{ "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$0" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "\n", "from sympy import *\n", "x = Symbol('x')\n", "\n", "p = plot((1-x)**3*x, (x, 0, 1),\n", " legend=True, show=False)\n", "p.show()" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/bob/anaconda3/lib/python3.8/site-packages/sympy/plotting/experimental_lambdify.py:233: UserWarning: The evaluation of the expression is problematic. We are trying a failback method that may still work. Please report this as a bug.\n", " warnings.warn('The evaluation of the expression is'\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "p = plot(-log((1-x)**3*x), (x, 0.0, 1.0),\n", " legend=True, show=False)\n", "p.show()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle - \\frac{- 3 x \\left(1 - x\\right)^{2} + \\left(1 - x\\right)^{3}}{x \\left(1 - x\\right)^{3}}$" ], "text/plain": [ "-(-3*x*(1 - x)**2 + (1 - x)**3)/(x*(1 - x)**3)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "diff(-log((1-x)**3*x),x)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{1 - 4 x}{x \\left(x - 1\\right)}$" ], "text/plain": [ "(1 - 4*x)/(x*(x - 1))" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "simplify(diff(-log((1-x)**3*x),x))" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[1/4]" ] }, "execution_count": 5, "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": "3.8.3" }, "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 }