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lincomb

PURPOSE ^

Computes a linear combination of tangent vectors in the Manopt framework.

SYNOPSIS ^

function vec = lincomb(M, x, vecs, coeffs)

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 ^

This function calls: This function is called by:

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

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