Home > manopt > tools > dexpm.m

# dexpm

## PURPOSE Fréchet derivative of the matrix exponential.

## SYNOPSIS function D = dexpm(X, H)

## DESCRIPTION ``` Fréchet derivative of the matrix exponential.

function D = dexpm(X, H)

Computes the directional derivative (the Fréchet derivative) of expm at X
along H (square matrices).

Thus, D = lim_(t -> 0) (expm(X + tH) - expm(X)) / t.

Note: the adjoint of dexpm(X, .) is dexpm(X', .), which is a fact often
useful to derive gradients of matrix functions involving expm(X).
(This is wrt the inner product inner = @(A, B) real(trace(A'*B))).

See also: dfunm dlogm dsqrtm```

## CROSS-REFERENCE INFORMATION This function calls:
• dfunm Fréchet derivative of matrix functions.
This function is called by:

## SOURCE CODE ```0001 function D = dexpm(X, H)
0002 % Fréchet derivative of the matrix exponential.
0003 %
0004 % function D = dexpm(X, H)
0005 %
0006 % Computes the directional derivative (the Fréchet derivative) of expm at X
0007 % along H (square matrices).
0008 %
0009 % Thus, D = lim_(t -> 0) (expm(X + tH) - expm(X)) / t.
0010 %
0011 % Note: the adjoint of dexpm(X, .) is dexpm(X', .), which is a fact often
0012 % useful to derive gradients of matrix functions involving expm(X).
0013 % (This is wrt the inner product inner = @(A, B) real(trace(A'*B))).
0014 %
0015 % See also: dfunm dlogm dsqrtm
0016
0017 % This file is part of Manopt: www.manopt.org.
0018 % Original author: Nicolas Boumal, July 3, 2015.
0019 % Contributors:
0020 % Change log:
0021
0022     D = dfunm(@expm, X, H);
0023
0024 end```

Generated on Mon 10-Sep-2018 11:48:06 by m2html © 2005