MatrixExp

Copyright (c) 2020 Jae-Seung Lee

License: MIT License

MatrixExp is a Swift package for numerically evaluating matrix exponentiation.

References

1. N. J. Higham, The scaling and squaring method for the matrix exponential revisited. SIAM J. Matrix Anal. Appl., 26(4), (2005), pp. 1179-1193. doi:10.1137/04061101X
2. A. H. Al-Mohy and N. J. Higham, A new scaling and squaring algorithm for the matrix exponential, SIAM J. Matrix Anal. Appl., 31(3), (2009), pp. 970-989. doi:10.1137/09074721X

Dependencies

1. Swift Numerics
2. LANumerics

Usage

Initialize a matrix using LANumerics' Matrix<Element> and instantiate an instance of MatrixExponentiator<Element>. Then, call compute() to get the result, which is either Matrix<Element> or nil.

let M1 = Matrix<Double>(rows: [[0, 1], [1, 0]])
let result = MatrixExponentiator<Double>(M1).compute()

let M2 = Matrix<Complex<Double>>(rows: [[Complex<Double>(0,0), Complex<Double>(0, -1)], [Complex<Double>(0, 1), Complex<Double>(0, 0)]])
let result = MatrixExponentiator<Complex>(M2).compute()

Update History

Version 0.3.0 (11/29/2023)

• Update LANumerics to 0.1.12 and swift-numerics to 0.1.0
• Update the interface and usage

Version 0.2.0 (12/10/2020)

Implement a function corresponding to normest1 in Matlab or onenormest in Scipy to estimate the 1-norm of the powers of a given matrix [1]

[1] Nicholas J. Higham and Fran\c{c}oise Tisseur, A Block Algorithm for Matrix 1-Norm Estimation with an Application to 1-Norm Pseudospectra, SIAM J. Matrix Anal. App. 21, 1185-1201, 2000. doi: 10.1137/S0895479899356080