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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: 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

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