| Name | twiss JSON |
| Version |
0.2.4
JSON |
| download |
| home_page | |
| Summary | Differentiable Wolski twiss matrices computation for arbitrary dimension stable symplectic matrices |
| upload_time | 2023-09-24 14:17:59 |
| maintainer | |
| docs_url | None |
| author | Ivan Morozov |
| requires_python | >=3.10 |
| license | MIT |
| keywords |
torch
twiss
differentiable
symplectic
matrix
|
| VCS |
|
| bugtrack_url |
|
| requirements |
No requirements were recorded.
|
| Travis-CI |
No Travis.
|
| coveralls test coverage |
No coveralls.
|
# twiss, 2022-2023
Coupled twiss parameters (Wolski twiss matrices) computation for arbitrary even dimension.
# Install & build
```
$ pip install git+https://github.com/i-a-morozov/twiss.git@main
```
or
```
$ pip install twiss -U
```
# Documentation
[](https://colab.research.google.com/github/i-a-morozov/twiss/blob/main/docs/source/examples/twiss.ipynb)
[https://i-a-morozov.github.io/twiss/](https://i-a-morozov.github.io/twiss/)
# Twiss
Compute tunes, normalization matrix and twiss matrices.
```python
>>> from math import pi
>>> import torch
>>> from twiss.matrix import rotation
>>> from twiss.wolski import twiss
>>> m = rotation(2*pi*torch.tensor(0.88, dtype=torch.float64))
>>> t, n, w = twiss(m)
>>> t
tensor([0.8800], dtype=torch.float64)
>>> n
tensor([[1.0000, 0.0000],
[0.0000, 1.0000]], dtype=torch.float64)
>>> w
tensor([[[1.0000, 0.0000],
[0.0000, 1.0000]]], dtype=torch.float64)
```
Input matrices can have arbitrary even dimension.
```python
>>> from math import pi
>>> import torch
>>> from twiss.matrix import rotation
>>> from twiss.wolski import twiss
>>> m = rotation(*(2*pi*torch.linspace(0.1, 0.9, 9, dtype=torch.float64)))
>>> t, n, w = twiss(m)
>>> t
tensor([0.1000, 0.2000, 0.3000, 0.4000, 0.5000, 0.6000, 0.7000, 0.8000, 0.9000],
dtype=torch.float64)
```
Can be mapped over a batch of input matrices.
```python
>>> from math import pi
>>> import torch
>>> from twiss.matrix import rotation
>>> from twiss.wolski import twiss
>>> m = torch.func.vmap(rotation)(2*pi*torch.linspace(0.1, 0.9, 9, dtype=torch.float64))
>>> t, n, w = torch.func.vmap(twiss)(m)
>>> t
tensor([[0.1000],
[0.2000],
[0.3000],
[0.4000],
[0.5000],
[0.6000],
[0.7000],
[0.8000],
[0.9000]], dtype=torch.float64)
```
Can be used to compute derivatives of observables.
```python
>>> from math import pi
>>> import torch
>>> from twiss.matrix import rotation
>>> from twiss.wolski import twiss
>>> def fn(k):
... m = rotation(2*pi*torch.tensor(0.88, dtype=torch.float64))
... i = torch.ones_like(k)
... o = torch.zeros_like(k)
... m = m @ torch.stack([i, k, o, i]).reshape(m.shape)
... t, *_ = twiss(m)
... return t
>>> k = torch.tensor(0.0, dtype=torch.float64)
>>> fn(k)
tensor([0.8800], dtype=torch.float64)
>>> torch.func.jacfwd(fn)(k)
tensor([0.0796], dtype=torch.float64)
```
Raw data
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"description": "# twiss, 2022-2023\n\nCoupled twiss parameters (Wolski twiss matrices) computation for arbitrary even dimension.\n\n# Install & build\n\n```\n$ pip install git+https://github.com/i-a-morozov/twiss.git@main\n```\nor \n```\n$ pip install twiss -U\n```\n\n# Documentation\n\n[](https://colab.research.google.com/github/i-a-morozov/twiss/blob/main/docs/source/examples/twiss.ipynb)\n\n[https://i-a-morozov.github.io/twiss/](https://i-a-morozov.github.io/twiss/)\n\n# Twiss\n\nCompute tunes, normalization matrix and twiss matrices.\n\n```python\n>>> from math import pi\n>>> import torch\n>>> from twiss.matrix import rotation\n>>> from twiss.wolski import twiss\n>>> m = rotation(2*pi*torch.tensor(0.88, dtype=torch.float64))\n>>> t, n, w = twiss(m)\n>>> t\ntensor([0.8800], dtype=torch.float64)\n>>> n\ntensor([[1.0000, 0.0000],\n [0.0000, 1.0000]], dtype=torch.float64)\n>>> w\ntensor([[[1.0000, 0.0000],\n [0.0000, 1.0000]]], dtype=torch.float64)\n```\n\nInput matrices can have arbitrary even dimension.\n\n```python\n>>> from math import pi\n>>> import torch\n>>> from twiss.matrix import rotation\n>>> from twiss.wolski import twiss\n>>> m = rotation(*(2*pi*torch.linspace(0.1, 0.9, 9, dtype=torch.float64)))\n>>> t, n, w = twiss(m)\n>>> t\ntensor([0.1000, 0.2000, 0.3000, 0.4000, 0.5000, 0.6000, 0.7000, 0.8000, 0.9000],\ndtype=torch.float64)\n```\n\nCan be mapped over a batch of input matrices.\n\n```python\n>>> from math import pi\n>>> import torch\n>>> from twiss.matrix import rotation\n>>> from twiss.wolski import twiss\n>>> m = torch.func.vmap(rotation)(2*pi*torch.linspace(0.1, 0.9, 9, dtype=torch.float64))\n>>> t, n, w = torch.func.vmap(twiss)(m)\n>>> t\ntensor([[0.1000],\n [0.2000],\n [0.3000],\n [0.4000],\n [0.5000],\n [0.6000],\n [0.7000],\n [0.8000],\n [0.9000]], dtype=torch.float64)\n```\n\nCan be used to compute derivatives of observables.\n\n```python\n >>> from math import pi\n >>> import torch\n >>> from twiss.matrix import rotation\n >>> from twiss.wolski import twiss\n >>> def fn(k):\n ... m = rotation(2*pi*torch.tensor(0.88, dtype=torch.float64))\n ... i = torch.ones_like(k)\n ... o = torch.zeros_like(k)\n ... m = m @ torch.stack([i, k, o, i]).reshape(m.shape)\n ... t, *_ = twiss(m)\n ... return t\n >>> k = torch.tensor(0.0, dtype=torch.float64)\n >>> fn(k)\n tensor([0.8800], dtype=torch.float64)\n >>> torch.func.jacfwd(fn)(k)\n tensor([0.0796], dtype=torch.float64)\n```\n",
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