SNR_neutron.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1062fbf28>]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np, matplotlib.pyplot as plt, scipy.integrate as INT\n",
    "%matplotlib inline\n",
    "Noise_ET=np.loadtxt('ET_D_data.txt')\n",
    "freq=Noise_ET[:,0]\n",
    "noise1=Noise_ET[:,1]\n",
    "noise2=Noise_ET[:,2]\n",
    "noise3=Noise_ET[:,3]\n",
    "plt.yscale('log')\n",
    "plt.xscale('log')\n",
    "plt.plot(freq,noise3,'k-')#,freq,noise2,'r-',freq,noise3,'b-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def Sn(f):\n",
    "    return np.interp(f,freq,noise3**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import scipy as sci"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "######## A table#################\n",
    "y101=0.6437\n",
    "y102=0.1469\n",
    "y103=-0.4098\n",
    "y104=-0.1331\n",
    "###############################################\n",
    "y111=0.827\n",
    "y112=-0.1228\n",
    "y113=-0.03523\n",
    "y114=-0.08172\n",
    "###############################################\n",
    "y121=-0.2706\n",
    "y122=-0.02609\n",
    "y123=0.1008\n",
    "y124=0.1451\n",
    "###############################################\n",
    "y201=-0.05822\n",
    "y202=-0.0249\n",
    "y203=1.829\n",
    "y204=-0.2714\n",
    "###############################################\n",
    "y211=-3.935\n",
    "y212=0.1701\n",
    "y213=-0.02017\n",
    "y214=0.1279\n",
    "###############################################\n",
    "y301=-7.092\n",
    "y302=2.325\n",
    "y303=-2.87\n",
    "y304=4.922\n",
    "\n",
    "x102=-920.9\n",
    "x112=492.1\n",
    "x122=135\n",
    "x202=6742\n",
    "x212=-1053\n",
    "x302=-1.34e4\n",
    "###########################\n",
    "x103=1.702e4\n",
    "x113=-9566\n",
    "x123=-2182\n",
    "x203=-1.214e5\n",
    "x213=2.075e4\n",
    "x303=2.386e5\n",
    "###########################\n",
    "x104=-1.254e5\n",
    "x114=7.507e4\n",
    "x124=1.338e4\n",
    "x204=8.735e5\n",
    "x214=-1.657e5\n",
    "x304=-1.694e6\n",
    "###########################\n",
    "x105=0\n",
    "x115=0\n",
    "x125=0\n",
    "x205=0\n",
    "x215=0\n",
    "x305=0\n",
    "###########################\n",
    "x106=-8.898e5\n",
    "x116=6.31e5\n",
    "x126=5.068e4\n",
    "x206=5.981e6\n",
    "x216=-1.415e6\n",
    "x306=-1.128e7\n",
    "###########################\n",
    "x107=8.696e5\n",
    "x117=-6.71e5\n",
    "x127=-3.008e4\n",
    "x207=-5.838e6\n",
    "x217=1.514e6\n",
    "x307=1.089e7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def F1(theta,phi,psi):\n",
    "    plus=-0.433*((1.0+np.cos(theta)**2)*np.sin(2.0*phi)*np.cos(2.0*psi)+2.0*np.cos(theta)*np.cos(2.0*phi)*np.sin(2.0*psi))\n",
    "    cross=0.433*((1.0+np.cos(theta)**2)*np.sin(2.0*phi)*np.sin(2.0*psi)-2.0*np.cos(theta)*np.cos(2.0*phi)*np.cos(2.0*psi))\n",
    "    return [plus,cross]\n",
    "# Mi is the mass of individual BH, in solar masses. chi_i is the reduced spin of BH.\n",
    "GMsun=1.32754125e26 # cgs unit\n",
    "DKPC=3.086e+21 # cgs unit\n",
    "c=3e10 #cgs\n",
    "def C(M1,M2,Deff,i,theta,phi,psi):\n",
    "    M=M1+M2\n",
    "#    factor=M*15.4787466e-6 #second;\n",
    "    eta=M1*M2/M**2\n",
    "#    result1=(GMsun*M)**0.83333/(2.0*D*DKPC*2.1433*c**1.5)*\\\n",
    "#    (0.208333*eta)**0.5*np.sqrt((1.0+np.cos(i)**2)**2*F1(theta,phi,psi)[0]**2+\\\n",
    "#                                4.0*np.cos(i)**2*F1(theta,phi,psi)[1]**2)   \n",
    "    #Deff=D/np.sqrt((0.5*(1.0+np.cos(i)**2))**2*F1(theta,phi,psi)[0]**2+np.cos(i)**2*F1(theta,phi,psi)[1]**2)\n",
    "    result=0.21*(GMsun*M*0.435)**0.83333/(Deff*DKPC)/c**1.5\n",
    "    return result\n",
    "Lorentz = lambda x1,x2,x3: 1.0/3.14159*0.5*x3/((x1-x2)**2+(0.5*x3)**2)\n",
    "def gamma(f,M1,M2,chi1,chi2): # the input value is with unit Hz    \n",
    "    M=M1+M2;\n",
    "    eta=M1*M2/M**2;\n",
    "    factor=M*15.4787466e-6 #second;\n",
    "    ft=f*factor # convert the input frequency to a dimensionless one\n",
    "    delta=(M1-M2)/M; # delta is independent with the total mass\n",
    "    chi=(1+delta)*chi1*0.5+(1-delta)*chi2*0.5 #spin\n",
    "    ###############################################\n",
    "    mu01=1-4.455*(1-chi)**0.217+3.521*(1-chi)**0.26 # independent of the total mass\n",
    "    mu02=(1-0.63*(1-chi)**0.3)*0.5\n",
    "    mu03=(1-0.63*(1-chi)**0.3)*(1-chi)**0.45*0.25\n",
    "    mu04=0.3236+0.04894*chi+0.01346*chi**2\n",
    "    ###############################################\n",
    "    f0=np.pi*1e-3\n",
    "    f1=mu01+y101*eta+y111*eta*chi+y121*eta*chi**2+y201*eta**2+y211*eta**2*chi+y301*eta**3; \n",
    "    f2=mu02+y102*eta+y112*eta*chi+y122*eta*chi**2+y202*eta**2+y212*eta**2*chi+y302*eta**3;\n",
    "    sigma=mu03+y103*eta+y113*eta*chi+y123*eta*chi**2+y203*eta**2+y213*eta**2*chi+y303*eta**3;\n",
    "    f3=mu04+y104*eta+y114*eta*chi+y124*eta*chi**2+y204*eta**2+y214*eta**2*chi+y304*eta**3;  #these are indepened with the total mass\n",
    "    ###############################################\n",
    "    alpha2=-323.0/224+451.0*eta/168.0\n",
    "    alpha3=(27.0/8-11.0*eta/6.0)*chi\n",
    "    epsilon1=1.4547*chi-1.8897\n",
    "    epsilon2=-1.8153*chi-1.6557\n",
    "    ################################################    \n",
    "    fp=ft/f1;\n",
    "    v=ft**0.3333    \n",
    "    Wm=(1+alpha2*v**2+alpha3*v**3)/(1+epsilon1*v+epsilon2*v**2)\n",
    "    Wr=Wm*(f2/f1)**(-2.0/3)*(1+epsilon1*v+epsilon2*v**2)/Lorentz(f2,f2,sigma)\n",
    "    if (ft<f1) and (ft>f0):\n",
    "        result=(ft/factor)**(-7.0/6)*(1+alpha2*v**2+alpha3*v**3);\n",
    "    elif (ft>=f1) and (ft<f2):\n",
    "        result=Wm*(f1/factor)**(-7.0/6)*fp**(-2.0/3)*(1+epsilon1*v+epsilon2*v**2);\n",
    "    elif ft>=f2 and ft<f3:\n",
    "        result=Wr*(f1/factor)**(-7.0/6)*Lorentz(ft,f2,sigma)\n",
    "    else: \n",
    "        result=0\n",
    "    return [result,f1/factor,f2/factor,f3/factor]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Rowc9evQAYMeOHcyYMYOZM2cyd+5cnn/+eUaMGAFAYmIi55xzTt6UnJxMTMzRxkmUDr1796ZBgwaYGdnZ2QwfPpzhw4dTu3ZtJk6cSN++fYmIiODnn49vvYmJiTz33HMMGjSoVA4mPJkUJCJhqGrVqvTu3ZvevXsDcPDgQRYvXszcuXOZO3cus2fPzvtrOi4ujtatW+cFS7t27ahTp06p+XJs0aIFLVq04JdffuGKK65g3rx5XHHFFYwZMyao8Tq9evbkpdGjSUtLo0uXLsVYcdmjIBEpAeLi4vKC4rANGzbkBcu8efMYPXo0//rXv4DcIDrrrLPypuTkZJo2bUp0dLRXH+GE/frrr4wdO5YXXniB6OhoJk6cSP/+/YNeb+fOnakxcSLPPvusgiRIChKREqpu3br06dOHPn36AHDo0CEWL17MokWLWLJkCUuWLOHFF1/MOxMsJiaG5s2bk5yczFlnnUXz5s1JTEykXr16YXV5F+ccq1atIi0tjZkzZzJ16lR2795Np06deOutt6hXr16xbCcmJoZbbrmFBx54gAULFtC2bdtiWW9ZpCARKSViY2M5++yzOfvss/PasrOzWblyZV6wLFmyhGnTpjF+/Pgjlq1VqxaJiYnUr18/7zEhIYEaNWpQs2ZNatasSdWqVYv9nvfOOXbv3s369euZM2cOM2bMIC0tLe+kglq1alG3bl12797Nl19+SVRU8X5l3XrrrTz//PM88MADfPbZZ8W67rJEQSJSikVFRdG0aVOaNm3KgAED8tq3bNnCTz/9xLp161i7dm3e49KlS0lNTT3qeJaIiAiqV69OzZo1qVatGhUqVKB8+fJHnSIjI3HOkZOTkzft27ePjIyMI6bffvvtiG0lJCTQuXNnOnXqRKdOnWjcuDGPPfYYDz30ULGHGOSePXf33Xdz5513MmvWLDp06FDs2ygLFCQiZdCpp57KqaeeetT3nHNs27aN33777Ygv/a1bt+Y93759O7/99hv79+/Pmw4cOMC+ffuOuEJvfjExMXm9m5o1a9KkSRNq1qxJQkICCQkJtG3bNu/srJPppptuYuTIkdx///2kpaWVmpMUTiYFiYgcwcyoUaMGNWrUOO5lnXMcOnQIn89HRERE3mRmREZGhuWXdPny5bnvvvsYOnQor7zyCkOGDPG6pBJHQSIixcbMiv3Aff/+/WnZsmVIQ+i6667j448/5vrrr2f16tU88cQTIdmVVlrpJyUiYa1Ro0b06NEjpEESExPDJ598wg033MDTTz9N3759ycrKCtn2ShsFiYiEtRUrVjB16tRjHnspLtHR0bz44os8++yzfPDBBwwZMiTk2ywttGtLRMLau+++y8MPP0xOTk7It2Vm3H777ezZs4eHH36YWrVq8dRTT4V8uyWdgkREpIAHH3yQLVu28PTTT2Nm6pkUQkEiIlKAmTFmzBh8Ph9PPfUUDRo08LqksKZjJCIiRxEZGcnLL7/M6NGj+eWXX8jKymL+/PlelxWWwj5IzOx0M3vNzN7P19bMzCab2UtmdrmX9YlI6WVm3HzzzfTv3x/nHOeccw633XYb+/bt87q0sBLSIDGz180sw8yWFWjvZmYrzGyVmd0daB3OudXOucEFmrsD/3bO3QgMKuayRSSMXHXVVXzzzTee1pCYmEhMTAw33ngjo0aNol27dvz000+e1hROQt0jGQ90y99gZpHAC+SGQTNggL+H0cLMUgtMR7/xMrwF9DezEUC1ENYvIh5LSkqic+fOYTEq/oUXXuDLL79k69attG3blvfff7/whcqAkAaJc24msKNAcztglb+nkQm8C/R0zi11zl1aYMo4xnoznHN/B+4GtoXyM4iIt5YuXco777wTNmdO/fnPf2bRokU0b9487zL+Gzdu9LosT3lxjKQOsD7f6w3+tqMys2pmNhZoaWb3+NuSzGwcMAEYcYzlhpjZQjNbuHXr1uKrXkROqg8//JCBAwd6XcYR6taty8yZM3n88cdJTU2lSZMmjBgx4qhXTS4Lwv5gu3Nuu3PuBufcn5xzT/rb1jjnhjjnBjrnZh9juXHOuTbOuTYncvE5EZFAYmJiuPfee1m+fDmdOnXirrvuolGjRkyYMOGkDJ4MJ14EyUYg/y3O6vrbRERKnNNPP53U1FS+/vpratWqxVVXXUWXLl3K1MF4L4JkAdDQzE4zsxigP5DiQR0iUooU+RDKCRxrKcrxmS5dujB//nxeffVVfvjhB5KTk7n33nvZuXPncW+vpAn16b8TgblAYzPbYGaDnXPZwFDgc+BHYLJzbnko6xARORkiIiIYPHgwP/30E3369OHJJ5/ktNNOY/jw4ezZs8fr8kIm1GdtDXDOJTjnop1zdZ1zr/nbpznnGvmPezweyhpEpGS77rrrWLhwYZHnL/JZwsd5OvHxnH5cq1Yt3n77bZYsWULHjh154IEHOP300xk5ciQHDhw4ru2WBGF/sF1EyrbatWvTunXrsBhHcrySk5NJSUlh3rx5nHXWWdxxxx00bNiQsWPHkpmZ6XV5xUZBIiJhLT09nXHjxoXNOJIT0b59e7744gu++eYbEhMTufHGG2nSpAljx44tFT0UBYmIhLXU1FSuv/56r8soFp07d2b27NlMmzaNGjVqcOONN5KYmMhjjz3G9u3bvS7vhClIREROIjOje/fuzJs3j7S0NNq1a8eDDz5I/fr1ufXWW1mzZo3XJR43BYmIiAfMjE6dOpGamsrSpUvp06cPL774Ig0aNOD//u//WLx4sdclFpmCRETEY2eccQbjx4/n119/ZdiwYaSmptKqVSu6du3K9OnTw/74kIJERCRM1K1blxEjRrBu3Tqeeuopli9fzkUXXUTz5s0ZPXo0u3bt8rrEo1KQiEhYGzp0KCtWrPC6jJOqSpUq/POf/+TXX3/ljTfeID4+nltvvZW6desybNgw1q5d63WJR1CQiEhYq1atGo0aNSqR40iCFRsby9VXX838+fNJT0/nsssuY8yYMfzpT3/i8ssv58svvwyLC0QqSEQkrM2ZM4dnn3027I8ThFqrVq2YMGECq1evZtiwYaSlpdG1a1caNWrEM888g5e3y1CQiEhY++KLL/jHP/7hdRlho169eowYMYINGzbw9ttvU7t2bf75z39Sp04dBgwYQFpa2kkPXQWJiEgJFBcXx8CBA5k5cybLly/npptu4rPPPqNLly40bdqU5557jh07Ct6gNjQUJCIiJVyzZs14/vnn2bRpE+PHj6dq1arcfvvt1K5dmyuvvJLZs2eHtJeiIBERKSXKlSvHVVddxZw5c/jhhx/429/+RkpKCh06dKBFixb8+9//DskpxAoSEZFSqEWLFowZM4ZNmzbx6quvUr58eW655RZq167NoEGD+Oqrr/D5fMWyLQWJiIS122+/nY0bdTfuE1WhQgUGDx7Md999x6JFixg0aBApKSlccMEFJCUlce+99/Ljjz8GtQ0FiYiEtfj4eGrXrl0mx5EUt5YtWzJ27Fg2b97MpEmTSE5O5plnnqFZs2a0a9eOMWPGsG3btuNer4JERMJaWloaDz/8cJkfR1KcypUrR9++fUlNTWXjxo2MHDmSrKwsbr75ZhISEujVqxcffvhhkdenIBGRsJaWlsYjjzyiHkmI1KpVi2HDhrF48WK+//57brvtNubPn89f//rXIq9DQSIiIgCceeaZjBgxgvXr1/Ppp58WeTkFiYiIHCEqKopu3boVeX4FiYiIBEVBIiIiQVGQiEhYu+eee/j999+9LkMCiPK6ABGRQGJjY4mNjfW6DAlAPRIRCWuff/45d9xxh9dlSABFChIza2Rmr5jZdDP7+vAU6uJERObOncvIkSO9LkMCKOqurfeAscArQPFc5UtEpBgVeeD7CYyQ16j6wIoaJNnOuZdCWomISDEo8gB4jZQvNkU9RjLVzG4yswQzq3p4CmllIiJhRJdoObai9kiu8j/ema/NAacXbzkiIlLSFKlH4pw77SiTQkREQk5X/g1/AXskZna+c+5rM7vsaO8754p+neETZGa9gEuASsBrzrnpZnY6cB9Q2Tl3eahrEBGRYyusR9LJ/9jjKNOlha3czF43swwzW1agvZuZrTCzVWZ2d6B1OOemOOeuA24A+vnbVjvnBhe2fREp+aZOncqQIUO8LkMCCNgjcc495H+85gTXPx4YA0w43GBmkcALQFdgA7DAzFKASODJAstf65zL8D+/37+ciJQh6enpvPLKK4wbN87rUuQYinyJFDO7BGgOxB1uc849GmgZ59xMM0sq0NwOWOWcW+1f77tAT+fckxyll2O5p0o8BXzqnFtU1HpFROTkKOrI9rHk7la6GTCgD5B4gtusA6zP93qDv+1YbgYuAC43sxv89VTz19TSzO45Rs1DzGyhmS3cunXrCZYqIiKFKWqP5Fzn3Jlm9oNz7hEzexYo+u2zguCcGw2MLtC2ndxjJoGWGweMA2jTpo1O+RARCZGiDkg86H/cb2a1gSwg4QS3uRGol+91XX+biMgfxMTEULFiRa/LkACOZ2R7FWAEsAhYA7xzgttcADQ0s9PMLAboD6Sc4LpEpJS799572bNnj9dlSACF7toyswjgK+fcLuADM0sF4pxzu4uw7ESgM1DdzDYADznnXjOzocDn5J6p9bpzbnkwH0JERLxTaJA453LM7AWgpf/1IeBQUVbunBtwjPZpwLTjqFNEyqgPPviADz74gHfeOdGdIBJqRd219ZWZ/dV01TIROcmWLl3KxIkTvS5DAihqkFxP7j1JDpnZ72a2x8x0E2URESna6b/OufhQFyIiIiVTUQckflWUNhERKXsKu/pvHFCe3LOuTiF3VDvkXok30Gh0EZFiER8fT0LCiQ5bk5OhsB7J9UA60MT/uNA/fUzuxRhFRELqjjvuYNOmTV6XIQEUFiRzgHOBf/hvZPUIsAyYwYkPSBQRkVKksCB5GTjknPu3mXUk9zLvbwK78V/HSkQklN555x169OjhdRkSQGFnbUU653b4n/cDxjnnPiB3hPuS0JYmIgIrVqwgNTXV6zIkgMJ6JJFmdjhs/gx8ne+9It/LRERESq/CwmAiMMPMtgEHgFkAZtaA3N1bIiJSxhV2q93H/eNFEoDpzrnD9/WIIPeGUyIiUsYV5aKN847S9nNoyhEROVK1atVo2LCh12VIAEW91paIiCduueUWfv5Zf7uGMwWJiIgERUEiImHtjTfeoHPnzoXOl3cEt9hmzL/I8S9TlihIRCSsrVmzhhkzZhR5/iLfNek4b6+k2zEdm4JERESCoiAREZGgKEhERCQoChIRCWsJCQm0atXK6zIkAAWJiIS1G264gfT0dK/LkAAUJCIiEhQFiYiEtbFjx9K6dWuvy5AAFCQiEtY2b97MokWLvC5DAlCQiIhIUBQkIiISFAWJiIgERUEiImEtKSmJTp06eV2GBKAgEZGwds0115CWluZ1GRKAgkRERIKiIBGRsDZ69GgaNWrkdRkSQKH3bPeamfUCLgEqAa8556abWVPgVqA68JVz7iUvaxSR0Nm+fTsrV670ugwJIKQ9EjN73cwyzGxZgfZuZrbCzFaZ2d2B1uGcm+Kcuw64Aejnb/vROXcD0Bc4L1T1i4hI4UK9a2s80C1/g5lFAi8A3YFmwAAza2ZmLcwstcBUM9+i9/uXO7yevwCfANNC/BlERCSAkO7acs7NNLOkAs3tgFXOudUAZvYu0NM59yRwacF1WO79LZ8CPnXO5V0nwTmXAqSY2SfAO6H5BCIiUhgvjpHUAdbne70BaB9g/puBC4DKZtbAOTfWzDoDlwGxHKNHYmZDgCEA9evXL4ayRcQLjRo14tJL//A3poSRsD/Y7pwbDYwu0JYGpBWy3DhgHECbNm1ciMoTkRAbOHAgAwcO9LoMCcCL0383AvXyva7rbxMRkRLIiyBZADQ0s9PMLAboD6R4UIeIlAAjRoygTp06XpchAYT69N+JwFygsZltMLPBzrlsYCjwOfAjMNk5tzyUdYhIybVnzx42b97sdRkSQKjP2hpwjPZp6LRdEZFSQZdIERGRoChIREQkKAoSEQlrLVq0YMCAo+4llzAR9uNIRKRs69OnD3369Cl0PlfU0WJFnjH/IhqKFogBpSZuAAAIyUlEQVR6JCJSqpgV94yHZz+++csSBYmIhLXhw4dTqVIlr8uQABQkIhLWMjMz2bt3r9dlSAAKEhERCYqCREREgqIgERGRoChIRCSstW7dmuuuu87rMiQAjSMRkbDWs2dPevbs6XUZEoB6JCIiEhQFiYiEtQcffJCICH1VhTP9dkREJCgKEhERCYqCREREgqIgERGRoChIRCSsnXvuudx+++1elyEBaByJiIS1bt260a1bN6/LkADUIxGRsHbo0CH27NnjdRkSgIJERMLa448/TuXKlb0uQwJQkIiISFAUJCIiEhQFiYiIBEVBIiIiQdHpvyIS1rp06UJkZKTXZUgAChIRCWtdunShS5cuXpchAWjXloiEtd9//51NmzZ5XYYEoCARkbA2YsQI6tWr53UZEoCCREREgqIgERGRoIR9kJhZLzN7xcwmmdmF/rbOZjbLzMaaWWePSxQRKdNCGiRm9rqZZZjZsgLt3cxshZmtMrO7A63DOTfFOXcdcAPQ73AzsBeIAzaEonYRKVmcK+4Z8y9y/MuUJaE+/Xc8MAaYcLjBzCKBF4Cu5IbAAjNLASKBJwssf61zLsP//H7/cgCznHMzzKwWMBIYGLJPICKe6tatG6ecckqR5zcr7hkPz35885clIQ0S59xMM0sq0NwOWOWcWw1gZu8CPZ1zTwKXFlyH5f72ngI+dc4t8q83x//2TiA2NNWLSDg477zzOO+887wuQwLwYkBiHWB9vtcbgPYB5r8ZuACobGYNnHNjzewy4CKgCrk9nj8wsyHAEID69esXR90i4oFt27axY8cOGjVq5HUpcgxhP7LdOTcaGF2g7UPgw0KWGweMA2jTpo12cIqUUKNGjeKJJ57A5/N5XYocgxdnbW0E8o8uqutvExGREsiLIFkANDSz08wsBugPpHhQh4iIFINQn/47EZgLNDazDWY22DmXDQwFPgd+BCY755aHsg4REQmdUJ+1NeAY7dOAaaHctoiInBxhf7BdRMq2v/zlLzrzMswpSEQkrLVt25a2bdt6XYYEEPbX2hKRsm3jxo2kp6d7XYYEoCARkbA2duxY2rVr53UZEoCCREREgqIgERGRoChIREQkKAoSEREJik7/FZGwdvnll9OsWTOvy5AAFCQiEtaSk5NJTk72ugwJQLu2RCSs/frrr6SlpXldhgSgIBGRsPb666/z5z//2esyJAAFiYiIBEVBIiIiQVGQiIhIUBQkIiISFJ3+KyJhbeDAgbpoY5hTkIhIWGvSpAlNmjTxugwJQLu2RCSs/fTTT0ydOtXrMiQABYmIhLX//Oc/9OrVy+syJAAFiYiIBMWcc17XEHJmtgdY4XUdIiIlTKJzrkZhM5WVg+0rnHNtvC5CRKQ00q4tEREJioJERESCUlaCZJzXBYiIlFZl4mC7iIiETlnpkYiISIgoSEREJCgKEhERCUpZGUdyBDOrALwIZAJpzrn/eFySiEiJVWp6JGb2upllmNmyAu3dzGyFma0ys7v9zZcB7zvnrgP+ctKLFREpRUpNkADjgW75G8wsEngB6A40AwaYWTOgLrDeP5vvJNYoIlLqlJogcc7NBHYUaG4HrHLOrXbOZQLvAj2BDeSGCZSin4GIiBdK+5doHf7X84DcAKkDfAj81cxeAnSjAxGRIJTJg+3OuX3ANV7XISJSGpT2HslGoF6+13X9bSIiUkxKe5AsABqa2WlmFgP0B1I8rklEpFQpNUFiZhOBuUBjM9tgZoOdc9nAUOBz4EdgsnNuuZd1ioiUNrpoo4iIBKXU9EhERMQbChIREQmKgkRERIKiIBERkaAoSEREJCgKEhERCYqCRMoUM/OZ2ZJ8U5LXNRUnM2tpZq/5n19tZmMKvJ9mZm0CLP+umTUMdZ1SupTJa21JmXbAOXfWsd40syj/QNaS6l5geBDLvwTcBVxXPOVIWaAeiZR5/r/cU8zsa+Arf9udZrbAzH4ws0fyzXufmf1sZrPNbKKZ/cPfnveXvplVN7M1/ueRZjYi37qu97d39i/zvpn9ZGb/MTPzv9fWzOaY2fdm9p2ZxZvZTDM7K18ds80sucDniAfOdM59X4TP/Jd8vbIVZvar/61ZwAVmpj8ypcj0j0XKmnJmtsT//FfnXG//81bkfgnvMLMLgYbk3s/GgBQz6wjsI/d6bWeR+39nEZBeyPYGA7udc23NLBb41sym+99rCTQHNgHfAueZ2XfAJKCfc26BmVUCDgCvAVcDt5lZIyDuKIHRBlhWoK2fmf2/fK8bADjnUvBfd87MJgMz/O05ZrYKSC7CZxMBFCRS9hxr19YXzrnDN0a70D8t9r+uSG6wxAMfOef2A5hZUS4AeiFwppld7n9d2b+uTOA759wG/7qWAEnAbmCzc24BgHPud//77wEPmNmdwLXk3hG0oARga4G2Sc65oYdfmFla/jfN7C5yfyYv5GvOAGqjIJEiUpCI5NqX77kBTzrnXs4/g5ndFmD5bP63qziuwLpuds59XmBdnYFD+Zp8BPj/6Jzbb2ZfkHuHz75A66PMdqDAtgMyswuAPkDHAm/F+dclUiQ6RiLyR58D15pZRQAzq2NmNYGZQC8zK+c/HtEj3zJr+N+X++UF1nWjmUX719XIzCoE2PYKIMHM2vrnj893vOJVYDSwwDm38yjL/oh/11VhzCwReAHo45wrGBqN+OMuMpFjUo9EpADn3HQzawrM9R//3gtc4ZxbZGaTgO/J3f2zIN9i/wImm9kQ4JN87a+Su8tqkf9g+lagV4BtZ5pZP+DfZlaO3J7BBcBe51y6mf0OvHGMZX8ys8pmFu+c21PIx7waqAZM8X/GTc65i82sFrm7urYUsrxIHl1GXuQEmdnD5H7B/+skba82kAY0cc7lHGOeYcAe59yrJ7iNYcDvzrnXTrhQKXO0a0ukBDCzQcB84L5jhYjfSxx57OV47QLeDGJ5KYPUIxERkaCoRyIiIkFRkIiISFAUJCIiEhQFiYiIBEVBIiIiQVGQiIhIUP4/GazvPms7alMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "MM=[73,74,75,76]\n",
    "LS=['k-','r-','b-','k--','r--','b--']\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "plt.xlabel('Frequency (Hz)')\n",
    "plt.ylabel('Strain')\n",
    "plt.plot(freq,noise3/np.sqrt(freq),'k-')\n",
    "plt.xlim([1,1.5])\n",
    "for i in range(0,len(MM)):\n",
    "    Signal=[C(MM[i],MM[i],1e3,0.,0.,0.,0.)*gamma(f,MM[i],MM[i],0.,0.)[0] for f in freq]\n",
    "    plt.plot(freq,Signal,LS[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# M0=1.5\n",
    "# chi0=0\n",
    "# D0=1e3 # in order of Kpc\n",
    "# factor=2.0*M0*15.4787466e-6 #second;\n",
    "# def INT(y): \n",
    "#         fp=np.exp(y)\n",
    "#         result=fp*gamma(fp/factor,M0,M0,chi0,chi0)[0]**2/Sn(fp/factor)\n",
    "#         return result*1e-48\n",
    "# f0=np.pi*1e-3\n",
    "# delta=(M0-M0)/(2.0*M0); # delta is independent with the total mass\n",
    "# chi=chi0\n",
    "# eta=0.25\n",
    "# ###############################################\n",
    "# mu01=1-4.455*(1-chi)**0.217+3.521*(1-chi)**0.26 # independent of the total mass\n",
    "# mu02=(1-0.63*(1-chi)**0.3)*0.5\n",
    "# mu03=(1-0.63*(1-chi)**0.3)*(1-chi)**0.45*0.25\n",
    "# mu04=0.3236+0.04894*chi+0.01346*chi**2\n",
    "# ###############################################\n",
    "# f0=np.pi*1e-3\n",
    "# #f1=mu01+y101*eta+y111*eta*chi+y121*eta*chi**2+y201*eta**2+y211*eta**2*chi+y301*eta**3; \n",
    "# #f2=mu02+y102*eta+y112*eta*chi+y122*eta*chi**2+y202*eta**2+y212*eta**2*chi+y302*eta**3;\n",
    "# #sigma=mu03+y103*eta+y113*eta*chi+y123*eta*chi**2+y203*eta**2+y213*eta**2*chi+y303*eta**3;\n",
    "# f3=mu04+y104*eta+y114*eta*chi+y124*eta*chi**2+y204*eta**2+y214*eta**2*chi+y304*eta**3;  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'f0' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-8-37c50a96e3d5>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mylow\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0myhigh\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mrhosq\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msci\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mintegrate\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mquad\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mINT\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mylow\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0myhigh\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mrhosq\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m4.0\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mC\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mM0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mM0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mD0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mrhosq\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;36m1e48\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mfactor\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mrho\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msqrt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrhosq\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'f0' is not defined"
     ]
    }
   ],
   "source": [
    "# ylow=np.log(f0)\n",
    "# yhigh=np.log(f3)\n",
    "# rhosq=sci.integrate.quad(INT,ylow,yhigh)\n",
    "# rhosq=4.0*C(M0,M0,D0,0,0,0,0)**2*rhosq[0]*1e48/factor\n",
    "# rho=np.sqrt(rhosq)\n",
    "# print(\"SNR=%e\" % rho)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def rho0M(Mchirp,D0=1e3): #input red-shifted chirp mass (solar mass), give you the standard SNR\n",
    "    m0=Mchirp/0.87; # from chirp mass to individual mass of an equal mass binary.\n",
    "    factor=2.0*m0*15.4787466e-6 #second;\n",
    "    f0=np.pi*1e-3\n",
    "    delta=0; # delta is independent with the total mass\n",
    "    chi=0;\n",
    "    eta=0.25\n",
    "    def INTT(y): \n",
    "        fp=np.exp(y)\n",
    "        if fp/factor>min(freq)+2.:\n",
    "            result=fp*gamma(fp/factor,m0,m0,chi,chi)[0]**2/Sn(fp/factor)\n",
    "        else:\n",
    "            result=0\n",
    "        return result*1e-48\n",
    "    ###############################################\n",
    "    mu01=1-4.455*(1-chi)**0.217+3.521*(1-chi)**0.26 # independent of the total mass\n",
    "    mu02=(1-0.63*(1-chi)**0.3)*0.5\n",
    "    mu03=(1-0.63*(1-chi)**0.3)*(1-chi)**0.45*0.25\n",
    "    mu04=0.3236+0.04894*chi+0.01346*chi**2\n",
    "    ###############################################\n",
    "    f3=mu04+y104*eta+y114*eta*chi+y124*eta*chi**2+y204*eta**2+y214*eta**2*chi+y304*eta**3;  \n",
    "    ylow=max(np.log(f0),np.log(min(freq*factor)))\n",
    "    yhigh=np.log(f3)    \n",
    "    rhosq=sci.integrate.quad(INTT,ylow,yhigh)\n",
    "    rho=np.sqrt(4.0*C(m0,m0,D0,0,0,0,0)**2*rhosq[0]*1e48/factor)\n",
    "    #rho=np.sqrt(rhosq)\n",
    "    #print(ylow,yhigh)\n",
    "    #rho=np.sqrt(4.0*C(m0,m0,D0,0,0,0,0)**2*rhosq[0]*1e48)\n",
    "    return rho"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/Cellar/python3/3.6.2/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/scipy/integrate/quadpack.py:364: IntegrationWarning: The maximum number of subdivisions (50) has been achieved.\n",
      "  If increasing the limit yields no improvement it is advised to analyze \n",
      "  the integrand in order to determine the difficulties.  If the position of a \n",
      "  local difficulty can be determined (singularity, discontinuity) one will \n",
      "  probably gain from splitting up the interval and calling the integrator \n",
      "  on the subranges.  Perhaps a special-purpose integrator should be used.\n",
      "  warnings.warn(msg, IntegrationWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1322522.8478091469"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rho0M(74)\n",
    "# Sn(np.exp(-5.)/4800.4787466e-6)*1e48\n",
    "# #print(np.exp(-2.)/60.4787466e-6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/Cellar/python3/3.6.2/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/scipy/integrate/quadpack.py:364: IntegrationWarning: The maximum number of subdivisions (50) has been achieved.\n",
      "  If increasing the limit yields no improvement it is advised to analyze \n",
      "  the integrand in order to determine the difficulties.  If the position of a \n",
      "  local difficulty can be determined (singularity, discontinuity) one will \n",
      "  probably gain from splitting up the interval and calling the integrator \n",
      "  on the subranges.  Perhaps a special-purpose integrator should be used.\n",
      "  warnings.warn(msg, IntegrationWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Mz=np.linspace(7,800.,50);\n",
    "RHO=[rho0M(mz) for mz in Mz];\n",
    "RHO2=[rho0M(20.)*(mz/20.)**0.8333 for mz in Mz];\n",
    "plt.yscale('log')\n",
    "plt.xscale('log')\n",
    "plt.xlabel(r'$\\mathcal{M}_z\\,(M_\\odot)$',fontsize=14)\n",
    "plt.ylabel(r'$\\rho_{0,\\mathcal{M}_z}$',fontsize=14)\n",
    "plt.plot(Mz,RHO,'b',label='real SNR vs Mz')\n",
    "plt.plot(Mz,RHO2,'r--',label='5/6 scaling')\n",
    "plt.legend(frameon=False)\n",
    "plt.savefig('MvsSNR.eps')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "GWtool_BHB.rho0M(1.31)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "GWtool_BHB.initialMtable()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}