Orthonormalizes a basis of tangent vectors twice for increased accuracy. function [orthobasis, R] = orthogonalizetwice(M, x, basis) See help for orthogonalize. This function calls that algorithm twice. This is useful if elements in the input basis are close to being linearly dependent (ill conditioned). See in code for details. See also: orthogonalize grammatrix tangentorthobasis

- orthogonalize Orthonormalizes a basis of tangent vectors in the Manopt framework.

0001 function [Q, R] = orthogonalizetwice(M, x, A) 0002 % Orthonormalizes a basis of tangent vectors twice for increased accuracy. 0003 % 0004 % function [orthobasis, R] = orthogonalizetwice(M, x, basis) 0005 % 0006 % See help for orthogonalize. This function calls that algorithm twice. 0007 % This is useful if elements in the input basis are close to being linearly 0008 % dependent (ill conditioned). See in code for details. 0009 % 0010 % See also: orthogonalize grammatrix tangentorthobasis 0011 0012 % This file is part of Manopt: www.manopt.org. 0013 % Original author: Nicolas Boumal, Oct. 5, 2017. 0014 % Contributors: 0015 % Change log: 0016 0017 [Q1, R1] = orthogonalize(M, x, A); 0018 [Q , R2] = orthogonalize(M, x, Q1); 0019 0020 R = R2*R1; % This is upper triangular since R1 and R2 are. 0021 0022 end

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