{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 07wk-2: Numpy 활용 (2)\n",
"\n",
"최규빈 \n",
"2023-04-19\n",
"\n",
"
\n",
"\n",
"# 강의영상\n",
"\n",
"> youtube:\n",
"> \n",
"\n",
"# imports"
],
"id": "64f20989-642d-41f5-bad0-f49a8252f5bf"
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"import pandas as pd\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt"
],
"id": "50c7a38b-5e82-4939-96c4-e8397b140413"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 예비학습: matplotlib\n",
"\n",
"## 범례추가\n",
"\n",
"`-` 예시1"
],
"id": "84a4d1e3-5732-487c-a706-5c5b7f8642aa"
},
{
"cell_type": "code",
"execution_count": 122,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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Gd7AjTFWP3BnlEgMUG2OOi0gYcBnWRc+yFgK/Bb4BxgDLjTHl+9mVUh4yf306Ly/bwb6j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\n"
}
}
],
"source": [
"y1= [1.0, 2.0, 3.0, 4.0]\n",
"y2= [1.1, 2.2, 2.8, 0.0]\n",
"plt.plot(y1,'--o',label='y1')\n",
"plt.plot(y2,'--o',label='y2')\n",
"plt.legend()"
],
"id": "26e7eebd-6449-4148-b18e-f5ba8bc4b2e4"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`-` 예시2"
],
"id": "bb9838da-b2f0-45ed-a4dc-925bd8861504"
},
{
"cell_type": "code",
"execution_count": 123,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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Su7Wown7oItIPWA5sBIqdi58CEgCMMVOdSX8ycDlWt8XbjTHn7WSu/dBrUEEO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\nSikf8f8BLBb5Efk0whwAAAAASUVORK5CYII=\n"
}
}
],
"source": [
"y1= [1.0, 2.0, 3.0, 4.0]\n",
"y2= [1.1, 2.2, 2.8, 0.0]\n",
"plt.plot(y1,'--o',label=r'$y_1$')\n",
"plt.plot(y2,'--o',label=r'$y_2$')\n",
"plt.legend()"
],
"id": "3634695a-d3d7-41e2-8774-ec5e22403833"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 넘파이 활용 (2단계)\n",
"\n",
"## 변환을 의미하는 행렬\n",
"\n",
"`1-3`. 아래는 우산모양의 scatter plot을 그릴 수 있는 $(x_i,y_i)$\n",
"좌표값을 불러와서 시각화하는 코드이다."
],
"id": "42d1e014-cd82-4329-a432-d92937bdd54c"
},
{
"cell_type": "code",
"execution_count": 67,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"# 자료저장 \n",
"data_raw = np.array(pd.read_csv('https://raw.githubusercontent.com/guebin/2021IR/master/_notebooks/round2.csv')).T\n",
"data_raw"
],
"id": "fdd7dcbb-9447-4926-ac29-65fee51bcae1"
},
{
"cell_type": "code",
"execution_count": 68,
"metadata": {},
"outputs": [],
"source": [
"# 저장된 자료를 x,y로 분해 \n",
"x_raw,y_raw = data_raw\n",
"x_raw,y_raw"
],
"id": "866a9e6e-3fe4-48cb-965f-ad333f8bf5e0"
},
{
"cell_type": "code",
"execution_count": 69,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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4nY9jLipGK8/vlGDGO8YLsOw7YvFngoRV7LvTmHgZUnEXQmwSQtwshGgA8GcA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\n"
}
}
],
"source": [
"# 시각화\n",
"plt.figure(figsize=(6,6)) # 그림크기고정\n",
"plt.plot(x_raw,y_raw,'o')"
],
"id": "622ab35d-e5a2-4b97-93d4-524da3cfeb2b"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`1`. `x_raw`와 `y_raw`를 각각 표준화하고 `x`, `y`에 저장하라. 결과를\n",
"시각화하라. 그리고 `x`, `y`를 바탕으로 `data` matrix를 다시 구성하라.\n",
"\n",
"`(풀이)`\n",
"\n",
"**표준화**"
],
"id": "84714c30-4944-4170-bf55-7ab7e8f682c6"
},
{
"cell_type": "code",
"execution_count": 70,
"metadata": {},
"outputs": [],
"source": [
"x= (x_raw-np.mean(x_raw)) / np.std(x_raw,ddof=1)\n",
"y= (y_raw-np.mean(y_raw)) / np.std(y_raw,ddof=1)"
],
"id": "bedbe015-9272-4fb3-a973-3c86440e0e1c"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**시각화**"
],
"id": "b3004a0d-b38a-4ad1-8ebf-fe363c52da5f"
},
{
"cell_type": "code",
"execution_count": 71,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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dZPn7kb2bLL+bZiQq7QmiFq8KzUcuhPiiEOKsEOLs9evXw3rbhuO0FVy6oLXGh7j96Gnb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\nAAAASUVORK5CYII=\n"
}
}
],
"source": [
"plt.figure(figsize=(6,6)) # 그림크기고정\n",
"plt.plot(x,y,'o')"
],
"id": "e9235959-1de3-4385-bf0a-96a6e16a4638"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**data matrix** 재구성"
],
"id": "b882f6df-f742-4186-b1ed-9183d19e5280"
},
{
"cell_type": "code",
"execution_count": 72,
"metadata": {},
"outputs": [],
"source": [
"data = np.array([x,y])\n",
"data"
],
"id": "6be9a76b-2e2d-473c-a0d0-13312032adb7"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`2`. 아래와 같은 규칙에 따라 $(x_i,y_i)$를 $(\\tilde{x}_i,\\tilde{y}_i$)로\n",
"변환하라. 단 여기에서 $\\theta= \\frac{\\pi}{4}$로 가정한다.\n",
"\n",
"- ${\\tt xx}_i = \\tilde{x}_i = (\\cos\\theta) x_i - (\\sin\\theta) y_i$\n",
"- ${\\tt yy}_i = \\tilde{y}_i = (\\sin\\theta) x_i + (\\cos\\theta) y_i$\n",
"\n",
"$(x_i,y_i)$와 $(\\tilde{x}_i, \\tilde{y}_i)$를 겹쳐서 시각화 하라. 이\n",
"변환이 의미하는 바는 무엇이라고 생각하는가?\n",
"\n",
"`(풀이1)`"
],
"id": "8117b093-d2c3-4aa2-8a2f-b5c663f457f7"
},
{
"cell_type": "code",
"execution_count": 73,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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Pv+jEeT2NIxMS2eE+3ZBKG1SOKMHym4Y7fwLNCA0ClN2a/ta4HI0sUEJY9iYP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\nAB4HC07+HaV0qRPHNWPZq7vxPc59H+6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isM6LAi30/lZyeKMleOApZawXzmg1vDCSbt+5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\n"
}
}
],
"source": [
"theta = np.pi/4 \n",
"xx = np.cos(theta)*x - np.sin(theta)*y\n",
"yy = np.sin(theta)*x + np.cos(theta)*y\n",
"plt.figure(figsize=(6,6))\n",
"plt.plot(x,y,'o', label=r'$(x,y)$') \n",
"plt.plot(xx,yy,'o', label=r'$(xx,yy)$')\n",
"plt.legend()"
],
"id": "65f421e8-5f62-4074-a06b-99246d2d523f"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`(풀이2)`\n",
"\n",
"아래의 규칙을 다시 고려하자.\n",
"\n",
"- ${\\tt xx}_i = \\tilde{x}_i = (\\cos\\theta) x_i - (\\sin\\theta) y_i$\n",
"- ${\\tt yy}_i = \\tilde{y}_i = (\\sin\\theta) x_i + (\\cos\\theta) y_i$\n",
"\n",
"이는 아래와 같이 재표현가능하다.\n",
"\n",
"- $\\begin{cases} {\\tt xx}_1 = (\\cos\\theta)x_1 - (\\sin\\theta)y_1 \\\\ {\\tt yy}_1 = (\\sin\\theta)x_1 + (\\cos\\theta)y_1 \\end{cases}$\n",
"\n",
"- $\\begin{cases} {\\tt xx}_2 = (\\cos\\theta)x_2 - (\\sin\\theta)y_2 \\\\ {\\tt yy}_2 = (\\sin\\theta)x_2 + (\\cos\\theta)y_2 \\end{cases}$\n",
"\n",
"- $\\dots$\n",
"\n",
"- $\\begin{cases} {\\tt xx}_n = (\\cos\\theta)x_n - (\\sin\\theta)y_1 \\\\ {\\tt yy}_n = (\\sin\\theta)x_n + (\\cos\\theta)y_n \\end{cases}$\n",
"\n",
"이는 다시 아래와 같이 재 표현가능하다.\n",
"\n",
"- $\\begin{bmatrix} {\\tt xx}_1 \\\\ {\\tt yy}_1 \\end{bmatrix} = \\begin{bmatrix} \\cos\\theta & - \\sin\\theta \\\\ \\sin\\theta & \\cos\\theta \\end{bmatrix} \\begin{bmatrix} x_1 \\\\ y_1 \\end{bmatrix}$\n",
"\n",
"- $\\begin{bmatrix} {\\tt xx}_2 \\\\ {\\tt yy}_2 \\end{bmatrix} = \\begin{bmatrix} \\cos\\theta & - \\sin\\theta \\\\ \\sin\\theta & \\cos\\theta \\end{bmatrix} \\begin{bmatrix} x_2 \\\\ y_2 \\end{bmatrix}$\n",
"\n",
"- $\\dots$\n",
"\n",
"- $\\begin{bmatrix} {\\tt xx}_n \\\\ {\\tt yy}_n \\end{bmatrix} = \\begin{bmatrix} \\cos\\theta & - \\sin\\theta \\\\ \\sin\\theta & \\cos\\theta \\end{bmatrix} \\begin{bmatrix} x_n \\\\ y_n \\end{bmatrix}$\n",
"\n",
"이는 다시 아래와 같이 재 표현가능하다. (이게 처음엔 생각하기 어려워요!!\n",
"$\\star\\star\\star$)\n",
"\n",
"- $\\begin{bmatrix} {\\tt xx}_1 & {\\tt xx}_2 & \\dots & {\\tt xx}_n \\\\ {\\tt yy}_1 & {\\tt yy}_2 & \\dots & {\\tt yy}_n \\end{bmatrix} = \\begin{bmatrix} \\cos\\theta & - \\sin\\theta \\\\ \\sin\\theta & \\cos\\theta \\end{bmatrix} \\begin{bmatrix} x_1 & x_2 & \\dots & x_n \\\\ y_1 & y_2 & \\dots & y_n \\end{bmatrix}$\n",
"\n",
"위의 수식에 맞추어 변환을 진행하면"
],
"id": "f299bfaa-2ebb-4571-bb1e-54c925b5f961"
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [],
"source": [
"theta = np.pi/4 \n",
"R = np.array([[np.cos(theta), -np.sin(theta)],[np.sin(theta),np.cos(theta)]])\n",
"R "
],
"id": "4bbf1f64-6ff4-4813-8be5-b107b002f9ed"
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [],
"source": [
"R @ data"
],
"id": "9bf10657-7e5a-480d-a54f-b3254efac201"
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {},
"outputs": [],
"source": [
"xx,yy = R @ data "
],
"id": "1909373d-bffa-409d-9d56-68706463b3b8"
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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Pv+jEeT2NIxMS2eE+3ZBKG1SOKMHym4Y7fwLNCA0ClN2a/ta4HI0sUEJY9iYP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\nAB4HC07+HaV0qRPHNWPZq7vxPc59H+6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isM6LAi30/lZyeKMleOApZawXzmg1vDCSbt+5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\n"
}
}
],
"source": [
"plt.figure(figsize=(6,6))\n",
"plt.plot(x,y,'o', label=r'$(x,y)$') \n",
"plt.plot(xx,yy,'o', label=r'$(xx,yy)$')\n",
"plt.legend()"
],
"id": "47171e1e-1209-43cb-8dcc-381df078c44f"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`3`. 2번과 같은 변환을 8번 연속진행한 결과를 시각화하라.\n",
"\n",
"`(풀이)`"
],
"id": "04e10032-e18f-4d8a-87ec-5c6dbfb15597"
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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Mp0+fxm233Za0zzvvvBM1NTXYuXOn7fJ//dd/xQc/+MG0x69HOgSVOcYCVm4FdRwr0Rw8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\nhCJHhFwQBKHI+f8BhgdLMYpMXXQAAAAASUVORK5CYII=\n"
}
}
],
"source": [
"plt.figure(figsize=(6,6))\n",
"xx,yy=np.linalg.matrix_power(R,8) @ data\n",
"plt.plot(x,y,'o',label=r'$data=(x,y)$') \n",
"plt.plot(xx,yy,'o',label=r'$R^8@data=(xx,yy)$')\n",
"plt.legend()"
],
"id": "21f2fb31"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`4`. 2번의 변환을 역변환하는 코드를 구현하라. 원본, 변환, 역변환한\n",
"자료를 순서대로 시각화 하라. 결과를 아래와 같이 저장하라.\n",
"\n",
"- 원본: ${\\tt x}, {\\tt y}$\n",
"- 2번변환: ${\\tt xx}, {\\tt yy}$\n",
"- 2번의역변환 ${\\tt xxx}, {\\tt yyy}$\n",
"\n",
"`(풀이)`"
],
"id": "603b7029-4b7d-4b13-a51b-7ceadec60775"
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {},
"outputs": [],
"source": [
"xx,yy = R@data \n",
"xxx,yyy = np.linalg.inv(R)@data"
],
"id": "e36a3109-6868-4b75-98a4-ab314d3f44a9"
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
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VEaOzvkpSvQXa9oLHMvye5zkhcxGsmiVli+pNpA64iW+LM7Gj9KULwLSKEyq1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\n+eU8uCSTHs+sZt7GPOqdQd02h8jxGishCXPRBzufjPyoqMNhxFqZhKX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nm+x+tLFNuppdCHGFRKPjtR82/r0Kn2DjWXmBVlONQi01TpfVPg5QucFiPk6bnpimiL7aXbFdsd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\nTAIcU8hNTExMApz/D9+p7DMtT0B+AAAAAElFTkSuQmCC\n"
}
}
],
"source": [
"plt.figure(figsize=(6,6))\n",
"plt.plot(x,y,'.', label=r'$data = (x,y)$') \n",
"plt.plot(xx,yy,'.', label=r'$R@data = (xx,yy)$')\n",
"plt.plot(xxx,yyy,'.', label=r'$R^{-1}@data = (xxx,yyy)$')\n",
"plt.legend()"
],
"id": "4bb0fc93-18a7-4825-9f4d-549d871bcf11"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`5-8`. 시계열 자료와 이동평균\n",
"\n",
"`5`. 아래의 수식에 따르는 수열 $x_t$를 생성하라. 단, $T=1000$ 으로\n",
"설정하고 랜덤시드는 `np.random.seed(2)`와 같이 설정한다.\n",
"\n",
"- $x_1=\\epsilon_1$\n",
"- $x_2=\\epsilon_1+\\epsilon_2$\n",
"- $x_3=\\epsilon_1+\\epsilon_2+\\epsilon_3$\n",
"- $\\dots$\n",
"- $x_T=\\sum_{t=1}^{T} \\epsilon_t$\n",
"\n",
"생성결과를 시각화하라.\n",
"\n",
"**hint** 아래의 코드를 활용하면 쉽다."
],
"id": "e49e6303-aea4-4b91-875c-384949427144"
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"np.cumsum([1,2,3,4])"
],
"id": "d0e88d26-bba3-43b8-871e-dd59321c24e4"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`(풀이)`"
],
"id": "df95465a-4f5b-458d-8ff2-ac4f155af41a"
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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ypdQ2pdTZIbdUxKRas4e6+4hRFKSzS/PgG907YF/81sKotCtaMlKSvKmaPzvQ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\neaXUG0qpzUF+lgA/AO4IpQF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vjKCfqO/zGcBurXWV1roDeA7jvU/099ljoO9rSO93IgT5\ntcAkc2begTGB80KU2xQWSikF/AXYorV+wHLqBcAzw34Vxli95/jXzFn6BUC95WthzNNa3661HqW1\nLsF4H9/SWl8BvA18ybzM//V6/g5fMq+Pu96u1voQUK6UOsY8tBj4jAR9nzGGaRYopdLMf+Oe15vQ\n77PFQN/XV4GzlFK55regs8xj/RPtSYkwTWycB2wHdgI/jHZ7wvi6FmJ8ldsEbDB/zsMYj3wT2AG8\nAeSZ1yuMlUY7gU8wVi9E/XUM8rWfCrxo3h4PrAHKgGeAFPO407xfZp4fH+12h/B6ZwOl5nv9PJCb\nyO8z8BNgK7AZ+BuQkojvM/AUxrxDB8Y3tusG874C15qvvwy4ZiBtkLQGQgiRwBJhuEYIIUQPJMgL\nIUQCkyAvhBAJTIK8EEIkMAnyQgiRwCTICyFEApMgL4QQCez/A89apwacAYGmAAAAAElFTkSuQmCC\n"
}
}
],
"source": [
"T = 1000\n",
"np.random.seed(2)\n",
"epsilon = np.random.randn(1000)\n",
"x = epsilon.cumsum()\n",
"plt.plot(x)"
],
"id": "9bd9725b"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`6`. 아래와 같은 변환을 수행하고 결과를 시각화 하라.\n",
"\n",
"- ${\\tt xx}_1= \\frac{1}{3}(x_1+x_2)$\n",
"- ${\\tt xx}_2= \\frac{1}{3}(x_1+x_2+x_3)$\n",
"- ${\\tt xx}_3= \\frac{1}{3}(x_2+x_3+x_4)$\n",
"- $\\dots$\n",
"- ${\\tt xx}_{T-1}= \\frac{1}{3}(x_{T-1}+x_{T-1}+x_T)$\n",
"- ${\\tt xx}_{T}= \\frac{1}{3}(x_{T-1}+x_T)$\n",
"\n",
"**hint** 아래의 수식을 이용하라.\n",
"\n",
"- $\\begin{bmatrix} {\\tt xx}_1 \\\\ {\\tt xx}_2 \\\\ {\\tt xx}_3 \\\\ \\dots \\\\ {\\tt xx}_{T-1} \\\\ {\\tt xx}_T \\end{bmatrix}= \\begin{bmatrix} 1/3 & 1/3 & 0 & 0 & 0 & \\dots & 0 & 0 & 0 & 0 \\\\ 1/3 & 1/3 & 1/3 & 0 & 0 & \\dots & 0 & 0 & 0 & 0 \\\\ 0 & 1/3 & 1/3 & 1/3 & 0 & \\dots & 0 & 0 & 0 & 0 \\\\ \\dots & \\dots & \\dots & \\dots & \\dots & \\dots & \\dots & \\dots & \\dots & \\dots \\\\ 0 & 0 & 0 & 0 & 0 & \\dots & 0 & 1/3 & 1/3 & 1/3 \\\\ 0 & 0 & 0 & 0 & 0 & \\dots & 0 & 0 & 1/3 & 1/3 \\\\ \\end{bmatrix}\\begin{bmatrix} x_1 \\\\ x_2 \\\\ x_3 \\\\ \\dots \\\\ x_{T-1} \\\\ x_T \\end{bmatrix}$\n",
"\n",
"`(풀이)`"
],
"id": "63a600dd-33ee-4db8-a5b8-a1b1d03c0300"
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"M = np.array([[abs(i-j)<2 for i in range(T)] for j in range(T)])*1/3\n",
"M"
],
"id": "ad07aa2f"
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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PCyWpTQsATm8TzvanRjO047HfenSRrtbp0rlfA/CNfRhzHQNo26EzJkcxf5ru5ZLibxr2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\nURSlGVNJXlEUpRlTSV5RFKUZ+3/jm9eIr3FllwAAAABJRU5ErkJggg==\n"
}
}
],
"source": [
"plt.plot(x,label=r'$x$')\n",
"plt.plot(M@x,'--',label=r'$M@x$')\n",
"plt.legend()"
],
"id": "0b178079"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- 끝이 올라간 이유? 마지막에 $\\frac{1}{3}(x_{T-1}+x_T+x_{T+1})$ 대신에\n",
" $\\frac{1}{3}(x_{T-1}+x_T+0)$ 을 이용하였기 때문\n",
"\n",
"`7`. 아래와 같은 변환을 수행하고 결과를 시각화하라.\n",
"\n",
"- ${\\tt xx}_1= \\frac{1}{3}(x_1+x_1+x_2)$\n",
"- ${\\tt xx}_2= \\frac{1}{3}(x_1+x_2+x_3)$\n",
"- ${\\tt xx}_3= \\frac{1}{3}(x_2+x_3+x_4)$\n",
"- $\\dots$\n",
"- ${\\tt xx}_{T-1}= \\frac{1}{3}(x_{T-1}+x_{T-1}+x_T)$\n",
"- ${\\tt xx}_{T}= \\frac{1}{3}(x_{T-1}+x_T+x_T)$\n",
"\n",
"`(풀이)`"
],
"id": "0565582f-52b6-46bb-8d54-399cc8319874"
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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pvDh7YpvJ1ZowCICXyq9mu/UK0kQJDc6m0aVc+/XeM9Psz/Ck6/fc5LiBeWmP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\n"
}
}
],
"source": [
"M[0,0] = 2/3 \n",
"M[-1,-1] = 2/3 \n",
"plt.plot(x,label=r'$x$')\n",
"plt.plot(M@x,label=r'$M@x$')\n",
"plt.legend()"
],
"id": "bad96f88-8fe7-425a-a7a6-48fa4bc70b21"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`8`. 7번의 변환을 100번 반복하고 시각화하라.\n",
"\n",
"`(풀이)`"
],
"id": "73190970-f7ed-49ec-809e-67c390343b92"
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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b5bpt0bZW9cOxY+Jh2+085LibRJXCL+bHuXbvk/w6dz4vz9zEvu/up69xM0tb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\nQV4IIQKYBHkhhAhgEuSFECKA/T934D/wbixcBAAAAABJRU5ErkJggg==\n"
}
}
],
"source": [
"plt.plot(x,label=r'$x$')\n",
"plt.plot(np.linalg.matrix_power(M,100)@x,label=r'$M^{100}@x$')\n",
"plt.legend()"
],
"id": "6bb6a2a4"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`9`. 7번의 변환을 1000번 반복하고 시각화하라."
],
"id": "c4f5fbd2-c95b-473c-8544-f073205207fe"
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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X6EdGXlGlKW0fGNaKmz9bxw1/hbMpYQoRXMXaSX6YEldByl5Mp3bTR2ViMNjI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\n4vJeAAAAAElFTkSuQmCC\n"
}
}
],
"source": [
"plt.plot(x,label=r'$x$')\n",
"plt.plot(np.linalg.matrix_power(M,1000)@x,label=r'$M^{1000}@x$')\n",
"plt.legend()"
],
"id": "5765bcf1"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# HW\n",
"\n",
"없음"
],
"id": "a9a7c504-f9eb-423e-be08-ce80046e43db"
}
],
"nbformat": 4,
"nbformat_minor": 5,
"metadata": {
"kernelspec": {
"name": "python3",
"display_name": "Python 3 (ipykernel)",
"language": "python"
},
"language_info": {
"name": "python",
"codemirror_mode": {
"name": "ipython",
"version": "3"
},
"file_extension": ".py",
"mimetype": "text/x-python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.16"
}
}
}