{ "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.そのまま計算させてもいいですが,対数とって計算してそれを戻してください." ] }, { "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": "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": "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", "\n", "``` python\n", "a = 2\n", "n = 3\n", "```\n", "\n", "として再度同時plotせよ.\n" ] }, { "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": "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": "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": "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.yscale = 'log' \n", "```\n", "を加えて対数プロットを作成せよ." ] }, { "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": "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": "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": "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": "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$0" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "\n", "from sympy import *\n", "x = Symbol('x')\n", "\n", "p = plot((1-x)**3*x, (x, 0, 1),\n", " legend=True, show=False)\n", "p.show()" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/bob/anaconda3/lib/python3.8/site-packages/sympy/plotting/experimental_lambdify.py:233: UserWarning: The evaluation of the expression is problematic. We are trying a failback method that may still work. Please report this as a bug.\n", " warnings.warn('The evaluation of the expression is'\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "p = plot(-log((1-x)**3*x), (x, 0.0, 1.0),\n", " legend=True, show=False)\n", "p.show()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle - \\frac{- 3 x \\left(1 - x\\right)^{2} + \\left(1 - x\\right)^{3}}{x \\left(1 - x\\right)^{3}}$" ], "text/plain": [ "-(-3*x*(1 - x)**2 + (1 - x)**3)/(x*(1 - x)**3)" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "diff(-log((1-x)**3*x),x)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{1 - 4 x}{x \\left(x - 1\\right)}$" ], "text/plain": [ "(1 - 4*x)/(x*(x - 1))" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "simplify(diff(-log((1-x)**3*x),x))" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[1/4]" ] }, "execution_count": 20, "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 } }, "nbformat": 4, "nbformat_minor": 4 }