test_pi_flux.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# API"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "source": [
    "import numpy as np\n",
    "import scipy.sparse as sp\n",
    "import scipy.sparse.linalg as sla\n",
    "import scipy.linalg as la\n",
    "import scipy.stats\n",
    "import matplotlib.pyplot as plt\n",
    "import time\n",
    "import pickle\n",
    "from copy import copy\n",
    "# %load_ext line_profiler"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "source": [
    "plt.rcParams['text.usetex']=True\n",
    "plt.rcParams['font.family']='serif'\n",
    "plt.rcParams['font.size']=9\n",
    "plt.rcParams['axes.titlesize']=plt.rcParams['font.size']\n",
    "plt.rcParams['figure.figsize']=(6.8,4)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "source": [
    "# ipcluster start --engines=MPI -n 4\n",
    "import ipyparallel as ipp\n",
    "rc = ipp.Client()\n",
    "rc[:].execute(\"from pi_flux import *\")\n",
    "rc[:].execute(\"import numpy as np\")"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "<AsyncResult: execute>"
      ]
     },
     "metadata": {},
     "execution_count": 143
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "source": [
    "# %%writefile pi_flux.py\n",
    "import numpy as np\n",
    "import scipy.linalg as la\n",
    "import numpy.linalg as nla\n",
    "import numpy.matlib\n",
    "\n",
    "class Params:\n",
    "    def __init__(self,\n",
    "            Lx=16,\n",
    "            Ly=16,\n",
    "            t=1,\n",
    "            Delta=1,\n",
    "            m=0,\n",
    "            bcx=-1,\n",
    "            bcy=1,\n",
    "            T=0,\n",
    "            history=False,\n",
    "            ):\n",
    "        self.Lx=Lx\n",
    "        self.Ly=Ly\n",
    "        self.t = t\n",
    "        self.Delta = Delta\n",
    "        self.m = m\n",
    "        self.bcx = bcx\n",
    "        self.bcy = bcy\n",
    "        self.T = T\n",
    "        self.history = history\n",
    "        if Lx<np.inf and Ly<np.inf:\n",
    "            hopx = np.diag(np.ones(Lx-1), -1)\n",
    "            hopx[0, -1] = bcx\n",
    "            hopy = np.diag(np.ones(Ly-1), -1)\n",
    "            hopy[0, -1] = bcy\n",
    "            hopxmat = np.kron(np.eye(Ly),hopx)\n",
    "            hopymat = np.kron(hopy,np.eye(Lx))\n",
    "            hop11mat= np.kron(hopy,hopx)\n",
    "            hop1m1mat=np.kron(hopy.T,hopx)\n",
    "            onsitemat = np.eye(Lx*Ly)\n",
    "            H00=np.array([[m,-t,-1j*Delta,t],\n",
    "                            [-t,-m,t,1j*Delta],\n",
    "                            [1j*Delta,t,m,t],\n",
    "                            [t,-1j*Delta,t,-m]])\n",
    "            H10=np.array([[0,-t,1j*Delta,0],\n",
    "                            [0,0,0,0],\n",
    "                            [0,0,0,0],\n",
    "                            [0,1j*Delta,t,0]])\n",
    "            H01=np.array([[0,0,1j*Delta,t],\n",
    "                            [0,0,t,-1j*Delta],\n",
    "                            [0,0,0,0],\n",
    "                            [0,0,0,0]])\n",
    "            H11=np.array([[0,0,-1j*Delta,0],\n",
    "                            [0,0,0,0],\n",
    "                            [0,0,0,0],\n",
    "                            [0,0,0,0]])\n",
    "            H1m1=np.array([[0,0,0,0],\n",
    "                            [0,0,0,0],\n",
    "                            [0,0,0,0],\n",
    "                            [0,-1j*Delta,0,0]])\n",
    "            H00mat=np.kron(onsitemat,H00)\n",
    "            H10mat=np.kron(hopxmat,H10)\n",
    "            H01mat=np.kron(hopymat,H01)\n",
    "            H11mat=np.kron(hop11mat,H11)\n",
    "            H1m1mat=np.kron(hop1m1mat,H1m1)\n",
    "            self.Hamiltonian=H00mat+H10mat+H10mat.T.conj()+H01mat+H01mat.T.conj()+H11mat+H11mat.T.conj()+H1m1mat+H1m1mat.T.conj()\n",
    "\n",
    "    def bandstructure(self):\n",
    "        val, vec = nla.eigh(self.Hamiltonian)\n",
    "        sortindex = np.argsort(val)\n",
    "        self.val = val[sortindex]\n",
    "        self.vec = vec[:, sortindex]\n",
    "\n",
    "    def fermi_dist(self, energy, E_F):\n",
    "        if self.T == 0:\n",
    "            return np.heaviside(E_F-energy, 0)\n",
    "        else:\n",
    "            return 1/(1+np.exp((energy-E_F)/self.T))\n",
    "\n",
    "    def correlation_matrix(self, E_F=0):\n",
    "        '''\n",
    "        G_{ij}=<f_i^\\dagger f_j>\n",
    "        '''\n",
    "        if not (hasattr(self, 'val') and hasattr(self, 'vec')):\n",
    "            self.bandstructure()\n",
    "        occupancy_mat = np.matlib.repmat(self.fermi_dist(self.val, E_F), self.vec.shape[0], 1)\n",
    "        self.C_f = ((occupancy_mat*self.vec)@self.vec.T.conj())\n",
    "\n",
    "    def covariance_matrix(self, E_F=0):\n",
    "        '''\n",
    "        c.f. notes\n",
    "        Maybe differs by a minus sign\n",
    "        '''\n",
    "        if not hasattr(self, 'C_f'):\n",
    "            if self.Lx < np.inf and self.Ly<np.inf:\n",
    "                self.correlation_matrix()\n",
    "            else:\n",
    "                self.correlation_matrix_inf_fft()\n",
    "        G = self.C_f\n",
    "        Gamma_11 = 1j*(G-G.T)\n",
    "        Gamma_21 = -(np.eye(G.shape[0])-G-G.T)\n",
    "        Gamma_12 = -Gamma_21.T\n",
    "        Gamma_22 = -1j*(G.T-G)\n",
    "        Gamma = np.zeros((2*G.shape[0], 2*G.shape[0]), dtype=complex)\n",
    "        even = np.arange(2*G.shape[0])[::2]\n",
    "        odd = np.arange(2*G.shape[0])[1::2]\n",
    "        Gamma[np.ix_(even, even)] = Gamma_11\n",
    "        Gamma[np.ix_(even, odd)] = Gamma_12\n",
    "        Gamma[np.ix_(odd, even)] = Gamma_21\n",
    "        Gamma[np.ix_(odd, odd)] = Gamma_22\n",
    "        assert np.abs(np.imag(Gamma)).max() < 1e-10, \"Covariance matrix not real {:.5f}\".format(np.abs(np.imag(Gamma)).max())\n",
    "        self.C_m = np.real(Gamma-Gamma.T.conj())/2\n",
    "        self.C_m_history = [self.C_m]\n",
    "\n",
    "    def linearize_index(self, subregion, n, proj=False, k=2):\n",
    "        '''\n",
    "        If proj ==True, then the index used for projection operator will be returned\n",
    "        k, the size of measurement, is useful only when proj=True\n",
    "        n=8 ususally, for 4 atoms in one unit cell and 2 Majorana operator \n",
    "        '''\n",
    "        subregion_x, subregion_y = (subregion)\n",
    "        subregion_x = np.array(subregion_x)\n",
    "        subregion_y = np.array(subregion_y)\n",
    "        \n",
    "        X, Y = np.meshgrid(subregion_x, subregion_y)\n",
    "        if self.Ly<np.inf:\n",
    "            assert subregion_x.max()<self.Lx and subregion_y.max()<self.Ly, 'Range exceeds'\n",
    "            linear_index = ((X+Y*self.Lx).flatten('F'))\n",
    "        else:\n",
    "            assert subregion_x.max()<self.dxmax and subregion_y.max()<self.dymax, 'Range exceeds'\n",
    "            linear_index = ((X+Y*self.dxmax).flatten('F'))\n",
    "        if proj:\n",
    "            return sorted(np.concatenate([n*linear_index+i for i in range(0, n, k)]))\n",
    "        else:\n",
    "            return sorted(np.concatenate([n*linear_index+i for i in range(n)]))\n",
    "\n",
    "    def square_index(self, subregion):\n",
    "        '''\n",
    "        Convert indices in covariance matrix\n",
    "        '''\n",
    "        subregion=np.unique(np.array(subregion)//8)\n",
    "        if self.Lx<np.inf and self.Ly<np.inf:\n",
    "            return subregion%self.Lx,subregion//self.Lx\n",
    "        else:\n",
    "            return subregion%self.dxmax,subregion//self.dxmax\n",
    "\n",
    "    def c_subregion_f(self, subregion, linear=True):\n",
    "        '''\n",
    "        subregion: [subregoin_x, subregion_y] index of unit cell\n",
    "        '''\n",
    "        if not hasattr(self, 'C_f'):\n",
    "            self.correlation_matrix()\n",
    "        try:\n",
    "            subregion = list(subregion)\n",
    "        except:\n",
    "            raise ValueError(\"The subregion is ill-defined\"+subregion)\n",
    "\n",
    "        if len(subregion) == 2:\n",
    "            if isinstance(subregion[0], int) and isinstance(subregion[1], int):\n",
    "                linear = True\n",
    "            elif (not isinstance(subregion[0], int)) and (not isinstance(subregion[1], int)):\n",
    "                linear = False\n",
    "            else:\n",
    "                raise ValueError('Illegal subregion')\n",
    "        else:\n",
    "            linear = True\n",
    "\n",
    "        if linear:\n",
    "            # linearized index\n",
    "            subregion_index = subregion\n",
    "        else:\n",
    "            # 2D index\n",
    "            subregion_index = self.linearize_index(subregion, 2)\n",
    "        # This is a dumb way...\n",
    "        return self.C_f[np.ix_(subregion_index, subregion_index)]\n",
    "\n",
    "    def von_Neumann_entropy_f(self, subregion):\n",
    "        c_A = self.c_subregion_f(subregion)\n",
    "        val = nla.eigvalsh(c_A)\n",
    "        self.val_sh = val\n",
    "        val = np.sort(val)\n",
    "        return np.real(-np.sum(val*np.log(val+1e-18j))-np.sum((1-val)*np.log(1-val+1e-18j)))\n",
    "\n",
    "    def c_subregion_m(self, subregion, Gamma=None):\n",
    "        '''\n",
    "        subregion: [subregoin_x, subregion_y] index of unit cell\n",
    "        '''\n",
    "        if not hasattr(self, 'C_m'):\n",
    "            self.covariance_matrix()\n",
    "        if Gamma is None:\n",
    "            Gamma = self.C_m_history[-1]\n",
    "        try:\n",
    "            subregion = list(subregion)\n",
    "        except:\n",
    "            raise ValueError(\"The subregion is ill-defined\"+subregion)\n",
    "\n",
    "        if len(subregion) == 2:\n",
    "            if isinstance(subregion[0], int) and isinstance(subregion[1], int):\n",
    "                linear = True\n",
    "            elif (not isinstance(subregion[0], int)) and (not isinstance(subregion[1], int)):\n",
    "                linear = False\n",
    "            else:\n",
    "                raise ValueError('Illegal subregion')\n",
    "        else:\n",
    "            linear = True\n",
    "        if linear:\n",
    "            # linearized index\n",
    "            subregion_index = subregion\n",
    "        else:\n",
    "            # 2D index\n",
    "            subregion_index = self.linearize_index(subregion, 4)\n",
    "\n",
    "        return Gamma[np.ix_(subregion_index, subregion_index)]\n",
    "\n",
    "    def von_Neumann_entropy_m(self, subregion):\n",
    "        c_A = self.c_subregion_m(subregion)\n",
    "        val = nla.eigvalsh(1j*c_A)\n",
    "        self.val_sh = val\n",
    "        val = np.sort(val)\n",
    "        val = (1-val)/2+1e-18j  # \\lambda=(1-\\xi)/2\n",
    "        return np.real(-np.sum(val*np.log(val))-np.sum((1-val)*np.log(1-val)))/2\n",
    "\n",
    "    def mutual_information_f(self, subregion_A, subregion_B):\n",
    "        subregion_A = self.linearize_index(subregion_A, 2)\n",
    "        subregion_B = self.linearize_index(subregion_B, 2)\n",
    "        s_A = self.von_Neumann_entropy_f(subregion_A)\n",
    "        s_B = self.von_Neumann_entropy_f(subregion_B)\n",
    "        assert np.intersect1d(\n",
    "            subregion_A, subregion_B).size == 0, \"Subregion A and B overlap\"\n",
    "        subregion_AB = np.concatenate([subregion_A, subregion_B])\n",
    "        s_AB = self.von_Neumann_entropy_f(subregion_AB)\n",
    "        return s_A+s_B-s_AB\n",
    "\n",
    "    def mutual_information_m(self, subregion_A, subregion_B):\n",
    "        subregion_A = self.linearize_index(subregion_A, 4)\n",
    "        subregion_B = self.linearize_index(subregion_B, 4)\n",
    "        assert np.intersect1d(\n",
    "            subregion_A, subregion_B).size == 0, \"Subregion A and B overlap\"\n",
    "        s_A = self.von_Neumann_entropy_m(subregion_A)\n",
    "        s_B = self.von_Neumann_entropy_m(subregion_B)\n",
    "        subregion_AB = np.concatenate([subregion_A, subregion_B])\n",
    "        s_AB = self.von_Neumann_entropy_m(subregion_AB)\n",
    "        return s_A+s_B-s_AB\n",
    "        \n",
    "    def log_neg(self, subregion_A, subregion_B, Gamma=None,linear=False):\n",
    "        if not linear:\n",
    "            subregion_A = self.linearize_index(subregion_A, 4)\n",
    "            subregion_B = self.linearize_index(subregion_B, 4)\n",
    "        assert np.intersect1d(\n",
    "            subregion_A, subregion_B).size == 0, \"Subregion A and B overlap\"\n",
    "        if not hasattr(self, 'C_m'):\n",
    "            self.covariance_matrix()\n",
    "\n",
    "        if Gamma is None:\n",
    "            Gamma = self.C_m_history[-1]\n",
    "        subregion_A = np.array(subregion_A)\n",
    "        subregion_B = np.array(subregion_B)\n",
    "        Gm_p = np.block([\n",
    "            [-Gamma[np.ix_(subregion_A, subregion_A)], 1j *\n",
    "             Gamma[np.ix_(subregion_A, subregion_B)]],\n",
    "            [1j*Gamma[np.ix_(subregion_B, subregion_A)],\n",
    "             Gamma[np.ix_(subregion_B, subregion_B)]]\n",
    "        ])\n",
    "        Gm_n = np.block([\n",
    "            [-Gamma[np.ix_(subregion_A, subregion_A)], -1j *\n",
    "             Gamma[np.ix_(subregion_A, subregion_B)]],\n",
    "            [-1j*Gamma[np.ix_(subregion_B, subregion_A)],\n",
    "             Gamma[np.ix_(subregion_B, subregion_B)]]\n",
    "        ])\n",
    "        idm = np.eye(Gm_p.shape[0])\n",
    "        # Gm_x=idm-(idm+1j*Gm_p)@nla.inv(idm-Gm_n@Gm_p)@(idm+1j*Gm_n)\n",
    "        Gm_x = idm-(idm+1j*Gm_p)@(la.solve((idm-Gm_n@Gm_p), (idm+1j*Gm_n)))\n",
    "        Gm_x = (Gm_x+Gm_x.T.conj())/2\n",
    "        xi = nla.eigvalsh(Gm_x)\n",
    "        subregion_AB = np.concatenate([subregion_A, subregion_B])\n",
    "        eA = np.sum(np.log(((1+xi+0j)/2)**0.5+((1-xi+0j)/2)**0.5))/2\n",
    "        chi = nla.eigvalsh(1j*Gamma[np.ix_(subregion_AB, subregion_AB)])\n",
    "        sA = np.sum(np.log(((1+chi)/2)**2+((1-chi)/2)**2))/4\n",
    "        self.eA=eA\n",
    "        self.sA=sA\n",
    "        return np.real(eA+sA)\n",
    "\n",
    "\n",
    "\n",
    "    def projection(self, s,type='onsite',ignore=False):\n",
    "            '''\n",
    "            For type:'onsite'\n",
    "                occupancy number: s= 0,1 \n",
    "                (-1)^0 even parity, (-1)^1 odd parity\n",
    "            For type:'link'\n",
    "                (o,+)|(o,-)|(e,+)|(e,-)\n",
    "            '''\n",
    "            if type=='onsite':\n",
    "                assert (s == 0 or s == 1), \"s={} is either 0 or 1\".format(s)\n",
    "                blkmat = np.array([[0, -(-1)**s, 0, 0],\n",
    "                                [(-1)**s, 0, 0, 0],\n",
    "                                [0, 0, 0, (-1)**s],\n",
    "                                [0, 0, -(-1)**s, 0]])\n",
    "                return blkmat\n",
    "            if type=='link':\n",
    "                assert (s in ['o+','o-','e+','e-']), \"s={} for {} is not defined\".format(s,type)\n",
    "                if s=='o+':\n",
    "                    antidiag=[1,-1,1,-1]\n",
    "                    blkmat=np.diag(antidiag)\n",
    "                    blkmat=np.fliplr(blkmat)\n",
    "                if s=='o-':\n",
    "                    antidiag=[-1,1,-1,1]\n",
    "                    blkmat=np.diag(antidiag)\n",
    "                    blkmat=np.fliplr(blkmat)\n",
    "                if not ignore:\n",
    "                    if s=='e+':\n",
    "                        blkmat=np.array([[0,-1,0,0],\n",
    "                                        [1,0,0,0],\n",
    "                                        [0,0,0,-1],\n",
    "                                        [0,0,1,0]])\n",
    "                    if s=='e-':\n",
    "                        blkmat=-np.array([[0,-1,0,0],\n",
    "                                        [1,0,0,0],\n",
    "                                        [0,0,0,-1],\n",
    "                                        [0,0,1,0]])\n",
    "                else:\n",
    "                    if s=='e+':\n",
    "                        antidiag=[-1,-1,1,1]\n",
    "                        blkmat=np.diag(antidiag)\n",
    "                        blkmat=np.fliplr(blkmat)\n",
    "                    if s=='e-':\n",
    "                        antidiag=[1,1,-1,-1]\n",
    "                        blkmat=np.diag(antidiag)\n",
    "                        blkmat=np.fliplr(blkmat)\n",
    "                proj=np.zeros((8,8))\n",
    "                proj[:4,:4]=blkmat\n",
    "                proj[4:,4:]=blkmat.T\n",
    "                return proj            \n",
    "            raise ValueError(\"type '{}' is not defined\".format(type))\n",
    "\n",
    "    def measure(self, s, ix,type='onsite',ignore=False):\n",
    "        if not hasattr(self, 'C_m'):\n",
    "            self.covariance_matrix()\n",
    "        if not hasattr(self, 's_history'):\n",
    "            self.s_history = []\n",
    "        if not hasattr(self, 'i_history'):\n",
    "            self.i_history = []\n",
    "\n",
    "        mat = self.C_m_history[-1].copy()\n",
    "\n",
    "        for i_ind, i in enumerate(ix):\n",
    "            mat[[i, -(len(ix)-i_ind)]] = mat[[-(len(ix)-i_ind), i]]\n",
    "            mat[:, [i, -(len(ix)-i_ind)]] = mat[:, [-(len(ix)-i_ind), i]]\n",
    "\n",
    "        self.mat = mat\n",
    "\n",
    "        Gamma_LL = mat[:-len(ix), :-len(ix)]\n",
    "        Gamma_LR = mat[:-len(ix), -len(ix):]\n",
    "        Gamma_RR = mat[-len(ix):, -len(ix):]\n",
    "\n",
    "        proj = self.projection(s,type=type,ignore=ignore)\n",
    "        Upsilon_LL = proj[:-len(ix), :-len(ix)]\n",
    "        Upsilon_RR = proj[-len(ix):, -len(ix):]\n",
    "        Upsilon_RL = proj[-len(ix):, :-len(ix)]\n",
    "        zero = np.zeros((mat.shape[0]-len(ix), len(ix)))\n",
    "        zero0 = np.zeros((len(ix), len(ix)))\n",
    "        mat1 = np.block([[Gamma_LL, zero], [zero.T, Upsilon_RR]])\n",
    "        mat2 = np.block([[Gamma_LR, zero], [zero0, Upsilon_RL]])\n",
    "        mat3 = np.block([[Gamma_RR, np.eye(len(ix))],\n",
    "                        [-np.eye(len(ix)), Upsilon_LL]])\n",
    "        self.mat2 = mat2\n",
    "        if np.count_nonzero(mat2):\n",
    "            Psi = mat1+mat2@(la.solve(mat3, mat2.T))\n",
    "            # Psi=mat1+mat2@(la.lstsq(mat3,mat2.T)[0])\n",
    "            assert np.abs(\n",
    "                np.trace(Psi)) < 1e-5, \"Not trace zero {:e}\".format(np.trace(Psi))\n",
    "        else:\n",
    "            Psi = mat1\n",
    "\n",
    "        for i_ind, i in enumerate(ix):\n",
    "            Psi[[i, -(len(ix)-i_ind)]] = Psi[[-(len(ix)-i_ind), i]]\n",
    "            Psi[:, [i, -(len(ix)-i_ind)]] = Psi[:, [-(len(ix)-i_ind), i]]\n",
    "        Psi = (Psi-Psi.T)/2   # Anti-symmetrize\n",
    "        if self.history:\n",
    "            self.C_m_history.append(Psi)\n",
    "            self.s_history.append(s)\n",
    "            self.i_history.append(ix[0])\n",
    "        else:\n",
    "            self.C_m_history = [Psi]\n",
    "            self.s_history = [s]\n",
    "            self.i_history = [ix[0]]\n",
    "\n",
    "\n",
    "    def measure_all_Born(self, proj_range,prob=None,linear=False,type='onsite',pool=4,ignore=False):\n",
    "        if not linear:\n",
    "            if type=='onsite':\n",
    "                proj_range = self.linearize_index(proj_range, 8, proj=True)\n",
    "            if type=='link_2':\n",
    "                # assert self.m==0, \"Cannot perform link measurement 2, m ({:d})should be zero\".format(self.m)\n",
    "                proj_range = self.linearize_index(proj_range, 8, proj=True,k=4)\n",
    "        # self.proj_range=proj_range\n",
    "        # print(proj_range)\n",
    "        self.P_0_list = []\n",
    "        self.f_parity= []\n",
    "        if not hasattr(self, 'C_m'):\n",
    "            self.covariance_matrix()\n",
    "        if type=='onsite':\n",
    "            for index,i in enumerate(proj_range):\n",
    "                if prob is None:\n",
    "                    P_0 = (self.C_m_history[-1][i, i+1]+1)/2    # Use Born rule\n",
    "                else:\n",
    "                    if isinstance(prob,list):\n",
    "                        assert len(prob)==len(proj_range), \"len of prob {:d} not equal to len of proj_range {:d}\".format(len(prob),len(proj_range))\n",
    "                        P_0=prob[index]\n",
    "                    else:    \n",
    "                        P_0=prob\n",
    "                self.P_0_list.append(P_0)\n",
    "                if np.random.rand() < P_0:\n",
    "                    self.measure(0, [i, i+1])\n",
    "                    self.f_parity.append(0)\n",
    "                else:\n",
    "                    self.measure(1, [i, i+1])\n",
    "                    self.f_parity.append(1)\n",
    "            return self\n",
    "\n",
    "        if type=='link_2':\n",
    "            for i in proj_range:\n",
    "                Gamma=self.C_m_history[-1][i:i+4,i:i+4]\n",
    "                P={}\n",
    "                gamma1234=-Gamma[0,1]*Gamma[2,3]+Gamma[0,2]*Gamma[1,3]-Gamma[0,3]*Gamma[1,2]\n",
    "                if prob is None:\n",
    "                    P['o+']=(1+Gamma[1,2]-Gamma[0,3]+gamma1234)/4\n",
    "                    P['o-']=(1-Gamma[1,2]+Gamma[0,3]+gamma1234)/4\n",
    "                    if not ignore:\n",
    "                        P['e+']=(1+Gamma[0,1]+Gamma[2,3]-gamma1234)/4\n",
    "                        P['e-']=(1-Gamma[0,1]-Gamma[2,3]-gamma1234)/4\n",
    "                    else:\n",
    "                        #ignore symmetry\n",
    "                        P['e+']=(1+Gamma[1,2]+Gamma[0,3]-gamma1234)/4\n",
    "                        P['e-']=(1-Gamma[1,2]-Gamma[0,3]-gamma1234)/4\n",
    "                else:\n",
    "                    P['o+'],P['o-'],P['e+'],P['e-']=tuple(prob)\n",
    "\n",
    "                # print((P.values()))\n",
    "                if pool==4:\n",
    "                    s=np.random.choice(['o+','o-','e+','e-'],p=[P['o+'],P['o-'],P['e+'],P['e-']])\n",
    "                elif pool==2:\n",
    "                    s=np.random.choice(['o+','o-'],p=[P['o+']/(P['o+']+P['o-']),P['o-']/(P['o+']+P['o-'])])\n",
    "                elif pool==-2:\n",
    "                    s=np.random.choice(['e+','e-'],p=[P['e+']/(P['e+']+P['e-']),P['e-']/(P['e+']+P['e-'])])\n",
    "                self.measure(s,[i,i+1,i+2,i+3],type='link',ignore=ignore)\n",
    "            return self\n",
    "\n",
    "        ValueError('No such type of measurement')\n",
    "        "
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Overwriting pi_flux.py\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "# test"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "source": [
    "params=Params(m=0)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "source": [
    "params.covariance_matrix()"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "source": [
    "params.Lx//4"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "metadata": {},
     "execution_count": 7
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "source": [
    "params.mutual_information_f([np.arange(params.Lx//4),np.arange(params.Ly)],[np.arange(params.Lx//2,3*params.Lx//4),np.arange(params.Ly)])"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "0.02628849427926383"
      ]
     },
     "metadata": {},
     "execution_count": 8
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "source": [
    "params.mutual_information_m([np.arange(params.Lx//4),np.arange(params.Ly)],[np.arange(params.Lx//2,3*params.Lx//4),np.arange(params.Ly)])"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "0.0262884942790933"
      ]
     },
     "metadata": {},
     "execution_count": 9
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "source": [
    "params.log_neg([np.arange(params.Lx//4),np.arange(params.Ly)],[np.arange(params.Lx//2,3*params.Lx//4),np.arange(params.Ly)])"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "0.03895508916636459"
      ]
     },
     "metadata": {},
     "execution_count": 10
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "source": [
    "(params.Hamiltonian.T.conj()-params.Hamiltonian).nonzero()"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "(array([], dtype=int64), array([], dtype=int64))"
      ]
     },
     "metadata": {},
     "execution_count": 55
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Bandstructure"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "source": [
    "m_list=np.linspace(-5,5)\n",
    "Delta=1\n",
    "eigval_pbc_new_list=[]\n",
    "for m in m_list:\n",
    "    params_new=Params(m=m,Delta=Delta,bcx=0,bcy=1,Lx=8,Ly=8)\n",
    "    params_new.bandstructure()\n",
    "    eigval_pbc_new_list.append(params_new.val)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "Delta=1\n",
    "eigval_apbc_new_list=[]\n",
    "for m in m_list:\n",
    "    params_new=Params(m=m,Delta=Delta,bcx=0,bcy=1,test='new',Lx=8,Ly=8)\n",
    "    params_new.bandstructure()\n",
    "    eigval_apbc_new_list.append(params_new.val)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "source": [
    "def h(m,t,Delta,kx,ky):\n",
    "    mat=np.array([[m,-t*(1+np.exp(-1j*kx)),-1j*Delta*(1-np.exp(-1j*kx))*(1-np.exp(-1j*ky)),t*(1+np.exp(-1j*ky))],\n",
    "                  [-t*(1+np.exp(1j*kx)),-m,t*(1+np.exp(-1j*ky)),1j*Delta*(1-np.exp(1j*kx))*(1-np.exp(-1j*ky))],\n",
    "                  [1j*Delta*(1-np.exp(1j*kx))*(1-np.exp(1j*ky)),t*(1+np.exp(1j*ky)),m,t*(1+np.exp(1j*kx))],\n",
    "                  [t*(1+np.exp(1j*ky)),-1j*Delta*(1-np.exp(-1j*kx))*(1-np.exp(1j*ky)),t*(1+np.exp(-1j*kx)),-m]])\n",
    "    return nla.eigvalsh(mat)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "source": [
    "bottom_list=[]\n",
    "top_list=[]\n",
    "# m_list=np.linspace(-5,5)\n",
    "for m in m_list:\n",
    "    en=np.abs(np.array([h(m,1,Delta,kx,ky) for kx in np.linspace(-np.pi,np.pi,10) for ky in np.linspace(-np.pi,np.pi,10)]))\n",
    "    bottom_list.append(en.min())\n",
    "    top_list.append(en.max())"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "source": [
    "Delta_list=np.linspace(-1,1)\n",
    "m=0\n",
    "eigval_pbc_Delta_m0_list=[]\n",
    "for Delta in Delta_list:\n",
    "    params_Delta=Params(m=m,Delta=Delta,bcx=1,bcy=1,Lx=8,Ly=8)\n",
    "    params_Delta.bandstructure()\n",
    "    eigval_pbc_Delta_m0_list.append(params_Delta.val)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "source": [
    "Delta_list=np.linspace(-1,1)\n",
    "m=0\n",
    "eigval_apbc_Delta_m0_list=[]\n",
    "for Delta in Delta_list:\n",
    "    params_Delta=Params(m=m,Delta=Delta,bcx=-1,bcy=1,Lx=8,Ly=8)\n",
    "    params_Delta.bandstructure()\n",
    "    eigval_apbc_Delta_m0_list.append(params_Delta.val)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "source": [
    "bottom_Delta_list=[]\n",
    "top_Delta_list=[]\n",
    "# Delta_list=np.linspace(-5,5)\n",
    "for Delta in Delta_list:\n",
    "    en=np.abs(np.array([h(m,1,Delta,kx,ky) for kx in np.linspace(-np.pi,np.pi,10) for ky in np.linspace(-np.pi,np.pi,10)]))\n",
    "    bottom_Delta_list.append(en.min())\n",
    "    top_Delta_list.append(en.max())"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "source": [
    "plt.plot(m_list,eigval_pbc_new_list,'c',lw=0.5)\n"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
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      ]
     },
     "metadata": {},
     "execution_count": 16
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 489.6x288 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "source": [
    "fig,ax=plt.subplots(2,2,tight_layout=True)\n",
    "ax[0,0].plot(m_list,eigval_apbc_new_list,'c',lw=0.5)\n",
    "ax[0,1].plot(m_list,eigval_pbc_new_list,'c',lw=0.5)\n",
    "\n",
    "ax[0,1].plot(m_list,bottom_list,'r',lw=3)\n",
    "ax[0,1].plot(m_list,top_list,'r',lw=3)\n",
    "ax[0,0].set_title('x: APBC, y: PBC')\n",
    "ax[0,1].set_title('x,y: PBC')\n",
    "[ax.text(.5,.9,r'$\\Delta$=1',transform=ax.transAxes,ha='center') for ax in ax[0]]\n",
    "\n",
    "\n",
    "ax[1,0].plot(Delta_list,eigval_apbc_Delta_m0_list,'c',lw=0.5)\n",
    "ax[1,1].plot(Delta_list,eigval_pbc_Delta_m0_list,'c',lw=0.5)\n",
    "ax[1,1].plot(Delta_list,bottom_Delta_list,'r',lw=3)\n",
    "ax[1,1].plot(Delta_list,top_Delta_list,'r',lw=3)\n",
    "\n",
    "[ax.text(.5,.9,'m=0',transform=ax.transAxes,ha='center') for ax in ax[1]]\n",
    "\n",
    "[ax.margins(x=0) for ax in ax.flatten()]\n",
    "[ax.set_xlabel(r'm') for ax in ax[0]]\n",
    "[ax.set_xlabel(r'$\\Delta$') for ax in ax[1]]\n",
    "[ax.set_ylabel(r'Energy') for ax in ax[:,0]]\n",
    "\n",
    "fig.savefig('/mnt/d/kitp/Rp_SPT/10/bs.pdf',bbox_inches='tight')"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 489.6x288 with 4 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "# No measurement "
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## m dependence"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "source": [
    "m_list=(lambda x:(x-4)**3+4 )(np.linspace(3,5,24))\n",
    "# m_list=np.linspace(3,5,20)\n",
    "LN_m_no_list=[]\n",
    "MI_m_no_list=[]\n",
    "Lx=32\n",
    "Ly=4\n",
    "def run(p):\n",
    "    m,Lx,Ly=p\n",
    "    params=Params(m=m,Lx=Lx,Ly=Ly)\n",
    "    MI=(params.mutual_information_m([np.arange(params.Lx//4),np.arange(params.Ly)],[np.arange(params.Lx//4)+params.Lx//2,np.arange(params.Ly)]))\n",
    "    LN=(params.log_neg([np.arange(params.Lx//4),np.arange(params.Ly)],[np.arange(params.Lx//4)+params.Lx//2,np.arange(params.Ly)]))\n",
    "    return MI,LN\n",
    "\n",
    "inputs=[(m,Lx,Ly) for m in m_list]\n",
    "async_result=(rc[:].map_sync(run,inputs))\n",
    "\n",
    "for index,results in enumerate(async_result):\n",
    "    MI_m_no_list.append(results[0])\n",
    "    LN_m_no_list.append(results[1])\n"
   ],
   "outputs": [
    {
     "output_type": "error",
     "ename": "NameError",
     "evalue": "name 'rc' is not defined",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-17-72455720cea8>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     13\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     14\u001b[0m \u001b[0minputs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mLx\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mLy\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mm\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mm_list\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 15\u001b[0;31m \u001b[0masync_result\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrc\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmap_sync\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0minputs\u001b[0m\u001b[0;34m)\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     16\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     17\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mindex\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mresults\u001b[0m \u001b[0;32min\u001b[0m \u001b[0menumerate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0masync_result\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'rc' is not defined"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "source": [
    "fig,ax=plt.subplots()\n",
    "ax.plot(m_list,LN_m_no_list/np.log(2),'.-',label='LN')\n",
    "ax.plot(m_list,MI_m_no_list/np.log(2),'.-',label='MI')\n",
    "ax.legend()\n",
    "ax.set_xlabel('m')\n",
    "ax.grid('on')\n",
    "ax.set_ylabel('[log(2)]')\n",
    "ax.set_title('Finite system')\n",
    "fig.savefig('/mnt/d/kitp/Rp_SPT/10/LN_CI_no_Lx{:d}_Ly{:d}.pdf'.format(Lx,Ly),bbox_inches='tight')"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 489.6x288 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Delta dependence"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "source": [
    "Delta_list=(lambda x:(x)**3)(np.linspace(-1,1,24))\n",
    "# Delta_list=np.linspace(-1,1,20)\n",
    "LN_Delta_no_list=[]\n",
    "MI_Delta_no_list=[]\n",
    "Lx=32\n",
    "Ly=4\n",
    "def run(p):\n",
    "    Delta,Lx,Ly=p\n",
    "    params=Params(m=0,Lx=Lx,Ly=Ly,Delta=Delta)\n",
    "    MI=(params.mutual_information_m([np.arange(params.Lx//4),np.arange(params.Ly)],[np.arange(params.Lx//4)+params.Lx//2,np.arange(params.Ly)]))\n",
    "    LN=(params.log_neg([np.arange(params.Lx//4),np.arange(params.Ly)],[np.arange(params.Lx//4)+params.Lx//2,np.arange(params.Ly)]))\n",
    "    return MI,LN\n",
    "\n",
    "inputs=[(Delta,Lx,Ly) for Delta in Delta_list]\n",
    "async_result=(rc[:].map_sync(run,inputs))\n",
    "\n",
    "for index,results in enumerate(async_result):\n",
    "    MI_Delta_no_list.append(results[0])\n",
    "    LN_Delta_no_list.append(results[1])\n"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "source": [
    "fig,ax=plt.subplots()\n",
    "ax.plot(Delta_list,LN_Delta_no_list/np.log(2),'.-',label='LN')\n",
    "ax.plot(Delta_list,MI_Delta_no_list/np.log(2),'.-',label='MI')\n",
    "ax.legend()\n",
    "ax.set_xlabel(r'$\\Delta$')\n",
    "ax.grid('on')\n",
    "ax.set_ylabel('[log(2)]')\n",
    "ax.set_title('Finite system')\n",
    "fig.savefig('/mnt/d/kitp/Rp_SPT/10/LN_CI_no_Delta_Lx{:d}_Ly{:d}.pdf'.format(Lx,Ly),bbox_inches='tight')"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 489.6x288 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Force measurement"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "source": [
    "params=Params(m=10,Lx=Lx,Ly=Ly)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "source": [
    "params.covariance_matrix()"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "source": [
    "np.diag(params.C_f)"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
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       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j,\n",
       "       0.01025816+0.j, 0.98974184+0.j, 0.01025816+0.j, 0.98974184+0.j])"
      ]
     },
     "metadata": {},
     "execution_count": 47
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "source": [
    "run((0,Lx,Ly))"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "(1.583534666949049e-05, 1.783450871339909e-05)"
      ]
     },
     "metadata": {},
     "execution_count": 32
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "source": [
    "m_list=(lambda x:(x-4)**3+4 )(np.linspace(3,5,24))\n",
    "# m_list=np.linspace(3,5,20)\n",
    "LN_m_no_list=[]\n",
    "MI_m_no_list=[]\n",
    "Lx=32\n",
    "Ly=4\n",
    "def run(p):\n",
    "    m,Lx,Ly=p\n",
    "    params=Params(m=m,Lx=Lx,Ly=Ly,bcx=-1,bcy=1)\n",
    "    params.measure_all_Born([np.arange(params.Lx//4,params.Lx//2),np.arange(params.Ly)],prob=([1,0,0,1]*(params.Lx//4*params.Ly)))\n",
    "    MI=(params.mutual_information_m([np.arange(params.Lx//4),np.arange(params.Ly)],[np.arange(params.Lx//4)+params.Lx//2,np.arange(params.Ly)]))\n",
    "    LN=(params.log_neg([np.arange(params.Lx//4),np.arange(params.Ly)],[np.arange(params.Lx//4)+params.Lx//2,np.arange(params.Ly)]))\n",
    "    return MI,LN\n",
    "\n",
    "inputs=[(m,Lx,Ly) for m in m_list]\n",
    "async_result=(rc[:].map_sync(run,inputs))\n",
    "\n",
    "for index,results in enumerate(async_result):\n",
    "    MI_m_no_list.append(results[0])\n",
    "    LN_m_no_list.append(results[1])\n"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "# Check ground state now"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "# Ground state? Charge? Particle number conserved"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "source": [
    "plt.plot(m_list,MI_m_no_list)"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f12f9941e20>]"
      ]
     },
     "metadata": {},
     "execution_count": 53
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 489.6x288 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "source": [
    "Delta_list=(lambda x:(x)**3)(np.linspace(-1,1,24))\n",
    "# Delta_list=np.linspace(-1,1,20)\n",
    "LN_Delta_no_list=[]\n",
    "MI_Delta_no_list=[]\n",
    "Lx=32\n",
    "Ly=4\n",
    "def run(p):\n",
    "    Delta,Lx,Ly=p\n",
    "    params=Params(m=1,Lx=Lx,Ly=Ly,Delta=Delta,bcx=-1,bcy=1)\n",
    "    # params.measure_all_Born([np.arange(params.Lx//4,params.Lx//2),np.arange(params.Ly)],prob=([0,1,0,1]*(params.Lx//4*params.Ly)))\n",
    "    params.measure_all_Born([np.arange(params.Lx//4,params.Lx//2),np.arange(params.Ly)],prob=[1,0,0,0],type='link_2')\n",
    "\n",
    "    MI=(params.mutual_information_m([np.arange(params.Lx//4),np.arange(params.Ly)],[np.arange(params.Lx//4)+params.Lx//2,np.arange(params.Ly)]))\n",
    "    LN=(params.log_neg([np.arange(params.Lx//4),np.arange(params.Ly)],[np.arange(params.Lx//4)+params.Lx//2,np.arange(params.Ly)]))\n",
    "    return MI,LN\n",
    "\n",
    "inputs=[(Delta,Lx,Ly) for Delta in Delta_list]\n",
    "async_result=(rc[:].map_sync(run,inputs))\n",
    "\n",
    "for index,results in enumerate(async_result):\n",
    "    MI_Delta_no_list.append(results[0])\n",
    "    LN_Delta_no_list.append(results[1])\n"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "source": [
    "plt.plot(Delta_list,MI_Delta_no_list)\n",
    "plt.plot(Delta_list,LN_Delta_no_list)"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f12e87d4be0>]"
      ]
     },
     "metadata": {},
     "execution_count": 147
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 489.6x288 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "source": [
    "params=Params(m=0,Lx=Lx,Ly=Ly,Delta=Delta,bcx=-1,bcy=1)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "source": [
    "params.covariance_matrix()"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "source": [
    "(np.diag(params.C_m_history[-1],1)[::2]+1)/2"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n",
       "       0.5, 0.5, 0.5, 0.5, 0.5])"
      ]
     },
     "metadata": {},
     "execution_count": 118
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "source": [
    "params.measure_all_Born([np.arange(params.Lx//4,params.Lx//2),np.arange(params.Ly)],prob=([1,0,1,0]*(params.Lx//4*params.Ly)))\n"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "<__main__.Params at 0x7f12f9563580>"
      ]
     },
     "metadata": {},
     "execution_count": 119
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "source": [
    "(np.diag(params.C_m_history[-1],1)[::2]+1)/2"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.50000005, 0.49999995,\n",
       "       0.5       , 0.49999995, 0.50000066, 0.49999934, 0.50000005,\n",
       "       0.49999935, 0.50001121, 0.49998879, 0.50000065, 0.4999954 ,\n",
       "       0.50027698, 0.49972302, 0.5000046 , 0.50038891, 0.5290549 ,\n",
       "       0.4709451 , 0.49961109, 1.        , 0.        , 1.        ,\n",
       "       0.        , 1.        , 0.        , 1.        , 0.        ,\n",
       "       1.        , 0.        , 1.        , 0.        , 1.        ,\n",
       "       0.        , 1.        , 0.        , 1.        , 0.        ,\n",
       "       1.        , 0.        , 1.        , 0.        , 1.        ,\n",
       "       0.        , 1.        , 0.        , 1.        , 0.        ,\n",
       "       1.        , 0.        , 1.        , 0.        , 0.4709451 ,\n",
       "       0.49961109, 0.50038891, 0.5290549 , 0.49972302, 0.5000046 ,\n",
       "       0.4999954 , 0.50027698, 0.49998879, 0.50000065, 0.49999935,\n",
       "       0.50001121, 0.49999934, 0.50000005, 0.49999995, 0.50000066,\n",
       "       0.49999995, 0.5       , 0.5       , 0.50000005, 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.50000005, 0.49999995, 0.5       , 0.49999995,\n",
       "       0.50000066, 0.49999934, 0.50000005, 0.49999935, 0.50001121,\n",
       "       0.49998879, 0.50000065, 0.4999954 , 0.50027698, 0.49972302,\n",
       "       0.5000046 , 0.50038891, 0.5290549 , 0.4709451 , 0.49961109,\n",
       "       1.        , 0.        , 1.        , 0.        , 1.        ,\n",
       "       0.        , 1.        , 0.        , 1.        , 0.        ,\n",
       "       1.        , 0.        , 1.        , 0.        , 1.        ,\n",
       "       0.        , 1.        , 0.        , 1.        , 0.        ,\n",
       "       1.        , 0.        , 1.        , 0.        , 1.        ,\n",
       "       0.        , 1.        , 0.        , 1.        , 0.        ,\n",
       "       1.        , 0.        , 0.4709451 , 0.49961109, 0.50038891,\n",
       "       0.5290549 , 0.49972302, 0.5000046 , 0.4999954 , 0.50027698,\n",
       "       0.49998879, 0.50000065, 0.49999935, 0.50001121, 0.49999934,\n",
       "       0.50000005, 0.49999995, 0.50000066, 0.49999995, 0.5       ,\n",
       "       0.5       , 0.50000005, 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.50000005,\n",
       "       0.49999995, 0.5       , 0.49999995, 0.50000066, 0.49999934,\n",
       "       0.50000005, 0.49999935, 0.50001121, 0.49998879, 0.50000065,\n",
       "       0.4999954 , 0.50027698, 0.49972302, 0.5000046 , 0.50038891,\n",
       "       0.5290549 , 0.4709451 , 0.49961109, 1.        , 0.        ,\n",
       "       1.        , 0.        , 1.        , 0.        , 1.        ,\n",
       "       0.        , 1.        , 0.        , 1.        , 0.        ,\n",
       "       1.        , 0.        , 1.        , 0.        , 1.        ,\n",
       "       0.        , 1.        , 0.        , 1.        , 0.        ,\n",
       "       1.        , 0.        , 1.        , 0.        , 1.        ,\n",
       "       0.        , 1.        , 0.        , 1.        , 0.        ,\n",
       "       0.4709451 , 0.49961109, 0.50038891, 0.5290549 , 0.49972302,\n",
       "       0.5000046 , 0.4999954 , 0.50027698, 0.49998879, 0.50000065,\n",
       "       0.49999935, 0.50001121, 0.49999934, 0.50000005, 0.49999995,\n",
       "       0.50000066, 0.49999995, 0.5       , 0.5       , 0.50000005,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.50000005, 0.49999995, 0.5       ,\n",
       "       0.49999995, 0.50000066, 0.49999934, 0.50000005, 0.49999935,\n",
       "       0.50001121, 0.49998879, 0.50000065, 0.4999954 , 0.50027698,\n",
       "       0.49972302, 0.5000046 , 0.50038891, 0.5290549 , 0.4709451 ,\n",
       "       0.49961109, 1.        , 0.        , 1.        , 0.        ,\n",
       "       1.        , 0.        , 1.        , 0.        , 1.        ,\n",
       "       0.        , 1.        , 0.        , 1.        , 0.        ,\n",
       "       1.        , 0.        , 1.        , 0.        , 1.        ,\n",
       "       0.        , 1.        , 0.        , 1.        , 0.        ,\n",
       "       1.        , 0.        , 1.        , 0.        , 1.        ,\n",
       "       0.        , 1.        , 0.        , 0.4709451 , 0.49961109,\n",
       "       0.50038891, 0.5290549 , 0.49972302, 0.5000046 , 0.4999954 ,\n",
       "       0.50027698, 0.49998879, 0.50000065, 0.49999935, 0.50001121,\n",
       "       0.49999934, 0.50000005, 0.49999995, 0.50000066, 0.49999995,\n",
       "       0.5       , 0.5       , 0.50000005, 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       , 0.5       , 0.5       , 0.5       ,\n",
       "       0.5       , 0.5       ])"
      ]
     },
     "metadata": {},
     "execution_count": 120
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "source": [
    "(params.mutual_information_m([np.arange(params.Lx//4),np.arange(params.Ly)],[np.arange(params.Lx//4)+params.Lx//2,np.arange(params.Ly)]))"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "1.5835346790282756e-05"
      ]
     },
     "metadata": {},
     "execution_count": 121
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "source": [
    "plt.plot(np.diag(params.C_m_history[-1],1)[::2],'.')"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f12f9540640>]"
      ]
     },
     "metadata": {},
     "execution_count": 122
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 489.6x288 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "source": [
    "plt.plot(Delta_list,MI_Delta_no_list)"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f12f95d86d0>]"
      ]
     },
     "metadata": {},
     "execution_count": 81
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 489.6x288 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Born measurement"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Onsite, m dep"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "source": [
    "m_list=(lambda x:(x-4)**3+4 )(np.linspace(3,5,24))\n",
    "es=20\n",
    "LN_Born_list=np.zeros((len(m_list),es))\n",
    "MI_Born_list=np.zeros((len(m_list),es))\n",
    "Lx,Ly=32,4\n",
    "def run(p):\n",
    "    m,Lx,Ly=p\n",
    "    params=Params(m=m,Lx=Lx,Ly=Ly,bcx=-1,bcy=1)\n",
    "    params.measure_all_Born([np.arange(Lx//4,Lx//2),np.arange(Ly)])\n",
    "    LN=params.log_neg([np.arange(Lx//4),np.arange(Ly)],[np.arange(Lx//4)+Lx//2,np.arange(Ly)])\n",
    "    MI=params.mutual_information_m([np.arange(Lx//4),np.arange(Ly)],[np.arange(Lx//4)+Lx//2,np.arange(Ly)])\n",
    "    return MI,LN\n",
    "for m_i,m in enumerate(m_list):\n",
    "    st=time.time()\n",
    "    # # Serial\n",
    "    # params0=Params(m=m,Lx=Lx,Ly=Ly)\n",
    "    # for es_i in range(es):\n",
    "    #     params=copy(params0)\n",
    "    #     params.measure_all_Born([np.arange(params.Lx//4,params.Lx//2),np.arange(params.Ly)])\n",
    "    #     # MI_Born_list[m_i,es_i]=params.mutual_information_m([np.arange(params.Lx//4),np.arange(params.Ly)],[np.arange(params.Lx//4)+params.Lx//2,np.arange(params.Ly)])\n",
    "    #     LN_Born_list[m_i,es_i]=params.log_neg([np.arange(params.Lx//4),np.arange(params.Ly)],[np.arange(params.Lx//4)+params.Lx//2,np.arange(params.Ly)])\n",
    "\n",
    "    # Parallel\n",
    "    inputs=[(m,Lx,Ly) for _ in range(es)]\n",
    "    async_result=rc[:].map_sync(run,inputs)\n",
    "\n",
    "    for index,results in enumerate(async_result):\n",
    "        MI_Born_list[m_i,index],LN_Born_list[m_i,index]=results\n",
    "\n",
    "    print('{:d}:{:.1f}'.format(m_i,time.time()-st))\n"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "0:24.6\n",
      "1:24.1\n",
      "2:24.7\n",
      "3:26.5\n",
      "4:25.5\n",
      "5:23.8\n",
      "6:25.9\n",
      "7:25.4\n",
      "8:24.7\n",
      "9:24.1\n",
      "10:24.6\n",
      "11:24.3\n",
      "12:24.5\n",
      "13:23.9\n",
      "14:24.5\n",
      "15:25.1\n",
      "16:23.6\n",
      "17:25.6\n",
      "18:25.5\n",
      "19:24.8\n",
      "20:24.2\n",
      "21:26.4\n",
      "22:25.9\n",
      "23:26.9\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "source": [
    "fig,ax=plt.subplots()\n",
    "# ax.plot(m_list,LN_no_list,'.-',label='No measurement')\n",
    "\n",
    "ax.errorbar(m_list,LN_Born_list.mean(axis=1)/np.log(2),LN_Born_list.std(axis=1)/np.log(2)/np.sqrt(es-1),capsize=3,fmt='.-',label='Onsite measurement (LN)')\n",
    "ax.errorbar(m_list,MI_Born_list.mean(axis=1)/np.log(2),MI_Born_list.std(axis=1)/np.log(2)/np.sqrt(es-1),capsize=3,fmt='.-',label='Onsite measurement (MI)')\n",
    "\n",
    "ax.legend()\n",
    "ax.grid('on')\n",
    "ax.set_xlabel(r'm')\n",
    "ax.set_ylabel(r'[log(2)]')\n",
    "ax.margins(x=0)\n",
    "ax.set_title('Ensemble Size={:d}, Lx={:d}, Ly={:d}'.format(es,Lx,Ly))\n",
    "fig.savefig('/mnt/d/KITP/Rp_SPT/10/LN_CI_Born_onsite_En{:d}_Lx{:d}_Ly{:d}.pdf'.format(es,Lx,Ly),bbox_inches='tight')"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 489.6x288 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Onsite, $\\Delta$ dep"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "source": [
    "Delta_list=(lambda x:(x)**3)(np.linspace(-1,1,24))\n",
    "es=20\n",
    "LN_Born_Delta_list=np.zeros((len(Delta_list),es))\n",
    "MI_Born_Delta_list=np.zeros((len(Delta_list),es))\n",
    "Lx,Ly=32,4\n",
    "def run(p):\n",
    "    Delta,Lx,Ly=p\n",
    "    params=Params(m=0,Delta=Delta,Lx=Lx,Ly=Ly,bcx=-1,bcy=1)\n",
    "    params.measure_all_Born([np.arange(Lx//4,Lx//2),np.arange(Ly)])\n",
    "    LN=params.log_neg([np.arange(Lx//4),np.arange(Ly)],[np.arange(Lx//4)+Lx//2,np.arange(Ly)])\n",
    "    MI=params.mutual_information_m([np.arange(Lx//4),np.arange(Ly)],[np.arange(Lx//4)+Lx//2,np.arange(Ly)])\n",
    "    return MI,LN\n",
    "for Delta_i,Delta in enumerate(Delta_list):\n",
    "    st=time.time()\n",
    "    # # Serial\n",
    "    # params0=Params(Delta=Delta,Lx=Lx,Ly=Ly)\n",
    "    # for es_i in range(es):\n",
    "    #     params=copy(params0)\n",
    "    #     params.measure_all_Born([np.arange(params.Lx//4,params.Lx//2),np.arange(params.Ly)])\n",
    "    #     # MI_Born_Delta_list[Delta_i,es_i]=params.mutual_information_m([np.arange(params.Lx//4),np.arange(params.Ly)],[np.arange(params.Lx//4)+params.Lx//2,np.arange(params.Ly)])\n",
    "    #     LN_Born_Delta_list[Delta_i,es_i]=params.log_neg([np.arange(params.Lx//4),np.arange(params.Ly)],[np.arange(params.Lx//4)+params.Lx//2,np.arange(params.Ly)])\n",
    "\n",
    "    # Parallel\n",
    "    inputs=[(Delta,Lx,Ly) for _ in range(es)]\n",
    "    async_result=rc[:].map_sync(run,inputs)\n",
    "\n",
    "    for index,results in enumerate(async_result):\n",
    "        MI_Born_Delta_list[Delta_i,index],LN_Born_Delta_list[Delta_i,index]=results\n",
    "\n",
    "    print('{:d}:{:.1f}'.format(Delta_i,time.time()-st))\n"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "0:25.5\n",
      "1:24.8\n",
      "2:24.9\n",
      "3:24.5\n",
      "4:24.6\n",
      "5:24.4\n",
      "6:24.8\n",
      "7:23.9\n",
      "8:24.4\n",
      "9:25.2\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "source": [
    "fig,ax=plt.subplots()\n",
    "# ax.plot(Delta_list,LN_no_list,'.-',label='No measurement')\n",
    "\n",
    "ax.errorbar(Delta_list,LN_Born_list.mean(axis=1)/np.log(2),LN_Born_list.std(axis=1)/np.log(2)/np.sqrt(es-1),capsize=3,fmt='.-',label='Onsite measurement (LN)')\n",
    "ax.errorbar(Delta_list,MI_Born_list.mean(axis=1)/np.log(2),MI_Born_list.std(axis=1)/np.log(2)/np.sqrt(es-1),capsize=3,fmt='.-',label='Onsite measurement (MI)')\n",
    "\n",
    "ax.legend()\n",
    "ax.grid('on')\n",
    "ax.set_xlabel(r'$\\Delta$')\n",
    "ax.set_ylabel(r'[log(2)]')\n",
    "ax.margins(x=0)\n",
    "ax.set_title('Ensemble Size={:d}, Lx={:d}, Ly={:d}'.format(es,Lx,Ly))\n",
    "fig.savefig('/mnt/d/KITP/Rp_SPT/10/LN_CI_Born_Delta_onsite_En{:d}_Lx{:d}_Ly{:d}.pdf'.format(es,Lx,Ly),bbox_inches='tight')"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 489.6x288 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Link $\\Delta$ dep"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "source": [
    "Delta_list=(lambda x:(x)**3)(np.linspace(-1,1,8))\n",
    "es=20\n",
    "LN_Born_link_Delta_list=np.zeros((len(Delta_list),es))\n",
    "MI_Born_link_Delta_list=np.zeros((len(Delta_list),es))\n",
    "Lx,Ly=32,4\n",
    "def run(p):\n",
    "    Delta,Lx,Ly=p\n",
    "    params=Params(m=0,Delta=Delta,Lx=Lx,Ly=Ly,bcx=-1,bcy=1)\n",
    "    params.measure_all_Born([np.arange(Lx//4,Lx//2),np.arange(Ly)],type='link_2')\n",
    "    LN=params.log_neg([np.arange(Lx//4),np.arange(Ly)],[np.arange(Lx//4)+Lx//2,np.arange(Ly)])\n",
    "    MI=params.mutual_information_m([np.arange(Lx//4),np.arange(Ly)],[np.arange(Lx//4)+Lx//2,np.arange(Ly)])\n",
    "    return MI,LN\n",
    "for Delta_i,Delta in enumerate(Delta_list):\n",
    "    st=time.time()\n",
    "    # Parallel\n",
    "    inputs=[(Delta,Lx,Ly) for _ in range(es)]\n",
    "    async_result=rc[:].map_sync(run,inputs)\n",
    "\n",
    "    for index,results in enumerate(async_result):\n",
    "        MI_Born_link_Delta_list[Delta_i,index],LN_Born_link_Delta_list[Delta_i,index]=results\n",
    "\n",
    "    print('{:d}:{:.1f}'.format(Delta_i,time.time()-st))\n"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "0:14.5\n",
      "1:14.1\n",
      "2:14.3\n",
      "3:14.4\n",
      "4:13.6\n",
      "5:15.1\n",
      "6:13.6\n",
      "7:13.7\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "source": [
    "fig,ax=plt.subplots()\n",
    "# ax.plot(Delta_list,LN_no_list,'.-',label='No measurement')\n",
    "\n",
    "ax.errorbar(Delta_list,LN_Born_link_Delta_list.mean(axis=1)/np.log(2),LN_Born_link_Delta_list.std(axis=1)/np.log(2)/np.sqrt(es-1),capsize=3,fmt='.-',label='Onsite measurement (LN)')\n",
    "ax.errorbar(Delta_list,MI_Born_link_Delta_list.mean(axis=1)/np.log(2),MI_Born_link_Delta_list.std(axis=1)/np.log(2)/np.sqrt(es-1),capsize=3,fmt='.-',label='Onsite measurement (MI)')\n",
    "\n",
    "ax.legend()\n",
    "ax.grid('on')\n",
    "ax.set_xlabel(r'$\\Delta$')\n",
    "ax.set_ylabel(r'[log(2)]')\n",
    "ax.margins(x=0)\n",
    "ax.set_title('Ensemble Size={:d}, Lx={:d}, Ly={:d}'.format(es,Lx,Ly))\n",
    "fig.savefig('/mnt/d/KITP/Rp_SPT/10/LN_CI_Born_link_Delta_En{:d}_Lx{:d}_Ly{:d}.pdf'.format(es,Lx,Ly),bbox_inches='tight')"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 489.6x288 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Link force to o+"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "source": [
    "params=Params(m=0,Delta=1,Lx=32,Ly=Ly,bcx=-1,bcy=1,history=True)\n",
    "params.measure_all_Born([np.arange(Lx//4,Lx//2),np.arange(Ly)],type='link_2',pool=-2)\n",
    "params.log_neg([np.arange(Lx//4),np.arange(Ly)],[np.arange(Lx//4)+Lx//2,np.arange(Ly)])"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "1.789907180871353e-05"
      ]
     },
     "metadata": {},
     "execution_count": 29
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "source": [
    "params.s_history"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "['e+',\n",
       " 'e-',\n",
       " 'e-',\n",
       " 'e-',\n",
       " 'e+',\n",
       " 'e-',\n",
       " 'e-',\n",
       " 'e+',\n",
       " 'e-',\n",
       " 'e+',\n",
       " 'e-',\n",
       " 'e+',\n",
       " 'e+',\n",
       " 'e+',\n",
       " 'e-',\n",
       " 'e+',\n",
       " 'e+',\n",
       " 'e-',\n",
       " 'e+',\n",
       " 'e-',\n",
       " 'e+',\n",
       " 'e-',\n",
       " 'e-',\n",
       " 'e+',\n",
       " 'e-',\n",
       " 'e+',\n",
       " 'e-',\n",
       " 'e+',\n",
       " 'e-',\n",
       " 'e+',\n",
       " 'e-',\n",
       " 'e+',\n",
       " 'e-',\n",
       " 'e+',\n",
       " 'e+',\n",
       " 'e-',\n",
       " 'e+',\n",
       " 'e-',\n",
       " 'e-',\n",
       " 'e+',\n",
       " 'e-',\n",
       " 'e-',\n",
       " 'e-',\n",
       " 'e+',\n",
       " 'e-',\n",
       " 'e-',\n",
       " 'e-',\n",
       " 'e+',\n",
       " 'e+',\n",
       " 'e-',\n",
       " 'e-',\n",
       " 'e+',\n",
       " 'e+',\n",
       " 'e-',\n",
       " 'e+',\n",
       " 'e+',\n",
       " 'e+',\n",
       " 'e-',\n",
       " 'e+',\n",
       " 'e-',\n",
       " 'e+',\n",
       " 'e-',\n",
       " 'e-',\n",
       " 'e+']"
      ]
     },
     "metadata": {},
     "execution_count": 30
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "source": [
    "Delta_list=(lambda x:(x)**3)(np.linspace(-1,1,24))\n",
    "# m_list=np.linspace(1,3,10)\n",
    "LN_Born_link_op_list=[]\n",
    "MI_Born_link_op_list=[]\n",
    "Lx,Ly=32,4\n",
    "def run(p):\n",
    "    Delta,Lx,Ly=p\n",
    "    params=Params(m=0,Delta=Delta,Lx=Lx,Ly=Ly,bcx=-1,bcy=1)\n",
    "    params.measure_all_Born([np.arange(Lx//4,Lx//2),np.arange(Ly)],type='link_2',prob=[1,0,0,0])\n",
    "    LN=params.log_neg([np.arange(Lx//4),np.arange(Ly)],[np.arange(Lx//4)+Lx//2,np.arange(Ly)])\n",
    "    MI=params.mutual_information_m([np.arange(Lx//4),np.arange(Ly)],[np.arange(Lx//4)+Lx//2,np.arange(Ly)])\n",
    "    return MI,LN\n",
    "\n",
    "    \n",
    "inputs=[(Delta,Lx,Ly) for Delta in Delta_list]\n",
    "async_result=(rc[:].map_sync(run,inputs))\n",
    "\n",
    "for index,results in enumerate(async_result):\n",
    "    MI_Born_link_op_list.append(results[0])\n",
    "    LN_Born_link_op_list.append(results[1])\n"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "source": [
    "fig,ax=plt.subplots()\n",
    "# ax.plot(Delta_list,LN_no_list,'.-',label='No measurement')\n",
    "\n",
    "ax.plot(Delta_list,LN_Born_link_op_list/np.log(2),'.-',label='Link (o+) measurement (LN)')\n",
    "ax.plot(Delta_list,MI_Born_link_op_list/np.log(2),'.-',label='Link (o+) measurement (MI)')\n",
    "# ax.set_yticks(np.arange(0.5,1.8,.1))\n",
    "ax.legend()\n",
    "ax.grid('on')\n",
    "ax.set_xlabel(r'$\\Delta$')\n",
    "ax.set_ylabel(r'log neg [log(2)]')\n",
    "ax.margins(x=0)\n",
    "ax.set_title('Lx={:d}, Ly={:d}'.format(Lx,Ly))\n",
    "fig.savefig('/mnt/d/KITP/Rp_SPT/10/LN_CI_Born_link_op_Lx{:d}_Ly{:d}.pdf'.format(Lx,Ly),bbox_inches='tight')"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 489.6x288 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Link force to o-"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "source": [
    "Delta_list=(lambda x:(x)**3)(np.linspace(-1,1,24))\n",
    "# m_list=np.linspace(1,3,10)\n",
    "LN_Born_link_om_list=[]\n",
    "MI_Born_link_om_list=[]\n",
    "Lx,Ly=32,4\n",
    "def run(p):\n",
    "    Delta,Lx,Ly=p\n",
    "    params=Params(m=0,Delta=Delta,Lx=Lx,Ly=Ly,bcx=-1,bcy=1)\n",
    "    params.measure_all_Born([np.arange(Lx//4,Lx//2),np.arange(Ly)],type='link_2',prob=[0,1,0,0])\n",
    "    LN=params.log_neg([np.arange(Lx//4),np.arange(Ly)],[np.arange(Lx//4)+Lx//2,np.arange(Ly)])\n",
    "    MI=params.mutual_information_m([np.arange(Lx//4),np.arange(Ly)],[np.arange(Lx//4)+Lx//2,np.arange(Ly)])\n",
    "    return MI,LN\n",
    "\n",
    "    \n",
    "inputs=[(Delta,Lx,Ly) for Delta in Delta_list]\n",
    "async_result=(rc[:].map_sync(run,inputs))\n",
    "\n",
    "for index,results in enumerate(async_result):\n",
    "    MI_Born_link_om_list.append(results[0])\n",
    "    LN_Born_link_om_list.append(results[1])\n"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "source": [
    "fig,ax=plt.subplots()\n",
    "# ax.plot(Delta_list,LN_no_list,'.-',label='No measurement')\n",
    "\n",
    "ax.plot(Delta_list,LN_Born_link_om_list/np.log(2),'.-',label='Link (o+) measurement (LN)')\n",
    "ax.plot(Delta_list,MI_Born_link_om_list/np.log(2),'.-',label='Link (o+) measurement (MI)')\n",
    "ax.set_yticks(np.arange(0.5,1.8,.1))\n",
    "ax.legend()\n",
    "ax.grid('on')\n",
    "ax.set_xlabel(r'$\\Delta$')\n",
    "ax.set_ylabel(r'log neg [log(2)]')\n",
    "ax.margins(x=0)\n",
    "ax.set_title('Lx={:d}, Ly={:d}'.format(Lx,Ly))\n",
    "fig.savefig('/mnt/d/KITP/Rp_SPT/10/LN_CI_Born_link_om_Lx{:d}_Ly{:d}.pdf'.format(Lx,Ly),bbox_inches='tight')"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 489.6x288 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Link, Born but with only {o+,o-}"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "source": [
    "Delta_list=(lambda x:(x)**3)(np.linspace(-1,1,8))\n",
    "# Delta_list=np.linspace(1,3,10)\n",
    "es=20\n",
    "LN_Born_link_pool2_list=np.zeros((len(Delta_list),es))\n",
    "MI_Born_link_pool2_list=np.zeros((len(Delta_list),es))\n",
    "Lx,Ly=32,4\n",
    "def run(p):\n",
    "    Delta,Lx,Ly=p\n",
    "    params=Params(m=0,Delta=Delta,Lx=Lx,Ly=Ly,bcx=-1,bcy=1)\n",
    "    params.measure_all_Born([np.arange(Lx//4,Lx//2),np.arange(Ly)],type='link_2',pool=2)\n",
    "    LN=params.log_neg([np.arange(Lx//4),np.arange(Ly)],[np.arange(Lx//4)+Lx//2,np.arange(Ly)])\n",
    "    MI=params.mutual_information_m([np.arange(Lx//4),np.arange(Ly)],[np.arange(Lx//4)+Lx//2,np.arange(Ly)])\n",
    "    return MI,LN\n",
    "for Delta_i,Delta in enumerate(Delta_list):\n",
    "    st=time.time()\n",
    "\n",
    "    inputs=[(Delta,Lx,Ly) for _ in range(es)]\n",
    "    async_result=rc[:].map_sync(run,inputs)\n",
    "\n",
    "    for index,results in enumerate(async_result):\n",
    "        MI_Born_link_pool2_list[Delta_i,index],LN_Born_link_pool2_list[Delta_i,index]=results\n",
    "\n",
    "    print('{:d}:{:.1f}'.format(Delta_i,time.time()-st))\n"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "0:151.2\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "source": [
    "fig,ax=plt.subplots()\n",
    "# ax.plot(Delta_list,LN_no_list,'.-',label='No measurement')\n",
    "\n",
    "ax.errorbar(Delta_list,LN_Born_link_pool2_list.mean(axis=1)/np.log(2),LN_Born_link_pool2_list.std(axis=1)/np.log(2)/np.sqrt(es-1),capsize=3,fmt='.-',label='Link measurement (LN)')\n",
    "ax.errorbar(Delta_list,MI_Born_link_pool2_list.mean(axis=1)/np.log(2),MI_Born_link_pool2_list.std(axis=1)/np.log(2)/np.sqrt(es-1),capsize=3,fmt='.-',label='Link measurement (MI)')\n",
    "\n",
    "ax.legend()\n",
    "ax.grid('on')\n",
    "ax.set_xlabel(r'm')\n",
    "ax.set_ylabel(r'log neg [log(2)]')\n",
    "ax.margins(x=0)\n",
    "ax.set_title('Ensemble Size={:d}, Lx={:d}, Ly={:d}'.format(es,Lx,Ly))\n",
    "fig.savefig('/mnt/d/KITP/Rp_SPT/10/LN_CI_Born_link_pool2_En{:d}_Lx{:d}_Ly{:d}.pdf'.format(es,Lx,Ly),bbox_inches='tight')"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 489.6x288 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Link, Born but with only {e+,e-}"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "run(())"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "source": [
    "Delta_list=(lambda x:(x)**3)(np.linspace(-1,1,8))\n",
    "# Delta_list=np.linspace(1,3,10)\n",
    "es=20\n",
    "LN_Born_link_poolm2_list=np.zeros((len(Delta_list),es))\n",
    "MI_Born_link_poolm2_list=np.zeros((len(Delta_list),es))\n",
    "Lx,Ly=64,4\n",
    "def run(p):\n",
    "    m,Lx,Ly=p\n",
    "    params=Params(m=m,Lx=Lx,Ly=Ly,bcx=-1,bcy=1)\n",
    "    params.measure_all_Born([np.arange(Lx//4,Lx//2),np.arange(Ly)],type='link_2',pool=-1)\n",
    "    LN=params.log_neg([np.arange(Lx//4),np.arange(Ly)],[np.arange(Lx//4)+Lx//2,np.arange(Ly)])\n",
    "    MI=params.mutual_information_m([np.arange(Lx//4),np.arange(Ly)],[np.arange(Lx//4)+Lx//2,np.arange(Ly)])\n",
    "    return MI,LN\n",
    "for m_i,m in enumerate(Delta_list):\n",
    "    st=time.time()\n",
    "\n",
    "    inputs=[(m,Lx,Ly) for _ in range(es)]\n",
    "    async_result=rc[:].map_sync(run,inputs)\n",
    "\n",
    "    for index,results in enumerate(async_result):\n",
    "        MI_Born_link_poolm2_list[m_i,index],LN_Born_link_poolm2_list[m_i,index]=results\n",
    "\n",
    "    print('{:d}:{:.1f}'.format(m_i,time.time()-st))\n"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "0:3.8\n",
      "1:3.7\n",
      "2:3.8\n",
      "3:3.7\n",
      "4:3.8\n",
      "5:3.7\n",
      "6:3.7\n",
      "7:3.7\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "source": [
    "fig,ax=plt.subplots()\n",
    "# ax.plot(Delta_list,LN_no_list,'.-',label='No measurement')\n",
    "\n",
    "ax.errorbar(Delta_list,LN_Born_link_poolm2_list.mean(axis=1)/np.log(2),LN_Born_link_poolm2_list.std(axis=1)/np.log(2)/np.sqrt(es-1),capsize=3,fmt='.-',label='Link measurement (LN)')\n",
    "ax.errorbar(Delta_list,MI_Born_link_poolm2_list.mean(axis=1)/np.log(2),MI_Born_link_poolm2_list.std(axis=1)/np.log(2)/np.sqrt(es-1),capsize=3,fmt='.-',label='Link measurement (MI)')\n",
    "\n",
    "ax.legend()\n",
    "ax.grid('on')\n",
    "ax.set_xlabel(r'm')\n",
    "ax.set_ylabel(r'log neg [log(2)]')\n",
    "ax.margins(x=0)\n",
    "ax.set_title('Ensemble Size={:d}, Lx={:d}, Ly={:d}'.format(es,Lx,Ly))\n",
    "fig.savefig('/mnt/d/KITP/Rp_SPT/10/LN_CI_Born_link_poolm2_En{:d}_Lx{:d}_Ly{:d}.pdf'.format(es,Lx,Ly),bbox_inches='tight')"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 489.6x288 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "# LN scaling"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## fix dist, |A|_x, increase |A|_y"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "source": [
    "Ly_list=np.arange(1,16)\n",
    "Lx=32\n",
    "LN_Ay=[Params(m=0,Lx=Lx,Ly=Ly).log_neg([np.arange(Lx//4),np.arange(Ly)],[np.arange(Lx//4)+Lx//2,np.arange(Ly)]) for Ly in Ly_list]\n"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "source": [
    "fig,ax=plt.subplots()\n",
    "ax.plot(Ly_list,LN_Ay/np.log(2),'.',label=r'$L_x={:d}$'.format(Lx),color='b')\n",
    "ax.set_xlabel(r'$L_y$')\n",
    "ax.set_ylabel(r'LN [log 2]')\n",
    "lr=scipy.stats.linregress(Ly_list,LN_Ay/np.log(2))\n",
    "xfit=Ly_list[[0,-1]]\n",
    "ax.plot(xfit,lr.slope*xfit+lr.intercept,'c',label=r'LN={:e}~$L_y$+ {:e}'.format(lr.slope,lr.intercept))\n",
    "\n",
    "ax.legend()\n",
    "\n",
    "fig.savefig('//mnt/d/kitp/Rp_SPT/10/LN_Ay.pdf',bbox_inches='tight')"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 489.6x288 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## fix dist, |A|_y, increase |A|_x"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "source": [
    "Lx_list=np.arange(8,20)\n",
    "Ly=32\n",
    "dist=8\n",
    "# LN_Ax=[Params(m=0,Lx=2*Lx+2*dist,Ly=Ly).log_neg([np.arange(Lx),np.arange(Ly)],[np.arange(Lx)+dist+Lx,np.arange(Ly)]) for Lx in Lx_list]\n",
    "LN_Ax=[]\n",
    "# for Lx in Lx_list:\n",
    "#     st=time.time()\n",
    "#     LN_Ax.append(Params(m=0,Lx=2*Lx+2*dist,Ly=Ly).log_neg([np.arange(Lx),np.arange(Ly)],[np.arange(Lx)+dist+Lx,np.arange(Ly)]))\n",
    "#     print('{:d}:{:.1f}'.format(Lx,time.time()-st))\n",
    "\n",
    "def run(p):\n",
    "    Lx,Ly,dist=p\n",
    "    return Params(m=0,Lx=2*Lx+2*dist,Ly=Ly).log_neg([np.arange(Lx),np.arange(Ly)],[np.arange(Lx)+dist+Lx,np.arange(Ly)])\n",
    "\n",
    "inputs=[(Lx,Ly,dist) for Lx in Lx_list]\n",
    "async_result=(rc[:].map_sync(run,inputs))\n",
    "\n",
    "for index,results in enumerate(async_result):\n",
    "    LN_Ax.append(results)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "source": [
    "fig,ax=plt.subplots()\n",
    "ax.plot(Lx_list,LN_Ax/np.log(2),'.',label=r'$L_y={:d}$'.format(Ly),color='b')\n",
    "ax.set_xlabel(r'$A_x$')\n",
    "ax.set_ylabel(r'LN [log 2]')\n",
    "# lr=scipy.stats.linregress(Lx_list,LN_Ax/np.log(2))\n",
    "# xfit=Lx_list[[0,-1]]\n",
    "# ax.plot(xfit,lr.slope*xfit+lr.intercept,'c',label=r'LN={:e}~$L_x$+ {:e}'.format(lr.slope,lr.intercept))\n",
    "\n",
    "ax.legend()\n",
    "\n",
    "fig.savefig('//mnt/d/kitp/Rp_SPT/10/LN_Ax.pdf',bbox_inches='tight')"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 489.6x288 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## fix |A|_x, |A|_y, increase dist "
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "source": [
    "dist_list=np.arange(2,16)\n",
    "Lx=32\n",
    "Ly=4\n",
    "dist=8\n",
    "# LN_dist=[Params(m=1,Lx=2*Lx+2*dist,Ly=Ly).log_neg([np.arange(Lx),np.arange(Ly)],[np.arange(Lx)+dist+Lx,np.arange(Ly)]) for dist in dist_list]\n",
    "LN_dist=[]\n",
    "for dist in dist_list:\n",
    "    st=time.time()\n",
    "    LN_dist.append(Params(m=0,Lx=2*Lx+2*dist,Ly=Ly).log_neg([np.arange(Lx),np.arange(Ly)],[np.arange(Lx)+dist+Lx,np.arange(Ly)]))\n",
    "    print(\"{:d}:{:.2f}\".format(dist,time.time()-st))\n",
    "    with open('dist.pickle','wb') as f:\n",
    "        pickle.dump([dist_list,LN_dist],f)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "2:1.83\n",
      "3:2.00\n",
      "4:2.04\n",
      "5:2.40\n",
      "6:3.05\n",
      "7:5.11\n",
      "8:3.09\n",
      "9:3.11\n",
      "10:7.89\n",
      "11:4.93\n",
      "12:3.78\n",
      "13:3.86\n",
      "14:3.67\n",
      "15:4.53\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "source": [
    "dist_list=np.array(dist_list)\n",
    "LN_dist=np.array(LN_dist)\n",
    "fig,ax=plt.subplots(3,1,figsize=(6.8,8),tight_layout=True)\n",
    "ax[0].plot((dist_list),(LN_dist/np.log(2)),'.')\n",
    "ax[0].set_title('Linear(x)-Linear(y)')\n",
    "ax[1].plot((dist_list),(LN_dist/np.log(2)),'.')\n",
    "ax[1].set_yscale('log')\n",
    "ax[1].set_title('Linear(x)-Log(y)')\n",
    "\n",
    "ax[2].plot((dist_list),(LN_dist/np.log(2)),'.')\n",
    "ax[2].set_xscale('log')\n",
    "ax[2].set_yscale('log')\n",
    "ax[2].set_title('Log(x)-Log(y)')\n",
    "\n",
    "ax[-1].set_xlabel(r'$A^\\prime_x$')\n",
    "[ax.set_ylabel(r'LN [log 2]') for ax in ax]\n",
    "\n",
    "mask=dist_list<14\n",
    "lr=scipy.stats.linregress((dist_list[mask]),np.log(LN_dist[mask]/np.log(2)))\n",
    "xfit=dist_list[mask]\n",
    "ax[1].plot(xfit,np.exp(lr.slope*xfit+lr.intercept),'c',label=r'LN=exp({:.4f}~d+ {:.4f}) $~R^2={:.4f}$'.format(lr.slope,lr.intercept,lr.rvalue))\n",
    "ax[1].legend()\n",
    "mask=dist_list<10\n",
    "lr=scipy.stats.linregress(np.log(dist_list[mask]),np.log(LN_dist[mask]/np.log(2)))\n",
    "xfit=dist_list[mask]\n",
    "ax[2].plot(xfit,np.exp(lr.slope*np.log(xfit)+lr.intercept),'c',label=r'LN=exp({:.4f}~log(d)+ {:.4f}) $~R^2={:.4f}$'.format(lr.slope,lr.intercept,lr.rvalue))# ax[0].legend()\n",
    "ax[2].legend()\n",
    "\n",
    "fig.savefig('//mnt/d/kitp/Rp_SPT/10/LN_dist.pdf',bbox_inches='tight')"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 489.6x576 with 3 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## label"
   ],
   "metadata": {}
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "6aee4f39eba147985a2c1cbf1db4ebecc02362fa8877deaa860706b7b1b97f3d"
  },
  "kernelspec": {
   "name": "python3",
   "display_name": "Python 3.8.8 64-bit ('base': conda)"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.8"
  },
  "orig_nbformat": 2
 },
 "nbformat": 4,
 "nbformat_minor": 2
}