{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 補間\n", " 補間は、データ解析で広く利用されています。積分や微分とは直接関係はありませんが、同様の数学的方法を使用します。\n", "\n", " 関数 $f(x)$ の 2 点 $x = a, b$ での値が与えられ、その間の別の点 $x$ での関数の値を知りたいとします。 どうすれば良いと思いますか?\n", "\n", " 簡単な例として関数 $f(x)$ が sin(x)である場合について考えてみましょう。" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from math import pi\n", "\n", "f = lambda x: np.sin(x) \n", "x_min, x_max = 0, pi\n", "npt0 = 100\n", "npt1 = 4\n", "\n", "x0 = np.linspace(x_min, x_max, npt0)\n", "x1 = np.linspace(x_min, x_max, npt1) \n", "\n", "plt.plot(x0,f(x0),label='ideal function')\n", "plt.scatter(x1,f(x1), color='r', label='available points')\n", "\n", "plt.legend()\n", "plt.xlabel('x')\n", "plt.ylabel('sin(x)')\n", "plt.xlim([0,pi])\n", "#plt.title('いくつかの点から元の関数を再構築せよ')\n", "plt.title('use the available points to reconstruct the ideal function')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 線形補間\n", " 最も単純なのは線形補間です。 関数は $f(a)$ から $f(b)$ への直線に従うと仮定します。現実には関数は 2 点間で曲線に従う可能性がありますが、この仮定では、いくつかの初等幾何学で $f(x)$ を計算することができます。\n", "\n", "直線近似の傾きは\n", "\n", "$$m = \\frac{f(b)-f(a)}{b-a}$$\n", "\n", "これは、台形公式を用いた積分で行ったことと同じです。\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from math import pi\n", "\n", "f = lambda x: np.sin(x) \n", "x_min, x_max = 0, pi\n", "npt0 = 100 #ideal function\n", "npt1 = 4 #available points\n", "npt2 = 10 #number of points you want to interpolate bewteen two known points\n", "\n", "x0 = np.linspace(x_min, x_max, npt0) #ideal function\n", "x1 = np.linspace(x_min, x_max, npt1) #available points\n", "\n", "\n", "#---------To interpolate based on the available points\n", "\n", "x2 = []\n", "y2 = []\n", "\n", "for i in range(npt1-1):\n", " slope = (f(x1[i+1])-f(x1[i]))/(x1[i+1]-x1[i])\n", " delta = (x1[i+1]-x1[i])/npt2\n", " for j in range(npt2+1):\n", " x2.append(x1[i]+delta*j)\n", " y2.append(f(x1[i]) + slope*delta*j)\n", "#---------To interpolate based on the available points\n", "\n", "\n", "\n", "#plot all points\n", "plt.plot(x0,f(x0),label='ideal function')\n", "plt.scatter(x1,f(x1), color='r', label='available points')\n", "plt.plot(x2,y2, '*b', label='linear interpolation')\n", "\n", "plt.legend()\n", "plt.xlabel('x')\n", "plt.ylabel('f(x)')\n", "plt.xlim([0,pi])\n", "plt.title('use the available points to reconstruct the ideal function')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## スプライン補間\n", " 理想的な関数が線形からかけ離れている場合には、線形補間は適切な近似ではありません。したがって、場合によっては重大なエラーが発生する可能性があります。 \n", "\n", " 積分の時に行ったことと同様に、より精度の良い近似は多項式関数を使用することです。**スプライン補間**は、補間関数がスプラインと呼ばれる特殊なタイプの多項式である補間の形式です。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**線形補間**は、実際にはスプライン補間の最も単純なバージョンです。\n", "\n", "$$S_i(x) = y_i + \\frac{y_{i+1}-y_i}{x_{i+1}-x_i}(x-x_i) $$\n", "\n", "\n", "**二次スプライン補間**を行う場合、関係はもう少し複雑になります。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "簡単な例から始めましょう。$(-1,0), (0,1), (1,3)$の3つの点があたえられていると仮定します。\n", "\n", "求めたい二次スプラインは次のとおりです。\n", "\n", "$$ p_1(x) = a_1 + b_1x + c_1x^2 ~~~[-1,0]$$\n", "\n", "$$ p_2(x) = a_2 + b_2x + c_2x^2 ~~~[0,1] $$\n", "\n", "以下の条件を満たす必要があります。\n", "\n", "$$p_1(-1)=a_1-b_1+c_1 = 0$$\n", "\n", "$$p_1(0) = a_1 = 1 $$\n", "\n", "$$p_2(0) = a_2 = 1 $$\n", "\n", "$$p_2(1) = a_2 + b_2 + c_2 = 3 $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "さらに、曲線を連続にしたいので、 $p_1(0)' = p_ 2(0)'$ は、\n", "\n", "$$b_1 = b_2$$\n", "\n", "となります。\n", "\n", "全部で 6 つの変数がありますが、式は 5 つしかないため、別の条件を定義する必要があります。\n", "\n", "通常、両端の導関数についても制約を課すことができます。たとえば$p_1(-1)'$=0とすると、\n", "\n", "$$b_1 - 2c_1 = 0$$\n", "\n", "したがって、方程式を解くことで二次スプライン関数のすべての係数を取得できます。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$ p_1(x) = 1 + 2x + x^2 ~~~[-1,0]$$\n", "$$ p_2(x) = 1 + 2x ~~~~~~~~[0,1] $$\n", "\n", "一連の点を補間すると、一般化された関係は次のようになります。\n", "\n", "$$S_i(x) = y_i + z_i(x-x_i) + \\frac{z_{i+1}-z_i}{2(x_{i+1}-x_i)}(x-x_i)^2$$\n", "\n", "$z$ シリーズは次の方法で取得できます\n", "\n", "$$z_{i+1} = -z_i + 2\\frac{y_{i+1}-y_i}{x_{i+1}-x_i}$$\n", "\n", "$z_0$ は 1 番目の点の導関数です。" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from math import pi\n", "\n", "f = lambda x: np.sin(x) \n", "x_min, x_max = 0, pi\n", "npt0 = 100 #ideal function\n", "npt1 = 4 #available points\n", "npt2 = 10 #number of points you want to interpolate bewteen two known points\n", "\n", "x0 = np.linspace(x_min, x_max, npt0) #ideal function\n", "x1 = np.linspace(x_min, x_max, npt1) #available points\n", "\n", "\n", "#---------To interpolate based on the available points\n", "x2 = []\n", "y2 = []\n", "z = np.empty(npt1)\n", "z[0] = 1 # try to play with different values here\n", "\n", "for i in range(npt1-1):\n", " slope = (f(x1[i+1])-f(x1[i]))/(x1[i+1]-x1[i])\n", " delta = (x1[i+1]-x1[i])/npt2\n", " z[i+1] = -z[i] + 2*slope\n", "\n", "\n", " for j in range(npt2+1):\n", " x2.append(x1[i]+delta*j)\n", " y2.append(f(x1[i]) + z[i]*delta*j + (z[i+1]-z[i])*delta*j*j/2/npt2)\n", " #print(x2[-1],y2[-1]) \n", "#---------To interpolate based on the available points\n", "\n", "\n", "#plot all points\n", "plt.plot(x0,f(x0),label='ideal function')\n", "plt.scatter(x1,f(x1), color='r', label='available points')\n", "plt.plot(x2,y2, 'b', label='quadratic spline')\n", "\n", "\n", "plt.legend()\n", "plt.xlabel('x')\n", "plt.ylabel('f(x)')\n", "plt.xlim([0,pi])\n", "plt.title('use the available points to reconstruct the ideal function')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "同様に、高次多項式も実行できます。 たとえば**3 次スプライン**は、多くの分野で使用されている一般的な方法です。 ロジックは、多項式関数と条件の拡張に他なりません。\n", "\n", "$$S_i(x) = \\frac{z_{i+1}(x-x_i)^3 + z_i(x_{i+1}-x)^3} {6h_i} + (\\frac{y_{i+1}}{h_i}-\\frac{h_i}{6}z_{i+1}) + (\\frac{y_i}{h_i}-\\frac{h_i}{6}z_i) (x_{i+1}-x_i)$$\n", "\n", "ここで、$h_i = x_{i+1} - x_i $、および $z$ シリーズは次の方法で取得できます。\n", "\n", "$$h_{i-1}z_{i-1} + 2(h_{i-1}+h_i)z_i + h_iz_{i+1} =6(\\frac{y_{i+1}}{h_i}-\\frac{y_i-y_{i-1}}{h_{i-1}}) $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Scipy の高度なライブラリ\n", " 実用上は、このようなコードをゼロから書くよりも、既にあるコードを理解する方が簡単です。 実際、3 次スプラインはすでにライブラリに実装されており、非常に便利なものになっています。 \n", "\n", " 幸いなことに、科学的プログラミングのための基本的なライブラリが構築されています。 Python で最も重要なのは scipy です。\n", "\n", "https://scipy.org/\n", "\n", " scipy を使用した後、ここで行ったようなれらの低レベルの作業は回避できることがすぐにわかります。しかし、少なくともこれらの機能の原理は知っておく必要があります。 何も知らずに関数を使うのは非常に危険です。\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### scipy での積分の例" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.75 1.942890293094024e-14\n" ] } ], "source": [ "import numpy as np\n", "from scipy import integrate\n", "\n", "f = lambda x: 3*x**3 + 1\n", "x_min, x_max = 0, 1\n", "I, err = integrate.quad(f,x_min,x_max)\n", "print(I, err)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### scipy での補間の例" ] }, { "cell_type": "code", "execution_count": 5, "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", "from math import pi\n", "from scipy.interpolate import *\n", "from random import random\n", "\n", "f = lambda x: np.sin(x)+random()\n", "x_min, x_max = 0, 2*pi\n", "npt0 = 100 #ideal function\n", "npt1 = 4 #available points\n", "npt2 = 10 #number of points you want to interpolate bewteen two known points\n", "\n", "x0 = np.linspace(x_min, x_max, npt0) #ideal function\n", "x1 = np.linspace(x_min, x_max, npt1) #available points\n", "\n", "f_spline1 = interpolate.interp1d(x1, f(x1), kind='linear')\n", "f_spline2 = interpolate.interp1d(x1, f(x1), kind='quadratic')\n", "f_spline3 = interpolate.interp1d(x1, f(x1), kind='cubic')\n", "\n", "\n", "#plot all points\n", "plt.plot(x0,f(x0),label='ideal function')\n", "plt.plot(x0,f_spline1(x0), '--', label='linear')\n", "plt.plot(x0,f_spline2(x0), '-', label='quadratic')\n", "plt.plot(x0,f_spline3(x0), '-.', label='cubic')\n", "plt.scatter(x1,f(x1), c='r', s=180, marker='*', label='available points')\n", "\n", "\n", "plt.legend()\n", "plt.xlabel('x')\n", "plt.ylabel('f(x)')\n", "plt.xlim([x_min, x_max])\n", "plt.title('interpolation with built-in function in scipy')\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 補完における次数の選び方\n", "\n", "曲線が連続的であるためには、各セグメントが出会ったときに等しい値を与えることを確認する必要があります\n", "\n", "$f_i(x_i) = f_{i+1}(x_i)$\n", "\n", "これが線形スプラインの機能です。\n", "\n", "曲線を滑らかにするために、1次導関数が等しくなるように求めます\n", "\n", "$(f_i(x_i))' = (f_{i+1}(x_i))'$\n", "\n", "これは二次スプライン補間で使用されています。\n", "\n", "セグメントが接するときに同じ曲率を持つようにするには、以下を課します。\n", "\n", "$(f_i(x_i))'' = (f_{i+1}(x_i))''$\n", "\n", "この条件を満たすには、3 次スプラインを使用する必要があります。 これが、人々が補間を行うときに 3 次スプラインが最も一般的な選択肢である理由です。 \n", "\n", "高次の方程式はさらに滑らかな曲線を与えますが、コストが高くなり、変化がより微妙になります。精度と複雑さの間にはトレードオフがあります。\n", "\n" ] }, { "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": [ "import matplotlib.pyplot as plt\n", "\n", "x = np.linspace(0,10, 100)\n", "plt.plot(x, x, label='y=x')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 7, "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(-10, 10, 100)\n", "plt.plot(x, x**3 - 2*x**2- 10*x + 20, label='2nd')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.11.6" } }, "nbformat": 4, "nbformat_minor": 4 }