Computes a linear combination of tangent vectors in the Manopt framework. vec = lincomb(M, x, vecs, coeffs) M is a Manopt manifold structure obtained from a factory. x is a point on the manifold M. vecs is a cell containing n tangent vectors at x. coeffs is a vector of length n vec is a tangent vector at x obtained as the linear combination vec = coeffs(1)*vecs{1} + ... + coeffs(n)*vecs{n} If vecs is an orthonormal basis, then tangent2vec is the inverse of lincomb. See also: grammatrix orthogonalize tangentorthobasis tangent2vec

- getGradient Computes the gradient of the cost function at x.
- getGradientFD Computes an approx. of the gradient w/ finite differences of the cost.
- fixedrankMNquotientfactory Manifold of m-by-n matrices of rank k with two factor quotient geometry.
- fixedrankembeddedfactory Manifold struct to optimize fixed-rank matrices w/ an embedded geometry.
- fixedrankfactory_2factors Manifold of m-by-n matrices of rank k with balanced quotient geometry.
- fixedrankfactory_2factors_preconditioned Manifold of m-by-n matrices of rank k with two factor quotient geometry.
- fixedrankfactory_2factors_subspace_projection Manifold of m-by-n matrices of rank k with two factor quotient geometry.
- fixedrankfactory_3factors Manifold of m-by-n matrices of rank k with polar quotient geometry.
- fixedrankfactory_3factors_preconditioned Manifold of m-by-n matrices of rank k with three factor quotient geometry.
- fixedrankfactory_tucker_preconditioned Manifold of fixed multilinear rank tensors in Tucker format.
- fixedranktensorembeddedfactory Manifold of tensors with fixed multilinear rank in Tucker format
- arc_lanczos Subproblem solver for ARC based on a Lanczos process.
- approxgradientFD Gradient approx. fnctn handle based on finite differences of the cost.
- tCG_rejectedstep Helper for trs_tCG_cached: mimics the latter's behavior, exploiting cache
- trs_gep Solves trust-region subproblem with TRSgep in a subspace of tangent space.
- trs_tCG Truncated (Steihaug-Toint) Conjugate-Gradient method.
- trs_tCG_cached Truncated (Steihaug-Toint) Conjugate-Gradient method with caching.
- powermanifold Returns a structure describing a power manifold M^n = M x M x ... x M.
- productmanifold Returns a structure describing a product manifold M = M1 x M2 x ... x Mn.
- smallestinconvexhull Computes a minimal norm convex combination of given tangent vectors in Manopt.

0001 function vec = lincomb(M, x, vecs, coeffs) 0002 % Computes a linear combination of tangent vectors in the Manopt framework. 0003 % 0004 % vec = lincomb(M, x, vecs, coeffs) 0005 % 0006 % M is a Manopt manifold structure obtained from a factory. 0007 % x is a point on the manifold M. 0008 % vecs is a cell containing n tangent vectors at x. 0009 % coeffs is a vector of length n 0010 % 0011 % vec is a tangent vector at x obtained as the linear combination 0012 % 0013 % vec = coeffs(1)*vecs{1} + ... + coeffs(n)*vecs{n} 0014 % 0015 % If vecs is an orthonormal basis, then tangent2vec is the inverse of 0016 % lincomb. 0017 % 0018 % See also: grammatrix orthogonalize tangentorthobasis tangent2vec 0019 0020 % This file is part of Manopt: www.manopt.org. 0021 % Original author: Nicolas Boumal, April 28, 2016. 0022 % Contributors: 0023 % Change log: 0024 0025 0026 n = numel(vecs); 0027 assert(numel(coeffs) == n); 0028 0029 switch n 0030 0031 case 0 0032 0033 vec = M.zerovec(x); 0034 0035 case 1 0036 0037 vec = M.lincomb(x, coeffs(1), vecs{1}); 0038 0039 otherwise 0040 0041 vec = M.lincomb(x, coeffs(1), vecs{1}, coeffs(2), vecs{2}); 0042 0043 for k = 3 : n 0044 0045 vec = M.lincomb(x, 1, vec, coeffs(k), vecs{k}); 0046 0047 end 0048 0049 end 0050 0051 0052 end

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