Invariant

Invariant utils

twiss.invariant.cs_invariant(twiss: torch.Tensor, orbit: torch.Tensor) → torch.Tensor[source]

Compute linear invariants for a given CS twiss and orbit

Parameters:

twiss (Tensor) – CS twiss ax, bx, ay, by
orbit (Tensor) – orbit

Returns:

[jx, jy] for each turn

Return type:

Tensor

Note

Orbit is assumed to have the form […, [qx_i, px_i, qy_i, py_i], …]

Examples

>>> from math import pi
>>> from twiss.matrix import rotation
>>> from twiss.wolski import twiss
>>> from twiss.convert import wolski_to_cs
>>> m = rotation(*2*pi*torch.tensor([0.12, 0.31], dtype=torch.float64))
>>> t, n, w = twiss(m)
>>> cs = wolski_to_cs(w)
>>> x = torch.tensor([[1, 0, 1, 0]], dtype=torch.float64)
>>> torch.allclose(cs_invariant(cs, x), cs_invariant(cs, torch.func.vmap(lambda x: m @ x)(x)))
True

twiss.invariant.invariant(normal: torch.Tensor, orbit: torch.Tensor) → torch.Tensor[source]

Compute linear invariants for a given normalization matrix and orbit

Parameters:

normal (Tensor, even-dimension, symplectic) – normalization matrix
orbit (Tensor) – orbit

Returns:

[jx, jy] for each turn

Return type:

Tensor

Note

Orbit is assumed to have the form […, [qx_i, px_i, qy_i, py_i], …]

Examples

>>> from math import pi
>>> from twiss.matrix import rotation
>>> from twiss.wolski import twiss
>>> m = rotation(*2*pi*torch.tensor([0.12, 0.31], dtype=torch.float64))
>>> t, n, w = twiss(m)
>>> x = torch.tensor([[1, 0, 1, 0]], dtype=torch.float64)
>>> torch.allclose(invariant(n, x), invariant(n, torch.func.vmap(lambda x: m @ x)(x)))
True

twiss.invariant.lb_invariant(twiss: torch.Tensor, orbit: torch.Tensor) → torch.Tensor[source]

Compute linear invariants for a given LB twiss and orbit

Parameters:

twiss (Tensor) – LB twiss a1x, b1x, a2x, b2x, a1y, b1y, a2y, b2y, u, v1, v2
orbit (Tensor) – orbit

Returns:

[jx, jy] for each turn

Return type:

Tensor

Note

Orbit is assumed to have the form […, [qx_i, px_i, qy_i, py_i], …]

Examples

>>> from math import pi
>>> from twiss.matrix import rotation
>>> from twiss.wolski import twiss
>>> from twiss.convert import wolski_to_lb
>>> m = rotation(*2*pi*torch.tensor([0.12, 0.31], dtype=torch.float64))
>>> t, n, w = twiss(m)
>>> lb = wolski_to_lb(w)
>>> x = torch.tensor([[1, 0, 1, 0]], dtype=torch.float64)
>>> torch.allclose(lb_invariant(lb, x), lb_invariant(lb, torch.func.vmap(lambda x: m @ x)(x)))
True