{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fitting Data and Making FOMs\n",
    "\n",
    "Here I will go through an example of how to fit data to a transfer function. Later this TF will be used to make a full system model.\n",
    "\n",
    "First imports:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/Ian/Desktop/Research/GQuEST/2024/buzz/src/buzz/ssutil.py:1251: SyntaxWarning: assertion is always true, perhaps remove parentheses?\n",
      "  assert(orig_pole_zero_diff == new_pole_zero_diff, \"The number diffrence between the number of poles and zeros must be the same for the new P system as the old P system.\\n There is some problem with the movement of the poles and zeros in the P system.\")\n",
      "/Users/Ian/Desktop/Research/GQuEST/2024/buzz/src/buzz/ssutil.py:1267: SyntaxWarning: assertion is always true, perhaps remove parentheses?\n",
      "  assert(len(P_new_zeros) == len(P_new_poles), \"P_new_zeros and P_new_poles must have the same length\")\n",
      "/Users/Ian/Desktop/Research/GQuEST/2024/buzz/src/buzz/ssutil.py:1316: SyntaxWarning: assertion is always true, perhaps remove parentheses?\n",
      "  assert(iodutil.getNamespace(F1)!='F3', 'The namespace of F1 is F3. This will cause a conflict with the F3 system')\n",
      "/Users/Ian/Desktop/Research/GQuEST/2024/buzz/src/buzz/ssutil.py:1317: SyntaxWarning: assertion is always true, perhaps remove parentheses?\n",
      "  assert(iodutil.getNamespace(F2)!='F3', 'The namespace of F2 is F3. This will cause a conflict with the F3 system')\n"
     ]
    }
   ],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import control\n",
    "import scipy.signal as signal\n",
    "from scipy import interpolate\n",
    "import scipy.linalg\n",
    "from scipy.stats import gmean\n",
    "import gwinc\n",
    "import yaml\n",
    "from wield.iirrational.v2 import data2filter\n",
    "from wield.control.AAA import tfAAA\n",
    "from wield.utilities.file_io import load, save\n",
    "from wield.control.ss_bare.ss import BareStateSpace\n",
    "from scipy.signal import cheby2\n",
    "from wield.control import SISO\n",
    "from buzz import ssutil\n",
    "from physunits import m, s, kg, Hz\n",
    "from scipy.constants import c, G"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Getting the LIGO Sensitivity Curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Power Spectral Density [strain/hz]')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f_Hz = np.geomspace(1e-2, 1e4, 2000)\n",
    "budget = gwinc.load_budget('aLIGO', freq=f_Hz)\n",
    "trace_PSD = budget.run(freq=f_Hz).psd\n",
    "\n",
    "plt.title(\"ALIGO BUDGET\")\n",
    "plt.loglog(f_Hz, trace_PSD)\n",
    "plt.xlabel(\"Frequency [Hz]\")\n",
    "plt.ylabel(\"Power Spectral Density [strain/hz]\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lastly for this step we will combine the twu curves to make a FOM. we divide the BNS PSD by the LIGO Noise spectrum without the controls noise. From the paper:\n",
    "$$\\mathrm{SNR}^2 = 4\\int_{0}^{\\infty} \\frac{\\left |h_\\mathrm{gw}(f)\\right |^2}{S_h(f)} df$$\n",
    "\n",
    "where $S_h(f)$ is the noise spectrum of the detector. This can be written as:\n",
    "\n",
    "$$ S_h(f) = S_{\\mathrm{det}}(f) + |C(f)|^2 S_{\\mathrm{p}}(f)$$\n",
    "\n",
    "where $S_{\\mathrm{det}}(f)$ is the detector noise spectrum without controls noise, $S_{\\mathrm{p}}(f)$ is the control noise spectrum, and $C(f)$ is the coupling function from the controls noise in the control loop to DARM. By using the taylor series of A/(B+x) to linearize the integral. i.e.:\n",
    "\n",
    "$$\\frac{A}{B+x}=\\frac{A}{B} - \\frac{Ax}{B^2} + \\frac{Ax^2}{B^3} - \\frac{Ax^3}{B^4} + \\frac{Ax^4}{B^5} - \\frac{Ax^5}{B^6} + O(x^6)$$\n",
    "\n",
    "taking the first two terms of the taylor series and applying it to the SNR equation we get:\n",
    "\n",
    "$$\\mathrm{SNR}^2 = 4\\int_{0}^{\\infty} \\frac{\\left | h_{\\mathrm{signal}}(f)\\right |^2}{S_{\\mathrm{det}}(f)} \\ df - 4\\int_{0}^{\\infty} \\frac{\\left |C\\right |^2\\left | h_{\\mathrm{signal}}(f)\\right |^2 }{S_{\\mathrm{det}}(f)^2}  S_{\\mathrm{p}}(f) \\ df$$\n",
    "\n",
    "To get range we need to use the $\\mathrm{SNR}$ not the $\\mathrm{SNR}^2$ so we take the square root of the above equation which has a different linearization. as $A \\rightarrow \\infty$ \n",
    "\n",
    "$$\\sqrt{A+B} = \\sqrt{A} \\sqrt{1+\\frac{B}{A}} = \\sqrt{A} (1+\\frac{B}{2 \\sqrt{A}})$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Frequency [Hz]')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from inspiral_range import inspiral_range as ir\n",
    "linearization_PSD = trace_PSD**2\n",
    "FOM_intgrand = ir.sensemon_range(f_Hz, psd=linearization_PSD, m1=1.4, m2=1.4, horizon=False, integrate=False, detection_snr=8)**2\n",
    "\n",
    "f_Hz = np.geomspace(1e-2, 1e4, 2000)\n",
    "budget = gwinc.load_budget('aLIGO', freq=f_Hz)\n",
    "trace_PSD = budget.run(freq=f_Hz).psd\n",
    "\n",
    "plt.title(\"ALIGO BUDGET\")\n",
    "plt.loglog(f_Hz, FOM_intgrand)\n",
    "plt.xlabel(\"Frequency [Hz]\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.547336892714717e+25\n",
      "4.547336892714716e+25\n"
     ]
    }
   ],
   "source": [
    "print(ir.sensemon_range(f_Hz, psd=linearization_PSD, m1=1.4, m2=1.4, horizon=False, integrate=True, detection_snr=8))\n",
    "FOM_intgrand = ir.sensemon_range(f_Hz, psd=linearization_PSD, m1=1.4, m2=1.4, horizon=False, integrate=False, detection_snr=8)**2\n",
    "print(np.trapezoid(FOM_intgrand, f_Hz)**0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/Ian/miniconda3/envs/controls/lib/python3.10/site-packages/wield/control/SISO/zpk.py:164: NumericalWarning: StateSpace is large (>50 states), using reduced response fiducial auditing heuristics. TODO to make this smarter\n",
      "  warnings.warn(f\"StateSpace is large (>{self.N_MAX_FID} states), using reduced response fiducial auditing heuristics. TODO to make this smarter\", util.NumericalWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x12c900c40>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Hand Fit the DARM**2 ZPK\n",
    "shift_sq = 0.8\n",
    "z_hand_sq = np.array([-0.07]*18) * 2 * np.pi * shift_sq\n",
    "mp_sq = -0.75 -0.075j\n",
    "mul_sq = 9\n",
    "p_hand_sq = np.array([mp_sq]*mul_sq + [np.real(mp_sq)-np.imag(mp_sq)*1j]*mul_sq)*2 * 2 * np.pi * shift_sq\n",
    "p_hand_sq = np.append(p_hand_sq, np.array([-150]*1 +[-300]*1 +[-700]*1 + [-7500]*1))\n",
    "k_hand_sq = 1e36\n",
    "\n",
    "##making steeper roll off\n",
    "mp_sq = mp_sq * 2.25\n",
    "p_hand_sq = np.append(p_hand_sq, np.array([mp_sq]*8 +[np.real(mp_sq)-np.imag(mp_sq)*1j]*8+ [-1]*8)* 2 * np.pi * shift_sq)\n",
    "z_hand_sq = np.append(z_hand_sq, np.array([-1]*24)* 2 * np.pi * shift_sq)\n",
    "\n",
    "#k_hand_sq = k_hand_sq *1e9\n",
    "\n",
    "#plt.loglog(F_bug, Div_PSD**0.5, label = \"Full FOM ASD\")\n",
    "plt.loglog(f_Hz, FOM_intgrand**0.5, label = \"Downsampled FOM ASD\")\n",
    "#plt.loglog(F_Hz, abs(TF_all), label = 'ALL ZPK Fit Bary. (order {})'.format(results.order))\n",
    "fq_plot = np.logspace(-2, 5, 10000)\n",
    "\n",
    "\n",
    "hand_sys = SISO.zpk(z_hand_sq, p_hand_sq, k_hand_sq, convention='IIRrational')\n",
    "#fr_hand = hand_sys.fresponse(f=fq_plot)\n",
    "fr_hand = hand_sys.fresponse(f=f_Hz)\n",
    "\n",
    "plt.loglog(-np.real(p_hand_sq), np.array([1e27]*len(p_hand_sq)), color='black', linestyle='', marker='o')\n",
    "plt.loglog(-np.real(z_hand_sq), np.array([1e27]*len(z_hand_sq)), color='r', linestyle='', marker='x')\n",
    "plt.loglog(*fr_hand.fplot_mag, label = 'Hand fit to DARM**2 ZPK')\n",
    "plt.xlabel(\"Frequency [Hz]\")\n",
    "plt.ylabel(\"ASD\")\n",
    "\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "\n",
    "#plt.savefig('FOM_BNS_fit.pdf', bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we calculate what this spectrum will look like from this FOM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x169ca1000>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "LLO_O4_DARM = np.loadtxt('O4_data/L1_darm_measured.txt').T\n",
    "LLO_O4_DARM_known = np.loadtxt('O4_data/L1_darm_known_measured.txt').T\n",
    "LLO_O4_SUS_damping = np.loadtxt('O4_data/L1_sus_damping.txt').T\n",
    "\n",
    "L_arm = 3995\n",
    "\n",
    "BNS_range_inv = ir.sensemon_range(f_Hz, psd=np.ones_like(f_Hz), m1=1.4, m2=1.4, horizon=False, integrate=False, detection_snr=8)**2\n",
    "det_PSD_from_FOM = ((BNS_range_inv)/fr_hand.mag**2)**0.5\n",
    "plt.loglog(f_Hz, trace_PSD**0.5*L_arm , label = 'Detector Spectrum from GWINC', color='green')\n",
    "# plt.loglog(LLO_O4_DARM[0], LLO_O4_DARM[1]*L_arm , label = 'Measured DARM LLO O4', color='red')\n",
    "plt.loglog(LLO_O4_SUS_damping[0], LLO_O4_SUS_damping[1]*L_arm , label = 'SUS Damping', color='orange')\n",
    "plt.loglog(LLO_O4_DARM_known[0], LLO_O4_DARM_known[1]*L_arm , label = 'Measured Known noises LLO O4', color='black')\n",
    "plt.loglog(f_Hz, det_PSD_from_FOM**0.5*L_arm , label = 'Detector Spectrum from FOM', color='dodgerblue')\n",
    "plt.xlabel(\"Frequency [Hz]\")\n",
    "plt.ylabel(\"DARM [m/rtHz]\")\n",
    "\n",
    "# plt.xlim([6, 10000])\n",
    "# plt.ylim([1e-20, 1e-15])\n",
    "\n",
    "plt.grid()\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we will save our result so it can be loaded by the make full system example file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 940x680 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "out_z = z_hand_sq\n",
    "out_p = p_hand_sq\n",
    "out_k = k_hand_sq\n",
    "\n",
    "pre_save_sys = SISO.zpk(out_z, out_p, out_k, convention='IIRrational')\n",
    "from wield.utilities.mpl import mplfigB\n",
    "plotting_omega = np.logspace(-2, 4, 1000)\n",
    "plt.close()\n",
    "axB = mplfigB(Nrows = 2)\n",
    "fr = pre_save_sys.fresponse(f=plotting_omega)\n",
    "axB.ax0.loglog(*fr.fplot_mag, label='test')\n",
    "axB.ax1.semilogx(*fr.fplot_deg225, label='test')\n",
    "\n",
    "\n",
    "sys_save = SISO.zpk(out_z, out_p, out_k, convention='IIRrational')\n",
    "assert(ssutil.isStable(sys_save))\n",
    "zpk_dict = {\n",
    "            'z' : [str(zero) for zero in np.asarray(tuple(sys_save.z)).tolist()],\n",
    "            'p' : [str(pole) for pole in np.asarray(tuple(sys_save.p)).tolist()],\n",
    "            'k' : float(sys_save.k)\n",
    "            }\n",
    "\n",
    "#save('BNS_FOM_IR.yml', zpk_dict) #Uncomment to save the ZPK"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now it is saved. To open it use the following code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'numpy.float64'>\n",
      "49\n",
      "52\n"
     ]
    }
   ],
   "source": [
    "with open('BNS_FOM.yml', 'r') as file:\n",
    "    filt_dict = yaml.safe_load(file)\n",
    "p = np.array(filt_dict['p'], dtype=np.complex128)\n",
    "z = np.array(filt_dict['z'], dtype=np.complex128)\n",
    "k = np.float64(filt_dict['k'])\n",
    "print(type(k))\n",
    "print(len(z))\n",
    "print(len(p))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "controls",
   "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": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
