{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\t
\n", "\t\tSageでのグラフの使い方について、説明します。\n", "\t\tレファレンスマニュアル\n", "\t\tを参考にしながら見てください。\n", "\t
\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "テーブル用のCSSの読み込み、jupyter用のdisplayメソッド、sage_utilを読み込みます。\n", "
\n", "" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "\n", "\t\tplotの呼び出しは、以下の形式で覚えると便利です。\n", "
\n", "plot(関数, [変数名, 最小, 最大], オプション)\n", "\n", "\t\tオプションは、省略可能です。plotのオプションは、plot.optionsで知ることができます。\n", "\t\tそれ以外にもGraphicsのオプションも使えます。よく使うオプションを以下にしめします。\n", "\t\n", "\t\t
\n", "\t\t3次元多項式の場合には、最初にプロットで使用する変数xをvar関数で定義します。\n", "\t\t次に関数fを定義します。今回はplotの結果をf_pltに代入していますので、最後に\n", "\t\tshow関数でf_pltを表示します。\n", "\t
\n", "\t\n", "\t\tf_plt変数に代入することによって、後で他のグラフと重ね合わせて表示することが\n", "\t\tできます。\n", "\t
\n", "" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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yYeTnSy++KN1yi1SnjutqAACJgEA+jPfek9atkx54wHUlAIBEQevMn/A8qWVL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\nnP59QkcAAAAASUVORK5CYII=\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = var('x')\n", "f = x^3 - x^2 - 2*x\n", "f_plt = plot(f, [x, -2.5, 2.5])\n", "show(f_plt, figsize=5) " ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "\n", "\t\n", "\t\tplot.optionsを知るには、plot?でヘルプを表示したり、plot_optionsを表示するとよいでしょう。\n", "\t
\n", "" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "{'adaptive_recursion': 5,\n", " 'adaptive_tolerance': 0.01,\n", " 'alpha': 1,\n", " 'aspect_ratio': 'automatic',\n", " 'detect_poles': False,\n", " 'exclude': None,\n", " 'fill': False,\n", " 'fillalpha': 0.5,\n", " 'fillcolor': 'automatic',\n", " 'legend_label': None,\n", " 'plot_points': 200,\n", " 'rgbcolor': (0, 0, 1),\n", " 'thickness': 1}" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# plotのオプションを知る\n", "plot.options " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\t\n", "\t\t点$(x_0, y_0)$での接線の傾きは、関数fの微分の$x_0$での値から得ることができますので、\n", "\t\t接線の式は、以下のように求めることができます。\n", "$$\n", "\t\t(y - y_0) = f'(x_0) (x - x_0)\n", "$$\t\t\n", "\t\t$y_0$の値は、$f(x_0)$ですから、接線の式は以下のようになります。\n", "$$\n", "\t\ty = f'(x_0) (x - x_0) + f(x_0)\n", "$$\n", "\t
\n", "\t\n", "\t\n", "\t\tこの計算をSageを使って計算してみましょう。まずSageの変数x0を定義し、y0にf(x=x0)の値を代入します。\n", "\t\tf1にfの微分をセットします。\n", "\t
\t\n", "" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "3*x^2 - 2*x - 2" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# (x0, y0)での接線を求める\n", "x0 = var('x0')\n", "y0 = f(x=x0)\n", "f1 = diff(f, x)\n", "show(f1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\t\n", "\t\t材料がそろったので、接線の式を定義し表示します。確認のために$x_0 = 0$での式も表示します。\n", "\t
\n", "\t\n", "\t\t$x_0 = 0$での接線は、原点を通り傾き-2と求まりました。\n", "\t
\n", "" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "x0^3 + (3*x0^2 - 2*x0 - 2)*(x - x0) - x0^2 - 2*x0" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/plain": [ "-2*x" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# x0 = 0での接線の式\n", "y = f1(x=x0)*(x - x0) + y0\n", "show(y)\n", "show(y(x0 = 0))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\t\n", "\t\tこの直線をプロットしてみましょう。\n", "\t\tx0=0での接線の式なので、plotの引数にはyではなく、y(x0=0)が渡されていることに注意してください。\n", "\t
\n", "\t\n", "\t\t重ね合わせたときに区別できるように線の色を緑にします。線の色は、rgbcolorオプションで指定します。\n", "\t
\n", "" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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DrHazkDoyFbcKb0ERrsDmM5tFZ+kkDjKRDkpISEB6ejocHR1FpxBp\nRJv6baAMVaJbk24YtHUQgncH42HpQ9FZOoWDTKRjbty4gUmTJiE2Nhampqaic4g0xt7CHpv6b0JE\nrwjEnI6Ba4Qrvsv7TnSWzuAgE+kQtVqNYcOGYfr06WjWrJnoHCKNkyQJY13GIis4CyYyE7SKbIVv\nM7/lZTfBQSbSKYsXL0aVKlUwYcIE0SlEWtW8RnNkjMnAKKdRGL93PPpt7oe7xXdFZwnFQSYSJDY2\nFjY2NrCxsYGtrS2OHTuGFStWICoqSnQaUaWwNLPEqp6rsG3gNiRfToYiTIHjV4+LzhKGt18kEqSo\nqAh5eXlPf79582bMmTMHkiQ9fVt5eTlkMhkaNGiAixcvPvM4T26/6OPj85fvOQcGBiIwMFA7fwEi\nDbqafxWDtw3Gyesn8X8d/g8ftvsQJjIT0VmVioNMpCPu3buHW7du/eFt3t7eGDZsGEaOHImmTZs+\n8+N4P2QyFGUVZZifMh8Lji1Ah9c7IMY/Bo62xnOmAX+Ek0hHVKtWDdWqVfvD28zMzFC7du2/HWMi\nQ2IqM8X8TvPh1cgLQ7YPgTxMjii/KPR+q7fotErB7yET6bDfv3xNZCw6vt4RqlAV2tRvA994X0za\nNwmPyh6JztI6vmRNpOf4kjUZKrVaja8zvsa0Q9PQvEZzxPeLx1vV3xKdpTV8hkxERDpJkiS85/4e\nTo0+hYelD+ES4YJoZbTBnrPMQSYiIp3mVMcJ2cHZGNBiAEbuHImghCAUlBSIztI4DjIREek86yrW\niPKLQox/DHaf2w3ncGdk3sgUnaVRHGQiItIbQ1oOQW5ILqpZVoPHWg98fuJzVKgrRGdpBAeZiIj0\nShOHJkgblYbJ7pMx7dA09IztibwHef/+gTqOg0xERHqnikkVfOb9GfYN2Yfsm9mQh8lx6OdDorNe\nCQeZiIj0Vvc3ukMVqsJ/av0H3WK6YebhmSgtLxWd9VI4yEREpNfq2NTBgaADWNR5EZadXIZ2Ue1w\n6d4l0VkvjINMRER6TybJMMNzBlJHpiKvKA+KcAU2fb9JdNYL4SATEZHBaF2vNXJDctH9je4I2BaA\nsbvGouhxkeis58JBJiIig2JvYY/4fvFY3Xs1Nn63Ea6Rrjidd1p01r/iIBMZiICAAPj6+iIuLk50\nCpFwkiRhtPNoZAVnwUxmBrdIN6zMWKnTl93kzSWI9BxvLkH0z4pLi/HBwQ+wKmsV+rzdB2t818DB\n0kF01l/wGTIRERk0SzNLrOy5EtsHbkfK5RQowhRIvZIqOusvOMhERGQU/Jv5QxmqREP7hui4riPm\np8xHeUW56KynOMhERGQ0Gtg1QPLwZMxpNwfzUuah8/rOuF5wXXQWAA4yEREZGVOZKeZ1moekYUm4\ncPcC5GFy7Dq3S3QWB5mIiIxTh9c7QBmqRNv6beEX74f39r2HR2WPhPVwkImIyGhVr1odOwN2YkX3\nFQjPDkfr1a1x7s45IS0cZCIiMmqSJGGi+0Skj0nHo7JHcI5wRlRuVKWfs8xBJiIiAqCorUB2cDYG\ntRiEUbtGYcj2ISgoKai0x+cgExER/Y9VFSus9VuL2L6xSDyfCKdwJ2TcyKiUx+YgExER/UngfwKR\nG5KL1yxfQ9u1bfFZ2meoUFdo9TE5yERERM/QxKEJjo86jimtp2D64enosbEH8h7kae3xOMhERER/\no4pJFSztuhT7h+xH7i+5kIfJcfDng1p5LA4yERHRv+j2RjeoQlVoWaslusV0w4xDM1BaXqrRx+Ag\nExERPYfa1rWxP2g/lnRZgi9OfQHPKE9cvHdRY8fn7ReJ9NyT2y/6+PjA1NQUgYGBCAwMFJ1FZNDS\nr6cjcFsg7CzskBOcA0mSXvmYHGQiPcf7IROJkf8oHzcLb6JZjWYaOZ6pRo5CRERkZOws7GBnYaex\n4/F7yERERDqAg0xERKQDOMhEREQ6gINMRESkAzjIREREOoCnPRHpObVajcLCQtjY2GjkXEgiEoOD\nTEREpAP4kjUREZEO4CATERHpAA4yERGRDuAgExER6QAOMhERkQ7gIBMREekADjIREZEO+H9De4v4\n40F0mwAAAABJRU5ErkJggg==\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "y_plt = plot(y(x0=0), [x, -2.5, 2.5], rgbcolor='green')\n", "show(y_plt, figsize=5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\t\n", "\t\t接線を計算したポイントを示すために、point関数を使って点を表示します。\n", "\t
\n", "\t\n", "\t\tpoint関数の使い方は、以下の通りです。座標は、リストまたはタプル形式で与えます。\n", "
\n", "point(座標, オプション属性(pointsize, rgccolor, faceted等))\n", "\n", "\t\n", "" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# x = 0のポイントをセット\n", "pt = (0, f(x=0))\n", "pt_plt = point(pt, rgbcolor='red', pointsize=30)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\t
\n", "\t\tSageのグラフ表示機能の最大の特徴は、重ね合わせです。\n", "\t\tこれまで計算した以下の結果を同時に表示してみましょう。\n", "\t\t
\n", "\t\t重ね合わせは至って簡単で上記の3つの変数を足し合わせて、showメソッドで表示するだけです。\n", "\t
\n", "" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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58CnIfmL8eHjuObMIyLXX2p5G3ERBDjzHC4+z4MtT7zkrzsFBQfYDH34IcXHw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\niAsoyCIiIi6gIIuIiLiAgiwiIuIC/w/lj7snV5aF3gAAAABJRU5ErkJggg==\n", "text/plain": [ "Graphics object consisting of 3 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "(f_plt + y_plt + pt_plt).show(figsize=5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "\t\tインタラクティブ機能とアニメーション機能は、SageMathカーネルでは動作しませんので、ここでは省略します。\n", "\t
\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\t\n", "\t\tSageのプロット結果は、縦に表示されてしまうため、結果を比較したときには不便です。\n", "\t
\n", "\t\n", "\t\tこのような場合には、htmlコマンドにプロットしたいグラフのリストを渡すと、\n", "\t\t表形式に変換して表示してくれます。表示するグラフのオプションにfigsizeでグラフの\n", "\t\t大きさを小さくしておくとよいでしょう。\n", "\t
\n", "\t\n", "\t\t以下にsin曲線とcos曲線の表示例を示します。\n", "\t
\n", "\n" ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "sin曲線 | cos曲線 |
---|---|
\n", "\t\tデータを表示するのに便利なのが、list_plot関数です。\n", "\t
\n", "\t\n", "\t\tlist_plot関数は、以下のように使用します。\n", "
\n", "list_plot(プロットするリスト, オプション)\t\n", "\t\t\n", "\t\n", "\t
\n", "\t\tリストの要素に[x, y]形式で座標を指定すると分布図が表示されます。\n", "\t\tまた、plot関数でエラーで表示できない場合の代替手段としてlist_plot関数を使うこともあります。\n", "\t
\n", "\t\n", "\t\t以下にデータ点のプロットの場合とデータを結ぶ場合の例を示します。\n", "\t
\n", "" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# データを結ぶ\n", "list_plot([1, 2, 4, 3, 6], plotjoined=True, figsize=5) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\t\n", "\t\t異なるデータを同時に表示する場合には、rgbcolorオプションで色をセットしたり、\n", "\t\tlegen_labelでデータの種類をセットすると便利です。\n", "\t
\n", "" ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# データ(座標)のプロット\n", "c1 = [[1,2],[1,4],[2,4]]\n", "c2 = [[2,1],[5,1],[4,2]]\n", "# プロットして分布を確認\n", "pl1 = list_plot(c1, rgbcolor='red', legend_label='c1')\n", "pl2 = list_plot(c2, rgbcolor ='blue', legend_label='c2')\n", "(pl1+pl2).show(xmin=0, xmax=5, ymin=0, figsize=5) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\t\n", "\t\tプロットしたい関数ではなく、条件などの関係式を表示したいときがあります。\n", "\t\tこのような場合には、implicit_plotを使うと便利です。\n", "\t
\n", "\t\n", "\t\timplicit_plotの例として、単位円を表示してみます。\n", "\t\t単位円の条件は、以下のように与えられます。\n", "$$\n", "\t\tx^2 + y^2 = 1\n", "$$\t\t\n", "\t
\n", "\t\n", "\t\tこれをimplicit_plotで表示すると以下のようになります。\n", "\t
\n", "\n" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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K8UjPPy8LKMyfr7oSIucVFADTp0uPmuho1dWYh1Mhn52dDYvFAn9//8se9/f3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\n9OjROHbsGMaPH+9sOZVKTk5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"text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# 関係を満たすグラフを表示する\n", "x, y = var('x y')\n", "i_plt = implicit_plot(x^2 + y^2 == 1, [x, -1.5, 1.5], [y, -1.5, 1.5])\n", "i_plt.show(aspect_ratio=1, figsize=5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\t\n", "\t\tx, yが時間変数t(パラメータ)によって表される場合、parametric_plot関数\n", "\t\tを使って表示すると簡単です。\n", "\t
\n", "\t\n", "\t\tパラメトリックプロットの例として、以下のサイクロイド曲線をparametric_plot関数\n", "\t\tで表示してみます。\n", "\t\t\n", "$$\n", "\t\t\\begin{eqnarray}\n", "\t\t\tx = 2 (t - sin(t)) \\\\\n", "\t\t\ty = 2 (1 - cos(t))\n", "\t\t\\end{eqnarray}\n", "$$\n", "\t\t
\t\n", "" ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# 媒介変数表示\n", "t = var('t')\n", "x = 2*(t-sin(t))\n", "y = 2*(1-cos(t))\n", "# サイクロイドのプロット(パラメトリックプロットの例)\n", "parametric_plot([x, y], (t, 0, 2*pi), figsize=5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\t\n", "\t\t3次元のグラフには、plot3d関数を使用します。重ね合わせは2次元のグラフと同じように使えます。\n", "\t
\n", "\t\n", "\t\t表示された3次元図形はマウスで自由に拡大、回転することができます。(驚きました)\t\t\n", "\t
\n", "\n" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "