orthogonalise_solve_svd() [1/2]

template<typename Vector , typename Iterator >

std::pair< typename std::remove_reference< Vector >::type, DenseTensor< 2 > > syten::orthogonalise_solve_svd	(	Vector &&	target,
		Iterator	first,
		Iterator	last,
		bool	careful
	)

Generic implementation of orthogonalisation against a set of vectors using SVD-based orthogonalisation.

Parameters

[in]	target	input vector which is to be orthogonalised
[in]	first	iterator pointing to the first element of the range of vectors against which we orthogonalise
[in]	last	iterator pointing one past the end of the range of vectors against which we orthogonalise
[in]	careful	if true, does not apply orthogonalisation against a specific element of [*first, *last) if the resulting vector would have norm 1e-3 smaller than the input vector.

Returns

a pair {Vec, DenseTensor<2>} which holds the orthogonalised vector and the overlap matrix

Remarks

As this function uses the SVD-based orthogonalisation, the vectors [*first, *last) don't have to be orthogonal. However, they should be normalised to one or one should be a good reference value to decide whether a particular overlap is small or large.

The SVD-based orthogonalisation requires the calculation of the full overlap matrix for all elements of [*first, last). If you have this matrix already available, you should supply it and use the other overload.

References conj(), syten::MPS::distance(), std::move(), orthogonalise_solve_svd(), overlap(), pseudo_inverse_svd_cm(), SYTEN_SMALL_THRESHOLD, and underThreshold().

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