| Name | ndmap JSON |
| Version |
0.1.7
JSON |
| download |
| home_page | |
| Summary | Higher order partial derivatives computation with respect to one or several tensor-like variables, application to nonlinear dynamics |
| upload_time | 2023-09-19 14:19:34 |
| maintainer | |
| docs_url | None |
| author | Ivan Morozov |
| requires_python | >=3.10 |
| license | MIT |
| keywords |
torch
derivative
|
| VCS |
|
| bugtrack_url |
|
| requirements |
No requirements were recorded.
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| Travis-CI |
No Travis.
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| coveralls test coverage |
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# ndmap, 2022-2023
<p align="center">
<img width="100" height="100" src="https://github.com/i-a-morozov/ndmap/blob/main/docs/pics/logo.svg">
</p>
Higher order partial derivatives computation with respect to one or several tensor-like variables.
Taylor series function approximation (derivative table and series function representation).
Parametric fixed point computation.
# Install & build
```
$ pip install git+https://github.com/i-a-morozov/ndmap.git@main
```
or
```
$ pip install ndmap -U
```
# Documentation
[https://i-a-morozov.github.io/ndmap/](https://i-a-morozov.github.io/ndmap/)
# Derivative (composable jacobian)
Compute higher order function (partial) derivatives.
```python
>>> from ndmap.derivative import derivative
>>> def fn(x):
... return 1 + x + x**2 + x**3 + x**4 + x**5
...
>>> import torch
>>> x = torch.tensor(0.0)
>>> derivative(5, fn, x)
[tensor(1.), tensor(1.), tensor(2.), tensor(6.), tensor(24.), tensor(120.)]
```
```python
>>> from ndmap.derivative import derivative
>>> def fn(x):
... x1, x2 = x
... return x1**2 + x1*x2 + x2**2
...
>>> import torch
>>> x = torch.tensor([0.0, 0.0])
>>> derivative(2, fn, x, intermediate=False)
tensor([[2., 1.],
[1., 2.]])
```
```python
>>> from ndmap.derivative import derivative
>>> def fn(x, y):
... x1, x2 = x
... return x1**2*(1 + y) + x2**2*(1 - y)
...
>>> import torch
>>> x = torch.tensor([0.0, 0.0])
>>> y = torch.tensor(0.0)
>>> derivative((2, 1), fn, x, y)
[[tensor(0.), tensor(0.)], [tensor([0., 0.]), tensor([0., 0.])], [tensor([[2., 0.],
[0., 2.]]), tensor([[ 2., 0.],
[ 0., -2.]])]]
```
# Derivative (gradient)
Compute higher order function (partial) derivatives.
```python
>>> from ndmap.gradient import series
>>> def fn(x):
... return 1 + x + x**2 + x**3 + x**4 + x**5
...
>>> import torch
>>> x = torch.tensor([0.0])
>>> series((5, ), fn, x, retain=False, series=False)
{(0,): tensor([1.]),
(1,): tensor([1.]),
(2,): tensor([2.]),
(3,): tensor([6.]),
(4,): tensor([24.]),
(5,): tensor([120.])}
```
```python
>>> from ndmap.gradient import series
>>> def fn(x):
... x1, x2 = x
... return x1**2 + x1*x2 + x2**2
...
>>> import torch
>>> x = torch.tensor([0.0, 0.0])
>>> series((2, ), fn, x, intermediate=False, retain=False, series=False)
{(2, 0): tensor(2.), (1, 1): tensor(1.), (0, 2): tensor(2.)}
```
```python
>>> from ndmap.gradient import series
>>> def fn(x, y):
... x1, x2 = x
... y1, = y
... return x1**2*(1 + y1) + x2**2*(1 - y1)
...
>>> import torch
>>> x = torch.tensor([0.0, 0.0])
>>> y = torch.tensor([0.0])
>>> series((2, 1), fn, x, y, retain=False, series=False)
{(0, 0, 0): tensor(0.),
(0, 0, 1): tensor(0.),
(1, 0, 0): tensor(0.),
(0, 1, 0): tensor(0.),
(1, 0, 1): tensor(0.),
(0, 1, 1): tensor(-0.),
(2, 0, 0): tensor(2.),
(1, 1, 0): tensor(0.),
(0, 2, 0): tensor(2.),
(2, 0, 1): tensor(2.),
(1, 1, 1): tensor(0.),
(0, 2, 1): tensor(-2.)}
```
# Desription
```python
>>> import ndmap
>>> ndmap.__about__
```
# Animations
Stable and unstable invariant manifolds approximation
<p align="center">
<img width="576" height="576" src="https://github.com/i-a-morozov/ndmap/blob/main/docs/pics/manifold.gif">
</p>
Collision of fixed points
<p align="center">
<img width="576" height="576" src="https://github.com/i-a-morozov/ndmap/blob/main/docs/pics/collision.gif">
</p>
Reduce real part of a hyperbolic fixed point
<p align="center">
<img width="576" height="576" src="https://github.com/i-a-morozov/ndmap/blob/main/docs/pics/change.gif">
</p>
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"description": "# ndmap, 2022-2023\n\n<p align=\"center\">\n <img width=\"100\" height=\"100\" src=\"https://github.com/i-a-morozov/ndmap/blob/main/docs/pics/logo.svg\">\n</p>\n\nHigher order partial derivatives computation with respect to one or several tensor-like variables.\nTaylor series function approximation (derivative table and series function representation).\nParametric fixed point computation.\n\n# Install & build\n\n```\n$ pip install git+https://github.com/i-a-morozov/ndmap.git@main\n```\nor\n```\n$ pip install ndmap -U\n```\n\n# Documentation\n\n[https://i-a-morozov.github.io/ndmap/](https://i-a-morozov.github.io/ndmap/)\n\n# Derivative (composable jacobian)\n\nCompute higher order function (partial) derivatives.\n\n```python\n>>> from ndmap.derivative import derivative\n>>> def fn(x):\n... return 1 + x + x**2 + x**3 + x**4 + x**5\n... \n>>> import torch\n>>> x = torch.tensor(0.0)\n>>> derivative(5, fn, x)\n[tensor(1.), tensor(1.), tensor(2.), tensor(6.), tensor(24.), tensor(120.)]\n```\n\n```python\n>>> from ndmap.derivative import derivative\n>>> def fn(x):\n... x1, x2 = x\n... return x1**2 + x1*x2 + x2**2\n... \n>>> import torch\n>>> x = torch.tensor([0.0, 0.0])\n>>> derivative(2, fn, x, intermediate=False)\ntensor([[2., 1.],\n [1., 2.]])\n```\n\n```python\n>>> from ndmap.derivative import derivative\n>>> def fn(x, y):\n... x1, x2 = x\n... return x1**2*(1 + y) + x2**2*(1 - y)\n... \n>>> import torch\n>>> x = torch.tensor([0.0, 0.0])\n>>> y = torch.tensor(0.0)\n>>> derivative((2, 1), fn, x, y)\n[[tensor(0.), tensor(0.)], [tensor([0., 0.]), tensor([0., 0.])], [tensor([[2., 0.],\n [0., 2.]]), tensor([[ 2., 0.],\n [ 0., -2.]])]]\n```\n\n# Derivative (gradient)\n\nCompute higher order function (partial) derivatives.\n\n```python\n>>> from ndmap.gradient import series\n>>> def fn(x):\n... return 1 + x + x**2 + x**3 + x**4 + x**5\n... \n>>> import torch\n>>> x = torch.tensor([0.0])\n>>> series((5, ), fn, x, retain=False, series=False)\n{(0,): tensor([1.]),\n (1,): tensor([1.]),\n (2,): tensor([2.]),\n (3,): tensor([6.]),\n (4,): tensor([24.]),\n (5,): tensor([120.])}\n```\n\n```python\n>>> from ndmap.gradient import series\n>>> def fn(x):\n... x1, x2 = x\n... return x1**2 + x1*x2 + x2**2\n...\n>>> import torch\n>>> x = torch.tensor([0.0, 0.0])\n>>> series((2, ), fn, x, intermediate=False, retain=False, series=False)\n{(2, 0): tensor(2.), (1, 1): tensor(1.), (0, 2): tensor(2.)}\n\n```\n\n```python\n>>> from ndmap.gradient import series\n>>> def fn(x, y):\n... x1, x2 = x\n... y1, = y\n... return x1**2*(1 + y1) + x2**2*(1 - y1)\n...\n>>> import torch\n>>> x = torch.tensor([0.0, 0.0])\n>>> y = torch.tensor([0.0])\n>>> series((2, 1), fn, x, y, retain=False, series=False)\n{(0, 0, 0): tensor(0.),\n (0, 0, 1): tensor(0.),\n (1, 0, 0): tensor(0.),\n (0, 1, 0): tensor(0.),\n (1, 0, 1): tensor(0.),\n (0, 1, 1): tensor(-0.),\n (2, 0, 0): tensor(2.),\n (1, 1, 0): tensor(0.),\n (0, 2, 0): tensor(2.),\n (2, 0, 1): tensor(2.),\n (1, 1, 1): tensor(0.),\n (0, 2, 1): tensor(-2.)}\n```\n\n# Desription\n\n```python\n>>> import ndmap\n>>> ndmap.__about__\n```\n\n# Animations\n\nStable and unstable invariant manifolds approximation\n\n<p align=\"center\">\n <img width=\"576\" height=\"576\" src=\"https://github.com/i-a-morozov/ndmap/blob/main/docs/pics/manifold.gif\">\n</p>\n\nCollision of fixed points\n\n<p align=\"center\">\n <img width=\"576\" height=\"576\" src=\"https://github.com/i-a-morozov/ndmap/blob/main/docs/pics/collision.gif\">\n</p>\n\nReduce real part of a hyperbolic fixed point\n\n<p align=\"center\">\n <img width=\"576\" height=\"576\" src=\"https://github.com/i-a-morozov/ndmap/blob/main/docs/pics/change.gif\">\n</p>\n",
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