https://github.com/mrcdr/lambda-lanczos
C++ adaptive and header-only Lanczos algorithm library
https://github.com/mrcdr/lambda-lanczos
c-plus-plus eigenvector-calculation header-only lanczos lanczos-algorithm matrix
Last synced: 25 days ago
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C++ adaptive and header-only Lanczos algorithm library
- Host: GitHub
- URL: https://github.com/mrcdr/lambda-lanczos
- Owner: mrcdr
- License: mit
- Created: 2018-09-30T10:33:07.000Z (over 6 years ago)
- Default Branch: master
- Last Pushed: 2023-11-23T08:43:30.000Z (over 1 year ago)
- Last Synced: 2025-03-30T22:32:15.343Z (2 months ago)
- Topics: c-plus-plus, eigenvector-calculation, header-only, lanczos, lanczos-algorithm, matrix
- Language: C++
- Homepage:
- Size: 413 KB
- Stars: 26
- Watchers: 2
- Forks: 3
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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Lambda Lanczos
===========
C++ adaptive and header-only Lanczos algorithm library
## Overview
**Lambda Lanczos** calculates the smallest or largest eigenvalue and
the corresponding eigenvector of a symmetric (Hermitian) matrix.
The characteristic feature is the matrix-vector multiplication routine used in
the Lanczos algorithm is adaptable:
```c++
#include
using lambda_lanczos::LambdaLanczos;
/* Some include and using declarations are omitted */
void sample() {
const int n = 3;
double matrix[n][n] = { {2.0, 1.0, 1.0},
{1.0, 2.0, 1.0},
{1.0, 1.0, 2.0} };
// Its eigenvalues are {4, 1, 1}
/* Prepare matrix-vector multiplication routine used in Lanczos algorithm */
auto mv_mul = [&](const vector& in, vector& out) {
for(int i = 0;i < n;i++) {
for(int j = 0;j < n;j++) {
out[i] += matrix[i][j]*in[j];
}
}
};
/* Execute Lanczos algorithm */
LambdaLanczos engine(mv_mul, n, true, 1); // Find 1 maximum eigenvalue
vector eigenvalues;
vector> eigenvectors;
engine.run(eigenvalues, eigenvectors);
//// If C++17 is available, the following notation does the same thing:
// auto [eigenvalues, eigenvectors] = engine.run()
/* Print result */
cout << "Eigenvalue: " << setprecision(16) << eigenvalues[0] << endl;
cout << "Eigenvector:";
for(int i = 0; i < n; i++) {
cout << eigenvectors[0][i] << " ";
}
cout << endl;
}
```
This feature allows you to
- easily combine **Lambda Lanczos** with existing matrix libraries
(e.g. [Eigen](http://eigen.tuxfamily.org/index.php);
see a [sample code](https://github.com/mrcdr/lambda-lanczos/blob/master/src/samples/sample4_use_Eigen_library.cpp)).
- use a matrix whose elements are partially given,
e.g. a sparse matrix whose non-zero elements are stored
as a list of {row-index, column-index, value} tuples.
## Interfaces
Lambda Lanczos provides the following two interfaces:
### 1. Eigenvalue problem
`LambdaLanczos` class computes maximum (minimum) eigenvalues and
corresponding eigenvectors. Degenerate eigenvalues are taken into account.
This class aims problems that require one or a few eigenpairs
(e.g. low-energy excitation of a quantum system).
### 2. Exponentiation
`Exponentiator` class computes the following type of matrix-vector multiplication:
$$\boldsymbol{v}'=e^{\delta A} \boldsymbol{v},$$
where $A$ is a symmetric (Hermitian) matrix and $\delta$ is a scalar parameter.
This class is based on the same theory of the Lanczos algorithm (Krylov subspace method).
As an application, this class may be used for
time evolution of a quantum many-body system:
$$ \ket{\psi(t+\Delta t)} = e^{-iH\Delta t} \ket{\psi(t)},$$
and more sophisticated algorithms, such as [TDVP](https://arxiv.org/abs/1408.5056) and other tensor networks.
## Sample programs
See [here](https://github.com/mrcdr/lambda-lanczos/tree/master/src/samples).
## API reference
[API reference](https://mrcdr.github.io/lib-docs/lambda-lanczos/)
## Requirement
C++11 compatible environment
## Dependencies
**Lambda Lanczos** itself does not depend on any libraries.
In order to run tests, [Google Test](https://github.com/google/googletest) is required.
## Installation
**Lambda Lanczos** is a header-only library.
So the installation step is as follows:
1. Clone or download the latest version from [Github](https://github.com/mrcdr/lambda-lanczos/).
2. Place the `include/lambda_lanczos` directory anywhere your project can find.
## License
[MIT](https://github.com/mrcdr/lambda-lanczos/blob/master/LICENSE)
## Author
[mrcdr](https://github.com/mrcdr)