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{
"metadata": {
"name": "FFT Introduction"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We are solving 1D Poisson equation:\n",
"$$\n",
"{d^2\\over dx^2}V(x) = -4\\pi n(x)\n",
"$$\n",
"Using Fast Fourier Transform (FFT). And then calculating the Hartree energy using:\n",
"$$\n",
"E_H = 2\\pi \\sum_{{\\bf G}\\ne 0} {|n({\\bf G})|^2\\over G^2}\n",
"$$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%pylab inline\n",
"from pylab import plot, semilogy\n",
"from numpy import loadtxt, linspace\n",
"from numpy.fft import fft, fftfreq\n",
"from sympy import exp, sin, pi, var, Integral"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\n",
"For more information, type 'help(pylab)'.\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's setup the right hand side:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"var(\"x\")\n",
"L = 2 # domain [0, L]\n",
"rho = exp(sin(2*pi*x/L))\n",
"#rho = sin(2*pi*x/L)\n",
"integ = Integral(rho, (x, 0, L)).n()\n",
"rho -= integ / L\n",
"print \"rho(x) =\", rho\n",
"print \"Integral of rho =\", Integral(rho, (x, 0, L)).n()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"rho(x) = exp(sin(pi*x)) - 1.26606587775201\n",
"Integral of rho = "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"-1.41156085310944e-16\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"D = []\n",
"for m in range(1, 15):\n",
" #2m+1 terms -Gmax, ..., 0, ..., Gmax\n",
" n = 2*m+1\n",
" xj = linspace(0, L, n+1)[:-1]\n",
" rhoj = array([float(rho.subs(x, val).n(20)) for val in xj])\n",
" nr = fft(rhoj) / n\n",
" # re-order -> -Gmax, ... Gmax\n",
" f = fftfreq(n)\n",
" idx = f.argsort()\n",
" f = f[idx]\n",
" nr = nr[idx]\n",
" nr[m] = 0 # set G=0 term = 0\n",
" G = array([float((2*pi*j/L)) for j in range(-m, m+1)])\n",
" G[m] = 1\n",
" tmp = array([complex(2*pi*abs(nr[j])**2/G[j]**2) for j in range(n)])\n",
" E = sum(tmp).real * L\n",
" print n, E\n",
" D.append((n, E))\n",
"D = array(D)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"3 0.857623650249\n",
"5 0.825420490259\n",
"7 0.825230159883\n",
"9 0.825229196177\n",
"11"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" 0.825229191862\n",
"13 0.825229191846\n",
"15 0.825229191846\n",
"17"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" 0.825229191846\n",
"19 0.825229191846\n",
"21"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" 0.825229191846\n",
"23 0.825229191846\n",
"25"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" 0.825229191846\n",
"27 0.825229191846\n",
"29"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" 0.825229191846\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"N = D[:, 0]\n",
"E = D[:, 1]\n",
"E_exact = E[-1]\n",
"figure(figsize=(8, 6), dpi=80)\n",
"semilogy(N, abs(E-E_exact), \"bo-\")\n",
"grid()\n",
"title(\"Convergence of an FFT Poisson solver (semilogy)\")\n",
"xlabel(\"N (number of PW in each direction)\")\n",
"ylabel(\"E - E_exact [a.u.]\")\n",
"\n",
"figure(figsize=(8, 6), dpi=80)\n",
"loglog(N, abs(E-E_exact), \"bo-\", label=\"calculated\")\n",
"grid()\n",
"title(\"Convergence of an FFT Poisson solver (loglog)\")\n",
"xlabel(\"N (number of PW in each direction)\")\n",
"ylabel(\"E - E_exact [a.u.]\")"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 8,
"text": [
"<matplotlib.text.Text at 0x515eb90>"
]
},
{
"output_type": "display_data",
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vRu/evZUOy2I9eCgJANq3Bzp0AObOVSYeU/ZwrqhkzJM0zJN0zJV8FCsAQkND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\nJsZqG6qv6+Hhwccff0x4eDh6vZ7w8HCKi4txdHTk66+/Zsy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},
{
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Z1gwQmScmA0QmoG5dYO1aIDISyMuTOhoiqm1YM0BkQiZNAmQyYPVqqSMhInPC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\n82YMHjxYqnCIyIxxNUKimjFKMhAaGgo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}
],
"prompt_number": 8
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}

Xet Storage Details

Size:
62.1 kB
·
Xet hash:
8ffd247923c0432b04667a29578cd4aa071e88f4fb06b1fc98f622e1c2dfce9d

Xet efficiently stores files, intelligently splitting them into unique chunks and accelerating uploads and downloads. More info.