FROM_ARRAY Approximate full array by TTeMPS tensor of prescribed rank
or within a prescribed tolerance.
X = TTeMPS.from_array( A, tol ) approximates the given array A by a
TTeMPS tensor such that the the error is in the order of tol.
X = TTeMPS.from_array( A, r ), with r a vector of length (ndims(A))+1),
approximates the given array A by a rank-r TTeMPS tensor, such that
X.rank = r.0001 function x = from_array(A,opt) 0002 %FROM_ARRAY Approximate full array by TTeMPS tensor of prescribed rank 0003 % or within a prescribed tolerance. 0004 % 0005 % X = TTeMPS.from_array( A, tol ) approximates the given array A by a 0006 % TTeMPS tensor such that the the error is in the order of tol. 0007 % 0008 % X = TTeMPS.from_array( A, r ), with r a vector of length (ndims(A))+1), 0009 % approximates the given array A by a rank-r TTeMPS tensor, such that 0010 % X.rank = r. 0011 % 0012 0013 % TTeMPS Toolbox. 0014 % Michael Steinlechner, 2013-2016 0015 % Questions and contact: michael.steinlechner@epfl.ch 0016 % BSD 2-clause license, see LICENSE.txt 0017 0018 n = size(A); 0019 d = length(n); 0020 0021 if length(opt) == 1 0022 useTol = true; 0023 tol = opt; 0024 r = ones(1,d+1); 0025 else 0026 useTol = false; 0027 r = opt; 0028 if r(1) ~= 1 || r(d+1) ~= 1 0029 error('Invalid rank specified') 0030 end 0031 end 0032 0033 U = cell(1,d); 0034 0035 % process from left to right 0036 % first core 0037 A = reshape( A, n(1), prod(n(2:end))); 0038 [u,s,v] = svd(A,'econ'); 0039 if useTol 0040 r(2) = trunc_singular( diag(s), tol ); 0041 end 0042 U{1} = reshape( u(:,1:r(2)), [1, n(1), r(2)] ); 0043 A = s(1:r(2),1:r(2))*v(:,1:r(2))'; 0044 0045 % middle cores 0046 for i = 2:d-1 0047 A = reshape( A, n(i)*r(i), prod(n(i+1:end))); 0048 [u,s,v] = svd(A,'econ'); 0049 if useTol 0050 r(i+1) = trunc_singular( diag(s), tol ); 0051 end 0052 U{i} = reshape( u(:,1:r(i+1)), [r(i), n(i), r(i+1)] ); 0053 A = s(1:r(i+1),1:r(i+1)) * v(:,1:r(i+1))'; 0054 end 0055 0056 %last core 0057 U{d} = reshape(A, [r(d), n(d), 1]); 0058 0059 x = TTeMPS( U ); 0060 end