{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " Group works No.1: 恒等式,関数,プロット \n", "
\n", "
\n", " cc by Shigeto R. Nishitani, 2020-10-08 \n", "
\n", "\n", "* file: ./math_python/group_works/gw_1_exp_log_ans.ipynb" ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "指数,対数の恒等式,関数を題材に,jupyter notebookを使ってpythonでのplotをbrush upしていく様子を見てもらいます.その過程で指数,対数で数値を取ることの意義を理解してもらいます.\n", "\n", "# 課題1(指数と対数の意味)\n", "下の図は\n", "$10^x$と$1/10^x$を(x,-3,3)で同時にlogplotした結果である.\n", "\n", "![image.png](attachment:image.png)\n", "\n", "この図の意味を解説せよ.\n", "\n", "というのが第一目標です.でも,じっと眺めているだけでは何もわかりません.\n", "ネットにも答えはありません(多分).\n", "そこで,いろいろ段階を踏んでこのplotを組み上げていきます.\n", "\n", "指数と対数がなぜできたのかを思いだすために,\n", "$$ \\frac{1500 \\times 230}{4} $$\n", "を考えましょう.そのまま計算させるだけでなく,対数とってevalfで打ち出して手計算して,それを戻してください." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "86250.0\n" ] } ], "source": [ "print(1500 * 230 /4);" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "7.31322038709030\n", "5.43807930892320\n", "1.38629436111989\n" ] } ], "source": [ "from sympy import *\n", "\n", "print(log(1500).evalf());\n", "print(log(230).evalf());\n", "print(log(4).evalf());" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "11.364\n" ] } ], "source": [ "val = 7.31+5.44-1.386;\n", "print(val);" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "86163.3334371859\n" ] } ], "source": [ "print(exp(val).evalf());" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## $2^x$のplot\n", "指数関数を思い出してもらうために,まずはベタ打ちです.\n", "\n", "$2^x$を(x,-3,3)でplotせよ.\n", "sympyのplotを使ってください.\n", "\n" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%matplotlib inline\n", "\n", "from sympy import *\n", "x = Symbol('x')\n", "plot(2**x,(x,-3,3))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "普通に$2, 2^2, 2^3, 2^4$と確認できますが,$1/2, 1/2^2, 1/2^3$なんかも数値で確認できるでしょう." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## $2^x$と$1/2^x$の同時plot\n", "2つの関数を同時にplotする練習を兼ねて,\n", "$2^x$と$1/2^x$を(x,-3,3)で同時にplotせよ." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "p = plot(2**x, (1/2)**x, (x, -3,3), \n", " legend=True, show=False)\n", "p[0].line_color = 'b'\n", "p[1].line_color = 'r'\n", "p.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`2**x`と`0.5**x`がどういう変化をするかがわかるでしょう.\n", "\n", "* `2**x`は,xの増加に従って,単調に増加していきます.\n", "* `2**x`は,xの減少に伴って,単調に減少しますが,これは,`1/2**x`でxを増加していくのと等価です.\n", "\n", "こうしてx=0に対して対称になっていることが確認できます." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 変数への変換\n", "変数にパラメータを入れることで,変更箇所を出来るだけまとめて一般化しましょう.\n", "2とか3として直打ちしている数値を変数に変更しましょう.\n", "\n", "``` python\n", "a = 2\n", "n = 3\n", "```\n", "\n", "として再度同時plotせよ.\n" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "a = 2\n", "n = 3\n", "p = plot(a**x, (1/a)**x, (x, -n, n), ylim=[0,a**n],\n", " legend=True, show=False)\n", "p[0].line_color = 'b'\n", "p[1].line_color = 'r'\n", "p.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "ここでは出力は変わりません." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## $10^x$と$1/10^x$の同時plot\n", "先ほど調整した`a,n`を変更するだけで,出力結果が変わることを確認してください.\n", "\n", "$10^x$と$1/10^x$を(x,-3,3)で同時にplotせよ.\n" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "a = 10\n", "n = 3\n", "p = plot(a**x, (1/a)**x, (x, -n, n), \n", " legend=True, show=False)\n", "p[0].line_color = 'b'\n", "p[1].line_color = 'r'\n", "p.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "グラフの概形が変わっているのに気が付きますか? 指数の底を2から10に変更することで,\n", "変化がより顕著な関数になっていることが確認できます.\n", "こうなると,小さな値の変化も微妙だし,大きな値の変化もわかりづらくなります." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 指数関数の和の公式\n", "\n", "## $a^r a^q = a^{r+q}$\n", "\n", "a=10, r=3, q=-1.5 で $a^r a^q = a^{r+q}$を確認せよ." ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(31.622776601683793, 31.622776601683793, 31.6227766016838)" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a**3*a**(-1.5), a**(3-1.5), a**3*(1/a)**1.5" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 指数関数の解\n", "\n", "グラフから数値を読み取り,$10^x=150$となる$x$の値を小数点以下2桁で求めよ" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "149.96848355023738" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a**2*a**0.1*a**0.07*a**0.006" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "解を求める関数を使えばすぐですが,グラフを拡大するなどして確認することができます.\n", "先ほどの和の公式を使えば,指数関数は単調増加関数なので,正ならどんな実数も表現できることがわかるでしょう." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 対数プロット\n", "\n", "## logplot\n", "\n", "```python\n", "p = plot(a**x, (1/a)**x, (x, -n, n),\n", " legend=True, show=False)\n", "```\n", "としたとして,\n", "``` python\n", "p.yscale = 'log' \n", "```\n", "を加えて対数プロットを作成せよ.\n", "対数プロットの意味がわからない場合は,matplotlib, yscale, logでGoogleってください.\n" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "p = plot(a**x, (1/a)**x, (x, -n, n),\n", " legend=True, show=False)\n", "p[0].line_color = 'b'\n", "p[1].line_color = 'r'\n", "p.yscale = 'log' \n", "p.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 手動logplot\n", "\n", "$\\log(a^x,a), \\log((1/a)^x,a)$をyscale='linear'でplotせよ.\n", "先ほどのlogplotとの違いを指摘せよ." ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "image/png": 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ElMo2MDOjQ7clqc4r6liR517+O1DX6A3d3IMqiIUFsHcvLfX99RcwdCgVVWRmyo6MMaZFSjpuo06dOqhatSrOnDkDIQQ2btz4yugJdRo2bBhmzpwJX1/fV2aRxcT8icaNbREbC5w6FYS+fTujXr1XF47atm2LXbt24enTp0hLS8Ovv/6Ktm3bonXr1ti7dy/S09Px5MkT7Nu3L9/n+SZeXl7YuHEjhBA4c+YMqlWrhjp16gBQ3+gN/UpQAL118PGhdklKJTB1KtC8ORAWJjsyxpiW8Pb2hkqlgr29Pdzc3DB//nzUrl0bvXr1goWFBWxsbNC/f384OjqiWrVqAICuXbu+krBWrFgBPz8/WFpaonHjxujcuTMAYNWqVVi1ahUA4Pbt27CwsMB3332HWbNmwcLCAqmpqYWOc+PGjShbtiz69euHiRMnIiwsDEeOHMH9+8CWLUfRtm1X1KkDREf/AU/P9q/d3tHREQMHDkSLFi3g4uICPz8/NGvWDM7OzvDy8oJKpULnzp1hZ2dX4PNcunQpLCwsEB8fD5VKBT8/PwBAly5d0KhRI1haWmLIkCFYsWJF3m2OHj2Krl27Fvp5FqigNudCU+M2StuePUKYmwthZCTEV18JkZYmOyKmx3jcRsF43EbJZWQIERtLIzGaN28r4uPvi7i4OOHp6Vnk+3r+PNPS0kTz5s1FRERE3vdat24tHjx4UOw427ZtK+7fv5/v93Rr3EZp694daNcO+PprYNEiYNcu6vOn7goixphe0MZxG8+bu8bFUYWeiUky/P3HwtzcFIApDhSjBdzQoUMRExOD9PR0fPrpp3B8abzRokWLcOvWLVSvXr3I95ucnIyxY8fC1NS0yLf9N+0bt1Gajh4Fhgyh/Sl/f6r6++eyljF14HEbBeNxG8WTkQH8/TedaSpThrpBmJjIjqr4dHvcRmlydQUuXKB9qW+/pT2qvXtlR8WYwXjLG2L2EiGo4/ilS8CTJ4CZGXWD0OXkVNT//4aVoACgYkVg2jTg1CmgRg3Aywvo148GJDLGSo2JiQlSUlI4SRXCs2fAlSu0pFelCr2XrlVL+5u7vokQAikpKTApQoY1rCW+f8vMpKGIs2YBVasCS5dSBaAu/xYwqXiJr2BZWVmIj48v1BkbQyUEkJpKQwSNjOg9tLYNESwJExMTWFhYvNb6CQUs8Rl2gnru0iVg8GBKWObmwIoVwEstPBgrLE5QrLjCw6ljW1YWtRtdsoSW9QwE70EVSKmkeVODB1PbJKUSWLWKymUYY6wUPXsGTJgAuLjQTsO8eTRRyICSU4E4QT1XpgyNlb94EWjRAhg+HHBzA2JjZUfGGNNTx47R1dKCBfT++NIlOhnDCCeof2vUCDh0iPr4RUa++O3JzpYdGWNMT6Sm0nvgDh1ooSY4GAgIAIpx7EivcYLKj0IBDBpE7ZI8PWnulJsbEBUlOzLGmI7bv58KhwMCqK/1xYv08sJexwnqTd57D9i5k4omrl4FnJxo5HxGhuzIGGM6JjkZ8PUFunUDbtygmauLFtHJF5Y/TlBvo1AA3t50NdWvH5WkN2sGnD4tOzLGmA4QAvjlFxr8vW0bHcM8fx5wdpYdmfbjBFVYNWsCGzYABw4AaWlA69bAmDF0xJsxxvIRHw/06EHHKxs1As6do0Y25crJjkw3cIIqKk9PIDoa+OILOqjg6kpFFYwx9o/cXNpjGjQIOHyYtrFPnQLUMCLJoHCCKo4qVYBly4Djx4E6dQAPD6oRffBAdmSMMcmuXQM6dqQh38bG1P7zyy9fHSTICocTVEm0bQts3QpMmkTLfzY2VFTBGDM4OTlU9KBS0VLe6tVUsWdpKTsy3cUJqqRMTIA5c4CzZ4HatYFevYDevYHbt2VHxtQgLi4Orq6usLGxgVKpxJIlS2SHxLRQdDRtS48bB3TqRDVVfn7c1rOkOEGpi6MjJak5c4B9++hqKjCQSniYzjI2NsaiRYsQExODM2fOYPny5YiJiZEdFtMSGRlUlefoSI1df/mFZqKam8uOTD9wglKnsmVpuS8yknZDZ8+mooqbN2VHxoqpTp06eZNGq1SpAmtrayQkJEiOimmD0FCgeXNg+nSgb19g40b6L181qQ8nqNJgZUXTe0eMoCa0trbADz9w81kdd/PmTZw/fx4uLi6vfD0gIABOTk5wcnJCMs8V03tpadQBolUr4NEjWjD5+WfgnXdkR6Z/eNxGafv7byrnOXgQ+OADYM0agMde65wnT56gffv28Pf3R8+ePQv8OR63od+OHAGGDAGuX6deevPm0Sg5VmI8bkOK+vXpcO+GDTQi08EBmD+fhr4wnZCVlYVevXrB19f3jcmJ6a+HDykxjR5NK/nHjlEHNE5OpYsTlCYoFMCAAVTa06MHsGcPjfQ4d052ZOwthBAYPHgwrK2tMXbsWNnhMAl276aap3XrgC5d6J9tu3ayozIMnKA06d136dzUV19RGXqLFlRU8eyZ7MhYAUJCQvDzzz/jyJEjcHBwgIODA3777TfZYTENuHOHih4++oiGB4aGAt9+y81dNYn3oGR58AAYP57mTjVpQntTbdvKjoqVEO9B6T4hgP/7vxetNqdMoYm3ZcvKjkyv8R6UVjE1paR06BCQmUlrBiNG0CQzxpgUt27ROIzZs6kYNzIS8Pfn5CQLJyjZ3N3pGPqYMcDKlbRXdeCA7KgYMyi5uVT0oFRSAcTYsdRqkwtu5eIEpQ0qVQIWL6Z2x9ev007sgAFASorsyBjTe3/+SaPXR4ygs03R0cDQodzcVRtwgtImLVsCYWE0tXfzZnr7tnUrt0tirBRkZ9NVk0pFY9fXraPjig0ayI6MPccJStuULw/MmAFERAD16lEZUc+eQGKi7MgY0xuRkYCLCzByJPCf/wCXLwMDB3KbIm3DCUpbqVTAmTN0qDcoCPjsM6r446spxootPZ2KHpycgIQEWqBYvZoGETDtwwlKmxkbUyn6hQvUecLPj3r5X78uOzLGdM7p09TIZc4cumqKiaHpOEx7cYLSBe+/T3OjV62ikR52dsD339OENMbYGz1+TEt5Xl60gn7wIO031aghOzL2NpygdIWRETWdjYkBXF1phnTr1sClS7IjY0xrHTxIwwSWLwd8fICTJwEPD9lRscLiBKVrLCyAvXtpGOK1a0CzZlRUkZEhOzLGtEZKCvDppzSOrWJFSkxLlwJVqsiOjBUFJyhdpFAA/fpR6VHv3tQp/YMPqESdMQMmBLB9O9CnD7BpE/DNN8D58/TPg+keTlC6rFYt+lf4ww/U2bJlS2DcOODpU9mRMaZxSUlU9NCnD+01hYcDM2cCJiayI2PFxQlKH3TpQntRQ4YAixZRifrRo7KjYkwjhKCiBxsb6hL27be0Cm5vLzsyVlKcoPRFtWpU5fc8Mbm5UVHFo0dy42KsFN24QUUPgwZRcWtUFHUeNzaWHRlTB05Q+qZDBzo3NX48dUvv04feTjKmR3JygIAAqtALDaWWRX/8QZNrmP7gBKWPKlakDhRnz9JgRC8vqrFNTpYdGWMlFhNDo9NmzaJhAJcuAcOH00kMpl/4f6k+a96cdopnzAB27KDms4GB3C6J6aTMTEpKzZpRB/K5c4Fdu4C6dWVHxkoLJyh9V64cdUePjKSOFP37A927A3FxsiNjrNDCwwFnZ/pV7tmTrqJ8fbm5q77jBGUobGzotOL331MhxWefUVFFbq7syBgr0NOnVPTg4gLcuwfs3k2TaMzMZEfGNIETlCEpUwYYPZomslWsSAv3bm5AbKzsyBh7zYkTVCq+YAEweDDtNXl5yY6KaRInKEPUsCG9FV27lpb+VCp6FcjOlh0ZY0hNpfdOPXtSa6LgYKrYq15ddmRM0zhBGSqFgg6PxMRQw7IJE6gTRVSU7MiYAdu/H1AqKSENGEBXUW5usqNisnCCMnTvvQfs3EmT2+LiaJLbokXcfJZp1L17VL/TrRudOT91in4NK1WSHRmTiRMUo6upPn3oamrIEOqw2awZTXhjrBQJAfzyC9CuHb1HmjYNOHeOiiIY4wTFXqhZk47k//orkJZG86bGjAGePJEdGdNDCQlAjx50htzenhLT1Kl0MoIxgBMUy4+nJ1X6jRgBLFlCTc4OHZIdFdMTQgCrV9PJh8OHaSnv//6P2hYx9jJOUCx/VarQGI8TJ2h2gY8P8PnnwIMHsiNjOuzaNaBjR2DoUGp0cvEiMHYsnYBg7N84QbE3a9OGStEnTKDmszY2VFTBWBHk5AA//kgnGiIi6AoqOBho3Fh2ZEybcYJib2diQgkqLAyoXZumwvXuTY1oGXuLixeBVq2Ar7+mPaeYGMDPj9sUsbfjBMUKr1kz6pA+Zw6wbx9dTW3YwM1nWb4yMqjowdERuHmTrqA2bQLMzWVHxnQFJyhWNGXLApMm0bKfjQ1dWfXsCfz9t+zImBY5c4YS04wZwCef0FVT37581cSKhhMUKx4rK+D4cbqaOnyYjv8vW6Z3zWcHDRoEMzMz2HKJWaGkpQETJwKdOlHLon37gJ9/Bt55R3ZkTBdxgmLFZ2REXTyjo6mYYuRIOnF55YrsyNRm4MCBCAoKkh2GTggOphMJ335LlXmXLgFdu8qOiukyTlCs5OrXBw4coP2omBh6+zxvHpCVJTuyEmvXrh1q1KghOwyt9vAhFT24uwPGxsCxY8D06UDVqrIjY7qOExRTD4WCuntevgx89BHtU7VoQe0B9FxAQACcnJzg5OSE5ORk2eFo1K5dtBW5fj1V6UVF0UU0Y+rACYqp17vv0gHfnTupDL1FC0pWz57JjqzUDB06FOHh4QgPD0etWrVkh6MRd+4Aw4YB3t40PDA0lC6aK1SQHRnTJ5ygWOnw9qblvoED6ZXLwYFaVDOdJgQVPdjY0Bj2WbPoeFzz5rIjY/qIExQrPaam1H3i0CH63NOT+vulpsqOjBXDrVtU9DBgANC0KfXP8/enkweMlQZOUKz0ubtTidfgwcDKldQV9MAB2VEVio+PD1q1aoWrV6/CwsICa9eulR2SxuXmUpN7pZJOFixdSi0ara1lR8b0nUK8uQsAtwhg6nXmDCWqmBiaULd4sV4dknFyckJ4eLjsMNTm6lW66A0OpuLMgACgQQPZUTE9lO8Rbr6CYprVsiVV9k2ZQpPq7O2Bbdu4XZKWycqirUN7e+o0vm4dcPAgJyemWZygmOaVL08HZSIiADc34OOPqagiMVF2ZAzA+fM00XbSJNpz2rCBal24TRHTNE5QTB6Vit6aL1hAb89tbIC1a/lqSpL0dOB//wOcnem9wvbtwI4d1MCeMRk4QTG5jI2BceNoJoODw4uWBNevy47MoISEAO3b0x7Tf/5DW4S9esmOihk6TlBMO1haAkeO0EyGsDAaILRkCU26Y6Xm8WNqodi2LR2+3bKFLmq5uxPTBpygmPYwMqJZ4M/fvo8ZA7RuTV1HmdodPEgV/8uXU5KKjqZx7IxpC05QTPtYWNCr5qZNwF9/0aDEGTOAzEzZkemF+/ep6MHTE6hYkc40LVkCVK4sOzLGXsUJimknhQLw8aGrqT59aDRr8+Y00ZcV244dVJty9ix1gTh/ni5SGdNGnKCYdqtVCwgMBPbuBR48oL2padOAp09lR6ZTkpJo1bR3b+rnGxhIffRMTGRHxljBOEEx3dCtG+1FDR1KB3zt7ICjR2VHpfWEoKIHGxvgt99omGBoKK2aMqbtOEEx3VGtGvXyW7WKlgDd3Gjmw6NHsiPTSjduUMn4oEGUz6OigAkTqLKfMV3ACYrpng4dgAsXgPHjqVu6jQ0tATIAVJm/ZAlV6F2+TI1e//gDaNJEdmSMFQ0nKKabKlYE5s+n9aqaNQEvL2DUKMDAJtr+W0wM0KYNVei3b08Tb4cPpwp+xnQN/9oy3ebkRJPzpk8Hfv+dZkBs2mRw7ZIyM4GZM2lvKTaWZjXt3w/UrSs7MsaKjxMU033lylF39B07qCOFry/QvTsQFyc7Mo2IiKD+eVOmAD170lWUry83d2W6jxMU0x9KJTWVW7yYKvyUSiqoyM2VHVmpePqUih66dwcyMoDdu4HNmwEzM9mRMaYenKCYfilThjZgoqNpZsTo0XTQNzZWdmRqdewYzWpasIAq8E+fpm04xvQJJyimnxo2pD2pdetoHKxKRUUV2dmyIyuR1FQqeujQgS4Mg4OpA7mpqezIGFM/TlBMfykUQL9+tCnj6Ql8/TVN9I2Kkh1ZsezfT6uWAQHA2LE0ocTNTXZUjJUeTlBM/733HrBzJ7B1KxVOODkBkyfTxo0OuHePRmZ160ZnlU+dAhYtokp7xvQZJyhmGBQK2ouKiaGrqpUraZ3s9GnZkRVICOrqZG1NK5UzZwLnztHWGmOGgBMUMyw1awIbNlC5W2IitfIeMwZ48kR2ZK+Ijwd69KCG7o0aUVHEN99QRT1jhoITFDNMnTpRpd8XX1BfIDs74NAh2VEhNxf4+Wfaazp8GPjuO1rSs7WVHRljmscJihmuKlWAZcuA48fp0sTDgzqrPnggJZxr12ii7ZdfAu3aURHEl19S5TxjhogTFGNt21Jl36RJtPz3ySdUVKEh2dlU9KBS0R7TvHnAnj1A48YaC4ExrcQJijGAJvfNmUN9g+7efTHd7/btUn3YCxeADz6gKr1OnaiGw8+P2xQxBnCCYuxVDg40D33OHGDfPhrlsWGD2pvPZmTQFPsvvgBu3qRqvV27AHNztT4MYzqNExRj/1a2LC33RUZSgho4EOjcmTKJGoSGAs2bAzNmAA0a0KDgvn35qomxf+MExVhBrKyogGLZMpoCaGtLnxez+WxaGnWAaNWKhgDv309jMWrVUnPcjOkJhXjz0oVhDdVhOuvu3bsICQlBYmIiKlSoAFtbWzg5OcFIXZP6/v6bxssfPEhnp9auBZo2fe3HnJycEB4e/trXjxyhm1+7Rst6c+cCVauqJzTG9EC+6wd8BcV02tGjR/Hhhx+ia9euOHDgAJKSkhATE4NZs2bBzs4OU6dORWpqaskfqH594MAB2o+KiaFW4nPnAllZb7zZw4dU9NCxI93k2DFg+XJOTowVhrHsABgrid9++w2rV69GvXr1XvtednY29u3bh0OHDqFXr17FfoygoCCMHj0aOTk58PPzw8TLl4H//hfw9wfOnKFqB0fH1263axddLd29C0ycSAMFK1QodhiMGRxe4mPsDXJyctCkSRMcOnQIFhYWcHZ2xubNm2FjY0NVfkOGAMnJwPjxwJQpcGrbFvv3h2PkSGDbNrpqWruWiiIYYwXiJT6mv/7zn//g0aNHeX++efMmOnbsWOL7PXv2LCwtLdGoUSOUK1cOn3zyCXbv3k3f7NaNlvs+/RSYNw/CwQGpiU9gY0PTbWfPBsLCODkxVlycoJheaNOmDVxcXPKW/Dw8PDBmzJgS329CQgLq1q2b92cLCwskJCS8+AFTU2DtWtwJPIQ7cZmomnQV8ytMxYWTqfjf/6hinTFWPG9c4vP09BT37t1TywMlJyejlgHW0/Lz1pwnT57g6tWrMDY2ho2NDcqqITs8ePAAqampqF+/PgAgJSUFaWlpr+x53bjxBPfvV4QRcmGMaNgpcgFjYyqsqFatxDHoCv5dNyzqfN4REREHhRCer31DCPGmD7Vp3ry5Ou9OZ/Dz1oyNGzeK999/X2zatElMnDhRNGvWTERGRpb4fk+dOiU8PDzy/jxnzhwxZ84cIYQQV64I0aaNEIAQnToJceOGEBUrVhTi9GkhbGzoG//5jxD37pU4Dl3Av+uGRc3PO98cxEt8TC/s2LEDJ0+ehI+PD+bOnYtVq1Zh4MCBJb5fZ2dnxMbG4saNG8jMzMQvv/yCzp298MMPVABx6RKwfj0dj2rQ4J8btWxJXV8nT6a5U9bWNM1Xze2SGNN3nKCYXti1axfMzMzy/tyiRQuEhoaW+H6NjY2xbNkyfPjhh7C2tkabNiMxaJASCxcCXl4vaiRea1NUvjz1MoqIAOrVo8979qQhiYyxQtFYgho6dKimHkqr8PMuXbNmzcL9+/fz/V65cuVw5MgR7Nu3r0SP0aVLF1y48Cc++eQv/PijHxITaZDg1q1A7dqv/uw777zz6hdUKjorNWwYEBREvf3WrtXLqyn+XTcsmnjefA6K6bTdu3dj/vz5MDExgaOjI2rVqoX09HTExsYiMjIS7u7u+N///leizdyQEGDwYODqVeCzz4CFC4EaNfL/2YJaHQGgPkd+ftROws0NWL2a5rkzxvgcFNM/27dvR0hICD788EMolUrk5OSgatWq6N+/P86ePYvFixcXOzk9eQJ89RXNM0xPp32mn34qODm9laUlNeVbtYoOSNnaAosXUyNaxthrNJqgJk+eDJVKBQcHB3h4eCDRQNbjx48fDysrK6hUKnh7e+Phw4eyQ9KIbdu2QalUwsjIqOCrihKKiIhAYmIiAgMD4eXlhWHDhmHAgAFwdnbGs2fPin2/Bw8CSiUQHg6MHAlER9NE+DcJCgpCdHQ0LC0tMW/evPx/yMiIlvtiYqhB365d1Hz20qVixyrboEGDYGZmBltbW9mhaExcXBxcXV1hY2MDpVKJJUuWyA5JY9LT09GiRQvY29tDqVRi6tSppfdgBZX3CTWXmQshxKNHj/I+X7JkiRg2bJi6H0IrHTx4UGRlZQkhhJgwYYKYMGGC5Ig0IyYmRly5ckW0b99ehIWFlcpjLFmyRFhZWYly5cqJhg0b5n00aNBANGzYsMj3l5IixKefUoW4lZUQISGFu112drZo1KiRsLW1FRkZGUKlUolLly69+Ua5uUJs3izEO+8IUbasENOnC5GRUeSYZTt27JiIiIgQSqVSdigak5iYKCIiIoQQQqSmpor333//7f+/9URubq54/PixEEKIzMxM0aJFC3H69OmS3q38MvOqL7VwTktLg8JAJrR5eHjA2Jj68rZs2RLx8fGSI9IMa2trNM1nJIU6jRo1CpcvX8agQYNw/fr1vI8bN27g+vXrRbqv7dupIjwwkPrAnj9P49gL43lLpPLly7/eEqkgCgXwySd0NdWnDzWddXKi5T8d0q5dO9Qo9rqnbqpTpw4c/2kQXKVKFVhbW7/aYUSPKRQKVK5cGQCQlZWFrKysUnst1/gelL+/P+rWrYvAwEDMmDFD0w8v3U8//YTOnTvLDkPvrFy5sti3TUqiVbc+fQALC8oPs2YBJiaFv4+3tkR6k1q1KCvu2QPcv08bX+PHA0+fFvGZMBlu3ryJ8+fPw8XFRXYoGpOTkwMHBweYmZmhU6dOpfbc1Z6g3N3dYWtr+9rH83eTs2fPRlxcHHx9fbFs2TJ1P7w0b3veAD13Y2Nj+Pr6SoxUvQrzvLWVEMC6dVT5HRJC451CQwEHB0kBde9Oe1EODlQqqFIBf/whKRhWGE+ePEGvXr3w/fffv7JCpO/KlCmDyMhIxMfH4+zZs4iOji6Vx1H7PKjDhw8X6ud8fX3RpUsXTJ8+Xd0hSPG2571+/Xrs27cPwcHBerW0Wdj/39rmxg1g6FDg8GGq0luzBmjSpPj3Z25ujri4uLw/x8fHw9zcvOh3VK0asHQp4O1NozxcXSnQ+fMNqq+fLsjKykKvXr3g6+uLnj17yg5HiurVq8PV1RVBQUGlUiSj0SW+2NjYvM93794NKysrTT68NEFBQZg/fz727NmDihUryg7HoOXkAEuWUIV3aCiwYgVdpJQkOQEvWiJlZGTktUTy8vIq/h26ugIXLgDjxlH2tLGhJUCmFYQQGDx4MKytrTF27FjZ4WhUcnJyXiXys2fPcOjQodJ7LS+oekKUQhVfz549hVKpFHZ2dqJbt24iPj5e3Q+hlRo3biwsLCyEvb29sLe3N5jqxZ07dwpzc3NRrlw5YWZm9krTVRkuXaLerYAQnTsLceuWeu9///79onz58qJRo0Zi1qxZ6rvjs2eFsLMTol07IXx8hLh7V333rQaffPKJqF27tjA2Nhbm5uZizZo1skMqdSdOnBAAhJ2dXd6/6/3798sOSyOioqKEg4ODsLOzE0qlUkyfPl0dd5tvDuJOEkzvZWUB334LzJwJVK4MrFxJBRGlsdL6xk4SJZGZ+eJJVK1Kl4H9+pXOk2BM87iTBDM8ERFUuT15MvVqvXwZ+PhjHXxdL1eOnsT589SRon9/Kqp4ad+LMX3DCYrppWfPqCqvRQvg3j0awb55M/BSw3PdpFRSyeHixcDRo4CPD10S5ubKjowxteMExfTOsWNUof2//9FxokuXaDSG3ihTBhgzBrh4EXjvPeCLL6j57EtFSIzpA05QTG+kpgLDhwMdOtAFRXAwMG8eUL267MhKSaNGwJYtNL4jMpKy8oIFQHa27MgYUwtOUEwv/PYbrX4FBABjx1KFtpub7Kg0QKEABg2idkmensA33wA9egBRUbIjY6zEOEExnXbvHp1n7duXzrGeOgUsWgRUqiQ7Mg177z1g506aohge/qIyJCNDdmSMFRsnKKaThAB++YWau27YAEyfDpw7BxhQO7TXKRR09RQTQyXos2YBzZoBp0/LjoyxYuEExXROQgK9Dvv4AA0bUin52LFUiS1LWFgYVCoVhBBIS0uDUqkstf5kb1WzJmXtAweAtDTg88+BUaNoAiNjOoQTFNMZubm0x2RjQz30Fi2iiwM7O9mRUasjLy8vJCQkYMKECejfv7/8AX6enjRpsUsX4Icf6C/q0CG5MTFWBNxJgumEa9eAr7+mbRZXV2D1aqBxY9lRvSozMxPVq1eHnZ0dTp06hTJlysgO6YWTJwE/P+DqVSqqWLgQMDWVHRVjz3EnCaZ7srPpSkmlAu7epcQUHKx9yQkAUlJSkJOTg8ePHyM9PV12OK9q04ZK0SdNouW/jh0p2zOmxThBMa118SJNtB03DujUiYoi/Py0t03RsGHDYG5uDl9fX3z99deyw3mdiQkwZw5NZGzYEOjVi5oS3r4tOzLG8sUJimmdjAyafu7oCNy8SYlp1y6gOOOVNGXjxo0oW7YsatSogYkTJyIsLAxHjhyRHVb+mjWjv9Q5c4C9e2lTb8MGKo1kTIvwHhTTKmFhwGefUXui/v2p5dw778iOqvBKrZt5ablyhS5LQ0KoNHLJEqB+fdlRMcPDe1BMe6WlUam4iwu9Pu7bB/z8s24lJ51kZQUcPw4sW0Zl6Eolfc7NZ5kW4ATFpAsOpgroxYvpyM7mzUDXrrKjMiBGRsCIEdTTr00bYORIoF07urpiTCJOUEyahw9pdcndHTA2pi7kK1bQPD4mQf36dLh3wwYanGVvT/tUWVmyI2MGihMUk2LXLpq3t349nW+KiqI37UwyhQIYMIDaJX30EeDvT5V+587JjowZIE5QTKPu3KGJtt7edKUUGkojMSpUkB0Ze8W779Ioj337gLNnafLjxIk0CZIxDeEExTRCCCp6sLGh6bazZ9NVVPPmsiNjb9S1K5VUDhwIfPst4OAAnDghOypmIDhBsVJ36xa1gxswgIrGoqJo2m3ZsrIjY4ViagqsWUN9/DIzaS12xAjg8WPZkTE9xwmKlZrcXGDdOqpcPnGC+pWeOEFJShds27YNSqUSRkZGunW2qbS4u1Pz2TFjgJUrgd69qaiCsVLCCYqViqtXgfbtqWL5eVPt//6XKpp1ha2tLXbu3Il2XL3xQqVKdB4gJARIT39xaZySIjsypod06OWC6YKsLCp6sLenrYvly2nIa4MGsiMrOmtrazRt2lR2GNqpVSvg999pau/mzTQ5cutWbpfE1IoTFFOb8+epE8SkSUC3blSp/Omn2tvcVV0CAgLg5OQEJycnJCcnyw5Hc8qXB2bMoImR9esDfftSeWZiouzImJ7gBMVKLD2dXqfataPXpu3b6aN2bdmRvZ27uztsbW1f+9i9e3eh72Po0KEIDw9HeHg4atWqVYrRaimViiZHLlgAHDxI70rWrOGrKVZixrIDYLotJAQYPJj2nCZOBCZM0K05eIcPH5Ydgn4wNqa5KD16AEOHAkOG0NLf6tVAo0ayo2M6iq+gWLE8fkwFEG3b0hXUwYPA3Lm6lZxYKXj/fWqu+OOP1Jre1paKKnJyZEfGdBAnKFZkwcH0urN8OSWp6GjAw0N2VOr366+/wsLCAqdPn0bXrl3x4Ycfyg5JNxgZ0VVUTAxN7h07FvD1pV8UxoqA50GxQrt/H/jyS1q5ad8emDYNaN1adlTaRefmQZU2IWi0/OefA48eUW+/SZOAcuVkR8a0C8+DYsUjBBU9WFsDgYG0z7R3LycnVggKBY2Wj4mhprPTplF/q7Aw2ZExHcAJir1RUhK9vvTpA1hYAOHhwKxZgImJ7MiYTqlVi97d7NkDPHgAtGxJRRVPn8qOjGkxTlAsX0JQmyKVCrh2jQ7fhoZSr1DGiq17dzrBPWQIHex1cQGOHpUdFdNSnKDYa27coKKHQYNoWW/bNprZZMyHEpg6VKsGrFpF7e2fPQPc3IBhw2iPirGXcIJieXJygKVLqULvzBmabvvHHwB3+2Glon174MIFYPx4OthrY0Obm4z9gxMUA0B72L1707ZA+/a0CjN8uG41d2U6qGJFYP58Wj+uWZMu1X18AENqGcUKxC8/Bi4ri4oemjUDjh+nfez9+4F69WRHxgyKkxNV4AweTGXp1tbApk3cLsnAcYIyYOHh9LoweTLQsydw+TJV6+l7c1empcqVA776iroOv/8+He7t3h2Ii5MdGZOEE5QBevqUzjJ9/jlw7x6NYN+8GTAzkx0ZY6C9qJMnqUXS0aOAnx8VVeTmyo6MaRgnKANz7BjNalqwAHB0pL0mLy/ZUTH2L2XK0OTeixfpz8OHU7VfbKzUsJhmcYIyEI8e0RVThw70RjQ4GAgIAKpXlx0ZY2/QqBEQFASsXQtERtLBvAULgOxs2ZExDeAEZQD27wf696fJB199RW9K3dxkR8VYISkUdCgvJgbw9KT1aV9fICpKdmSslHGC0mPJyfTvuFs34PZt4NQpYOFCquxlTOe89x5V+G3ZQhU9zyt8MjJkR8ZKCScoPSQE8MsvtNe8bRv15wwJoa4yjOk0hQL4+GMqnujX78UZiVOnZEfGSgEnKD2TkEAzmnx8aPn+3Dlg6lSebsD0TM2awIYNwIEDQFoa0KYNMHo08OSJ7MiYGnGC0hNC0B6TjQ3w0080TPDUKWpbxJje8vSkQYhffEFVP56ewKFDsqNiasIJSg9cu0aDS4cOpVE7Fy/Sv9cyZWRHxpgGVKkCLFtGpanJyS86HT94IDsyVkKcoHRYTg41dFWpgIgIuoIKDgYaN5YdGWMSfPABVfZNmgRs3EjLCTt3yo6KlQAnKB0VHQ20akVHQjw9qQLXz4/bFDEDZ2ICzJkDnD0L1K5N0zZ796YyVqZzOEHpmIwMqspzdARu3qRBgjt2AObmsiNjTIs4OlKSmjMH2LePlv3Wr+fmszqGE5QOCQ2lPabp04G+femqqW9fvmpiLF9ly9JyX1QUoFQCn30GdO4M/P237MhYIXGC0gFpacCMGbSk9+gRvSH8+WfgnXdkR8aYDmjalObILFtGBwKVSvqcm89qPU5QWi44GLCzo7NM/v7U3LVrV9lRMaZjjIyAESNo87ZNGzos2K4dcOWK7MjYG3CC0lIPHwJDhgDu7oCxMXUhnzkTqFpVdmSM6bD69elw74YNtEZubw/Mng1kZsqOjOWDE5QW2rWLKmTXraMJ2FFR9GaPMaYGCgUwYAD18+vRgxKWiwu1XWFahROUFrlzhw7b9u1LwwNDQ6lKr0IF2ZExpofefRfYuhUYN47K0Fu0oKKKZ89kR8b+wQlKCwhBRQ82NrTysHAhEBZGFXuMsVL20Ue03DdwIL0jdHAATpyQHBQDOEFJd+sWFT0MGABYWdFMtpEjqUKWMaYhpqbAmjXUxy8zk9bUR4wAHj+WHZlB4wQlSW4utSlSKoHjx4GlS+lNm7W17MgYM2Du7lTpN2YMsHIlTfo8cEB2VAaLE5QEV6/SwfZ58+hsU3Q0XTUZ8f8NxuSrVAlYvJjOTN26BXTpQkscKSmyIzM4/JKoQVlZlJTs7am567x5wMGDQIMGsiNjjL2mVSvgzBlgyhRg82Za3ti6ldslaRAnKA05f54qWSdNohHsly/TQFBuU6S9xo8fDysrK6hUKnh7e+Phw4eyQ2KaVr489RaLiKAzVH37At7eNBmUlTpOUKUsPZ06QDg7A4mJwPbt9FG7tuzI2Nt06tQJ0dHRuHDhApo0aYK5c+fKDonJolIBp0/T+IDffwf69AHWruWrqVLGCaoUhYRQU+Vdu16cC+zVS3ZUrLA8PDxgbGwMAGjZsiXi4+MlR8SkMjamM1MXLgDlytF8G3d34Pp12ZHpLU5QpeDxYyp6aNsWePoUWLKExrCbmsqOjBXXTz/9hM6dO+f7vYCAADg5OcHJyQnJyckajoxpnKUlcOQI8OOPdGDR1paKKnJyZEemdxTizZeofP1aRAcPUjeIuDhKUrNnA5Ury46KFcTd3R238xlmN3v2bPTo0SPv8/DwcOzcuROKt2waOjk5ITw8vFRiZVooPh4YPpxGDLRvT13SbW1lR6WL8v2HZazpKPTV/fvA2LHUCcLKis40tW4tOyr2NocPH37j99evX499+/YhODj4rcmJGSALC2DPHuCXX2jMvKMjbTpPmkTLgKxEeIlPDXbsAJo1A06epN/N8+c5OemDoKAgzJ8/H3v27EHFihVlh8O0lUIB+PhQgurTh0ZeN29OE31ZiXCCKoGkJKBnT6B3bxoeuH07MGsWYGIiOzKmDv/973/x+PFjdOrUCQ4ODvj8889lh8S0Wa1aNBhxzx7gwQM6R/XVV7QRzYqFl/iKQQhg/Xpa0ktPB779lj435r9NvXLt2jXZITBd1L079fL7+mvgu++AGzdoQ9rVVXZkOoevoIroxg1qUzRoEE26jYoCJkzg5MQYe0m1asCqVcAff9AYbDc3qp569Eh2ZDqFE1Qh5eRQubivL81pWrGCfveaNJEdGWNMa7VvT5vS48bRwV4bG2DvXtlR6QxOUIUQEwO0aUMNjhs2pDdEw4dzc1fGWCFUrEgdKM6cAWrWBLy8qKji7l3ZkWk9fol9g8xMYOZMqtCLjQX+7//oo25d2ZExxnSOszMQHg7MmAEcPUon+Tdt4nZJb8AJqgDh4fT7NGUKVerFxNDyHh+FYYwVW7lywOTJlKBq1KAXle7d6WQ/ew0nqH95+pTOMrm4APfuAbt3U6d9MzPZkTHG9Ia1NR2c/P57SlZKJRVV5ObKjkyrcIJ6ybFjNKvp5Elg8GC6avLykh0VY0wvlSkDjB4NXLwItGhBG9tubrSfwABwggIApKbS70aHDvQGZupUICCAKkUZY6xUNWoEHDpEVX6RkcDnn1NRRXa27MikM/gEtX8/XV0HBNCh74sX6U0MY4xpjEJBhysvXaK2NBMmAC1b0kFLA2awCSo5Gejfn6bbVq9Os8gWLqSKUMYYk8LcnBrPbt1KhRNOTlRUkZEhOzIpDC5BCUH//9u0AQ4fpr6OERG0BMwYY9IpFNR0NiYG6NePGnw6ONA5KgNjUAkqPh7o0YPOyFWrRglq6lTuis8Y00I1a9L8ngMHgMaNgQ8+oG4BT57IjkxjDCJB5ebSHpNSSUlp0SJa0uO5YowxrefpSWddRoygfmt2dlRUYQD0PkFduwZ07AgMG0YjWi5epM7jZcrIjowxxgqpShXghx9oEmr58i86Vj94IDuyUqW3CSo7m66U3NyAc+eA1auB4GC6UmaMMZ3Upg2Vok+aRO+2lUrg119lR1Vq9DJBXbxIy7XjxlGVXkwM4OfHbYoYY3rAxASYM4f2Ld59l3qx9ekD3L4tOzK106sElZFBRQ+OjsDNm1Stt3w5VW4yxpheadaMxsrPmUMjPGxsaOy8HjWf1ZsEFRpKe0wzZgCffEJXTX378lUTY0yPlS1Ly32RkZSghg+nF8C//5YdmVrofIJKS6Ok1KoVDavctw/4+Wc6jM0YYwbBygo4fpwKKZ63x1m2TOebz+p0ggoOporLqVOpA/mlS0DXrrKjYowxCYyMXrRLatMGGDkSaNcOuHJFdmTFppMJ6uFDYMgQwN0dMDamLuQzZwJVq8qOjDHGJKtfnw73bthAex1Dh9I+VVaW7MiKTOcS1L59tNS6bh3w9dfUS7FdO9lRMcaYFlEogAEDgMuXqVu6vz9NYD13TnZkRaIzCerOHSp6GD2aqvJCQ4F584AKFWRHxhhjWurdd4H164GdO+lFtEULYOJE4Nkz2ZEVitYnKCGo6MHGBti1i5ZYQ0KoYo8xxlgheHvTct/AgcC339K5qRMnZEf1VlqdoG7dArp0oSvVpk2pktLfn5u7MsZYkZmaAmvWUB+/lBTaGxkxAnj8WHZkBdLKBJWbS1elSiUl+aVL6b/W1rIjY4wxHefuTl2zx4wBVq6kF9oDB2RHlS+tS1BXrwLt29PU4y5dgOhoqpbk5q6MMaYmlSoBixcDp05RI9ouXajqLCVFdmSv0JoElZVFRQ/29pSUVq2iVkUNGsiOjDHG9FTLllTZN3MmvehaW9M0Xy1pl6QVCer8ecDFhTp2dO1KlZEDB3KbIsYYK3XlywPffEP7KPXqUbm0tzeQmCg7MrkJKj39RXl+YiKwfTuwYwdQu7bMqBhjzACpVDRWfsEC4OBBKp1eu1bq1ZS0BBUSAvj60gHnAQOoArJXL1nRMMYYg7ExzSm6eBFwcKA5RX36ANevSwlH4wnq8WMqemjbFggPp4rHn34CatTQdCSMvdnkyZOhUqng4OAADw8PJGrBkgdjGmFpCRw5Avz4I3D3LmBrS0UVOTkaDUMh3nz5ptZru4MHqS1UXBwlqdmzgcqV1fkIjKlPamoqqv7T4HHp0qWIiYnBqlWr3ngbJycnhIeHayI8xjQjPp7Kqvfvp2KBNWsoYalXvhUHGrmCun8f+PRTwNMTqFgROHkSWLKEkxPTblVf6j6clpYGBVftMENkYUEDETdtAv76iybCTp8OZGaW+kNrJEFFRNBz8/enir0PPtDEozJWcv7+/qhbty4CAwMxY8YM2eEwJodCAfj4ULFA797AwoUaGTGvsSW+uDigbl113Rtj6uHu7o7b+fxDmz17Nnr06JH357lz5yI9PR3Tp09/7WcDAgIQEBAAAEhOTsbfejLNlLECqf8FPd/lCY3uQTGmq27duoUuXbogOjr6jT/He1CMFYu8PSjGdFFsbGze57t374aVlZXEaBgzPMayA2BMW02cOBFXr16FkZER6tev/9YKPsaYenGCYqwAO3bskB0CYwaNl/gYY4xpJU5QjDHGtBInKMYYY1qJExRjjDGtxAmKMcaYVuIExRhjTCtxgmKMMaaV3tbqiDFWBAqFIkgI4Sk7Dsb0AScoxhhjWomX+BhjjGklTlCMMca0EicoxhhjWokTFGOMMa3ECYoxxphW+n9sOHgtkS9mtwAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "p = plot(log(a**x,a), log((1/a)**x,a), (x, -n, n),\n", " legend=True, show=False)\n", "p[0].line_color = 'b'\n", "p[1].line_color = 'r'\n", "p.yscale = '' \n", "p.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\log_{10} 10^x = x \\log_{10} 10 = x$と変形できますよね.\n", "だから直線になります.\n", "\n", "さて,以上の変形,誘導をまとめて,先ほどのlogplot図の意図を解説してください." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 対数の公式\n", "## $\\log xy = \\log x + \\log y$\n", "\n", "$\\log xy = \\log x + \\log y$を $x=10^2, y = 10^{4}$で確認せよ." ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "(6, 6)" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "log(a**2,a)+log(a**4,a), log(a**2*a**4,a)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## $\\log_{10}(10^x10^y)$のplot3d\n", "\n", "$\\log_{10}(10^x10^y)$を (x,-n,n),(y,-n,n)でplotせよ.\n", "\n", "plot3dはテキストで紹介しているが,例はこんな感じ.\n", "``` python\n", "%matplotlib inline\n", "from sympy import *\n", "from sympy.plotting import plot3d\n", "x,y = symbols('x,y')\n", "\n", "plot3d(sin(x)*cos(y), (x,-3, 3),(y,-3, 3))\n", "```" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%matplotlib inline\n", "from sympy import *\n", "from sympy.plotting import plot3d\n", "x,y = symbols('x,y')\n", "\n", "plot3d(log(a**x*a**y,a), (x,-n,n),(y,-n,n))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## $\\log_{10} 10^x + \\log _{10} 10^y$のplot3d\n", "\n", "$\\log_{10} 10^x + \\log _{10} 10^y$を (x,-n,n),(y,-n,n)でplotせよ." ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot3d(log(a**x,a)+log(a**y,a), (x,-n,n),(y,-n,n))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "これらの公式から,対数を取ることによって,積の計算が和の計算に変換されることが確認できるでしょう.\n", "コンピュータが苦手とする大きな数と小さな数の掛け算が,たし算に変換できます.\n", "AIの中身である確率計算にとっても便利です.\n", "なぜなら確率は必ず正の値をとり,さらに指数計算が頻出するからです." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# おまけ(交差エントロピー誤差)\n", "\n", "対数を取るのは確率を考えるときに便利と述べました.\n", "実際にロジスティック回帰と呼ばれる手法では,確率の対数をとって,\n", "交差エントロピー誤差を考えます(p.215-9あたり).\n", "\n", "その様子を示したのが下のプロットです.\n", "$$f(x) = (1-x)^3x$$\n", "に対して$-\\log(f(x))$をとり,その様子をplotしています.\n", "\n", "* 大きな数での変化が緩やかになっていること,\n", "* 小さな数での変化が大きくなっていること,\n", "* 最大位置(最小位置)が変わらないこと\n", "\n", "に注意ください.\n", "なお,定義域は$0" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "\n", "from sympy import *\n", "x = Symbol('x')\n", "\n", "p = plot((1-x)**3*x, (x, 0, 1),\n", " legend=True, show=False)\n", "p.show()" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "p = plot(-log((1-x)**3*x), (x, 0.0, 1.0),\n", " legend=True, show=False)\n", "p.show()" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle - \\frac{- 3 x \\left(1 - x\\right)^{2} + \\left(1 - x\\right)^{3}}{x \\left(1 - x\\right)^{3}}$" ], "text/plain": [ "-(-3*x*(1 - x)**2 + (1 - x)**3)/(x*(1 - x)**3)" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "diff(-log((1-x)**3*x),x)" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{1 - 4 x}{x \\left(x - 1\\right)}$" ], "text/plain": [ "(1 - 4*x)/(x*(x - 1))" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "simplify(diff(-log((1-x)**3*x),x))" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[1/4]" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solve(diff(-log((1-x)**3*x),x))" ] }, { "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": "3.8.5" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": true }, "vscode": { "interpreter": { "hash": "f3f87633aac09da3bda522f97956bee375b5501d1579e6458804e567301cb62a" } } }, "nbformat": 4, "nbformat_minor": 4 }