Description of lincomb

DESCRIPTION

 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

CROSS-REFERENCE INFORMATION

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.

SOURCE CODE

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

lincomb

PURPOSE

SYNOPSIS

DESCRIPTION

CROSS-REFERENCE INFORMATION

SOURCE CODE