{ "cells": [ { "attachments": {}, "cell_type": "markdown", "id": "10aa1938-c5bf-4e9e-96d2-9b00f5958672", "metadata": {}, "source": [ "# Example-31: Orbit (dispersion)" ] }, { "cell_type": "code", "execution_count": 1, "id": "7780a2b3-9159-42ba-bbed-82b225a4b3c5", "metadata": {}, "outputs": [], "source": [ "# In this example 1st and 2nd order derivatives of closed orbit with respect to momentum deviation are computed\n", "# First, dispersion at BPMs is computed from linear fit and compared with ELEGANT\n", "# Next, 1st and 2ns derivatives of closed orbit are computed" ] }, { "cell_type": "code", "execution_count": 2, "id": "dd81fcd8-b0b9-46a5-b4b3-eeb1c7a9071e", "metadata": {}, "outputs": [], "source": [ "# Import\n", "\n", "from pprint import pprint\n", "\n", "import torch\n", "\n", "from pathlib import Path\n", "\n", "import matplotlib\n", "from matplotlib import pyplot as plt\n", "from matplotlib.patches import Rectangle\n", "matplotlib.rcParams['text.usetex'] = True\n", "\n", "from twiss import twiss\n", "\n", "from model.library.line import Line\n", "\n", "from model.command.util import select\n", "from model.command.util import chop\n", "from model.command.util import evaluate\n", "from model.command.util import series\n", "\n", "from model.command.external import load_sdds\n", "from model.command.external import load_lattice\n", "\n", "from model.command.build import build\n", "\n", "from model.command.layout import Layout\n", "\n", "from model.command.orbit import orbit\n", "from model.command.orbit import parametric_orbit" ] }, { "cell_type": "code", "execution_count": 3, "id": "300a98a3-6c22-4c0a-9a3c-4f59e726f116", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Load ELEGANT twiss\n", "\n", "path = Path('ic.twiss')\n", "parameters, columns = load_sdds(path)\n", "\n", "# Set tunes\n", "\n", "nu_qx:float = parameters['nux'] % 1\n", "nu_qy:float = parameters['nuy'] % 1\n", "\n", "# Set dispersion at monitors\n", "\n", "kinds = select(columns, 'ElementType', keep=False)\n", "\n", "eta_qx = select(columns, 'etax' , keep=False)\n", "eta_px = select(columns, 'etaxp', keep=False)\n", "eta_qy = select(columns, 'etay' , keep=False)\n", "eta_py = select(columns, 'etayp', keep=False)\n", "\n", "eta_qx = {key: value for (key, value), kind in zip(eta_qx.items(), kinds.values()) if kind == 'MONI'}\n", "eta_px = {key: value for (key, value), kind in zip(eta_px.items(), kinds.values()) if kind == 'MONI'}\n", "eta_qy = {key: value for (key, value), kind in zip(eta_qy.items(), kinds.values()) if kind == 'MONI'}\n", "eta_py = {key: value for (key, value), kind in zip(eta_py.items(), kinds.values()) if kind == 'MONI'}\n", "\n", "positions = select(columns, 's', keep=False).items()\n", "positions = [value for (key, value), kind in zip(positions, kinds.values()) if kind == 'MONI']\n", "\n", "# Plot dispersion at monitors\n", "\n", "plt.figure(figsize=(16, 4))\n", "plt.plot(positions, eta_qx.values(), color='red', alpha=0.75, marker='o', label=r'$\\eta_{qx}$')\n", "plt.plot(positions, eta_px.values(), color='blue', alpha=0.75, marker='o', label=r'$\\eta_{px}$')\n", "plt.xticks(ticks=positions, labels=eta_qx.keys())\n", "plt.legend()\n", "plt.ylim(-1.50, 1.50)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 4, "id": "e29bce3a-b2ce-422b-97e1-6a6f560fadcf", "metadata": {}, "outputs": [], "source": [ "# Build and setup lattice\n", "\n", "path = Path('ic.lte')\n", "data = load_lattice(path)\n", "\n", "ring:Line = build('RING', 'ELEGANT', data)\n", "ring.propagate = True\n", "ring.flatten()\n", "ring.merge()\n", "ring.split((None, ['BPM'], None, None))\n", "ring.roll(1)\n", "ring.splice()" ] }, { "cell_type": "code", "execution_count": 5, "id": "ebb95921-3c96-4485-b11a-e9b1a1a063e2", "metadata": {}, "outputs": [], "source": [ "# Generate data for layout plot\n", "\n", "layout = Layout(ring)\n", "rectangles = layout.profile_1d(scale=0.75, shift=-1.25, text=False, exclude=['BPM'])" ] }, { "cell_type": "code", "execution_count": 6, "id": "f1344016-6bb0-4f15-96d5-6923f6e6736a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "tensor(3.1086e-15, dtype=torch.float64)\n", "tensor(5.5511e-16, dtype=torch.float64)\n" ] } ], "source": [ "# Compare linear tunes\n", "\n", "state = torch.tensor(4*[0.0], dtype=torch.float64)\n", "\n", "matrix = torch.func.jacrev(ring)(state)\n", "\n", "(nuqx, nuqy), *_ = twiss(matrix)\n", "\n", "print(nu_qx - nuqx)\n", "print(nu_qy - nuqy)" ] }, { "cell_type": "code", "execution_count": 7, "id": "7de88086-6f58-44c0-9a2f-3369bc2e6f43", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "torch.Size([16, 5, 4])\n", "\n", "tensor([[-8.0639e-03, 1.5204e-02, -1.6705e-47, -1.0023e-46],\n", " [ 5.4760e-03, -6.2632e-03, -1.1567e-46, -2.1361e-46],\n", " [ 6.0119e-01, 9.4899e-01, -1.2796e-46, 1.6479e-46],\n", " [ 2.1306e-04, 3.5665e-04, -1.7803e-48, 1.0495e-46],\n", " [ 1.9312e-04, -3.4532e-04, 1.3538e-46, 2.0140e-46],\n", " [ 6.0213e-01, -9.4895e-01, 2.2986e-47, -7.7907e-47],\n", " [ 5.5166e-03, 6.3179e-03, -5.1114e-47, -2.4426e-47],\n", " [-8.2339e-03, -1.5569e-02, -1.8418e-46, 2.8539e-46],\n", " [-8.0136e-03, 1.5570e-02, -6.4499e-47, -3.5286e-47],\n", " [ 5.4415e-03, -6.2309e-03, 7.7971e-47, 1.9323e-46],\n", " [ 6.3304e-01, 9.4904e-01, 1.1570e-46, -1.0752e-46],\n", " [ 1.4893e-04, 2.5326e-04, 5.7455e-47, -1.7626e-46],\n", " [ 1.4627e-04, -2.5477e-04, -1.1789e-46, -2.1735e-46],\n", " [ 6.1073e-01, -9.4905e-01, -7.4501e-47, -4.1134e-48],\n", " [ 5.4673e-03, 6.2236e-03, -5.9414e-48, 1.1262e-46],\n", " [-8.1900e-03, -1.5703e-02, 1.4993e-46, -1.9653e-46]],\n", " dtype=torch.float64)\n", "\n" ] } ], "source": [ "# First, we use orbit funtion to compute dispersion from linear fit\n", "\n", "dps = torch.linspace(-1.0E-6, 1.0E-6, 5, dtype=torch.float64)\n", "\n", "def fn(dp):\n", " guess = torch.tensor(4*[0.0], dtype=torch.float64) \n", " table, *_ = orbit(ring, \n", " guess, \n", " [dp], \n", " ('dp', None, None, None), \n", " alignment=False, \n", " advance=True, \n", " full=False, \n", " limit=16,\n", " epsilon=None)\n", " return table\n", "\n", "data = torch.func.vmap(fn)(dps).swapaxes(0, 1)\n", "print(data.shape)\n", "print()\n", "\n", "solution = torch.linalg.lstsq(dps.unsqueeze(1).expand(16, -1, -1), data).solution.squeeze()\n", "etaqx, etapx, etaqy, etapy = solution.T\n", "\n", "print(solution)\n", "print()" ] }, { "cell_type": "code", "execution_count": 8, "id": "5291b352-d89b-4593-93ef-ef4f2aa3fa78", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "tensor([ 2.2442e-10, -2.2744e-10, 6.9459e-11, 7.6277e-11, -1.3798e-10,\n", " -5.3663e-11, 1.4376e-10, -1.7885e-10, -1.6939e-10, 1.5748e-10,\n", " -6.4322e-11, 5.5576e-13, 1.0362e-10, -3.3488e-11, -1.3350e-10,\n", " 2.5610e-10], dtype=torch.float64)\n", "\n", "tensor([-4.5285e-10, 3.1612e-10, 2.4220e-10, 1.5288e-11, 1.1806e-10,\n", " 1.3037e-10, 1.9701e-10, -3.3796e-10, 3.3938e-10, -2.2205e-10,\n", " -1.9500e-10, 5.4374e-11, -1.2243e-10, -8.7487e-12, -1.3556e-10,\n", " 4.6687e-10], dtype=torch.float64)\n", "\n" ] } ], "source": [ "# Compare fitted values with ELEGANT\n", "\n", "print(etaqx - torch.tensor([*eta_qx.values()], dtype=torch.float64))\n", "print()\n", "\n", "print(etapx - torch.tensor([*eta_px.values()], dtype=torch.float64))\n", "print()" ] }, { "cell_type": "code", "execution_count": 9, "id": "2b57d437-a14e-4ce0-a563-a07787fb499d", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot dispersion\n", "\n", "plt.figure(figsize=(16, 4))\n", "plt.plot(positions, eta_qx.values(), color='red', alpha=0.75, marker='o', label=r'$\\eta_{q_x}$')\n", "plt.plot(positions, eta_px.values(), color='blue', alpha=0.75, marker='o', label=r'$\\eta_{p_x}$')\n", "plt.errorbar(ring.locations().cpu().numpy(), etaqx.cpu().numpy(), fmt=' ', ms=8, color='black', alpha=0.75, marker='x')\n", "plt.errorbar(ring.locations().cpu().numpy(), etapx.cpu().numpy(), fmt=' ', ms=8, color='black', alpha=0.75, marker='x')\n", "plt.xticks(ticks=positions, labels=eta_qx.keys())\n", "plt.legend()\n", "for rectangle in rectangles:\n", " plt.gca().add_patch(Rectangle(**rectangle))\n", "plt.ylim(-1.50, 1.50)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 10, "id": "e06bfdc3-6e68-460d-8c6e-d76e6c8a3062", "metadata": {}, "outputs": [], "source": [ "# Compute parametric closed orbit (1st and 2nd derivatives of closed orbit with respect to momentum deviation)\n", "# Note, all parameters after groups are shown with default values\n", "\n", "fp = torch.tensor(4*[0.0], dtype=torch.float64)\n", "dp = torch.tensor(1*[0.0], dtype=torch.float64)\n", "\n", "def solve(matrix, vector):\n", " return torch.linalg.lstsq(matrix, vector.unsqueeze(1)).solution.squeeze()\n", "\n", "orbits, table, orders = parametric_orbit(ring, # -- input line\n", " fp, # -- dynamical closed orbit (at given starting location)\n", " [dp], # -- list of deviation variables\n", " (1 + 1, 'dp', None, None, None), # -- deviation variables group(s), (order, key, kinds, names and names to exclude)\n", " start=None, # -- new lattice start\n", " alignment=False, # -- flag to use alignment\n", " advance=True, # -- flag to propagate orbit (orbits for at the end of all first level elements/lines are returned)\n", " full=False, # -- full propagation flag (compute and return orbit at the last element/line, should match the first element of the output)\n", " power=1, # -- fixed point power/order\n", " solve=solve, # -- linear system solver (A x = b)\n", " jacobian=torch.func.jacrev) # -- jacobian" ] }, { "cell_type": "code", "execution_count": 11, "id": "7604927f-fddb-44cd-b0f2-9a7022a982fd", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[(None, None, 'dp')]\n", "(2,)\n" ] } ], "source": [ "# Deviation groups specification is similar to command.wrapper.group or command.orbit.orbit, with first element being the derivative order\n", "\n", "# Here, only one group (1 + 1, 'dp', None, None, None) is used\n", "# 1 + 1 -- derivative order with respect to dp\n", "# 'dp' -- deviation paramter to bind in matched elements (see element.data())\n", "# None -- list of element kinds to match (use None to match all or a list of kinds)\n", "# None -- list of element names to match (use None to match all or a list of names)\n", "# None -- list of element names to exclude (use None to exclude none or a list of names) \n", "\n", "# Several groups can be passed\n", "# In this case list of deviation variables is expected to match\n", "# Table returns group info in command.wrapper.wrapper format\n", "\n", "print(table)\n", "\n", "# Tuple of derivative orders is also returned\n", "# The computed derivative is partial with respect to deviation groups\n", "# See Example-01 and Example-02 in https://i-a-morozov.github.io/ndmap/examples/ndmap.html for details\n", "\n", "print(orders)" ] }, { "cell_type": "code", "execution_count": 12, "id": "bdc5ad5a-3f34-4461-89ef-fc37fe1ca00d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[tensor([0., 0., 0., 0.], dtype=torch.float64),\n", " tensor([[-0.0081],\n", " [ 0.0152],\n", " [ 0.0000],\n", " [ 0.0000]], dtype=torch.float64),\n", " tensor([[[-14.6125]],\n", "\n", " [[ 24.3816]],\n", "\n", " [[ 0.0000]],\n", "\n", " [[ 0.0000]]], dtype=torch.float64)]]\n", "\n", "tensor([-1.5370e-05, 2.7395e-05, 0.0000e+00, 0.0000e+00],\n", " dtype=torch.float64)\n", "\n", "tensor([-1.5370e-05, 2.7395e-05, 0.0000e+00, 0.0000e+00],\n", " dtype=torch.float64)\n", "\n" ] } ], "source": [ "# Each orbit in orbits is represented as a special Table\n", "\n", "# This is a redundent multivariate series representation\n", "# It can be evaluated using model.command.util.evaluate function (alias of ndmap.evaluate.evaluate)\n", "# model.command.util.chop can be used to clean small values (alias of ndmap.signature.chop)\n", "\n", "local, *_ = orbits\n", "chop(local)\n", "\n", "pprint(local)\n", "print()\n", "\n", "# Evaluate table at non-zero deviation\n", "# Note, here dynamical fixed point is required but has no effect\n", "\n", "print(evaluate(local, [fp, dp + 1.0E-3]))\n", "print()\n", "\n", "# With only one deviation group the above is equivalent to \n", "\n", "(x, dxdp, dxdpdp), *_ = local\n", "print(x + dxdp @ (dp + 1.0E-3) + 0.5 * dxdpdp @ (dp + 1.0E-3) @ (dp + 1.0E-3))\n", "print()" ] }, { "cell_type": "code", "execution_count": 13, "id": "1a7220d4-f0ee-42ec-9abe-60ddbe9b9ca2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "{(0, 0, 0, 0, 0): tensor([0., 0., 0., 0.], dtype=torch.float64),\n", " (0, 0, 0, 0, 1): tensor([-0.0081, 0.0152, 0.0000, 0.0000], dtype=torch.float64),\n", " (0, 0, 0, 0, 2): tensor([-7.3062, 12.1908, 0.0000, 0.0000], dtype=torch.float64)}\n", "\n", "tensor([-1.5370e-05, 2.7395e-05, 0.0000e+00, 0.0000e+00],\n", " dtype=torch.float64)\n", "\n", "tensor([-1.5370e-05, 2.7395e-05, 0.0000e+00, 0.0000e+00],\n", " dtype=torch.float64)\n", "\n" ] } ], "source": [ "# Derivative table representation can be also converted to series using model.command.util.series function (alias of ndmap.series.series)\n", "\n", "local, *_ = orbits\n", "pprint(series((4, 1), (0, 1 + 1), local))\n", "print()\n", "\n", "# model.command.util.evaluate can also be used with series\n", "\n", "print(evaluate(local, [fp, dp + 1.0E-3]))\n", "print()\n", "\n", "print(evaluate(series((4, 1), (0, 1 + 1), local), [fp, dp + 1.0E-3]))\n", "print()" ] }, { "cell_type": "code", "execution_count": 14, "id": "490d52ae-69da-4eee-83fc-e8fddbae1fd1", "metadata": {}, "outputs": [], "source": [ "# Extract 1st and 2nd order dispersion values from series representation\n", "\n", "eta1_qx = torch.stack([series((4, 1), (0, 2), local)[(0, 0, 0, 0, 1)][0] for local in orbits])\n", "eta1_px = torch.stack([series((4, 1), (0, 2), local)[(0, 0, 0, 0, 1)][1] for local in orbits])\n", "\n", "eta2_qx = torch.stack([series((4, 1), (0, 2), local)[(0, 0, 0, 0, 2)][0] for local in orbits])\n", "eta2_px = torch.stack([series((4, 1), (0, 2), local)[(0, 0, 0, 0, 2)][1] for local in orbits])" ] }, { "cell_type": "code", "execution_count": 15, "id": "b538d1ef-e996-497d-abd5-bcbc9238d681", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "tensor([ 1.0004e-14, -1.3037e-14, 5.9952e-15, 1.2807e-15, -9.5464e-15,\n", " 1.3323e-15, 9.5436e-15, -1.4350e-14, -1.3914e-14, 9.5748e-15,\n", " 8.8818e-16, -8.9525e-15, 5.2589e-16, 6.7724e-15, -1.3343e-14,\n", " 9.5809e-15], dtype=torch.float64)\n", "\n", "tensor([-2.1778e-14, 1.9190e-14, 1.4433e-14, -3.7748e-15, 1.0540e-14,\n", " 3.9968e-15, 1.0880e-14, -2.7096e-14, 2.7100e-14, -1.1074e-14,\n", " -4.1078e-15, -1.0103e-14, 4.2984e-15, -1.5210e-14, -2.0095e-14,\n", " 2.1663e-14], dtype=torch.float64)\n", "\n" ] } ], "source": [ "# Compare with ELEGANT\n", "\n", "print(eta1_qx - torch.tensor([*eta_qx.values()], dtype=torch.float64))\n", "print()\n", "\n", "print(eta1_px - torch.tensor([*eta_px.values()], dtype=torch.float64))\n", "print()" ] }, { "cell_type": "code", "execution_count": 16, "id": "42b4cfad-8e2c-4954-aca9-7eefd7e10843", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot dispersion\n", "\n", "plt.figure(figsize=(16, 4))\n", "plt.plot(positions, eta_qx.values(), color='red', alpha=0.75, marker='o', label=r'$\\eta_{q_x}$')\n", "plt.plot(positions, eta_px.values(), color='blue', alpha=0.75, marker='o', label=r'$\\eta_{p_x}$')\n", "plt.errorbar(ring.locations().cpu().numpy(), eta1_qx.cpu().numpy(), fmt=' ', ms=8, color='black', alpha=0.75, marker='x')\n", "plt.errorbar(ring.locations().cpu().numpy(), eta1_px.cpu().numpy(), fmt=' ', ms=8, color='black', alpha=0.75, marker='x')\n", "plt.xticks(ticks=positions, labels=eta_qx.keys())\n", "plt.legend()\n", "for rectangle in rectangles:\n", " plt.gca().add_patch(Rectangle(**rectangle))\n", "plt.ylim(-1.50, 1.50)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 17, "id": "b8b80c69-81b4-4281-92f9-210508ce0af9", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot second order dispersion\n", "\n", "plt.figure(figsize=(16, 4))\n", "plt.errorbar(ring.locations().cpu().numpy(), eta2_qx.cpu().numpy(), fmt='-', ms=8, color='red', alpha=0.75, marker='x')\n", "plt.errorbar(ring.locations().cpu().numpy(), eta2_px.cpu().numpy(), fmt='-', ms=8, color='blue', alpha=0.75, marker='x')\n", "plt.xticks(ticks=positions, labels=eta_qx.keys())\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 18, "id": "2ddc8116-d360-4981-baa7-6ed3bccf8578", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Compute dispersion at the exit of each element\n", "\n", "ring.flatten()\n", "\n", "fp = torch.tensor(4*[0.0], dtype=torch.float64)\n", "dp = torch.tensor(1*[0.0], dtype=torch.float64)\n", "\n", "orbits, *_ = parametric_orbit(ring, fp, [dp], (1, 'dp', None, None, None), advance=True, full=True)\n", "\n", "dispersion = torch.stack([series((4, 1), (0, 2), local)[(0, 0, 0, 0, 1)][0] for local in orbits])\n", "\n", "plt.figure(figsize=(16, 4))\n", "plt.errorbar(ring.locations('all').cpu().numpy(), dispersion.cpu().numpy(), fmt='-', color='red', alpha=0.75, label=r'$\\eta$')\n", "plt.errorbar(positions, eta_qx.values(), fmt=' ', ms=8, color='black', alpha=0.75, marker='x')\n", "plt.xticks(ticks=positions, labels=eta_qx.keys())\n", "plt.legend()\n", "for rectangle in rectangles:\n", " plt.gca().add_patch(Rectangle(**rectangle))\n", "plt.ylim(-1.50, 1.50)\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": { "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 }