Jacobian \(\mathbf{J}_{\boldsymbol{\psi}}\) of the additive logistic map

Returns the Jacobian of additive_logistic(), \(\mathbf{J}_{\boldsymbol{\psi}}\in\mathcal{M}_{J\times(J-1)}\) with entries \((\mathbf{J}_{\boldsymbol{\psi}})_{i,j}=\partial p_i/\partial\rho_j\).

Usage

jacobian_additive_logistic(rho)

Arguments

rho

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

Value

Numeric matrix of size \(J\times(J-1)\).

Examples

jacobian_additive_logistic(c(0.2, -0.5))
#>             [,1]        [,2]
#> [1,]  0.24536327 -0.09263461
#> [2,] -0.09263461  0.16847742
#> [3,] -0.15272866 -0.07584281