Second derivatives (Hessian tensor) of the additive logistic map

Tensor of mixed partials of additive_logistic(), \(\partial^{2}p_i/(\partial\rho_k\partial\rho_j)\), stored as an array of size \((J-1)\times(J-1)\times J\).

Usage

hessian_additive_logistic(rho)

Arguments

rho

Numeric vector \(\boldsymbol{\rho}\in\mathbb{R}^{J-1}\).

Value

Numeric array used in the constrained Hessian chain rule.

Examples

hessian_additive_logistic(c(0.2, -0.5))
#> , , 1
#> 
#>             [,1]        [,2]
#> [1,]  0.03341530 -0.01261563
#> [2,] -0.01261563 -0.05289836
#> 
#> , , 2
#> 
#>             [,1]        [,2]
#> [1,] -0.01261563 -0.05289836
#> [2,] -0.05289836  0.09620788
#> 
#> , , 3
#> 
#>             [,1]        [,2]
#> [1,] -0.02079966  0.06551400
#> [2,]  0.06551400 -0.04330952
#>