Normal

Normalization matrix utils

twiss.normal.cs_normal(pars: torch.Tensor) → torch.Tensor[source]

Generate Courant-Snyder normalization matrix

Parameters:: pars (Tensor) – Courant-Snyder twiss parameters ax, bx, ay, by
Returns:: normalization matrix N, M = N R N^-1
Return type:: Tensor

Note

[ax, bx, ay, by] are CS twiss parameters

Examples

>>> import torch
>>> from twiss.matrix import is_symplectic
>>> pars = torch.tensor([0, 1, 0, 1], dtype=torch.float64)
>>> is_symplectic(cs_normal(pars))
True

twiss.normal.lb_normal(pars: torch.Tensor) → torch.Tensor[source]

Generate Lebedev-Bogacz normalization matrix

Parameters:: pars (Tensor) – Lebedev-Bogacz twiss parameters a1x, b1x, a2x, b2x, a1y, b1y, a2y, b2y, u, v1, v2
Returns:: normalization matrix N, M = N R N^-1
Return type:: Tensor

Note

[a1x, b1x, a2x, b2x, a1y, b1y, a2y, b2y, u, v1, v2] are LB twiss parameters [a1x, b1x, a2y, b2y] are ‘in-plane’ twiss parameters

Examples

>>> import torch
>>> from twiss.matrix import is_symplectic
>>> pars = torch.tensor([0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0], dtype=torch.float64)
>>> is_symplectic(lb_normal(pars))
True

twiss.normal.normal_to_wolski(n: torch.Tensor) → torch.Tensor[source]

Compute Wolski twiss matrices for a given normalization matrix

Parameters:: n (torch.Tensor, even-dimension, symplectic) – normalization matrix
Return type:: Tensor

Examples

>>> from math import pi
>>> import torch
>>> from twiss.matrix import  rotation
>>> m = rotation(2*pi*torch.tensor(0.88, dtype=torch.float64))
>>> t, n, w = twiss(m)
>>> torch.allclose(normal_to_wolski(n), w)
True

twiss.normal.parametric(pars: torch.Tensor) → torch.Tensor[source]

Generate ‘parametric’ 4x4 normalization matrix for given free elements

Parameters:: pars (Tensor) – free matrix elements n11, n33, n21, n43, n13, n31, n14, n41
Returns:: normalization matrix N M = N R N^-1
Return type:: Tensor

Note

Elements denoted with x are computed for given free elements using symplectic condition For n11 > 0 & n33 > 0, all matrix elements are not singular in uncoupled limit

n11 0 n13 n14 n21 x x x n31 x n33 0 n41 x n43 x

Examples

>>> import torch
>>> from twiss.matrix import is_symplectic
>>> pars = torch.tensor([1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])
>>> is_symplectic(parametric(pars))
True

twiss.normal.wolski_to_normal(w: torch.Tensor, *, epsilon: float = 1e-12) → torch.Tensor[source]

Compute normalization matrix for given Wolski twiss matrices

Parameters:

w (Tensor) – Wolski twiss matrices
epsilon (float, optional, default=1.0E-12) – tolerance epsilon

Return type:

Tensor

Note

Normalization matrix is computed using fake one-turn matrix with fixed tunes

Examples

>>> from math import pi
>>> import torch
>>> from twiss.matrix import  rotation
>>> m = rotation(2*pi*torch.tensor(0.88, dtype=torch.float64))
>>> t, n, w = twiss(m)
>>> torch.allclose(wolski_to_normal(w), n)
True