{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "85d6656d-13d2-4cb4-8404-d1fdf6af354e",
   "metadata": {},
   "source": [
    "# Example-05: Drift (element)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "942d635e-4ba0-4b82-89f3-a55e423f5f10",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Comparison of drift element with MADX-PTC and other features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "94da4e4d-ea80-4f6d-8b7c-d541629a3c23",
   "metadata": {},
   "outputs": [],
   "source": [
    "from pathlib import Path\n",
    "from os import system\n",
    "\n",
    "import torch\n",
    "from model.library.drift import Drift"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5c39499a-c10e-4dfb-99f7-abd58e326dcc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.0025373134328358204, -0.005, -0.003507462686567164, 0.001]\n",
      "[0.0025373134328358204, -0.005, -0.0035074626865671645, 0.001]\n",
      "[0.0, 0.0, 4.336808689942018e-19, 0.0]\n"
     ]
    }
   ],
   "source": [
    "# Tracking (paraxial)\n",
    "\n",
    "ptc = Path('ptc')\n",
    "obs = Path('track.obs0001.p0001')\n",
    "\n",
    "exact = False\n",
    "align = False\n",
    "\n",
    "dp = 0.005\n",
    "length = 1.5\n",
    "state = torch.tensor([0.01, -0.005, -0.005, 0.001], dtype=torch.float64)\n",
    "qx, px, qy, py = state.tolist()\n",
    "\n",
    "dx = align*torch.tensor(0.05, dtype=torch.float64)\n",
    "dy = align*torch.tensor(-0.02, dtype=torch.float64)\n",
    "dz = align*torch.tensor(0.05, dtype=torch.float64)\n",
    "\n",
    "wx = align*torch.tensor(0.005, dtype=torch.float64)\n",
    "wy = align*torch.tensor(-0.005, dtype=torch.float64)\n",
    "wz = align*torch.tensor(0.1, dtype=torch.float64)\n",
    "\n",
    "error = {'dx': dx, 'dy': dy, 'dz': dz, 'wx': wx, 'wy': wy, 'wz': wz}\n",
    "\n",
    "code = f\"\"\"\n",
    "mag:drift,l={length} ;\n",
    "map:line=(mag) ;\n",
    "beam,energy=1.0E+6,particle=electron ;\n",
    "set,format=\"20.20f\",\"-20s\" ;\n",
    "use,period=map ;\n",
    "select,flag=error,pattern=\"mag\" ;\n",
    "ealign,dx={dx.item()},dy={dy.item()},ds={dz.item()},dphi={wx.item()},dtheta={wy.item()},dpsi={wz.item()} ;\n",
    "ptc_create_universe,sector_nmul_max=10,sector_nmul=10 ;\n",
    "ptc_create_layout,model=1,method=6,nst=1000,exact={str(exact).lower()} ;\n",
    "ptc_setswitch,fringe=false,time=true,totalpath=true,exact_mis=true ;\n",
    "ptc_align ;\n",
    "ptc_start,x={qx},px={px},y={qy},py={py},pt={dp},t=0.0 ;\n",
    "ptc_track,icase=5,deltap=0.,turns=1,file=track,maxaper={{1.,1.,1.,1.,1.,1.}} ;\n",
    "ptc_track_end ;\n",
    "ptc_end ;\n",
    "\"\"\" \n",
    "\n",
    "with ptc.open('w') as stream:\n",
    "    stream.write(code)\n",
    "    \n",
    "system(f'madx < {str(ptc)} > /dev/null')\n",
    "\n",
    "with obs.open('r') as stream:\n",
    "    for line in stream:\n",
    "        continue\n",
    "    _, _, qx, px, qy, py, *_ = line.split()\n",
    "    \n",
    "ref = torch.tensor([float(x) for x in (qx, px, qy, py)], dtype=torch.float64)\n",
    "\n",
    "D = Drift('D', length=length, dp=dp, exact=exact)\n",
    "res = D(state, alignment=align, data={**D.data(), **error})\n",
    "\n",
    "print(ref.tolist())\n",
    "print(res.tolist())\n",
    "print((ref - res).tolist())\n",
    "\n",
    "ptc.unlink()\n",
    "obs.unlink()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5ae0a652-05ba-4f39-b7ae-009373ddfa3f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.002537217378977325, -0.005, -0.003507443475795465, 0.001]\n",
      "[0.002537217378977325, -0.005, -0.0035074434757954654, 0.001]\n",
      "[0.0, 0.0, 4.336808689942018e-19, 0.0]\n"
     ]
    }
   ],
   "source": [
    "# Tracking (exact)\n",
    "\n",
    "ptc = Path('ptc')\n",
    "obs = Path('track.obs0001.p0001')\n",
    "\n",
    "exact = True\n",
    "align = False\n",
    "\n",
    "dp = 0.005\n",
    "length = 1.5\n",
    "state = torch.tensor([0.01, -0.005, -0.005, 0.001], dtype=torch.float64)\n",
    "qx, px, qy, py = state.tolist()\n",
    "\n",
    "dx = align*torch.tensor(0.05, dtype=torch.float64)\n",
    "dy = align*torch.tensor(-0.02, dtype=torch.float64)\n",
    "dz = align*torch.tensor(0.05, dtype=torch.float64)\n",
    "\n",
    "wx = align*torch.tensor(0.005, dtype=torch.float64)\n",
    "wy = align*torch.tensor(-0.005, dtype=torch.float64)\n",
    "wz = align*torch.tensor(0.1, dtype=torch.float64)\n",
    "\n",
    "error = {'dx': dx, 'dy': dy, 'dz': dz, 'wx': wx, 'wy': wy, 'wz': wz}\n",
    "\n",
    "code = f\"\"\"\n",
    "mag:drift,l={length} ;\n",
    "map:line=(mag) ;\n",
    "beam,energy=1.0E+6,particle=electron ;\n",
    "set,format=\"20.20f\",\"-20s\" ;\n",
    "use,period=map ;\n",
    "select,flag=error,pattern=\"mag\" ;\n",
    "ealign,dx={dx.item()},dy={dy.item()},ds={dz.item()},dphi={wx.item()},dtheta={wy.item()},dpsi={wz.item()} ;\n",
    "ptc_create_universe,sector_nmul_max=10,sector_nmul=10 ;\n",
    "ptc_create_layout,model=1,method=6,nst=1000,exact={str(exact).lower()} ;\n",
    "ptc_setswitch,fringe=false,time=true,totalpath=true,exact_mis=true ;\n",
    "ptc_align ;\n",
    "ptc_start,x={qx},px={px},y={qy},py={py},pt={dp},t=0.0 ;\n",
    "ptc_track,icase=5,deltap=0.,turns=1,file=track,maxaper={{1.,1.,1.,1.,1.,1.}} ;\n",
    "ptc_track_end ;\n",
    "ptc_end ;\n",
    "\"\"\" \n",
    "\n",
    "with ptc.open('w') as stream:\n",
    "    stream.write(code)\n",
    "    \n",
    "system(f'madx < {str(ptc)} > /dev/null')\n",
    "\n",
    "with obs.open('r') as stream:\n",
    "    for line in stream:\n",
    "        continue\n",
    "    _, _, qx, px, qy, py, *_ = line.split()\n",
    "    \n",
    "ref = torch.tensor([float(x) for x in (qx, px, qy, py)], dtype=torch.float64)\n",
    "\n",
    "D = Drift('D', length=length, dp=dp, exact=exact)\n",
    "res = D(state, alignment=align, data={**D.data(), **error})\n",
    "\n",
    "print(ref.tolist())\n",
    "print(res.tolist())\n",
    "print((ref - res).tolist())\n",
    "\n",
    "ptc.unlink()\n",
    "obs.unlink()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e0bba0d5-03e3-43ad-9955-05aa21a0b360",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.0025372170792497145, -0.0049999999999999975, -0.003507395297032926, 0.0010000000000000009]\n",
      "[0.0025372170792497166, -0.004999999999999999, -0.0035073952970329247, 0.0010000000000000018]\n",
      "[-2.168404344971009e-18, 1.734723475976807e-18, -1.3010426069826053e-18, -8.673617379884035e-19]\n"
     ]
    }
   ],
   "source": [
    "# Tracking (exact, alignment)\n",
    "\n",
    "ptc = Path('ptc')\n",
    "obs = Path('track.obs0001.p0001')\n",
    "\n",
    "exact = False\n",
    "align = True\n",
    "\n",
    "dp = 0.005\n",
    "length = 1.5\n",
    "state = torch.tensor([0.01, -0.005, -0.005, 0.001], dtype=torch.float64)\n",
    "qx, px, qy, py = state.tolist()\n",
    "\n",
    "dx = align*torch.tensor(0.05, dtype=torch.float64)\n",
    "dy = align*torch.tensor(-0.02, dtype=torch.float64)\n",
    "dz = align*torch.tensor(0.05, dtype=torch.float64)\n",
    "\n",
    "wx = align*torch.tensor(0.005, dtype=torch.float64)\n",
    "wy = align*torch.tensor(-0.005, dtype=torch.float64)\n",
    "wz = align*torch.tensor(0.1, dtype=torch.float64)\n",
    "\n",
    "error = {'dx': dx, 'dy': dy, 'dz': dz, 'wx': wx, 'wy': wy, 'wz': wz}\n",
    "\n",
    "code = f\"\"\"\n",
    "mag:drift,l={length} ;\n",
    "map:line=(mag) ;\n",
    "beam,energy=1.0E+6,particle=electron ;\n",
    "set,format=\"20.20f\",\"-20s\" ;\n",
    "use,period=map ;\n",
    "select,flag=error,pattern=\"mag\" ;\n",
    "ealign,dx={dx.item()},dy={dy.item()},ds={dz.item()},dphi={wx.item()},dtheta={wy.item()},dpsi={wz.item()} ;\n",
    "ptc_create_universe,sector_nmul_max=10,sector_nmul=10 ;\n",
    "ptc_create_layout,model=1,method=6,nst=1000,exact={str(exact).lower()} ;\n",
    "ptc_setswitch,fringe=false,time=true,totalpath=true,exact_mis=true ;\n",
    "ptc_align ;\n",
    "ptc_start,x={qx},px={px},y={qy},py={py},pt={dp},t=0.0 ;\n",
    "ptc_track,icase=5,deltap=0.,turns=1,file=track,maxaper={{1.,1.,1.,1.,1.,1.}} ;\n",
    "ptc_track_end ;\n",
    "ptc_end ;\n",
    "\"\"\" \n",
    "\n",
    "with ptc.open('w') as stream:\n",
    "    stream.write(code)\n",
    "    \n",
    "system(f'madx < {str(ptc)} > /dev/null')\n",
    "\n",
    "with obs.open('r') as stream:\n",
    "    for line in stream:\n",
    "        continue\n",
    "    _, _, qx, px, qy, py, *_ = line.split()\n",
    "    \n",
    "ref = torch.tensor([float(x) for x in (qx, px, qy, py)], dtype=torch.float64)\n",
    "\n",
    "D = Drift('D', length=length, dp=dp, exact=exact)\n",
    "res = D(state, alignment=align, data={**D.data(), **error})\n",
    "\n",
    "print(ref.tolist())\n",
    "print(res.tolist())\n",
    "print((ref - res).tolist())\n",
    "\n",
    "ptc.unlink()\n",
    "obs.unlink()\n",
    "\n",
    "# Note, for some reason drift is not invariant under WX ans WY rotations in MADX"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c3422dd0-926f-4f3b-9150-a2e7c2042351",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([ 0.0025, -0.0050, -0.0035,  0.0010], dtype=torch.float64)\n",
      "\n",
      "tensor([ 0.0100, -0.0050, -0.0050,  0.0010], dtype=torch.float64)\n",
      "\n",
      "tensor([ 0.0025, -0.0050, -0.0035,  0.0010], dtype=torch.float64)\n",
      "\n",
      "tensor([0., 0., 0., 0.], dtype=torch.float64)\n"
     ]
    }
   ],
   "source": [
    "# Deviation/error variables\n",
    "\n",
    "dp = 0.005\n",
    "length = 1.5\n",
    "state = torch.tensor([0.01, -0.005, -0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "dx = torch.tensor(0.05, dtype=torch.float64)\n",
    "dy = torch.tensor(-0.02, dtype=torch.float64)\n",
    "dz = torch.tensor(0.05, dtype=torch.float64)\n",
    "\n",
    "wx = torch.tensor(0.005, dtype=torch.float64)\n",
    "wy = torch.tensor(-0.005, dtype=torch.float64)\n",
    "wz = torch.tensor(0.1, dtype=torch.float64)\n",
    "\n",
    "error = {'dx': dx, 'dy': dy, 'dz': dz, 'wx': wx, 'wy': wy, 'wz': wz}\n",
    "\n",
    "D = Drift('D', length, dp)\n",
    "\n",
    "# Each element has two variant of a call method\n",
    "# In the first case only state is passed, it is transformed using parameters specified on initializaton\n",
    "\n",
    "print(D(state))\n",
    "print()\n",
    "\n",
    "# Deviation errors can be also passed to call method\n",
    "# These variables are added to corresponding parameters specified on initializaton\n",
    "# For example, element lenght can changed\n",
    "\n",
    "print(D(state, data={**D.data(), **{'dl': torch.tensor(-length, dtype=D.dtype)}}))\n",
    "print()\n",
    "\n",
    "# In the above D.data() creates default deviation dictionary (with zero values for each deviaton)\n",
    "# {**D.data(), **{'dl': torch.tensor(-length, dtype=DR.dtype)}} replaces the 'dl' key value \n",
    "\n",
    "# Additionaly, alignment errors are passed as deivation variables\n",
    "# They are used if alignment flag is raised\n",
    "\n",
    "print(D(state, data={**D.data(), **error}, alignment=True))\n",
    "print()\n",
    "\n",
    "# The following elements can be made equivalent using deviation variables\n",
    "\n",
    "DA = Drift('DA', length, dp)\n",
    "DB = Drift('DB', length - 0.1, dp)\n",
    "\n",
    "print(DA(state) - DB(state, data={**DB.data(), **{'dl': torch.tensor(+0.1, dtype=DB.dtype)}}))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "3850f79d-c1b7-40c5-8407-1802852021cb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([0., 0., 0., 0.], dtype=torch.float64)\n",
      "tensor([-0.0005,  0.0000,  0.0001,  0.0000], dtype=torch.float64)\n",
      "tensor([-9.7502e-08,  0.0000e+00,  1.9500e-08,  0.0000e+00],\n",
      "       dtype=torch.float64)\n"
     ]
    }
   ],
   "source": [
    "# Insertion element\n",
    "\n",
    "# In this mode elements are treated as thin insertions (at the center)\n",
    "# Using parameters specified on initialization, transport two matrices are computed\n",
    "# These matrices are used to insert the element\n",
    "# Input state is transformed from the element center to its entrance\n",
    "# Next, transformation from the entrance frame to the exit frame is performed\n",
    "# This transformation can contain errors\n",
    "# The final step is to transform state from the exit frame back to the element center\n",
    "# Without errors, this results in identity transformation for linear elements\n",
    "\n",
    "dp = 0.0\n",
    "length = 1.5\n",
    "state = torch.tensor([0.01, -0.005, -0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "dx = torch.tensor(0.05, dtype=torch.float64)\n",
    "dy = torch.tensor(-0.02, dtype=torch.float64)\n",
    "dz = torch.tensor(0.05, dtype=torch.float64)\n",
    "\n",
    "wx = torch.tensor(0.005, dtype=torch.float64)\n",
    "wy = torch.tensor(-0.005, dtype=torch.float64)\n",
    "wz = torch.tensor(0.1, dtype=torch.float64)\n",
    "\n",
    "error = {'dx': dx, 'dy': dy, 'dz': dz, 'wx': wx, 'wy': wy, 'wz': wz}\n",
    "\n",
    "D = Drift('D', length, dp, exact=False, insertion=True)\n",
    "\n",
    "# Identity transformation without errors\n",
    "\n",
    "print(D(state) - state)\n",
    "\n",
    "# Represents effect of an error\n",
    "\n",
    "print(D(state, data={**D.data(), **{'dl': 0.1}}) - state)\n",
    "\n",
    "# Exact tracking corresponds to inclusion of kinematic term as errors\n",
    "\n",
    "D = Drift('D', length, dp, exact=True, insertion=True)\n",
    "\n",
    "print(D(state) - state)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b5146cc0-6f5b-47b9-9317-939ca62bbc9b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([512, 4])\n",
      "torch.Size([512, 4])\n"
     ]
    }
   ],
   "source": [
    "# Mapping over a set of initial conditions\n",
    "\n",
    "# Call method can be used to map over a set of initial conditions\n",
    "# Note, device can be set to cpu or gpu via base element classvariables\n",
    "\n",
    "dp = 0.0\n",
    "length = 1.5\n",
    "\n",
    "dx = torch.tensor(0.05, dtype=torch.float64)\n",
    "dy = torch.tensor(-0.02, dtype=torch.float64)\n",
    "dz = torch.tensor(0.05, dtype=torch.float64)\n",
    "\n",
    "wx = torch.tensor(0.005, dtype=torch.float64)\n",
    "wy = torch.tensor(-0.005, dtype=torch.float64)\n",
    "wz = torch.tensor(0.1, dtype=torch.float64)\n",
    "\n",
    "error = {'dx': dx, 'dy': dy, 'dz': dz, 'wx': wx, 'wy': wy, 'wz': wz}\n",
    "\n",
    "D = Drift('D', length, dp, exact=True)\n",
    "\n",
    "state = 1.0E-3*torch.randn((512, 4), dtype=D.dtype, device=D.device)\n",
    "\n",
    "print(torch.vmap(D)(state).shape)\n",
    "\n",
    "# To map over deviations parameters a wrapper function (or a lambda expression) can be used\n",
    "\n",
    "def wrapper(state, dp):\n",
    "    return D(state, data={**D.data(), **{'dp': dp}})\n",
    "\n",
    "dp = 1.0E-3*torch.randn(512, dtype=D.dtype, device=D.device)\n",
    "\n",
    "print(torch.vmap(wrapper)(state, dp).shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "3020a87b-b812-4657-a53f-f163959d9d67",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[1.0000, 1.5000, 0.0000, 0.0000],\n",
      "        [0.0000, 1.0000, 0.0000, 0.0000],\n",
      "        [0.0000, 0.0000, 1.0000, 1.5000],\n",
      "        [0.0000, 0.0000, 0.0000, 1.0000]], dtype=torch.float64)\n",
      "\n",
      "tensor([-0.0050,  0.0000,  0.0010,  0.0000], dtype=torch.float64)\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor(-0., dtype=torch.float64)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Differentiability\n",
    "\n",
    "# Both call methods are differentiable\n",
    "# Derivative with respect to state can be computed directly\n",
    "# For deviation variables, wrapping is required\n",
    "\n",
    "dp = 0.0\n",
    "length = 1.5\n",
    "state = torch.tensor([0.01, -0.005, -0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "dx = torch.tensor(0.05, dtype=torch.float64)\n",
    "dy = torch.tensor(-0.02, dtype=torch.float64)\n",
    "dz = torch.tensor(0.05, dtype=torch.float64)\n",
    "\n",
    "wx = torch.tensor(0.005, dtype=torch.float64)\n",
    "wy = torch.tensor(-0.005, dtype=torch.float64)\n",
    "wz = torch.tensor(0.1, dtype=torch.float64)\n",
    "\n",
    "error = {'dx': dx, 'dy': dy, 'dz': dz, 'wx': wx, 'wy': wy, 'wz': wz}\n",
    "\n",
    "D = Drift('D', length, dp, exact=False)\n",
    "\n",
    "# Compute derivative with respect to state\n",
    "\n",
    "print(torch.func.jacrev(D)(state))\n",
    "print()\n",
    "\n",
    "# Compute derivative with respect to a deviation variable\n",
    "\n",
    "dl = torch.tensor(0.0, dtype=torch.float64)\n",
    "\n",
    "def wrapper(state, dl):\n",
    "    return D(state, data={**D.data(), **{'dl': dl}})\n",
    "\n",
    "print(torch.func.jacrev(wrapper, 1)(state, dl))\n",
    "print()\n",
    "\n",
    "# Compositional derivative (compute derivative of jacobian trace with respect momentum deviation)\n",
    "\n",
    "dp = torch.tensor(0.0, dtype=torch.float64)\n",
    "\n",
    "def trace(state, dp):\n",
    "    return (torch.func.jacrev(lambda state: D(state, data={**D.data(), **{'dp': dp}}))(state)).trace()\n",
    "\n",
    "torch.func.jacrev(trace, 1)(state, dp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "c906a277-85a1-451c-9d08-79505a16a072",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([ 0.0025, -0.0050, -0.0035,  0.0010], dtype=torch.float64)\n",
      "torch.Size([10, 4])\n",
      "torch.Size([10, 4, 4])\n",
      "torch.Size([100, 4])\n",
      "torch.Size([100, 4, 4])\n"
     ]
    }
   ],
   "source": [
    "# Output at each step\n",
    "\n",
    "# It is possible to collect output of state or tangent matrix at each integration step\n",
    "# Number of integratin steps is controlled by ns parameter on initialization\n",
    "# Alternatively, desired integration step length can be passed\n",
    "# Number of integration steps is computed as ceil(length/ds)\n",
    "\n",
    "dp = 0.0\n",
    "length = 1.5\n",
    "state = torch.tensor([0.01, -0.005, -0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "dx = torch.tensor(0.05, dtype=torch.float64)\n",
    "dy = torch.tensor(-0.02, dtype=torch.float64)\n",
    "dz = torch.tensor(0.05, dtype=torch.float64)\n",
    "\n",
    "wx = torch.tensor(0.005, dtype=torch.float64)\n",
    "wy = torch.tensor(-0.005, dtype=torch.float64)\n",
    "wz = torch.tensor(0.1, dtype=torch.float64)\n",
    "\n",
    "error = {'dx': dx, 'dy': dy, 'dz': dz, 'wx': wx, 'wy': wy, 'wz': wz}\n",
    "\n",
    "D = Drift('D', length, dp, exact=False, ns=10, output=True, matrix=True)\n",
    "\n",
    "# Final state is still returned\n",
    "\n",
    "print(D(state))\n",
    "\n",
    "# Data is added to special attributes (state and tangent matrix)\n",
    "\n",
    "print(D.container_output.shape)\n",
    "print(D.container_matrix.shape)\n",
    "\n",
    "# Number of integration steps can be changed\n",
    "\n",
    "D.ns = 100\n",
    "\n",
    "D(state)\n",
    "print(D.container_output.shape)\n",
    "print(D.container_matrix.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "4c9992c3-1047-43ae-8be5-c90bb10c9123",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.002499902498098708, -0.005, -0.003499980499619743, 0.001]\n",
      "[0.002499902498098709, -0.005, -0.0034999804996197477, 0.001]\n",
      "[-8.673617379884035e-19, 0.0, 4.7704895589362195e-18, 0.0]\n",
      "\n",
      "[0, 1, 0, 1, 0, 1, 0]\n",
      "[0.6756035959798289, 1.3512071919596578, -0.17560359597982877, -1.7024143839193153, -0.17560359597982877, 1.3512071919596578, 0.6756035959798289]\n"
     ]
    }
   ],
   "source": [
    "# Integration order is set on initialization (default value is zero)\n",
    "# This order is related to difference order as 2n + 2\n",
    "# Thus, zero corresponds to second order difference method\n",
    "\n",
    "dp = 0.0\n",
    "length = 1.5\n",
    "state = torch.tensor([0.01, -0.005, -0.005, 0.001], dtype=torch.float64)\n",
    "\n",
    "dx = torch.tensor(0.05, dtype=torch.float64)\n",
    "dy = torch.tensor(-0.02, dtype=torch.float64)\n",
    "dz = torch.tensor(0.05, dtype=torch.float64)\n",
    "\n",
    "wx = torch.tensor(0.005, dtype=torch.float64)\n",
    "wy = torch.tensor(-0.005, dtype=torch.float64)\n",
    "wz = torch.tensor(0.1, dtype=torch.float64)\n",
    "\n",
    "error = {'dx': dx, 'dy': dy, 'dz': dz, 'wx': wx, 'wy': wy, 'wz': wz}\n",
    "\n",
    "D = Drift('D', length, dp, order=1, exact=True)\n",
    "\n",
    "# For drift integration is performed only with exact flag\n",
    "# In this case, kinematic term error is added\n",
    "# This term actually commutes with paraxial drift map\n",
    "# But integration is still performed for consistency with matrix-kick-matrix split\n",
    "# Only one integration step is required to get exact result\n",
    "\n",
    "D.ns = 1\n",
    "ref = D(state)\n",
    "\n",
    "D.ns = 10\n",
    "res = D(state)\n",
    "\n",
    "print(ref.tolist())\n",
    "print(res.tolist())\n",
    "print((ref - res).tolist())\n",
    "print()\n",
    "\n",
    "# Integrator parameters are stored in data attribute (if integration is actually performed)\n",
    "\n",
    "maps, weights = D._data\n",
    "print(maps)\n",
    "print(weights)"
   ]
  }
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