ELETTRA-35: ID feed forward
[1]:
# In this example corrections are computed for two ID parameters
# And switching between ID parameters is demonstrated
[2]:
# Import
import torch
from torch import Tensor
from pathlib import Path
import matplotlib
from matplotlib import pyplot as plt
from matplotlib.patches import Rectangle
matplotlib.rcParams['text.usetex'] = True
from model.library.element import Element
from model.library.line import Line
from model.library.corrector import Corrector
from model.library.quadrupole import Quadrupole
from model.library.matrix import Matrix
from model.command.external import load_lattice
from model.command.build import build
from model.command.tune import tune
from model.command.orbit import dispersion
from model.command.orbit import ORM
from model.command.twiss import twiss
from model.command.advance import advance
from model.command.coupling import coupling
from model.command.wrapper import Wrapper
from model.command.wrapper import forward
from model.command.wrapper import inverse
from model.command.wrapper import normalize
[3]:
# Set data type and device
Element.dtype = dtype = torch.float64
Element.device = device = torch.device('cpu')
[4]:
# Load lattice (ELEGANT table)
# Note, lattice is allowed to have repeated elements
path = Path('elettra.lte')
data = load_lattice(path)
[5]:
# Build and setup lattice
ring:Line = build('RING', 'ELEGANT', data)
# Flatten sublines
ring.flatten()
# Remove all marker elements but the ones starting with MLL (long straight section centers)
ring.remove_group(pattern=r'^(?!MLL_).*', kinds=['Marker'])
# Replace all sextupoles with quadrupoles
def factory(element:Element) -> None:
table = element.serialize
table.pop('ms', None)
return Quadrupole(**table)
ring.replace_group(pattern=r'', factory=factory, kinds=['Sextupole'])
# Set linear dipoles
def apply(element:Element) -> None:
element.linear = True
ring.apply(apply, kinds=['Dipole'])
# Insert correctors
for name, *_ in ring.layout():
if name.startswith('CH'):
corrector = Corrector(f'{name}_CXY', factor=1)
ring.split((1 + 1, None, [name], None), paste=[corrector])
# Merge drifts
ring.merge()
# Change lattice start start
ring.start = "BPM_S01_01"
# Split BPMs
ring.split((None, ['BPM'], None, None))
# Roll lattice
ring.roll(1)
# Splice
ring.splice()
# Describe
ring.describe
[5]:
{'BPM': 168,
'Drift': 732,
'Dipole': 156,
'Quadrupole': 360,
'Corrector': 24,
'Marker': 12}
[6]:
# Compute tunes (fractional part)
nux, nuy = tune(ring, [], matched=True, limit=1)
[7]:
# Compute dispersion
orbit = torch.tensor(4*[0.0], dtype=dtype)
etaqx, etapx, etaqy, etapy = dispersion(ring, orbit, [], limit=1)
[8]:
# Compute twiss parameters
ax, bx, ay, by = twiss(ring, [], matched=True, advance=True, full=False).T
[9]:
# Compute phase advances
mux, muy = advance(ring, [], alignment=False, matched=True).T
[10]:
# Compute coupling
c = coupling(ring, [])
[11]:
# Quadrupole names for global tune correction
QF = [f'QF_S{i:02}_{j:02}' for j in [2, 3] for i in range(1, 12 + 1)]
QD = [f'QD_S{i:02}_{j:02}' for j in [2, 3] for i in range(1, 12 + 1)]
[12]:
# Global tune responce matrix
def global_observable(knobs):
kf, kd = knobs
kn = torch.stack(len(QF)*[kf] + len(QD)*[kd])
return tune(ring, [kn], ('kn', None, QF + QD, None), matched=True, limit=1)
knobs = torch.tensor([0.0, 0.0], dtype=dtype)
global_target = global_observable(knobs)
global_matrix = torch.func.jacfwd(global_observable)(knobs)
print(global_target)
print(global_matrix)
tensor([0.2994, 0.1608], dtype=torch.float64)
tensor([[ 5.8543, 2.0964],
[-2.9918, -1.2602]], dtype=torch.float64)
[13]:
# Local knobs
nkn = ['OCT_S01_02', 'QF_S01_02', 'QD_S01_02', 'QD_S01_03', 'QF_S01_03', 'OCT_S01_03']
nks = ['SD_S01_05', 'SH_S01_02', 'SH_S01_03', 'SD_S01_06']
[14]:
# Define knobs to magnets mixing matrices
Sn = torch.tensor([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0], [0.0, 0.0, 1.0], [0.0, 1.0, 0.0], [1.0, 0.0, 0.0]], dtype=dtype)
print(Sn)
print()
Ss = torch.tensor([[+1.0, 0.0], [0.0, +1.0], [0.0, -1.0], [-1.0, 0.0]], dtype=dtype)
print(Ss)
print()
tensor([[1., 0., 0.],
[0., 1., 0.],
[0., 0., 1.],
[0., 0., 1.],
[0., 1., 0.],
[1., 0., 0.]], dtype=torch.float64)
tensor([[ 1., 0.],
[ 0., 1.],
[ 0., -1.],
[-1., 0.]], dtype=torch.float64)
[15]:
# Define observables for 'mixed' knobs
def observable_twiss(kn, ks):
return twiss(ring, [kn, ks], ('kn', None, nkn, None), ('ks', None, nks, None), matched=True, advance=True, full=False, convert=False)
def observable_dispersion(kn, ks):
orbit = torch.tensor(4*[0.0], dtype=dtype)
etax, _, etay, _ = dispersion(ring,
orbit,
[kn, ks],
('kn', None, nkn, None),
('ks', None, nks, None))
return torch.stack([etax, etay]).T
def observable(knobs):
kn, ks = torch.split(knobs, [3, 2])
kn = Sn @ kn
ks = Ss @ ks
betas = observable_twiss(kn, ks)
etas = observable_dispersion(kn, ks)
return torch.cat([betas.flatten(), etas.flatten()])
knobs = torch.tensor((3 + 2)*[0.0], dtype=dtype)
print((target := observable(knobs)).shape)
print((matrix := torch.func.jacfwd(observable)(knobs)).shape)
torch.Size([5712])
torch.Size([5712, 5])
[16]:
# 1st ID setting
[17]:
# Define ID model
A = torch.tensor([[-9.54791e-03, -3.26154e-11, 1.44707e-09, 5.43034e-04],
[-3.26149e-11, -1.29258e-02, 6.98380e-04, -1.05053e-09],
[ 1.44707e-09, 6.98380e-04, 2.07735e-02, -2.55925e-09],
[ 5.43034e-04, -1.05053e-09, -2.55925e-09, 2.90246e-02]], dtype=dtype)
ID = Matrix('ID', length=0.0, A=A[torch.triu(torch.ones_like(A, dtype=torch.bool))].tolist())
[18]:
# Insert ID into the existing lattice
# This will replace the target marker
error = ring.clone()
error.flatten()
error.insert(ID, 'MLL_S01', position=0.0)
error.splice()
# Describe
error.describe
[18]:
{'BPM': 168,
'Drift': 732,
'Dipole': 156,
'Quadrupole': 360,
'Corrector': 24,
'Matrix': 1,
'Marker': 11}
[19]:
# Compute tunes (fractional part)
nux_id, nuy_id = tune(error, [], matched=True, limit=1)
[20]:
# Compute dispersion
orbit = torch.tensor(4*[0.0], dtype=dtype)
etaqx_id, etapx_id, etaqy_id, etapy_id = dispersion(error, orbit, [], limit=1)
[21]:
# Compute twiss parameters
ax_id, bx_id, ay_id, by_id = twiss(error, [], matched=True, advance=True, full=False).T
[22]:
# Compute phase advances
mux_id, muy_id = advance(error, [], alignment=False, matched=True).T
[23]:
# Compute coupling
c_id = coupling(error, [])
[24]:
# Tune shifts
print((nux - nux_id))
print((nuy - nuy_id))
tensor(0.0072, dtype=torch.float64)
tensor(-0.0041, dtype=torch.float64)
[25]:
# Coupling (minimal tune distance)
print(c)
print(c_id)
tensor(0., dtype=torch.float64)
tensor(0.0001, dtype=torch.float64)
[26]:
# Define parametric observable vector
def global_observable(knobs):
kf, kd = knobs
kn = torch.stack(len(QF)*[kf] + len(QD)*[kd])
return tune(error, [kn], ('kn', None, QF + QD, None), matched=True, limit=1)
def observable_twiss(kn, ks):
return twiss(error, [kn, ks], ('kn', None, nkn, None), ('ks', None, nks, None), matched=True, advance=True, full=False, convert=False)
def observable_dispersion(kn, ks):
orbit = torch.tensor(4*[0.0], dtype=dtype)
etax, _, etay, _ = dispersion(error,
orbit,
[kn, ks],
('kn', None, nkn, None),
('ks', None, nks, None))
return torch.stack([etax, etay]).T
def observable(knobs):
kn, ks = torch.split(knobs, [3, 2])
kn = Sn @ kn
ks = Ss @ ks
betas = observable_twiss(kn, ks)
etas = observable_dispersion(kn, ks)
return torch.cat([betas.flatten(), etas.flatten()])
[27]:
# Check the residual vector norm
global_knobs = torch.tensor(2*[0.0], dtype=dtype)
knobs = torch.tensor((3 + 2)*[0.0], dtype=dtype)
print(((global_observable(global_knobs) - global_target)**2).sum())
print(((observable(knobs) - target)**2).sum())
tensor(6.9010e-05, dtype=torch.float64)
tensor(17.4004, dtype=torch.float64)
[28]:
# Optimization loop (local)
# Responce matrix (jacobian)
M = matrix.clone()
# Weighting covariance (sensitivity) matrix
epsilon = 1.0E-9
C = M @ M.T
C = C + epsilon*torch.eye(len(C), dtype=dtype)
# Cholesky decomposition
L = torch.linalg.cholesky(C)
# Whiten response
M = torch.linalg.solve_triangular(L, M, upper=False)
# Additional weights
# Can be used to extra weight selected observables, e.g. tunes
weights = torch.ones(len(M), dtype=dtype)
weights = weights.sqrt()
# Whiten response with additional weights
M = M*weights.unsqueeze(1)
# Iterative correction
lr = 0.75
# Initial value
knobs = torch.tensor((3 + 2)*[0.0], dtype=dtype)
# Correction loop
for _ in range(8):
value = observable(knobs)
residual = target - value
residual = torch.linalg.solve_triangular(L, residual.unsqueeze(-1), upper=False).squeeze(-1)
residual = residual*weights
delta = torch.linalg.lstsq(M, residual, driver="gels").solution
knobs += lr*delta
print(((value - target)**2).sum())
print()
tensor(17.4004, dtype=torch.float64)
tensor(1.1182, dtype=torch.float64)
tensor(0.0923, dtype=torch.float64)
tensor(0.0272, dtype=torch.float64)
tensor(0.0231, dtype=torch.float64)
tensor(0.0229, dtype=torch.float64)
tensor(0.0229, dtype=torch.float64)
tensor(0.0229, dtype=torch.float64)
[29]:
# Apply final corrections
kn, ks = torch.split(knobs, [3, 2])
kn = Sn @ kn
ks = Ss @ ks
error.flatten()
for name, knob in zip(nkn, kn):
error[name].kn = (error[name].kn + knob).item()
for name, knob in zip(nks, ks):
error[name].ks = (error[name].ks + knob).item()
error.splice()
[30]:
# Optimization loop (global)
# Responce matrix (jacobian)
M = global_matrix.clone()
# Weighting covariance (sensitivity) matrix
epsilon = 1.0E-9
C = M @ M.T
C = C + epsilon*torch.eye(len(C), dtype=dtype)
# Cholesky decomposition
L = torch.linalg.cholesky(C)
# Whiten response
M = torch.linalg.solve_triangular(L, M, upper=False)
# Additional weights
# Can be used to extra weight selected observables, e.g. tunes
weights = torch.ones(len(M), dtype=dtype)
weights = weights.sqrt()
# Whiten response with additional weights
M = M*weights.unsqueeze(1)
# Iterative correction
lr = 0.75
# Initial value
global_knobs = torch.tensor(2*[0.0], dtype=dtype)
# Correction loop
for _ in range(4):
value = global_observable(global_knobs)
residual = global_target - value
residual = torch.linalg.solve_triangular(L, residual.unsqueeze(-1), upper=False).squeeze(-1)
residual = residual*weights
delta = torch.linalg.lstsq(M, residual, driver="gels").solution
global_knobs += lr*delta
print(((value - global_target)**2).sum())
print()
tensor(1.9252e-05, dtype=torch.float64)
tensor(1.2772e-06, dtype=torch.float64)
tensor(8.9138e-08, dtype=torch.float64)
tensor(6.3411e-09, dtype=torch.float64)
[31]:
# Apply final corrections
kd, kf = global_knobs
error.flatten()
for name in QF:
error[name].kn = (error[name].kn + kd).item()
for name in QD:
error[name].kn = (error[name].kn + kf).item()
error.splice()
[32]:
# Compute tunes (fractional part)
nux_result, nuy_result = tune(error, [], matched=True, limit=1)
[33]:
# Compute dispersion
orbit = torch.tensor(4*[0.0], dtype=dtype)
etaqx_result, etapx_result, etaqy_result, etapy_result = dispersion(error, orbit, [], limit=1)
[34]:
# Compute twiss parameters
ax_result, bx_result, ay_result, by_result = twiss(error, [], matched=True, advance=True, full=False).T
[35]:
# Compute phase advances
mux_result, muy_result = advance(error, [], alignment=False, matched=True).T
[36]:
# Compute coupling
c_result = coupling(error, [])
[37]:
# Tune shifts
print((nux - nux_id).abs())
print((nuy - nuy_id).abs())
print()
print((nux - nux_result).abs())
print((nuy - nuy_result).abs())
print()
tensor(0.0072, dtype=torch.float64)
tensor(0.0041, dtype=torch.float64)
tensor(7.6696e-06, dtype=torch.float64)
tensor(1.9920e-05, dtype=torch.float64)
[38]:
# Coupling (minimal tune distance)
print(c)
print(c_id)
print(c_result)
tensor(0., dtype=torch.float64)
tensor(0.0001, dtype=torch.float64)
tensor(2.6848e-06, dtype=torch.float64)
[39]:
# Beta-beating and dispersion
bx_ref_bb = 100.0*(bx - bx_id) / bx
by_ref_bb = 100.0*(by - by_id) / by
bx_res_bb = 100.0*(bx - bx_result)/ bx
by_res_bb = 100.0*(by - by_result)/ by
def rms(x):
return (x**2).mean().sqrt()
rms_x_ref = rms(bx_ref_bb).item()
ptp_x_ref = (bx_ref_bb.max() - bx_ref_bb.min()).item()
rms_y_ref = rms(by_ref_bb).item()
ptp_y_ref = (by_ref_bb.max() - by_ref_bb.min()).item()
rms_x_res = rms(bx_res_bb).item()
ptp_x_res = (bx_res_bb.max() - bx_res_bb.min()).item()
rms_y_res = rms(by_res_bb).item()
ptp_y_res = (by_res_bb.max() - by_res_bb.min()).item()
s = ring.locations().cpu().numpy()
bx_ref_np = bx_ref_bb.cpu().numpy()
by_ref_np = by_ref_bb.cpu().numpy()
bx_res_np = bx_res_bb.cpu().numpy()
by_res_np = by_res_bb.cpu().numpy()
etax_ref = etaqx - etaqx_id
etay_ref = etaqy - etaqy_id
etax_res = etaqx - etaqx_result
etay_res = etaqy - etaqy_result
rms_etax_ref = rms(etax_ref).item()
ptp_etax_ref = (etax_ref.max() - etax_ref.min()).item()
rms_etay_ref = rms(etay_ref).item()
ptp_etay_ref = (etay_ref.max() - etay_ref.min()).item()
rms_etax_res = rms(etax_res).item()
ptp_etax_res = (etax_res.max() - etax_res.min()).item()
rms_etay_res = rms(etay_res).item()
ptp_etay_res = (etay_res.max() - etay_res.min()).item()
etax_ref_np = etax_ref.cpu().numpy()
etay_ref_np = etay_ref.cpu().numpy()
etax_res_np = etax_res.cpu().numpy()
etay_res_np = etay_res.cpu().numpy()
fig, (ax, ay) = plt.subplots(
2, 1, figsize=(16, 10),
sharex=True,
gridspec_kw={'hspace': 0.3}
)
ax.errorbar(s, bx_ref_np, fmt='-', marker='x', color='blue', alpha=0.75, lw=2.0, label=r'initial, $\beta_x$')
ax.errorbar(s, by_ref_np, fmt='-', marker='x', color='red', alpha=0.75, lw=2.0, label=r'initial, $\beta_y$')
ax.errorbar(s, bx_res_np, fmt='-', marker='o', color='blue', alpha=0.75, lw=2.0, label=r'final, $\beta_x$')
ax.errorbar(s, by_res_np, fmt='-', marker='o', color='red', alpha=0.75, lw=2.0, label=r'final, $\beta_y$')
ax.set_xlabel('s [m]', fontsize=18)
ax.set_ylabel(r'$\Delta \beta / \beta$ [\%]', fontsize=18)
ax.tick_params(width=2, labelsize=16)
ax.tick_params(axis='x', length=8, direction='in')
ax.tick_params(axis='y', length=8, direction='in')
title = (
rf'RMS$_x$={rms_x_ref:05.2f}\% \quad RMS$_y$={rms_y_ref:05.2f}\% \quad '
rf'PTP$_x$={ptp_x_ref:05.2f}\% \quad PTP$_y$={ptp_y_ref:05.2f}\% \quad '
rf'$\Delta \nu_x$={(lambda x: '-' if x < 0 else '~')(nux - nux_id)}{(nux - nux_id).abs().item():.4f} \quad $\Delta \nu_y$={(lambda x: '-' if x < 0 else '~')(nuy - nuy_id)}{(nuy - nuy_id).abs().item():.4f}'
rf'\quad C={c_id.item():.6f}'
)
ax.text(0.0, 1.10, title, transform=ax.transAxes, ha='left', va='bottom', fontsize=16, fontfamily='monospace')
title = (
rf'RMS$_x$={rms_x_res:05.2f}\% \quad RMS$_y$={rms_y_res:05.2f}\% \quad '
rf'PTP$_x$={ptp_x_res:05.2f}\% \quad PTP$_y$={ptp_y_res:05.2f}\% \quad '
rf'$\Delta \nu_x$={(lambda x: '-' if x < 0 else '~')(nux - nux_result)}{(nux - nux_result).abs().item():.4f} \quad $\Delta \nu_y$={(lambda x: '-' if x < 0 else '~')(nuy - nuy_result)}{(nuy - nuy_result).abs().item():.4f}'
rf'\quad C={c_result.item():.6f}'
)
ax.text(0.0, 1.025, title, transform=ax.transAxes, ha='left', va='bottom', fontsize=16, fontfamily='monospace')
ax.legend(loc='upper right', frameon=False, fontsize=14, ncol=4)
ax.set_ylim(-10, 10)
ay.errorbar(s, etax_ref_np, fmt='-', marker='x', color='blue', alpha=0.75, lw=2.0, label=r'initial, $\eta_x$')
ay.errorbar(s, etay_ref_np, fmt='-', marker='x', color='red', alpha=0.75, lw=2.0, label=r'initial, $\eta_y$')
ay.errorbar(s, etax_res_np, fmt='-', marker='o', color='blue',alpha=0.75, lw=2.0, label=r'final, $\eta_x$')
ay.errorbar(s, etay_res_np, fmt='-', marker='o', color='red', alpha=0.75, lw=2.0, label=r'final, $\eta_y$')
ay.set_xlabel('s [m]', fontsize=18)
ay.set_ylabel(r'$\Delta \eta$ [m]', fontsize=18)
ay.tick_params(width=2, labelsize=16)
ay.tick_params(axis='x', length=8, direction='in')
ay.tick_params(axis='y', length=8, direction='in')
title = (
rf'RMS$_x$={rms_etax_ref:.4E} m \quad RMS$_y$={rms_etay_ref:.4E} m \quad '
rf'PTP$_x$={ptp_etax_ref:.4E} m \quad PTP$_y$={ptp_etay_ref:.4E} m \quad '
)
ay.text(0.0, 1.125, title, transform=ay.transAxes, ha='left', va='bottom', fontsize=16, fontfamily='monospace')
title = (
rf'RMS$_x$={rms_etax_res:.4E} m \quad RMS$_y$={rms_etay_res:.4E} m \quad '
rf'PTP$_x$={ptp_etax_res:.4E} m \quad PTP$_y$={ptp_etay_res:.4E} m \quad '
)
ay.text(0.0, 1.05, title, transform=ay.transAxes, ha='left', va='bottom', fontsize=16, fontfamily='monospace')
ay.set_ylim(-1E-4, +1E-4)
plt.setp(ax.spines.values(), linewidth=2.0)
plt.setp(ay.spines.values(), linewidth=2.0)
plt.show()
[40]:
# Save corrections
kla = knobs.clone()
kga = global_knobs.clone()
[41]:
# 2nd ID setting
[42]:
# Define ID model
A = torch.tensor([[-7.09028e-02, -7.46370e-09, 2.52021e-09, 2.87339e-03],
[-7.46371e-09, -9.05582e-02, 2.78757e-03, 2.67785e-08],
[ 2.52021e-09, 2.78757e-03, 9.68052e-02, 2.76621e-08],
[ 2.87339e-03, 2.67785e-08, 2.76621e-08, 1.48760e-01]], dtype=dtype)
ID = Matrix('ID', length=0.0, A=A[torch.triu(torch.ones_like(A, dtype=torch.bool))].tolist())
[43]:
# Insert ID into the existing lattice
# This will replace the target marker
error = ring.clone()
error.flatten()
error.insert(ID, 'MLL_S01', position=0.0)
error.splice()
# Describe
error.describe
[43]:
{'BPM': 168,
'Drift': 732,
'Dipole': 156,
'Quadrupole': 360,
'Corrector': 24,
'Matrix': 1,
'Marker': 11}
[44]:
# Compute tunes (fractional part)
nux_id, nuy_id = tune(error, [], matched=True, limit=1)
[45]:
# Compute dispersion
orbit = torch.tensor(4*[0.0], dtype=dtype)
etaqx_id, etapx_id, etaqy_id, etapy_id = dispersion(error, orbit, [], limit=1)
[46]:
# Compute twiss parameters
ax_id, bx_id, ay_id, by_id = twiss(error, [], matched=True, advance=True, full=False).T
[47]:
# Compute phase advances
mux_id, muy_id = advance(error, [], alignment=False, matched=True).T
[48]:
# Compute coupling
c_id = coupling(error, [])
[49]:
# Tune shifts
print((nux - nux_id))
print((nuy - nuy_id))
tensor(0.0522, dtype=torch.float64)
tensor(-0.0198, dtype=torch.float64)
[50]:
# Coupling (minimal tune distance)
print(c)
print(c_id)
tensor(0., dtype=torch.float64)
tensor(0.0009, dtype=torch.float64)
[51]:
# Define parametric observable vector
def global_observable(knobs):
kf, kd = knobs
kn = torch.stack(len(QF)*[kf] + len(QD)*[kd])
return tune(error, [kn], ('kn', None, QF + QD, None), matched=True, limit=1)
def observable_twiss(kn, ks):
return twiss(error, [kn, ks], ('kn', None, nkn, None), ('ks', None, nks, None), matched=True, advance=True, full=False, convert=False)
def observable_dispersion(kn, ks):
orbit = torch.tensor(4*[0.0], dtype=dtype)
etax, _, etay, _ = dispersion(error,
orbit,
[kn, ks],
('kn', None, nkn, None),
('ks', None, nks, None))
return torch.stack([etax, etay]).T
def observable(knobs):
kn, ks = torch.split(knobs, [3, 2])
kn = Sn @ kn
ks = Ss @ ks
betas = observable_twiss(kn, ks)
etas = observable_dispersion(kn, ks)
return torch.cat([betas.flatten(), etas.flatten()])
[52]:
# Check the residual vector norm
global_knobs = torch.tensor(2*[0.0], dtype=dtype)
knobs = torch.tensor((3 + 2)*[0.0], dtype=dtype)
print(((global_observable(global_knobs) - global_target)**2).sum())
print(((observable(knobs) - target)**2).sum())
tensor(0.0031, dtype=torch.float64)
tensor(880.7403, dtype=torch.float64)
[53]:
# Optimization loop (local)
# Responce matrix (jacobian)
M = matrix.clone()
# Weighting covariance (sensitivity) matrix
epsilon = 1.0E-9
C = M @ M.T
C = C + epsilon*torch.eye(len(C), dtype=dtype)
# Cholesky decomposition
L = torch.linalg.cholesky(C)
# Whiten response
M = torch.linalg.solve_triangular(L, M, upper=False)
# Additional weights
# Can be used to extra weight selected observables, e.g. tunes
weights = torch.ones(len(M), dtype=dtype)
weights = weights.sqrt()
# Whiten response with additional weights
M = M*weights.unsqueeze(1)
# Iterative correction
lr = 0.75
# Initial value
knobs = torch.tensor((3 + 2)*[0.0], dtype=dtype)
# Correction loop
for _ in range(8):
value = observable(knobs)
residual = target - value
residual = torch.linalg.solve_triangular(L, residual.unsqueeze(-1), upper=False).squeeze(-1)
residual = residual*weights
delta = torch.linalg.lstsq(M, residual, driver="gels").solution
knobs += lr*delta
print(((value - target)**2).sum())
print()
tensor(880.7403, dtype=torch.float64)
tensor(34.1142, dtype=torch.float64)
tensor(4.5410, dtype=torch.float64)
tensor(1.1710, dtype=torch.float64)
tensor(0.9594, dtype=torch.float64)
tensor(0.9483, dtype=torch.float64)
tensor(0.9477, dtype=torch.float64)
tensor(0.9477, dtype=torch.float64)
[54]:
# Apply final corrections
kn, ks = torch.split(knobs, [3, 2])
kn = Sn @ kn
ks = Ss @ ks
error.flatten()
for name, knob in zip(nkn, kn):
error[name].kn = (error[name].kn + knob).item()
for name, knob in zip(nks, ks):
error[name].ks = (error[name].ks + knob).item()
error.splice()
[55]:
# Optimization loop (global)
# Responce matrix (jacobian)
M = global_matrix.clone()
# Weighting covariance (sensitivity) matrix
epsilon = 1.0E-9
C = M @ M.T
C = C + epsilon*torch.eye(len(C), dtype=dtype)
# Cholesky decomposition
L = torch.linalg.cholesky(C)
# Whiten response
M = torch.linalg.solve_triangular(L, M, upper=False)
# Additional weights
# Can be used to extra weight selected observables, e.g. tunes
weights = torch.ones(len(M), dtype=dtype)
weights = weights.sqrt()
# Whiten response with additional weights
M = M*weights.unsqueeze(1)
# Iterative correction
lr = 0.75
# Initial value
global_knobs = torch.tensor(2*[0.0], dtype=dtype)
# Correction loop
for _ in range(4):
value = global_observable(global_knobs)
residual = global_target - value
residual = torch.linalg.solve_triangular(L, residual.unsqueeze(-1), upper=False).squeeze(-1)
residual = residual*weights
delta = torch.linalg.lstsq(M, residual, driver="gels").solution
global_knobs += lr*delta
print(((value - global_target)**2).sum())
print()
tensor(0.0003, dtype=torch.float64)
tensor(2.8347e-05, dtype=torch.float64)
tensor(3.1027e-06, dtype=torch.float64)
tensor(3.7248e-07, dtype=torch.float64)
[56]:
# Apply final corrections
kd, kf = global_knobs
error.flatten()
for name in QF:
error[name].kn = (error[name].kn + kd).item()
for name in QD:
error[name].kn = (error[name].kn + kf).item()
error.splice()
[57]:
# Compute tunes (fractional part)
nux_result, nuy_result = tune(error, [], matched=True, limit=1)
[58]:
# Compute dispersion
orbit = torch.tensor(4*[0.0], dtype=dtype)
etaqx_result, etapx_result, etaqy_result, etapy_result = dispersion(error, orbit, [], limit=1)
[59]:
# Compute twiss parameters
ax_result, bx_result, ay_result, by_result = twiss(error, [], matched=True, advance=True, full=False).T
[60]:
# Compute phase advances
mux_result, muy_result = advance(error, [], alignment=False, matched=True).T
[61]:
# Compute coupling
c_result = coupling(error, [])
[62]:
# Tune shifts
print((nux - nux_id).abs())
print((nuy - nuy_id).abs())
print()
print((nux - nux_result).abs())
print((nuy - nuy_result).abs())
print()
tensor(0.0522, dtype=torch.float64)
tensor(0.0198, dtype=torch.float64)
tensor(0.0001, dtype=torch.float64)
tensor(0.0002, dtype=torch.float64)
[63]:
# Coupling (minimal tune distance)
print(c)
print(c_id)
print(c_result)
tensor(0., dtype=torch.float64)
tensor(0.0009, dtype=torch.float64)
tensor(1.0800e-05, dtype=torch.float64)
[64]:
# Beta-beating and dispersion
bx_ref_bb = 100.0*(bx - bx_id) / bx
by_ref_bb = 100.0*(by - by_id) / by
bx_res_bb = 100.0*(bx - bx_result)/ bx
by_res_bb = 100.0*(by - by_result)/ by
def rms(x):
return (x**2).mean().sqrt()
rms_x_ref = rms(bx_ref_bb).item()
ptp_x_ref = (bx_ref_bb.max() - bx_ref_bb.min()).item()
rms_y_ref = rms(by_ref_bb).item()
ptp_y_ref = (by_ref_bb.max() - by_ref_bb.min()).item()
rms_x_res = rms(bx_res_bb).item()
ptp_x_res = (bx_res_bb.max() - bx_res_bb.min()).item()
rms_y_res = rms(by_res_bb).item()
ptp_y_res = (by_res_bb.max() - by_res_bb.min()).item()
s = ring.locations().cpu().numpy()
bx_ref_np = bx_ref_bb.cpu().numpy()
by_ref_np = by_ref_bb.cpu().numpy()
bx_res_np = bx_res_bb.cpu().numpy()
by_res_np = by_res_bb.cpu().numpy()
etax_ref = etaqx - etaqx_id
etay_ref = etaqy - etaqy_id
etax_res = etaqx - etaqx_result
etay_res = etaqy - etaqy_result
rms_etax_ref = rms(etax_ref).item()
ptp_etax_ref = (etax_ref.max() - etax_ref.min()).item()
rms_etay_ref = rms(etay_ref).item()
ptp_etay_ref = (etay_ref.max() - etay_ref.min()).item()
rms_etax_res = rms(etax_res).item()
ptp_etax_res = (etax_res.max() - etax_res.min()).item()
rms_etay_res = rms(etay_res).item()
ptp_etay_res = (etay_res.max() - etay_res.min()).item()
etax_ref_np = etax_ref.cpu().numpy()
etay_ref_np = etay_ref.cpu().numpy()
etax_res_np = etax_res.cpu().numpy()
etay_res_np = etay_res.cpu().numpy()
fig, (ax, ay) = plt.subplots(
2, 1, figsize=(16, 10),
sharex=True,
gridspec_kw={'hspace': 0.3}
)
ax.errorbar(s, bx_ref_np, fmt='-', marker='x', color='blue', alpha=0.75, lw=2.0, label=r'initial, $\beta_x$')
ax.errorbar(s, by_ref_np, fmt='-', marker='x', color='red', alpha=0.75, lw=2.0, label=r'initial, $\beta_y$')
ax.errorbar(s, bx_res_np, fmt='-', marker='o', color='blue', alpha=0.75, lw=2.0, label=r'final, $\beta_x$')
ax.errorbar(s, by_res_np, fmt='-', marker='o', color='red', alpha=0.75, lw=2.0, label=r'final, $\beta_y$')
ax.set_xlabel('s [m]', fontsize=18)
ax.set_ylabel(r'$\Delta \beta / \beta$ [\%]', fontsize=18)
ax.tick_params(width=2, labelsize=16)
ax.tick_params(axis='x', length=8, direction='in')
ax.tick_params(axis='y', length=8, direction='in')
title = (
rf'RMS$_x$={rms_x_ref:05.2f}\% \quad RMS$_y$={rms_y_ref:05.2f}\% \quad '
rf'PTP$_x$={ptp_x_ref:05.2f}\% \quad PTP$_y$={ptp_y_ref:05.2f}\% \quad '
rf'$\Delta \nu_x$={(lambda x: '-' if x < 0 else '~')(nux - nux_id)}{(nux - nux_id).abs().item():.4f} \quad $\Delta \nu_y$={(lambda x: '-' if x < 0 else '~')(nuy - nuy_id)}{(nuy - nuy_id).abs().item():.4f}'
rf'\quad C={c_id.item():.6f}'
)
ax.text(0.0, 1.10, title, transform=ax.transAxes, ha='left', va='bottom', fontsize=16, fontfamily='monospace')
title = (
rf'RMS$_x$={rms_x_res:05.2f}\% \quad RMS$_y$={rms_y_res:05.2f}\% \quad '
rf'PTP$_x$={ptp_x_res:05.2f}\% \quad PTP$_y$={ptp_y_res:05.2f}\% \quad '
rf'$\Delta \nu_x$={(lambda x: '-' if x < 0 else '~')(nux - nux_result)}{(nux - nux_result).abs().item():.4f} \quad $\Delta \nu_y$={(lambda x: '-' if x < 0 else '~')(nuy - nuy_result)}{(nuy - nuy_result).abs().item():.4f}'
rf'\quad C={c_result.item():.6f}'
)
ax.text(0.0, 1.025, title, transform=ax.transAxes, ha='left', va='bottom', fontsize=16, fontfamily='monospace')
ax.legend(loc='upper right', frameon=False, fontsize=14, ncol=4)
ax.set_ylim(-50, 50)
ay.errorbar(s, etax_ref_np, fmt='-', marker='x', color='blue', alpha=0.75, lw=2.0, label=r'initial, $\eta_x$')
ay.errorbar(s, etay_ref_np, fmt='-', marker='x', color='red', alpha=0.75, lw=2.0, label=r'initial, $\eta_y$')
ay.errorbar(s, etax_res_np, fmt='-', marker='o', color='blue',alpha=0.75, lw=2.0, label=r'final, $\eta_x$')
ay.errorbar(s, etay_res_np, fmt='-', marker='o', color='red', alpha=0.75, lw=2.0, label=r'final, $\eta_y$')
ay.set_xlabel('s [m]', fontsize=18)
ay.set_ylabel(r'$\Delta \eta$ [m]', fontsize=18)
ay.tick_params(width=2, labelsize=16)
ay.tick_params(axis='x', length=8, direction='in')
ay.tick_params(axis='y', length=8, direction='in')
title = (
rf'RMS$_x$={rms_etax_ref:.4E} m \quad RMS$_y$={rms_etay_ref:.4E} m \quad '
rf'PTP$_x$={ptp_etax_ref:.4E} m \quad PTP$_y$={ptp_etay_ref:.4E} m \quad '
)
ay.text(0.0, 1.125, title, transform=ay.transAxes, ha='left', va='bottom', fontsize=16, fontfamily='monospace')
title = (
rf'RMS$_x$={rms_etax_res:.4E} m \quad RMS$_y$={rms_etay_res:.4E} m \quad '
rf'PTP$_x$={ptp_etax_res:.4E} m \quad PTP$_y$={ptp_etay_res:.4E} m \quad '
)
ay.text(0.0, 1.05, title, transform=ay.transAxes, ha='left', va='bottom', fontsize=16, fontfamily='monospace')
ay.set_ylim(-5E-4, +5E-4)
plt.setp(ax.spines.values(), linewidth=2.0)
plt.setp(ay.spines.values(), linewidth=2.0)
plt.show()
[65]:
# Save corrections
klb = knobs.clone()
kgb = global_knobs.clone()
[66]:
# Model feed forward (change of ID settings)
[67]:
# Define ID model
A = torch.tensor([[-9.54791e-03, -3.26154e-11, 1.44707e-09, 5.43034e-04],
[-3.26149e-11, -1.29258e-02, 6.98380e-04, -1.05053e-09],
[ 1.44707e-09, 6.98380e-04, 2.07735e-02, -2.55925e-09],
[ 5.43034e-04, -1.05053e-09, -2.55925e-09, 2.90246e-02]], dtype=dtype)
ID = Matrix('ID', length=0.0, A=A[torch.triu(torch.ones_like(A, dtype=torch.bool))].tolist())
[68]:
# Insert ID into the existing lattice
# This will replace the target marker
error = ring.clone()
error.flatten()
error.insert(ID, 'MLL_S01', position=0.0)
error.splice()
# Describe
error.describe
[68]:
{'BPM': 168,
'Drift': 732,
'Dipole': 156,
'Quadrupole': 360,
'Corrector': 24,
'Matrix': 1,
'Marker': 11}
[69]:
# Compute tunes (fractional part)
nux_id, nuy_id = tune(error, [], matched=True, limit=1)
[70]:
# Compute dispersion
orbit = torch.tensor(4*[0.0], dtype=dtype)
etaqx_id, etapx_id, etaqy_id, etapy_id = dispersion(error, orbit, [], limit=1)
[71]:
# Compute twiss parameters
ax_id, bx_id, ay_id, by_id = twiss(error, [], matched=True, advance=True, full=False).T
[72]:
# Compute phase advances
mux_id, muy_id = advance(error, [], alignment=False, matched=True).T
[73]:
# Compute coupling
c_id = coupling(error, [])
[74]:
# Tune shifts
print((nux - nux_id))
print((nuy - nuy_id))
tensor(0.0072, dtype=torch.float64)
tensor(-0.0041, dtype=torch.float64)
[75]:
# Coupling (minimal tune distance)
print(c)
print(c_id)
tensor(0., dtype=torch.float64)
tensor(0.0001, dtype=torch.float64)
[76]:
# Apply final corrections (local)
kn, ks = torch.split(kla, [3, 2])
kn = Sn @ kn
ks = Ss @ ks
error.flatten()
for name, knob in zip(nkn, kn):
error[name].kn = (error[name].kn + knob).item()
for name, knob in zip(nks, ks):
error[name].ks = (error[name].ks + knob).item()
error.splice()
[77]:
# Apply final corrections (global)
kd, kf = kga
error.flatten()
for name in QF:
error[name].kn = (error[name].kn + kd).item()
for name in QD:
error[name].kn = (error[name].kn + kf).item()
error.splice()
[78]:
# Compute tunes (fractional part)
nux_result, nuy_result = tune(error, [], matched=True, limit=1)
[79]:
# Compute dispersion
orbit = torch.tensor(4*[0.0], dtype=dtype)
etaqx_result, etapx_result, etaqy_result, etapy_result = dispersion(error, orbit, [], limit=1)
[80]:
# Compute twiss parameters
ax_result, bx_result, ay_result, by_result = twiss(error, [], matched=True, advance=True, full=False).T
[81]:
# Compute phase advances
mux_result, muy_result = advance(error, [], alignment=False, matched=True).T
[82]:
# Compute coupling
c_result = coupling(error, [])
[83]:
# Tune shifts
print((nux - nux_id).abs())
print((nuy - nuy_id).abs())
print()
print((nux - nux_result).abs())
print((nuy - nuy_result).abs())
print()
tensor(0.0072, dtype=torch.float64)
tensor(0.0041, dtype=torch.float64)
tensor(7.6696e-06, dtype=torch.float64)
tensor(1.9920e-05, dtype=torch.float64)
[84]:
# Coupling (minimal tune distance)
print(c)
print(c_id)
print(c_result)
tensor(0., dtype=torch.float64)
tensor(0.0001, dtype=torch.float64)
tensor(2.6848e-06, dtype=torch.float64)
[85]:
# Beta-beating and dispersion
bx_ref_bb = 100.0*(bx - bx_id) / bx
by_ref_bb = 100.0*(by - by_id) / by
bx_res_bb = 100.0*(bx - bx_result)/ bx
by_res_bb = 100.0*(by - by_result)/ by
def rms(x):
return (x**2).mean().sqrt()
rms_x_ref = rms(bx_ref_bb).item()
ptp_x_ref = (bx_ref_bb.max() - bx_ref_bb.min()).item()
rms_y_ref = rms(by_ref_bb).item()
ptp_y_ref = (by_ref_bb.max() - by_ref_bb.min()).item()
rms_x_res = rms(bx_res_bb).item()
ptp_x_res = (bx_res_bb.max() - bx_res_bb.min()).item()
rms_y_res = rms(by_res_bb).item()
ptp_y_res = (by_res_bb.max() - by_res_bb.min()).item()
s = ring.locations().cpu().numpy()
bx_ref_np = bx_ref_bb.cpu().numpy()
by_ref_np = by_ref_bb.cpu().numpy()
bx_res_np = bx_res_bb.cpu().numpy()
by_res_np = by_res_bb.cpu().numpy()
etax_ref = etaqx - etaqx_id
etay_ref = etaqy - etaqy_id
etax_res = etaqx - etaqx_result
etay_res = etaqy - etaqy_result
rms_etax_ref = rms(etax_ref).item()
ptp_etax_ref = (etax_ref.max() - etax_ref.min()).item()
rms_etay_ref = rms(etay_ref).item()
ptp_etay_ref = (etay_ref.max() - etay_ref.min()).item()
rms_etax_res = rms(etax_res).item()
ptp_etax_res = (etax_res.max() - etax_res.min()).item()
rms_etay_res = rms(etay_res).item()
ptp_etay_res = (etay_res.max() - etay_res.min()).item()
etax_ref_np = etax_ref.cpu().numpy()
etay_ref_np = etay_ref.cpu().numpy()
etax_res_np = etax_res.cpu().numpy()
etay_res_np = etay_res.cpu().numpy()
fig, (ax, ay) = plt.subplots(
2, 1, figsize=(16, 10),
sharex=True,
gridspec_kw={'hspace': 0.3}
)
ax.errorbar(s, bx_ref_np, fmt='-', marker='x', color='blue', alpha=0.75, lw=2.0, label=r'initial, $\beta_x$')
ax.errorbar(s, by_ref_np, fmt='-', marker='x', color='red', alpha=0.75, lw=2.0, label=r'initial, $\beta_y$')
ax.errorbar(s, bx_res_np, fmt='-', marker='o', color='blue', alpha=0.75, lw=2.0, label=r'final, $\beta_x$')
ax.errorbar(s, by_res_np, fmt='-', marker='o', color='red', alpha=0.75, lw=2.0, label=r'final, $\beta_y$')
ax.set_xlabel('s [m]', fontsize=18)
ax.set_ylabel(r'$\Delta \beta / \beta$ [\%]', fontsize=18)
ax.tick_params(width=2, labelsize=16)
ax.tick_params(axis='x', length=8, direction='in')
ax.tick_params(axis='y', length=8, direction='in')
title = (
rf'RMS$_x$={rms_x_ref:05.2f}\% \quad RMS$_y$={rms_y_ref:05.2f}\% \quad '
rf'PTP$_x$={ptp_x_ref:05.2f}\% \quad PTP$_y$={ptp_y_ref:05.2f}\% \quad '
rf'$\Delta \nu_x$={(lambda x: '-' if x < 0 else '~')(nux - nux_id)}{(nux - nux_id).abs().item():.4f} \quad $\Delta \nu_y$={(lambda x: '-' if x < 0 else '~')(nuy - nuy_id)}{(nuy - nuy_id).abs().item():.4f}'
rf'\quad C={c_id.item():.6f}'
)
ax.text(0.0, 1.10, title, transform=ax.transAxes, ha='left', va='bottom', fontsize=16, fontfamily='monospace')
title = (
rf'RMS$_x$={rms_x_res:05.2f}\% \quad RMS$_y$={rms_y_res:05.2f}\% \quad '
rf'PTP$_x$={ptp_x_res:05.2f}\% \quad PTP$_y$={ptp_y_res:05.2f}\% \quad '
rf'$\Delta \nu_x$={(lambda x: '-' if x < 0 else '~')(nux - nux_result)}{(nux - nux_result).abs().item():.4f} \quad $\Delta \nu_y$={(lambda x: '-' if x < 0 else '~')(nuy - nuy_result)}{(nuy - nuy_result).abs().item():.4f}'
rf'\quad C={c_result.item():.6f}'
)
ax.text(0.0, 1.025, title, transform=ax.transAxes, ha='left', va='bottom', fontsize=16, fontfamily='monospace')
ax.legend(loc='upper right', frameon=False, fontsize=14, ncol=4)
ax.set_ylim(-20, 20)
ay.errorbar(s, etax_ref_np, fmt='-', marker='x', color='blue', alpha=0.75, lw=2.0, label=r'initial, $\eta_x$')
ay.errorbar(s, etay_ref_np, fmt='-', marker='x', color='red', alpha=0.75, lw=2.0, label=r'initial, $\eta_y$')
ay.errorbar(s, etax_res_np, fmt='-', marker='o', color='blue',alpha=0.75, lw=2.0, label=r'final, $\eta_x$')
ay.errorbar(s, etay_res_np, fmt='-', marker='o', color='red', alpha=0.75, lw=2.0, label=r'final, $\eta_y$')
ay.set_xlabel('s [m]', fontsize=18)
ay.set_ylabel(r'$\Delta \eta$ [m]', fontsize=18)
ay.tick_params(width=2, labelsize=16)
ay.tick_params(axis='x', length=8, direction='in')
ay.tick_params(axis='y', length=8, direction='in')
title = (
rf'RMS$_x$={rms_etax_ref:.4E} m \quad RMS$_y$={rms_etay_ref:.4E} m \quad '
rf'PTP$_x$={ptp_etax_ref:.4E} m \quad PTP$_y$={ptp_etay_ref:.4E} m \quad '
)
ay.text(0.0, 1.125, title, transform=ay.transAxes, ha='left', va='bottom', fontsize=16, fontfamily='monospace')
title = (
rf'RMS$_x$={rms_etax_res:.4E} m \quad RMS$_y$={rms_etay_res:.4E} m \quad '
rf'PTP$_x$={ptp_etax_res:.4E} m \quad PTP$_y$={ptp_etay_res:.4E} m \quad '
)
ay.text(0.0, 1.05, title, transform=ay.transAxes, ha='left', va='bottom', fontsize=16, fontfamily='monospace')
ay.set_ylim(-5E-4, +5E-4)
plt.setp(ax.spines.values(), linewidth=2.0)
plt.setp(ay.spines.values(), linewidth=2.0)
plt.show()
[86]:
# Define ID model
A = torch.tensor([[-7.09028e-02, -7.46370e-09, 2.52021e-09, 2.87339e-03],
[-7.46371e-09, -9.05582e-02, 2.78757e-03, 2.67785e-08],
[ 2.52021e-09, 2.78757e-03, 9.68052e-02, 2.76621e-08],
[ 2.87339e-03, 2.67785e-08, 2.76621e-08, 1.48760e-01]], dtype=dtype)
ID = Matrix('ID', length=0.0, A=A[torch.triu(torch.ones_like(A, dtype=torch.bool))].tolist())
[87]:
# Change ID settings
error.flatten()
error.replace('ID', ID)
error.splice()
[88]:
# Compute tunes (fractional part)
nux_id, nuy_id = tune(error, [], matched=True, limit=1)
[89]:
# Compute dispersion
orbit = torch.tensor(4*[0.0], dtype=dtype)
etaqx_id, etapx_id, etaqy_id, etapy_id = dispersion(error, orbit, [], limit=1)
[90]:
# Compute twiss parameters
ax_id, bx_id, ay_id, by_id = twiss(error, [], matched=True, advance=True, full=False).T
[91]:
# Compute phase advances
mux_id, muy_id = advance(error, [], alignment=False, matched=True).T
[92]:
# Compute coupling
c_id = coupling(error, [])
[93]:
# Tune shifts
print((nux - nux_id))
print((nuy - nuy_id))
tensor(0.0442, dtype=torch.float64)
tensor(-0.0158, dtype=torch.float64)
[94]:
# Coupling (minimal tune distance)
print(c)
print(c_id)
tensor(0., dtype=torch.float64)
tensor(0.0007, dtype=torch.float64)
[95]:
# Apply final corrections (local)
kn, ks = torch.split(klb - kla, [3, 2])
kn = Sn @ kn
ks = Ss @ ks
error.flatten()
for name, knob in zip(nkn, kn):
error[name].kn = (error[name].kn + knob).item()
for name, knob in zip(nks, ks):
error[name].ks = (error[name].ks + knob).item()
error.splice()
[96]:
# Apply final corrections (global)
kd, kf = kgb - kga
error.flatten()
for name in QF:
error[name].kn = (error[name].kn + kd).item()
for name in QD:
error[name].kn = (error[name].kn + kf).item()
error.splice()
[97]:
# Compute tunes (fractional part)
nux_result, nuy_result = tune(error, [], matched=True, limit=1)
[98]:
# Compute dispersion
orbit = torch.tensor(4*[0.0], dtype=dtype)
etaqx_result, etapx_result, etaqy_result, etapy_result = dispersion(error, orbit, [], limit=1)
[99]:
# Compute twiss parameters
ax_result, bx_result, ay_result, by_result = twiss(error, [], matched=True, advance=True, full=False).T
[100]:
# Compute phase advances
mux_result, muy_result = advance(error, [], alignment=False, matched=True).T
[101]:
# Compute coupling
c_result = coupling(error, [])
[102]:
# Tune shifts
print((nux - nux_id).abs())
print((nuy - nuy_id).abs())
print()
print((nux - nux_result).abs())
print((nuy - nuy_result).abs())
print()
tensor(0.0442, dtype=torch.float64)
tensor(0.0158, dtype=torch.float64)
tensor(0.0001, dtype=torch.float64)
tensor(0.0002, dtype=torch.float64)
[103]:
# Coupling (minimal tune distance)
print(c)
print(c_id)
print(c_result)
tensor(0., dtype=torch.float64)
tensor(0.0007, dtype=torch.float64)
tensor(1.0800e-05, dtype=torch.float64)
[104]:
# Beta-beating and dispersion
bx_ref_bb = 100.0*(bx - bx_id) / bx
by_ref_bb = 100.0*(by - by_id) / by
bx_res_bb = 100.0*(bx - bx_result)/ bx
by_res_bb = 100.0*(by - by_result)/ by
def rms(x):
return (x**2).mean().sqrt()
rms_x_ref = rms(bx_ref_bb).item()
ptp_x_ref = (bx_ref_bb.max() - bx_ref_bb.min()).item()
rms_y_ref = rms(by_ref_bb).item()
ptp_y_ref = (by_ref_bb.max() - by_ref_bb.min()).item()
rms_x_res = rms(bx_res_bb).item()
ptp_x_res = (bx_res_bb.max() - bx_res_bb.min()).item()
rms_y_res = rms(by_res_bb).item()
ptp_y_res = (by_res_bb.max() - by_res_bb.min()).item()
s = ring.locations().cpu().numpy()
bx_ref_np = bx_ref_bb.cpu().numpy()
by_ref_np = by_ref_bb.cpu().numpy()
bx_res_np = bx_res_bb.cpu().numpy()
by_res_np = by_res_bb.cpu().numpy()
etax_ref = etaqx - etaqx_id
etay_ref = etaqy - etaqy_id
etax_res = etaqx - etaqx_result
etay_res = etaqy - etaqy_result
rms_etax_ref = rms(etax_ref).item()
ptp_etax_ref = (etax_ref.max() - etax_ref.min()).item()
rms_etay_ref = rms(etay_ref).item()
ptp_etay_ref = (etay_ref.max() - etay_ref.min()).item()
rms_etax_res = rms(etax_res).item()
ptp_etax_res = (etax_res.max() - etax_res.min()).item()
rms_etay_res = rms(etay_res).item()
ptp_etay_res = (etay_res.max() - etay_res.min()).item()
etax_ref_np = etax_ref.cpu().numpy()
etay_ref_np = etay_ref.cpu().numpy()
etax_res_np = etax_res.cpu().numpy()
etay_res_np = etay_res.cpu().numpy()
fig, (ax, ay) = plt.subplots(
2, 1, figsize=(16, 10),
sharex=True,
gridspec_kw={'hspace': 0.3}
)
ax.errorbar(s, bx_ref_np, fmt='-', marker='x', color='blue', alpha=0.75, lw=2.0, label=r'initial, $\beta_x$')
ax.errorbar(s, by_ref_np, fmt='-', marker='x', color='red', alpha=0.75, lw=2.0, label=r'initial, $\beta_y$')
ax.errorbar(s, bx_res_np, fmt='-', marker='o', color='blue', alpha=0.75, lw=2.0, label=r'final, $\beta_x$')
ax.errorbar(s, by_res_np, fmt='-', marker='o', color='red', alpha=0.75, lw=2.0, label=r'final, $\beta_y$')
ax.set_xlabel('s [m]', fontsize=18)
ax.set_ylabel(r'$\Delta \beta / \beta$ [\%]', fontsize=18)
ax.tick_params(width=2, labelsize=16)
ax.tick_params(axis='x', length=8, direction='in')
ax.tick_params(axis='y', length=8, direction='in')
title = (
rf'RMS$_x$={rms_x_ref:05.2f}\% \quad RMS$_y$={rms_y_ref:05.2f}\% \quad '
rf'PTP$_x$={ptp_x_ref:05.2f}\% \quad PTP$_y$={ptp_y_ref:05.2f}\% \quad '
rf'$\Delta \nu_x$={(lambda x: '-' if x < 0 else '~')(nux - nux_id)}{(nux - nux_id).abs().item():.4f} \quad $\Delta \nu_y$={(lambda x: '-' if x < 0 else '~')(nuy - nuy_id)}{(nuy - nuy_id).abs().item():.4f}'
rf'\quad C={c_id.item():.6f}'
)
ax.text(0.0, 1.10, title, transform=ax.transAxes, ha='left', va='bottom', fontsize=16, fontfamily='monospace')
title = (
rf'RMS$_x$={rms_x_res:05.2f}\% \quad RMS$_y$={rms_y_res:05.2f}\% \quad '
rf'PTP$_x$={ptp_x_res:05.2f}\% \quad PTP$_y$={ptp_y_res:05.2f}\% \quad '
rf'$\Delta \nu_x$={(lambda x: '-' if x < 0 else '~')(nux - nux_result)}{(nux - nux_result).abs().item():.4f} \quad $\Delta \nu_y$={(lambda x: '-' if x < 0 else '~')(nuy - nuy_result)}{(nuy - nuy_result).abs().item():.4f}'
rf'\quad C={c_result.item():.6f}'
)
ax.text(0.0, 1.025, title, transform=ax.transAxes, ha='left', va='bottom', fontsize=16, fontfamily='monospace')
ax.legend(loc='upper right', frameon=False, fontsize=14, ncol=4)
ax.set_ylim(-50, 50)
ay.errorbar(s, etax_ref_np, fmt='-', marker='x', color='blue', alpha=0.75, lw=2.0, label=r'initial, $\eta_x$')
ay.errorbar(s, etay_ref_np, fmt='-', marker='x', color='red', alpha=0.75, lw=2.0, label=r'initial, $\eta_y$')
ay.errorbar(s, etax_res_np, fmt='-', marker='o', color='blue',alpha=0.75, lw=2.0, label=r'final, $\eta_x$')
ay.errorbar(s, etay_res_np, fmt='-', marker='o', color='red', alpha=0.75, lw=2.0, label=r'final, $\eta_y$')
ay.set_xlabel('s [m]', fontsize=18)
ay.set_ylabel(r'$\Delta \eta$ [m]', fontsize=18)
ay.tick_params(width=2, labelsize=16)
ay.tick_params(axis='x', length=8, direction='in')
ay.tick_params(axis='y', length=8, direction='in')
title = (
rf'RMS$_x$={rms_etax_ref:.4E} m \quad RMS$_y$={rms_etay_ref:.4E} m \quad '
rf'PTP$_x$={ptp_etax_ref:.4E} m \quad PTP$_y$={ptp_etay_ref:.4E} m \quad '
)
ay.text(0.0, 1.125, title, transform=ay.transAxes, ha='left', va='bottom', fontsize=16, fontfamily='monospace')
title = (
rf'RMS$_x$={rms_etax_res:.4E} m \quad RMS$_y$={rms_etay_res:.4E} m \quad '
rf'PTP$_x$={ptp_etax_res:.4E} m \quad PTP$_y$={ptp_etay_res:.4E} m \quad '
)
ay.text(0.0, 1.05, title, transform=ay.transAxes, ha='left', va='bottom', fontsize=16, fontfamily='monospace')
ay.set_ylim(-5E-4, +5E-4)
plt.setp(ax.spines.values(), linewidth=2.0)
plt.setp(ay.spines.values(), linewidth=2.0)
plt.show()
