https://github.com/mrcdr/pylanczos

Python wrapper for Lambda Lanczos
https://github.com/mrcdr/pylanczos

eigenvector-calculation lanczos-algorithm matrix numpy python

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Python wrapper for Lambda Lanczos

• Host: GitHub
• URL: https://github.com/mrcdr/pylanczos
• Owner: mrcdr
• License: mit
• Created: 2020-03-09T19:07:15.000Z (almost 5 years ago)
• Default Branch: master
• Last Pushed: 2023-12-02T08:15:15.000Z (about 1 year ago)
• Last Synced: 2025-01-15T22:23:27.866Z (about 1 month ago)
• Topics: eigenvector-calculation, lanczos-algorithm, matrix, numpy, python
• Language: Python
• Homepage:
• Size: 64.5 KB
• Stars: 17
• Watchers: 1
• Forks: 0
• Open Issues: 2
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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# PyLanczos

## Overview

**PyLanczos** is a Lanczos diagonalization library.

Its core part is written in C++ as [LambdaLanczos](https://github.com/mrcdr/lambda-lanczos).

## Usage

All samples are available [here](https://github.com/mrcdr/pylanczos/tree/master/sample).

### NumPy and SciPy matrix

``` python

matrix = np.array([[2.0, 1.0, 1.0],

                   [1.0, 2.0, 1.0],

                   [1.0, 1.0, 2.0]])

engine = PyLanczos(matrix, True, 2)  # Find 2 maximum eigenpairs

eigenvalues, eigenvectors = engine.run()

print("Eigenvalue: {}".format(eigenvalues))

print("Eigenvector:")

print(eigenvectors)

```

Note: Use of SciPy sparse matrix is recommended to take full advantage of Lanczos algorithm.

### Customized operation

You can also attach your customized function:

```python

tensor = np.zeros((2, 2, 2, 2), dtype='float64')

tensor[0, 0, 0, 0] = 1

# and so on...

## Matrix-vector (or tensor-matrix) multiplication function

def mv_mul(v_in, v_out):

    v_in.shape = (2, 2)

    v_out.shape = (2, 2)

    np.einsum("ijkl, kl -> ij", tensor, v_in, out=v_out, optimize="optimal")

## Calculate an "eigenmatrix" for the 4th-order tensor.

engine = PyLanczos.create_custom(mv_mul, n, 'float64', False, 1) # Find 1 minimum eigenpair

eigenvalues, eigenmatrices = engine.run()

eigenmatrices.shape = (2, 2)

print("Eigenvalue: {}".format(eigenvalues))

print("Eigenmatrix:")

print(eigenmatrices)

```

There is [a full sample](https://github.com/mrcdr/pylanczos/tree/master/sample/sample3_custom.py) with detailed description.

## Installation

```sh

pip install pylanczos

```

## Requirements

C++11 compatible environment

## License

[MIT](https://github.com/mrcdr/lambda-lanczos/blob/master/LICENSE)

## Author

[mrcdr](https://github.com/mrcdr)

## PyPI repository

[pylanczos](https://pypi.org/project/pylanczos/)