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edy555/RiemannZeta.ipynb

Created June 2, 2015 21:51
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ゼータ関数を描いてみたipython notebook
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RiemannZeta.ipynb
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"%matplotlib inline\n",
"%config InlineBackend.figure_format='svg'\n",
"import numpy as np\n",
"import pylab as pl"
],
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"\u307e\u305a\u306f\u30ca\u30a4\u30fc\u30d6\u306a\u8a08\u7b97\u3002 $\\displaystyle \\zeta(s) = \\sum_{n=1}^{\\infty}\\frac{1}{n^s}$"
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"input": [
"def zeta0(s):\n",
" x = 0\n",
" for i in range(1,1000000):\n",
" x += 1 / (i ** s)\n",
" return x"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 7
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"zeta0(0.5+14.134j)"
],
"language": "python",
"metadata": {},
"outputs": [
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"metadata": {},
"output_type": "pyout",
"prompt_number": 8,
"text": [
"(35.44160211530015+61.18274604837292j)"
]
}
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"source": [
"scipy.special\u306b\u30bc\u30fc\u30bf\u95a2\u6570\u304c\u3042\u308b\u3051\u3069\u3001\u8907\u7d20\u6570\u3067\u306f\u4f7f\u3048\u306a\u3044\u3088\u3046\u3060"
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"input": [
"#import scipy.special\n",
"#scipy.special.zeta(0.5+14.134j, 0)"
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"\u8fbb\u541b\u306e\u30da\u30fc\u30b8\u304b\u3089\u5f15\u7528(http://tsujimotter.hatenablog.com/entry/riemann-zeta-function )"
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"source": [
"$$\\zeta(s) = \\frac{1}{1-2^{1-s}} \\sum_{m=1}^{\\infty} 2^{-m} \\sum_{j=1}^{m} (-1)^{j-1} \\binom {m-1}{j-1} j^{-s}$$"
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"cell_type": "code",
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"input": [
"import scipy.misc as scm\n",
"scm.comb(1000000, 10)"
],
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"metadata": {},
"output_type": "pyout",
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"text": [
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"input": [
"from scipy.misc import comb\n",
"LOWER_THRESHOLD=1.0e-6\n",
"UPPER_BOUND=1.0e+4\n",
"INFINITY=300\n",
"\n",
"def zeta(s):\n",
" outer_sum = 0.0\n",
" prev = np.inf\n",
" if s == 1:\n",
" return np.inf\n",
" for m in range(1,INFINITY):\n",
" inner_sum = 0.0\n",
" for j in range(1, m+1):\n",
" k = comb(m-1, j-1, exact=True) * j**(-s)\n",
" inner_sum += k if j%2 else -k\n",
" inner_sum = inner_sum * 2**(-m)\n",
" outer_sum += inner_sum\n",
" if abs(prev - inner_sum) < LOWER_THRESHOLD:\n",
" break\n",
" if abs(outer_sum) > UPPER_BOUND:\n",
" break\n",
" prev = inner_sum\n",
" return outer_sum / (1-(2**(1-s)))"
],
"language": "python",
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"\u6700\u521d\u306e\u96f6\u70b9\u4ed8\u8fd1\u3067\u8a66\u3059"
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"cell_type": "code",
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"input": [
"zeta(0.5+14.134j)"
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"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 14,
"text": [
"(9.031587952272404e-05-0.000568140412905536j)"
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}
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"input": [
"x = np.linspace(0,50,1000)\n",
"%time y = np.vectorize(zeta)(0.5 + x*1j)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"CPU times: user 6.38 s, sys: 83.9 ms, total: 6.47 s\n",
"Wall time: 6.46 s\n"
]
}
],
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"source": [
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"input": [
"#x = np.linspace(0,30,1000)\n",
"#%time y = np.vectorize(zeta)(0.8 + x*1j)\n",
"pl.grid()\n",
"pl.plot(x, np.abs(y))\n",
"pl.figure()\n",
"pl.grid()\n",
"pl.plot(np.real(y), np.imag(y))"
],
"language": "python",
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"output_type": "pyout",
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"[<matplotlib.lines.Line2D at 0x11151d050>]"
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{
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"#%matplotlib \n",
"%matplotlib inline\n",
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"#ax.plot_surface(RE, IM, np.log(np.abs(Z)), rstride=1, cstride=1, cmap='hot')"
],
"language": "python",
"metadata": {},
"outputs": [
{
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