{"repo":"mrcdr/lambda-lanczos","free":true,"listed":false,"github":"https://github.com/mrcdr/lambda-lanczos","clone":"git clone https://github.com/mrcdr/lambda-lanczos.git","description":"C++ adaptive and header-only Lanczos algorithm library","language":"C++","stars":34,"topics":["c-plus-plus","header-only","lanczos-algorithm","eigenvector-calculation","matrix","lanczos"],"license":"MIT","category":"chat-messaging","readme_excerpt":"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: This feature allows you to - easily combine Lambda Lanczos with existing matrix libraries (e.g. Eigen; see a sample code). - 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 and other tensor network","default_branch":null,"files":null,"tree":[],"storefront":"/r/mrcdr","claimed":false,"request_supported":{"post":"https://gitbuyer.com/r/mrcdr/lambda-lanczos/request-supported","requests":0},"note":"indexed from public GitHub; nothing is for sale on this page. Clone it from GitHub. Paid listings live at /search."}