subspacea - Angles between subspaces

Angles between subspaces and canonical correlations in general scalar products.

Andrew Knyazev

Version 4.6 (11,9 ko)

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20 déc. 2021

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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.

The input A can be provided as a matrix as well as a string of a function name, e.g., funcA giving the product funcA(X) = A*X.

[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

Citation pour cette source

Andrew Knyazev (2026). subspacea - Angles between subspaces (https://fr.mathworks.com/matlabcentral/fileexchange/55-subspacea-angles-between-subspaces), MATLAB Central File Exchange. Extrait(e) le juin 4, 2026.

Knyazev, Andrew V., and Merico E. Argentati. “Principal Angles between Subspaces in an A-Based Scalar Product: Algorithms and Perturbation Estimates.” SIAM Journal on Scientific Computing, vol. 23, no. 6, Society for Industrial & Applied Mathematics (SIAM), Jan. 2002, pp. 2008–40, doi:10.1137/s1064827500377332.

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Inspiré par : subspace.m, ortha.m

A inspiré : subspace.m

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Version	Publié le	Notes de version	Action
4.6	20 déc. 2021	Fix error handling, code beautification.	Toolbox Zip
1.2	15 mai 2015	Updated description. added a conversion to a toolbox	Toolbox Zip
1.1.0.0	19 mai 2009	License update to free software (BSD). Comments update.	Télécharger
1.0.0.0	28 juin 2005	minor update for MATLAB R14	Télécharger

MLA	Knyazev, Andrew V., and Merico E. Argentati. “Principal Angles between Subspaces in an A-Based Scalar Product: Algorithms and Perturbation Estimates.” SIAM Journal on Scientific Computing, vol. 23, no. 6, Society for Industrial & Applied Mathematics (SIAM), Jan. 2002, pp. 2008–40, doi:10.1137/s1064827500377332.
APA	Knyazev, A. V., & Argentati, M. E. (2002). Principal Angles between Subspaces in an A-Based Scalar Product: Algorithms and Perturbation Estimates. SIAM Journal on Scientific Computing, 23(6), 2008–2040. Society for Industrial & Applied Mathematics (SIAM). Retrieved from https://doi.org/10.1137%2Fs1064827500377332
BibTeX	@article{Knyazev_2002, doi = {10.1137/s1064827500377332}, url = {https://doi.org/10.1137%2Fs1064827500377332}, year = 2002, month = {jan}, publisher = {Society for Industrial {\&} Applied Mathematics ({SIAM})}, volume = {23}, number = {6}, pages = {2008--2040}, author = {Andrew V. Knyazev and Merico E. Argentati}, title = {Principal Angles between Subspaces in an A-Based Scalar Product: Algorithms and Perturbation Estimates}, journal = {{SIAM} Journal on Scientific Computing} }