5k+dyuSQ3L1gij+d56cJe\n65h+8OBBPPvss3jsscfw2WefhcX88enTp2PQoEGYO3eu5vaxY8ciNzcXkyZNwt69exEfH98hw60A\n9aELKA6HQxJOdrsdTqfTzS4OFOyLy/M8zGaz4ipMHl5l98m3uVwuNDQ0wGAwIDo6OiBfahJ5BEHo\niUAVPcidPPbDWlxphWxb+hrMldMa22Wz2bB8+XIcPXoUubm5uPnmm9vq7bWKL7/8EqNGjcLgwYMl\nkfzaa6+hvLwcHMdh1qxZAIDZs2ejqKgIsbGxyMvLQ3p6eohXHlBo9FcocDqdkivH3K64uLiAviar\nVlJXrgK+8+SYkBNFEWaz2a3/UCARRZFy8giCCEuCXcEqF3lyV08u8tj/fUVOfI3t+uqrr7BkyRLM\nmjULTz75pC6KOTo4JOhCgVzQsdBnoJowiqIIm80Gu92OqKgoxRfXl5DjeV5qJKl19RYqSOQRBBFK\nwqkVibr4gv3Ic/jUTp63sV01NTVYunQpLl++jA0bNnTYvDMdQoIuFMgFncvlQl1dHTp37tymr6Gu\nXDWbzX5XrgqCIIWCtZJjwxEK1RIEEQzCScx5Qn6Ml4s8dl43GAyIiopCQ0ODVMkqiiI+++wz/Od/\n/icWLFiAxx9/POyP+4QCEnShwOVygW8aUs3zPGpqahAfH98mz82KFpiVLg+RNqdy1WQyISoqStc2\nO4k8giDaCj0IOU+wlBue56U2IzzPY/ny5Xj77bcxaNAgAI3tVJYvX4677rrLzbkjwh4SdKFALugE\nQcC1a9fQtWvXVj8va0ECQKpcBaBZuaoWcvLKVXU+RXuCRB5BEM1Bz0JOPrbLZDIpcqfZ9vz8fHz4\n4Yfo06cP6urqcODAAZSXl2PQoEGYPHkyFixYEMJ3QDQDj4KO2pYEEPkXSl6Y0FJ7myW3+lO5Khdz\n8spVjuM0m0i2N6h9CkEQ/qJnMScf2xUTE+NWzHbhwgUsWLAACQkJyM/PV6T91NbW4vDhw5LxQOgb\ncugCCOs1xKisrFSM2fIXQRBQX18vJbdGRUW1qHI1OjoaERERlC8hg0QeQXRc9Czk1GO75OcFoPG8\nsXnzZuTl5WHlypX42c9+Rsf+9gE5dKGgtdMiBEFAQ0ODVLmqnrmqx8rVcIOcPILomOhZzPka23X6\n9GlkZ2fj9ttvR0lJCcxmcyiWSQQZcugCiCAIcDqd0u2qqirExsb67O8mr1yNjIyE2Wz2W8jpsXJV\nD5DII4j2gZ6FnNyV0zq+8zyPt99+G//zP/+DtWvXYvjw4SFcLREgyKELB3w5dOrK1U6dOrm1IPG3\nctXfUV2Ef5CTRxD6Rs9CDvA9tuvbb7/F/Pnzce+992LXrl1SlSvRcSCHLoAwgcaoqamRch3UtKZy\nlVU3tffK1XCD/d45jpP6/5HII4jwQ89iztfYLqfTiXXr1mHXrl3Izc3FrbfeGsLVEkGAHLpwwGAw\nuDl0LpcL9fX1UoWS/MvKxr/IhZynylWt6iYiMLD8REEQ3ApNyMkjiPBBz0IOuN7ZwJMrd+jQITz7\n7LP493//dxQXF7f77gWEd8ihCzB2u136f319veTmsKRWqlzVD22Zn0gijyACi57FnCiKXsd22Ww2\nrFixAkeOHEFubi5uvvnmEK2UCAHUWDhUOBwOyZVjvYI4jpOSWs1ms99Cjud52O12uFwuqlwNIvJE\n5EBO1iCRRxCtR89CDrg+9zsiIkJxfgAaj0Vff/01XnjhBcycORPTp0+nFJuOBwm6UMEEnSiKqK2t\nldydllauavUbIgKDPKxtMBgQHR0d9JAGiTyC8B89iznWpsrlcmmm0NTU1OCll17CxYsXsWHDBvTu\n3TtEKyVCDAm6UOFwONDQ0ACbzQaO42AwGBAXFweg481c1RPe8uRCiSiKGB/361AvgyDCCj0LOX/G\ndhUXF+OVV17B/PnzMWnSpLA4FhEhgwRdqLhy5QoEQYDZbJbyIpig86dy1Wg0hsQZ6qjosY8fiTyi\no6JnIQcox3aZzWY3V+7q1atYvHgxAGDNmjXo3r17QNczY8YM7NixAwkJCTh8+LDb9i+++ALjxo1D\n//79AQATJkzAkiVLAromwg0SdKHCbrdLos3lcqGurg6xsbGKma6eKleZM0QEnmDlyQULCtUS7R09\nizn5RbtWGo0oiigoKMDatWuxdOlSPPzww0G5sNyzZw8sFguysrI8Cro33ngD27dvD/haCI9Q25JQ\nYTQaJSeOtSGpra2F0WhU/LArNapcDS7qPDmtMTp6hNqnEO0VPQs5wPfYrgsXLmDhwoXo3r07Pvvs\nM3Tu3Dloaxs5ciTKy8u97tOc8ZVEcCFBF2CYiGMFD3FxcdJ9PM/D4XBI24xGIyIjI3XtDOkJdmBl\nIlrdGqC9QSKP0Dtbf9oEp9MJo9Gou+Okr7FdgiDgv//7v/Huu+9i5cqV+PnPfx6WF/V79+7F0KFD\nkZiYiFWrVmHQoEGhXhLRBAm6APOb3/wGly5dQnp6OjIyMpCRkYEbbrgBlZWVWLlyJR599FEMHToU\nEREREARBIfLULp7BYAjLL7jekFeT6SVPLlCQyCP0wLbqPMVFMM/zAOB2jFTnI4cLcldOq0FweXk5\nsrOzcdttt6GkpAQxMTGhWKZPMjIyUF5ejpiYGBQWFmL8+PE4ceJEqJdFNEE5dAFGFEX89NNPKCsr\ng9VqhdVqxbFjx1BVVYVRo0Zh6tSpGDVqFCwWi1sOBc/zcLlc0oEMcD+A6e0qNZSoq4bV1WSEZ0jk\nEaHAU3hVnsIi/wHCS+T5GtvF8zzeeecdfPDBB1i7di2GDx8e8mNSeXk5HnnkEc0cOjU33XQT9u/f\nj65duwZhZUQTlEMXKjiOQ/fu3fGLX/wCV69eRV5eHoYOHYpnnnkGV69eRVlZGTZt2oS6ujrccsst\nkpM3ePBgREZGKooimIPn7SqVcu/cYXlyNpsNRqOx3eTJBRNy8ohg4y1Xjok0g8GgmHutTmfROkYa\nDIagRDt8je3617/+hfnz5+NnP/sZSkpKEBkZGdD1+Av7PWpx8eJFJCQkAACsVitEUSTfhA+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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sympy.abc import h, s\n", + "from devito import Operator, time\n", + "\n", + "# Reset our initial condition in both buffers\n", + "init_hat(field=u.data[0], dx=dx, dy=dy, value=2.)\n", + "init_hat(field=u.data[1], dx=dx, dy=dy, value=2.)\n", + "\n", + "# Create an operator that updates the forward stencil point\n", + "op = Operator(Eq(u.forward, stencil), subs={h: dx, s:dt})\n", + "\n", + "# Apply the operator for a number of timesteps\n", + "op(time=nt+1)\n", + "\n", + "plot_field(u.data[0, :, :])\n", + "\n", + "# Some small sanity checks for the testing framework\n", + "assert (u.data[0, 45:55, 45:55] > 1.8).all()\n", + "assert np.allclose(u.data[0], u_ref, rtol=3.e-2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Great, that looks to have done the same thing as the original NumPy example, so we seem to be doing something right, at least.\n", + "\n", + "**A note on performance:** During the code generation phase of the previous operatorm Devito has created some log output with information about two optimisation steps: The DSE (Devito Symbolics Engine) and the DLE (Devito Loop Engine). We can ignore these for now, because our exmaple is tiny - but for large runs where performance matters, these are the engines that make the Devito kernel run very fast in comparison to raw Python/NumPy.\n", + "\n", + "Now, despite getting a correct looking result, there is still one problem with the above operator: It doesn't set any boundary conditions as part of the time loop. We also note that the operator includes a time loop, but at this point Devito doesn;t actually provide any language constructs to explicitly define different types of boundary conditions (Devito is probably still a kind of prototype at this point). Luckily though, Devito provides a backdoor for us to insert custom expression in the so-called \"indexed\" or \"low-level\" API that allow us to encode the Dirichlet boundary condition of the original example.\n", + "\n", + "#### The \"indexed\" or low-level API\n", + "The `TimeData` field we created earlier behaves symbolically like a `sympy.Function` object with the appropriate indices, eg. `u(t, x, y)`. If we take a simple first-order derivative of that we have a term that includes the spacing variable `h`, which Devito uses as the default for encoding $dx$ or $dy$. For example, `u.dx` simply expands to `-u(t, x, y)/h + u(t, x + h, y)/h`.\n", + "\n", + "Now, when the `Operator` creates explicit C-code from that expression, it at some point \"lowers\" that expression by resolving explicit data accesses (or indices) into our grid by transforming it into a `sympy.Indexed` object. During this process all occurences of `h` in data accesses get replaced with integers, so that the expression now looks like `-u[t, x, y]/h + u[t, x + 1, y]/h`. This is the \"indexed\" notation and we can create custom expression of the same kind by using the `u.indexed` property with explicit indices in square-bracket notation. These custom expressions can then be injected them into our operator like this:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "CustomCompiler: compiled /tmp/devito-1000/79af1d1041662300b14c729f097a980d80c1827a.c [0.18 s]\n", + "=========================================================================================\n", + "Section loop_y_1<101,81> with OI=0.00 computed in 0.000 s [Perf: 0.00 GFlops/s]\n", + "Section loop_x_2<101,81> with OI=0.00 computed in 0.000 s [Perf: 0.00 GFlops/s]\n", + "Section main<101,80,80> with OI=0.61 computed in 0.001 s [Perf: 5.87 GFlops/s]\n", + "=========================================================================================\n" + ] + }, + { + "data": { + "image/png": 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rVwTiqw6B4MUcC9wcj8fo9/uoVqtYW1tDs9kshZgDshFGmqah1+uh1+tBUZRM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\nxNWrV0O8K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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from devito import t, x, y\n", + "\n", + "# Reset our data field and ICs in both buffers\n", + "init_hat(field=u.data[0], dx=dx, dy=dy, value=2.)\n", + "init_hat(field=u.data[1], dx=dx, dy=dy, value=2.)\n", + "\n", + "# For defining BCs, we want to explicitly set rows/columns in our field\n", + "# We can use Devito's \"indexed\" notation to do this:\n", + "bc_left = Eq(u.indexed[t + 1, 0, y], 1.)\n", + "bc_right = Eq(u.indexed[t + 1, nx-1, y], 1.)\n", + "bc_top = Eq(u.indexed[t + 1, x, ny-1], 1.)\n", + "bc_bottom = Eq(u.indexed[t + 1, x, 0], 1.)\n", + "\n", + "# Now combine the BC expressions with the stencil to form operator\n", + "expressions = [Eq(u.forward, stencil)]\n", + "expressions += [bc_left, bc_right, bc_top, bc_bottom]\n", + "op = Operator(expressions=expressions, subs={h: dx, s:dt},\n", + " dle=None, dse=None) # <-- Turn off performance optimisations\n", + "op(time=nt+1)\n", + "\n", + "plot_field(u.data[0, :, :])\n", + "\n", + "# Some small sanity checks for the testing framework\n", + "assert (u.data[0, 45:55, 45:55] > 1.8).all()\n", + "assert np.allclose(u.data[0], u_ref, rtol=3.e-2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You might have noticed that we used the arguments `dle=None` and `dse=None` in the creation of the previous operator. This suppresses the various performance optimisation steps in the code-generation pipeline, which makes the auto-generated C code much easier to look at. So, for the brave, let's have a little peek under the hood... " + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "#define _POSIX_C_SOURCE 200809L\n", + "#include \"stdlib.h\"\n", + "#include \"math.h\"\n", + "#include \"sys/time.h\"\n", + "\n", + "struct profiler\n", + "{\n", + " double loop_x_0;\n", + " double loop_y_1;\n", + " double loop_x_2;\n", + "} ;\n", + "\n", + "\n", + "int Kernel(float *restrict u_vec, const int t_size, const int x_size, const int y_size, const int time_size, struct profiler *timings)\n", + "{\n", + " float (*restrict u)[x_size][y_size] __attribute__((aligned(64))) = (float (*)[x_size][y_size]) u_vec;\n", + " for (int time = 0; time < time_size - 1; time += 1)\n", + " {\n", + " int t0 = (time) % 2;\n", + " int t1 = (time + 1) % 2;\n", + " struct timeval start_loop_x_0, end_loop_x_0;\n", + " gettimeofday(&start_loop_x_0, NULL);\n", + " for (int x = 1; x < x_size; x += 1)\n", + " {\n", + " for (int y = 1; y < y_size; y += 1)\n", + " {\n", + " u[t1][x][y] = 6.0e-1F*u[t0][x][y] + 2.0e-1F*u[t0][x][y - 1] + 2.0e-1F*u[t0][x - 1][y];\n", + " }\n", + " }\n", + " gettimeofday(&end_loop_x_0, NULL);\n", + " timings->loop_x_0 += (double)(end_loop_x_0.tv_sec-start_loop_x_0.tv_sec)+(double)(end_loop_x_0.tv_usec-start_loop_x_0.tv_usec)/1000000;\n", + " struct timeval start_loop_y_1, end_loop_y_1;\n", + " gettimeofday(&start_loop_y_1, NULL);\n", + " for (int y = 0; y < y_size; y += 1)\n", + " {\n", + " u[t1][0][y] = 1.00000000000000F;\n", + " u[t1][80][y] = 1.00000000000000F;\n", + " }\n", + " gettimeofday(&end_loop_y_1, NULL);\n", + " timings->loop_y_1 += (double)(end_loop_y_1.tv_sec-start_loop_y_1.tv_sec)+(double)(end_loop_y_1.tv_usec-start_loop_y_1.tv_usec)/1000000;\n", + " struct timeval start_loop_x_2, end_loop_x_2;\n", + " gettimeofday(&start_loop_x_2, NULL);\n", + " for (int x = 0; x < x_size; x += 1)\n", + " {\n", + " u[t1][x][80] = 1.00000000000000F;\n", + " u[t1][x][0] = 1.00000000000000F;\n", + " }\n", + " gettimeofday(&end_loop_x_2, NULL);\n", + " timings->loop_x_2 += (double)(end_loop_x_2.tv_sec-start_loop_x_2.tv_sec)+(double)(end_loop_x_2.tv_usec-start_loop_x_2.tv_usec)/1000000;\n", + " }\n", + " return 0;\n", + "}\n" + ] + } + ], + "source": [ + "print(op.ccode)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "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": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/examples/cfd/tools.py b/examples/cfd/tools.py new file mode 100644 index 0000000000..eb6a508e2e --- /dev/null +++ b/examples/cfd/tools.py @@ -0,0 +1,46 @@ +from mpl_toolkits.mplot3d import Axes3D # noqa + +import numpy as np +from matplotlib import pyplot, cm + + +def plot_field(field, xmax=2., ymax=2., view=None, linewidth=0): + """Utility plotting routine for 2D data + + :param field: Numpy array with field data to plot + :param xmax: (Optional) Length of the x-axis + :param ymax: (Optional) Length of the y-axis + :param view: (Optional) View point to intialise + """ + x_coord = np.linspace(0, xmax, field.shape[0]) + y_coord = np.linspace(0, ymax, field.shape[1]) + fig = pyplot.figure(figsize=(11, 7), dpi=100) + ax = fig.gca(projection='3d') + X, Y = np.meshgrid(x_coord, y_coord) + ax.plot_surface(X, Y, field[:], cmap=cm.viridis, rstride=1, cstride=1, + linewidth=linewidth, antialiased=False) + + # Enforce axis measures and set view if given + ax.set_xlim(0., xmax) + ax.set_ylim(0., ymax) + if view is not None: + ax.view_init(*view) + + # Label axis + ax.set_xlabel('$x$') + ax.set_ylabel('$y$') + + +def init_hat(field, dx, dy, value=2., bgvalue=1.): + """Set "hat function" initial condition on an array: + + u(.5<=x<=1 && .5<=y<=1 ) is 2 + + :param field: Numpy array with field data to plot + :param dx: Spacing in the x-dimension + :param dy: Spacing in the y-dimension + :param value: Value of the top part of the function, default=2. + :param bgvalue: Background value for the bottom of the function, default=1. + """ + field[:] = bgvalue + field[int(.5 / dx):int(1 / dx + 1), int(.5 / dy):int(1 / dy + 1)] = value From 79bee1dc229fb8b076e00b0fb621379f35610ed6 Mon Sep 17 00:00:00 2001 From: Michael Lange Date: Mon, 29 May 2017 12:10:22 +0100 Subject: [PATCH 02/12] CFD: Add tutorial notebook for non-linear convection --- .../cfd/test_02_convection_nonlinear.ipynb | 354 ++++++++++++++++++ 1 file changed, 354 insertions(+) create mode 100644 examples/cfd/test_02_convection_nonlinear.ipynb diff --git a/examples/cfd/test_02_convection_nonlinear.ipynb b/examples/cfd/test_02_convection_nonlinear.ipynb new file mode 100644 index 0000000000..c35ce5d428 --- /dev/null +++ b/examples/cfd/test_02_convection_nonlinear.ipynb @@ -0,0 +1,354 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Example 2: Nonlinear convection in 2D\n", + "\n", + "Following the initial convection tutorial with a single steat variable $u$, we will now look at non-linear convection (step 6 in the original). This brings one new crucial challenge: computing a pair of coupled equations and thus updating two time-dependent variables $u$ and $v$.\n", + "\n", + "The full set of coupled equations is now\n", + "\n", + "$$\\frac{\\partial u}{\\partial t} + u \\frac{\\partial u}{\\partial x} + v \\frac{\\partial u}{\\partial y} = 0$$\n", + " \n", + "$$\\frac{\\partial v}{\\partial t} + u \\frac{\\partial v}{\\partial x} + v \\frac{\\partial v}{\\partial y} = 0$$\n", + "\n", + "and rearranging the discretised version gives us an expression for the update of both variables\n", + "\n", + "$$u_{i,j}^{n+1} = u_{i,j}^n - u_{i,j} \\frac{\\Delta t}{\\Delta x} (u_{i,j}^n-u_{i-1,j}^n) - v_{i,j}^n \\frac{\\Delta t}{\\Delta y} (u_{i,j}^n-u_{i,j-1}^n)$$\n", + " \n", + "$$v_{i,j}^{n+1} = v_{i,j}^n - u_{i,j} \\frac{\\Delta t}{\\Delta x} (v_{i,j}^n-v_{i-1,j}^n) - v_{i,j}^n \\frac{\\Delta t}{\\Delta y} (v_{i,j}^n-v_{i,j-1}^n)$$\n", + "\n", + "So, for starters we will re-create the original example run in pure NumPy array notation, before demonstrating \n", + "the Devito version. LEt's start again with some utilities and parameters:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from examples.cfd import plot_field, init_hat\n", + "import numpy as np\n", + "%matplotlib inline\n", + "\n", + "# Some variable declarations\n", + "nx = 101\n", + "ny = 101\n", + "nt = 80\n", + "c = 1.\n", + "dx = 2. / (nx - 1)\n", + "dy = 2. / (ny - 1)\n", + "sigma = .2\n", + "dt = sigma * dx" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's re-create the initial setup with a 2D \"hat function\", but this time for two state variables." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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VQqGgr4+r154rqoGuHgY5ouCwE4I9cQ4yF2hnaZVq9WrQsbi7PQa6JlmVLQlD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\nJjjtuLi6VQu4J1krngG0Wq0upwyQe9imiB1bkQD3z94WFBRAo9Fgy5Y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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Allocate fields and assign initial conditions\n", + "u = np.empty((nx, ny))\n", + "v = np.empty((nx, ny))\n", + "\n", + "init_hat(field=u, dx=dx, dy=dy, value=2.)\n", + "init_hat(field=v, dx=dx, dy=dy, value=2.)\n", + "\n", + "plot_field(u)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can create the two stencil expression for our two coupled equations according to the discretised equation above. We again use some simple Dirichlet boundary conditions to keep the values on all sides constant." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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QSQjr41qkoLvjjjvw5je/GQDw0pe+FBdeeCG+//3vF7a/PCGXawLYosdKj7Cs\nss3NzVo+ceW1iPN9Vqusq1clfLKHN0aQxBJRFJ9/9ucxtlpQJBs9n7IgY7uF8XzqNXzKlkTxgum4\nts5UluvH+VnqgOU4ui/uHoJuqXjj5neodAnIQhcXtr56yUPQsWxaP17ykpfg7//+7/HTP/3TOHHi\nBH74wx/ioosuyrS/siBBlwDbtrGzs+N2MGDirq4XZ1ahwbfnYtlIZdTVE0kgWZaFyWTiJnuIHjeZ\nFVHOuwhUvTD/9+NvRENqYUNZjF/TbAWa7Qgxv/g5PulBjshyZbxgdtGNqFE3tNtLsXRf3D209L7x\neJy6WDJBZG37dfPNN+Oee+7BqVOncMEFF+D222931/GjR4/id3/3d/GOd7wDV111FQDgD/7gD3Dm\nmWfmNfxCIUGXAEmSsLGx4S7YfDeIOpKlzyhfILnsunoiCLokQk6E8SZFluWluU0Lrjjc+cy/R8Pn\n69gx22jLy7XnklrnLCxv/AWrjzPlvViiZ4wzsKFMArfxP4dXQuY6UvzIOAtnyrt4z0P/FX/7E7+T\nuFjyqlD1g0BdCDpPWQXdnXfeGfr6i170Itx9992pt18lJOgSoiiKuzh7s1zrRlKhIVKB5KrOO19+\npQ6ZzHHxzoU6z+t1glnnTFvCjrmYmBCU3XrK3HB/PkfZSbQ/r6hLwgPjC/Dq/ndx84vvW6rHmaUr\nBrGahAm6gwcPVjAi8SFBlxB+4auj5cWPpH1Gqy6QXMWNPIuQq+M8YTEmtGiKxx8/9R+wpQBjy3G3\nDs02uvPYNN46d8rYS2pgFjrFU2/uhYDEh33KaOH36bwGXVz+5/DKRO+P0xWDdeRhlmNZlqEoSqqG\n71USFBtGLBIm6A4dWnblEyToMsEW6roufFFj9na6EKVhfJkCqW61BbPC95a1bXthwWSvE9Xx34+/\nEVuKibHVQleeLYg5AHhhQcSZ8/+TuVtNyK4V7yxluPT6C1bfLZMyNDsLbteh3cY3R04AuSL5h6Mc\naj0Veyy80GMPkXH6gAY1fCfqT1aX6ypT/epcM/gbwyrcJPz6jObRnqtIyi6I3G63M9XQq4uFzrZt\nDAYDqKqKbrfrurzYosksI6PRiBbNCvjoU2+DgpYr1Lxsm11OxOVTTPiUueGbPRsXy5YX4ujyIE4f\nUJGFXl0NAGUSZighQRcMCbqM+AmiOsGLDW+gv2hCrgwMw8B0Os1FyNUB3iIHwO0tyxpj89+/bdsY\njUbodDrPMnRMAAAgAElEQVTuoslcYBTrVDwKbFeo8Va57XlpkbxEnJfnjQ2coy5b6vz46vAydOXg\nbNgsMXhR1F3oEcsECbozzjijgtGIDwm6hHgnGMsGrOuiL0nSUp9V0d2KRVi8vEKu1+vldlMX0ULn\njYvs9/sYDoexXOp+hZKTBLUrikILZkL+y+O/hobcxJYnq1S3wx+4Fnq3BvRr5TEDas3zou5Z3Skm\nvG9em87rdhWNuEKPfzhh7+dDDvJ6OKmzAaAsws4RWeiCIUGXEREX67iwG9hoNKpVfFie55wVRDYM\nI3chJyKs5MxkMoEsy26CCzufaRebpEHtZBmJjyPmFq1vzCrX9XGHMkvdC2YPCldnLsz1eUDdjhxH\nlKXuq8PLIrchEmFCjzJuxcUwDDSbyZJ01gUSdBmpo6DjRQwrktxq+Vd9F5ksT7r8Oeh0OoV2thBh\njgQJOYb32PO0TqYNamfWkXVfMMdWE1vyxLXO+Vnlhlw/1jSu12cNx+pm2TL2N4LF3fPGhu/fhxE9\nYBuyAd2qx3IT5+Eki9AjC100Qeeo6vuo6NTjChMIv4WvDpMsqD3XaDSK/rBgZLkZ6rqO6XQK0zTX\nokVZlJCrgigXGEvAIMsI8J8eexe2VEfIbc9FE4tRm1oNdOUZXjD6aMjLmaxxrXNeTsxdqvsb2xhb\ni5YQ0/a34P/z8GJ0lOWCxqtEXkKvDutF1USJ3lW/7tNCgi4jogs61p5rOp3Csqyl9lyijz+IpMko\nrEVZFb1mJUkqvaNIkUKuKAtDFheYN9ZpFfgvj/8agHDXEl+mBMiWGGF5xNoJfWspNu6ksYGz527X\ngdl14+iS8ILlX/uursQVepqmufcBFrtK4Qb+hFno6DwFQ4IuIXWx0PF9VgGg3W779lkVdfxRxBm3\n1ypZVq/ZKvETcqqqxjrmKJFc1XkLWzCZNW8VMxfHVtO1zjF0S8G25VjqWnOrnJ91jqgev3lrWRbG\n4zGazebKztsiGQ6H6PdX64EgT0jQZaQK60sY/ILO4uPC2nPVVdCFIZqQK+McewV8t9utrC1bWUiS\ntJSVGxWf52cVEfEc/afH3oWJ2XAzU/vKYtP7VgkibmqrmHKJEMwVyzMwu/ju+DwAwMRsoKPoGFvN\n0NIl6wyba0nn7boJvbAadFtby/OQcCBBlxC/siWmWUz9pyR4+6zGtcyIJkjj4ieSotzLq4hXyFXZ\nX1cEViFz8bbv34aW3EBfdUSRaUvYNjqRIum03nN/lmOUKAGAc5vRvVyT1KHjMW05sFsEsQjV0FuE\nigqngwRdRqq2cNm2jel06rbnShorVfX408KPO657uSqKOMdFCLm6zoU4pIlz8lrzylosk1jfdswO\nMH+elEOEWxDPaZsAnPpz+xvB4o7PbuXj6IhkJI0BSyL0NE1bqKFX50zxoH63p0+fpqLCIZCgSwG/\n8FW1CPJ9VhuNhlvhPyl1XsTZArxO1qmyLHKrfA55/IReXKsI/968ztfRf30/trjnMdNe3u6u2cKu\n6ZQZasj5WcBO6Juhos6Pe3cuwqY6DX1PEe2/1p1VsESngSx04ZCgy0jZgijvPqt1FHRsEY0bJ1g1\neZxjcq2WR1yrCGuPFtbbNsn3c9v3b8NWY886t2s0F0qBnJq7VKMseHHdrX6c0B2L3Za6mL367GwL\n5zazW+UeGF+Aq7tPZt5OXSk6S7PoGnplEXSednZ2SNCFQIIuBVVY6LztufLss1oXQccSPliMXLPZ\nRLfbXWlRwxI8xmNngS1SyMWZy0nLxawSXqGnKApms9lCb9ssbc+mZiNQrE3M5TAK3jqXxt3KCGr3\nFcbJgALDRDhV3WvrJvTCYuguvPDCwvdfV0jQZYT1ci0K0zQxmUyg63oh7bnqYKHzy9zVNK02PUHT\nnGPRMnWJYKIWS1ZaJazt2X/8/v+xYFkDgJmlYjbvrsCEXhnZrYBjkTvQCm8H9uj4nFLGsmqIdA0n\nEXos+c/7gFJmIsZgMCALXQgk6FJQRsFDb7P4brdbSJ9VkW4uXsJqqun66lal54sgk5CrL3Hj8255\n+P+GKjfRb8wwNNrYiIhJ88OCjFOa099V4YShPO8WcU4KdykTdc/OnDIRz2kbubhdCfEJEnq8yIt6\nSMki9Mjlmg4SdBlhJui8BB0ru1FWs3gRLXRxiuOKOO4g4o5VBCFXl3NaV/zi8zabU4yNvY4Q27pT\nOLg9j5/zs8qd1PpQ54kGfMKBn5gDgOe1PRepBWdO7Q8oWcK7d5mYywO+n+ufPXMTbjnvb3Pbdl2o\ne7gCnxDEKKK0StB5GgwGlOUaAgm6FHgnWlZxEdRntYwLn41dhBuNXy29oBIsdRJ0UYgg5ACxrbUi\nksf8+5Xv/J+udQ4ArHlWa9unL+pprQdVdtxeag5Zoye0TTeLdn8rmeXt29sXYLMxWfo7FRdeP/Ku\noRd2XW1vb5OgC4EEXQ6kFRd85qJt25Us5iIs4ryQUxQldi29ugi6oPnBkh2qFnJB+I1llYR0HmT5\nvhwxtyfMdvUWuuqyCDqtOdmtTMwVwYnZRixRR27XbIjw4FwWWYQe4MSPexMxdnZ2qFNECPkHZa0h\nSRc5JmB2dnYwmUzQ6XSwtbWFVqtVmWWmikWaFUUeDAbQdR39fh8bGxuxxFydb4qGYWA4HGJ3dxfN\nZrPS794LibXymJp7z9O7emvhtYHWxUDrYmy0vB8rjBOzjaVs2pPact/M57TFDNcdox24TdOmJYaH\nri+4ok1VVTSbTTdGvNfrod1uu3F7zNjxJ3/yJ3jlK1+Jw4cPQ9d1HDt2DI888kjiDk233nor9u/f\nj6uuuirwPffccw+uvfZaXHnllXj1q1+d6TirgK62FHgX3riZrkzAbG9vu+UONjc3K7fMlC3oWA05\nJuQ2NjYSF0auk6WIjZUXco1GA1tbW2i320IIOaDeIrluvOmb/xf6jUVrHLPO7WjBAslLnPg5HhY/\nF8Rzs+VyJF5R9/SEXF5ZoOvMHz4RQ5ZldDod9Ho93HLLLfj4xz+O1772tRiPx/jTP/1TvPa1r8Xm\n5iauu+46HDlyJNZacOTIEdx9992Br29vb+M973kPjh07hocffhh//dd/nefhlQK5XHMgSlwwi9xk\nMknVnqtoyhJH3jZlabtbAPUSdIbhBLUPh0N0Op3S4iMJMXnd138PrXny4NhooKs68XJMyDWVcMtD\nHvFzgH8XiiTs6B3fODqCyILXLd3tdnHttdfimmuuwWc+8xkcO3YMgHM//d73vofHH3881v30xhtv\nxBNPPBH4+p133om3vOUtOP/88wEAZ599dsYjKR8SdCmImxTBt+fKKmCKpGhxxAu5LG3K6gZLdGGC\nLu8agkVCgrM4WoozH3gxt6s30VaCa8zx8XMnpz33Z752nbeOHWN/O1nM23OzDZybMEkiiD9/5DrY\ntgTLkvD2y+7LZZt1JqhHKRGNZVkL525jYwOvfOUr8cpXvjKX7f/whz+Erut49atfjd3dXdx22224\n5ZZbctl2Waz+qloCXkGUd3uuoilK0Hn7zeZ5HkS20PFCjlnkTp8+LbxIEvmcrgqv+af/jI3Wnvja\n1Z1yJX5irjkXcS/MOgvJE0Hu1CBOTBfdqOe0dyM/89xsY0EgntT6OLsZ/TmeP3/kOvdnWd7b1j07\nl+GSzolE2yLWh7AuEZubm4Xt1zAMfPvb38aXv/xljEYj3HDDDbjhhhtw8cUXF7bPvCFBlwOSJLkZ\nO5PJpJD2XEWS90JehqAVUXzwXT28pWdWpWWWiOe9Ltz4lT/A2b3wosFjo4GmYmIway+IOD/iWOf8\neH7qxMQZloxzO3uWuKlPezEvDw9eBADY10pe/PjsxhAn9fVuGbYK94CiCRN0RWa4Hjx4EOeccw7a\n7Tba7Tb+3b/7d3jggQdqJejI9psC72Rj5Ue2t7chSRK2trbQ6/VqIeaA/BZpy7IwHo+xvb0N27ax\nubmJfr9fm/OQFtM0sbu7i52dHSiKgn379qHT6dCNm1igpZqYGg1XfFkBMWyD2WJSRBbrXBCG5dz6\nn5vEF1h+Ga9B/M2jwZmEDNZOap0eENbpWNMSJuiydolgJVP8eOMb34h//Md/hGmaGI/H+PrXv47L\nL7880/7Khix0KWHtp6bTKTRNc4VcHeMjsgo63iJXlmVSBEuR1yIX1tVDhPFGUYcx1pXX/NN/RmOe\n7DBmbtZ5/NzMVDGblzBpsMLBEda5PHlusoHN5rLF7blJH+d2krlZAeBzP7wakuw/j04bXffnoEKz\nfH/QVXwoWsVjKoOsgu7mm2/GPffcg1OnTuGCCy7A7bff7q7dR48exWWXXYZf+IVfwFVXXQVFUXD0\n6FFcccUVOR5B8ZCgS8nu7i40TUO73cbGxgbG43EtxRyQfiGvQsgxqhQfSYQcQQCAZiquoBORHa29\nIOr4xItYnzfa2IzRg/bz/3o13vTyBwAA7bZjiWRWE9M03UbwlmW5CQR+3QToeltdghJHsgq6O++8\nM/I9H/jAB/CBD3wg9T6qhgRdSlgxREmSau82YDGAcfHGClZhmaxC0HmFXLfbjX3cdbJ+MZeDrusL\nC6miKLU5BpH4ma/+AXrNxZpzuqlAN52Hn6bqJEQ0CuwEEcXUVDGNsMg9cvocbETEzt31WHKLRlhH\nAb4RvJ/QY9a8LI3gy4Ri6KIJOkenT5+mtl8RkKBLSaPRcEVQnRZrP+KO3zRN18XcarWEcDGXcYMU\n8biLgK+X2Gq13NIyrD2PYRiuVZZfSOu0oJbNq778X9FQgYnuJBx0Gos9WpmYC+P0xHFTSjGSINh7\nzmqPU43XS5TbNawWnWVLiZI1vPCFZnl4a14ejeAJsQi6p+/s7ODAgQMVjKg+kKBLCT/hRGpwn5Yw\nQSeioCnjPOd53CKLft7iqqoqtra2IEmSG1+iKIpbCHsymbhiji2omqaReyyAhrpndWNJECOtGVo8\neKTttftKK4hOTbsLv9u2hLM7IwB7CRF+PDfpp97vsR8cgqIGH9f/89D/lnibfkiStFTHMqo/qPcB\npKp5Wec1omq2t7fJQhcBCbocqPsFGjR+3sUoipDjKaoUCC9wRDzuvOBjIFutFlqtlrvgBYlPthD6\nLahe9xjrtbiu1rxX/N1/Q6e1KI6CxNxEb2ACRzQrGaxaYZycOHFx+1rZuzsMZu1UpUuKIovbtiyh\nJ+oDnWgUmeW66pCgywlmsahjiQ6v9Uh0IVcURQo5kSx03mQWdpzjcXo3nZ97LMpq4hcDtUpCT4mR\nqTqcOtY4VYkfwxrlbo3i1FzYnTW32E3NxWXAu/3nJn1sTzuxxycSYW5bXuhpmuaG0BT9ALJKc7wI\nSNClhwRdSuK2/6oDbOxZgv6rIM/6eetgkfO2YPNmJec9h9cp2N3LtXd9GM0moOkK2k1jqebcaNaE\nGpH1yguruGLNDzug3t2pSc8VdTwvTLo4s5NM3H/1sUsSvf+Ryf5E78+btA8g62hpLpOw+w+5XKMh\nQZcTdRZ07Oa1s7NTqzIcedfPK1LIVTk/+GQHEVrRRVlNTNMMXUwVRRHamveKv/tvaDb3LG5TTUWz\n4Yg33VCgG8Hnvih3K8P0xM+dmvTQa84ybXNHj2+9a7Sik0CqIuwBhBd6LDkoqduW4ufi43eehsNh\noa2/VgESdClZBQudt3n8vn37anXDyat+3ipb5FgvXUVRsLGxsRT7JhJxrCaGYYQmYYjwPZqGDKW5\n7EKdzBq+rtUk7taqGc7aS6VL7n/yYOhnJMlesBLed/IC/OTZTxYyviLIIz6vjqE4VRAmem3bpvMY\ngbh395pRJ0HnbR7f6/UwGAyqHlbhrEshZNu2oWkaJpMJZFlGv9+PJeTi1CMse57HXUxZDFTVrrFr\n7/qw798ns8U+qVHu1p1xGzIXgxc0fOaW3eykT1A4PenijLmLdTCPlePdrk+f3oeNTjYr3ioSx9LM\nW/QYs9mM3LYBBAm6uqytVUOCLiV1tNB5hRzfPL6OxD3nVQq5MmE9hSeTCSRJQq/Xc8uNpEHkuZE0\nBqqMjMZrvvgRSJIjvnRdRaPhWL69bk4vu5O9MiVsNEnEHADsTPb6v7J4vTN60XFw2ry4MS/qyuDR\n4Tml7atsguYmsy6zYvTr2PYsK3ROwiFBlxMsy1VEWM9Z0zTRbrd9hVxRJUCKJErQiSTkihT8vJAD\ngE6ng0ajUavvMg/Susb8apSl2//i96tpzu1VUZ37Au9anUybe5+b9z3N+9s6PdqrRbevG12q5PSk\nmzj54luPXQClIeZ9TyT4udls7n331PZskaA1yDCMlXwIzxsSdDmRtH1WGbBF3rKsQCHHqIOF0Q+/\nMVuW5caOiZAEwCji/LLv2LbtzEKurnMgiiwdB+JaTA79zcegtvesaUGncTqd15qbi7ugJvZ5Mxh3\nYJoy9vXi16B7YdINfX0wc6yCpi67os40lNDiwgBw/MQZOOOC7LXwVoF1zgT3I6xLxNbWVgUjqhck\n6FIiqsuVmfaZkOt0Omg2m5EXvCjjT4L3mKLKclRJ3ufXMAyMx+NE33FS6maxTUpUxwFe5PlZTJj4\nAwCYMkxdgdpcFDPMOgcsi7kqGIw6iUTdeG5JHE5aFEeXkSTXU5aHkDrH5wWdo8FgQDXoYkCCLgP8\nIl21IEor5BhVjz8NbMwiCzmePM4v+46Z+7zVapV+067bPEkCbzHhxV5YIdpDf/MxSE3nnBiaM+8U\nVqZk6mxDUtKdszjxczzeend+MFHH4ucYu5MWNrrxkyseffwAJHK3xiaP6ybqIUTktmdZoKLC8SBB\nlxNVCSI+foq53dJYa+oo6IC9+ECRhRyQPZiXL/pcZkKL94m5rvMkK34WE03TcN3nPgWoMsBlrTIx\nl2j73M9yjA4TWRmMOui2tVSf9Std4sW2pNLcyXWiiGs2j7Iqogg9stBlgwRdBqq00HkD4dvtdia3\nW50Wat4iJ8uy8PXVsuDt3lFk0WfvfK7TnKgCSZIA1YbkcbMac6ucrEaUgAkQPNNxk3uT81+nm058\nMUxzOdN2OGpjo7cozIbjdiIrXRJk2YZl1csylCdlX0tRZVWqaHsWBRObXshCF4/VXAUroKws16Iy\nGuuwePMdD1RVRbvdhm3btRBzSc/vurQjqzM/8ZefAtqArTvfSxz3Ix8/p425kjLc5euXaTrhRZ4P\nvV7+8W0vvNBHO0BIDmdt378T4VRtAWNjELXtGVnosiH+SigwZbqiyihNIaqg8wo5ZpGbzWbQdb3q\n4cUmac08EnKC07YAJr7msWu2uXw9WroCRTFgTlWYfH/WHF2So1Fr4fe4Fj1mpeNr4fFMx01fUXfi\nGVpcV4kwt20ebc+ysrOzg4MHwzuSECTocifvzEBW9X86ddwgRdUYE9FCF6d1lWhjDiLq+xKhHZmI\nc0BUDv2PjwMeI5WtKUBABqs5DbnVBlnnMlzik9GeRa/TWxZkvAvWK+bydLtathSYwHH1//dHeOAN\n78tlP3UgyJ0oMnm1PYu7XoVZ6M4888xcjmmVIUGXE3zMUR5iy9u+qdvtQlXVUuKnqsYr5IJaV4ng\nvkiC3/mtS4YuQ8R6i2XjiLnwc2AbMkxj7or1yXAtM2FgMmqi2TYCX/dLYBiOl12qeZcuefmLf5zb\ntuqAKPfXPEja9iyu2zZo/aQYuniQoMtAEbXovEKu1+sVKuQYIizUcYUcQyQRGoXfjYu5kesg5Ig9\nJEOCrc+/z6btultdZgrgV6YkYReGvLBMGdNRE20fS10annv8TKC13qI+LXV7CE1Klvg8RVEC7+fb\n29s444wzyjqM2kKCLkeYKEqzMPNihgm5LH04k1KlOPITsXGOvU6CDti7sUW5kauibuezCg79j48D\nLe4caTLQmP9uSICxeO2nrT9XBNO5GzaOsNPDXMREKtb12oqKz+PbngHAeDyGLMt49NFH8Xd/93e4\n4oorMB6PqVNEDOiqzYD3aUuW5cQXbdVCjlHFYp5WyNUVy7Kwvb0NWZYjrY+EmEiGBNtPpE1lQHX+\n7vt64h1l30QQ3hIm+sS55poxhN4wIHmCiMeqW+iS4BV6tm1jNBqh1+u51rtnn30WX/7yl3H//ffj\nwgsvxJVXXolDhw65/2644YZIA8qtt96KY8eOYf/+/XjwwQcD33fffffhhhtuwF/91V/hzW9+c67H\nWha0ouRIElGU1L1YNGUKuryEXB0sSiw7eTwew7Zt9Pv92ojWOpzfMrnq03+y/EdTcv7FZaICkg33\nrHIfDWzywLlqlW5wLNzehsJf1kcNNHrh2eHWRIXccfYVlOmahdOzDs5oUT9XYg8WP8fctocOHcIf\n/uEfAgBe97rX4bOf/SwefvhhPPzww/jWt76FP//zP8c999wTud0jR47gfe97Hw4fPhz4Hsuy8Du/\n8zv4xV/8xbwOpxJI0GUgTQydtwRH1UKOUcbinXd8oMiCw6/wM4uXI+rH1X/6CUABIAGSJsNuemLI\n1IB5OJ5bD3JKbjTHy/eKMJFn+RQUzsLk2d7C77YuU/uvmKx6b+SsBJ0fdo8/99xz8ZrXvAavec1r\nEm33xhtvxBNPPBH6nj/6oz/CW9/6Vtx3332Jti0a1SuJFSJMYPDZjHwtNVEoUhwVmeghoqDztmJr\nNBpuoWCRiTMHRBbRReJ1o0qzuZvIR8hJEybiyjlP5lhdMO8p3ejajH5WOm3URLOnYXY6umiwNJNh\nc4kRpi5DCRF2kmTDjtFndpVZx+smT4oSw8888ww+//nP48tf/jK+8Y1vFLKPshBHUawAfoudtyyF\naEKOUcRC7bVSdbvdXGvose2I8uRrGAbG4zEsy1rqqSvC+Ih0XPPxTwAt7LlHWS1hj5iTpjLsvMuM\npciMtUaOFViOcKvqo0ZulkMe01CgqMn72a4DdB8IJug+rmlaoZ6N3/7t38YHP/jBhfWkroinLGqE\nn8uVlf6wLMuNkatDWYo8BV0ZXS0AcW6OhmFgMpnANE202220Wq1Q1wFRL+wYl600jamMAgoHZzJe\nBXzYGjWAtkdYRcT7aaPgFmOzJzYgA7ByLFkym80q6xtaJnTtR1NVDbpvfvOb+JVf+RXYto2TJ0/i\nrrvuQqPRwE033VTYPouCBF1GeCEkyzI0TcN4PMZsNquFkPOSxdpVlpDjybOYc1JM08RkMoGu6+h0\nOuj3+4HjqMNCxc9l27bdoqCs0nsdjiFvrvm4EzsnGXvHzixzMnO7RmW1ltgcYMmgN5rf4nsxkilC\nmI6buSXeNlp7Y5EkKbQuWZHtpKpgVY6jTLa3tzOXLGElUvz4t3/7N/fnI0eO4A1veEMtxRxAgi43\nLMuCpmkwDAOyLNdOyGXpdFGFkKsSXsi12230er3MrW1EgY93ZDfA2Wy2UF6AFQddZYsKAFz34U9C\nViWYnGDzi5nzpcROEIHw1riR6i/qdhWg7+8e5TNdi+Bfn3oRmtfsWQT96pL5tZPihR6xOoS1/cpi\nobv55ptxzz334NSpU7jgggtw++23Q9M0SJKEo0ePLry37nOKBF1GbNt2LXKqqro1xupIUrerCEKu\nzCB9ltigaRparVaifqt1uFEYhrN4TyYTdDqdhRACVundMAw3LjRr30bRsVXAbC3OLXkmua8tvT9i\nKshjebG+nM9pMnsFxp7FKK8in27kNga/lmJhxOkbappm4nZSIiD6g5wIhAm6LF0i7rzzztjv/dSn\nPpV6PyJAgi4ju7u7kCQJm5ubAIDhcFjxiNITVxwxd9x4PAbglOTgEwDKpAxBl0XIeRHxxs7HAALA\n5uYmJElyBd5b9t0KAPjc9qdckdftdpcadGua5rvQ1tFl+5Mf+iTQAmTNGbPVDMhe93G3KhMJkDkX\nrd9hB5wKZRw8r3yFVpLgu6myGFM3ju9BUJ9qw2ynv86yZLjy7aRYcLxfOylN03wfMkRw21IMXTTs\nu/NCfVzjQ4IuIxsbG+7FytwDdSZs/EzITSYT30zOqijqnFuWhel0itlshmazmUnIAeJZ6bwxgL1e\nD4PBwB3nmzbesfD+N2+9c2kbn9v+VGjfRsMwAhdaUa1513/wkzD7e1qJiTkpxHClTGTYPtYoO8Ii\nlwRltCzAzO5egkJUQqykS4Cuwt7wuFFD3K5ZUb+x4WYFm9fn97Abx5rH3LbsQYW5aquy5ok41+vA\nYDDAWWedVfUwagEJuozIsuzeMJi1SEQrTBzCrF3MtSqSkAOKuUl6S83kFQ8pSg033uLIxwDyY/v3\nnbfH2pafyAMcoccTx20mShC85amQoMzdrBZr7cXdNZWJj8AvMQmCF3lWlxNlSbpXFETjvv6CiNWm\nKtRmseVM0jaH58VeEfNPhOtedILWzZ2dHVx00UUVjKh+kKDLkSyJBSLgN2ZRhRwj73IrRQg5UYhj\ncTx8/m257CvMmufnNuMXWd6a511oi+YnP/RJmBHtSpUJ506dTw8/61zZyHNxZ0XEwElDHysdnPi5\nvGjcJ04ccRJrXpHzT6T7poiElS3JEkO3TpCgy0ia9l+iwo9ddCHHyON8e9uxFVX8uaq5EUeoxrXI\nZSHMmsefb17klV3SQjIAtu6bzT03pmQAUAFlKu2JuLy1fooiwn64wq4dUi/OGz+3u/e7MlLceD1r\noqJ5Mtm10Pl2Z9nVLOAt0c+aB8Sbf3WNDRWZqurQrRIk6HKm7oLOMAzMZjNYlhVaJHcV8LYkE7WL\nR1r441MUxff4yhByUSSJzQsqaeGNj0ozZ3/yQ5+EzdXVVbRF96syTVjOJyh+Lq/LKSLRQBnJMHuO\nqJN0Ma5hQ1PcBInzzh1UPBp/4rhtw2JD2T+eunptRGAwGODMM8+sehi1YHVWr4pYFQudYRjQdd3t\nP1oXIZfmfLNyK+Px2O0tW2RrGe++y9gHf3z9fl9IIRdGktg8JvK81hQ/kRc0p6//4CchSVgQdAxl\nBlhFWeXyImBa8aKOR91VYGRMhGD9XG1dhtSwYOoy+g9F+KtrSly3bVCmt2matVwXyoQsdNkhQZcz\ndRPqOWUAACAASURBVBN0fMkKtgC229HNuUUhyfkuurdsFGXshwk5wP/4RBdyUQRZ83iiYqP8hJ4t\nYclyJlmOmIuLOlncQHILnQSjn19bLXerOVvn5Jkc2P5LMgUWvQUQNwmDCbrRaJToQWNdCLuHT6dT\ndDqdEkdTX0jQ5QxfjFVkmJAzDMNtWzWbzdyM3ToRR9DxQqeqThZFin1WFzAo5rHuQi6MuNY8XuTx\n1ryf/9BfAPNnGFlfznK1fASKou397BQUzmcuqbv+KbJJhR5fYkXWpMA6eozmQIHRW35P52kVZszn\nu437V9M6lxQ/a95sNoNt22g0GokeNNYFZp0LOuYs5aLWCRJ0GfFOQFmWhbbQ+Qk5dgx1sy4C0WOu\nS3JHWkzTxHg8dr9Pr6t8lYVcFHGteQuCxQbkuVjz6wahTOc/JFlfcoif8wq9pAJPHckwPK7XMLcr\nnxgRB1uPf0LO33869ntXCSba/JIwgsIGRCvpUzZ1W4+qhgRdzogqingh1263fRvJizr2MIIsorwr\nWRQhl+f5NU0T0+nUrSXn932us5gLwivyfvz+n3Ksc56p4RVz6tTfUhdEhsYIsVCHewLK6IfPKdnj\ncvWtnQdAHUm+Vjr3c1MpsFvE1kONhdZnkh1+Do6fOGNthZ0XSZKWYlzjlPQRvUB3EqKSRup+fGVB\ngi4jfqJIJJert5G838LPqKug48fstViFHW8d4WvJBbUhIyEXjx+//6dgK3M3q08yBOC8JuvB24jq\n31oG6tCZ31HCzs9KF4ZfZ4osdB7oYHL1JNdt1oWgtlZB8G5bv5I+UUkYdXPbBgm66XRaq5juqiFB\nlwO8qBBFFHmFHOsGEIYoY09DEuFaFVnOL19LLqgoMAm5ZMgmYM41i7xUosT53zfAXwAR54e668x3\nsxNiZfNY59RdBfJyjWEAQPN0vOtn66FyMsTrTF731bhJGCL3tfUjSNANBgNsbW1VMKJ6QoIuZ6oW\nRWmEHKPqsaeB9Zfd2dkJtFjVGb7ocZVFgVeNH7//pyAHhIj5CZwk7taqCXOdSlZyq6IyRWBihDRL\nfq0Nj70I9qUmsN+p/Xff//7ribdRR4oSUWk7YdQhCYNKliSDBF0OeC10VbhcvUKu2+0mFjZ1EnSs\nH+lsNoMkSbUQcklLrNShKHBdkU2nEwSPa5VLeFdUR/Mf5uthYLkSAEYv2bZ9iTGFgkSdMslpDHP2\nfVeBlXIVeea5fQjwdK8cVdxXgzphBGV7l9XX1o8wCx0JuviQoMuZsrNceSGX1UJVB0Hn7Ufa6/Uw\nnU6FF3Nx4WvlSZLkW/SYhFw2Tvz2TwGYu1lDFIWfu1UdcxauFNmrrvjj4T5rdONtxyXkclVHUujx\nBX0mLDEiMTZ8z81Z31Fw+mfz200dEMUCFtTJIqwTi1+2bZ5QUeF8IEGXM2WJIj7LMW9Xo4htarwx\nZMz1aBgBAUACErfECuvWsWpFgUXgufc6Ys77LUghFTqUyV5/16KTINTx8t8Si7yofYyirXSdZySY\nBdZyzfuYiGzEcduapgnDMApJwggTdGeccUaqba4jJOhygJ+IbNEuShQVKeTYeEUSdFGN5etgVYwi\nqsQKCbn88LpTWYFgt7UX97oyT8isOpNVHWNBgYaJIckT7dHYBfR+8Pub2/Nt+gg8ZYJAUSfPZGw+\nJsY9og6IdE9NAu+2ZZ4Cv762QSVVkrhtg1yuBw4cyP24VhUSdDlT1EXLYsaKEHI8otx0+GQAVVV9\nY8iAegk6b3wl7y4PKrFCYi4/Tr570TrnN9PdwsHIQcjFuZTivMczvZnbNs9YuMXtx7sHyAZgqXv/\nE8HU5R4VhyRJGKZpxrLmhVnoLr300sKPaVWgyzAHggr05iGOyhJyjKoFUpxkgLrDf6dBmcgk5PJl\n8I4bIBuArQNmA1C4Fl+SAUBx+rayuLlEYo776oouKMyLO3XkFPDVI4Qds9IpXAm4OG7XMPb9YPlA\nk2bQWttNaJesT106UR6WiyJuSRU+CYPF5DELn3fdJJdrMlZrpRQEZonJIrz4RT+o7lgRVCXoeCEn\ny7JvMoAfVQvQpOi6HvqdkpArBkuVYM5bjSo+hYJ5MRfEglgRYG2W5tO+MbfYeYUd329W8dFNvgka\nABrbwfsM6xYRigTfBI7mI6vfdL1O96e8iWvNYx6Z2WyGZ599Fh/5yEfw8pe/HKdPn165B/oioTOV\nA3n2c/VmcZZdjqNsgcRndQJAr9eDqqqJn2ZFjlFhcYBMrFItuXIZvOOGpb9JJoCG42INcxdWHT+X\nhMYIMIJi3szwWnpZLXZx6X6n41pI1w1R709V4LXmsc4+kiRhY2MDL3vZy3D//ffjX/7lX/DZz34W\n5557Lg4dOoSrrroKV111FW666abIDhK33norjh07hv379+PBBx9cev3OO+/EBz/4QUiShH6/jz/+\n4z/GoUOHCjnesiBBVwBpRFHVQo5RlqBjBYHHYyetzy+rMw4iJnIw2FPndDqFoijodrvQdX1BzJGQ\nK5YXfn0eN+czNYLEnDLbE0aS5fwOhFjoAqZdkPu1qAxPyYxOguAJ6hChTgHDs1byxYX93K3ecURZ\nO9eJdbbQxYXdvyVJwv79+/He974XAPCmN70JDzzwAH784x/jwQcfxEMPPYS/+Iu/wE033RS5zSNH\njuB973sfDh8+7Pv6RRddhK9+9avY2trCl770JbzrXe/Cvffem+txlQ0JugJIIoq8Qs7PelMmZQg6\nZpGzLMs3qzMpIgo5XdcxHo8hyzL6/T5UVYWm7fnASMiVgzKzYbac+cHqzimz6CB+NW6Ga0IxB/iX\nJgECLGQpLsW4ok4dU/mQshDtHiUSYevNbDZDt9vFJZdcgksuuQRvectbYm/3xhtvxBNPPBH4+qte\n9aqFn48fPx5726JCgi4HgpIiwhBNyDGKFHRR5TnSIlIcHRNywLL7WJIk/Oq5/7HK4a0V27fcALMl\nueJKsoPFHB9v5ifiyoif84tpWxBc3BSXIqY7fzyAE0OnIFrodU6Ev04kR5R7k+h41wK++1LRfPKT\nn8TrXve6wvdTNCToCiBMYIgq5BhFiCPTNDEej904Cb/yHFkQQdAx93GQ1ZEscuUjG3vWuSBU1u4r\nSsRVRIMTeXoCa1qamDg/QemtRbf1iA2rGbM3tB1uqTzrOwpG5zv3B1F7iebFKh9bVqLCZYo+d//w\nD/+AO+64A1/72tcK3U8ZkKDLAT8Lnbefq2VZbjxVUJN1EchTHHn7y+Yt5ETAK1ZbrRaVIBGA7Vtu\ngC0Dsm7DbEpQNBtWw5O85BNDJoKIC6LBuWq9yQ9hnS78aO5kH09ezGazynuJFknVD5uiEyToyjhv\nDz74II4ePYovfelLK1EehQRdTvBCSJZlmKZzh43qdCAafmI0KXw3i6A6a3lShYUujlglIVcNo7e+\nyrHOzS1JXjGnTp25YqnFzMnCa9EhngXO7z1Jkia88EWX86Tb7Ub2EuVFXh2teXUbb5kECbrJZIJu\nN1uQJ5tXfjz55JN4y1vegj/7sz/DS1/60kz7EQUSdAXARNFkMqmNkGNkEUdlF0FmlCnoeJd50DGS\nkKsWqwFXzHmRjeV5ktoqV/AaHRUnF6djhDpaPr7GLvd6gsSI/lPZrzFbXm5P9uatdwIAPrf9Kd96\nZUzkBRWlFd2aRxa6dAwGA+zbty/152+++Wbcc889OHXqFC644ALcfvvt0DQNkiTh6NGj+L3f+z28\n8MIL+M3f/E3Yto1Go4FvfOMbOR5B+ZCgywm+h6uu6zAMI7DmmMjUteRK0TdN3tJKRYHFZfLL17s/\nK/OuEICT7QrsldMIs86pEzu4+8PC38PFQ1pLWCQeQaSO9kqKAICcssZb57k9cedXusSPPNt+MWHn\n5XPbn1r43a/FFLPmeUWeKNY8EcYgKkEWuqyC7s477wx9/ROf+AQ+8YlPpN6+iJCgywnbtl2LHLup\n9PtF3dGLI4mg84qcqsRrkTdLvqdskKWVhJwYjN76KqedlyQtiDmvRciLOpmLvZyfQRq7CLTiRbXr\nSryvUf7bDELWlhMjQoWdjUzWTD+h97ntTy1dh7zI4615WRrG5wFZ6MIpStCtIyTocmJ3dxeWZWFj\nYwOSJGE4HFY9pFTEEXSixQUW4XKN01OWhJxYyOZirJyiLcbK8cVuixJxC4TohYZPRmlaQSabe9v0\n24b3781h8n1t/ZtzvszobnylkMWaF7dhfJ6QhS6YIEG3vb1Ngi4hJOhyYmNjw00mYDePOhImjnhr\nlaqqviKnCvIUdHwrMkmSfHvKkpATj8kvXw+jHb1ougkRSooFNoG7NQ18bBuQrhVXGndrVBydXx/Y\nICSr2kzhONY8v4bxmqa5CRj8P0VRMosxstClgwRdcqpfjVcE/qIXuR1VHLw3oDjWqlWACTnbtn1b\nkZGQExPtF38Ssm5DkaW9unP2onVOndiw51M2UswFxc+VDEt6kGwbej/eQBQNMJvcNmKKsc5z8/ev\nYPeItNY8TdMWyql4RV6Se3sd14GyYELay/b2Ng4ePFjBiOrL6q3KFeEVdMxqVLcLmR8vL+RkWfa1\nVolAVgtdVAcLEnJiY6sSzJazILDkByZqXNdqxJ1O5PpzANDYdY5D74bfT2TN+edNyPC6XZPE3G39\nyIos0JwGJhy3D9+Arf/3X3LffhRprHmGYfha81jcdFA9tbqtA2US5nI9dOhQBSOqLyToCkKE7gVp\nYONmRZCB5RZWopG2dh5fSy6ogwWJObGZ/PL1kPXF60yynCh8dWqHWuNEF3F+NOfCTotpsVv6fAWh\nveferwG2Y2k88ROt8geQgDTWPNM0YRjGkjWPiTwSdOEErZPkck0OCbqcSNPPVTRs24ZhOOXzp9Op\nr9tRVJKca75eXlDhYxJy4sNcrX7CLEjMKTMbFmflaoznFryg0iTy8t/mryyOpecZRNJLJuGtorlr\nQ+tLbkKEl8buYhII4J+IEUbc0iV+SKaz/3Pv32sqa0sS9n97hueuWRR1OxdK2Eq3m9IIs+YxrwVv\nzeOzbPm/ebtgEA6UFJEPJOgKom6CjsWPMUtXv9+vTf28uDdGKgq8Wtiq5LT2akmQdQtWI57JrTF2\n5rgt+8wbPzEXg+Zo0ULMC0TdK/YSIIXcQ5q7NoxOdlHQfd6GHrCdrR+lT+46537NV9jaCoCUtfJE\nIkjkybK8EGM8Ho/d373FkVex1VlSwlyuq9COq0xI0BVEHi20ysAvfmx7e7vqYSUiSjzHKbNCQq5e\nGD//ClfMAU52pTKzlvq1AoCi266A8BNpRSc+NEb+94GkQs+vnl5jdy9hQtY8r41s6L3gg+Pj6BqT\nYFGXhrMfmg/Gpwbdga9PcfJqx/TXOw6Mzs9tt5UT5LL9q1N/siDyVr3VWRKobEl+kKDLCe+EZLET\nosKEHGsqz8eP1c26GDReb5kVEnKrgfHzr/C3rnHIuu3G1tk+rteoz5cBL/Qk28dtG3c7u/GzYMvA\nFXMxOfNfxX/wzcp/OOvo0t9WtdVZEsLWGcMw0Gw2A18nliFBVxCiiqI4TeVFHXtcvNm5VBR4dbB+\n9icg6xbM1p4wV2a2r2XOS1lJEGktfrzbNo64k7j4ucauHdi/1t3+0Nk+bxn0i6tjpUs2nzSXtsk6\ncPDdIvguEWc/PIus0WerEoy2E6O3zqxyq7OkeMdc5/WnSkjQ5YToosg0TUyn09BEAIZoY4+C76Nr\nGAbG4zEAUFHgFcRqyJD1PeHDiznJsKEYrEwJ6w6RYHELip8reH2UfC41V9zZCHWbRhHpdh3Hu86V\nmR1ZuuTsh2fBL0pYSvxQncsU2xfJKKlrWS2oe6uzJERlAIs4ZpEhQZcjvBASJYaOz+gMSgTwUkdB\nZ1kWhsMhLMtCt9ulosAriP0z1y5Z5xjKzErX/WFhByhcvCVifgk2RjYkE5Fu1ebIci17rCNGWpjY\nSoJk2skENBGburU6i0uQoKNSL+kgQVcQVYsiPqOz2WzGEnKMqseeBNM0MR6PYds2ms0mWq0WlSBZ\nQeyfuRa2IkHWLNiSBKu5N5eVmSfDVPVfCFSW3RpQogRcXF2g2zSn7NU0hMXKKfN4QV7UuZ8bBV/L\n6tiC0Q0+DkWLduUCwFn/uuc/lWw70u164OtTyJqJF15OtrksiNjqLA+GwyH6/X70G4kFSNAVRFUW\nOj6js9ls+iYCRFEHQcfHArZaLTcmkIeE3GogXX8VoFuQTGnJOucUEfZHnZhu8kMRSRBB2asAoPWL\nEXusY0RYuRI/6xx/nhojy1eM8pmu3ZMBBe58OON7kwUxTFSLCK3O4hKW4bq1JXp1QvEgQZcjvBAq\nO8s1TmmOuIgs6PxcyJIkuV0tABJyq4YtSUuCQZk5goPVnuPdrerEeS2RiEtonYuiubss9vxEnl/8\nXNztB4lG2QzvkMHoJBBteWFLUmhtPaI4ymp1lgQqWZIvJOgKoixR5C3N4ZfRmRRR4v94vJZH3oXM\nzjMJudVDvvYK2IYFu6m41jkmCPhCwup0LuJSJkGUgZ/IC3Tbxrh1hIk6L16rXJh1EQCUqQWzHb5t\nWbOx9Vj6VFWrqaA1sNAaANb/+hOQv/Lt1Nsi0hFWHJknSauzJNa8IEF3+vRpKiqcAhJ0OcJPzKIF\nHV+aQ1GUXIQcQyQLHS9YgyyPb+jeUtHoiCKRr70CtqLAbjrft2uVm8fPKdM9C1OYkLPjWN8qYkFY\n2YDuZ8ULMaQ1d62l7FN1YgOwU7t9N56O18Zh3yOTeFbQkGST3vEJRud3MHxJS/j2X+tCmMs2bqsz\nr8hLas0jC106SNAVBF9KI8/YA2+NNb/SHFkRQdDFEaxkkVtdlCsvhRUzZEDUwsFpaOwu14rLSnMY\n7lrlEyMak2TXvWTZtT3XRDLitjrjRV5UqzNWZsXLzs4OCboUkKDLEa+FLk9s23b7rQJOjTVVVQvL\nSKpK0PHHKUkS1ZJbV9i89t7rLRvy1ITt07dVnpkwu8u3NHVsuD8vZrjOfwm4hPQ+t62K3LN+VjbZ\nXLw2G7uWr2UvjPYLJoxOOtGo6MDmo+PFbGLLTpQYYasSJEMMLwCRnihrHiOs1RkzIMiyjIceegiX\nXnoptre3ceGFF5Z1GCsDCboCYbFoWZrce4vldjqdpRpreVNV2rqu66HHSUJuPVAOXQar1YCkm7Bb\nCiTDhK3Gu4aUuXhbsNrN55CvmAuhscsLwcX3G/3017QvnLbhEyWauxZg2tAj9ucn6rwxdkHZrTy9\nZ2a+df6AeMWFQ2vR+RQXZqgxCxwT9SBubN54PHazaHd3d/He974Xjz76KPbv34+XvOQlePTRR3H1\n1Vfj6quvxvnnnx9rbbr11ltx7Ngx7N+/Hw8++KDve2677Tbcdddd6PV6+PSnP41rrrkm3YEKRrmF\nlNaMrJmuuq5jOBxiNBqh3W5jc3MTzWazcMFVtsvVMIzI4yQxtwZIMpTLX+b8OBdzAAALkDTTsQJ5\nkDUTysSAMjGWXnM2VMy1ou6avv9yZ26Na+yaaPhsn/WrdcflcZn6JWIkRdEWt7n5aHTVYcpkJby8\neeud7j8G61HbbDZxxhln4J//+Z/x9NNP4+d+7ufwmte8BoPBAB/5yEfwile8AmeffTZ++MMfRu7n\nyJEjuPvuuwNfv+uuu/DYY4/hkUcewcc//nG8+93vzuX4RIAsdDmSV/svwzAwmUxgmiY6nU4pIo6n\nLEHH15LrdDq+fWVJyK0B0jzJ4bKLAVWGHdXJxLAgGXOh4hc/V2G3Aj9Rl6c1r7FrwgxwlTZ2raVj\nb+wa0HuL+2+/4IxRnVihble/TFdllv99YeORHQwv2cx9u4T4+MWYN5tNTCYT/Oqv/iouueQS9+8n\nTpzAmWeeGbnNG2+8EU888UTg61/4whdw+PBhAMD111+P7e1tnDhxAvv37095FOJAgq5AkgojJuQM\nwwgUOGVQtKDja8kF9ZUlIbcmeMScY5lz/ibNTNiNRTEiz3TYPiEMiQLz+bkWJ0kz4zWYp8iTTRvy\nrhnpgg0iqFyJOrbQGkRnt/YfH8FW83XsWN0GOs9rUC+9GMYPHs1124RY+BU3DqpD5y1bkpfgOn78\nOF784he7v59//vk4fvw4CTpikbQWOt5S1W63KxNyjKIydPl2ZEF9ZUnIrQlzISfJEpSXvBgwTGDe\nMkrSDNjNxVuTZJqQTI8wirDEKRMDZndeYkGwRMzGcNFFzBIw4hYabgSIOnVkwujlHN+XM0HFhbUD\nm5B/UMGAiMLxCjlG0Bqzs7NTWKcIvzVZhHZneUCCrkCiBJ1pmphOp6GWqiooIkM3qh0ZCbk1QZK5\nH+diDgAU2RF1jcVbkjxzrEbMKuRnnVt8PyeUJAnKeP75oDktwxV9VcISMIwed/xmuLrzxs8pU3/r\nW2NkLrldw1Bmpm9iRP/x0cLvkmE72aoZSpdYTQWyVn7HCqI8wsRcEJZl5VZX1cvBgwfx1FNPub8/\n/fTTOO+88wrZV9mQoMsRPwudX8cFv/ZVfrV4qoSJ0SziztvFgoTcGuMRcgCg7D9373XDhD0Xc8w6\nJ0V0K5Enc7GmSHue0xTzlYk+P8oWeyqXWWt0ojJbjcXSKmwbcysdn6XLaA50mJ3lz3ROTGEFZLcC\ni4kRkmH5u13DSpeEFBcGAHUwhbGvHfwGonYECTkv3jUmj3Af5mHy46abbsLHPvYxvO1tb8O9996L\nffv2rYS7FSBBVyiyLMPk3ES8y9Hbvko0ssTReYsfU1HgNcZHyEmKAvnss7hac3P3q+4IEOaOY/Fz\nvHiQp9rCZ+IQZp2LIkjsGb1m7P17iZsB2hgZ0DmLnbf+HBAu6oJQJoYr6qISIxjdJ4cAoi2kYbQf\neX7vF9uC9r+ck3pbhNjEEXNRBoO0xoSbb74Z99xzD06dOoULLrgAt99+OzRNgyRJOHr0KF7/+tfj\ni1/8Ii6++GL0ej3ccccdqfYjIiTocoYXQnwsWpTLUTTSCDq/4sdUFHiN4eLkAEfIAYB81pmOmFPk\nZWHmU29Oms4tTVHZqwvJDsWGLqgjzffvWYSeX422xsg5dl7YLb0nQNQtbifY7apOHEuoPDNDrXRx\n8daia//bSd/3NX/0PIzz9rIWm8cHACVG1Jq4Vjkg2BIX1D0iLnfeeWfkez760Y+m3r7IkKArGMMw\nMBgMAvuQikqaDN3xeAzLstDtdn2LH5OYWxMCrHJSpwOp23FEnDJ/jz63gHnb15kWJNMRGmFFhass\nUeKHn9BLI/IkT829xsiA2Q5xiQbEz/E0A7JYGzv+4pRtt318ZynbOC5BYg6SDNgW1KdOwnjx2QAA\nq9eGPNUgKQpsbwIMITRJhBxPUIbr5iaVsUkDCbqcYXFzLHYMgK/LUXTiCro4NfNIyK0JAUIOquoI\nOibmLMsRdGyeNBqApgGqCkABNB1QmLvVR0gIGqYQhFfkpY3LU3d1GH3ns7JuBb7m7FP3bYMWl6DE\niCS0H30+Vjsw9amTsM6aZzSaFqRmE9A0EnU1Ia2YCytZUlSG66pTL5VRA2azGUajERRFQbfbxXQ6\nrZ2YA+Jl6EaVWiEhtyYECTkAUBRI7RYkVXWEWrPhCDk+o1XjBA8n5hZ2oRuwFUewSJO990vyspt1\nIWZODo7Ft3qtmAeYLwtxeRZg9qMFHiukrO7qsd2iythYEHX873wcnTwzYLX871Ht4zuB4wmqR9f8\n0Sn/AcnScrcPRQZMC/JzL8A613G/yvu2YG3vwB5Hd6QgqiOtkGOECbp9+/Zl2va6Uj+lUQNY7Bhr\nRFxHggRdnAxdEnJrhCdODpiLOUVxRFxDdRZx09oTc4Dzd93wjZlzMU1AVSDNNECWIU3nQshNpsgW\nMyePZj7H42zH6maIhYsLa3axq0OybRj9ePsMinXzWuni0Hp+UTTx21ZmyxYyyTQXEiO8pUsCxVwM\n5NF07+de16lLSJY6Ickq5sIgQZceEnQ502633czWrL1cq8Qr6LyJHSTk1pwAq5xt2Y6Ym4s66Ibj\nQpMlwDAc96rh03eVWbFN0/kHONuZeeK7SqrTKI+X48qKFnnqrrPPKGEn6RYU3XIte/I0JKN1bpVT\nt5ePJ7D/7Zzms0PXCifpy107lt7/xDxeTorpEp/H0TmDUYDRGOh1AQD2dLY3DwhhyFPIkYUuf0jQ\nlUDeHRfKgmXosnjAoMQOEnJrhI+Qc/8uyZAUOKJLVZ0FWVH2LGnSXNQx8aY6gg+AY8Fjf/OStkRJ\n0lC7iGvUT+QB+Qs9dehYDs2IZAplV19y16q7eqx2ZnEJc63yNJ486X/+wmrT+XF6G2g2IPV7zu8z\n51yQla568rbKBa2Lp0+fXmr7RcSDBF3O8BNUkqRcCvRWhWEY2N7ehqIoVEuOcGAWFUmGbdlurJwk\nS85rzDrHCTe2GEts/rDMVmYB9hNsUdngmga05zFwFV9bqax5MSIxlJEGybBChV2Ydc7dzthY+JnF\n0TVeGLtFnL1xdM1nh9EDnNN4MiCT1Y+QODpnxw1A0x1Xq6a7c8xmn7HrGcJSZ4pyr9q27VueZGdn\nBwcOHChkn6sOCbqCKbrRfd6wWnKz+ZNxv9+nWnLEHl4LnW0tJkAoiiPUmIVunvggqSpsw9h7r1+i\nkJ91TuMSCLwxc9PlGDjJ4+6zK0p88Iq8MIEXVWhYGWmBok4ZazA925bHOiwuk1YZTmG141sR5Znp\nJK2ExTfOUZ8+ufe92Hau4lpqNvD/t3fu4VHU9/5/z2w2ySYbCCAEQriIBhIUCQkBL0irR7RWBOSg\nIKeECgXtrwg0gIJiET0KCAJCIuWojbScEqpHDAdMPDUSC2qy4SaXYkGFAJGbJIRc9zIzvz+S7zAz\nO5vdJHtNPq/nyQM7O7v73U125j3vzw22xgsCzmCA5HA90YPwPr7Mk2uOqqoqcuhaCQk6L6M3/itU\nBJ3dbkddU2VZeHg4RFEkMUc00kwlK3NRWP8wTinm7A7A2CjmnLDZm9yZJpeJFRBx3I1QbEta8yAt\nEQAAIABJREFUlOjkbnHawgdN+E8y+aH4AU0CT3EcEE0uhKaLYwUTdZzd2aFSijo2Dq0thF3Rd+dY\nHh0rjAg7d6Xxd6UNq0qi53l0AKSrlZBEEXznxt5jYl0dIAjgIiIgCQKFWwOAP8Qc5dB5HxJ0PsbV\nPNdgQq+XnNKlA0jIdWj08uYUIVeOFwGeuyHm0OSqaJ/GYIBkb3LpbBrh4S7E2saKVlcoW6AokaK8\n7OxphBpff+O7Jblwz1irEoah1gYx3LNDttalUz1PnUMeocbZHHLY1RV6eXSGCy2oZtXJo5OuVqhf\ng+chVqlbpEhNxx9qNOw//OnKkaDzPiTovIz2DzSYK12VveRMJpOqlxxzFknIEUrHRRIldaiV5TQ1\n5TjJ+XJKgWZ3AAYDJFHj0hncuDgBbCDM1TmHc70u8gBABLim8KzkQXEFX2/Vdff0Qq9AY7gVaJyB\n6y7sylsd4K9ed57a4UWkq5XOGzkOkCRwPA9JFJvGwhkaXTqeg2hzPcmC8B7+DrE2J+go5No6SND5\nmGAMuSp7yUVGRiI6Otrpi/VYp6cCtDoi6GjGoQOUTYRv7MfynpyeSrFNYi4da2kCgIuMbN0abXYg\nwo3gakm1pQ6+Fnl8TaP4ctfwmIk63ubQbFe7nnydfvjVUFUHyUUjYRUu8uj4S5U3XFKWN8dcOHZb\nE3Z1EnJsYkhzGAyQbDZ1+JaKIrxOoHLlXFFdXU2jv1oJCTofE0yCThRFNDQ0wGq1UlNgwjN0GgfL\nJ9imk7Ys3gRR33WTJFmwSYoec7qwvnOuQqyuwq08L7e4kHEn8LyAL0Qea3gsRWjn294IO/L1VqfP\n0J0Lp7yfszpkUcfCrvzVppCn3e7SpeMvVsiOmqehb6nymvudNC6dpHTlSMT5hEALOVcOnSRJITPz\nPNggQedlgrEogpoCE62GiTbmxvEK94WJPVYcocyb4zm5EEJ25fQEgHLCRAsS6T1CK/AYpla6gB6i\nK/JaWnwhiODqrG0Sh2zyghR5Q5yx3LmWwjlEoMrzViaAIk/OVei8yaUT6xvAmyIhKquWOZ6qWn3I\nn8s3oLa2FjzPg+d5GAwG8Dwvt9ryNa7OiYE+V4Y6JOh8gFLEBbIogpoCE21CR2Apc+jYPk55c9ox\nYIBazDEBaLOBU5zs1U2Bm8RihEIINefOtYT6Bv3tPhR6cvGFKN1opeLBYYGJQ62w46wOAA55O2dt\nFD/uXDquumnUV7im1cmlppCoNsTKwq4V11y7qtqwKwCpQuHKiaLb35Go+Z1IgqB2ggmvwFw51jRe\nFEUIggC73Q5RFOXecEzgsR9vizzmzrl63lDs2xoMkKDzMTzPw27375WmJEmw2Wyor68Hz/PUFJho\nHQrRpt6sceua9pGaktjBIoMcf6MQQhlCZQJQeZLXEXMAIFltalHnS/SEnimycbsXxZ7cSkUSIUWZ\nGre5uejjrtfp9tTTc/E8KYAA1GFXJ5oJu97Ik3MOu0qVVW5fFwDE2jrd7VTN6js+rHxX/j8TUzzP\nq84NoijKP0qhpxR3SjfP2zgcDgq3tgESdD5A69D5y0ZmTYHr6+sBANHR0U595AASc0Tb0c2pU+9w\n4/9tbDkiWW0ePY7zhcPGRJ5W7LXmtbQTEgBwdY3fVXnqBXBjaoJ231qrS1GnzV1UDrrnGuyQIo03\n3DmgcdJGk0vHVboJpTK3jY1yc4GkaTuiQuHSSU3HJ9Vj9YQcOXNe4W9X/wuSJEEQBHnOOBN0TNQx\nmGhTwpw89mO1WiGKovxYpZvnacjWVf7c9evX0blz5za+444LCTof4y9Bx4ScKIqIioqC0Wh0+sKQ\nkCNahU6jWF2XDoAku3OK+/VMF46HxIQLz90YC9aGViWSq5w5AJy3CyRcuXmeohUr7PncPAdXa3UO\ni9pszo9TCDagUdSxJs+q57M61PN1tZWtTKS5OUlL16rc7iPW1t1oSs1zkESJhJyP2XE9RxZZLKTK\n/lWGXIEbxQjsvMGEHcdxMBgMKuesuZCtNlyr5+a5EnTXrl2jHnRtgASdD9DOc/WloNNrCkxCjvA6\n2pMsx6tdOs19HsNyrrSTJJoRB1x4y0OwemLP5yLPU4GnPD7UNzQ6dMrHOjSip8GqdvTY45p7vTpn\nVwwAcN21OydVVDq3nmEuXVO4tVlXTgHLkWM5mKJdZ3JI4w4ePR/RPLlX/ghRFFFTUwMAsshiwoyJ\nLJbfzdw3peBT9iTVunmehmxtNpucl6cM2brKK6emwm2DBJ2P8ZWgUzYFjoyMVDUFZpCQI3yCosmw\n8136jp1KGLSxmlVy0WiW04ocd8/ja5GnFXiePDdzLd05ds2JOvZYjUsHQO3SKT9HpUunh16+nFYM\n6uyjLXYAoC/mSMh5hbyaLarbzElj4VY2AUgURZW4MxgMqqiOVtwxASYIgizQWhOyFQQBDodDfr76\n+noYDAbs378f8fHxqKysJEHXBkjQ+Rgm6FxZzC1F2RSYeskRAUHHrWv8x/Xftxxa43ioYrDy5qbH\nGgytyrMDAKlBP+TaEqHnSuRJVmvbxR57blF0FmN6iCJQW6cWglonUytuXVXw6lFXrx/idghynpur\nBtFsTBenfXyTqNMTci4LHkjMeQWtmAPUTpoyn1op8piTxooftEKPnV+8EbJla7BarfL+oigiJycH\nRUVFqK+vR48ePVBdXY2UlBSkpKQgOTkZ4R648gUFBZg/fz5EUcTMmTPx/PPPq+4/d+4cpk+fjmvX\nrkEURaxYsQIPP/xwKz7p4IVz4x5RU5hWwK5CGBUVFYiNjXUSXi1BkiTU19fDarUiPDwcJpOJhBwR\nPDTjuimnSzR7vzuac5BaSEvdPKfHN4msVgk9ZbhJklwXRCj3Y6+hFXTaz85qA7RVwfUNzhWrxrAb\nYVjlcSQsDFJNbeP/Deo+g403OIjsfrZJcxwSNcKa8uR8i56Qaw1Kgab8UQoybQGEXshWqyn0QrZW\nqxUcxzkJtU2bNuHixYvo2bMnDh8+jMOHD+P06dPYuXMnxowZ43Ltoihi4MCBKCwsRHx8PNLT05Gb\nm4ukpCR5n6effhqpqal4+umnceLECfzyl7/E6dOnvfLZ+RmXB0xy6PxAW+a5Ui85IiRw0eKk8S72\nt3/jxK4WcR62KdCKGUYrhJ6em9daJ08eIt9aB4+tpbkZqlbnyRCN23UEnN42bRsSZU6dsgJVI9YA\ntUunFXNKtEKOPdZ5I4k5b+EtMQc0X/ygdPJY2FUp8loasmVuIPuXYbPZMGrUKEycOFHeVldX59YM\nsVgsSExMRL9+/QAAU6ZMQV5enkrQ8TyP69cbneVr166hd+/ebfzEgg8SdD7AG9MilL3kDAYD9ZIj\nQgNXJ2u9ebDsITonfb0wn0v0hF5r3Dybi36R4Z4Nq1eFa0VJv42K1p1TvX5T+DQ8XH/OqdWqDr+y\n/pZNAk6qqQWnFYXK0GeTqJOaxBxn1PmMlE2ANaPcZDGnzaUTxRtzedk2EnI+xZtCrjlchWy1OXEs\nL08ZslU6esrHWK1WCIIAnuflx7Nz5IULF3D33Xer1hAVFeV2neXl5ejTp498OyEhARaLRbXPsmXL\n8OCDD2LDhg2oq6vDZ5991paPJighQecHWiLoWC85dlVCveSIdoGi9YmymMJVuNVVvpXHQq+Fbp5T\nLphyLS1185ren6TJI2u2T57y+GCzNbpieo4fE43a+5pm4Ep2e6Ook2879IWbzn1M6OlNdlA5c4ri\nB62QA3R+dyTkvIa/hJw7WNhVaTJoQ7Z2u10VsuU4Tm4cbDabVdWuDocDH3/8MfLz8/Hkk0+2eD16\n51etsbJt2zY89dRT+P3vf4/i4mL86le/wvHjx1v8WsEMCTof0FqHjgk5ANRLjmh/NNPPTotfhV4z\nbp7kor1Ca0K2SoHX3PQL9h5Zfp5UVw9O4xIqQ6NcRDgknWk0ko6ok6prdEO3YnVjewvt5yjV1jvn\n6cFDIQeQmPMiwSLmXOEqZMsK+RwOh+zKXb16FdOmTcNtt92GxMRE7Nq1C0lJSTh8+DA6derU4tdO\nSEjA2bNn5dvnz59HfHy8ap/33nsPn376KQDgzjvvRENDA3766SfcdNNNrXzHwQcVRfgAFi5l1NTU\nwGg0IsJFjo3D4UBdXR1EUaReckTHxMNWJh4XUKCFYVvtY5uStV0JupY8hy6K4y4XES6LPS4ywlkY\nKQolmLCTtK0/NJ8LZzTKgq7xdphahCpPuopjFafarhBt2jC54vVJyPmWYBdyzcEa3huNRkRGRsrn\nNavViqKiInzyySc4dOgQfvrpJ1y+fBlJSUlydetTTz2FmJgYj15HEAQMGjQIhYWF6NWrF0aMGIFt\n27YhOTlZ3ueRRx7BE088genTp+PEiRMYM2YMzp8/75P37WOoKCKQKKuBlCh7yZlMJkRERJCQIzom\negKg2QIL5W7ed/N0e921MC9PJZSaEXdK505qsDaKPebIacaASfUN+uuw2VW5flJtnWo/JwHY1CBY\nzvtjIdSmAogb25t+B6J0owk0e19N83ud3xCJOW8RqmKOuXJscpE2//vHH3/EH//4RwwbNgx79+6F\nyWRCXV0djh07hkOHDuHQoUMtmulqMBiQlZWFBx98UG5bkpycjGXLliE9PR1jx47FmjVrMGvWLKxb\ntw48z2PLltD8bJuDHDofYVUkSNfX10OSJDm5U9lLLjIyUnXlwiAhRxA6+MDJA9rg5rWm+EKS1AKv\nuUIJvUkN2tdWhpHDjerijqZ9mAhzcuD05uzqhaU5HpLjxvPqhspJyHmNUBVyLAe8oaEB4eHhTiaF\nw+HA5s2bkZeXh/Xr12P48OEBXG3IQg6dv1HmzTGHThRFNDQ0wGq1UlNggmgNPnDygDZU2raywlbl\n3rnYXxIEWcBx4eFqMYemHDttzlt9g3qbw6EKGzs1ClY4b5Ak59eQb9/Y7vTZkpDzKqEq5pSuXHR0\ntJPD9s9//hMLFy7EmDFjsGfPHt1iP6JtkEPnI9gMOwCyiBNFkZoCE4S/8MDN84uTpxRszRxvncSZ\nUlw1iSi5uEFxn8p1YwJQuY2FW1kLEodD9dlIDju48HB1WFZHpJEr51tCVcixnHFmVGhzwG02G9au\nXYt9+/YhKysLgwcPDuBq2wXk0Pkb5sqxpsAAqCkwQfgTD9w8vzh5ChdPEiUX/d8kSKJCULnKC9Rp\nQyI7eXqFDsr3q+wr1/TZyBW1LvLi2GehHt0GEnJeJFSFHHAjDxyAkysnSRIOHTqE559/Hk888QT+\n/ve/tygvjmg5JOh8hNVqRW1tLXieh8lkgtVqpT9mggg0ARR57HmVTpiuuJNE1bhbp/Ux8cVeg72+\nqwIFpUgTBGeR1sx7oZ5yviVUxRybYMRmimtdubq6OqxYsQInTpzAX/7yFwwYMCCAq+04UMjVR1RX\nV4PjOBiNRgiCgOrqasTGxrrcn5w6gggivB2u9eT5mEBTiCZVE2aDwSNBpc2Tc3LX2D6K9VM41b+E\nqpADGgsb6uvrZbNCmT4kSRK+/PJLvPTSS3j66afx61//uk0zzAldXB54SND5CIfDAaHpQCqKIqqq\nqtClS5cWPQeJPIIIIrwk8iRRch2mbRJR7H6V0NLep3HPOIPBZasW7eu72cHtcxCtJ1TFnCRJaGho\ngN1uR2RkpFPj++vXr+MPf/gDKioqsHHjRvTq1SuAq23XkKDzN0pBJ0kSKisr0aVLF6f2JC2FRB5B\nBBEtFHkuJ2M05765yFuTREn3ueWQKgm3oCJUhRxww5UzGAyIjIx0cuX+/ve/47XXXsOiRYvw+OOP\nt/k8RzQLFUX4G+UftDf/uHfVb3XaRiKPIAJES3Ly2L56bVZ0ChGUr6EUa0qhpifa3IZPOZ7EnB8J\nZSGndOVMJpNTq5GrV69i8eLFMBgMKCgoQLdu3QK0UgIgh85nCIIAh6K6rbKyUrfvnK8gkUcQIYSH\nDZPdohWNJNwCSiiLOVdju4BGoffRRx9hw4YNWL58OR5++GFy5fwHOXT+RvvHzdqY+EvQkZNHECGE\nVng156J5ItZIyAWUUBZyrAG+IAi6Y7suXLiAhQsXolevXigsLESnTp18tpbz588jIyMDFy9ehMFg\nwKxZszB37lyn/ebOnYv8/HxER0fj/fffR0pKis/WFMyQoPMTyskRgYJEHkGECCTWQpZQFXPasV0m\nk0llTIiiiK1btyInJwdvvPEGRo8e7XNXLiwsDGvXrkVKSgpqamqQlpaGBx98EElJSfI++fn5+P77\n73Hq1CmUlJTgmWeeQXFxsU/XFayQoPMR2j90nucDLui0iKKI7T9tdpopSyKPIAiiZYSqkAPcj+06\nffo0FixYgKFDh6KoqAgmk8kv6+rZsyd69uwJADCbzUhOTkZ5eblK0OXl5SEjIwMAMHLkSFRVVeHS\npUuIi4vzyxqDCRJ0fiIYHDoGS3RlV2LK3D5JkpBXswVi0/xHjuPAcRzGm6cHcskEQRBBy19+3Ija\n2loYDAb5JxT6rynHdoWHhyMqKkplRgiCgM2bN2PHjh1Yv3490tPTA7bWM2fO4PDhwxg5cqRqe3l5\nOfr06SPf7t27N8rLy0nQEb4jGAQd6+7NEl2Vo8gkSYIoik5CjrHjeg4aGhrgcDjkzuATYn4diLdB\nEAQRFOTVbJGPnYIgQBAEeW43AJXAMxgMTsfVQNLc2C4AOHHiBBYuXIj7778fe/bsQXh4eCCWCQCo\nqanBpEmT8NZbb8FsNqvu0zuvBstn7G9I0PkIvaKIQAk6lhtRV1cHnucRExMjJ7qyg5EkSZAkyemA\noxzxEh4ejpiYGPl+vRADOXkEQbR3lMc+juNkwcZgx1Mm8mw2GwRBgCRJTiKP53m/ChB3Y7tsNhvW\nr1+PL774AllZWbjtttv8tjY9HA4HJk2ahGnTpmH8+PFO9yckJODcuXPy7fPnzyM+Pt6fSwwaSND5\nEKWIY1Wu/oaVnkuShKioKLm7N1sXO8hwHOfULJJZ8WFhYTCbzR6FEEjkEQTRnvEkV45dGPM8r+rd\npnTyHA6H7Ob5S+QJgiBf2Osd0w8dOoTnnnsOjz/+OD777LOgmD8+Y8YMDB48GPPmzdO9f9y4ccjO\nzsbkyZNRXFyM2NjYDhluBagPnU+x2WyycLJarbDb7U52sa9gX1xBEGAymVRXYcrwKtumvM/hcKCh\noQE8zyMyMtInX2oSeQRBhBK+KnpQOnnsh7W40gvZtvY1mCunN7arvr4eK1aswLFjx5CdnY1bbrnF\nW2+vTXz55ZcYPXo0hgwZIovk119/HWVlZeA4DrNnzwYAzJkzBwUFBYiOjkZOTg5SU1MDvHKfQqO/\nAoHdbpddOeZ2xcTE+PQ1WbWStnIVcJ8nx4ScJEkwmUxO/Yd8iSRJlJNHEERQ4u8KVqXIU7p6SpHH\n/u8ucuJubNdXX32FpUuXYvbs2XjqqadCopijg0OCLhAoBR0LffqqCaMkSaivr4fVakVERITqi+tO\nyAmCIDeS1Lt6CxQk8giCCCTB1IpEW3zBfpQ5fFonr7mxXdXV1Vi2bBmuXLmCjRs3dti8sxCEBF0g\nUAo6h8OB2tpadO7c2auvoa1cNZlMHleuiqIoh4L1kmODEQrVEgThD4JJzLlCeYxXijx2Xud5HhER\nEWhoaJArWSVJwmeffYb//M//xMKFC/HEE08E/XGfUEGCLhA4HA4ITUO3BUFAdXU1YmNjvfLcrGiB\nWenKEGlLKleNRiMiIiJC2mYnkUcQhLcIBSHnCpZyIwiC3GZEEASsWLEC77zzDgYPHgygsZ3KihUr\ncPfddzs5d0TQQ4IuECgFnSiKuHbtGrp27drm52UtSADIlasAdCtXtUJOWbmqzadoT5DIIwiiJYSy\nkFOO7TIajarcaXZ/bm4uPvzwQ/Tp0we1tbU4ePAgysrKMHjwYEyZMgULFy4M4DsgWoBLQUdtS3yI\n8gulLExorb3Nkls9qVxVijll5SrHcbpNJNsb1D6FIAhPCWUxpxzbFRUV5VTMdvHiRSxcuBBxcXHI\nzc1Vpf3U1NTgyJEjsvFAhDbk0PkQ1muIUVlZqRqz5SmiKKKurk5Obo2IiGhV5WpkZCTCwsIoX0IB\niTyC6LiEspDTju1SnheAxvPG1q1bkZOTg1WrVuFnP/sZHfvbB+TQBYK2TosQRRENDQ1y5ap25moo\nVq4GG+TkEUTHJJTFnLuxXWfOnEFmZibuuOMOFBUVwWQyBWKZhJ8hh86HiKIIu90u366qqkJ0dLTb\n/m7KytXw8HCYTCaPhVwoVq6GAiTyCKJ9EMpCTunK6R3fBUHAO++8g//5n//BunXrMGLEiACulvAR\n5NAFA+4cOm3laqdOnZxakHhauerpqC7CM8jJI4jQJpSFHOB+bNe3336LBQsW4L777sOePXvkKlei\n40AOnQ9hAo1RXV0t5zpoaUvlKqtuau+Vq8EG+9w5jpP7/5HII4jgI5TFnLuxXXa7HevXr8eePXuQ\nnZ2N2267LYCrJfwAOXTBAM/zTg6dw+FAXV2dXKGk/LKy8S9KIeeqclWvuonwDSw/URRFp0ITcvII\nIngIZSEH3Ohs4MqVO3z4MJ577jn8+7//OwoLC9t99wKiecih8zFWq1X+f11dnezmsKRWqlwNHbyZ\nn0gijyB8SyiLOUmSmh3bVV9fj5UrV+Lo0aPIzs7GLbfcEqCVEgGAGgsHCpvNJrtyrFcQx3FyUqvJ\nZPJYyAmCAKvVCofDQZWrfkSZiOzLyRok8gii7YSykANuzP0OCwtTnR+AxmPR119/jRdffBGzZs3C\njBkzKMWm40GCLlAwQSdJEmpqamR3p7WVq3r9hgjfoAxr8zyPyMhIv4c0SOQRhOeEsphjbaocDodu\nCk11dTVefvllXLp0CRs3bkTv3r0DtFIiwJCgCxQ2mw0NDQ2or68Hx3HgeR4xMTEAOt7M1VCiuTy5\nQCJJEibE/DrQyyCIoCKUhZwnY7sKCwvx6quvYsGCBZg8eXJQHIuIgEGCLlBcvXoVoijCZDLJeRFM\n0HlSuWowGALiDHVUQrGPH4k8oqMSykIOUI/tMplMTq5cRUUFlixZAgBYu3Ytunfv7tP1zJw5E7t2\n7UJcXByOHDnidP8XX3yB8ePHY8CAAQCAiRMnYunSpT5dE+EECbpAYbVaZdHmcDhQW1uL6Oho1UxX\nV5WrzBkifI+/8uT8BYVqifZOKIs55UW7XhqNJEnIy8vDunXrsGzZMjzyyCN+ubDct28fzGYzMjIy\nXAq6N998Ezt37vT5WgiXUNuSQGEwGGQnjrUhqampgcFgUP2wKzWqXPUv2jw5vTE6oQi1TyHaK6Es\n5AD3Y7suXryIRYsWoXv37vjss8/QuXNnv61t1KhRKCsra3afloyvJPwLCTofw0QcK3iIiYmRtwmC\nAJvNJt9nMBgQHh4e0s5QKMEOrExEa1sDtDdI5BGhzvafNsNut8NgMITccdLd2C5RFPHf//3feO+9\n97Bq1Sr8/Oc/D8qL+uLiYgwbNgzx8fFYvXo1Bg8eHOglEU2QoPMxv/nNb3D58mWkpqYiLS0NaWlp\nuOmmm1BZWYlVq1bhsccew7BhwxAWFgZRFFUiT+vi8TwflF/wUENZTRYqeXK+gkQeEQrsuJ6juggW\nBAEAnI6R2nzkYEHpyuk1CC4rK0NmZiZuv/12FBUVISoqKhDLdEtaWhrKysoQFRWF/Px8TJgwASdP\nngz0sogmKIfOx0iShJ9++gmlpaWwWCywWCw4fvw4qqqqMHr0aEybNg2jR4+G2Wx2yqEQBAEOh0M+\nkAHOB7BQu0oNJNqqYW01GeEaEnlEIHAVXlWmsCh/gOASee7GdgmCgHfffRcffPAB1q1bhxEjRgT8\nmFRWVoZHH31UN4dOy80334wDBw6ga9euflgZ0QTl0AUKjuPQvXt3/OIXv0BFRQVycnIwbNgwPPvs\ns6ioqEBpaSk2b96M2tpa3HrrrbKTN2TIEISHh6uKIpiD19xVKuXeOcPy5Orr62EwGNpNnpw/ISeP\n8DfN5coxkcbzvGrutTadRe8YyfO8X6Id7sZ2/etf/8KCBQvws5/9DEVFRQgPD/fpejyFfY56XLp0\nCXFxcQAAi8UCSZJIzAUR5ND5iYMHD+J3v/sdVq9ejVGjRjndLwgCTp48iZKSEpSWluLo0aMQRRG3\n3XYbhg0bhuHDh2PQoEEqIcK+eEoXTxAE8Dyve5XaEVHmyem1BSC8C4k8oq14u+hBeSHMfiRJ8llK\ni3Zsl/Yi226346233sLnn3+OrKws3H777W1+TW8xdepUFBUV4erVq4iLi8Py5cths9nAcRxmz56N\n7OxsbNq0CUajESaTCevWrcPIkSMDveyOBrUtCQaUrUo82ddms+HIkSNyuPbkyZOIjIzE0KFDZSev\nb9++qis/1qxYewBTirywsLB2n4+nzJOjMWn+RRlmioiIwBPdZgd6SUSI4K8KVl+JPOXYrsjISCdX\n7ptvvsGiRYswceJEzJ07ly4widZAgq49wMaHHThwAKWlpSgtLcW5c+cQGxsru3is6EIvH0/5016L\nLpRigsak+RdlaNvVCY1BTh6hJBhakShFHvu/p8dJ5QWkyWRyqphvaGjAypUr8c033yA7Oxu33nqr\nP98a0b4gQddekSQJV69elV280tJS/PTTT+jdu7fs4g0bNsxl0QX7cTgc8hVqWFhYUCQUtwTtdA3l\nrFzC93gjtE0ir2MSDGLOFZ5cDLMQa3h4uO7YruLiYrz44ouYMWMGfvOb39BxiWgrJOg6EpIk4dy5\nc3I+3sGDB1FbW4tbbrkFqampGD58uFx0oe2D5EnVWLAdkFhjYMqT8z/KfCFftIAhkdd+CWYh1xzK\nDgQ2m00uIDAYDDh+/DiOHDmC1NRU9O/fHytWrMCFCxewceNGJCQkBHjlRDuBBF1HhxVdsNYpLSm6\n0LZP4ThO5eIFquiC8uQCh9IRdRde9TYk8kKbUBVyDL2xXUDjMfbrr7/Gn/70Jxw+fBiaalB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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "for n in range(nt + 1): ##loop across number of time steps\n", + " un = u.copy()\n", + " vn = v.copy()\n", + " u[1:, 1:] = (un[1:, 1:] - \n", + " (un[1:, 1:] * c * dt / dx * (un[1:, 1:] - un[1:, :-1])) -\n", + " vn[1:, 1:] * c * dt / dy * (un[1:, 1:] - un[:-1, 1:]))\n", + " v[1:, 1:] = (vn[1:, 1:] -\n", + " (un[1:, 1:] * c * dt / dx * (vn[1:, 1:] - vn[1:, :-1])) -\n", + " vn[1:, 1:] * c * dt / dy * (vn[1:, 1:] - vn[:-1, 1:]))\n", + " \n", + " u[0, :] = 1\n", + " u[-1, :] = 1\n", + " u[:, 0] = 1\n", + " u[:, -1] = 1\n", + " \n", + " v[0, :] = 1\n", + " v[-1, :] = 1\n", + " v[:, 0] = 1\n", + " v[:, -1] = 1\n", + " \n", + "plot_field(u)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Excellent, we gain get a wave that resembles the one from the oiginal examples.\n", + "\n", + "Now we can set up our coupled problem in Devito. Let's start by creating two initial state variables $u$ and $v$, as before, and intialising them our \"hat function." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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VQqGgr4+r154rqoGuHgY5ouCwE4I9cQ4yF2hnaZVq9WrQsbi7PQa6JlmVLQlD\nf09zn9VMJoOenp6Gb/qwBVKnrIJoo+llono+8N0f4JmvXsidi+Q71tCrxqLCrWGga1PQI1yapqFY\nLOrtuZrtsxr08bfKeNxOp5eJ6inOyletczKvceqUiyUFp9k1YM0EvXK5XFVDz1hHL2ofUOxGeffs\n2cOiwnUw0LXAGCaCCkTGPquJRAL9/f0t9VmNaqADoC80FkGu0fQyUSN9fX2OR0WA+i2KiLzSrTX0\nOEJXHwNdm/wORG73WY1ioBMXUafrBIma0UxnAU3TkMvlOuJi6RYGXHtePzde19Dzi93zNDw8zEBX\nBwNdC4IYoTO353Kzz2pUAp3Y8CHWyCWTSfT19fHiQb4wB714PI5SqYR0Ou34YhmPx/l67WJBnWuj\nFvTqraE79NBDPb//qGKga5Po5eoVRVFQKBRQqVQ8ac8VhRE6q5275XKZF0cKhUYXS0VRqnqFdvJi\ndmosTP/PzQQ9sfnP/AHFz9fu4OAgR+jqYKBrgR8FD83N4vv6+jwpBRCmk4uZMciZd+5WKpWgD4+o\nLquLpdP1eVFdzA5wyrUT2AU9Y8jz8kMKp1xbw0DXJnHCdeskJspu+NUsPowjdPWCnBDG4yZqpNH6\nPDGaF5apL3JX1MOucUOQ4EVpFbvnaXBwkLtc62Cga4Hb3Rbs+qz68cYXxx6GE41VLT27EiwMdBQ0\nN19/7exaNJZXCfo9TN3H7Rp69d5XQ0NDDHR1MNC5oNVwYayfpmlaIIVww3ABMAa5eDzuuJYeAx0F\nzev3T701TmI0r1uKzXaCMHxw9ks7QQ/Yu37cPBo9PDzMThF1MNC5oNlAZ9ytCQRfP83NKeNmiCBX\nKBTQ09ODbDbruJZet5wUiaxIktR0+yirZvBevI+6KbQ0ix9CG49GK4pS9dq97777cM8992Dq1Kmo\nVCpYvXo1jjnmGEyZMqWpSg8LFy7E6tWrMTAwgM2bN1v+zNq1a/GVr3wFlUoF+++/P5566qm2Hqvf\nGOhaYD5ZOd3pap5SDDrICX5PX5q7W7RSFJlTrkTVurXYbNTwubUmPnQA0K+PAHD++efjpJNOwiuv\nvILvf//7uOeee/DKK6/gr3/9K6ZOnYqZM2fihz/8YcPndcGCBbjsssswf/58y+8PDQ3hy1/+Mv77\nv/8bkyZNwnvvvefuA/QBA50LGoUL80hUs+25vOZXOHIjyAkMdETOOC1NwbZnFAbmEd6+vj7Mnj0b\ns2bNwv0WcgxdAAAgAElEQVT334/Vq1cDAEZGRvDqq6/ijTfecPTanDt3LrZu3Wr7/QceeABnn302\nJk2aBADYb7/92nwk/mOga4HTTRHG9lztBhgveR2OjEGunTZlROSedsqqMOi1xq5HKTWmqmrVc9ff\n34+TTjoJJ510kiu3v2XLFlQqFXzkIx/B6OgoFi9ejPPPP9+V2/YLr6ouMAcit9tzec2rQGfuN+vm\n88AROiL3NdP2zG7alu9Lake9LhFjxozx7H5lWcbzzz+PJ598ErlcDieffDJOPvlkHH744Z7dp9sY\n6FwgSZJ+oisUCp605/KS2+HIj0DLQEfkn2bW5wFAPp9n2zML3DDSWL1A5+UO18mTJ2P//fdHKpVC\nKpXCvHnz8OKLL0Yq0HHstwXmF5soPzI0NARJkjB27FhkMplIhDnAvXCkqiry+TyGhoagaRrGjBmD\nbDYbmeeBiJojpm0TiQR6e3v1hex9fX3o7e3VN4yVy2XkcjnkcjkUCgWUSiW9nVQ3fTDrpsfaqnqB\nrt0uEWKk2cqZZ56J3/zmN1AUBfl8Hs8++yymTZvW1v35jSN0LRLtp4rFIsrlsh7korg+ot1AZxyR\n82tkkiN0ROEj3pNiNK/b2p450YmPyQ/tBrrzzjsPa9euxa5du3DwwQdj6dKl+rV70aJFmDp1Kv7+\n7/8eM2fORDwex6JFizB9+nQXH4H3GOhaNDo6inK5jFQqhf7+fn2KIYpaDUdBBDmBgY4ovKxCC9ue\nkRN2G0faDXQPPPBAw59ZsmQJlixZ0vJ9BI2BrkWpVAp9fX2QJCny0wZiDaBT5rWCQYxMBhHoFEVB\noVDw9T6JOl03tT3jGrrG7J6jPXv2sO1XAwx0LUokEnoIivpokdPjVxRFn2Lu7e0NxRSzHydI8+Mm\nIu+x7Vl3sjunDw8PY8KECQEcUXQw0LXI+IILU4P7VtULdGEMcn48z2F83ERh5sc5MMxtzxqJ8jUi\naENDQxyha4CBzgVRf4PaHb+YYqxUKqEMNF71oDVOKYfxcUdFalMfirPyQR8GdYEotD2L8iyOn7zc\n5drpGOhcIrbnR7FEh3nKNexBzisMckSdJYxtz6I+AOA1BrrWMdC1yGn7rygQx24McmLTR5gDjZv1\n8xjkiLoH256FU73zOadcG2Ogc0mUA504eQ0PDyOVSiGTyUTiROV2/TwGOaL2RHmNmBttz+pN20b5\nufGb1fM0MjLiaeuvTsBA16JOGKGTZRmFQgGyLAMAxo0bF6kTjlv18xjkiMiOG+vzorgUJwj1Qq+m\naXweG2Cgc0mUAp0xyKXTaWQyGQwODgZ9WJ4LshAyEXWWRuvzRGkVMaInlEolTtvasAt0Ubm2Bo2B\nrkVRHKEzB7lsNhvpk4nT55xBjoj8Yrc+T5ZlvdVUt7Y9axefk/oY6FwidrmGkeg5qygKUqmUZZDz\nqgSIlxoFOgY5albU3gNhw+fPmnHaNplM6l9n27Nqdq8fWZZ57naAgc4lzbbP8kOlUkGhUICqqrZB\nTojCCKMVq2NWVRWlUgnFYhGJRIJBjhzL5XIcMSHfdFPbMyfqdYkYO3ZsAEcULQx0LQrrlKsY2hdB\nLp1OI5lMNnzDh+X4m2F+TJqmoVgsMshRyzKZTNUaqHojJmK6jMiJZkYvu7Xtmd1zNDg4yBp0DjDQ\ntcEYgoIORK0GOSHo42+FseUagxy5wThiYmwvVa8QbaFQiPyF1C2ccrXnxvk1ym3P2sGiws4w0Lkk\nqECkaZo+tappWtNBTohioAPeXx/IIEdeshoxKZfLUBQFiURCv5CWy+WuXf9EjXnx/x+FtmdOcYSu\nPQx0bQhyhM4Y5AAglUq1FOSEKAU644hcLBZDf39/zadWIq+JC6DViIndhdTrtlIUXn6fX8PY9qwR\nETbNOELnDK+CLvFrl6s5yKXTaSQSibbfdFEIdJqmoVQqoVAooKenB6lUCpqm+R7mnv/WP+G4b93h\n631SdNhdSI0XUav1T+ZF7gx6nScM/6dhbnvGEbr2MNC1wfjC8zoQeRXkzPcRRuYgJ0bkSqUSKpVK\n0IdH5Ii4EBo5LVth3G0bZlxDF01etz1r1/DwMCZPnuz67XYaBjqXuX1C0zQN5XIZxWIRgDdBDgjn\nCJ0IcsViEfF43HJqNWzHTNQMJ+ufFEXRL6SdspuxG9lNJ4aZW23PnL4+643Q7bPPPq48pk7GQOcS\n8cJ3K9CJICd20PX19aGnp8ezE3eYAp05yGWzWctpVV7EqFMZp8USiQSA8IyWUGvCcn51Q7Ntz5x+\nELG7fnINnTMMdG3wohadOchlMhlPg5wQhsLIToOcEKYQSuS1ZkZLFEXhaF4Idfpz3876vHg8bns+\nHxoawvjx4/16GJHFQOciEYpaKZ1hDDMiyIlP5n4IMhxZhVgnj52Bjqi1i6hXtcm4hs5et56rGq3P\nM64fBYB8Po9YLIbXXnsNv/71rzF9+nTk83l2inCAga4N5hNXLBZr+k0bdJATgghHrQY5IqqPLaXC\nic/n+8yvUU3TkMvlkMlk9A8eO3bswJNPPolNmzbh0EMPxTHHHIMZM2bov04++eSGAygLFy7E6tWr\nMTAwgM2bN9v+3IYNG3DyySfjJz/5Cc466yxXH6tfGOhc1EwoanZ60Wt+Bjq3ghxH6Iia005LKfa1\nJS+J0V3xGp0xYwZuuOEGAMBpp52Gn//853j55Zfx8ssvY+PGjXjwwQexdu3ahre7YMECXHbZZZg/\nf77tz6iqiq997Wv4+Mc/7tbDCQQDXRtaWUNnLsERdJAT/AhHbq8PZKAjckejllKN+to2s5OxW3E6\nuj6750ec4w844AB89KMfxUc/+tGmbnfu3LnYunVr3Z+57bbbcM4552DDhg1N3XbYBJ8kOki9gGHs\nbmCspRYWXoYjLzd6MNAReaPZvrbi/RyLxVCpVDhta8JzVXu8eh395S9/wcMPP4wnn3wS69ev9+Q+\n/BKeRNEBrEKRuXF82IKc4EWgMxdD7uvrc7WGnrgdfvIl8k+9TRiiXqZxRI8lVd7XjY/ZKbvzeLlc\n9nRt9RVXXIHly5dXXU+iKnzJIkKsplxF6Q9VVfU1clFoHO9moPOjqwXAkyNRWBhH88y18+ptwrDa\nbduJohwS/BJUDbrnnnsOn/vc56BpGt577z2sWbMGiUQCZ5xxhmf36RUGujYZg1AsFkO5XEY+n0ep\nVIpEkDNrZ7TLryBn5GYxZyJqj/m92Gpf207dhNEpj8NPQ0NDbZcsESPIVv73f/9X//OCBQvwyU9+\nMpJhDmCgc41YSyLLMmKxWOSCXDudLoIIckFSFCXoQyCKtG7oa0vNqdf2q50RuvPOOw9r167Frl27\ncPDBB2Pp0qUol8uQJAmLFi2q+tmov6YY6NqkaZo+ItfT04NYLIZsNhv0YbWk2WnXMAQ5P3e6qqqK\nQqGAcrnsy/0RdZNO7mvLWYTG6gW6drpEPPDAA45/9oc//GHL9xMGDHRtGh0dhSRJGDNmDABgZGQk\n4CNqndNwpGkaZFlGPp8HAKRSKSSTyUBOWH4EOmOQ6+3tZcVyIh856WurKArK5XJo+9pyDV1j4v/O\njH1cnWOga1N/f7/+ZhXTA1FW7/hFkCsUClBVFel0OrAgZz4uL6iqimKxiFKphGQyibFjx1qecIho\nL79GoprtawugZgOG36N5QZ8no2pwcBD77rtv0IcRCQx0bYrFYvoJQ4wWRXV4vd5ol5haDVOQA7w5\nSZpLzURtPSRRt2q1Oby53Znb55Wof9D3g911c3h4GFOmTAngiKKHgc5F7WwsCAOrYw5rkBPcLrfC\nIEdORfV93m3C0teWr5X66pUtaWcNXTdhoGtTK+2/wsp47GEPcoIbz7e5HVtYiz8TkXvq9bUVI3l2\nJVWM7c7CeF6MoqDq0HUSXrVcFvVAJ8sySqUSVFVFKpVCb29vx56wzC3JGORo1q9uxabTFwd9GJHV\nCaOWTqZtZVmuuwnDajQw6s9LUAYHB7HPPvsEfRiRwKtXmzplhE6WZVQqFWiahnQ6HZkg18rzLcqt\n5PN5vbesl61lutkhP4hj68Ws20fR5nTa1tjX1hjuFEWJ5HXBTxyhax8DncuiFujErlVFUfT1IqlU\nKujDcqyZ59vr3rJE1F2cbsIQgS6Xy1m2O+v2c1C9c3ixWEQ6nfbxaKKLgc5lxn6uYSaCnCzLSKfT\nyGazKJVKkeyC4CTQiRE5oPM7WVB7xAgLXx/N49Si9WheqVSCpmlIJBJd39fWinjd2D1mlotyhoGu\nTeYXYCwWC/UInVWQE48haqOLQONjjsrmDgqPfD4fqS4EFA0itFltwhDtzrqpr60TUbseBY2BzmVh\nDUXGIJdKpaqCnBDWY6/HbkTUOJXMIEfNyGQyjroQRGEknsJPkqSazVjGaVtjyLPahCF220ZZo5Hd\nqD8+vzDQtckqFIXpRK8oCgqFAiqVim2QE6Ia6IzHrCgK8vm85QgkkRNnj1sIAPivoeq+juYF8MZ1\nUSxnQfXYtbWyY5y2NYY9p5swojaibBfoisVipNZ0B42BzgXGUBGWUGQOcplMpuGbOyzH3opmgiuR\nE2eNvajma/819EN9ykx8eEsmkw3LWRinzDqV8RxI1dw6rzrdhBHmvrZW7ALd4OAge2c3gYHOZUGH\nolaCnBD0sbdC9JcdHh5Gb28v+62Sp6xCHlB/NE9RFMiyzHVRXc6r/+NWO2FEYRMGS5Y0h4HOBeYR\nuiCmXM1Brq+vr+lgE6VAp6oqCoUCSqUSJElikKNA1RvNEzUOnayLcrPVFIVHEOdVu04Y5mUDfve1\ntVJvhI6BzjkGOpf5vcvVGOTaHaGKQqBTVRXFYhGlUgnJZBKZTAbFYpFhjkKn3mie1boou1ZTQVxg\nyX1h+X+z62Rh3G1rtwnDq6UDLCrsDgY6l/kVihRFQbFYRLlcdn2qMYy1pDRNQ7FYRLFYRDKZxJgx\nYxCPxyHLctCHRtSURmvzgMYX2DBOl4XxvEHOOJm2tVs64MbrsF6gGz9+fEu32Y0Y6FxgfCGKQOfV\nyc3LICeON0wnZmOQSyQSepATojCqSNRIM2vz7GqWsQNBeIXpnNoM47St1dIBsRHIrqRKM69DuynX\nCRMmuP64OhUDncu8etOKNWNeBDmjsJx0NE1DqVRCoVBAT08P+vv7a2o1AQx01NnsRvOM6i1+N4e8\nsIzmdZtOOkc1swlDURRHo3n1RuiOOuoozx9Tp2Cgc4FdgV43Tpx+BTkh6ICkaRrK5TIKhQLi8bht\nkCPqVk6mbAH7xe9elbKI6iiUXzr9uXFaUsVqVFl8ADG/hjjl2hxeKT0gdrq2E7yMQS6ZTPq2izOo\nQGcMcrFYDJlMRh/iryfoAEoUBq2UU2l2FIVa083nJ6ejeWJGplQqYceOHbj11ltx9NFHY8+ePfxA\n3wQ+Uy5ws5+reRen3+U4/A5Imqbp/VaBvW2Xenp6mr6QcHSAqFYzGzCcFKbthDZTQeHz9j7zaJ7o\n7CNJEvr7+3HkkUdi06ZN+P3vf4+f//znOOCAAzBjxgzMnDkTM2fOxBlnnNGwg8TChQuxevVqDAwM\nYPPmzTXff+CBB7B8+XJIkoRsNos777wTM2bM8OTx+oWBzgOthKKgg5zgV6ATBYHz+TwAIJ1OI5FI\nNH3SC+NGDqIwa3U0z67NFENefd08QueUOH9LkoSBgQFceumlAIBPfepTePHFF/HOO+9g8+bNeOml\nl7Bq1SqcccYZDW9zwYIFuOyyyzB//nzL70+ZMgX/8z//g7Fjx+LRRx/FJZdcgnXr1rn6uPzGQOeB\nZkKROciZd3H6zY9AJ0bkVFVFOp1GMpls64LAiwlR+1oZzTO2OhPvw3K53BWtzprB58FevetNqVRC\nX18fjjjiCBxxxBE4++yzHd/u3LlzsXXrVtvvf+ADH6j68/bt2x3fdlgx0LnAblNEPWELcoKXgU6W\nZRQKBSiK4kqQE7iOjsgbzYzmVSoVfcE7W529j+cmZ8yvCT97A//gBz/Aaaed5vn9eI2BzgP1AkZY\ng5zgRThSFAX5fF5fJ5HNZl19kzLQEfnLKuj9ZNd/IBaL6Wub2OrsfZ382NrVaLmM18/dU089hZUr\nV+KZZ57x9H78wEDnAqsROnM/V1VVUSqVbAvkhoWb4cjcX9btIEdE4fHZfRdZfr3bW53xw2Z9doHO\nj+dt8+bNWLRoER599NGOKI/CQOcSYxCKxWJQFAVA404HYWMVRptl7GaRSqWQyWQ8PSlzhI4ovDq1\n1Vkzona8frILdIVCAX19fW3ftt214a233sLZZ5+NH//4xzjssMPaup+wYKDzgAhFhUIhMkFOaCcc\n+V0EWfAz0IkpcyJqnV3Is6pXFvVWZ/yw2ZrBwUGMGzeu5X9/3nnnYe3atdi1axcOPvhgLF26FOVy\nGZIkYdGiRfj2t7+N3bt345/+6Z+gaRoSiQTWr1/v4iPwHwOdS4w9XCuVCmRZRiwWi0yQE6JacsXr\nk6ZxpDWZTHp6X0TdqJ3iyGFvdRaGYwgruxG6dgPdAw88UPf7d999N+6+++6Wbz+MGOhcommaPiIn\nTirZbDbow2paM4HOHHKCCq9eniyNPWWjNNJK1CnC2urMKY7Q1edVoOtGDHQuGR0dhaqq6O/vhyRJ\nGBkZCfqQWuIk0IVtXaAXU67sKUsUXlFrdcYROnt2gW5oaIiBrkm8Qrmkv79f30wgTh5RVC8cGUer\nenp6QhNy3Ax0xlZkkiRZ9pT9RPoLwDUfdOX+iMg9YWx1xhG61jDQNS/4q3GHML7po96OynwC6pbR\nKhHkNE2zbEX2ifQXAjw6ImqFV63Omjm3R/E64BcRpM2GhoYwefLkAI4oujrvqhwQc6ATo0ZReyMb\nj9cY5GKxmOVoVRi0O0LXqIMFgxxR52m31Zk55NlN2UbxOuCnelOuM2bMCOCIoouBziNRrY0mjlsU\nQQaATCaDnp6e0J6UWq2dZyx8bNfBgmGOqHu0MpqnKErdVmcMdPXZXSc55do8BjqXtNLPNWw0TYMs\nywCAYrFoOe0YVs0818Z6eXaFjxnkiEioN5onZi3qtToTX+uWVmfN4qYIdzDQeSRqgU6sHxMjXdls\nNjLlOZyeGI318uwKHzPIEZET9YojG9cY5/N5/e/d0OqsWfWmXDuhHZefGOg84kYLLT9YrR8bGhoK\n+rCa0ig8OymzwiBHRO2ym7L9ya7/qOln28mtzprBsiXuYaBzifkFKdZOhJUIcrIs16wfi9root3x\nmsusMMgF45AfxLH1YiXowyAKzGf3XVTztU5tddaMetcZWZbZladJDHQeCWsoMm4ESKVSlhsBwnrs\nTpl351qVWWGQI6IgdXKrs2aZjznK158gMdC5JOyhSFEUFIvFuhsBhLAdeyPGPrqyLCOfzwOAfVFg\nIqKQinqrs2Y02gEcxmMOMwY6FxmDUFjW0Bl3dNptBDCLYqBTVRUjIyNQVRV9fX0sCkxEHSNqrc6c\nsgt0LPXSGgY6jwQdiow7OpPJpKMgJwR97M1QFAX5fB6apiGZTKK3t5clSIioK4Sx1ZkbRkZGkM1m\ngz6MyGGg80hQI3TGHZ3JZNJyI0AjUQh0xrWAvb29+ppAIwY5Iuo2YWh15lS9Ha5jx451/f46HQOd\ni4xByO9drk5KczgV5kBnNYUsSZLe1QJgkCMiMvOr1VkzWLLEXQx0HvErFJlLc1jt6GxWWNb/GZlH\nHo1TyOJ5ZpAjInKuXnFko2ZanTUzmmcX6Pbs2cOiwi1goHOR8YXpdaAzluaIx+OuBDkhTCN0xsBq\nN/L4yb7zAzo6IqLOUm/K1mmrM3PIa3Y0jyN0rWGg84ixlIabaw/MNdasSnO0KwyBzklg5YgcEZE/\nnLY6M4a8Rq3ORJkVs+HhYQa6FjDQucg8QucmTdP0fqvA3hprPT09nu1ICirQGR+nJEmsJUdEFFKN\nRvOEeq3OxABCLBbDSy+9hKOOOgpDQ0M49NBD/XoYHYOBzkNiLVo7Te7NxXLT6XRNjTW3BbVtvVKp\n1H2cDHJEROHndG1ePp/Xd9GOjo7i0ksvxWuvvYaBgQEccsgheO2113Dsscfi2GOPxaRJkxxdmxYu\nXIjVq1djYGAAmzdvtvyZxYsXY82aNchkMrj33nsxa9as1h5oyDgrTEYtaXena6VSwcjICHK5HFKp\nFMaMGYNkMul54PJ7ylWW5YaPk2GOiCi6zhp7kf5LED1qk8kkxo8fj9/97nfYtm0bPvaxj+GjH/0o\nBgcHceutt+KEE07Afvvthy1btjS8nwULFuCxxx6z/f6aNWvw+uuv489//jPuuusufOlLX3Ll8YUB\nR+hc5Fb7L1mWUSgUoCgK0um0LyHOyK9AZ6wll06nLfvKMsgREXUmqzXmyWQShUIBn//853HEEUfo\nX9+5cyf22Wefhrc5d+5cbN261fb7jzzyCObPnw8AmDNnDoaGhrBz504MDAy0+CjCg4HOQ80GIxHk\nZFm2DTh+8DrQGWvJ2fWVZZAjIuosVsWN7erQmcuWuBW4tm/fjoMOOkj/+6RJk7B9+3YGOqrW6gid\ncaQqlUoFFuQEr3boGtuR2fWVZZAjIuos5iAn2F1jhoeHPesUYXVNDkO7Mzcw0HmoUaBTFAXFYrHu\nSFUQvNih26gdGYMcEVHnqRfm7Kiq6lpdVbPJkyfj7bff1v++bds2TJw40ZP78hsDnYusRuisOi5Y\nta+yqsUTJBFG2wl35i4WDHJERN3BLsiZma8xbiz3ETNMVs444wysWLEC5557LtatW4dx48Z1xHQr\nwEDnqVgsBkVR9L8bpxzN7avCpp11dObixywKTETUPZyEuUYDBq0OJpx33nlYu3Ytdu3ahYMPPhhL\nly5FuVyGJElYtGgRTj/9dPzqV7/C4Ycfjkwmg5UrV7Z0P2HEQOcyYxAyrkVrNOUYNq0EOqvixywK\nTETUHZyOygH2I3F23SOceuCBBxr+zO23397y7YcZA53HZFnG4OCgbR/SsGplh24+n4eqqujr67Ms\nfswwR1Hwl2s+iInLfxf0YRBFRjNBzshuh+uYMWPaPaSuxEDnMrFuTqwdA2A55Rh2TgOdk5p5DHIU\nJcVZ+aAPgSgyWg1z9UqWeLXDtdNFK2VEQKlUQi6XQzweR19fH4rFYuTCHOBsh26jUiudHOQmLv8d\n/nLNB4M+DCKiQLQa5IR6gW7cuHFt3Xa3il7SiACxdkw0Io4iu0DnZIduJwc5IqJu126Yq4eBrnUM\ndC5LpVL6ztZ2e7kGyRzozBs7GOSIiLqLm0GOI3TuY6DzgdsdF/widuiK9YB2GzsY5IiIOpvbo3J2\n18U9e/bUtP0iZxjoXGZ8gUqS5EqB3qDIsoyhoSHE43HWkiMi6kJeTa9qmmZZnmR4eBgTJkzw5D47\nHQOdx7xudO82UUuuVCoBALLZLGvJERF1GS/XydUzNDTEEboWMdC5zKr9V1QCXaVSQT6/t2RDMpmE\nqqoMc0REXcaPMMc1dO5joPOYXT/XMLGqJWccpQMY5IiIOp2fo3IMdO5joHOZ+QUa5p2uxlpy6XS6\nqpacGFlkkCMi6nx+T7HWC3Sccm0NA53Hwjjlaqwll0qlkMlkat5Ynx6zIKCjIwoe239RtwhqrZyd\nkZERtv5qEQOdx8IU6FRVRbFYRKlUYlFgIqIuFnSQsxuh0zQtMj3Pw4aBzmVh3BTBosBEzk35/Kag\nD4HIU/+5/VbkcjnEYjHEYjHE43HEYjG91JbX7K6JQV8ro46BzgPGEBfkpggWBaawOOQHcWy9WAn6\nMOpikKNOJ0blRNF4VVWhKAoqlQpUVdVrw4mAJ365HfLE6Jzd7UaxbmsYMNB5LBaLoVKp+Hqfmqah\nXC6jUCggFouxKDBRAwxz1Ol+tucH+p9FmIrFYlXXBlVV9V/GoGcMd8bRPLfJsszp1jYw0HnAPELn\n1zCyKApcKBQAAJlMpqaOHMAwRyQwyFGn+8mu/4CmaVAURe8zLgKdCHWCCG1GYiRP/CqVSlBVVf+3\nxtE8p1O2duvnhoeHMXbs2DYfcfdioPOYX4FOBDlVVdHX14dEIlHzhmGQI9qLQY66wS+GV+ohS0yp\nit+NU67A+5sRxHVDBDtJkhCPx6tGzupN2Zqna61G8+wC3eDgIGvQtYGBzgPmfq5eBjqrosAMckTW\nGOSoG6x69/tQVRWjo6MAoIcsEcxEyBLru8XomzHwGWuSmkfznE7ZlstlfV2eccrWbl05iwq3h4HO\nY14FOmNR4FQqVVUUWGCQI3ofwxx1ukdGf1T1dzGSJqZbRQcgVVWrwl08Hq+a1TGHOxHAFEXRA1or\nU7aKokCWZf32CoUC4vE4nnvuOUycOBF79uxhoGsDA53HRKCzG2JulrEoMGvJETXGIEfdwBzmgOqR\nNON6amPIEyNpYvODOeiJ64sbU7biGEqlkv7zqqpi5cqVWLt2LQqFAg444ACMjIxg1qxZmDVrFqZN\nm4ZkMtnw8T/66KO44ooroKoqFi5ciGuuuabq+2+//TYuuOACDA4OQlVVLFu2DKeddloLz3R4SQ1G\nj1gUpgXiU4iwe/dujBs3riZ4NUPTNBQKBZRKJSSTSaTTaQa5ACkfPR47T+gN+jBCb+C59/sB+122\nhEGOuoFVkGuFMaAZfxkDmXkDhNWUrTlTWE3ZlkolSJJUE9TuvPNO7NixAxMmTMCmTZuwadMmvPHG\nG/jlL3+JU045xfbYVVXFkUceiSeeeAITJ07EiSeeiFWrVmHq1Kn6z3zxi1/Ecccdhy9+8Yt49dVX\ncfrpp+ONN95w5bnzme3IEEfofNBOP1fWkgsf5aPHA9gbVhjqwolhjrqBW2EOqL/5wTiSJ6ZdjSGv\n2SlbMRoofhfK5TLmzp2Ls846S/9aPp9vOBiyfv16HHHEETjkkEMAAJ/73OfwyCOPVAW6WCyG4eFh\nAHs3X0yaNKnNZyx8GOg84Ea3CGMtuXg8zlpyIRJ/YiOA94MdhQeDHHUDN4NcPXZTtuY1cWJdnnHK\n1n0sr2kAACAASURBVDiiZ/w3pVIJiqIgFovp/15cI9955x188IMfrDqGvr6+hse5fft2HHTQQfrf\nJ0+ejPXr11f9zHXXXYdTTz0Vt956K/L5PB5//PF2nppQYqDzQTOBTtSSE59KWEsuvOJPbMTEJ6q/\n9pdrPmj9w+QpBjnqBn4FuUbEtKtxkME8ZVupVKqmbCVJ0gsHZ7PZqt2usizj4Ycfxpo1a/D5z3++\n6eOxur6aB1YefPBBLFiwAF/5ylewbt06fOELX8Arr7zS9H2FGQOdB1odoRNBDgBryUXUxOW/q/ka\nQ553GOSoW4QlzNmxm7IVG/lkWdZH5Xbt2oXzzz8fRx99NI444gisXr0aU6dOxaZNmzBmzJim73vy\n5Ml466239L9v27YNEydOrPqZe+65B4899hgA4AMf+ACKxSLee+897Lfffi0+4vBhoPNBo0AnyzLy\n+TxUVWUtuQ7EkOcNhjnqBmEPcvWIOqmJRAKZTEa/rvX29uLKK6/Er371Kzz44IN477338Oyzz+LZ\nZ5/Vd7cuWLAA/f39ju7nxBNPxGuvvYatW7fiwAMPxKpVq/Dggw9W/cwhhxyCxx9/HBdccAFeffVV\nlEqljgpzAAOdL4y7gYyMteTS6TR6e3sZ5LoEQ17rGOSoW0Q1zIlROdG5yLz++y9/+Qu+//3vY/bs\n2fjNb36DdDqNfD6Pl19+GS+88AJeeOGFpnq6xuNx3H777Tj11FP1siXTpk3DddddhxNPPBGf+MQn\n8G//9m+45JJLcNNNNyEWi+FHP4rmc1sPy5Z4pFR6v1xDoVCApmn64k5jLblUKoVUKsUgR5aiHvLc\nLFvCIEfdIqpBTqwBLxaLSCaTNYMUsizjrrvuwiOPPIKbb74ZJ5xwQoBHG1ksW+I34zSrGKFTVRXF\nYhGlUolFgckRjuQxyFF3iWqYM47KZTKZmhG2P/zhD1iyZAlOOeUUPPXUU5ab/ag9DHQ+kWUZQ0ND\nSCaTDHLUFquQB3Rm0GOYo24R1SAnSmyJgQrzGvByuYwbb7wRzzzzDO644w5Mnz49wKPtbAx0HhGj\ncqIoMAAWBSZPddJoHoMcdYuoBjng/XXgAGpG5TRNwwsvvIBrrrkGn/3sZ/HrX/+6qXVx1DwGOo+U\nSiXkcjnEYjGk02mUSiW+mMl3UQt5DHLUTaIa5kQHI9FT3Dwql8/nsWzZMrz66qv48Y9/jClTpgR4\ntN2DmyI8MjIyAkmSkEgkoCgKRkZGMG7cONuf50gdBcmrkNfMpgiGOeoWUQ1ywPulSMRghXH5kKZp\n+O1vf4v/9//+H774xS/iwgsvbKuHOVnipgi/pdNpKMreC5iTwsKrC/fVfI0hj/wS5Egegxx1k6iG\nOU3TUCwWUalUkEqlagrfDw8P45vf/CZ2796Nhx9+GAceeGCAR9udOELnEVmW9UCnaRr27NmD8ePH\n15QnaRZDHgWp2ZBXb4SOQY66SVSDHPD+qFw8HkcqlaoZlfv1r3+N73znO7j66qvxmc98pu3rHNXF\nETq/GV/Qbr64OZJHQXJjJI9BjrpJlIOccVQunU7XlBrZtWsXvva1ryEej+PRRx/FvvvuG9CREsAR\nOs8oigJZlvW/79mzx7JciVcY8ihIIuQZR+gAIP7ExiAOhygQUQ5zlUpFb9tlLn6vaRr+67/+C7fe\neiuWLl2K0047jaNy/rF9ohnoPKKqKiqViv73wcFBZLPZmhYofmLIIyLyXpSDnCiArygK0ul0zTXr\nnXfewZIlS3DggQfi+uuvx5gxYzw7lm3btmH+/PnYsWMH4vE4LrnkEixevLjm5xYvXow1a9Ygk8ng\n3nvvxaxZszw7phDglGvQnGyM8Bqna4mIvBXVMGdu25VOp6tG3VRVxX333YeVK1fie9/7HubNm+f5\nqFxPTw9uvPFGzJo1C6Ojozj++ONx6qmnYurUqfrPrFmzBq+//jr+/Oc/49lnn8WXvvQlrFu3ztPj\nCisGOo+YX+ixWCzwQGemqioeeu+ump6yDHlERM2JapADGrfteuONN3DVVVfh2GOPxdq1a5FOp305\nrgkTJmDChAkAgGw2i2nTpmH79u1Vge6RRx7B/PnzAQBz5szB0NAQdu7ciYGBAV+OMUwY6HwShhE6\nQSx0FZ/EjGv7NE3DI6M/gqqqAPYetyRJODN7QZCHTEQUWj/+y23I5XKIx+P6ryjUXzO27Uomk+jr\n66sajFAUBXfddRd+8Ytf4Oabb8aJJ54Y2LG++eab2LRpE+bMmVP19e3bt+Oggw7S/z5p0iRs376d\ngY68E4ZAJ6p7i4WuxlZkmqZBVdWaICf8YnglisUiZFnWK4N/qv/CIB4GEVEoPDL6I/3cqSgKFEVB\nqVTSz6PGgBePx2vOq0Gq17YLAF599VUsWbIEf/d3f4ennnoKyWQyiMMEAIyOjuKcc87BLbfcgmw2\nW/U9q+tqWJ5jvzHQecT8ggoy0Im1Efl8HrFYDP39/fpCV3Ey0jQNmqbVnHCMLV6SyST6+/v171tN\nMXAkj4g6nfHcJ0mSHtgEcT4VIa9cLkNRFGiaVhPyYrGYrwGkUduucrmMm2++GU8//TRuv/12HH30\n0b4dmxVZlnHOOefg/PPPx5lnnlnz/cmTJ+Ptt9/W/75t2zZMnDjRz0MMDQY6DxlDnCRJ+qc2P4mt\n55qmoa+vT6/uLY5LnGQkSaopFimG4nt6epDNZh1NITDkEVEnc7JWTnwwjsViVbXbjCN5sizro3l+\nhTxFUfQP9lbn9BdeeAFf/epX8ZnPfAaPP/54KPqPX3TRRZg+fTouv/xyy++fccYZWLFiBc4991ys\nW7cO48aN68rpVoBlSzxVLpf14FQqlVCpVGqGi70i3rhi67nxU5hxelV8zfg9WZZRLBYRi8WQSqU8\neVMz5BFRlHi16cE4kid+qaqKWCxmOWXb6n2IUTmrtl2FQgHLli3Dyy+/jBUrVuCwww5z6+G15be/\n/S3mzZuHGTNm6CH5u9/9LrZu3QpJkrBo0SIAwKWXXopHH30UmUwGK1euxHHHHRfwkXuKdeiCUKlU\n9FE5MdrV39/v6X2K3UrmnatA43VyIshpmmZZf8hLmqZxTR4RhZLfO1iNIc84qmcMeeLPjWZOGrXt\n+t3vfodvfOMbWLRoERYsWBCJzRxdjoEuCMZAJ6Y+vSrCqGkaCoUCSqUSent7q964jYKcoih6IUmr\nT29BYcgjoiCFqRSJefOF+GVcw2ceyavXtmtkZATXXXcd3n33Xdx2221du+4sghjogmAMdLIsI5fL\nYezYsa7eh3nnajqddrxzVVVVfSrYanFsGHGqloj8EKYwZ8d4jjeGPHFdj8Vi6O3tRbFY1HeyapqG\nxx9/HP/6r/+KJUuW4LOf/Wzoz/tUhYEuCLIsQ1EUAHtHwUZGRjBu3DhXbltsWhBD6cYp0mZ2riYS\nCfT29kZ6mJ0hj4jcEoUgZ0csuVEURS8zoigKli1bhrvvvhvTp08HsLecyrJly/DBD36wZuSOQo+B\nLgjGQKeqKgYHB7HPPvu0fbuiBAkAfecqAMudq+YgZ9y5al5P0UkY8oioGVEOcsa2XYlEomrttPj+\nqlWr8LOf/QwHHXQQcrkcnn/+eWzduhXTp0/H5z73OSxZsiTAR0BNYC/XIBjfUMaNCa0Ob4vFrU52\nrhrDnHHnqiRJlkUkOw3LpxCRU1EOc8a2XX19fTWb2Xbs2IElS5ZgYGAAq1atqlr2Mzo6is2bN+sD\nDxRtHKHzkKg1JOzZs6eqzZZTqqoin8/ri1t7e3tb2rmaSqXQ09PD9RIGDHlE3SvKQc7ctst4XQD2\nXjfuu+8+rFy5EsuXL8eHP/xhnvs7A0fogtButwhVVVEsFvWdq+aeq1HcuRo2HMkj6k5RDnON2na9\n+eabuPLKKzFz5kysXbsW6XQ6iMMkn3GEzkOqqqJSqeh/HxoaQiaTaVjfzbhzNZlMIp1OOw5yUdy5\nGgUMeUSdIcpBzjgqZ3V+VxQFd999N37+85/jpptuwkknnRTg0ZJHOEIXBo1G6Mw7V8eMGVNTgsTp\nzlWnrbrIGY7kEUVblIMc0Lht1x//+EdcddVV+MhHPoKnnnpK3+VK3YMjdB4SAU0YGRnR1zqYtbNz\nVexu6vSdq2EjnndJkvT6fwx5ROET5TDXqG1XpVLBzTffjKeeegorVqzA0UcfHeDRkg84QhcGsVis\nZoROlmXk83l9h5LxzSravxiDnN3OVavdTeQNsT5RVdWajSYcySMKjygHOeD9ygZ2o3KbNm3CV7/6\nVZx99tl44oknOr56AdXHETqPlUol/c/5fF4fzRGLWrlzNTrcXJ/IkEfkrSiHOU3T6rbtKhQKuP76\n6/HSSy9hxYoVOOywwwI6UgoACwsHpVwu66NyolaQJEn6otZ0Ou04yCmKglKpBFmWuXPVR8aFyF52\n1mDII2pflIMc8H7f756enqrrA7D3XPT73/8eX//613HJJZfgoosu4hKb7sNAFxQR6DRNw+joqD66\n0+rOVat6Q+QN47R2LBZDKpXyfUqDIY/IuSiHOVGmSpZlyyU0IyMj+Na3voWdO3fitttuw6RJkwI6\nUgoYA11QyuUyisUiCoUCJElCLBZDf38/gO7ruRol9dbJBUnTNHyq/8KgD4MoVKIc5Jy07XriiSfw\n7W9/G1dddRXOPffcUJyLKDAMdEHZtWsXVFVFOp3W10WIQOdk52o8Hg9kZKhbRbGOH0MedasoBzmg\num1XOp2uGZXbvXs3rr32WgDAjTfeiP3339/T41m4cCFWr16NgYEBbN68ueb7Tz/9NM4880xMmTIF\nAHDWWWfhG9/4hqfHRDUY6IJSKpX00CbLMnK5HDKZTFVPV7udq2JkiLzn1zo5v3CqljpdlMOc8UO7\n1TIaTdPwyCOP4KabbsJ1112Hf/iHf/Dlg+UzzzyDbDaL+fPn2wa6f//3f8cvf/lLz4+FbLFsSVDi\n8bg+EifKkIyOjiIej1f9Ep/UuHPVX+Z1clZtdKKI5VOoU0U5yAGN23bt2LEDV199Nfbff388/vjj\nGDt2rG/HNnfuXGzdurXuzzTTvpL8xUDnMRHixIaH/v5+/WuKoqBcLuvfi8fjSCaTkR4ZihJxYhUh\n2lwaoNMw5FHUPfTeXahUKojH45E7TzZq26WqKu6//37cc889WL58Of72b/82lB/q161bh9mzZ2Pi\nxIm44YYbMH369KAPif4PA53HLr74Yvz1r3/Fcccdh+OPPx7HH3889ttvP+zZswfLly/Hpz/9acye\nPRs9PT1QVbUq5JlH8WKxWCjf4FFj3E0WlXVyXmHIoyj4xfDKqg/BiqIAQM050rweOSyMo3JWBYK3\nbt2KK6+8EscccwzWrl2Lvr6+IA6zoeOPPx5bt25FX18f1qxZg0996lPYsmVL0IdF/4dr6DymaRre\ne+89bNiwAevXr8f69evxyiuvYGhoCPPmzcP555+PefPmIZvN1qyhUBQFsizrJzKg9gQWtU+pQTLv\nGjbvJiN7DHkUBLvpVeMSFuMvIFwhr1HbLkVR8IMf/AA//elPcdNNN+Gkk04K/Jy0detWfPKTn7Rc\nQ2d26KGHYuPGjdhnn318ODL6P1xDFxRJkrD//vvj4x//OHbv3o2VK1di9uzZuOyyy7B7925s2LAB\nd911F3K5HA4//HB9JG/GjBlIJpNVmyLECF69T6lce1dLrJMrFAqIx+Mds07OTxzJI7/VWysnQlos\nFqvqe21ezmJ1jozFYr7MdjRq2/WnP/0JV111FT784Q9j7dq1SCaTnh6PU+J5tLJz504MDAwAANav\nXw9N0xjmQoQjdD55/vnn8eUvfxk33HAD5s6dW/N9RVGwZcsWPPvss9iwYQNeeuklqKqKo48+GrNn\nz8YJJ5yAo446qiqIiDeecRRPURTEYjHLT6ndyLhOzqosALmLIY/a5famB+MHYfFL0zTPlrSY23aZ\nP2RXKhXccsstePLJJ3H77bfjmGOOafs+3XLeeedh7dq12LVrFwYGBrB06VKUy2VIkoRFixZhxYoV\nuPPOO5FIJJBOp3HTTTdhzpw5QR92t2HZkjAwlipx8rPlchmbN2/Wp2u3bNmCVCqFY489Vh/JO/jg\ng6s++YlixeYTmDHk9fT0dPx6POM6ObZJ85dxmqm3txef3XdR0IdEEeHXDlavQp6xbVcqlaoZlXvx\nxRdx9dVX46yzzsLixYv5AZNawUDXCUT7sI0bN2LDhg3YsGED3n77bYwbN04fxRObLqzW4xl/deqm\nC2OYYJs0fxmntu0uaAJH8sgoDKVIjCFP/NnpedL4ATKdTtfsmC8Wi7j++uvx4osvYsWKFTj88MP9\nfGjUWRjoOpWmadi1a5c+irdhwwa89957mDRpkj6KN3v2bNtNF+KXLMv6J9Senp5QLChuhrm7hrFX\nLnnPjalthrzuFIYwZ8fJh2ExxZpMJi3bdq1btw5f//rXcdFFF+Hiiy/meYnaxUDXTTRNw9tvv62v\nx3v++eeRy+Vw2GGH4bjjjsMJJ5ygb7ow10FysmssbCckURiY6+T8Z1wv5EUJGIa8zhXmIFePsQJB\nuVzWNxDE43G88sor2Lx5M4477jj8zd/8DZYtW4Z33nkHt912GyZPnhzwkVOHYKDrdmLThSid0sym\nC3P5FEmSqkbxgtp0wXVywTGOiDaaXnUbQ160RTXICVZtu4C959jf//73+OEPf4hNmzbhjTfewKRJ\nk/Cxj30MJ5xwAo477jjMmDEDqVQq4EdAEcdAR9XMmy42bNiALVu2oLe3FzNnztSLILey6cLrkMd1\ncsEyFkkNS79hhrxoiHqYU1UV+XweAJBOp2vKH+3ZswfXXnstFEXBd77zHbzzzjt4/vnnsXHjRmzc\nuBFDQ0N48803Azhy6iAMdNSYpmnI5XL6pov169dXbboQIW///fevWSeiqmrVKJ4Xmy6CHBWivRez\nUqmESqUSiRFRhrzwiHqQa9S2S9M0/PKXv8SNN96Ib37zm/jEJz5h+d6QZTkUH4Ao0hjoqDXmTRfP\nPfcc3n33XUycOFFfjzdr1iz09/c3vbNW1GdyEgrEOjkgPKNC3cIYpBOJBHp7eyMZpDVNw6f6Lwz6\nMLpO1MOccUTaalRux44duPrqq7Hvvvvie9/7HsaNGxfEYVL3YKAj94hNF2I93gsvvIDR0VF904Xo\ndGGeCm1l0wXXyQXLGKStLmZRx5DnnagHuUZtu1RVxYMPPoi7774b119/PT7ykY/w3ER+YKAjbxk3\nXWzYsAGbN2+GpmmYNm2aPpJ35JFH1oysmUOeLMuQJEkvB6AoimU5APJWNwdpTtW2J+pBDqhu22VV\nAumtt97ClVdeiWnTpuHb3/42+vr6AjpS6kIMdOQvsebkpZdequp0ITZdiJBn3nQhyzJef/11TJgw\nQf+6qqpsZ+YT41qhRCLBIP1/GPKciXqYM5bhsfogoygK7rnnHvzkJz/BjTfeiDlz5vD9QX5joKPg\nmTddbNiwAW+99RbGjh2L2bNnY/z48bjvvvswadIkPPTQQ/ponnlnrSzLesgzlk/phE4XQRKjEpIk\ndeT0qtsY8t4X9SAH7H395/N52w1XW7ZswZVXXol58+bh2muv1cuVEPmMgc4rjz76KK644gqoqoqF\nCxfimmuuqfp+uVzG/PnzsXHjRuy333546KGHcPDBBwd0tOGjaRqef/55XH755XjllVdwyimnYOvW\nrTWdLlrZdMGQ54y5bZG5mTg5140hL+phTtM0FAoF27ZdlUoFt956Kx5//HHcfvvtmDFjRkBHSgSA\ngc4bqqriyCOPxBNPPIGJEyfixBNPxKpVqzB16lT9Z+6880689NJLuOOOO/DQQw/hF7/4BVatWhXg\nUYfLDTfcgOuvvx5XXnklrrzySqTT6apNF6LTxejoKKZMmaKXTrHadGFVBBkIf6eLoBinV1nPzzud\nGvKiHuSAvWGtUCjYLi/YvHkzlixZgk9/+tO4/PLLubuewoCBzgvr1q3D0qVLsWbNGgDA9ddfD0mS\nqkbpPv7xj2Pp0qWYM2cOFEXBhAkT8O677wZ1yKHzzDPPYMqUKZg4cWLdn1NVtabThaIomD59elOb\nLqxCXjeOSIkyJLFYDKlUitOrPot6yIt6mFNVFYVCAaqqWrYLLBaLWL58OV544QWsWLECRxxxREBH\nSlTD9mLFjxtt2L59Ow466CD975MnT8b69ettfyYej2PcuHHYvXs39tlnH1+PNazmzp3r6OdisRim\nTp2KqVOnYv78+QCAUqmEl19+GevXr8cdd9yBP/3pT0gmk1WdLg455BAkEgl9GkW0MxOjeKVSCfl8\nvms2XRgvZGLRN/lHLLr/8V9uqylQG4WQF/UgZ27b1dfXVzPK/+yzz+Kf//mfsWDBAixbtowj+hQZ\nDHRtsBrdNIcA889omtaRQSEIvb29enD7x3/8R33TxfPPP48NGzbgX/7lX6o2XYifPeCAA5BMJvXb\nMW+6qFQqVe3MxMaLKK/HM7dLM1/IyHtieq+npwfZbLYmKFiFpbCEvKgHOaD6w0wmk6kZlR4dHcXS\npUuxfft2/OxnP8PkyZMDOlKi1jDQtWHy5Ml466239L9v27atZurwoIMOwttvv42JEydCURQMDw9j\n/Pjxfh9qV5AkCdlsFvPmzcO8efMA7A0yu3fv1kun/Od//ifeffddTJgwQQ94YtOF8QRv3HQhyzJK\npVIkN12I0ch6QYK8ZQwSfX19Ta3DCkPIi3qYc9K266mnnsLSpUtxxRVX4POf/7zn75GFCxdi9erV\nGBgYwObNmy1/ZvHixVizZg0ymQzuvfdezJo1y9NjoujjGro2KIqCo446Ck888QQOPPBAnHTSSXjw\nwQcxbdo0/WfuuOMOvPzyy7jjjjuwatUqPPzww9wUETBN07Bt27aqThcjIyOYMmWKvrN25sz/3969\nB0V1nn8A/+7CqsBqABtWcREkWS42RARWvHYaG+PYIKBjRkorzuhIbUvEoiZ4yRDjxCZCrDXLWDq2\n1NaJWJ1YrIRNZ7AkmJRdiPFanUDUFUmUjgoaURZ2z+8Pf+d0bwgq7EW+nxlnXDgzvOsiPPue9/s8\nz/caurAt9ARBsNvFE2/VekORZ7FYcO/evV7PCdHgcmfoZDCKPF8v5IC+x3bdvHkTGzduhNlsxo4d\nOxAWFuaWdR07dgxKpRI5OTkuC7rq6mrodDpUVVXBYDAgPz8f9fX1blkbeT2GIgaLXq9Hfn6+1Lak\nsLAQRUVF0Gq1SEtLQ1dXF5YsWYIvv/wSo0ePRkVFBaKiojy9bHJgtVrR1NQEg8EgTbqwWCyIj4+X\ndvJiY2MfKXTh7mStbXNUVzsSNPi8oaff4xR5vl7M2R4x6G1X7siRIygpKcGmTZuQnp7u9v8jJpMJ\n8+fPd1nQrVy5Ei+88AIWL14MAIiPj0dtbS1UKpVb10heiQUd0cMym81S6MJoNNqFLsRkbWRkpF2x\nJoYuHNunyGQyu128wQhd2B747q05Kg2uviYNeFpfRd7Bm7u9apf5UfQ1tuvatWtYt24dQkJCUFxc\njODgYI+s80EF3fz587F+/XpMnz4dAPDiiy9i27ZtSEpKcvcyyfsw5Ur0sIYNG4akpCQkJSVh5cqV\nTqGLLVu2wGQyYdSoUZg8eTJSUlKk0IVjsvZBoYuBKPLEW0uCIDz0OS16fLbFtEKhcGqE7S16O5N3\n8OZuWCwWmM1mr9hlfhR9FdNWqxUVFRX4wx/+gN/85jeYPXu2V75GQP8Cd0SO+FOfqJ8eFLpobGyE\nwWCwC13YTroYNWqUU+jCarVKu3hms/mRQhe8vep5tmcVfbGYFos8x9Y+4hsQXyjyxF05Pz8/l8Gf\nlpYWFBQUIDY2Fv/6178QFBTkoZX2j1qtRktLi/TYVeCOyJFv/eQh8jIymQyjR4/G3LlzMXfuXAD2\noYtPP/0UO3bswO3btzFhwgTpPJ4YurCdB9lXsla8ZSsWbLY7Qkyvul9f57R8lXi7VS6XP7DI6+np\ngUwm85rzoq7GdlksFpSXl6OiogLbt29Hamqq17xG4r+pK+np6SgtLcXixYtRX1+P4OBgnp+jPvEM\nHZEbiKEL20kXPT09iI+Pl3by4uLi+hW6EP/PymQyDB8+HAqFgsWcm/V1TmsocDxKYHtetLc3IQOp\nr7FdX331FdasWYMZM2Zg48aNdm+ePC07Oxu1tbW4fv06VCoVNm/eDLPZDJlMhtzcXABAXl4e9Ho9\ngoKCUF5ezvNzJGIogsjb2IYuGhoacP78eQwbNgwJCQnSTl5UVJRULLS1taG2thZz586VGiOLt23F\nX6KO7VNoYFmtVty7d6/XQe5DXW9F3kCeFxVfA4vF4rIdT3d3N3Q6HT7++GPodDo8//zzA/HUiLwF\nCzpyH71ej9WrV0utXGxn2wLAnj17sG7dOqkTe15eHpYtW+aJpXoVQRDQ2dmJ48ePS0WeyWSCUqmE\nUqlEXV0dFi1ahJKSEqdk7WD/Eh3qHEMPrnaEyLWB+v7sz2tw+vRprF27Funp6fj1r3/tc+cZH8fZ\ns2dx6NAhzJkzB6mpqcjKymLP0ycTU67kHlarFXl5eaipqUF4eDi0Wi0yMjIQFxdnd11WVhZ27tzp\noVV6J5lMhqCgIMyaNQuzZs0CANTV1eGXv/wl/Pz8sGLFCvznP//BnDlzoFKp7CZd9Ba6EM/jiaEL\nuVxut4vn7ZMuvIFtc1pXI6PowWxvwYoeNvnd19iue/fuYdu2bTh+/Dj+9Kc/QaPRuPtpetzt27eh\nUCggCAKam5uhVCo9vSRyMxZ0NKCMRiM0Gg0iIyMB3C/cKisrnQq6PnaGCcC7774LnU6H9957D6+8\n8opUeAmCgNbWVpehC9tJFyNGjICfn590e/ZJGWfmLkwQD56HKfJkMhkEQYC/vz8CAgKcGgQbjUZs\n2LABS5cuxdatW4fkeUYAmDp1Kn7729/i9ddfx969e6UedjR0sKCjAdXa2oqIiAjpsVqthtFoSQPl\nLQAAETFJREFUdLruww8/RF1dHWJiYrB9+3YOwnYhOzsbv/rVr5zeactkMqjVaqjVaixcuBCAfeji\n0KFDePPNN2GxWBAXFyft5ImhC9vbULZNkMXbWYD3tqdwF/HAPeffuo9jkWexWNDZ2Qngfk9IcZcu\nJycH33zzDZ5//nm0t7fj9u3b2Lt3L5555hlPLt8riO1Y/v3vf2PVqlUeXg25Gws6GlD9aYiZnp6O\n7OxsKBQKlJWVYenSpaipqXHXEn2GbWHcF7lcjtjYWMTGxmLJkiUA7hclZ86cgcFgQFlZGc6fPw+F\nQmE36SIqKsqpyLPdJXHVg2wwk4ueZntrzxd7yj0J+moHs3fvXhw4cABVVVXo7OxEe3s7EhIS8P3v\nfx8pKSmYO3cuMjMzPfgMPGf8+PE4cOAAampqUFpa6unlkJvxpxUNKLVajcuXL0uPXTXEDAkJkf6+\nYsUKp9AEDQyFQoHJkydj8uTJ0qQLMXTR0NCAt99+G5cuXZImXYg7eSqVymnShSAIUhNkMWH4JIUu\nBEGA2WxGV1cXhg0bhsDAQJ99Lr5M3JWTy+Uud0bb29uxceNG3L17F+Xl5QgLCwMA3LlzBydPnkRj\nYyP++9//emLpHrd792788Ic/RHh4ODIyMjy9HPIAplxpQFksFsTGxqKmpgZjx47FlClTsG/fPsTH\nx0vXXL16FWPGjAEAHDp0CMXFxfj88889teQhTRAE3Lx5U5p00djYiLa2NqhUKuk8XlJSEkaNGuV0\ndulByUVxF88XzuOJPeVkMhkCAgIYevAA2105V2O7BEFAVVUViouLsWHDBmRmZnr995W71dTUoLOz\nE01NTcjLy5POztITh21LyH30ej3y8/OltiWFhYUoKiqCVqtFWloaNmzYgMOHD0OhUCA0NBS7du1C\nTEyMp5dN/882dNHQ0IAvvvgCt2/fRlRUlN2kC8e2EbahC/GPN4cu+pr9Se5hO7ZrxIgRTrtybW1t\neO211zBq1CgUFxfb7fATDUEs6Ijo0VmtVjQ3N8NgMKChoQGnTp1Cd3e3NOkiJSXF5aQLx2StOOnC\nVRNkdxVT7CnnHfoa22W1WrF//36UlZVh69at+NGPfsTXiYgFHRENNDF0Ie7knTt3zi50kZycjAkT\nJjjtuLi6VQu4J1krngG0Wq0upwyQe9imiB1bkQD3z94WFBRAo9Fgy5Y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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from devito import TimeData\n", + "\n", + "# First we need two time-dependent data fields, both initialised with the hat function\n", + "u = TimeData(name='u', shape=(nx, ny))\n", + "init_hat(field=u.data[0], dx=dx, dy=dy, value=2.)\n", + "\n", + "v = TimeData(name='u', shape=(nx, ny))\n", + "init_hat(field=v.data[0], dx=dx, dy=dy, value=2.)\n", + "\n", + "plot_field(u.data[0])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using the tow `TimeData` objects we can again derive our dicretized equation, rearrange for the forward stenicl point in time and define our variable update expression - only we have to do everything twice now! We again use foward differences for time via `u.dt` and backward differnces in space via `u.dxl` and `u.dyl` to match the original tutorial." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "U update:\n", + "Eq(u(t + s, x, y), (h*u(t, x, y) - s*u(t, x, y)**2 - s*u(t, x, y)*u(t, x, y) + s*u(t, x, y)*u(t, x - h, y) + s*u(t, x, y)*u(t, x, y - h))/h)\n", + "\n", + "V update:\n", + "Eq(u(t + s, x, y), (h*u(t, x, y) - s*u(t, x, y)*u(t, x, y) + s*u(t, x, y)*u(t, x - h, y) - s*u(t, x, y)**2 + s*u(t, x, y)*u(t, x, y - h))/h)\n", + "\n" + ] + } + ], + "source": [ + "from sympy import Eq, solve\n", + "from devito import Operator\n", + "\n", + "eq_u = Eq(u.dt + u*u.dxl + v*u.dyl)\n", + "eq_v = Eq(v.dt + u*v.dxl + v*v.dyl)\n", + "\n", + "# We can use the same SymPy trick to generate two\n", + "# stencil expressions, one for each field update.\n", + "stencil_u = solve(eq_u, u.forward)[0]\n", + "stencil_v = solve(eq_v, v.forward)[0]\n", + "update_u = Eq(u.forward, stencil_u)\n", + "update_v = Eq(v.forward, stencil_v)\n", + "\n", + "print(\"U update:\\n%s\\n\" % update_u)\n", + "print(\"V update:\\n%s\\n\" % update_v)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We then set Dirichlet boundary conditions at all sides of the domain to $1$." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from devito import t, x, y\n", + "bc_u = [Eq(u.indexed[t+1, 0, y], 1.)] # left\n", + "bc_u += [Eq(u.indexed[t+1, nx-1, y], 1.)] # right\n", + "bc_u += [Eq(u.indexed[t+1, x, ny-1], 1.)] # top\n", + "bc_u += [Eq(u.indexed[t+1, x, 0], 1.)] # bottom\n", + "bc_v = [Eq(v.indexed[t+1, 0, y], 1.)] # left\n", + "bc_v += [Eq(v.indexed[t+1, nx-1, y], 1.)] # right\n", + "bc_v += [Eq(v.indexed[t+1, x, ny-1], 1.)] # top\n", + "bc_v += [Eq(v.indexed[t+1, x, 0], 1.)] # bottom" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And finally we can put it all together to buuild an operator and solve our coupled problem." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "DSE: extract_time_invariants [flops: 9, elapsed: 0.00] >>\n", + " eliminate_inter_stencil_redundancies [flops: 9, elapsed: 0.00] >>\n", + " eliminate_intra_stencil_redundancies [flops: 9, elapsed: 0.00] >>\n", + " factorize [flops: 8, elapsed: 0.01] >>\n", + " finalize [flops: 8, elapsed: 0.00]\n", + " [Total elapsed: 0.02 s]\n", + "DSE: extract_time_invariants [flops: 0, elapsed: 0.00] >>\n", + " eliminate_inter_stencil_redundancies [flops: 0, elapsed: 0.00] >>\n", + " eliminate_intra_stencil_redundancies [flops: 0, elapsed: 0.00] >>\n", + " factorize [flops: 0, elapsed: 0.00] >>\n", + " finalize [flops: 0, elapsed: 0.00]\n", + " [Total elapsed: 0.01 s]\n", + "DSE: extract_time_invariants [flops: 0, elapsed: 0.00] >>\n", + " eliminate_inter_stencil_redundancies [flops: 0, elapsed: 0.00] >>\n", + " eliminate_intra_stencil_redundancies [flops: 0, elapsed: 0.00] >>\n", + " factorize [flops: 0, elapsed: 0.00] >>\n", + " finalize [flops: 0, elapsed: 0.00]\n", + " [Total elapsed: 0.01 s]\n", + "DLE: analyze [elapsed: 0.01] >>\n", + " avoid_denormals [elapsed: 0.00] >>\n", + " loop_fission [elapsed: 0.00] >>\n", + " create_elemental_functions [elapsed: 0.00] >>\n", + " loop_blocking [elapsed: 0.03] >>\n", + " simdize [elapsed: 1.15]\n", + " [Total elapsed: 1.19 s]\n", + "CustomCompiler: compiled /tmp/devito-1000/dda6c0ed48805e2c8ec8b6701e0d44f2becdd123.c [0.55 s]\n", + "=========================================================================================\n", + "Section loop_y_1<81,101> with OI=0.00 computed in 0.000 s [Perf: 0.00 GFlops/s]\n", + "Section loop_x_2<81,101> with OI=0.00 computed in 0.000 s [Perf: 0.00 GFlops/s]\n", + "Section main<81,100,100> with OI=0.98 computed in 0.001 s [Perf: 5.20 GFlops/s]\n", + "=========================================================================================\n" + ] + }, + { + "data": { + "image/png": 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AgJe85CU4//zz8cgjjxS2vzwhC10C2KLHSo+w8gHr6+uVfOLKs88oK5BcZl29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\nHLhIQ9Pv+RP2/PUa1a7MzbPW+9TZkws8SZA1c4jQ1dogRikP1ZxN6WC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evAi9Xo9Zs2Zh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\nA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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sympy.abc import h, s\n", + "from devito import Operator\n", + "\n", + "# Reset our data field and ICs\n", + "init_hat(field=u.data[0], dx=dx, dy=dy, value=2.)\n", + "init_hat(field=v.data[0], dx=dx, dy=dy, value=2.)\n", + "\n", + "op = Operator([update_u, update_v] + bc_u + bc_v,\n", + " subs={h: dx, s: dt})\n", + "op(time=nt+1)\n", + "\n", + "plot_field(u.data[0, :, :])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "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": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} From c6a91dd35fb5d71b596eabe542db6a4040625694 Mon Sep 17 00:00:00 2001 From: Michael Lange Date: Mon, 29 May 2017 12:10:37 +0100 Subject: [PATCH 03/12] CFD: Add tutorial notebook for diffusion --- examples/cfd/test_03_diffusion.ipynb | 381 +++++++++++++++++++++++++++ examples/cfd/tools.py | 4 +- 2 files changed, 384 insertions(+), 1 deletion(-) create mode 100644 examples/cfd/test_03_diffusion.ipynb diff --git a/examples/cfd/test_03_diffusion.ipynb b/examples/cfd/test_03_diffusion.ipynb new file mode 100644 index 0000000000..37cf0b76f6 --- /dev/null +++ b/examples/cfd/test_03_diffusion.ipynb @@ -0,0 +1,381 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Example 3: Diffusion \n", + "\n", + "In this example we will look at the diffusion equation and how to handle second-order derivatives. For this we will introduce Devito's `.laplace` short-hand expression and demonstrate it using the examples from step 7 of the original tutorial.\n", + "\n", + "So, the equation we are now trying to implement is\n", + "\n", + "$$\\frac{\\partial u}{\\partial t} = \\nu \\frac{\\partial ^2 u}{\\partial x^2} + \\nu \\frac{\\partial ^2 u}{\\partial y^2}$$\n", + "\n", + "To discretize this equation we will use central differences and reorganizing the terms yields\n", + "\n", + "\\begin{align}\n", + "u_{i,j}^{n+1} = u_{i,j}^n &+ \\frac{\\nu \\Delta t}{\\Delta x^2}(u_{i+1,j}^n - 2 u_{i,j}^n + u_{i-1,j}^n) \\\\\n", + "&+ \\frac{\\nu \\Delta t}{\\Delta y^2}(u_{i,j+1}^n-2 u_{i,j}^n + u_{i,j-1}^n)\n", + "\\end{align}\n", + "\n", + "As usual, we establish our baseline experiment by re-creating some of the original example runs. So let's start by defining some parameters." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from examples.cfd import plot_field, init_hat\n", + "import numpy as np\n", + "%matplotlib inline\n", + "\n", + "# Some variable declarations\n", + "nx = 31\n", + "ny = 31\n", + "nt = 17\n", + "nu = .05\n", + "dx = 2. / (nx - 1)\n", + "dy = 2. / (ny - 1)\n", + "sigma = .25\n", + "dt = sigma * dx * dy / nu" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We now set up the diffusion operator as a separate function, so that we can re-use if for several runs." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def diffuse(u, nt):\n", + " for n in range(nt + 1): \n", + " un = u.copy()\n", + " u[1:-1, 1:-1] = (un[1:-1,1:-1] + \n", + " nu * dt / dx**2 * (un[1:-1, 2:] - 2 * un[1:-1, 1:-1] + un[1:-1, 0:-2]) +\n", + " nu * dt / dy**2 * (un[2:,1: -1] - 2 * un[1:-1, 1:-1] + un[0:-2, 1:-1]))\n", + " u[0, :] = 1\n", + " u[-1, :] = 1\n", + " u[:, 0] = 1\n", + " u[:, -1] = 1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's take this for a spin. In the next two cells we run the same diffusion operator for a varying nuper of timesteps to see our \"hat function\" dissipate to varying degrees." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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XpWQy2VK1SiQSHVfNyEzM+ahWq7Fa5elkdXFcQxCDXPx5nZ9nnqtHvY099FoF\n1VS41zHQuWD8pYui2apXxgqWpmlIJBIYGhqK1YXAvLo46O3GvHB6jkQd5OJ4LsdNt/Otevmm3Y+6\nnQPWTdATO6gYzxkxTy9uFWC7Ku/Ro0djtXND2BjoXDDe+OJ0E7SqYAFArVaL1S+7IG58cW+mG3WQ\nsxL18/cb9s+jbvRrDz1W6NpjoPMoDoGuXQWrXq9Lf/xm4kYXxr6xfrA7R2QMciQPp9UZ2ebncSWi\nvaDfm6B76IXF7n0aGxtjoGuDgc6FuFTozI2O7YKPrMdvZnw9jUYDmUwG+Xw+djcPcwuVgYEBKV6D\nk3O523Yx5L9+rc70gqiutXELeu3m0L3lLW8J/PnjioHOo0QiId0qV7HPqmh0nM/nbfvjyRxIBRHk\njBW5Wq0Wm03XjSuJxbxFmYIc9QY3/dDMvdA4bBs8md7fboKeWPxnPFeMc/TCMDIywgpdGwx0Lsja\n8NAY5JLJJAqFAtLpdNu/E/Uxt2MMcolEoqVxc71ej/rwHNM0DZqmYWJiIpa7U1C8hT0/T4ZrIXlj\nF/SMIc843O/3nE4OubrDQOeRKEFHeRHTdb259VgqlUKxWHS8z6qMFbp2QU6Q8bjNjPvFKooSi5XE\n4kZfr9dRr9dju0qO2nO7etJqdwOeF87FPex26rno14cDu/dpZGSEq1zbYKBzwXyiRRUujDtWpNNp\nDA4OOg5ygjh2GS405qHidhVGmQOdeWg1l8thYmIi8vfXCVVVUSqVAKBZCTXOqRFhT3x6j8NrCoqs\n558XfszPE9cT6g9+99Brd+6Mjo4y0LXBQOeDsMOFMch53WdVhhuym6Fi8fdkYqzI5XK55tCquPHJ\nTMyRqVaryOfzSCaTzcoi8PoNXSxIEXuZ9nv7jH56nU7n54kRA+Mcq347L+zI8ME5LF6CHoBmj1Rj\nFXhsbIw7RbTBQOeDsAKd2DuyVqt5DnJGUQ0ZiyBXLpddDRXLwi7IxYFxxW0ikWi2TzEv9BE3dEU5\ntndxMpnseGHm8Fzvswp6ExMTyOVyLVufsX/eMbJ/sAtDpyqwmHMszpkf/OAH+M53voP58+ejXq9j\n27ZteNvb3oa5c+c6vv+99NJLWLNmDQ4dOoRkMonLLrsM69evn/K49evXY/v27SgUCvjud7+LpUuX\n+vKaw8JA54L54hP0SldN01Aul1Gv1zEwMNCy9Zgfwq4wmuf8eRkqjpLTICfDsZoZh4VFiOt2WNjL\n8Jwx7PU5iY68AAAgAElEQVTLzbxfiPPCqprHDwByfRiVifGcER8uAWD16tU4/fTT8dRTT+Gb3/wm\nvvOd7+Cpp57C//7v/2L+/PlYsmQJbrnllrbvayqVwrXXXoulS5diYmICy5cvx3vf+17Mnz+/+Zjt\n27fjmWeewa9+9Ss8/PDDuPzyy7Fr165gX7TPGOh8ENQNW1VVVCqVwIKcEFbg8CPICVGGJLcVORmG\nW8zz+4KoJrYbnhNDtaza9B/2zyMnzNfJfD6PZcuWYenSpbjtttuwbds2AMD4+Dh+8Ytf4Lnnnut4\nPsycORMzZ84EABSLRSxYsAAHDx5sCXR333031qxZAwBYsWIFRkdHcfjwYcyYMcPvlxgYBjoXgl4U\nYQwM2WwWhUIh0AtY0OHIGOTcLt6Qgfnn4jQMyXDz0TQNpVLJcQgN4pgVRZnyc5d91wMKntteaHGc\nn2e3Ryl1JqaFCIODgzj99NNx+umnd/V9nn/+eezduxcrVqxo+fODBw/ixBNPbP7/7NmzcfDgQQa6\nfuNXIDLvIBDWXKygAl2j0Wgudkin077N+QPCrdC5DXIyMA7Xdzr2KKqebqs2cbyZ9wu/KtFh988j\nObTbJWLatGmevvfExARWrVqF66+/HsViccrzmsXt3GGg84FYyeiGaAMhVg9GsYOA3zdyczsVP4Oc\nEEb4MA55ew1yYS88MQc5v6q8YYU+u6qNMeS1u5mLBRxxuyBTe15WTprnbUZxbsgw7UJ27QKdlxWu\nqqpi1apVWL16NS644IIpX58zZw5efPHF5v+/9NJLmDVrluvniwIDnQt+DLmKIFculwEA2Ww2ss3Z\n/bpJ+9lOJUpBhaEwNBoNDIy+HWkAi3/6cTx5/oaeGuLp1NhU0zSoqtpsn8Fh2/4Ql/l5si2OklG7\nQOdll4hLLrkECxcuxBVXXGH59fPPPx833XQTPvzhD2PXrl2YPn16rIZbAQY614whqJsKnXGDeQDI\n5XJIp9OR3mC8BrooglwQlaIgg1zQlS0R5Ix+9Z5bgdFbpzy2ftw+y+8h42pcJ4w3c+McvXZzsLiH\naTBkO3+6mZ8X1kpsnmfueAl0P/vZz3Dbbbdh8eLFWLZsGRRFwdVXX40DBw5AURSsW7cO5513Hu69\n916ccsopKBQK2Lp1q8+vIHgMdD4Q3dHbMW9nJUOQE9zeyKOsyPkZPnqhIteN9NHF1l/IxGuJfide\n5mBxyzNvZH/PvA7p80NAcOwWjngJdO9+97ubH+ba+frXv+7q+8uCgc4lc4XOLlxYbWdl3pc0at3O\nAWw0GiiXy80Gx0G1U2nHj0AXZpALYp5it0Guk+m1dx77j2OzAJABMFl41NfniFqnOViirUqnoble\nGsam13Ua0vf6IYBz6Dqze4+OHj3Kbb86YKDzgdXN2txzrZtdEMLmNGwYd6oIsi9eN9xcIONckdN1\nHZmRJaE9X2Fyeev/A0AVmEz1T9Azb20lbuTi96Zer7Ni08P8nJ9Hndld08fGxpq95MianAkjBown\nnLiwi3+MrTri0nOtXaCTMci5uTiag1w+nw/tdXit0Om6juWbbsa+K2728ajcMwc9oPeqeUD7Ydt6\nvQ5VVaVdURmFfqpAuZmfBwC1Wo07pbgwOjrKCl0H8ieNGBC/kKVSCbVaLbBWHUGxu6AEveWYV05b\ngUQZ5LwyBrl91ouzpGEV8oDeC3oioCWTyWarIaC7io1oq0K9p938vFKphEQiwfl5bQS1yrUfMNB5\nJOaTAcdOxDgFOcFcPZI9yDkl0+votkInKr2D5XdIH+Q6sQp6b/3px7H3vKmbY8dZp4qNmJ8ndsPg\njby/iJ9rJpNp/hkX6UzFQOceA51LjUYDk5OTzWHIRCKBbDYbuzAHvB424lbJsgtJMg4ROyVWQxdL\npyHT+eGx9av33ApMTm2p0mvVPMD5alv2zus/cemfF5Z2H3o55NoZA51LmqZBUZRmWFBVVboeTE6J\nG8rY2FisFglYVRZlDXKdKnT9EuQ66bdhWzc3cpnnX/XTHLpudfPeeOmfZ67oxZHVcY+Pj3ve+qvX\nMdC5JKpyQhybshr3KAWA6dOnx+oCYKwsyhrkOhGT6wuTy/s6yHXSz4swALS0VOH8q/7l5PyI87B+\nu9Cr63osR8DCxEDnkzgFOmOQy+VyKBQKGBkZifqwuiZaw6iqKn2QM58fDHLe9Us1Dzh2/phXy5uH\nbcVNvNeH5eIqyOqlk/MjDnsf271Hcbm3Ro2BziXzSReHQGcOcl42m4+SWIiiaRoSiYTUQc5M13Wo\nqor8xKkMcgHpp0UYboZtzduexfEaEEdh3x+cNtGO097HshyHrBjofJJIJLrabSFM9XodlUoFmqYh\nm81aBjmnLUCiZNyhYmBgAOl0GplMJhZhTlEUqKqKwfI7GOQi0O+LMADn21p5qdbIfg2JmgzvjR8L\nMYJqu2N3/qiqyuFWBxjofNLt9llhqNfrKJfLzV5Z7SpyMlcYzUFOVOQmJiakPWYjVVUxVF0R9WGQ\nBWM1rxfDnVGnba00TYtVtYb8JUPbnXa7RAwNDbn+vv2Cgc4lWYdcxZCeCHK5XA6ZTKbjL5ksx29k\nF+QE2W8sqqoiN74M6agPhDo6NiTb3d/phWqUsVpjnINlVa0Rm5ubh2w5bOtMXM8Xp213/FioY/ce\njYyMsAedAwx0HhhDUNSByG2QE6I+fiNjkMtkMrZz5GQ6ZiMGufh4608/HvUhSMntTVw8zrjfLR0j\n47XKrU7z84wVXz8W6rCpsDMMdD6JKlyI1ZLlchm6rncd5AQZwpHTICfIcMxGmqYhO7aUQS4GGOS6\n52TulejHKa5H3PKsVa+/9m4qvlZBTyx0M2OFzhkGOg+irNAZgxwAZLNZV0FOiDIcNRoNVCoVVKtV\nR0FONgxy8cEg5z9zNU8svjJX8+LaG80vMn34DJvT+XmapjXPlUQigX/4h3/AnDlzUKlUkM/nIzr6\n+GCg80lYq1zNQS6XyyGdTnu+GEYR6LwGuagXojDIxQeDXPiMN/F0+thvSadhW6uWKr0U9HrptfjB\nHPTK5TJSqRSSySQ0TUOhUMDOnTvx5JNP4plnnsGWLVuwePFivO1tb8PixYtx5pln4k1velPb57j0\n0kuxbds2zJgxA8PDw1O+PjY2ho997GN44YUXoGkarrzySnziE58I4uUGjoHOA+MvZ9CBKKggZ36O\nMPhVkYuqqthoNDAw+nYGuZhgmAtPp4n/XltmxH1LK+rMWMHdsGEDAOD666/HvHnzsGTJEjz55JPY\nt28f/umf/gmDg4MdA93atWvx6U9/GmvWrLH8+k033YRFixbhnnvuwauvvop58+bhYx/72JRGzXEQ\nvyOWnN8rmcQen5VKBUAwQQ4IJxwFMbQaZqATQY7igUEuPmRomRE0EU7JXrtVrieccALmzZuHefPm\n4aKLLnL8PVeuXIkDBw7Yfl1RFIyPjwM4tl/s8ccfH8swBzDQ+UZ88vQr0IkgVy6XkUgkkM/nkUql\nAt06JqhwZA5y06ZN86VJZFgXbwa5eHEb5Jbee0PP7SYRd05X28ahd14/z6Fzyu7+GeQq1z/90z/F\n+eefj1mzZmFiYgJ33nlnIM8TBgY6D4LoRWcOcoVCIdAgJwQxHy2oICeEMcydGVkS2Pcnf7Ei1x+8\nDNsa5+hFEfJkCJYyaxfojjvuuECe8yc/+QmWLVuGBx98EM888wzOPvtsDA8Po1gsBvJ8QWKg85EI\nRW5Ci67rqFarqFQqzSAnJhKHwc9wFHSQE4IKdLquo1KpYFrldN+/N/mPQU4eUTbPbTdsa1xF6UcD\nXDdYoWuv3fsTZIVu69at+MIXvgAAOPnkk/GWt7wFv/zlL3HaaacF8nxBYqDzwPyLn0gkuv6ljTrI\nCX6Eo7CCXFDEz6JcLiOdTmPx9f8fAGDfFTdHfGRkJYggV6vVpBuqI28URZkyJ8o8bOtXA1wnx0Lt\nWb1Hk5OTnipm4udt5c1vfjPuv/9+vPvd78bhw4exf/9+zJ071/VzRYmBzkfdhCJjkEsmkygWi5FO\nxPQS6KIKcn5V6IxBLpVKYXBwsOVnIYKdEUNedIKsyInV5Mabu1UrDYq3boZtxZZnPBeC1am663ZB\nycUXX4wdO3bgyJEjOOmkk7Bp0ybUajUoioJ169bhi1/8Ij7xiU9gyZJj02u+8pWv4A1veIOr54oa\nA50HbubQmcND1EFOcBOOjEEunU6HXpHzGuiM8xWTyeSUINeOVcgDGPSCFMbQ6sDAQPO/Ow3Vicdw\nm6ve4WXfUmNLFatzIa57uYbF7v3x+qH99ttvb/v1N73pTfjJT37i6TlkEX2S6CHtAoaYl1WpVCyr\nQFHrJhw1Go1mdTGKIGfk5pfdauGJX8PcrOYFI4p5cu2G6kQ3e6ttrqKeeB+lXmzN4XTfUrveeeIf\nzqHzpt9+l9yQJ1H0AKtQZAxy6XRauiAnOK0uGl9L1HPkxC+400++YjitVCqFOl+R1Tz3ZFvwYL65\nm7e5ElsXuangULw43be0Vqs1OwiIKTYctp3K7jpeq9UimVceR/IlixixGnIVv7gyVbGccFpdlOm1\nOL0QmnfZyOfzgTRn7harefZkC3KddBqqa1fB4e4HvcXqXGg0GiiVSkin080Krzn0myu7/XY+RNGD\nrtcw0HlkDEKJRAK1Wg2lUimyeWVeGX+pZA1yRu2aOYexXZrf+j3kxS3IteOkgtNu0/pkMhm7Gzvn\niVkT74m50uR0yzPj+dBvRkdHMTQ0FPVhxAIDnU9EaV1VVSQSCSnDTzvGnS4ASB/kOhFBrtFoIJfL\nIZPJxPZi2A9Dtr0U5DoxVnDsNq1XVdV294N+vbH3ok5bnnUK/b00bNtu2y9W6JxhoPNI1/VmRS6V\nSiGRSMSyw7QQ5apVN8xDxb0U5DrphWpePwW5dpy20RDzsXr5xt6Luq1cOgn95mFbq7l5cTof2gW6\noHaJ6DUMdB5NTExAURRMmzYNAJqb/MaJGFrVdR2qqkq7cMOKCHSqqqJcLkPTtJ4Pcu3EpZrHIOeM\nkzYanZri9tqq0zjyY4Wrly3P4jBX026FNOfQORePu7bEBgcHm7+s4pcoLsxz5BKJBHK5XGzCHPB6\nhVQEuWKx6MsF69QvfcOHo5OHTNU8mcPc0ntvwN7z1kd9GG3JXM3jHDp7Qb0vnYZtRS/FuA7bjoyM\n4Pjjj4/6MGIhPnduSSUSiWYncVEtkv2iZtcTb2xsLDaBVNO05tCqaAcj83suo7CreTIHuV7gtCmu\n3dy8OA7TxUUU19W4nQ92982xsbHYbsUVNgY6HxkXFsh4Uey0xZWMx2wmgly9Xkc2m0UqlZJ+5Wrc\n+F3N69UgJ+vvuZGbLa7Mc7Fkrt7EiQzvodth2zB657VrW8I5dM4w0HnkZvuvsHUKcoKMxy5omoZK\npYJarYZsNotCoQBFUaBpmrTH3EvchLxeDXK9oNstrqKu3lCw7IZtjSHPrmG2Xy122IfOOwY6n8kU\nipwGOUGmYxcajQbK5TJqtRoGBgYwNDTESd6SsAp5laWlCI6E/OCmemOu3IibPbWKQzXXitWiGnPD\n7HYtdvwI/iMjI3jDG97g9aX0BQY6j2Ss0HUb5AQZjl1wGuRkOmaiXtRN9QYAyuVy7Fto+K2XrlFO\ntzzrdhifFTrvGOh8FmXAEEFO7BfYbfsRGcJRo9Fo9sLLZDIdK3IyHDO9Lrs3zypdn7Cq3kxMTGBg\nYKB5c49iLpasev21djuMbx62FY83v0+VSgW5XC7U1xJXDHQ+M+7nGhZzkCsWi65aj0Rx7II5yHXT\n1JiBjkgeVjtZiP1L7W7qvb6Pab9eo9oN4xvPCVVVAQClUgmJRAJ79uzB3r17sWjRomZLLeqMgc4j\n84UnkUiE9svrV5AToqh2ed0vlhU6IvkpijLl2mS+qVs1xDUHvTiL+/H7yRz0xBSbfD7fbEX1/PPP\n49/+7d/wxBNPYObMmVi8eDGWLFmCxYsXY+nSpVi2bFnb57j00kuxbds2zJgxA8PDw5aP2bFjB/7s\nz/4M9XodJ5xwAh566CHfX2uYlA43Q94pO9B1HbVarfn/5XIZuq4jn88H+pzGIOdXM+BarYZqtYrB\nwUEfjrI9c5DL5XKuthmrVCrQNA2FQsHX4+u1xsJhivuQq9PGwmIi+MDAQMBHFB8TExPNFehumRvi\nin+MQ3TGXQ/iEJSq1SoURUEmk4n6UKSkaRqq1eqU+6au6zj33HNx5513Yt++fdi3bx+Gh4ehaRru\nuOOOtt9z586dKBaLWLNmjWWgGx0dxRlnnIF///d/x+zZs/Hqq6/ijW98o6+vKyC2JzwrdB5ZLYoI\natjSHOQKhUJznz8/hFHtcrtgww4rdES9pdNcLOOQbVy2t7Lb1oqOsVsQIebPzZkzB3PmzMG5557r\n+HuuXLkSBw4csP367bffjosuugizZ88GgLiEubYY6HxgDBVBBAxRBSyXy0gkEr4HOSHIcOR1wQYR\nyc14DfRbp5WVnba38qNPmhf80NmeXaAbGRnB0NBQIM+5f/9+1Ot1nHXWWZiYmMD69euxevXqQJ4r\nLLyj+szPUBRWkBPiGEZZoSPqX06qee36pFkt4AjyWKk7QbYsUVUVjz32GB588EFMTk7iXe96F971\nrnfhlFNOCeT5wsBA5wNzhc7rkGvYQU6IYxgNItBFtdKX5LD03hvw6Dl/IuXQHXXmpE+aCHphbVbP\nD53ttavQBRXo5syZgxNOOAHZbBbZbBZnnnkmnnjiCQY6ep2XVa5RBTnBj3Ck6zrq9TrK5TIAoFAo\nIJVKBXpj9OtiaWydQv2tWq02b/ZsktsbjNU8cV0190kTIS+Iah7PGXtBNRUWP18rF1xwAT796U83\nF2Q8/PDD2LBhg+vnkgEDnc/chKKog5zV8XR78TEHuVwuh3Q6HfhFzI/vb1xxK3rgUX/L5/Mdt7wS\nvyeaprGah3hub+V0u7NarRZaNa8ftQt0xx13nKvvefHFF2PHjh04cuQITjrpJGzatAm1Wg2KomDd\nunWYP38+zjnnHCxZsgTJZBLr1q3DwoULvb6USDHQ+cB4IopA5+TiJluQE8fbzYVZ13WoqopS6Vir\nirCCnOClqmhcceumBx71tk7zs0TAq1Qqkc/PIn853fXA6R6mcQy7YbMbcp05c6ar73f77bd3fMzG\njRuxceNGV99fRgx0PnPyS2sV5IIelnSqm2MQFblGo4FcLodMJhP6a/BaEeWKW/+9+dtJHPikFvVh\nBMJY0Wk0GkgkEi1bXXWq6ES92pLcc1rNE3uYGn/24jH82VtrV6GbN29eBEcUT7yL+cCqF53VCSpz\nkBOcBCRRkYsyyLkhhoXF9jJRV0Spdzip6NittpS1d1q3+rUK5eRnDxybl+mkmtePghhy7UcMdAEQ\nK12NGw7LHuSEdoFOVVWUy2VomoZsNouBgYHIX4OTABrFQg0iJxUdu9WWcdsJgVoZf/bi+i92QWg3\nL5Nz81oF2bakFzHQ+cBuP1fxi1ypVAAcm2gd5vwyN6wCkghyqqoil8uhWCxK9xrsPuEZh4Xj8P5T\n72u32tJuX1OrlbYUL+JnZq7mAa0hz7gTRr+ssra7fo+NjbFC1wUGuoCIoT0g/IUCXhgDnaZpKJfL\nqNfryGazUgY5u0nHxmpinIaFqT+1q+aJkNePN/pe4GSOr/gZmv+eXTWv10I+h1z9wUDnIzG0Jy7A\ncawIiTYMExMTzSDndbPtoBmPTdM0lEolqauJRE4pijJlwU6ndipRDdv16xw6J9y8L1Zz84D21Txz\n0ItDyG8XeKvVKgYGBkI8mnhjoPOJmCMHoDmUkslkIj6q7hgnbmezWQwNDcViQ2kRQkulki/VxFO/\n9A2fj5DIP15barCdSrj83iXCrprXbsjeKujJxmoRodWfkz0GOh+IxrRiaFUEu7hoNBool8uo1WpI\nJBLIZrPNCbyyExetiYkJDAwMxCaEUvzJtJ2T1wa5bKcSrDAarHc7ZC/LApxOlV2ek84x0PkgmUy2\n7C4gVrnKzrjVVSaTwdDQUHNpvezM23QVCoXYVUQp/mS/2bCdSvSivJ7aDdl3quaF+fO3C3RxuA/J\nhoHOJ8bFBIlEApomb2NVqyAnPtnJHkattumanJzkTYd8tfTeG7D3vPVRH0Yggmqnwjl09mR6Xzr9\n/EXQC6udjt15Uy6XYzNSJAsGugC42b0gDMYwZLfVlczHbrdNl6zHTBQnXtup8HfQWlzel07VXOOQ\nbRhzM0dGRtiDrksMdD4xhgrZAoaTICfIeOxOtumS6Zipt7f/6ifdzs0CgEqlwnYqJnF9/cafv/G6\n66Sa63Rupl2FjoGuewx0AZAlFBmrWqlUytGepTIdu3l3DbttuuJ6sSSKK6u5WbVaDZqmIZlMStVO\nJWoyXE/91q6a22luprmax0DnHwa6AEQdikSQq1QqXW8+L8Oxd7tNV9THTK+b8Ug16kOgCCUSiZYP\nXmynckyvvi4jtyutRaDTNK0l6HPbr+4x0PnE+Asb1cICc1WrWCw6DnJClOFIBDld17vaXYOBjkhO\nbKfSmxW6bnSamycCfqVSga7r+PCHP4yZM2fiuOOOw8DAAA4fPowZM2Z09ZyXXnoptm3bhhkzZmB4\neNj2cXv27MG73vUu/OhHP8KFF17o+jXKgg27AmAsJYdBVORGR0dRrVZRKBQwbdq0rsOc8fuFSVVV\njI+PY3JyEgMDA5g2bRq36iLqYeImn06nMTAwgHw+j0Kh0PJBTmzfNzk5iVKphEql0hzWjVtI4rWs\nlXFenqjqFgoF5PN5/O3f/i1++7d/G6+88goeeOABLFy4EDNmzMDZZ5+NjRs3Yv/+/R2//9q1a/GT\nn/yk7WMajQY+//nP433ve59fLytyrND5xFyhE1WjIH+RjcOTiqI4Gp7sJMwLj1/bdLFCRxQ9r9e7\noNqpRI3tXNozvj+JRALLly/H8uXLcfjwYaxbtw7nnHMOXn75ZTzxxBMYHh52dK1fuXIlDhw40PYx\nN954I1atWoU9e/b48jpkwEAXkCBDhnmeWTfDk52I4w7yIqRpGsrlsi/bdAHy984jIve8tlORYQFG\n1M8vM7v7pJhDpygKZs+ejdmzZ+O8887z5Tlffvll3HXXXXjwwQexe/duX76nDBjofGL+hQ0i0Om6\nDlVVUSqVAPgb5IQgLzzGLcb83qaLFTqi/uFmqyurkBdG0OK1qTOrn0OQiyI+85nPYPPmzaFPjwoa\nA11A/A50oiLXaDSQy+UCnWPm93CxcWeKIPZb5adfCkK9XpemwkPO2G11ZVyAEUU7FZ4/9uzuNaOj\nozjuuOMCec5HHnkEH/nIR6DrOl599VVs374d6XQa559/fiDPFxYGuoD4NQwYZpAT/Aqj5m26/A5y\ngp/huVc+qZF3xgqPVYsNaiWGO2XTaZVl0O1UeE1pr12g81KhEz9jK88++2zzv9euXYsPfOADsQ9z\nAAOdb8wnpNetcMQKL03TkM1mMTAwENqnPK8Bqd02XUHwI9AZW74QAUA2mwVg32IDeP3ck3lSPk0V\ndjsVnhPW2l23VVVFJpNx9X0vvvhi7NixA0eOHMFJJ52ETZs2oVarQVEUrFu3ruWxvfSzYaALiNuQ\nIYKc15WfXrg9di8NjaNi1ciY/BH37b+W3nsD5n50LwDgX0dvmVLhqVZfb6Is+6R8csZJNc9uBwRj\nqDdiha4zv9+z22+/3fFjb7nlFk/PJRO577Yx4nVRhN8rP73o9tj9aGjshdsAahzOzufzvi8wod5x\n4dAlln/+w1e+2VJFsJuU30+7IvQar+1UGOjsdZqrzd+R7jDQ+cgYLJzOoTMHuUKhEPlJ7DQgWVW3\n7PZbDVK3gc44nB3WvETqTR854fIpf/avo62f+J0M4/XCkG2/9Vtz2k4FQPPDLiu3rezOmX47l/zC\nQBeQTiFD07Rm5/MgVn564SQgud2mKwhOA51MVVDqXVbVPKshWxH0jJU8DtnGm1U1b2JiAvl8vqWa\nJ0M7FZmNj4+jWCxGfRixw0AXELsKXZC92PzSLiCJPnhhrrr1Kg7vOfU2uyHbfx29pWV6Aodse4tx\nxEbGdipRa7fCdWhoKIIjijcGOh8Zg5B5lauxF1uQLTz8YBXozIs1wlx124ldAA2rbQqRW3bVPKO4\nDNlyrpg9q59J1O1UZBBUy5J+xUAXEBEy4hTkBGN1MU7DlOLiEHbbFCI/xXnIVtZrQ1S6Dblht1OJ\nml2gO3r0aGBNhXsZA52PzCdmo9HA6OgoMplMrEKFCHSTk5Oo1WrSLNawY9y+Ray2dds25dQvfSOI\nQyTyhEO28eXH+xxEOxWZsULnDgOdz4zDfABi0YvNSHz6ExW5OFQUxafgsbExKIoS2WpborD10pBt\nLwpyGNprOxUZft52FbqxsTEGOhfikzRioFarYWxsrDnMNzo6GpuqnDGIik+C+Xw+6sPqSCzSABD6\njhpEMopqyJatJqxF0RjeSTsVGYbo7baLGx0dxVve8pZQjqGXMND5yDzMJ4YuZQ51xiAngqhYFSoz\nTdNQKpWaveQajQZSqRRvKEQWOGQbDVkWirSr5ln9vMNqp2L3IWBkZIQVOhcY6HxkHlr1up9rkNpt\n09VuU+Oo2S3SEEPcROScn0O2Ml83oiRz8JW1nQqHXN1hoPOR1+2/wuBkmy4Zj9u4Wtiql5yMx0zx\n38+1H7kdsgW4I4JZHK9JYbZTaVeh4yrX7jHQBUimkNHNNl2yHbeTXnIyHTP1jmfvWIq5H90b9WFE\nzi7kJRKJ5gfCdjsi9POQbS+8zqDaqbTrQ8dA1z0GOh/JWqGr1+vNhQNOtukSxx3lJGf2kiOSW7t5\neUb9vMpWhut/kLy2U2m3ypU7RXSPgS5AUQc6t9t0Rb2M3U0vuajfayI6Js6NkYMQ52N3o5t2KgBQ\nKpWQSCTw3HPPYf/+/ViyZElzkRt1h++Yj6wqdFb7uQZNbNOlaZrrVh4iIIW5fN3pkLAVBjoieTkZ\nsnxxvDAAACAASURBVAV6b5Utr0mvM7dT0XUdk5OTyOVy0DQNhw4dwve+9z08/fTTeO211/Dbv/3b\nePvb3978Z/HixR1baV166aXYtm0bZsyYgeHh4Slfv/3227F582YoioJisYibb74ZixcvDuolh07p\ncMLxbOxStVpt/nelUoGmaSgUCqE8t3EFqNf9VkdGRjA4OBjKMKexkpjP5zsOCVuZnJxEIpFALpfz\ndCzcKcKbGY9Up/xZ3BdFcA5duDoN2YrAF4ch22q1CkVRkMlkoj4U6Yj2WOb7o67rOOecc3D11Vfj\niSeewN69e/HEE09gcHAQ//mf/9n2e+7cuRPFYhFr1qyxDHS7du3CggULMDQ0hPvuuw9f+tKXsGvX\nLl9fVwhsT3BW6HxmrBSFVTUSvxh+btMVxrGbe8k5HRK2ItNFnIjc66UhWzZbtmd3f2k0Gkin0zjr\nrLNw1llndXy80cqVK3HgwAHbr7/zne9s+e+DBw92ccTyY6ALUNChqFMrDy+CPHa7XnJecMiVqHfF\neciWgc6e3QrXadOmOXqsF9/+9rdx7rnn+vo9o8ZA57MwKnROW3l4EcSxBx1Ao5ivSETRiMMqW37I\ntNeuZUnQK1wfeughbN26FTt37gz0ecLGQBcgv0OR1TZdQc1x8/PYwwigRESAfEO2rNBZaxfogtwl\nYnh4GOvWrcN9993Xc73uGOh8ZjxB/aoaGXuypVIpx608vPAj0IXZS86P42WFzxurBRFEMohqyJYV\nuu55DXTttqB74YUXcNFFF+H73/8+Tj75ZNfPISsGugB53cvVvE1XGEFO8BKQojhur8crKojkP27/\nRTIKa8iWFTprQVToLr74YuzYsQNHjhzBSSedhE2bNqFWq0FRFKxbtw5XXXUVXnvtNXzqU5+CrutI\np9PYvXu315ciDQa6EHS70snYk01RlK57svml24DktZecV26O19jE2GoiLhH1Fz+HbMWf0VR298Wj\nR4+6Hgq9/fbb2359y5Yt2LJli6vvHQcMdD4zD7l226C32226gtLtcLEfveS8iGNgJqJ4cDtkCxzr\nRxrXxshBEuHXbGxsDDNnzozgiOKPgS5gTocC3W7TFRSnz23sJed2Vwo/uHmfjcFTfNomMnv2jqVs\nLkxTOBmynZiYaDY778e9bN0YHR3tucUKYWGg85nV/Il2QcOPbbqC0Om4zc2M/egl50Wn47XbRUMM\nnWiahg8OfgL43BnhHTQR9RzZVtnKKqpVrr2MgS5gdkOX5oARdSAyswtIQfaSC0K7XTTEBfWC4scj\nPkoi6mVxbowcFAY6/zHQ+cx8gppXugaxTVcQzIFO9l5y3RyvXZB7mdU5IgpJHBojB6ldoOOQqzsM\ndAEzzs+KU2XLOBwZVi85L5wcLytyRCS7fh+yHR8fZ8cBlxjoQiBaY8hY2Wqn0WhgdHQ09B54bojq\nnNXxMsgRUZw5HbI1VvJkH7K1q9Dpui5l0SAO5L1Dx5RxfpaoyCUSCWkrW2a6rjdXguq6jmKxKH1L\nD3G8ACxXrjLIEVGvifOQrd0CNvbs84aBzmdiyK9UKiGVSiGbzcbmE4e5dcrk5KTUYc7YMiWXy0FV\n1ZaqXHPlKhFRn4jDkK2oztl936irh3HFQOczsapVDPnVajVUq3LvcSmCkaqqzZYeADA5Odn1Lhdh\nsGuZUi6Xm588WZWTC7f/IoqOn0O2xmqe31RVjUXxQ1YMdAEoFArNViV+bBoflE695Lrd5SJonVau\nAmBFjojIgXYhz8g8ZFutVluGbI3VPKdDtnb3lbGxMQwNDbl/UX2OgS5gMgY6pytuZTl2rlwlIgpe\nu3l5TodszcO1VtU8u0A3MjLCHnQeMNAFwKrKJYNue8lFfexiz9VSqcSVq0REEXE7ZFur1Zrz8oxD\ntnbbLLKpsDcMdAGLOhQB7Stc7UR57PV6HeVyGbquc+UqEZFk3AzZapoGVVWbga5cLiOZTOKRRx7B\nrFmzcPToUQY6DxjoAmZseBv2XDRd15s98Nz0kosi0JlXrmYyGes9V4lC9OwdSzH3o3ujPgwiqXUa\nshVdE6rVanN4ttFoYOvWrdixYwfK5TJ+4zd+A+Pj41i6dCmWLl2KBQsWIJPJdHzuSy+9FNu2bcOM\nGTMwPDxs+Zj169dj+/btKBQK+O53v4ulS5e6f7ESYqALgHnIFbCfMxAUMVQJHFuk4bb9SFiBrt0C\nDVbliIjiyxj0RJ+8RCLRvC9t2bIFAHDzzTfj0KFDmDlzJn7yk59g8+bNeO6553DPPffg7LPPbvsc\na9euxac//WmsWbPG8uvbt2/HM888g1/96ld4+OGHcfnll2PXrl1+vDxpMNCFwLyfa5CMveSMQ5Vu\nhNVgslwuWy7QYJAjIuodd776rWZj40Qi0fy3UKvVsHLlSlx44YXNPxNzqDtZuXIlDhw4YPv1u+++\nuxn2VqxYgdHRURw+fBgzZszw8IrkwkAXAHMQCmPo0qqXnNdAFuRxc+UqEVF/uHvi1pa2J5qmIZFI\nNOfUiXvNr3/9a5xxxhktfzefz/tyDAcPHsSJJ57Y/P/Zs2fj4MGDDHTUnSCDUadecl4EcdzGeX3J\nZJIrV4mIetj3X74Rk5OTUBSl2Ti4WCy2rHZVVRV33XUXtm/fjo9+9KOBHIfVvUyWHqt+YaALQBgV\nOqe95Lzw+7jt5vUxyBER9Za7J25tXtvL5TJUVW1W5Y4cOYLVq1dj0aJFeOtb34pt27Zh/vz52Lt3\nL6ZNmxbI8cyZMwcvvvhi8/9feuklzJo1K5Dnioq/CYAs+RmMxJyz0dFR6LqOoaEh5PN538Mc4N9x\nq6qK8fFxTE5OIpvNYtq0aUin0y0rVxnmet+bv80tfYj6wd0TtwI4du2fnJxEMpnEtGnTMDg4iGnT\npmFoaAgbNmyApmm444478Nxzz+HWW2/F7/zO7+CSSy7BDTfcgPHx8a6fV9xTrJx//vn43ve+BwDY\ntWsXpk+f3lPDrQArdKEQ+7t64baXnBdeA52maSiXy6jX68jlcly5SkTUw0SQE1U5sTjP3C7r5Zdf\nxje/+U0sW7YM//Vf/4VcLodSqYQnn3wSjz/+OB5//PGu728XX3wxduzYgSNHjuCkk07Cpk2bUKvV\noCgK1q1bh/POOw/33nsvTjnlFBQKBWzdutW31y0LpcMNW44tDmKoWq02/9vYILdb5t0SrH45glKr\n1VCtVjE4ONjV3zMPB+dyuVgEuZc/d0bnB5GtGY9UOz7mwCe1EI4kGOxDR2RNBDlxvxK7EZkX56mq\nim9961u4++67cd111+G0006L6pDjzHbiHyt0ATFWt9xW6PzqJedWtxW6dluLyRzkiIjIHauqXKFQ\nmFJhe/rpp7Fx40acffbZeOihh0K/n/UDBroQdBuMjL3kjLslhM3pcZtXrrIFCRFRbzNW5cRozsDA\nwJT7Va1Ww7XXXoudO3fiG9/4BhYuXBjVIfc8BrqAmCt0ToKRec6ZH73kvHBy3Fy5SkTUX0SYE/cs\nAFOqcrqu4/HHH8fnPvc5/NEf/RH+4z/+I/B53/2OgS4EnYZczb3kCoWCFP1x2gU6ux0pxOO55yoR\nUW8xVuWq1SpqtZplVa5UKuHLX/4yfvGLX+D73/8+5s6dG9Uh9xW2LQmI8eS22/qr0WigVCphdHQU\niqJgaGioZQFB1KwCnaZpmJiYwPj4eHOenPhlFlW5D+RXxy7McUGEN04WRMTds3f01kbeRN0wtiKZ\nmJiApmkoFostI0m6rmPnzp14//vfj0WLFmHbtm0McyFihS4E5mDUbvGAjERvH7sqIodXiYh6k7Eq\nV6lUUK/Xkc1mp+wTPjY2hr/+67/Ga6+9hrvuugtvetObojrkvsVAFwJj9UosHkilUqH0kvNC/LKW\ny2VUq1WuXCUi6iPGqpxY9FYsFlsKELqu4z/+4z/w93//9/jsZz+LP/zDP5RmlKnfMNAFxOqEHhsb\nQyKRaNm/VFZi5RJw7JeZK1eJiPqDVVUul8tNaTVy5MgRfP7zn0cymcR9992H448/PorDpf8jd6ro\nAcZVoFG2IHFKNIYsl8tQFAWKojRXLzHIERH1NhHmxH0gnU5jcHCw5b6l6zr+9V//FTfccAM2bdqE\nc889V+r7Wr+Qd+JWzGmahrGxseb+pYqiIJlMSn3Siz1Xy+UycrkcBgcHkUgk0Gg0uOcq+YL7uRLJ\n6e6JW3H3xK3NxXqVSgX5fH7KQr1f//rX+NjHPoaf//zneOCBB3DeeecFdl976aWX8Lu/+7tYuHAh\nFi9ejBtuuMHycevXr8db3/pWLF26FHv39u+OLqzQBURRlJatTyqVii8b3QfB2P8un8+3VBEVRYGq\nqvjQtLURHyVR9KxWQ8/a/N8RHAmRP+y27TIHuUajgR/84AfYunUrvvKVr+DMM88MvECRSqVw7bXX\nYunSpZiYmMDy5cvx3ve+F/Pnz28+Zvv27XjmmWfwq1/9Cg8//DAuv/xy7Nq1K9DjkhUDXUBSqRSy\n2Wzz/+1al0SpXf87Mbx68YxPRXyURHJ7+XNnMNRRLDndtuu5557DlVdeibe//e3YsWMHcrlcKMc3\nc+ZMzJw5EwBQLBaxYMECHDx4sCXQ3X333VizZg0AYMWKFRgdHcXhw4cxY8aMUI5RJgx0Iel2+68g\ncc9VIn8wyFEcWW3blclkkM/nW6pumqbhW9/6Fn784x/juuuuwzve8Y6oDhnPP/889u7dixUrVrT8\n+cGDB3HiiSc2/3/27Nk4ePAgAx0FR4ZAJ7p7i4muXLlK5A6DHMWVk227AOAXv/gFNm7ciN/93d/F\nQw89hEwmE/qxChMTE1i1ahWuv/56FIvFlq9Z3VdlnqseJAa6gJhPqCgDnZgbUSqVprRNYZAj6g7D\nHMWR0227arUarrvuOvz0pz/F17/+dSxatCiqQwZwbLHeqlWrsHr1alxwwQVTvj5nzhy8+OKLzf9/\n6aWXMGvWrDAPURpc5Rog4y9Jp/1cg1Kv15srV/P5fDPMid0fuHKVyJm5H93LMEexZKzK2W3bBQCP\nP/443v/+92P69Om4//77Iw9zAHDJJZdg4cKFuOKKKyy/fv755+N73/seAGDXrl2YPn16Xw63AqzQ\nhSaRSEDTtNCeT9M0lEolaJo2pf8dq3JEzs39aP+2QaB4s6rKWW3bVS6X8eUvfxlPPvkkvve97+Hk\nk0+O6pBb/OxnP8Ntt92GxYsXY9myZVAUBVdffTUOHDgARVGwbt06nHfeebj33ntxyimnoFAoYOvW\nrVEfdmSUDsOAcszij6l6vd6syomJp4ODg4E+p3nlquiBBzDItWPVjoKcm/FI1fFjD3wyvA82XjHM\nUVxZbduVzWanbNv13//93/jiF7+IdevWYe3atVLvK04AANsJgqzQhSToOXS6rjf3XB0YGODKVSIP\nGOQorn48trV5v2m3bdf4+Dj+5m/+Bq+88gp+/OMf9+28s17CQBeSoAIdV64S+YdBjuLqzle/1Zwj\nJ+41iUQC2WwW5XIZiUSiuYXj/fffj7/7u7/Dxo0b8Ud/9Ed9uyq01zDQBci8KMLPQCf6B4lSOleu\nUly8+dtJ6YZdGeQozswNgjVNa7YZqdfr+MpXvoItW7Zg4cKFAIBkMol/+Id/wBlnnMEw10MY6ELi\n5ypX0YIEONY/SJTSRWDUNA0fHPyEL8/VD7TfW9787xmPVHH4tIEIj4bCxjBHcWW1bVc6nZ7SIPiq\nq67CokWL8M///M848cQTMTk5icsvvxwHDhzAwoUL8ZGPfAQbN26M6mWQTxjoAmSu0AHHfvHcfiIS\nk1u5ctUf5iBH/YVBjuLMatuufD7fHKkRDh06hI0bN2LGjBn44Q9/iKGhoebXJiYmMDw8HGoHBgoO\nA11IFEVpDrt2G+gajQZKpVJzcmuxWGSQ88AY5Kj/MMhRnDndtqvRaOAHP/gBtm7dis2bN+M973nP\nlHtPsVjEGWdwhX+vYKALkNfdIhqNBiqVCleu+ohhrr8xzFGcOd226/nnn8eGDRuwZMkS7NixA7lc\nLvRjpfAx0IXIaaAzrlzNZDIMcj5KPvAoAAa7fsMgR3FmVZWz2rZL0zRs2bIF//Iv/4Kvfe1rOP30\n06M6ZIoAA12IOgU688pVtiAJjgh2Rgx5vYdBjuLOWJUT+3EXi8UpDYB/+ctf4sorr8RZZ52Fhx56\nqLnKlfoHA12ArIZc7Va6cuVq9ETIm/XA63/GHSTii2GO4szptl31eh3XXXcdHnroIdx0001S7L9K\n0WCgC1EikZhSoVNVFaVSqblCyfjLqus6g1zErDZjZ8iTG4McxZ152y67qtzevXvx53/+57jooovw\nwAMPTJlLR/2FgS5A7RZFiEmtYuXqwMAAV67GBEOenBjkKO6MVbl223aVy2Vcc8012LdvH2699Vac\nfPLJURwuSUbpMEk/uM1H+0StVmuGONErSFGU5qTWXC7HINeD+i3gddvHz++dIhjmKM5EkAOODaGW\ny2WkUqmW+wNw7B7x85//HH/5l3+Jyy67DJdccsmUqh31PNu+Zwx0AROBTtd1TExMoF6vN4McV672\nl14OeW4aM/sR6hjkKO6MDYIrlQpUVbVsEDw+Po4vfelLOHz4MG688UbMnj07isOl6NkGOg65hkC0\nIFEUBel0GoVCAQCDXL/hUK1/GOQo7uy27RocHJxSlXvggQdw1VVX4corr8SHP/xh7r9KllihC9iR\nI0fQaDSQy+Wa8yIGBwcBHJtHJ3aO4MIHEuIY8sKs0DHMUdxZbduVy+WmVOVee+01fOELXwAAXHvt\ntTjhhBMCPa5LL70U27Ztw4wZMzA8PDzl6z/96U9xwQUXYO7cuQCACy+8EF/84hcDPSaagkOuUalW\nq83QpqoqJicnUSgUWrYAM86hU1UVlUoFiqLg/838kygPnSQic8hzuw9ut4GOQY7izqoql8lkWhbF\nia/ffffd+NrXvoa/+Zu/wfvf//5QqnI7d+5EsVjEmjVrbAPdP/7jP+Kee+4J/FjIFodco5JMJpuV\nONGGZGJiAslksuUf8UlN13Vks1mkUqmWibIAODTbx/p5uJZBjnqB0227Dh06hM9+9rM44YQTcP/9\n92NoaCi0Y1y5ciUOHDjQ9jHdbF9J4WKgC5gIcaKh8ODgYPPPNE1DrVZrfi2ZTCKTydiuWjIHPIAh\nr5/1Q8hjmKO4c7ptV6PRwG233YbvfOc72Lx5M37nd35Hyrlyu3btwrJlyzBr1ix89atfxcKFC6M+\nJPo/DHQB++QnP4n//d//xamnnorly5dj+fLleOMb34ijR49i8+bN+NCHPoRly5YhlUqh0Wi0hDxz\nFS+RSEz5BWfII6NeCXkMctQLrKpyVg2CDxw4gA0bNuBtb3sbduzYgXw+H/qxOrF8+XIcOHAA+Xwe\n27dvxwc/+EHs378/6sOi/8M5dAHTdR2vvvoq9uzZg927d2P37t146qmnMDo6ijPPPBOrV6/GmWee\niWKxOGUOhaZpUFW1Wc0DYBnynGDIIyM/Q56fc+gY5KgXON22S9M0fPvb38Y//dM/4Wtf+xpOP/30\nyKtyBw4cwAc+8AHLOXRmb3nLW/Doo4/iDW94QwhHRv+Hc+iioigKTjjhBLzvfe/Da6+9hq1bt2LZ\nsmX49Kc/jddeew179uzBt771LUxOTuKUU05pVvIWL16MTCbTsupJVPBEFc8q5KVSKcsLAit5ZCRj\nJY9hjnqB0227/ud//gdXXnkl3vOe92DHjh3IZDJRHO4UYr63lcOHD2PGjBkAgN27d0PXdYY5ibBC\nF5LHHnsMf/Inf4KvfvWrWLly5ZSva5qG/fv34+GHH8aePXuwb98+NBoNLFq0CMuWLcNpp52GefPm\ntUygFb94xiqepmlIJBJTKnlOPvUx4JGZk5DntULHIEe9wG7bLvOH7Hq9juuvvx4PPvggvv71r+Nt\nb3tbVIc8xcUXX4wdO3bgyJEjmDFjBjZt2oRarQZFUbBu3TrcdNNNuPnmm5FOp5HL5fC1r30NK1as\niPqw+w3blsjA2KrEyWNrtRqGh4ebw7X79+9HNpvF29/+9mYl76STTmr55CeaFRsDnjnkpVIpy/l4\nVhjyyMwc8twGuuQDj/pxOESRstu2K5vNTqnKPfHEE/jsZz+LCy+8EOvXr5/Sd47IAQa6XiC2D3v0\n0UexZ88e7NmzBy+++CKmT5/erOKJRRdW8/GM/zhddGGFIY/MtN9b7vixDHLUK6y27crlckin0y2P\nq1QquOaaa/DEE0/gpptuwimnnBLF4VJvYKDrVbqu48iRI80q3p49e/Dqq69i9uzZzSresmXLbBdd\niH9UVYWu680KnnGoliGPumUX8BjmqBfcduim5jVSDLFmMhlks9kp19ldu3bhL//yL3HJJZfgk5/8\npOOFbEQ2GOj6ia7rePHFF5vz8R577DFMTk7i5JNPxqmnnorTTjutuejC3AfJXMkDuLKWiEi4a/y7\nzQ/BtVqtuYAgmUziqaeewvDwME499VT85m/+Jr785S/j17/+NW688UbMmTMn4iOnHsFA1+/EogvR\nOqWbRRfm9imKorRU8ZwuugAY8ogontpt2wUcu8b+/Oc/xy233IK9e/fiueeew+zZs/H7v//7OO20\n03Dqqadi8eLFyGazUb4Mij8GOmplXnSxZ88e7N+/HwMDA1iyZEmzCbKbRRdcWUtEvcQ4V65UKgEA\ncrnclG27jh49ii984QvQNA1///d/j1//+td47LHH8Oijj+LRRx/F6Ogonn/++bAPn3oLAx11pus6\nJicnm4sudu/e3bLoQoS8E044Yco8kUaj0VLF46ILIoo7p9t26bqOe+65B9deey3++q//Gn/wB39g\nea1TVZUrW8krBjpyx7zo4pFHHsErr7yCWbNmNefjLV26FIODg12vrBX9mRjyiEg2Vtt2WVXlDh06\nhM9+9rM4/vjj8ZWvfAXTp08P/ViprzDQkX/EogsxH+/xxx/HxMREc9GF2OliYGDA86ILYzsA89Y5\nDHlE5Den23Y1Gg3ccccd2LJlC6655hqcddZZkW/bRX2BgY6CZVx0sWfPHgwPD0PXdSxYsKBZyfut\n3/qtKcMN5pCnqioURWm2A9A0zbIdgB2GPCJyw9gg2LhtVy6Xm7Ky/4UXXsCGDRuwYMECXHXVVcjn\n82EfLvUvBjoKl5hzsm/fvpadLsSiCxHyzIsuVFXFM888g5kzZzb/vNFouF50ATDkEVF7Vtt2WVXl\nNE3Dd77zHfzoRz/CtddeixUrVrAqR2FjoKPomRdd7NmzBy+88AKGhoawbNkyHHfccfjBD36A2bNn\n484772xW88wra1VVbYY8Y/sULrogom6Yq3KlUsl22679+/djw4YNOPPMM/GFL3yh2a6EKGQMdEG5\n77778JnPfAaNRgOXXnopPve5z7V8vVarYc2aNXj00Ufxxje+EXfeeSdOOumkiI5WPrqu47HHHsMV\nV1yBp556CmeffTYOHDgwZacLN4suGPKIyI6xKlcul2237arX67jhhhtw//334+tf/zoWL14cxeES\nCQx0QWg0Gvit3/otPPDAA5g1axbe8Y534Ic//CHmz5/ffMzNN9+Mffv24Rvf+AbuvPNO/PjHP8YP\nf/jDCI9aLl/96ldxzTXXYMOGDdiwYQNyuVzLogux08XExATmzp3bbJ1itejCqgkywJ0uiOh1xqpc\nvV5HuVxGOp22nKc7PDyMjRs34kMf+hCuuOIKthwhGTDQBWHXrl3YtGkTtm/fDgC45pproChKS5Xu\nfe97HzZt2oQVK1ZA0zTMnDkTr7zySlSHLJ2dO3di7ty5mDVrVtvHNRqNKTtdaJqGhQsXdrXowirk\nifYpTjDkEcWXsUFwuVxGo9FALpebct2oVCrYvHkzHn/8cdx0001461vfGsXhElmxvVnx44YHBw8e\nxIknntj8/zlz5mD37t22j0kmk5g+fTpee+01vOENbwj1WGW1cuVKR49LJBKYP38+5s+fjzVr1gAA\nqtUqnnzySezevRvf+MY38D//8z/IZDItO128+c1vRjqdbg6jiO3MRBWvWq2iVCo5XnRh/HQvMOQR\nyc1u2658Pj+lyv/www/jL/7iL7B27Vp8+f9v7/6Doq7zP4A/F1gRWQ3wYhEXQTp+eaHIT3/P5WWN\nE790bCQucUZGzu5IONTCHw2ho11CnmeQcdMd2TmBp5PhSWw3Q1FYxy5E/jydMHUFSmk0EMVY2P18\n//C7n9tf6GKwP/T5+MuFT/JCTJ68Pp/X+/XaazZ39IkcjYHuZ7DW3TQPAebXCILAqagR4unpKQa3\nF154QRy6aG1tRXNzM7Zu3WoydGG41t/fH2PGjBF/H/Ohi4GBAZN1ZobBi6Gex2PII3Je1rpy3t7e\nFgcE37x5E8XFxejs7MShQ4egUCgcUS7RfWOg+xkUCgUuX74svu7o6LC4dRgUFIT29nYEBgZCp9Ph\nxo0b8PX1tXepDwWJRAKZTIYFCxZgwYIFAO6EtevXr4tHp7z33nv44YcfEBAQIAY8w9CF8T/wxkMX\ng4OD6O/vH9bQhXnIY8Ajsq/hrO369NNPUVxcjPz8fDz33HOj3pXLzs7G0aNHIZfLcfLkSavXrF27\nFnV1dfD29sa7776LmJiYUa2JXB+fofsZdDodIiIiUF9fj0mTJiExMRFVVVWIiooSr3nrrbdw+vRp\nvPXWW6iursaHH37IoQgHEwQBHR0dJpsuent7ERoaKk7WTp8+fcihC+OgJwiCSRfPcKuWk7VEjmPr\n2q4ff/wRmzdvhlarxe7du+Hv72+X+o4dOwaZTIasrCyrga6urg5lZWWora2FSqVCXl4empqa7FIb\nOT0ORYwWpVKJvLw88diSwsJCFBUVISEhAcnJyejv78eKFSvw9ddfY+LEiaiurkZISIijyyYzer0e\nbW1tUKlU4qYLnU6HqKgosZMXERFxX0MXnKwlsg9ra7uG6sodPXoUpaWl2LJlC1JTU+3+KIxGkAkN\nZgAAFWxJREFUo0FKSorVQLdmzRo88cQTWL58OQAgKioKDQ0NkMvldq2RnBIDHdFwabVacehCrVab\nDF0YJmuDg4NNwpph6ML8+BSJRGLSxeOmC6KRM5y1XVevXsWGDRvg6+uLkpIS+Pj42LtcAHcPdCkp\nKdi4cSPmzJkDAHjyySexc+dOxMbG2rtMcj6cciUarjFjxiA2NhaxsbFYs2aNxdDFtm3boNFoMGHC\nBMycORPx8fHi0IX5ZO3dhi44WUt0/2xd26XX61FdXY2//vWveO2117Bw4UKnHVCzZeCOyBwDHZGN\n7jZ00dLSApVKZTJ0YbzpYsKECRZDF3q9XuziabXa+xq6MHwTy3h0jX3+EIichLWunLu7O2QymUVX\nrr29HQUFBYiIiMCnn34Kb29ve5c7LAqFAu3t7eJrawN3ROZ4y5VohBkPXRg2XfT29mLq1Kni83i2\nDF2YrzMz3LI1/DeG87SkUik8PT0tvomxi0cPKmtdOWtru3Q6HSorK1FdXY1du3YhKSnJaTpdly5d\nQkpKCk6dOmXxvo8++gjl5eWora1FU1MT8vPzORRBBnyGjsiRDEMXxpsuBgcHERUVJXbyIiMjbRq6\nMPw/K5FI4OnpCalUyqELeigMZ23XN998g3Xr1mHu3LnYvHkzPD097V3ukDIzM9HQ0IBr165BLpej\nuLgYWq0WEokEOTk5AIDc3FwolUp4e3ujsrKSz8+RAQMdkbMxHrpobm7GuXPnMGbMGERHR4udvJCQ\nEDGsdXV1oaGhAU8//bR4MLLhtq1EIrF6fIotGPLIFRgfEPzTTz9Bp9NZXds1MDCAsrIyfPzxxygr\nK8P06dMdUS7RaGGgI/tRKpXIz88Xj3Ix3m0LAPv27cOGDRvEk9hzc3OxatUqR5TqVARBQF9fH1pb\nW8WQp9FoIJPJIJPJ0NjYiGXLlqG0tNRistZaJ8/WoQtrGPLIWVhb2zVUV+7UqVNYv349UlNT8cc/\n/tEi7D3Izpw5g8OHD2PRokVISkpCRkYGzzx9MHHKlexDr9cjNzcX9fX1CAwMREJCAtLS0hAZGWly\nXUZGBvbs2eOgKp2TRCKBt7c35s+fj/nz5wMAGhsb8fvf/x7u7u5YvXo1/vvf/2LRokWQy+Ummy6G\nGrowHJ9iGLpwc3Mz6eJxnRk5sw973wVw77VdP/30E3bu3InW1lb8/e9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m5iz7xhEk6DzT7XYxMzPTd634b11JhG3iSW/XwSObkPObQ8e7inG/BsIcfhPm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sW3336LkpISYYQWQRAhhYSOIIJNfX097r33Xrz//vuwWq0YNmwY7rvvPqe5owThL6ShC7PZjDNn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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Initialise u with hat function\n", + "u = np.empty((nx, ny))\n", + "init_hat(field=u, dx=dx, dy=dy, value=2.)\n", + "plot_field(u, zmax=2.5)\n", + "\n", + "diffuse(u, nt=10)\n", + "plot_field(u, zmax=2.5)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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t+G9daYRN4mlv18Ejm8j5zaHjo4pJvwbCHH4S5pnm/DzaCcEa9h4Haaw9DaJn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\n8V2OyNt21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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Initialise u with hat function\n", + "u = np.empty((nx, ny))\n", + "init_hat(field=u, dx=dx, dy=dy, value=2.)\n", + " \n", + "diffuse(u, nt=50)\n", + "plot_field(u, zmax=2.5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Excellent. Now for the Devito part we need to note one important detail to our previous examples: we noe have a second-order derivative. So, when creating our `TimeData` object we need to tell it about our spatial discretisation by setting `space_order=2`. Only then can we use the shorthand notation `u.dx2` and `u.dx2` to denote second derivatives." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Eq(u(t + s, x, y), (-4*a*s*u(t, x, y) + a*s*u(t, x, y - h) + a*s*u(t, x, y + h) + a*s*u(t, x - h, y) + a*s*u(t, x + h, y) + h**2*u(t, x, y))/h**2)\n" + ] + } + ], + "source": [ + "from devito import TimeData\n", + "from sympy import Eq, solve\n", + "from sympy.abc import a\n", + "\n", + "# Initialize `u` for space order 2\n", + "u = TimeData(name='u', shape=(nx, ny), space_order=2)\n", + "\n", + "# Create an equation with second-order derivatives\n", + "eq = Eq(u.dt, a * (u.dx2 + u.dy2))\n", + "stencil = solve(eq, u.forward)[0]\n", + "eq_stencil = Eq(u.forward, stencil)\n", + "\n", + "print(eq_stencil)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, there is another trick here! Note how the above formulation explicitly uses `u.dx2` and `u.dy2` to denote the laplace operator, which makes this equation dependent on the spatial dimension. We can instead use the notation `u.laplace` to denote all second derivatives in space, allowing us to reuse this code for 2D and 3D examples." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Eq(u(t + s, x, y), (-4*a*s*u(t, x, y) + a*s*u(t, x, y - h) + a*s*u(t, x, y + h) + a*s*u(t, x - h, y) + a*s*u(t, x + h, y) + h**2*u(t, x, y))/h**2)\n" + ] + } + ], + "source": [ + "eq = Eq(u.dt, a * u.laplace)\n", + "stencil = solve(eq, u.forward)[0]\n", + "eq_stencil = Eq(u.forward, stencil)\n", + "\n", + "print(eq_stencil)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Great. Now all that is left is to pu it all together to build the operator and use it on our examples. For illustration purposes we will do this in one cell, including update equation and boundary conditions." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "DSE: extract_time_invariants [flops: 7, elapsed: 0.00] >>\n", + " eliminate_inter_stencil_redundancies [flops: 7, elapsed: 0.00] >>\n", + " eliminate_intra_stencil_redundancies [flops: 7, elapsed: 0.00] >>\n", + " factorize [flops: 4, elapsed: 0.00] >>\n", + " finalize [flops: 4, elapsed: 0.00]\n", + " [Total elapsed: 0.01 s]\n", + "DSE: extract_time_invariants [flops: 0, elapsed: 0.00] >>\n", + " eliminate_inter_stencil_redundancies [flops: 0, elapsed: 0.00] >>\n", + " eliminate_intra_stencil_redundancies [flops: 0, elapsed: 0.00] >>\n", + " factorize [flops: 0, elapsed: 0.00] >>\n", + " finalize [flops: 0, elapsed: 0.00]\n", + " [Total elapsed: 0.01 s]\n", + "DSE: extract_time_invariants [flops: 0, elapsed: 0.00] >>\n", + " eliminate_inter_stencil_redundancies [flops: 0, elapsed: 0.00] >>\n", + " eliminate_intra_stencil_redundancies [flops: 0, elapsed: 0.00] >>\n", + " factorize [flops: 0, elapsed: 0.00] >>\n", + " finalize [flops: 0, elapsed: 0.00]\n", + " [Total elapsed: 0.01 s]\n", + "DLE: analyze [elapsed: 0.02] >>\n", + " avoid_denormals [elapsed: 0.00] >>\n", + " loop_fission [elapsed: 0.00] >>\n", + " create_elemental_functions [elapsed: 0.00] >>\n", + " loop_blocking [elapsed: 0.14] >>\n", + " simdize [elapsed: 1.10]\n", + " [Total elapsed: 1.25 s]\n", + "CustomCompiler: compiled /tmp/devito-1000/d1566594c733db316918dd7a4c44d109f1879cb5.c [0.46 s]\n", + "=========================================================================================\n", + "Section loop_y_1<10,31> with OI=0.00 computed in 0.000 s [Perf: 0.00 GFlops/s]\n", + "Section loop_x_2<10,31> with OI=0.00 computed in 0.000 s [Perf: 0.00 GFlops/s]\n", + "Section main<10,30,30> with OI=0.47 computed in 0.000 s [Perf: 2.00 GFlops/s]\n", + "=========================================================================================\n" + ] + }, + { + "data": { + "image/png": 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IOEbUQi+JgoXwR9gtVuxCrlQU0Q8JuiGCbz3CutsXCoVENQNWFEX6GYisCrfT6SCdTiOf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\n2Wxf5aonMaekXIu5VC5nKubcEoYzJ7ogwivH7eq6rtT1Em7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QPiIprWBGSVE3U0tHJG+J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fz584iKijK7Jjo6GlVVVQAAk8mE69evo1evXi55fUKINQp0hBDix86ePYvDhw9j1KhRZn9veVt0\nwIABVqHPWenp6Th9+jT0ej0MBgMKCgowYcIEs2vGjx+PrVu3AgB27tyJBx980CWvTQgRR7dcCSHE\nTzU0NOCJJ57AG2+8AZVKZfY+KbdFnaVQKJCbm4uHH34YDMNg9uzZSExMxIoVK5Ceno5x48Zh9uzZ\nmDFjBuLi4tC7d28UFBS45LUJIeJolishhPgho9GIcePG4bHHHkNWVpbV++fOnYsHHngAU6dOBQAk\nJCTgq6++glqt9vRSCSGuQ7NcCSGkK5k1axaGDBkiGuYAYMKECfjggw8AAGVlZYiIiKAwR0gXRhU6\nQgjxM9988w3GjBmDYcOGQSaTQSaT4dVXX4Ver4dMJsOcOXMAAJmZmSguLkZYWBjy8/ORkpLi5ZUT\nQjrJZoWOAh0hhBBCiH+gW66EEEIIIV0VBTpCCCGEED/X0bEldKw3IYQQQoiPowodIYQQQoifo0BH\nCCGEEOLnKNARQgghhPg5CnSEEEIIIX6OAh0hhBBCiJ+jQEcIIYQQ4uf+P3Z/owkJVomXAAAAAElF\nTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sympy import Eq, solve\n", + "from sympy.abc import h, s, a\n", + "from devito import Operator, t, x, y\n", + "\n", + "# Reset our data field and ICs\n", + "init_hat(field=u.data[0], dx=dx, dy=dy, value=2.)\n", + "\n", + "# Create an operator with seond-order derivatives\n", + "eq = Eq(u.dt, a * u.laplace)\n", + "stencil = solve(eq, u.forward)[0]\n", + "eq_stencil = Eq(u.forward, stencil)\n", + "\n", + "# Create boundary condition expressions\n", + "bc = [Eq(u.indexed[t+1, 0, y], 1.)] # left\n", + "bc += [Eq(u.indexed[t+1, nx-1, y], 1.)] # right\n", + "bc += [Eq(u.indexed[t+1, x, ny-1], 1.)] # top\n", + "bc += [Eq(u.indexed[t+1, x, 0], 1.)] # bottom\n", + "\n", + "op = Operator([eq_stencil] + bc,\n", + " subs={h: dx, s: dt, a: nu})\n", + "op(time=10)\n", + "\n", + "plot_field(u.data[0], zmax=2.5)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "And now let's use the same operator again to show the more diffused field. In fact, instead of resetting the previously used object `u`, we can also create a new `TimeData` object and tell our operator to use this." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "=========================================================================================\n", + "Section loop_y_1<50,31> with OI=0.00 computed in 0.000 s [Perf: 0.00 GFlops/s]\n", + "Section loop_x_2<50,31> with OI=0.00 computed in 0.000 s [Perf: 0.00 GFlops/s]\n", + "Section main<50,30,30> with OI=0.47 computed in 0.000 s [Perf: 1.53 GFlops/s]\n", + "=========================================================================================\n" + ] + }, + { + "data": { + "image/png": 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H4uLiMGrFf+tKI2wST3u7Dh7VRM7vGjo+qpj0ayCs4Sdhnmlen0c7IdjD3uMg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\npZgzZw527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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "u2 = TimeData(name='u2', shape=(nx, ny), space_order=2)\n", + "init_hat(field=u2.data[0], dx=dx, dy=dy, value=2.)\n", + "\n", + "op(u=u2, time=50)\n", + "\n", + "plot_field(u2.data[0], zmax=2.5)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "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": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/examples/cfd/tools.py b/examples/cfd/tools.py index eb6a508e2e..b4dc2d904e 100644 --- a/examples/cfd/tools.py +++ b/examples/cfd/tools.py @@ -4,7 +4,7 @@ from matplotlib import pyplot, cm -def plot_field(field, xmax=2., ymax=2., view=None, linewidth=0): +def plot_field(field, xmax=2., ymax=2., zmax=None, view=None, linewidth=0): """Utility plotting routine for 2D data :param field: Numpy array with field data to plot @@ -23,6 +23,8 @@ def plot_field(field, xmax=2., ymax=2., view=None, linewidth=0): # Enforce axis measures and set view if given ax.set_xlim(0., xmax) ax.set_ylim(0., ymax) + if zmax is not None: + ax.set_zlim(1., zmax) if view is not None: ax.view_init(*view) From 1accaade51e126a4b7b4df823ce64b4a779c7f3b Mon Sep 17 00:00:00 2001 From: Michael Lange Date: Mon, 15 May 2017 11:58:48 +0100 Subject: [PATCH 04/12] CFD: Add tutorial notebook for 2D Burger's equation --- examples/cfd/test_04_burgers.ipynb | 319 +++++++++++++++++++++++++++++ 1 file changed, 319 insertions(+) create mode 100644 examples/cfd/test_04_burgers.ipynb diff --git a/examples/cfd/test_04_burgers.ipynb b/examples/cfd/test_04_burgers.ipynb new file mode 100644 index 0000000000..54df4ed96d --- /dev/null +++ b/examples/cfd/test_04_burgers.ipynb @@ -0,0 +1,319 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Example 4: Burgers' equation\n", + "\n", + "Now that we have seen how to construct the non-linear convection and diffusion examples, we can combine them to form Burgers' equations. We again create a set of coupled equations which are actually starting to form quite complicated stencil expressions, even if we are only using a low-order discretisations.\n", + "\n", + "Let's start with the definition fo the governing equations:\n", + "$$ \\frac{\\partial u}{\\partial t} + u \\frac{\\partial u}{\\partial x} + v \\frac{\\partial u}{\\partial y} = \\nu \\; \\left(\\frac{\\partial ^2 u}{\\partial x^2} + \\frac{\\partial ^2 u}{\\partial y^2}\\right)$$\n", + " \n", + "$$ \\frac{\\partial v}{\\partial t} + u \\frac{\\partial v}{\\partial x} + v \\frac{\\partial v}{\\partial y} = \\nu \\; \\left(\\frac{\\partial ^2 v}{\\partial x^2} + \\frac{\\partial ^2 v}{\\partial y^2}\\right)$$\n", + "\n", + "The discretized and rearranged form then looks like this:\n", + "$$u_{i,j}^{n+1} = u_{i,j}^n - \\frac{\\Delta t}{\\Delta x} u_{i,j}^n (u_{i,j}^n - u_{i-1,j}^n) - \\frac{\\Delta t}{\\Delta y} v_{i,j}^n (u_{i,j}^n - u_{i,j-1}^n)+ $$\n", + "$$ \\frac{\\nu \\Delta t}{\\Delta x^2}(u_{i+1,j}^n-2u_{i,j}^n+u_{i-1,j}^n) + \\frac{\\nu \\Delta t}{\\Delta y^2} (u_{i,j+1}^n - 2u_{i,j}^n + u_{i,j+1}^n)$$ \n", + "\n", + "$$v_{i,j}^{n+1} = v_{i,j}^n - \\frac{\\Delta t}{\\Delta x} u_{i,j}^n (v_{i,j}^n - v_{i-1,j}^n) - \\frac{\\Delta t}{\\Delta y} v_{i,j}^n (v_{i,j}^n - v_{i,j-1}^n)+ $$\n", + "$$ \\frac{\\nu \\Delta t}{\\Delta x^2}(v_{i+1,j}^n-2v_{i,j}^n+v_{i-1,j}^n) + \\frac{\\nu \\Delta t}{\\Delta y^2} (v_{i,j+1}^n - 2v_{i,j}^n + v_{i,j+1}^n)$$\n", + "\n", + "Great. Now before we look at the Devito implementation, let's re-create the NumPy-based implementation form the original." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from examples.cfd import plot_field, init_hat\n", + "import numpy as np\n", + "%matplotlib inline\n", + "\n", + "# Some variable declarations\n", + "nx = 41\n", + "ny = 41\n", + "nt = 120\n", + "c = 1\n", + "dx = 2. / (nx - 1)\n", + "dy = 2. / (ny - 1)\n", + "sigma = .0009\n", + "nu = 0.01\n", + "dt = sigma * dx * dy / nu" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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vL+jDCC0GujZJkhSqfq6iz2qhUNDXx9VrzxXVQFcPgxxRcNgJwZ44B5kLtLO0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\nzcp3SAAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Assign initial conditions\n", + "u = np.empty((nx, ny))\n", + "v = np.empty((nx, ny))\n", + "\n", + "init_hat(field=u, dx=dx, dy=dy, value=2.)\n", + "init_hat(field=v, dx=dx, dy=dy, value=2.)\n", + "\n", + "plot_field(u)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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q+bFCQucDRVEwOjpqXrD5aRAyElSMrA2Sk+6rJ4LQ+RG5KNfLonNpbLdGwSa1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\nRyq6kM7j7d69G1evXpWLLqRJF9aPQm+n6ILn5FzLPEjb+2Xm6biL5zi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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "for n in range(nt + 1): ##loop across number of time steps\n", + " un = u.copy()\n", + " vn = v.copy()\n", + "\n", + " u[1:-1, 1:-1] = (un[1:-1, 1:-1] -\n", + " dt / dx * un[1:-1, 1:-1] * \n", + " (un[1:-1, 1:-1] - un[1:-1, 0:-2]) - \n", + " dt / dy * vn[1:-1, 1:-1] * \n", + " (un[1:-1, 1:-1] - un[0:-2, 1:-1]) + \n", + " nu * dt / dx**2 * \n", + " (un[1:-1,2:] - 2 * un[1:-1, 1:-1] + un[1:-1, 0:-2]) + \n", + " nu * dt / dy**2 * \n", + " (un[2:, 1:-1] - 2 * un[1:-1, 1:-1] + un[0:-2, 1:-1]))\n", + " \n", + " v[1:-1, 1:-1] = (vn[1:-1, 1:-1] - \n", + " dt / dx * un[1:-1, 1:-1] *\n", + " (vn[1:-1, 1:-1] - vn[1:-1, 0:-2]) -\n", + " dt / dy * vn[1:-1, 1:-1] * \n", + " (vn[1:-1, 1:-1] - vn[0:-2, 1:-1]) + \n", + " nu * dt / dx**2 * \n", + " (vn[1:-1, 2:] - 2 * vn[1:-1, 1:-1] + vn[1:-1, 0:-2]) +\n", + " nu * dt / dy**2 *\n", + " (vn[2:, 1:-1] - 2 * vn[1:-1, 1:-1] + vn[0:-2, 1:-1]))\n", + " \n", + " u[0, :] = 1\n", + " u[-1, :] = 1\n", + " u[:, 0] = 1\n", + " u[:, -1] = 1\n", + " \n", + " v[0, :] = 1\n", + " v[-1, :] = 1\n", + " v[:, 0] = 1\n", + " v[:, -1] = 1\n", + " \n", + "plot_field(u)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Nice, our wave looks just like the original. Now we shall attempt to write our entire Burgers' equation operator in a single cell - but before we can demonstrate this, there is one slight problem.\n", + "\n", + "The diffusion term in our equation requires a second-order space discretisation on our velocity fields, which we set through the `TimeData` constructor for $u$ and $v$. The `TimeData` objects will store this dicretisation information and use it as default whenever we use the shorthnad notations for derivative, like `u.dxl` or `u.dyl`. For the advection term, however, we want to use a first-order discretisation, which we now have to create by hand when combining terms with different stencil discretisations. To illustrate let's consider the following example: " + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Space order 1:\n", + "u1(t, x, y)/h - u1(t, x - h, y)/h\n", + "\n", + "Space order 2:\n", + "3*u2(t, x, y)/(2*h) + u2(t, x - 2*h, y)/(2*h) - 2*u2(t, x - h, y)/h\n", + "\n", + "Explicit space order 1:\n", + "u2(t, x, y)/h - u2(t, x - h, y)/h\n", + "\n" + ] + } + ], + "source": [ + "from devito import TimeData, first_derivative, left, x\n", + "\n", + "u1 = TimeData(name='u1', shape=(nx, ny), space_order=1)\n", + "print(\"Space order 1:\\n%s\\n\" % u1.dxl)\n", + "\n", + "u2 = TimeData(name='u2', shape=(nx, ny), space_order=2)\n", + "print(\"Space order 2:\\n%s\\n\" % u2.dxl)\n", + "\n", + "# We use u2 to create the explicit first-order derivative\n", + "u1_dx = first_derivative(u2, dim=x, side=left, order=1)\n", + "print(\"Explicit space order 1:\\n%s\\n\" % u1_dx)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Ok, so by constructing derivative terms explicitly we again have full control of the spatial discretisation - the power of symbolic computation. Armed with that trick, we can now build and execute our advection-diffusion operator from scratch in one cell." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "DSE: extract_time_invariants [flops: 40, elapsed: 0.01] >>\n", + " eliminate_inter_stencil_redundancies [flops: 40, elapsed: 0.01] >>\n", + " eliminate_intra_stencil_redundancies [flops: 38, elapsed: 0.03] >>\n", + " factorize [flops: 28, elapsed: 0.08] >>\n", + " finalize [flops: 28, elapsed: 0.01]\n", + " [Total elapsed: 0.14 s]\n", + "DSE: extract_time_invariants [flops: 0, elapsed: 0.00] >>\n", + " eliminate_inter_stencil_redundancies [flops: 0, elapsed: 0.01] >>\n", + " eliminate_intra_stencil_redundancies [flops: 0, elapsed: 0.00] >>\n", + " factorize [flops: 0, elapsed: 0.00] >>\n", + " finalize [flops: 0, elapsed: 0.00]\n", + " [Total elapsed: 0.02 s]\n", + "DSE: extract_time_invariants [flops: 0, elapsed: 0.00] >>\n", + " eliminate_inter_stencil_redundancies [flops: 0, elapsed: 0.01] >>\n", + " eliminate_intra_stencil_redundancies [flops: 0, elapsed: 0.00] >>\n", + " factorize [flops: 0, elapsed: 0.00] >>\n", + " finalize [flops: 0, elapsed: 0.00]\n", + " [Total elapsed: 0.02 s]\n", + "DLE: analyze [elapsed: 0.01] >>\n", + " avoid_denormals [elapsed: 0.00] >>\n", + " loop_fission [elapsed: 0.01] >>\n", + " create_elemental_functions [elapsed: 0.01] >>\n", + " loop_blocking [elapsed: 0.19] >>\n", + " simdize [elapsed: 1.10]\n", + " [Total elapsed: 1.32 s]\n", + "CustomCompiler: compiled /tmp/devito-1000/6242e625bd0b906e96ef83dcda3de90d96873a5f.c [0.40 s]\n", + "=========================================================================================\n", + "Section loop_y_1<121,41> with OI=0.00 computed in 0.000 s [Perf: 0.00 GFlops/s]\n", + "Section loop_x_2<121,41> with OI=0.00 computed in 0.000 s [Perf: 0.00 GFlops/s]\n", + "Section main<121,40,40> with OI=1.67 computed in 0.001 s [Perf: 4.57 GFlops/s]\n", + "=========================================================================================\n" + ] + }, + { + "data": { + "image/png": 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ShOHhYeOCbZ4GISJBxcjaIDnpvno8CJ0fkYtjvWlut4Zhq1KwnWbhhFnq4pQ5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\nQEdERETk5RjoiIiIiLwcAx0RERGRl/s/GH3UIJmp1rwAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sympy import Eq, solve\n", + "from sympy.abc import h, s, a\n", + "from devito import Operator, TimeData, first_derivative, left, x, y, t\n", + "\n", + "# Define our velocity fields and initialise with hat function\n", + "u = TimeData(name='u', shape=(nx, ny), space_order=2)\n", + "v = TimeData(name='v', shape=(nx, ny), space_order=2)\n", + "init_hat(field=u.data[0], dx=dx, dy=dy, value=2.)\n", + "init_hat(field=v.data[0], dx=dx, dy=dy, value=2.)\n", + "\n", + "# Write down the equations with explicit backward differences\n", + "u_dx = first_derivative(u, dim=x, side=left, order=1)\n", + "u_dy = first_derivative(u, dim=y, side=left, order=1)\n", + "v_dx = first_derivative(v, dim=x, side=left, order=1)\n", + "v_dy = first_derivative(v, dim=y, side=left, order=1)\n", + "eq_u = Eq(u.dt + u*u_dx + v*u_dy, a*u.laplace)\n", + "eq_v = Eq(v.dt + u*v_dx + v*v_dy, a*v.laplace)\n", + "\n", + "# Let SymPy rearrange our stencils to form the update expressions\n", + "stencil_u = solve(eq_u, u.forward)[0]\n", + "stencil_v = solve(eq_v, v.forward)[0]\n", + "update_u = Eq(u.forward, stencil_u)\n", + "update_v = Eq(v.forward, stencil_v)\n", + "\n", + "# Create Dirichlet BC expressions using the low-level API\n", + "bc_u = [Eq(u.indexed[t+1, 0, y], 1.)] # left\n", + "bc_u += [Eq(u.indexed[t+1, nx-1, y], 1.)] # right\n", + "bc_u += [Eq(u.indexed[t+1, x, ny-1], 1.)] # top\n", + "bc_u += [Eq(u.indexed[t+1, x, 0], 1.)] # bottom\n", + "bc_v = [Eq(v.indexed[t+1, 0, y], 1.)] # left\n", + "bc_v += [Eq(v.indexed[t+1, nx-1, y], 1.)] # right\n", + "bc_v += [Eq(v.indexed[t+1, x, ny-1], 1.)] # top\n", + "bc_v += [Eq(v.indexed[t+1, x, 0], 1.)] # bottom\n", + "\n", + "# Create the operator\n", + "op = Operator([update_u, update_v] + bc_u + bc_v,\n", + " subs={h: dx, s:dt, a: nu})\n", + "\n", + "# Execute the operator for a number of timesteps\n", + "op(time=nt + 1)\n", + "\n", + "plot_field(u.data[0])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "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": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} From 10e11b823a539638d0ca8aa8bfc51cd6e09d5694 Mon Sep 17 00:00:00 2001 From: Michael Lange Date: Mon, 15 May 2017 11:59:21 +0100 Subject: [PATCH 05/12] CFD: Add basic CFD Laplace example (steady-state heat equation) --- examples/cfd/test_05_laplace.ipynb | 408 +++++++++++++++++++++++++++++ 1 file changed, 408 insertions(+) create mode 100644 examples/cfd/test_05_laplace.ipynb diff --git a/examples/cfd/test_05_laplace.ipynb b/examples/cfd/test_05_laplace.ipynb new file mode 100644 index 0000000000..f074ed70ad --- /dev/null +++ b/examples/cfd/test_05_laplace.ipynb @@ -0,0 +1,408 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Example 5: Laplace equation\n", + "\n", + "In this tutorial we will look constructing the steady-state heat example using the Laplace equation. In contrast to the previous tutorials this example is entirely driven by the prescribed Dirichlet and Neumann boundary conditions, instead of an initial condition. We will also demonstrate how to use Devito to solve a steady-state problem without time derivatives and how to switch buffers explicitly without having to re-compile the kernel.\n", + "\n", + "First, we again define our governing equation:\n", + "$$\\frac{\\partial ^2 p}{\\partial x^2} + \\frac{\\partial ^2 p}{\\partial y^2} = 0$$\n", + "\n", + "And in a discretised form, rearranged to update the state of $p$:\n", + "$$p_{i,j}^n = \\frac{\\Delta y^2(p_{i+1,j}^n+p_{i-1,j}^n)+\\Delta x^2(p_{i,j+1}^n + p_{i,j-1}^n)}{2(\\Delta x^2 + \\Delta y^2)}$$\n", + "\n", + "And, as always, we first re-create the original implementation to see what we are aiming for. Here we initialise the field $p$ to $0$ and apply the following bounday conditions:\n", + "\n", + "$p=0$ at $x=0$\n", + " \n", + "$p=y$ at $x=2$\n", + " \n", + "$\\frac{\\partial p}{\\partial y}=0$ at $y=0, \\ 1$\n", + "\n", + "**Developer note:**\n", + "The original tutorial stores the field data in the layout `(ny, nx)`. Until now we have used `(x, y)` notation for creating our Devito examples, but for this one we will adopt the `(y, x)` layout for compatibility reasons." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from examples.cfd import plot_field\n", + "import numpy as np\n", + "%matplotlib inline\n", + "\n", + "# Some variable declarations\n", + "nx = 31\n", + "ny = 31\n", + "c = 1\n", + "dx = 2. / (nx - 1)\n", + "dy = 1. / (ny - 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def laplace2d(p, bc_y, dx, dy, l1norm_target):\n", + " l1norm = 1\n", + " pn = np.empty_like(p)\n", + "\n", + " while l1norm > l1norm_target:\n", + " pn = p.copy()\n", + " p[1:-1, 1:-1] = ((dy**2 * (pn[1:-1, 2:] + pn[1:-1, 0:-2]) +\n", + " dx**2 * (pn[2:, 1:-1] + pn[0:-2, 1:-1])) /\n", + " (2 * (dx**2 + dy**2)))\n", + " \n", + " p[:, 0] = 0 # p = 0 @ x = 0\n", + " p[:, -1] = bc_right # p = y @ x = 2\n", + " p[0, :] = p[1, :] # dp/dy = 0 @ y = 0\n", + " p[-1, :] = p[-2, :] # dp/dy = 0 @ y = 1\n", + " l1norm = (np.sum(np.abs(p[:]) - np.abs(pn[:])) /\n", + " np.sum(np.abs(pn[:])))\n", + " \n", + " return p" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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Raha9y2QyKBQKJQK/PHrn57ZfAAVdTSSTSbzzzjslj+kneP1idq9E4arBdVal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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Out initial condition is 0 everywhere,except at the boundary\n", + "p = np.zeros((ny, nx))\n", + "\n", + "# Boundary conditions\n", + "bc_right = np.linspace(0, 1, ny)\n", + "p[:, 0] = 0 # p = 0 @ x = 0\n", + "p[:, -1] = bc_right # p = y @ x = 2\n", + "p[0, :] = p[1, :] # dp/dy = 0 @ y = 0\n", + "p[-1, :] = p[-2, :] # dp/dy = 0 @ y = 1\n", + "\n", + "plot_field(p, ymax=1.0, view=(30, 225))" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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esf1YJmJuMPGPyUTdf9h8bGHbJO4czwO9I7hw4wnh31UTIXSvqSuDkEh7/mFr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\nOHbsGKZMm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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "p = laplace2d(p, bc_right, dx, dy, 1e-4)\n", + "plot_field(p, ymax=1.0, view=(30, 225))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Ok, nice. Now, to re-create this example in Devito we need to look a little bit further under the hood. There are two things that make this different to the examples we covered so far:\n", + "* We have no time dependence in the `p` field, but we still need to advance the state of p in between buffers. So, instead of using `TimeData` objects that provide multiple data buffers for timestepping schemes, we will use `DenseData` objects that have no time dimension and only allocate a single buffer according to the space dimensions. However, since we are still implementing a pseudo-timestepping loop, we will need to objects, say `p` and `pn`, to act as alternating buffers.\n", + "* If we're using two different symbols to denote our buffers, any operator we create will only perform a single timestep. This is desired though, since we need to check a convergence criteria outside of the main stencil update to determine when we stop iterating. As a result we will need to call the operator repeatedly after instantiating it outside the convergence loop.\n", + "\n", + "So, how do we make sure our operator doesn't accidentally overwrite values in the same buffer? Well, we can again let SymPy reorganise our Laplace equation based on `pn` to generate the stencil, but when we create the update expression, we set the LHS to our second buffer variable `p`." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Update stencil:\n", + "Eq(p(x, y), pn(x, y - h)/4 + pn(x, y + h)/4 + pn(x - h, y)/4 + pn(x + h, y)/4)\n", + "\n" + ] + } + ], + "source": [ + "from devito import DenseData\n", + "from sympy import Eq, solve\n", + "from sympy.abc import a\n", + "\n", + "# Create two explicit buffers for pseudo-timestepping\n", + "p = DenseData(name='p', shape=(nx, ny), space_order=2)\n", + "pn = DenseData(name='pn', shape=(nx, ny), space_order=2)\n", + "\n", + "# Create Laplace equation base on `pn`\n", + "eq = Eq(a * pn.laplace)\n", + "# Let SymPy solve for the central stencil point\n", + "stencil = solve(eq, pn)[0]\n", + "# Now we let our stencil populate our second buffer `p`\n", + "eq_stencil = Eq(p, stencil)\n", + "\n", + "# In the resulting stencil `pn` is exclusively used on the RHS\n", + "# and `p` on the LHS is the grid the kernel will update\n", + "print(\"Update stencil:\\n%s\\n\" % eq_stencil)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can add our boundary conditions. We have already seen how to prescribe constant Dirichlet BCs by simply setting values using the low-level notation. This time we will go a little further by setting a prescribed profile, which we create first as a custom 1D symbol and supply with the BC values." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from devito import x\n", + "\n", + "bc_right = DenseData(name='bc_right', shape=(nx, ), dimensions=(x, ))\n", + "bc_right.data[:] = np.linspace(0, 1, nx)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can create a set of expressions for the BCs again, where we wet prescribed values on the right and left of our grid. For the Neuman BCs along the top and bottom boundaries we simply copy the second rwo from the outside into the outermost row, just as the original tutorial did. Using these expressions and our stencil update we can now create an operator." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "DLE: analyze [elapsed: 0.00] >>\n", + " avoid_denormals [elapsed: 0.00] >>\n", + " loop_fission [elapsed: 0.00] >>\n", + " create_elemental_functions [elapsed: 0.00] >>\n", + " loop_blocking [elapsed: 0.13] >>\n", + " simdize [elapsed: 1.18]\n", + " [Total elapsed: 1.31 s]\n" + ] + } + ], + "source": [ + "from devito import Operator, x, y\n", + "from sympy.abc import h, a\n", + "\n", + "# Create boundary condition expressions\n", + "bc = [Eq(p.indexed[x, 0], 0.)] # p = 0 @ x = 0\n", + "bc += [Eq(p.indexed[x, ny-1], bc_right.indexed[x])] # p = y @ x = 2\n", + "bc += [Eq(p.indexed[0, y], p.indexed[1, y])] # dp/dy = 0 @ y = 0\n", + "bc += [Eq(p.indexed[nx-1, y], p.indexed[nx-2, y])] # dp/dy = 0 @ y = 1\n", + "\n", + "# Now we can build the operator that we need\n", + "op = Operator(expressions=[eq_stencil] + bc, subs={h: dx, a: 1.})" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can now use this single-step operator repeatedly in a Python loop, where we can arbitrarily execute other code in between invocations. This allows us to update our L1 norm and check for convergence. Using our pre0compiled operator now comes down to a single function call that supplies the relevant data symbols. One thing to note is that we now do exactly the same thing as the original NumPy loop, in that we deep-copy the data between each iteration of the loop, which we will look at after this." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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K5QIOqN8Tzk/Cxi8YReGA/RM+o3DuYdnrF+P/fOAuw+f0Hmf6RfROit65QRB5jXLvO0VR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\nl9qF6GOkoRN9S0VFBZmZmezatQuANWvWoFAorHbpVqxYQVhYGAsXLnR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8n7n71/CnP/ZOo2NXDVnlbL/fDyN2o9EIjUajtJGhdRC6qlOaPnSrwHVdXH31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\n8Riw1tZW7NixA+Xl5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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Silence the runtime performance logging\n", + "from devito import configuration\n", + "configuration['log_level'] = 'ERROR'\n", + "\n", + "# Initialise the two buffer fields\n", + "p.data[:] = 0.\n", + "p.data[:, -1] = np.linspace(0, 1, ny)\n", + "pn.data[:] = 0.\n", + "pn.data[:, -1] = np.linspace(0, 1, ny)\n", + "\n", + "# Visualize the initial condition\n", + "plot_field(p.data, ymax=1.0, view=(30, 225))\n", + "\n", + "# Run the convergence loop with deep data copies\n", + "l1norm_target = 1.e-4\n", + "l1norm = 1\n", + "while l1norm > l1norm_target:\n", + " # This call implies a deep data copy\n", + " pn.data[:] = p.data[:]\n", + " op(p=p, pn=pn)\n", + " \n", + " l1norm = (np.sum(np.abs(p.data[:]) - np.abs(pn.data[:])) /\n", + " np.sum(np.abs(pn.data[:])))\n", + "\n", + "# Visualize the converged steady-state\n", + "plot_field(p.data, ymax=1.0, view=(30, 225))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One crucial detail about the code above is that the deep data copy between iterations will really hurt performance if we were to run this on a large grid. However, we have already seen how we can match data symbols to symbolic names when calling the pre-compiled operator, which we can now use to actually switch the roles of `pn` and `p` between iterations, eg. `op(p=pn, pn=p)`. Thus, we can implement a simple buffer-switching scheme by simply testing for odd and even time-steps, without ever having to shuffle data around." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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K5QIOqN8Tzk/Cxi8YReGA/RM+o3DuYdnrF+P/fOAuw+f0Hmf6RfROit65QRB5jXLvO0VR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\nl9qF6GOkoRN9S0VFBZmZmezatQuANWvWoFAorHbpVqxYQVhYGAsXLnR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RbH8/c9ev489+5B1G+64assrZfr8fRuxGoxEajUZpI0PrIHRVpzR96FaB67q4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\nq4QdQMSdGcJu01cvm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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Initialise the two buffer fields\n", + "p.data[:] = 0.\n", + "p.data[:, -1] = np.linspace(0, 1, ny)\n", + "pn.data[:] = 0.\n", + "pn.data[:, -1] = np.linspace(0, 1, ny)\n", + "\n", + "# Visualize the initial condition\n", + "plot_field(p.data, ymax=1.0, view=(30, 225))\n", + "\n", + "# Run the convergence loop by explicitly flipping buffers\n", + "l1norm_target = 1.e-4\n", + "l1norm = 1\n", + "counter = 0\n", + "while l1norm > l1norm_target:\n", + " # Determine buffer order\n", + " if counter % 2 == 0:\n", + " _p = p\n", + " _pn = pn\n", + " else:\n", + " _p = pn\n", + " _pn = p\n", + "\n", + " # Apply operator\n", + " op(p=_p, pn=_pn)\n", + " \n", + " # Compute L1 norm\n", + " l1norm = (np.sum(np.abs(_p.data[:]) - np.abs(_pn.data[:])) /\n", + " np.sum(np.abs(_pn.data[:])))\n", + " counter += 1\n", + " \n", + "plot_field(p.data, ymax=1.0, view=(30, 225))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "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": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} From 39a1e592c6997826e680cb2a8917e89f744efa5a Mon Sep 17 00:00:00 2001 From: Michael Lange Date: Wed, 17 May 2017 09:02:15 +0100 Subject: [PATCH 06/12] CFD: Add Poisson example with pseudo-timestepping via Python and Devito --- examples/cfd/test_06_poisson.ipynb | 312 +++++++++++++++++++++++++++++ 1 file changed, 312 insertions(+) create mode 100644 examples/cfd/test_06_poisson.ipynb diff --git a/examples/cfd/test_06_poisson.ipynb b/examples/cfd/test_06_poisson.ipynb new file mode 100644 index 0000000000..cca0dbdf5f --- /dev/null +++ b/examples/cfd/test_06_poisson.ipynb @@ -0,0 +1,312 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Example 6: Poisson equation\n", + "\n", + "In the previous example we have seen how to solve the steady-state Laplace equation with a prescribed boundary condition and BCs that contain derivatives (Neumann BC). For this we used a pseudo-timestepping to illustrate the use of two explicit data symbols of type `DenseData` to derive at a steady state. In this example we are going to solve the Poisson equation (step 10 of the original tutorial series) with an initial condition to demonstrate how we can combine time-dependent functions of type `TimeData` with time-constant `DenseData` functions. We will again implement a Python-driven outer loop for the diffusion kernel, before demonstrating how we can change the expression defining our operator to internalize the pseudo-timestepping and thus get the full performance advantage of compiled kernel loops.\n", + "\n", + "Our governing equation is the Poisson equation with a souce term as the RHS:\n", + "$$\\frac{\\partial ^2 p}{\\partial x^2} + \\frac{\\partial ^2 p}{\\partial y^2} = b$$\n", + "\n", + "Discretizing and rearranging our stencil expression yields\n", + "$$p_{i,j}^{n}=\\frac{(p_{i+1,j}^{n}+p_{i-1,j}^{n})\\Delta y^2+(p_{i,j+1}^{n}+p_{i,j-1}^{n})\\Delta x^2-b_{i,j}^{n}\\Delta x^2\\Delta y^2}{2(\\Delta x^2+\\Delta y^2)}$$\n", + "\n", + "The key difference to the Laplace example in the previous tutorial is that this example hassimple Dirichlet boundary conditions $p = 0$ on all boundaries and is instead driven by the source term $b$ defined as\n", + "\n", + "$b_{i,j}=100$ at $i=nx/4, j=ny/4$\n", + "\n", + "$b_{i,j}=-100$ at $i=nx*3/4, j=3/4 ny$\n", + "\n", + "$b_{i,j}=0$ everywhere else.\n", + "\n", + "And of course, we will demonstrate the original example first using pure NumPy notation." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from examples.cfd import plot_field, init_hat\n", + "import numpy as np\n", + "%matplotlib inline\n", + "\n", + "# Some variable declarations\n", + "nx = 50\n", + "ny = 50\n", + "nt = 100\n", + "xmin = 0.\n", + "xmax = 2.\n", + "ymin = 0.\n", + "ymax = 1.\n", + "\n", + "dx = (xmax - xmin) / (nx - 1)\n", + "dy = (ymax - ymin) / (ny - 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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OR1hI0IUkaNoxa1E4NyYl5crbirBzlvfi7CyYvYo/hkRh3U+1hovO/cvyNvwL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\n6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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Initialization\n", + "p = np.zeros((nx, ny))\n", + "pd = np.zeros((nx, ny))\n", + "b = np.zeros((nx, ny))\n", + "\n", + "# Source\n", + "b[int(nx / 4), int(ny / 4)] = 100\n", + "b[int(3 * nx / 4), int(3 * ny / 4)] = -100\n", + "\n", + "for it in range(nt):\n", + " pd = p.copy()\n", + " p[1:-1,1:-1] = (((pd[1:-1, 2:] + pd[1:-1, :-2]) * dy**2 +\n", + " (pd[2:, 1:-1] + pd[:-2, 1:-1]) * dx**2 -\n", + " b[1:-1, 1:-1] * dx**2 * dy**2) / \n", + " (2 * (dx**2 + dy**2)))\n", + "\n", + " p[0, :] = 0\n", + " p[nx-1, :] = 0\n", + " p[:, 0] = 0\n", + " p[:, ny-1] = 0\n", + " \n", + "plot_field(p, xmax=xmax, ymax=ymax, view=(30, 225))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can now pretty much use our previous implementation, although we will use `pd` instead of `pn` for consistency with the original. Our boundary conditions are even simpler since they are $0$ everywhere. Our source term is neatly wrapped in the smbol `b` and we can again use a Python-driven timestepping loop with switching buffers to repeatedly execute the operator we create." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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EnY4Htg/72waAH9484393eP0sHsFhXPb+9/rLHnzTzb54o2kJjuMEXLNimSgm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\nJ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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from devito import TimeData, DenseData, Operator, x, y, t, configuration\n", + "from sympy import Eq, solve\n", + "from sympy.abc import h, a\n", + "\n", + "# Silence the runtime performance logging\n", + "configuration['log_level'] = 'ERROR'\n", + "\n", + "# Now with Devito we will turn `p` into `TimeData` object \n", + "# to make all the buffer switching implicit\n", + "p = DenseData(name='p', shape=(nx, ny), space_order=2)\n", + "pd = DenseData(name='pd', shape=(nx, ny), space_order=2)\n", + "p.data[:] = 0.\n", + "pd.data[:] = 0.\n", + "\n", + "# Initialise the source term `b`\n", + "b = DenseData(name='b', shape=(nx, ny))\n", + "b.data[:] = 0.\n", + "b.data[int(nx / 4), int(ny / 4)] = 100\n", + "b.data[int(3 * nx / 4), int(3 * ny / 4)] = -100\n", + "\n", + "# Create Laplace equation base on `pd`\n", + "eq = Eq(a * pd.laplace, b)\n", + "# Let SymPy solve for the central stencil point\n", + "stencil = solve(eq, pd)[0]\n", + "# Now we let our stencil populate our second buffer `p`\n", + "eq_stencil = Eq(p, stencil)\n", + "\n", + "# Create boundary condition expressions\n", + "bc = [Eq(p.indexed[x, 0], 0.)]\n", + "bc += [Eq(p.indexed[x, ny-1], 0.)]\n", + "bc += [Eq(p.indexed[0, y], 0.)]\n", + "bc += [Eq(p.indexed[nx-1, y], 0.)]\n", + " \n", + "# Now we can build the operator that we need\n", + "op = Operator([eq_stencil] + bc, subs={h: dx, a: 1.})\n", + "\n", + "# Run the outer loop explicitly in Python\n", + "for i in range(nt):\n", + " # Determine buffer order\n", + " if i % 2 == 0:\n", + " _p = p\n", + " _pd = pd\n", + " else:\n", + " _p = pd\n", + " _pd = p\n", + "\n", + " # Apply operator\n", + " op(p=_p, pd=_pd)\n", + " \n", + "plot_field(p.data, xmax=xmax, ymax=ymax, view=(30, 225))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Nice, we get the same spikes as the pure NumPy implementation. But we still drive the time loop though Python, which is slow. So let's try and utilise Devito's time-stepping mechanism that we saw earlier for this \"pseudo-timestepping\". \n", + "\n", + "The trick here is to again use `TimeData` objects, despite the lack of a time-dependence. This will cause Devito to allocate two grid buffers instead of one, which we can directly address them via the terms `p` and `p.forward`. This will now create an internal time loop in the kernel that we can again control by supplying the `time` argument to the create operator during invocation.\n", + "\n", + "One caveat, however, is that a `TimeData` object has an implicit time dimension `t`, so the symbol is denoted as `p(t, x, y)`. This entails that, when creating our boundary condition expressions, we now need honour the leading time dimension in the \"low-level\" notation, and ensure that we update the index `t + 1` (the equivalent to `u.forward`)." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "DSE: extract_time_invariants [flops: 9, elapsed: 0.00] >>\n", + " eliminate_inter_stencil_redundancies [flops: 9, elapsed: 0.00] >>\n", + " eliminate_intra_stencil_redundancies [flops: 9, elapsed: 0.00] >>\n", + " factorize [flops: 6, elapsed: 0.01] >>\n", + " finalize [flops: 6, elapsed: 0.00]\n", + " [Total elapsed: 0.02 s]\n", + "DSE: extract_time_invariants [flops: 0, elapsed: 0.00] >>\n", + " eliminate_inter_stencil_redundancies [flops: 0, elapsed: 0.00] >>\n", + " eliminate_intra_stencil_redundancies [flops: 0, elapsed: 0.00] >>\n", + " factorize [flops: 0, elapsed: 0.00] >>\n", + " finalize [flops: 0, elapsed: 0.00]\n", + " [Total elapsed: 0.01 s]\n", + "DSE: extract_time_invariants [flops: 0, elapsed: 0.00] >>\n", + " eliminate_inter_stencil_redundancies [flops: 0, elapsed: 0.00] >>\n", + " eliminate_intra_stencil_redundancies [flops: 0, elapsed: 0.00] >>\n", + " factorize [flops: 0, elapsed: 0.00] >>\n", + " finalize [flops: 0, elapsed: 0.00]\n", + " [Total elapsed: 0.01 s]\n", + "DLE: analyze [elapsed: 0.01] >>\n", + " avoid_denormals [elapsed: 0.00] >>\n", + " loop_fission [elapsed: 0.00] >>\n", + " create_elemental_functions [elapsed: 0.00] >>\n", + " loop_blocking [elapsed: 0.00] >>\n", + " simdize [elapsed: 0.00]\n", + " [Total elapsed: 0.03 s]\n", + "CustomCompiler: compiled /tmp/devito-1000/f294f71d1bb0738982398a054025606bc3b6ad8d.c [0.32 s]\n", + "=========================================================================================\n", + "Section loop_x_1<101,50> with OI=0.00 computed in 0.000 s [Perf: 0.00 GFlops/s]\n", + "Section loop_y_2<101,50> with OI=0.00 computed in 0.000 s [Perf: 0.00 GFlops/s]\n", + "Section main<101,49,49> with OI=0.48 computed in 0.000 s [Perf: 4.79 GFlops/s]\n", + "=========================================================================================\n" + ] + }, + { + "data": { + "image/png": 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ifgfLcANexf6rondUMYCid6aR4jJ8BoTruqU5lqSw0BmwsbGB06dPY3Nzc9W7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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from devito import TimeData, DenseData, Operator, x, y, t, configuration\n", + "from sympy import Eq, solve\n", + "from sympy.abc import h, a\n", + "\n", + "# Now with Devito we will turn `p` into `TimeData` object \n", + "# to make all the buffer switching implicit\n", + "p = TimeData(name='p', shape=(nx, ny), space_order=2)\n", + "p.data[:] = 0.\n", + "\n", + "# Initialise the source term `b`\n", + "b = DenseData(name='b', shape=(nx, ny))\n", + "b.data[:] = 0.\n", + "b.data[int(nx / 4), int(ny / 4)] = 100\n", + "b.data[int(3 * nx / 4), int(3 * ny / 4)] = -100\n", + "\n", + "# Create Laplace equation base on `p`\n", + "eq = Eq(a * p.laplace, b)\n", + "# Let SymPy solve for the central stencil point\n", + "stencil = solve(eq, p)[0]\n", + "# Let our stencil populate the buffer `p.forward`\n", + "eq_stencil = Eq(p.forward, stencil)\n", + "\n", + "# Create boundary condition expressions\n", + "# Note that we now add an explicit \"t + 1\" for the time dimension.\n", + "bc = [Eq(p.indexed[t + 1, x, 0], 0.)]\n", + "bc += [Eq(p.indexed[t + 1, x, ny-1], 0.)]\n", + "bc += [Eq(p.indexed[t + 1, 0, y], 0.)]\n", + "bc += [Eq(p.indexed[t + 1, nx-1, y], 0.)]\n", + "\n", + "# We can even switch performance logging back on,\n", + "# since we only require a single kernel invocation.\n", + "configuration['log_level'] = 'INFO'\n", + " \n", + "# Create and execute the operator for a number of timesteps\n", + "op = Operator([eq_stencil] + bc, subs={h: dx, a: 1.})\n", + "op(time=nt + 1)\n", + " \n", + "plot_field(p.data[0], xmax=xmax, ymax=ymax, view=(30, 225))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "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": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} From 371d9f5bad5efb2f6be1053cc397f84e42d54a37 Mon Sep 17 00:00:00 2001 From: Michael Lange Date: Sun, 28 May 2017 05:13:37 +0100 Subject: [PATCH 07/12] Acoustic: Notation fix - use `dt**2` instead of `dt * dt` --- examples/seismic/acoustic/operators.py | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/examples/seismic/acoustic/operators.py b/examples/seismic/acoustic/operators.py index f4b7db490f..22909da52c 100644 --- a/examples/seismic/acoustic/operators.py +++ b/examples/seismic/acoustic/operators.py @@ -49,7 +49,7 @@ def ForwardOperator(model, source, receiver, time_order=2, space_order=4, # u[ti + 1, ...] - accesses the forward stencil value ti = u.indices[0] src_term = src.inject(field=u, u_t=ti + 1, offset=model.nbpml, - expr=src * dt * dt / m, p_t=time) + expr=src * dt**2 / m, p_t=time) # Create interpolation expression for receivers rec_term = rec.interpolate(expr=u, u_t=ti, offset=model.nbpml) @@ -95,7 +95,7 @@ def AdjointOperator(model, source, receiver, time_order=2, space_order=4, **kwar # Construct expression to inject receiver values ti = v.indices[0] receivers = rec.inject(field=v, u_t=ti - 1, offset=model.nbpml, - expr=rec * dt * dt / m, p_t=time) + expr=rec * dt**2 / m, p_t=time) # Create interpolation expression for the adjoint-source source_a = srca.interpolate(expr=v, u_t=ti, offset=model.nbpml) From 96918e66563ab17b65c1a5307848e61fa2d60c64 Mon Sep 17 00:00:00 2001 From: Michael Lange Date: Mon, 5 Jun 2017 15:47:01 +0100 Subject: [PATCH 08/12] Docs: Add tutorials to the tutorial section of the docs. --- docs/tutorials.rst | 28 ++++++++++++++++++++++++---- 1 file changed, 24 insertions(+), 4 deletions(-) diff --git a/docs/tutorials.rst b/docs/tutorials.rst index 6f9153b7a5..3881767e98 100644 --- a/docs/tutorials.rst +++ b/docs/tutorials.rst @@ -12,14 +12,34 @@ by checking out our the repository on github_ Computational Fluid Dynamics ---------------------------- -**COMING SOON:** A tutorial series that introduces the core features -of Devito through a set of classic examples from Computational Fluid -Dynamics (CFD). The series is based on the excellent tutorial blog -`CFD Python: 12 steps to Navier-Stokes +A tutorial series that introduces the core features of Devito through +a set of classic examples from Computational Fluid Dynamics (CFD). The +series is based on the excellent tutorial blog `CFD Python: 12 steps +to Navier-Stokes `_ by the Lorena A. Barba Group and focusses on the implementation with Devito rather than pure CFD or finite difference theory. +* `01 - Linear convection + `_ + - Building a linear operator with simple zero BCs. +* `02 - Nonlinear convection + `_ + - Building an operator with coupled equations and simple BCs. +* `03 - Diffusion + `_ + - Building an second-order operator with simple BCs. +* `04 - Burgers' equation + `_ + - Coupled operator with mixed discretizations and simple BCs. +* `05 - Laplace equation + `_ + - Steady-state example with Python convergence loop and Neumann BCs. +* `06 - Poisson equation + `_ + - Pseudo-timestepping example with kernel-driven diffusion loop. + + Seismic Modelling and Inversion ------------------------------- From a67f7a2e5aac8ba41c31ee5e33941d6f94b18345 Mon Sep 17 00:00:00 2001 From: Michael Lange Date: Mon, 5 Jun 2017 15:49:07 +0100 Subject: [PATCH 09/12] Docs: Suppress the no-change-bailout, since it prevents tutorial updates. Did I already mention we might want to check out `doctr`? --- docs/deploy.sh | 7 ++++--- 1 file changed, 4 insertions(+), 3 deletions(-) diff --git a/docs/deploy.sh b/docs/deploy.sh index 53764ee392..008c94639c 100755 --- a/docs/deploy.sh +++ b/docs/deploy.sh @@ -45,9 +45,10 @@ git config user.name "Travis CI" git config user.email "$COMMIT_AUTHOR_EMAIL" # If there are no changes to the compiled out (e.g. this is a README update) then just bail. -if git diff --quiet; then - echo "No changes to the output on this push; exiting." - exit 0 +# NOTE: Disabled since it also suppresses re-compiled tutorial links, etc. +#if git diff --quiet; then +# echo "No changes to the output on this push; exiting." +# exit 0 fi # Commit the "changes", i.e. the new version. From e26fba26a70c9c635bfec6ca35aa8a5fdc473f01 Mon Sep 17 00:00:00 2001 From: Michael Lange Date: Mon, 5 Jun 2017 15:58:28 +0100 Subject: [PATCH 10/12] CFD: Moving the legacy diffusion example to CFD and adding note. --- .travis.yml | 1 - .../{diffusion => cfd}/example_diffusion.py | 11 ++++++- examples/diffusion/README.md | 32 ------------------- 3 files changed, 10 insertions(+), 34 deletions(-) rename examples/{diffusion => cfd}/example_diffusion.py (95%) delete mode 100644 examples/diffusion/README.md diff --git a/.travis.yml b/.travis.yml index e4b1c19ecc..b4119c176c 100644 --- a/.travis.yml +++ b/.travis.yml @@ -55,6 +55,5 @@ script: - python examples/benchmark.py test -P acoustic -a - python examples/seismic/acoustic/acoustic_example.py - py.test -vs examples/seismic/tutorials - - py.test -vs examples/diffusion/example_diffusion.py - py.test -vs examples/cfd - if [[ $DEVITO_ARCH == 'gcc-5' ]]; then ./docs/deploy.sh; fi diff --git a/examples/diffusion/example_diffusion.py b/examples/cfd/example_diffusion.py similarity index 95% rename from examples/diffusion/example_diffusion.py rename to examples/cfd/example_diffusion.py index e18cca20d9..3fab9295db 100644 --- a/examples/diffusion/example_diffusion.py +++ b/examples/cfd/example_diffusion.py @@ -1,7 +1,16 @@ """ +NOTE: This is a legacy example. For more up-to-date examples +please see the tutorials under `examples/cfd/`. + This example encodes multiple ways to solve the 2D diffusion equations using an explicit finite difference scheme with fixed boundary values -and a given initial value for the density. +and a given initial value for the density. The example also includes +demo implementations using more traditional methods, including pure +Python, vectorized NumPy and a vectorized symbolic implementation +using SymPy's `lambdify()` functionality. For a visual demonstration +and comparison between pure Python and NumPy, for example, run: + +python example_diffusion.py run -m python numpy --show """ import time from argparse import ArgumentParser diff --git a/examples/diffusion/README.md b/examples/diffusion/README.md deleted file mode 100644 index 4a2c60e689..0000000000 --- a/examples/diffusion/README.md +++ /dev/null @@ -1,32 +0,0 @@ -# Devito diffusion example - -A simple example demonstrating how to solve the 2D diffusion equation -using Devito's `Operator` API can be found in -`example_diffusion.py`. The example also includes demo implementations -using more traditional methods, including pure Python, vectorized -NumPy and a vectorized symbolic implementation using SymPy's -`lambdify()` functionality. For a visual demonstration and comparison -between pure Python and NumPy, for example, run: -``` -python example_diffusion.py run -m python numpy --show -``` -The above runs highlight the performance gains from using NumPy's -array vectorization, but the baseline test is still fairly small. To -demonstrate Devito's performance in relation to NumPy please run: -``` -python example_diffusion.py run -m numpy devito --spacing 0.001 --timesteps 500 -``` - -### Benchmarking and plotting - -The diffusion example also provides a benchmarking mode that depends -on the [opescibench](https://github.com/opesci/opescibench) utility -package. As an example, on the benchmarking architecture you can run -the following command to generate performance data: -``` -python example_diffusion.py bench -m numpy lambdify devito --spacing 0.001 -t 500 --resultsdir='results' -``` -This will store the generated performance data in a sub-directory `results`, which can then be used to create a comparison plot with: -``` -python example_diffusion.py plot -m numpy lambdify devito --spacing 0.001 -t 500 --resultsdir='results' --plotdir='plots' -``` \ No newline at end of file From bc6d0d6beda66909c16e4dcf4eda5ca28641c7cb Mon Sep 17 00:00:00 2001 From: Michael Lange Date: Mon, 5 Jun 2017 16:18:50 +0100 Subject: [PATCH 11/12] CFD: Add `pyplot.show()` to utility plotting function --- examples/cfd/tools.py | 2 ++ 1 file changed, 2 insertions(+) diff --git a/examples/cfd/tools.py b/examples/cfd/tools.py index b4dc2d904e..c455b35c35 100644 --- a/examples/cfd/tools.py +++ b/examples/cfd/tools.py @@ -32,6 +32,8 @@ def plot_field(field, xmax=2., ymax=2., zmax=None, view=None, linewidth=0): ax.set_xlabel('$x$') ax.set_ylabel('$y$') + pyplot.show() + def init_hat(field, dx, dy, value=2., bgvalue=1.): """Set "hat function" initial condition on an array: From 2a128f9abe8c0e2c326385701669da5d8f79d51d Mon Sep 17 00:00:00 2001 From: Michael Lange Date: Wed, 7 Jun 2017 05:13:02 +0100 Subject: [PATCH 12/12] CFD: Fixing typos, comments and other small fixes across tutorials --- examples/cfd/test_01_convection.ipynb | 31 ++++++++++--------- .../cfd/test_02_convection_nonlinear.ipynb | 8 ++--- examples/cfd/test_03_diffusion.ipynb | 2 +- examples/cfd/test_04_burgers.ipynb | 12 ++++--- examples/cfd/test_05_laplace.ipynb | 2 +- 5 files changed, 31 insertions(+), 24 deletions(-) diff --git a/examples/cfd/test_01_convection.ipynb b/examples/cfd/test_01_convection.ipynb index cdab463777..309af2c4de 100644 --- a/examples/cfd/test_01_convection.ipynb +++ b/examples/cfd/test_01_convection.ipynb @@ -71,7 +71,7 @@ "data": { "image/png": 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NBn0YocVA1yJJkkLVz1X0WS0UCvr6uFrtuaIa6GphkCMKDjsh2BPnIHOBdpZW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\n+QjPTeQHBjrylnHTxcaNG9Hf3w9N0zBjxgx9JO/II48cM7J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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -98,14 +98,15 @@ "cell_type": "code", "execution_count": 3, "metadata": { - "collapsed": false + "collapsed": false, + "scrolled": true }, "outputs": [ { "data": { "image/png": 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Q6XTgOA7W19c9pwyIhsjndBX4zJlfnPl+y1rP/TW3rTq2rbrv43zO3pbVhIFk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\nC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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -156,7 +157,7 @@ "* They behave symbolically like `sympy.Function` objects, so that we can construct derivatives and use them in symbolic expressions, thus inheriting all the power of automated symbolic manipulation that SymPy provides.\n", "* They act as containers for user data by providing a `.data` property that wraps automatically allocated memory space in a neat NumPy array.\n", "\n", - "The particular `TimeData` type that we will declare our variable $u$ as in this case is aware of the fact that we will want to implement a timestepping algorithm with it. So the object `u` it will declare two buffers of shape `(nx, ny)` for us and present them as `u.data[0]` and `u.data[1]`. Let's fill the initial buffer with some data and look at it:" + "The particular `TimeData` type that we will declare our variable $u$ as in this case is aware of the fact that we will want to implement a timestepping algorithm with it. So the object `u` will declare two buffers of shape `(nx, ny)` for us and present them as `u.data[0]` and `u.data[1]`. Let's fill the initial buffer with some data and look at it:" ] }, { @@ -170,7 +171,7 @@ "data": { "image/png": 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NBn0YocVA1yJJkkLVz1X0WS0UCvr6uFrtuaIa6GphkCMKDjsh2BPnIHOBdpZW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\n+QjPTeQHBjrylnHTxcaNG9Hf3w9N0zBjxgx9JO/II48cM7J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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -280,12 +281,12 @@ " avoid_denormals [elapsed: 0.00] >>\n", " loop_fission [elapsed: 0.00] >>\n", " create_elemental_functions [elapsed: 0.00] >>\n", - " loop_blocking [elapsed: 0.02] >>\n", - " simdize [elapsed: 1.10]\n", - " [Total elapsed: 1.13 s]\n", - "CustomCompiler: compiled /tmp/devito-1000/6aaf870464b3b177e4afd85a712be00325a70519.c [0.23 s]\n", + " loop_blocking [elapsed: 0.03] >>\n", + " simdize [elapsed: 1.16]\n", + " [Total elapsed: 1.20 s]\n", + "CustomCompiler: compiled /tmp/devito-1000/6aaf870464b3b177e4afd85a712be00325a70519.c [0.64 s]\n", "=========================================================================================\n", - "Section main<101,80,80> with OI=0.49 computed in 0.000 s [Perf: 6.06 GFlops/s]\n", + "Section main<101,80,80> with OI=0.49 computed in 0.001 s [Perf: 4.54 GFlops/s]\n", "=========================================================================================\n" ] }, @@ -293,7 +294,7 @@ "data": { "image/png": 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XcM0119ifuf/++/GDH/wATz75JL72ta/hN3/zN/Hwww9nd8AJIUFHxCZMxirrLZpGS6oy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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -304,7 +305,9 @@ "from sympy.abc import h, s\n", "from devito import Operator, time\n", "\n", - "# Reset our initial condition in both buffers\n", + "# Reset our initial condition in both buffers.\n", + "# This is required to avoid 0s propagating into\n", + "# our solution, which has a background value of 1.\n", "init_hat(field=u.data[0], dx=dx, dy=dy, value=2.)\n", "init_hat(field=u.data[1], dx=dx, dy=dy, value=2.)\n", "\n", @@ -352,7 +355,7 @@ "=========================================================================================\n", "Section loop_y_1<101,81> with OI=0.00 computed in 0.000 s [Perf: 0.00 GFlops/s]\n", "Section loop_x_2<101,81> with OI=0.00 computed in 0.000 s [Perf: 0.00 GFlops/s]\n", - "Section main<101,80,80> with OI=0.61 computed in 0.001 s [Perf: 5.87 GFlops/s]\n", + "Section main<101,80,80> with OI=0.61 computed in 0.001 s [Perf: 5.33 GFlops/s]\n", "=========================================================================================\n" ] }, @@ -360,7 +363,7 @@ "data": { "image/png": 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rVwTiqw6B4MUcC9wcj8fo9/uoVqtYW1tDs9kshZgDshFGmqah1+uh1+tBUZRM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\nOg9BQwXm/2QAAAAASUVORK5CYII=\n", "text/plain": [ - "" + "" ] }, "metadata": {}, diff --git a/examples/cfd/test_02_convection_nonlinear.ipynb b/examples/cfd/test_02_convection_nonlinear.ipynb index c35ce5d428..5e0164e455 100644 --- a/examples/cfd/test_02_convection_nonlinear.ipynb +++ b/examples/cfd/test_02_convection_nonlinear.ipynb @@ -6,7 +6,7 @@ "source": [ "### Example 2: Nonlinear convection in 2D\n", "\n", - "Following the initial convection tutorial with a single steat variable $u$, we will now look at non-linear convection (step 6 in the original). This brings one new crucial challenge: computing a pair of coupled equations and thus updating two time-dependent variables $u$ and $v$.\n", + "Following the initial convection tutorial with a single state variable $u$, we will now look at non-linear convection (step 6 in the original). This brings one new crucial challenge: computing a pair of coupled equations and thus updating two time-dependent variables $u$ and $v$.\n", "\n", "The full set of coupled equations is now\n", "\n", @@ -21,7 +21,7 @@ "$$v_{i,j}^{n+1} = v_{i,j}^n - u_{i,j} \\frac{\\Delta t}{\\Delta x} (v_{i,j}^n-v_{i-1,j}^n) - v_{i,j}^n \\frac{\\Delta t}{\\Delta y} (v_{i,j}^n-v_{i,j-1}^n)$$\n", "\n", "So, for starters we will re-create the original example run in pure NumPy array notation, before demonstrating \n", - "the Devito version. LEt's start again with some utilities and parameters:" + "the Devito version. Let's start again with some utilities and parameters:" ] }, { @@ -138,7 +138,7 @@ "source": [ "Excellent, we gain get a wave that resembles the one from the oiginal examples.\n", "\n", - "Now we can set up our coupled problem in Devito. Let's start by creating two initial state variables $u$ and $v$, as before, and intialising them our \"hat function." + "Now we can set up our coupled problem in Devito. Let's start by creating two initial state variables $u$ and $v$, as before, and intialising them with our \"hat function." ] }, { @@ -176,7 +176,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Using the tow `TimeData` objects we can again derive our dicretized equation, rearrange for the forward stenicl point in time and define our variable update expression - only we have to do everything twice now! We again use foward differences for time via `u.dt` and backward differnces in space via `u.dxl` and `u.dyl` to match the original tutorial." + "Using the tow `TimeData` objects we can again derive our dicretized equation, rearrange for the forward stencil point in time and define our variable update expression - only we have to do everything twice now! We again use foward differences for time via `u.dt` and backward differnces in space via `u.dxl` and `u.dyl` to match the original tutorial." ] }, { diff --git a/examples/cfd/test_03_diffusion.ipynb b/examples/cfd/test_03_diffusion.ipynb index 37cf0b76f6..f1008980c2 100644 --- a/examples/cfd/test_03_diffusion.ipynb +++ b/examples/cfd/test_03_diffusion.ipynb @@ -148,7 +148,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Excellent. Now for the Devito part we need to note one important detail to our previous examples: we noe have a second-order derivative. So, when creating our `TimeData` object we need to tell it about our spatial discretisation by setting `space_order=2`. Only then can we use the shorthand notation `u.dx2` and `u.dx2` to denote second derivatives." + "Excellent. Now for the Devito part we need to note one important detail to our previous examples: we now have a second-order derivative. So, when creating our `TimeData` object we need to tell it about our spatial discretisation by setting `space_order=2`. Only then can we use the shorthand notation `u.dx2` and `u.dx2` to denote second derivatives." ] }, { diff --git a/examples/cfd/test_04_burgers.ipynb b/examples/cfd/test_04_burgers.ipynb index 54df4ed96d..a584f9604d 100644 --- a/examples/cfd/test_04_burgers.ipynb +++ b/examples/cfd/test_04_burgers.ipynb @@ -14,11 +14,15 @@ "$$ \\frac{\\partial v}{\\partial t} + u \\frac{\\partial v}{\\partial x} + v \\frac{\\partial v}{\\partial y} = \\nu \\; \\left(\\frac{\\partial ^2 v}{\\partial x^2} + \\frac{\\partial ^2 v}{\\partial y^2}\\right)$$\n", "\n", "The discretized and rearranged form then looks like this:\n", - "$$u_{i,j}^{n+1} = u_{i,j}^n - \\frac{\\Delta t}{\\Delta x} u_{i,j}^n (u_{i,j}^n - u_{i-1,j}^n) - \\frac{\\Delta t}{\\Delta y} v_{i,j}^n (u_{i,j}^n - u_{i,j-1}^n)+ $$\n", - "$$ \\frac{\\nu \\Delta t}{\\Delta x^2}(u_{i+1,j}^n-2u_{i,j}^n+u_{i-1,j}^n) + \\frac{\\nu \\Delta t}{\\Delta y^2} (u_{i,j+1}^n - 2u_{i,j}^n + u_{i,j+1}^n)$$ \n", + "\\begin{aligned}\n", + "u_{i,j}^{n+1} &= u_{i,j}^n - \\frac{\\Delta t}{\\Delta x} u_{i,j}^n (u_{i,j}^n - u_{i-1,j}^n) - \\frac{\\Delta t}{\\Delta y} v_{i,j}^n (u_{i,j}^n - u_{i,j-1}^n) \\\\\n", + "&+ \\frac{\\nu \\Delta t}{\\Delta x^2}(u_{i+1,j}^n-2u_{i,j}^n+u_{i-1,j}^n) + \\frac{\\nu \\Delta t}{\\Delta y^2} (u_{i,j+1}^n - 2u_{i,j}^n + u_{i,j+1}^n)\n", + "\\end{aligned}\n", "\n", - "$$v_{i,j}^{n+1} = v_{i,j}^n - \\frac{\\Delta t}{\\Delta x} u_{i,j}^n (v_{i,j}^n - v_{i-1,j}^n) - \\frac{\\Delta t}{\\Delta y} v_{i,j}^n (v_{i,j}^n - v_{i,j-1}^n)+ $$\n", - "$$ \\frac{\\nu \\Delta t}{\\Delta x^2}(v_{i+1,j}^n-2v_{i,j}^n+v_{i-1,j}^n) + \\frac{\\nu \\Delta t}{\\Delta y^2} (v_{i,j+1}^n - 2v_{i,j}^n + v_{i,j+1}^n)$$\n", + "\\begin{aligned}\n", + "v_{i,j}^{n+1} &= v_{i,j}^n - \\frac{\\Delta t}{\\Delta x} u_{i,j}^n (v_{i,j}^n - v_{i-1,j}^n) - \\frac{\\Delta t}{\\Delta y} v_{i,j}^n (v_{i,j}^n - v_{i,j-1}^n) \\\\\n", + "&+ \\frac{\\nu \\Delta t}{\\Delta x^2}(v_{i+1,j}^n-2v_{i,j}^n+v_{i-1,j}^n) + \\frac{\\nu \\Delta t}{\\Delta y^2} (v_{i,j+1}^n - 2v_{i,j}^n + v_{i,j+1}^n)\n", + "\\end{aligned}\n", "\n", "Great. Now before we look at the Devito implementation, let's re-create the NumPy-based implementation form the original." ] diff --git a/examples/cfd/test_05_laplace.ipynb b/examples/cfd/test_05_laplace.ipynb index f074ed70ad..50385d3d08 100644 --- a/examples/cfd/test_05_laplace.ipynb +++ b/examples/cfd/test_05_laplace.ipynb @@ -11,7 +11,7 @@ "First, we again define our governing equation:\n", "$$\\frac{\\partial ^2 p}{\\partial x^2} + \\frac{\\partial ^2 p}{\\partial y^2} = 0$$\n", "\n", - "And in a discretised form, rearranged to update the state of $p$:\n", + "We are again discretizing second-order derivatives using a central difference scheme to construct a diffusion problem (see tutorial 3). This time we have no time-dependent term in our equation though, since there is no term $p_{i,j}^{n+1}$. This means that we are simply updating our field variable $p$ over and over again, until we have reached an equilibrium state. In a discretised form, after rearranging to update the central point $p_{i,j}^n$ we have\n", "$$p_{i,j}^n = \\frac{\\Delta y^2(p_{i+1,j}^n+p_{i-1,j}^n)+\\Delta x^2(p_{i,j+1}^n + p_{i,j-1}^n)}{2(\\Delta x^2 + \\Delta y^2)}$$\n", "\n", "And, as always, we first re-create the original implementation to see what we are aiming for. Here we initialise the field $p$ to $0$ and apply the following bounday conditions:\n",