subspacea - Angles between subspaces

Angles between subspaces and canonical correlations in general scalar products.

Andrew Knyazev

Versione 4.6 (11,9 KB)

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20 dic 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

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Andrew Knyazev (2026). subspacea - Angles between subspaces (https://it.mathworks.com/matlabcentral/fileexchange/55-subspacea-angles-between-subspaces), MATLAB Central File Exchange. Recuperato aprile 9, 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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Ispirato da: subspace.m, ortha.m

Ispirato: subspace.m

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Versione	Pubblicato	Note della release	Action
4.6	20 dic 2021	Fix error handling, code beautification.	Toolbox Zip
1.2	15 mag 2015	Updated description. added a conversion to a toolbox	Toolbox Zip
1.1.0.0	19 mag 2009	License update to free software (BSD). Comments update.	Scarica
1.0.0.0	28 giu 2005	minor update for MATLAB R14	Scarica

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} }