{"cells":[{"cell_type":"markdown","metadata":{},"source":["
\n"," 2022年度 数式処理演習 pair試験問題 \n","
\n","
\n"," cc by Shigeto R. Nishitani, 2022/11/24実施 \n","
\n","\n","- file: ~/symbolic_math/22_pair/22_pair_ans.ipynb\n","- make problem: ruby text_dir/bin/pick_works_from_ans.rb 22_pair/22_pair_ans.ipynb -1 '27' '8 9 10 28 32'\n","\n","以下の問題を python で解き,LUNA へ提出せよ.LUNA へは ipynb と pdf 形式の2種類を提出すること.\n"]},{"cell_type":"markdown","metadata":{},"source":["# 問 1 微積分\n","\n","## 1(a) 関数の概形(15 点)\n","\n","(テキスト p.144 の図 4.35 の確認)\n","\n","ガウス関数\n","\n","\\begin{equation*}\n","y= \\exp\\left(-\\frac{x^2}{2 {\\rm sigma}^2}\\right)\n","\\end{equation*}\n","\n","の概形を\n","\n","```python\n","sigma = 2\n","plt.xlim(-10,10)\n","plt.ylim(-0.5,1.5)\n","```\n","\n","で描け.\n"]},{"cell_type":"markdown","metadata":{},"source":["## 1(b) 関数の積分(15 点)\n","\n","sympy において,\n","\n","```python\n","sigma = symbols('sigma',positive = True)\n","```\n","\n","を指定することで,\n","\\begin{equation*}\n","\\int_{-\\infty}^{\\infty} \\exp\\left(-\\frac{x^2}{2\\sigma^2}\\right) dx\n","\\end{equation*}\n","を求めよ.\n"]},{"cell_type":"markdown","metadata":{},"source":["# 問 2 線形代数\n","\n","## 2(a) 共分散の逆行列(15 点)\n","\n","ここでは$\\Sigma$を共分散とする.\n","sigma = np.array([[2,1],[1,2]])\n","の逆行列$\\Sigma^{-1}$を求めよ.\n","\n","さらに検算せよ.\n"]},{"cell_type":"markdown","metadata":{},"source":["## 2(b) 一般的な 2 次元ガウス関数(15 点)\n","\n","さらに,sympy で\n","v = Matrix([x0,x1])\n","として,\n","$v^{T} \\Sigma^{-1} v$を求めよ.\n","\n","得られた式を$\\exp$の指数部に入れて規格化した関数の 3d プロットは以下の通りとなる(テキストp.150, 図4.37)\n","\n","注意 :: 配列同士の内積にはテキストでは,\n","numpy.matmulのoperator ’@’を使っている.\n","2次元配列(行列)の内積では, numpy.dotから呼び出され同じ結果を返す.\n","マニュアルではmatmulの使用を推奨している( https://numpy.org/doc/stable/reference/generated/numpy.dot.html#numpy.dot )."]},{"cell_type":"code","execution_count":5,"metadata":{},"outputs":[],"source":["%matplotlib inline\n","import numpy as np\n","import matplotlib.pyplot as plt\n","\n","def gauss(x0, x1, mu, sigma):\n"," x = np.array([x0,x1])\n"," a=1/(2*np.pi)*1/(np.linalg.det(sigma) ** (1/2))\n"," inv_sigma = np.linalg.inv(sigma)\n"," y=a * np.exp(\n"," (-1/2)*(x-mu).T @ inv_sigma @(x-mu))\n"," return y"]},{"cell_type":"code","execution_count":6,"metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{"needs_background":"light"},"output_type":"display_data"}],"source":["mu=np.array([0,0])\n","sigma =np.array([[2,1],[1,1]])\n","x0_min, x0_max = -3,3\n","x1_min, x1_max = -3,3\n","\n","x0_n, x1_n = 40, 40\n","x0 =np.linspace(x0_min,x0_max, x0_n)\n","x1 =np.linspace(x1_min,x1_max, x1_n)\n","\n","f = np.zeros((x1_n, x0_n))\n","for i0 in range(x0_n):\n"," for i1 in range(x1_n):\n"," f[i1,i0] = gauss(x0[i0],x1[i1], mu, sigma)\n","xx0, xx1 = np.meshgrid(x0,x1)\n","\n","plt.figure(figsize=(7,3))\n","\n","plt.subplot(1,2,1)\n","cont = plt.contour(xx0, xx1, f, levels=15, colors=\"black\")\n","plt.grid()\n"]},{"cell_type":"markdown","metadata":{},"source":["# 問 3 センター試験原題(20 点)\n","\n","(2020 大学入試センター試験 数学 II・B/追試験 第 2 問)\n","\n","$a, b, c$ を実数とし,\n","関数$f(x)=x^3 -1$, $g(x) = x^3+ax^2+bx+c$を考える.\n","座標平面上の曲線$y=f(x)$を$C_1$とし,\n","曲線$y=g(x)$ を$C_2$とする.\n","$C_2$は点 A(-1,-2)を通り,\n","$C_2$の A における接線は\n","$C_1$の A における接線と一致するものとする.\n","\n","(1) 曲線$C_1$の点 A における接線を$l$とする.\n","$f'(-1) = \\fbox{ ア }$により,\n","$l$の方程式は\n","$y=\\fbox{ イ }x + \\fbox{ ウ }$である.\n","また,原点 O の直線$l$の距離は\n","$\\frac{\\sqrt{\\fbox{ エオ }}}{\\fbox{ エオ }}$である.\n","\n","ヒント:問4での数値改変に備えて,x0=-1, y0=f.subs({x:x0})として問題を解いていけ.\n"]},{"cell_type":"markdown","metadata":{},"source":["(2) 曲線$C_2$の点 A における接線は(1)の直線$l$と一致しているので,\n","$g'(-1) = \\fbox{ カ }$である.\n","したがって,$b,c$を$a$を用いて表すと,\n","$b=\\fbox{ キ }a$, $c= \\fbox{ ク }-\\fbox{ ケ }$となる.\n"]},{"cell_type":"markdown","metadata":{},"source":["(3) $a=-2$のとき,関数$g(x)$は\n","$\\frac{\\fbox{ コサ }}{\\fbox{ シ }}$で極大値\n","$\\frac{\\fbox{ スセソ }}{\\fbox{ タチ }}$をとり,\n","$\\fbox{ ツ }$で極小値\n","$\\fbox{ テトナ }$をとる.\n","\n","## 解答注意\n","- 極大値は浮動小数点数でも良い.(分数で出したかったらRationalを使え)\n","- $\\fbox{ ア }, \\fbox{ イ }, \\fbox{ ウ }, \\ldots$ を明示する(あるいは書き出す)必要はない.\n","- 以下は関数$f(x), g(x: a=-2, x0=-1)$のplotである.解答の検算の参考とせよ."]},{"cell_type":"code","execution_count":20,"metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{"needs_background":"light"},"output_type":"display_data"}],"source":["%matplotlib inline\n","import numpy as np\n","import matplotlib.pyplot as plt\n","\n","g_curve = x**3 - 2*x**2 - 4*x - 3\n","xx_n = 100\n","xx =np.linspace(-2, 4, xx_n)\n","\n","gY = np.zeros(xx_n)\n","fY = np.zeros(xx_n)\n","for i0 in range(xx_n):\n"," gY[i0] = g_curve.subs({x:xx[i0]})\n"," fY[i0] = f.subs({x:xx[i0]})\n","\n","plt.plot(xx, fY)\n","plt.plot(xx, gY)\n","plt.xlim(-2,4)\n","plt.ylim(-12,2)\n","plt.show()"]},{"cell_type":"markdown","metadata":{},"source":["# 問 4 センター試験改変(20 点)\n","\n","点 A の$x$座標を$-1/2$として同様に求めると,\n","$a=-2$では$g(x)= x^3 - 2x^2 - 2x - 3/2$となることを確かめよ.\n","\n","\n","\n","さらに, 点 A の$x$座標が$-1.1$で, $a=-2$の時の$g(x)$を求めよ.\n","f(x)およびg(x; a=-2, x0=-1.1)を同時プロットすると以下の通りとなる."]},{"cell_type":"code","execution_count":23,"metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{"needs_background":"light"},"output_type":"display_data"}],"source":["%matplotlib inline\n","import numpy as np\n","import matplotlib.pyplot as plt\n","\n","xx_n = 100\n","xx =np.linspace(-2, 4, xx_n)\n","\n","gY = np.zeros(xx_n)\n","fY = np.zeros(xx_n)\n","for i0 in range(xx_n):\n"," gY[i0] = g_curve.subs({x:xx[i0]})\n"," fY[i0] = f.subs({x:xx[i0]})\n","\n","plt.plot(xx, fY)\n","plt.plot(xx, gY)\n","plt.xlim(-2,4)\n","plt.ylim(-12,2)\n","plt.show()"]}],"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"},"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":false},"vscode":{"interpreter":{"hash":"f3f87633aac09da3bda522f97956bee375b5501d1579e6458804e567301cb62a"}}},"nbformat":4,"nbformat_minor":2}