{ "cells": [ { "cell_type": "markdown", "metadata": { "toc": "true" }, "source": [ "

Table of Contents

\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "
\n", "\n", "
\n", "代数方程式(fsolve)\n", "
\n", "
\n", "
\n", "file:/Users/bob/Github/TeamNishitani/jupyter_num_calc/fsolve\n", "
\n", "https://github.com/daddygongon/jupyter_num_calc/tree/master/notebooks_python\n", "
\n", "cc by Shigeto R. Nishitani 2017-23\n", "
\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 概要\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "代数方程式の解$f(x)=0$を数値的に求めることを考える.標準的な\n", "> 二分法(bisection method)とニュートン法(Newton's method)\n", "\n", "の考え方と例を説明し,\n", ">収束性(convergency)と安定性(stability)\n", "\n", "について議論する.さらに収束判定条件について言及する.\n", "\n", "\n", "二分法のアイデアは単純.中間値の定理より連続な関数では,関数の符号が変わる二つの変数の間には根が必ず存在する.したがって,この方法は収束性は決して高くはないが,\n", "確実.一方,Newton法は関数の微分を用いて収束性を速めた方法である.しかし,不幸にして収束しない場合や微分に時間がかかる場合があり,初期値や使用対象には注意\n", "を要する.\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# pythonの標準関数による解法\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "pythonでは代数方程式の解は,solveで求まる.\n", "\n", "$$\n", "x^2-4x+1 = 0\n", "$$\n", "の解を考える.未知の問題では時として異常な振る舞いをする関数を相手にすることがあるので,先ずは関数の概形を見ることを常に心がけるべき." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "from sympy import *\n", "\n", "x = symbols('x')\n", "\n", "def func(x):\n", " return x**2-4*x+1\n", "\n", "x = np.linspace(-1, 5, 100) #0から2πまでの範囲を100分割したnumpy配列\n", "y = func(x)\n", "plt.plot(x, y, color = 'b')\n", "\n", "plt.plot(0, 0, \"o\", color = 'k')\n", "# plot([x1, x2], [y1, y2], color='k', linestyle='-', linewidth=2)\n", "plt.hlines(0, -1, 5, color='k', linestyle='-', linewidth=2)\n", "plt.vlines(0, -4, 6, color='k', linestyle='-', linewidth=2)\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "もし,解析解が容易に求まるなら,その結果を使うほうがよい.\n", "pythonの解析解を求めるsolveは,sympyから呼び出して," ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[2 - √3, √3 + 2]\n" ] } ], "source": [ "from sympy import *\n", "\n", "x = symbols('x')\n", "\n", "def func(x):\n", " return x**2-4*x+1\n", "\n", "pprint(solve(func(x), x))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "と即座に求めてくれる.数値解は以下の通り求められる.\n", "コメントを外してみてください.ちょっと注意が必要ということがわかるでしょうか?" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0.26794919]\n", "[2.01500001]\n", "[0.26794919 3.73205081]\n", "[0.26794919 0.26794919]\n" ] } ], "source": [ "from scipy.optimize import fsolve\n", "def func(x):\n", " return x**2-4*x+1\n", "\n", "pprint(fsolve(func, 0))\n", "pprint(fsolve(func, 2.0))\n", "pprint(fsolve(func, [0, 5]))\n", "pprint(fsolve(func, [0, 0.8]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 二分法とNewton法の原理\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 二分法(bisection) \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "二分法は領域の端$x_1, x_2$で関数値$f(x_1),f(x_2)$を求め,中間の値を次々に計算して,解を囲い込んでいく方法である.\n", "\n", "|$x_1$ | $x_2$ |$f(x_1)$ | $f(x_2)$ |\n", "|:----|:----|:----|:----|\n", "|0.0 | 0.8 |      |      |\n", "|    |     |     |      |\n", "|    |     |     |      |\n", "|    |     |     |      |\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "def func(x):\n", " return x**2-4*x+1\n", "\n", "x = np.linspace(0, 0.8, 100) #0から2πまでの範囲を100分割したnumpy配列\n", "y = func(x)\n", "plt.plot(x, y)\n", "\n", "plt.plot(0, func(0), \"o\", color = 'r')\n", "plt.plot(0.8, func(0.8), \"o\", color = 'r')\n", "# plot([x1, x2], [y1, y2], color='k', linestyle='-', linewidth=2)\n", "plt.hlines(0, 0, 0.8, color='k', linestyle='-', linewidth=2)\n", "plt.vlines(0, -2, 1, color='k', linestyle='-', linewidth=2)\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Newton法(あるいはNewton-Raphson法) \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Newton法は最初の点$x_1$から接線をひき,それが$x$軸(y=0)と交わった点を新たな点$x_2$とする.さらにそこでの接線を求めて...\n", "\n", "という操作を繰り返しながら解を求める方法である.関数の微分をdf(x)とすると,これらの間には\n", "\n", "|   $x_{i+1} = x_i + \\ldots$   |\n", "|:----|\n", "|       |\n", "という関係が成り立つ.\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2⋅x - 4\n", "-2.0⋅x\n", "0 -2.00000000000000\n", "1.00000000000000 -3.00000000000000\n" ] } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from sympy import *\n", "\n", "x = symbols('x')\n", "\n", "def func(x):\n", " return x**2-4*x+1\n", "\n", "def df(x):\n", " return diff(func(x), x)\n", "\n", "pprint(df(x))\n", "\n", "x1 = 1.0\n", "df(x).subs(x, x1)*(x-x1)+func(x1)\n", "\n", "def line_f(x, x1):\n", " return df(x).subs(x, x1)*(x-x1)+func(x1)\n", "\n", "\n", "pprint(line_f(x, 1.0))\n", "x0 = 0.0\n", "x1 = 1.0\n", "\n", "y0 = line_f(x, x1).subs(x, x0)\n", "y1 = line_f(x, x1).subs(x, x1)\n", "print(y0, y1)\n", "\n", "yy0 = line_f(x, x0).subs(x, x0)\n", "yy1 = line_f(x, x0).subs(x, x1)\n", "print(yy0, yy1)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x = np.linspace(x0-0.05, x1+0.05, 100)\n", "y = func(x)\n", "plt.plot(x, y)\n", "\n", "plt.plot(x0, func(x0), \"o\", color = 'r')\n", "plt.plot(x1, func(x1), \"o\", color = 'r')\n", "# plot([x1, x2], [y1, y2], color='k', linestyle='-', linewidth=2)\n", "plt.hlines(0, x0, x1, color='k', linestyle='-', linewidth=2)\n", "plt.vlines(0, -3.5,1.5, color='k', linestyle='-', linewidth=2)\n", "\n", "plt.plot([x0, x1], [y0, y1], color='b', linestyle='--', linewidth=1)\n", "plt.plot([x0, x1], [yy0, yy1], color='r', linestyle='--', linewidth=1)\n", "\n", "plt.grid()\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "|$x_1$ |$f(x_1)$ | $df(x_1)$ |\n", "|:----|:----|:----|\n", "|1.0 |      |      |\n", "|       |         |         |\n", "|       |         |         |\n", "|       |         |         |\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 二分法とNewton法のコード\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 二分法(bisection) \n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x1 x2 f1 f2 \n", "0.000 0.800 1.000 -1.560\n", "0.000 0.400 1.000 -0.440\n", "0.200 0.400 0.240 -0.440\n", "0.200 0.300 0.240 -0.110\n", "0.250 0.300 0.062 -0.110\n", "0.250 0.275 0.062 -0.024\n" ] } ], "source": [ "x1, x2 = 0.0, 0.8\n", "f1, f2 = func(x1), func(x2)\n", "print('%-6s %-6s %-6s %-6s' % ('x1','x2','f1','f2'))\n", "print('%-6.3f %-6.3f %-6.3f %-6.3f' % (x1,x2,f1,f2))\n", "for i in range(0, 5):\n", " x = (x1 + x2)/2\n", " f = func(x)\n", " if (f*f1>=0.0):\n", " x1, f1 = x, f\n", " else:\n", " x2, f2 = x, f\n", " print('%-6.3f %-6.3f %-6.3f %-6.3f' % (x1,x2,f1,f2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Newton法(あるいはNewton-Raphson法) \n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "#from sympy import *\n", "\n", "#x = symbols('x')\n", "def func(x):\n", " return x**2-4*x+1\n", "def df(x):\n", " return 2*x - 4" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.0000000000 -2.0000000000000000000000000\n", "0.0000000000 1.0000000000000000000000000\n", "0.2500000000 0.0625000000000000000000000\n", "0.2678571429 0.0003188775510204466812070\n", "0.2679491900 0.0000000084726737847873324\n", "0.2679491924 0.0000000000000000000000000\n" ] } ], "source": [ "epsilon = 10**(-10)\n", "x1 = 1.0\n", "f1 = func(x1)\n", "print('%-15.10f %-24.25f' % (x1,f1))\n", "for i in range(0, 5):\n", " x1 = x1 - f1 / df(x1)\n", " f1 =func(x1)\n", " print('%-15.10f %-24.25f' % (x1,f1))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 収束性と安定性" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "実際のコードの出力からも分かる通り,解の収束の速さは2つの手法で極端に違う.2分法では一回の操作で解の区間が半分になる.このように繰り返しごとに誤差幅が前回の誤差幅の定数($<1$)倍になる方法は1次収束(linear convergence)するという.Newton法では関数・初期値が素直な場合($f^{\\prime}(x) <> 0$)に,収束が誤差の2乗に比例する2次収束を示す.以下はその導出をMapleで示した.\n", "\n", "\n", "```maple\n", "> restart; ff:=subs(xi-x[f]=ei,series(f(xi),xi=x[f],4));\n", "```\n", "\n", "$$\n", "{\\it ff}\\, := \\,f \\left( x_{{f}} \\right) +D \\left( f \\right) \\left( x_{{f}} \\right) {\\it ei}+\\frac{1}{2}\\, D^{ \\left( 2 \\right) } \\left( f \\right) \\left( x_{{f}} \\right) {{\\it ei}}^{2} +\\frac{1}{6}\\, \n", "D^{ \\left( 3 \\right) } \\left( f \\right) \\left( x_{{f}} \\right) {{\\it ei}}^{3}+O \\left( {{\\it ei}}^{4} \\right)\n", "$$\n", "```maple\n", "> dff:=subs({0=x[f],x=ei},series(diff(f(x),x),x,3));\n", "```\n", "$$\n", "{\\it dff}\\, := \\,D \\left( f \\right) \\left( x_{{f}} \\right) + \n", "D^{ \\left( 2 \\right) } \\left( f \\right) \\left( x_{{f}} \\right) {\\it ei}+\n", "\\frac{1}{2}\\, D^{ \\left( 3 \\right) } \\left( f \\right) \\left( x_{{f}} \\right) {{\\it ei}}^{2} +O \\left( {{\\it ei}}^{3} \\right)\n", "$$\n", "```maple\n", "> ei1:=ei-ff/dff;\n", "```\n", "$$\n", "{\\it ei1}\\, := \\,{\\it ei}-{\\frac {f \\left( x_{{f}} \\right) +D \\left( f \\right) \\left( x_{{f}} \\right) {\\it ei}+\\frac{1}{2}\\, D^{ \\left( 2 \\right) } \\left( f \\right) \\left( x_{{f}} \\right) {{\\it ei}}^{2}+\\frac{1}{6}\\, D^{ \\left( 3 \\right) } \\left( f \\right) \\left( x_{{f}} \\right) {{\\it ei}}^{3}+O \\left( {{\\it ei}}^{4} \\right) }{D \\left( f \\right) \\left( x_{{f}} \\right) + D^{ \\left( 2 \\right) } \\left( f \\right) \\left( x_{{f}} \\right) {\\it ei} +\\frac{1}{2}\\, D^{ \\left( 3 \\right) } \\left( f \\right) \\left( x_{{f}} \\right) {{\\it ei}}^{2}+O \\left( {{\\it ei}}^{3} \\right) }}\n", "$$\n", "```maple\n", "> ei2:=simplify(convert(ei1,polynom));\n", "```\n", "$$\n", "{\\it ei2}\\, := \\,\\frac{1}{3}\\,\\frac {3\\, D^{ \\left( 2 \\right) } \\left( f \\right) \\left( x_{{f}} \\right) {{\\it ei}}^{2}+2\\, D^{ \\left( 3 \\right) } \\left( f \\right) \\left( x_{{f}} \\right) {{\\it ei}}^{3}\n", "-6\\,f \\left( x_{{f}} \\right) }{2\\,D \\left( f \\right) \\left( x_{{f}} \\right) +2\\, D^{ \\left( 2 \\right) } \\left( f \\right) \\left( x_{{f}} \\right) {\\it ei}+ D^{ \\left( 3 \\right) } \\left( f \\right) \\left( x_{{f}} \\right) {{\\it ei}}^{2}\n", "}\n", "$$\n", "```maple\n", "> ei3:=series(ei2,ei,3);\n", "```\n", "$$\n", "{\\it ei3}\\, := \\,-{\\frac {f \\left( x_{{f}} \\right) }{D \\left( f \\right) \\left( x_{{f}} \\right) }}+{\\frac {f \\left( x_{{f}} \\right) \\left( D^{ \\left( 2 \\right) } \\right) \\left( f \\right) \\left( x_{{f}} \\right) {\\it ei}}{ \\left( D \\left( f \\right) \\left( x_{{f}} \\right) \\right) ^{2}}}+ \\\\\n", "\\frac{1}{6}\\, \\frac{ 3\\, \\left( D^{ \\left( 2 \\right) } \\right) \\left( f \\right) \\left( x_{{f}} \\right) +3\\,{\\frac {f \\left( x_{{f}} \\right) \\left( D^{ \\left( 3 \\right) } \\right) \\left( f \\right) \\left( x_{{f}} \\right) }{D \\left( f \\right) \\left( x_{{f}} \\right) }}-6\\,{\\frac {f \\left( x_{{f}} \\right) \\left( \\left( D^{ \\left( 2 \\right) } \\right) \\left( f \\right) \\left( x_{{f}} \\right) \\right) ^{2}}{ \\left( D \\left( f \\right) \\left( x_{{f}} \\right) \\right) ^{2}}}}\n", "{ \\left( D \\left( f \\right) \\left( x_{{f}} \\right) \\right)}{{\\it ei}}^{2} +O \\left( {{\\it ei}}^{3} \\right)\n", "$$\n", "```maple\n", "> subs(f(x[f])=0,ei3);\n", "```\n", "$$\n", "\\frac{1}{2}\\,{\\frac { D^{ \\left( 2 \\right) } \\left( f \\right) \\left( x_{{f}} \\right) {{\\it ei}}^{2}}{D \\left( f \\right) \\left( x_{{f}} \\right) }}+O \\left( {{\\it ei}}^{3} \\right)\n", "$$\n", "注意すべきは,この収束性には一回の計算時間の差は入っていないことである.Newton法で解析的に微分が求まらない場合,数値的に求めるという手法がとられるが,これにかかる計算時間はばかにできない.二分法を改良した割線法(secant method)がより速い場合がある(NumRecipe9章参照).\n", "\n", "二分法では,収束は遅いが,正負の関数値の間に連続関数では必ず解が存在するという意味で解が保証されている.しかし,Newton法では,収束は速いが,必ずしも素直に解に収束するとは限らない.解を確実に囲い込む,あるいは解に近い値を初期値に選ぶ手法が種々考案されている.解が安定であるかどうかは,問題,解法,初期値に大きく依存する.収束性と安定性のコントロールが数値計算のツボとなる.\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 収束判定条件\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "どこまで値が解に近づけば計算を打ち切るかを決める条件を収束判定条件と呼ぶ.以下のような条件がある.\n", "\n", "\n", "|手法|判定条件|解説\n", "|:----|:----|:----|\n", "|$\\varepsilon$(イプシロン,epsilon)法 | |\n", "|$\\delta$(デルタ,delta)法 | |\n", "|占部法 | $ \\left| f(x_{i+1})\\right| > \\left| f(x_i)\\right| $ | 数値計算の際の丸め誤差までも含めて判定する条件\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### $\\epsilon, \\delta$を説明するための図 \n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "def func(x):\n", " return 0.4*(x**2-4*x+1)\n", "x1=0.25\n", "x0=0.4\n", "x = np.linspace(0.2, 0.4, 100)\n", "y = func(x)\n", "plt.plot(x, y, color = 'k')\n", "plt.plot(x1, func(x1), \"o\", color = 'r')\n", "plt.plot(x0, func(x0), \"o\", color = 'r')\n", "plt.plot([0.2,0.45],[0,0], color = 'k')\n", "plt.plot([x1,x0],[func(x1),func(x1)], color = 'b')\n", "plt.plot([x0,x0],[func(x0),func(x1)], color = 'b')\n", "\n", "plt.text(0.41, -0.07, r'$\\epsilon$', size='24') \n", "plt.text(0.32, 0.05, r'$\\delta$', size='24') \n", "\n", "\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "#from sympy import *\n", "\n", "#x = symbols('x')\n", "def func(x):\n", " return x**2-4*x+1\n", "def df(x):\n", " return 2*x - 4" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.0000000000 -2.0000000000000000000000000\n", "1.0000000000 -2.0000000000000000000000000\n", "0.0000000000 1.0000000000000000000000000\n", "0.2500000000 0.0625000000000000000000000\n", "0.2678571429 0.0003188775510204466812070\n", "0.2679491900 0.0000000084726737847873324\n", "0.2679491924 0.0000000000000000000000000\n" ] } ], "source": [ "epsilon = 10**(-10)\n", "x1 = 1.0\n", "f1 = func(x1)\n", "print('%-15.10f %-24.25f' % (x1,f1))\n", "for i in range(0, 20):\n", " x2 = x1 - f1 / df(x1)\n", " f2 =func(x2)\n", " print('%-15.10f %-24.25f' % (x1,f1))\n", " if abs(f2-f1) restart;\n", "> f:=(x,y)->4*x+2*y-6*x*y; g:=(x,y)->10*x-2*y+1;\n", "```\n", "$$\n", "f\\, := \\,( {x,y} )\\mapsto 4\\,x+2\\,y-6\\,xy \\\\\n", "g\\, := \\,( {x,y} )\\mapsto 10\\,x-2\\,y+1 \n", "$$\n", "```maple\n", "> p1:=plot3d({f(x,y)},x=-2..2,y=-2..2,color=red):\n", " p2:=plot3d({g(x,y)},x=-2..2,y=-2..2,color=blue):\n", " p3:=plot3d({0},x=-2..2,y=-2..2,color=gray):\n", " with(plots):\n", " display([p1,p2,p3],axes=boxed,orientation=[-150,70]);\n", "```\n", "\n", "\n", "解のある程度近くからは,Newton法で効率良く求められる.\n", "```maple\n", "> fsolve({f(x,y)=0,g(x,y)=0},{x,y});\n", "```\n", "$$\n", "\\left\\{ x=- 0.07540291160,y= 0.1229854420 \\right\\}\n", "$$\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "scrolled": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ ":21: MatplotlibDeprecationWarning: Axes3D(fig) adding itself to the figure is deprecated since 3.4. Pass the keyword argument auto_add_to_figure=False and use fig.add_axes(ax) to suppress this warning. The default value of auto_add_to_figure will change to False in mpl3.5 and True values will no longer work in 3.6. This is consistent with other Axes classes.\n", " plot3d = Axes3D(fig)\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "8ea97a408bdd4de5af20e70784bca926", "version_major": 2, "version_minor": 0 }, "image/png": 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\n", " \n", "
\n", " " ], "text/plain": [ "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib notebook\n", "\n", "\n", "import ipympl\n", "import matplotlib.pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D\n", "import numpy as np\n", "\n", "def f(x,y):\n", " return 4*x+2*y-6*x*y\n", "def g(x,y):\n", " return 10*x-2*y+1\n", "\n", "x = np.arange(-3, 3, 0.25)\n", "y = np.arange(-3, 3, 0.25)\n", "X, Y = np.meshgrid(x, y)\n", "Z1 = f(X,Y)\n", "Z2 = g(X,Y)\n", "\n", "fig = plt.figure()\n", "plot3d = Axes3D(fig)\n", "plot3d.plot_surface(X,Y,Z1) \n", "plot3d.plot_surface(X,Y,Z2, color='r') \n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 2020年度課題(中筋さんありがとう)\n", "\n", "1. 次に示した「例題:二分法とNewton法の収束性」および「解答例」をコピペして,pythonが動作することを確認せよ.\n", "\n", "1. 対象の関数を $f(x) = \\exp(-x)-2\\exp(-2x)$ として解答せよ.\n", "提出は2.だけでよい.\n", "\n", "ただし,func, dfuncは以下を使え.下の「exp関数に関する注意」参照" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "def func(x):\n", " return np.exp(-x)-2*np.exp(-2*x)\n", "\n", "def df(x):\n", " return -np.exp(-x) + 4*np.exp(-2*x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 例題:二分法とNewton法の収束性\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "代数方程式に関する次の課題に答えよ.(2004年度期末試験)\n", "1. $\\exp(-x) = x^2$を二分法およびニュートン法で解け.\n", "1. $n$回目の値$x_n$と小数点以下10桁まで求めた値$x_f=0.7034674225$との差$\\Delta x_n$の絶対値(abs)のlogを$n$の関数としてプロットし,その収束性を比較せよ.また,その傾きの違いを両解法の原理から説明せよ.\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 解答例 \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "+ funcで関数を定義.\n", "+ 関数をplotして概形を確認.\n", "+ 組み込みコマンドで正解を確認しておく.\n", "$$\n", "0.7034674224983916520498186018599021303429\n", "$$\n", "テキストからプログラムをコピーして走らせてみる.環境によっては,printf分の中の\"\\\"が文字化けしているので,その場合は修正して使用せよ.\n", "\n", "+ プロットのためにリストをlist_bisecで作成している.\n", "+ 同様にNewton法での結果をlist_newtonに入れる.\n", "+ list_bisec, list_newtonを片対数プロットして同時に表示.\n", "\n", "2分法で求めた解は,Newton法で求めた解よりもゆっくりと精密解へ収束している.これは,二分法が原理的に計算回数について一次収束なのに対して,Newton法は2次収束であるためである.解の差($\\delta$)だけでなく,関数値$f(x),\\epsilon$をとっても同様の振る舞いを示す.\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-2*x - exp(-x)\n" ] } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "from sympy import *\n", "\n", "x = symbols('x')\n", "\n", "\n", "def func(x):\n", " return exp(-x)-x**2\n", "\n", "def df(x):\n", " return diff(func(x), x)\n", "\n", "print(df(x))\n" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "8ea97a408bdd4de5af20e70784bca926", 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", 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\n", " \n", "
\n", " " ], "text/plain": [ "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def func(x):\n", " return np.exp(-x)-x**2\n", "def df(x):\n", " return -2*x - np.exp(-x)\n", "\n", "x0=0.0\n", "x1=1.0\n", "x = np.linspace(x0, x1, 100)\n", "y = func(x)\n", "plt.plot(x, y, color = 'k')\n", "plt.plot([x0,x1],[0,0])\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.7034674224983918" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from scipy.optimize import fsolve\n", "x0 = fsolve(func, 0.0)[0]\n", "x0" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " x1 x2 f1 f2\n", " +0.0000000000 +1.0000000000 +1.0000000000 -0.6321205588\n", " +0.5000000000 +1.0000000000 +0.3565306597 -0.6321205588\n", " +0.5000000000 +0.7500000000 +0.3565306597 -0.0901334473\n", " +0.6250000000 +0.7500000000 +0.1446364285 -0.0901334473\n", " +0.6875000000 +0.7500000000 +0.0301753280 -0.0901334473\n", " +0.6875000000 +0.7187500000 +0.0301753280 -0.0292404858\n", " +0.7031250000 +0.7187500000 +0.0006511313 -0.0292404858\n", " +0.7031250000 +0.7109375000 +0.0006511313 -0.0142486319\n", " +0.7031250000 +0.7070312500 +0.0006511313 -0.0067872536\n", " +0.7031250000 +0.7050781250 +0.0006511313 -0.0030651888\n", " +0.7031250000 +0.7041015625 +0.0006511313 -0.0012063109\n", " +0.7031250000 +0.7036132812 +0.0006511313 -0.0002774104\n", " +0.7033691406 +0.7036132812 +0.0001869053 -0.0002774104\n", " +0.7033691406 +0.7034912109 +0.0001869053 -0.0000452413\n", " +0.7034301758 +0.7034912109 +0.0000708348 -0.0000452413\n", " +0.7034606934 +0.7034912109 +0.0000127975 -0.0000452413\n", " +0.7034606934 +0.7034759521 +0.0000127975 -0.0000162218\n", " +0.7034606934 +0.7034683228 +0.0000127975 -0.0000017121\n", " +0.7034645081 +0.7034683228 +0.0000055427 -0.0000017121\n", " +0.7034664154 +0.7034683228 +0.0000019153 -0.0000017121\n", " +0.7034673691 +0.7034683228 +0.0000001016 -0.0000017121\n", "\n" ] } ], "source": [ "x1, x2 = 0.0, 1.0\n", "f1, f2 = func(x1), func(x2)\n", "print('%+15s %+15s %+15s %+15s' % ('x1','x2','f1','f2'))\n", "print('%+15.10f %+15.10f %+15.10f %+15.10f' % (x1,x2,f1,f2))\n", "\n", "list_bisec = [[0],[abs(x1-x0)]]\n", "for i in range(0, 20):\n", " x = (x1 + x2)/2\n", " f = func(x)\n", " if (f*f1>=0.0):\n", " x1, f1 = x, f\n", " list_bisec[0].append(i)\n", " list_bisec[1].append(abs(x1-x0))\n", " else:\n", " x2, f2 = x, f\n", " list_bisec[0].append(i)\n", " list_bisec[1].append(abs(x2-x0))\n", "\n", " print('%+15.10f %+15.10f %+15.10f %+15.10f' % (x1,x2,f1,f2))\n", "\n", "list_bisec\n", "print()" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-0.7182818284590451" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df(-1.0)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.0000000000 -0.6321205588285576659757226\n", "0.7330436052 -0.0569084480040253914978621\n", "0.7038077863 -0.0006473915387465445370196\n", "0.7034674683 -0.0000000871660306156485376\n", "0.7034674225 -0.0000000000000014988010832\n", "\n" ] } ], "source": [ "x1 = 1.0\n", "f1 = func(x1)\n", "list_newton = [[0],[x1]]\n", "print('%-15.10f %+24.25f' % (x1,f1))\n", "for i in range(0, 4):\n", " x1 = x1 - f1 / df(x1)\n", " f1 =func(x1)\n", " print('%-15.10f %+24.25f' % (x1,f1))\n", " list_newton[0].append(i)\n", " list_newton[1].append(abs(x1-x0))\n", "\n", "list_newton\n", "print()" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "\n", "X = list_bisec[0]\n", "Y = list_bisec[1]\n", "plt.plot(X, Y)\n", "\n", "X = list_newton[0]\n", "Y = list_newton[1]\n", "plt.plot(X, Y)\n", "\n", "plt.yscale(\"log\") # y軸を対数目盛に\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## exp関数に関する注意\n", "exp関数のimport元で振る舞いが違うみたい.\n", "```python\n", "ValueError: sequence too large; cannot be greater than 32\n", "```\n", "がplot作成の前段階で出る.\n", "numpyでやるときには,np.exp(-x)などとしてる.\n", "\n", "でも,diffには通らない.そのあたり,覚悟して使う関数を決めないと..." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "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" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": false, "user_envs_cfg": false }, "toc": { "base_numbering": 1, "nav_menu": { "height": "12px", "width": "252px" }, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": true, "toc_position": {}, "toc_section_display": "block", "toc_window_display": true }, "vscode": { "interpreter": { "hash": "f3f87633aac09da3bda522f97956bee375b5501d1579e6458804e567301cb62a" } } }, "nbformat": 4, "nbformat_minor": 2 }