{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Vacuum Neutrino Oscillations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here is a notebook for homogeneous gas model." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we are talking about a homogeneous gas bulk of neutrinos with single energy. The EoM is\n", "$$\n", "i \\partial_t \\rho_E = \\left[ \\frac{\\delta m^2}{2E}B ,\\rho_E \\right]\n", "$$\n", "\n", "while the EoM for antineutrinos is\n", "$$\n", "i \\partial_t \\bar\\rho_E = \\left[- \\frac{\\delta m^2}{2E}B ,\\bar\\rho_E \\right]\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Initial:\n", "Homogeneous, Isotropic, Monoenergetic $\\nu_e$ and $\\bar\\nu_e$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The equations becomes\n", "$$\n", "i \\partial_t \\rho_E = \\left[ \\frac{\\delta m^2}{2E} B ,\\rho_E \\right]\n", "$$\n", "$$\n", "i \\partial_t \\bar\\rho_E = \\left[- \\frac{\\delta m^2}{2E}B,\\bar\\rho_E \\right]\n", "$$\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define $\\omega=\\frac{\\delta m^2}{2E}$, $\\omega = \\frac{\\delta m^2}{-2E}$, $\\mu=\\sqrt{2}G_F n_\\nu$\n", "$$\n", "i \\partial_t \\rho_E = \\left[ \\omega B ,\\rho_E \\right]\n", "$$\n", "$$\n", "i \\partial_t \\bar\\rho_E = \\left[\\bar\\omega B,\\bar\\rho_E \\right]\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "where\n", "\n", "$$\n", "B = \\frac{1}{2} \\begin{pmatrix} \n", "-\\cos 2\\theta_v & \\sin 2\\theta_v \\\\\n", "\\sin 2\\theta_v & \\cos 2\\theta_v\n", "\\end{pmatrix}\n", "$$\n", "\n", "or just use theta =0.2rad\n", "\n", "\n", "$$\n", "L = \\begin{pmatrix}\n", "1 & 0 \\\\\n", "0 & 0\n", "\\end{pmatrix}\n", "$$\n", "\n", "Initial condition \n", "$$\n", "\\rho(t=0) = \\begin{pmatrix}\n", "1 & 0 \\\\\n", "0 & 0\n", "\\end{pmatrix}\n", "$$\n", "\n", "$$\n", "\\bar\\rho(t=0) =\\begin{pmatrix}\n", "1 & 0 \\\\\n", "0 & 0\n", "\\end{pmatrix}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "define the following quantities\n", "\n", "1. hbar$=\\hbar$\n", "%2. delm2E$= \\delta m^2/2E$\n", "%3. lamb $= \\lambda$, lambb $= \\bar\\lambda$\n", "%4. gF $= G_F$\n", "%5. mu $=\\mu$\n", "6. omega $=\\omega$, omegab $=-\\bar\\omega$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Numerical" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# This line configures matplotlib to show figures embedded in the notebook, \n", "# instead of opening a new window for each figure. More about that later. \n", "# If you are using an old version of IPython, try using '%pylab inline' instead.\n", "%matplotlib inline\n", "%load_ext snakeviz\n", "\n", "import numpy as np\n", "from scipy.optimize import minimize\n", "from scipy.special import expit\n", "import matplotlib.pyplot as plt\n", "\n", "from matplotlib.lines import Line2D\n", "\n", "import timeit\n", "\n", "import pandas as pd\n", "\n", "import plotly.plotly as py\n", "from plotly.graph_objs import *\n", "import plotly.tools as tls" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-0.49003329 0.09933467]\n", " [ 0.09933467 0.49003329]]\n" ] } ], "source": [ "# hbar=1.054571726*10**(-34)\n", "hbar=1.0\n", "delm2E=1.0\n", "# lamb=1.0 ## lambda for neutrinos\n", "# lambb=1.0 ## lambda for anti neutrinos\n", "# gF=1.0\n", "# nd=1.0 ## number density\n", "# ndb=1.0 ## number density\n", "omega=1.0\n", "omegab=-1.0\n", "\n", "## Here are some matrices to be used\n", "\n", "elM = np.array([[1.0,0.0],[0.0,0.0]])\n", "#bM = 1.0/2*np.array( [ [ - 0.38729833462,0.31622776601] , [0.31622776601,0.38729833462] ] )\n", "bM = 1.0/2*np.array( [ [ -np.cos(0.2),np.sin(0.2)] , [np.sin(0.2),np.cos(0.2)] ] )\n", "\n", "print bM\n", "## sqareroot of 2\n", "sqrt2=np.sqrt(2.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I am going to substitute all density matrix elements using their corrosponding network expressions.\n", "\n", "So first of all, I need the network expression for the unknown functions.\n", "\n", "A function is written as\n", "\n", "$$ y_i= initial+t_i v_k f(t_i w_k+u_k) ,$$\n", "\n", "while it's derivative is\n", "\n", "$$v_k f(t w_k+u_k) + t v_k f(tw_k+u_k) (1-f(tw_k+u_k)) w_k .$$\n", "\n", "Now I can write down the equations using these two forms." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def trigf(x):\n", " #return 1/(1+np.exp(-x)) # It's not bad to define this function here for people could use other functions other than expit(x).\n", " return expit(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "rho = [[r11, a+ib ], [a-ib,r22]], the following rho4 function is rho4 = [r11,a, b, r22]" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false }, "outputs": [], "source": [ "## The time derivative part\n", "\n", "### Here are the initial conditions\n", "\n", "init = np.array( [1.0, 0.0, 0.0, 0.0] )\n", "\n", "### For neutrinos\n", "\n", "def rho4(x,ti,initialCondition): # x is the input structure arrays, ti is a time point\n", "\n", " elem0 = np.sum(ti * x[0] * trigf( ti*x[1] + x[2] ) )\n", " elem1 = np.sum(ti * x[3] * trigf( ti*x[4] + x[5] ) )\n", " elem2 = np.sum(ti * x[6] * trigf( ti*x[7] + x[8] ) )\n", " elem3 = np.sum(ti * x[9] * trigf( ti*x[10] + x[11] ) )\n", " \n", " return initialCondition + np.array([ elem0 , elem1, elem2, elem3 ])\n" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "array([ 1.88079708, 0.88079708, 0.88079708, 0.88079708])" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "## Test\n", "xtemp=np.ones(12)\n", "rho4(xtemp,1,init)" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-0.49003329 0.09933467 0.09933467 0.49003329]\n" ] } ], "source": [ "## Define Hamiltonians for both\n", "\n", "hamilv = delm2E*bM.flatten()\n", "\n", "print hamilv" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-0.49003329 0.09933467]\n", " [ 0.09933467 0.49003329]]\n", "[-0.49003329 0.09933467 0.09933467 0.49003329]\n" ] } ], "source": [ "## Test\n", "\n", "print bM\n", "\n", "print hamilv" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A function is written as\n", "\n", "$$ y_i= initial+t_i v_k f(t_i w_k+u_k) ,$$\n", "\n", "while it's derivative is\n", "\n", "$$v_k f(t w_k+u_k) + t v_k f(tw_k+u_k) (1-f(tw_k+u_k)) w_k .$$" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false }, "outputs": [], "source": [ "## The COST of the eqn set\n", "#remember that commutator is[1.0j* e0, e1 + 1.0j*e2 , - e1 + 1.0j*e2 ,1.0j*e3 ], where exs are the elements of the commv\n", "\n", "regularization = 0.0001\n", "npsum = np.sum\n", "\n", "def costvTi(x,ti,initialCondition): # l is total length of x\n", " \n", " list = np.linspace(0,3,4)\n", "\n", " fvec = []\n", " rho4i = rho4(x,ti,initialCondition)\n", " a0 = 2.0*rho4i[2]*hamilv[1]\n", " a1 = -2.0*rho4i[2]*hamilv[0]\n", " a2 = 2.0*rho4i[1]*hamilv[0] + hamilv[1]*( rho4i[3] - rho4i[0] )\n", " a3 = -2.0*rho4i[2]*hamilv[2]\n", " added = np.array([a0,a1,a2,a3])\n", " fvecappend = fvec.append\n", " \n", " for i in list:\n", " fvecappend(np.asarray(trigf(ti*1.0*x[i*3+1] + 1.0*x[i*3+2]) ) )\n", " \n", " fvec = np.array(fvec)\n", " \n", " rhoprime = np.zeros(4)\n", " \n", " for i in list:\n", " rhoprime[i] = ( np.sum (1.0*x[i*3]*fvec[i] + 1.0*ti * x[i*3]* fvec[i] * ( 1.0 - fvec[i] ) * x[i*3+1] ) )\n", "\n", " costi = rhoprime + added\n", " \n", " costiTemp = np.sum(costi**2)\n", "\n", " \n", " return costiTemp\n" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "11.7835898849\n" ] } ], "source": [ "print costvTi(xtemp,2,init)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "## Calculate the total cost\n", "\n", "def costv(x,t,initialCondition):\n", "\n", " t = np.array(t)\n", " \n", " costvTotal = np.sum( costvTList(x,t,initialCondition) )\n", " \n", " return costvTotal\n", " \n", "\n", "def costvTList(x,t,initialCondition): ## This is the function WITHOUT the square!!! \n", " \n", " t = np.array(t)\n", " \n", " costvList = np.asarray([])\n", " \n", " for temp in t:\n", " tempElement = costvTi(x,temp,initialCondition)\n", " costvList = np.append(costvList, tempElement)\n", " \n", " return np.array(costvList)\n", "\n", " " ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0. 0.20408163 0.40816327 0.6122449 0.81632653\n", " 1.02040816 1.2244898 1.42857143 1.63265306 1.83673469\n", " 2.04081633 2.24489796 2.44897959 2.65306122 2.85714286\n", " 3.06122449 3.26530612 3.46938776 3.67346939 3.87755102\n", " 4.08163265 4.28571429 4.48979592 4.69387755 4.89795918\n", " 5.10204082 5.30612245 5.51020408 5.71428571 5.91836735\n", " 6.12244898 6.32653061 6.53061224 6.73469388 6.93877551\n", " 7.14285714 7.34693878 7.55102041 7.75510204 7.95918367\n", " 8.16326531 8.36734694 8.57142857 8.7755102 8.97959184\n", " 9.18367347 9.3877551 9.59183673 9.79591837 10. ]\n" ] } ], "source": [ "ttemp = np.linspace(0,10)\n", "print ttemp" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 2.00241504 2.52486601 3.12957558 3.82314867 4.61583765\n", " 5.52007582 6.548817 7.71415413 9.0264291 10.49383832\n", " 12.12242401 13.91630864 15.87804541 18.00899333 20.30966179\n", " 22.77999828 25.41961232 28.22793954 31.20435522 34.34824788\n", " 37.65906304 41.13632579 44.77964879 48.58873118 52.56335186\n", " 56.70335997 61.00866425 65.47922231 70.11503074 74.91611611\n", " 79.88252726 85.01432875 90.31159553 95.77440856 101.40285145\n", " 107.19700781 113.15695936 119.28278448 125.57455727 132.03234697\n", " 138.65621761 145.4462279 152.4024313 159.52487616 166.81360596\n", " 174.26865961 181.89007178 189.67787322 197.63209112 205.75274943]\n", "3592.25842934\n" ] } ], "source": [ "ttemp = np.linspace(0,10)\n", "print costvTList(xtemp,ttemp,init)\n", "print costv(xtemp,ttemp,init)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## Minimization" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "Here is the minimization" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [], "source": [ "endpoint = 10\n", "tlin = np.linspace(0,endpoint,20)\n", "# tlinTest = np.linspace(0,14,10) + 0.5\n", "# initGuess = np.ones(120)\n", "# initGuess = np.asarray(np.split(np.random.rand(1,720)[0],12))\n", "initGuess = np.asarray(np.split(np.random.rand(1,60)[0],12))\n", " \n", "\n", "\n", "costvF = lambda x: costv(x,tlin,init)\n", "#costvFTest = lambda x: costv(x,tlinTest,init)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "10483.2460234\n" ] } ], "source": [ "print costv(initGuess,tlin,init)#, costv(initGuess,tlinTest,init)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "22.0414690971\n", " status: 0\n", " success: True\n", " njev: 44\n", " nfev: 2745\n", " fun: 0.029594802355524336\n", " x: array([ -1.59252118e-03, 3.51014982e+00, 1.65251562e+00,\n", " -1.74724687e-01, -2.04199807e-01, -9.39817008e-01,\n", " 1.19918520e-01, -1.04374519e-01, -7.08835998e+00,\n", " 1.56467928e-03, 6.42148180e+00, 2.63351999e+00,\n", " 2.74194493e-01, 6.04660148e-01, 8.27430694e-01,\n", " 9.41868026e-01, 9.55032063e-01, 2.71249180e-01,\n", " 6.63824188e-01, 6.47188705e-01, 8.24388861e-01,\n", " 4.96686894e-01, 8.53520987e-01, 6.36443930e-02,\n", " 3.37829263e-01, 5.43065972e-02, 3.08361127e-01,\n", " 8.36703782e-01, 3.90895320e-01, 1.91154610e-02,\n", " 5.54548230e-02, 5.61579367e-01, 8.69265422e-01,\n", " 3.13275701e-01, 2.83225135e-02, 5.01541153e-01,\n", " 4.92425726e-01, 6.16425625e-01, 9.44842566e-02,\n", " 9.27639463e-01, 7.72354571e-01, 8.12257532e-01,\n", " 6.47191868e-01, 7.61174793e-01, 8.18460476e-01,\n", " 1.37300048e-01, 5.09062206e-01, 8.67575780e-01,\n", " 1.77022215e-02, 8.47841558e-01, 4.94487180e-01,\n", " 5.93556947e-01, 9.99917064e-01, 7.53008878e-01,\n", " 2.76437081e-01, 8.67706376e-01, 5.50429901e-01,\n", " 6.06363724e-01, 8.78098759e-01, 2.77274115e-01])\n", " message: 'Optimization terminated successfully.'\n", " jac: array([ -1.17622549e-03, -3.59956175e-07, -8.19563866e-08,\n", " 3.20923305e-03, 4.90120612e-04, 5.18076122e-05,\n", " -5.90027310e-04, 8.09070189e-05, -7.06948340e-05,\n", " 1.03940256e-04, -2.79396772e-08, 2.23983079e-07,\n", " 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n", " 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n", " 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n", " 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n", " 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n", " 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n", " 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n", " 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n", " 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n", " 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n", " 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n", " 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n", " 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n", " 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n", " 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n", " 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n", " 0.00000000e+00])\n", " nit: 44\n", " \n", "*** Profile stats marshalled to file u'/var/folders/mj/1sl30v6x2g5_lnlgdnngtd3c0000gn/T/tmpbh57FC'. \n" ] } ], "source": [ "#%%snakeviz\n", "startSLSQP = timeit.default_timer()\n", "costvFResultSLSQP = minimize(costvF,initGuess,method=\"SLSQP\")\n", "stopSLSQP = timeit.default_timer()\n", "\n", "print stopSLSQP - startSLSQP\n", "\n", "print costvFResultSLSQP" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#np.savetxt('./assets/homogen/optimize_ResultSLSQPT2120_Vac.txt', costvFResultSLSQP.get('x'), delimiter = ',')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Functions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Find the solutions to each elements." ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# costvFResultSLSQPx = np.genfromtxt('./assets/homogen/optimize_ResultSLSQP.txt', delimiter = ',')" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ -1.59252118e-03 3.51014982e+00 1.65251562e+00 -1.74724687e-01\n", " -2.04199807e-01 -9.39817008e-01 1.19918520e-01 -1.04374519e-01\n", " -7.08835998e+00 1.56467928e-03 6.42148180e+00 2.63351999e+00\n", " 2.74194493e-01 6.04660148e-01 8.27430694e-01 9.41868026e-01\n", " 9.55032063e-01 2.71249180e-01 6.63824188e-01 6.47188705e-01\n", " 8.24388861e-01 4.96686894e-01 8.53520987e-01 6.36443930e-02\n", " 3.37829263e-01 5.43065972e-02 3.08361127e-01 8.36703782e-01\n", " 3.90895320e-01 1.91154610e-02 5.54548230e-02 5.61579367e-01\n", " 8.69265422e-01 3.13275701e-01 2.83225135e-02 5.01541153e-01\n", " 4.92425726e-01 6.16425625e-01 9.44842566e-02 9.27639463e-01\n", " 7.72354571e-01 8.12257532e-01 6.47191868e-01 7.61174793e-01\n", " 8.18460476e-01 1.37300048e-01 5.09062206e-01 8.67575780e-01\n", " 1.77022215e-02 8.47841558e-01 4.94487180e-01 5.93556947e-01\n", " 9.99917064e-01 7.53008878e-01 2.76437081e-01 8.67706376e-01\n", " 5.50429901e-01 6.06363724e-01 8.78098759e-01 2.77274115e-01]\n", "[ 1. 0.9998582 0.99970599 0.99954735 0.99938508 0.99922104\n", " 0.99905637 0.99889172 0.99872741 0.99856357 0.99840023 0.99823737\n", " 0.99807491 0.99791279 0.99775096 0.99758935 0.99742792 0.99726663\n", " 0.99710544 0.99694434 0.9967833 0.9966223 0.99646134 0.99630041\n", " 0.99613949 0.99597859 0.9958177 0.99565682 0.99549594 0.99533507\n", " 0.9951742 0.99501333 0.99485247 0.9946916 0.99453074 0.99436988\n", " 0.99420902 0.99404816 0.99388729 0.99372643 0.99356557 0.99340471\n", " 0.99324385 0.99308299 0.99292213 0.99276127 0.99260041 0.99243955\n", " 0.99227869 0.99211782 0.99195696 0.9917961 0.99163524 0.99147438\n", " 0.99131352 0.99115266 0.9909918 0.99083094 0.99067008 0.99050922\n", " 0.99034836 0.9901875 0.99002664 0.98986577 0.98970491 0.98954405\n", " 0.98938319 0.98922233 0.98906147 0.98890061 0.98873975 0.98857889\n", " 0.98841803 0.98825717 0.98809631 0.98793545 0.98777458 0.98761372\n", " 0.98745286 0.987292 0.98713114 0.98697028 0.98680942 0.98664856\n", " 0.9864877 0.98632684 0.98616598 0.98600512 0.98584426 0.9856834\n", " 0.98552253 0.98536167 0.98520081 0.98503995 0.98487909 0.98471823\n", " 0.98455737 0.98439651 0.98423565 0.98407479]\n", "[ 0. -0.00488505 -0.00962502 -0.01422196 -0.01867792 -0.02299496\n", " -0.02717519 -0.03122071 -0.03513365 -0.03891614 -0.04257033 -0.04609838\n", " -0.04950246 -0.05278473 -0.05594737 -0.05899256 -0.06192248 -0.0647393\n", " -0.06744519 -0.07004234 -0.0725329 -0.07491904 -0.0772029 -0.07938664\n", " -0.08147237 -0.08346222 -0.08535831 -0.08716271 -0.08887752 -0.09050479\n", " -0.09204656 -0.09350487 -0.09488172 -0.09617911 -0.09739899 -0.09854332\n", " -0.09961403 -0.10061301 -0.10154215 -0.10240331 -0.1031983 -0.10392896\n", " -0.10459704 -0.10520433 -0.10575253 -0.10624337 -0.10667851 -0.10705962\n", " -0.10738832 -0.1076662 -0.10789484 -0.10807578 -0.10821053 -0.1083006\n", " -0.10834743 -0.10835247 -0.10831712 -0.10824275 -0.10813073 -0.10798237\n", " -0.10779897 -0.10758181 -0.10733212 -0.10705113 -0.10674002 -0.10639995\n", " -0.10603207 -0.10563749 -0.10521729 -0.10477253 -0.10430424 -0.10381345\n", " -0.10330112 -0.10276824 -0.10221572 -0.10164449 -0.10105543 -0.10044942\n", " -0.09982729 -0.09918987 -0.09853795 -0.09787233 -0.09719374 -0.09650294\n", " -0.09580063 -0.0950875 -0.09436424 -0.09363149 -0.0928899 -0.09214007\n", " -0.09138262 -0.09061811 -0.08984711 -0.08907016 -0.0882878 -0.08750052\n", " -0.08670884 -0.08591322 -0.08511412 -0.084312 ]\n", "[ 0.00000000e+00 9.99719455e-06 1.97848692e-05 2.93663146e-05\n", " 3.87447756e-05 4.79234516e-05 5.69054976e-05 6.56940242e-05\n", " 7.42920987e-05 8.27027454e-05 9.09289461e-05 9.89736409e-05\n", " 1.06839729e-04 1.14530067e-04 1.22047474e-04 1.29394728e-04\n", " 1.36574568e-04 1.43589694e-04 1.50442767e-04 1.57136414e-04\n", " 1.63673220e-04 1.70055737e-04 1.76286479e-04 1.82367925e-04\n", " 1.88302519e-04 1.94092669e-04 1.99740750e-04 2.05249102e-04\n", " 2.10620033e-04 2.15855817e-04 2.20958695e-04 2.25930878e-04\n", " 2.30774543e-04 2.35491838e-04 2.40084877e-04 2.44555746e-04\n", " 2.48906502e-04 2.53139168e-04 2.57255743e-04 2.61258194e-04\n", " 2.65148460e-04 2.68928452e-04 2.72600053e-04 2.76165121e-04\n", " 2.79625484e-04 2.82982944e-04 2.86239278e-04 2.89396237e-04\n", " 2.92455544e-04 2.95418901e-04 2.98287981e-04 3.01064434e-04\n", " 3.03749888e-04 3.06345943e-04 3.08854179e-04 3.11276151e-04\n", " 3.13613391e-04 3.15867409e-04 3.18039692e-04 3.20131707e-04\n", " 3.22144895e-04 3.24080681e-04 3.25940464e-04 3.27725626e-04\n", " 3.29437525e-04 3.31077502e-04 3.32646876e-04 3.34146947e-04\n", " 3.35578994e-04 3.36944278e-04 3.38244043e-04 3.39479511e-04\n", " 3.40651886e-04 3.41762357e-04 3.42812091e-04 3.43802240e-04\n", " 3.44733937e-04 3.45608299e-04 3.46426426e-04 3.47189400e-04\n", " 3.47898287e-04 3.48554137e-04 3.49157985e-04 3.49710849e-04\n", " 3.50213730e-04 3.50667616e-04 3.51073479e-04 3.51432275e-04\n", " 3.51744947e-04 3.52012422e-04 3.52235614e-04 3.52415421e-04\n", " 3.52552729e-04 3.52648408e-04 3.52703317e-04 3.52718299e-04\n", " 3.52694186e-04 3.52631795e-04 3.52531933e-04 3.52395390e-04]\n", "[ 0. 0.00015233 0.00031001 0.00046933 0.00062882 0.00078803\n", " 0.0009469 0.00110549 0.00126388 0.00142214 0.00158031 0.00173843\n", " 0.00189652 0.0020546 0.00221266 0.00237072 0.00252877 0.00268682\n", " 0.00284487 0.00300292 0.00316097 0.00331902 0.00347706 0.00363511\n", " 0.00379316 0.00395121 0.00410926 0.00426731 0.00442536 0.0045834\n", " 0.00474145 0.0048995 0.00505755 0.0052156 0.00537365 0.00553169\n", " 0.00568974 0.00584779 0.00600584 0.00616389 0.00632194 0.00647998\n", " 0.00663803 0.00679608 0.00695413 0.00711218 0.00727023 0.00742828\n", " 0.00758632 0.00774437 0.00790242 0.00806047 0.00821852 0.00837657\n", " 0.00853461 0.00869266 0.00885071 0.00900876 0.00916681 0.00932486\n", " 0.0094829 0.00964095 0.009799 0.00995705 0.0101151 0.01027315\n", " 0.0104312 0.01058924 0.01074729 0.01090534 0.01106339 0.01122144\n", " 0.01137949 0.01153753 0.01169558 0.01185363 0.01201168 0.01216973\n", " 0.01232778 0.01248582 0.01264387 0.01280192 0.01295997 0.01311802\n", " 0.01327607 0.01343412 0.01359216 0.01375021 0.01390826 0.01406631\n", " 0.01422436 0.01438241 0.01454045 0.0146985 0.01485655 0.0150146\n", " 0.01517265 0.0153307 0.01548874 0.01564679]\n", "[ 1. 0. 0. 0.]\n" ] } ], "source": [ "## The first element of neutrino density matrix\n", "xresult = np.asarray(costvFResultSLSQP.get('x'))\n", "#xresult = np.asarray(costvFResultNM.get('x'))\n", "#xresult = np.asarray(costvFResultBFGS.get('x'))\n", "\n", "print xresult\n", "\n", "plttlin=np.linspace(0,endpoint,100)\n", "\n", "pltdata11 = np.array([])\n", "pltdata11Test = np.array([])\n", "pltdata22 = np.array([])\n", "pltdata12 = np.array([])\n", "pltdata21 = np.array([])\n", "\n", "for i in plttlin:\n", " pltdata11 = np.append(pltdata11 ,rho4(xresult,i,init)[0] )\n", " \n", "print pltdata11\n", "\n", "for i in plttlin:\n", " pltdata12 = np.append(pltdata12 ,rho4(xresult,i,init)[1] )\n", " \n", "print pltdata12\n", "\n", "for i in plttlin:\n", " pltdata21 = np.append(pltdata21 ,rho4(xresult,i,init)[2] )\n", " \n", "print pltdata21\n", "\n", "#for i in plttlin:\n", "# pltdata11Test = np.append(pltdata11Test ,rho(xresultTest,i,init)[0,0] )\n", "# \n", "#print pltdata11Test\n", "\n", "\n", "for i in plttlin:\n", " pltdata22 = np.append(pltdata22 ,rho4(xresult,i,init)[3] )\n", " \n", "print pltdata22\n", "\n", "print rho4(xresult,0,init)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "array([ 9.98416546e-01, -4.22106245e-02, 9.01145420e-05,\n", " 1.56449654e-03])" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rho4(xresult,1,init)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#np.savetxt('./assets/homogen/optimize_pltdatar11.txt', pltdata11, delimiter = ',')\n", "#np.savetxt('./assets/homogen/optimize_pltdatar22.txt', pltdata22, delimiter = ',')" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAA78AAAI6CAYAAADv6v9FAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3XmYnWV9//H3yYJhESaoiKwRqIgiFUUUCzpo6QSpiFRQ\n", "q9VWi2hFUVsFFH6OWim4L3WrqKi4gqKIgoAVcAM3iIAJEnaQJYkVdwX8/P547kxOxkkyk5yZ+yzv\n", "13WdK895njNzvnyvS+GT+3m+N0iSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmS\n", "JFXzUeAO4Iq1fOY9wDXAImDPtvMLgSXl2jFt57cEzgd+BpwHDHWwXkmSJEmSpmw/mkC7pvD7FOBr\n", "5fixwCXleDawFFgAzAUuB3Yr194CvKYcHwOc1NGKJUmSJElaDwtYc/j9IPDMtvdLgK2BfYBz284f\n", "W14rP/PAcrx1eS9JkiRJ0hrNqvz92wI3t72/pZzbZg3noQm+d5TjO1gVhCVJkiRJmlDt8AvQmuRn\n", 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"plt.show()\n", "#py.iplot_mpl(plt.gcf(),filename=\"vac_HG-rho11\")\n", "\n", "\n", "# tls.embed(\"https://plot.ly/~emptymalei/73/\")" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAA8AAAAI6CAYAAADoqCFQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3XmYnHWd7v93dRJ2JOICAaJR3BBHRRyFcdR2YQiKG4K4\n", "4jLjcV9+buBBx1bUUfTMzFFHRQV14OC+oKIIqDk4IOiIbMoa9iVh1d/IoIPOff6oJ+HpTnenKl1V\n", "33qq3q/r6itVXdVVdz5cJLnr+T7fByRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJ\n", "kiRJkhppJXARcClw6BzP+Vj1+LnAHl3+rCRJkiRJxS0CLgNWAEuAc4DdZjznacD3q9uPBc7s4mcl\n", "SZIkSVpvouB7P4Z2ib0SuBP4MvCsGc95JvDF6vZZwFJgxw5/VpIkSZKk9UoW4J2Ba2r3r62+18lz\n", "durgZyVJkiRJWq9kAU6Hz2v1NYUkSZIkaSwsLvje1wHLa/eX0z6SO99zdqmes6SDnwXuH7i8B1El\n", "SZIkSUNoNfCA0iE6sZh22BXAZmx8E6y9uGsTrE5+FiCQX0OW9jK4VMBU6QBSD0yVDiD1yFTpAFIP\n", "TJUOIPVIpyuLgbJHgP8EvB74Ie1dnY8GLgReVT1+FO3y+zTaG17dDrx8Iz87m52BfYGv9Px3IEmS\n", 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"plt.plot(np.linspace(0,15,4501),MMA_optmize_Vac_pltdata,\"r-\",label=\"MMAVacrho11\")\n", "plt.plot(plttlin,pltdata11,\"b4-\",label=\"vac_rho11\")\n", "plt.show()\n", "#py.iplot_mpl(plt.gcf(),filename=\"MMA-rho11-Vac-80-60\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Practice" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "xtemp1 = np.arange(4)\n", "xtemp1.shape = (2,2)\n", "print xtemp1\n", "xtemp1[0,1]\n", "np.dot(xtemp1,xtemp1)\n", "xtemp1[0,1]" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.6" } }, "nbformat": 4, "nbformat_minor": 0 }