# Overview

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`trigmv`

, `trighmv`

- **The action of trigonometric and hyperbolic matrix functions**

## About

`trigmv`

contains two MATLAB functions for computing cosm(tA)b and sinm(tA)b - `trigmv`

- as well as coshm(tA)b and sinh(tA)b - `trighmv`

, where A is an n-by-n matrix and b an n-by-1 vector.

The functionality of trigmv`and trighmv`

is based on `expmv`

by Al-Mohy and Higham.

Furthermore, the function `expmv`

is extended - see expmv.m for more details.

That the original functionality and interface is preserved.

The basic functionality is as follows:

- trigmv(t,A,b) computes [cosm(t
*A)b, sinm(t*A)b] - trigmv(t,A,B) computes [cosm(t
*A)B, sinm(t*A)B], for a skinny n-by-m matrix B - trighmv(t,A,b) computes [coshm(t
*A)b, sinhm(t*A)b] - trighmv(t,A,B) computes [coshm(t
*A)B, sinhm(t*A)B], for a tall, skinny n-by-m matrix B

The functions work for any matrix A and only use matrix-vector products with A and A^*.

Function `test.m`

runs some simple test code.

Detail on the underlying algorithms can be found in the preprint:

N. J. Higham and P. Kandolf, "Computing the Action of Trigonometric and Hyperbolic Matrix Functions" MIMS Eprint 2016.40, University of Manchester

## External contribution

Parts of this code are from `expmv`

- **Matrix exponential times a vector**.

For more information on `expmv`

by Al-Mohy and Higham visit the homepage or read the corresponding publication:

A. H. Al-Mohy and N. J. Higham, "Computing the action of the matrix exponential, with an application to exponential integrators" SIAM J. Sci. Comput., 33(2):488--511, 2011.