3BodyPotentials.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Molecules Calculations Compact"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Old stuff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'boToAtomicMatrix' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-22-c458e3471c38>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[0mrmInd\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0mboMatrixInAtomic\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mboToAtomicMatrix\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mT\u001b[0m\u001b[1;33m@\u001b[0m\u001b[0mcreateBOMatrix2\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mC_3_val\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrv\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0mboBasis\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mastype\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfloat\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m@\u001b[0m\u001b[0mboToAtomicMatrix\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      3\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mi0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0m_\u001b[0m \u001b[1;32min\u001b[0m \u001b[0menumerate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mboMatrixInAtomic\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m     \u001b[0misUncoupled\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mTrue\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m     \u001b[1;32mfor\u001b[0m \u001b[0mi1\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mboMatrixInAtomic\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'boToAtomicMatrix' is not defined"
     ]
    }
   ],
   "source": [
    "rmInd = []\n",
    "boMatrixInAtomic = boToAtomicMatrix.T@createBOMatrix2(C_3_val, rv, *boBasis).astype(float)@boToAtomicMatrix\n",
    "for i0, _ in enumerate(boMatrixInAtomic):\n",
    "    isUncoupled=True\n",
    "    for i1 in range(len(boMatrixInAtomic)):\n",
    "        if i1 != i0:\n",
    "            if boMatrixInAtomic[i1,i0] != 0:\n",
    "                isUncoupled = False\n",
    "                break\n",
    "    for i2 in range(len(boMatrixInAtomic[i0])):\n",
    "        if i2 != i0:\n",
    "            if boMatrixInAtomic[i0,i2] != 0:\n",
    "                isUncoupled = False\n",
    "                break\n",
    "    if isUncoupled:\n",
    "        rmInd.append(i0)            \n",
    "print(rmInd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2 Atoms J Basis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Okay so I want to try to start creating some analysis for analyzing 3-body systems. The first thought is to take the fine-structure analysis and instead of calculating things in terms of the BO basis, to calculate it in terms of the atomic basis. I already have some analysis for working in the atomic basis since this is where the fine structure or hyperfine structure is diagonal, so this doesn't sound too hard. If I can express the BO energies in the atomic basis, it seems like it should be not too hard to add a 3rd atom and add all of the individual 2-body interactions to that picture. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "np.set_printoptions(precision=1,suppress=True,linewidth=100000, edgeitems=10000)\n",
    "from IPython.display import Latex\n",
    "import MarksConstants as mc\n",
    "import Miscellaneous as misc\n",
    "import matplotlib.pyplot as plt\n",
    "import sympy as sp\n",
    "sp.init_printing(use_latex=True)\n",
    "from sympy.physics.quantum import Bra, Ket, qapply, Dagger as Dag\n",
    "from sympy.physics.quantum.cg import CG"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "g = 0\n",
    "u = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "class multiplyableDict(dict):\n",
    "    # This class exists so that I can take a basis ref and use it in np.kron()\n",
    "    # to programatically get the basis ref for multi-particle systems.\n",
    "    def __mul__(self, other):\n",
    "        assert(type(other) == type(self))\n",
    "        newDict = multiplyableDict()\n",
    "        for key, value in self.items():\n",
    "            newDict.update({key+\"_1\": value})\n",
    "        for key, value in other.items():\n",
    "            newDict.update({key+\"_2\": value})\n",
    "        return newDict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "def createLargerBasisRefs(Lvals, Svals, Ivals, forceExcited=False):\n",
    "    fBasisRef = []\n",
    "    for Lv in Lvals:\n",
    "        for Sv in Svals:\n",
    "            Jvals = set(np.arange(abs(Sv - Lv), Sv + Lv+1, 1))\n",
    "            for Jv in Jvals:\n",
    "                for Iv in Ivals:\n",
    "                    FVals = set(np.arange(abs(Jv - Iv), Jv + Iv+1, 1))\n",
    "                    for Fv in FVals:\n",
    "                        for mf in np.arange(-Fv,Fv+1,1):\n",
    "                            fBasisRef.append(multiplyableDict({\"F\":Fv, \"mF\": mf, \"J\":Jv, \"L\":Lv, \"S\":Sv, \"I\":Iv}))\n",
    "    jiBasisRef = []\n",
    "    for Lv in Lvals:\n",
    "        for Sv in Svals:\n",
    "            Jvals = set(np.arange(abs(Sv - Lv), Sv + Lv+1, 1))\n",
    "            for Jv in Jvals:\n",
    "                for mJ in np.arange(-Jv,Jv+1,1):\n",
    "                    for Iv in Ivals:\n",
    "                        for mi in np.arange(-Iv,Iv+1,1):\n",
    "                            jiBasisRef.append(multiplyableDict({\"J\":Jv, \"mJ\":mJ, \"L\":Lv, \"S\":Sv, \"I\":Iv, \"mI\":mi}))\n",
    "    lsiBasisRef = []\n",
    "    for Lv in Lvals:\n",
    "        for mL in np.arange(-Lv,Lv+1,1):\n",
    "            for Sv in Svals:\n",
    "                for mS in np.arange(-Sv, Sv+1,1):\n",
    "                    for Iv in Ivals:\n",
    "                        for mi in np.arange(-Iv,Iv+1,1):\n",
    "                            lsiBasisRef.append(multiplyableDict({\"L\":Lv, \"mL\":mL, \"S\":Sv, \"mS\":mS, \"I\":Iv, \"mI\":mi}))\n",
    "    return lsiBasisRef, jiBasisRef, fBasisRef, np.kron(lsiBasisRef,lsiBasisRef), np.kron(jiBasisRef,jiBasisRef), np.kron(fBasisRef,fBasisRef)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fsOp(basis):\n",
    "    # expects a two-particle basis, so each element of the basis should \n",
    "    # have J_1, mJ_1, L_1, S_1, and J_2, mJ_2, L_2, S_2 values.\n",
    "    op = np.zeros((len(basis),len(basis)))\n",
    "    J1,mJ1,L1,S1,J2,mJ2,L2,S2 = [0 for _ in range(8)]\n",
    "    names = ['J','mJ','L','S']\n",
    "    for s1num, state1 in enumerate(basis):\n",
    "        for s2num, state2 in enumerate(basis):\n",
    "            val = 1\n",
    "            qNums = [0 for _ in range(8)]\n",
    "            for num, name in enumerate(names):\n",
    "                if state2[name+\"_1\"] != state1[name+\"_1\"]:\n",
    "                    # matrix is diagonal.\n",
    "                    val = 0\n",
    "                qNums[num] = state1[name+\"_1\"]\n",
    "            for num, name in enumerate(names):\n",
    "                if state2[name+\"_2\"] != state1[name+\"_2\"]:\n",
    "                    # matrix is diagonal.\n",
    "                    val = 0\n",
    "                qNums[num+4] = state1[name+\"_2\"]\n",
    "            J1,mJ1,L1,S1,J2,mJ2,L2,S2 = qNums\n",
    "            # the matrix element is A/2 (L1 . S1 + L2 . S2), A=1\n",
    "            val *= 0.5*(J1*(J1+1)-L1*(L1+1)-S1*(S1+1)+ J2*(J2+1)-L2*(L2+1)-S2*(S2+1) )\n",
    "            op[s1num,s2num] = val            \n",
    "    return op"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "def createBOMatrix2(C3, R, *states):\n",
    "    # expects states to be a list of lists where the low level list has the values of L, Lambda, S,Sigma, and sigma.\n",
    "    matrix = np.array([[0.0 for _ in states] for _ in states])\n",
    "    # the matrix is diagonal.\n",
    "    for num, state in enumerate(states):\n",
    "        #L, Lambda, S, Sigma, sigma = state\n",
    "        sigma = g if state[\"sigma\"]==\"g\" else u\n",
    "        p = (-1)**(state[\"S\"]+sigma)\n",
    "        L = state[\"L\"]\n",
    "        matrix[num,num] = -p*(3*state[\"Lambda\"]**2-L*(L+1))/R**3 * C3\n",
    "    return matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "def createBornOppenheimerBasisHFS(Lvals, Svals, Ivals, sigmavals=[\"g\",\"u\"]):\n",
    "    # Normal Notaion is |L Lambda sigma S Sigma>, but I need to keep track of more than that for the splittings caused by other interactions.\n",
    "    # Therefore this creates a very big basis which is probably unnecessary, but the size of the matrices isn't actually prohibitive in these \n",
    "    # calculations so it's okay to have degeneracies.\n",
    "    boBasisRef = []\n",
    "    for sigma in sigmavals:\n",
    "        for Lv in Lvals:\n",
    "            for Lambda in np.arange(-Lv,Lv+1,1):\n",
    "                for Sv in Svals:\n",
    "                    for Sigma in np.arange(-Sv, Sv+1,1):\n",
    "                        for i1 in Ivals:\n",
    "                            for i2 in Ivals:\n",
    "                                for I in np.arange(abs(i2-i1), i2+i1+1,1):\n",
    "                                    for iota in np.arange(-I,I+1,1):\n",
    "                                        state = multiplyableDict({\"L\":Lv, \"Lambda\": Lambda, \"sigma\": sigma, \"S\":Sv, \"Sigma\":Sigma, \"i\":I, \"iota\":iota, \"i1\":i1, \"i2\":i2,\n",
    "                                                                  \"Omega\":Sigma+Lambda, \"phi\": Sigma+Lambda+iota })\n",
    "                                        if state not in boBasisRef:\n",
    "                                            boBasisRef.append(state)\n",
    "    boBasisRef = list(sorted(boBasisRef, key=lambda state: abs(state[\"Omega\"]) + 100 * ord(state[\"sigma\"])))\n",
    "    boBasisFancy = []\n",
    "    for state in boBasisRef:\n",
    "        spinT = 2*state[\"S\"]+1\n",
    "        omega = state[\"Omega\"]\n",
    "        parity = state[\"sigma\"]\n",
    "        LambdaSymbol = \"\\Sigma\" if state[\"Lambda\"]==0 else \"\\Pi\"\n",
    "        boBasisFancy.append(Latex(r\"$^{\"+str(spinT)+ \"}\" + LambdaSymbol + \"_{\"+ str(abs(omega)) + \",\" + parity + \"}$\"))        \n",
    "    return boBasisRef, boBasisFancy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "def createCouplingMatrix(states, op, offset=-1/2, boBasis=None):\n",
    "    num = len(states)\n",
    "    coupleM = np.array([[0.0 for _ in states] for _ in states])\n",
    "    for num, _ in enumerate(states):\n",
    "        coupleM[num,num] = offset\n",
    "    for num1, state1 in enumerate(states):\n",
    "        misc.reportProgress(num1, len(states))\n",
    "        for num2, state2 in enumerate(states):\n",
    "            matElem = state2.T@op@state1\n",
    "            if boBasis is not None:\n",
    "                if boBasis[num1]['sigma'] != boBasis[num2]['sigma'] and not math.isclose(matElem, 0, abs_tol=0):\n",
    "                    continue\n",
    "                    print(boBasis[num1], '\\n', boBasis[num2],'\\n', matElem, '\\n')\n",
    "            coupleM[num1,num2] += matElem\n",
    "    return coupleM    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "def BohrOppenheimerToAtomic( oalNums, spinNums, nuclearNums, sigma, \n",
    "                             lsBasis, \n",
    "                             basisChange=None, naturalKronBasis=None, finalBasis=None ):\n",
    "    \"\"\"\n",
    "    oalNums = (L, Lambda, la, lb)\n",
    "    L is the total molecular orbital angular momentum \\vec{L} = \\vec{l1}+\\vec{l2}\n",
    "    Lambda is the projection of L on the internuclear axis.\n",
    "    l1 is the orbital angular momentum of atom 1.\n",
    "    l2 is the orbital angular momentum of atom 2.\n",
    "    \n",
    "    spinNums = (S, Sigma, sa, sb)\n",
    "    S is the total molecular spin angular momentum \\vec{s} = \\vec{s1}+\\vec{s2}\n",
    "    Sigma is the projection of S on the internuclear axis.\n",
    "    s1 is the spin angular momentum of atom 1.\n",
    "    s2 is the spin angular momentum of atom 2.\n",
    "    \n",
    "    nuclearNums = (I, iota, ia, ib)\n",
    "    \n",
    "    sigma is the spatial symmetry of the electronic wavefunctions, \n",
    "        either 0 for g (\"gerude\" or symmetric wavefunctions) \n",
    "        or 1 for u (\"ungerude\" or antisymmetric wavefunctions)\n",
    "    \"\"\"\n",
    "    (L, Lambda, la, lb) = oalNums\n",
    "    (S, Sigma, sa, sb) = spinNums\n",
    "    (I, iota, ia, ib) = nuclearNums\n",
    "    state = 0\n",
    "    p = (-1)**(S+sigma)\n",
    "    indvCont = []\n",
    "    lsiBasisStates = []\n",
    "    otherBasisStates = []\n",
    "    for mla in np.arange(-la,la+1,1):\n",
    "        mlb = Lambda-mla\n",
    "        if abs(mlb) > lb:\n",
    "            continue\n",
    "        for msa in np.arange(-sa,sa+1,1):\n",
    "            msb = Sigma-msa\n",
    "            if abs(msb) > sb:\n",
    "                continue\n",
    "            for mia in np.arange(-ia, ia+1, 1):\n",
    "                mib = iota-mia\n",
    "                if abs(mib) > ib:\n",
    "                    continue\n",
    "                # CG notation is <j1,mj1,j2,mj2|j3,mj3>\n",
    "                oalCoef = float(CG(la,mla,lb,mlb,L,Lambda).doit())\n",
    "                spinCoef = float(CG(sa,msa,sb,msb,S,Sigma).doit())\n",
    "                nuclearCoef = float(CG(ia,mia,ib,mib,I,iota).doit())\n",
    "                aState1 = getColumnState(lsiBasis, {'L':la,'mL':mla,'S':sa,'mS':msa, 'I':ia,'mI':mia})\n",
    "                bState1 = getColumnState(lsiBasis, {'L':lb,'mL':mlb,'S':sb,'mS':msb, 'I':ib,'mI':mib})\n",
    "                aState2 = getColumnState(lsiBasis, {'L':lb,'mL':mlb,'S':sa,'mS':msa, 'I':ia,'mI':mia})\n",
    "                bState2 = getColumnState(lsiBasis, {'L':la,'mL':mla,'S':sb,'mS':msb, 'I':ib,'mI':mib})\n",
    "                if oalCoef != 0 and nuclearCoef != 0 and spinCoef != 0:\n",
    "                    lsiBasisStates.append([aState1, bState1, aState2, bState2])\n",
    "                if basisChange is not None:\n",
    "                    aState1 = basisChange@aState1\n",
    "                    bState1 = basisChange@bState1\n",
    "                    aState2 = basisChange@aState2\n",
    "                    bState2 = basisChange@bState2\n",
    "                newpart = nuclearCoef*oalCoef*spinCoef * (np.kron(aState1,bState1) + p * np.kron(aState2,bState2))\n",
    "                \n",
    "                state += newpart\n",
    "                if oalCoef != 0 and nuclearCoef != 0 and spinCoef != 0:\n",
    "                    indvCont.append(newpart)\n",
    "                    otherBasisStates.append([aState1, bState1, aState2, bState2])\n",
    "    if np.linalg.norm(state) == 0:\n",
    "        raise ValueError(\"State has zero norm!\")\n",
    "    state /= np.linalg.norm(state)\n",
    "    if finalBasis is not None:\n",
    "        state = convertToReducedBasis(state, finalBasis, naturalKronBasis)\n",
    "    return state, np.array(indvCont), np.array(lsiBasisStates), np.array(otherBasisStates)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "def convertToReducedBasis(state, finBasis, origBasis):\n",
    "    assert(len(state) == len(origBasis))\n",
    "    newState = np.zeros((len(finBasis),1))\n",
    "    for num, origState in enumerate(origBasis):\n",
    "        if state[num] != 0:\n",
    "            comp = state[num]*getColumnState(finBasis, origState)\n",
    "            newState += comp\n",
    "    return newState"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "def getColumnState(basis, quantumNums):\n",
    "    assert(len(basis[0])==len(quantumNums))\n",
    "    colState = [[0] for _ in range(len(basis))]\n",
    "    for num, state in enumerate(basis):\n",
    "        match = True\n",
    "        for qnum, val in quantumNums.items():\n",
    "            if val != state[qnum]:\n",
    "                match = False\n",
    "        if match:\n",
    "            colState[num][0] = 1\n",
    "            return colState\n",
    "    raise ValueError(\"No Match! nums were\" + str(quantumNums))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lsiToJi(lsiBasis, jiBasis):\n",
    "    # expects single atom bases\n",
    "    assert(len(lsiBasis)==len(jiBasis))\n",
    "    op = np.zeros((len(lsiBasis),len(jiBasis)))\n",
    "    for lsnum, lsiState in enumerate(lsiBasis):\n",
    "        for jnum, jiState in enumerate(jiBasis):\n",
    "            # there should be some repeats because of the i values in each basis\n",
    "            L, mL, S, mS, I_lsi, mI_lsi = [lsiState[key] for key in ['L','mL','S','mS', 'I', 'mI']]\n",
    "            J, mJ, JL, JS, I_ji, mI_ji = [jiState[key] for key in ['J','mJ', 'L', 'S', 'I', 'mI']]\n",
    "            # needing to handle this case makes me feel like the actual clebsh gordon coef should be written as\n",
    "            # <L,mL,S,mS|J,mJ,L2,S2> or so instead of <L,mL,S,mS|J,mJ> as it usually is written. \n",
    "            if JL != L or JS != S or I_lsi != I_ji or mI_lsi != mI_ji:\n",
    "                op[jnum,lsnum] = 0\n",
    "            else:\n",
    "                op[jnum,lsnum] += float(CG(L, mL, S, mS, J, mJ).doit())\n",
    "    return op"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "# plugging in zero nuclear spin effectively avoids i in all of these bases. \n",
    "lsiBasis, jiBasis, fBasis, lsiBasis2Atom, jiBasis2Atom, fBasis2Atom = createLargerBasisRefs([0,1], [1/2], [0])\n",
    "JbasisR = []\n",
    "for state in jiBasis2Atom:\n",
    "    if (state['L_1'] == 0 and state['L_2'] == 0) or (state['L_1'] == 1 and state['L_2'] == 1):\n",
    "        continue\n",
    "    JbasisR.append(state)\n",
    "#fsOperator = fsOp(jiBasis2Atom)\n",
    "fsRed = fsOp(JbasisR)\n",
    "lsiToJiop = lsiToJi(lsiBasis,jiBasis)\n",
    "boBasisDict_g, boBasisLatex_g = createBornOppenheimerBasisHFS([1],[0,1], [0], sigmavals=['g'])\n",
    "boBasisDict_u, boBasisLatex_u = createBornOppenheimerBasisHFS([1],[0,1], [0], sigmavals=['u'])\n",
    "boBasisDict_full, boBasisLatex_full = createBornOppenheimerBasisHFS([1],[0,1], [0], sigmavals=['g', 'u'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "boBasis0mg = []\n",
    "boBasisDict_full;\n",
    "boQns = ['L','Lambda', 'S', 'Sigma','sigma']\n",
    "stateList = [[1, 0, 1, 0, 'g'], [1, -1, 1, 1, 'g'], [1, 1, 1, -1, 'g'], [1,0,0,0,'g']]\n",
    "for boVals in stateList:\n",
    "    for bostate in boBasisDict_full:\n",
    "        match=True\n",
    "        for qn, val in zip(boQns, boVals):\n",
    "            if bostate[qn] != val:\n",
    "                match=False\n",
    "                break\n",
    "        if match:\n",
    "            boBasis0mg.append(bostate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "boBasis = boBasisDict_full"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "boToAtomicMatrix = []\n",
    "for st in boBasis: \n",
    "    sigmaV = g if st['sigma']=='g' else u\n",
    "    phase = (-1)**(sigmaV+st['S'])\n",
    "    state1, _,_,_ = BohrOppenheimerToAtomic( [st['L'],st['Lambda'],st['L'],0],\n",
    "                                                [st['S'],st['Sigma'],1/2,1/2],\n",
    "                                                [st['i'],st['iota'],0,0],\n",
    "                                                sigmaV, lsiBasis, basisChange=lsiToJiop, naturalKronBasis=jiBasis2Atom, finalBasis=JbasisR)\n",
    "    boToAtomicMatrix.append(state1.T[0])\n",
    "boToAtomicMatrix = np.array(boToAtomicMatrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "A_gs = (mc.Rb87_Ground_ToF2-mc.Rb87_Ground_ToF1)/2\n",
    "A_12 = (mc.Rb87_5P12_ToF2-mc.Rb87_5P12_ToF1)/2\n",
    "A_32 = (mc.Rb87_5P32_ToF3-mc.Rb87_5P32_ToF0)/6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.7197635548748796e-21 5.94492796981645e-48\n"
     ]
    }
   ],
   "source": [
    "lifetime = (mc.Rb87_D1_Lifetime+mc.Rb87_D2_Lifetime)/2\n",
    "transFreq = 2*np.pi*(mc.Rb87_D2LineFrequency+mc.Rb87_D1LineFrequency)/2\n",
    "DeltaVal = mc.h*(mc.Rb87_D2LineFrequency-mc.Rb87_D1LineFrequency)# / mc.h\n",
    "C_3_val = mc.Rb87_C3\n",
    "print(DeltaVal, C_3_val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100%                         \r"
     ]
    }
   ],
   "source": [
    "Rvals = np.linspace( 0.5*20*mc.a0, 10*20*mc.a0, 20000 )\n",
    "data = []\n",
    "#eEnergy = electronicEnergy(jiBasis2Atom)\n",
    "for rnum, rv in enumerate(Rvals):\n",
    "    misc.reportProgress(rnum, len(Rvals))\n",
    "    t1 = boToAtomicMatrix.T@createBOMatrix2(C_3_val, rv, *boBasis).astype(float)@boToAtomicMatrix\n",
    "    t2 = fsRed * 2 * DeltaVal / 3\n",
    "    rmatrix = t1 + t2\n",
    "    eigVals = np.linalg.eigvalsh(rmatrix)\n",
    "    data.append(eigVals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Miniconda3\\lib\\site-packages\\IPython\\core\\pylabtools.py:132: UserWarning: Creating legend with loc=\"best\" can be slow with large amounts of data.\n",
      "  fig.canvas.print_figure(bytes_io, **kw)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "colors, _ = misc.getColors(len(misc.transpose(data))+1)\n",
    "linestyles = ['-',':','--']\n",
    "yoff = 0\n",
    "for datanum, (mdata, color) in enumerate(zip(misc.transpose(data), colors)):\n",
    "    ax.plot(Rvals*1e9, np.array(mdata) * 1e-9 / mc.h + yoff, linewidth=1, label=datanum, color='#0000AA', linestyle='-')\n",
    "ax.legend(ncol=5)\n",
    "ax.set_xlim(1,5)\n",
    "ax.set_ylim(-20000,15000)\n",
    "ax.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2 Atoms LS Basis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lsiToJi(lsiBasis, jiBasis):\n",
    "    # expects single atom bases\n",
    "    assert(len(lsiBasis)==len(jiBasis))\n",
    "    op = np.zeros((len(lsiBasis),len(jiBasis)))\n",
    "    for lsnum, lsiState in enumerate(lsiBasis):\n",
    "        for jnum, jiState in enumerate(jiBasis):\n",
    "            # there should be some repeats because of the i values in each basis\n",
    "            L, mL, S, mS, I_lsi, mI_lsi = [lsiState[key] for key in ['L','mL','S','mS', 'I', 'mI']]\n",
    "            J, mJ, JL, JS, I_ji, mI_ji = [jiState[key] for key in ['J','mJ', 'L', 'S', 'I', 'mI']]\n",
    "            # needing to handle this case makes me feel like the actual clebsh gordon coef should be written as\n",
    "            # <L,mL,S,mS|J,mJ,L2,S2> or so instead of <L,mL,S,mS|J,mJ> as it usually is written. \n",
    "            if JL != L or JS != S or I_lsi != I_ji or mI_lsi != mI_ji:\n",
    "                op[jnum,lsnum] = 0\n",
    "            else:\n",
    "                op[jnum,lsnum] += float(CG(L, mL, S, mS, J, mJ).doit())\n",
    "    return op"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {},
   "outputs": [],
   "source": [
    "def J_to_LS(lsiBasis, jiBasis):\n",
    "    assert(len(lsiBasis)==len(jiBasis))\n",
    "    op = np.zeros((len(lsiBasis),len(jiBasis)))\n",
    "    for lsnum, lsiState in enumerate(lsiBasis):\n",
    "        for jnum, jiState in enumerate(jiBasis):\n",
    "            # there should be some repeats because of the i values in each basis unless I=0\n",
    "            L1, mL1, S1, mS1, I_lsi1, mI_lsi1 = [lsiState[key] for key in ['L_1','mL_1','S_1','mS_1', 'I_1', 'mI_1']]\n",
    "            J1, mJ1, JL1, JS1, I_ji1, mI_ji1 = [jiState[key] for key in ['J_1','mJ_1', 'L_1', 'S_1', 'I_1', 'mI_1']]\n",
    "            L2, mL2, S2, mS2, I_lsi2, mI_lsi2 = [lsiState[key] for key in ['L_2','mL_2','S_2','mS_2', 'I_2', 'mI_2']]\n",
    "            J2, mJ2, JL2, JS2, I_ji2, mI_ji2 = [jiState[key] for key in ['J_2','mJ_2', 'L_2', 'S_2', 'I_2', 'mI_2']]\n",
    "            # needing to handle this case makes me feel like the actual clebsh gordon coef should be written as\n",
    "            # <L,mL,S,mS|J,mJ,L2,S2> or so instead of <L,mL,S,mS|J,mJ> as it usually is written. \n",
    "            if JL1 != L1 or JS1 != S1 or I_lsi1 != I_ji1 or mI_lsi1 != mI_ji1:\n",
    "                op[jnum,lsnum] = 0\n",
    "            elif JL2 != L2 or JS2 != S2 or I_lsi2 != I_ji2 or mI_lsi2 != mI_ji2:\n",
    "                op[jnum,lsnum] = 0\n",
    "            else:\n",
    "                op[jnum,lsnum] += float(CG(L1, mL1, S1, mS1, J1, mJ1).doit())*float(CG(L2, mL2, S2, mS2, J2, mJ2).doit())\n",
    "    return op"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "24\n",
      "(8, 8)\n"
     ]
    }
   ],
   "source": [
    "# plugging in zero nuclear spin effectively avoids i in all of these bases. \n",
    "lsiBasis, jiBasis, fBasis, lsiBasis2Atom, jiBasis2Atom, fBasis2Atom = createLargerBasisRefs([0,1], [1/2], [0])\n",
    "lsBasisR, jBasisR = [], []\n",
    "for state in lsiBasis2Atom:\n",
    "    if (state['L_1'] == 0 and state['L_2'] == 0) or (state['L_1'] == 1 and state['L_2'] == 1):\n",
    "        continue\n",
    "    lsBasisR.append(state)\n",
    "for state in jiBasis2Atom:\n",
    "    if (state['L_1'] == 0 and state['L_2'] == 0) or (state['L_1'] == 1 and state['L_2'] == 1):\n",
    "        continue\n",
    "    jBasisR.append(state)\n",
    "fsOperator = fsOp(jBasisR)\n",
    "J_to_LS_op = J_to_LS(lsBasisR,jBasisR)\n",
    "fsOp_LS = J_to_LS_op@fsOperator@J_to_LS_op.T\n",
    "print(len(lsBasisR))\n",
    "lsiToJiop = lsiToJi(lsiBasis,jiBasis)\n",
    "print(lsiToJiop.shape)\n",
    "#fsLsi = lsiToJiop.T@fsOperator@lsiToJiop\n",
    "#boBasisDict_g, boBasisLatex_g = createBornOppenheimerBasisHFS([1],[0,1], [0], sigmavals=['g'])\n",
    "#boBasisDict_u, boBasisLatex_u = createBornOppenheimerBasisHFS([1],[0,1], [0], sigmavals=['u'])\n",
    "#boBasisDict_full, boBasisLatex_full = createBornOppenheimerBasisHFS([1],[0,1], [0], sigmavals=['g', 'u'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [],
   "source": [
    "boBasis = boBasisDict_full"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [],
   "source": [
    "boToAtomicMatrix = []\n",
    "for st in boBasis: \n",
    "    sigmaV = g if st['sigma']=='g' else u\n",
    "    phase = (-1)**(sigmaV+st['S'])\n",
    "    state1, _,_,_ = BohrOppenheimerToAtomic( [st['L'],st['Lambda'],st['L'],0],\n",
    "                                                [st['S'],st['Sigma'],1/2,1/2],\n",
    "                                                [st['i'],st['iota'],0,0],\n",
    "                                                sigmaV, lsiBasis, basisChange=lsiToJiop, naturalKronBasis=jiBasis2Atom, finalBasis=jBasisR)\n",
    "    boToAtomicMatrix.append(state1.T[0])\n",
    "boToAtomicMatrix = np.array(boToAtomicMatrix)\n",
    "#boToAtomicMatrix = J_to_LS_op @ np.array(boToAtomicMatrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {},
   "outputs": [],
   "source": [
    "A_gs = (mc.Rb87_Ground_ToF2-mc.Rb87_Ground_ToF1)/2\n",
    "A_12 = (mc.Rb87_5P12_ToF2-mc.Rb87_5P12_ToF1)/2\n",
    "A_32 = (mc.Rb87_5P32_ToF3-mc.Rb87_5P32_ToF0)/6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.7197635548748796e-21 5.94492796981645e-48\n"
     ]
    }
   ],
   "source": [
    "lifetime = (mc.Rb87_D1_Lifetime+mc.Rb87_D2_Lifetime)/2\n",
    "transFreq = 2*np.pi*(mc.Rb87_D2LineFrequency+mc.Rb87_D1LineFrequency)/2\n",
    "DeltaVal = mc.h*(mc.Rb87_D2LineFrequency-mc.Rb87_D1LineFrequency)# / mc.h\n",
    "C_3_val = mc.Rb87_C3\n",
    "print(DeltaVal, C_3_val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0], [0], [1], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0]]\n",
      "{'J_1': 1.5, 'mJ_1': 1.5, 'L_1': 1, 'S_1': 0.5, 'I_1': 0, 'mI_1': 0, 'J_2': 0.5, 'mJ_2': -0.5, 'L_2': 0, 'S_2': 0.5, 'I_2': 0, 'mI_2': 0}\n",
      "{'L_1': 1, 'mL_1': 1, 'S_1': 0.5, 'mS_1': 0.5, 'I_1': 0, 'mI_1': 0, 'L_2': 0, 'mL_2': 0, 'S_2': 0.5, 'mS_2': -0.5, 'I_2': 0, 'mI_2': 0}\n"
     ]
    }
   ],
   "source": [
    "print(getColumnState(jBasisR, jBasisR[2]))\n",
    "print(jBasisR[-2])\n",
    "print(lsBasisR[-2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {},
   "outputs": [],
   "source": [
    "def HC(matrix):\n",
    "    return matrix.conj().T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {},
   "outputs": [],
   "source": [
    "toAtomic = boToAtomicMatrix@HC(J_to_LS_op)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100%                        \r"
     ]
    }
   ],
   "source": [
    "Rvals = np.linspace( 0.5*20*mc.a0, 5*20*mc.a0, 5000 )\n",
    "data = []\n",
    "for rnum, rv in enumerate(Rvals):\n",
    "    misc.reportProgress(rnum, len(Rvals))\n",
    "    #t1 = J_to_LS_op@boToAtomicMatrix.T@createBOMatrix2(C_3_val, rv, *boBasis).astype(float)@boToAtomicMatrix@J_to_LS_op.T\n",
    "    t1 = HC(toAtomic)@createBOMatrix2(C_3_val, rv, *boBasis).astype(float)@toAtomic\n",
    "    t2 = fsOp_LS * 2 * DeltaVal / 3\n",
    "    rmatrix = t1 + t2\n",
    "    eigVals = np.linalg.eigvalsh(rmatrix)\n",
    "    data.append(eigVals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "colors, _ = misc.getColors(len(misc.transpose(data))+1)\n",
    "linestyles = ['-',':','--']\n",
    "for datanum, (mdata, color) in enumerate(zip(misc.transpose(data), colors)):\n",
    "    ax.plot(Rvals*1e9, np.array(mdata) * 1e-9 / mc.h, linewidth=1, label=datanum, color='#0000AA', linestyle='-')\n",
    "ax.legend(ncol=5)\n",
    "ax.set_xlim(1,5)\n",
    "ax.set_ylim(-20000,15000)\n",
    "ax.grid()\n",
    "ax.set_title('Result in LSI Basis');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "so close..."
   ]
  },
  {
   "attachments": {
    "8c4d6609-0a85-45cb-9cc3-51c36457d0f5.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:8c4d6609-0a85-45cb-9cc3-51c36457d0f5.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2-Atoms Rotated"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "this should give the same result as above since I'm rotating the whole basis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### constructing the rotation operator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "R(\\theta) = \\exp\\{-\\frac{i\\theta}{\\hbar}\\hat{n}\\bullet\\vec{J}\\}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2.7, 0. ],\n",
       "       [0. , 0.4]])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.linalg import expm, sinm, cosm\n",
    "expm([[1,0],[0,-1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rotateM(theta, Sz):\n",
    "    #sigmax = np.array([[0,1],[1,0]])\n",
    "    #sigmay = np.array([[0,1j],[-1j,0]])\n",
    "    #sigmaz = np.array([[1,0],[0,-1]])\n",
    "    return expm(-1j*theta/2*Sz)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.-0.j, -0.+0.j,  0.+0.j],\n",
       "       [ 0.+0.j,  1.+0.j,  0.+0.j],\n",
       "       [ 0.+0.j,  0.+0.j,  1.+0.j]])"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rotateM(4*np.pi, createSpinMatrix(1,\"Sz\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [],
   "source": [
    "def delta(ms1,ms2):\n",
    "    if ms1==ms2:\n",
    "        return 1\n",
    "    return 0\n",
    "def createSpinMatrix(spin, which):\n",
    "    assert(which == \"Sx\" or which == \"Sy\" or which == \"Sz\")\n",
    "    assert(int(2*spin) == float(2*spin))\n",
    "    mS_vals = np.arange(-spin,spin+1,1)\n",
    "    Sm = np.zeros((len(mS_vals),len(mS_vals)), dtype=complex)\n",
    "    for i1, ms1 in enumerate(mS_vals):\n",
    "        for i2, ms2 in enumerate(mS_vals):\n",
    "            if which == \"Sx\":\n",
    "                Sm[i1,i2] = (delta(ms2,ms1+1) + delta(ms2+1,ms1)) * 0.5 * np.sqrt(spin*(spin+1)-ms1*ms2)\n",
    "            elif which == \"Sy\":\n",
    "                Sm[i1,i2] = (delta(ms2,ms1+1) - delta(ms2+1,ms1)) * 0.5j * np.sqrt(spin*(spin+1)-ms1*ms2)\n",
    "            elif which == \"Sz\":\n",
    "                Sm[i1,i2] = delta(ms2,ms1)*ms1\n",
    "    return Sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.+0.j , 0.+0.7j, 0.+0.j ],\n",
       "       [0.-0.7j, 0.+0.j , 0.+0.7j],\n",
       "       [0.+0.j , 0.-0.7j, 0.+0.j ]])"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "createSpinMatrix(1,'Sy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [],
   "source": [
    "def createRotationMatrix(basis, theta, spinToRotate):\n",
    "    Rm = np.zeros((len(basis), len(basis)), dtype=complex)\n",
    "    for i1, state1 in enumerate(basis):\n",
    "        for i2, state2 in enumerate(basis):\n",
    "            coupled=True\n",
    "            for k1,k2 in zip(state1.keys(), state2.keys()):\n",
    "                assert(k1==k2)\n",
    "                if (k1 != \"m\" + spinToRotate) and state1[k1] != state2[k2]:\n",
    "                    coupled=False\n",
    "            if not coupled:\n",
    "                Rm[i1, i2] = 0\n",
    "            else:\n",
    "                assert(state1[spinToRotate] == state2[spinToRotate])\n",
    "                spv = state1[spinToRotate]\n",
    "                rm_small = rotateM(theta, createSpinMatrix(spv,\"Sx\"))\n",
    "                rm_i1 = list(np.arange(-spv, spv+1)).index(state1[\"m\"+spinToRotate])\n",
    "                rm_i2 = list(np.arange(-spv, spv+1)).index(state2[\"m\"+spinToRotate])\n",
    "                Rm[i1,i2] = rm_small[rm_i1,rm_i2]\n",
    "    return Rm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fullRotation(theta):\n",
    "    RmL1 = createRotationMatrix(lsBasisR, theta, 'L_1')\n",
    "    RmL2 = createRotationMatrix(lsBasisR, theta, 'L_2')\n",
    "    RmS1 = createRotationMatrix(lsBasisR, theta, 'S_1')\n",
    "    RmS2 = createRotationMatrix(lsBasisR, theta, 'S_2')\n",
    "    return RmL1@RmL2@RmS1@RmS2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## analysis..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "24\n",
      "(8, 8)\n"
     ]
    }
   ],
   "source": [
    "# plugging in zero nuclear spin effectively avoids i in all of these bases. \n",
    "lsiBasis, jiBasis, fBasis, lsiBasis2Atom, jiBasis2Atom, fBasis2Atom = createLargerBasisRefs([0,1], [1/2], [0])\n",
    "lsBasisR, jBasisR = [], []\n",
    "for state in lsiBasis2Atom:\n",
    "    if (state['L_1'] == 0 and state['L_2'] == 0) or (state['L_1'] == 1 and state['L_2'] == 1):\n",
    "        continue\n",
    "    lsBasisR.append(state)\n",
    "for state in jiBasis2Atom:\n",
    "    if (state['L_1'] == 0 and state['L_2'] == 0) or (state['L_1'] == 1 and state['L_2'] == 1):\n",
    "        continue\n",
    "    jBasisR.append(state)\n",
    "fsOperator = fsOp(jBasisR)\n",
    "J_to_LS_op = J_to_LS(lsBasisR,jBasisR)\n",
    "fsOp_LS = J_to_LS_op@fsOperator@J_to_LS_op.T\n",
    "print(len(lsBasisR))\n",
    "lsiToJiop = lsiToJi(lsiBasis,jiBasis)\n",
    "print(lsiToJiop.shape)\n",
    "#fsLsi = lsiToJiop.T@fsOperator@lsiToJiop\n",
    "#boBasisDict_g, boBasisLatex_g = createBornOppenheimerBasisHFS([1],[0,1], [0], sigmavals=['g'])\n",
    "#boBasisDict_u, boBasisLatex_u = createBornOppenheimerBasisHFS([1],[0,1], [0], sigmavals=['u'])\n",
    "boBasisDict_full, boBasisLatex_full = createBornOppenheimerBasisHFS([1],[0,1], [0], sigmavals=['g', 'u'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "metadata": {},
   "outputs": [],
   "source": [
    "boBasis = boBasisDict_full"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "metadata": {},
   "outputs": [],
   "source": [
    "boToAtomicMatrix = []\n",
    "for st in boBasis: \n",
    "    sigmaV = g if st['sigma']=='g' else u\n",
    "    phase = (-1)**(sigmaV+st['S'])\n",
    "    state1, _,_,_ = BohrOppenheimerToAtomic( [st['L'],st['Lambda'],st['L'],0],\n",
    "                                                [st['S'],st['Sigma'],1/2,1/2],\n",
    "                                                [st['i'],st['iota'],0,0],\n",
    "                                                sigmaV, lsiBasis, basisChange=lsiToJiop, naturalKronBasis=jiBasis2Atom, finalBasis=jBasisR)\n",
    "    boToAtomicMatrix.append(state1.T[0])\n",
    "boToAtomicMatrix = np.array(boToAtomicMatrix)\n",
    "#boToAtomicMatrix = J_to_LS_op @ np.array(boToAtomicMatrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "metadata": {},
   "outputs": [],
   "source": [
    "A_gs = (mc.Rb87_Ground_ToF2-mc.Rb87_Ground_ToF1)/2\n",
    "A_12 = (mc.Rb87_5P12_ToF2-mc.Rb87_5P12_ToF1)/2\n",
    "A_32 = (mc.Rb87_5P32_ToF3-mc.Rb87_5P32_ToF0)/6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.7197635548748796e-21 5.94492796981645e-48\n"
     ]
    }
   ],
   "source": [
    "lifetime = (mc.Rb87_D1_Lifetime+mc.Rb87_D2_Lifetime)/2\n",
    "transFreq = 2*np.pi*(mc.Rb87_D2LineFrequency+mc.Rb87_D1LineFrequency)/2\n",
    "DeltaVal = mc.h*(mc.Rb87_D2LineFrequency-mc.Rb87_D1LineFrequency)# / mc.h\n",
    "C_3_val = mc.Rb87_C3\n",
    "print(DeltaVal, C_3_val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0], [0], [1], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0]]\n",
      "{'J_1': 1.5, 'mJ_1': 1.5, 'L_1': 1, 'S_1': 0.5, 'I_1': 0, 'mI_1': 0, 'J_2': 0.5, 'mJ_2': -0.5, 'L_2': 0, 'S_2': 0.5, 'I_2': 0, 'mI_2': 0}\n",
      "{'L_1': 1, 'mL_1': 1, 'S_1': 0.5, 'mS_1': 0.5, 'I_1': 0, 'mI_1': 0, 'L_2': 0, 'mL_2': 0, 'S_2': 0.5, 'mS_2': -0.5, 'I_2': 0, 'mI_2': 0}\n"
     ]
    }
   ],
   "source": [
    "print(getColumnState(jBasisR, jBasisR[2]))\n",
    "print(jBasisR[-2])\n",
    "print(lsBasisR[-2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 215,
   "metadata": {},
   "outputs": [],
   "source": [
    "def HC(matrix):\n",
    "    return matrix.conj().T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {},
   "outputs": [],
   "source": [
    "toAtomic = boToAtomicMatrix@HC(J_to_LS_op)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100%                        \r"
     ]
    }
   ],
   "source": [
    "Rvals = np.linspace( 0.5*20*mc.a0, 5*20*mc.a0, 5000 )\n",
    "data = []\n",
    "rotMatrix = fullRotation(1)\n",
    "for rnum, rv in enumerate(Rvals):\n",
    "    misc.reportProgress(rnum, len(Rvals))\n",
    "    #t1 = J_to_LS_op@boToAtomicMatrix.T@createBOMatrix2(C_3_val, rv, *boBasis).astype(float)@boToAtomicMatrix@J_to_LS_op.T\n",
    "    t1 = HC(toAtomic)@createBOMatrix2(C_3_val, rv, *boBasis).astype(float)@toAtomic\n",
    "    t2 = fsOp_LS * 2 * DeltaVal / 3\n",
    "    rmatrix = t1 + t2\n",
    "    rotatedH = HC(rotMatrix)@rmatrix@rotMatrix\n",
    "    eigVals = np.linalg.eigvalsh(rotatedH)\n",
    "    data.append(eigVals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "colors, _ = misc.getColors(len(misc.transpose(data))+1)\n",
    "linestyles = ['-',':','--']\n",
    "for datanum, (mdata, color) in enumerate(zip(misc.transpose(data), colors)):\n",
    "    ax.plot(Rvals*1e9, np.array(mdata) * 1e-9 / mc.h, linewidth=1, label=datanum, color='#0000AA', linestyle='-')\n",
    "ax.legend(ncol=5)\n",
    "ax.set_xlim(1,5)\n",
    "ax.set_ylim(-20000,15000)\n",
    "ax.grid()\n",
    "ax.set_title('Result in LSI Basis');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "for ref:"
   ]
  },
  {
   "attachments": {
    "dfa5667b-d326-4dd1-a23b-12e8cab92f55.png": {
     "image/png": 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ELND+14Lg4uIimKQOmXNHJ/VqKsICnQxUBRcXVcHE/26RoMFJJHO7d/9PN2+eoz/7bL6uVIk0X331O+/MdmdnmtTIAu0fKMHFxUUw8b9wZSFy5wo1govg4kfArZW54n+3CJlLIpljGo4YsVbXqJGpX3hhqiF0qFvnzt3sztA0qJEF2j9IgouLi2Dif+HKQuTOFWoEF8HFj4BbK3PF/24RMpdkMsdUvOWW0SaQMF6tNWr00WedlauR2qVbkQXaP2KCi4uLYOJ/4cpC5M4VagQXwcWPgFsrc8X/bhEyVwZkbuXKbSZXa3b2CpO3tX79fvqNN2a6szTFa2SB9g+Q4OLiIpj4X7iyELlzhRrBRXDxI+DWylzxv1uEzJUBmWM6fvjhXN26dZ5++ukpRt16xBG99OTJG9yZmsI1skD7B0dwcXERTPwvXFmI3LlCjeAiuPgRcGtlrvjfLULmyojM7dnzP6Ne/fjjubpu3SxjR9e06QC9Y0f6eLfKAu2+WKgRXFxcBBP/C1cWIneuUCO4CC5+BNxamSv+d4uQuTIic0zJGTM2GXXr8OFrjbq1SZP++h//SJ9gwrJAuy8WagQXFxfBxP/CLeuFiJyW1apVM0nb3VFKnZqS4LJhwwZ9zTXX6EaNGunGjRtrsl1UhBIcM4sLadmIp/eHP/xBjx07tiJ0s1Afgn0OfvHBBx+Y5PP03QZKtpgEz0u34yVLlug2bdqYeUvf3nvvPdOFWMdZ4sx5iJuvKlFx5nwT7OWXp+vLLx+m33hjhiF0xx7bR/fuHcox6Ds/lepkgfaPhuDi4iKYpAaZI1/p+PHjKySZu+WWW/Tnn39uJh/ZLSB3FaEEx8wSFxbvWbNm6fPOO69Ckrlgn+0Y5uXl6QsvvFBv377dVJGDl2Ixseel457sFjyXtj8E9Z4+fbqOdZyFzPmYm6cumWQOtepJJ/XX3367SJ9xxiCT7otMEeRzTfUiC7R/hAQXFxfBJDXIHCMTmSbJHa3yr4l3gd60aZM+7rjjNGmRKmKxYxaJS0Ulc4yh7bMdz+uuu04PHDjQfszfR2KS/0UaH1x55ZU6JycnvwfFjbOQOQ9x81XVrt0gH9RkHEyYsF5Xq9Zbz5y5SR90UIZG3XrmmYP0zp2pbT8nC7R/NgguLi6CiZA5d1ZEr4l3gZ44caI+7bTT9K233qqbNWum77zzTk2O1opSLLGJxKW4RT6d+2/7bPtAiqsXXnhBn3766frcc8/VY8aMMV9FYmLPT9c9/a5Vq5bmD4otxY2zkDkfc/PU7bNP3aQ7Jrz++kx93nmDdV7eapO7tVmzAfrvf59oxzIl97JA+4dFcHFxEUyEzLmzInpNvAs0dmOVKlXSv/zyi7noQw89pJ977rnoN0izbyyxicSluEU+zbpZqLm2z7byxBNP1A8++KCRvo4ePTpfEhuJiT0/HfebN2/WLVq00BkZGYWaX9w4C5nzEDdfFWTu4ouHFgI30R8IGnzOOXn6zTdn6UcemWjCldSu3deoXxN9r0RdTxZoP5KCi4uLYOKSOaW6mj9uidy7yLs1kYuke0bpahLZH3ut4lq0cuVKXadOnfzTfv75Z33ZZZflf07UgW1PIvextM2OWSRxKW6Rj+XaxZ2TyL7aaxV3T763fbbnXnLJJYWcy+rWravXrFmTcJs528ZE7m0fitrv3LlTX3zxxbpTp07OacWNs5A5H3Pz1NWq1cA4J3z//SIH5ERWLFy4xXi3Tpq0QbdsOVBXqdLDqF/Hjl2XyNsk7FqyQPuhFFxcXAQTl8yBUuTi7CKX+JrIRTLxdyj9FUuCS+vWrY1TAHd/8cUX9WOPPVb6hqTIFeyYReJS3CKfIs0vUTNsn+2PO3furJ9//nnzcfbs2bpmzZpGSheJiT0/nfbYenbo0EE//PDD3mYXN85C5jzEzVeFA8S9947T++3XXa9bt8MLdqIqv/56oT7hhGy9du024wzRqFG2rlUrU5M1ItWKLND+ERFcXFwEk9Qgc+3bt9fVq1fXlStX1jVq1NBdunRxBysFakqyQGM317JlS33yySfrq666Sq9fvz4FelL6JgTH7NhjjzVj1qNHDzN+++67rz7qqKOMRKf0d0qdKwT7bOcpHso33XST8cRu3ry5zs3NNQ0uyVxJnZ6GWjJs2DCtlDJzF9tAtqysLB3rOAuZ8zE3Tx1kbs+ePYZUEdg3mQWGfuuto/VNN/2ip0/fqCtV6maCC5O/ddu23cm8ddzXlgXaD5ng4uIimKQGmXNHJjVrKsICnQxkBRcXVcHE/26RoMFRyBxTaMGCzbpy5W5JD+z7+++79MknD9Cffjrf2Myhu2/VapC+/vqRmswRqVJkgfaPhODi4iKY+F+4shC5c4UawUVw8SPg1spc8b9bhMwVQeaYRqhB//CHrnrQoFXurEpgzaxZvxn7ufHj1+uHHpqg99mnq27ePEc/+mjqZIiQBdo/4IKLi4tg4n/hykLkzhVqBBfBxY+AWytzxf9uSQUy94VSao1SalqAV1VVSg1USs0N7w8Pf/cHpdQHSql5SqkpSqkWgd/cGj6f33BsS0ul1NTwb/gt1yiyRAYNbtdupN5//+Tbz/300xKTtxU7vUsuGWru2aBBP/3ee3PcGV0ONbJA+0EXXFxcBBP/C1cWIneuUCO4CC5+BNxamSv+d0sqkLlzw6QsSObeVEo9FWZc7P8VPr5MKZUdJmRnKqVGh+shfwuUUuwhfhxbAjhGKdUq/Bt+e2mRTE4pFUnmsJ8jbEjDhv2MLZ07vRJXgyTuwguH6O3bd+nGjbN11ao9NSm/unZdkriblPBKskD7gRNcXFwEE/8LVxYid65QI7gILn4E3FqZK/53SyqQObjVcRGSudlKqWPCpIs9nymfKqVuCB+zs+dRx3e22PP47SxbGf5t8LzAVwWHkWSO6bR8+e/Gu/Waa0a4syuBNcSfu/TSn/Xf/jZeY0t3xBG9dJ06mZqUX1lZKxJ4p/gvJQu0HzPBxcVFMPG/cGUhcucKNYKL4OJHwK2VueJ/t6QqmdtYQK3M0Ybw575KqdaB73KVUqcqpR5TSj0XqH8+XMd3gwL15yiluEaRxUfmmFJDh64xtmyvvTbDnWEJrNm4cacJV/Lxx3MNiSTlFyFLSAGWbNu9orohC7QfHcHFxUUw8b9wZSFy5wo1govg4kfArZW54n+3pBuZy/KQOWziHveQuUeVUqd5yFxmFCZ3dxiMcdWqVTORp1mQIreHHsoyDhGvv97f+S7y3NJ8/u67Qfrww7vpt98eoL/7bqDed9+uun79DF2lSjf9wQc5Sb13tHZnZmaWy32jtSdV6gUX9zkRTAbrCRMmGJLC4mO3DRs25B/bumTuiUd1zjnnaP6gNm7cWL/xxhtlev9Y+xYvLuPHjzcxuogxx3bIIYfo119/PSX7FisG9rybb75ZH3nkkfqEE07QFhfSlTVo0MDEXLviiiv0kiVLKkRffX22dVdffXX+GNeuXdsc853FxJ6Xjvtoz2Ws48y7JXL9S1UyZ9Wn8K6UULMG/x/cdtsY/cc/dtOzZhUkxg1+n6jjIUPWGGnchAnr9eTJG8w9iT+HhG7kyF8TdZuYr8PkkeIiILgIJi4C/n/PLDxlWVasWKEhPhTuDSGYPn16WTYhpnuVBpfdu3fro48+Wi9alNyMPTF1JAEnDR061IwZuUktLgMGDNC7du0yV3/iiSc0W0UqwT77+vWPf/xDd+zY0XxlMfGdly510Z7LWMc5lYMGR9rMvRXhAIFDBOXyCAcInBsoOD4sDDs94PjAMXWUsUopnCXwYsUBAieKIks0NWtwopx55iCN+nP16uRmaujWbalxgJg/f7MePnytCSp87rl5JoxJXt7qYJOSfiykxQ+x4OLiIpikBpmLHJkrr7xS5+TkRFaX++fSLNAsgGeddVa59yGRDbCprXy4kCXgxhtvTOTtUuJats+RjSGwPqm85swJRXXwYRL5m3T77HsuixrnVCVzPyilViqldimlliml7lRKHaGUwh6OMCPsLTGDkH2slJofDjeCTZwtd4TDjxC25HZbGbapw1OW33wUS2iSY49tUOxcwMOVsCFHHtnLOCoU+4NSnPDJJ/N0/fr9DHHEbo9AxmefnWvuXZZOEbJA+wdRcHFxEUxSj8yxWNaqVUtv2pRcjYI7G4qvKc0Cffvtt+sPP/yw+Juk0RmW2PhwQc367bffplFvYmuq7XPk2UjtSNtmiw8T+1067qM9l0WNc6qSuQDvSpXDunrp0t+LnRfbtu0yXqbHH99X79q1p9jzS3PC889P1S1bDtSbNu00KlbUvGecMdDcv3v3paW5dMy/lQXaD5Xg4uIimKQWmdu8ebNu0aKFzsjIcAcrBWpKukCTv/OII47Qq1YlN6h7WUNkiU0kLq+88or+y1/+YhLOl3Wbkn0/2+fI+9x777367bffzq+OxCT/izQ8iPZcFjfOQuZi5Ip//GM9fdxxfWOKKbd27TZ9yCE9TDoupHXJKoiaCVeCzdxvv+3UZIrYd9/uukWLHH3MMX000rtkF1mg/QgLLi4ugolL5kjTl+jNRd6t2blzp0nM3qlTJ/fLBNQkuk9cL9bSq1cv3bZt21hPj/u88uqbJTZB4vLVV1/pM888U//+e/GChrg7GvhBefc50BRjJ3jUUUfppUsLBBZBTILnlvS4vPob7bmMZZyFzMVI5urVa2hiyt1119iY5seiRVuM/VyzZjkxEcCYLuo5iTytd989Trdunac3b96lp07dqA84IEPXr59lVL5PPDE5qblcZYH2DIrWxqvI/83eWytzxSVzzIZEL0TFzTD+BHbo0EE//PDDxZ1art+XFJd27drpL774olzbnoybR5K57Oxs4926Zs2aZNwuJa5p+xxsDP0+99xzg1Vl/gwVunmCPkR7LmMdZyFzMZI5HCBQXZKTtV+/2AL1QugOPDDD5FNNpoQOQnfnnWM1ThBbtuwy6mCyRBBU+PTTB+p27Ubpbdt2J2jKFb6MLNCF8bCfBBeLRMFeMEkNMjds2DCtlDJhHU455RTNlpWVVTBQKXJUEjKHhKpq1ap648aNKdKLxDSjffv2unr16rpy5cr62GOP1V26dNH16tUzTgB2DO+5557E3CxFrhLsc40aNUyfadqtt96qO3fuXKiVJZkrhS6QAh+iPZexjrOQuRjJ3MEH1zPDfcMNo4yEbuXK2DxWFyzYbAgdtm3JJnSER4HQYUOHlA67PbxryR6B5G7VqtjaHM+8lgXaj5bg4uIimKQGmXNHJjVrKsICnQxkBRcXVcHE/25JlThzMdKssjqtrpHMQcjwIq1RIzNmcgahC2Vs6KdxkEhWIe3XvfeOM04Ra9ZsNw4YZ5wxSFeu3FW3bz9K16qVqceMWZfQ28sC7YdTcHFxEUz8L1xZiNy5Qo3gIrj4EXBrZa743y1C5jz88NBD6+v99++uN2zYYTbI2SWXDHVnVZQaJHlVq/YyjglcI1kFvfuzz07VjRtn6yVLQkaxqGBRD1977QgTuuSrrxYm7PayQPuhFFxcXAQT/wtXFiJ3rlAjuAgufgTcWpkr/neLkDkPmcNm7thj+xipF1NpzJhfTU7Wjh2nuTMrSs2mTTuMdOyww3rGFOYkymViqn777Vm6Tp2+etasUHT5zz+fb9rbqtUg4xjxwAMT9PbtpbejkwXaPxyCi4uLYOJ/4cpC5M4VagQXwcWPgFsrc8X/bhEyF4XMkaprn326aogS5ZNP5hqJV7duS9zZFaVmx449+sQT+xspH9kbklm+/HKhcYIYPDiUFYLQJUgUjzmmt5EqEsJkzpzSpRKSBdo/goKLi4tg4n/hykLkzhVqBBfBxY+AWytzxf9uETIXhcwxhV57bYYhdORFpTz00ASTTgtJXawFu7u//GW4uc6nn86P9WclOi83d7UhdF98scD8HhXvSSf115UqddW33DLaqF2//bbk+QtlgfYPi+Di4iKY+F+4shC5c2CvIOsAACAASURBVIUawUVw8SPg1spc8b9bhMwVQeaYRniMoiq1zgyXXfaz8XBdvDi+wI0vvjjNSPbuu2+cOzsTWDNz5iZdr16WfuqpKfkx5/7xj0nm3uefP1g3atTPELuNG3fGfVdZoP2QCS4uLoKJ/4UrC5E7V6gRXAQXPwJurcwV/7tFyFwxZA5VKc4MrVrlmlmFpO3kk/sbghevc0OPHktNXlVCl/z+e/I8Xdeu3a7POSdPX3HFML1+fcgBA/UrcfCqVeulr712pK5du6/OyYkvBY4s0O6LhRrBxcVFMPG/cMt6Idq2bZs+7bTTdNOmTXWTJk30Cy+84A5WCtSUBJd33nnH9OnEE0/UxCmjrxWhkGu2WrVqmn5ZXJ577rn8WIFkvFi+fHlF6Gp+H4J9tpUTJ07UZ5xxhomNSG7W0aNHm68sJva8dNwvWbJEt2nTRjdu3NjM4ffee890I9ZxljhzHuLmq8IBIlhmzNhk1KvkR6VA8Aj9QaBeYrzFU7Bbq1att0kBNnZsYkOHBNuxc+ce/cgjE3Xdull6woT15ivaeuaZg4zK9+qrRxhCd88940x6sOBvox3LAu1HRnBxcRFMUoPM4fFO/kcK6YNOP/10PWrUKHfAyrkm3gV62bJl+rjjjtNbt241Lb/uuuv0l19+Wc69SMztSSw/fvz4QmRu06ZN+Rd///33dUULGhzss+0opLVfv37mI4GuzzvvPHMc71yx10ul/YoVK8wY0yb606BBAz19+nQd6zgLmfMxN09dJJkDcOzdCPmRmRn6R4RkjZyoeL1aFWysk2XXrj26bdshhlT9618zY/1Zic778cclxlbO2tFxEbxd//jHbrpmzUx93XUjTR7a7OyVxV5fFmg/RIKLi4tgkhpkLjgyZExo3ry5/uWXX4LVKXEc7wINmatZs6Zet26dyd95+eWX6wEDBqREXxLRCJvayofLa6+9pkk+X9GK7bPt18UXX6x//PFH8/H777/XN9xwgzn2YWJ/k677K6+8Uufk5BRqflHjLGTOQ9x8VT4yB8rkaq1cuZvG05VC+BHUloQFQVoXb8FTFo/Z008fZK4V7+9jPX/69E0mFl2HDqNNxgh+t3btNpN6jPvjoIGdHerXpUuj2wLKAu1HXHBxcRFMUofM7d6926iqDjroIP3EE0+4g5UCNSVZoFFN0acjjzxS33jjjSnQi8Q1wRKbIC7PPPOMIbCoXytijlbbZ4sihKVWrVqmz6Q1W7Qo5LwXxMSem857+k0/rVQulnEWMudjbp66aGSOCYOa8tBDe+STr3XrdhibOtSu8apcud60aRt19ep9TPgSbOqSVcjjevfd4/Txx2fpESMKwqR8/PFc49BBftcOHX7RRxzRy4RjQU0bWWSBjkQk9FlwcXERTFKHzNnR2bBhg7HTmTo1ZC5i61NhH+8CvX79en3++ecbUoP6+KqrrtLffvttKnQlIW2wxMaHCxKbVLV9LE3nbZ/tNR588EHdvXt38/Gnn37SF154oTn2YWJ/k257TCBatGihMzIynKYXNc5C5jzEzVdVFJlDRYp6FUmWzb+KIwSEDCkdEq94C9ch1ypq3CuvHF4iKV+s9+zVa5k++uje+oUXppkUYPwOlTE5Xbk/gYbxeiU+XqTqVRZoP8qCi4uLYOKSOaW66kRvLvJF17z00kv6rbfeKvqkOL9NdJ+4XnGla9eu+o477sg/7euvv9b33Xdf/udEHZRH32i7JTY+4oKECulcskp599n269BDD9XYfFLYH3LIIebYh4n9TUn25dVf/oSgSu7UqZO32UWNs5A5H3Pz1BVF5kB99eptJiCv9XClDkJEsvsqVXoUqar0jlq4Eo9TpH4E+40nOHFR1/R9t2LF1vxAwhMnhmLocd6wYWsM0SO/69VXDzfZIy6+eKieMmWjuYws0D40xZvVh4rMFZfMgVOiFyIf9sE61HFI5Cg4C7Ru3VpnZmYGT0mJ43hxwe4P71zsAFnob7nlFv3BBx+kRF8S0YhIMjdnzpz8y9LPa665Jv9zRTmwfbb9wdPTvkcGDRpkJFh8F+9csddLpT1ztkOHDvrhhx8u1KxYx1nInIe4+aqqVq1fCGDfB+zm9t23uwn/Yb9HakeQXvK6xhNY2P6ePddA3YmUDJUuatxkFCYTWSPwrCUm3datBem+XnllhlG9HnpohmkLXrvkfO3WbVAympL217QvnLTvSAI7IJikBpmbPHmybtasmQlrgTSnY8eOCRzlxF2qJAs0qsZGjRoZKdXNN9+st2/fnrgGleOVCLNSvXp1XblyZY2tWJcuXfTVV19t+nnyySfrK664QuMAUpFKsM81atQwfR42bJghcITVwQt73LhQjNaSzJVUw4q+KaXyw82ccsopGo/dWMdZyJyPuXnqKleuqwcOLD4G2y+//GpCltx++5j8uYLK9PLLhxnHhu++K3m2hYkT15vwJzhcvPRS7Dlh8xsS48HKlduMR2uDBv20TQXGT/HQhVTiIIGDx403jtKHHNLNhDvhN1IKEBDiUoCFPRJMUoPM2fFI9X1FWKCTgbHg4qIqmPjfLRI02EPmatZsYEKOrFpVPGnp12+FITx///vEQrPu8cdDWReeeWZKofp4P0DkCCNy5JG98sOixHuNWM7v2XOZiTvXrt0ovWRJgUfr8uW/69atc42ksEaN7vr660fqww/vqR99dJJRN8dy7Yp+jhAXd4QFE/8LVxYid65QI7gILn4E3FqZK/53i5A5D5nDZu7ZZ6dq7MX27AkZYLpTqqDmp5+WGEL34IMTCiq11l99tdDUt2kzON/ZoNAJMX7AS/aqq4YbQtW06QA9b14oCGiMP4/5NOz+cIzAo/Wf/5yut20rUL2iVj7hhB6mDY0bZ+t27UKkjlRhRYUzifnmaXyiEBd38AQT/wtXFiJ3rlAjuAgufgTcWpkr/neLkLkoZA7btdat8/Srr85wZ5Onpnv3pYa4ReZenTx5g3GKQLJG9ofSFDJRNGmSbQjVRRcN0clSdy5cuEVfc80IE8bk++8X5xNaFmhCqZCODJu+hg37mfOQ1BHDjr7ujUWIizvqgon/hSsLkTtXqBFcBBc/Am6tzBX/u0XIXBQyxxRC4kSGh6ysFe6M8tT07r3cEDqcBYIFideppw409nXBTAzBc+I57t9/pbFjw56NUCbJcpLAhu6MMwbpU04ZoFEn5+Xl5Tdz6tSN+epXQrVA/tgjzSTnKw4We0sR4uKOtGDif+HKQuTOFWoEF8HFj4BbK3PF/24RMlcEmWMaEWAXj89Zs2KTqmVlLTek7U9/+jk/Dp2djtaO7sILh8SdAsxeI7hHGgiBgtSRa5WQKYkukDLs6U44IVs3bdpTDxtWEHCYeyEd/OtfR5g+4/162WU/G4/eRo2y9bvvztbr1yfHGzfR/SzN9YS4uOgJJv4XrixE7lyhRnARXPwIuLUyV/zvFiFzxZA5ptJnn83XkJONG3e6M8tTM3bsOhOeBPu2yDRfhCxBLXnIIT0KeY96LhNz1ddfL9Q1avQxqk/s80qrzvXdePfu/+knn8w2eVzPO2+wI31D+vi3v43XBx/cw5DLli1zDLE77LCe+o47xuhx49b7Llsh6oS4uMMomPhfuLIQuXOFGsFFcPEj4NbKXPG/W4TMxUDmmE733z9eI23zpblyp5vWixZt0RCZGjUyHTUo9njWoaF9+1Glco4I3htVKHZs2LM1a5aTMLJo78ECTdu/+WaRkdSddtpAI7WLdBL58cclJhcs7UBNfcUVw4xauEWLHP3++3P0mjUVIx5UEBd7LPsQAkLm/C/c8lqIyM9KvDkS0qdiKQku5GYldh7Bg999991U7FaJ2nT77bfratWqmb5F4kL2DuKTrV1bWENSohul0I+CfbbNmjRpkj7zzDP1SSedZGLr2dylkZjY8/emvcSZ8xA3X5UvAwQkDhUiabditQfbtGmHITEHHpihiUkXWUithYSOjeNEFSSDEC3IFAF/8UyFhJW2BBdoCFxGxlINQUMF27nzPE3+12BZvPh3Y0u3337ddaVKXXXTpv1127ZDdJUqPY2tH7+PlFwGf58ux0Fc0qXNyW6nYJJaZI6UQTfccEOFIXPkl4XIkQFi165dJm9nMHp+sud3Mq8/dOhQPX78eIfMLVmyxKR/ql27doUjc8E+W2xPPfVUPWTIEPPxP//5j37uuefMsZA5/7tFJHMeNlevXkM7nwrtISuQJMKWxFoIIgwJxK6NpPaRBZKFdA7iRTy3kuR2jbym/cy1IJ8HHJBhYtUhDSxNWBPfAg2xzctbbSSNhDR57LFJGm/YYAEDAiijdqaf2NadfXauyQOLl+/dd4/TgwatSgjhDN63rI59uJTVvVP1PoKJ/4VbHgvR0qVL9QUXXKBzc3MrDJkjN+udd96ZP/1ffvll/a9//Sv/c7of2NRWwflCCi+kVXXq1KlwZI7xsn22Y0cuVis4gciecMIJ5qsgJvbcvW0vkjkPcfNVHXBAvfxJFDlJUBHWr99Pf/LJvMivivxMiiyIDPHZIDeRZfz49bpmzUzjSPDAA+O950T+JtbP3O/TT+cbKSFJhblPx47T4nbCKG6BXrBgiwkmXLVqL0Pu+vZd4RA0YuY99dRk47hBWyBzpC2D6OFoArEj+0YiJImx4lPa84rDpbTXT8ffCyapQ+YgAaRCYkwqipqVxaxBgwb6119/NdI51HEPPPBAOj4q3jZbYmOJS+/evfVDDz1kzt1byFyrVq10r169TJ+RLB988MHm2GLiBW4vqRQy52Nunrr9969nnB6izQukW9jCERQ4npKTs9JIyXBWWLDAH/j3ww/nmHMOPjhDf/75/HguH9O53PeGG0bpgw7KMNLC008fFHNmiVgXaAgbTiOENcFmjiwYc+e6/cWu8K67xhpVcJDYEQoFYkeIFzxpuV4ql1hxSeU+JLptgklqkLnMzEx93333meGtSGSODpGztHnz5vqcc87R99xzj37kkUcSPY3L7XpBMocqmdykGzduNO3ZW8jczJkzddu2bU1+1pdeeklXrVrV9F/InP/dkupq1kVKqalKqUmBhlZVSg1USs0N7w8P87E/KKU+UErNU0pNUUq1CPC0W8Pn8xuOiyx16jQwEqNly7ZGfZhnztxkiMq338aXf3XDhh1GClWpUjf973/7pXtIpSA5qGYhQz16LI3ajtJ8QVw8yBz32X//7ppAxMSwi1ZKskATj45UZ5AzvGD/858F3nAlkcQOuzqkdXjFYlN4ySVD9YcfznVUuNHaWpb1JcGlLNtXHvcSTNwXLn9YEr0VN7ZPPfWUJnE5BODoo4/WBxxwgL7pppuK+1lc3ye6T1wv3vL000/rjz/+ON6fFXt+efUtSOamTJliHCIYQ7ZKlSrpWrVq6ZUro7+ri+1YESeUd599TZs9e7Y+7bTTzFdC5tx3C8AEOFKR/Ka8voTMHRlx8zeVUk+F69j/K3x8mVIqWykFqTtTKTU6XA/5W6CUYg/x49gSwIhLhz7iAPHii9P0n/88LKq6FfCmT99k1IU//LDYN/+KrHv66SlG7XruuXlRJU/YvOEJCtmqVStTE8MuGQXyiETw5JMH5BM7HBWQJAZLaRZoHB2Ii0dMOsgZ2JJdwid1Ix/sE09M1g0ahDxzyU1br16WkfShlj3xxP6aNGJ47/p+H2xzWRyXBpeyaF953EMw8b9wy3MhYkwqipqVOb169WoztRcvXqwbNWqk16+vOOGPgmQu8vndWyRzdnwxE+rQoYPGCYJSns9Q5FiU1+d0VLP6yNxspdQxYRbGns+UT5VSN4SP2dnzqOM7WyLPs/X5e8gc5OOkk/obwlHUgCF5ql69j/7yy/hUrlwTr1O8TZGKFSXhIzAvYVGwuYPUEVcuWYV+v/cexK6/IXb77tvdpO+iLjs7NyG3JV4ffbj00p/1oYf20NdfP1JDiH1x/CCaZM2A9OLIwb9G4vThQQupI64d33XsON0EeI41dExCOhK+iBAXF03BRMicOyui15RkgW7durUxim/atKkeNGhQ9Iun2Tft27fX1atX15UrV9bHHnusUScHu1ARyVywz0iSUaETega7SLYnn3wyX7BSkrkSxK8iHKcjmVuolJqglBqvlLo7zLY25rOu0MGG8Oe+SqnWge9ylVKnKqUeU0o9F6h/PlwXqCp8aEOTjB69Th99dG+9fHl0dSsTA5Vr7dp99dtvz4p7nvCvg3yuEDUcAYryZkVihUcqKlpi2CE9TKajANeGdJ13Xp4mvApEin7SXnK0JqKsXbvdOGfg8YvEDlUv6lTUrr5CftpHHplo4thVrtzN4AYhhngjyYMcQhLJqTtkyBq9detu32USWifExYVTMEk9MueOUurUyALtHwvBxcVFMPG/W1JdzXpsmGYdpZSarJQ6VykVjcxlechcS6XU4x4y92hh+mY+QRbHsRGwkcWI7bbb+uqWLXvq3Ny8/Dr7XXD/00+DdO3aGfrGGzNNDtPgd7Ec/+c/A3W1at2NNKxdu0wTRiDa75CQXXVVH73vvl115cpd9Tnn9NLffz+wyPZFu1Y89e++21u3bdtbH354N0PsuH/Dhj30rbdm6oyM3FLfv18/JGz99SWX9NZVqnTT9ev3MHi+884APWCAH/933x1g2gR2EGII56GHdtM1anTXxx7bXe+3X1fdpEkPDab//Gd/3bNn6dsZiRlG5pF1e/tnwWSwnjBhglEJsfjYbcOGDfnHtk72v2nBpWCOBOeD4OLiIpj8Zt4tkWtMqpO5IOd6KSxRs+pTvkuamtX+H0A6ddZZufqdd2bbqqh7pEzEobv55l/0tm0lkwgh3SPILuE9irORQ6pH/lOkZZAY7MoIQUJ9MgqTx5Zt23aZe5FnFilhiET1MFK8N9+caXK22nNLsid9GHlgn3tuqnHSQGqHqrlTp9l6ypSN+SL34LXp9+DBq/U994wzkjtwpF2HHJJh0pCBD2rZunWzdLt2o4wkFeldae3ugrgE27M3Hwsm/n/PLNRSXAQEFxcTagQXFxfBxP9uSWUyd5BS6pAwm+N4pFLqT0qptyIcIHCIoFwe4QAxJlyP4wPqWpwe2DimLmqxalY7jebP32y8WydN2mCrou7JUXrddSONyhRbt5IUroGjAJKmJk2yNTHoiiuoPVEvonqExEB8Ro50s04Ud52ivi9qgUY9/NprM4yTAsQLEoWNG2FGUItiH1iasn79DuNAAVE7/vgsY6cIzh98MEdPnLhBQ/58hTAyzz8/VbdqlaurVg2RThxKIKDYH7LRziZN+utbbx2tP/porsHtt99iy8PLPYvCxdemvaFOMPG/cGUh8s9+wUVw8SPg1spc8b9bUpnM1Q2rVlGvTldKPRtmX0copbCHI8wIe0vM8GL9WCk1PxzOBHs5W+4IhywhbMnttjLaPpLMMZ2wHWPBh2gVV0h19dJL04zEbMKE4olYtOvNmfObPvXUUFouQojEkr0BSSLOCo0bZxsyWKVKD33TTb/E9Nto7bD18SzQpDIj9Aq2cDiIQEyx9YM8Udep0yxNuq+SFgIUMyaEcGnUKNukCIPMQih//nmNk1rM3gfpHdkmHnxwgnHsAB+IJ+rqww7rYbyTaS9OKUjw/vKX4fqFF6aZ1GXEyovMQ8t148HFtqOi7wWT0AvXRrC34y0LkUWi8F5wKYyH/SS4WCQK9ns7JrxT0tEBIhrfSmq9j8wBIKQI6U3kC7pgmhU+6tp1iZHodemyIObfFL5C6BNSLbw3IUSofPGgjaVAqMi2QIBjCAuSKaRZvjyxsVyvNAs0JIpQIvfeO043axaKHUebCDtSp05fk6sVEhrN8aG49q1evc0QLqSAqLqRthFq5Y47xpi8sePGrY+aBxYPXmLuQfCQ4OFQgfSO9kHqSFNGvD/wwxGEYMgENH7rrVkm4PJ33w1KqiNKcX1Pxe9LM1dSsT8ladOCBQtM2qXg+2JvX4ii4Si4+JERXFxc9mZMeJesXbtW826JLKksmUsqYSvq4j4yB3DkZiUcBtkNYi3EouM32NGV3jZrtbkWpI5rYh8Wa0Hl+/jjk4y0id9DSrB3I2dqrB6xiV6gIVG9ei0z0jWIF1kvIFBI8AgyDGmC/P300xINMY2nbN++W48Zs87kwyU/LXjRZyScf/vbeCM1RA1dlDqVbBmoca+9dqSRdNr20UZU2ahqq1XrpQ86qJsmhAsq8WuuGWFy9xJqBhLuC7cSTz/S9dxEz5V0xGHnzp3mpcu/aLvhFGGPZS+4FDcHZL4UzBGL1d6OCUSOd0tkETLnYXXRyBzgzZr1m5G2IemJtaCaRUKEOjAW+7firotkDgkdpIzUYDgcxOP0QHtQc2LPBgnhOqg/kToWZWdXFgs0xBKSSlBlyCbtoo2WQPGZuHIQMtSshGuJtUCmhw5dY5xZbr99jFGzIsGz6lRCvWRkLNWot6MRXHAGf6SISGpbtMgxnreVKoUkeRBRUqURC48sFrQdG0LOa99+lCF6ZMHA8WLp0t+9attY+5PK55XFXEnl/kdrm+DiR0ZwEVz8CLi1MldcTKgRMhcnmQM01KcY4a9bF5+06L//XWwkTthgIZUqbYEMtGs30kiJIA3Yd0XL+VrUvVC7Ir3CKxZix7WwucPZAGJliWJ5PkSkQfvxxyVGUte6da4heahAIXmoRCFOtPnKK4eb+Ht4AvOb4gqkjTiBSP/wnOX3xx3X16hXsZG8+uoRhlhCHMHJd02LC/OhW7clJjsF9nuoxg8/vIe2RA9saTPkDqkekkLUzNwPh5X77huvX399ppGWYveHyrk8giAXh1ks31tMYjl3bzpHcPGPtuAiuPgRcGtlrriYUCNkrgRkDuBIJ0WA23gXWwIQ4wCAVCwW71j/sBWuhWx9/PFcY3sGuUF6hQdnLM4aha+kjUTq++8XGXUh14EosdWsmWni2XXpMj9uEht5j0R+hoxBsv71r5mG2IIrNm6QJEv0IE8QJkggpBWp5LBhazThVaIVsGN8IHlkl7jxxpAUDqkbgaSRDiLd++c/p+tnn802Es1Vq7ZFtY3kXhBj2olEDxUytowHHlgQHy9EpLsZkkcIFaSGYI+tHnaGZMp47LFJRvXbs+cy0+8lS35PyB+DaDiUtF5euH7kBBfBxY+Av1bmi4uLYOJiQo2QuRKSOUJhIH1BmhI0cPbDXLiW80n/RZ5RSOGmTa7+u/AvYv+EivCGG0YZ6Q/kgLRcEL2SSgIhiqgmkdIRFBmCAUlCwkTGBSSDqUbwLFr0GaKH3Rter2SyQKVKlghIEv0glAufccLAcQJJHLaFpBBDJR6JG2OHRBSPWGwnn3pqim7Tprf5LSQSaRvZKMg9+/DDE406tkePZcZ+D7tFnzcs7bUqYNS32AlefPFQY+eHTd5++4WIqSWnEFXwZyyw3WOcuS+SVdTvt9wy2kgT6Xe3bkv18OFrNeF1yiIbhsVeXrgWicJ7waUwHvaT4GKRKLwXXArjwSfBxMWEGiFzJSRzgAcJQxVH+qmSFDwwkRThKYkKNl5SWNw9kQRdcMFgs/Cz4Ddq1M+oIH2qwuKuxff2IeL3X3210NiANWzYL5/goZ5F2gRpgqRmZi4vkXQwlrYk4hycKnJyVprAyxCoSy4ZasgvoUkgR5bwYQeHpAzpJJI/iBbjho0djg6dO+fkO7cwJ5DoQeAIAH3//eON6habObxkwQjiePbZuQY/JG0QOGz1SB+HpA3nDV9hvkAiP/xwjondRyxCJHx16/Y1Nnr77ltA+hhvG3MQ4sd96Q9EEBXv8cf3NbEQkfZBXvHMZUyzslYYxw1UvCWR7Np227liP8s+hIDg4p8Jgovg4kfArZW54mJCjZC5UpA5ACTeGYt///4r/QjHUDtixFqjRmvdOs8ki4/hJ3GfArEjr6uNq0abCVNCuBBrE1fcRYt6iCBG2Is98MB4Ix3i+lbVCZlAZYvUCNUkksLJkzfEfN/i2pXM7+kXKlnaTN/AEAJFNgkkq0jHIE5IzdhbL1cIW/PmOYYg4lhCiBiuAWkbMGClHjhwpbGNe+ONmYbwcd2WLQcaMgxuOFBgc9emzWBD+gi5wrlIdLOzV5pAyStWbPU6aiDlQyKJdBFHEu4PUYVQom5GbUs7LVml7WyQVu4NKWTP99Shpj7mmD6mPeeck2fmDST0zTdnacLuQFyZX4wpZBSv77y8vGQOS9peu6hnKG07lYCGCy5+EAUXFxfBxMWEGiFzpSRzgEjaKUJplCZAMGpbFmpID0b4iUpk7xt2ktXjDYqalMWajeP77htniEs0cleSh4jMEIQ/4X7nnz/YqDmRclkCBNHDI5eQIahssfWDFOLIEa0dvj6VZx24YLsHrj16LDV2cWB5xRXDjPoVbCG3kCIkZLbv7CFN2OEhtUMFDOG66KLB+uqrhxt16f/931h9993j9N13jzUe0ajQkQw2bTrA/Iaxw/kDcgmG2GN26DDaSO5eeWWGibGHqjUvb7VJg4bNZqTkD8cNvJgZJ36DlBJnmrPOGmQIHJJj/gRAAK0zhyWA9MGSPiSBtIc6NsYWUopEk7AtrVoNMpjg2Y2zyQcfzDYeyYSnoX2otQnMvGbNdqeN5Tm+ibx3SZ6hRN4/Va8luPhHRnBxcRFMXEyoETKXADIHkEhckF6wGJWmkNOV/KOQQ4zuyUOazAJhQjpHLDXaz8LMBsGCjJDr1cZ4S/RDhCoPNeVDD03QbdsOMcQhZCMW8lKFMEAgkIDhqUqoEqRMVr1JHLfSqAIThWtJcIH8kdEDiS4YQ24IRAzmZ545yPQXEgUZQuULUYIgWRLFGEEMIYJHHNHTjB1SN1TpxOxr3nyAkfRBDlENgx/SQrCEQHJNro/0j0DJ2H9CFCFy2AEiBSSDxw8/LDaSwFGjfjVev9j9YXu3e/duExYGEoiTCE4lqGsZn8svH6ZPOCFDo4IP9sFK+2wf7N6SNQNUqQAAIABJREFUPzv32PMd9ZbsYo+ICp9r0icklkgzkfQiJURN/OWXC0zKNzDFTpA0bzyPtJl4gtHsFRM1D2K5TknmSizXTfdzBBf/CAouLi6CiYsJNULmEkTmABODeEKWoP4qbcH2igUViQ4LPItTWRTIHQ4PSJZwngg6PBxzTHcjNcQWLJbUYqVtL+m+kHSRGg2igZoWKReEj3YFF31IH+pDbMFIgQY5sepNbMzI8EB8uGSQv7J8uTA+2M5BZJFoffLJXIMPkk8km5BiHDkgb0jEwAoHD6RkkYTQEiakbeAHwUNqik1d1aq9DPHj9/yxgEzZcCpcB+w5H3IISWSuYAeI4wfeulde2ceQLDyB+XPCs/H994uNHSUqWeI0sjHXevdepr/5ZqF+//3ZRjJLX9q3H2kkkPQFAkdfuBd9OeCA7obkWSmgJYXBvSWIwb3tL+0HD/rKnOEZow/cB+ILucVTHZtEnEn4s0E4oXffna2//Xah6QO2i5hHQBiJPclcRaKIirko0liWc6W0z19Z/l5w8aMtuLi4CCYuJtQImUsgmQPQV1+dYVRgJXUyiBwmpCCdO88zJBGJDfHOkN6VZaEvSNAuuaS3kfqwoLIwsqAjOcJ7Ey9QVHTYlyF1KquCtykqaVSz5GVFLUnMNghd/fr9TBiRSPUmbWdBR6oFQUCiRR9YxPktxBH7OCSA2Ll1777UqCFZsH19S8eXC7jRH0ghMflwfkC69swzUwyRv/HGUUbCRggWbPkghxBlJG0hUoVnM44VqFYLJIaRhIo5wvfgjZQNaSLEkY1j6oKkjGO+I9sGc6t69d6GaCFxbNZsgCH0EFbm2223hYjWiy9ONU4kSBIh7m+/PVO/8sp0/dxzUwyh5I/J7bePNqFdLr10qMbur2XLHKP6RbWNFBrSClnlvrZflrRCCIP98h37zgn1PWSDCHmE/B54YOiZgSAjCYdE1q+fZRypkDiiisZpCXU50nL+kEBun3xysukTHsq8AyDAeXmrNBJTzDvINIPH8rJlW/XatduNcxbvCcw30qGk4zNUFrgKLi7KgomLCTVC5hJM5vBIxVgdI/lEpnKCRCBdwpCdxfTxxyeXWqXrnxLRa4MPEe2BuEHgWFhJl8XiywLGYsdCzQKJrRRtJu8p6sSJE9d7CVH0uyb2G9qNPR5erJ9/Pt8QNgggabhQ40ICIS7YLoIz0hvIhe2XXcgt6YAQHnxwN2O/xm+QHGLPBvHmeqgCkVRBKHCCIM4cOEA+ke5Apggng7QtMgxKYnteNldDcoha/vvvB5q+gTNqWPpMphLUyUi6UI9CVlDJghMxAEMEq7+uV6+vwZ94fkjO+PNAPD7GIUj+fATKjo/dByVzkcfBcxhfyBvzFuLFuHJf5rQlXrVrZ+q6dTN148ZZRj194onZ+uST2QaYMW/WrL8hnEj3kFTyTDCXkPhh04jU/uiju+maNfvoY47pbeYMEk/uwb24J0TS9pP2QIRpWyx9tf0pas91uB7z1xJs7mfJJvMd+0hwZ/5DplFvQzrpA/2hbxBP5jjEmPG7/PKfzTPEnwBsIiGgjz020fw5ePnl6Wbs8dr+9NN5RgpL4HW83XNzVxpC+tlnA8yfMqScSP0xwYCYErvx11+3m3cpUk/sPSGoifb8L5unI/67BN+58f+6Yv5CMPGPq5C5BJM5YOZFQ0iKRBM6O4TYAWEnhNE8L9SPPpprVDz2+2TtY32ISLGFNIuFmwUbgsSCwGJlFyUWEz6zYLNAIAEi3dUTT0w2Cz92T7NmbSoysG+y+lnUdSFcLDSovVEBE2PvnnuyzKKFNA+1HOo5pEeohQn2y2JODDj6ysJNv1lAi5L8gBMYQV44F6kOCz6LLOMOnkjKrI0cGHM/bMm4NyQJkg2mSHcgrBBq7NoYF0g4kjgkj3i9EigatS3kC5KOMwIOHUjvcJAg6DFELdYS61yJ9XrFnUfb8OIlBiDtxpuXvjBGSLKQ2kEmyLCBxJV5xp8uHEsg2zicIA3DSQccIZZNm/Y3+CK9g6hDwPiDggoawoMUj3GBCFkP4GQQsEhyxtywzxHf2c8hkgYpDW3MndDGnyu2kJSQuIVsfLbH9nPonFB/7Pn2OvTNbsxNNu5pN9uOYNsi257Mz/b+tj22jbSZPlipMISZcWP8kNrzXOFExLMZNC/geUUFjzQaNT/PMFJ85gNSf549bE4h7fyB41ln3px++kAjYSU6AWGaILs4LWH6gckMzkXXXRd6NsnZzfNJHEzsVfmjQ1inJ57gOZ2ib7utr9E48Efovfdm608+mWfeOZglYM+KrTaS9ZycVSZF4MiRPLvrTHikGTM26rlzf9MLFvxmvMwhx5gAQZAxCYAkr1+/w2S1wayH5wczFCS6vOf444vJQKoR57J+txT37kmV74XMJYHMMbiW0EG2eFCSUcg+QVwwHCV4GbGAk/cTKU8ySqIeItS2kCGIENIq1Jq89Hgx8vKE7PDytYsCe17IvICRZPBStWpRXpIQRl6GEBUWa6RALOLcg3/5ybCTC+KbKFwgJLQVMhwkJBBj1KCoEOkfZAwiAkELEZERZqFg0YAUM+dQjbLAgCnSQohfiJD0yZcIoVZkMQNvCImVCNlF2uJf1AIcXED5nV04IRRW4oN9I/ewC2fQJg9iiroRVSfts4slbYbkF14oB5o/Bnjt0kdIF5Ih5g4kjP5DZFGVQ8xYOJGMQmqZI9gUMtfAjAUU6SDzhoDYSJIgu+DKYspcIqwLWEP+OnacZhZVJKvYjGI/h8oTm0XmG3OZMYI44hUMOSb9HFJJpLDMR8jyK6/0NxIpnI769l2ue/Zcar7nfH739dcL9GefzdOdO8/VH300xyzgLOSvvhpSG7PI//3vE/X994/T99wzxvSB/lx//Qj9178ONzaLqJIvvHCwIfbYMYIVZB81Nc8N0nKICBhDTJC6gT1jAGGFxEBaedYgN4wXhMfOFZ5DxpQ5EyKyIYkpz2wB2SsgeZArO09imVNFzTf5rniVf7phFJwbkceWmNu9lVQHibqdc/ZPR4i42z8rofeafRcxXyHzltAzl3k3sUHuQwS/4F0VIvrYEYek9Jbw82wguWbjWeE9FiL/vM96mz8APE/8CeDZQqpfp07o/YaEPvSHIMs8g/zZt38MeDZ5RpF+I+HnDwJScP4kYD+MgAhTDCINoM3gfd+mDX8YBoua1cPlVMOGDYNrdYmPIXQsErxME2VDF60xeOuxGLBoQex4ibPwQAoS9c8qUaQlWh989VYtmpu7yiyWSJSQgNFPjNSZ3Ex+Hg5IQVDyxQMfuXjwmXqrTuPhZbHigbQ2TCxyXBNCxNjx0EAWII4QZiRvEIMOHX4xHqgY+/OP2kq9SPHFAsxibxd6u8izwEPOWNhRM7Goo27FKQCJGN6hqF5RR+OwwfhZtRNSJzwzkZShygz9i+af9C7zT9r+mw79o+ZfdeySNB/2kXVcj3sxl2kHUjtUxLQTSR5tpx9IxF57rb/pJ/2l75AdiA/SMcgQ9o04tkCWkJJBUCBTSCfw6oVsobIjFiJ4Q8ogZ5A0yBpjAXljXCBzkDrIHeMF2YO8MH68DCG1IRJToPZkjFEbWjLDy5YXLxJP5gHqRV7QqFh5YUNqmFvMFZ4vS25QS7IQWILDImFJDguI3ZhvSLoguXbRsYsQe7s42cXKLl52H7nI2c/ltXDb+8eyt32IZ1+AR4FNZfBe0a4VyznRflvW9cG2Juu4vOaH3Lc8SLca5+Mze3VdosgciyFEioUels0CWBYFuxICy5JqjH/dLE78e0dqh4qwpKU8yFxJ2xr8HSQE8gP5ILAtpAkihTQEsgW5gFigusa2DSIBWYQ4IOmBMEDoII5W4sU/KP5RQQaOPrq7IQLgDAHgX5uVZth/fXaxZ6EPLvCFpRmFVVfBF7y8HMvj5Vg+9wyOeyKPg2SlJPOpJG0J3rOoY65tv4fQxrtZ1TL7eH8bPN+2oTR725d48WJMgr8pyRjJb8rnmU0N3IXMOcQ1kWQOUgGhwwgYSQAeZ2VZuDf3xNgf+ynIBgSPNE6EjEAVGWvOznQlc8nGO5VxgciyIa1jQ3rHhoSNDekeG/YybJBeNqRvSADZCPzMhvqejT8lbKiD2ZAYskGW7XG3boPyv7fns7fXsNdkb+/DPe1m28Hets221SeRDEolkyWZjHUe8czRBmyPaDt9wsOU/nftOkgvXLjFOC/NnLnJSDUJb4I0Fs/UIUNW6+zsFcYWCg9yHAawlXrjjRlG3fv005P1o49O1A88MMHY++GlG1KzjjTq5CuvHGYkl0itsZ/EbgtpJSoapJQ4a/BHpHHjAjUrqm0rmQxKJYMSyaA0MiiJtH9OrOQx1j8nkJbUWAClHRV1HILEOHgcSdSDZD54XPAHwdqeWttLq8IN2Zzuv7/NlV2gwg2pcUOOVJEq3EMPzdBVqoS2kPo2ZAuNPTQxQ9liU+FimtInX4UrNnMOlVMJU7NGvvwxXkWNg3SovAoLDR5jqL5QASNpwv6FFz3G+6RoQqrHosy5wZLKpCXYzrI+FlxcxGPFhDmG7SeeipAeDLMx1IbwoMIl7Axkh7y1/PFAjUs6tL59V+iePZcZmzTMC8iegpQVZyAcO1DHE84D0oNtHH9krrpqmPGshuRAcLBFQf1qJawQGozdsX1BuopaFXUqqngkq5a4WMKCKpCFwS4UyV4U7X3Yc9/QwlNgp2bVt9aJwUqArdrX2gr59vYcuy/sGIGKOKQmtvcIYRBytAgugHahtG1NNibFXd+2w2JmcbMqbvpB38CKvvMutHZUBTaeIXsp6xzBH2JseyG+1taTP8ghO6h+Zj5h7wlptrZPzDUINfMOE5hzzsF0I8+YiuDtjxaAGI04R+BZjxkHZgZt2/bKt+3EBAETk0cemWC0CMxvnCTQKrz66gxjVvPOO7OMeQfhrDBt4D1PfEdr2oFZB8/PkCFr9PDha/To0YS2WRf2JN5kPP159+MoYf988UfEOksQoQGTHv6khP5U7TYexjzDZeVlHOu7xX0rVewaIXNlSOaYShhE8zIYOHBVyswsJHN4/yG9e/jhifqCC4aYNqIqRLWIgwVptp58MtukLuNBLyowasp0rIwaki4vF8YMaREvZDzagjZvBPAlCC5ptSDz2PRZezcC/n744VyjjmbRIIAuCwnOAiwwkCXmCIsQdm1t25JurIexW2vSpL8JycHCxz9PFkjIBIsoCyuLMQstxIgFNrS4hhbYSAJhF2BLovi9XayLWtTtOZwfvAftgKhB2Jjr/BtmkcZ2DmlVKP5btjGRCHkLE4rDGh3jcDHYpF4j/RqSMDbs+IgTx0LNuSzeGC9jZsHiXrNmt7AzSogMhLxj8abE+Bovy9C/e8gFWNi+2j4U1c94vrPXg4hZTCyhgcxYXCC04MI7izEMYgNhgQyTgxgPToyy6TfkBGJyzTXDDSFhfmC+gF0kksWOHacZ4vH++3OMswcSyJdeyjYSyaFDV+sxY7AZ3WCklkgvIfXkwCbvL+8epLshu9GdhlBU5HAl6fJuKaNXrbmNYOJHW8hcGZM5hoF/Rfz7599TKhdemkhD+HfHAn7RRaFQKBiFs9DiVcpihbcgEhCM2pGQ9Omz3PwO431IAyqwilyivVz4p8q/V9z/+ZdbHHmC6IN1UeQJO0gfecKrCeKNhBUPVjymkDIhYcJIH2LAYs+4QahYoFmYOQ/SgkMAEio2jqlD0gCpwRvLSqz4XVBiBSEKGfYXkLNIUgFxgDRwHucfckiGIXY8A1ybMA94rSK9wFMLG0UkFZBD8szibQoRwFkCpx68ekndRc5Z60CSnb3cBNLt3n2JsYXkjwlmBHii/uMfIc9fpHPEQwMr7gUZoX8hotkrTDQzDEYQHEsWI/sT/GxJUXAf+T19B/+Q1KurIY+RIWbAHRUopBH7TAgixBhzCGw4IUPYdCKFISgyHq+EpiAsBdJKiDiEHGcUyA+2scw55h5zELVvpKQ9lZ7JaM9QKrWxPNoiuLioCyYuJtQImSsHMgfwxIpr1CjbSMJ40aZDCT5ESHhQhUH2CACKlyJeicRNYiGG5NE/iB/SBQgF5I9FG29DFmwWq3btQkFG8WQkJ2hhlcFsIxEiRliXLgvyVQbcj4Wcvd0gQmxIk9hY6OyGmgGShAOIVcVZr0pCfeB9yqJP9gP6QGgK2gNxIvwH6mfaiQqEWFFILlGVsPCyANeqlWHsEJHqQHSQbNBnFnWkHUh+wAHyhN0k0iqkGWB03nkhL1kkGThdYP+ENycqcAgMmNA2iDLkBDUiRIXNOm48+ugkYz+FWobrgC2SEqQmEDJUQdhhIG2BUEBUIB+WdITIViieHfYd9MFmXoDwoIrHWxQv0muvHWHIJE49SGtpA+oc1DiQiilTNhhbuf79c73kAWIP0Rg5cq2R/jGuEDT6iZSP0CF4DHM/QmlAKiGSkB/aBp5gG2y/7Qd76iFhkZs9P9TX0LiAh+0rpA4SjBQNssc4Q6TuumuMsVFjjnz88RyTzou+EhIIKSZ2bpMmFU7phQoq2jMdfIbS4ZkvqzYKLn6kBRcXF8HExYQaIXPlROYAn3/NqGZYODhO9VLShwiJALH2UJVMmbLRLICE4yCjBUQLYgK5QoUHQWBhRwqByhdSc/fdIVUeRBHpChIbu0GA7EYYCzYWYbtBwtj4LRItyBkkrSA452T97LOhWGIs2OTDhaDQHogTRBJpI+0kQCe2WqjIf/4Ze5NQcM6vvx5o+rZ8+VZjW8Jijg1JcZIQFnzCjoAFpAb1ExIYJJ2E2yCkBpIzVFwQQogMJMWSF4gJEh/II6QE0oOUC+kchOTKK4cbyRZ9hSTTHwgvRvaor1C3FtfG4JyEwGNvSXuxUwMn1K2QT8KHQCIhfrShatVuJrCujzwGSRfEDHIZ3Czx4jskeahA6RsSQyRqqDEZf8YStd1bb80044S6rkePZcYmiD8ZqOr404RqjvkXjWAF+5js45I+Q8luV3lfX3Dxj4Dg4uIimLiYUCNkrhzJHAPAog9pYdEmVlcqF3mI/KNjcdmxY7dRcyG5QdoEEUWaR/wzpD4QEjIHoOq0hAViA5GBkKESxZAaaR+SKX4LYUFiSMw6ros90apV2CyWTJoLecPRgHyeBLLluhAyVHlIVFHVIo2zbY0kkLQXQkmbIZL0hXPY+Ey/2Pbbr6tR5SIZPPXUHCPVQ8L5+OMTDWnnvgTZhXxBDiHGEEwIMQbWFdUm084V/0zae2sFF//YCy4uLoKJiwk1QubKmczZYUFigj0SUqp4pCX292Wx31sfonXrtmuCFkNAkHJBsiA9qEwhYKRKsuQsRGRC0iTswZCuIUlCooj6lswBEBg8mrdsSUxmELzNiJ1HWq4XXpiqb7ttjDFCR4qF+pA2IuGyql8rGeMzZAwPPlSYbJBKS8owxseejPyj2HDdfPMo88cDKR/G66iusY8cNmyt8YaDiOFMw/zdW+dKcc+h4OJHSHARXPwIuLUyV1xMqBEylyJkjsFAMoE9FYvxli27/CNWjrUV8SGCCBHXC0kaalhUhdj6QYCQNlmShiQKxwHs3iBoF188xJzfsSNplrINOUMNmaiCh964ceuM9Iq0UpBBVKdIzXAcgHjRJoiZlZZBzCBj1jsT9SRt5jycD7CDo+2XXDLEqF8hl9ji4XABwYSUMQfBBOeN0pSKOFdKg4f9reBikSi8F1wK42E/CS4WiYK9YFKARfBIyFwKkTkGBhKHygv7IFRqqVTS8SFCpYixOk4E2NZh00WsP0iPJWpIoiA+qARxbMAJAekT0lJsxIpTacaDC1Ir4jiF8nTOMM4VEEjUsJA02mXt4mgfBA1CBrnkezaOOQ8vST43bz7AOA1gu4b9H2FEUMliN4ZNHjZ8ZV3iwaSs21ae9xNc/OgLLoKLHwG3VuaKiwk1QuZSjMzZYYJIYPiOUX4qGG7TrlR9iNas2WaSlePVSYwriDC2aZAdpFaQNQgQcb5wNkFVigcmqs7du0tme2bHKRIXrkdeVRwaCO6JHRqBQyFdOAMECSQkjThjSPtQh2IvFzoP79/uRkpLDlJIGmQUFXz//itNuwmum8p2Zak6V4LjVh7HgosfdcFFcPEj4NbKXHExoUbIXIqSOQYHCQ5BSFu1yjVeef4hLLva8nyIkGiRDYAI56gcCcIKQbN2YKhECQ1CuBAka3haYkeGujLRBc9jPHFxTCB90vHHZxh7R0ijtUfDDg0bSAgaqlHChJBCCbJGmhjIGxK5O+4YY6SAkD8is0+fvsl4Xia6zWV9vfKcK2Xd13juJ7j40RJcBBc/Am6tzBUXE2qEzKUwmWOAkL5gNA9xwa6rPKV0ZfUQEewUOy6yCkCCyAuJRIsNezDIEfHUkFYR2wwv0kSXzZt3GsJG3Lk//WmoCaZLOyKlfcRBa9gww6hnQ7H1+hkJHKSNz8RNg/QhVcNrk/AseDBX9FJWcyXdcBRc/CMmuAgufgTcWpkrLibUCJlLcTJnh23+/M0mTRLBZssrhEmiHyKkbUSsf/nl6SbeHsFtrXQLmzDUpXiOQmJRXRZnu2aximePByYhMggBAvlCumfbwB5SBqHE+QAVLs4Dp52WY+K6Qe4IgNy2bUgdjmqc2GblYaMWT5/L4txEz5WyaHNZ3ENw8aMsuAgufgTcWpkrLibU7C1k7k9KqdlKqXlKqac8/K1QVcOGDf1olXMt5AfigS0dQXWJx1WWpbQP0eLFW/Sbb84ypIiQF6hIkbYR8Bb16P33jzehLhLpFWrxIaURHpvEfiM7gs1MgVoUlSjqUJwfrr56uHFAQZVLaA9IJSpRslUgpSOLBF6f2KwxHpTS4mLbWJH2gol/NAUXwcWPgL9W5ouLi2DiYkLN3kDmKiml5iul6iql9lVKTVZKNSnE3iI+pCqZs0NIvlPClxDY9ZtvFpWZIXw8DxFSNGzACPfRqFE/E+YD4oSaFJJELldityXCAcHiYvekiyL11VVXDTex4CBr1hECZwMSpN9111j91FOT9f33j9OtW+cZVS5SOTJykEAeG7Zffvk1JsIcDy62jRV9L5j4R1hwEVz8CPhrZb64uAgmLibU7A1krpVSakCArz2tlGKLWlKdzNmhhGycdtpA4yAxdmzyw5gU9RBhy0c4DFJREfqD8BrYl5GPlXyekE6kY4kueLJ+/PFck7qqdu3M/NhreIqSSYF8pQTS7dRppknjRbBfpG3EksOe7a23Zunc3NUmtlpJ21YULiW9Zrr/TjDxj6DgIrj4EfDXynxxcRFMXEyo2RvI3LVKqS4B5tZBKfVR4LM9vDsMxrhq1aoZ1RmTJtW33Nw8/cQT2bpq1e76kkt66x9+GJS0NmdmZha69rvvDtAXXthbH3lkKOQG5I2k81dc0Ud/8MEAnZeXV+j80mKZk5OrX365v7FRq1kzw2ReQOK2//5djUfp5Zf30U8+2U8/91w/ff31mfqkk3qY7447LkNffHFvff/9Wfr99wforKzchLYrEpfS9rMi/F4w8b87BBfBJZ7nW+aLO18EExcT5tTeQOau85C5Dy2D8+3TRTIX5OckEidJfdWqvUzKJWy6El0yMnJNUFritZFVAOkbOWVxHkBKmOiyceMOkxwexwNs3LCvwymB4L7t2o0y6atIGo+37/XXjzRSQLx+L798mH7llRnGe7Qs7Ap5kKQURkAwKYyH/SS4WCQK7wWXwnjYT4KLRaJgL5gUYBE82hvIXIVVswYH0h5jT/fggxNMKBOyGEDySlMgaRAlSBJSMDIlEAi3e/clCbd3I43U66/PMInpUZNyP1SiePDi8DFhwjqNOhnVKIQNb9ITT+yv7713nMkTOnv2b/lOCaXpc7y/lZeLi5hg4mJCjeAiuPgR8NfKfHFxEUxcTKjZG8hcZaXUAqXU8QEHiBN9Ejlbl46SucjhJZ5Zhw6jTeBaJHa//hqbpA4PzczM5SZYMY4DSMOQhJHHs2vXQZG3KdVnAvqSiQGnA0gi5A0S17p1rglHsmLF7ybbQSR5w+u1W7elevXqbaW6f6J+LC8XF0nBxMWEGsFFcPEj4K+V+eLiIpi4mFCzN5A5ONplSqk5Ya/WZy1pi7avCGTODvfcuZuN5ybqV6RbBOT1FTxPyUhAJgVs38iwgPoyGCYkEQ/RyJFrjVMCoUkgiqS4wruVAMDEfFu3bofJiYoXLOdAJJG8de26JGXIWyR+icAl8prp/lkw8Y+g4CK4+BHw18p8cXERTFxMqNlbyFw03uatr0hkzg77kiW/G/UrMd0gR6gkp0zZYMJ3IIHD/g0C9+9/z4uqPi3JQ7Rjxx7dufNc43Frc5MSt+2++8aZ+yMJJAhyx47TzTlI5lChkiweIpoOpSS4pEO/StNGwcSPnuAiuPgR8NfKfHFxEUxcTKgRMuehcxWRzNnhnzfvN5PpAKkYak2kX2+8MSOmHKaxPkQ4Xzz++CQjVbPSt7POyjVEEXJHGJO8vNWGXNaqlanr1++nH310knFYSEYuVdv3ZO1jxSVZ90/F6wom/lERXAQXPwL+WpkvLi6CiYsJNULm9hIyR15Q1JmQKxwHSPCOGrVZsxxDpt55Z7besGGHf5aEa4t6iFDfPvTQBBNjDpKIWve660Zq1KoU1LU9ey7Tt9wy2jhTkPEBj9Np0zaWi9NCkR2N88uicInzUhXmdMHEP5SCi+DiR8BfK/PFxUUwcTGhRshcBSZzSMEImHvkkb0MiSNgLlkXggU154gR2LH9YpwQCDMyevQ6L8GKfIhwQIDAkYkCAsd9br11tFHhcg8kcP37rzR1ODi0aTPYqE9R+VakEolLRepbSfsimPiRE1wEFz8C/lqZLy4ugomLCTVC5iogmVu69HeTS5RYcIT2IHXV+vVFS92YDIQ1efXVGUZS16RJf5NHdcWKrfkzh4do5849+q23Zpo0WRA4QpbgrID6lmLHV0kbAAAgAElEQVTJIR6n5JAlET0SQJwbKmqRl4s7soKJiwk1govg4kfAXyvzxcVFMHExoUbIXAUic1OnbjQx2lClYov2xRcL/KNeTC2EjGTyd9451kjrcEh47rmpunHjHrpSpW4mMT15T3GgsAWyBhGsVy9Ln3BCtv7nP6enjQOD7UNJ9/JycZETTFxMqBFcBBc/Av5amS8uLoKJiwk1QuYqAJkbOnSNPumk/kaVShDdSFWqf+iLryVMCDZuhCtBCofH67nn5um+fVdoVLhI6bCDu+KKYRov2bvvHhdVRVv83dL3DHm5uGMnmLiYUCO4CC5+BPy1Ml9cXAQTFxNqhMylMZkbM+ZXIwVDEnfmmYM0krlElH79VpisC1yXNFrPPDNF//77Lt29+yD9wQdz9OmnDzTqW0KaoI799NP5esuWXYm4dVpeQ14u7rAJJi4m1AgugosfAX+tzBcXF8HExYQaIXNpSOYgbaS4gmxhkzZnTshezT/EsdUiaSOcCBI2JHCtWuVqJH62oHp9550BJi4dzgx4qj7xxGTj1HDooT30X/86Qn/11cKYM03Y61aEvbxc3FEUTFxMqBFcBBc/Av5amS8uLoKJiwk1QubSiMytXbvNkCdIXNOmA/TEiev9oxpHLSFFrrlmhMZZ4uCDe5jYb5s3F0jZIHnffLPIhDCpXTvDxIoLfs+tSBX29dcLDaGD2J133mCTjmvSpA1er9g4mpcWp8rLxR0mwcTFhBrBRXDxI+Cvlfni4iKYuJhQI2QuDcjcnj179N/+Nt44H+DYMGxYgcTMP6zF10IEkb5BDAktQuaHYMH79bXXZpjvLrxwiM7KWqFzc/OCp3iPt27dbXK74s1KMODq1fsYu7v//nexJphwRSzycnFHVTBxMaFGcBFc/Aj4a2W+uLgIJi4m1AiZS3Eyh+ry4IMzjI3axx/P9Y9iHLUQwcaNsw2JO/nk/ibrQvDna9du108/PcUE/SVmHNI1W0ryEM2fv1l/8sk8o54lWHHLlgNNjtjMzOXFBim29031fUlwSfU+lbZ9gokfQcFFcPEj4K+V+eLiIpi4mFAjZC5Fydzy5b8bVSr2a8RxIwBvaQr2b40a9TMkjtRas2ZtKnQ51K2PPRaymbvnnnF64cIthb7nQ2kfIrxff/55jX755ekaaR9qXTJQPPzwRN2jx7K0tbcrLS4O0BWgQjDxD6LgIrj4EfDXynxxcRFMXEyoETKXgmQO71HiuTVo0K/Uzg2QOK6DOrV161w9b17h5PWoPh95ZKJxfHjggQm6qOwMiX6IsMcj+wTq3EsuGaoPOaSH8Y6FvOIhi1SwtCTWP+0TW5toXBLbuvK5mmDix11wEVz8CPhrZb64uAgmLibUCJlLITJHntIaNfroP/6xm+7UaZZ/xGKsRfJ2yikDDIk755w8h8ThxICEjByq2LcFMz1Eu0WyHyIkd+PHrzdqWeLbNWqUbaR3OFQ8+eRkI70juwWetalUko1LKvU11rYIJn6kBBfBxY+Av1bmi4uLYOJiQo2QuRQhc88/P9WEBDnttIGlsiXD47Vt2yFhm7gBJpF9cOghTNjeHXNMH33DDaMckhc8N/K4PB4iHDHI79qx43R96aU/m7h35IBt23aoCY3yww+L9cyZm/Tu3eVH8MoDl8ixSbXPgol/RAQXwcWPgL9W5ouLi2DiYkKNkLlyJnPYquGQQGgQAvKWtKCORD2JjV3Nmpk6J2elcymcDvAwvfjioUYC5pxQTEUqPERI5ZYt22qyUJAy7OqrR+jjj8/SBx2UYbxz8frF4QL1Ms4cZVFSAZey6Gc89xBM/GgJLoKLHwF/rcwXFxfBxMWEGiFz5UjmfvxxiVGpks8U9WFJCzHeIDNsXbrMdy4ze/Zv+rLLfjZqy+xsl+Q5P4hSkcoP0YYNO/SQIWv0u+/O1nfdNdYQO7xnjzqqt4nNhyoZiSTnJJrkpTIuUYYy6dWCiR9iwUVw8SPgr5X54uIimLiYUCNkrhzIHHHjCPuBU8IDD4z3j0wMtWR+IKl9NI/X337baVSRRxzRS7/99iyTTzWGy0Y9Jd0eIivFy8lZZUje//3fWI0nLyQPTEiB1qHDaGM7+P33i/XYsev0xo07o/Y/2hfphku0fiSyXjDxoym4CC5+BPy1Ml9cXAQTFxNqhMyVMZnDpg1JHMnrUXuWpEAGb7ttjCGDZIJYsKCwhyrX7NVrmVG3QhpjcW6IpR0V5SGC5KHeHjZsrf7iiwUmrt611440DiNIN8lHS0BlnDBwEiEDBiFVFi/+3WubV1FwiWUOxHqOYOJHSnARXPwI+Gtlvri4CCYuJtQImStDMjd8+Fq9//7d9XHH9dWrV2/zj0gxtdiCkT/1wAMzNGrayAJJgZgQjgSVYiLL3vAQQfQgv+DcpcsC/dRTU4yjCBI9MmXsu29o/Nq0GWwI9YsvTtNPPpmt8/JWawIkb9++O5GQp+219oa5UpLBEVz8qAkugosfAbdW5oqLCTVC5sqIzBE3DXXoVVcN10jW4i3EZCOZPapZvDq3bSvIn8q1ICGQD6RKZHDYti3xpEIeIm3I2ty5m/XAgasM3s89N1W3bdtbE/6FVGuElcHblrAw2Cmi2n3ppWn688/n6379VpjYedjsMV4Vuchc8Y+u4CK4+BHw18p8cXERTFxMqBEyVwZk7r77xhkShhSnJAXPVLIlkMSeMB2RBe9OQnWQKiuYfivyvNJ+lofIj2AQlz17QirccePW6969lxvPWggfnsZ4EZ94Yn992GE9jZodL1wkfpB0sm688MI046TRrdtSo9bFcQXHjnQkfkFM/KjtnbWCi3/cBRfBxY+AWytzxcWEGiFzSSRzSODOP3+wCTvSvftS/wgUURu0jSMEhy8bwk8/LTEem9h2+b4v4vJxfyUPkR+ykuDy+++7THYPbPEgb3jaQubuvXecIXeQPMLIkBUD+0qkfpB1pH0QQ1Kvvf76TP3ZZ/N1RsZSo1KfMmWjXr58a0qoekuCiR/dilUruPjHU3ARXPwIuLUyV1xMqBEylyQyB7EikT02cpMnFySr9w+DW0vaLbJB8PsePVwiiNflzTf/ohs27KfHjFnnXiAJNfIQ+UFNNi5bt+7WixZt0aNHrzNOM6jT33hjpvFUvvPOsfovfxlu1LxNmvTXRx/d26h6ceSoXbuvbt48x+TBvf76kfq++8ZrpITvvDNb/+c/CwwJHDRolfHiRXVMajfU+YkoycYkEW0sj2sILn7UBRfBxY+AWytzxcWEGiFzSSBzpMqqU6evrlKlh/GA9EMfvfa99+aY3KwtWuR4s0GMHPmruT6L85YthW3nol+19N/IQ+THMNVwQS1LWJqFC7do1L2EZiFTxkcfzTWZNB5+eKJx3kC9i+SYeVa3bpYJ10JO4AMOyDAZQghmTfgW8ua2azdK3333OP3445P1q6/OMNciviFSQa7PnJw6daO556+/btcDBuT5wdrLa1NtrqTKcAgu/pEQXFxcBBMXE2qEzCWYzBF6BAP46tX76HXrdvhRj1KLWhXnBhwlyG4QWVikCYpLIFzsscq6yEPkR7wi4cIc4w8CdpjTp2/SI0asNY4bxOHr3HmeUe3i4Ys6GMkwUsELLxyizzhjkEYyiDQQb+tKlboaCSHH1PEd53Auv+G3/BmBHGIigLTw3/+epyGIqJ2zslbowYNXG2kkJBFPYTy1N23amXRzAv8oJ6a2Is2VxCASuorg4kdTcHFxEUxcTKgRMpdAMgd5Y/Ei9Eikt6kf/oJaYpiRLxX12C+//FrwRfgItSp2c6eeOlAvWLDF+b4sKuQh8qMsuLi4gAlhWpDSISGEkCG9Q4qHNA/ShqQQdfGzz07VSAuR/EHymOd/+tPP+txz88x8hwjyTPEnBhtC/uzgNUzwZ54Z4jaefPIAQxaRNF5++TATnoc4gZDOv/99ogkxg1cx90PyDTH98suFRmLZo8cyQ1gJL0Mbx49fb4gsBBJSSx8guImwSZW54s4VagQXwcWPgFsrc8XFhBohcwkicxC5qlVDRC5euyOcI1icTjqpv960yZXm4aHKgkXe0fKMY1aSh2jr1l0ar8zc3FX6228X6bfemmVsve6+e6y+8cZfTKiWiy4aos8+O9cY+LNw01cM/pFuEmqlatVexgMUb168eiG8qAJxDCDuG9iR2za4oS60m623n9nbOrvnGmxcj+tiq0gsP+5lPYlRm+OJyjgjfaVt2KgdcUQ3XaNGpmkz6nVUljgvoKbEe5XAzqgyTzttoAlGTBgTSAceyDg0EK7mmmtG6PbtRxkyg4MD3q1kB4GIPPnkZGPrhrQWMoIUCyJEuBMCGv/442Lds2dImoUN3LBha4wdHA4RYL948Ra9atVWIylGsgUxYR7t3v2/pHnKlmSu+F9Rbi3SQ54xPH1x+MDeD7vUUaN+1bm5q41dIY5BkDVw6tRptlENP//8VDP3HnpogiGOBNRGfQz+qJKJHYhauVmzHJNZBW9jyKKN60hYIOYOc4IMIsQdZKyZs4wvgabPO69gXJFAYqsIQb3jjjGGWF59daZxXiF8EN7tqKx5Jt5/P0QwsWUMjekSDcns23eFIcDEjIRoojanrzNnbjLSStIAErNy/fodGvMOQhIlc1zd0UhMTTLnS2JaWD5XEVxc3AUTFxNqhMwlgMyFiFwvY8cWL5F75pkpJmwJEgRfgehBHFBzlXfhIWIhXbRoi+7adYlRj2GAj2qYxQzpCcQLIoT0RKnQxiIIaYKAQYZYIFkoITssnCyCF1wwWF9xxTDdrt1I46354IMT9FNPTTYL3iuvTM9f8FDFkbXhu+8W6e7dl+jevZeZcC1IVVjwCPZrNzxF7bHdh+pW66FDQ9uQIasN0RwwYKVZOMmcgZrvv/9dpL/6aqHJddu581z9wQdzjIr7zTdn6tdem6E7dpymIQeoHK+/PtOQLtrMOBJb7rbbRuubbvrFLOZ//etw/ec/DzM4QVwhDa1b5xrigKQVJwUkS5ACHFogs2CJehInGEgtUikIBMQCidT/t3cmYHJV1dpeEGYRISQCEiATCQLKoBcuXq4MXhWEC3iBiyDoVXBgePxRBhH8AX9ADMNVCSggg6IiZE66M3QmRhkCBgIhBMIYiAkkCGEwzPt/3l3ndJ+uvaq7utOdHurbz1Ndp1adrqrz7r3P+c5aa++NhyoXtfAuiloEB/zhntdBa8/sy4P/y8WuJ2z5XkQtv4Pfg6DdcsuJUdgMGFAX+wACZ+utx8S1gDkmxCzHiJhFLHHsMCDkiog66KCSoD3iiJKgZYk1BC2CnzV1Tz31oXDGGQ8H+goC6MILFwTq4Ve/eiJO/YKoxdOHqMXrV1+/JDCdD3WMwJs7F0/ba3H0MB7wpUtL3ja83bkAwutG226p8P67734Q/4e5AhFSCMn581+LIotJwQkN05ZY3YXfwsTeiDMGrfzmN0+Fk0+eHC65ZGE8BkYvI+pOO+3hQNtBwHPctJsjj7wnhqMR+7QZvJSwo59x00c7oQ9xE0EdcKPDzQd1lve9vM9RZ9QXbQgBSruijoYPL91sMCci7bBUN003GvTrQw65O3pKEaXcfCGA6fOlm425sW4YWc1x0B9+9rPHokDlGLnpoN8wUpt+Sz3Rd6kr+i95nJxH4HTBBdMiM+ZixHuLKKc/s0oLIpbBPwjZhx56NXCTQgrAwoWvR/5EKqhXvKiE4hnIwzk5r18GEHFelshtqXX3nPck5vy6kphbTTHHFBOcJDlBtiW0Sn4c4SBOvJzgygsXDk6MeKgI+6zJwnFwQj3nnEeiwEJo4IFab70mcYD3ios5FwUuBBwLF188DVxUCRWzkgLH2dtLTzi5MP8dQoT2ineOi92yZavC4sVvRZFDGPTBB18JCBIupFxUGUWNGMGjiscIUYsHCU9SLmhpI2eeOS+KWTyJXOS52H/pSxPjyhmIEgZaINQPOOCOKEwQcngn99prZthjj5JAQfAhUlhrmNVLaFcIWtp/UdByY4NnlJuC3FOLiPE8tUVR2xZhmwvfcoGbi9zcg4uILnpwEU38JsQ24onfmQtezhH0ob59RzcKX44NTy7HyfHizUWkcZMDB3jQ93bdtSSGmZpmjz1KooupaxDFiDx4cjOE6GMuQzgfeGDJ64sYRCwffPCd8YaCmwoehxxSehx66F2BB15EPJQ859v5a95H1DU9Sp9BndLv+Q6EH9/L93/xi7dHob7//qUbF7yV++wzO/7WvfeeHb3w/H7qHwFJLuUOO4yL55HPfGZ6FP4ITI4dBtwQwGT48CmxbXCzg5CFHQwRqOkNT8mLn7cLhG3eBjjnUofUHTdE1Bc3oaUbk0lRIHM+5zv4Ltojwpc6wdPO7+L3cYNCnXCTwjFwU8rxNdXJ7YU6uTNyghkcYUw6Aav1IJTxyiOW8eKSHsByjXhzDzpoUvQik1/KjQ2in5QEPPbcBJBziuceMU26AoKaGx6uHXjyOR8zhdGIEY/HfouXmrxr+vHIkYsahTZTHCG2uemgr+PV5mYW4U3/R3z/+c/PR6cC5wQ83whxbnwR43iRx49/MeZyT5q0JApzvMqcR6ZOXRpvuLnJYbJ1ogecY7jxyW/Aucnm3EOOLuKdmzAEPDM1sGY210BuyhDzv/vdjCjoOWdxI7VgwcroqUbcE4ngBovZIEiTQOjjfEDsc65D8OPN59qE8Merjfjn5ox0CjzcePy5EWAQGTd7RDI4b+L1JqLBjQHnUm4OOK+2dhO4pq5/3VXMnW9mS8zs4ezxlYLm+omZPWVmT5jZlwv2AzIb751VsA8ys/vNbJGZ3Wpm6xXeczeHDRtWFX+ECp2dkwCVXW2hgXBi4mRCwy0vfBYXQU50NLjOKvx+OhAXYy6unBQRaVzMOPlx4cRzhmcJL9n//b9T4zqwtSDQ2sK8J4i5thxPR+zbnZlw8s3FLSdo+hsnbk7inNw56XMhIJT5yCOvxosJ/RQv7owZS+MFquTBXVzw4OJ5K4ndyy9fGD2HCF4uqOTqcZHFs/i1r9WFH/3ooejROuWUueGkkx6MAviEEx6IXjku5HjmuLhzDiD8zoUf8YVwQjQhmBBuhOoRSvRd0hQQSJwzEMjcYBWFUS6WEUaIEsQRwhGhwjksF88IpG23rYvrOuP145yAJx3vK4K0f/8J8byASEWsIloR1ggiPLaIWUQtj403LqUpILZzwZ0LYJ451/DAm7jOOiWBhcji3JM/ENClR8lrjBDjkQvt4nMuwrvbc/E3FrcrHUtuz4+z+JrtJiY5m/Jn9mn+yHm257m8Ttryurgv28XX7fkt/A/HVv6/rTMp/R//W86z/HWxjsq329O2yj+j+Lr8u/PX3vGUHzOvc6Y8d2cxd7qjtHY0s3lmtr6ZIdKeNrM+2YPtwZlYYx/2pYwys69l21eb2YnZdsWnasUcJ01OWG1ZZ5XQTB7yWLLkreS6ibeEuz1CTR29JBd3LFxQOOFzJ0qjovFwkuZiwMUFrxojcr3SnS/Q3u9dU7buygXRwl0kd5bcaXL3yR1pLla4k20KEb4cw82EKLnTJqyPx5jw2MiRT8aQGfl6hDjPO68kTPAK4CGg3RBeRpAQhkOM7LffhChE8O7gjSiKEDxJeC/wLOHNwKuB+CCEiMcD4YEHZMcdfdExaFDJm4X3pOS5K4qOSdEDRpvmZoRHufBoEh8l716T+GjKySwKELw7G25Y8sLlAiQXIXl4Oz+plp9wy0/K+cnaey6e5L3t9lxI9D9N0QSxEIve3QbswYqipgvfwDPniTm8cjzy0mBme2UPtvOS77eWma0ws3WyN9i3uF++f7PnasQcrnJO5E8++XrVmoELJxcGLlJebh2fxR0yd/Id4bp99NFX44WWCyMXHxoyIo6QB54C3NZtKd1VtLTlGDpj3yIX6g0Rjsse0YRgIkRA7g9hBkIRhCsQSoyoZGTlxRcviAMcyA0j345wC6FJ8skQPdw0IHAI9ZTypEoDQxAlCBGEB56O/K4XoZCftHJRUC4ecntxP/bJ73rXW290bDO0V0JRfA9el1L4sGnwB14bcuWKYSm8ztttNzaGyBBniDTEGseBeOPGIQ9FkTeXhwYJB+KB4tjz8NMxx9wbxWEeeiKECyPEIwOCimEn8uoIOXHDwuTIiE6mPUGA4iVDjBJuuuyyhXFQBOEmcroQq+R1UR/XXPNUIdRUyu8izIS4Jcfr1lufD+Sxjhr1fPjzn0thqOuueyqGoPkc8viaPHOEuuaXeeYmhdNOmxsYhEFYmqX+SE84/vj7oxA+7rj7AsdM7ig5hIcdRkizFCqlPRDCxCNXEsPwLIX58MLhRScESH/PPW9DhxKSrA/bbUcdMUiH+poUPvGJiWGrrch3nBC22IL6ZFAPYWHqmIE+hB/Hhk02oe4JR5ZCkhttxMCgMQVxy6Ch/NHUBhG1uZDN217e5njO2117n4ufVdzOv6v8Of8t+XO56C73chSPifM8j6KQz7eLnka2Ef2lRyn0X7oRKG3nNwitPdPf8n022GBU43Zuq/xcGrTF+8XvzbfLfyuv8+No/pzXZ+k5vVFpOk/kPHnOmRfro1L9Fvfh/0qexFKbKdZFqR5KvzP//euvD5NSO6Rd4lApPUoeYc5TpXQH2nH+aEp9yNMfuMnjZo/IGg9uAHmQDsEDbzTnN7zTPEj3oO9wA8mD/oQnO0+V4NzM9ZsH3m76HqkTeL/xgvPg3LjDDqUHHnK0wE475eF7QvilHGPO95w76dOE8zmH4uThPEpYnwfnUx44Z3h0Z8/cc2b2iJndYGabZWrrSjM7tqC8rjezI7LHdQX7cWbGvv2ykGz+1jZmNj9/Ufb83QzGg/37949D5blIe4+jj66LDfeqqxrc973/ueKKhhhK+PSnx4VZs2Yl//eb30wPffuOCaedNiV5z/s8z9bQMCv+/6c+xRJQpRMmOTqf+9yEcNZZUwLve/9Xra2urm61/r/a71mT+82aNTtMnjwrjBo1M/z+9zPCVVdND5de2hDOP39aOPPMqTFh/Vvfqg9HHVUXDj54Uth//4lhzz0nhF12GR+GDx8XttmGkY2jwsYbc+IrhX84MZVOOKPDRz86OmyyCdNolJ7Z/shHyNchrFQ6iXHCy/+H9zbddHT4+MfHxEEEgwePjflEtJs99hgfPv/5CeHLX54YDj10Uhx4cdxxdeH44+vDiSfWhx/+cEo466yp4bzzpoaf/3xauPzyaWHkyOnh6qunhxtumBH++McZ4S9/mRnGjp0VJk2aFaZOnR1mzpzdKXXa1rZCn6irmxVuuWVG/K30rcsvbwgXXjgt/PSnU8Lpp0+JdXHCCfXh2GPrwpFH1oVDDpkUDjhgYthvv4lh770nRD677TY+7LzzuMhs++3HBvghLAcMYCLkMZFrv36jw2ableqE+oH5hhuOinVCHVIvhP2oEy40XHgqXZRye35xarowlT6Dz+IzaQ/UeeniPCp+J20mbxv8Hvoqv42632KLMfH3br312NjGOIaBA0vHM2TI2MCxDRtG2xgbPvnJcWHHHceFnXYaF4+dtkL73GWXcWHXXceF3XYbF3bfncf4+IBRycZzaZv9ePA/n/70+MA5BI4778zN57j4HXzX8OFND34Dj6FDxwZ+E6wHDWLlkTHxMWBAqQ1vtdXosOWWHNfo0L//qNhfNt10VPjYx0aFj34UFiU+cIJ5zhSW1APsNtxwdOxj8IJVv36luqROYbTttiU+JTal+m/iMT7sumvpWD/72fHhX/5lfOzDe+01IZ4b//3fJ8R+tc8+E2P//sIXJoYvfnFi7GcHHDAp5q3R92lvhx02KXz1q3XhiCNKbZDzAteDY46pC8ceWx++8Y368D//Ux++/e362C+/853J4XvfmxxOPHFybL+nnDI5/OAHU8Kpp06J/ZXz/RlnTAk//vHU8JOfTA1nnz01/PSnU8O5506N56Czz54QB4dcdNG0cPHF08KIEQ3xcdllDYHH//5vQ/jlLxvCr37VEH7964ZwxRXTY5/nPMbjt78t9f9rrpkec83IN7v++lIfu/HGGfGc94c/zAg33TQj/OlPM+Pj5ptnxvPELbfMjOdFzo1jxpTOG+PGzQrjx88KEybMChMnlvos/ZZz6JQps+M5hQnDecyYUTq/cI6dPbvjzjNtPbesyetJV35XV4q5mZmwQlwVH4ea2RZZ6HRtM7soE3Ror6scMXe4mR1pZuVibqSZ9XfE3KNlIi552ZJnjsRPTtwkh1ZbyK/hzoWEV6+QJModAomjbS0MVsCzg+rnd3GHhVrH60B4rSMLDbU7F5JTSXRl1BtesHzVA7wzJA0TuiZZm7sY7pbwUlIvTD3CnReeL+6Ecg9SKUm7FAbkzgivB//HvuQHcbHhLrp//9HxLmrffWfH/EKSl/G84B1iVB+hSjw7jHBkVC1JvORkkXhLvhb5W92t4DmGJcnHJCyPHr04juylXeE5ZgQj3jFCqnjS8K6Ru8WdI0nrpQtsfUxMhzOePTwEeDi4825JJNGOSxdyBDKejpJ3EOZ8FnfP1AF3xNz5cofLXSx3q4Ru8fYxTx3ec3LOjj763uj1wqOHN+xHPyqNvuQ4SA7nmMh3w1t6883PxcRuRkozAIQpX+i/PBg5PXHiC7EeJ0x4IXro8LKSLE4d54ND8AQyUhUvIWFoPIiEoGl/++47MebAEXbmd5IwT3vj9+NN466+OEIVbwQsEDh4SPC6kJ+GV4GkfzwE/A9tF+60XzjQdsmnI7eO72LQA+cfpmIhyb40Wrjk3aRv5CNS+d3k+cEFDybHxChckuM55+WjUEl8J+mdcxYTPNPfaCf5CFQS2Elex/vPVCr56FMS05l3EK81IX9SVBiMgyDgfIVXu5qRxd2tv3TW7+nu59zOOu6WPldMfDpdKeYSEVXBMLDgTcvDp/muazTMyugZLv5cqKstiD9OxoRTvMJJkYuTN+0+B9UAACAASURBVBDC2x8bAxAYicRFjAsfgoK8JOYX68zSFZ2IsCUjjLggIHq54HKh4QLEhYn8Ky6ChP+42HEhxC3NRSxfj5RRXozquvDCx2J4mYs54TrCWISsCEtxcURkIBIQbog+RpMx9QijN/leLuiESxk9xUWIEU2UruBSXs9cAMnHpB0hvAj5MaqNMCQhSpLoEQ/kp3HRRwBwrBw3QgvRwPHTnnLPCM+5qOImgXaGkODGg/9lFCZhA4QIn0tdwI0QKd5DhBMDZxA3/B5GxsGQOQfnzFkROfKbV658p8VRz7QBppcg54+RaQgDhAKj4RgxRx+jfphTjrpCjBBqpZ4ZBYi4ZkBBPp9cHrrOxTlhYo6J46N/5wIfG2IJAU/YA9HF/9K2GIyAOOJzyRMsCcW5jUIR9oR2GT1IX2W0IGKIQUTkJPK7GdmHuGfkd2n6lJVxJB5Ch/bFgAyOuxbETXfoQ+V9qju8Fpe0FsQkZYKlu4q5rXK1ZmY/NLNbstc7lQ2AeCbz4JETxzaDIhitygAI9qWMLhsAcVJmr/jkeea44ODB4WRebcmFHHfnXuEul7trPDXVFHLuuIggWvBYMBUAd8JrqnRGJ2J4N3fqDFXHw4EXDS8G+UGIVZgjNhiFxyS7CBNG33KRxCvC/8GFucMYfYj3i/mt8IYgLBAu5E/wOYg2bHiUuNAiLvAoMG8VXrL2esg6igteVo6FpdoQPxwnQgGhjtcLQYEIo83gpUKAITyKAozXCC+OmTwQxAheWzw25KrhsWKUJIzxxiC08CohABFHfD+ekvaOWEZ44WEhlMs0AXj2qCNEHPOtIbgQ44gtBDm/A88ZXjTEJl5TRBbHSd4K9Yag5JjwynE8iHfyR+iLeJ0Qj3BCuCHg+GwEHZ4lvo+pFmgr+UoPHCeeIybjJqcRDyT1z4hWhFNnlo5qK535G7vis8XFpy4uKRcxSZlg6a5i7o9mRjiUnLlJZlYUd+dko1iZmuTAgiJj+pIns/fYJy+McJ2ThVsRdoyEbbF4Yg4hQDJktSf71oQcFxi8G1w8WyuEOPAe4CkhrESidnsvtq19V0vvt7cTwYzwCvMN4aXgIo4oJTTERZpj48JM+IcLMcdH6AaRxSjMYuGCi/cJAcLncDGHCeIWAYAIxBtFeAhRxAUbzx4io7NKJS6IIryl1B8eKhLbSWDH88dvRWzhDSp6xBBmHAsCFtGGV4j98SASzkT8MKcUoUHme8Kz88wzb7gDatp6vLkQw1sGez4bEfb73z8bv48QHMzxWCKgCK0yoIG+gchiQAZiklAgeU38dkQXvx2xRv0isgk/IiI5BjxWCC2+B08VdUudMfKaMFxPX4u1vA4qtZXy/Wrttbj4NS4uKRcxSZlg6a5irkWx1dlvlos5wkVccLmDr6bg5cCbUMkjh1hBwOAVqFTIWcIzw0Wd72aut2q/v9Jnrq69tU6El42LMBdmwpqMysSbRM4T+U2Ep/CK4TFhH4QsYSSvICzIK2NiSnLPEAOMFkIokJdFzg8hNQQbHrk1ucwZU8rwvXj3CNeSUI3nC0FDGBIxlocqETcINoQZIUk8T3ja+D9GFF9zzdNxtQLEbrU3Ch6vog12iF4mzGTiTYQxggzuiGU8WHjD8NIRHsVzh7DE40tdcZOBQCOfi1wrcr1ILSB0iABjYlHqZdq0pXGST9IPaJuI5vwYWmsrxd9bS9vi4te2uIiLTyC1qq2kTLBIzDnKsCjmJk9eEsNYeEGqKSQBI+Qq5dXhkeOiz8XbK4g4vBdcWBEBhI3WpFDxflNuK3Yi8sXI88HrxKz/CCyEFlNU4C1jDjIEBGE2wm6tFfKhyIlDMPD/5HIheMn1wiPEdBCE7RCMnVkYkEBOF9NLkAeFACXci9ghrJmHNBFsDHHHw8bs9eRjIfr5P0K9eMs60nsKQ4QyOXvkWXJDQEiadoYwIwSNoIQZ3s68LvCM4a3EK8bUJ/wP3lGm2yBvixnXyQFkcuqObGfFttKZ9dXTPltc/BoTF3HxCaRWtZWUCRaJuRbEHJPncmFk7qdqCvOJ4UUjnOYVRlcSqkWUlBc8Gnjy8hAbXpSOFAPl39eW17mXjOHzeHUYLYdYII8Nrw0hTVaSICRWbWFJFUZ4fve7D0bPEDle5EwRQmQuNt7vrIJnDXFOzhjCEbGGMKPu8KjhTeP3kOCPJ405v/AO8j/MBVheL+09ucCVXC0Gd+DlQvyST4ZAY/AGeXKEKskbQ0jimSSsSbgVbnjZ8JQhzPh/RvHiIUOQdnVpL5Ou/t2d/f3i4hMWF3HxCaRWtZWUCRaJuRbEHBd5LujlF28PJZ4YhB85UV4hLEdCN7lI5YUJSxFHPEjcrub7yj+jI1/j/cLrxoSqJMvnEycynxfiAe8QS5K1pZD7hncNbxcChWR2RAmT5pIj1d7BB5V+AwwZJUgolO8haR6BlnvWqCtCn+SjcYxwZ3H2th4X3++dXBBqjEakvglzkuOH+CpNT3FbnFSS38AoXEKaeADxnuHRZAAHQpdEfULIsOPzelLxmPSk399Zv1VcfLLiIi4+gdSqtpIywSIxV0HMkc9UbZ4cie7ktiEMPCFGYjdhOqZTKBbEBmFJPEGEVr3/Le7fmdvkpxG6Y7oFEtkRsggvRiCSe4WYaEsnYn9yqZhxnykr4EOOFuINT1RHije8ZZdc8njMRSPsSXg6n1aDY2FEKwn77EPYt6M4I/wQaxdcwAS9T8SFsHNPH940HngvCXMycIHFr5lCg/ZAvmQ14efOrPPO/Oy2tJXO/B3d7bPFxa8RcREXn0BqVVtJmWCRmHPE3MCB28e8NzxTrRXCo+QpIcry5O/i/xB6Zb6qO+9smkKEKSi46OMlIpTWlrVdi5+9OttMzkluF2FTlh7Ba4jXiJAd+VNeaa0TIeAI9TFwA1HFoAdEKrlZHRH6Q4QRzmVkKKNf8awhhBFueN0YbMHUJXjB8JR2RCGpn2ksCIEi8Jkkl9ArcwMyWACxxkzyhEYRqjBF4OGV62netI7glX9Ga20l36/WnsXFr3FxERefQGpVW0mZYJGYc8Rcnz6D4wShPrLmVubuwgPDxbu8MH8aIwOZJDQvTFlCOJUcLcJoa7LwG5nbDi8V4gdBxIhQxEc1wqNSJyJMioAjp4tpQsh7I0xbzWe2dPyIXAQSHj1CvQws4YGXE+4MDmGwgieiW/rc8vcIK+OZZAAGIU7y0WCDYKNuGUTAyFwGYjA3HWFmcvpy72IlLuXfU0uvxcSvbXERF5+Ab1V7SbmIScoEi8ScI+bWWmtwnJXeR9ZkJQxJKHa+M1ccoVfytBgcQMEzhRcObxzTanRUqK/p1/hbTFGBV4k5wQh1MtUEI2pJvG9rKXYiFpLn2BhBiVcSAcfkx6sj4ODIiEtyyPB64XFjAWVWdMDzhVdudbkhEAlzEhZlolk+m+9ihDEjQk85ZW6caJZRyS+++M+qjqfIpa1Me+v+YuLXrLiIi0/At6q9pFzEJGWCRWLOEXMDBmzv0ypYGbSAMGNgQ3khhIlww3NEwQNHHhceJTxWnV2YNoRwH0sN4YFDwDESsz3J/cXfymLJzOaPZ4/51PBWIYxyD1Vx32q2yXU744yH44z/DAZAvOENYx626657uipBXel78Lax7BM5f6ed9nAUaoSSGXDAmpVMLMy0KuQtri4XnVzSWhCTlAkWcREXn4BvVXtJuYhJygSLxJwj5orzzHnYyIMj3McIyPKCZwqRwwhJRA6eHkQf85C9/37nLhXE3HWEOxFELLTNAtnM37a6Ba8ik9sOHFjKEUPIemHl1r6HcCheQgZE5IMUyCckfxA7uYTtKTAnTIpgRbgRIsULSS4g67cy3QcjSlnZYHU8h5V+m04uKRkxSZlgERdx8Qn4VrWXlIuYpEywSMy1UczhxUEoMCeaV37xi8djjhVhTMKFTP775z8/5+3aITYEEmtOEkZFGDF3Gh6vjijLlq2KC83zuXj3Lrusoc1iCAFFiJQBEYhaPHBMMMzkuu31iCEuZ89+KU6Ay0hRpjnJJxhm5Ynp05fF9UU7gkE1n6GTS0pJTFImWMRFXHwCvlXtJeUiJikTLBJzbRRzu+zSED1fXtI93h8GPBB6JLxJWA8x0xmFCXqZWBgRw2AARqES3u2IQq4Ya3ASkmQ0ar5aRbWd6Lnn3oyrQnD8hE4JLxPyZZ3S9hSEMYKVsPUee8yMA0iYPJc52VgWjDU8u7JUy6Urf+Oa/m4x8YmLi7j4BHyr2kvKRUxSJlgk5tog5hA2DHhArJQX5g1DtJx77qNxugxCfZ7gK/+/tr5mFCULlbPcFQKJqUA6qiA8WTsVEYdwKhdJLXUipjNhQAghXgQc04bwWe1ZT5ZBG0xnwmAI5ogjP49QLF43Fn+vtJ5rR3Fo6+e0xKWtn9Vb9hcTvybFRVx8Ar5V7SXlIiYpEywSc1WKOaatIEzI1CLlhRn6Waz8kEPuivuQt9XRBW8Zc8IhtAhbMu1JRxV+/1lnPRLDlQjFSiNdyzsRYpVwKblp+eAFBG9bvZF8DiNVzz9/flzcnXy6/fa7LYo3Jlru7PVYV5djOZfV/bze8P9i4teiuIiLT8C3qr2kXMQkZYJFYq4KMUduF9NXsKB5eSGhPl8uikER11zzVPkuq/UajxchT/LCCCt2xICG/Ae9884HcXkuvGnf/vacVkVY3onmzFkRBxkwYS9rhh5yyN1xtYf8c6t5RkAijFnCCi8jE/5yfA0NSztkguFqfkNH7ZNz6ajP6w2fIyZ+LYqLuPgEfKvaS8pFTFImWCTmqhBzLCxP2NCb4+xXv3oi5sch5Orr02lKfOytWxGQ55zzaBRxiLlKqzK0/kn+Hkwxwjx4hC9Zdqu1wrGfeOLksPXWk6L38VOfmhZuvvk5l0mlzyI8zSTADB5hEAnfzcjY9oRiK31HV9h1ckmpi0nKBIu4iItPwLeqvaRcxCRlgkVirhUxx9qiCLWFC1cmBO+9d3kcrbreeqPjmp/JDu0wMJ3JjTc+GwdSsLzW4sUdO4CCPDg8jCy1xeCB1qbqYPJj9mcU6rrrjgpHHXVPWLKk+t9EyJVVFfbcc2b0wDFh8vjxL7Z7JGs7kHb6v+jkkiIWk5QJFnERF5+Ab1V7SbmIScoEi8RcC2IOAYeQQ9CVlxUrVkWBw4CIxx5r3bNV/v/ea9YAZdoO1v5kMtuOLIg21ixlmhFWa2htkXe8aEx3wvEThmXk7KxZs6r6SUxpwrq2jLIlPIyAmzZtaWAy495YdHJJa1VMUiZYxEVcfAK+Ve0l5SImKRMsEnMtiDmWqdp99+kJOUKOrK3ap8+osGBB6rFL/qEVA9OMnHzy3+L6o6yd2t4VFSp9Dd49lqoiXMyqCC0VQq540RjsMWhQfRg3rmld2ZY6Efl3TB9C/tymm44PeBUZkYq9t5eWuPT2Y690fGLikxEXcfEJ+Fa1l5SLmKRMsEjMVRBzZ501L4ZQly9flZDbccdpUezMm/dq8l5bDSwHxrqgxx//QPjHP95p67+3uD/euBtueCZ64y68cEGLU6XgiWPVCEQc+XDenHBeJ4IBU4gwLQtLmPF9TC1SS8XjUkvH7x2rmHhU5JnzqYiLuFQikNp1bkmZYJGYc8TcoEHbx/DiyJFPJtRYlotpOG655fnkvbYYEG7kom2//ZS4dmtb/reafRktypJijBJ9+OHKopOF51lFARHH9Cr33FM5vJt3IsKlLJ1FGHXrreviQI1Fi96o5mf1yn1yLr3y4Np5UGLigxMXcfEJ+Fa1l5SLmKRMsEjMOWJu3XUHRxFUjoylshBy3/veA+Vvten1bbe9FAjhsth7Z0yAy0TCzP3GvHSVVoVgbjcm+SUnbsCAusA8eq2VsWNnxbngttpqUlxfdezYF1r09rX2eb3lfZ1c0poUk5QJFnERF5+Ab1V7SbmIScoEi8ScI+bMBgc8VsXCFBoIOVYkaG9OG/ljTMrLkl/ViKfi91ezTVj1yisXxZCnN7lx/hksar/xxmPjYvfXXfd0bq74TF4ggxg++tHRcVWHaqYyqfhhvfANnVzSShWTlAkWcREXn4BvVXtJuYhJygSLxJwj5rbYYmgzWuSPEYbcaKOxgeW02lNYwYFRqgcffFfFFRba87n5/7z99vtx4l/CqpVCnozOJZSKNw5x1tpyY4yoPeywu+No1gsueCxMmlTdaNb8N9XKs04uaU2LScoEi7iIi0/At6q9pFzEJGWCRWLOEXPDhg1rpMWcasyxxvqg11//TKO9LRuEVQlN/vznC9rt1Wvp+5gKhMELrETBZMPlhdG3LAGGiNt11+mtTtLL+qf77ntbnItu5MhFjSsyqBOVky29FpeUi5ikTLCIi7j4BHyr2kvKRUxSJlgk5loQc3iuEGHMzfaFL9zW6gS75YgJe15++RNhiy0mhunTl5W/3SGvGdxA/t255853heIDD7wSV69AkLYWUmVf5pYbOLA+TlxcPi+cOpFfZeKSchGTlAkWcREXn4BvVXtJuYhJygSLxFwLYg7vFIu+9+07rs0L2yOETjjhgegJY9qPziizZ78U8+MYWeqV73//wRge3mef2WHlysrTnjD3HF49cvnIDaw0N5w6kUdZF2iPitqKR0VtxaciLuJSiUBq17klZYJFYq6CmLvkktIyXoQlWc2gLYVpQZik96CD7nLDnm35rEr7jh79QhRyCLrywlqneNfWW29MXD+1/P389fLlb4eTTvpb/JxLL13YGE7N3y9/VicqJ1J6LS4pFzFJmWARF3HxCfhWtZeUi5ikTLBIzDlibrvtSvPMHX74X8Nee81yw5c+zhDXUt1pp2lxRYfWBhhU+ozW7HjP8KI99FA6f9w11zwdWGLsk5+cGrwJj/lsvIYseM9Ev6ecMjesWPF2a18Z31cn8jGJS8pFTFImWMRFXHwCvlXtJeUiJikTLBJzjphbe+3BYa+9ZsZRnJ5g8lGG8OSTr8dBA3i5yJfrjHLJJQvjHHJPP918kl4GOTDylFG3rF5RqTAYY4cdpsbcuPnz27amrDqRT1VcUi5ikjLBIi7i4hPwrWovKRcxSZlg6Uoxd6SZPWZmH5rZZ8s01U/M7Ckze8LMvlx474DMxntnFeyDzOx+M1tkZrea2XrZe+tnr9mf9wcW/qfiJmLuW9+6P44A9bGlVuZew1v2u9+1Pm9b+t/VWUaMeDwMHTolvPDCW83+gTnxttuuPmy44Vh3GS52fuWVd+KSYUwQPH78i+0Sm+pEzbA3vhCXRhSNG2LSiKLZhrg0w9H4QlwaUTTbEJdmOOILMUmZYOlKMfdJMxtuZreXibkdzWyemSHEEGlPm1mf7MH24EyssQ/7UkaZ2dey7avN7MRs+yQz4zWF9xF6rZatthoaR7GS+1ZNYRQoI1Zvvnn1lvhq6bt+8YvH49JfzFdXLLNmLQsbbDAmDB48OQq24nts4yH8y1+ejyNaCamuXFndMZV/Dq/ViTwq4uJRUVvxqKit+FTERVwqEUjtOrekTLB0pZjLRVW5mMMrxyMvDWa2V/ZgOy/5fmuZ2QozWyd7g33z/fL/5S3eZz/2b7Gsv/6Q8Mc/PucTK7P+7W//iLlnEya8WPZOx7287LKFcbLfciFH7hxzxx1xxD2BMGt5efnlt2PolVUr7r238pqr5f9X6bU6kU9GXFIuYpIywSIu4uIT8K1qLykXMUmZYOmOYu5KMzu2oLauN7Mjssd1BftxZsa+/bKQbP7WNmY2P3vB84D8jczLx/4tlg03HFJVGJKcsy23nBTGjes8IcdExYRQy0OrTAJMftyFFy5wa7a+/u/Ru3jmmfMCq0N0RFEn8imKS8pFTFImWMRFXHwCvlXtJeUiJikTLJ0t5mZmwgpRVXwcWlBT5Z65qxwxd7iZkWNXLuZGmll/R8w9mn0+OXnlYm7zwncXN7+bwXhw8823iCddGk2lx5/+NDP06zcmnH321Ir7VPrfau0XXDAt9O07Jtx004zG75g1a1bYY4/x0SN37rnpd0+ZMjv8539OCltsMSb88pcNjf9X7Xe2tF9dXV2Hfl5L39WT3hOXtJ+IScqENi0u4tKWc5vaS9pexCRlQpvqbDFXFEuVtsvFXB4+zffPQ6XF8Cnv5ft1eJi1uJyXp4HxkuEtu/bazhvswKhTpg558MF/NP4EQqnMe0eO3Jw5adj08cdXBqZF+frX7wvV5vs1fngVGzQYlZSAuIhJSsC3qK2Ii0/At6q9pFzEJGWCpTuKuZ3KBkA8kw1+IOeNbQZFMFqVARDsSxldNgCCgQ+Uk8sGQDBQotXSkphjAAGL2TMgobPKggUro5CbObNpCTBWZRg+fErYeOOxwVtR4tZbF8dlxxCYnTUtijqRX+PiknIRk5QJFnERF5+Ab1V7SbmIScoES1eKua+a2Ytm9o6ZvVQYtIDYOifLb2NqkgML6usrZvZk9h775IURrnOycCvCjpGwlA0yocfUJLzPfq2WSmKOyXZZu5RlsjpLMDGB75Ahk+PaqHmVvfXWe9ETuOmm48PSpatyc3xG5JE/x2hWBmN0ZlEn8umKS8pFTFImWMRFXHwCvlXtJeUiJikTLF0p5loVVV21gyfmEG/HH/9AXKKrs1Z2QJh9/vOzA4MW8oKQY/46Qq7MFVcsvGb92IMPviv84x/N3yvu11Hb6kQ+SXFJuYhJygSLuIiLT8C3qr2kXMQkZYJFYs5RjJ6YY+WF3Xab3mlrrSIWv/3tOeHQQ+9uXD4McUduHkLujTfea1aDCxe+HicQPv30h8P773fOahPNvlAXonIcja91cmlE0bghJo0omm2ISzMcjS/EpRFFsw1xaYYjvhCTlAkWibkqxNz06cviNB+LFzdfecFH2j7rlVcuirl4uWjD+zds2JRAaLXcI0cu3cc/PjFcd90z7fuydv6XOpEPTlxSLmKSMsEiLuLiE/Ctai8pFzFJmWCRmGtFzD3zzJtxdYfbb3/ZJ9gB1vvuWxG9b4sWldZbZdTqLrs0hI03HpfkyLHKBEKO0a5ruqgT+cTFJeUiJikTLOIiLj4B36r2knIRk5QJFom5FsQc+WpMBfLLXz7h0+sA6/Llb4dtt62P66XmH/eFL9we11ktH7U6cuSisPXWdYF1YLuiqBP51MUl5SImKRMs4iIuPgHfqvaSchGTlAkWibkWxNwJJzwQjjnmvk4buUquG6NjiwMeGCnbp8/o8NBDTSNTyac777z5MUcOT2FXFXUin7y4pFzEJGWCRVzExSfgW9VeUi5ikjLBIjFXQcwxb9vQoVPC66+3f2F6H3mT9aKLFsTRq/noWNZgZYmu4jqvCLlTT30oegiXLWs+LUnTJ62ZLXUin7O4pFzEJGWCRVzExSfgW9VeUi5ikjLBIjHniLlBg4bFHLYHHnjFp9YBVj6bUar5oIqJE5dEIXf55QsbPx0h98MfPhQ+85kZa2TqkcYvrrChTuSDEZeUi5ikTLCIi7j4BHyr2kvKRUxSJlgk5hwxt8EGQ8KllzaJKh9d+61vvvleHKl6yy2L44c89dQbYZ11RgfCunlByJ122sNh992ndwshx+9SJ8prp/mzuDTnobaS8sgtais5iebP4tKcR/5KXHISTc9i0sSiuCUx54i5jTYa0jjXWxFWR22TF3fccffHj2MuuX79JsQ57PLPR8j9+MfzYmi1fFqSfJ+ueFYn8qmLS8pFTFImWMRFXHwCvlXtJeUiJikTLBJzjpgbOnSYT6sDrHV1S8LAgfXhtddKuXif+9ysOJccI2fzwrqvO+88LbC0V3cq6kR+bYhLykVMUiZYxEVcfAK+Ve0l5SImKRMsEnOOmPNWgPDxtc366qvvxKlF8jnrzjjj4Thydf78pqlGbrjhmSj2liz5Z9s+fA3srU7kQxaXlIuYpEywiIu4+AR8q9pLykVMUiZYJObWoJj7znceCIRYKUz6y8jVP/zh2caamTRpSdhyy0mBpbq6Y1En8mtFXFIuYpIywSIu4uIT8K1qLykXMUmZYJGYW0Nibvbsl8KAAXVh5cp3AyHVj3xkbDjssLsba+Xee1fE3Ln77++8EbSNX9bODXUiH5y4pFzEJGWCRVzExSfgW9VeUi5ikjLBIjG3BsQc4m3IkMkBzxtlzz1nxmlJWLaLwvQkW201qfH9aOyGf9SJ/EoRl5SLmKRMsIiLuPgEfKvaS8pFTFImWCTm1oCYO+OMeeFrX7s31sDFFz8e1l57VFiwYGV8zTQlu+02PYwY8bhfQ93Iqk7kV4a4pFzEJGWCRVzExSfgW9VeUi5ikjLBIjHXyWKOwQ1MPfLSS6vCk0++HoXcJZeUhNsHH3wYDj/8r+Eb37i/05YM86u9fVZ1Ip+buKRcxCRlgkVcxMUn4FvVXlIuYpIywSIx14lijvni9t//9nDFFU9G+tttVx/njsur4vzz54e99poVVq16Pzd162d1Ir96xCXlIiYpEyziIi4+Ad+q9pJyEZOUCRaJuU4Uc6NGLQ6f+lRDYO3Vs86aF9Zdd3RYvry0vmpDw9KYJ/f3v3e/KUj8pqILkbhUIpDadcJNmWARF3HxCfhWtZeUi5ikTLBIzHWSmCMXbptt6sIdd7wcFi5cGcOrV121KNbCCy+8FbbYYmKcnsSvlu5pVSfy60VcUi5ikjLBIi7i4hPwrWovKRcxSZlgkZjrJDF39tmPhGOOuS9S33bb+rjGKi/effeD8G//NitcdNECv0a6sVWdyK8ccUm5iEnKBIu4iItPwLeqvaRcxCRlgkVirhPE3PPPvxX69p0QXnzxn+FnP5sf1lmnKbzKyNYDD7yzU9d+9at69a3qRD5DcUm5iEnKBIu4iItPwLeqvaRcxCRlgkVirhPE3De/eX8455xHwyuvvBOF3IUXlrxwM2cui8t5LV/evdZc9ZtGalUnSplgEZeUi5ikTNRWfCbiIi6VCaTv6NySMsEiMdfBYm7evFfDxz8+D5Zo6QAAEzhJREFUMa70sPfes+KqD4BmXVZy6KZNW+rXRA+wqhP5lSQuKRcxSZlgERdx8Qn4VrWXlIuYpEywSMx1sJg74IA741QkU6b8Pa69+sADpeW5vv71+8LJJ//Nr4UeYlUn8itKXFIuYpIywSIu4uIT8K1qLykXMUmZYJGY60AxRxiVZbtWrXovbLbZ+Ma1V2+9dXEYPnxqXJPVr4aeYVUn8utJXFIuYpIywSIu4uIT8K1qLykXMUmZYJGY6yAxxwTBn/3sjHDLLYvDGWc8HDbYYEwUdcuWrYph1zlzSh46vxp6hlWdyK8ncUm5iEnKBIu4iItPwLeqvaRcxCRlgkViroPE3KRJS8IuuzTEXDlGr7IGK+Woo+4NZ545z6ffw6zqRH6FiUvKRUxSJljERVx8Ar5V7SXlIiYpEywScx0g5vDK7b779DBu3Ivh0EPvDv37T4y06+v/HgYPntzjw6t501Enykk0fxaX5jx4JSYpE3HxmYiLuFQmkL6jc0vKBIvEXAeIuYkTS145VnpYa61Rgdevv/5uYLLgGTOW+eR7oFWdyK80cUm5iEnKBIu4iItPwLeqvaRcxCRlgkVibjXFHF653XYreeUIs+6887RI+gc/mBuYb643FXUivzbFJeUiJikTLOIiLj4B36r2knIRk5QJlq4Uc0ea2WNm9qGZfbagqQaa2Sozezh7XF147zNm9qiZPWVmV5jZWtl7fc1shpktyp43y+y8z37s/4iZ7V74rIqbw4YN82k5Vrxwu+46PcyYsTR65RYsWBnmzv1HXHt1xYqeOTmwc5jRpE7kkxGXlIuYpEywiIu4+AR8q9pLykVMUiZYulLMfdLMhpvZ7Y6Ym19Bac0xs70yETfVzA7M9rvEzM7KtnkekW1/xczYD1H3r2Z2f4XPbWauVszluXLjx78YBg2qD/vtd1vAxtqr11zztE+8B1vVifzKE5eUi5ikTLCIi7j4BHyr2kvKRUxSJli6UszlAqpaMbeVmS3M/8nMjjaza7LXT5gZ71N45jWF99kvL8X9clvyXK2Ymz59Wdhpp2kBMUeu3AsvvBVuvvn5GHZ9//0PfeI92KpO5FeeuKRcxCRlgkVcxMUn4FvVXlIuYpIywdJdxdxbZvaQmd1hZv+eqS1CsTMLygt7ffb6tYKdzVez17y/d+G9WWVewMJbTZvVirkvfvGOcOONz8Yluw488M7w5pvvxe277lru0+7hVnUivwLFJeUiJikTLOIiLj4B36r2knIRk5QJls4Wc4gvQqblj0ObpFMSZl3fzDbP3idH7gUz28TM/sURc3XZfpXE3GRHzPGZXvluBuPB/v37x5MujabS49prp4d+/caEs8+eEr1y48bNCscdVx/2339ixf+p9Fk9xV5XV9drj2116kBc0n4iJikT2pi4iEtbzjVqL2l7EZOUCW2qs8WcJ5rKbeVh1krvd6sw69FH3xsuvXRhHOjwX//11/Dcc2+Gvn0nxFCrr5t7vpUGo5ISEBcxSQn4FrUVcfEJ+Fa1l5SLmKRMsHRHMdffzPpkim6wmS0xM0arUh7IBjIwoIGBDQxwoFxaNgCCARGUg8oGQDCAotXSWpj12WdLwu3aa58Oa689Krz66jtxGpJzznnUp9xLrOpEfkWKS8pFTFImWMRFXHwCvlXtJeUiJikTLF0p5r5qZi+a2Ttm9pKZNWQq6/BsypJ5ZjbXzP6zoL7ImyNk+7SZXVmYmoSwLPlwTE3Ccy7+EH1XZfszpUlxCpTCxzbfbE3MMYccS3QNGFAXDjnk7vDoo6/FVR9ee+1dn3IvsaoT+RUpLikXMUmZYBEXcfEJ+Fa1l5SLmKRMsHSlmGuuoLrRq5bEHIJts83Gh5tuejbmyi1duiou4XX55U/4hHuRVZ3Ir0xxSbmIScoEi7iIi0/At6q9pFzEJGWCRWLOEZEtiblf//rJcNRR94btt58S9tlndvjrX5eHbbapC6tWve8T7kVWdSK/MsUl5SImKRMs4iIuPgHfqvaSchGTlAkWibk2iLkPPvgwDBs2JVx77VPRK/fEEyvD5z8/O9xwwzM+3V5mVSfyK1RcUi5ikjLBIi7i4hPwrWovKRcxSZlgkZhrg5hraFgaWH91110bwu67Tw8zZy4Lw4dPDe+994FPt5dZ1Yn8ChWXlIuYpEywiIu4+AR8q9pLykVMUiZYJObaIOYOPviucPHFC6JXbs6cFdErd9NNz/lke6FVncivVHFJuYhJygSLuIiLT8C3qr2kXMQkZYJFYq5KMff002+EzTefEL785TvCwIH14Y47Xg5DhkyuGa8cjUWdyO9E4pJyEZOUifqQz0RcxKUygfQdnVtSJlgk5qoUc6ef/nA49dS5oU+f0eH3v382/Md/3B6uv742cuXypqNOlJNo/iwuzXnwSkxSJuLiMxEXcalMIH1H55aUCRaJuSrE3Ntvvx/nkTvhhDlh443HhXvuWRG2264+vPtubeTK5U1HnSgn0fxZXJrz4JWYpEzExWciLuJSmUD6js4tKRMsEnNViLlRoxaH/fa7LWyyybjAhMEHHnhn+O1vn/KJ9mKrOpFfueKSchGTlAkWcREXn4BvVXtJuYhJygSLxFwVYu5LX7ojnHTSgzHEet99y8NWW00KeOtqragT+TUuLikXMUmZYBEXcfEJ+Fa1l5SLmKRMsEjMtSLmnnuutA7roEH1AVH3zW/eHy66aIFPs5db1Yn8ChaXlIuYpEywiIu4+AR8q9pLykVMUiZYJOZaEXPnnTc/HHvsfcFsVLjzzpfDppuOD6+88o5Ps5db1Yn8ChaXlIuYpEywiIu4+AR8q9pLykVMUiZYJOZaEHPvv/9h2Hbb+pgvx4CHs89+JJx88t98kjVgVSfyK1lcUi5ikjLBIi7i4hPwrWovKRcxSZlgkZhrQcxNm7Y0rvSw/vpjwogRj4d+/SaERYve8EnWgFWdyK9kcUm5iEnKBIu4iItPwLeqvaRcxCRlgkVirgUx99//fU846qh7wrrrjg4jRz4RDjvsbp9ijVjVifyKFpeUi5ikTLCIi7j4BHyr2kvKRUxSJlgk5iqIuZUr341TkRBeZRmv7befEnPmfIy1YVUn8utZXFIuYpIywSIu4uIT8K1qLykXMUmZYJGYqyDmbryxtMoDAx9Y6WGXXRrChx9+6FOsEas6kV/R4pJyEZOUCRZxERefgG9Ve0m5iEnKBIvEXAUxx3Jde+45Mw6AILx69dW1N0lweZNRJyonUnotLikXMUmZYBEXcfEJ+Fa1l5SLmKRMsEjMOWJu8OBhcQqSDTYYE37yk0fCZpuND2+88Z5PsIas6kR+ZYtLykVMUiZYxEVcfAK+Ve0l5SImKRMsEnOOmOvff2icjqRPn9FxOpKTTqrd6UiKzUadqEijaVtcmljkW2KSk2j+LC7NeeSvxCUn0fxZXJrz4JWYpEywSMw5Ym799YeE4cOnxDDrJz4xKTz66Gs+vRqzqhP5FS4uKRcxSZlgERdx8Qn4VrWXlIuYpEywSMw5Yq5Pn8FhrbVGhR//eF7Ye+/ZPrkatKoT+ZUuLikXMUmZYBEXcfEJ+Fa1l5SLmKRMsEjMOWJuww2HhI02GhvXYv3Tn57zydWgVZ3Ir3RxSbmIScoEi7iIi0/At6q9pFzEJGWCRWLOEXPrrDM4HHDAHaFv3wnhn/983ydXg1Z1Ir/SxSXlIiYpEyziIi4+Ad+q9pJyEZOUCRaJOUfMmQ0OP/jB3PD97z/oU6tRqzqRX/HiknIRk5QJFnERF5+Ab1V7SbmIScoEi8ScI+bImWPFh/vuW+FTq1GrOpFf8eKSchGTlAkWcREXn4BvVXtJuYhJygSLxJwj5jbffGjYYYepNb/iQ3mTUScqJ1J6LS4pFzFJmWARF3HxCfhWtZeUi5ikTLBIzDli7mMfGxpGjHjcJ1bDVnUiv/LFJeUiJikTLOIiLj4B36r2knIRk5QJFok5R8ytvfbgsGTJP31iNWxVJ/IrX1xSLmKSMsEiLuLiE/Ctai8pFzFJmWCRmHPE3Ec+MsSnVeNWdSK/AYhLykVMUiZYxEVcfAK+Ve0l5SImKRMsEnOOmNtuu+19WjVuVSfyG4C4pFzEJGWCRVzExSfgW9VeUi5ikjLB0pVi7lIzW2hmj5jZeDPbtKCrfmJmT5nZE2b25YL9gMzGe2cV7IPM7H4zW2Rmt5rZetl762ev2Z/3Bxb+p+LmsGHDfFo1blUn8huAuKRcxCRlgkVcxMUn4FvVXlIuYpIywdKVYu5LZrZOpqhGmBkPyo5mNs/MEGKItKfNrE/2YHtwJtbYh30po8zsa9n21WZ2YrZ9kpnxmsL7CL1Wi8Sc31jUicTFJ5Ba1VZSJljERVx8Ar5V7SXlIiYpEyxdKeaKouqrZvbnzIBXjkdeGsxsr+zBdl7y/dYysxUFYci++X75//I/CEf2Y/8Wi8Sc31jUicTFJ5Ba1VZSJljERVx8Ar5V7SXlIiYpEyzdRczVmdmxmcK6srCN6XozOyJ7XFdQYceZGfv2y0Ky+VvbmNn87AXPA/I3Mi8f+7dYJOb8xqJOJC4+gdSqtpIywSIu4uIT8K1qLykXMUmZYOlsMTczE1aIquLj0IKaOifLmcs9Zlc5Yu5wMzvSzMrF3Egz6++IuUezz3/MEXObF767uPndDMaDZvZ2YZvXepQYPCcWblsQl7SPiEnKhPOIuIhLW64nai9pexGTlAlt6o2ioFnT2980s3vNbKPCF+fh09yUh0qL4VPey/fr8DBrJljy79dzEwEajEpKQFzEJCXgW9RWxMUn4FvVXlIuYpIywdJlXBiZuiDzrBV/2k5lAyCeyQY/kPPGNoMiGK3KAAj2pYwuGwDBwAfKyWUDIBgoUU3pMijV/Lgu3EdcfPjiknIRk5QJFnERF5+Ab1V7SbmIScoES5dxYbqQF8zs4eyRjzrlRxF6ZeQqU5McWPjdXzGzJ7P32CcvjHCdk4VbEXaMhKVskAk9vov32a+a0mVQqvlxXbiPuPjwxSXlIiYpEyziIi4+Ad+q9pJyEZOUCRZxcbiQP6eSEhCXlAkWcUm5iEnKRG3FZyIu4lKZQPqOzi0pEyzi4nORVQREQAREQAREQAREQAREQAREQAREQAREQAREoFMI3GBmLxfmpCv/EkbJXpHl4bHk2O7lO/TS161x2dfMVhZyHc/tpRyKh8XchbeZ2eNmxnQ3/6f4ZrZdi+2lGi612F7I1SVHl0FatJefOe2lXUsNOp/Tk0zVcPkfM1teOL+c0JMOcDV+K6scPWRm9c5n1GJbyTG0xKVW2wpTszD9GuMNvDy5mrsWfT4TaPkEw3njyZ8ZbDE1WzHiX7O1XfP3evNza1y4OHsnnN7MZKuCmP9oNggnX0ouP+5abC/VcKnF9sLJdOOsYaybnTs4hxRLu5YaLH5AD9yuhgsXaCaDr7XyIzO7ucK5tRbbSl7/LXGp1baCmGtp8YNavBbZwBY8c9eY2dF5i8pG1nLxqoXSEpdavDiX1/lEM/timbGW20uOwuNS6+2FOTTnmtmeOaTsOZ8/k5dVLzVY9hk9+WUlLrV4gWaVollmtn8FMVerbaU1LrXYVujzrYm5mrwWtSRa8D7tXThb0tk+W3jdmzdb4sLF+ZUshITnMp/rrzfzKB4bbBab2SZFY3YSrtX2AopKXGq1vRAeIgzyppmNKGsrvGzXUoPO5/Q0U2tcuEAvNTNSW8aYGaH83l44zs+YWaUbn1ptK61xqcW2Ql94NrtB/FuFEaw1qV1aEi2THTFHh6uF0hIXREweQsKdu6gWgGTHyHHTgf7LOeZabi8tcanl9kIz2TTLt9y5rM20ZanBsn/tFS8rcWG5xXye0O+b2execbSVD+JgM/tN9nYlMVeLbaUaLrXWVvJW9Ils4+OZU4XUqGKpyWtRS6KlJl2VWYtoiUux0bDdmsu3fP+e+prcJ8Id5HB4pVbbS2tcylnVSnspHvd5ZnZ60ZC1JZYopNRimJXj9riUiJT+4sVjsFVvLheb2YvZeXSZmf3TzP5UdsC1GGathksRUy20leLx5tvnO+eWmrwWtSRaDiobAMHotFopLXHZMhsUAos9spAjic29uXB8N5nZr1o4yFpsL9VwqcX20j/zyNFcNjSzu8wMT0OxtHepweJn9LTtargU85K/amb39bSDXI3fW8kzV4ttpYixEpdabCsfMTMG4VHYvsfMWBq1WGruWvSXLDfjvezO6Hgzw63Pg8KF6qps6TCGAddKvlxrXE7Jpltg2gVOtJ/LePXmJ3LhQpbHky8/R4i51ttLNVxqsb18Optmgrwv8p3y6Xv+n5kdknWU9i412JP7WTVc8MgQVuT8wnRAO/TkA27jby+KllpvK0V0lbjUYlthSVL6Rj7tUb6saa1fi4rtRdsiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIi0HMJ/H8+pLJauadEWAAAAABJRU5ErkJggg=="
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:dfa5667b-d326-4dd1-a23b-12e8cab92f55.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3-Atoms attempt 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Okay so the basic idea is going to be to calculate the energy of a pair *once* at all the distances using the normal method above, and then rotate the states if needed and then convert them to 3-Atom basis. the last part might be a bit slow, but should work out fine I think."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2.7, 0. ],\n",
       "       [0. , 0.4]])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.linalg import expm, sinm, cosm\n",
    "expm([[1,0],[0,-1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rotateM(theta, Sz):\n",
    "    #sigmax = np.array([[0,1],[1,0]])\n",
    "    #sigmay = np.array([[0,1j],[-1j,0]])\n",
    "    #sigmaz = np.array([[1,0],[0,-1]])\n",
    "    return expm(-1j*theta/2*Sz)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 383,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fsOp3(basis):\n",
    "    # expects a two-particle basis, so each element of the basis should \n",
    "    # have J_1, mJ_1, L_1, S_1, and J_2, mJ_2, L_2, S_2 values.\n",
    "    op = np.zeros((len(basis),len(basis)))\n",
    "    J1,mJ1,L1,S1,J2,mJ2,L2,S2 = [0 for _ in range(8)]\n",
    "    names = ['J','mJ','L','S']\n",
    "    for s1num, state1 in enumerate(basis):\n",
    "        for s2num, state2 in enumerate(basis):\n",
    "            val = 1\n",
    "            qNums = [0 for _ in range(12)]\n",
    "            for num, name in enumerate(names):\n",
    "                if state2[name+\"_1\"] != state1[name+\"_1\"]:\n",
    "                    # matrix is diagonal.\n",
    "                    val = 0\n",
    "                qNums[num] = state1[name+\"_1\"]\n",
    "            for num, name in enumerate(names):\n",
    "                if state2[name+\"_2\"] != state1[name+\"_2\"]:\n",
    "                    # matrix is diagonal.\n",
    "                    val = 0\n",
    "                qNums[num+4] = state1[name+\"_2\"]\n",
    "            for num, name in enumerate(names):\n",
    "                if state2[name+\"_3\"] != state1[name+\"_3\"]:\n",
    "                    # matrix is diagonal.\n",
    "                    val = 0\n",
    "                qNums[num+8] = state1[name+\"_3\"]\n",
    "            J1,mJ1,L1,S1,J2,mJ2,L2,S2,J3,mJ3,L3,S3, = qNums\n",
    "            # the matrix element is A/2 (L1 . S1 + L2 . S2), A=1\n",
    "            val *= 0.5*(J1*(J1+1)-L1*(L1+1)-S1*(S1+1)+ J2*(J2+1)-L2*(L2+1)-S2*(S2+1) + J3*(J3+1)-L3*(L3+1)-S3*(S3+1))\n",
    "            #val *= 0.5*(J1*(J1+1)-L1*(L1+1)-S1*(S1+1)+ J2*(J2+1)-L2*(L2+1)-S2*(S2+1))\n",
    "            op[s1num,s2num] = val\n",
    "    return op"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 276,
   "metadata": {},
   "outputs": [],
   "source": [
    "def J_to_LS3(lsiBasis, jiBasis):\n",
    "    assert(len(lsiBasis)==len(jiBasis))\n",
    "    op = np.zeros((len(lsiBasis),len(jiBasis)))\n",
    "    for lsnum, lsiState in enumerate(lsiBasis):\n",
    "        for jnum, jiState in enumerate(jiBasis):\n",
    "            # there should be some repeats because of the i values in each basis unless I=0\n",
    "            L1, mL1, S1, mS1, I_lsi1, mI_lsi1 = [lsiState[key] for key in ['L_1','mL_1','S_1','mS_1', 'I_1', 'mI_1']]\n",
    "            J1, mJ1, JL1, JS1, I_ji1, mI_ji1 = [jiState[key] for key in ['J_1','mJ_1', 'L_1', 'S_1', 'I_1', 'mI_1']]\n",
    "            L2, mL2, S2, mS2, I_lsi2, mI_lsi2 = [lsiState[key] for key in ['L_2','mL_2','S_2','mS_2', 'I_2', 'mI_2']]\n",
    "            J2, mJ2, JL2, JS2, I_ji2, mI_ji2 = [jiState[key] for key in ['J_2','mJ_2', 'L_2', 'S_2', 'I_2', 'mI_2']]\n",
    "            L3, mL3, S3, mS3, I_lsi3, mI_lsi3 = [lsiState[key] for key in ['L_3','mL_3','S_3','mS_3', 'I_3', 'mI_3']]\n",
    "            J3, mJ3, JL3, JS3, I_ji3, mI_ji3 = [jiState[key] for key in ['J_3','mJ_3', 'L_3', 'S_3', 'I_3', 'mI_3']]\n",
    "            # needing to handle this case makes me feel like the actual clebsh gordon coef should be written as\n",
    "            # <L,mL,S,mS|J,mJ,L2,S2> or so instead of <L,mL,S,mS|J,mJ> as it usually is written. \n",
    "            if JL1 != L1 or JS1 != S1 or I_lsi1 != I_ji1 or mI_lsi1 != mI_ji1:\n",
    "                op[jnum,lsnum] = 0\n",
    "            elif JL2 != L2 or JS2 != S2 or I_lsi2 != I_ji2 or mI_lsi2 != mI_ji2:\n",
    "                op[jnum,lsnum] = 0\n",
    "            elif JL3 != L3 or JS3 != S3 or I_lsi3 != I_ji3 or mI_lsi3 != mI_ji3:\n",
    "                op[jnum,lsnum] = 0\n",
    "            else:\n",
    "                op[jnum,lsnum] += float(CG(L1, mL1, S1, mS1, J1, mJ1).doit())*float(CG(L2, mL2, S2, mS2, J2, mJ2).doit())*float(CG(L3, mL3, S3, mS3, J3, mJ3).doit())\n",
    "    return op"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 256,
   "metadata": {},
   "outputs": [],
   "source": [
    "def delta(ms1,ms2):\n",
    "    if ms1==ms2:\n",
    "        return 1\n",
    "    return 0\n",
    "def createSpinMatrix(spin, which):\n",
    "    assert(which == \"Sx\" or which == \"Sy\" or which == \"Sz\")\n",
    "    assert(int(2*spin) == float(2*spin))\n",
    "    mS_vals = np.arange(-spin,spin+1,1)\n",
    "    Sm = np.zeros((len(mS_vals),len(mS_vals)), dtype=complex)\n",
    "    for i1, ms1 in enumerate(mS_vals):\n",
    "        for i2, ms2 in enumerate(mS_vals):\n",
    "            if which == \"Sx\":\n",
    "                Sm[i1,i2] = (delta(ms2,ms1+1) + delta(ms2+1,ms1)) * 0.5 * np.sqrt(spin*(spin+1)-ms1*ms2)\n",
    "            elif which == \"Sy\":\n",
    "                Sm[i1,i2] = (delta(ms2,ms1+1) - delta(ms2+1,ms1)) * 0.5j * np.sqrt(spin*(spin+1)-ms1*ms2)\n",
    "            elif which == \"Sz\":\n",
    "                Sm[i1,i2] = delta(ms2,ms1)*ms1\n",
    "    return Sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 258,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fullRotation(theta):\n",
    "    RmL1 = createRotationMatrix(lsBasisR, theta, 'L_1')\n",
    "    RmL2 = createRotationMatrix(lsBasisR, theta, 'L_2')\n",
    "    RmS1 = createRotationMatrix(lsBasisR, theta, 'S_1')\n",
    "    RmS2 = createRotationMatrix(lsBasisR, theta, 'S_2')\n",
    "    return RmL1@RmL2@RmS1@RmS2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 302,
   "metadata": {},
   "outputs": [],
   "source": [
    "def HC(matrix):\n",
    "    return matrix.conj().T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 404,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.linalg import expm, sinm, cosm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 405,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rotateM(theta, Sz):\n",
    "    #sigmax = np.array([[0,1],[1,0]])\n",
    "    #sigmay = np.array([[0,1j],[-1j,0]])\n",
    "    #sigmaz = np.array([[1,0],[0,-1]])\n",
    "    return expm(-1j*theta/2*Sz)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 407,
   "metadata": {},
   "outputs": [],
   "source": [
    "def delta(ms1,ms2):\n",
    "    if ms1==ms2:\n",
    "        return 1\n",
    "    return 0\n",
    "def createSpinMatrix(spin, which):\n",
    "    assert(which == \"Sx\" or which == \"Sy\" or which == \"Sz\")\n",
    "    assert(int(2*spin) == float(2*spin))\n",
    "    mS_vals = np.arange(-spin,spin+1,1)\n",
    "    Sm = np.zeros((len(mS_vals),len(mS_vals)), dtype=complex)\n",
    "    for i1, ms1 in enumerate(mS_vals):\n",
    "        for i2, ms2 in enumerate(mS_vals):\n",
    "            if which == \"Sx\":\n",
    "                Sm[i1,i2] = (delta(ms2,ms1+1) + delta(ms2+1,ms1)) * 0.5 * np.sqrt(spin*(spin+1)-ms1*ms2)\n",
    "            elif which == \"Sy\":\n",
    "                Sm[i1,i2] = (delta(ms2,ms1+1) - delta(ms2+1,ms1)) * 0.5j * np.sqrt(spin*(spin+1)-ms1*ms2)\n",
    "            elif which == \"Sz\":\n",
    "                Sm[i1,i2] = delta(ms2,ms1)*ms1\n",
    "    return Sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 409,
   "metadata": {},
   "outputs": [],
   "source": [
    "def createRotationMatrix(basis, theta, spinToRotate):\n",
    "    Rm = np.zeros((len(basis), len(basis)), dtype=complex)\n",
    "    for i1, state1 in enumerate(basis):\n",
    "        for i2, state2 in enumerate(basis):\n",
    "            coupled=True\n",
    "            for k1,k2 in zip(state1.keys(), state2.keys()):\n",
    "                assert(k1==k2)\n",
    "                if (k1 != \"m\" + spinToRotate) and state1[k1] != state2[k2]:\n",
    "                    coupled=False\n",
    "            if not coupled:\n",
    "                Rm[i1, i2] = 0\n",
    "            else:\n",
    "                assert(state1[spinToRotate] == state2[spinToRotate])\n",
    "                spv = state1[spinToRotate]\n",
    "                rm_small = rotateM(theta, createSpinMatrix(spv,\"Sx\"))\n",
    "                rm_i1 = list(np.arange(-spv, spv+1)).index(state1[\"m\"+spinToRotate])\n",
    "                rm_i2 = list(np.arange(-spv, spv+1)).index(state2[\"m\"+spinToRotate])\n",
    "                Rm[i1,i2] = rm_small[rm_i1,rm_i2]\n",
    "    return Rm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 303,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "24\n",
      "(8, 8)\n"
     ]
    }
   ],
   "source": [
    "# plugging in zero nuclear spin effectively avoids i in all of these bases. \n",
    "lsiBasis, jiBasis, fBasis, lsiBasis2Atom, jiBasis2Atom, fBasis2Atom = createLargerBasisRefs([0,1], [1/2], [0])\n",
    "lsBasisR, jBasisR = [], []\n",
    "for state in lsiBasis2Atom:\n",
    "    if (state['L_1'] == 0 and state['L_2'] == 0) or (state['L_1'] == 1 and state['L_2'] == 1):\n",
    "        continue\n",
    "    lsBasisR.append(state)\n",
    "for state in jiBasis2Atom:\n",
    "    if (state['L_1'] == 0 and state['L_2'] == 0) or (state['L_1'] == 1 and state['L_2'] == 1):\n",
    "        continue\n",
    "    jBasisR.append(state)\n",
    "fsOperator = fsOp(jBasisR)\n",
    "J_to_LS_op = J_to_LS(lsBasisR,jBasisR)\n",
    "fsOp_LS = J_to_LS_op@fsOperator@J_to_LS_op.T\n",
    "print(len(lsBasisR))\n",
    "lsiToJiop = lsiToJi(lsiBasis,jiBasis)\n",
    "print(lsiToJiop.shape)\n",
    "#fsLsi = lsiToJiop.T@fsOperator@lsiToJiop\n",
    "#boBasisDict_g, boBasisLatex_g = createBornOppenheimerBasisHFS([1],[0,1], [0], sigmavals=['g'])\n",
    "#boBasisDict_u, boBasisLatex_u = createBornOppenheimerBasisHFS([1],[0,1], [0], sigmavals=['u'])\n",
    "boBasisDict_full, boBasisLatex_full = createBornOppenheimerBasisHFS([1],[0,1], [0], sigmavals=['g', 'u'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 304,
   "metadata": {},
   "outputs": [],
   "source": [
    "boBasis = boBasisDict_full"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 305,
   "metadata": {},
   "outputs": [],
   "source": [
    "boToAtomicMatrix = []\n",
    "for st in boBasis: \n",
    "    sigmaV = g if st['sigma']=='g' else u\n",
    "    phase = (-1)**(sigmaV+st['S'])\n",
    "    state1, _,_,_ = BohrOppenheimerToAtomic( [st['L'],st['Lambda'],st['L'],0],\n",
    "                                                [st['S'],st['Sigma'],1/2,1/2],\n",
    "                                                [st['i'],st['iota'],0,0],\n",
    "                                                sigmaV, lsiBasis, basisChange=lsiToJiop, naturalKronBasis=jiBasis2Atom, finalBasis=jBasisR)\n",
    "    boToAtomicMatrix.append(state1.T[0])\n",
    "boToAtomicMatrix = np.array(boToAtomicMatrix)\n",
    "#boToAtomicMatrix = J_to_LS_op @ np.array(boToAtomicMatrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 306,
   "metadata": {},
   "outputs": [],
   "source": [
    "toAtomic = boToAtomicMatrix@HC(J_to_LS_op)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 307,
   "metadata": {},
   "outputs": [],
   "source": [
    "A_gs = (mc.Rb87_Ground_ToF2-mc.Rb87_Ground_ToF1)/2\n",
    "A_12 = (mc.Rb87_5P12_ToF2-mc.Rb87_5P12_ToF1)/2\n",
    "A_32 = (mc.Rb87_5P32_ToF3-mc.Rb87_5P32_ToF0)/6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 308,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.7197635548748796e-21 5.94492796981645e-48\n"
     ]
    }
   ],
   "source": [
    "lifetime = (mc.Rb87_D1_Lifetime+mc.Rb87_D2_Lifetime)/2\n",
    "transFreq = 2*np.pi*(mc.Rb87_D2LineFrequency+mc.Rb87_D1LineFrequency)/2\n",
    "DeltaVal = mc.h*(mc.Rb87_D2LineFrequency-mc.Rb87_D1LineFrequency)# / mc.h\n",
    "C_3_val = mc.Rb87_C3\n",
    "print(DeltaVal, C_3_val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 386,
   "metadata": {},
   "outputs": [],
   "source": [
    "# plugging in zero nuclear spin effectively avoids i in all of these bases. \n",
    "lsiBasis, jiBasis, fBasis, lsiBasis3Atom, jiBasis3Atom, fBasis3Atom = createLargerBasisRefs3Atoms([0,1], [1/2], [0])\n",
    "lsBasisR3, jBasisR3 = [], []\n",
    "for state in lsiBasis3Atom:\n",
    "    totalElectronicAngularMomentum = state['L_1'] + state['L_2'] + state['L_3']\n",
    "    if totalElectronicAngularMomentum != 1:\n",
    "        continue\n",
    "    lsBasisR3.append(state)\n",
    "for state in jiBasis3Atom:\n",
    "    totalElectronicAngularMomentum = state['L_1'] + state['L_2'] + state['L_3']\n",
    "    if totalElectronicAngularMomentum != 1:\n",
    "        continue\n",
    "    jBasisR3.append(state)\n",
    "fsOperator3 = fsOp3(jBasisR3)\n",
    "J_to_LS_op3 = J_to_LS3(lsBasisR3,jBasisR3)\n",
    "fsOp_LS3 = J_to_LS_op3@fsOperator3@J_to_LS_op3.T\n",
    "#print(len(lsBasisR))\n",
    "#lsiToJiop = lsiToJi(lsiBasis,jiBasis)\n",
    "#print(lsiToJiop.shape)\n",
    "#fsLsi = lsiToJiop.T@fsOperator@lsiToJiop\n",
    "#boBasisDict_g, boBasisLatex_g = createBornOppenheimerBasisHFS([1],[0,1], [0], sigmavals=['g'])\n",
    "#boBasisDict_u, boBasisLatex_u = createBornOppenheimerBasisHFS([1],[0,1], [0], sigmavals=['u'])\n",
    "#boBasisDict_full, boBasisLatex_full = createBornOppenheimerBasisHFS([1],[0,1], [0], sigmavals=['g', 'u'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 371,
   "metadata": {},
   "outputs": [],
   "source": [
    "def convertHTo3Atom(H2atom, basis3,basis2, atomPair):\n",
    "    for num in range(3):\n",
    "        if num+1 not in atomPair:\n",
    "            which3=num+1\n",
    "    H3atom = np.zeros((len(basis3),len(basis3)), dtype=complex)\n",
    "    for i31, state31 in enumerate(basis3):\n",
    "        for i32, state32 in enumerate(basis3):\n",
    "            if state31['L_'+str(which3)] == 1:\n",
    "                continue\n",
    "            shouldExist=True\n",
    "            relevantLabels1, relevantLabels2 = {}, {}\n",
    "            for k1, k2 in zip(state31.keys(), state32.keys()):\n",
    "                assert(k1==k2)\n",
    "                if k1[-1] == str(which3) and state31[k1] != state32[k2]:\n",
    "                    shouldExist=False\n",
    "                    break\n",
    "                if k1[-1] == str(atomPair[0]):\n",
    "                    kv1 = k1[:-1] + '1'\n",
    "                    kv2 = k2[:-1] + '1'\n",
    "                elif k1[-1] == str(atomPair[1]):\n",
    "                    kv1 = k1[:-1] + '2'\n",
    "                    kv2 = k2[:-1] + '2'\n",
    "                else:\n",
    "                    continue\n",
    "                relevantLabels1.update({kv1:state31[k1]})\n",
    "                relevantLabels2.update({kv2:state32[k2]})\n",
    "            if not shouldExist:\n",
    "                continue\n",
    "            i21 = basis2.index(relevantLabels1)\n",
    "            i22 = basis2.index(relevantLabels2)\n",
    "            H3atom[i31, i32] = H2atom[i21,i22]\n",
    "    return H3atom"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2 distances held constant, angles change"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 520,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.5+0.j ,  0. -0.7j, -0.5+0.j ],\n",
       "       [ 0. -0.7j,  0.1+0.j ,  0. -0.7j],\n",
       "       [-0.5+0.j ,  0. -0.7j,  0.5+0.j ]])"
      ]
     },
     "execution_count": 520,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rotateM(3, createSpinMatrix(1,\"Sx\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 429,
   "metadata": {},
   "outputs": [],
   "source": [
    "def createRotationMatrix(basis, theta, spinToRotate):\n",
    "    Rm = np.zeros((len(basis), len(basis)), dtype=complex)\n",
    "    for i1, state1 in enumerate(basis):\n",
    "        for i2, state2 in enumerate(basis):\n",
    "            coupled=True\n",
    "            for k1,k2 in zip(state1.keys(), state2.keys()):\n",
    "                assert(k1==k2)\n",
    "                if (k1 != \"m\" + spinToRotate) and state1[k1] != state2[k2]:\n",
    "                    coupled=False\n",
    "            if not coupled:\n",
    "                Rm[i1, i2] = 0\n",
    "            else:\n",
    "                assert(state1[spinToRotate] == state2[spinToRotate])\n",
    "                spv = state1[spinToRotate]\n",
    "                #print(theta)\n",
    "                #if np.isnan(theta):\n",
    "                #    print('nan!')\n",
    "                rm_small = rotateM(theta, createSpinMatrix(spv,\"Sx\"))\n",
    "                rm_i1 = list(np.arange(-spv, spv+1)).index(state1[\"m\"+spinToRotate])\n",
    "                rm_i2 = list(np.arange(-spv, spv+1)).index(state2[\"m\"+spinToRotate])\n",
    "                Rm[i1,i2] = rm_small[rm_i1,rm_i2]\n",
    "    return Rm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 434,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fullRotation3(theta):\n",
    "    RmL1 = createRotationMatrix(lsBasisR3, theta, 'L_1')\n",
    "    RmL2 = createRotationMatrix(lsBasisR3, theta, 'L_2')\n",
    "    RmL3 = createRotationMatrix(lsBasisR3, theta, 'L_3')\n",
    "    RmS1 = createRotationMatrix(lsBasisR3, theta, 'S_1')\n",
    "    RmS2 = createRotationMatrix(lsBasisR3, theta, 'S_2')\n",
    "    RmS3 = createRotationMatrix(lsBasisR3, theta, 'S_3')\n",
    "    return RmL1@RmL2@RmL3@RmS1@RmS2@RmS3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 341,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100%                        \r"
     ]
    }
   ],
   "source": [
    "Rvals = np.linspace( 0.5*20*mc.a0, 5*20*mc.a0, 5000 )\n",
    "rotMatrix = fullRotation(1)\n",
    "HamiltoniansAtAllPositions = []\n",
    "for rnum, rv in enumerate(Rvals):\n",
    "    misc.reportProgress(rnum, len(Rvals))\n",
    "    totalM =  HC(toAtomic)@createBOMatrix2(C_3_val, rv, *boBasis).astype(complex)@toAtomic\n",
    "    #totalM += fsOp_LS * 2 * DeltaVal / 3\n",
    "    rotatedH = HC(rotMatrix)@totalM@rotMatrix\n",
    "    HamiltoniansAtAllPositions.append(rotatedH)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 514,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "99.6%                      \r"
     ]
    }
   ],
   "source": [
    "data = []\n",
    "incr = 20\n",
    "r_23 = r_13 = 5e-9\n",
    "H_13 = HamiltoniansAtAllPositions[np.argmin(abs(Rvals-r_13))]\n",
    "H_23 = HamiltoniansAtAllPositions[np.argmin(abs(Rvals-r_23))]\n",
    "for num in range(0,len(HamiltoniansAtAllPositions),incr):\n",
    "    misc.reportProgress(num, len(HamiltoniansAtAllPositions))\n",
    "    r_12 = Rvals[num]\n",
    "    if r_12 > (r_23+r_13):\n",
    "        print('Impossible Geometry Reached')\n",
    "        break\n",
    "    \n",
    "    H_12 = HamiltoniansAtAllPositions[num]\n",
    "    # calculate the angles to rotate the 23 and 13 interactions by.\n",
    "    theta213 = np.arccos((r_13**2+r_12**2-r_23**2)/(2*r_13*r_12))\n",
    "    theta123 = np.pi - np.arccos((r_23**2+r_12**2-r_13**2)/(2*r_23*r_12))\n",
    "    # create rotation matrices\n",
    "    R_13 = fullRotation(theta213)\n",
    "    R_23 = fullRotation(theta123)\n",
    "    # calculate all interaction energies, using the rotation matrices to \n",
    "    # rotate the different BO energies to have the same quantization axis.\n",
    "    H12 = convertHTo3Atom(H_12, lsBasisR3, lsBasisR, [1,2] ) \n",
    "    H13 = convertHTo3Atom(HC(R_13)@H_13@R_13, lsBasisR3, lsBasisR, [1,3] )\n",
    "    H23 = convertHTo3Atom(HC(R_23)@H_23@R_23, lsBasisR3, lsBasisR, [2,3] )\n",
    "    totalEnergy = H12 + H13 + H23 + fsOp_LS3 * 2 * DeltaVal / 3 \n",
    "    # and diagonalize to find the eigenenergies. \n",
    "    eigVals = np.linalg.eigvalsh(totalEnergy)\n",
    "    data.append(eigVals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 515,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(15, 10))\n",
    "colors, _ = misc.getColors(len(misc.transpose(data))+1)\n",
    "linestyles = ['-',':','--']\n",
    "for datanum, (mdata, color) in enumerate(zip(misc.transpose(data), colors)):\n",
    "    #print(len(mdata))\n",
    "    ax.plot(Rvals[:len(mdata)*incr:incr]*1e9, np.array(mdata) * 1e-9 / mc.h, linewidth=1, label=datanum, color='#0000AA', linestyle='-')\n",
    "#ax.legend(ncol=5)\n",
    "ax.set_xlim(1,5)\n",
    "ax.set_xlabel(r'$r_{12}$ (nm)',fontsize=22)\n",
    "ax.set_ylim(-20000,15000)\n",
    "ax.grid()\n",
    "ax.set_title('$r_{23} = r_{13} = ' + str(r_13*1e9) + \" $nm (fixed)\", fontsize=24);\n",
    "ax.set_ylabel('Energy (GHz)', fontsize=22)\n",
    "plt.savefig('3BodyEnergyDiagrams/' + '$r_{23} = r_{13} = ' + str(r_13*1e9) + \" $nm (fixed)\" + \".png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### basic single interaction in expanded basis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 402,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "99.0%                     \r"
     ]
    }
   ],
   "source": [
    "data = []\n",
    "incr = 50\n",
    "\n",
    "for num, H_ in enumerate(HamiltoniansAtAllPositions[::incr]):\n",
    "    misc.reportProgress(num, len(HamiltoniansAtAllPositions[::incr]))\n",
    "    #int short for interaction...\n",
    "    int12 = convertHTo3Atom(H_, lsBasisR3, lsBasisR, [3,2] ) \n",
    "    int13 = 0\n",
    "    int23 = 0\n",
    "    totalEnergy = int12 + int13 + int23 + fsOp_LS3 * 2 * DeltaVal / 3 \n",
    "    eigVals = np.linalg.eigvalsh(totalEnergy)\n",
    "    data.append(eigVals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 403,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "colors, _ = misc.getColors(len(misc.transpose(data))+1)\n",
    "linestyles = ['-',':','--']\n",
    "for datanum, (mdata, color) in enumerate(zip(misc.transpose(data), colors)):\n",
    "    ax.plot(Rvals[::incr]*1e9, np.array(mdata) * 1e-9 / mc.h, linewidth=1, label=datanum, color='#0000AA', linestyle='-')\n",
    "#ax.legend(ncol=5)\n",
    "ax.set_xlim(1,5)\n",
    "ax.set_ylim(-20000,15000)\n",
    "ax.grid()\n",
    "ax.set_title('Result in LSI Basis');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## problems with extra couplings..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 343,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "colors, _ = misc.getColors(len(misc.transpose(data))+1)\n",
    "linestyles = ['-',':','--']\n",
    "for datanum, (mdata, color) in enumerate(zip(misc.transpose(data), colors)):\n",
    "    ax.plot(Rvals[::incr]*1e9, np.array(mdata) * 1e-9 / mc.h, linewidth=1, label=datanum, color='#0000AA', linestyle='-')\n",
    "#ax.legend(ncol=5)\n",
    "ax.set_xlim(1,5)\n",
    "ax.set_ylim(-20000,15000)\n",
    "ax.grid()\n",
    "ax.set_title('Result in LSI Basis');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "colors, _ = misc.getColors(len(misc.transpose(data))+1)\n",
    "linestyles = ['-',':','--']\n",
    "for datanum, (mdata, color) in enumerate(zip(misc.transpose(data), colors)):\n",
    "    ax.plot(Rvals[::incr]*1e9, np.array(mdata) * 1e-9 / mc.h, linewidth=1, label=datanum, color='#0000AA', linestyle='-')\n",
    "#ax.legend(ncol=5)\n",
    "ax.set_xlim(1,5)\n",
    "ax.set_ylim(-20000,15000)\n",
    "ax.grid()\n",
    "ax.set_title('Result in LSI Basis');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 318,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "colors, _ = misc.getColors(len(misc.transpose(data))+1)\n",
    "linestyles = ['-',':','--']\n",
    "for datanum, (mdata, color) in enumerate(zip(misc.transpose(data), colors)):\n",
    "    ax.plot(Rvals[::incr]*1e9, np.array(mdata) * 1e-9 / mc.h, linewidth=1, label=datanum, color='#0000AA', linestyle='-')\n",
    "#ax.legend(ncol=5)\n",
    "ax.set_xlim(1,5)\n",
    "ax.set_ylim(-20000,15000)\n",
    "ax.grid()\n",
    "ax.set_title('Result in LSI Basis');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "attachments": {
    "e6d3e7ce-92af-417d-a00d-b86d51b703bd.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For reference:\n",
    "![image.png](attachment:e6d3e7ce-92af-417d-a00d-b86d51b703bd.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3-Atoms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "np.set_printoptions(precision=1,suppress=True,linewidth=100000, edgeitems=10000)\n",
    "from IPython.display import Latex\n",
    "import MarksConstants as mc\n",
    "import Miscellaneous as misc\n",
    "import matplotlib.pyplot as plt\n",
    "import sympy as sp\n",
    "sp.init_printing(use_latex=True)\n",
    "from sympy.physics.quantum import Bra, Ket, qapply, Dagger as Dag\n",
    "from sympy.physics.quantum.cg import CG"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "def J_to_LS(lsiBasis, jiBasis):\n",
    "    assert(len(lsiBasis)==len(jiBasis))\n",
    "    op = np.zeros((len(lsiBasis),len(jiBasis)))\n",
    "    for lsnum, lsiState in enumerate(lsiBasis):\n",
    "        for jnum, jiState in enumerate(jiBasis):\n",
    "            # there should be some repeats because of the i values in each basis unless I=0\n",
    "            L1, mL1, S1, mS1, I_lsi1, mI_lsi1 = [lsiState[key] for key in ['L_1','mL_1','S_1','mS_1', 'I_1', 'mI_1']]\n",
    "            J1, mJ1, JL1, JS1, I_ji1, mI_ji1 = [jiState[key] for key in ['J_1','mJ_1', 'L_1', 'S_1', 'I_1', 'mI_1']]\n",
    "            L2, mL2, S2, mS2, I_lsi2, mI_lsi2 = [lsiState[key] for key in ['L_2','mL_2','S_2','mS_2', 'I_2', 'mI_2']]\n",
    "            J2, mJ2, JL2, JS2, I_ji2, mI_ji2 = [jiState[key] for key in ['J_2','mJ_2', 'L_2', 'S_2', 'I_2', 'mI_2']]\n",
    "            # needing to handle this case makes me feel like the actual clebsh gordon coef should be written as\n",
    "            # <L,mL,S,mS|J,mJ,L2,S2> or so instead of <L,mL,S,mS|J,mJ> as it usually is written. \n",
    "            if JL1 != L1 or JS1 != S1 or I_lsi1 != I_ji1 or mI_lsi1 != mI_ji1:\n",
    "                op[jnum,lsnum] = 0\n",
    "            elif JL2 != L2 or JS2 != S2 or I_lsi2 != I_ji2 or mI_lsi2 != mI_ji2:\n",
    "                op[jnum,lsnum] = 0\n",
    "            else:\n",
    "                op[jnum,lsnum] += float(CG(L1, mL1, S1, mS1, J1, mJ1).doit())*float(CG(L2, mL2, S2, mS2, J2, mJ2).doit())\n",
    "    return op"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "def createLargerBasisRefs3Atoms(Lvals, Svals, Ivals, forceExcited=False):\n",
    "    fBasisRef = []\n",
    "    for Lv in Lvals:\n",
    "        for Sv in Svals:\n",
    "            Jvals = set(np.arange(abs(Sv - Lv), Sv + Lv+1, 1))\n",
    "            for Jv in Jvals:\n",
    "                for Iv in Ivals:\n",
    "                    FVals = set(np.arange(abs(Jv - Iv), Jv + Iv+1, 1))\n",
    "                    for Fv in FVals:\n",
    "                        for mf in np.arange(-Fv,Fv+1,1):\n",
    "                            fBasisRef.append(multiplyableDictMulti({\"F\":Fv, \"mF\": mf, \"J\":Jv, \"L\":Lv, \"S\":Sv, \"I\":Iv}))\n",
    "    jiBasisRef = []\n",
    "    for Lv in Lvals:\n",
    "        for Sv in Svals:\n",
    "            Jvals = set(np.arange(abs(Sv - Lv), Sv + Lv+1, 1))\n",
    "            for Jv in Jvals:\n",
    "                for mJ in np.arange(-Jv,Jv+1,1):\n",
    "                    for Iv in Ivals:\n",
    "                        for mi in np.arange(-Iv,Iv+1,1):\n",
    "                            jiBasisRef.append(multiplyableDictMulti({\"J\":Jv, \"mJ\":mJ, \"L\":Lv, \"S\":Sv, \"I\":Iv, \"mI\":mi}))\n",
    "    lsiBasisRef = []\n",
    "    for Lv in Lvals:\n",
    "        for mL in np.arange(-Lv,Lv+1,1):\n",
    "            for Sv in Svals:\n",
    "                for mS in np.arange(-Sv, Sv+1,1):\n",
    "                    for Iv in Ivals:\n",
    "                        for mi in np.arange(-Iv,Iv+1,1):\n",
    "                            lsiBasisRef.append(multiplyableDictMulti({\"L\":Lv, \"mL\":mL, \"S\":Sv, \"mS\":mS, \"I\":Iv, \"mI\":mi}))\n",
    "    return lsiBasisRef, jiBasisRef, fBasisRef, np.kron(np.kron(lsiBasisRef,lsiBasisRef),lsiBasisRef), np.kron(np.kron(jiBasisRef,jiBasisRef), jiBasisRef), np.kron(np.kron(fBasisRef,fBasisRef), fBasisRef)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "def createBornOppenheimerBasisHFS(Lvals, Svals, Ivals, sigmavals=[\"g\",\"u\"]):\n",
    "    # Normal Notaion is |L Lambda sigma S Sigma>, but I need to keep track of more than that for the splittings caused by other interactions.\n",
    "    # Therefore this creates a very big basis which is probably unnecessary, but the size of the matrices isn't actually prohibitive in these \n",
    "    # calculations so it's okay to have degeneracies.\n",
    "    boBasisRef = []\n",
    "    for sigma in sigmavals:\n",
    "        for Lv in Lvals:\n",
    "            for Lambda in np.arange(-Lv,Lv+1,1):\n",
    "                for Sv in Svals:\n",
    "                    for Sigma in np.arange(-Sv, Sv+1,1):\n",
    "                        for i1 in Ivals:\n",
    "                            for i2 in Ivals:\n",
    "                                for I in np.arange(abs(i2-i1), i2+i1+1,1):\n",
    "                                    for iota in np.arange(-I,I+1,1):\n",
    "                                        state = multiplyableDictMulti({\"L\":Lv, \"Lambda\": Lambda, \"sigma\": sigma, \"S\":Sv, \"Sigma\":Sigma, \"i\":I, \"iota\":iota, \"i1\":i1, \"i2\":i2,\n",
    "                                                                  \"Omega\":Sigma+Lambda, \"phi\": Sigma+Lambda+iota })\n",
    "                                        if state not in boBasisRef:\n",
    "                                            boBasisRef.append(state)\n",
    "    boBasisRef = list(sorted(boBasisRef, key=lambda state: abs(state[\"Omega\"]) + 100 * ord(state[\"sigma\"])))\n",
    "    boBasisFancy = []\n",
    "    for state in boBasisRef:\n",
    "        spinT = 2*state[\"S\"]+1\n",
    "        omega = state[\"Omega\"]\n",
    "        parity = state[\"sigma\"]\n",
    "        LambdaSymbol = \"\\Sigma\" if state[\"Lambda\"]==0 else \"\\Pi\"\n",
    "        boBasisFancy.append(Latex(r\"$^{\"+str(spinT)+ \"}\" + LambdaSymbol + \"_{\"+ str(abs(omega)) + \",\" + parity + \"}$\"))        \n",
    "    return boBasisRef, boBasisFancy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fsOp3(basis):\n",
    "    # expects a two-particle basis, so each element of the basis should \n",
    "    # have J_1, mJ_1, L_1, S_1, and J_2, mJ_2, L_2, S_2 values.\n",
    "    op = np.zeros((len(basis),len(basis)))\n",
    "    J1,mJ1,L1,S1,J2,mJ2,L2,S2 = [0 for _ in range(8)]\n",
    "    names = ['J','mJ','L','S']\n",
    "    for s1num, state1 in enumerate(basis):\n",
    "        for s2num, state2 in enumerate(basis):\n",
    "            val = 1\n",
    "            qNums = [0 for _ in range(8)]\n",
    "            for num, name in enumerate(names):\n",
    "                if state2[name+\"_1\"] != state1[name+\"_1\"]:\n",
    "                    # matrix is diagonal.\n",
    "                    val = 0\n",
    "                qNums[num] = state1[name+\"_1\"]\n",
    "            for num, name in enumerate(names):\n",
    "                if state2[name+\"_2\"] != state1[name+\"_2\"]:\n",
    "                    # matrix is diagonal.\n",
    "                    val = 0\n",
    "                qNums[num+4] = state1[name+\"_2\"]\n",
    "            J1,mJ1,L1,S1,J2,mJ2,L2,S2 = qNums\n",
    "            # the matrix element is A/2 (L1 . S1 + L2 . S2), A=1\n",
    "            val *= 0.5*(J1*(J1+1)-L1*(L1+1)-S1*(S1+1)+ J2*(J2+1)-L2*(L2+1)-S2*(S2+1) )\n",
    "            op[s1num,s2num] = val            \n",
    "    return op"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "g = 0\n",
    "u = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "class multiplyableDictMulti(dict):\n",
    "    # This class exists so that I can take a basis ref and use it in np.kron()\n",
    "    # to programatically get the basis ref for multi-particle systems.\n",
    "    def __mul__(self, other):\n",
    "        #assert(type(other) == type(self))\n",
    "        newDict = multiplyableDictMulti()\n",
    "        for key, value in self.items():\n",
    "            keyCore = key\n",
    "            if len(keyCore) > 1 and keyCore[-2] == \"_\":\n",
    "                keyCore = keyCore[:-2]\n",
    "            for num in range(3):\n",
    "                if keyCore + \"_\" + str(num+1) not in newDict:\n",
    "                    newDict.update({keyCore+\"_\" + str(num+1): value})\n",
    "                    break\n",
    "        for key, value in other.items():\n",
    "            keyCore = key\n",
    "            if len(keyCore) > 1 and  keyCore[-2] == \"_\":\n",
    "                keyCore = keyCore[:-2]\n",
    "            for num in range(3):\n",
    "                if keyCore + \"_\" + str(num+1) not in newDict:\n",
    "                    newDict.update({keyCore+\"_\" + str(num+1): value})\n",
    "                    break\n",
    "        return newDict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "def BohrOppenheimerToAtomic( oalNums, spinNums, nuclearNums, sigma, \n",
    "                             lsBasis, \n",
    "                             basisChange=None, naturalKronBasis=None, finalBasis=None ):\n",
    "    \"\"\"\n",
    "    oalNums = (L, Lambda, la, lb)\n",
    "    L is the total molecular orbital angular momentum \\vec{L} = \\vec{l1}+\\vec{l2}\n",
    "    Lambda is the projection of L on the internuclear axis.\n",
    "    l1 is the orbital angular momentum of atom 1.\n",
    "    l2 is the orbital angular momentum of atom 2.\n",
    "    \n",
    "    spinNums = (S, Sigma, sa, sb)\n",
    "    S is the total molecular spin angular momentum \\vec{s} = \\vec{s1}+\\vec{s2}\n",
    "    Sigma is the projection of S on the internuclear axis.\n",
    "    s1 is the spin angular momentum of atom 1.\n",
    "    s2 is the spin angular momentum of atom 2.\n",
    "    \n",
    "    nuclearNums = (I, iota, ia, ib)\n",
    "    \n",
    "    sigma is the spatial symmetry of the electronic wavefunctions, \n",
    "        either 0 for g (\"gerude\" or symmetric wavefunctions) \n",
    "        or 1 for u (\"ungerude\" or antisymmetric wavefunctions)\n",
    "    \"\"\"\n",
    "    (L, Lambda, la, lb) = oalNums\n",
    "    (S, Sigma, sa, sb) = spinNums\n",
    "    (I, iota, ia, ib) = nuclearNums\n",
    "    state = 0\n",
    "    p = (-1)**(S+sigma)\n",
    "    indvCont = []\n",
    "    lsiBasisStates = []\n",
    "    otherBasisStates = []\n",
    "    for mla in np.arange(-la,la+1,1):\n",
    "        mlb = Lambda-mla\n",
    "        if abs(mlb) > lb:\n",
    "            continue\n",
    "        for msa in np.arange(-sa,sa+1,1):\n",
    "            msb = Sigma-msa\n",
    "            if abs(msb) > sb:\n",
    "                continue\n",
    "            for mia in np.arange(-ia, ia+1, 1):\n",
    "                mib = iota-mia\n",
    "                if abs(mib) > ib:\n",
    "                    continue\n",
    "                # CG notation is <j1,mj1,j2,mj2|j3,mj3>\n",
    "                oalCoef = float(CG(la,mla,lb,mlb,L,Lambda).doit())\n",
    "                spinCoef = float(CG(sa,msa,sb,msb,S,Sigma).doit())\n",
    "                nuclearCoef = float(CG(ia,mia,ib,mib,I,iota).doit())\n",
    "                aState1 = getColumnState(lsiBasis, {'L':la,'mL':mla,'S':sa,'mS':msa, 'I':ia,'mI':mia})\n",
    "                bState1 = getColumnState(lsiBasis, {'L':lb,'mL':mlb,'S':sb,'mS':msb, 'I':ib,'mI':mib})\n",
    "                aState2 = getColumnState(lsiBasis, {'L':lb,'mL':mlb,'S':sa,'mS':msa, 'I':ia,'mI':mia})\n",
    "                bState2 = getColumnState(lsiBasis, {'L':la,'mL':mla,'S':sb,'mS':msb, 'I':ib,'mI':mib})\n",
    "                if oalCoef != 0 and nuclearCoef != 0 and spinCoef != 0:\n",
    "                    lsiBasisStates.append([aState1, bState1, aState2, bState2])\n",
    "                if basisChange is not None:\n",
    "                    aState1 = basisChange@aState1\n",
    "                    bState1 = basisChange@bState1\n",
    "                    aState2 = basisChange@aState2\n",
    "                    bState2 = basisChange@bState2\n",
    "                newpart = nuclearCoef*oalCoef*spinCoef * (np.kron(aState1,bState1) + p * np.kron(aState2,bState2))\n",
    "                \n",
    "                state += newpart\n",
    "                if oalCoef != 0 and nuclearCoef != 0 and spinCoef != 0:\n",
    "                    indvCont.append(newpart)\n",
    "                    otherBasisStates.append([aState1, bState1, aState2, bState2])\n",
    "    if np.linalg.norm(state) == 0:\n",
    "        raise ValueError(\"State has zero norm!\")\n",
    "    state /= np.linalg.norm(state)\n",
    "    if finalBasis is not None:\n",
    "        state = convertToReducedBasis(state, finalBasis, naturalKronBasis)\n",
    "    return state, np.array(indvCont), np.array(lsiBasisStates), np.array(otherBasisStates)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "192\n"
     ]
    }
   ],
   "source": [
    "# plugging in zero nuclear spin effectively avoids i in all of these bases. \n",
    "lsiBasis, jiBasis, fBasis, lsiBasis3Atom, jiBasis3Atom, fBasis3Atom = createLargerBasisRefs3Atoms([0,1], [1/2], [0])\n",
    "lsBasisR, jBasisR = [], []\n",
    "for state in lsiBasis3Atom:\n",
    "    if (state['L_1'] == 0 and state['L_2'] == 0) or (state['L_1'] == 1 and state['L_2'] == 1):\n",
    "        continue\n",
    "    lsBasisR.append(state)\n",
    "for state in jiBasis3Atom:\n",
    "    if (state['L_1'] == 0 and state['L_2'] == 0) or (state['L_1'] == 1 and state['L_2'] == 1):\n",
    "        continue\n",
    "    jBasisR.append(state)\n",
    "fsOperator = fsOp3(jBasisR)\n",
    "J_to_LS_op = J_to_LS(lsBasisR,jBasisR)\n",
    "fsOp_LS = J_to_LS_op@fsOperator@J_to_LS_op.T\n",
    "print(len(lsBasisR))\n",
    "lsiToJiop = lsiToJi(lsiBasis,jiBasis)\n",
    "#print(lsiToJiop.shape)\n",
    "#fsLsi = lsiToJiop.T@fsOperator@lsiToJiop\n",
    "#boBasisDict_g, boBasisLatex_g = createBornOppenheimerBasisHFS([1],[0,1], [0], sigmavals=['g'])\n",
    "#boBasisDict_u, boBasisLatex_u = createBornOppenheimerBasisHFS([1],[0,1], [0], sigmavals=['u'])\n",
    "boBasisDict_full, boBasisLatex_full = createBornOppenheimerBasisHFS([1],[0,1], [0], sigmavals=['g', 'u'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "boBasis = boBasisDict_full"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "ename": "AssertionError",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAssertionError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-75-18b46097f919>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      6\u001b[0m                                                 \u001b[1;33m[\u001b[0m\u001b[0mst\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'S'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mst\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'Sigma'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m/\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m/\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      7\u001b[0m                                                 \u001b[1;33m[\u001b[0m\u001b[0mst\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'i'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mst\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'iota'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 8\u001b[1;33m                                                 sigmaV, lsiBasis, basisChange=lsiToJiop, naturalKronBasis=jiBasis2Atom, finalBasis=jBasisR)\n\u001b[0m\u001b[0;32m      9\u001b[0m     \u001b[0mboToAtomicMatrix\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mstate1\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mT\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     10\u001b[0m \u001b[0mboToAtomicMatrix\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mboToAtomicMatrix\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<ipython-input-72-80334573135d>\u001b[0m in \u001b[0;36mBohrOppenheimerToAtomic\u001b[1;34m(oalNums, spinNums, nuclearNums, sigma, lsBasis, basisChange, naturalKronBasis, finalBasis)\u001b[0m\n\u001b[0;32m     66\u001b[0m     \u001b[0mstate\u001b[0m \u001b[1;33m/=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlinalg\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mnorm\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mstate\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     67\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mfinalBasis\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 68\u001b[1;33m         \u001b[0mstate\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mconvertToReducedBasis\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mstate\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfinalBasis\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnaturalKronBasis\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     69\u001b[0m     \u001b[1;32mreturn\u001b[0m \u001b[0mstate\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mindvCont\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlsiBasisStates\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0motherBasisStates\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<ipython-input-47-2630e77de126>\u001b[0m in \u001b[0;36mconvertToReducedBasis\u001b[1;34m(state, finBasis, origBasis)\u001b[0m\n\u001b[0;32m      4\u001b[0m     \u001b[1;32mfor\u001b[0m \u001b[0mnum\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0morigState\u001b[0m \u001b[1;32min\u001b[0m \u001b[0menumerate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0morigBasis\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mstate\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mnum\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m!=\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 6\u001b[1;33m             \u001b[0mcomp\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mstate\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mnum\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mgetColumnState\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfinBasis\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0morigState\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      7\u001b[0m             \u001b[0mnewState\u001b[0m \u001b[1;33m+=\u001b[0m \u001b[0mcomp\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      8\u001b[0m     \u001b[1;32mreturn\u001b[0m \u001b[0mnewState\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<ipython-input-48-a2685795d154>\u001b[0m in \u001b[0;36mgetColumnState\u001b[1;34m(basis, quantumNums)\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mgetColumnState\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mbasis\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mquantumNums\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m     \u001b[1;32massert\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mbasis\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m==\u001b[0m\u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mquantumNums\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      3\u001b[0m     \u001b[0mcolState\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0m_\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mbasis\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m     \u001b[1;32mfor\u001b[0m \u001b[0mnum\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mstate\u001b[0m \u001b[1;32min\u001b[0m \u001b[0menumerate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mbasis\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m         \u001b[0mmatch\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;32mTrue\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mAssertionError\u001b[0m: "
     ]
    }
   ],
   "source": [
    "boToAtomicMatrix = []\n",
    "for st in boBasis: \n",
    "    sigmaV = g if st['sigma']=='g' else u\n",
    "    phase = (-1)**(sigmaV+st['S'])\n",
    "    state1, _,_,_ = BohrOppenheimerToAtomic( [st['L'],st['Lambda'],st['L'],0],\n",
    "                                                [st['S'],st['Sigma'],1/2,1/2],\n",
    "                                                [st['i'],st['iota'],0,0],\n",
    "                                                sigmaV, lsiBasis, basisChange=lsiToJiop, naturalKronBasis=jiBasis2Atom, finalBasis=jBasisR)\n",
    "    boToAtomicMatrix.append(state1.T[0])\n",
    "boToAtomicMatrix = np.array(boToAtomicMatrix)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "A_gs = (mc.Rb87_Ground_ToF2-mc.Rb87_Ground_ToF1)/2\n",
    "A_12 = (mc.Rb87_5P12_ToF2-mc.Rb87_5P12_ToF1)/2\n",
    "A_32 = (mc.Rb87_5P32_ToF3-mc.Rb87_5P32_ToF0)/6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "lifetime = (mc.Rb87_D1_Lifetime+mc.Rb87_D2_Lifetime)/2\n",
    "transFreq = 2*np.pi*(mc.Rb87_D2LineFrequency+mc.Rb87_D1LineFrequency)/2\n",
    "DeltaVal = mc.h*(mc.Rb87_D2LineFrequency-mc.Rb87_D1LineFrequency)# / mc.h\n",
    "C_3_val = mc.Rb87_C3\n",
    "print(DeltaVal, C_3_val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(getColumnState(jBasisR, jBasisR[2]))\n",
    "print(jBasisR[-2])\n",
    "print(lsBasisR[-2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def HC(matrix):\n",
    "    return matrix.conj().T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "toAtomic = boToAtomicMatrix@HC(J_to_LS_op)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Rvals = np.linspace( 0.5*20*mc.a0, 5*20*mc.a0, 5000 )\n",
    "data = []\n",
    "rotMatrix = fullRotation(1)\n",
    "for rnum, rv in enumerate(Rvals):\n",
    "    misc.reportProgress(rnum, len(Rvals))\n",
    "    #t1 = J_to_LS_op@boToAtomicMatrix.T@createBOMatrix2(C_3_val, rv, *boBasis).astype(float)@boToAtomicMatrix@J_to_LS_op.T\n",
    "    t1 = HC(toAtomic)@createBOMatrix2(C_3_val, rv, *boBasis).astype(float)@toAtomic\n",
    "    t2 = fsOp_LS * 2 * DeltaVal / 3\n",
    "    rmatrix = t1 + t2\n",
    "    rotatedH = HC(rotMatrix)@rmatrix@rotMatrix\n",
    "    eigVals = np.linalg.eigvalsh(rotatedH)\n",
    "    data.append(eigVals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "colors, _ = misc.getColors(len(misc.transpose(data))+1)\n",
    "linestyles = ['-',':','--']\n",
    "for datanum, (mdata, color) in enumerate(zip(misc.transpose(data), colors)):\n",
    "    ax.plot(Rvals*1e9, np.array(mdata) * 1e-9 / mc.h, linewidth=1, label=datanum, color='#0000AA', linestyle='-')\n",
    "ax.legend(ncol=5)\n",
    "ax.set_xlim(1,5)\n",
    "ax.set_ylim(-20000,15000)\n",
    "ax.grid()\n",
    "ax.set_title('Result in LSI Basis');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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