{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# 微分\n", " 数値積分の反対は数値微分です。数値積分よりも数値微分の計算は簡単です。\n", " \n", " 導関数の標準的な定義は次のとおりです。\n", "\n", "$$\\frac{df}{dx} = \\lim_{h \\to 0} \\frac{f(x+h)-f(x)}{h}$$ \n", "\n", " [0,3] の間の $f(x) = -x^4 + 4x^3 + 2$ について考えてみましょう。\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "plt.rcParams['font.family'] = \"Hiragino sans\" #for Mac\n", "#plt.rcParams['font.family'] = \"MS Gothic\" #for Windows\n", "\n", "#define the function\n", "f = lambda x: -x**4 + 4*x**3 + 2\n", "\n", "#define the parameters\n", "x_min, x_max = 0, 3\n", "npoints = 100\n", "x0 = (x_min+x_max)/2\n", "deltax = 0.5" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [], "source": [ "#draw the plot\n", "x = np.linspace(x_min, x_max, npoints)\n", "plt.plot(x,f(x))\n", "\n", "#draw the derivative\n", "x_1 = np.array([x0-deltax, x0, x0+deltax])\n", "plt.plot(x_1,f(x_1),'-o')\n", "\n", "for point in x_1:\n", " linex, liney = [point, point], [0, f(point)]\n", " plt.plot(linex, liney, color='black', linewidth=2.0) \n", "\n", "plt.text(x_1[0]+deltax/2, f(x_1[0]+deltax/2)+1, r'後方差分', {'ha': 'left', 'va': 'bottom'}, rotation=90) \n", "plt.text(x_1[1]+deltax/2, f(x_1[1]+deltax/2)+1, r'前方差分', {'ha': 'left', 'va': 'bottom'}, rotation=90) " ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ " \n", "plt.xlabel('x')\n", "plt.ylabel('$f(x)$')\n", "plt.xlim([0,3])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## 前方差分, 後方差分, 中央差分\n", "\n", " 点 $x$ で数値微分することを考えます。プログラミングで数値微分では、微分を差分で近似します。\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### 前方差分\n", "$$\\frac{df}{dx} = \\lim_{h \\to 0} \\frac{f(x+h)-f(x)}{h}$$ \n", "\n", "### 後方差分\n", "$$\\frac{df}{dx} = \\lim_{h \\to 0} \\frac{f(x)-f(x-h)}{h}$$ \n", "\n", " 通常、前方差分と後方差分はほぼ同じ答えを示し、多くの場合どちらを使用してもかまいませんが、ほとんどの場合で前方差分を使用します。\n", "\n", "\n", "\n", "### 中央差分\n", "$$\\frac{df}{dx} = \\lim_{h \\to 0} \\frac{f(x+h/2)-f(x-h/2)}{h}$$ \n", "\n", " 点 $x$ で関数の導関数に不連続がある場合は注意が必要です。" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## 演習:前方差分と後方差分のプログラムを作成せよ" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "#define the function\n", "f = lambda x: -x**4 + 4*x**3 + 2\n", "\n", "#-----------------------------------------------------\n", "#define the derivative(f, x, h) here\n", "#-----------------------------------------------------\n", "\n", "h = 0.001\n", "xrange = np.arange(0, 3, h)\n", "data = []\n", "\n", "for x in xrange:\n", " data.append(derivative(f, x, h))\n", "\n", "plt.plot(xrange, data)\n", "#plt.plot(xrange, xrange**3 - 2*xrange**2 +1) # 解析的に求めた例も追加した\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## 2階微分\n", " 関数 $f(x)$ の 2次導関数の数値近似を導出することもできます。2次導関数は1次導関数の導関数であるため、1次導関数の式を2回適用することで計算できます。\n", "\n", " たとえば、中心差分の式から始めて、$x + h/2$ と $x − h/2$ で一次導関数の式を次のように書くことができます。\n", "\n", "$$f'(x+h/2) \\approx \\frac{f(x+h)-f(x)}{h}$$\n", "$$f'(x-h/2) \\approx \\frac{f(x)-f(x-h)}{h}$$\n", "\n", "\n", "$$f\"(x) \\approx \\frac{f(x+h)-2f(x)+f(x-h)}{h^2}$$ \n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## 課題:二次導関数を計算するプログラムを作成せよ\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## ばらつきが大きいデータの微分\n", " グラフにプロットすると下の図のように見える量の測定値があるとします。 \n", " \n", " " ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "x,y = np.loadtxt('noise.dat', unpack=True)\n", "#data = np.column_stack([x,y])\n", "#np.savetxt('noise.dat', data)\n", "\n", "plt.plot(x,y)\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ " 実験で得られるデータは、このようにノイズが含まれます。曲線の全体的な形状は分かりますが滑らかではありません。 \n", "\n", " ここで、この曲線の一次導関数を計算したい場合、各点での前方差分を計算し、取得した値をプロットするプログラムを作成します。 " ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def derivative(x, h):\n", " res = x[1:] - x[:-1]\n", " return res/(2*h)\n", "\n", "#for x in xrange:\n", "# data.append(derivative(func, x, h))\n", "\n", "#誤差が多い方法\n", "yd = derivative(y, x[1] - x[0])\n", "\n", "plt.plot(yd)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ " みてわかるように、微分をとることでノイズの問題がさらに悪化しました。もうこの曲線の形状を確認することは不可能です。これは数値微分によくある問題です。微分をとる曲線にノイズがある場合、微分をとることによってノイズが大幅に誇張され、結果が役に立たなくなることが多々あります。" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ " 残念ながらこの種の問題は実験で取得したデータでは一般的であり、これが数値微分が数値積分よりも使用されない理由の1つです。この問題を軽減するためにできることはいくつかありますが、それらはすべて結果の精度を低下させることになります。\n", "\n", "- h の値を増やす\n", "\n", "- 導関数が必要な点の近くのデータの一部に曲線を当てはめる\n", "\n", "- 微分する前に他の方法でデータを平滑化する" ] } ], "metadata": { "celltoolbar": "Slideshow", "kernelspec": { "display_name": "Python [conda env:base] *", "language": "python", "name": "conda-base-py" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.12" } }, "nbformat": 4, "nbformat_minor": 4 }