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Highlights from subspacea.m

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subspacea.m

Andrew Knyazev (view profile)

20 Sep 2000 (Updated )

Angles between subspaces. Canonical correlations.

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Description

subspacea(F,G,A) Finds all min(size(orth(F),2),size(orth(G),2)) principal angles between two subspaces spanned by the columns of matrices F and G in the A-based scalar product x'*A*y, where A is Hermitian and positive definite. COS of principal angles is called canonical correlations in statistics.
[theta,U,V] = subspacea(F,G,A) also computes left and right
principal (canonical) vectors - columns of U and V, respectively.

If F and G are vectors of unit length and A=I, the angle is ACOS(F'*G) in exact arithmetic. If A is not provided as a third argument, than A=I and the function gives the same largest angle as SUBSPACE.m by Andrew Knyazev. MATLAB's SUBSPACE.m function is still badly designed and fails to compute some angles accurately.

The algorithm is described in A. V. Knyazev and M. E. Argentati, Principal Angles between Subspaces in an A-Based Scalar Product: Algorithms and Perturbation Estimates. SIAM J. Scientific Computing, 23 (2002), no. 6, 2009-2041. http://dx.doi.org/10.1137/S1064827500377332

Acknowledgements

Subspace.M and Ortha.M inspired this file.

This file inspired Subspace.M.

Required Products MATLAB
MATLAB release MATLAB 5.2 (R10)
MATLAB Search Path
`/`
13 Jul 2010 Ken Crounse

Ken Crounse (view profile)

20 Jun 2005 jeff arndt
05 Oct 2001

new revision

19 May 2009 1.1