MULTIHCONJ Hermitian conjugating arrays of matrices. B = MULTIHCONJ(A) is equivalent to B = MULTIHCONJ(A, DIM), where DIM = 1. B = MULTIHCONJ(A, DIM) is equivalent to B = PERMUTE(A, [1:DIM-1, DIM+1, DIM, DIM+2:NDIMS(A)]), where A is an array containing N P-by-Q matrices along its dimensions DIM and DIM+1, and B is an array containing the Q-by-P Hermitian conjugate (') of those N matrices along the same dimensions. N = NUMEL(A) / (P*Q), i.e. N is equal to the number of elements in A divided by the number of elements in each matrix. Example: A 5-by-9-by-3-by-2 array may be considered to be a block array containing ten 9-by-3 matrices along dimensions 2 and 3. In this case, its size is so indicated: 5-by-(9-by-3)-by-2 or 5x(9x3)x2. If A is ................ a 5x(9x3)x2 array of 9x3 matrices, C = MULTIHCONJ(A, 2) is a 5x(3x9)x2 array of 3x9 matrices. See also MULTITRANSP MULTIHERM.

- multitransp Transposing arrays of matrices.

- grassmanncomplexfactory Returns a manifold struct to optimize over the set of subspaces in C^n.
- stiefelcomplexfactory Returns a manifold struct. to optimize over complex orthonormal matrices.
- multiherm Returns the Hermitian parts of the matrices in the 3D matrix X

0001 function b = multihconj(a, dim) 0002 %MULTIHCONJ Hermitian conjugating arrays of matrices. 0003 % B = MULTIHCONJ(A) is equivalent to B = MULTIHCONJ(A, DIM), where 0004 % DIM = 1. 0005 % 0006 % B = MULTIHCONJ(A, DIM) is equivalent to 0007 % B = PERMUTE(A, [1:DIM-1, DIM+1, DIM, DIM+2:NDIMS(A)]), where A is an 0008 % array containing N P-by-Q matrices along its dimensions DIM and DIM+1, 0009 % and B is an array containing the Q-by-P Hermitian conjugate (') of 0010 % those N matrices along the same dimensions. N = NUMEL(A) / (P*Q), i.e. 0011 % N is equal to the number of elements in A divided by the number of 0012 % elements in each matrix. 0013 % 0014 % 0015 % Example: 0016 % A 5-by-9-by-3-by-2 array may be considered to be a block array 0017 % containing ten 9-by-3 matrices along dimensions 2 and 3. In this 0018 % case, its size is so indicated: 5-by-(9-by-3)-by-2 or 5x(9x3)x2. 0019 % If A is ................ a 5x(9x3)x2 array of 9x3 matrices, 0020 % C = MULTIHCONJ(A, 2) is a 5x(3x9)x2 array of 3x9 matrices. 0021 % 0022 % See also MULTITRANSP MULTIHERM. 0023 0024 % This file is part of Manopt: www.manopt.org. 0025 % Original author: Hiroyuki Sato, April 27, 2015. 0026 % Contributors: 0027 % Change log: 0028 0029 % Setting DIM if not supplied. 0030 if nargin == 1, dim = 1; end 0031 0032 % Transposing 0033 b = multitransp(a, dim); 0034 0035 %Conjugating 0036 b = conj(b); 0037 0038 end

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