{
    "metadata": {
        "name": "smooth_dos"
    }, 
    "nbformat": 2, 
    "worksheets": [
        {
            "cells": [
                {
                    "cell_type": "code", 
                    "collapsed": true, 
                    "input": [
                        "from sympy import *", 
                        "import numpy as np", 
                        "import math"
                    ], 
                    "language": "python", 
                    "outputs": [], 
                    "prompt_number": 1
                }, 
                {
                    "cell_type": "markdown", 
                    "source": [
                        "<h2>Strutinsky Energy Averaging Method</h2>"
                    ]
                }, 
                {
                    "cell_type": "markdown", 
                    "source": [
                        "Define a callable class for computing the smooth part of the density of states $\\tilde{g}_m(E)$ with curvature", 
                        "correction of order $2M$."
                    ]
                }, 
                {
                    "cell_type": "code", 
                    "collapsed": true, 
                    "input": [
                        "class SmoothDOS(object):", 
                        "", 
                        "    def __init__(self, energies):", 
                        "        self.energies = energies", 
                        "", 
                        "    def gaussian_smoothing_func(self, M, x):", 
                        "        return (mpmath.laguerre(M,0.5,x**2)*exp(-x**2)/sqrt(pi)).evalf()", 
                        "", 
                        "    def __call__(self, e, M=3, gamma=1.0):", 
                        "        return sum(self.gaussian_smoothing_func(M, (e-ei)/gamma)/gamma for ei in self.energies)"
                    ], 
                    "language": "python", 
                    "outputs": [], 
                    "prompt_number": 2
                }, 
                {
                    "cell_type": "code", 
                    "collapsed": true, 
                    "input": [
                        "def avgf(M, x):", 
                        "    return (mpmath.laguerre(M,0.5,x**2)*exp(-x**2)/sqrt(pi)).evalf()"
                    ], 
                    "language": "python", 
                    "outputs": [], 
                    "prompt_number": 3
                }, 
                {
                    "cell_type": "code", 
                    "collapsed": true, 
                    "input": [
                        "def smooth_dos(gamma, M, e, energies):", 
                        "    return sum(avgf(M, (e-ei)/gamma)/gamma for ei in energies)"
                    ], 
                    "language": "python", 
                    "outputs": [], 
                    "prompt_number": 4
                }, 
                {
                    "cell_type": "markdown", 
                    "source": [
                        "<h2>1D Simple Harmonic Oscillator DOS</h2>"
                    ]
                }, 
                {
                    "cell_type": "code", 
                    "collapsed": true, 
                    "input": [
                        "def sho_smooth_dos(e):", 
                        "    \"\"\"Compute the exact smooth DOS.\"\"\"", 
                        "    return 1"
                    ], 
                    "language": "python", 
                    "outputs": [], 
                    "prompt_number": 5
                }, 
                {
                    "cell_type": "code", 
                    "collapsed": true, 
                    "input": [
                        "def sho_spectrum(nmax):", 
                        "    \"\"\"Compute the first nmax energies of the 1D SHO.\"\"\"", 
                        "    return [n+0.5 for n in range(nmax)]"
                    ], 
                    "language": "python", 
                    "outputs": [], 
                    "prompt_number": 6
                }, 
                {
                    "cell_type": "code", 
                    "collapsed": true, 
                    "input": [
                        "sho_evalues = np.linspace(0.0,20,100)"
                    ], 
                    "language": "python", 
                    "outputs": [], 
                    "prompt_number": 7
                }, 
                {
                    "cell_type": "code", 
                    "collapsed": true, 
                    "input": [
                        "sho_dos = SmoothDOS(sho_spectrum(30))"
                    ], 
                    "language": "python", 
                    "outputs": [], 
                    "prompt_number": 8
                }, 
                {
                    "cell_type": "code", 
                    "collapsed": true, 
                    "input": [
                        "sho_exact_dos = [sho_smooth_dos(e) for e in sho_evalues]"
                    ], 
                    "language": "python", 
                    "outputs": [], 
                    "prompt_number": 10
                }, 
                {
                    "cell_type": "code", 
                    "collapsed": true, 
                    "input": [
                        "sho_approx_dos = [sho_dos(e,M=3,gamma=10.0) for e in sho_evalues]"
                    ], 
                    "language": "python", 
                    "outputs": [], 
                    "prompt_number": 23
                }, 
                {
                    "cell_type": "code", 
                    "collapsed": false, 
                    "input": [
                        "plot(sho_evalues, sho_exact_dos, label=\"exact\")", 
                        "plot(sho_evalues, sho_approx_dos, label=\"approx\")", 
                        "title(\"Smooth part of the DOS for the 1D SHO\")", 
                        "xlabel(\"Energy\"); ylabel(\"$g(E)$\")", 
                        "legend(loc=4)"
                    ], 
                    "language": "python", 
                    "outputs": [
                        {
                            "output_type": "pyout", 
                            "prompt_number": 24, 
                            "text": [
                                "&lt;matplotlib.legend.Legend at 0x7f1790f77990&gt;"
                            ]
                        }, 
                        {
                            "output_type": "display_data", 
                            "png": 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POpZ0PEX50VoiXSjeZYcIIYS0LU66nry8vBAdHY2CggLo6elhxYoV4PP5AAB/f3/k5ubC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\nFhUKQgghzaJCQQghpFlUKAghhDTr/wCAVvjlY6wV8gAAAABJRU5ErkJggg==\n"
                        }
                    ], 
                    "prompt_number": 24
                }, 
                {
                    "cell_type": "markdown", 
                    "source": [
                        "Note how the exact smoothed DOS and the Strutinsky approximation agree once the energy is away from", 
                        "0. In general, these are edge effects and are also present at the right limit if you don't use enough energy", 
                        "levels.  Here we have used 30, so the right side doesn't show these artifacts."
                    ]
                }, 
                {
                    "cell_type": "markdown", 
                    "source": [
                        "<h2>1D Particle in a BOX (PIAB) DOS</h2>"
                    ]
                }, 
                {
                    "cell_type": "code", 
                    "collapsed": true, 
                    "input": [
                        "def piab_smooth_dos(e):", 
                        "    \"\"\"Compute the exact smooth DOS.\"\"\"", 
                        "    return 1.0/(2.0*math.sqrt(e*math.pi**2/2))"
                    ], 
                    "language": "python", 
                    "outputs": [], 
                    "prompt_number": 16
                }, 
                {
                    "cell_type": "code", 
                    "collapsed": true, 
                    "input": [
                        "def piab_spectrum(nmax):", 
                        "    \"\"\"Compute the first nmax energies of the 1D PIAB.\"\"\"", 
                        "    return [0.5*math.pi**2*(n+1)**2 for n in range(nmax)]"
                    ], 
                    "language": "python", 
                    "outputs": [], 
                    "prompt_number": 17
                }, 
                {
                    "cell_type": "code", 
                    "collapsed": true, 
                    "input": [
                        "piab_evalues = linspace(1.0,1000.0,100)"
                    ], 
                    "language": "python", 
                    "outputs": [], 
                    "prompt_number": 18
                }, 
                {
                    "cell_type": "code", 
                    "collapsed": true, 
                    "input": [
                        "piab_dos = SmoothDOS(piab_spectrum(20))"
                    ], 
                    "language": "python", 
                    "outputs": [], 
                    "prompt_number": 19
                }, 
                {
                    "cell_type": "code", 
                    "collapsed": true, 
                    "input": [
                        "piab_exact_dos = [piab_smooth_dos(e) for e in piab_evalues]"
                    ], 
                    "language": "python", 
                    "outputs": [], 
                    "prompt_number": 20
                }, 
                {
                    "cell_type": "code", 
                    "collapsed": true, 
                    "input": [
                        "piab_approx_dos = [piab_dos(e, M=4, gamma=150.0) for e in piab_evalues]"
                    ], 
                    "language": "python", 
                    "outputs": [], 
                    "prompt_number": 21
                }, 
                {
                    "cell_type": "code", 
                    "collapsed": false, 
                    "input": [
                        "plot(piab_evalues, piab_exact_dos, label=\"exact\")", 
                        "plot(piab_evalues, piab_approx_dos, label=\"approx\")", 
                        "title(\"Smooth part of the DOS for the 1D PIAB\")", 
                        "xlabel(\"Energy\"); ylabel(\"$g(E)$\")", 
                        "legend(loc=1)"
                    ], 
                    "language": "python", 
                    "outputs": [
                        {
                            "output_type": "pyout", 
                            "prompt_number": 22, 
                            "text": [
                                "&lt;matplotlib.legend.Legend at 0x6107410&gt;"
                            ]
                        }, 
                        {
                            "output_type": "display_data", 
                            "png": 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MeHt7V7gNhgsRkfmY/LCYKeiHKwv84x9AUpK5a0NE9HR4qg+LmQp7LkRE5sNw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\nIiIyOoYLEREZHcOFiIiM7v8D5L89YpM7o1sAAAAASUVORK5CYII=\n"
                        }
                    ], 
                    "prompt_number": 22
                }, 
                {
                    "cell_type": "code", 
                    "collapsed": true, 
                    "input": [], 
                    "language": "python", 
                    "outputs": []
                }
            ]
        }
    ]
}