HWP_sim-UHF.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.optimize as opt\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_HWP_transfer_matrix(thicks,thetas,no,ne,wavelength):\n",
    "    ## this code caculats the transfer matrix assumng x-y input and output\n",
    "    ################\n",
    "    ## thick --- the thickness of each layer, use mm\n",
    "    ## theta --- the angle of the ordinary axis relative to the x axis\n",
    "    ## no    --- the index along the ordinary axis\n",
    "    ## ne    --- the index along the extrodinary axis\n",
    "    ## wavelength  --- the wavelenght, use mm\n",
    "    ################\n",
    "    # set up the input layer, assumed to be vacuume\n",
    "    TF = np.matrix([[1,0],\n",
    "                    [0,1]])\n",
    "    theta_prev = 0.\n",
    "    # now iterate through the layers of HWP\n",
    "    N_layers = np.size(thicks)\n",
    "    i = 0\n",
    "    while (i < N_layers):\n",
    "        d_th = thetas[i] - theta_prev\n",
    "        Mrot = np.matrix([[np.cos(d_th),np.sin(d_th)],\n",
    "                         [-np.sin(d_th),np.cos(d_th)]])\n",
    "        k = 2 * np.pi / wavelength\n",
    "        phi_o = k * no * thicks[i]\n",
    "        phi_e = k * ne * thicks[i]\n",
    "        Mphase = np.matrix([[np.exp(np.complex(0,1)*phi_o),0],\n",
    "                         [0, np.exp(np.complex(0,1)*phi_e)]])\n",
    "        TF_layer = np.matmul(Mphase,Mrot)\n",
    "        TF = np.matmul(TF_layer,TF)\n",
    "        ## now iterate\n",
    "        theta_prev = thetas[i]\n",
    "        i+=1\n",
    "    # now do the last layer\n",
    "    d_th = 0 - theta_prev\n",
    "    Mrot = np.matrix([[np.cos(d_th),np.sin(d_th)],\n",
    "                      [-np.sin(d_th),np.cos(d_th)]])\n",
    "    TF = np.matmul(Mrot,TF)\n",
    "    return(TF)\n",
    "\n",
    "##########\n",
    "wavelength = 2.\n",
    "no = 3\n",
    "ne = 3.1\n",
    "thicks = np.array([1/(ne-no)*wavelength/2.])\n",
    "thetas = np.array([np.pi/4.])\n",
    "\n",
    "\n",
    "print(thicks)\n",
    "print(thetas)\n",
    "\n",
    "tmp = make_HWP_transfer_matrix(thicks,thetas,no,ne,wavelength)\n",
    "\n",
    "print(\"the transfer matrix\")\n",
    "print(tmp)\n",
    "print(\"checking unitatity\")\n",
    "print(np.matmul(np.conj(tmp),tmp))\n",
    "\n",
    "print(tmp[0,0])\n",
    "print(tmp[1,0])   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rotate_HWP(TF,psi):\n",
    "    Mrot = np.matrix([[np.cos(psi),np.sin(psi)],\n",
    "                      [-np.sin(psi),np.cos(psi)]])\n",
    "    out = np.matmul(TF,Mrot)\n",
    "    out = np.matmul(np.transpose(Mrot),out)\n",
    "    return(out)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sim_rot_HWP(TF,nsamps):\n",
    "    angs = np.arange(nsamps)/nsamps * 2 * np.pi\n",
    "    Ex_out = np.zeros(nsamps) * np.complex(0,1)\n",
    "    Ey_out = np.zeros(nsamps) * np.complex(0,1)\n",
    "    i = 0\n",
    "    while(i<nsamps):\n",
    "        TF_tmp = rotate_HWP(TF,angs[i])\n",
    "        Ex_out[i] = TF_tmp[0,0]\n",
    "        Ey_out[i] = TF_tmp[1,0]\n",
    "        i+=1\n",
    "    return(angs,Ex_out,Ey_out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1066befd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3.33333333]\n"
     ]
    }
   ],
   "source": [
    "## setup a HWP for 2 mm\n",
    "wavelength = 2.\n",
    "no = 3.05\n",
    "ne = 3.35\n",
    "thicks = np.array([1/(ne-no)*wavelength/2.])\n",
    "thetas = np.array([np.pi/4.])\n",
    "\n",
    "\n",
    "\n",
    "## make the transfer funciton\n",
    "wavelength = 2.\n",
    "TF = make_HWP_transfer_matrix(thicks,thetas,no,ne,wavelength)\n",
    "\n",
    "# simulate its output vs angle for x poliazed input\n",
    "n_angles = 128\n",
    "angs,Exo,Eyo = sim_rot_HWP(TF,n_angles)\n",
    "\n",
    "## plot the results\n",
    "plt.plot(angs,(np.abs(Exo))**2,\"b.\")\n",
    "plt.plot(angs,(np.abs(Eyo))**2,\"r.\")\n",
    "plt.show()\n",
    "\n",
    "print(thicks)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x103c0dcc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 3.75000000e-01+0.00000000e+00j -2.58158612e-17+1.60768989e-17j\n",
      " -4.03767227e-17-1.31022784e-17j -3.35645003e-17-6.25840893e-18j\n",
      "  1.87500000e-01+2.85362012e-16j  2.90777807e-17+9.98593750e-18j\n",
      "  7.02341155e-18-9.14254992e-19j  1.06868768e-17+1.02286366e-17j]\n",
      "[ 1.23569707e-17-1.30203285e-18j  1.06868768e-17-1.02286366e-17j\n",
      "  7.02341155e-18+9.14254992e-19j  2.90777807e-17-9.98593750e-18j\n",
      "  1.87500000e-01+1.61329283e-16j -3.35645003e-17+6.25840893e-18j\n",
      " -4.03767227e-17+1.31022784e-17j -2.58158612e-17-1.60768989e-17j]\n",
      "1.0\n"
     ]
    }
   ],
   "source": [
    "## make the transfer funciton\n",
    "wavelength = 3.0\n",
    "TF = make_HWP_transfer_matrix(thicks,thetas,no,ne,wavelength)\n",
    "\n",
    "# simulate its output vs angle for x poliazed input\n",
    "n_angles = 128\n",
    "angs,Exo,Eyo = sim_rot_HWP(TF,n_angles)\n",
    "\n",
    "## plot the results\n",
    "plt.plot(angs*180/np.pi,(np.abs(Exo))**2,\"b.\")\n",
    "plt.plot(angs*180/np.pi,(np.abs(Eyo))**2,\"r.\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "## fit fourier modes to the output\n",
    "\n",
    "tmp = ( np.fft.ifft((np.abs(Eyo))**2))\n",
    "\n",
    "print(tmp[0:8])\n",
    "print(tmp[-8:])\n",
    "\n",
    "print(2*np.abs(tmp[4])/np.abs(tmp[0]))\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0.7500000000000007, 2.842170943040401e-14)\n"
     ]
    }
   ],
   "source": [
    "def mod_eff_and_phase(E):\n",
    "    tmp = np.fft.ifft((np.abs(E))**2)\n",
    "    mod_eff = 2. * np.abs(tmp[4]) /.5 #/ np.abs(tmp[0])\n",
    "    ##\n",
    "    tmp = np.arctan2(np.imag(tmp[4]),np.real(tmp[4]))\n",
    "    phase =  45 + 180/np.pi * tmp/4.\n",
    "    return(mod_eff,phase)\n",
    "\n",
    "print(mod_eff_and_phase(Exo))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1069ac240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## wavelenght range\n",
    "wavelengths = ((np.arange(0,500)+1)/500.)*10. + 1\n",
    "freq_GHZ = 1./wavelengths * 300./1.  ## \n",
    "mod_effs = np.zeros(np.shape(wavelengths))\n",
    "phases =   np.zeros(np.shape(wavelengths))\n",
    "\n",
    "## numer of angles to use in the simulations of the HWP\n",
    "n_angles = 32\n",
    "\n",
    "## setup a HWP for 2 mm\n",
    "wavelength = 2.\n",
    "no = 3.05\n",
    "ne = 3.35\n",
    "thicks = np.array([1/(ne-no)*wavelength/2.])\n",
    "thetas = np.array([np.pi/4.])\n",
    "\n",
    "\n",
    "\n",
    "## make the transfer funciton\n",
    "i = 0\n",
    "while (i < np.size(wavelengths)):\n",
    "    wavelength = wavelengths[i]\n",
    "    TF = make_HWP_transfer_matrix(thicks,thetas,no,ne,wavelengths[i])\n",
    "    angs,Exo,Eyo = sim_rot_HWP(TF,n_angles)\n",
    "    mod_eff,phase = mod_eff_and_phase(Exo)\n",
    "    mod_effs[i] = mod_eff\n",
    "    phases[i] = phase\n",
    "    i +=1\n",
    "\n",
    "\n",
    "mod_effs_single = np.copy(mod_effs)\n",
    "mod_phsses_single = np.copy(phases)\n",
    "\n",
    "plt.plot(freq_GHZ,mod_effs_single) \n",
    "plt.show()\n",
    "\n",
    "\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106997588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 4.89873243e-01+0.00000000e+00j -1.87136807e-17+1.68724832e-17j\n",
      " -6.95216274e-17-4.55285637e-19j -3.13424964e-17-2.96640732e-18j\n",
      "  2.44936622e-01+3.54750951e-16j  4.57087354e-17-1.87979620e-18j\n",
      "  5.66845454e-18+2.84595803e-17j  1.46170949e-17+1.92287114e-17j]\n"
     ]
    }
   ],
   "source": [
    "wavelength = 2.2\n",
    "n_angles = 128\n",
    "\n",
    "TF = make_HWP_transfer_matrix(thicks,thetas,no,ne,wavelength)\n",
    "angs,Exo,Eyo = sim_rot_HWP(TF,n_angles)\n",
    "mod_eff,phase = mod_eff_and_phase(Exo)\n",
    "\n",
    "\n",
    "## plot the results\n",
    "plt.plot(angs*180./np.pi,(np.abs(Exo))**2,\"b.\")\n",
    "plt.plot(angs*180./np.pi,(np.abs(Eyo))**2,\"r.\")\n",
    "plt.xlim(0,45)\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "## fit fourier modes to the output\n",
    "\n",
    "tmp = ( np.fft.ifft((np.abs(Eyo))**2)[0:8])\n",
    "\n",
    "print(tmp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.3566889860503669\n",
      "0.3566889860503669\n"
     ]
    }
   ],
   "source": [
    "## compute the fraction of the simualted band that is usable, defined as above a threshold\n",
    "#def fractional_BW_usable(mod_eff,thresshold):\n",
    "#    ok = np.where(mod_eff > thresshold )\n",
    "#    return(np.size(ok)/np.size(mod_eff))\n",
    "\n",
    "def fractional_BW_usable(mod_eff):\n",
    "    tmp = np.sum(mod_eff)\n",
    "    tmp = tmp / np.size(mod_eff)\n",
    "    return(tmp)\n",
    "\n",
    "print(fractional_BW_usable(mod_effs_single))\n",
    "print(fractional_BW_usable(mod_effs))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "## calcuatle the dispersion in the phase angle\n",
    "def phase_angle_dispersion(phase_angle,frequency):\n",
    "    phase_angle  = np.unwrap(phase_angle*4.*np.pi/180)/4. * 180/np.pi\n",
    "    #low_band = np.where(frequency  < 112.)\n",
    "    #high_band =np.where(frequency > 122.)\n",
    "    #out = np.std(phase_angle[low_band])\n",
    "    #out += np.std(phase_angle[high_band])\n",
    "    out = np.std(phase_angle)\n",
    "    return(out)\n",
    "\n",
    "#print(phase_angle_dispersion(mod_phsses_single))\n",
    "#print(phase_angle_dispersion(phases))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def optomization_function(mod_effs,phase_angles,frequency):\n",
    "    ## the bandwidth part, this is multiplitative, with small values being bad\n",
    "    fBW = fractional_BW_usable(mod_effs)\n",
    "    alpha = 0.05 ## smaller aphpah penalizes more for loss of BW\n",
    "                ## 0.1 means 10% bw loss results in a 70% penalty\n",
    "    BW_penalty = ( ((1-fBW)/alpha))\n",
    "    ## the phase constancy part, small is good\n",
    "    rms_phi = np.sqrt(phase_angle_dispersion(phase_angles,frequency)**2)\n",
    "    ## optomization funciton should get small as things improe\n",
    "    opt = rms_phi + BW_penalty ## consider addign a thickness penalty\n",
    "    return(opt)\n",
    "\n",
    "#print(optomization_function(mod_effs,phases))\n",
    "#print(optomization_function(mod_effs_single,mod_phsses_single))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "54.12038835777537\n"
     ]
    }
   ],
   "source": [
    "def evaluate_HWP(params):\n",
    "    ##unpack the params\n",
    "    thicks = np.abs(params[:int(np.size(params)/2)])\n",
    "    thetas = params[int(np.size(params)/2):]*np.pi/180.\n",
    "    ne = 3.2 + 0.31/2.\n",
    "    no = 3.2 - 0.31/2.\n",
    "    ## set up the wavelenght range\n",
    "    freq_GHZ = np.arange(120) + 190.  ## from 70 to 170 GHz \n",
    "    #ok = np.where(np.logical_or(freq_GHZ < 112, freq_GHZ > 122))\n",
    "    #freq_GHZ = freq_GHZ[ok]\n",
    "    wavelengths = 1./freq_GHZ *300.  ## convert to mm\n",
    "    ## set up the outputs for the calcaulation\n",
    "    mod_effs = np.zeros(np.shape(wavelengths))\n",
    "    phases =   np.zeros(np.shape(wavelengths))\n",
    "\n",
    "    ## numer of angles to use in the simulations of the HWP\n",
    "    n_angles = 32\n",
    "    \n",
    "    ## make the transfer funciton\n",
    "    i = 0\n",
    "    while (i < np.size(wavelengths)):\n",
    "        wavelength = wavelengths[i]\n",
    "        TF = make_HWP_transfer_matrix(thicks,thetas,no,ne,wavelengths[i])\n",
    "        angs,Exo,Eyo = sim_rot_HWP(TF,n_angles)\n",
    "        mod_eff,phase = mod_eff_and_phase(Exo)\n",
    "        mod_effs[i] = mod_eff\n",
    "        phases[i] = phase\n",
    "        i +=1 \n",
    "    \n",
    "    phases  = np.unwrap(phases*4.*np.pi/180)/4. * 180/np.pi\n",
    "    ## plots for debugging\n",
    "    if (np.random.random_sample() < .002):  ## very important for speeding it up\n",
    "        print(\"thicks: \", thicks)\n",
    "        print(\"agnles: \", thetas*180./np.pi)\n",
    "        plt.plot(freq_GHZ,mod_effs,\"b.\")\n",
    "        plt.ylim(0,1)\n",
    "        plt.show()\n",
    "        plt.plot(freq_GHZ,phases-np.mean(phases),\"r.\")\n",
    "        plt.show()\n",
    "\n",
    "    return(optomization_function(mod_effs,phases,freq_GHZ))\n",
    "\n",
    "\n",
    "freq_GHZ = np.arange(100) + 70.  ## from 70 to 170 GHz \n",
    "\n",
    "thicks = np.ones(5)* 1/(.3)*2./2.*1.4\n",
    "angles = np.array([0,25,85,25,0])*np.pi/180.\n",
    "params = np.concatenate((thicks,angles))\n",
    "print(evaluate_HWP(params))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "thicks:  [1.89013379 1.83092158 1.90040552 1.83092158 1.89013379]\n",
      "agnles:  [ 2.28995060e+01 -5.00009221e+01 -3.03941004e-04  4.99993932e+01\n",
      " -2.29007311e+01]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106b0e2b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106be05c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "thicks:  [1.89991233 1.89938589 1.90000361 1.8993859  1.8999123 ]\n",
      "agnles:  [ 2.28999956e+01 -5.00000082e+01 -2.70527186e-06  4.99999946e+01\n",
      " -2.29000065e+01]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106c99080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106d5c3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "thicks:  [1.89936482 1.89939407 1.9035856  1.8993949  1.8993546 ]\n",
      "agnles:  [ 2.29797262e+01 -5.01020800e+01  1.38290065e-03  5.01054134e+01\n",
      " -2.29763419e+01]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106d5c940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106b18c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "thicks:  [1.89995452 1.89937027 1.90076078 1.8993701  1.89994245]\n",
      "agnles:  [ 2.36970868e+01 -5.10821140e+01  1.96386425e-02  5.10751118e+01\n",
      " -2.37164499e+01]\n"
     ]
    },
    {
     "data": {
      "image/png": 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8vt5ld4uVCzbcu7OkdwGHquov+jb130rhOuBjfeO/2n0C4KXAd05evllqC/WSZAvwB8DWqvpe31P2Adu7TwCsBzYAnzmfNS9kUC9V9fmqurSqLquqy+j9Q7uyqr7OBB8XOO3v2UfpXd8lyeXAKnp3IFxWx6ZzFHh5t/xK4Ivd8sQemyRT6T49luTHgFfRew/hLnq3UIFT//0vr1usLPU7ukv1AH6G3suqB4H7u8e19K6j3UnvF/RO4Bn12Lvru+ldl/s8ML3UPYzQyyy964Qnx27te84NXS+H6T7pMAmPhXqZN+fLPPZpmYk9LkOOzSrgb4EvAJ8FXrlcj003fh+9T/ncA7x40o8N8ELgc10vXwBu7MafS+8/01l6r0JOfprpid36bLf9uUvdw7CHtx+QpAZdsJdlJKllhrskNchwl6QGGe6S1CDDXZIaZLhLUoMMd0lq0P8D6WHrtuvTq0wAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1066bb7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106a949e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "thicks:  [1.89988027 1.89937148 1.90122431 1.89937114 1.89987742]\n",
      "agnles:  [ 2.37051564e+01 -5.11008256e+01  2.32041959e-02  5.10967893e+01\n",
      " -2.37222997e+01]\n"
     ]
    },
    {
     "data": {
      "image/png": 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8vt5ld4uVCzbcu7OkdwGHquov+jb130rhOuBjfeO/2n0C4KXAd05evllqC/WSZAvwB8DWqvpe31P2Adu7TwCsBzYAnzmfNS9kUC9V9fmqurSqLquqy+j9Q7uyqr7OBB8XOO3v2UfpXd8lyeXAKnp3IFxWx6ZzFHh5t/xK4Ivd8sQemyRT6T49luTHgFfRew/hLnq3UIFT//0vr1usLPU7ukv1AH6G3suqB4H7u8e19K6j3UnvF/RO4Bn12Lvru+ldl/s8ML3UPYzQyyy964Qnx27te84NXS+H6T7pMAmPhXqZN+fLPPZpmYk9LkOOzSrgb4EvAJ8FXrlcj003fh+9T/ncA7x40o8N8ELgc10vXwBu7MafS+8/01l6r0JOfprpid36bLf9uUvdw7CHtx+QpAZdsJdlJKllhrskNchwl6QGGe6S1CDDXZIaZLhLUoMMd0lq0P8D6WHrtuvTq0wAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106c7b908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10698ba58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "thicks:  [1.89995422 1.89935737 1.9010134  1.89935737 1.89996033]\n",
      "agnles:  [ 2.32592539e+01 -5.14475153e+01  1.28094826e-03  5.14512692e+01\n",
      " -2.32551960e+01]\n"
     ]
    },
    {
     "data": {
      "image/png": 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8vt5ld4uVCzbcu7OkdwGHquov+jb130rhOuBjfeO/2n0C4KXAd05evllqC/WSZAvwB8DWqvpe31P2Adu7TwCsBzYAnzmfNS9kUC9V9fmqurSqLquqy+j9Q7uyqr7OBB8XOO3v2UfpXd8lyeXAKnp3IFxWx6ZzFHh5t/xK4Ivd8sQemyRT6T49luTHgFfRew/hLnq3UIFT//0vr1usLPU7ukv1AH6G3suqB4H7u8e19K6j3UnvF/RO4Bn12Lvru+ldl/s8ML3UPYzQyyy964Qnx27te84NXS+H6T7pMAmPhXqZN+fLPPZpmYk9LkOOzSrgb4EvAJ8FXrlcj003fh+9T/ncA7x40o8N8ELgc10vXwBu7MafS+8/01l6r0JOfprpid36bLf9uUvdw7CHtx+QpAZdsJdlJKllhrskNchwl6QGGe6S1CDDXZIaZLhLUoMMd0lq0P8D6WHrtuvTq0wAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106a62780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1069bb4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "thicks:  [1.89995422 1.89935737 1.9010134  1.89935737 1.89996033]\n",
      "agnles:  [ 2.32592539e+01 -5.14475153e+01  1.28093335e-03  5.14512692e+01\n",
      " -2.32551960e+01]\n"
     ]
    },
    {
     "data": {
      "image/png": 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8vt5ld4uVCzbcu7OkdwGHquov+jb130rhOuBjfeO/2n0C4KXAd05evllqC/WSZAvwB8DWqvpe31P2Adu7TwCsBzYAnzmfNS9kUC9V9fmqurSqLquqy+j9Q7uyqr7OBB8XOO3v2UfpXd8lyeXAKnp3IFxWx6ZzFHh5t/xK4Ivd8sQemyRT6T49luTHgFfRew/hLnq3UIFT//0vr1usLPU7ukv1AH6G3suqB4H7u8e19K6j3UnvF/RO4Bn12Lvru+ldl/s8ML3UPYzQyyy964Qnx27te84NXS+H6T7pMAmPhXqZN+fLPPZpmYk9LkOOzSrgb4EvAJ8FXrlcj003fh+9T/ncA7x40o8N8ELgc10vXwBu7MafS+8/01l6r0JOfprpid36bLf9uUvdw7CHtx+QpAZdsJdlJKllhrskNchwl6QGGe6S1CDDXZIaZLhLUoMMd0lq0P8D6WHrtuvTq0wAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106b96b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106fcf518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "thicks:  [2.07053812 2.07225969 2.06913146 2.07222393 2.07129558]\n",
      "agnles:  [ 22.76459745 -51.1675197   -0.19097204  50.51257774 -23.48552943]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106b8aac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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RPIgsW5aNQnwTxsopYvRnfVqtVszMzJRrJJ9j9b9izOqtmA+5/vosH7JsGZx5ZjY68fe3b5IeiIhWr3q+RUo/2ld6+KIls3paKB/iILJkHEj60eniRP8PaVYvzocMjQNJP3xxolm9OR8yVA4k/fDFiWb11H59SB5EnA8ZKAeSfvniRLN6cT6kNhxIzKx5nA+pFQcSM2uG4s0WL77Y+ZAacSAxs/pqDx4HDoCUBRDnQ2rDgeRI+OJEs6VXzIG0B4+JiazM+ZBacCBZLF+caLb02nMg7cHDt3+vFQeSxfLFiWZLY6EcyIoVDh415kCyWL440ay84vQwwC23wE03wcGDzoE0kAPJYvniRLMjNz19eNDIp6sOHID8BrLOgTSOA8mR8MWJZv1rn7L65S/ng0Z+DUj+XvI0VgM5kJhZdfqZsioGjaOOyl7z0cl73uPrQRrIgaQMLwO2cVYcaTzzzOHXevSasioGDfD3qOEcSI6UlwHbOOkWNIorq5Ytm0+SL3bKyt+dRqskkEjaBPw52WNxvxARn2zbvwK4BXg98Azwjoj4Ydq3DTgfOAR8MCJ2LtRmeo77DuA44FvAuyPiQBX9WBQvA7ZR0j4ltZigAfOvxRGHp6zGRulAImkCuBb4PWAOuF/SVEQ8Uqh2PvBsRJwq6VzgauAdktaTPb/9NOAkYJekV6ZjurV5NXBNROyQdF1q+/Nl+7FoXgZsTbVQHiMPAL/6VX9BI3/f6VoP8JTVmKhiRLIBmI2IRwEk7QA2A8VAshm4PG3fAXxWklL5jojYDzwmaTa1R6c2JX0feBPwrlTn5tTu4AOJlwFbEyw2j9E+JdVP0Mjb7vQ98PdiLFQRSFYDjxfezwGnd6sTEQclPQesTOX3tB27Om13anMl8LOIONih/mEkbQW2AkxOTi6uR/3yMmCrkyryGPkqquKIpN+gYWOrikCiDmXRZ51u5csWWf+FhRHbge0ArVarYx2zxlps0ID+8xhweNsOGtZDFYFkDji58H4N8ESXOnOSlgPHAPt6HNup/KfAyyQtT6OSTr9rOLwU2JZK2aCRv19MHsP/D9siVBFI7gfWpdVUPyZLnr+rrc4UsAWYBs4B7o6IkDQFfFnSp8mS7euA+8hGHi9oMx3zjdTGjtTmVyvoQzleCmxVW+gGhkcSNJzHsCVUOpCknMdFwE6ypbo3RsTDkq4AZiJiCrgBuDUl0/eRBQZSvdvJEvMHgQsj4hBApzbTr/wosEPSnwDfTm0Pl5cCWxV6PcQJygcNsyWgiNFPH7RarZiZmVm6X+ARiZXRfiPDTg9xOnTIQcMGTtIDEdHqVc9XtlfBS4GtX93yHcUbGXZ7iJODhtWUA0lVvBTYuukn3+G731qDOZCYLaVuzx2HzstxfSsRayAHkqp5GbDluj13HPwIWRspDiRVctLd+n3uuPMdNkIcSKrkZcDjq9fKKz933EaYA0mVfEfg8bLQI2T93HEbIw4kVfIy4PHRKYnulVc2phxIquZlwKMtH4Xs3Ts/jdntEbL+/8DGhAPJUvIKrtHRngOZmIDl6etTvGjQn7WNIQeSpeIVXM23UA4E4IILYHLSwcPGngPJUvEKrmbrlQM5+mhPX5klnR4gZVXIV3BNTHgFV9MULyTMb5Y4MTH/Wb7vfR5hmhV4RLJUvIKrmfKRSLcLCf1Zmr2AA8lS8gqu5mhfjeULCc365kAyCF69VV+9VmM5iJj1VCqQSDoOuA1YC/wQ+BcR8WyHeluAf5/e/klE3JzKXw98EXgxcCfwofQ43Y7tSnoVcBPwOuDSiPizMuc/EF69VV/5Z+PVWGallE22XwLcFRHrgLvS+8OkoPBx4HRgA/BxScem3Z8HtpI9q30dsKlHu/uADwL1DyC5Tqu3bLimp+Gqq7KRyIEDnVdjbdvmIGLWp7JTW5uBM9L2zcBusmeqF50FfD0i9gFI+jqwSdJu4KURMZ3KbwHeBnytW7sR8RTwlKR/WvK8B8f336qX4gixOI3lK9LNjljZQPKKiHgSICKelPTyDnVWA48X3s+lstVpu72833abwau36qP9+SDgaSyzCvQMJJJ2ASd02HVpn79DHcpigfJKSNpKNm3G5ORkVc0emeLqLSfeB2uh54P4okKzSvQMJBFxZrd9kn4i6cQ0ajgReKpDtTnmp6kA1pBNVc2l7WL5E2m7n3Z7nfd2YDtAq9WqLECV4sT7YHV7zK2X9ZpVqmyyfQrYkra3AF/tUGcn8BZJx6Yk+1uAnWnq6heS3iBJwHmF4/tpt3mceB+M9mR6+9XpK1Y4iJhVqGyO5JPA7ZLOB/YCbweQ1ALeHxHvjYh9kj4B3J+OuSJPvAMfYH7579fSz0LtngDMAC8Fnpd0MbA+In5esh+D4cT70uuWTPcdes2WjCLqMeuzlFqtVszMzAz7NDLFOXv/UatWnkzftWt+BOJkutkRk/RARLR61fOV7YOW/zFzrqRane6R5WS62UA4kAyDbzFfHd8jy2zoHEiGwbmS8nyPLLPacCAZBl+kWI7vkWVWKw4kw+KLFBevfRrLTyw0qwUHkmHzRYr98T2yzGrLgWTYnHjvzffIMqs1B5Jha0+8r1yZXZXtP5AZL+s1qz0HkmErJt7zGwt6msvLes0axIGkDvLE+1VXeZoLFr7NiYOIWe04kNTJuF9f0j4KOXQoK3c+xKzWHEjqpH2aK7878Kj/8ex1caHzIWa15kBSN+N2Ly5fXGjWeA4kdTQOS4J9caHZyHAgqaNRXxLsiwvNRooDSR2N8pJgX1xoNnIcSOqq05Lg/fuzP8JNWwJbfJjXxRf74kKzEVPqme2SjpP0dUk/SK/Hdqm3JdX5gaQthfLXS/qupFlJf5Ge3d61XUl/KOk76ef/SPrNMuffCPk017Jl2R/fXbuyaaHp6WGfWX/yaazLLoMLLzw8iJx5ZvNHWGZWLpAAlwB3RcQ64K70/jCSjgM+DpwObAA+Xgg4nwe2AuvSz6Ye7T4G/E5EvAb4BLC95PnXXz7NdeaZ88HkwIFsuexVV9U7oBSnsQ4dmn/87cQErFjRvJGVmXVU6pntkvYAZ0TEk5JOBHZHxD9qq/POVOd96f1/Anann29ExKva6/XZ7rHA9yJida/zrNUz249Ue4Jayq65qFveZKFprBUr4DOf8bPqzRpiUM9sf0VEPAmQ/ui/vEOd1cDjhfdzqWx12m4v77fd84GvlTz/5igm4Pfuheuvr1fepP2iQikLIL5HltnI6xlIJO0CTuiw69I+f4c6lMUC5b0blH6XLJC8cYE6W8mmzZicnOyn2frLE/DT03DzzfP/2t+1C775zcGPTNpHH8WLCpctmx85+R5ZZiOtZyCJiDO77ZP0E0knFqagnupQbQ44o/B+Ddm01lzaLpY/kba7tivpNcAXgLMj4pkFzns7KYfSarWOfP6ujvLRyeWXZ0GkmDdZ6icttgePAwfmRx/Fiwo9jWU2NspObU0BW4BPptevdqizE/iPhQT7W4BtEbFP0i8kvQG4FzgP+MuF2pU0CXwFeHdE/E3Jc2+2jRuzQPLNb87nTYr3qqr6wr5eU1f56MMXFZqNnbLJ9pXA7cAksBd4ewoQLeD9EfHeVO89wL9Lh10ZETel8hbwReDFZPmOP4qIWKDdLwB/APwotXWwn0TQSCTbuyneaiTPm0D2R/1FLzp8VACLG7H0M3X1/PPZ1JVHH2Yjp99ke6lA0hQjHUhynW5+WPxjX1zpVRw1wHywKAacbqMP6BykHDzMRo4DScFYBBJYePpJaW1DMY9x1FHZ669+NT9FtXx5Vla8kWJ7QPLUldlYGNTyX6uTfFXXeee9MCGej0jyABGRBRCYDxjPP//CMifOzawHB5JRlAcUgFe/ej4vAi98gFS3EclSJe3NbOQ4kIy6YlDJ3+cjlmICvj1HstTLiM1sZDhHYmZmHfWbIyl700YzMxtzDiRmZlaKA4mZmZXiQGJmZqU4kJiZWSkOJGZmVspYLP+V9DTzN3qsq+OBnw77JCrivtTTKPUFRqs/de3LP4iIVb0qjUUgaQJJM/2s124C96WeRqkvMFr9aXpfPLVlZmalOJCYmVkpDiT1sX3YJ1Ah96WeRqkvMFr9aXRfnCMxM7NSPCIxM7NSHEgGQNLJkr4h6fuSHpb0oVR+nKSvS/pBej02lUvSX0ialfQdSa8bbg/mLdCXT0n663S+/03SywrHbEt92SPprOGd/Qt1609h/7+VFJKOT+8b99mkfX+U/vs/LOlPC+W1/GwW+P/stZLukfSgpBlJG1J5nT+XF0m6T9JDqS//IZWfIune9P2/TdLRqXxFej+b9q8d5vn3JSL8s8Q/wInA69L23wf+BlgP/ClwSSq/BLg6bb8V+Bog4A3AvcPuQx99eQuwPJVfXejLeuAhYAVwCvB/gYlh96NXf9L7k4GdZNcgHd/gz+Z3gV3AirTv5XX/bBboy18BZxc+i90N+FwEvCRtHwXcm87xduDcVH4d8IG0/a+A69L2ucBtw+5Drx+PSAYgIp6MiG+l7V8A3wdWA5uBm1O1m4G3pe3NwC2RuQd4maQTB3zaHXXrS0T8VUQcTNXuAdak7c3AjojYHxGPAbPAhkGfdzcLfDYA1wAfAYqJxMZ9NsAHgE9GxP6076l0SG0/mwX6EsBLU7VjgCfSdp0/l4iIv01vj0o/AbwJuCOVt3//878LdwBvlqQBne4RcSAZsDRM/S2yf5W8IiKehOyLA7w8VVsNPF44bI75P2610daXoveQ/esQGtIXOLw/kn4f+HFEPNRWrRH9aftsXgn8kzRN8j8l/Xaq1sS+XAx8StLjwJ8B21K1WvdF0oSkB4GngK+Tjf5+VvjHV/F8f92XtP85YOVgz3hxHEgGSNJLgP8KXBwRP1+oaoeyWi2v69YXSZcCB4Ev5UUdDq9VX+Dw/pCd/6XAxzpV7VBWq/50+GyWA8eSTaf8MXB7+hduE/vyAeDDEXEy8GHghrxqh8Nr05eIOBQRryUbqW8A/nGnaum11n3pxIFkQCQdRfaF+FJEfCUV/yQffqfXfMphjmx+PreG+SH80HXpC5K2AP8M+MNIE7zUvC/QsT//kCxn8JCkH5Kd87cknUDN+9Pls5kDvpKmWO4Dnie7t1MT+7IFyLf/C/NTcbXuSy4ifgbsJgvqL5O0PO0qnu+v+5L2HwPsG+yZLo4DyQCkf/3dAHw/Ij5d2DVF9sUgvX61UH5eWonyBuC5fAps2Lr1RdIm4KPA70fE3xUOmQLOTStRTgHWAfcN8pwX0qk/EfHdiHh5RKyNiLVkX+zXRcT/o4GfDfDfyebjkfRK4GiyGwTW9rNZoC9PAL+Ttt8E/CBt1/lzWaW0ilHSi4EzyXI+3wDOSdXav//534VzgLsL/zCrp2Fn+8fhB3gj2dD0O8CD6eetZPOed5F9Ge4Cjkv1BVxLNo/6XaA17D700ZdZsnndvOy6wjGXpr7sIa24qctPt/601fkh86u2mvjZHA38Z+B7wLeAN9X9s1mgL28EHiBbbXYv8PoGfC6vAb6d+vI94GOp/DfIAvcs2egqX1X3ovR+Nu3/jWH3odePr2w3M7NSPLVlZmalOJCYmVkpDiRmZlaKA4mZmZXiQGJmZqU4kJiZWSkOJGZmVooDiZmZlfL/AVLBenuvH7GyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10709f320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "thicks:  [1.8697344  1.86826627 1.87293644 1.86827    1.86953201]\n",
      "agnles:  [ 22.85641607 -51.26801509  -0.20904587  50.61933754 -23.56555016]\n"
     ]
    },
    {
     "data": {
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8vt5ld4uVCzbcu7OkdwGHquov+jb130rhOuBjfeO/2n0C4KXAd05evllqC/WSZAvwB8DWqvpe31P2Adu7TwCsBzYAnzmfNS9kUC9V9fmqurSqLquqy+j9Q7uyqr7OBB8XOO3v2UfpXd8lyeXAKnp3IFxWx6ZzFHh5t/xK4Ivd8sQemyRT6T49luTHgFfRew/hLnq3UIFT//0vr1usLPU7ukv1AH6G3suqB4H7u8e19K6j3UnvF/RO4Bn12Lvru+ldl/s8ML3UPYzQyyy964Qnx27te84NXS+H6T7pMAmPhXqZN+fLPPZpmYk9LkOOzSrgb4EvAJ8FXrlcj003fh+9T/ncA7x40o8N8ELgc10vXwBu7MafS+8/01l6r0JOfprpid36bLf9uUvdw7CHtx+QpAZdsJdlJKllhrskNchwl6QGGe6S1CDDXZIaZLhLUoMMd0lq0P8D6WHrtuvTq0wAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1069d6b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x103b8b0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-14-31d7b2239639>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      2\u001b[0m                   22.9, -50, 0,  50,  -22.9])\n\u001b[1;32m      3\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0mtmp\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mopt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbasinhopping\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mevaluate_HWP\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mparams\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mniter\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m100\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mT\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m5.0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstepsize\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1.0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/scipy/optimize/_basinhopping.py\u001b[0m in \u001b[0;36mbasinhopping\u001b[0;34m(func, x0, niter, T, stepsize, minimizer_kwargs, take_step, accept_test, callback, interval, disp, niter_success, seed)\u001b[0m\n\u001b[1;32m    640\u001b[0m                \" successfully\"]\n\u001b[1;32m    641\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mniter\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 642\u001b[0;31m         \u001b[0mnew_global_min\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbh\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mone_cycle\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    643\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    644\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcallback\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcollections\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mCallable\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/scipy/optimize/_basinhopping.py\u001b[0m in \u001b[0;36mone_cycle\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    149\u001b[0m         \u001b[0mnew_global_min\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    150\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 151\u001b[0;31m         \u001b[0maccept\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mminres\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_monte_carlo_step\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    152\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    153\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0maccept\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/scipy/optimize/_basinhopping.py\u001b[0m in \u001b[0;36m_monte_carlo_step\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    104\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    105\u001b[0m         \u001b[0;31m# do a local minimization\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 106\u001b[0;31m         \u001b[0mminres\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mminimizer\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx_after_step\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    107\u001b[0m         \u001b[0mx_after_quench\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mminres\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    108\u001b[0m         \u001b[0menergy_after_quench\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mminres\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/scipy/optimize/_basinhopping.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self, x0)\u001b[0m\n\u001b[1;32m    280\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mminimizer\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    281\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 282\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mminimizer\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfunc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    283\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    284\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/scipy/optimize/_minimize.py\u001b[0m in \u001b[0;36mminimize\u001b[0;34m(fun, x0, args, method, jac, hess, hessp, bounds, constraints, tol, callback, options)\u001b[0m\n\u001b[1;32m    479\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0m_minimize_cg\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mjac\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcallback\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0moptions\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    480\u001b[0m     \u001b[0;32melif\u001b[0m \u001b[0mmeth\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'bfgs'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 481\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0m_minimize_bfgs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mjac\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcallback\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0moptions\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    482\u001b[0m     \u001b[0;32melif\u001b[0m \u001b[0mmeth\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'newton-cg'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    483\u001b[0m         return _minimize_newtoncg(fun, x0, args, jac, hess, hessp, callback,\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/scipy/optimize/optimize.py\u001b[0m in \u001b[0;36m_minimize_bfgs\u001b[0;34m(fun, x0, args, jac, callback, gtol, norm, eps, maxiter, disp, return_all, **unknown_options)\u001b[0m\n\u001b[1;32m    962\u001b[0m             \u001b[0malpha_k\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mold_fval\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mold_old_fval\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgfkp1\u001b[0m \u001b[0;34m=\u001b[0m\u001b[0;31m \u001b[0m\u001b[0;31m\\\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    963\u001b[0m                      _line_search_wolfe12(f, myfprime, xk, pk, gfk,\n\u001b[0;32m--> 964\u001b[0;31m                                           old_fval, old_old_fval, amin=1e-100, amax=1e100)\n\u001b[0m\u001b[1;32m    965\u001b[0m         \u001b[0;32mexcept\u001b[0m \u001b[0m_LineSearchError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    966\u001b[0m             \u001b[0;31m# Line search failed to find a better solution.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/scipy/optimize/optimize.py\u001b[0m in \u001b[0;36m_line_search_wolfe12\u001b[0;34m(f, fprime, xk, pk, gfk, old_fval, old_old_fval, **kwargs)\u001b[0m\n\u001b[1;32m    781\u001b[0m     ret = line_search_wolfe1(f, fprime, xk, pk, gfk,\n\u001b[1;32m    782\u001b[0m                              \u001b[0mold_fval\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mold_old_fval\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 783\u001b[0;31m                              **kwargs)\n\u001b[0m\u001b[1;32m    784\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    785\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mret\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mextra_condition\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/scipy/optimize/linesearch.py\u001b[0m in \u001b[0;36mline_search_wolfe1\u001b[0;34m(f, fprime, xk, pk, gfk, old_fval, old_old_fval, args, c1, c2, amax, amin, xtol)\u001b[0m\n\u001b[1;32m     99\u001b[0m     stp, fval, old_fval = scalar_search_wolfe1(\n\u001b[1;32m    100\u001b[0m             \u001b[0mphi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mderphi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mold_fval\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mold_old_fval\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mderphi0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 101\u001b[0;31m             c1=c1, c2=c2, amax=amax, amin=amin, xtol=xtol)\n\u001b[0m\u001b[1;32m    102\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    103\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mstp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfc\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgc\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfval\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mold_fval\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgval\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/scipy/optimize/linesearch.py\u001b[0m in \u001b[0;36mscalar_search_wolfe1\u001b[0;34m(phi, derphi, phi0, old_phi0, derphi0, c1, c2, amax, amin, xtol)\u001b[0m\n\u001b[1;32m    173\u001b[0m             \u001b[0malpha1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mstp\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    174\u001b[0m             \u001b[0mphi1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mphi\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 175\u001b[0;31m             \u001b[0mderphi1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mderphi\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    176\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    177\u001b[0m             \u001b[0;32mbreak\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/scipy/optimize/linesearch.py\u001b[0m in \u001b[0;36mderphi\u001b[0;34m(s)\u001b[0m\n\u001b[1;32m     88\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     89\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mderphi\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 90\u001b[0;31m         \u001b[0mgval\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfprime\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mxk\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0ms\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mpk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0mnewargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     91\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mgradient\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     92\u001b[0m             \u001b[0mgc\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/scipy/optimize/optimize.py\u001b[0m in \u001b[0;36mfunction_wrapper\u001b[0;34m(*wrapper_args)\u001b[0m\n\u001b[1;32m    290\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mfunction_wrapper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mwrapper_args\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    291\u001b[0m         \u001b[0mncalls\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 292\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mfunction\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mwrapper_args\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    293\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    294\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mncalls\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfunction_wrapper\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/scipy/optimize/optimize.py\u001b[0m in \u001b[0;36mapprox_fprime\u001b[0;34m(xk, f, epsilon, *args)\u001b[0m\n\u001b[1;32m    701\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    702\u001b[0m     \"\"\"\n\u001b[0;32m--> 703\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0m_approx_fprime_helper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mxk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mepsilon\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    704\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    705\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/scipy/optimize/optimize.py\u001b[0m in \u001b[0;36m_approx_fprime_helper\u001b[0;34m(xk, f, epsilon, args, f0)\u001b[0m\n\u001b[1;32m    641\u001b[0m         \u001b[0mei\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1.0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    642\u001b[0m         \u001b[0md\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mepsilon\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mei\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 643\u001b[0;31m         \u001b[0mgrad\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mxk\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0md\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mf0\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0md\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    644\u001b[0m         \u001b[0mei\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m0.0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    645\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mgrad\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/scipy/optimize/optimize.py\u001b[0m in \u001b[0;36mfunction_wrapper\u001b[0;34m(*wrapper_args)\u001b[0m\n\u001b[1;32m    290\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mfunction_wrapper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mwrapper_args\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    291\u001b[0m         \u001b[0mncalls\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 292\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mfunction\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mwrapper_args\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    293\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    294\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mncalls\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfunction_wrapper\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-13-400ca957d486>\u001b[0m in \u001b[0;36mevaluate_HWP\u001b[0;34m(params)\u001b[0m\n\u001b[1;32m     22\u001b[0m         \u001b[0mwavelength\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mwavelengths\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     23\u001b[0m         \u001b[0mTF\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmake_HWP_transfer_matrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mthicks\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mthetas\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mno\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mne\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mwavelengths\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 24\u001b[0;31m         \u001b[0mangs\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mExo\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mEyo\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msim_rot_HWP\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mTF\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mn_angles\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     25\u001b[0m         \u001b[0mmod_eff\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mphase\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmod_eff_and_phase\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mExo\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     26\u001b[0m         \u001b[0mmod_effs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmod_eff\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-4-6a739fc2b1f3>\u001b[0m in \u001b[0;36msim_rot_HWP\u001b[0;34m(TF, nsamps)\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0mi\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m     \u001b[0;32mwhile\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m<\u001b[0m\u001b[0mnsamps\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m         \u001b[0mTF_tmp\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mrotate_HWP\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mTF\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mangs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      8\u001b[0m         \u001b[0mEx_out\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mTF_tmp\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[0m\n\u001b[1;32m      9\u001b[0m         \u001b[0mEy_out\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mTF_tmp\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-3-7c31d5332d5b>\u001b[0m in \u001b[0;36mrotate_HWP\u001b[0;34m(TF, psi)\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mrotate_HWP\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mTF\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mpsi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m     Mrot = np.matrix([[np.cos(psi),np.sin(psi)],\n\u001b[0;32m----> 3\u001b[0;31m                       [-np.sin(psi),np.cos(psi)]])\n\u001b[0m\u001b[1;32m      4\u001b[0m     \u001b[0mout\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmatmul\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mTF\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mMrot\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0mout\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmatmul\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtranspose\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mMrot\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mout\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/numpy/matrixlib/defmatrix.py\u001b[0m in \u001b[0;36m__new__\u001b[0;34m(subtype, data, dtype, copy)\u001b[0m\n\u001b[1;32m    253\u001b[0m         ret = N.ndarray.__new__(subtype, shape, arr.dtype,\n\u001b[1;32m    254\u001b[0m                                 \u001b[0mbuffer\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0marr\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 255\u001b[0;31m                                 order=order)\n\u001b[0m\u001b[1;32m    256\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mret\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    257\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/numpy/matrixlib/defmatrix.py\u001b[0m in \u001b[0;36m__array_finalize__\u001b[0;34m(self, obj)\u001b[0m\n\u001b[1;32m    256\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mret\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    257\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 258\u001b[0;31m     \u001b[0;32mdef\u001b[0m \u001b[0m__array_finalize__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mobj\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    259\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_getitem\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    260\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mobj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmatrix\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mobj\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_getitem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;32mreturn\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "params = np.array([ 1.9,  1.9 ,  1.9,  1.9 ,1.9,\n",
    "                  22.9, -50, 0,  50,  -22.9])\n",
    "\n",
    "tmp = opt.basinhopping(evaluate_HWP, params, niter=100, T=5.0, stepsize=1.0)\n",
    "             \n",
    "             \n",
    "print(tmp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2. 2. 2. 2. 2.]\n",
      "[ 23.2 -51.4   0.   51.4 -23.2]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jeffmcm/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:17: RuntimeWarning: divide by zero encountered in true_divide\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106ce6518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9999551706583251\n",
      "0.9999551706583251\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106b8a278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106af4320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## fiducial SO design\n",
    "no = 3.05\n",
    "ne = 3.35\n",
    "thick_HWP = 2.0\n",
    "thicks = np.array([ 1,1,1,1,1])* thick_HWP \n",
    "\n",
    "psi_A = 23.2\n",
    "psi_B = 51.4\n",
    "thetas = np.array([psi_A, -psi_B, 0,  psi_B,  -psi_A])*np.pi/180. \n",
    "\n",
    "print(thicks)\n",
    "print(thetas*180./np.pi)\n",
    "\n",
    "\n",
    "## setup the sim\n",
    "freq_GHZ = np.arange(600)  ## from 70 to 170 GHz \n",
    "wavelengths = 1./freq_GHZ *300.  ## convert to mm\n",
    "\n",
    "mod_effs = np.zeros(np.shape(wavelengths))\n",
    "phases = np.zeros(np.shape(wavelengths))\n",
    "\n",
    "## make the transfer funciton\n",
    "i = 0\n",
    "while (i < np.size(wavelengths)):\n",
    "    wavelength = wavelengths[i]\n",
    "    TF = make_HWP_transfer_matrix(thicks,thetas,no,ne,wavelengths[i])\n",
    "    angs,Exo,Eyo = sim_rot_HWP(TF,n_angles)\n",
    "    mod_eff,phase = mod_eff_and_phase(Exo)\n",
    "    mod_effs[i] = mod_eff\n",
    "    phases[i] = phase\n",
    "    i +=1\n",
    "\n",
    "\n",
    "\n",
    "plt.plot(freq_GHZ,mod_effs) \n",
    "#plt.plot(freq_GHZ,mod_effs_single)\n",
    "plt.ylim(0.9,1.0)\n",
    "plt.xlim(175,325)\n",
    "plt.plot(np.array([1,1])*195,np.array([0,1]),\"r\")\n",
    "plt.plot(np.array([1,1])*248,np.array([0,1]),\"r\")\n",
    "plt.plot(np.array([1,1])*250,np.array([0,1]),\"g\")\n",
    "plt.plot(np.array([1,1])*305,np.array([0,1]),\"g\")\n",
    "#plt.plot(np.array([1,1])*195,np.array([0,1]),\"b\")\n",
    "#plt.plot(np.array([1,1])*250,np.array([0,1]),\"b\")\n",
    "plt.show()\n",
    "\n",
    "print(np.mean(mod_effs[np.where(np.logical_and(freq_GHZ>190,freq_GHZ<310))]))\n",
    "print(np.mean(mod_effs[np.where(np.logical_and(freq_GHZ>190,freq_GHZ<310))]))\n",
    "\n",
    "plt.plot(freq_GHZ,mod_effs) \n",
    "#plt.plot(freq_GHZ,mod_effs_single)\n",
    "plt.ylim(0.0,1.0)\n",
    "plt.xlim(175,325)\n",
    "plt.plot(np.array([1,1])*195,np.array([0,1]),\"r\")\n",
    "plt.plot(np.array([1,1])*248,np.array([0,1]),\"r\")\n",
    "plt.plot(np.array([1,1])*250,np.array([0,1]),\"g\")\n",
    "plt.plot(np.array([1,1])*305,np.array([0,1]),\"g\")\n",
    "#plt.plot(np.array([1,1])*195,np.array([0,1]),\"b\")\n",
    "#plt.plot(np.array([1,1])*250,np.array([0,1]),\"b\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "plt.plot(freq_GHZ,phases - np.mean(phases[50:150])) \n",
    "plt.xlim(175,325)\n",
    "plt.ylim(np.array([-1,1])*0.1 )\n",
    "plt.plot(np.array([1,1])*195,np.array([-1,1]),\"r\")\n",
    "plt.plot(np.array([1,1])*248,np.array([-1,1]),\"r\")\n",
    "plt.plot(np.array([1,1])*250,np.array([-1,1]),\"g\")\n",
    "plt.plot(np.array([1,1])*305,np.array([-1,1]),\"g\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "#plt.plot(freq_GHZ,phases-np.mean(phases))\n",
    "\n",
    "#phase_angle_s  = np.unwrap(mod_phsses_single*4.*np.pi/180)/4. * 180/np.pi\n",
    "\n",
    "#plt.plot(freq_GHZ,phase_angle_s)\n",
    "#plt.show() \n",
    "\n",
    "#plt.plot(freq_GHZ,phases)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106ff5978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9999551706583251\n",
      "0.9999551706583251\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1070231d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106c11ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "\n",
    "plt.plot(freq_GHZ,mod_effs) \n",
    "#plt.plot(freq_GHZ,mod_effs_single)\n",
    "plt.ylim(0.9,1.0)\n",
    "plt.xlim(0,600)\n",
    "plt.plot(np.array([1,1])*195,np.array([0,1]),\"r\")\n",
    "plt.plot(np.array([1,1])*248,np.array([0,1]),\"r\")\n",
    "plt.plot(np.array([1,1])*250,np.array([0,1]),\"g\")\n",
    "plt.plot(np.array([1,1])*305,np.array([0,1]),\"g\")\n",
    "#plt.plot(np.array([1,1])*195,np.array([0,1]),\"b\")\n",
    "#plt.plot(np.array([1,1])*250,np.array([0,1]),\"b\")\n",
    "plt.show()\n",
    "\n",
    "print(np.mean(mod_effs[np.where(np.logical_and(freq_GHZ>190,freq_GHZ<310))]))\n",
    "print(np.mean(mod_effs[np.where(np.logical_and(freq_GHZ>190,freq_GHZ<310))]))\n",
    "\n",
    "plt.plot(freq_GHZ,mod_effs) \n",
    "#plt.plot(freq_GHZ,mod_effs_single)\n",
    "plt.ylim(0.0,1.0)\n",
    "plt.xlim(0,600)\n",
    "plt.plot(np.array([1,1])*195,np.array([0,1]),\"r\")\n",
    "plt.plot(np.array([1,1])*248,np.array([0,1]),\"r\")\n",
    "plt.plot(np.array([1,1])*250,np.array([0,1]),\"g\")\n",
    "plt.plot(np.array([1,1])*305,np.array([0,1]),\"g\")\n",
    "#plt.plot(np.array([1,1])*195,np.array([0,1]),\"b\")\n",
    "#plt.plot(np.array([1,1])*250,np.array([0,1]),\"b\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "plt.plot(freq_GHZ,phases - np.mean(phases[50:150])) \n",
    "plt.xlim(0,600)\n",
    "plt.ylim(np.array([-1,1])*0.1 )\n",
    "plt.plot(np.array([1,1])*195,np.array([-1,1]),\"r\")\n",
    "plt.plot(np.array([1,1])*248,np.array([-1,1]),\"r\")\n",
    "plt.plot(np.array([1,1])*250,np.array([-1,1]),\"g\")\n",
    "plt.plot(np.array([1,1])*305,np.array([-1,1]),\"g\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "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": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}