sum_to_zero_constrain() [4/6]

template<bool Jacobian, typename T , require_std_vector_t< T > * = nullptr>

auto stan::math::sum_to_zero_constrain ( const T &  y, return_type_t< T > &  lp  )

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 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

Jacobian	unused
Vec	A standard vector with inner type inheriting from Eigen::DenseBase or a var_value with inner type inheriting from Eigen::DenseBase with compile time dynamic rows and 1 column

Parameters

[in]	y	free vector
[in,out]	lp	unused

Returns

Zero-sum vectors of dimensionality one greater than y

Definition at line 158 of file sum_to_zero_constrain.hpp.