sum_to_zero_free() [1/2]

template<typename Vec , require_eigen_vector_t< Vec > * = nullptr>

plain_type_t< Vec > stan::math::sum_to_zero_free ( const Vec &  z )

inline

Return an unconstrained vector.

The sum-to-zero transform is defined using a modified version of the isometric log ratio transform (ILR). See: Egozcue, Juan Jose; Pawlowsky-Glahn, Vera; Mateu-Figueras, Gloria; Barcelo-Vidal, Carles (2003), "Isometric logratio transformations for compositional data analysis", Mathematical Geology, 35 (3): 279–300, doi:10.1023/A:1023818214614, S2CID 122844634

This implementation is closer to the description of the same using "pivot coordinates" in Filzmoser, P., Hron, K., Templ, M. (2018). Geometrical Properties of Compositional Data. In: Applied Compositional Data Analysis. Springer Series in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-96422-5_3

Template Parameters

ColVec

a column vector type

Parameters

z	Vector of length K.

Returns

Free vector of length (K-1).

Exceptions

std::domain_error

if z does not sum to zero

Definition at line 38 of file sum_to_zero_free.hpp.