https://github.com/famura/ndc
Numerical differentiation leveraging convolutions based on PyTorch
https://github.com/famura/ndc
convolution finite-differences numerical-differentiation pytorch signal-processing
Last synced: 3 months ago
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Numerical differentiation leveraging convolutions based on PyTorch
- Host: GitHub
- URL: https://github.com/famura/ndc
- Owner: famura
- License: mit
- Created: 2022-04-11T17:35:57.000Z (about 4 years ago)
- Default Branch: main
- Last Pushed: 2022-04-19T09:29:00.000Z (about 4 years ago)
- Last Synced: 2025-04-24T14:01:56.888Z (about 1 year ago)
- Topics: convolution, finite-differences, numerical-differentiation, pytorch, signal-processing
- Language: Python
- Homepage:
- Size: 11.7 KB
- Stars: 1
- Watchers: 1
- Forks: 1
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE.txt
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README
# Numerical Differentiation Leveraging Convolution (ndc)
[](https://opensource.org/licenses/MIT)
[](https://codecov.io/gh/famura/ndc)
[](https://pycqa.github.io/isort/)
[](https://github.com/psf/black)
**What for?**
Differentiate signals stored as PyTorch tensors, e.g. measurements obtained from a device or simulation, where automatic differentiation can not be applied.
**Features**
* Theoretically **any order, any stencils, and any step size** (see [this Wiki page](https://en.wikipedia.org/wiki/Finite_difference_coefficient) for information). Be aware that there are numerical limits when computing the filter kernel's coefficients, e.g. small step sized and high orders lead to numerical issues.
* Works for **multidimensional signals**, assuming that all dimensions share the same step size.
* Computations can be executed on **CUDA**. However, this has not been tested extensively.
* Straightforward implementation which you can easily adapt to your needs.
**How?**
The idea of this small repository is to use the duality between convolution, i.e., filtering, and [numerical differentiation](https://en.wikipedia.org/wiki/Numerical_differentiation) to leverage the existing functions for 1-dimensional convolution in order to compute the (time) derivatives.
**Why PyTorch?**
More often then not I received (recorded) simulation data as PyTorch tensors rather than numpy arrays.
Thus, I think it is nice to have a function to differentiate measurement signals without switching the data type or computation device.
Moreover, the `torch.conv1d` function fits perfectly for this purpose.
## Citing
If you use code or ideas from this repository for your projects or research, please cite it.
```
@misc{Muratore_ncd,
author = {Fabio Muratore},
title = {ndc - Numerical differentiation leveraging convolutions},
year = {2022},
publisher = {GitHub},
journal = {GitHub repository},
howpublished = {\url{https://github.com/famura/ndc}}
}
```
## Installation
To install the core part of the package run
```
pip install ndc
```
For (local) development install the dependencies with
```
pip install -e .[dev]
```
## Usage
Consider a signal `x`, e.g. a measurement you obtained form a device. This package assumes that the signal to differentiate is of shape `(num_steps, dim_data)`
```python
import torch
import ndc
# Assuming you got x(t) from somewhere.
assert isinstance(x, torch.Tensor)
num_steps, dim_data = x.shape
# Specify the derivative. Here, the first order central derivative.
stencils = [-1, 0, 1]
order = 1
step_size = dt # should be known from your signal x(t), else use 1
padding = True # if true, the initial and final values are repeated as often as necessary to match the length of x
dx_dt_num = ndc.differentiate_numerically(x, stencils, order, step_size, padding)
assert dx_dt_num.device == x.device
if padding:
assert dx_dt_num.shape == (num_steps, dim_data)
else:
assert dx_dt_num.shape == (num_steps - sum(s != 0 for s in stencils), dim_data)
```
## Contributions
Maybe you want another padding mode, or you found a way to improve the CUDA support. Please feel free to leave a pull request or issue.