Linear combination function for tangent vectors represented as matrices. function v = lincomb(x, a1, d1) function v = lincomb(x, a1, d1, a2, d2) Given a point x, two tangent vectors d1 and d2 at x, and two real coefficients a1 and a2, returns a tangent vector at x representing a1*d1 + a2*d2, if d1 and d2 are represented as matrices (or more generally as arrays in Matlab). If a2 and d2 are omitted, the returned tangent vector is a1*d1. The input x is actually unused. This function is a helper to define manifolds in Manopt.

- complexcirclefactory Returns a manifold struct to optimize over unit-modulus complex numbers.
- realphasefactory Returns a manifold struct to optimize over phases of fft's of real signals
- essentialfactory Manifold structure to optimize over the space of essential matrices.
- centeredmatrixfactory Linear manifold struct. for optimization over matrices with centered cols
- constantfactory Returns a manifold struct representing the singleton.
- euclideancomplexfactory Returns a manifold struct to optimize over complex matrices.
- euclideanfactory Returns a manifold struct to optimize over real matrices.
- shapefitfactory Linear manifold structure for optimization over the ShapeFit search space
- skewsymmetricfactory Returns a manifold struct to optimize over k skew-symmetric matrices of size n
- symmetricfactory Returns a manifold struct to optimize over k symmetric matrices of size n
- grassmanncomplexfactory Returns a manifold struct to optimize over the set of subspaces in C^n.
- grassmannfactory Returns a manifold struct to optimize over the space of vector subspaces.
- grassmanngeneralizedfactory Returns a manifold struct of "scaled" vector subspaces.
- multinomialdoublystochasticfactory Manifold of n-by-n doubly-stochastic matrices with positive entries.
- multinomialfactory Manifold of n-by-m column-stochastic matrices with positive entries.
- multinomialsymmetricfactory Manifold of n-by-n symmetric stochastic matrices with positive entries.
- obliquecomplexfactory Returns a manifold struct defining complex matrices w/ unit-norm columns.
- obliquefactory Returns a manifold struct to optimize over matrices w/ unit-norm columns.
- positivefactory Manifold of m-by-n matrices with positive entries; scale invariant metric
- rotationsfactory Returns a manifold structure to optimize over rotation matrices.
- spherecomplexfactory Returns a manifold struct to optimize over unit-norm complex matrices.
- spherefactory Returns a manifold struct to optimize over unit-norm vectors or matrices.
- spheresymmetricfactory Returns a manifold struct to optimize over unit-norm symmetric matrices.
- stiefelcomplexfactory Returns a manifold struct. to optimize over complex orthonormal matrices.
- stiefelfactory Returns a manifold structure to optimize over orthonormal matrices.
- stiefelgeneralizedfactory Returns a manifold structure of "scaled" orthonormal matrices.
- stiefelstackedfactory Stiefel(k, d)^m, represented as matrices of size m*d-by-k.
- elliptopefactory Manifold of n-by-n psd matrices of rank k with unit diagonal elements.
- spectrahedronfactory Manifold of n-by-n symmetric positive semidefinite matrices of rank k
- symfixedrankYYcomplexfactory Manifold of n x n complex Hermitian pos. semidefinite matrices of rank k.
- symfixedrankYYfactory Manifold of n-by-n symmetric positive semidefinite matrices of rank k.
- sympositivedefinitefactory Manifold of n-by-n symmetric positive definite matrices with

0001 function v = matrixlincomb(x, a1, d1, a2, d2) %#ok<INUSL> 0002 % Linear combination function for tangent vectors represented as matrices. 0003 % 0004 % function v = lincomb(x, a1, d1) 0005 % function v = lincomb(x, a1, d1, a2, d2) 0006 % 0007 % Given a point x, two tangent vectors d1 and d2 at x, and two real 0008 % coefficients a1 and a2, returns a tangent vector at x representing 0009 % a1*d1 + a2*d2, if d1 and d2 are represented as matrices (or more 0010 % generally as arrays in Matlab). 0011 % 0012 % If a2 and d2 are omitted, the returned tangent vector is a1*d1. 0013 % 0014 % The input x is actually unused. 0015 % 0016 % This function is a helper to define manifolds in Manopt. 0017 0018 % This file is part of Manopt: www.manopt.org. 0019 % Original author: Nicolas Boumal, July 2, 2015. 0020 % Contributors: 0021 % Change log: 0022 0023 if nargin == 3 0024 v = a1*d1; 0025 elseif nargin == 5 0026 v = a1*d1 + a2*d2; 0027 else 0028 error('matrixlincomb takes either 3 or 5 inputs.'); 0029 end 0030 0031 end

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