The Matrix Means Toolbox includes the following files:
alm.m  Computes the AndoLiMathias mean of k matrices [1]
cheap.m  Computes the cheap mean of k matrices [3]
dist.m  Computes the Riemannian and Euclidean distance between A and B
explog.m  Computes the explog mean of k matrices [2]
karcher.m  Computes the Karcher mean of k matrices using a Richardsonlike iteration [4]
mean2.m  Computes the geometric mean of two matrices with three algorithms [6]
nbmp.m  Computes the Nakamura/BiniMeiniPoloni mean of k matrices [5,7]
random.m  Generates k random positive definite matrices
sharp.m  Computes $A\#_t B$
Bibliography
[1] T. Ando, C.K. Li and R. Mathias, Geometric means, Linear Algebra Appl., 3851 (2004) pp. 305334.
[2] V. Arsigny, P. Fillard, X. Pennec and N. Ayache, Geometric means in a novel vector space structure on symmetric positivedefinite matrices, SIAM J. Matrix Anal. Appl., 291 (2006/07), pp. 328347.
[3] D. A. Bini and B. Iannazzo, A note on computing matrix geometric means, Advances Comp. Math., 352/4 (2010), pp. 175192.
[4] D. A. Bini and B. Iannazzo, Computing the Karcher mean of symmetric positive definite matrices, to appear in Linear Algebra Appl., 2012.
[5] D. A. Bini, B. Meini and F. Poloni, An effective matrix geometric mean satisfying the AndoLiMathias properties, Math. Comp., 79 (2010), pp. 437452.
[6] B. Iannazzo, The geometric mean of two matrices from a computational viewpoint, arXiv preprint arXiv:1201.0101, 2011.
[7] K. Nakamura, Geometric Means of Positive Operators, Kyungpook Math. J. 49 (2009), 167181
History
mmtoolbox 2.3  July 14, 2014  Fixed a bug in the stepsize computation in
karcher.m, updated the file dist.m (thanks to J. Todd).
mmtoolbox 2.2  Febraury 13, 2014  Fixed a bug, removed unused files, fixed
indent, optimized the Richardson iteration.
mmtoolbox 2.1  February 11, 2014  removed unused cycle and duplicated
Cholesky factorization in mean2.m. In karcher.m changed log1 with log1p.
mmtoolbox 2.0  January 10, 2014  rewritten all files again with major adjustments. Included full Matlab and cellarray support.
Removed gradient.m and rich.m for the Karcher mean; now there is the file karcher.m which computes the Karcher mean using the Richardson iteration, starting from the arithmetic mean
and with the exponential at the end. Changed geomean.m to mean2.m. Many bugs have been removed.
mmtoolbox 1.1b2  November 26, 2011  Some minor adjustments to the formatting
of the files.
mmtoolbox 1.1b1  August, 19, 2011  rewritten all files from scratch with a uniform style, help in line,
and more; changed the square root computation to the Cholesky factor whenever possible;
changed the name of the file manton.m to gradient.m; changed the name of the file bmp.m to nbmp.m, as
soon as the reference [8] was individuated; fixed a bug in dist.m.
mmtoolbox 1.0  July 11, 2010  first release
