{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Visualising complex functions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### One-dimensional functions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider a \"normal\" plot of $\\sin(t)$:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import sympy\n", "sympy.init_printing()\n", "\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "t = sympy.Symbol('t')" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sympy.plot(sympy.sin(t))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This allows us to see exactly what the of $\\sin(t)$ is for every value of $t$. To do this, we need two dimensions: one for the value of $t$ and one for $\\sin(t)$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we want to plot a function of two variables we start needing three dimensions. The following plot shows a \"fake\" 3d plot. It's fake because in fact there are only two dimensions available on your computer screen. So we're already in a bit of trouble when trying to visualise the relationships represented by higher dimensional functions." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "x, y = sympy.symbols('x, y')" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "f2 = sympy.sin(x) + sympy.cos(y)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sympy.plotting.plot3d(f2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can make up for some of this lack by using colors to represent another axis." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "import numpy\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "f2numeric = sympy.lambdify((x, y), f2, 'numpy')" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "xx, yy = numpy.mgrid[-10:10:0.1, -10:10:0.1]" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "zz = f2numeric(xx, yy)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.pcolor(xx, yy, zz)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For transfer functions, we have an even bigger challenge, because we have two input variables (the real and imaginary part of $s$) and two output variables (the real and imaginary part of $G(s)$). One solution to the problem is to use colors for $\\angle G(s)$ and brightness for $|G(s)|$. This is known as [domain colouring](https://en.wikipedia.org/wiki/Domain_coloring) and is supplied by `mpmath.cplot`." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "try:\n", " import mpmath\n", "except:\n", " from sympy import mpmath" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "s = sympy.Symbol('s')\n", "\n", "G = 1/(s**2 + s + 1)\n", "Gnumeric = sympy.lambdify(s, G)\n", "mpmath.cplot(Gnumeric)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can get a smoother result by plotting with more points" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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5hsEnEpdwsbLsoWQYF5RpiBiojmAXXPnhumQtnoHkRXD5ZcxmHvmpuibZOYJp788jw4uiOa1mGl44rRdOlsJpCKaBQOCMsVfMAwxgZQZqGSZoZISe4/rd2zDIO5TZs0jTSvFKLxnC044J1/a31j40AWWIzEL8cxwl5iFjJ52YG2maZyATTmPIDKo20SrzaLAVfdc9pzC/2A2oNY0Tx0ROlF1kXHCMQzWNC9LHC/I8F7hkGcO1spbSKWxsA6EppuGX1wPGzO8cvXqMozTVlmmcGIKyCuefD6De5sqZaJu6RstUOx/BPAKBwFbYL+aB0pjQwkKGBWUJU05jwzUVeStXRkcauyp86cqedhzKUmg+03VeaZmhxmQ3MahF2Wd1JDuhY6ljflJlHIuSeVCPgViQv5jBPFKNzkI4v9gNMMxDCqvWcewsJuY+F7jNOC56JiIv8pCtXjLgAKVVxTOPpRGp8iZAA2rGQUW6LestJlMb/ACAnuVbMwy1jsxnHj3tY2in/P0H7SM0j0AgcMbYL+ahmocMw629bVKaDpDyhDoSNF3aPdPo6CPFfjSpLBV1Tl0by0UZB6wLe5txVNYYwAxVJUtS5qEL5tZW8xA9hDRNw0VHAylOm3MXm1hb/BJ8v3nPiXn7J2pdUQeWtXSx1DUumuYvyj0vSrMXU5mSiSTLihHFDp0O4hmIP1EOaJ03q2HJOFqbGPc3My5RWk7ajEN/r2wdmWYePe1juOeYDXIawTwCgcBW2D/mcYrKz8PCq9fZMiOhPrGZ0/rvbu1TMYT2tqo5eGtLl4FY5rEo2YrqIfWiOvNcSSBxfUwayBBeXxyZSjK+LsRW4RfRJQaiC+UaSwxTJ5ytIU3qbZWScaSFcF7XODWV1LpyLHlHQ56yiIst5iFpl6SZi+ysLcmXo4wDwIHTQfKiN2rGiydPDKTUOlp+Hp5ppI2kuNQz2paTXp4P6+X19V/zmIepYyfECM0jEAicOXb28SCiZxLRbxDR+4jovUT06l31JRAIbI5dTltOAbyGme8notsAvJ2I3sLMfzRWiVZUr+uyTMv7O1VbVohIaeYgS3kLaSog6T0B1V57s66fvnhh1eapRpic0KrpS65TmW91+qLTloVOo/LLONEpDMm0ZaHmXBFSq8V11nXZXaQOHBT3bwqm657LubR1bOq46YpOJy7K+7ok8Uum+UvQNHUKG9L99CW7ouf3mBfCyTQliaD9aUu9K1hbKC3Pm5W/M2d25SR66pk8/WlLbZJ1AndjP9Ip4bRpqnW7qM/FzpgHM3+Ume+X60cAvA/AM3bVn0AgsBkeF4IpET0bwFcA+IPRgl4wrb2qu6ykGiAbVkk16x4clEW8+7pN84KpZysrNeWaz3RlxnXmXBVUC8cy79Kelbihr4mB5DorcRxbL65LnTYDSSbbhWUe5QujDvNg+yK9O7ouZkuiqFQ6MubC6/Ksx8omhvhlGQUvy/NeNrdRFuLFVGUg2S1dGUhGdgoTE62M4ksumceiJZhqXuV6ro5euU4WRE+LMLOKaeZRC6Z9h6++ibbPPNgxj71bGEdEtwL4BQDfwcwPN/LvJaI/JKI/vHp9/oMFAoGzxU6ZBw3rx38BwBuY+Y2tMsx8H4D7AODpT1oyrWpHsI00jxk6Sdq1WpmIUIJC89Cwo3kcuLi1Tp66tLQRzaJkKS3HssRAvOnWhUDWQa4K88BCxuikhaj2oQzEnI27cPPfDvMozvnQKsnVfCjE6hR2JGWPjJYjzOOyjOZXhDVclvwUmndxKTmHqTl3yLzgNJBsjs2VD5y2kc63dWbXluaRl9kL80jWV3UFz+8vX8tu9+5g3b4ZNl/X5le/lYKpw22GMe4ItqfMg4Zlmz8J4H3M/IO76kcgENgOu2QeLwTwSgDvJqJ3Str3MPObRmudIn/y9CNpPoF9zYOKOk2Xdk1wcQ0PGweY9nZlXyXrB4oQyFsVKvM4UeXfO5ZZnSTpI6UeQi60dCW5rguLOFpck7LKQJSRiAayMMwjua5LkG6gjmdDUGgefutA0THouoxwEvK13MeL8sKuyI2uyLu4RZrwDASwzmFDqMv180I5fZ9qwbHMw7ujq8PekL6UEXzRZB6aJhsxOXbByEsDPNPwjCMtTuQ5mseUBWUsr8UuUFx7q8tc7Ozjwcy/i9rFPxAI7AkeF9aW2eBhWp5GW2UIi7IMgOrD2zum1V6n9rSsW4Bn6yQF4LBMUOtKzxpjr0+FRRzqsnoJDyQ8NM91KGUPEgORUNep6SK7xrpwTgxk0DpWy2tSSUO1xhybB1Tm4V9yyTyKE+9XJeNgZRzXyvDgKI+yt8r4kcMBV+QdXZHfoPTzGHAxWVeKnlXhgXn3B+wYh3cxV+uYPa5P/oiUaayFYSSLiWpHbJibs7b0rCxjG/tMaR5jG/vMsbbU/h3hnh4IBM4Be8c8Cs1DP5jFirUhyJaYUutoah6epRy0yxYOmK69hQxzykS8j0iLeXhLzEkVN56RjpXksLTQLMy78DrIWvI+s3h0yF/KGK4MZHk9V07L+fWlKNVQXxFdBJdfZNq0WBgHXZOR8qqMlI8O8dvMbPU2mfvfJlVvQRmqleWSYTgXXajbDh4mXw1hdCjjQItxqLeo+moM4dpYTjLTKEM4Hw5qWFu8l6hnGrX2MV/raG1m7K0ubV8OdNKCeQQCgXNAfDwCgcBW2O9pixNOAUPVpwTTBuPzYmo1nWlMW3JdKuLqCX4oodXf1M39tDN9USH1xHzak+OTpF1wYqsXUgFgqbvLO//q9XLo/CNLcehdXpZyt+fKyYyrruv6ALo3iETNeSrJJKvTlEekMw8PbdwuL+EJRhzUO94m7amJ9or8CGqivWR+ZBVI1T09uaGrs51McbwDGJDNtwsVwyV9naYgg2hMZkc24nKaotMWP12xu4H1hNGpacxQxk89phe5TZtmW5aCsSnNNIJ5BAKBrbBXzIO8qdazDKBaP10xjYZnr9m4UuqQi7u2bDvJrCvpHZF1abbCWjg2kk23EjZc2pWFKAM5TgxEwqWGRmSVtAPd/GtZPtdqOYyy1w4+KwVuS3Vp+ZikiSt7Yh7yIBo1i9zwmIymwjTos0PnLh8PhZ8olZ5onut2eU9qor1F8nQhnF8EB9jzWnThW8k0siPYkG6Zh2caaxxJurIJL4q28tqMg4x7PycBtBRO/W7mdXrOmzK3jptqW2Kojec06yRGIZgGAoGzxl4xj57mUbinKytJB81Khmcc1qTpmYVjLUkzaOokVORVx8I6hzObthQGclEG80oLMc+VNhd3esiRhJck/aKpczGxEtFHdCd51UIk/vHDRwAAxwefypUP7pQyV4dQz3wR5qEDK181ptrPyij7qSG88MgQPlny75JnuMMMbqp13MqqcUiYdkjXZfe50mEyzZaah56jcuCWzK8Mi1gnTUNCllDTnZ4xlC2dwLzWQZVDWF/b6DIQS2vZM4spBzCTp5S3WijX8HRMDMbmBfMIBAJnjP1jHieorS1jB2YkJtKJA3mKqYxDQ00/cHF77ZmGHg/rNZFGXc9ODoWBXJKJvt0CQC0wqoso8ziWdNVArph3cU0YxmV5nssSvyTPc0HME0vp8wOHD6a6LJaXQxo2dzvA4Eimi8PW4ld2+pncyZOPDw3Rg0Mnni5lnyJF7pRB7XbzXMo4rsiIedkxjXzurGEeiWFImHYzH7ASFpH1jLyjfGYYJdPohUCLaTito3IIaziDOcuJj48tWOszkDmWk17cXoe1JRAInCP2i3kAgLW26AjWYB6VRUZH+WUZB5AZhz+gpcNAivamQhEwRpnHiprph2Y12CVxeFDpxLu0ZyaS66geck3CWzVcluEtB8pQshD0AH106IOEF2mwyCzlBa/EQHP00TySnQxFcY+0c7cslLtL5t+3y8h2qxnhrkh7l9N5s7KhT/LhWEtol9Wrj8ZQZiXMYg1Z4KeMgyTkvOCvYhxJ+yh9OKjQL8a3Emz6anROd+sxkPb2gF7baC1kQ1G2zzTG3NND8wgEAueI/WIe4ufhjx+wu4L47fkqXWRVpgOGjSzKeJVu2YNaLHQw8sesa7pqILauP/GgEy7MajqtfyBs5LKuWZf2ExMxxzVki8yQdiTPo1rIY9LXuyR8MuU/h7tlAdyH6YMAgAv05wCAi/Iij/58GKGOP5if6/PEevRk6esTV0N7yjhuEXHnsjm1/qKkXWT1EpUwbSGoLz9rEKc8CC4rYRoLGkJmxzycvjFce03Dh6cuNJqGWpy4tK5QYgi15tHTNvp6Rra8ZNbCrm7NIrjLMFrsAiN5wTwCgcAZY++YR2FtkUG2sLZ4VuLZSctCs3Rp3ktVGchpXSdZYpQ1HLhQ65jD65NFRkN3iH1qqz7wPoWaJ8tScOmKdMecM5A8Vp2FxltqrsvDXDV/DleF0jxKA9V5aPF+AMBKbrB8/9DJOy/l0e9WOczpivTtijzHJXFYuaDswoxZep29QsWqJGzhFIOfyUqsPQCwEMbBLsxMwzOP2lsUHW9RHw7t+y0Fe6yiXp/CjpXUTKOlRZQMo7+sPrMEz0ZqJtJnHtTMm0Ywj0AgsBXi4xEIBLbC/k1bjGDaNNX66UlvumIF0xWNl/HTGhhR9dTFNTwoXcDJvumTsgz89EUPdDOL6VLaUS+U+5nNwC7LdlyHEvr9VnVv01N5sJV5KeoMprua3/HQQLsX//E1AID16rsAAJ+hO1Kdq+qpn7YHkIVqMm2hxlil05MTPCbxISSSnd5FHCXkByNvkq2mKzo1qZfXgzvTFPkhs8nWTkFWzbBe5FabW734WU9n/DQD8NOSusy02ZWSm/r0tIUbaXMQzCMQCGyF/WMeJ4ZNjDCPipX0hNSRvB4DaaZNhJZ5JAH2sMxTdpG2/c5e1XkPngslw1B2IgM1yDiW0WNSVkTVhWwIeijxC5qezv41Apyc7kafGjrFfzwsnlt9RG588j8BALcdf0mqcyvfJc0oZRJXdhmZj0X0PKEsfiZmkZiGsgofGhdzpVvJ+UvD8b1Gy7y2CDp2glvvzNja7GrLzNuch2aYXaliClNm17HQIky1gUDgHLF/zMOaSxtOYvCsxJtzPTMx7fgytas7VXWwbMdTHc9EYJiGZyWaLgvWyJhdyR1GQhc6odVJLrq0Cy60x8cD+aQ3IG3sg0/KIrM/k7YeHh6M138yJBybH2T1pCFk3fvc/3mVWgTQ0it8WDt6obeoTbUNbpthh+v2Jj39M1LqNNUxqLt03rKEtrbRN8Pa66mFa9swj1b9zUy0imAegUBgK+wd86ATdNkF0NBDpkKgdjqbcjQDqoV3FdPw+onVS7zzmWMgLQtNleYdzRwjsWm+rP7qam1hOXuFTszI9pgs+npIHvrjknddmcfHh/jKPNjpoItgPTAP5uGG7HZkooI+9pbEewev2tFr2sGrtpzUJ9C33cap4fBVaxtek7gRd/Ha4avn6FXnt9sZT++VDc0jEAicMWYzDyJ6PoC/C+DpAK4BeA+AtzLzQ2fUtxrqnt5iD3BpnkWMMY9eXs9SM6eM11FalpqeLtLQSeBZifMngWMVxbWGnhUp1jIqGubBctobPSztf1ZGXdnMGCxr8tf5hrwSS8xazDhr51iSb2iuvdXDsYbGObC9E+i9VaRmF/benmH0NtwB+uxhzMV8ngZxIyzCblbcuhpvq1f2JjIPIvrnRHQ/gNdhOEbj/QA+AeArAbyFiH6aiD5v9h0DgcDnBOYwj1sAvJCZr7Uyieh5AL4IwIdvZsea6DAPKsQIF7r0ionYyynW0mIenTJd3QSY3Dag0k/stWcPnom0tJWOdpPGGD1v1hzgpEcq8FUZxR+TMokADJ6gvDYPthb/i7WYd3gp9/FjlJ3ft5lAzRqsTtIuS5WnZ3+5u98g2G+4M49F9Pwvcpmch07ZPiNQL9HsfrMpixiL9/LmM4/Jjwcz/xgAENEzmfkvbB4R3c3M75x9t0Ag8DmDTQTTDxLRfyWiKybtTTe7Q4FAYD+wian23QB+B8DvENE/ZuY/RVuyPDt4J7Gxu09MXzYp25rqdNv1AupY3SnX+ZY5uSfENqdHI+1Z6BqqtZlOnKqIOlTi65KnW7qLG3nBcte6o5f+WU3dODfQn2rUptMUfO+HAAAgAElEQVS+uDnuAt5Om+OQ1Z4CbDIF2Wxa0Zs69OtQSplbd25eH5swD2bm/wzg2wH8ChF9/dZ3FRDRy4jo/UT0ASL67htpKxAInC82YR4EAMz8v4noJQD+G4AvGa8y0hjREsCPAfgaAA8AeBsR/TIz/1G3kgqmzZ6N9Xpm+hRLmVGHlKZU6XWd2Q5tY3k9pjOn3VEhTpmGiqko47pQzZhQs9dZo7n2jRuFN2ECm5lD22llJ+ul7BbbiJJzhcsbZQZTZeaO82fjJPa1qXnmjwJ4MYCXbVDf4wUAPsDMf8bMxwB+DsA33EB7gUDgHDHJPIjomwH8rHwwEpj5FMBvE9EXAHgaM//uhvd+BgBrvXkAwN8erbEN85iDmfVpTrmbUWYkv+rDJqzLxdnnN8y86cDXxFpU85CFasUI7ReV6aY56Y6NTm4+MlMjbV4bm5Tp50/rC9vc7/FS9yaaagHcBeAdRPR2AG8H8CCASwC+EMCLAHwSwDZ6RevPvia6RPcCuBcAnjDrf28gEDgPzPHz+BEi+lEM05QXAvhyDO7p7wPwSmbe1jnsAQDPNPF7APxl4/73AbgPAJ6xPOB6HTlwXqIHm3jrqoyPtbXN6j1yfbhx0YPmjDLVYbtC/WRToqbbvW/CX9yg5NHdWW8qnMobSzdplVTUi88tM5Y+lTe3zFxCscH4PEswZeYVgLfIv5uFtwH4IiJ6DoCPAPhGAN90E9sPBAJniE0Wxj0HwL8C8Gxbj5lfsc2NmfmUiL4NwK9jGL/+CzO/d6IXKJnHOTl6jI7qZZzV4uBMKdxkETfg6NHdjcgO/zMdPdTCQGZ494fHpH0PhYFclDpm20PIJkbQxXrqhk8jw17PNcOHN+Dm0ZJleuyFNWPazWOaxYzl3Vw3j83r9vJuNvMQ/CKAnwTwK6i3NNoKzPwmhJdqILCX2OTjcZ2Z/9OZ9WQWCEOXe0wBI3ljLGK8jLKG8uiAuY4XcxjBFKuw136xmV9vn+twl5X4Z9djAszwvhA/jsVwYls+dkIYiDAOvs2MI1fEh+KiLKrrbQHQYgJtQ00KuV4X19+zeGx1/RTD2cCtpDpKdkxbmWhrtMxUOhpuKXO1lqm8EWzy8fgRIvpeAG+G2debme/f7taBQGCfscnH48sAvBKD1cV+c198szsVCAQe/9jk4/EPAXy+eIPuCCqYummFoV004fOdpyDW1cinlYImVVMQ2257msIjU5AsqpZ53AmH6962YAeSf+jK2bz2VmLZhCpjwcJ44C3kHJXlwxJXk+2jQ3iLTFGeaN7j7fJDXJbn0l3gF44XW7Or266DXdg4eqWayqRwVYatjcTS4j839eGxqY6fyrg4j0x1vDA7aWYuyrr3tsmUp1dnquwGgukm7unvAnDHZKlAIPBXApswj6cC+GMiehtKzWMrU+12aDOPMceoHqtom0F74uf2plOeJX6WLKIO8zV7psF+a3SzfToOO6FbMr+omQctH5OioowuZU/RxaeH+z5B6jzF7DJ+5zCU8S2Sd+ja15G53jy9DtX7/UTatMfNejbSCdlvbWqvPUu5iabhIq/HWnpMpFW3a1YeqTOV3it7Rqba792gbCAQ+BzH7I8HM//WWXZkHgiMQ/NxrBlBn2mMuXGX7KE2zdbmVk5ll824ZyLc2ArdM46KVRiHuDrtgsR9eNHU0euLRRmtS9JW3m/VUIIDOa3+8DapIvuDLj42xJ8qQ+mzsgTGT5Kh7BYpe6DvUaAHutWHv4GPOqE/jtak8cl4WDEQoDb9eiaiOkahk7i0DhPhMZ2kZ9Zt7FfU1UXWrugWbKVAK+9mMg8ieqRzawLAzHz7/NsFAoHPFcxZGHfbeXRkHnpOYmPOW202YXf0VpaSrSueiUjImT1QtQ9gW8eo9Qyb5y0kpY7BZJlHyRo4sQkNLxVhmSbnqHRD3WbdjBFLGfovfAoAsLhF+nj4waHoXxuG97XdDuoudV1Xt3RJ1xH7mgsB6J78KbzeCY9yHThWwk4fgWcidr8iZSXeYjNioanZCZd1GpqHt954i0zlYLaFXrIV89jEKW0CcWJcIBDYCvt1Vq1YW2pdo2YefR+N+e7iuY2Wn/XUMW+lxYQL5uHzlIH44+vNkffKOFiYBpVMQ9lFZhkAy2n1TEO4lvgRDW1clzZPpc8rM99diBBy5cKzAQB33PYFQ/pd7xna+rqBkTxyRzaDXJUNkNeyy1B6EzJCk+oWR3mI48c05DLeYSTDtdRXNpLalXyvrVhLjddBeuEI8/Bu8BUDsdczw+aeSj1/kg1c6DdiK8CZ+XkEAoFAwh4yjwP0rSJaBqjZQ0/XyFqG6hg146hPPsu6xUE7LscPMNXMw2sb6qPhLSZsfDa8plExDr4i97sl1bkm93lE7p1dKYYh61jC63Lq29V1Hnauymj0qIQPLe8EAKx+4AeGN3L6LwEAd5rjGm6VIeyKtHtFJvaXZIS8oO4f9k3IIx7Iq1W3ksRE9PA5q5NomtdFpK2kj8iNkhYyPLykSZiYCLu4uV9PH/Feqg3fEHYbSE9pIcV1bwFe60SJiqVw0b4Pi2sbBvMIBAJnjfh4BAKBrbCH0xbrnl5OX4YS8/bKKE215bSkN12h4nX5Mt7RqxRDMeLw1XP0smbXtVyThAsM05RTqPg59OPEcFmdnhy58JqEjwkfflgo9acNVX9QaP2HRZy88MVD2YsnQ8YRfzEA4NhsYft5Mid4sqiOTxSufrtQd/Vav2woumz9kcJD6X6azuhrNl7368My1Nlfmr4cuHTrYObc4CsHs5ZjmV7rz+8dzRou7X5qM+Vg1pq2TE5XGvu6VtOgWQvwXN2ZCOYRCAS2wt4xD8aBYRe1qVaXuxPNN7uq2JkdyJYuvWQXw30kTQRRcuZXvwitFD+nGMcQrjkzD6JBGD2RutfkOU9kOf2J9P3Y+EgfSd41SbsqO4U9KnUfln1KPyV1P3aan+8BGa0PnzuEF581hEthESsMCUf8nFTnE7Iv1D0yJN8tI/NdEt6+GureakboK9Le5cRAhOkoA0lr7PKweCDWaHn1WC9FHJSfNjEPFwKZhaQ0b1lvbAFQiaraf71fSzD1AulcJgLU2wZ0BNQ55t2uw1krLwTTQCBwHtgz5gEAB/Ab7ZSm2vZmPH1dw9RJJtu2nlHWGdc4/JL5lqs5V45fpdZxYn6eazIknMowodrGcQpV1yBTRxiHhI9K+LAMgw/Jc39ChtYHjJcYP2141sOnDfHjJwz3yavrnyD9eVqqc8LD9f9b/elwfxmpH5NR9k4Jbzej361yfcXpIaqBKAO5YEZZ1UV0k/YDMd0ulAmksGQkZZ4rc+LST+o66ec/dekNxzJelSZaz1Iq1jLiYMYubJpq5+oj9r9Ki5UE8wgEAmeNPWMeam0Zs5z0rCttXWNI6y1qKxlHy8WcKsbRdjkvNY+21qFMQ/2hVtZyIsPOibiNn8gQcSSu4EeSfs0yDxnWHpW8R6TsZ6TIp6T5j0v89MlmKHvq0Jf1HUN4fFkc8nTenZzT8uZyfPpUaWjYuvAvTz8xPIc4aR3LCH19le9zTUbeW1el9uE1kItmZE46iOQpE0nyhbzqhfwJsBkia+ZRlkmhJZmelXQYSGvpf+VApu17JjBmbdnAQlMxDX+fMbayIZUI5hEIBLbCHjKP7J4+tkkPnMu5ZxXUsLagwzRynZp5qKZB5H03vPZhNumhckGaelOfinx+KsP7qRlalGmoNeVY2IRqHNeFVVwzh4E/JnmPyrD3sGR9WkaaT0r8SDdduCvfj54gJ9xfGYZTXsr7Skvj5Z2tr6Q6WA06CK/uGoquBg71oDAR1QFWZoQ+kbRjubX6ghwJq7iUGEiuc6FjkTlQLUTeYzKoGH94SgxDtA7SuIT6p2A1Dy3r/txSHccqbFpiI779iomYxYIzfUKsTpJ1kbKv3jJT1PGsJ6wtgUDgPLBXzIPFz8MzjpblpNY6epsON/LECUCtLt6iMtRpaxzU0TpOzf30Q6+WE9U2lGmcQnWNlreoMBBd1AbVOgZcNXPax2QUeUTiD0vepyX9qg7dYkkhYwbhW3RjHzfM5q2v5WHMtgFrWZS3HjaXY2EiV1eD6+enV1LZaB4ruc2phImJSFwZySXLPKR65ZWqzMMxkaV5J2nrZ7kgxzx05GUzAqdrzzi0jmof9ogJzzj8cn7fhvURcYzAW2QqLcRez9U+bPuGpXAwj0AgcNbYK+bR0zy4wTz6TMMzkVZeyTR8fLgu16x4f451WmsywFpOVjIBXSVto/TdOE2WlfxUx2pdUQYizV2nknk8Ziatsqodj0jSZyX9YVKmIQXkvFm+YoayS/Iel24oPta4TqLtYVbiEas6yErElPXQu4dXnwQALMz8Plsj5J1IFzQ8lfDE1FHGoSvt01J/KXPgmYi53VL6rWwk+RtXTMRoEJ5xdJhI4ZXqGU2PtTT2pqp8P/R+c6wtPvRO2LaOTwtrSyAQOA/ExyMQCGyFPZ+29PcWrU22bZdzm0Yd0yy7RW42TQXSPE0hiQ9YOVHUXp+iPW1JoVn5dEwqmA7QLT3VRHtVRVDzVHKqLB5J0xe5uFXewRWJy9myZFVJOe2NF9Kw7jKWlrc7tQ1AWgO/ll3O1rKCTacx61uHfqweTlUWbhGYUvZ1mr7IOzJdO/VTGi6dxSoB1QqmTkStpi/ymEv75+FmbtWUpCGypj+/03bZXKc0Gdu6XlytFtc1FtN1RVU/jQGyqEomHoJpIBA4a+wd8+AJ5uGF0jmCae80+bzHqF92D6zl+jQxjeEzvnZiaLbQ5eHvtCOMqt7WOCQNx1L9SMoq80hHoch9HzMjx6MplPtdFKH0csk4VBzlC2YsUaFUFERS5pGcp0RkLWya6qct/uFrFVAvF+HpOh/C8qjsuE7eAUoE1MxA8m2ymCoMTRfRuVDTD43YeuDYSMVA5D1aq6uykYX738Ij7KHPNFx+QzBNIrKWXbfjhfipf2gT92s5lgXzCAQC54qdMA8i+n4AX49hcP1TAP+CmT8zr/Y48/AMI699LrWPluaBrml2YCAn5rOcmEYKBySNQz7rK/GHPi2YhzqDSZ6Mdicygvll9kDWOrKJdgiTc5iGZsS8Ku0d6TAqjIMvSVw0DlLGcWCGnWU5rnCHeRQLrZLLuu7CI45yykDYMREAR+uBXy2FYlQaSGN+v9YNiRwrSavgk+ahDC/X9Q5kiYGsnQnXMg92obyahW5ziBppxHfxntbRdErzJloft45lU+bcluYxwkrmYFfM4y0AnsvMXw7gTwC8bkf9CAQCW2InzIOZ32yivw/gH82rScIsPOPou5r3Niou67RPd1urniEjmDnWJOVla4qmqwUFRX7JPFCkZeuKLnob8o/Nt/1IyqiTmB6adq3DQICsgyjToIvq161Ds5xlk1aWmbFkUQ5DSfNIjlCqedhSOoTp/oB+h2JxZTcu7cpKrq2Ho+J0dFcNJGshxmlrXSalo1G8hcZZXYCacXjt48CxDJuX/upSGdFH5LHNfk997cGzCh+26ngNJMXNO/FlNrhPYXXZM83jVQB+bdedCAQCm+HMmAcRvRXA3Y2s1zPzL0mZ12MYy94w0s69AO4FgCfQrWhrHn1Xcx9Sg3lkprGQUHUMb0nJ/Vo7a4rXPBLzSMvs80iuWocudsunAZSbGB+ZUUAtL7oQLllbHAO5bhjOWrUMYR6sjEPMESS+HMmyYtkGlUMQd5hHOeHvrG9X1/21HulmF9MNzGMt+/5dFw0kM5BSAxnakVCzlImsy9/JayJAZiFZJym1jpVjIrYvS884NO7KAYaN+P9hHS1kVPPQ0FtUxjSPDhPhm8g8zuzjwcxfPZZPRN8C4OUAXsLcPzGCme8DcB8APH35lG65QCBwvtiVteVlAL4LwIuY+epUeQvmJUA9djFD80hnyOYZWxakZYR2jKN9CLr349Cwo3mYz94JlWWOk/YhmkfzGIUhvC5519OSfMlXi83CzEQT05C0tHuOaB1p4i++HIvGsKNDVd5HAGWCebB0qRtKu7MPkgZiTnBKPiGyFaMwkCO1vjgNpLiP3wDHMRFlEcU6PGeJ8UyjxTy8BcZbX1K66SK5NN2cGUanGOIuNNc91qA+MAWL6Ph5dNNtey1LzAzsSvP4UQC3AXgLEb2TiH58R/0IBAJbYlfWli/cxX0DgcDNw965p28umKr5Vff+GLA2MgtTuZjNO35lDSrzupUz3yo7PHXTmVM3jQHsTuheOJXpSto1zJhqnYiqO4ol5zGJJ1EUSNMVqg46Uacw5dZSt+DdTtlbuQdNipyl4R3f62r6Yo9w0/1QyunLEQ/G5zRFsFpu/hGLLnSFVNPFQy+qOhOtjwO1ULp06Ss3jQFqr3NSkVXjaRojfc5Vm05nBRqCades25u+2Os0feG9M9UGAoE9xB4yj2U62a0WTu21ml1RhE5rk2su8nqbV9vFbSlNkk6pLJMdwUpXdJvnGcixE0yPTC8T05D76TktasJdK6s4NEOHMA5Wk6zkUfKMUhOtLoKDgRsS0wN7la0xTlZbbZWHyKYFh0PnpP3SoUxNt8eypr1kHs58y2VY7xhuWKYTUb1ru2cgQ9q4OdcLqDavEk71GXzcnmrXFUy1A6jhGYNnFa7tVpl9EUwDgcCeY8+Yx6Bp9M2x1rFLy2vY1jEA4+bsrJJe61ibUbYy0SYG4pmHhvmOJ8lJTOLJLd0zkDwUHDs95FiGkLTP6YUG80gaR8k02DOOhomWboB5ZBnEb9zpj1xDrYdwac49Scwj32fhRnVyXfGMo3Du6+ghPjwwWs7aMY2lIwCegQBWB+Eiz4etQT8RQUuoDRzRGq7HGIZFy1RLpjOheQQCgbPGnjEP0TySw5eMpMbxpjMNnrfxdGIgJXvxi9/stQ+9teUkpWd464qW8afB2YVxno1omOQDdfRqMg8JK8Yh5dSyYlzSuXqB3trihIWisJ+se+vLNPPgdGz9ED9e562RKubhf+REPeouVhYZbsctW6k3DCpDva0diacYR8VAzP3I52lCh4kMhdrxiomMWVtC8wgEAueBvWIejGHxWo9V2LQe42hbWwb4ZfU+fRbzSAvhJC7p5uhTk1ZaV7IGMoTHZHUSKsK1btaTjoxXl/OaeaSzV5JE5K0sI0OOd0/3zKPpnq5wzKOlebhlA7X2MbytNee3f7IermsGwkV87A+EO6FqHZat9HQRH7b8PPzmET1rS+Fi0ymT0htDvtc8ukzEah4tS1loHoFA4Kyxd8zjFPmLmQYWO/i5gXIjzUPCtKDKTfPHmEdeCCd+HTLaKgOxzOOkClUDKdnFiXH5PPHtpP30nJ6xNENHsq5I3DENqhhHMSwNqE1PnQxbyUelH5UGYjvnWInzDUkhgBP2zEP0Bd1AyDMP+/fhdZAUl7+phlfqwWzmkSstO6xkjuZRPZdnWFLO/nyejbQsMj009ZAZCOYRCAS2Qnw8AoHAVtiraQswmEJ1v40xwdS7nM+ZtlS7gqkzkLdSYmzaonGZirjpC9CatrTDwrFMzdLJxdyZYf30xV4nVa4USrnFfxO8rU/C1KURYuxVu+7J0PZ6Yrpipi0s0xbd+6M7BWh6U5Whn654k20rrQ6HC7sHiHcs22jaImFXMG0ItGlK03Ewyybb/kSG7U1mIJhHIBDYCnvFPBjDyN5jFYAZJZyjly/bWuQ2l4HYMjXj8KEykFxZT5k7JSeQdkIAWC1KhsGOadCIYFoxjzQ8acHGcOO9iyrK1jLVdka16tCSOcxDTbiOiQDQdeerxEBkT9YO8ygdsLjIq5lI/Sg9sy47s27LscwLpt5069nFULY0OXt2omXt371nJSnUvVRHfuJYGBcIBM4Ve8c8rOaRx74Gi3Dm1lrzoKpObyd0v/gNqHWQmnG0Q6B2BvMOZa06/a1ZZfRrMA/ybuh+IVw14jRMtTVlcwktQUGjHXenJvPQfU87Jlvrm+3y9Mzfno5ABY1ohz120UpL5/g4dmFlBn07nmn0Tbf5hj7Pu7+v3fPZ654+khzoWg5mJtzERT2YRyAQ2Ap7yjwG5LGvZhF5jZSMEo4pzLK2pFPhNJ4/9fUmQBLvhC339BRKWyeOgbCV03vOYEnX0KHHLG7rLICrncMUIxPjOZpHr65rnwsfab9ozrOT1jJ+v7nQ8PZVX+q6q9vruSH6GkdVxVpMHFvp7bie/j5h6rpwSvsA8i/nWYnnfsW70HBLChHMIxAIbIW9Yh6AWlsG+A1+hjQUaX5zIH/eis2rmYcPjfVDtxt0lpg5mkedJ33i0gpDxan1PtQhrMNAgIZ1Ra1U3toiKFdNDeiuKGzausqwkvMb96kWz41bX9p5w5/xKetpc+VvU9ytZ4kZZR7l83im0dJJesxj6dponTbnrTdT2octUzONkn013nzlIzIXwTwCgcBW2CvmwRhGfM8q7NS6d2xCb6MfILOIPuMoQ3udz6SV+AzLiWccye9DCzQHWxlBehv6NDSPPDn21pXegrgRq8QszaOjf3gGUjCPhUvzDKRloXE+IPDWl+FNVn4fMCPvJPPIlapFdC69xTyWLk17mhhHZ7OgIk3ia5eubdq36MskxoGybFPzMHkjClaFYB6BQGAr7B3zOIUdDGvNw7OR6rzZxEByHb/B8TzmoZYYZQ8DdJ7tGYitm7cqLK05qU9ezwDyehSneZD33WhqHm5SW61vGPMwdeHo2paZzKO1C+8E4+Cm5tHeZGgN9UAtR3egYYXoMY6Rx+p7nNZlFj7u+uQ1kKH/KMosXBmfb5/D6yI9q0uR12AycxDMIxAIbIX4eAQCga2wV9MWgAvBlN10Y7j2YcdUayhfdiCbN30B+gvivCt7NuHmG66cQJqFUjddsZ/25OdciqDs4oUD2OzpyghV723NNrowbu70xVw7V3auTLdji+n0gFYnnKIUTu11PX0pTZqtd8EuPmre1R6mKQ2XcVeuJZj6GZQ33dou+ufwouqYeByCaSAQOFfsFfNg9Jbkt9zT2cUHNE9/cyKqF0NnmWpd3AuoRV3n0p7VM8c4rEboTbE+nnyt7NDiBVMNeoyjJZx21LqmYNqpWyU3XZUkc9GOW1NtJa72GMjQ2ZWR1HumzDEWUT1iTzA1RaYYhzfljq7dc6zBMxHALON3dWcJpo28OQjmEQgEtsJeMQ9AncRKHaO5JL+jX7SW5CeGMZOB2OsplpLTzf3cfbrL7Vtm14qBuLJNzSMlAEBjKzod5UeGv42cxFz7o8ymmnlL+piTWC+vZBwarg3zWDlto2e6be3WN7q9oYt7xpHTy7Blqq22AJB0b/a1Ww14ptHTPApi6vKo8UhjCOYRCAS2wk6ZBxG9FsD3A3gyM39yqrzXPFoswi+W8xpHtaeNqZ/c1FWncNrERtaWTmivK0vJmKt578ixMYuKd0NPedWKuCIorqvj16sCps4MHcS2WXbO5XXiQJ95VBsL1axlJW9/ink0H2GSeXDrsohXWgfKdJvXc0tv/YqeaXgmsnDpNq/luj4HO2MeRPRMAF8D4MO76kMgENgeu2QePwTgOwH80twKjGHOmhe3lWxiKONYhKT3NBBbxusXmYGU6bb+piHQ0Do6Lg3FJi2T1pb5mkc9ZI65p3uJvyrQqNRpq5nX0zx6buutNMc0KkaSzVaqf1Tah9698VjeIlON0I3zbdMdHWvwJK+5qM71pdp8qOF2r5e9xXOtxXR7qXkQ0SsAfISZ37WL+wcCgRvHmTEPInorgLsbWa8H8D0AXjqznXsB3AsAl+m2wdqSrBViPRixtvQYSOvoBc8SqqMXTL+8HjK1nN+yo2pX3CnvUZNG1UC9gebRnC2j7aiQmMaU5mGerNI8NmEiG2geU16oPeuLSVvLsv2VG5Fb1pb0uzesHDa96dbSyWsxDl/He5L2tkG0/fW/sG9j7HCpTTWPM/t4MPNXt9KJ6MsAPAfAu8SV+h4A9xPRC5j5Y4127gNwHwDcsbx7w8cLBAJnhXPXPJj53QCeonEi+hCA58+xtgQCgccP9spJjDFQyESY087o1j19fJoy6iTWqdPaw1Tv3TPnVru4N/S+2aG59ubd5HLe9DH2UxqXnjDimOzthpvsnt67XXNhnM/TqYkTToGRacqMXcicuLpOjmQD0jSm8Vg6XfHTmFlmXZdeTVcaptosgnKzKDemIH7P1J7J1pbdVjDd+ceDmZ+96z4EAoHNsfOPx6ZYo97DdG0+wT0zbo+BDGltM+4cRy9vzu25w7vDSCX0LuYuHFk/Vls2G2KoYxrUYxhNwbQjlFaCaUNlnessZotWIm7vgRt5G+1/Wuat0+I5abEhjifG0WMLY8zDxXuMo7kyQAVSlGVaS/KrnctQlvUmW1u2EEw3oB7hnh4IBLbCXjEP1TzG3NO9DjLFQGxe75yWlmNZpXG4EWvtp+pjmocv25jmd02yXs8oJutlXjZpj2gcit6xaNs4iVVt28hMxtE866Xz4nrL+ovrkpVUzmPmbqvWo6LlLNa5Hok3SV+HcdRaSN38VpoHct4mmkcwj0AgsBX2jHkM2xD67Qdbu6d7BjLP2tJut32+7bjG4bUOGmMefjl9a3l9NUGdCIENFsJ5iwf6I2eleYwWkugci8ykqGMKTzEMH+8zD7W6qJLW1jxcj7TMFBMZGm7Ga+2jUXniddrkyqHMpY9qHqZuMI9AIHDm2CvmAQwjemYG5eiv+UXeBAMp60DK+LL9+0wxjrF1XVQxEAn7HtmNcAMdo4cdWlt81Tp95GVsanVBZhq9MmvZyrCleVQu7GN957Jsvr8vV+obtky9IK7oeVGp0kE6+oh9Lt9e5XY/gWAegUBgK+wh8+CKCZQbIHttY0De+q9mET2to2eFsde1J6nTLfySeSBpGeyGsMpLtLC2dMJefoFt2Mk21pYtUFX3bMKn2zzPNHreqXPqqvYhfwNmMV2lg3R0jKbc1K3TYHsT7ft4S/PoMVtDPdQAAAZCSURBVI6WhSbrIEPipkwimEcgENgK8fEIBAJbYa+mLQx/bktLyBwXO70zF4DuiXHzpkeuDz3nsBkL46qdxJqCqTPjjgmn1SylM30Z0T6r6UoqM2f39M6Uppl8A+7pfn+PEcG0zmMXl4VyDXrf3Wndxcvn0NArpy46Y/oy5iTWm64o/H4fQ5khZs24YaoNBAJnjr1iHsAmgmm7jGckgDXnQspoW+2wmTZldp0jfs7wi3Ie533hdDRNh6ERAbVHIuaYanuNzWEco0KpZE26sHfiRV7JNGq3dctmSweyTUy2vV3HunGTNmmiHTPVduq2zLHVc8xEMI9AILAV9op5MPyS/DIcrufpFk1TbXdRXV9bSYvN5i52a6V1zpQdcxKrSENj+OsvwXcX3iHMXm/FPDp2wxkz6u4S/Rmax7xFdcos1hPx3Ff9i9MSc7SOKcYxacq1aTPK9trLfxalvmGSCjf10DwCgcCZg3hDl9RdgogeBPDnZ9D0kwDsyx6q+9RXYL/6u099Bc6mv89i5ifPKbhXH4+zAhH9ITM/f9f9mIN96iuwX/3dp74Cu+9vTFsCgcBWiI9HIBDYCvHxGHDfrjuwAfapr8B+9Xef+grsuL+heQQCga0QzCMQCGyF+HgYENFriYiJ6Em77ssYiOj7ieiPiej/EtH/IKI7dt0nDyJ6GRG9n4g+QETfvev+jIGInklEv0FE7yOi9xLRq3fdpykQ0ZKI3kFEv7qrPsTHQ0BEzwTwNQA+vOu+zMBbADyXmb8cwJ8AeN2O+1OAiJYAfgzAPwDwpQD+KRF96W57NYpTAK9h5r8O4O8A+NbHeX8B4NUA3rfLDsTHI+OHAHwnbnhrrLMHM7+ZmU8l+vsA7tllfxp4AYAPMPOfMfMxgJ8D8A077lMXzPxRZr5frh/B8J/yGbvtVR9EdA+ArwPwE7vsR3w8ABDRKwB8hJnfteu+bIFXAfi1XXfC4RkA/sLEH8Dj+D+jBRE9G8BXAPiD3fZkFD+MYaBbTxU8S+zVwrgbARG9FcDdjazXA/geAC893x6NY6y/zPxLUub1GCj3G86zbzPQWpH3uGd0RHQrgF8A8B3M/PCu+9MCEb0cwCeY+e1E9FW77MtfmY8HM391K52IvgzAcwC8i4bVrfcAuJ+IXsDMHzvHLhbo9VdBRN8C4OUAXsKPP3v7AwCeaeL3APjLHfVlFojoEMOH4w3M/MZd92cELwTwCiL6WgCXANxORD/DzN983h0JPw8HIvoQgOcz8+N2gRQRvQzADwJ4ETM/uOv+eBDRAQYh9yUAPgLgbQC+iZnfu9OOdUDDqPHTAB5i5u/YdX/mQpjHa5n55bu4f2ge+4kfBXAbgLcQ0TuJ6Md33SELEXO/DcCvYxAf//vj9cMheCGAVwJ4sbzPd8rIHhhBMI9AILAVgnkEAoGtEB+PQCCwFeLjEQgEtkJ8PAKBwFaIj0cgENgK8fEIBAJbIT4egY1ARCvxg3gPEf3KnO0AiOgyEf2WrLZt5V8got8W57LAniA+HoFNcY2Zn8fMzwXwEIBvnVHnVQDeyMyrVqasvP1fAP7Jzetm4KwRH4/AjeD3YFbLEtG/IaK3ySZF/96U+2cAdDHf9xkvzo8Q0U9JmV+UcoE9QXw8AltBpiAvAfDLEn8pgC/CsJfH8wD8TSL6e0R0AcDnM/OHAICZ/y0zPw/AiwB8CoOrPQC8B8DfOteHCNwQ4uMR2BSXieidGP7j34lhVzNg2NLgpQDeAeB+AF+C4WPyJACfsQ3IQrQ3APghZn47AMiU5piIbjuPhwjcOOLjEdgU14Q5PAvABWTNgwD8B9FDnsfMX8jMPwngGoal4xb/DsADzPxTLv0igOtn1/XAzUR8PAJbgZk/C+DbAbxW9sL4dQCvkg11QETPIKKnMPOnASyJ6JKkvxzDXrHfbtsjorsAPMjMJ+f5HIHtER+PwNZg5ncAeBeAb2TmNwP4WQC/R0TvBvDzGLYNAIA3A/hKuX4NgKcD+D8imn6fpP99AG86t84HbhixJD9w5iCirwDwr5n5lSNl3gjgdcz8/vPrWeBGEMwjcOYQhvIbY05iAH4xPhz7hWAegUBgKwTzCAQCWyE+HoFAYCvExyMQCGyF+HgEAoGtEB+PQCCwFf4/QogzPjOLcVMAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mpmath.cplot(Gnumeric, points=10000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The roots of the denominator appear as two bright regions." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another solution is to plot the image of $G(s)$ as $s$ goes through a particular path. We will speak more of this when we cover the frequency domain, but have a look at this example. We generate values of $s$ in a circle of diameter 1 (radius 0.5) around the origin, then plot $G(s)$ for all these $s$ values. This is known as the image of $G(s)$ for these values of $s$." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "theta = numpy.linspace(0, 2*numpy.pi) # angles around the circle\n", "s = 0.5*(numpy.cos(theta) + numpy.sin(theta)*1j) # The circle with radius 0.5\n", "Gs = Gnumeric(s)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(s.real, s.imag)\n", "plt.plot(Gs.real, Gs.imag)\n", "plt.axis('equal');" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.5" } }, "nbformat": 4, "nbformat_minor": 2 }