{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "5cb92984-d64b-49ae-ad70-12261f26ddd0",
   "metadata": {},
   "source": [
    "# Example-18: Inverse tracking"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ba56d8c7-c426-4c33-8601-e7e853f575eb",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "\n",
    "from model.library.drift import Drift\n",
    "from model.library.quadrupole import Quadrupole\n",
    "from model.library.sextupole import Sextupole\n",
    "from model.library.octupole import Octupole\n",
    "from model.library.multipole import Multipole\n",
    "from model.library.dipole import Dipole\n",
    "from model.library.corrector import Corrector\n",
    "from model.library.gradient import Gradient\n",
    "from model.library.linear import Linear\n",
    "from model.library.bpm import BPM\n",
    "from model.library.marker import Marker\n",
    "from model.library.line import Line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "7e5f97a8-0dcc-4a56-b5f2-92a83d5d027e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0005, -0.0005,  0.0060,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([0., 0., 0., 0.], dtype=torch.float64)\n",
      "\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0005, -0.0005,  0.0060,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([0., 0., 0., 0.], dtype=torch.float64)\n",
      "\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0005, -0.0005,  0.0060,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([-8.6736e-19,  2.1684e-19,  0.0000e+00, -4.3368e-19],\n",
      "       dtype=torch.float64)\n",
      "\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([-2.7015e-10, -5.0000e-04,  6.0000e-03,  1.0000e-03],\n",
      "       dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([-2.6021e-18,  2.1684e-19,  8.6736e-19, -4.3368e-19],\n",
      "       dtype=torch.float64)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Drift\n",
    "\n",
    "MF = Drift('MAG', length=1.0, dp=0.001, dx=0.0, dy=0.0, dz=0.0, wx=0.0, wy=0.0, wz=0.0, ns=10, exact=False)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()\n",
    "\n",
    "MF = Drift('MAG', length=1.0, dp=0.001, dx=0.0, dy=0.0, dz=0.0, wx=0.0, wy=0.0, wz=0.0, ns=10, exact=True)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()\n",
    "\n",
    "MF = Drift('MAG', length=1.0, dp=0.001, dx=0.01, dy=0.01, dz=-0.01, wx=0.001, wy=-0.001, wz=0.001, ns=10, exact=True)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()\n",
    "\n",
    "MF = Drift('MAG', length=1.0, dp=0.001, dx=0.01, dy=0.01, dz=-0.01, wx=0.001, wy=-0.001, wz=0.001, ns=10, exact=True, insertion=True)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "15d0295c-1338-4cce-b921-4965cd9b27fc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([-0.0002, -0.0043,  0.0075,  0.0095], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 6.5052e-19,  0.0000e+00,  3.4694e-18, -8.6736e-19],\n",
      "       dtype=torch.float64)\n",
      "\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([-0.0002, -0.0043,  0.0075,  0.0095], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([-8.6736e-19, -7.0473e-18,  6.0715e-18, -2.1684e-18],\n",
      "       dtype=torch.float64)\n",
      "\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0046,  0.0135,  0.0046, -0.0031], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([-9.5410e-18,  1.1926e-18,  8.6736e-19, -7.8063e-18],\n",
      "       dtype=torch.float64)\n",
      "\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0005, -0.0005,  0.0055,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([-7.8063e-18, -3.9031e-18, -2.6021e-18, -8.6736e-19],\n",
      "       dtype=torch.float64)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Quadrupole\n",
    "\n",
    "MF = Quadrupole('MAG', length=0.5, kn=3.0, ks=-1.0, dp=0.001, dx=0.0, dy=0.0, dz=0.0, wx=0.0, wy=0.0, wz=0.0, ns=10, exact=False)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()\n",
    "\n",
    "MF = Quadrupole('MAG', length=0.5, kn=3.0, ks=-1.0, dp=0.001, dx=0.0, dy=0.0, dz=0.0, wx=0.0, wy=0.0, wz=0.0, ns=10, exact=True)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()\n",
    "\n",
    "MF = Quadrupole('MAG', length=0.5, kn=3.0, ks=-1.0, dp=0.001, dx=0.01, dy=0.01, dz=-0.01, wx=0.001, wy=-0.001, wz=0.001, ns=10, exact=True)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()\n",
    "\n",
    "MF = Quadrupole('MAG', length=0.5, kn=3.0, ks=-1.0, dp=0.001, dx=0.01, dy=0.01, dz=-0.01, wx=0.001, wy=-0.001, wz=0.001, ns=10, exact=True, insertion=True)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "43136280-898c-4273-92f1-e74d95ab942d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0009, -0.0005,  0.0053,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([0., 0., 0., 0.], dtype=torch.float64)\n",
      "\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0009, -0.0005,  0.0053,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([0., 0., 0., 0.], dtype=torch.float64)\n",
      "\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0009, -0.0006,  0.0053,  0.0011], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([-8.6736e-19,  1.0842e-19, -8.6736e-19, -4.3368e-19],\n",
      "       dtype=torch.float64)\n",
      "\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0007, -0.0006,  0.0053,  0.0011], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([-8.6736e-19,  1.0842e-19, -8.6736e-19,  0.0000e+00],\n",
      "       dtype=torch.float64)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Sextupole\n",
    "\n",
    "MF = Sextupole('MAG', length=0.25, ms=10.0, dp=0.001, dx=0.0, dy=0.0, dz=0.0, wx=0.0, wy=0.0, wz=0.0, ns=10, exact=False)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()\n",
    "\n",
    "MF = Sextupole('MAG', length=0.25, ms=10.0, dp=0.001, dx=0.0, dy=0.0, dz=0.0, wx=0.0, wy=0.0, wz=0.0, ns=10, exact=True)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()\n",
    "\n",
    "MF = Sextupole('MAG', length=0.25, ms=10.0, dp=0.001, dx=0.01, dy=0.01, dz=-0.01, wx=0.001, wy=-0.001, wz=0.001, ns=10, exact=True)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()\n",
    "\n",
    "MF = Sextupole('MAG', length=0.25, ms=10.0, dp=0.001, dx=0.01, dy=0.01, dz=-0.01, wx=0.001, wy=-0.001, wz=0.001, ns=10, exact=True, insertion=True)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "25457662-44b4-4600-b7d2-61d59644a7b2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0009, -0.0005,  0.0052,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([0., 0., 0., 0.], dtype=torch.float64)\n",
      "\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0009, -0.0005,  0.0052,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([0., 0., 0., 0.], dtype=torch.float64)\n",
      "\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0009, -0.0005,  0.0052,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([-8.6736e-19,  1.0842e-19,  0.0000e+00,  0.0000e+00],\n",
      "       dtype=torch.float64)\n",
      "\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0008, -0.0005,  0.0052,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([-8.6736e-19,  0.0000e+00,  8.6736e-19,  0.0000e+00],\n",
      "       dtype=torch.float64)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Octupole\n",
    "\n",
    "MF = Octupole('MAG', length=0.25, mo=25.0, dp=0.001, dx=0.0, dy=0.0, dz=0.0, wx=0.0, wy=0.0, wz=0.0, ns=10, exact=False)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()\n",
    "\n",
    "MF = Octupole('MAG', length=0.25, mo=25.0, dp=0.001, dx=0.0, dy=0.0, dz=0.0, wx=0.0, wy=0.0, wz=0.0, ns=10, exact=True)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()\n",
    "\n",
    "MF = Octupole('MAG', length=0.25, mo=25.0, dp=0.001, dx=0.01, dy=0.01, dz=-0.01, wx=0.001, wy=-0.001, wz=0.001, ns=10, exact=True)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()\n",
    "\n",
    "MF = Octupole('MAG', length=0.25, mo=25.0, dp=0.001, dx=0.01, dy=0.01, dz=-0.01, wx=0.001, wy=-0.001, wz=0.001, ns=10, exact=True, insertion=True)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c39b66b7-dc38-4e37-80db-126a0f625844",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0006, -0.0024,  0.0057,  0.0048], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 7.5894e-18, -4.3368e-19, -2.0817e-17, -2.8189e-18],\n",
      "       dtype=torch.float64)\n",
      "\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0006, -0.0024,  0.0057,  0.0048], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 7.3726e-18, -3.7947e-18, -2.0817e-17, -1.9516e-18],\n",
      "       dtype=torch.float64)\n",
      "\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0019,  0.0072,  0.0051, -0.0005], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([-4.4235e-17,  3.0358e-18,  1.6480e-17, -4.1200e-18],\n",
      "       dtype=torch.float64)\n",
      "\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0007, -0.0006,  0.0053,  0.0011], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([-3.7297e-17,  8.6736e-19,  9.5410e-18,  0.0000e+00],\n",
      "       dtype=torch.float64)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Multipole\n",
    "\n",
    "MF = Multipole('MAG', length=0.25, kn=3.0, ks=-1.0, ms=10.0, mo=25.0, dp=0.001, dx=0.0, dy=0.0, dz=0.0, wx=0.0, wy=0.0, wz=0.0, ns=10, exact=False)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()\n",
    "\n",
    "MF = Multipole('MAG', length=0.25, kn=3.0, ks=-1.0, ms=10.0, mo=25.0, dp=0.001, dx=0.0, dy=0.0, dz=0.0, wx=0.0, wy=0.0, wz=0.0, ns=10, exact=True)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()\n",
    "\n",
    "MF = Multipole('MAG', length=0.25, kn=3.0, ks=-1.0, ms=10.0, mo=25.0, dp=0.001, dx=0.01, dy=0.01, dz=-0.01, wx=0.001, wy=-0.001, wz=0.001, ns=10, exact=True)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()\n",
    "\n",
    "MF = Multipole('MAG', length=0.25, kn=3.0, ks=-1.0, ms=10.0, mo=25.0, dp=0.001, dx=0.01, dy=0.01, dz=-0.01, wx=0.001, wy=-0.001, wz=0.001, ns=10, exact=True, insertion=True)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "97072a39-c1d4-41e9-8b10-7054c1af59f5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([ 0.0010, -0.0005,  0.0050, -0.0010], dtype=torch.float64)\n",
      "tensor([-0.0116, -0.0136,  0.0722,  0.1266], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050, -0.0010], dtype=torch.float64)\n",
      "tensor([ 4.0549e-17, -4.4452e-17, -1.2663e-16,  2.5045e-16],\n",
      "       dtype=torch.float64)\n",
      "\n",
      "tensor([ 0.0010, -0.0005,  0.0050, -0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0306,  0.0215, -0.0687, -0.1470], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050, -0.0010], dtype=torch.float64)\n",
      "tensor([ 3.6689e-16, -8.8438e-16, -2.6489e-15,  4.6872e-15],\n",
      "       dtype=torch.float64)\n",
      "\n",
      "tensor([ 0.0010, -0.0005,  0.0050, -0.0010], dtype=torch.float64)\n",
      "tensor([-0.0021, -0.0006,  0.0069, -0.0007], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050, -0.0010], dtype=torch.float64)\n",
      "tensor([ 3.7297e-17,  3.1550e-17, -1.0408e-17,  2.1250e-17],\n",
      "       dtype=torch.float64)\n",
      "\n",
      "tensor([ 0.0010, -0.0005,  0.0050, -0.0010], dtype=torch.float64)\n",
      "tensor([-0.0097, -0.0101,  0.0171,  0.0200], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050, -0.0010], dtype=torch.float64)\n",
      "tensor([ 1.5400e-10, -2.2230e-10, -4.3635e-10,  5.0327e-10],\n",
      "       dtype=torch.float64)\n",
      "\n",
      "tensor([ 0.0010, -0.0005,  0.0050, -0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0304,  0.0215, -0.0691, -0.1473], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050, -0.0010], dtype=torch.float64)\n",
      "tensor([-6.6071e-09, -4.3597e-10,  9.8294e-09, -1.9903e-08],\n",
      "       dtype=torch.float64)\n",
      "\n",
      "tensor([ 0.0010, -0.0005,  0.0050, -0.0010], dtype=torch.float64)\n",
      "tensor([-0.0021, -0.0006,  0.0069, -0.0008], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050, -0.0010], dtype=torch.float64)\n",
      "tensor([-1.6908e-12,  1.4334e-11,  2.0711e-11, -3.7469e-11],\n",
      "       dtype=torch.float64)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Dipole\n",
    "\n",
    "MF = Dipole('MAG', length=2.0, angle=0.1, e1=0.01, e2=0.05, kn=3.0, ks=-1.0, ms=10.0, mo=25.0, dp=0.001, dx=0.0, dy=0.0, dz=0.0, wx=0.0, wy=0.0, wz=0.0, ns=10, exact=False)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, -0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()\n",
    "\n",
    "MF = Dipole('MAG', length=2.0, angle=0.1, e1=0.01, e2=0.05, kn=3.0, ks=-1.0, ms=10.0, mo=25.0, dp=0.001, dx=0.01, dy=0.01, dz=-0.01, wx=0.001, wy=-0.001, wz=0.001, ns=10, exact=False)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, -0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()\n",
    "\n",
    "MF = Dipole('MAG', length=2.0, angle=0.1, e1=0.01, e2=0.05, kn=3.0, ks=-1.0, ms=10.0, mo=25.0, dp=0.001, dx=0.01, dy=0.01, dz=-0.01, wx=0.001, wy=-0.001, wz=0.001, ns=10, exact=False, insertion=True)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, -0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()\n",
    "\n",
    "MF = Dipole('MAG', length=2.0, angle=0.1, e1=0.01, e2=0.05, kn=1.0, ks=-1.0, ms=5.0, mo=10.0, dp=0.001, dx=0.0, dy=0.0, dz=0.0, wx=0.0, wy=0.0, wz=0.0, ns=10, exact=True)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, -0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()\n",
    "\n",
    "MF = Dipole('MAG', length=2.0, angle=0.1, e1=0.01, e2=0.05, kn=3.0, ks=-1.0, ms=10.0, mo=25.0, dp=0.001, dx=0.01, dy=0.01, dz=-0.01, wx=0.001, wy=-0.001, wz=0.001, ns=10, exact=True)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, -0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()\n",
    "\n",
    "MF = Dipole('MAG', length=2.0, angle=0.1, e1=0.01, e2=0.05, kn=3.0, ks=-1.0, ms=10.0, mo=25.0, dp=0.001, dx=0.01, dy=0.01, dz=-0.01, wx=0.001, wy=-0.001, wz=0.001, ns=10, exact=True, insertion=True)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, -0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "71912186-90e0-4906-b9a0-49c30c287738",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([0.0010, 0.0095, 0.0050, 0.0510], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0000e+00, -4.3368e-19,  0.0000e+00,  8.6736e-19],\n",
      "       dtype=torch.float64)\n",
      "\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([0.0011, 0.0095, 0.0055, 0.0510], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 8.6736e-19, -6.5052e-19,  0.0000e+00,  1.4962e-17],\n",
      "       dtype=torch.float64)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Corrector\n",
    "\n",
    "MF = Corrector('MAG', cx=0.01, cy=0.05, dp=0.001, dx=0.0, dy=0.0, dz=0.0, wx=0.0, wy=0.0, wz=0.0)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()\n",
    "\n",
    "MF = Corrector('MAG', cx=0.01, cy=0.05, dp=0.001, dx=0.01, dy=0.01, dz=-0.01, wx=0.001, wy=-0.001, wz=0.001)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "791ff0ad-e469-457c-b98c-38861f60c9b1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([0.0010, 0.0019, 0.0050, 0.0020], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([0., 0., 0., 0.], dtype=torch.float64)\n",
      "\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0031,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 6.5052e-19,  1.0842e-18, -1.7347e-18, -2.1684e-19],\n",
      "       dtype=torch.float64)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Gradient\n",
    "\n",
    "MF = Gradient('MAG', kn=0.1, ks=0.5, dp=0.001, dx=0.0, dy=0.0, dz=0.0, wx=0.0, wy=0.0, wz=0.0)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()\n",
    "\n",
    "MF = Gradient('MAG', kn=0.1, ks=0.5, dp=0.001, dx=0.01, dy=0.01, dz=-0.01, wx=0.001, wy=-0.001, wz=0.001)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "567cd2b1-562b-4d4d-a9f2-a7abe30b2779",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0056,  0.0107,  0.0026, -0.0038], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([-2.8189e-18,  0.0000e+00,  5.2042e-18,  2.1684e-18],\n",
      "       dtype=torch.float64)\n",
      "\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([-0.0009, -0.0046,  0.0097,  0.0083], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 8.6736e-19,  2.9273e-18, -1.7347e-18, -8.6736e-19],\n",
      "       dtype=torch.float64)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Linear\n",
    "\n",
    "# Note, gives correct inverse for zero vector\n",
    "\n",
    "length = 1.0\n",
    "kn = - 2.0\n",
    "ks = + 1.5\n",
    "dp = 0.001\n",
    "Q = Quadrupole('Q', length, kn, ks, dp)\n",
    "\n",
    "state = torch.tensor([0.0, 0.0, 0.0, 0.0], dtype=torch.float64)\n",
    "\n",
    "matrix = torch.func.jacrev(lambda state, dp: Q(state, data={**Q.data(), **{'dp': dp}}), 0)(state, Q.dp)\n",
    "vector = torch.zeros_like(state)\n",
    "\n",
    "\n",
    "MF = Linear('MAG', (dp*vector).tolist(), matrix.tolist(), dp=0.001, dx=0.0, dy=0.0, dz=0.0, wx=0.0, wy=0.0, wz=0.0)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()\n",
    "\n",
    "\n",
    "MF = Linear('MAG', (dp*vector).tolist(), matrix.tolist(), dp=0.001, dx=0.01, dy=0.01, dz=-0.01, wx=0.001, wy=-0.001, wz=0.001)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "3ad43cda-127a-4f67-b0b8-c02fede912cd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([0., 0., 0., 0.], dtype=torch.float64)\n",
      "\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 4.3368e-19,  2.1684e-19, -1.7347e-18, -4.3368e-19],\n",
      "       dtype=torch.float64)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Marker\n",
    "\n",
    "MF = Marker('MAG', dp=0.001, dx=0.0, dy=0.0, dz=0.0, wx=0.0, wy=0.0, wz=0.0)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()\n",
    "\n",
    "MF =  Marker('MAG', dp=0.001, dx=0.01, dy=0.01, dz=-0.01, wx=0.001, wy=-0.001, wz=0.001)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "45a8ed92-0026-48cc-8f92-2075241a996c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0011, -0.0005,  0.0047,  0.0011], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([-2.1684e-19,  1.0842e-19,  0.0000e+00,  0.0000e+00],\n",
      "       dtype=torch.float64)\n",
      "\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0054,  0.0010], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([ 2.1684e-19,  0.0000e+00,  0.0000e+00, -2.1684e-19],\n",
      "       dtype=torch.float64)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# BPM\n",
    "\n",
    "xx = torch.tensor(+0.05, dtype=torch.float64)\n",
    "xy = torch.tensor(+0.01, dtype=torch.float64)\n",
    "yx = torch.tensor(+0.05, dtype=torch.float64)\n",
    "yy = torch.tensor(-0.06, dtype=torch.float64)\n",
    "\n",
    "MF = BPM('MAG', dp=0.001, dx=0.0, dy=0.0, dz=0.0, wx=0.0, wy=0.0, wz=0.0)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data={**MF.data(), **{'xx': xx, 'xy': xy, 'yx': yx, 'yy': yy}}, alignment=True))\n",
    "print(local := MI(local, data={**MI.data(), **{'xx': xx, 'xy': xy, 'yx': yx, 'yy': yy}}, alignment=True))\n",
    "print(local - state)\n",
    "print()\n",
    "\n",
    "MF =  BPM('MAG', dp=0.001, dx=0.01, dy=0.01, dz=-0.01, wx=0.001, wy=-0.001, wz=0.001)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data={**MF.data(), **{'xx': xx, 'xy': xy, 'yx': yx, 'yy': yy}}, alignment=True))\n",
    "print(local := MI(local, data={**MI.data(), **{'xx': xx, 'xy': xy, 'yx': yx, 'yy': yy}}, alignment=True))\n",
    "print(local - state)\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "e896c00b-0bbe-49c1-b20e-cc1477c67ea8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([-0.0043, -0.0001,  0.0121, -0.0014], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([5.5793e-16, 1.2804e-16, 1.7347e-18, 8.6736e-19], dtype=torch.float64)\n",
      "\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([-0.0380, -0.0058,  0.0121, -0.0015], dtype=torch.float64)\n",
      "tensor([ 0.0010, -0.0005,  0.0050,  0.0010], dtype=torch.float64)\n",
      "tensor([-9.8145e-13, -1.4483e-13,  1.8322e-12, -7.0449e-13],\n",
      "       dtype=torch.float64)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Line\n",
    "\n",
    "QF = Quadrupole('QF', 1.0, +0.25)\n",
    "QD = Quadrupole('QD', 1.0, -0.20)\n",
    "SF = Sextupole('SF', 0.25)\n",
    "SD = Sextupole('SD', 0.25)\n",
    "DR = Drift('DR', 0.25)\n",
    "BM = Dipole('BM', 3.50, torch.pi/8.0)\n",
    "\n",
    "MF = Line('FODO', \n",
    "          [QF, DR, SF, DR, BM, DR, SD, DR, QD, DR, SD, DR, BM, DR, SF, DR], \n",
    "          propagate=True, \n",
    "          dp=0.001, \n",
    "          exact=False, \n",
    "          output=False,\n",
    "          matrix = False)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()\n",
    "\n",
    "\n",
    "MF = Line('FODO', \n",
    "          [QF, DR, SF, DR, BM, DR, SD, DR, QD, DR, SD, DR, BM, DR, SF, DR], \n",
    "          propagate=True, \n",
    "          dp=0.001, \n",
    "          exact=True, \n",
    "          output=False,\n",
    "          matrix = False)\n",
    "MI = MF.inverse()\n",
    "\n",
    "state = torch.tensor([0.001, -0.0005, 0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "print(local := state)\n",
    "print(local := MF(local, data=MF.data(), alignment=True))\n",
    "print(local := MI(local, data=MI.data(), alignment=True))\n",
    "print(local - state)\n",
    "print()"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [
    "myt0_gMIOq7b",
    "5d97819c"
   ],
   "name": "03_frequency.ipynb",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.12.1"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autoclose": false,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}