{
 "cells": [

{
   "cell_type": "markdown",
   "id": "5fc18d8f",
   "metadata": {},
   "source": [
    "# <font  color = \"#0093AF\">DIPSHIFT</font>"
   ]
},
{
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a href=\"https://githubtocolab.com/alsinmr/SLEEPY_tutorial/blob/main/ColabNotebooks/Chapter3/Ch3_DIPSHIFT.ipynb\" target=\"_blank\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\"></a>"
     
            ]
},
{
   "cell_type": "markdown",
   "id": "c35e7d08",
   "metadata": {},
   "source": [
    "DIPSHIFT$^1$ (DIPpolar-coupling chemical-SHIFT correlation) is a method for measuring dipolar couplings under magic-angle spinning conditions. The DIPSHIFT experiment lasts two rotor periods. In the first rotor period, homonuclear decoupling is applied for part of the rotor period, and heteronuclear decoupling is applied in the remaining part. The fraction of heteronuclear/homonuclear decoupling is varied over multiple timesteps. With homonuclear decoupling, heteronuclear dipolar couplings are active and lead to modulation of transverse magnetization (in the example here, on the $^{13}$C spin). The second rotor period follows a $\\pi$-pulse and is used for refocusing the dephasing on the transverse magnetization due to chemical shift or CSA.\n",
    "\n",
    "DIPSHIFT is a nice example for SLEEPY, because we can see how one-bond dipole couplings are averaged by dynamics and furthermore investigate the timescale dependence of that averaging, where sufficiently slow motions will not average the coupling, and intermediate timescale motion will broaden and damp the DIPSHIFT curve. Furthermore, DIPSHIFT requires two different decoupling sequences: usually frequency-switched Lee-Goldburg decoupling (flsg)$^2$ is applied for homonuclear decoupling, and we apply continuous-wave (cw) irradiation for heteronuclear decoupling (SPINAL may also be tested by setting the flag `SPINAL=True` below$^3$). Therefore, in this example, we can see how one may input a decoupling sequence into SLEEPY and how SLEEPY handles stepping through the sequence.\n",
    "\n",
    "[1] M.G. Munowitz, R.G. Griffin, G. Bodenhausen, T.H. Huang. [*J. Am. Chem. Soc.*](https://doi.org/10.1021/ja00400a007), **1981**, 103, 2529-2533.\n",
    "\n",
    "[2] A. Bielecki, A.C. Kolbert, M.H. Levitt. [*Chem. Phys. Lett.*](https://doi.org/10.1016/0009-2614(89)87166-0), **1989**, 155, 341-346.\n",
    "\n",
    "[3] B.M. Fung, A.K. Khitrin, K. Ermolaev. [*J. Magn. Reson.*](https://doi.org/10.1006/jmre.1999.1896), **2000**, 142, 97-101."
   ]
},
{
   "cell_type": "markdown",
   "id": "d4f8d0b8",
   "metadata": {},
   "source": [
    "## Setup"
   ]
}
,
    {
     "cell_type": "code",
     "execution_count": 0,
     "metadata": {"tags": [
        "remove-cell"
    ]},
     "outputs": [],
     "source": [
      "# SETUP SLEEPY\n",
      "import sys\n",
      "if 'google.colab' in sys.modules:\n",
      "  !pip install sleepy-nmr"
     ]
    },
{
   "cell_type": "code",
   "execution_count": 2,
   "id": "c6356b3a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import SLEEPY as sl\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from time import time"
   ]
},
{
   "cell_type": "markdown",
   "id": "9dea7b5d",
   "metadata": {},
   "source": [
    "## Parameter setup"
   ]
},
{
   "cell_type": "code",
   "execution_count": 3,
   "id": "006c8920",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "S = -0.325\n"
     ]
    }
   ],
   "source": [
    "vr=3000    #MAS frequency\n",
    "v1=65000  #1H Decoupling field strength (Homonuclear)\n",
    "v1het=90000\n",
    "N=17       #Number of time points in rotor period\n",
    "\n",
    "phi=70*np.pi/180  #Opening angle of hopping (~tetrahedral)\n",
    "S=-1/2+3/2*np.cos(phi)**2\n",
    "print(f'S = {S:.3f}')"
   ]
},
{
   "cell_type": "code",
   "execution_count": 4,
   "id": "46fb4c2d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "delta(H-C)*S : -15.14 / kHz\n"
     ]
    }
   ],
   "source": [
    "# Some calculated parameters\n",
    "magic=np.arccos(np.sqrt(1/3)) # Magic angle (for fslg)\n",
    "\n",
    "tetra=magic*2 #Tetrahedral angle\n",
    "distCC=.109  #nm\n",
    "dHC=sl.Tools.dipole_coupling(distCC,'1H','13C')\n",
    "print(f'delta(H-C)*S : {dHC*S/1e3:.2f} / kHz')  \n",
    "#This is the anisotropy, whereas one often reports half this value"
   ]
},
{
   "cell_type": "markdown",
   "id": "febe028a",
   "metadata": {},
   "source": [
    "## Build the system"
   ]
},
{
   "cell_type": "code",
   "execution_count": 5,
   "id": "29ac96b1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set up experimental system, create Liouvillian\n",
    "ex0=sl.ExpSys(600,Nucs=['13C','1H'],vr=vr,pwdavg=sl.PowderAvg(q=2),n_gamma=30)\n",
    "ex0.set_inter('dipole',delta=dHC,i0=0,i1=1)\n",
    "ex0.set_inter('CSA',delta=20,i=0,euler=[0,tetra,-np.pi/3])\n",
    "ex0.set_inter('CSA',delta=4,i=1)\n",
    "\n",
    "# This builds a 3-site symmetric exchange, with opening angle phi\n",
    "L=sl.Tools.Setup3siteSym(ex0,tc=1e-9,phi=phi)"
   ]
},
{
   "cell_type": "markdown",
   "id": "b9dffc52",
   "metadata": {},
   "source": [
    "## Decoupling"
   ]
},
{
   "cell_type": "markdown",
   "id": "8fb8a091",
   "metadata": {},
   "source": [
    "Decoupling is input just like any other sequence. Note that one may input the decoupling on one channel and pulses on another channel. The decoupling and pulses do not need to be synchronized (SLEEPY will generate a single time-axis for switching on all channels). \n",
    "\n",
    "If a sequence is used to generate a propagator that has a length shorter than the sequence itself, then the next propagator generated by the sequence will start where the previous propagator stopped. When the end of the sequence is reached, it will be repeated."
   ]
},
{
   "cell_type": "code",
   "execution_count": 6,
   "id": "3fb2c4ff",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Build decoupling sequences\n",
    "voff=v1/np.tan(magic) #fslg offset\n",
    "veff=v1/np.sin(magic) #fslg effective field\n",
    "tau=1/veff   #fslg pulse length\n",
    "\n",
    "# FSLG decoupling\n",
    "fslg=L.Sequence()\n",
    "fslg.add_channel('1H',t=[0,tau,2*tau],v1=v1,phase=[0,np.pi],voff=[voff,-voff])\n",
    "\n",
    "# Heteronuclear decoupling (cw or SPINAL)\n",
    "SPINAL=False\n",
    "if SPINAL:\n",
    "    v1het=165/360*64*vr #Rotor synchronize SPINAL\n",
    "    dt=1/v1het*165/360 #165 degree pulse\n",
    "    #Spinal (phase angles)\n",
    "    Q=[10,-10,15,-15,20,-20,15,-15]\n",
    "    Qb=[-10,10,-15,15,-20,20,-15,15]\n",
    "    phase=np.concatenate((Q,Qb,Qb,Q,Qb,Q,Q,Qb))*np.pi/180\n",
    "    \n",
    "    # SPINAL time axis (length of phase+1)\n",
    "    t=dt*np.arange(len(phase)+1)\n",
    "    \n",
    "    dec=L.Sequence()\n",
    "    dec.add_channel('1H',t=t,v1=v1het,phase=phase)\n",
    "else:\n",
    "    dec=L.Sequence().add_channel('1H',v1=v1het)  #Uncomment to use cw coupling"
   ]
},
{
   "cell_type": "markdown",
   "id": "499b1a6e",
   "metadata": {},
   "source": [
    "When we use `rho.DetProp(...)` with a sequence, `rho` will automatically try to determine how the calculation may be reduced. On the other hand, if we generate propagators outside of `rho.DetProp`, we do not automatically know how the calculation could be reduced without using `rho`. However, rho has functionality to set up a reduced calculation via the `rho.ReducedSetup(...)` function. We may input sequences and propagators into this function to reduce their basis. Note that we need to input ALL sequences and propagators that will be used in the simulation; otherwise, we may leave out states that are required for the calculations (if we later introduce sequences/propagators not included in this setup, SLEEPY will produce an error). "
   ]
},
{
   "cell_type": "code",
   "execution_count": 7,
   "id": "4bb3ea53",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "State-space reduction: 48->24\n"
     ]
    }
   ],
   "source": [
    "# Setup Reduced-matrix processing\n",
    "rho=sl.Rho('13Cx','13Cx')\n",
    "Upi=L.Udelta('13C',np.pi)\n",
    "rho,dec,fslg,Upi,Ueye=rho.ReducedSetup(dec,fslg,Upi,L.Ueye())"
   ]
},
{
   "cell_type": "markdown",
   "id": "57cff324",
   "metadata": {},
   "source": [
    "Plot the sequences"
   ]
},
{
   "cell_type": "code",
   "execution_count": 8,
   "id": "9804f892",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Fi0gcEuVaJSnTRCSpggPOzJ4Ajgc+Alblb1PKU1Z6tm7dCkDPnj0DVyIiWdMRc02ZJiJJFfO/22uA1fnrX3YYv/71r4H2r4P56KOP8tRTT3HjjTey336VPve1iATS4XJNmSYiSRWcCO7+XEcKyCajR49m9OjcnuUFCxYwZMgQBg8ezIwZM/aYb8mSJYwcOZKlS5eGKFNEAuiIuaZME5Gkov/vYP/+/enfvz+NjY1ceeWVPProo6xatYp77rmHVatW7Z6vS5cu1NbWMnTo0IDVioi0TZkmIkll9qDmtGzZkjt14B/+8AcGDx68+wSpkydPpq6ujhNPPBGA739/79N8iYhkjzJNRJKKfvD3yCOPANCjRw/69++/e3pVVRXLli0LVZaISEmUaSKSVPSDvy996UsAPP300/s8lz+nl4hIh6FME5Gkoh/8HXPMMUDuf8Xr16/fPX3Dhg3069cvVFkiIiVRpolIUtF/4WPz5s1s3ryZkSNHsnbtWl599VV27tzJ3LlzGTduXOjyRKQDM7P+Zvakma02s9+b2Tfz0480s4Vmtjb/84i01qlME5Gkoh/8LViwgAULFrD//vszc+ZMxowZw9ChQ5k0aRLDhg0LXZ6IdGwfA3/j7kOB04ArzexEYDqwyN2PBxblH6dCmSYiSZm7h66haDU1NV5fX1/QvJs3bwbg6KOPLmdJIhKQmS1395oM1FEHzMzfznL3TWbWF1js7kPaem2huaZME+kcyplr0R/zp4AUkUows4HAycAyoI+7bwLIDwB7p7UeZZqIJBX9bt+NGzeycePG0GWISMTMrAdwH/Atd3+/iNdNM7N6M6t/6623CnqNMk1Ekop+8Ldw4UIWLlwYugwRiZSZdSU38Kt19/vzk9/M7+4l/3NLS69191nuXuPuNb169Spofco0EUkq+t2+5513XugSRCRSljux3i+B1e7+T82eehC4FJiR/1mX1jqVaSKSVPSDv969UzvURkRkb58Hvga8ZGYr8tO+Q27QN8/MLgNeByamtUJlmogkFf3gr+kkqM0vgyQikgZ3fwpo7bIao8uxTmWaiCQV/TF/ixYtYtGiRaHLEBFJhTJNRJKK/pO/Cy64IHQJIiKpUaaJSFIVG/yZWX/gTuBo4BNglrvfbGZHAvcCA4EGYJK7b0trvT179kxrUSIiwSnTRCSpSu72rfhlkAAaGhpoaGhIc5EiIsEo00QkqYoN/tx9k7s/l7+/HVgNHAOMB+bkZ5sDXJjmehcvXszixYvTXKSISDDKNBFJKsgxf6VcBsnMpgHTAAYMGFDwusaPH5+0XBGRzFCmiUhSFR/87X0ZpNw5Utvn7rOAWZC7AHqh6zviiCNKKVNEJJOUaSKSVEVP9ZLkMkilWrduHevWrUtzkSIiwSjTRCSpSn7bt+KXQQJYsmQJAIMGDUpzsSIiQSjTRCSpSu72rfhlkAC+8pWvpLk4EZGglGkiklTFBn8hLoMEcNhhh5Vr0SIiFadME5Gkor+82yuvvMIrr7wSugwRkVQo00QkqegHf0899RRPPfUUCxYsYMiQIQwePJgZM2a0OO+UKVOYP3/+PtPPOuss6uvrdz9uaGhg+PDhZatZRKQ1yjQRSSr6a/tOmDCBxsZGRowYwcKFC6mqqmLkyJGMGzeOE088MXR5IiJFUaaJSFLRf/LXo0cPVq1axeDBgxk0aBAHHHAAkydPpq6u7S8Vf/e732XKlCl88sknbc53+eWXU11dTXV1Nb169eKGG25Is3wRkT0o00Qkqeg/+VuzZg3PPPMM/fv33z2tqqqKZcuWtfqaa6+9lvfee4877riDppNQX3LJJXTv3h2AnTt3st9+uXHz7bffDsBrr73GmDFjmDJlSpl+ExERZZqIJBf9J39Lly7l5Zdf3md6a1cWufHGG3n33Xf5+c9/vsc8tbW1rFixghUrVvDII4/s8ZqPPvqIiRMnMnPmTI499th0fwERkWaUaSKSVPSDv0mTJjFhwgTWr1+/e9qGDRvo169fi/OPHDmS5cuX88477xS8jiuuuIKLLrqIs88+O3G9IiJtUaaJSFLRD/4OOuggvvCFL7B27VpeffVVdu7cydy5cxk3blyL848dO5bp06dz/vnns3379naXf+utt7J9+3amT5+edukiIvtQpolIUtEf87d69WoAZs6cyZgxY2hsbGTq1KkMGzas1ddMnDiR7du3M27cuH12h+ztpptuomvXrlRXVwO5/zFfccUVqdUvItKcMk1EkjJ3D11D0Wpqarz5OaraMnv2bAAdtCwSMTNb7u41oetIotBcU6aJdA7lzLXoP/mbPHly6BJERFKjTBORpKIf/HXr1i10CSIiqVGmiUhS0X/hY+XKlaxcuTJ0GSIiqVCmiUhS0X/y13QMja5bKSIxUKaJSFLRD/4uueSS0CWIiKRGmSYiSUU/+OvatWvoEkREUqNME5Gkoj/m78UXX+TFF18MXYaISCqUaSKSVPSf/D333HMAnHTSSYErERFJTpkmIklFP/j72te+FroEEZHUKNNEJKlM7PY1s7FmtsbMXjGzVC8o2aVLF7p06ZLmIkVE2lWuXFOmiUhSwQd/ZtYFuBU4FzgRuNjMTkxr+StWrGDFihVpLU5EpF3lzDVlmogklYXdvp8FXnH3dQBmNhcYD6xKY+Hz7riDDz78kGfqHkxjcSJSAX88+I/4xW9/G7qMJMqWa8o0kY4pS7mWhcHfMcD6Zo83AKfuPZOZTQOm5R9+YGZrilhHT2BryRWmK0u1gOppS5ZqgU5Uz7Itb3K7WTEvGVKOOhIod65l7W+hWB25ftUeTkeuv+eyLW9uLTLXji1XMVkY/LW0JXyfCe6zgFklrcCs3t1rSnlt2rJUC6ietmSpFlA9bTGz+tA17KWsuZalbV+Kjly/ag+nI9eftdqDH/NH7n/E/Zs9rgLeCFSLiEgalGsikllZGPw9CxxvZseZ2QHAZEAHs4hIR6ZcE5HMCr7b190/NrOrgH8HugC/cvffp7yaknYXl0mWagHV05Ys1QKqpy1ZqqUSuZap37cEHbl+1R5OR64/U7Wb+z6HoYiIiIhIpLKw21dEREREKkSDPxEREZFOJOrBXzkvG1dEDQ1m9pKZrWg6HYWZHWlmC81sbf7nEWVc/6/MbIuZrWw2rdX1m9m389trjZmNqUAt/2BmG/PbZ4WZnVehWvqb2ZNmttrMfm9m38xPD7VtWqsn1PbpZmbPmNkL+XpuyE+v+PZpo5Yg2ya0LORaqVrKwywrNj+zpNi8zZJS8jkrSsnyINw9yhu5g6z/AAwCDgBeAE4MUEcD0HOvaT8EpufvTwd+UMb1jwJGACvbWz+5y1C9ABwIHJfffl3KXMs/ANe0MG+5a+kLjMjfPwR4Ob/OUNumtXpCbR8DeuTvdwWWAaeF2D5t1BJk24S8ZSXXEtS/Tx5m+VZMfmbtVkzeZu1WbD5n6VZsloe6xfzJ3+7LK7n7TqDp8kpZMB6Yk78/B7iwXCty9yXAOwWufzww193/291fBV4htx3LWUtryl3LJnd/Ln9/O7Ca3FUZQm2b1uppTbnrcXf/IP+wa/7mBNg+bdTSmrJum8CynGvRKTI/M6XIvM2UEvI5M0rI8iBiHvy1dHmlEA1w4DEzW265SzkB9HH3TZD7QwF6V7im1tYfaptdZWYv5ndTNH2MX7FazGwgcDK5T5SCb5u96oFA28fMupjZCmALsNDdg22fVmqBwH87AXT0362lPOxoQud3Ui29ZzKrwHzOpAKzPIiYB38FXV6pAj7v7iOAc4ErzWxUgBoKFWKb/Qz4I6Aa2AT8v0rWYmY9gPuAb7n7+23NGqieYNvH3RvdvZrc1Sk+a2bD25i9rPW0UkvQv51AOvrv1pHyMEatvWcyqYh8zpwisjyImAd/mbi8kru/kf+5BXiA3G6bN82sL0D+55YKl9Xa+iu+zdz9zfw/7J8Av+DT3XNlr8XMupJ7c9a6+/35ycG2TUv1hNw+Tdz9XWAxMJbAfzvNa8nCtgmgQ/9ureRhRxM6v0vWxnsmc4rM50wpMsuDiHnwF/zySmZ2sJkd0nQfOAdYma/j0vxslwJ1layrjfU/CEw2swPN7DjgeOCZchbS9EbO+wq57VP2WszMgF8Cq939n5o9FWTbtFZPwO3Ty8wOz9/vDpwN/CcBtk9rtYTaNoEFz7VStZGHHU3o/C5ZG++ZTCkhnzOjhCwPI/Q3Tsp5A84j902bPwDXB1j/IHLfxnsB+H1TDcBRwCJgbf7nkWWs4R5yHzHvIvepwWVtrR+4Pr+91gDnVqCWu4CXgBfJvbH7VqiWM8jtLnsRWJG/nRdw27RWT6jtcxLwfH69K4G/b+9vt1z1tFFLkG0T+hY61xLU3WIeZvlWbH5m6VZs3mbpVko+Z+VWSpaHuOnybiIiIiKdSMy7fUVERERkLxr8iYiIiHQiGvyJiIiIdCIa/ImIiIh0Ihr8iYiIiHQiGvyJiIiIdCIa/ImIiIh0Ihr8iYiIiHQiGvyJiIiIdCIa/ImIiIh0Ihr8iYiIiHQi+4cuoBQ9e/b0gQMHhi5DRDJi+fLlW929V+g6klCuiUhz5cy1Djn4GzhwIPX19QXN+5vf/AaAM888s5wliUhAZvZa6BqSKjTXlGnxUm/jVUpvy5lrHXLwV4y33347dAkiIqlRpsVLvY1X1npr7h66hqLV1NR4oZ/8iUj8zGy5u9eEriMJ5ZqINFfOXNMXPkREREQ6kegHf08++SRPPvlk6DJERFKhTIuXehuvrPU2+mP+3n///dAliIikRpkWL/U2XlnrrY75E5EOT8f8iUhsdMyfiIiIiKQi+sHf448/zuOPPx66DBGRVCjT4qXexitrvY3+mL8PP/wwdAkiIqlRpsVLvY1X1nqrY/5EpMPTMX8iEpty5lr0n/xt/j//h/9e/Z/87dKneWLDBo7q1o3HvjwOgL95+reMPqaK8449dvf8J869h1WTLw5VrogABw49gaO/853QZWRSU6YByjWRDiRLuRb9MX9LGxt59qijmDDoj5jzxdGhyxERSaQp0wDlWmSePeqo3b2VuDx71FEsbWwMXcZu0X/yd8CIEQCc/5Mf09DQQNcLLuDYu+4EoMeUKfS64AKOnTBh9/z2wP27nxcRyZqmTDv2/PM5FpRrEVn58MNArrcSl6beZkX0g7/z23kT/e3f/i3f//73K1SNiEgy7WUaKNc6qkJ6Kx1T1nob/eCvPT/60Y+Y0Ox/yD169AhYjYhIcso1EWlL9Mf8LViwgAULFoQuQ0QkFcq0eKm38cpab6Mf/ImIiIjIp6Lf7Tt27FgALr74YhYvXszWrVupqqrihhtuCFyZiMTAzA4HbgeGAw5MBdYA9wIDgQZgkrtvS2N9TZkGyrXYNO+txCVrvdVJnkWkwwt5kmczmwP8h7vfbmYHAAcB3wHecfcZZjYdOMLdr2trOco1EWmunLkW/W7fhx9+mIcz9hVrEYmDmR0KjAJ+CeDuO939XWA8MCc/2xzgwrTWqUyLl3obr6z1NvrBX9euXenatWvoMkQkToOAt4A7zOx5M7vdzA4G+rj7JoD8z94tvdjMpplZvZnVv/XWWwWtUJkWL/U2XlnrbUV3+5rZXwOXkzsu5iXg6+R2kRR1bIx2j4hIc6F2+5pZDfA74PPuvszMbgbeB65298ObzbfN3Y9oa1nKNRFpLordvmZ2DPA/gRp3Hw50ASYD04FF7n48sCj/WESkI9gAbHD3ZfnH84ERwJtm1hcg/3NLoPpERPZR6d2++wPdzWx/cp/4vUEZj40BeOihh3jooYfSXKSICADuvhlYb2ZD8pNGA6uAB4FL89MuBerSWqcyLV7qbbyy1tuKnerF3Tea2U3A68CHwGPu/piZ7XFsjJm1emwMMA1gwIABBa+3e/fuiWsXEWnD1UBt/pu+68gdzrIfMM/MLiOXeRPTWpkyLV7qbbyy1tuKHfNnZkcA9wF/DrwL/Cu5XSQzdWyMiCQR8lQvaVGuiUhzURzzB5wNvOrub7n7LuB+4HPo2BgRERGRiqnk4O914DQzO8jMjNyxMasp47ExAHV1ddTVpbpIEZFglGnxUm/jlbXeVvKYv2VmNh94DvgYeB6YBfSgTMfGABx66KFpLk5EJChlWrzU23hlrbe6vJuIdHg65k9EYhPLMX8iIiIiElj0g7/777+f+++/P3QZIiKpUKbFS72NV9Z6W7Fj/kI56qijQpcgIpIaZVq81Nt4Za230Q/+zjzzzNAliIikRpkWL/U2XlnrbfS7fUVERETkU9EP/ubPn8/8+fNDlyEikgplWrzU23hlrbfR7/Y9+uijQ5cgIpIaZVq81Nt4Za230Q/+zjjjjNAliIikRpkWL/U2XlnrbfS7fUVERETkU9EP/ubNm8e8efNClyEikgplWrzU23hlrbfR7/atqqoKXYKISGqUafFSb+OVtd5GP/j73Oc+F7oEEZHUKNPipd7GK2u9jX63r4iIiIh8KvrB3z333MM999wTugwRkVQo0+Kl3sYra72NfrfvcccdF7oEEZHUKNPipd7GK2u9jX7wd9ppp4UuQUQkNcq0eKm38cpab6Pf7SsiIiIin4p+8FdbW0ttbW3oMkREUqFMi5d6G6+s9Tb63b6f+cxnQpcgIpIaZVq81Nt4Za23FR38mdnhwO3AcMCBqcAa4F5gINAATHL3bWmtc+TIkWktSkQkOGVavNTbeGWttwXv9jWzRWZ23l7TZhW5vpuBBe5+AvAnwGpgOrDI3Y8HFuUfi4iUXUq5JiLSoRRzzN9xwHVm9r1m02oKfbGZHQqMAn4J4O473f1dYDwwJz/bHODCImpq15133smdd96Z5iJFJB6Jci0EZVq81Nt4Za23xez2fRcYDfzUzB4CvlrkugYBbwF3mNmfAMuBbwJ93H0TgLtvMrPeLb3YzKYB0wAGDBhQ8EqHDRtWZJki0om8S7JcqzhlWrzU23hlrbfFDP7M3T8GvmFmU4CngCOKXNcI4Gp3X2ZmN1PELl53nwXMAqipqfFCX3fKKacUUaKIdDJJc63ilGnxUm/jlbXeFrPb97amO+4+G7gUeKyI128ANrj7svzj+eQGg2+aWV+A/M8tRSxTRCSJpLkmItLhtPvJn5ndQu6buZjZT/d6+oNCV+Tum81svZkNcfc15Ha1rMrfLgVm5H/WFbrMQsyePRuAKVOmpLlYEenA0sq1EJRp8VJv45W13hay27e+2f0bgO+1NmMBrgZqzewAYB3wdXKfPs4zs8uA14GJCZa/j+rq6jQXJyJxSC3XzKxLfnkb3f0CMzuSMp6+SpkWL/U2XlnrrbkXfPgcZva8u59cxnoKUlNT4/X19e3PKCKdgpktd/eSvqWbNNfM7H+R+4bwofnB3w+Bd9x9hplNB45w9+vaW45yTUSaS5Jr7Sn28m6FjxQzorGxkcbGxtBliEh2lZxrZlYFnE/u5PVNynr6KmVavNTbeGWtt9Ff2/euu+7irrvuCl2GiMTpJ8C1wCfNpu1x+iqgxdNXQe4UVmZWb2b1b731VkErVKbFS72NV9Z6W8gXPraT+5+xAd3N7P2mpwB390PLWF9iI0aMCF2CiGRMGrlmZhcAW9x9uZmdVUodpZzCSpkWL/U2XlnrbbuDP3c/pBKFlMtJJ50UugQRyZiUcu3zwLj85eG6AYea2d3kT1+VP2l96qevUqbFS72NV9Z6W8y1ffc5Q6GZfTndctK3a9cudu3aFboMEcmgJLnm7t929yp3HwhMBp5w968CD5I7bRWU4fRVyrR4qbfxylpviznm7xdm9sdND8zsYuDv0i8pXbW1tdTW1oYuQ0SyqRy5NgP4kpmtBb6Uf5waZVq81Nt4Za23xVzebQIw38wuAc4A/hI4pyxVpaimJtPXaBeRsFLJNXdfDCzO33+b3Ensy0KZFi/1Nl5Z623Bgz93X2dmk4F/A9YD57j7h+UqLC3Dhw8PXYKIZFRHzDVlWrzU23hlrbeFfNv3JfY8D9aRQBdgmZnh7tk6inEvH330EQDdunULXImIZEVHzjVlWrzU23hlrbeFfPJ3QdmrKKO5c+cC2bmenohkQofNNWVavNTbeGWtt4Wc6uW1ShRSLqeeemroEkQkYzpyrinT4qXexitrvS3mCx8d0tChQ0OXICKSGmVavNTbeGWtt9Ff3m3Hjh3s2LEjdBkiIqlQpsVLvY1X1nrb7uDPzE43M6tEMeUwb9485s2bF7oMEcmQjpxryrR4qbfxylpvC9nteylwq5m9DCwAFrj75vKWlZ7TTz89dAkikj0dNteUafFSb+OVtd4W8oWPKwDM7ATgXGC2mR0GPEkuNH/r7o1lrTKBIUOGhC5BRDKmI+eaMi1e6m28stbbgo/5c/f/dPcfu/tY4IvAU8BEYFm5ikvDBx98wAcffBC6DBHJoI6Ya8q0eKm38cpab0v6tm/+DPiP5G+ZNn/+fCA759YRkWzqKLmmTIuXehuvrPU2+lO9nHHGGaFLEBFJjTItXuptvLLW24oO/sysC1APbHT3C8zsSOBeYCDQAExy921prnPw4MFpLk5EJChlWrzU23hlrbeVPs/fN4HVzR5PBxa5+/HAovzjVL333nu89957aS9WRCQIZVq81Nt4Za23iQd/ZnZdgfNVAecDtzebPB6Yk78/B7gwaT17e+CBB3jggQfSXqyIRKzQXAtBmRYv9TZeWett0bt9zaz5WQoNqAZ+UMBLfwJcCxzSbFofd98E4O6bzKx3G+udBkwDGDBgQMH1jho1quB5RaRzSpBrFadMi5d6G6+s9baUY/7ed/fLmx6Y2c/ae4GZXQBscfflZnZWCevE3WcBswBqamq80NcNGjSolNWJSOdSdK6FokyLl3obr6z1tuDdvmb2tJl9Efj+Xk9dX8DLPw+MM7MGYC7wRTO7G3jTzPrml98X2FJoPYXatm0b27al+h0SEYlEwlwLQpkWL/U2XlnrbTHH/E0DrgR+aWa7r1Pi7u+090J3/7a7V7n7QGAy8IS7fxV4kNxllsj/rCuinoLU1dVRV5f6YkUkDiXnWijKtHipt/HKWm8L3u3r7iuBPzOzEcD/zl8T/e/cfUWC9c8A5pnZZcDr5M6sn6qzzjor7UWKSCTKlGtlpUyLl3obr6z1tpRj/l4BbgS+Tu6cfUUtw90XA4vz998GRpdQQ8EGDhxYzsWLSBwS5VolKdPipd7GK2u9LeaYvyfMbD2wHPgOsA2YUqa6UrN161a2bt3a7nyPPvoo119/PZ988kkFqhKRLOiIuaZMi1ehvS2F/h7Cytr7tphj/q4BPuPux7v7+PxxfHeXq7C0/PrXv+bXv/41AAsWLGDIkCEMHjyYGTNm7DHfkiVLGDlyJEuXLg1RpoiE0eFyTZkWr+a9nTp1Kr1792b48OF7zPPjH/+YYcOGMXz4cC6++GI++ugjoO2/BdDfQ2hZe98WPPhz9+fyFz7vUEaPHs3o0aNpbGzkyiuv5NFHH2XVqlXcc889rFq1avd8Xbp0oba2lqFDhwasVkQqqSPmmjItXk29BZgyZQoLFizY4/mNGzfy05/+lPr6elauXEljYyNz585t928B9PcQWtbet5k9riUt/fv3B2Dp0qUMHjx497l2Jk+eTF1dHSeeeCIA3//+3md6EBHJHmVavJp6C7mTAjc0NOwzz8cff8yHH35I165d2bFjB/369eOZZ55p828B9PcQWtbet5W+tm/FbdmyhS1btrBx48Y93lhVVVVs3LgxYGUiIsVTpsWrqbetOeaYY7jmmmsYMGAAffv25bDDDuOcc87R30IHkLX3bfSf/D3yyCMAHHzwwfs8lz+tg4hIh6FMi1dTb6dMmdLi89u2baOuro5XX32Vww8/nIkTJ3L33Xdz4IEH7jOv/hayJWvv2+gHf1/60pcAeP3111m/fv3u6Rs2bKBfv36hyhIRKYkyLV5NvW3N448/znHHHUevXr0AuOiii3j66af52te+pr+FjMva+zb6wd8xxxwDQJ8+fVi7di2vvvoqxxxzDHPnzuVf/uVfAlcnIlIcZVq8mnrbmgEDBvC73/2OHTt20L17dxYtWkRNTQ0jR47U30LGZe19G/3gb/PmzQAcffTRzJw5kzFjxtDY2MjUqVMZNmxY4OpEpCMzs/7AncDRwCfALHe/2cyOBO4FBgINwCR3T+XCnsq0eDXv7cUXX8zixYvZunUrVVVV3HDDDVx22WVMmDCBESNGsP/++3PyySczbdo09t9/f/0tZFzW3rfm7hVfaVI1NTVeX19f0LyzZ88GWj+GQkQ6PjNb7u41AdbbF+jr7s+Z2SHkThZ9IbkTRb/j7jPMbDpwhLtf19ayCs01ZVq81Nt4ldLbcuZa9J/8jR07NnQJIhIpd98EbMrf325mq4FjgPHAWfnZ5pC7pGWbg79CKdPipd7GK2u9jX7wd/TRR4cuQUQ6ATMbCJwMLAP65AeGuPsmM+vdymumAdMgdzxXIZRp8VJv45W13kZ/nr+NGzfqfEciUlZm1gO4D/iWu79f6OvcfZa717h7TdM3ONujTIuXehuvrPU2+sHfwoULWbhwYegyRCRSZtaV3MCv1t3vz09+M388YNNxga2fubdIyrR4qbfxylpvo9/te95554UuQUQiZbmzs/4SWO3u/9TsqQeBS4EZ+Z91aa1TmRYv9TZeWett9IO/3r1bPNRGRCQNnwe+BrxkZivy075DbtA3z8wuA14HJqa1QmVavNTbeGWtt9EP/prOpN38WnoiImlw96eA1q7NNLoc61SmxUu9jVfWehv9MX+LFi1i0aJFocsQEUmFMi1e6m28stbb6D/5u+CCC0KXICKSGmVavNTbeGWttxUb/IW4DBJAz54901qUiEhwyrR4qbfxylpvK7nb92Pgb9x9KHAacKWZnQhMBxa5+/HAovzj1DQ0NNDQ0JDmIkVEglGmxUu9jVfWeluxwZ+7b3L35/L3twPNL4M0Jz/bHHLXxUzN4sWLWbx4cZqLFBEJRpkWL/U2XlnrbZBj/ip1GSSA8ePHJy1XRCQzlGnxUm/jlbXeVnzwt/dlkHLnSG2fu88CZgHU1NR4oes74ogjSilTRCSTlGnxUm/jlbXeVvRUL5W+DBLAunXrWLduXZqLFBEJRpkWL/U2XlnrbSW/7VvxyyABLFmyBIBBgwaluVgRkSCUafFSb+OVtd5WcrdvxS+DBPCVr3wlzcWJiASlTIuXehuvrPW2YoO/EJdBAjjssMPKtWgRkYpTpsVLvY1X1nob/eXdXnnlFV555ZXQZYiIpEKZFi/1Nl5Z6230g7+nnnqKp556igULFjBkyBAGDx7MjBkzWpx3ypQpzJ8/f5/pZ511FvX19bsfNzQ0MHz48LLVLCLSmqZMA2hsbOTkk0/e59JRt9xyC0OGDGHYsGFce+21+yxj8eLFLV5uavbs2Vx11VV7TNs7/6R8mvd2b88++yxdunTZ49+od999lwkTJnDCCScwdOhQli5dus/r9O9aNqQxFjGzxWZW0+zxQDNbWUo90V/bd8KECTQ2NjJixAgWLlxIVVUVI0eOZNy4cZx44omhyxMRKcqECRN237/55psZOnQo77///u5pTz75JHV1dbz44osceOCBbNmS6gkUpIya97a5xsZGrrvuOsaMGbPH9G9+85uMHTuW+fPns3PnTnbs2FGJMqUEWRuLRP/JX48ePVi1ahWDBw9m0KBBHHDAAUyePJm6ura/VPzd736XKVOm8Mknn7Q53+WXX051dTXV1dX06tWLG264Ic3yRUT20KNHD3r06MGGDRt4+OGHufzyy/d4/mc/+xnTp0/nwAMPBKB37xbPm7/bs88+y8knn9zuaSgefPDB3Vk3ZMgQjjvuuGS/iOyjqbd7u+WWW/izP/uzPXr5/vvvs2TJEi677DIADjjgAA4//PA2l69/18IpdSxiZjea2Wwza3O8Zma3m9mK/O0tM/teW/NH/8nfmjVreOaZZ+jfv//uaVVVVSxbtqzV11x77bW899573HHHHTSdhPqSSy6he/fuAOzcuZP99sv14fbbbwfgtddeY8yYMUyZMqVMv4mISC7TAK6//np++MMfsn379j2ef/nll/mP//gPrr/+erp168ZNN93EyJEjW1zW008/zdVXX01dXR0DBgxgyZIl3HvvvXvsemw6TmncuHGMGzcOgEmTJnHmmWeW49fr1Jp6O2TIkN3TNm7cyAMPPMATTzzBs88+u3v6unXr6NWrF1//+td54YUXOOWUU7j55ps5+OCDW1y2/l0Lq5SxCFAF9Aa+7u6e71utmX2Yf/4A4BMAd78cwMyOBf4dmN3WgqP/5G/p0qW8/PLL+0xv7coiN954I++++y4///nP95intraWFStWsGLFCh555JE9XvPRRx8xceJEZs6cybHHHpvuLyAi0szSpUv52c9+Ru/evTnllFP2ef7jjz9m27Zt/O53v+NHP/oRkyZNwn3fiyKtXr2aadOm8dBDD+1xycw///M/3511K1asoKamZo/X/fCHP6R79+5ceeWV6f9yndzSpUv3OW7vW9/6Fj/4wQ/o0qXLHtM//vhjnnvuOf7qr/6K559/noMPPrjVY8j071p4pYxFgC7u/j98zzfwJe5e7e7VwHl7Lasb8K/AVe7+Wlv1RD/4mzRpEhMmTGD9+vW7p23YsIF+/fq1OP/IkSNZvnw577zzTsHruOKKK7jooos4++yzE9crItKWSZMmsf/++/Pggw8ycOBAJk+ezBNPPMFXv/pVIPdpwkUXXYSZ8dnPfpb99tuPrVu37rOcvn370q1bN55//vmC171o0SL+9V//ldtuuy2130c+NWnSJLZt27Z7l+sbb7xBfX09kydPZuDAgcyfP59vfOMb/Nu//RtVVVVUVVVx6qmnArljyp577rkWl6t/18IrZSwCHGRmRxaxmtuA+9398fZmjH7wd9BBB/GFL3yBtWvX8uqrr7Jz507mzp27e/fF3saOHcv06dM5//zz99md0pJbb72V7du3M3369LRLFxHZx0EHHcRNN93Ehg0baGhoYO7cuXzxi1/k7rvvBuDCCy/kiSeeAHK7gHfu3EnPnj33Wc7hhx/Oww8/zHe+8x0WL17c7npfe+01vvGNbzBv3rzduwolXQcddBB//dd/vfvTuH79+vHqq6/S0NBAQ0MDEyZM4J//+Z+58MILOfroo+nfv//uXcWLFi1q9YsD+nctvFLGIsBm4GEzO6S95ZvZlcAh7t7yx797if6Yv9WrVwMwc+ZMxowZQ2NjI1OnTmXYsGGtvmbixIls376dcePG7fNR+N5uuukmunbtSnV1NZD739IVV1yRWv0iIs01ZdrQoUNbfH7q1KlMnTqV4cOHc8ABBzBnzpxWdy316dOHhx56iHPPPZdf/epXba539uzZvP3227uvVNCvX79281GK015v93bLLbdwySWXsHPnTgYNGsQdd9zR6rz6dy2sUsYiwDbgF8CDZnZeWzMC1wC7ml1B7TZ3b/UjemvpWJCsq6mp8ULPOzV79mwAHbAqEjEzW+7uNe3PmV2F5poyLV7qbbxK6W05cy36wd9HH30EQLdu3cpZkogE1JkGf8q0eKm38Sqlt+XMteh3++pNJCIxUabFS72NV9Z6G/0XPlauXMnKlSVd/UREJHOUafFSb+OVtd5G/8lf024UXbNQRGKgTIuXehuvrPU2+mP+du3aBUDXrl3LWZKIBNSZjvlTpsVLvY1XKb3VMX8J6E0kIjFRpsVLvY1X1nob/TF/L774Ii+++GLoMkREUqFMi5d6G6+s9Tb6T/6aLndz0kknBa5ERCQ5ZVq81Nt4Za230R/z19jYCLDPRbFFJB6d6Zg/ZVq81Nt4ldLbcuZaJnb7mtlYM1tjZq+YWaoXE+zSpYveSCJSceXKNWVavNTbeGWtt8EHf2bWBbgVOBc4EbjYzFq+OnUJmi6QLSJSKeXMNWVavNTbeGWtt1k45u+zwCvuvg7AzOYC44FVaSx8/vz5fPDBB5na6CLSturqan7yk5+ELiOJsuWaMi1e1dXVAOpthKqrq+nRo8fuHocW/Jg/M5sAjHX3y/OPvwac6u5X7TXfNGBa/uEQYE0Rq+kJbE2h3DRkqRZQPW3JUi2getoyxN0PCV1EkwrkWpa2fSk6cv2qPZyOXH8ptR/r7r3KUUwWPvmzFqbtMyJ191nArJJWYFaflYPBs1QLqJ62ZKkWUD1tMbPCvgFWOWXNtSxt+1J05PpVezgduf6s1R78mD9gA9C/2eMq4I1AtYiIpEG5JiKZlYXB37PA8WZ2nJkdAEwGHgxck4hIEso1Ecms4Lt93f1jM7sK+HegC/Ard/99yqspaXdxmWSpFlA9bclSLaB62pKlWiqRa5n6fUvQketX7eF05PozVXvwL3yIiIiISOVkYbeviIiIiFSIBn8iIiIinUjUg79yXjauiBoazOwlM1vRdDoKMzvSzBaa2dr8zyPKuP5fmdkWM1vZbFqr6zezb+e31xozG1OBWv7BzDbmt88KMzuvQrX0N7MnzWy1mf3ezL6Znx5q27RWT6jt083MnjGzF/L13JCfXvHt00YtQbZNaFnItVK1lIdZVmx+ZkmxeZslpeRzVpSS5UG4e5Q3cgdZ/wEYBBwAvACcGKCOBqDnXtN+CEzP358O/KCM6x8FjABWtrd+cpehegE4EDguv/26lLmWfwCuaWHectfSFxiRv38I8HJ+naG2TWv1hNo+BvTI3+8KLANOC7F92qglyLYJectKriWof588zPKtmPzM2q2YvM3ardh8ztKt2CwPdYv5k7/dl1dy951A0+WVsmA8MCd/fw5wYblW5O5LgHcKXP94YK67/7e7vwq8Qm47lrOW1pS7lk3u/lz+/nZgNXAM4bZNa/W0ptz1uLt/kH/YNX9zAmyfNmppTVm3TWBZzrXoFJmfmVJk3mZKCfmcGSVkeRAxD/6OAdY3e7yBMA1w4DEzW265SzkB9HH3TZD7QwF6V7im1tYfaptdZWYv5ndTNH2MX7FazGwgcDK5T5SCb5u96oFA28fMupjZCmALsNDdg22fVmqBwH87AXT0362lPOxoQud3Ui29ZzKrwHzOpAKzPIiYB38FXV6pAj7v7iOAc4ErzWxUgBoKFWKb/Qz4I6Aa2AT8v0rWYmY9gPuAb7n7+23NGqieYNvH3RvdvZrc1Sk+a2bD25i9rPW0UkvQv51AOvrv1pHyMEatvWcyqYh8zpwisjyImAd/mbi8kru/kf+5BXiA3G6bN82sL0D+55YKl9Xa+iu+zdz9zfw/7J8Av+DT3XNlr8XMupJ7c9a6+/35ycG2TUv1hNw+Tdz9XWAxMJbAfzvNa8nCtgmgQ/9ureRhRxM6v0vWxnsmc4rM50wpMsuDiHnwF/zySmZ2sJkd0nQfOAdYma/j0vxslwJ1layrjfU/CEw2swPN7DjgeOCZchbS9EbO+wq57VP2WszMgF8Cq939n5o9FWTbtFZPwO3Ty8wOz9/vDpwN/CcBtk9rtYTaNoEFz7VStZGHHU3o/C5ZG++ZTCkhnzOjhCwPI/Q3Tsp5A84j902bPwDXB1j/IHLfxnsB+H1TDcBRwCJgbf7nkWWs4R5yHzHvIvepwWVtrR+4Pr+91gDnVqCWu4CXgBfJvbH7VqiWM8jtLnsRWJG/nRdw27RWT6jtcxLwfH69K4G/b+9vt1z1tFFLkG0T+hY61xLU3WIeZvlWbH5m6VZs3mbpVko+Z+VWSpaHuOnybiIiIiKdSMy7fUVERERkLxr8iYiIiHQiGvyJiIiIdCIa/ImIiIh0Ihr8iYiIiHQiGvyJiIiIdCIa/ImIiIh0Ihr8SWaY2eFm9o125vm5mX2+UjWJiCShXJMs0uBPsuRwoM2QBE4Fflf+UkREUnE4yjXJGA3+JEtmAH9kZivM7Ed7P2lmQ4GX3b1xr+mLzWxI/v5RZrYyf/9gM3vYzF4ws5Vm9ueV+CVERJpRrknm7B+6AJFmpgPD3b26lefPBRa0MH0wuWs9Qu46sC/l748F3nD38wHM7LD0ShURKYhyTTJHn/xJRzKGvULSzI4FNrr7J/lJJ5G7cDbkwvJsM/uBmX3B3d+rXKkiIgVRrknFafAnHYKZHQQc7u5v7PVUNZ+GIsApTY/d/eX845eA/2tmf1+BUkVECqJck1A0+JMs2Q4c0spzfwo82cL0PwG6AZjZ8cB48rtHzKwfsMPd7wZuAkakXbCISDuUa5I5GvxJZrj728Bv8wcx731gdGvHxVQD+5nZC8DfA6uBS/PP/THwjJmtAK4Hvl+OukVEWqNckywydw9dg0i7zOw54FR337XX9FeAk919e5jKRERKo1yTUPRtX+kQ3H2fXRtmdgjwiQJSRDoi5ZqEok/+RERERDoRHfMnIiIi0olo8CciIiLSiWjwJyIiItKJaPAnIiIi0olo8CciIiLSiWjwJyIiItKJaPAnIiIi0on8f3ic/mH3PPj9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 648x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax=plt.subplots(2,2,figsize=[9,5])\n",
    "dec.plot(ax=ax.T[0])\n",
    "fslg.plot(ax=ax.T[1])\n",
    "_=fig.tight_layout()"
   ]
},
{
   "cell_type": "markdown",
   "id": "830dda29",
   "metadata": {},
   "source": [
    "Below, we build propagators for steps within the rotor period. The decoupling sequences are in \"cyclic\" mode by default (`cyclic=True`). In this mode, when we create a propagator from a sequence, it advances the time in the rotor period and the time in the sequence, so the second propagator starts where the previous propagator left off both in the rotor cycle and in the pulse sequence. At the end of the sequence, the propagators will come back to the beginning of the sequence.\n",
    "\n",
    "Here, we break the rotor cycle up into N-1 steps, and calculate the propagators for each of those steps. This will shorten the calculation time considerably, by avoiding recalculation of the propagators for each step in the DIPSHIFT cycle."
   ]
},
{
   "cell_type": "code",
   "execution_count": 9,
   "id": "34ab48c4",
   "metadata": {},
   "outputs": [],
   "source": [
    "L.reset_prop_time()\n",
    "\n",
    "step=L.taur/(N-1)\n",
    "#Propagators for 2*(N-1) steps through two rotor periods\n",
    "Udec=[dec.U(t0_seq=step*k,Dt=step) for k in range(2*(N-1))] \n",
    "Uref=L.Udelta('13C')\n",
    "\n",
    "L.reset_prop_time()\n",
    "Ufslg=[fslg.U(Dt=L.taur/(N-1)) for k in range(N-1)] #Propagators for N-1 steps through rotor period"
   ]
},
{
   "cell_type": "markdown",
   "id": "3b50b78b",
   "metadata": {},
   "source": [
    "Here, we calculate the refocusing period for the chemical shift. We apply an ideal $^{13}$C $\\pi$-pulse, followed by one rotor period of heteronuclear decoupling."
   ]
},
{
   "cell_type": "code",
   "execution_count": 10,
   "id": "26b0eabd",
   "metadata": {},
   "outputs": [],
   "source": [
    "Uref=Upi\n",
    "for m in range(N-1,2*(N-1)):\n",
    "    Uref=Udec[m]*Uref"
   ]
},
{
   "cell_type": "code",
   "execution_count": 11,
   "id": "dff4d211",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Run the sequence\n",
    "L.reset_prop_time()\n",
    "for k in range(N):\n",
    "    rho.reset()\n",
    "    U=Ueye #Initialize the propagator with an identity matrix\n",
    "    \n",
    "    # for the first step, we don't use any homonuclear decoupling\n",
    "    for m in range(k):  # k steps of homonuclear decoupling\n",
    "        U=Ufslg[m]*U\n",
    "    \n",
    "    # for the last step, we only use homonuclear decoupling\n",
    "    for m in range(k,N-1):  # N-k steps of heteronuclear decoupling\n",
    "        U=Udec[m]*U\n",
    "    # Multiply by the U constructed above, then apply the refocusing period, and finally detect\n",
    "    (Uref*U*rho)()"
   ]
},
{
   "cell_type": "code",
   "execution_count": 12,
   "id": "0dd44ba8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax=rho.plot()\n",
    "ax.figure.tight_layout()\n",
    "_=ax.set_ylim([0,1])"
   ]
},
{
   "cell_type": "markdown",
   "id": "452e99da",
   "metadata": {},
   "source": [
    "Above, we obtain a typical DIPSHIFT dephasing curve.\n",
    "\n",
    "Note that DIPSHIFT has a fixed evolution time (we switch between homonuclear and heteronuclear decoupling, but the total evolution time is fixed). Then, when plotting, SLEEPY just uses the Acquisition Number as the x-axis, since all the time points are the same (see `rho.t_axis`).\n",
    "\n",
    "One may use matplotlib functions to add a time axis, corresponding to the length of the homonuclear decoupling."
   ]
},
{
   "cell_type": "code",
   "execution_count": 13,
   "id": "9e7667fd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax=rho.plot()\n",
    "ff=lambda value,tick_number:f'{L.taur/16*value*1e6:.1f}'\n",
    "ax.set_xticklabels([],rotation=90)\n",
    "ax.xaxis.set_major_formatter(plt.FuncFormatter(ff))\n",
    "\n",
    "_=ax.set_xlabel(r'$\\tau$ / $\\mu$s')\n",
    "_=ax.set_ylim([0,1])"
   ]
},
{
   "cell_type": "markdown",
   "id": "d3eab01f",
   "metadata": {},
   "source": [
    "## DIPSHIFT as a function of correlation time"
   ]
},
{
   "cell_type": "markdown",
   "id": "d36f10f4",
   "metadata": {},
   "source": [
    "In the next section, we will vary the correlation time of motion to see how the DIPSHIFT sequence responses. \n",
    "\n",
    "Some caution should be taken when reusing objects. The Liouvillian for the sequences generated from `L` is `L` itself, so the edited `kex` will automatically be relayed to the sequences. However, the propagators are already calculated and will not be re-calculated when kex is changed."
   ]
},
{
   "cell_type": "code",
   "execution_count": 16,
   "id": "be511d88",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "log10(tc/s) = -9, 8 seconds elapsed\n",
      "log10(tc/s) = -8, 15 seconds elapsed\n",
      "log10(tc/s) = -7, 22 seconds elapsed\n",
      "log10(tc/s) = -6, 32 seconds elapsed\n",
      "log10(tc/s) = -5, 39 seconds elapsed\n",
      "log10(tc/s) = -4, 48 seconds elapsed\n",
      "log10(tc/s) = -3, 58 seconds elapsed\n",
      "log10(tc/s) = -2, 65 seconds elapsed\n",
      "log10(tc/s) = -1, 71 seconds elapsed\n"
     ]
    }
   ],
   "source": [
    "rho0=[]\n",
    "t0=time()\n",
    "tc0=np.logspace(-9,-1,9)\n",
    "for tc in tc0:\n",
    "    L.kex=sl.Tools.nSite_sym(n=3,tc=tc)\n",
    "    L.reset_prop_time()\n",
    "\n",
    "    rho0.append(rho.copy_reduced())\n",
    "\n",
    "    Ufslg=[fslg.U(Dt=L.taur/(N-1)) for k in range(N-1)] #Propagators for N steps through rotor period\n",
    "    Udec=[dec.U(t0_seq=step*k,Dt=step) for k in range(2*(N-1))] #Propagators for N steps through two rotor periods\n",
    "    \n",
    "    Uref=Upi\n",
    "    for m in range(N-1,2*(N-1)):\n",
    "        Uref=Udec[m]*Uref\n",
    "        \n",
    "    # Run the sequence\n",
    "    L.reset_prop_time()\n",
    "    for k in range(N):\n",
    "        rho0[-1].reset()\n",
    "        U=Ueye\n",
    "        for m in range(k):  # k steps of homonuclear decoupling\n",
    "            U=Ufslg[m]*U\n",
    "\n",
    "        for m in range(k,N-1):  # N-k steps of heteronuclear decoupling\n",
    "            U=Udec[m]*U\n",
    "        (Uref*U*rho0[-1])() #Propagate rho by U and refocus\n",
    "        \n",
    "    print(f'log10(tc/s) = {np.log10(tc):.0f}, {time()-t0:.0f} seconds elapsed')"
   ]
},
{
   "cell_type": "code",
   "execution_count": 15,
   "id": "2d2c5725",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x432 with 9 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax=plt.subplots(3,3,figsize=[7,6])\n",
    "for a,rho1,tc in zip(ax.flatten(),rho0,tc0):\n",
    "    rho1.plot(ax=a)\n",
    "    if not(a.is_first_col()):\n",
    "        a.set_ylabel('')\n",
    "        a.set_yticklabels([])\n",
    "    if not(a.is_last_row()):\n",
    "        a.set_xlabel('')\n",
    "        a.set_xticklabels([])\n",
    "    a.text(3,.2,fr'$\\log_{{10}}(\\tau_c / s)$ = {np.log10(tc):.0f}')\n",
    "    a.set_ylim([-.3,1])\n",
    "    \n",
    "fig.tight_layout()"
   ]
},
{
   "cell_type": "markdown",
   "id": "9218e644",
   "metadata": {},
   "source": [
    "Finally, we see the behavior of the DIPSHIFT curve as a function of correlation time. For short correlation times, we get a reduced dipole coupling, whereas for long correlation times, we obtain the full coupling. For intermediate times, we get a broadened curve. There is also significant signal loss for intermediate times, which may not be obvious experimentally since we usually reference these curves to their first time point."
   ]
}
],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}