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@akashin
Last active August 29, 2015 14:09
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CompMath, Task 2, Andrey Kashin
{
"metadata": {
"name": "",
"signature": "sha256:8a990c7a47921ab2a81c1be9cf13ba0b55e6b3b1afbf9f1c38b36c8215d3cf0a"
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"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"\u0417\u0430\u0434\u0430\u0447\u0430 2"
]
},
{
"cell_type": "heading",
"level": 5,
"metadata": {},
"source": [
"\u041a\u0430\u0448\u0438\u043d \u0410\u043d\u0434\u0440\u0435\u0439, 195 \u0433\u0440\u0443\u043f\u043f\u0430, \u0424\u0418\u0412\u0422 \u041c\u0424\u0422\u0418"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%pylab inline"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"def f0(x):\n",
" return math.sin(x)\n",
"\n",
"def f1(x):\n",
" return math.cos(x)\n",
"\n",
"(L, R) = (0, 2 * math.pi)\n",
"\n",
"class Spline:\n",
" @staticmethod\n",
" def interpolate(f0, f1, x0, x1):\n",
" a = np.array([[1, x0, x0**2, x0**3], [1, x1, x1**2, x1**3], [0, 1, 2 * x0, 3 * x0**2], [0, 1, 2 * x1, 3 * x1**2]])\n",
" b = np.array([f0(x0),f0(x1), f1(x0), f1(x1)])\n",
" x = np.linalg.solve(a, b)\n",
" return x\n",
" \n",
" @staticmethod\n",
" def P0(P, x):\n",
" return dot(P, [1, x, x**2, x**3])\n",
" \n",
" @staticmethod\n",
" def P1(P, x):\n",
" return dot(P, [0, 1, 2 * x, 3 * x**2])\n",
" \n",
" def __init__(self, f0, f1, L, R, N):\n",
" if N <= 1:\n",
" raise Exception(\"N should be > 1\")\n",
" self.f0 = f0\n",
" self.f1 = f1\n",
" self.L = L\n",
" self.R = R\n",
" self.N = N\n",
" self.h = (R - L)/(N - 1)\n",
" self.build()\n",
" \n",
" def build(self):\n",
" self.bucketP = [0] * (self.N - 1)\n",
" points = linspace(self.L, self.R, self.N)\n",
" for i in range(self.N - 1):\n",
" cL = points[i]\n",
" cR = points[i + 1]\n",
" self.bucketP[i] = Spline.interpolate(self.f0, self.f1, cL, cR)\n",
" \n",
" def evaluate(self, x):\n",
" if x < self.L or x > self.R:\n",
" raise Exception(\"x should be in range ({}, {})\".format(self.L, self.R))\n",
" \n",
" bucketIndex = int((x - 1e-9 - self.L) / self.h)\n",
" return Spline.P0(self.bucketP[bucketIndex], x)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 12
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"f = Spline(f0, f1, L, R, 30)\n",
"print(f.evaluate(0), f.evaluate(math.pi / 2), f.evaluate(math.pi))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(0.0, 0.999996777787585, -3.5527136788005009e-15)\n"
]
}
],
"prompt_number": 26
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def findError(N, density = 500):\n",
" f = Spline(f0, f1, L, R, N)\n",
" return max(abs(f0(x) - f.evaluate(x)) for x in linspace(L, R, N * density))\n",
"\n",
"def plotApproximation(N, density = 500):\n",
" X = linspace(L, R, N * density)\n",
" Y = [f0(x) for x in X]\n",
" f = Spline(f0, f1, L, R, N)\n",
" YP = [f.evaluate(x) for x in X]\n",
" \n",
" fig = plt.figure(figsize=(8, 6))\n",
" plt.plot(X, Y)\n",
" plt.plot(X, YP)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 27
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\\varepsilon(h) = O(h^k)$\n",
"\n",
"$\\varepsilon(h) = c h^k$\n",
"\n",
"$\\dfrac{\\varepsilon(h_1)}{\\varepsilon(h_2)} = \\left(\\dfrac{h_1}{h_2}\\right)^k$\n",
"\n",
"$k = log{\\left(\\frac{\\varepsilon(h_1)}{\\varepsilon(h_2)}\\right)} \\div log{\\left(\\frac{h_1}{h_2}\\right)}$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Ns = range(3, 30)\n",
"Ks = []\n",
"Cs = []\n",
"for N in Ns: \n",
" def n_h_eps(N):\n",
" return (N, (R - L)/(N - 1), findError(N))\n",
" \n",
" (N1, h1, eps1) = n_h_eps(N)\n",
" (N2, h2, eps2) = n_h_eps(N + 1)\n",
" k = log(eps1 / eps2) / log(h1 / h2)\n",
" Ks.append(k)\n",
" Cs.append(eps1 / h1**k)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 28
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print(Ks)\n",
"print\n",
"print(\"Mean: {}\".format(mean(Ks)))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[4.1192966369289961, 4.5879449395886871, 2.6179361695282068, 3.6816034002176976, 4.1328387047676216, 4.3785183352983355, 3.4403972774369169, 3.8402118889386805, 4.0952400877836874, 4.2706788156166322, 3.6501027891712186, 3.8940929516876897, 4.0733140635432976, 4.2099181604928697, 3.7457377534024063, 3.9209516451940645, 4.0594488986022252, 4.1712359784906861, 3.8005194154420359, 3.9368803728073836, 4.0499847922758727, 4.1444963711181728, 3.8358381636776873, 3.9475688205630757, 4.0429731464931979, 4.125085389709203, 3.8604718937988003]\n",
"\n",
"Mean: 3.94938099491\n"
]
}
],
"prompt_number": 29
},
{
"cell_type": "heading",
"level": 5,
"metadata": {},
"source": [
"\u0411\u043b\u0438\u0436\u0435 \u043a 4 :)"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print(mean(Cs))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"0.00251266368365\n"
]
}
],
"prompt_number": 30
},
{
"cell_type": "heading",
"level": 4,
"metadata": {},
"source": [
"\u041f\u043e\u0445\u043e\u0436\u0435 \u043d\u0430 1/400"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Ns = Ns[:20]\n",
"hs = [(R - L)/(N - 1) for N in Ns]\n",
"\n",
"fig = plt.figure(figsize=(8, 6))\n",
"plt.plot(Ns, [findError(N) for N in Ns])\n",
"plt.plot(Ns, [h**4 / 400 for h in hs])\n",
"\n",
"plt.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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OYW2CYGfNxCgAgIEgrE0QnMWMxTwAAANBWJvgywFmLOYBABgAwtoELJMJAAgFYW2CvgPM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\n",
"text": [
"<matplotlib.figure.Figure at 0x10d1b3910>"
]
}
],
"prompt_number": 31
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plotApproximation(2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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CRjUcJTsO6Tnn4s6Y7TEb7Ve2x90X2ev3aW0NtGgBrFihpnBEpJd0tkg/fCiW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\nhBBC6Ir6F58Db93XLNdUAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x10d0b7350>"
]
}
],
"prompt_number": 32
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plotApproximation(3)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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CypKrWb/e2OBFRCSyXKolXasWlKvykG8fZmJ3m91kSprJBulEImbBkQX47fMj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\nPn37eZ4ensyvM59fT/3KnENz7BNOePj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jA+7dnZWV1djb2yv+5/cNBsO+nJyc+kC3BeB2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\nQmiawiaNEEIITVPYpBFCCKFp6k//MO8G2uBurwAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x10d0b1f50>"
]
}
],
"prompt_number": 33
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plotApproximation(4)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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wRuqlb2VP7Ivxg4wLkBHRZ6hESU/YfBhFJDaoaecgOgpRrhrXpjXSC93EgTPR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\nAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x10d1bd050>"
]
}
],
"prompt_number": 34
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plotApproximation(5)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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3f/bs2b996jnDhw9fYmdnd9/R0fFaZGSk06eeM9X/IPKll0PjKnbZTSLSCL5d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\nzF88kg4NDXX73L+zsLBIeP7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UCl1vb+9lISEhzaKiohz8/f09bt++bf+jX5OIKKfkyQPM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\ngg==\n",
"text": [
"<matplotlib.figure.Figure at 0x10d0b1f50>"
]
}
],
"prompt_number": 35
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
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