{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "
\n", "数値計算2016解答例\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", " 2019/12/06 西谷滋人 \n", "
" ] }, { "cell_type": "markdown", "metadata": { "toc": "true" }, "source": [ "

Table of Contents

\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 数値解の収束性" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "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", "def func(x):\n", " return -3*np.exp(-x)+np.exp(-3*x)\n", "\n", "x1, x2 = -1.0, 0.0\n", "x = np.linspace(x1,x2, 101)\n", "y = func(x)\n", "plt.plot(x, y, color = 'k')\n", "plt.plot([x1,x2],[0,0])\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " 上では,funcの中身を修正している.plotの範囲(x1..x2)は変える必要はない.\n", "以下では, x0が解析解であるが,これは修正している." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " x1 x2 f1 f2\n", " -1.0000000000 +0.0000000000 +11.9306914378 -2.0000000000\n", " -1.0000000000 -0.5000000000 +11.9306914378 -0.4644747418\n", " -0.7500000000 -0.5000000000 +3.1367357865 -0.4644747418\n", " -0.6250000000 -0.5000000000 +0.9160812480 -0.4644747418\n", " -0.5625000000 -0.5000000000 +0.1407849543 -0.4644747418\n", " -0.5625000000 -0.5312500000 +0.1407849543 -0.1809993961\n", " -0.5625000000 -0.5468750000 +0.1407849543 -0.0251426693\n", " -0.5546875000 -0.5468750000 +0.0565301134 -0.0251426693\n", " -0.5507812500 -0.5468750000 +0.0153750461 -0.0251426693\n", " -0.5507812500 -0.5488281250 +0.0153750461 -0.0049629758\n", " -0.5498046875 -0.5488281250 +0.0051861813 -0.0049629758\n", "\n" ] } ], "source": [ "x1, x2 = -1.0, 0.0\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", "x0 = -1/2*np.log(3.0)\n", "list_bisec = [[0],[abs(x1-x0)]]\n", "for i in range(0, 10):\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": 14, "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", "\n", "X = list_bisec[0]\n", "Y = list_bisec[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": [ "# Gauss-Seidelの収束性\n", "\n", "* 以下のcodeはGauss-Seidelに直したコード.\n", "* np.set_printoptions(precision=6, suppress=True)\n", "で6桁で表示させて見やすくしている.\n", "* tt=0.2とした場合は,7回程度のループで収束しているのがわかる.\n", "* ttを変更した場合は,これで収束せず,iterのrangeを100回程度まで取らないと収束する回数は見えない.\n" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0 [ 2. 1.6 1.28]\n", "1 [ 1.424 1.4592 1.42336]\n", "2 [ 1.423488 1.43063 1.429176]\n", "3 [ 1.428039 1.428557 1.428681]\n", "4 [ 1.428552 1.428553 1.428579]\n", "5 [ 1.428574 1.42857 1.428571]\n", "6 [ 1.428572 1.428571 1.428571]\n", "7 [ 1.428571 1.428571 1.428571]\n", "8 [ 1.428571 1.428571 1.428571]\n", "9 [ 1.428571 1.428571 1.428571]\n" ] } ], "source": [ "import numpy as np\n", "np.set_printoptions(precision=6, suppress=True)\n", "\n", "tt=0.2\n", "A=np.array([[1,tt,tt],[tt,1,tt],[tt,tt,1]])\n", "b=np.array([2,2,2])\n", "n=3\n", "x0=np.zeros(n)\n", "x1=np.zeros(n)\n", "\n", "for iter in range(0, 10):\n", " for i in range(0, n):\n", " x1[i]=b[i]\n", " for j in range(0, n):\n", " x1[i]=x1[i]-A[i][j]*x0[j]\n", " x1[i]=x1[i]+A[i][i]*x0[i]\n", " x1[i]=x1[i]/A[i][i]\n", " x0[i]=x1[i]\n", " print(iter,x0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# FFTの強度表示\n", "```\n", "1.と2.を同時プロットして表示するよう工夫したバージョン.\n", "紅茶花伝の知恵.ありがとう.\n", "3.の答えとしては,「ピークの位置が違う」とかいう解答ではなく,\n", "「新たに高周波側に40チャンネルあたりにピークが出現している」\n", "とか\n", "「その強度は1/2のはずだが,期待したほど小さくなってない」\n", "などというコメントがあると点数が上がる.\n", "\n", "そこに点数をつける理由は,数値計算で必要なスキルを習得するコツだから.\n", "数値計算では,細かい数値だけでなく,プロットの図形の読み取りも大事で,\n", "それを定性的,定量的に言葉にすることで解の性質を把握する癖がついてくるから.\n", "```" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "from scipy import fft\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "\n", "def func(x):\n", " return np.cos(x/15)+np.cos(x/2)\n", "\n", "\n", "x = np.linspace(0, 256, 256) #0から2πまでの範囲を100分割したnumpy配列\n", "plt.plot(x, func(x), color = 'b')\n", "plt.plot(x, np.cos(x/15), color = 'r', linewidth=0.8)\n", "plt.plot(x, np.cos(x/2), color = 'r', linewidth=0.8)\n", "\n", "plt.grid()\n", "plt.show()\n", "\n", "yy = func(x)\n", "out = fft(yy)\n", "\n", "def spectrum_power(x):\n", " re, im = x.real, x.imag\n", " return np.sqrt(re**2+im**2)\n", "\n", "plt.plot(x,spectrum_power(out))\n", "plt.xlim(0,128)\n", "plt.show()\n", "\n", "plt.plot(x,spectrum_power(out))\n", "plt.xlim(0,128)\n", "plt.yscale('log')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "def func(x):\n", " return np.cos(x/15)+np.cos(x/2)+1/2.0*np.cos(x)\n", "\n", "\n", "x = np.linspace(0, 256, 256) #0から2πまでの範囲を100分割したnumpy配列\n", "plt.plot(x, func(x), color = 'b')\n", "plt.plot(x, np.cos(x/15), color = 'r', linewidth=0.8)\n", "plt.plot(x, np.cos(x/2), color = 'r', linewidth=0.8)\n", "\n", "plt.grid()\n", "plt.show()\n", "\n", "yy = func(x)\n", "out2 = fft(yy)\n", "\n", "plt.plot(x,spectrum_power(out2))\n", "plt.xlim(0,128)\n", "plt.show()\n", "\n", "plt.plot(x,spectrum_power(out2))\n", "plt.xlim(0,128)\n", "plt.yscale('log')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(x,spectrum_power(out2), color = 'b')\n", "plt.plot(x,spectrum_power(out), color = 'r')\n", "plt.xlim(0,128)\n", "# plt.yscale('log')\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 対数関数のニュートンの差分商補間\n", "\n", "章末課題に挙げていたlogを変更した問題です.\n", "解答例としてはこっちの方が見やすい(打ち間違いが少ない)でしょうね.\n", "桁数制御してないので,ちょっと誤差が出ています." ] }, { "cell_type": "code", "execution_count": 97, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.0\n" ] } ], "source": [ "import numpy as np\n", "\n", "np.set_printoptions(precision=7, suppress=True)\n", "print(np.tan(np.pi/4))" ] }, { "cell_type": "code", "execution_count": 98, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.684136808342 0.842288380463 1.02963855705 1.26015821755\n" ] } ], "source": [ "x0 = 0.6\n", "x1 = 0.7\n", "x2 = 0.8\n", "x3 = 0.9\n", "y0 =np.tan(x0)\n", "y1 =np.tan(x1)\n", "y2 =np.tan(x2)\n", "y3 =np.tan(x3)\n", "\n", "print(y0,y1,y2,y3)" ] }, { "cell_type": "code", "execution_count": 99, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.45993022329\n", "2.15847419563\n" ] } ], "source": [ "f1_01 = (y1-y0)/(x1-x0) #1.581516\n", "f1_12 = (y2-y1)/(x2-x1) #1.873506\n", "f2_012 = (f1_12-f1_01)/(x_2-x_0)\n", "print(f2_012)\n", "\n", "f1_23 = (y3-y2)/(x3-x2) # 2.305190\n", "f2_123 = (f1_23-f1_12)/(x_3-x_1)\n", "print(f2_123)" ] }, { "cell_type": "code", "execution_count": 100, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.0004615735170512" ] }, "execution_count": 100, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = 0.7853982\n", "F_0 = y0\n", "F_0 + (x-x_0)*(f1_01)+(x-x_0)*(x-x_1)*f2_012" ] }, { "cell_type": "code", "execution_count": 101, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.99992326268286946" ] }, "execution_count": 101, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f3_0123 = (f2_123-f2_012)/(x3-x0)#2.328233\n", "F_0 + (x-x_0)*(f1_01)+(x-x_0)*(x-x_1)*f2_012+(x-x_0)*(x-x_1)*(x-x_2)*f3_0123" ] }, { "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": "30px", "width": "251.7391357421875px" }, "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 } }, "nbformat": 4, "nbformat_minor": 2 }