godilation

README

go-dilation

Library to calculate a n-dilation of a square matrix contraction with real values

This project is licensed under the terms of the MIT license.

If you stumbled across this and are interested, found a bug or have another idea how to contribute, feel free to open an issue or a pull request.

The recipe to calculate the dilation follows the theory mentioned by Béla Szőkefalvi-Nagy in "Analyse harmonique des opérateurs de l'espace de Hilbert" (1967). The matrix square root needed for the dilation is calculated using the Exponential Method for Matrices.

Development

Run any common go tasks such as go test ./.... This project was built on go version go1.13.9.

Usage

Build n dilations by calling UnitaryNDilation(m, n), where t is of type *mat.Dense (see gonum) - the contraction that will be dilated, and n is of type int - the degree that the dilation will have. Note that the defect operator of t must have real eigenvalues. Import the library as github.com/acra5y/go-dilation.

For ill-conditionend matrices (e.g. with high eigenvalues or eigenvalues close to 0) the result might be imprecise.

Documentation

Overview

This project is licensed under the terms of the MIT license. It provides a function to calculate a unitary n-dilation for a given matrix contraction and a degree using the gonum library. The recipe to calculate the dilation follows the theory mentioned by Béla Szőkefalvi-Nagy in "Analyse harmonique des opérateurs de l'espace de Hilbert" (1967). The matrix square root needed for the dilation is calculated using the Exponential Method for Matrices.

Index

• func UnitaryNDilation(t *mat.Dense, n int) (*mat.Dense, error)

Functions

func UnitaryNDilation

func UnitaryNDilation(t *mat.Dense, n int) (*mat.Dense, error)

returns a unitary n-dilation for the given square matrix contraction t or an error, if t is not a contraction or not a square matrix