{ "cells": [ { "cell_type": "markdown", "id": "1ea11364", "metadata": {}, "source": [ "# Truncation Error\n", "**강좌**: *수치해석*" ] }, { "cell_type": "markdown", "id": "4800ebc0", "metadata": {}, "source": [ "## Taylor 급수\n", "Taylor 급수는 수치해석에서 매우 근본적인 이론을 제공한다. \n", "\n", "### Taylor 정리\n", "함수 $f$와 그것의 처음 $n+1$차까지의 미분이 $a$와 $x$를 포함하는 구간에서 연속적이라면, $x$에서의 함수 값은 다음과 같이 주어진다.\n", "\n", "$$\n", "\\begin{align}\n", "f(x) = f(a) &+ f'(a)(x-a) + \\frac{f''(a)}{2!}(x-a)^2 \\\\\n", " &+ \\frac{f^{(3)}(a)}{3!}(x-a)^3 + ... \\\\\n", " &+ \\frac{f^{(n)}(a)}{n!}(x-a)^n + R_n\n", "\\end{align}\n", "$$\n", "\n", "여기서 나머지 $R_n$ 은 다음과 같이 정의된다.\n", "\n", "$$\n", "R_n = \\int_a^x \\frac{(x-t)^{n+1}}{n+1!} f^{(n+1)} dt.\n", "$$\n", "\n", "다음 중간간 정리에 따르면 $\\xi \\in [a, x]$ 에 대해서 아래 식을 만족한다.\n", "\n", "$$\n", "\\int_a^x g(t)dt = g(\\xi)(x-a).\n", "$$\n", "\n", "이를 적용하면 $R_n$ 은 다음과 같다.\n", "\n", "$$\n", "R_n = \\frac{(x-a)^{n+1}}{n+1!} f^{(n+1)}(\\xi) = \\frac{h^{n+1}}{n+1!} f^{(n+1)}(\\xi).\n", "$$\n", "\n", "여기서 $h=x - a$ 이다." ] }, { "cell_type": "markdown", "id": "9794a983", "metadata": {}, "source": [ "### Taylor 급수를 이용한 근사화\n", "Taylor 급수를 이용하면 비선형 함수를 근사적으로 계산할 수 있다.\n", "\n", "#### 예제: $e^x$ 함수 근사화\n", "$e^x$ 함수를 원점 $(a=0)$ 에서 다항식으로 근사화해보자.\n", "\n", "$$\n", "e^x \\approx 1 + x + \\frac{x^2}{2} + \\frac{x^3}{3!} +... + \\frac{x^n}{n!}\n", "$$" ] }, { "cell_type": "code", "execution_count": 1, "id": "e561a016", "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "from matplotlib import pyplot as plt\n", "\n", "import numpy as np\n", "\n", "plt.style.use('ggplot')\n", "plt.rcParams['figure.dpi'] = 150" ] }, { "cell_type": "code", "execution_count": 2, "id": "903b8dca", "metadata": {}, "outputs": [], "source": [ "def factorial(n):\n", " \"\"\" Factorial 계산\n", " Parameters\n", " ----------\n", " n : integer\n", " n\n", " \"\"\"\n", " fac = 1\n", " for i in range(1, n+1):\n", " fac *= i\n", " \n", " return fac\n", "\n", "\n", "def approx_exp(n, x):\n", " \"\"\" Exponential 함수 근사\n", " Parameters\n", " ----------\n", " n : integer\n", " 항의 계수\n", " x : float\n", " 값\n", " \"\"\" \n", " exp = 0\n", " for i in range(n):\n", " exp += 1/factorial(i)*x**i\n", " \n", " ## Pythoniac\n", " # exp = sum([factorial(i)*x**i for i in range(n)])\n", " return exp" ] }, { "cell_type": "code", "execution_count": 3, "id": "cfd39259", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'y')" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-1, 1, 101)\n", "\n", "# Plot approximation\n", "for i in range(2, 5):\n", " plt.plot(x, approx_exp(i, x))\n", "\n", "# Plot exact \n", "plt.plot(x, np.exp(x), color='black')\n", "\n", "# Legend\n", "plt.legend([\n", " '1st order approximation',\n", " '2nd order approximation',\n", " '3rd order approximation',\n", " 'Exact ($e^x$)'\n", "])\n", "\n", "# Label\n", "plt.xlabel('x')\n", "plt.ylabel('y')" ] }, { "cell_type": "markdown", "id": "d3bb920d", "metadata": {}, "source": [ "### 전단오차 (Truncation error)\n", "Taylor 급수를 이용한 근사식의 경우 n차 항까지만 사용하므로 그 이상의 항은 절삭 (Truncation) 한다. 이에 따른 오차를 전단오차 (Truncation Error)라 한다.\n", "\n", "위 예제에서 $x=0.5$ 일 때 절대오차를 계산하면 다음과 같다." ] }, { "cell_type": "code", "execution_count": 4, "id": "e438f37b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Error using 1-th order terms: 1.48721e-01\n", "Error using 2-th order terms: 2.37213e-02\n", "Error using 3-th order terms: 2.88794e-03\n" ] } ], "source": [ "x = 0.5\n", "exact = np.exp(x)\n", "\n", "for i in range(2, 5):\n", " approx = approx_exp(i, x)\n", " error = exact - approx\n", " \n", " print(\"Error using {}-th order terms: {:.5e}\".format(i-1, error))" ] }, { "cell_type": "markdown", "id": "31e91553", "metadata": {}, "source": [ "x 크기를 바꿔가면서 그래프로 그려보면 아래와 같다." ] }, { "cell_type": "code", "execution_count": 5, "id": "415ab9a9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$\\\\epsilon$')" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(1e-3, 0.1, 100)\n", "exact = np.exp(x)\n", "\n", "# Plot error between approximation and exact values\n", "for i in range(2, 5):\n", " approx = approx_exp(i, x)\n", " error = exact - approx\n", " \n", " plt.loglog(x, error)\n", " \n", "# Same scale of x and y\n", "plt.axis('equal')\n", "\n", "# Legend\n", "plt.legend([\n", " '1st order approximation',\n", " '2nd order approximation',\n", " '3rd order approximation',\n", "])\n", "\n", "plt.xlabel('x')\n", "plt.ylabel('$\\epsilon$')" ] }, { "cell_type": "markdown", "id": "9b362b03", "metadata": {}, "source": [ "오차항 $R_n = C h^{n+1}$ 이므로 log scale 로 그렸을 때 기울기가 $n$ 이다.\n", "\n", "즉 아래 그래프를 보면 기울기가 각각 2, 3, 4차임일 알 수 있다.\n", "\n", "오차항을 다음과 같이 표현하기도 한다.\n", "\n", "$$\n", "R_n = O(h^{n+1})\n", "$$\n", "\n", "### DIY\n", "$\\sin(x)$ 를 $a=\\pi/4$ 를 기준으로 Taylor series를 이용하여 근사식을 구하고, $[0, \\pi/2]$ 구간에서 근사해와 이론해를 비교하시오. 전단오차의 크기를 확인하시오." ] }, { "cell_type": "markdown", "id": "5c179dcf", "metadata": {}, "source": [ "## 오차의 전파\n", "### 함수의 오차\n", "실제 공학 문제에서는 다양한 오차가 발생한다. 예를 들어 계측하는 과정에서 오차가 있을 수 있고, 이론식에서 가정에 의한 오차가 있을 수 있다. 특히 수치해석 과정에서는 Round-off error, Truncation error 등이 존재한다. \n", "\n", "독립변수 $x$에 대해서 오차가 있어서 근사값 $\\tilde{x}$을 사용하는 경우를 생각하자. 이때 함수 $f(x)$ 결과의 오차는 다음과 같다.\n", "\n", "$$\n", "\\Delta f(\\tilde{x}) = |f(x) - f(\\tilde{x})|\n", "$$\n", "\n", "Taylor expansion을 이용하면\n", "\n", "$$\n", "f(x) = f(\\tilde{x}) + f'(\\tilde{x})(x - \\tilde{x}) + \\frac{f''(\\tilde{x})}{2} (x - \\tilde{x})^2 + ...\n", "$$\n", "\n", "1차 항으로만 근사하면 함수 $f(x)$ 결과의 오차는 다음과 같다.\n", "\n", "$$\n", "\\Delta f(\\tilde{x}) \\approx |f'(\\tilde{x})| \\Delta \\tilde{x}\n", "$$\n", "\n", "#### 예제\n", "근사값 $\\tilde{x}=2.5$ 이고 이 값에 0.01의 오차가 있다. 이 경우 함수 $f(x)=x^3$ 계산시 발생하는 오차를 구해보자.\n", "\n", "위 근사식을 적용하면\n", "\n", "$$\n", "\\Delta f(\\tilde{x}) \\approx |f'(\\tilde{x})| \\Delta \\tilde{x} = 3(2.5)^2 0.01 = 0.1875\n", "$$\n", "\n", "즉 오차는 다음과 같이 정리할 수 있다.\n", "\n", "$$\n", "f(x) = f(\\tilde{x}) \\pm \\Delta f(\\tilde{x}) = 15.625 \\pm 0.1875\n", "$$\n", "\n", "다변함수의 경우 편미분을 이용한 Taylor expansion을 활용한다.\n", "\n", "$$\n", "f(x, y) \\approx f(\\tilde{x}, \\tilde{y}) \n", "+ \\frac{\\partial f}{\\partial x} \\Delta \\tilde{x}\n", "+ \\frac{\\partial f}{\\partial y} \\Delta \\tilde{y}\n", "+ O(\\Delta \\tilde{x}^2, \\Delta \\tilde{y}^2)\n", "$$\n", "\n", "### Condition Number\n", "수학에서 조건은 입력값의 변화에 대한 민감도이며, 작은 입력 오차에 따라 함수의 변화가 클수록 불안정해질 수 있다.\n", "\n", "Condition Number는 독립변수의 상대오차 대비 함수의 상대오차로 정의한다.\n", "\n", "$$\n", "Cond = \\frac{\\epsilon_{a, f(x)}}{\\epsilon_{a, x}}\n", "$$\n", "\n", "각각의 상대오차는 다음과 같다.\n", "\n", "$$\n", "\\begin{align}\n", "\\epsilon_{a, x} &= \\frac{\\Delta \\tilde{x}}{\\tilde{x}} \\\\\n", "\\epsilon_{a, f(x)} & = \\frac{\\Delta f(\\tilde{x})}{f(\\tilde{x})} \\approx \\frac{|f'(\\tilde{x})| \\Delta \\tilde{x}}{f(\\tilde{x})}\n", "\\end{align}\n", "$$\n", "\n", "Condition Number는 다음과 같다.\n", "\n", "$$\n", "Cond = \\frac{\\frac{|f'(\\tilde{x})| \\Delta \\tilde{x}}{f(\\tilde{x})}}{\\frac{\\Delta \\tilde{x}}{\\tilde{x}}}\n", "= \\frac{\\tilde{x} f'(\\tilde{x})}{f(\\tilde{x})}\n", "$$\n", "\n", "Condition Number가 큰 경우 작은 오차에도 함수가 매우 크게 바뀌므로 수치해석시 조심해야 한다. 이런 함수를 ill-conditioned라 한다.\n", "\n", "#### 예제\n", "$\\tan(\\tilde{x})$의 Condition Number는 다음과 같다.\n", "\n", "\n", "$$\n", "Cond = \\frac{\\tilde{x} f'(\\tilde{x})}{f(\\tilde{x})} = \\frac{\\tilde{x} 1/\\cos^2(\\tilde{x})}{\\tan{\\tilde{x}}}\n", "$$\n", "\n", "즉 $\\tilde{x} =\\pi/4, \\pi/2\\times0.999$ 에서 Condition Number는 다음과 같다." ] }, { "cell_type": "code", "execution_count": 6, "id": "bb120179", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.5707963267948963" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = np.pi/4\n", "\n", "Cond = x * 1/np.cos(x)**2 /np.tan(x)\n", "Cond" ] }, { "cell_type": "code", "execution_count": 7, "id": "19739388", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "999.0016432910481" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = np.pi/2*0.999\n", "\n", "Cond = x * 1/np.cos(x)**2 /np.tan(x)\n", "Cond" ] }, { "cell_type": "code", "execution_count": 8, "id": "3df89581", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-np.pi/2, np.pi/2, 101)[1:-1]\n", "plt.plot(x, np.tan(x))\n", "\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n", "\n", "plt.legend([\"$tan(x)$\"])" ] }, { "cell_type": "markdown", "id": "5858d20f", "metadata": {}, "source": [ "## 전체 수치 오차\n", "복습하면 수치 오차는 다음 두 가지로 구성된다.\n", "\n", "- Round-off Erorr: 숫자 표기 한계로 반올림에 의한 오차\n", "- Truncation Error: 계산 과정에서 절단애 의한 오차" ] }, { "cell_type": "markdown", "id": "5a8b1f1b", "metadata": {}, "source": [ "수치 해석에서는 2가지를 유의해야 한다.\n", "\n", "- Consistency: 수치 오차는 가급적 적어야 한다.\n", "- Stability: 발생한 수치 오차가 증폭되지 않아야 한다." ] } ], "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": "3.11.2" } }, "nbformat": 4, "nbformat_minor": 5 }