sum_to_zero_constrain() [1/6]

template<typename Vec , require_eigen_col_vector_t< Vec > * = nullptr, require_not_st_var< Vec > * = nullptr>

plain_type_t< Vec > stan::math::sum_to_zero_constrain ( const Vec &  y )

inline

Return a vector with sum zero corresponding to the specified free vector.

The sum-to-zero transform is defined using a modified version of the the inverse 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

This is a linear transform, with no Jacobian.

Template Parameters

Vec	type of the vector

Parameters

y	Free vector input of dimensionality K - 1.

Returns

Zero-sum vector of dimensionality K.

Definition at line 40 of file sum_to_zero_constrain.hpp.