{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "262a5ec8-2553-4237-ab62-319b6ca22089",
   "metadata": {},
   "source": [
    "# Example-50: Advance (Phase advance sensitivity)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a213b251-33ff-45b6-9731-9b6051c00e9c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# In this example effect of systematic quadruple errors on phase advances is illustrated"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8e0b7972-29a6-4702-a8e3-8a5a4e1fc254",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import\n",
    "\n",
    "from random import random\n",
    "from pprint import pprint\n",
    "\n",
    "import torch\n",
    "from torch import Tensor\n",
    "\n",
    "from pathlib import Path\n",
    "\n",
    "import matplotlib\n",
    "from matplotlib import pyplot as plt\n",
    "matplotlib.rcParams['text.usetex'] = True\n",
    "\n",
    "from model.library.line import Line\n",
    "\n",
    "from model.command.external import load_sdds\n",
    "from model.command.external import load_lattice\n",
    "from model.command.build import build\n",
    "from model.command.tune import tune\n",
    "from model.command.advance import advance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8e28283c-8719-4afb-9d6b-961e2a06eea7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load ELEGANT twiss\n",
    "\n",
    "path = Path('ic.twiss')\n",
    "parameters, columns = load_sdds(path)\n",
    "\n",
    "nu_qx:Tensor = torch.tensor(parameters['nux'] % 1, dtype=torch.float64)\n",
    "nu_qy:Tensor = torch.tensor(parameters['nuy'] % 1, dtype=torch.float64)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "592c1a33-d9aa-44d8-a8c5-3e6aa9309522",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Build and setup lattice\n",
    "\n",
    "# Note, sextupoles are turned off and dipoles are linear \n",
    "\n",
    "# Load ELEGANT table\n",
    "\n",
    "path = Path('ic.lte')\n",
    "data = load_lattice(path)\n",
    "\n",
    "# Build ELEGANT table\n",
    "\n",
    "ring:Line = build('RING', 'ELEGANT', data)\n",
    "ring.flatten()\n",
    "\n",
    "# Merge drifts\n",
    "\n",
    "ring.merge()\n",
    "\n",
    "# Split BPMs\n",
    "\n",
    "ring.split((None, ['BPM'], None, None))\n",
    "\n",
    "# Roll lattice start\n",
    "\n",
    "ring.roll(1)\n",
    "\n",
    "# Set linear dipoles\n",
    "\n",
    "for element in ring:\n",
    "    if element.__class__.__name__ == 'Dipole':\n",
    "        element.linear = True\n",
    "\n",
    "# Split lattice into lines by BPMs\n",
    "\n",
    "ring.splice()\n",
    "\n",
    "# Set number of elements of different kinds\n",
    "\n",
    "nb = ring.describe['BPM']\n",
    "nq = ring.describe['Quadrupole']\n",
    "ns = ring.describe['Sextupole']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5bf9f907-5837-419e-8afb-6b0bbf4d094a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Compute tunes (fractional part)\n",
    "\n",
    "guess = torch.tensor(4*[0.0], dtype=torch.float64)\n",
    "nuqx, nuqy = tune(ring, [], alignment=False, matched=True, guess=guess, limit=8, epsilon=1.0E-9)\n",
    "\n",
    "# Compare with elegant\n",
    "\n",
    "print(torch.allclose(nu_qx, nuqx))\n",
    "print(torch.allclose(nu_qy, nuqy))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "90f97c55-9824-442e-93b6-bc11e4dcaca8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([16])\n",
      "torch.Size([16])\n"
     ]
    }
   ],
   "source": [
    "# Compute nominal phase advances between BPMs\n",
    "\n",
    "kn = torch.zeros(nq, dtype=torch.float64)\n",
    "\n",
    "muqx_model, muqy_model = advance(ring, [kn], ('kn', ['Quadrupole'], None, None), matched=True, limit=1, epsilon=None).T\n",
    "\n",
    "print(muqx_model.shape)\n",
    "print(muqy_model.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "be79cad2-cb89-4e96-8102-5ffb1ef68e45",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([16, 8192])\n",
      "torch.Size([16, 8192])\n"
     ]
    }
   ],
   "source": [
    "# Compute phase advances between BPMs using MC\n",
    "\n",
    "kns = 0.01*torch.randn((8192, nq), dtype=torch.float64)\n",
    "\n",
    "muqxs, muqys = torch.vmap(lambda kn: advance(ring, [kn], ('kn', ['Quadrupole'], None, None), matched=True, limit=1, epsilon=None), chunk_size=1024)(kns).swapaxes(0, -1)\n",
    "\n",
    "dmuqxs = muqxs - muqx_model.unsqueeze(1)\n",
    "dmuqys = muqys - muqy_model.unsqueeze(1)\n",
    "\n",
    "print(dmuqxs.shape)\n",
    "print(dmuqys.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d88adea1-6bf1-4303-a757-805287fd992c",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 3400x200 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 4000x250 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot histograms\n",
    "\n",
    "fig, axs = plt.subplots(1, len(ring), figsize=(17*2, 2))\n",
    "for dmuqx, ax in zip(dmuqxs, axs):\n",
    "    ax.hist(dmuqx.cpu().numpy(), bins=100, color='blue', alpha=0.7)\n",
    "plt.tight_layout() \n",
    "plt.show()    \n",
    "\n",
    "fig, axs = plt.subplots(1, len(ring), figsize=(len(ring)*2.5, 2.5))\n",
    "for dmuqy, ax in zip(dmuqys, axs):\n",
    "    ax.hist(dmuqy.cpu().numpy(), bins=100, color='blue', alpha=0.7)    \n",
    "plt.tight_layout() \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "30fb1e48-3041-4c93-9f7b-fe8fe4c37da6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute and plot spreads\n",
    "\n",
    "sigma_dmuqxs = dmuqxs.std(1)\n",
    "sigma_dmuqys = dmuqys.std(1)\n",
    "\n",
    "plt.figure(figsize=(16, 2))\n",
    "plt.bar(range(len(sigma_dmuqxs)), sigma_dmuqxs.cpu().numpy(), color='blue', alpha=0.75, width=0.75)\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "plt.figure(figsize=(16, 2))\n",
    "plt.bar(range(len(sigma_dmuqys)), sigma_dmuqys.cpu().numpy(), color='blue', alpha=0.75, width=0.75)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "0c41ca06-b337-407c-85b2-03211bb9b230",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([16, 28])\n",
      "torch.Size([16, 28])\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute twiss derivatives and estimate spread from linear surrogate model using MC\n",
    "\n",
    "# Compute derivatives\n",
    "\n",
    "kn = torch.zeros(nq, dtype=torch.float64)\n",
    "dmuqx_dk, dmuqy_dk = torch.func.jacrev(lambda kn: advance(ring, [kn], ('kn', ['Quadrupole'], None, None), matched=True, limit=1, epsilon=None), chunk_size=1024)(kn).swapaxes(0, 1)\n",
    "\n",
    "print(dmuqx_dk.shape)\n",
    "print(dmuqy_dk.shape)\n",
    "\n",
    "# Sample\n",
    "\n",
    "kns = 0.01*torch.randn((8192, nq), dtype=torch.float64)\n",
    "\n",
    "dmuqxs = dmuqx_dk @ kns.T\n",
    "dmuqxy = dmuqy_dk @ kns.T\n",
    "\n",
    "# Compute and plot spreads\n",
    "\n",
    "sigma_dmuqxs = dmuqxs.std(1)\n",
    "sigma_dmuqys = dmuqys.std(1)\n",
    "\n",
    "plt.figure(figsize=(16, 2))\n",
    "plt.bar(range(len(sigma_dmuqxs)), sigma_dmuqxs.cpu().numpy(), color='blue', alpha=0.75, width=0.75)\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "plt.figure(figsize=(16, 2))\n",
    "plt.bar(range(len(sigma_dmuqys)), sigma_dmuqys.cpu().numpy(), color='blue', alpha=0.75, width=0.75)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "0b34036f-c6c2-4400-b3ac-d03a85ce91ba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute spread using error propagation\n",
    "\n",
    "sigma_dmuqxs = (dmuqx_dk @ (0.01*torch.eye(nq,  dtype=torch.float64))**2 @ dmuqx_dk.T).diag().sqrt()\n",
    "sigma_dmuqys = (dmuqy_dk @ (0.01*torch.eye(nq,  dtype=torch.float64))**2 @ dmuqy_dk.T).diag().sqrt()\n",
    "\n",
    "plt.figure(figsize=(16, 2))\n",
    "plt.bar(range(len(sigma_dmuqxs)), sigma_dmuqxs.cpu().numpy(), color='blue', alpha=0.75, width=0.75)\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "plt.figure(figsize=(16, 2))\n",
    "plt.bar(range(len(sigma_dmuqys)), sigma_dmuqys.cpu().numpy(), color='blue', alpha=0.75, width=0.75)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  }
 ],
 "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": {
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    "version": 3
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   "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",
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   "eqLabelWithNumbers": true,
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   "hotkeys": {
    "equation": "Ctrl-E",
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 },
 "nbformat": 4,
 "nbformat_minor": 5
}